LMFDB - Embedded newform 16.28.e.a.5.16

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			5.16
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6847.52 + 9345.01i) q^{2} +(2.95774e6 - 2.95774e6i) q^{3} +(-4.04408e7 - 1.27980e8i) q^{4} +(6.75988e8 + 6.75988e8i) q^{5} +(7.38694e9 + 4.78933e10i) q^{6} -3.29800e11i q^{7} +(1.47290e12 + 4.98428e11i) q^{8} -9.87086e12i q^{9} +O(q^{10})$	\(q+(-6847.52 + 9345.01i) q^{2} +(2.95774e6 - 2.95774e6i) q^{3} +(-4.04408e7 - 1.27980e8i) q^{4} +(6.75988e8 + 6.75988e8i) q^{5} +(7.38694e9 + 4.78933e10i) q^{6} -3.29800e11i q^{7} +(1.47290e12 + 4.98428e11i) q^{8} -9.87086e12i q^{9} +(-1.09460e13 + 1.68828e12i) q^{10} +(-1.51836e13 - 1.51836e13i) q^{11} +(-4.98146e14 - 2.58919e14i) q^{12} +(-4.13391e14 + 4.13391e14i) q^{13} +(3.08199e15 + 2.25831e15i) q^{14} +3.99880e15 q^{15} +(-1.47435e16 + 1.03512e16i) q^{16} -6.20711e16 q^{17} +(9.22433e16 + 6.75909e16i) q^{18} +(1.52280e17 - 1.52280e17i) q^{19} +(5.91757e16 - 1.13851e17i) q^{20} +(-9.75464e17 - 9.75464e17i) q^{21} +(2.45861e17 - 3.79209e16i) q^{22} -2.08390e18i q^{23} +(5.83066e18 - 2.88222e18i) q^{24} -6.53666e18i q^{25} +(-1.03244e18 - 6.69384e18i) q^{26} +(-6.64090e18 - 6.64090e18i) q^{27} +(-4.22079e19 + 1.33374e19i) q^{28} +(-1.58279e19 + 1.58279e19i) q^{29} +(-2.73818e19 + 3.73688e19i) q^{30} -1.09427e20 q^{31} +(4.22387e18 - 2.08658e20i) q^{32} -8.98182e19 q^{33} +(4.25033e20 - 5.80055e20i) q^{34} +(2.22941e20 - 2.22941e20i) q^{35} +(-1.26328e21 + 3.99185e20i) q^{36} +(7.19433e20 + 7.19433e20i) q^{37} +(3.80320e20 + 2.46581e21i) q^{38} +2.44540e21i q^{39} +(6.58729e20 + 1.33259e21i) q^{40} +8.61962e21i q^{41} +(1.57952e22 - 2.43622e21i) q^{42} +(1.75610e21 + 1.75610e21i) q^{43} +(-1.32916e21 + 2.55723e21i) q^{44} +(6.67259e21 - 6.67259e21i) q^{45} +(1.94741e22 + 1.42696e22i) q^{46} +1.47232e22 q^{47} +(-1.29911e22 + 7.42237e22i) q^{48} -4.30560e22 q^{49} +(6.10852e22 + 4.47599e22i) q^{50} +(-1.83590e23 + 1.83590e23i) q^{51} +(6.96237e22 + 3.61880e22i) q^{52} +(-2.01822e23 - 2.01822e23i) q^{53} +(1.07533e23 - 1.65856e22i) q^{54} -2.05278e22i q^{55} +(1.64382e23 - 4.85762e23i) q^{56} -9.00812e23i q^{57} +(-3.95301e22 - 2.56293e23i) q^{58} +(9.87753e22 + 9.87753e22i) q^{59} +(-1.61714e23 - 5.11767e23i) q^{60} +(-9.38493e23 + 9.38493e23i) q^{61} +(7.49306e23 - 1.02260e24i) q^{62} -3.25541e24 q^{63} +(1.92099e24 + 1.46826e24i) q^{64} -5.58894e23 q^{65} +(6.15032e23 - 8.39352e23i) q^{66} +(-2.27190e24 + 2.27190e24i) q^{67} +(2.51020e24 + 7.94387e24i) q^{68} +(-6.16365e24 - 6.16365e24i) q^{69} +(5.56795e23 + 3.60998e24i) q^{70} -9.77167e24i q^{71} +(4.91991e24 - 1.45387e25i) q^{72} +1.86587e25i q^{73} +(-1.16494e25 + 1.79678e24i) q^{74} +(-1.93337e25 - 1.93337e25i) q^{75} +(-2.56472e25 - 1.33306e25i) q^{76} +(-5.00755e24 + 5.00755e24i) q^{77} +(-2.28523e25 - 1.67449e25i) q^{78} +6.34834e25 q^{79} +(-1.69637e25 - 2.96911e24i) q^{80} +3.59871e25 q^{81} +(-8.05504e25 - 5.90230e25i) q^{82} +(-7.33394e25 + 7.33394e25i) q^{83} +(-8.53916e25 + 1.64289e26i) q^{84} +(-4.19593e25 - 4.19593e25i) q^{85} +(-2.84356e25 + 4.38584e24i) q^{86} +9.36295e25i q^{87} +(-1.47959e25 - 2.99317e25i) q^{88} -3.71102e26i q^{89} +(1.66647e25 + 1.08046e26i) q^{90} +(1.36336e26 + 1.36336e26i) q^{91} +(-2.66699e26 + 8.42746e25i) q^{92} +(-3.23658e26 + 3.23658e26i) q^{93} +(-1.00817e26 + 1.37588e26i) q^{94} +2.05880e26 q^{95} +(-6.04664e26 - 6.29650e26i) q^{96} -2.24795e26 q^{97} +(2.94827e26 - 4.02359e26i) q^{98} +(-1.49875e26 + 1.49875e26i) 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 $

$2$	−6847.52	+	9345.01i	−0.591055	+	0.806631i
$2$	−6847.52	+	9345.01i	−0.591055	+	0.806631i
$3$	2.95774e6	−	2.95774e6i	1.07108	−	1.07108i	0.0738107	−	0.997272i	$-0.476484\pi$
$3$	2.95774e6	−	2.95774e6i	1.07108	−	1.07108i	0.997272	−	0.0738107i	$-0.0235161\pi$
$4$	−4.04408e7	−	1.27980e8i	−0.301307	−	0.953527i
$5$	6.75988e8	+	6.75988e8i	0.247653	+	0.247653i	0.820007	−	0.572354i	$-0.193970\pi$
$5$	6.75988e8	+	6.75988e8i	0.247653	+	0.247653i	−0.572354	+	0.820007i	$0.693970\pi$
$6$	7.38694e9	+	4.78933e10i	0.230899	+	1.49704i
$7$		−	3.29800e11i		−	1.28655i	−0.765634	−	0.643277i	$-0.777575\pi$
$7$		−	3.29800e11i		−	1.28655i	0.765634	−	0.643277i	$-0.222425\pi$
$8$	1.47290e12	+	4.98428e11i	0.947234	+	0.320544i
$9$		−	9.87086e12i		−	1.29444i
$10$	−1.09460e13	+	1.68828e12i	−0.346142	+	0.0533880i
$11$	−1.51836e13	−	1.51836e13i	−0.132609	−	0.132609i	0.637687	−	0.770296i	$-0.279891\pi$
$11$	−1.51836e13	−	1.51836e13i	−0.132609	−	0.132609i	−0.770296	+	0.637687i	$0.779891\pi$
$12$	−4.98146e14	−	2.58919e14i	−1.34403	−	0.698582i
$13$	−4.13391e14	+	4.13391e14i	−0.378552	+	0.378552i	−0.870580	−	0.492028i	$-0.836256\pi$
$13$	−4.13391e14	+	4.13391e14i	−0.378552	+	0.378552i	0.492028	+	0.870580i	$0.336256\pi$
$14$	3.08199e15	+	2.25831e15i	1.03777	+	0.760424i
$15$	3.99880e15			0.530515
$16$	−1.47435e16	+	1.03512e16i	−0.818428	+	0.574609i
$17$	−6.20711e16			−1.51995			−0.759974	−	0.649953i	$-0.774788\pi$
$17$	−6.20711e16			−1.51995			−0.759974	+	0.649953i	$0.774788\pi$
$18$	9.22433e16	+	6.75909e16i	1.04413	+	0.765084i
$19$	1.52280e17	−	1.52280e17i	0.830750	−	0.830750i	−0.156869	−	0.987619i	$-0.550140\pi$
$19$	1.52280e17	−	1.52280e17i	0.830750	−	0.830750i	0.987619	+	0.156869i	$0.0501401\pi$
$20$	5.91757e16	−	1.13851e17i	0.161524	−	0.310764i
$21$	−9.75464e17	−	9.75464e17i	−1.37801	−	1.37801i
$22$	2.45861e17	−	3.79209e16i	0.185346	−	0.0285873i
$23$		−	2.08390e18i		−	0.862089i	−0.902331	−	0.431044i	$-0.858145\pi$
$23$		−	2.08390e18i		−	0.862089i	0.902331	−	0.431044i	$-0.141855\pi$
$24$	5.83066e18	−	2.88222e18i	1.35789	−	0.671237i
$25$		−	6.53666e18i		−	0.877336i
$26$	−1.03244e18	−	6.69384e18i	−0.0816065	−	0.529097i
$27$	−6.64090e18	−	6.64090e18i	−0.315367	−	0.315367i
$28$	−4.22079e19	+	1.33374e19i	−1.22676	+	0.387648i
$29$	−1.58279e19	+	1.58279e19i	−0.286451	+	0.286451i	−0.835675	−	0.549224i	$-0.814923\pi$
$29$	−1.58279e19	+	1.58279e19i	−0.286451	+	0.286451i	0.549224	+	0.835675i	$0.314923\pi$
$30$	−2.73818e19	+	3.73688e19i	−0.313563	+	0.427929i
$31$	−1.09427e20			−0.804902			−0.402451	−	0.915442i	$-0.631842\pi$
$31$	−1.09427e20			−0.804902			−0.402451	+	0.915442i	$0.631842\pi$
$32$	4.22387e18	−	2.08658e20i	0.0202389	−	0.999795i
$33$	−8.98182e19			−0.284070
$34$	4.25033e20	−	5.80055e20i	0.898373	−	1.22604i
$35$	2.22941e20	−	2.22941e20i	0.318619	−	0.318619i
$36$	−1.26328e21	+	3.99185e20i	−1.23428	+	0.390023i
$37$	7.19433e20	+	7.19433e20i	0.485587	+	0.485587i	0.906911	−	0.421323i	$-0.138434\pi$
$37$	7.19433e20	+	7.19433e20i	0.485587	+	0.485587i	−0.421323	+	0.906911i	$0.638434\pi$
$38$	3.80320e20	+	2.46581e21i	0.179090	+	1.16113i
$39$			2.44540e21i			0.810921i
$40$	6.58729e20	+	1.33259e21i	0.155202	+	0.313969i
$41$			8.61962e21i			1.45514i	0.686031	+	0.727572i	$0.259351\pi$
$41$			8.61962e21i			1.45514i	−0.686031	+	0.727572i	$0.740649\pi$
$42$	1.57952e22	−	2.43622e21i	1.92602	−	0.297064i
$43$	1.75610e21	+	1.75610e21i	0.155856	+	0.155856i	0.780728	−	0.624871i	$-0.214849\pi$
$43$	1.75610e21	+	1.75610e21i	0.155856	+	0.155856i	−0.624871	+	0.780728i	$0.714849\pi$
$44$	−1.32916e21	+	2.55723e21i	−0.0864902	+	0.166402i
$45$	6.67259e21	−	6.67259e21i	0.320572	−	0.320572i
$46$	1.94741e22	+	1.42696e22i	0.695387	+	0.509542i
$47$	1.47232e22			0.393260			0.196630	−	0.980478i	$-0.437000\pi$
$47$	1.47232e22			0.393260			0.196630	+	0.980478i	$0.437000\pi$
$48$	−1.29911e22	+	7.42237e22i	−0.261150	+	1.49206i
$49$	−4.30560e22			−0.655219
$50$	6.10852e22	+	4.47599e22i	0.707686	+	0.518554i
$51$	−1.83590e23	+	1.83590e23i	−1.62799	+	1.62799i
$52$	6.96237e22	+	3.61880e22i	0.475020	+	0.246899i
$53$	−2.01822e23	−	2.01822e23i	−1.06474	−	1.06474i	−0.997754	−	0.0669869i	$-0.978661\pi$
$53$	−2.01822e23	−	2.01822e23i	−1.06474	−	1.06474i	−0.0669869	−	0.997754i	$-0.521339\pi$
$54$	1.07533e23	−	1.65856e22i	0.440784	−	0.0679854i
$55$		−	2.05278e22i		−	0.0656821i
$56$	1.64382e23	−	4.85762e23i	0.412397	−	1.21867i
$57$		−	9.00812e23i		−	1.77961i
$58$	−3.95301e22	−	2.56293e23i	−0.0617518	−	0.400368i
$59$	9.87753e22	+	9.87753e22i	0.122503	+	0.122503i	0.765700	−	0.643197i	$-0.222393\pi$
$59$	9.87753e22	+	9.87753e22i	0.122503	+	0.122503i	−0.643197	+	0.765700i	$0.722393\pi$
$60$	−1.61714e23	−	5.11767e23i	−0.159848	−	0.505860i
$61$	−9.38493e23	+	9.38493e23i	−0.742127	+	0.742127i	−0.972987	−	0.230860i	$-0.925846\pi$
$61$	−9.38493e23	+	9.38493e23i	−0.742127	+	0.742127i	0.230860	+	0.972987i	$0.425846\pi$
$62$	7.49306e23	−	1.02260e24i	0.475742	−	0.649259i
$63$	−3.25541e24			−1.66536
$64$	1.92099e24	+	1.46826e24i	0.794503	+	0.607260i
$65$	−5.58894e23			−0.187499
$66$	6.15032e23	−	8.39352e23i	0.167901	−	0.229140i
$67$	−2.27190e24	+	2.27190e24i	−0.506266	+	0.506266i	−0.913378	−	0.407112i	$-0.866536\pi$
$67$	−2.27190e24	+	2.27190e24i	−0.506266	+	0.506266i	0.407112	+	0.913378i	$0.366536\pi$
$68$	2.51020e24	+	7.94387e24i	0.457971	+	1.44931i
$69$	−6.16365e24	−	6.16365e24i	−0.923368	−	0.923368i
$70$	5.56795e23	+	3.60998e24i	0.0686865	+	0.445330i
$71$		−	9.77167e24i		−	0.995362i	−0.867360	−	0.497681i	$-0.834185\pi$
$71$		−	9.77167e24i		−	0.995362i	0.867360	−	0.497681i	$-0.165815\pi$
$72$	4.91991e24	−	1.45387e25i	0.414924	−	1.22613i
$73$			1.86587e25i			1.30624i	0.757254	+	0.653121i	$0.226541\pi$
$73$			1.86587e25i			1.30624i	−0.757254	+	0.653121i	$0.773459\pi$
$74$	−1.16494e25	+	1.79678e24i	−0.678699	+	0.104681i
$75$	−1.93337e25	−	1.93337e25i	−0.939699	−	0.939699i
$76$	−2.56472e25	−	1.33306e25i	−1.04245	−	0.541832i
$77$	−5.00755e24	+	5.00755e24i	−0.170609	+	0.170609i
$78$	−2.28523e25	−	1.67449e25i	−0.654114	−	0.479299i
$79$	6.34834e25			1.53001			0.765005	−	0.644024i	$-0.222736\pi$
$79$	6.34834e25			1.53001			0.765005	+	0.644024i	$0.222736\pi$
$80$	−1.69637e25	−	2.96911e24i	−0.344990	−	0.0603826i
$81$	3.59871e25			0.618869
$82$	−8.05504e25	−	5.90230e25i	−1.17376	−	0.860070i
$83$	−7.33394e25	+	7.33394e25i	−0.907368	+	0.907368i	−0.996059	−	0.0886913i	$-0.971732\pi$
$83$	−7.33394e25	+	7.33394e25i	−0.907368	+	0.907368i	0.0886913	+	0.996059i	$0.471732\pi$
$84$	−8.53916e25	+	1.64289e26i	−0.898763	+	1.72917i
$85$	−4.19593e25	−	4.19593e25i	−0.376420	−	0.376420i
$86$	−2.84356e25	+	4.38584e24i	−0.217838	+	0.0335988i
$87$			9.36295e25i			0.613625i
$88$	−1.47959e25	−	2.99317e25i	−0.0831047	−	0.168119i
$89$		−	3.71102e26i		−	1.78949i	−0.446581	−	0.894743i	$-0.647359\pi$
$89$		−	3.71102e26i		−	1.78949i	0.446581	−	0.894743i	$-0.352641\pi$
$90$	1.66647e25	+	1.08046e26i	0.0691075	+	0.448059i
$91$	1.36336e26	+	1.36336e26i	0.487027	+	0.487027i
$92$	−2.66699e26	+	8.42746e25i	−0.822025	+	0.259753i
$93$	−3.23658e26	+	3.23658e26i	−0.862117	+	0.862117i
$94$	−1.00817e26	+	1.37588e26i	−0.232439	+	0.317216i
$95$	2.05880e26			0.411476
$96$	−6.04664e26	−	6.29650e26i	−1.04919	−	1.09254i
$97$	−2.24795e26			−0.339132			−0.169566	−	0.985519i	$-0.554237\pi$
$97$	−2.24795e26			−0.339132			−0.169566	+	0.985519i	$0.554237\pi$
$98$	2.94827e26	−	4.02359e26i	0.387271	−	0.528520i
$99$	−1.49875e26	+	1.49875e26i	−0.171654	+	0.171654i
$100$	−8.36563e26	+	2.64347e26i	−0.836563	+	0.264347i
$101$	−1.53698e27	−	1.53698e27i	−1.34378	−	1.34378i	−0.892259	−	0.451523i	$-0.850881\pi$
$101$	−1.53698e27	−	1.53698e27i	−1.34378	−	1.34378i	−0.451523	−	0.892259i	$-0.649119\pi$
$102$	−4.58515e26	−	2.97279e27i	−0.350955	−	2.27542i
$103$			7.26872e26i			0.487703i	0.969813	+	0.243851i	$0.0784109\pi$
$103$			7.26872e26i			0.487703i	−0.969813	+	0.243851i	$0.921589\pi$
$104$	−8.14926e26	+	4.02836e26i	−0.479919	+	0.237235i
$105$		−	1.31880e27i		−	0.682535i
$106$	3.26801e27	−	5.04049e26i	1.48817	−	0.229532i
$107$	−2.98510e27	−	2.98510e27i	−1.19751	−	1.19751i	−0.974911	−	0.222594i	$-0.928548\pi$
$107$	−2.98510e27	−	2.98510e27i	−1.19751	−	1.19751i	−0.222594	−	0.974911i	$-0.571452\pi$
$108$	−5.81341e26	+	1.11847e27i	−0.205689	+	0.395733i
$109$	−3.04835e27	+	3.04835e27i	−0.952374	+	0.952374i	−0.998916	−	0.0465423i	$-0.985180\pi$
$109$	−3.04835e27	+	3.04835e27i	−0.952374	+	0.952374i	0.0465423	+	0.998916i	$0.485180\pi$
$110$	1.91833e26	+	1.40565e26i	0.0529812	+	0.0388218i
$111$	4.25579e27			1.04021
$112$	3.41384e27	+	4.86241e27i	0.739265	+	1.05295i
$113$	−8.84264e27			−1.69833			−0.849167	−	0.528125i	$-0.822895\pi$
$113$	−8.84264e27			−1.69833			−0.849167	+	0.528125i	$0.822895\pi$
$114$	8.41810e27	+	6.16833e27i	1.43548	+	1.05185i
$115$	1.40869e27	−	1.40869e27i	0.213499	−	0.213499i
$116$	2.66575e27	+	1.38556e27i	0.359448	+	0.186829i
$117$	4.08052e27	+	4.08052e27i	0.490012	+	0.490012i
$118$	−1.59942e27	+	2.46691e26i	−0.171221	+	0.0264086i
$119$			2.04711e28i			1.95549i
$120$	5.88981e27	+	1.99311e27i	0.502521	+	0.170053i
$121$		−	1.26489e28i		−	0.964830i
$122$	−2.34388e27	−	1.51966e28i	−0.159985	−	1.03726i
$123$	2.54946e28	+	2.54946e28i	1.55858	+	1.55858i
$124$	4.42532e27	+	1.40045e28i	0.242523	+	0.767496i
$125$	9.45521e27	−	9.45521e27i	0.464928	−	0.464928i
$126$	2.22915e28	−	3.04219e28i	0.984322	−	1.34333i
$127$	2.84648e28			1.12969			0.564844	−	0.825198i	$-0.308936\pi$
$127$	2.84648e28			1.12969			0.564844	+	0.825198i	$0.308936\pi$
$128$	−2.68750e28	+	7.89773e27i	−0.959430	+	0.281947i
$129$	1.03881e28			0.333870
$130$	3.82704e27	−	5.22287e27i	0.110822	−	0.151243i
$131$	−8.53917e26	+	8.53917e26i	−0.0222974	+	0.0222974i	−0.718168	−	0.695870i	$-0.755019\pi$
$131$	−8.53917e26	+	8.53917e26i	−0.0222974	+	0.0222974i	0.695870	+	0.718168i	$0.255019\pi$
$132$	3.63232e27	+	1.14950e28i	0.0855925	+	0.270869i
$133$	−5.02222e28	−	5.02222e28i	−1.06880	−	1.06880i
$134$	−5.67405e27	−	3.67877e28i	−0.109139	−	0.707601i
$135$		−	8.97835e27i		−	0.156203i
$136$	−9.14242e28	−	3.09379e28i	−1.43975	−	0.487210i
$137$			4.81749e28i			0.687215i	0.939113	+	0.343608i	$0.111649\pi$
$137$			4.81749e28i			0.687215i	−0.939113	+	0.343608i	$0.888351\pi$
$138$	9.98050e28	−	1.53937e28i	1.29058	−	0.199056i
$139$	4.76219e28	+	4.76219e28i	0.558608	+	0.558608i	0.928911	−	0.370303i	$-0.120746\pi$
$139$	4.76219e28	+	4.76219e28i	0.558608	+	0.558608i	−0.370303	+	0.928911i	$0.620746\pi$
$140$	−3.75480e28	−	1.95162e28i	−0.399814	−	0.207810i
$141$	4.35473e28	−	4.35473e28i	0.421214	−	0.421214i
$142$	9.13164e28	+	6.69117e28i	0.802890	+	0.588314i
$143$	1.25535e28			0.100399
$144$	1.02176e29	+	1.45531e29i	0.743795	+	1.05940i
$145$	−2.13989e28			−0.141881
$146$	−1.74366e29	−	1.27766e29i	−1.05366	−	0.772061i
$147$	−1.27348e29	+	1.27348e29i	−0.701794	+	0.701794i
$148$	6.29788e28	−	1.21168e29i	0.316710	−	0.609331i
$149$	−9.80771e28	−	9.80771e28i	−0.450353	−	0.450353i	0.445119	−	0.895472i	$-0.353161\pi$
$149$	−9.80771e28	−	9.80771e28i	−0.450353	−	0.450353i	−0.895472	+	0.445119i	$0.853161\pi$
$150$	3.13062e29	−	4.82859e28i	1.31340	−	0.202576i
$151$		−	7.69720e28i		−	0.295219i	−0.989046	−	0.147609i	$-0.952842\pi$
$151$		−	7.69720e28i		−	0.295219i	0.989046	−	0.147609i	$-0.0471578\pi$
$152$	3.00194e29	−	1.48392e29i	1.05321	−	0.520623i
$153$			6.12695e29i			1.96748i
$154$	−1.25063e28	−	8.10849e28i	−0.0367790	−	0.238457i
$155$	−7.39716e28	−	7.39716e28i	−0.199337	−	0.199337i
$156$	3.12963e29	−	9.88940e28i	0.773235	−	0.244336i
$157$	−3.47803e29	+	3.47803e29i	−0.788294	+	0.788294i	−0.981214	−	0.192920i	$-0.938204\pi$
$157$	−3.47803e29	+	3.47803e29i	−0.788294	+	0.788294i	0.192920	+	0.981214i	$0.438204\pi$
$158$	−4.34704e29	+	5.93253e29i	−0.904321	+	1.23415i
$159$	−1.19387e30			−2.28085
$160$	1.43906e29	−	1.38195e29i	0.252615	−	0.242590i
$161$	−6.87273e29			−1.10912
$162$	−2.46422e29	+	3.36300e29i	−0.365786	+	0.499199i
$163$	−4.11153e29	+	4.11153e29i	−0.561657	+	0.561657i	−0.929778	−	0.368121i	$-0.880001\pi$
$163$	−4.11153e29	+	4.11153e29i	−0.561657	+	0.561657i	0.368121	+	0.929778i	$0.380001\pi$
$164$	1.10314e30	−	3.48584e29i	1.38752	−	0.438445i
$165$	−6.07160e28	−	6.07160e28i	−0.0703510	−	0.0703510i
$166$	−1.83165e29	−	1.18755e30i	−0.195606	−	1.26822i
$167$		−	3.00539e29i		−	0.295957i	−0.988991	−	0.147979i	$-0.952723\pi$
$167$		−	3.00539e29i		−	0.295957i	0.988991	−	0.147979i	$-0.0472767\pi$
$168$	−9.50559e29	−	1.92296e30i	−0.863582	−	1.74700i
$169$			8.50750e29i			0.713397i
$170$	6.79427e29	−	1.04793e29i	0.526117	−	0.0811470i
$171$	−1.50314e30	−	1.50314e30i	−1.07535	−	1.07535i
$172$	1.53728e29	−	2.95763e29i	0.101653	−	0.195574i
$173$	−2.99394e28	+	2.99394e28i	−0.0183072	+	0.0183072i	−0.716201	−	0.697894i	$-0.754121\pi$
$173$	−2.99394e28	+	2.99394e28i	−0.0183072	+	0.0183072i	0.697894	+	0.716201i	$0.254121\pi$
$174$	−8.74969e29	−	6.41130e29i	−0.494969	−	0.362686i
$175$	−2.15579e30			−1.12874
$176$	3.81028e29	+	6.66901e28i	0.184729	+	0.0323326i
$177$	5.84303e29			0.262421
$178$	3.46795e30	+	2.54113e30i	1.44346	+	1.05769i
$179$	6.93610e29	−	6.93610e29i	0.267670	−	0.267670i	−0.560491	−	0.828161i	$-0.689387\pi$
$179$	6.93610e29	−	6.93610e29i	0.267670	−	0.267670i	0.828161	+	0.560491i	$0.189387\pi$
$180$	−1.12380e30	−	5.84115e29i	−0.402264	−	0.209083i
$181$	2.78751e30	+	2.78751e30i	0.925882	+	0.925882i	0.997437	−	0.0715547i	$-0.0227961\pi$
$181$	2.78751e30	+	2.78751e30i	0.925882	+	0.925882i	−0.0715547	+	0.997437i	$0.522796\pi$
$182$	−2.20763e30	+	3.40499e29i	−0.680711	+	0.104991i
$183$			5.55164e30i			1.58976i
$184$	1.03868e30	−	3.06937e30i	0.276337	−	0.816599i
$185$			9.72657e29i			0.240515i
$186$	−8.08333e29	−	5.24084e30i	−0.185851	−	1.20497i
$187$	9.42461e29	+	9.42461e29i	0.201559	+	0.201559i
$188$	−5.95416e29	−	1.88427e30i	−0.118492	−	0.374984i
$189$	−2.19017e30	+	2.19017e30i	−0.405736	+	0.405736i
$190$	−1.40976e30	+	1.92395e30i	−0.243205	+	0.331909i
$191$	−1.50223e30			−0.241428			−0.120714	−	0.992687i	$-0.538518\pi$
$191$	−1.50223e30			−0.241428			−0.120714	+	0.992687i	$0.538518\pi$
$192$	1.00245e31	−	1.33905e30i	1.50140	−	0.200554i
$193$	4.65566e30			0.650066			0.325033	−	0.945703i	$-0.394625\pi$
$193$	4.65566e30			0.650066			0.325033	+	0.945703i	$0.394625\pi$
$194$	1.53929e30	−	2.10071e30i	0.200446	−	0.273554i
$195$	−1.65306e30	+	1.65306e30i	−0.200827	+	0.200827i
$196$	1.74122e30	+	5.51032e30i	0.197422	+	0.624769i
$197$	−6.57786e30	−	6.57786e30i	−0.696291	−	0.696291i	0.267318	−	0.963608i	$-0.413863\pi$
$197$	−6.57786e30	−	6.57786e30i	−0.696291	−	0.696291i	−0.963608	+	0.267318i	$0.913863\pi$
$198$	−3.74312e29	−	2.42686e30i	−0.0370044	−	0.239919i
$199$			3.71729e30i			0.343329i	0.985155	+	0.171664i	$0.0549145\pi$
$199$			3.71729e30i			0.343329i	−0.985155	+	0.171664i	$0.945086\pi$
$200$	3.25805e30	−	9.62782e30i	0.281224	−	0.831042i
$201$			1.34394e31i			1.08451i
$202$	2.48876e31	−	3.83859e30i	1.87819	−	0.289687i
$203$	5.22004e30	+	5.22004e30i	0.368534	+	0.368534i
$204$	3.09204e31	+	1.60714e31i	2.04286	+	1.06181i
$205$	−5.82676e30	+	5.82676e30i	−0.360371	+	0.360371i
$206$	−6.79263e30	−	4.97727e30i	−0.393396	−	0.288259i
$207$	−2.05699e31			−1.11592
$208$	1.81572e30	−	1.03739e31i	0.0922981	−	0.527337i
$209$	−4.62433e30			−0.220330
$210$	1.23242e31	+	9.03054e30i	0.550554	+	0.403416i
$211$	9.17660e30	−	9.17660e30i	0.384476	−	0.384476i	−0.488236	−	0.872712i	$-0.662359\pi$
$211$	9.17660e30	−	9.17660e30i	0.384476	−	0.384476i	0.872712	+	0.488236i	$0.162359\pi$
$212$	−1.76674e31	+	3.39910e31i	−0.694445	+	1.33607i
$213$	−2.89021e31	−	2.89021e31i	−1.06612	−	1.06612i
$214$	4.83363e31	−	7.45526e30i	1.67374	−	0.258153i
$215$			2.37420e30i			0.0771966i
$216$	−6.47135e30	−	1.30914e31i	−0.197637	−	0.399815i
$217$			3.60892e31i			1.03555i
$218$	−7.61325e30	−	4.93605e31i	−0.205309	−	1.33112i
$219$	5.51877e31	+	5.51877e31i	1.39909	+	1.39909i
$220$	−2.62716e30	+	8.30162e29i	−0.0626297	+	0.0197905i
$221$	2.56596e31	−	2.56596e31i	0.575379	−	0.575379i
$222$	−2.91416e31	+	3.97704e31i	−0.614821	+	0.839064i
$223$	−4.66837e31			−0.926936			−0.463468	−	0.886114i	$-0.653395\pi$
$223$	−4.66837e31			−0.926936			−0.463468	+	0.886114i	$0.653395\pi$
$224$	−6.88156e31	−	1.39304e30i	−1.28629	−	0.0260384i
$225$	−6.45225e31			−1.13566
$226$	6.05501e31	−	8.26346e31i	1.00381	−	1.36993i
$227$	5.46514e31	−	5.46514e31i	0.853595	−	0.853595i	−0.136979	−	0.990574i	$-0.543739\pi$
$227$	5.46514e31	−	5.46514e31i	0.853595	−	0.853595i	0.990574	+	0.136979i	$0.0437391\pi$
$228$	−1.15286e32	+	3.64295e31i	−1.69690	+	0.536208i
$229$	−7.96434e31	−	7.96434e31i	−1.10502	−	1.10502i	−0.993795	−	0.111226i	$-0.964522\pi$
$229$	−7.96434e31	−	7.96434e31i	−1.10502	−	1.10502i	−0.111226	−	0.993795i	$-0.535478\pi$
$230$	3.51821e30	+	2.28103e31i	0.0460252	+	0.298405i
$231$			2.96221e31i			0.365472i
$232$	−3.12019e31	+	1.54238e31i	−0.363156	+	0.179516i
$233$		−	2.25315e30i		−	0.0247449i	−0.999923	−	0.0123724i	$-0.996062\pi$
$233$		−	2.25315e30i		−	0.0247449i	0.999923	−	0.0123724i	$-0.00393837\pi$
$234$	−6.60739e31	+	1.01911e31i	−0.684883	+	0.105635i
$235$	9.95269e30	+	9.95269e30i	0.0973922	+	0.0973922i
$236$	8.64674e30	−	1.66358e31i	0.0798988	−	0.153721i
$237$	1.87767e32	−	1.87767e32i	1.63877	−	1.63877i
$238$	−1.91302e32	−	1.40176e32i	−1.57736	−	1.15581i
$239$	−1.66005e32			−1.29345			−0.646723	−	0.762725i	$-0.723861\pi$
$239$	−1.66005e32			−1.29345			−0.646723	+	0.762725i	$0.723861\pi$
$240$	−5.89562e31	+	4.13925e31i	−0.434188	+	0.304838i
$241$	1.43579e32			0.999682			0.499841	−	0.866117i	$-0.333392\pi$
$241$	1.43579e32			0.999682			0.499841	+	0.866117i	$0.333392\pi$
$242$	1.18204e32	+	8.66136e31i	0.778262	+	0.570268i
$243$	1.57081e32	−	1.57081e32i	0.978227	−	0.978227i
$244$	1.58062e32	+	8.21552e31i	0.931247	+	0.484030i
$245$	−2.91054e31	−	2.91054e31i	−0.162267	−	0.162267i
$246$	−4.12822e32	+	6.36726e31i	−2.17841	+	0.335992i
$247$			1.25903e32i			0.628964i
$248$	−1.61175e32	−	5.45416e31i	−0.762430	−	0.258006i
$249$			4.33838e32i			1.94373i
$250$	2.36143e31	+	1.53104e32i	0.100227	+	0.649824i
$251$	1.62237e32	+	1.62237e32i	0.652463	+	0.652463i	0.953585	−	0.301122i	$-0.0973613\pi$
$251$	1.62237e32	+	1.62237e32i	0.652463	+	0.652463i	−0.301122	+	0.953585i	$0.597361\pi$
$252$	1.31651e32	+	4.16629e32i	0.501786	+	1.58797i
$253$	−3.16411e31	+	3.16411e31i	−0.114321	+	0.114321i
$254$	−1.94913e32	+	2.66004e32i	−0.667708	+	0.911241i
$255$	−2.48210e32			−0.806354
$256$	1.10222e32	−	3.05227e32i	0.339649	−	0.940552i
$257$	5.19968e32			1.52012			0.760062	−	0.649850i	$-0.225168\pi$
$257$	5.19968e32			1.52012			0.760062	+	0.649850i	$0.225168\pi$
$258$	−7.11330e31	+	9.70774e31i	−0.197336	+	0.269310i
$259$	2.37269e32	−	2.37269e32i	0.624734	−	0.624734i
$260$	2.26021e31	+	7.15274e31i	0.0564948	+	0.178786i
$261$	1.56235e32	+	1.56235e32i	0.370792	+	0.370792i
$262$	−2.13265e30	−	1.38271e31i	−0.00480677	−	0.0311647i
$263$		−	8.65102e32i		−	1.85210i	−0.377400	−	0.926050i	$-0.623182\pi$
$263$		−	8.65102e32i		−	1.85210i	0.377400	−	0.926050i	$-0.376818\pi$
$264$	−1.32293e32	−	4.47679e31i	−0.269081	−	0.0910570i
$265$		−	2.72858e32i		−	0.527373i
$266$	8.13224e32	−	1.25430e32i	1.49385	−	0.230408i
$267$	−1.09762e33	−	1.09762e33i	−1.91669	−	1.91669i
$268$	3.82635e32	+	1.98881e32i	0.635280	+	0.330197i
$269$	5.40143e32	−	5.40143e32i	0.852812	−	0.852812i	−0.137667	−	0.990479i	$-0.543960\pi$
$269$	5.40143e32	−	5.40143e32i	0.852812	−	0.852812i	0.990479	+	0.137667i	$0.0439602\pi$
$270$	8.39027e31	+	6.14794e31i	0.125998	+	0.0923248i
$271$	−6.96792e32			−0.995447			−0.497723	−	0.867336i	$-0.665830\pi$
$271$	−6.96792e32			−0.995447			−0.497723	+	0.867336i	$0.665830\pi$
$272$	9.15144e32	−	6.42512e32i	1.24397	−	0.873376i
$273$	8.06495e32			1.04329
$274$	−4.50195e32	−	3.29878e32i	−0.554329	−	0.406182i
$275$	−9.92499e31	+	9.92499e31i	−0.116343	+	0.116343i
$276$	−5.39563e32	+	1.03809e33i	−0.602239	+	1.15867i
$277$	−4.09077e32	−	4.09077e32i	−0.434838	−	0.434838i	0.455432	−	0.890270i	$-0.349485\pi$
$277$	−4.09077e32	−	4.09077e32i	−0.434838	−	0.434838i	−0.890270	+	0.455432i	$0.849485\pi$
$278$	−7.71119e32	+	1.18936e32i	−0.780759	+	0.120422i
$279$			1.08014e33i			1.04190i
$280$	4.39489e32	−	2.17249e32i	0.403938	−	0.199675i
$281$			1.10011e33i			0.963608i	0.876279	+	0.481804i	$0.160018\pi$
$281$			1.10011e33i			0.963608i	−0.876279	+	0.481804i	$0.839982\pi$
$282$	1.08759e32	+	7.05141e32i	0.0908035	+	0.588726i
$283$	1.06729e33	+	1.06729e33i	0.849506	+	0.849506i	0.990071	−	0.140565i	$-0.0448920\pi$
$283$	1.06729e33	+	1.06729e33i	0.849506	+	0.849506i	−0.140565	+	0.990071i	$0.544892\pi$
$284$	−1.25058e33	+	3.95174e32i	−0.949105	+	0.299910i
$285$	6.08938e32	−	6.08938e32i	0.440725	−	0.440725i
$286$	−8.59603e31	+	1.17313e32i	−0.0593412	+	0.0809847i
$287$	2.84275e33			1.87212
$288$	−2.05964e33	−	4.16933e31i	−1.29417	−	0.0261979i
$289$	2.18511e33			1.31024
$290$	1.46530e32	−	1.99973e32i	0.0838595	−	0.114446i
$291$	−6.64886e32	+	6.64886e32i	−0.363238	+	0.363238i
$292$	2.38795e33	−	7.54573e32i	1.24554	−	0.393580i
$293$	3.55086e32	+	3.55086e32i	0.176856	+	0.176856i	0.789984	−	0.613128i	$-0.210089\pi$
$293$	3.55086e32	+	3.55086e32i	0.176856	+	0.176856i	−0.613128	+	0.789984i	$0.710089\pi$
$294$	−3.18052e32	−	2.06209e33i	−0.151290	−	0.980888i
$295$			1.33542e32i			0.0606765i
$296$	7.01065e32	+	1.41824e33i	0.304313	+	0.615617i
$297$			2.01665e32i			0.0836410i
$298$	1.58812e33	−	2.44947e32i	0.629452	−	0.0970851i
$299$	8.61466e32	+	8.61466e32i	0.326345	+	0.326345i
$300$	−1.69247e33	+	3.25621e33i	−0.612891	+	1.17917i
$301$	5.79161e32	−	5.79161e32i	0.200517	−	0.200517i
$302$	7.19304e32	+	5.27067e32i	0.238133	+	0.174491i
$303$	−9.09196e33			−2.87861
$304$	−6.68854e32	+	3.82144e33i	−0.202553	+	1.15727i
$305$	−1.26882e33			−0.367581
$306$	−5.72564e33	−	4.19544e33i	−1.58703	−	1.16289i
$307$	5.47615e32	−	5.47615e32i	0.145247	−	0.145247i	−0.630744	−	0.775991i	$-0.717250\pi$
$307$	5.47615e32	−	5.47615e32i	0.145247	−	0.145247i	0.775991	+	0.630744i	$0.217250\pi$
$308$	8.43377e32	+	4.38359e32i	0.214085	+	0.111274i
$309$	2.14990e33	+	2.14990e33i	0.522370	+	0.522370i
$310$	1.19779e33	−	1.84744e32i	0.278610	−	0.0429721i
$311$		−	3.44893e33i		−	0.768102i	−0.923312	−	0.384051i	$-0.874529\pi$
$311$		−	3.44893e33i		−	0.768102i	0.923312	−	0.384051i	$-0.125471\pi$
$312$	−1.21886e33	+	3.60183e33i	−0.259936	+	0.768132i
$313$		−	6.25226e33i		−	1.27699i	−0.769625	−	0.638496i	$-0.779557\pi$
$313$		−	6.25226e33i		−	1.27699i	0.769625	−	0.638496i	$-0.220443\pi$
$314$	−8.68636e32	−	5.63181e33i	−0.169937	−	1.10179i
$315$	−2.20062e33	−	2.20062e33i	−0.412433	−	0.412433i
$316$	−2.56732e33	−	8.12462e33i	−0.461003	−	1.45891i
$317$	−4.14179e33	+	4.14179e33i	−0.712669	+	0.712669i	−0.967093	−	0.254424i	$-0.918114\pi$
$317$	−4.14179e33	+	4.14179e33i	−0.712669	+	0.712669i	0.254424	+	0.967093i	$0.418114\pi$
$318$	8.17507e33	−	1.11568e34i	1.34811	−	1.83981i
$319$	4.80648e32			0.0759719
$320$	3.06039e32	+	2.29110e33i	0.0463716	+	0.347151i
$321$	−1.76583e34			−2.56525
$322$	4.70611e33	−	6.42257e33i	0.655553	−	0.894653i
$323$	−9.45221e33	+	9.45221e33i	−1.26270	+	1.26270i
$324$	−1.45534e33	−	4.60563e33i	−0.186470	−	0.590108i
$325$	2.70219e33	+	2.70219e33i	0.332117	+	0.332117i
$326$	−1.02685e33	−	6.65761e33i	−0.121079	−	0.785020i
$327$			1.80325e34i			2.04014i
$328$	−4.29625e33	+	1.26958e34i	−0.466437	+	1.37836i
$329$		−	4.85571e33i		−	0.505950i
$330$	9.83146e32	−	1.51638e32i	0.0983286	−	0.0151660i
$331$	−8.90363e33	−	8.90363e33i	−0.854849	−	0.854849i	0.135877	−	0.990726i	$-0.456615\pi$
$331$	−8.90363e33	−	8.90363e33i	−0.854849	−	0.854849i	−0.990726	+	0.135877i	$0.956615\pi$
$332$	1.23519e34	+	6.42010e33i	1.13860	+	0.591803i
$333$	7.10143e33	−	7.10143e33i	0.628562	−	0.628562i
$334$	2.80854e33	+	2.05795e33i	0.238728	+	0.174927i
$335$	−3.07155e33			−0.250757
$336$	2.44790e34	+	4.28449e33i	1.91961	+	0.335984i
$337$	2.13986e34			1.61206			0.806032	−	0.591872i	$-0.201611\pi$
$337$	2.13986e34			1.61206			0.806032	+	0.591872i	$0.201611\pi$
$338$	−7.95027e33	−	5.82552e33i	−0.575448	−	0.421657i
$339$	−2.61542e34	+	2.61542e34i	−1.81906	+	1.81906i
$340$	−3.67310e33	+	7.06683e33i	−0.245509	+	0.472345i
$341$	1.66150e33	+	1.66150e33i	0.106737	+	0.106737i
$342$	2.43396e34	−	3.75408e33i	1.50301	−	0.231820i
$343$		−	7.47208e33i		−	0.443579i
$344$	1.71126e33	+	3.46183e33i	0.0976735	+	0.197591i
$345$		−	8.33311e33i		−	0.457351i
$346$	−7.47736e31	−	4.84795e32i	−0.00394658	−	0.0255877i
$347$	−1.99529e33	−	1.99529e33i	−0.101288	−	0.101288i	0.654647	−	0.755935i	$-0.272817\pi$
$347$	−1.99529e33	−	1.99529e33i	−0.101288	−	0.101288i	−0.755935	+	0.654647i	$0.772817\pi$
$348$	1.19827e34	−	3.78645e33i	0.585108	−	0.184890i
$349$	−1.24581e34	+	1.24581e34i	−0.585205	+	0.585205i	−0.936329	−	0.351124i	$-0.885799\pi$
$349$	−1.24581e34	+	1.24581e34i	−0.585205	+	0.585205i	0.351124	+	0.936329i	$0.385799\pi$
$350$	1.47618e34	−	2.01459e34i	0.667147	−	0.910476i
$351$	5.49057e33			0.238766
$352$	−3.23231e33	+	3.10405e33i	−0.135266	+	0.129898i
$353$	3.75795e34			1.51353			0.756767	−	0.653684i	$-0.226778\pi$
$353$	3.75795e34			1.51353			0.756767	+	0.653684i	$0.226778\pi$
$354$	−4.00103e33	+	5.46032e33i	−0.155106	+	0.211677i
$355$	6.60553e33	−	6.60553e33i	0.246505	−	0.246505i
$356$	−4.74937e34	+	1.50077e34i	−1.70632	+	0.539185i
$357$	6.05481e34	+	6.05481e34i	2.09450	+	2.09450i
$358$	1.73229e33	+	1.12313e34i	0.0577031	+	0.374119i
$359$		−	2.81930e34i		−	0.904413i	−0.891913	−	0.452206i	$-0.850637\pi$
$359$		−	2.81930e34i		−	0.904413i	0.891913	−	0.452206i	$-0.149363\pi$
$360$	1.31538e34	−	6.50222e33i	0.406414	−	0.200899i
$361$		−	1.27780e34i		−	0.380292i
$362$	−4.51368e34	+	6.96179e33i	−1.29409	+	0.199598i
$363$	−3.74122e34	−	3.74122e34i	−1.03341	−	1.03341i
$364$	1.19348e34	−	2.29619e34i	0.317649	−	0.611138i
$365$	−1.26131e34	+	1.26131e34i	−0.323495	+	0.323495i
$366$	−5.18801e34	−	3.80150e34i	−1.28235	−	0.939636i
$367$	2.45541e34			0.584968			0.292484	−	0.956270i	$-0.405518\pi$
$367$	2.45541e34			0.584968			0.292484	+	0.956270i	$0.405518\pi$
$368$	2.15710e34	+	3.07240e34i	0.495364	+	0.705558i
$369$	8.50830e34			1.88359
$370$	−9.08949e33	−	6.66029e33i	−0.194007	−	0.142157i
$371$	−6.65609e34	+	6.65609e34i	−1.36985	+	1.36985i
$372$	5.45107e34	+	2.83328e34i	1.08181	+	0.562290i
$373$	5.63594e34	+	5.63594e34i	1.07869	+	1.07869i	0.996627	+	0.0820646i	$0.0261514\pi$
$373$	5.63594e34	+	5.63594e34i	1.07869	+	1.07869i	0.0820646	+	0.996627i	$0.473849\pi$
$374$	−1.52608e34	+	2.35379e33i	−0.281716	+	0.0434512i
$375$		−	5.59321e34i		−	0.995954i
$376$	2.16857e34	+	7.33843e33i	0.372509	+	0.126057i
$377$		−	1.30862e34i		−	0.216873i
$378$	−5.46995e33	−	3.54644e34i	−0.0874669	−	0.567092i
$379$	−8.23792e34	−	8.23792e34i	−1.27113	−	1.27113i	−0.945498	−	0.325627i	$-0.894424\pi$
$379$	−8.23792e34	−	8.23792e34i	−1.27113	−	1.27113i	−0.325627	−	0.945498i	$-0.605576\pi$
$380$	−8.32593e33	−	2.63485e34i	−0.123981	−	0.392354i
$381$	8.41916e34	−	8.41916e34i	1.20999	−	1.20999i
$382$	1.02866e34	−	1.40384e34i	0.142697	−	0.194743i
$383$	−3.19152e34			−0.427380			−0.213690	−	0.976901i	$-0.568548\pi$
$383$	−3.19152e34			−0.427380			−0.213690	+	0.976901i	$0.568548\pi$
$384$	−5.61297e34	+	1.02849e35i	−0.725640	+	1.32962i
$385$	−6.77009e33			−0.0845035
$386$	−3.18797e34	+	4.35072e34i	−0.384225	+	0.524363i
$387$	1.73342e34	−	1.73342e34i	0.201746	−	0.201746i
$388$	9.09089e33	+	2.87693e34i	0.102183	+	0.323371i
$389$	−1.11172e35	−	1.11172e35i	−1.20691	−	1.20691i	−0.972023	−	0.234886i	$-0.924528\pi$
$389$	−1.11172e35	−	1.11172e35i	−1.20691	−	1.20691i	−0.234886	−	0.972023i	$-0.575472\pi$
$390$	−4.12852e33	−	2.67673e34i	−0.0432935	−	0.280693i
$391$			1.29350e35i			1.31033i
$392$	−6.34170e34	−	2.14603e34i	−0.620646	−	0.210026i
$393$			5.05133e33i			0.0477646i
$394$	1.06512e35	−	1.64282e34i	0.973196	−	0.150103i
$395$	4.29140e34	+	4.29140e34i	0.378912	+	0.378912i
$396$	2.52421e34	+	1.31200e34i	0.215397	+	0.111956i
$397$	1.16980e35	−	1.16980e35i	0.964806	−	0.964806i	−0.0345956	−	0.999401i	$-0.511014\pi$
$397$	1.16980e35	−	1.16980e35i	0.964806	−	0.964806i	0.999401	+	0.0345956i	$0.0110143\pi$
$398$	−3.47382e34	−	2.54542e34i	−0.276940	−	0.202926i
$399$	−2.97088e35			−2.28956
$400$	6.76625e34	+	9.63732e34i	0.504125	+	0.718036i
$401$	−1.21213e35			−0.873175			−0.436588	−	0.899662i	$-0.643813\pi$
$401$	−1.21213e35			−0.873175			−0.436588	+	0.899662i	$0.643813\pi$
$402$	−1.25591e35	−	9.20262e34i	−0.874796	−	0.641003i
$403$	4.52362e34	−	4.52362e34i	0.304697	−	0.304697i
$404$	−1.34546e35	+	2.58859e35i	−0.876442	+	1.68622i
$405$	2.43268e34	+	2.43268e34i	0.153265	+	0.153265i
$406$	−8.45257e34	+	1.30370e34i	−0.515095	+	0.0794469i
$407$		−	2.18471e34i		−	0.128786i
$408$	−3.61915e35	+	1.78903e35i	−2.06393	+	1.02025i
$409$		−	1.70745e35i		−	0.942073i	−0.882114	−	0.471036i	$-0.843880\pi$
$409$		−	1.70745e35i		−	0.942073i	0.882114	−	0.471036i	$-0.156120\pi$
$410$	−1.45523e34	−	9.43500e34i	−0.0776872	−	0.503686i
$411$	1.42489e35	+	1.42489e35i	0.736065	+	0.736065i
$412$	9.30252e34	−	2.93952e34i	0.465038	−	0.146948i
$413$	3.25761e34	−	3.25761e34i	0.157606	−	0.157606i
$414$	1.40853e35	−	1.92226e35i	0.659570	−	0.900136i
$415$	−9.91532e34			−0.449425
$416$	8.45113e34	+	8.80035e34i	0.370813	+	0.386136i
$417$	2.81707e35			1.19663
$418$	3.16651e34	−	4.32144e34i	0.130227	−	0.177725i
$419$	2.29869e35	−	2.29869e35i	0.915360	−	0.915360i	−0.0813279	−	0.996687i	$-0.525916\pi$
$419$	2.29869e35	−	2.29869e35i	0.915360	−	0.915360i	0.996687	+	0.0813279i	$0.0259161\pi$
$420$	−1.68781e35	+	5.33335e34i	−0.650816	+	0.205653i
$421$	−5.69316e34	−	5.69316e34i	−0.212591	−	0.212591i	0.592776	−	0.805367i	$-0.298032\pi$
$421$	−5.69316e34	−	5.69316e34i	−0.212591	−	0.212591i	−0.805367	+	0.592776i	$0.798032\pi$
$422$	2.29185e34	+	1.48592e35i	0.0828836	+	0.537376i
$423$		−	1.45330e35i		−	0.509051i
$424$	−1.96669e35	−	3.97856e35i	−0.667262	−	1.34985i
$425$			4.05737e35i			1.33350i
$426$	4.67997e35	−	7.21828e34i	1.49009	−	0.229828i
$427$	3.09516e35	+	3.09516e35i	0.954786	+	0.954786i
$428$	−2.61314e35	+	5.02753e35i	−0.781037	+	1.50267i
$429$	3.71300e34	−	3.71300e34i	0.107535	−	0.107535i
$430$	−2.21869e34	−	1.62574e34i	−0.0622692	−	0.0456275i
$431$	4.46284e35			1.21386			0.606929	−	0.794756i	$-0.292401\pi$
$431$	4.46284e35			1.21386			0.606929	+	0.794756i	$0.292401\pi$
$432$	1.66652e35	+	2.91685e34i	0.439318	+	0.0768925i
$433$	2.56632e35			0.655729			0.327864	−	0.944725i	$-0.393671\pi$
$433$	2.56632e35			0.655729			0.327864	+	0.944725i	$0.393671\pi$
$434$	−3.37254e35	−	2.47121e35i	−0.835306	−	0.612067i
$435$	−6.32925e34	+	6.32925e34i	−0.151966	+	0.151966i
$436$	5.13407e35	+	2.66851e35i	1.19507	+	0.621157i
$437$	−3.17338e35	−	3.17338e35i	−0.716180	−	0.716180i
$438$	−8.93628e35	+	1.37831e35i	−1.95549	+	0.301610i
$439$			8.77578e34i			0.186215i	0.995656	+	0.0931075i	$0.0296800\pi$
$439$			8.77578e34i			0.186215i	−0.995656	+	0.0931075i	$0.970320\pi$
$440$	1.02316e34	−	3.02354e34i	0.0210540	−	0.0622163i
$441$			4.25000e35i			0.848140i
$442$	6.40847e34	+	4.15494e35i	0.124038	+	0.804199i
$443$	−2.09399e35	−	2.09399e35i	−0.393120	−	0.393120i	0.482678	−	0.875798i	$-0.339664\pi$
$443$	−2.09399e35	−	2.09399e35i	−0.393120	−	0.393120i	−0.875798	+	0.482678i	$0.839664\pi$
$444$	−1.72108e35	−	5.44658e35i	−0.313422	−	0.991867i
$445$	2.50861e35	−	2.50861e35i	0.443172	−	0.443172i
$446$	3.19667e35	−	4.36260e35i	0.547870	−	0.747695i
$447$	−5.80173e35			−0.964731
$448$	4.84234e35	−	6.33544e35i	0.781272	−	1.02217i
$449$	1.19419e35			0.186960			0.0934801	−	0.995621i	$-0.470201\pi$
$449$	1.19419e35			0.186960			0.0934801	+	0.995621i	$0.470201\pi$
$450$	4.41819e35	−	6.02963e35i	0.671236	−	0.916055i
$451$	1.30877e35	−	1.30877e35i	0.192965	−	0.192965i
$452$	3.57603e35	+	1.13168e36i	0.511720	+	1.61941i
$453$	−2.27663e35	−	2.27663e35i	−0.316204	−	0.316204i
$454$	1.36492e35	+	8.84944e35i	0.184014	+	1.19306i
$455$			1.84324e35i			0.241228i
$456$	4.48990e35	−	1.32680e36i	0.570441	−	1.68570i
$457$		−	2.34153e35i		−	0.288822i	−0.989518	−	0.144411i	$-0.953871\pi$
$457$		−	2.34153e35i		−	0.288822i	0.989518	−	0.144411i	$-0.0461288\pi$
$458$	1.28963e36	−	1.98909e35i	1.54447	−	0.238216i
$459$	4.12208e35	+	4.12208e35i	0.479341	+	0.479341i
$460$	−2.37254e35	−	1.23316e35i	−0.267906	−	0.139248i
$461$	−7.12299e35	+	7.12299e35i	−0.781088	+	0.781088i	−0.980014	−	0.198926i	$-0.936255\pi$
$461$	−7.12299e35	+	7.12299e35i	−0.781088	+	0.781088i	0.198926	+	0.980014i	$0.436255\pi$
$462$	−2.76819e35	−	2.02838e35i	−0.294801	−	0.216014i
$463$	−1.61150e36			−1.66682			−0.833408	−	0.552658i	$-0.813614\pi$
$463$	−1.61150e36			−1.66682			−0.833408	+	0.552658i	$0.813614\pi$
$464$	6.95201e34	−	3.97196e35i	0.0698421	−	0.399036i
$465$	−4.37578e35			−0.427012
$466$	2.10557e34	+	1.54285e34i	0.0199600	+	0.0146256i
$467$	7.61271e35	−	7.61271e35i	0.701070	−	0.701070i	−0.263570	−	0.964640i	$-0.584900\pi$
$467$	7.61271e35	−	7.61271e35i	0.701070	−	0.701070i	0.964640	+	0.263570i	$0.0849001\pi$
$468$	3.57207e35	−	6.87245e35i	0.319595	−	0.614883i
$469$	7.49272e35	+	7.49272e35i	0.651338	+	0.651338i
$470$	−1.61159e35	+	2.48568e34i	−0.136124	+	0.0209954i
$471$			2.05742e36i			1.68866i
$472$	9.62534e34	+	1.94718e35i	0.0767713	+	0.155306i
$473$		−	5.33276e34i		−	0.0413359i
$474$	4.68948e35	+	3.04043e36i	0.353279	+	2.29048i
$475$	−9.95405e35	−	9.95405e35i	−0.728847	−	0.728847i
$476$	2.61989e36	−	8.27865e35i	1.86462	−	0.589204i
$477$	−1.99215e36	+	1.99215e36i	−1.37824	+	1.37824i
$478$	1.13672e36	−	1.55131e36i	0.764498	−	1.04333i
$479$	2.26478e35			0.148080			0.0740401	−	0.997255i	$-0.476411\pi$
$479$	2.26478e35			0.148080			0.0740401	+	0.997255i	$0.476411\pi$
$480$	1.68904e34	−	8.34382e35i	0.0107370	−	0.530406i
$481$	−5.94814e35			−0.367640
$482$	−9.83161e35	+	1.34175e36i	−0.590867	+	0.806374i
$483$	−2.03277e36	+	2.03277e36i	−1.18796	+	1.18796i
$484$	−1.61881e36	+	5.11532e35i	−0.919991	+	0.290710i
$485$	−1.51959e35	−	1.51959e35i	−0.0839871	−	0.0839871i
$486$	3.92310e35	+	2.54354e36i	0.210882	+	1.36725i
$487$		−	3.16599e36i		−	1.65527i	−0.561269	−	0.827633i	$-0.689687\pi$
$487$		−	3.16599e36i		−	1.65527i	0.561269	−	0.827633i	$-0.310313\pi$
$488$	−1.85007e36	+	9.14532e35i	−0.940852	+	0.465084i
$489$			2.43217e36i			1.20316i
$490$	4.71289e35	−	7.26905e34i	0.226799	−	0.0349809i
$491$	5.47627e34	+	5.47627e34i	0.0256380	+	0.0256380i	0.719810	−	0.694172i	$-0.244229\pi$
$491$	5.47627e34	+	5.47627e34i	0.0256380	+	0.0256380i	−0.694172	+	0.719810i	$0.744229\pi$
$492$	2.23178e36	−	4.29382e36i	1.01654	−	1.95576i
$493$	9.82453e35	−	9.82453e35i	0.435390	−	0.435390i
$494$	−1.17656e36	−	8.62120e35i	−0.507342	−	0.371753i
$495$	−2.02628e35			−0.0850214
$496$	1.61334e36	−	1.13271e36i	0.658754	−	0.462504i
$497$	−3.22270e36			−1.28059
$498$	−4.05422e36	−	2.97071e36i	−1.56787	−	1.14885i
$499$	2.43774e36	−	2.43774e36i	0.917549	−	0.917549i	−0.0793017	−	0.996851i	$-0.525269\pi$
$499$	2.43774e36	−	2.43774e36i	0.917549	−	0.917549i	0.996851	+	0.0793017i	$0.0252691\pi$
$500$	−1.59246e36	−	8.27704e35i	−0.583408	−	0.303236i
$501$	−8.88917e35	−	8.88917e35i	−0.316995	−	0.316995i
$502$	−2.62703e36	+	4.05187e35i	−0.911939	+	0.140655i
$503$		−	1.87147e36i		−	0.632434i	−0.948687	−	0.316217i	$-0.897587\pi$
$503$		−	1.87147e36i		−	0.632434i	0.948687	−	0.316217i	$-0.102413\pi$
$504$	−4.79489e36	−	1.62259e36i	−1.57749	−	0.533822i
$505$		−	2.07796e36i		−	0.665584i
$506$	−7.90235e34	−	5.12350e35i	−0.0246448	−	0.159784i
$507$	2.51630e36	+	2.51630e36i	0.764107	+	0.764107i
$508$	−1.15114e36	−	3.64294e36i	−0.340383	−	1.07719i
$509$	3.22726e34	−	3.22726e34i	0.00929274	−	0.00929274i	−0.702445	−	0.711738i	$-0.747908\pi$
$509$	3.22726e34	−	3.22726e34i	0.00929274	−	0.00929274i	0.711738	+	0.702445i	$0.247908\pi$
$510$	1.69962e36	−	2.31952e36i	0.476600	−	0.650431i
$511$	6.15366e36			1.68055
$512$	2.09760e36	+	3.12007e36i	0.557927	+	0.829890i
$513$	−2.02256e36			−0.523983
$514$	−3.56049e36	+	4.85911e36i	−0.898478	+	1.22618i
$515$	−4.91357e35	+	4.91357e35i	−0.120781	+	0.120781i
$516$	−4.20105e35	−	1.32948e36i	−0.100597	−	0.318354i
$517$	−2.23550e35	−	2.23550e35i	−0.0521498	−	0.0521498i
$518$	5.92579e35	+	3.84199e36i	0.134677	+	0.873182i
$519$			1.77106e35i			0.0392170i
$520$	−8.23193e35	−	2.78568e35i	−0.177606	−	0.0601017i
$521$		−	6.33916e36i		−	1.33267i	−0.745653	−	0.666335i	$-0.767862\pi$
$521$		−	6.33916e36i		−	1.33267i	0.745653	−	0.666335i	$-0.232138\pi$
$522$	−2.52984e36	+	3.90196e35i	−0.518252	+	0.0799338i
$523$	5.50349e36	+	5.50349e36i	1.09866	+	1.09866i	0.994567	+	0.104098i	$0.0331955\pi$
$523$	5.50349e36	+	5.50349e36i	1.09866	+	1.09866i	0.104098	+	0.994567i	$0.466805\pi$
$524$	1.43818e35	+	7.47515e34i	0.0279795	+	0.0145428i
$525$	−6.37628e36	+	6.37628e36i	−1.20897	+	1.20897i
$526$	8.08439e36	+	5.92380e36i	1.49396	+	1.09469i
$527$	6.79227e36			1.22341
$528$	1.32423e36	−	9.29729e35i	0.232491	−	0.163229i
$529$	1.50056e36			0.256803
$530$	2.54986e36	+	1.86840e36i	0.425396	+	0.311707i
$531$	9.74997e35	−	9.74997e35i	0.158572	−	0.158572i
$532$	−4.39642e36	+	8.45847e36i	−0.697096	+	1.34117i
$533$	−3.56327e36	−	3.56327e36i	−0.550847	−	0.550847i
$534$	1.77733e37	−	2.74131e36i	2.67893	−	0.413191i
$535$		−	4.03578e36i		−	0.593132i
$536$	−4.47864e36	+	2.21389e36i	−0.641832	+	0.317272i
$537$		−	4.10304e36i		−	0.573394i
$538$	1.34901e36	+	8.74629e36i	0.183846	+	1.19196i
$539$	6.53744e35	+	6.53744e35i	0.0868880	+	0.0868880i
$540$	−1.14905e36	+	3.63091e35i	−0.148944	+	0.0470652i
$541$	−4.05454e36	+	4.05454e36i	−0.512600	+	0.512600i	−0.915322	−	0.402722i	$-0.868064\pi$
$541$	−4.05454e36	+	4.05454e36i	−0.512600	+	0.512600i	0.402722	+	0.915322i	$0.368064\pi$
$542$	4.77130e36	−	6.51153e36i	0.588364	−	0.802958i
$543$	1.64895e37			1.98339
$544$	−2.62180e35	+	1.29516e37i	−0.0307620	+	1.51964i
$545$	−4.12130e36			−0.471717
$546$	−5.52249e36	+	7.53671e36i	−0.616644	+	0.841552i
$547$	−4.78821e36	+	4.78821e36i	−0.521608	+	0.521608i	−0.918057	−	0.396449i	$-0.870242\pi$
$547$	−4.78821e36	+	4.78821e36i	−0.521608	+	0.521608i	0.396449	+	0.918057i	$0.370242\pi$
$548$	6.16543e36	−	1.94823e36i	0.655278	−	0.207063i
$549$	9.26374e36	+	9.26374e36i	0.960638	+	0.960638i
$550$	−2.47876e35	−	1.60711e36i	−0.0250806	−	0.162610i
$551$			4.82055e36i			0.475938i
$552$	−6.00628e36	−	1.21505e37i	−0.578666	−	1.17063i
$553$		−	2.09369e37i		−	1.96844i
$554$	6.62398e36	−	1.02167e36i	0.607767	−	0.0937405i
$555$	2.87687e36	+	2.87687e36i	0.257611	+	0.257611i
$556$	4.16880e36	−	8.02053e36i	0.364335	−	0.700961i
$557$	−1.20199e36	+	1.20199e36i	−0.102531	+	0.102531i	−0.756511	−	0.653980i	$-0.773098\pi$
$557$	−1.20199e36	+	1.20199e36i	−0.102531	+	0.102531i	0.653980	+	0.756511i	$0.273098\pi$
$558$	−1.00939e37	−	7.39629e36i	−0.840425	−	0.615818i
$559$	−1.45191e36			−0.117999
$560$	−9.79215e35	+	5.59465e36i	−0.0776854	+	0.443848i
$561$	5.57511e36			0.431772
$562$	−1.02805e37	−	7.53302e36i	−0.777276	−	0.569546i
$563$	1.30691e37	−	1.30691e37i	0.964676	−	0.964676i	−0.0347214	−	0.999397i	$-0.511054\pi$
$563$	1.30691e37	−	1.30691e37i	0.964676	−	0.964676i	0.999397	+	0.0347214i	$0.0110544\pi$
$564$	−7.33428e36	−	3.81211e36i	−0.528554	−	0.274724i
$565$	−5.97752e36	−	5.97752e36i	−0.420598	−	0.420598i
$566$	−1.72822e37	+	2.66556e36i	−1.18734	+	0.183133i
$567$		−	1.18686e37i		−	0.796208i
$568$	4.87047e36	−	1.43926e37i	0.319057	−	0.942841i
$569$		−	1.37520e37i		−	0.879734i	−0.898063	−	0.439867i	$-0.855026\pi$
$569$		−	1.37520e37i		−	0.879734i	0.898063	−	0.439867i	$-0.144974\pi$
$570$	1.52082e36	+	9.86025e36i	0.0950096	+	0.615995i
$571$	−1.12024e37	−	1.12024e37i	−0.683475	−	0.683475i	0.277306	−	0.960782i	$-0.410558\pi$
$571$	−1.12024e37	−	1.12024e37i	−0.683475	−	0.683475i	−0.960782	+	0.277306i	$0.910558\pi$
$572$	−5.07673e35	−	1.60660e36i	−0.0302509	−	0.0957329i
$573$	−4.44322e36	+	4.44322e36i	−0.258589	+	0.258589i
$574$	−1.94658e37	+	2.65656e37i	−1.10653	+	1.51011i
$575$	−1.36218e37			−0.756341
$576$	1.44930e37	−	1.89618e37i	0.786060	−	1.02844i
$577$	−2.78524e36			−0.147567			−0.0737835	−	0.997274i	$-0.523507\pi$
$577$	−2.78524e36			−0.147567			−0.0737835	+	0.997274i	$0.523507\pi$
$578$	−1.49625e37	+	2.04198e37i	−0.774426	+	1.05688i
$579$	1.37702e37	−	1.37702e37i	0.696274	−	0.696274i
$580$	8.65389e35	+	2.73864e36i	0.0427497	+	0.135287i
$581$	2.41874e37	+	2.41874e37i	1.16738	+	1.16738i
$582$	−1.66055e36	−	1.07662e37i	−0.0783053	−	0.507693i
$583$			6.12876e36i			0.282388i
$584$	−9.30003e36	+	2.74824e37i	−0.418708	+	1.23732i
$585$			5.51677e36i			0.242706i
$586$	−5.74973e36	+	8.86825e35i	−0.247189	+	0.0381259i
$587$	8.90381e36	+	8.90381e36i	0.374077	+	0.374077i	0.868960	−	0.494883i	$-0.164789\pi$
$587$	8.90381e36	+	8.90381e36i	0.374077	+	0.374077i	−0.494883	+	0.868960i	$0.664789\pi$
$588$	2.14482e37	+	1.11480e37i	0.880635	+	0.457724i
$589$	−1.66636e37	+	1.66636e37i	−0.668673	+	0.668673i
$590$	−1.24795e36	−	9.14431e35i	−0.0489435	−	0.0358632i
$591$	−3.89112e37			−1.49157
$592$	−1.80540e37	−	3.15993e36i	−0.676441	−	0.118395i
$593$	3.15514e37			1.15553			0.577764	−	0.816204i	$-0.303925\pi$
$593$	3.15514e37			1.15553			0.577764	+	0.816204i	$0.303925\pi$
$594$	−1.88457e36	−	1.38091e36i	−0.0674674	−	0.0494365i
$595$	−1.38382e37	+	1.38382e37i	−0.484285	+	0.484285i
$596$	−8.58562e36	+	1.65182e37i	−0.293729	+	0.565118i
$597$	1.09948e37	+	1.09948e37i	0.367734	+	0.367734i
$598$	−1.39493e37	+	2.15151e36i	−0.456128	+	0.0703521i
$599$		−	4.85861e37i		−	1.55328i	−0.629945	−	0.776640i	$-0.716923\pi$
$599$		−	4.85861e37i		−	1.55328i	0.629945	−	0.776640i	$-0.283077\pi$
$600$	−1.88401e37	−	3.81131e37i	−0.588900	−	1.19133i
$601$			2.24167e37i			0.685119i	0.939496	+	0.342559i	$0.111294\pi$
$601$			2.24167e37i			0.685119i	−0.939496	+	0.342559i	$0.888706\pi$
$602$	1.44645e36	+	9.37808e36i	0.0432266	+	0.280260i
$603$	2.24256e37	+	2.24256e37i	0.655330	+	0.655330i
$604$	−9.85089e36	+	3.11280e36i	−0.281499	+	0.0889515i
$605$	8.55052e36	−	8.55052e36i	0.238943	−	0.238943i
$606$	6.22574e37	−	8.49645e37i	1.70142	−	2.32197i
$607$	−5.58356e37			−1.49233			−0.746163	−	0.665764i	$-0.768106\pi$
$607$	−5.58356e37			−1.49233			−0.746163	+	0.665764i	$0.768106\pi$
$608$	−3.11314e37	−	3.24178e37i	−0.813767	−	0.847394i
$609$	3.08791e37			0.789461
$610$	8.68828e36	−	1.18572e37i	0.217261	−	0.296502i
$611$	−6.08642e36	+	6.08642e36i	−0.148869	+	0.148869i
$612$	7.84128e37	−	2.47778e37i	1.87604	−	0.592815i
$613$	−4.54117e37	−	4.54117e37i	−1.06280	−	1.06280i	−0.997891	−	0.0649094i	$-0.979324\pi$
$613$	−4.54117e37	−	4.54117e37i	−1.06280	−	1.06280i	−0.0649094	−	0.997891i	$-0.520676\pi$
$614$	1.36767e36	+	8.86727e36i	0.0313117	+	0.203010i
$615$			3.44681e37i			0.771975i
$616$	−9.87150e36	+	4.87970e36i	−0.216294	+	0.106919i
$617$			7.21982e37i			1.54766i	0.633391	+	0.773832i	$0.281662\pi$
$617$			7.21982e37i			1.54766i	−0.633391	+	0.773832i	$0.718338\pi$
$618$	−3.48123e37	+	5.36936e36i	−0.730110	+	0.112610i
$619$	2.37150e37	+	2.37150e37i	0.486631	+	0.486631i	0.907241	−	0.420611i	$-0.138184\pi$
$619$	2.37150e37	+	2.37150e37i	0.486631	+	0.486631i	−0.420611	+	0.907241i	$0.638184\pi$
$620$	−6.47544e36	+	1.24584e37i	−0.130011	+	0.250134i
$621$	−1.38390e37	+	1.38390e37i	−0.271874	+	0.271874i
$622$	3.22303e37	+	2.36166e37i	0.619575	+	0.453991i
$623$	−1.22390e38			−2.30227
$624$	−2.53130e37	−	3.60538e37i	−0.465962	−	0.663680i
$625$	−3.59187e37			−0.647054
$626$	5.84274e37	+	4.28124e37i	1.03006	+	0.754773i
$627$	−1.36776e37	+	1.36776e37i	−0.235992	+	0.235992i
$628$	5.85774e37	+	3.04465e37i	0.989178	+	0.514141i
$629$	−4.46560e37	−	4.46560e37i	−0.738067	−	0.738067i
$630$	3.56336e37	−	5.49604e36i	0.576451	−	0.0889104i
$631$		−	4.07038e37i		−	0.644524i	−0.946651	−	0.322262i	$-0.895557\pi$
$631$		−	4.07038e37i		−	0.644524i	0.946651	−	0.322262i	$-0.104443\pi$
$632$	9.35044e37	+	3.16419e37i	1.44928	+	0.490435i
$633$		−	5.42840e37i		−	0.823611i
$634$	−1.03441e37	−	6.70660e37i	−0.153634	−	0.996088i
$635$	1.92419e37	+	1.92419e37i	0.279771	+	0.279771i
$636$	4.82811e37	+	1.52792e38i	0.687237	+	2.17485i
$637$	1.77989e37	−	1.77989e37i	0.248034	−	0.248034i
$638$	−3.29124e36	+	4.49166e36i	−0.0449036	+	0.0612813i
$639$	−9.64548e37			−1.28843
$640$	−2.35059e37	−	1.28284e37i	−0.307431	−	0.167781i
$641$	6.68066e37			0.855532			0.427766	−	0.903890i	$-0.359301\pi$
$641$	6.68066e37			0.855532			0.427766	+	0.903890i	$0.359301\pi$
$642$	1.20915e38	−	1.65017e38i	1.51621	−	2.06921i
$643$	1.78363e37	−	1.78363e37i	0.219006	−	0.219006i	−0.589074	−	0.808079i	$-0.700507\pi$
$643$	1.78363e37	−	1.78363e37i	0.219006	−	0.219006i	0.808079	+	0.589074i	$0.200507\pi$
$644$	2.77938e37	+	8.79573e37i	0.334187	+	1.05758i
$645$	7.02227e36	+	7.02227e36i	0.0826840	+	0.0826840i
$646$	−2.36068e37	−	1.53055e38i	−0.272207	−	1.76485i
$647$			1.21791e38i			1.37533i	0.726029	+	0.687664i	$0.241364\pi$
$647$			1.21791e38i			1.37533i	−0.726029	+	0.687664i	$0.758636\pi$
$648$	5.30052e37	+	1.79369e37i	0.586214	+	0.198375i
$649$		−	2.99953e36i		−	0.0324900i
$650$	−4.37553e37	+	6.74871e36i	−0.464195	+	0.0715963i
$651$	1.06742e38	+	1.06742e38i	1.10916	+	1.10916i
$652$	6.92468e37	+	3.59921e37i	0.704786	+	0.366324i
$653$	1.49648e36	−	1.49648e36i	0.0149192	−	0.0149192i	−0.699608	−	0.714527i	$-0.746642\pi$
$653$	1.49648e36	−	1.49648e36i	0.0149192	−	0.0149192i	0.714527	+	0.699608i	$0.246642\pi$
$654$	−1.68514e38	−	1.23478e38i	−1.64564	−	1.20584i
$655$	−1.15448e36			−0.0110440
$656$	−8.92237e37	−	1.27083e38i	−0.836139	−	1.19093i
$657$	1.84178e38			1.69085
$658$	4.53766e37	+	3.32495e37i	0.408115	+	0.299045i
$659$	1.78430e37	−	1.78430e37i	0.157222	−	0.157222i	−0.624112	−	0.781335i	$-0.714539\pi$
$659$	1.78430e37	−	1.78430e37i	0.157222	−	0.157222i	0.781335	+	0.624112i	$0.214539\pi$
$660$	−5.31505e36	+	1.02259e37i	−0.0458843	+	0.0882788i
$661$	8.73764e37	+	8.73764e37i	0.739051	+	0.739051i	0.972394	−	0.233343i	$-0.0749666\pi$
$661$	8.73764e37	+	8.73764e37i	0.739051	+	0.739051i	−0.233343	+	0.972394i	$0.574967\pi$
$662$	1.44172e38	−	2.22368e37i	1.19481	−	0.184285i
$663$		−	1.51789e38i		−	1.23256i
$664$	−1.44576e38	+	7.14669e37i	−1.15034	+	0.568638i
$665$		−	6.78992e37i		−	0.529386i
$666$	1.77358e37	+	1.14990e38i	0.135503	+	0.878533i
$667$	3.29838e37	+	3.29838e37i	0.246946	+	0.246946i
$668$	−3.84631e37	+	1.21540e37i	−0.282203	+	0.0891740i
$669$	−1.38078e38	+	1.38078e38i	−0.992825	+	0.992825i
$670$	2.10325e37	−	2.87037e37i	0.148211	−	0.202268i
$671$	2.84994e37			0.196826
$672$	−2.07659e38	+	1.99419e38i	−1.40561	+	1.34983i
$673$	2.77590e37			0.184162			0.0920810	−	0.995752i	$-0.470648\pi$
$673$	2.77590e37			0.184162			0.0920810	+	0.995752i	$0.470648\pi$
$674$	−1.46528e38	+	1.99971e38i	−0.952819	+	1.30034i
$675$	−4.34093e37	+	4.34093e37i	−0.276683	+	0.276683i
$676$	1.08879e38	−	3.44050e37i	0.680243	−	0.214952i
$677$	7.45978e37	+	7.45978e37i	0.456855	+	0.456855i	0.897622	−	0.440766i	$-0.145293\pi$
$677$	7.45978e37	+	7.45978e37i	0.456855	+	0.456855i	−0.440766	+	0.897622i	$0.645293\pi$
$678$	−6.53201e37	−	4.23503e38i	−0.392144	−	2.54247i
$679$			7.41375e37i			0.436311i
$680$	−4.08880e37	−	8.27154e37i	−0.235899	−	0.477217i
$681$		−	3.23289e38i		−	1.82854i
$682$	−2.69039e37	+	4.14958e36i	−0.149185	+	0.0230099i
$683$	−4.36983e36	−	4.36983e36i	−0.0237566	−	0.0237566i	0.695129	−	0.718885i	$-0.255347\pi$
$683$	−4.36983e36	−	4.36983e36i	−0.0237566	−	0.0237566i	−0.718885	+	0.695129i	$0.755347\pi$
$684$	−1.31584e38	+	2.53160e38i	−0.701368	+	1.34939i
$685$	−3.25656e37	+	3.25656e37i	−0.170191	+	0.170191i
$686$	6.98267e37	+	5.11652e37i	0.357805	+	0.262180i
$687$	−4.71129e38			−2.36714
$688$	−4.40687e37	−	7.71322e36i	−0.217113	−	0.0380007i
$689$	1.66862e38			0.806119
$690$	7.78730e37	+	5.70611e37i	0.368913	+	0.270319i
$691$	2.38456e38	−	2.38456e38i	1.10778	−	1.10778i	0.114339	−	0.993442i	$-0.463525\pi$
$691$	2.38456e38	−	2.38456e38i	1.10778	−	1.10778i	0.993442	−	0.114339i	$-0.0364750\pi$
$692$	5.04243e36	+	2.62088e36i	0.0229725	+	0.0119403i
$693$	4.94288e37	+	4.94288e37i	0.220842	+	0.220842i
$694$	3.23088e37	−	4.98323e36i	0.141569	−	0.0218352i
$695$			6.43837e37i			0.276682i
$696$	−4.66675e37	+	1.37907e38i	−0.196694	+	0.581246i
$697$		−	5.35029e38i		−	2.21174i
$698$	−3.11140e37	−	2.01728e38i	−0.126156	−	0.817933i
$699$	−6.66423e36	−	6.66423e36i	−0.0265038	−	0.0265038i
$700$	8.71819e37	+	2.75899e38i	0.340097	+	1.07628i
$701$	1.52465e37	−	1.52465e37i	0.0583415	−	0.0583415i	−0.677334	−	0.735676i	$-0.736865\pi$
$701$	1.52465e37	−	1.52465e37i	0.0583415	−	0.0583415i	0.735676	+	0.677334i	$0.236865\pi$
$702$	−3.75968e37	+	5.13095e37i	−0.141124	+	0.192596i
$703$	2.19111e38			0.806803
$704$	−6.87403e36	−	5.14610e37i	−0.0248302	−	0.185886i
$705$	5.88749e37			0.208630
$706$	−2.57326e38	+	3.51181e38i	−0.894583	+	1.22086i
$707$	−5.06896e38	+	5.06896e38i	−1.72885	+	1.72885i
$708$	−2.36297e37	−	7.47793e37i	−0.0790695	−	0.250226i
$709$	1.66554e38	+	1.66554e38i	0.546803	+	0.546803i	0.925515	−	0.378712i	$-0.123633\pi$
$709$	1.66554e38	+	1.66554e38i	0.546803	+	0.546803i	−0.378712	+	0.925515i	$0.623633\pi$
$710$	1.64973e37	+	1.06960e38i	0.0531404	+	0.344536i
$711$		−	6.26636e38i		−	1.98050i
$712$	1.84968e38	−	5.46595e38i	0.573609	−	1.69506i
$713$			2.28036e38i			0.693897i
$714$	−9.80427e38	+	1.51219e38i	−2.92745	+	0.451522i
$715$	8.48602e36	+	8.48602e36i	0.0248641	+	0.0248641i
$716$	−1.16819e38	−	6.07183e37i	−0.335882	−	0.174580i
$717$	−4.90998e38	+	4.90998e38i	−1.38539	+	1.38539i
$718$	2.63464e38	+	1.93052e38i	0.729527	+	0.534558i
$719$	−4.39767e38			−1.19504			−0.597520	−	0.801854i	$-0.703847\pi$
$719$	−4.39767e38			−1.19504			−0.597520	+	0.801854i	$0.703847\pi$
$720$	−2.93077e37	+	1.67447e38i	−0.0781615	+	0.446568i
$721$	2.39723e38			0.627456
$722$	1.19411e38	+	8.74979e37i	0.306755	+	0.224774i
$723$	4.24670e38	−	4.24670e38i	1.07074	−	1.07074i
$724$	2.44017e38	−	4.69475e38i	0.603879	−	1.16183i
$725$	1.03461e38	+	1.03461e38i	0.251313	+	0.251313i
$726$	6.05798e38	−	9.34368e37i	1.44439	−	0.222779i
$727$		−	7.21887e38i		−	1.68949i	−0.535173	−	0.844743i	$-0.679754\pi$
$727$		−	7.21887e38i		−	1.68949i	0.535173	−	0.844743i	$-0.320246\pi$
$728$	1.32855e38	+	2.68763e38i	0.305215	+	0.617442i
$729$		−	6.54788e38i		−	1.47666i
$730$	−3.15011e37	−	2.04238e38i	−0.0697377	−	0.452145i
$731$	−1.09003e38	−	1.09003e38i	−0.236893	−	0.236893i
$732$	7.10500e38	−	2.24513e38i	1.51588	−	0.479006i
$733$	3.32283e38	−	3.32283e38i	0.695992	−	0.695992i	−0.267551	−	0.963544i	$-0.586214\pi$
$733$	3.32283e38	−	3.32283e38i	0.695992	−	0.695992i	0.963544	+	0.267551i	$0.0862144\pi$
$734$	−1.68135e38	+	2.29458e38i	−0.345749	+	0.471853i
$735$	−1.72172e38			−0.347603
$736$	−4.34824e38	−	8.80215e36i	−0.861912	−	0.0174477i
$737$	6.89910e37			0.134271
$738$	−5.82607e38	+	7.95102e38i	−1.11331	+	1.51936i
$739$	−3.95697e38	+	3.95697e38i	−0.742443	+	0.742443i	−0.973047	−	0.230605i	$-0.925930\pi$
$739$	−3.95697e38	+	3.95697e38i	−0.742443	+	0.742443i	0.230605	+	0.973047i	$0.425930\pi$
$740$	1.24481e38	−	3.93350e37i	0.229337	−	0.0724688i
$741$	3.72387e38	+	3.72387e38i	0.673673	+	0.673673i
$742$	−1.66236e38	−	1.07779e39i	−0.295305	−	1.91461i

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)

\(f(q)\)	\(=\)	\(q+(-6847.52 + 9345.01i) q^{2} +(2.95774e6 - 2.95774e6i) q^{3} +(-4.04408e7 - 1.27980e8i) q^{4} +(6.75988e8 + 6.75988e8i) q^{5} +(7.38694e9 + 4.78933e10i) q^{6} -3.29800e11i q^{7} +(1.47290e12 + 4.98428e11i) q^{8} -9.87086e12i q^{9} +O(q^{10})\)	\(q+(-6847.52 + 9345.01i) q^{2} +(2.95774e6 - 2.95774e6i) q^{3} +(-4.04408e7 - 1.27980e8i) q^{4} +(6.75988e8 + 6.75988e8i) q^{5} +(7.38694e9 + 4.78933e10i) q^{6} -3.29800e11i q^{7} +(1.47290e12 + 4.98428e11i) q^{8} -9.87086e12i q^{9} +(-1.09460e13 + 1.68828e12i) q^{10} +(-1.51836e13 - 1.51836e13i) q^{11} +(-4.98146e14 - 2.58919e14i) q^{12} +(-4.13391e14 + 4.13391e14i) q^{13} +(3.08199e15 + 2.25831e15i) q^{14} +3.99880e15 q^{15} +(-1.47435e16 + 1.03512e16i) q^{16} -6.20711e16 q^{17} +(9.22433e16 + 6.75909e16i) q^{18} +(1.52280e17 - 1.52280e17i) q^{19} +(5.91757e16 - 1.13851e17i) q^{20} +(-9.75464e17 - 9.75464e17i) q^{21} +(2.45861e17 - 3.79209e16i) q^{22} -2.08390e18i q^{23} +(5.83066e18 - 2.88222e18i) q^{24} -6.53666e18i q^{25} +(-1.03244e18 - 6.69384e18i) q^{26} +(-6.64090e18 - 6.64090e18i) q^{27} +(-4.22079e19 + 1.33374e19i) q^{28} +(-1.58279e19 + 1.58279e19i) q^{29} +(-2.73818e19 + 3.73688e19i) q^{30} -1.09427e20 q^{31} +(4.22387e18 - 2.08658e20i) q^{32} -8.98182e19 q^{33} +(4.25033e20 - 5.80055e20i) q^{34} +(2.22941e20 - 2.22941e20i) q^{35} +(-1.26328e21 + 3.99185e20i) q^{36} +(7.19433e20 + 7.19433e20i) q^{37} +(3.80320e20 + 2.46581e21i) q^{38} +2.44540e21i q^{39} +(6.58729e20 + 1.33259e21i) q^{40} +8.61962e21i q^{41} +(1.57952e22 - 2.43622e21i) q^{42} +(1.75610e21 + 1.75610e21i) q^{43} +(-1.32916e21 + 2.55723e21i) q^{44} +(6.67259e21 - 6.67259e21i) q^{45} +(1.94741e22 + 1.42696e22i) q^{46} +1.47232e22 q^{47} +(-1.29911e22 + 7.42237e22i) q^{48} -4.30560e22 q^{49} +(6.10852e22 + 4.47599e22i) q^{50} +(-1.83590e23 + 1.83590e23i) q^{51} +(6.96237e22 + 3.61880e22i) q^{52} +(-2.01822e23 - 2.01822e23i) q^{53} +(1.07533e23 - 1.65856e22i) q^{54} -2.05278e22i q^{55} +(1.64382e23 - 4.85762e23i) q^{56} -9.00812e23i q^{57} +(-3.95301e22 - 2.56293e23i) q^{58} +(9.87753e22 + 9.87753e22i) q^{59} +(-1.61714e23 - 5.11767e23i) q^{60} +(-9.38493e23 + 9.38493e23i) q^{61} +(7.49306e23 - 1.02260e24i) q^{62} -3.25541e24 q^{63} +(1.92099e24 + 1.46826e24i) q^{64} -5.58894e23 q^{65} +(6.15032e23 - 8.39352e23i) q^{66} +(-2.27190e24 + 2.27190e24i) q^{67} +(2.51020e24 + 7.94387e24i) q^{68} +(-6.16365e24 - 6.16365e24i) q^{69} +(5.56795e23 + 3.60998e24i) q^{70} -9.77167e24i q^{71} +(4.91991e24 - 1.45387e25i) q^{72} +1.86587e25i q^{73} +(-1.16494e25 + 1.79678e24i) q^{74} +(-1.93337e25 - 1.93337e25i) q^{75} +(-2.56472e25 - 1.33306e25i) q^{76} +(-5.00755e24 + 5.00755e24i) q^{77} +(-2.28523e25 - 1.67449e25i) q^{78} +6.34834e25 q^{79} +(-1.69637e25 - 2.96911e24i) q^{80} +3.59871e25 q^{81} +(-8.05504e25 - 5.90230e25i) q^{82} +(-7.33394e25 + 7.33394e25i) q^{83} +(-8.53916e25 + 1.64289e26i) q^{84} +(-4.19593e25 - 4.19593e25i) q^{85} +(-2.84356e25 + 4.38584e24i) q^{86} +9.36295e25i q^{87} +(-1.47959e25 - 2.99317e25i) q^{88} -3.71102e26i q^{89} +(1.66647e25 + 1.08046e26i) q^{90} +(1.36336e26 + 1.36336e26i) q^{91} +(-2.66699e26 + 8.42746e25i) q^{92} +(-3.23658e26 + 3.23658e26i) q^{93} +(-1.00817e26 + 1.37588e26i) q^{94} +2.05880e26 q^{95} +(-6.04664e26 - 6.29650e26i) q^{96} -2.24795e26 q^{97} +(2.94827e26 - 4.02359e26i) q^{98} +(-1.49875e26 + 1.49875e26i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more