LMFDB - Embedded newform 37.10.f.a.7.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(7,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.12
Character	$\chi$	$=$	37.7
Dual form			37.10.f.a.16.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.45759 + 2.71434i) q^{2} +(-52.8450 - 19.2340i) q^{3} +(-343.967 + 288.622i) q^{4} +(69.2798 + 392.905i) q^{5} +446.304 q^{6} +(-1588.46 - 9008.63i) q^{7} +(3813.41 - 6605.02i) q^{8} +(-12655.4 - 10619.1i) q^{9} +O(q^{10})$	\(q+(-7.45759 + 2.71434i) q^{2} +(-52.8450 - 19.2340i) q^{3} +(-343.967 + 288.622i) q^{4} +(69.2798 + 392.905i) q^{5} +446.304 q^{6} +(-1588.46 - 9008.63i) q^{7} +(3813.41 - 6605.02i) q^{8} +(-12655.4 - 10619.1i) q^{9} +(-1583.14 - 2742.08i) q^{10} +(-46098.7 + 79845.4i) q^{11} +(23728.3 - 8636.40i) q^{12} +(27580.5 - 23142.8i) q^{13} +(36298.6 + 62871.0i) q^{14} +(3896.06 - 22095.6i) q^{15} +(29410.5 - 166796. i) q^{16} +(-22379.7 - 18778.8i) q^{17} +(123203. + 44842.1i) q^{18} +(725288. + 263983. i) q^{19} +(-137231. - 115151. i) q^{20} +(-89329.7 + 506614. i) q^{21} +(127058. - 720582. i) q^{22} +(310176. + 537240. i) q^{23} +(-328561. + 275695. i) q^{24} +(1.68576e6 - 613567. i) q^{25} +(-142866. + 247452. i) q^{26} +(1.01798e6 + 1.76319e6i) q^{27} +(3.14647e6 + 2.64020e6i) q^{28} +(-160184. + 277447. i) q^{29} +(30919.9 + 175355. i) q^{30} +3.54047e6 q^{31} +(911492. + 5.16933e6i) q^{32} +(3.97184e6 - 3.33277e6i) q^{33} +(217870. + 79298.3i) q^{34} +(3.42949e6 - 1.24823e6i) q^{35} +7.41796e6 q^{36} +(-7.44733e6 + 8.63129e6i) q^{37} -6.12544e6 q^{38} +(-1.90262e6 + 692497. i) q^{39} +(2.85934e6 + 1.04071e6i) q^{40} +(225766. - 189440. i) q^{41} +(-708938. - 4.02059e6i) q^{42} +1.58412e7 q^{43} +(-7.18872e6 - 4.07693e7i) q^{44} +(3.29556e6 - 5.70807e6i) q^{45} +(-3.77142e6 - 3.16459e6i) q^{46} +(4.84871e6 + 8.39821e6i) q^{47} +(-4.76235e6 + 8.24863e6i) q^{48} +(-4.07122e7 + 1.48180e7i) q^{49} +(-1.09063e7 + 9.15146e6i) q^{50} +(821463. + 1.42282e6i) q^{51} +(-2.80725e6 + 1.59207e7i) q^{52} +(-5.15015e6 + 2.92080e7i) q^{53} +(-1.23776e7 - 1.03860e7i) q^{54} +(-3.45654e7 - 1.25808e7i) q^{55} +(-6.55596e7 - 2.38618e7i) q^{56} +(-3.32504e7 - 2.79004e7i) q^{57} +(441502. - 2.50388e6i) q^{58} +(2.38395e7 - 1.35201e8i) q^{59} +(5.03718e6 + 8.72465e6i) q^{60} +(6.77794e7 - 5.68737e7i) q^{61} +(-2.64034e7 + 9.61005e6i) q^{62} +(-7.55613e7 + 1.30876e8i) q^{63} +(2.25295e7 + 3.90223e7i) q^{64} +(1.10037e7 + 9.23319e6i) q^{65} +(-2.05741e7 + 3.56353e7i) q^{66} +(-2.09077e7 - 1.18573e8i) q^{67} +1.31178e7 q^{68} +(-6.05796e6 - 3.43564e7i) q^{69} +(-2.21876e7 + 1.86176e7i) q^{70} +(-9.85706e7 - 3.58768e7i) q^{71} +(-1.18400e8 + 4.30940e7i) q^{72} +2.47187e8 q^{73} +(3.21108e7 - 8.45831e7i) q^{74} -1.00886e8 q^{75} +(-3.25666e8 + 1.18533e8i) q^{76} +(7.92524e8 + 2.88455e8i) q^{77} +(1.23093e7 - 1.03287e7i) q^{78} +(-3.88668e7 - 2.20424e8i) q^{79} +6.75724e7 q^{80} +(3.65837e7 + 2.07476e8i) q^{81} +(-1.16947e6 + 2.02557e6i) q^{82} +(2.03742e8 + 1.70960e8i) q^{83} +(-1.15494e8 - 2.00041e8i) q^{84} +(5.82782e6 - 1.00941e7i) q^{85} +(-1.18137e8 + 4.29985e7i) q^{86} +(1.38014e7 - 1.15807e7i) q^{87} +(3.51587e8 + 6.08966e8i) q^{88} +(1.18825e8 - 6.73889e8i) q^{89} +(-9.08325e6 + 5.15137e7i) q^{90} +(-2.52295e8 - 2.11701e8i) q^{91} +(-2.61750e8 - 9.52691e7i) q^{92} +(-1.87096e8 - 6.80975e7i) q^{93} +(-5.89553e7 - 4.94694e7i) q^{94} +(-5.34726e7 + 3.03258e8i) q^{95} +(5.12591e7 - 2.90705e8i) q^{96} +(7.90911e8 + 1.36990e9i) q^{97} +(2.63394e8 - 2.21014e8i) q^{98} +(1.43129e9 - 5.20946e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9}+O(q^{10}) $ 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9	\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9} + 59997 q^{10} + 175689 q^{11} - 147411 q^{12} + 713586 q^{13} - 96867 q^{14} - 143316 q^{15} + 556665 q^{16} - 119334 q^{17} - 711948 q^{18} + 1752348 q^{19} + 4774248 q^{20} + 57972 q^{21} + 1413495 q^{22} - 5098719 q^{23} + 3891975 q^{24} + 10869768 q^{25} + 5518221 q^{26} + 13281609 q^{27} + 9017757 q^{28} - 2782023 q^{29} - 10231020 q^{30} + 8407836 q^{31} + 6197838 q^{32} - 8252229 q^{33} - 49656453 q^{34} - 23563824 q^{35} + 151165428 q^{36} - 23634336 q^{37} - 12277422 q^{38} + 100476834 q^{39} + 165006327 q^{40} + 74094072 q^{41} - 3662109 q^{42} - 90803088 q^{43} - 350087604 q^{44} - 184820799 q^{45} - 114643110 q^{46} + 158694333 q^{47} + 359750805 q^{48} + 36118224 q^{49} - 259200273 q^{50} + 176035647 q^{51} - 203883429 q^{52} - 31488120 q^{53} - 109796865 q^{54} + 23137227 q^{55} + 37371291 q^{56} - 12449808 q^{57} - 840994983 q^{58} - 77893794 q^{59} + 244178580 q^{60} - 980597586 q^{61} - 586588080 q^{62} - 48634623 q^{63} - 917012376 q^{64} + 1432770144 q^{65} - 177475497 q^{66} - 302695398 q^{67} + 1615796082 q^{68} + 699674787 q^{69} + 2092804794 q^{70} - 774435768 q^{71} - 2899807611 q^{72} - 2505680652 q^{73} + 1161236205 q^{74} - 2302474524 q^{75} + 1445475621 q^{76} - 1374645213 q^{77} + 2942410749 q^{78} - 29533980 q^{79} + 9154934064 q^{80} - 2232253221 q^{81} + 707552205 q^{82} - 392438496 q^{83} - 1388366664 q^{84} - 556053567 q^{85} + 852383496 q^{86} - 6650019951 q^{87} + 3660093510 q^{88} + 100313124 q^{89} + 12897388398 q^{90} + 684844038 q^{91} + 621259308 q^{92} + 2212599060 q^{93} + 3136220628 q^{94} + 1257937926 q^{95} - 6811500039 q^{96} + 70258497 q^{97} - 8202052869 q^{98} - 2679000153 q^{99}+O(q^{100}) \) 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9 + 59997 * q^10 + 175689 * q^11 - 147411 * q^12 + 713586 * q^13 - 96867 * q^14 - 143316 * q^15 + 556665 * q^16 - 119334 * q^17 - 711948 * q^18 + 1752348 * q^19 + 4774248 * q^20 + 57972 * q^21 + 1413495 * q^22 - 5098719 * q^23 + 3891975 * q^24 + 10869768 * q^25 + 5518221 * q^26 + 13281609 * q^27 + 9017757 * q^28 - 2782023 * q^29 - 10231020 * q^30 + 8407836 * q^31 + 6197838 * q^32 - 8252229 * q^33 - 49656453 * q^34 - 23563824 * q^35 + 151165428 * q^36 - 23634336 * q^37 - 12277422 * q^38 + 100476834 * q^39 + 165006327 * q^40 + 74094072 * q^41 - 3662109 * q^42 - 90803088 * q^43 - 350087604 * q^44 - 184820799 * q^45 - 114643110 * q^46 + 158694333 * q^47 + 359750805 * q^48 + 36118224 * q^49 - 259200273 * q^50 + 176035647 * q^51 - 203883429 * q^52 - 31488120 * q^53 - 109796865 * q^54 + 23137227 * q^55 + 37371291 * q^56 - 12449808 * q^57 - 840994983 * q^58 - 77893794 * q^59 + 244178580 * q^60 - 980597586 * q^61 - 586588080 * q^62 - 48634623 * q^63 - 917012376 * q^64 + 1432770144 * q^65 - 177475497 * q^66 - 302695398 * q^67 + 1615796082 * q^68 + 699674787 * q^69 + 2092804794 * q^70 - 774435768 * q^71 - 2899807611 * q^72 - 2505680652 * q^73 + 1161236205 * q^74 - 2302474524 * q^75 + 1445475621 * q^76 - 1374645213 * q^77 + 2942410749 * q^78 - 29533980 * q^79 + 9154934064 * q^80 - 2232253221 * q^81 + 707552205 * q^82 - 392438496 * q^83 - 1388366664 * q^84 - 556053567 * q^85 + 852383496 * q^86 - 6650019951 * q^87 + 3660093510 * q^88 + 100313124 * q^89 + 12897388398 * q^90 + 684844038 * q^91 + 621259308 * q^92 + 2212599060 * q^93 + 3136220628 * q^94 + 1257937926 * q^95 - 6811500039 * q^96 + 70258497 * q^97 - 8202052869 * q^98 - 2679000153 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.45759	+	2.71434i	−0.329582	+	0.119958i	−0.501511	−	0.865151i	$-0.667222\pi$
$2$	−7.45759	+	2.71434i	−0.329582	+	0.119958i	0.171929	+	0.985109i	$0.445000\pi$
$3$	−52.8450	−	19.2340i	−0.376668	−	0.137096i	0.146747	−	0.989174i	$-0.453120\pi$
$3$	−52.8450	−	19.2340i	−0.376668	−	0.137096i	−0.523414	+	0.852078i	$0.675342\pi$
$4$	−343.967	+	288.622i	−0.671810	+	0.563716i
$5$	69.2798	+	392.905i	0.0495726	+	0.281140i	0.999510	−	0.0313000i	$-0.00996472\pi$
$5$	69.2798	+	392.905i	0.0495726	+	0.281140i	−0.949937	+	0.312440i	$0.898854\pi$
$6$	446.304			0.140589
$7$	−1588.46	−	9008.63i	−0.250055	−	1.41813i	−0.808453	−	0.588561i	$-0.799695\pi$
$7$	−1588.46	−	9008.63i	−0.250055	−	1.41813i	0.558397	−	0.829574i	$-0.311417\pi$
$8$	3813.41	−	6605.02i	0.329161	−	0.570124i
$9$	−12655.4	−	10619.1i	−0.642961	−	0.539508i
$10$	−1583.14	−	2742.08i	−0.0500633	−	0.0867121i
$11$	−46098.7	+	79845.4i	−0.949341	+	1.64431i	−0.202522	+	0.979278i	$0.564914\pi$
$11$	−46098.7	+	79845.4i	−0.949341	+	1.64431i	−0.746818	+	0.665028i	$0.768419\pi$
$12$	23728.3	−	8636.40i	0.330332	−	0.120231i
$13$	27580.5	−	23142.8i	0.267828	−	0.224735i	−0.498976	−	0.866616i	$-0.666290\pi$
$13$	27580.5	−	23142.8i	0.267828	−	0.224735i	0.766804	+	0.641881i	$0.221846\pi$
$14$	36298.6	+	62871.0i	0.252530	+	0.437396i
$15$	3896.06	−	22095.6i	0.0198708	−	0.112693i
$16$	29410.5	−	166796.i	0.112192	−	0.636274i
$17$	−22379.7	−	18778.8i	−0.0649881	−	0.0545315i	0.609715	−	0.792621i	$-0.291284\pi$
$17$	−22379.7	−	18778.8i	−0.0649881	−	0.0545315i	−0.674703	+	0.738089i	$0.735728\pi$
$18$	123203.	+	44842.1i	0.276627	+	0.100684i
$19$	725288.	+	263983.i	1.27679	+	0.464713i	0.889369	−	0.457190i	$-0.151144\pi$
$19$	725288.	+	263983.i	1.27679	+	0.464713i	0.387420	+	0.921903i	$0.373366\pi$
$20$	−137231.	−	115151.i	−0.191787	−	0.160928i
$21$	−89329.7	+	506614.i	−0.100233	+	0.568447i
$22$	127058.	−	720582.i	0.115638	−	0.655815i
$23$	310176.	+	537240.i	0.231117	+	0.400307i	0.958137	−	0.286309i	$-0.0924285\pi$
$23$	310176.	+	537240.i	0.231117	+	0.400307i	−0.727020	+	0.686617i	$0.759095\pi$
$24$	−328561.	+	275695.i	−0.202146	+	0.169621i
$25$	1.68576e6	−	613567.i	0.863110	−	0.314146i
$26$	−142866.	+	247452.i	−0.0613127	+	0.106197i
$27$	1.01798e6	+	1.76319e6i	0.368639	+	0.638502i
$28$	3.14647e6	+	2.64020e6i	0.967415	+	0.811757i
$29$	−160184.	+	277447.i	−0.0420560	+	0.0728432i	−0.886287	−	0.463136i	$-0.846724\pi$
$29$	−160184.	+	277447.i	−0.0420560	+	0.0728432i	0.844231	+	0.535979i	$0.180057\pi$
$30$	30919.9	+	175355.i	0.00696935	+	0.0395251i
$31$	3.54047e6			0.688547			0.344274	−	0.938869i	$-0.388125\pi$
$31$	3.54047e6			0.688547			0.344274	+	0.938869i	$0.388125\pi$
$32$	911492.	+	5.16933e6i	0.153666	+	0.871484i
$33$	3.97184e6	−	3.33277e6i	0.583014	−	0.489206i
$34$	217870.	+	79298.3i	0.0279604	+	0.0101767i
$35$	3.42949e6	−	1.24823e6i	0.386299	−	0.140601i
$36$	7.41796e6			0.736077
$37$	−7.44733e6	+	8.63129e6i	−0.653270	+	0.757125i
$37$	−7.44733e6	+	8.63129e6i	−0.653270	+	0.757125i
$38$	−6.12544e6			−0.476553
$39$	−1.90262e6	+	692497.i	−0.131693	+	0.0479322i
$40$	2.85934e6	+	1.04071e6i	0.176602	+	0.0642779i
$41$	225766.	−	189440.i	0.0124776	−	0.0104700i	−0.636527	−	0.771254i	$-0.719630\pi$
$41$	225766.	−	189440.i	0.0124776	−	0.0104700i	0.649005	+	0.760784i	$0.275185\pi$
$42$	−708938.	−	4.02059e6i	−0.0351550	−	0.199374i
$43$	1.58412e7			0.706612			0.353306	−	0.935508i	$-0.385057\pi$
$43$	1.58412e7			0.706612			0.353306	+	0.935508i	$0.385057\pi$
$44$	−7.18872e6	−	4.07693e7i	−0.289144	−	1.63982i
$45$	3.29556e6	−	5.70807e6i	0.119804	−	0.207507i
$46$	−3.77142e6	−	3.16459e6i	−0.124192	−	0.104210i
$47$	4.84871e6	+	8.39821e6i	0.144939	+	0.251042i	0.929350	−	0.369199i	$-0.120368\pi$
$47$	4.84871e6	+	8.39821e6i	0.144939	+	0.251042i	−0.784411	+	0.620241i	$0.787035\pi$
$48$	−4.76235e6	+	8.24863e6i	−0.129490	+	0.224283i
$49$	−4.07122e7	+	1.48180e7i	−1.00889	+	0.367205i
$50$	−1.09063e7	+	9.15146e6i	−0.246781	+	0.207074i
$51$	821463.	+	1.42282e6i	0.0170029	+	0.0294498i
$52$	−2.80725e6	+	1.59207e7i	−0.0532434	+	0.301958i
$53$	−5.15015e6	+	2.92080e7i	−0.0896559	+	0.508464i	0.906599	+	0.421994i	$0.138670\pi$
$53$	−5.15015e6	+	2.92080e7i	−0.0896559	+	0.508464i	−0.996254	+	0.0864697i	$0.972441\pi$
$54$	−1.23776e7	−	1.03860e7i	−0.198090	−	0.166217i
$55$	−3.45654e7	−	1.25808e7i	−0.509342	−	0.185385i
$56$	−6.55596e7	−	2.38618e7i	−0.890821	−	0.324232i
$57$	−3.32504e7	−	2.79004e7i	−0.417215	−	0.350085i
$58$	441502.	−	2.50388e6i	0.00512279	−	0.0290528i
$59$	2.38395e7	−	1.35201e8i	0.256132	−	1.45259i	−0.537020	−	0.843570i	$-0.680450\pi$
$59$	2.38395e7	−	1.35201e8i	0.256132	−	1.45259i	0.793151	−	0.609025i	$-0.208439\pi$
$60$	5.03718e6	+	8.72465e6i	0.0501772	+	0.0869095i
$61$	6.77794e7	−	5.68737e7i	0.626778	−	0.525929i	−0.273148	−	0.961972i	$-0.588065\pi$
$61$	6.77794e7	−	5.68737e7i	0.626778	−	0.525929i	0.899926	+	0.436043i	$0.143620\pi$
$62$	−2.64034e7	+	9.61005e6i	−0.226933	+	0.0825967i
$63$	−7.55613e7	+	1.30876e8i	−0.604320	+	1.04671i
$64$	2.25295e7	+	3.90223e7i	0.167858	+	0.290738i
$65$	1.10037e7	+	9.23319e6i	0.0764589	+	0.0641567i
$66$	−2.05741e7	+	3.56353e7i	−0.133467	+	0.231171i
$67$	−2.09077e7	−	1.18573e8i	−0.126756	−	0.718871i	−0.980249	−	0.197766i	$-0.936631\pi$
$67$	−2.09077e7	−	1.18573e8i	−0.126756	−	0.718871i	0.853493	−	0.521105i	$-0.174480\pi$
$68$	1.31178e7			0.0743999
$69$	−6.05796e6	−	3.43564e7i	−0.0321740	−	0.182468i
$70$	−2.21876e7	+	1.86176e7i	−0.110451	+	0.0926793i
$71$	−9.85706e7	−	3.58768e7i	−0.460347	−	0.167552i	0.101428	−	0.994843i	$-0.467659\pi$
$71$	−9.85706e7	−	3.58768e7i	−0.460347	−	0.167552i	−0.561774	+	0.827290i	$0.689881\pi$
$72$	−1.18400e8	+	4.30940e7i	−0.519224	+	0.188982i
$73$	2.47187e8			1.01876			0.509382	−	0.860541i	$-0.329874\pi$
$73$	2.47187e8			1.01876			0.509382	+	0.860541i	$0.329874\pi$
$74$	3.21108e7	−	8.45831e7i	0.124483	−	0.327900i
$75$	−1.00886e8			−0.368174
$76$	−3.25666e8	+	1.18533e8i	−1.11973	+	0.407547i
$77$	7.92524e8	+	2.88455e8i	2.56924	+	0.935125i
$78$	1.23093e7	−	1.03287e7i	0.0376536	−	0.0315952i
$79$	−3.88668e7	−	2.20424e8i	−0.112268	−	0.636704i	−0.988067	−	0.154027i	$-0.950776\pi$
$79$	−3.88668e7	−	2.20424e8i	−0.112268	−	0.636704i	0.875798	−	0.482677i	$-0.160335\pi$
$80$	6.75724e7			0.184444
$81$	3.65837e7	+	2.07476e8i	0.0944289	+	0.535533i
$82$	−1.16947e6	+	2.02557e6i	−0.00285644	+	0.00494750i
$83$	2.03742e8	+	1.70960e8i	0.471226	+	0.395406i	0.847242	−	0.531208i	$-0.178262\pi$
$83$	2.03742e8	+	1.70960e8i	0.471226	+	0.395406i	−0.376015	+	0.926613i	$0.622706\pi$
$84$	−1.15494e8	−	2.00041e8i	−0.253105	−	0.438391i
$85$	5.82782e6	−	1.00941e7i	0.0121094	−	0.0209740i
$86$	−1.18137e8	+	4.29985e7i	−0.232887	+	0.0847638i
$87$	1.38014e7	−	1.15807e7i	0.0258277	−	0.0216720i
$88$	3.51587e8	+	6.08966e8i	0.624972	+	1.08248i
$89$	1.18825e8	−	6.73889e8i	0.200749	−	1.13850i	−0.703243	−	0.710950i	$-0.748265\pi$
$89$	1.18825e8	−	6.73889e8i	0.200749	−	1.13850i	0.903991	−	0.427551i	$-0.140624\pi$
$90$	−9.08325e6	+	5.15137e7i	−0.0145932	+	0.0827621i
$91$	−2.52295e8	−	2.11701e8i	−0.385676	−	0.323621i
$92$	−2.61750e8	−	9.52691e7i	−0.380926	−	0.138646i
$93$	−1.87096e8	−	6.80975e7i	−0.259354	−	0.0943970i
$94$	−5.89553e7	−	4.94694e7i	−0.0778839	−	0.0653523i
$95$	−5.34726e7	+	3.03258e8i	−0.0673558	+	0.381994i
$96$	5.12591e7	−	2.90705e8i	0.0615958	−	0.349327i
$97$	7.90911e8	+	1.36990e9i	0.907099	+	1.57114i	0.818074	+	0.575113i	$0.195042\pi$
$97$	7.90911e8	+	1.36990e9i	0.907099	+	1.57114i	0.0890249	+	0.996029i	$0.471625\pi$
$98$	2.63394e8	−	2.21014e8i	0.288462	−	0.242048i
$99$	1.43129e9	−	5.20946e8i	1.49751	−	0.545048i
$100$	−4.02757e8	+	6.97595e8i	−0.402757	+	0.697595i
$101$	6.43165e8	+	1.11399e9i	0.615002	+	1.06521i	0.990384	+	0.138344i	$0.0441781\pi$
$101$	6.43165e8	+	1.11399e9i	0.615002	+	1.06521i	−0.375382	+	0.926870i	$0.622489\pi$
$102$	−9.98814e6	−	8.38105e6i	−0.00913659	−	0.00766651i
$103$	7.46950e8	−	1.29376e9i	0.653919	−	1.13262i	−0.328244	−	0.944593i	$-0.606457\pi$
$103$	7.46950e8	−	1.29376e9i	0.653919	−	1.13262i	0.982164	−	0.188028i	$-0.0602097\pi$
$104$	−4.76828e7	−	2.70422e8i	−0.0399679	−	0.226669i
$105$	−2.05240e8			−0.164782
$106$	−4.08726e7	−	2.31800e8i	−0.0314453	−	0.178335i
$107$	−7.72624e8	+	6.48309e8i	−0.569825	+	0.478140i	−0.881588	−	0.472020i	$-0.843525\pi$
$107$	−7.72624e8	+	6.48309e8i	−0.569825	+	0.478140i	0.311763	+	0.950160i	$0.399080\pi$
$108$	−8.59047e8	−	3.12667e8i	−0.607589	−	0.221144i
$109$	3.62115e8	−	1.31799e8i	0.245712	−	0.0894320i	−0.216228	−	0.976343i	$-0.569376\pi$
$109$	3.62115e8	−	1.31799e8i	0.245712	−	0.0894320i	0.461941	+	0.886911i	$0.347153\pi$
$110$	2.91923e8			0.190108
$111$	5.59568e8	−	3.12879e8i	0.349864	−	0.195624i
$112$	−1.54932e9			−0.930377
$113$	−2.12678e9	+	7.74086e8i	−1.22707	+	0.446618i	−0.872594	−	0.488446i	$-0.837564\pi$
$113$	−2.12678e9	+	7.74086e8i	−1.22707	+	0.446618i	−0.354478	+	0.935064i	$0.615342\pi$
$114$	3.23699e8	+	1.17817e8i	0.179502	+	0.0653334i
$115$	−1.89596e8	+	1.59090e8i	−0.101085	+	0.0848207i
$116$	−2.49794e7	−	1.41665e8i	−0.0128092	−	0.0726445i
$117$	−5.94798e8			−0.293450
$118$	1.89195e8	+	1.07298e9i	0.0898340	+	0.509474i
$119$	−1.33622e8	+	2.31440e8i	−0.0610824	+	0.105798i
$120$	−1.31085e8	−	1.09993e8i	−0.0577081	−	0.0484228i
$121$	−3.07121e9	−	5.31950e9i	−1.30249	−	2.25599i
$122$	−3.51097e8	+	6.08117e8i	−0.143485	+	0.248524i
$123$	−1.55743e7	+	5.66859e6i	−0.00613530	+	0.00223307i
$124$	−1.21780e9	+	1.02186e9i	−0.462573	+	0.388145i
$125$	7.47479e8	+	1.29467e9i	0.273844	+	0.474313i
$126$	2.08263e8	−	1.18112e9i	0.0736113	−	0.417471i
$127$	7.42873e8	−	4.21304e9i	0.253395	−	1.43707i	−0.546764	−	0.837287i	$-0.684141\pi$
$127$	7.42873e8	−	4.21304e9i	0.253395	−	1.43707i	0.800159	−	0.599788i	$-0.204748\pi$
$128$	−2.33270e9	−	1.95737e9i	−0.768093	−	0.644507i
$129$	−8.37130e8	−	3.04691e8i	−0.266158	−	0.0968736i
$130$	−1.07123e8	−	3.89896e7i	−0.0328956	−	0.0119730i
$131$	−3.09774e8	−	2.59931e8i	−0.0919019	−	0.0771148i	0.595679	−	0.803222i	$-0.296883\pi$
$131$	−3.09774e8	−	2.59931e8i	−0.0919019	−	0.0771148i	−0.687581	+	0.726108i	$0.741327\pi$
$132$	−4.04269e8	+	2.29272e9i	−0.115901	+	0.657308i
$133$	1.22603e9	−	6.95318e9i	0.339758	−	1.92686i
$134$	4.77770e8	+	8.27521e8i	0.128011	+	0.221721i
$135$	−6.22241e8	+	5.22123e8i	−0.161234	+	0.135291i
$136$	−2.09377e8	+	7.62070e7i	−0.0524812	+	0.0191016i
$137$	−3.46225e9	+	5.99679e9i	−0.839684	+	1.45438i	0.0504749	+	0.998725i	$0.483927\pi$
$137$	−3.46225e9	+	5.99679e9i	−0.839684	+	1.45438i	−0.890159	+	0.455650i	$0.849407\pi$
$138$	1.38433e8	+	2.39773e8i	0.0324925	+	0.0562787i
$139$	6.62537e9	+	5.55935e9i	1.50537	+	1.26316i	0.872204	+	0.489143i	$0.162690\pi$
$139$	6.62537e9	+	5.55935e9i	1.50537	+	1.26316i	0.633168	+	0.774014i	$0.281754\pi$
$140$	−8.19363e8	+	1.41918e9i	−0.180260	+	0.312220i
$141$	−9.46989e7	−	5.37064e8i	−0.0201771	−	0.114430i
$142$	8.32481e8			0.171821
$143$	5.76417e8	+	3.26903e9i	0.115272	+	0.653742i
$144$	−2.14343e9	+	1.79855e9i	−0.415411	+	0.348571i
$145$	−1.20108e8	−	4.37157e7i	−0.0225640	−	0.00821262i
$146$	−1.84342e9	+	6.70950e8i	−0.335766	+	0.122209i
$147$	2.43645e9			0.430357
$148$	7.04501e7	−	5.11834e9i	0.0120699	−	0.876903i
$149$	8.04175e9			1.33663			0.668317	−	0.743877i	$-0.267015\pi$
$149$	8.04175e9			1.33663			0.668317	+	0.743877i	$0.267015\pi$
$150$	7.52363e8	−	2.73838e8i	0.121344	−	0.0441654i
$151$	2.86823e9	+	1.04395e9i	0.448970	+	0.163412i	0.556602	−	0.830779i	$-0.312105\pi$
$151$	2.86823e9	+	1.04395e9i	0.448970	+	0.163412i	−0.107632	+	0.994191i	$0.534327\pi$
$152$	4.50943e9	−	3.78386e9i	0.685214	−	0.574962i
$153$	8.38093e7	+	4.75306e8i	0.0123646	+	0.0701232i
$154$	−6.69328e9			−0.958949
$155$	2.45283e8	+	1.39107e9i	0.0341331	+	0.193578i
$156$	4.54568e8	−	7.87334e8i	0.0614523	−	0.106438i
$157$	2.83526e9	+	2.37907e9i	0.372430	+	0.312506i	0.809722	−	0.586814i	$-0.199618\pi$
$157$	2.83526e9	+	2.37907e9i	0.372430	+	0.312506i	−0.437292	+	0.899320i	$0.644062\pi$
$158$	8.88159e8	+	1.53834e9i	0.113379	+	0.196379i
$159$	8.33947e8	−	1.44444e9i	0.103479	−	0.179230i
$160$	−1.96791e9	+	7.16261e8i	−0.237392	+	0.0864035i
$161$	4.34710e9	−	3.64765e9i	0.509897	−	0.427855i
$162$	−8.35988e8	−	1.44797e9i	−0.0953635	−	0.165174i
$163$	−2.68434e8	+	1.52237e9i	−0.0297847	+	0.168918i	−0.996072	−	0.0885496i	$-0.971777\pi$
$163$	−2.68434e8	+	1.52237e9i	−0.0297847	+	0.168918i	0.966287	+	0.257467i	$0.0828879\pi$
$164$	−2.29793e7	+	1.30322e8i	−0.00248051	+	0.0140676i
$165$	1.58463e9	+	1.32966e9i	0.166437	+	0.139657i
$166$	−1.98347e9	−	7.21923e8i	−0.202740	−	0.0737912i
$167$	1.38430e10	+	5.03844e9i	1.37723	+	0.501270i	0.921337	−	0.388765i	$-0.127098\pi$
$167$	1.38430e10	+	5.03844e9i	1.37723	+	0.501270i	0.455892	+	0.890035i	$0.349320\pi$
$168$	3.00554e9	+	2.52195e9i	0.291093	+	0.244256i
$169$	−1.61636e9	+	9.16682e9i	−0.152422	+	0.864427i
$170$	−1.60627e7	+	9.10962e7i	−0.00147502	+	0.00836528i
$171$	−6.37553e9	−	1.10427e10i	−0.570209	−	0.987631i
$172$	−5.44886e9	+	4.57213e9i	−0.474709	+	0.398328i
$173$	−1.20967e9	+	4.40283e8i	−0.102673	+	0.0373701i	−0.392846	−	0.919604i	$-0.628509\pi$
$173$	−1.20967e9	+	4.40283e8i	−0.102673	+	0.0373701i	0.290173	+	0.956974i	$0.406287\pi$
$174$	−7.14908e7	+	1.23826e8i	−0.00591260	+	0.0102409i
$175$	−8.20517e9	−	1.42118e10i	−0.661327	−	1.14545i
$176$	1.19621e10	+	1.00374e10i	0.939721	+	0.788520i
$177$	−3.86025e9	+	6.68615e9i	−0.295621	+	0.512031i
$178$	9.43018e8	+	5.34812e9i	0.0704093	+	0.399311i
$179$	2.82096e9			0.205380			0.102690	−	0.994713i	$-0.467255\pi$
$179$	2.82096e9			0.205380			0.102690	+	0.994713i	$0.467255\pi$
$180$	5.13915e8	+	2.91456e9i	0.0364893	+	0.206941i
$181$	6.51375e9	−	5.46568e9i	0.451105	−	0.378522i	−0.388741	−	0.921347i	$-0.627090\pi$
$181$	6.51375e9	−	5.46568e9i	0.451105	−	0.378522i	0.839846	+	0.542825i	$0.182645\pi$
$182$	2.45614e9	+	8.93963e8i	0.165933	+	0.0603946i
$183$	−4.67572e9	+	1.70182e9i	−0.308190	+	0.112172i
$184$	4.73131e9			0.304300
$185$	−3.90723e9	−	2.32812e9i	−0.245243	−	0.146128i
$186$	1.58013e9			0.0968019
$187$	2.53107e9	−	9.21235e8i	0.151362	−	0.0550913i
$188$	−4.09171e9	−	1.48926e9i	−0.238888	−	0.0869481i
$189$	1.42669e10	−	1.19713e10i	0.813301	−	0.682441i
$190$	−4.24369e8	−	2.40672e9i	−0.0236240	−	0.133978i
$191$	−2.84359e10			−1.54602			−0.773012	−	0.634391i	$-0.781251\pi$
$191$	−2.84359e10			−1.54602			−0.773012	+	0.634391i	$0.781251\pi$
$192$	−4.40018e8	−	2.49546e9i	−0.0233676	−	0.132524i
$193$	−1.21997e10	+	2.11305e10i	−0.632909	+	1.09623i	0.354046	+	0.935228i	$0.384806\pi$
$193$	−1.21997e10	+	2.11305e10i	−0.632909	+	1.09623i	−0.986954	+	0.161002i	$0.948528\pi$
$194$	−9.61666e9	−	8.06933e9i	−0.487435	−	0.409006i
$195$	−4.03899e8	−	6.99573e8i	−0.0200040	−	0.0346480i
$196$	9.72683e9	−	1.68474e10i	0.470781	−	0.815417i
$197$	1.92086e10	−	6.99137e9i	0.908654	−	0.330723i	0.154939	−	0.987924i	$-0.450482\pi$
$197$	1.92086e10	−	6.99137e9i	0.908654	−	0.330723i	0.753715	+	0.657201i	$0.228260\pi$
$198$	−9.25993e9	+	7.77000e9i	−0.428168	+	0.359276i
$199$	−1.64360e10	−	2.84679e10i	−0.742945	−	1.28682i	−0.951149	−	0.308733i	$-0.900095\pi$
$199$	−1.64360e10	−	2.84679e10i	−0.742945	−	1.28682i	0.208204	−	0.978085i	$-0.433238\pi$
$200$	2.37588e9	−	1.34743e10i	0.105000	−	0.595485i
$201$	−1.17578e9	+	6.66816e9i	−0.0508092	+	0.288153i
$202$	−7.82022e9	−	6.56195e9i	−0.330475	−	0.277301i
$203$	2.75386e9	+	1.00232e9i	0.113818	+	0.0414263i
$204$	−6.93213e8	−	2.52309e8i	−0.0280240	−	0.0101999i
$205$	9.00732e7	+	7.55804e7i	0.00356207	+	0.00298894i
$206$	−2.05875e9	+	1.16758e10i	−0.0796530	+	0.451734i
$207$	1.77963e9	−	1.00928e10i	0.0673696	−	0.382072i
$208$	−3.04895e9	−	5.28094e9i	−0.112945	−	0.195626i
$209$	−5.45127e10	+	4.57416e10i	−1.97624	+	1.65826i
$210$	1.53060e9	−	5.57091e8i	0.0543092	−	0.0197669i
$211$	−1.52320e10	+	2.63826e10i	−0.529036	+	0.916317i	0.470391	+	0.882458i	$0.344113\pi$
$211$	−1.52320e10	+	2.63826e10i	−0.529036	+	0.916317i	−0.999427	+	0.0338590i	$0.989220\pi$
$212$	−6.65859e9	−	1.15330e10i	−0.226397	−	0.392132i
$213$	4.51891e9	+	3.79182e9i	0.150427	+	0.126223i
$214$	4.00218e9	−	6.93198e9i	0.130447	−	0.225941i
$215$	1.09748e9	+	6.22411e9i	0.0350286	+	0.198657i
$216$	1.55279e10			0.485367
$217$	−5.62391e9	−	3.18948e10i	−0.172175	−	0.976453i
$218$	−2.34276e9	+	1.96581e9i	−0.0702543	+	0.0589504i
$219$	−1.30626e10	−	4.75440e9i	−0.383735	−	0.139668i
$220$	1.55204e10	−	5.64898e9i	0.446686	−	0.162580i
$221$	−1.05183e9			−0.0296608
$222$	−3.32377e9	+	3.85218e9i	−0.0918423	+	0.106443i
$223$	1.66122e10			0.449837			0.224919	−	0.974378i	$-0.427788\pi$
$223$	1.66122e10			0.449837			0.224919	+	0.974378i	$0.427788\pi$
$224$	4.51207e10	−	1.64226e10i	1.19746	−	0.435839i
$225$	−2.78496e10	−	1.01364e10i	−0.724431	−	0.263671i
$226$	1.37595e10	−	1.15456e10i	0.350845	−	0.294394i
$227$	1.65123e9	+	9.36457e9i	0.0412753	+	0.234084i	0.998466	−	0.0553756i	$-0.0176356\pi$
$227$	1.65123e9	+	9.36457e9i	0.0412753	+	0.234084i	−0.957190	+	0.289459i	$0.906525\pi$
$228$	1.94897e10			0.477638
$229$	2.96601e9	+	1.68211e10i	0.0712709	+	0.404198i	0.999483	+	0.0321464i	$0.0102343\pi$
$229$	2.96601e9	+	1.68211e10i	0.0712709	+	0.404198i	−0.928212	+	0.372051i	$0.878655\pi$
$230$	9.82103e8	−	1.70105e9i	0.0231410	−	0.0400814i
$231$	−3.63328e10	−	3.04868e10i	−0.839547	−	0.704463i
$232$	1.22170e9	+	2.11604e9i	0.0276864	+	0.0479543i
$233$	−2.50859e10	+	4.34501e10i	−0.557607	+	0.965803i	0.440089	+	0.897954i	$0.354947\pi$
$233$	−2.50859e10	+	4.34501e10i	−0.557607	+	0.965803i	−0.997696	+	0.0678491i	$0.978386\pi$
$234$	4.43576e9	−	1.61449e9i	0.0967157	−	0.0352016i
$235$	−2.96379e9	+	2.48691e9i	−0.0633930	+	0.0531931i
$236$	3.08219e10	+	5.33851e10i	0.646778	+	1.12025i
$237$	−2.18573e9	+	1.23959e10i	−0.0450017	+	0.255218i
$238$	3.68290e8	−	2.08868e9i	0.00744035	−	0.0421963i
$239$	5.62845e10	+	4.72283e10i	1.11583	+	0.936293i	0.998386	−	0.0567863i	$-0.0180854\pi$
$239$	5.62845e10	+	4.72283e10i	1.11583	+	0.936293i	0.117444	+	0.993079i	$0.462530\pi$
$240$	−3.57087e9	−	1.29969e9i	−0.0694741	−	0.0252865i
$241$	−3.99005e10	−	1.45226e10i	−0.761906	−	0.277311i	−0.0682990	−	0.997665i	$-0.521757\pi$
$241$	−3.99005e10	−	1.45226e10i	−0.761906	−	0.277311i	−0.693607	+	0.720354i	$0.743979\pi$
$242$	3.73428e10	+	3.13343e10i	0.699903	+	0.587288i
$243$	9.01607e9	−	5.11327e10i	0.165878	−	0.940741i
$244$	−6.89885e9	+	3.91253e10i	−0.124601	+	0.706649i
$245$	−8.64262e9	−	1.49695e10i	−0.153249	−	0.265435i
$246$	1.00760e8	−	8.45480e7i	0.00175421	−	0.00147196i
$247$	2.61131e10	−	9.50439e9i	0.446398	−	0.162475i
$248$	1.35013e10	−	2.33849e10i	0.226643	−	0.392557i
$249$	−7.47851e9	−	1.29532e10i	−0.123287	−	0.213540i
$250$	−9.08857e9	−	7.62622e9i	−0.147152	−	0.123475i
$251$	4.86605e10	−	8.42824e10i	0.773828	−	1.34031i	−0.161622	−	0.986853i	$-0.551673\pi$
$251$	4.86605e10	−	8.42824e10i	0.773828	−	1.34031i	0.935451	−	0.353457i	$-0.114994\pi$
$252$	−1.17832e10	−	6.68257e10i	−0.184060	−	1.04386i
$253$	−5.71949e10			−0.877637
$254$	5.89559e9	+	3.34356e10i	0.0888742	+	0.504030i
$255$	−5.02121e8	+	4.21330e8i	−0.00743666	+	0.00624010i
$256$	1.03037e9	+	3.75024e8i	0.0149938	+	0.00545731i
$257$	8.09999e10	−	2.94816e10i	1.15821	−	0.421552i	0.309749	−	0.950818i	$-0.399755\pi$
$257$	8.09999e10	−	2.94816e10i	1.15821	−	0.421552i	0.848456	+	0.529266i	$0.177533\pi$
$258$	7.07001e9			0.0993416
$259$	8.95859e10	+	5.33797e10i	1.23706	+	0.737101i
$260$	−6.44981e9			−0.0875320
$261$	4.97344e9	−	1.81019e9i	0.0663399	−	0.0241458i
$262$	3.01571e9	+	1.09763e9i	0.0395397	+	0.0143913i
$263$	−4.64246e10	+	3.89549e10i	−0.598339	+	0.502066i	−0.890911	−	0.454178i	$-0.849933\pi$
$263$	−4.64246e10	+	3.89549e10i	−0.598339	+	0.502066i	0.292572	+	0.956243i	$0.405489\pi$
$264$	−6.86675e9	−	3.89433e10i	−0.0870029	−	0.493418i
$265$	−1.18328e10			−0.147394
$266$	9.73004e9	+	5.51818e10i	0.119165	+	0.675816i
$267$	−1.92409e10	+	3.33262e10i	−0.231699	+	0.401315i
$268$	4.14145e10	+	3.47509e10i	0.490395	+	0.411490i
$269$	8.09609e10	+	1.40228e11i	0.942736	+	1.63287i	0.760223	+	0.649662i	$0.225090\pi$
$269$	8.09609e10	+	1.40228e11i	0.942736	+	1.63287i	0.182513	+	0.983203i	$0.441577\pi$
$270$	3.22320e9	−	5.58275e9i	0.0369106	−	0.0639310i
$271$	−9.69044e10	+	3.52703e10i	−1.09139	+	0.397235i	−0.824137	−	0.566390i	$-0.808340\pi$
$271$	−9.69044e10	+	3.52703e10i	−1.09139	+	0.397235i	−0.267257	+	0.963625i	$0.586117\pi$
$272$	−3.79041e9	+	3.18054e9i	−0.0419881	+	0.0352322i
$273$	9.26069e9	+	1.60400e10i	0.100905	+	0.174772i
$274$	9.54270e9	−	5.41193e10i	0.102281	−	0.580063i
$275$	−2.87210e10	+	1.62885e11i	−0.302833	+	1.71745i
$276$	1.19998e10	+	1.00690e10i	0.124475	+	0.104447i
$277$	−2.48843e10	−	9.05713e9i	−0.253960	−	0.0924340i	0.211903	−	0.977291i	$-0.432034\pi$
$277$	−2.48843e10	−	9.05713e9i	−0.253960	−	0.0924340i	−0.465863	+	0.884857i	$0.654256\pi$
$278$	−6.44993e10	−	2.34758e10i	−0.647669	−	0.235732i
$279$	−4.48061e10	−	3.75968e10i	−0.442709	−	0.371477i
$280$	4.83345e9	−	2.74119e10i	0.0469944	−	0.266519i
$281$	1.06000e10	−	6.01157e10i	0.101421	−	0.575188i	−0.891168	−	0.453673i	$-0.850114\pi$
$281$	1.06000e10	−	6.01157e10i	0.101421	−	0.575188i	0.992590	−	0.121515i	$-0.0387753\pi$
$282$	2.16400e9	+	3.74816e9i	0.0203768	+	0.0352937i
$283$	7.36925e10	−	6.18354e10i	0.682943	−	0.573057i	−0.233922	−	0.972255i	$-0.575156\pi$
$283$	7.36925e10	−	6.18354e10i	0.682943	−	0.573057i	0.916865	+	0.399198i	$0.130711\pi$
$284$	4.42599e10	−	1.61093e10i	0.403718	−	0.146941i
$285$	8.65864e9	−	1.49972e10i	0.0777406	−	0.134651i
$286$	−1.31719e10	−	2.28145e10i	−0.116413	−	0.201634i
$287$	−2.06522e9	−	1.73292e9i	−0.0179679	−	0.0150769i
$288$	4.33586e10	−	7.50992e10i	0.371372	−	0.643234i
$289$	−2.04444e10	−	1.15946e11i	−0.172398	−	0.977720i
$290$	1.01438e9			0.00842185
$291$	−1.54471e10	−	8.76047e10i	−0.126278	−	0.716158i
$292$	−8.50242e10	+	7.13438e10i	−0.684415	+	0.574293i
$293$	9.49737e10	+	3.45676e10i	0.752834	+	0.274009i	0.689798	−	0.724002i	$-0.257699\pi$
$293$	9.49737e10	+	3.45676e10i	0.752834	+	0.274009i	0.0630360	+	0.998011i	$0.479922\pi$
$294$	−1.81700e10	+	6.61335e9i	−0.141838	+	0.0516248i
$295$	5.47726e10			0.421080
$296$	2.86101e10	+	8.21044e10i	0.216624	+	0.621661i
$297$	−1.87710e11			−1.39986
$298$	−5.99721e10	+	2.18280e10i	−0.440530	+	0.160340i
$299$	2.09880e10	+	7.63902e9i	0.151863	+	0.0552735i
$300$	3.47013e10	−	2.91178e10i	0.247343	−	0.207545i
$301$	−2.51632e10	−	1.42708e11i	−0.176692	−	1.00207i
$302$	−2.42237e10			−0.167575
$303$	−1.25615e10	−	7.12398e10i	−0.0856149	−	0.485546i
$304$	6.53623e10	−	1.13211e11i	0.438931	−	0.760251i
$305$	2.70417e10	+	2.26907e10i	0.178931	+	0.150141i
$306$	−1.91516e9	−	3.31715e9i	−0.0124870	−	0.0216281i
$307$	−2.86520e10	+	4.96267e10i	−0.184091	+	0.318855i	−0.943270	−	0.332027i	$-0.892267\pi$
$307$	−2.86520e10	+	4.96267e10i	−0.184091	+	0.318855i	0.759179	+	0.650882i	$0.225601\pi$
$308$	−3.55856e11	+	1.29521e11i	−2.25318	+	0.820092i
$309$	−6.43567e10	+	5.40017e10i	−0.401588	+	0.336972i
$310$	−5.60506e9	−	9.70825e9i	−0.0344709	−	0.0597054i
$311$	6.74760e8	−	3.82675e9i	0.00409004	−	0.0231958i	−0.982694	−	0.185234i	$-0.940696\pi$
$311$	6.74760e8	−	3.82675e9i	0.00409004	−	0.0231958i	0.986784	+	0.162038i	$0.0518068\pi$
$312$	−2.68151e9	+	1.52076e10i	−0.0160208	+	0.0908585i
$313$	−8.88275e10	−	7.45351e10i	−0.523116	−	0.438946i	0.342601	−	0.939481i	$-0.388692\pi$
$313$	−8.88275e10	−	7.45351e10i	−0.523116	−	0.438946i	−0.865716	+	0.500535i	$0.833137\pi$
$314$	−2.76018e10	−	1.00462e10i	−0.160234	−	0.0583203i
$315$	−5.66568e10	−	2.06214e10i	−0.324231	−	0.118010i
$316$	7.69883e10	+	6.46009e10i	0.434343	+	0.364457i
$317$	−1.06388e10	+	6.03357e10i	−0.0591734	+	0.335589i	−0.999995	−	0.00331463i	$-0.998945\pi$
$317$	−1.06388e10	+	6.03357e10i	−0.0591734	+	0.335589i	0.940821	+	0.338904i	$0.110056\pi$
$318$	−2.29853e9	+	1.30356e10i	−0.0126046	+	0.0714842i
$319$	−1.47686e10	−	2.55799e10i	−0.0798510	−	0.138306i
$320$	−1.37712e10	+	1.15554e10i	−0.0734171	+	0.0616043i
$321$	5.32989e10	−	1.93992e10i	0.280186	−	0.101979i
$322$	−2.25179e10	+	3.90021e10i	−0.116728	+	0.202179i
$323$	−1.12744e10	−	1.95279e10i	−0.0576346	−	0.0998260i
$324$	−7.24659e10	−	6.08061e10i	−0.365327	−	0.306545i
$325$	3.22945e10	−	5.59357e10i	0.160566	−	0.278108i
$326$	−2.13035e9	−	1.20818e10i	−0.0104465	−	0.0592451i
$327$	−2.16710e10			−0.104813
$328$	−3.90318e8	−	2.21360e9i	−0.00186203	−	0.0105601i
$329$	6.79544e10	−	5.70205e10i	0.319769	−	0.268318i
$330$	−1.54267e10	−	5.61485e9i	−0.0716077	−	0.0260631i
$331$	2.79439e11	−	1.01707e11i	1.27956	−	0.465722i	0.389274	−	0.921122i	$-0.372726\pi$
$331$	2.79439e11	−	1.01707e11i	1.27956	−	0.465722i	0.890287	+	0.455400i	$0.150504\pi$
$332$	−1.19423e11			−0.539471
$333$	1.85906e11	−	3.01482e10i	0.828502	−	0.134358i
$334$	−1.16911e11			−0.514041
$335$	4.51397e10	−	1.64295e10i	0.195820	−	0.0712726i
$336$	8.18737e10	+	2.97996e10i	0.350443	+	0.127551i
$337$	−9.06063e10	+	7.60277e10i	−0.382670	+	0.321098i	−0.813749	−	0.581216i	$-0.802577\pi$
$337$	−9.06063e10	+	7.60277e10i	−0.382670	+	0.321098i	0.431080	+	0.902314i	$0.358133\pi$
$338$	−1.28277e10	−	7.27497e10i	−0.0534595	−	0.303184i
$339$	1.27279e11			0.523428
$340$	9.08802e8	+	5.15407e9i	0.00368820	+	0.0209168i
$341$	−1.63211e11	+	2.82690e11i	−0.653666	+	1.13218i
$342$	7.75199e10	+	6.50469e10i	0.306405	+	0.257104i
$343$	1.35906e10	+	2.35397e10i	0.0530172	+	0.0918284i
$344$	6.04091e10	−	1.04632e11i	0.232589	−	0.402856i
$345$	1.30791e10	−	4.76041e9i	0.0497042	−	0.0180908i
$346$	7.82612e9	−	6.56689e9i	0.0293565	−	0.0246330i
$347$	−1.67895e11	−	2.90803e11i	−0.621664	−	1.07675i	−0.989176	−	0.146735i	$-0.953124\pi$
$347$	−1.67895e11	−	2.90803e11i	−0.621664	−	1.07675i	0.367512	−	0.930019i	$-0.380210\pi$
$348$	−1.40475e9	+	7.96676e9i	−0.00513445	+	0.0291189i
$349$	−4.08633e10	+	2.31747e11i	−0.147441	+	0.836181i	0.817933	+	0.575313i	$0.195120\pi$
$349$	−4.08633e10	+	2.31747e11i	−0.147441	+	0.836181i	−0.965374	+	0.260868i	$0.915991\pi$
$350$	9.97664e10	+	8.37140e10i	0.355368	+	0.298189i
$351$	6.88814e10	+	2.50708e10i	0.242226	+	0.0881629i
$352$	−4.54766e11	−	1.65521e11i	−1.57887	−	0.574661i
$353$	3.09184e11	+	2.59436e11i	1.05982	+	0.889291i	0.994091	−	0.108547i	$-0.0346197\pi$
$353$	3.09184e11	+	2.59436e11i	1.05982	+	0.889291i	0.0657246	+	0.997838i	$0.479064\pi$
$354$	1.06397e10	−	6.03406e10i	0.0360092	−	0.204218i
$355$	7.26722e9	−	4.12145e10i	0.0242852	−	0.137728i
$356$	1.53628e11	+	2.66091e11i	0.506926	+	0.878022i
$357$	1.15128e10	−	9.66035e9i	0.0375122	−	0.0314765i
$358$	−2.10376e10	+	7.65705e9i	−0.0676896	+	0.0246370i
$359$	1.97134e11	−	3.41446e11i	0.626378	−	1.08492i	−0.361895	−	0.932219i	$-0.617870\pi$
$359$	1.97134e11	−	3.41446e11i	0.626378	−	1.08492i	0.988273	−	0.152699i	$-0.0487967\pi$
$360$	−2.51346e10	−	4.35344e10i	−0.0788698	−	0.136607i
$361$	2.09162e11	+	1.75508e11i	0.648188	+	0.543894i
$362$	−3.37411e10	+	5.84413e10i	−0.103269	+	0.178868i
$363$	5.99831e10	+	3.40181e11i	0.181321	+	1.02832i
$364$	1.47883e11			0.441531
$365$	1.71251e10	+	9.71212e10i	0.0505028	+	0.286415i
$366$	3.02502e10	−	2.53830e10i	0.0881179	−	0.0739397i
$367$	6.11812e11	+	2.22681e11i	1.76044	+	0.640747i	0.999963	−	0.00862095i	$-0.00274417\pi$
$367$	6.11812e11	+	2.22681e11i	1.76044	+	0.640747i	0.760475	+	0.649368i	$0.224966\pi$
$368$	9.87317e10	−	3.59354e10i	0.280635	−	0.102143i
$369$	−4.86886e9			−0.0136712
$370$	3.54578e10	+	6.75662e9i	0.0983568	+	0.0187422i
$371$	2.71305e11			0.743489
$372$	8.40094e10	−	3.05769e10i	0.227449	−	0.0827848i
$373$	−2.36330e11	−	8.60170e10i	−0.632162	−	0.230088i	0.00600990	−	0.999982i	$-0.498087\pi$
$373$	−2.36330e11	−	8.60170e10i	−0.632162	−	0.230088i	−0.638172	+	0.769894i	$0.720309\pi$
$374$	−1.63752e10	+	1.37404e10i	−0.0432776	+	0.0363142i
$375$	−1.45988e10	−	8.27940e10i	−0.0381221	−	0.216201i
$376$	7.39605e10			0.190833
$377$	2.00294e9	+	1.13592e10i	0.00510659	+	0.0289609i
$378$	−7.39023e10	+	1.28003e11i	−0.186185	+	0.322482i
$379$	−3.49039e11	−	2.92879e11i	−0.868956	−	0.729141i	0.0949222	−	0.995485i	$-0.469740\pi$
$379$	−3.49039e11	−	2.92879e11i	−0.868956	−	0.729141i	−0.963878	+	0.266344i	$0.914184\pi$
$380$	−6.91343e10	−	1.19744e11i	−0.170086	−	0.294597i
$381$	−1.20291e11	+	2.08350e11i	−0.292463	+	0.506560i
$382$	2.12063e11	−	7.71846e10i	0.509542	−	0.185458i
$383$	4.35644e11	−	3.65548e11i	1.03452	−	0.868061i	0.0431340	−	0.999069i	$-0.486266\pi$
$383$	4.35644e11	−	3.65548e11i	1.03452	−	0.868061i	0.991381	+	0.131008i	$0.0418213\pi$
$384$	8.56236e10	+	1.48304e11i	0.200957	+	0.348067i
$385$	−5.84296e10	+	3.31371e11i	−0.135538	+	0.768672i
$386$	3.36250e10	−	1.90697e11i	0.0770937	−	0.437220i
$387$	−2.00477e11	−	1.68220e11i	−0.454324	−	0.381223i
$388$	−6.67430e11	−	2.42925e11i	−1.49508	−	0.544163i
$389$	7.84368e11	+	2.85487e11i	1.73679	+	0.632139i	0.999076	−	0.0429774i	$-0.0136843\pi$
$389$	7.84368e11	+	2.85487e11i	1.73679	+	0.632139i	0.737711	+	0.675116i	$0.235907\pi$
$390$	4.91099e9	+	4.12081e9i	0.0107493	+	0.00901970i
$391$	3.14708e9	−	1.78480e10i	0.00680946	−	0.0386184i
$392$	−5.73789e10	+	3.25412e11i	−0.122734	+	0.696060i
$393$	1.13705e10	+	1.96943e10i	0.0240443	+	0.0416460i
$394$	−1.24273e11	+	1.04278e11i	−0.259803	+	0.218001i
$395$	8.39133e10	−	3.05419e10i	0.173438	−	0.0631262i
$396$	−3.41959e11	+	5.92290e11i	−0.698788	+	1.21034i
$397$	−1.04991e11	−	1.81851e11i	−0.212127	−	0.367415i	0.740253	−	0.672329i	$-0.234706\pi$
$397$	−1.04991e11	−	1.81851e11i	−0.212127	−	0.367415i	−0.952380	+	0.304913i	$0.901372\pi$
$398$	1.99844e11	+	1.67689e11i	0.399225	+	0.334990i
$399$	−1.98527e11	+	3.43859e11i	−0.392141	+	0.679208i
$400$	−5.27611e10	−	2.99223e11i	−0.103049	−	0.584420i
$401$	−7.28623e11			−1.40719			−0.703596	−	0.710601i	$-0.748423\pi$
$401$	−7.28623e11			−1.40719			−0.703596	+	0.710601i	$0.748423\pi$
$402$	−9.33119e9	−	5.29198e10i	−0.0178205	−	0.101065i
$403$	9.76479e10	−	8.19363e10i	0.184412	−	0.154740i
$404$	−5.42751e11	−	1.97545e11i	−1.01364	−	0.368936i
$405$	−7.89841e10	+	2.87479e10i	−0.145879	+	0.0530955i
$406$	−2.32578e10			−0.0424817
$407$	−3.45856e11	−	9.92526e11i	−0.624770	−	1.79295i
$408$	1.25303e10			0.0223867
$409$	4.45501e11	−	1.62149e11i	0.787215	−	0.286523i	0.0830373	−	0.996546i	$-0.473538\pi$
$409$	4.45501e11	−	1.62149e11i	0.787215	−	0.286523i	0.704178	+	0.710024i	$0.251316\pi$
$410$	−8.76879e8	−	3.19158e8i	−0.00153254	−	0.000557800i
$411$	2.98305e11	−	2.50308e11i	0.515671	−	0.432699i
$412$	1.16481e11	+	6.60595e11i	0.199167	+	1.12953i
$413$	−1.25584e12			−2.12402
$414$	1.41235e10	+	8.00984e10i	0.0236288	+	0.134005i
$415$	−5.30559e10	+	9.18955e10i	−0.0878045	+	0.152082i
$416$	1.44772e11	+	1.21478e11i	0.237009	+	0.198874i
$417$	−2.43189e11	−	4.21217e11i	−0.393852	−	0.682171i
$418$	2.82375e11	−	4.89088e11i	0.452411	−	0.783599i
$419$	7.03303e11	−	2.55981e11i	1.11475	−	0.405738i	0.282019	−	0.959409i	$-0.408996\pi$
$419$	7.03303e11	−	2.55981e11i	1.11475	−	0.405738i	0.832735	+	0.553671i	$0.186774\pi$
$420$	7.05958e10	−	5.92369e10i	0.110702	−	0.0928903i
$421$	−3.64981e11	−	6.32165e11i	−0.566240	−	0.980756i	−0.996933	−	0.0782576i	$-0.975064\pi$
$421$	−3.64981e11	−	6.32165e11i	−0.566240	−	0.980756i	0.430694	−	0.902498i	$-0.358269\pi$
$422$	4.19826e10	−	2.38095e11i	0.0644411	−	0.365464i
$423$	2.78195e10	−	1.57772e11i	0.0422490	−	0.239606i
$424$	1.73280e11	+	1.45399e11i	0.260376	+	0.218481i
$425$	−4.92489e10	−	1.79251e10i	−0.0732227	−	0.0266509i
$426$	−4.39925e10	−	1.60120e10i	−0.0647195	−	0.0235560i
$427$	−6.20019e11	−	5.20258e11i	−0.902568	−	0.757344i
$428$	7.86406e10	−	4.45993e11i	0.113279	−	0.642438i
$429$	3.24157e10	−	1.83839e11i	0.0462059	−	0.262047i
$430$	−2.50789e10	−	4.34379e10i	−0.0353753	−	0.0612718i
$431$	−7.57523e11	+	6.35637e11i	−1.05742	+	0.887281i	−0.993854	−	0.110696i	$-0.964692\pi$
$431$	−7.57523e11	+	6.35637e11i	−1.05742	+	0.887281i	−0.0635666	+	0.997978i	$0.520248\pi$
$432$	3.24031e11	−	1.17938e11i	0.447621	−	0.162921i
$433$	−3.99534e11	+	6.92013e11i	−0.546208	+	0.946060i	0.452322	+	0.891855i	$0.350596\pi$
$433$	−3.99534e11	+	6.92013e11i	−0.546208	+	0.946060i	−0.998530	+	0.0542049i	$0.982738\pi$
$434$	1.28514e11	+	2.22593e11i	0.173879	+	0.301167i
$435$	5.50628e9	+	4.62032e9i	0.00737321	+	0.00618686i
$436$	−8.65154e10	+	1.49849e11i	−0.114658	+	0.198593i
$437$	8.31444e10	+	4.71535e11i	0.109060	+	0.618511i
$438$	1.10321e11			0.143227
$439$	1.43255e11	+	8.12438e11i	0.184085	+	1.04400i	0.927125	+	0.374752i	$0.122272\pi$
$439$	1.43255e11	+	8.12438e11i	0.184085	+	1.04400i	−0.743040	+	0.669247i	$0.766617\pi$
$440$	−2.14908e11	+	1.80329e11i	−0.273348	+	0.229366i
$441$	6.72584e11	+	2.44801e11i	0.846785	+	0.308204i
$442$	7.84415e9	−	2.85504e9i	0.00977565	−	0.00355805i
$443$	−4.26397e11			−0.526014			−0.263007	−	0.964794i	$-0.584714\pi$
$443$	−4.26397e11			−0.526014			−0.263007	+	0.964794i	$0.584714\pi$
$444$	−1.02169e11	+	2.69124e11i	−0.124766	+	0.328646i
$445$	2.73007e11			0.330030
$446$	−1.23887e11	+	4.50912e10i	−0.148258	+	0.0539616i
$447$	−4.24967e11	−	1.54675e11i	−0.503467	−	0.183247i
$448$	3.15750e11	−	2.64945e11i	0.370333	−	0.310746i
$449$	1.38188e11	+	7.83700e11i	0.160458	+	0.910000i	0.953625	+	0.300997i	$0.0973194\pi$
$449$	1.38188e11	+	7.83700e11i	0.160458	+	0.910000i	−0.793168	+	0.609004i	$0.791570\pi$
$450$	2.35204e11			0.270389
$451$	4.71839e9	+	2.67593e10i	0.00537031	+	0.0304566i
$452$	5.08124e11	−	8.80097e11i	0.572594	−	0.991762i
$453$	−1.31492e11	−	1.10335e11i	−0.146710	−	0.123104i
$454$	−3.77328e10	−	6.53551e10i	−0.0416838	−	0.0721985i
$455$	6.56994e10	−	1.13795e11i	0.0718638	−	0.124472i
$456$	−3.11080e11	+	1.13224e11i	−0.336923	+	0.122630i
$457$	−1.74139e11	+	1.46120e11i	−0.186755	+	0.156706i	−0.731372	−	0.681979i	$-0.761120\pi$
$457$	−1.74139e11	+	1.46120e11i	−0.186755	+	0.156706i	0.544617	+	0.838685i	$0.316675\pi$
$458$	−6.77773e10	−	1.17394e11i	−0.0719763	−	0.124667i
$459$	1.03285e10	−	5.85760e10i	0.0108613	−	0.0615974i
$460$	1.92978e10	−	1.09443e11i	0.0200954	−	0.113967i
$461$	−6.56806e11	−	5.51126e11i	−0.677303	−	0.568324i	0.237914	−	0.971286i	$-0.423536\pi$
$461$	−6.56806e11	−	5.51126e11i	−0.677303	−	0.568324i	−0.915217	+	0.402962i	$0.867981\pi$
$462$	3.53707e11	+	1.28739e11i	0.361205	+	0.131468i
$463$	1.56037e12	+	5.67928e11i	1.57802	+	0.574353i	0.974773	−	0.223201i	$-0.0716505\pi$
$463$	1.56037e12	+	5.67928e11i	1.57802	+	0.574353i	0.603248	+	0.797553i	$0.293873\pi$
$464$	4.15658e10	+	3.48779e10i	0.0416299	+	0.0349316i
$465$	1.37939e10	−	7.82290e10i	0.0136820	−	0.0775942i
$466$	6.91421e10	−	3.92124e11i	0.0679213	−	0.385201i
$467$	−2.23214e11	−	3.86617e11i	−0.217168	−	0.376145i	0.736773	−	0.676140i	$-0.236348\pi$
$467$	−2.23214e11	−	3.86617e11i	−0.217168	−	0.376145i	−0.953941	+	0.299995i	$0.903015\pi$
$468$	2.04591e11	−	1.71672e11i	0.197142	−	0.165422i
$469$	−1.03497e12	+	3.76699e11i	−0.987760	+	0.359515i
$470$	1.53524e10	−	2.65911e10i	0.0145123	−	0.0251360i
$471$	−1.04070e11	−	1.80255e11i	−0.0974392	−	0.168770i
$472$	−8.02092e11	−	6.73035e11i	−0.743850	−	0.624164i
$473$	−7.30261e11	+	1.26485e12i	−0.670815	+	1.16189i
$474$	−1.73464e10	−	9.83763e10i	−0.0157836	−	0.0895134i
$475$	1.38463e12			1.24800
$476$	−2.08372e10	−	1.18174e11i	−0.0186041	−	0.105509i
$477$	3.75341e11	−	3.14948e11i	0.331966	−	0.278552i
$478$	−5.47940e11	−	1.99434e11i	−0.480074	−	0.174732i
$479$	5.33793e11	−	1.94285e11i	0.463301	−	0.168628i	−0.0998146	−	0.995006i	$-0.531825\pi$
$479$	5.33793e11	−	1.94285e11i	0.463301	−	0.168628i	0.563115	+	0.826378i	$0.309603\pi$
$480$	1.17771e11			0.101263
$481$	−5.64894e9	+	4.10407e11i	−0.00481187	+	0.349592i
$482$	3.36980e11			0.284376
$483$	−2.99881e11	+	1.09148e11i	−0.250719	+	0.0912543i
$484$	2.59172e12	+	9.43310e11i	2.14676	+	0.781358i
$485$	−4.83446e11	+	4.05660e11i	−0.396744	+	0.332908i
$486$	7.15533e10	+	4.05799e11i	0.0581790	+	0.329950i
$487$	−1.34480e11			−0.108337			−0.0541686	−	0.998532i	$-0.517251\pi$
$487$	−1.34480e11			−0.108337			−0.0541686	+	0.998532i	$0.517251\pi$
$488$	−1.17181e11	−	6.64567e11i	−0.0935338	−	0.530457i
$489$	4.34666e10	−	7.52864e10i	0.0343769	−	0.0595425i
$490$	1.05085e11	+	8.81770e10i	0.0823492	+	0.0690992i
$491$	−4.27322e11	−	7.40143e11i	−0.331809	−	0.574710i	0.651058	−	0.759028i	$-0.274326\pi$
$491$	−4.27322e11	−	7.40143e11i	−0.331809	−	0.574710i	−0.982867	+	0.184318i	$0.940992\pi$
$492$	3.72097e9	−	6.44490e9i	0.00286294	−	0.00495876i
$493$	8.79498e9	−	3.20111e9i	0.00670539	−	0.00244056i
$494$	−1.68942e11	+	1.41760e11i	−0.127634	+	0.107098i
$495$	3.03842e11	+	5.26270e11i	0.227470	+	0.393990i
$496$	1.04127e11	−	5.90535e11i	0.0772497	−	0.438105i
$497$	−1.66625e11	+	9.44975e11i	−0.122500	+	0.694731i
$498$	9.09309e10	+	7.63001e10i	0.0662491	+	0.0555896i
$499$	1.45220e12	+	5.28556e11i	1.04851	+	0.381627i	0.808101	−	0.589045i	$-0.200496\pi$
$499$	1.45220e12	+	5.28556e11i	1.04851	+	0.381627i	0.240410	+	0.970671i	$0.422718\pi$
$500$	−6.30779e11	−	2.29585e11i	−0.451349	−	0.164278i
$501$	−6.34625e11	−	5.32513e11i	−0.450036	−	0.377625i
$502$	−1.34119e11	+	7.60625e11i	−0.0942589	+	0.534569i
$503$	3.38495e11	−	1.91970e12i	0.235774	−	1.33714i	−0.605202	−	0.796072i	$-0.706908\pi$
$503$	3.38495e11	−	1.91970e12i	0.235774	−	1.33714i	0.840977	−	0.541071i	$-0.181981\pi$
$504$	5.76292e11	+	9.98168e11i	0.397837	+	0.689074i
$505$	−3.93136e11	+	3.29881e11i	−0.268987	+	0.225707i
$506$	4.26536e11	−	1.55246e11i	0.289253	−	0.105280i
$507$	2.61731e11	−	4.53332e11i	0.175922	−	0.304705i
$508$	9.60455e11	+	1.66356e12i	0.639868	+	1.10828i
$509$	2.56573e11	+	2.15290e11i	0.169426	+	0.142166i	0.723558	−	0.690263i	$-0.242505\pi$
$509$	2.56573e11	+	2.15290e11i	0.169426	+	0.142166i	−0.554132	+	0.832429i	$0.686950\pi$
$510$	2.60098e9	−	4.50503e9i	0.00170244	−	0.00294871i
$511$	−3.92648e11	−	2.22682e12i	−0.254747	−	1.44474i
$512$	1.55040e12			0.997078
$513$	2.72875e11	+	1.54755e12i	0.173954	+	0.986544i
$514$	−5.24041e11	+	4.39723e11i	−0.331155	+	0.277872i
$515$	5.60072e11	+	2.03850e11i	0.350842	+	0.127696i
$516$	3.75886e11	−	1.36811e11i	0.233417	−	0.0849567i
$517$	−8.94078e11			−0.550387
$518$	−8.12985e11	−	1.54917e11i	−0.496134	−	0.0945401i
$519$	7.23933e10			0.0437971
$520$	1.02947e11	−	3.74696e10i	0.0617446	−	0.0224732i
$521$	−1.66497e11	−	6.06000e10i	−0.0990005	−	0.0360332i	0.292045	−	0.956405i	$-0.405664\pi$
$521$	−1.66497e11	−	6.06000e10i	−0.0990005	−	0.0360332i	−0.391046	+	0.920371i	$0.627887\pi$
$522$	−3.21764e10	+	2.69992e10i	−0.0189680	+	0.0159160i
$523$	1.93969e11	+	1.10005e12i	0.113364	+	0.642917i	0.987547	+	0.157322i	$0.0502860\pi$
$523$	1.93969e11	+	1.10005e12i	0.113364	+	0.642917i	−0.874184	+	0.485595i	$0.838603\pi$
$524$	1.81574e11			0.105211
$525$	1.60253e11	+	9.08840e11i	0.0920639	+	0.522120i
$526$	2.40479e11	−	4.16521e11i	0.136975	−	0.237247i
$527$	−7.92346e10	−	6.64857e10i	−0.0447473	−	0.0375475i
$528$	−4.39077e11	−	7.60503e11i	−0.245860	−	0.425842i
$529$	7.08158e11	−	1.22657e12i	0.393169	−	0.680989i
$530$	8.82439e10	−	3.21182e10i	0.0485784	−	0.0176811i
$531$	−1.73741e12	+	1.45786e12i	−0.948369	+	0.795776i
$532$	1.58513e12	+	2.74552e12i	0.857950	+	1.48601i
$533$	1.84257e9	−	1.04497e10i	0.000988895	−	0.00560830i
$534$	5.30320e10	−	3.00760e11i	0.0282230	−	0.160060i
$535$	−3.08251e11	−	2.58654e11i	−0.162672	−	0.136498i
$536$	−8.62910e11	−	3.14073e11i	−0.451569	−	0.164358i
$537$	−1.49074e11	−	5.42584e10i	−0.0773601	−	0.0281568i
$538$	−9.84400e11	−	8.26010e11i	−0.506584	−	0.425074i
$539$	6.93630e11	−	3.93377e12i	0.353980	−	2.00752i
$540$	6.33341e10	−	3.59186e11i	0.0320528	−	0.181780i
$541$	5.06978e11	+	8.78111e11i	0.254449	+	0.440719i	0.964746	−	0.263184i	$-0.0847725\pi$
$541$	5.06978e11	+	8.78111e11i	0.254449	+	0.440719i	−0.710297	+	0.703903i	$0.751439\pi$
$542$	6.26938e11	−	5.26063e11i	0.312052	−	0.261843i
$543$	−4.49346e11	+	1.63549e11i	−0.221810	+	0.0807324i
$544$	7.66748e10	−	1.32805e11i	0.0375368	−	0.0650157i
$545$	7.68718e10	+	1.33146e11i	0.0373236	+	0.0646463i
$546$	−1.12600e11	−	9.44830e10i	−0.0542217	−	0.0454974i
$547$	−1.09868e12	+	1.90297e12i	−0.524720	+	0.908841i	0.474866	+	0.880058i	$0.342497\pi$
$547$	−1.09868e12	+	1.90297e12i	−0.524720	+	0.908841i	−0.999586	+	0.0287833i	$0.990837\pi$
$548$	−5.39910e11	−	3.06198e12i	−0.255746	−	1.45041i
$549$	−1.46173e12			−0.686737
$550$	−2.27936e11	−	1.29269e12i	−0.106214	−	0.602367i
$551$	−1.89421e11	+	1.58943e11i	−0.0875479	+	0.0734614i
$552$	−2.50026e11	−	9.10021e10i	−0.114620	−	0.0417182i
$553$	−1.92398e12	+	7.00273e11i	−0.874859	+	0.318423i
$554$	2.10161e11			0.0947890
$555$	1.61698e11	+	1.98181e11i	0.0723415	+	0.0886634i
$556$	−3.88346e12			−1.72339
$557$	−3.12904e12	+	1.13888e12i	−1.37741	+	0.501336i	−0.921392	−	0.388635i	$-0.872947\pi$
$557$	−3.12904e12	+	1.13888e12i	−1.37741	+	0.501336i	−0.456018	+	0.889971i	$0.650725\pi$
$558$	4.36196e11	+	1.58762e11i	0.190471	+	0.0693256i
$559$	4.36909e11	−	3.66610e11i	0.189251	−	0.158800i
$560$	−1.07336e11	−	6.08735e11i	−0.0461212	−	0.261566i
$561$	−1.51474e11			−0.0645661
$562$	8.41239e10	+	4.77090e11i	0.0355718	+	0.201738i
$563$	1.05687e12	−	1.83055e12i	0.443336	−	0.767881i	−0.554599	−	0.832118i	$-0.687128\pi$
$563$	1.05687e12	−	1.83055e12i	0.443336	−	0.767881i	0.997935	+	0.0642374i	$0.0204615\pi$
$564$	1.87582e11	+	1.57400e11i	0.0780612	+	0.0655011i
$565$	−4.51486e11	−	7.81996e11i	−0.186391	−	0.322839i
$566$	−3.81726e11	+	6.61169e11i	−0.156343	+	0.270794i
$567$	1.81097e12	−	6.59138e11i	0.735845	−	0.267826i
$568$	−6.12857e11	+	5.14248e11i	−0.247054	+	0.207303i
$569$	3.21328e11	+	5.56557e11i	0.128512	+	0.222589i	0.923100	−	0.384559i	$-0.125647\pi$
$569$	3.21328e11	+	5.56557e11i	0.128512	+	0.222589i	−0.794588	+	0.607149i	$0.792313\pi$
$570$	−2.38650e10	+	1.35345e11i	−0.00946947	+	0.0537040i
$571$	−1.01346e11	+	5.74763e11i	−0.0398975	+	0.226270i	−0.998236	−	0.0593636i	$-0.981093\pi$
$571$	−1.01346e11	+	5.74763e11i	−0.0398975	+	0.226270i	0.958339	+	0.285633i	$0.0922040\pi$
$572$	−1.14178e12	−	9.58069e11i	−0.445965	−	0.374209i
$573$	1.50269e12	+	5.46936e11i	0.582338	+	0.211954i
$574$	2.01053e10	+	7.31773e9i	0.00773049	+	0.00281367i
$575$	8.52516e11	+	7.15346e11i	0.325235	+	0.272905i
$576$	1.29263e11	−	7.33086e11i	0.0489297	−	0.277494i
$577$	−6.71708e11	+	3.80945e12i	−0.252284	+	1.43077i	0.550666	+	0.834726i	$0.314374\pi$
$577$	−6.71708e11	+	3.80945e12i	−0.252284	+	1.43077i	−0.802949	+	0.596047i	$0.796737\pi$
$578$	4.67182e11	+	8.09183e11i	0.174105	+	0.301558i
$579$	1.05112e12	−	8.81992e11i	0.388685	−	0.326145i
$580$	5.39305e10	−	1.96291e10i	0.0197883	−	0.00720235i
$581$	1.21648e12	−	2.10700e12i	0.442906	−	0.767136i
$582$	3.52987e11	+	6.11391e11i	0.127528	+	0.220885i
$583$	−2.09471e12	−	1.75767e12i	−0.750956	−	0.630127i
$584$	9.42627e11	−	1.63268e12i	0.335337	−	0.580821i
$585$	−4.12075e10	−	2.33700e11i	−0.0145471	−	0.0825005i
$586$	−8.02103e11			−0.280990
$587$	−8.11547e11	−	4.60251e12i	−0.282126	−	1.60001i	−0.715376	−	0.698740i	$-0.753745\pi$
$587$	−8.11547e11	−	4.60251e12i	−0.282126	−	1.60001i	0.433250	−	0.901274i	$-0.357367\pi$
$588$	−8.38057e11	+	7.03213e11i	−0.289118	+	0.242599i
$589$	2.56786e12	+	9.34625e11i	0.879129	+	0.319977i
$590$	−4.08472e11	+	1.48672e11i	−0.138780	+	0.0505119i
$591$	−1.14955e12			−0.387601
$592$	1.22063e12	+	1.49603e12i	0.408448	+	0.500602i
$593$	1.67556e11			0.0556435			0.0278217	−	0.999613i	$-0.491143\pi$
$593$	1.67556e11			0.0556435			0.0278217	+	0.999613i	$0.491143\pi$
$594$	1.39986e12	−	5.09509e11i	0.461367	−	0.167924i
$595$	−1.00191e11	−	3.64666e10i	−0.0327720	−	0.0119280i
$596$	−2.76609e12	+	2.32103e12i	−0.897964	+	0.753481i
$597$	3.21007e11	+	1.82052e12i	0.103426	+	0.586558i
$598$	−1.77255e11			−0.0566817
$599$	−8.75572e11	−	4.96562e12i	−0.277889	−	1.57599i	−0.729633	−	0.683839i	$-0.760309\pi$
$599$	−8.75572e11	−	4.96562e12i	−0.277889	−	1.57599i	0.451744	−	0.892147i	$-0.350802\pi$
$600$	−3.84718e11	+	6.66351e11i	−0.121189	+	0.209905i
$601$	−8.46616e11	−	7.10395e11i	−0.264698	−	0.222108i	0.500772	−	0.865579i	$-0.333049\pi$
$601$	−8.46616e11	−	7.10395e11i	−0.264698	−	0.222108i	−0.765471	+	0.643471i	$0.777494\pi$
$602$	5.75015e11	+	9.95954e11i	0.178441	+	0.309069i
$603$	−9.94553e11	+	1.72262e12i	−0.306337	+	0.530592i
$604$	−1.28788e12	+	4.68751e11i	−0.393741	+	0.143310i
$605$	1.87729e12	−	1.57523e12i	0.569681	−	0.478019i
$606$	2.87047e11	+	4.97181e11i	0.0864623	+	0.149757i
$607$	−9.76783e11	+	5.53961e12i	−0.292044	+	1.65627i	0.386933	+	0.922108i	$0.373534\pi$
$607$	−9.76783e11	+	5.53961e12i	−0.292044	+	1.65627i	−0.678978	+	0.734159i	$0.737577\pi$
$608$	−7.03522e11	+	3.98987e12i	−0.208791	+	1.18411i
$609$	−1.26249e11	−	1.05936e11i	−0.0371921	−	0.0312079i
$610$	−2.63256e11	−	9.58175e10i	−0.0769830	−	0.0280195i
$611$	3.28088e11	+	1.19414e11i	0.0952367	+	0.0346633i
$612$	−1.66012e11	−	1.39300e11i	−0.0478362	−	0.0401394i
$613$	2.20781e11	−	1.25211e12i	0.0631523	−	0.358155i	−0.936813	−	0.349830i	$-0.886239\pi$
$613$	2.20781e11	−	1.25211e12i	0.0631523	−	0.358155i	0.999965	−	0.00832419i	$-0.00264970\pi$
$614$	7.89710e10	−	4.47867e11i	0.0224238	−	0.127172i
$615$	−3.30620e9	−	5.72651e9i	−0.000931948	−	0.00161418i
$616$	4.92747e12	−	4.13464e12i	1.37883	−	1.15698i
$617$	1.85262e12	−	6.74299e11i	0.514640	−	0.187313i	−0.0716273	−	0.997431i	$-0.522819\pi$
$617$	1.85262e12	−	6.74299e11i	0.514640	−	0.187313i	0.586267	+	0.810118i	$0.300597\pi$
$618$	3.33367e11	−	5.77408e11i	0.0919336	−	0.159234i
$619$	1.75418e11	+	3.03832e11i	0.0480248	+	0.0831813i	0.889039	−	0.457832i	$-0.151374\pi$
$619$	1.75418e11	+	3.03832e11i	0.0480248	+	0.0831813i	−0.841014	+	0.541014i	$0.818041\pi$
$620$	−4.85864e11	−	4.07688e11i	−0.132054	−	0.110807i
$621$	−6.31504e11	+	1.09380e12i	−0.170398	+	0.295138i
$622$	5.35503e9	+	3.03699e10i	0.00143451	+	0.00813554i
$623$	−6.25957e12			−1.66475
$624$	5.95483e10	+	3.37715e11i	0.0157231	+	0.0891702i
$625$	2.22718e12	−	1.86882e12i	0.583841	−	0.489901i
$626$	8.64753e11	+	3.14744e11i	0.225065	+	0.0819168i
$627$	3.76052e12	−	1.36872e12i	0.971726	−	0.353679i
$628$	−1.66189e12			−0.426367
$629$	3.28754e11	−	5.33137e10i	0.0837419	−	0.0135803i
$630$	4.78496e11			0.121017
$631$	5.71158e12	−	2.07885e12i	1.43425	−	0.522024i	0.496103	−	0.868264i	$-0.334764\pi$
$631$	5.71158e12	−	2.07885e12i	1.43425	−	0.522024i	0.938146	+	0.346240i	$0.112542\pi$
$632$	−1.60412e12	−	5.83853e11i	−0.399955	−	0.145572i
$633$	1.31238e12	−	1.10122e12i	0.324894	−	0.272619i
$634$	−8.44317e10	−	4.78836e11i	−0.0207541	−	0.117702i
$635$	1.70679e12			0.416581
$636$	1.30047e11	+	7.37534e11i	0.0315169	+	0.178741i
$637$	−7.79932e11	+	1.35088e12i	−0.187685	+	0.325080i
$638$	1.79571e11	+	1.50678e11i	0.0429084	+	0.0360044i
$639$	8.66471e11	+	1.50077e12i	0.205589	+	0.356091i
$640$	6.07451e11	−	1.05214e12i	0.143120	−	0.247892i
$641$	6.46966e11	−	2.35476e11i	0.151363	−	0.0550917i	−0.265228	−	0.964186i	$-0.585447\pi$
$641$	6.46966e11	−	2.35476e11i	0.151363	−	0.0550917i	0.416591	+	0.909094i	$0.363225\pi$
$642$	−3.44825e11	+	2.89343e11i	−0.0801109	+	0.0672210i
$643$	−1.26248e12	−	2.18667e12i	−0.291255	−	0.504469i	0.682852	−	0.730557i	$-0.260740\pi$
$643$	−1.26248e12	−	2.18667e12i	−0.291255	−	0.504469i	−0.974107	+	0.226088i	$0.927406\pi$
$644$	−4.42464e11	+	2.50934e12i	−0.101366	+	0.574874i
$645$	6.17183e10	−	3.50022e11i	0.0140409	−	0.0796300i
$646$	1.37085e11	+	1.15028e11i	0.0309702	+	0.0259871i
$647$	3.75386e12	+	1.36629e12i	0.842189	+	0.306532i	0.726851	−	0.686795i	$-0.240983\pi$
$647$	3.75386e12	+	1.36629e12i	0.842189	+	0.306532i	0.115337	+	0.993326i	$0.463205\pi$
$648$	1.50989e12	+	5.49557e11i	0.336402	+	0.122440i
$649$	9.69616e12	+	8.13605e12i	2.14535	+	1.80017i
$650$	−8.90105e10	+	5.04803e11i	−0.0195583	+	0.110921i
$651$	−3.16269e11	+	1.79365e12i	−0.0690149	+	0.391403i
$652$	−3.47056e11	−	6.01119e11i	−0.0752118	−	0.130271i
$653$	−3.66412e12	+	3.07456e12i	−0.788606	+	0.661719i	−0.945400	−	0.325912i	$-0.894329\pi$
$653$	−3.66412e12	+	3.07456e12i	−0.788606	+	0.661719i	0.156794	+	0.987631i	$0.449884\pi$
$654$	1.61613e11	−	5.88225e10i	0.0345444	−	0.0125731i
$655$	8.06673e10	−	1.39720e11i	0.0171243	−	0.0296601i
$656$	−2.49579e10	−	4.32283e10i	−0.00526187	−	0.00911383i
$657$	−3.12825e12	−	2.62492e12i	−0.655025	−	0.549631i
$658$	−3.52003e11	+	6.09687e11i	−0.0732031	+	0.126792i
$659$	1.49787e12	+	8.49484e12i	0.309378	+	1.75457i	0.602145	+	0.798387i	$0.294313\pi$
$659$	1.49787e12	+	8.49484e12i	0.309378	+	1.75457i	−0.292767	+	0.956184i	$0.594576\pi$
$660$	−9.28831e11			−0.190541
$661$	−3.00975e11	−	1.70691e12i	−0.0613230	−	0.347780i	−0.999996	−	0.00297033i	$-0.999055\pi$
$661$	−3.00975e11	−	1.70691e12i	−0.0613230	−	0.347780i	0.938673	−	0.344810i	$-0.112057\pi$
$662$	−1.80787e12	+	1.51699e12i	−0.365853	+	0.306987i
$663$	5.55842e10	+	2.02310e10i	0.0111723	+	0.00406637i
$664$	1.90615e12	−	6.93780e11i	0.380540	−	0.138505i
$665$	2.81688e12			0.558562
$666$	−1.30458e12	+	7.29444e11i	−0.256942	+	0.143667i
$667$	−1.98741e11			−0.0388795
$668$	−6.21574e12	+	2.26234e12i	−1.20781	+	0.439607i
$669$	−8.77873e11	−	3.19520e11i	−0.169439	−	0.0616708i
$670$	−2.92038e11	+	2.45049e11i	−0.0559890	+	0.0469803i
$671$	1.41655e12	+	8.03368e12i	0.269763	+	1.52990i
$672$	−2.70028e12			−0.510795
$673$	−1.24943e12	−	7.08585e12i	−0.234770	−	1.33145i	−0.843097	−	0.537762i	$-0.819270\pi$
$673$	−1.24943e12	−	7.08585e12i	−0.234770	−	1.33145i	0.608326	−	0.793687i	$-0.291841\pi$
$674$	4.69339e11	−	8.12920e11i	0.0876027	−	0.151732i
$675$	2.79790e12	+	2.34772e12i	0.518759	+	0.435291i
$676$	−2.08978e12	−	3.61960e12i	−0.384893	−	0.666653i
$677$	8.23034e11	−	1.42554e12i	0.150580	−	0.260813i	−0.780861	−	0.624705i	$-0.785219\pi$
$677$	8.23034e11	−	1.42554e12i	0.150580	−	0.260813i	0.931441	+	0.363892i	$0.118552\pi$
$678$	−9.49192e11	+	3.45478e11i	−0.172512	+	0.0627894i
$679$	1.10846e13	−	9.30106e12i	2.00127	−	1.67926i
$680$	−4.44478e10	−	7.69858e10i	−0.00797186	−	0.0138077i
$681$	9.28592e10	−	5.26630e11i	0.0165448	−	0.0938305i
$682$	4.49845e11	−	2.55120e12i	0.0796221	−	0.451559i
$683$	9.45962e10	+	7.93757e10i	0.0166334	+	0.0139571i	0.651066	−	0.759021i	$-0.274322\pi$
$683$	9.45962e10	+	7.93757e10i	0.0166334	+	0.0139571i	−0.634433	+	0.772978i	$0.718766\pi$
$684$	5.38016e12	+	1.95822e12i	0.939815	+	0.342065i
$685$	−2.59604e12	−	9.44880e11i	−0.450509	−	0.163972i
$686$	−1.65248e11	−	1.38660e11i	−0.0284891	−	0.0239052i
$687$	1.66798e11	−	9.45958e11i	0.0285683	−	0.162019i
$688$	4.65899e11	−	2.64225e12i	0.0792764	−	0.449599i
$689$	5.33910e11	+	9.24759e11i	0.0902571	+	0.156330i
$690$	−8.46174e10	+	7.10024e10i	−0.0142115	+	0.0119248i
$691$	−1.00899e13	+	3.67241e12i	−1.68358	+	0.612774i	−0.993794	−	0.111238i	$-0.964518\pi$
$691$	−1.00899e13	+	3.67241e12i	−1.68358	+	0.612774i	−0.689788	+	0.724012i	$0.742296\pi$
$692$	2.89010e11	−	5.00579e11i	0.0479110	−	0.0829842i
$693$	−6.96656e12	−	1.20664e13i	−1.14741	−	1.98737i
$694$	2.04143e12	+	1.71296e12i	0.334054	+	0.280305i
$695$	−1.72529e12	+	2.98830e12i	−0.280499	+	0.485839i
$696$	−2.38606e10	−	1.35320e11i	−0.00385425	−	0.0218585i
$697$	−8.61003e9			−0.00138184
$698$	−3.24300e11	−	1.83919e12i	−0.0517127	−	0.293277i
$699$	2.16138e12	−	1.81362e12i	0.342440	−	0.287341i
$700$	6.92414e12	+	2.52018e12i	1.09000	+	0.396726i
$701$	4.44388e12	−	1.61744e12i	0.695074	−	0.252986i	0.0297676	−	0.999557i	$-0.490523\pi$
$701$	4.44388e12	−	1.61744e12i	0.695074	−	0.252986i	0.665306	+	0.746571i	$0.268301\pi$
$702$	−5.81740e11			−0.0904090
$703$	−7.67997e12	+	4.29420e12i	−1.18593	+	0.663106i
$704$	−4.15433e12			−0.637417
$705$	2.04455e11	−	7.44154e10i	0.0311707	−	0.0113452i
$706$	−3.00996e12	−	1.09554e12i	−0.455974	−	0.165961i
$707$	9.01392e12	−	7.56358e12i	1.35683	−	1.13852i
$708$	−6.01974e11	−	3.41397e12i	−0.0900385	−	0.510634i
$709$	−1.08528e13			−1.61300			−0.806502	−	0.591232i	$-0.798642\pi$
$709$	−1.08528e13			−1.61300			−0.806502	+	0.591232i	$0.798642\pi$
$710$	5.76741e10	+	3.27086e11i	0.00851763	+	0.0483059i
$711$	−1.84884e12	+	3.20229e12i	−0.271323	+	0.469946i
$712$	−3.99793e12	−	3.35466e12i	−0.583008	−	0.489202i
$713$	1.09817e12	+	1.90209e12i	0.159135	+	0.275630i
$714$	−5.96359e10	+	1.03292e11i	−0.00858749	+	0.0148740i
$715$	−1.24448e12	+	4.52955e11i	−0.178079	+	0.0648154i
$716$	−9.70317e11	+	8.14193e11i	−0.137976	+	0.115776i
$717$	−2.06597e12	−	3.57836e12i	−0.291936	−	0.505647i
$718$	−5.43343e11	+	3.08145e12i	−0.0762982	+	0.432709i
$719$	−3.30130e11	+	1.87226e12i	−0.0460686	+	0.261268i	−0.999139	−	0.0414796i	$-0.986793\pi$
$719$	−3.30130e11	+	1.87226e12i	−0.0460686	+	0.261268i	0.953071	+	0.302748i	$0.0979040\pi$
$720$	−8.55156e11	−	7.17561e11i	−0.118590	−	0.0995091i
$721$	−1.28415e13	−	4.67391e12i	−1.76973	−	0.644128i
$722$	−2.03623e12	−	7.41129e11i	−0.278875	−	0.101502i
$723$	1.82921e12	+	1.53489e12i	0.248967	+	0.208908i
$724$	−6.62994e11	+	3.76003e12i	−0.0896781	+	0.508590i
$725$	−9.97999e10	+	5.65993e11i	−0.0134156	+	0.0760835i
$726$	−1.37070e12	−	2.37411e12i	−0.183116	−	0.317166i
$727$	−2.17670e12	+	1.82647e12i	−0.288998	+	0.242498i	−0.775747	−	0.631044i	$-0.782627\pi$
$727$	−2.17670e12	+	1.82647e12i	−0.288998	+	0.242498i	0.486750	+	0.873542i	$0.338182\pi$
$728$	−2.36039e12	+	8.59113e11i	−0.311453	+	0.113360i
$729$	6.13438e11	−	1.06251e12i	0.0804445	−	0.139334i
$730$	−3.91332e11	−	6.77807e11i	−0.0510026	−	0.0883391i
$731$	−3.54522e11	−	2.97479e11i	−0.0459213	−	0.0385326i
$732$	1.11711e12	−	1.93489e12i	0.143812	−	0.249090i
$733$	−6.47095e11	−	3.66986e12i	−0.0827942	−	0.469549i	−0.997811	−	0.0661332i	$-0.978934\pi$
$733$	−6.47095e11	−	3.66986e12i	−0.0827942	−	0.469549i	0.915017	−	0.403416i	$-0.132177\pi$
$734$	−5.16707e12			−0.657071
$735$	1.68797e11	+	9.57294e11i	0.0213339	+	0.120991i
$736$	−2.49445e12	+	2.09309e12i	−0.313346	+	0.262929i
$737$	1.04314e13	+	3.79670e12i	1.30238	+	0.474027i
$738$	3.63099e10	−	1.32157e10i	0.00450580	−	0.00163998i
$739$	2.52673e12			0.311644			0.155822	−	0.987785i	$-0.450197\pi$
$739$	2.52673e12			0.311644			0.155822	+	0.987785i	$0.450197\pi$
$740$	2.01590e12	−	3.26918e11i	0.247131	−	0.0400770i
$741$	−1.56275e12			−0.190418
$742$	−2.02328e12	+	7.36413e11i	−0.245041	+	0.0891875i
$743$	−5.10231e12	−	1.85709e12i	−0.614211	−	0.223554i	0.0161339	−	0.999870i	$-0.494864\pi$
$743$	−5.10231e12	−	1.85709e12i	−0.614211	−	0.223554i	−0.630345	+	0.776315i	$0.717086\pi$
$744$	−1.16326e12	+	9.76092e11i	−0.139187	+	0.116792i
$745$	5.57131e11	+	3.15965e12i	0.0662604	+	0.375781i
$746$	1.99593e12			0.235950
$747$	−7.62990e11	−	4.32713e12i	−0.0896554	−	0.508461i
$748$	−6.04716e11	+	1.04740e12i	−0.0706308	+	0.122336i
$749$	7.06766e12	+	5.93047e12i	0.820554	+	0.688527i
$750$	3.33603e11	+	5.77817e11i	0.0384994	+	0.0666830i
$751$	3.94396e12	−	6.83114e12i	0.452432	−	0.783634i	−0.546105	−	0.837717i	$-0.683890\pi$
$751$	3.94396e12	−	6.83114e12i	0.452432	−	0.783634i	0.998536	+	0.0540824i	$0.0172234\pi$
$752$	1.54339e12	−	5.61747e11i	0.175993	−	0.0640561i
$753$	−4.19255e12	+	3.51797e12i	−0.475227	+	0.398763i
$754$	−4.57699e10	−	7.92758e10i	−0.00515714	−	0.00893242i
$755$	−2.11463e11	+	1.19927e12i	−0.0236850	+	0.134324i
$756$	−1.45214e12	+	8.23549e12i	−0.161681	+	0.916941i
$757$	1.02801e13	+	8.62599e12i	1.13780	+	0.954723i	0.999364	−	0.0356487i	$-0.0113497\pi$
$757$	1.02801e13	+	8.62599e12i	1.13780	+	0.954723i	0.138431	+	0.990372i	$0.455794\pi$
$758$	3.39796e12	+	1.23676e12i	0.373858	+	0.136073i
$759$	3.02247e12	+	1.10009e12i	0.330578	+	0.120320i
$760$	1.79911e12	+	1.50964e12i	0.195613	+	0.164139i
$761$	5.12839e11	−	2.90845e12i	0.0554306	−	0.314363i	−0.944468	−	0.328604i	$-0.893422\pi$
$761$	5.12839e11	−	2.90845e12i	0.0554306	−	0.314363i	0.999899	+	0.0142408i	$0.00453313\pi$
$762$	3.31547e11	−	1.88030e12i	0.0356245	−	0.202036i
$763$	−1.76254e12	−	3.05280e12i	−0.188268	−	0.326091i
$764$	9.78099e12	−	8.20723e12i	1.03863	−	0.871518i
$765$	−1.80944e11	+	6.58582e10i	−0.0191015	+	0.00695238i
$766$	−2.25663e12	+	3.90859e12i	−0.236827	+	0.410196i
$767$	−2.47141e12	−	4.28061e12i	−0.257849	−	0.446608i
$768$	−4.72367e10	−	3.96363e10i	−0.00489952	−	0.00411119i
$769$	1.31997e12	−	2.28625e12i	0.136112	−	0.235752i	−0.789910	−	0.613223i	$-0.789873\pi$
$769$	1.31997e12	−	2.28625e12i	0.136112	−	0.235752i	0.926022	+	0.377471i	$0.123206\pi$
$770$	−4.63709e11	−	2.62983e12i	−0.0475376	−	0.269599i
$771$	−4.84749e12			−0.494052
$772$	−1.90244e12	−	1.07893e13i	−0.192767	−	1.09324i
$773$	−1.19483e13	+	1.00258e13i	−1.20365	+	1.00998i	−0.204128	+	0.978944i	$0.565436\pi$
$773$	−1.19483e13	+	1.00258e13i	−1.20365	+	1.00998i	−0.999518	+	0.0310354i	$0.990120\pi$
$774$	1.95168e12	+	7.10355e11i	0.195468	+	0.0711444i
$775$	5.96839e12	−	2.17232e12i	0.594292	−	0.216305i
$776$	1.20643e13			1.19433
$777$	−3.70746e12	−	4.54395e12i	−0.364907	−	0.447238i
$778$	−6.62440e12			−0.648244
$779$	2.13754e11	−	7.78003e10i	0.0207968	−	0.00756942i
$780$	3.40840e11	+	1.24056e11i	0.0329705	+	0.0120003i
$781$	7.40858e12	−	6.21654e12i	0.712533	−	0.597886i
$782$	2.49759e10	+	1.41645e11i	0.00238831	+	0.0135448i
$783$	−6.52256e11			−0.0620140
$784$	1.27421e12	+	7.22642e12i	0.120454	+	0.683126i
$785$	−7.38322e11	+	1.27881e12i	−0.0693957	+	0.120197i
$786$	−1.38253e11	−	1.16008e11i	−0.0129204	−	0.0108415i
$787$	−7.67634e12	−	1.32958e13i	−0.713293	−	1.23546i	−0.963614	−	0.267297i	$-0.913870\pi$
$787$	−7.67634e12	−	1.32958e13i	−0.713293	−	1.23546i	0.250321	−	0.968163i	$-0.419464\pi$
$788$	−4.58927e12	+	7.94884e12i	−0.424009	+	0.734405i
$789$	3.20257e12	−	1.16564e12i	0.294206	−	0.107082i
$790$	−5.42889e11	+	4.55538e11i	−0.0495895	+	0.0416105i
$791$	1.03518e13	+	1.79298e13i	0.940200	+	1.62847i
$792$	2.01723e12	−	1.14403e13i	0.182176	−	1.03317i
$793$	5.53174e11	−	3.13721e12i	0.0496744	−	0.281718i
$794$	1.27659e12	+	1.07118e12i	0.113988	+	0.0956471i
$795$	6.25303e11	+	2.27592e11i	0.0555186	+	0.0202071i
$796$	1.38699e13	+	5.04824e12i	1.22452	+	0.445688i
$797$	1.28414e13	+	1.07752e13i	1.12733	+	0.945939i	0.998951	−	0.0457865i	$-0.0145794\pi$
$797$	1.28414e13	+	1.07752e13i	1.12733	+	0.945939i	0.128375	+	0.991726i	$0.459024\pi$
$798$	5.47184e11	−	3.10323e12i	0.0477661	−	0.270895i
$799$	4.91956e10	−	2.79002e11i	0.00427037	−	0.0242185i
$800$	4.70829e12	+	8.15500e12i	0.406404	+	0.703913i
$801$	−8.65990e12	+	7.26652e12i	−0.743305	+	0.623707i
$802$	5.43377e12	−	1.97773e12i	0.463785	−	0.168804i
$803$	−1.13950e13	+	1.97368e13i	−0.967153	+	1.67516i
$804$	−1.52015e12	−	2.63298e12i	−0.128302	−	0.222226i
$805$	1.73435e12	+	1.45529e12i	0.145564	+	0.122143i
$806$	−5.05815e11	+	8.76097e11i	−0.0422167	+	0.0731214i
$807$	−1.58123e12	−	8.96757e12i	−0.131239	−	0.744293i
$808$	9.81061e12			0.809739
$809$	−8.81642e10	−	5.00004e11i	−0.00723642	−	0.0410398i	0.980976	−	0.194130i	$-0.0621885\pi$
$809$	−8.81642e10	−	5.00004e11i	−0.00723642	−	0.0410398i	−0.988212	+	0.153091i	$0.951077\pi$
$810$	5.10999e11	−	4.28779e11i	0.0417098	−	0.0349987i
$811$	−8.47637e12	−	3.08515e12i	−0.688044	−	0.250427i	−0.0257464	−	0.999669i	$-0.508196\pi$
$811$	−8.47637e12	−	3.08515e12i	−0.688044	−	0.250427i	−0.662297	+	0.749241i	$0.730418\pi$
$812$	−1.23653e12	+	4.50060e11i	−0.0998166	+	0.0363303i
$813$	5.79931e12			0.465553
$814$	5.27330e12	+	6.46308e12i	0.420991	+	0.515976i
$815$	−6.16743e11			−0.0489660
$816$	2.61479e11	−	9.51706e10i	0.0206458	−	0.00751445i
$817$	1.14895e13	+	4.18182e12i	0.902194	+	0.328372i
$818$	−2.88223e12	+	2.41848e12i	−0.225081	+	0.188866i
$819$	9.44816e11	+	5.35832e12i	0.0733787	+	0.416151i
$820$	−5.27964e10			−0.00407795
$821$	−4.94193e11	−	2.80271e12i	−0.0379623	−	0.215295i	0.959926	−	0.280255i	$-0.0904190\pi$
$821$	−4.94193e11	−	2.80271e12i	−0.0379623	−	0.215295i	−0.997888	+	0.0649603i	$0.979308\pi$
$822$	−1.54522e12	+	2.67639e12i	−0.118050	+	0.204469i
$823$	−1.38419e13	−	1.16148e13i	−1.05171	−	0.882493i	−0.0584419	−	0.998291i	$-0.518613\pi$
$823$	−1.38419e13	−	1.16148e13i	−1.05171	−	0.882493i	−0.993273	+	0.115797i	$0.963058\pi$
$824$	−5.69685e12	−	9.86724e12i	−0.430490	−	0.745630i
$825$	4.65070e12	−	8.05524e12i	0.349523	−	0.605391i
$826$	9.36553e12	−	3.40878e12i	0.700039	−	0.254793i
$827$	−1.36526e13	+	1.14559e13i	−1.01494	+	0.851635i	−0.988983	−	0.148028i	$-0.952707\pi$
$827$	−1.36526e13	+	1.14559e13i	−1.01494	+	0.851635i	−0.0259557	+	0.999663i	$0.508263\pi$
$828$	2.30087e12	+	3.98523e12i	0.170120	+	0.294657i
$829$	3.90955e12	−	2.21722e13i	0.287496	−	1.63047i	−0.408735	−	0.912653i	$-0.634030\pi$
$829$	3.90955e12	−	2.21722e13i	0.287496	−	1.63047i	0.696231	−	0.717817i	$-0.254859\pi$
$830$	1.46233e11	−	8.29330e11i	0.0106953	−	0.0606563i
$831$	1.14080e12	+	9.57249e11i	0.0829864	+	0.0696338i
$832$	1.52446e12	+	5.54857e11i	0.110296	+	0.0401445i
$833$	1.18939e12	+	4.32903e11i	0.0855898	+	0.0311521i
$834$	2.95693e12	+	2.48116e12i	0.211638	+	0.177586i
$835$	−1.02059e12	+	5.78805e12i	−0.0726544	+	0.412044i
$836$	5.54851e12	−	3.14672e13i	0.392869	−	2.22807i
$837$	3.60412e12	+	6.24252e12i	0.253825	+	0.439638i
$838$	−4.55012e12	+	3.81801e12i	−0.318732	+	0.267448i
$839$	1.41614e13	−	5.15434e12i	0.986684	−	0.359124i	0.202249	−	0.979334i	$-0.435175\pi$
$839$	1.41614e13	−	5.15434e12i	0.986684	−	0.359124i	0.784436	+	0.620210i	$0.212953\pi$
$840$	−7.82665e11	+	1.35561e12i	−0.0542399	+	0.0939463i
$841$	7.20226e12	+	1.24747e13i	0.496463	+	0.859898i
$842$	4.43778e12	+	3.72374e12i	0.304272	+	0.255314i
$843$	−1.71643e12	+	2.97294e12i	−0.117058	+	0.202750i
$844$	−2.37530e12	−	1.34710e13i	−0.161131	−	0.913817i
$845$	−3.71367e12			−0.250581
$846$	2.20781e11	+	1.25211e12i	0.0148182	+	0.0840380i
$847$	−4.30429e13	+	3.61173e13i	−2.87360	+	2.41124i
$848$	4.72029e12	+	1.71804e12i	0.313464	+	0.114091i
$849$	−5.08363e12	+	1.85029e12i	−0.335807	+	0.122224i
$850$	4.15933e11			0.0273299
$851$	−6.94706e12	−	1.32379e12i	−0.454065	−	0.0865237i
$852$	−2.64876e12			−0.172212
$853$	1.73875e13	−	6.32855e12i	1.12452	−	0.409292i	0.288221	−	0.957564i	$-0.406936\pi$
$853$	1.73875e13	−	6.32855e12i	1.12452	−	0.409292i	0.836300	+	0.548272i	$0.184714\pi$
$854$	6.03601e12	+	2.19693e12i	0.388320	+	0.141337i
$855$	3.89706e12	−	3.27002e12i	0.249396	−	0.209268i
$856$	1.33576e12	+	7.57547e12i	0.0850347	+	0.482256i
$857$	−2.22712e13			−1.41036			−0.705181	−	0.709027i	$-0.749134\pi$
$857$	−2.22712e13			−1.41036			−0.705181	+	0.709027i	$0.749134\pi$
$858$	2.57257e11	+	1.45898e12i	0.0162060	+	0.0919087i
$859$	4.89372e12	−	8.47617e12i	0.306669	−	0.531166i	−0.670963	−	0.741491i	$-0.734119\pi$
$859$	4.89372e12	−	8.47617e12i	0.306669	−	0.531166i	0.977631	+	0.210325i	$0.0674523\pi$
$860$	−2.17391e12	−	1.82413e12i	−0.135519	−	0.113714i
$861$	7.58055e10	+	1.31299e11i	0.00470096	+	0.00814230i
$862$	3.92396e12	−	6.79649e12i	0.242070	−	0.419278i
$863$	−2.10694e13	+	7.66864e12i	−1.29302	+	0.470620i	−0.894716	−	0.446635i	$-0.852622\pi$
$863$	−2.10694e13	+	7.66864e12i	−1.29302	+	0.470620i	−0.398301	+	0.917255i	$0.630400\pi$
$864$	−8.18663e12	+	6.86940e12i	−0.499797	+	0.419379i
$865$	−2.56795e11	−	4.44782e11i	−0.0155960	−	0.0270131i
$866$	1.10120e12	−	6.24522e12i	0.0665328	−	0.377326i
$867$	−1.14972e12	+	6.52038e12i	−0.0691044	+	0.391911i
$868$	1.11400e13	+	9.34757e12i	0.666110	+	0.558933i
$869$	1.93916e13	+	7.05796e12i	1.15352	+	0.419846i
$870$	−5.36047e10	−	1.95105e10i	−0.00317224	−	0.00115460i
$871$	−3.32076e12	−	2.78645e12i	−0.195504	−	0.164047i
$872$	5.10357e11	−	2.89438e12i	0.0298917	−	0.169524i
$873$	4.53785e12	−	2.57354e13i	0.264415	−	1.49957i
$874$	−1.89996e12	−	3.29083e12i	−0.110140	−	0.190768i
$875$	1.04759e13	−	8.79030e12i	0.604163	−	0.506953i
$876$	5.86533e12	−	2.13481e12i	0.336530	−	0.122487i
$877$	−4.00923e12	+	6.94419e12i	−0.228856	+	0.396391i	−0.957469	−	0.288535i	$-0.906832\pi$
$877$	−4.00923e12	+	6.94419e12i	−0.228856	+	0.396391i	0.728613	+	0.684925i	$0.240165\pi$
$878$	−3.27357e12	−	5.66999e12i	−0.185907	−	0.322001i
$879$	−4.35401e12	−	3.65345e12i	−0.246003	−	0.206421i
$880$	−3.11500e12	+	5.39534e12i	−0.175100	+	0.303282i
$881$	−3.77122e12	−	2.13877e13i	−0.210907	−	1.19611i	−0.887870	−	0.460095i	$-0.847815\pi$
$881$	−3.77122e12	−	2.13877e13i	−0.210907	−	1.19611i	0.676963	−	0.736017i	$-0.263296\pi$
$882$	−5.68033e12			−0.316056
$883$	−5.12288e12	−	2.90533e13i	−0.283590	−	1.60832i	−0.710279	−	0.703920i	$-0.751431\pi$
$883$	−5.12288e12	−	2.90533e13i	−0.283590	−	1.60832i	0.426689	−	0.904398i	$-0.359680\pi$
$884$	3.61796e11	−	3.03583e11i	0.0199264	−	0.0167202i
$885$	−2.89446e12	−	1.05350e12i	−0.158607	−	0.0577283i
$886$	3.17989e12	−	1.15739e12i	0.173365	−	0.0630996i
$887$	2.82089e13			1.53014			0.765069	−	0.643948i	$-0.222705\pi$
$887$	2.82089e13			1.53014			0.765069	+	0.643948i	$0.222705\pi$
$888$	6.72947e10	−	4.88910e12i	0.00363181	−	0.263858i
$889$	−3.91338e13			−2.10133
$890$	−2.03597e12	+	7.41034e11i	−0.108772	+	0.0395898i
$891$	−1.82525e13	−	6.64336e12i	−0.970225	−	0.353133i
$892$	−5.71405e12	+	4.79466e12i	−0.302205	+	0.253580i
$893$	1.29972e12	+	7.37110e12i	0.0683942	+	0.387883i
$894$	3.58907e12			0.187916
$895$	1.95436e11	+	1.10837e12i	0.0101812	+	0.0577406i
$896$	−1.39278e13	+	2.41236e13i	−0.721932	+	1.25042i
$897$	−9.62184e11	−	8.07368e11i	−0.0496240	−	0.0416395i
$898$	−3.15778e12	−	5.46943e12i	−0.162046	−	0.280672i
$899$	−5.67127e11	+	9.82294e11i	−0.0289576	+	0.0501560i
$900$	1.25049e13	−	4.55142e12i	0.635316	−	0.231236i
$901$	6.63749e11	−	5.56951e11i	0.0335538	−	0.0281550i
$902$	−1.07822e11	−	1.86753e11i	−0.00542347	−	0.00939372i
$903$	−1.41509e12	+	8.02539e12i	−0.0708255	+	0.401672i
$904$	−2.99744e12	+	1.69993e13i	−0.149277	+	0.846592i
$905$	2.59877e12	+	2.18063e12i	0.128780	+	0.108059i
$906$	1.28010e12	+	4.65919e11i	0.0631201	+	0.0229738i
$907$	8.21090e12	+	2.98852e12i	0.402864	+	0.146630i	0.535502	−	0.844534i	$-0.320123\pi$
$907$	8.21090e12	+	2.98852e12i	0.402864	+	0.146630i	−0.132638	+	0.991165i	$0.542345\pi$
$908$	−3.27079e12	−	2.74452e12i	−0.159686	−	0.133992i
$909$	3.69016e12	−	2.09279e13i	0.179270	−	1.01669i
$910$	−1.81082e11	+	1.02697e12i	−0.00875363	+	0.0496443i
$911$	1.23866e13	+	2.14542e13i	0.595826	+	1.03200i	0.993430	+	0.114443i	$0.0365084\pi$
$911$	1.23866e13	+	2.14542e13i	0.595826	+	1.03200i	−0.397604	+	0.917557i	$0.630158\pi$
$912$	−5.63157e12	+	4.72545e12i	−0.269558	+	0.226186i
$913$	−2.30426e13	+	8.38683e12i	−1.09752	+	0.399465i
$914$	9.02037e11	−	1.56237e12i	0.0427530	−	0.0740504i
$915$	−9.92588e11	−	1.71921e12i	−0.0468138	−	0.0810839i
$916$	−5.87514e12	−	4.92983e12i	−0.275733	−	0.231367i
$917$	−1.84956e12	+	3.20353e12i	−0.0863786	+	0.149612i
$918$	8.19693e10	+	4.64871e11i	0.00380942	+	0.0216043i
$919$	2.46689e13			1.14085			0.570426	−	0.821349i	$-0.306778\pi$
$919$	2.46689e13			1.14085			0.570426	+	0.821349i	$0.306778\pi$
$920$	3.27784e11	+	1.85896e12i	0.0150849	+	0.0855509i
$921$	2.46864e12	−	2.07143e12i	0.113055	−	0.0948642i
$922$	6.39413e12	+	2.32727e12i	0.291402	+	0.106062i
$923$	−3.54891e12	+	1.29170e12i	−0.160949	+	0.0585806i
$924$	2.12965e13			0.961133
$925$	−7.25854e12	+	1.91197e13i	−0.325996	+	0.858705i
$926$	−1.31781e13			−0.588985
$927$	−2.31915e13	+	8.44103e12i	−1.03150	+	0.375436i
$928$	−1.58022e12	−	5.75154e11i	−0.0699443	−	0.0254576i
$929$	9.12179e12	−	7.65409e12i	0.401799	−	0.337150i	−0.419389	−	0.907807i	$-0.637756\pi$
$929$	9.12179e12	−	7.65409e12i	0.401799	−	0.337150i	0.821189	+	0.570657i	$0.193311\pi$
$930$	1.09471e11	+	6.20841e11i	0.00479872	+	0.0272149i
$931$	−3.34398e13			−1.45878
$932$	−3.91194e12	−	2.21857e13i	−0.169833	−	0.963168i
$933$	−1.09262e11	+	1.89246e11i	−0.00472063	+	0.00817637i
$934$	2.71405e12	+	2.27736e12i	0.116696	+	0.0979197i
$935$	5.37311e11	+	9.30649e11i	0.0229918	+	0.0398230i
$936$	−2.26821e12	+	3.92866e12i	−0.0965922	+	0.167303i
$937$	8.13666e12	−	2.96150e12i	0.344840	−	0.125512i	−0.163793	−	0.986495i	$-0.552373\pi$
$937$	8.13666e12	−	2.96150e12i	0.344840	−	0.125512i	0.508634	+	0.860983i	$0.330151\pi$
$938$	6.69591e12	−	5.61854e12i	0.282421	−	0.236979i
$939$	3.26048e12	+	5.64732e12i	0.136863	+	0.237054i
$940$	3.01666e11	−	1.71083e12i	0.0126023	−	0.0714713i
$941$	3.26051e12	−	1.84913e13i	0.135560	−	0.768800i	−0.838908	−	0.544274i	$-0.816805\pi$
$941$	3.26051e12	−	1.84913e13i	0.135560	−	0.768800i	0.974468	−	0.224527i	$-0.0720836\pi$
$942$	1.26539e12	+	1.06179e12i	0.0523594	+	0.0439348i
$943$	1.71802e11	+	6.25309e10i	0.00707499	+	0.00257509i
$944$	−2.18497e13	−	7.95264e12i	−0.895512	−	0.325940i
$945$	5.69202e12	+	4.77617e12i	0.232179	+	0.194821i
$946$	2.01275e12	−	1.14149e13i	0.0817110	−	0.463406i
$947$	3.34541e12	−	1.89728e13i	0.135168	−	0.766577i	−0.839574	−	0.543245i	$-0.817195\pi$
$947$	3.34541e12	−	1.89728e13i	0.135168	−	0.766577i	0.974742	−	0.223332i	$-0.0716935\pi$
$948$	−2.82591e12	−	4.89463e12i	−0.113637	−	0.196826i
$949$	6.81754e12	−	5.72060e12i	0.272854	−	0.228951i
$950$	−1.03260e13	+	3.75837e12i	−0.411318	+	0.149707i
$951$	1.72271e12	−	2.98381e12i	0.0682966	−	0.118293i
$952$	1.01911e12	+	1.76515e12i	0.0402119	+	0.0696490i
$953$	5.61071e12	+	4.70795e12i	0.220343	+	0.184890i	0.746277	−	0.665636i	$-0.231840\pi$
$953$	5.61071e12	+	4.70795e12i	0.220343	+	0.184890i	−0.525934	+	0.850526i	$0.676284\pi$
$954$	−1.94426e12	+	3.36756e12i	−0.0759953	+	0.131628i
$955$	−1.97003e12	−	1.11726e13i	−0.0766405	−	0.434650i
$956$	−3.29911e13			−1.27743
$957$	2.88441e11	+	1.63583e12i	0.0111161	+	0.0630427i
$958$	−3.45345e12	+	2.89779e12i	−0.132467	+	0.111153i
$959$	5.95226e13	+	2.16644e13i	2.27247	+	0.827111i
$960$	9.49997e11	−	3.45771e11i	0.0360996	−	0.0131392i
$961$	−1.39047e13			−0.525903
$962$	−1.07186e12	−	3.07598e12i	−0.0403505	−	0.115796i
$963$	1.66624e13			0.624336
$964$	1.79160e13	−	6.52088e12i	0.668181	−	0.243198i
$965$	−9.14748e12	−	3.32941e12i	−0.339569	−	0.123593i
$966$	1.94013e12	−	1.62796e12i	0.0716858	−	0.0601515i
$967$	2.80405e12	+	1.59026e13i	0.103126	+	0.584855i	0.991952	+	0.126611i	$0.0404101\pi$
$967$	2.80405e12	+	1.59026e13i	0.103126	+	0.584855i	−0.888827	+	0.458244i	$0.848479\pi$
$968$	−4.68472e13			−1.71492
$969$	2.20198e11	+	1.24880e12i	0.00802335	+	0.0455027i
$970$	2.50424e12	−	4.33748e12i	0.0908247	−	0.157313i
$971$	2.21437e13	+	1.85808e13i	0.799398	+	0.670775i	0.948052	−	0.318114i	$-0.103050\pi$
$971$	2.21437e13	+	1.85808e13i	0.799398	+	0.670775i	−0.148654	+	0.988889i	$0.547494\pi$
$972$	1.16568e13	+	2.01902e13i	0.418872	+	0.725507i
$973$	3.95579e13	−	6.85164e13i	1.41490	−	2.45068i
$974$	1.00290e12	−	3.65025e11i	0.0357060	−	0.0129959i
$975$	−2.78247e12	+	2.33477e12i	−0.0986075	+	0.0827415i
$976$	−7.49285e12	−	1.29780e13i	−0.264316	−	0.457808i
$977$	1.69183e12	−	9.59486e12i	0.0594062	−	0.336909i	−0.940590	−	0.339544i	$-0.889727\pi$
$977$	1.69183e12	−	9.59486e12i	0.0594062	−	0.336909i	0.999997	+	0.00263425i	$0.000838508\pi$
$978$	−1.19803e11	+	6.79438e11i	−0.00418739	+	0.0237479i
$979$	4.83293e13	+	4.05531e13i	1.68147	+	1.41092i
$980$	7.29329e12	+	2.65454e12i	0.252584	+	0.0919332i
$981$	−5.98230e12	−	2.17738e12i	−0.206233	−	0.0750626i
$982$	5.19579e12	+	4.35978e12i	0.178299	+	0.149611i
$983$	−2.43319e12	+	1.37993e13i	−0.0831160	+	0.471374i	0.914631	+	0.404289i	$0.132481\pi$
$983$	−2.43319e12	+	1.37993e13i	−0.0831160	+	0.471374i	−0.997747	+	0.0670850i	$0.978630\pi$
$984$	−2.19501e10	+	1.24485e11i	−0.000746378	+	0.00423292i
$985$	4.07772e12	+	7.06282e12i	0.138024	+	0.239064i
$986$	−5.69005e10	+	4.77452e10i	−0.00191721	+	0.00160873i
$987$	−4.68779e12	+	1.70621e12i	−0.157232	+	0.0572277i
$988$	−6.23885e12	+	1.08060e13i	−0.208304	+	0.360794i
$989$	4.91357e12	+	8.51055e12i	0.163310	+	0.282862i
$990$	−3.69440e12	−	3.09997e12i	−0.122232	−	0.102565i
$991$	−1.50136e13	+	2.60044e13i	−0.494487	+	0.856476i	−0.999980	−	0.00635462i	$-0.997977\pi$
$991$	−1.50136e13	+	2.60044e13i	−0.494487	+	0.856476i	0.505493	+	0.862831i	$0.331311\pi$
$992$	3.22711e12	+	1.83019e13i	0.105806	+	0.600058i
$993$	−1.67232e13			−0.545818
$994$	−1.32237e12	−	7.49951e12i	−0.0429648	−	0.243666i
$995$	1.00465e13	−	8.43004e12i	0.324947	−	0.272663i
$996$	6.31093e12	+	2.29699e12i	0.203201	+	0.0739592i
$997$	3.12848e13	−	1.13867e13i	1.00278	−	0.364982i	0.212123	−	0.977243i	$-0.431962\pi$
$997$	3.12848e13	−	1.13867e13i	1.00278	−	0.364982i	0.790656	+	0.612261i	$0.209740\pi$
$998$	−1.22646e13			−0.391349
$999$	−2.27998e13	−	4.34459e12i	−0.724247	−	0.138008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.f.a.7.12	✓	162
37.16	even	9	inner	37.10.f.a.16.12	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.f.a.7.12	✓	162	1.1	even	1	trivial
37.10.f.a.16.12	yes	162	37.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.45759 + 2.71434i) q^{2} +(-52.8450 - 19.2340i) q^{3} +(-343.967 + 288.622i) q^{4} +(69.2798 + 392.905i) q^{5} +446.304 q^{6} +(-1588.46 - 9008.63i) q^{7} +(3813.41 - 6605.02i) q^{8} +(-12655.4 - 10619.1i) q^{9} +O(q^{10})\)	\(q+(-7.45759 + 2.71434i) q^{2} +(-52.8450 - 19.2340i) q^{3} +(-343.967 + 288.622i) q^{4} +(69.2798 + 392.905i) q^{5} +446.304 q^{6} +(-1588.46 - 9008.63i) q^{7} +(3813.41 - 6605.02i) q^{8} +(-12655.4 - 10619.1i) q^{9} +(-1583.14 - 2742.08i) q^{10} +(-46098.7 + 79845.4i) q^{11} +(23728.3 - 8636.40i) q^{12} +(27580.5 - 23142.8i) q^{13} +(36298.6 + 62871.0i) q^{14} +(3896.06 - 22095.6i) q^{15} +(29410.5 - 166796. i) q^{16} +(-22379.7 - 18778.8i) q^{17} +(123203. + 44842.1i) q^{18} +(725288. + 263983. i) q^{19} +(-137231. - 115151. i) q^{20} +(-89329.7 + 506614. i) q^{21} +(127058. - 720582. i) q^{22} +(310176. + 537240. i) q^{23} +(-328561. + 275695. i) q^{24} +(1.68576e6 - 613567. i) q^{25} +(-142866. + 247452. i) q^{26} +(1.01798e6 + 1.76319e6i) q^{27} +(3.14647e6 + 2.64020e6i) q^{28} +(-160184. + 277447. i) q^{29} +(30919.9 + 175355. i) q^{30} +3.54047e6 q^{31} +(911492. + 5.16933e6i) q^{32} +(3.97184e6 - 3.33277e6i) q^{33} +(217870. + 79298.3i) q^{34} +(3.42949e6 - 1.24823e6i) q^{35} +7.41796e6 q^{36} +(-7.44733e6 + 8.63129e6i) q^{37} -6.12544e6 q^{38} +(-1.90262e6 + 692497. i) q^{39} +(2.85934e6 + 1.04071e6i) q^{40} +(225766. - 189440. i) q^{41} +(-708938. - 4.02059e6i) q^{42} +1.58412e7 q^{43} +(-7.18872e6 - 4.07693e7i) q^{44} +(3.29556e6 - 5.70807e6i) q^{45} +(-3.77142e6 - 3.16459e6i) q^{46} +(4.84871e6 + 8.39821e6i) q^{47} +(-4.76235e6 + 8.24863e6i) q^{48} +(-4.07122e7 + 1.48180e7i) q^{49} +(-1.09063e7 + 9.15146e6i) q^{50} +(821463. + 1.42282e6i) q^{51} +(-2.80725e6 + 1.59207e7i) q^{52} +(-5.15015e6 + 2.92080e7i) q^{53} +(-1.23776e7 - 1.03860e7i) q^{54} +(-3.45654e7 - 1.25808e7i) q^{55} +(-6.55596e7 - 2.38618e7i) q^{56} +(-3.32504e7 - 2.79004e7i) q^{57} +(441502. - 2.50388e6i) q^{58} +(2.38395e7 - 1.35201e8i) q^{59} +(5.03718e6 + 8.72465e6i) q^{60} +(6.77794e7 - 5.68737e7i) q^{61} +(-2.64034e7 + 9.61005e6i) q^{62} +(-7.55613e7 + 1.30876e8i) q^{63} +(2.25295e7 + 3.90223e7i) q^{64} +(1.10037e7 + 9.23319e6i) q^{65} +(-2.05741e7 + 3.56353e7i) q^{66} +(-2.09077e7 - 1.18573e8i) q^{67} +1.31178e7 q^{68} +(-6.05796e6 - 3.43564e7i) q^{69} +(-2.21876e7 + 1.86176e7i) q^{70} +(-9.85706e7 - 3.58768e7i) q^{71} +(-1.18400e8 + 4.30940e7i) q^{72} +2.47187e8 q^{73} +(3.21108e7 - 8.45831e7i) q^{74} -1.00886e8 q^{75} +(-3.25666e8 + 1.18533e8i) q^{76} +(7.92524e8 + 2.88455e8i) q^{77} +(1.23093e7 - 1.03287e7i) q^{78} +(-3.88668e7 - 2.20424e8i) q^{79} +6.75724e7 q^{80} +(3.65837e7 + 2.07476e8i) q^{81} +(-1.16947e6 + 2.02557e6i) q^{82} +(2.03742e8 + 1.70960e8i) q^{83} +(-1.15494e8 - 2.00041e8i) q^{84} +(5.82782e6 - 1.00941e7i) q^{85} +(-1.18137e8 + 4.29985e7i) q^{86} +(1.38014e7 - 1.15807e7i) q^{87} +(3.51587e8 + 6.08966e8i) q^{88} +(1.18825e8 - 6.73889e8i) q^{89} +(-9.08325e6 + 5.15137e7i) q^{90} +(-2.52295e8 - 2.11701e8i) q^{91} +(-2.61750e8 - 9.52691e7i) q^{92} +(-1.87096e8 - 6.80975e7i) q^{93} +(-5.89553e7 - 4.94694e7i) q^{94} +(-5.34726e7 + 3.03258e8i) q^{95} +(5.12591e7 - 2.90705e8i) q^{96} +(7.90911e8 + 1.36990e9i) q^{97} +(2.63394e8 - 2.21014e8i) q^{98} +(1.43129e9 - 5.20946e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9}+O(q^{10}) \) 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9	\( 162 q - 57 q^{2} - 228 q^{3} + 249 q^{4} - 3420 q^{5} - 12 q^{6} + 5808 q^{7} + 61698 q^{8} - 30198 q^{9} + 59997 q^{10} + 175689 q^{11} - 147411 q^{12} + 713586 q^{13} - 96867 q^{14} - 143316 q^{15} + 556665 q^{16} - 119334 q^{17} - 711948 q^{18} + 1752348 q^{19} + 4774248 q^{20} + 57972 q^{21} + 1413495 q^{22} - 5098719 q^{23} + 3891975 q^{24} + 10869768 q^{25} + 5518221 q^{26} + 13281609 q^{27} + 9017757 q^{28} - 2782023 q^{29} - 10231020 q^{30} + 8407836 q^{31} + 6197838 q^{32} - 8252229 q^{33} - 49656453 q^{34} - 23563824 q^{35} + 151165428 q^{36} - 23634336 q^{37} - 12277422 q^{38} + 100476834 q^{39} + 165006327 q^{40} + 74094072 q^{41} - 3662109 q^{42} - 90803088 q^{43} - 350087604 q^{44} - 184820799 q^{45} - 114643110 q^{46} + 158694333 q^{47} + 359750805 q^{48} + 36118224 q^{49} - 259200273 q^{50} + 176035647 q^{51} - 203883429 q^{52} - 31488120 q^{53} - 109796865 q^{54} + 23137227 q^{55} + 37371291 q^{56} - 12449808 q^{57} - 840994983 q^{58} - 77893794 q^{59} + 244178580 q^{60} - 980597586 q^{61} - 586588080 q^{62} - 48634623 q^{63} - 917012376 q^{64} + 1432770144 q^{65} - 177475497 q^{66} - 302695398 q^{67} + 1615796082 q^{68} + 699674787 q^{69} + 2092804794 q^{70} - 774435768 q^{71} - 2899807611 q^{72} - 2505680652 q^{73} + 1161236205 q^{74} - 2302474524 q^{75} + 1445475621 q^{76} - 1374645213 q^{77} + 2942410749 q^{78} - 29533980 q^{79} + 9154934064 q^{80} - 2232253221 q^{81} + 707552205 q^{82} - 392438496 q^{83} - 1388366664 q^{84} - 556053567 q^{85} + 852383496 q^{86} - 6650019951 q^{87} + 3660093510 q^{88} + 100313124 q^{89} + 12897388398 q^{90} + 684844038 q^{91} + 621259308 q^{92} + 2212599060 q^{93} + 3136220628 q^{94} + 1257937926 q^{95} - 6811500039 q^{96} + 70258497 q^{97} - 8202052869 q^{98} - 2679000153 q^{99}+O(q^{100}) \) 162 * q - 57 * q^2 - 228 * q^3 + 249 * q^4 - 3420 * q^5 - 12 * q^6 + 5808 * q^7 + 61698 * q^8 - 30198 * q^9 + 59997 * q^10 + 175689 * q^11 - 147411 * q^12 + 713586 * q^13 - 96867 * q^14 - 143316 * q^15 + 556665 * q^16 - 119334 * q^17 - 711948 * q^18 + 1752348 * q^19 + 4774248 * q^20 + 57972 * q^21 + 1413495 * q^22 - 5098719 * q^23 + 3891975 * q^24 + 10869768 * q^25 + 5518221 * q^26 + 13281609 * q^27 + 9017757 * q^28 - 2782023 * q^29 - 10231020 * q^30 + 8407836 * q^31 + 6197838 * q^32 - 8252229 * q^33 - 49656453 * q^34 - 23563824 * q^35 + 151165428 * q^36 - 23634336 * q^37 - 12277422 * q^38 + 100476834 * q^39 + 165006327 * q^40 + 74094072 * q^41 - 3662109 * q^42 - 90803088 * q^43 - 350087604 * q^44 - 184820799 * q^45 - 114643110 * q^46 + 158694333 * q^47 + 359750805 * q^48 + 36118224 * q^49 - 259200273 * q^50 + 176035647 * q^51 - 203883429 * q^52 - 31488120 * q^53 - 109796865 * q^54 + 23137227 * q^55 + 37371291 * q^56 - 12449808 * q^57 - 840994983 * q^58 - 77893794 * q^59 + 244178580 * q^60 - 980597586 * q^61 - 586588080 * q^62 - 48634623 * q^63 - 917012376 * q^64 + 1432770144 * q^65 - 177475497 * q^66 - 302695398 * q^67 + 1615796082 * q^68 + 699674787 * q^69 + 2092804794 * q^70 - 774435768 * q^71 - 2899807611 * q^72 - 2505680652 * q^73 + 1161236205 * q^74 - 2302474524 * q^75 + 1445475621 * q^76 - 1374645213 * q^77 + 2942410749 * q^78 - 29533980 * q^79 + 9154934064 * q^80 - 2232253221 * q^81 + 707552205 * q^82 - 392438496 * q^83 - 1388366664 * q^84 - 556053567 * q^85 + 852383496 * q^86 - 6650019951 * q^87 + 3660093510 * q^88 + 100313124 * q^89 + 12897388398 * q^90 + 684844038 * q^91 + 621259308 * q^92 + 2212599060 * q^93 + 3136220628 * q^94 + 1257937926 * q^95 - 6811500039 * q^96 + 70258497 * q^97 - 8202052869 * q^98 - 2679000153 * q^99

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