LMFDB - Embedded newform 43.11.d.a.37.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, 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:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.18
Character	$\chi$	$=$	43.37
Dual form			43.11.d.a.7.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.41302i q^{2} +(42.4427 + 24.5043i) q^{3} +994.699 q^{4} +(1000.11 + 577.412i) q^{5} +(132.642 - 229.743i) q^{6} +(-21227.5 + 12255.7i) q^{7} -10927.3i q^{8} +(-28323.6 - 49057.9i) q^{9} +O(q^{10})$	\(q-5.41302i q^{2} +(42.4427 + 24.5043i) q^{3} +994.699 q^{4} +(1000.11 + 577.412i) q^{5} +(132.642 - 229.743i) q^{6} +(-21227.5 + 12255.7i) q^{7} -10927.3i q^{8} +(-28323.6 - 49057.9i) q^{9} +(3125.54 - 5413.60i) q^{10} -122185. q^{11} +(42217.7 + 24374.4i) q^{12} +(-265812. - 460400. i) q^{13} +(66340.4 + 114905. i) q^{14} +(28298.2 + 49013.9i) q^{15} +959423. q^{16} +(983096. + 1.70277e6i) q^{17} +(-265551. + 153316. i) q^{18} +(-2.64211e6 - 1.52542e6i) q^{19} +(994806. + 574352. i) q^{20} -1.20127e6 q^{21} +661392. i q^{22} +(4.11108e6 - 7.12060e6i) q^{23} +(267765. - 463782. i) q^{24} +(-4.21600e6 - 7.30233e6i) q^{25} +(-2.49215e6 + 1.43885e6i) q^{26} -5.67011e6i q^{27} +(-2.11150e7 + 1.21908e7i) q^{28} +(-7.84645e6 + 4.53015e6i) q^{29} +(265313. - 153178. i) q^{30} +(2.94580e6 - 5.10227e6i) q^{31} -1.63829e7i q^{32} +(-5.18588e6 - 2.99407e6i) q^{33} +(9.21713e6 - 5.32151e6i) q^{34} -2.83064e7 q^{35} +(-2.81734e7 - 4.87978e7i) q^{36} +(-5.42299e7 - 3.13096e7i) q^{37} +(-8.25714e6 + 1.43018e7i) q^{38} -2.60542e7i q^{39} +(6.30953e6 - 1.09284e7i) q^{40} -1.05884e8 q^{41} +6.50250e6i q^{42} +(9.19026e7 + 1.14741e8i) q^{43} -1.21538e8 q^{44} -6.54175e7i q^{45} +(-3.85439e7 - 2.22533e7i) q^{46} -2.76335e8 q^{47} +(4.07205e7 + 2.35100e7i) q^{48} +(1.59168e8 - 2.75687e8i) q^{49} +(-3.95276e7 + 2.28213e7i) q^{50} +9.63603e7i q^{51} +(-2.64403e8 - 4.57960e8i) q^{52} +(5.92347e7 - 1.02598e8i) q^{53} -3.06924e7 q^{54} +(-1.22199e8 - 7.05514e7i) q^{55} +(1.33921e8 + 2.31959e8i) q^{56} +(-7.47589e7 - 1.29486e8i) q^{57} +(2.45218e7 + 4.24730e7i) q^{58} -4.28718e8 q^{59} +(2.81482e7 + 4.87541e7i) q^{60} +(1.37229e8 - 7.92292e7i) q^{61} +(-2.76187e7 - 1.59456e7i) q^{62} +(1.20248e9 + 6.94252e8i) q^{63} +8.93768e8 q^{64} -6.13933e8i q^{65} +(-1.62069e7 + 2.80713e7i) q^{66} +(-9.81598e8 + 1.70018e9i) q^{67} +(9.77885e8 + 1.69375e9i) q^{68} +(3.48971e8 - 2.01478e8i) q^{69} +1.53223e8i q^{70} +(1.90625e8 - 1.10057e8i) q^{71} +(-5.36068e8 + 3.09499e8i) q^{72} +(2.41472e9 - 1.39414e9i) q^{73} +(-1.69480e8 + 2.93547e8i) q^{74} -4.13241e8i q^{75} +(-2.62811e9 - 1.51734e9i) q^{76} +(2.59369e9 - 1.49747e9i) q^{77} -1.41032e8 q^{78} +(1.30084e9 + 2.25311e9i) q^{79} +(9.59526e8 + 5.53982e8i) q^{80} +(-1.53354e9 + 2.65616e9i) q^{81} +5.73154e8i q^{82} +(1.77799e8 - 3.07956e8i) q^{83} -1.19490e9 q^{84} +2.27061e9i q^{85} +(6.21092e8 - 4.97470e8i) q^{86} -4.44033e8 q^{87} +1.33515e9i q^{88} +(2.93454e9 + 1.69426e9i) q^{89} -3.54106e8 q^{90} +(1.12851e10 + 6.51544e9i) q^{91} +(4.08929e9 - 7.08285e9i) q^{92} +(2.50055e8 - 1.44369e8i) q^{93} +1.49581e9i q^{94} +(-1.76160e9 - 3.05117e9i) q^{95} +(4.01451e8 - 6.95333e8i) q^{96} -1.60853e10 q^{97} +(-1.49230e9 - 8.61577e8i) q^{98} +(3.46073e9 + 5.99416e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) $ 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9 - 127061 * q^10 + 521524 * q^11 - 606618 * q^12 + 796742 * q^13 - 865794 * q^14 - 433513 * q^15 + 22423366 * q^16 - 1768471 * q^17 - 11957547 * q^18 - 122844 * q^19 + 419841 * q^20 - 26778860 * q^21 + 16414886 * q^23 + 8684578 * q^24 + 70516989 * q^25 + 3069 * q^26 - 97624092 * q^28 + 118701393 * q^29 - 1455921 * q^30 + 10824883 * q^31 + 315141798 * q^33 + 47529561 * q^34 - 333788722 * q^35 - 597728908 * q^36 - 169881246 * q^37 - 88887452 * q^38 + 570788831 * q^40 - 543049070 * q^41 + 408159179 * q^43 - 754130886 * q^44 + 270181896 * q^46 + 348527658 * q^47 + 175039227 * q^48 + 781091547 * q^49 - 663244398 * q^50 - 1853993086 * q^52 + 219922736 * q^53 + 3104867360 * q^54 + 2154394182 * q^55 + 2010912675 * q^56 + 349107351 * q^57 + 2023447828 * q^58 + 2247595680 * q^59 - 2906780465 * q^60 + 508093974 * q^61 - 3451752063 * q^62 + 158921973 * q^63 - 13473879716 * q^64 + 1277847051 * q^66 - 2812410281 * q^67 + 13614613118 * q^68 - 5113655829 * q^69 + 2418191196 * q^71 + 26243329290 * q^72 - 6537901611 * q^73 - 2632816966 * q^74 - 10170994206 * q^76 - 16936463889 * q^77 - 24146069696 * q^78 + 5397136602 * q^79 + 7242149661 * q^80 - 15745886176 * q^81 + 4998656042 * q^83 + 44726677232 * q^84 - 27688564866 * q^86 + 37895576172 * q^87 - 12151857357 * q^89 - 96024912764 * q^90 + 36633770214 * q^91 - 31643971023 * q^92 + 59768940153 * q^93 - 19802964089 * q^95 - 3289705262 * q^96 - 40329658574 * q^97 + 19243888221 * q^98 + 18506221111 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	5.41302i		−	0.169157i	−0.996417	−	0.0845784i	$-0.973046\pi$
$2$		−	5.41302i		−	0.169157i	0.996417	−	0.0845784i	$-0.0269543\pi$
$3$	42.4427	+	24.5043i	0.174661	+	0.100841i	0.584782	−	0.811191i	$-0.301180\pi$
$3$	42.4427	+	24.5043i	0.174661	+	0.100841i	−0.410121	+	0.912031i	$0.634513\pi$
$4$	994.699			0.971386
$5$	1000.11	+	577.412i	0.320034	+	0.184772i	0.651408	−	0.758728i	$-0.274179\pi$
$5$	1000.11	+	577.412i	0.320034	+	0.184772i	−0.331374	+	0.943500i	$0.607512\pi$
$6$	132.642	−	229.743i	0.0170579	−	0.0295451i
$7$	−21227.5	+	12255.7i	−1.26302	+	0.729203i	−0.973657	−	0.228017i	$-0.926776\pi$
$7$	−21227.5	+	12255.7i	−1.26302	+	0.729203i	−0.289360	+	0.957220i	$0.593442\pi$
$8$		−	10927.3i		−	0.333473i
$9$	−28323.6	−	49057.9i	−0.479662	−	0.830799i
$10$	3125.54	−	5413.60i	0.0312554	−	0.0541360i
$11$	−122185.			−0.758675			−0.379338	−	0.925258i	$-0.623848\pi$
$11$	−122185.			−0.758675			−0.379338	+	0.925258i	$0.623848\pi$
$12$	42217.7	+	24374.4i	0.169664	+	0.0979553i
$13$	−265812.	−	460400.i	−0.715909	−	1.23999i	−0.962608	−	0.270899i	$-0.912679\pi$
$13$	−265812.	−	460400.i	−0.715909	−	1.23999i	0.246698	−	0.969092i	$-0.420654\pi$
$14$	66340.4	+	114905.i	0.123350	+	0.213648i
$15$	28298.2	+	49013.9i	0.0372651	+	0.0645450i
$16$	959423.			0.914977
$17$	983096.	+	1.70277e6i	0.692391	+	1.19926i	0.971052	+	0.238867i	$0.0767759\pi$
$17$	983096.	+	1.70277e6i	0.692391	+	1.19926i	−0.278662	+	0.960389i	$0.589891\pi$
$18$	−265551.	+	153316.i	−0.140535	+	0.0811381i
$19$	−2.64211e6	−	1.52542e6i	−1.06705	−	0.616059i	−0.139673	−	0.990198i	$-0.544605\pi$
$19$	−2.64211e6	−	1.52542e6i	−1.06705	−	0.616059i	−0.927373	+	0.374139i	$0.877938\pi$
$20$	994806.	+	574352.i	0.310877	+	0.179485i
$21$	−1.20127e6			−0.294134
$22$			661392.i			0.128335i
$23$	4.11108e6	−	7.12060e6i	0.638729	−	1.10631i	−0.346983	−	0.937871i	$-0.612794\pi$
$23$	4.11108e6	−	7.12060e6i	0.638729	−	1.10631i	0.985712	−	0.168440i	$-0.0538729\pi$
$24$	267765.	−	463782.i	0.0336277	−	0.0582449i
$25$	−4.21600e6	−	7.30233e6i	−0.431719	−	0.747759i
$26$	−2.49215e6	+	1.43885e6i	−0.209753	+	0.121101i
$27$		−	5.67011e6i		−	0.395160i
$28$	−2.11150e7	+	1.21908e7i	−1.22688	+	0.708338i
$29$	−7.84645e6	+	4.53015e6i	−0.382546	+	0.220863i	−0.678925	−	0.734207i	$-0.737554\pi$
$29$	−7.84645e6	+	4.53015e6i	−0.382546	+	0.220863i	0.296380	+	0.955070i	$0.404221\pi$
$30$	265313.	−	153178.i	0.0109182	−	0.00630364i
$31$	2.94580e6	−	5.10227e6i	0.102895	−	0.178219i	−0.809981	−	0.586456i	$-0.800523\pi$
$31$	2.94580e6	−	5.10227e6i	0.102895	−	0.178219i	0.912876	+	0.408236i	$0.133856\pi$
$32$		−	1.63829e7i		−	0.488248i
$33$	−5.18588e6	−	2.99407e6i	−0.132511	−	0.0765054i
$34$	9.21713e6	−	5.32151e6i	0.202862	−	0.117123i
$35$	−2.83064e7			−0.538945
$36$	−2.81734e7	−	4.87978e7i	−0.465937	−	0.807027i
$37$	−5.42299e7	−	3.13096e7i	−0.782042	−	0.451512i	0.0551116	−	0.998480i	$-0.482449\pi$
$37$	−5.42299e7	−	3.13096e7i	−0.782042	−	0.451512i	−0.837153	+	0.546968i	$0.815782\pi$
$38$	−8.25714e6	+	1.43018e7i	−0.104211	+	0.180498i
$39$		−	2.60542e7i		−	0.288771i
$40$	6.30953e6	−	1.09284e7i	0.0616165	−	0.106723i
$41$	−1.05884e8			−0.913929			−0.456965	−	0.889485i	$-0.651063\pi$
$41$	−1.05884e8			−0.913929			−0.456965	+	0.889485i	$0.651063\pi$
$42$			6.50250e6i			0.0497547i
$43$	9.19026e7	+	1.14741e8i	0.625152	+	0.780503i
$43$	9.19026e7	+	1.14741e8i	0.625152	+	0.780503i
$44$	−1.21538e8			−0.736967
$45$		−	6.54175e7i		−	0.354513i
$46$	−3.85439e7	−	2.22533e7i	−0.187140	−	0.108045i
$47$	−2.76335e8			−1.20489			−0.602444	−	0.798161i	$-0.705806\pi$
$47$	−2.76335e8			−1.20489			−0.602444	+	0.798161i	$0.705806\pi$
$48$	4.07205e7	+	2.35100e7i	0.159811	+	0.0922670i
$49$	1.59168e8	−	2.75687e8i	0.563475	−	0.975967i
$50$	−3.95276e7	+	2.28213e7i	−0.126488	+	0.0730281i
$51$			9.63603e7i			0.279285i
$52$	−2.64403e8	−	4.57960e8i	−0.695424	−	1.20451i
$53$	5.92347e7	−	1.02598e8i	0.141644	−	0.245334i	−0.786472	−	0.617626i	$-0.788095\pi$
$53$	5.92347e7	−	1.02598e8i	0.141644	−	0.245334i	0.928116	+	0.372292i	$0.121428\pi$
$54$	−3.06924e7			−0.0668439
$55$	−1.22199e8	−	7.05514e7i	−0.242802	−	0.140182i
$56$	1.33921e8	+	2.31959e8i	0.243170	+	0.421182i
$57$	−7.47589e7	−	1.29486e8i	−0.124248	−	0.215203i
$58$	2.45218e7	+	4.24730e7i	0.0373605	+	0.0647102i
$59$	−4.28718e8			−0.599670			−0.299835	−	0.953991i	$-0.596932\pi$
$59$	−4.28718e8			−0.599670			−0.299835	+	0.953991i	$0.596932\pi$
$60$	2.81482e7	+	4.87541e7i	0.0361988	+	0.0626981i
$61$	1.37229e8	−	7.92292e7i	0.162479	−	0.0938071i	−0.416556	−	0.909110i	$-0.636763\pi$
$61$	1.37229e8	−	7.92292e7i	0.162479	−	0.0938071i	0.579035	+	0.815303i	$0.303430\pi$
$62$	−2.76187e7	−	1.59456e7i	−0.0301470	−	0.0174054i
$63$	1.20248e9	+	6.94252e8i	1.21164	+	0.699543i
$64$	8.93768e8			0.832386
$65$		−	6.13933e8i		−	0.529120i
$66$	−1.62069e7	+	2.80713e7i	−0.0129414	+	0.0224152i
$67$	−9.81598e8	+	1.70018e9i	−0.727042	+	1.25927i	0.231085	+	0.972934i	$0.425772\pi$
$67$	−9.81598e8	+	1.70018e9i	−0.727042	+	1.25927i	−0.958128	+	0.286341i	$0.907561\pi$
$68$	9.77885e8	+	1.69375e9i	0.672579	+	1.16494i
$69$	3.48971e8	−	2.01478e8i	0.223123	−	0.128820i
$70$			1.53223e8i			0.0911662i
$71$	1.90625e8	−	1.10057e8i	0.105655	−	0.0609997i	−0.446242	−	0.894913i	$-0.647238\pi$
$71$	1.90625e8	−	1.10057e8i	0.105655	−	0.0609997i	0.551896	+	0.833913i	$0.313904\pi$
$72$	−5.36068e8	+	3.09499e8i	−0.277049	+	0.159955i
$73$	2.41472e9	−	1.39414e9i	1.16480	−	0.672500i	0.212353	−	0.977193i	$-0.431887\pi$
$73$	2.41472e9	−	1.39414e9i	1.16480	−	0.672500i	0.952451	+	0.304693i	$0.0985539\pi$
$74$	−1.69480e8	+	2.93547e8i	−0.0763763	+	0.132288i
$75$		−	4.13241e8i		−	0.174139i
$76$	−2.62811e9	−	1.51734e9i	−1.03651	−	0.598431i
$77$	2.59369e9	−	1.49747e9i	0.958220	−	0.553229i
$78$	−1.41032e8			−0.0488476
$79$	1.30084e9	+	2.25311e9i	0.422753	+	0.732230i	0.996208	−	0.0870073i	$-0.0277304\pi$
$79$	1.30084e9	+	2.25311e9i	0.422753	+	0.732230i	−0.573454	+	0.819237i	$0.694397\pi$
$80$	9.59526e8	+	5.53982e8i	0.292824	+	0.169062i
$81$	−1.53354e9	+	2.65616e9i	−0.439814	+	0.761780i
$82$			5.73154e8i			0.154597i
$83$	1.77799e8	−	3.07956e8i	0.0451376	−	0.0781806i	−0.842574	−	0.538581i	$-0.818961\pi$
$83$	1.77799e8	−	3.07956e8i	0.0451376	−	0.0781806i	0.887712	+	0.460400i	$0.152294\pi$
$84$	−1.19490e9			−0.285717
$85$			2.27061e9i			0.511737i
$86$	6.21092e8	−	4.97470e8i	0.132027	−	0.105749i
$87$	−4.44033e8			−0.0890879
$88$			1.33515e9i			0.252998i
$89$	2.93454e9	+	1.69426e9i	0.525520	+	0.303409i	0.739190	−	0.673497i	$-0.235208\pi$
$89$	2.93454e9	+	1.69426e9i	0.525520	+	0.303409i	−0.213670	+	0.976906i	$0.568542\pi$
$90$	−3.54106e8			−0.0599682
$91$	1.12851e10	+	6.51544e9i	1.80841	+	1.04409i
$92$	4.08929e9	−	7.08285e9i	0.620453	−	1.07466i
$93$	2.50055e8	−	1.44369e8i	0.0359436	−	0.0207520i
$94$			1.49581e9i			0.203815i
$95$	−1.76160e9	−	3.05117e9i	−0.227661	−	0.394320i
$96$	4.01451e8	−	6.95333e8i	0.0492353	−	0.0852780i
$97$	−1.60853e10			−1.87315			−0.936573	−	0.350472i	$-0.886021\pi$
$97$	−1.60853e10			−1.87315			−0.936573	+	0.350472i	$0.886021\pi$
$98$	−1.49230e9	−	8.61577e8i	−0.165091	−	0.0953156i
$99$	3.46073e9	+	5.99416e9i	0.363908	+	0.630307i
$100$	−4.19365e9	−	7.26362e9i	−0.419365	−	0.726362i
$101$	−5.55491e9	−	9.62138e9i	−0.528530	−	0.915441i	−0.999447	−	0.0332636i	$-0.989410\pi$
$101$	−5.55491e9	−	9.62138e9i	−0.528530	−	0.915441i	0.470916	−	0.882178i	$-0.343923\pi$
$102$	5.21600e8			0.0472429
$103$	6.41776e8	+	1.11159e9i	0.0553602	+	0.0958867i	0.892377	−	0.451290i	$-0.149036\pi$
$103$	6.41776e8	+	1.11159e9i	0.0553602	+	0.0958867i	−0.837017	+	0.547177i	$0.815703\pi$
$104$	−5.03091e9	+	2.90460e9i	−0.413504	+	0.238737i
$105$	−1.20140e9	−	6.93629e8i	−0.0941329	−	0.0543476i
$106$	−5.55362e8	−	3.20639e8i	−0.0414999	−	0.0239600i
$107$	1.61111e10			1.14870			0.574351	−	0.818609i	$-0.305254\pi$
$107$	1.61111e10			1.14870			0.574351	+	0.818609i	$0.305254\pi$
$108$		−	5.64005e9i		−	0.383852i
$109$	−5.30190e7	+	9.18317e7i	−0.00344587	+	0.00596843i	−0.867743	−	0.497013i	$-0.834430\pi$
$109$	−5.30190e7	+	9.18317e7i	−0.00344587	+	0.00596843i	0.864297	+	0.502981i	$0.167764\pi$
$110$	−3.81896e8	+	6.61463e8i	−0.0237127	+	0.0410716i
$111$	−1.53444e9	−	2.65773e9i	−0.0910616	−	0.157723i
$112$	−2.03662e10	+	1.17584e10i	−1.15563	+	0.667204i
$113$		−	3.04877e10i		−	1.65475i	−0.561651	−	0.827375i	$-0.689833\pi$
$113$		−	3.04877e10i		−	1.65475i	0.561651	−	0.827375i	$-0.310167\pi$
$114$	−7.00911e8	+	4.04671e8i	−0.0364031	+	0.0210173i
$115$	8.22304e9	−	4.74758e9i	0.408831	−	0.236038i
$116$	−7.80486e9	+	4.50614e9i	−0.371600	+	0.214543i
$117$	−1.50575e10	+	2.60804e10i	−0.686790	+	1.18955i
$118$			2.32066e9i			0.101438i
$119$	−4.17374e10	−	2.40971e10i	−1.74900	−	1.00979i
$120$	5.35587e8	−	3.09221e8i	0.0215240	−	0.0124269i
$121$	−1.10081e10			−0.424412
$122$	−4.28869e8	−	7.42822e8i	−0.0158681	−	0.0274844i
$123$	−4.49402e9	−	2.59462e9i	−0.159628	−	0.0921613i
$124$	2.93018e9	−	5.07522e9i	0.0999508	−	0.173120i
$125$		−	2.10151e10i		−	0.688622i
$126$	3.75800e9	−	6.50904e9i	0.118332	−	0.204958i
$127$	9.26831e9			0.280532			0.140266	−	0.990114i	$-0.455204\pi$
$127$	9.26831e9			0.280532			0.140266	+	0.990114i	$0.455204\pi$
$128$		−	2.16140e10i		−	0.629051i
$129$	1.08896e9	+	7.12191e9i	0.0304833	+	0.199365i
$130$	−3.32323e9			−0.0895042
$131$			3.59493e10i			0.931825i	0.884831	+	0.465912i	$0.154274\pi$
$131$			3.59493e10i			0.931825i	−0.884831	+	0.465912i	$0.845726\pi$
$132$	−5.15839e9	−	2.97820e9i	−0.128720	−	0.0743163i
$133$	7.47806e10			1.79693
$134$	9.20309e9	+	5.31341e9i	0.213015	+	0.122984i
$135$	3.27399e9	−	5.67072e9i	0.0730144	−	0.126465i
$136$	1.86066e10	−	1.07425e10i	0.399920	−	0.230894i
$137$			8.57751e10i			1.77729i	0.458595	+	0.888646i	$0.348353\pi$
$137$			8.57751e10i			1.77729i	−0.458595	+	0.888646i	$0.651647\pi$
$138$	−1.09061e9	−	1.88898e9i	−0.0217907	−	0.0377427i
$139$	−1.82866e9	+	3.16732e9i	−0.0352418	+	0.0610406i	−0.883108	−	0.469169i	$-0.844553\pi$
$139$	−1.82866e9	+	3.16732e9i	−0.0352418	+	0.0610406i	0.847867	+	0.530210i	$0.177887\pi$
$140$	−2.81564e10			−0.523524
$141$	−1.17284e10	−	6.77140e9i	−0.210447	−	0.121502i
$142$	−5.95742e8	−	1.03186e9i	−0.0103185	−	0.0178722i
$143$	3.24784e10	+	5.62542e10i	0.543143	+	0.940751i
$144$	−2.71743e10	−	4.70672e10i	−0.438880	−	0.760162i
$145$	−1.04631e10			−0.163237
$146$	−7.54650e9	−	1.30709e10i	−0.113758	−	0.197034i
$147$	1.35110e10	−	7.80059e9i	0.196835	−	0.113642i
$148$	−5.39424e10	−	3.11437e10i	−0.759664	−	0.438592i
$149$	6.23631e10	+	3.60054e10i	0.849174	+	0.490271i	0.860372	−	0.509667i	$-0.170231\pi$
$149$	6.23631e10	+	3.60054e10i	0.849174	+	0.490271i	−0.0111983	+	0.999937i	$0.503565\pi$
$150$	−2.23688e9			−0.0294568
$151$			6.03532e10i			0.768804i	0.923166	+	0.384402i	$0.125592\pi$
$151$			6.03532e10i			0.768804i	−0.923166	+	0.384402i	$0.874408\pi$
$152$	−1.66687e10	+	2.88710e10i	−0.205439	+	0.355831i
$153$	5.56896e10	−	9.64572e10i	0.664227	−	1.15048i
$154$	−8.10583e9	−	1.40397e10i	−0.0935824	−	0.162089i
$155$	5.89223e9	−	3.40188e9i	0.0658599	−	0.0380242i
$156$		−	2.59161e10i		−	0.280509i
$157$	5.51263e10	−	3.18272e10i	0.577911	−	0.333657i	−0.182392	−	0.983226i	$-0.558384\pi$
$157$	5.51263e10	−	3.18272e10i	0.577911	−	0.333657i	0.760303	+	0.649569i	$0.225051\pi$
$158$	1.21961e10	−	7.04144e9i	0.123862	−	0.0715116i
$159$	5.02817e9	−	2.90301e9i	0.0494793	−	0.0285669i
$160$	9.45967e9	−	1.63846e10i	0.0902145	−	0.156256i
$161$			2.01537e11i			1.86305i
$162$	1.43779e10	+	8.30106e9i	0.128860	+	0.0743975i
$163$	9.58471e10	−	5.53373e10i	0.832992	−	0.480928i	−0.0218839	−	0.999761i	$-0.506966\pi$
$163$	9.58471e10	−	5.53373e10i	0.832992	−	0.480928i	0.854876	+	0.518832i	$0.173633\pi$
$164$	−1.05323e11			−0.887778
$165$	−3.45762e9	−	5.98878e9i	−0.0282721	−	0.0489687i
$166$	−1.66697e9	−	9.62427e8i	−0.0132248	−	0.00763532i
$167$	7.23243e10	−	1.25269e11i	0.556803	−	0.964411i	−0.440958	−	0.897528i	$-0.645361\pi$
$167$	7.23243e10	−	1.25269e11i	0.556803	−	0.964411i	0.997761	−	0.0668834i	$-0.0213055\pi$
$168$			1.31266e10i			0.0980857i
$169$	−7.23830e10	+	1.25371e11i	−0.525053	+	0.909418i
$170$	1.22908e10			0.0865638
$171$			1.72822e11i			1.18200i
$172$	9.14155e10	+	1.14132e11i	0.607264	+	0.758170i
$173$	2.05728e11			1.32758			0.663792	−	0.747917i	$-0.268946\pi$
$173$	2.05728e11			1.32758			0.663792	+	0.747917i	$0.268946\pi$
$174$			2.40356e9i			0.0150698i
$175$	1.78991e11	+	1.03340e11i	1.09054	+	0.629621i
$176$	−1.17227e11			−0.694170
$177$	−1.81960e10	−	1.05054e10i	−0.104739	−	0.0604711i
$178$	9.17103e9	−	1.58847e10i	0.0513237	−	0.0888953i
$179$	1.22573e11	−	7.07677e10i	0.667007	−	0.385097i	−0.127935	−	0.991783i	$-0.540835\pi$
$179$	1.22573e11	−	7.07677e10i	0.667007	−	0.385097i	0.794942	+	0.606686i	$0.207501\pi$
$180$		−	6.50708e10i		−	0.344368i
$181$	2.15852e10	+	3.73867e10i	0.111113	+	0.192453i	0.916219	−	0.400678i	$-0.131225\pi$
$181$	2.15852e10	+	3.73867e10i	0.111113	+	0.192453i	−0.805107	+	0.593130i	$0.797892\pi$
$182$	3.52682e10	−	6.10863e10i	0.176614	−	0.305905i
$183$	7.76582e9			0.0378383
$184$	−7.78086e10	−	4.49228e10i	−0.368925	−	0.212999i
$185$	−3.61571e10	−	6.26260e10i	−0.166854	−	0.288999i
$186$	−7.81474e8	−	1.35355e9i	−0.00351034	−	0.00608010i
$187$	−1.20120e11	−	2.08054e11i	−0.525300	−	0.909846i
$188$	−2.74870e11			−1.17041
$189$	6.94913e10	+	1.20362e11i	0.288152	+	0.499093i
$190$	−1.65161e10	+	9.53555e9i	−0.0667019	+	0.0385104i
$191$	−3.42858e11	−	1.97949e11i	−1.34880	−	0.778729i	−0.360719	−	0.932674i	$-0.617469\pi$
$191$	−3.42858e11	−	1.97949e11i	−1.34880	−	0.778729i	−0.988079	+	0.153945i	$0.950802\pi$
$192$	3.79339e10	+	2.19012e10i	0.145386	+	0.0839385i
$193$	−3.60615e11			−1.34666			−0.673329	−	0.739343i	$-0.735136\pi$
$193$	−3.60615e11			−1.34666			−0.673329	+	0.739343i	$0.735136\pi$
$194$			8.70702e10i			0.316855i
$195$	1.50440e10	−	2.60570e10i	0.0533569	−	0.0924168i
$196$	1.58324e11	−	2.74225e11i	0.547352	−	0.948041i
$197$	−9.01186e10	−	1.56090e11i	−0.303727	−	0.526070i	0.673250	−	0.739415i	$-0.264898\pi$
$197$	−9.01186e10	−	1.56090e11i	−0.303727	−	0.526070i	−0.976977	+	0.213344i	$0.931564\pi$
$198$	3.24465e10	−	1.87330e10i	0.106621	−	0.0615575i
$199$			2.38161e11i			0.763141i	0.924340	+	0.381570i	$0.124617\pi$
$199$			2.38161e11i			0.763141i	−0.924340	+	0.381570i	$0.875383\pi$
$200$	−7.97944e10	+	4.60693e10i	−0.249358	+	0.143967i
$201$	−8.33234e10	+	4.81068e10i	−0.253972	+	0.146631i
$202$	−5.20807e10	+	3.00688e10i	−0.154853	+	0.0894045i
$203$	1.11041e11	−	1.92328e11i	0.322108	−	0.557907i
$204$			9.58495e10i			0.271293i
$205$	−1.05896e11	−	6.11389e10i	−0.292489	−	0.168868i
$206$	6.01705e9	−	3.47395e9i	0.0162199	−	0.00936455i
$207$	−4.65762e11			−1.22550
$208$	−2.55026e11	−	4.41718e11i	−0.655041	−	1.13456i
$209$	3.22827e11	+	1.86384e11i	0.809541	+	0.467389i
$210$	−3.75462e9	+	6.50320e9i	−0.00919327	+	0.0159232i
$211$			5.09908e11i			1.21921i	0.792704	+	0.609607i	$0.208673\pi$
$211$			5.09908e11i			1.21921i	−0.792704	+	0.609607i	$0.791327\pi$
$212$	5.89208e10	−	1.02054e11i	0.137591	−	0.238314i
$213$	1.07875e10			0.0246050
$214$		−	8.72099e10i		−	0.194311i
$215$	2.56599e10	+	1.67819e11i	0.0558550	+	0.365298i
$216$	−6.19587e10			−0.131775
$217$			1.44411e11i			0.300126i
$218$	4.97086e8	+	2.86993e8i	0.00100960	+	0.000582893i
$219$	1.36650e11			0.271262
$220$	−1.21551e11	−	7.01774e10i	−0.235855	−	0.136171i
$221$	5.22638e11	−	9.05235e11i	0.991378	−	1.71712i
$222$	−1.43863e10	+	8.30596e9i	−0.0266800	+	0.0154037i
$223$		−	9.77505e11i		−	1.77253i	−0.463175	−	0.886267i	$-0.653290\pi$
$223$		−	9.77505e11i		−	1.77253i	0.463175	−	0.886267i	$-0.346710\pi$
$224$	2.00784e11	+	3.47768e11i	0.356032	+	0.616665i
$225$	−2.38825e11	+	4.13656e11i	−0.414158	+	0.717343i
$226$	−1.65030e11			−0.279912
$227$	−3.19561e11	−	1.84499e11i	−0.530181	−	0.306100i	0.210909	−	0.977506i	$-0.432358\pi$
$227$	−3.19561e11	−	1.84499e11i	−0.530181	−	0.306100i	−0.741090	+	0.671405i	$0.765691\pi$
$228$	−7.43626e10	−	1.28800e11i	−0.120693	−	0.209046i
$229$	3.48261e11	+	6.03205e11i	0.553002	+	0.957828i	0.998056	+	0.0623243i	$0.0198513\pi$
$229$	3.48261e11	+	6.03205e11i	0.553002	+	0.957828i	−0.445054	+	0.895504i	$0.646815\pi$
$230$	−2.56987e10	−	4.45115e10i	−0.0399275	−	0.0691564i
$231$	1.46778e11			0.223152
$232$	4.95021e10	+	8.57402e10i	0.0736519	+	0.127569i
$233$	3.95792e11	−	2.28510e11i	0.576351	−	0.332756i	−0.183331	−	0.983051i	$-0.558688\pi$
$233$	3.95792e11	−	2.28510e11i	0.576351	−	0.332756i	0.759682	+	0.650295i	$0.225355\pi$
$234$	1.41173e11	+	8.15065e10i	0.201221	+	0.116175i
$235$	−2.76365e11	−	1.59559e11i	−0.385606	−	0.222629i
$236$	−4.26446e11			−0.582511
$237$			1.27504e11i			0.170523i
$238$	−1.30438e11	+	2.25925e11i	−0.170812	+	0.295856i
$239$	−3.81992e11	+	6.61630e11i	−0.489852	+	0.848449i	−0.999932	−	0.0116785i	$-0.996283\pi$
$239$	−3.81992e11	+	6.61630e11i	−0.489852	+	0.848449i	0.510080	+	0.860127i	$0.329616\pi$
$240$	2.71499e10	+	4.70250e10i	0.0340967	+	0.0590572i
$241$	8.47211e11	−	4.89138e11i	1.04209	−	0.601653i	0.121668	−	0.992571i	$-0.461176\pi$
$241$	8.47211e11	−	4.89138e11i	1.04209	−	0.601653i	0.920425	+	0.390918i	$0.127842\pi$
$242$			5.95873e10i			0.0717921i
$243$	−4.20133e11	+	2.42564e11i	−0.495855	+	0.286282i
$244$	1.36502e11	−	7.88092e10i	0.157830	−	0.0911230i
$245$	3.18370e11	−	1.83811e11i	0.360663	−	0.208229i
$246$	−1.40447e10	+	2.43262e10i	−0.0155897	+	0.0270022i
$247$			1.62190e12i			1.76417i
$248$	−5.57538e10	−	3.21895e10i	−0.0594314	−	0.0343127i
$249$	1.50925e10	−	8.71367e9i	0.0157676	−	0.00910341i
$250$	−1.13755e11			−0.116485
$251$	−7.72038e11	−	1.33721e12i	−0.774944	−	1.34224i	−0.934826	−	0.355106i	$-0.884445\pi$
$251$	−7.72038e11	−	1.33721e12i	−0.774944	−	1.34224i	0.159883	−	0.987136i	$-0.448888\pi$
$252$	1.19611e12	+	6.90572e11i	1.17697	+	0.679526i
$253$	−5.02314e11	+	8.70034e11i	−0.484588	+	0.839331i
$254$		−	5.01695e10i		−	0.0474538i
$255$	−5.56396e10	+	9.63707e10i	−0.0516040	+	0.0893807i
$256$	7.98221e11			0.725978
$257$		−	1.98701e12i		−	1.77229i	−0.463410	−	0.886144i	$-0.653374\pi$
$257$		−	1.98701e12i		−	1.77229i	0.463410	−	0.886144i	$-0.346626\pi$
$258$	3.85510e10	−	5.89454e9i	0.0337239	−	0.00515646i
$259$	1.53489e12			1.31698
$260$		−	6.10679e11i		−	0.513980i
$261$	4.44479e11	+	2.56620e11i	0.366986	+	0.211879i
$262$	1.94594e11			0.157624
$263$	9.45478e11	+	5.45872e11i	0.751403	+	0.433822i	0.826200	−	0.563376i	$-0.190498\pi$
$263$	9.45478e11	+	5.45872e11i	0.751403	+	0.433822i	−0.0747979	+	0.997199i	$0.523831\pi$
$264$	−3.27169e10	+	5.66674e10i	−0.0255125	+	0.0441890i
$265$	1.18482e11	−	6.84057e10i	0.0906617	−	0.0523436i
$266$		−	4.04789e11i		−	0.303963i
$267$	8.30331e10	+	1.43818e11i	0.0611920	+	0.105988i
$268$	−9.76395e11	+	1.69117e12i	−0.706239	+	1.22324i
$269$	−2.45725e12			−1.74457			−0.872283	−	0.489001i	$-0.837362\pi$
$269$	−2.45725e12			−1.74457			−0.872283	+	0.489001i	$0.837362\pi$
$270$	−3.06957e10	−	1.77222e10i	−0.0213923	−	0.0123509i
$271$	8.72099e11	+	1.51052e12i	0.596650	+	1.03343i	0.993312	+	0.115463i	$0.0368351\pi$
$271$	8.72099e11	+	1.51052e12i	0.596650	+	1.03343i	−0.396662	+	0.917965i	$0.629832\pi$
$272$	9.43204e11	+	1.63368e12i	0.633521	+	1.09729i
$273$	3.19313e11	+	5.53066e11i	0.210573	+	0.364723i
$274$	4.64302e11			0.300641
$275$	5.15134e11	+	8.92238e11i	0.327534	+	0.567306i
$276$	3.47121e11	−	2.00410e11i	0.216738	−	0.125134i
$277$	−9.40483e11	−	5.42988e11i	−0.576703	−	0.332959i	0.183119	−	0.983091i	$-0.441381\pi$
$277$	−9.40483e11	−	5.42988e11i	−0.576703	−	0.332959i	−0.759822	+	0.650131i	$0.774714\pi$
$278$	1.71448e10	+	9.89854e9i	0.0103254	+	0.00596139i
$279$	−3.33742e11			−0.197419
$280$			3.09311e11i			0.179724i
$281$	1.40891e12	−	2.44030e12i	0.804176	−	1.39287i	−0.112670	−	0.993633i	$-0.535940\pi$
$281$	1.40891e12	−	2.44030e12i	0.804176	−	1.39287i	0.916846	−	0.399241i	$-0.130726\pi$
$282$	−3.66537e10	+	6.34860e10i	−0.0205529	+	0.0355986i
$283$	1.18559e11	+	2.05351e11i	0.0653136	+	0.113126i	0.896833	−	0.442369i	$-0.145862\pi$
$283$	1.18559e11	+	2.05351e11i	0.0653136	+	0.113126i	−0.831519	+	0.555496i	$0.812529\pi$
$284$	1.89615e11	−	1.09474e11i	0.102631	−	0.0592542i
$285$		−	1.72667e11i		−	0.0918300i
$286$	3.04505e11	−	1.75806e11i	0.159134	−	0.0918763i
$287$	2.24766e12	−	1.29769e12i	1.15431	−	0.666440i
$288$	−8.03709e11	+	4.64022e11i	−0.405636	+	0.234194i
$289$	−9.24958e11	+	1.60207e12i	−0.458810	+	0.794682i
$290$			5.66367e10i			0.0276127i
$291$	−6.82705e11	−	3.94160e11i	−0.327166	−	0.188889i
$292$	2.40192e12	−	1.38675e12i	1.13147	−	0.653257i
$293$	−8.48561e11			−0.392957			−0.196478	−	0.980508i	$-0.562951\pi$
$293$	−8.48561e11			−0.392957			−0.196478	+	0.980508i	$0.562951\pi$
$294$	−4.22247e10	−	7.31353e10i	−0.0192234	−	0.0332959i
$295$	−4.28764e11	−	2.47547e11i	−0.191915	−	0.110802i
$296$	−3.42128e11	+	5.92583e11i	−0.150567	+	0.260790i
$297$			6.92805e11i			0.299798i
$298$	1.94898e11	−	3.37573e11i	0.0829326	−	0.143643i
$299$	−4.37110e12			−1.82909
$300$		−	4.11050e11i		−	0.169157i
$301$	−3.35709e12	−	1.30933e12i	−1.35872	−	0.529926i
$302$	3.26693e11			0.130048
$303$		−	5.44477e11i		−	0.213190i
$304$	−2.53490e12	−	1.46353e12i	−0.976322	−	0.563680i
$305$	1.82992e11			0.0693317
$306$	−5.22124e11	−	3.01449e11i	−0.194611	−	0.112359i
$307$	1.93868e11	−	3.35789e11i	0.0710908	−	0.123133i	−0.828289	−	0.560301i	$-0.810685\pi$
$307$	1.93868e11	−	3.35789e11i	0.0710908	−	0.123133i	0.899380	+	0.437168i	$0.144019\pi$
$308$	2.57995e12	−	1.48953e12i	0.930802	−	0.537399i
$309$			6.29052e10i			0.0223303i
$310$	−1.84144e10	−	3.18947e10i	−0.00643205	−	0.0111406i
$311$	1.11110e12	−	1.92448e12i	0.381900	−	0.661471i	−0.609433	−	0.792837i	$-0.708603\pi$
$311$	1.11110e12	−	1.92448e12i	0.381900	−	0.661471i	0.991334	+	0.131366i	$0.0419364\pi$
$312$	−2.84700e11			−0.0962975
$313$	−2.63060e12	−	1.51878e12i	−0.875656	−	0.505560i	−0.00643254	−	0.999979i	$-0.502048\pi$
$313$	−2.63060e12	−	1.51878e12i	−0.875656	−	0.505560i	−0.869224	+	0.494419i	$0.835381\pi$
$314$	−1.72281e11	−	2.98400e11i	−0.0564403	−	0.0977575i
$315$	8.01739e11	+	1.38865e12i	0.258512	+	0.447755i
$316$	1.29394e12	+	2.24117e12i	0.410657	+	0.711278i
$317$	−5.03131e12			−1.57176			−0.785878	−	0.618382i	$-0.787788\pi$
$317$	−5.03131e12			−1.57176			−0.785878	+	0.618382i	$0.787788\pi$
$318$	−1.57141e10	−	2.72175e10i	−0.00483229	−	0.00836977i
$319$	9.58722e11	−	5.53519e11i	0.290228	−	0.167563i
$320$	8.93864e11	+	5.16073e11i	0.266392	+	0.153802i
$321$	6.83800e11	+	3.94792e11i	0.200634	+	0.115836i
$322$	1.09092e12			0.315148
$323$		−	5.99855e12i		−	1.70621i
$324$	−1.52541e12	+	2.64208e12i	−0.427229	+	0.739983i
$325$	−2.24133e12	+	3.88210e12i	−0.618143	+	1.07066i
$326$	−2.99542e11	−	5.18822e11i	−0.0813522	−	0.140906i
$327$	−4.50054e9	+	2.59839e9i	−0.00120372	+	0.000694969i
$328$			1.15703e12i			0.304771i
$329$	5.86591e12	−	3.38668e12i	1.52179	−	0.878608i
$330$	−3.24174e10	+	1.87162e10i	−0.00828339	+	0.00478242i
$331$	−7.65396e11	+	4.41902e11i	−0.192640	+	0.111221i	−0.593218	−	0.805042i	$-0.702143\pi$
$331$	−7.65396e11	+	4.41902e11i	−0.192640	+	0.111221i	0.400578	+	0.916263i	$0.368809\pi$
$332$	1.76856e11	−	3.06324e11i	0.0438460	−	0.0759435i
$333$			3.54720e12i			0.866293i
$334$	−6.78085e11	−	3.91492e11i	−0.163137	−	0.0941870i
$335$	−1.96341e12	+	1.13357e12i	−0.465357	+	0.268674i
$336$	−1.15253e12			−0.269125
$337$	−9.91252e11	−	1.71690e12i	−0.228052	−	0.394998i	0.729178	−	0.684324i	$-0.239902\pi$
$337$	−9.91252e11	−	1.71690e12i	−0.228052	−	0.394998i	−0.957231	+	0.289325i	$0.906569\pi$
$338$	6.78635e11	+	3.91810e11i	0.153834	+	0.0888162i
$339$	7.47079e11	−	1.29398e12i	0.166866	−	0.289021i
$340$			2.25857e12i			0.497095i
$341$	−3.59933e11	+	6.23423e11i	−0.0780639	+	0.135211i
$342$	9.35487e11			0.199943
$343$			8.78984e11i			0.185144i
$344$	1.25380e12	−	1.00424e12i	0.260277	−	0.208471i
$345$	4.65344e11			0.0952092
$346$		−	1.11361e12i		−	0.224570i
$347$	−2.02012e12	−	1.16631e12i	−0.401540	−	0.231829i	0.285608	−	0.958346i	$-0.407804\pi$
$347$	−2.02012e12	−	1.16631e12i	−0.401540	−	0.231829i	−0.687148	+	0.726517i	$0.741138\pi$
$348$	−4.41679e11			−0.0865388
$349$	−6.19937e12	−	3.57921e12i	−1.19735	−	0.691289i	−0.237385	−	0.971416i	$-0.576290\pi$
$349$	−6.19937e12	−	3.57921e12i	−1.19735	−	0.691289i	−0.959963	+	0.280126i	$0.909624\pi$
$350$	5.59383e11	−	9.68879e11i	0.106505	−	0.184472i
$351$	−2.61052e12	+	1.50718e12i	−0.489995	+	0.282898i
$352$			2.00175e12i			0.370422i
$353$	−1.40048e12	−	2.42571e12i	−0.255508	−	0.442553i	0.709525	−	0.704680i	$-0.248909\pi$
$353$	−1.40048e12	−	2.42571e12i	−0.255508	−	0.442553i	−0.965033	+	0.262127i	$0.915576\pi$
$354$	−5.68661e10	+	9.84950e10i	−0.0102291	+	0.0177173i
$355$	2.54194e11			0.0450841
$356$	2.91898e12	+	1.68527e12i	0.510483	+	0.294727i
$357$	−1.18097e12	−	2.04549e12i	−0.203655	−	0.352742i
$358$	−3.83067e11	−	6.63491e11i	−0.0651417	−	0.112829i
$359$	−3.49976e12	−	6.06177e12i	−0.586903	−	1.01655i	−0.994635	−	0.103445i	$-0.967014\pi$
$359$	−3.49976e12	−	6.06177e12i	−0.586903	−	1.01655i	0.407732	−	0.913102i	$-0.366320\pi$
$360$	−7.14834e11			−0.118220
$361$	1.58830e12	+	2.75101e12i	0.259057	+	0.448701i
$362$	2.02375e11	−	1.16841e11i	0.0325547	−	0.0187954i
$363$	−4.67215e11	−	2.69747e11i	−0.0741283	−	0.0427980i
$364$	1.12253e13	+	6.48090e12i	1.75667	+	1.01421i
$365$	3.21997e12			0.497036
$366$		−	4.20365e10i		−	0.00640061i
$367$	−5.68368e12	+	9.84442e12i	−0.853688	+	1.47863i	0.0241683	+	0.999708i	$0.492306\pi$
$367$	−5.68368e12	+	9.84442e12i	−0.853688	+	1.47863i	−0.877857	+	0.478924i	$0.841027\pi$
$368$	3.94426e12	−	6.83166e12i	0.584422	−	1.01225i
$369$	2.99902e12	+	5.19446e12i	0.438377	+	0.759292i
$370$	−3.38995e11	+	1.95719e11i	−0.0488861	+	0.0282244i
$371$			2.90386e12i			0.413148i
$372$	2.48730e11	−	1.43604e11i	0.0349151	−	0.0201582i
$373$	1.04329e13	−	6.02343e12i	1.44497	−	0.834256i	0.446798	−	0.894635i	$-0.352564\pi$
$373$	1.04329e13	−	6.02343e12i	1.44497	−	0.834256i	0.998176	+	0.0603785i	$0.0192308\pi$
$374$	−1.12620e12	+	6.50211e11i	−0.153907	+	0.0888580i
$375$	5.14960e11	−	8.91936e11i	0.0694412	−	0.120276i
$376$			3.01958e12i			0.401798i
$377$	4.17137e12	+	2.40834e12i	0.547736	+	0.316236i
$378$	6.51523e11	−	3.76157e11i	0.0844250	−	0.0487428i
$379$	7.42405e12			0.949390			0.474695	−	0.880150i	$-0.342558\pi$
$379$	7.42405e12			0.949390			0.474695	+	0.880150i	$0.342558\pi$
$380$	−1.75226e12	−	3.03500e12i	−0.221147	−	0.383037i
$381$	3.93372e11	+	2.27113e11i	0.0489980	+	0.0282890i
$382$	−1.07150e12	+	1.85589e12i	−0.131727	+	0.228158i
$383$			9.03964e12i			1.09688i	0.836191	+	0.548438i	$0.184777\pi$
$383$			9.03964e12i			1.09688i	−0.836191	+	0.548438i	$0.815223\pi$
$384$	5.29637e11	−	9.17358e11i	0.0634340	−	0.109871i
$385$	3.45863e12			0.408884
$386$			1.95201e12i			0.227796i
$387$	3.02592e12	−	7.75841e12i	0.348580	−	0.893754i
$388$	−1.60001e13			−1.81955
$389$			1.17439e13i			1.31845i	0.751944	+	0.659227i	$0.229116\pi$
$389$			1.17439e13i			1.31845i	−0.751944	+	0.659227i	$0.770884\pi$
$390$	−1.41047e11	−	8.14334e10i	−0.0156329	−	0.00902567i
$391$	1.61663e13			1.76900
$392$	−3.01250e12	−	1.73927e12i	−0.325459	−	0.187904i
$393$	−8.80913e11	+	1.52579e12i	−0.0939659	+	0.162754i
$394$	−8.44918e11	+	4.87813e11i	−0.0889884	+	0.0513775i
$395$			3.00447e12i			0.312452i
$396$	3.44238e12	+	5.96238e12i	0.353495	+	0.612272i
$397$	3.40150e12	−	5.89157e12i	0.344920	−	0.597418i	−0.640419	−	0.768025i	$-0.721239\pi$
$397$	3.40150e12	−	5.89157e12i	0.344920	−	0.597418i	0.985339	+	0.170607i	$0.0545728\pi$
$398$	1.28917e12			0.129090
$399$	3.17389e12	+	1.83245e12i	0.313854	+	0.181204i
$400$	−4.04493e12	−	7.00602e12i	−0.395013	−	0.684182i
$401$	−3.19388e12	−	5.53196e12i	−0.308032	−	0.533528i	0.669899	−	0.742452i	$-0.266337\pi$
$401$	−3.19388e12	−	5.53196e12i	−0.308032	−	0.533528i	−0.977932	+	0.208924i	$0.933004\pi$
$402$	2.60403e11	+	4.51031e11i	0.0248036	+	0.0429611i
$403$	−3.13211e12			−0.294654
$404$	−5.52546e12	−	9.57038e12i	−0.513407	−	0.889247i
$405$	−3.06740e12	+	1.77097e12i	−0.281511	+	0.162531i
$406$	−1.04107e12	−	6.01064e11i	−0.0943738	−	0.0544867i
$407$	6.62610e12	+	3.82558e12i	0.593316	+	0.342551i
$408$	1.05295e12			0.0931340
$409$			2.99841e12i			0.261984i	0.991383	+	0.130992i	$0.0418162\pi$
$409$			2.99841e12i			0.261984i	−0.991383	+	0.130992i	$0.958184\pi$
$410$	−3.30946e11	+	5.73215e11i	−0.0285652	+	0.0494765i
$411$	−2.10186e12	+	3.64053e12i	−0.179223	+	0.310424i
$412$	6.38375e11	+	1.10570e12i	0.0537761	+	0.0931430i
$413$	9.10063e12	−	5.25425e12i	0.757393	−	0.437281i
$414$			2.52118e12i			0.207301i
$415$	3.55636e11	−	2.05326e11i	0.0288911	−	0.0166803i
$416$	−7.54268e12	+	4.35477e12i	−0.605423	+	0.349541i
$417$	−1.55226e11	+	8.96199e10i	−0.0123108	+	0.00710762i
$418$	1.00890e12	−	1.74747e12i	0.0790620	−	0.136939i
$419$		−	1.52112e13i		−	1.17786i	−0.808185	−	0.588929i	$-0.799550\pi$
$419$		−	1.52112e13i		−	1.17786i	0.808185	−	0.588929i	$-0.200450\pi$
$420$	−1.19503e12	−	6.89952e11i	−0.0914394	−	0.0527925i
$421$	−1.71660e13	+	9.91079e12i	−1.29795	+	0.749373i	−0.980050	−	0.198751i	$-0.936311\pi$
$421$	−1.71660e13	+	9.91079e12i	−1.29795	+	0.749373i	−0.317902	+	0.948124i	$0.602978\pi$
$422$	2.76014e12			0.206238
$423$	7.82680e12	+	1.35564e13i	0.577939	+	1.00102i
$424$	−1.12111e12	−	6.47273e11i	−0.0818123	−	0.0472344i
$425$	8.28947e12	−	1.43578e13i	0.597836	−	1.03548i
$426$		−	5.83930e10i		−	0.00416210i
$427$	−1.94202e12	+	3.36368e12i	−0.136809	+	0.236960i
$428$	1.60257e13			1.11583
$429$			3.18344e12i			0.219084i
$430$	9.08405e11	−	1.38897e11i	0.0617927	−	0.00944825i
$431$	1.53254e12			0.103045			0.0515224	−	0.998672i	$-0.483593\pi$
$431$	1.53254e12			0.103045			0.0515224	+	0.998672i	$0.483593\pi$
$432$		−	5.44003e12i		−	0.361562i
$433$	−1.46560e13	−	8.46162e12i	−0.962886	−	0.555922i	−0.0658256	−	0.997831i	$-0.520968\pi$
$433$	−1.46560e13	−	8.46162e12i	−0.962886	−	0.555922i	−0.897060	+	0.441909i	$0.854301\pi$
$434$	7.81701e11			0.0507683
$435$	−4.44081e11	−	2.56390e11i	−0.0285112	−	0.0164610i
$436$	−5.27380e10	+	9.13449e10i	−0.00334727	+	0.00579765i
$437$	−2.17239e13	+	1.25423e13i	−1.36311	+	0.786990i
$438$		−	7.39687e11i		−	0.0458857i
$439$	−1.37398e12	−	2.37981e12i	−0.0842671	−	0.145955i	0.820812	−	0.571199i	$-0.193522\pi$
$439$	−1.37398e12	−	2.37981e12i	−0.0842671	−	0.145955i	−0.905079	+	0.425244i	$0.860188\pi$
$440$	−7.70933e11	+	1.33529e12i	−0.0467469	+	0.0809680i
$441$	−1.80328e13			−1.08111
$442$	−4.90005e12	−	2.82905e12i	−0.290462	−	0.167698i
$443$	−1.58024e13	−	2.73705e13i	−0.926197	−	1.60422i	−0.789625	−	0.613589i	$-0.789725\pi$
$443$	−1.58024e13	−	2.73705e13i	−0.926197	−	1.60422i	−0.136571	−	0.990630i	$-0.543608\pi$
$444$	−1.52631e12	−	2.64364e12i	−0.0884560	−	0.153210i
$445$	1.95657e12	+	3.38887e12i	0.112123	+	0.194203i
$446$	−5.29125e12			−0.299836
$447$	1.76457e12	+	3.05633e12i	0.0988785	+	0.171263i
$448$	−1.89725e13	+	1.09538e13i	−1.05132	+	0.606979i
$449$	−9.42763e12	−	5.44304e12i	−0.516619	−	0.298270i	0.218931	−	0.975740i	$-0.429743\pi$
$449$	−9.42763e12	−	5.44304e12i	−0.516619	−	0.298270i	−0.735550	+	0.677470i	$0.763076\pi$
$450$	2.23913e12	+	1.29276e12i	0.121343	+	0.0700577i
$451$	1.29375e13			0.693376
$452$		−	3.03261e13i		−	1.60740i
$453$	−1.47891e12	+	2.56155e12i	−0.0775268	+	0.134280i
$454$	−9.98693e11	+	1.72979e12i	−0.0517789	+	0.0896837i
$455$	7.52419e12	+	1.30323e13i	0.385836	+	0.668288i
$456$	−1.41493e12	+	8.16909e11i	−0.0717646	+	0.0414333i
$457$			1.37791e13i			0.691259i	0.938371	+	0.345630i	$0.112335\pi$
$457$			1.37791e13i			0.691259i	−0.938371	+	0.345630i	$0.887665\pi$
$458$	3.26516e12	−	1.88514e12i	0.162023	−	0.0935441i
$459$	9.65490e12	−	5.57426e12i	0.473897	−	0.273605i
$460$	8.17945e12	−	4.72241e12i	0.397132	−	0.229284i
$461$	1.36367e13	−	2.36195e13i	0.654946	−	1.13440i	−0.326961	−	0.945038i	$-0.606025\pi$
$461$	1.36367e13	−	2.36195e13i	0.654946	−	1.13440i	0.981907	−	0.189362i	$-0.0606421\pi$
$462$		−	7.94511e11i		−	0.0377477i
$463$	2.82374e13	+	1.63029e13i	1.32715	+	0.766231i	0.984858	−	0.173362i	$-0.0554631\pi$
$463$	2.82374e13	+	1.63029e13i	1.32715	+	0.766231i	0.342293	+	0.939593i	$0.388796\pi$
$464$	−7.52807e12	+	4.34633e12i	−0.350020	+	0.202084i
$465$	3.33443e11			0.0153376
$466$	−1.23693e12	−	2.14243e12i	−0.0562880	−	0.0974937i
$467$	9.07944e12	+	5.24201e12i	0.408766	+	0.236001i	0.690259	−	0.723562i	$-0.257496\pi$
$467$	9.07944e12	+	5.24201e12i	0.408766	+	0.236001i	−0.281494	+	0.959563i	$0.590830\pi$
$468$	−1.49777e13	+	2.59421e13i	−0.667138	+	1.15552i
$469$		−	4.81208e13i		−	2.12065i
$470$	−8.63697e11	+	1.49597e12i	−0.0376593	+	0.0652278i
$471$	3.11961e12			0.134585
$472$			4.68471e12i			0.199974i
$473$	−1.12292e13	−	1.40196e13i	−0.474287	−	0.592149i
$474$	6.90183e11			0.0288451
$475$			2.57248e13i			1.06386i
$476$	−4.15162e13	−	2.39694e13i	−1.69896	−	0.980893i
$477$	−6.71096e12			−0.271765
$478$	3.58141e12	+	2.06773e12i	0.143521	+	0.0828618i
$479$	−5.70127e12	+	9.87489e12i	−0.226097	+	0.391611i	−0.956648	−	0.291247i	$-0.905930\pi$
$479$	−5.70127e12	+	9.87489e12i	−0.226097	+	0.391611i	0.730551	+	0.682858i	$0.239263\pi$
$480$	8.02988e11	−	4.63605e11i	0.0315140	−	0.0181946i
$481$			3.32899e13i			1.29297i
$482$	−2.64771e12	−	4.58597e12i	−0.101774	−	0.176277i
$483$	−4.93852e12	+	8.55377e12i	−0.187872	+	0.325403i
$484$	−1.09498e13			−0.412267
$485$	−1.60871e13	−	9.28788e12i	−0.599471	−	0.346105i
$486$	1.31300e12	+	2.27418e12i	0.0484266	+	0.0838773i
$487$	1.43291e13	+	2.48187e13i	0.523087	+	0.906013i	0.999639	+	0.0268671i	$0.00855309\pi$
$487$	1.43291e13	+	2.48187e13i	0.523087	+	0.906013i	−0.476552	+	0.879146i	$0.658114\pi$
$488$	−8.65757e11	−	1.49954e12i	−0.0312822	−	0.0541823i
$489$	5.42401e12			0.193989
$490$	−9.94971e11	−	1.72334e12i	−0.0352233	−	0.0610085i
$491$	2.45190e13	−	1.41561e13i	0.859203	−	0.496061i	−0.00454237	−	0.999990i	$-0.501446\pi$
$491$	2.45190e13	−	1.41561e13i	0.859203	−	0.496061i	0.863745	+	0.503929i	$0.168113\pi$
$492$	−4.47020e12	−	2.58087e12i	−0.155061	−	0.0895242i
$493$	−1.54276e13	−	8.90715e12i	−0.529742	−	0.305847i
$494$	8.77939e12			0.298421
$495$			7.99307e12i			0.268960i
$496$	2.82626e12	−	4.89523e12i	0.0941465	−	0.163067i
$497$	−2.69767e12	+	4.67249e12i	−0.0889623	+	0.154087i
$498$	−4.71672e10	−	8.16960e10i	−0.00153990	−	0.00266719i
$499$	2.26384e13	−	1.30703e13i	0.731718	−	0.422457i	−0.0873325	−	0.996179i	$-0.527834\pi$
$499$	2.26384e13	−	1.30703e13i	0.731718	−	0.422457i	0.819050	+	0.573722i	$0.194501\pi$
$500$		−	2.09037e13i		−	0.668918i
$501$	6.13927e12	−	3.54451e12i	0.194504	−	0.112297i
$502$	−7.23833e12	+	4.17905e12i	−0.227049	+	0.131087i
$503$	5.05383e13	−	2.91783e13i	1.56957	−	0.906191i	0.573350	−	0.819311i	$-0.305644\pi$
$503$	5.05383e13	−	2.91783e13i	1.56957	−	0.906191i	0.996219	−	0.0868802i	$-0.0276897\pi$
$504$	7.58626e12	−	1.31398e13i	0.233279	−	0.404051i
$505$		−	1.28299e13i		−	0.390630i
$506$	4.70951e12	+	2.71903e12i	0.141979	+	0.0819713i
$507$	−6.14426e12	+	3.54739e12i	−0.183413	+	0.105893i
$508$	9.21918e12			0.272504
$509$	−5.47658e12	−	9.48571e12i	−0.160295	−	0.277639i	0.774679	−	0.632354i	$-0.217911\pi$
$509$	−5.47658e12	−	9.48571e12i	−0.160295	−	0.277639i	−0.934975	+	0.354715i	$0.884578\pi$
$510$	5.21656e11	+	3.01178e11i	0.0151194	+	0.00872916i
$511$	−3.41724e13	+	5.91883e13i	−0.980778	+	1.69876i
$512$		−	2.64536e13i		−	0.751856i
$513$	−8.64931e12	+	1.49811e13i	−0.243442	+	0.421653i
$514$	−1.07557e13			−0.299794
$515$			1.48228e12i			0.0409160i
$516$	1.08319e12	+	7.08416e12i	0.0296111	+	0.193660i
$517$	3.37641e13			0.914119
$518$		−	8.30837e12i		−	0.222775i
$519$	8.73164e12	+	5.04121e12i	0.231878	+	0.133875i
$520$	−6.70860e12			−0.176447
$521$	4.18942e13	+	2.41876e13i	1.09135	+	0.630092i	0.933936	−	0.357440i	$-0.116350\pi$
$521$	4.18942e13	+	2.41876e13i	1.09135	+	0.630092i	0.157416	+	0.987532i	$0.449684\pi$
$522$	1.38909e12	−	2.40597e12i	0.0358408	−	0.0620781i
$523$	−4.52009e13	+	2.60968e13i	−1.15515	+	0.666927i	−0.950137	−	0.311832i	$-0.899057\pi$
$523$	−4.52009e13	+	2.60968e13i	−1.15515	+	0.666927i	−0.205014	+	0.978759i	$0.565724\pi$
$524$			3.57588e13i			0.905162i
$525$	5.06456e12	+	8.77208e12i	0.126983	+	0.219941i
$526$	2.95481e12	−	5.11789e12i	0.0733840	−	0.127105i
$527$	1.15840e13			0.284974
$528$	−4.97545e12	−	2.87258e12i	−0.121245	−	0.0700007i
$529$	−1.30887e13	−	2.26703e13i	−0.315950	−	0.547241i
$530$	−3.70281e11	−	6.41346e11i	−0.00885427	−	0.0153360i
$531$	1.21428e13	+	2.10320e13i	0.287639	+	0.498205i
$532$	7.43842e13			1.74551
$533$	2.81454e13	+	4.87492e13i	0.654291	+	1.13326i
$534$	7.78487e11	−	4.49459e11i	0.0179285	−	0.0103510i
$535$	1.61129e13	+	9.30277e12i	0.367624	+	0.212248i
$536$	1.85783e13	+	1.07262e13i	0.419934	+	0.242449i
$537$	6.93645e12			0.155334
$538$			1.33011e13i			0.295105i
$539$	−1.94480e13	+	3.36849e13i	−0.427495	+	0.740442i
$540$	3.25664e12	−	5.64066e12i	0.0709252	−	0.122846i
$541$	−4.44134e12	−	7.69263e12i	−0.0958359	−	0.165993i	0.814121	−	0.580695i	$-0.197219\pi$
$541$	−4.44134e12	−	7.69263e12i	−0.0958359	−	0.165993i	−0.909957	+	0.414702i	$0.863886\pi$
$542$	8.17647e12	−	4.72069e12i	0.174811	−	0.100927i
$543$			2.11572e12i			0.0448187i
$544$	2.78963e13	−	1.61059e13i	0.585534	−	0.338058i
$545$	−1.06049e11	+	6.12277e10i	−0.00220560	+	0.00127340i
$546$	2.99375e12	−	1.72844e12i	0.0616954	−	0.0356199i
$547$	9.94615e12	−	1.72272e13i	0.203104	−	0.351786i	−0.746423	−	0.665472i	$-0.768230\pi$
$547$	9.94615e12	−	1.72272e13i	0.203104	−	0.351786i	0.949527	+	0.313685i	$0.101564\pi$
$548$			8.53205e13i			1.72644i
$549$	−7.77363e12	−	4.48811e12i	−0.155870	−	0.0899915i
$550$	4.82970e12	−	2.78843e12i	0.0959637	−	0.0554046i
$551$	2.76416e13			0.544258
$552$	−2.20160e12	−	3.81329e12i	−0.0429580	−	0.0744054i
$553$	−5.52271e13	−	3.18854e13i	−1.06789	−	0.616546i
$554$	−2.93920e12	+	5.09085e12i	−0.0563223	+	0.0975531i
$555$		−	3.54402e12i		−	0.0673025i
$556$	−1.81896e12	+	3.15054e12i	−0.0342334	+	0.0592940i
$557$	−5.12839e12			−0.0956545			−0.0478273	−	0.998856i	$-0.515230\pi$
$557$	−5.12839e12			−0.0956545			−0.0478273	+	0.998856i	$0.515230\pi$
$558$			1.80655e12i			0.0333948i
$559$	2.83977e13	−	7.28114e13i	0.520265	−	1.33395i
$560$	−2.71578e13			−0.493122
$561$		−	1.17738e13i		−	0.211887i
$562$	−1.32094e13	−	7.62644e12i	−0.235614	−	0.136032i
$563$	−7.84151e13			−1.38630			−0.693151	−	0.720792i	$-0.743778\pi$
$563$	−7.84151e13			−1.38630			−0.693151	+	0.720792i	$0.743778\pi$
$564$	−1.16662e13	−	6.73550e12i	−0.204426	−	0.118025i
$565$	1.76040e13	−	3.04910e13i	0.305751	−	0.529577i
$566$	1.11157e12	−	6.41763e11i	0.0191361	−	0.0110482i
$567$		−	7.51784e13i		−	1.28286i
$568$	−1.20262e12	−	2.08301e12i	−0.0203418	−	0.0352330i
$569$	−1.69450e13	+	2.93497e13i	−0.284107	+	0.492087i	−0.972392	−	0.233353i	$-0.925030\pi$
$569$	−1.69450e13	+	2.93497e13i	−0.284107	+	0.492087i	0.688285	+	0.725440i	$0.258364\pi$
$570$	−9.34648e11			−0.0155337
$571$	4.91124e13	+	2.83551e13i	0.809116	+	0.467143i	0.846649	−	0.532152i	$-0.178617\pi$
$571$	4.91124e13	+	2.83551e13i	0.809116	+	0.467143i	−0.0375329	+	0.999295i	$0.511950\pi$
$572$	3.23062e13	+	5.59560e13i	0.527601	+	0.913833i
$573$	−9.70121e12	−	1.68030e13i	−0.157055	−	0.272028i
$574$	−7.02441e12	−	1.21666e13i	−0.112733	−	0.195259i
$575$	−6.93293e13			−1.10301
$576$	−2.53147e13	−	4.38464e13i	−0.399264	−	0.691546i
$577$	3.42140e13	−	1.97535e13i	0.534965	−	0.308862i	−0.208071	−	0.978114i	$-0.566718\pi$
$577$	3.42140e13	−	1.97535e13i	0.534965	−	0.308862i	0.743036	+	0.669252i	$0.233385\pi$
$578$	8.67205e12	+	5.00681e12i	0.134426	+	0.0776108i
$579$	−1.53055e13	−	8.83662e12i	−0.235209	−	0.135798i
$580$	−1.04076e13			−0.158566
$581$			8.71620e12i			0.131658i
$582$	−2.13360e12	+	3.69550e12i	−0.0319519	+	0.0553424i
$583$	−7.23762e12	+	1.25359e13i	−0.107462	+	0.186129i
$584$	−1.52341e13	−	2.63863e13i	−0.224261	−	0.388431i
$585$	−3.01182e13	+	1.73888e13i	−0.439593	+	0.253799i
$586$			4.59327e12i			0.0664713i
$587$	−4.00402e13	+	2.31172e13i	−0.574520	+	0.331700i	−0.758953	−	0.651146i	$-0.774289\pi$
$587$	−4.00402e13	+	2.31172e13i	−0.574520	+	0.331700i	0.184432	+	0.982845i	$0.440955\pi$
$588$	1.34394e13	−	7.75924e12i	0.191202	−	0.110391i
$589$	−1.55662e13	+	8.98717e12i	−0.219587	+	0.126779i
$590$	−1.33998e12	+	2.32091e12i	−0.0187429	+	0.0324637i
$591$		−	8.83317e12i		−	0.122512i
$592$	−5.20294e13	−	3.00392e13i	−0.715550	−	0.413123i
$593$	−5.30450e13	+	3.06255e13i	−0.723387	+	0.417648i	−0.815998	−	0.578055i	$-0.803812\pi$
$593$	−5.30450e13	+	3.06255e13i	−0.723387	+	0.417648i	0.0926110	+	0.995702i	$0.470479\pi$
$594$	3.75016e12			0.0507128
$595$	−2.78279e13	−	4.81994e13i	−0.373161	−	0.646333i
$596$	6.20325e13	+	3.58145e13i	0.824875	+	0.476242i
$597$	−5.83596e12	+	1.01082e13i	−0.0769557	+	0.133291i
$598$			2.36608e13i			0.309403i
$599$	8.81691e12	−	1.52713e13i	0.114336	−	0.198035i	−0.803178	−	0.595739i	$-0.796859\pi$
$599$	8.81691e12	−	1.52713e13i	0.114336	−	0.198035i	0.917514	+	0.397703i	$0.130193\pi$
$600$	−4.51559e12			−0.0580708
$601$		−	8.01006e13i		−	1.02156i	−0.859712	−	0.510779i	$-0.829357\pi$
$601$		−	8.01006e13i		−	1.02156i	0.859712	−	0.510779i	$-0.170643\pi$
$602$	−7.08740e12	+	1.81720e13i	−0.0896406	+	0.229837i
$603$	1.11210e14			1.39494
$604$			6.00333e13i			0.746805i
$605$	−1.10093e13	−	6.35624e12i	−0.135826	−	0.0784193i
$606$	−2.94726e12			−0.0360625
$607$	−8.18150e13	−	4.72359e13i	−0.992863	−	0.573230i	−0.0867340	−	0.996232i	$-0.527643\pi$
$607$	−8.18150e13	−	4.72359e13i	−0.992863	−	0.573230i	−0.906129	+	0.423002i	$0.860976\pi$
$608$	−2.49908e13	+	4.32854e13i	−0.300789	+	0.520983i
$609$	9.42572e12	−	5.44194e12i	0.112520	−	0.0649632i
$610$		−	9.90536e11i		−	0.0117279i
$611$	7.34532e13	+	1.27225e14i	0.862591	+	1.49405i
$612$	5.53944e13	−	9.59459e13i	0.645221	−	1.11756i
$613$	6.25955e13			0.723170			0.361585	−	0.932339i	$-0.382236\pi$
$613$	6.25955e13			0.723170			0.361585	+	0.932339i	$0.382236\pi$
$614$	−1.81763e12	−	1.04941e12i	−0.0208288	−	0.0120255i
$615$	−2.99633e12	−	5.18980e12i	−0.0340577	−	0.0589896i
$616$	−1.63632e13	−	2.83420e13i	−0.184487	−	0.319541i
$617$	−6.74559e13	−	1.16837e14i	−0.754387	−	1.30664i	−0.945679	−	0.325103i	$-0.894601\pi$
$617$	−6.74559e13	−	1.16837e14i	−0.754387	−	1.30664i	0.191292	−	0.981533i	$-0.438732\pi$
$618$	3.40507e11			0.00377731
$619$	−2.66055e13	−	4.60821e13i	−0.292764	−	0.507083i	0.681698	−	0.731634i	$-0.261242\pi$
$619$	−2.66055e13	−	4.60821e13i	−0.292764	−	0.507083i	−0.974462	+	0.224551i	$0.927908\pi$
$620$	5.86099e12	−	3.38385e12i	0.0639754	−	0.0369362i
$621$	−4.03746e13	−	2.33103e13i	−0.437169	−	0.252400i
$622$	−1.04172e13	−	6.01439e12i	−0.111892	−	0.0646010i
$623$	−8.30573e13			−0.884988
$624$		−	2.49970e13i		−	0.264219i
$625$	−2.90375e13	+	5.02945e13i	−0.304481	+	0.527376i
$626$	−8.22118e12	+	1.42395e13i	−0.0855190	+	0.148123i
$627$	9.13445e12	+	1.58213e13i	0.0942637	+	0.163270i
$628$	5.48341e13	−	3.16585e13i	0.561374	−	0.324110i
$629$		−	1.23121e14i		−	1.25049i
$630$	7.51680e12	−	4.33983e12i	0.0757408	−	0.0437290i
$631$	4.02151e13	−	2.32182e13i	0.402015	−	0.232103i	−0.285338	−	0.958427i	$-0.592106\pi$
$631$	4.02151e13	−	2.32182e13i	0.402015	−	0.232103i	0.687353	+	0.726323i	$0.258773\pi$
$632$	2.46203e13	−	1.42146e13i	0.244179	−	0.140977i
$633$	−1.24949e13	+	2.16419e13i	−0.122946	+	0.212949i
$634$			2.72346e13i			0.265873i
$635$	9.26930e12	+	5.35163e12i	0.0897797	+	0.0518344i
$636$	5.00151e12	−	2.88762e12i	0.0480635	−	0.0277495i
$637$	−1.69235e14			−1.61359
$638$	−2.99620e12	−	5.18958e12i	−0.0283445	−	0.0490940i
$639$	−1.07984e13	−	6.23444e12i	−0.101357	−	0.0585185i
$640$	1.24802e13	−	2.16164e13i	0.116231	−	0.201318i
$641$			8.19028e13i			0.756848i	0.925632	+	0.378424i	$0.123534\pi$
$641$			8.19028e13i			0.756848i	−0.925632	+	0.378424i	$0.876466\pi$
$642$	2.13702e12	−	3.70142e12i	0.0195944	−	0.0339386i
$643$	7.10457e13			0.646373			0.323186	−	0.946335i	$-0.395246\pi$
$643$	7.10457e13			0.646373			0.323186	+	0.946335i	$0.395246\pi$
$644$			2.00469e14i			1.80974i
$645$	−3.02320e12	+	7.75145e12i	−0.0270813	+	0.0694360i
$646$	−3.24702e13			−0.288618
$647$			3.67794e13i			0.324401i	0.986758	+	0.162201i	$0.0518592\pi$
$647$			3.67794e13i			0.324401i	−0.986758	+	0.162201i	$0.948141\pi$
$648$	2.90246e13	+	1.67573e13i	0.254033	+	0.146666i
$649$	5.23831e13			0.454955
$650$	2.10139e13	+	1.21324e13i	0.181109	+	0.104563i
$651$	−3.53870e12	+	6.12921e12i	−0.0302649	+	0.0524203i
$652$	9.53390e13	−	5.50440e13i	0.809157	−	0.467167i
$653$		−	5.80141e13i		−	0.488616i	−0.969698	−	0.244308i	$-0.921439\pi$
$653$		−	5.80141e13i		−	0.488616i	0.969698	−	0.244308i	$-0.0785608\pi$
$654$	1.40651e10	+	2.43615e10i	0.000117559	+	0.000203618i
$655$	−2.07576e13	+	3.59532e13i	−0.172175	+	0.298216i
$656$	−1.01588e14			−0.836224
$657$	−1.36787e14	−	7.89741e13i	−1.11742	−	0.645146i
$658$	−1.83322e13	−	3.17523e13i	−0.148622	−	0.257422i
$659$	8.68215e13	+	1.50379e14i	0.698554	+	1.20993i	0.968968	+	0.247187i	$0.0795062\pi$
$659$	8.68215e13	+	1.50379e14i	0.698554	+	1.20993i	−0.270414	+	0.962744i	$0.587160\pi$
$660$	−3.43930e12	−	5.95704e12i	−0.0274631	−	0.0475675i
$661$	−1.64113e14			−1.30058			−0.650289	−	0.759687i	$-0.725352\pi$
$661$	−1.64113e14			−1.30058			−0.650289	+	0.759687i	$0.725352\pi$
$662$	2.39202e12	+	4.14310e12i	0.0188137	+	0.0325864i
$663$	4.43643e13	−	2.56137e13i	0.346311	−	0.199943i
$664$	−3.36512e12	−	1.94285e12i	−0.0260711	−	0.0150522i
$665$	7.47887e13	+	4.31793e13i	0.575079	+	0.332022i
$666$	1.92011e13			0.146539
$667$			7.44953e13i			0.564286i
$668$	7.19409e13	−	1.24605e14i	0.540871	−	0.936816i
$669$	2.39531e13	−	4.14879e13i	0.178744	−	0.309593i
$670$	6.13605e12	+	1.06280e13i	0.0454480	+	0.0787183i
$671$	−1.67674e13	+	9.68065e12i	−0.123269	+	0.0711692i
$672$			1.96803e13i			0.143610i
$673$	−1.00151e14	+	5.78220e13i	−0.725402	+	0.418811i	−0.816738	−	0.577009i	$-0.804220\pi$
$673$	−1.00151e14	+	5.78220e13i	−0.725402	+	0.418811i	0.0913359	+	0.995820i	$0.470886\pi$
$674$	−9.29360e12	+	5.36566e12i	−0.0668166	+	0.0385766i
$675$	−4.14050e13	+	2.39052e13i	−0.295484	+	0.170598i
$676$	−7.19993e13	+	1.24706e14i	−0.510029	+	0.883396i
$677$		−	3.20311e13i		−	0.225231i	−0.993639	−	0.112615i	$-0.964077\pi$
$677$		−	3.20311e13i		−	0.225231i	0.993639	−	0.112615i	$-0.0359228\pi$
$678$	−7.00433e12	−	4.04395e12i	−0.0488898	−	0.0282265i
$679$	3.41452e14	−	1.97137e14i	2.36582	−	1.36590i
$680$	2.48115e13			0.170651
$681$	−9.04202e12	−	1.56612e13i	−0.0617348	−	0.106928i
$682$	3.37460e12	+	1.94833e12i	0.0228718	+	0.0132050i
$683$	1.33166e14	−	2.30650e14i	0.895961	−	1.55185i	0.0633494	−	0.997991i	$-0.479822\pi$
$683$	1.33166e14	−	2.30650e14i	0.895961	−	1.55185i	0.832611	−	0.553858i	$-0.186845\pi$
$684$			1.71906e14i			1.14818i
$685$	−4.95276e13	+	8.57843e13i	−0.328394	+	0.568794i
$686$	4.75795e12			0.0313184
$687$			3.41355e13i			0.223061i
$688$	8.81734e13	+	1.10085e14i	0.571999	+	0.714142i
$689$	−6.29813e13			−0.405616
$690$		−	2.51892e12i		−	0.0161053i
$691$	1.17244e14	+	6.76911e13i	0.744221	+	0.429676i	0.823602	−	0.567168i	$-0.191961\pi$
$691$	1.17244e14	+	6.76911e13i	0.744221	+	0.429676i	−0.0793813	+	0.996844i	$0.525294\pi$
$692$	2.04637e14			1.28960
$693$	−1.46925e14	−	8.48274e13i	−0.919244	−	0.530726i
$694$	−6.31328e12	+	1.09349e13i	−0.0392155	+	0.0679232i
$695$	−3.65770e12	+	2.11178e12i	−0.0225572	+	0.0130234i
$696$			4.85206e12i			0.0297084i
$697$	−1.04094e14	−	1.80297e14i	−0.632796	−	1.09604i
$698$	−1.93743e13	+	3.35573e13i	−0.116936	+	0.202540i
$699$	2.23980e13			0.134222
$700$	1.78042e14	+	1.02793e14i	1.05933	+	0.611605i
$701$	9.81283e13	+	1.69963e14i	0.579701	+	1.00407i	0.995513	+	0.0946216i	$0.0301641\pi$
$701$	9.81283e13	+	1.69963e14i	0.579701	+	1.00407i	−0.415812	+	0.909451i	$0.636503\pi$
$702$	8.15841e12	+	1.41308e13i	0.0478542	+	0.0828859i
$703$	9.55209e13	+	1.65447e14i	0.556316	+	0.963568i
$704$	−1.09205e14			−0.631511
$705$	−7.81978e12	−	1.35442e13i	−0.0449002	−	0.0777695i
$706$	−1.31304e13	+	7.58084e12i	−0.0748608	+	0.0432209i
$707$	2.35834e14	+	1.36159e14i	1.33509	+	0.770812i
$708$	−1.80995e13	−	1.04498e13i	−0.101742	−	0.0587408i
$709$	−2.03110e13			−0.113371			−0.0566853	−	0.998392i	$-0.518053\pi$
$709$	−2.03110e13			−0.113371			−0.0566853	+	0.998392i	$0.518053\pi$
$710$		−	1.37596e12i		−	0.00762628i
$711$	7.36886e13	−	1.27632e14i	0.405558	−	0.702446i
$712$	1.85136e13	−	3.20664e13i	0.101179	−	0.175247i
$713$	−2.42208e13	−	4.19517e13i	−0.131444	−	0.227668i
$714$	−1.10723e13	+	6.39258e12i	−0.0596686	+	0.0344497i
$715$			7.50137e13i			0.401430i
$716$	1.21924e14	−	7.03926e13i	0.647921	−	0.374078i
$717$	−3.24256e13	+	1.87209e13i	−0.171116	+	0.0987941i
$718$	−3.28124e13	+	1.89443e13i	−0.171956	+	0.0992786i
$719$	−1.72683e14	+	2.99097e14i	−0.898683	+	1.55656i	−0.0695031	+	0.997582i	$0.522141\pi$
$719$	−1.72683e14	+	2.99097e14i	−0.898683	+	1.55656i	−0.829180	+	0.558982i	$0.811192\pi$
$720$		−	6.27631e13i		−	0.324371i
$721$	−2.72467e13	−	1.57309e13i	−0.139842	−	0.0807377i
$722$	1.48913e13	−	8.59748e12i	0.0759007	−	0.0438213i
$723$	4.79439e13			0.242684
$724$	2.14708e13	+	3.71885e13i	0.107933	+	0.186946i
$725$	6.61613e13	+	3.81983e13i	0.330304	+	0.190701i
$726$	−1.46014e12	+	2.52904e12i	−0.00723957	+	0.0125393i
$727$		−	7.92403e13i		−	0.390188i	−0.980785	−	0.195094i	$-0.937499\pi$
$727$		−	7.92403e13i		−	0.390188i	0.980785	−	0.195094i	$-0.0625012\pi$
$728$	7.11958e13	−	1.23315e14i	0.348175	−	0.603057i
$729$	1.57332e14			0.764153
$730$		−	1.74298e13i		−	0.0840771i
$731$	−1.05028e14	+	2.69290e14i	−0.503174	+	1.29013i
$732$	7.72466e12			0.0367556
$733$		−	3.22963e14i		−	1.52627i	−0.646236	−	0.763137i	$-0.723658\pi$
$733$		−	3.22963e14i		−	1.52627i	0.646236	−	0.763137i	$-0.276342\pi$
$734$	5.32880e13	+	3.07659e13i	0.250120	+	0.144407i
$735$	1.80166e13			0.0839918
$736$	−1.16656e14	−	6.73513e13i	−0.540154	−	0.311858i
$737$	1.19937e14	−	2.07737e14i	0.551589	−	0.955381i
$738$	2.81177e13	−	1.62338e13i	0.128439	−	0.0741545i
$739$			4.43717e13i			0.201319i	0.994921	+	0.100659i	$0.0320952\pi$
$739$			4.43717e13i			0.201319i	−0.994921	+	0.100659i	$0.967905\pi$
$740$	−3.59655e13	−	6.22940e13i	−0.162079	−	0.280729i
$741$	−3.97436e13	+	6.88380e13i	−0.177900	+	0.308132i
$742$	1.57186e13			0.0698868
$743$	−2.27636e14	−	1.31426e14i	−1.00530	−	0.580412i	−0.0954900	−	0.995430i	$-0.530442\pi$
$743$	−2.27636e14	−	1.31426e14i	−1.00530	−	0.580412i	−0.909813	+	0.415018i	$0.863775\pi$
$744$	−1.57756e12	−	2.73242e12i	−0.00692024	−	0.0119862i
$745$	4.15799e13	+	7.20185e13i	0.181176	+	0.313807i
$746$	−3.26049e13	−	5.64733e13i	−0.141120	−	0.244427i
$747$	−2.01436e13			−0.0866032
$748$	−1.19483e14	−	2.06951e14i	−0.510269	−	0.883812i
$749$	−3.42000e14	+	1.97454e14i	−1.45083	+	0.837637i
$750$	−4.82807e12	−	2.78749e12i	−0.0203454	−	0.0117464i
$751$	−2.63033e14	−	1.51862e14i	−1.10106	−	0.635697i	−0.164560	−	0.986367i	$-0.552621\pi$
$751$	−2.63033e14	−	1.51862e14i	−1.10106	−	0.635697i	−0.936499	+	0.350670i	$0.885954\pi$
$752$	−2.65122e14			−1.10244
$753$		−	7.56730e13i		−	0.312584i
$754$	1.30364e13	−	2.25797e13i	0.0534934	−	0.0926533i
$755$	−3.48487e13	+	6.03597e13i	−0.142053	+	0.246044i
$756$	6.91229e13	+	1.19724e14i	0.279906	+	0.484812i
$757$	1.71427e14	−	9.89734e13i	0.689604	−	0.398143i	−0.113860	−	0.993497i	$-0.536321\pi$
$757$	1.71427e14	−	9.89734e13i	0.689604	−	0.398143i	0.803464	+	0.595354i	$0.202988\pi$
$758$		−	4.01865e13i		−	0.160596i
$759$	−4.26391e13	+	2.46177e13i	−0.169278	+	0.0977325i
$760$	−3.33409e13	+	1.92494e13i	−0.131495	+	0.0759188i
$761$	−1.50473e14	+	8.68759e13i	−0.589572	+	0.340389i	−0.764928	−	0.644116i	$-0.777226\pi$
$761$	−1.50473e14	+	8.68759e13i	−0.589572	+	0.340389i	0.175356	+	0.984505i	$0.443892\pi$
$762$	1.22937e12	−	2.12933e12i	0.00478528	−	0.00828834i
$763$		−	2.59915e12i		−	0.0100510i
$764$	−3.41040e14	−	1.96900e14i	−1.31020	−	0.756447i
$765$	1.11391e14	−	6.43117e13i	0.425151	−	0.245461i
$766$	4.89317e13			0.185544
$767$	1.13959e14	+	1.97382e14i	0.429309	+	0.743585i
$768$	3.38787e13	+	1.95599e13i	0.126800	+	0.0732082i
$769$	9.46715e12	−	1.63976e13i	0.0352036	−	0.0609745i	−0.847887	−	0.530177i	$-0.822125\pi$
$769$	9.46715e12	−	1.63976e13i	0.0352036	−	0.0609745i	0.883090	+	0.469203i	$0.155459\pi$
$770$		−	1.87216e13i		−	0.0691656i
$771$	4.86903e13	−	8.43340e13i	0.178719	−	0.309550i
$772$	−3.58703e14			−1.30812
$773$		−	3.76252e14i		−	1.36327i	−0.731692	−	0.681635i	$-0.761269\pi$
$773$		−	3.76252e14i		−	1.36327i	0.731692	−	0.681635i	$-0.238731\pi$
$774$	−4.19964e13	−	1.63793e13i	−0.151184	−	0.0589646i
$775$	−4.96779e13			−0.177687
$776$			1.75769e14i			0.624644i
$777$	6.51448e13	+	3.76114e13i	0.230025	+	0.132805i
$778$	6.35700e13			0.223025
$779$	2.79758e14	+	1.61518e14i	0.975204	+	0.563034i
$780$	1.49643e13	−	2.59188e13i	0.0518301	−	0.0897724i
$781$	−2.32916e13	+	1.34474e13i	−0.0801575	+	0.0462790i
$782$		−	8.75087e13i		−	0.299238i
$783$	2.56865e13	+	4.44902e13i	0.0872761	+	0.151167i
$784$	1.52709e14	−	2.64500e14i	0.515566	−	0.892987i
$785$	7.35097e13			0.246602
$786$	8.25911e12	+	4.76840e12i	0.0275309	+	0.0158950i
$787$	1.02124e14	+	1.76884e14i	0.338262	+	0.585888i	0.984106	−	0.177582i	$-0.0568276\pi$
$787$	1.02124e14	+	1.76884e14i	0.338262	+	0.585888i	−0.645844	+	0.763470i	$0.723494\pi$
$788$	−8.96409e13	−	1.55263e14i	−0.295036	−	0.511017i
$789$	2.67524e13	+	4.63366e13i	0.0874940	+	0.151544i
$790$	1.62633e13			0.0528533
$791$	3.73648e14	+	6.47178e14i	1.20665	+	2.08998i
$792$	6.54997e13	−	3.78163e13i	0.210191	−	0.121354i
$793$	−7.29543e13	−	4.21202e13i	−0.232640	−	0.134315i
$794$	−3.18912e13	−	1.84124e13i	−0.101057	−	0.0583455i
$795$	6.70494e12			0.0211135
$796$			2.36898e14i			0.741304i
$797$	−5.66311e13	+	9.80879e13i	−0.176102	+	0.305017i	−0.940542	−	0.339678i	$-0.889682\pi$
$797$	−5.66311e13	+	9.80879e13i	−0.176102	+	0.305017i	0.764440	+	0.644694i	$0.223015\pi$
$798$	9.91907e12	−	1.71803e13i	0.0306518	−	0.0530905i
$799$	−2.71664e14	−	4.70535e14i	−0.834253	−	1.44497i
$800$	−1.19633e14	+	6.90702e13i	−0.365091	+	0.210786i
$801$		−	1.91949e14i		−	0.582136i
$802$	−2.99446e13	+	1.72885e13i	−0.0902498	+	0.0521058i
$803$	−2.95044e14	+	1.70344e14i	−0.883708	+	0.510209i
$804$	−8.28817e13	+	4.78518e13i	−0.246705	+	0.142435i
$805$	−1.16370e14	+	2.01559e14i	−0.344240	+	0.596241i
$806$			1.69542e13i			0.0498427i
$807$	−1.04292e14	−	6.02132e13i	−0.304708	−	0.175923i
$808$	−1.05135e14	+	6.06999e13i	−0.305275	+	0.176251i
$809$	4.47911e13			0.129255			0.0646277	−	0.997909i	$-0.479414\pi$
$809$	4.47911e13			0.129255			0.0646277	+	0.997909i	$0.479414\pi$
$810$	9.58627e12	+	1.66039e13i	0.0274931	+	0.0476195i
$811$	8.82130e13	+	5.09298e13i	0.251437	+	0.145167i	0.620422	−	0.784268i	$-0.286961\pi$
$811$	8.82130e13	+	5.09298e13i	0.251437	+	0.145167i	−0.368985	+	0.929435i	$0.620295\pi$
$812$	1.10452e14	−	1.91308e14i	0.312891	−	0.541943i
$813$			8.54807e13i			0.240666i
$814$	2.07079e13	−	3.58672e13i	0.0579448	−	0.100363i
$815$	1.27810e14			0.355448
$816$			9.24503e13i			0.255539i
$817$	−6.77889e13	−	4.43348e14i	−0.186230	−	1.21796i
$818$	1.62304e13			0.0443163
$819$		−	7.38162e14i		−	2.00324i
$820$	−1.05334e14	−	6.08149e13i	−0.284120	−	0.164036i
$821$	−6.62619e14			−1.77643			−0.888215	−	0.459428i	$-0.848054\pi$
$821$	−6.62619e14			−1.77643			−0.888215	+	0.459428i	$0.848054\pi$
$822$	1.97062e13	+	1.13774e13i	0.0525103	+	0.0303168i
$823$	7.88479e13	−	1.36569e14i	0.208829	−	0.361702i	−0.742517	−	0.669827i	$-0.766368\pi$
$823$	7.88479e13	−	1.36569e14i	0.208829	−	0.361702i	0.951346	+	0.308125i	$0.0997015\pi$
$824$	1.21466e13	−	7.01285e12i	0.0319756	−	0.0184611i
$825$			5.04920e13i			0.132115i
$826$	−2.84413e13	−	4.92619e13i	−0.0739690	−	0.128118i
$827$	−1.64372e13	+	2.84700e13i	−0.0424913	+	0.0735971i	−0.886489	−	0.462750i	$-0.846863\pi$
$827$	−1.64372e13	+	2.84700e13i	−0.0424913	+	0.0735971i	0.843998	+	0.536347i	$0.180196\pi$
$828$	−4.63293e14			−1.19043
$829$	3.53058e14	+	2.03838e14i	0.901723	+	0.520610i	0.877759	−	0.479103i	$-0.159038\pi$
$829$	3.53058e14	+	2.03838e14i	0.901723	+	0.520610i	0.0239643	+	0.999713i	$0.492371\pi$
$830$	−1.11143e12	−	1.92506e12i	−0.00282159	−	0.00488713i
$831$	−2.66111e13	−	4.60918e13i	−0.0671518	−	0.116310i
$832$	−2.37574e14	−	4.11491e14i	−0.595913	−	1.03215i
$833$	6.25908e14			1.56058
$834$	4.85114e11	+	8.40242e11i	0.00120230	+	0.00208245i
$835$	1.44664e14	−	8.35218e13i	0.356392	−	0.205763i
$836$	3.21116e14	+	1.85397e14i	0.786377	+	0.454015i
$837$	−2.89304e13	−	1.67030e13i	−0.0704251	−	0.0406599i
$838$	−8.23384e13			−0.199243
$839$		−	6.24597e13i		−	0.150242i	−0.997174	−	0.0751208i	$-0.976066\pi$
$839$		−	6.24597e13i		−	0.150242i	0.997174	−	0.0751208i	$-0.0239342\pi$
$840$	−7.57946e12	+	1.31280e13i	−0.0181235	+	0.0313908i
$841$	−1.69309e14	+	2.93252e14i	−0.402439	+	0.697045i
$842$	5.36473e13	+	9.29198e13i	0.126761	+	0.219557i
$843$	1.19596e14	−	6.90487e13i	0.280917	−	0.162187i
$844$			5.07205e14i			1.18433i
$845$	−1.44782e14	+	8.35896e13i	−0.336070	+	0.194030i
$846$	7.33811e13	−	4.23666e13i	0.169329	−	0.0977623i
$847$	2.33676e14	−	1.34913e14i	0.536039	−	0.309482i
$848$	5.68312e13	−	9.84345e13i	0.129601	−	0.224475i
$849$			1.16209e13i			0.0263451i
$850$	−7.77189e13	−	4.48710e13i	−0.175159	−	0.101128i
$851$	−4.45887e14	+	2.57433e14i	−0.999026	+	0.576788i
$852$	1.07303e13			0.0239010
$853$	1.32851e14	+	2.30105e14i	0.294185	+	0.509543i	0.974795	−	0.223103i	$-0.0716186\pi$
$853$	1.32851e14	+	2.30105e14i	0.294185	+	0.509543i	−0.680610	+	0.732646i	$0.738285\pi$
$854$	1.82076e13	+	1.05122e13i	0.0400834	+	0.0231422i
$855$	−9.97894e13	+	1.72840e14i	−0.218401	+	0.378281i
$856$		−	1.76050e14i		−	0.383061i
$857$	2.17708e14	−	3.77082e14i	0.470946	−	0.815702i	−0.528502	−	0.848932i	$-0.677246\pi$
$857$	2.17708e14	−	3.77082e14i	0.470946	−	0.815702i	0.999448	+	0.0332298i	$0.0105793\pi$
$858$	1.72320e13			0.0370595
$859$			6.41514e13i			0.137164i	0.997645	+	0.0685820i	$0.0218475\pi$
$859$			6.41514e13i			0.137164i	−0.997645	+	0.0685820i	$0.978153\pi$
$860$	2.55239e13	+	1.66929e14i	0.0542568	+	0.354846i
$861$	1.27196e14			0.268817
$862$		−	8.29567e12i		−	0.0174307i
$863$	6.40031e14	+	3.69522e14i	1.33705	+	0.771945i	0.986369	−	0.164551i	$-0.0526174\pi$
$863$	6.40031e14	+	3.69522e14i	1.33705	+	0.771945i	0.350679	+	0.936496i	$0.385951\pi$
$864$	−9.28927e13			−0.192936
$865$	2.05750e14	+	1.18790e14i	0.424873	+	0.245300i
$866$	−4.58029e13	+	7.93329e13i	−0.0940380	+	0.162879i
$867$	−7.85154e13	+	4.53309e13i	−0.160273	+	0.0925335i
$868$			1.43646e14i			0.291538i
$869$	−1.58943e14	−	2.75298e14i	−0.320733	−	0.555525i
$870$	−1.38784e12	+	2.40382e12i	−0.00278448	+	0.00482286i
$871$	1.04368e15			2.08199
$872$	1.00347e12	+	5.79352e11i	0.00199031	+	0.00114911i
$873$	4.55594e14	+	7.89113e14i	0.898478	+	1.55621i
$874$	6.78915e13	+	1.17592e14i	0.133125	+	0.230579i
$875$	2.57555e14	+	4.46098e14i	0.502145	+	0.869741i
$876$	1.35925e14			0.263500
$877$	1.65954e14	+	2.87440e14i	0.319882	+	0.554051i	0.980463	−	0.196703i	$-0.0630235\pi$
$877$	1.65954e14	+	2.87440e14i	0.319882	+	0.554051i	−0.660581	+	0.750754i	$0.729690\pi$
$878$	−1.28819e13	+	7.43738e12i	−0.0246893	+	0.0142544i
$879$	−3.60152e13	−	2.07934e13i	−0.0686344	−	0.0396261i
$880$	−1.17240e14	−	6.76886e13i	−0.222158	−	0.128263i
$881$	−8.84214e14			−1.66601			−0.833005	−	0.553265i	$-0.813382\pi$
$881$	−8.84214e14			−1.66601			−0.833005	+	0.553265i	$0.813382\pi$
$882$			9.76118e13i			0.182877i
$883$	−3.79168e13	+	6.56739e13i	−0.0706364	+	0.122346i	−0.899180	−	0.437578i	$-0.855836\pi$
$883$	−3.79168e13	+	6.56739e13i	−0.0706364	+	0.122346i	0.828544	+	0.559924i	$0.189170\pi$
$884$	5.19867e14	−	9.00437e14i	0.963011	−	1.66798i
$885$	−1.21319e13	−	2.10131e13i	−0.0223467	−	0.0387057i
$886$	−1.48157e14	+	8.55384e13i	−0.271365	+	0.156672i
$887$		−	3.86570e14i		−	0.704060i	−0.935989	−	0.352030i	$-0.885491\pi$
$887$		−	3.86570e14i		−	0.704060i	0.935989	−	0.352030i	$-0.114509\pi$
$888$	−2.90417e13	+	1.67672e13i	−0.0525965	+	0.0303666i
$889$	−1.96743e14	+	1.13590e14i	−0.354316	+	0.204565i
$890$	1.83440e13	−	1.05909e13i	0.0328507	−	0.0189664i
$891$	1.87376e14	−	3.24545e14i	0.333676	−	0.577944i
$892$		−	9.72323e14i		−	1.72181i
$893$	7.30108e14	+	4.21528e14i	1.28567	+	0.742282i
$894$	1.65440e13	−	9.55166e12i	0.0289702	−	0.0167260i
$895$	1.63449e14			0.284620
$896$	2.64896e14	+	4.58813e14i	0.458706	+	0.794503i
$897$	−1.85521e14	−	1.07111e14i	−0.319471	−	0.184447i
$898$	−2.94633e13	+	5.10319e13i	−0.0504544	+	0.0873897i
$899$			5.33796e13i			0.0909028i
$900$	−2.37559e14	+	4.11464e14i	−0.402308	+	0.696817i
$901$	2.32934e14			0.392291
$902$		−	7.00310e13i		−	0.117289i
$903$	−1.10400e14	−	1.37835e14i	−0.183878	−	0.229572i
$904$	−3.33147e14			−0.551815
$905$			4.98543e13i			0.0821220i
$906$	1.38657e13	+	8.00538e12i	0.0227144	+	0.0131142i
$907$	−5.95915e14			−0.970840			−0.485420	−	0.874281i	$-0.661333\pi$
$907$	−5.95915e14			−0.970840			−0.485420	+	0.874281i	$0.661333\pi$
$908$	−3.17867e14	−	1.83521e14i	−0.515010	−	0.297341i
$909$	−3.14670e14	+	5.45024e14i	−0.507032	+	0.878206i
$910$	7.05439e13	−	4.07286e13i	0.113045	−	0.0652668i
$911$			5.99070e14i			0.954741i	0.878702	+	0.477371i	$0.158410\pi$
$911$			5.99070e14i			0.954741i	−0.878702	+	0.477371i	$0.841590\pi$
$912$	−7.17254e13	−	1.24232e14i	−0.113684	−	0.196906i
$913$	−2.17244e13	+	3.76278e13i	−0.0342448	+	0.0593137i
$914$	7.45867e13			0.116931
$915$	7.76666e12	+	4.48408e12i	0.0121096	+	0.00699146i
$916$	3.46415e14	+	6.00008e14i	0.537179	+	0.930421i
$917$	−4.40585e14	−	7.63115e14i	−0.679490	−	1.17691i
$918$	−3.01736e13	−	5.22621e13i	−0.0462821	−	0.0801630i
$919$	1.12166e15			1.71113			0.855567	−	0.517692i	$-0.173208\pi$
$919$	1.12166e15			1.71113			0.855567	+	0.517692i	$0.173208\pi$
$920$	−5.18780e13	−	8.98552e13i	−0.0787125	−	0.136334i
$921$	1.64565e13	−	9.50118e12i	0.0248336	−	0.0143377i
$922$	−1.27853e14	−	7.38158e13i	−0.191891	−	0.110789i
$923$	−1.01341e14	−	5.85092e13i	−0.151278	−	0.0873405i
$924$	1.46000e14			0.216767
$925$			5.28006e14i			0.779705i
$926$	8.82478e13	−	1.52850e14i	0.129613	−	0.224497i
$927$	3.63548e13	−	6.29684e13i	0.0531084	−	0.0919865i
$928$	7.42169e13	+	1.28547e14i	0.107836	+	0.186777i
$929$	2.33395e14	−	1.34750e14i	0.337297	−	0.194738i	−0.321779	−	0.946815i	$-0.604281\pi$
$929$	2.33395e14	−	1.34750e14i	0.337297	−	0.194738i	0.659076	+	0.752076i	$0.270948\pi$
$930$		−	1.80493e12i		−	0.00259445i
$931$	−8.41077e14	+	4.85596e14i	−1.20251	+	0.694268i
$932$	3.93694e14	−	2.27299e14i	0.559859	−	0.323235i
$933$	9.43159e13	−	5.44533e13i	0.133406	−	0.0770223i
$934$	2.83751e13	−	4.91471e13i	0.0399212	−	0.0691455i
$935$		−	2.77435e14i		−	0.388243i
$936$	2.84987e14	+	1.64537e14i	0.396685	+	0.229026i
$937$	5.91229e14	−	3.41346e14i	0.818574	−	0.472604i	−0.0313504	−	0.999508i	$-0.509981\pi$
$937$	5.91229e14	−	3.41346e14i	0.818574	−	0.472604i	0.849925	+	0.526904i	$0.176647\pi$
$938$	−2.60479e14			−0.358722
$939$	−7.44333e13	−	1.28922e14i	−0.101962	−	0.176604i
$940$	−2.74900e14	−	1.58713e14i	−0.374572	−	0.216259i
$941$	2.89397e14	−	5.01251e14i	0.392235	−	0.679371i	−0.600509	−	0.799618i	$-0.705035\pi$
$941$	2.89397e14	−	5.01251e14i	0.392235	−	0.679371i	0.992744	+	0.120247i	$0.0383687\pi$
$942$		−	1.68865e13i		−	0.0227659i
$943$	−4.35299e14	+	7.53960e14i	−0.583753	+	1.01109i
$944$	−4.11322e14			−0.548684
$945$			1.60500e14i			0.212969i
$946$	−7.58884e13	+	6.07836e13i	−0.100166	+	0.0802289i
$947$	3.90949e14			0.513299			0.256650	−	0.966505i	$-0.417381\pi$
$947$	3.90949e14			0.513299			0.256650	+	0.966505i	$0.417381\pi$
$948$			1.26828e14i			0.165644i
$949$	−1.28372e15	−	7.41159e14i	−1.66779	−	0.962898i
$950$	1.39248e14			0.179959
$951$	−2.13542e14	−	1.23289e14i	−0.274525	−	0.158497i
$952$	−2.63315e14	+	4.56075e14i	−0.336737	+	0.583246i
$953$	−8.52182e14	+	4.92007e14i	−1.08410	+	0.625903i	−0.931998	−	0.362462i	$-0.881936\pi$
$953$	−8.52182e14	+	4.92007e14i	−1.08410	+	0.625903i	−0.152098	+	0.988365i	$0.548603\pi$
$954$			3.63265e13i			0.0459708i
$955$	−2.28596e14	−	3.95941e14i	−0.287775	−	0.498440i
$956$	−3.79967e14	+	6.58123e14i	−0.475835	+	0.824171i
$957$	5.42544e13			0.0675888
$958$	5.34529e13	+	3.08611e13i	0.0662436	+	0.0382458i
$959$	−1.05124e15	−	1.82079e15i	−1.29601	−	2.24475i
$960$	2.52920e13	+	4.38070e13i	0.0310189	+	0.0537264i
$961$	3.92459e14	+	6.79758e14i	0.478825	+	0.829350i
$962$	1.80199e14			0.218714
$963$	−4.56325e14	−	7.90378e14i	−0.550989	−	0.954341i
$964$	8.42720e14	−	4.86545e14i	1.01227	−	0.584437i
$965$	−3.60654e14	−	2.08224e14i	−0.430977	−	0.248825i
$966$	4.63017e13	+	2.67323e13i	0.0550442	+	0.0317798i
$967$	7.79584e14			0.921999			0.461000	−	0.887400i	$-0.347491\pi$
$967$	7.79584e14			0.921999			0.461000	+	0.887400i	$0.347491\pi$
$968$			1.20289e14i			0.141530i
$969$	1.46990e14	−	2.54595e14i	0.172056	−	0.298010i
$970$	−5.02754e13	+	8.70796e13i	−0.0585460	+	0.101405i
$971$	−2.62290e13	−	4.54299e13i	−0.0303868	−	0.0526315i	0.850432	−	0.526085i	$-0.176341\pi$
$971$	−2.62290e13	−	4.54299e13i	−0.0303868	−	0.0526315i	−0.880819	+	0.473453i	$0.843007\pi$
$972$	−4.17905e14	+	2.41278e14i	−0.481667	+	0.278090i
$973$		−	8.96460e13i		−	0.102794i
$974$	1.34344e14	−	7.75636e13i	0.153258	−	0.0884837i
$975$	−1.90256e14	+	1.09844e14i	−0.215931	+	0.124668i
$976$	1.31661e14	−	7.60143e13i	0.148664	−	0.0858314i
$977$	6.46602e14	−	1.11995e15i	0.726380	−	1.25813i	−0.232023	−	0.972710i	$-0.574534\pi$
$977$	6.46602e14	−	1.11995e15i	0.726380	−	1.25813i	0.958403	−	0.285417i	$-0.0921322\pi$
$978$		−	2.93603e13i		−	0.0328145i
$979$	−3.58558e14	−	2.07013e14i	−0.398699	−	0.230189i
$980$	3.16682e14	−	1.82836e14i	0.350343	−	0.202270i
$981$	6.00675e12			0.00661142
$982$	−7.66270e13	−	1.32722e14i	−0.0839121	−	0.145340i
$983$	−2.14635e14	−	1.23920e14i	−0.233848	−	0.135012i	0.378498	−	0.925602i	$-0.376441\pi$
$983$	−2.14635e14	−	1.23920e14i	−0.233848	−	0.135012i	−0.612346	+	0.790590i	$0.709774\pi$
$984$	−2.83521e13	+	4.91073e13i	−0.0307333	+	0.0532317i
$985$		−	2.08142e14i		−	0.224481i
$986$	−4.82145e13	+	8.35100e13i	−0.0517361	+	0.0896095i
$987$	3.31953e14			0.354398
$988$			1.61331e15i			1.71369i
$989$	1.19484e15	−	1.82694e14i	1.26278	−	0.193083i
$990$	4.32666e13			0.0454964
$991$			1.23420e15i			1.29127i	0.763645	+	0.645637i	$0.223408\pi$
$991$			1.23420e15i			1.29127i	−0.763645	+	0.645637i	$0.776592\pi$
$992$	−8.35898e13	−	4.82606e13i	−0.0870152	−	0.0502383i
$993$	−4.33140e13			−0.0448623
$994$	2.52923e13	+	1.46025e13i	0.0260649	+	0.0150486i
$995$	−1.37517e14	+	2.38186e14i	−0.141007	+	0.244231i
$996$	1.50125e13	−	8.66748e12i	0.0153164	−	0.00884293i
$997$		−	2.12779e13i		−	0.0215999i	−0.999942	−	0.0108000i	$-0.996562\pi$
$997$		−	2.12779e13i		−	0.0215999i	0.999942	−	0.0108000i	$-0.00343780\pi$
$998$	−7.07498e13	−	1.22542e14i	−0.0714615	−	0.123775i
$999$	−1.77529e14	+	3.07489e14i	−0.178419	+	0.309031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.37.18	yes	72
43.7	odd	6	inner	43.11.d.a.7.19	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.19	✓	72	43.7	odd	6	inner
43.11.d.a.37.18	yes	72	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.41302i q^{2} +(42.4427 + 24.5043i) q^{3} +994.699 q^{4} +(1000.11 + 577.412i) q^{5} +(132.642 - 229.743i) q^{6} +(-21227.5 + 12255.7i) q^{7} -10927.3i q^{8} +(-28323.6 - 49057.9i) q^{9} +O(q^{10})\)	\(q-5.41302i q^{2} +(42.4427 + 24.5043i) q^{3} +994.699 q^{4} +(1000.11 + 577.412i) q^{5} +(132.642 - 229.743i) q^{6} +(-21227.5 + 12255.7i) q^{7} -10927.3i q^{8} +(-28323.6 - 49057.9i) q^{9} +(3125.54 - 5413.60i) q^{10} -122185. q^{11} +(42217.7 + 24374.4i) q^{12} +(-265812. - 460400. i) q^{13} +(66340.4 + 114905. i) q^{14} +(28298.2 + 49013.9i) q^{15} +959423. q^{16} +(983096. + 1.70277e6i) q^{17} +(-265551. + 153316. i) q^{18} +(-2.64211e6 - 1.52542e6i) q^{19} +(994806. + 574352. i) q^{20} -1.20127e6 q^{21} +661392. i q^{22} +(4.11108e6 - 7.12060e6i) q^{23} +(267765. - 463782. i) q^{24} +(-4.21600e6 - 7.30233e6i) q^{25} +(-2.49215e6 + 1.43885e6i) q^{26} -5.67011e6i q^{27} +(-2.11150e7 + 1.21908e7i) q^{28} +(-7.84645e6 + 4.53015e6i) q^{29} +(265313. - 153178. i) q^{30} +(2.94580e6 - 5.10227e6i) q^{31} -1.63829e7i q^{32} +(-5.18588e6 - 2.99407e6i) q^{33} +(9.21713e6 - 5.32151e6i) q^{34} -2.83064e7 q^{35} +(-2.81734e7 - 4.87978e7i) q^{36} +(-5.42299e7 - 3.13096e7i) q^{37} +(-8.25714e6 + 1.43018e7i) q^{38} -2.60542e7i q^{39} +(6.30953e6 - 1.09284e7i) q^{40} -1.05884e8 q^{41} +6.50250e6i q^{42} +(9.19026e7 + 1.14741e8i) q^{43} -1.21538e8 q^{44} -6.54175e7i q^{45} +(-3.85439e7 - 2.22533e7i) q^{46} -2.76335e8 q^{47} +(4.07205e7 + 2.35100e7i) q^{48} +(1.59168e8 - 2.75687e8i) q^{49} +(-3.95276e7 + 2.28213e7i) q^{50} +9.63603e7i q^{51} +(-2.64403e8 - 4.57960e8i) q^{52} +(5.92347e7 - 1.02598e8i) q^{53} -3.06924e7 q^{54} +(-1.22199e8 - 7.05514e7i) q^{55} +(1.33921e8 + 2.31959e8i) q^{56} +(-7.47589e7 - 1.29486e8i) q^{57} +(2.45218e7 + 4.24730e7i) q^{58} -4.28718e8 q^{59} +(2.81482e7 + 4.87541e7i) q^{60} +(1.37229e8 - 7.92292e7i) q^{61} +(-2.76187e7 - 1.59456e7i) q^{62} +(1.20248e9 + 6.94252e8i) q^{63} +8.93768e8 q^{64} -6.13933e8i q^{65} +(-1.62069e7 + 2.80713e7i) q^{66} +(-9.81598e8 + 1.70018e9i) q^{67} +(9.77885e8 + 1.69375e9i) q^{68} +(3.48971e8 - 2.01478e8i) q^{69} +1.53223e8i q^{70} +(1.90625e8 - 1.10057e8i) q^{71} +(-5.36068e8 + 3.09499e8i) q^{72} +(2.41472e9 - 1.39414e9i) q^{73} +(-1.69480e8 + 2.93547e8i) q^{74} -4.13241e8i q^{75} +(-2.62811e9 - 1.51734e9i) q^{76} +(2.59369e9 - 1.49747e9i) q^{77} -1.41032e8 q^{78} +(1.30084e9 + 2.25311e9i) q^{79} +(9.59526e8 + 5.53982e8i) q^{80} +(-1.53354e9 + 2.65616e9i) q^{81} +5.73154e8i q^{82} +(1.77799e8 - 3.07956e8i) q^{83} -1.19490e9 q^{84} +2.27061e9i q^{85} +(6.21092e8 - 4.97470e8i) q^{86} -4.44033e8 q^{87} +1.33515e9i q^{88} +(2.93454e9 + 1.69426e9i) q^{89} -3.54106e8 q^{90} +(1.12851e10 + 6.51544e9i) q^{91} +(4.08929e9 - 7.08285e9i) q^{92} +(2.50055e8 - 1.44369e8i) q^{93} +1.49581e9i q^{94} +(-1.76160e9 - 3.05117e9i) q^{95} +(4.01451e8 - 6.95333e8i) q^{96} -1.60853e10 q^{97} +(-1.49230e9 - 8.61577e8i) q^{98} +(3.46073e9 + 5.99416e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9 - 127061 * q^10 + 521524 * q^11 - 606618 * q^12 + 796742 * q^13 - 865794 * q^14 - 433513 * q^15 + 22423366 * q^16 - 1768471 * q^17 - 11957547 * q^18 - 122844 * q^19 + 419841 * q^20 - 26778860 * q^21 + 16414886 * q^23 + 8684578 * q^24 + 70516989 * q^25 + 3069 * q^26 - 97624092 * q^28 + 118701393 * q^29 - 1455921 * q^30 + 10824883 * q^31 + 315141798 * q^33 + 47529561 * q^34 - 333788722 * q^35 - 597728908 * q^36 - 169881246 * q^37 - 88887452 * q^38 + 570788831 * q^40 - 543049070 * q^41 + 408159179 * q^43 - 754130886 * q^44 + 270181896 * q^46 + 348527658 * q^47 + 175039227 * q^48 + 781091547 * q^49 - 663244398 * q^50 - 1853993086 * q^52 + 219922736 * q^53 + 3104867360 * q^54 + 2154394182 * q^55 + 2010912675 * q^56 + 349107351 * q^57 + 2023447828 * q^58 + 2247595680 * q^59 - 2906780465 * q^60 + 508093974 * q^61 - 3451752063 * q^62 + 158921973 * q^63 - 13473879716 * q^64 + 1277847051 * q^66 - 2812410281 * q^67 + 13614613118 * q^68 - 5113655829 * q^69 + 2418191196 * q^71 + 26243329290 * q^72 - 6537901611 * q^73 - 2632816966 * q^74 - 10170994206 * q^76 - 16936463889 * q^77 - 24146069696 * q^78 + 5397136602 * q^79 + 7242149661 * q^80 - 15745886176 * q^81 + 4998656042 * q^83 + 44726677232 * q^84 - 27688564866 * q^86 + 37895576172 * q^87 - 12151857357 * q^89 - 96024912764 * q^90 + 36633770214 * q^91 - 31643971023 * q^92 + 59768940153 * q^93 - 19802964089 * q^95 - 3289705262 * q^96 - 40329658574 * q^97 + 19243888221 * q^98 + 18506221111 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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