LMFDB - Embedded newform 5.21.c.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,21,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	5.c (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:	$12.6756882551$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 7326009 x^{16} + 21914129354136 x^{14} + \cdots + 79\!\cdots\!76 $ x^18 + 7326009x^16 + 21914129354136x^14 + 34716886079362208784x^12 + 31708037646565185778430976x^10 + 17074068956994774485619232997376x^8 + 5289719974975064649188570034899779584x^6 + 860456443567863287787024826102919920091136x^4 + 56032264901085762369236000491606259366923075584x^2 + 797517854172776133766249661927470942176176766976
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{16}\cdot 5^{32} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.2
Root			$1196.41i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.21.c.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1196.41 - 1196.41i) q^{2} +(-49580.3 + 49580.3i) q^{3} +1.81424e6i q^{4} +(-9.20993e6 + 3.24723e6i) q^{5} +1.18637e8 q^{6} +(2.14321e8 + 2.14321e8i) q^{7} +(9.16051e8 - 9.16051e8i) q^{8} -1.42964e9i q^{9} +O(q^{10})$	\(q+(-1196.41 - 1196.41i) q^{2} +(-49580.3 + 49580.3i) q^{3} +1.81424e6i q^{4} +(-9.20993e6 + 3.24723e6i) q^{5} +1.18637e8 q^{6} +(2.14321e8 + 2.14321e8i) q^{7} +(9.16051e8 - 9.16051e8i) q^{8} -1.42964e9i q^{9} +(1.49039e10 + 7.13386e9i) q^{10} -2.93214e10 q^{11} +(-8.99506e10 - 8.99506e10i) q^{12} +(-1.74406e11 + 1.74406e11i) q^{13} -5.12834e11i q^{14} +(2.95633e11 - 6.17631e11i) q^{15} -2.89586e11 q^{16} +(2.79395e11 + 2.79395e11i) q^{17} +(-1.71044e12 + 1.71044e12i) q^{18} -4.94427e12i q^{19} +(-5.89126e12 - 1.67090e13i) q^{20} -2.12522e13 q^{21} +(3.50805e13 + 3.50805e13i) q^{22} +(-1.73176e13 + 1.73176e13i) q^{23} +9.08363e13i q^{24} +(7.42784e13 - 5.98136e13i) q^{25} +4.17324e14 q^{26} +(-1.01994e14 - 1.01994e14i) q^{27} +(-3.88830e14 + 3.88830e14i) q^{28} -4.41901e14i q^{29} +(-1.09264e15 + 3.85243e14i) q^{30} +4.37243e14 q^{31} +(-6.14084e14 - 6.14084e14i) q^{32} +(1.45376e15 - 1.45376e15i) q^{33} -6.68545e14i q^{34} +(-2.66983e15 - 1.27793e15i) q^{35} +2.59371e15 q^{36} +(5.59455e15 + 5.59455e15i) q^{37} +(-5.91540e15 + 5.91540e15i) q^{38} -1.72942e16i q^{39} +(-5.46214e15 + 1.14114e16i) q^{40} -5.55775e15 q^{41} +(2.54265e16 + 2.54265e16i) q^{42} +(-1.34424e16 + 1.34424e16i) q^{43} -5.31960e16i q^{44} +(4.64237e15 + 1.31669e16i) q^{45} +4.14381e16 q^{46} +(2.63557e16 + 2.63557e16i) q^{47} +(1.43578e16 - 1.43578e16i) q^{48} +1.20748e16i q^{49} +(-1.60430e17 - 1.73058e16i) q^{50} -2.77050e16 q^{51} +(-3.16415e17 - 3.16415e17i) q^{52} +(4.22158e16 - 4.22158e16i) q^{53} +2.44054e17i q^{54} +(2.70048e17 - 9.52134e16i) q^{55} +3.92658e17 q^{56} +(2.45139e17 + 2.45139e17i) q^{57} +(-5.28697e17 + 5.28697e17i) q^{58} -2.78863e17i q^{59} +(1.12053e18 + 5.36349e17i) q^{60} -2.38765e17 q^{61} +(-5.23124e17 - 5.23124e17i) q^{62} +(3.06401e17 - 3.06401e17i) q^{63} +1.77305e18i q^{64} +(1.03993e18 - 2.17261e18i) q^{65} -3.47861e18 q^{66} +(-7.63239e17 - 7.63239e17i) q^{67} +(-5.06890e17 + 5.06890e17i) q^{68} -1.71723e18i q^{69} +(1.66529e18 + 4.72317e18i) q^{70} +2.33338e18 q^{71} +(-1.30962e18 - 1.30962e18i) q^{72} +(2.47479e18 - 2.47479e18i) q^{73} -1.33868e19i q^{74} +(-7.17166e17 + 6.64833e18i) q^{75} +8.97010e18 q^{76} +(-6.28419e18 - 6.28419e18i) q^{77} +(-2.06911e19 + 2.06911e19i) q^{78} +1.18600e19i q^{79} +(2.66707e18 - 9.40355e17i) q^{80} +1.50986e19 q^{81} +(6.64937e18 + 6.64937e18i) q^{82} +(-6.17199e17 + 6.17199e17i) q^{83} -3.85566e19i q^{84} +(-3.48047e18 - 1.66595e18i) q^{85} +3.21653e19 q^{86} +(2.19096e19 + 2.19096e19i) q^{87} +(-2.68599e19 + 2.68599e19i) q^{88} -1.09458e19i q^{89} +(1.01988e19 - 2.13072e19i) q^{90} -7.47579e19 q^{91} +(-3.14183e19 - 3.14183e19i) q^{92} +(-2.16787e19 + 2.16787e19i) q^{93} -6.30646e19i q^{94} +(1.60552e19 + 4.55364e19i) q^{95} +6.08930e19 q^{96} +(-1.00851e20 - 1.00851e20i) q^{97} +(1.44465e19 - 1.44465e19i) q^{98} +4.19190e19i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1196.41	−	1196.41i	−1.16837	−	1.16837i	−0.982591	−	0.185783i	$-0.940518\pi$
$2$	−1196.41	−	1196.41i	−1.16837	−	1.16837i	−0.185783	−	0.982591i	$-0.559482\pi$
$3$	−49580.3	+	49580.3i	−0.839648	+	0.839648i	−0.988812	−	0.149165i	$-0.952342\pi$
$3$	−49580.3	+	49580.3i	−0.839648	+	0.839648i	0.149165	+	0.988812i	$0.452342\pi$
$4$			1.81424e6i			1.73019i
$5$	−9.20993e6	+	3.24723e6i	−0.943097	+	0.332517i
$5$	−9.20993e6	+	3.24723e6i	−0.943097	+	0.332517i
$6$	1.18637e8			1.96204
$7$	2.14321e8	+	2.14321e8i	0.758725	+	0.758725i	0.976090	−	0.217365i	$-0.0697462\pi$
$7$	2.14321e8	+	2.14321e8i	0.758725	+	0.758725i	−0.217365	+	0.976090i	$0.569746\pi$
$8$	9.16051e8	−	9.16051e8i	0.853139	−	0.853139i
$9$		−	1.42964e9i		−	0.410016i
$10$	1.49039e10	+	7.13386e9i	1.49039	+	0.713386i
$11$	−2.93214e10			−1.13047			−0.565233	−	0.824931i	$-0.691214\pi$
$11$	−2.93214e10			−1.13047			−0.565233	+	0.824931i	$0.691214\pi$
$12$	−8.99506e10	−	8.99506e10i	−1.45275	−	1.45275i
$13$	−1.74406e11	+	1.74406e11i	−1.26511	+	1.26511i	−0.316527	+	0.948584i	$0.602517\pi$
$13$	−1.74406e11	+	1.74406e11i	−1.26511	+	1.26511i	−0.948584	+	0.316527i	$0.897483\pi$
$14$		−	5.12834e11i		−	1.77295i
$15$	2.95633e11	−	6.17631e11i	0.512672	−	1.07107i
$16$	−2.89586e11			−0.263377
$17$	2.79395e11	+	2.79395e11i	0.138589	+	0.138589i	0.772998	−	0.634409i	$-0.218756\pi$
$17$	2.79395e11	+	2.79395e11i	0.138589	+	0.138589i	−0.634409	+	0.772998i	$0.718756\pi$
$18$	−1.71044e12	+	1.71044e12i	−0.479052	+	0.479052i
$19$		−	4.94427e12i		−	0.806430i	−0.915105	−	0.403215i	$-0.867893\pi$
$19$		−	4.94427e12i		−	0.806430i	0.915105	−	0.403215i	$-0.132107\pi$
$20$	−5.89126e12	−	1.67090e13i	−0.575319	−	1.63174i
$21$	−2.12522e13			−1.27412
$22$	3.50805e13	+	3.50805e13i	1.32081	+	1.32081i
$23$	−1.73176e13	+	1.73176e13i	−0.418032	+	0.418032i	−0.884525	−	0.466493i	$-0.845517\pi$
$23$	−1.73176e13	+	1.73176e13i	−0.418032	+	0.418032i	0.466493	+	0.884525i	$0.345517\pi$
$24$			9.08363e13i			1.43267i
$25$	7.42784e13	−	5.98136e13i	0.778865	−	0.627191i
$26$	4.17324e14			2.95624
$27$	−1.01994e14	−	1.01994e14i	−0.495379	−	0.495379i
$28$	−3.88830e14	+	3.88830e14i	−1.31274	+	1.31274i
$29$		−	4.41901e14i		−	1.05038i	−0.850986	−	0.525188i	$-0.823995\pi$
$29$		−	4.41901e14i		−	1.05038i	0.850986	−	0.525188i	$-0.176005\pi$
$30$	−1.09264e15	+	3.85243e14i	−1.85040	+	0.652413i
$31$	4.37243e14			0.533465			0.266732	−	0.963771i	$-0.414056\pi$
$31$	4.37243e14			0.533465			0.266732	+	0.963771i	$0.414056\pi$
$32$	−6.14084e14	−	6.14084e14i	−0.545416	−	0.545416i
$33$	1.45376e15	−	1.45376e15i	0.949193	−	0.949193i
$34$		−	6.68545e14i		−	0.323848i
$35$	−2.66983e15	−	1.27793e15i	−0.967841	−	0.463263i
$36$	2.59371e15			0.709407
$37$	5.59455e15	+	5.59455e15i	1.16345	+	1.16345i	0.983715	+	0.179736i	$0.0575245\pi$
$37$	5.59455e15	+	5.59455e15i	1.16345	+	1.16345i	0.179736	+	0.983715i	$0.442476\pi$
$38$	−5.91540e15	+	5.91540e15i	−0.942211	+	0.942211i
$39$		−	1.72942e16i		−	2.12449i
$40$	−5.46214e15	+	1.14114e16i	−0.520910	+	1.08828i
$41$	−5.55775e15			−0.414057			−0.207029	−	0.978335i	$-0.566379\pi$
$41$	−5.55775e15			−0.414057			−0.207029	+	0.978335i	$0.566379\pi$
$42$	2.54265e16	+	2.54265e16i	1.48865	+	1.48865i
$43$	−1.34424e16	+	1.34424e16i	−0.622001	+	0.622001i	−0.946043	−	0.324042i	$-0.894958\pi$
$43$	−1.34424e16	+	1.34424e16i	−0.622001	+	0.622001i	0.324042	+	0.946043i	$0.394958\pi$
$44$		−	5.31960e16i		−	1.95593i
$45$	4.64237e15	+	1.31669e16i	0.136337	+	0.386685i
$46$	4.14381e16			0.976836
$47$	2.63557e16	+	2.63557e16i	0.501066	+	0.501066i	0.911769	−	0.410703i	$-0.134717\pi$
$47$	2.63557e16	+	2.63557e16i	0.501066	+	0.501066i	−0.410703	+	0.911769i	$0.634717\pi$
$48$	1.43578e16	−	1.43578e16i	0.221144	−	0.221144i
$49$			1.20748e16i			0.151328i
$50$	−1.60430e17	−	1.73058e16i	−1.64280	−	0.177211i
$51$	−2.77050e16			−0.232732
$52$	−3.16415e17	−	3.16415e17i	−2.18889	−	2.18889i
$53$	4.22158e16	−	4.22158e16i	0.241388	−	0.241388i	−0.576036	−	0.817424i	$-0.695401\pi$
$53$	4.22158e16	−	4.22158e16i	0.241388	−	0.241388i	0.817424	+	0.576036i	$0.195401\pi$
$54$			2.44054e17i			1.15757i
$55$	2.70048e17	−	9.52134e16i	1.06614	−	0.375899i
$56$	3.92658e17			1.29460
$57$	2.45139e17	+	2.45139e17i	0.677117	+	0.677117i
$58$	−5.28697e17	+	5.28697e17i	−1.22723	+	1.22723i
$59$		−	2.78863e17i		−	0.545595i	−0.962071	−	0.272798i	$-0.912051\pi$
$59$		−	2.78863e17i		−	0.545595i	0.962071	−	0.272798i	$-0.0879490\pi$
$60$	1.12053e18	+	5.36349e17i	1.85315	+	0.887023i
$61$	−2.38765e17			−0.334713			−0.167357	−	0.985896i	$-0.553523\pi$
$61$	−2.38765e17			−0.334713			−0.167357	+	0.985896i	$0.553523\pi$
$62$	−5.23124e17	−	5.23124e17i	−0.623286	−	0.623286i
$63$	3.06401e17	−	3.06401e17i	0.311090	−	0.311090i
$64$			1.77305e18i			1.53788i
$65$	1.03993e18	−	2.17261e18i	0.772452	−	1.61379i
$66$	−3.47861e18			−2.21802
$67$	−7.63239e17	−	7.63239e17i	−0.418709	−	0.418709i	0.466049	−	0.884759i	$-0.345677\pi$
$67$	−7.63239e17	−	7.63239e17i	−0.418709	−	0.418709i	−0.884759	+	0.466049i	$0.845677\pi$
$68$	−5.06890e17	+	5.06890e17i	−0.239786	+	0.239786i
$69$		−	1.71723e18i		−	0.702000i
$70$	1.66529e18	+	4.72317e18i	0.589535	+	1.67206i
$71$	2.33338e18			0.716805			0.358403	−	0.933567i	$-0.383322\pi$
$71$	2.33338e18			0.716805			0.358403	+	0.933567i	$0.383322\pi$
$72$	−1.30962e18	−	1.30962e18i	−0.349801	−	0.349801i
$73$	2.47479e18	−	2.47479e18i	0.575849	−	0.575849i	−0.357908	−	0.933757i	$-0.616510\pi$
$73$	2.47479e18	−	2.47479e18i	0.575849	−	0.575849i	0.933757	+	0.357908i	$0.116510\pi$
$74$		−	1.33868e19i		−	2.71869i
$75$	−7.17166e17	+	6.64833e18i	−0.127352	+	1.18059i
$76$	8.97010e18			1.39528
$77$	−6.28419e18	−	6.28419e18i	−0.857713	−	0.857713i
$78$	−2.06911e19	+	2.06911e19i	−2.48220	+	2.48220i
$79$			1.18600e19i			1.25261i	0.779578	+	0.626305i	$0.215433\pi$
$79$			1.18600e19i			1.25261i	−0.779578	+	0.626305i	$0.784567\pi$
$80$	2.66707e18	−	9.40355e17i	0.248390	−	0.0875774i
$81$	1.50986e19			1.24190
$82$	6.64937e18	+	6.64937e18i	0.483774	+	0.483774i
$83$	−6.17199e17	+	6.17199e17i	−0.0397781	+	0.0397781i	−0.726716	−	0.686938i	$-0.758954\pi$
$83$	−6.17199e17	+	6.17199e17i	−0.0397781	+	0.0397781i	0.686938	+	0.726716i	$0.258954\pi$
$84$		−	3.85566e19i		−	2.20448i
$85$	−3.48047e18	−	1.66595e18i	−0.176786	−	0.0846199i
$86$	3.21653e19			1.45346
$87$	2.19096e19	+	2.19096e19i	0.881946	+	0.881946i
$88$	−2.68599e19	+	2.68599e19i	−0.964445	+	0.964445i
$89$		−	1.09458e19i		−	0.351033i	−0.984476	−	0.175517i	$-0.943840\pi$
$89$		−	1.09458e19i		−	0.351033i	0.984476	−	0.175517i	$-0.0561596\pi$
$90$	1.01988e19	−	2.13072e19i	0.292500	−	0.611085i
$91$	−7.47579e19			−1.91974
$92$	−3.14183e19	−	3.14183e19i	−0.723277	−	0.723277i
$93$	−2.16787e19	+	2.16787e19i	−0.447922	+	0.447922i
$94$		−	6.30646e19i		−	1.17087i
$95$	1.60552e19	+	4.55364e19i	0.268151	+	0.760542i
$96$	6.08930e19			0.915915
$97$	−1.00851e20	−	1.00851e20i	−1.36762	−	1.36762i	−0.863827	−	0.503789i	$-0.831939\pi$
$97$	−1.00851e20	−	1.00851e20i	−1.36762	−	1.36762i	−0.503789	−	0.863827i	$-0.668061\pi$
$98$	1.44465e19	−	1.44465e19i	0.176808	−	0.176808i
$99$			4.19190e19i			0.463509i
$100$	1.08516e20	+	1.34759e20i	1.08516	+	1.34759i
$101$	−1.02541e19			−0.0928288			−0.0464144	−	0.998922i	$-0.514779\pi$
$101$	−1.02541e19			−0.0928288			−0.0464144	+	0.998922i	$0.514779\pi$
$102$	3.31467e19	+	3.31467e19i	0.271918	+	0.271918i
$103$	1.15445e20	−	1.15445e20i	0.859017	−	0.859017i	−0.132205	−	0.991222i	$-0.542206\pi$
$103$	1.15445e20	−	1.15445e20i	0.859017	−	0.859017i	0.991222	+	0.132205i	$0.0422058\pi$
$104$			3.19530e20i			2.15863i
$105$	1.95732e20	−	6.90110e19i	1.20162	−	0.423668i
$106$	−1.01015e20			−0.564063
$107$	4.78756e19	+	4.78756e19i	0.243375	+	0.243375i	0.818245	−	0.574870i	$-0.194947\pi$
$107$	4.78756e19	+	4.78756e19i	0.243375	+	0.243375i	−0.574870	+	0.818245i	$0.694947\pi$
$108$	1.85042e20	−	1.85042e20i	0.857101	−	0.857101i
$109$			2.40232e20i			1.01476i	0.861721	+	0.507382i	$0.169387\pi$
$109$			2.40232e20i			1.01476i	−0.861721	+	0.507382i	$0.830613\pi$
$110$	−4.37004e20	−	2.09175e20i	−1.68484	−	0.806459i
$111$	−5.54760e20			−1.95378
$112$	−6.20645e19	−	6.20645e19i	−0.199831	−	0.199831i
$113$	−1.70164e20	+	1.70164e20i	−0.501282	+	0.501282i	−0.911836	−	0.410554i	$-0.865335\pi$
$113$	−1.70164e20	+	1.70164e20i	−0.501282	+	0.501282i	0.410554	+	0.911836i	$0.365335\pi$
$114$		−	5.86575e20i		−	1.58225i
$115$	1.03260e20	−	2.15729e20i	0.255242	−	0.533248i
$116$	8.01715e20			1.81736
$117$	2.49338e20	+	2.49338e20i	0.518715	+	0.518715i
$118$	−3.33636e20	+	3.33636e20i	−0.637459	+	0.637459i
$119$			1.19761e20i			0.210302i
$120$	−2.94967e20	−	8.36596e20i	−0.476388	−	1.35115i
$121$	1.86994e20			0.277954
$122$	2.85662e20	+	2.85662e20i	0.391070	+	0.391070i
$123$	2.75555e20	−	2.75555e20i	0.347662	−	0.347662i
$124$			7.93263e20i			0.922998i
$125$	−4.89870e20	+	7.92079e20i	−0.525994	+	0.850488i
$126$	−7.33166e20			−0.726938
$127$	7.32576e18	+	7.32576e18i	0.00671144	+	0.00671144i	0.710455	−	0.703743i	$-0.248489\pi$
$127$	7.32576e18	+	7.32576e18i	0.00671144	+	0.00671144i	−0.703743	+	0.710455i	$0.748489\pi$
$128$	1.47739e21	−	1.47739e21i	1.25140	−	1.25140i
$129$		−	1.33295e21i		−	1.04452i
$130$	−3.84353e21	+	1.35515e21i	−2.78802	+	0.983001i
$131$	7.38693e20			0.496308			0.248154	−	0.968721i	$-0.420176\pi$
$131$	7.38693e20			0.496308			0.248154	+	0.968721i	$0.420176\pi$
$132$	2.63748e21	+	2.63748e21i	1.64229	+	1.64229i
$133$	1.05966e21	−	1.05966e21i	0.611859	−	0.611859i
$134$			1.82630e21i			0.978418i
$135$	1.27056e21	+	6.08160e20i	0.631912	+	0.302469i
$136$	5.11881e20			0.236472
$137$	−6.22559e20	−	6.22559e20i	−0.267285	−	0.267285i	0.560720	−	0.828005i	$-0.310524\pi$
$137$	−6.22559e20	−	6.22559e20i	−0.267285	−	0.267285i	−0.828005	+	0.560720i	$0.810524\pi$
$138$	−2.05452e21	+	2.05452e21i	−0.820198	+	0.820198i
$139$		−	1.41346e21i		−	0.524971i	−0.964936	−	0.262486i	$-0.915458\pi$
$139$		−	1.41346e21i		−	0.524971i	0.964936	−	0.262486i	$-0.0845423\pi$
$140$	2.31848e21	−	4.84372e21i	0.801535	−	1.67455i
$141$	−2.61345e21			−0.841438
$142$	−2.79168e21	−	2.79168e21i	−0.837496	−	0.837496i
$143$	5.11383e21	−	5.11383e21i	1.43016	−	1.43016i
$144$			4.14003e20i			0.107989i
$145$	1.43496e21	+	4.06988e21i	0.349268	+	0.990608i
$146$	−5.92174e21			−1.34561
$147$	−5.98673e20	−	5.98673e20i	−0.127062	−	0.127062i
$148$	−1.01499e22	+	1.01499e22i	−2.01300	+	2.01300i
$149$		−	1.55356e21i		−	0.288047i	−0.989574	−	0.144024i	$-0.953996\pi$
$149$		−	1.55356e21i		−	0.288047i	0.989574	−	0.144024i	$-0.0460042\pi$
$150$	8.81219e21	−	7.09613e21i	1.52817	−	1.23058i
$151$	−6.13413e21			−0.995368			−0.497684	−	0.867358i	$-0.665816\pi$
$151$	−6.13413e21			−0.995368			−0.497684	+	0.867358i	$0.665816\pi$
$152$	−4.52921e21	−	4.52921e21i	−0.687997	−	0.687997i
$153$	3.99434e20	−	3.99434e20i	0.0568238	−	0.0568238i
$154$			1.50370e22i			2.00426i
$155$	−4.02698e21	+	1.41983e21i	−0.503109	+	0.177386i
$156$	3.13759e22			3.67579
$157$	6.43373e21	+	6.43373e21i	0.707077	+	0.707077i	0.965919	−	0.258843i	$-0.0833411\pi$
$157$	6.43373e21	+	6.43373e21i	0.707077	+	0.707077i	−0.258843	+	0.965919i	$0.583341\pi$
$158$	1.41895e22	−	1.41895e22i	1.46352	−	1.46352i
$159$			4.18614e21i			0.405362i
$160$	7.64975e21	+	3.66160e21i	0.695741	+	0.333021i
$161$	−7.42306e21			−0.634343
$162$	−1.80642e22	−	1.80642e22i	−1.45101	−	1.45101i
$163$	−1.77300e22	+	1.77300e22i	−1.33916	+	1.33916i	−0.442289	+	0.896873i	$0.645833\pi$
$163$	−1.77300e22	+	1.77300e22i	−1.33916	+	1.33916i	−0.896873	+	0.442289i	$0.854167\pi$
$164$		−	1.00831e22i		−	0.716399i
$165$	−8.66836e21	+	1.81098e22i	−0.579559	+	1.21080i
$166$	1.47685e21			0.0929514
$167$	1.23329e22	+	1.23329e22i	0.730973	+	0.730973i	0.970812	−	0.239840i	$-0.0770949\pi$
$167$	1.23329e22	+	1.23329e22i	0.730973	+	0.730973i	−0.239840	+	0.970812i	$0.577095\pi$
$168$	−1.94681e22	+	1.94681e22i	−1.08701	+	1.08701i
$169$		−	4.18301e22i		−	2.20101i
$170$	2.17092e21	+	6.15726e21i	0.107685	+	0.305420i
$171$	−7.06852e21			−0.330649
$172$	−2.43877e22	−	2.43877e22i	−1.07618	−	1.07618i
$173$	8.11002e21	−	8.11002e21i	0.337723	−	0.337723i	−0.517787	−	0.855510i	$-0.673244\pi$
$173$	8.11002e21	−	8.11002e21i	0.337723	−	0.337723i	0.855510	+	0.517787i	$0.173244\pi$
$174$		−	5.24260e22i		−	2.06089i
$175$	2.87387e22	+	3.10010e21i	1.06681	+	0.115079i
$176$	8.49107e21			0.297739
$177$	1.38261e22	+	1.38261e22i	0.458108	+	0.458108i
$178$	−1.30957e22	+	1.30957e22i	−0.410138	+	0.410138i
$179$			4.46583e21i			0.132243i	0.997812	+	0.0661214i	$0.0210625\pi$
$179$			4.46583e21i			0.132243i	−0.997812	+	0.0661214i	$0.978938\pi$
$180$	−2.38879e22	+	8.42237e21i	−0.669040	+	0.235890i
$181$	−1.86352e22			−0.493798			−0.246899	−	0.969041i	$-0.579412\pi$
$181$	−1.86352e22			−0.493798			−0.246899	+	0.969041i	$0.579412\pi$
$182$	8.94414e22	+	8.94414e22i	2.24298	+	2.24298i
$183$	1.18381e22	−	1.18381e22i	0.281041	−	0.281041i
$184$			3.17277e22i			0.713280i
$185$	−6.96923e22	−	3.33586e22i	−1.48411	−	0.710381i
$186$	5.18733e22			1.04668
$187$	−8.19225e21	−	8.19225e21i	−0.156671	−	0.156671i
$188$	−4.78155e22	+	4.78155e22i	−0.866942	+	0.866942i
$189$		−	4.37190e22i		−	0.751713i
$190$	3.52718e22	−	7.36892e22i	0.575296	−	1.20190i
$191$	−3.56893e21			−0.0552338			−0.0276169	−	0.999619i	$-0.508792\pi$
$191$	−3.56893e21			−0.0552338			−0.0276169	+	0.999619i	$0.508792\pi$
$192$	−8.79085e22	−	8.79085e22i	−1.29128	−	1.29128i
$193$	6.02224e22	−	6.02224e22i	0.839817	−	0.839817i	−0.149018	−	0.988835i	$-0.547611\pi$
$193$	6.02224e22	−	6.02224e22i	0.839817	−	0.839817i	0.988835	+	0.149018i	$0.0476111\pi$
$194$			2.41320e23i			3.19577i
$195$	5.61585e22	+	1.59279e23i	0.706430	+	2.00360i
$196$	−2.19066e22			−0.261827
$197$	−8.42092e22	−	8.42092e22i	−0.956527	−	0.956527i	0.0425664	−	0.999094i	$-0.486447\pi$
$197$	−8.42092e22	−	8.42092e22i	−0.956527	−	0.956527i	−0.999094	+	0.0425664i	$0.986447\pi$
$198$	5.01524e22	−	5.01524e22i	0.541552	−	0.541552i
$199$			3.79978e22i			0.390147i	0.980789	+	0.195073i	$0.0624945\pi$
$199$			3.79978e22i			0.390147i	−0.980789	+	0.195073i	$0.937506\pi$
$200$	1.32504e22	−	1.22835e23i	0.129399	−	1.19956i
$201$	7.56833e22			0.703136
$202$	1.22681e22	+	1.22681e22i	0.108459	+	0.108459i
$203$	9.47087e22	−	9.47087e22i	0.796948	−	0.796948i
$204$		−	5.02636e22i		−	0.402672i
$205$	5.11865e22	−	1.80473e22i	0.390496	−	0.137681i
$206$	−2.76239e23			−2.00731
$207$	2.47579e22	+	2.47579e22i	0.171400	+	0.171400i
$208$	5.05056e22	−	5.05056e22i	0.333201	−	0.333201i
$209$			1.44973e23i			0.911642i
$210$	−3.16742e23	−	1.51610e23i	−1.89895	−	0.908942i
$211$	−7.97216e22			−0.455776			−0.227888	−	0.973687i	$-0.573182\pi$
$211$	−7.97216e22			−0.455776			−0.227888	+	0.973687i	$0.573182\pi$
$212$	7.65895e22	+	7.65895e22i	0.417648	+	0.417648i
$213$	−1.15690e23	+	1.15690e23i	−0.601864	+	0.601864i
$214$		−	1.14558e23i		−	0.568707i
$215$	8.01528e22	−	1.67454e23i	0.379782	−	0.793433i
$216$	−1.86864e23			−0.845254
$217$	9.37104e22	+	9.37104e22i	0.404753	+	0.404753i
$218$	2.87417e23	−	2.87417e23i	1.18562	−	1.18562i
$219$			2.45401e23i			0.967021i
$220$	1.72740e23	+	4.89932e23i	0.650378	+	1.84463i
$221$	−9.74565e22			−0.350662
$222$	6.63723e23	+	6.63723e23i	2.28274	+	2.28274i
$223$	1.61406e23	−	1.61406e23i	0.530727	−	0.530727i	−0.390062	−	0.920789i	$-0.627546\pi$
$223$	1.61406e23	−	1.61406e23i	0.530727	−	0.530727i	0.920789	+	0.390062i	$0.127546\pi$
$224$		−	2.63222e23i		−	0.827642i
$225$	−8.55118e22	−	1.06191e23i	−0.257159	−	0.319347i
$226$	4.07172e23			1.17137
$227$	−2.65588e23	−	2.65588e23i	−0.731053	−	0.731053i	0.239775	−	0.970828i	$-0.422926\pi$
$227$	−2.65588e23	−	2.65588e23i	−0.731053	−	0.731053i	−0.970828	+	0.239775i	$0.922926\pi$
$228$	−4.44741e23	+	4.44741e23i	−1.17154	+	1.17154i
$229$		−	3.77109e23i		−	0.950850i	−0.879756	−	0.475425i	$-0.842294\pi$
$229$		−	3.77109e23i		−	0.950850i	0.879756	−	0.475425i	$-0.157706\pi$
$230$	−3.81642e23	+	1.34559e23i	−0.921251	+	0.324814i
$231$	6.23145e23			1.44035
$232$	−4.04804e23	−	4.04804e23i	−0.896118	−	0.896118i
$233$	−4.66152e23	+	4.66152e23i	−0.988482	+	0.988482i	−0.999934	−	0.0114524i	$-0.996355\pi$
$233$	−4.66152e23	+	4.66152e23i	−0.988482	+	0.988482i	0.0114524	+	0.999934i	$0.496355\pi$
$234$		−	5.96622e23i		−	1.21211i
$235$	−3.28317e23	−	1.57151e23i	−0.639167	−	0.305941i
$236$	5.05924e23			0.943986
$237$	−5.88025e23	−	5.88025e23i	−1.05175	−	1.05175i
$238$	1.43283e23	−	1.43283e23i	0.245712	−	0.245712i
$239$			6.49626e23i			1.06828i	0.845397	+	0.534139i	$0.179364\pi$
$239$			6.49626e23i			1.06828i	−0.845397	+	0.534139i	$0.820636\pi$
$240$	−8.56112e22	+	1.78857e23i	−0.135026	+	0.282094i
$241$	−1.27189e23			−0.192432			−0.0962160	−	0.995360i	$-0.530674\pi$
$241$	−1.27189e23			−0.192432			−0.0962160	+	0.995360i	$0.530674\pi$
$242$	−2.23722e23	−	2.23722e23i	−0.324754	−	0.324754i
$243$	−3.92965e23	+	3.92965e23i	−0.547382	+	0.547382i
$244$		−	4.33178e23i		−	0.579119i
$245$	−3.92097e22	−	1.11208e23i	−0.0503191	−	0.142717i
$246$	−6.59356e23			−0.812399
$247$	8.62312e23	+	8.62312e23i	1.02022	+	1.02022i
$248$	4.00537e23	−	4.00537e23i	0.455120	−	0.455120i
$249$		−	6.12018e22i		−	0.0667992i
$250$	1.53374e24	−	3.61567e23i	1.60825	−	0.379131i
$251$	1.17496e24			1.18382			0.591908	−	0.806006i	$-0.298375\pi$
$251$	1.17496e24			1.18382			0.591908	+	0.806006i	$0.298375\pi$
$252$	5.55886e23	+	5.55886e23i	0.538245	+	0.538245i
$253$	5.07777e23	−	5.07777e23i	0.472572	−	0.472572i
$254$		−	1.75293e22i		−	0.0156829i
$255$	2.55161e23	−	8.99647e22i	0.219489	−	0.0773874i
$256$	−1.67597e24			−1.38633
$257$	−1.48158e24	−	1.48158e24i	−1.17868	−	1.17868i	−0.980082	−	0.198593i	$-0.936363\pi$
$257$	−1.48158e24	−	1.48158e24i	−1.17868	−	1.17868i	−0.198593	−	0.980082i	$-0.563637\pi$
$258$	−1.59477e24	+	1.59477e24i	−1.22039	+	1.22039i
$259$			2.39806e24i			1.76548i
$260$	3.94163e24	+	1.88669e24i	2.79217	+	1.33649i
$261$	−6.31758e23			−0.430671
$262$	−8.83784e23	−	8.83784e23i	−0.579873	−	0.579873i
$263$	−1.72033e24	+	1.72033e24i	−1.08656	+	1.08656i	−0.0906825	+	0.995880i	$0.528905\pi$
$263$	−1.72033e24	+	1.72033e24i	−1.08656	+	1.08656i	−0.995880	+	0.0906825i	$0.971095\pi$
$264$		−	2.66345e24i		−	1.61959i
$265$	−2.51720e23	+	5.25889e23i	−0.147387	+	0.307918i
$266$	−2.53559e24			−1.42976
$267$	5.42698e23	+	5.42698e23i	0.294744	+	0.294744i
$268$	1.38470e24	−	1.38470e24i	0.724448	−	0.724448i
$269$		−	8.77807e23i		−	0.442462i	−0.975221	−	0.221231i	$-0.928993\pi$
$269$		−	8.77807e23i		−	0.442462i	0.975221	−	0.221231i	$-0.0710075\pi$
$270$	−7.92502e23	−	2.24772e24i	−0.384913	−	1.09171i
$271$	2.79394e24			1.30775			0.653875	−	0.756603i	$-0.273142\pi$
$271$	2.79394e24			1.30775			0.653875	+	0.756603i	$0.273142\pi$
$272$	−8.09090e22	−	8.09090e22i	−0.0365013	−	0.0365013i
$273$	3.70652e24	−	3.70652e24i	1.61191	−	1.61191i
$274$			1.48968e24i			0.624578i
$275$	−2.17794e24	+	1.75382e24i	−0.880481	+	0.709019i
$276$	3.11546e24			1.21460
$277$	−2.74788e24	−	2.74788e24i	−1.03324	−	1.03324i	−0.999428	−	0.0338103i	$-0.989236\pi$
$277$	−2.74788e24	−	2.74788e24i	−1.03324	−	1.03324i	−0.0338103	−	0.999428i	$-0.510764\pi$
$278$	−1.69108e24	+	1.69108e24i	−0.613363	+	0.613363i
$279$		−	6.25099e23i		−	0.218729i
$280$	−3.61636e24	+	1.27505e24i	−1.22093	+	0.430475i
$281$	2.10242e24			0.684947			0.342474	−	0.939527i	$-0.388735\pi$
$281$	2.10242e24			0.684947			0.342474	+	0.939527i	$0.388735\pi$
$282$	3.12676e24	+	3.12676e24i	0.983115	+	0.983115i
$283$	1.49812e24	−	1.49812e24i	0.454657	−	0.454657i	−0.442240	−	0.896897i	$-0.645816\pi$
$283$	1.49812e24	−	1.49812e24i	0.454657	−	0.454657i	0.896897	+	0.442240i	$0.145816\pi$
$284$			4.23330e24i			1.24021i
$285$	−3.05374e24	−	1.46169e24i	−0.863740	−	0.413434i
$286$	−1.22365e25			−3.34193
$287$	−1.19114e24	−	1.19114e24i	−0.314156	−	0.314156i
$288$	−8.77918e23	+	8.77918e23i	−0.223629	+	0.223629i
$289$		−	3.90811e24i		−	0.961586i
$290$	3.15246e24	−	6.58607e24i	0.749324	−	1.56548i
$291$	1.00005e25			2.29663
$292$	4.48985e24	+	4.48985e24i	0.996331	+	0.996331i
$293$	−3.88101e24	+	3.88101e24i	−0.832278	+	0.832278i	−0.987828	−	0.155550i	$-0.950285\pi$
$293$	−3.88101e24	+	3.88101e24i	−0.832278	+	0.832278i	0.155550	+	0.987828i	$0.450285\pi$
$294$			1.43252e24i			0.296912i
$295$	9.05533e23	+	2.56831e24i	0.181420	+	0.514550i
$296$	1.02498e25			1.98517
$297$	2.99061e24	+	2.99061e24i	0.560009	+	0.560009i
$298$	−1.85870e24	+	1.85870e24i	−0.336547	+	0.336547i
$299$		−	6.04060e24i		−	1.05771i
$300$	−1.20617e25	−	1.30111e24i	−2.04265	−	0.220344i
$301$	−5.76196e24			−0.943855
$302$	7.33897e24	+	7.33897e24i	1.16296	+	1.16296i
$303$	5.08401e23	−	5.08401e23i	0.0779435	−	0.0779435i
$304$			1.43179e24i			0.212395i
$305$	2.19901e24	−	7.75327e23i	0.315667	−	0.111298i
$306$	−9.55777e23			−0.132783
$307$	6.32096e24	+	6.32096e24i	0.849962	+	0.849962i	0.990128	−	0.140166i	$-0.0447637\pi$
$307$	6.32096e24	+	6.32096e24i	0.849962	+	0.849962i	−0.140166	+	0.990128i	$0.544764\pi$
$308$	1.14010e25	−	1.14010e25i	1.48401	−	1.48401i
$309$			1.14476e25i			1.44254i
$310$	6.51664e24	+	3.11923e24i	0.795073	+	0.380566i
$311$	−1.64752e25			−1.94638			−0.973189	−	0.230006i	$-0.926126\pi$
$311$	−1.64752e25			−1.94638			−0.973189	+	0.230006i	$0.926126\pi$
$312$	−1.58424e25	−	1.58424e25i	−1.81249	−	1.81249i
$313$	6.68081e24	−	6.68081e24i	0.740262	−	0.740262i	−0.232366	−	0.972628i	$-0.574647\pi$
$313$	6.68081e24	−	6.68081e24i	0.740262	−	0.740262i	0.972628	+	0.232366i	$0.0746467\pi$
$314$		−	1.53948e25i		−	1.65226i
$315$	−1.82698e24	+	3.81690e24i	−0.189945	+	0.396830i
$316$	−2.15170e25			−2.16726
$317$	−1.17083e25	−	1.17083e25i	−1.14262	−	1.14262i	−0.987969	−	0.154649i	$-0.950575\pi$
$317$	−1.17083e25	−	1.17083e25i	−1.14262	−	1.14262i	−0.154649	−	0.987969i	$-0.549425\pi$
$318$	5.00836e24	−	5.00836e24i	0.473614	−	0.473614i
$319$			1.29572e25i			1.18742i
$320$	−5.75752e24	−	1.63297e25i	−0.511370	−	1.45037i
$321$	−4.74738e24			−0.408699
$322$	8.88106e24	+	8.88106e24i	0.741150	+	0.741150i
$323$	1.38141e24	−	1.38141e24i	0.111763	−	0.111763i
$324$			2.73926e25i			2.14873i
$325$	−2.52274e24	+	2.33865e25i	−0.191884	+	1.77882i
$326$	4.24249e25			3.12928
$327$	−1.19108e25	−	1.19108e25i	−0.852044	−	0.852044i
$328$	−5.09118e24	+	5.09118e24i	−0.353249	+	0.353249i
$329$			1.12971e25i			0.760344i
$330$	3.20378e25	−	1.12959e25i	2.09181	−	0.737531i
$331$	2.04862e24			0.129772			0.0648862	−	0.997893i	$-0.479332\pi$
$331$	2.04862e24			0.129772			0.0648862	+	0.997893i	$0.479332\pi$
$332$	−1.11975e24	−	1.11975e24i	−0.0688238	−	0.0688238i
$333$	7.99818e24	−	7.99818e24i	0.477034	−	0.477034i
$334$		−	2.95106e25i		−	1.70810i
$335$	9.50780e24	+	4.55097e24i	0.534111	+	0.255656i
$336$	6.15436e24			0.335575
$337$	5.27760e24	+	5.27760e24i	0.279343	+	0.279343i	0.832847	−	0.553504i	$-0.186710\pi$
$337$	5.27760e24	+	5.27760e24i	0.279343	+	0.279343i	−0.553504	+	0.832847i	$0.686710\pi$
$338$	−5.00461e25	+	5.00461e25i	−2.57160	+	2.57160i
$339$		−	1.68735e25i		−	0.841801i
$340$	3.02243e24	−	6.31441e24i	0.146409	−	0.305875i
$341$	−1.28206e25			−0.603064
$342$	8.45688e24	+	8.45688e24i	0.386322	+	0.386322i
$343$	1.45133e25	−	1.45133e25i	0.643909	−	0.643909i
$344$			2.46278e25i			1.06131i
$345$	5.57624e24	+	1.58156e25i	0.233427	+	0.662054i
$346$	−1.94059e25			−0.789174
$347$	−1.49336e25	−	1.49336e25i	−0.590023	−	0.590023i	0.347614	−	0.937638i	$-0.386992\pi$
$347$	−1.49336e25	−	1.49336e25i	−0.590023	−	0.590023i	−0.937638	+	0.347614i	$0.886992\pi$
$348$	−3.97493e25	+	3.97493e25i	−1.52594	+	1.52594i
$349$		−	5.09445e25i		−	1.90039i	−0.311652	−	0.950196i	$-0.600882\pi$
$349$		−	5.09445e25i		−	1.90039i	0.311652	−	0.950196i	$-0.399118\pi$
$350$	−3.06745e25	−	3.80925e25i	−1.11198	−	1.38089i
$351$	3.55768e25			1.25342
$352$	1.80058e25	+	1.80058e25i	0.616575	+	0.616575i
$353$	2.24167e25	−	2.24167e25i	0.746146	−	0.746146i	−0.227607	−	0.973753i	$-0.573090\pi$
$353$	2.24167e25	−	2.24167e25i	0.746146	−	0.746146i	0.973753	+	0.227607i	$0.0730901\pi$
$354$		−	3.30835e25i		−	1.07048i
$355$	−2.14902e25	+	7.57702e24i	−0.676017	+	0.238350i
$356$	1.98584e25			0.607356
$357$	−5.93777e24	−	5.93777e24i	−0.176580	−	0.176580i
$358$	5.34299e24	−	5.34299e24i	0.154509	−	0.154509i
$359$			6.64973e25i			1.87008i	0.354547	+	0.935038i	$0.384635\pi$
$359$			6.64973e25i			1.87008i	−0.354547	+	0.935038i	$0.615365\pi$
$360$	1.63142e25	+	7.80888e24i	0.446211	+	0.213582i
$361$	1.31441e25			0.349671
$362$	2.22955e25	+	2.22955e25i	0.576941	+	0.576941i
$363$	−9.27122e24	+	9.27122e24i	−0.233384	+	0.233384i
$364$		−	1.35629e26i		−	3.32153i
$365$	−1.47564e25	+	3.08288e25i	−0.351602	+	0.734562i
$366$	−2.83265e25			−0.656723
$367$	−5.04090e25	−	5.04090e25i	−1.13723	−	1.13723i	−0.988945	−	0.148283i	$-0.952625\pi$
$367$	−5.04090e25	−	5.04090e25i	−1.13723	−	1.13723i	−0.148283	−	0.988945i	$-0.547375\pi$
$368$	5.01495e24	−	5.01495e24i	0.110100	−	0.110100i
$369$			7.94557e24i			0.169770i
$370$	4.34701e25	+	1.23292e26i	0.904011	+	2.56399i
$371$	1.80955e25			0.366294
$372$	−3.93303e25	−	3.93303e25i	−0.774993	−	0.774993i
$373$	2.16900e24	−	2.16900e24i	0.0416075	−	0.0416075i	−0.685997	−	0.727604i	$-0.740634\pi$
$373$	2.16900e24	−	2.16900e24i	0.0416075	−	0.0416075i	0.727604	+	0.685997i	$0.240634\pi$
$374$			1.96027e25i			0.366100i
$375$	−1.49836e25	−	6.35595e25i	−0.272461	−	1.15576i
$376$	4.82863e25			0.854959
$377$	7.70703e25	+	7.70703e25i	1.32884	+	1.32884i
$378$	−5.23060e25	+	5.23060e25i	−0.878281	+	0.878281i
$379$		−	1.46080e25i		−	0.238890i	−0.992841	−	0.119445i	$-0.961888\pi$
$379$		−	1.46080e25i		−	0.238890i	0.992841	−	0.119445i	$-0.0381115\pi$
$380$	−8.26140e25	+	2.91280e25i	−1.31588	+	0.463954i
$381$	−7.26428e23			−0.0112705
$382$	4.26992e24	+	4.26992e24i	0.0645337	+	0.0645337i
$383$	−2.01225e24	+	2.01225e24i	−0.0296275	+	0.0296275i	−0.721765	−	0.692138i	$-0.756669\pi$
$383$	−2.01225e24	+	2.01225e24i	−0.0296275	+	0.0296275i	0.692138	+	0.721765i	$0.256669\pi$
$384$			1.46499e26i			2.10147i
$385$	7.82832e25	+	3.74708e25i	1.09411	+	0.523703i
$386$	−1.44102e26			−1.96244
$387$	1.92177e25	+	1.92177e25i	0.255030	+	0.255030i
$388$	1.82968e26	−	1.82968e26i	2.36624	−	2.36624i
$389$		−	3.34967e25i		−	0.422189i	−0.977466	−	0.211094i	$-0.932297\pi$
$389$		−	3.34967e25i		−	0.422189i	0.977466	−	0.211094i	$-0.0677027\pi$
$390$	1.23375e26	−	2.57752e26i	1.51558	−	3.16633i
$391$	−9.67692e24			−0.115870
$392$	1.10611e25	+	1.10611e25i	0.129104	+	0.129104i
$393$	−3.66247e25	+	3.66247e25i	−0.416724	+	0.416724i
$394$			2.01498e26i			2.23516i
$395$	−3.85124e25	−	1.09230e26i	−0.416514	−	1.18133i
$396$	−7.60510e25			−0.801961
$397$	1.23637e24	+	1.23637e24i	0.0127129	+	0.0127129i	0.713435	−	0.700722i	$-0.247139\pi$
$397$	1.23637e24	+	1.23637e24i	0.0127129	+	0.0127129i	−0.700722	+	0.713435i	$0.747139\pi$
$398$	4.54611e25	−	4.54611e25i	0.455837	−	0.455837i
$399$			1.05077e26i			1.02749i
$400$	−2.15100e25	+	1.73212e25i	−0.205135	+	0.165188i
$401$	1.17346e26			1.09150			0.545751	−	0.837947i	$-0.316244\pi$
$401$	1.17346e26			1.09150			0.545751	+	0.837947i	$0.316244\pi$
$402$	−9.05486e25	−	9.05486e25i	−0.821526	−	0.821526i
$403$	−7.62579e25	+	7.62579e25i	−0.674892	+	0.674892i
$404$		−	1.86033e25i		−	0.160612i
$405$	−1.39057e26	+	4.90288e25i	−1.17124	+	0.412954i
$406$	−2.26622e26			−1.86226
$407$	−1.64040e26	−	1.64040e26i	−1.31524	−	1.31524i
$408$	−2.53792e25	+	2.53792e25i	−0.198553	+	0.198553i
$409$		−	1.21391e26i		−	0.926729i	−0.886168	−	0.463365i	$-0.846642\pi$
$409$		−	1.21391e26i		−	0.926729i	0.886168	−	0.463365i	$-0.153358\pi$
$410$	−8.28324e25	−	3.96482e25i	−0.617108	−	0.295383i
$411$	6.17334e25			0.448851
$412$	2.09444e26	+	2.09444e26i	1.48627	+	1.48627i
$413$	5.97662e25	−	5.97662e25i	0.413957	−	0.413957i
$414$		−	5.92415e25i		−	0.400518i
$415$	3.68017e24	−	7.68855e24i	0.0242877	−	0.0507415i
$416$	2.14200e26			1.38002
$417$	7.00799e25	+	7.00799e25i	0.440791	+	0.440791i
$418$	1.73448e26	−	1.73448e26i	1.06514	−	1.06514i
$419$		−	4.61542e25i		−	0.276739i	−0.990381	−	0.138370i	$-0.955814\pi$
$419$		−	4.61542e25i		−	0.276739i	0.990381	−	0.138370i	$-0.0441862\pi$
$420$	1.25202e26	+	3.55104e26i	0.733027	+	2.07904i
$421$	−1.54078e26			−0.880885			−0.440443	−	0.897781i	$-0.645178\pi$
$421$	−1.54078e26			−0.880885			−0.440443	+	0.897781i	$0.645178\pi$
$422$	9.53801e25	+	9.53801e25i	0.532517	+	0.532517i
$423$	3.76790e25	−	3.76790e25i	0.205445	−	0.205445i
$424$		−	7.73436e25i		−	0.411875i
$425$	3.74647e25	+	4.04138e24i	0.194864	+	0.0210203i
$426$	2.76825e26			1.40640
$427$	−5.11725e25	−	5.11725e25i	−0.253956	−	0.253956i
$428$	−8.68579e25	+	8.68579e25i	−0.421087	+	0.421087i
$429$			5.07091e26i			2.40167i
$430$	−2.96240e26	+	1.04448e26i	−1.37075	+	0.483299i
$431$	2.18994e26			0.990056			0.495028	−	0.868877i	$-0.335158\pi$
$431$	2.18994e26			0.990056			0.495028	+	0.868877i	$0.335158\pi$
$432$	2.95361e25	+	2.95361e25i	0.130471	+	0.130471i
$433$	−1.63256e26	+	1.63256e26i	−0.704679	+	0.704679i	−0.965411	−	0.260732i	$-0.916036\pi$
$433$	−1.63256e26	+	1.63256e26i	−0.704679	+	0.704679i	0.260732	+	0.965411i	$0.416036\pi$
$434$		−	2.24233e26i		−	0.945806i
$435$	−2.72932e26	−	1.30640e26i	−1.12502	−	0.538499i
$436$	−4.35838e26			−1.75574
$437$	8.56231e25	+	8.56231e25i	0.337114	+	0.337114i
$438$	2.93602e26	−	2.93602e26i	1.12984	−	1.12984i
$439$		−	3.89138e26i		−	1.46372i	−0.681454	−	0.731861i	$-0.738652\pi$
$439$		−	3.89138e26i		−	1.46372i	0.681454	−	0.731861i	$-0.261348\pi$
$440$	1.60158e26	−	3.34598e26i	0.588872	−	1.23026i
$441$	1.72626e25			0.0620469
$442$	1.16598e26	+	1.16598e26i	0.409704	+	0.409704i
$443$	−3.45555e26	+	3.45555e26i	−1.18708	+	1.18708i	−0.209207	+	0.977871i	$0.567088\pi$
$443$	−3.45555e26	+	3.45555e26i	−1.18708	+	1.18708i	−0.977871	+	0.209207i	$0.932912\pi$
$444$		−	1.00647e27i		−	3.38041i
$445$	3.55437e25	+	1.00810e26i	0.116725	+	0.331059i
$446$	−3.86217e26			−1.24018
$447$	7.70258e25	+	7.70258e25i	0.241858	+	0.241858i
$448$	−3.80002e26	+	3.80002e26i	−1.16683	+	1.16683i
$449$			1.98774e26i			0.596891i	0.954427	+	0.298446i	$0.0964682\pi$
$449$			1.98774e26i			0.596891i	−0.954427	+	0.298446i	$0.903532\pi$
$450$	−2.47410e25	+	2.29356e26i	−0.0726595	+	0.673574i
$451$	1.62961e26			0.468078
$452$	−3.08718e26	−	3.08718e26i	−0.867315	−	0.867315i
$453$	3.04132e26	−	3.04132e26i	0.835758	−	0.835758i
$454$			6.35506e26i			1.70829i
$455$	6.88515e26	−	2.42756e26i	1.81050	−	0.638347i
$456$	4.49120e26			1.15535
$457$	6.98484e24	+	6.98484e24i	0.0175790	+	0.0175790i	0.715842	−	0.698263i	$-0.246043\pi$
$457$	6.98484e24	+	6.98484e24i	0.0175790	+	0.0175790i	−0.698263	+	0.715842i	$0.746043\pi$
$458$	−4.51179e26	+	4.51179e26i	−1.11095	+	1.11095i
$459$		−	5.69933e25i		−	0.137308i
$460$	3.91383e26	+	1.87338e26i	0.922622	+	0.441619i
$461$	1.70849e26			0.394097			0.197048	−	0.980394i	$-0.436864\pi$
$461$	1.70849e26			0.394097			0.197048	+	0.980394i	$0.436864\pi$
$462$	−7.45540e26	−	7.45540e26i	−1.68287	−	1.68287i
$463$	−4.68474e25	+	4.68474e25i	−0.103484	+	0.103484i	−0.756953	−	0.653469i	$-0.773313\pi$
$463$	−4.68474e25	+	4.68474e25i	−0.103484	+	0.103484i	0.653469	+	0.756953i	$0.273313\pi$
$464$			1.27969e26i			0.276645i
$465$	1.29263e26	−	2.70055e26i	0.273493	−	0.571376i
$466$	1.11542e27			2.30983
$467$	−7.48416e25	−	7.48416e25i	−0.151696	−	0.151696i	0.627179	−	0.778875i	$-0.284209\pi$
$467$	−7.48416e25	−	7.48416e25i	−0.151696	−	0.151696i	−0.778875	+	0.627179i	$0.784209\pi$
$468$	−4.52358e26	+	4.52358e26i	−0.897478	+	0.897478i
$469$		−	3.27156e26i		−	0.635371i
$470$	2.04786e26	+	5.80821e26i	0.389333	+	1.10424i
$471$	−6.37974e26			−1.18739
$472$	−2.55453e26	−	2.55453e26i	−0.465469	−	0.465469i
$473$	3.94149e26	−	3.94149e26i	0.703151	−	0.703151i
$474$			1.40704e27i			2.45767i
$475$	−2.95735e26	−	3.67253e26i	−0.505786	−	0.628100i
$476$	−2.17274e26			−0.363864
$477$	−6.03532e25	−	6.03532e25i	−0.0989730	−	0.0989730i
$478$	7.77222e26	−	7.77222e26i	1.24815	−	1.24815i
$479$			8.69333e26i			1.36720i	0.729858	+	0.683599i	$0.239586\pi$
$479$			8.69333e26i			1.36720i	−0.729858	+	0.683599i	$0.760414\pi$
$480$	−5.60821e26	+	1.97734e26i	−0.863797	+	0.304557i
$481$	−1.95145e27			−2.94379
$482$	1.52170e26	+	1.52170e26i	0.224833	+	0.224833i
$483$	3.68038e26	−	3.68038e26i	0.532625	−	0.532625i
$484$			3.39252e26i			0.480915i
$485$	1.25632e27	+	6.01346e26i	1.74455	+	0.835040i
$486$	9.40297e26			1.27909
$487$	2.80032e26	+	2.80032e26i	0.373180	+	0.373180i	0.868634	−	0.495454i	$-0.164998\pi$
$487$	2.80032e26	+	2.80032e26i	0.373180	+	0.373180i	−0.495454	+	0.868634i	$0.664998\pi$
$488$	−2.18721e26	+	2.18721e26i	−0.285557	+	0.285557i
$489$		−	1.75812e27i		−	2.24885i
$490$	−8.61400e25	+	1.79962e26i	−0.107955	+	0.225538i
$491$	7.67970e26			0.943038			0.471519	−	0.881856i	$-0.343706\pi$
$491$	7.67970e26			0.943038			0.471519	+	0.881856i	$0.343706\pi$
$492$	4.99923e26	+	4.99923e26i	0.601523	+	0.601523i
$493$	1.23465e26	−	1.23465e26i	0.145571	−	0.145571i
$494$		−	2.06337e27i		−	2.38400i
$495$	−1.36121e26	−	3.86071e26i	−0.154125	−	0.437134i
$496$	−1.26620e26			−0.140502
$497$	5.00092e26	+	5.00092e26i	0.543858	+	0.543858i
$498$	−7.32228e25	+	7.32228e25i	−0.0780464	+	0.0780464i
$499$			3.66801e26i			0.383200i	0.981473	+	0.191600i	$0.0613675\pi$
$499$			3.66801e26i			0.383200i	−0.981473	+	0.191600i	$0.938632\pi$
$500$	−1.43702e27	−	8.88742e26i	−1.47151	−	0.910071i
$501$	−1.22294e27			−1.22752
$502$	−1.40573e27	−	1.40573e27i	−1.38314	−	1.38314i
$503$	−1.42014e27	+	1.42014e27i	−1.36978	+	1.36978i	−0.509030	+	0.860749i	$0.669996\pi$
$503$	−1.42014e27	+	1.42014e27i	−1.36978	+	1.36978i	−0.860749	+	0.509030i	$0.830004\pi$
$504$		−	5.61359e26i		−	0.530805i
$505$	9.44393e25	−	3.32974e25i	0.0875466	−	0.0308671i
$506$	−1.21502e27			−1.10428
$507$	2.07395e27	+	2.07395e27i	1.84807	+	1.84807i
$508$	−1.32907e25	+	1.32907e25i	−0.0116121	+	0.0116121i
$509$		−	1.80843e27i		−	1.54926i	−0.632413	−	0.774631i	$-0.717936\pi$
$509$		−	1.80843e27i		−	1.54926i	0.632413	−	0.774631i	$-0.282064\pi$
$510$	−4.12914e26	−	1.97644e26i	−0.346863	−	0.166028i
$511$	1.06080e27			0.873823
$512$	4.55992e26	+	4.55992e26i	0.368348	+	0.368348i
$513$	−5.04287e26	+	5.04287e26i	−0.399488	+	0.399488i
$514$			3.54517e27i			2.75427i
$515$	−6.88362e26	+	1.43811e27i	−0.524499	+	1.09577i
$516$	2.41830e27			1.80723
$517$	−7.72785e26	−	7.72785e26i	−0.566439	−	0.566439i
$518$	2.86908e27	−	2.86908e27i	2.06274	−	2.06274i
$519$			8.04195e26i			0.567137i
$520$	−1.03759e27	−	2.94285e27i	−0.717781	−	2.03580i
$521$	−2.04840e27			−1.39007			−0.695036	−	0.718975i	$-0.744612\pi$
$521$	−2.04840e27			−1.39007			−0.695036	+	0.718975i	$0.744612\pi$
$522$	7.55845e26	+	7.55845e26i	0.503185	+	0.503185i
$523$	4.12173e26	−	4.12173e26i	0.269192	−	0.269192i	−0.559582	−	0.828775i	$-0.689038\pi$
$523$	4.12173e26	−	4.12173e26i	0.269192	−	0.269192i	0.828775	+	0.559582i	$0.189038\pi$
$524$			1.34017e27i			0.858709i
$525$	−1.57858e27	+	1.27117e27i	−0.992370	+	0.799119i
$526$	4.11646e27			2.53902
$527$	1.22164e26	+	1.22164e26i	0.0739325	+	0.0739325i
$528$	−4.20990e26	+	4.20990e26i	−0.249996	+	0.249996i
$529$			1.11636e27i			0.650498i
$530$	9.30342e26	−	3.28020e26i	0.531966	−	0.187560i
$531$	−3.98673e26			−0.223703
$532$	1.92248e27	+	1.92248e27i	1.05863	+	1.05863i
$533$	9.69306e26	−	9.69306e26i	0.523828	−	0.523828i
$534$		−	1.29858e27i		−	0.688743i
$535$	−5.96395e26	−	2.85468e26i	−0.310453	−	0.148600i
$536$	−1.39833e27			−0.714435
$537$	−2.21417e26	−	2.21417e26i	−0.111037	−	0.111037i
$538$	−1.05022e27	+	1.05022e27i	−0.516961	+	0.516961i
$539$		−	3.54050e26i		−	0.171071i
$540$	−1.10335e27	+	2.30510e27i	−0.523329	+	1.09333i
$541$	3.15171e27			1.46748			0.733741	−	0.679429i	$-0.237772\pi$
$541$	3.15171e27			1.46748			0.733741	+	0.679429i	$0.237772\pi$
$542$	−3.34271e27	−	3.34271e27i	−1.52794	−	1.52794i
$543$	9.23942e26	−	9.23942e26i	0.414616	−	0.414616i
$544$		−	3.43144e26i		−	0.151178i
$545$	−7.80089e26	−	2.21252e27i	−0.337426	−	0.957022i
$546$	−8.86907e27			−3.76662
$547$	−2.53967e27	−	2.53967e27i	−1.05902	−	1.05902i	−0.998145	−	0.0608740i	$-0.980611\pi$
$547$	−2.53967e27	−	2.53967e27i	−1.05902	−	1.05902i	−0.0608740	−	0.998145i	$-0.519389\pi$
$548$	1.12947e27	−	1.12947e27i	0.462455	−	0.462455i
$549$			3.41348e26i			0.137238i
$550$	4.70402e27	+	5.07430e26i	1.85713	+	0.200332i
$551$	−2.18488e27			−0.847055
$552$	−1.57307e27	−	1.57307e27i	−0.598904	−	0.598904i
$553$	−2.54186e27	+	2.54186e27i	−0.950386	+	0.950386i
$554$			6.57522e27i			2.41442i
$555$	5.10930e27	−	1.80144e27i	1.84260	−	0.649664i
$556$	2.56436e27			0.908302
$557$	2.68665e27	+	2.68665e27i	0.934672	+	0.934672i	0.997993	−	0.0633210i	$-0.0201692\pi$
$557$	2.68665e27	+	2.68665e27i	0.934672	+	0.934672i	−0.0633210	+	0.997993i	$0.520169\pi$
$558$	−7.47877e26	+	7.47877e26i	−0.255557	+	0.255557i
$559$		−	4.68886e27i		−	1.57380i
$560$	7.73148e26	+	3.70072e26i	0.254907	+	0.122013i
$561$	8.12350e26			0.263096
$562$	−2.51537e27	−	2.51537e27i	−0.800274	−	0.800274i
$563$	9.50027e26	−	9.50027e26i	0.296929	−	0.296929i	−0.542881	−	0.839810i	$-0.682667\pi$
$563$	9.50027e26	−	9.50027e26i	0.296929	−	0.296929i	0.839810	+	0.542881i	$0.182667\pi$
$564$		−	4.74142e27i		−	1.45585i
$565$	1.01463e27	−	2.11976e27i	0.306073	−	0.639443i
$566$	−3.58476e27			−1.06242
$567$	3.23596e27	+	3.23596e27i	0.942263	+	0.942263i
$568$	2.13749e27	−	2.13749e27i	0.611535	−	0.611535i
$569$		−	1.36717e27i		−	0.384325i	−0.981363	−	0.192163i	$-0.938450\pi$
$569$		−	1.36717e27i		−	0.384325i	0.981363	−	0.192163i	$-0.0615501\pi$
$570$	1.90475e27	+	5.40232e27i	0.526125	+	1.49222i
$571$	−6.73150e26			−0.182705			−0.0913526	−	0.995819i	$-0.529119\pi$
$571$	−6.73150e26			−0.182705			−0.0913526	+	0.995819i	$0.529119\pi$
$572$	9.27772e27	+	9.27772e27i	2.47446	+	2.47446i
$573$	1.76949e26	−	1.76949e26i	0.0463769	−	0.0463769i
$574$			2.85020e27i			0.734102i
$575$	−2.50495e26	+	2.32215e27i	−0.0634045	+	0.587777i
$576$	2.53482e27			0.630554
$577$	−1.87699e27	−	1.87699e27i	−0.458884	−	0.458884i	0.439405	−	0.898289i	$-0.355189\pi$
$577$	−1.87699e27	−	1.87699e27i	−0.458884	−	0.458884i	−0.898289	+	0.439405i	$0.855189\pi$
$578$	−4.67572e27	+	4.67572e27i	−1.12349	+	1.12349i
$579$			5.97169e27i			1.41030i
$580$	−7.38374e27	+	2.60336e27i	−1.71394	+	0.604301i
$581$	−2.64557e26			−0.0603613
$582$	−1.19647e28	−	1.19647e28i	−2.68332	−	2.68332i
$583$	−1.23782e27	+	1.23782e27i	−0.272881	+	0.272881i
$584$		−	4.53406e27i		−	0.982560i
$585$	−3.10604e27	−	1.48673e27i	−0.661681	−	0.316718i
$586$	9.28659e27			1.94482
$587$	4.82140e26	+	4.82140e26i	0.0992641	+	0.0992641i	0.754995	−	0.655731i	$-0.227639\pi$
$587$	4.82140e26	+	4.82140e26i	0.0992641	+	0.0992641i	−0.655731	+	0.754995i	$0.727639\pi$
$588$	1.08614e27	−	1.08614e27i	0.219842	−	0.219842i
$589$		−	2.16185e27i		−	0.430202i
$590$	1.98937e27	−	4.15616e27i	0.389220	−	0.813152i
$591$	8.35024e27			1.60629
$592$	−1.62011e27	−	1.62011e27i	−0.306427	−	0.306427i
$593$	−3.11622e27	+	3.11622e27i	−0.579537	+	0.579537i	−0.934776	−	0.355239i	$-0.884400\pi$
$593$	−3.11622e27	+	3.11622e27i	−0.579537	+	0.579537i	0.355239	+	0.934776i	$0.384400\pi$
$594$		−	7.15601e27i		−	1.30860i
$595$	−3.88891e26	−	1.10299e27i	−0.0699291	−	0.198336i
$596$	2.81852e27			0.498378
$597$	−1.88394e27	−	1.88394e27i	−0.327586	−	0.327586i
$598$	−7.22706e27	+	7.22706e27i	−1.23581	+	1.23581i
$599$		−	9.36431e26i		−	0.157474i	−0.996895	−	0.0787368i	$-0.974911\pi$
$599$		−	9.36431e26i		−	0.157474i	0.996895	−	0.0787368i	$-0.0250887\pi$
$600$	5.43325e27	+	6.74717e27i	0.898560	+	1.11586i
$601$	5.90837e27			0.960999			0.480500	−	0.876995i	$-0.340455\pi$
$601$	5.90837e27			0.960999			0.480500	+	0.876995i	$0.340455\pi$
$602$	6.89370e27	+	6.89370e27i	1.10278	+	1.10278i
$603$	−1.09116e27	+	1.09116e27i	−0.171677	+	0.171677i
$604$		−	1.11288e28i		−	1.72218i
$605$	−1.72220e27	+	6.07213e26i	−0.262138	+	0.0924245i
$606$	−1.21652e27			−0.182134
$607$	−3.67524e27	−	3.67524e27i	−0.541252	−	0.541252i	0.382644	−	0.923896i	$-0.375014\pi$
$607$	−3.67524e27	−	3.67524e27i	−0.541252	−	0.541252i	−0.923896	+	0.382644i	$0.875014\pi$
$608$	−3.03620e27	+	3.03620e27i	−0.439840	+	0.439840i
$609$			9.39139e27i			1.33831i
$610$	−3.55855e27	−	1.70332e27i	−0.498855	−	0.238780i
$611$	−9.19318e27			−1.26781
$612$	7.24669e26	+	7.24669e26i	0.0983163	+	0.0983163i
$613$	3.37619e27	−	3.37619e27i	0.450633	−	0.450633i	−0.444932	−	0.895564i	$-0.646772\pi$
$613$	3.37619e27	−	3.37619e27i	0.450633	−	0.450633i	0.895564	+	0.444932i	$0.146772\pi$
$614$		−	1.51250e28i		−	1.98615i
$615$	−1.64305e27	+	3.43264e27i	−0.212276	+	0.443483i
$616$	−1.15133e28			−1.46350
$617$	−3.94445e27	−	3.94445e27i	−0.493327	−	0.493327i	0.416026	−	0.909353i	$-0.363423\pi$
$617$	−3.94445e27	−	3.94445e27i	−0.493327	−	0.493327i	−0.909353	+	0.416026i	$0.863423\pi$
$618$	1.36960e28	−	1.36960e28i	1.68543	−	1.68543i
$619$			1.09070e28i			1.32068i	0.750968	+	0.660339i	$0.229587\pi$
$619$			1.09070e28i			1.32068i	−0.750968	+	0.660339i	$0.770413\pi$
$620$	−2.57591e27	−	7.30590e27i	−0.306912	−	0.870477i
$621$	3.53259e27			0.414169
$622$	1.97112e28	+	1.97112e28i	2.27410	+	2.27410i
$623$	2.34592e27	−	2.34592e27i	0.266338	−	0.266338i
$624$			5.00818e27i			0.559543i
$625$	1.93960e27	−	8.88572e27i	0.213262	−	0.976995i
$626$	−1.59860e28			−1.72981
$627$	−7.18781e27	−	7.18781e27i	−0.765458	−	0.765458i
$628$	−1.16723e28	+	1.16723e28i	−1.22338	+	1.22338i
$629$			3.12618e27i			0.322484i
$630$	6.75241e27	−	2.38076e27i	0.685573	−	0.241719i
$631$	−7.10178e26			−0.0709698			−0.0354849	−	0.999370i	$-0.511298\pi$
$631$	−7.10178e26			−0.0709698			−0.0354849	+	0.999370i	$0.511298\pi$
$632$	1.08644e28	+	1.08644e28i	1.06865	+	1.06865i
$633$	3.95262e27	−	3.95262e27i	0.382691	−	0.382691i
$634$			2.80160e28i			2.67001i
$635$	−9.12583e25	−	4.36813e25i	−0.00856121	−	0.00409787i
$636$	−7.59467e27			−0.701355
$637$	−2.10592e27	−	2.10592e27i	−0.191447	−	0.191447i
$638$	1.55021e28	−	1.55021e28i	1.38735	−	1.38735i
$639$		−	3.33588e27i		−	0.293902i
$640$	−8.80924e27	+	1.84041e28i	−0.764080	+	1.59630i
$641$	2.21422e28			1.89078			0.945388	−	0.325947i	$-0.105683\pi$
$641$	2.21422e28			1.89078			0.945388	+	0.325947i	$0.105683\pi$
$642$	5.67983e27	+	5.67983e27i	0.477513	+	0.477513i
$643$	5.26267e26	−	5.26267e26i	0.0435609	−	0.0435609i	−0.684991	−	0.728552i	$-0.740194\pi$
$643$	5.26267e26	−	5.26267e26i	0.0435609	−	0.0435609i	0.728552	+	0.684991i	$0.240194\pi$
$644$		−	1.34672e28i		−	1.09754i
$645$	4.32841e27	+	1.22764e28i	0.347321	+	0.985087i
$646$	−3.30547e27			−0.261161
$647$	−7.91724e27	−	7.91724e27i	−0.615929	−	0.615929i	0.328555	−	0.944485i	$-0.393438\pi$
$647$	−7.91724e27	−	7.91724e27i	−0.615929	−	0.615929i	−0.944485	+	0.328555i	$0.893438\pi$
$648$	1.38311e28	−	1.38311e28i	1.05952	−	1.05952i
$649$			8.17665e27i			0.616777i
$650$	3.09982e28	−	2.49617e28i	2.30251	−	1.85413i
$651$	−9.29239e27			−0.679700
$652$	−3.21665e28	−	3.21665e28i	−2.31701	−	2.31701i
$653$	−1.03979e28	+	1.03979e28i	−0.737585	+	0.737585i	−0.972110	−	0.234525i	$-0.924646\pi$
$653$	−1.03979e28	+	1.03979e28i	−0.737585	+	0.737585i	0.234525	+	0.972110i	$0.424646\pi$
$654$			2.85004e28i			1.99101i
$655$	−6.80332e27	+	2.39871e27i	−0.468067	+	0.165031i
$656$	1.60945e27			0.109053
$657$	−3.53805e27	−	3.53805e27i	−0.236107	−	0.236107i
$658$	1.35161e28	−	1.35161e28i	0.888365	−	0.888365i
$659$		−	7.93283e27i		−	0.513539i	−0.966473	−	0.256770i	$-0.917342\pi$
$659$		−	7.93283e27i		−	0.513539i	0.966473	−	0.256770i	$-0.0826582\pi$
$660$	−3.28555e28	−	1.57265e28i	−2.09493	−	1.00275i
$661$	−2.04441e28			−1.28397			−0.641984	−	0.766718i	$-0.721889\pi$
$661$	−2.04441e28			−1.28397			−0.641984	+	0.766718i	$0.721889\pi$
$662$	−2.45100e27	−	2.45100e27i	−0.151623	−	0.151623i
$663$	4.83193e27	−	4.83193e27i	0.294432	−	0.294432i
$664$			1.13077e27i			0.0678725i
$665$	−6.31845e27	+	1.32004e28i	−0.373589	+	0.780496i
$666$	−1.91383e28			−1.11471
$667$	7.65268e27	+	7.65268e27i	0.439092	+	0.439092i
$668$	−2.23749e28	+	2.23749e28i	−1.26472	+	1.26472i
$669$			1.60051e28i			0.891248i
$670$	−5.93043e27	−	1.68201e28i	−0.325340	−	0.922743i
$671$	7.00093e27			0.378382
$672$	1.30507e28	+	1.30507e28i	0.694928	+	0.694928i
$673$	6.17120e27	−	6.17120e27i	0.323757	−	0.323757i	−0.526449	−	0.850206i	$-0.676477\pi$
$673$	6.17120e27	−	6.17120e27i	0.323757	−	0.323757i	0.850206	+	0.526449i	$0.176477\pi$
$674$		−	1.26284e28i		−	0.652754i
$675$	−1.36766e28	−	1.47532e27i	−0.696530	−	0.0751359i
$676$	7.58898e28			3.80817
$677$	1.72768e28	+	1.72768e28i	0.854233	+	0.854233i	0.990651	−	0.136418i	$-0.0435592\pi$
$677$	1.72768e28	+	1.72768e28i	0.854233	+	0.854233i	−0.136418	+	0.990651i	$0.543559\pi$
$678$	−2.01877e28	+	2.01877e28i	−0.983538	+	0.983538i
$679$		−	4.32291e28i		−	2.07529i
$680$	−4.71439e27	+	1.66220e27i	−0.223016	+	0.0786309i
$681$	2.63358e28			1.22765
$682$	1.53387e28	+	1.53387e28i	0.704604	+	0.704604i
$683$	1.73339e28	−	1.73339e28i	0.784676	−	0.784676i	−0.195940	−	0.980616i	$-0.562776\pi$
$683$	1.73339e28	−	1.73339e28i	0.784676	−	0.784676i	0.980616	+	0.195940i	$0.0627757\pi$
$684$		−	1.28240e28i		−	0.572087i
$685$	7.75532e27	+	3.71213e27i	0.340953	+	0.163199i
$686$	−3.47278e28			−1.50465
$687$	1.86972e28	+	1.86972e28i	0.798379	+	0.798379i
$688$	3.89272e27	−	3.89272e27i	0.163821	−	0.163821i
$689$			1.47254e28i			0.610765i
$690$	1.22505e28	−	2.55935e28i	0.500797	−	1.04626i
$691$	−4.30122e28			−1.73305			−0.866525	−	0.499134i	$-0.833652\pi$
$691$	−4.30122e28			−1.73305			−0.866525	+	0.499134i	$0.833652\pi$
$692$	1.47135e28	+	1.47135e28i	0.584327	+	0.584327i
$693$	−8.98412e27	+	8.98412e27i	−0.351676	+	0.351676i
$694$			3.57335e28i			1.37873i
$695$	4.58984e27	+	1.30179e28i	0.174562	+	0.495099i
$696$	4.01407e28			1.50485
$697$	−1.55281e27	−	1.55281e27i	−0.0573839	−	0.0573839i
$698$	−6.09508e28	+	6.09508e28i	−2.22037	+	2.22037i
$699$		−	4.62240e28i		−	1.65995i
$700$	−5.62432e27	+	5.21390e28i	−0.199108	+	1.84579i
$701$	6.49768e27			0.226766			0.113383	−	0.993551i	$-0.463831\pi$
$701$	6.49768e27			0.226766			0.113383	+	0.993551i	$0.463831\pi$
$702$	−4.25646e28	−	4.25646e28i	−1.46446	−	1.46446i
$703$	2.76610e28	−	2.76610e28i	0.938242	−	0.938242i
$704$		−	5.19883e28i		−	1.73852i
$705$	2.40697e28	−	8.48647e27i	0.793558	−	0.279792i
$706$	−5.36393e28			−1.74356
$707$	−2.19766e27	−	2.19766e27i	−0.0704315	−	0.0704315i
$708$	−2.50839e28	+	2.50839e28i	−0.792615	+	0.792615i
$709$		−	2.98077e28i		−	0.928681i	−0.885657	−	0.464341i	$-0.846291\pi$
$709$		−	2.98077e28i		−	0.928681i	0.885657	−	0.464341i	$-0.153709\pi$
$710$	3.47765e28	+	1.66460e28i	1.06832	+	0.511359i
$711$	1.69556e28			0.513590
$712$	−1.00269e28	−	1.00269e28i	−0.299480	−	0.299480i
$713$	−7.57201e27	+	7.57201e27i	−0.223006	+	0.223006i
$714$			1.42081e28i			0.412623i
$715$	−3.04922e28	+	6.37039e28i	−0.873231	+	1.82434i
$716$	−8.10209e27			−0.228806
$717$	−3.22087e28	−	3.22087e28i	−0.896977	−	0.896977i
$718$	7.95583e28	−	7.95583e28i	2.18495	−	2.18495i
$719$			7.37727e27i			0.199805i	0.994997	+	0.0999026i	$0.0318531\pi$
$719$			7.37727e27i			0.199805i	−0.994997	+	0.0999026i	$0.968147\pi$
$720$	−1.34437e27	−	3.81294e27i	−0.0359081	−	0.101844i
$721$	4.94845e28			1.30352
$722$	−1.57258e28	−	1.57258e28i	−0.408546	−	0.408546i
$723$	6.30605e27	−	6.30605e27i	0.161575	−	0.161575i
$724$		−	3.38088e28i		−	0.854366i
$725$	−2.64317e28	−	3.28237e28i	−0.658787	−	0.818102i
$726$	2.21844e28			0.545359
$727$	−3.40646e28	−	3.40646e28i	−0.825961	−	0.825961i	0.160994	−	0.986955i	$-0.448530\pi$
$727$	−3.40646e28	−	3.40646e28i	−0.825961	−	0.825961i	−0.986955	+	0.160994i	$0.948530\pi$
$728$	−6.84820e28	+	6.84820e28i	−1.63781	+	1.63781i
$729$			1.36791e28i			0.322687i
$730$	5.45388e28	−	1.92293e28i	1.26905	−	0.447439i
$731$	−7.51146e27			−0.172405
$732$	2.14771e28	+	2.14771e28i	0.486256	+	0.486256i
$733$	1.28126e28	−	1.28126e28i	0.286152	−	0.286152i	−0.549404	−	0.835557i	$-0.685145\pi$
$733$	1.28126e28	−	1.28126e28i	0.286152	−	0.286152i	0.835557	+	0.549404i	$0.185145\pi$
$734$			1.20620e29i			2.65741i
$735$	7.45777e27	+	3.56971e27i	0.162082	+	0.0775817i
$736$	2.12690e28			0.456003
$737$	2.23792e28	+	2.23792e28i	0.473337	+	0.473337i
$738$	9.50619e27	−	9.50619e27i	0.198355	−	0.198355i
$739$			5.86884e28i			1.20811i	0.796941	+	0.604057i	$0.206450\pi$
$739$			5.86884e28i			1.20811i	−0.796941	+	0.604057i	$0.793550\pi$
$740$	6.05206e28	−	1.26439e29i	1.22910	−	2.56781i
$741$	−8.55075e28			−1.71325
$742$	−2.16497e28	−	2.16497e28i	−0.427969	−	0.427969i
$743$	2.31918e27	−	2.31918e27i	0.0452320	−	0.0452320i	−0.684129	−	0.729361i	$-0.739817\pi$
$743$	2.31918e27	−	2.31918e27i	0.0452320	−	0.0452320i	0.729361	+	0.684129i	$0.239817\pi$
$744$			3.97175e28i			0.764281i
$745$	5.04476e27	+	1.43081e28i	0.0957806	+	0.271657i
$746$	−5.19005e27			−0.0972262
$747$	8.82370e26	+	8.82370e26i	0.0163097	+	0.0163097i
$748$	1.48627e28	−	1.48627e28i	0.271070	−	0.271070i
$749$			2.05215e28i			0.369310i
$750$	−5.81169e28	+	9.39701e28i	−1.03202	+	1.66870i
$751$	−8.33254e28			−1.46008			−0.730042	−	0.683402i	$-0.760500\pi$
$751$	−8.33254e28			−1.46008			−0.730042	+	0.683402i	$0.760500\pi$
$752$	−7.63224e27	−	7.63224e27i	−0.131969	−	0.131969i
$753$	−5.82547e28	+	5.82547e28i	−0.993988	+	0.993988i
$754$		−	1.84416e29i		−	3.10517i
$755$	5.64950e28	−	1.99190e28i	0.938729	−	0.330977i
$756$	7.93167e28			1.30061
$757$	1.60145e28	+	1.60145e28i	0.259152	+	0.259152i	0.824709	−	0.565557i	$-0.191339\pi$
$757$	1.60145e28	+	1.60145e28i	0.259152	+	0.259152i	−0.565557	+	0.824709i	$0.691339\pi$
$758$	−1.74772e28	+	1.74772e28i	−0.279113	+	0.279113i
$759$			5.03515e28i			0.793587i
$760$	5.64211e28	+	2.70063e28i	0.877619	+	0.420078i
$761$	4.42838e28			0.679827			0.339913	−	0.940457i	$-0.389602\pi$
$761$	4.42838e28			0.679827			0.339913	+	0.940457i	$0.389602\pi$
$762$	8.69109e26	+	8.69109e26i	0.0131681	+	0.0131681i
$763$	−5.14867e28	+	5.14867e28i	−0.769927	+	0.769927i
$764$		−	6.47490e27i		−	0.0955651i
$765$	−2.38170e27	+	4.97582e27i	−0.0346955	+	0.0724853i
$766$	4.81497e27			0.0692319
$767$	4.86354e28	+	4.86354e28i	0.690238	+	0.690238i
$768$	8.30950e28	−	8.30950e28i	1.16403	−	1.16403i
$769$			4.55545e28i			0.629895i	0.949109	+	0.314947i	$0.101987\pi$
$769$			4.55545e28i			0.629895i	−0.949109	+	0.314947i	$0.898013\pi$
$770$	−4.88287e28	−	1.38490e29i	−0.666450	−	1.89021i
$771$	1.46915e29			1.97934
$772$	1.09258e29	+	1.09258e29i	1.45305	+	1.45305i
$773$	8.51224e28	−	8.51224e28i	1.11750	−	1.11750i	0.125397	−	0.992107i	$-0.459979\pi$
$773$	8.51224e28	−	8.51224e28i	1.11750	−	1.11750i	0.992107	−	0.125397i	$-0.0400205\pi$
$774$		−	4.59847e28i		−	0.595941i
$775$	3.24777e28	−	2.61531e28i	0.415497	−	0.334585i
$776$	−1.84770e29			−2.33353
$777$	−1.18897e29	−	1.18897e29i	−1.48238	−	1.48238i
$778$	−4.00760e28	+	4.00760e28i	−0.493274	+	0.493274i
$779$			2.74790e28i			0.333908i
$780$	−2.88970e29	+	1.01885e29i	−3.46662	+	1.22226i
$781$	−6.84178e28			−0.810324
$782$	1.15776e28	+	1.15776e28i	0.135379	+	0.135379i
$783$	−4.50713e28	+	4.50713e28i	−0.520334	+	0.520334i
$784$		−	3.49670e27i		−	0.0398564i
$785$	−8.01461e28	−	3.83624e28i	−0.901957	−	0.431727i
$786$	8.76366e28			0.973778
$787$	2.76326e28	+	2.76326e28i	0.303161	+	0.303161i	0.842249	−	0.539088i	$-0.181231\pi$
$787$	2.76326e28	+	2.76326e28i	0.303161	+	0.303161i	−0.539088	+	0.842249i	$0.681231\pi$
$788$	1.52776e29	−	1.52776e29i	1.65498	−	1.65498i
$789$		−	1.70589e29i		−	1.82466i
$790$	−8.46080e28	+	1.76761e29i	−0.893594	+	1.86688i
$791$	−7.29393e28			−0.760671
$792$	3.83999e28	+	3.83999e28i	0.395438	+	0.395438i
$793$	4.16422e28	−	4.16422e28i	0.423449	−	0.423449i
$794$		−	2.95842e27i		−	0.0297068i
$795$	−1.35934e28	−	3.85541e28i	−0.134790	−	0.382296i
$796$	−6.89372e28			−0.675029
$797$	8.55491e28	+	8.55491e28i	0.827242	+	0.827242i	0.987134	−	0.159893i	$-0.0511148\pi$
$797$	8.55491e28	+	8.55491e28i	0.827242	+	0.827242i	−0.159893	+	0.987134i	$0.551115\pi$
$798$	1.25715e29	−	1.25715e29i	1.20049	−	1.20049i
$799$			1.47273e28i			0.138885i
$800$	−8.23438e28	−	8.88256e27i	−0.766886	−	0.0827253i
$801$	−1.56486e28			−0.143929
$802$	−1.40394e29	−	1.40394e29i	−1.27528	−	1.27528i
$803$	−7.25641e28	+	7.25641e28i	−0.650978	+	0.650978i
$804$			1.37308e29i			1.21656i
$805$	6.83659e28	−	2.41044e28i	0.598248	−	0.210930i
$806$	1.82472e29			1.57705
$807$	4.35220e28	+	4.35220e28i	0.371512	+	0.371512i
$808$	−9.39326e27	+	9.39326e27i	−0.0791959	+	0.0791959i
$809$		−	1.68938e29i		−	1.40683i	−0.710777	−	0.703417i	$-0.751657\pi$
$809$		−	1.68938e29i		−	1.40683i	0.710777	−	0.703417i	$-0.248343\pi$
$810$	2.25029e29	+	1.07712e29i	1.85092	+	0.885956i
$811$	5.74314e28			0.466596			0.233298	−	0.972405i	$-0.425048\pi$
$811$	5.74314e28			0.466596			0.233298	+	0.972405i	$0.425048\pi$
$812$	1.71824e29	+	1.71824e29i	1.37887	+	1.37887i
$813$	−1.38525e29	+	1.38525e29i	−1.09805	+	1.09805i
$814$			3.92520e29i			3.07339i
$815$	1.05719e29	−	2.20866e29i	0.817666	−	1.70825i
$816$	8.02300e27			0.0612964
$817$	6.64627e28	+	6.64627e28i	0.501600	+	0.501600i
$818$	−1.45234e29	+	1.45234e29i	−1.08277	+	1.08277i
$819$			1.06877e29i			0.787125i
$820$	3.27422e28	+	9.28646e28i	0.238215	+	0.675634i
$821$	−4.77197e28			−0.342978			−0.171489	−	0.985186i	$-0.554858\pi$
$821$	−4.77197e28			−0.342978			−0.171489	+	0.985186i	$0.554858\pi$
$822$	−7.38587e28	−	7.38587e28i	−0.524425	−	0.524425i
$823$	1.56756e29	−	1.56756e29i	1.09958	−	1.09958i	0.105120	−	0.994460i	$-0.466477\pi$
$823$	1.56756e29	−	1.56756e29i	1.09958	−	1.09958i	0.994460	−	0.105120i	$-0.0335228\pi$
$824$		−	2.11507e29i		−	1.46572i
$825$	2.10283e28	−	1.94938e29i	0.143968	−	1.33462i
$826$	−1.43010e29			−0.967313
$827$	−3.72004e28	−	3.72004e28i	−0.248595	−	0.248595i	0.571799	−	0.820394i	$-0.306246\pi$
$827$	−3.72004e28	−	3.72004e28i	−0.248595	−	0.248595i	−0.820394	+	0.571799i	$0.806246\pi$
$828$	−4.49168e28	+	4.49168e28i	−0.296555	+	0.296555i
$829$		−	3.22756e28i		−	0.210537i	−0.994444	−	0.105269i	$-0.966430\pi$
$829$		−	3.22756e28i		−	0.210537i	0.994444	−	0.105269i	$-0.0335702\pi$
$830$	−1.36017e28	+	4.79568e27i	−0.0876622	+	0.0309079i
$831$	2.72482e29			1.73511
$832$	−3.09231e29	−	3.09231e29i	−1.94558	−	1.94558i
$833$	−3.37364e27	+	3.37364e27i	−0.0209724	+	0.0209724i
$834$		−	1.67689e29i		−	1.03002i
$835$	−1.53633e29	−	7.35375e28i	−0.932439	−	0.446318i
$836$	−2.63016e29			−1.57732
$837$	−4.45962e28	−	4.45962e28i	−0.264267	−	0.264267i
$838$	−5.52196e28	+	5.52196e28i	−0.323335	+	0.323335i
$839$			2.95132e29i			1.70764i	0.520566	+	0.853821i	$0.325721\pi$
$839$			2.95132e29i			1.70764i	−0.520566	+	0.853821i	$0.674279\pi$
$840$	1.16083e29	−	2.42518e29i	0.663704	−	1.38660i
$841$	−1.82821e28			−0.103292
$842$	1.84341e29	+	1.84341e29i	1.02920	+	1.02920i
$843$	−1.04239e29	+	1.04239e29i	−0.575114	+	0.575114i
$844$		−	1.44634e29i		−	0.788581i
$845$	1.35832e29	+	3.85252e29i	0.731872	+	2.07576i
$846$	−9.01595e28			−0.480074
$847$	4.00767e28	+	4.00767e28i	0.210891	+	0.210891i
$848$	−1.22251e28	+	1.22251e28i	−0.0635761	+	0.0635761i
$849$			1.48555e29i			0.763503i
$850$	−3.99881e28	−	4.96584e28i	−0.203115	−	0.252234i
$851$	−1.93769e29			−0.972720
$852$	−2.09889e29	−	2.09889e29i	−1.04134	−	1.04134i
$853$	−1.03027e29	+	1.03027e29i	−0.505195	+	0.505195i	−0.913048	−	0.407853i	$-0.866278\pi$
$853$	−1.03027e29	+	1.03027e29i	−0.505195	+	0.505195i	0.407853	+	0.913048i	$0.366278\pi$
$854$			1.22447e29i			0.593430i
$855$	6.51006e28	−	2.29531e28i	0.311834	−	0.109946i
$856$	8.77131e28			0.415266
$857$	−2.31862e29	−	2.31862e29i	−1.08498	−	1.08498i	−0.996037	−	0.0889409i	$-0.971652\pi$
$857$	−2.31862e29	−	2.31862e29i	−1.08498	−	1.08498i	−0.0889409	−	0.996037i	$-0.528348\pi$
$858$	6.06691e29	−	6.06691e29i	2.80605	−	2.80605i
$859$		−	5.07455e28i		−	0.231988i	−0.993250	−	0.115994i	$-0.962995\pi$
$859$		−	5.07455e28i		−	0.231988i	0.993250	−	0.115994i	$-0.0370054\pi$
$860$	3.03801e29	+	1.45416e29i	1.37279	+	0.657096i
$861$	1.18115e29			0.527560
$862$	−2.62008e29	−	2.62008e29i	−1.15676	−	1.15676i
$863$	1.10319e29	−	1.10319e29i	0.481440	−	0.481440i	−0.424151	−	0.905591i	$-0.639428\pi$
$863$	1.10319e29	−	1.10319e29i	0.481440	−	0.481440i	0.905591	+	0.424151i	$0.139428\pi$
$864$			1.25266e29i			0.540375i
$865$	−4.83576e28	+	1.01028e29i	−0.206207	+	0.430805i
$866$	3.90645e29			1.64666
$867$	1.93765e29	+	1.93765e29i	0.807393	+	0.807393i
$868$	−1.70013e29	+	1.70013e29i	−0.700302	+	0.700302i
$869$		−	3.47753e29i		−	1.41603i
$870$	1.70239e29	+	4.82840e29i	0.685279	+	1.94362i
$871$	2.66227e29			1.05943
$872$	2.20065e29	+	2.20065e29i	0.865736	+	0.865736i
$873$	−1.44181e29	+	1.44181e29i	−0.560744	+	0.560744i
$874$		−	2.04881e29i		−	0.787750i
$875$	−2.74749e29	+	6.47698e28i	−1.04437	+	0.246202i
$876$	−4.45217e29			−1.67313
$877$	1.66160e29	+	1.66160e29i	0.617350	+	0.617350i	0.944851	−	0.327501i	$-0.106206\pi$
$877$	1.66160e29	+	1.66160e29i	0.617350	+	0.617350i	−0.327501	+	0.944851i	$0.606206\pi$
$878$	−4.65570e29	+	4.65570e29i	−1.71017	+	1.71017i
$879$		−	3.84844e29i		−	1.39764i
$880$	−7.82022e28	+	2.75725e28i	−0.280797	+	0.0990033i
$881$	−2.72720e29			−0.968184			−0.484092	−	0.875017i	$-0.660850\pi$
$881$	−2.72720e29			−0.968184			−0.484092	+	0.875017i	$0.660850\pi$
$882$	−2.06532e28	−	2.06532e28i	−0.0724940	−	0.0724940i
$883$	−1.83574e29	+	1.83574e29i	−0.637095	+	0.637095i	−0.949838	−	0.312743i	$-0.898752\pi$
$883$	−1.83574e29	+	1.83574e29i	−0.637095	+	0.637095i	0.312743	+	0.949838i	$0.398752\pi$
$884$		−	1.76809e29i		−	0.606712i
$885$	−1.72234e29	−	8.24410e28i	−0.584369	−	0.279712i
$886$	8.26853e29			2.77390
$887$	−1.14631e29	−	1.14631e29i	−0.380248	−	0.380248i	0.490943	−	0.871191i	$-0.336652\pi$
$887$	−1.14631e29	−	1.14631e29i	−0.380248	−	0.380248i	−0.871191	+	0.490943i	$0.836652\pi$
$888$	−5.08189e29	+	5.08189e29i	−1.66684	+	1.66684i
$889$			3.14013e27i			0.0101843i
$890$	7.80860e28	−	1.63136e29i	0.250422	−	0.523178i
$891$	−4.42713e29			−1.40393
$892$	2.92829e29	+	2.92829e29i	0.918261	+	0.918261i
$893$	1.30310e29	−	1.30310e29i	0.404075	−	0.404075i
$894$		−	1.84310e29i		−	0.565162i
$895$	−1.45016e28	−	4.11300e28i	−0.0439730	−	0.124718i
$896$	6.33272e29			1.89894
$897$	2.99495e29	+	2.99495e29i	0.888107	+	0.888107i
$898$	2.37816e29	−	2.37816e29i	0.697392	−	0.697392i
$899$		−	1.93218e29i		−	0.560339i
$900$	1.92656e29	−	1.55139e29i	0.552533	−	0.444934i
$901$	2.35898e28			0.0669076
$902$	−1.94969e29	−	1.94969e29i	−0.546890	−	0.546890i
$903$	2.85680e29	−	2.85680e29i	0.792506	−	0.792506i
$904$			3.11757e29i			0.855327i
$905$	1.71629e29	−	6.05130e28i	0.465700	−	0.164196i
$906$	−7.27737e29			−1.95296
$907$	2.12686e29	+	2.12686e29i	0.564504	+	0.564504i	0.930583	−	0.366080i	$-0.119300\pi$
$907$	2.12686e29	+	2.12686e29i	0.564504	+	0.564504i	−0.366080	+	0.930583i	$0.619300\pi$
$908$	4.81839e29	−	4.81839e29i	1.26486	−	1.26486i
$909$			1.46596e28i			0.0380613i
$910$	−1.11419e30	−	5.33312e29i	−2.86117	−	1.36952i
$911$	−3.29124e29			−0.835941			−0.417971	−	0.908461i	$-0.637259\pi$
$911$	−3.29124e29			−0.835941			−0.417971	+	0.908461i	$0.637259\pi$
$912$	−7.09889e28	−	7.09889e28i	−0.178337	−	0.178337i
$913$	1.80971e28	−	1.80971e28i	0.0449678	−	0.0449678i
$914$		−	1.67135e28i		−	0.0410777i
$915$	−7.05869e28	+	1.47469e29i	−0.171598	+	0.358500i
$916$	6.84166e29			1.64515
$917$	1.58318e29	+	1.58318e29i	0.376561	+	0.376561i
$918$	−6.81876e28	+	6.81876e28i	−0.160427	+	0.160427i
$919$			5.70189e28i			0.132698i	0.997796	+	0.0663490i	$0.0211351\pi$
$919$			5.70189e28i			0.132698i	−0.997796	+	0.0663490i	$0.978865\pi$
$920$	−1.03027e29	−	2.92210e29i	−0.237178	−	0.672692i
$921$	−6.26791e29			−1.42734
$922$	−2.04406e29	−	2.04406e29i	−0.460452	−	0.460452i
$923$	−4.06955e29	+	4.06955e29i	−0.906838	+	0.906838i
$924$			1.13053e30i			2.49209i
$925$	7.50185e29	+	8.09237e28i	1.63588	+	0.176465i
$926$	1.12098e29			0.241817
$927$	−1.65044e29	−	1.65044e29i	−0.352211	−	0.352211i
$928$	−2.71365e29	+	2.71365e29i	−0.572893	+	0.572893i
$929$		−	3.99844e29i		−	0.835090i	−0.908656	−	0.417545i	$-0.862891\pi$
$929$		−	3.99844e29i		−	0.835090i	0.908656	−	0.417545i	$-0.137109\pi$
$930$	−4.77750e29	+	1.68445e29i	−0.987123	+	0.348039i
$931$	5.97012e28			0.122035
$932$	−8.45712e29	−	8.45712e29i	−1.71027	−	1.71027i
$933$	8.16847e29	−	8.16847e29i	1.63427	−	1.63427i
$934$			1.79083e29i			0.354475i
$935$	1.02052e29	+	4.88480e28i	0.199851	+	0.0956600i
$936$	4.56812e29			0.885073
$937$	−7.20749e28	−	7.20749e28i	−0.138162	−	0.138162i	0.634643	−	0.772805i	$-0.281147\pi$
$937$	−7.20749e28	−	7.20749e28i	−0.138162	−	0.138162i	−0.772805	+	0.634643i	$0.781147\pi$
$938$	−3.91415e29	+	3.91415e29i	−0.742350	+	0.742350i
$939$			6.62474e29i			1.24312i
$940$	2.85109e29	−	5.95646e29i	0.529338	−	1.10588i
$941$	2.14884e29			0.394738			0.197369	−	0.980329i	$-0.436760\pi$
$941$	2.14884e29			0.394738			0.197369	+	0.980329i	$0.436760\pi$
$942$	7.63281e29	+	7.63281e29i	1.38732	+	1.38732i
$943$	9.62470e28	−	9.62470e28i	0.173089	−	0.173089i
$944$			8.07549e28i			0.143697i
$945$	1.41966e29	+	4.02649e29i	0.249957	+	0.708938i
$946$	−9.43130e29			−1.64309
$947$	−4.27310e29	−	4.27310e29i	−0.736619	−	0.736619i	0.235303	−	0.971922i	$-0.424392\pi$
$947$	−4.27310e29	−	4.27310e29i	−0.736619	−	0.736619i	−0.971922	+	0.235303i	$0.924392\pi$
$948$	1.06682e30	−	1.06682e30i	1.81973	−	1.81973i
$949$			8.63236e29i			1.45703i
$950$	−8.55647e28	+	7.93208e29i	−0.142909	+	1.32480i
$951$	1.16100e30			1.91879
$952$	1.09707e29	+	1.09707e29i	0.179417	+	0.179417i
$953$	−2.97726e29	+	2.97726e29i	−0.481823	+	0.481823i	−0.905714	−	0.423890i	$-0.860664\pi$
$953$	−2.97726e29	+	2.97726e29i	−0.481823	+	0.481823i	0.423890	+	0.905714i	$0.360664\pi$
$954$			1.44415e29i			0.231275i
$955$	3.28696e28	−	1.15892e28i	0.0520908	−	0.0183662i
$956$	−1.17858e30			−1.84833
$957$	−6.42420e29	−	6.42420e29i	−0.997011	−	0.997011i
$958$	1.04008e30	−	1.04008e30i	1.59740	−	1.59740i
$959$		−	2.66855e29i		−	0.405592i
$960$	1.09509e30	+	5.24172e29i	1.64717	+	0.788427i
$961$	−4.80609e29			−0.715415
$962$	2.33474e30	+	2.33474e30i	3.43944	+	3.43944i
$963$	6.84448e28	−	6.84448e28i	0.0997878	−	0.0997878i
$964$		−	2.30750e29i		−	0.332945i
$965$	−3.59088e29	+	7.50200e29i	−0.512776	+	1.07128i
$966$	−8.80652e29			−1.24461
$967$	1.69534e29	+	1.69534e29i	0.237134	+	0.237134i	0.815662	−	0.578529i	$-0.196373\pi$
$967$	1.69534e29	+	1.69534e29i	0.237134	+	0.237134i	−0.578529	+	0.815662i	$0.696373\pi$
$968$	1.71296e29	−	1.71296e29i	0.237134	−	0.237134i
$969$			1.36981e29i			0.187682i
$970$	−7.83622e29	−	2.22254e30i	−1.06265	−	3.01392i
$971$	−9.61412e29			−1.29038			−0.645189	−	0.764023i	$-0.723221\pi$
$971$	−9.61412e29			−1.29038			−0.645189	+	0.764023i	$0.723221\pi$
$972$	−7.12932e29	−	7.12932e29i	−0.947077	−	0.947077i
$973$	3.02934e29	−	3.02934e29i	0.398309	−	0.398309i
$974$		−	6.70070e29i		−	0.872028i
$975$	−1.03443e30	−	1.28459e30i	−1.33246	−	1.65469i
$976$	6.91432e28			0.0881559
$977$	3.21663e29	+	3.21663e29i	0.405934	+	0.405934i	0.880318	−	0.474384i	$-0.157329\pi$
$977$	3.21663e29	+	3.21663e29i	0.405934	+	0.405934i	−0.474384	+	0.880318i	$0.657329\pi$
$978$	−2.10344e30	+	2.10344e30i	−2.62749	+	2.62749i
$979$			3.20947e29i			0.396831i
$980$	2.01758e29	−	7.11359e28i	0.246928	−	0.0870618i
$981$	3.43444e29			0.416070
$982$	−9.18810e29	−	9.18810e29i	−1.10182	−	1.10182i
$983$	9.95944e29	−	9.95944e29i	1.18222	−	1.18222i	0.203057	−	0.979167i	$-0.434912\pi$
$983$	9.95944e29	−	9.95944e29i	1.18222	−	1.18222i	0.979167	−	0.203057i	$-0.0650877\pi$
$984$		−	5.04845e29i		−	0.593209i
$985$	1.04901e30	+	5.02114e29i	1.22016	+	0.584037i
$986$	−2.95431e29			−0.340163
$987$	−5.60117e29	−	5.60117e29i	−0.638421	−	0.638421i
$988$	−1.56444e30	+	1.56444e30i	−1.76518	+	1.76518i
$989$		−	4.65579e29i		−	0.520033i
$990$	−2.99044e29	+	6.24758e29i	−0.330661	+	0.690812i
$991$	9.41450e29			1.03053			0.515265	−	0.857031i	$-0.327693\pi$
$991$	9.41450e29			1.03053			0.515265	+	0.857031i	$0.327693\pi$
$992$	−2.68504e29	−	2.68504e29i	−0.290960	−	0.290960i
$993$	−1.01571e29	+	1.01571e29i	−0.108963	+	0.108963i
$994$		−	1.19663e30i		−	1.27086i
$995$	−1.23388e29	−	3.49957e29i	−0.129730	−	0.367946i
$996$	1.11035e29			0.115576
$997$	−4.74000e28	−	4.74000e28i	−0.0488458	−	0.0488458i	0.682262	−	0.731108i	$-0.260996\pi$
$997$	−4.74000e28	−	4.74000e28i	−0.0488458	−	0.0488458i	−0.731108	+	0.682262i	$0.760996\pi$
$998$	4.38846e29	−	4.38846e29i	0.447720	−	0.447720i
$999$		−	1.14122e30i		−	1.15270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.21.c.a.2.2	✓	18
3.2	odd	2		45.21.g.a.37.8		18
5.2	odd	4		25.21.c.b.18.8		18
5.3	odd	4	inner	5.21.c.a.3.2	yes	18
5.4	even	2		25.21.c.b.7.8		18
15.8	even	4		45.21.g.a.28.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.21.c.a.2.2	✓	18	1.1	even	1	trivial
5.21.c.a.3.2	yes	18	5.3	odd	4	inner
25.21.c.b.7.8		18	5.4	even	2
25.21.c.b.18.8		18	5.2	odd	4
45.21.g.a.28.8		18	15.8	even	4
45.21.g.a.37.8		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1196.41 - 1196.41i) q^{2} +(-49580.3 + 49580.3i) q^{3} +1.81424e6i q^{4} +(-9.20993e6 + 3.24723e6i) q^{5} +1.18637e8 q^{6} +(2.14321e8 + 2.14321e8i) q^{7} +(9.16051e8 - 9.16051e8i) q^{8} -1.42964e9i q^{9} +O(q^{10})\)	\(q+(-1196.41 - 1196.41i) q^{2} +(-49580.3 + 49580.3i) q^{3} +1.81424e6i q^{4} +(-9.20993e6 + 3.24723e6i) q^{5} +1.18637e8 q^{6} +(2.14321e8 + 2.14321e8i) q^{7} +(9.16051e8 - 9.16051e8i) q^{8} -1.42964e9i q^{9} +(1.49039e10 + 7.13386e9i) q^{10} -2.93214e10 q^{11} +(-8.99506e10 - 8.99506e10i) q^{12} +(-1.74406e11 + 1.74406e11i) q^{13} -5.12834e11i q^{14} +(2.95633e11 - 6.17631e11i) q^{15} -2.89586e11 q^{16} +(2.79395e11 + 2.79395e11i) q^{17} +(-1.71044e12 + 1.71044e12i) q^{18} -4.94427e12i q^{19} +(-5.89126e12 - 1.67090e13i) q^{20} -2.12522e13 q^{21} +(3.50805e13 + 3.50805e13i) q^{22} +(-1.73176e13 + 1.73176e13i) q^{23} +9.08363e13i q^{24} +(7.42784e13 - 5.98136e13i) q^{25} +4.17324e14 q^{26} +(-1.01994e14 - 1.01994e14i) q^{27} +(-3.88830e14 + 3.88830e14i) q^{28} -4.41901e14i q^{29} +(-1.09264e15 + 3.85243e14i) q^{30} +4.37243e14 q^{31} +(-6.14084e14 - 6.14084e14i) q^{32} +(1.45376e15 - 1.45376e15i) q^{33} -6.68545e14i q^{34} +(-2.66983e15 - 1.27793e15i) q^{35} +2.59371e15 q^{36} +(5.59455e15 + 5.59455e15i) q^{37} +(-5.91540e15 + 5.91540e15i) q^{38} -1.72942e16i q^{39} +(-5.46214e15 + 1.14114e16i) q^{40} -5.55775e15 q^{41} +(2.54265e16 + 2.54265e16i) q^{42} +(-1.34424e16 + 1.34424e16i) q^{43} -5.31960e16i q^{44} +(4.64237e15 + 1.31669e16i) q^{45} +4.14381e16 q^{46} +(2.63557e16 + 2.63557e16i) q^{47} +(1.43578e16 - 1.43578e16i) q^{48} +1.20748e16i q^{49} +(-1.60430e17 - 1.73058e16i) q^{50} -2.77050e16 q^{51} +(-3.16415e17 - 3.16415e17i) q^{52} +(4.22158e16 - 4.22158e16i) q^{53} +2.44054e17i q^{54} +(2.70048e17 - 9.52134e16i) q^{55} +3.92658e17 q^{56} +(2.45139e17 + 2.45139e17i) q^{57} +(-5.28697e17 + 5.28697e17i) q^{58} -2.78863e17i q^{59} +(1.12053e18 + 5.36349e17i) q^{60} -2.38765e17 q^{61} +(-5.23124e17 - 5.23124e17i) q^{62} +(3.06401e17 - 3.06401e17i) q^{63} +1.77305e18i q^{64} +(1.03993e18 - 2.17261e18i) q^{65} -3.47861e18 q^{66} +(-7.63239e17 - 7.63239e17i) q^{67} +(-5.06890e17 + 5.06890e17i) q^{68} -1.71723e18i q^{69} +(1.66529e18 + 4.72317e18i) q^{70} +2.33338e18 q^{71} +(-1.30962e18 - 1.30962e18i) q^{72} +(2.47479e18 - 2.47479e18i) q^{73} -1.33868e19i q^{74} +(-7.17166e17 + 6.64833e18i) q^{75} +8.97010e18 q^{76} +(-6.28419e18 - 6.28419e18i) q^{77} +(-2.06911e19 + 2.06911e19i) q^{78} +1.18600e19i q^{79} +(2.66707e18 - 9.40355e17i) q^{80} +1.50986e19 q^{81} +(6.64937e18 + 6.64937e18i) q^{82} +(-6.17199e17 + 6.17199e17i) q^{83} -3.85566e19i q^{84} +(-3.48047e18 - 1.66595e18i) q^{85} +3.21653e19 q^{86} +(2.19096e19 + 2.19096e19i) q^{87} +(-2.68599e19 + 2.68599e19i) q^{88} -1.09458e19i q^{89} +(1.01988e19 - 2.13072e19i) q^{90} -7.47579e19 q^{91} +(-3.14183e19 - 3.14183e19i) q^{92} +(-2.16787e19 + 2.16787e19i) q^{93} -6.30646e19i q^{94} +(1.60552e19 + 4.55364e19i) q^{95} +6.08930e19 q^{96} +(-1.00851e20 - 1.00851e20i) q^{97} +(1.44465e19 - 1.44465e19i) q^{98} +4.19190e19i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Introduction

L-functions

Modular forms

Varieties

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