LMFDB - Embedded newform 20.20.e.b.3.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,20,Mod(3,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("20.3");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	20.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:	$45.7633393113$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.50
Character	$\chi$	$=$	20.3
Dual form			20.20.e.b.7.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(698.639 + 190.241i) q^{2} +(-31214.8 + 31214.8i) q^{3} +(451905. + 265819. i) q^{4} +(648675. + 4.31888e6i) q^{5} +(-2.77462e7 + 1.58695e7i) q^{6} +(-3.60017e7 - 3.60017e7i) q^{7} +(2.65149e8 + 2.71683e8i) q^{8} -7.86460e8i q^{9} +(-3.68437e8 + 3.14074e9i) q^{10} +1.35477e10i q^{11} +(-2.24036e10 + 5.80861e9i) q^{12} +(-5.93370e9 - 5.93370e9i) q^{13} +(-1.83032e10 - 3.20011e10i) q^{14} +(-1.55061e11 - 1.14564e11i) q^{15} +(1.33558e11 + 2.40250e11i) q^{16} +(-6.05914e11 + 6.05914e11i) q^{17} +(1.49617e11 - 5.49452e11i) q^{18} +2.07691e12 q^{19} +(-8.54902e11 + 2.12415e12i) q^{20} +2.24757e12 q^{21} +(-2.57732e12 + 9.46492e12i) q^{22} +(6.76866e12 - 6.76866e12i) q^{23} +(-1.67571e13 - 2.03954e11i) q^{24} +(-1.82319e13 + 5.60310e12i) q^{25} +(-3.01668e12 - 5.27434e12i) q^{26} +(-1.17306e13 - 1.17306e13i) q^{27} +(-6.69939e12 - 2.58393e13i) q^{28} -1.06685e14i q^{29} +(-8.65368e13 - 1.09538e14i) q^{30} +1.97706e13i q^{31} +(4.76035e13 + 1.93256e14i) q^{32} +(-4.22887e14 - 4.22887e14i) q^{33} +(-5.38584e14 + 3.08045e14i) q^{34} +(1.32133e14 - 1.78840e14i) q^{35} +(2.09056e14 - 3.55405e14i) q^{36} +(1.20369e13 - 1.20369e13i) q^{37} +(1.45101e15 + 3.95113e14i) q^{38} +3.70438e14 q^{39} +(-1.00137e15 + 1.32138e15i) q^{40} -2.08906e15 q^{41} +(1.57024e15 + 4.27579e14i) q^{42} +(1.49558e15 - 1.49558e15i) q^{43} +(-3.60123e15 + 6.12225e15i) q^{44} +(3.39662e15 - 5.10157e14i) q^{45} +(6.01652e15 - 3.44117e15i) q^{46} +(7.49783e14 + 7.49783e14i) q^{47} +(-1.16683e16 - 3.33037e15i) q^{48} -8.80666e15i q^{49} +(-1.38035e16 + 4.46086e14i) q^{50} -3.78269e16i q^{51} +(-1.10417e15 - 4.25876e15i) q^{52} +(1.34040e16 + 1.34040e16i) q^{53} +(-5.96379e15 - 1.04271e16i) q^{54} +(-5.85106e16 + 8.78803e15i) q^{55} +(2.35231e14 - 1.93268e16i) q^{56} +(-6.48302e16 + 6.48302e16i) q^{57} +(2.02959e16 - 7.45344e16i) q^{58} +4.82890e16 q^{59} +(-3.96193e16 - 9.29904e16i) q^{60} -7.43386e16 q^{61} +(-3.76117e15 + 1.38125e16i) q^{62} +(-2.83139e16 + 2.83139e16i) q^{63} +(-3.50760e15 + 1.44072e17i) q^{64} +(2.17779e16 - 2.94760e16i) q^{65} +(-2.14995e17 - 3.75895e17i) q^{66} +(-2.26777e17 - 2.26777e17i) q^{67} +(-4.34879e17 + 1.12752e17i) q^{68} +4.22564e17i q^{69} +(1.26336e17 - 9.98075e16i) q^{70} +2.81605e17i q^{71} +(2.13667e17 - 2.08529e17i) q^{72} +(-2.08722e17 - 2.08722e17i) q^{73} +(1.06994e16 - 6.11954e15i) q^{74} +(3.94206e17 - 7.44004e17i) q^{75} +(9.38565e17 + 5.52082e17i) q^{76} +(4.87738e17 - 4.87738e17i) q^{77} +(2.58802e17 + 7.04724e16i) q^{78} +1.57651e18 q^{79} +(-9.50975e17 + 7.32665e17i) q^{80} +1.64640e18 q^{81} +(-1.45950e18 - 3.97424e17i) q^{82} +(-7.69941e17 + 7.69941e17i) q^{83} +(1.01569e18 + 5.97446e17i) q^{84} +(-3.00991e18 - 2.22383e18i) q^{85} +(1.32939e18 - 7.60349e17i) q^{86} +(3.33015e18 + 3.33015e18i) q^{87} +(-3.68066e18 + 3.59214e18i) q^{88} +4.16046e18i q^{89} +(2.47007e18 + 2.89761e17i) q^{90} +4.27246e17i q^{91} +(4.85803e18 - 1.25955e18i) q^{92} +(-6.17134e17 - 6.17134e17i) q^{93} +(3.81188e17 + 6.66467e17i) q^{94} +(1.34724e18 + 8.96991e18i) q^{95} +(-7.51838e18 - 4.54652e18i) q^{96} +(-1.04131e18 + 1.04131e18i) q^{97} +(1.67539e18 - 6.15267e18i) q^{98} +1.06547e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 1026 q^{2} - 7131840 q^{5} - 50939608 q^{6} + 1332591828 q^{8} + 1805468790 q^{10} + 25565343280 q^{12} - 99498527404 q^{13} + 759936037048 q^{16} + 1103360788948 q^{17} - 2932289137902 q^{18} - 4821918866500 q^{20}+ \cdots + 66\!\cdots\!58 q^{98}+O(q^{100}) $ 108 * q - 1026 * q^2 - 7131840 * q^5 - 50939608 * q^6 + 1332591828 * q^8 + 1805468790 * q^10 + 25565343280 * q^12 - 99498527404 * q^13 + 759936037048 * q^16 + 1103360788948 * q^17 - 2932289137902 * q^18 - 4821918866500 * q^20 + 3306300862704 * q^21 + 26555173338440 * q^22 - 57672549609740 * q^25 - 151870176076556 * q^26 + 145347487073040 * q^28 + 265510366207880 * q^30 + 451426657209224 * q^32 - 229672757216560 * q^33 - 2556468817119620 * q^36 - 2904533279226852 * q^37 + 4500710811976960 * q^38 + 2246744304601900 * q^40 - 4721437306521104 * q^41 + 452761724453480 * q^42 - 970083854699780 * q^45 + 8478786115826952 * q^46 + 16046505545373280 * q^48 + 56844159661370 * q^50 - 101281742222079732 * q^52 - 27665397406960484 * q^53 - 10433774450699008 * q^56 + 83589162043122240 * q^57 - 22879145244078184 * q^58 + 145234473586307920 * q^60 - 6358689987281664 * q^61 - 371338823915128280 * q^62 - 91631698278804820 * q^65 + 331374884002311600 * q^66 - 694094458817479804 * q^68 - 165782163012631200 * q^70 - 215667461842637436 * q^72 + 1087298370549745276 * q^73 + 1949878275840327200 * q^76 - 1250723257104163920 * q^77 + 668342418678475560 * q^78 + 4071497833979030320 * q^80 - 12135903560578575228 * q^81 - 3459475352437471112 * q^82 + 14947305238413951060 * q^85 + 11624244909135363112 * q^86 - 5598373834541334880 * q^88 - 9907327634674956330 * q^90 + 27521624775955257680 * q^92 - 25916131489404857680 * q^93 - 50213774290767283648 * q^96 + 8468568053676169148 * q^97 + 66196294974841827558 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	698.639	+	190.241i	0.964868	+	0.262736i
$2$	698.639	+	190.241i	0.964868	+	0.262736i
$3$	−31214.8	+	31214.8i	−0.915605	+	0.915605i	−0.996706	−	0.0811013i	$-0.974156\pi$
$3$	−31214.8	+	31214.8i	−0.915605	+	0.915605i	0.0811013	+	0.996706i	$0.474156\pi$
$4$	451905.	+	265819.i	0.861940	+	0.507010i
$5$	648675.	+	4.31888e6i	0.148529	+	0.988908i
$5$	648675.	+	4.31888e6i	0.148529	+	0.988908i
$6$	−2.77462e7	+	1.58695e7i	−1.12400	+	0.642876i
$7$	−3.60017e7	−	3.60017e7i	−0.337203	−	0.337203i	0.518111	−	0.855314i	$-0.326635\pi$
$7$	−3.60017e7	−	3.60017e7i	−0.337203	−	0.337203i	−0.855314	+	0.518111i	$0.826635\pi$
$8$	2.65149e8	+	2.71683e8i	0.698449	+	0.715660i
$9$		−	7.86460e8i		−	0.676663i
$10$	−3.68437e8	+	3.14074e9i	−0.116510	+	0.993190i
$11$			1.35477e10i			1.73234i	0.499748	+	0.866171i	$0.333426\pi$
$11$			1.35477e10i			1.73234i	−0.499748	+	0.866171i	$0.666574\pi$
$12$	−2.24036e10	+	5.80861e9i	−1.25342	+	0.324975i
$13$	−5.93370e9	−	5.93370e9i	−0.155190	−	0.155190i	0.625241	−	0.780431i	$-0.285000\pi$
$13$	−5.93370e9	−	5.93370e9i	−0.155190	−	0.155190i	−0.780431	+	0.625241i	$0.785000\pi$
$14$	−1.83032e10	−	3.20011e10i	−0.236761	−	0.413951i
$15$	−1.55061e11	−	1.14564e11i	−1.04144	−	0.769455i
$16$	1.33558e11	+	2.40250e11i	0.485881	+	0.874025i
$17$	−6.05914e11	+	6.05914e11i	−1.23921	+	1.23921i	−0.278890	+	0.960323i	$0.589966\pi$
$17$	−6.05914e11	+	6.05914e11i	−1.23921	+	1.23921i	−0.960323	+	0.278890i	$0.910034\pi$
$18$	1.49617e11	−	5.49452e11i	0.177784	−	0.652891i
$19$	2.07691e12			1.47658			0.738292	−	0.674481i	$-0.235633\pi$
$19$	2.07691e12			1.47658			0.738292	+	0.674481i	$0.235633\pi$
$20$	−8.54902e11	+	2.12415e12i	−0.373363	+	0.927685i
$21$	2.24757e12			0.617489
$22$	−2.57732e12	+	9.46492e12i	−0.455148	+	1.67148i
$23$	6.76866e12	−	6.76866e12i	0.783589	−	0.783589i	−0.196846	−	0.980434i	$-0.563070\pi$
$23$	6.76866e12	−	6.76866e12i	0.783589	−	0.783589i	0.980434	+	0.196846i	$0.0630698\pi$
$24$	−1.67571e13	−	2.03954e11i	−1.29476	−	0.0157589i
$25$	−1.82319e13	+	5.60310e12i	−0.955878	+	0.293764i
$26$	−3.01668e12	−	5.27434e12i	−0.108964	−	0.190512i
$27$	−1.17306e13	−	1.17306e13i	−0.296048	−	0.296048i
$28$	−6.69939e12	−	2.58393e13i	−0.119683	−	0.461614i
$29$		−	1.06685e14i		−	1.36560i	−0.730606	−	0.682799i	$-0.760762\pi$
$29$		−	1.06685e14i		−	1.36560i	0.730606	−	0.682799i	$-0.239238\pi$
$30$	−8.65368e13	−	1.09538e14i	−0.802692	−	1.01605i
$31$			1.97706e13i			0.134302i	0.997743	+	0.0671511i	$0.0213910\pi$
$31$			1.97706e13i			0.134302i	−0.997743	+	0.0671511i	$0.978609\pi$
$32$	4.76035e13	+	1.93256e14i	0.239174	+	0.970977i
$33$	−4.22887e14	−	4.22887e14i	−1.58614	−	1.58614i
$34$	−5.38584e14	+	3.08045e14i	−1.52126	+	0.870091i
$35$	1.32133e14	−	1.78840e14i	0.283378	−	0.383547i
$36$	2.09056e14	−	3.55405e14i	0.343075	−	0.583243i
$37$	1.20369e13	−	1.20369e13i	0.0152264	−	0.0152264i	−0.699453	−	0.714679i	$-0.746573\pi$
$37$	1.20369e13	−	1.20369e13i	0.0152264	−	0.0152264i	0.714679	+	0.699453i	$0.246573\pi$
$38$	1.45101e15	+	3.95113e14i	1.42471	+	0.387951i
$39$	3.70438e14			0.284185
$40$	−1.00137e15	+	1.32138e15i	−0.603982	+	0.796998i
$41$	−2.08906e15			−0.996560			−0.498280	−	0.867016i	$-0.666035\pi$
$41$	−2.08906e15			−0.996560			−0.498280	+	0.867016i	$0.666035\pi$
$42$	1.57024e15	+	4.27579e14i	0.595795	+	0.162236i
$43$	1.49558e15	−	1.49558e15i	0.453794	−	0.453794i	−0.442818	−	0.896612i	$-0.646021\pi$
$43$	1.49558e15	−	1.49558e15i	0.453794	−	0.453794i	0.896612	+	0.442818i	$0.146021\pi$
$44$	−3.60123e15	+	6.12225e15i	−0.878315	+	1.49317i
$45$	3.39662e15	−	5.10157e14i	0.669158	−	0.100504i
$46$	6.01652e15	−	3.44117e15i	0.961936	−	0.550183i
$47$	7.49783e14	+	7.49783e14i	0.0977250	+	0.0977250i	0.754279	−	0.656554i	$-0.227987\pi$
$47$	7.49783e14	+	7.49783e14i	0.0977250	+	0.0977250i	−0.656554	+	0.754279i	$0.727987\pi$
$48$	−1.16683e16	−	3.33037e15i	−1.24514	−	0.355386i
$49$		−	8.80666e15i		−	0.772589i
$50$	−1.38035e16	+	4.46086e14i	−0.999478	+	0.0323001i
$51$		−	3.78269e16i		−	2.26926i
$52$	−1.10417e15	−	4.25876e15i	−0.0550815	−	0.212447i
$53$	1.34040e16	+	1.34040e16i	0.557976	+	0.557976i	0.928731	−	0.370755i	$-0.120901\pi$
$53$	1.34040e16	+	1.34040e16i	0.557976	+	0.557976i	−0.370755	+	0.928731i	$0.620901\pi$
$54$	−5.96379e15	−	1.04271e16i	−0.207865	−	0.363430i
$55$	−5.85106e16	+	8.78803e15i	−1.71313	+	0.257304i
$56$	2.35231e14	−	1.93268e16i	0.00580375	−	0.476841i
$57$	−6.48302e16	+	6.48302e16i	−1.35197	+	1.35197i
$58$	2.02959e16	−	7.45344e16i	0.358791	−	1.31762i
$59$	4.82890e16			0.725695			0.362847	−	0.931849i	$-0.381805\pi$
$59$	4.82890e16			0.725695			0.362847	+	0.931849i	$0.381805\pi$
$60$	−3.96193e16	−	9.29904e16i	−0.507540	−	1.19125i
$61$	−7.43386e16			−0.813919			−0.406959	−	0.913446i	$-0.633411\pi$
$61$	−7.43386e16			−0.813919			−0.406959	+	0.913446i	$0.633411\pi$
$62$	−3.76117e15	+	1.38125e16i	−0.0352860	+	0.129584i
$63$	−2.83139e16	+	2.83139e16i	−0.228173	+	0.228173i
$64$	−3.50760e15	+	1.44072e17i	−0.0243389	+	0.999704i
$65$	2.17779e16	−	2.94760e16i	0.130418	−	0.176519i
$66$	−2.14995e17	−	3.75895e17i	−1.11368	−	1.94715i
$67$	−2.26777e17	−	2.26777e17i	−1.01833	−	1.01833i	−0.999829	−	0.0185005i	$-0.994111\pi$
$67$	−2.26777e17	−	2.26777e17i	−1.01833	−	1.01833i	−0.0185005	−	0.999829i	$-0.505889\pi$
$68$	−4.34879e17	+	1.12752e17i	−1.69642	+	0.439834i
$69$			4.22564e17i			1.43492i
$70$	1.26336e17	−	9.98075e16i	0.374194	−	0.295619i
$71$			2.81605e17i			0.728930i	0.931217	+	0.364465i	$0.118748\pi$
$71$			2.81605e17i			0.728930i	−0.931217	+	0.364465i	$0.881252\pi$
$72$	2.13667e17	−	2.08529e17i	0.484261	−	0.472615i
$73$	−2.08722e17	−	2.08722e17i	−0.414955	−	0.414955i	0.468506	−	0.883460i	$-0.344793\pi$
$73$	−2.08722e17	−	2.08722e17i	−0.414955	−	0.414955i	−0.883460	+	0.468506i	$0.844793\pi$
$74$	1.06994e16	−	6.11954e15i	0.0186920	−	0.0106910i
$75$	3.94206e17	−	7.44004e17i	0.606235	−	1.14418i
$76$	9.38565e17	+	5.52082e17i	1.27273	+	0.748643i
$77$	4.87738e17	−	4.87738e17i	0.584150	−	0.584150i
$78$	2.58802e17	+	7.04724e16i	0.274201	+	0.0746655i
$79$	1.57651e18			1.47992			0.739961	−	0.672650i	$-0.234844\pi$
$79$	1.57651e18			1.47992			0.739961	+	0.672650i	$0.234844\pi$
$80$	−9.50975e17	+	7.32665e17i	−0.792162	+	0.610310i
$81$	1.64640e18			1.21879
$82$	−1.45950e18	−	3.97424e17i	−0.961549	−	0.261832i
$83$	−7.69941e17	+	7.69941e17i	−0.452080	+	0.452080i	−0.896045	−	0.443964i	$-0.853572\pi$
$83$	−7.69941e17	+	7.69941e17i	−0.452080	+	0.452080i	0.443964	+	0.896045i	$0.353572\pi$
$84$	1.01569e18	+	5.97446e17i	0.532238	+	0.313073i
$85$	−3.00991e18	−	2.22383e18i	−1.40953	−	1.04141i
$86$	1.32939e18	−	7.60349e17i	0.557079	−	0.318623i
$87$	3.33015e18	+	3.33015e18i	1.25035	+	1.25035i
$88$	−3.68066e18	+	3.59214e18i	−1.23977	+	1.20995i
$89$			4.16046e18i			1.25874i	0.777106	+	0.629370i	$0.216687\pi$
$89$			4.16046e18i			1.25874i	−0.777106	+	0.629370i	$0.783313\pi$
$90$	2.47007e18	+	2.89761e17i	0.672055	+	0.0788381i
$91$			4.27246e17i			0.104661i
$92$	4.85803e18	−	1.25955e18i	1.07269	−	0.278119i
$93$	−6.17134e17	−	6.17134e17i	−0.122968	−	0.122968i
$94$	3.81188e17	+	6.66467e17i	0.0686159	+	0.119968i
$95$	1.34724e18	+	8.96991e18i	0.219316	+	1.46021i
$96$	−7.51838e18	−	4.54652e18i	−1.10802	−	0.670042i
$97$	−1.04131e18	+	1.04131e18i	−0.139074	+	0.139074i	−0.773217	−	0.634142i	$-0.781353\pi$
$97$	−1.04131e18	+	1.04131e18i	−0.139074	+	0.139074i	0.634142	+	0.773217i	$0.281353\pi$
$98$	1.67539e18	−	6.15267e18i	0.202986	−	0.745446i
$99$	1.06547e19			1.17221
$100$	−9.72851e18	−	2.31433e18i	−0.972851	−	0.231433i
$101$	4.89330e18			0.445194			0.222597	−	0.974911i	$-0.428547\pi$
$101$	4.89330e18			0.445194			0.222597	+	0.974911i	$0.428547\pi$
$102$	7.19622e18	−	2.64273e19i	0.596215	−	2.18953i
$103$	2.69659e18	−	2.69659e18i	0.203639	−	0.203639i	−0.597918	−	0.801557i	$-0.704005\pi$
$103$	2.69659e18	−	2.69659e18i	0.203639	−	0.203639i	0.801557	+	0.597918i	$0.204005\pi$
$104$	3.87702e16	−	3.18539e18i	0.00267104	−	0.219455i
$105$	1.45794e18	+	9.70696e18i	0.0917152	+	0.610640i
$106$	6.81459e18	+	1.19146e19i	0.391773	+	0.684973i
$107$	7.05348e17	+	7.05348e17i	0.0370901	+	0.0370901i	0.725409	−	0.688319i	$-0.241651\pi$
$107$	7.05348e17	+	7.05348e17i	0.0370901	+	0.0370901i	−0.688319	+	0.725409i	$0.741651\pi$
$108$	−2.18289e18	−	8.41930e18i	−0.105076	−	0.405276i
$109$			3.21216e19i			1.41659i	0.705915	+	0.708296i	$0.250536\pi$
$109$			3.21216e19i			1.41659i	−0.705915	+	0.708296i	$0.749464\pi$
$110$	−4.25497e19	−	4.99146e18i	−1.72054	−	0.201835i
$111$			7.51458e17i			0.0278828i
$112$	3.84109e18	−	1.34577e19i	0.130883	−	0.458564i
$113$	2.56642e19	+	2.56642e19i	0.803680	+	0.803680i	0.983669	−	0.179988i	$-0.0576060\pi$
$113$	2.56642e19	+	2.56642e19i	0.803680	+	0.803680i	−0.179988	+	0.983669i	$0.557606\pi$
$114$	−5.76262e19	+	3.29595e19i	−1.65968	+	0.949260i
$115$	3.36237e19	+	2.48424e19i	0.891283	+	0.658511i
$116$	2.83590e19	−	4.82115e19i	0.692372	−	1.17706i
$117$	−4.66661e18	+	4.66661e18i	−0.105011	+	0.105011i
$118$	3.37366e19	+	9.18654e18i	0.700199	+	0.190666i
$119$	4.36278e19			0.835732
$120$	−9.98903e18	−	7.25040e19i	−0.176726	−	1.28274i
$121$	−1.22380e20			−2.00101
$122$	−5.19359e19	−	1.41422e19i	−0.785324	−	0.213845i
$123$	6.52094e19	−	6.52094e19i	0.912455	−	0.912455i
$124$	−5.25540e18	+	8.93442e18i	−0.0680926	+	0.115760i
$125$	−3.60257e19	−	7.51069e19i	−0.432481	−	0.901643i
$126$	−2.51676e19	+	1.43947e19i	−0.280106	+	0.160208i
$127$	1.44328e19	+	1.44328e19i	0.149010	+	0.149010i	0.777676	−	0.628666i	$-0.216399\pi$
$127$	1.44328e19	+	1.44328e19i	0.149010	+	0.149010i	−0.628666	+	0.777676i	$0.716399\pi$
$128$	−2.98590e19	+	9.99874e19i	−0.286142	+	0.958187i
$129$			9.33682e19i			0.830992i
$130$	2.08224e19	−	1.64500e19i	0.172214	−	0.136052i
$131$			4.14322e19i			0.318611i	0.987229	+	0.159306i	$0.0509255\pi$
$131$			4.14322e19i			0.318611i	−0.987229	+	0.159306i	$0.949074\pi$
$132$	−7.86930e19	−	3.03516e20i	−0.562968	−	2.17135i
$133$	−7.47722e19	−	7.47722e19i	−0.497908	−	0.497908i
$134$	−1.15293e20	−	2.01577e20i	−0.715002	−	1.25010i
$135$	4.30535e19	−	5.82721e19i	0.248793	−	0.336737i
$136$	−3.25273e20	−	3.95898e18i	−1.75238	−	0.0213286i
$137$	−5.44687e19	+	5.44687e19i	−0.273717	+	0.273717i	−0.830594	−	0.556878i	$-0.811999\pi$
$137$	−5.44687e19	+	5.44687e19i	−0.273717	+	0.273717i	0.556878	+	0.830594i	$0.311999\pi$
$138$	−8.03889e19	+	2.95220e20i	−0.377003	+	1.38450i
$139$	7.40281e19			0.324157			0.162079	−	0.986778i	$-0.448180\pi$
$139$	7.40281e19			0.324157			0.162079	+	0.986778i	$0.448180\pi$
$140$	1.07251e20	−	4.56951e19i	0.438717	−	0.186919i
$141$	−4.68085e19			−0.178955
$142$	−5.35727e19	+	1.96740e20i	−0.191516	+	0.703321i
$143$	8.03876e19	−	8.03876e19i	0.268842	−	0.268842i
$144$	1.88947e20	−	1.05038e20i	0.591421	−	0.328778i
$145$	4.60760e20	−	6.92040e19i	1.35045	−	0.202832i
$146$	−1.06114e20	−	1.85529e20i	−0.291353	−	0.509400i
$147$	2.74898e20	+	2.74898e20i	0.707386	+	0.707386i
$148$	8.63917e18	−	2.23989e18i	0.0208442	−	0.00540432i
$149$			6.37057e20i			1.44181i	0.693032	+	0.720907i	$0.256274\pi$
$149$			6.37057e20i			1.44181i	−0.693032	+	0.720907i	$0.743726\pi$
$150$	4.16948e20	−	4.44796e20i	0.885553	−	0.944701i
$151$			6.54094e20i			1.30425i	0.758113	+	0.652123i	$0.226121\pi$
$151$			6.54094e20i			1.30425i	−0.758113	+	0.652123i	$0.773879\pi$
$152$	5.50689e20	+	5.64260e20i	1.03132	+	1.05673i
$153$	4.76527e20	+	4.76527e20i	0.838530	+	0.838530i
$154$	4.33540e20	−	2.47965e20i	0.717105	−	0.410151i
$155$	−8.53867e19	+	1.28247e19i	−0.132813	+	0.0199478i
$156$	1.67403e20	+	9.84695e19i	0.244951	+	0.144085i
$157$	−5.62588e19	+	5.62588e19i	−0.0774718	+	0.0774718i	−0.744781	−	0.667309i	$-0.767446\pi$
$157$	−5.62588e19	+	5.62588e19i	−0.0774718	+	0.0774718i	0.667309	+	0.744781i	$0.267446\pi$
$158$	1.10141e21	+	2.99916e20i	1.42793	+	0.388828i
$159$	−8.36808e20			−1.02177
$160$	−8.03771e20	+	3.30954e20i	−0.924682	+	0.380740i
$161$	−4.87366e20			−0.528457
$162$	1.15024e21	+	3.13213e20i	1.17597	+	0.320219i
$163$	−4.69649e20	+	4.69649e20i	−0.452888	+	0.452888i	−0.896312	−	0.443424i	$-0.853764\pi$
$163$	−4.69649e20	+	4.69649e20i	−0.452888	+	0.452888i	0.443424	+	0.896312i	$0.353764\pi$
$164$	−9.44055e20	−	5.55312e20i	−0.858975	−	0.505266i
$165$	1.55208e21	−	2.10071e21i	1.33296	−	1.80413i
$166$	−6.84385e20	+	3.91437e20i	−0.554976	+	0.317420i
$167$	−3.41519e20	−	3.41519e20i	−0.261582	−	0.261582i	0.564114	−	0.825697i	$-0.309218\pi$
$167$	−3.41519e20	−	3.41519e20i	−0.261582	−	0.261582i	−0.825697	+	0.564114i	$0.809218\pi$
$168$	5.95939e20	+	6.10624e20i	0.431284	+	0.441912i
$169$		−	1.39150e21i		−	0.951832i
$170$	−1.67978e21	−	2.12626e21i	−1.08639	−	1.37515i
$171$		−	1.63341e21i		−	0.999150i
$172$	1.07341e21	−	2.78305e20i	0.621221	−	0.161065i
$173$	−1.82907e21	−	1.82907e21i	−1.00183	−	1.00183i	−0.999998	−	0.00183021i	$-0.999417\pi$
$173$	−1.82907e21	−	1.82907e21i	−1.00183	−	1.00183i	−0.00183021	−	0.999998i	$-0.500583\pi$
$174$	1.69304e21	+	2.96010e21i	0.877910	+	1.53493i
$175$	8.58100e20	+	4.54659e20i	0.421383	+	0.223267i
$176$	−3.25482e21	+	1.80940e21i	−1.51411	+	0.841712i
$177$	−1.50733e21	+	1.50733e21i	−0.664449	+	0.664449i
$178$	−7.91489e20	+	2.90666e21i	−0.330716	+	1.21452i
$179$	−1.47798e21			−0.585551			−0.292776	−	0.956181i	$-0.594579\pi$
$179$	−1.47798e21			−0.585551			−0.292776	+	0.956181i	$0.594579\pi$
$180$	1.67056e21	+	6.72346e20i	0.627731	+	0.252641i
$181$	5.99135e20			0.213589			0.106794	−	0.994281i	$-0.465941\pi$
$181$	5.99135e20			0.213589			0.106794	+	0.994281i	$0.465941\pi$
$182$	−8.12796e19	+	2.98491e20i	−0.0274981	+	0.100984i
$183$	2.32046e21	−	2.32046e21i	0.745228	−	0.745228i
$184$	3.63363e21	+	4.42257e19i	1.10808	+	0.0134867i
$185$	5.97939e19	+	4.41779e19i	0.0173191	+	0.0127960i
$186$	−3.13750e20	−	5.48558e20i	−0.0863396	−	0.150956i
$187$	−8.20871e21	−	8.20871e21i	−2.14674	−	2.14674i
$188$	1.39524e20	+	5.38137e20i	0.0346855	+	0.133781i
$189$			8.44639e20i			0.199657i
$190$	−7.65210e20	+	6.52303e21i	−0.172037	+	1.46653i
$191$			2.28579e21i			0.488899i	0.969662	+	0.244449i	$0.0786072\pi$
$191$			2.28579e21i			0.488899i	−0.969662	+	0.244449i	$0.921393\pi$
$192$	−4.38770e21	−	4.60668e21i	−0.893049	−	0.937618i
$193$	−3.02061e21	−	3.02061e21i	−0.585194	−	0.585194i	0.351132	−	0.936326i	$-0.385797\pi$
$193$	−3.02061e21	−	3.02061e21i	−0.585194	−	0.585194i	−0.936326	+	0.351132i	$0.885797\pi$
$194$	−9.25597e20	+	5.29398e20i	−0.170728	+	0.0976486i
$195$	2.40294e20	+	1.59988e21i	0.0422098	+	0.281033i
$196$	2.34098e21	−	3.97977e21i	0.391710	−	0.665925i
$197$	4.92576e20	−	4.92576e20i	0.0785315	−	0.0785315i	−0.666750	−	0.745281i	$-0.732315\pi$
$197$	4.92576e20	−	4.92576e20i	0.0785315	−	0.0785315i	0.745281	+	0.666750i	$0.232315\pi$
$198$	7.44378e21	+	2.02696e21i	1.13103	+	0.307982i
$199$	−8.99027e21			−1.30217			−0.651086	−	0.759004i	$-0.725686\pi$
$199$	−8.99027e21			−1.30217			−0.651086	+	0.759004i	$0.725686\pi$
$200$	−6.35643e21	−	3.46764e21i	−0.877867	−	0.478905i
$201$	1.41576e22			1.86477
$202$	3.41865e21	+	9.30906e20i	0.429553	+	0.116968i
$203$	−3.84084e21	+	3.84084e21i	−0.460484	+	0.460484i
$204$	1.00551e22	−	1.70942e22i	1.15054	−	1.95596i
$205$	−1.35512e21	−	9.02238e21i	−0.148019	−	0.985507i
$206$	2.39695e21	−	1.37094e21i	0.249989	−	0.142982i
$207$	−5.32328e21	−	5.32328e21i	−0.530226	−	0.530226i
$208$	6.33078e20	−	2.21806e21i	0.0602359	−	0.211044i
$209$			2.81372e22i			2.55795i
$210$	−8.28087e20	+	7.05902e21i	−0.0719437	+	0.613283i
$211$			4.16282e21i			0.345704i	0.984948	+	0.172852i	$0.0552982\pi$
$211$			4.16282e21i			0.345704i	−0.984948	+	0.172852i	$0.944702\pi$
$212$	2.49430e21	+	9.62041e21i	0.198042	+	0.763841i
$213$	−8.79022e21	−	8.79022e21i	−0.667411	−	0.667411i
$214$	3.58598e20	+	6.26970e20i	0.0260421	+	0.0455319i
$215$	7.42936e21	+	5.48907e21i	0.516162	+	0.381359i
$216$	7.66462e19	−	6.29733e21i	0.00509542	−	0.418645i
$217$	7.11773e20	−	7.11773e20i	0.0452871	−	0.0452871i
$218$	−6.11083e21	+	2.24414e22i	−0.372189	+	1.36682i
$219$	1.30304e22			0.759869
$220$	−2.87773e22	−	1.15819e22i	−1.60707	−	0.646792i
$221$	7.19061e21			0.384627
$222$	−1.42958e20	+	5.24998e20i	−0.00732580	+	0.0269032i
$223$	1.83906e22	−	1.83906e22i	0.903026	−	0.903026i	−0.0926711	−	0.995697i	$-0.529541\pi$
$223$	1.83906e22	−	1.83906e22i	0.903026	−	0.903026i	0.995697	+	0.0926711i	$0.0295405\pi$
$224$	5.24374e21	−	8.67135e21i	0.246766	−	0.408066i
$225$	4.40661e21	+	1.43387e22i	0.198779	+	0.646808i
$226$	1.30477e22	+	2.28124e22i	0.564290	+	0.986601i
$227$	2.18473e22	+	2.18473e22i	0.906049	+	0.906049i	0.995951	−	0.0899016i	$-0.0286553\pi$
$227$	2.18473e22	+	2.18473e22i	0.906049	+	0.906049i	−0.0899016	+	0.995951i	$0.528655\pi$
$228$	−4.65302e22	+	1.20640e22i	−1.85078	+	0.479854i
$229$		−	3.52273e22i		−	1.34413i	−0.740491	−	0.672066i	$-0.765407\pi$
$229$		−	3.52273e22i		−	1.34413i	0.740491	−	0.672066i	$-0.234593\pi$
$230$	1.87648e22	+	2.37524e22i	0.686956	+	0.869548i
$231$			3.04492e22i			1.06970i
$232$	2.89845e22	−	2.82874e22i	0.977305	−	0.953801i
$233$	−3.48184e22	−	3.48184e22i	−1.12701	−	1.12701i	−0.990661	−	0.136347i	$-0.956464\pi$
$233$	−3.48184e22	−	3.48184e22i	−1.12701	−	1.12701i	−0.136347	−	0.990661i	$-0.543536\pi$
$234$	−4.14806e21	+	2.37250e21i	−0.128912	+	0.0737319i
$235$	−2.75185e21	+	3.72458e21i	−0.0821260	+	0.111156i
$236$	2.18220e22	+	1.28361e22i	0.625505	+	0.367935i
$237$	−4.92103e22	+	4.92103e22i	−1.35502	+	1.35502i
$238$	3.04801e22	+	8.29979e21i	0.806371	+	0.219577i
$239$	5.45576e22			1.38700			0.693498	−	0.720459i	$-0.256069\pi$
$239$	5.45576e22			1.38700			0.693498	+	0.720459i	$0.256069\pi$
$240$	6.81449e21	−	5.25544e22i	0.166505	−	1.28411i
$241$	5.25020e22			1.23315			0.616573	−	0.787298i	$-0.288521\pi$
$241$	5.25020e22			1.23315			0.616573	+	0.787298i	$0.288521\pi$
$242$	−8.54993e22	−	2.32816e22i	−1.93071	−	0.525736i
$243$	−3.77581e22	+	3.77581e22i	−0.819881	+	0.819881i
$244$	−3.35940e22	−	1.97606e22i	−0.701549	−	0.412665i
$245$	3.80349e22	−	5.71266e21i	0.764019	−	0.114752i
$246$	5.79633e22	−	3.31523e22i	1.12013	−	0.640664i
$247$	−1.23237e22	−	1.23237e22i	−0.229151	−	0.229151i
$248$	−5.37132e21	+	5.24214e21i	−0.0961147	+	0.0938032i
$249$		−	4.80671e22i		−	0.827854i
$250$	−1.08806e22	−	5.93262e22i	−0.180394	−	0.983594i
$251$		−	2.05203e22i		−	0.327554i	−0.986497	−	0.163777i	$-0.947632\pi$
$251$		−	2.05203e22i		−	0.327554i	0.986497	−	0.163777i	$-0.0523678\pi$
$252$	−2.03215e22	+	5.26880e21i	−0.312357	+	0.0809853i
$253$	9.16994e22	+	9.16994e22i	1.35744	+	1.35744i
$254$	7.33762e21	+	1.28290e22i	0.104625	+	0.182925i
$255$	1.63370e23	−	2.45374e22i	2.24409	−	0.337051i
$256$	−3.98824e22	+	6.41747e22i	−0.527839	+	0.849345i
$257$	−9.28402e22	+	9.28402e22i	−1.18405	+	1.18405i	−0.205369	+	0.978685i	$0.565839\pi$
$257$	−9.28402e22	+	9.28402e22i	−1.18405	+	1.18405i	−0.978685	+	0.205369i	$0.934161\pi$
$258$	−1.77624e22	+	6.52306e22i	−0.218331	+	0.801797i
$259$	−8.66697e20			−0.0102688
$260$	1.76768e22	−	7.53135e21i	0.201910	−	0.0860252i
$261$	−8.39036e22			−0.924051
$262$	−7.88211e21	+	2.89462e22i	−0.0837105	+	0.307418i
$263$	−2.18462e22	+	2.18462e22i	−0.223767	+	0.223767i	−0.810083	−	0.586316i	$-0.800578\pi$
$263$	−2.18462e22	+	2.18462e22i	−0.223767	+	0.223767i	0.586316	+	0.810083i	$0.300578\pi$
$264$	2.76310e21	−	2.27019e23i	0.0272998	−	2.24297i
$265$	−4.91956e22	+	6.65853e22i	−0.468911	+	0.634662i
$266$	−3.80140e22	−	6.64635e22i	−0.349597	−	0.611234i
$267$	−1.29868e23	−	1.29868e23i	−1.15251	−	1.15251i
$268$	−4.21999e22	−	1.62763e23i	−0.361436	−	1.39404i
$269$			1.38110e23i			1.14177i	0.821030	+	0.570885i	$0.193400\pi$
$269$			1.38110e23i			1.14177i	−0.821030	+	0.570885i	$0.806600\pi$
$270$	4.11646e22	−	3.25207e22i	0.328525	−	0.259540i
$271$			2.01091e23i			1.54948i	0.632283	+	0.774738i	$0.282118\pi$
$271$			2.01091e23i			1.54948i	−0.632283	+	0.774738i	$0.717882\pi$
$272$	−2.26495e23	−	6.46462e22i	−1.68521	−	0.480992i
$273$	−1.33364e22	−	1.33364e22i	−0.0958280	−	0.0958280i
$274$	−4.84161e22	+	2.76918e22i	−0.336016	+	0.192185i
$275$	−7.59088e22	−	2.47000e23i	−0.508899	−	1.65591i
$276$	−1.12326e23	+	1.90959e23i	−0.727517	+	1.23681i
$277$	8.94767e22	−	8.94767e22i	0.559954	−	0.559954i	−0.369340	−	0.929294i	$-0.620416\pi$
$277$	8.94767e22	−	8.94767e22i	0.559954	−	0.559954i	0.929294	+	0.369340i	$0.120416\pi$
$278$	5.17189e22	+	1.40832e22i	0.312769	+	0.0851676i
$279$	1.55488e22			0.0908774
$280$	8.36227e22	−	1.15209e22i	0.472414	−	0.0650856i
$281$	5.66140e22			0.309182			0.154591	−	0.987979i	$-0.450594\pi$
$281$	5.66140e22			0.309182			0.154591	+	0.987979i	$0.450594\pi$
$282$	−3.27023e22	−	8.90490e21i	−0.172668	−	0.0470178i
$283$	−1.67208e22	+	1.67208e22i	−0.0853662	+	0.0853662i	−0.748500	−	0.663134i	$-0.769226\pi$
$283$	−1.67208e22	+	1.67208e22i	−0.0853662	+	0.0853662i	0.663134	+	0.748500i	$0.269226\pi$
$284$	−7.48560e22	+	1.27259e23i	−0.369575	+	0.628294i
$285$	−3.22047e23	−	2.37940e23i	−1.53778	−	1.13616i
$286$	7.14550e22	−	4.08689e22i	0.330031	−	0.188763i
$287$	7.52095e22	+	7.52095e22i	0.336043	+	0.336043i
$288$	1.51988e23	−	3.74382e22i	0.657025	−	0.161840i
$289$		−	4.95190e23i		−	2.07130i
$290$	3.35070e23	+	3.93068e22i	1.35630	+	0.159106i
$291$		−	6.50083e22i		−	0.254674i
$292$	−3.88401e22	−	1.49805e23i	−0.147280	−	0.568052i
$293$	3.59270e23	+	3.59270e23i	1.31880	+	1.31880i	0.914728	+	0.404069i	$0.132405\pi$
$293$	3.59270e23	+	3.59270e23i	1.31880	+	1.31880i	0.404069	+	0.914728i	$0.367595\pi$
$294$	1.39757e23	+	2.44351e23i	0.496678	+	0.868389i
$295$	3.13239e22	+	2.08554e23i	0.107787	+	0.717645i
$296$	6.46178e21	+	7.86478e19i	0.0215318	+	0.000262069i
$297$	1.58921e23	−	1.58921e23i	0.512857	−	0.512857i
$298$	−1.21194e23	+	4.45073e23i	−0.378816	+	1.39116i
$299$	−8.03263e22			−0.243210
$300$	3.75914e23	−	2.31432e23i	1.10265	−	0.678845i
$301$	−1.07687e23			−0.306041
$302$	−1.24435e23	+	4.56976e23i	−0.342672	+	1.25842i
$303$	−1.52743e23	+	1.52743e23i	−0.407621	+	0.407621i
$304$	2.77388e23	+	4.98977e23i	0.717445	+	1.29057i
$305$	−4.82216e22	−	3.21059e23i	−0.120891	−	0.804891i
$306$	2.42265e23	+	4.23575e23i	0.588759	+	1.02938i
$307$	−4.08161e23	−	4.08161e23i	−0.961649	−	0.961649i	0.0376421	−	0.999291i	$-0.488015\pi$
$307$	−4.08161e23	−	4.08161e23i	−0.961649	−	0.961649i	−0.999291	+	0.0376421i	$0.988015\pi$
$308$	3.50061e23	−	9.07609e22i	0.799673	−	0.207332i
$309$			1.68347e23i			0.372906i
$310$	−6.20943e22	−	7.28421e21i	−0.133388	−	0.0156476i
$311$			4.14179e22i			0.0862908i	0.999069	+	0.0431454i	$0.0137379\pi$
$311$			4.14179e22i			0.0862908i	−0.999069	+	0.0431454i	$0.986262\pi$
$312$	9.82210e22	+	1.00641e23i	0.198489	+	0.203380i
$313$	2.72892e23	+	2.72892e23i	0.534958	+	0.534958i	0.922044	−	0.387086i	$-0.126518\pi$
$313$	2.72892e23	+	2.72892e23i	0.534958	+	0.534958i	−0.387086	+	0.922044i	$0.626518\pi$
$314$	−5.00073e22	+	2.86018e22i	−0.0951046	+	0.0543954i
$315$	−1.40651e23	−	1.03918e23i	−0.259532	−	0.191752i
$316$	7.12431e23	+	4.19066e23i	1.27560	+	0.750335i
$317$	4.66550e23	−	4.66550e23i	0.810654	−	0.810654i	−0.174078	−	0.984732i	$-0.555694\pi$
$317$	4.66550e23	−	4.66550e23i	0.810654	−	0.810654i	0.984732	+	0.174078i	$0.0556944\pi$
$318$	−5.84627e23	−	1.59195e23i	−0.985873	−	0.268455i
$319$	1.44533e24			2.36568
$320$	−6.24507e23	+	7.83074e22i	−0.992230	+	0.124416i
$321$	−4.40345e22			−0.0679197
$322$	−3.40493e23	−	9.27169e22i	−0.509891	−	0.138844i
$323$	−1.25843e24	+	1.25843e24i	−1.82980	+	1.82980i
$324$	7.44018e23	+	4.37646e23i	1.05052	+	0.617939i
$325$	1.41430e23	+	7.49356e22i	0.193932	+	0.102753i
$326$	−4.17461e23	+	2.38768e23i	−0.555967	+	0.317987i
$327$	−1.00267e24	−	1.00267e24i	−1.29704	−	1.29704i
$328$	−5.53911e23	−	5.67560e23i	−0.696046	−	0.713199i
$329$		−	5.39868e22i		−	0.0659063i
$330$	1.48398e24	−	1.17237e24i	1.76014	−	1.39054i
$331$		−	1.92287e23i		−	0.221608i	−0.993842	−	0.110804i	$-0.964657\pi$
$331$		−	1.92287e23i		−	0.221608i	0.993842	−	0.110804i	$-0.0353425\pi$
$332$	−5.52606e23	+	1.43275e23i	−0.618876	+	0.160457i
$333$	−9.46654e21	−	9.46654e21i	−0.0103032	−	0.0103032i
$334$	−1.73627e23	−	3.03569e23i	−0.183665	−	0.321119i
$335$	8.32317e23	−	1.12653e24i	0.855782	−	1.15829i
$336$	3.00180e23	+	5.39978e23i	0.300026	+	0.539701i
$337$	−1.79914e23	+	1.79914e23i	−0.174816	+	0.174816i	−0.789092	−	0.614275i	$-0.789448\pi$
$337$	−1.79914e23	+	1.79914e23i	−0.174816	+	0.174816i	0.614275	+	0.789092i	$0.289448\pi$
$338$	2.64721e23	−	9.72158e23i	0.250080	−	0.918392i
$339$	−1.60221e24			−1.47171
$340$	−7.69056e23	−	1.80505e24i	−0.686923	−	1.61228i
$341$	−2.67845e23			−0.232657
$342$	3.10740e23	−	1.14116e24i	0.262512	−	0.964048i
$343$	−7.27433e23	+	7.27433e23i	−0.597722	+	0.597722i
$344$	8.02873e23	+	9.77195e21i	0.641714	+	0.00781045i
$345$	−1.82500e24	+	2.74107e23i	−1.41900	+	0.213127i
$346$	−9.29898e23	−	1.62583e24i	−0.703416	−	1.22985i
$347$	5.73666e23	+	5.73666e23i	0.422210	+	0.422210i	0.885964	−	0.463754i	$-0.153498\pi$
$347$	5.73666e23	+	5.73666e23i	0.422210	+	0.422210i	−0.463754	+	0.885964i	$0.653498\pi$
$348$	6.19693e23	+	2.39013e24i	0.443786	+	1.71166i
$349$		−	1.55959e23i		−	0.108685i	−0.998522	−	0.0543424i	$-0.982694\pi$
$349$		−	1.55959e23i		−	0.108685i	0.998522	−	0.0543424i	$-0.0173063\pi$
$350$	5.13008e23	+	4.80888e23i	0.347918	+	0.326135i
$351$			1.39211e23i			0.0918874i
$352$	−2.61817e24	+	6.44915e23i	−1.68206	+	0.414331i
$353$	1.91273e23	+	1.91273e23i	0.119617	+	0.119617i	0.764381	−	0.644764i	$-0.223045\pi$
$353$	1.91273e23	+	1.91273e23i	0.119617	+	0.119617i	−0.644764	+	0.764381i	$0.723045\pi$
$354$	−1.33983e24	+	7.66323e23i	−0.815680	+	0.466531i
$355$	−1.21622e24	+	1.82670e23i	−0.720844	+	0.108267i
$356$	−1.10593e24	+	1.88013e24i	−0.638194	+	1.08496i
$357$	−1.36183e24	+	1.36183e24i	−0.765200	+	0.765200i
$358$	−1.03258e24	−	2.81172e23i	−0.564980	−	0.153845i
$359$	2.38393e24			1.27027			0.635136	−	0.772401i	$-0.280944\pi$
$359$	2.38393e24			1.27027			0.635136	+	0.772401i	$0.280944\pi$
$360$	1.03921e24	+	7.87536e23i	0.539299	+	0.408692i
$361$	2.33513e24			1.18030
$362$	4.18579e23	+	1.13980e23i	0.206085	+	0.0561174i
$363$	3.82005e24	−	3.82005e24i	1.83213	−	1.83213i
$364$	−1.13570e23	+	1.93074e23i	−0.0530642	+	0.0902114i
$365$	7.66051e23	−	1.03684e24i	0.348719	−	0.471985i
$366$	2.06261e24	−	1.17972e24i	0.914844	−	0.523249i
$367$	1.07890e24	+	1.07890e24i	0.466288	+	0.466288i	0.900710	−	0.434421i	$-0.143047\pi$
$367$	1.07890e24	+	1.07890e24i	0.466288	+	0.466288i	−0.434421	+	0.900710i	$0.643047\pi$
$368$	2.53018e24	+	7.22162e23i	1.06561	+	0.304145i
$369$			1.64296e24i			0.674336i
$370$	3.33699e22	+	4.22396e22i	0.0133487	+	0.0168968i
$371$		−	9.65136e23i		−	0.376302i
$372$	−1.14840e23	−	4.42932e23i	−0.0436449	−	0.168337i
$373$	−1.10379e24	−	1.10379e24i	−0.408934	−	0.408934i	0.472433	−	0.881367i	$-0.343376\pi$
$373$	−1.10379e24	−	1.10379e24i	−0.408934	−	0.408934i	−0.881367	+	0.472433i	$0.843376\pi$
$374$	−4.17329e24	−	7.29655e24i	−1.50730	−	2.63535i
$375$	3.46898e24	+	1.21991e24i	1.22153	+	0.429566i
$376$	−4.89900e21	+	4.02507e23i	−0.00168199	+	0.138194i
$377$	−6.33037e23	+	6.33037e23i	−0.211927	+	0.211927i
$378$	−1.60685e23	+	5.90098e23i	−0.0524569	+	0.192642i
$379$	−1.10478e24			−0.351725			−0.175863	−	0.984415i	$-0.556271\pi$
$379$	−1.10478e24			−0.351725			−0.175863	+	0.984415i	$0.556271\pi$
$380$	−1.77555e24	+	4.41167e24i	−0.551302	+	1.36981i
$381$	−9.01034e23			−0.272869
$382$	−4.34850e23	+	1.59694e24i	−0.128451	+	0.471723i
$383$	−9.77352e23	+	9.77352e23i	−0.281619	+	0.281619i	−0.833755	−	0.552135i	$-0.813813\pi$
$383$	−9.77352e23	+	9.77352e23i	−0.281619	+	0.281619i	0.552135	+	0.833755i	$0.313813\pi$
$384$	−2.18904e24	−	4.05312e24i	−0.615328	−	1.13931i
$385$	2.42286e24	+	1.79010e24i	0.664434	+	0.490907i
$386$	−1.53567e24	−	2.68496e24i	−0.410884	−	0.718386i
$387$	−1.17621e24	−	1.17621e24i	−0.307066	−	0.307066i
$388$	−7.47371e23	+	1.93772e23i	−0.190386	+	0.0493617i
$389$		−	5.27127e24i		−	1.31037i	−0.755468	−	0.655185i	$-0.772590\pi$
$389$		−	5.27127e24i		−	1.31037i	0.755468	−	0.655185i	$-0.227410\pi$
$390$	−1.36483e23	+	1.16345e24i	−0.0331104	+	0.282250i
$391$			8.20245e24i			1.94207i
$392$	2.39261e24	−	2.33507e24i	0.552911	−	0.539613i
$393$	−1.29330e24	−	1.29330e24i	−0.291722	−	0.291722i
$394$	4.37840e23	−	2.50424e23i	0.0964055	−	0.0551395i
$395$	1.02264e24	+	6.80874e24i	0.219812	+	1.46351i
$396$	4.81490e24	+	2.83222e24i	1.01038	+	0.594323i
$397$	−2.58217e24	+	2.58217e24i	−0.529024	+	0.529024i	−0.920281	−	0.391257i	$-0.872040\pi$
$397$	−2.58217e24	+	2.58217e24i	−0.529024	+	0.529024i	0.391257	+	0.920281i	$0.372040\pi$
$398$	−6.28095e24	−	1.71032e24i	−1.25642	−	0.342127i
$399$	4.66799e24			0.911774
$400$	−3.78117e24	−	3.63188e24i	−0.721200	−	0.692727i
$401$	9.29628e22			0.0173156			0.00865780	−	0.999963i	$-0.497244\pi$
$401$	9.29628e22			0.0173156			0.00865780	+	0.999963i	$0.497244\pi$
$402$	9.89103e24	+	2.69335e24i	1.79926	+	0.489942i
$403$	1.17313e23	−	1.17313e23i	0.0208423	−	0.0208423i
$404$	2.21131e24	+	1.30073e24i	0.383730	+	0.225718i
$405$	1.06798e24	+	7.11062e24i	0.181026	+	1.20527i
$406$	−3.41405e24	+	1.95268e24i	−0.565291	+	0.323320i
$407$	1.63072e23	+	1.63072e23i	0.0263774	+	0.0263774i
$408$	1.02769e25	−	1.00297e25i	1.62402	−	1.58496i
$409$			1.04183e25i			1.60851i	0.594284	+	0.804256i	$0.297436\pi$
$409$			1.04183e25i			1.60851i	−0.594284	+	0.804256i	$0.702564\pi$
$410$	7.69686e23	−	6.56119e24i	0.116109	−	0.989773i
$411$		−	3.40045e24i		−	0.501232i
$412$	1.93541e24	−	5.01797e23i	0.278772	−	0.0722777i
$413$	−1.73848e24	−	1.73848e24i	−0.244706	−	0.244706i
$414$	−2.70635e24	−	4.73176e24i	−0.372289	−	0.650907i
$415$	−3.82472e24	−	2.82584e24i	−0.514213	−	0.379919i
$416$	8.64260e23	−	1.42919e24i	0.113568	−	0.187803i
$417$	−2.31077e24	+	2.31077e24i	−0.296800	+	0.296800i
$418$	−5.35285e24	+	1.96578e25i	−0.672064	+	2.46808i
$419$	7.03079e23			0.0862920			0.0431460	−	0.999069i	$-0.486262\pi$
$419$	7.03079e23			0.0862920			0.0431460	+	0.999069i	$0.486262\pi$
$420$	−1.92145e24	+	4.77417e24i	−0.230547	+	0.572835i
$421$	1.52805e25			1.79249			0.896247	−	0.443556i	$-0.146283\pi$
$421$	1.52805e25			1.79249			0.896247	+	0.443556i	$0.146283\pi$
$422$	−7.91938e23	+	2.90831e24i	−0.0908287	+	0.333558i
$423$	5.89674e23	−	5.89674e23i	0.0661269	−	0.0661269i
$424$	−8.75807e22	+	7.19571e24i	−0.00960357	+	0.789038i
$425$	7.65198e24	−	1.44420e25i	0.820501	−	1.54857i
$426$	−4.46893e24	−	7.81345e24i	−0.468611	−	0.819316i
$427$	2.67631e24	+	2.67631e24i	0.274456	+	0.274456i
$428$	1.31255e23	+	5.06245e23i	0.0131644	+	0.0507744i
$429$			5.01856e24i			0.492306i
$430$	4.14620e24	+	5.24825e24i	0.397832	+	0.503575i
$431$		−	1.95237e25i		−	1.83243i	−0.400687	−	0.916215i	$-0.631229\pi$
$431$		−	1.95237e25i		−	1.83243i	0.400687	−	0.916215i	$-0.368771\pi$
$432$	1.25156e24	−	4.38498e24i	0.114909	−	0.402598i
$433$	−1.26879e25	−	1.26879e25i	−1.13960	−	1.13960i	−0.988521	−	0.151082i	$-0.951724\pi$
$433$	−1.26879e25	−	1.26879e25i	−1.13960	−	1.13960i	−0.151082	−	0.988521i	$-0.548276\pi$
$434$	6.32681e23	−	3.61864e23i	0.0555946	−	0.0317975i
$435$	−1.22223e25	+	1.65427e25i	−1.05077	+	1.42219i
$436$	−8.53853e24	+	1.45159e25i	−0.718227	+	1.22102i
$437$	1.40579e25	−	1.40579e25i	1.15703	−	1.15703i
$438$	9.10355e24	+	2.47891e24i	0.733173	+	0.199645i
$439$	−1.42105e25			−1.11994			−0.559972	−	0.828511i	$-0.689188\pi$
$439$	−1.42105e25			−1.11994			−0.559972	+	0.828511i	$0.689188\pi$
$440$	−1.79016e25	−	1.35662e25i	−1.38067	−	1.04630i
$441$	−6.92608e24			−0.522782
$442$	5.02364e24	+	1.36795e24i	0.371114	+	0.101055i
$443$	8.99738e24	−	8.99738e24i	0.650550	−	0.650550i	−0.302576	−	0.953125i	$-0.597846\pi$
$443$	8.99738e24	−	8.99738e24i	0.650550	−	0.650550i	0.953125	+	0.302576i	$0.0978465\pi$
$444$	−1.99752e23	+	3.39587e23i	−0.0141369	+	0.0240333i
$445$	−1.79685e25	+	2.69879e24i	−1.24478	+	0.186960i
$446$	1.63470e25	−	9.34976e24i	1.10856	−	0.634044i
$447$	−1.98856e25	−	1.98856e25i	−1.32013	−	1.32013i
$448$	5.31313e24	−	5.06057e24i	0.345310	−	0.328896i
$449$			2.05350e25i			1.30664i	0.757083	+	0.653318i	$0.226624\pi$
$449$			2.05350e25i			1.30664i	−0.757083	+	0.653318i	$0.773376\pi$
$450$	3.50829e23	+	1.08559e25i	0.0218563	+	0.676310i
$451$		−	2.83018e25i		−	1.72638i
$452$	4.77574e24	+	1.84199e25i	0.285250	+	1.10020i
$453$	−2.04174e25	−	2.04174e25i	−1.19417	−	1.19417i
$454$	1.11071e25	+	1.94196e25i	0.636166	+	1.11227i
$455$	−1.84522e24	+	2.77144e23i	−0.103500	+	0.0155452i
$456$	−3.48029e25	−	4.23594e23i	−1.91183	−	0.0232693i
$457$	1.92398e25	−	1.92398e25i	1.03513	−	1.03513i	0.0357748	−	0.999360i	$-0.488610\pi$
$457$	1.92398e25	−	1.92398e25i	1.03513	−	1.03513i	0.999360	−	0.0357748i	$-0.0113899\pi$
$458$	6.70167e24	−	2.46112e25i	0.353151	−	1.29691i
$459$	1.42154e25			0.733734
$460$	8.59112e24	+	2.01642e25i	0.434361	+	1.01949i
$461$	−2.09764e25			−1.03890			−0.519449	−	0.854502i	$-0.673863\pi$
$461$	−2.09764e25			−1.03890			−0.519449	+	0.854502i	$0.673863\pi$
$462$	−5.79269e24	+	2.12730e25i	−0.281049	+	1.03212i
$463$	−2.37309e25	+	2.37309e25i	−1.12796	+	1.12796i	−0.137457	+	0.990508i	$0.543893\pi$
$463$	−2.37309e25	+	2.37309e25i	−1.12796	+	1.12796i	−0.990508	+	0.137457i	$0.956107\pi$
$464$	2.56311e25	−	1.42487e25i	1.19357	−	0.663519i
$465$	2.26501e24	−	3.06564e24i	0.103339	−	0.139868i
$466$	−1.77016e25	−	3.09493e25i	−0.791309	−	1.38352i
$467$	2.47296e25	+	2.47296e25i	1.08319	+	1.08319i	0.996210	+	0.0869854i	$0.0277234\pi$
$467$	2.47296e25	+	2.47296e25i	1.08319	+	1.08319i	0.0869854	+	0.996210i	$0.472277\pi$
$468$	−3.34934e24	+	8.68389e23i	−0.143755	+	0.0372717i
$469$			1.63287e25i			0.686767i
$470$	−2.63112e24	+	2.07862e24i	−0.108445	+	0.0856735i
$471$		−	3.51221e24i		−	0.141867i
$472$	1.28038e25	+	1.31193e25i	0.506860	+	0.519351i
$473$	2.02616e25	+	2.02616e25i	0.786126	+	0.786126i
$474$	−4.37420e25	+	2.50184e25i	−1.66343	+	0.951405i
$475$	−3.78660e25	+	1.16371e25i	−1.41143	+	0.433767i
$476$	1.97156e25	+	1.15971e25i	0.720351	+	0.423725i
$477$	1.05417e25	−	1.05417e25i	0.377562	−	0.377562i
$478$	3.81160e25	+	1.03791e25i	1.33827	+	0.364413i
$479$	−1.53012e25			−0.526671			−0.263336	−	0.964704i	$-0.584823\pi$
$479$	−1.53012e25			−0.526671			−0.263336	+	0.964704i	$0.584823\pi$
$480$	1.47589e25	−	3.54202e25i	0.498036	−	1.19525i
$481$	−1.42847e23			−0.00472598
$482$	3.66800e25	+	9.98803e24i	1.18982	+	0.323991i
$483$	1.52130e25	−	1.52130e25i	0.483857	−	0.483857i
$484$	−5.53040e25	−	3.25309e25i	−1.72475	−	1.01453i
$485$	−5.17275e24	−	3.82181e24i	−0.158188	−	0.116875i
$486$	−3.35624e25	+	1.91962e25i	−1.00649	+	0.575665i
$487$	−3.04285e25	−	3.04285e25i	−0.894859	−	0.894859i	0.100116	−	0.994976i	$-0.468078\pi$
$487$	−3.04285e25	−	3.04285e25i	−0.894859	−	0.894859i	−0.994976	+	0.100116i	$0.968078\pi$
$488$	−1.97108e25	−	2.01965e25i	−0.568481	−	0.582489i
$489$		−	2.93199e25i		−	0.829333i
$490$	2.76594e25	+	3.24470e24i	0.767327	+	0.0900143i
$491$		−	1.74396e24i		−	0.0474528i	−0.999718	−	0.0237264i	$-0.992447\pi$
$491$		−	1.74396e24i		−	0.0474528i	0.999718	−	0.0237264i	$-0.00755305\pi$
$492$	4.68024e25	−	1.21345e25i	1.24911	−	0.323858i
$493$	6.46420e25	+	6.46420e25i	1.69227	+	1.69227i
$494$	−6.26537e24	−	1.09543e25i	−0.160894	−	0.281306i
$495$	6.91143e24	+	4.60163e25i	0.174108	+	1.15921i
$496$	−4.74988e24	+	2.64052e24i	−0.117383	+	0.0652549i
$497$	1.01382e25	−	1.01382e25i	0.245797	−	0.245797i
$498$	9.14432e24	−	3.35815e25i	0.217507	−	0.798770i
$499$	4.99228e25			1.16505			0.582524	−	0.812814i	$-0.302065\pi$
$499$	4.99228e25			1.16505			0.582524	+	0.812814i	$0.302065\pi$
$500$	3.68467e24	−	4.35175e25i	0.0843692	−	0.996435i
$501$	2.13208e25			0.479012
$502$	3.90380e24	−	1.43363e25i	0.0860602	−	0.316047i
$503$	7.13141e24	−	7.13141e24i	0.154269	−	0.154269i	−0.625752	−	0.780022i	$-0.715208\pi$
$503$	7.13141e24	−	7.13141e24i	0.154269	−	0.154269i	0.780022	+	0.625752i	$0.215208\pi$
$504$	−1.51998e25	−	1.85000e23i	−0.322661	−	0.00392718i
$505$	3.17416e24	+	2.11336e25i	0.0661243	+	0.440256i
$506$	4.66198e25	+	8.15098e25i	0.953105	+	1.66640i
$507$	4.34354e25	+	4.34354e25i	0.871502	+	0.871502i
$508$	2.68574e24	+	1.03588e25i	0.0528882	+	0.203988i
$509$		−	5.13242e24i		−	0.0991981i	−0.998769	−	0.0495991i	$-0.984206\pi$
$509$		−	5.13242e24i		−	0.0991981i	0.998769	−	0.0495991i	$-0.0157944\pi$
$510$	1.18804e26	+	1.39368e25i	2.25380	+	0.264391i
$511$			1.50287e25i			0.279848i
$512$	−4.00720e25	+	3.72477e25i	−0.732448	+	0.680823i
$513$	−2.43633e25	−	2.43633e25i	−0.437140	−	0.437140i
$514$	−8.25238e25	+	4.71998e25i	−1.45355	+	0.831362i
$515$	1.33955e25	+	9.89705e24i	0.231627	+	0.171134i
$516$	−2.48191e25	+	4.21935e25i	−0.421321	+	0.716265i
$517$	−1.01578e25	+	1.01578e25i	−0.169293	+	0.169293i
$518$	−6.05508e23	−	1.64881e23i	−0.00990803	−	0.00269798i
$519$	1.14188e26			1.83456
$520$	1.37825e25	−	1.89884e24i	0.217418	−	0.0299542i
$521$	−1.02641e26			−1.58987			−0.794934	−	0.606696i	$-0.792495\pi$
$521$	−1.02641e26			−1.58987			−0.794934	+	0.606696i	$0.792495\pi$
$522$	−5.86183e25	−	1.59619e25i	−0.891587	−	0.242781i
$523$	−5.26195e25	+	5.26195e25i	−0.785925	+	0.785925i	−0.980823	−	0.194899i	$-0.937562\pi$
$523$	−5.26195e25	+	5.26195e25i	−0.785925	+	0.785925i	0.194899	+	0.980823i	$0.437562\pi$
$524$	−1.10135e25	+	1.87234e25i	−0.161539	+	0.274624i
$525$	−4.09775e25	+	1.25933e25i	−0.590244	+	0.181396i
$526$	−1.94186e25	+	1.11065e25i	−0.274697	+	0.157114i
$527$	−1.19793e25	−	1.19793e25i	−0.166429	−	0.166429i
$528$	4.51186e25	−	1.58078e26i	0.615650	−	2.15700i
$529$		−	1.70140e25i		−	0.228023i
$530$	−4.70372e25	+	3.71601e25i	−0.619185	+	0.489166i
$531$		−	3.79773e25i		−	0.491051i
$532$	−1.39140e25	−	5.36658e25i	−0.176723	−	0.681612i
$533$	1.23958e25	+	1.23958e25i	0.154656	+	0.154656i
$534$	−6.60245e25	−	1.15437e26i	−0.809214	−	1.41482i
$535$	−2.58877e24	+	3.50385e24i	−0.0311697	+	0.0421876i
$536$	1.48174e24	−	1.21741e26i	0.0175269	−	1.44003i
$537$	4.61348e25	−	4.61348e25i	0.536134	−	0.536134i
$538$	−2.62742e25	+	9.64891e25i	−0.299984	+	1.10166i
$539$	1.19309e26			1.33839
$540$	3.49460e25	−	1.48890e25i	0.385173	−	0.164106i
$541$	−7.43013e25			−0.804679			−0.402339	−	0.915491i	$-0.631803\pi$
$541$	−7.43013e25			−0.804679			−0.402339	+	0.915491i	$0.631803\pi$
$542$	−3.82558e25	+	1.40490e26i	−0.407102	+	1.49504i
$543$	−1.87019e25	+	1.87019e25i	−0.195563	+	0.195563i
$544$	−1.45940e26	−	8.82530e25i	−1.49963	−	0.906859i
$545$	−1.38729e26	+	2.08365e25i	−1.40088	+	0.210406i
$546$	−6.78019e24	−	1.18544e25i	−0.0672840	−	0.117639i
$547$	−1.24455e24	−	1.24455e24i	−0.0121376	−	0.0121376i	0.701012	−	0.713150i	$-0.252732\pi$
$547$	−1.24455e24	−	1.24455e24i	−0.0121376	−	0.0121376i	−0.713150	+	0.701012i	$0.752732\pi$
$548$	−3.90935e25	+	1.01358e25i	−0.374705	+	0.0971502i
$549$			5.84643e25i			0.550749i
$550$	−6.04342e24	−	1.87005e26i	−0.0559548	−	1.73144i
$551$		−	2.21575e26i		−	2.01642i
$552$	−1.14803e26	+	1.12042e26i	−1.02691	+	1.00221i
$553$	−5.67569e25	−	5.67569e25i	−0.499034	−	0.499034i
$554$	7.95341e25	−	4.54898e25i	0.687401	−	0.393162i
$555$	−3.24545e24	+	4.87452e23i	−0.0275735	+	0.00414141i
$556$	3.34536e25	+	1.96781e25i	0.279404	+	0.164351i
$557$	−1.53828e25	+	1.53828e25i	−0.126302	+	0.126302i	−0.767432	−	0.641130i	$-0.778466\pi$
$557$	−1.53828e25	+	1.53828e25i	−0.126302	+	0.126302i	0.641130	+	0.767432i	$0.278466\pi$
$558$	1.08630e25	+	2.95801e24i	0.0876847	+	0.0238767i
$559$	−1.77486e25			−0.140848
$560$	6.06138e25	+	7.85952e24i	0.472918	+	0.0613210i
$561$	5.12465e26			3.93113
$562$	3.95528e25	+	1.07703e25i	0.298320	+	0.0812330i
$563$	−2.77535e24	+	2.77535e24i	−0.0205820	+	0.0205820i	−0.717323	−	0.696741i	$-0.754633\pi$
$563$	−2.77535e24	+	2.77535e24i	−0.0205820	+	0.0205820i	0.696741	+	0.717323i	$0.254633\pi$
$564$	−2.11530e25	−	1.24426e25i	−0.154248	−	0.0907320i
$565$	−9.41930e25	+	1.27489e26i	−0.675396	+	0.914136i
$566$	−1.48628e25	+	8.50083e24i	−0.104796	+	0.0599384i
$567$	−5.92733e25	−	5.92733e25i	−0.410979	−	0.410979i
$568$	−7.65071e25	+	7.46671e25i	−0.521666	+	0.509120i
$569$			2.36459e26i			1.58558i	0.609493	+	0.792791i	$0.291373\pi$
$569$			2.36459e26i			1.58558i	−0.609493	+	0.792791i	$0.708627\pi$
$570$	−1.79729e26	−	2.27501e26i	−1.18524	−	1.50028i
$571$			4.88621e25i			0.316905i	0.987367	+	0.158453i	$0.0506505\pi$
$571$			4.88621e25i			0.316905i	−0.987367	+	0.158453i	$0.949350\pi$
$572$	5.76962e25	−	1.49590e25i	0.368031	−	0.0954200i
$573$	−7.13503e25	−	7.13503e25i	−0.447638	−	0.447638i
$574$	3.82364e25	+	6.68522e25i	0.235947	+	0.412527i
$575$	−8.54802e25	+	1.61331e26i	−0.518825	+	0.979205i
$576$	1.13307e26	+	2.75859e24i	0.676463	+	0.0164692i
$577$	−8.07504e25	+	8.07504e25i	−0.474214	+	0.474214i	−0.903275	−	0.429061i	$-0.858844\pi$
$577$	−8.07504e25	+	8.07504e25i	−0.474214	+	0.474214i	0.429061	+	0.903275i	$0.358844\pi$
$578$	9.42054e25	−	3.45959e26i	0.544203	−	1.99853i
$579$	1.88575e26			1.07161
$580$	2.26616e26	+	9.12053e25i	1.26685	+	0.509864i
$581$	5.54383e25			0.304886
$582$	1.23672e25	−	4.54173e25i	0.0669120	−	0.245727i
$583$	−1.81593e26	+	1.81593e26i	−0.966604	+	0.966604i
$584$	1.36377e24	−	1.12048e26i	0.00714197	−	0.586791i
$585$	−2.31817e25	−	1.71274e25i	−0.119444	−	0.0882493i
$586$	1.82652e26	+	3.19348e26i	0.925970	+	1.61896i
$587$	−2.42370e26	−	2.42370e26i	−1.20898	−	1.20898i	−0.971359	−	0.237617i	$-0.923634\pi$
$587$	−2.42370e26	−	2.42370e26i	−1.20898	−	1.20898i	−0.237617	−	0.971359i	$-0.576366\pi$
$588$	5.11544e25	+	1.97301e26i	0.251072	+	0.968376i
$589$			4.10617e25i			0.198309i
$590$	−1.77915e25	+	1.51663e26i	−0.0845507	+	0.720752i
$591$			3.07512e25i			0.143808i
$592$	4.49949e24	+	1.28424e24i	0.0207065	+	0.00591004i
$593$	−6.07326e25	−	6.07326e25i	−0.275044	−	0.275044i	0.556083	−	0.831127i	$-0.312304\pi$
$593$	−6.07326e25	−	6.07326e25i	−0.275044	−	0.275044i	−0.831127	+	0.556083i	$0.812304\pi$
$594$	1.41262e26	−	8.07954e25i	0.629585	−	0.360093i
$595$	2.83003e25	+	1.88423e26i	0.124131	+	0.826462i
$596$	−1.69342e26	+	2.87889e26i	−0.731014	+	1.24276i
$597$	2.80629e26	−	2.80629e26i	1.19227	−	1.19227i
$598$	−5.61191e25	−	1.52814e25i	−0.234666	−	0.0638999i
$599$	2.81532e26			1.15871			0.579353	−	0.815077i	$-0.303305\pi$
$599$	2.81532e26			1.15871			0.579353	+	0.815077i	$0.303305\pi$
$600$	3.06656e26	−	9.01729e25i	1.24227	−	0.365291i
$601$	2.14735e25			0.0856239			0.0428119	−	0.999083i	$-0.486368\pi$
$601$	2.14735e25			0.0856239			0.0428119	+	0.999083i	$0.486368\pi$
$602$	−7.52340e25	−	2.04864e25i	−0.295289	−	0.0804079i
$603$	−1.78351e26	+	1.78351e26i	−0.689066	+	0.689066i
$604$	−1.73871e26	+	2.95588e26i	−0.661266	+	1.12418i
$605$	−7.93847e25	−	5.28543e26i	−0.297208	−	1.97881i
$606$	−1.35770e26	+	7.76544e25i	−0.500397	+	0.286204i
$607$	−3.00158e26	−	3.00158e26i	−1.08907	−	1.08907i	−0.995624	−	0.0934493i	$-0.970211\pi$
$607$	−3.00158e26	−	3.00158e26i	−1.08907	−	1.08907i	−0.0934493	−	0.995624i	$-0.529789\pi$
$608$	9.88681e25	+	4.01376e26i	0.353160	+	1.43373i
$609$		−	2.39782e26i		−	0.843242i
$610$	2.73891e25	−	2.33478e26i	0.0948297	−	0.808376i
$611$		−	8.89796e24i		−	0.0303319i
$612$	8.86747e25	+	3.42015e26i	0.297619	+	1.14791i
$613$	−4.23810e25	−	4.23810e25i	−0.140055	−	0.140055i	0.633603	−	0.773658i	$-0.281575\pi$
$613$	−4.23810e25	−	4.23810e25i	−0.140055	−	0.140055i	−0.773658	+	0.633603i	$0.781575\pi$
$614$	−2.07508e26	−	3.62806e26i	−0.675205	−	1.18052i
$615$	3.23931e26	+	2.39332e26i	1.03786	+	0.766808i
$616$	2.61833e26	+	3.18683e24i	0.826052	+	0.0100541i
$617$	−1.52252e26	+	1.52252e26i	−0.472993	+	0.472993i	−0.902882	−	0.429889i	$-0.858553\pi$
$617$	−1.52252e26	+	1.52252e26i	−0.472993	+	0.472993i	0.429889	+	0.902882i	$0.358553\pi$
$618$	−3.20265e25	+	1.17614e26i	−0.0979758	+	0.359805i
$619$	1.06008e26			0.319359			0.159680	−	0.987169i	$-0.448954\pi$
$619$	1.06008e26			0.319359			0.159680	+	0.987169i	$0.448954\pi$
$620$	−4.19957e25	−	1.69019e25i	−0.124590	−	0.0501435i
$621$	−1.58800e26			−0.463960
$622$	−7.87938e24	+	2.89362e25i	−0.0226717	+	0.0832592i
$623$	1.49783e26	−	1.49783e26i	0.424451	−	0.424451i
$624$	4.94749e25	+	8.89977e25i	0.138080	+	0.248385i
$625$	3.01008e26	−	2.04311e26i	0.827406	−	0.561605i
$626$	1.38738e26	+	2.42568e26i	0.375611	+	0.656716i
$627$	−8.78297e26	−	8.78297e26i	−2.34207	−	2.34207i
$628$	−4.03783e25	+	1.04689e25i	−0.106055	+	0.0274970i
$629$			1.45866e25i			0.0377376i
$630$	−7.84946e25	−	9.93584e25i	−0.200034	−	0.253203i
$631$			1.72041e26i			0.431871i	0.976408	+	0.215935i	$0.0692800\pi$
$631$			1.72041e26i			0.431871i	−0.976408	+	0.215935i	$0.930720\pi$
$632$	4.18009e26	+	4.28310e26i	1.03365	+	1.05912i
$633$	−1.29941e26	−	1.29941e26i	−0.316528	−	0.316528i
$634$	4.14707e26	−	2.37193e26i	0.995162	−	0.569186i
$635$	−5.29714e25	+	7.16958e25i	−0.125225	+	0.169490i
$636$	−3.78158e26	−	2.22440e26i	−0.880705	−	0.518048i
$637$	−5.22560e25	+	5.22560e25i	−0.119898	+	0.119898i
$638$	1.00977e27	+	2.74961e26i	2.28257	+	0.621549i
$639$	2.21471e26			0.493240
$640$	−4.51202e26	−	6.40981e25i	−0.990060	−	0.140649i
$641$	8.07007e26			1.74472			0.872361	−	0.488862i	$-0.162588\pi$
$641$	8.07007e26			1.74472			0.872361	+	0.488862i	$0.162588\pi$
$642$	−3.07642e25	−	8.37717e24i	−0.0655335	−	0.0178449i
$643$	−4.93246e25	+	4.93246e25i	−0.103528	+	0.103528i	−0.756974	−	0.653445i	$-0.773323\pi$
$643$	−4.93246e25	+	4.93246e25i	−0.103528	+	0.103528i	0.653445	+	0.756974i	$0.273323\pi$
$644$	−2.20243e26	−	1.29551e26i	−0.455498	−	0.267933i
$645$	−4.03246e26	+	6.05656e25i	−0.821774	+	0.123427i
$646$	−1.11859e27	+	6.39782e26i	−2.24627	+	1.28476i
$647$	5.54465e26	+	5.54465e26i	1.09719	+	1.09719i	0.994737	+	0.102457i	$0.0326703\pi$
$647$	5.54465e26	+	5.54465e26i	1.09719	+	1.09719i	0.102457	+	0.994737i	$0.467330\pi$
$648$	4.36542e26	+	4.47299e26i	0.851262	+	0.872239i
$649$			6.54202e26i			1.25715i
$650$	8.45526e25	+	7.92587e25i	0.160122	+	0.150096i
$651$			4.44357e25i			0.0829301i
$652$	−3.37078e26	+	8.73948e25i	−0.619981	+	0.160743i
$653$	−2.26279e25	−	2.26279e25i	−0.0410175	−	0.0410175i	0.686301	−	0.727318i	$-0.259233\pi$
$653$	−2.26279e25	−	2.26279e25i	−0.0410175	−	0.0410175i	−0.727318	+	0.686301i	$0.759233\pi$
$654$	−5.09754e26	−	8.91250e26i	−0.910693	−	1.59225i
$655$	−1.78941e26	+	2.68761e25i	−0.315077	+	0.0473231i
$656$	−2.79010e26	−	5.01896e26i	−0.484210	−	0.871019i
$657$	−1.64151e26	+	1.64151e26i	−0.280785	+	0.280785i
$658$	1.02705e25	−	3.77173e25i	0.0173159	−	0.0635909i
$659$	−5.85286e26			−0.972650			−0.486325	−	0.873778i	$-0.661663\pi$
$659$	−5.85286e26			−0.972650			−0.486325	+	0.873778i	$0.661663\pi$
$660$	1.25980e27	−	5.36749e26i	2.06364	−	0.879233i
$661$	1.25441e26			0.202547			0.101273	−	0.994859i	$-0.467708\pi$
$661$	1.25441e26			0.202547			0.101273	+	0.994859i	$0.467708\pi$
$662$	3.65809e25	−	1.34339e26i	0.0582242	−	0.213822i
$663$	−2.24453e26	+	2.24453e26i	−0.352166	+	0.352166i
$664$	−4.13329e26	−	5.03072e24i	−0.639291	−	0.00778096i
$665$	2.74429e26	−	3.71435e26i	0.418431	−	0.566339i
$666$	−4.81277e24	−	8.41461e24i	−0.00723419	−	0.0126482i
$667$	−7.22116e26	−	7.22116e26i	−1.07007	−	1.07007i
$668$	−6.35517e25	−	2.45116e26i	−0.0928433	−	0.358093i
$669$			1.14812e27i			1.65363i
$670$	7.95801e26	−	6.28695e26i	1.13004	−	0.892748i
$671$		−	1.00711e27i		−	1.40999i
$672$	1.06992e26	+	4.34356e26i	0.147687	+	0.599567i
$673$	3.41022e26	+	3.41022e26i	0.464129	+	0.464129i	0.900006	−	0.435877i	$-0.143562\pi$
$673$	3.41022e26	+	3.41022e26i	0.464129	+	0.464129i	−0.435877	+	0.900006i	$0.643562\pi$
$674$	−1.59922e26	+	9.14682e25i	−0.214605	+	0.122744i
$675$	2.79598e26	+	1.48143e26i	0.369954	+	0.196018i
$676$	3.69888e26	−	6.28827e26i	0.482589	−	0.820422i
$677$	−4.51163e26	+	4.51163e26i	−0.580418	+	0.580418i	−0.935018	−	0.354600i	$-0.884617\pi$
$677$	−4.51163e26	+	4.51163e26i	−0.580418	+	0.580418i	0.354600	+	0.935018i	$0.384617\pi$
$678$	−1.11936e27	−	3.04805e26i	−1.42000	−	0.386670i
$679$	7.49775e25			0.0937926
$680$	−1.93898e26	−	1.40738e27i	−0.239188	−	1.73611i
$681$	−1.36391e27			−1.65917
$682$	−1.87127e26	−	5.09550e25i	−0.224484	−	0.0611273i
$683$	2.40283e26	−	2.40283e26i	0.284267	−	0.284267i	−0.550541	−	0.834808i	$-0.685579\pi$
$683$	2.40283e26	−	2.40283e26i	0.284267	−	0.284267i	0.834808	+	0.550541i	$0.185579\pi$
$684$	4.34191e26	−	7.38144e26i	0.506579	−	0.861208i
$685$	−2.70576e26	−	1.99911e26i	−0.311336	−	0.230026i
$686$	−6.46601e26	+	3.69826e26i	−0.733765	+	0.419680i
$687$	1.09961e27	+	1.09961e27i	1.23069	+	1.23069i
$688$	5.59059e26	+	1.59566e26i	0.617117	+	0.176137i
$689$		−	1.59071e26i		−	0.173184i
$690$	−1.32716e27	−	1.55688e26i	−1.42514	−	0.167182i
$691$			5.12749e26i			0.543080i	0.962427	+	0.271540i	$0.0875329\pi$
$691$			5.12749e26i			0.543080i	−0.962427	+	0.271540i	$0.912467\pi$
$692$	−3.40364e26	−	1.31277e27i	−0.355579	−	1.37145i
$693$	−3.83586e26	−	3.83586e26i	−0.395273	−	0.395273i
$694$	2.91651e26	+	5.09920e26i	0.296448	+	0.518307i
$695$	4.80202e25	+	3.19718e26i	0.0481469	+	0.320562i
$696$	−2.17589e25	+	1.78773e27i	−0.0215203	+	1.76813i
$697$	1.26579e27	−	1.26579e27i	1.23495	−	1.23495i
$698$	2.96698e25	−	1.08959e26i	0.0285554	−	0.104866i
$699$	2.17369e27			2.06379
$700$	2.66923e26	+	4.33562e26i	0.250008	+	0.406088i
$701$	4.74256e25			0.0438220			0.0219110	−	0.999760i	$-0.493025\pi$
$701$	4.74256e25			0.0438220			0.0219110	+	0.999760i	$0.493025\pi$
$702$	−2.64836e25	+	9.72583e25i	−0.0241421	+	0.0886592i
$703$	2.49995e25	−	2.49995e25i	0.0224831	−	0.0224831i
$704$	−1.95184e27	−	4.75197e25i	−1.73183	−	0.0421632i
$705$	−3.03636e25	−	2.02160e26i	−0.0265801	−	0.176970i
$706$	9.72426e25	+	1.70018e26i	0.0839870	+	0.146842i
$707$	−1.76167e26	−	1.76167e26i	−0.150121	−	0.150121i
$708$	−1.08185e27	+	2.80492e26i	−0.909598	+	0.235833i
$709$		−	2.78694e26i		−	0.231200i	−0.993296	−	0.115600i	$-0.963121\pi$
$709$		−	2.78694e26i		−	0.231200i	0.993296	−	0.115600i	$-0.0368791\pi$
$710$	−8.84448e26	−	1.03754e26i	−0.723965	−	0.0849276i
$711$		−	1.23986e27i		−	1.00141i
$712$	−1.13032e27	+	1.10314e27i	−0.900830	+	0.879166i
$713$	1.33820e26	+	1.33820e26i	0.105238	+	0.105238i
$714$	−1.21050e27	+	6.92352e26i	−0.939362	+	0.537272i
$715$	3.99330e26	+	2.95039e26i	0.305791	+	0.225929i
$716$	−6.67907e26	−	3.92876e26i	−0.504710	−	0.296881i
$717$	−1.70300e27	+	1.70300e27i	−1.26994	+	1.26994i
$718$	1.66551e27	+	4.53521e26i	1.22564	+	0.333745i
$719$	2.54275e27			1.84663			0.923314	−	0.384046i	$-0.125470\pi$
$719$	2.54275e27			1.84663			0.923314	+	0.384046i	$0.125470\pi$
$720$	5.76212e26	+	7.47904e26i	0.412975	+	0.536027i
$721$	−1.94164e26			−0.137336
$722$	1.63141e27	+	4.44237e26i	1.13883	+	0.310107i
$723$	−1.63884e27	+	1.63884e27i	−1.12907	+	1.12907i
$724$	2.70752e26	+	1.59262e26i	0.184101	+	0.108292i
$725$	5.97768e26	+	1.94508e27i	0.401163	+	1.30535i
$726$	3.39557e27	−	1.94211e27i	2.24913	−	1.28640i
$727$	2.05632e26	+	2.05632e26i	0.134435	+	0.134435i	0.771122	−	0.636687i	$-0.219696\pi$
$727$	2.05632e26	+	2.05632e26i	0.134435	+	0.134435i	−0.636687	+	0.771122i	$0.719696\pi$
$728$	−1.16075e26	+	1.13284e26i	−0.0749017	+	0.0731003i
$729$		−	4.43669e26i		−	0.282584i
$730$	7.32442e26	−	5.78640e26i	0.460475	−	0.363782i
$731$			1.81238e27i			1.12469i
$732$	1.66545e27	−	4.31804e26i	1.02018	−	0.264504i
$733$	1.59151e26	+	1.59151e26i	0.0962326	+	0.0962326i	0.753584	−	0.657352i	$-0.228323\pi$
$733$	1.59151e26	+	1.59151e26i	0.0962326	+	0.0962326i	−0.657352	+	0.753584i	$0.728323\pi$
$734$	5.48512e26	+	9.59014e26i	0.327396	+	0.572417i
$735$	−1.00893e27	+	1.36557e27i	−0.594472	+	0.804607i
$736$	1.63030e27	+	9.85874e26i	0.948261	+	0.573432i
$737$	3.07229e27	−	3.07229e27i	1.76409	−	1.76409i
$738$	−3.12558e26	+	1.14784e27i	−0.177172	+	0.650645i
$739$	1.56915e27			0.878094			0.439047	−	0.898464i	$-0.355316\pi$
$739$	1.56915e27			0.878094			0.439047	+	0.898464i	$0.355316\pi$
$740$	1.52778e25	+	3.58586e25i	0.00844035	+	0.0198103i
$741$	7.69365e26			0.419623
$742$	1.83608e26	−	6.74282e26i	0.0988679	−	0.363082i
$743$	1.30558e27	−	1.30558e27i	0.694078	−	0.694078i	−0.269049	−	0.963127i	$-0.586709\pi$
$743$	1.30558e27	−	1.30558e27i	0.694078	−	0.694078i	0.963127	+	0.269049i	$0.0867093\pi$
$744$	4.03229e24	−	3.31297e26i	0.00211645	−	0.173890i
$745$	−2.75137e27	+	4.13243e26i	−1.42582	+	0.214152i
$746$	−5.61166e26	−	9.81138e26i	−0.287126	−	0.502009i
$747$	6.05528e26	+	6.05528e26i	0.305906	+	0.305906i
$748$	−1.52752e27	−	5.89159e27i	−0.761942	−	2.93878i
$749$		−	5.07874e25i		−	0.0250137i
$750$	2.19149e27	+	1.51222e27i	1.06575	+	0.735414i
$751$		−	2.22914e26i		−	0.107043i	−0.998567	−	0.0535214i	$-0.982955\pi$
$751$		−	2.22914e26i		−	0.107043i	0.998567	−	0.0535214i	$-0.0170445\pi$
$752$	−7.99958e25	+	2.80275e26i	−0.0379313	+	0.132897i
$753$	6.40536e26	+	6.40536e26i	0.299910	+	0.299910i
$754$	−5.62694e26	+	3.21835e26i	−0.260162	+	0.148801i
$755$	−2.82495e27	+	4.24295e26i	−1.28978	+	0.193719i
$756$	−2.24521e26	+	3.81696e26i	−0.101228	+	0.172092i
$757$	1.60168e27	−	1.60168e27i	0.713126	−	0.713126i	−0.254062	−	0.967188i	$-0.581767\pi$
$757$	1.60168e27	−	1.60168e27i	0.713126	−	0.713126i	0.967188	+	0.254062i	$0.0817667\pi$
$758$	−7.71843e26	−	2.10174e26i	−0.339368	−	0.0924108i
$759$	−5.72475e27			−2.48576
$760$	−2.07975e27	+	2.74438e27i	−0.891830	+	1.17683i
$761$	2.40513e27			1.01855			0.509277	−	0.860603i	$-0.329913\pi$
$761$	2.40513e27			1.01855			0.509277	+	0.860603i	$0.329913\pi$
$762$	−6.29497e26	−	1.71413e26i	−0.263282	−	0.0716923i
$763$	1.15643e27	−	1.15643e27i	0.477679	−	0.477679i
$764$	−6.07607e26	+	1.03296e27i	−0.247877	+	0.421401i
$765$	−1.74895e27	+	2.36717e27i	−0.704683	+	0.953776i
$766$	−8.68748e26	+	4.96884e26i	−0.345717	+	0.197734i
$767$	−2.86532e26	−	2.86532e26i	−0.112620	−	0.112620i
$768$	−7.58278e26	−	3.24811e27i	−0.294372	−	1.26096i
$769$			9.73378e26i			0.373234i	0.982433	+	0.186617i	$0.0597524\pi$
$769$			9.73378e26i			0.373234i	−0.982433	+	0.186617i	$0.940248\pi$
$770$	1.35216e27	+	1.71156e27i	0.512113	+	0.648231i
$771$		−	5.79597e27i		−	2.16825i
$772$	−5.62091e26	−	2.16796e27i	−0.207703	−	0.801102i
$773$	−5.68243e25	−	5.68243e25i	−0.0207410	−	0.0207410i	0.696660	−	0.717401i	$-0.254669\pi$
$773$	−5.68243e25	−	5.68243e25i	−0.0207410	−	0.0207410i	−0.717401	+	0.696660i	$0.754669\pi$
$774$	−5.97984e26	−	1.04551e27i	−0.215601	−	0.376955i
$775$	−1.10776e26	−	3.60456e26i	−0.0394531	−	0.128377i
$776$	−5.59006e26	−	6.80379e24i	−0.196666	−	0.00239367i
$777$	2.70537e25	−	2.70537e25i	0.00940215	−	0.00940215i
$778$	1.00281e27	−	3.68272e27i	0.344281	−	1.26433i
$779$	−4.33878e27			−1.47151
$780$	−3.16688e26	+	7.86866e26i	−0.106104	+	0.263634i
$781$	−3.81508e27			−1.26275
$782$	−1.56044e27	+	5.73055e27i	−0.510250	+	1.87384i
$783$	−1.25148e27	+	1.25148e27i	−0.404283	+	0.404283i
$784$	2.11580e27	−	1.17620e27i	0.675262	−	0.375386i
$785$	−2.79468e26	−	2.06481e26i	−0.0881193	−	0.0651056i
$786$	−6.57510e26	−	1.14959e27i	−0.204827	−	0.358119i
$787$	4.09631e27	+	4.09631e27i	1.26076	+	1.26076i	0.950725	+	0.310036i	$0.100341\pi$
$787$	4.09631e27	+	4.09631e27i	1.26076	+	1.26076i	0.310036	+	0.950725i	$0.399659\pi$
$788$	3.53533e26	−	9.16612e25i	0.107506	−	0.0278732i
$789$		−	1.36384e27i		−	0.409763i
$790$	−5.80844e26	+	4.95140e27i	−0.172426	+	1.46984i
$791$		−	1.84791e27i		−	0.542006i
$792$	2.82507e27	+	2.89469e27i	0.818730	+	0.838905i
$793$	4.41103e26	+	4.41103e26i	0.126312	+	0.126312i
$794$	−2.29524e27	+	1.31277e27i	−0.649431	+	0.371445i
$795$	−5.42817e26	−	3.61407e27i	−0.151763	−	1.01044i
$796$	−4.06275e27	−	2.38979e27i	−1.12239	−	0.660215i
$797$	−3.54044e27	+	3.54044e27i	−0.966502	+	0.966502i	−0.999457	−	0.0329550i	$-0.989508\pi$
$797$	−3.54044e27	+	3.54044e27i	−0.966502	+	0.966502i	0.0329550	+	0.999457i	$0.489508\pi$
$798$	3.26124e27	+	8.88042e26i	0.879742	+	0.239555i
$799$	−9.08607e26			−0.242204
$800$	−1.95074e27	−	3.25671e27i	−0.513859	−	0.857875i
$801$	3.27203e27			0.851744
$802$	6.49474e25	+	1.76853e25i	0.0167073	+	0.00454942i
$803$	2.82769e27	−	2.82769e27i	0.718843	−	0.718843i
$804$	6.39787e27	+	3.76336e27i	1.60732	+	0.945459i
$805$	−3.16142e26	−	2.10487e27i	−0.0784913	−	0.522595i
$806$	1.04277e26	−	5.96415e25i	0.0255861	−	0.0146341i
$807$	−4.31107e27	−	4.31107e27i	−1.04541	−	1.04541i
$808$	1.29745e27	+	1.32942e27i	0.310945	+	0.318607i
$809$		−	7.68845e27i		−	1.82107i	−0.413427	−	0.910537i	$-0.635668\pi$
$809$		−	7.68845e27i		−	1.82107i	0.413427	−	0.910537i	$-0.364332\pi$
$810$	−6.06597e26	+	5.17093e27i	−0.142001	+	1.21049i
$811$			1.98262e27i			0.458713i	0.973342	+	0.229357i	$0.0736622\pi$
$811$			1.98262e27i			0.458713i	−0.973342	+	0.229357i	$0.926338\pi$
$812$	−2.75667e27	+	7.14725e26i	−0.630379	+	0.163439i
$813$	−6.27701e27	−	6.27701e27i	−1.41871	−	1.41871i
$814$	8.29053e25	+	1.44951e26i	0.0185204	+	0.0323810i
$815$	−2.33300e27	−	1.72371e27i	−0.515132	−	0.380597i
$816$	9.08791e27	−	5.05208e27i	1.98339	−	1.10259i
$817$	3.10618e27	−	3.10618e27i	0.670065	−	0.670065i
$818$	−1.98198e27	+	7.27861e27i	−0.422613	+	1.55200i
$819$	3.36012e26			0.0708202
$820$	1.78594e27	−	4.43748e27i	0.372079	−	0.924495i
$821$	−3.88417e27			−0.799905			−0.399952	−	0.916536i	$-0.630973\pi$
$821$	−3.88417e27			−0.799905			−0.399952	+	0.916536i	$0.630973\pi$
$822$	6.46905e26	−	2.37569e27i	0.131692	−	0.483623i
$823$	−3.35134e27	+	3.35134e27i	−0.674403	+	0.674403i	−0.958728	−	0.284325i	$-0.908231\pi$
$823$	−3.35134e27	+	3.35134e27i	−0.674403	+	0.674403i	0.284325	+	0.958728i	$0.408231\pi$
$824$	1.44762e27	+	1.76193e25i	0.287968	+	0.00350493i
$825$	1.00795e28	+	5.34056e27i	1.98211	+	1.05021i
$826$	−8.83842e26	−	1.54530e27i	−0.171816	−	0.300402i
$827$	−2.13590e26	−	2.13590e26i	−0.0410467	−	0.0410467i	0.686286	−	0.727332i	$-0.259240\pi$
$827$	−2.13590e26	−	2.13590e26i	−0.0410467	−	0.0410467i	−0.727332	+	0.686286i	$0.759240\pi$
$828$	−9.90585e26	−	3.82065e27i	−0.188193	−	0.725853i
$829$		−	3.25013e27i		−	0.610425i	−0.952284	−	0.305213i	$-0.901272\pi$
$829$		−	3.25013e27i		−	0.610425i	0.952284	−	0.305213i	$-0.0987275\pi$
$830$	−2.13451e27	−	2.70186e27i	−0.396330	−	0.501674i
$831$			5.58599e27i			1.02539i
$832$	8.75695e26	−	8.34069e26i	0.158921	−	0.151367i
$833$	5.33607e27	+	5.33607e27i	0.957402	+	0.957402i
$834$	−2.05399e27	+	1.17479e27i	−0.364353	+	0.208393i
$835$	1.25344e27	−	1.69651e27i	0.219828	−	0.297533i
$836$	−7.47942e27	+	1.27154e28i	−1.29691	+	2.20480i
$837$	2.31920e26	−	2.31920e26i	0.0397600	−	0.0397600i
$838$	4.91198e26	+	1.33754e26i	0.0832604	+	0.0226720i
$839$	−1.55367e27			−0.260387			−0.130194	−	0.991489i	$-0.541560\pi$
$839$	−1.55367e27			−0.260387			−0.130194	+	0.991489i	$0.541560\pi$
$840$	−2.25064e27	+	2.96988e27i	−0.372952	+	0.492137i
$841$	−5.27846e27			−0.864860
$842$	1.06756e28	+	2.90697e27i	1.72952	+	0.470952i
$843$	−1.76719e27	+	1.76719e27i	−0.283088	+	0.283088i
$844$	−1.10656e27	+	1.88120e27i	−0.175275	+	0.297976i
$845$	6.00973e27	−	9.02634e26i	0.941274	−	0.141375i
$846$	5.24149e26	−	2.99789e26i	0.0811777	−	0.0464299i
$847$	4.40587e27	+	4.40587e27i	0.674745	+	0.674745i
$848$	−1.43011e27	+	5.01054e27i	−0.216575	+	0.758794i
$849$		−	1.04387e27i		−	0.156323i
$850$	8.09342e27	−	8.63400e27i	1.19854	−	1.27859i
$851$		−	1.62947e26i		−	0.0238625i
$852$	−1.63573e27	−	6.30895e27i	−0.236884	−	0.913653i
$853$	2.00183e27	+	2.00183e27i	0.286690	+	0.286690i	0.835770	−	0.549080i	$-0.185022\pi$
$853$	2.00183e27	+	2.00183e27i	0.286690	+	0.286690i	−0.549080	+	0.835770i	$0.685022\pi$
$854$	1.36063e27	+	2.37892e27i	0.192704	+	0.336923i
$855$	7.05448e27	−	1.05955e27i	0.988068	−	0.148403i
$856$	−4.60867e24	+	3.78653e26i	−0.000638374	+	0.0524494i
$857$	−5.89031e27	+	5.89031e27i	−0.806901	+	0.806901i	−0.984164	−	0.177263i	$-0.943276\pi$
$857$	−5.89031e27	+	5.89031e27i	−0.806901	+	0.806901i	0.177263	+	0.984164i	$0.443276\pi$
$858$	−9.54735e26	+	3.50616e27i	−0.129346	+	0.475010i
$859$	2.00469e27			0.268604			0.134302	−	0.990940i	$-0.457121\pi$
$859$	2.00469e27			0.268604			0.134302	+	0.990940i	$0.457121\pi$
$860$	1.89826e27	+	4.45541e27i	0.251548	+	0.590408i
$861$	−4.69529e27			−0.615365
$862$	3.71420e27	−	1.36400e28i	0.481444	−	1.76805i
$863$	7.75431e27	−	7.75431e27i	0.994124	−	0.994124i	−0.00585924	−	0.999983i	$-0.501865\pi$
$863$	7.75431e27	−	7.75431e27i	0.994124	−	0.994124i	0.999983	+	0.00585924i	$0.00186506\pi$
$864$	1.70859e27	−	2.82542e27i	0.216649	−	0.358263i
$865$	6.71307e27	−	9.08602e27i	0.841915	−	1.13952i
$866$	−6.45049e27	−	1.12780e28i	−0.800152	−	1.39898i
$867$	1.54572e28	+	1.54572e28i	1.89649	+	1.89649i
$868$	5.10857e26	−	1.32451e26i	0.0619958	−	0.0160737i
$869$			2.13580e28i			2.56373i
$870$	−1.16861e28	+	9.23219e27i	−1.38751	+	1.09615i
$871$			2.69125e27i			0.316069i
$872$	−8.72687e27	+	8.51699e27i	−1.01380	+	0.989417i
$873$	8.18946e26	+	8.18946e26i	0.0941066	+	0.0941066i
$874$	1.24958e28	−	7.14700e27i	1.42038	−	0.812391i
$875$	−1.40699e27	+	4.00096e27i	−0.158203	+	0.449870i
$876$	5.88850e27	+	3.46373e27i	0.654961	+	0.385261i
$877$	−7.94606e27	+	7.94606e27i	−0.874290	+	0.874290i	−0.992937	−	0.118646i	$-0.962145\pi$
$877$	−7.94606e27	+	7.94606e27i	−0.874290	+	0.874290i	0.118646	+	0.992937i	$0.462145\pi$
$878$	−9.92801e27	−	2.70342e27i	−1.08060	−	0.294249i
$879$	−2.24290e28			−2.41499
$880$	−9.92589e27	−	1.28835e28i	−1.05727	−	1.37230i
$881$	9.14701e27			0.963847			0.481924	−	0.876213i	$-0.339938\pi$
$881$	9.14701e27			0.963847			0.481924	+	0.876213i	$0.339938\pi$
$882$	−4.83883e27	−	1.31762e27i	−0.504416	−	0.137354i
$883$	1.03054e28	−	1.03054e28i	1.06276	−	1.06276i	0.0648705	−	0.997894i	$-0.479337\pi$
$883$	1.03054e28	−	1.03054e28i	1.06276	−	1.06276i	0.997894	−	0.0648705i	$-0.0206634\pi$
$884$	3.24947e27	+	1.91140e27i	0.331525	+	0.195010i
$885$	−7.48773e27	−	5.53220e27i	−0.755770	−	0.558389i
$886$	7.99759e27	−	4.57425e27i	0.798617	−	0.456772i
$887$	−5.17943e27	−	5.17943e27i	−0.511691	−	0.511691i	0.403354	−	0.915044i	$-0.367844\pi$
$887$	−5.17943e27	−	5.17943e27i	−0.511691	−	0.511691i	−0.915044	+	0.403354i	$0.867844\pi$
$888$	−2.04158e26	+	1.99248e26i	−0.0199546	+	0.0194747i
$889$		−	1.03921e27i		−	0.100493i
$890$	−1.30669e28	−	1.53287e27i	−1.25017	−	0.146656i
$891$			2.23049e28i			2.11136i
$892$	1.31994e28	−	3.42223e27i	1.23620	−	0.320511i
$893$	1.55723e27	+	1.55723e27i	0.144299	+	0.144299i
$894$	−1.01098e28	−	1.76759e28i	−0.926906	−	1.62060i
$895$	−9.58730e26	−	6.38322e27i	−0.0869716	−	0.579057i
$896$	4.67469e27	−	2.52474e27i	0.419591	−	0.226616i
$897$	2.50737e27	−	2.50737e27i	0.222684	−	0.222684i
$898$	−3.90660e27	+	1.43466e28i	−0.343300	+	1.26073i
$899$	2.10923e27			0.183403
$900$	−1.82013e27	+	7.65108e27i	−0.156602	+	0.658293i
$901$	−1.62434e28			−1.38290
$902$	5.38416e27	−	1.97728e28i	0.453582	−	1.66573i
$903$	3.36141e27	−	3.36141e27i	0.280213	−	0.280213i
$904$	−1.67688e26	+	1.37774e28i	−0.0138325	+	1.13649i
$905$	3.88644e26	+	2.58759e27i	0.0317242	+	0.211220i
$906$	−1.03802e28	−	1.81486e28i	−0.838468	−	1.46597i
$907$	−6.16818e27	−	6.16818e27i	−0.493046	−	0.493046i	0.416218	−	0.909265i	$-0.363355\pi$
$907$	−6.16818e27	−	6.16818e27i	−0.493046	−	0.493046i	−0.909265	+	0.416218i	$0.863355\pi$
$908$	4.06546e27	+	1.56803e28i	0.321584	+	1.24034i
$909$		−	3.84839e27i		−	0.301246i
$910$	−1.34187e27	−	1.57413e26i	−0.103948	−	0.0121941i
$911$			6.95820e27i			0.533423i	0.963776	+	0.266712i	$0.0859371\pi$
$911$			6.95820e27i			0.533423i	−0.963776	+	0.266712i	$0.914063\pi$
$912$	−2.42341e28	−	6.91687e27i	−1.83855	−	0.524757i
$913$	−1.04309e28	−	1.04309e28i	−0.783158	−	0.783158i
$914$	1.71019e28	−	9.78148e27i	1.27073	−	0.726802i
$915$	1.15270e28	+	8.51656e27i	0.847650	+	0.626273i
$916$	9.36409e27	−	1.59194e28i	0.681489	−	1.15856i
$917$	1.49163e27	−	1.49163e27i	0.107437	−	0.107437i
$918$	9.93143e27	+	2.70435e27i	0.707956	+	0.192778i
$919$	1.89221e28			1.33497			0.667485	−	0.744623i	$-0.267371\pi$
$919$	1.89221e28			1.33497			0.667485	+	0.744623i	$0.267371\pi$
$920$	2.16604e27	+	1.57219e28i	0.151245	+	1.09779i
$921$	2.54813e28			1.76098
$922$	−1.46550e28	−	3.99057e27i	−1.00240	−	0.272955i
$923$	1.67096e27	−	1.67096e27i	0.113123	−	0.113123i
$924$	−8.09400e27	+	1.37602e28i	−0.542349	+	0.922018i
$925$	−1.52012e26	+	2.86900e26i	−0.0100816	+	0.0190276i
$926$	−2.10940e28	+	1.20648e28i	−1.38469	+	0.791981i
$927$	−2.12076e27	−	2.12076e27i	−0.137795	−	0.137795i
$928$	2.06176e28	−	5.07858e27i	1.32596	−	0.326616i
$929$			8.53754e27i			0.543480i	0.962371	+	0.271740i	$0.0875991\pi$
$929$			8.53754e27i			0.543480i	−0.962371	+	0.271740i	$0.912401\pi$
$930$	2.16563e27	−	1.71088e27i	0.136457	−	0.107803i
$931$		−	1.82906e28i		−	1.14079i
$932$	−6.47919e27	−	2.49900e28i	−0.400009	−	1.54282i
$933$	−1.29285e27	−	1.29285e27i	−0.0790083	−	0.0790083i
$934$	1.25725e28	+	2.19816e28i	0.760546	+	1.32973i
$935$	3.01276e28	−	4.07772e28i	1.80407	−	2.44178i
$936$	−2.50518e27	−	3.04912e25i	−0.148497	−	0.00180740i
$937$	3.23066e27	−	3.23066e27i	0.189568	−	0.189568i	−0.605941	−	0.795509i	$-0.707203\pi$
$937$	3.23066e27	−	3.23066e27i	0.189568	−	0.189568i	0.795509	+	0.605941i	$0.207203\pi$
$938$	−3.10638e27	+	1.14079e28i	−0.180438	+	0.662639i
$939$	−1.70365e28			−0.979619
$940$	−2.23364e27	+	9.51662e26i	−0.127145	+	0.0541711i
$941$	−2.85360e28			−1.60802			−0.804009	−	0.594617i	$-0.797304\pi$
$941$	−2.85360e28			−1.60802			−0.804009	+	0.594617i	$0.797304\pi$
$942$	6.68165e26	−	2.45376e27i	0.0372735	−	0.136883i
$943$	−1.41401e28	+	1.41401e28i	−0.780894	+	0.780894i
$944$	6.44938e27	+	1.16014e28i	0.352602	+	0.634275i
$945$	−3.64789e27	+	5.47896e26i	−0.197442	+	0.0296549i
$946$	1.03009e28	+	1.80101e28i	0.551964	+	0.965051i
$947$	−1.52270e28	−	1.52270e28i	−0.807773	−	0.807773i	0.176524	−	0.984296i	$-0.443515\pi$
$947$	−1.52270e28	−	1.52270e28i	−0.807773	−	0.807773i	−0.984296	+	0.176524i	$0.943515\pi$
$948$	−3.53194e28	+	9.15732e27i	−1.85496	+	0.480938i
$949$			2.47698e27i			0.128794i
$950$	−2.86686e28	+	9.26480e26i	−1.47581	+	0.0476938i
$951$			2.91265e28i			1.48448i
$952$	1.15678e28	+	1.18529e28i	0.583716	+	0.598100i
$953$	1.94254e28	+	1.94254e28i	0.970481	+	0.970481i	0.999577	−	0.0290953i	$-0.00926264\pi$
$953$	1.94254e28	+	1.94254e28i	0.970481	+	0.970481i	−0.0290953	+	0.999577i	$0.509263\pi$
$954$	9.37035e27	−	5.35940e27i	0.463496	−	0.265098i
$955$	−9.87204e27	+	1.48273e27i	−0.483476	+	0.0726158i
$956$	2.46548e28	+	1.45025e28i	1.19551	+	0.703221i
$957$	−4.51157e28	+	4.51157e28i	−2.16603	+	2.16603i
$958$	−1.06900e28	−	2.91092e27i	−0.508168	−	0.138375i
$959$	3.92192e27			0.184596
$960$	1.70495e28	−	2.19382e28i	0.794574	−	1.02241i
$961$	2.12798e28			0.981963
$962$	−9.97982e25	−	2.71753e25i	−0.00455994	−	0.00124168i
$963$	5.54728e26	−	5.54728e26i	0.0250975	−	0.0250975i
$964$	2.37259e28	+	1.39561e28i	1.06290	+	0.625217i
$965$	1.10862e28	−	1.50050e28i	0.491785	−	0.665622i
$966$	1.35225e28	−	7.73426e27i	0.593985	−	0.339732i
$967$	7.39163e27	+	7.39163e27i	0.321506	+	0.321506i	0.849345	−	0.527839i	$-0.176997\pi$
$967$	7.39163e27	+	7.39163e27i	0.321506	+	0.321506i	−0.527839	+	0.849345i	$0.676997\pi$
$968$	−3.24488e28	−	3.32484e28i	−1.39760	−	1.43204i
$969$		−	7.85630e28i		−	3.35075i
$970$	−2.88682e27	−	3.65413e27i	−0.121924	−	0.154331i
$971$		−	1.56188e28i		−	0.653227i	−0.945158	−	0.326613i	$-0.894092\pi$
$971$		−	1.56188e28i		−	0.653227i	0.945158	−	0.326613i	$-0.105908\pi$
$972$	−2.70999e28	+	7.02624e27i	−1.12238	+	0.291000i
$973$	−2.66513e27	−	2.66513e27i	−0.109307	−	0.109307i
$974$	−1.54698e28	−	2.70472e28i	−0.628310	−	1.09853i
$975$	−6.75379e27	+	2.07560e27i	−0.271646	+	0.0834833i
$976$	−9.92852e27	−	1.78599e28i	−0.395468	−	0.711385i
$977$	1.88319e28	−	1.88319e28i	0.742843	−	0.742843i	−0.230281	−	0.973124i	$-0.573965\pi$
$977$	1.88319e28	−	1.88319e28i	0.742843	−	0.742843i	0.973124	+	0.230281i	$0.0739647\pi$
$978$	5.57785e27	−	2.04840e28i	0.217895	−	0.800196i
$979$	−5.63644e28			−2.18057
$980$	1.87067e28	+	7.52883e27i	0.716719	+	0.288456i
$981$	2.52623e28			0.958556
$982$	3.31772e26	−	1.21840e27i	0.0124675	−	0.0457857i
$983$	−1.09141e28	+	1.09141e28i	−0.406190	+	0.406190i	−0.880408	−	0.474218i	$-0.842731\pi$
$983$	−1.09141e28	+	1.09141e28i	−0.406190	+	0.406190i	0.474218	+	0.880408i	$0.342731\pi$
$984$	3.50064e28	+	4.26071e26i	1.29031	+	0.0157047i
$985$	2.44690e27	+	1.80785e27i	0.0893246	+	0.0659962i
$986$	3.28639e28	+	5.74590e28i	1.18820	+	2.07743i
$987$	1.68519e27	+	1.68519e27i	0.0603441	+	0.0603441i
$988$	−2.29327e27	−	8.84505e27i	−0.0813325	−	0.313696i
$989$		−	2.02461e28i		−	0.711176i
$990$	−3.92558e27	+	3.34636e28i	−0.136575	+	1.16423i
$991$			5.11418e28i			1.76229i	0.472850	+	0.881143i	$0.343225\pi$
$991$			5.11418e28i			1.76229i	−0.472850	+	0.881143i	$0.656775\pi$
$992$	−3.82079e27	+	9.41148e26i	−0.130404	+	0.0321216i
$993$	6.00220e27	+	6.00220e27i	0.202905	+	0.202905i
$994$	9.01167e27	−	5.15426e27i	0.301741	−	0.172582i
$995$	−5.83176e27	−	3.88279e28i	−0.193411	−	1.28773i
$996$	1.27772e28	−	2.17217e28i	0.419730	−	0.713560i
$997$	−1.81837e28	+	1.81837e28i	−0.591668	+	0.591668i	−0.938082	−	0.346414i	$-0.887399\pi$
$997$	−1.81837e28	+	1.81837e28i	−0.591668	+	0.591668i	0.346414	+	0.938082i	$0.387399\pi$
$998$	3.48780e28	+	9.49736e27i	1.12412	+	0.306100i
$999$	−2.82399e26			−0.00901552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.20.e.b.3.50	yes	108
4.3	odd	2	inner	20.20.e.b.3.22	✓	108
5.2	odd	4	inner	20.20.e.b.7.22	yes	108
20.7	even	4	inner	20.20.e.b.7.50	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.20.e.b.3.22	✓	108	4.3	odd	2	inner
20.20.e.b.3.50	yes	108	1.1	even	1	trivial
20.20.e.b.7.22	yes	108	5.2	odd	4	inner
20.20.e.b.7.50	yes	108	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(698.639 + 190.241i) q^{2} +(-31214.8 + 31214.8i) q^{3} +(451905. + 265819. i) q^{4} +(648675. + 4.31888e6i) q^{5} +(-2.77462e7 + 1.58695e7i) q^{6} +(-3.60017e7 - 3.60017e7i) q^{7} +(2.65149e8 + 2.71683e8i) q^{8} -7.86460e8i q^{9} +(-3.68437e8 + 3.14074e9i) q^{10} +1.35477e10i q^{11} +(-2.24036e10 + 5.80861e9i) q^{12} +(-5.93370e9 - 5.93370e9i) q^{13} +(-1.83032e10 - 3.20011e10i) q^{14} +(-1.55061e11 - 1.14564e11i) q^{15} +(1.33558e11 + 2.40250e11i) q^{16} +(-6.05914e11 + 6.05914e11i) q^{17} +(1.49617e11 - 5.49452e11i) q^{18} +2.07691e12 q^{19} +(-8.54902e11 + 2.12415e12i) q^{20} +2.24757e12 q^{21} +(-2.57732e12 + 9.46492e12i) q^{22} +(6.76866e12 - 6.76866e12i) q^{23} +(-1.67571e13 - 2.03954e11i) q^{24} +(-1.82319e13 + 5.60310e12i) q^{25} +(-3.01668e12 - 5.27434e12i) q^{26} +(-1.17306e13 - 1.17306e13i) q^{27} +(-6.69939e12 - 2.58393e13i) q^{28} -1.06685e14i q^{29} +(-8.65368e13 - 1.09538e14i) q^{30} +1.97706e13i q^{31} +(4.76035e13 + 1.93256e14i) q^{32} +(-4.22887e14 - 4.22887e14i) q^{33} +(-5.38584e14 + 3.08045e14i) q^{34} +(1.32133e14 - 1.78840e14i) q^{35} +(2.09056e14 - 3.55405e14i) q^{36} +(1.20369e13 - 1.20369e13i) q^{37} +(1.45101e15 + 3.95113e14i) q^{38} +3.70438e14 q^{39} +(-1.00137e15 + 1.32138e15i) q^{40} -2.08906e15 q^{41} +(1.57024e15 + 4.27579e14i) q^{42} +(1.49558e15 - 1.49558e15i) q^{43} +(-3.60123e15 + 6.12225e15i) q^{44} +(3.39662e15 - 5.10157e14i) q^{45} +(6.01652e15 - 3.44117e15i) q^{46} +(7.49783e14 + 7.49783e14i) q^{47} +(-1.16683e16 - 3.33037e15i) q^{48} -8.80666e15i q^{49} +(-1.38035e16 + 4.46086e14i) q^{50} -3.78269e16i q^{51} +(-1.10417e15 - 4.25876e15i) q^{52} +(1.34040e16 + 1.34040e16i) q^{53} +(-5.96379e15 - 1.04271e16i) q^{54} +(-5.85106e16 + 8.78803e15i) q^{55} +(2.35231e14 - 1.93268e16i) q^{56} +(-6.48302e16 + 6.48302e16i) q^{57} +(2.02959e16 - 7.45344e16i) q^{58} +4.82890e16 q^{59} +(-3.96193e16 - 9.29904e16i) q^{60} -7.43386e16 q^{61} +(-3.76117e15 + 1.38125e16i) q^{62} +(-2.83139e16 + 2.83139e16i) q^{63} +(-3.50760e15 + 1.44072e17i) q^{64} +(2.17779e16 - 2.94760e16i) q^{65} +(-2.14995e17 - 3.75895e17i) q^{66} +(-2.26777e17 - 2.26777e17i) q^{67} +(-4.34879e17 + 1.12752e17i) q^{68} +4.22564e17i q^{69} +(1.26336e17 - 9.98075e16i) q^{70} +2.81605e17i q^{71} +(2.13667e17 - 2.08529e17i) q^{72} +(-2.08722e17 - 2.08722e17i) q^{73} +(1.06994e16 - 6.11954e15i) q^{74} +(3.94206e17 - 7.44004e17i) q^{75} +(9.38565e17 + 5.52082e17i) q^{76} +(4.87738e17 - 4.87738e17i) q^{77} +(2.58802e17 + 7.04724e16i) q^{78} +1.57651e18 q^{79} +(-9.50975e17 + 7.32665e17i) q^{80} +1.64640e18 q^{81} +(-1.45950e18 - 3.97424e17i) q^{82} +(-7.69941e17 + 7.69941e17i) q^{83} +(1.01569e18 + 5.97446e17i) q^{84} +(-3.00991e18 - 2.22383e18i) q^{85} +(1.32939e18 - 7.60349e17i) q^{86} +(3.33015e18 + 3.33015e18i) q^{87} +(-3.68066e18 + 3.59214e18i) q^{88} +4.16046e18i q^{89} +(2.47007e18 + 2.89761e17i) q^{90} +4.27246e17i q^{91} +(4.85803e18 - 1.25955e18i) q^{92} +(-6.17134e17 - 6.17134e17i) q^{93} +(3.81188e17 + 6.66467e17i) q^{94} +(1.34724e18 + 8.96991e18i) q^{95} +(-7.51838e18 - 4.54652e18i) q^{96} +(-1.04131e18 + 1.04131e18i) q^{97} +(1.67539e18 - 6.15267e18i) q^{98} +1.06547e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 1026 q^{2} - 7131840 q^{5} - 50939608 q^{6} + 1332591828 q^{8} + 1805468790 q^{10} + 25565343280 q^{12} - 99498527404 q^{13} + 759936037048 q^{16} + 1103360788948 q^{17} - 2932289137902 q^{18} - 4821918866500 q^{20}+ \cdots + 66\!\cdots\!58 q^{98}+O(q^{100}) \) 108 * q - 1026 * q^2 - 7131840 * q^5 - 50939608 * q^6 + 1332591828 * q^8 + 1805468790 * q^10 + 25565343280 * q^12 - 99498527404 * q^13 + 759936037048 * q^16 + 1103360788948 * q^17 - 2932289137902 * q^18 - 4821918866500 * q^20 + 3306300862704 * q^21 + 26555173338440 * q^22 - 57672549609740 * q^25 - 151870176076556 * q^26 + 145347487073040 * q^28 + 265510366207880 * q^30 + 451426657209224 * q^32 - 229672757216560 * q^33 - 2556468817119620 * q^36 - 2904533279226852 * q^37 + 4500710811976960 * q^38 + 2246744304601900 * q^40 - 4721437306521104 * q^41 + 452761724453480 * q^42 - 970083854699780 * q^45 + 8478786115826952 * q^46 + 16046505545373280 * q^48 + 56844159661370 * q^50 - 101281742222079732 * q^52 - 27665397406960484 * q^53 - 10433774450699008 * q^56 + 83589162043122240 * q^57 - 22879145244078184 * q^58 + 145234473586307920 * q^60 - 6358689987281664 * q^61 - 371338823915128280 * q^62 - 91631698278804820 * q^65 + 331374884002311600 * q^66 - 694094458817479804 * q^68 - 165782163012631200 * q^70 - 215667461842637436 * q^72 + 1087298370549745276 * q^73 + 1949878275840327200 * q^76 - 1250723257104163920 * q^77 + 668342418678475560 * q^78 + 4071497833979030320 * q^80 - 12135903560578575228 * q^81 - 3459475352437471112 * q^82 + 14947305238413951060 * q^85 + 11624244909135363112 * q^86 - 5598373834541334880 * q^88 - 9907327634674956330 * q^90 + 27521624775955257680 * q^92 - 25916131489404857680 * q^93 - 50213774290767283648 * q^96 + 8468568053676169148 * q^97 + 66196294974841827558 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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