LMFDB - Embedded newform 37.10.c.a.10.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.c (of order $3$, degree $2$, 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:	$54$
Relative dimension:	$27$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.21
Character	$\chi$	$=$	37.10
Dual form			37.10.c.a.26.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.4973 - 21.6460i) q^{2} +(-65.5823 - 113.592i) q^{3} +(-56.3672 - 97.6309i) q^{4} +(1069.92 + 1853.15i) q^{5} -3278.42 q^{6} +(-1698.03 - 2941.08i) q^{7} +9979.52 q^{8} +(1239.41 - 2146.72i) q^{9} +O(q^{10})$	\(q+(12.4973 - 21.6460i) q^{2} +(-65.5823 - 113.592i) q^{3} +(-56.3672 - 97.6309i) q^{4} +(1069.92 + 1853.15i) q^{5} -3278.42 q^{6} +(-1698.03 - 2941.08i) q^{7} +9979.52 q^{8} +(1239.41 - 2146.72i) q^{9} +53484.4 q^{10} +42114.7 q^{11} +(-7393.39 + 12805.7i) q^{12} +(79955.9 + 138488. i) q^{13} -84883.5 q^{14} +(140335. - 243068. i) q^{15} +(153577. - 266004. i) q^{16} +(-12344.2 + 21380.7i) q^{17} +(-30978.7 - 53656.7i) q^{18} +(-545548. - 944916. i) q^{19} +(120616. - 208914. i) q^{20} +(-222722. + 385765. i) q^{21} +(526321. - 911615. i) q^{22} +1.78643e6 q^{23} +(-654480. - 1.13359e6i) q^{24} +(-1.31288e6 + 2.27397e6i) q^{25} +3.99695e6 q^{26} -2.90685e6 q^{27} +(-191427. + 331561. i) q^{28} -5.83438e6 q^{29} +(-3.50763e6 - 6.07540e6i) q^{30} +9.76036e6 q^{31} +(-1.28387e6 - 2.22372e6i) q^{32} +(-2.76198e6 - 4.78389e6i) q^{33} +(308539. + 534404. i) q^{34} +(3.63350e6 - 6.29341e6i) q^{35} -279449. q^{36} +(9.07388e6 - 6.90120e6i) q^{37} -2.72716e7 q^{38} +(1.04874e7 - 1.81647e7i) q^{39} +(1.06772e7 + 1.84935e7i) q^{40} +(1.10772e7 + 1.91862e7i) q^{41} +(5.56686e6 + 9.64209e6i) q^{42} +1.44716e7 q^{43} +(-2.37389e6 - 4.11169e6i) q^{44} +5.30427e6 q^{45} +(2.23257e7 - 3.86692e7i) q^{46} -4.37626e7 q^{47} -4.02879e7 q^{48} +(1.44102e7 - 2.49592e7i) q^{49} +(3.28150e7 + 5.68372e7i) q^{50} +3.23824e6 q^{51} +(9.01379e6 - 1.56123e7i) q^{52} +(1.62965e7 - 2.82264e7i) q^{53} +(-3.63279e7 + 6.29218e7i) q^{54} +(4.50591e7 + 7.80447e7i) q^{55} +(-1.69455e7 - 2.93505e7i) q^{56} +(-7.15566e7 + 1.23940e8i) q^{57} +(-7.29143e7 + 1.26291e8i) q^{58} +(-1.96702e7 + 3.40698e7i) q^{59} -3.16412e7 q^{60} +(-5.59491e6 - 9.69067e6i) q^{61} +(1.21979e8 - 2.11273e8i) q^{62} -8.41824e6 q^{63} +9.30837e7 q^{64} +(-1.71092e8 + 2.96341e8i) q^{65} -1.38070e8 q^{66} +(2.35185e7 + 4.07352e7i) q^{67} +2.78323e6 q^{68} +(-1.17158e8 - 2.02924e8i) q^{69} +(-9.08183e7 - 1.57302e8i) q^{70} +(9.67325e7 + 1.67546e8i) q^{71} +(1.23687e7 - 2.14233e7i) q^{72} -8.23371e6 q^{73} +(-3.59842e7 - 2.82660e8i) q^{74} +3.44406e8 q^{75} +(-6.15020e7 + 1.06525e8i) q^{76} +(-7.15120e7 - 1.23862e8i) q^{77} +(-2.62129e8 - 4.54021e8i) q^{78} +(-1.26604e8 - 2.19284e8i) q^{79} +6.57260e8 q^{80} +(1.66243e8 + 2.87941e8i) q^{81} +5.53740e8 q^{82} +(-1.03937e8 + 1.80024e8i) q^{83} +5.02168e7 q^{84} -5.28289e7 q^{85} +(1.80856e8 - 3.13252e8i) q^{86} +(3.82633e8 + 6.62739e8i) q^{87} +4.20284e8 q^{88} +(-2.76177e8 + 4.78352e8i) q^{89} +(6.62892e7 - 1.14816e8i) q^{90} +(2.71535e8 - 4.70313e8i) q^{91} +(-1.00696e8 - 1.74411e8i) q^{92} +(-6.40107e8 - 1.10870e9i) q^{93} +(-5.46916e8 + 9.47286e8i) q^{94} +(1.16738e9 - 2.02196e9i) q^{95} +(-1.68398e8 + 2.91674e8i) q^{96} -1.20069e9 q^{97} +(-3.60178e8 - 6.23847e8i) q^{98} +(5.21974e7 - 9.04085e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) $ 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9 - 82404 * q^10 - 108196 * q^11 + 45492 * q^12 - 29827 * q^13 - 504992 * q^14 + 87135 * q^15 - 1561814 * q^16 + 116991 * q^17 + 1767678 * q^18 - 599677 * q^19 + 4122556 * q^20 - 221017 * q^21 - 257914 * q^22 + 1752736 * q^23 + 1149408 * q^24 - 6037260 * q^25 - 16731604 * q^26 - 1916582 * q^27 + 1917318 * q^28 - 11336100 * q^29 - 20390006 * q^30 + 14447580 * q^31 - 873740 * q^32 - 4494200 * q^33 + 13736524 * q^34 - 8546699 * q^35 + 61692836 * q^36 - 1919410 * q^37 - 85447920 * q^38 - 14035313 * q^39 + 3210182 * q^40 + 28676571 * q^41 - 101904850 * q^42 + 56602028 * q^43 + 153011074 * q^44 + 104234980 * q^45 + 99535572 * q^46 - 147509100 * q^47 - 203670880 * q^48 - 201857540 * q^49 - 91421384 * q^50 + 328228338 * q^51 - 69374156 * q^52 + 59137361 * q^53 + 201615042 * q^54 - 219079762 * q^55 + 202573590 * q^56 - 5989161 * q^57 - 157098688 * q^58 + 137993791 * q^59 + 413427232 * q^60 - 244884419 * q^61 + 109345558 * q^62 - 995908592 * q^63 + 184008092 * q^64 + 248745395 * q^65 + 1965122248 * q^66 - 130143913 * q^67 + 667610796 * q^68 + 246927272 * q^69 - 291173360 * q^70 + 473387559 * q^71 + 366188748 * q^72 + 923638972 * q^73 - 885443390 * q^74 - 2185997392 * q^75 - 337459826 * q^76 - 586609928 * q^77 - 261025842 * q^78 + 563110723 * q^79 - 4210381784 * q^80 + 713813329 * q^81 + 3458576264 * q^82 - 663594441 * q^83 - 2635249016 * q^84 - 1417287750 * q^85 - 2269028474 * q^86 + 314944482 * q^87 - 7714172 * q^88 + 655027619 * q^89 + 588021376 * q^90 - 1833870961 * q^91 - 2384055268 * q^92 - 90092600 * q^93 - 1449940302 * q^94 + 2787158841 * q^95 + 2383567424 * q^96 - 2751583248 * q^97 + 4970876154 * q^98 + 2668760954 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	12.4973	−	21.6460i	0.552310	−	0.956629i	−0.445798	−	0.895134i	$-0.647080\pi$
$2$	12.4973	−	21.6460i	0.552310	−	0.956629i	0.998107	−	0.0614949i	$-0.0195868\pi$
$3$	−65.5823	−	113.592i	−0.467457	−	0.809659i	0.531852	−	0.846837i	$-0.321496\pi$
$3$	−65.5823	−	113.592i	−0.467457	−	0.809659i	−0.999309	+	0.0371787i	$0.988163\pi$
$4$	−56.3672	−	97.6309i	−0.110092	−	0.190685i
$5$	1069.92	+	1853.15i	0.765570	+	1.32601i	0.939945	+	0.341326i	$0.110876\pi$
$5$	1069.92	+	1853.15i	0.765570	+	1.32601i	−0.174375	+	0.984679i	$0.555791\pi$
$6$	−3278.42			−1.03272
$7$	−1698.03	−	2941.08i	−0.267303	−	0.462983i	0.700861	−	0.713298i	$-0.252799\pi$
$7$	−1698.03	−	2941.08i	−0.267303	−	0.462983i	−0.968165	+	0.250315i	$0.919466\pi$
$8$	9979.52			0.861399
$9$	1239.41	−	2146.72i	0.0629686	−	0.109065i
$10$	53484.4			1.69133
$11$	42114.7			0.867294			0.433647	−	0.901083i	$-0.357227\pi$
$11$	42114.7			0.867294			0.433647	+	0.901083i	$0.357227\pi$
$12$	−7393.39	+	12805.7i	−0.102927	+	0.178274i
$13$	79955.9	+	138488.i	0.776436	+	1.34483i	0.933984	+	0.357315i	$0.116308\pi$
$13$	79955.9	+	138488.i	0.776436	+	1.34483i	−0.157548	+	0.987511i	$0.550359\pi$
$14$	−84883.5			−0.590537
$15$	140335.	−	243068.i	0.715741	−	1.23970i
$16$	153577.	−	266004.i	0.585852	−	1.01472i
$17$	−12344.2	+	21380.7i	−0.0358461	+	0.0620872i	−0.883392	−	0.468635i	$-0.844746\pi$
$17$	−12344.2	+	21380.7i	−0.0358461	+	0.0620872i	0.847546	+	0.530722i	$0.178079\pi$
$18$	−30978.7	−	53656.7i	−0.0695564	−	0.120475i
$19$	−545548.	−	944916.i	−0.960376	−	1.66342i	−0.721555	−	0.692357i	$-0.756572\pi$
$19$	−545548.	−	944916.i	−0.960376	−	1.66342i	−0.238821	−	0.971064i	$-0.576761\pi$
$20$	120616.	−	208914.i	0.168567	−	0.291966i
$21$	−222722.	+	385765.i	−0.249906	+	0.432849i
$22$	526321.	−	911615.i	0.479015	−	0.829678i
$23$	1.78643e6			1.33110			0.665551	−	0.746352i	$-0.268196\pi$
$23$	1.78643e6			1.33110			0.665551	+	0.746352i	$0.268196\pi$
$24$	−654480.	−	1.13359e6i	−0.402667	−	0.697439i
$25$	−1.31288e6	+	2.27397e6i	−0.672193	+	1.16427i
$26$	3.99695e6			1.71533
$27$	−2.90685e6			−1.05265
$28$	−191427.	+	331561.i	−0.0588561	+	0.101942i
$29$	−5.83438e6			−1.53181			−0.765903	−	0.642956i	$-0.777708\pi$
$29$	−5.83438e6			−1.53181			−0.765903	+	0.642956i	$0.777708\pi$
$30$	−3.50763e6	−	6.07540e6i	−0.790622	−	1.36940i
$31$	9.76036e6			1.89818			0.949091	−	0.315001i	$-0.102005\pi$
$31$	9.76036e6			1.89818			0.949091	+	0.315001i	$0.102005\pi$
$32$	−1.28387e6	−	2.22372e6i	−0.216443	−	0.374891i
$33$	−2.76198e6	−	4.78389e6i	−0.405422	−	0.702212i
$34$	308539.	+	534404.i	0.0395963	+	0.0685827i
$35$	3.63350e6	−	6.29341e6i	0.409279	−	0.708892i
$36$	−279449.			−0.0277294
$37$	9.07388e6	−	6.90120e6i	0.795949	−	0.605364i
$37$	9.07388e6	−	6.90120e6i	0.795949	−	0.605364i
$38$	−2.72716e7			−2.12170
$39$	1.04874e7	−	1.81647e7i	0.725900	−	1.25730i
$40$	1.06772e7	+	1.84935e7i	0.659461	+	1.14222i
$41$	1.10772e7	+	1.91862e7i	0.612211	+	1.06038i	0.990867	+	0.134843i	$0.0430529\pi$
$41$	1.10772e7	+	1.91862e7i	0.612211	+	1.06038i	−0.378656	+	0.925537i	$0.623614\pi$
$42$	5.56686e6	+	9.64209e6i	0.276051	+	0.478134i
$43$	1.44716e7			0.645517			0.322759	−	0.946481i	$-0.395390\pi$
$43$	1.44716e7			0.645517			0.322759	+	0.946481i	$0.395390\pi$
$44$	−2.37389e6	−	4.11169e6i	−0.0954823	−	0.165380i
$45$	5.30427e6			0.192828
$46$	2.23257e7	−	3.86692e7i	0.735181	−	1.27337i
$47$	−4.37626e7			−1.30816			−0.654082	−	0.756423i	$-0.726945\pi$
$47$	−4.37626e7			−1.30816			−0.654082	+	0.756423i	$0.726945\pi$
$48$	−4.02879e7			−1.09544
$49$	1.44102e7	−	2.49592e7i	0.357098	−	0.618511i
$50$	3.28150e7	+	5.68372e7i	0.742518	+	1.28608i
$51$	3.23824e6			0.0670259
$52$	9.01379e6	−	1.56123e7i	0.170959	−	0.296110i
$53$	1.62965e7	−	2.82264e7i	0.283696	−	0.491376i	−0.688596	−	0.725145i	$-0.741773\pi$
$53$	1.62965e7	−	2.82264e7i	0.283696	−	0.491376i	0.972292	+	0.233769i	$0.0751059\pi$
$54$	−3.63279e7	+	6.29218e7i	−0.581391	+	1.00700i
$55$	4.50591e7	+	7.80447e7i	0.663974	+	1.15004i
$56$	−1.69455e7	−	2.93505e7i	−0.230255	−	0.398813i
$57$	−7.15566e7	+	1.23940e8i	−0.897869	+	1.55515i
$58$	−7.29143e7	+	1.26291e8i	−0.846032	+	1.46537i
$59$	−1.96702e7	+	3.40698e7i	−0.211337	+	0.366046i	−0.952133	−	0.305684i	$-0.901115\pi$
$59$	−1.96702e7	+	3.40698e7i	−0.211337	+	0.366046i	0.740796	+	0.671730i	$0.234448\pi$
$60$	−3.16412e7			−0.315190
$61$	−5.59491e6	−	9.69067e6i	−0.0517379	−	0.0896127i	0.838997	−	0.544137i	$-0.183143\pi$
$61$	−5.59491e6	−	9.69067e6i	−0.0517379	−	0.0896127i	−0.890734	+	0.454524i	$0.849809\pi$
$62$	1.21979e8	−	2.11273e8i	1.04838	−	1.81586i
$63$	−8.41824e6			−0.0673270
$64$	9.30837e7			0.693528
$65$	−1.71092e8	+	2.96341e8i	−1.18883	+	2.05912i
$66$	−1.38070e8			−0.895674
$67$	2.35185e7	+	4.07352e7i	0.142585	+	0.246964i	0.928469	−	0.371409i	$-0.121125\pi$
$67$	2.35185e7	+	4.07352e7i	0.142585	+	0.246964i	−0.785885	+	0.618373i	$0.787792\pi$
$68$	2.78323e6			0.0157855
$69$	−1.17158e8	−	2.02924e8i	−0.622233	−	1.07774i
$70$	−9.08183e7	−	1.57302e8i	−0.452097	−	0.783056i
$71$	9.67325e7	+	1.67546e8i	0.451762	+	0.782475i	0.998496	−	0.0548319i	$-0.0174623\pi$
$71$	9.67325e7	+	1.67546e8i	0.451762	+	0.782475i	−0.546734	+	0.837307i	$0.684129\pi$
$72$	1.23687e7	−	2.14233e7i	0.0542412	−	0.0939484i
$73$	−8.23371e6			−0.0339346			−0.0169673	−	0.999856i	$-0.505401\pi$
$73$	−8.23371e6			−0.0339346			−0.0169673	+	0.999856i	$0.505401\pi$
$74$	−3.59842e7	−	2.82660e8i	−0.139498	−	1.09578i
$75$	3.44406e8			1.25688
$76$	−6.15020e7	+	1.06525e8i	−0.211460	+	0.366259i
$77$	−7.15120e7	−	1.23862e8i	−0.231831	−	0.401542i
$78$	−2.62129e8	−	4.54021e8i	−0.801844	−	1.38883i
$79$	−1.26604e8	−	2.19284e8i	−0.365699	−	0.633410i	0.623189	−	0.782071i	$-0.285837\pi$
$79$	−1.26604e8	−	2.19284e8i	−0.365699	−	0.633410i	−0.988888	+	0.148662i	$0.952503\pi$
$80$	6.57260e8			1.79404
$81$	1.66243e8	+	2.87941e8i	0.429101	+	0.743225i
$82$	5.53740e8			1.35252
$83$	−1.03937e8	+	1.80024e8i	−0.240391	+	0.416369i	−0.960826	−	0.277154i	$-0.910609\pi$
$83$	−1.03937e8	+	1.80024e8i	−0.240391	+	0.416369i	0.720435	+	0.693523i	$0.243942\pi$
$84$	5.02168e7			0.110051
$85$	−5.28289e7			−0.109771
$86$	1.80856e8	−	3.13252e8i	0.356525	−	0.617520i
$87$	3.82633e8	+	6.62739e8i	0.716053	+	1.24024i
$88$	4.20284e8			0.747086
$89$	−2.76177e8	+	4.78352e8i	−0.466586	+	0.808151i	−0.999272	−	0.0381624i	$-0.987850\pi$
$89$	−2.76177e8	+	4.78352e8i	−0.466586	+	0.808151i	0.532685	+	0.846313i	$0.321183\pi$
$90$	6.62892e7	−	1.14816e8i	0.106501	−	0.184464i
$91$	2.71535e8	−	4.70313e8i	0.415088	−	0.718954i
$92$	−1.00696e8	−	1.74411e8i	−0.146544	−	0.253822i
$93$	−6.40107e8	−	1.10870e9i	−0.887318	−	1.53688i
$94$	−5.46916e8	+	9.47286e8i	−0.722512	+	1.25143i
$95$	1.16738e9	−	2.02196e9i	1.47047	−	2.54693i
$96$	−1.68398e8	+	2.91674e8i	−0.202356	+	0.350491i
$97$	−1.20069e9			−1.37707			−0.688536	−	0.725202i	$-0.741746\pi$
$97$	−1.20069e9			−1.37707			−0.688536	+	0.725202i	$0.741746\pi$
$98$	−3.60178e8	−	6.23847e8i	−0.394457	−	0.683220i
$99$	5.21974e7	−	9.04085e7i	0.0546123	−	0.0945913i
$100$	2.96013e8			0.296013
$101$	−1.13148e9			−1.08193			−0.540966	−	0.841044i	$-0.681941\pi$
$101$	−1.13148e9			−1.08193			−0.540966	+	0.841044i	$0.681941\pi$
$102$	4.04694e7	−	7.00950e7i	0.0370191	−	0.0641189i
$103$	−1.20663e9			−1.05634			−0.528171	−	0.849138i	$-0.677122\pi$
$103$	−1.20663e9			−1.05634			−0.528171	+	0.849138i	$0.677122\pi$
$104$	7.97922e8	+	1.38204e9i	0.668822	+	1.15843i
$105$	−9.53174e8			−0.765280
$106$	−4.07327e8	−	7.05510e8i	−0.313376	−	0.542784i
$107$	−3.24286e8	−	5.61680e8i	−0.239167	−	0.414250i	0.721308	−	0.692614i	$-0.243541\pi$
$107$	−3.24286e8	−	5.61680e8i	−0.239167	−	0.414250i	−0.960476	+	0.278364i	$0.910208\pi$
$108$	1.63851e8	+	2.83798e8i	0.115889	+	0.200726i
$109$	−8.57300e8	+	1.48489e9i	−0.581720	+	1.00757i	0.413556	+	0.910479i	$0.364287\pi$
$109$	−8.57300e8	+	1.48489e9i	−0.581720	+	1.00757i	−0.995276	+	0.0970895i	$0.969047\pi$
$110$	2.25248e9			1.46688
$111$	−1.37901e9	−	5.78123e8i	−0.862210	−	0.361465i
$112$	−1.04312e9			−0.626401
$113$	−1.70799e8	+	2.95833e8i	−0.0985447	+	0.170684i	−0.911082	−	0.412224i	$-0.864752\pi$
$113$	−1.70799e8	+	2.95833e8i	−0.0985447	+	0.170684i	0.812538	+	0.582909i	$0.198085\pi$
$114$	1.78853e9	+	3.09783e9i	0.991803	+	1.71785i
$115$	1.91133e9	+	3.31053e9i	1.01905	+	1.76505i
$116$	3.28868e8	+	5.69616e8i	0.168640	+	0.292093i
$117$	3.96393e8			0.195565
$118$	4.91651e8	+	8.51565e8i	0.233447	+	0.404342i
$119$	8.38431e7			0.0383271
$120$	1.40048e9	−	2.42570e9i	0.616539	−	1.06788i
$121$	−5.84304e8			−0.247802
$122$	−2.79686e8			−0.114301
$123$	1.45293e9	−	2.51655e9i	0.572364	−	0.991363i
$124$	−5.50164e8	−	9.52912e8i	−0.208975	−	0.361956i
$125$	−1.43932e9			−0.527304
$126$	−1.05206e8	+	1.82222e8i	−0.0371853	+	0.0644069i
$127$	−1.08706e9	+	1.88284e9i	−0.370796	+	0.642237i	−0.989688	−	0.143239i	$-0.954248\pi$
$127$	−1.08706e9	+	1.88284e9i	−0.370796	+	0.642237i	0.618892	+	0.785476i	$0.287582\pi$
$128$	1.82064e9	−	3.15344e9i	0.599486	−	1.03834i
$129$	−9.49080e8	−	1.64385e9i	−0.301751	−	0.522648i
$130$	4.27640e9	+	7.40694e9i	1.31321	+	2.27454i
$131$	−1.47586e9	+	2.55626e9i	−0.437848	+	0.758375i	−0.997523	−	0.0703369i	$-0.977593\pi$
$131$	−1.47586e9	+	2.55626e9i	−0.437848	+	0.758375i	0.559675	+	0.828712i	$0.310926\pi$
$132$	−3.11370e8	+	5.39309e8i	−0.0892677	+	0.154616i
$133$	−1.85271e9	+	3.20900e9i	−0.513424	+	0.889276i
$134$	1.17567e9			0.315004
$135$	−3.11008e9	−	5.38682e9i	−0.805880	−	1.39582i
$136$	−1.23189e8	+	2.13369e8i	−0.0308778	+	0.0534819i
$137$	1.82004e9			0.441407			0.220704	−	0.975341i	$-0.429165\pi$
$137$	1.82004e9			0.441407			0.220704	+	0.975341i	$0.429165\pi$
$138$	−5.85668e9			−1.37466
$139$	1.46939e9	−	2.54506e9i	0.333865	−	0.578271i	−0.649401	−	0.760446i	$-0.724980\pi$
$139$	1.46939e9	−	2.54506e9i	0.333865	−	0.578271i	0.983266	+	0.182175i	$0.0583138\pi$
$140$	−8.19242e8			−0.180234
$141$	2.87005e9	+	4.97107e9i	0.611510	+	1.05917i
$142$	4.83560e9			0.998050
$143$	3.36732e9	+	5.83236e9i	0.673398	+	1.16636i
$144$	−3.80692e8	−	6.59377e8i	−0.0737806	−	0.127792i
$145$	−6.24230e9	−	1.08120e10i	−1.17270	−	2.03118i
$146$	−1.02900e8	+	1.78227e8i	−0.0187424	+	0.0324628i
$147$	−3.78021e9			−0.667711
$148$	−1.18524e9	−	4.96889e8i	−0.203062	−	0.0851299i
$149$	3.14173e9			0.522192			0.261096	−	0.965313i	$-0.415916\pi$
$149$	3.14173e9			0.522192			0.261096	+	0.965313i	$0.415916\pi$
$150$	4.30417e9	−	7.45503e9i	0.694190	−	1.20237i
$151$	−3.86846e9	−	6.70037e9i	−0.605539	−	1.04882i	−0.991966	−	0.126504i	$-0.959624\pi$
$151$	−3.86846e9	−	6.70037e9i	−0.605539	−	1.04882i	0.386428	−	0.922320i	$-0.373709\pi$
$152$	−5.44430e9	−	9.42981e9i	−0.827268	−	1.43287i
$153$	3.05990e7	+	5.29990e7i	0.00451436	+	0.00781909i
$154$	−3.57484e9			−0.512169
$155$	1.04428e10	+	1.80874e10i	1.45319	+	2.51700i
$156$	−2.36458e9			−0.319664
$157$	−5.26176e9	+	9.11363e9i	−0.691166	+	1.19713i	0.280290	+	0.959915i	$0.409569\pi$
$157$	−5.26176e9	+	9.11363e9i	−0.691166	+	1.19713i	−0.971456	+	0.237219i	$0.923764\pi$
$158$	−6.32883e9			−0.807917
$159$	−4.27506e9			−0.530463
$160$	2.74726e9	−	4.75839e9i	0.331405	−	0.574010i
$161$	−3.03342e9	−	5.25404e9i	−0.355808	−	0.616278i
$162$	8.31036e9			0.947987
$163$	3.83095e9	−	6.63540e9i	0.425072	−	0.736246i	−0.571355	−	0.820703i	$-0.693582\pi$
$163$	3.83095e9	−	6.63540e9i	0.425072	−	0.736246i	0.996427	+	0.0844566i	$0.0269154\pi$
$164$	1.24878e9	−	2.16295e9i	0.134799	−	0.233479i
$165$	5.91017e9	−	1.02367e10i	0.620758	−	1.07518i
$166$	2.59787e9	+	4.49964e9i	0.265540	+	0.459929i
$167$	−3.49154e9	−	6.04752e9i	−0.347370	−	0.601663i	0.638411	−	0.769696i	$-0.279592\pi$
$167$	−3.49154e9	−	6.04752e9i	−0.347370	−	0.601663i	−0.985781	+	0.168032i	$0.946259\pi$
$168$	−2.22266e9	+	3.84975e9i	−0.215269	+	0.372856i
$169$	−7.48366e9	+	1.29621e10i	−0.705706	+	1.22232i
$170$	−6.60221e8	+	1.14354e9i	−0.0606274	+	0.105010i
$171$	−2.70463e9			−0.241894
$172$	−8.15723e8	−	1.41287e9i	−0.0710664	−	0.123091i
$173$	6.80849e9	−	1.17927e10i	0.577888	−	1.00093i	−0.417833	−	0.908524i	$-0.637210\pi$
$173$	6.80849e9	−	1.17927e10i	0.577888	−	1.00093i	0.995721	−	0.0924075i	$-0.0294562\pi$
$174$	1.91276e10			1.58193
$175$	8.91723e9			0.718719
$176$	6.46786e9	−	1.12027e10i	0.508105	−	0.880064i
$177$	5.16008e9			0.395163
$178$	6.90295e9	+	1.19563e10i	0.515400	+	0.892699i
$179$	−1.73405e10			−1.26248			−0.631239	−	0.775589i	$-0.717453\pi$
$179$	−1.73405e10			−1.26248			−0.631239	+	0.775589i	$0.717453\pi$
$180$	−2.98987e8	−	5.17860e8i	−0.0212288	−	0.0367694i
$181$	4.46568e9	+	7.73479e9i	0.309267	+	0.535667i	0.978202	−	0.207654i	$-0.0665828\pi$
$181$	4.46568e9	+	7.73479e9i	0.309267	+	0.535667i	−0.668935	+	0.743321i	$0.733249\pi$
$182$	−6.78694e9	−	1.17553e10i	−0.458514	−	0.794170i
$183$	−7.33855e8	+	1.27107e9i	−0.0483705	+	0.0837801i
$184$	1.78277e10			1.14661
$185$	2.24972e10	+	9.43154e9i	1.41207	+	0.591984i
$186$	−3.19986e10			−1.96030
$187$	−5.19870e8	+	9.00441e8i	−0.0310891	+	0.0538478i
$188$	2.46677e9	+	4.27258e9i	0.144019	+	0.249448i
$189$	4.93592e9	+	8.54927e9i	0.281378	+	0.487361i
$190$	−2.91783e10	−	5.05383e10i	−1.62431	−	2.81339i
$191$	1.09004e10			0.592644			0.296322	−	0.955088i	$-0.404240\pi$
$191$	1.09004e10			0.592644			0.296322	+	0.955088i	$0.404240\pi$
$192$	−6.10465e9	−	1.05736e10i	−0.324194	−	0.561521i
$193$	−1.31662e10			−0.683052			−0.341526	−	0.939872i	$-0.610944\pi$
$193$	−1.31662e10			−0.683052			−0.341526	+	0.939872i	$0.610944\pi$
$194$	−1.50054e10	+	2.59901e10i	−0.760570	+	1.31735i
$195$	4.48825e10			2.22291
$196$	−3.24905e9			−0.157255
$197$	−3.67671e9	+	6.36825e9i	−0.173925	+	0.301246i	−0.939789	−	0.341756i	$-0.888978\pi$
$197$	−3.67671e9	+	6.36825e9i	−0.173925	+	0.301246i	0.765864	+	0.643003i	$0.222312\pi$
$198$	−1.30466e9	−	2.25973e9i	−0.0603258	−	0.104487i
$199$	−2.31675e10			−1.04723			−0.523613	−	0.851956i	$-0.675416\pi$
$199$	−2.31675e10			−1.04723			−0.523613	+	0.851956i	$0.675416\pi$
$200$	−1.31019e10	+	2.26931e10i	−0.579027	+	1.00290i
$201$	3.08479e9	−	5.34302e9i	0.133304	−	0.230890i
$202$	−1.41405e10	+	2.44920e10i	−0.597562	+	1.03501i
$203$	9.90697e9	+	1.71594e10i	0.409457	+	0.709201i
$204$	−1.82530e8	−	3.16152e8i	−0.00737903	−	0.0127809i
$205$	−2.37032e10	+	4.10552e10i	−0.937380	+	1.62359i
$206$	−1.50796e10	+	2.61187e10i	−0.583428	+	1.01053i
$207$	2.21413e9	−	3.83498e9i	0.0838177	−	0.145177i
$208$	4.91177e10			1.81951
$209$	−2.29755e10	−	3.97948e10i	−0.832928	−	1.44267i
$210$	−1.19121e10	+	2.06324e10i	−0.422672	+	0.732089i
$211$	3.47287e10			1.20619			0.603097	−	0.797667i	$-0.293933\pi$
$211$	3.47287e10			1.20619			0.603097	+	0.797667i	$0.293933\pi$
$212$	−3.67436e9			−0.124931
$213$	1.26879e10	−	2.19761e10i	0.422358	−	0.731546i
$214$	−1.62109e10			−0.528378
$215$	1.54834e10	+	2.68180e10i	0.494188	+	0.855959i
$216$	−2.90089e10			−0.906755
$217$	−1.65734e10	−	2.87060e10i	−0.507391	−	0.878827i
$218$	2.14280e10	+	3.71143e10i	0.642579	+	1.11298i
$219$	5.39986e8	+	9.35283e8i	0.0158630	+	0.0274754i
$220$	5.07972e9	−	8.79833e9i	0.146197	−	0.253220i
$221$	−3.94796e9			−0.111329
$222$	−2.97480e10	+	2.26250e10i	−0.821995	+	0.625174i
$223$	−1.52140e10			−0.411977			−0.205988	−	0.978554i	$-0.566041\pi$
$223$	−1.52140e10			−0.411977			−0.205988	+	0.978554i	$0.566041\pi$
$224$	−4.36009e9	+	7.55189e9i	−0.115712	+	0.200419i
$225$	3.25439e9	+	5.63677e9i	0.0846542	+	0.146625i
$226$	4.26908e9	+	7.39426e9i	0.108854	+	0.188541i
$227$	1.02165e10	+	1.76954e10i	0.255379	+	0.442329i	0.964998	−	0.262256i	$-0.0844666\pi$
$227$	1.02165e10	+	1.76954e10i	0.255379	+	0.442329i	−0.709620	+	0.704585i	$0.751133\pi$
$228$	1.61338e10			0.395394
$229$	−2.54869e10	−	4.41446e10i	−0.612431	−	1.06076i	−0.990829	−	0.135118i	$-0.956859\pi$
$229$	−2.54869e10	−	4.41446e10i	−0.612431	−	1.06076i	0.378399	−	0.925643i	$-0.376475\pi$
$230$	9.55464e10			2.25133
$231$	−9.37985e9	+	1.62464e10i	−0.216741	+	0.375407i
$232$	−5.82243e10			−1.31950
$233$	4.19495e10			0.932450			0.466225	−	0.884666i	$-0.345614\pi$
$233$	4.19495e10			0.932450			0.466225	+	0.884666i	$0.345614\pi$
$234$	4.95386e9	−	8.58035e9i	0.108012	−	0.187083i
$235$	−4.68223e10	−	8.10985e10i	−1.00149	−	1.73463i
$236$	4.43502e9			0.0930662
$237$	−1.66059e10	+	2.87623e10i	−0.341897	+	0.592183i
$238$	1.04782e9	−	1.81487e9i	0.0211684	−	0.0366648i
$239$	−5.99685e9	+	1.03868e10i	−0.118887	+	0.205917i	−0.919327	−	0.393495i	$-0.871266\pi$
$239$	−5.99685e9	+	1.03868e10i	−0.118887	+	0.205917i	0.800440	+	0.599413i	$0.204599\pi$
$240$	−4.31047e10	−	7.46595e10i	−0.838636	−	1.45256i
$241$	−7.90909e9	−	1.36989e10i	−0.151025	−	0.261584i	0.780579	−	0.625057i	$-0.214924\pi$
$241$	−7.90909e9	−	1.36989e10i	−0.151025	−	0.261584i	−0.931605	+	0.363473i	$0.881591\pi$
$242$	−7.30225e9	+	1.26479e10i	−0.136863	+	0.237054i
$243$	−6.80259e9	+	1.17824e10i	−0.125154	+	0.216774i
$244$	−6.30739e8	+	1.09247e9i	−0.0113919	+	0.0197313i
$245$	6.16707e10			1.09353
$246$	−3.63156e10	−	6.29004e10i	−0.632244	−	1.09508i
$247$	8.72396e10	−	1.51103e11i	1.49134	−	2.58308i
$248$	9.74036e10			1.63509
$249$	2.72657e10			0.449489
$250$	−1.79876e10	+	3.11555e10i	−0.291235	+	0.504434i
$251$	−5.52840e10			−0.879159			−0.439580	−	0.898204i	$-0.644873\pi$
$251$	−5.52840e10			−0.879159			−0.439580	+	0.898204i	$0.644873\pi$
$252$	4.74513e8	+	8.21881e8i	0.00741218	+	0.0128383i
$253$	7.52350e10			1.15446
$254$	2.71706e10	+	4.70609e10i	0.409588	+	0.709428i
$255$	3.46464e9	+	6.00093e9i	0.0513130	+	0.0888767i
$256$	−2.16769e10	−	3.75454e10i	−0.315440	−	0.546358i
$257$	2.56076e10	−	4.43537e10i	0.366159	−	0.634206i	−0.622802	−	0.782379i	$-0.714006\pi$
$257$	2.56076e10	−	4.43537e10i	0.366159	−	0.634206i	0.988961	+	0.148173i	$0.0473393\pi$
$258$	−4.74439e10			−0.666641
$259$	−3.57047e10	−	1.49685e10i	−0.493033	−	0.206695i
$260$	3.85760e10			0.523525
$261$	−7.23120e9	+	1.25248e10i	−0.0964558	+	0.167066i
$262$	3.68886e10	+	6.38929e10i	0.483656	+	0.837716i
$263$	1.15448e10	+	1.99962e10i	0.148794	+	0.257719i	0.930782	−	0.365575i	$-0.119128\pi$
$263$	1.15448e10	+	1.99962e10i	0.148794	+	0.257719i	−0.781988	+	0.623294i	$0.785794\pi$
$264$	−2.75632e10	−	4.77409e10i	−0.349230	−	0.604885i
$265$	6.97437e10			0.868757
$266$	4.63080e10	+	8.02078e10i	0.567138	+	0.982312i
$267$	7.24492e10			0.872435
$268$	2.65134e9	−	4.59226e9i	0.0313949	−	0.0543776i
$269$	3.69527e10			0.430290			0.215145	−	0.976582i	$-0.430978\pi$
$269$	3.69527e10			0.430290			0.215145	+	0.976582i	$0.430978\pi$
$270$	−1.55471e11			−1.78038
$271$	−4.53966e10	+	7.86292e10i	−0.511283	+	0.885568i	0.488632	+	0.872490i	$0.337496\pi$
$271$	−4.53966e10	+	7.86292e10i	−0.511283	+	0.885568i	−0.999914	+	0.0130777i	$0.995837\pi$
$272$	3.79157e9	+	6.56719e9i	0.0420010	+	0.0727478i
$273$	−7.12317e10			−0.776143
$274$	2.27457e10	−	3.93967e10i	0.243793	−	0.422263i
$275$	−5.52914e10	+	9.57675e10i	−0.582989	+	1.00977i
$276$	−1.32078e10	+	2.28766e10i	−0.137006	+	0.237301i
$277$	−6.05287e10	−	1.04839e11i	−0.617735	−	1.06995i	−0.989898	−	0.141781i	$-0.954717\pi$
$277$	−6.05287e10	−	1.04839e11i	−0.617735	−	1.06995i	0.372163	−	0.928168i	$-0.378616\pi$
$278$	−3.67270e10	−	6.36130e10i	−0.368794	−	0.638769i
$279$	1.20971e10	−	2.09528e10i	0.119526	−	0.207025i
$280$	3.62606e10	−	6.28052e10i	0.352553	−	0.610639i
$281$	−4.42940e10	+	7.67195e10i	−0.423805	+	0.734053i	−0.996308	−	0.0858503i	$-0.972639\pi$
$281$	−4.42940e10	+	7.67195e10i	−0.423805	+	0.734053i	0.572503	+	0.819903i	$0.305973\pi$
$282$	1.43472e11			1.35097
$283$	−2.90738e10	−	5.03573e10i	−0.269440	−	0.466684i	0.699277	−	0.714851i	$-0.253505\pi$
$283$	−2.90738e10	−	5.03573e10i	−0.269440	−	0.466684i	−0.968717	+	0.248166i	$0.920172\pi$
$284$	1.09051e10	−	1.88882e10i	0.0994710	−	0.172289i
$285$	−3.06238e11			−2.74952
$286$	1.68330e11			1.48770
$287$	3.76187e10	−	6.51575e10i	0.327292	−	0.566886i
$288$	−6.36495e9			−0.0545166
$289$	5.89892e10	+	1.02172e11i	0.497430	+	0.861574i
$290$	−3.12049e11			−2.59078
$291$	7.87438e10	+	1.36388e11i	0.643721	+	1.11496i
$292$	4.64112e8	+	8.03865e8i	0.00373594	+	0.00647083i
$293$	−1.66020e10	−	2.87555e10i	−0.131600	−	0.227938i	0.792693	−	0.609621i	$-0.208678\pi$
$293$	−1.66020e10	−	2.87555e10i	−0.131600	−	0.227938i	−0.924294	+	0.381682i	$0.875345\pi$
$294$	−4.72426e10	+	8.18266e10i	−0.368783	+	0.638751i
$295$	−8.41819e10			−0.647172
$296$	9.05529e10	−	6.88706e10i	0.685630	−	0.521460i
$297$	−1.22421e11			−0.912960
$298$	3.92633e10	−	6.80060e10i	0.288412	−	0.499544i
$299$	1.42836e11	+	2.47399e11i	1.03352	+	1.79010i
$300$	−1.94132e10	−	3.36247e10i	−0.138373	−	0.239670i
$301$	−2.45732e10	−	4.25620e10i	−0.172549	−	0.298864i
$302$	−1.93382e11			−1.33778
$303$	7.42050e10	+	1.28527e11i	0.505756	+	0.875996i
$304$	−3.35135e11			−2.25055
$305$	1.19722e10	−	2.07364e10i	0.0792180	−	0.137210i
$306$	1.52963e9			0.00997329
$307$	2.92799e11			1.88125			0.940627	−	0.339443i	$-0.110239\pi$
$307$	2.92799e11			1.88125			0.940627	+	0.339443i	$0.110239\pi$
$308$	−8.06187e9	+	1.39636e10i	−0.0510455	+	0.0884134i
$309$	7.91333e10	+	1.37063e11i	0.493794	+	0.855277i
$310$	5.22027e11			3.21045
$311$	−2.43421e10	+	4.21618e10i	−0.147549	+	0.255563i	−0.930321	−	0.366746i	$-0.880472\pi$
$311$	−2.43421e10	+	4.21618e10i	−0.147549	+	0.255563i	0.782772	+	0.622309i	$0.213805\pi$
$312$	1.04659e11	−	1.81275e11i	0.625290	−	1.08303i
$313$	4.61426e10	−	7.99213e10i	0.271739	−	0.470666i	−0.697568	−	0.716519i	$-0.745735\pi$
$313$	4.61426e10	−	7.99213e10i	0.271739	−	0.470666i	0.969307	+	0.245852i	$0.0790678\pi$
$314$	1.31516e11	+	2.27792e11i	0.763476	+	1.32238i
$315$	−9.00681e9	−	1.56003e10i	−0.0515435	−	0.0892759i
$316$	−1.42726e10	+	2.47208e10i	−0.0805213	+	0.139467i
$317$	8.31234e10	−	1.43974e11i	0.462335	−	0.800787i	−0.536742	−	0.843746i	$-0.680345\pi$
$317$	8.31234e10	−	1.43974e11i	0.462335	−	0.800787i	0.999077	+	0.0429592i	$0.0136785\pi$
$318$	−5.34269e10	+	9.25380e10i	−0.292980	+	0.507456i
$319$	−2.45713e11			−1.32853
$320$	9.95918e10	+	1.72498e11i	0.530944	+	0.919622i
$321$	−4.25349e10	+	7.36726e10i	−0.223601	+	0.387288i
$322$	−1.51639e11			−0.786066
$323$	2.69373e10			0.137703
$324$	1.87413e10	−	3.24608e10i	0.0944815	−	0.163647i
$325$	−4.19890e11			−2.08766
$326$	−9.57535e10	−	1.65850e11i	−0.469543	−	0.813272i
$327$	2.24895e11			1.08772
$328$	1.10545e11	+	1.91469e11i	0.527358	+	0.913411i
$329$	7.43102e10	+	1.28709e11i	0.349677	+	0.605658i
$330$	−1.47723e11	−	2.55863e11i	−0.685701	−	1.18767i
$331$	8.97156e10	−	1.55392e11i	0.410811	−	0.711545i	−0.584168	−	0.811633i	$-0.698579\pi$
$331$	8.97156e10	−	1.55392e11i	0.410811	−	0.711545i	0.994979	+	0.100088i	$0.0319123\pi$
$332$	2.34345e10			0.105861
$333$	−3.56870e9	−	2.80325e10i	−0.0159042	−	0.124929i
$334$	−1.74540e11			−0.767424
$335$	−5.03256e10	+	8.71665e10i	−0.218317	+	0.378136i
$336$	6.84101e10	+	1.18490e11i	0.292815	+	0.507171i
$337$	−3.48032e10	−	6.02809e10i	−0.146989	−	0.254592i	0.783124	−	0.621865i	$-0.213625\pi$
$337$	−3.48032e10	−	6.02809e10i	−0.146989	−	0.254592i	−0.930113	+	0.367273i	$0.880291\pi$
$338$	1.87052e11	+	3.23983e11i	0.779537	+	1.35020i
$339$	4.48057e10			0.184262
$340$	2.97782e9	+	5.15773e9i	0.0120849	+	0.0209317i
$341$	4.11054e11			1.64628
$342$	−3.38007e10	+	5.85446e10i	−0.133601	+	0.231403i
$343$	−2.34919e11			−0.916421
$344$	1.44419e11			0.556048
$345$	2.50699e11	−	4.34224e11i	0.952725	−	1.65017i
$346$	−1.70176e11	−	2.94754e11i	−0.638346	−	1.10565i
$347$	−1.15562e11			−0.427890			−0.213945	−	0.976846i	$-0.568631\pi$
$347$	−1.15562e11			−0.427890			−0.213945	+	0.976846i	$0.568631\pi$
$348$	4.31359e10	−	7.47135e10i	0.157664	−	0.273082i
$349$	2.02615e11	−	3.50939e11i	0.731066	−	1.26624i	−0.225362	−	0.974275i	$-0.572356\pi$
$349$	2.02615e11	−	3.50939e11i	0.731066	−	1.26624i	0.956428	−	0.291968i	$-0.0943102\pi$
$350$	1.11442e11	−	1.93023e11i	0.396955	−	0.687547i
$351$	−2.32420e11	−	4.02563e11i	−0.817318	−	1.41564i
$352$	−5.40695e10	−	9.36512e10i	−0.187720	−	0.325141i
$353$	−3.96628e10	+	6.86979e10i	−0.135956	+	0.235482i	−0.925962	−	0.377617i	$-0.876744\pi$
$353$	−3.96628e10	+	6.86979e10i	−0.135956	+	0.235482i	0.790007	+	0.613098i	$0.210077\pi$
$354$	6.44873e10	−	1.11695e11i	0.218252	−	0.378024i
$355$	−2.06991e11	+	3.58519e11i	−0.691710	+	1.19808i
$356$	6.22692e10			0.205470
$357$	−5.49863e9	−	9.52390e9i	−0.0179163	−	0.0310319i
$358$	−2.16711e11	+	3.75354e11i	−0.697279	+	1.20772i
$359$	−5.03521e11			−1.59990			−0.799949	−	0.600068i	$-0.795140\pi$
$359$	−5.03521e11			−1.59990			−0.799949	+	0.600068i	$0.795140\pi$
$360$	5.29340e10			0.166102
$361$	−4.33901e11	+	7.51538e11i	−1.34465	+	2.32899i
$362$	2.23237e11			0.683246
$363$	3.83200e10	+	6.63722e10i	0.115837	+	0.200635i
$364$	−6.12228e10			−0.182792
$365$	−8.80938e9	−	1.52583e10i	−0.0259793	−	0.0449975i
$366$	1.83425e10	+	3.17701e10i	0.0534310	+	0.0925452i
$367$	1.61534e11	+	2.79784e11i	0.464799	+	0.805056i	0.999192	−	0.0401800i	$-0.0127931\pi$
$367$	1.61534e11	+	2.79784e11i	0.464799	+	0.805056i	−0.534393	+	0.845236i	$0.679460\pi$
$368$	2.74356e11	−	4.75198e11i	0.779829	−	1.35070i
$369$	5.49166e10			0.154200
$370$	4.85311e11	−	3.69107e11i	1.34621	−	1.02387i
$371$	−1.10688e11			−0.303332
$372$	−7.21621e10	+	1.24988e11i	−0.195374	+	0.338397i
$373$	−2.64521e11	−	4.58164e11i	−0.707571	−	1.22555i	−0.965755	−	0.259454i	$-0.916457\pi$
$373$	−2.64521e11	−	4.58164e11i	−0.707571	−	1.22555i	0.258184	−	0.966096i	$-0.416876\pi$
$374$	1.29940e10	+	2.25063e10i	0.0343416	+	0.0594814i
$375$	9.43937e10	+	1.63495e11i	0.246492	+	0.426936i
$376$	−4.36729e11			−1.12685
$377$	−4.66494e11	−	8.07991e11i	−1.18935	−	2.06001i
$378$	2.46744e11			0.621631
$379$	−5.84509e10	+	1.01240e11i	−0.145517	+	0.252044i	−0.929566	−	0.368656i	$-0.879818\pi$
$379$	−5.84509e10	+	1.01240e11i	−0.145517	+	0.252044i	0.784048	+	0.620700i	$0.213151\pi$
$380$	−2.63208e11			−0.647549
$381$	2.85167e11			0.693324
$382$	1.36226e11	−	2.35951e11i	0.327323	−	0.566940i
$383$	−1.57617e11	−	2.73000e11i	−0.374290	−	0.648289i	0.615931	−	0.787800i	$-0.288780\pi$
$383$	−1.57617e11	−	2.73000e11i	−0.374290	−	0.648289i	−0.990220	+	0.139512i	$0.955447\pi$
$384$	−4.77607e11			−1.12093
$385$	1.53024e11	−	2.65045e11i	0.354965	−	0.614817i
$386$	−1.64543e11	+	2.84997e11i	−0.377256	+	0.653427i
$387$	1.79362e10	−	3.10665e10i	0.0406473	−	0.0704033i
$388$	6.76793e10	+	1.17224e11i	0.151605	+	0.262587i
$389$	1.65429e11	+	2.86532e11i	0.366302	+	0.634454i	0.988984	−	0.148021i	$-0.0472904\pi$
$389$	1.65429e11	+	2.86532e11i	0.366302	+	0.634454i	−0.622682	+	0.782475i	$0.713957\pi$
$390$	5.60912e11	−	9.71529e11i	1.22773	−	2.12650i
$391$	−2.20520e10	+	3.81952e10i	−0.0477148	+	0.0826444i
$392$	1.43807e11	−	2.49080e11i	0.307604	−	0.532785i
$393$	3.87161e11			0.818700
$394$	9.18982e10	+	1.59172e11i	0.192121	+	0.332763i
$395$	2.70910e11	−	4.69231e11i	0.559936	−	0.969838i
$396$	−1.17689e10			−0.0240496
$397$	2.28205e11			0.461072			0.230536	−	0.973064i	$-0.425952\pi$
$397$	2.28205e11			0.461072			0.230536	+	0.973064i	$0.425952\pi$
$398$	−2.89532e11	+	5.01485e11i	−0.578393	+	1.00181i
$399$	4.86021e11			0.960014
$400$	4.03257e11	+	6.98462e11i	0.787611	+	1.36418i
$401$	−6.16496e11			−1.19064			−0.595320	−	0.803489i	$-0.702975\pi$
$401$	−6.16496e11			−1.19064			−0.595320	+	0.803489i	$0.702975\pi$
$402$	−7.71035e10	−	1.33547e11i	−0.147250	−	0.255045i
$403$	7.80399e11	+	1.35169e12i	1.47382	+	2.55273i
$404$	6.37783e10	+	1.10467e11i	0.119112	+	0.206309i
$405$	−3.55731e11	+	6.16145e11i	−0.657014	+	1.13798i
$406$	4.95243e11			0.904589
$407$	3.82143e11	−	2.90641e11i	0.690321	−	0.525028i
$408$	3.23160e10			0.0577361
$409$	−4.86481e11	+	8.42609e11i	−0.859628	+	1.48892i	0.0126559	+	0.999920i	$0.495971\pi$
$409$	−4.86481e11	+	8.42609e11i	−0.859628	+	1.48892i	−0.872284	+	0.489000i	$0.837362\pi$
$410$	5.92455e11	+	1.02616e12i	1.03545	+	1.79345i
$411$	−1.19363e11	−	2.06742e11i	−0.206339	−	0.357389i
$412$	6.80141e10	+	1.17804e11i	0.116295	+	0.201429i
$413$	1.33603e11			0.225964
$414$	−5.53414e10	−	9.58541e10i	−0.0925867	−	0.160365i
$415$	−4.44814e11			−0.736143
$416$	2.05305e11	−	3.55599e11i	0.336109	−	0.582158i
$417$	−3.85464e11			−0.624269
$418$	−1.14853e12			−1.84014
$419$	−1.81958e11	+	3.15160e11i	−0.288408	+	0.499537i	−0.973430	−	0.228985i	$-0.926459\pi$
$419$	−1.81958e11	+	3.15160e11i	−0.288408	+	0.499537i	0.685022	+	0.728522i	$0.259793\pi$
$420$	5.37278e10	+	9.30593e10i	0.0842514	+	0.145928i
$421$	7.80534e10			0.121094			0.0605469	−	0.998165i	$-0.480716\pi$
$421$	7.80534e10			0.121094			0.0605469	+	0.998165i	$0.480716\pi$
$422$	4.34017e11	−	7.51739e11i	0.666193	−	1.15388i
$423$	−5.42398e10	+	9.39462e10i	−0.0823733	+	0.142675i
$424$	1.62631e11	−	2.81686e11i	0.244376	−	0.423271i
$425$	−3.24128e10	−	5.61405e10i	−0.0481910	−	0.0834692i
$426$	−3.17130e11	−	5.49285e11i	−0.466545	−	0.808080i
$427$	−1.90007e10	+	3.29101e10i	−0.0276595	+	0.0479076i
$428$	−3.65582e10	+	6.33207e10i	−0.0526609	+	0.0912114i
$429$	4.41673e11	−	7.65000e11i	0.629569	−	1.09044i
$430$	7.74004e11			1.09178
$431$	−1.96953e10	−	3.41133e10i	−0.0274926	−	0.0476186i	0.851952	−	0.523620i	$-0.175419\pi$
$431$	−1.96953e10	−	3.41133e10i	−0.0274926	−	0.0476186i	−0.879444	+	0.476002i	$0.842086\pi$
$432$	−4.46427e11	+	7.73233e11i	−0.616699	+	1.06815i
$433$	−5.73361e11			−0.783849			−0.391924	−	0.919997i	$-0.628191\pi$
$433$	−5.73361e11			−0.783849			−0.391924	+	0.919997i	$0.628191\pi$
$434$	−8.28494e11			−1.12095
$435$	−8.18769e11	+	1.41815e12i	−1.09638	+	1.89898i
$436$	1.93295e11			0.256171
$437$	−9.74585e11	−	1.68803e12i	−1.27836	−	2.21418i
$438$	2.69936e10			0.0350451
$439$	−3.54601e11	−	6.14186e11i	−0.455669	−	0.789241i	0.543058	−	0.839695i	$-0.317266\pi$
$439$	−3.54601e11	−	6.14186e11i	−0.455669	−	0.789241i	−0.998726	+	0.0504540i	$0.983933\pi$
$440$	4.49668e11	+	7.78849e11i	0.571946	+	0.990640i
$441$	−3.57203e10	−	6.18694e10i	−0.0449719	−	0.0778936i
$442$	−4.93390e10	+	8.54576e10i	−0.0614879	+	0.106500i
$443$	4.08024e11			0.503348			0.251674	−	0.967812i	$-0.419019\pi$
$443$	4.08024e11			0.503348			0.251674	+	0.967812i	$0.419019\pi$
$444$	2.12881e10	+	1.67221e11i	0.0259965	+	0.204205i
$445$	−1.18194e12			−1.42882
$446$	−1.90135e11	+	3.29324e11i	−0.227539	+	0.394109i
$447$	−2.06042e11	−	3.56875e11i	−0.244102	−	0.422797i
$448$	−1.58059e11	−	2.73766e11i	−0.185382	−	0.321092i
$449$	−4.99398e10	−	8.64983e10i	−0.0579880	−	0.100438i	0.835574	−	0.549378i	$-0.185135\pi$
$449$	−4.99398e10	−	8.64983e10i	−0.0579880	−	0.100438i	−0.893562	+	0.448940i	$0.851802\pi$
$450$	1.62685e11			0.187021
$451$	4.66511e11	+	8.08020e11i	0.530966	+	0.919661i
$452$	3.85100e10			0.0433961
$453$	−5.07405e11	+	8.78852e11i	−0.566126	+	0.980559i
$454$	5.10715e11			0.564192
$455$	1.16208e12			1.27112
$456$	−7.14100e11	+	1.23686e12i	−0.773424	+	1.33961i
$457$	1.48157e11	+	2.56615e11i	0.158891	+	0.275207i	0.934469	−	0.356044i	$-0.115875\pi$
$457$	1.48157e11	+	2.56615e11i	0.158891	+	0.275207i	−0.775578	+	0.631252i	$0.782542\pi$
$458$	−1.27407e12			−1.35301
$459$	3.58826e10	−	6.21505e10i	0.0377335	−	0.0653563i
$460$	2.15473e11	−	3.73210e11i	0.224379	−	0.388637i
$461$	−5.19454e10	+	8.99721e10i	−0.0535665	+	0.0927799i	−0.891565	−	0.452892i	$-0.850392\pi$
$461$	−5.19454e10	+	8.99721e10i	−0.0535665	+	0.0927799i	0.837999	+	0.545672i	$0.183726\pi$
$462$	2.34446e11	+	4.06073e11i	0.239417	+	0.414682i
$463$	−5.00060e11	−	8.66130e11i	−0.505717	−	0.875928i	−0.999978	−	0.00661457i	$-0.997895\pi$
$463$	−5.00060e11	−	8.66130e11i	−0.505717	−	0.875928i	0.494261	−	0.869314i	$-0.335439\pi$
$464$	−8.96030e11	+	1.55197e12i	−0.897412	+	1.55436i
$465$	1.36972e12	−	2.37243e12i	1.35861	−	2.35318i
$466$	5.24258e11	−	9.08041e11i	0.515001	−	0.892008i
$467$	1.64699e12			1.60238			0.801190	−	0.598409i	$-0.204200\pi$
$467$	1.64699e12			1.60238			0.801190	+	0.598409i	$0.204200\pi$
$468$	−2.23436e10	−	3.87003e10i	−0.0215301	−	0.0372913i
$469$	7.98702e10	−	1.38339e11i	0.0762267	−	0.132029i
$470$	−2.34062e12			−2.21253
$471$	1.38031e12			1.29236
$472$	−1.96299e11	+	3.40000e11i	−0.182045	+	0.315312i
$473$	6.09465e11			0.559853
$474$	4.15060e11	+	7.18905e11i	0.377666	+	0.654137i
$475$	2.86495e12			2.58223
$476$	−4.72600e9	−	8.18568e9i	−0.00421952	−	0.00730842i
$477$	−4.03962e10	−	6.99683e10i	−0.0357279	−	0.0618826i
$478$	1.49889e11	+	2.59616e11i	0.131324	+	0.227460i
$479$	−3.41982e11	+	5.92330e11i	−0.296820	+	0.514108i	−0.975407	−	0.220413i	$-0.929260\pi$
$479$	−3.41982e11	+	5.92330e11i	−0.296820	+	0.514108i	0.678586	+	0.734521i	$0.262593\pi$
$480$	−7.20686e11			−0.619670
$481$	1.68124e12	+	7.04829e11i	1.43211	+	0.600387i
$482$	−3.95371e11			−0.333651
$483$	−3.97878e11	+	6.89144e11i	−0.332650	+	0.576167i
$484$	3.29356e10	+	5.70461e10i	0.0272811	+	0.0472522i
$485$	−1.28463e12	−	2.22505e12i	−1.05424	−	1.82600i
$486$	1.70029e11	+	2.94498e11i	0.138248	+	0.239453i
$487$	−1.69252e11			−0.136350			−0.0681748	−	0.997673i	$-0.521718\pi$
$487$	−1.69252e11			−0.136350			−0.0681748	+	0.997673i	$0.521718\pi$
$488$	−5.58345e10	−	9.67082e10i	−0.0445670	−	0.0771924i
$489$	−1.00497e12			−0.794811
$490$	7.70720e11	−	1.33493e12i	0.603969	−	1.04610i
$491$	1.83687e12			1.42630			0.713151	−	0.701011i	$-0.247267\pi$
$491$	1.83687e12			1.42630			0.713151	+	0.701011i	$0.247267\pi$
$492$	−3.27591e11			−0.252051
$493$	7.20206e10	−	1.24743e11i	0.0549092	−	0.0951056i
$494$	−2.18053e12	−	3.77678e12i	−1.64737	−	2.85332i
$495$	2.23387e11			0.167238
$496$	1.49897e12	−	2.59629e12i	1.11205	−	1.92613i
$497$	3.28510e11	−	5.68995e11i	0.241515	−	0.418316i
$498$	3.40748e11	−	5.90193e11i	0.248257	−	0.429994i
$499$	3.70590e11	+	6.41880e11i	0.267572	+	0.463448i	0.968234	−	0.250045i	$-0.0804453\pi$
$499$	3.70590e11	+	6.41880e11i	0.267572	+	0.463448i	−0.700662	+	0.713493i	$0.747112\pi$
$500$	8.11303e10	+	1.40522e11i	0.0580521	+	0.100549i
$501$	−4.57967e11	+	7.93221e11i	−0.324761	+	0.562503i
$502$	−6.90903e11	+	1.19668e12i	−0.485568	+	0.841029i
$503$	1.55218e11	−	2.68846e11i	0.108115	−	0.187261i	−0.806891	−	0.590700i	$-0.798852\pi$
$503$	1.55218e11	−	2.68846e11i	0.108115	−	0.187261i	0.915007	+	0.403439i	$0.132185\pi$
$504$	−8.40100e10			−0.0579954
$505$	−1.21059e12	−	2.09680e12i	−0.828294	−	1.43465i
$506$	9.40238e11	−	1.62854e12i	0.637618	−	1.10439i
$507$	1.96318e12			1.31955
$508$	2.45097e11			0.163287
$509$	−1.58954e11	+	2.75317e11i	−0.104964	+	0.181804i	−0.913724	−	0.406336i	$-0.866806\pi$
$509$	−1.58954e11	+	2.75317e11i	−0.104964	+	0.181804i	0.808759	+	0.588140i	$0.200140\pi$
$510$	1.73195e11			0.113363
$511$	1.39811e10	+	2.42160e10i	0.00907084	+	0.0157112i
$512$	7.80721e11			0.502090
$513$	1.58582e12	+	2.74673e12i	1.01094	+	1.75101i
$514$	−6.40054e11	−	1.10861e12i	−0.404466	−	0.700556i
$515$	−1.29099e12	−	2.23606e12i	−0.808704	−	1.40072i
$516$	−1.06994e11	+	1.85319e11i	−0.0664410	+	0.115079i
$517$	−1.84304e12			−1.13456
$518$	−7.70223e11	+	5.85798e11i	−0.470037	+	0.357490i
$519$	−1.78607e12			−1.08055
$520$	−1.70742e12	+	2.95734e12i	−1.02406	+	1.77372i
$521$	7.77851e11	+	1.34728e12i	0.462516	+	0.801101i	0.999086	−	0.0427551i	$-0.0136135\pi$
$521$	7.77851e11	+	1.34728e12i	0.462516	+	0.801101i	−0.536570	+	0.843856i	$0.680280\pi$
$522$	1.80742e11	+	3.13054e11i	0.106547	+	0.184545i
$523$	1.09694e12	+	1.89995e12i	0.641098	+	1.11041i	0.985188	+	0.171478i	$0.0548542\pi$
$523$	1.09694e12	+	1.89995e12i	0.641098	+	1.11041i	−0.344090	+	0.938937i	$0.611812\pi$
$524$	3.32760e11			0.192815
$525$	−5.84813e11	−	1.01293e12i	−0.335970	−	0.581917i
$526$	5.77117e11			0.328722
$527$	−1.20483e11	+	2.08683e11i	−0.0680424	+	0.117853i
$528$	−1.69671e12			−0.950069
$529$	1.39019e12			0.771834
$530$	8.71610e11	−	1.50967e12i	0.479823	−	0.831078i
$531$	4.87590e10	+	8.44531e10i	0.0266152	+	0.0460989i
$532$	4.17730e11			0.226096
$533$	−1.77137e12	+	3.06810e12i	−0.950685	+	1.64663i
$534$	9.05423e11	−	1.56824e12i	0.481854	−	0.834596i
$535$	6.93918e11	−	1.20190e12i	0.366198	−	0.634274i
$536$	2.34703e11	+	4.06518e11i	0.122822	+	0.212734i
$537$	1.13723e12	+	1.96974e12i	0.590154	+	1.02218i
$538$	4.61811e11	−	7.99880e11i	0.237653	−	0.411628i
$539$	6.06880e11	−	1.05115e12i	0.309709	−	0.536431i
$540$	−3.50614e11	+	6.07281e11i	−0.177442	+	0.307339i
$541$	−2.88583e12			−1.44838			−0.724192	−	0.689599i	$-0.757787\pi$
$541$	−2.88583e12			−1.44838			−0.724192	+	0.689599i	$0.757787\pi$
$542$	1.13467e12	+	1.96531e12i	0.564773	+	0.978216i
$543$	5.85740e11	−	1.01453e12i	0.289138	−	0.500802i
$544$	6.33930e10			0.0310346
$545$	−3.66896e12			−1.78139
$546$	−8.90207e11	+	1.54188e12i	−0.428671	+	0.742480i
$547$	−8.68728e11			−0.414898			−0.207449	−	0.978246i	$-0.566516\pi$
$547$	−8.68728e11			−0.414898			−0.207449	+	0.978246i	$0.566516\pi$
$548$	−1.02591e11	−	1.77693e11i	−0.0485955	−	0.0841699i
$549$	−2.77376e10			−0.0130315
$550$	1.38199e12	+	2.39368e12i	0.643981	+	1.11541i
$551$	3.18293e12	+	5.51300e12i	1.47111	+	2.54804i
$552$	−1.16919e12	−	2.02509e12i	−0.535991	−	0.928364i
$553$	−4.29954e11	+	7.44702e11i	−0.195505	+	0.338625i
$554$	−3.02579e12			−1.36473
$555$	−4.04074e11	−	3.17405e12i	−0.180777	−	1.42002i
$556$	−3.31302e11			−0.147024
$557$	1.53100e12	−	2.65177e12i	0.673949	−	1.16731i	−0.302826	−	0.953046i	$-0.597930\pi$
$557$	1.53100e12	−	2.65177e12i	0.673949	−	1.16731i	0.976775	−	0.214268i	$-0.0687366\pi$
$558$	−3.02363e11	−	5.23709e11i	−0.132031	−	0.228684i
$559$	1.15709e12	+	2.00414e12i	0.501203	+	0.868109i
$560$	−1.11605e12	−	1.93305e12i	−0.479553	−	0.830611i
$561$	1.36377e11			0.0581311
$562$	1.10711e12	+	1.91758e12i	0.468144	+	0.810849i
$563$	−4.72440e11			−0.198179			−0.0990897	−	0.995079i	$-0.531593\pi$
$563$	−4.72440e11			−0.198179			−0.0990897	+	0.995079i	$0.531593\pi$
$564$	3.23554e11	−	5.60411e11i	0.134645	−	0.233212i
$565$	−7.30964e11			−0.301771
$566$	−1.45338e12			−0.595258
$567$	5.64570e11	−	9.77865e11i	0.229401	−	0.397333i
$568$	9.65343e11	+	1.67202e12i	0.389148	+	0.674023i
$569$	1.04979e12			0.419853			0.209927	−	0.977717i	$-0.432677\pi$
$569$	1.04979e12			0.419853			0.209927	+	0.977717i	$0.432677\pi$
$570$	−3.82716e12	+	6.62884e12i	−1.51859	+	2.63027i
$571$	−4.32696e11	+	7.49451e11i	−0.170341	+	0.295040i	−0.938539	−	0.345173i	$-0.887820\pi$
$571$	−4.32696e11	+	7.49451e11i	−0.170341	+	0.295040i	0.768198	+	0.640213i	$0.221154\pi$
$572$	3.79613e11	−	6.57508e11i	0.148272	−	0.256814i
$573$	−7.14876e11	−	1.23820e12i	−0.277035	−	0.479839i
$574$	−9.40268e11	−	1.62859e12i	−0.361533	−	0.626194i
$575$	−2.34537e12	+	4.06230e12i	−0.894758	+	1.54977i
$576$	1.15369e11	−	1.99825e11i	0.0436705	−	0.0756395i
$577$	7.08175e11	−	1.22659e12i	0.265980	−	0.460691i	−0.701840	−	0.712335i	$-0.747638\pi$
$577$	7.08175e11	−	1.22659e12i	0.265980	−	0.460691i	0.967820	+	0.251644i	$0.0809711\pi$
$578$	2.94883e12			1.09894
$579$	8.63473e11	+	1.49558e12i	0.319297	+	0.553039i
$580$	−7.03722e11	+	1.21888e12i	−0.258211	+	0.447235i
$581$	7.05952e11			0.257029
$582$	3.93635e12			1.42213
$583$	6.86323e11	−	1.18875e12i	0.246048	−	0.426168i
$584$	−8.21685e10			−0.0292313
$585$	4.24108e11	+	7.34576e11i	0.149718	+	0.259320i
$586$	−8.29924e11			−0.290736
$587$	−6.96091e11	−	1.20566e12i	−0.241988	−	0.419136i	0.719292	−	0.694708i	$-0.244466\pi$
$587$	−6.96091e11	−	1.20566e12i	−0.241988	−	0.419136i	−0.961281	+	0.275572i	$0.911133\pi$
$588$	2.13080e11	+	3.69066e11i	0.0735098	+	0.127323i
$589$	−5.32474e12	−	9.22272e12i	−1.82297	−	3.15748i
$590$	−1.05205e12	+	1.82220e12i	−0.357439	+	0.619103i
$591$	9.64509e11			0.325209
$592$	−4.42203e11	−	3.47356e12i	−0.147970	−	1.16232i
$593$	2.71066e12			0.900179			0.450090	−	0.892983i	$-0.351392\pi$
$593$	2.71066e12			0.900179			0.450090	+	0.892983i	$0.351392\pi$
$594$	−1.52994e12	+	2.64993e12i	−0.504237	+	0.873363i
$595$	8.97051e10	+	1.55374e11i	0.0293421	+	0.0508220i
$596$	−1.77091e11	−	3.06730e11i	−0.0574893	−	0.0995744i
$597$	1.51938e12	+	2.63164e12i	0.489533	+	0.847896i
$598$	7.14028e12			2.28328
$599$	6.79496e11	+	1.17692e12i	0.215658	+	0.373531i	0.953476	−	0.301469i	$-0.0974770\pi$
$599$	6.79496e11	+	1.17692e12i	0.215658	+	0.373531i	−0.737818	+	0.675000i	$0.764144\pi$
$600$	3.43701e12			1.08268
$601$	3.49978e11	−	6.06179e11i	0.109422	−	0.189525i	−0.806114	−	0.591760i	$-0.798433\pi$
$601$	3.49978e11	−	6.06179e11i	0.109422	−	0.189525i	0.915536	+	0.402235i	$0.131767\pi$
$602$	−1.22840e12			−0.381202
$603$	1.16596e11			0.0359134
$604$	−4.36109e11	+	7.55363e11i	−0.133330	+	0.230935i
$605$	−6.25156e11	−	1.08280e12i	−0.189710	−	0.328587i
$606$	3.70946e12			1.11734
$607$	−2.56217e12	+	4.43781e12i	−0.766054	+	1.32684i	0.173633	+	0.984810i	$0.444449\pi$
$607$	−2.56217e12	+	4.43781e12i	−0.766054	+	1.32684i	−0.939688	+	0.342034i	$0.888884\pi$
$608$	−1.40082e12	+	2.42629e12i	−0.415734	+	0.720073i
$609$	1.29944e12	−	2.25070e12i	0.382807	−	0.663041i
$610$	−2.99241e11	−	5.18300e11i	−0.0875057	−	0.151564i
$611$	−3.49908e12	−	6.06058e12i	−1.01571	−	1.75925i
$612$	3.44956e9	−	5.97482e9i	0.000993991	−	0.00172164i
$613$	5.50118e11	−	9.52832e11i	0.157356	−	0.272549i	−0.776558	−	0.630045i	$-0.783036\pi$
$613$	5.50118e11	−	9.52832e11i	0.157356	−	0.272549i	0.933914	+	0.357497i	$0.116370\pi$
$614$	3.65921e12	−	6.33794e12i	1.03903	−	1.79966i
$615$	6.21806e12			1.75274
$616$	−7.13655e11	−	1.23609e12i	−0.199699	−	0.345888i
$617$	−3.33133e12	+	5.77004e12i	−0.925411	+	1.60286i	−0.134513	+	0.990912i	$0.542947\pi$
$617$	−3.33133e12	+	5.77004e12i	−0.925411	+	1.60286i	−0.790898	+	0.611947i	$0.790386\pi$
$618$	3.95582e12			1.09091
$619$	−6.09077e12			−1.66749			−0.833747	−	0.552146i	$-0.813809\pi$
$619$	−6.09077e12			−1.66749			−0.833747	+	0.552146i	$0.813809\pi$
$620$	1.17726e12	−	2.03907e12i	0.319970	−	0.554205i
$621$	−5.19289e12			−1.40119
$622$	6.08424e11	+	1.05382e12i	0.162986	+	0.282299i
$623$	1.87583e12			0.498880
$624$	−3.22126e12	−	5.57938e12i	−0.850540	−	1.47318i
$625$	1.02427e12	+	1.77408e12i	0.268505	+	0.465065i
$626$	−1.15332e12	−	1.99761e12i	−0.300168	−	0.519907i
$627$	−3.01358e12	+	5.21967e12i	−0.778716	+	1.34878i
$628$	1.18636e12			0.304368
$629$	3.55431e10	+	2.79195e11i	0.00905374	+	0.0711182i
$630$	−4.50245e11			−0.113872
$631$	6.08255e11	−	1.05353e12i	0.152740	−	0.264554i	−0.779494	−	0.626410i	$-0.784524\pi$
$631$	6.08255e11	−	1.05353e12i	0.152740	−	0.264554i	0.932234	+	0.361856i	$0.117857\pi$
$632$	−1.26344e12	−	2.18835e12i	−0.315013	−	0.545619i
$633$	−2.27759e12	−	3.94490e12i	−0.563844	−	0.976606i
$634$	−2.07764e12	−	3.59858e12i	−0.510704	−	0.884565i
$635$	−4.65223e12			−1.13548
$636$	2.40973e11	+	4.17378e11i	0.0583998	+	0.101151i
$637$	4.60872e12			1.10905
$638$	−3.07076e12	+	5.31871e12i	−0.733758	+	1.27091i
$639$	4.79565e11			0.113787
$640$	7.79172e12			1.83579
$641$	2.91163e12	−	5.04309e12i	0.681200	−	1.17987i	−0.293414	−	0.955985i	$-0.594792\pi$
$641$	2.91163e12	−	5.04309e12i	0.681200	−	1.17987i	0.974615	−	0.223888i	$-0.0718751\pi$
$642$	1.06315e12	+	1.84142e12i	0.246994	+	0.427805i
$643$	4.53196e12			1.04553			0.522765	−	0.852477i	$-0.324901\pi$
$643$	4.53196e12			1.04553			0.522765	+	0.852477i	$0.324901\pi$
$644$	−3.41971e11	+	5.92311e11i	−0.0783435	+	0.135695i
$645$	2.03087e12	−	3.51757e12i	0.462023	−	0.800247i
$646$	3.36645e11	−	5.83086e11i	0.0760546	−	0.131730i
$647$	−2.85138e12	−	4.93873e12i	−0.639713	−	1.10802i	−0.985496	−	0.169701i	$-0.945720\pi$
$647$	−2.85138e12	−	4.93873e12i	−0.639713	−	1.10802i	0.345783	−	0.938315i	$-0.387613\pi$
$648$	1.65902e12	+	2.87351e12i	0.369628	+	0.640214i
$649$	−8.28404e11	+	1.43484e12i	−0.183291	+	0.317469i
$650$	−5.24750e12	+	9.08894e12i	−1.15304	+	1.99712i
$651$	−2.17384e12	+	3.76521e12i	−0.474366	+	0.821627i
$652$	−8.63761e11			−0.187189
$653$	2.20974e11	+	3.82739e11i	0.0475590	+	0.0823746i	0.888825	−	0.458247i	$-0.151522\pi$
$653$	2.20974e11	+	3.82739e11i	0.0475590	+	0.0823746i	−0.841266	+	0.540622i	$0.818189\pi$
$654$	2.81059e12	−	4.86809e12i	0.600756	−	1.04054i
$655$	−6.31617e12			−1.34081
$656$	6.80481e12			1.43466
$657$	−1.02050e10	+	1.76755e10i	−0.00213682	+	0.00370107i
$658$	3.71472e12			0.772520
$659$	−4.95702e11	−	8.58582e11i	−0.102385	−	0.177336i	0.810282	−	0.586041i	$-0.199314\pi$
$659$	−4.95702e11	−	8.58582e11i	−0.102385	−	0.177336i	−0.912667	+	0.408704i	$0.865981\pi$
$660$	−1.33256e12			−0.273362
$661$	2.52506e12	+	4.37354e12i	0.514477	+	0.891100i	0.999859	+	0.0167975i	$0.00534707\pi$
$661$	2.52506e12	+	4.37354e12i	0.514477	+	0.891100i	−0.485382	+	0.874302i	$0.661320\pi$
$662$	−2.24241e12	−	3.88397e12i	−0.453790	−	0.785987i
$663$	2.58916e11	+	4.48456e11i	0.0520413	+	0.0901382i
$664$	−1.03724e12	+	1.79655e12i	−0.207072	+	0.358660i
$665$	−7.92899e12			−1.57225
$666$	−6.51393e11	−	2.73084e11i	−0.128295	−	0.0537851i
$667$	−1.04227e13			−2.03899
$668$	−3.93617e11	+	6.81764e11i	−0.0764856	+	0.132477i
$669$	9.97772e11	+	1.72819e12i	0.192581	+	0.333560i
$670$	1.25787e12	+	2.17870e12i	0.241157	+	0.417696i
$671$	−2.35628e11	−	4.08119e11i	−0.0448720	−	0.0777205i
$672$	1.14378e12			0.216362
$673$	−1.55037e12	−	2.68531e12i	−0.291317	−	0.504577i	0.682804	−	0.730602i	$-0.260760\pi$
$673$	−1.55037e12	−	2.68531e12i	−0.291317	−	0.504577i	−0.974122	+	0.226025i	$0.927427\pi$
$674$	−1.73979e12			−0.324733
$675$	3.81634e12	−	6.61009e12i	0.707587	−	1.22558i
$676$	1.68733e12			0.310771
$677$	4.81093e12			0.880197			0.440098	−	0.897950i	$-0.354944\pi$
$677$	4.81093e12			0.880197			0.440098	+	0.897950i	$0.354944\pi$
$678$	5.59952e11	−	9.69866e11i	0.101769	−	0.176270i
$679$	2.03880e12	+	3.53131e12i	0.368096	+	0.637561i
$680$	−5.27207e11			−0.0945564
$681$	1.34004e12	−	2.32102e12i	0.238757	−	0.413539i
$682$	5.13708e12	−	8.89769e12i	0.909258	−	1.57488i
$683$	2.34447e11	−	4.06075e11i	0.0412242	−	0.0714024i	−0.844677	−	0.535276i	$-0.820208\pi$
$683$	2.34447e11	−	4.06075e11i	0.0412242	−	0.0714024i	0.885901	+	0.463874i	$0.153541\pi$
$684$	1.52453e11	+	2.64056e11i	0.0266307	+	0.0461257i
$685$	1.94729e12	+	3.37281e12i	0.337928	+	0.585308i
$686$	−2.93587e12	+	5.08507e12i	−0.506148	+	0.876674i
$687$	−3.34298e12	+	5.79021e12i	−0.572570	+	0.991720i
$688$	2.22251e12	−	3.84950e12i	0.378177	−	0.655022i
$689$	5.21202e12			0.881088
$690$	−6.26616e12	−	1.08533e13i	−1.05240	−	1.82281i
$691$	1.58927e12	−	2.75270e12i	0.265184	−	0.459312i	−0.702428	−	0.711755i	$-0.747901\pi$
$691$	1.58927e12	−	2.75270e12i	0.265184	−	0.459312i	0.967612	+	0.252443i	$0.0812339\pi$
$692$	−1.53510e12			−0.254484
$693$	−3.54531e11			−0.0583922
$694$	−1.44422e12	+	2.50146e12i	−0.236328	+	0.409332i
$695$	6.28850e12			1.02239
$696$	3.81849e12	+	6.61382e12i	0.616808	+	1.06834i
$697$	−5.46953e11			−0.0877814
$698$	−5.06429e12	−	8.77161e12i	−0.807550	−	1.39872i
$699$	−2.75115e12	−	4.76513e12i	−0.435880	−	0.754966i
$700$	−5.02640e11	−	8.70597e11i	−0.0791253	−	0.137049i
$701$	1.38798e12	−	2.40405e12i	0.217096	−	0.376021i	−0.736823	−	0.676086i	$-0.763675\pi$
$701$	1.38798e12	−	2.40405e12i	0.217096	−	0.376021i	0.953919	+	0.300065i	$0.0970082\pi$
$702$	−1.16185e13			−1.80565
$703$	−1.14713e13	−	4.80912e12i	−1.77139	−	0.742620i
$704$	3.92019e12			0.601492
$705$	−6.14143e12	+	1.06373e13i	−0.936307	+	1.62173i
$706$	9.91359e11	+	1.71708e12i	0.150179	+	0.260118i
$707$	1.92129e12	+	3.32776e12i	0.289204	+	0.500916i
$708$	−2.90859e11	−	5.03783e11i	−0.0435044	−	0.0753518i
$709$	4.34021e12			0.645064			0.322532	−	0.946559i	$-0.395466\pi$
$709$	4.34021e12			0.645064			0.322532	+	0.946559i	$0.395466\pi$
$710$	5.17368e12	+	8.96108e12i	0.764077	+	1.32342i
$711$	−6.27656e11			−0.0921104
$712$	−2.75611e12	+	4.77372e12i	−0.401917	+	0.696141i
$713$	1.74362e13			2.52668
$714$	−2.74873e11			−0.0395813
$715$	−7.20549e12	+	1.24803e13i	−1.03107	+	1.78586i
$716$	9.77438e11	+	1.69297e12i	0.138989	+	0.240736i
$717$	1.57315e12			0.222297
$718$	−6.29267e12	+	1.08992e13i	−0.883640	+	1.53051i
$719$	7.39650e11	−	1.28111e12i	0.103216	−	0.178775i	−0.809792	−	0.586717i	$-0.800420\pi$
$719$	7.39650e11	−	1.28111e12i	0.103216	−	0.178775i	0.913008	+	0.407942i	$0.133753\pi$
$720$	8.14616e11	−	1.41096e12i	0.112968	−	0.195667i
$721$	2.04889e12	+	3.54878e12i	0.282364	+	0.489069i
$722$	1.08452e13	+	1.87845e13i	1.48532	+	2.57265i
$723$	−1.03739e12	+	1.79682e12i	−0.141196	+	0.244558i
$724$	5.03436e11	−	8.71977e11i	0.0680959	−	0.117946i
$725$	7.65983e12	−	1.32672e13i	1.02967	−	1.78344i
$726$	1.91559e12			0.255911
$727$	6.51550e12	+	1.12852e13i	0.865053	+	1.49832i	0.866995	+	0.498318i	$0.166049\pi$
$727$	6.51550e12	+	1.12852e13i	0.865053	+	1.49832i	−0.00194158	+	0.999998i	$0.500618\pi$
$728$	2.70979e12	−	4.69350e12i	0.357557	−	0.619306i
$729$	8.32883e12			1.09222
$730$	−4.40375e11			−0.0573945
$731$	−1.78639e11	+	3.09413e11i	−0.0231392	+	0.0400784i
$732$	1.65462e11			0.0213009
$733$	−1.91571e12	−	3.31811e12i	−0.245111	−	0.424545i	0.717052	−	0.697020i	$-0.245491\pi$
$733$	−1.91571e12	−	3.31811e12i	−0.245111	−	0.424545i	−0.962163	+	0.272475i	$0.912158\pi$
$734$	8.07496e12			1.02685
$735$	−4.04451e12	−	7.00530e12i	−0.511179	−	0.885388i
$736$	−2.29354e12	−	3.97253e12i	−0.288109	−	0.499019i
$737$	9.90473e11	+	1.71555e12i	0.123663	+	0.214190i
$738$	6.86312e11	−	1.18873e12i	0.0851663	−	0.147512i
$739$	−1.59259e12			−0.196428			−0.0982142	−	0.995165i	$-0.531313\pi$
$739$	−1.59259e12			−0.196428			−0.0982142	+	0.995165i	$0.531313\pi$
$740$	−3.47297e11	−	2.72805e12i	−0.0425753	−	0.334434i
$741$	−2.28855e13			−2.78855
$742$	−1.38331e12	+	2.39596e12i	−0.167533	+	0.290176i
$743$	4.61388e12	+	7.99147e12i	0.555414	+	0.962005i	0.997871	+	0.0652152i	$0.0207734\pi$
$743$	4.61388e12	+	7.99147e12i	0.555414	+	0.962005i	−0.442458	+	0.896789i	$0.645893\pi$
$744$	−6.38796e12	−	1.10643e13i	−0.764335	−	1.32387i
$745$	3.36139e12	+	5.82209e12i	0.399774	+	0.692430i
$746$	−1.32232e13			−1.56319
$747$	2.57641e11	+	4.46247e11i	0.0302742	+	0.0524364i
$748$	1.17215e11			0.0136907
$749$	−1.10130e12	+	1.90750e12i	−0.127860	+	0.221461i
$750$	4.71868e12			0.544559
$751$	7.88249e12			0.904240			0.452120	−	0.891957i	$-0.350668\pi$
$751$	7.88249e12			0.904240			0.452120	+	0.891957i	$0.350668\pi$
$752$	−6.72094e12	+	1.16410e13i	−0.766390	+	1.32743i
$753$	3.62565e12	+	6.27982e12i	0.410969	+	0.711819i
$754$	−2.33197e13			−2.62756
$755$	8.27785e12	−	1.43377e13i	0.927164	−	1.60589i
$756$	5.56448e11	−	9.63797e11i	0.0619551	−	0.107309i
$757$	4.52507e12	−	7.83765e12i	0.500834	−	0.867470i	−0.499165	−	0.866507i	$-0.666360\pi$
$757$	4.52507e12	−	7.83765e12i	0.500834	−	0.867470i	1.00000		0.000963489i	$-0.000306688\pi$
$758$	1.46096e12	+	2.53046e12i	0.160741	+	0.278412i
$759$	−4.93409e12	−	8.54609e12i	−0.539658	−	0.934716i
$760$	1.16499e13	−	2.01782e13i	1.26666	−	2.19392i
$761$	−8.00585e12	+	1.38665e13i	−0.865319	+	1.49878i	0.00141012	+	0.999999i	$0.499551\pi$
$761$	−8.00585e12	+	1.38665e13i	−0.865319	+	1.49878i	−0.866730	+	0.498778i	$0.833782\pi$
$762$	3.56382e12	−	6.17273e12i	0.382930	−	0.663254i
$763$	5.82289e12			0.621983
$764$	−6.14427e11	−	1.06422e12i	−0.0652455	−	0.113008i
$765$	−6.54767e10	+	1.13409e11i	−0.00691211	+	0.0119721i
$766$	−7.87916e12			−0.826895
$767$	−6.29100e12			−0.656358
$768$	−2.84324e12	+	4.92463e12i	−0.294909	+	0.510797i
$769$	−1.57893e13			−1.62815			−0.814076	−	0.580759i	$-0.802756\pi$
$769$	−1.57893e13			−1.62815			−0.814076	+	0.580759i	$0.802756\pi$
$770$	−3.82478e12	−	6.62471e12i	−0.392101	−	0.679139i
$771$	−6.71762e12			−0.684654
$772$	7.42144e11	+	1.28543e12i	0.0751987	+	0.130248i
$773$	9.43351e12	+	1.63393e13i	0.950311	+	1.64599i	0.744752	+	0.667342i	$0.232568\pi$
$773$	9.43351e12	+	1.63393e13i	0.950311	+	1.64599i	0.205559	+	0.978645i	$0.434099\pi$
$774$	−4.48311e11	−	7.76497e11i	−0.0448998	−	0.0777688i
$775$	−1.28142e13	+	2.21948e13i	−1.27595	+	2.21000i
$776$	−1.19823e13			−1.18621
$777$	6.41293e11	+	5.03743e12i	0.0631193	+	0.495810i
$778$	8.26971e12			0.809249
$779$	1.20862e13	−	2.09340e13i	1.17591	−	2.03673i
$780$	−2.52990e12	−	4.38192e12i	−0.244725	−	0.423876i
$781$	4.07385e12	+	7.05612e12i	0.391810	+	0.678635i
$782$	5.51183e11	+	9.54678e11i	0.0527067	+	0.0912907i
$783$	1.69597e13			1.61246
$784$	−4.42616e12	−	7.66633e12i	−0.418413	−	0.724712i
$785$	−2.25186e13			−2.11654
$786$	4.83848e12	−	8.38049e12i	0.452176	−	0.783192i
$787$	3.93055e12			0.365231			0.182615	−	0.983184i	$-0.441544\pi$
$787$	3.93055e12			0.365231			0.182615	+	0.983184i	$0.441544\pi$
$788$	8.28984e11			0.0765910
$789$	1.51427e12	−	2.62279e12i	0.139110	−	0.240945i
$790$	−6.77132e12	−	1.17283e13i	−0.618517	−	1.07130i
$791$	1.16009e12			0.105365
$792$	5.20905e11	−	9.02234e11i	0.0470430	−	0.0814809i
$793$	8.94693e11	−	1.54965e12i	0.0803424	−	0.139157i
$794$	2.85196e12	−	4.93974e12i	0.254654	−	0.441074i
$795$	−4.57395e12	−	7.92232e12i	−0.406106	−	0.703396i
$796$	1.30589e12	+	2.26186e12i	0.115291	+	0.199691i
$797$	9.56952e10	−	1.65749e11i	0.00840094	−	0.0145508i	−0.861794	−	0.507258i	$-0.830659\pi$
$797$	9.56952e10	−	1.65749e11i	0.00840094	−	0.0145508i	0.870195	+	0.492707i	$0.163993\pi$
$798$	6.07398e12	−	1.05204e13i	0.530225	−	0.918376i
$799$	5.40212e11	−	9.35675e11i	0.0468926	−	0.0812203i
$800$	6.74223e12			0.581968
$801$	6.84593e11	+	1.18575e12i	0.0587606	+	0.101776i
$802$	−7.70456e12	+	1.33447e13i	−0.657602	+	1.13900i
$803$	−3.46760e11			−0.0294313
$804$	−6.95525e11			−0.0587031
$805$	6.49101e12	−	1.12428e13i	0.544792	−	0.943608i
$806$	3.90116e13			3.25602
$807$	−2.42345e12	−	4.19753e12i	−0.201142	−	0.348388i
$808$	−1.12916e13			−0.931976
$809$	−8.11208e12	−	1.40505e13i	−0.665831	−	1.15325i	−0.979059	−	0.203575i	$-0.934744\pi$
$809$	−8.11208e12	−	1.40505e13i	−0.665831	−	1.15325i	0.313228	−	0.949678i	$-0.398589\pi$
$810$	8.89139e12	+	1.54003e13i	0.725750	+	1.25704i
$811$	1.21349e12	+	2.10183e12i	0.0985014	+	0.170609i	0.911065	−	0.412264i	$-0.135262\pi$
$811$	1.21349e12	+	2.10183e12i	0.0985014	+	0.170609i	−0.812563	+	0.582873i	$0.801928\pi$
$812$	1.11686e12	−	1.93445e12i	0.0901561	−	0.156155i
$813$	1.19089e13			0.956010
$814$	−1.51546e12	−	1.19041e13i	−0.120986	−	0.950359i
$815$	1.63952e13			1.30169
$816$	4.97320e11	−	8.61384e11i	0.0392672	−	0.0680129i
$817$	−7.89493e12	−	1.36744e13i	−0.619939	−	1.07377i
$818$	1.21594e13	+	2.10608e13i	0.949562	+	1.64469i
$819$	−6.73089e11	−	1.16582e12i	−0.0522751	−	0.0905431i
$820$	5.34435e12			0.412793
$821$	−3.69222e11	−	6.39511e11i	−0.0283624	−	0.0491251i	0.851496	−	0.524361i	$-0.175696\pi$
$821$	−3.69222e11	−	6.39511e11i	−0.0283624	−	0.0491251i	−0.879858	+	0.475236i	$0.842363\pi$
$822$	−5.96687e12			−0.455851
$823$	9.71959e12	−	1.68348e13i	0.738497	−	1.27911i	−0.214675	−	0.976685i	$-0.568869\pi$
$823$	9.71959e12	−	1.68348e13i	0.738497	−	1.27911i	0.953172	−	0.302428i	$-0.0977973\pi$
$824$	−1.20415e13			−0.909933
$825$	1.45046e13			1.09009
$826$	1.66968e12	−	2.89197e12i	0.124802	−	0.216164i
$827$	4.94479e12	+	8.56463e12i	0.367598	+	0.636698i	0.989189	−	0.146643i	$-0.0468469\pi$
$827$	4.94479e12	+	8.56463e12i	0.367598	+	0.636698i	−0.621591	+	0.783342i	$0.713514\pi$
$828$	−4.99217e11			−0.0369107
$829$	4.36568e12	−	7.56159e12i	0.321038	−	0.556055i	−0.659664	−	0.751560i	$-0.729302\pi$
$829$	4.36568e12	−	7.56159e12i	0.321038	−	0.556055i	0.980703	+	0.195506i	$0.0626348\pi$
$830$	−5.55900e12	+	9.62847e12i	−0.406579	+	0.704216i
$831$	−7.93923e12	+	1.37511e13i	−0.577529	+	1.00031i
$832$	7.44260e12	+	1.28910e13i	0.538480	+	0.932675i
$833$	3.55763e11	+	6.16200e11i	0.0256011	+	0.0443424i
$834$	−4.81728e12	+	8.34377e12i	−0.344790	+	0.597194i
$835$	7.47131e12	−	1.29407e13i	0.531872	−	0.921230i
$836$	−2.59014e12	+	4.48625e12i	−0.183398	+	0.317654i
$837$	−2.83719e13			−1.99813
$838$	4.54798e12	+	7.87733e12i	0.318581	+	0.551799i
$839$	6.07919e12	−	1.05295e13i	0.423562	−	0.733631i	−0.572723	−	0.819749i	$-0.694113\pi$
$839$	6.07919e12	−	1.05295e13i	0.423562	−	0.733631i	0.996285	+	0.0861182i	$0.0274463\pi$
$840$	−9.51222e12			−0.659212
$841$	1.95329e13			1.34643
$842$	9.75460e11	−	1.68955e12i	0.0668813	−	0.115842i
$843$	1.16196e13			0.792443
$844$	−1.95756e12	−	3.39060e12i	−0.132793	−	0.230004i
$845$	−3.20275e13			−2.16107
$846$	1.35571e12	+	2.34815e12i	0.0909912	+	0.157601i
$847$	9.92166e11	+	1.71848e12i	0.0662383	+	0.114728i
$848$	−5.00556e12	−	8.66988e12i	−0.332408	−	0.575747i
$849$	−3.81345e12	+	6.60510e12i	−0.251903	+	0.436309i
$850$	−1.62029e12			−0.106465
$851$	1.62099e13	−	1.23285e13i	1.05949	−	0.805802i
$852$	−2.86072e12			−0.185993
$853$	−1.15356e13	+	1.99802e13i	−0.746051	+	1.29220i	0.203652	+	0.979043i	$0.434719\pi$
$853$	−1.15356e13	+	1.99802e13i	−0.746051	+	1.29220i	−0.949702	+	0.313154i	$0.898614\pi$
$854$	4.74916e11	+	8.22579e11i	0.0305532	+	0.0529197i
$855$	−2.89373e12	−	5.01209e12i	−0.185187	−	0.320753i
$856$	−3.23622e12	−	5.60530e12i	−0.206018	−	0.356834i
$857$	1.15948e13			0.734257			0.367128	−	0.930170i	$-0.380341\pi$
$857$	1.15948e13			0.734257			0.367128	+	0.930170i	$0.380341\pi$
$858$	−1.10395e13	−	1.91209e13i	−0.695434	−	1.20453i
$859$	4.97284e11			0.0311627			0.0155814	−	0.999879i	$-0.495040\pi$
$859$	4.97284e11			0.0311627			0.0155814	+	0.999879i	$0.495040\pi$
$860$	1.74551e12	−	3.02331e12i	0.108813	−	0.188469i
$861$	−9.86850e12			−0.611979
$862$	−9.84558e11			−0.0607377
$863$	1.07028e13	−	1.85378e13i	0.656823	−	1.13765i	−0.324611	−	0.945848i	$-0.605233\pi$
$863$	1.07028e13	−	1.85378e13i	0.656823	−	1.13765i	0.981434	−	0.191802i	$-0.0614333\pi$
$864$	3.73200e12	+	6.46402e12i	0.227840	+	0.394630i
$865$	2.91381e13			1.76965
$866$	−7.16549e12	+	1.24110e13i	−0.432927	+	0.749852i
$867$	7.73730e12	−	1.34014e13i	0.465054	−	0.805497i
$868$	−1.86839e12	+	3.23615e12i	−0.111720	+	0.193504i
$869$	−5.33187e12	−	9.23506e12i	−0.317169	−	0.549352i
$870$	2.04649e13	+	3.54462e13i	1.21108	+	2.09765i
$871$	−3.76088e12	+	6.51404e12i	−0.221416	+	0.383503i
$872$	−8.55545e12	+	1.48185e13i	−0.501093	+	0.867919i
$873$	−1.48814e12	+	2.57754e12i	−0.0867123	+	0.150190i
$874$	−4.87189e13			−2.82420
$875$	2.44400e12	+	4.23314e12i	0.140950	+	0.244133i
$876$	6.08751e10	−	1.05439e11i	0.00349278	−	0.00604967i
$877$	−1.97760e13			−1.12886			−0.564431	−	0.825480i	$-0.690904\pi$
$877$	−1.97760e13			−1.12886			−0.564431	+	0.825480i	$0.690904\pi$
$878$	−1.77263e13			−1.00668
$879$	−2.17760e12	+	3.77171e12i	−0.123035	+	0.213102i
$880$	2.76803e13			1.55596
$881$	1.03036e13	+	1.78464e13i	0.576234	+	0.998067i	0.995906	+	0.0903914i	$0.0288118\pi$
$881$	1.03036e13	+	1.78464e13i	0.576234	+	0.998067i	−0.419672	+	0.907676i	$0.637855\pi$
$882$	−1.78564e12			−0.0993537
$883$	−1.01379e13	−	1.75593e13i	−0.561208	−	0.972040i	−0.997391	−	0.0721827i	$-0.977004\pi$
$883$	−1.01379e13	−	1.75593e13i	−0.561208	−	0.972040i	0.436184	−	0.899858i	$-0.356330\pi$
$884$	2.22535e11	+	3.85443e11i	0.0122564	+	0.0212288i
$885$	5.52085e12	+	9.56239e12i	0.302525	+	0.523988i
$886$	5.09921e12	−	8.83209e12i	0.278004	−	0.481517i
$887$	−1.76706e13			−0.958507			−0.479254	−	0.877676i	$-0.659093\pi$
$887$	−1.76706e13			−0.958507			−0.479254	+	0.877676i	$0.659093\pi$
$888$	−1.37618e13	−	5.76938e12i	−0.742707	−	0.311366i
$889$	7.38342e12			0.396460
$890$	−1.47711e13	+	2.55844e13i	−0.789149	+	1.36685i
$891$	7.00125e12	+	1.21265e13i	0.372157	+	0.644594i
$892$	8.57573e11	+	1.48536e12i	0.0453554	+	0.0785579i
$893$	2.38746e13	+	4.13520e13i	1.25633	+	2.17603i
$894$	−1.02999e13			−0.539280
$895$	−1.85529e13	−	3.21346e13i	−0.966514	−	1.67405i
$896$	−1.23660e13			−0.640978
$897$	1.87350e13	−	3.24500e13i	0.966248	−	1.67359i
$898$	−2.49646e12			−0.128109
$899$	−5.69457e13			−2.90765
$900$	3.66882e11	−	6.35459e11i	0.0186395	−	0.0322846i
$901$	4.02334e11	+	6.96863e11i	0.0203388	+	0.0352278i
$902$	2.33206e13			1.17303
$903$	−3.22314e12	+	5.58263e12i	−0.161318	+	0.279412i
$904$	−1.70450e12	+	2.95227e12i	−0.0848864	+	0.147028i
$905$	−9.55581e12	+	1.65511e13i	−0.473532	+	0.820181i
$906$	1.26824e13	+	2.19666e13i	0.625354	+	1.08314i
$907$	−5.34097e12	−	9.25083e12i	−0.262052	−	0.453887i	0.704735	−	0.709470i	$-0.251066\pi$
$907$	−5.34097e12	−	9.25083e12i	−0.262052	−	0.453887i	−0.966787	+	0.255583i	$0.917732\pi$
$908$	1.15175e12	−	1.99489e12i	0.0562304	−	0.0973939i
$909$	−1.40237e12	+	2.42897e12i	−0.0681278	+	0.118001i
$910$	1.45229e13	−	2.51544e13i	0.702049	−	1.21599i
$911$	−3.27180e12			−0.157382			−0.0786908	−	0.996899i	$-0.525074\pi$
$911$	−3.27180e12			−0.157382			−0.0786908	+	0.996899i	$0.525074\pi$
$912$	2.19790e13	+	3.80687e13i	1.05204	+	1.82218i
$913$	−4.37726e12	+	7.58164e12i	−0.208489	+	0.361114i
$914$	7.40628e12			0.351028
$915$	−3.14065e12			−0.148124
$916$	−2.87325e12	+	4.97661e12i	−0.134848	+	0.233563i
$917$	1.00242e13			0.468153
$918$	−8.96875e11	−	1.55343e12i	−0.0416812	−	0.0721939i
$919$	2.19419e13			1.01474			0.507370	−	0.861728i	$-0.330618\pi$
$919$	2.19419e13			1.01474			0.507370	+	0.861728i	$0.330618\pi$
$920$	1.90742e13	+	3.30375e13i	0.877811	+	1.52041i
$921$	−1.92025e13	−	3.32596e13i	−0.879404	−	1.52317i
$922$	1.29836e12	+	2.24882e12i	0.0591706	+	0.102486i
$923$	−1.54687e13	+	2.67925e13i	−0.701529	+	1.21508i
$924$	2.11487e12			0.0954462
$925$	3.78023e12	+	2.96942e13i	0.169778	+	1.33362i
$926$	−2.49977e13			−1.11725
$927$	−1.49551e12	+	2.59029e12i	−0.0665165	+	0.115210i
$928$	7.49056e12	+	1.29740e13i	0.331550	+	0.574261i
$929$	1.28252e13	+	2.22138e13i	0.564926	+	0.978481i	0.997057	+	0.0766700i	$0.0244288\pi$
$929$	1.28252e13	+	2.22138e13i	0.564926	+	0.978481i	−0.432130	+	0.901811i	$0.642238\pi$
$930$	−3.42358e13	−	5.92981e13i	−1.50074	−	2.59937i
$931$	−3.14458e13			−1.37179
$932$	−2.36458e12	−	4.09557e12i	−0.102656	−	0.177805i
$933$	6.38565e12			0.275891
$934$	2.05830e13	−	3.56509e13i	0.885011	−	1.53288i
$935$	−2.22487e12			−0.0952034
$936$	3.95582e12			0.168459
$937$	1.36843e13	−	2.37019e13i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636404\pi$
$937$	1.36843e13	−	2.37019e13i	0.579955	−	1.00451i	0.995484	−	0.0949311i	$-0.0302631\pi$
$938$	−1.99633e12	−	3.45775e12i	−0.0842015	−	0.145841i
$939$	−1.21046e13			−0.508105
$940$	−5.27848e12	+	9.14260e12i	−0.220513	+	0.381939i
$941$	2.02407e13	−	3.50579e13i	0.841534	−	1.45758i	−0.0470626	−	0.998892i	$-0.514986\pi$
$941$	2.02407e13	−	3.50579e13i	0.841534	−	1.45758i	0.888597	−	0.458689i	$-0.151681\pi$
$942$	1.72503e13	−	2.98783e13i	0.713784	−	1.23631i
$943$	1.97886e13	+	3.42749e13i	0.814915	+	1.41147i
$944$	6.04181e12	+	1.04647e13i	0.247624	+	0.428897i
$945$	−1.05620e13	+	1.82940e13i	−0.430829	+	0.746217i
$946$	7.61670e12	−	1.31925e13i	0.309212	−	0.535571i
$947$	−8.74229e12	+	1.51421e13i	−0.353224	+	0.611802i	−0.986812	−	0.161868i	$-0.948248\pi$
$947$	−8.74229e12	+	1.51421e13i	−0.353224	+	0.611802i	0.633588	+	0.773670i	$0.281581\pi$
$948$	3.74412e12			0.150561
$949$	−6.58334e11	−	1.14027e12i	−0.0263481	−	0.0456362i
$950$	3.58043e13	−	6.20148e13i	1.42619	−	2.47024i
$951$	−2.18057e13			−0.864486
$952$	8.36714e11			0.0330150
$953$	−8.50814e12	+	1.47365e13i	−0.334131	+	0.578732i	−0.983318	−	0.181897i	$-0.941776\pi$
$953$	−8.50814e12	+	1.47365e13i	−0.334131	+	0.578732i	0.649187	+	0.760629i	$0.275109\pi$
$954$	−2.01938e12			−0.0789316
$955$	1.16625e13	+	2.02001e13i	0.453710	+	0.785848i
$956$	1.35210e12			0.0523539
$957$	1.61144e13	+	2.79110e13i	0.621028	+	1.07565i
$958$	8.54774e12	+	1.48051e13i	0.327874	+	0.567894i
$959$	−3.09049e12	−	5.35289e12i	−0.117990	−	0.204364i
$960$	1.30629e13	−	2.26256e13i	0.496386	−	0.859766i
$961$	6.88249e13			2.60310
$962$	3.62678e13	−	2.75837e13i	1.36532	−	1.03840i
$963$	−1.60770e12			−0.0602401
$964$	−8.91627e11	+	1.54434e12i	−0.0332534	+	0.0575967i
$965$	−1.40868e13	−	2.43990e13i	−0.522924	−	0.905731i
$966$	9.94483e12	+	1.72249e13i	0.367452	+	0.636445i
$967$	−1.07396e13	−	1.86015e13i	−0.394973	−	0.684114i	0.598125	−	0.801403i	$-0.295913\pi$
$967$	−1.07396e13	−	1.86015e13i	−0.394973	−	0.684114i	−0.993098	+	0.117289i	$0.962579\pi$
$968$	−5.83107e12			−0.213456
$969$	−1.76661e12	−	3.05986e12i	−0.0643701	−	0.111492i
$970$	−6.42180e13			−2.32908
$971$	1.44486e13	−	2.50257e13i	0.521602	−	0.903441i	−0.478083	−	0.878315i	$-0.658668\pi$
$971$	1.44486e13	−	2.50257e13i	0.521602	−	0.903441i	0.999684	−	0.0251257i	$-0.00799859\pi$
$972$	1.53377e12			0.0551141
$973$	−9.98029e12			−0.356973
$974$	−2.11520e12	+	3.66364e12i	−0.0753072	+	0.130436i
$975$	2.75373e13	+	4.76961e13i	0.975891	+	1.69029i
$976$	−3.43701e12			−0.121243
$977$	−1.43589e13	+	2.48703e13i	−0.504190	+	0.873283i	0.495798	+	0.868438i	$0.334876\pi$
$977$	−1.43589e13	+	2.48703e13i	−0.504190	+	0.873283i	−0.999988	+	0.00484512i	$0.998458\pi$
$978$	−1.25595e13	+	2.17536e13i	−0.438982	+	0.760339i
$979$	−1.16311e13	+	2.01456e13i	−0.404667	+	0.700904i
$980$	−3.47621e12	−	6.02097e12i	−0.120389	−	0.208521i
$981$	2.12510e12	+	3.68078e12i	0.0732602	+	0.126890i
$982$	2.29560e13	−	3.97609e13i	0.787761	−	1.36444i
$983$	2.49581e13	−	4.32286e13i	0.852550	−	1.47666i	−0.0263487	−	0.999653i	$-0.508388\pi$
$983$	2.49581e13	−	4.32286e13i	0.852550	−	1.47666i	0.878899	−	0.477008i	$-0.158279\pi$
$984$	1.44996e13	−	2.51140e13i	0.493034	−	0.853960i
$985$	−1.57351e13			−0.532606
$986$	−1.80013e12	−	3.11792e12i	−0.0606538	−	0.105056i
$987$	9.74688e12	−	1.68821e13i	0.326918	−	0.566238i
$988$	−1.96698e13			−0.656741
$989$	2.58525e13			0.859250
$990$	2.79175e12	−	4.83545e12i	0.0923672	−	0.159985i
$991$	4.58686e12			0.151072			0.0755361	−	0.997143i	$-0.475933\pi$
$991$	4.58686e12			0.151072			0.0755361	+	0.997143i	$0.475933\pi$
$992$	−1.25310e13	−	2.17043e13i	−0.410849	−	0.711612i
$993$	−2.35350e13			−0.768145
$994$	−8.21099e12	−	1.42219e13i	−0.266782	−	0.462081i
$995$	−2.47873e13	−	4.29328e13i	−0.801724	−	1.38863i
$996$	−1.53689e12	−	2.66197e12i	−0.0494852	−	0.0857110i
$997$	−4.58409e12	+	7.93987e12i	−0.146935	+	0.254498i	−0.930093	−	0.367324i	$-0.880274\pi$
$997$	−4.58409e12	+	7.93987e12i	−0.146935	+	0.254498i	0.783158	+	0.621822i	$0.213607\pi$
$998$	1.85255e13			0.591131
$999$	−2.63764e13	+	2.00607e13i	−0.837858	+	0.637239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.c.a.10.21	✓	54
37.26	even	3	inner	37.10.c.a.26.21	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.c.a.10.21	✓	54	1.1	even	1	trivial
37.10.c.a.26.21	yes	54	37.26	even	3	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.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.4973 - 21.6460i) q^{2} +(-65.5823 - 113.592i) q^{3} +(-56.3672 - 97.6309i) q^{4} +(1069.92 + 1853.15i) q^{5} -3278.42 q^{6} +(-1698.03 - 2941.08i) q^{7} +9979.52 q^{8} +(1239.41 - 2146.72i) q^{9} +O(q^{10})\)	\(q+(12.4973 - 21.6460i) q^{2} +(-65.5823 - 113.592i) q^{3} +(-56.3672 - 97.6309i) q^{4} +(1069.92 + 1853.15i) q^{5} -3278.42 q^{6} +(-1698.03 - 2941.08i) q^{7} +9979.52 q^{8} +(1239.41 - 2146.72i) q^{9} +53484.4 q^{10} +42114.7 q^{11} +(-7393.39 + 12805.7i) q^{12} +(79955.9 + 138488. i) q^{13} -84883.5 q^{14} +(140335. - 243068. i) q^{15} +(153577. - 266004. i) q^{16} +(-12344.2 + 21380.7i) q^{17} +(-30978.7 - 53656.7i) q^{18} +(-545548. - 944916. i) q^{19} +(120616. - 208914. i) q^{20} +(-222722. + 385765. i) q^{21} +(526321. - 911615. i) q^{22} +1.78643e6 q^{23} +(-654480. - 1.13359e6i) q^{24} +(-1.31288e6 + 2.27397e6i) q^{25} +3.99695e6 q^{26} -2.90685e6 q^{27} +(-191427. + 331561. i) q^{28} -5.83438e6 q^{29} +(-3.50763e6 - 6.07540e6i) q^{30} +9.76036e6 q^{31} +(-1.28387e6 - 2.22372e6i) q^{32} +(-2.76198e6 - 4.78389e6i) q^{33} +(308539. + 534404. i) q^{34} +(3.63350e6 - 6.29341e6i) q^{35} -279449. q^{36} +(9.07388e6 - 6.90120e6i) q^{37} -2.72716e7 q^{38} +(1.04874e7 - 1.81647e7i) q^{39} +(1.06772e7 + 1.84935e7i) q^{40} +(1.10772e7 + 1.91862e7i) q^{41} +(5.56686e6 + 9.64209e6i) q^{42} +1.44716e7 q^{43} +(-2.37389e6 - 4.11169e6i) q^{44} +5.30427e6 q^{45} +(2.23257e7 - 3.86692e7i) q^{46} -4.37626e7 q^{47} -4.02879e7 q^{48} +(1.44102e7 - 2.49592e7i) q^{49} +(3.28150e7 + 5.68372e7i) q^{50} +3.23824e6 q^{51} +(9.01379e6 - 1.56123e7i) q^{52} +(1.62965e7 - 2.82264e7i) q^{53} +(-3.63279e7 + 6.29218e7i) q^{54} +(4.50591e7 + 7.80447e7i) q^{55} +(-1.69455e7 - 2.93505e7i) q^{56} +(-7.15566e7 + 1.23940e8i) q^{57} +(-7.29143e7 + 1.26291e8i) q^{58} +(-1.96702e7 + 3.40698e7i) q^{59} -3.16412e7 q^{60} +(-5.59491e6 - 9.69067e6i) q^{61} +(1.21979e8 - 2.11273e8i) q^{62} -8.41824e6 q^{63} +9.30837e7 q^{64} +(-1.71092e8 + 2.96341e8i) q^{65} -1.38070e8 q^{66} +(2.35185e7 + 4.07352e7i) q^{67} +2.78323e6 q^{68} +(-1.17158e8 - 2.02924e8i) q^{69} +(-9.08183e7 - 1.57302e8i) q^{70} +(9.67325e7 + 1.67546e8i) q^{71} +(1.23687e7 - 2.14233e7i) q^{72} -8.23371e6 q^{73} +(-3.59842e7 - 2.82660e8i) q^{74} +3.44406e8 q^{75} +(-6.15020e7 + 1.06525e8i) q^{76} +(-7.15120e7 - 1.23862e8i) q^{77} +(-2.62129e8 - 4.54021e8i) q^{78} +(-1.26604e8 - 2.19284e8i) q^{79} +6.57260e8 q^{80} +(1.66243e8 + 2.87941e8i) q^{81} +5.53740e8 q^{82} +(-1.03937e8 + 1.80024e8i) q^{83} +5.02168e7 q^{84} -5.28289e7 q^{85} +(1.80856e8 - 3.13252e8i) q^{86} +(3.82633e8 + 6.62739e8i) q^{87} +4.20284e8 q^{88} +(-2.76177e8 + 4.78352e8i) q^{89} +(6.62892e7 - 1.14816e8i) q^{90} +(2.71535e8 - 4.70313e8i) q^{91} +(-1.00696e8 - 1.74411e8i) q^{92} +(-6.40107e8 - 1.10870e9i) q^{93} +(-5.46916e8 + 9.47286e8i) q^{94} +(1.16738e9 - 2.02196e9i) q^{95} +(-1.68398e8 + 2.91674e8i) q^{96} -1.20069e9 q^{97} +(-3.60178e8 - 6.23847e8i) q^{98} +(5.21974e7 - 9.04085e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9 - 82404 * q^10 - 108196 * q^11 + 45492 * q^12 - 29827 * q^13 - 504992 * q^14 + 87135 * q^15 - 1561814 * q^16 + 116991 * q^17 + 1767678 * q^18 - 599677 * q^19 + 4122556 * q^20 - 221017 * q^21 - 257914 * q^22 + 1752736 * q^23 + 1149408 * q^24 - 6037260 * q^25 - 16731604 * q^26 - 1916582 * q^27 + 1917318 * q^28 - 11336100 * q^29 - 20390006 * q^30 + 14447580 * q^31 - 873740 * q^32 - 4494200 * q^33 + 13736524 * q^34 - 8546699 * q^35 + 61692836 * q^36 - 1919410 * q^37 - 85447920 * q^38 - 14035313 * q^39 + 3210182 * q^40 + 28676571 * q^41 - 101904850 * q^42 + 56602028 * q^43 + 153011074 * q^44 + 104234980 * q^45 + 99535572 * q^46 - 147509100 * q^47 - 203670880 * q^48 - 201857540 * q^49 - 91421384 * q^50 + 328228338 * q^51 - 69374156 * q^52 + 59137361 * q^53 + 201615042 * q^54 - 219079762 * q^55 + 202573590 * q^56 - 5989161 * q^57 - 157098688 * q^58 + 137993791 * q^59 + 413427232 * q^60 - 244884419 * q^61 + 109345558 * q^62 - 995908592 * q^63 + 184008092 * q^64 + 248745395 * q^65 + 1965122248 * q^66 - 130143913 * q^67 + 667610796 * q^68 + 246927272 * q^69 - 291173360 * q^70 + 473387559 * q^71 + 366188748 * q^72 + 923638972 * q^73 - 885443390 * q^74 - 2185997392 * q^75 - 337459826 * q^76 - 586609928 * q^77 - 261025842 * q^78 + 563110723 * q^79 - 4210381784 * q^80 + 713813329 * q^81 + 3458576264 * q^82 - 663594441 * q^83 - 2635249016 * q^84 - 1417287750 * q^85 - 2269028474 * q^86 + 314944482 * q^87 - 7714172 * q^88 + 655027619 * q^89 + 588021376 * q^90 - 1833870961 * q^91 - 2384055268 * q^92 - 90092600 * q^93 - 1449940302 * q^94 + 2787158841 * q^95 + 2383567424 * q^96 - 2751583248 * q^97 + 4970876154 * q^98 + 2668760954 * q^99

Introduction

L-functions

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