LMFDB - Embedded newform 16.28.e.a.5.10

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			5.10
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9666.34 - 6385.89i) q^{2} +(-1.23946e6 + 1.23946e6i) q^{3} +(5.26586e7 + 1.23456e8i) q^{4} +(3.17355e9 + 3.17355e9i) q^{5} +(1.98961e10 - 4.06599e9i) q^{6} +1.31495e11i q^{7} +(2.79363e11 - 1.52964e12i) q^{8} +4.55307e12i q^{9} +O(q^{10})$	\(q+(-9666.34 - 6385.89i) q^{2} +(-1.23946e6 + 1.23946e6i) q^{3} +(5.26586e7 + 1.23456e8i) q^{4} +(3.17355e9 + 3.17355e9i) q^{5} +(1.98961e10 - 4.06599e9i) q^{6} +1.31495e11i q^{7} +(2.79363e11 - 1.52964e12i) q^{8} +4.55307e12i q^{9} +(-1.04107e13 - 5.09425e13i) q^{10} +(5.98696e13 + 5.98696e13i) q^{11} +(-2.18288e14 - 8.77512e13i) q^{12} +(-1.10551e15 + 1.10551e15i) q^{13} +(8.39711e14 - 1.27107e15i) q^{14} -7.86698e15 q^{15} +(-1.24686e16 + 1.30021e16i) q^{16} -4.51231e16 q^{17} +(2.90754e16 - 4.40115e16i) q^{18} +(-1.81383e17 + 1.81383e17i) q^{19} +(-2.24680e17 + 5.58909e17i) q^{20} +(-1.62983e17 - 1.62983e17i) q^{21} +(-1.96399e17 - 9.61041e17i) q^{22} +6.64533e17i q^{23} +(1.54967e18 + 2.24219e18i) q^{24} +1.26922e19i q^{25} +(1.77459e19 - 3.62658e18i) q^{26} +(-1.50950e19 - 1.50950e19i) q^{27} +(-1.62339e19 + 6.92433e18i) q^{28} +(2.78644e19 - 2.78644e19i) q^{29} +(7.60449e19 + 5.02377e19i) q^{30} -5.58783e19 q^{31} +(2.03555e20 - 4.60596e19i) q^{32} -1.48412e20 q^{33} +(4.36176e20 + 2.88151e20i) q^{34} +(-4.17305e20 + 4.17305e20i) q^{35} +(-5.62105e20 + 2.39758e20i) q^{36} +(1.13775e20 + 1.13775e20i) q^{37} +(2.91160e21 - 5.95018e20i) q^{38} -2.74048e21i q^{39} +(5.74096e21 - 3.96782e21i) q^{40} -4.53327e21i q^{41} +(5.34657e20 + 2.61624e21i) q^{42} +(3.64051e21 + 3.64051e21i) q^{43} +(-4.23864e21 + 1.05439e22i) q^{44} +(-1.44494e22 + 1.44494e22i) q^{45} +(4.24364e21 - 6.42361e21i) q^{46} +3.53860e22 q^{47} +(-6.61276e20 - 3.15699e22i) q^{48} +4.84215e22 q^{49} +(8.10510e22 - 1.22687e23i) q^{50} +(5.59284e22 - 5.59284e22i) q^{51} +(-1.94697e23 - 7.82679e22i) q^{52} +(1.54555e23 + 1.54555e23i) q^{53} +(4.95184e22 + 2.42308e23i) q^{54} +3.79998e23i q^{55} +(2.01140e23 + 3.67348e22i) q^{56} -4.49634e23i q^{57} +(-4.47286e23 + 9.14079e22i) q^{58} +(-1.66157e21 - 1.66157e21i) q^{59} +(-4.14264e23 - 9.71229e23i) q^{60} +(-1.46942e24 + 1.46942e24i) q^{61} +(5.40139e23 + 3.56833e23i) q^{62} -5.98704e23 q^{63} +(-2.26176e24 - 8.54652e23i) q^{64} -7.01679e24 q^{65} +(1.43460e24 + 9.47744e23i) q^{66} +(9.06100e23 - 9.06100e23i) q^{67} +(-2.37612e24 - 5.57074e24i) q^{68} +(-8.23664e23 - 8.23664e23i) q^{69} +(6.69867e24 - 1.36895e24i) q^{70} -1.54392e25i q^{71} +(6.96457e24 + 1.27196e24i) q^{72} +2.66330e25i q^{73} +(-3.73232e23 - 1.82634e24i) q^{74} +(-1.57315e25 - 1.57315e25i) q^{75} +(-3.19442e25 - 1.28415e25i) q^{76} +(-7.87254e24 + 7.87254e24i) q^{77} +(-1.75004e25 + 2.64904e25i) q^{78} +7.42240e25 q^{79} +(-8.08322e25 + 1.69315e24i) q^{80} +2.69949e24 q^{81} +(-2.89489e25 + 4.38201e25i) q^{82} +(2.79222e25 - 2.79222e25i) q^{83} +(1.15388e25 - 2.87037e25i) q^{84} +(-1.43200e26 - 1.43200e26i) q^{85} +(-1.19425e25 - 5.84383e25i) q^{86} +6.90738e25i q^{87} +(1.08305e26 - 7.48538e25i) q^{88} -1.66487e26i q^{89} +(2.31945e26 - 4.74004e25i) q^{90} +(-1.45369e26 - 1.45369e26i) q^{91} +(-8.20409e25 + 3.49934e25i) q^{92} +(6.92590e25 - 6.92590e25i) q^{93} +(-3.42053e26 - 2.25971e26i) q^{94} -1.15125e27 q^{95} +(-1.95210e26 + 3.09388e26i) q^{96} -4.26550e26 q^{97} +(-4.68059e26 - 3.09214e26i) q^{98} +(-2.72590e26 + 2.72590e26i) 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 $

$2$	−9666.34	−	6385.89i	−0.834367	−	0.551209i
$2$	−9666.34	−	6385.89i	−0.834367	−	0.551209i
$3$	−1.23946e6	+	1.23946e6i	−0.448845	+	0.448845i	−0.894970	−	0.446126i	$-0.852803\pi$
$3$	−1.23946e6	+	1.23946e6i	−0.448845	+	0.448845i	0.446126	+	0.894970i	$0.352803\pi$
$4$	5.26586e7	+	1.23456e8i	0.392337	+	0.919822i
$5$	3.17355e9	+	3.17355e9i	1.16265	+	1.16265i	0.983893	+	0.178759i	$0.0572083\pi$
$5$	3.17355e9	+	3.17355e9i	1.16265	+	1.16265i	0.178759	+	0.983893i	$0.442792\pi$
$6$	1.98961e10	−	4.06599e9i	0.621909	−	0.127094i
$7$			1.31495e11i			0.512962i	0.966549	+	0.256481i	$0.0825631\pi$
$7$			1.31495e11i			0.512962i	−0.966549	+	0.256481i	$0.917437\pi$
$8$	2.79363e11	−	1.52964e12i	0.179661	−	0.983729i
$9$			4.55307e12i			0.597077i
$10$	−1.04107e13	−	5.09425e13i	−0.329214	−	1.61094i
$11$	5.98696e13	+	5.98696e13i	0.522884	+	0.522884i	0.918441	−	0.395557i	$-0.129449\pi$
$11$	5.98696e13	+	5.98696e13i	0.522884	+	0.522884i	−0.395557	+	0.918441i	$0.629449\pi$
$12$	−2.18288e14	−	8.77512e13i	−0.588956	−	0.236759i
$13$	−1.10551e15	+	1.10551e15i	−1.01234	+	1.01234i	−0.0124221	+	0.999923i	$0.503954\pi$
$13$	−1.10551e15	+	1.10551e15i	−1.01234	+	1.01234i	−0.999923	+	0.0124221i	$0.996046\pi$
$14$	8.39711e14	−	1.27107e15i	0.282749	−	0.427998i
$15$	−7.86698e15			−1.04370
$16$	−1.24686e16	+	1.30021e16i	−0.692144	+	0.721760i
$17$	−4.51231e16			−1.10494			−0.552470	−	0.833533i	$-0.686315\pi$
$17$	−4.51231e16			−1.10494			−0.552470	+	0.833533i	$0.686315\pi$
$18$	2.90754e16	−	4.40115e16i	0.329114	−	0.498181i
$19$	−1.81383e17	+	1.81383e17i	−0.989515	+	0.989515i	−0.999946	−	0.0104303i	$-0.996680\pi$
$19$	−1.81383e17	+	1.81383e17i	−0.989515	+	0.989515i	0.0104303	+	0.999946i	$0.496680\pi$
$20$	−2.24680e17	+	5.58909e17i	−0.613281	+	1.52558i
$21$	−1.62983e17	−	1.62983e17i	−0.230240	−	0.230240i
$22$	−1.96399e17	−	9.61041e17i	−0.148059	−	0.724495i
$23$			6.64533e17i			0.274910i	0.990508	+	0.137455i	$0.0438923\pi$
$23$			6.64533e17i			0.274910i	−0.990508	+	0.137455i	$0.956108\pi$
$24$	1.54967e18	+	2.24219e18i	0.360902	+	0.522182i
$25$			1.26922e19i			1.70352i
$26$	1.77459e19	−	3.62658e18i	1.40268	−	0.286653i
$27$	−1.50950e19	−	1.50950e19i	−0.716840	−	0.716840i
$28$	−1.62339e19	+	6.92433e18i	−0.471833	+	0.201254i
$29$	2.78644e19	−	2.78644e19i	0.504286	−	0.504286i	−0.408481	−	0.912767i	$-0.633941\pi$
$29$	2.78644e19	−	2.78644e19i	0.504286	−	0.504286i	0.912767	+	0.408481i	$0.133941\pi$
$30$	7.60449e19	+	5.02377e19i	0.870830	+	0.575297i
$31$	−5.58783e19			−0.411017			−0.205509	−	0.978655i	$-0.565885\pi$
$31$	−5.58783e19			−0.411017			−0.205509	+	0.978655i	$0.565885\pi$
$32$	2.03555e20	−	4.60596e19i	0.975342	−	0.220697i
$33$	−1.48412e20			−0.469387
$34$	4.36176e20	+	2.88151e20i	0.921926	+	0.609053i
$35$	−4.17305e20	+	4.17305e20i	−0.596396	+	0.596396i
$36$	−5.62105e20	+	2.39758e20i	−0.549204	+	0.234255i
$37$	1.13775e20	+	1.13775e20i	0.0767931	+	0.0767931i	0.744460	−	0.667667i	$-0.232707\pi$
$37$	1.13775e20	+	1.13775e20i	0.0767931	+	0.0767931i	−0.667667	+	0.744460i	$0.732707\pi$
$38$	2.91160e21	−	5.95018e20i	1.37105	−	0.280189i
$39$		−	2.74048e21i		−	0.908772i
$40$	5.74096e21	−	3.96782e21i	1.35262	−	0.934851i
$41$		−	4.53327e21i		−	0.765296i	−0.923894	−	0.382648i	$-0.875012\pi$
$41$		−	4.53327e21i		−	0.765296i	0.923894	−	0.382648i	$-0.124988\pi$
$42$	5.34657e20	+	2.61624e21i	0.0651943	+	0.319015i
$43$	3.64051e21	+	3.64051e21i	0.323101	+	0.323101i	0.849955	−	0.526855i	$-0.176629\pi$
$43$	3.64051e21	+	3.64051e21i	0.323101	+	0.323101i	−0.526855	+	0.849955i	$0.676629\pi$
$44$	−4.23864e21	+	1.05439e22i	−0.275813	+	0.686106i
$45$	−1.44494e22	+	1.44494e22i	−0.694192	+	0.694192i
$46$	4.24364e21	−	6.42361e21i	0.151533	−	0.229376i
$47$	3.53860e22			0.945172			0.472586	−	0.881285i	$-0.343321\pi$
$47$	3.53860e22			0.945172			0.472586	+	0.881285i	$0.343321\pi$
$48$	−6.61276e20	−	3.15699e22i	−0.0132931	−	0.634623i
$49$	4.84215e22			0.736870
$50$	8.10510e22	−	1.22687e23i	0.938996	−	1.42136i
$51$	5.59284e22	−	5.59284e22i	0.495947	−	0.495947i
$52$	−1.94697e23	−	7.82679e22i	−1.32836	−	0.533997i
$53$	1.54555e23	+	1.54555e23i	0.815379	+	0.815379i	0.985434	−	0.170055i	$-0.0543947\pi$
$53$	1.54555e23	+	1.54555e23i	0.815379	+	0.815379i	−0.170055	+	0.985434i	$0.554395\pi$
$54$	4.95184e22	+	2.42308e23i	0.202979	+	0.993236i
$55$			3.79998e23i			1.21586i
$56$	2.01140e23	+	3.67348e22i	0.504615	+	0.0921593i
$57$		−	4.49634e23i		−	0.888278i
$58$	−4.47286e23	+	9.14079e22i	−0.698727	+	0.142793i
$59$	−1.66157e21	−	1.66157e21i	−0.00206070	−	0.00206070i	0.706076	−	0.708136i	$-0.250464\pi$
$59$	−1.66157e21	−	1.66157e21i	−0.00206070	−	0.00206070i	−0.708136	+	0.706076i	$0.750464\pi$
$60$	−4.14264e23	−	9.71229e23i	−0.409482	−	0.960019i
$61$	−1.46942e24	+	1.46942e24i	−1.16197	+	1.16197i	−0.177922	+	0.984045i	$0.556937\pi$
$61$	−1.46942e24	+	1.46942e24i	−1.16197	+	1.16197i	−0.984045	+	0.177922i	$0.943063\pi$
$62$	5.40139e23	+	3.56833e23i	0.342939	+	0.226557i
$63$	−5.98704e23			−0.306277
$64$	−2.26176e24	−	8.54652e23i	−0.935444	−	0.353476i
$65$	−7.01679e24			−2.35401
$66$	1.43460e24	+	9.47744e23i	0.391641	+	0.258731i
$67$	9.06100e23	−	9.06100e23i	0.201914	−	0.201914i	−0.598906	−	0.800820i	$-0.704398\pi$
$67$	9.06100e23	−	9.06100e23i	0.201914	−	0.201914i	0.800820	+	0.598906i	$0.204398\pi$
$68$	−2.37612e24	−	5.57074e24i	−0.433509	−	1.01635i
$69$	−8.23664e23	−	8.23664e23i	−0.123392	−	0.123392i
$70$	6.69867e24	−	1.36895e24i	0.826352	−	0.168874i
$71$		−	1.54392e25i		−	1.57267i	−0.617803	−	0.786333i	$-0.711977\pi$
$71$		−	1.54392e25i		−	1.57267i	0.617803	−	0.786333i	$-0.288023\pi$
$72$	6.96457e24	+	1.27196e24i	0.587361	+	0.107271i
$73$			2.66330e25i			1.86449i	0.361823	+	0.932247i	$0.382154\pi$
$73$			2.66330e25i			1.86449i	−0.361823	+	0.932247i	$0.617846\pi$
$74$	−3.73232e23	−	1.82634e24i	−0.0217446	−	0.106403i
$75$	−1.57315e25	−	1.57315e25i	−0.764616	−	0.764616i
$76$	−3.19442e25	−	1.28415e25i	−1.29840	−	0.521954i
$77$	−7.87254e24	+	7.87254e24i	−0.268219	+	0.268219i
$78$	−1.75004e25	+	2.64904e25i	−0.500923	+	0.758249i
$79$	7.42240e25			1.78887			0.894435	−	0.447198i	$-0.147578\pi$
$79$	7.42240e25			1.78887			0.894435	+	0.447198i	$0.147578\pi$
$80$	−8.08322e25	+	1.69315e24i	−1.64388	+	0.0344334i
$81$	2.69949e24			0.0464230
$82$	−2.89489e25	+	4.38201e25i	−0.421838	+	0.638537i
$83$	2.79222e25	−	2.79222e25i	0.345458	−	0.345458i	−0.512956	−	0.858415i	$-0.671450\pi$
$83$	2.79222e25	−	2.79222e25i	0.345458	−	0.345458i	0.858415	+	0.512956i	$0.171450\pi$
$84$	1.15388e25	−	2.87037e25i	0.121448	−	0.302112i
$85$	−1.43200e26	−	1.43200e26i	−1.28466	−	1.28466i
$86$	−1.19425e25	−	5.84383e25i	−0.0914886	−	0.447681i
$87$			6.90738e25i			0.452693i
$88$	1.08305e26	−	7.48538e25i	0.608318	−	0.420434i
$89$		−	1.66487e26i		−	0.802815i	−0.915900	−	0.401408i	$-0.868521\pi$
$89$		−	1.66487e26i		−	0.802815i	0.915900	−	0.401408i	$-0.131479\pi$
$90$	2.31945e26	−	4.74004e25i	0.961856	−	0.196566i
$91$	−1.45369e26	−	1.45369e26i	−0.519294	−	0.519294i
$92$	−8.20409e25	+	3.49934e25i	−0.252868	+	0.107857i
$93$	6.92590e25	−	6.92590e25i	0.184483	−	0.184483i
$94$	−3.42053e26	−	2.25971e26i	−0.788620	−	0.520987i
$95$	−1.15125e27			−2.30092
$96$	−1.95210e26	+	3.09388e26i	−0.338719	+	0.536836i
$97$	−4.26550e26			−0.643504			−0.321752	−	0.946824i	$-0.604272\pi$
$97$	−4.26550e26			−0.643504			−0.321752	+	0.946824i	$0.604272\pi$
$98$	−4.68059e26	−	3.09214e26i	−0.614820	−	0.406170i
$99$	−2.72590e26	+	2.72590e26i	−0.312202	+	0.312202i
$100$	−1.56693e27	+	6.68353e26i	−1.56693	+	0.668353i
$101$	−6.96327e26	−	6.96327e26i	−0.608800	−	0.608800i	0.333833	−	0.942632i	$-0.391658\pi$
$101$	−6.96327e26	−	6.96327e26i	−0.608800	−	0.608800i	−0.942632	+	0.333833i	$0.891658\pi$
$102$	−8.97776e26	+	1.83470e26i	−0.687172	+	0.140431i
$103$			5.12049e26i			0.343565i	0.985135	+	0.171783i	$0.0549527\pi$
$103$			5.12049e26i			0.343565i	−0.985135	+	0.171783i	$0.945047\pi$
$104$	1.38220e27	+	1.99988e27i	0.813994	+	1.17775i
$105$		−	1.03447e27i		−	0.535379i
$106$	−5.07011e26	−	2.48096e27i	−0.230881	−	1.12977i
$107$	2.74083e27	+	2.74083e27i	1.09952	+	1.09952i	0.994467	+	0.105048i	$0.0334996\pi$
$107$	2.74083e27	+	2.74083e27i	1.09952	+	1.09952i	0.105048	+	0.994467i	$0.466500\pi$
$108$	1.06869e27	−	2.65845e27i	0.378122	−	0.940607i
$109$	−1.06504e27	+	1.06504e27i	−0.332741	+	0.332741i	−0.853627	−	0.520885i	$-0.825602\pi$
$109$	−1.06504e27	+	1.06504e27i	−0.332741	+	0.332741i	0.520885	+	0.853627i	$0.325602\pi$
$110$	2.42663e27	−	3.67319e27i	0.670195	−	1.01448i
$111$	−2.82039e26			−0.0689364
$112$	−1.70970e27	−	1.63955e27i	−0.370235	−	0.355043i
$113$	9.46566e27			1.81799			0.908995	−	0.416806i	$-0.136851\pi$
$113$	9.46566e27			1.81799			0.908995	+	0.416806i	$0.136851\pi$
$114$	−2.87131e27	+	4.34632e27i	−0.489627	+	0.741150i
$115$	−2.10893e27	+	2.10893e27i	−0.319625	+	0.319625i
$116$	4.90734e27	+	1.97274e27i	0.661704	+	0.266003i
$117$	−5.03347e27	−	5.03347e27i	−0.604447	−	0.604447i
$118$	5.45069e24	+	2.66718e25i	0.000583504	+	0.00285526i
$119$		−	5.93346e27i		−	0.566792i
$120$	−2.19774e27	+	1.20337e28i	−0.187513	+	1.02672i
$121$		−	5.94125e27i		−	0.453185i
$122$	2.35875e28	−	4.82036e27i	1.60999	−	0.329020i
$123$	5.61881e27	+	5.61881e27i	0.343499	+	0.343499i
$124$	−2.94247e27	−	6.89853e27i	−0.161257	−	0.378063i
$125$	−1.66345e28	+	1.66345e28i	−0.817948	+	0.817948i
$126$	5.78728e27	+	3.82326e27i	0.255548	+	0.168823i
$127$	3.89415e28			1.54548			0.772738	−	0.634725i	$-0.218887\pi$
$127$	3.89415e28			1.54548			0.772738	+	0.634725i	$0.218887\pi$
$128$	1.64053e28	+	2.27047e28i	0.585664	+	0.810554i
$129$	−9.02455e27			−0.290044
$130$	6.78267e28	+	4.48085e28i	1.96411	+	1.29755i
$131$	2.67814e27	−	2.67814e27i	0.0699312	−	0.0699312i	−0.671276	−	0.741207i	$-0.734254\pi$
$131$	2.67814e27	−	2.67814e27i	0.0699312	−	0.0699312i	0.741207	+	0.671276i	$0.234254\pi$
$132$	−7.81517e27	−	1.83224e28i	−0.184158	−	0.431753i
$133$	−2.38509e28	−	2.38509e28i	−0.507584	−	0.507584i
$134$	−1.45449e28	+	2.97242e27i	−0.279767	+	0.0571735i
$135$		−	9.58093e28i		−	1.66687i
$136$	−1.26057e28	+	6.90223e28i	−0.198515	+	1.08696i
$137$		−	1.99662e28i		−	0.284818i	−0.989808	−	0.142409i	$-0.954515\pi$
$137$		−	1.99662e28i		−	0.284818i	0.989808	−	0.142409i	$-0.0454849\pi$
$138$	2.70199e27	+	1.32216e28i	0.0349394	+	0.170969i
$139$	1.06382e29	+	1.06382e29i	1.24786	+	1.24786i	0.956661	+	0.291203i	$0.0940556\pi$
$139$	1.06382e29	+	1.06382e29i	1.24786	+	1.24786i	0.291203	+	0.956661i	$0.405944\pi$
$140$	−7.34936e28	−	2.95443e28i	−0.782566	−	0.314590i
$141$	−4.38596e28	+	4.38596e28i	−0.424236	+	0.424236i
$142$	−9.85929e28	+	1.49240e29i	−0.866868	+	1.31218i
$143$	−1.32373e29			−1.05868
$144$	−5.91993e28	−	5.67701e28i	−0.430946	−	0.413263i
$145$	1.76858e29			1.17262
$146$	1.70075e29	−	2.57443e29i	1.02773	−	1.55567i
$147$	−6.00166e28	+	6.00166e28i	−0.330740	+	0.330740i
$148$	−8.05500e27	+	2.00374e28i	−0.0405072	+	0.100765i
$149$	−1.46707e29	−	1.46707e29i	−0.673654	−	0.673654i	0.284902	−	0.958557i	$-0.408039\pi$
$149$	−1.46707e29	−	1.46707e29i	−0.673654	−	0.673654i	−0.958557	+	0.284902i	$0.908039\pi$
$150$	5.16065e28	+	2.52526e29i	0.216507	+	1.05943i
$151$		−	3.28281e29i		−	1.25909i	−0.776963	−	0.629546i	$-0.783241\pi$
$151$		−	3.28281e29i		−	1.25909i	0.776963	−	0.629546i	$-0.216759\pi$
$152$	2.26779e29	+	3.28123e29i	0.795637	+	1.15119i
$153$		−	2.05449e29i		−	0.659734i
$154$	1.26372e29	−	2.58255e28i	0.371638	−	0.0759484i
$155$	−1.77332e29	−	1.77332e29i	−0.477870	−	0.477870i
$156$	3.38330e29	−	1.44310e29i	0.835908	−	0.356545i
$157$	1.53562e27	−	1.53562e27i	0.00348048	−	0.00348048i	−0.705364	−	0.708845i	$-0.749217\pi$
$157$	1.53562e27	−	1.53562e27i	0.00348048	−	0.00348048i	0.708845	+	0.705364i	$0.249217\pi$
$158$	−7.17475e29	−	4.73986e29i	−1.49257	−	0.986042i
$159$	−3.83131e29			−0.731957
$160$	7.92164e29	+	4.99819e29i	1.39058	+	0.877390i
$161$	−8.73827e28			−0.141018
$162$	−2.60942e28	−	1.72386e28i	−0.0387338	−	0.0255888i
$163$	−9.01481e29	+	9.01481e29i	−1.23147	+	1.23147i	−0.268072	+	0.963399i	$0.586386\pi$
$163$	−9.01481e29	+	9.01481e29i	−1.23147	+	1.23147i	−0.963399	+	0.268072i	$0.913614\pi$
$164$	5.59661e29	−	2.38715e29i	0.703935	−	0.300254i
$165$	−4.70993e29	−	4.70993e29i	−0.545734	−	0.545734i
$166$	−4.48214e29	+	9.15975e28i	−0.478659	+	0.0978192i
$167$		−	1.32830e30i		−	1.30805i	−0.756475	−	0.654023i	$-0.773080\pi$
$167$		−	1.32830e30i		−	1.30805i	0.756475	−	0.654023i	$-0.226920\pi$
$168$	−2.94837e29	+	2.03774e29i	−0.267859	+	0.185129i
$169$		−	1.25178e30i		−	1.04968i
$170$	4.69762e29	+	2.29869e30i	0.363762	+	1.78000i
$171$	−8.25848e29	−	8.25848e29i	−0.590816	−	0.590816i
$172$	−2.57740e29	+	6.41148e29i	−0.170431	+	0.423960i
$173$	−4.26730e29	+	4.26730e29i	−0.260934	+	0.260934i	−0.825434	−	0.564499i	$-0.809069\pi$
$173$	−4.26730e29	+	4.26730e29i	−0.260934	+	0.260934i	0.564499	+	0.825434i	$0.309069\pi$
$174$	4.41098e29	−	6.67691e29i	0.249528	−	0.377712i
$175$	−1.66896e30			−0.873840
$176$	−1.52492e30	+	3.19416e28i	−0.739307	+	0.0154859i
$177$	4.11890e27			0.00184987
$178$	−1.06317e30	+	1.60932e30i	−0.442519	+	0.669843i
$179$	1.77478e30	−	1.77478e30i	0.684903	−	0.684903i	−0.276198	−	0.961101i	$-0.589075\pi$
$179$	1.77478e30	−	1.77478e30i	0.684903	−	0.684903i	0.961101	+	0.276198i	$0.0890745\pi$
$180$	−2.54475e30	−	1.02298e30i	−0.910890	−	0.366176i
$181$	−9.00742e29	−	9.00742e29i	−0.299185	−	0.299185i	0.541510	−	0.840695i	$-0.317853\pi$
$181$	−9.00742e29	−	9.00742e29i	−0.299185	−	0.299185i	−0.840695	+	0.541510i	$0.817853\pi$
$182$	4.76877e29	+	2.33350e30i	0.147042	+	0.719522i
$183$		−	3.64258e30i		−	1.04309i
$184$	1.01650e30	+	1.85646e29i	0.270437	+	0.0493907i
$185$			7.22138e29i			0.178567i
$186$	−1.11176e30	+	2.27201e29i	−0.255615	+	0.0522378i
$187$	−2.70150e30	−	2.70150e30i	−0.577755	−	0.577755i
$188$	1.86338e30	+	4.36863e30i	0.370826	+	0.869390i
$189$	1.98491e30	−	1.98491e30i	0.367711	−	0.367711i
$190$	1.11284e31	+	7.35178e30i	1.91982	+	1.26829i
$191$	9.78026e29			0.157181			0.0785905	−	0.996907i	$-0.474958\pi$
$191$	9.78026e29			0.157181			0.0785905	+	0.996907i	$0.474958\pi$
$192$	3.86268e30	−	1.74406e30i	0.578525	−	0.261213i
$193$	−1.09659e31			−1.53116			−0.765580	−	0.643340i	$-0.777548\pi$
$193$	−1.09659e31			−1.53116			−0.765580	+	0.643340i	$0.777548\pi$
$194$	4.12318e30	+	2.72390e30i	0.536919	+	0.354705i
$195$	8.69705e30	−	8.69705e30i	1.05659	−	1.05659i
$196$	2.54981e30	+	5.97794e30i	0.289101	+	0.677789i
$197$	3.12440e29	+	3.12440e29i	0.0330729	+	0.0330729i	0.723450	−	0.690377i	$-0.242555\pi$
$197$	3.12440e29	+	3.12440e29i	0.0330729	+	0.0330729i	−0.690377	+	0.723450i	$0.742555\pi$
$198$	4.37568e30	−	8.94219e29i	0.432579	−	0.0884024i
$199$			6.69195e30i			0.618068i	0.951051	+	0.309034i	$0.100006\pi$
$199$			6.69195e30i			0.618068i	−0.951051	+	0.309034i	$0.899994\pi$
$200$	1.94145e31	+	3.54573e30i	1.67580	+	0.306056i
$201$			2.24615e30i			0.181256i
$202$	2.28427e30	+	1.11776e31i	0.172386	+	0.843538i
$203$	3.66403e30	+	3.66403e30i	0.258680	+	0.258680i
$204$	9.84983e30	+	3.95961e30i	0.650761	+	0.261604i
$205$	1.43865e31	−	1.43865e31i	0.889772	−	0.889772i
$206$	3.26989e30	−	4.94964e30i	0.189376	−	0.286659i
$207$	−3.02566e30			−0.164142
$208$	−5.89812e29	−	2.81581e31i	−0.0299819	−	1.43136i
$209$	−2.17186e31			−1.03480
$210$	−6.60599e30	+	9.99951e30i	−0.295106	+	0.446702i
$211$	−5.61857e30	+	5.61857e30i	−0.235403	+	0.235403i	−0.814944	−	0.579540i	$-0.803232\pi$
$211$	−5.61857e30	+	5.61857e30i	−0.235403	+	0.235403i	0.579540	+	0.814944i	$0.303232\pi$
$212$	−1.09422e31	+	2.72195e31i	−0.430100	+	1.06991i
$213$	1.91363e31	+	1.91363e31i	0.705883	+	0.705883i
$214$	−8.99116e30	−	4.39964e31i	−0.311336	−	1.52346i
$215$			2.31067e31i			0.751308i
$216$	−2.73069e31	+	1.88730e31i	−0.833964	+	0.576387i
$217$		−	7.34770e30i		−	0.210836i
$218$	1.70962e31	−	3.49380e30i	0.461038	−	0.0942183i
$219$	−3.30105e31	−	3.30105e31i	−0.836868	−	0.836868i
$220$	−4.69132e31	+	2.00101e31i	−1.11838	+	0.477028i
$221$	4.98842e31	−	4.98842e31i	1.11858	−	1.11858i
$222$	2.72628e30	+	1.80107e30i	0.0575183	+	0.0379984i
$223$	6.31630e31			1.25414			0.627072	−	0.778962i	$-0.284253\pi$
$223$	6.31630e31			1.25414			0.627072	+	0.778962i	$0.284253\pi$
$224$	6.05660e30	+	2.67664e31i	0.113209	+	0.500313i
$225$	−5.77885e31			−1.01713
$226$	−9.14983e31	−	6.04466e31i	−1.51687	−	1.00209i
$227$	−7.30045e31	+	7.30045e31i	−1.14025	+	1.14025i	−0.151848	+	0.988404i	$0.548522\pi$
$227$	−7.30045e31	+	7.30045e31i	−1.14025	+	1.14025i	−0.988404	+	0.151848i	$0.951478\pi$
$228$	5.55102e31	−	2.36771e31i	0.817057	−	0.348504i
$229$	−5.06155e31	−	5.06155e31i	−0.702271	−	0.702271i	0.262627	−	0.964897i	$-0.415411\pi$
$229$	−5.06155e31	−	5.06155e31i	−0.702271	−	0.702271i	−0.964897	+	0.262627i	$0.915411\pi$
$230$	3.38530e31	−	6.91823e30i	0.442865	−	0.0905043i
$231$		−	1.95154e31i		−	0.240778i
$232$	−3.48383e31	−	5.04069e31i	−0.405480	−	0.586682i
$233$		−	3.85841e31i		−	0.423744i	−0.977297	−	0.211872i	$-0.932044\pi$
$233$		−	3.85841e31i		−	0.423744i	0.977297	−	0.211872i	$-0.0679560\pi$
$234$	1.65121e31	+	8.07985e31i	0.171154	+	0.837508i
$235$	1.12299e32	+	1.12299e32i	1.09891	+	1.09891i
$236$	1.17635e29	−	2.92627e29i	0.00108699	−	0.00270397i
$237$	−9.19979e31	+	9.19979e31i	−0.802925	+	0.802925i
$238$	−3.78904e31	+	5.73548e31i	−0.312421	+	0.472913i
$239$	−1.78211e32			−1.38855			−0.694276	−	0.719709i	$-0.744275\pi$
$239$	−1.78211e32			−1.38855			−0.694276	+	0.719709i	$0.744275\pi$
$240$	9.80898e31	−	1.02287e32i	0.722391	−	0.753301i
$241$	−1.08186e32			−0.753256			−0.376628	−	0.926365i	$-0.622916\pi$
$241$	−1.08186e32			−0.753256			−0.376628	+	0.926365i	$0.622916\pi$
$242$	−3.79402e31	+	5.74302e31i	−0.249800	+	0.378123i
$243$	1.11762e32	−	1.11762e32i	0.696003	−	0.696003i
$244$	−2.58787e32	−	1.04032e32i	−1.52468	−	0.612919i
$245$	1.53668e32	+	1.53668e32i	0.856724	+	0.856724i
$246$	−1.84322e31	−	9.01945e31i	−0.0972645	−	0.475944i
$247$		−	4.01042e32i		−	2.00346i
$248$	−1.56103e31	+	8.54739e31i	−0.0738439	+	0.404330i
$249$			6.92170e31i			0.310114i
$250$	2.67022e32	−	5.45688e31i	1.13333	−	0.231609i
$251$	3.01734e32	+	3.01734e32i	1.21347	+	1.21347i	0.969878	+	0.243590i	$0.0783253\pi$
$251$	3.01734e32	+	3.01734e32i	1.21347	+	1.21347i	0.243590	+	0.969878i	$0.421675\pi$
$252$	−3.15269e31	−	7.39139e31i	−0.120164	−	0.281721i
$253$	−3.97854e31	+	3.97854e31i	−0.143746	+	0.143746i
$254$	−3.76422e32	−	2.48676e32i	−1.28949	−	0.851881i
$255$	3.54983e32			1.15323
$256$	−1.35891e31	−	3.24234e32i	−0.0418745	−	0.999123i
$257$	3.73463e32			1.09182			0.545909	−	0.837844i	$-0.316184\pi$
$257$	3.73463e32			1.09182			0.545909	+	0.837844i	$0.316184\pi$
$258$	8.72344e31	+	5.76298e31i	0.242003	+	0.159875i
$259$	−1.49608e31	+	1.49608e31i	−0.0393919	+	0.0393919i
$260$	−3.69494e32	−	8.66268e32i	−0.923565	−	2.16527i
$261$	1.26869e32	+	1.26869e32i	0.301098	+	0.301098i
$262$	−4.29901e31	+	8.78551e30i	−0.0968949	+	0.0198016i
$263$			2.69119e32i			0.576157i	0.957607	+	0.288079i	$0.0930164\pi$
$263$			2.69119e32i			0.576157i	−0.957607	+	0.288079i	$0.906984\pi$
$264$	−4.14609e31	+	2.27018e32i	−0.0843307	+	0.461750i
$265$			9.80976e32i			1.89600i
$266$	7.82417e31	+	3.82860e32i	0.143726	+	0.703296i
$267$	2.06354e32	+	2.06354e32i	0.360340	+	0.360340i
$268$	1.59578e32	+	6.41499e31i	0.264943	+	0.106506i
$269$	−6.24780e32	+	6.24780e32i	−0.986441	+	0.986441i	−0.999909	−	0.0134685i	$-0.995713\pi$
$269$	−6.24780e32	+	6.24780e32i	−0.986441	+	0.986441i	0.0134685	+	0.999909i	$0.495713\pi$
$270$	−6.11828e32	+	9.26125e32i	−0.918794	+	1.39078i
$271$	1.11265e32			0.158954			0.0794771	−	0.996837i	$-0.474675\pi$
$271$	1.11265e32			0.158954			0.0794771	+	0.996837i	$0.474675\pi$
$272$	5.62620e32	−	5.86694e32i	0.764777	−	0.797502i
$273$	3.60359e32			0.466165
$274$	−1.27502e32	+	1.93000e32i	−0.156995	+	0.237643i
$275$	−7.59878e32	+	7.59878e32i	−0.890743	+	0.890743i
$276$	5.83136e31	−	1.45059e32i	0.0650874	−	0.161910i
$277$	−6.31879e32	−	6.31879e32i	−0.671671	−	0.671671i	0.286430	−	0.958101i	$-0.407531\pi$
$277$	−6.31879e32	−	6.31879e32i	−0.671671	−	0.671671i	−0.958101	+	0.286430i	$0.907531\pi$
$278$	−3.48980e32	−	1.70766e33i	−0.353343	−	1.72901i
$279$		−	2.54418e32i		−	0.245409i
$280$	5.21748e32	+	7.54907e32i	0.479543	+	0.693841i
$281$		−	4.51095e32i		−	0.395124i	−0.980290	−	0.197562i	$-0.936698\pi$
$281$		−	4.51095e32i		−	0.395124i	0.980290	−	0.197562i	$-0.0633023\pi$
$282$	7.04045e32	−	1.43879e32i	0.587811	−	0.120126i
$283$	1.07108e33	+	1.07108e33i	0.852518	+	0.852518i	0.990443	−	0.137925i	$-0.0440432\pi$
$283$	1.07108e33	+	1.07108e33i	0.852518	+	0.852518i	−0.137925	+	0.990443i	$0.544043\pi$
$284$	1.90606e33	−	8.13005e32i	1.44657	−	0.617015i
$285$	1.42693e33	−	1.42693e33i	1.03276	−	1.03276i
$286$	1.27957e33	+	8.45321e32i	0.883326	+	0.583553i
$287$	5.96101e32			0.392567
$288$	2.09713e32	+	9.26799e32i	0.131773	+	0.582354i
$289$	3.68386e32			0.220893
$290$	−1.70957e33	−	1.12940e33i	−0.978395	−	0.646359i
$291$	5.28692e32	−	5.28692e32i	0.288833	−	0.288833i
$292$	−3.28801e33	+	1.40245e33i	−1.71500	+	0.731509i
$293$	7.77212e32	+	7.77212e32i	0.387103	+	0.387103i	0.873653	−	0.486550i	$-0.161745\pi$
$293$	7.77212e32	+	7.77212e32i	0.387103	+	0.387103i	−0.486550	+	0.873653i	$0.661745\pi$
$294$	9.63400e32	−	1.96882e32i	0.458266	−	0.0936518i
$295$		−	1.05461e31i		−	0.00479176i
$296$	2.05819e32	−	1.42250e32i	0.0893403	−	0.0617468i
$297$		−	1.80746e33i		−	0.749648i
$298$	4.81266e32	+	2.35498e33i	0.190751	+	0.933400i
$299$	−7.34650e32	−	7.34650e32i	−0.278304	−	0.278304i
$300$	1.11376e33	−	2.77055e33i	0.403323	−	1.00330i
$301$	−4.78708e32	+	4.78708e32i	−0.165738	+	0.165738i
$302$	−2.09637e33	+	3.17328e33i	−0.694023	+	1.05055i
$303$	1.72614e33			0.546513
$304$	−9.67712e31	−	4.61993e33i	−0.0293057	−	1.39908i
$305$	−9.32655e33			−2.70192
$306$	−1.31197e33	+	1.98594e33i	−0.363651	+	0.550460i
$307$	3.70682e33	−	3.70682e33i	0.983180	−	0.983180i	−0.0166807	−	0.999861i	$-0.505310\pi$
$307$	3.70682e33	−	3.70682e33i	0.983180	−	0.983180i	0.999861	+	0.0166807i	$0.00530989\pi$
$308$	−1.38647e33	−	5.57359e32i	−0.351946	−	0.141482i
$309$	−6.34666e32	−	6.34666e32i	−0.154207	−	0.154207i
$310$	5.81730e32	+	2.84658e33i	0.135313	+	0.662126i
$311$			3.11139e33i			0.692930i	0.938063	+	0.346465i	$0.112618\pi$
$311$			3.11139e33i			0.692930i	−0.938063	+	0.346465i	$0.887382\pi$
$312$	−4.19196e33	−	7.65590e32i	−0.893985	−	0.163271i
$313$		−	2.78059e33i		−	0.567921i	−0.958836	−	0.283960i	$-0.908352\pi$
$313$		−	2.78059e33i		−	0.567921i	0.958836	−	0.283960i	$-0.0916484\pi$
$314$	−2.46502e31	+	5.03754e30i	−0.00482247	+	0.000985525i
$315$	−1.90002e33	−	1.90002e33i	−0.356094	−	0.356094i
$316$	3.90853e33	+	9.16343e33i	0.701840	+	1.64544i
$317$	−6.86600e33	+	6.86600e33i	−1.18142	+	1.18142i	−0.202042	+	0.979377i	$0.564758\pi$
$317$	−6.86600e33	+	6.86600e33i	−1.18142	+	1.18142i	−0.979377	+	0.202042i	$0.935242\pi$
$318$	3.70347e33	+	2.44663e33i	0.610721	+	0.403462i
$319$	3.33647e33			0.527366
$320$	−4.46554e33	−	9.89009e33i	−0.676626	−	1.49856i
$321$	−6.79431e33			−0.987024
$322$	8.44671e32	+	5.58016e32i	0.117661	+	0.0777307i
$323$	8.18456e33	−	8.18456e33i	1.09336	−	1.09336i
$324$	1.42151e32	+	3.33269e32i	0.0182135	+	0.0427009i
$325$	−1.40314e34	−	1.40314e34i	−1.72455	−	1.72455i
$326$	1.44708e34	−	2.95727e33i	1.70630	−	0.348701i
$327$		−	2.64014e33i		−	0.298698i
$328$	−6.93428e33	−	1.26643e33i	−0.752843	−	0.137494i
$329$			4.65308e33i			0.484837i
$330$	1.54507e33	+	7.56049e33i	0.154529	+	0.756156i
$331$	−8.03864e33	−	8.03864e33i	−0.771800	−	0.771800i	0.206621	−	0.978421i	$-0.433753\pi$
$331$	−8.03864e33	−	8.03864e33i	−0.771800	−	0.771800i	−0.978421	+	0.206621i	$0.933753\pi$
$332$	4.91752e33	+	1.97683e33i	0.453296	+	0.182224i
$333$	−5.18023e32	+	5.18023e32i	−0.0458514	+	0.0458514i
$334$	−8.48236e33	+	1.28398e34i	−0.721007	+	1.09139i
$335$	5.75110e33			0.469511
$336$	4.15127e33	−	8.69544e31i	0.325537	−	0.00681885i
$337$	−1.80793e34			−1.36200			−0.681002	−	0.732281i	$-0.738456\pi$
$337$	−1.80793e34			−1.36200			−0.681002	+	0.732281i	$0.738456\pi$
$338$	−7.99375e33	+	1.21002e34i	−0.578596	+	0.875822i
$339$	−1.17323e34	+	1.17323e34i	−0.815996	+	0.815996i
$340$	1.01383e34	−	2.52197e34i	0.677639	−	1.68568i
$341$	−3.34541e33	−	3.34541e33i	−0.214914	−	0.214914i
$342$	2.70915e33	+	1.32567e34i	0.167294	+	0.818621i
$343$			1.50080e34i			0.890948i
$344$	6.58571e33	−	4.55166e33i	0.375892	−	0.259795i
$345$		−	5.22787e33i		−	0.286924i
$346$	6.84997e33	−	1.39987e33i	0.361544	−	0.0738856i
$347$	1.55749e34	+	1.55749e34i	0.790637	+	0.790637i	0.981598	−	0.190960i	$-0.0611602\pi$
$347$	1.55749e34	+	1.55749e34i	0.790637	+	0.790637i	−0.190960	+	0.981598i	$0.561160\pi$
$348$	−8.52760e33	+	3.63733e33i	−0.416397	+	0.177608i
$349$	2.26052e34	−	2.26052e34i	1.06185	−	1.06185i	0.0638978	−	0.997956i	$-0.479647\pi$
$349$	2.26052e34	−	2.26052e34i	1.06185	−	1.06185i	0.997956	−	0.0638978i	$-0.0203532\pi$
$350$	1.61327e34	+	1.06578e34i	0.729104	+	0.481669i
$351$	3.33754e34			1.45138
$352$	1.49443e34	+	9.42919e33i	0.625390	+	0.394592i
$353$	3.09462e34			1.24637			0.623187	−	0.782073i	$-0.285837\pi$
$353$	3.09462e34			1.24637			0.623187	+	0.782073i	$0.285837\pi$
$354$	−3.98146e31	−	2.63028e31i	−0.00154347	−	0.00101967i
$355$	4.89969e34	−	4.89969e34i	1.82846	−	1.82846i
$356$	2.05539e34	−	8.76697e33i	0.738447	−	0.314974i
$357$	7.35429e33	+	7.35429e33i	0.254402	+	0.254402i
$358$	−2.84892e34	+	5.82208e33i	−0.948985	+	0.193936i
$359$			4.70824e33i			0.151037i	0.997144	+	0.0755185i	$0.0240612\pi$
$359$			4.70824e33i			0.151037i	−0.997144	+	0.0755185i	$0.975939\pi$
$360$	1.80657e34	+	2.61390e34i	0.558177	+	0.807616i
$361$		−	3.21988e34i		−	0.958281i
$362$	2.95484e33	+	1.44589e34i	0.0847166	+	0.414544i
$363$	7.36396e33	+	7.36396e33i	0.203410	+	0.203410i
$364$	1.02918e34	−	2.56017e34i	0.273920	−	0.681396i
$365$	−8.45209e34	+	8.45209e34i	−2.16776	+	2.16776i
$366$	−2.32611e34	+	3.52105e34i	−0.574958	+	0.870316i
$367$	−2.82302e34			−0.672546			−0.336273	−	0.941764i	$-0.609167\pi$
$367$	−2.82302e34			−0.672546			−0.336273	+	0.941764i	$0.609167\pi$
$368$	−8.64031e33	−	8.28577e33i	−0.198419	−	0.190277i
$369$	2.06403e34			0.456940
$370$	4.61150e33	−	6.98043e33i	0.0984280	−	0.148991i
$371$	−2.03232e34	+	2.03232e34i	−0.418258	+	0.418258i
$372$	1.21975e34	+	4.90339e33i	0.242071	+	0.0973120i
$373$	−4.21563e34	−	4.21563e34i	−0.806850	−	0.806850i	0.177306	−	0.984156i	$-0.443262\pi$
$373$	−4.21563e34	−	4.21563e34i	−0.806850	−	0.806850i	−0.984156	+	0.177306i	$0.943262\pi$
$374$	8.86216e33	+	4.33652e34i	0.163596	+	0.800524i
$375$		−	4.12358e34i		−	0.734264i
$376$	9.88555e33	−	5.41280e34i	0.169811	−	0.929793i
$377$			6.16090e34i			1.02102i
$378$	−3.18623e34	+	6.51141e33i	−0.509492	+	0.104120i
$379$	−6.55736e33	−	6.55736e33i	−0.101181	−	0.101181i	0.654704	−	0.755885i	$-0.272793\pi$
$379$	−6.55736e33	−	6.55736e33i	−0.101181	−	0.101181i	−0.755885	+	0.654704i	$0.772793\pi$
$380$	−6.06233e34	−	1.42130e35i	−0.902737	−	2.11644i
$381$	−4.82665e34	+	4.82665e34i	−0.693679	+	0.693679i
$382$	−9.45394e33	−	6.24557e33i	−0.131147	−	0.0866396i
$383$	9.87716e34			1.32266			0.661330	−	0.750095i	$-0.269992\pi$
$383$	9.87716e34			1.32266			0.661330	+	0.750095i	$0.269992\pi$
$384$	−4.84754e34	−	7.80794e33i	−0.626685	−	0.100940i
$385$	−4.99678e34			−0.623692
$386$	1.06000e35	+	7.00270e34i	1.27755	+	0.843990i
$387$	−1.65755e34	+	1.65755e34i	−0.192916	+	0.192916i
$388$	−2.24615e34	−	5.26603e34i	−0.252470	−	0.591909i
$389$	−4.35349e34	−	4.35349e34i	−0.472627	−	0.472627i	0.430137	−	0.902764i	$-0.358465\pi$
$389$	−4.35349e34	−	4.35349e34i	−0.472627	−	0.472627i	−0.902764	+	0.430137i	$0.858465\pi$
$390$	−1.39607e35	+	2.85302e34i	−1.46398	+	0.299180i
$391$		−	2.99858e34i		−	0.303759i
$392$	1.35272e34	−	7.40676e34i	0.132387	−	0.724880i
$393$			6.63890e33i			0.0627765i
$394$	−1.02494e33	−	5.01535e33i	−0.00936484	−	0.0458250i
$395$	2.35553e35	+	2.35553e35i	2.07983	+	2.07983i
$396$	−4.80072e34	−	1.92988e34i	−0.409658	−	0.164682i
$397$	−1.52435e34	+	1.52435e34i	−0.125722	+	0.125722i	−0.767168	−	0.641446i	$-0.778335\pi$
$397$	−1.52435e34	+	1.52435e34i	−0.125722	+	0.125722i	0.641446	+	0.767168i	$0.278335\pi$
$398$	4.27340e34	−	6.46866e34i	0.340685	−	0.515695i
$399$	5.91246e34			0.455653
$400$	−1.65025e35	−	1.58253e35i	−1.22953	−	1.17908i
$401$	−9.82453e34			−0.707722			−0.353861	−	0.935298i	$-0.615131\pi$
$401$	−9.82453e34			−0.707722			−0.353861	+	0.935298i	$0.615131\pi$
$402$	1.43437e34	−	2.17121e34i	0.0999100	−	0.151234i
$403$	6.17742e34	−	6.17742e34i	0.416091	−	0.416091i
$404$	4.92984e34	−	1.22634e35i	0.321133	−	0.798842i
$405$	8.56695e33	+	8.56695e33i	0.0539738	+	0.0539738i
$406$	−1.20197e34	−	5.88158e34i	−0.0732472	−	0.358420i
$407$			1.36233e34i			0.0803078i
$408$	−6.99262e34	−	1.01175e35i	−0.398775	−	0.576979i
$409$			2.01963e35i			1.11432i	0.830407	+	0.557158i	$0.188108\pi$
$409$			2.01963e35i			1.11432i	−0.830407	+	0.557158i	$0.811892\pi$
$410$	−2.30936e35	+	4.71943e34i	−1.23285	+	0.251946i
$411$	2.47474e34	+	2.47474e34i	0.127839	+	0.127839i
$412$	−6.32157e34	+	2.69638e34i	−0.316019	+	0.134793i
$413$	2.18487e32	−	2.18487e32i	0.00105706	−	0.00105706i
$414$	2.92471e34	+	1.93216e34i	0.136955	+	0.0904768i
$415$	1.77225e35			0.803296
$416$	−1.74113e35	+	2.75952e35i	−0.763962	+	1.21080i
$417$	−2.63712e35			−1.12020
$418$	2.09940e35	+	1.38693e35i	0.863406	+	0.570393i
$419$	9.10927e34	−	9.10927e34i	0.362739	−	0.362739i	−0.502081	−	0.864820i	$-0.667432\pi$
$419$	9.10927e34	−	9.10927e34i	0.362739	−	0.362739i	0.864820	+	0.502081i	$0.167432\pi$
$420$	1.27712e35	−	5.44735e34i	0.492453	−	0.210049i
$421$	2.34412e35	+	2.34412e35i	0.875329	+	0.875329i	0.993047	−	0.117718i	$-0.0375580\pi$
$421$	2.34412e35	+	2.34412e35i	0.875329	+	0.875329i	−0.117718	+	0.993047i	$0.537558\pi$
$422$	9.01905e34	−	1.84314e34i	0.326169	−	0.0666563i
$423$			1.61115e35i			0.564340i
$424$	2.79591e35	−	1.93237e35i	0.948604	−	0.655620i
$425$		−	5.72712e35i		−	1.88229i
$426$	−6.27756e34	−	3.07180e35i	−0.199876	−	0.978055i
$427$	−1.93221e35	−	1.93221e35i	−0.596044	−	0.596044i
$428$	−1.94045e35	+	4.82701e35i	−0.579977	+	1.44274i
$429$	1.64072e35	−	1.64072e35i	0.475182	−	0.475182i
$430$	1.47557e35	−	2.23357e35i	0.414128	−	0.626866i
$431$	−1.89345e35			−0.515003			−0.257502	−	0.966278i	$-0.582899\pi$
$431$	−1.89345e35			−0.515003			−0.257502	+	0.966278i	$0.582899\pi$
$432$	3.84479e35	−	8.05346e33i	1.01354	−	0.0212301i
$433$	−1.93502e35			−0.494423			−0.247212	−	0.968961i	$-0.579514\pi$
$433$	−1.93502e35			−0.494423			−0.247212	+	0.968961i	$0.579514\pi$
$434$	−4.69216e34	+	7.10254e34i	−0.116215	+	0.175915i
$435$	−2.19209e35	+	2.19209e35i	−0.526324	+	0.526324i
$436$	−1.87569e35	−	7.54022e34i	−0.436609	−	0.175516i
$437$	−1.20535e35	−	1.20535e35i	−0.272028	−	0.272028i
$438$	1.08289e35	+	5.29893e35i	0.236966	+	1.15954i
$439$			6.88144e35i			1.46019i	0.683347	+	0.730093i	$0.260523\pi$
$439$			6.88144e35i			1.46019i	−0.683347	+	0.730093i	$0.739477\pi$
$440$	5.81261e35	+	1.06157e35i	1.19608	+	0.218444i
$441$			2.20466e35i			0.439968i
$442$	−8.00753e35	+	1.63643e35i	−1.54988	+	0.316735i
$443$	−1.56255e35	−	1.56255e35i	−0.293349	−	0.293349i	0.545053	−	0.838402i	$-0.316510\pi$
$443$	−1.56255e35	−	1.56255e35i	−0.293349	−	0.293349i	−0.838402	+	0.545053i	$0.816510\pi$
$444$	−1.48518e34	−	3.48195e34i	−0.0270463	−	0.0634092i
$445$	5.28355e35	−	5.28355e35i	0.933395	−	0.933395i
$446$	−6.10555e35	−	4.03352e35i	−1.04642	−	0.691295i
$447$	3.63676e35			0.604733
$448$	1.12382e35	−	2.97410e35i	0.181319	−	0.479847i
$449$	−4.36625e35			−0.683571			−0.341785	−	0.939778i	$-0.611032\pi$
$449$	−4.36625e35			−0.683571			−0.341785	+	0.939778i	$0.611032\pi$
$450$	5.58603e35	+	3.69031e35i	0.848661	+	0.560652i
$451$	2.71405e35	−	2.71405e35i	0.400161	−	0.400161i
$452$	4.98448e35	+	1.16860e36i	0.713265	+	1.67223i
$453$	4.06892e35	+	4.06892e35i	0.565137	+	0.565137i
$454$	1.17189e36	−	2.39488e35i	1.57991	−	0.322871i
$455$		−	9.22672e35i		−	1.20752i
$456$	−6.87780e35	−	1.25611e35i	−0.873824	−	0.159589i
$457$			5.52893e35i			0.681981i	0.940067	+	0.340990i	$0.110762\pi$
$457$			5.52893e35i			0.681981i	−0.940067	+	0.340990i	$0.889238\pi$
$458$	1.66042e35	+	8.12492e35i	0.198853	+	0.973049i
$459$	6.81133e35	+	6.81133e35i	0.792065	+	0.792065i
$460$	−3.71414e35	−	1.49307e35i	−0.419399	−	0.168597i
$461$	4.21755e35	−	4.21755e35i	0.462485	−	0.462485i	−0.436984	−	0.899469i	$-0.643953\pi$
$461$	4.21755e35	−	4.21755e35i	0.462485	−	0.462485i	0.899469	+	0.436984i	$0.143953\pi$
$462$	−1.24623e35	+	1.88643e35i	−0.132719	+	0.200897i
$463$	−6.61682e35			−0.684393			−0.342197	−	0.939628i	$-0.611171\pi$
$463$	−6.61682e35			−0.684393			−0.342197	+	0.939628i	$0.611171\pi$
$464$	1.48662e34	+	7.09724e35i	0.0149351	+	0.713012i
$465$	4.39593e35			0.428979
$466$	−2.46394e35	+	3.72967e35i	−0.233572	+	0.353558i
$467$	4.36861e35	−	4.36861e35i	0.402314	−	0.402314i	−0.476734	−	0.879048i	$-0.658179\pi$
$467$	4.36861e35	−	4.36861e35i	0.402314	−	0.402314i	0.879048	+	0.476734i	$0.158179\pi$
$468$	3.56359e35	−	8.86470e35i	0.318837	−	0.793131i
$469$	1.19147e35	+	1.19147e35i	0.103574	+	0.103574i
$470$	−3.68392e35	−	1.80265e36i	−0.311164	−	1.52262i
$471$			3.80669e33i			0.00312439i
$472$	−3.00578e33	+	2.07742e33i	−0.00239740	+	0.00165694i
$473$			4.35912e35i			0.337888i
$474$	1.47677e36	−	3.01795e35i	1.11251	−	0.227355i
$475$	−2.30215e36	−	2.30215e36i	−1.68566	−	1.68566i
$476$	7.32523e35	−	3.12447e35i	0.521348	−	0.222373i
$477$	−7.03700e35	+	7.03700e35i	−0.486844	+	0.486844i
$478$	1.72265e36	+	1.13803e36i	1.15856	+	0.765383i
$479$	−2.22281e36			−1.45336			−0.726678	−	0.686978i	$-0.758937\pi$
$479$	−2.22281e36			−1.45336			−0.726678	+	0.686978i	$0.758937\pi$
$480$	−1.60136e36	+	3.62350e35i	−1.01797	+	0.230341i
$481$	−2.51559e35			−0.155482
$482$	1.04577e36	+	6.90866e35i	0.628492	+	0.415202i
$483$	1.08307e35	−	1.08307e35i	0.0632954	−	0.0632954i
$484$	7.33485e35	−	3.12858e35i	0.416849	−	0.177801i
$485$	−1.35368e36	−	1.35368e36i	−0.748171	−	0.748171i
$486$	−1.79404e36	+	3.66631e35i	−0.964365	+	0.197079i
$487$		−	2.95075e36i		−	1.54274i	−0.636390	−	0.771368i	$-0.719573\pi$
$487$		−	2.95075e36i		−	1.54274i	0.636390	−	0.771368i	$-0.280427\pi$
$488$	1.83719e36	+	2.65819e36i	0.934299	+	1.35182i
$489$		−	2.23470e36i		−	1.10548i
$490$	−5.04100e35	−	2.46671e36i	−0.242588	−	1.18706i
$491$	−1.39440e35	−	1.39440e35i	−0.0652813	−	0.0652813i	0.673712	−	0.738994i	$-0.264699\pi$
$491$	−1.39440e35	−	1.39440e35i	−0.0652813	−	0.0652813i	−0.738994	+	0.673712i	$0.764699\pi$
$492$	−3.97800e35	+	9.89557e35i	−0.181190	+	0.450725i
$493$	−1.25733e36	+	1.25733e36i	−0.557206	+	0.557206i
$494$	−2.56101e36	+	3.87661e36i	−1.10433	+	1.67162i
$495$	−1.73016e36			−0.725964
$496$	6.96721e35	−	7.26534e35i	0.284483	−	0.296656i
$497$	2.03017e36			0.806717
$498$	4.42012e35	−	6.69076e35i	0.170938	−	0.258749i
$499$	−2.67083e36	+	2.67083e36i	−1.00529	+	1.00529i	−0.00529915	+	0.999986i	$0.501687\pi$
$499$	−2.67083e36	+	2.67083e36i	−1.00529	+	1.00529i	−0.999986	+	0.00529915i	$0.998313\pi$
$500$	−2.92959e36	−	1.17769e36i	−1.07328	−	0.431455i
$501$	1.64637e36	+	1.64637e36i	0.587110	+	0.587110i
$502$	−9.89823e35	−	4.84350e36i	−0.343603	−	1.68135i
$503$			1.14761e36i			0.387817i	0.981020	+	0.193909i	$0.0621165\pi$
$503$			1.14761e36i			0.387817i	−0.981020	+	0.193909i	$0.937883\pi$
$504$	−1.67256e35	+	9.15804e35i	−0.0550262	+	0.301294i
$505$		−	4.41965e36i		−	1.41564i
$506$	6.38644e35	−	1.30514e35i	0.199171	−	0.0407029i
$507$	1.55154e36	+	1.55154e36i	0.471146	+	0.471146i
$508$	2.05060e36	+	4.80758e36i	0.606347	+	1.42156i
$509$	1.23788e36	−	1.23788e36i	0.356441	−	0.356441i	−0.506058	−	0.862499i	$-0.668898\pi$
$509$	1.23788e36	−	1.23788e36i	0.356441	−	0.356441i	0.862499	+	0.506058i	$0.168898\pi$
$510$	−3.43138e36	−	2.26688e36i	−0.962215	−	0.635669i
$511$	−3.50210e36			−0.956414
$512$	−1.93917e36	+	3.22093e36i	−0.515787	+	0.856717i
$513$	5.47594e36			1.41865
$514$	−3.61002e36	−	2.38489e36i	−0.910977	−	0.601820i
$515$	−1.62501e36	+	1.62501e36i	−0.399447	+	0.399447i
$516$	−4.75220e35	−	1.11414e36i	−0.113795	−	0.266789i
$517$	2.11855e36	+	2.11855e36i	0.494215	+	0.494215i
$518$	2.40154e35	−	4.90781e34i	0.0545805	−	0.0111541i
$519$		−	1.05783e36i		−	0.234238i
$520$	−1.96023e36	+	1.07332e37i	−0.422924	+	2.31571i
$521$			1.22145e36i			0.256783i	0.991724	+	0.128392i	$0.0409814\pi$
$521$			1.22145e36i			0.256783i	−0.991724	+	0.128392i	$0.959019\pi$
$522$	−4.16186e35	−	2.03652e36i	−0.0852582	−	0.417194i
$523$	−3.74804e36	−	3.74804e36i	−0.748224	−	0.748224i	0.225921	−	0.974146i	$-0.427461\pi$
$523$	−3.74804e36	−	3.74804e36i	−0.748224	−	0.748224i	−0.974146	+	0.225921i	$0.927461\pi$
$524$	4.71660e35	+	1.89606e35i	0.0917608	+	0.0368876i
$525$	2.06861e36	−	2.06861e36i	0.392219	−	0.392219i
$526$	1.71856e36	−	2.60139e36i	0.317583	−	0.480727i
$527$	2.52140e36			0.454150
$528$	1.85049e36	−	1.92967e36i	0.324884	−	0.338785i
$529$	5.40161e36			0.924424
$530$	6.26441e36	−	9.48245e36i	1.04509	−	1.58196i
$531$	7.56522e33	−	7.56522e33i	0.00123040	−	0.00123040i
$532$	1.68859e36	−	4.20050e36i	0.267743	−	0.666030i
$533$	5.01158e36	+	5.01158e36i	0.774743	+	0.774743i
$534$	−6.76936e35	−	3.31245e36i	−0.102033	−	0.499278i
$535$			1.73963e37i			2.55671i
$536$	−1.13288e36	−	1.63914e36i	−0.162352	−	0.234904i
$537$			4.39955e36i			0.614830i
$538$	1.00291e37	−	2.04956e36i	1.36679	−	0.279319i
$539$	2.89898e36	+	2.89898e36i	0.385298	+	0.385298i
$540$	1.18283e37	−	5.04518e36i	1.53322	−	0.653975i
$541$	4.95448e36	−	4.95448e36i	0.626375	−	0.626375i	−0.320779	−	0.947154i	$-0.603945\pi$
$541$	4.95448e36	−	4.95448e36i	0.626375	−	0.626375i	0.947154	+	0.320779i	$0.103945\pi$
$542$	−1.07552e36	−	7.10524e35i	−0.132626	−	0.0876170i
$543$	2.23287e36			0.268575
$544$	−9.18504e36	+	2.07836e36i	−1.07770	+	0.243857i
$545$	−6.75988e36			−0.773725
$546$	−3.48335e36	−	2.30121e36i	−0.388953	−	0.256955i
$547$	9.19559e36	−	9.19559e36i	1.00173	−	1.00173i	0.00173101	−	0.999999i	$-0.499449\pi$
$547$	9.19559e36	−	9.19559e36i	1.00173	−	1.00173i	0.999999	−	0.00173101i	$-0.000550999\pi$
$548$	2.46496e36	−	1.05139e36i	0.261982	−	0.111745i
$549$	−6.69037e36	−	6.69037e36i	−0.693783	−	0.693783i
$550$	1.21977e37	−	2.49274e36i	1.23419	−	0.252221i
$551$			1.01083e37i			0.997998i
$552$	−1.49001e36	+	1.02981e36i	−0.143553	+	0.0992155i
$553$			9.76007e36i			0.917622i
$554$	2.07285e36	+	1.01431e37i	0.190189	+	0.930652i
$555$	−8.95063e35	−	8.95063e35i	−0.0801490	−	0.0801490i
$556$	−7.53160e36	+	1.87354e37i	−0.658230	+	1.63740i
$557$	−5.29169e36	+	5.29169e36i	−0.451387	+	0.451387i	−0.895815	−	0.444428i	$-0.853407\pi$
$557$	−5.29169e36	+	5.29169e36i	−0.451387	+	0.451387i	0.444428	+	0.895815i	$0.353407\pi$
$558$	−1.62468e36	+	2.45929e36i	−0.135272	+	0.204761i
$559$	−8.04926e36			−0.654179
$560$	−2.22640e35	−	1.06290e37i	−0.0176630	−	0.843246i
$561$	6.69683e36			0.518645
$562$	−2.88064e36	+	4.36044e36i	−0.217796	+	0.329678i
$563$	2.12198e36	−	2.12198e36i	0.156631	−	0.156631i	−0.624441	−	0.781072i	$-0.714673\pi$
$563$	2.12198e36	−	2.12198e36i	0.156631	−	0.156631i	0.781072	+	0.624441i	$0.214673\pi$
$564$	−7.72434e36	−	3.10517e36i	−0.556664	−	0.223778i
$565$	3.00397e37	+	3.00397e37i	2.11369	+	2.11369i
$566$	−3.51361e36	−	1.71932e37i	−0.241397	−	1.18123i
$567$			3.54968e35i			0.0238132i
$568$	−2.36164e37	−	4.31314e36i	−1.54708	−	0.282547i
$569$		−	1.61527e36i		−	0.103331i	−0.998664	−	0.0516653i	$-0.983547\pi$
$569$		−	1.61527e36i		−	0.103331i	0.998664	−	0.0516653i	$-0.0164529\pi$
$570$	−2.29055e37	+	4.68099e36i	−1.43096	+	0.292434i
$571$	−1.11771e37	−	1.11771e37i	−0.681934	−	0.681934i	0.278501	−	0.960436i	$-0.410162\pi$
$571$	−1.11771e37	−	1.11771e37i	−0.681934	−	0.681934i	−0.960436	+	0.278501i	$0.910162\pi$
$572$	−6.97059e36	−	1.63423e37i	−0.415358	−	0.973795i
$573$	−1.21223e36	+	1.21223e36i	−0.0705499	+	0.0705499i
$574$	−5.76211e36	−	3.80663e36i	−0.327545	−	0.216387i
$575$	−8.43440e36			−0.468315
$576$	3.89128e36	−	1.02980e37i	0.211052	−	0.558532i
$577$	−1.55705e37			−0.824952			−0.412476	−	0.910969i	$-0.635336\pi$
$577$	−1.55705e37			−0.824952			−0.412476	+	0.910969i	$0.635336\pi$
$578$	−3.56095e36	−	2.35247e36i	−0.184306	−	0.121758i
$579$	1.35918e37	−	1.35918e37i	0.687254	−	0.687254i
$580$	9.31310e36	+	2.18343e37i	0.460062	+	1.07860i
$581$	3.67163e36	+	3.67163e36i	0.177207	+	0.177207i
$582$	−8.48669e36	+	1.73435e36i	−0.400201	+	0.0817855i
$583$			1.85063e37i			0.852697i
$584$	4.07389e37	+	7.44027e36i	1.83416	+	0.334977i
$585$		−	3.19479e37i		−	1.40552i
$586$	−2.54961e36	−	1.24760e37i	−0.109611	−	0.536361i
$587$	−1.11793e37	−	1.11793e37i	−0.469680	−	0.469680i	0.432131	−	0.901811i	$-0.357762\pi$
$587$	−1.11793e37	−	1.11793e37i	−0.469680	−	0.469680i	−0.901811	+	0.432131i	$0.857762\pi$
$588$	−1.05698e37	−	4.24904e36i	−0.433984	−	0.174461i
$589$	1.01354e37	−	1.01354e37i	0.406708	−	0.406708i
$590$	−6.73463e34	+	1.01942e35i	−0.00264126	+	0.00399809i
$591$	−7.74514e35			−0.0296892
$592$	−2.89791e36	+	6.07009e34i	−0.108578	+	0.00227432i
$593$	−4.68786e37			−1.71687			−0.858433	−	0.512925i	$-0.828562\pi$
$593$	−4.68786e37			−1.71687			−0.858433	+	0.512925i	$0.828562\pi$
$594$	−1.15423e37	+	1.74715e37i	−0.413213	+	0.625481i
$595$	1.88301e37	−	1.88301e37i	0.658982	−	0.658982i
$596$	1.03866e37	−	2.58374e37i	0.355342	−	0.883941i
$597$	−8.29441e36	−	8.29441e36i	−0.277416	−	0.277416i
$598$	2.40998e36	+	1.17928e37i	0.0788040	+	0.385611i
$599$		−	1.72430e37i		−	0.551253i	−0.961265	−	0.275626i	$-0.911115\pi$
$599$		−	1.72430e37i		−	0.551253i	0.961265	−	0.275626i	$-0.0888853\pi$
$600$	−2.84584e37	+	1.96688e37i	−0.889546	+	0.614803i
$601$		−	5.60779e36i		−	0.171390i	−0.996321	−	0.0856952i	$-0.972689\pi$
$601$		−	5.60779e36i		−	0.171390i	0.996321	−	0.0856952i	$-0.0273111\pi$
$602$	7.68433e36	−	1.57038e36i	0.229643	−	0.0469301i
$603$	4.12553e36	+	4.12553e36i	0.120558	+	0.120558i
$604$	4.05284e37	−	1.72868e37i	1.15814	−	0.493988i
$605$	1.88548e37	−	1.88548e37i	0.526896	−	0.526896i
$606$	−1.66855e37	−	1.10229e37i	−0.455993	−	0.301243i
$607$	−5.23038e37			−1.39793			−0.698965	−	0.715156i	$-0.746356\pi$
$607$	−5.23038e37			−1.39793			−0.698965	+	0.715156i	$0.746356\pi$
$608$	−2.85670e37	+	4.52758e37i	−0.746734	+	1.18350i
$609$	−9.08285e36			−0.232214
$610$	9.01536e37	+	5.95583e37i	2.25440	+	1.48933i
$611$	−3.91197e37	+	3.91197e37i	−0.956840	+	0.956840i
$612$	2.53639e37	−	1.08186e37i	0.606838	−	0.258838i
$613$	1.63422e37	+	1.63422e37i	0.382467	+	0.382467i	0.871990	−	0.489523i	$-0.162829\pi$
$613$	1.63422e37	+	1.63422e37i	0.382467	+	0.382467i	−0.489523	+	0.871990i	$0.662829\pi$
$614$	−5.95027e37	+	1.21600e37i	−1.36227	+	0.278395i
$615$			3.56631e37i			0.798740i
$616$	9.84288e36	+	1.42415e37i	0.215666	+	0.312044i
$617$		−	2.53027e37i		−	0.542397i	−0.962523	−	0.271198i	$-0.912580\pi$
$617$		−	2.53027e37i		−	0.542397i	0.962523	−	0.271198i	$-0.0874199\pi$
$618$	2.08199e36	+	1.01878e37i	0.0436651	+	0.213666i
$619$	−2.38274e37	−	2.38274e37i	−0.488938	−	0.488938i	0.419033	−	0.907971i	$-0.362369\pi$
$619$	−2.38274e37	−	2.38274e37i	−0.488938	−	0.488938i	−0.907971	+	0.419033i	$0.862369\pi$
$620$	1.25547e37	−	3.12309e37i	0.252069	−	0.627042i
$621$	1.00311e37	−	1.00311e37i	0.197067	−	0.197067i
$622$	1.98690e37	−	3.00758e37i	0.381949	−	0.578158i
$623$	2.18922e37			0.411814
$624$	3.56319e37	+	3.41698e37i	0.655915	+	0.629001i
$625$	−1.10167e37			−0.198459
$626$	−1.77565e37	+	2.68781e37i	−0.313043	+	0.473854i
$627$	2.69194e37	−	2.69194e37i	0.464466	−	0.464466i
$628$	2.70446e35	+	1.08719e35i	0.00456694	+	0.00183590i
$629$	−5.13387e36	−	5.13387e36i	−0.0848518	−	0.0848518i
$630$	6.23291e36	+	3.04995e37i	0.100831	+	0.493396i
$631$		−	1.14370e38i		−	1.81099i	−0.424358	−	0.905494i	$-0.639500\pi$
$631$		−	1.14370e38i		−	1.81099i	0.424358	−	0.905494i	$-0.360500\pi$
$632$	2.07355e37	−	1.13536e38i	0.321390	−	1.75976i
$633$		−	1.39280e37i		−	0.211319i
$634$	1.10215e38	−	2.25236e37i	1.63695	−	0.334528i
$635$	1.23583e38	+	1.23583e38i	1.79685	+	1.79685i
$636$	−2.01751e37	−	4.72999e37i	−0.287174	−	0.673270i
$637$	−5.35306e37	+	5.35306e37i	−0.745967	+	0.745967i
$638$	−3.22514e37	−	2.13063e37i	−0.440017	−	0.290689i
$639$	7.02956e37			0.939002
$640$	−1.99916e37	+	1.24117e38i	−0.261468	+	1.62332i
$641$	−1.51408e38			−1.93894			−0.969472	−	0.245204i	$-0.921145\pi$
$641$	−1.51408e38			−1.93894			−0.969472	+	0.245204i	$0.921145\pi$
$642$	6.56761e37	+	4.33877e37i	0.823540	+	0.544056i
$643$	8.02116e37	−	8.02116e37i	0.984894	−	0.984894i	−0.0149941	−	0.999888i	$-0.504773\pi$
$643$	8.02116e37	−	8.02116e37i	0.984894	−	0.984894i	0.999888	+	0.0149941i	$0.00477294\pi$
$644$	−4.60145e36	−	1.07879e37i	−0.0553267	−	0.129712i
$645$	−2.86398e37	−	2.86398e37i	−0.337221	−	0.337221i
$646$	−1.31380e38	+	2.68491e37i	−1.51493	+	0.309592i
$647$			3.59086e37i			0.405500i	0.979231	+	0.202750i	$0.0649879\pi$
$647$			3.59086e37i			0.405500i	−0.979231	+	0.202750i	$0.935012\pi$
$648$	7.54137e35	−	4.12925e36i	0.00834042	−	0.0456677i
$649$		−	1.98955e35i		−	0.00215502i
$650$	4.60293e37	+	2.25235e38i	0.488320	+	2.38949i
$651$	9.10720e36	+	9.10720e36i	0.0946328	+	0.0946328i
$652$	−1.58764e38	−	6.38229e37i	−1.61588	−	0.649582i
$653$	−4.02202e37	+	4.02202e37i	−0.400974	+	0.400974i	−0.878576	−	0.477602i	$-0.841506\pi$
$653$	−4.02202e37	+	4.02202e37i	−0.400974	+	0.400974i	0.477602	+	0.878576i	$0.341506\pi$
$654$	−1.68597e37	+	2.55205e37i	−0.164645	+	0.249224i
$655$	1.69984e37			0.162611
$656$	5.89418e37	+	5.65233e37i	0.552360	+	0.529694i
$657$	−1.21262e38			−1.11325
$658$	2.97140e37	−	4.49782e37i	0.267247	−	0.404532i
$659$	1.11797e38	−	1.11797e38i	0.985093	−	0.985093i	−0.0147975	−	0.999891i	$-0.504710\pi$
$659$	1.11797e38	−	1.11797e38i	0.985093	−	0.985093i	0.999891	+	0.0147975i	$0.00471037\pi$
$660$	3.33453e37	−	8.29489e37i	0.287867	−	0.716090i
$661$	5.04640e36	+	5.04640e36i	0.0426837	+	0.0426837i	0.728127	−	0.685443i	$-0.240391\pi$
$661$	5.04640e36	+	5.04640e36i	0.0426837	+	0.0426837i	−0.685443	+	0.728127i	$0.740391\pi$
$662$	2.63704e37	+	1.29038e38i	0.218541	+	1.06939i
$663$			1.23659e38i			1.00414i
$664$	−3.49106e37	−	5.05115e37i	−0.277772	−	0.401903i
$665$		−	1.51384e38i		−	1.18029i
$666$	8.31543e36	−	1.69935e36i	0.0635306	−	0.0129832i
$667$	1.85168e37	+	1.85168e37i	0.138634	+	0.138634i
$668$	1.63987e38	−	6.99462e37i	1.20317	−	0.513194i
$669$	−7.82882e37	+	7.82882e37i	−0.562916	+	0.562916i
$670$	−5.55921e37	−	3.67259e37i	−0.391745	−	0.258799i
$671$	−1.75947e38			−1.21515
$672$	−4.06829e37	−	2.56690e37i	−0.275376	−	0.173750i
$673$	4.49802e37			0.298413			0.149207	−	0.988806i	$-0.452328\pi$
$673$	4.49802e37			0.298413			0.149207	+	0.988806i	$0.452328\pi$
$674$	1.74761e38	+	1.15453e38i	1.13641	+	0.750749i
$675$	1.91589e38	−	1.91589e38i	1.22115	−	1.22115i
$676$	1.54541e38	−	6.59171e37i	0.965523	−	0.411830i
$677$	1.95050e38	+	1.95050e38i	1.19453	+	1.19453i	0.975780	+	0.218753i	$0.0701989\pi$
$677$	1.95050e38	+	1.95050e38i	1.19453	+	1.19453i	0.218753	+	0.975780i	$0.429801\pi$
$678$	1.88330e38	−	3.84873e37i	1.13062	−	0.231056i
$679$		−	5.60891e37i		−	0.330093i
$680$	−2.59050e38	+	1.79041e38i	−1.49456	+	1.03295i
$681$		−	1.80973e38i		−	1.02359i
$682$	1.09745e37	+	5.37013e37i	0.0608547	+	0.297780i
$683$	−2.44442e37	−	2.44442e37i	−0.132891	−	0.132891i	0.637532	−	0.770423i	$-0.279955\pi$
$683$	−2.44442e37	−	2.44442e37i	−0.132891	−	0.132891i	−0.770423	+	0.637532i	$0.779955\pi$
$684$	5.84682e37	−	1.45444e38i	0.311647	−	0.775245i
$685$	6.33637e37	−	6.33637e37i	0.331145	−	0.331145i
$686$	9.58395e37	−	1.45072e38i	0.491099	−	0.743378i
$687$	1.25472e38			0.630421
$688$	−9.27260e37	+	1.94228e36i	−0.456833	+	0.00956903i
$689$	−3.41726e38			−1.65089
$690$	−3.33846e37	+	5.05344e37i	−0.158155	+	0.239400i
$691$	−2.08737e37	+	2.08737e37i	−0.0969720	+	0.0969720i	−0.753928	−	0.656956i	$-0.771844\pi$
$691$	−2.08737e37	+	2.08737e37i	−0.0969720	+	0.0969720i	0.656956	+	0.753928i	$0.271844\pi$
$692$	−7.51536e37	−	3.02116e37i	−0.342387	−	0.137639i
$693$	−3.58442e37	−	3.58442e37i	−0.160148	−	0.160148i
$694$	−5.10927e37	−	2.50012e38i	−0.223875	−	1.09549i
$695$			6.75215e38i			2.90166i
$696$	1.05658e38	+	1.92967e37i	0.445327	+	0.0813313i
$697$			2.04555e38i			0.845606i
$698$	−3.62864e38	+	7.41552e37i	−1.47128	+	0.300672i
$699$	4.78236e37	+	4.78236e37i	0.190195	+	0.190195i
$700$	−8.78850e37	−	2.06044e38i	−0.342840	−	0.803777i
$701$	1.85808e38	−	1.85808e38i	0.711002	−	0.711002i	−0.255743	−	0.966745i	$-0.582320\pi$
$701$	1.85808e38	−	1.85808e38i	0.711002	−	0.711002i	0.966745	+	0.255743i	$0.0823199\pi$
$702$	−3.22618e38	−	2.13132e38i	−1.21098	−	0.800013i
$703$	−4.12735e37			−0.151976
$704$	−8.42433e37	−	1.86579e38i	−0.304302	−	0.673955i
$705$	−2.78381e38			−0.986477
$706$	−2.99136e38	−	1.97619e38i	−1.03993	−	0.687013i
$707$	9.15633e37	−	9.15633e37i	0.312291	−	0.312291i
$708$	2.16895e35	+	5.08504e35i	0.000725773	+	0.00170155i
$709$	2.44920e38	+	2.44920e38i	0.804082	+	0.804082i	0.983731	−	0.179649i	$-0.0574961\pi$
$709$	2.44920e38	+	2.44920e38i	0.804082	+	0.804082i	−0.179649	+	0.983731i	$0.557496\pi$
$710$	−7.86510e38	+	1.60732e38i	−2.53348	+	0.517744i
$711$			3.37947e38i			1.06809i
$712$	−2.54666e38	−	4.65104e37i	−0.789752	−	0.144235i
$713$		−	3.71330e37i		−	0.112993i
$714$	−2.41254e37	−	1.18053e38i	−0.0720359	−	0.352493i
$715$	−4.20093e38	−	4.20093e38i	−1.23087	−	1.23087i
$716$	3.12566e38	+	1.25651e38i	0.898701	+	0.361276i
$717$	2.20886e38	−	2.20886e38i	0.623245	−	0.623245i
$718$	3.00663e37	−	4.55114e37i	0.0832530	−	0.126020i
$719$	−4.30429e37			−0.116966			−0.0584832	−	0.998288i	$-0.518626\pi$
$719$	−4.30429e37			−0.116966			−0.0584832	+	0.998288i	$0.518626\pi$
$720$	−7.70901e36	−	3.68034e38i	−0.0205594	−	0.981521i
$721$	−6.73318e37			−0.176236
$722$	−2.05618e38	+	3.11245e38i	−0.528213	+	0.799558i
$723$	1.34093e38	−	1.34093e38i	0.338095	−	0.338095i
$724$	6.37706e37	−	1.58634e38i	0.157816	−	0.392578i
$725$	3.53661e38	+	3.53661e38i	0.859062	+	0.859062i
$726$	−2.41571e37	−	1.18208e38i	−0.0575971	−	0.281840i
$727$			4.92863e38i			1.15348i	0.816927	+	0.576742i	$0.195676\pi$
$727$			4.92863e38i			1.15348i	−0.816927	+	0.576742i	$0.804324\pi$
$728$	−2.62974e38	+	1.81752e38i	−0.604142	+	0.417548i
$729$			2.97636e38i			0.671218i
$730$	1.35675e39	−	2.77267e38i	3.00359	−	0.613817i
$731$	−1.64271e38	−	1.64271e38i	−0.357007	−	0.357007i
$732$	4.49700e38	−	1.91813e38i	0.959452	−	0.409241i
$733$	−3.72845e38	+	3.72845e38i	−0.780953	+	0.780953i	−0.979992	−	0.199039i	$-0.936218\pi$
$733$	−3.72845e38	+	3.72845e38i	−0.780953	+	0.780953i	0.199039	+	0.979992i	$0.436218\pi$
$734$	2.72883e38	+	1.80275e38i	0.561151	+	0.370714i
$735$	−3.80931e38			−0.769072
$736$	3.06082e37	+	1.35269e38i	0.0606718	+	0.268132i
$737$	1.08496e38			0.211155
$738$	−1.99516e38	−	1.31806e38i	−0.381256	−	0.251870i
$739$	5.17772e38	−	5.17772e38i	0.971491	−	0.971491i	−0.0281134	−	0.999605i	$-0.508950\pi$
$739$	5.17772e38	−	5.17772e38i	0.971491	−	0.971491i	0.999605	+	0.0281134i	$0.00894994\pi$
$740$	−8.91526e37	+	3.80268e37i	−0.164250	+	0.0700585i
$741$	4.97076e38	+	4.97076e38i	0.899244	+	0.899244i
$742$	3.26233e38	−	6.66693e37i	0.579529

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)

\(f(q)\)	\(=\)	\(q+(-9666.34 - 6385.89i) q^{2} +(-1.23946e6 + 1.23946e6i) q^{3} +(5.26586e7 + 1.23456e8i) q^{4} +(3.17355e9 + 3.17355e9i) q^{5} +(1.98961e10 - 4.06599e9i) q^{6} +1.31495e11i q^{7} +(2.79363e11 - 1.52964e12i) q^{8} +4.55307e12i q^{9} +O(q^{10})\)	\(q+(-9666.34 - 6385.89i) q^{2} +(-1.23946e6 + 1.23946e6i) q^{3} +(5.26586e7 + 1.23456e8i) q^{4} +(3.17355e9 + 3.17355e9i) q^{5} +(1.98961e10 - 4.06599e9i) q^{6} +1.31495e11i q^{7} +(2.79363e11 - 1.52964e12i) q^{8} +4.55307e12i q^{9} +(-1.04107e13 - 5.09425e13i) q^{10} +(5.98696e13 + 5.98696e13i) q^{11} +(-2.18288e14 - 8.77512e13i) q^{12} +(-1.10551e15 + 1.10551e15i) q^{13} +(8.39711e14 - 1.27107e15i) q^{14} -7.86698e15 q^{15} +(-1.24686e16 + 1.30021e16i) q^{16} -4.51231e16 q^{17} +(2.90754e16 - 4.40115e16i) q^{18} +(-1.81383e17 + 1.81383e17i) q^{19} +(-2.24680e17 + 5.58909e17i) q^{20} +(-1.62983e17 - 1.62983e17i) q^{21} +(-1.96399e17 - 9.61041e17i) q^{22} +6.64533e17i q^{23} +(1.54967e18 + 2.24219e18i) q^{24} +1.26922e19i q^{25} +(1.77459e19 - 3.62658e18i) q^{26} +(-1.50950e19 - 1.50950e19i) q^{27} +(-1.62339e19 + 6.92433e18i) q^{28} +(2.78644e19 - 2.78644e19i) q^{29} +(7.60449e19 + 5.02377e19i) q^{30} -5.58783e19 q^{31} +(2.03555e20 - 4.60596e19i) q^{32} -1.48412e20 q^{33} +(4.36176e20 + 2.88151e20i) q^{34} +(-4.17305e20 + 4.17305e20i) q^{35} +(-5.62105e20 + 2.39758e20i) q^{36} +(1.13775e20 + 1.13775e20i) q^{37} +(2.91160e21 - 5.95018e20i) q^{38} -2.74048e21i q^{39} +(5.74096e21 - 3.96782e21i) q^{40} -4.53327e21i q^{41} +(5.34657e20 + 2.61624e21i) q^{42} +(3.64051e21 + 3.64051e21i) q^{43} +(-4.23864e21 + 1.05439e22i) q^{44} +(-1.44494e22 + 1.44494e22i) q^{45} +(4.24364e21 - 6.42361e21i) q^{46} +3.53860e22 q^{47} +(-6.61276e20 - 3.15699e22i) q^{48} +4.84215e22 q^{49} +(8.10510e22 - 1.22687e23i) q^{50} +(5.59284e22 - 5.59284e22i) q^{51} +(-1.94697e23 - 7.82679e22i) q^{52} +(1.54555e23 + 1.54555e23i) q^{53} +(4.95184e22 + 2.42308e23i) q^{54} +3.79998e23i q^{55} +(2.01140e23 + 3.67348e22i) q^{56} -4.49634e23i q^{57} +(-4.47286e23 + 9.14079e22i) q^{58} +(-1.66157e21 - 1.66157e21i) q^{59} +(-4.14264e23 - 9.71229e23i) q^{60} +(-1.46942e24 + 1.46942e24i) q^{61} +(5.40139e23 + 3.56833e23i) q^{62} -5.98704e23 q^{63} +(-2.26176e24 - 8.54652e23i) q^{64} -7.01679e24 q^{65} +(1.43460e24 + 9.47744e23i) q^{66} +(9.06100e23 - 9.06100e23i) q^{67} +(-2.37612e24 - 5.57074e24i) q^{68} +(-8.23664e23 - 8.23664e23i) q^{69} +(6.69867e24 - 1.36895e24i) q^{70} -1.54392e25i q^{71} +(6.96457e24 + 1.27196e24i) q^{72} +2.66330e25i q^{73} +(-3.73232e23 - 1.82634e24i) q^{74} +(-1.57315e25 - 1.57315e25i) q^{75} +(-3.19442e25 - 1.28415e25i) q^{76} +(-7.87254e24 + 7.87254e24i) q^{77} +(-1.75004e25 + 2.64904e25i) q^{78} +7.42240e25 q^{79} +(-8.08322e25 + 1.69315e24i) q^{80} +2.69949e24 q^{81} +(-2.89489e25 + 4.38201e25i) q^{82} +(2.79222e25 - 2.79222e25i) q^{83} +(1.15388e25 - 2.87037e25i) q^{84} +(-1.43200e26 - 1.43200e26i) q^{85} +(-1.19425e25 - 5.84383e25i) q^{86} +6.90738e25i q^{87} +(1.08305e26 - 7.48538e25i) q^{88} -1.66487e26i q^{89} +(2.31945e26 - 4.74004e25i) q^{90} +(-1.45369e26 - 1.45369e26i) q^{91} +(-8.20409e25 + 3.49934e25i) q^{92} +(6.92590e25 - 6.92590e25i) q^{93} +(-3.42053e26 - 2.25971e26i) q^{94} -1.15125e27 q^{95} +(-1.95210e26 + 3.09388e26i) q^{96} -4.26550e26 q^{97} +(-4.68059e26 - 3.09214e26i) q^{98} +(-2.72590e26 + 2.72590e26i) 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