LMFDB - Embedded newform 38.10.e.b.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, 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("38.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.e (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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	38.17
Dual form			38.10.e.b.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.77837 - 15.7569i) q^{2} +(-172.140 - 144.442i) q^{3} +(-240.561 - 87.5572i) q^{4} +(432.938 - 157.576i) q^{5} +(-2754.24 + 2311.08i) q^{6} +(4035.63 + 6989.91i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(5350.58 + 30344.6i) q^{9} +O(q^{10})$	\(q+(2.77837 - 15.7569i) q^{2} +(-172.140 - 144.442i) q^{3} +(-240.561 - 87.5572i) q^{4} +(432.938 - 157.576i) q^{5} +(-2754.24 + 2311.08i) q^{6} +(4035.63 + 6989.91i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(5350.58 + 30344.6i) q^{9} +(-1280.06 - 7259.57i) q^{10} +(-11823.5 + 20478.9i) q^{11} +(28763.2 + 49819.3i) q^{12} +(-3580.47 + 3004.37i) q^{13} +(121352. - 44168.5i) q^{14} +(-97286.6 - 35409.4i) q^{15} +(50203.5 + 42125.7i) q^{16} +(7702.60 - 43683.6i) q^{17} +493004. q^{18} +(514037. - 241773. i) q^{19} -117945. q^{20} +(314948. - 1.78616e6i) q^{21} +(289835. + 243200. i) q^{22} +(169614. + 61734.6i) q^{23} +(864915. - 314803. i) q^{24} +(-1.33358e6 + 1.11900e6i) q^{25} +(37391.7 + 64764.4i) q^{26} +(1.25050e6 - 2.16593e6i) q^{27} +(-358799. - 2.03485e6i) q^{28} +(185746. + 1.05342e6i) q^{29} +(-828242. + 1.43456e6i) q^{30} +(24726.1 + 42826.8i) q^{31} +(803256. - 674012. i) q^{32} +(4.99333e6 - 1.81742e6i) q^{33} +(-666919. - 242739. i) q^{34} +(2.84862e6 + 2.39028e6i) q^{35} +(1.36975e6 - 7.76823e6i) q^{36} +2.13625e7 q^{37} +(-2.38141e6 - 8.77137e6i) q^{38} +1.05030e6 q^{39} +(-327695. + 1.85845e6i) q^{40} +(-9.10559e6 - 7.64050e6i) q^{41} +(-2.72693e7 - 9.92522e6i) q^{42} +(1.55527e7 - 5.66070e6i) q^{43} +(4.63736e6 - 3.89121e6i) q^{44} +(7.09807e6 + 1.22942e7i) q^{45} +(1.44400e6 - 2.50108e6i) q^{46} +(8.20862e6 + 4.65534e7i) q^{47} +(-2.55728e6 - 1.45030e7i) q^{48} +(-1.23958e7 + 2.14702e7i) q^{49} +(1.39269e7 + 2.41221e7i) q^{50} +(-7.63570e6 + 6.40711e6i) q^{51} +(1.12438e6 - 409239. i) q^{52} +(3.66350e7 + 1.33340e7i) q^{53} +(-3.06540e7 - 2.57217e7i) q^{54} +(-1.89185e6 + 1.07292e7i) q^{55} -3.30599e7 q^{56} +(-1.23408e8 - 3.26301e7i) q^{57} +1.71147e7 q^{58} +(-2.81848e7 + 1.59844e8i) q^{59} +(2.03030e7 + 1.70363e7i) q^{60} +(-8.50821e7 - 3.09673e7i) q^{61} +(743517. - 270618. i) q^{62} +(-1.90513e8 + 1.59860e8i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-1.07670e6 + 1.86490e6i) q^{65} +(-1.47637e7 - 8.37289e7i) q^{66} +(-1.24379e7 - 7.05390e7i) q^{67} +(-5.67776e6 + 9.83417e6i) q^{68} +(-2.02803e7 - 3.51265e7i) q^{69} +(4.55780e7 - 3.82445e7i) q^{70} +(3.72113e8 - 1.35438e8i) q^{71} +(-1.18598e8 - 4.31660e7i) q^{72} +(-1.72810e8 - 1.45005e8i) q^{73} +(5.93530e7 - 3.36608e8i) q^{74} +3.91193e8 q^{75} +(-1.44826e8 + 1.31535e7i) q^{76} -1.90861e8 q^{77} +(2.91812e6 - 1.65495e7i) q^{78} +(5.14602e8 + 4.31803e8i) q^{79} +(2.83730e7 + 1.03269e7i) q^{80} +(4.17995e7 - 1.52138e7i) q^{81} +(-1.45689e8 + 1.22248e8i) q^{82} +(3.49377e8 + 6.05138e8i) q^{83} +(-2.32155e8 + 4.02105e8i) q^{84} +(-3.54877e6 - 2.01260e7i) q^{85} +(-4.59842e7 - 2.60790e8i) q^{86} +(1.20184e8 - 2.08164e8i) q^{87} +(-4.84291e7 - 8.38817e7i) q^{88} +(2.66466e7 - 2.23592e7i) q^{89} +(2.13440e8 - 7.76858e7i) q^{90} +(-3.54497e7 - 1.29026e7i) q^{91} +(-3.53974e7 - 2.97019e7i) q^{92} +(1.92967e6 - 1.09437e7i) q^{93} +7.56345e8 q^{94} +(1.84448e8 - 1.85673e8i) q^{95} -2.35628e8 q^{96} +(1.67278e8 - 9.48683e8i) q^{97} +(3.03864e8 + 2.54972e8i) q^{98} +(-6.84688e8 - 2.49206e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9 - 55221 * q^11 - 62208 * q^12 + 21777 * q^13 + 28464 * q^14 - 280011 * q^15 + 1055055 * q^17 + 6083232 * q^18 + 2408220 * q^19 + 523776 * q^20 - 5105673 * q^21 - 2513280 * q^22 - 456708 * q^23 + 135168 * q^24 + 19417530 * q^25 - 1077120 * q^26 - 11729661 * q^27 - 30720 * q^28 + 4679889 * q^29 + 4879158 * q^31 - 12360834 * q^33 + 9206400 * q^34 - 47475759 * q^35 + 2035968 * q^36 + 119843604 * q^37 - 39471312 * q^38 + 16552668 * q^39 + 60082911 * q^41 + 59187024 * q^42 + 109939059 * q^43 - 40212480 * q^44 + 3067236 * q^45 - 4919424 * q^46 + 198627789 * q^47 - 4325376 * q^48 - 182954115 * q^49 - 229688016 * q^50 - 228228021 * q^51 - 49495296 * q^52 - 370799859 * q^53 + 111760416 * q^54 - 60369543 * q^55 + 211427328 * q^56 + 128158266 * q^57 + 166196064 * q^58 - 382689396 * q^59 - 36777216 * q^60 - 850085550 * q^61 + 42954480 * q^62 - 803298357 * q^63 - 402653184 * q^64 + 261122181 * q^65 + 516819888 * q^66 + 1146400764 * q^67 + 125611008 * q^68 - 178115667 * q^69 - 759612144 * q^70 + 363378456 * q^71 - 65150976 * q^72 + 1407478230 * q^73 - 12153360 * q^74 + 1715917770 * q^75 - 128288256 * q^76 - 193134048 * q^77 - 1199414208 * q^78 - 2098405449 * q^79 + 3082805319 * q^81 + 961326576 * q^82 + 358330707 * q^83 + 502249728 * q^84 - 1961566422 * q^85 - 588638592 * q^86 - 1222269090 * q^87 - 226185216 * q^88 - 368108670 * q^89 + 1740707616 * q^90 - 3296437032 * q^91 - 819648768 * q^92 + 6597152658 * q^93 + 2953278144 * q^94 - 881990403 * q^95 + 509607936 * q^96 - 3752161206 * q^97 - 458055696 * q^98 + 6061589742 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	2.77837	−	15.7569i	0.122788	−	0.696364i
$2$	2.77837	−	15.7569i	0.122788	−	0.696364i
$3$	−172.140	−	144.442i	−1.22698	−	1.02955i	−0.998430	−	0.0560211i	$-0.982159\pi$
$3$	−172.140	−	144.442i	−1.22698	−	1.02955i	−0.228546	−	0.973533i	$-0.573397\pi$
$4$	−240.561	−	87.5572i	−0.469846	−	0.171010i
$5$	432.938	−	157.576i	0.309785	−	0.112753i	−0.182449	−	0.983215i	$-0.558403\pi$
$5$	432.938	−	157.576i	0.309785	−	0.112753i	0.492234	+	0.870463i	$0.336180\pi$
$6$	−2754.24	+	2311.08i	−0.867602	+	0.728005i
$7$	4035.63	+	6989.91i	0.635287	+	1.10035i	0.986454	+	0.164037i	$0.0524516\pi$
$7$	4035.63	+	6989.91i	0.635287	+	1.10035i	−0.351167	+	0.936313i	$0.614215\pi$
$8$	−2048.00	+	3547.24i	−0.176777	+	0.306186i
$9$	5350.58	+	30344.6i	0.271838	+	1.54167i
$10$	−1280.06	−	7259.57i	−0.0404790	−	0.229568i
$11$	−11823.5	+	20478.9i	−0.243489	+	0.421736i	−0.961706	−	0.274084i	$-0.911625\pi$
$11$	−11823.5	+	20478.9i	−0.243489	+	0.421736i	0.718217	+	0.695820i	$0.244959\pi$
$12$	28763.2	+	49819.3i	0.400426	+	0.693557i
$13$	−3580.47	+	3004.37i	−0.0347692	+	0.0291748i	−0.660007	−	0.751260i	$-0.729447\pi$
$13$	−3580.47	+	3004.37i	−0.0347692	+	0.0291748i	0.625237	+	0.780435i	$0.285002\pi$
$14$	121352.	−	44168.5i	0.844250	−	0.307282i
$15$	−97286.6	−	35409.4i	−0.496183	−	0.180596i
$16$	50203.5	+	42125.7i	0.191511	+	0.160697i
$17$	7702.60	−	43683.6i	0.0223675	−	0.126852i	−0.971579	−	0.236714i	$-0.923930\pi$
$17$	7702.60	−	43683.6i	0.0223675	−	0.126852i	0.993947	+	0.109861i	$0.0350407\pi$
$18$	493004.			1.10694
$19$	514037.	−	241773.i	0.904905	−	0.425614i
$19$	514037.	−	241773.i	0.904905	−	0.425614i
$20$	−117945.			−0.164833
$21$	314948.	−	1.78616e6i	0.353388	−	2.00416i
$22$	289835.	+	243200.i	0.263784	+	0.221341i
$23$	169614.	+	61734.6i	0.126383	+	0.0459995i	0.404437	−	0.914566i	$-0.367467\pi$
$23$	169614.	+	61734.6i	0.126383	+	0.0459995i	−0.278055	+	0.960565i	$0.589690\pi$
$24$	864915.	−	314803.i	0.532136	−	0.193682i
$25$	−1.33358e6	+	1.11900e6i	−0.682791	+	0.572929i
$26$	37391.7	+	64764.4i	0.0160471	+	0.0277943i
$27$	1.25050e6	−	2.16593e6i	0.452841	−	0.784344i
$28$	−358799.	−	2.03485e6i	−0.110316	−	0.625636i
$29$	185746.	+	1.05342e6i	0.0487672	+	0.276572i	0.999434	−	0.0336415i	$-0.0107104\pi$
$29$	185746.	+	1.05342e6i	0.0487672	+	0.276572i	−0.950667	+	0.310214i	$0.899599\pi$
$30$	−828242.	+	1.43456e6i	−0.186686	+	0.323349i
$31$	24726.1	+	42826.8i	0.00480870	+	0.00832890i	0.868420	−	0.495830i	$-0.165136\pi$
$31$	24726.1	+	42826.8i	0.00480870	+	0.00832890i	−0.863611	+	0.504159i	$0.831803\pi$
$32$	803256.	−	674012.i	0.135419	−	0.113630i
$33$	4.99333e6	−	1.81742e6i	0.732955	−	0.266774i
$34$	−666919.	−	242739.i	−0.0855890	−	0.0311519i
$35$	2.84862e6	+	2.39028e6i	0.320870	+	0.269242i
$36$	1.36975e6	−	7.76823e6i	0.135919	−	0.770834i
$37$	2.13625e7			1.87389			0.936946	−	0.349473i	$-0.113639\pi$
$37$	2.13625e7			1.87389			0.936946	+	0.349473i	$0.113639\pi$
$38$	−2.38141e6	−	8.77137e6i	−0.185271	−	0.682404i
$39$	1.05030e6			0.0726980
$40$	−327695.	+	1.85845e6i	−0.0202395	+	0.114784i
$41$	−9.10559e6	−	7.64050e6i	−0.503246	−	0.422274i	0.355499	−	0.934677i	$-0.384311\pi$
$41$	−9.10559e6	−	7.64050e6i	−0.503246	−	0.422274i	−0.858745	+	0.512403i	$0.828755\pi$
$42$	−2.72693e7	−	9.92522e6i	−1.35224	−	0.492174i
$43$	1.55527e7	−	5.66070e6i	0.693740	−	0.252501i	0.0290040	−	0.999579i	$-0.490766\pi$
$43$	1.55527e7	−	5.66070e6i	0.693740	−	0.252501i	0.664736	+	0.747079i	$0.268544\pi$
$44$	4.63736e6	−	3.89121e6i	0.186523	−	0.156512i
$45$	7.09807e6	+	1.22942e7i	0.258038	+	0.446935i
$46$	1.44400e6	−	2.50108e6i	0.0475507	−	0.0823602i
$47$	8.20862e6	+	4.65534e7i	0.245375	+	1.39159i	0.819621	+	0.572906i	$0.194184\pi$
$47$	8.20862e6	+	4.65534e7i	0.245375	+	1.39159i	−0.574246	+	0.818683i	$0.694705\pi$
$48$	−2.55728e6	−	1.45030e7i	−0.0695332	−	0.394342i
$49$	−1.23958e7	+	2.14702e7i	−0.307180	+	0.532051i
$50$	1.39269e7	+	2.41221e7i	0.315129	+	0.545820i
$51$	−7.63570e6	+	6.40711e6i	−0.158046	+	0.132616i
$52$	1.12438e6	−	409239.i	0.0213254	−	0.00776180i
$53$	3.66350e7	+	1.33340e7i	0.637756	+	0.232124i	0.640603	−	0.767872i	$-0.278684\pi$
$53$	3.66350e7	+	1.33340e7i	0.637756	+	0.232124i	−0.00284782	+	0.999996i	$0.500906\pi$
$54$	−3.06540e7	−	2.57217e7i	−0.490586	−	0.411650i
$55$	−1.89185e6	+	1.07292e7i	−0.0278775	+	0.158101i
$56$	−3.30599e7			−0.449216
$57$	−1.23408e8	−	3.26301e7i	−1.54849	−	0.409431i
$58$	1.71147e7			0.198583
$59$	−2.81848e7	+	1.59844e8i	−0.302818	+	1.71737i	0.330784	+	0.943706i	$0.392687\pi$
$59$	−2.81848e7	+	1.59844e8i	−0.302818	+	1.71737i	−0.633602	+	0.773659i	$0.718424\pi$
$60$	2.03030e7	+	1.70363e7i	0.202246	+	0.169705i
$61$	−8.50821e7	−	3.09673e7i	−0.786781	−	0.286365i	−0.0827838	−	0.996568i	$-0.526381\pi$
$61$	−8.50821e7	−	3.09673e7i	−0.786781	−	0.286365i	−0.703997	+	0.710203i	$0.748603\pi$
$62$	743517.	−	270618.i	0.00639040	−	0.00232592i
$63$	−1.90513e8	+	1.59860e8i	−1.52368	+	1.27852i
$64$	−8.38861e6	−	1.45295e7i	−0.0625000	−	0.108253i
$65$	−1.07670e6	+	1.86490e6i	−0.00748144	+	0.0129582i
$66$	−1.47637e7	−	8.37289e7i	−0.0957738	−	0.543160i
$67$	−1.24379e7	−	7.05390e7i	−0.0754069	−	0.427654i	−0.999017	−	0.0443214i	$-0.985887\pi$
$67$	−1.24379e7	−	7.05390e7i	−0.0754069	−	0.427654i	0.923610	−	0.383333i	$-0.125224\pi$
$68$	−5.67776e6	+	9.83417e6i	−0.0322023	+	0.0557761i
$69$	−2.02803e7	−	3.51265e7i	−0.107709	−	0.186558i
$70$	4.55780e7	−	3.82445e7i	0.226889	−	0.190383i
$71$	3.72113e8	−	1.35438e8i	1.73785	−	0.632526i	0.738713	−	0.674020i	$-0.235434\pi$
$71$	3.72113e8	−	1.35438e8i	1.73785	−	0.632526i	0.999139	+	0.0414939i	$0.0132117\pi$
$72$	−1.18598e8	−	4.31660e7i	−0.520092	−	0.189298i
$73$	−1.72810e8	−	1.45005e8i	−0.712223	−	0.597626i	0.212999	−	0.977052i	$-0.431677\pi$
$73$	−1.72810e8	−	1.45005e8i	−0.712223	−	0.597626i	−0.925222	+	0.379427i	$0.876121\pi$
$74$	5.93530e7	−	3.36608e8i	0.230091	−	1.30491i
$75$	3.91193e8			1.42763
$76$	−1.44826e8	+	1.31535e7i	−0.497950	+	0.0452252i
$77$	−1.90861e8			−0.618742
$78$	2.91812e6	−	1.65495e7i	0.00892643	−	0.0506243i
$79$	5.14602e8	+	4.31803e8i	1.48645	+	1.24728i	0.898948	+	0.438055i	$0.144332\pi$
$79$	5.14602e8	+	4.31803e8i	1.48645	+	1.24728i	0.587501	+	0.809224i	$0.300112\pi$
$80$	2.83730e7	+	1.03269e7i	0.0774463	+	0.0281881i
$81$	4.17995e7	−	1.52138e7i	0.107892	−	0.0392694i
$82$	−1.45689e8	+	1.22248e8i	−0.355849	+	0.298593i
$83$	3.49377e8	+	6.05138e8i	0.808058	+	1.39960i	0.914207	+	0.405248i	$0.132815\pi$
$83$	3.49377e8	+	6.05138e8i	0.808058	+	1.39960i	−0.106149	+	0.994350i	$0.533852\pi$
$84$	−2.32155e8	+	4.02105e8i	−0.508770	+	0.881216i
$85$	−3.54877e6	−	2.01260e7i	−0.00737381	−	0.0418190i
$86$	−4.59842e7	−	2.60790e8i	−0.0906496	−	0.514099i
$87$	1.20184e8	−	2.08164e8i	0.224910	−	0.389556i
$88$	−4.84291e7	−	8.38817e7i	−0.0860864	−	0.149106i
$89$	2.66466e7	−	2.23592e7i	0.0450181	−	0.0377747i	−0.620001	−	0.784601i	$-0.712868\pi$
$89$	2.66466e7	−	2.23592e7i	0.0450181	−	0.0377747i	0.665019	+	0.746826i	$0.268423\pi$
$90$	2.13440e8	−	7.76858e7i	0.342914	−	0.124810i
$91$	−3.54497e7	−	1.29026e7i	−0.0541909	−	0.0197239i
$92$	−3.53974e7	−	2.97019e7i	−0.0515140	−	0.0432254i
$93$	1.92967e6	−	1.09437e7i	0.00267491	−	0.0151702i
$94$	7.56345e8			0.999182
$95$	1.84448e8	−	1.85673e8i	0.232337	−	0.233879i
$96$	−2.35628e8			−0.283144
$97$	1.67278e8	−	9.48683e8i	0.191852	−	1.08805i	−0.724978	−	0.688772i	$-0.758150\pi$
$97$	1.67278e8	−	9.48683e8i	0.191852	−	1.08805i	0.916831	−	0.399276i	$-0.130739\pi$
$98$	3.03864e8	+	2.54972e8i	0.332783	+	0.279238i
$99$	−6.84688e8	−	2.49206e8i	−0.716365	−	0.260736i
$100$	4.18783e8	−	1.52425e8i	0.418783	−	0.152425i
$101$	3.33209e8	−	2.79596e8i	0.318618	−	0.267353i	−0.469425	−	0.882972i	$-0.655539\pi$
$101$	3.33209e8	−	2.79596e8i	0.318618	−	0.267353i	0.788043	+	0.615620i	$0.211094\pi$
$102$	7.97416e7	+	1.38116e8i	0.0729431	+	0.126341i
$103$	2.14980e8	−	3.72356e8i	0.188205	−	0.325980i	−0.756447	−	0.654055i	$-0.773066\pi$
$103$	2.14980e8	−	3.72356e8i	0.188205	−	0.325980i	0.944652	+	0.328075i	$0.106400\pi$
$104$	−3.32442e6	−	1.88537e7i	−0.00278654	−	0.0158033i
$105$	−1.45104e8	−	8.22924e8i	−0.116500	−	0.660706i
$106$	3.11889e8	−	5.40207e8i	0.239952	−	0.415608i
$107$	3.88100e8	+	6.72209e8i	0.286231	+	0.495767i	0.972907	−	0.231197i	$-0.0742642\pi$
$107$	3.88100e8	+	6.72209e8i	0.286231	+	0.495767i	−0.686676	+	0.726964i	$0.740931\pi$
$108$	−4.90464e8	+	4.11548e8i	−0.346897	+	0.291081i
$109$	1.38735e9	−	5.04955e8i	0.941386	−	0.342636i	0.174673	−	0.984627i	$-0.444113\pi$
$109$	1.38735e9	−	5.04955e8i	0.941386	−	0.342636i	0.766713	+	0.641990i	$0.221891\pi$
$110$	1.63803e8	+	5.96195e7i	0.106673	+	0.0388258i
$111$	−3.67734e9	−	3.08566e9i	−2.29922	−	1.92927i
$112$	−9.18526e7	+	5.20922e8i	−0.0551582	+	0.312818i
$113$	−2.98361e9			−1.72143			−0.860716	−	0.509086i	$-0.829984\pi$
$113$	−2.98361e9			−1.72143			−0.860716	+	0.509086i	$0.829984\pi$
$114$	−8.57024e8	+	1.85388e9i	−0.475249	+	1.02804i
$115$	8.31604e7			0.0443380
$116$	4.75509e7	−	2.69674e8i	0.0243836	−	0.138286i
$117$	−1.10324e8	−	9.25729e7i	−0.0544294	−	0.0456717i
$118$	2.44034e9	+	8.88213e8i	1.15873	+	0.421743i
$119$	3.36430e8	−	1.22450e8i	0.153792	−	0.0559756i
$120$	3.24849e8	−	2.72580e8i	0.143010	−	0.119999i
$121$	8.99383e8	+	1.55778e9i	0.381426	+	0.660649i
$122$	−7.24340e8	+	1.25459e9i	−0.296021	+	0.512724i
$123$	4.63822e8	+	2.63047e9i	0.182717	+	1.03624i
$124$	−2.19834e6	−	1.24674e7i	−0.000835021	−	0.00473564i
$125$	−8.50951e8	+	1.47389e9i	−0.311752	+	0.539971i
$126$	1.98958e9	+	3.44606e9i	0.703225	+	1.21802i
$127$	−3.28760e9	+	2.75862e9i	−1.12140	+	0.940970i	−0.998675	−	0.0514706i	$-0.983609\pi$
$127$	−3.28760e9	+	2.75862e9i	−1.12140	+	0.940970i	−0.122729	+	0.992440i	$0.539165\pi$
$128$	−2.52247e8	+	9.18103e7i	−0.0830579	+	0.0302306i
$129$	−3.49488e9	−	1.27203e9i	−1.11116	−	0.404431i
$130$	2.63936e7	+	2.21469e7i	0.00810502	+	0.00680092i
$131$	−5.44101e8	+	3.08575e9i	−0.161420	+	0.915460i	0.791258	+	0.611482i	$0.209426\pi$
$131$	−5.44101e8	+	3.08575e9i	−0.161420	+	0.915460i	−0.952679	+	0.303979i	$0.901685\pi$
$132$	−1.36033e9			−0.389997
$133$	3.76443e9	+	2.61737e9i	1.04320	+	0.725325i
$134$	−1.14603e9			−0.307062
$135$	2.00089e8	−	1.13476e9i	0.0518467	−	0.294037i
$136$	1.39181e8	+	1.16787e8i	0.0348864	+	0.0292732i
$137$	−2.70833e9	−	9.85751e8i	−0.656838	−	0.239070i	−0.00796768	−	0.999968i	$-0.502536\pi$
$137$	−2.70833e9	−	9.85751e8i	−0.656838	−	0.239070i	−0.648871	+	0.760899i	$0.724758\pi$
$138$	−6.09832e8	+	2.21961e8i	−0.143138	+	0.0520979i
$139$	1.03890e9	−	8.71740e8i	0.236051	−	0.198071i	−0.517087	−	0.855933i	$-0.672984\pi$
$139$	1.03890e9	−	8.71740e8i	0.236051	−	0.198071i	0.753138	+	0.657862i	$0.228539\pi$
$140$	−4.75982e8	−	8.24426e8i	−0.104716	−	0.181374i
$141$	5.31126e9	−	9.19936e9i	1.13165	−	1.96007i
$142$	−1.10022e9	−	6.23966e9i	−0.227082	−	1.28784i
$143$	−1.91925e7	−	1.08846e8i	−0.00383814	−	0.0217672i
$144$	−1.00967e9	+	1.74880e9i	−0.195681	+	0.338930i
$145$	2.46410e8	+	4.26794e8i	0.0462916	+	0.0801794i
$146$	−2.76496e9	+	2.32008e9i	−0.503617	+	0.422585i
$147$	5.23501e9	−	1.90539e9i	0.924677	−	0.336555i
$148$	−5.13900e9	−	1.87044e9i	−0.880442	−	0.320455i
$149$	6.74494e8	+	5.65968e8i	0.112109	+	0.0940705i	0.697119	−	0.716956i	$-0.254465\pi$
$149$	6.74494e8	+	5.65968e8i	0.112109	+	0.0940705i	−0.585010	+	0.811026i	$0.698909\pi$
$150$	1.08688e9	−	6.16400e9i	0.175295	−	0.994150i
$151$	8.77634e9			1.37378			0.686890	−	0.726762i	$-0.258975\pi$
$151$	8.77634e9			1.37378			0.686890	+	0.726762i	$0.258975\pi$
$152$	−1.95122e8	+	2.31856e9i	−0.0296490	+	0.352308i
$153$	1.36678e9			0.201645
$154$	−5.30284e8	+	3.00739e9i	−0.0759740	+	0.430870i
$155$	1.74533e7	+	1.46451e7i	0.00242877	+	0.00203798i
$156$	−2.52661e8	−	9.19612e7i	−0.0341569	−	0.0124321i
$157$	−6.38720e9	+	2.32475e9i	−0.839000	+	0.305371i	−0.725547	−	0.688172i	$-0.758413\pi$
$157$	−6.38720e9	+	2.32475e9i	−0.839000	+	0.305371i	−0.113453	+	0.993543i	$0.536191\pi$
$158$	8.23364e9	−	6.90884e9i	1.05108	−	0.881959i
$159$	−4.38034e9	−	7.58696e9i	−0.543526	−	0.941415i
$160$	2.41551e8	−	4.18379e8i	0.0291387	−	0.0504697i
$161$	2.52981e8	+	1.43473e9i	0.0296737	+	0.168288i
$162$	−1.23588e8	−	7.00901e8i	−0.0140980	−	0.0799538i
$163$	−1.54236e9	+	2.67145e9i	−0.171137	+	0.296417i	−0.938817	−	0.344415i	$-0.888077\pi$
$163$	−1.54236e9	+	2.67145e9i	−0.171137	+	0.296417i	0.767681	+	0.640832i	$0.221411\pi$
$164$	1.52147e9	+	2.63527e9i	0.164235	+	0.284464i
$165$	1.87542e9	−	1.57366e9i	0.196979	−	0.165285i
$166$	1.05058e10	−	3.82381e9i	1.07385	−	0.390849i
$167$	−1.39347e10	−	5.07183e9i	−1.38636	−	0.504592i	−0.462257	−	0.886746i	$-0.652960\pi$
$167$	−1.39347e10	−	5.07183e9i	−1.38636	−	0.504592i	−0.924099	+	0.382154i	$0.875182\pi$
$168$	5.69092e9	+	4.77525e9i	0.551177	+	0.462492i
$169$	−1.83766e9	+	1.04219e10i	−0.173290	+	0.982779i
$170$	−3.26984e8			−0.0300266
$171$	1.00869e10	+	1.43046e10i	0.902142	+	1.27936i
$172$	−4.23700e9			−0.369131
$173$	−2.64736e9	+	1.50139e10i	−0.224702	+	1.27435i	0.638553	+	0.769578i	$0.279533\pi$
$173$	−2.64736e9	+	1.50139e10i	−0.224702	+	1.27435i	−0.863255	+	0.504768i	$0.831578\pi$
$174$	−2.94612e9	−	2.47208e9i	−0.243657	−	0.204452i
$175$	−1.32036e10	−	4.80570e9i	−1.06419	−	0.387334i
$176$	−1.45627e9	+	5.30040e8i	−0.114402	+	0.0416391i
$177$	2.79400e10	−	2.34445e10i	2.13967	−	1.79540i
$178$	−2.78277e8	−	4.81991e8i	−0.0207772	−	0.0359872i
$179$	1.04684e9	−	1.81317e9i	0.0762150	−	0.132008i	−0.825399	−	0.564550i	$-0.809050\pi$
$179$	1.04684e9	−	1.81317e9i	0.0762150	−	0.132008i	0.901614	+	0.432542i	$0.142383\pi$
$180$	−6.31074e8	−	3.57900e9i	−0.0448079	−	0.254118i
$181$	−2.34469e9	−	1.32974e10i	−0.162380	−	0.920900i	−0.951725	−	0.306951i	$-0.900691\pi$
$181$	−2.34469e9	−	1.32974e10i	−0.162380	−	0.920900i	0.789346	−	0.613949i	$-0.210420\pi$
$182$	−3.01798e8	+	5.22730e8i	−0.0203890	+	0.0353148i
$183$	1.01730e10	+	1.76202e10i	0.670533	+	1.16140i
$184$	−5.66358e8	+	4.75231e8i	−0.0364259	+	0.0305650i
$185$	9.24864e9	−	3.36623e9i	0.580504	−	0.211286i
$186$	−1.67078e8	−	6.08113e7i	−0.0102355	−	0.00372542i
$187$	8.03522e8	+	6.74235e8i	0.0480519	+	0.0403203i
$188$	2.10141e9	−	1.19177e10i	0.122687	−	0.695794i
$189$	2.01862e10			1.15074
$190$	−2.41316e9	−	3.42220e9i	−0.134337	−	0.190509i
$191$	−2.39326e10			−1.30119			−0.650594	−	0.759426i	$-0.725480\pi$
$191$	−2.39326e10			−1.30119			−0.650594	+	0.759426i	$0.725480\pi$
$192$	−6.54663e8	+	3.71278e9i	−0.0347666	+	0.197171i
$193$	1.94750e10	+	1.63414e10i	1.01034	+	0.847779i	0.988384	−	0.151980i	$-0.0485650\pi$
$193$	1.94750e10	+	1.63414e10i	1.01034	+	0.847779i	0.0219597	+	0.999759i	$0.493009\pi$
$194$	−1.44836e10	−	5.27158e9i	−0.734121	−	0.267198i
$195$	4.54714e8	−	1.65502e8i	0.0225208	−	0.00819688i
$196$	4.86182e9	−	4.07955e9i	0.235313	−	0.197451i
$197$	−7.74398e9	−	1.34130e10i	−0.366325	−	0.634493i	0.622663	−	0.782490i	$-0.286051\pi$
$197$	−7.74398e9	−	1.34130e10i	−0.366325	−	0.634493i	−0.988988	+	0.147997i	$0.952717\pi$
$198$	−5.82904e9	+	1.00962e10i	−0.269528	+	0.466836i
$199$	1.59115e9	+	9.02388e9i	0.0719239	+	0.407901i	0.999420	+	0.0340667i	$0.0108459\pi$
$199$	1.59115e9	+	9.02388e9i	0.0719239	+	0.407901i	−0.927496	+	0.373834i	$0.878043\pi$
$200$	−1.23821e9	−	7.02223e9i	−0.0547216	−	0.310342i
$201$	−8.04776e9	+	1.39391e10i	−0.347771	+	0.602356i
$202$	−3.47979e9	−	6.02717e9i	−0.147052	−	0.254702i
$203$	−6.61369e9	+	5.54954e9i	−0.273345	+	0.229364i
$204$	2.39784e9	−	8.72743e8i	0.0969359	−	0.0352818i
$205$	−5.14612e9	−	1.87303e9i	−0.203511	−	0.0740718i
$206$	−5.26990e9	−	4.42197e9i	−0.203892	−	0.171085i
$207$	−9.65779e8	+	5.47720e9i	−0.0365604	+	0.207344i
$208$	−3.06313e8			−0.0113470
$209$	−1.12648e9	+	1.33855e10i	−0.0408380	+	0.485263i
$210$	−1.33699e10			−0.474397
$211$	−7.92917e9	+	4.49686e10i	−0.275396	+	1.56185i	0.462307	+	0.886720i	$0.347022\pi$
$211$	−7.92917e9	+	4.49686e10i	−0.275396	+	1.56185i	−0.737703	+	0.675126i	$0.764089\pi$
$212$	−7.64546e9	−	6.41531e9i	−0.259952	−	0.218125i
$213$	−8.36186e10	−	3.04347e10i	−2.78352	−	1.01312i
$214$	1.16702e10	−	4.24762e9i	0.380380	−	0.138447i
$215$	5.84134e9	−	4.90147e9i	0.186440	−	0.156442i
$216$	5.12204e9	+	8.87163e9i	0.160104	+	0.277308i
$217$	−1.99570e8	+	3.45666e8i	−0.00610980	+	0.0105825i
$218$	−4.10196e9	−	2.32634e10i	−0.123009	−	0.697619i
$219$	8.80263e9	+	4.99222e10i	0.258591	+	1.46654i
$220$	1.39453e9	−	2.41539e9i	0.0401351	−	0.0695160i
$221$	1.03663e8	+	1.79549e8i	0.00292319	+	0.00506312i
$222$	−5.88374e10	+	4.93705e10i	−1.62579	+	1.36420i
$223$	4.15884e10	−	1.51369e10i	1.12616	−	0.409889i	0.289264	−	0.957249i	$-0.406589\pi$
$223$	4.15884e10	−	1.51369e10i	1.12616	−	0.409889i	0.836897	+	0.547360i	$0.184367\pi$
$224$	7.95293e9	+	2.89463e9i	0.211062	+	0.0768204i
$225$	−4.10911e10	−	3.44796e10i	−1.06887	−	0.896893i
$226$	−8.28959e9	+	4.70126e10i	−0.211371	+	1.19874i
$227$	3.42345e10			0.855751			0.427875	−	0.903838i	$-0.359262\pi$
$227$	3.42345e10			0.855751			0.427875	+	0.903838i	$0.359262\pi$
$228$	2.68303e10	+	1.86548e10i	0.657535	+	0.457177i
$229$	4.40650e10			1.05885			0.529425	−	0.848357i	$-0.322408\pi$
$229$	4.40650e10			1.05885			0.529425	+	0.848357i	$0.322408\pi$
$230$	2.31050e8	−	1.31035e9i	0.00544417	−	0.0308754i
$231$	3.28548e10	+	2.75685e10i	0.759181	+	0.637029i
$232$	−4.11713e9	−	1.49851e9i	−0.0933036	−	0.0339597i
$233$	−7.43706e10	+	2.70687e10i	−1.65310	+	0.601680i	−0.989257	−	0.146189i	$-0.953299\pi$
$233$	−7.43706e10	+	2.70687e10i	−1.65310	+	0.601680i	−0.663846	+	0.747869i	$0.731077\pi$
$234$	−1.76518e9	+	1.48117e9i	−0.0384874	+	0.0322948i
$235$	1.08895e10	+	1.88612e10i	0.232919	+	0.403427i
$236$	2.07757e10	−	3.59845e10i	0.435965	−	0.755113i
$237$	−2.62129e10	−	1.48661e11i	−0.539695	−	3.06076i
$238$	−9.94715e8	−	5.64131e9i	−0.0200957	−	0.113968i
$239$	9.75958e9	−	1.69041e10i	0.193482	−	0.335121i	−0.752920	−	0.658112i	$-0.771355\pi$
$239$	9.75958e9	−	1.69041e10i	0.193482	−	0.335121i	0.946402	+	0.322992i	$0.104689\pi$
$240$	−3.39248e9	−	5.87594e9i	−0.0660034	−	0.114321i
$241$	−1.42266e9	+	1.19375e9i	−0.0271659	+	0.0227949i	−0.656270	−	0.754527i	$-0.727867\pi$
$241$	−1.42266e9	+	1.19375e9i	−0.0271659	+	0.0227949i	0.629104	+	0.777321i	$0.283422\pi$
$242$	2.70446e10	−	9.84342e9i	0.506887	−	0.184492i
$243$	−5.56512e10	−	2.02554e10i	−1.02387	−	0.372660i
$244$	1.77560e10	+	1.48991e10i	0.320695	+	0.269095i
$245$	−1.98342e9	+	1.12485e10i	−0.0351696	+	0.199457i
$246$	4.27368e10			0.744035
$247$	−1.11412e9	+	2.41001e9i	−0.0190456	+	0.0411987i
$248$	−2.02556e8			−0.00340026
$249$	2.72660e10	−	1.54633e11i	0.449495	−	2.54921i
$250$	2.08597e10	+	1.75034e10i	0.337737	+	0.283395i
$251$	3.35092e10	+	1.21964e10i	0.532884	+	0.193954i	0.594426	−	0.804151i	$-0.297379\pi$
$251$	3.35092e10	+	1.21964e10i	0.532884	+	0.193954i	−0.0615415	+	0.998105i	$0.519602\pi$
$252$	5.98270e10	−	2.17753e10i	0.934534	−	0.340143i
$253$	−3.26970e9	+	2.74360e9i	−0.0501724	+	0.0420997i
$254$	3.43332e10	+	5.94669e10i	0.517563	+	0.896445i
$255$	−2.29617e9	+	3.97709e9i	−0.0340074	+	0.0589026i
$256$	7.45813e8	+	4.22972e9i	0.0108530	+	0.0615505i
$257$	−2.24787e10	−	1.27483e11i	−0.321420	−	1.82286i	−0.533722	−	0.845660i	$-0.679207\pi$
$257$	−2.24787e10	−	1.27483e11i	−0.321420	−	1.82286i	0.212302	−	0.977204i	$-0.431904\pi$
$258$	−2.97534e10	+	5.15343e10i	−0.418068	+	0.724116i
$259$	8.62112e10	+	1.49322e11i	1.19046	+	2.06194i
$260$	4.22298e8	−	3.54350e8i	0.00573112	−	0.00480898i
$261$	−3.09717e10	+	1.12728e10i	−0.413126	+	0.150366i
$262$	4.71102e10	+	1.71467e10i	0.617673	+	0.224815i
$263$	1.19179e10	+	1.00003e10i	0.153602	+	0.128888i	0.716350	−	0.697741i	$-0.245811\pi$
$263$	1.19179e10	+	1.00003e10i	0.153602	+	0.128888i	−0.562748	+	0.826629i	$0.690256\pi$
$264$	−3.77950e9	+	2.14346e10i	−0.0478869	+	0.271580i
$265$	1.79618e10			0.223740
$266$	5.17007e10	−	5.20438e10i	0.633182	−	0.637385i
$267$	−7.81656e9			−0.0941271
$268$	−3.18411e9	+	1.80580e10i	−0.0377035	+	0.213827i
$269$	6.35558e10	+	5.33297e10i	0.740065	+	0.620988i	0.932855	−	0.360252i	$-0.117309\pi$
$269$	6.35558e10	+	5.33297e10i	0.740065	+	0.620988i	−0.192790	+	0.981240i	$0.561754\pi$
$270$	−1.73244e10	−	6.30557e9i	−0.198391	−	0.0722084i
$271$	−4.00077e10	+	1.45616e10i	−0.450590	+	0.164001i	−0.557340	−	0.830285i	$-0.688178\pi$
$271$	−4.00077e10	+	1.45616e10i	−0.450590	+	0.164001i	0.106750	+	0.994286i	$0.465956\pi$
$272$	2.22690e9	−	1.86859e9i	0.0246684	−	0.0206993i
$273$	4.23862e9	+	7.34150e9i	0.0461841	+	0.0799932i
$274$	−2.30571e10	+	3.99361e10i	−0.247131	+	0.428044i
$275$	−7.14843e9	−	4.05408e10i	−0.0753726	−	0.427459i
$276$	1.80308e9	+	1.02258e10i	0.0187035	+	0.106073i
$277$	3.59726e10	−	6.23064e10i	0.367124	−	0.635878i	−0.621990	−	0.783025i	$-0.713676\pi$
$277$	3.59726e10	−	6.23064e10i	0.367124	−	0.635878i	0.989115	+	0.147147i	$0.0470091\pi$
$278$	−1.08495e10	−	1.87919e10i	−0.108945	−	0.188698i
$279$	−1.16726e9	+	9.79451e8i	−0.0115332	+	0.00967752i
$280$	−1.43129e10	+	5.20946e9i	−0.139160	+	0.0506502i
$281$	−3.00411e10	−	1.09340e10i	−0.287433	−	0.104617i	0.194280	−	0.980946i	$-0.437763\pi$
$281$	−3.00411e10	−	1.09340e10i	−0.287433	−	0.104617i	−0.481713	+	0.876329i	$0.659985\pi$
$282$	−1.30197e11	−	1.09248e11i	−1.22597	−	1.02871i
$283$	5.89436e9	−	3.34286e10i	0.0546258	−	0.309798i	−0.945237	−	0.326386i	$-0.894169\pi$
$283$	5.89436e9	−	3.34286e10i	0.0546258	−	0.309798i	0.999862	+	0.0165876i	$0.00528024\pi$
$284$	−1.01375e11			−0.924692
$285$	−5.85699e10	+	5.31948e9i	−0.525863	+	0.0477603i
$286$	−1.76841e9			−0.0156291
$287$	1.66596e10	−	9.44815e10i	0.144943	−	0.822012i
$288$	2.47505e10	+	2.07682e10i	0.211991	+	0.177882i
$289$	1.09587e11	+	3.98865e10i	0.924101	+	0.336345i
$290$	7.40959e9	−	2.69687e9i	0.0615181	−	0.0223908i
$291$	−1.65825e11	+	1.39144e11i	−1.35560	+	1.13749i
$292$	2.88752e10	+	5.00133e10i	0.232435	+	0.402589i
$293$	7.11736e10	−	1.23276e11i	0.564176	−	0.977181i	−0.432950	−	0.901418i	$-0.642527\pi$
$293$	7.11736e10	−	1.23276e11i	0.564176	−	0.977181i	0.997126	−	0.0757634i	$-0.0241394\pi$
$294$	−1.54783e10	−	8.77816e10i	−0.120826	−	0.685237i
$295$	1.29854e10	+	7.36438e10i	0.0998289	+	0.566158i
$296$	−4.37504e10	+	7.57780e10i	−0.331261	+	0.573760i
$297$	2.95706e10	+	5.12177e10i	0.220524	+	0.381959i
$298$	1.07919e10	−	9.05548e9i	0.0792729	−	0.0665179i
$299$	−7.92772e8	+	2.88545e8i	−0.00573625	+	0.00208782i
$300$	−9.41059e10	−	3.42518e10i	−0.670766	−	0.244139i
$301$	1.02333e11	+	8.58672e10i	0.718563	+	0.602946i
$302$	2.43839e10	−	1.38288e11i	0.168683	−	0.956651i
$303$	−9.77441e10			−0.666191
$304$	3.59913e10	+	9.51635e9i	0.241694	+	0.0639056i
$305$	−4.17150e10			−0.276021
$306$	3.79741e9	−	2.15362e10i	0.0247595	−	0.140418i
$307$	9.16037e10	+	7.68646e10i	0.588560	+	0.493860i	0.887745	−	0.460335i	$-0.152271\pi$
$307$	9.16037e10	+	7.68646e10i	0.588560	+	0.493860i	−0.299186	+	0.954195i	$0.596715\pi$
$308$	4.59138e10	+	1.67113e10i	0.290714	+	0.105811i
$309$	−9.07907e10	+	3.30451e10i	−0.566537	+	0.206203i
$310$	2.79253e8	−	2.34321e8i	0.00171740	−	0.00144107i
$311$	−6.18622e10	−	1.07148e11i	−0.374976	−	0.649478i	0.615347	−	0.788256i	$-0.289016\pi$
$311$	−6.18622e10	−	1.07148e11i	−0.374976	−	0.649478i	−0.990323	+	0.138778i	$0.955682\pi$
$312$	−2.15101e9	+	3.72566e9i	−0.0128513	+	0.0222591i
$313$	1.68917e10	+	9.57978e10i	0.0994775	+	0.564165i	0.993283	+	0.115710i	$0.0369144\pi$
$313$	1.68917e10	+	9.57978e10i	0.0994775	+	0.564165i	−0.893805	+	0.448455i	$0.851974\pi$
$314$	1.88849e10	+	1.07102e11i	0.109631	+	0.621746i
$315$	−5.72904e10	+	9.92298e10i	−0.327857	+	0.567864i
$316$	−8.59860e10	−	1.48932e11i	−0.485105	−	0.840227i
$317$	5.47497e10	−	4.59404e10i	0.304519	−	0.255522i	−0.477703	−	0.878521i	$-0.658530\pi$
$317$	5.47497e10	−	4.59404e10i	0.304519	−	0.255522i	0.782222	+	0.622999i	$0.214086\pi$
$318$	−1.31717e11	+	4.79412e10i	−0.722306	+	0.262898i
$319$	−2.37690e10	−	8.65121e9i	−0.128515	−	0.0467755i
$320$	−5.92125e9	−	4.96852e9i	−0.0315674	−	0.0264882i
$321$	3.02881e10	−	1.71772e11i	0.159220	−	0.902984i
$322$	2.33098e10			0.120833
$323$	−6.60208e9	−	2.43173e10i	−0.0337497	−	0.124309i
$324$	−1.13874e10			−0.0574080
$325$	1.41293e9	−	8.01311e9i	0.00702497	−	0.0398406i
$326$	3.78086e10	+	3.17252e10i	0.185401	+	0.155570i
$327$	−3.11756e11	−	1.13470e11i	−1.50782	−	0.548801i
$328$	4.57509e10	−	1.66520e10i	0.218257	−	0.0794389i
$329$	−2.92277e11	+	2.45250e11i	−1.37535	+	1.15406i
$330$	−1.95855e10	−	3.39230e10i	−0.0909120	−	0.157464i
$331$	3.09306e9	−	5.35734e9i	0.0141632	−	0.0245314i	−0.858857	−	0.512216i	$-0.828825\pi$
$331$	3.09306e9	−	5.35734e9i	0.0141632	−	0.0245314i	0.873020	+	0.487684i	$0.162158\pi$
$332$	−3.10624e10	−	1.76163e11i	−0.140318	−	0.795782i
$333$	1.14302e11	+	6.48238e11i	0.509394	+	2.88892i
$334$	−1.18632e11	+	2.05477e11i	−0.521607	+	0.903450i
$335$	−1.65001e10	−	2.85791e10i	−0.0715790	−	0.123979i
$336$	9.10547e10	−	7.64040e10i	0.389741	−	0.327031i
$337$	2.07474e10	−	7.55142e9i	0.0876250	−	0.0318929i	−0.297836	−	0.954617i	$-0.596265\pi$
$337$	2.07474e10	−	7.55142e9i	0.0876250	−	0.0318929i	0.385461	+	0.922724i	$0.374043\pi$
$338$	1.59111e11	+	5.79117e10i	0.663094	+	0.241347i
$339$	5.13599e11	+	4.30961e11i	2.11215	+	1.77231i
$340$	−9.08484e8	+	5.15227e9i	−0.00368691	+	0.0209095i
$341$	−1.16940e9			−0.00468346
$342$	2.53422e11	−	1.19195e11i	1.00168	−	0.471129i
$343$	1.25605e11			0.489985
$344$	−1.17720e10	+	6.67621e10i	−0.0453248	+	0.257050i
$345$	−1.43152e10	−	1.20119e10i	−0.0544017	−	0.0456484i
$346$	2.29218e11	+	8.34286e10i	0.859818	+	0.312948i
$347$	−2.40106e11	+	8.73915e10i	−0.889038	+	0.323584i	−0.745852	−	0.666112i	$-0.767957\pi$
$347$	−2.40106e11	+	8.73915e10i	−0.889038	+	0.323584i	−0.143187	+	0.989696i	$0.545735\pi$
$348$	−4.71378e10	+	3.95534e10i	−0.172291	+	0.144570i
$349$	−8.80388e10	−	1.52488e11i	−0.317658	−	0.550200i	0.662341	−	0.749203i	$-0.269563\pi$
$349$	−8.80388e10	−	1.52488e11i	−0.317658	−	0.550200i	−0.979999	+	0.199003i	$0.936230\pi$
$350$	−1.12407e11	+	1.94695e11i	−0.400395	+	0.693505i
$351$	2.02987e9	+	1.15120e10i	0.00713817	+	0.0404826i
$352$	4.30573e9	+	2.44190e10i	0.0149487	+	0.0847786i
$353$	−6.38293e10	+	1.10556e11i	−0.218793	+	0.378961i	−0.954439	−	0.298405i	$-0.903545\pi$
$353$	−6.38293e10	+	1.10556e11i	−0.218793	+	0.378961i	0.735646	+	0.677366i	$0.236879\pi$
$354$	−2.91785e11	−	5.05386e11i	−0.987525	−	1.71044i
$355$	1.39760e11	−	1.17273e11i	0.467042	−	0.391894i
$356$	−8.36785e9	+	3.04565e9i	−0.0276114	+	0.0100497i
$357$	−7.56000e10	−	2.75162e10i	−0.246329	−	0.0896563i
$358$	−2.56616e10	−	2.15326e10i	−0.0825675	−	0.0692824i
$359$	9.60419e10	−	5.44681e11i	0.305166	−	1.73068i	−0.317558	−	0.948239i	$-0.602863\pi$
$359$	9.60419e10	−	5.44681e11i	0.305166	−	1.73068i	0.622724	−	0.782442i	$-0.286026\pi$
$360$	−5.81474e10			−0.182461
$361$	2.05780e11	−	2.48560e11i	0.637706	−	0.770280i
$362$	−2.16040e11			−0.661220
$363$	7.01895e10	−	3.98064e11i	0.212174	−	1.20330i
$364$	7.39811e9	+	6.20775e9i	0.0220884	+	0.0185344i
$365$	−9.76653e10	−	3.55473e10i	−0.288020	−	0.104831i
$366$	3.05904e11	−	1.11340e11i	0.891088	−	0.324330i
$367$	−5.36136e10	+	4.49872e10i	−0.154269	+	0.129447i	−0.716655	−	0.697428i	$-0.754328\pi$
$367$	−5.36136e10	+	4.49872e10i	−0.154269	+	0.129447i	0.562386	+	0.826875i	$0.309883\pi$
$368$	5.91462e9	+	1.02444e10i	0.0168117	+	0.0291187i
$369$	1.83128e11	−	3.17187e11i	0.514205	−	0.890629i
$370$	−2.73453e10	−	1.55083e11i	−0.0758533	−	0.430186i
$371$	5.46413e10	+	3.09886e11i	0.149740	+	0.849220i
$372$	−1.42240e9	+	2.46367e9i	−0.00385105	+	0.00667021i
$373$	−5.98696e10	−	1.03697e11i	−0.160146	−	0.277381i	0.774775	−	0.632237i	$-0.217863\pi$
$373$	−5.98696e10	−	1.03697e11i	−0.160146	−	0.277381i	−0.934921	+	0.354856i	$0.884530\pi$
$374$	1.28564e10	−	1.07878e10i	0.0339778	−	0.0285108i
$375$	3.59375e11	−	1.30802e11i	0.938442	−	0.341565i
$376$	−1.81947e11	−	6.62234e10i	−0.469462	−	0.170870i
$377$	−3.82991e9	−	3.21367e9i	−0.00976454	−	0.00819343i
$378$	5.60847e10	−	3.18072e11i	0.141296	−	0.801332i
$379$	−4.60581e11			−1.14665			−0.573324	−	0.819329i	$-0.694346\pi$
$379$	−4.60581e11			−1.14665			−0.573324	+	0.819329i	$0.694346\pi$
$380$	−6.06281e10	+	2.85159e10i	−0.149158	+	0.0701553i
$381$	9.64389e11			2.34471
$382$	−6.64937e10	+	3.77104e11i	−0.159770	+	0.906101i
$383$	−5.89360e11	−	4.94532e11i	−1.39954	−	1.17436i	−0.961302	−	0.275498i	$-0.911157\pi$
$383$	−5.89360e11	−	4.94532e11i	−1.39954	−	1.17436i	−0.438241	−	0.898858i	$-0.644398\pi$
$384$	5.66830e10	+	2.06309e10i	0.133034	+	0.0484204i
$385$	−8.26311e10	+	3.00753e10i	−0.191677	+	0.0697647i
$386$	3.11600e11	−	2.61463e11i	0.714421	−	0.599470i
$387$	2.54988e11	+	4.41652e11i	0.577856	+	1.00088i
$388$	−1.23305e11	+	2.13570e11i	−0.276208	+	0.478407i
$389$	9.23512e10	+	5.23750e11i	0.204489	+	1.15971i	0.898242	+	0.439500i	$0.144845\pi$
$389$	9.23512e10	+	5.23750e11i	0.204489	+	1.15971i	−0.693754	+	0.720212i	$0.744044\pi$
$390$	−1.34445e9	−	7.62473e9i	−0.00294274	−	0.0166891i
$391$	4.00326e9	−	6.93386e9i	0.00866201	−	0.0150030i
$392$	−5.07732e10	−	8.79418e10i	−0.108604	−	0.188108i
$393$	5.39374e11	−	4.52589e11i	1.14058	−	0.957056i
$394$	−2.32863e11	+	8.47551e10i	−0.486819	+	0.177187i
$395$	2.90833e11	+	1.05854e11i	0.601114	+	0.218787i
$396$	1.42890e11	+	1.19899e11i	0.291993	+	0.245011i
$397$	3.18522e10	−	1.80643e11i	0.0643549	−	0.364975i	−0.935575	−	0.353128i	$-0.885118\pi$
$397$	3.18522e10	−	1.80643e11i	0.0643549	−	0.364975i	0.999930	−	0.0118466i	$-0.00377099\pi$
$398$	1.46609e11			0.292879
$399$	−2.69949e11	−	9.94297e11i	−0.533217	−	1.96398i
$400$	−1.14089e11			−0.222830
$401$	−2.34399e10	+	1.32934e11i	−0.0452695	+	0.256736i	−0.999040	−	0.0437986i	$-0.986054\pi$
$401$	−2.34399e10	+	1.32934e11i	−0.0452695	+	0.256736i	0.953771	+	0.300535i	$0.0971651\pi$
$402$	1.97278e11	+	1.65536e11i	0.376757	+	0.316137i
$403$	−2.17198e8	−	7.90537e7i	−0.000410189	−	0.000149296i
$404$	−1.04638e11	+	3.80851e10i	−0.195422	+	0.0711277i
$405$	1.56993e10	−	1.31732e10i	0.0289956	−	0.0243302i
$406$	6.90684e10	+	1.19630e11i	0.126157	+	0.218511i
$407$	−2.52580e11	+	4.37482e11i	−0.456272	+	0.790287i
$408$	−7.08965e9	−	4.02074e10i	−0.0126664	−	0.0718349i
$409$	1.31643e11	+	7.46585e11i	0.232618	+	1.31924i	0.847573	+	0.530679i	$0.178063\pi$
$409$	1.31643e11	+	7.46585e11i	0.232618	+	1.31924i	−0.614955	+	0.788562i	$0.710826\pi$
$410$	−4.38111e10	+	7.58830e10i	−0.0765696	+	0.132622i
$411$	3.23827e11	+	5.60884e11i	0.559789	+	0.969583i
$412$	−8.43183e10	+	7.07515e10i	−0.144173	+	0.120976i
$413$	−1.23104e12	+	4.48062e11i	−2.08208	+	0.757815i
$414$	8.36206e10	+	3.04354e10i	0.139898	+	0.0509187i
$415$	2.46614e11	+	2.06934e11i	0.408133	+	0.342464i
$416$	−8.51051e8	+	4.82655e9i	−0.00139327	+	0.00790164i
$417$	−3.04752e11			−0.493554
$418$	2.07785e11	+	5.49398e10i	0.332905	+	0.0880225i
$419$	7.63543e11			1.21024			0.605118	−	0.796135i	$-0.293126\pi$
$419$	7.63543e11			1.21024			0.605118	+	0.796135i	$0.293126\pi$
$420$	−3.71466e10	+	2.10669e11i	−0.0582501	+	0.330353i
$421$	−1.75112e11	−	1.46937e11i	−0.271674	−	0.227961i	0.496764	−	0.867885i	$-0.334521\pi$
$421$	−1.75112e11	−	1.46937e11i	−0.271674	−	0.227961i	−0.768438	+	0.639924i	$0.778966\pi$
$422$	6.86536e11	+	2.49879e11i	1.05380	+	0.383551i
$423$	−1.36872e12	+	4.98175e11i	−2.07866	+	0.756572i
$424$	−1.22327e11	+	1.02645e11i	−0.183814	+	0.154238i
$425$	3.86101e10	+	6.68747e10i	0.0574051	+	0.0994286i
$426$	−7.11880e11	+	1.23301e12i	−1.04728	+	1.81395i
$427$	−1.26901e11	−	7.19689e11i	−0.184730	−	1.04766i
$428$	−3.45052e10	−	1.95688e11i	−0.0497035	−	0.281883i
$429$	−1.24182e10	+	2.15090e10i	−0.0177012	+	0.0306593i
$430$	−6.10026e10	−	1.05660e11i	−0.0860479	−	0.149039i
$431$	1.65814e11	−	1.39135e11i	0.231459	−	0.194217i	−0.519680	−	0.854361i	$-0.673949\pi$
$431$	1.65814e11	−	1.39135e11i	0.231459	−	0.194217i	0.751140	+	0.660143i	$0.229505\pi$
$432$	1.54021e11	−	5.60589e10i	0.212766	−	0.0774404i
$433$	−1.07037e12	−	3.89581e11i	−1.46331	−	0.532601i	−0.517035	−	0.855964i	$-0.672964\pi$
$433$	−1.07037e12	−	3.89581e11i	−1.46331	−	0.532601i	−0.946275	+	0.323363i	$0.895187\pi$
$434$	4.89215e9	+	4.10500e9i	0.00661906	+	0.00555405i
$435$	1.92303e10	−	1.09060e11i	0.0257504	−	0.146038i
$436$	−3.77956e11			−0.500901
$437$	1.02114e11	−	9.27425e9i	0.133942	−	0.0121650i
$438$	8.11077e11			1.05300
$439$	2.30253e11	−	1.30583e12i	0.295880	−	1.67802i	−0.367725	−	0.929935i	$-0.619863\pi$
$439$	2.30253e11	−	1.30583e12i	0.295880	−	1.67802i	0.663605	−	0.748083i	$-0.269026\pi$
$440$	−3.41846e10	−	2.86843e10i	−0.0434804	−	0.0364844i
$441$	−7.17829e11	−	2.61268e11i	−0.903748	−	0.328937i
$442$	3.11716e9	−	1.13455e9i	0.00388471	−	0.00141392i
$443$	−2.49384e11	+	2.09258e11i	−0.307647	+	0.258146i	−0.783519	−	0.621368i	$-0.786577\pi$
$443$	−2.49384e11	+	2.09258e11i	−0.307647	+	0.258146i	0.475872	+	0.879515i	$0.342133\pi$
$444$	6.14455e11	+	1.06427e12i	0.750354	+	1.29965i
$445$	8.01305e9	−	1.38790e10i	0.00968674	−	0.0167779i
$446$	−1.22964e11	−	6.97362e11i	−0.147153	−	0.834548i
$447$	−3.43575e10	−	1.94851e11i	−0.0407041	−	0.230844i
$448$	6.77066e10	−	1.17271e11i	0.0794109	−	0.137544i
$449$	2.46815e11	+	4.27496e11i	0.286591	+	0.496391i	0.972994	−	0.230831i	$-0.0741445\pi$
$449$	2.46815e11	+	4.27496e11i	0.286591	+	0.496391i	−0.686403	+	0.727222i	$0.740811\pi$
$450$	−6.57458e11	+	5.51673e11i	−0.755809	+	0.634199i
$451$	2.64129e11	−	9.61352e10i	0.300623	−	0.109418i
$452$	7.17742e11	+	2.61237e11i	0.808808	+	0.294382i
$453$	−1.51076e12	−	1.26768e12i	−1.68559	−	1.41438i
$454$	9.51161e10	−	5.39430e11i	0.105076	−	0.595914i
$455$	−1.73807e10			−0.0190115
$456$	3.68487e11	−	3.70933e11i	0.399099	−	0.401748i
$457$	1.56256e12			1.67577			0.837886	−	0.545845i	$-0.183791\pi$
$457$	1.56256e12			1.67577			0.837886	+	0.545845i	$0.183791\pi$
$458$	1.22429e11	−	6.94329e11i	0.130014	−	0.737345i
$459$	−8.49834e10	−	7.13096e10i	−0.0893670	−	0.0749878i
$460$	−2.00052e10	−	7.28129e9i	−0.0208321	−	0.00758225i
$461$	−1.32611e12	+	4.82664e11i	−1.36749	+	0.497726i	−0.918363	−	0.395740i	$-0.870488\pi$
$461$	−1.32611e12	+	4.82664e11i	−1.36749	+	0.497726i	−0.449130	+	0.893467i	$0.648266\pi$
$462$	5.25677e11	−	4.41096e11i	0.536822	−	0.450447i
$463$	−5.73100e11	−	9.92638e11i	−0.579583	−	1.00387i	−0.995527	−	0.0944769i	$-0.969882\pi$
$463$	−5.73100e11	−	9.92638e11i	−0.579583	−	1.00387i	0.415944	−	0.909390i	$-0.363451\pi$
$464$	−3.50508e10	+	6.07098e10i	−0.0351049	+	0.0608034i
$465$	−8.89042e8	−	5.04201e9i	−0.000881828	−	0.00500110i
$466$	2.19890e11	+	1.24706e12i	0.216008	+	1.22504i
$467$	−2.58486e11	+	4.47710e11i	−0.251484	+	0.435583i	−0.963935	−	0.266139i	$-0.914252\pi$
$467$	−2.58486e11	+	4.47710e11i	−0.251484	+	0.435583i	0.712451	+	0.701722i	$0.247585\pi$
$468$	1.84343e10	+	3.19291e10i	0.0177631	+	0.0307667i
$469$	4.42867e11	−	3.71609e11i	0.422664	−	0.354657i
$470$	3.27450e11	−	1.19182e11i	0.309532	−	0.112660i
$471$	1.43528e12	+	5.22401e11i	1.34383	+	0.489114i
$472$	−5.09283e11	−	4.27339e11i	−0.472302	−	0.396309i
$473$	−6.79619e10	+	3.85431e11i	−0.0624296	+	0.354056i
$474$	−2.41527e12			−2.19767
$475$	−4.14963e11	+	8.97631e11i	−0.374014	+	0.809052i
$476$	−9.16534e10			−0.0818309
$477$	−2.08598e11	+	1.18302e12i	−0.184492	+	1.04631i
$478$	−2.39241e11	−	2.00747e11i	−0.209609	−	0.175883i
$479$	−2.35792e11	−	8.58212e10i	−0.204653	−	0.0744877i	0.237660	−	0.971349i	$-0.423620\pi$
$479$	−2.35792e11	−	8.58212e10i	−0.204653	−	0.0744877i	−0.442313	+	0.896861i	$0.645842\pi$
$480$	−1.02012e11	+	3.71295e10i	−0.0877137	+	0.0319252i
$481$	−7.64878e10	+	6.41809e10i	−0.0651537	+	0.0546705i
$482$	1.48572e10	+	2.57334e10i	0.0125379	+	0.0217163i
$483$	1.63688e11	−	2.83515e11i	0.136853	−	0.237036i
$484$	−7.99622e10	−	4.53488e11i	−0.0662339	−	0.375631i
$485$	−7.70689e10	−	4.37080e11i	−0.0632472	−	0.358693i
$486$	−4.73782e11	+	8.20615e11i	−0.385226	+	0.667231i
$487$	1.00985e12	+	1.74911e12i	0.813534	+	1.40908i	0.910376	+	0.413783i	$0.135793\pi$
$487$	1.00985e12	+	1.74911e12i	0.813534	+	1.40908i	−0.0968414	+	0.995300i	$0.530874\pi$
$488$	2.84097e11	−	2.38385e11i	0.226766	−	0.190279i
$489$	6.51374e11	−	2.37081e11i	0.515158	−	0.187502i
$490$	1.71732e11	+	6.25052e10i	0.134576	+	0.0489817i
$491$	−3.93534e11	−	3.30214e11i	−0.305573	−	0.256406i	0.477086	−	0.878857i	$-0.341693\pi$
$491$	−3.93534e11	−	3.30214e11i	−0.305573	−	0.256406i	−0.782660	+	0.622450i	$0.786137\pi$
$492$	1.18739e11	−	6.73400e11i	0.0913585	−	0.518120i
$493$	4.74478e10			0.0361747
$494$	3.48790e10	+	2.42510e10i	0.0263507	+	0.0183214i
$495$	−3.35697e11			−0.251318
$496$	−5.62775e8	+	3.19166e9i	−0.000417511	+	0.00236782i
$497$	2.44841e12	+	2.05446e12i	1.80003	+	1.51041i
$498$	−2.36079e12	−	8.59257e11i	−1.71999	−	0.626024i
$499$	1.69315e12	−	6.16256e11i	1.22248	−	0.444948i	0.351467	−	0.936200i	$-0.385683\pi$
$499$	1.69315e12	−	6.16256e11i	1.22248	−	0.444948i	0.871017	+	0.491253i	$0.163461\pi$
$500$	3.33756e11	−	2.80054e11i	0.238816	−	0.200391i
$501$	1.66614e12	+	2.88583e12i	1.18152	+	2.04645i
$502$	2.85278e11	−	4.94117e11i	0.200494	−	0.347266i
$503$	1.88389e11	+	1.06841e12i	0.131220	+	0.744185i	0.977418	+	0.211316i	$0.0677750\pi$
$503$	1.88389e11	+	1.06841e12i	0.131220	+	0.744185i	−0.846198	+	0.532869i	$0.821114\pi$
$504$	−1.76889e11	−	1.00319e12i	−0.122114	−	0.692541i
$505$	1.00201e11	−	1.73554e11i	0.0685585	−	0.118747i
$506$	3.41463e10	+	5.91431e10i	0.0231561	+	0.0401076i
$507$	1.82170e12	−	1.52858e12i	1.22445	−	1.02743i
$508$	1.03241e12	−	3.75765e11i	0.687803	−	0.250340i
$509$	−6.25864e10	−	2.27796e10i	−0.0413285	−	0.0150424i	0.321273	−	0.946987i	$-0.395889\pi$
$509$	−6.25864e10	−	2.27796e10i	−0.0413285	−	0.0150424i	−0.362602	+	0.931944i	$0.618111\pi$
$510$	5.62870e10	+	4.72304e10i	0.0368420	+	0.0309141i
$511$	3.16174e11	−	1.79311e12i	0.205131	−	1.16336i
$512$	6.87195e10			0.0441942
$513$	1.19140e11	−	1.41570e12i	0.0759506	−	0.902492i
$514$	−2.07120e12			−1.30884
$515$	3.43984e10	−	1.95083e11i	0.0215479	−	0.122204i
$516$	7.29357e11	+	6.12003e11i	0.452915	+	0.380041i
$517$	−1.05042e12	−	3.82321e11i	−0.646628	−	0.235354i
$518$	2.59238e12	−	9.43551e11i	1.58203	−	0.575813i
$519$	2.62437e12	−	2.20211e12i	1.58771	−	1.33225i
$520$	−4.41017e9	−	7.63864e9i	−0.00264509	−	0.00458143i
$521$	1.79021e11	−	3.10073e11i	0.106447	−	0.184371i	−0.807882	−	0.589345i	$-0.799386\pi$
$521$	1.79021e11	−	3.10073e11i	0.106447	−	0.184371i	0.914328	+	0.404973i	$0.132719\pi$
$522$	9.15734e10	+	5.19338e11i	0.0539824	+	0.306149i
$523$	−3.58950e11	−	2.03570e12i	−0.209786	−	1.18975i	−0.889729	−	0.456489i	$-0.849107\pi$
$523$	−3.58950e11	−	2.03570e12i	−0.209786	−	1.18975i	0.679943	−	0.733265i	$-0.262004\pi$
$524$	4.01069e11	−	6.94672e11i	0.232396	−	0.402521i
$525$	1.57871e12	+	2.73441e12i	0.906955	+	1.57089i
$526$	1.90686e11	−	1.60005e11i	0.108613	−	0.0911374i
$527$	2.06128e9	−	7.50246e8i	0.00116410	−	0.000423698i
$528$	3.27243e11	+	1.19107e11i	0.183239	+	0.0666934i
$529$	−1.35481e12	−	1.13682e12i	−0.752188	−	0.631161i
$530$	4.99045e10	−	2.83023e11i	0.0274725	−	0.155804i
$531$	−5.00122e12			−2.72992
$532$	−6.76407e11	−	9.59240e11i	−0.366105	−	0.519189i
$533$	5.55571e10			0.0298172
$534$	−2.17173e10	+	1.23165e11i	−0.0115577	+	0.0655468i
$535$	2.73948e11	+	2.29869e11i	0.144569	+	0.121308i
$536$	2.75692e11	+	1.00344e11i	0.144272	+	0.0525107i
$537$	−4.42102e11	+	1.60912e11i	−0.229424	+	0.0835033i
$538$	1.01689e12	−	8.53274e11i	0.523305	−	0.439105i
$539$	−2.93124e11	−	5.07706e11i	−0.149590	−	0.259097i
$540$	−1.47490e11	+	2.55460e11i	−0.0746433	+	0.129286i
$541$	3.68025e11	+	2.08717e12i	0.184710	+	1.04754i	0.926328	+	0.376718i	$0.122947\pi$
$541$	3.68025e11	+	2.08717e12i	0.184710	+	1.04754i	−0.741618	+	0.670822i	$0.765941\pi$
$542$	1.18290e11	+	6.70856e11i	0.0588777	+	0.333912i
$543$	−1.51709e12	+	2.62768e12i	−0.748881	+	1.29710i
$544$	−2.32561e10	−	4.02808e10i	−0.0113852	−	0.0197198i
$545$	5.21068e11	−	4.37228e11i	0.252994	−	0.212287i
$546$	1.27456e11	−	4.63902e10i	0.0613752	−	0.0223388i
$547$	−2.55527e12	−	9.30040e11i	−1.22037	−	0.444180i	−0.350084	−	0.936718i	$-0.613847\pi$
$547$	−2.55527e12	−	9.30040e11i	−1.22037	−	0.444180i	−0.870291	+	0.492539i	$0.836069\pi$
$548$	5.65209e11	+	4.74267e11i	0.267730	+	0.224652i
$549$	4.84455e11	−	2.74748e12i	0.227603	−	1.29080i
$550$	−6.58659e11			−0.306922
$551$	3.50167e11	+	4.96586e11i	0.161843	+	0.229516i
$552$	1.66136e11			0.0761620
$553$	−9.41520e11	+	5.33962e12i	−0.428121	+	2.42799i
$554$	−8.81812e11	−	7.39928e11i	−0.397724	−	0.333730i
$555$	−2.07829e12	−	7.56434e11i	−0.929795	−	0.338418i
$556$	−3.26246e11	+	1.18744e11i	−0.144780	+	0.0526956i
$557$	2.94008e12	−	2.46702e12i	1.29423	−	1.08599i	0.303115	−	0.952954i	$-0.401973\pi$
$557$	2.94008e12	−	2.46702e12i	1.29423	−	1.08599i	0.991112	−	0.133032i	$-0.0424712\pi$
$558$	1.21900e10	+	2.11138e10i	0.00532294	+	0.00921960i
$559$	−3.86789e10	+	6.69939e10i	−0.0167541	+	0.0290190i
$560$	4.23186e10	+	2.40001e11i	0.0181838	+	0.103126i
$561$	−4.09300e10	−	2.32126e11i	−0.0174465	−	0.0989441i
$562$	−2.55752e11	+	4.42976e11i	−0.108145	+	0.187312i
$563$	1.58800e12	+	2.75049e12i	0.666134	+	1.15378i	0.978977	+	0.203973i	$0.0653853\pi$
$563$	1.58800e12	+	2.75049e12i	0.666134	+	1.15378i	−0.312843	+	0.949805i	$0.601281\pi$
$564$	−2.08315e12	+	1.74797e12i	−0.866892	+	0.727409i
$565$	−1.29172e12	+	4.70148e11i	−0.533274	+	0.194096i
$566$	−5.10355e11	−	1.85754e11i	−0.209025	−	0.0760789i
$567$	2.75030e11	+	2.30778e11i	0.111752	+	0.0937714i
$568$	−2.81656e11	+	1.59735e12i	−0.113541	+	0.643922i
$569$	−2.22467e12			−0.889733			−0.444866	−	0.895597i	$-0.646749\pi$
$569$	−2.22467e12			−0.889733			−0.444866	+	0.895597i	$0.646749\pi$
$570$	−7.89103e10	+	9.37661e11i	−0.0313110	+	0.372057i
$571$	−2.73304e12			−1.07593			−0.537965	−	0.842967i	$-0.680807\pi$
$571$	−2.73304e12			−1.07593			−0.537965	+	0.842967i	$0.680807\pi$
$572$	−4.91329e9	+	2.78647e10i	−0.00191907	+	0.0108836i
$573$	4.11976e12	+	3.45689e12i	1.59653	+	1.33964i
$574$	−1.44245e12	−	5.25009e11i	−0.554623	−	0.201866i
$575$	−2.95275e11	+	1.07471e11i	−0.112647	+	0.0410003i
$576$	3.96008e11	−	3.32290e11i	0.149901	−	0.125781i
$577$	−7.33219e11	−	1.26997e12i	−0.275387	−	0.476984i	0.694846	−	0.719159i	$-0.255473\pi$
$577$	−7.33219e11	−	1.26997e12i	−0.275387	−	0.476984i	−0.970233	+	0.242175i	$0.922139\pi$
$578$	9.32962e11	−	1.61594e12i	0.347687	−	0.602212i
$579$	−9.92020e11	−	5.62603e12i	−0.366832	−	2.08041i
$580$	−2.19078e10	−	1.24245e11i	−0.00803845	−	0.0455883i
$581$	−2.81991e12	+	4.88423e12i	−1.02670	+	1.77829i
$582$	1.73176e12	+	2.99949e12i	0.625653	+	1.08366i
$583$	−7.06221e11	+	5.92590e11i	−0.253182	+	0.212445i
$584$	8.68281e11	−	3.16028e11i	0.308889	−	0.112426i
$585$	−6.23508e10	−	2.26938e10i	−0.0220110	−	0.00801136i
$586$	−1.74471e12	−	1.46398e12i	−0.611200	−	0.512858i
$587$	4.69996e11	−	2.66548e12i	0.163389	−	0.926626i	−0.787321	−	0.616544i	$-0.788532\pi$
$587$	4.69996e11	−	2.66548e12i	0.163389	−	0.926626i	0.950710	−	0.310082i	$-0.100357\pi$
$588$	−1.42617e12			−0.492010
$589$	2.30644e10	+	1.60365e10i	0.00789631	+	0.00549022i
$590$	1.19648e12			0.406510
$591$	−6.04355e11	+	3.42747e12i	−0.203774	+	1.15566i
$592$	1.07247e12	+	8.99912e11i	0.358871	+	0.301129i
$593$	−3.26851e12	−	1.18964e12i	−1.08544	−	0.395066i	−0.263508	−	0.964657i	$-0.584879\pi$
$593$	−3.26851e12	−	1.18964e12i	−1.08544	−	0.395066i	−0.821928	+	0.569591i	$0.807102\pi$
$594$	8.89192e11	−	3.23639e11i	0.293060	−	0.106665i
$595$	1.26358e11	−	1.06027e11i	0.0413310	−	0.0346808i
$596$	−1.12703e11	−	1.95207e11i	−0.0365869	−	0.0633704i
$597$	1.02953e12	−	1.78320e12i	0.331707	−	0.574533i
$598$	2.34397e9	+	1.32933e10i	0.000749545	+	0.00425088i
$599$	3.47631e11	+	1.97151e12i	0.110331	+	0.625718i	0.988956	+	0.148207i	$0.0473501\pi$
$599$	3.47631e11	+	1.97151e12i	0.110331	+	0.625718i	−0.878625	+	0.477512i	$0.841539\pi$
$600$	−8.01163e11	+	1.38766e12i	−0.252372	+	0.437120i
$601$	1.44129e11	+	2.49639e11i	0.0450626	+	0.0780507i	0.887677	−	0.460467i	$-0.152318\pi$
$601$	1.44129e11	+	2.49639e11i	0.0450626	+	0.0780507i	−0.842614	+	0.538517i	$0.818985\pi$
$602$	1.63732e12	−	1.37388e12i	0.508101	−	0.426347i
$603$	2.07393e12	−	7.54849e11i	0.638802	−	0.232505i
$604$	−2.11125e12	−	7.68431e11i	−0.645465	−	0.234930i
$605$	6.34846e11	+	5.32699e11i	0.192650	+	0.161653i
$606$	−2.71569e11	+	1.54015e12i	−0.0818001	+	0.463912i
$607$	−3.25935e12			−0.974499			−0.487249	−	0.873263i	$-0.662000\pi$
$607$	−3.25935e12			−0.974499			−0.487249	+	0.873263i	$0.662000\pi$
$608$	2.49945e11	−	5.40672e11i	0.0741787	−	0.160460i
$609$	1.94007e12			0.571530
$610$	−1.15900e11	+	6.57300e11i	−0.0338921	+	0.192211i
$611$	−1.69254e11	−	1.42021e11i	−0.0491308	−	0.0412257i
$612$	−3.28794e11	−	1.19671e11i	−0.0947419	−	0.0344832i
$613$	8.74343e11	−	3.18235e11i	0.250098	−	0.0910281i	−0.213929	−	0.976849i	$-0.568626\pi$
$613$	8.74343e11	−	3.18235e11i	0.250098	−	0.0910281i	0.464027	+	0.885821i	$0.346404\pi$
$614$	1.46566e12	−	1.22983e12i	0.416174	−	0.349212i
$615$	6.15306e11	+	1.06574e12i	0.173442	+	0.300410i
$616$	3.90884e11	−	6.77031e11i	0.109379	−	0.189450i
$617$	−4.76670e11	−	2.70333e12i	−0.132414	−	0.750958i	−0.976626	−	0.214948i	$-0.931042\pi$
$617$	−4.76670e11	−	2.70333e12i	−0.132414	−	0.750958i	0.844211	−	0.536011i	$-0.180069\pi$
$618$	2.68439e11	+	1.52239e12i	0.0740283	+	0.419835i
$619$	2.84306e12	−	4.92433e12i	0.778357	−	1.34815i	−0.154531	−	0.987988i	$-0.549387\pi$
$619$	2.84306e12	−	4.92433e12i	0.778357	−	1.34815i	0.932888	−	0.360166i	$-0.117280\pi$
$620$	−2.91632e9	−	5.05121e9i	−0.000792633	−	0.00137288i
$621$	3.45815e11	−	2.90173e11i	0.0933107	−	0.0782970i
$622$	−1.86021e12	+	6.77060e11i	−0.498316	+	0.181372i
$623$	2.63824e11	+	9.60243e10i	0.0701647	+	0.0255379i
$624$	5.27287e10	+	4.42446e10i	0.0139225	+	0.0116823i
$625$	4.54265e11	−	2.57627e12i	0.119083	−	0.675353i
$626$	1.55641e12			0.405079
$627$	2.12735e12	−	2.14147e12i	0.549712	−	0.553361i
$628$	1.74006e12			0.446423
$629$	1.64547e11	−	9.33192e11i	0.0419143	−	0.237708i
$630$	1.40438e12	+	1.17842e12i	0.355184	+	0.298034i
$631$	2.42524e12	+	8.82714e11i	0.609007	+	0.221660i	0.628069	−	0.778158i	$-0.283846\pi$
$631$	2.42524e12	+	8.82714e11i	0.609007	+	0.221660i	−0.0190617	+	0.999818i	$0.506068\pi$
$632$	−2.58561e12	+	9.41086e11i	−0.644669	+	0.234640i
$633$	7.86030e12	−	6.59557e12i	1.94591	−	1.63281i
$634$	−5.71765e11	−	9.90326e11i	−0.140545	−	0.243431i
$635$	−9.88632e11	+	1.71236e12i	−0.241297	+	0.417940i
$636$	3.89446e11	+	2.20866e12i	0.0943823	+	0.535269i
$637$	−2.01215e10	−	1.14115e11i	−0.00484209	−	0.0274609i
$638$	−2.02356e11	+	3.50490e11i	−0.0483528	+	0.0837496i
$639$	6.10085e12	+	1.05670e13i	1.44756	+	2.50724i
$640$	−9.47400e10	+	7.94963e10i	−0.0223215	+	0.0187300i
$641$	−5.87370e12	+	2.13785e12i	−1.37420	+	0.500169i	−0.920416	−	0.390941i	$-0.872150\pi$
$641$	−5.87370e12	+	2.13785e12i	−1.37420	+	0.500169i	−0.453788	+	0.891110i	$0.649927\pi$
$642$	−2.62245e12	−	9.54493e11i	−0.609255	−	0.221751i
$643$	−4.76530e12	−	3.99856e12i	−1.09936	−	0.922475i	−0.101980	−	0.994786i	$-0.532518\pi$
$643$	−4.76530e12	−	3.99856e12i	−1.09936	−	0.922475i	−0.997382	+	0.0723117i	$0.976962\pi$
$644$	6.47632e10	−	3.67290e11i	0.0148369	−	0.0841440i
$645$	−1.71351e12			−0.389823
$646$	−4.01508e11	+	3.64661e10i	−0.0907086	+	0.00823840i
$647$	−2.19222e11			−0.0491831			−0.0245915	−	0.999698i	$-0.507829\pi$
$647$	−2.19222e11			−0.0491831			−0.0245915	+	0.999698i	$0.507829\pi$
$648$	−3.16385e10	+	1.79431e11i	−0.00704901	+	0.0399769i
$649$	−2.94019e12	−	2.46712e12i	−0.650541	−	0.545869i
$650$	−1.22336e11	−	4.45268e10i	−0.0268810	−	0.00978388i
$651$	8.42829e10	−	3.06765e10i	0.0183918	−	0.00669408i
$652$	6.04938e11	−	5.07603e11i	0.131098	−	0.110004i
$653$	2.25566e12	+	3.90692e12i	0.485473	+	0.840864i	0.999861	−	0.0166939i	$-0.00531408\pi$
$653$	2.25566e12	+	3.90692e12i	0.485473	+	0.840864i	−0.514388	+	0.857558i	$0.671981\pi$
$654$	−2.65411e12	+	4.59705e12i	−0.567308	+	0.982605i
$655$	2.50680e11	+	1.42167e12i	0.0532149	+	0.301797i
$656$	−1.35271e11	−	7.67159e11i	−0.0285192	−	0.161740i
$657$	3.47548e12	−	6.01971e12i	0.727731	−	1.26047i
$658$	3.05233e12	+	5.28678e12i	0.634767	+	1.09945i
$659$	−3.23634e12	+	2.71561e12i	−0.668452	+	0.560898i	−0.912607	−	0.408838i	$-0.865934\pi$
$659$	−3.23634e12	+	2.71561e12i	−0.668452	+	0.560898i	0.244155	+	0.969736i	$0.421490\pi$
$660$	−5.88938e11	+	2.14356e11i	−0.120815	+	0.0439732i
$661$	6.70026e11	+	2.43870e11i	0.136517	+	0.0496880i	0.409375	−	0.912366i	$-0.365747\pi$
$661$	6.70026e11	+	2.43870e11i	0.136517	+	0.0496880i	−0.272858	+	0.962054i	$0.587969\pi$
$662$	−7.58215e10	−	6.36218e10i	−0.0153437	−	0.0128749i
$663$	8.09004e9	−	4.58809e10i	0.00162607	−	0.00922191i
$664$	−2.86210e12			−0.571384
$665$	2.04220e12	+	5.39972e11i	0.404950	+	0.107072i
$666$	1.05318e13			2.07429
$667$	−3.35271e10	+	1.90141e11i	−0.00655887	+	0.0371972i
$668$	2.90808e12	+	2.44017e12i	0.565084	+	0.474161i
$669$	−9.34544e12	−	3.40146e12i	−1.80377	−	0.656520i
$670$	−4.96162e11	+	1.80588e11i	−0.0951232	+	0.0346220i
$671$	1.64015e12	−	1.37625e12i	0.312343	−	0.262087i
$672$	−9.50908e11	−	1.64702e12i	−0.179878	−	0.311557i
$673$	1.49741e12	−	2.59360e12i	0.281367	−	0.487343i	−0.690354	−	0.723471i	$-0.742545\pi$
$673$	1.49741e12	−	2.59360e12i	0.281367	−	0.487343i	0.971722	+	0.236129i	$0.0758787\pi$
$674$	−6.13433e10	−	3.47895e11i	−0.0114498	−	0.0649350i
$675$	7.56044e11	+	4.28774e12i	0.140178	+	0.794989i
$676$	1.35458e12	−	2.34620e12i	0.249485	−	0.432121i
$677$	−4.22800e12	−	7.32310e12i	−0.773545	−	1.33982i	−0.935609	−	0.353039i	$-0.885148\pi$
$677$	−4.22800e12	−	7.32310e12i	−0.773545	−	1.33982i	0.162064	−	0.986780i	$-0.448185\pi$
$678$	8.21758e12	−	6.89537e12i	1.49352	−	1.25321i
$679$	7.30628e12	−	2.65927e12i	1.31911	−	0.480118i
$680$	7.86598e10	+	2.86298e10i	0.0141079	+	0.00513486i
$681$	−5.89312e12	−	4.94491e12i	−1.04999	−	0.881042i
$682$	−3.24902e9	+	1.84261e10i	−0.000575072	+	0.00326139i
$683$	−8.42903e12			−1.48212			−0.741062	−	0.671437i	$-0.765677\pi$
$683$	−8.42903e12			−1.48212			−0.741062	+	0.671437i	$0.765677\pi$
$684$	−1.17404e12	−	4.32432e12i	−0.205084	−	0.755380i
$685$	−1.32787e12			−0.230434
$686$	3.48977e11	−	1.97915e12i	0.0601642	−	0.341208i
$687$	−7.58534e12	−	6.36486e12i	−1.29918	−	1.09014i
$688$	1.01926e12	+	3.70980e11i	0.173435	+	0.0631251i
$689$	−1.71231e11	+	6.23228e10i	−0.0289464	+	0.0105356i
$690$	−2.29044e11	+	1.92190e11i	−0.0384678	+	0.0322783i
$691$	2.62420e12	+	4.54525e12i	0.437870	+	0.758414i	0.997525	−	0.0703122i	$-0.0223995\pi$
$691$	2.62420e12	+	4.54525e12i	0.437870	+	0.758414i	−0.559655	+	0.828726i	$0.689066\pi$
$692$	1.95143e12	−	3.37998e12i	0.323501	−	0.560321i
$693$	−1.02122e12	−	5.79162e12i	−0.168197	−	0.953894i
$694$	7.09917e11	+	4.02614e12i	0.116169	+	0.658827i
$695$	3.12413e11	−	5.41115e11i	0.0507922	−	0.0879748i
$696$	4.92273e11	+	8.52641e11i	0.0795178	+	0.137729i
$697$	−4.03901e11	+	3.38914e11i	−0.0648228	+	0.0543928i
$698$	−2.64734e12	+	9.63554e11i	−0.422144	+	0.153648i
$699$	1.67120e13	+	6.08268e12i	2.64778	+	0.963713i
$700$	2.75549e12	+	2.31213e12i	0.433768	+	0.363975i
$701$	−4.41246e11	+	2.50243e12i	−0.0690161	+	0.391409i	0.930658	+	0.365890i	$0.119235\pi$
$701$	−4.41246e11	+	2.50243e12i	−0.0690161	+	0.391409i	−0.999674	+	0.0255199i	$0.991876\pi$
$702$	1.87033e11			0.0290671
$703$	1.09811e13	−	5.16487e12i	1.69569	−	0.797555i
$704$	3.96731e11			0.0608723
$705$	8.49840e11	−	4.81968e12i	0.129565	−	0.734797i
$706$	1.56468e12	+	1.31292e12i	0.237030	+	0.198892i
$707$	3.29906e12	+	1.20076e12i	0.496596	+	0.180746i
$708$	−8.77402e12	+	3.19348e12i	−1.31235	+	0.477655i
$709$	−1.92405e12	+	1.61447e12i	−0.285962	+	0.239951i	−0.774473	−	0.632607i	$-0.781985\pi$
$709$	−1.92405e12	+	1.61447e12i	−0.285962	+	0.239951i	0.488511	+	0.872558i	$0.337540\pi$
$710$	−1.45955e12	−	2.52802e12i	−0.215554	−	0.373351i
$711$	−1.03495e13	+	1.79258e13i	−1.51882	+	2.63067i
$712$	2.47411e10	+	1.40313e11i	0.00360793	+	0.0204616i
$713$	1.55000e9	+	8.79049e9i	0.000224610	+	0.00127383i
$714$	−6.43615e11	+	1.11477e12i	−0.0926796	+	0.160526i
$715$	−2.54608e10	−	4.40994e10i	−0.00364330	−	0.00631038i
$716$	−4.10585e11	+	3.44522e11i	−0.0583841	+	0.0489900i
$717$	−4.12168e12	+	1.50017e12i	−0.582423	+	0.211984i
$718$	−8.31565e12	−	3.02665e12i	−1.16771	−	0.425013i
$719$	6.67827e12	+	5.60374e12i	0.931932	+	0.781984i	0.976163	−	0.217038i	$-0.0696394\pi$
$719$	6.67827e12	+	5.60374e12i	0.931932	+	0.781984i	−0.0442313	+	0.999021i	$0.514084\pi$
$720$	−1.61555e11	+	9.16224e11i	−0.0224039	+	0.127059i
$721$	3.47032e12			0.478256
$722$	−3.34481e12	−	3.93305e12i	−0.458093	−	0.538656i
$723$	4.17325e11			0.0568005
$724$	−6.00240e11	+	3.40413e12i	−0.0811898	+	0.460450i
$725$	−1.42648e12	−	1.19696e12i	−0.191754	−	0.160901i
$726$	−6.07726e12	−	2.21194e12i	−0.811882	−	0.295501i
$727$	−6.30286e12	+	2.29405e12i	−0.836822	+	0.304578i	−0.724656	−	0.689111i	$-0.758001\pi$
$727$	−6.30286e12	+	2.29405e12i	−0.836822	+	0.304578i	−0.112166	+	0.993689i	$0.535779\pi$
$728$	1.18370e11	−	9.93240e10i	0.0156189	−	0.0131058i
$729$	6.21628e12	+	1.07669e13i	0.815186	+	1.41194i
$730$	−8.31466e11	+	1.44014e12i	−0.108366	+	0.187695i
$731$	−1.27484e11	−	7.22999e11i	−0.0165131	−	0.0936503i
$732$	−9.04461e11	−	5.12945e12i	−0.116437	−	0.660346i
$733$	−3.82159e12	+	6.61919e12i	−0.488964	+	0.846910i	−0.999919	−	0.0126971i	$-0.995958\pi$
$733$	−3.82159e12	+	6.61919e12i	−0.488964	+	0.846910i	0.510956	+	0.859607i	$0.329292\pi$
$734$	5.59901e11	+	9.69777e11i	0.0711999	+	0.123322i
$735$	1.96619e12	−	1.64983e12i	0.248504	−	0.208519i
$736$	1.77854e11	−	6.47334e10i	0.0223415	−	0.00813164i
$737$	1.59162e12	+	5.79303e11i	0.198718	+	0.0723273i
$738$	−4.48909e12	−	3.76680e12i	−0.557064	−	0.467432i
$739$	1.86856e12	−	1.05971e13i	0.230466	−	1.30704i	−0.621488	−	0.783424i	$-0.713472\pi$
$739$	1.86856e12	−	1.05971e13i	0.230466	−	1.30704i	0.851954	−	0.523616i	$-0.175417\pi$
$740$	−2.51960e12			−0.308880
$741$	5.39892e11	−	2.53934e11i	0.0657848	−	0.0309413i
$742$	5.03467e12			0.609752
$743$	−3.75715e11	+	2.13079e12i	−0.0452281	+	0.256502i	−0.999035	−	0.0439186i	$-0.986016\pi$
$743$	−3.75715e11	+	2.13079e12i	−0.0452281	+	0.256502i	0.953807	+	0.300420i	$0.0971269\pi$
$744$	3.48679e10	+	2.92577e10i	0.00417204	+	0.00350075i
$745$	3.81197e11	+	1.38744e11i	0.0453363	+	0.0165011i
$746$	−1.80029e12	+	6.55252e11i	−0.212823	+	0.0774611i
$747$	−1.64933e13	+	1.38396e13i	−1.93805	+	1.62622i
$748$	−1.34262e11	−	2.32549e11i	−0.0156818	−	0.0271617i
$749$	−3.13246e12	+	5.42557e12i	−0.363678	+	0.629908i
$750$	−1.06256e12	−	6.02606e12i	−0.122624	−	0.695437i
$751$	2.66094e12	+	1.50909e13i	0.305249	+	1.73115i	0.622329	+	0.782756i	$0.286187\pi$
$751$	2.66094e12	+	1.50909e13i	0.305249	+	1.73115i	−0.317079	+	0.948399i	$0.602702\pi$
$752$	−1.54899e12	+	2.68294e12i	−0.176632	+	0.305936i
$753$	−4.00660e12	−	6.93964e12i	−0.454150	−	0.786610i
$754$	−6.12785e10	+	5.14188e10i	−0.00690458	+	0.00579363i
$755$	3.79961e12	−	1.38294e12i	0.425576	−	0.154897i
$756$	−4.85602e12	−	1.76744e12i	−0.540670	−	0.196788i
$757$	6.47807e12	+	5.43575e12i	0.716992	+	0.601628i	0.926551	−	0.376168i	$-0.122759\pi$
$757$	6.47807e12	+	5.43575e12i	0.716992	+	0.601628i	−0.209559	+	0.977796i	$0.567203\pi$
$758$	−1.27967e12	+	7.25734e12i	−0.140794	+	0.798484i
$759$	9.59138e11			0.104904
$760$	2.80875e11	+	1.03454e12i	0.0305388	+	0.112483i
$761$	2.97114e12			0.321138			0.160569	−	0.987025i	$-0.448667\pi$
$761$	2.97114e12			0.321138			0.160569	+	0.987025i	$0.448667\pi$
$762$	2.67943e12	−	1.51958e13i	0.287902	−	1.63277i
$763$	9.12843e12	+	7.65966e12i	0.975070	+	0.818181i
$764$	5.75726e12	+	2.09547e12i	0.611358	+	0.222516i
$765$	5.91730e11	−	2.15372e11i	0.0624665	−	0.0227359i
$766$	−9.42976e12	+	7.91251e12i	−0.989626	+	0.830395i
$767$	−3.79316e11	−	6.56994e11i	−0.0395751	−	0.0685461i
$768$	4.82567e11	−	8.35830e11i	0.0500532	−	0.0866947i
$769$	4.73589e11	+	2.68586e12i	0.0488352	+	0.276958i	0.999441	−	0.0334437i	$-0.0106475\pi$
$769$	4.73589e11	+	2.68586e12i	0.0488352	+	0.276958i	−0.950605	+	0.310402i	$0.899536\pi$
$770$	2.44314e11	+	1.38557e12i	0.0250461	+	0.142043i
$771$	−1.45445e13	+	2.51918e13i	−1.48236	+	2.56753i
$772$	−3.25411e12	−	5.63629e12i	−0.329727	−	0.571105i
$773$	−5.10186e11	+	4.28097e11i	−0.0513950	+	0.0431255i	−0.668123	−	0.744051i	$-0.732902\pi$
$773$	−5.10186e11	+	4.28097e11i	−0.0513950	+	0.0431255i	0.616728	+	0.787176i	$0.288458\pi$
$774$	7.66752e12	−	2.79075e12i	0.767928	−	0.279503i
$775$	−8.08974e10	−	2.94442e10i	−0.00805521	−	0.00293186i
$776$	3.02262e12	+	2.53628e12i	0.299230	+	0.251084i
$777$	6.72808e12	−	3.81569e13i	0.662212	−	3.75559i
$778$	8.50927e12			0.832691
$779$	−6.52787e12	−	1.72601e12i	−0.635116	−	0.167929i
$780$	−1.23878e11			−0.0119830
$781$	−1.62606e12	+	9.22184e12i	−0.156389	+	0.886927i
$782$	−9.81337e10	−	8.23439e10i	−0.00938400	−	0.00787411i
$783$	2.51390e12	+	9.14983e11i	0.239012	+	0.0869932i
$784$	−1.52676e12	+	5.55695e11i	−0.144327	+	0.0525308i
$785$	−2.39893e12	+	2.01294e12i	−0.225478	+	0.189199i
$786$	−5.63283e12	−	9.75634e12i	−0.526411	−	0.911770i
$787$	7.60031e12	−	1.31641e13i	0.706228	−	1.22322i	−0.260018	−	0.965604i	$-0.583728\pi$
$787$	7.60031e12	−	1.31641e13i	0.706228	−	1.22322i	0.966246	−	0.257620i	$-0.0829382\pi$
$788$	6.88501e11	+	3.90468e12i	0.0636116	+	0.360760i
$789$	−6.07076e11	−	3.44290e12i	−0.0557694	−	0.316284i
$790$	2.47598e12	−	4.28853e12i	0.226165	−	0.391730i
$791$	−1.20408e13	−	2.08552e13i	−1.09360	−	1.89418i
$792$	2.28624e12	−	1.91838e12i	0.206470	−	0.173249i
$793$	3.97671e11	−	1.44740e11i	0.0357104	−	0.0129975i
$794$	−2.75788e12	−	1.00378e12i	−0.246254	−	0.0896290i
$795$	−3.09194e12	−	2.59445e12i	−0.274523	−	0.230352i
$796$	4.07335e11	−	2.31011e12i	0.0359619	−	0.203950i
$797$	−6.00307e12			−0.527001			−0.263500	−	0.964659i	$-0.584877\pi$
$797$	−6.00307e12			−0.527001			−0.263500	+	0.964659i	$0.584877\pi$
$798$	−1.64171e13	+	1.49105e12i	−1.43312	+	0.130160i
$799$	2.09685e12			0.182015
$800$	−3.16981e11	+	1.79769e12i	−0.0273608	+	0.155171i
$801$	8.21055e11	+	6.88947e11i	0.0704736	+	0.0591343i
$802$	2.02951e12	+	7.38681e11i	0.173223	+	0.0630481i
$803$	5.01276e12	−	1.82450e12i	0.425458	−	0.154854i
$804$	3.15645e12	−	2.64858e12i	0.266408	−	0.223543i
$805$	3.35605e11	+	5.81284e11i	0.0281674	+	0.0487873i
$806$	−1.84910e9	+	3.20274e9i	−0.000154331	+	0.000267309i
$807$	−3.23742e12	−	1.83603e13i	−0.268700	−	1.52387i
$808$	3.09381e11	+	1.75459e12i	0.0255354	+	0.144818i
$809$	1.61606e12	−	2.79910e12i	0.132644	−	0.229747i	−0.792051	−	0.610455i	$-0.790987\pi$
$809$	1.61606e12	−	2.79910e12i	0.132644	−	0.229747i	0.924695	+	0.380708i	$0.124320\pi$
$810$	−1.63951e11	−	2.83972e11i	−0.0133824	−	0.0231789i
$811$	1.33865e13	−	1.12326e13i	1.08661	−	0.911776i	0.0901592	−	0.995927i	$-0.471262\pi$
$811$	1.33865e13	−	1.12326e13i	1.08661	−	0.911776i	0.996453	+	0.0841515i	$0.0268180\pi$
$812$	2.07690e12	−	7.55930e11i	0.167654	−	0.0610210i
$813$	8.99023e12	+	3.27218e12i	0.721711	+	0.262681i
$814$	6.19160e12	+	5.19537e12i	0.494303	+	0.414769i
$815$	−2.46790e11	+	1.39961e12i	−0.0195938	+	0.111122i
$816$	−6.53243e11			−0.0515785
$817$	6.62603e12	−	6.67001e12i	0.520301	−	0.523754i
$818$	1.21296e13			0.947235
$819$	2.01850e11	−	1.14475e12i	0.0156765	−	0.0889061i
$820$	1.07396e12	+	9.01159e11i	0.0829517	+	0.0696048i
$821$	9.06110e12	+	3.29797e12i	0.696044	+	0.253339i	0.665721	−	0.746201i	$-0.268124\pi$
$821$	9.06110e12	+	3.29797e12i	0.696044	+	0.253339i	0.0303233	+	0.999540i	$0.490346\pi$
$822$	9.73752e12	−	3.54417e12i	0.743919	−	0.270764i
$823$	2.64538e11	−	2.21974e11i	0.0200997	−	0.0168656i	−0.632682	−	0.774411i	$-0.718046\pi$
$823$	2.64538e11	−	2.21974e11i	0.0200997	−	0.0168656i	0.652782	+	0.757546i	$0.273602\pi$
$824$	8.80558e11	+	1.52517e12i	0.0665404	+	0.115251i
$825$	−4.62528e12	+	8.01122e12i	−0.347612	+	0.602082i
$826$	3.63979e12	+	2.06423e13i	0.272061	+	1.54294i
$827$	−3.02729e11	−	1.71686e12i	−0.0225050	−	0.127632i	0.971485	−	0.237099i	$-0.0761967\pi$
$827$	−3.02729e11	−	1.71686e12i	−0.0225050	−	0.127632i	−0.993990	+	0.109467i	$0.965086\pi$
$828$	7.11897e11	−	1.23304e12i	0.0526358	−	0.0911678i
$829$	4.45208e12	+	7.71123e12i	0.327392	+	0.567059i	0.981993	−	0.188915i	$-0.0604970\pi$
$829$	4.45208e12	+	7.71123e12i	0.327392	+	0.567059i	−0.654602	+	0.755974i	$0.727164\pi$
$830$	3.94582e12	−	3.31094e12i	0.288593	−	0.242159i
$831$	−1.51920e13	+	5.52944e12i	−1.10512	+	0.402232i
$832$	7.36871e10	+	2.68199e10i	0.00533134	+	0.00194045i
$833$	8.42415e11	+	7.06870e11i	0.0606210	+	0.0508671i
$834$	−8.46714e11	+	4.80196e12i	−0.0606024	+	0.343693i
$835$	−6.83207e12			−0.486366
$836$	1.44299e12	−	3.12141e12i	0.102172	−	0.221015i
$837$	1.23680e11			0.00871030
$838$	2.12141e12	−	1.20311e13i	0.148602	−	0.842766i
$839$	−8.46418e12	−	7.10229e12i	−0.589734	−	0.494846i	0.298393	−	0.954443i	$-0.403549\pi$
$839$	−8.46418e12	−	7.10229e12i	−0.589734	−	0.494846i	−0.888127	+	0.459597i	$0.847994\pi$
$840$	3.21628e12	+	1.17063e12i	0.222893	+	0.0811266i
$841$	1.25571e13	−	4.57040e12i	0.865579	−	0.315045i
$842$	−2.80180e12	+	2.35099e12i	−0.192102	+	0.161193i
$843$	3.59192e12	+	6.22139e12i	0.244964	+	0.424290i
$844$	5.84477e12	−	1.01234e13i	0.396485	−	0.686732i
$845$	8.46651e11	+	4.80160e12i	0.0571280	+	0.323989i
$846$	4.04688e12	+	2.29510e13i	0.271615	+	1.54041i
$847$	−7.25915e12	+	1.25732e13i	−0.484630	+	0.839404i
$848$	1.27750e12	+	2.21269e12i	0.0848357	+	0.146940i
$849$	−5.84316e12	+	4.90299e12i	−0.385979	+	0.323875i
$850$	1.16101e12	−	4.22574e11i	0.0762872	−	0.0277663i
$851$	3.62339e12	+	1.31881e12i	0.236828	+	0.0861982i
$852$	1.74506e13	+	1.46428e13i	1.13457	+	0.952020i
$853$	1.09589e12	−	6.21512e12i	0.0708757	−	0.401956i	−0.928644	−	0.370972i	$-0.879025\pi$
$853$	1.09589e12	−	6.21512e12i	0.0708757	−	0.401956i	0.999520	−	0.0309845i	$-0.00986425\pi$
$854$	−1.16927e13			−0.752234
$855$	6.62107e12	+	4.60356e12i	0.423722	+	0.294609i
$856$	−3.17932e12			−0.202396
$857$	4.81095e12	−	2.72842e13i	0.304661	−	1.72782i	−0.320434	−	0.947271i	$-0.603829\pi$
$857$	4.81095e12	−	2.72842e13i	0.304661	−	1.72782i	0.625095	−	0.780548i	$-0.285060\pi$
$858$	3.04413e11	+	2.55433e11i	0.0191766	+	0.0160911i
$859$	2.41348e13	+	8.78434e12i	1.51243	+	0.550478i	0.959243	−	0.282582i	$-0.0911909\pi$
$859$	2.41348e13	+	8.78434e12i	1.51243	+	0.550478i	0.553183	+	0.833060i	$0.313413\pi$
$860$	−1.83436e12	+	6.67652e11i	−0.114351	+	0.0416205i
$861$	−1.65149e13	+	1.38577e13i	−1.02415	+	0.859362i
$862$	−1.73164e12	−	2.99929e12i	−0.106826	−	0.185027i
$863$	1.17157e13	−	2.02923e13i	0.718988	−	1.24532i	−0.242414	−	0.970173i	$-0.577939\pi$
$863$	1.17157e13	−	2.02923e13i	0.718988	−	1.24532i	0.961401	−	0.275150i	$-0.0887276\pi$
$864$	−4.55390e11	−	2.58264e12i	−0.0278017	−	0.157671i
$865$	1.21970e12	+	6.91727e12i	0.0740766	+	0.420109i
$866$	−9.11247e12	+	1.57833e13i	−0.550561	+	0.953600i
$867$	−1.31030e13	−	2.26951e13i	−0.787564	−	1.36410i
$868$	7.82745e10	−	6.56801e10i	0.00468038	−	0.00392731i
$869$	−1.49273e13	+	5.43308e12i	−0.887956	+	0.323190i
$870$	−1.66503e12	−	6.06020e11i	−0.0985337	−	0.0358633i
$871$	2.56459e11	+	2.15194e11i	0.0150986	+	0.0126692i
$872$	−1.05010e12	+	5.95542e12i	−0.0615045	+	0.348809i
$873$	2.96825e13			1.72956
$874$	1.37576e11	−	1.63477e12i	0.00797520	−	0.0947664i
$875$	−1.37365e13			−0.792209
$876$	2.25347e12	−	1.27801e13i	0.129296	−	0.733272i
$877$	6.72078e10	+	5.63941e10i	0.00383638	+	0.00321911i	0.644704	−	0.764432i	$-0.276981\pi$
$877$	6.72078e10	+	5.63941e10i	0.00383638	+	0.00321911i	−0.640867	+	0.767652i	$0.721425\pi$
$878$	−1.99361e13	−	7.25616e12i	−1.13218	−	0.412080i
$879$	−3.00581e13	+	1.09403e13i	−1.69829	+	0.618127i
$880$	−5.46953e11	+	4.58948e11i	−0.0307453	+	0.0257983i
$881$	3.96881e12	+	6.87417e12i	0.221957	+	0.384440i	0.955402	−	0.295308i	$-0.0954223\pi$
$881$	3.96881e12	+	6.87417e12i	0.221957	+	0.384440i	−0.733445	+	0.679748i	$0.762089\pi$
$882$	−6.11118e12	+	1.05849e13i	−0.340029	+	0.588948i
$883$	2.79049e12	+	1.58257e13i	0.154475	+	0.876071i	0.959264	+	0.282510i	$0.0911671\pi$
$883$	2.79049e12	+	1.58257e13i	0.154475	+	0.876071i	−0.804789	+	0.593561i	$0.797722\pi$
$884$	−9.21644e9	−	5.22690e10i	−0.000507607	−	0.00287878i
$885$	8.40199e12	−	1.45527e13i	0.460403	−	0.797441i
$886$	2.60439e12	+	4.51093e12i	0.141989	+	0.245931i
$887$	2.04979e13	−	1.71998e13i	1.11187	−	0.932968i	0.113703	−	0.993515i	$-0.463729\pi$
$887$	2.04979e13	−	1.71998e13i	1.11187	−	0.932968i	0.998165	+	0.0605466i	$0.0192844\pi$
$888$	1.84768e13	−	6.72499e12i	0.997166	−	0.362939i
$889$	−3.25501e13	−	1.18473e13i	−1.74781	−	0.636150i
$890$	−1.96427e11	−	1.64822e11i	−0.0104941	−	0.00880563i
$891$	−1.82655e11	+	1.03589e12i	−0.00970918	+	0.0550635i
$892$	−1.13299e13			−0.599218
$893$	1.54749e13	+	2.19455e13i	0.814320	+	1.15482i
$894$	−3.16571e12			−0.165750
$895$	1.67502e11	−	9.49949e11i	0.00872600	−	0.0494876i
$896$	−1.65972e12	−	1.39267e12i	−0.0860298	−	0.0721876i
$897$	1.78146e11	+	6.48398e10i	0.00918776	+	0.00334407i
$898$	7.42177e12	−	2.70130e12i	0.380859	−	0.138621i
$899$	−4.05217e10	+	3.40017e10i	−0.00206904	+	0.00173613i
$900$	6.86601e12	+	1.18923e13i	0.348829	+	0.604190i
$901$	8.64664e11	−	1.49764e12i	0.0437105	−	0.0757088i
$902$	−7.80946e11	−	4.42896e12i	−0.0392818	−	0.222778i
$903$	−5.21264e12	−	2.95623e13i	−0.260893	−	1.47960i
$904$	6.11044e12	−	1.05836e13i	0.304309	−	0.527079i
$905$	−3.11046e12	−	5.38747e12i	−0.154137	−	0.266973i
$906$	−2.41721e13	+	2.02828e13i	−1.19189	+	1.00012i
$907$	−7.25060e12	+	2.63900e12i	−0.355747	+	0.129481i	−0.513710	−	0.857964i	$-0.671729\pi$
$907$	−7.25060e12	+	2.63900e12i	−0.355747	+	0.129481i	0.157963	+	0.987445i	$0.449507\pi$
$908$	−8.23549e12	−	2.99747e12i	−0.402071	−	0.146342i
$909$	1.02671e13	+	8.61512e12i	0.498781	+	0.418527i
$910$	−4.82900e10	+	2.73866e11i	−0.00233437	+	0.0132389i
$911$	1.61730e13			0.777960			0.388980	−	0.921246i	$-0.372828\pi$
$911$	1.61730e13			0.777960			0.388980	+	0.921246i	$0.372828\pi$
$912$	−4.82097e12	−	6.83681e12i	−0.230758	−	0.327248i
$913$	−1.65235e13			−0.787014
$914$	4.34138e12	−	2.46212e13i	0.205764	−	1.16695i
$915$	7.18081e12	+	6.02542e12i	0.338671	+	0.284179i
$916$	−1.06003e13	−	3.85821e12i	−0.497496	−	0.181074i
$917$	−2.37649e13	+	8.64972e12i	−1.10987	+	0.403961i
$918$	−1.35973e12	+	1.14095e12i	−0.0631920	+	0.0530244i
$919$	−1.13670e13	−	1.96883e13i	−0.525687	−	0.910517i	−0.999552	−	0.0299195i	$-0.990475\pi$
$919$	−1.13670e13	−	1.96883e13i	−0.525687	−	0.910517i	0.473865	−	0.880597i	$-0.342858\pi$
$920$	−1.70313e11	+	2.94990e11i	−0.00783793	+	0.0135757i
$921$	−4.66613e12	−	2.64629e13i	−0.213692	−	1.21191i
$922$	3.92088e12	+	2.22364e13i	0.178688	+	1.01339i
$923$	−9.25433e11	+	1.60290e12i	−0.0419699	+	0.0726939i
$924$	−5.48978e12	−	9.50859e12i	−0.247760	−	0.429133i
$925$	−2.84885e13	+	2.39047e13i	−1.27948	+	1.07361i
$926$	−1.72332e13	+	6.27237e12i	−0.770223	+	0.280338i
$927$	1.24493e13	+	4.53117e12i	0.553714	+	0.201535i
$928$	8.59216e11	+	7.20968e11i	0.0380309	+	0.0319117i
$929$	−5.60083e11	+	3.17639e12i	−0.0246707	+	0.139914i	−0.994655	−	0.103252i	$-0.967075\pi$
$929$	−5.60083e11	+	3.17639e12i	−0.0246707	+	0.139914i	0.969985	+	0.243167i	$0.0781862\pi$
$930$	−8.19166e10			−0.00359086
$931$	−1.18100e12	+	1.40334e13i	−0.0515202	+	0.612195i
$932$	2.02608e13			0.879598
$933$	−4.82784e12	+	2.73801e13i	−0.208586	+	1.18295i
$934$	6.33637e12	+	5.31684e12i	0.272445	+	0.228609i
$935$	4.54119e11	+	1.65286e11i	0.0194320	+	0.00707267i
$936$	5.54322e11	−	2.01757e11i	0.0236059	−	0.00859185i
$937$	−1.25960e13	+	1.05693e13i	−0.533833	+	0.447939i	−0.869423	−	0.494069i	$-0.835509\pi$
$937$	−1.25960e13	+	1.05693e13i	−0.533833	+	0.447939i	0.335590	+	0.942008i	$0.391064\pi$
$938$	−4.62497e12	−	8.01068e12i	−0.195073	−	0.337876i
$939$	1.09295e13	−	1.89305e13i	0.458782	−	0.794634i
$940$	−9.68166e11	−	5.49074e12i	−0.0404459	−	0.229380i
$941$	2.32310e12	+	1.31750e13i	0.0965862	+	0.547768i	0.994250	+	0.107086i	$0.0341521\pi$
$941$	2.32310e12	+	1.31750e13i	0.0965862	+	0.547768i	−0.897664	+	0.440682i	$0.854737\pi$
$942$	1.22192e13	−	2.11642e13i	0.505607	−	0.875737i
$943$	−1.07276e12	−	1.85807e12i	−0.0441772	−	0.0765172i
$944$	−8.14853e12	+	6.83743e12i	−0.333968	+	0.280233i
$945$	8.73936e12	−	3.18087e12i	0.356481	−	0.129749i
$946$	5.88439e12	+	2.14174e12i	0.238886	+	0.0869475i
$947$	−2.38117e13	−	1.99804e13i	−0.962090	−	0.807290i	0.0192014	−	0.999816i	$-0.493888\pi$
$947$	−2.38117e13	−	1.99804e13i	−0.962090	−	0.807290i	−0.981292	+	0.192526i	$0.938332\pi$
$948$	−6.71051e12	+	3.80572e13i	−0.269847	+	1.53038i
$949$	1.05439e12			0.0421990
$950$	1.29910e13	+	9.03249e12i	0.517470	+	0.359792i
$951$	−1.60604e13			−0.636712
$952$	−2.54647e11	+	1.44418e12i	−0.0100478	+	0.0569841i
$953$	1.15775e12	+	9.71467e11i	0.0454670	+	0.0381514i	0.665238	−	0.746631i	$-0.268330\pi$
$953$	1.15775e12	+	9.71467e11i	0.0454670	+	0.0381514i	−0.619771	+	0.784783i	$0.712775\pi$
$954$	1.80612e13	+	6.57373e12i	0.705957	+	0.256948i
$955$	−1.03613e13	+	3.77122e12i	−0.403089	+	0.146712i
$956$	−3.82785e12	+	3.21195e12i	−0.148216	+	0.124368i
$957$	2.84199e12	+	4.92247e12i	0.109526	+	0.189705i
$958$	−2.00740e12	+	3.47691e12i	−0.0769995	+	0.133367i
$959$	−4.03949e12	−	2.29091e13i	−0.154221	−	0.874630i
$960$	3.01618e11	+	1.71056e12i	0.0114614	+	0.0650007i
$961$	1.32186e13	−	2.28953e13i	0.499954	−	0.865945i
$962$	7.98782e11	+	1.38353e12i	0.0300705	+	0.0520836i
$963$	−1.83214e13	+	1.53735e13i	−0.686499	+	0.576041i
$964$	4.46758e11	−	1.62607e11i	0.0166620	−	0.00606446i
$965$	1.10065e13	+	4.00603e12i	0.408578	+	0.148710i
$966$	−4.01254e12	−	3.36692e12i	−0.148259	−	0.124404i
$967$	−8.21202e12	+	4.65727e13i	−0.302017	+	1.71282i	0.335208	+	0.942144i	$0.391193\pi$
$967$	−8.21202e12	+	4.65727e13i	−0.302017	+	1.71282i	−0.637225	+	0.770678i	$0.719918\pi$
$968$	−7.36774e12			−0.269709
$969$	−2.37597e12	+	5.13959e12i	−0.0865731	+	0.187271i
$970$	−7.10116e12			−0.257547
$971$	−3.69717e12	+	2.09677e13i	−0.133470	+	0.756944i	0.842443	+	0.538785i	$0.181116\pi$
$971$	−3.69717e12	+	2.09677e13i	−0.133470	+	0.756944i	−0.975913	+	0.218160i	$0.929995\pi$
$972$	1.16140e13	+	9.74533e12i	0.417335	+	0.350186i
$973$	1.02860e13	+	3.74380e12i	0.367907	+	0.133907i
$974$	3.03663e13	−	1.10524e13i	1.08113	−	0.393498i
$975$	−1.40065e12	+	1.17529e12i	−0.0496375	+	0.0416508i
$976$	−2.96690e12	−	5.13881e12i	−0.104659	−	0.181275i
$977$	4.29810e12	−	7.44452e12i	0.150921	−	0.261403i	−0.780645	−	0.624975i	$-0.785109\pi$
$977$	4.29810e12	−	7.44452e12i	0.150921	−	0.261403i	0.931566	+	0.363571i	$0.118443\pi$
$978$	−1.92590e12	−	1.09223e13i	−0.0673147	−	0.381760i
$979$	1.42835e11	+	8.10058e11i	0.00496950	+	0.0281834i
$980$	1.46202e12	−	2.53230e12i	0.0506334	−	0.0876996i
$981$	2.27458e13	+	3.93969e13i	0.784135	+	1.35816i
$982$	−6.29654e12	+	5.28343e12i	−0.216073	+	0.181307i
$983$	−4.62321e12	+	1.68271e12i	−0.157926	+	0.0574803i	−0.419773	−	0.907629i	$-0.637890\pi$
$983$	−4.62321e12	+	1.68271e12i	−0.157926	+	0.0574803i	0.261848	+	0.965109i	$0.415668\pi$
$984$	−1.02808e13	−	3.74191e12i	−0.349582	−	0.127238i
$985$	−5.46623e12	−	4.58671e12i	−0.185023	−	0.155252i
$986$	1.31827e11	−	7.47631e11i	0.00444181	−	0.0251907i
$987$	8.57370e13			2.87568
$988$	4.79028e11	−	4.82207e11i	0.0159939	−	0.0161001i
$989$	2.98742e12			0.0992915
$990$	−9.32690e11	+	5.28955e12i	−0.0308588	+	0.175009i
$991$	−3.82624e13	−	3.21059e13i	−1.26020	−	1.05744i	−0.995660	−	0.0930619i	$-0.970335\pi$
$991$	−3.82624e13	−	3.21059e13i	−1.26020	−	1.05744i	−0.264543	−	0.964374i	$-0.585221\pi$
$992$	4.87271e10	+	1.77352e10i	0.00159760	+	0.000581479i
$993$	−1.30627e12	+	4.75442e11i	−0.0426344	+	0.0155176i
$994$	3.91746e13	−	3.28714e13i	1.27282	−	1.06802i
$995$	2.11082e12	+	3.65605e12i	0.0682728	+	0.118252i
$996$	−2.00984e13	+	3.48115e13i	−0.647134	+	1.12087i
$997$	4.90062e12	+	2.77928e13i	0.157081	+	0.890849i	0.956859	+	0.290553i	$0.0938394\pi$
$997$	4.90062e12	+	2.77928e13i	0.157081	+	0.890849i	−0.799778	+	0.600296i	$0.795049\pi$
$998$	−5.00611e12	−	2.83910e13i	−0.159740	−	0.905928i
$999$	2.67138e13	−	4.62696e13i	0.848576	−	1.46978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.b.17.1	yes	48
19.9	even	9	inner	38.10.e.b.9.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.b.9.1	✓	48	19.9	even	9	inner
38.10.e.b.17.1	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.77837 - 15.7569i) q^{2} +(-172.140 - 144.442i) q^{3} +(-240.561 - 87.5572i) q^{4} +(432.938 - 157.576i) q^{5} +(-2754.24 + 2311.08i) q^{6} +(4035.63 + 6989.91i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(5350.58 + 30344.6i) q^{9} +O(q^{10})\)	\(q+(2.77837 - 15.7569i) q^{2} +(-172.140 - 144.442i) q^{3} +(-240.561 - 87.5572i) q^{4} +(432.938 - 157.576i) q^{5} +(-2754.24 + 2311.08i) q^{6} +(4035.63 + 6989.91i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(5350.58 + 30344.6i) q^{9} +(-1280.06 - 7259.57i) q^{10} +(-11823.5 + 20478.9i) q^{11} +(28763.2 + 49819.3i) q^{12} +(-3580.47 + 3004.37i) q^{13} +(121352. - 44168.5i) q^{14} +(-97286.6 - 35409.4i) q^{15} +(50203.5 + 42125.7i) q^{16} +(7702.60 - 43683.6i) q^{17} +493004. q^{18} +(514037. - 241773. i) q^{19} -117945. q^{20} +(314948. - 1.78616e6i) q^{21} +(289835. + 243200. i) q^{22} +(169614. + 61734.6i) q^{23} +(864915. - 314803. i) q^{24} +(-1.33358e6 + 1.11900e6i) q^{25} +(37391.7 + 64764.4i) q^{26} +(1.25050e6 - 2.16593e6i) q^{27} +(-358799. - 2.03485e6i) q^{28} +(185746. + 1.05342e6i) q^{29} +(-828242. + 1.43456e6i) q^{30} +(24726.1 + 42826.8i) q^{31} +(803256. - 674012. i) q^{32} +(4.99333e6 - 1.81742e6i) q^{33} +(-666919. - 242739. i) q^{34} +(2.84862e6 + 2.39028e6i) q^{35} +(1.36975e6 - 7.76823e6i) q^{36} +2.13625e7 q^{37} +(-2.38141e6 - 8.77137e6i) q^{38} +1.05030e6 q^{39} +(-327695. + 1.85845e6i) q^{40} +(-9.10559e6 - 7.64050e6i) q^{41} +(-2.72693e7 - 9.92522e6i) q^{42} +(1.55527e7 - 5.66070e6i) q^{43} +(4.63736e6 - 3.89121e6i) q^{44} +(7.09807e6 + 1.22942e7i) q^{45} +(1.44400e6 - 2.50108e6i) q^{46} +(8.20862e6 + 4.65534e7i) q^{47} +(-2.55728e6 - 1.45030e7i) q^{48} +(-1.23958e7 + 2.14702e7i) q^{49} +(1.39269e7 + 2.41221e7i) q^{50} +(-7.63570e6 + 6.40711e6i) q^{51} +(1.12438e6 - 409239. i) q^{52} +(3.66350e7 + 1.33340e7i) q^{53} +(-3.06540e7 - 2.57217e7i) q^{54} +(-1.89185e6 + 1.07292e7i) q^{55} -3.30599e7 q^{56} +(-1.23408e8 - 3.26301e7i) q^{57} +1.71147e7 q^{58} +(-2.81848e7 + 1.59844e8i) q^{59} +(2.03030e7 + 1.70363e7i) q^{60} +(-8.50821e7 - 3.09673e7i) q^{61} +(743517. - 270618. i) q^{62} +(-1.90513e8 + 1.59860e8i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-1.07670e6 + 1.86490e6i) q^{65} +(-1.47637e7 - 8.37289e7i) q^{66} +(-1.24379e7 - 7.05390e7i) q^{67} +(-5.67776e6 + 9.83417e6i) q^{68} +(-2.02803e7 - 3.51265e7i) q^{69} +(4.55780e7 - 3.82445e7i) q^{70} +(3.72113e8 - 1.35438e8i) q^{71} +(-1.18598e8 - 4.31660e7i) q^{72} +(-1.72810e8 - 1.45005e8i) q^{73} +(5.93530e7 - 3.36608e8i) q^{74} +3.91193e8 q^{75} +(-1.44826e8 + 1.31535e7i) q^{76} -1.90861e8 q^{77} +(2.91812e6 - 1.65495e7i) q^{78} +(5.14602e8 + 4.31803e8i) q^{79} +(2.83730e7 + 1.03269e7i) q^{80} +(4.17995e7 - 1.52138e7i) q^{81} +(-1.45689e8 + 1.22248e8i) q^{82} +(3.49377e8 + 6.05138e8i) q^{83} +(-2.32155e8 + 4.02105e8i) q^{84} +(-3.54877e6 - 2.01260e7i) q^{85} +(-4.59842e7 - 2.60790e8i) q^{86} +(1.20184e8 - 2.08164e8i) q^{87} +(-4.84291e7 - 8.38817e7i) q^{88} +(2.66466e7 - 2.23592e7i) q^{89} +(2.13440e8 - 7.76858e7i) q^{90} +(-3.54497e7 - 1.29026e7i) q^{91} +(-3.53974e7 - 2.97019e7i) q^{92} +(1.92967e6 - 1.09437e7i) q^{93} +7.56345e8 q^{94} +(1.84448e8 - 1.85673e8i) q^{95} -2.35628e8 q^{96} +(1.67278e8 - 9.48683e8i) q^{97} +(3.03864e8 + 2.54972e8i) q^{98} +(-6.84688e8 - 2.49206e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9 - 55221 * q^11 - 62208 * q^12 + 21777 * q^13 + 28464 * q^14 - 280011 * q^15 + 1055055 * q^17 + 6083232 * q^18 + 2408220 * q^19 + 523776 * q^20 - 5105673 * q^21 - 2513280 * q^22 - 456708 * q^23 + 135168 * q^24 + 19417530 * q^25 - 1077120 * q^26 - 11729661 * q^27 - 30720 * q^28 + 4679889 * q^29 + 4879158 * q^31 - 12360834 * q^33 + 9206400 * q^34 - 47475759 * q^35 + 2035968 * q^36 + 119843604 * q^37 - 39471312 * q^38 + 16552668 * q^39 + 60082911 * q^41 + 59187024 * q^42 + 109939059 * q^43 - 40212480 * q^44 + 3067236 * q^45 - 4919424 * q^46 + 198627789 * q^47 - 4325376 * q^48 - 182954115 * q^49 - 229688016 * q^50 - 228228021 * q^51 - 49495296 * q^52 - 370799859 * q^53 + 111760416 * q^54 - 60369543 * q^55 + 211427328 * q^56 + 128158266 * q^57 + 166196064 * q^58 - 382689396 * q^59 - 36777216 * q^60 - 850085550 * q^61 + 42954480 * q^62 - 803298357 * q^63 - 402653184 * q^64 + 261122181 * q^65 + 516819888 * q^66 + 1146400764 * q^67 + 125611008 * q^68 - 178115667 * q^69 - 759612144 * q^70 + 363378456 * q^71 - 65150976 * q^72 + 1407478230 * q^73 - 12153360 * q^74 + 1715917770 * q^75 - 128288256 * q^76 - 193134048 * q^77 - 1199414208 * q^78 - 2098405449 * q^79 + 3082805319 * q^81 + 961326576 * q^82 + 358330707 * q^83 + 502249728 * q^84 - 1961566422 * q^85 - 588638592 * q^86 - 1222269090 * q^87 - 226185216 * q^88 - 368108670 * q^89 + 1740707616 * q^90 - 3296437032 * q^91 - 819648768 * q^92 + 6597152658 * q^93 + 2953278144 * q^94 - 881990403 * q^95 + 509607936 * q^96 - 3752161206 * q^97 - 458055696 * q^98 + 6061589742 * q^99

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