LMFDB - Embedded newform 16.28.e.a.5.1

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			5.1
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11581.2 + 305.932i) q^{2} +(-2.33243e6 + 2.33243e6i) q^{3} +(1.34031e8 - 7.08611e6i) q^{4} +(-3.25506e9 - 3.25506e9i) q^{5} +(2.62988e10 - 2.77259e10i) q^{6} -4.57721e11i q^{7} +(-1.55007e12 + 1.23070e11i) q^{8} -3.25487e12i q^{9} +O(q^{10})$	\(q+(-11581.2 + 305.932i) q^{2} +(-2.33243e6 + 2.33243e6i) q^{3} +(1.34031e8 - 7.08611e6i) q^{4} +(-3.25506e9 - 3.25506e9i) q^{5} +(2.62988e10 - 2.77259e10i) q^{6} -4.57721e11i q^{7} +(-1.55007e12 + 1.23070e11i) q^{8} -3.25487e12i q^{9} +(3.86933e13 + 3.67017e13i) q^{10} +(7.31216e13 + 7.31216e13i) q^{11} +(-2.96089e14 + 3.29145e14i) q^{12} +(-1.05155e15 + 1.05155e15i) q^{13} +(1.40031e14 + 5.30096e15i) q^{14} +1.51844e16 q^{15} +(1.79140e16 - 1.89951e15i) q^{16} -3.52795e16 q^{17} +(9.95769e14 + 3.76953e16i) q^{18} +(-1.46140e17 + 1.46140e17i) q^{19} +(-4.59343e17 - 4.13212e17i) q^{20} +(1.06760e18 + 1.06760e18i) q^{21} +(-8.69206e17 - 8.24465e17i) q^{22} -2.95092e18i q^{23} +(3.32837e18 - 3.90248e18i) q^{24} +1.37403e19i q^{25} +(1.18565e19 - 1.24999e19i) q^{26} +(-1.01944e19 - 1.01944e19i) q^{27} +(-3.24346e18 - 6.13486e19i) q^{28} +(-3.27394e19 + 3.27394e19i) q^{29} +(-1.75854e20 + 4.64539e18i) q^{30} -7.52814e18 q^{31} +(-2.06884e20 + 2.74791e19i) q^{32} -3.41102e20 q^{33} +(4.08579e20 - 1.07931e19i) q^{34} +(-1.48991e21 + 1.48991e21i) q^{35} +(-2.30644e19 - 4.36253e20i) q^{36} +(-2.52539e20 - 2.52539e20i) q^{37} +(1.64777e21 - 1.73718e21i) q^{38} -4.90532e21i q^{39} +(5.44616e21 + 4.64496e21i) q^{40} +3.98696e21i q^{41} +(-1.26907e22 - 1.20375e22i) q^{42} +(1.03084e22 + 1.03084e22i) q^{43} +(1.03187e22 + 9.28238e21i) q^{44} +(-1.05948e22 + 1.05948e22i) q^{45} +(9.02779e20 + 3.41752e22i) q^{46} -2.78056e22 q^{47} +(-3.73526e22 + 4.62136e22i) q^{48} -1.43796e23 q^{49} +(-4.20358e21 - 1.59129e23i) q^{50} +(8.22869e22 - 8.22869e22i) q^{51} +(-1.33488e23 + 1.48391e23i) q^{52} +(-3.83935e21 - 3.83935e21i) q^{53} +(1.21182e23 + 1.14945e23i) q^{54} -4.76030e23i q^{55} +(5.63316e22 + 7.09498e23i) q^{56} -6.81723e23i q^{57} +(3.69145e23 - 3.89177e23i) q^{58} +(-5.02923e23 - 5.02923e23i) q^{59} +(2.03517e24 - 1.07598e23i) q^{60} +(-1.45871e24 + 1.45871e24i) q^{61} +(8.71849e22 - 2.30310e21i) q^{62} -1.48982e24 q^{63} +(2.38756e24 - 3.81533e23i) q^{64} +6.84570e24 q^{65} +(3.95037e24 - 1.04354e23i) q^{66} +(-3.20060e24 + 3.20060e24i) q^{67} +(-4.72853e24 + 2.49994e23i) q^{68} +(6.88281e24 + 6.88281e24i) q^{69} +(1.67991e25 - 1.77108e25i) q^{70} +2.21358e24i q^{71} +(4.00577e23 + 5.04527e24i) q^{72} -8.58412e24i q^{73} +(3.00196e24 + 2.84744e24i) q^{74} +(-3.20482e25 - 3.20482e25i) q^{75} +(-1.85516e25 + 2.06228e25i) q^{76} +(3.34693e25 - 3.34693e25i) q^{77} +(1.50069e24 + 5.68095e25i) q^{78} +2.53654e25 q^{79} +(-6.44941e25 - 5.21280e25i) q^{80} +7.23759e25 q^{81} +(-1.21974e24 - 4.61738e25i) q^{82} +(-4.74091e25 + 4.74091e25i) q^{83} +(1.50657e26 + 1.35526e26i) q^{84} +(1.14837e26 + 1.14837e26i) q^{85} +(-1.22537e26 - 1.16230e26i) q^{86} -1.52725e26i q^{87} +(-1.22342e26 - 1.04344e26i) q^{88} -7.83314e25i q^{89} +(1.19459e26 - 1.25942e26i) q^{90} +(4.81315e26 + 4.81315e26i) q^{91} +(-2.09105e25 - 3.95513e26i) q^{92} +(1.75589e25 - 1.75589e25i) q^{93} +(3.22022e26 - 8.50660e24i) q^{94} +9.51389e26 q^{95} +(4.18450e26 - 5.46636e26i) q^{96} -7.63225e26 q^{97} +(1.66533e27 - 4.39918e25i) q^{98} +(2.38002e26 - 2.38002e26i) 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}+O(q^{10}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8	$ 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}+ \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

Display 100 coefficients 10 coefficients

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 $

$2$	−11581.2	+	305.932i	−0.999651	+	0.0264070i
$2$	−11581.2	+	305.932i	−0.999651	+	0.0264070i
$3$	−2.33243e6	+	2.33243e6i	−0.844641	+	0.844641i	−0.989458	−	0.144818i	$-0.953740\pi$
$3$	−2.33243e6	+	2.33243e6i	−0.844641	+	0.844641i	0.144818	+	0.989458i	$0.453740\pi$
$4$	1.34031e8	−	7.08611e6i	0.998605	−	0.0527956i
$5$	−3.25506e9	−	3.25506e9i	−1.19252	−	1.19252i	−0.976359	−	0.216157i	$-0.930648\pi$
$5$	−3.25506e9	−	3.25506e9i	−1.19252	−	1.19252i	−0.216157	−	0.976359i	$-0.569352\pi$
$6$	2.62988e10	−	2.77259e10i	0.822042	−	0.866650i
$7$		−	4.57721e11i		−	1.78557i	−0.450481	−	0.892786i	$-0.648748\pi$
$7$		−	4.57721e11i		−	1.78557i	0.450481	−	0.892786i	$-0.351252\pi$
$8$	−1.55007e12	+	1.23070e11i	−0.996863	+	0.0791474i
$9$		−	3.25487e12i		−	0.426835i
$10$	3.86933e13	+	3.67017e13i	1.22359	+	1.16061i
$11$	7.31216e13	+	7.31216e13i	0.638623	+	0.638623i	0.950216	−	0.311593i	$-0.100863\pi$
$11$	7.31216e13	+	7.31216e13i	0.638623	+	0.638623i	−0.311593	+	0.950216i	$0.600863\pi$
$12$	−2.96089e14	+	3.29145e14i	−0.798869	+	0.888056i
$13$	−1.05155e15	+	1.05155e15i	−0.962928	+	0.962928i	−0.999337	−	0.0364094i	$-0.988408\pi$
$13$	−1.05155e15	+	1.05155e15i	−0.962928	+	0.962928i	0.0364094	+	0.999337i	$0.488408\pi$
$14$	1.40031e14	+	5.30096e15i	0.0471516	+	1.78495i
$15$	1.51844e16			2.01449
$16$	1.79140e16	−	1.89951e15i	0.994425	−	0.105444i
$17$	−3.52795e16			−0.863896			−0.431948	−	0.901898i	$-0.642174\pi$
$17$	−3.52795e16			−0.863896			−0.431948	+	0.901898i	$0.642174\pi$
$18$	9.95769e14	+	3.76953e16i	0.0112714	+	0.426686i
$19$	−1.46140e17	+	1.46140e17i	−0.797251	+	0.797251i	−0.982661	−	0.185410i	$-0.940639\pi$
$19$	−1.46140e17	+	1.46140e17i	−0.797251	+	0.797251i	0.185410	+	0.982661i	$0.440639\pi$
$20$	−4.59343e17	−	4.13212e17i	−1.25381	−	1.12789i
$21$	1.06760e18	+	1.06760e18i	1.50817	+	1.50817i
$22$	−8.69206e17	−	8.24465e17i	−0.655264	−	0.621536i
$23$		−	2.95092e18i		−	1.22076i	−0.792108	−	0.610381i	$-0.791016\pi$
$23$		−	2.95092e18i		−	1.22076i	0.792108	−	0.610381i	$-0.208984\pi$
$24$	3.32837e18	−	3.90248e18i	0.775140	−	0.908842i
$25$			1.37403e19i			1.84419i
$26$	1.18565e19	−	1.24999e19i	0.937164	−	0.988020i
$27$	−1.01944e19	−	1.01944e19i	−0.484118	−	0.484118i
$28$	−3.24346e18	−	6.13486e19i	−0.0942704	−	1.78308i
$29$	−3.27394e19	+	3.27394e19i	−0.592512	+	0.592512i	−0.938309	−	0.345797i	$-0.887608\pi$
$29$	−3.27394e19	+	3.27394e19i	−0.592512	+	0.592512i	0.345797	+	0.938309i	$0.387608\pi$
$30$	−1.75854e20	+	4.64539e18i	−2.01379	+	0.0531968i
$31$	−7.52814e18			−0.0553739			−0.0276869	−	0.999617i	$-0.508814\pi$
$31$	−7.52814e18			−0.0553739			−0.0276869	+	0.999617i	$0.508814\pi$
$32$	−2.06884e20	+	2.74791e19i	−0.991294	+	0.131667i
$33$	−3.41102e20			−1.07881
$34$	4.08579e20	−	1.07931e19i	0.863595	−	0.0228129i
$35$	−1.48991e21	+	1.48991e21i	−2.12932	+	2.12932i
$36$	−2.30644e19	−	4.36253e20i	−0.0225350	−	0.426240i
$37$	−2.52539e20	−	2.52539e20i	−0.170453	−	0.170453i	0.616725	−	0.787178i	$-0.288459\pi$
$37$	−2.52539e20	−	2.52539e20i	−0.170453	−	0.170453i	−0.787178	+	0.616725i	$0.788459\pi$
$38$	1.64777e21	−	1.73718e21i	0.775920	−	0.818026i
$39$		−	4.90532e21i		−	1.62666i
$40$	5.44616e21	+	4.64496e21i	1.28316	+	1.09439i
$41$			3.98696e21i			0.673070i	0.941671	+	0.336535i	$0.109255\pi$
$41$			3.98696e21i			0.673070i	−0.941671	+	0.336535i	$0.890745\pi$
$42$	−1.26907e22	−	1.20375e22i	−1.54747	−	1.46781i
$43$	1.03084e22	+	1.03084e22i	0.914884	+	0.914884i	0.996651	−	0.0817674i	$-0.0260565\pi$
$43$	1.03084e22	+	1.03084e22i	0.914884	+	0.914884i	−0.0817674	+	0.996651i	$0.526056\pi$
$44$	1.03187e22	+	9.28238e21i	0.671449	+	0.604016i
$45$	−1.05948e22	+	1.05948e22i	−0.509008	+	0.509008i
$46$	9.02779e20	+	3.41752e22i	0.0322367	+	1.22034i
$47$	−2.78056e22			−0.742695			−0.371348	−	0.928494i	$-0.621104\pi$
$47$	−2.78056e22			−0.742695			−0.371348	+	0.928494i	$0.621104\pi$
$48$	−3.73526e22	+	4.62136e22i	−0.750870	+	0.928994i
$49$	−1.43796e23			−2.18827
$50$	−4.20358e21	−	1.59129e23i	−0.0486995	−	1.84354i
$51$	8.22869e22	−	8.22869e22i	0.729682	−	0.729682i
$52$	−1.33488e23	+	1.48391e23i	−0.910746	+	1.01242i
$53$	−3.83935e21	−	3.83935e21i	−0.0202550	−	0.0202550i	0.696907	−	0.717162i	$-0.254559\pi$
$53$	−3.83935e21	−	3.83935e21i	−0.0202550	−	0.0202550i	−0.717162	+	0.696907i	$0.754559\pi$
$54$	1.21182e23	+	1.14945e23i	0.496733	+	0.471165i
$55$		−	4.76030e23i		−	1.52313i
$56$	5.63316e22	+	7.09498e23i	0.141323	+	1.77997i
$57$		−	6.81723e23i		−	1.34678i
$58$	3.69145e23	−	3.89177e23i	0.576659	−	0.607952i
$59$	−5.02923e23	−	5.02923e23i	−0.623734	−	0.623734i	0.322750	−	0.946484i	$-0.395393\pi$
$59$	−5.02923e23	−	5.02923e23i	−0.623734	−	0.623734i	−0.946484	+	0.322750i	$0.895393\pi$
$60$	2.03517e24	−	1.07598e23i	2.01168	−	0.106356i
$61$	−1.45871e24	+	1.45871e24i	−1.15350	+	1.15350i	−0.167651	+	0.985846i	$0.553618\pi$
$61$	−1.45871e24	+	1.45871e24i	−1.15350	+	1.15350i	−0.985846	+	0.167651i	$0.946382\pi$
$62$	8.71849e22	−	2.30310e21i	0.0553546	−	0.00146226i
$63$	−1.48982e24			−0.762145
$64$	2.38756e24	−	3.81533e23i	0.987471	−	0.157798i
$65$	6.84570e24			2.29661
$66$	3.95037e24	−	1.04354e23i	1.07844	−	0.0284882i
$67$	−3.20060e24	+	3.20060e24i	−0.713216	+	0.713216i	−0.967207	−	0.253991i	$-0.918257\pi$
$67$	−3.20060e24	+	3.20060e24i	−0.713216	+	0.713216i	0.253991	+	0.967207i	$0.418257\pi$
$68$	−4.72853e24	+	2.49994e23i	−0.862692	+	0.0456100i
$69$	6.88281e24	+	6.88281e24i	1.03111	+	1.03111i
$70$	1.67991e25	−	1.77108e25i	2.07235	−	2.18481i
$71$			2.21358e24i			0.225480i	0.993625	+	0.112740i	$0.0359627\pi$
$71$			2.21358e24i			0.225480i	−0.993625	+	0.112740i	$0.964037\pi$
$72$	4.00577e23	+	5.04527e24i	0.0337829	+	0.425496i
$73$		−	8.58412e24i		−	0.600948i	−0.953790	−	0.300474i	$-0.902855\pi$
$73$		−	8.58412e24i		−	0.600948i	0.953790	−	0.300474i	$-0.0971449\pi$
$74$	3.00196e24	+	2.84744e24i	0.174895	+	0.165893i
$75$	−3.20482e25	−	3.20482e25i	−1.55767	−	1.55767i
$76$	−1.85516e25	+	2.06228e25i	−0.754048	+	0.838231i
$77$	3.34693e25	−	3.34693e25i	1.14031	−	1.14031i
$78$	1.50069e24	+	5.68095e25i	0.0429551	+	1.62609i
$79$	2.53654e25			0.611329			0.305665	−	0.952139i	$-0.401121\pi$
$79$	2.53654e25			0.611329			0.305665	+	0.952139i	$0.401121\pi$
$80$	−6.44941e25	−	5.21280e25i	−1.31161	−	1.06012i
$81$	7.23759e25			1.24465
$82$	−1.21974e24	−	4.61738e25i	−0.0177738	−	0.672835i
$83$	−4.74091e25	+	4.74091e25i	−0.586554	+	0.586554i	−0.936696	−	0.350143i	$-0.886133\pi$
$83$	−4.74091e25	+	4.74091e25i	−0.586554	+	0.586554i	0.350143	+	0.936696i	$0.386133\pi$
$84$	1.50657e26	+	1.35526e26i	1.58569	+	1.42644i
$85$	1.14837e26	+	1.14837e26i	1.03021	+	1.03021i
$86$	−1.22537e26	−	1.16230e26i	−0.938724	−	0.890406i
$87$		−	1.52725e26i		−	1.00092i
$88$	−1.22342e26	−	1.04344e26i	−0.687165	−	0.586074i
$89$		−	7.83314e25i		−	0.377721i	−0.982004	−	0.188860i	$-0.939521\pi$
$89$		−	7.83314e25i		−	0.377721i	0.982004	−	0.188860i	$-0.0604794\pi$
$90$	1.19459e26	−	1.25942e26i	0.495389	−	0.522272i
$91$	4.81315e26	+	4.81315e26i	1.71938	+	1.71938i
$92$	−2.09105e25	−	3.95513e26i	−0.0644509	−	1.21906i
$93$	1.75589e25	−	1.75589e25i	0.0467710	−	0.0467710i
$94$	3.22022e26	−	8.50660e24i	0.742436	−	0.0196124i
$95$	9.51389e26			1.90147
$96$	4.18450e26	−	5.46636e26i	0.726076	−	0.948498i
$97$	−7.63225e26			−1.15142			−0.575711	−	0.817653i	$-0.695275\pi$
$97$	−7.63225e26			−1.15142			−0.575711	+	0.817653i	$0.695275\pi$
$98$	1.66533e27	−	4.39918e25i	2.18750	−	0.0577856i
$99$	2.38002e26	−	2.38002e26i	0.272587	−	0.272587i
$100$	9.73650e25	+	1.84161e27i	0.0973650	+	1.84161i
$101$	5.79920e26	+	5.79920e26i	0.507025	+	0.507025i	0.913612	−	0.406587i	$-0.133281\pi$
$101$	5.79920e26	+	5.79920e26i	0.507025	+	0.507025i	−0.406587	+	0.913612i	$0.633281\pi$
$102$	−9.27807e26	+	9.78156e26i	−0.710159	+	0.748696i
$103$			1.50880e27i			1.01235i	0.862432	+	0.506173i	$0.168940\pi$
$103$			1.50880e27i			1.01235i	−0.862432	+	0.506173i	$0.831060\pi$
$104$	1.50055e27	−	1.75938e27i	0.883694	−	1.03612i
$105$		−	6.95022e27i		−	3.59702i
$106$	4.56388e25	+	4.32897e25i	0.0207829	+	0.0197131i
$107$	−2.05125e27	−	2.05125e27i	−0.822882	−	0.822882i	0.163638	−	0.986520i	$-0.447677\pi$
$107$	−2.05125e27	−	2.05125e27i	−0.822882	−	0.822882i	−0.986520	+	0.163638i	$0.947677\pi$
$108$	−1.43860e27	−	1.29412e27i	−0.509002	−	0.457884i
$109$	8.30595e26	−	8.30595e26i	0.259497	−	0.259497i	−0.565353	−	0.824849i	$-0.691260\pi$
$109$	8.30595e26	−	8.30595e26i	0.259497	−	0.259497i	0.824849	+	0.565353i	$0.191260\pi$
$110$	1.45633e26	+	5.51300e27i	0.0402215	+	1.52260i
$111$	1.17806e27			0.287943
$112$	−8.69446e26	−	8.19960e27i	−0.188278	−	1.77562i
$113$	−3.54387e26			−0.0680642			−0.0340321	−	0.999421i	$-0.510835\pi$
$113$	−3.54387e26			−0.0680642			−0.0340321	+	0.999421i	$0.510835\pi$
$114$	2.08561e26	+	7.89516e27i	0.0355645	+	1.34631i
$115$	−9.60541e27	+	9.60541e27i	−1.45578	+	1.45578i
$116$	−4.15608e27	+	4.62007e27i	−0.560404	+	0.622968i
$117$	3.42265e27	+	3.42265e27i	0.411011	+	0.411011i
$118$	5.97831e27	+	5.67059e27i	0.639988	+	0.607046i
$119$			1.61482e28i			1.54255i
$120$	−2.35368e28	+	1.86874e27i	−2.00817	+	0.159442i
$121$		−	2.41646e27i		−	0.184322i
$122$	1.64474e28	−	1.73399e28i	1.12263	−	1.18356i
$123$	−9.29931e27	−	9.29931e27i	−0.568502	−	0.568502i
$124$	−1.00900e27	+	5.33452e25i	−0.0552966	+	0.00292350i
$125$	2.04733e28	−	2.04733e28i	1.00671	−	1.00671i
$126$	1.72540e28	−	4.55784e26i	0.761879	−	0.0201260i
$127$	−2.55876e28			−1.01550			−0.507749	−	0.861505i	$-0.669522\pi$
$127$	−2.55876e28			−1.01550			−0.507749	+	0.861505i	$0.669522\pi$
$128$	−2.75341e28	+	5.14904e27i	−0.982960	+	0.183819i
$129$	−4.80872e28			−1.54550
$130$	−7.92814e28	+	2.09432e27i	−2.29581	+	0.0606467i
$131$	2.79898e28	−	2.79898e28i	0.730866	−	0.730866i	−0.239925	−	0.970791i	$-0.577123\pi$
$131$	2.79898e28	−	2.79898e28i	0.730866	−	0.730866i	0.970791	+	0.239925i	$0.0771229\pi$
$132$	−4.57181e28	+	2.41709e27i	−1.07731	+	0.0569566i
$133$	6.68913e28	+	6.68913e28i	1.42355	+	1.42355i
$134$	3.60876e28	−	3.80459e28i	0.694134	−	0.731801i
$135$			6.63669e28i			1.15464i
$136$	5.46855e28	−	4.34184e27i	0.861186	−	0.0683752i
$137$		−	3.84396e28i		−	0.548342i	−0.961681	−	0.274171i	$-0.911597\pi$
$137$		−	3.84396e28i		−	0.548342i	0.961681	−	0.274171i	$-0.0884034\pi$
$138$	−8.18169e28	−	7.76055e28i	−1.05797	−	1.00352i
$139$	4.45967e28	+	4.45967e28i	0.523122	+	0.523122i	0.918513	−	0.395391i	$-0.129391\pi$
$139$	4.45967e28	+	4.45967e28i	0.523122	+	0.523122i	−0.395391	+	0.918513i	$0.629391\pi$
$140$	−1.89136e29	+	2.10251e29i	−2.01393	+	2.23877i
$141$	6.48546e28	−	6.48546e28i	0.627310	−	0.627310i
$142$	−6.77204e26	−	2.56359e28i	−0.00595425	−	0.225401i
$143$	−1.53782e29			−1.22989
$144$	−6.18267e27	−	5.83077e28i	−0.0450072	−	0.424456i
$145$	2.13137e29			1.41316
$146$	2.62615e27	+	9.94144e28i	0.0158693	+	0.600739i
$147$	3.35395e29	−	3.35395e29i	1.84830	−	1.84830i
$148$	−3.56374e28	−	3.20584e28i	−0.179215	−	0.161216i
$149$	−1.57873e29	−	1.57873e29i	−0.724924	−	0.724924i	0.244680	−	0.969604i	$-0.421317\pi$
$149$	−1.57873e29	−	1.57873e29i	−0.724924	−	0.724924i	−0.969604	+	0.244680i	$0.921317\pi$
$150$	3.80961e29	+	3.61352e29i	1.59826	+	1.51600i
$151$			2.28490e29i			0.876353i	0.898889	+	0.438176i	$0.144375\pi$
$151$			2.28490e29i			0.876353i	−0.898889	+	0.438176i	$0.855625\pi$
$152$	2.08541e29	−	2.44512e29i	0.731650	−	0.857851i
$153$			1.14830e29i			0.368741i
$154$	−3.77375e29	+	3.97854e29i	−1.10980	+	1.17002i
$155$	2.45046e28	+	2.45046e28i	0.0660342	+	0.0660342i
$156$	−3.47597e28	−	6.57463e29i	−0.0858803	−	1.62439i
$157$	2.21273e29	−	2.21273e29i	0.501515	−	0.501515i	−0.410394	−	0.911908i	$-0.634609\pi$
$157$	2.21273e29	−	2.21273e29i	0.501515	−	0.501515i	0.911908	+	0.410394i	$0.134609\pi$
$158$	−2.93761e29	+	7.76007e27i	−0.611116	+	0.0161434i
$159$	1.79100e28			0.0342165
$160$	7.62866e29	+	5.83974e29i	1.33915	+	1.02512i
$161$	−1.35070e30			−2.17976
$162$	−8.38199e29	+	2.21421e28i	−1.24421	+	0.0328674i
$163$	5.65042e29	−	5.65042e29i	0.771877	−	0.771877i	−0.206557	−	0.978434i	$-0.566226\pi$
$163$	5.65042e29	−	5.65042e29i	0.771877	−	0.771877i	0.978434	+	0.206557i	$0.0662260\pi$
$164$	2.82520e28	+	5.34375e29i	0.0355351	+	0.672131i
$165$	1.11031e30	+	1.11031e30i	1.28650	+	1.28650i
$166$	5.34551e29	−	5.63558e29i	0.570860	−	0.601838i
$167$		−	3.86533e29i		−	0.380640i	−0.981722	−	0.190320i	$-0.939047\pi$
$167$		−	3.86533e29i		−	0.380640i	0.981722	−	0.190320i	$-0.0609526\pi$
$168$	−1.78625e30	−	1.52347e30i	−1.62280	−	1.38407i
$169$		−	1.01897e30i		−	0.854459i
$170$	−1.36508e30	−	1.29482e30i	−1.05706	−	1.00265i
$171$	4.75667e29	+	4.75667e29i	0.340295	+	0.340295i
$172$	1.45468e30	+	1.30859e30i	0.961910	+	0.865306i
$173$	1.26544e30	−	1.26544e30i	0.773781	−	0.773781i	−0.204984	−	0.978765i	$-0.565714\pi$
$173$	1.26544e30	−	1.26544e30i	0.773781	−	0.773781i	0.978765	+	0.204984i	$0.0657144\pi$
$174$	4.67233e28	+	1.76873e30i	0.0264313	+	1.00057i
$175$	6.28921e30			3.29293
$176$	1.44879e30	+	1.17100e30i	0.702401	+	0.567724i
$177$	2.34607e30			1.05366
$178$	2.39641e28	+	9.07172e29i	0.00997448	+	0.377589i
$179$	2.23221e30	−	2.23221e30i	0.861427	−	0.861427i	−0.130077	−	0.991504i	$-0.541522\pi$
$179$	2.23221e30	−	2.23221e30i	0.861427	−	0.861427i	0.991504	+	0.130077i	$0.0415224\pi$
$180$	−1.34495e30	+	1.49510e30i	−0.481424	+	0.535171i
$181$	3.53051e30	+	3.53051e30i	1.17267	+	1.17267i	0.981570	+	0.191103i	$0.0612063\pi$
$181$	3.53051e30	+	3.53051e30i	1.17267	+	1.17267i	0.191103	+	0.981570i	$0.438794\pi$
$182$	−5.72146e30	−	5.42696e30i	−1.76418	−	1.67337i
$183$		−	6.80469e30i		−	1.94858i
$184$	3.63169e29	+	4.57412e30i	0.0966202	+	1.21693i
$185$			1.64406e30i			0.406536i
$186$	−1.97981e29	+	2.08725e29i	−0.0455196	+	0.0479898i
$187$	−2.57969e30	−	2.57969e30i	−0.551704	−	0.551704i
$188$	−3.72679e30	+	1.97033e29i	−0.741659	+	0.0392111i
$189$	−4.66620e30	+	4.66620e30i	−0.864428	+	0.864428i
$190$	−1.10182e31	+	2.91060e29i	−1.90081	+	0.0502121i
$191$	1.31825e30			0.211860			0.105930	−	0.994374i	$-0.466218\pi$
$191$	1.31825e30			0.211860			0.105930	+	0.994374i	$0.466218\pi$
$192$	−4.67892e30	+	6.45872e30i	−0.700776	+	0.967341i
$193$	7.20451e30			1.00596			0.502980	−	0.864298i	$-0.332237\pi$
$193$	7.20451e30			1.00596			0.502980	+	0.864298i	$0.332237\pi$
$194$	8.83906e30	−	2.33495e29i	1.15102	−	0.0304056i
$195$	−1.59671e31	+	1.59671e31i	−1.93981	+	1.93981i
$196$	−1.92731e31	+	1.01896e30i	−2.18522	+	0.115531i
$197$	−6.67235e29	−	6.67235e29i	−0.0706293	−	0.0706293i	0.670910	−	0.741539i	$-0.265904\pi$
$197$	−6.67235e29	−	6.67235e29i	−0.0706293	−	0.0706293i	−0.741539	+	0.670910i	$0.765904\pi$
$198$	−2.68353e30	+	2.82916e30i	−0.265293	+	0.279690i
$199$		−	5.07434e30i		−	0.468666i	−0.972156	−	0.234333i	$-0.924709\pi$
$199$		−	5.07434e30i		−	0.468666i	0.972156	−	0.234333i	$-0.0752905\pi$
$200$	−1.69101e30	−	2.12983e31i	−0.145963	−	1.83840i
$201$		−	1.49303e31i		−	1.20482i
$202$	−6.89358e30	−	6.53875e30i	−0.520237	−	0.493459i
$203$	1.49855e31	+	1.49855e31i	1.05797	+	1.05797i
$204$	1.04459e31	−	1.16121e31i	0.690140	−	0.767188i
$205$	1.29778e31	−	1.29778e31i	0.802646	−	0.802646i
$206$	−4.61589e29	−	1.74737e31i	−0.0267330	−	1.01199i
$207$	−9.60486e30			−0.521065
$208$	−1.68400e31	+	2.08348e31i	−0.856025	+	1.05909i
$209$	−2.13720e31			−1.01829
$210$	2.12629e30	+	8.04919e31i	0.0949867	+	3.59577i
$211$	−2.32488e31	+	2.32488e31i	−0.974064	+	0.974064i	−0.999672	−	0.0256082i	$-0.991848\pi$
$211$	−2.32488e31	+	2.32488e31i	−0.974064	+	0.974064i	0.0256082	+	0.999672i	$0.491848\pi$
$212$	−5.41796e29	−	4.87384e29i	−0.0212962	−	0.0191574i
$213$	−5.16302e30	−	5.16302e30i	−0.190449	−	0.190449i
$214$	2.43835e31	+	2.31284e31i	0.844325	+	0.800865i
$215$		−	6.71088e31i		−	2.18203i
$216$	1.70566e31	+	1.45474e31i	0.520916	+	0.444283i
$217$			3.44579e30i			0.0988740i
$218$	−9.36518e30	+	9.87339e30i	−0.252554	+	0.266259i
$219$	2.00219e31	+	2.00219e31i	0.507585	+	0.507585i
$220$	−3.37320e30	−	6.38026e31i	−0.0804149	−	1.52101i
$221$	3.70980e31	−	3.70980e31i	0.831870	−	0.831870i
$222$	−1.36433e31	+	3.60406e29i	−0.287843	+	0.00760372i
$223$	9.24558e31			1.83577			0.917885	−	0.396846i	$-0.129895\pi$
$223$	9.24558e31			1.83577			0.917885	+	0.396846i	$0.129895\pi$
$224$	1.25777e31	+	9.46952e31i	0.235101	+	1.77003i
$225$	4.47228e31			0.787164
$226$	4.10423e30	−	1.08418e29i	0.0680405	−	0.00179737i
$227$	4.20968e29	−	4.20968e29i	0.00657506	−	0.00657506i	−0.703812	−	0.710387i	$-0.748520\pi$
$227$	4.20968e29	−	4.20968e29i	0.00657506	−	0.00657506i	0.710387	+	0.703812i	$0.248520\pi$
$228$	−4.83076e30	−	9.13717e31i	−0.0711042	−	1.34490i
$229$	−9.87624e31	−	9.87624e31i	−1.37029	−	1.37029i	−0.860005	−	0.510286i	$-0.829539\pi$
$229$	−9.87624e31	−	9.87624e31i	−1.37029	−	1.37029i	−0.510286	−	0.860005i	$-0.670461\pi$
$230$	1.08304e32	−	1.14181e32i	1.41683	−	1.49371i
$231$			1.56130e32i			1.92630i
$232$	4.67189e31	−	5.47774e31i	0.543757	−	0.637549i
$233$			3.06787e30i			0.0336925i	0.999858	+	0.0168462i	$0.00536258\pi$
$233$			3.06787e30i			0.0336925i	−0.999858	+	0.0168462i	$0.994637\pi$
$234$	−4.06855e31	−	3.85913e31i	−0.421722	−	0.400015i
$235$	9.05088e31	+	9.05088e31i	0.885675	+	0.885675i
$236$	−7.09708e31	−	6.38433e31i	−0.655795	−	0.589934i
$237$	−5.91630e31	+	5.91630e31i	−0.516354	+	0.516354i
$238$	−4.94023e30	−	1.87015e32i	−0.0407341	−	1.54201i
$239$	−6.57096e31			−0.511985			−0.255992	−	0.966679i	$-0.582402\pi$
$239$	−6.57096e31			−0.511985			−0.255992	+	0.966679i	$0.582402\pi$
$240$	2.72013e32	−	2.88429e31i	2.00326	−	0.212416i
$241$	−1.93403e32			−1.34658			−0.673292	−	0.739377i	$-0.735120\pi$
$241$	−1.93403e32			−1.34658			−0.673292	+	0.739377i	$0.735120\pi$
$242$	7.39272e29	+	2.79855e31i	0.00486740	+	0.184258i
$243$	−9.10733e31	+	9.10733e31i	−0.567161	+	0.567161i
$244$	−1.85175e32	+	2.05848e32i	−1.09099	+	1.21279i
$245$	4.68065e32	+	4.68065e32i	2.60954	+	2.60954i
$246$	1.10542e32	+	1.04852e32i	0.583316	+	0.553291i
$247$		−	3.07346e32i		−	1.53539i
$248$	1.16691e31	−	9.26487e29i	0.0552002	−	0.00438270i
$249$		−	2.21157e32i		−	0.990854i
$250$	−2.30842e32	+	2.43369e32i	−0.979770	+	1.03294i
$251$	−2.66170e32	−	2.66170e32i	−1.07044	−	1.07044i	−0.997323	−	0.0731219i	$-0.976704\pi$
$251$	−2.66170e32	−	2.66170e32i	−1.07044	−	1.07044i	−0.0731219	−	0.997323i	$-0.523296\pi$
$252$	−1.99682e32	+	1.05571e31i	−0.761082	+	0.0402379i
$253$	2.15776e32	−	2.15776e32i	0.779607	−	0.779607i
$254$	2.96335e32	−	7.82805e30i	1.01514	−	0.0268163i
$255$	−5.35698e32			−1.74031
$256$	3.17302e32	−	6.80555e31i	0.977763	−	0.209712i
$257$	−6.34528e32			−1.85504			−0.927520	−	0.373772i	$-0.878064\pi$
$257$	−6.34528e32			−1.85504			−0.927520	+	0.373772i	$0.878064\pi$
$258$	5.56907e32	−	1.47114e31i	1.54496	−	0.0408120i
$259$	−1.15592e32	+	1.15592e32i	−0.304356	+	0.304356i
$260$	9.17533e32	−	4.85094e31i	2.29341	−	0.121251i
$261$	1.06562e32	+	1.06562e32i	0.252905	+	0.252905i
$262$	−3.15593e32	+	3.32719e32i	−0.711312	+	0.749912i
$263$			4.34305e31i			0.0929806i	0.998919	+	0.0464903i	$0.0148037\pi$
$263$			4.34305e31i			0.0929806i	−0.998919	+	0.0464903i	$0.985196\pi$
$264$	5.28731e32	−	4.19794e31i	1.07543	−	0.0853853i
$265$			2.49946e31i			0.0483089i
$266$	−7.95146e32	−	7.54217e32i	−1.46064	−	1.38546i
$267$	1.82703e32	+	1.82703e32i	0.319038	+	0.319038i
$268$	−4.06298e32	+	4.51658e32i	−0.674567	+	0.749876i
$269$	−1.89230e32	+	1.89230e32i	−0.298768	+	0.298768i	−0.840531	−	0.541763i	$-0.817757\pi$
$269$	−1.89230e32	+	1.89230e32i	−0.298768	+	0.298768i	0.541763	+	0.840531i	$0.317757\pi$
$270$	−2.03037e31	−	7.68608e32i	−0.0304905	−	1.15423i
$271$	8.92317e32			1.27478			0.637388	−	0.770543i	$-0.280015\pi$
$271$	8.92317e32			1.27478			0.637388	+	0.770543i	$0.280015\pi$
$272$	−6.31996e32	+	6.70137e31i	−0.859080	+	0.0910927i
$273$	−2.24527e33			−2.90451
$274$	1.17599e31	+	4.45177e32i	0.0144801	+	0.548151i
$275$	−1.00471e33	+	1.00471e33i	−1.17774	+	1.17774i
$276$	9.71279e32	+	8.73735e32i	1.08411	+	0.975230i
$277$	−7.99909e31	−	7.99909e31i	−0.0850283	−	0.0850283i	0.663313	−	0.748342i	$-0.269150\pi$
$277$	−7.99909e31	−	7.99909e31i	−0.0850283	−	0.0850283i	−0.748342	+	0.663313i	$0.769150\pi$
$278$	−5.30127e32	−	5.02839e32i	−0.536753	−	0.509125i
$279$			2.45032e31i			0.0236355i
$280$	2.12610e33	−	2.49282e33i	1.95411	−	2.29117i
$281$		−	1.15405e33i		−	1.01085i	−0.862870	−	0.505426i	$-0.831335\pi$
$281$		−	1.15405e33i		−	1.01085i	0.862870	−	0.505426i	$-0.168665\pi$
$282$	−7.31252e32	+	7.70934e32i	−0.610526	+	0.643657i
$283$	−4.10239e32	−	4.10239e32i	−0.326528	−	0.326528i	0.524737	−	0.851265i	$-0.324164\pi$
$283$	−4.10239e32	−	4.10239e32i	−0.326528	−	0.326528i	−0.851265	+	0.524737i	$0.824164\pi$
$284$	1.56857e31	+	2.96687e32i	0.0119043	+	0.225165i
$285$	−2.21905e33	+	2.21905e33i	−1.60606	+	1.60606i
$286$	1.78098e33	−	4.70467e31i	1.22947	−	0.0324779i
$287$	1.82492e33			1.20181
$288$	8.94409e31	+	6.73382e32i	0.0562001	+	0.423119i
$289$	−4.23070e32			−0.253683
$290$	−2.46838e33	+	6.52054e31i	−1.41267	+	0.0373173i
$291$	1.78017e33	−	1.78017e33i	0.972537	−	0.972537i
$292$	−6.08280e31	−	1.15053e33i	−0.0317274	−	0.600110i
$293$	−5.20348e32	−	5.20348e32i	−0.259168	−	0.259168i	0.565548	−	0.824716i	$-0.308665\pi$
$293$	−5.20348e32	−	5.20348e32i	−0.259168	−	0.259168i	−0.824716	+	0.565548i	$0.808665\pi$
$294$	−3.78167e33	+	3.98688e33i	−1.79885	+	1.89646i
$295$			3.27409e33i			1.48763i
$296$	4.22532e32	+	3.60372e32i	0.183409	+	0.156427i
$297$		−	1.49086e33i		−	0.618338i
$298$	1.87665e33	+	1.78006e33i	0.743814	+	0.705528i
$299$	3.10303e33	+	3.10303e33i	1.17551	+	1.17551i
$300$	−4.52254e33	−	4.06834e33i	−1.63774	−	1.47326i
$301$	4.71836e33	−	4.71836e33i	1.63359	−	1.63359i
$302$	−6.99024e31	−	2.64619e33i	−0.0231419	−	0.876047i
$303$	−2.70525e33			−0.856508
$304$	−2.34035e33	+	2.89554e33i	−0.708741	+	0.876872i
$305$	9.49639e33			2.75113
$306$	−3.51302e31	−	1.32987e33i	−0.00973736	−	0.368613i
$307$	−3.95492e33	+	3.95492e33i	−1.04899	+	1.04899i	−0.0502504	+	0.998737i	$0.516002\pi$
$307$	−3.95492e33	+	3.95492e33i	−1.04899	+	1.04899i	−0.998737	+	0.0502504i	$0.983998\pi$
$308$	4.24874e33	−	4.72307e33i	1.07851	−	1.19892i
$309$	−3.51917e33	−	3.51917e33i	−0.855068	−	0.855068i
$310$	−2.91289e32	−	2.76295e32i	−0.0677549	−	0.0642674i
$311$		−	1.43621e33i		−	0.319854i	−0.987129	−	0.159927i	$-0.948874\pi$
$311$		−	1.43621e33i		−	0.319854i	0.987129	−	0.159927i	$-0.0511259\pi$
$312$	6.03697e32	+	7.60358e33i	0.128746	+	1.62155i
$313$		−	1.23917e33i		−	0.253094i	−0.991961	−	0.126547i	$-0.959610\pi$
$313$		−	1.23917e33i		−	0.253094i	0.991961	−	0.126547i	$-0.0403895\pi$
$314$	−2.49491e33	+	2.63030e33i	−0.488096	+	0.514583i
$315$	4.84947e33	+	4.84947e33i	0.908870	+	0.908870i
$316$	3.39973e33	−	1.79742e32i	0.610477	−	0.0322755i
$317$	7.03040e33	−	7.03040e33i	1.20971	−	1.20971i	0.238586	−	0.971121i	$-0.423316\pi$
$317$	7.03040e33	−	7.03040e33i	1.20971	−	1.20971i	0.971121	−	0.238586i	$-0.0766838\pi$
$318$	−2.07420e32	+	5.47924e30i	−0.0342045	+	0.000903555i
$319$	−4.78791e33			−0.756783
$320$	−9.01356e33	−	6.52974e33i	−1.36575	−	0.989398i
$321$	9.56880e33			1.39008
$322$	1.56427e34	−	4.13221e32i	2.17900	−	0.0575610i
$323$	5.15574e33	−	5.15574e33i	0.688743	−	0.688743i
$324$	9.70058e33	−	5.12863e32i	1.24291	−	0.0657119i
$325$	−1.44485e34	−	1.44485e34i	−1.77582	−	1.77582i
$326$	−6.37100e33	+	6.71673e33i	−0.751225	+	0.791991i
$327$			3.87461e33i			0.438363i
$328$	−4.90675e32	−	6.18005e33i	−0.0532717	−	0.670958i
$329$			1.27272e34i			1.32614i
$330$	−1.31984e34	−	1.25190e34i	−1.32003	−	1.25208i
$331$	−1.93968e33	−	1.93968e33i	−0.186231	−	0.186231i	0.607833	−	0.794065i	$-0.292039\pi$
$331$	−1.93968e33	−	1.93968e33i	−0.186231	−	0.186231i	−0.794065	+	0.607833i	$0.792039\pi$
$332$	−6.01832e33	+	6.69022e33i	−0.554768	+	0.616703i
$333$	−8.21982e32	+	8.21982e32i	−0.0727554	+	0.0727554i
$334$	1.18253e32	+	4.47652e33i	0.0100516	+	0.380507i
$335$	2.08363e34			1.70104
$336$	2.11529e34	+	1.70971e34i	1.65879	+	1.34073i
$337$	1.39572e33			0.105147			0.0525733	−	0.998617i	$-0.483258\pi$
$337$	1.39572e33			0.105147			0.0525733	+	0.998617i	$0.483258\pi$
$338$	3.11735e32	+	1.18009e34i	0.0225637	+	0.854161i
$339$	8.26583e32	−	8.26583e32i	0.0574898	−	0.0574898i
$340$	1.62054e34	+	1.45779e34i	1.08316	+	0.974382i
$341$	−5.50470e32	−	5.50470e32i	−0.0353630	−	0.0353630i
$342$	−5.65432e33	−	5.36327e33i	−0.349163	−	0.331190i
$343$			3.57406e34i			2.12174i
$344$	−1.72473e34	−	1.47100e34i	−0.984425	−	0.839603i
$345$		−	4.48079e34i		−	2.45922i
$346$	−1.42681e34	+	1.50424e34i	−0.753078	+	0.793944i
$347$	1.00271e34	+	1.00271e34i	0.509010	+	0.509010i	0.914222	−	0.405213i	$-0.132803\pi$
$347$	1.00271e34	+	1.00271e34i	0.509010	+	0.509010i	−0.405213	+	0.914222i	$0.632803\pi$
$348$	−1.08222e33	−	2.04698e34i	−0.0528442	−	0.999523i
$349$	−1.43790e34	+	1.43790e34i	−0.675436	+	0.675436i	−0.958964	−	0.283528i	$-0.908495\pi$
$349$	−1.43790e34	+	1.43790e34i	−0.675436	+	0.675436i	0.283528	+	0.958964i	$0.408495\pi$
$350$	−7.28365e34	+	1.92407e33i	−3.29178	+	0.0869564i
$351$	2.14398e34			0.932341
$352$	−1.71370e34	−	1.31184e34i	−0.717148	−	0.548977i
$353$	−1.48507e34			−0.598118			−0.299059	−	0.954235i	$-0.596673\pi$
$353$	−1.48507e34			−0.598118			−0.299059	+	0.954235i	$0.596673\pi$
$354$	−2.71703e34	+	7.17736e32i	−1.05329	+	0.0278241i
$355$	7.20533e33	−	7.20533e33i	0.268888	−	0.268888i
$356$	−5.55065e32	−	1.04988e34i	−0.0199420	−	0.377194i
$357$	−3.76645e34	−	3.76645e34i	−1.30290	−	1.30290i
$358$	−2.51687e34	+	2.65345e34i	−0.838379	+	0.883875i
$359$		−	1.54110e33i		−	0.0494376i	−0.999694	−	0.0247188i	$-0.992131\pi$
$359$		−	1.54110e33i		−	0.0494376i	0.999694	−	0.0247188i	$-0.00786904\pi$
$360$	1.51188e34	−	1.77266e34i	0.467124	−	0.547698i
$361$		−	9.11314e33i		−	0.271219i
$362$	−4.19676e34	−	3.98074e34i	−1.20323	−	1.14130i
$363$	5.63623e33	+	5.63623e33i	0.155686	+	0.155686i
$364$	6.79216e34	+	6.11003e34i	1.80775	+	1.62620i
$365$	−2.79418e34	+	2.79418e34i	−0.716640	+	0.716640i
$366$	2.08177e33	+	7.88064e34i	0.0514562	+	1.94790i
$367$	−4.83897e34			−1.15282			−0.576410	−	0.817161i	$-0.695547\pi$
$367$	−4.83897e34			−1.15282			−0.576410	+	0.817161i	$0.695547\pi$
$368$	−5.60530e33	−	5.28626e34i	−0.128722	−	1.21396i
$369$	1.29771e34			0.287290
$370$	−5.02970e32	−	1.90402e34i	−0.0107354	−	0.406394i
$371$	−1.75735e33	+	1.75735e33i	−0.0361668	+	0.0361668i
$372$	2.22900e33	−	2.47785e33i	0.0442365	−	0.0491751i
$373$	7.21823e34	+	7.21823e34i	1.38153	+	1.38153i	0.841901	+	0.539632i	$0.181437\pi$
$373$	7.21823e34	+	7.21823e34i	1.38153	+	1.38153i	0.539632	+	0.841901i	$0.318563\pi$
$374$	3.06651e34	+	2.90867e34i	0.566080	+	0.536943i
$375$			9.55051e34i			1.70061i
$376$	4.31005e34	−	3.42202e33i	0.740365	−	0.0587824i
$377$		−	6.88540e34i		−	1.14109i
$378$	5.26126e34	−	5.54677e34i	0.841299	−	0.886953i
$379$	2.71495e34	+	2.71495e34i	0.418921	+	0.418921i	0.884832	−	0.465911i	$-0.154273\pi$
$379$	2.71495e34	+	2.71495e34i	0.418921	+	0.418921i	−0.465911	+	0.884832i	$0.654273\pi$
$380$	1.27515e35	−	6.74164e33i	1.89882	−	0.100389i
$381$	5.96813e34	−	5.96813e34i	0.857731	−	0.857731i
$382$	−1.52670e34	+	4.03296e32i	−0.211786	+	0.00559459i
$383$	6.33334e34			0.848104			0.424052	−	0.905638i	$-0.360607\pi$
$383$	6.33334e34			0.848104			0.424052	+	0.905638i	$0.360607\pi$
$384$	5.22116e34	−	7.62311e34i	0.674987	−	0.985509i
$385$	−2.17889e35			−2.71967
$386$	−8.34368e34	+	2.20409e33i	−1.00561	+	0.0265644i
$387$	3.35525e34	−	3.35525e34i	0.390505	−	0.390505i
$388$	−1.02296e35	+	5.40830e33i	−1.14982	+	0.0607900i
$389$	−4.61855e34	−	4.61855e34i	−0.501401	−	0.501401i	0.410472	−	0.911873i	$-0.365364\pi$
$389$	−4.61855e34	−	4.61855e34i	−0.501401	−	0.501401i	−0.911873	+	0.410472i	$0.865364\pi$
$390$	1.80034e35	−	1.89803e35i	1.88791	−	1.99036i
$391$			1.04107e35i			1.05461i
$392$	2.22894e35	−	1.76970e34i	2.18140	−	0.173196i
$393$			1.30569e35i			1.23464i
$394$	7.93151e33	+	7.52325e33i	0.0724698	+	0.0687396i
$395$	−8.25658e34	−	8.25658e34i	−0.729020	−	0.729020i
$396$	3.02130e34	−	3.35860e34i	0.257815	−	0.286598i
$397$	1.22128e35	−	1.22128e35i	1.00726	−	1.00726i	0.00728905	−	0.999973i	$-0.497680\pi$
$397$	1.22128e35	−	1.22128e35i	1.00726	−	1.00726i	0.999973	−	0.00728905i	$-0.00232020\pi$
$398$	1.55240e33	+	5.87669e34i	0.0123761	+	0.468502i
$399$	−3.12039e35			−2.40478
$400$	2.60998e34	+	2.46143e35i	0.194458	+	1.83391i
$401$	1.65864e35			1.19482			0.597410	−	0.801936i	$-0.296197\pi$
$401$	1.65864e35			1.19482			0.597410	+	0.801936i	$0.296197\pi$
$402$	4.56767e33	+	1.72911e35i	0.0318158	+	1.20440i
$403$	7.91620e33	−	7.91620e33i	0.0533210	−	0.0533210i
$404$	8.18364e34	+	7.36176e34i	0.533087	+	0.479549i
$405$	−2.35588e35	−	2.35588e35i	−1.48426	−	1.48426i
$406$	−1.78134e35	−	1.68965e35i	−1.08554	−	1.02967i
$407$		−	3.69321e34i		−	0.217710i
$408$	−1.17423e35	+	1.37677e35i	−0.669640	+	0.785145i
$409$		−	1.49964e35i		−	0.827415i	−0.910410	−	0.413707i	$-0.864234\pi$
$409$		−	1.49964e35i		−	0.827415i	0.910410	−	0.413707i	$-0.135766\pi$
$410$	−1.46328e35	+	1.54269e35i	−0.781170	+	0.823561i
$411$	8.96577e34	+	8.96577e34i	0.463152	+	0.463152i
$412$	1.06915e34	+	2.02225e35i	0.0534474	+	1.01093i
$413$	−2.30199e35	+	2.30199e35i	−1.11372	+	1.11372i
$414$	1.11236e35	−	2.93843e33i	0.520883	−	0.0137598i
$415$	3.08639e35			1.39895
$416$	1.88653e35	−	2.46444e35i	0.827759	−	1.08133i
$417$	−2.08037e35			−0.883700
$418$	2.47513e35	−	6.53836e33i	1.01793	−	0.0268899i
$419$	−3.00753e35	+	3.00753e35i	−1.19763	+	1.19763i	−0.222751	+	0.974875i	$0.571504\pi$
$419$	−3.00753e35	+	3.00753e35i	−1.19763	+	1.19763i	−0.974875	+	0.222751i	$0.928496\pi$
$420$	−4.92501e34	−	9.31542e35i	−0.189907	−	3.59201i
$421$	4.02468e34	+	4.02468e34i	0.150287	+	0.150287i	0.778246	−	0.627959i	$-0.216109\pi$
$421$	4.02468e34	+	4.02468e34i	0.150287	+	0.150287i	−0.627959	+	0.778246i	$0.716109\pi$
$422$	2.62136e35	−	2.76361e35i	0.948002	−	0.999446i
$423$			9.05036e34i			0.317008i
$424$	6.42375e33	+	5.47874e33i	0.0217946	+	0.0185884i
$425$		−	4.84749e35i		−	1.59319i
$426$	6.13735e34	+	5.82144e34i	0.195412	+	0.185354i
$427$	6.67683e35	+	6.67683e35i	2.05965	+	2.05965i
$428$	−2.89466e35	−	2.60395e35i	−0.865179	−	0.778290i
$429$	3.58685e35	−	3.58685e35i	1.03882	−	1.03882i
$430$	2.05307e34	+	7.77200e35i	0.0576208	+	2.18127i
$431$	−2.02475e35			−0.550717			−0.275358	−	0.961342i	$-0.588796\pi$
$431$	−2.02475e35			−0.550717			−0.275358	+	0.961342i	$0.588796\pi$
$432$	−2.01987e35	−	1.63258e35i	−0.532467	−	0.430372i
$433$	2.11043e35			0.539242			0.269621	−	0.962966i	$-0.413102\pi$
$433$	2.11043e35			0.539242			0.269621	+	0.962966i	$0.413102\pi$
$434$	−1.05418e33	−	3.99064e34i	−0.00261097	−	0.0988395i
$435$	−4.97128e35	+	4.97128e35i	−1.19361	+	1.19361i
$436$	1.05439e35	−	1.17211e35i	0.245434	−	0.272835i
$437$	4.31247e35	+	4.31247e35i	0.973255	+	0.973255i
$438$	−2.38003e35	−	2.25752e35i	−0.520812	−	0.494005i
$439$			4.45130e34i			0.0944531i	0.998884	+	0.0472265i	$0.0150383\pi$
$439$			4.45130e34i			0.0944531i	−0.998884	+	0.0472265i	$0.984962\pi$
$440$	5.85850e34	+	7.37879e35i	0.120552	+	1.51836i
$441$			4.68039e35i			0.934030i
$442$	−4.18290e35	+	4.40989e35i	−0.809612	+	0.853547i
$443$	−4.85605e35	−	4.85605e35i	−0.911660	−	0.911660i	0.0847429	−	0.996403i	$-0.472993\pi$
$443$	−4.85605e35	−	4.85605e35i	−0.911660	−	0.911660i	−0.996403	+	0.0847429i	$0.972993\pi$
$444$	1.57896e35	−	8.34786e33i	0.287542	−	0.0152021i
$445$	−2.54974e35	+	2.54974e35i	−0.450438	+	0.450438i
$446$	−1.07075e36	+	2.82851e34i	−1.83513	+	0.0484772i
$447$	7.36455e35			1.22460
$448$	−1.74636e35	−	1.09284e36i	−0.281760	−	1.76320i
$449$	−4.71509e35			−0.738184			−0.369092	−	0.929393i	$-0.620331\pi$
$449$	−4.71509e35			−0.738184			−0.369092	+	0.929393i	$0.620331\pi$
$450$	−5.17944e35	+	1.36821e34i	−0.786889	+	0.0207867i
$451$	−2.91533e35	+	2.91533e35i	−0.429838	+	0.429838i
$452$	−4.74987e34	+	2.51122e33i	−0.0679693	+	0.00359349i
$453$	−5.32938e35	−	5.32938e35i	−0.740203	−	0.740203i
$454$	−4.74653e33	+	5.00410e33i	−0.00639914	+	0.00674640i
$455$		−	3.13342e36i		−	4.10077i
$456$	8.38995e34	+	1.05672e36i	0.106594	+	1.34256i
$457$		−	1.20700e36i		−	1.48881i	−0.667728	−	0.744405i	$-0.732733\pi$
$457$		−	1.20700e36i		−	1.48881i	0.667728	−	0.744405i	$-0.267267\pi$
$458$	1.17400e36	+	1.11357e36i	1.40600	+	1.33363i
$459$	3.59653e35	+	3.59653e35i	0.418228	+	0.418228i
$460$	−1.21935e36	+	1.35548e36i	−1.37689	+	1.53061i
$461$	−4.20312e35	+	4.20312e35i	−0.460903	+	0.460903i	−0.898951	−	0.438049i	$-0.855670\pi$
$461$	−4.20312e35	+	4.20312e35i	−0.460903	+	0.460903i	0.438049	+	0.898951i	$0.355670\pi$
$462$	−4.77650e34	−	1.80817e36i	−0.0508678	−	1.92563i
$463$	1.27380e36			1.31752			0.658762	−	0.752351i	$-0.271080\pi$
$463$	1.27380e36			1.31752			0.658762	+	0.752351i	$0.271080\pi$
$464$	−5.24303e35	+	6.48681e35i	−0.526732	+	0.651686i
$465$	−1.14310e35			−0.111550
$466$	−9.38560e32	−	3.55297e34i	−0.000889718	−	0.0336807i
$467$	2.52284e35	−	2.52284e35i	0.232333	−	0.232333i	−0.581333	−	0.813666i	$-0.697469\pi$
$467$	2.52284e35	−	2.52284e35i	0.232333	−	0.232333i	0.813666	+	0.581333i	$0.197469\pi$
$468$	4.82994e35	+	4.34487e35i	0.432138	+	0.388739i
$469$	1.46498e36	+	1.46498e36i	1.27350	+	1.27350i
$470$	−1.07589e36	−	1.02051e36i	−0.908755	−	0.861978i
$471$			1.03221e36i			0.847199i
$472$	8.41459e35	+	7.17670e35i	0.671144	+	0.572410i
$473$			1.50753e36i			1.16853i
$474$	6.67078e35	−	7.03278e35i	0.502538	−	0.529809i
$475$	−2.00800e36	−	2.00800e36i	−1.47028	−	1.47028i
$476$	1.14428e35	+	2.16435e36i	0.0814399	+	1.54040i
$477$	−1.24966e34	+	1.24966e34i	−0.00864557	+	0.00864557i
$478$	7.60996e35	−	2.01026e34i	0.511806	−	0.0135200i
$479$	−1.59000e36			−1.03960			−0.519802	−	0.854287i	$-0.673994\pi$
$479$	−1.59000e36			−1.03960			−0.519802	+	0.854287i	$0.673994\pi$
$480$	−3.14141e36	+	4.17253e35i	−1.99696	+	0.265242i
$481$	5.31113e35			0.328268
$482$	2.23984e36	−	5.91681e34i	1.34611	−	0.0355593i
$483$	3.15041e36	−	3.15041e36i	1.84111	−	1.84111i
$484$	−1.71233e34	−	3.23880e35i	−0.00973140	−	0.184065i
$485$	2.48434e36	+	2.48434e36i	1.37309	+	1.37309i
$486$	1.02688e36	−	1.08260e36i	0.551986	−	0.581940i
$487$			2.21222e36i			1.15661i	0.815820	+	0.578307i	$0.196286\pi$
$487$			2.21222e36i			1.15661i	−0.815820	+	0.578307i	$0.803714\pi$
$488$	2.08158e36	−	2.44062e36i	1.05858	−	1.24118i
$489$			2.63584e36i			1.30392i
$490$	−5.56395e36	−	5.27756e36i	−2.67754	−	2.53972i
$491$	3.23979e35	+	3.23979e35i	0.151676	+	0.151676i	0.778866	−	0.627190i	$-0.215795\pi$
$491$	3.23979e35	+	3.23979e35i	0.151676	+	0.151676i	−0.627190	+	0.778866i	$0.715795\pi$
$492$	−1.31229e36	−	1.18050e36i	−0.597723	−	0.537695i
$493$	1.15503e36	−	1.15503e36i	0.511869	−	0.511869i
$494$	9.40269e34	+	3.55944e36i	0.0405451	+	1.53486i
$495$	−1.54942e36			−0.650128
$496$	−1.34859e35	+	1.42998e34i	−0.0550652	+	0.00583884i
$497$	1.01320e36			0.402610
$498$	6.76589e34	+	2.56126e36i	0.0261655	+	0.990508i
$499$	1.92777e36	−	1.92777e36i	0.725600	−	0.725600i	−0.244140	−	0.969740i	$-0.578506\pi$
$499$	1.92777e36	−	1.92777e36i	0.725600	−	0.725600i	0.969740	+	0.244140i	$0.0785056\pi$
$500$	2.59897e36	−	2.88912e36i	0.952152	−	1.05845i
$501$	9.01562e35	+	9.01562e35i	0.321504	+	0.321504i
$502$	3.16400e36	+	3.00114e36i	1.09834	+	1.04180i
$503$		−	4.17654e36i		−	1.41140i	−0.708512	−	0.705698i	$-0.750633\pi$
$503$		−	4.17654e36i		−	1.41140i	0.708512	−	0.705698i	$-0.249367\pi$
$504$	2.30933e36	−	1.83352e35i	0.759754	−	0.0603218i
$505$		−	3.77535e36i		−	1.20927i
$506$	−2.43293e36	+	2.56495e36i	−0.758748	+	0.799922i
$507$	2.37668e36	+	2.37668e36i	0.721711	+	0.721711i
$508$	−3.42952e36	+	1.81316e35i	−1.01408	+	0.0536139i
$509$	3.84305e36	−	3.84305e36i	1.10659	−	1.10659i	0.112992	−	0.993596i	$-0.463957\pi$
$509$	3.84305e36	−	3.84305e36i	1.10659	−	1.10659i	0.993596	−	0.112992i	$-0.0360434\pi$
$510$	6.20402e36	−	1.63887e35i	1.73971	−	0.0459565i
$511$	−3.92913e36			−1.07304
$512$	−3.65392e36	+	8.85237e35i	−0.971884	+	0.235459i
$513$	2.97962e36			0.771928
$514$	7.34859e36	−	1.94122e35i	1.85439	−	0.0489861i
$515$	4.91123e36	−	4.91123e36i	1.20724	−	1.20724i
$516$	−6.44515e36	+	3.40751e35i	−1.54334	+	0.0815954i
$517$	−2.03319e36	−	2.03319e36i	−0.474302	−	0.474302i
$518$	1.30333e36	−	1.37406e36i	0.296213	−	0.312287i
$519$			5.90309e36i			1.30713i
$520$	−1.06113e37	+	8.42499e35i	−2.28941	+	0.181771i
$521$			1.75125e36i			0.368163i	0.982911	+	0.184081i	$0.0589310\pi$
$521$			1.75125e36i			0.368163i	−0.982911	+	0.184081i	$0.941069\pi$
$522$	−1.26672e36	−	1.20152e36i	−0.259495	−	0.246138i
$523$	−2.20670e36	−	2.20670e36i	−0.440524	−	0.440524i	0.451664	−	0.892188i	$-0.350831\pi$
$523$	−2.20670e36	−	2.20670e36i	−0.440524	−	0.440524i	−0.892188	+	0.451664i	$0.850831\pi$
$524$	3.55315e36	−	3.94983e36i	0.691261	−	0.768434i
$525$	−1.46691e37	+	1.46691e37i	−2.78134	+	2.78134i
$526$	−1.32868e34	−	5.02977e35i	−0.00245534	−	0.0929482i
$527$	2.65589e35			0.0478373
$528$	−6.11049e36	+	6.47927e35i	−1.07280	+	0.113754i
$529$	−2.86470e36			−0.490261
$530$	−7.64664e33	−	2.89468e35i	−0.00127569	−	0.0482921i
$531$	−1.63695e36	+	1.63695e36i	−0.266232	+	0.266232i
$532$	9.43948e36	+	8.49148e36i	1.49672	+	1.34641i
$533$	−4.19248e36	−	4.19248e36i	−0.648117	−	0.648117i
$534$	−2.17181e36	−	2.06002e36i	−0.327352	−	0.310502i
$535$			1.33539e37i			1.96260i
$536$	4.56724e36	−	5.35503e36i	0.654530	−	0.767428i
$537$			1.04129e37i			1.45519i
$538$	2.13362e36	−	2.24940e36i	0.290774	−	0.306553i
$539$	−1.05146e37	−	1.05146e37i	−1.39748	−	1.39748i
$540$	4.70283e35	+	8.89519e36i	0.0609598	+	1.15303i
$541$	5.57551e36	−	5.57551e36i	0.704890	−	0.704890i	−0.260566	−	0.965456i	$-0.583909\pi$
$541$	5.57551e36	−	5.57551e36i	0.704890	−	0.704890i	0.965456	+	0.260566i	$0.0839092\pi$
$542$	−1.03341e37	+	2.72988e35i	−1.27433	+	0.0336630i
$543$	−1.64693e37			−1.98097
$544$	7.29876e36	−	9.69446e35i	0.856375	−	0.113747i
$545$	−5.40728e36			−0.618907
$546$	2.60029e37	−	6.86899e35i	2.90350	−	0.0766995i
$547$	−3.06093e36	+	3.06093e36i	−0.333445	+	0.333445i	−0.853893	−	0.520448i	$-0.825765\pi$
$547$	−3.06093e36	+	3.06093e36i	−0.333445	+	0.333445i	0.520448	+	0.853893i	$0.325765\pi$
$548$	−2.72387e35	−	5.15208e36i	−0.0289500	−	0.547577i
$549$	4.74792e36	+	4.74792e36i	0.492353	+	0.492353i
$550$	1.13284e37	−	1.19431e37i	1.14623	−	1.20843i
$551$		−	9.56905e36i		−	0.944762i
$552$	−1.15159e37	−	9.82175e36i	−1.10948	−	0.946262i
$553$		−	1.16103e37i		−	1.09157i
$554$	9.50862e35	+	9.01918e35i	0.0872440	+	0.0827533i
$555$	−3.83465e36	−	3.83465e36i	−0.343377	−	0.343377i
$556$	6.29333e36	+	5.66130e36i	0.550011	+	0.494774i
$557$	−1.01026e37	+	1.01026e37i	−0.861765	+	0.861765i	−0.991543	−	0.129778i	$-0.958573\pi$
$557$	−1.01026e37	+	1.01026e37i	−0.861765	+	0.861765i	0.129778	+	0.991543i	$0.458573\pi$
$558$	−7.49629e33	−	2.83776e35i	−0.000624144	−	0.0236273i
$559$	−2.16795e37			−1.76193
$560$	−2.38601e37	+	2.95203e37i	−1.89293	+	2.34198i
$561$	1.20339e37			0.931983
$562$	3.53059e35	+	1.33652e37i	0.0266936	+	1.01050i
$563$	−2.85063e36	+	2.85063e36i	−0.210416	+	0.210416i	−0.804444	−	0.594028i	$-0.797537\pi$
$563$	−2.85063e36	+	2.85063e36i	−0.210416	+	0.210416i	0.594028	+	0.804444i	$0.297537\pi$
$564$	8.23292e36	−	9.15206e36i	0.593316	−	0.659555i
$565$	1.15355e36	+	1.15355e36i	0.0811676	+	0.0811676i
$566$	4.87657e36	+	4.62555e36i	0.335037	+	0.317791i
$567$		−	3.31280e37i		−	2.22241i
$568$	−2.72425e35	−	3.43119e36i	−0.0178461	−	0.224772i
$569$			1.12984e37i			0.722775i	0.932416	+	0.361388i	$0.117697\pi$
$569$			1.12984e37i			0.722775i	−0.932416	+	0.361388i	$0.882303\pi$
$570$	2.50204e37	−	2.63781e37i	1.56309	−	1.64791i
$571$	9.87170e36	+	9.87170e36i	0.602288	+	0.602288i	0.940919	−	0.338631i	$-0.109964\pi$
$571$	9.87170e36	+	9.87170e36i	0.602288	+	0.602288i	−0.338631	+	0.940919i	$0.609964\pi$
$572$	−2.06114e37	+	1.08971e36i	−1.22818	+	0.0649331i
$573$	−3.07474e36	+	3.07474e36i	−0.178946	+	0.178946i
$574$	−2.11347e37	+	5.58300e35i	−1.20140	+	0.0317363i
$575$	4.05464e37			2.25131
$576$	−1.24184e36	−	7.77121e36i	−0.0673539	−	0.421488i
$577$	1.53120e37			0.811259			0.405629	−	0.914038i	$-0.367052\pi$
$577$	1.53120e37			0.811259			0.405629	+	0.914038i	$0.367052\pi$
$578$	4.89966e36	−	1.29431e35i	0.253595	−	0.00669901i
$579$	−1.68040e37	+	1.68040e37i	−0.849675	+	0.849675i
$580$	2.85669e37	−	1.51031e36i	1.41119	−	0.0746086i
$581$	2.17002e37	+	2.17002e37i	1.04733	+	1.04733i
$582$	−2.00719e37	+	2.11611e37i	−0.946516	+	0.997880i
$583$		−	5.61478e35i		−	0.0258707i
$584$	1.05645e36	+	1.33060e37i	0.0475635	+	0.599063i
$585$		−	2.22819e37i		−	0.980275i
$586$	6.18544e36	+	5.86706e36i	0.265921	+	0.252234i
$587$	1.22724e37	+	1.22724e37i	0.515604	+	0.515604i	0.916238	−	0.400634i	$-0.131210\pi$
$587$	1.22724e37	+	1.22724e37i	0.515604	+	0.515604i	−0.400634	+	0.916238i	$0.631210\pi$
$588$	4.25765e37	−	4.73298e37i	1.74814	−	1.94330i
$589$	1.10016e36	−	1.10016e36i	0.0441469	−	0.0441469i
$590$	−1.00165e36	−	3.79179e37i	−0.0392838	−	1.48711i
$591$	3.11256e36			0.119313
$592$	−5.00367e36	−	4.04427e36i	−0.187476	−	0.151530i
$593$	−4.00738e36			−0.146765			−0.0733825	−	0.997304i	$-0.523379\pi$
$593$	−4.00738e36			−0.146765			−0.0733825	+	0.997304i	$0.523379\pi$
$594$	4.56102e35	+	1.72660e37i	0.0163285	+	0.618122i
$595$	5.25632e37	−	5.25632e37i	1.83951	−	1.83951i
$596$	−2.22785e37	−	2.00411e37i	−0.762186	−	0.685640i
$597$	1.18356e37	+	1.18356e37i	0.395854	+	0.395854i
$598$	−3.68861e37	−	3.49875e37i	−1.20614	−	1.14405i
$599$			2.52974e37i			0.808749i	0.914594	+	0.404374i	$0.132511\pi$
$599$			2.52974e37i			0.808749i	−0.914594	+	0.404374i	$0.867489\pi$
$600$	5.36210e37	+	4.57327e37i	1.67607	+	1.42950i
$601$		−	1.83437e37i		−	0.560637i	−0.959907	−	0.280318i	$-0.909560\pi$
$601$		−	1.83437e37i		−	0.560637i	0.959907	−	0.280318i	$-0.0904400\pi$
$602$	−5.32008e37	+	5.60878e37i	−1.58988	+	1.67616i
$603$	1.04175e37	+	1.04175e37i	0.304426	+	0.304426i
$604$	1.61911e36	+	3.06247e37i	0.0462676	+	0.875131i
$605$	−7.86573e36	+	7.86573e36i	−0.219807	+	0.219807i
$606$	3.13300e37	−	8.27621e35i	0.856209	−	0.0226178i
$607$	−2.15299e37			−0.575432			−0.287716	−	0.957716i	$-0.592896\pi$
$607$	−2.15299e37			−0.575432			−0.287716	+	0.957716i	$0.592896\pi$
$608$	2.62182e37	−	3.42498e37i	0.685339	−	0.895282i
$609$	−6.99053e37			−1.78721
$610$	−1.09980e38	+	2.90525e36i	−2.75017	+	0.0726491i
$611$	2.92389e37	−	2.92389e37i	0.715162	−	0.715162i
$612$	8.13700e35	+	1.53908e37i	0.0194679	+	0.368227i
$613$	−2.58608e37	−	2.58608e37i	−0.605237	−	0.605237i	0.336460	−	0.941698i	$-0.390770\pi$
$613$	−2.58608e37	−	2.58608e37i	−0.605237	−	0.605237i	−0.941698	+	0.336460i	$0.890770\pi$
$614$	4.45928e37	−	4.70127e37i	1.02092	−	1.07632i
$615$			6.05397e37i			1.35589i
$616$	−4.77606e37	+	5.59987e37i	−1.04648	+	1.22698i
$617$		−	2.00824e37i		−	0.430493i	−0.976560	−	0.215247i	$-0.930944\pi$
$617$		−	2.00824e37i		−	0.430493i	0.976560	−	0.215247i	$-0.0690555\pi$
$618$	4.18328e37	+	3.96796e37i	0.877350	+	0.832190i
$619$	1.73371e37	+	1.73371e37i	0.355755	+	0.355755i	0.862246	−	0.506490i	$-0.169057\pi$
$619$	1.73371e37	+	1.73371e37i	0.355755	+	0.355755i	−0.506490	+	0.862246i	$0.669057\pi$
$620$	3.45800e36	+	3.11072e36i	0.0694284	+	0.0624558i
$621$	−3.00829e37	+	3.00829e37i	−0.590993	+	0.590993i
$622$	4.39382e35	+	1.66330e37i	0.00844640	+	0.319743i
$623$	−3.58539e37			−0.674448
$624$	−9.31771e36	−	8.78738e37i	−0.171521	−	1.61759i
$625$	−3.09107e37			−0.556837
$626$	3.79102e35	+	1.43511e37i	0.00668347	+	0.253006i
$627$	4.98486e37	−	4.98486e37i	0.860085	−	0.860085i
$628$	2.80894e37	−	3.12253e37i	0.474337	−	0.527293i
$629$	8.90944e36	+	8.90944e36i	0.147254	+	0.147254i
$630$	−5.76463e37	−	5.46791e37i	−0.932554	−	0.884552i
$631$		−	5.73798e37i		−	0.908579i	−0.890854	−	0.454290i	$-0.849893\pi$
$631$		−	5.73798e37i		−	0.908579i	0.890854	−	0.454290i	$-0.150107\pi$
$632$	−3.93180e37	+	3.12171e36i	−0.609412	+	0.0483851i
$633$		−	1.08452e38i		−	1.64547i
$634$	−7.92697e37	+	8.35713e37i	−1.17734	+	1.24123i
$635$	8.32892e37	+	8.32892e37i	1.21100	+	1.21100i
$636$	2.40049e36	−	1.26912e35i	0.0341687	−	0.00180648i
$637$	1.51209e38	−	1.51209e38i	2.10714	−	2.10714i
$638$	5.54497e37	−	1.46477e36i	0.756519	−	0.0199844i
$639$	7.20492e36			0.0962427
$640$	1.06385e38	+	7.28647e37i	1.39140	+	0.952988i
$641$	−6.74215e37			−0.863406			−0.431703	−	0.902016i	$-0.642087\pi$
$641$	−6.74215e37			−0.863406			−0.431703	+	0.902016i	$0.642087\pi$
$642$	−1.10818e38	+	2.92740e36i	−1.38959	+	0.0367079i
$643$	−9.60356e37	+	9.60356e37i	−1.17919	+	1.17919i	−0.199241	+	0.979951i	$0.563848\pi$
$643$	−9.60356e37	+	9.60356e37i	−1.17919	+	1.17919i	−0.979951	+	0.199241i	$0.936152\pi$
$644$	−1.81035e38	+	9.57119e36i	−2.17672	+	0.115082i
$645$	1.56527e38	+	1.56527e38i	1.84303	+	1.84303i
$646$	−5.81323e37	+	6.12869e37i	−0.670315	+	0.706690i
$647$			4.86931e37i			0.549869i	0.961463	+	0.274934i	$0.0886562\pi$
$647$			4.86931e37i			0.549869i	−0.961463	+	0.274934i	$0.911344\pi$
$648$	−1.12187e38	+	8.90729e36i	−1.24074	+	0.0985106i
$649$		−	7.35491e37i		−	0.796662i
$650$	1.71752e38	+	1.62911e38i	1.82209	+	1.72830i
$651$	−8.03707e36	−	8.03707e36i	−0.0835130	−	0.0835130i
$652$	7.17289e37	−	7.97368e37i	0.730049	−	0.811552i
$653$	9.96444e37	−	9.96444e37i	0.993401	−	0.993401i	−0.00657695	−	0.999978i	$-0.502094\pi$
$653$	9.96444e37	−	9.96444e37i	0.993401	−	0.993401i	0.999978	+	0.00657695i	$0.00209352\pi$
$654$	−1.18537e36	−	4.48726e37i	−0.0115759	−	0.438210i
$655$	−1.82217e38			−1.74314
$656$	7.57327e36	+	7.14223e37i	0.0709711	+	0.669317i
$657$	−2.79402e37			−0.256506
$658$	−3.89365e36	−	1.47396e38i	−0.0350193	−	1.32567i
$659$	1.08343e36	−	1.08343e36i	0.00954661	−	0.00954661i	−0.702317	−	0.711864i	$-0.747851\pi$
$659$	1.08343e36	−	1.08343e36i	0.00954661	−	0.00954661i	0.711864	+	0.702317i	$0.247851\pi$
$660$	1.56683e38	+	1.40947e38i	1.35263	+	1.21679i
$661$	1.01016e38	+	1.01016e38i	0.854419	+	0.854419i	0.990674	−	0.136255i	$-0.0435066\pi$
$661$	1.01016e38	+	1.01016e38i	0.854419	+	0.854419i	−0.136255	+	0.990674i	$0.543507\pi$
$662$	2.30572e37	+	2.18704e37i	0.191084	+	0.181248i
$663$			1.73057e38i			1.40526i
$664$	6.76527e37	−	7.93219e37i	0.538289	−	0.631138i
$665$		−	4.35471e38i		−	3.39521i
$666$	9.26807e36	−	9.77101e36i	0.0708088	−	0.0746513i
$667$	9.66111e37	+	9.66111e37i	0.723316	+	0.723316i
$668$	−2.73902e36	−	5.18073e37i	−0.0200961	−	0.380109i
$669$	−2.15647e38	+	2.15647e38i	−1.55057	+	1.55057i
$670$	−2.41309e38	+	6.37448e36i	−1.70045	+	0.0449195i
$671$	−2.13327e38			−1.47330
$672$	−2.50207e38	−	1.91533e38i	−1.69361	−	1.29646i
$673$	−3.17797e37			−0.210837			−0.105418	−	0.994428i	$-0.533618\pi$
$673$	−3.17797e37			−0.210837			−0.105418	+	0.994428i	$0.533618\pi$
$674$	−1.61641e37	+	4.26995e35i	−0.105110	+	0.00277661i
$675$	1.40074e38	−	1.40074e38i	0.892804	−	0.892804i
$676$	−7.22054e36	−	1.36573e38i	−0.0451117	−	0.853267i
$677$	−3.46930e36	−	3.46930e36i	−0.0212468	−	0.0212468i	0.696404	−	0.717650i	$-0.254782\pi$
$677$	−3.46930e36	−	3.46930e36i	−0.0212468	−	0.0212468i	−0.717650	+	0.696404i	$0.754782\pi$
$678$	−9.31995e36	+	9.82570e36i	−0.0559516	+	0.0589879i
$679$			3.49344e38i			2.05595i
$680$	−1.92138e38	−	1.63872e38i	−1.10852	−	0.945440i
$681$			1.96376e36i			0.0111071i
$682$	6.54350e36	+	6.20669e36i	0.0362845	+	0.0344168i
$683$	−3.49900e37	−	3.49900e37i	−0.190223	−	0.190223i	0.605569	−	0.795793i	$-0.292945\pi$
$683$	−3.49900e37	−	3.49900e37i	−0.190223	−	0.190223i	−0.795793	+	0.605569i	$0.792945\pi$
$684$	6.71245e37	+	6.03833e37i	0.357787	+	0.321854i
$685$	−1.25123e38	+	1.25123e38i	−0.653906	+	0.653906i
$686$	−1.09342e37	−	4.13919e38i	−0.0560288	−	2.12100i
$687$	4.60713e38			2.31481
$688$	2.04245e38	+	1.65083e38i	1.00625	+	0.813315i
$689$	8.07451e36			0.0390083
$690$	1.37082e37	+	5.18930e38i	0.0649406	+	2.45836i
$691$	−1.58069e38	+	1.58069e38i	−0.734333	+	0.734333i	−0.971475	−	0.237142i	$-0.923789\pi$
$691$	−1.58069e38	+	1.58069e38i	−0.734333	+	0.734333i	0.237142	+	0.971475i	$0.423789\pi$
$692$	1.60640e38	−	1.78574e38i	0.731849	−	0.813554i
$693$	−1.08938e38	−	1.08938e38i	−0.486723	−	0.486723i
$694$	−1.19193e38	−	1.13058e38i	−0.522274	−	0.495391i
$695$		−	2.90330e38i		−	1.24766i
$696$	1.87958e37	+	2.36733e38i	0.0792202	+	0.997779i
$697$		−	1.40658e38i		−	0.581462i
$698$	1.62127e38	−	1.70924e38i	0.657364	−	0.693036i
$699$	−7.15561e36	−	7.15561e36i	−0.0284580	−	0.0284580i
$700$	8.42946e38	−	4.45660e37i	3.28834	−	0.173852i
$701$	−2.09073e38	+	2.09073e38i	−0.800026	+	0.800026i	−0.983099	−	0.183073i	$-0.941395\pi$
$701$	−2.09073e38	+	2.09073e38i	−0.800026	+	0.800026i	0.183073	+	0.983099i	$0.441395\pi$
$702$	−2.48299e38	+	6.55912e36i	−0.932016	+	0.0246204i
$703$	7.38120e37			0.271788
$704$	2.02480e38	+	1.46684e38i	0.731395	+	0.529848i
$705$	−4.22211e38			−1.49615
$706$	1.71988e38	−	4.54329e36i	0.597910	−	0.0157945i
$707$	2.65442e38	−	2.65442e38i	0.905330	−	0.905330i
$708$	3.14445e38	−	1.66245e37i	1.05219	−	0.0556288i
$709$	−1.35313e38	−	1.35313e38i	−0.444236	−	0.444236i	0.449197	−	0.893433i	$-0.351710\pi$
$709$	−1.35313e38	−	1.35313e38i	−0.444236	−	0.444236i	−0.893433	+	0.449197i	$0.851710\pi$
$710$	−8.12421e37	+	8.56507e37i	−0.261694	+	0.275895i
$711$		−	8.25611e37i		−	0.260937i
$712$	9.64023e36	+	1.21419e38i	0.0298956	+	0.376536i
$713$			2.22149e37i			0.0675983i
$714$	4.47722e38	+	4.24677e38i	1.33685	+	1.26804i
$715$	5.00569e38	+	5.00569e38i	1.46667	+	1.46667i
$716$	2.83366e38	−	3.15002e38i	0.814746	−	0.905705i
$717$	1.53263e38	−	1.53263e38i	0.432443	−	0.432443i
$718$	4.71473e35	+	1.78478e37i	0.00130550	+	0.0494203i
$719$	−4.16658e38			−1.13224			−0.566122	−	0.824321i	$-0.691557\pi$
$719$	−4.16658e38			−1.13224			−0.566122	+	0.824321i	$0.691557\pi$
$720$	−1.69670e38	+	2.09920e38i	−0.452498	+	0.559842i
$721$	6.90609e38			1.80762
$722$	2.78800e36	+	1.05541e38i	0.00716210	+	0.271125i
$723$	4.51100e38	−	4.51100e38i	1.13738	−	1.13738i
$724$	4.98214e38	+	4.48179e38i	1.23295	+	1.10913i
$725$	−4.49847e38	−	4.49847e38i	−1.09270	−	1.09270i
$726$	−6.69986e37	−	6.35500e37i	−0.159743	−	0.151520i
$727$			9.24040e37i			0.216260i	0.994137	+	0.108130i	$0.0344863\pi$
$727$			9.24040e37i			0.216260i	−0.994137	+	0.108130i	$0.965514\pi$
$728$	−8.05306e38	−	6.86835e38i	−1.85007	−	1.57790i
$729$			1.27065e38i			0.286552i
$730$	3.15052e38	−	3.32148e38i	0.697466	−	0.735315i
$731$	−3.63674e38	−	3.63674e38i	−0.790365	−	0.790365i
$732$	−4.82188e37	−	9.12036e38i	−0.102877	−	1.94586i
$733$	−2.10372e38	+	2.10372e38i	−0.440640	+	0.440640i	−0.892227	−	0.451587i	$-0.850858\pi$
$733$	−2.10372e38	+	2.10372e38i	−0.440640	+	0.440640i	0.451587	+	0.892227i	$0.350858\pi$
$734$	5.60411e38	−	1.48039e37i	1.15242	−	0.0304425i
$735$	−2.18346e39			−4.40825
$736$	8.10884e37	+	6.10498e38i	0.160734	+	1.21013i
$737$	−4.68065e38			−0.910952
$738$	−1.50290e38	+	3.97009e36i	−0.287190	+	0.00758647i
$739$	4.09334e37	−	4.09334e37i	0.0768030	−	0.0768030i	−0.667662	−	0.744465i	$-0.732705\pi$
$739$	4.09334e37	−	4.09334e37i	0.0768030	−	0.0768030i	0.744465	+	0.667662i	$0.232705\pi$
$740$	1.16500e37	+	2.20354e38i	0.0214633	+	0.405969i
$741$	7.16864e38	+	7.16864e38i	1.29685	+	1.29685i
$742$	1.98146e37	−	2.08899e37i	0.0351992	−	0.0371093i

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)

\(f(q)\)	\(=\)	\(q+(-11581.2 + 305.932i) q^{2} +(-2.33243e6 + 2.33243e6i) q^{3} +(1.34031e8 - 7.08611e6i) q^{4} +(-3.25506e9 - 3.25506e9i) q^{5} +(2.62988e10 - 2.77259e10i) q^{6} -4.57721e11i q^{7} +(-1.55007e12 + 1.23070e11i) q^{8} -3.25487e12i q^{9} +O(q^{10})\)	\(q+(-11581.2 + 305.932i) q^{2} +(-2.33243e6 + 2.33243e6i) q^{3} +(1.34031e8 - 7.08611e6i) q^{4} +(-3.25506e9 - 3.25506e9i) q^{5} +(2.62988e10 - 2.77259e10i) q^{6} -4.57721e11i q^{7} +(-1.55007e12 + 1.23070e11i) q^{8} -3.25487e12i q^{9} +(3.86933e13 + 3.67017e13i) q^{10} +(7.31216e13 + 7.31216e13i) q^{11} +(-2.96089e14 + 3.29145e14i) q^{12} +(-1.05155e15 + 1.05155e15i) q^{13} +(1.40031e14 + 5.30096e15i) q^{14} +1.51844e16 q^{15} +(1.79140e16 - 1.89951e15i) q^{16} -3.52795e16 q^{17} +(9.95769e14 + 3.76953e16i) q^{18} +(-1.46140e17 + 1.46140e17i) q^{19} +(-4.59343e17 - 4.13212e17i) q^{20} +(1.06760e18 + 1.06760e18i) q^{21} +(-8.69206e17 - 8.24465e17i) q^{22} -2.95092e18i q^{23} +(3.32837e18 - 3.90248e18i) q^{24} +1.37403e19i q^{25} +(1.18565e19 - 1.24999e19i) q^{26} +(-1.01944e19 - 1.01944e19i) q^{27} +(-3.24346e18 - 6.13486e19i) q^{28} +(-3.27394e19 + 3.27394e19i) q^{29} +(-1.75854e20 + 4.64539e18i) q^{30} -7.52814e18 q^{31} +(-2.06884e20 + 2.74791e19i) q^{32} -3.41102e20 q^{33} +(4.08579e20 - 1.07931e19i) q^{34} +(-1.48991e21 + 1.48991e21i) q^{35} +(-2.30644e19 - 4.36253e20i) q^{36} +(-2.52539e20 - 2.52539e20i) q^{37} +(1.64777e21 - 1.73718e21i) q^{38} -4.90532e21i q^{39} +(5.44616e21 + 4.64496e21i) q^{40} +3.98696e21i q^{41} +(-1.26907e22 - 1.20375e22i) q^{42} +(1.03084e22 + 1.03084e22i) q^{43} +(1.03187e22 + 9.28238e21i) q^{44} +(-1.05948e22 + 1.05948e22i) q^{45} +(9.02779e20 + 3.41752e22i) q^{46} -2.78056e22 q^{47} +(-3.73526e22 + 4.62136e22i) q^{48} -1.43796e23 q^{49} +(-4.20358e21 - 1.59129e23i) q^{50} +(8.22869e22 - 8.22869e22i) q^{51} +(-1.33488e23 + 1.48391e23i) q^{52} +(-3.83935e21 - 3.83935e21i) q^{53} +(1.21182e23 + 1.14945e23i) q^{54} -4.76030e23i q^{55} +(5.63316e22 + 7.09498e23i) q^{56} -6.81723e23i q^{57} +(3.69145e23 - 3.89177e23i) q^{58} +(-5.02923e23 - 5.02923e23i) q^{59} +(2.03517e24 - 1.07598e23i) q^{60} +(-1.45871e24 + 1.45871e24i) q^{61} +(8.71849e22 - 2.30310e21i) q^{62} -1.48982e24 q^{63} +(2.38756e24 - 3.81533e23i) q^{64} +6.84570e24 q^{65} +(3.95037e24 - 1.04354e23i) q^{66} +(-3.20060e24 + 3.20060e24i) q^{67} +(-4.72853e24 + 2.49994e23i) q^{68} +(6.88281e24 + 6.88281e24i) q^{69} +(1.67991e25 - 1.77108e25i) q^{70} +2.21358e24i q^{71} +(4.00577e23 + 5.04527e24i) q^{72} -8.58412e24i q^{73} +(3.00196e24 + 2.84744e24i) q^{74} +(-3.20482e25 - 3.20482e25i) q^{75} +(-1.85516e25 + 2.06228e25i) q^{76} +(3.34693e25 - 3.34693e25i) q^{77} +(1.50069e24 + 5.68095e25i) q^{78} +2.53654e25 q^{79} +(-6.44941e25 - 5.21280e25i) q^{80} +7.23759e25 q^{81} +(-1.21974e24 - 4.61738e25i) q^{82} +(-4.74091e25 + 4.74091e25i) q^{83} +(1.50657e26 + 1.35526e26i) q^{84} +(1.14837e26 + 1.14837e26i) q^{85} +(-1.22537e26 - 1.16230e26i) q^{86} -1.52725e26i q^{87} +(-1.22342e26 - 1.04344e26i) q^{88} -7.83314e25i q^{89} +(1.19459e26 - 1.25942e26i) q^{90} +(4.81315e26 + 4.81315e26i) q^{91} +(-2.09105e25 - 3.95513e26i) q^{92} +(1.75589e25 - 1.75589e25i) q^{93} +(3.22022e26 - 8.50660e24i) q^{94} +9.51389e26 q^{95} +(4.18450e26 - 5.46636e26i) q^{96} -7.63225e26 q^{97} +(1.66533e27 - 4.39918e25i) q^{98} +(2.38002e26 - 2.38002e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) 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

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