LMFDB - Embedded newform 16.28.e.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,28,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	16.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:	$73.8968919741$
Analytic rank:	$0$
Dimension:	$106$
Relative dimension:	$53$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	16.13
Dual form			16.28.e.a.5.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9065.18 + 7213.90i) q^{2} +(-3.30251e6 - 3.30251e6i) q^{3} +(3.01372e7 - 1.30790e8i) q^{4} +(3.04061e8 - 3.04061e8i) q^{5} +(5.37618e10 + 6.11388e9i) q^{6} +2.05985e11i q^{7} +(6.70310e11 + 1.40305e12i) q^{8} +1.41875e13i q^{9} +(-5.62903e11 + 4.94983e12i) q^{10} +(-7.46488e13 + 7.46488e13i) q^{11} +(-5.31465e14 + 3.32408e14i) q^{12} +(4.03416e14 + 4.03416e14i) q^{13} +(-1.48595e15 - 1.86729e15i) q^{14} -2.00833e15 q^{15} +(-1.61979e16 - 7.88331e15i) q^{16} -2.29769e14 q^{17} +(-1.02347e17 - 1.28613e17i) q^{18} +(1.92943e17 + 1.92943e17i) q^{19} +(-3.06047e16 - 4.89318e16i) q^{20} +(6.80267e17 - 6.80267e17i) q^{21} +(1.38196e17 - 1.21521e18i) q^{22} -9.65370e17i q^{23} +(2.41986e18 - 6.84727e18i) q^{24} +7.26567e18i q^{25} +(-6.56723e18 - 7.46836e17i) q^{26} +(2.16709e19 - 2.16709e19i) q^{27} +(2.69409e19 + 6.20780e18i) q^{28} +(-5.76285e19 - 5.76285e19i) q^{29} +(1.82058e19 - 1.44879e19i) q^{30} +1.11797e20 q^{31} +(2.03706e20 - 4.53864e19i) q^{32} +4.93057e20 q^{33} +(2.08290e18 - 1.65753e18i) q^{34} +(6.26320e19 + 6.26320e19i) q^{35} +(1.85559e21 + 4.27572e20i) q^{36} +(-1.14792e21 + 1.14792e21i) q^{37} +(-3.14094e21 - 3.57192e20i) q^{38} -2.66457e21i q^{39} +(6.30426e20 + 2.22796e20i) q^{40} +2.52651e21i q^{41} +(-1.25937e21 + 1.10741e22i) q^{42} +(3.23875e19 - 3.23875e19i) q^{43} +(7.51365e21 + 1.20131e22i) q^{44} +(4.31387e21 + 4.31387e21i) q^{45} +(6.96408e21 + 8.75125e21i) q^{46} +1.55896e22 q^{47} +(2.74590e22 + 7.95284e22i) q^{48} +2.32826e22 q^{49} +(-5.24138e22 - 6.58646e22i) q^{50} +(7.58816e20 + 7.58816e20i) q^{51} +(6.49207e22 - 4.06051e22i) q^{52} +(1.50907e23 - 1.50907e23i) q^{53} +(-4.01189e22 + 3.52781e23i) q^{54} +4.53955e22i q^{55} +(-2.89006e23 + 1.38074e23i) q^{56} -1.27439e24i q^{57} +(9.38139e23 + 1.06687e23i) q^{58} +(6.11665e23 - 6.11665e23i) q^{59} +(-6.05253e22 + 2.62670e23i) q^{60} +(-1.55517e24 - 1.55517e24i) q^{61} +(-1.01346e24 + 8.06489e23i) q^{62} -2.92242e24 q^{63} +(-1.51922e24 + 1.88095e24i) q^{64} +2.45326e23 q^{65} +(-4.46965e24 + 3.55686e24i) q^{66} +(-1.01732e24 - 1.01732e24i) q^{67} +(-6.92460e21 + 3.00517e22i) q^{68} +(-3.18814e24 + 3.18814e24i) q^{69} +(-1.01959e24 - 1.15949e23i) q^{70} -6.70294e24i q^{71} +(-1.99058e25 + 9.51005e24i) q^{72} +2.33739e25i q^{73} +(2.12511e24 - 1.86870e25i) q^{74} +(2.39950e25 - 2.39950e25i) q^{75} +(3.10499e25 - 1.94204e25i) q^{76} +(-1.53765e25 - 1.53765e25i) q^{77} +(1.92219e25 + 2.41548e25i) q^{78} -5.61337e25 q^{79} +(-7.32215e24 + 2.52814e24i) q^{80} -3.49480e25 q^{81} +(-1.82260e25 - 2.29033e25i) q^{82} +(3.04605e25 + 3.04605e25i) q^{83} +(-6.84712e25 - 1.09474e26i) q^{84} +(-6.98639e22 + 6.98639e22i) q^{85} +(-5.99585e22 + 5.27239e23i) q^{86} +3.80637e26i q^{87} +(-1.54773e26 - 5.46978e25i) q^{88} +4.02988e26i q^{89} +(-7.02259e25 - 7.98620e24i) q^{90} +(-8.30976e25 + 8.30976e25i) q^{91} +(-1.26261e26 - 2.90935e25i) q^{92} +(-3.69209e26 - 3.69209e26i) q^{93} +(-1.41322e26 + 1.12461e26i) q^{94} +1.17333e26 q^{95} +(-8.22631e26 - 5.22853e26i) q^{96} -1.05860e27 q^{97} +(-2.11061e26 + 1.67958e26i) q^{98} +(-1.05908e27 - 1.05908e27i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−9065.18	+	7213.90i	−0.782477	+	0.622680i
$2$	−9065.18	+	7213.90i	−0.782477	+	0.622680i
$3$	−3.30251e6	−	3.30251e6i	−1.19593	−	1.19593i	−0.975373	−	0.220560i	$-0.929211\pi$
$3$	−3.30251e6	−	3.30251e6i	−1.19593	−	1.19593i	−0.220560	−	0.975373i	$-0.570789\pi$
$4$	3.01372e7	−	1.30790e8i	0.224539	−	0.974465i
$5$	3.04061e8	−	3.04061e8i	0.111395	−	0.111395i	−0.649212	−	0.760607i	$-0.724901\pi$
$5$	3.04061e8	−	3.04061e8i	0.111395	−	0.111395i	0.760607	+	0.649212i	$0.224901\pi$
$6$	5.37618e10	+	6.11388e9i	1.68047	+	0.191106i
$7$			2.05985e11i			0.803548i	0.915739	+	0.401774i	$0.131606\pi$
$7$			2.05985e11i			0.803548i	−0.915739	+	0.401774i	$0.868394\pi$
$8$	6.70310e11	+	1.40305e12i	0.431083	+	0.902312i
$9$			1.41875e13i			1.86051i
$10$	−5.62903e11	+	4.94983e12i	−0.0178005	+	0.156527i
$11$	−7.46488e13	+	7.46488e13i	−0.651961	+	0.651961i	−0.953465	−	0.301504i	$-0.902511\pi$
$11$	−7.46488e13	+	7.46488e13i	−0.651961	+	0.651961i	0.301504	+	0.953465i	$0.402511\pi$
$12$	−5.31465e14	+	3.32408e14i	−1.43393	+	0.896861i
$13$	4.03416e14	+	4.03416e14i	0.369418	+	0.369418i	0.867265	−	0.497847i	$-0.165876\pi$
$13$	4.03416e14	+	4.03416e14i	0.369418	+	0.369418i	−0.497847	+	0.867265i	$0.665876\pi$
$14$	−1.48595e15	−	1.86729e15i	−0.500353	−	0.628758i
$15$	−2.00833e15			−0.266442
$16$	−1.61979e16	−	7.88331e15i	−0.899164	−	0.437612i
$17$	−2.29769e14			−0.00562642			−0.00281321	−	0.999996i	$-0.500895\pi$
$17$	−2.29769e14			−0.00562642			−0.00281321	+	0.999996i	$0.500895\pi$
$18$	−1.02347e17	−	1.28613e17i	−1.15851	−	1.45581i
$19$	1.92943e17	+	1.92943e17i	1.05258	+	1.05258i	0.998539	+	0.0540436i	$0.0172110\pi$
$19$	1.92943e17	+	1.92943e17i	1.05258	+	1.05258i	0.0540436	+	0.998539i	$0.482789\pi$
$20$	−3.06047e16	−	4.89318e16i	−0.0835379	−	0.133563i
$21$	6.80267e17	−	6.80267e17i	0.960990	−	0.960990i
$22$	1.38196e17	−	1.21521e18i	0.104181	−	0.916107i
$23$		−	9.65370e17i		−	0.399363i	−0.979861	−	0.199682i	$-0.936009\pi$
$23$		−	9.65370e17i		−	0.399363i	0.979861	−	0.199682i	$-0.0639908\pi$
$24$	2.41986e18	−	6.84727e18i	0.563559	−	1.59465i
$25$			7.26567e18i			0.975182i
$26$	−6.56723e18	−	7.46836e17i	−0.519090	−	0.0590317i
$27$	2.16709e19	−	2.16709e19i	1.02912	−	1.02912i
$28$	2.69409e19	+	6.20780e18i	0.783030	+	0.180428i
$29$	−5.76285e19	−	5.76285e19i	−1.04295	−	1.04295i	−0.999035	−	0.0439173i	$-0.986016\pi$
$29$	−5.76285e19	−	5.76285e19i	−1.04295	−	1.04295i	−0.0439173	−	0.999035i	$-0.513984\pi$
$30$	1.82058e19	−	1.44879e19i	0.208485	−	0.165908i
$31$	1.11797e20			0.822329			0.411165	−	0.911561i	$-0.365122\pi$
$31$	1.11797e20			0.822329			0.411165	+	0.911561i	$0.365122\pi$
$32$	2.03706e20	−	4.53864e19i	0.976067	−	0.217471i
$33$	4.93057e20			1.55940
$34$	2.08290e18	−	1.65753e18i	0.00440254	−	0.00350346i
$35$	6.26320e19	+	6.26320e19i	0.0895112	+	0.0895112i
$36$	1.85559e21	+	4.27572e20i	1.81301	+	0.417759i
$37$	−1.14792e21	+	1.14792e21i	−0.774794	+	0.774794i	−0.978940	−	0.204146i	$-0.934558\pi$
$37$	−1.14792e21	+	1.14792e21i	−0.774794	+	0.774794i	0.204146	+	0.978940i	$0.434558\pi$
$38$	−3.14094e21	−	3.57192e20i	−1.47904	−	0.168199i
$39$		−	2.66457e21i		−	0.883598i
$40$	6.30426e20	+	2.22796e20i	0.148533	+	0.0524926i
$41$			2.52651e21i			0.426520i	0.976995	+	0.213260i	$0.0684081\pi$
$41$			2.52651e21i			0.426520i	−0.976995	+	0.213260i	$0.931592\pi$
$42$	−1.25937e21	+	1.10741e22i	−0.153563	+	1.35034i
$43$	3.23875e19	−	3.23875e19i	0.00287444	−	0.00287444i	−0.705668	−	0.708543i	$-0.749353\pi$
$43$	3.23875e19	−	3.23875e19i	0.00287444	−	0.00287444i	0.708543	+	0.705668i	$0.249353\pi$
$44$	7.51365e21	+	1.20131e22i	0.488922	+	0.781704i
$45$	4.31387e21	+	4.31387e21i	0.207252	+	0.207252i
$46$	6.96408e21	+	8.75125e21i	0.248675	+	0.312492i
$47$	1.55896e22			0.416402			0.208201	−	0.978086i	$-0.433239\pi$
$47$	1.55896e22			0.416402			0.208201	+	0.978086i	$0.433239\pi$
$48$	2.74590e22	+	7.95284e22i	0.551986	+	1.59869i
$49$	2.32826e22			0.354310
$50$	−5.24138e22	−	6.58646e22i	−0.607226	−	0.763057i
$51$	7.58816e20	+	7.58816e20i	0.00672882	+	0.00672882i
$52$	6.49207e22	−	4.06051e22i	0.442933	−	0.277036i
$53$	1.50907e23	−	1.50907e23i	0.796134	−	0.796134i	−0.186350	−	0.982483i	$-0.559666\pi$
$53$	1.50907e23	−	1.50907e23i	0.796134	−	0.796134i	0.982483	+	0.186350i	$0.0596657\pi$
$54$	−4.01189e22	+	3.52781e23i	−0.164450	+	1.44607i
$55$			4.53955e22i			0.145250i
$56$	−2.89006e23	+	1.38074e23i	−0.725051	+	0.346396i
$57$		−	1.27439e24i		−	2.51764i
$58$	9.38139e23	+	1.06687e23i	1.46551	+	0.166660i
$59$	6.11665e23	−	6.11665e23i	0.758598	−	0.758598i	−0.217469	−	0.976067i	$-0.569780\pi$
$59$	6.11665e23	−	6.11665e23i	0.758598	−	0.758598i	0.976067	+	0.217469i	$0.0697801\pi$
$60$	−6.05253e22	+	2.62670e23i	−0.0598267	+	0.259638i
$61$	−1.55517e24	−	1.55517e24i	−1.22978	−	1.22978i	−0.964048	−	0.265727i	$-0.914388\pi$
$61$	−1.55517e24	−	1.55517e24i	−1.22978	−	1.22978i	−0.265727	−	0.964048i	$-0.585612\pi$
$62$	−1.01346e24	+	8.06489e23i	−0.643453	+	0.512048i
$63$	−2.92242e24			−1.49501
$64$	−1.51922e24	+	1.88095e24i	−0.628335	+	0.777943i
$65$	2.45326e23			0.0823025
$66$	−4.46965e24	+	3.55686e24i	−1.22020	+	0.971009i
$67$	−1.01732e24	−	1.01732e24i	−0.226699	−	0.226699i	0.584613	−	0.811312i	$-0.301246\pi$
$67$	−1.01732e24	−	1.01732e24i	−0.226699	−	0.226699i	−0.811312	+	0.584613i	$0.801246\pi$
$68$	−6.92460e21	+	3.00517e22i	−0.00126335	+	0.00548275i
$69$	−3.18814e24	+	3.18814e24i	−0.477612	+	0.477612i
$70$	−1.01959e24	−	1.15949e23i	−0.125777	−	0.0143036i
$71$		−	6.70294e24i		−	0.682775i	−0.939923	−	0.341388i	$-0.889103\pi$
$71$		−	6.70294e24i		−	0.682775i	0.939923	−	0.341388i	$-0.110897\pi$
$72$	−1.99058e25	+	9.51005e24i	−1.67877	+	0.802036i
$73$			2.33739e25i			1.63634i	0.574978	+	0.818169i	$0.305011\pi$
$73$			2.33739e25i			1.63634i	−0.574978	+	0.818169i	$0.694989\pi$
$74$	2.12511e24	−	1.86870e25i	0.123810	−	1.08871i
$75$	2.39950e25	−	2.39950e25i	1.16625	−	1.16625i
$76$	3.10499e25	−	1.94204e25i	1.26205	−	0.789358i
$77$	−1.53765e25	−	1.53765e25i	−0.523882	−	0.523882i
$78$	1.92219e25	+	2.41548e25i	0.550199	+	0.691395i
$79$	−5.61337e25			−1.35288			−0.676438	−	0.736499i	$-0.736478\pi$
$79$	−5.61337e25			−1.35288			−0.676438	+	0.736499i	$0.736478\pi$
$80$	−7.32215e24	+	2.52814e24i	−0.148910	+	0.0514146i
$81$	−3.49480e25			−0.601000
$82$	−1.82260e25	−	2.29033e25i	−0.265585	−	0.333742i
$83$	3.04605e25	+	3.04605e25i	0.376862	+	0.376862i	0.869969	−	0.493107i	$-0.164139\pi$
$83$	3.04605e25	+	3.04605e25i	0.376862	+	0.376862i	−0.493107	+	0.869969i	$0.664139\pi$
$84$	−6.84712e25	−	1.09474e26i	−0.720671	−	1.15223i
$85$	−6.98639e22	+	6.98639e22i	−0.000626754	+	0.000626754i
$86$	−5.99585e22	+	5.27239e23i	−0.000459326	+	0.00403904i
$87$			3.80637e26i			2.49460i
$88$	−1.54773e26	−	5.46978e25i	−0.869322	−	0.307223i
$89$			4.02988e26i			1.94324i	0.236538	+	0.971622i	$0.423987\pi$
$89$			4.02988e26i			1.94324i	−0.236538	+	0.971622i	$0.576013\pi$
$90$	−7.02259e25	−	7.98620e24i	−0.291221	−	0.0331182i
$91$	−8.30976e25	+	8.30976e25i	−0.296845	+	0.296845i
$92$	−1.26261e26	−	2.90935e25i	−0.389165	−	0.0896727i
$93$	−3.69209e26	−	3.69209e26i	−0.983451	−	0.983451i
$94$	−1.41322e26	+	1.12461e26i	−0.325825	+	0.259285i
$95$	1.17333e26			0.234505
$96$	−8.22631e26	−	5.22853e26i	−1.42739	−	0.907231i
$97$	−1.05860e27			−1.59703			−0.798513	−	0.601978i	$-0.794380\pi$
$97$	−1.05860e27			−1.59703			−0.798513	+	0.601978i	$0.794380\pi$
$98$	−2.11061e26	+	1.67958e26i	−0.277239	+	0.220622i
$99$	−1.05908e27	−	1.05908e27i	−1.21298	−	1.21298i
$100$	9.50281e26	+	2.18967e26i	0.950281	+	0.218967i
$101$	−5.90888e26	+	5.90888e26i	−0.516615	+	0.516615i	−0.916545	−	0.399931i	$-0.869034\pi$
$101$	−5.90888e26	+	5.90888e26i	−0.516615	+	0.516615i	0.399931	+	0.916545i	$0.369034\pi$
$102$	−1.23528e25	−	1.40478e24i	−0.00945505	−	0.00107524i
$103$		−	2.53300e27i		−	1.69955i	−0.527147	−	0.849774i	$-0.676738\pi$
$103$		−	2.53300e27i		−	1.69955i	0.527147	−	0.849774i	$-0.323262\pi$
$104$	−2.95597e26	+	8.36424e26i	−0.174080	+	0.492580i
$105$		−	4.13685e26i		−	0.214099i
$106$	−2.79372e26	+	2.45663e27i	−0.127220	+	1.11869i
$107$	2.28539e27	−	2.28539e27i	0.916810	−	0.916810i	−0.0799861	−	0.996796i	$-0.525488\pi$
$107$	2.28539e27	−	2.28539e27i	0.916810	−	0.916810i	0.996796	+	0.0799861i	$0.0254876\pi$
$108$	−2.18124e27	−	3.48744e27i	−0.771762	−	1.23392i
$109$	2.29278e27	+	2.29278e27i	0.716317	+	0.716317i	0.967849	−	0.251532i	$-0.0809343\pi$
$109$	2.29278e27	+	2.29278e27i	0.716317	+	0.716317i	−0.251532	+	0.967849i	$0.580934\pi$
$110$	−3.27479e26	−	4.11519e26i	−0.0904444	−	0.113655i
$111$	7.58200e27			1.85321
$112$	1.62384e27	−	3.33652e27i	0.351642	−	0.722522i
$113$	−8.72077e27			−1.67493			−0.837464	−	0.546493i	$-0.815963\pi$
$113$	−8.72077e27			−1.67493			−0.837464	+	0.546493i	$0.815963\pi$
$114$	9.19334e27	+	1.15526e28i	1.56768	+	1.96999i
$115$	−2.93531e26	−	2.93531e26i	−0.0444870	−	0.0444870i
$116$	−9.27402e27	+	5.80050e27i	−1.25050	+	0.782137i
$117$	−5.72347e27	+	5.72347e27i	−0.687307	+	0.687307i
$118$	−1.13237e27	+	9.95735e27i	−0.121221	+	1.06595i
$119$		−	4.73290e25i		−	0.00452110i
$120$	−1.34620e27	−	2.81777e27i	−0.114859	−	0.240414i
$121$			1.96511e27i			0.149894i
$122$	2.53168e28	+	2.87906e27i	1.72803	+	0.196514i
$123$	8.34383e27	−	8.34383e27i	0.510090	−	0.510090i
$124$	3.36923e27	−	1.46219e28i	0.184645	−	0.801331i
$125$	4.47464e27	+	4.47464e27i	0.220025	+	0.220025i
$126$	2.64922e28	−	2.10820e28i	1.16981	−	0.930915i
$127$	2.20177e28			0.873820			0.436910	−	0.899505i	$-0.356073\pi$
$127$	2.20177e28			0.873820			0.436910	+	0.899505i	$0.356073\pi$
$128$	2.03022e26	−	2.80106e28i	0.00724783	−	0.999974i
$129$	−2.13920e26			−0.00687528
$130$	−2.22392e27	+	1.76976e27i	−0.0643998	+	0.0512481i
$131$	3.49163e28	+	3.49163e28i	0.911728	+	0.911728i	0.996408	−	0.0846801i	$-0.0269868\pi$
$131$	3.49163e28	+	3.49163e28i	0.911728	+	0.911728i	−0.0846801	+	0.996408i	$0.526987\pi$
$132$	1.48593e28	−	6.44871e28i	0.350148	−	1.51958i
$133$	−3.97434e28	+	3.97434e28i	−0.845801	+	0.845801i
$134$	1.65611e28	+	1.88336e27i	0.318548	+	0.0362258i
$135$		−	1.31785e28i		−	0.229277i
$136$	−1.54017e26	−	3.22377e26i	−0.00242545	−	0.00507678i
$137$			1.04934e29i			1.49688i	0.663200	+	0.748442i	$0.269198\pi$
$137$			1.04934e29i			1.49688i	−0.663200	+	0.748442i	$0.730802\pi$
$138$	5.90215e27	−	5.19000e28i	0.0763208	−	0.671119i
$139$	2.75751e28	−	2.75751e28i	0.323457	−	0.323457i	−0.526634	−	0.850092i	$-0.676546\pi$
$139$	2.75751e28	−	2.75751e28i	0.323457	−	0.323457i	0.850092	+	0.526634i	$0.176546\pi$
$140$	1.00792e28	−	6.30411e27i	0.107324	−	0.0671268i
$141$	−5.14846e28	−	5.14846e28i	−0.497989	−	0.497989i
$142$	4.83543e28	+	6.07634e28i	0.425151	+	0.534256i
$143$	−6.02290e28			−0.481692
$144$	1.11845e29	−	2.29808e29i	0.814183	−	1.67291i
$145$	−3.50452e28			−0.232359
$146$	−1.68617e29	−	2.11889e29i	−1.01891	−	1.28040i
$147$	−7.68909e28	−	7.68909e28i	−0.423731	−	0.423731i
$148$	1.15541e29	+	1.84731e29i	0.581038	+	0.928982i
$149$	−5.62779e28	+	5.62779e28i	−0.258418	+	0.258418i	−0.824410	−	0.565992i	$-0.808493\pi$
$149$	−5.62779e28	+	5.62779e28i	−0.258418	+	0.258418i	0.565992	+	0.824410i	$0.308493\pi$
$150$	−4.44214e28	+	3.90616e29i	−0.186363	+	1.63877i
$151$			3.30214e29i			1.26651i	0.773945	+	0.633253i	$0.218281\pi$
$151$			3.30214e29i			1.26651i	−0.773945	+	0.633253i	$0.781719\pi$
$152$	−1.41376e29	+	4.00040e29i	−0.496007	+	1.40351i
$153$		−	3.25986e27i		−	0.0104680i
$154$	2.50316e29	+	2.84663e28i	0.736136	+	0.0837146i
$155$	3.39930e28	−	3.39930e28i	0.0916033	−	0.0916033i
$156$	−3.48500e29	−	8.03025e28i	−0.861035	−	0.198402i
$157$	−1.99675e29	−	1.99675e29i	−0.452561	−	0.452561i	0.443643	−	0.896204i	$-0.353686\pi$
$157$	−1.99675e29	−	1.99675e29i	−0.452561	−	0.452561i	−0.896204	+	0.443643i	$0.853686\pi$
$158$	5.08862e29	−	4.04943e29i	1.05859	−	0.842409i
$159$	−9.96746e29			−1.90425
$160$	4.81389e28	−	7.57393e28i	0.0845038	−	0.132954i
$161$	1.98852e29			0.320908
$162$	3.16810e29	−	2.52111e29i	0.470268	−	0.374230i
$163$	−5.13733e28	−	5.13733e28i	−0.0701786	−	0.0701786i	0.671146	−	0.741325i	$-0.265802\pi$
$163$	−5.13733e28	−	5.13733e28i	−0.0701786	−	0.0701786i	−0.741325	+	0.671146i	$0.765802\pi$
$164$	3.30444e29	+	7.61419e28i	0.415629	+	0.0957705i
$165$	1.49919e29	−	1.49919e29i	0.173710	−	0.173710i
$166$	−4.95869e29	−	5.63910e28i	−0.529551	−	0.0602214i
$167$		−	2.19792e29i		−	0.216441i	−0.994127	−	0.108220i	$-0.965485\pi$
$167$		−	2.19792e29i		−	0.216441i	0.994127	−	0.108220i	$-0.0345152\pi$
$168$	1.41044e30	+	4.98456e29i	1.28138	+	0.452847i
$169$		−	8.67045e29i		−	0.727061i
$170$	1.29338e26	−	1.13732e27i	0.000100153	−	0.000880688i
$171$	−2.73739e30	+	2.73739e30i	−1.95834	+	1.95834i
$172$	−3.25991e27	−	5.21205e27i	−0.00215562	−	0.00344647i
$173$	1.51128e30	+	1.51128e30i	0.924110	+	0.924110i	0.997317	−	0.0732069i	$-0.0233233\pi$
$173$	1.51128e30	+	1.51128e30i	0.924110	+	0.924110i	−0.0732069	+	0.997317i	$0.523323\pi$
$174$	−2.74588e30	−	3.45055e30i	−1.55334	−	1.95197i
$175$	−1.49662e30			−0.783606
$176$	1.79763e30	−	6.20674e29i	0.871525	−	0.300914i
$177$	−4.04006e30			−1.81447
$178$	−2.90712e30	−	3.65316e30i	−1.21002	−	1.52054i
$179$	−1.59571e30	−	1.59571e30i	−0.615798	−	0.615798i	0.328653	−	0.944451i	$-0.393405\pi$
$179$	−1.59571e30	−	1.59571e30i	−0.615798	−	0.615798i	−0.944451	+	0.328653i	$0.893405\pi$
$180$	6.94222e29	−	4.34206e29i	0.248496	−	0.155424i
$181$	−1.57311e30	+	1.57311e30i	−0.522514	+	0.522514i	−0.918330	−	0.395816i	$-0.870462\pi$
$181$	−1.57311e30	+	1.57311e30i	−0.522514	+	0.522514i	0.395816	+	0.918330i	$0.370462\pi$
$182$	1.53837e29	−	1.35275e30i	0.0474348	−	0.417114i
$183$			1.02719e31i			2.94146i
$184$	1.35446e30	−	6.47097e29i	0.360350	−	0.172159i
$185$			6.98072e29i			0.172616i
$186$	6.01038e30	+	6.83511e29i	1.38190	+	0.157152i
$187$	1.71520e28	−	1.71520e28i	0.00366820	−	0.00366820i
$188$	4.69825e29	−	2.03897e30i	0.0934986	−	0.405769i
$189$	4.46387e30	+	4.46387e30i	0.826946	+	0.826946i
$190$	−1.06364e30	+	8.46428e29i	−0.183494	+	0.146021i
$191$	−1.72098e30			−0.276583			−0.138291	−	0.990392i	$-0.544161\pi$
$191$	−1.72098e30			−0.276583			−0.138291	+	0.990392i	$0.544161\pi$
$192$	1.12291e31	−	1.19462e30i	1.68181	−	0.178921i
$193$	−3.75238e30			−0.523942			−0.261971	−	0.965076i	$-0.584373\pi$
$193$	−3.75238e30			−0.523942			−0.261971	+	0.965076i	$0.584373\pi$
$194$	9.59636e30	−	7.63660e30i	1.24964	−	0.994436i
$195$	−8.10191e29	−	8.10191e29i	−0.0984283	−	0.0984283i
$196$	7.01670e29	−	3.04514e30i	0.0795566	−	0.345263i
$197$	1.03921e31	−	1.03921e31i	1.10004	−	1.10004i	0.105636	−	0.994405i	$-0.466312\pi$
$197$	1.03921e31	−	1.03921e31i	1.10004	−	1.10004i	0.994405	−	0.105636i	$-0.0336878\pi$
$198$	1.72409e31	+	1.96066e30i	1.70443	+	0.193831i
$199$			5.35860e30i			0.494920i	0.968898	+	0.247460i	$0.0795959\pi$
$199$			5.35860e30i			0.494920i	−0.968898	+	0.247460i	$0.920404\pi$
$200$	−1.01941e31	+	4.87025e30i	−0.879919	+	0.420385i
$201$			6.71945e30i			0.542234i
$202$	1.09390e30	−	9.61911e30i	0.0825533	−	0.725924i
$203$	1.18706e31	−	1.18706e31i	0.838063	−	0.838063i
$204$	1.22114e29	−	7.63773e28i	0.00806788	−	0.00504611i
$205$	7.68214e29	+	7.68214e29i	0.0475122	+	0.0475122i
$206$	1.82728e31	+	2.29621e31i	1.05827	+	1.32986i
$207$	1.36962e31			0.743021
$208$	−3.35424e30	−	9.71474e30i	−0.170506	−	0.493828i
$209$	−2.88060e31			−1.37248
$210$	2.98428e30	+	3.75013e30i	0.133315	+	0.167527i
$211$	−7.10583e30	−	7.10583e30i	−0.297716	−	0.297716i	0.542403	−	0.840119i	$-0.317515\pi$
$211$	−7.10583e30	−	7.10583e30i	−0.297716	−	0.297716i	−0.840119	+	0.542403i	$0.817515\pi$
$212$	−1.51893e31	−	2.42852e31i	−0.597041	−	0.954568i
$213$	−2.21365e31	+	2.21365e31i	−0.816554	+	0.816554i
$214$	−4.23090e30	+	3.72040e31i	−0.146503	+	1.28826i
$215$		−	1.96956e28i		−	0.000640397i
$216$	4.49314e31	+	1.58790e31i	1.37222	+	0.484951i
$217$			2.30284e31i			0.660781i
$218$	−3.73244e31	−	4.24459e30i	−1.00654	−	0.114465i
$219$	7.71926e31	−	7.71926e31i	1.95695	−	1.95695i
$220$	5.93731e30	+	1.36809e30i	0.141541	+	0.0326144i
$221$	−9.26926e28	−	9.26926e28i	−0.00207850	−	0.00207850i
$222$	−6.87322e31	+	5.46957e31i	−1.45009	+	1.15395i
$223$	−8.33436e31			−1.65484			−0.827421	−	0.561582i	$-0.810193\pi$
$223$	−8.33436e31			−1.65484			−0.827421	+	0.561582i	$0.810193\pi$
$224$	9.34891e30	+	4.19604e31i	0.174748	+	0.784317i
$225$	−1.03082e32			−1.81434
$226$	7.90554e31	−	6.29107e31i	1.31059	−	1.04294i
$227$	6.12716e30	+	6.12716e30i	0.0956997	+	0.0956997i	0.753336	−	0.657636i	$-0.228444\pi$
$227$	6.12716e30	+	6.12716e30i	0.0956997	+	0.0956997i	−0.657636	+	0.753336i	$0.728444\pi$
$228$	−1.66679e32	−	3.84066e31i	−2.45335	−	0.565309i
$229$	3.14572e30	−	3.14572e30i	0.0436457	−	0.0436457i	−0.684947	−	0.728593i	$-0.740175\pi$
$229$	3.14572e30	−	3.14572e30i	0.0436457	−	0.0436457i	0.728593	+	0.684947i	$0.240175\pi$
$230$	4.77841e30	+	5.43409e29i	0.0625112	+	0.00710888i
$231$			1.01562e32i			1.25306i
$232$	4.22264e31	−	1.19484e32i	0.491470	−	1.39067i
$233$		−	1.27066e32i		−	1.39548i	−0.716350	−	0.697741i	$-0.754188\pi$
$233$		−	1.27066e32i		−	1.39548i	0.716350	−	0.697741i	$-0.245812\pi$
$234$	1.05958e31	−	9.31729e31i	0.109829	−	0.965774i
$235$	4.74017e30	−	4.74017e30i	0.0463851	−	0.0463851i
$236$	−6.15662e31	−	9.84339e31i	−0.568892	−	0.909562i
$237$	1.85382e32	+	1.85382e32i	1.61795	+	1.61795i
$238$	3.41427e29	+	4.29046e29i	0.00281520	+	0.00353765i
$239$	1.72079e32			1.34077			0.670386	−	0.742012i	$-0.266128\pi$
$239$	1.72079e32			1.34077			0.670386	+	0.742012i	$0.266128\pi$
$240$	3.25307e31	+	1.58323e31i	0.239575	+	0.116598i
$241$	−1.35645e32			−0.944436			−0.472218	−	0.881482i	$-0.656546\pi$
$241$	−1.35645e32			−0.944436			−0.472218	+	0.881482i	$0.656546\pi$
$242$	−1.41761e31	−	1.78141e31i	−0.0933360	−	0.117289i
$243$	−4.98372e31	−	4.98372e31i	−0.310363	−	0.310363i
$244$	−2.50270e32	+	1.56533e32i	−1.47451	+	0.922240i
$245$	7.07931e30	−	7.07931e30i	0.0394684	−	0.0394684i
$246$	−1.54468e31	+	1.35830e32i	−0.0815106	+	0.716756i
$247$			1.55673e32i			0.777685i
$248$	7.49384e31	+	1.56856e32i	0.354492	+	0.741998i
$249$		−	2.01192e32i		−	0.901405i
$250$	−7.28429e31	−	8.28382e30i	−0.309170	−	0.0351593i
$251$	1.53881e31	−	1.53881e31i	0.0618856	−	0.0618856i	−0.675487	−	0.737372i	$-0.736066\pi$
$251$	1.53881e31	−	1.53881e31i	0.0618856	−	0.0618856i	0.737372	+	0.675487i	$0.236066\pi$
$252$	−8.80734e31	+	3.82225e32i	−0.335689	+	1.45684i
$253$	7.20637e31	+	7.20637e31i	0.260369	+	0.260369i
$254$	−1.99594e32	+	1.58833e32i	−0.683744	+	0.544110i
$255$	4.61452e29			0.00149911
$256$	2.00225e32	+	2.55386e32i	0.616992	+	0.786969i
$257$	−2.58993e32			−0.757165			−0.378583	−	0.925567i	$-0.623588\pi$
$257$	−2.58993e32			−0.757165			−0.378583	+	0.925567i	$0.623588\pi$
$258$	1.93922e30	−	1.54320e30i	0.00537975	−	0.00428110i
$259$	−2.36453e32	−	2.36453e32i	−0.622585	−	0.622585i
$260$	7.39343e30	−	3.20863e31i	0.0184802	−	0.0802009i
$261$	8.17607e32	−	8.17607e32i	1.94043	−	1.94043i
$262$	−5.68404e32	−	6.46399e31i	−1.28112	−	0.145691i
$263$			2.74826e32i			0.588376i	0.955748	+	0.294188i	$0.0950492\pi$
$263$			2.74826e32i			0.588376i	−0.955748	+	0.294188i	$0.904951\pi$
$264$	3.30501e32	+	6.91781e32i	0.672233	+	1.40707i
$265$		−	9.17700e31i		−	0.177371i
$266$	7.35763e31	−	6.46986e32i	0.135156	−	1.18848i
$267$	1.33087e33	−	1.33087e33i	2.32399	−	2.32399i
$268$	−1.63716e32	+	1.02397e32i	−0.271813	+	0.170008i
$269$	1.10355e32	+	1.10355e32i	0.174235	+	0.174235i	0.788837	−	0.614602i	$-0.210683\pi$
$269$	1.10355e32	+	1.10355e32i	0.174235	+	0.174235i	−0.614602	+	0.788837i	$0.710683\pi$
$270$	9.50684e31	+	1.19466e32i	0.142766	+	0.179404i
$271$	−1.60178e31			−0.0228833			−0.0114417	−	0.999935i	$-0.503642\pi$
$271$	−1.60178e31			−0.0228833			−0.0114417	+	0.999935i	$0.503642\pi$
$272$	3.72178e30	+	1.81134e30i	0.00505907	+	0.00246218i
$273$	5.48861e32			0.710014
$274$	−7.56982e32	−	9.51244e32i	−0.932079	−	1.17128i
$275$	−5.42374e32	−	5.42374e32i	−0.635781	−	0.635781i
$276$	3.20897e32	+	5.13060e32i	0.358173	+	0.572659i
$277$	9.77915e32	−	9.77915e32i	1.03950	−	1.03950i	0.0403123	−	0.999187i	$-0.487165\pi$
$277$	9.77915e32	−	9.77915e32i	1.03950	−	1.03950i	0.999187	−	0.0403123i	$-0.0128353\pi$
$278$	−5.10493e31	+	4.48897e32i	−0.0516874	+	0.454508i
$279$			1.58612e33i			1.52996i
$280$	−4.58926e31	+	1.29858e32i	−0.0421803	+	0.119354i
$281$		−	1.21410e33i		−	1.06346i	−0.846915	−	0.531728i	$-0.821543\pi$
$281$		−	1.21410e33i		−	1.06346i	0.846915	−	0.531728i	$-0.178457\pi$
$282$	8.38122e32	+	9.53126e31i	0.699752	+	0.0795770i
$283$	−4.00884e32	+	4.00884e32i	−0.319081	+	0.319081i	−0.848414	−	0.529333i	$-0.822442\pi$
$283$	−4.00884e32	+	4.00884e32i	−0.319081	+	0.319081i	0.529333	+	0.848414i	$0.322442\pi$
$284$	−8.76681e32	−	2.02008e32i	−0.665341	−	0.153310i
$285$	−3.87493e32	−	3.87493e32i	−0.280452	−	0.280452i
$286$	5.45987e32	−	4.34486e32i	0.376912	−	0.299940i
$287$	−5.20424e32			−0.342729
$288$	6.43921e32	+	2.89009e33i	0.404607	+	1.81599i
$289$	−1.66766e33			−0.999968
$290$	3.17691e32	−	2.52812e32i	0.181816	−	0.144685i
$291$	3.49602e33	+	3.49602e33i	1.90994	+	1.90994i
$292$	3.05709e33	+	7.04424e32i	1.59455	+	0.367422i
$293$	−1.87597e33	+	1.87597e33i	−0.934358	+	0.934358i	−0.997974	−	0.0636162i	$-0.979737\pi$
$293$	−1.87597e33	+	1.87597e33i	−0.934358	+	0.934358i	0.0636162	+	0.997974i	$0.479737\pi$
$294$	1.25171e33	+	1.42347e32i	0.595409	+	0.0677109i
$295$		−	3.71967e32i		−	0.169008i
$296$	−2.38004e33	−	8.41118e32i	−1.03311	−	0.365106i
$297$			3.23541e33i			1.34189i
$298$	1.04186e32	−	9.16151e32i	0.0412944	−	0.363118i
$299$	3.89445e32	−	3.89445e32i	0.147532	−	0.147532i
$300$	−2.41517e33	−	3.86145e33i	−0.874603	−	1.39834i
$301$	6.67134e30	+	6.67134e30i	0.00230975	+	0.00230975i
$302$	−2.38213e33	−	2.99345e33i	−0.788628	−	0.991011i
$303$	3.90283e33			1.23567
$304$	−1.60424e33	−	4.64631e33i	−0.485822	−	1.40707i
$305$	−9.45734e32			−0.273982
$306$	2.35163e31	+	2.95512e31i	0.00651823	+	0.00819099i
$307$	−1.63853e33	−	1.63853e33i	−0.434595	−	0.434595i	0.455593	−	0.890188i	$-0.349427\pi$
$307$	−1.63853e33	−	1.63853e33i	−0.434595	−	0.434595i	−0.890188	+	0.455593i	$0.849427\pi$
$308$	−2.47451e33	+	1.54770e33i	−0.628137	+	0.392873i
$309$	−8.36527e33	+	8.36527e33i	−2.03255	+	2.03255i
$310$	−6.29306e31	+	5.53374e32i	−0.0146379	+	0.128717i
$311$		−	4.94909e33i		−	1.10220i	−0.834439	−	0.551100i	$-0.814208\pi$
$311$		−	4.94909e33i		−	1.10220i	0.834439	−	0.551100i	$-0.185792\pi$
$312$	3.73851e33	−	1.78609e33i	0.797281	−	0.380904i
$313$		−	1.65900e33i		−	0.338843i	−0.985544	−	0.169422i	$-0.945810\pi$
$313$		−	1.65900e33i		−	0.338843i	0.985544	−	0.169422i	$-0.0541899\pi$
$314$	3.25052e33	+	3.69654e32i	0.635919	+	0.0723178i
$315$	−8.88593e32	+	8.88593e32i	−0.166537	+	0.166537i
$316$	−1.69171e33	+	7.34176e33i	−0.303774	+	1.31833i
$317$	−4.70672e33	−	4.70672e33i	−0.809875	−	0.809875i	0.174739	−	0.984615i	$-0.444092\pi$
$317$	−4.70672e33	−	4.70672e33i	−0.809875	−	0.809875i	−0.984615	+	0.174739i	$0.944092\pi$
$318$	9.03568e33	−	7.19042e33i	1.49003	−	1.18574i
$319$	8.60380e33			1.35993
$320$	1.09988e32	+	1.03386e33i	0.0166656	+	0.156652i
$321$	−1.50950e34			−2.19289
$322$	−1.80263e33	+	1.43449e33i	−0.251103	+	0.199823i
$323$	−4.43325e31	−	4.43325e31i	−0.00592226	−	0.00592226i
$324$	−1.05323e33	+	4.57086e33i	−0.134948	+	0.585653i
$325$	−2.93109e33	+	2.93109e33i	−0.360250	+	0.360250i
$326$	8.36310e32	+	9.51065e31i	0.0986120	+	0.0112143i
$327$		−	1.51439e34i		−	1.71334i
$328$	−3.54481e33	+	1.69355e33i	−0.384854	+	0.183866i
$329$			3.21121e33i			0.334599i
$330$	−2.77543e32	+	2.44055e33i	−0.0277582	+	0.244089i
$331$	−1.10862e34	+	1.10862e34i	−1.06440	+	1.06440i	−0.0666228	+	0.997778i	$0.521222\pi$
$331$	−1.10862e34	+	1.10862e34i	−1.06440	+	1.06440i	−0.997778	+	0.0666228i	$0.978778\pi$
$332$	4.90194e33	−	3.06595e33i	0.451860	−	0.282619i
$333$	−1.62861e34	−	1.62861e34i	−1.44152	−	1.44152i
$334$	1.58556e33	+	1.99245e33i	0.134773	+	0.169360i
$335$	−6.18657e32			−0.0505063
$336$	−1.63817e34	+	5.65615e33i	−1.28463	+	0.443548i
$337$	5.40659e33			0.407305			0.203652	−	0.979043i	$-0.434719\pi$
$337$	5.40659e33			0.407305			0.203652	+	0.979043i	$0.434719\pi$
$338$	6.25477e33	+	7.85991e33i	0.452726	+	0.568908i
$339$	2.88004e34	+	2.88004e34i	2.00310	+	2.00310i
$340$	7.03203e30	+	1.12430e31i	0.000470019	+	0.000751481i
$341$	−8.34548e33	+	8.34548e33i	−0.536126	+	0.536126i
$342$	5.06768e33	−	4.45622e34i	0.312937	−	2.75178i
$343$			1.83316e34i			1.08825i
$344$	6.71508e31	+	2.37315e31i	0.00383277	+	0.00135452i
$345$			1.93878e33i			0.106407i
$346$	−2.46023e34	−	2.79781e33i	−1.29852	−	0.147670i
$347$	2.00821e33	−	2.00821e33i	0.101944	−	0.101944i	−0.654295	−	0.756239i	$-0.727035\pi$
$347$	2.00821e33	−	2.00821e33i	0.101944	−	0.101944i	0.756239	+	0.654295i	$0.227035\pi$
$348$	4.97838e34	+	1.14713e34i	2.43090	+	0.560137i
$349$	−1.84746e34	−	1.84746e34i	−0.867824	−	0.867824i	0.124408	−	0.992231i	$-0.460297\pi$
$349$	−1.84746e34	−	1.84746e34i	−0.867824	−	0.867824i	−0.992231	+	0.124408i	$0.960297\pi$
$350$	1.35671e34	−	1.07965e34i	0.613153	−	0.487936i
$351$	1.74847e34			0.760349
$352$	−1.18184e34	+	1.85945e34i	−0.494575	+	0.778140i
$353$	4.51337e34			1.81778			0.908892	−	0.417031i	$-0.136929\pi$
$353$	4.51337e34			1.81778			0.908892	+	0.417031i	$0.136929\pi$
$354$	3.66239e34	−	2.91446e34i	1.41978	−	1.12983i
$355$	−2.03810e33	−	2.03810e33i	−0.0760577	−	0.0760577i
$356$	5.27070e34	+	1.21449e34i	1.89362	+	0.436335i
$357$	−1.56305e32	+	1.56305e32i	−0.00540693	+	0.00540693i
$358$	2.59767e34	+	2.95411e33i	0.865293	+	0.0984025i
$359$			4.04626e32i			0.0129801i	0.999979	+	0.00649006i	$0.00206586\pi$
$359$			4.04626e32i			0.0129801i	−0.999979	+	0.00649006i	$0.997934\pi$
$360$	−3.16093e33	+	8.94419e33i	−0.0976631	+	0.276349i
$361$			4.08536e34i			1.21586i
$362$	2.91227e33	−	2.56088e34i	0.0834960	−	0.734214i
$363$	6.48980e33	−	6.48980e33i	0.179263	−	0.179263i
$364$	8.36405e33	+	1.33727e34i	0.222612	+	0.355918i
$365$	7.10709e33	+	7.10709e33i	0.182280	+	0.182280i
$366$	−7.41007e34	−	9.31170e34i	−1.83159	−	2.30162i
$367$	1.68697e34			0.401896			0.200948	−	0.979602i	$-0.435598\pi$
$367$	1.68697e34			0.401896			0.200948	+	0.979602i	$0.435598\pi$
$368$	−7.61031e33	+	1.56370e34i	−0.174766	+	0.359093i
$369$	−3.58450e34			−0.793547
$370$	−5.03582e33	−	6.32815e33i	−0.107485	−	0.135068i
$371$	3.10846e34	+	3.10846e34i	0.639732	+	0.639732i
$372$	−5.94160e34	+	3.71621e34i	−1.17916	+	0.737515i
$373$	−1.68074e34	+	1.68074e34i	−0.321685	+	0.321685i	−0.849413	−	0.527728i	$-0.823044\pi$
$373$	−1.68074e34	+	1.68074e34i	−0.321685	+	0.321685i	0.527728	+	0.849413i	$0.323044\pi$
$374$	−3.17532e31	+	2.79219e32i	−0.000586167	+	0.00515440i
$375$		−	2.95551e34i		−	0.526271i
$376$	1.04498e34	+	2.18728e34i	0.179504	+	0.375724i
$377$		−	4.64965e34i		−	0.770570i
$378$	−7.26677e34	−	8.26389e33i	−1.16199	−	0.132143i
$379$	−1.66209e34	+	1.66209e34i	−0.256463	+	0.256463i	−0.823614	−	0.567151i	$-0.808046\pi$
$379$	−1.66209e34	+	1.66209e34i	−0.256463	+	0.256463i	0.567151	+	0.823614i	$0.308046\pi$
$380$	3.53608e33	−	1.53460e34i	0.0526555	−	0.228517i
$381$	−7.27137e34	−	7.27137e34i	−1.04503	−	1.04503i
$382$	1.56010e34	−	1.24150e34i	0.216420	−	0.172223i
$383$	2.59069e34			0.346922			0.173461	−	0.984841i	$-0.444505\pi$
$383$	2.59069e34			0.346922			0.173461	+	0.984841i	$0.444505\pi$
$384$	−9.31759e34	+	9.18349e34i	−1.20457	+	1.18723i
$385$	−9.35080e33			−0.116716
$386$	3.40160e34	−	2.70693e34i	0.409973	−	0.326248i
$387$	4.59499e32	+	4.59499e32i	0.00534794	+	0.00534794i
$388$	−3.19031e34	+	1.38454e35i	−0.358595	+	1.55625i
$389$	5.02498e34	−	5.02498e34i	0.545525	−	0.545525i	−0.379618	−	0.925143i	$-0.623945\pi$
$389$	5.02498e34	−	5.02498e34i	0.545525	−	0.545525i	0.925143	+	0.379618i	$0.123945\pi$
$390$	1.31892e34	+	1.49989e33i	0.138307	+	0.0157285i
$391$			2.21812e32i			0.00224698i
$392$	1.56065e34	+	3.26665e34i	0.152737	+	0.319698i
$393$		−	2.30623e35i		−	2.18073i
$394$	−1.92387e34	+	1.69174e35i	−0.175783	+	1.54573i
$395$	−1.70681e34	+	1.70681e34i	−0.150704	+	0.150704i
$396$	−1.70436e35	+	1.06600e35i	−1.45437	+	0.909647i
$397$	−4.80211e34	−	4.80211e34i	−0.396059	−	0.396059i	0.480781	−	0.876840i	$-0.340353\pi$
$397$	−4.80211e34	−	4.80211e34i	−0.396059	−	0.396059i	−0.876840	+	0.480781i	$0.840353\pi$
$398$	−3.86564e34	−	4.85767e34i	−0.308177	−	0.387263i
$399$	2.62506e35			2.02304
$400$	5.72776e34	−	1.17689e35i	0.426751	−	0.876849i
$401$	−1.61818e35			−1.16568			−0.582839	−	0.812587i	$-0.698058\pi$
$401$	−1.61818e35			−1.16568			−0.582839	+	0.812587i	$0.698058\pi$
$402$	−4.84734e34	−	6.09130e34i	−0.337638	−	0.424286i
$403$	4.51005e34	+	4.51005e34i	0.303783	+	0.303783i
$404$	5.94748e34	+	9.50902e34i	0.387422	+	0.619423i
$405$	−1.06263e34	+	1.06263e34i	−0.0669483	+	0.0669483i
$406$	−2.19759e34	+	1.93243e35i	−0.133920	+	1.17761i
$407$		−	1.71381e35i		−	1.01027i
$408$	−5.56011e32	+	1.57329e33i	−0.00317082	+	0.00897218i
$409$			1.92583e35i			1.06256i	0.847197	+	0.531279i	$0.178289\pi$
$409$			1.92583e35i			1.06256i	−0.847197	+	0.531279i	$0.821711\pi$
$410$	−1.25058e34	−	1.42218e33i	−0.0667620	−	0.00759229i
$411$	3.46545e35	−	3.46545e35i	1.79017	−	1.79017i
$412$	−3.31293e35	−	7.63376e34i	−1.65615	−	0.381615i
$413$	1.25994e35	+	1.25994e35i	0.609570	+	0.609570i
$414$	−1.24159e35	+	9.88031e34i	−0.581396	+	0.462664i
$415$	1.85237e34			0.0839611
$416$	1.00488e35	+	6.38687e34i	0.440914	+	0.280239i
$417$	−1.82134e35			−0.773667
$418$	2.61131e35	−	2.07803e35i	1.07394	−	0.854619i
$419$	9.70453e33	+	9.70453e33i	0.0386443	+	0.0386443i	0.726165	−	0.687521i	$-0.241301\pi$
$419$	9.70453e33	+	9.70453e33i	0.0386443	+	0.0386443i	−0.687521	+	0.726165i	$0.741301\pi$
$420$	−5.41061e34	−	1.24673e34i	−0.208632	−	0.0480736i
$421$	−2.89305e35	+	2.89305e35i	−1.08031	+	1.08031i	−0.0838275	+	0.996480i	$0.526714\pi$
$421$	−2.89305e35	+	2.89305e35i	−1.08031	+	1.08031i	−0.996480	+	0.0838275i	$0.973286\pi$
$422$	1.15676e35	+	1.31549e34i	0.418337	+	0.0475740i
$423$			2.21177e35i			0.774722i
$424$	3.12885e35	+	1.10575e35i	1.06156	+	0.375162i
$425$		−	1.66943e33i		−	0.00548678i
$426$	4.09810e34	−	3.60362e35i	0.130483	−	1.14739i
$427$	3.20342e35	−	3.20342e35i	0.988184	−	0.988184i
$428$	−2.30032e35	−	3.67782e35i	−0.687539	−	1.09926i
$429$	1.98907e35	+	1.98907e35i	0.576071	+	0.576071i
$430$	1.42082e32	+	1.78544e32i	0.000398762	+	0.000501095i
$431$	−3.51318e35			−0.955557			−0.477779	−	0.878480i	$-0.658558\pi$
$431$	−3.51318e35			−0.955557			−0.477779	+	0.878480i	$0.658558\pi$
$432$	−5.21860e35	+	1.80184e35i	−1.37570	+	0.474992i
$433$	−6.43365e35			−1.64388			−0.821941	−	0.569573i	$-0.807109\pi$
$433$	−6.43365e35			−1.64388			−0.821941	+	0.569573i	$0.807109\pi$
$434$	−1.66125e35	−	2.08757e35i	−0.411455	−	0.517046i
$435$	1.15737e35	+	1.15737e35i	0.277886	+	0.277886i
$436$	3.68972e35	−	2.30776e35i	0.858868	−	0.537185i
$437$	1.86262e35	−	1.86262e35i	0.420362	−	0.420362i
$438$	−1.42905e35	+	1.25662e36i	−0.312714	+	2.74982i
$439$			7.57628e35i			1.60763i	0.594882	+	0.803813i	$0.297199\pi$
$439$			7.57628e35i			1.60763i	−0.594882	+	0.803813i	$0.702801\pi$
$440$	−6.36920e34	+	3.04291e34i	−0.131061	+	0.0626149i
$441$			3.30322e35i			0.659199i
$442$	1.50895e33	+	1.71600e32i	0.00292061	+	0.000332137i
$443$	5.60049e34	−	5.60049e34i	0.105142	−	0.105142i	−0.652579	−	0.757721i	$-0.726313\pi$
$443$	5.60049e34	−	5.60049e34i	0.105142	−	0.105142i	0.757721	+	0.652579i	$0.226313\pi$
$444$	2.28500e35	−	9.91653e35i	0.416118	−	1.80588i
$445$	1.22533e35	+	1.22533e35i	0.216468	+	0.216468i
$446$	7.55525e35	−	6.01232e35i	1.29488	−	1.03044i
$447$	3.71716e35			0.618102
$448$	−3.87448e35	−	3.12937e35i	−0.625115	−	0.504897i
$449$	1.94251e35			0.304114			0.152057	−	0.988372i	$-0.451410\pi$
$449$	1.94251e35			0.304114			0.152057	+	0.988372i	$0.451410\pi$
$450$	9.34457e35	−	7.43623e35i	1.41968	−	1.12975i
$451$	−1.88601e35	−	1.88601e35i	−0.278074	−	0.278074i
$452$	−2.62819e35	+	1.14059e36i	−0.376087	+	1.63216i
$453$	1.09054e36	−	1.09054e36i	1.51466	−	1.51466i
$454$	−9.97445e34	−	1.13431e34i	−0.134473	−	0.0152925i
$455$			5.05334e34i			0.0661340i
$456$	1.78803e36	−	8.54239e35i	2.27169	−	1.08531i
$457$		−	5.66586e35i		−	0.698872i	−0.936960	−	0.349436i	$-0.886373\pi$
$457$		−	5.66586e35i		−	0.698872i	0.936960	−	0.349436i	$-0.113627\pi$
$458$	−5.82362e33	+	5.12094e34i	−0.00697443	+	0.0613290i
$459$	−4.97930e33	+	4.97930e33i	−0.00579025	+	0.00579025i
$460$	−4.72373e34	+	2.95449e34i	−0.0533401	+	0.0333620i
$461$	−1.03642e35	−	1.03642e35i	−0.113651	−	0.113651i	0.647994	−	0.761645i	$-0.275608\pi$
$461$	−1.03642e35	−	1.03642e35i	−0.113651	−	0.113651i	−0.761645	+	0.647994i	$0.775608\pi$
$462$	−7.32659e35	−	9.20680e35i	−0.780253	−	0.980487i
$463$	−1.30902e36			−1.35395			−0.676976	−	0.736005i	$-0.736710\pi$
$463$	−1.30902e36			−1.35395			−0.676976	+	0.736005i	$0.736710\pi$
$464$	4.79158e35	+	1.38776e36i	0.481377	+	1.39419i
$465$	−2.24524e35			−0.219103
$466$	9.16641e35	+	1.15188e36i	0.868939	+	1.09193i
$467$	−9.34032e35	−	9.34032e35i	−0.860170	−	0.860170i	0.131188	−	0.991358i	$-0.458121\pi$
$467$	−9.34032e35	−	9.34032e35i	−0.860170	−	0.860170i	−0.991358	+	0.131188i	$0.958121\pi$
$468$	5.76087e35	+	9.21065e35i	0.515429	+	0.824084i
$469$	2.09554e35	−	2.09554e35i	0.182164	−	0.182164i
$470$	−8.77540e33	+	7.71656e34i	−0.00741218	+	0.0651783i
$471$			1.31885e36i			1.08247i
$472$	1.26820e36	+	4.48189e35i	1.01151	+	0.357474i
$473$			4.83538e33i			0.00374805i
$474$	−3.01785e36	−	3.43195e35i	−2.27347	−	0.258543i
$475$	−1.40186e36	+	1.40186e36i	−1.02646	+	1.02646i
$476$	−6.19019e33	−	1.42636e33i	−0.00440565	−	0.00101516i
$477$	2.14100e36	+	2.14100e36i	1.48122	+	1.48122i
$478$	−1.55992e36	+	1.24136e36i	−1.04912	+	0.834872i
$479$	−1.45139e36			−0.948977			−0.474488	−	0.880262i	$-0.657367\pi$
$479$	−1.45139e36			−0.948977			−0.474488	+	0.880262i	$0.657367\pi$
$480$	−4.09109e35	+	9.11507e34i	−0.260065	+	0.0579433i
$481$	−9.26174e35			−0.572445
$482$	1.22964e36	−	9.78526e35i	0.738999	−	0.588081i
$483$	−6.56709e35	−	6.56709e35i	−0.383784	−	0.383784i
$484$	2.57018e35	+	5.92229e34i	0.146067	+	0.0336571i
$485$	−3.21878e35	+	3.21878e35i	−0.177901	+	0.177901i
$486$	8.11304e35	+	9.22628e34i	0.436108	+	0.0495949i
$487$		−	1.68312e36i		−	0.879984i	−0.898002	−	0.439992i	$-0.854981\pi$
$487$		−	1.68312e36i		−	0.879984i	0.898002	−	0.439992i	$-0.145019\pi$
$488$	1.13953e36	−	3.22443e36i	0.579506	−	1.63978i
$489$			3.39322e35i			0.167858i
$490$	−1.31058e34	+	1.15245e35i	−0.00630691	+	0.0554592i
$491$	−2.72215e36	+	2.72215e36i	−1.27442	+	1.27442i	−0.330672	+	0.943746i	$0.607275\pi$
$491$	−2.72215e36	+	2.72215e36i	−1.27442	+	1.27442i	−0.943746	+	0.330672i	$0.892725\pi$
$492$	−8.39834e35	−	1.34275e36i	−0.382529	−	0.611600i
$493$	1.32413e34	+	1.32413e34i	0.00586808	+	0.00586808i
$494$	−1.12301e36	−	1.41120e36i	−0.484249	−	0.608520i
$495$	−6.44051e35			−0.270240
$496$	−1.81087e36	−	8.81327e35i	−0.739409	−	0.359861i
$497$	1.38071e36			0.548643
$498$	1.45138e36	+	1.82384e36i	0.561287	+	0.705328i
$499$	1.54633e36	+	1.54633e36i	0.582029	+	0.582029i	0.935460	−	0.353432i	$-0.114985\pi$
$499$	1.54633e36	+	1.54633e36i	0.582029	+	0.582029i	−0.353432	+	0.935460i	$0.614985\pi$
$500$	7.20093e35	−	4.50387e35i	0.263811	−	0.165003i
$501$	−7.25865e35	+	7.25865e35i	−0.258849	+	0.258849i
$502$	−2.84877e34	+	2.50504e35i	−0.00988911	+	0.0869589i
$503$		−	5.41126e35i		−	0.182865i	−0.995811	−	0.0914325i	$-0.970855\pi$
$503$		−	5.41126e35i		−	0.182865i	0.995811	−	0.0914325i	$-0.0291446\pi$
$504$	−1.95893e36	−	4.10029e36i	−0.644475	−	1.34897i
$505$			3.59332e35i			0.115096i
$506$	−1.17313e36	−	1.33410e35i	−0.365859	−	0.0416061i
$507$	−2.86342e36	+	2.86342e36i	−0.869517	+	0.869517i
$508$	6.63551e35	−	2.87971e36i	0.196207	−	0.851507i
$509$	−4.49220e36	−	4.49220e36i	−1.29351	−	1.29351i	−0.932602	−	0.360907i	$-0.882467\pi$
$509$	−4.49220e36	−	4.49220e36i	−1.29351	−	1.29351i	−0.360907	−	0.932602i	$-0.617533\pi$
$510$	−4.18315e33	+	3.32887e33i	−0.00117302	+	0.000933468i
$511$	−4.81468e36			−1.31488
$512$	−3.65741e36	−	8.70715e35i	−0.972812	−	0.231596i
$513$	8.36249e36			2.16646
$514$	2.34782e36	−	1.86835e36i	0.592464	−	0.471472i
$515$	−7.70188e35	−	7.70188e35i	−0.189321	−	0.189321i
$516$	−6.44695e33	+	2.79787e34i	−0.00154377	+	0.00669972i
$517$	−1.16374e36	+	1.16374e36i	−0.271478	+	0.271478i
$518$	3.84924e36	+	4.37742e35i	0.874829	+	0.0994870i
$519$		−	9.98206e36i		−	2.21035i
$520$	1.64444e35	+	3.44203e35i	0.0354792	+	0.0742626i
$521$			4.42671e36i			0.930620i	0.885148	+	0.465310i	$0.154057\pi$
$521$			4.42671e36i			0.930620i	−0.885148	+	0.465310i	$0.845943\pi$
$522$	−1.51362e36	+	1.33099e37i	−0.310074	+	2.72661i
$523$	6.40929e36	−	6.40929e36i	1.27949	−	1.27949i	0.338537	−	0.940953i	$-0.390068\pi$
$523$	6.40929e36	−	6.40929e36i	1.27949	−	1.27949i	0.940953	−	0.338537i	$-0.109932\pi$
$524$	5.61899e36	−	3.51444e36i	1.09317	−	0.683728i
$525$	4.94260e36	+	4.94260e36i	0.937141	+	0.937141i
$526$	−1.98256e36	−	2.49135e36i	−0.366370	−	0.460390i
$527$	−2.56874e34			−0.00462677
$528$	−7.98648e36	−	3.88692e36i	−1.40216	−	0.682413i
$529$	4.91127e36			0.840509
$530$	6.62019e35	+	8.31912e35i	0.110445	+	0.138788i
$531$	8.67802e36	+	8.67802e36i	1.41138	+	1.41138i
$532$	4.00031e36	+	6.39581e36i	0.634288	+	1.01412i
$533$	−1.01923e36	+	1.01923e36i	−0.157564	+	0.157564i
$534$	−2.46382e36	+	2.16654e37i	−0.371366	+	3.26557i
$535$		−	1.38980e36i		−	0.204256i
$536$	7.45430e35	−	2.10928e36i	0.106827	−	0.302280i
$537$			1.05397e37i			1.47291i
$538$	−1.79647e36	−	2.04298e35i	−0.244827	−	0.0278422i
$539$	−1.73801e36	+	1.73801e36i	−0.230996	+	0.230996i
$540$	−1.72362e36	−	3.97163e35i	−0.223423	−	0.0514817i
$541$	−7.33992e36	−	7.33992e36i	−0.927958	−	0.927958i	0.0696156	−	0.997574i	$-0.477823\pi$
$541$	−7.33992e36	−	7.33992e36i	−0.927958	−	0.927958i	−0.997574	+	0.0696156i	$0.977823\pi$
$542$	1.45205e35	−	1.15551e35i	0.0179056	−	0.0142490i
$543$	1.03904e37			1.24978
$544$	−4.68055e34	+	1.04284e34i	−0.00549176	+	0.00122358i
$545$	1.39429e36			0.159588
$546$	−4.97552e36	+	3.95943e36i	−0.555569	+	0.442111i
$547$	−7.96527e36	−	7.96527e36i	−0.867704	−	0.867704i	0.124514	−	0.992218i	$-0.460263\pi$
$547$	−7.96527e36	−	7.96527e36i	−0.867704	−	0.867704i	−0.992218	+	0.124514i	$0.960263\pi$
$548$	1.37244e37	+	3.16241e36i	1.45866	+	0.336109i
$549$	2.20641e37	−	2.20641e37i	2.28802	−	2.28802i
$550$	8.82934e36	+	1.00409e36i	0.893371	+	0.101596i
$551$		−	2.22381e37i		−	2.19559i
$552$	−6.61015e36	−	2.33606e36i	−0.636845	−	0.225065i
$553$		−	1.15627e37i		−	1.08710i
$554$	−1.81040e36	+	1.59196e37i	−0.166109	+	1.46066i
$555$	2.30539e36	−	2.30539e36i	0.206438	−	0.206438i
$556$	−2.77552e36	−	4.43759e36i	−0.242569	−	0.387827i
$557$	4.22207e36	+	4.22207e36i	0.360148	+	0.360148i	0.863867	−	0.503720i	$-0.168036\pi$
$557$	4.22207e36	+	4.22207e36i	0.360148	+	0.360148i	−0.503720	+	0.863867i	$0.668036\pi$
$558$	−1.14421e37	−	1.43784e37i	−0.952673	−	1.19715i
$559$	2.61313e34			0.00212374
$560$	−5.20759e35	−	1.50825e36i	−0.0413141	−	0.119656i
$561$	−1.13289e35			−0.00877385
$562$	8.75840e36	+	1.10060e37i	0.662193	+	0.832129i
$563$	3.05274e35	+	3.05274e35i	0.0225334	+	0.0225334i	0.718284	−	0.695750i	$-0.244928\pi$
$563$	3.05274e35	+	3.05274e35i	0.0225334	+	0.0225334i	−0.695750	+	0.718284i	$0.744928\pi$
$564$	−8.28530e36	+	5.18210e36i	−0.597091	+	0.373455i
$565$	−2.65165e36	+	2.65165e36i	−0.186578	+	0.186578i
$566$	7.42149e35	−	6.52602e36i	0.0509882	−	0.448359i
$567$		−	7.19876e36i		−	0.482932i
$568$	9.40453e36	−	4.49305e36i	0.616077	−	0.294333i
$569$		−	3.28180e36i		−	0.209941i	−0.994475	−	0.104970i	$-0.966525\pi$
$569$		−	3.28180e36i		−	0.209941i	0.994475	−	0.104970i	$-0.0334748\pi$
$570$	6.30803e36	+	7.17359e35i	0.394079	+	0.0448153i
$571$	−2.22460e37	+	2.22460e37i	−1.35726	+	1.35726i	−0.479987	+	0.877275i	$0.659359\pi$
$571$	−2.22460e37	+	2.22460e37i	−1.35726	+	1.35726i	−0.877275	+	0.479987i	$0.840641\pi$
$572$	−1.81513e36	+	7.87738e36i	−0.108159	+	0.469392i
$573$	5.68355e36	+	5.68355e36i	0.330775	+	0.330775i
$574$	4.71773e36	−	3.75428e36i	0.268178	−	0.213411i
$575$	7.01406e36			0.389452
$576$	−2.66861e37	−	2.15540e37i	−1.44737	−	1.16903i
$577$	−2.42403e36			−0.128429			−0.0642147	−	0.997936i	$-0.520454\pi$
$577$	−2.42403e36			−0.128429			−0.0642147	+	0.997936i	$0.520454\pi$
$578$	1.51176e37	−	1.20303e37i	0.782452	−	0.622660i
$579$	1.23923e37	+	1.23923e37i	0.626600	+	0.626600i
$580$	−1.05616e36	+	4.58357e36i	−0.0521738	+	0.226426i
$581$	−6.27441e36	+	6.27441e36i	−0.302827	+	0.302827i
$582$	−5.69120e37	−	6.47213e36i	−2.68376	−	0.305202i
$583$			2.25301e37i			1.03810i
$584$	−3.27947e37	+	1.56678e37i	−1.47649	+	0.705397i
$585$			3.48057e36i			0.153125i
$586$	3.47295e36	−	3.05391e37i	0.149307	−	1.31292i
$587$	−1.82714e37	+	1.82714e37i	−0.767641	+	0.767641i	−0.977691	−	0.210050i	$-0.932637\pi$
$587$	−1.82714e37	+	1.82714e37i	−0.767641	+	0.767641i	0.210050	+	0.977691i	$0.432637\pi$
$588$	−1.23739e37	+	7.73932e36i	−0.508056	+	0.317767i
$589$	2.15704e37	+	2.15704e37i	0.865569	+	0.865569i
$590$	2.68333e36	+	3.37195e36i	0.105238	+	0.132245i
$591$	−6.86399e37			−2.63115
$592$	2.76432e37	−	9.54445e36i	1.03573	−	0.357608i
$593$	−1.84307e37			−0.674999			−0.337500	−	0.941326i	$-0.609581\pi$
$593$	−1.84307e37			−0.674999			−0.337500	+	0.941326i	$0.609581\pi$
$594$	−2.33399e37	−	2.93295e37i	−0.835568	−	1.05000i
$595$	−1.43909e34	−	1.43909e34i	−0.000503627	−	0.000503627i
$596$	5.66455e36	+	9.05666e36i	0.193794	+	0.309844i
$597$	1.76968e37	−	1.76968e37i	0.591892	−	0.591892i
$598$	−7.20973e35	+	6.33981e36i	−0.0235751	+	0.207305i
$599$			6.18104e36i			0.197606i	0.995107	+	0.0988028i	$0.0315013\pi$
$599$			6.18104e36i			0.197606i	−0.995107	+	0.0988028i	$0.968499\pi$
$600$	4.97501e37	+	1.75819e37i	1.55508	+	0.549573i
$601$			1.44078e37i			0.440343i	0.975461	+	0.220172i	$0.0706618\pi$
$601$			1.44078e37i			0.440343i	−0.975461	+	0.220172i	$0.929338\pi$
$602$	−1.08603e35	−	1.23505e34i	−0.00324556	−	0.000369091i
$603$	1.44333e37	−	1.44333e37i	0.421777	−	0.421777i
$604$	4.31889e37	+	9.95172e36i	1.23417	+	0.284380i
$605$	5.97513e35	+	5.97513e35i	0.0166974	+	0.0166974i
$606$	−3.53798e37	+	2.81546e37i	−0.966885	+	0.769429i
$607$	1.17063e37			0.312875			0.156438	−	0.987688i	$-0.449999\pi$
$607$	1.17063e37			0.312875			0.156438	+	0.987688i	$0.449999\pi$
$608$	4.80607e37	+	3.05467e37i	1.25630	+	0.798485i
$609$	−7.84056e37			−2.00453
$610$	8.57325e36	−	6.82243e36i	0.214384	−	0.170603i
$611$	6.28907e36	+	6.28907e36i	0.153826	+	0.153826i
$612$	−4.26359e35	−	9.82430e34i	−0.0102007	−	0.00235048i
$613$	3.64520e37	−	3.64520e37i	0.853109	−	0.853109i	−0.137406	−	0.990515i	$-0.543876\pi$
$613$	3.64520e37	−	3.64520e37i	0.853109	−	0.853109i	0.990515	+	0.137406i	$0.0438765\pi$
$614$	2.66737e37	+	3.03337e36i	0.610675	+	0.0694469i
$615$		−	5.07406e36i		−	0.113643i
$616$	1.12669e37	−	3.18810e37i	0.246869	−	0.698542i
$617$		−	1.86352e37i		−	0.399469i	−0.979850	−	0.199735i	$-0.935992\pi$
$617$		−	1.86352e37i		−	0.399469i	0.979850	−	0.199735i	$-0.0640080\pi$
$618$	1.54865e37	−	1.36179e38i	0.324794	−	2.85605i
$619$	5.41285e37	−	5.41285e37i	1.11071	−	1.11071i	0.117660	−	0.993054i	$-0.462461\pi$
$619$	5.41285e37	−	5.41285e37i	1.11071	−	1.11071i	0.993054	−	0.117660i	$-0.0375392\pi$
$620$	−3.42151e36	−	5.47041e36i	−0.0686957	−	0.109833i
$621$	−2.09204e37	−	2.09204e37i	−0.410992	−	0.410992i
$622$	3.57023e37	+	4.48644e37i	0.686318	+	0.862446i
$623$	−8.30095e37			−1.56149
$624$	−2.10056e37	+	4.31604e37i	−0.386673	+	0.794500i
$625$	−5.14124e37			−0.926163
$626$	1.19679e37	+	1.50392e37i	0.210991	+	0.265137i
$627$	9.51320e37	+	9.51320e37i	1.64140	+	1.64140i
$628$	−3.21332e37	+	2.00979e37i	−0.542623	+	0.339387i
$629$	2.63756e35	−	2.63756e35i	0.00435932	−	0.00435932i
$630$	1.64504e36	−	1.44655e37i	0.0266120	−	0.234010i
$631$			4.51978e37i			0.715683i	0.933782	+	0.357842i	$0.116487\pi$
$631$			4.51978e37i			0.715683i	−0.933782	+	0.357842i	$0.883513\pi$
$632$	−3.76270e37	−	7.87582e37i	−0.583202	−	1.22072i
$633$			4.69342e37i			0.712097i
$634$	7.66210e37	+	8.71347e36i	1.13800	+	0.129415i
$635$	6.69472e36	−	6.69472e36i	0.0973391	−	0.0973391i
$636$	−3.00391e37	+	1.30365e38i	−0.427578	+	1.85562i
$637$	9.39255e36	+	9.39255e36i	0.130888	+	0.130888i
$638$	−7.79950e37	+	6.20669e37i	−1.06411	+	0.846800i
$639$	9.50983e37			1.27031
$640$	−8.45521e36	−	8.57867e36i	−0.110585	−	0.112199i
$641$	−6.29462e37			−0.806094			−0.403047	−	0.915179i	$-0.632049\pi$
$641$	−6.29462e37			−0.806094			−0.403047	+	0.915179i	$0.632049\pi$
$642$	1.36839e38	−	1.08894e38i	1.71588	−	1.36547i
$643$	−5.14310e37	−	5.14310e37i	−0.631505	−	0.631505i	0.316941	−	0.948445i	$-0.397344\pi$
$643$	−5.14310e37	−	5.14310e37i	−0.631505	−	0.631505i	−0.948445	+	0.316941i	$0.897344\pi$
$644$	5.99282e36	−	2.60079e37i	0.0720564	−	0.312713i
$645$	−6.50447e34	+	6.50447e34i	−0.000765872	+	0.000765872i
$646$	7.21691e35	+	8.20719e34i	0.00832171	+	0.000946358i
$647$		−	5.60498e37i		−	0.632945i	−0.948602	−	0.316473i	$-0.897501\pi$
$647$		−	5.60498e37i		−	0.632945i	0.948602	−	0.316473i	$-0.102499\pi$
$648$	−2.34260e37	−	4.90336e37i	−0.259081	−	0.542289i
$649$			9.13202e37i			0.989153i
$650$	5.42627e36	−	4.77154e37i	0.0575667	−	0.506207i
$651$	7.60516e37	−	7.60516e37i	0.790250	−	0.790250i
$652$	−8.26739e36	+	5.17089e36i	−0.0841445	+	0.0526288i
$653$	−7.44579e37	−	7.44579e37i	−0.742306	−	0.742306i	0.230716	−	0.973021i	$-0.425893\pi$
$653$	−7.44579e37	−	7.44579e37i	−0.742306	−	0.742306i	−0.973021	+	0.230716i	$0.925893\pi$
$654$	1.09246e38	+	1.37282e38i	1.06686	+	1.34065i
$655$	2.12333e37			0.203124
$656$	1.99173e37	−	4.09242e37i	0.186650	−	0.383511i
$657$	−3.31618e38			−3.04443
$658$	−2.31654e37	−	2.91102e37i	−0.208348	−	0.261816i
$659$	8.17724e37	+	8.17724e37i	0.720532	+	0.720532i	0.968714	−	0.248181i	$-0.0798329\pi$
$659$	8.17724e37	+	8.17724e37i	0.720532	+	0.720532i	−0.248181	+	0.968714i	$0.579833\pi$
$660$	−1.50899e37	−	2.41261e37i	−0.130269	−	0.208279i
$661$	2.29366e36	−	2.29366e36i	0.0194003	−	0.0194003i	−0.697340	−	0.716740i	$-0.745633\pi$
$661$	2.29366e36	−	2.29366e36i	0.0194003	−	0.0194003i	0.716740	+	0.697340i	$0.245633\pi$
$662$	2.05237e37	−	1.80473e38i	0.170088	−	1.49565i
$663$			6.12236e35i			0.00497149i
$664$	−2.23195e37	+	6.31555e37i	−0.177589	+	0.502507i
$665$			2.41688e37i			0.188436i
$666$	2.65122e38	+	3.01501e37i	2.02556	+	0.230349i
$667$	−5.56328e37	+	5.56328e37i	−0.416517	+	0.416517i
$668$	−2.87467e37	−	6.62391e36i	−0.210914	−	0.0485995i
$669$	2.75243e38	+	2.75243e38i	1.97908	+	1.97908i
$670$	5.60824e36	−	4.46293e36i	0.0395200	−	0.0314492i
$671$	2.32184e38			1.60353
$672$	1.07700e38	−	1.69450e38i	0.729004	−	1.14698i
$673$	−2.81473e38			−1.86738			−0.933691	−	0.358080i	$-0.883431\pi$
$673$	−2.81473e38			−1.86738			−0.933691	+	0.358080i	$0.883431\pi$
$674$	−4.90117e37	+	3.90026e37i	−0.318707	+	0.253621i
$675$	1.57453e38	+	1.57453e38i	1.00358	+	1.00358i
$676$	−1.13401e38	−	2.61303e37i	−0.708496	−	0.163254i
$677$	−2.53880e37	+	2.53880e37i	−0.155483	+	0.155483i	−0.780562	−	0.625079i	$-0.785067\pi$
$677$	−2.53880e37	+	2.53880e37i	−0.155483	+	0.155483i	0.625079	+	0.780562i	$0.285067\pi$
$678$	−4.68844e38	−	5.33177e37i	−2.81467	−	0.320089i
$679$		−	2.18055e38i		−	1.28329i
$680$	−1.44853e35	−	5.11917e34i	−0.000835711	−	0.000295345i
$681$		−	4.04700e37i		−	0.228901i
$682$	1.54498e37	−	1.35857e38i	0.0856712	−	0.753342i
$683$	1.62063e38	−	1.62063e38i	0.881055	−	0.881055i	−0.112587	−	0.993642i	$-0.535914\pi$
$683$	1.62063e38	−	1.62063e38i	0.881055	−	0.881055i	0.993642	+	0.112587i	$0.0359135\pi$
$684$	2.75527e38	+	4.40522e38i	1.46861	+	2.34806i
$685$	3.19063e37	+	3.19063e37i	0.166745	+	0.166745i
$686$	−1.32242e38	−	1.66179e38i	−0.677634	−	0.851533i
$687$	−2.07775e37			−0.104395
$688$	−7.79931e35	+	2.69289e35i	−0.00384248	+	0.00132671i
$689$	1.21757e38			0.588212
$690$	−1.39861e37	−	1.75754e37i	−0.0662575	−	0.0832610i
$691$	2.35093e38	+	2.35093e38i	1.09216	+	1.09216i	0.995298	+	0.0968623i	$0.0308806\pi$
$691$	2.35093e38	+	2.35093e38i	1.09216	+	1.09216i	0.0968623	+	0.995298i	$0.469119\pi$
$692$	2.43207e38	−	1.52116e38i	1.10801	−	0.693014i
$693$	2.18155e38	−	2.18155e38i	0.974690	−	0.974690i
$694$	−3.71776e36	+	3.26918e37i	−0.0162903	+	0.143247i
$695$		−	1.67690e37i		−	0.0720631i
$696$	−5.34052e38	+	2.55145e38i	−2.25091	+	1.07538i
$697$		−	5.80515e35i		−	0.00239978i
$698$	3.00749e38	+	3.42017e37i	1.21943	+	0.138675i
$699$	−4.19637e38	+	4.19637e38i	−1.66890	+	1.66890i
$700$	−4.51039e37	+	1.95744e38i	−0.175950	+	0.763597i
$701$	−3.65097e38	−	3.65097e38i	−1.39706	−	1.39706i	−0.808330	−	0.588730i	$-0.799628\pi$
$701$	−3.65097e38	−	3.65097e38i	−1.39706	−	1.39706i	−0.588730	−	0.808330i	$-0.700372\pi$
$702$	−1.58502e38	+	1.26133e38i	−0.594955	+	0.473454i
$703$	−4.42965e38			−1.63107
$704$	−2.70027e37	−	2.53819e38i	−0.0975387	−	0.916838i
$705$	−3.13089e37			−0.110947
$706$	−4.09145e38	+	3.25590e38i	−1.42237	+	1.13190i
$707$	−1.21714e38	−	1.21714e38i	−0.415125	−	0.415125i
$708$	−1.21756e38	+	5.28402e38i	−0.407419	+	1.76813i
$709$	2.34645e38	−	2.34645e38i	0.770348	−	0.770348i	−0.207819	−	0.978167i	$-0.566637\pi$
$709$	2.34645e38	−	2.34645e38i	0.770348	−	0.770348i	0.978167	+	0.207819i	$0.0666367\pi$
$710$	3.31784e37	+	3.77310e36i	0.106873	+	0.0121538i
$711$		−	7.96399e38i		−	2.51705i
$712$	−5.65411e38	+	2.70127e38i	−1.75341	+	0.837700i
$713$		−	1.07925e38i		−	0.328408i
$714$	2.89364e35	−	2.54449e36i	0.000864010	−	0.00759759i
$715$	−1.83133e37	+	1.83133e37i	−0.0536580	+	0.0536580i
$716$	−2.56794e38	+	1.60614e38i	−0.738345	+	0.461803i
$717$	−5.68291e38	−	5.68291e38i	−1.60348	−	1.60348i
$718$	−2.91893e36	−	3.66801e36i	−0.00808246	−	0.0101566i
$719$	−1.62402e38			−0.441318			−0.220659	−	0.975351i	$-0.570821\pi$
$719$	−1.62402e38			−0.441318			−0.220659	+	0.975351i	$0.570821\pi$
$720$	−3.58681e37	−	1.03883e38i	−0.0956577	−	0.277049i
$721$	5.21761e38			1.36567
$722$	−2.94714e38	−	3.70345e38i	−0.757091	−	0.951381i
$723$	4.47967e38	+	4.47967e38i	1.12948	+	1.12948i
$724$	1.58339e38	+	2.53157e38i	0.391847	+	0.626497i
$725$	4.18710e38	−	4.18710e38i	1.01707	−	1.01707i
$726$	−1.20144e37	+	1.05648e38i	−0.0286457	+	0.251893i
$727$		−	1.27856e38i		−	0.299232i	−0.988744	−	0.149616i	$-0.952196\pi$
$727$		−	1.27856e38i		−	0.299232i	0.988744	−	0.149616i	$-0.0478037\pi$
$728$	−1.72291e38	−	6.08885e37i	−0.395812	−	0.139882i
$729$			5.95675e38i			1.34335i
$730$	−1.15697e38	−	1.31572e37i	−0.256132	−	0.0291277i
$731$	−7.44166e33	+	7.44166e33i	−1.61728e−5	+	1.61728e-5i
$732$	1.34347e39	+	3.09567e38i	2.86635	+	0.660474i
$733$	4.14426e38	+	4.14426e38i	0.868047	+	0.868047i	0.992256	−	0.124209i	$-0.0396395\pi$
$733$	4.14426e38	+	4.14426e38i	0.868047	+	0.868047i	−0.124209	+	0.992256i	$0.539639\pi$
$734$	−1.52926e38	+	1.21696e38i	−0.314475	+	0.250253i
$735$	−4.67590e37			−0.0944031
$736$	−4.38146e37	−	1.96652e38i	−0.0868498	−	0.389805i
$737$	1.51884e38			0.295598
$738$	3.24941e38	−	2.58582e38i	0.620932	−	0.494126i
$739$	4.16254e38	+	4.16254e38i	0.781014	+	0.781014i	0.980002	−	0.198988i	$-0.0637655\pi$
$739$	4.16254e38	+	4.16254e38i	0.781014	+	0.781014i	−0.198988	+	0.980002i	$0.563766\pi$
$740$	9.13012e37	+	2.10379e37i	0.168209	+	0.0387592i
$741$	5.14110e38	−	5.14110e38i	0.930059	−	0.930059i
$742$	−5.06029e38	−	5.75465e37i	−0.898924	−	0.102227i
$743$		−	1.10351e39i		−	1.92498i	−0.271314	−	0.962491i	$-0.587458\pi$
$743$		−	1.10351e39i		−	1.92498i	0.271314	−	0.962491i	$-0.412542\pi$
$744$	2.70533e38	−	7.65502e38i	0.463431	−	1.31133i
$745$			3.42238e37i			0.0575729i
$746$	3.11152e37	−	2.73608e38i	0.0514042	−	0.452018i
$747$	−4.32159e38	+	4.32159e38i	−0.701158	+	0.701158i
$748$	−1.72641e36	−	2.76023e36i	−0.00275088	−	0.00439819i
$749$	4.70756e38	+	4.70756e38i	0.736701	+	0.736701i
$750$	2.13207e38	+	2.67922e38i	0.327699	+	0.411795i
$751$	−9.93115e37			−0.149920			−0.0749601	−	0.997187i	$-0.523883\pi$
$751$	−9.93115e37			−0.149920			−0.0749601	+	0.997187i	$0.523883\pi$
$752$	−2.52518e38	−	1.22897e38i	−0.374414	−	0.182222i
$753$	−1.01639e38			−0.148022
$754$	3.35421e38	+	4.21499e38i	0.479818	+	0.602953i
$755$	1.00405e38	+	1.00405e38i	0.141082	+	0.141082i
$756$	7.18360e38	−	4.49303e38i	0.991512	−	0.620148i
$757$	−8.65995e38	+	8.65995e38i	−1.17414	+	1.17414i	−0.192931	+	0.981212i	$0.561799\pi$
$757$	−8.65995e38	+	8.65995e38i	−1.17414	+	1.17414i	−0.981212	+	0.192931i	$0.938201\pi$
$758$	3.07699e37	−	2.70572e38i	0.0409819	−	0.360371i
$759$		−	4.75982e38i		−	0.622768i
$760$	7.86495e37	+	1.64623e38i	0.101091	+	0.211596i
$761$			3.39164e38i			0.428269i	0.976804	+	0.214134i	$0.0686931\pi$
$761$			3.39164e38i			0.428269i	−0.976804	+	0.214134i	$0.931307\pi$
$762$	1.18371e39	+	1.34614e38i	1.46843	+	0.166992i
$763$	−4.72279e38	+	4.72279e38i	−0.575596	+	0.575596i
$764$	−5.18654e37	+	2.25088e38i	−0.0621037	+	0.269520i
$765$	−9.91196e35	−	9.91196e35i	−0.00116609	−	0.00116609i
$766$	−2.34850e38	+	1.86889e38i	−0.271458	+	0.216021i
$767$	4.93511e38			0.560479
$768$	1.82168e38	−	1.50466e39i	0.203281	−	1.67904i
$769$	7.51316e37			0.0823791			0.0411895	−	0.999151i	$-0.486885\pi$
$769$	7.51316e37			0.0823791			0.0411895	+	0.999151i	$0.486885\pi$
$770$	8.47667e37	−	6.74557e37i	0.0913272	−	0.0726765i
$771$	8.55326e38	+	8.55326e38i	0.905520	+	0.905520i
$772$	−1.13086e38	+	4.90776e38i	−0.117646	+	0.510563i
$773$	4.60267e38	−	4.60267e38i	0.470529	−	0.470529i	−0.431557	−	0.902086i	$-0.642035\pi$
$773$	4.60267e38	−	4.60267e38i	0.470529	−	0.470529i	0.902086	+	0.431557i	$0.142035\pi$
$774$	−7.48022e36	−	8.50663e35i	−0.00751469	−	0.000854583i
$775$			8.12278e38i			0.801921i
$776$	−7.09588e38	−	1.48526e39i	−0.688451	−	1.44102i
$777$			1.56178e39i			1.48914i
$778$	−9.30266e37	+	8.18020e38i	−0.0871731	+	0.766548i
$779$	−4.87474e38	+	4.87474e38i	−0.448947	+	0.448947i
$780$	−1.30382e38	+	8.15484e37i	−0.118016	+	0.0738139i
$781$	5.00367e38	+	5.00367e38i	0.445143	+	0.445143i
$782$	−1.60013e36	−	2.01077e36i	−0.00139915	−	0.00175821i
$783$	−2.49772e39			−2.14664
$784$	−3.77129e38	−	1.83544e38i	−0.318583	−	0.155050i
$785$	−1.21426e38			−0.100826
$786$	1.66369e39	+	2.09063e39i	1.35790	+	1.70637i
$787$	1.00678e38	+	1.00678e38i	0.0807746	+	0.0807746i	0.746340	−	0.665565i	$-0.231809\pi$
$787$	1.00678e38	+	1.00678e38i	0.0807746	+	0.0807746i	−0.665565	+	0.746340i	$0.731809\pi$
$788$	−1.04600e39	−	1.67237e39i	−0.824949	−	1.31895i
$789$	9.07615e38	−	9.07615e38i	0.703659	−	0.703659i
$790$	3.15978e37	−	2.77852e38i	0.0240819	−	0.211762i
$791$		−	1.79635e39i		−	1.34589i
$792$	7.76027e38	−	2.19585e39i	0.571593	−	1.61739i
$793$		−	1.25476e39i		−	0.908601i
$794$	7.81738e38	+	8.89005e37i	0.556525	+	0.0632889i
$795$	−3.03071e38	+	3.03071e38i	−0.212123	+	0.212123i
$796$	7.00854e38	+	1.61493e38i	0.482282	+	0.111129i
$797$	8.65594e38	+	8.65594e38i	0.585635	+	0.585635i	0.936446	−	0.350811i	$-0.114094\pi$
$797$	8.65594e38	+	8.65594e38i	0.585635	+	0.585635i	−0.350811	+	0.936446i	$0.614094\pi$
$798$	−2.37966e39	+	1.89369e39i	−1.58298	+	1.25971i
$799$	−3.58200e36			−0.00234285
$800$	3.29763e38	+	1.48006e39i	0.212074	+	0.951843i
$801$	−5.71741e39			−3.61543
$802$	1.46691e39	−	1.16734e39i	0.912116	−	0.725845i
$803$	−1.74483e39	−	1.74483e39i	−1.06683	−	1.06683i
$804$	8.78840e38	+	2.02505e38i	0.528388	+	0.121753i
$805$	6.04630e37	−	6.04630e37i	0.0357475	−	0.0357475i
$806$	−7.34194e38	−	8.34938e37i	−0.426863	−	0.0485435i
$807$		−	7.28895e38i		−	0.416747i
$808$	−1.22512e39	−	4.32964e38i	−0.688851	−	0.243444i
$809$			1.14023e38i			0.0630502i	0.999503	+	0.0315251i	$0.0100364\pi$
$809$			1.14023e38i			0.0630502i	−0.999503	+	0.0315251i	$0.989964\pi$
$810$	1.96723e37	−	1.72986e38i	0.0106981	−	0.0940729i
$811$	8.12692e38	−	8.12692e38i	0.434655	−	0.434655i	−0.455553	−	0.890208i	$-0.650559\pi$
$811$	8.12692e38	−	8.12692e38i	0.434655	−	0.434655i	0.890208	+	0.455553i	$0.150559\pi$
$812$	−1.19482e39	−	1.91031e39i	−0.628485	−	1.00484i
$813$	5.28991e37	+	5.28991e37i	0.0273669	+	0.0273669i
$814$	1.23632e39	+	1.55360e39i	0.629076	+	0.790514i
$815$	−3.12412e37			−0.0156351
$816$	−6.30924e36	−	1.82732e37i	−0.00310570	−	0.00899492i
$817$	1.24979e37			0.00605117
$818$	−1.38927e39	−	1.74580e39i	−0.661634	−	0.831427i
$819$	−1.17895e39	−	1.17895e39i	−0.552284	−	0.552284i
$820$	1.23627e38	−	7.73232e37i	0.0569673	−	0.0356306i
$821$	1.01983e39	−	1.01983e39i	0.462269	−	0.462269i	−0.437129	−	0.899399i	$-0.644005\pi$
$821$	1.01983e39	−	1.01983e39i	0.462269	−	0.462269i	0.899399	+	0.437129i	$0.144005\pi$
$822$	−6.41553e38	+	5.64143e39i	−0.286064	+	2.51547i
$823$			1.01341e39i			0.444517i	0.974988	+	0.222259i	$0.0713429\pi$
$823$			1.01341e39i			0.444517i	−0.974988	+	0.222259i	$0.928657\pi$
$824$	3.55392e39	−	1.69790e39i	1.53352	−	0.732646i
$825$			3.58239e39i			1.52070i
$826$	−2.05106e39	−	2.33250e38i	−0.856542	−	0.0974073i
$827$	2.80573e39	−	2.80573e39i	1.15271	−	1.15271i	0.166706	−	0.986007i	$-0.446687\pi$
$827$	2.80573e39	−	2.80573e39i	1.15271	−	1.15271i	0.986007	−	0.166706i	$-0.0533132\pi$
$828$	4.12765e38	−	1.79133e39i	0.166837	−	0.724048i
$829$	2.31506e39	+	2.31506e39i	0.920610	+	0.920610i	0.997072	−	0.0764628i	$-0.0243626\pi$
$829$	2.31506e39	+	2.31506e39i	0.920610	+	0.920610i	−0.0764628	+	0.997072i	$0.524363\pi$
$830$	−1.67921e38	+	1.33628e38i	−0.0656976	+	0.0522809i
$831$	−6.45915e39			−2.48634
$832$	−1.37168e39	+	1.45928e38i	−0.519504	+	0.0552679i
$833$	−5.34962e36			−0.00199350
$834$	1.65108e39	−	1.31390e39i	0.605377	−	0.481747i
$835$	−6.68301e37	−	6.68301e37i	−0.0241104	−	0.0241104i
$836$	−8.68130e38	+	3.76755e39i	−0.308177	+	1.33744i
$837$	2.42273e39	−	2.42273e39i	0.846274	−	0.846274i
$838$	−1.57981e38	−	1.79658e37i	−0.0543013	−	0.00617523i
$839$			5.11615e39i			1.73044i	0.501392	+	0.865220i	$0.332821\pi$
$839$			5.11615e39i			1.73044i	−0.501392	+	0.865220i	$0.667179\pi$
$840$	5.80419e38	−	2.77297e38i	0.193184	−	0.0922944i
$841$			3.58896e39i			1.17550i
$842$	5.35585e38	−	4.70962e39i	0.172630	−	1.51800i
$843$	−4.00958e39	+	4.00958e39i	−1.27182	+	1.27182i
$844$	−1.14353e39	+	7.15226e38i	−0.356963	+	0.223265i
$845$	−2.63634e38	−	2.63634e38i	−0.0809909	−	0.0809909i
$846$	−1.59555e39	−	2.00501e39i	−0.482404	−	0.606202i
$847$	−4.04783e38			−0.120447
$848$	−3.63403e39	+	1.25473e39i	−1.06425	+	0.367458i
$849$	2.64784e39			0.763200
$850$	1.20431e37	+	1.51337e37i	0.00341651	+	0.00429328i
$851$	1.10816e39	+	1.10816e39i	0.309424	+	0.309424i
$852$	2.22812e39	+	3.56238e39i	0.612355	+	0.979052i
$853$	1.30454e39	−	1.30454e39i	0.352894	−	0.352894i	−0.508291	−	0.861185i	$-0.669723\pi$
$853$	1.30454e39	−	1.30454e39i	0.352894	−	0.352894i	0.861185	+	0.508291i	$0.169723\pi$
$854$	−5.93044e38	+	5.21487e39i	−0.157909	+	1.38855i
$855$			1.66467e39i			0.436299i
$856$	4.73842e39	+	1.67459e39i	1.22247	+	0.432028i
$857$		−	4.57806e39i		−	1.16263i	−0.813680	−	0.581313i	$-0.802539\pi$
$857$		−	4.57806e39i		−	1.16263i	0.813680	−	0.581313i	$-0.197461\pi$
$858$	−3.23802e39	−	3.68233e38i	−0.809470	−	0.0920543i
$859$	1.29831e39	−	1.29831e39i	0.319500	−	0.319500i	−0.529075	−	0.848575i	$-0.677461\pi$
$859$	1.29831e39	−	1.29831e39i	0.319500	−	0.319500i	0.848575	+	0.529075i	$0.177461\pi$
$860$	−2.57599e36	−	5.93568e35i	−0.000624044	−	0.000143794i
$861$	1.71870e39	+	1.71870e39i	0.409882	+	0.409882i
$862$	3.18476e39	−	2.53437e39i	0.747701	−	0.595006i
$863$	−3.94389e39			−0.911546			−0.455773	−	0.890096i	$-0.650637\pi$
$863$	−3.94389e39			−0.911546			−0.455773	+	0.890096i	$0.650637\pi$
$864$	3.43093e39	−	5.39805e39i	0.780685	−	1.22829i
$865$	9.19044e38			0.205882
$866$	5.83221e39	−	4.64116e39i	1.28630	−	1.02361i
$867$	5.50746e39	+	5.50746e39i	1.19590	+	1.19590i
$868$	3.01190e39	+	6.94011e38i	0.643908	+	0.148371i
$869$	4.19032e39	−	4.19032e39i	0.882023	−	0.882023i
$870$	−1.88409e39	−	2.14262e38i	−0.390474	−	0.0444053i
$871$		−	8.20810e38i		−	0.167493i
$872$	−1.68000e39	+	4.75376e39i	−0.337550	+	0.955134i
$873$		−	1.50189e40i		−	2.97129i
$874$	−3.44823e38	+	3.03217e39i	−0.0671725	+	0.590675i
$875$	−9.21708e38	+	9.21708e38i	−0.176801	+	0.176801i
$876$	−7.76969e39	−	1.24224e40i	−1.46757	−	2.34639i
$877$	1.85080e39	+	1.85080e39i	0.344242	+	0.344242i	0.857960	−	0.513717i	$-0.171732\pi$
$877$	1.85080e39	+	1.85080e39i	0.344242	+	0.344242i	−0.513717	+	0.857960i	$0.671732\pi$
$878$	−5.46545e39	−	6.86803e39i	−1.00104	−	1.25793i
$879$	1.23908e40			2.23486
$880$	3.57867e38	−	7.35313e38i	0.0635632	−	0.130604i
$881$	3.87424e38			0.0677660			0.0338830	−	0.999426i	$-0.489213\pi$
$881$	3.87424e38			0.0677660			0.0338830	+	0.999426i	$0.489213\pi$
$882$	−2.38291e39	−	2.99443e39i	−0.410470	−	0.515808i
$883$	−8.20275e38	−	8.20275e38i	−0.139152	−	0.139152i	0.634099	−	0.773252i	$-0.281371\pi$
$883$	−8.20275e38	−	8.20275e38i	−0.139152	−	0.139152i	−0.773252	+	0.634099i	$0.781371\pi$
$884$	−1.49168e37	+	9.32982e36i	−0.00249213	+	0.00155872i
$885$	−1.22842e39	+	1.22842e39i	−0.202122	+	0.202122i
$886$	−1.03681e38	+	9.11708e38i	−0.0168013	+	0.147741i
$887$		−	9.14863e39i		−	1.46011i	−0.683386	−	0.730057i	$-0.739493\pi$
$887$		−	9.14863e39i		−	1.46011i	0.683386	−	0.730057i	$-0.260507\pi$
$888$	5.08229e39	+	1.06379e40i	0.798885	+	1.67217i
$889$			4.53532e39i			0.702156i
$890$	−1.99472e39	−	2.26843e38i	−0.304171	−	0.0345908i
$891$	2.60882e39	−	2.60882e39i	0.391828	−	0.391828i
$892$	−2.51174e39	+	1.09006e40i	−0.371577	+	1.61259i
$893$	3.00790e39	+	3.00790e39i	0.438297	+	0.438297i
$894$	−3.36967e39	+	2.68152e39i	−0.483650	+	0.384880i
$895$	−9.70387e38			−0.137194
$896$	5.76977e39	+	4.18194e37i	0.803527	+	0.00582398i
$897$	−2.57229e39			−0.352876
$898$	−1.76092e39	+	1.40130e39i	−0.237962	+	0.189366i
$899$	−6.44267e39	−	6.44267e39i	−0.857650	−	0.857650i
$900$	−3.10660e39	+	1.34821e40i	−0.407391	+	1.76801i
$901$	−3.46739e37	+	3.46739e37i	−0.00447938	+	0.00447938i
$902$	3.07025e39	+	3.49154e38i	0.390738	+	0.0444354i
$903$		−	4.40643e37i		−	0.00552462i
$904$	−5.84562e39	−	1.22356e40i	−0.722033	−	1.51131i
$905$			9.56642e38i			0.116411i
$906$	−2.01889e39	+	1.77529e40i	−0.242037	+	2.12833i
$907$	5.93960e39	−	5.93960e39i	0.701550	−	0.701550i	−0.263193	−	0.964743i	$-0.584776\pi$
$907$	5.93960e39	−	5.93960e39i	0.701550	−	0.701550i	0.964743	+	0.263193i	$0.0847757\pi$
$908$	9.86030e38	−	6.16719e38i	0.114744	−	0.0717676i
$909$	−8.38324e39	−	8.38324e39i	−0.961169	−	0.961169i
$910$	−3.64543e38	−	4.58095e38i	−0.0411803	−	0.0517483i
$911$	4.87917e38			0.0543060			0.0271530	−	0.999631i	$-0.491356\pi$
$911$	4.87917e38			0.0543060			0.0271530	+	0.999631i	$0.491356\pi$
$912$	−1.00464e40	+	2.06425e40i	−1.10175	+	2.26377i
$913$	−4.54768e39			−0.491399
$914$	4.08729e39	+	5.13621e39i	0.435173	+	0.546851i
$915$	3.12330e39	+	3.12330e39i	0.327664	+	0.327664i
$916$	−3.16627e38	−	5.06233e38i	−0.0327310	−	0.0523313i
$917$	−7.19223e39	+	7.19223e39i	−0.732618	+	0.732618i
$918$	9.21809e36	−	8.10584e37i	0.000925262	−	0.00813620i
$919$		−	1.16631e40i		−	1.15360i	−0.816885	−	0.576801i	$-0.804301\pi$
$919$		−	1.16631e40i		−	1.15360i	0.816885	−	0.576801i	$-0.195699\pi$
$920$	2.15081e38	−	6.08594e38i	0.0209636	−	0.0593188i
$921$			1.08225e40i			1.03949i
$922$	1.68719e39	+	1.91870e38i	0.159697	+	0.0181610i
$923$	2.70407e39	−	2.70407e39i	0.252229	−	0.252229i
$924$	1.32834e40	+	3.06080e39i	1.22106	+	0.281360i
$925$	−8.34038e39	−	8.34038e39i	−0.755566	−	0.755566i
$926$	1.18665e40	−	9.44314e39i	1.05944	−	0.843078i
$927$	3.59371e40			3.16203
$928$	−1.43548e40	−	9.12374e39i	−1.24480	−	0.791180i
$929$	9.32143e39			0.796655			0.398328	−	0.917243i	$-0.369591\pi$
$929$	9.32143e39			0.796655			0.398328	+	0.917243i	$0.369591\pi$
$930$	2.03535e39	−	1.61969e39i	0.171443	−	0.136431i
$931$	4.49221e39	+	4.49221e39i	0.372941	+	0.372941i
$932$	−1.66190e40	−	3.82941e39i	−1.35985	−	0.313341i
$933$	−1.63444e40	+	1.63444e40i	−1.31816	+	1.31816i
$934$	1.52052e40	+	1.72916e39i	1.20867	+	0.137452i
$935$		−	1.04305e37i		−	0.000817238i
$936$	−1.18668e40	−	4.19379e39i	−0.916452	−	0.323879i
$937$		−	1.04934e40i		−	0.798785i	−0.916780	−	0.399392i	$-0.869221\pi$
$937$		−	1.04934e40i		−	0.798785i	0.916780	−	0.399392i	$-0.130779\pi$
$938$	−3.87943e38	+	3.41134e39i	−0.0291092	+	0.255969i
$939$	−5.47887e39	+	5.47887e39i	−0.405234	+	0.405234i
$940$	−4.77114e38	−	7.62825e38i	−0.0347853	−	0.0556159i
$941$	−1.12863e40	−	1.12863e40i	−0.811134	−	0.811134i	0.173670	−	0.984804i	$-0.444437\pi$
$941$	−1.12863e40	−	1.12863e40i	−0.811134	−	0.811134i	−0.984804	+	0.173670i	$0.944437\pi$
$942$	−9.51407e39	−	1.19556e40i	−0.674030	−	0.847005i
$943$	2.43902e39			0.170336
$944$	−1.47296e40	+	5.08575e39i	−1.01408	+	0.350133i
$945$	2.71458e39			0.184235
$946$	−3.48819e37	−	4.38336e37i	−0.00233383	−	0.00293276i
$947$	−9.07914e39	−	9.07914e39i	−0.598853	−	0.598853i	0.341154	−	0.940007i	$-0.389182\pi$
$947$	−9.07914e39	−	9.07914e39i	−0.598853	−	0.598853i	−0.940007	+	0.341154i	$0.889182\pi$
$948$	2.98331e40	−	1.86593e40i	1.93993	−	1.21334i
$949$	−9.42941e39	+	9.42941e39i	−0.604492	+	0.604492i
$950$	2.59524e39	−	2.28210e40i	0.164025	−	1.44234i
$951$			3.10880e40i			1.93711i
$952$	6.64048e37	−	3.17251e37i	0.00407944	−	0.00194897i
$953$			2.36197e40i			1.43061i	0.698814	+	0.715303i	$0.253711\pi$
$953$			2.36197e40i			1.43061i	−0.698814	+	0.715303i	$0.746289\pi$
$954$	−3.48535e40	−	3.96360e39i	−2.08134	−	0.236694i
$955$	−5.23282e38	+	5.23282e38i	−0.0308099	+	0.0308099i
$956$	5.18596e39	−	2.25062e40i	0.301056	−	1.30654i
$957$	−2.84141e40	−	2.84141e40i	−1.62638	−	1.62638i
$958$	1.31571e40	−	1.04702e40i	0.742552	−	0.590909i
$959$	−2.16148e40			−1.20282
$960$	3.05109e39	−	3.77756e39i	0.167415	−	0.207277i
$961$	−5.98423e39			−0.323775
$962$	8.39593e39	−	6.68132e39i	0.447925	−	0.356450i
$963$	3.24240e40	+	3.24240e40i	1.70574	+	1.70574i
$964$	−4.08794e39	+	1.77410e40i	−0.212063	+	0.920320i
$965$	−1.14095e39	+	1.14095e39i	−0.0583645	+	0.0583645i
$966$	1.06906e40	+	1.21575e39i	0.539277	+	0.0613274i
$967$			1.39220e40i			0.692537i	0.938135	+	0.346269i	$0.112551\pi$
$967$			1.39220e40i			0.692537i	−0.938135	+	0.346269i	$0.887449\pi$
$968$	−2.75714e39	+	1.31723e39i	−0.135251	+	0.0646168i
$969$			2.92817e38i			0.0141653i
$970$	5.95887e38	−	5.23987e39i	0.0284279	−	0.249978i
$971$	−1.33184e40	+	1.33184e40i	−0.626604	+	0.626604i	−0.947212	−	0.320608i	$-0.896113\pi$
$971$	−1.33184e40	+	1.33184e40i	−0.626604	+	0.626604i	0.320608	+	0.947212i	$0.396113\pi$
$972$	−8.02019e39	+	5.01628e39i	−0.372126	+	0.232749i
$973$	5.68005e39	+	5.68005e39i	0.259914	+	0.259914i
$974$	1.21419e40	+	1.52578e40i	0.547949	+	0.688567i
$975$	1.93599e40			0.861669
$976$	1.29306e40	+	3.74504e40i	0.567606	+	1.64393i
$977$	−1.76152e40			−0.762626			−0.381313	−	0.924446i	$-0.624528\pi$
$977$	−1.76152e40			−0.762626			−0.381313	+	0.924446i	$0.624528\pi$
$978$	−2.44783e39	−	3.07601e39i	−0.104522	−	0.131345i
$979$	−3.00826e40	−	3.00826e40i	−1.26692	−	1.26692i
$980$	−7.12556e38	−	1.13926e39i	−0.0295983	−	0.0473227i
$981$	−3.25290e40	+	3.25290e40i	−1.33272	+	1.33272i
$982$	5.03947e39	−	4.43141e40i	0.203648	−	1.79076i
$983$		−	3.97049e40i		−	1.58260i	−0.611428	−	0.791300i	$-0.709405\pi$
$983$		−	3.97049e40i		−	1.58260i	0.611428	−	0.791300i	$-0.290595\pi$
$984$	1.72997e40	+	6.11382e39i	0.680151	+	0.240369i
$985$		−	6.31965e39i		−	0.245078i
$986$	−2.15556e38	−	2.45133e37i	−0.00824558	−	0.000937700i
$987$	1.06051e40	−	1.06051e40i	0.400158	−	0.400158i
$988$	2.03605e40	+	4.69153e39i	0.757827	+	0.174621i
$989$	−3.12659e37	−	3.12659e37i	−0.00114795	−	0.00114795i
$990$	5.83844e39	−	4.64612e39i	0.211457	−	0.168273i
$991$	−3.88755e40			−1.38894			−0.694468	−	0.719524i	$-0.744360\pi$
$991$	−3.88755e40			−1.38894			−0.694468	+	0.719524i	$0.744360\pi$
$992$	2.27737e40	−	5.07404e39i	0.802648	−	0.178833i
$993$	7.32246e40			2.54591
$994$	−1.25163e40	+	9.96027e39i	−0.429300	+	0.341629i
$995$	1.62934e39	+	1.62934e39i	0.0551316	+	0.0551316i
$996$	−2.63140e40	−	6.06336e39i	−0.878388	−	0.202401i
$997$	−2.03439e40	+	2.03439e40i	−0.669961	+	0.669961i	−0.957707	−	0.287746i	$-0.907094\pi$
$997$	−2.03439e40	+	2.03439e40i	−0.669961	+	0.669961i	0.287746	+	0.957707i	$0.407094\pi$
$998$	−2.51728e40	−	2.86269e39i	−0.817841	−	0.0930062i
$999$			4.97526e40i			1.59471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.13.12	yes	106
16.5	even	4	inner	16.28.e.a.5.12	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.12	✓	106	16.5	even	4	inner
16.28.e.a.13.12	yes	106	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9065.18 + 7213.90i) q^{2} +(-3.30251e6 - 3.30251e6i) q^{3} +(3.01372e7 - 1.30790e8i) q^{4} +(3.04061e8 - 3.04061e8i) q^{5} +(5.37618e10 + 6.11388e9i) q^{6} +2.05985e11i q^{7} +(6.70310e11 + 1.40305e12i) q^{8} +1.41875e13i q^{9} +(-5.62903e11 + 4.94983e12i) q^{10} +(-7.46488e13 + 7.46488e13i) q^{11} +(-5.31465e14 + 3.32408e14i) q^{12} +(4.03416e14 + 4.03416e14i) q^{13} +(-1.48595e15 - 1.86729e15i) q^{14} -2.00833e15 q^{15} +(-1.61979e16 - 7.88331e15i) q^{16} -2.29769e14 q^{17} +(-1.02347e17 - 1.28613e17i) q^{18} +(1.92943e17 + 1.92943e17i) q^{19} +(-3.06047e16 - 4.89318e16i) q^{20} +(6.80267e17 - 6.80267e17i) q^{21} +(1.38196e17 - 1.21521e18i) q^{22} -9.65370e17i q^{23} +(2.41986e18 - 6.84727e18i) q^{24} +7.26567e18i q^{25} +(-6.56723e18 - 7.46836e17i) q^{26} +(2.16709e19 - 2.16709e19i) q^{27} +(2.69409e19 + 6.20780e18i) q^{28} +(-5.76285e19 - 5.76285e19i) q^{29} +(1.82058e19 - 1.44879e19i) q^{30} +1.11797e20 q^{31} +(2.03706e20 - 4.53864e19i) q^{32} +4.93057e20 q^{33} +(2.08290e18 - 1.65753e18i) q^{34} +(6.26320e19 + 6.26320e19i) q^{35} +(1.85559e21 + 4.27572e20i) q^{36} +(-1.14792e21 + 1.14792e21i) q^{37} +(-3.14094e21 - 3.57192e20i) q^{38} -2.66457e21i q^{39} +(6.30426e20 + 2.22796e20i) q^{40} +2.52651e21i q^{41} +(-1.25937e21 + 1.10741e22i) q^{42} +(3.23875e19 - 3.23875e19i) q^{43} +(7.51365e21 + 1.20131e22i) q^{44} +(4.31387e21 + 4.31387e21i) q^{45} +(6.96408e21 + 8.75125e21i) q^{46} +1.55896e22 q^{47} +(2.74590e22 + 7.95284e22i) q^{48} +2.32826e22 q^{49} +(-5.24138e22 - 6.58646e22i) q^{50} +(7.58816e20 + 7.58816e20i) q^{51} +(6.49207e22 - 4.06051e22i) q^{52} +(1.50907e23 - 1.50907e23i) q^{53} +(-4.01189e22 + 3.52781e23i) q^{54} +4.53955e22i q^{55} +(-2.89006e23 + 1.38074e23i) q^{56} -1.27439e24i q^{57} +(9.38139e23 + 1.06687e23i) q^{58} +(6.11665e23 - 6.11665e23i) q^{59} +(-6.05253e22 + 2.62670e23i) q^{60} +(-1.55517e24 - 1.55517e24i) q^{61} +(-1.01346e24 + 8.06489e23i) q^{62} -2.92242e24 q^{63} +(-1.51922e24 + 1.88095e24i) q^{64} +2.45326e23 q^{65} +(-4.46965e24 + 3.55686e24i) q^{66} +(-1.01732e24 - 1.01732e24i) q^{67} +(-6.92460e21 + 3.00517e22i) q^{68} +(-3.18814e24 + 3.18814e24i) q^{69} +(-1.01959e24 - 1.15949e23i) q^{70} -6.70294e24i q^{71} +(-1.99058e25 + 9.51005e24i) q^{72} +2.33739e25i q^{73} +(2.12511e24 - 1.86870e25i) q^{74} +(2.39950e25 - 2.39950e25i) q^{75} +(3.10499e25 - 1.94204e25i) q^{76} +(-1.53765e25 - 1.53765e25i) q^{77} +(1.92219e25 + 2.41548e25i) q^{78} -5.61337e25 q^{79} +(-7.32215e24 + 2.52814e24i) q^{80} -3.49480e25 q^{81} +(-1.82260e25 - 2.29033e25i) q^{82} +(3.04605e25 + 3.04605e25i) q^{83} +(-6.84712e25 - 1.09474e26i) q^{84} +(-6.98639e22 + 6.98639e22i) q^{85} +(-5.99585e22 + 5.27239e23i) q^{86} +3.80637e26i q^{87} +(-1.54773e26 - 5.46978e25i) q^{88} +4.02988e26i q^{89} +(-7.02259e25 - 7.98620e24i) q^{90} +(-8.30976e25 + 8.30976e25i) q^{91} +(-1.26261e26 - 2.90935e25i) q^{92} +(-3.69209e26 - 3.69209e26i) q^{93} +(-1.41322e26 + 1.12461e26i) q^{94} +1.17333e26 q^{95} +(-8.22631e26 - 5.22853e26i) q^{96} -1.05860e27 q^{97} +(-2.11061e26 + 1.67958e26i) q^{98} +(-1.05908e27 - 1.05908e27i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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