LMFDB - Embedded newform 16.28.e.a.5.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,28,Mod(5,16)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			5.22
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3056.43 + 11174.8i) q^{2} +(3.04594e6 - 3.04594e6i) q^{3} +(-1.15534e8 - 6.83100e7i) q^{4} +(-2.58085e9 - 2.58085e9i) q^{5} +(2.47280e10 + 4.33475e10i) q^{6} +3.57176e11i q^{7} +(1.11647e12 - 1.08228e12i) q^{8} -1.09299e13i q^{9} +(3.67287e13 - 2.09523e13i) q^{10} +(2.32427e13 + 2.32427e13i) q^{11} +(-5.59979e14 + 1.43842e14i) q^{12} +(4.99297e14 - 4.99297e14i) q^{13} +(-3.99137e15 - 1.09169e15i) q^{14} -1.57222e16 q^{15} +(8.68188e15 + 1.57843e16i) q^{16} +5.74935e16 q^{17} +(1.22140e17 + 3.34066e16i) q^{18} +(1.65649e16 - 1.65649e16i) q^{19} +(1.21878e17 + 4.74474e17i) q^{20} +(1.08794e18 + 1.08794e18i) q^{21} +(-3.30773e17 + 1.88693e17i) q^{22} -1.98076e18i q^{23} +(1.04134e17 - 6.69729e18i) q^{24} +5.87099e18i q^{25} +(4.05347e18 + 7.10561e18i) q^{26} +(-1.00648e19 - 1.00648e19i) q^{27} +(2.43987e19 - 4.12661e19i) q^{28} +(7.73440e18 - 7.73440e18i) q^{29} +(4.80540e19 - 1.75693e20i) q^{30} +2.11243e20 q^{31} +(-2.02922e20 + 4.87746e19i) q^{32} +1.41592e20 q^{33} +(-1.75725e20 + 6.42477e20i) q^{34} +(9.21819e20 - 9.21819e20i) q^{35} +(-7.46624e20 + 1.26278e21i) q^{36} +(-1.64489e21 - 1.64489e21i) q^{37} +(1.34480e20 + 2.35739e20i) q^{38} -3.04166e21i q^{39} +(-5.67466e21 - 8.82339e19i) q^{40} +8.07062e21i q^{41} +(-1.54827e22 + 8.83227e21i) q^{42} +(-2.51612e20 - 2.51612e20i) q^{43} +(-1.09762e21 - 4.27304e21i) q^{44} +(-2.82085e22 + 2.82085e22i) q^{45} +(2.21346e22 + 6.05408e21i) q^{46} -6.40741e22 q^{47} +(7.45225e22 + 2.16335e22i) q^{48} -6.18626e22 q^{49} +(-6.56071e22 - 1.79443e22i) q^{50} +(1.75122e23 - 1.75122e23i) q^{51} +(-9.17929e22 + 2.35789e22i) q^{52} +(-2.38498e23 - 2.38498e23i) q^{53} +(1.43234e23 - 8.17096e22i) q^{54} -1.19972e23i q^{55} +(3.86567e23 + 3.98778e23i) q^{56} -1.00911e23i q^{57} +(6.27906e22 + 1.10070e23i) q^{58} +(-7.80016e23 - 7.80016e23i) q^{59} +(1.81646e24 + 1.07399e24i) q^{60} +(9.25564e23 - 9.25564e23i) q^{61} +(-6.45650e23 + 2.36060e24i) q^{62} +3.90391e24 q^{63} +(7.51710e22 - 2.41668e24i) q^{64} -2.57722e24 q^{65} +(-4.32767e23 + 1.58226e24i) q^{66} +(-5.48866e23 + 5.48866e23i) q^{67} +(-6.64246e24 - 3.92738e24i) q^{68} +(-6.03329e24 - 6.03329e24i) q^{69} +(7.48365e24 + 1.31186e25i) q^{70} -1.74997e25i q^{71} +(-1.18293e25 - 1.22030e25i) q^{72} -7.20999e24i q^{73} +(2.34088e25 - 1.33538e25i) q^{74} +(1.78827e25 + 1.78827e25i) q^{75} +(-3.04536e24 + 7.82263e23i) q^{76} +(-8.30176e24 + 8.30176e24i) q^{77} +(3.39899e25 + 9.29664e24i) q^{78} +1.84456e25 q^{79} +(1.83302e25 - 6.31435e25i) q^{80} +2.20337e25 q^{81} +(-9.01875e25 - 2.46673e25i) q^{82} +(-4.38234e25 + 4.38234e25i) q^{83} +(-5.13769e25 - 2.00011e26i) q^{84} +(-1.48382e26 - 1.48382e26i) q^{85} +(3.58075e24 - 2.04268e24i) q^{86} -4.71170e25i q^{87} +(5.11052e25 + 7.94622e23i) q^{88} +2.81106e26i q^{89} +(-2.29007e26 - 4.01442e26i) q^{90} +(1.78337e26 + 1.78337e26i) q^{91} +(-1.35306e26 + 2.28846e26i) q^{92} +(6.43434e26 - 6.43434e26i) q^{93} +(1.95838e26 - 7.16015e26i) q^{94} -8.55031e25 q^{95} +(-4.69523e26 + 7.66652e26i) q^{96} -4.69139e26 q^{97} +(1.89079e26 - 6.91301e26i) q^{98} +(2.54042e26 - 2.54042e26i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3056.43	+	11174.8i	−0.263821	+	0.964572i
$2$	−3056.43	+	11174.8i	−0.263821	+	0.964572i
$3$	3.04594e6	−	3.04594e6i	1.10302	−	1.10302i	0.108979	−	0.994044i	$-0.465242\pi$
$3$	3.04594e6	−	3.04594e6i	1.10302	−	1.10302i	0.994044	−	0.108979i	$-0.0347582\pi$
$4$	−1.15534e8	−	6.83100e7i	−0.860796	−	0.508949i
$5$	−2.58085e9	−	2.58085e9i	−0.945513	−	0.945513i	0.0530770	−	0.998590i	$-0.483097\pi$
$5$	−2.58085e9	−	2.58085e9i	−0.945513	−	0.945513i	−0.998590	+	0.0530770i	$0.983097\pi$
$6$	2.47280e10	+	4.33475e10i	0.772944	+	1.35495i
$7$			3.57176e11i			1.39335i	0.717389	+	0.696673i	$0.245337\pi$
$7$			3.57176e11i			1.39335i	−0.717389	+	0.696673i	$0.754663\pi$
$8$	1.11647e12	−	1.08228e12i	0.718015	−	0.696028i
$9$		−	1.09299e13i		−	1.43332i
$10$	3.67287e13	−	2.09523e13i	1.16146	−	0.662569i
$11$	2.32427e13	+	2.32427e13i	0.202995	+	0.202995i	0.801282	−	0.598287i	$-0.204152\pi$
$11$	2.32427e13	+	2.32427e13i	0.202995	+	0.202995i	−0.598287	+	0.801282i	$0.704152\pi$
$12$	−5.59979e14	+	1.43842e14i	−1.51086	+	0.388096i
$13$	4.99297e14	−	4.99297e14i	0.457219	−	0.457219i	−0.440523	−	0.897741i	$-0.645207\pi$
$13$	4.99297e14	−	4.99297e14i	0.457219	−	0.457219i	0.897741	+	0.440523i	$0.145207\pi$
$14$	−3.99137e15	−	1.09169e15i	−1.34398	−	0.367595i
$15$	−1.57222e16			−2.08585
$16$	8.68188e15	+	1.57843e16i	0.481941	+	0.876204i
$17$	5.74935e16			1.40786			0.703928	−	0.710272i	$-0.251428\pi$
$17$	5.74935e16			1.40786			0.703928	+	0.710272i	$0.251428\pi$
$18$	1.22140e17	+	3.34066e16i	1.38254	+	0.378141i
$19$	1.65649e16	−	1.65649e16i	0.0903681	−	0.0903681i	−0.660478	−	0.750846i	$-0.729646\pi$
$19$	1.65649e16	−	1.65649e16i	0.0903681	−	0.0903681i	0.750846	+	0.660478i	$0.229646\pi$
$20$	1.21878e17	+	4.74474e17i	0.332676	+	1.29511i
$21$	1.08794e18	+	1.08794e18i	1.53689	+	1.53689i
$22$	−3.30773e17	+	1.88693e17i	−0.249358	+	0.142249i
$23$		−	1.98076e18i		−	0.819421i	−0.912216	−	0.409710i	$-0.865630\pi$
$23$		−	1.98076e18i		−	0.819421i	0.912216	−	0.409710i	$-0.134370\pi$
$24$	1.04134e17	−	6.69729e18i	0.0242517	−	1.55972i
$25$			5.87099e18i			0.787991i
$26$	4.05347e18	+	7.10561e18i	0.320396	+	0.561644i
$27$	−1.00648e19	−	1.00648e19i	−0.477963	−	0.477963i
$28$	2.43987e19	−	4.12661e19i	0.709143	−	1.19939i
$29$	7.73440e18	−	7.73440e18i	0.139976	−	0.139976i	−0.633647	−	0.773623i	$-0.718443\pi$
$29$	7.73440e18	−	7.73440e18i	0.139976	−	0.139976i	0.773623	+	0.633647i	$0.218443\pi$
$30$	4.80540e19	−	1.75693e20i	0.550291	−	2.01195i
$31$	2.11243e20			1.55382			0.776908	−	0.629614i	$-0.216787\pi$
$31$	2.11243e20			1.55382			0.776908	+	0.629614i	$0.216787\pi$
$32$	−2.02922e20	+	4.87746e19i	−0.972307	+	0.233705i
$33$	1.41592e20			0.447817
$34$	−1.75725e20	+	6.42477e20i	−0.371423	+	1.35798i
$35$	9.21819e20	−	9.21819e20i	1.31743	−	1.31743i
$36$	−7.46624e20	+	1.26278e21i	−0.729488	+	1.23380i
$37$	−1.64489e21	−	1.64489e21i	−1.11023	−	1.11023i	−0.993119	−	0.117112i	$-0.962636\pi$
$37$	−1.64489e21	−	1.64489e21i	−1.11023	−	1.11023i	−0.117112	−	0.993119i	$-0.537364\pi$
$38$	1.34480e20	+	2.35739e20i	0.0633255	+	0.111008i
$39$		−	3.04166e21i		−	1.00865i
$40$	−5.67466e21	−	8.82339e19i	−1.33700	−	0.0207886i
$41$			8.07062e21i			1.36246i	0.732068	+	0.681231i	$0.238555\pi$
$41$			8.07062e21i			1.36246i	−0.732068	+	0.681231i	$0.761445\pi$
$42$	−1.54827e22	+	8.83227e21i	−1.88791	+	1.07698i
$43$	−2.51612e20	−	2.51612e20i	−0.0223310	−	0.0223310i	0.695853	−	0.718184i	$-0.255026\pi$
$43$	−2.51612e20	−	2.51612e20i	−0.0223310	−	0.0223310i	−0.718184	+	0.695853i	$0.755026\pi$
$44$	−1.09762e21	−	4.27304e21i	−0.0714234	−	0.278052i
$45$	−2.82085e22	+	2.82085e22i	−1.35522	+	1.35522i
$46$	2.21346e22	+	6.05408e21i	0.790390	+	0.216181i
$47$	−6.40741e22			−1.71144			−0.855720	−	0.517439i	$-0.826885\pi$
$47$	−6.40741e22			−1.71144			−0.855720	+	0.517439i	$0.826885\pi$
$48$	7.45225e22	+	2.16335e22i	1.49807	+	0.434881i
$49$	−6.18626e22			−0.941415
$50$	−6.56071e22	−	1.79443e22i	−0.760074	−	0.207889i
$51$	1.75122e23	−	1.75122e23i	1.55290	−	1.55290i
$52$	−9.17929e22	+	2.35789e22i	−0.626273	+	0.160871i
$53$	−2.38498e23	−	2.38498e23i	−1.25823	−	1.25823i	−0.951937	−	0.306293i	$-0.900911\pi$
$53$	−2.38498e23	−	2.38498e23i	−1.25823	−	1.25823i	−0.306293	−	0.951937i	$-0.599089\pi$
$54$	1.43234e23	−	8.17096e22i	0.587126	−	0.334933i
$55$		−	1.19972e23i		−	0.383870i
$56$	3.86567e23	+	3.98778e23i	0.969808	+	1.00044i
$57$		−	1.00911e23i		−	0.199356i
$58$	6.27906e22	+	1.10070e23i	0.0980882	+	0.171945i
$59$	−7.80016e23	−	7.80016e23i	−0.967390	−	0.967390i	0.0320953	−	0.999485i	$-0.489782\pi$
$59$	−7.80016e23	−	7.80016e23i	−0.967390	−	0.967390i	−0.999485	+	0.0320953i	$0.989782\pi$
$60$	1.81646e24	+	1.07399e24i	1.79549	+	1.06159i
$61$	9.25564e23	−	9.25564e23i	0.731903	−	0.731903i	−0.239093	−	0.970997i	$-0.576850\pi$
$61$	9.25564e23	−	9.25564e23i	0.731903	−	0.731903i	0.970997	+	0.239093i	$0.0768502\pi$
$62$	−6.45650e23	+	2.36060e24i	−0.409930	+	1.49877i
$63$	3.90391e24			1.99711
$64$	7.51710e22	−	2.41668e24i	0.0310900	−	0.999517i
$65$	−2.57722e24			−0.864613
$66$	−4.32767e23	+	1.58226e24i	−0.118144	+	0.431952i
$67$	−5.48866e23	+	5.48866e23i	−0.122309	+	0.122309i	−0.765612	−	0.643303i	$-0.777564\pi$
$67$	−5.48866e23	+	5.48866e23i	−0.122309	+	0.122309i	0.643303	+	0.765612i	$0.277564\pi$
$68$	−6.64246e24	−	3.92738e24i	−1.21188	−	0.716527i
$69$	−6.03329e24	−	6.03329e24i	−0.903840	−	0.903840i
$70$	7.48365e24	+	1.31186e25i	0.923188	+	1.61832i
$71$		−	1.74997e25i		−	1.78255i	−0.453462	−	0.891276i	$-0.649811\pi$
$71$		−	1.74997e25i		−	1.78255i	0.453462	−	0.891276i	$-0.350189\pi$
$72$	−1.18293e25	−	1.22030e25i	−0.997631	−	1.02915i
$73$		−	7.20999e24i		−	0.504750i	−0.967630	−	0.252375i	$-0.918788\pi$
$73$		−	7.20999e24i		−	0.504750i	0.967630	−	0.252375i	$-0.0812117\pi$
$74$	2.34088e25	−	1.33538e25i	1.36380	−	0.777995i
$75$	1.78827e25	+	1.78827e25i	0.869173	+	0.869173i
$76$	−3.04536e24	+	7.82263e23i	−0.123781	+	0.0317958i
$77$	−8.30176e24	+	8.30176e24i	−0.282843	+	0.282843i
$78$	3.39899e25	+	9.29664e24i	0.972911	+	0.266102i
$79$	1.84456e25			0.444556			0.222278	−	0.974983i	$-0.428651\pi$
$79$	1.84456e25			0.444556			0.222278	+	0.974983i	$0.428651\pi$
$80$	1.83302e25	−	6.31435e25i	0.372780	−	1.28414i
$81$	2.20337e25			0.378912
$82$	−9.01875e25	−	2.46673e25i	−1.31419	−	0.359447i
$83$	−4.38234e25	+	4.38234e25i	−0.542190	+	0.542190i	−0.924170	−	0.381981i	$-0.875242\pi$
$83$	−4.38234e25	+	4.38234e25i	−0.542190	+	0.542190i	0.381981	+	0.924170i	$0.375242\pi$
$84$	−5.13769e25	−	2.00011e26i	−0.540752	−	2.10515i
$85$	−1.48382e26	−	1.48382e26i	−1.33115	−	1.33115i
$86$	3.58075e24	−	2.04268e24i	0.0274312	−	0.0156484i
$87$		−	4.71170e25i		−	0.308793i
$88$	5.11052e25	+	7.94622e23i	0.287044	+	0.00446318i
$89$			2.81106e26i			1.35552i	0.735285	+	0.677758i	$0.237048\pi$
$89$			2.81106e26i			1.35552i	−0.735285	+	0.677758i	$0.762952\pi$
$90$	−2.29007e26	−	4.01442e26i	−0.949673	−	1.66475i
$91$	1.78337e26	+	1.78337e26i	0.637064	+	0.637064i
$92$	−1.35306e26	+	2.28846e26i	−0.417044	+	0.705355i
$93$	6.43434e26	−	6.43434e26i	1.71389	−	1.71389i
$94$	1.95838e26	−	7.16015e26i	0.451515	−	1.65081i
$95$	−8.55031e25			−0.170889
$96$	−4.69523e26	+	7.66652e26i	−0.814695	+	1.33026i
$97$	−4.69139e26			−0.707755			−0.353877	−	0.935292i	$-0.615137\pi$
$97$	−4.69139e26			−0.707755			−0.353877	+	0.935292i	$0.615137\pi$
$98$	1.89079e26	−	6.91301e26i	0.248365	−	0.908062i
$99$	2.54042e26	−	2.54042e26i	0.290958	−	0.290958i
$100$	4.01048e26	−	6.78300e26i	0.401048	−	0.678300i
$101$	6.81207e26	+	6.81207e26i	0.595581	+	0.595581i	0.939133	−	0.343553i	$-0.111630\pi$
$101$	6.81207e26	+	6.81207e26i	0.595581	+	0.595581i	−0.343553	+	0.939133i	$0.611630\pi$
$102$	1.42170e27	+	2.49220e27i	1.08819	+	1.90757i
$103$		−	1.48639e27i		−	0.997312i	−0.866800	−	0.498656i	$-0.833827\pi$
$103$		−	1.48639e27i		−	0.997312i	0.866800	−	0.498656i	$-0.166173\pi$
$104$	1.70699e25	−	1.09783e27i	0.0100527	−	0.646527i
$105$		−	5.61561e27i		−	2.90631i
$106$	3.39412e27	−	1.93621e27i	1.54560	−	0.881705i
$107$	1.95755e27	+	1.95755e27i	0.785295	+	0.785295i	0.980719	−	0.195424i	$-0.0626082\pi$
$107$	1.95755e27	+	1.95755e27i	0.785295	+	0.785295i	−0.195424	+	0.980719i	$0.562608\pi$
$108$	4.75301e26	+	1.85035e27i	0.168170	+	0.654688i
$109$	2.33683e27	−	2.33683e27i	0.730077	−	0.730077i	−0.240558	−	0.970635i	$-0.577330\pi$
$109$	2.33683e27	−	2.33683e27i	0.730077	−	0.730077i	0.970635	+	0.240558i	$0.0773304\pi$
$110$	1.34066e27	+	3.66687e26i	0.370270	+	0.101273i
$111$	−1.00205e28			−2.44922
$112$	−5.63777e27	+	3.10096e27i	−1.22086	+	0.671511i
$113$	−5.28508e27			−1.01506			−0.507531	−	0.861634i	$-0.669442\pi$
$113$	−5.28508e27			−1.01506			−0.507531	+	0.861634i	$0.669442\pi$
$114$	1.12766e27	+	3.08429e26i	0.192293	+	0.0525945i
$115$	−5.11206e27	+	5.11206e27i	−0.774773	+	0.774773i
$116$	−1.42192e27	+	3.65250e26i	−0.191731	+	0.0492501i
$117$	−5.45728e27	−	5.45728e27i	−0.655341	−	0.655341i
$118$	1.11006e28	−	6.33245e27i	1.18833	−	0.677898i
$119$			2.05353e28i			1.96163i
$120$	−1.75534e28	+	1.70159e28i	−1.49767	+	1.45181i
$121$		−	1.20295e28i		−	0.917586i
$122$	7.51406e27	+	1.31719e28i	0.512881	+	0.899065i
$123$	2.45826e28	+	2.45826e28i	1.50283	+	1.50283i
$124$	−2.44058e28	−	1.44300e28i	−1.33752	−	0.790813i
$125$	−4.07668e27	+	4.07668e27i	−0.200457	+	0.200457i
$126$	−1.19320e28	+	4.36254e28i	−0.526881	+	1.92636i
$127$	−7.21903e27			−0.286503			−0.143251	−	0.989686i	$-0.545756\pi$
$127$	−7.21903e27			−0.286503			−0.143251	+	0.989686i	$0.545756\pi$
$128$	2.67762e28	+	8.22645e27i	0.955903	+	0.293682i
$129$	−1.53279e27			−0.0492631
$130$	7.87711e27	−	2.87999e28i	0.228103	−	0.833981i
$131$	3.54708e28	−	3.54708e28i	0.926208	−	0.926208i	−0.0712505	−	0.997458i	$-0.522699\pi$
$131$	3.54708e28	−	3.54708e28i	0.926208	−	0.926208i	0.997458	+	0.0712505i	$0.0226990\pi$
$132$	−1.63587e28	−	9.67216e27i	−0.385480	−	0.227916i
$133$	5.91659e27	+	5.91659e27i	0.125914	+	0.125914i
$134$	−4.45589e27	−	7.81104e27i	−0.0857077	−	0.150243i
$135$			5.19515e28i			0.903841i
$136$	6.41899e28	−	6.22243e28i	1.01086	−	0.979907i
$137$		−	3.62426e28i		−	0.517001i	−0.966011	−	0.258501i	$-0.916772\pi$
$137$		−	3.62426e28i		−	0.517001i	0.966011	−	0.258501i	$-0.0832284\pi$
$138$	8.58611e28	−	4.89804e28i	1.11027	−	0.633366i
$139$	5.66472e28	+	5.66472e28i	0.664475	+	0.664475i	0.956432	−	0.291956i	$-0.0943062\pi$
$139$	5.66472e28	+	5.66472e28i	0.664475	+	0.664475i	−0.291956	+	0.956432i	$0.594306\pi$
$140$	−1.69471e29	+	4.35321e28i	−1.80454	+	0.463533i
$141$	−1.95166e29	+	1.95166e29i	−1.88776	+	1.88776i
$142$	1.95555e29	+	5.34866e28i	1.71940	+	0.470275i
$143$	2.32101e28			0.185627
$144$	1.72521e29	−	9.48923e28i	1.25588	−	0.690776i
$145$	−3.99226e28			−0.264698
$146$	8.05702e28	+	2.20369e28i	0.486867	+	0.133164i
$147$	−1.88430e29	+	1.88430e29i	−1.03840	+	1.03840i
$148$	7.76785e28	+	3.02403e29i	0.390632	+	1.52073i
$149$	−6.11552e28	−	6.11552e28i	−0.280814	−	0.280814i	0.552620	−	0.833434i	$-0.313628\pi$
$149$	−6.11552e28	−	6.11552e28i	−0.280814	−	0.280814i	−0.833434	+	0.552620i	$0.813628\pi$
$150$	−2.54493e29	+	1.45178e29i	−1.06769	+	0.609073i
$151$		−	2.84534e29i		−	1.09130i	−0.838013	−	0.545651i	$-0.816282\pi$
$151$		−	2.84534e29i		−	1.09130i	0.838013	−	0.545651i	$-0.183718\pi$
$152$	5.66320e26	−	3.64222e28i	0.00198689	−	0.127784i
$153$		−	6.28399e29i		−	2.01791i
$154$	−6.73966e28	−	1.18144e29i	−0.198202	−	0.347442i
$155$	−5.45186e29	−	5.45186e29i	−1.46915	−	1.46915i
$156$	−2.07776e29	+	3.51416e29i	−0.513349	+	0.868238i
$157$	3.34799e29	−	3.34799e29i	0.758820	−	0.758820i	−0.217288	−	0.976108i	$-0.569721\pi$
$157$	3.34799e29	−	3.34799e29i	0.758820	−	0.758820i	0.976108	+	0.217288i	$0.0697209\pi$
$158$	−5.63777e28	+	2.06125e29i	−0.117283	+	0.428806i
$159$	−1.45290e30			−2.77571
$160$	6.49590e29	+	3.97830e29i	1.14030	+	0.698358i
$161$	7.07482e29			1.14174
$162$	−6.73444e28	+	2.46221e29i	−0.0999652	+	0.365488i
$163$	8.83909e29	−	8.83909e29i	1.20747	−	1.20747i	0.235622	−	0.971845i	$-0.424287\pi$
$163$	8.83909e29	−	8.83909e29i	1.20747	−	1.20747i	0.971845	−	0.235622i	$-0.0757126\pi$
$164$	5.51304e29	−	9.32432e29i	0.693425	−	1.17280i
$165$	−3.65428e29	−	3.65428e29i	−0.423417	−	0.423417i
$166$	−3.55774e29	−	6.23660e29i	−0.379940	−	0.666022i
$167$		−	6.38354e29i		−	0.628621i	−0.949320	−	0.314311i	$-0.898227\pi$
$167$		−	6.38354e29i		−	0.628621i	0.949320	−	0.314311i	$-0.101773\pi$
$168$	2.39211e30	+	3.71944e28i	2.17323	+	0.0337911i
$169$			6.93938e29i			0.581902i
$170$	2.11166e30	−	1.20462e30i	1.63517	−	0.932801i
$171$	−1.81053e29	−	1.81053e29i	−0.129527	−	0.129527i
$172$	1.18822e28	+	4.62574e28i	0.00785708	+	0.0305877i
$173$	−1.78211e30	+	1.78211e30i	−1.08971	+	1.08971i	−0.0941569	+	0.995557i	$0.530016\pi$
$173$	−1.78211e30	+	1.78211e30i	−1.08971	+	1.08971i	−0.995557	+	0.0941569i	$0.969984\pi$
$174$	5.26523e29	+	1.44010e29i	0.297853	+	0.0814663i
$175$	−2.09698e30			−1.09794
$176$	−1.65079e29	+	5.68661e29i	−0.0800335	+	0.275697i
$177$	−4.75177e30			−2.13411
$178$	−3.14130e30	−	8.59181e29i	−1.30749	−	0.357614i
$179$	2.10602e30	−	2.10602e30i	0.812731	−	0.812731i	−0.172312	−	0.985042i	$-0.555124\pi$
$179$	2.10602e30	−	2.10602e30i	0.812731	−	0.812731i	0.985042	+	0.172312i	$0.0551236\pi$
$180$	5.18597e30	−	1.33212e30i	1.85631	−	0.476832i
$181$	1.73682e30	+	1.73682e30i	0.576890	+	0.576890i	0.934045	−	0.357155i	$-0.116253\pi$
$181$	1.73682e30	+	1.73682e30i	0.576890	+	0.576890i	−0.357155	+	0.934045i	$0.616253\pi$
$182$	−2.53796e30	+	1.44780e30i	−0.782565	+	0.446423i
$183$		−	5.63843e30i		−	1.61461i
$184$	−2.14375e30	−	2.21147e30i	−0.570340	−	0.588356i
$185$			8.49042e30i			2.09948i
$186$	5.22363e30	+	9.15685e30i	1.20101	+	2.10534i
$187$	1.33631e30	+	1.33631e30i	0.285788	+	0.285788i
$188$	7.40275e30	+	4.37691e30i	1.47320	+	0.871036i
$189$	3.59491e30	−	3.59491e30i	0.665968	−	0.665968i
$190$	2.61334e29	−	9.55479e29i	0.0450841	−	0.164834i
$191$	−2.10898e30			−0.338940			−0.169470	−	0.985535i	$-0.554206\pi$
$191$	−2.10898e30			−0.338940			−0.169470	+	0.985535i	$0.554206\pi$
$192$	−7.13211e30	−	7.59004e30i	−1.06820	−	1.13678i
$193$	−8.57994e30			−1.19801			−0.599005	−	0.800745i	$-0.704437\pi$
$193$	−8.57994e30			−1.19801			−0.599005	+	0.800745i	$0.704437\pi$
$194$	1.43389e30	−	5.24253e30i	0.186721	−	0.682680i
$195$	−7.85007e30	+	7.85007e30i	−0.953688	+	0.953688i
$196$	7.14724e30	+	4.22583e30i	0.810366	+	0.479132i
$197$	−1.09480e31	−	1.09480e31i	−1.15889	−	1.15889i	−0.984715	−	0.174174i	$-0.944275\pi$
$197$	−1.09480e31	−	1.09480e31i	−1.15889	−	1.15889i	−0.174174	−	0.984715i	$-0.555725\pi$
$198$	2.06240e30	+	3.61532e30i	0.203889	+	0.357410i
$199$			8.38789e30i			0.774705i	0.921932	+	0.387352i	$0.126610\pi$
$199$			8.38789e30i			0.774705i	−0.921932	+	0.387352i	$0.873390\pi$
$200$	6.35408e30	+	6.55480e30i	0.548464	+	0.565789i
$201$			3.34363e30i			0.269818i
$202$	−9.69441e30	+	5.53028e30i	−0.731607	+	0.417353i
$203$	2.76254e30	+	2.76254e30i	0.195035	+	0.195035i
$204$	−3.21951e31	+	8.26997e30i	−2.12707	+	0.546383i
$205$	2.08291e31	−	2.08291e31i	1.28823	−	1.28823i
$206$	1.66101e31	+	4.54306e30i	0.961979	+	0.263112i
$207$	−2.16496e31			−1.17449
$208$	1.22159e31	+	3.54621e30i	0.620969	+	0.180264i
$209$	7.70028e29			0.0366886
$210$	6.27533e31	+	1.71637e31i	2.80334	+	0.766746i
$211$	−1.00151e31	+	1.00151e31i	−0.419607	+	0.419607i	−0.885068	−	0.465461i	$-0.845889\pi$
$211$	−1.00151e31	+	1.00151e31i	−0.419607	+	0.419607i	0.465461	+	0.885068i	$0.345889\pi$
$212$	1.12628e31	+	4.38464e31i	0.442705	+	1.72346i
$213$	−5.33030e31	−	5.33030e31i	−1.96620	−	1.96620i
$214$	−2.78584e31	+	1.58921e31i	−0.964651	+	0.550296i
$215$			1.29875e30i			0.0422284i
$216$	−2.21300e31	−	3.44095e29i	−0.675860	−	0.0105088i
$217$			7.54510e31i			2.16500i
$218$	1.89712e31	+	3.32559e31i	0.511601	+	0.896821i
$219$	−2.19612e31	−	2.19612e31i	−0.556751	−	0.556751i
$220$	−8.19530e30	+	1.38609e31i	−0.195370	+	0.330434i
$221$	2.87063e31	−	2.87063e31i	0.643698	−	0.643698i
$222$	3.06269e31	−	1.11977e32i	0.646157	−	2.36245i
$223$	−4.29850e29			−0.00853495			−0.00426748	−	0.999991i	$-0.501358\pi$
$223$	−4.29850e29			−0.00853495			−0.00426748	+	0.999991i	$0.501358\pi$
$224$	−1.74211e31	−	7.24788e31i	−0.325633	−	1.35476i
$225$	6.41695e31			1.12944
$226$	1.61535e31	−	5.90596e31i	0.267795	−	0.979099i
$227$	3.71539e31	−	3.71539e31i	0.580304	−	0.580304i	−0.354683	−	0.934987i	$-0.615411\pi$
$227$	3.71539e31	−	3.71539e31i	0.580304	−	0.580304i	0.934987	+	0.354683i	$0.115411\pi$
$228$	−6.89326e30	+	1.16587e31i	−0.101462	+	0.171605i
$229$	−9.12339e29	−	9.12339e29i	−0.0126584	−	0.0126584i	0.700749	−	0.713408i	$-0.252849\pi$
$229$	−9.12339e29	−	9.12339e29i	−0.0126584	−	0.0126584i	−0.713408	+	0.700749i	$0.752849\pi$
$230$	−4.15015e31	−	7.27508e31i	−0.542922	−	0.951726i
$231$			5.05734e31i			0.623965i
$232$	2.64423e29	−	1.70061e31i	0.00307760	−	0.197932i
$233$		−	8.96901e31i		−	0.985007i	−0.870310	−	0.492504i	$-0.836082\pi$
$233$		−	8.96901e31i		−	0.985007i	0.870310	−	0.492504i	$-0.163918\pi$
$234$	7.76638e31	−	4.43042e31i	0.805016	−	0.459230i
$235$	1.65366e32	+	1.65366e32i	1.61819	+	1.61819i
$236$	3.68356e31	+	1.43401e32i	0.340373	+	1.32508i
$237$	5.61841e31	−	5.61841e31i	0.490356	−	0.490356i
$238$	−2.29478e32	−	6.27648e31i	−1.89213	−	0.517520i
$239$	−4.78542e31			−0.372862			−0.186431	−	0.982468i	$-0.559692\pi$
$239$	−4.78542e31			−0.372862			−0.186431	+	0.982468i	$0.559692\pi$
$240$	−1.36499e32	−	2.48164e32i	−1.00526	−	1.82763i
$241$	−1.77505e31			−0.123589			−0.0617946	−	0.998089i	$-0.519682\pi$
$241$	−1.77505e31			−0.123589			−0.0617946	+	0.998089i	$0.519682\pi$
$242$	1.34428e32	+	3.67675e31i	0.885077	+	0.242079i
$243$	1.43863e32	−	1.43863e32i	0.895912	−	0.895912i
$244$	−1.70160e32	+	4.37090e31i	−1.00252	+	0.257518i
$245$	1.59658e32	+	1.59658e32i	0.890120	+	0.890120i
$246$	−3.49841e32	+	1.99571e32i	−1.84606	+	1.05311i
$247$		−	1.65416e31i		−	0.0826360i
$248$	2.35847e32	−	2.28625e32i	1.11566	−	1.08150i
$249$			2.66967e32i			1.19610i
$250$	−3.30960e31	−	5.80162e31i	−0.140470	−	0.246240i
$251$	2.95369e31	+	2.95369e31i	0.118787	+	0.118787i	0.764002	−	0.645214i	$-0.223232\pi$
$251$	2.95369e31	+	2.95369e31i	0.118787	+	0.118787i	−0.645214	+	0.764002i	$0.723232\pi$
$252$	−4.51035e32	−	2.66676e32i	−1.71911	−	1.01643i
$253$	4.60384e31	−	4.60384e31i	0.166339	−	0.166339i
$254$	2.20645e31	−	8.06712e31i	0.0755856	−	0.276352i
$255$	−9.03926e32			−2.93657
$256$	−1.73768e32	+	2.74074e32i	−0.535465	+	0.844557i
$257$	−1.52877e32			−0.446937			−0.223468	−	0.974711i	$-0.571738\pi$
$257$	−1.52877e32			−0.446937			−0.223468	+	0.974711i	$0.571738\pi$
$258$	4.68488e30	−	1.71286e31i	0.0129967	−	0.0475178i
$259$	5.87516e32	−	5.87516e32i	1.54694	−	1.54694i
$260$	2.97757e32	+	1.76050e32i	0.744255	+	0.440044i
$261$	−8.45364e31	−	8.45364e31i	−0.200630	−	0.200630i
$262$	2.87965e32	+	5.04793e32i	0.649040	+	1.13775i
$263$		−	4.21835e32i		−	0.903108i	−0.892244	−	0.451554i	$-0.850870\pi$
$263$		−	4.21835e32i		−	0.903108i	0.892244	−	0.451554i	$-0.149130\pi$
$264$	1.58084e32	−	1.53243e32i	0.321539	−	0.311693i
$265$			1.23105e33i			2.37935i
$266$	−8.42003e31	+	4.80330e31i	−0.154672	+	0.0882343i
$267$	8.56232e32	+	8.56232e32i	1.49517	+	1.49517i
$268$	1.00906e32	−	2.59197e31i	0.167532	−	0.0430339i
$269$	3.87413e32	−	3.87413e32i	0.611671	−	0.611671i	−0.331710	−	0.943381i	$-0.607626\pi$
$269$	3.87413e32	−	3.87413e32i	0.611671	−	0.611671i	0.943381	+	0.331710i	$0.107626\pi$
$270$	−5.80547e32	−	1.58786e32i	−0.871819	−	0.238453i
$271$	3.21230e32			0.458914			0.229457	−	0.973319i	$-0.426305\pi$
$271$	3.21230e32			0.458914			0.229457	+	0.973319i	$0.426305\pi$
$272$	4.99151e32	+	9.07493e32i	0.678504	+	1.23357i
$273$	1.08641e33			1.40539
$274$	4.05003e32	+	1.10773e32i	0.498685	+	0.136396i
$275$	−1.36458e32	+	1.36458e32i	−0.159959	+	0.159959i
$276$	2.84917e32	+	1.10919e33i	0.318014	+	1.23803i
$277$	7.78749e32	+	7.78749e32i	0.827791	+	0.827791i	0.987211	−	0.159420i	$-0.0509624\pi$
$277$	7.78749e32	+	7.78749e32i	0.827791	+	0.827791i	−0.159420	+	0.987211i	$0.550962\pi$
$278$	−8.06159e32	+	4.59882e32i	−0.816237	+	0.465631i
$279$		−	2.30887e33i		−	2.22712i
$280$	3.15151e31	−	2.02686e33i	0.0289658	−	1.86290i
$281$			7.81296e32i			0.684353i	0.939636	+	0.342176i	$0.111164\pi$
$281$			7.81296e32i			0.684353i	−0.939636	+	0.342176i	$0.888836\pi$
$282$	−1.58443e33	−	2.77745e33i	−1.32285	−	2.31891i
$283$	−5.11473e32	−	5.11473e32i	−0.407104	−	0.407104i	0.473623	−	0.880728i	$-0.342946\pi$
$283$	−5.11473e32	−	5.11473e32i	−0.407104	−	0.407104i	−0.880728	+	0.473623i	$0.842946\pi$
$284$	−1.19540e33	+	2.02181e33i	−0.907228	+	1.53441i
$285$	−2.60437e32	+	2.60437e32i	−0.188494	+	0.188494i
$286$	−7.09401e31	+	2.59368e32i	−0.0489723	+	0.179050i
$287$	−2.88263e33			−1.89838
$288$	5.33103e32	+	2.21792e33i	0.334975	+	1.39363i
$289$	1.63779e33			0.982057
$290$	1.22021e32	−	4.46127e32i	0.0698331	−	0.255320i
$291$	−1.42897e33	+	1.42897e33i	−0.780670	+	0.780670i
$292$	−4.92515e32	+	8.33001e32i	−0.256892	+	0.434487i
$293$	1.52919e33	+	1.52919e33i	0.761637	+	0.761637i	0.976618	−	0.214981i	$-0.0689691\pi$
$293$	1.52919e33	+	1.52919e33i	0.761637	+	0.761637i	−0.214981	+	0.976618i	$0.568969\pi$
$294$	−1.52974e33	−	2.68159e33i	−0.727661	−	1.27557i
$295$			4.02621e33i			1.82936i
$296$	−3.61671e33	−	5.62354e31i	−1.56991	−	0.0244102i
$297$		−	4.67867e32i		−	0.194049i
$298$	8.70314e32	−	4.96480e32i	0.344950	−	0.196780i
$299$	−9.88990e32	−	9.88990e32i	−0.374654	−	0.374654i
$300$	−8.44495e32	−	3.28763e33i	−0.305816	−	1.19055i
$301$	8.98699e31	−	8.98699e31i	0.0311148	−	0.0311148i
$302$	3.17960e33	+	8.69658e32i	1.05264	+	0.287909i
$303$	4.14983e33			1.31388
$304$	4.05280e32	+	1.17651e32i	0.122733	+	0.0356288i
$305$	−4.77748e33			−1.38405
$306$	7.02223e33	+	1.92066e33i	1.94642	+	0.532368i
$307$	−2.29932e32	+	2.29932e32i	−0.0609861	+	0.0609861i	−0.736942	−	0.675956i	$-0.763731\pi$
$307$	−2.29932e32	+	2.29932e32i	−0.0609861	+	0.0609861i	0.675956	+	0.736942i	$0.263731\pi$
$308$	1.52623e33	−	3.92043e32i	0.387423	−	0.0995175i
$309$	−4.52747e33	−	4.52747e33i	−1.10006	−	1.10006i
$310$	7.75867e33	−	4.42602e33i	1.80470	−	1.02951i
$311$			3.27978e33i			0.730432i	0.930923	+	0.365216i	$0.119005\pi$
$311$			3.27978e33i			0.730432i	−0.930923	+	0.365216i	$0.880995\pi$
$312$	−3.29194e33	−	3.39593e33i	−0.702046	−	0.724222i
$313$		−	1.95829e33i		−	0.399970i	−0.979799	−	0.199985i	$-0.935911\pi$
$313$		−	1.95829e33i		−	0.399970i	0.979799	−	0.199985i	$-0.0640893\pi$
$314$	2.71802e33	+	4.76460e33i	0.531743	+	0.932129i
$315$	−1.00754e34	−	1.00754e34i	−1.88830	−	1.88830i
$316$	−2.13109e33	−	1.26002e33i	−0.382672	−	0.226256i
$317$	4.32393e33	−	4.32393e33i	0.744010	−	0.744010i	−0.229337	−	0.973347i	$-0.573656\pi$
$317$	4.32393e33	−	4.32393e33i	0.744010	−	0.744010i	0.973347	+	0.229337i	$0.0736559\pi$
$318$	4.44070e33	−	1.62359e34i	0.732293	−	2.67738i
$319$	3.59537e32			0.0568290
$320$	−6.43110e33	+	6.04309e33i	−0.974452	+	0.915660i
$321$	1.19252e34			1.73240
$322$	−2.16237e33	+	7.90596e33i	−0.301215	+	1.10129i
$323$	9.52374e32	−	9.52374e32i	0.127225	−	0.127225i
$324$	−2.54564e33	−	1.50512e33i	−0.326166	−	0.192847i
$325$	2.93137e33	+	2.93137e33i	0.360284	+	0.360284i
$326$	7.17589e33	+	1.25791e34i	0.846132	+	1.48324i
$327$		−	1.42357e34i		−	1.61058i
$328$	8.73471e33	+	9.01062e33i	0.948312	+	0.978268i
$329$		−	2.28858e34i		−	2.38463i
$330$	5.20049e33	−	2.96667e33i	0.520123	−	0.296710i
$331$	−7.31312e33	−	7.31312e33i	−0.702141	−	0.702141i	0.262728	−	0.964870i	$-0.415378\pi$
$331$	−7.31312e33	−	7.31312e33i	−0.702141	−	0.702141i	−0.964870	+	0.262728i	$0.915378\pi$
$332$	8.05667e33	−	2.06952e33i	0.742662	−	0.190768i
$333$	−1.79785e34	+	1.79785e34i	−1.59132	+	1.59132i
$334$	7.13347e33	+	1.95109e33i	0.606350	+	0.165844i
$335$	2.83308e33			0.231289
$336$	−7.72697e33	+	2.66177e34i	−0.605939	+	2.08732i
$337$	−1.23450e34			−0.930011			−0.465005	−	0.885308i	$-0.653948\pi$
$337$	−1.23450e34			−0.930011			−0.465005	+	0.885308i	$0.653948\pi$
$338$	−7.75461e33	−	2.12098e33i	−0.561286	−	0.153518i
$339$	−1.60980e34	+	1.60980e34i	−1.11964	+	1.11964i
$340$	7.00721e33	+	2.72792e34i	0.468360	+	1.82333i
$341$	4.90987e33	+	4.90987e33i	0.315417	+	0.315417i
$342$	2.57661e33	−	1.46985e33i	0.159109	−	0.0907657i
$343$			1.37505e33i			0.0816297i
$344$	−5.53234e32	−	8.60210e30i	−0.0315769	−	0.000490982i
$345$			3.11420e34i			1.70919i
$346$	−1.44678e34	−	2.53616e34i	−0.763617	−	1.33860i
$347$	−2.23413e34	−	2.23413e34i	−1.13413	−	1.13413i	−0.989484	−	0.144641i	$-0.953797\pi$
$347$	−2.23413e34	−	2.23413e34i	−1.13413	−	1.13413i	−0.144641	−	0.989484i	$-0.546203\pi$
$348$	−3.21857e33	+	5.44363e33i	−0.157160	+	0.265808i
$349$	7.52393e33	−	7.52393e33i	0.353428	−	0.353428i	−0.507955	−	0.861384i	$-0.669598\pi$
$349$	7.52393e33	−	7.52393e33i	0.353428	−	0.353428i	0.861384	+	0.507955i	$0.169598\pi$
$350$	6.40928e33	−	2.34333e34i	0.289661	−	1.05905i
$351$	−1.00506e34			−0.437067
$352$	−5.85011e33	−	3.58280e33i	−0.244815	−	0.149933i
$353$	1.34410e34			0.541343			0.270672	−	0.962672i	$-0.412754\pi$
$353$	1.34410e34			0.541343			0.270672	+	0.962672i	$0.412754\pi$
$354$	1.45235e34	−	5.31000e34i	0.563023	−	2.05850i
$355$	−4.51640e34	+	4.51640e34i	−1.68543	+	1.68543i
$356$	1.92023e34	−	3.24773e34i	0.689889	−	1.16682i
$357$	6.25494e34	+	6.25494e34i	2.16372	+	2.16372i
$358$	1.70974e34	+	2.99713e34i	0.569521	+	0.998353i
$359$		−	4.74222e34i		−	1.52127i	−0.649179	−	0.760636i	$-0.724887\pi$
$359$		−	4.74222e34i		−	1.52127i	0.649179	−	0.760636i	$-0.275113\pi$
$360$	−9.64391e32	+	6.20237e34i	−0.0297968	+	1.91634i
$361$			3.30518e34i			0.983667i
$362$	−2.47170e34	+	1.41001e34i	−0.708648	+	0.404256i
$363$	−3.66413e34	−	3.66413e34i	−1.01212	−	1.01212i
$364$	−8.42182e33	−	3.27862e34i	−0.224149	−	0.872616i
$365$	−1.86079e34	+	1.86079e34i	−0.477248	+	0.477248i
$366$	6.30083e34	+	1.72335e34i	1.55741	+	0.425970i
$367$	−1.61651e34			−0.385111			−0.192556	−	0.981286i	$-0.561678\pi$
$367$	−1.61651e34			−0.385111			−0.192556	+	0.981286i	$0.561678\pi$
$368$	3.12649e34	−	1.71968e34i	0.717979	−	0.394913i
$369$	8.82113e34			1.95285
$370$	−9.48787e34	−	2.59504e34i	−2.02510	−	0.553887i
$371$	8.51858e34	−	8.51858e34i	1.75315	−	1.75315i
$372$	−1.18292e35	+	3.03856e34i	−2.34760	+	0.603029i
$373$	2.06144e34	+	2.06144e34i	0.394550	+	0.394550i	0.876306	−	0.481756i	$-0.160001\pi$
$373$	2.06144e34	+	2.06144e34i	0.394550	+	0.394550i	−0.481756	+	0.876306i	$0.660001\pi$
$374$	−1.90173e34	+	1.08486e34i	−0.351060	+	0.200266i
$375$			2.48347e34i			0.442218i
$376$	−7.15370e34	+	6.93465e34i	−1.22884	+	1.19121i
$377$		−	7.72352e33i		−	0.127999i
$378$	2.91847e34	+	5.11599e34i	0.466677	+	0.818070i
$379$	5.83455e34	+	5.83455e34i	0.900281	+	0.900281i	0.995460	−	0.0951796i	$-0.0303425\pi$
$379$	5.83455e34	+	5.83455e34i	0.900281	+	0.900281i	−0.0951796	+	0.995460i	$0.530343\pi$
$380$	9.87852e33	+	5.84072e33i	0.147100	+	0.0869736i
$381$	−2.19888e34	+	2.19888e34i	−0.316019	+	0.316019i
$382$	6.44597e33	−	2.35674e34i	0.0894196	−	0.326932i
$383$	−1.00903e35			−1.35120			−0.675601	−	0.737268i	$-0.736116\pi$
$383$	−1.00903e35			−1.35120			−0.675601	+	0.737268i	$0.736116\pi$
$384$	1.06616e35	−	5.65014e34i	1.37832	−	0.730445i
$385$	4.28512e34			0.534864
$386$	2.62240e34	−	9.58791e34i	0.316061	−	1.15557i
$387$	−2.75010e33	+	2.75010e33i	−0.0320074	+	0.0320074i
$388$	5.42015e34	+	3.20469e34i	0.609233	+	0.360211i
$389$	1.09517e35	+	1.09517e35i	1.18895	+	1.18895i	0.977359	+	0.211586i	$0.0678627\pi$
$389$	1.09517e35	+	1.09517e35i	1.18895	+	1.18895i	0.211586	+	0.977359i	$0.432137\pi$
$390$	−6.37297e34	−	1.11716e35i	−0.668297	−	1.17150i
$391$		−	1.13881e35i		−	1.15363i
$392$	−6.90679e34	+	6.69529e34i	−0.675950	+	0.655251i
$393$		−	2.16084e35i		−	2.04326i
$394$	1.55804e35	−	8.88800e34i	1.42357	−	0.812091i
$395$	−4.76053e34	−	4.76053e34i	−0.420334	−	0.420334i
$396$	−4.67041e34	+	1.19969e34i	−0.398538	+	0.102373i
$397$	−6.09021e34	+	6.09021e34i	−0.502297	+	0.502297i	−0.912151	−	0.409854i	$-0.865580\pi$
$397$	−6.09021e34	+	6.09021e34i	−0.502297	+	0.502297i	0.409854	+	0.912151i	$0.365580\pi$
$398$	−9.37329e34	−	2.56370e34i	−0.747258	−	0.204384i
$399$	3.60432e34			0.277772
$400$	−9.26694e34	+	5.09712e34i	−0.690441	+	0.379765i
$401$	−9.47322e34			−0.682415			−0.341207	−	0.939988i	$-0.610836\pi$
$401$	−9.47322e34			−0.682415			−0.341207	+	0.939988i	$0.610836\pi$
$402$	−3.73644e34	−	1.02196e34i	−0.260259	−	0.0711839i
$403$	1.05473e35	−	1.05473e35i	0.710433	−	0.710433i
$404$	−3.21694e34	−	1.25236e35i	−0.209553	−	0.815794i
$405$	−5.68655e34	−	5.68655e34i	−0.358267	−	0.358267i
$406$	−3.93144e34	+	2.24273e34i	−0.239580	+	0.136671i
$407$		−	7.64635e34i		−	0.450744i
$408$	5.98705e33	−	3.85050e35i	0.0341429	−	2.19586i
$409$			2.37502e35i			1.31040i	0.755457	+	0.655198i	$0.227415\pi$
$409$			2.37502e35i			1.31040i	−0.755457	+	0.655198i	$0.772585\pi$
$410$	1.69098e35	+	2.96423e35i	0.902725	+	1.58245i
$411$	−1.10393e35	−	1.10393e35i	−0.570265	−	0.570265i
$412$	−1.01536e35	+	1.71729e35i	−0.507581	+	0.858483i
$413$	2.78603e35	−	2.78603e35i	1.34791	−	1.34791i
$414$	6.61706e34	−	2.41930e35i	0.309856	−	1.13288i
$415$	2.26203e35			1.02530
$416$	−7.69652e34	+	1.25671e35i	−0.337703	+	0.551411i
$417$	3.45088e35			1.46586
$418$	−2.35354e33	+	8.60490e33i	−0.00967925	+	0.0353888i
$419$	−1.33631e35	+	1.33631e35i	−0.532130	+	0.532130i	−0.921206	−	0.389076i	$-0.872794\pi$
$419$	−1.33631e35	+	1.33631e35i	−0.532130	+	0.532130i	0.389076	+	0.921206i	$0.372794\pi$
$420$	−3.83603e35	+	6.48795e35i	−1.47916	+	2.50174i
$421$	−1.32147e35	−	1.32147e35i	−0.493456	−	0.493456i	0.415937	−	0.909393i	$-0.363454\pi$
$421$	−1.32147e35	−	1.32147e35i	−0.493456	−	0.493456i	−0.909393	+	0.415937i	$0.863454\pi$
$422$	−8.13063e34	−	1.42527e35i	−0.294040	−	0.515443i
$423$			7.00326e35i			2.45304i
$424$	−5.24399e35	−	8.15375e33i	−1.77919	−	0.0276642i
$425$			3.37544e35i			1.10938i
$426$	7.58566e35	−	4.32732e35i	2.41526	−	1.37781i
$427$	3.30590e35	+	3.30590e35i	1.01980	+	1.01980i
$428$	−9.24438e34	−	3.59885e35i	−0.276304	−	1.07565i
$429$	7.06966e34	−	7.06966e34i	0.204750	−	0.204750i
$430$	−1.45132e34	−	3.96953e33i	−0.0407324	−	0.0111408i
$431$	−7.27782e35			−1.97951			−0.989756	−	0.142770i	$-0.954399\pi$
$431$	−7.27782e35			−1.97951			−0.989756	+	0.142770i	$0.954399\pi$
$432$	7.14842e34	−	2.46247e35i	0.188443	−	0.649143i
$433$	1.69859e35			0.434013			0.217007	−	0.976170i	$-0.430371\pi$
$433$	1.69859e35			0.434013			0.217007	+	0.976170i	$0.430371\pi$
$434$	−8.43149e35	−	2.30611e35i	−2.08830	−	0.571174i
$435$	−1.21602e35	+	1.21602e35i	−0.291968	+	0.291968i
$436$	−4.29612e35	+	1.10355e35i	−1.00002	+	0.256875i
$437$	−3.28112e34	−	3.28112e34i	−0.0740495	−	0.0740495i
$438$	3.12535e35	−	1.78289e35i	0.683909	−	0.390143i
$439$		−	2.63494e35i		−	0.559113i	−0.960129	−	0.279556i	$-0.909813\pi$
$439$		−	2.63494e35i		−	0.559113i	0.960129	−	0.279556i	$-0.0901874\pi$
$440$	−1.29844e35	−	1.33946e35i	−0.267184	−	0.275624i
$441$			6.76154e35i			1.34935i
$442$	2.33048e35	+	4.08526e35i	0.451071	+	0.790714i
$443$	4.72993e35	+	4.72993e35i	0.887982	+	0.887982i	0.994329	−	0.106347i	$-0.0339154\pi$
$443$	4.72993e35	+	4.72993e35i	0.887982	+	0.887982i	−0.106347	+	0.994329i	$0.533915\pi$
$444$	1.15771e36	+	6.84499e35i	2.10828	+	1.24653i
$445$	7.25492e35	−	7.25492e35i	1.28166	−	1.28166i
$446$	1.31381e33	−	4.80348e33i	0.00225170	−	0.00823257i
$447$	−3.72550e35			−0.619489
$448$	8.63182e35	+	2.68493e34i	1.39267	+	0.0433191i
$449$	3.12732e35			0.489606			0.244803	−	0.969573i	$-0.421277\pi$
$449$	3.12732e35			0.489606			0.244803	+	0.969573i	$0.421277\pi$
$450$	−1.96130e35	+	7.17081e35i	−0.297972	+	1.08943i
$451$	−1.87583e35	+	1.87583e35i	−0.276574	+	0.276574i
$452$	6.10607e35	+	3.61024e35i	0.873761	+	0.516615i
$453$	−8.66673e35	−	8.66673e35i	−1.20373	−	1.20373i
$454$	3.01629e35	+	5.28745e35i	0.406648	+	0.712841i
$455$		−	9.20523e35i		−	1.20470i
$456$	−1.09215e35	−	1.12665e35i	−0.138758	−	0.143141i
$457$			9.52053e35i			1.17434i	0.809465	+	0.587168i	$0.199757\pi$
$457$			9.52053e35i			1.17434i	−0.809465	+	0.587168i	$0.800243\pi$
$458$	1.29837e34	−	7.40669e33i	0.0155494	−	0.00887034i
$459$	−5.78660e35	−	5.78660e35i	−0.672903	−	0.672903i
$460$	9.39822e35	−	2.41412e35i	1.06124	−	0.272602i
$461$	−2.11549e34	+	2.11549e34i	−0.0231979	+	0.0231979i	−0.718611	−	0.695413i	$-0.755222\pi$
$461$	−2.11549e34	+	2.11549e34i	−0.0231979	+	0.0231979i	0.695413	+	0.718611i	$0.255222\pi$
$462$	−5.65147e35	−	1.54574e35i	−0.601859	−	0.164615i
$463$	2.32586e35			0.240569			0.120284	−	0.992739i	$-0.461619\pi$
$463$	2.32586e35			0.240569			0.120284	+	0.992739i	$0.461619\pi$
$464$	1.89231e35	+	5.49328e34i	0.190108	+	0.0551873i
$465$	−3.32121e36			−3.24102
$466$	1.00227e36	+	2.74132e35i	0.950110	+	0.259866i
$467$	4.10953e35	−	4.10953e35i	0.378455	−	0.378455i	−0.492089	−	0.870545i	$-0.663767\pi$
$467$	4.10953e35	−	4.10953e35i	0.378455	−	0.378455i	0.870545	+	0.492089i	$0.163767\pi$
$468$	2.57715e35	+	1.00329e36i	0.230580	+	0.897650i
$469$	−1.96042e35	−	1.96042e35i	−0.170418	−	0.170418i
$470$	−2.35336e36	+	1.34250e36i	−1.98777	+	1.13395i
$471$		−	2.03956e36i		−	1.67399i
$472$	−1.71507e36	−	2.66671e34i	−1.36793	−	0.0212696i
$473$		−	1.16963e34i		−	0.00906616i
$474$	4.56123e35	+	7.99569e35i	0.343617	+	0.602349i
$475$	9.72524e34	+	9.72524e34i	0.0712093	+	0.0712093i
$476$	1.40277e36	−	2.37253e36i	0.998371	−	1.68856i
$477$	−2.60676e36	+	2.60676e36i	−1.80345	+	1.80345i
$478$	1.46263e35	−	5.34760e35i	0.0983690	−	0.359652i
$479$	−7.67223e35			−0.501640			−0.250820	−	0.968034i	$-0.580700\pi$
$479$	−7.67223e35			−0.501640			−0.250820	+	0.968034i	$0.580700\pi$
$480$	3.19038e36	−	7.66845e35i	2.02808	−	0.487474i
$481$	−1.64258e36			−1.01524
$482$	5.42532e34	−	1.98358e35i	0.0326055	−	0.119211i
$483$	2.15495e36	−	2.15495e36i	1.25936	−	1.25936i
$484$	−8.21738e35	+	1.38982e36i	−0.467005	+	0.789855i
$485$	1.21078e36	+	1.21078e36i	0.669192	+	0.669192i
$486$	1.16793e36	+	2.04735e36i	0.627810	+	1.10053i
$487$			1.74210e36i			0.910821i	0.890282	+	0.455410i	$0.150507\pi$
$487$			1.74210e36i			0.910821i	−0.890282	+	0.455410i	$0.849493\pi$
$488$	3.16431e34	−	2.03509e36i	0.0160921	−	1.03494i
$489$		−	5.38467e36i		−	2.66373i
$490$	−2.27213e36	+	1.29616e36i	−1.09342	+	0.623752i
$491$	8.48223e35	+	8.48223e35i	0.397109	+	0.397109i	0.877212	−	0.480103i	$-0.159401\pi$
$491$	8.48223e35	+	8.48223e35i	0.397109	+	0.397109i	−0.480103	+	0.877212i	$0.659401\pi$
$492$	−1.16089e36	−	4.51937e36i	−0.528766	−	2.05849i
$493$	4.44677e35	−	4.44677e35i	0.197066	−	0.197066i
$494$	1.84849e35	+	5.05584e34i	0.0797083	+	0.0218011i
$495$	−1.31129e36			−0.550209
$496$	1.83399e36	+	3.33432e36i	0.748848	+	1.36146i
$497$	6.25047e36			2.48371
$498$	−2.98330e36	−	8.15966e35i	−1.15372	−	0.315556i
$499$	2.56679e35	−	2.56679e35i	0.0966126	−	0.0966126i	−0.657149	−	0.753761i	$-0.728238\pi$
$499$	2.56679e35	−	2.56679e35i	0.0966126	−	0.0966126i	0.753761	+	0.657149i	$0.228238\pi$
$500$	7.49474e35	−	1.92518e35i	0.274576	−	0.0705303i
$501$	−1.94439e36	−	1.94439e36i	−0.693384	−	0.693384i
$502$	−4.20346e35	+	2.39791e35i	−0.145917	+	0.0832401i
$503$			8.33207e35i			0.281569i	0.990040	+	0.140785i	$0.0449625\pi$
$503$			8.33207e35i			0.281569i	−0.990040	+	0.140785i	$0.955037\pi$
$504$	4.35861e36	−	4.22514e36i	1.43396	−	1.39005i
$505$		−	3.51619e36i		−	1.12626i
$506$	3.73756e35	+	6.55183e35i	0.116562	+	0.204329i
$507$	2.11369e36	+	2.11369e36i	0.641852	+	0.641852i
$508$	8.34045e35	+	4.93132e35i	0.246621	+	0.145815i
$509$	−1.18360e36	+	1.18360e36i	−0.340813	+	0.340813i	−0.856673	−	0.515860i	$-0.827472\pi$
$509$	−1.18360e36	+	1.18360e36i	−0.340813	+	0.340813i	0.515860	+	0.856673i	$0.327472\pi$
$510$	2.76279e36	−	1.01012e37i	0.774730	−	2.83253i
$511$	2.57524e36			0.703292
$512$	−2.53161e36	−	2.77952e36i	−0.673368	−	0.739307i
$513$	−3.33445e35			−0.0863852
$514$	4.67260e35	−	1.70837e36i	0.117912	−	0.431103i
$515$	−3.83616e36	+	3.83616e36i	−0.942972	+	0.942972i
$516$	1.77090e35	+	1.04705e35i	0.0424055	+	0.0250724i
$517$	−1.48926e36	−	1.48926e36i	−0.347414	−	0.347414i
$518$	4.76966e36	+	8.36107e36i	1.08402	+	1.90025i
$519$			1.08564e37i			2.40396i
$520$	−2.87740e36	+	2.78929e36i	−0.620804	+	0.601795i
$521$		−	3.45656e36i		−	0.726665i	−0.931659	−	0.363333i	$-0.881639\pi$
$521$		−	3.45656e36i		−	0.726665i	0.931659	−	0.363333i	$-0.118361\pi$
$522$	1.20306e36	−	6.86297e35i	0.246453	−	0.140592i
$523$	6.41317e35	+	6.41317e35i	0.128027	+	0.128027i	0.768217	−	0.640190i	$-0.221144\pi$
$523$	6.41317e35	+	6.41317e35i	0.128027	+	0.128027i	−0.640190	+	0.768217i	$0.721144\pi$
$524$	−6.52110e36	+	1.67508e36i	−1.26867	+	0.325884i
$525$	−6.38728e36	+	6.38728e36i	−1.21106	+	1.21106i
$526$	4.71391e36	+	1.28931e36i	0.871112	+	0.238259i
$527$	1.21451e37			2.18755
$528$	1.22929e36	+	2.23493e36i	0.215822	+	0.392379i
$529$	1.91978e36			0.328549
$530$	−1.37568e37	−	3.76264e36i	−2.29505	−	0.627723i
$531$	−8.52552e36	+	8.52552e36i	−1.38658	+	1.38658i
$532$	−2.79406e35	−	1.08773e36i	−0.0443025	−	0.172470i
$533$	4.02964e36	+	4.02964e36i	0.622943	+	0.622943i
$534$	−1.21852e37	+	6.95120e36i	−1.83665	+	1.04774i
$535$		−	1.01043e37i		−	1.48501i
$536$	−1.87646e34	+	1.20682e36i	−0.00268915	+	0.172950i
$537$		−	1.28296e37i		−	1.79292i
$538$	3.14516e36	+	5.51336e36i	0.428629	+	0.751373i
$539$	−1.43786e36	−	1.43786e36i	−0.191103	−	0.191103i
$540$	3.54881e36	−	6.00217e36i	0.460009	−	0.778023i
$541$	−2.86551e36	+	2.86551e36i	−0.362275	+	0.362275i	−0.864650	−	0.502375i	$-0.832460\pi$
$541$	−2.86551e36	+	2.86551e36i	−0.362275	+	0.362275i	0.502375	+	0.864650i	$0.332460\pi$
$542$	−9.81820e35	+	3.58968e36i	−0.121071	+	0.442655i
$543$	1.05805e37			1.27265
$544$	−1.16667e37	+	2.80422e36i	−1.36887	+	0.329023i
$545$	−1.20620e37			−1.38059
$546$	−3.32054e36	+	1.21404e37i	−0.370773	+	1.35560i
$547$	5.01342e36	−	5.01342e36i	0.546141	−	0.546141i	−0.379181	−	0.925322i	$-0.623794\pi$
$547$	5.01342e36	−	5.01342e36i	0.546141	−	0.546141i	0.925322	+	0.379181i	$0.123794\pi$
$548$	−2.47573e36	+	4.18726e36i	−0.263127	+	0.445033i
$549$	−1.01163e37	−	1.01163e37i	−1.04905	−	1.04905i
$550$	−1.10781e36	−	1.94196e36i	−0.112091	−	0.196492i
$551$		−	2.56239e35i		−	0.0252987i
$552$	−1.32657e37	−	2.06266e35i	−1.27807	−	0.0198724i
$553$			6.58832e36i			0.619420i
$554$	−1.10826e37	+	6.32216e36i	−1.01685	+	0.580075i
$555$	2.58613e37	+	2.58613e37i	2.31577	+	2.31577i
$556$	−2.67512e36	−	1.04143e37i	−0.233794	−	0.910162i
$557$	8.33414e36	−	8.33414e36i	0.710912	−	0.710912i	−0.255814	−	0.966726i	$-0.582343\pi$
$557$	8.33414e36	−	8.33414e36i	0.710912	−	0.710912i	0.966726	+	0.255814i	$0.0823435\pi$
$558$	2.58011e37	+	7.05691e36i	2.14821	+	0.587561i
$559$	−2.51258e35			−0.0204203
$560$	2.25534e37	+	6.54712e36i	1.78926	+	0.519412i
$561$	8.14062e36			0.630462
$562$	−8.73082e36	−	2.38798e36i	−0.660107	−	0.180547i
$563$	8.92867e36	−	8.92867e36i	0.659057	−	0.659057i	−0.296100	−	0.955157i	$-0.595686\pi$
$563$	8.92867e36	−	8.92867e36i	0.659057	−	0.659057i	0.955157	+	0.296100i	$0.0956860\pi$
$564$	3.58801e37	−	9.21655e36i	2.58575	−	0.664202i
$565$	1.36400e37	+	1.36400e37i	0.959754	+	0.959754i
$566$	7.27888e36	−	4.15232e36i	0.500084	−	0.285278i
$567$			7.86990e36i			0.527956i
$568$	−1.89396e37	−	1.95379e37i	−1.24071	−	1.27990i
$569$		−	7.51124e36i		−	0.480503i	−0.970711	−	0.240251i	$-0.922770\pi$
$569$		−	7.51124e36i		−	0.480503i	0.970711	−	0.240251i	$-0.0772299\pi$
$570$	−2.11432e36	−	3.70634e36i	−0.132087	−	0.231545i
$571$	−9.25930e36	−	9.25930e36i	−0.564925	−	0.564925i	0.365777	−	0.930702i	$-0.380803\pi$
$571$	−9.25930e36	−	9.25930e36i	−0.564925	−	0.564925i	−0.930702	+	0.365777i	$0.880803\pi$
$572$	−2.68156e36	−	1.58548e36i	−0.159787	−	0.0944745i
$573$	−6.42384e36	+	6.42384e36i	−0.373858	+	0.373858i
$574$	8.81058e36	−	3.22128e37i	0.500834	−	1.83113i
$575$	1.16290e37			0.645696
$576$	−2.64142e37	−	8.21613e35i	−1.43263	−	0.0445619i
$577$	1.26778e37			0.671691			0.335845	−	0.941917i	$-0.390978\pi$
$577$	1.26778e37			0.671691			0.335845	+	0.941917i	$0.390978\pi$
$578$	−5.00579e36	+	1.83019e37i	−0.259088	+	0.947264i
$579$	−2.61340e37	+	2.61340e37i	−1.32143	+	1.32143i
$580$	4.61243e36	+	2.72712e36i	0.227851	+	0.134718i
$581$	−1.56527e37	−	1.56527e37i	−0.755458	−	0.755458i
$582$	−1.16009e37	−	2.03360e37i	−0.547055	−	0.958970i
$583$		−	1.10867e37i		−	0.510830i
$584$	−7.80327e36	−	8.04976e36i	−0.351320	−	0.362418i
$585$			2.81689e37i			1.23927i
$586$	−2.17622e37	+	1.24145e37i	−0.935589	+	0.533717i
$587$	−7.64264e36	−	7.64264e36i	−0.321092	−	0.321092i	0.528094	−	0.849186i	$-0.322907\pi$
$587$	−7.64264e36	−	7.64264e36i	−0.321092	−	0.321092i	−0.849186	+	0.528094i	$0.822907\pi$
$588$	3.46417e37	−	8.89843e36i	1.42235	−	0.365359i
$589$	3.49922e36	−	3.49922e36i	0.140415	−	0.140415i
$590$	−4.49920e37	−	1.23058e37i	−1.76455	−	0.482624i
$591$	−6.66941e37			−2.55656
$592$	1.16827e37	−	4.02441e37i	0.437722	−	1.50785i
$593$	7.05269e36			0.258295			0.129148	−	0.991625i	$-0.458776\pi$
$593$	7.05269e36			0.258295			0.129148	+	0.991625i	$0.458776\pi$
$594$	5.22832e36	+	1.43001e36i	0.187174	+	0.0511942i
$595$	5.29985e37	−	5.29985e37i	1.85475	−	1.85475i
$596$	2.88800e36	+	1.12430e37i	0.0988036	+	0.384644i
$597$	2.55490e37	+	2.55490e37i	0.854517	+	0.854517i
$598$	1.40745e37	−	8.02897e36i	0.460223	−	0.262539i
$599$		−	2.26859e37i		−	0.725260i	−0.931933	−	0.362630i	$-0.881879\pi$
$599$		−	2.26859e37i		−	0.725260i	0.931933	−	0.362630i	$-0.118121\pi$
$600$	3.93197e37	+	6.11373e35i	1.22905	+	0.0191101i
$601$			1.66138e37i			0.507767i	0.967235	+	0.253884i	$0.0817080\pi$
$601$			1.66138e37i			0.507767i	−0.967235	+	0.253884i	$0.918292\pi$
$602$	7.29596e35	+	1.27896e36i	0.0218037	+	0.0382212i
$603$	5.99907e36	+	5.99907e36i	0.175307	+	0.175307i
$604$	−1.94365e37	+	3.28734e37i	−0.555417	+	0.939389i
$605$	−3.10464e37	+	3.10464e37i	−0.867590	+	0.867590i
$606$	−1.26837e37	+	4.63735e37i	−0.346629	+	1.26733i
$607$	2.03778e37			0.544640			0.272320	−	0.962207i	$-0.412209\pi$
$607$	2.03778e37			0.544640			0.272320	+	0.962207i	$0.412209\pi$
$608$	−2.55343e36	+	4.16932e36i	−0.0667461	+	0.108985i
$609$	1.68291e37			0.430256
$610$	1.46021e37	−	5.33874e37i	0.365142	−	1.33501i
$611$	−3.19920e37	+	3.19920e37i	−0.782502	+	0.782502i
$612$	−4.29260e37	+	7.26016e37i	−1.02701	+	1.73701i
$613$	−5.31158e35	−	5.31158e35i	−0.0124310	−	0.0124310i	0.700864	−	0.713295i	$-0.252798\pi$
$613$	−5.31158e35	−	5.31158e35i	−0.0124310	−	0.0124310i	−0.713295	+	0.700864i	$0.752798\pi$
$614$	−1.86667e36	−	3.27221e36i	−0.0427360	−	0.0749148i
$615$		−	1.26888e38i		−	2.84189i
$616$	−2.83820e35	+	1.82536e37i	−0.00621876	+	0.399952i
$617$		−	6.93443e37i		−	1.48649i	−0.669022	−	0.743243i	$-0.733287\pi$
$617$		−	6.93443e37i		−	1.48649i	0.669022	−	0.743243i	$-0.266713\pi$
$618$	6.44314e37	−	3.67556e37i	1.35130	−	0.770866i
$619$	−1.46679e37	−	1.46679e37i	−0.300985	−	0.300985i	0.540414	−	0.841399i	$-0.318268\pi$
$619$	−1.46679e37	−	1.46679e37i	−0.300985	−	0.300985i	−0.841399	+	0.540414i	$0.818268\pi$
$620$	2.57460e37	+	1.00229e38i	0.516917	+	2.01237i
$621$	−1.99360e37	+	1.99360e37i	−0.391653	+	0.391653i
$622$	−3.66509e37	−	1.00244e37i	−0.704554	−	0.192704i
$623$	−1.00404e38			−1.88870
$624$	4.80104e37	−	2.64073e37i	0.883779	−	0.486108i
$625$	6.47849e37			1.16706
$626$	2.18834e37	+	5.98537e36i	0.385800	+	0.105521i
$627$	2.34546e36	−	2.34546e36i	0.0404684	−	0.0404684i
$628$	−6.15508e37	+	1.58106e37i	−1.03939	+	0.266989i
$629$	−9.45704e37	−	9.45704e37i	−1.56305	−	1.56305i
$630$	1.43385e38	−	8.17958e37i	2.31957	−	1.32322i
$631$		−	2.39552e37i		−	0.379317i	−0.981850	−	0.189659i	$-0.939262\pi$
$631$		−	2.39552e37i		−	0.379317i	0.981850	−	0.189659i	$-0.0607382\pi$
$632$	2.05940e37	−	1.99634e37i	0.319198	−	0.309423i
$633$			6.10110e37i			0.925674i
$634$	3.51032e37	+	6.15348e37i	0.521365	+	0.913936i
$635$	1.86312e37	+	1.86312e37i	0.270892	+	0.270892i
$636$	1.67860e38	+	9.92477e37i	2.38933	+	1.41270i
$637$	−3.08878e37	+	3.08878e37i	−0.430432	+	0.430432i
$638$	−1.09890e36	+	4.01775e36i	−0.0149927	+	0.0548156i
$639$	−1.91270e38			−2.55497
$640$	−4.78740e37	−	9.03365e37i	−0.626138	−	1.18150i
$641$	7.86343e37			1.00700			0.503499	−	0.863996i	$-0.332046\pi$
$641$	7.86343e37			1.00700			0.503499	+	0.863996i	$0.332046\pi$
$642$	−3.64486e37	+	1.33262e38i	−0.457044	+	1.67102i
$643$	−2.05779e37	+	2.05779e37i	−0.252669	+	0.252669i	−0.822064	−	0.569395i	$-0.807178\pi$
$643$	−2.05779e37	+	2.05779e37i	−0.252669	+	0.252669i	0.569395	+	0.822064i	$0.307178\pi$
$644$	−8.17383e37	−	4.83281e37i	−0.982803	−	0.581086i
$645$	3.95591e36	+	3.95591e36i	0.0465790	+	0.0465790i
$646$	7.73171e36	+	1.35534e37i	0.0891531	+	0.156283i
$647$			1.63042e38i			1.84116i	0.390558	+	0.920578i	$0.372282\pi$
$647$			1.63042e38i			1.84116i	−0.390558	+	0.920578i	$0.627718\pi$
$648$	2.46000e37	−	2.38467e37i	0.272065	−	0.263734i
$649$		−	3.62594e37i		−	0.392751i
$650$	−4.17170e37	+	2.37979e37i	−0.442571	+	0.252469i
$651$	2.29819e38	+	2.29819e38i	2.38805	+	2.38805i
$652$	−1.62502e38	+	4.17418e37i	−1.65392	+	0.424844i
$653$	−5.67306e36	+	5.67306e36i	−0.0565574	+	0.0565574i	−0.734820	−	0.678262i	$-0.762733\pi$
$653$	−5.67306e36	+	5.67306e36i	−0.0565574	+	0.0565574i	0.678262	+	0.734820i	$0.262733\pi$
$654$	1.59081e38	+	4.35104e37i	1.55352	+	0.424906i
$655$	−1.83090e38			−1.75148
$656$	−1.27389e38	+	7.00681e37i	−1.19379	+	0.656627i
$657$	−7.88047e37			−0.723469
$658$	2.55744e38	+	6.99488e37i	2.30015	+	0.629116i
$659$	4.50335e37	−	4.50335e37i	0.396810	−	0.396810i	−0.480296	−	0.877106i	$-0.659471\pi$
$659$	4.50335e37	−	4.50335e37i	0.396810	−	0.396810i	0.877106	+	0.480296i	$0.159471\pi$
$660$	1.72570e37	+	6.71818e37i	0.148978	+	0.579974i
$661$	7.29781e37	+	7.29781e37i	0.617267	+	0.617267i	0.944829	−	0.327563i	$-0.106227\pi$
$661$	7.29781e37	+	7.29781e37i	0.617267	+	0.617267i	−0.327563	+	0.944829i	$0.606227\pi$
$662$	1.04075e38	−	5.93705e37i	0.862505	−	0.492026i
$663$		−	1.74876e38i		−	1.42003i
$664$	−1.49823e36	+	9.63569e37i	−0.0119209	+	0.766679i
$665$		−	3.05397e37i		−	0.238107i
$666$	−1.45956e38	−	2.55856e38i	−1.11512	−	1.95476i
$667$	−1.53200e37	−	1.53200e37i	−0.114699	−	0.114699i
$668$	−4.36060e37	+	7.37516e37i	−0.319936	+	0.541115i
$669$	−1.30930e36	+	1.30930e36i	−0.00941425	+	0.00941425i
$670$	−8.65913e36	+	3.16591e37i	−0.0610189	+	0.223095i
$671$	4.30253e37			0.297146
$672$	−2.73830e38	−	1.67702e38i	−1.85351	−	1.13515i
$673$	2.19840e38			1.45849			0.729246	−	0.684251i	$-0.239871\pi$
$673$	2.19840e38			1.45849			0.729246	+	0.684251i	$0.239871\pi$
$674$	3.77317e37	−	1.37953e38i	0.245357	−	0.897062i
$675$	5.90903e37	−	5.90903e37i	0.376631	−	0.376631i
$676$	4.74029e37	−	8.01735e37i	0.296159	−	0.500899i
$677$	1.47102e38	+	1.47102e38i	0.900890	+	0.900890i	0.995513	−	0.0946230i	$-0.0301646\pi$
$677$	1.47102e38	+	1.47102e38i	0.900890	+	0.900890i	−0.0946230	+	0.995513i	$0.530165\pi$
$678$	−1.30690e38	−	2.29095e38i	−0.784585	−	1.37535i
$679$		−	1.67565e38i		−	0.986148i
$680$	−3.26256e38	−	5.07288e36i	−1.88230	−	0.0292674i
$681$		−	2.26337e38i		−	1.28018i
$682$	−6.98734e37	+	3.98601e37i	−0.387457	+	0.221029i
$683$	1.44182e38	+	1.44182e38i	0.783848	+	0.783848i	0.980478	−	0.196630i	$-0.0629997\pi$
$683$	1.44182e38	+	1.44182e38i	0.783848	+	0.783848i	−0.196630	+	0.980478i	$0.563000\pi$
$684$	8.55008e36	+	3.32856e37i	0.0455735	+	0.177418i
$685$	−9.35367e37	+	9.35367e37i	−0.488832	+	0.488832i
$686$	−1.53659e37	−	4.20275e36i	−0.0787376	−	0.0215357i
$687$	−5.55786e36			−0.0279249
$688$	1.78705e36	−	6.15598e36i	0.00880426	−	0.0303287i
$689$	−2.38163e38			−1.15057
$690$	−3.48006e38	−	9.51836e37i	−1.64863	−	0.450920i
$691$	−1.29961e38	+	1.29961e38i	−0.603753	+	0.603753i	−0.941306	−	0.337553i	$-0.890401\pi$
$691$	−1.29961e38	+	1.29961e38i	−0.603753	+	0.603753i	0.337553	+	0.941306i	$0.390401\pi$
$692$	3.27631e38	−	8.41587e37i	1.49263	−	0.383413i
$693$	9.07376e37	+	9.07376e37i	0.405405	+	0.405405i
$694$	3.17944e38	−	1.81375e38i	1.39315	−	0.794738i
$695$		−	2.92396e38i		−	1.25654i
$696$	−5.09941e37	−	5.26049e37i	−0.214929	−	0.221718i
$697$			4.64008e38i			1.91815i
$698$	6.10819e37	+	1.07075e38i	0.247665	+	0.434149i
$699$	−2.73191e38	−	2.73191e38i	−1.08649	−	1.08649i
$700$	2.42273e38	+	1.43245e38i	0.945107	+	0.558798i
$701$	−7.46218e37	+	7.46218e37i	−0.285544	+	0.285544i	−0.835315	−	0.549772i	$-0.814715\pi$
$701$	−7.46218e37	+	7.46218e37i	−0.285544	+	0.285544i	0.549772	+	0.835315i	$0.314715\pi$
$702$	3.07192e37	−	1.12314e38i	0.115308	−	0.421582i
$703$	−5.44949e37			−0.200659
$704$	5.79175e37	−	5.44232e37i	0.209208	−	0.196586i
$705$	1.00739e39			3.56980
$706$	−4.10815e37	+	1.50200e38i	−0.142818	+	0.522164i
$707$	−2.43311e38	+	2.43311e38i	−0.829850	+	0.829850i
$708$	5.48991e38	+	3.24593e38i	1.83703	+	1.08615i
$709$	−1.25629e38	−	1.25629e38i	−0.412445	−	0.412445i	0.470144	−	0.882590i	$-0.344202\pi$
$709$	−1.25629e38	−	1.25629e38i	−0.412445	−	0.412445i	−0.882590	+	0.470144i	$0.844202\pi$
$710$	−3.66657e38	−	6.42739e38i	−1.18106	−	2.07037i
$711$		−	2.01609e38i		−	0.637191i
$712$	3.04237e38	+	3.13847e38i	0.943477	+	0.973280i
$713$		−	4.18423e38i		−	1.27323i
$714$	−8.90154e38	+	5.07798e38i	−2.65790	+	1.51623i
$715$	−5.99017e37	−	5.99017e37i	−0.175512	−	0.175512i
$716$	−3.87180e38	+	9.94550e37i	−1.11323	+	0.285957i
$717$	−1.45761e38	+	1.45761e38i	−0.411275	+	0.411275i
$718$	5.29933e38	+	1.44943e38i	1.46738	+	0.401344i
$719$	2.19389e38			0.596177			0.298088	−	0.954538i	$-0.403651\pi$
$719$	2.19389e38			0.596177			0.298088	+	0.954538i	$0.403651\pi$
$720$	−6.90154e38	−	2.00348e38i	−1.84059	−	0.534314i
$721$	5.30905e38			1.38960
$722$	−3.69347e38	−	1.01021e38i	−0.948817	−	0.259513i
$723$	−5.40670e37	+	5.40670e37i	−0.136322	+	0.136322i
$724$	−8.20197e37	−	3.19304e38i	−0.202977	−	0.790193i
$725$	4.54086e37	+	4.54086e37i	0.110300	+	0.110300i
$726$	5.21450e38	−	2.97467e38i	1.24328	−	0.709242i
$727$		−	6.12438e38i		−	1.43333i	−0.697415	−	0.716667i	$-0.745667\pi$
$727$		−	6.12438e38i		−	1.43333i	0.697415	−	0.716667i	$-0.254333\pi$
$728$	3.92120e38	+	6.09698e36i	0.900836	+	0.0140069i
$729$		−	7.08379e38i		−	1.59751i
$730$	−1.51066e38	−	2.64813e38i	−0.334431	−	0.586248i
$731$	−1.44661e37	−	1.44661e37i	−0.0314388	−	0.0314388i
$732$	−3.85161e38	+	6.51431e38i	−0.821756	+	1.38985i
$733$	−5.00010e38	+	5.00010e38i	−1.04731	+	1.04731i	−0.0484865	+	0.998824i	$0.515440\pi$
$733$	−5.00010e38	+	5.00010e38i	−1.04731	+	1.04731i	−0.998824	+	0.0484865i	$0.984560\pi$
$734$	4.94075e37	−	1.80641e38i	0.101601	−	0.371467i
$735$	9.72618e38			1.96365
$736$	9.66109e37	+	4.01940e38i	0.191503	+	0.796729i
$737$	−2.55143e37			−0.0496562
$738$	−2.69612e38	+	9.85742e38i	−0.515203	+	1.88366i
$739$	4.91520e38	−	4.91520e38i	0.922235	−	0.922235i	−0.0749520	−	0.997187i	$-0.523880\pi$
$739$	4.91520e38	−	4.91520e38i	0.922235	−	0.922235i	0.997187	+	0.0749520i	$0.0238803\pi$
$740$	5.79981e38	−	9.80934e38i	1.06853	−	1.80722i
$741$	−5.03848e37	−	5.03848e37i	−0.0911494	−	0.0911494i
$742$	6.91568e38	+	1.21230e39i	1.22852	+	2.15356i
$743$			7.35304e38i			1.28268i	0.767257	+	0.641339i	$0.221621\pi$
$743$			7.35304e38i			1.28268i	−0.767257	+	0.641339i	$0.778379\pi$
$744$	2.19977e37	−	1.41476e39i	0.0376827	−	2.42352i
$745$			3.15665e38i			0.531027i
$746$	−2.93368e38	+	1.67355e38i	−0.484662	+	0.276481i
$747$	4.78986e38	+	4.78986e38i	0.777132	+	0.777132i
$748$	−6.31059e37	−	2.45672e38i	−0.100554	−	0.391457i
$749$	−6.99192e38	+	6.99192e38i	−1.09419	+	1.09419i
$750$	−2.77522e38	−	7.59056e37i	−0.426551	−	0.116667i
$751$	−1.46544e37			−0.0221222			−0.0110611	−	0.999939i	$-0.503521\pi$
$751$	−1.46544e37			−0.0221222			−0.0110611	+	0.999939i	$0.503521\pi$
$752$	−5.56284e38	−	1.01136e39i	−0.824813	−	1.49957i
$753$	1.79935e38			0.262050
$754$	8.63088e37	+	2.36064e37i	0.123464	+	0.0337689i
$755$	−7.34339e38	+	7.34339e38i	−1.03184	+	1.03184i
$756$	−6.60903e38	+	1.69766e38i	−0.912207	+	0.234319i
$757$	6.99815e38	+	6.99815e38i	0.948831	+	0.948831i	0.998753	−	0.0499218i	$-0.0158972\pi$
$757$	6.99815e38	+	6.99815e38i	0.948831	+	0.948831i	−0.0499218	+	0.998753i	$0.515897\pi$
$758$	−8.30328e38	+	4.73669e38i	−1.10590	+	0.630872i
$759$		−	2.80461e38i		−	0.366951i
$760$	−9.54618e37	+	9.25387e37i	−0.122700	+	0.118943i
$761$		−	2.25174e38i		−	0.284332i	−0.989843	−	0.142166i	$-0.954593\pi$
$761$		−	2.25174e38i		−	0.284332i	0.989843	−	0.142166i	$-0.0454067\pi$
$762$	−1.78513e38	−	3.12927e38i	−0.221450	−	0.388196i
$763$	8.34659e38	+	8.34659e38i	1.01725	+	1.01725i
$764$	2.43659e38	+	1.44065e38i	0.291758	+	0.172503i
$765$	−1.62180e39	+	1.62180e39i	−1.90796	+	1.90796i
$766$	3.08403e38	−	1.12757e39i	0.356476	−	1.30333i
$767$	−7.78920e38			−0.884617
$768$	3.05526e38	+	1.36410e39i	0.340935	+	1.52220i
$769$	−7.71512e38			−0.845935			−0.422967	−	0.906145i	$-0.639012\pi$
$769$	−7.71512e38			−0.845935			−0.422967	+	0.906145i	$0.639012\pi$
$770$	−1.30972e38	+	4.78853e38i	−0.141109	+	0.515914i
$771$	−4.65656e38	+	4.65656e38i	−0.492982	+	0.492982i
$772$	9.91277e38	+	5.86096e38i	1.03124	+	0.609727i
$773$	−5.02687e38	−	5.02687e38i	−0.513895	−	0.513895i	0.401823	−	0.915717i	$-0.368377\pi$
$773$	−5.02687e38	−	5.02687e38i	−0.513895	−	0.513895i	−0.915717	+	0.401823i	$0.868377\pi$
$774$	−2.23263e37	−	3.91373e37i	−0.0224292	−	0.0393177i
$775$			1.24021e39i			1.22439i
$776$	−5.23781e38	+	5.07742e38i	−0.508178	+	0.492617i
$777$		−	3.57908e39i		−	3.41261i
$778$	−1.55856e39	+	8.89098e38i	−1.46049	+	0.833153i
$779$	1.33689e38	+	1.33689e38i	0.123123	+	0.123123i
$780$	1.44319e39	−	3.70713e38i	1.30631	−	0.335552i
$781$	4.06740e38	−	4.06740e38i	0.361850	−	0.361850i
$782$	1.27260e39	+	3.48070e38i	1.11275	+	0.304351i
$783$	−1.55690e38			−0.133807
$784$	−5.37084e38	−	9.76456e38i	−0.453706	−	0.824871i
$785$	−1.72813e39			−1.43495
$786$	2.41469e39	+	6.60447e38i	1.97087	+	0.539055i
$787$	7.85518e38	−	7.85518e38i	0.630228	−	0.630228i	−0.317898	−	0.948125i	$-0.602977\pi$
$787$	7.85518e38	−	7.85518e38i	0.630228	−	0.630228i	0.948125	+	0.317898i	$0.102977\pi$
$788$	5.17011e38	+	2.01273e39i	0.407752	+	1.58738i
$789$	−1.28488e39	−	1.28488e39i	−0.996149	−	0.996149i
$790$	6.77481e38	−	3.86476e38i	0.516335	−	0.294549i
$791$		−	1.88770e39i		−	1.41433i
$792$	8.68516e36	−	5.58576e38i	0.00639717	−	0.411426i
$793$		−	9.24263e38i		−	0.669280i
$794$	−4.94425e38	−	8.66712e38i	−0.351985	−	0.617018i
$795$	3.74972e39	+	3.74972e39i	2.62448	+	2.62448i
$796$	5.72977e38	−	9.69088e38i	0.394285	−	0.666863i
$797$	4.65812e38	−	4.65812e38i	0.315155	−	0.315155i	−0.531748	−	0.846903i	$-0.678465\pi$
$797$	4.65812e38	−	4.65812e38i	0.315155	−	0.315155i	0.846903	+	0.531748i	$0.178465\pi$
$798$	−1.10164e38	+	4.02775e38i	−0.0732823	+	0.267931i
$799$	−3.68384e39			−2.40946
$800$	−2.86355e38	−	1.19135e39i	−0.184158	−	0.766170i
$801$	3.07247e39			1.94289
$802$	2.89543e38	−	1.05861e39i	0.180036	−	0.658238i
$803$	1.67580e38	−	1.67580e38i	0.102462	−	0.102462i
$804$	2.28403e38	−	3.86303e38i	0.137324	−	0.232259i
$805$	−1.82591e39	−	1.82591e39i	−1.07953	−	1.07953i
$806$	8.56268e38	+	1.50101e39i	0.497836	+	0.872691i
$807$		−	2.36007e39i		−	1.34938i
$808$	1.49781e39	+	2.32891e37i	0.842177	+	0.0130948i
$809$		−	4.91042e38i		−	0.271528i	−0.990741	−	0.135764i	$-0.956651\pi$
$809$		−	4.91042e38i		−	0.271528i	0.990741	−	0.135764i	$-0.0433488\pi$
$810$	8.09266e38	−	4.61655e38i	0.440092	−	0.251055i
$811$	1.19416e39	+	1.19416e39i	0.638678	+	0.638678i	0.950229	−	0.311552i	$-0.100849\pi$
$811$	1.19416e39	+	1.19416e39i	0.638678	+	0.638678i	−0.311552	+	0.950229i	$0.600849\pi$
$812$	−1.30459e38	−	5.07878e38i	−0.0686225	−	0.267148i
$813$	9.78449e38	−	9.78449e38i	0.506193	−	0.506193i
$814$	8.54464e38	+	2.33706e38i	0.434775	+	0.118916i
$815$	−4.56247e39			−2.28335
$816$	4.28456e39	+	1.24379e39i	2.10906	+	0.612249i
$817$	−8.33586e36			−0.00403601
$818$	−2.65404e39	−	7.25909e38i	−1.26397	−	0.345711i
$819$	1.94921e39	−	1.94921e39i	0.913117	−	0.913117i
$820$	−3.82930e39	+	9.83634e38i	−1.76454	+	0.453259i
$821$	−9.54069e38	−	9.54069e38i	−0.432461	−	0.432461i	0.457004	−	0.889465i	$-0.348923\pi$
$821$	−9.54069e38	−	9.54069e38i	−0.432461	−	0.432461i	−0.889465	+	0.457004i	$0.848923\pi$
$822$	1.57103e39	−	8.96208e38i	0.700509	−	0.399613i
$823$			1.86119e39i			0.816379i	0.912897	+	0.408190i	$0.133840\pi$
$823$			1.86119e39i			0.816379i	−0.912897	+	0.408190i	$0.866160\pi$
$824$	−1.60870e39	−	1.65952e39i	−0.694157	−	0.716085i
$825$			8.31286e38i			0.352876i
$826$	2.26180e39	+	3.96487e39i	0.944547	+	1.65576i
$827$	−2.86515e39	−	2.86515e39i	−1.17713	−	1.17713i	−0.980473	−	0.196655i	$-0.936992\pi$
$827$	−2.86515e39	−	2.86515e39i	−1.17713	−	1.17713i	−0.196655	−	0.980473i	$-0.563008\pi$
$828$	2.50127e39	+	1.47889e39i	1.01100	+	0.597757i
$829$	−1.60711e37	+	1.60711e37i	−0.00639086	+	0.00639086i	−0.710295	−	0.703904i	$-0.751438\pi$
$829$	−1.60711e37	+	1.60711e37i	−0.00639086	+	0.00639086i	0.703904	+	0.710295i	$0.251438\pi$
$830$	−6.91375e38	+	2.52777e39i	−0.270495	+	0.988971i
$831$	4.74405e39			1.82615
$832$	−1.16911e39	−	1.24418e39i	−0.442783	−	0.471212i
$833$	−3.55669e39			−1.32538
$834$	−1.05474e39	+	3.85629e39i	−0.386726	+	1.41393i
$835$	−1.64750e39	+	1.64750e39i	−0.594370	+	0.594370i
$836$	−8.89645e37	−	5.26006e37i	−0.0315814	−	0.0186727i
$837$	−2.12612e39	−	2.12612e39i	−0.742666	−	0.742666i
$838$	−1.08486e39	−	1.90173e39i	−0.372890	−	0.653664i
$839$		−	3.01868e39i		−	1.02101i	−0.859875	−	0.510505i	$-0.829458\pi$
$839$		−	3.01868e39i		−	1.02101i	0.859875	−	0.510505i	$-0.170542\pi$
$840$	−6.07769e39	−	6.26968e39i	−2.02287	−	2.08677i
$841$			2.93349e39i			0.960813i
$842$	1.88061e39	−	1.07281e39i	0.606158	−	0.345789i
$843$	2.37978e39	+	2.37978e39i	0.754857	+	0.754857i
$844$	1.84122e39	−	4.72955e38i	0.574756	−	0.147638i
$845$	1.79095e39	−	1.79095e39i	0.550196	−	0.550196i
$846$	−7.82599e39	−	2.14050e39i	−2.36613	−	0.647165i
$847$	4.29667e39			1.27851
$848$	1.69391e39	−	5.83513e39i	0.496073	−	1.70886i
$849$	−3.11583e39			−0.898091
$850$	−3.77198e39	−	1.03168e39i	−1.07007	−	0.292678i
$851$	−3.25814e39	+	3.25814e39i	−0.909747	+	0.909747i
$852$	2.51719e39	+	9.79944e39i	0.691800	+	2.69319i
$853$	7.67894e38	+	7.67894e38i	0.207725	+	0.207725i	0.803300	−	0.595575i	$-0.203076\pi$
$853$	7.67894e38	+	7.67894e38i	0.207725	+	0.207725i	−0.595575	+	0.803300i	$0.703076\pi$
$854$	−4.70470e39	+	2.68384e39i	−1.25271	+	0.714621i
$855$			9.34542e38i			0.244938i
$856$	4.30419e39	+	6.69248e37i	1.11044	+	0.0172660i
$857$			7.14582e39i			1.81473i	0.420347	+	0.907363i	$0.361908\pi$
$857$			7.14582e39i			1.81473i	−0.420347	+	0.907363i	$0.638092\pi$
$858$	5.73940e38	+	1.00610e39i	0.143479	+	0.251514i
$859$	1.92290e39	+	1.92290e39i	0.473204	+	0.473204i	0.902950	−	0.429746i	$-0.141397\pi$
$859$	1.92290e39	+	1.92290e39i	0.473204	+	0.473204i	−0.429746	+	0.902950i	$0.641397\pi$
$860$	8.87174e37	−	1.50050e38i	0.0214921	−	0.0363501i
$861$	−8.78033e39	+	8.78033e39i	−2.09396	+	2.09396i
$862$	2.22442e39	−	8.13281e39i	0.522238	−	1.90938i
$863$	−4.56077e39			−1.05413			−0.527063	−	0.849826i	$-0.676707\pi$
$863$	−4.56077e39			−1.05413			−0.527063	+	0.849826i	$0.676707\pi$
$864$	2.53327e39	+	1.55146e39i	0.576429	+	0.353024i
$865$	9.19873e39			2.06068
$866$	−5.19164e38	+	1.89814e39i	−0.114502	+	0.418637i
$867$	4.98861e39	−	4.98861e39i	1.08323	−	1.08323i
$868$	5.15406e39	−	8.71717e39i	1.10188	−	1.86363i
$869$	4.28726e38	+	4.28726e38i	0.0902428	+	0.0902428i
$870$	−9.87208e38	−	1.73055e39i	−0.204597	−	0.358652i
$871$			5.48095e38i			0.111843i
$872$	7.98912e37	−	5.13811e39i	0.0160519	−	1.03236i
$873$			5.12765e39i			1.01444i
$874$	4.66943e38	−	2.66373e38i	0.0909619	−	0.0518902i
$875$	−1.45609e39	−	1.45609e39i	−0.279306	−	0.279306i
$876$	1.03710e39	+	4.03744e39i	0.195891	+	0.762607i
$877$	4.90878e39	−	4.90878e39i	0.913017	−	0.913017i	−0.0834918	−	0.996508i	$-0.526607\pi$
$877$	4.90878e39	−	4.90878e39i	0.913017	−	0.913017i	0.996508	+	0.0834918i	$0.0266073\pi$
$878$	2.94449e39	+	8.05352e38i	0.539304	+	0.147506i
$879$	9.31563e39			1.68021
$880$	1.89367e39	−	1.04158e39i	0.336348	−	0.185003i
$881$	8.65971e39			1.51471			0.757354	−	0.653005i	$-0.226492\pi$
$881$	8.65971e39			1.51471			0.757354	+	0.653005i	$0.226492\pi$
$882$	−7.55587e39	−	2.06662e39i	−1.30154	−	0.355987i
$883$	5.10375e39	−	5.10375e39i	0.865805	−	0.865805i	−0.126200	−	0.992005i	$-0.540278\pi$
$883$	5.10375e39	−	5.10375e39i	0.865805	−	0.865805i	0.992005	+	0.126200i	$0.0402781\pi$
$884$	−5.27749e39	+	1.35563e39i	−0.881702	+	0.226483i
$885$	1.22636e40	+	1.22636e40i	2.01783	+	2.01783i
$886$	−6.73127e39	+	3.83992e39i	−1.09079	+	0.622254i
$887$			1.00183e39i			0.159891i	0.996799	+	0.0799456i	$0.0254747\pi$
$887$			1.00183e39i			0.159891i	−0.996799	+	0.0799456i	$0.974525\pi$
$888$	−1.11876e40	+	1.08450e40i	−1.75858	+	1.70473i
$889$		−	2.57847e39i		−	0.399198i
$890$	5.88980e39	+	1.03246e40i	0.898122	+	1.57438i
$891$	5.12123e38	+	5.12123e38i	0.0769175	+	0.0769175i
$892$	4.96623e37	+	2.93630e37i	0.00734686	+	0.00434386i
$893$	−1.06138e39	+	1.06138e39i	−0.154660	+	0.154660i
$894$	1.13868e39	−	4.16317e39i	0.163434	−	0.597541i
$895$	−1.08706e40			−1.53690
$896$	−2.93829e39	+	9.56381e39i	−0.409201	+	1.33190i
$897$	−6.02481e39			−0.826505
$898$	−9.55844e38	+	3.49471e39i	−0.129168	+	0.472260i
$899$	1.63384e39	−	1.63384e39i	0.217497	−	0.217497i
$900$	−7.41377e39	−	4.38342e39i	−0.972221	−	0.574830i
$901$	−1.37121e40	−	1.37121e40i	−1.77141	−	1.77141i
$902$	−1.52287e39	−	2.66954e39i	−0.193809	−	0.339741i
$903$		−	5.47477e38i		−	0.0686406i
$904$	−5.90064e39	+	5.71996e39i	−0.728829	+	0.706511i
$905$		−	8.96493e39i		−	1.09092i
$906$	1.23338e40	−	7.03596e39i	1.47866	−	0.843515i
$907$	−4.69561e39	−	4.69561e39i	−0.554617	−	0.554617i	0.373153	−	0.927770i	$-0.378277\pi$
$907$	−4.69561e39	−	4.69561e39i	−0.554617	−	0.554617i	−0.927770	+	0.373153i	$0.878277\pi$
$908$	−6.83053e39	+	1.75456e39i	−0.794868	+	0.204178i
$909$	7.44554e39	−	7.44554e39i	0.853658	−	0.853658i
$910$	1.02866e40	+	2.81352e39i	1.16202	+	0.317827i
$911$	6.00086e39			0.667906			0.333953	−	0.942590i	$-0.391617\pi$
$911$	6.00086e39			0.667906			0.333953	+	0.942590i	$0.391617\pi$
$912$	1.59281e39	−	8.76101e38i	0.174677	−	0.0960780i
$913$	−2.03715e39			−0.220124
$914$	−1.06390e40	−	2.90989e39i	−1.13273	−	0.309815i
$915$	−1.45519e40	+	1.45519e40i	−1.52664	+	1.52664i
$916$	4.30844e37	+	1.67728e38i	0.00445381	+	0.0173387i
$917$	1.26693e40	+	1.26693e40i	1.29053	+	1.29053i
$918$	8.23504e39	−	4.69777e39i	0.826589	−	0.471537i
$919$			1.33502e40i			1.32047i	0.751059	+	0.660235i	$0.229543\pi$
$919$			1.33502e40i			1.32047i	−0.751059	+	0.660235i	$0.770457\pi$
$920$	−1.74771e38	+	1.12402e40i	−0.0170346	+	1.09556i
$921$			1.40072e39i			0.134538i
$922$	−1.71743e38	−	3.01060e38i	−0.0162559	−	0.0284961i
$923$	−8.73753e39	−	8.73753e39i	−0.815015	−	0.815015i
$924$	3.45467e39	−	5.84295e39i	0.317566	−	0.537107i
$925$	9.65713e39	−	9.65713e39i	0.874852	−	0.874852i
$926$	−7.10883e38	+	2.59910e39i	−0.0634672	+	0.232046i
$927$	−1.62462e40			−1.42947
$928$	−1.19223e39	+	1.94672e39i	−0.103387	+	0.168813i
$929$	6.08461e39			0.520021			0.260010	−	0.965606i	$-0.416274\pi$
$929$	6.08461e39			0.520021			0.260010	+	0.965606i	$0.416274\pi$
$930$	1.01511e40	−	3.71139e40i	0.855051	−	3.12620i
$931$	−1.02475e39	+	1.02475e39i	−0.0850739	+	0.0850739i
$932$	−6.12673e39	+	1.03623e40i	−0.501319	+	0.847891i
$933$	9.99003e39	+	9.99003e39i	0.805684	+	0.805684i
$934$	3.33626e39	+	5.84837e39i	0.265203	+	0.464892i
$935$		−	6.89761e39i		−	0.540433i
$936$	−1.19992e40	−	1.86573e38i	−0.926680	−	0.0144087i
$937$		−	1.02857e40i		−	0.782976i	−0.920183	−	0.391488i	$-0.871960\pi$
$937$		−	1.02857e40i		−	0.782976i	0.920183	−	0.391488i	$-0.128040\pi$
$938$	2.78992e39	−	1.59154e39i	0.209341	−	0.119421i
$939$	−5.96482e39	−	5.96482e39i	−0.441176	−	0.441176i
$940$	−7.80925e39	−	3.04015e40i	−0.569355	−	2.21651i
$941$	−7.95073e39	+	7.95073e39i	−0.571409	+	0.571409i	−0.932522	−	0.361113i	$-0.882397\pi$
$941$	−7.95073e39	+	7.95073e39i	−0.571409	+	0.571409i	0.361113	+	0.932522i	$0.382397\pi$
$942$	2.27916e40	+	6.23377e39i	1.61469	+	0.441635i
$943$	1.59860e40			1.11643
$944$	5.53999e39	−	1.90840e40i	0.381405	−	1.31385i
$945$	−1.85558e40			−1.25936
$946$	1.30704e38	+	3.57490e37i	0.00874496	+	0.00239185i
$947$	−1.50682e40	+	1.50682e40i	−0.993883	+	0.993883i	−0.999981	−	0.00609841i	$-0.998059\pi$
$947$	−1.50682e40	+	1.50682e40i	−0.993883	+	0.993883i	0.00609841	+	0.999981i	$0.498059\pi$
$948$	−1.03291e40	+	2.65325e39i	−0.671662	+	0.172530i
$949$	−3.59993e39	−	3.59993e39i	−0.230781	−	0.230781i
$950$	−1.38402e39	+	7.89530e38i	−0.0874730	+	0.0498999i
$951$		−	2.63409e40i		−	1.64132i
$952$	2.22251e40	+	2.29271e40i	1.36535	+	1.40848i
$953$		−	1.64290e40i		−	0.995080i	−0.867441	−	0.497540i	$-0.834237\pi$
$953$		−	1.64290e40i		−	0.995080i	0.867441	−	0.497540i	$-0.165763\pi$
$954$	−2.11626e40	−	3.70974e40i	−1.26377	−	2.21534i
$955$	5.44297e39	+	5.44297e39i	0.320472	+	0.320472i
$956$	5.52879e39	+	3.26892e39i	0.320958	+	0.189768i
$957$	1.09513e39	−	1.09513e39i	0.0626837	−	0.0626837i
$958$	2.34497e39	−	8.57355e39i	0.132343	−	0.483867i
$959$	1.29450e40			0.720362
$960$	−1.18186e39	+	3.79957e40i	−0.0648490	+	2.08484i
$961$	2.61409e40			1.41434
$962$	5.02043e39	−	1.83555e40i	0.267841	−	0.979268i
$963$	2.13959e40	−	2.13959e40i	1.12558	−	1.12558i
$964$	2.05079e39	+	1.21254e39i	0.106385	+	0.0629006i
$965$	2.21435e40	+	2.21435e40i	1.13274	+	1.13274i
$966$	1.74946e40	+	3.06676e40i	0.882499	+	1.54699i
$967$			1.17924e40i			0.586604i	0.956020	+	0.293302i	$0.0947542\pi$
$967$			1.17924e40i			0.586604i	−0.956020	+	0.293302i	$0.905246\pi$
$968$	−1.30194e40	−	1.34307e40i	−0.638665	−	0.658840i
$969$		−	5.80175e39i		−	0.280665i
$970$	−1.72308e40	+	9.82952e39i	−0.822030	+	0.468936i
$971$	4.48448e39	+	4.48448e39i	0.210985	+	0.210985i	0.804686	−	0.593701i	$-0.202334\pi$
$971$	4.48448e39	+	4.48448e39i	0.210985	+	0.210985i	−0.593701	+	0.804686i	$0.702334\pi$
$972$	−2.64484e40	+	6.79382e39i	−1.22717	+	0.315224i
$973$	−2.02331e40	+	2.02331e40i	−0.925844	+	0.925844i
$974$	−1.94676e40	−	5.32463e39i	−0.878552	−	0.240294i
$975$	1.78576e40			0.794804
$976$	2.26450e40	+	6.57373e39i	0.994031	+	0.288562i
$977$	−1.91315e40			−0.828273			−0.414136	−	0.910215i	$-0.635916\pi$
$977$	−1.91315e40			−0.828273			−0.414136	+	0.910215i	$0.635916\pi$
$978$	6.01726e40	+	1.64579e40i	2.56936	+	0.702748i
$979$	−6.53367e39	+	6.53367e39i	−0.275164	+	0.275164i
$980$	−7.53971e39	−	2.93522e40i	−0.313186	−	1.21924i
$981$	−2.55413e40	−	2.55413e40i	−1.04643	−	1.04643i
$982$	−1.20713e40	+	6.88618e39i	−0.487806	+	0.278274i
$983$			2.18468e40i			0.870795i	0.900238	+	0.435398i	$0.143392\pi$
$983$			2.18468e40i			0.870795i	−0.900238	+	0.435398i	$0.856608\pi$
$984$	5.40512e40	+	8.40430e38i	2.12506	+	0.0330421i
$985$			5.65104e40i			2.19149i
$986$	3.61005e39	+	6.32830e39i	0.138094	+	0.242074i
$987$	−6.97087e40	−	6.97087e40i	−2.63030	−	2.63030i
$988$	−1.12996e39	+	1.91112e39i	−0.0420575	+	0.0711328i
$989$	−4.98384e38	+	4.98384e38i	−0.0182985	+	0.0182985i
$990$	4.00786e39	−	1.46533e40i	0.145157	−	0.530715i
$991$	−2.52460e40			−0.901982			−0.450991	−	0.892528i	$-0.648929\pi$
$991$	−2.52460e40			−0.901982			−0.450991	+	0.892528i	$0.648929\pi$
$992$	−4.28658e40	+	1.03033e40i	−1.51079	+	0.363135i
$993$	−4.45507e40			−1.54896
$994$	−1.91041e40	+	6.98476e40i	−0.655256	+	2.39572i
$995$	2.16479e40	−	2.16479e40i	0.732494	−	0.732494i
$996$	1.82365e40	−	3.08438e40i	0.608752	−	1.02960i
$997$	7.91279e39	+	7.91279e39i	0.260582	+	0.260582i	0.825291	−	0.564708i	$-0.191011\pi$
$997$	7.91279e39	+	7.91279e39i	0.260582	+	0.260582i	−0.564708	+	0.825291i	$0.691011\pi$
$998$	2.08382e39	+	3.65286e39i	0.0677013	+	0.118678i
$999$			3.31110e40i			1.06130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.5.22	✓	106
16.13	even	4	inner	16.28.e.a.13.22	yes	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.22	✓	106	1.1	even	1	trivial
16.28.e.a.13.22	yes	106	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3056.43 + 11174.8i) q^{2} +(3.04594e6 - 3.04594e6i) q^{3} +(-1.15534e8 - 6.83100e7i) q^{4} +(-2.58085e9 - 2.58085e9i) q^{5} +(2.47280e10 + 4.33475e10i) q^{6} +3.57176e11i q^{7} +(1.11647e12 - 1.08228e12i) q^{8} -1.09299e13i q^{9} +(3.67287e13 - 2.09523e13i) q^{10} +(2.32427e13 + 2.32427e13i) q^{11} +(-5.59979e14 + 1.43842e14i) q^{12} +(4.99297e14 - 4.99297e14i) q^{13} +(-3.99137e15 - 1.09169e15i) q^{14} -1.57222e16 q^{15} +(8.68188e15 + 1.57843e16i) q^{16} +5.74935e16 q^{17} +(1.22140e17 + 3.34066e16i) q^{18} +(1.65649e16 - 1.65649e16i) q^{19} +(1.21878e17 + 4.74474e17i) q^{20} +(1.08794e18 + 1.08794e18i) q^{21} +(-3.30773e17 + 1.88693e17i) q^{22} -1.98076e18i q^{23} +(1.04134e17 - 6.69729e18i) q^{24} +5.87099e18i q^{25} +(4.05347e18 + 7.10561e18i) q^{26} +(-1.00648e19 - 1.00648e19i) q^{27} +(2.43987e19 - 4.12661e19i) q^{28} +(7.73440e18 - 7.73440e18i) q^{29} +(4.80540e19 - 1.75693e20i) q^{30} +2.11243e20 q^{31} +(-2.02922e20 + 4.87746e19i) q^{32} +1.41592e20 q^{33} +(-1.75725e20 + 6.42477e20i) q^{34} +(9.21819e20 - 9.21819e20i) q^{35} +(-7.46624e20 + 1.26278e21i) q^{36} +(-1.64489e21 - 1.64489e21i) q^{37} +(1.34480e20 + 2.35739e20i) q^{38} -3.04166e21i q^{39} +(-5.67466e21 - 8.82339e19i) q^{40} +8.07062e21i q^{41} +(-1.54827e22 + 8.83227e21i) q^{42} +(-2.51612e20 - 2.51612e20i) q^{43} +(-1.09762e21 - 4.27304e21i) q^{44} +(-2.82085e22 + 2.82085e22i) q^{45} +(2.21346e22 + 6.05408e21i) q^{46} -6.40741e22 q^{47} +(7.45225e22 + 2.16335e22i) q^{48} -6.18626e22 q^{49} +(-6.56071e22 - 1.79443e22i) q^{50} +(1.75122e23 - 1.75122e23i) q^{51} +(-9.17929e22 + 2.35789e22i) q^{52} +(-2.38498e23 - 2.38498e23i) q^{53} +(1.43234e23 - 8.17096e22i) q^{54} -1.19972e23i q^{55} +(3.86567e23 + 3.98778e23i) q^{56} -1.00911e23i q^{57} +(6.27906e22 + 1.10070e23i) q^{58} +(-7.80016e23 - 7.80016e23i) q^{59} +(1.81646e24 + 1.07399e24i) q^{60} +(9.25564e23 - 9.25564e23i) q^{61} +(-6.45650e23 + 2.36060e24i) q^{62} +3.90391e24 q^{63} +(7.51710e22 - 2.41668e24i) q^{64} -2.57722e24 q^{65} +(-4.32767e23 + 1.58226e24i) q^{66} +(-5.48866e23 + 5.48866e23i) q^{67} +(-6.64246e24 - 3.92738e24i) q^{68} +(-6.03329e24 - 6.03329e24i) q^{69} +(7.48365e24 + 1.31186e25i) q^{70} -1.74997e25i q^{71} +(-1.18293e25 - 1.22030e25i) q^{72} -7.20999e24i q^{73} +(2.34088e25 - 1.33538e25i) q^{74} +(1.78827e25 + 1.78827e25i) q^{75} +(-3.04536e24 + 7.82263e23i) q^{76} +(-8.30176e24 + 8.30176e24i) q^{77} +(3.39899e25 + 9.29664e24i) q^{78} +1.84456e25 q^{79} +(1.83302e25 - 6.31435e25i) q^{80} +2.20337e25 q^{81} +(-9.01875e25 - 2.46673e25i) q^{82} +(-4.38234e25 + 4.38234e25i) q^{83} +(-5.13769e25 - 2.00011e26i) q^{84} +(-1.48382e26 - 1.48382e26i) q^{85} +(3.58075e24 - 2.04268e24i) q^{86} -4.71170e25i q^{87} +(5.11052e25 + 7.94622e23i) q^{88} +2.81106e26i q^{89} +(-2.29007e26 - 4.01442e26i) q^{90} +(1.78337e26 + 1.78337e26i) q^{91} +(-1.35306e26 + 2.28846e26i) q^{92} +(6.43434e26 - 6.43434e26i) q^{93} +(1.95838e26 - 7.16015e26i) q^{94} -8.55031e25 q^{95} +(-4.69523e26 + 7.66652e26i) q^{96} -4.69139e26 q^{97} +(1.89079e26 - 6.91301e26i) q^{98} +(2.54042e26 - 2.54042e26i) 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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