LMFDB - Embedded newform 75.10.e.f.68.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, 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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.7
Character	$\chi$	$=$	75.68
Dual form			75.10.e.f.32.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.35582 - 6.35582i) q^{2} +(-0.342183 + 140.296i) q^{3} -431.207i q^{4} +(893.869 - 889.519i) q^{6} +(7866.00 - 7866.00i) q^{7} +(-5994.85 + 5994.85i) q^{8} +(-19682.8 - 96.0135i) q^{9} +O(q^{10})$	\(q+(-6.35582 - 6.35582i) q^{2} +(-0.342183 + 140.296i) q^{3} -431.207i q^{4} +(893.869 - 889.519i) q^{6} +(7866.00 - 7866.00i) q^{7} +(-5994.85 + 5994.85i) q^{8} +(-19682.8 - 96.0135i) q^{9} -50710.2i q^{11} +(60496.5 + 147.552i) q^{12} +(4944.61 + 4944.61i) q^{13} -99989.7 q^{14} -144574. q^{16} +(174648. + 174648. i) q^{17} +(124490. + 125710. i) q^{18} -36012.9i q^{19} +(1.10087e6 + 1.10626e6i) q^{21} +(-322305. + 322305. i) q^{22} +(-995471. + 995471. i) q^{23} +(-839001. - 843104. i) q^{24} -62854.1i q^{26} +(20205.4 - 2.76137e6i) q^{27} +(-3.39187e6 - 3.39187e6i) q^{28} +1.37690e6 q^{29} -5.36776e6 q^{31} +(3.98825e6 + 3.98825e6i) q^{32} +(7.11442e6 + 17352.1i) q^{33} -2.22007e6i q^{34} +(-41401.7 + 8.48735e6i) q^{36} +(4.18640e6 - 4.18640e6i) q^{37} +(-228892. + 228892. i) q^{38} +(-695400. + 692016. i) q^{39} -1.69845e7i q^{41} +(34214.8 - 1.40281e7i) q^{42} +(-4.04862e6 - 4.04862e6i) q^{43} -2.18666e7 q^{44} +1.26541e7 q^{46} +(-3.93367e7 - 3.93367e7i) q^{47} +(49470.6 - 2.02831e7i) q^{48} -8.33943e7i q^{49} +(-2.45622e7 + 2.44426e7i) q^{51} +(2.13215e6 - 2.13215e6i) q^{52} +(-4.34114e7 + 4.34114e7i) q^{53} +(-1.76792e7 + 1.74224e7i) q^{54} +9.43110e7i q^{56} +(5.05246e6 + 12323.0i) q^{57} +(-8.75132e6 - 8.75132e6i) q^{58} -1.26412e8 q^{59} -1.56468e8 q^{61} +(3.41165e7 + 3.41165e7i) q^{62} +(-1.55580e8 + 1.54069e8i) q^{63} +2.33245e7i q^{64} +(-4.51077e7 - 4.53283e7i) q^{66} +(7.00756e7 - 7.00756e7i) q^{67} +(7.53096e7 - 7.53096e7i) q^{68} +(-1.39320e8 - 1.40001e8i) q^{69} +3.78414e7i q^{71} +(1.18571e8 - 1.17420e8i) q^{72} +(-1.07957e8 - 1.07957e8i) q^{73} -5.32159e7 q^{74} -1.55290e7 q^{76} +(-3.98886e8 - 3.98886e8i) q^{77} +(8.81817e6 + 21507.6i) q^{78} -6.60075e7i q^{79} +(3.87402e8 + 3.77962e6i) q^{81} +(-1.07950e8 + 1.07950e8i) q^{82} +(3.05096e8 - 3.05096e8i) q^{83} +(4.77026e8 - 4.74705e8i) q^{84} +5.14646e7i q^{86} +(-471151. + 1.93173e8i) q^{87} +(3.04000e8 + 3.04000e8i) q^{88} +4.49257e7 q^{89} +7.77887e7 q^{91} +(4.29254e8 + 4.29254e8i) q^{92} +(1.83676e6 - 7.53074e8i) q^{93} +5.00034e8i q^{94} +(-5.60899e8 + 5.58169e8i) q^{96} +(1.77817e8 - 1.77817e8i) q^{97} +(-5.30039e8 + 5.30039e8i) q^{98} +(-4.86886e6 + 9.98117e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7}+O(q^{10}) $ 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7	$ 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7} - 191940 q^{12} - 114260 q^{13} - 1494724 q^{16} - 994800 q^{18} + 592212 q^{21} - 308260 q^{22} - 4786830 q^{27} + 12953300 q^{28} + 16124104 q^{31} - 19638120 q^{33} - 48943956 q^{36} + 35578660 q^{37} - 46648260 q^{42} + 118721020 q^{43} + 3145024 q^{46} - 275395140 q^{48} - 64226868 q^{51} + 157103680 q^{52} - 48163500 q^{57} + 209634300 q^{58} + 63607744 q^{61} - 89858580 q^{63} + 358931400 q^{66} - 153311540 q^{67} + 1534046760 q^{72} - 628070360 q^{73} - 2457023472 q^{76} + 403337880 q^{78} + 2250542952 q^{81} - 4138031440 q^{82} + 2878139760 q^{87} + 595851300 q^{88} - 4369040216 q^{91} + 293672640 q^{93} + 7291125636 q^{96} - 3987642200 q^{97}+O(q^{100}) $ 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7 - 191940 * q^12 - 114260 * q^13 - 1494724 * q^16 - 994800 * q^18 + 592212 * q^21 - 308260 * q^22 - 4786830 * q^27 + 12953300 * q^28 + 16124104 * q^31 - 19638120 * q^33 - 48943956 * q^36 + 35578660 * q^37 - 46648260 * q^42 + 118721020 * q^43 + 3145024 * q^46 - 275395140 * q^48 - 64226868 * q^51 + 157103680 * q^52 - 48163500 * q^57 + 209634300 * q^58 + 63607744 * q^61 - 89858580 * q^63 + 358931400 * q^66 - 153311540 * q^67 + 1534046760 * q^72 - 628070360 * q^73 - 2457023472 * q^76 + 403337880 * q^78 + 2250542952 * q^81 - 4138031440 * q^82 + 2878139760 * q^87 + 595851300 * q^88 - 4369040216 * q^91 + 293672640 * q^93 + 7291125636 * q^96 - 3987642200 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−6.35582	−	6.35582i	−0.280890	−	0.280890i	0.552574	−	0.833464i	$-0.313646\pi$
$2$	−6.35582	−	6.35582i	−0.280890	−	0.280890i	−0.833464	+	0.552574i	$0.813646\pi$
$3$	−0.342183	+	140.296i	−0.00243900	+	0.999997i
$3$	−0.342183	+	140.296i	−0.00243900	+	0.999997i
$4$		−	431.207i		−	0.842201i
$5$		0			0
$5$		0			0
$6$	893.869	−	889.519i	0.281574	−	0.280204i
$7$	7866.00	−	7866.00i	1.23826	−	1.23826i	0.277552	−	0.960711i	$-0.410477\pi$
$7$	7866.00	−	7866.00i	1.23826	−	1.23826i	0.960711	−	0.277552i	$-0.0895230\pi$
$8$	−5994.85	+	5994.85i	−0.517456	+	0.517456i
$9$	−19682.8	−	96.0135i	−0.999988	−	0.00487799i
$10$		0			0
$11$		−	50710.2i		−	1.04431i	−0.852852	−	0.522153i	$-0.825129\pi$
$11$		−	50710.2i		−	1.04431i	0.852852	−	0.522153i	$-0.174871\pi$
$12$	60496.5	+	147.552i	0.842199	+	0.00205413i
$13$	4944.61	+	4944.61i	0.0480161	+	0.0480161i	0.730707	−	0.682691i	$-0.239190\pi$
$13$	4944.61	+	4944.61i	0.0480161	+	0.0480161i	−0.682691	+	0.730707i	$0.739190\pi$
$14$	−99989.7			−0.695632
$15$		0			0
$16$	−144574.			−0.551505
$17$	174648.	+	174648.i	0.507159	+	0.507159i	0.913653	−	0.406494i	$-0.133249\pi$
$17$	174648.	+	174648.i	0.507159	+	0.507159i	−0.406494	+	0.913653i	$0.633249\pi$
$18$	124490.	+	125710.i	0.279517	+	0.282257i
$19$		−	36012.9i		−	0.0633968i	−0.999497	−	0.0316984i	$-0.989908\pi$
$19$		−	36012.9i		−	0.0633968i	0.999497	−	0.0316984i	$-0.0100916\pi$
$20$		0			0
$21$	1.10087e6	+	1.10626e6i	1.23524	+	1.24128i
$22$	−322305.	+	322305.i	−0.293336	+	0.293336i
$23$	−995471.	+	995471.i	−0.741743	+	0.741743i	−0.972913	−	0.231170i	$-0.925745\pi$
$23$	−995471.	+	995471.i	−0.741743	+	0.741743i	0.231170	+	0.972913i	$0.425745\pi$
$24$	−839001.	−	843104.i	−0.516193	−	0.518717i
$25$		0			0
$26$		−	62854.1i		−	0.0269745i
$27$	20205.4	−	2.76137e6i	0.00731695	−	0.999973i
$28$	−3.39187e6	−	3.39187e6i	−1.04287	−	1.04287i
$29$	1.37690e6			0.361502			0.180751	−	0.983529i	$-0.442147\pi$
$29$	1.37690e6			0.361502			0.180751	+	0.983529i	$0.442147\pi$
$30$		0			0
$31$	−5.36776e6			−1.04392			−0.521958	−	0.852971i	$-0.674798\pi$
$31$	−5.36776e6			−1.04392			−0.521958	+	0.852971i	$0.674798\pi$
$32$	3.98825e6	+	3.98825e6i	0.672369	+	0.672369i
$33$	7.11442e6	+	17352.1i	1.04430	+	0.00254707i
$34$		−	2.22007e6i		−	0.284912i
$35$		0			0
$36$	−41401.7	+	8.48735e6i	−0.00410825	+	0.842191i
$37$	4.18640e6	−	4.18640e6i	0.367225	−	0.367225i	−0.499239	−	0.866464i	$-0.666387\pi$
$37$	4.18640e6	−	4.18640e6i	0.367225	−	0.367225i	0.866464	+	0.499239i	$0.166387\pi$
$38$	−228892.	+	228892.i	−0.0178075	+	0.0178075i
$39$	−695400.	+	692016.i	−0.0481331	+	0.0478989i
$40$		0			0
$41$		−	1.69845e7i		−	0.938695i	−0.883014	−	0.469347i	$-0.844489\pi$
$41$		−	1.69845e7i		−	0.938695i	0.883014	−	0.469347i	$-0.155511\pi$
$42$	34214.8	−	1.40281e7i	0.00169665	−	0.695630i
$43$	−4.04862e6	−	4.04862e6i	−0.180592	−	0.180592i	0.611022	−	0.791614i	$-0.290759\pi$
$43$	−4.04862e6	−	4.04862e6i	−0.180592	−	0.180592i	−0.791614	+	0.611022i	$0.790759\pi$
$44$	−2.18666e7			−0.879517
$45$		0			0
$46$	1.26541e7			0.416697
$47$	−3.93367e7	−	3.93367e7i	−1.17587	−	1.17587i	−0.980788	−	0.195078i	$-0.937504\pi$
$47$	−3.93367e7	−	3.93367e7i	−1.17587	−	1.17587i	−0.195078	−	0.980788i	$-0.562496\pi$
$48$	49470.6	−	2.02831e7i	0.00134512	−	0.551503i
$49$		−	8.33943e7i		−	2.06659i
$50$		0			0
$51$	−2.45622e7	+	2.44426e7i	−0.508395	+	0.505921i
$52$	2.13215e6	−	2.13215e6i	0.0404393	−	0.0404393i
$53$	−4.34114e7	+	4.34114e7i	−0.755723	+	0.755723i	−0.975541	−	0.219818i	$-0.929454\pi$
$53$	−4.34114e7	+	4.34114e7i	−0.755723	+	0.755723i	0.219818	+	0.975541i	$0.429454\pi$
$54$	−1.76792e7	+	1.74224e7i	−0.282938	+	0.278827i
$55$		0			0
$56$			9.43110e7i			1.28149i
$57$	5.05246e6	+	12323.0i	0.0633966	+	0.000154625i
$58$	−8.75132e6	−	8.75132e6i	−0.101542	−	0.101542i
$59$	−1.26412e8			−1.35817			−0.679083	−	0.734062i	$-0.737622\pi$
$59$	−1.26412e8			−1.35817			−0.679083	+	0.734062i	$0.737622\pi$
$60$		0			0
$61$	−1.56468e8			−1.44691			−0.723455	−	0.690372i	$-0.757447\pi$
$61$	−1.56468e8			−1.44691			−0.723455	+	0.690372i	$0.757447\pi$
$62$	3.41165e7	+	3.41165e7i	0.293226	+	0.293226i
$63$	−1.55580e8	+	1.54069e8i	−1.24429	+	1.23221i
$64$			2.33245e7i			0.173781i
$65$		0			0
$66$	−4.51077e7	−	4.53283e7i	−0.292619	−	0.294050i
$67$	7.00756e7	−	7.00756e7i	0.424845	−	0.424845i	−0.462023	−	0.886868i	$-0.652876\pi$
$67$	7.00756e7	−	7.00756e7i	0.424845	−	0.424845i	0.886868	+	0.462023i	$0.152876\pi$
$68$	7.53096e7	−	7.53096e7i	0.427130	−	0.427130i
$69$	−1.39320e8	−	1.40001e8i	−0.739932	−	0.743550i
$70$		0			0
$71$			3.78414e7i			0.176727i	0.996088	+	0.0883637i	$0.0281638\pi$
$71$			3.78414e7i			0.176727i	−0.996088	+	0.0883637i	$0.971836\pi$
$72$	1.18571e8	−	1.17420e8i	0.519974	−	0.514926i
$73$	−1.07957e8	−	1.07957e8i	−0.444937	−	0.444937i	0.448730	−	0.893667i	$-0.351876\pi$
$73$	−1.07957e8	−	1.07957e8i	−0.444937	−	0.444937i	−0.893667	+	0.448730i	$0.851876\pi$
$74$	−5.32159e7			−0.206300
$75$		0			0
$76$	−1.55290e7			−0.0533929
$77$	−3.98886e8	−	3.98886e8i	−1.29313	−	1.29313i
$78$	8.81817e6	+	21507.6i	0.0269744	+	6.57910e-5i
$79$		−	6.60075e7i		−	0.190665i	−0.995445	−	0.0953325i	$-0.969609\pi$
$79$		−	6.60075e7i		−	0.190665i	0.995445	−	0.0953325i	$-0.0303914\pi$
$80$		0			0
$81$	3.87402e8	+	3.77962e6i	0.999952	+	0.00975587i
$82$	−1.07950e8	+	1.07950e8i	−0.263670	+	0.263670i
$83$	3.05096e8	−	3.05096e8i	0.705643	−	0.705643i	−0.259973	−	0.965616i	$-0.583714\pi$
$83$	3.05096e8	−	3.05096e8i	0.705643	−	0.705643i	0.965616	+	0.259973i	$0.0837135\pi$
$84$	4.77026e8	−	4.74705e8i	1.04541	−	1.04032i
$85$		0			0
$86$			5.14646e7i			0.101453i
$87$	−471151.	+	1.93173e8i	−0.000881705	+	0.361501i
$88$	3.04000e8	+	3.04000e8i	0.540383	+	0.540383i
$89$	4.49257e7			0.0758996			0.0379498	−	0.999280i	$-0.487917\pi$
$89$	4.49257e7			0.0758996			0.0379498	+	0.999280i	$0.487917\pi$
$90$		0			0
$91$	7.77887e7			0.118913
$92$	4.29254e8	+	4.29254e8i	0.624697	+	0.624697i
$93$	1.83676e6	−	7.53074e8i	0.00254611	−	1.04391i
$94$			5.00034e8i			0.660578i
$95$		0			0
$96$	−5.60899e8	+	5.58169e8i	−0.674006	+	0.670727i
$97$	1.77817e8	−	1.77817e8i	0.203939	−	0.203939i	−0.597746	−	0.801685i	$-0.703937\pi$
$97$	1.77817e8	−	1.77817e8i	0.203939	−	0.203939i	0.801685	+	0.597746i	$0.203937\pi$
$98$	−5.30039e8	+	5.30039e8i	−0.580484	+	0.580484i
$99$	−4.86886e6	+	9.98117e8i	−0.00509412	+	1.04429i
$100$		0			0
$101$		−	1.39974e9i		−	1.33844i	−0.743062	−	0.669222i	$-0.766627\pi$
$101$		−	1.39974e9i		−	1.33844i	0.743062	−	0.669222i	$-0.233373\pi$
$102$	3.11466e8	+	759668.i	0.284911	+	0.000694902i
$103$	5.51324e8	+	5.51324e8i	0.482657	+	0.482657i	0.905979	−	0.423322i	$-0.139136\pi$
$103$	5.51324e8	+	5.51324e8i	0.482657	+	0.482657i	−0.423322	+	0.905979i	$0.639136\pi$
$104$	−5.92845e7			−0.0496925
$105$		0			0
$106$	5.51831e8			0.424551
$107$	7.91408e8	+	7.91408e8i	0.583678	+	0.583678i	0.935912	−	0.352234i	$-0.114578\pi$
$107$	7.91408e8	+	7.91408e8i	0.583678	+	0.583678i	−0.352234	+	0.935912i	$0.614578\pi$
$108$	−1.19072e9	−	8.71271e6i	−0.842179	−	0.00616235i
$109$			5.27319e8i			0.357811i	0.983866	+	0.178906i	$0.0572557\pi$
$109$			5.27319e8i			0.357811i	−0.983866	+	0.178906i	$0.942744\pi$
$110$		0			0
$111$	5.85901e8	+	5.88766e8i	0.366328	+	0.368120i
$112$	−1.13722e9	+	1.13722e9i	−0.682907	+	0.682907i
$113$	−3.16112e8	+	3.16112e8i	−0.182385	+	0.182385i	−0.792394	−	0.610009i	$-0.791166\pi$
$113$	−3.16112e8	+	3.16112e8i	−0.182385	+	0.182385i	0.610009	+	0.792394i	$0.291166\pi$
$114$	−3.20342e7	−	3.21908e7i	−0.0177640	−	0.0178509i
$115$		0			0
$116$		−	5.93729e8i		−	0.304458i
$117$	−9.68489e7	−	9.77984e7i	−0.0477814	−	0.0482498i
$118$	8.03449e8	+	8.03449e8i	0.381495	+	0.381495i
$119$	2.74757e9			1.25599
$120$		0			0
$121$	−2.13575e8			−0.0905765
$122$	9.94483e8	+	9.94483e8i	0.406423	+	0.406423i
$123$	2.38285e9	+	5.81179e6i	0.938692	+	0.00228948i
$124$			2.31462e9i			0.879187i
$125$		0			0
$126$	1.96807e9	+	9.60037e6i	0.695623	+	0.00339329i
$127$	−3.79059e9	+	3.79059e9i	−1.29298	+	1.29298i	−0.360039	+	0.932937i	$0.617237\pi$
$127$	−3.79059e9	+	3.79059e9i	−1.29298	+	1.29298i	−0.932937	+	0.360039i	$0.882763\pi$
$128$	2.19023e9	−	2.19023e9i	0.721182	−	0.721182i
$129$	5.69389e8	−	5.66619e8i	0.181032	−	0.180151i
$130$		0			0
$131$		−	1.46363e9i		−	0.434220i	−0.976147	−	0.217110i	$-0.930337\pi$
$131$		−	1.46363e9i		−	0.434220i	0.976147	−	0.217110i	$-0.0696631\pi$
$132$	7.48237e6	−	3.06779e9i	0.00214514	−	0.879514i
$133$	−2.83278e8	−	2.83278e8i	−0.0785019	−	0.0785019i
$134$	−8.90776e8			−0.238669
$135$		0			0
$136$	−2.09398e9			−0.524865
$137$	−3.31214e9	−	3.31214e9i	−0.803278	−	0.803278i	0.180328	−	0.983606i	$-0.442284\pi$
$137$	−3.31214e9	−	3.31214e9i	−0.803278	−	0.803278i	−0.983606	+	0.180328i	$0.942284\pi$
$138$	−4.33001e6	+	1.77531e9i	−0.00101632	+	0.416696i
$139$		−	3.71186e8i		−	0.0843382i	−0.999110	−	0.0421691i	$-0.986573\pi$
$139$		−	3.71186e8i		−	0.0843382i	0.999110	−	0.0421691i	$-0.0134268\pi$
$140$		0			0
$141$	5.53223e9	−	5.50531e9i	1.17873	−	1.17299i
$142$	2.40513e8	−	2.40513e8i	0.0496410	−	0.0496410i
$143$	2.50742e8	−	2.50742e8i	0.0501436	−	0.0501436i
$144$	2.84561e9	+	1.38810e7i	0.551498	+	0.00269024i
$145$		0			0
$146$			1.37231e9i			0.249957i
$147$	1.16999e10	+	2.85361e7i	2.06658	+	0.00504042i
$148$	−1.80520e9	−	1.80520e9i	−0.309278	−	0.309278i
$149$	8.72697e8			0.145053			0.0725263	−	0.997367i	$-0.476894\pi$
$149$	8.72697e8			0.145053			0.0725263	+	0.997367i	$0.476894\pi$
$150$		0			0
$151$	−9.56872e9			−1.49781			−0.748907	−	0.662676i	$-0.769421\pi$
$151$	−9.56872e9			−1.49781			−0.748907	+	0.662676i	$0.769421\pi$
$152$	2.15892e8	+	2.15892e8i	0.0328051	+	0.0328051i
$153$	−3.42079e9	−	3.45433e9i	−0.504679	−	0.509627i
$154$			5.07050e9i			0.726453i
$155$		0			0
$156$	2.98402e8	+	2.99861e8i	0.0403405	+	0.0405378i
$157$	−3.24277e9	+	3.24277e9i	−0.425958	+	0.425958i	−0.887249	−	0.461291i	$-0.847387\pi$
$157$	−3.24277e9	+	3.24277e9i	−0.425958	+	0.425958i	0.461291	+	0.887249i	$0.347387\pi$
$158$	−4.19531e8	+	4.19531e8i	−0.0535559	+	0.0535559i
$159$	−6.07558e9	−	6.10529e9i	−0.753878	−	0.757564i
$160$		0			0
$161$			1.56608e10i			1.83695i
$162$	−2.43823e9	−	2.48628e9i	−0.278136	−	0.283617i
$163$	7.02766e9	+	7.02766e9i	0.779770	+	0.779770i	0.979791	−	0.200022i	$-0.0641013\pi$
$163$	7.02766e9	+	7.02766e9i	0.779770	+	0.779770i	−0.200022	+	0.979791i	$0.564101\pi$
$164$	−7.32382e9			−0.790570
$165$		0			0
$166$	−3.87827e9			−0.396417
$167$	1.64630e9	+	1.64630e9i	0.163789	+	0.163789i	0.784243	−	0.620454i	$-0.213052\pi$
$167$	1.64630e9	+	1.64630e9i	0.163789	+	0.163789i	−0.620454	+	0.784243i	$0.713052\pi$
$168$	−1.32314e10	−	3.22716e7i	−1.28149	−	0.00312557i
$169$		−	1.05556e10i		−	0.995389i
$170$		0			0
$171$	−3.45773e6	+	7.08834e8i	−0.000309249	+	0.0633960i
$172$	−1.74579e9	+	1.74579e9i	−0.152095	+	0.152095i
$173$	−2.85951e9	+	2.85951e9i	−0.242708	+	0.242708i	−0.817969	−	0.575262i	$-0.804900\pi$
$173$	−2.85951e9	+	2.85951e9i	−0.242708	+	0.242708i	0.575262	+	0.817969i	$0.304900\pi$
$174$	1.23077e9	−	1.22478e9i	0.101790	−	0.101294i
$175$		0			0
$176$			7.33135e9i			0.575940i
$177$	4.32559e7	−	1.77350e10i	0.00331257	−	1.35816i
$178$	−2.85539e8	−	2.85539e8i	−0.0213195	−	0.0213195i
$179$	−3.29534e9			−0.239918			−0.119959	−	0.992779i	$-0.538276\pi$
$179$	−3.29534e9			−0.239918			−0.119959	+	0.992779i	$0.538276\pi$
$180$		0			0
$181$	2.04260e10			1.41458			0.707292	−	0.706922i	$-0.249917\pi$
$181$	2.04260e10			1.41458			0.707292	+	0.706922i	$0.249917\pi$
$182$	−4.94411e8	−	4.94411e8i	−0.0334015	−	0.0334015i
$183$	5.35407e7	−	2.19518e10i	0.00352902	−	1.44691i
$184$		−	1.19354e10i		−	0.767639i
$185$		0			0
$186$	−4.79807e9	+	4.77473e9i	−0.293940	+	0.292510i
$187$	8.85645e9	−	8.85645e9i	0.529630	−	0.529630i
$188$	−1.69623e10	+	1.69623e10i	−0.990316	+	0.990316i
$189$	−2.15620e10	−	2.18799e10i	−1.22917	−	1.24729i
$190$		0			0
$191$		−	2.74055e10i		−	1.49000i	−0.667062	−	0.745002i	$-0.732448\pi$
$191$		−	2.74055e10i		−	1.49000i	0.667062	−	0.745002i	$-0.267552\pi$
$192$	−3.27233e9	−	7.98125e6i	−0.173781	−	0.000423853i
$193$	1.40018e10	+	1.40018e10i	0.726401	+	0.726401i	0.969901	−	0.243500i	$-0.0782956\pi$
$193$	1.40018e10	+	1.40018e10i	0.726401	+	0.726401i	−0.243500	+	0.969901i	$0.578296\pi$
$194$	−2.26034e9			−0.114569
$195$		0			0
$196$	−3.59602e10			−1.74048
$197$	−8.56540e9	−	8.56540e9i	−0.405181	−	0.405181i	0.474873	−	0.880054i	$-0.342494\pi$
$197$	−8.56540e9	−	8.56540e9i	−0.405181	−	0.405181i	−0.880054	+	0.474873i	$0.842494\pi$
$198$	6.37479e9	−	6.31290e9i	0.294763	−	0.291901i
$199$			4.05778e10i			1.83421i	0.398643	+	0.917106i	$0.369481\pi$
$199$			4.05778e10i			1.83421i	−0.398643	+	0.917106i	$0.630519\pi$
$200$		0			0
$201$	9.80733e9	+	9.85528e9i	0.423807	+	0.425880i
$202$	−8.89648e9	+	8.89648e9i	−0.375956	+	0.375956i
$203$	1.08307e10	−	1.08307e10i	0.447635	−	0.447635i
$204$	1.05398e10	+	1.05914e10i	0.426087	+	0.428171i
$205$		0			0
$206$		−	7.00823e9i		−	0.271147i
$207$	1.96892e10	−	1.94981e10i	0.745353	−	0.738116i
$208$	−7.14861e8	−	7.14861e8i	−0.0264811	−	0.0264811i
$209$	−1.82622e9			−0.0662057
$210$		0			0
$211$	−3.17708e10			−1.10346			−0.551730	−	0.834023i	$-0.686032\pi$
$211$	−3.17708e10			−1.10346			−0.551730	+	0.834023i	$0.686032\pi$
$212$	1.87193e10	+	1.87193e10i	0.636471	+	0.636471i
$213$	−5.30898e9	−	1.29487e7i	−0.176727	−	0.000431039i
$214$		−	1.00601e10i		−	0.327899i
$215$		0			0
$216$	1.64329e10	+	1.66752e10i	0.513656	+	0.521229i
$217$	−4.22228e10	+	4.22228e10i	−1.29264	+	1.29264i
$218$	3.35154e9	−	3.35154e9i	0.100506	−	0.100506i
$219$	1.51829e10	−	1.51090e10i	0.446021	−	0.443850i
$220$		0			0
$221$			1.72714e9i			0.0487037i
$222$	1.82096e7	−	7.46597e9i	0.000503166	−	0.206299i
$223$	1.95375e8	+	1.95375e8i	0.00529049	+	0.00529049i	0.709747	−	0.704457i	$-0.248809\pi$
$223$	1.95375e8	+	1.95375e8i	0.00529049	+	0.00529049i	−0.704457	+	0.709747i	$0.748809\pi$
$224$	6.27431e10			1.66514
$225$		0			0
$226$	4.01831e9			0.102460
$227$	−2.33229e10	−	2.33229e10i	−0.582996	−	0.582996i	0.352730	−	0.935725i	$-0.385254\pi$
$227$	−2.33229e10	−	2.33229e10i	−0.582996	−	0.582996i	−0.935725	+	0.352730i	$0.885254\pi$
$228$	5.31377e6	−	2.17866e9i	0.000130225	−	0.0533927i
$229$			3.65209e9i			0.0877570i	0.999037	+	0.0438785i	$0.0139714\pi$
$229$			3.65209e9i			0.0877570i	−0.999037	+	0.0438785i	$0.986029\pi$
$230$		0			0
$231$	5.60985e10	−	5.58255e10i	1.29628	−	1.28997i
$232$	−8.25431e9	+	8.25431e9i	−0.187062	+	0.187062i
$233$	−4.92890e9	+	4.92890e9i	−0.109559	+	0.109559i	−0.759761	−	0.650202i	$-0.774684\pi$
$233$	−4.92890e9	+	4.92890e9i	−0.109559	+	0.109559i	0.650202	+	0.759761i	$0.274684\pi$
$234$	−6.03485e6	+	1.23714e9i	−0.000131582	+	0.0269742i
$235$		0			0
$236$			5.45096e10i			1.14385i
$237$	9.26056e9	+	2.25866e7i	0.190664	+	0.000465033i
$238$	−1.74630e10	−	1.74630e10i	−0.352796	−	0.352796i
$239$	−8.39359e10			−1.66402			−0.832008	−	0.554764i	$-0.812809\pi$
$239$	−8.39359e10			−1.66402			−0.832008	+	0.554764i	$0.812809\pi$
$240$		0			0
$241$	4.41718e10			0.843468			0.421734	−	0.906720i	$-0.361422\pi$
$241$	4.41718e10			0.843468			0.421734	+	0.906720i	$0.361422\pi$
$242$	1.35744e9	+	1.35744e9i	0.0254421	+	0.0254421i
$243$	−6.62827e8	+	5.43495e10i	−0.0121947	+	0.999926i
$244$			6.74701e10i			1.21859i
$245$		0			0
$246$	−1.51080e10	−	1.51819e10i	−0.263026	−	0.264312i
$247$	1.78070e8	−	1.78070e8i	0.00304407	−	0.00304407i
$248$	3.21789e10	−	3.21789e10i	0.540181	−	0.540181i
$249$	4.26993e10	+	4.29081e10i	0.703920	+	0.707362i
$250$		0			0
$251$		−	5.85609e10i		−	0.931271i	−0.884977	−	0.465635i	$-0.845826\pi$
$251$		−	5.85609e10i		−	0.931271i	0.884977	−	0.465635i	$-0.154174\pi$
$252$	6.64358e10	+	6.70871e10i	1.03777	+	1.04794i
$253$	5.04805e10	+	5.04805e10i	0.774607	+	0.774607i
$254$	4.81847e10			0.726369
$255$		0			0
$256$	−1.58993e10			−0.231365
$257$	8.17663e10	+	8.17663e10i	1.16916	+	1.16916i	0.982406	+	0.186758i	$0.0597980\pi$
$257$	8.17663e10	+	8.17663e10i	1.16916	+	1.16916i	0.186758	+	0.982406i	$0.440202\pi$
$258$	−7.22026e9	−	1.76103e7i	−0.101453	−	0.000247445i
$259$		−	6.58604e10i		−	0.909442i
$260$		0			0
$261$	−2.71012e10	−	1.32201e8i	−0.361498	−	0.00176341i
$262$	−9.30256e9	+	9.30256e9i	−0.121968	+	0.121968i
$263$	3.66174e10	−	3.66174e10i	0.471940	−	0.471940i	−0.430602	−	0.902542i	$-0.641699\pi$
$263$	3.66174e10	−	3.66174e10i	0.471940	−	0.471940i	0.902542	+	0.430602i	$0.141699\pi$
$264$	−4.27539e10	+	4.25459e10i	−0.541699	+	0.539063i
$265$		0			0
$266$			3.60092e9i			0.0441008i
$267$	−1.53728e7	+	6.30288e9i	−0.000185119	+	0.0758994i
$268$	−3.02171e10	−	3.02171e10i	−0.357805	−	0.357805i
$269$	3.89647e10			0.453718			0.226859	−	0.973928i	$-0.427154\pi$
$269$	3.89647e10			0.453718			0.226859	+	0.973928i	$0.427154\pi$
$270$		0			0
$271$	9.85169e10			1.10956			0.554778	−	0.831999i	$-0.312803\pi$
$271$	9.85169e10			1.10956			0.554778	+	0.831999i	$0.312803\pi$
$272$	−2.52495e10	−	2.52495e10i	−0.279701	−	0.279701i
$273$	−2.66179e7	+	1.09134e10i	−0.000290030	+	0.118913i
$274$			4.21027e10i			0.451266i
$275$		0			0
$276$	−6.03694e10	+	6.00757e10i	−0.626219	+	0.623172i
$277$	5.82731e10	−	5.82731e10i	0.594715	−	0.594715i	−0.344186	−	0.938901i	$-0.611845\pi$
$277$	5.82731e10	−	5.82731e10i	0.594715	−	0.594715i	0.938901	+	0.344186i	$0.111845\pi$
$278$	−2.35919e9	+	2.35919e9i	−0.0236898	+	0.0236898i
$279$	1.05652e11	+	5.15378e8i	1.04390	+	0.00509221i
$280$		0			0
$281$		−	8.27366e10i		−	0.791625i	−0.918331	−	0.395812i	$-0.870463\pi$
$281$		−	8.27366e10i		−	0.791625i	0.918331	−	0.395812i	$-0.129537\pi$
$282$	−7.01526e10	−	1.71103e8i	−0.660576	−	0.00161115i
$283$	−1.95137e8	−	1.95137e8i	−0.00180843	−	0.00180843i	0.706202	−	0.708010i	$-0.250407\pi$
$283$	−1.95137e8	−	1.95137e8i	−0.00180843	−	0.00180843i	−0.708010	+	0.706202i	$0.750407\pi$
$284$	1.63175e10			0.148840
$285$		0			0
$286$	−3.18734e9			−0.0281697
$287$	−1.33600e11	−	1.33600e11i	−1.16235	−	1.16235i
$288$	−7.81168e10	−	7.88827e10i	−0.669081	−	0.675640i
$289$		−	5.75838e10i		−	0.485579i
$290$		0			0
$291$	2.48861e10	+	2.50078e10i	0.203441	+	0.204436i
$292$	−4.65519e10	+	4.65519e10i	−0.374727	+	0.374727i
$293$	3.12698e10	−	3.12698e10i	0.247868	−	0.247868i	−0.572227	−	0.820095i	$-0.693920\pi$
$293$	3.12698e10	−	3.12698e10i	0.247868	−	0.247868i	0.820095	+	0.572227i	$0.193920\pi$
$294$	−7.41808e10	−	7.45436e10i	−0.579067	−	0.581898i
$295$		0			0
$296$			5.01937e10i			0.380046i
$297$	−1.40030e11	−	1.02462e9i	−1.04428	−	0.00764114i
$298$	−5.54671e9	−	5.54671e9i	−0.0407438	−	0.0407438i
$299$	−9.84444e9			−0.0712313
$300$		0			0
$301$	−6.36929e10			−0.447241
$302$	6.08171e10	+	6.08171e10i	0.420721	+	0.420721i
$303$	1.96377e11	+	4.78966e8i	1.33844	+	0.00326447i
$304$			5.20652e9i			0.0349636i
$305$		0			0
$306$	−2.13156e8	+	4.36970e10i	−0.00138980	+	0.284909i
$307$	9.44092e10	−	9.44092e10i	0.606585	−	0.606585i	−0.335467	−	0.942052i	$-0.608894\pi$
$307$	9.44092e10	−	9.44092e10i	0.606585	−	0.606585i	0.942052	+	0.335467i	$0.108894\pi$
$308$	−1.72003e11	+	1.72003e11i	−1.08907	+	1.08907i
$309$	−7.75370e10	+	7.71597e10i	−0.483833	+	0.481479i
$310$		0			0
$311$		−	3.38874e10i		−	0.205408i	−0.994712	−	0.102704i	$-0.967251\pi$
$311$		−	3.38874e10i		−	0.205408i	0.994712	−	0.102704i	$-0.0327494\pi$
$312$	2.02861e7	−	8.31736e9i	0.000121200	−	0.0496924i
$313$	−7.82383e10	−	7.82383e10i	−0.460755	−	0.460755i	0.438148	−	0.898903i	$-0.355635\pi$
$313$	−7.82383e10	−	7.82383e10i	−0.460755	−	0.460755i	−0.898903	+	0.438148i	$0.855635\pi$
$314$	4.12209e10			0.239295
$315$		0			0
$316$	−2.84629e10			−0.160578
$317$	1.18735e11	+	1.18735e11i	0.660408	+	0.660408i	0.955476	−	0.295068i	$-0.0953423\pi$
$317$	1.18735e11	+	1.18735e11i	0.660408	+	0.660408i	−0.295068	+	0.955476i	$0.595342\pi$
$318$	−1.88827e8	+	7.74195e10i	−0.00103548	+	0.424549i
$319$		−	6.98228e10i		−	0.377519i
$320$		0			0
$321$	−1.11302e11	+	1.10760e11i	−0.585100	+	0.582253i
$322$	9.95369e10	−	9.95369e10i	0.515980	−	0.515980i
$323$	6.28960e9	−	6.28960e9i	0.0321523	−	0.0321523i
$324$	1.62980e9	−	1.67051e11i	0.00821641	−	0.842161i
$325$		0			0
$326$		−	8.93330e10i		−	0.438059i
$327$	−7.39806e10	−	1.80439e8i	−0.357810	−	0.000872703i
$328$	1.01819e11	+	1.01819e11i	0.485733	+	0.485733i
$329$	−6.18845e11			−2.91206
$330$		0			0
$331$	−1.30971e10			−0.0599721			−0.0299861	−	0.999550i	$-0.509546\pi$
$331$	−1.30971e10			−0.0599721			−0.0299861	+	0.999550i	$0.509546\pi$
$332$	−1.31560e11	−	1.31560e11i	−0.594294	−	0.594294i
$333$	−8.28018e10	+	8.19979e10i	−0.369012	+	0.365430i
$334$		−	2.09272e10i		−	0.0920137i
$335$		0			0
$336$	−1.59157e11	−	1.59936e11i	−0.681240	−	0.684571i
$337$	1.77881e11	−	1.77881e11i	0.751266	−	0.751266i	−0.223449	−	0.974716i	$-0.571732\pi$
$337$	1.77881e11	−	1.77881e11i	0.751266	−	0.751266i	0.974716	+	0.223449i	$0.0717318\pi$
$338$	−6.70895e10	+	6.70895e10i	−0.279595	+	0.279595i
$339$	−4.42411e10	−	4.44574e10i	−0.181939	−	0.182829i
$340$		0			0
$341$			2.72200e11i			1.09017i
$342$	4.52720e9	−	4.48324e9i	0.0178942	−	0.0177205i
$343$	−3.38558e11	−	3.38558e11i	−1.32072	−	1.32072i
$344$	4.85418e10			0.186897
$345$		0			0
$346$	3.63490e10			0.136348
$347$	−4.96304e10	−	4.96304e10i	−0.183766	−	0.183766i	0.609229	−	0.792995i	$-0.291479\pi$
$347$	−4.96304e10	−	4.96304e10i	−0.183766	−	0.183766i	−0.792995	+	0.609229i	$0.791479\pi$
$348$	8.32976e10	+	2.03164e8i	0.304457	+	0.000742574i
$349$		−	2.91123e11i		−	1.05042i	−0.850973	−	0.525210i	$-0.823987\pi$
$349$		−	2.91123e11i		−	1.05042i	0.850973	−	0.525210i	$-0.176013\pi$
$350$		0			0
$351$	1.37538e10	−	1.35540e10i	0.0483662	−	0.0476635i
$352$	2.02245e11	−	2.02245e11i	0.702159	−	0.702159i
$353$	−1.10166e11	+	1.10166e11i	−0.377627	+	0.377627i	−0.870245	−	0.492619i	$-0.836040\pi$
$353$	−1.10166e11	+	1.10166e11i	−0.377627	+	0.377627i	0.492619	+	0.870245i	$0.336040\pi$
$354$	−1.12995e11	+	1.12446e11i	−0.382425	+	0.380564i
$355$		0			0
$356$		−	1.93723e10i		−	0.0639228i
$357$	−9.40170e8	+	3.85472e11i	−0.00306337	+	1.25599i
$358$	2.09446e10	+	2.09446e10i	0.0673905	+	0.0673905i
$359$	5.74004e11			1.82385			0.911926	−	0.410355i	$-0.134595\pi$
$359$	5.74004e11			1.82385			0.911926	+	0.410355i	$0.134595\pi$
$360$		0			0
$361$	3.21391e11			0.995981
$362$	−1.29824e11	−	1.29824e11i	−0.397343	−	0.397343i
$363$	7.30816e7	−	2.99636e10i	0.000220916	−	0.0905762i
$364$		−	3.35430e10i		−	0.100149i
$365$		0			0
$366$	−1.39862e11	+	1.39181e11i	−0.407413	+	0.405430i
$367$	−1.24345e11	+	1.24345e11i	−0.357793	+	0.357793i	−0.862999	−	0.505206i	$-0.831417\pi$
$367$	−1.24345e11	+	1.24345e11i	−0.357793	+	0.357793i	0.505206	+	0.862999i	$0.331417\pi$
$368$	1.43919e11	−	1.43919e11i	0.409075	−	0.409075i
$369$	−1.63074e9	+	3.34301e11i	−0.00457895	+	0.938683i
$370$		0			0
$371$			6.82949e11i			1.87157i
$372$	−3.24731e11	−	7.92022e8i	−0.879185	−	0.00214434i
$373$	4.38495e10	+	4.38495e10i	0.117294	+	0.117294i	0.763317	−	0.646024i	$-0.223569\pi$
$373$	4.38495e10	+	4.38495e10i	0.117294	+	0.117294i	−0.646024	+	0.763317i	$0.723569\pi$
$374$	−1.12580e11			−0.297536
$375$		0			0
$376$	4.71636e11			1.21692
$377$	6.80823e9	+	6.80823e9i	0.0173579	+	0.0173579i
$378$	−2.02033e9	+	2.76109e11i	−0.00508990	+	0.695613i
$379$		−	2.97574e11i		−	0.740829i	−0.928867	−	0.370414i	$-0.879216\pi$
$379$		−	2.97574e11i		−	0.740829i	0.928867	−	0.370414i	$-0.120784\pi$
$380$		0			0
$381$	−5.30507e11	−	5.33101e11i	−1.28982	−	1.29613i
$382$	−1.74184e11	+	1.74184e11i	−0.418528	+	0.418528i
$383$	5.03468e11	−	5.03468e11i	1.19558	−	1.19558i	0.220099	−	0.975478i	$-0.429362\pi$
$383$	5.03468e11	−	5.03468e11i	1.19558	−	1.19558i	0.975478	−	0.220099i	$-0.0706380\pi$
$384$	3.06530e11	+	3.08029e11i	0.719421	+	0.722939i
$385$		0			0
$386$		−	1.77986e11i		−	0.408078i
$387$	7.92993e10	+	8.00768e10i	0.179709	+	0.181471i
$388$	−7.66758e10	−	7.66758e10i	−0.171757	−	0.171757i
$389$	5.78423e11			1.28077			0.640387	−	0.768052i	$-0.278774\pi$
$389$	5.78423e11			1.28077			0.640387	+	0.768052i	$0.278774\pi$
$390$		0			0
$391$	−3.47715e11			−0.752364
$392$	4.99937e11	+	4.99937e11i	1.06937	+	1.06937i
$393$	2.05341e11	+	5.00829e8i	0.434219	+	0.00105907i
$394$			1.08880e11i			0.227623i
$395$		0			0
$396$	4.30395e11	+	2.09949e9i	0.879506	+	0.00429028i
$397$	4.21765e11	−	4.21765e11i	0.852145	−	0.852145i	−0.138252	−	0.990397i	$-0.544148\pi$
$397$	4.21765e11	−	4.21765e11i	0.852145	−	0.852145i	0.990397	+	0.138252i	$0.0441484\pi$
$398$	2.57905e11	−	2.57905e11i	0.515212	−	0.515212i
$399$	3.98396e10	−	3.96457e10i	0.0786931	−	0.0783102i
$400$		0			0
$401$		−	8.61243e11i		−	1.66332i	−0.555284	−	0.831661i	$-0.687391\pi$
$401$		−	8.61243e11i		−	1.66332i	0.555284	−	0.831661i	$-0.312609\pi$
$402$	3.04808e8	−	1.24972e11i	0.000582116	−	0.238669i
$403$	−2.65415e10	−	2.65415e10i	−0.0501248	−	0.0501248i
$404$	−6.03577e11			−1.12724
$405$		0			0
$406$	−1.37676e11			−0.251472
$407$	−2.12293e11	−	2.12293e11i	−0.383496	−	0.383496i
$408$	7.16525e8	−	2.93777e11i	0.00128015	−	0.524864i
$409$			7.20641e11i			1.27340i	0.771113	+	0.636699i	$0.219701\pi$
$409$			7.20641e11i			1.27340i	−0.771113	+	0.636699i	$0.780299\pi$
$410$		0			0
$411$	4.65812e11	−	4.63545e11i	0.805235	−	0.801317i
$412$	2.37735e11	−	2.37735e11i	0.406495	−	0.406495i
$413$	−9.94353e11	+	9.94353e11i	−1.68177	+	1.68177i
$414$	−2.49067e11	−	1.21496e9i	−0.416692	−	0.00203264i
$415$		0			0
$416$			3.94407e10i			0.0645691i
$417$	5.20757e10	+	1.27013e8i	0.0843380	+	0.000205701i
$418$	1.16071e10	+	1.16071e10i	0.0185965	+	0.0185965i
$419$	2.26098e11			0.358371			0.179186	−	0.983815i	$-0.442654\pi$
$419$	2.26098e11			0.358371			0.179186	+	0.983815i	$0.442654\pi$
$420$		0			0
$421$	4.17388e11			0.647545			0.323773	−	0.946135i	$-0.395049\pi$
$421$	4.17388e11			0.647545			0.323773	+	0.946135i	$0.395049\pi$
$422$	2.01929e11	+	2.01929e11i	0.309951	+	0.309951i
$423$	7.70478e11	+	7.78032e11i	1.17012	+	1.18159i
$424$		−	5.20491e11i		−	0.782108i
$425$		0			0
$426$	3.36606e10	+	3.38252e10i	0.0495198	+	0.0497619i
$427$	−1.23078e12	+	1.23078e12i	−1.79165	+	1.79165i
$428$	3.41261e11	−	3.41261e11i	0.491575	−	0.491575i
$429$	3.50923e10	+	3.52639e10i	0.0500211	+	0.0502657i
$430$		0			0
$431$			1.02113e11i			0.142540i	0.997457	+	0.0712698i	$0.0227051\pi$
$431$			1.02113e11i			0.142540i	−0.997457	+	0.0712698i	$0.977295\pi$
$432$	−2.92117e9	+	3.99222e11i	−0.00403533	+	0.551490i
$433$	1.23064e10	+	1.23064e10i	0.0168243	+	0.0168243i	0.715469	−	0.698645i	$-0.246213\pi$
$433$	1.23064e10	+	1.23064e10i	0.0168243	+	0.0168243i	−0.698645	+	0.715469i	$0.746213\pi$
$434$	5.36721e11			0.726181
$435$		0			0
$436$	2.27384e11			0.301349
$437$	3.58498e10	+	3.58498e10i	0.0470241	+	0.0470241i
$438$	−1.92530e11	−	4.69582e8i	−0.249956	−	0.000609646i
$439$			1.44584e12i			1.85793i	0.370167	+	0.928965i	$0.379300\pi$
$439$			1.44584e12i			1.85793i	−0.370167	+	0.928965i	$0.620700\pi$
$440$		0			0
$441$	−8.00698e9	+	1.64143e12i	−0.0100808	+	2.06656i
$442$	1.09774e10	−	1.09774e10i	0.0136804	−	0.0136804i
$443$	−4.21001e11	+	4.21001e11i	−0.519357	+	0.519357i	−0.917377	−	0.398020i	$-0.869698\pi$
$443$	−4.21001e11	+	4.21001e11i	−0.519357	+	0.519357i	0.398020	+	0.917377i	$0.369698\pi$
$444$	2.53880e11	−	2.52645e11i	0.310031	−	0.308522i
$445$		0			0
$446$		−	2.48353e9i		−	0.00297210i
$447$	−2.98622e8	+	1.22436e11i	−0.000353784	+	0.145052i
$448$	1.83471e11	+	1.83471e11i	0.215187	+	0.215187i
$449$	3.49856e10			0.0406238			0.0203119	−	0.999794i	$-0.493534\pi$
$449$	3.49856e10			0.0406238			0.0203119	+	0.999794i	$0.493534\pi$
$450$		0			0
$451$	−8.61285e11			−0.980285
$452$	1.36310e11	+	1.36310e11i	0.153605	+	0.153605i
$453$	3.27425e9	−	1.34245e12i	0.00365317	−	1.49781i
$454$			2.96472e11i			0.327516i
$455$		0			0
$456$	−3.03626e10	+	3.02149e10i	−0.0328850	+	0.0327250i
$457$	−2.46966e11	+	2.46966e11i	−0.264859	+	0.264859i	−0.827024	−	0.562166i	$-0.809968\pi$
$457$	−2.46966e11	+	2.46966e11i	−0.264859	+	0.264859i	0.562166	+	0.827024i	$0.309968\pi$
$458$	2.32120e10	−	2.32120e10i	0.0246501	−	0.0246501i
$459$	4.85798e11	−	4.78741e11i	0.510856	−	0.503435i
$460$		0			0
$461$		−	7.54635e11i		−	0.778185i	−0.921199	−	0.389093i	$-0.872789\pi$
$461$		−	7.54635e11i		−	0.778185i	0.921199	−	0.389093i	$-0.127211\pi$
$462$	−7.11369e11	−	1.73504e9i	−0.726451	−	0.00177182i
$463$	−4.00214e9	−	4.00214e9i	−0.00404742	−	0.00404742i	0.705080	−	0.709128i	$-0.250911\pi$
$463$	−4.00214e9	−	4.00214e9i	−0.00404742	−	0.00404742i	−0.709128	+	0.705080i	$0.750911\pi$
$464$	−1.99063e11			−0.199370
$465$		0			0
$466$	6.26543e10			0.0615481
$467$	−9.82015e10	−	9.82015e10i	−0.0955416	−	0.0955416i	0.657721	−	0.753262i	$-0.271521\pi$
$467$	−9.82015e10	−	9.82015e10i	−0.0955416	−	0.0955416i	−0.753262	+	0.657721i	$0.771521\pi$
$468$	−4.21714e10	+	4.17619e10i	−0.0406360	+	0.0402415i
$469$		−	1.10243e12i		−	1.05214i
$470$		0			0
$471$	−4.53836e11	−	4.56056e11i	−0.424918	−	0.426996i
$472$	7.57819e11	−	7.57819e11i	0.702791	−	0.702791i
$473$	−2.05306e11	+	2.05306e11i	−0.188594	+	0.188594i
$474$	−5.87149e10	−	5.90020e10i	−0.0534252	−	0.0536864i
$475$		0			0
$476$		−	1.18477e12i		−	1.05780i
$477$	8.58625e11	−	8.50289e11i	0.759401	−	0.752028i
$478$	5.33482e11	+	5.33482e11i	0.467406	+	0.467406i
$479$	−1.05362e12			−0.914477			−0.457239	−	0.889344i	$-0.651161\pi$
$479$	−1.05362e12			−0.914477			−0.457239	+	0.889344i	$0.651161\pi$
$480$		0			0
$481$	4.14002e10			0.0352655
$482$	−2.80748e11	−	2.80748e11i	−0.236922	−	0.236922i
$483$	−2.19714e12	−	5.35884e9i	−1.83694	−	0.00448032i
$484$			9.20949e10i			0.0762837i
$485$		0			0
$486$	3.49649e11	−	3.41223e11i	0.284295	−	0.277444i
$487$	1.03714e12	−	1.03714e12i	0.835519	−	0.835519i	−0.152747	−	0.988265i	$-0.548812\pi$
$487$	1.03714e12	−	1.03714e12i	0.835519	−	0.835519i	0.988265	+	0.152747i	$0.0488118\pi$
$488$	9.38003e11	−	9.38003e11i	0.748712	−	0.748712i
$489$	−9.88355e11	+	9.83545e11i	−0.781669	+	0.777865i
$490$		0			0
$491$			2.09833e12i			1.62932i	0.579936	+	0.814662i	$0.303078\pi$
$491$			2.09833e12i			1.62932i	−0.579936	+	0.814662i	$0.696922\pi$
$492$	2.50608e9	−	1.02750e12i	0.00192820	−	0.790568i
$493$	2.40473e11	+	2.40473e11i	0.183339	+	0.183339i
$494$	−2.26356e9			−0.00171010
$495$		0			0
$496$	7.76037e11			0.575724
$497$	2.97660e11	+	2.97660e11i	0.218835	+	0.218835i
$498$	1.32708e9	−	5.44105e11i	0.000966862	−	0.396415i
$499$		−	6.19886e11i		−	0.447568i	−0.974639	−	0.223784i	$-0.928159\pi$
$499$		−	6.19886e11i		−	0.447568i	0.974639	−	0.223784i	$-0.0718411\pi$
$500$		0			0
$501$	−2.31533e11	+	2.30406e11i	−0.164188	+	0.163389i
$502$	−3.72203e11	+	3.72203e11i	−0.261585	+	0.261585i
$503$	1.09703e12	−	1.09703e12i	0.764125	−	0.764125i	−0.212940	−	0.977065i	$-0.568304\pi$
$503$	1.09703e12	−	1.09703e12i	0.764125	−	0.764125i	0.977065	+	0.212940i	$0.0683040\pi$
$504$	9.05514e9	−	1.85630e12i	0.00625112	−	1.28148i
$505$		0			0
$506$		−	6.41690e11i		−	0.435159i
$507$	1.48091e12	+	3.61194e9i	0.995386	+	0.00242776i
$508$	1.63453e12	+	1.63453e12i	1.08895	+	1.08895i
$509$	1.18313e12			0.781271			0.390636	−	0.920545i	$-0.372255\pi$
$509$	1.18313e12			0.781271			0.390636	+	0.920545i	$0.372255\pi$
$510$		0			0
$511$	−1.69838e12			−1.10190
$512$	−1.02034e12	−	1.02034e12i	−0.656194	−	0.656194i
$513$	−9.94452e10	−	7.27655e8i	−0.0633951	−	0.000463871i
$514$		−	1.03938e12i		−	0.656813i
$515$		0			0
$516$	−2.44330e11	−	2.45525e11i	−0.151724	−	0.152466i
$517$	−1.99477e12	+	1.99477e12i	−1.22796	+	1.22796i
$518$	−4.18597e11	+	4.18597e11i	−0.255453	+	0.255453i
$519$	−4.00198e11	−	4.02155e11i	−0.242115	−	0.243299i
$520$		0			0
$521$			2.35572e12i			1.40073i	0.713785	+	0.700364i	$0.246979\pi$
$521$			2.35572e12i			1.40073i	−0.713785	+	0.700364i	$0.753021\pi$
$522$	1.71410e11	+	1.73090e11i	0.101046	+	0.102037i
$523$	−2.19998e12	−	2.19998e12i	−1.28577	−	1.28577i	−0.937334	−	0.348432i	$-0.886714\pi$
$523$	−2.19998e12	−	2.19998e12i	−1.28577	−	1.28577i	−0.348432	−	0.937334i	$-0.613286\pi$
$524$	−6.31127e11			−0.365701
$525$		0			0
$526$	−4.65468e11			−0.265127
$527$	−9.37470e11	−	9.37470e11i	−0.529432	−	0.529432i
$528$	−1.02856e12	−	2.50866e9i	−0.575938	−	0.00140472i
$529$		−	1.80774e11i		−	0.100366i
$530$		0			0
$531$	2.48813e12	+	1.21372e10i	1.35815	+	0.00662512i
$532$	−1.22151e11	+	1.22151e11i	−0.0661144	+	0.0661144i
$533$	8.39816e10	−	8.39816e10i	0.0450725	−	0.0450725i
$534$	4.01577e10	−	3.99623e10i	0.0213714	−	0.0212674i
$535$		0			0
$536$			8.40186e11i			0.439677i
$537$	1.12761e9	−	4.62323e11i	0.000585160	−	0.239917i
$538$	−2.47652e11	−	2.47652e11i	−0.127445	−	0.127445i
$539$	−4.22894e12			−2.15815
$540$		0			0
$541$	−1.83286e12			−0.919901			−0.459951	−	0.887944i	$-0.652133\pi$
$541$	−1.83286e12			−0.919901			−0.459951	+	0.887944i	$0.652133\pi$
$542$	−6.26156e11	−	6.26156e11i	−0.311663	−	0.311663i
$543$	−6.98941e9	+	2.86567e12i	−0.00345018	+	1.41458i
$544$			1.39308e12i			0.681996i
$545$		0			0
$546$	6.95329e10	−	6.91945e10i	0.0334829	−	0.0333200i
$547$	4.88169e11	−	4.88169e11i	0.233146	−	0.233146i	−0.580859	−	0.814004i	$-0.697283\pi$
$547$	4.88169e11	−	4.88169e11i	0.233146	−	0.233146i	0.814004	+	0.580859i	$0.197283\pi$
$548$	−1.42822e12	+	1.42822e12i	−0.676522	+	0.676522i
$549$	3.07972e12	+	1.50230e10i	1.44689	+	0.00705801i
$550$		0			0
$551$		−	4.95862e10i		−	0.0229181i
$552$	1.67449e12	+	4.08409e9i	0.767637	+	0.00187228i
$553$	−5.19215e11	−	5.19215e11i	−0.236093	−	0.236093i
$554$	−7.40746e11			−0.334099
$555$		0			0
$556$	−1.60058e11			−0.0710298
$557$	1.00208e12	+	1.00208e12i	0.441117	+	0.441117i	0.892387	−	0.451270i	$-0.149029\pi$
$557$	1.00208e12	+	1.00208e12i	0.441117	+	0.441117i	−0.451270	+	0.892387i	$0.649029\pi$
$558$	−6.68232e11	−	6.74783e11i	−0.291792	−	0.294653i
$559$		−	4.00377e10i		−	0.0173427i
$560$		0			0
$561$	1.23949e12	+	1.24555e12i	0.528336	+	0.530920i
$562$	−5.25859e11	+	5.25859e11i	−0.222360	+	0.222360i
$563$	−2.02348e12	+	2.02348e12i	−0.848813	+	0.848813i	−0.989985	−	0.141172i	$-0.954913\pi$
$563$	−2.02348e12	+	2.02348e12i	−0.848813	+	0.848813i	0.141172	+	0.989985i	$0.454913\pi$
$564$	−2.37393e12	−	2.38554e12i	−0.987897	−	0.992728i
$565$		0			0
$566$			2.48051e9i			0.00101594i
$567$	3.07703e12	−	3.01757e12i	1.25028	−	1.22612i
$568$	−2.26853e11	−	2.26853e11i	−0.0914488	−	0.0914488i
$569$	2.23601e12			0.894268			0.447134	−	0.894467i	$-0.352445\pi$
$569$	2.23601e12			0.894268			0.447134	+	0.894467i	$0.352445\pi$
$570$		0			0
$571$	−3.80656e12			−1.49855			−0.749273	−	0.662262i	$-0.769597\pi$
$571$	−3.80656e12			−1.49855			−0.749273	+	0.662262i	$0.769597\pi$
$572$	−1.08122e11	−	1.08122e11i	−0.0422310	−	0.0422310i
$573$	3.84487e12	+	9.37769e9i	1.49000	+	0.00363413i
$574$			1.69827e12i			0.652986i
$575$		0			0
$576$	2.23947e9	−	4.59091e11i	0.000847703	−	0.173779i
$577$	−2.99148e12	+	2.99148e12i	−1.12356	+	1.12356i	−0.132354	+	0.991203i	$0.542254\pi$
$577$	−2.99148e12	+	2.99148e12i	−1.12356	+	1.12356i	−0.991203	+	0.132354i	$0.957746\pi$
$578$	−3.65992e11	+	3.65992e11i	−0.136394	+	0.136394i
$579$	−1.96918e12	+	1.95960e12i	−0.728170	+	0.724627i
$580$		0			0
$581$		−	4.79977e12i		−	1.74754i
$582$	7.73450e8	−	3.17116e11i	0.000279434	−	0.114568i
$583$	2.20140e12	+	2.20140e12i	0.789207	+	0.789207i
$584$	1.29437e12			0.460471
$585$		0			0
$586$	−3.97490e11			−0.139247
$587$	2.62999e12	+	2.62999e12i	0.914288	+	0.914288i	0.996606	−	0.0823184i	$-0.0262325\pi$
$587$	2.62999e12	+	2.62999e12i	0.914288	+	0.914288i	−0.0823184	+	0.996606i	$0.526232\pi$
$588$	1.23050e10	−	5.04506e12i	0.00424505	−	1.74048i
$589$			1.93309e11i			0.0661809i
$590$		0			0
$591$	1.20462e12	−	1.19876e12i	0.406168	−	0.404192i
$592$	−6.05242e11	+	6.05242e11i	−0.202526	+	0.202526i
$593$	3.66646e12	−	3.66646e12i	1.21759	−	1.21759i	0.249116	−	0.968474i	$-0.419860\pi$
$593$	3.66646e12	−	3.66646e12i	1.21759	−	1.21759i	0.968474	−	0.249116i	$-0.0801400\pi$
$594$	8.83492e11	+	8.96516e11i	0.291181	+	0.295474i
$595$		0			0
$596$		−	3.76313e11i		−	0.122163i
$597$	−5.69289e12	−	1.38850e10i	−1.83421	−	0.00447365i
$598$	6.25695e10	+	6.25695e10i	0.0200082	+	0.0200082i
$599$	5.56905e12			1.76750			0.883752	−	0.467956i	$-0.155009\pi$
$599$	5.56905e12			1.76750			0.883752	+	0.467956i	$0.155009\pi$
$600$		0			0
$601$	2.42777e12			0.759054			0.379527	−	0.925181i	$-0.376087\pi$
$601$	2.42777e12			0.759054			0.379527	+	0.925181i	$0.376087\pi$
$602$	4.04821e11	+	4.04821e11i	0.125626	+	0.125626i
$603$	−1.38601e12	+	1.37255e12i	−0.426912	+	0.422767i
$604$			4.12610e12i			1.26146i
$605$		0			0
$606$	−1.24509e12	−	1.25118e12i	−0.375038	−	0.376872i
$607$	7.92074e11	−	7.92074e11i	0.236819	−	0.236819i	−0.578712	−	0.815532i	$-0.696445\pi$
$607$	7.92074e11	−	7.92074e11i	0.236819	−	0.236819i	0.815532	+	0.578712i	$0.196445\pi$
$608$	1.43629e11	−	1.43629e11i	0.0426260	−	0.0426260i
$609$	1.51579e12	+	1.52320e12i	0.446542	+	0.448725i
$610$		0			0
$611$		−	3.89010e11i		−	0.112921i
$612$	−1.48953e12	+	1.47507e12i	−0.429209	+	0.425042i
$613$	2.77694e12	+	2.77694e12i	0.794318	+	0.794318i	0.982193	−	0.187875i	$-0.0601601\pi$
$613$	2.77694e12	+	2.77694e12i	0.794318	+	0.794318i	−0.187875	+	0.982193i	$0.560160\pi$
$614$	−1.20010e12			−0.340767
$615$		0			0
$616$	4.78253e12			1.33827
$617$	−8.48981e11	−	8.48981e11i	−0.235839	−	0.235839i	0.579286	−	0.815124i	$-0.303331\pi$
$617$	−8.48981e11	−	8.48981e11i	−0.235839	−	0.235839i	−0.815124	+	0.579286i	$0.803331\pi$
$618$	9.83224e11	+	2.39809e9i	0.271147	+	0.000661330i
$619$		−	5.11215e12i		−	1.39957i	−0.714352	−	0.699787i	$-0.753278\pi$
$619$		−	5.11215e12i		−	1.39957i	0.714352	−	0.699787i	$-0.246722\pi$
$620$		0			0
$621$	2.72876e12	+	2.76898e12i	0.736296	+	0.747151i
$622$	−2.15382e11	+	2.15382e11i	−0.0576970	+	0.0576970i
$623$	3.53385e11	−	3.53385e11i	0.0939837	−	0.0939837i
$624$	1.00536e11	−	1.00047e11i	0.0265456	−	0.0264165i
$625$		0			0
$626$			9.94537e11i			0.258843i
$627$	6.24902e8	−	2.56211e11i	0.000161476	−	0.0662055i
$628$	1.39830e12	+	1.39830e12i	0.358743	+	0.358743i
$629$	1.46229e12			0.372483
$630$		0			0
$631$	5.72205e12			1.43688			0.718438	−	0.695591i	$-0.244857\pi$
$631$	5.72205e12			1.43688			0.718438	+	0.695591i	$0.244857\pi$
$632$	3.95705e11	+	3.95705e11i	0.0986608	+	0.0986608i
$633$	1.08714e10	−	4.45730e12i	0.00269134	−	1.10346i
$634$		−	1.50932e12i		−	0.371004i
$635$		0			0
$636$	−2.63265e12	+	2.61984e12i	−0.638022	+	0.634917i
$637$	4.12353e11	−	4.12353e11i	0.0992296	−	0.0992296i
$638$	−4.43781e11	+	4.43781e11i	−0.106041	+	0.106041i
$639$	3.63328e9	−	7.44823e11i	0.000862075	−	0.176725i
$640$		0			0
$641$		−	3.81433e12i		−	0.892396i	−0.894934	−	0.446198i	$-0.852778\pi$
$641$		−	3.81433e12i		−	0.892396i	0.894934	−	0.446198i	$-0.147222\pi$
$642$	1.41139e12	+	3.44239e9i	0.327898	+	0.000799747i
$643$	−3.52135e12	−	3.52135e12i	−0.812382	−	0.812382i	0.172609	−	0.984990i	$-0.444780\pi$
$643$	−3.52135e12	−	3.52135e12i	−0.812382	−	0.812382i	−0.984990	+	0.172609i	$0.944780\pi$
$644$	6.75303e12			1.54708
$645$		0			0
$646$	−7.99511e10			−0.0180625
$647$	1.80018e12	+	1.80018e12i	0.403874	+	0.403874i	0.879596	−	0.475722i	$-0.157813\pi$
$647$	1.80018e12	+	1.80018e12i	0.403874	+	0.403874i	−0.475722	+	0.879596i	$0.657813\pi$
$648$	−2.34508e12	+	2.29976e12i	−0.522480	+	0.512383i
$649$			6.41035e12i			1.41834i
$650$		0			0
$651$	−5.90923e12	−	5.93813e12i	−1.28949	−	1.29579i
$652$	3.03038e12	−	3.03038e12i	0.656723	−	0.656723i
$653$	−2.94935e12	+	2.94935e12i	−0.634772	+	0.634772i	−0.949261	−	0.314489i	$-0.898167\pi$
$653$	−2.94935e12	+	2.94935e12i	−0.634772	+	0.634772i	0.314489	+	0.949261i	$0.398167\pi$
$654$	4.69060e11	+	4.71354e11i	0.100260	+	0.100751i
$655$		0			0
$656$			2.45550e12i			0.517694i
$657$	2.11453e12	+	2.13526e12i	0.442761	+	0.447102i
$658$	3.93327e12	+	3.93327e12i	0.817969	+	0.817969i
$659$	−8.33097e12			−1.72072			−0.860362	−	0.509684i	$-0.829762\pi$
$659$	−8.33097e12			−1.72072			−0.860362	+	0.509684i	$0.829762\pi$
$660$		0			0
$661$	−2.97082e12			−0.605298			−0.302649	−	0.953102i	$-0.597871\pi$
$661$	−2.97082e12			−0.605298			−0.302649	+	0.953102i	$0.597871\pi$
$662$	8.32429e10	+	8.32429e10i	0.0168456	+	0.0168456i
$663$	−2.42310e11	−	5.90996e8i	−0.0487035	−	0.000118788i
$664$			3.65801e12i			0.730279i
$665$		0			0
$666$	1.04744e12	+	5.10945e9i	0.206297	+	0.00100633i
$667$	−1.37066e12	+	1.37066e12i	−0.268142	+	0.268142i
$668$	7.09898e11	−	7.09898e11i	0.137944	−	0.137944i
$669$	−2.74771e10	+	2.73434e10i	−0.00530338	+	0.00527757i
$670$		0			0
$671$			7.93452e12i			1.51102i
$672$	−2.14696e10	+	8.80259e12i	−0.00406128	+	1.66513i
$673$	−5.60387e12	−	5.60387e12i	−1.05298	−	1.05298i	−0.998516	−	0.0544645i	$-0.982655\pi$
$673$	−5.60387e12	−	5.60387e12i	−1.05298	−	1.05298i	−0.0544645	−	0.998516i	$-0.517345\pi$
$674$	−2.26115e12			−0.422047
$675$		0			0
$676$	−4.55165e12			−0.838318
$677$	1.89913e12	+	1.89913e12i	0.347462	+	0.347462i	0.859163	−	0.511702i	$-0.170985\pi$
$677$	1.89913e12	+	1.89913e12i	0.347462	+	0.347462i	−0.511702	+	0.859163i	$0.670985\pi$
$678$	−1.37500e9	+	5.63751e11i	−0.000249901	+	0.102460i
$679$		−	2.79741e12i		−	0.505059i
$680$		0			0
$681$	3.28008e12	−	3.26412e12i	0.584416	−	0.581572i
$682$	1.73005e12	−	1.73005e12i	0.306218	−	0.306218i
$683$	8.58489e11	−	8.58489e11i	0.150953	−	0.150953i	−0.627591	−	0.778544i	$-0.715959\pi$
$683$	8.58489e11	−	8.58489e11i	0.150953	−	0.150953i	0.778544	+	0.627591i	$0.215959\pi$
$684$	3.05654e11	+	1.49100e9i	0.0533922	+	0.000260450i
$685$		0			0
$686$			4.30363e12i			0.741952i
$687$	−5.12373e11	−	1.24968e9i	−0.0877568	−	0.000214040i
$688$	5.85324e11	+	5.85324e11i	0.0995974	+	0.0995974i
$689$	−4.29306e11			−0.0725738
$690$		0			0
$691$	1.37889e11			0.0230080			0.0115040	−	0.999934i	$-0.496338\pi$
$691$	1.37889e11			0.0230080			0.0115040	+	0.999934i	$0.496338\pi$
$692$	1.23304e12	+	1.23304e12i	0.204409	+	0.204409i
$693$	7.81289e12	+	7.88948e12i	1.28680	+	1.29942i
$694$			6.30883e11i			0.103236i
$695$		0			0
$696$	−1.15522e12	−	1.16087e12i	−0.186605	−	0.187517i
$697$	2.96631e12	−	2.96631e12i	0.476068	−	0.476068i
$698$	−1.85033e12	+	1.85033e12i	−0.295052	+	0.295052i
$699$	−6.89816e11	−	6.93190e11i	−0.109291	−	0.109826i
$700$		0			0
$701$		−	3.87887e12i		−	0.606700i	−0.952879	−	0.303350i	$-0.901895\pi$
$701$		−	3.87887e12i		−	0.606700i	0.952879	−	0.303350i	$-0.0981051\pi$
$702$	−1.73564e11	−	1.26999e9i	−0.0269738	−	0.000197371i
$703$	−1.50764e11	−	1.50764e11i	−0.0232809	−	0.0232809i
$704$	1.18279e12			0.181481
$705$		0			0
$706$	1.40039e12			0.212143
$707$	−1.10103e13	−	1.10103e13i	−1.65735	−	1.65735i
$708$	−7.64746e12	−	1.86522e10i	−1.14385	−	0.00278985i
$709$		−	5.90342e12i		−	0.877396i	−0.898635	−	0.438698i	$-0.855440\pi$
$709$		−	5.90342e12i		−	0.877396i	0.898635	−	0.438698i	$-0.144560\pi$
$710$		0			0
$711$	−6.33761e9	+	1.29921e12i	−0.000930063	+	0.190663i
$712$	−2.69323e11	+	2.69323e11i	−0.0392747	+	0.0392747i
$713$	5.34345e12	−	5.34345e12i	0.774318	−	0.774318i
$714$	2.45597e12	−	2.44401e12i	0.353655	−	0.351934i
$715$		0			0
$716$			1.42098e12i			0.202059i
$717$	2.87214e10	−	1.17759e13i	0.00405854	−	1.66401i
$718$	−3.64826e12	−	3.64826e12i	−0.512302	−	0.512302i
$719$	−9.82340e12			−1.37082			−0.685412	−	0.728155i	$-0.740378\pi$
$719$	−9.82340e12			−1.37082			−0.685412	+	0.728155i	$0.740378\pi$
$720$		0			0
$721$	8.67342e12			1.19531
$722$	−2.04270e12	−	2.04270e12i	−0.279761	−	0.279761i
$723$	−1.51148e10	+	6.19711e12i	−0.00205722	+	0.843465i
$724$		−	8.80782e12i		−	1.19136i
$725$		0			0
$726$	−1.90908e11	+	1.89979e11i	−0.0255040	+	0.0253799i
$727$	6.87876e11	−	6.87876e11i	0.0913283	−	0.0913283i	−0.659967	−	0.751295i	$-0.729430\pi$
$727$	6.87876e11	−	6.87876e11i	0.0913283	−	0.0913283i	0.751295	+	0.659967i	$0.229430\pi$
$728$	−4.66332e11	+	4.66332e11i	−0.0615324	+	0.0615324i
$729$	−7.62478e12	−	1.11589e11i	−0.999893	−	0.0146335i
$730$		0			0
$731$		−	1.41417e12i		−	0.183178i
$732$	−9.46577e12	−	2.30871e10i	−1.21859	−	0.00297214i
$733$	−4.37758e12	−	4.37758e12i	−0.560101	−	0.560101i	0.369235	−	0.929336i	$-0.379620\pi$
$733$	−4.37758e12	−	4.37758e12i	−0.560101	−	0.560101i	−0.929336	+	0.369235i	$0.879620\pi$
$734$	1.58063e12			0.201001
$735$		0			0
$736$	−7.94038e12			−0.997450
$737$	−3.55355e12	−	3.55355e12i	−0.443668	−	0.443668i
$738$	2.13512e12	−	2.11439e12i	0.264953	−	0.262381i
$739$		−	7.92748e12i		−	0.977766i	−0.872349	−	0.488883i	$-0.837404\pi$
$739$		−	7.92748e12i		−	0.977766i	0.872349	−	0.488883i	$-0.162596\pi$
$740$		0			0
$741$	2.49215e10	+	2.50434e10i	0.00303664	+	0.00305148i
$742$	4.34070e12	−	4.34070e12i	0.525705	−	0.525705i
$743$	3.83077e12	−	3.83077e12i	0.461143	−	0.461143i	−0.437887	−	0.899030i	$-0.644273\pi$
$743$	3.83077e12	−	3.83077e12i	0.461143	−	0.461143i	0.899030	+	0.437887i	$0.144273\pi$
$744$	4.50356e12	+	4.52558e12i	0.538862	+	0.541497i
$745$		0			0
$746$		−	5.57399e11i		−	0.0658933i
$747$	−6.03443e12	+	5.97584e12i	−0.709077	+	0.702193i
$748$	−3.81896e12	−	3.81896e12i	−0.446055	−	0.446055i
$749$	1.24504e13			1.44549
$750$		0			0
$751$	8.72058e11			0.100038			0.0500191	−	0.998748i	$-0.484072\pi$
$751$	8.72058e11			0.100038			0.0500191	+	0.998748i	$0.484072\pi$
$752$	5.68705e12	+	5.68705e12i	0.648495	+	0.648495i
$753$	8.21584e12	+	2.00385e10i	0.931268	+	0.00227137i
$754$		−	8.65438e10i		−	0.00975135i
$755$		0			0
$756$	−9.43477e12	+	9.29770e12i	−1.05047	+	1.03521i
$757$	−7.87026e10	+	7.87026e10i	−0.00871079	+	0.00871079i	−0.711449	−	0.702738i	$-0.751961\pi$
$757$	−7.87026e10	+	7.87026e10i	−0.00871079	+	0.00871079i	0.702738	+	0.711449i	$0.251961\pi$
$758$	−1.89132e12	+	1.89132e12i	−0.208092	+	0.208092i
$759$	−7.09948e12	+	7.06493e12i	−0.776494	+	0.772716i
$760$		0			0
$761$		−	1.29237e13i		−	1.39687i	−0.715673	−	0.698435i	$-0.753880\pi$
$761$		−	1.29237e13i		−	1.39687i	0.715673	−	0.698435i	$-0.246120\pi$
$762$	−1.64880e10	+	6.76010e12i	−0.00177162	+	0.726366i
$763$	4.14789e12	+	4.14789e12i	0.443065	+	0.443065i
$764$	−1.18174e13			−1.25488
$765$		0			0
$766$	−6.39990e12			−0.671651
$767$	−6.25056e11	−	6.25056e11i	−0.0652139	−	0.0652139i
$768$	5.44045e9	−	2.23060e12i	0.000564299	−	0.231364i
$769$		−	4.15909e12i		−	0.428875i	−0.976738	−	0.214437i	$-0.931208\pi$
$769$		−	4.15909e12i		−	0.428875i	0.976738	−	0.214437i	$-0.0687918\pi$
$770$		0			0
$771$	−1.14994e13	+	1.14435e13i	−1.17201	+	1.16631i
$772$	6.03768e12	−	6.03768e12i	0.611776	−	0.611776i
$773$	−1.07320e13	+	1.07320e13i	−1.08112	+	1.08112i	−0.0847149	+	0.996405i	$0.526998\pi$
$773$	−1.07320e13	+	1.07320e13i	−1.08112	+	1.08112i	−0.996405	+	0.0847149i	$0.973002\pi$
$774$	4.94130e9	−	1.01297e12i	0.000494888	−	0.101452i
$775$		0			0
$776$			2.13197e12i			0.211059i
$777$	9.23993e12	+	2.25363e10i	0.909440	+	0.00221813i
$778$	−3.67635e12	−	3.67635e12i	−0.359757	−	0.359757i
$779$	−6.11660e11			−0.0595102
$780$		0			0
$781$	1.91894e12			0.184558
$782$	2.21001e12	+	2.21001e12i	0.211332	+	0.211332i
$783$	2.78208e10	−	3.80213e12i	0.00264510	−	0.361493i
$784$			1.20566e13i			1.13973i
$785$		0			0
$786$	−1.30193e12	−	1.30829e12i	−0.121670	−	0.122265i
$787$	8.43461e12	−	8.43461e12i	0.783752	−	0.783752i	−0.196709	−	0.980462i	$-0.563026\pi$
$787$	8.43461e12	−	8.43461e12i	0.783752	−	0.783752i	0.980462	+	0.196709i	$0.0630256\pi$
$788$	−3.69346e12	+	3.69346e12i	−0.341244	+	0.341244i
$789$	5.12474e12	+	5.14980e12i	0.470788	+	0.473090i
$790$		0			0
$791$			4.97308e12i			0.451681i
$792$	−5.95438e12	−	6.01275e12i	−0.537741	−	0.543013i
$793$	−7.73674e11	−	7.73674e11i	−0.0694750	−	0.0694750i
$794$	−5.36133e12			−0.478718
$795$		0			0
$796$	1.74974e13			1.54478
$797$	1.25806e13	+	1.25806e13i	1.10443	+	1.10443i	0.993870	+	0.110559i	$0.0352641\pi$
$797$	1.25806e13	+	1.25806e13i	1.10443	+	1.10443i	0.110559	+	0.993870i	$0.464736\pi$
$798$	−5.05194e11	−	1.23217e9i	−0.0441007	−	0.000107562i
$799$		−	1.37402e13i		−	1.19270i
$800$		0			0
$801$	−8.84262e11	−	4.31347e9i	−0.0758987	−	0.000370238i
$802$	−5.47391e12	+	5.47391e12i	−0.467211	+	0.467211i
$803$	−5.47453e12	+	5.47453e12i	−0.464651	+	0.464651i
$804$	4.24967e12	−	4.22899e12i	0.358676	−	0.356931i
$805$		0			0
$806$			3.37386e11i			0.0281591i
$807$	−1.33330e10	+	5.46657e12i	−0.00110662	+	0.453716i
$808$	8.39122e12	+	8.39122e12i	0.692586	+	0.692586i
$809$	−2.93830e12			−0.241173			−0.120586	−	0.992703i	$-0.538477\pi$
$809$	−2.93830e12			−0.241173			−0.120586	+	0.992703i	$0.538477\pi$
$810$		0			0
$811$	5.94961e12			0.482942			0.241471	−	0.970408i	$-0.422370\pi$
$811$	5.94961e12			0.482942			0.241471	+	0.970408i	$0.422370\pi$
$812$	−4.67027e12	−	4.67027e12i	−0.376999	−	0.376999i
$813$	−3.37108e10	+	1.38215e13i	−0.00270621	+	1.10955i
$814$			2.69859e12i			0.215440i
$815$		0			0
$816$	3.55104e12	−	3.53376e12i	0.280382	−	0.279018i
$817$	−1.45803e11	+	1.45803e11i	−0.0114490	+	0.0114490i
$818$	4.58026e12	−	4.58026e12i	0.357685	−	0.357685i
$819$	−1.53110e12	−	7.46876e9i	−0.118912	−	0.000580058i
$820$		0			0
$821$		−	1.03206e13i		−	0.792791i	−0.918080	−	0.396396i	$-0.870261\pi$
$821$		−	1.03206e13i		−	0.792791i	0.918080	−	0.396396i	$-0.129739\pi$
$822$	−5.90683e12	−	1.44068e10i	−0.451265	−	0.00110064i
$823$	−1.36701e13	−	1.36701e13i	−1.03866	−	1.03866i	−0.999222	−	0.0394373i	$-0.987443\pi$
$823$	−1.36701e13	−	1.36701e13i	−1.03866	−	1.03866i	−0.0394373	−	0.999222i	$-0.512557\pi$
$824$	−6.61021e12			−0.499508
$825$		0			0
$826$	1.26399e13			0.944783
$827$	−1.01334e13	−	1.01334e13i	−0.753321	−	0.753321i	0.221777	−	0.975097i	$-0.428814\pi$
$827$	−1.01334e13	−	1.01334e13i	−0.753321	−	0.753321i	−0.975097	+	0.221777i	$0.928814\pi$
$828$	−8.40770e12	−	8.49013e12i	−0.621642	−	0.627737i
$829$			1.93590e12i			0.142360i	0.997463	+	0.0711798i	$0.0226764\pi$
$829$			1.93590e12i			0.142360i	−0.997463	+	0.0711798i	$0.977324\pi$
$830$		0			0
$831$	8.15552e12	+	8.19540e12i	0.593263	+	0.596164i
$832$	−1.15331e11	+	1.15331e11i	−0.00834430	+	0.00834430i
$833$	1.45647e13	−	1.45647e13i	1.04809	−	1.04809i
$834$	−3.30177e11	−	3.31791e11i	−0.0236319	−	0.0237475i
$835$		0			0
$836$			7.87480e11i			0.0557585i
$837$	−1.08458e11	+	1.48224e13i	−0.00763828	+	1.04389i
$838$	−1.43704e12	−	1.43704e12i	−0.100663	−	0.100663i
$839$	2.51651e13			1.75336			0.876679	−	0.481076i	$-0.159754\pi$
$839$	2.51651e13			1.75336			0.876679	+	0.481076i	$0.159754\pi$
$840$		0			0
$841$	−1.26113e13			−0.869316
$842$	−2.65284e12	−	2.65284e12i	−0.181889	−	0.181889i
$843$	1.16076e13	+	2.83110e10i	0.791622	+	0.00193078i
$844$			1.36998e13i			0.929336i
$845$		0			0
$846$	4.80100e10	−	9.84205e12i	0.00322230	−	0.660570i
$847$	−1.67998e12	+	1.67998e12i	−0.112157	+	0.112157i
$848$	6.27615e12	−	6.27615e12i	0.416785	−	0.416785i
$849$	2.74437e10	−	2.73101e10i	0.00181283	−	0.00180401i
$850$		0			0
$851$			8.33487e12i			0.544774i
$852$	−5.58355e9	+	2.28927e12i	−0.000363022	+	0.148840i
$853$	1.17360e13	+	1.17360e13i	0.759011	+	0.759011i	0.976142	−	0.217131i	$-0.0696700\pi$
$853$	1.17360e13	+	1.17360e13i	0.759011	+	0.759011i	−0.217131	+	0.976142i	$0.569670\pi$
$854$	1.56452e13			1.00652
$855$		0			0
$856$	−9.48875e12			−0.604056
$857$	1.66550e13	+	1.66550e13i	1.05471	+	1.05471i	0.998414	+	0.0562930i	$0.0179281\pi$
$857$	1.66550e13	+	1.66550e13i	1.05471	+	1.05471i	0.0562930	+	0.998414i	$0.482072\pi$
$858$	1.09065e9	−	4.47171e11i	6.87060e−5	−	0.0281696i
$859$			2.91922e11i			0.0182936i	0.999958	+	0.00914678i	$0.00291155\pi$
$859$			2.91922e11i			0.0182936i	−0.999958	+	0.00914678i	$0.997088\pi$
$860$		0			0
$861$	1.87892e13	−	1.86978e13i	1.16518	−	1.15951i
$862$	6.49015e11	−	6.49015e11i	0.0400380	−	0.0400380i
$863$	1.93117e11	−	1.93117e11i	0.0118514	−	0.0118514i	−0.701156	−	0.713008i	$-0.747332\pi$
$863$	1.93117e11	−	1.93117e11i	0.0118514	−	0.0118514i	0.713008	+	0.701156i	$0.247332\pi$
$864$	1.10936e13	−	1.09325e13i	0.677270	−	0.667431i
$865$		0			0
$866$		−	1.56435e11i		−	0.00945154i
$867$	8.07876e12	+	1.97042e10i	0.485578	+	0.00118433i
$868$	1.82068e13	+	1.82068e13i	1.08866	+	1.08866i
$869$	−3.34725e12			−0.199113
$870$		0			0
$871$	6.92994e11			0.0407988
$872$	−3.16120e12	−	3.16120e12i	−0.185152	−	0.185152i
$873$	−3.51700e12	+	3.48285e12i	−0.204931	+	0.202941i
$874$		−	4.55710e11i		−	0.0264172i
$875$		0			0
$876$	−6.51510e12	−	6.54696e12i	−0.373812	−	0.375639i
$877$	−2.01420e13	+	2.01420e13i	−1.14975	+	1.14975i	−0.163153	+	0.986601i	$0.552166\pi$
$877$	−2.01420e13	+	2.01420e13i	−1.14975	+	1.14975i	−0.986601	+	0.163153i	$0.947834\pi$
$878$	9.18949e12	−	9.18949e12i	0.521874	−	0.521874i
$879$	4.37631e12	+	4.39771e12i	0.247263	+	0.248472i
$880$		0			0
$881$			2.60113e13i			1.45469i	0.686271	+	0.727346i	$0.259246\pi$
$881$			2.60113e13i			1.45469i	−0.686271	+	0.727346i	$0.740754\pi$
$882$	1.04835e13	−	1.03817e13i	0.583309	−	0.577646i
$883$	−3.17625e12	−	3.17625e12i	−0.175829	−	0.175829i	0.613706	−	0.789535i	$-0.289678\pi$
$883$	−3.17625e12	−	3.17625e12i	−0.175829	−	0.175829i	−0.789535	+	0.613706i	$0.789678\pi$
$884$	7.44754e11			0.0410183
$885$		0			0
$886$	5.35161e12			0.291765
$887$	−1.34489e12	−	1.34489e12i	−0.0729506	−	0.0729506i	0.669690	−	0.742641i	$-0.266427\pi$
$887$	−1.34489e12	−	1.34489e12i	−0.0729506	−	0.0729506i	−0.742641	+	0.669690i	$0.766427\pi$
$888$	−7.04195e12	−	1.71754e10i	−0.380045	−	0.000926934i
$889$			5.96336e13i			3.20209i
$890$		0			0
$891$	1.91665e11	−	1.96452e13i	0.0101881	−	1.04426i
$892$	8.42469e10	−	8.42469e10i	0.00445566	−	0.00445566i
$893$	−1.41663e12	+	1.41663e12i	−0.0745461	+	0.0745461i
$894$	7.80077e11	−	7.76281e11i	0.0408431	−	0.0406443i
$895$		0			0
$896$		−	3.44567e13i		−	1.78603i
$897$	3.36860e9	−	1.38113e12i	0.000173733	−	0.0712311i
$898$	−2.22362e11	−	2.22362e11i	−0.0114108	−	0.0114108i
$899$	−7.39086e12			−0.377378
$900$		0			0
$901$	−1.51635e13			−0.766544
$902$	5.47417e12	+	5.47417e12i	0.275352	+	0.275352i
$903$	2.17946e10	−	8.93584e12i	0.00109082	−	0.447240i
$904$		−	3.79010e12i		−	0.188752i
$905$		0			0
$906$	−8.55318e12	+	8.51156e12i	−0.421746	+	0.419694i
$907$	5.42622e12	−	5.42622e12i	0.266235	−	0.266235i	−0.561346	−	0.827581i	$-0.689716\pi$
$907$	5.42622e12	−	5.42622e12i	0.266235	−	0.266235i	0.827581	+	0.561346i	$0.189716\pi$
$908$	−1.00570e13	+	1.00570e13i	−0.491000	+	0.491000i
$909$	−1.34394e11	+	2.75507e13i	−0.00652892	+	1.33843i
$910$		0			0
$911$		−	6.40196e12i		−	0.307950i	−0.988075	−	0.153975i	$-0.950792\pi$
$911$		−	6.40196e12i		−	0.307950i	0.988075	−	0.153975i	$-0.0492076\pi$
$912$	−7.30452e11	−	1.78158e9i	−0.0349635	−	8.52764e-5i
$913$	−1.54715e13	−	1.54715e13i	−0.736908	−	0.736908i
$914$	3.13934e12			0.148792
$915$		0			0
$916$	1.57481e12			0.0739091
$917$	−1.15129e13	−	1.15129e13i	−0.537679	−	0.537679i
$918$	−6.13043e12	−	4.48573e10i	−0.284904	−	0.00208469i
$919$		−	4.29393e13i		−	1.98580i	−0.118951	−	0.992900i	$-0.537953\pi$
$919$		−	4.29393e13i		−	1.98580i	0.118951	−	0.992900i	$-0.462047\pi$
$920$		0			0
$921$	1.32129e13	+	1.32775e13i	0.605103	+	0.608062i
$922$	−4.79633e12	+	4.79633e12i	−0.218585	+	0.218585i
$923$	−1.87111e11	+	1.87111e11i	−0.00848577	+	0.00848577i
$924$	−2.40724e13	−	2.41901e13i	−1.08641	−	1.09173i
$925$		0			0
$926$			5.08738e10i			0.00227376i
$927$	−1.07986e13	−	1.09045e13i	−0.480297	−	0.485006i
$928$	5.49142e12	+	5.49142e12i	0.243063	+	0.243063i
$929$	1.64282e13			0.723635			0.361817	−	0.932249i	$-0.382156\pi$
$929$	1.64282e13			0.723635			0.361817	+	0.932249i	$0.382156\pi$
$930$		0			0
$931$	−3.00327e12			−0.131015
$932$	2.12538e12	+	2.12538e12i	0.0922707	+	0.0922707i
$933$	4.75426e12	+	1.15957e10i	0.205407	+	0.000500990i
$934$			1.24830e12i			0.0536734i
$935$		0			0
$936$	1.16688e12	+	5.69211e9i	0.0496919	+	0.000242400i
$937$	−4.14059e12	+	4.14059e12i	−0.175483	+	0.175483i	−0.789383	−	0.613901i	$-0.789600\pi$
$937$	−4.14059e12	+	4.14059e12i	−0.175483	+	0.175483i	0.613901	+	0.789383i	$0.289600\pi$
$938$	−7.00684e12	+	7.00684e12i	−0.295535	+	0.295535i
$939$	1.10033e13	−	1.09497e13i	0.461877	−	0.459630i
$940$		0			0
$941$			1.41870e13i			0.589845i	0.955521	+	0.294923i	$0.0952939\pi$
$941$			1.41870e13i			0.589845i	−0.955521	+	0.294923i	$0.904706\pi$
$942$	−1.41051e10	+	5.78311e12i	−0.000583641	+	0.239294i
$943$	1.69075e13	+	1.69075e13i	0.696270	+	0.696270i
$944$	1.82758e13			0.749035
$945$		0			0
$946$	2.60978e12			0.105948
$947$	−7.85040e12	−	7.85040e12i	−0.317188	−	0.317188i	0.530498	−	0.847686i	$-0.322005\pi$
$947$	−7.85040e12	−	7.85040e12i	−0.317188	−	0.317188i	−0.847686	+	0.530498i	$0.822005\pi$
$948$	9.73951e9	−	3.99322e12i	0.000391651	−	0.160578i
$949$		−	1.06761e12i		−	0.0427283i
$950$		0			0
$951$	−1.66987e13	+	1.66174e13i	−0.662017	+	0.658795i
$952$	−1.64713e13	+	1.64713e13i	−0.649921	+	0.649921i
$953$	−6.02425e12	+	6.02425e12i	−0.236584	+	0.236584i	−0.815434	−	0.578850i	$-0.803502\pi$
$953$	−6.02425e12	+	6.02425e12i	−0.236584	+	0.236584i	0.578850	+	0.815434i	$0.303502\pi$
$954$	−1.08616e13	−	5.29832e10i	−0.424546	−	0.00207095i
$955$		0			0
$956$			3.61938e13i			1.40144i
$957$	9.79584e12	+	2.38922e10i	0.377518	+	0.000920771i
$958$	6.69660e12	+	6.69660e12i	0.256868	+	0.256868i
$959$	−5.21066e13			−1.98934
$960$		0			0
$961$	2.37323e12			0.0897605
$962$	−2.63132e11	−	2.63132e11i	−0.00990573	−	0.00990573i
$963$	−1.55011e13	−	1.56531e13i	−0.580824	−	0.586519i
$964$		−	1.90472e13i		−	0.710370i
$965$		0			0
$966$	1.39305e13	+	1.39987e13i	0.514720	+	0.517237i
$967$	−1.66636e12	+	1.66636e12i	−0.0612843	+	0.0612843i	−0.737085	−	0.675800i	$-0.763798\pi$
$967$	−1.66636e12	+	1.66636e12i	−0.0612843	+	0.0612843i	0.675800	+	0.737085i	$0.263798\pi$
$968$	1.28035e12	−	1.28035e12i	0.0468694	−	0.0468694i
$969$	8.80251e11	+	8.84556e11i	0.0320737	+	0.0322306i
$970$		0			0
$971$		−	1.46235e13i		−	0.527915i	−0.964534	−	0.263957i	$-0.914972\pi$
$971$		−	1.46235e13i		−	0.527915i	0.964534	−	0.263957i	$-0.0850278\pi$
$972$	2.34359e13	+	2.85816e11i	0.842139	+	0.0102704i
$973$	−2.91975e12	−	2.91975e12i	−0.104433	−	0.104433i
$974$	−1.31837e13			−0.469378
$975$		0			0
$976$	2.26212e13			0.797977
$977$	3.58161e13	+	3.58161e13i	1.25763	+	1.25763i	0.952221	+	0.305409i	$0.0987933\pi$
$977$	3.58161e13	+	3.58161e13i	1.25763	+	1.25763i	0.305409	+	0.952221i	$0.401207\pi$
$978$	1.25330e13	+	3.05682e10i	0.438058	+	0.00106843i
$979$		−	2.27819e12i		−	0.0792625i
$980$		0			0
$981$	5.06298e10	−	1.03791e13i	0.00174540	−	0.357807i
$982$	1.33366e13	−	1.33366e13i	0.457661	−	0.457661i
$983$	−2.78530e13	+	2.78530e13i	−0.951440	+	0.951440i	−0.998874	−	0.0474345i	$-0.984895\pi$
$983$	−2.78530e13	+	2.78530e13i	−0.951440	+	0.951440i	0.0474345	+	0.998874i	$0.484895\pi$
$984$	−1.43197e13	+	1.42500e13i	−0.486917	+	0.484547i
$985$		0			0
$986$		−	3.05681e12i		−	0.102996i
$987$	2.11758e11	−	8.68213e13i	0.00710253	−	2.91205i
$988$	−7.67851e10	−	7.67851e10i	−0.00256372	−	0.00256372i
$989$	8.06057e12			0.267906
$990$		0			0
$991$	−5.83129e13			−1.92058			−0.960292	−	0.278998i	$-0.909998\pi$
$991$	−5.83129e13			−1.92058			−0.960292	+	0.278998i	$0.909998\pi$
$992$	−2.14080e13	−	2.14080e13i	−0.701896	−	0.701896i
$993$	4.48161e9	−	1.83747e12i	0.000146272	−	0.0599720i
$994$		−	3.78375e12i		−	0.122937i
$995$		0			0
$996$	1.85023e13	−	1.84122e13i	0.595742	−	0.592843i
$997$	−1.76105e13	+	1.76105e13i	−0.564473	+	0.564473i	−0.930575	−	0.366102i	$-0.880692\pi$
$997$	−1.76105e13	+	1.76105e13i	−0.564473	+	0.564473i	0.366102	+	0.930575i	$0.380692\pi$
$998$	−3.93988e12	+	3.93988e12i	−0.125718	+	0.125718i
$999$	−1.14756e13	−	1.16448e13i	−0.364528	−	0.369902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.f.68.7		32
3.2	odd	2	inner	75.10.e.f.68.10		32
5.2	odd	4	inner	75.10.e.f.32.10		32
5.3	odd	4		15.10.e.a.2.7	✓	32
5.4	even	2		15.10.e.a.8.10	yes	32
15.2	even	4	inner	75.10.e.f.32.7		32
15.8	even	4		15.10.e.a.2.10	yes	32
15.14	odd	2		15.10.e.a.8.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.e.a.2.7	✓	32	5.3	odd	4
15.10.e.a.2.10	yes	32	15.8	even	4
15.10.e.a.8.7	yes	32	15.14	odd	2
15.10.e.a.8.10	yes	32	5.4	even	2
75.10.e.f.32.7		32	15.2	even	4	inner
75.10.e.f.32.10		32	5.2	odd	4	inner
75.10.e.f.68.7		32	1.1	even	1	trivial
75.10.e.f.68.10		32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.35582 - 6.35582i) q^{2} +(-0.342183 + 140.296i) q^{3} -431.207i q^{4} +(893.869 - 889.519i) q^{6} +(7866.00 - 7866.00i) q^{7} +(-5994.85 + 5994.85i) q^{8} +(-19682.8 - 96.0135i) q^{9} +O(q^{10})\)	\(q+(-6.35582 - 6.35582i) q^{2} +(-0.342183 + 140.296i) q^{3} -431.207i q^{4} +(893.869 - 889.519i) q^{6} +(7866.00 - 7866.00i) q^{7} +(-5994.85 + 5994.85i) q^{8} +(-19682.8 - 96.0135i) q^{9} -50710.2i q^{11} +(60496.5 + 147.552i) q^{12} +(4944.61 + 4944.61i) q^{13} -99989.7 q^{14} -144574. q^{16} +(174648. + 174648. i) q^{17} +(124490. + 125710. i) q^{18} -36012.9i q^{19} +(1.10087e6 + 1.10626e6i) q^{21} +(-322305. + 322305. i) q^{22} +(-995471. + 995471. i) q^{23} +(-839001. - 843104. i) q^{24} -62854.1i q^{26} +(20205.4 - 2.76137e6i) q^{27} +(-3.39187e6 - 3.39187e6i) q^{28} +1.37690e6 q^{29} -5.36776e6 q^{31} +(3.98825e6 + 3.98825e6i) q^{32} +(7.11442e6 + 17352.1i) q^{33} -2.22007e6i q^{34} +(-41401.7 + 8.48735e6i) q^{36} +(4.18640e6 - 4.18640e6i) q^{37} +(-228892. + 228892. i) q^{38} +(-695400. + 692016. i) q^{39} -1.69845e7i q^{41} +(34214.8 - 1.40281e7i) q^{42} +(-4.04862e6 - 4.04862e6i) q^{43} -2.18666e7 q^{44} +1.26541e7 q^{46} +(-3.93367e7 - 3.93367e7i) q^{47} +(49470.6 - 2.02831e7i) q^{48} -8.33943e7i q^{49} +(-2.45622e7 + 2.44426e7i) q^{51} +(2.13215e6 - 2.13215e6i) q^{52} +(-4.34114e7 + 4.34114e7i) q^{53} +(-1.76792e7 + 1.74224e7i) q^{54} +9.43110e7i q^{56} +(5.05246e6 + 12323.0i) q^{57} +(-8.75132e6 - 8.75132e6i) q^{58} -1.26412e8 q^{59} -1.56468e8 q^{61} +(3.41165e7 + 3.41165e7i) q^{62} +(-1.55580e8 + 1.54069e8i) q^{63} +2.33245e7i q^{64} +(-4.51077e7 - 4.53283e7i) q^{66} +(7.00756e7 - 7.00756e7i) q^{67} +(7.53096e7 - 7.53096e7i) q^{68} +(-1.39320e8 - 1.40001e8i) q^{69} +3.78414e7i q^{71} +(1.18571e8 - 1.17420e8i) q^{72} +(-1.07957e8 - 1.07957e8i) q^{73} -5.32159e7 q^{74} -1.55290e7 q^{76} +(-3.98886e8 - 3.98886e8i) q^{77} +(8.81817e6 + 21507.6i) q^{78} -6.60075e7i q^{79} +(3.87402e8 + 3.77962e6i) q^{81} +(-1.07950e8 + 1.07950e8i) q^{82} +(3.05096e8 - 3.05096e8i) q^{83} +(4.77026e8 - 4.74705e8i) q^{84} +5.14646e7i q^{86} +(-471151. + 1.93173e8i) q^{87} +(3.04000e8 + 3.04000e8i) q^{88} +4.49257e7 q^{89} +7.77887e7 q^{91} +(4.29254e8 + 4.29254e8i) q^{92} +(1.83676e6 - 7.53074e8i) q^{93} +5.00034e8i q^{94} +(-5.60899e8 + 5.58169e8i) q^{96} +(1.77817e8 - 1.77817e8i) q^{97} +(-5.30039e8 + 5.30039e8i) q^{98} +(-4.86886e6 + 9.98117e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7}+O(q^{10}) \) 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7	\( 32 q + 150 q^{3} - 4548 q^{6} + 9760 q^{7} - 191940 q^{12} - 114260 q^{13} - 1494724 q^{16} - 994800 q^{18} + 592212 q^{21} - 308260 q^{22} - 4786830 q^{27} + 12953300 q^{28} + 16124104 q^{31} - 19638120 q^{33} - 48943956 q^{36} + 35578660 q^{37} - 46648260 q^{42} + 118721020 q^{43} + 3145024 q^{46} - 275395140 q^{48} - 64226868 q^{51} + 157103680 q^{52} - 48163500 q^{57} + 209634300 q^{58} + 63607744 q^{61} - 89858580 q^{63} + 358931400 q^{66} - 153311540 q^{67} + 1534046760 q^{72} - 628070360 q^{73} - 2457023472 q^{76} + 403337880 q^{78} + 2250542952 q^{81} - 4138031440 q^{82} + 2878139760 q^{87} + 595851300 q^{88} - 4369040216 q^{91} + 293672640 q^{93} + 7291125636 q^{96} - 3987642200 q^{97}+O(q^{100}) \) 32 * q + 150 * q^3 - 4548 * q^6 + 9760 * q^7 - 191940 * q^12 - 114260 * q^13 - 1494724 * q^16 - 994800 * q^18 + 592212 * q^21 - 308260 * q^22 - 4786830 * q^27 + 12953300 * q^28 + 16124104 * q^31 - 19638120 * q^33 - 48943956 * q^36 + 35578660 * q^37 - 46648260 * q^42 + 118721020 * q^43 + 3145024 * q^46 - 275395140 * q^48 - 64226868 * q^51 + 157103680 * q^52 - 48163500 * q^57 + 209634300 * q^58 + 63607744 * q^61 - 89858580 * q^63 + 358931400 * q^66 - 153311540 * q^67 + 1534046760 * q^72 - 628070360 * q^73 - 2457023472 * q^76 + 403337880 * q^78 + 2250542952 * q^81 - 4138031440 * q^82 + 2878139760 * q^87 + 595851300 * q^88 - 4369040216 * q^91 + 293672640 * q^93 + 7291125636 * q^96 - 3987642200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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