LMFDB - Embedded newform 20.20.e.b.3.16

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			3.16
Character	$\chi$	$=$	20.3
Dual form			20.20.e.b.7.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-427.698 - 584.262i) q^{2} +(-45979.8 + 45979.8i) q^{3} +(-158436. + 499776. i) q^{4} +(2.76408e6 - 3.38132e6i) q^{5} +(4.65297e7 + 7.19877e6i) q^{6} +(-3.16871e7 - 3.16871e7i) q^{7} +(3.59763e8 - 1.21185e8i) q^{8} -3.06602e9i q^{9} +(-3.15777e9 - 1.68760e8i) q^{10} +1.21297e10i q^{11} +(-1.56947e10 - 3.02644e10i) q^{12} +(1.32322e10 + 1.32322e10i) q^{13} +(-4.96106e9 + 3.20661e10i) q^{14} +(2.83808e10 + 2.82564e11i) q^{15} +(-2.24674e11 - 1.58365e11i) q^{16} +(-4.04727e11 + 4.04727e11i) q^{17} +(-1.79136e12 + 1.31133e12i) q^{18} -1.51776e12 q^{19} +(1.25197e12 + 1.91714e12i) q^{20} +2.91393e12 q^{21} +(7.08694e12 - 5.18786e12i) q^{22} +(-1.32433e12 + 1.32433e12i) q^{23} +(-1.09698e13 + 2.21139e13i) q^{24} +(-3.79322e12 - 1.86925e13i) q^{25} +(2.07169e12 - 1.33905e13i) q^{26} +(8.75343e13 + 8.75343e13i) q^{27} +(2.08569e13 - 1.08161e13i) q^{28} +3.40394e13i q^{29} +(1.52953e14 - 1.37434e14i) q^{30} -8.97267e13i q^{31} +(3.56561e12 + 1.99001e14i) q^{32} +(-5.57722e14 - 5.57722e14i) q^{33} +(4.09568e14 + 6.33657e13i) q^{34} +(-1.94730e14 + 1.95588e13i) q^{35} +(1.53232e15 + 4.85769e14i) q^{36} +(-4.64329e14 + 4.64329e14i) q^{37} +(6.49143e14 + 8.86770e14i) q^{38} -1.21683e15 q^{39} +(5.84648e14 - 1.55144e15i) q^{40} -2.13183e14 q^{41} +(-1.24628e15 - 1.70250e15i) q^{42} +(-1.94630e15 + 1.94630e15i) q^{43} +(-6.06214e15 - 1.92179e15i) q^{44} +(-1.03672e16 - 8.47471e15i) q^{45} +(1.34017e15 + 2.07343e14i) q^{46} +(2.11340e15 + 2.11340e15i) q^{47} +(1.76121e16 - 3.04884e15i) q^{48} -9.39075e15i q^{49} +(-9.29896e15 + 1.02110e16i) q^{50} -3.72186e16i q^{51} +(-8.70960e15 + 4.51667e15i) q^{52} +(1.89585e16 + 1.89585e16i) q^{53} +(1.37047e16 - 8.85812e16i) q^{54} +(4.10145e16 + 3.35275e16i) q^{55} +(-1.52399e16 - 7.55986e15i) q^{56} +(6.97863e16 - 6.97863e16i) q^{57} +(1.98879e16 - 1.45586e16i) q^{58} -6.88149e16 q^{59} +(-1.45715e17 - 3.05844e16i) q^{60} +1.25032e17 q^{61} +(-5.24239e16 + 3.83760e16i) q^{62} +(-9.71533e16 + 9.71533e16i) q^{63} +(1.14744e17 - 8.71956e16i) q^{64} +(8.13173e16 - 8.16753e15i) q^{65} +(-8.73191e16 + 5.64392e17i) q^{66} +(-4.25112e16 - 4.25112e16i) q^{67} +(-1.38149e17 - 2.66397e17i) q^{68} -1.21785e17i q^{69} +(9.47132e16 + 1.05408e17i) q^{70} -7.48331e17i q^{71} +(-3.71555e17 - 1.10304e18i) q^{72} +(-1.09903e17 - 1.09903e17i) q^{73} +(4.69882e17 + 7.26971e16i) q^{74} +(1.03389e18 + 6.85065e17i) q^{75} +(2.40469e17 - 7.58540e17i) q^{76} +(3.84356e17 - 3.84356e17i) q^{77} +(5.20435e17 + 7.10946e17i) q^{78} +5.77533e17 q^{79} +(-1.15650e18 + 3.21960e17i) q^{80} -4.48610e18 q^{81} +(9.11780e16 + 1.24555e17i) q^{82} +(1.34675e17 - 1.34675e17i) q^{83} +(-4.61674e17 + 1.45631e18i) q^{84} +(2.49816e17 + 2.48721e18i) q^{85} +(1.96958e18 + 3.04721e17i) q^{86} +(-1.56512e18 - 1.56512e18i) q^{87} +(1.46994e18 + 4.36382e18i) q^{88} -3.17509e18i q^{89} +(-5.17421e17 + 9.68178e18i) q^{90} -8.38582e17i q^{91} +(-4.52047e17 - 8.71693e17i) q^{92} +(4.12562e18 + 4.12562e18i) q^{93} +(3.30882e17 - 2.13868e18i) q^{94} +(-4.19521e18 + 5.13204e18i) q^{95} +(-9.31396e18 - 8.98607e18i) q^{96} +(-7.79061e18 + 7.79061e18i) q^{97} +(-5.48666e18 + 4.01641e18i) q^{98} +3.71899e19 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 $

$2$	−427.698	−	584.262i	−0.590680	−	0.806906i
$2$	−427.698	−	584.262i	−0.590680	−	0.806906i
$3$	−45979.8	+	45979.8i	−1.34870	+	1.34870i	−0.461622	+	0.887077i	$0.652732\pi$
$3$	−45979.8	+	45979.8i	−1.34870	+	1.34870i	−0.887077	+	0.461622i	$0.847268\pi$
$4$	−158436.	+	499776.i	−0.302194	+	0.953247i
$5$	2.76408e6	−	3.38132e6i	0.632900	−	0.774233i
$5$	2.76408e6	−	3.38132e6i	0.632900	−	0.774233i
$6$	4.65297e7	+	7.19877e6i	1.88492	+	0.291623i
$7$	−3.16871e7	−	3.16871e7i	−0.296792	−	0.296792i	0.542964	−	0.839756i	$-0.317302\pi$
$7$	−3.16871e7	−	3.16871e7i	−0.296792	−	0.296792i	−0.839756	+	0.542964i	$0.817302\pi$
$8$	3.59763e8	−	1.21185e8i	0.947680	−	0.319222i
$9$		−	3.06602e9i		−	2.63798i
$10$	−3.15777e9	−	1.68760e8i	−0.998575	−	0.0533666i
$11$			1.21297e10i			1.55103i	0.631329	+	0.775515i	$0.282510\pi$
$11$			1.21297e10i			1.55103i	−0.631329	+	0.775515i	$0.717490\pi$
$12$	−1.56947e10	−	3.02644e10i	−0.878074	−	1.69321i
$13$	1.32322e10	+	1.32322e10i	0.346075	+	0.346075i	0.858645	−	0.512570i	$-0.171307\pi$
$13$	1.32322e10	+	1.32322e10i	0.346075	+	0.346075i	−0.512570	+	0.858645i	$0.671307\pi$
$14$	−4.96106e9	+	3.20661e10i	−0.0641739	+	0.414792i
$15$	2.83808e10	+	2.82564e11i	0.190615	+	1.89780i
$16$	−2.24674e11	−	1.58365e11i	−0.817358	−	0.576130i
$17$	−4.04727e11	+	4.04727e11i	−0.827748	+	0.827748i	−0.987205	−	0.159457i	$-0.949026\pi$
$17$	−4.04727e11	+	4.04727e11i	−0.827748	+	0.827748i	0.159457	+	0.987205i	$0.449026\pi$
$18$	−1.79136e12	+	1.31133e12i	−2.12860	+	1.55820i
$19$	−1.51776e12			−1.07906			−0.539528	−	0.841968i	$-0.681397\pi$
$19$	−1.51776e12			−1.07906			−0.539528	+	0.841968i	$0.681397\pi$
$20$	1.25197e12	+	1.91714e12i	0.546777	+	0.837278i
$21$	2.91393e12			0.800565
$22$	7.08694e12	−	5.18786e12i	1.25154	−	0.916163i
$23$	−1.32433e12	+	1.32433e12i	−0.153314	+	0.153314i	−0.779597	−	0.626282i	$-0.784576\pi$
$23$	−1.32433e12	+	1.32433e12i	−0.153314	+	0.153314i	0.626282	+	0.779597i	$0.284576\pi$
$24$	−1.09698e13	+	2.21139e13i	−0.847600	+	1.70867i
$25$	−3.79322e12	−	1.86925e13i	−0.198874	−	0.980025i
$26$	2.07169e12	−	1.33905e13i	0.0748303	−	0.483670i
$27$	8.75343e13	+	8.75343e13i	2.20914	+	2.20914i
$28$	2.08569e13	−	1.08161e13i	0.372604	−	0.193227i
$29$			3.40394e13i			0.435713i	0.975981	+	0.217856i	$0.0699065\pi$
$29$			3.40394e13i			0.435713i	−0.975981	+	0.217856i	$0.930094\pi$
$30$	1.52953e14	−	1.37434e14i	1.41875	−	1.27480i
$31$		−	8.97267e13i		−	0.609517i	−0.952430	−	0.304758i	$-0.901424\pi$
$31$		−	8.97267e13i		−	0.609517i	0.952430	−	0.304758i	$-0.0985757\pi$
$32$	3.56561e12	+	1.99001e14i	0.0179147	+	0.999840i
$33$	−5.57722e14	−	5.57722e14i	−2.09187	−	2.09187i
$34$	4.09568e14	+	6.33657e13i	1.15685	+	0.178980i
$35$	−1.94730e14	+	1.95588e13i	−0.417625	+	0.0419464i
$36$	1.53232e15	+	4.85769e14i	2.51464	+	0.797179i
$37$	−4.64329e14	+	4.64329e14i	−0.587366	+	0.587366i	−0.936917	−	0.349551i	$-0.886334\pi$
$37$	−4.64329e14	+	4.64329e14i	−0.587366	+	0.587366i	0.349551	+	0.936917i	$0.386334\pi$
$38$	6.49143e14	+	8.86770e14i	0.637377	+	0.870696i
$39$	−1.21683e15			−0.933502
$40$	5.84648e14	−	1.55144e15i	0.352635	−	0.935761i
$41$	−2.13183e14			−0.101696			−0.0508482	−	0.998706i	$-0.516192\pi$
$41$	−2.13183e14			−0.101696			−0.0508482	+	0.998706i	$0.516192\pi$
$42$	−1.24628e15	−	1.70250e15i	−0.472878	−	0.645980i
$43$	−1.94630e15	+	1.94630e15i	−0.590554	+	0.590554i	−0.937781	−	0.347227i	$-0.887123\pi$
$43$	−1.94630e15	+	1.94630e15i	−0.590554	+	0.590554i	0.347227	+	0.937781i	$0.387123\pi$
$44$	−6.06214e15	−	1.92179e15i	−1.47851	−	0.468711i
$45$	−1.03672e16	−	8.47471e15i	−2.04241	−	1.66958i
$46$	1.34017e15	+	2.07343e14i	0.214270	+	0.0331505i
$47$	2.11340e15	+	2.11340e15i	0.275456	+	0.275456i	0.831292	−	0.555836i	$-0.187602\pi$
$47$	2.11340e15	+	2.11340e15i	0.275456	+	0.275456i	−0.555836	+	0.831292i	$0.687602\pi$
$48$	1.76121e16	−	3.04884e15i	1.87940	−	0.325344i
$49$		−	9.39075e15i		−	0.823829i
$50$	−9.29896e15	+	1.02110e16i	−0.673317	+	0.739354i
$51$		−	3.72186e16i		−	2.23276i
$52$	−8.70960e15	+	4.51667e15i	−0.434477	+	0.225313i
$53$	1.89585e16	+	1.89585e16i	0.789194	+	0.789194i	0.981362	−	0.192168i	$-0.0615519\pi$
$53$	1.89585e16	+	1.89585e16i	0.789194	+	0.789194i	−0.192168	+	0.981362i	$0.561552\pi$
$54$	1.37047e16	−	8.85812e16i	0.477671	−	3.08746i
$55$	4.10145e16	+	3.35275e16i	1.20086	+	0.981648i
$56$	−1.52399e16	−	7.55986e15i	−0.376006	−	0.186521i
$57$	6.97863e16	−	6.97863e16i	1.45532	−	1.45532i
$58$	1.98879e16	−	1.45586e16i	0.351579	−	0.257367i
$59$	−6.88149e16			−1.03416			−0.517080	−	0.855937i	$-0.672981\pi$
$59$	−6.88149e16			−1.03416			−0.517080	+	0.855937i	$0.672981\pi$
$60$	−1.45715e17	−	3.05844e16i	−1.86667	−	0.391799i
$61$	1.25032e17			1.36895			0.684476	−	0.729035i	$-0.260031\pi$
$61$	1.25032e17			1.36895			0.684476	+	0.729035i	$0.260031\pi$
$62$	−5.24239e16	+	3.83760e16i	−0.491823	+	0.360030i
$63$	−9.71533e16	+	9.71533e16i	−0.782929	+	0.782929i
$64$	1.14744e17	−	8.71956e16i	0.796194	−	0.605041i
$65$	8.13173e16	−	8.16753e15i	0.486974	−	0.0489118i
$66$	−8.73191e16	+	5.64392e17i	−0.452316	+	2.92357i
$67$	−4.25112e16	−	4.25112e16i	−0.190894	−	0.190894i	0.605188	−	0.796082i	$-0.293098\pi$
$67$	−4.25112e16	−	4.25112e16i	−0.190894	−	0.190894i	−0.796082	+	0.605188i	$0.793098\pi$
$68$	−1.38149e17	−	2.66397e17i	−0.538907	−	1.03919i
$69$		−	1.21785e17i		−	0.413550i
$70$	9.47132e16	+	1.05408e17i	0.280530	+	0.312207i
$71$		−	7.48331e17i		−	1.93704i	−0.248930	−	0.968521i	$-0.580079\pi$
$71$		−	7.48331e17i		−	1.93704i	0.248930	−	0.968521i	$-0.419921\pi$
$72$	−3.71555e17	−	1.10304e18i	−0.842101	−	2.49996i
$73$	−1.09903e17	−	1.09903e17i	−0.218496	−	0.218496i	0.589368	−	0.807864i	$-0.299377\pi$
$73$	−1.09903e17	−	1.09903e17i	−0.218496	−	0.218496i	−0.807864	+	0.589368i	$0.799377\pi$
$74$	4.69882e17	+	7.26971e16i	0.820895	+	0.127004i
$75$	1.03389e18	+	6.85065e17i	1.58998	+	1.05354i
$76$	2.40469e17	−	7.58540e17i	0.326084	−	1.02861i
$77$	3.84356e17	−	3.84356e17i	0.460333	−	0.460333i
$78$	5.20435e17	+	7.10946e17i	0.551401	+	0.753248i
$79$	5.77533e17			0.542150			0.271075	−	0.962558i	$-0.412621\pi$
$79$	5.77533e17			0.542150			0.271075	+	0.962558i	$0.412621\pi$
$80$	−1.15650e18	+	3.21960e17i	−0.963365	+	0.268193i
$81$	−4.48610e18			−3.32094
$82$	9.11780e16	+	1.24555e17i	0.0600701	+	0.0820594i
$83$	1.34675e17	−	1.34675e17i	0.0790761	−	0.0790761i	−0.666462	−	0.745539i	$-0.732192\pi$
$83$	1.34675e17	−	1.34675e17i	0.0790761	−	0.0790761i	0.745539	+	0.666462i	$0.232192\pi$
$84$	−4.61674e17	+	1.45631e18i	−0.241926	+	0.763136i
$85$	2.49816e17	+	2.48721e18i	0.116988	+	1.16475i
$86$	1.96958e18	+	3.04721e17i	0.825351	+	0.127693i
$87$	−1.56512e18	−	1.56512e18i	−0.587645	−	0.587645i
$88$	1.46994e18	+	4.36382e18i	0.495123	+	1.46988i
$89$		−	3.17509e18i		−	0.960618i	−0.877099	−	0.480309i	$-0.840525\pi$
$89$		−	3.17509e18i		−	0.960618i	0.877099	−	0.480309i	$-0.159475\pi$
$90$	−5.17421e17	+	9.68178e18i	−0.140780	+	2.63422i
$91$		−	8.38582e17i		−	0.205424i
$92$	−4.52047e17	−	8.71693e17i	−0.0998158	−	0.192477i
$93$	4.12562e18	+	4.12562e18i	0.822055	+	0.822055i
$94$	3.30882e17	−	2.13868e18i	0.0595606	−	0.384974i
$95$	−4.19521e18	+	5.13204e18i	−0.682935	+	0.835441i
$96$	−9.31396e18	−	8.98607e18i	−1.37264	−	1.32432i
$97$	−7.79061e18	+	7.79061e18i	−1.04050	+	1.04050i	−0.0413503	+	0.999145i	$0.513166\pi$
$97$	−7.79061e18	+	7.79061e18i	−1.04050	+	1.04050i	−0.999145	+	0.0413503i	$0.986834\pi$
$98$	−5.48666e18	+	4.01641e18i	−0.664753	+	0.486620i
$99$	3.71899e19			4.09158
$100$	9.94304e18	+	1.06581e18i	0.994304	+	0.106581i
$101$	1.83896e19			1.67309			0.836547	−	0.547896i	$-0.184571\pi$
$101$	1.83896e19			1.67309			0.836547	+	0.547896i	$0.184571\pi$
$102$	−2.17454e19	+	1.59183e19i	−1.80163	+	1.31885i
$103$	1.19719e19	−	1.19719e19i	0.904089	−	0.904089i	−0.0916982	−	0.995787i	$-0.529229\pi$
$103$	1.19719e19	−	1.19719e19i	0.904089	−	0.904089i	0.995787	+	0.0916982i	$0.0292295\pi$
$104$	6.36400e18	+	3.15692e18i	0.438443	+	0.217494i
$105$	8.05434e18	−	9.85296e18i	0.506678	−	0.619824i
$106$	2.96822e18	−	1.91853e19i	0.170644	−	1.10297i
$107$	−5.71673e18	−	5.71673e18i	−0.300609	−	0.300609i	0.540643	−	0.841252i	$-0.318181\pi$
$107$	−5.71673e18	−	5.71673e18i	−0.300609	−	0.300609i	−0.841252	+	0.540643i	$0.818181\pi$
$108$	−5.76161e19	+	2.98789e19i	−2.77344	+	1.43826i
$109$			1.44964e19i			0.639305i	0.947535	+	0.319653i	$0.103566\pi$
$109$			1.44964e19i			0.639305i	−0.947535	+	0.319653i	$0.896434\pi$
$110$	2.04701e18	−	3.83029e19i	0.0827732	−	1.54882i
$111$		−	4.26995e19i		−	1.58436i
$112$	2.10112e18	+	1.21374e19i	0.0715945	+	0.413576i
$113$	−1.55116e19	−	1.55116e19i	−0.485748	−	0.485748i	0.421214	−	0.906961i	$-0.361604\pi$
$113$	−1.55116e19	−	1.55116e19i	−0.485748	−	0.485748i	−0.906961	+	0.421214i	$0.861604\pi$
$114$	−7.06209e19	−	1.09260e19i	−2.03394	−	0.314677i
$115$	8.17440e17	+	8.13857e18i	0.0216684	+	0.215734i
$116$	−1.70120e19	−	5.39308e18i	−0.415342	−	0.131670i
$117$	4.05702e19	−	4.05702e19i	0.912938	−	0.912938i
$118$	2.94320e19	+	4.02059e19i	0.610858	+	0.834470i
$119$	2.56493e19			0.491337
$120$	4.44529e19	+	9.82168e19i	0.786462	+	1.73766i
$121$	−8.59710e19			−1.40569
$122$	−5.34760e19	−	7.30516e19i	−0.808613	−	1.10462i
$123$	9.80210e18	−	9.80210e18i	0.137158	−	0.137158i
$124$	4.48432e19	+	1.42160e19i	0.581020	+	0.184192i
$125$	−7.36902e19	−	3.88414e19i	−0.884636	−	0.466283i
$126$	9.83153e19	+	1.52107e19i	1.09421	+	0.169289i
$127$	5.27142e19	+	5.27142e19i	0.544243	+	0.544243i	0.924770	−	0.380527i	$-0.124257\pi$
$127$	5.27142e19	+	5.27142e19i	0.544243	+	0.544243i	−0.380527	+	0.924770i	$0.624257\pi$
$128$	−1.00021e20	−	2.97470e19i	−0.958507	−	0.285068i
$129$		−	1.78981e20i		−	1.59296i
$130$	−3.95512e19	−	4.40174e19i	−0.327113	−	0.364051i
$131$		−	1.68250e20i		−	1.29383i	−0.762563	−	0.646914i	$-0.776059\pi$
$131$		−	1.68250e20i		−	1.29383i	0.762563	−	0.646914i	$-0.223941\pi$
$132$	3.67099e20	−	1.90372e20i	2.62622	−	1.36192i
$133$	4.80935e19	+	4.80935e19i	0.320255	+	0.320255i
$134$	−6.65572e18	+	4.30196e19i	−0.0412761	+	0.266791i
$135$	5.37933e20	−	5.40302e19i	3.10855	−	0.312223i
$136$	−9.65592e19	+	1.94653e20i	−0.520204	+	1.04868i
$137$	5.58824e19	−	5.58824e19i	0.280821	−	0.280821i	−0.552615	−	0.833436i	$-0.686370\pi$
$137$	5.58824e19	−	5.58824e19i	0.280821	−	0.280821i	0.833436	+	0.552615i	$0.186370\pi$
$138$	−7.11544e19	+	5.20873e19i	−0.333696	+	0.244276i
$139$	−2.44897e20			−1.07237			−0.536183	−	0.844102i	$-0.680134\pi$
$139$	−2.44897e20			−1.07237			−0.536183	+	0.844102i	$0.680134\pi$
$140$	2.10774e19	−	1.00420e20i	0.0862185	−	0.410776i
$141$	−1.94347e20			−0.743015
$142$	−4.37221e20	+	3.20060e20i	−1.56301	+	1.14417i
$143$	−1.60503e20	+	1.60503e20i	−0.536773	+	0.536773i
$144$	−4.85551e20	+	6.88853e20i	−1.51982	+	2.15617i
$145$	1.15098e20	+	9.40875e19i	0.337343	+	0.275763i
$146$	−1.72069e19	+	1.11218e20i	−0.0472444	+	0.305367i
$147$	4.31784e20	+	4.31784e20i	1.11110	+	1.11110i
$148$	−1.58494e20	−	3.05627e20i	−0.382407	−	0.737403i
$149$			2.34906e20i			0.531648i	0.964022	+	0.265824i	$0.0856441\pi$
$149$			2.34906e20i			0.531648i	−0.964022	+	0.265824i	$0.914356\pi$
$150$	−4.19346e19	−	8.97063e20i	−0.0890647	−	1.90527i
$151$		−	5.62967e20i		−	1.12254i	−0.827633	−	0.561270i	$-0.810313\pi$
$151$		−	5.62967e20i		−	1.12254i	0.827633	−	0.561270i	$-0.189687\pi$
$152$	−5.46034e20	+	1.83929e20i	−1.02260	+	0.344459i
$153$	1.24090e21	+	1.24090e21i	2.18358	+	2.18358i
$154$	−3.88953e20	−	6.01763e19i	−0.643355	−	0.0995356i
$155$	−3.03395e20	−	2.48012e20i	−0.471908	−	0.385764i
$156$	1.92790e20	−	6.08141e20i	0.282098	−	0.889858i
$157$	1.33071e20	−	1.33071e20i	0.183247	−	0.183247i	−0.609522	−	0.792769i	$-0.708639\pi$
$157$	1.33071e20	−	1.33071e20i	0.183247	−	0.183247i	0.792769	+	0.609522i	$0.208639\pi$
$158$	−2.47010e20	−	3.37431e20i	−0.320237	−	0.437464i
$159$	−1.74342e21			−2.12877
$160$	6.82742e20	+	5.37998e20i	0.785447	+	0.618929i
$161$	8.39287e19			0.0910049
$162$	1.91870e21	+	2.62106e21i	1.96161	+	2.67969i
$163$	1.45004e21	−	1.45004e21i	1.39829	−	1.39829i	0.593331	−	0.804958i	$-0.297812\pi$
$163$	1.45004e21	−	1.45004e21i	1.39829	−	1.39829i	0.804958	−	0.593331i	$-0.202188\pi$
$164$	3.37759e19	−	1.06544e20i	0.0307320	−	0.0969418i
$165$	−3.42742e21	+	3.44251e20i	−2.94354	+	0.295650i
$166$	−1.36286e20	−	2.10853e19i	−0.110516	−	0.0170983i
$167$	−2.41363e19	−	2.41363e19i	−0.0184869	−	0.0184869i	0.697803	−	0.716290i	$-0.254161\pi$
$167$	−2.41363e19	−	2.41363e19i	−0.0184869	−	0.0184869i	−0.716290	+	0.697803i	$0.754161\pi$
$168$	1.04833e21	−	3.53124e20i	0.758679	−	0.255558i
$169$		−	1.11174e21i		−	0.760464i
$170$	1.34634e21	−	1.20973e21i	0.870742	−	0.782394i
$171$			4.65348e21i			2.84652i
$172$	−6.64349e20	−	1.28108e21i	−0.384482	−	0.741406i
$173$	6.25877e20	+	6.25877e20i	0.342808	+	0.342808i	0.857422	−	0.514614i	$-0.172065\pi$
$173$	6.25877e20	+	6.25877e20i	0.342808	+	0.342808i	−0.514614	+	0.857422i	$0.672065\pi$
$174$	−2.45042e20	+	1.58384e21i	−0.127064	+	0.821285i
$175$	−4.72115e20	+	7.12508e20i	−0.231839	+	0.349887i
$176$	1.92093e21	−	2.72523e21i	0.893595	−	1.26775i
$177$	3.16409e21	−	3.16409e21i	1.39477	−	1.39477i
$178$	−1.85508e21	+	1.35798e21i	−0.775128	+	0.567418i
$179$	3.04524e20			0.120647			0.0603237	−	0.998179i	$-0.480787\pi$
$179$	3.04524e20			0.120647			0.0603237	+	0.998179i	$0.480787\pi$
$180$	5.87800e21	−	3.83857e21i	2.20872	−	1.44238i
$181$	−4.24832e21			−1.51450			−0.757252	−	0.653123i	$-0.773458\pi$
$181$	−4.24832e21			−1.51450			−0.757252	+	0.653123i	$0.773458\pi$
$182$	−4.89951e20	+	3.58660e20i	−0.165758	+	0.121340i
$183$	−5.74895e21	+	5.74895e21i	−1.84630	+	1.84630i
$184$	−3.15957e20	+	6.36935e20i	−0.0963516	+	0.194234i
$185$	2.86605e20	+	2.85349e21i	0.0830142	+	0.826503i
$186$	6.45922e20	−	4.17496e21i	0.177749	−	1.14889i
$187$	−4.90923e21	−	4.90923e21i	−1.28386	−	1.28386i
$188$	−1.39107e21	+	7.21387e20i	−0.345819	+	0.179337i
$189$		−	5.54742e21i		−	1.31131i
$190$	4.79274e21	+	2.56137e20i	1.07752	+	0.0575856i
$191$		−	6.44917e21i		−	1.37939i	−0.724101	−	0.689694i	$-0.757745\pi$
$191$		−	6.44917e21i		−	1.37939i	0.724101	−	0.689694i	$-0.242255\pi$
$192$	−1.26666e21	+	9.28512e21i	−0.257808	+	1.88984i
$193$	3.14770e21	+	3.14770e21i	0.609817	+	0.609817i	0.942898	−	0.333081i	$-0.108088\pi$
$193$	3.14770e21	+	3.14770e21i	0.609817	+	0.609817i	−0.333081	+	0.942898i	$0.608088\pi$
$194$	7.88379e21	+	1.21973e21i	1.45418	+	0.224981i
$195$	−3.36341e21	+	4.11449e21i	−0.590814	+	0.722749i
$196$	4.69327e21	+	1.48784e21i	0.785313	+	0.248956i
$197$	−4.87382e19	+	4.87382e19i	−0.00777034	+	0.00777034i	−0.710981	−	0.703211i	$-0.751749\pi$
$197$	−4.87382e19	+	4.87382e19i	−0.00777034	+	0.00777034i	0.703211	+	0.710981i	$0.251749\pi$
$198$	−1.59061e22	−	2.17287e22i	−2.41682	−	3.30152i
$199$	−2.58531e21			−0.374462			−0.187231	−	0.982316i	$-0.559951\pi$
$199$	−2.58531e21			−0.374462			−0.187231	+	0.982316i	$0.559951\pi$
$200$	−3.62991e21	−	6.26519e21i	−0.501315	−	0.865265i
$201$	3.90931e21			0.514917
$202$	−7.86522e21	−	1.07444e22i	−0.988263	−	1.35003i
$203$	1.07861e21	−	1.07861e21i	0.129316	−	0.129316i
$204$	1.86009e22	+	5.89678e21i	2.12837	+	0.674727i
$205$	−5.89254e20	+	7.20841e20i	−0.0643637	+	0.0787368i
$206$	−1.21151e22	−	1.87437e21i	−1.26354	−	0.195487i
$207$	4.06043e21	+	4.06043e21i	0.404440	+	0.404440i
$208$	−8.77405e20	−	5.06845e21i	−0.0834830	−	0.482252i
$209$		−	1.84100e22i		−	1.67365i
$210$	−9.20154e21	−	4.91756e20i	−0.799424	−	0.0427234i
$211$		−	1.13239e22i		−	0.940401i	−0.882560	−	0.470201i	$-0.844182\pi$
$211$		−	1.13239e22i		−	0.940401i	0.882560	−	0.470201i	$-0.155818\pi$
$212$	−1.24787e22	+	6.47129e21i	−0.990786	+	0.513807i
$213$	3.44081e22	+	3.44081e22i	2.61249	+	2.61249i
$214$	−8.95034e20	+	5.78510e21i	−0.0649993	+	0.420127i
$215$	1.20135e21	+	1.19608e22i	0.0834647	+	0.830989i
$216$	4.20994e22	+	2.08838e22i	2.79876	+	1.38835i
$217$	−2.84318e21	+	2.84318e21i	−0.180900	+	0.180900i
$218$	8.46970e21	−	6.20008e21i	0.515859	−	0.377625i
$219$	1.01067e22			0.589370
$220$	−2.32544e22	+	1.51861e22i	−1.29864	+	0.848067i
$221$	−1.07109e22			−0.572926
$222$	−2.49477e22	+	1.82625e22i	−1.27843	+	0.935850i
$223$	3.54410e21	−	3.54410e21i	0.174024	−	0.174024i	−0.614721	−	0.788745i	$-0.710731\pi$
$223$	3.54410e21	−	3.54410e21i	0.174024	−	0.174024i	0.788745	+	0.614721i	$0.210731\pi$
$224$	6.19279e21	−	6.41875e21i	0.291427	−	0.302061i
$225$	−5.73115e22	+	1.16301e22i	−2.58528	+	0.524625i
$226$	−2.42855e21	+	1.56971e22i	−0.105031	+	0.678874i
$227$	1.09704e21	+	1.09704e21i	0.0454966	+	0.0454966i	0.729489	−	0.683992i	$-0.239758\pi$
$227$	1.09704e21	+	1.09704e21i	0.0454966	+	0.0454966i	−0.683992	+	0.729489i	$0.739758\pi$
$228$	2.38208e22	+	4.59342e22i	0.947491	+	1.82707i
$229$		−	2.95241e22i		−	1.12652i	−0.826280	−	0.563260i	$-0.809547\pi$
$229$		−	2.95241e22i		−	1.12652i	0.826280	−	0.563260i	$-0.190453\pi$
$230$	4.40544e21	−	3.95845e21i	0.161278	−	0.144914i
$231$			3.53452e22i			1.24170i
$232$	4.12505e21	+	1.22461e22i	0.139089	+	0.412916i
$233$	−7.66411e21	−	7.66411e21i	−0.248074	−	0.248074i	0.572106	−	0.820180i	$-0.306127\pi$
$233$	−7.66411e21	−	7.66411e21i	−0.248074	−	0.248074i	−0.820180	+	0.572106i	$0.806127\pi$
$234$	−4.10554e22	−	6.35183e21i	−1.27591	−	0.197400i
$235$	1.29877e22	−	1.30449e21i	0.387604	−	0.0389310i
$236$	1.09028e22	−	3.43920e22i	0.312517	−	0.985810i
$237$	−2.65548e22	+	2.65548e22i	−0.731197	+	0.731197i
$238$	−1.09702e22	−	1.49859e22i	−0.290223	−	0.396463i
$239$	2.80760e22			0.713764			0.356882	−	0.934150i	$-0.383840\pi$
$239$	2.80760e22			0.713764			0.356882	+	0.934150i	$0.383840\pi$
$240$	3.83720e22	−	6.79793e22i	0.937578	−	1.66100i
$241$	2.74946e22			0.645780			0.322890	−	0.946436i	$-0.395346\pi$
$241$	2.74946e22			0.645780			0.322890	+	0.946436i	$0.395346\pi$
$242$	3.67696e22	+	5.02296e22i	0.830316	+	1.13426i
$243$	1.04532e23	−	1.04532e23i	2.26981	−	2.26981i
$244$	−1.98097e22	+	6.24880e22i	−0.413689	+	1.30495i
$245$	−3.17532e22	−	2.59568e22i	−0.637836	−	0.521402i
$246$	−9.91934e21	−	1.53466e21i	−0.191690	−	0.0296570i
$247$	−2.00833e22	−	2.00833e22i	−0.373435	−	0.373435i
$248$	−1.08735e22	−	3.22804e22i	−0.194571	−	0.577627i
$249$			1.23847e22i			0.213300i
$250$	8.82359e21	+	5.96668e22i	0.146290	+	0.989242i
$251$			1.95835e22i			0.312601i	0.987710	+	0.156301i	$0.0499569\pi$
$251$			1.95835e22i			0.312601i	−0.987710	+	0.156301i	$0.950043\pi$
$252$	−3.31622e22	−	6.39475e22i	−0.509728	−	0.982921i
$253$	−1.60638e22	−	1.60638e22i	−0.237795	−	0.237795i
$254$	8.25315e21	−	5.33447e22i	0.117679	−	0.760626i
$255$	−1.25848e23	−	1.02875e23i	−1.72868	−	1.41312i
$256$	2.53987e22	+	7.11611e22i	0.336148	+	0.941809i
$257$	4.88855e22	−	4.88855e22i	0.623469	−	0.623469i	−0.322948	−	0.946417i	$-0.604674\pi$
$257$	4.88855e22	−	4.88855e22i	0.623469	−	0.623469i	0.946417	+	0.322948i	$0.104674\pi$
$258$	−1.04572e23	+	7.65499e22i	−1.28537	+	0.940930i
$259$	2.94265e22			0.348651
$260$	−8.80169e21	+	4.19344e22i	−0.100535	+	0.478987i
$261$	1.04365e23			1.14940
$262$	−9.83018e22	+	7.19600e22i	−1.04400	+	0.764239i
$263$	3.92108e21	−	3.92108e21i	0.0401630	−	0.0401630i	−0.686740	−	0.726903i	$-0.740959\pi$
$263$	3.92108e21	−	3.92108e21i	0.0401630	−	0.0401630i	0.726903	+	0.686740i	$0.240959\pi$
$264$	−2.68235e23	−	1.33060e23i	−2.65020	−	1.31465i
$265$	1.16508e23	−	1.17021e22i	1.11050	−	0.111539i
$266$	7.52970e21	−	4.86687e22i	0.0692472	−	0.447584i
$267$	1.45990e23	+	1.45990e23i	1.29558	+	1.29558i
$268$	2.79814e22	−	1.45107e22i	0.239656	−	0.124282i
$269$			2.27073e20i			0.00187723i	1.00000		0.000938616i	$0.000298771\pi$
$269$			2.27073e20i			0.00187723i	−1.00000		0.000938616i	$0.999701\pi$
$270$	−2.61641e23	−	2.91186e23i	−2.08809	−	2.32388i
$271$			1.27249e23i			0.980497i	0.871583	+	0.490248i	$0.163094\pi$
$271$			1.27249e23i			0.980497i	−0.871583	+	0.490248i	$0.836906\pi$
$272$	1.55026e23	−	2.68368e22i	1.15346	−	0.199676i
$273$	3.85578e22	+	3.85578e22i	0.277056	+	0.277056i
$274$	−5.65508e22	−	8.74916e21i	−0.392471	−	0.0607206i
$275$	2.26735e23	−	4.60107e22i	1.52005	−	0.308460i
$276$	6.08653e22	+	1.92952e22i	0.394215	+	0.124972i
$277$	−6.38089e22	+	6.38089e22i	−0.399322	+	0.399322i	−0.877994	−	0.478672i	$-0.841118\pi$
$277$	−6.38089e22	+	6.38089e22i	−0.399322	+	0.399322i	0.478672	+	0.877994i	$0.341118\pi$
$278$	1.04742e23	+	1.43084e23i	0.633425	+	0.865298i
$279$	−2.75104e23			−1.60789
$280$	−6.76865e22	+	3.06349e22i	−0.382385	+	0.173067i
$281$	1.40329e23			0.766368			0.383184	−	0.923672i	$-0.374828\pi$
$281$	1.40329e23			0.766368			0.383184	+	0.923672i	$0.374828\pi$
$282$	8.31221e22	+	1.13550e23i	0.438884	+	0.599543i
$283$	−4.65354e22	+	4.65354e22i	−0.237581	+	0.237581i	−0.815848	−	0.578267i	$-0.803729\pi$
$283$	−4.65354e22	+	4.65354e22i	−0.237581	+	0.237581i	0.578267	+	0.815848i	$0.303729\pi$
$284$	3.73997e23	+	1.18563e23i	1.84648	+	0.585362i
$285$	−4.30753e22	−	4.28865e23i	−0.205685	−	2.04783i
$286$	1.62423e23	+	2.51290e22i	0.750187	+	0.116064i
$287$	6.75516e21	+	6.75516e21i	0.0301827	+	0.0301827i
$288$	6.10140e23	−	1.09322e22i	2.63755	−	0.0472586i
$289$		−	8.85361e22i		−	0.370332i
$290$	5.74448e21	−	1.07489e23i	0.0232525	−	0.435092i
$291$		−	7.16421e23i		−	2.80663i
$292$	7.23396e22	−	3.75143e22i	0.274309	−	0.142252i
$293$	−1.66605e23	−	1.66605e23i	−0.611570	−	0.611570i	0.331785	−	0.943355i	$-0.392349\pi$
$293$	−1.66605e23	−	1.66605e23i	−0.611570	−	0.611570i	−0.943355	+	0.331785i	$0.892349\pi$
$294$	6.76019e22	−	4.36949e23i	0.240248	−	1.55285i
$295$	−1.90210e23	+	2.32685e23i	−0.654521	+	0.800682i
$296$	−1.10779e23	+	2.23318e23i	−0.369135	+	0.744136i
$297$	−1.06177e24	+	1.06177e24i	−3.42644	+	3.42644i
$298$	1.37247e23	−	1.00469e23i	0.428990	−	0.314034i
$299$	−3.50477e22			−0.106117
$300$	−5.06184e23	+	4.08173e23i	−1.48476	+	1.19727i
$301$	1.23345e23			0.350543
$302$	−3.28920e23	+	2.40780e23i	−0.905784	+	0.663062i
$303$	−8.45551e23	+	8.45551e23i	−2.25650	+	2.25650i
$304$	3.41001e23	+	2.40361e23i	0.881975	+	0.621677i
$305$	3.45599e23	−	4.22774e23i	0.866410	−	1.05989i
$306$	1.94280e23	−	1.25574e24i	0.472145	−	3.05174i
$307$	2.43443e23	+	2.43443e23i	0.573566	+	0.573566i	0.933123	−	0.359557i	$-0.117072\pi$
$307$	2.43443e23	+	2.43443e23i	0.573566	+	0.573566i	−0.359557	+	0.933123i	$0.617072\pi$
$308$	1.31196e23	+	2.52988e23i	0.299701	+	0.577920i
$309$			1.10093e24i			2.43869i
$310$	−1.51423e22	+	2.83337e23i	−0.0325279	+	0.608648i
$311$		−	1.28917e23i		−	0.268587i	−0.990942	−	0.134294i	$-0.957123\pi$
$311$		−	1.28917e23i		−	0.268587i	0.990942	−	0.134294i	$-0.0428766\pi$
$312$	−4.37770e23	+	1.47461e23i	−0.884661	+	0.297995i
$313$	−3.43355e23	−	3.43355e23i	−0.673088	−	0.673088i	0.285339	−	0.958427i	$-0.407894\pi$
$313$	−3.43355e23	−	3.43355e23i	−0.673088	−	0.673088i	−0.958427	+	0.285339i	$0.907894\pi$
$314$	−1.34663e23	−	2.08342e22i	−0.256104	−	0.0396227i
$315$	5.99675e22	+	5.97046e23i	0.110654	+	1.10169i
$316$	−9.15023e22	+	2.88637e23i	−0.163834	+	0.516803i
$317$	3.18137e23	−	3.18137e23i	0.552779	−	0.552779i	−0.374463	−	0.927242i	$-0.622173\pi$
$317$	3.18137e23	−	3.18137e23i	0.552779	−	0.552779i	0.927242	+	0.374463i	$0.122173\pi$
$318$	7.45656e23	+	1.01861e24i	1.25742	+	1.71772i
$319$	−4.12888e23			−0.675804
$320$	2.23240e22	−	6.29001e23i	0.0354689	−	0.999371i
$321$	5.25708e23			0.810862
$322$	−3.58962e22	−	4.90364e22i	−0.0537548	−	0.0734323i
$323$	6.14279e23	−	6.14279e23i	0.893186	−	0.893186i
$324$	7.10762e23	−	2.24204e24i	1.00357	−	3.16568i
$325$	1.97150e23	−	2.97536e23i	0.270337	−	0.407988i
$326$	−1.46738e24	−	2.27024e23i	−1.95423	−	0.302346i
$327$	−6.66541e23	−	6.66541e23i	−0.862230	−	0.862230i
$328$	−7.66953e22	+	2.58345e22i	−0.0963757	+	0.0324638i
$329$		−	1.33935e23i		−	0.163506i
$330$	1.66704e24	+	1.85528e24i	1.97726	+	2.20053i
$331$			9.77956e22i			0.112708i	0.998411	+	0.0563538i	$0.0179475\pi$
$331$			9.77956e22i			0.112708i	−0.998411	+	0.0563538i	$0.982053\pi$
$332$	4.59699e22	+	8.86448e22i	0.0514828	+	0.0992754i
$333$	1.42364e24	+	1.42364e24i	1.54946	+	1.54946i
$334$	−3.77887e21	+	2.44250e22i	−0.00399734	+	0.0258370i
$335$	−2.61248e23	+	2.62398e22i	−0.268613	+	0.0269796i
$336$	−6.54684e23	−	4.61466e23i	−0.654348	−	0.461229i
$337$	−3.91966e22	+	3.91966e22i	−0.0380859	+	0.0380859i	−0.725893	−	0.687807i	$-0.758573\pi$
$337$	−3.91966e22	+	3.91966e22i	−0.0380859	+	0.0380859i	0.687807	+	0.725893i	$0.258573\pi$
$338$	−6.49546e23	+	4.75488e23i	−0.613623	+	0.449191i
$339$	1.42644e24			1.31025
$340$	−1.28263e24	−	2.69213e23i	−1.14565	−	0.240462i
$341$	1.08836e24			0.945379
$342$	2.71885e24	−	1.99029e24i	2.29688	−	1.68139i
$343$	−6.58764e23	+	6.58764e23i	−0.541297	+	0.541297i
$344$	−4.64345e23	+	9.36070e23i	−0.371138	+	0.748175i
$345$	−4.11795e23	−	3.36624e23i	−0.320184	−	0.261736i
$346$	9.79898e22	−	6.33363e23i	0.0741239	−	0.479104i
$347$	2.43972e23	+	2.43972e23i	0.179560	+	0.179560i	0.791164	−	0.611604i	$-0.209475\pi$
$347$	2.43972e23	+	2.43972e23i	0.179560	+	0.179560i	−0.611604	+	0.791164i	$0.709475\pi$
$348$	1.03018e24	−	5.34238e23i	0.737754	−	0.382588i
$349$		−	2.46619e24i		−	1.71864i	−0.511439	−	0.859320i	$-0.670887\pi$
$349$		−	2.46619e24i		−	1.71864i	0.511439	−	0.859320i	$-0.329113\pi$
$350$	6.18214e23	−	2.88994e22i	0.419269	−	0.0195994i
$351$			2.31654e24i			1.52905i
$352$	−2.41383e24	+	4.32499e22i	−1.55078	+	0.0277862i
$353$	−1.82317e24	−	1.82317e24i	−1.14016	−	1.14016i	−0.988420	−	0.151744i	$-0.951511\pi$
$353$	−1.82317e24	−	1.82317e24i	−1.14016	−	1.14016i	−0.151744	−	0.988420i	$-0.548489\pi$
$354$	−3.20194e24	−	4.95383e23i	−1.94931	−	0.301585i
$355$	−2.53035e24	−	2.06844e24i	−1.49972	−	1.22596i
$356$	1.58683e24	+	5.03050e23i	0.915706	+	0.290293i
$357$	−1.17935e24	+	1.17935e24i	−0.662666	+	0.662666i
$358$	−1.30244e23	−	1.77922e23i	−0.0712640	−	0.0973510i
$359$	−2.66261e24			−1.41876			−0.709382	−	0.704824i	$-0.751026\pi$
$359$	−2.66261e24			−1.41876			−0.709382	+	0.704824i	$0.751026\pi$
$360$	−4.75674e24	−	1.79254e24i	−2.46852	−	0.930241i
$361$	3.25177e23			0.164362
$362$	1.81700e24	+	2.48213e24i	0.894587	+	1.22206i
$363$	3.95293e24	−	3.95293e24i	1.89586	−	1.89586i
$364$	4.19103e23	+	1.32862e23i	0.195820	+	0.0620780i
$365$	−6.75400e23	+	6.78373e22i	−0.307453	+	0.0308806i
$366$	5.81771e24	+	9.00078e23i	2.58037	+	0.399218i
$367$	1.07337e24	+	1.07337e24i	0.463899	+	0.463899i	0.899931	−	0.436032i	$-0.143617\pi$
$367$	1.07337e24	+	1.07337e24i	0.463899	+	0.463899i	−0.436032	+	0.899931i	$0.643617\pi$
$368$	5.07272e23	−	8.78143e22i	0.213642	−	0.0369837i
$369$			6.53623e23i			0.268273i
$370$	1.54460e24	−	1.38788e24i	0.617875	−	0.555184i
$371$		−	1.20148e24i		−	0.468452i
$372$	−2.71553e24	+	1.40823e24i	−1.03204	+	0.535201i
$373$	−1.26225e24	−	1.26225e24i	−0.467642	−	0.467642i	0.433508	−	0.901150i	$-0.357276\pi$
$373$	−1.26225e24	−	1.26225e24i	−0.467642	−	0.467642i	−0.901150	+	0.433508i	$0.857276\pi$
$374$	−7.68608e23	+	4.96795e24i	−0.277603	+	1.79431i
$375$	5.17418e24	−	1.60234e24i	1.82198	−	0.564231i
$376$	1.01644e24	+	5.04212e23i	0.348976	+	0.173113i
$377$	−4.50416e23	+	4.50416e23i	−0.150789	+	0.150789i
$378$	−3.24115e24	+	2.37262e24i	−1.05810	+	0.774563i
$379$	1.80568e24			0.574867			0.287433	−	0.957801i	$-0.407198\pi$
$379$	1.80568e24			0.574867			0.287433	+	0.957801i	$0.407198\pi$
$380$	−1.90019e24	−	2.90977e24i	−0.590003	−	0.903470i
$381$	−4.84758e24			−1.46804
$382$	−3.76800e24	+	2.75830e24i	−1.11304	+	0.814778i
$383$	−3.81931e23	+	3.81931e23i	−0.110052	+	0.110052i	−0.759988	−	0.649937i	$-0.774795\pi$
$383$	−3.81931e23	+	3.81931e23i	−0.110052	+	0.110052i	0.649937	+	0.759988i	$0.274795\pi$
$384$	5.96669e24	−	3.23117e24i	1.67721	−	0.908267i
$385$	−2.37242e23	−	2.36202e24i	−0.0650601	−	0.647750i
$386$	4.92817e23	−	3.18535e24i	0.131858	−	0.852271i
$387$	5.96740e24	+	5.96740e24i	1.55787	+	1.55787i
$388$	−2.65924e24	−	5.12787e24i	−0.677417	−	1.30628i
$389$		−	1.19323e24i		−	0.296621i	−0.988941	−	0.148310i	$-0.952617\pi$
$389$		−	1.19323e24i		−	0.296621i	0.988941	−	0.148310i	$-0.0473835\pi$
$390$	3.84246e24	+	2.05352e23i	0.932172	+	0.0498179i
$391$		−	1.07199e24i		−	0.253811i
$392$	−1.13802e24	−	3.37844e24i	−0.262985	−	0.780727i
$393$	7.73607e24	+	7.73607e24i	1.74498	+	1.74498i
$394$	4.93211e22	+	7.63064e21i	0.0108597	+	0.00168014i
$395$	1.59635e24	−	1.95283e24i	0.343127	−	0.419751i
$396$	−5.89224e24	+	1.85866e25i	−1.23645	+	3.90028i
$397$	5.49190e24	−	5.49190e24i	1.12516	−	1.12516i	0.134202	−	0.990954i	$-0.457153\pi$
$397$	5.49190e24	−	5.49190e24i	1.12516	−	1.12516i	0.990954	−	0.134202i	$-0.0428472\pi$
$398$	1.10573e24	+	1.51050e24i	0.221187	+	0.302156i
$399$	−4.42265e24			−0.863854
$400$	−2.10801e24	+	4.80043e24i	−0.402070	+	0.915609i
$401$	7.02378e24			1.30828			0.654138	−	0.756375i	$-0.273032\pi$
$401$	7.02378e24			1.30828			0.654138	+	0.756375i	$0.273032\pi$
$402$	−1.67200e24	−	2.28406e24i	−0.304151	−	0.415490i
$403$	1.18728e24	−	1.18728e24i	0.210939	−	0.210939i
$404$	−2.91359e24	+	9.19069e24i	−0.505598	+	1.59487i
$405$	−1.23999e25	+	1.51690e25i	−2.10182	+	2.57118i
$406$	−1.09151e24	−	1.68871e23i	−0.180730	−	0.0279614i
$407$	−5.63218e24	−	5.63218e24i	−0.911023	−	0.911023i
$408$	−4.51032e24	−	1.33899e25i	−0.712748	−	2.11595i
$409$			6.00851e24i			0.927673i	0.885921	+	0.463837i	$0.153528\pi$
$409$			6.00851e24i			0.927673i	−0.885921	+	0.463837i	$0.846472\pi$
$410$	6.73183e23	+	3.59768e22i	0.101552	+	0.00542719i
$411$			5.13892e24i			0.757486i
$412$	4.08649e24	+	7.88008e24i	0.588610	+	1.13503i
$413$	2.18055e24	+	2.18055e24i	0.306930	+	0.306930i
$414$	6.35717e23	−	4.10900e24i	0.0874501	−	0.565239i
$415$	−8.31277e22	−	8.27633e23i	−0.0111761	−	0.111271i
$416$	−2.58604e24	+	2.68040e24i	−0.339820	+	0.352220i
$417$	1.12603e25	−	1.12603e25i	1.44630	−	1.44630i
$418$	−1.07563e25	+	7.87393e24i	−1.35048	+	0.988591i
$419$	−1.14899e24			−0.141021			−0.0705106	−	0.997511i	$-0.522463\pi$
$419$	−1.14899e24			−0.141021			−0.0705106	+	0.997511i	$0.522463\pi$
$420$	3.64817e24	+	5.58643e24i	0.437730	+	0.670296i
$421$	−9.07116e24			−1.06410			−0.532051	−	0.846713i	$-0.678578\pi$
$421$	−9.07116e24			−1.06410			−0.532051	+	0.846713i	$0.678578\pi$
$422$	−6.61613e24	+	4.84322e24i	−0.758815	+	0.555476i
$423$	6.47973e24	−	6.47973e24i	0.726647	−	0.726647i
$424$	9.11806e24	+	4.52309e24i	0.999831	+	0.495975i
$425$	9.10059e24	+	6.03014e24i	0.975831	+	0.646596i
$426$	5.38706e24	−	3.48196e25i	0.564886	−	3.65118i
$427$	−3.96191e24	−	3.96191e24i	−0.406294	−	0.406294i
$428$	3.76282e24	−	1.95134e24i	0.377396	−	0.195712i
$429$		−	1.47598e25i		−	1.44789i
$430$	6.47444e24	−	5.81752e24i	0.621229	−	0.558197i
$431$			1.59071e25i			1.49299i	0.665391	+	0.746495i	$0.268265\pi$
$431$			1.59071e25i			1.49299i	−0.665391	+	0.746495i	$0.731735\pi$
$432$	−5.80425e24	−	3.35291e25i	−0.532905	−	3.07840i
$433$	−1.13785e25	−	1.13785e25i	−1.02200	−	1.02200i	−0.999753	−	0.0222471i	$-0.992918\pi$
$433$	−1.13785e25	−	1.13785e25i	−1.02200	−	1.02200i	−0.0222471	−	0.999753i	$-0.507082\pi$
$434$	2.87719e24	+	4.45140e23i	0.252823	+	0.0391151i
$435$	−9.61831e24	+	9.66065e23i	−0.826896	+	0.0830536i
$436$	−7.24495e24	−	2.29676e24i	−0.609416	−	0.193194i
$437$	2.01002e24	−	2.01002e24i	0.165435	−	0.165435i
$438$	−4.32260e24	−	5.90493e24i	−0.348129	−	0.475566i
$439$	1.88846e25			1.48831			0.744157	−	0.668005i	$-0.232851\pi$
$439$	1.88846e25			1.48831			0.744157	+	0.668005i	$0.232851\pi$
$440$	1.88185e25	+	7.09162e24i	1.45139	+	0.546947i
$441$	−2.87922e25			−2.17324
$442$	4.58102e24	+	6.25796e24i	0.338416	+	0.462297i
$443$	−1.56992e25	+	1.56992e25i	−1.13512	+	1.13512i	−0.145807	+	0.989313i	$0.546578\pi$
$443$	−1.56992e25	+	1.56992e25i	−1.13512	+	1.13512i	−0.989313	+	0.145807i	$0.953422\pi$
$444$	2.13402e25	+	6.76515e24i	1.51029	+	0.478784i
$445$	−1.07360e25	−	8.77619e24i	−0.743742	−	0.607976i
$446$	−3.58649e24	−	5.54878e23i	−0.243214	−	0.0376285i
$447$	−1.08009e25	−	1.08009e25i	−0.717033	−	0.717033i
$448$	−6.39888e24	−	8.72921e23i	−0.415875	−	0.0567327i
$449$		−	1.69649e25i		−	1.07947i	−0.841835	−	0.539735i	$-0.818524\pi$
$449$		−	1.69649e25i		−	1.07947i	0.841835	−	0.539735i	$-0.181476\pi$
$450$	3.13071e25	+	2.85108e25i	1.95040	+	1.77619i
$451$		−	2.58585e24i		−	0.157734i
$452$	1.02099e25	−	5.29471e24i	0.609827	−	0.316247i
$453$	2.58851e25	+	2.58851e25i	1.51397	+	1.51397i
$454$	1.71758e23	−	1.11017e24i	0.00983751	−	0.0635854i
$455$	−2.83552e24	−	2.31791e24i	−0.159046	−	0.130013i
$456$	1.66495e25	−	3.35636e25i	0.914608	−	1.84375i
$457$	−1.91033e25	+	1.91033e25i	−1.02779	+	1.02779i	−0.0281898	+	0.999603i	$0.508974\pi$
$457$	−1.91033e25	+	1.91033e25i	−1.02779	+	1.02779i	−0.999603	+	0.0281898i	$0.991026\pi$
$458$	−1.72498e25	+	1.26274e25i	−0.908996	+	0.665413i
$459$	−7.08550e25			−3.65721
$460$	−4.19697e24	−	8.80909e23i	−0.212196	−	0.0445381i
$461$	2.13088e25			1.05536			0.527680	−	0.849443i	$-0.323062\pi$
$461$	2.13088e25			1.05536			0.527680	+	0.849443i	$0.323062\pi$
$462$	2.06509e25	−	1.51171e25i	1.00194	−	0.733448i
$463$	−4.63353e23	+	4.63353e23i	−0.0220238	+	0.0220238i	−0.718033	−	0.696009i	$-0.754957\pi$
$463$	−4.63353e23	+	4.63353e23i	−0.0220238	+	0.0220238i	0.696009	+	0.718033i	$0.254957\pi$
$464$	5.39066e24	−	7.64775e24i	0.251027	−	0.356133i
$465$	2.53536e25	−	2.54652e24i	1.15674	−	0.116183i
$466$	−1.19992e24	+	7.75578e24i	−0.0536398	+	0.346704i
$467$	1.31288e25	+	1.31288e25i	0.575063	+	0.575063i	0.933539	−	0.358476i	$-0.116703\pi$
$467$	1.31288e25	+	1.31288e25i	0.575063	+	0.575063i	−0.358476	+	0.933539i	$0.616703\pi$
$468$	1.38482e25	+	2.67038e25i	0.594371	+	1.14614i
$469$			2.69411e24i			0.113312i
$470$	−6.31698e24	−	7.03030e24i	−0.260363	−	0.289764i
$471$			1.22372e25i			0.494291i
$472$	−2.47570e25	+	8.33931e24i	−0.980053	+	0.330127i
$473$	−2.36081e25	−	2.36081e25i	−0.915968	−	0.915968i
$474$	2.68724e25	+	4.15753e24i	1.02191	+	0.158103i
$475$	5.75721e24	+	2.83707e25i	0.214596	+	1.05750i
$476$	−4.06379e24	+	1.28189e25i	−0.148479	+	0.468365i
$477$	5.81272e25	−	5.81272e25i	2.08187	−	2.08187i
$478$	−1.20080e25	−	1.64037e25i	−0.421606	−	0.575940i
$479$	2.07362e25			0.713743			0.356871	−	0.934154i	$-0.383843\pi$
$479$	2.07362e25			0.713743			0.356871	+	0.934154i	$0.383843\pi$
$480$	−5.61294e25	+	6.65533e24i	−1.89408	+	0.224583i
$481$	−1.22882e25			−0.406546
$482$	−1.17594e25	−	1.60640e25i	−0.381450	−	0.521084i
$483$	−3.85902e24	+	3.85902e24i	−0.122738	+	0.122738i
$484$	1.36209e25	−	4.29662e25i	0.424792	−	1.33997i
$485$	4.80872e24	+	4.78764e25i	0.147056	+	1.46412i
$486$	−1.05782e26	−	1.63660e25i	−3.17226	−	0.490791i
$487$	3.05006e25	+	3.05006e25i	0.896980	+	0.896980i	0.995168	−	0.0981883i	$-0.0313047\pi$
$487$	3.05006e25	+	3.05006e25i	0.896980	+	0.896980i	−0.0981883	+	0.995168i	$0.531305\pi$
$488$	4.49820e25	−	1.51520e25i	1.29733	−	0.437000i
$489$			1.33345e26i			3.77174i
$490$	−1.58478e24	+	2.96538e25i	−0.0439650	+	0.822656i
$491$		−	3.92713e25i		−	1.06857i	−0.845306	−	0.534283i	$-0.820582\pi$
$491$		−	3.92713e25i		−	1.06857i	0.845306	−	0.534283i	$-0.179418\pi$
$492$	3.34584e24	+	6.45186e24i	0.0892970	+	0.172193i
$493$	−1.37767e25	−	1.37767e25i	−0.360660	−	0.360660i
$494$	−3.14432e24	+	2.03235e25i	−0.0807460	+	0.521907i
$495$	1.02796e26	−	1.25751e26i	2.58956	−	3.16784i
$496$	−1.42096e25	+	2.01592e25i	−0.351161	+	0.498194i
$497$	−2.37125e25	+	2.37125e25i	−0.574898	+	0.574898i
$498$	7.23589e24	−	5.29690e24i	0.172113	−	0.125992i
$499$	−8.09336e25			−1.88875			−0.944374	−	0.328874i	$-0.893331\pi$
$499$	−8.09336e25			−1.88875			−0.944374	+	0.328874i	$0.893331\pi$
$500$	3.10872e25	−	3.06747e25i	0.711814	−	0.702368i
$501$	2.21956e24			0.0498665
$502$	1.14419e25	−	8.37585e24i	0.252240	−	0.184648i
$503$	−1.90819e25	+	1.90819e25i	−0.412787	+	0.412787i	−0.882708	−	0.469922i	$-0.844282\pi$
$503$	−1.90819e25	+	1.90819e25i	−0.412787	+	0.412787i	0.469922	+	0.882708i	$0.344282\pi$
$504$	−2.31787e25	+	4.67257e25i	−0.492038	+	0.991895i
$505$	5.08304e25	−	6.21813e25i	1.05890	−	1.29536i
$506$	−2.51501e24	+	1.62559e25i	−0.0514174	+	0.332339i
$507$	5.11174e25	+	5.11174e25i	1.02564	+	1.02564i
$508$	−3.46972e25	+	1.79934e25i	−0.683264	+	0.354331i
$509$			5.89389e25i			1.13916i	0.821937	+	0.569578i	$0.192893\pi$
$509$			5.89389e25i			1.13916i	−0.821937	+	0.569578i	$0.807107\pi$
$510$	−6.28100e24	+	1.17528e26i	−0.119155	+	2.22958i
$511$			6.96504e24i			0.129695i
$512$	3.07138e25	−	4.52749e25i	0.561395	−	0.827548i
$513$	−1.32856e26	−	1.32856e26i	−2.38378	−	2.38378i
$514$	−4.94701e25	−	7.65370e24i	−0.871352	−	0.134810i
$515$	−7.38963e24	−	7.35724e25i	−0.127777	−	1.27217i
$516$	8.94504e25	+	2.83571e25i	1.51848	+	0.481382i
$517$	−2.56350e25	+	2.56350e25i	−0.427241	+	0.427241i
$518$	−1.25857e25	−	1.71928e25i	−0.205941	−	0.281328i
$519$	−5.75554e25			−0.924690
$520$	2.82652e25	−	1.27928e25i	0.445882	−	0.201806i
$521$	6.75661e25			1.04657			0.523287	−	0.852156i	$-0.324705\pi$
$521$	6.75661e25			1.04657			0.523287	+	0.852156i	$0.324705\pi$
$522$	−4.46368e25	−	6.09767e25i	−0.678928	−	0.927458i
$523$	2.69343e25	−	2.69343e25i	0.402290	−	0.402290i	−0.476749	−	0.879039i	$-0.658185\pi$
$523$	2.69343e25	−	2.69343e25i	0.402290	−	0.402290i	0.879039	+	0.476749i	$0.158185\pi$
$524$	8.40870e25	+	2.66569e25i	1.23334	+	0.390987i
$525$	−1.10532e25	−	5.44687e25i	−0.159212	−	0.784574i
$526$	−3.96798e24	−	6.13900e23i	−0.0561312	−	0.00868426i
$527$	3.63149e25	+	3.63149e25i	0.504526	+	0.504526i
$528$	3.69816e25	+	2.13629e26i	0.504618	+	2.91500i
$529$			7.11078e25i			0.952989i
$530$	−5.66672e25	−	6.30661e25i	−0.745953	−	0.830186i
$531$			2.10988e26i			2.72809i
$532$	−3.16557e25	+	1.64162e25i	−0.402061	+	0.208503i
$533$	−2.82088e24	−	2.82088e24i	−0.0351946	−	0.0351946i
$534$	2.28567e25	−	1.47736e26i	0.280138	−	1.81069i
$535$	−3.51316e25	+	3.52863e24i	−0.422997	+	0.0424859i
$536$	−2.04457e25	−	1.01422e25i	−0.241844	−	0.119969i
$537$	−1.40019e25	+	1.40019e25i	−0.162717	+	0.162717i
$538$	1.32670e23	−	9.71186e22i	0.00151475	−	0.00110884i
$539$	1.13907e26			1.27778
$540$	−5.82253e25	+	2.77406e26i	−0.641758	+	3.05757i
$541$	−1.61812e26			−1.75242			−0.876209	−	0.481931i	$-0.839936\pi$
$541$	−1.61812e26			−1.75242			−0.876209	+	0.481931i	$0.839936\pi$
$542$	7.43468e25	−	5.44242e25i	0.791168	−	0.579160i
$543$	1.95337e26	−	1.95337e26i	2.04261	−	2.04261i
$544$	−8.19842e25	−	7.90980e25i	−0.842444	−	0.812786i
$545$	4.90170e25	+	4.00692e25i	0.494972	+	0.404617i
$546$	6.03676e24	−	3.90190e25i	0.0599065	−	0.387209i
$547$	−1.87941e25	−	1.87941e25i	−0.183292	−	0.183292i	0.609497	−	0.792788i	$-0.291371\pi$
$547$	−1.87941e25	−	1.87941e25i	−0.183292	−	0.183292i	−0.792788	+	0.609497i	$0.791371\pi$
$548$	1.90749e25	+	3.67825e25i	0.182829	+	0.352554i
$549$		−	3.83351e26i		−	3.61126i
$550$	−1.23856e26	−	1.12794e26i	−1.14676	−	1.04433i
$551$		−	5.16636e25i		−	0.470159i
$552$	−1.47585e25	−	4.38138e25i	−0.132014	−	0.391913i
$553$	−1.83004e25	−	1.83004e25i	−0.160906	−	0.160906i
$554$	6.45721e25	+	9.99017e24i	0.558087	+	0.0863436i
$555$	−1.44381e26	−	1.18025e26i	−1.22666	−	1.00274i
$556$	3.88006e25	−	1.22394e26i	0.324062	−	1.02223i
$557$	1.21375e25	−	1.21375e25i	0.0996560	−	0.0996560i	−0.655521	−	0.755177i	$-0.727551\pi$
$557$	1.21375e25	−	1.21375e25i	0.0996560	−	0.0996560i	0.755177	+	0.655521i	$0.227551\pi$
$558$	1.17661e26	+	1.60733e26i	0.949750	+	1.29742i
$559$	−5.15078e25			−0.408753
$560$	4.68482e25	+	2.64442e25i	0.365516	+	0.206321i
$561$	4.51451e26			3.46308
$562$	−6.00184e25	−	8.19889e25i	−0.452678	−	0.618386i
$563$	1.69009e26	−	1.69009e26i	1.25337	−	1.25337i	0.299174	−	0.954199i	$-0.403289\pi$
$563$	1.69009e26	−	1.69009e26i	1.25337	−	1.25337i	0.954199	−	0.299174i	$-0.0967111\pi$
$564$	3.07917e25	−	9.71302e25i	0.224534	−	0.708276i
$565$	−9.53249e25	+	9.57446e24i	−0.683512	+	0.0686521i
$566$	4.70920e25	+	7.28576e24i	0.332040	+	0.0513711i
$567$	1.42152e26	+	1.42152e26i	0.985627	+	0.985627i
$568$	−9.06863e25	−	2.69222e26i	−0.618347	−	1.83570i
$569$			1.05542e26i			0.707719i	0.935299	+	0.353859i	$0.115131\pi$
$569$			1.05542e26i			0.707719i	−0.935299	+	0.353859i	$0.884869\pi$
$570$	−2.32146e26	+	2.08592e26i	−1.53091	+	1.37558i
$571$			1.80291e26i			1.16932i	0.811280	+	0.584658i	$0.198771\pi$
$571$			1.80291e26i			1.16932i	−0.811280	+	0.584658i	$0.801229\pi$
$572$	−5.47860e25	−	1.05645e26i	−0.349468	−	0.673887i
$573$	2.96531e26	+	2.96531e26i	1.86038	+	1.86038i
$574$	1.05761e24	−	6.83595e24i	0.00652626	−	0.0421828i
$575$	2.97786e25	+	1.97316e25i	0.180742	+	0.119762i
$576$	−2.67343e26	−	3.51806e26i	−1.59608	−	2.10034i
$577$	−2.07428e26	+	2.07428e26i	−1.21814	+	1.21814i	−0.249857	+	0.968283i	$0.580384\pi$
$577$	−2.07428e26	+	2.07428e26i	−1.21814	+	1.21814i	−0.968283	+	0.249857i	$0.919616\pi$
$578$	−5.17283e25	+	3.78668e25i	−0.298823	+	0.218748i
$579$	−2.89461e26			−1.64492
$580$	−6.52584e25	+	4.26164e25i	−0.364813	+	0.238238i
$581$	−8.53494e24			−0.0469383
$582$	−4.18578e26	+	3.06412e26i	−2.26468	+	1.65782i
$583$	−2.29962e26	+	2.29962e26i	−1.22406	+	1.22406i
$584$	−5.28577e25	−	2.62205e25i	−0.276813	−	0.137315i
$585$	−2.50418e25	−	2.49320e26i	−0.129028	−	1.28463i
$586$	−2.60844e25	+	1.68598e26i	−0.132237	+	0.854722i
$587$	−2.42138e26	−	2.42138e26i	−1.20782	−	1.20782i	−0.971733	−	0.236084i	$-0.924136\pi$
$587$	−2.42138e26	−	2.42138e26i	−1.20782	−	1.20782i	−0.236084	−	0.971733i	$-0.575864\pi$
$588$	−2.84206e26	+	1.47385e26i	−1.39492	+	0.723383i
$589$			1.36184e26i			0.657703i
$590$	2.17302e26	+	1.16132e25i	1.03269	+	0.0551897i
$591$		−	4.48194e24i		−	0.0209597i
$592$	1.77856e26	−	3.07888e25i	0.818488	−	0.141689i
$593$	−1.38270e26	−	1.38270e26i	−0.626192	−	0.626192i	0.320916	−	0.947108i	$-0.396009\pi$
$593$	−1.38270e26	−	1.38270e26i	−0.626192	−	0.626192i	−0.947108	+	0.320916i	$0.896009\pi$
$594$	1.07447e27	+	1.66234e26i	4.78874	+	0.740883i
$595$	7.08967e25	−	8.67286e25i	0.310967	−	0.380409i
$596$	−1.17400e26	−	3.72177e25i	−0.506792	−	0.160661i
$597$	1.18872e26	−	1.18872e26i	0.505037	−	0.505037i
$598$	1.49898e25	+	2.04771e25i	0.0626810	+	0.0856261i
$599$	−1.23448e26			−0.508077			−0.254039	−	0.967194i	$-0.581759\pi$
$599$	−1.23448e26			−0.508077			−0.254039	+	0.967194i	$0.581759\pi$
$600$	4.54974e26	+	1.21170e26i	1.84310	+	0.490859i
$601$	−1.99112e26			−0.793946			−0.396973	−	0.917830i	$-0.629939\pi$
$601$	−1.99112e26			−0.793946			−0.396973	+	0.917830i	$0.629939\pi$
$602$	−5.27546e25	−	7.20661e25i	−0.207059	−	0.282855i
$603$	−1.30340e26	+	1.30340e26i	−0.503574	+	0.503574i
$604$	2.81357e26	+	8.91944e25i	1.07006	+	0.339224i
$605$	−2.37631e26	+	2.90696e26i	−0.889665	+	1.08834i
$606$	8.55664e26	+	1.32383e26i	3.15365	+	0.487912i
$607$	1.48760e26	+	1.48760e26i	0.539752	+	0.539752i	0.923456	−	0.383704i	$-0.125352\pi$
$607$	1.48760e26	+	1.48760e26i	0.539752	+	0.539752i	−0.383704	+	0.923456i	$0.625352\pi$
$608$	−5.41175e24	−	3.02036e26i	−0.0193310	−	1.07888i
$609$			9.91885e25i			0.348816i
$610$	−3.94823e26	−	2.11004e25i	−1.36700	−	0.0730563i
$611$			5.59299e25i			0.190657i
$612$	−8.16776e26	+	4.23568e26i	−2.74135	+	1.42162i
$613$	1.03161e25	+	1.03161e25i	0.0340911	+	0.0340911i	0.723947	−	0.689856i	$-0.242326\pi$
$613$	1.03161e25	+	1.03161e25i	0.0340911	+	0.0340911i	−0.689856	+	0.723947i	$0.742326\pi$
$614$	3.81144e25	−	2.46355e26i	0.124020	−	0.801608i
$615$	−6.05031e24	−	6.02379e25i	−0.0193849	−	0.192999i
$616$	9.16990e25	−	1.84855e26i	0.289300	−	0.583197i
$617$	3.05115e25	−	3.05115e25i	0.0947881	−	0.0947881i	−0.658123	−	0.752911i	$-0.728649\pi$
$617$	3.05115e25	−	3.05115e25i	0.0947881	−	0.0947881i	0.752911	+	0.658123i	$0.228649\pi$
$618$	6.43234e26	−	4.70868e26i	1.96779	−	1.44048i
$619$	2.03477e26			0.612991			0.306495	−	0.951872i	$-0.400844\pi$
$619$	2.03477e26			0.612991			0.306495	+	0.951872i	$0.400844\pi$
$620$	1.72019e26	−	1.12335e26i	0.510335	−	0.333270i
$621$	−2.31849e26			−0.677385
$622$	−7.53212e25	+	5.51375e25i	−0.216725	+	0.158649i
$623$	−1.00609e26	+	1.00609e26i	−0.285103	+	0.285103i
$624$	2.73389e26	+	1.92703e26i	0.763006	+	0.537819i
$625$	−3.35021e26	+	1.41810e26i	−0.920898	+	0.389803i
$626$	−5.37570e25	+	3.47461e26i	−0.145539	+	0.940699i
$627$	8.46488e26	+	8.46488e26i	2.25725	+	2.25725i
$628$	4.54225e25	+	8.75892e25i	0.119304	+	0.230056i
$629$		−	3.75853e26i		−	0.972382i
$630$	3.23184e26	−	2.90392e26i	0.823596	−	0.740031i
$631$			1.04807e26i			0.263094i	0.991310	+	0.131547i	$0.0419944\pi$
$631$			1.04807e26i			0.263094i	−0.991310	+	0.131547i	$0.958006\pi$
$632$	2.07775e26	−	6.99882e25i	0.513785	−	0.173066i
$633$	5.20671e26	+	5.20671e26i	1.26832	+	1.26832i
$634$	−3.21942e26	−	4.98088e25i	−0.772557	−	0.119525i
$635$	3.23950e26	−	3.25376e25i	0.765822	−	0.0769194i
$636$	2.76221e26	−	8.71318e26i	0.643300	−	2.02924i
$637$	1.24260e26	−	1.24260e26i	0.285107	−	0.285107i
$638$	1.76591e26	+	2.41235e26i	0.399184	+	0.545310i
$639$	−2.29439e27			−5.10987
$640$	−3.77049e26	+	2.55980e26i	−0.827349	+	0.561689i
$641$	−9.55018e25			−0.206471			−0.103236	−	0.994657i	$-0.532920\pi$
$641$	−9.55018e25			−0.206471			−0.103236	+	0.994657i	$0.532920\pi$
$642$	−2.24844e26	−	3.07151e26i	−0.478960	−	0.654289i
$643$	3.45371e26	−	3.45371e26i	0.724906	−	0.724906i	−0.244694	−	0.969600i	$-0.578688\pi$
$643$	3.45371e26	−	3.45371e26i	0.724906	−	0.724906i	0.969600	+	0.244694i	$0.0786876\pi$
$644$	−1.32974e25	+	4.19455e25i	−0.0275011	+	0.0867501i
$645$	−6.05193e26	−	4.94718e26i	−1.23332	−	1.00818i
$646$	−6.21626e26	−	9.61740e25i	−1.24830	−	0.193129i
$647$	−2.62715e26	−	2.62715e26i	−0.519869	−	0.519869i	0.397663	−	0.917532i	$-0.369821\pi$
$647$	−2.62715e26	−	2.62715e26i	−0.519869	−	0.519869i	−0.917532	+	0.397663i	$0.869821\pi$
$648$	−1.61393e27	+	5.43647e26i	−3.14719	+	1.06012i
$649$		−	8.34705e26i		−	1.60401i
$650$	−2.58160e26	+	1.20681e25i	−0.488890	+	0.0228539i
$651$		−	2.61458e26i		−	0.487958i
$652$	4.94955e26	+	9.54433e26i	0.910361	+	1.75547i
$653$	7.30194e26	+	7.30194e26i	1.32362	+	1.32362i	0.910824	+	0.412795i	$0.135447\pi$
$653$	7.30194e26	+	7.30194e26i	1.32362	+	1.32362i	0.412795	+	0.910824i	$0.364553\pi$
$654$	−1.04356e26	+	6.74513e26i	−0.186436	+	1.20504i
$655$	−5.68906e26	−	4.65055e26i	−1.00172	−	0.818864i
$656$	4.78966e25	+	3.37608e25i	0.0831224	+	0.0585904i
$657$	−3.36965e26	+	3.36965e26i	−0.576387	+	0.576387i
$658$	−7.82533e25	+	5.72839e25i	−0.131934	+	0.0965799i
$659$	−3.08110e26			−0.512028			−0.256014	−	0.966673i	$-0.582409\pi$
$659$	−3.08110e26			−0.512028			−0.256014	+	0.966673i	$0.582409\pi$
$660$	3.70981e26	−	1.76749e27i	0.607692	−	2.89527i
$661$	1.13880e27			1.83879			0.919396	−	0.393334i	$-0.128678\pi$
$661$	1.13880e27			1.83879			0.919396	+	0.393334i	$0.128678\pi$
$662$	5.71383e25	−	4.18270e25i	0.0909445	−	0.0665742i
$663$	4.92484e26	−	4.92484e26i	0.772704	−	0.772704i
$664$	3.21306e25	−	6.47717e25i	0.0496960	−	0.100182i
$665$	2.95554e26	−	2.96855e25i	0.450641	−	0.0452625i
$666$	2.22891e26	−	1.44067e27i	0.335032	−	2.16550i
$667$	−4.50795e25	−	4.50795e25i	−0.0668011	−	0.0668011i
$668$	1.58868e25	−	8.23867e24i	0.0232092	−	0.0120360i
$669$			3.25914e26i			0.469413i
$670$	1.27066e26	+	1.41415e26i	0.180435	+	0.200809i
$671$			1.51661e27i			2.12329i
$672$	1.03900e25	+	5.79876e26i	0.0143419	+	0.800436i
$673$	1.17880e26	+	1.17880e26i	0.160434	+	0.160434i	0.782759	−	0.622325i	$-0.213812\pi$
$673$	1.17880e26	+	1.17880e26i	0.160434	+	0.160434i	−0.622325	+	0.782759i	$0.713812\pi$
$674$	3.96654e25	+	6.13678e24i	0.0532284	+	0.00823514i
$675$	1.30420e27	−	1.96827e27i	1.72567	−	2.60435i
$676$	5.55619e26	+	1.76140e26i	0.724910	+	0.229807i
$677$	9.77162e26	−	9.77162e26i	1.25711	−	1.25711i	0.304648	−	0.952465i	$-0.401461\pi$
$677$	9.77162e26	−	9.77162e26i	1.25711	−	1.25711i	0.952465	−	0.304648i	$-0.0985388\pi$
$678$	−6.10085e26	−	8.33413e26i	−0.773941	−	1.05725i
$679$	4.93724e26			0.617620
$680$	3.91287e26	+	8.64533e26i	0.482682	+	1.06647i
$681$	−1.00884e26			−0.122722
$682$	−4.65490e26	−	6.35888e26i	−0.558417	−	0.762832i
$683$	6.73263e26	−	6.73263e26i	0.796505	−	0.796505i	−0.186038	−	0.982543i	$-0.559565\pi$
$683$	6.73263e26	−	6.73263e26i	0.796505	−	0.796505i	0.982543	+	0.186038i	$0.0595647\pi$
$684$	−2.32570e27	−	7.37281e26i	−2.71344	−	0.860201i
$685$	−3.44932e25	−	3.43420e26i	−0.0396892	−	0.395153i
$686$	6.66643e26	+	1.03139e26i	0.756510	+	0.117042i
$687$	1.35751e27	+	1.35751e27i	1.51934	+	1.51934i
$688$	7.45510e26	−	1.29056e26i	0.822931	−	0.142458i
$689$			5.01726e26i			0.546241i
$690$	−2.05525e25	+	3.84570e26i	−0.0220698	+	0.412961i
$691$			7.49807e26i			0.794160i	0.917784	+	0.397080i	$0.129976\pi$
$691$			7.49807e26i			0.794160i	−0.917784	+	0.397080i	$0.870024\pi$
$692$	−4.11960e26	+	2.13637e26i	−0.430375	+	0.223186i
$693$	−1.17844e27	−	1.17844e27i	−1.21435	−	1.21435i
$694$	3.81973e25	−	2.46890e26i	0.0388255	−	0.250951i
$695$	−6.76914e26	+	8.28076e26i	−0.678700	+	0.830261i
$696$	−7.52742e26	−	3.73404e26i	−0.744489	−	0.369310i
$697$	8.62810e25	−	8.62810e25i	0.0841790	−	0.0841790i
$698$	−1.44090e27	+	1.05478e27i	−1.38678	+	1.01517i
$699$	7.04788e26			0.669153
$700$	−2.81294e26	−	3.48839e26i	−0.263469	−	0.326733i
$701$	−1.38487e27			−1.27964			−0.639818	−	0.768527i	$-0.720990\pi$
$701$	−1.38487e27			−1.27964			−0.639818	+	0.768527i	$0.720990\pi$
$702$	1.35347e27	−	9.90782e26i	1.23380	−	0.903182i
$703$	7.04740e26	−	7.04740e26i	0.633801	−	0.633801i
$704$	1.05766e27	+	1.39181e27i	0.938437	+	1.23492i
$705$	−5.37192e26	+	6.57152e26i	−0.470254	+	0.575267i
$706$	−2.85442e26	+	1.84497e27i	−0.246532	+	1.59348i
$707$	−5.82715e26	−	5.82715e26i	−0.496560	−	0.496560i
$708$	1.08003e27	+	2.08264e27i	0.908070	+	1.75105i
$709$		−	1.32760e27i		−	1.10136i	−0.834717	−	0.550680i	$-0.814369\pi$
$709$		−	1.32760e27i		−	1.10136i	0.834717	−	0.550680i	$-0.185631\pi$
$710$	−1.26288e26	+	2.36306e27i	−0.103373	+	1.93428i
$711$		−	1.77073e27i		−	1.43018i
$712$	−3.84772e26	−	1.14228e27i	−0.306651	−	0.910358i
$713$	1.18828e26	+	1.18828e26i	0.0934477	+	0.0934477i
$714$	1.19345e27	+	1.84644e26i	0.926132	+	0.143285i
$715$	9.90698e25	+	9.86356e26i	0.0758637	+	0.755311i
$716$	−4.82477e25	+	1.52194e26i	−0.0364588	+	0.115007i
$717$	−1.29093e27	+	1.29093e27i	−0.962652	+	0.962652i
$718$	1.13879e27	+	1.55566e27i	0.838036	+	1.14481i
$719$	−7.99366e25			−0.0580525			−0.0290263	−	0.999579i	$-0.509241\pi$
$719$	−7.99366e25			−0.0580525			−0.0290263	+	0.999579i	$0.509241\pi$
$720$	9.87135e26	+	3.54585e27i	0.707486	+	2.54133i
$721$	−7.58713e26			−0.536652
$722$	−1.39077e26	−	1.89988e26i	−0.0970853	−	0.132624i
$723$	−1.26419e27	+	1.26419e27i	−0.870963	+	0.870963i
$724$	6.73088e26	−	2.12320e27i	0.457673	−	1.44370i
$725$	6.36281e26	−	1.29119e26i	0.427010	−	0.0866521i
$726$	−4.00021e27	−	6.18886e26i	−2.64962	−	0.409933i
$727$	3.95129e25	+	3.95129e25i	0.0258322	+	0.0258322i	0.719905	−	0.694073i	$-0.244185\pi$
$727$	3.95129e25	+	3.95129e25i	0.0258322	+	0.0258322i	−0.694073	+	0.719905i	$0.744185\pi$
$728$	−1.01623e26	−	3.01691e26i	−0.0655760	−	0.194677i
$729$			4.39870e27i			2.80165i
$730$	3.28502e26	+	3.65597e26i	0.206524	+	0.229845i
$731$		−	1.57544e27i		−	0.977660i
$732$	−1.96234e27	−	3.78403e27i	−1.20204	−	2.31792i
$733$	−1.74792e27	−	1.74792e27i	−1.05690	−	1.05690i	−0.998280	−	0.0586207i	$-0.981330\pi$
$733$	−1.74792e27	−	1.74792e27i	−1.05690	−	1.05690i	−0.0586207	−	0.998280i	$-0.518670\pi$
$734$	1.68052e26	−	1.08621e27i	0.100307	−	0.648339i
$735$	2.65349e27	−	2.66517e26i	1.56346	−	0.157035i
$736$	−2.68266e26	−	2.58822e26i	−0.156036	−	0.150543i
$737$	5.15649e26	−	5.15649e26i	0.296082	−	0.296082i
$738$	3.81887e26	−	2.79553e26i	0.216471	−	0.158463i
$739$	9.27051e26			0.518778			0.259389	−	0.965773i	$-0.416479\pi$
$739$	9.27051e26			0.518778			0.259389	+	0.965773i	$0.416479\pi$
$740$	−1.47151e27	−	3.08858e26i	−0.812948	−	0.170631i
$741$	1.84685e27			1.00730
$742$	−7.01981e26	+	5.13872e26i	−0.377997	+	0.276706i
$743$	−1.12867e27	+	1.12867e27i	−0.600029	+	0.600029i	−0.940320	−	0.340291i	$-0.889474\pi$
$743$	−1.12867e27	+	1.12867e27i	−0.600029	+	0.600029i	0.340291	+	0.940320i	$0.389474\pi$
$744$	1.98421e27	+	9.84282e26i	1.04146	+	0.516627i
$745$	7.94293e26	+	6.49299e26i	0.411620	+	0.336480i
$746$	−1.97624e26	+	1.27735e27i	−0.101116	+	0.653569i
$747$	−4.12916e26	−	4.12916e26i	−0.208601	−	0.208601i
$748$	3.23132e27	−	1.67571e27i	1.61181	−	0.835862i
$749$			3.62294e26i			0.178436i
$750$	−3.14917e27	−	2.33776e27i	−1.53149	−	1.13689i
$751$		−	1.21768e27i		−	0.584729i	−0.956307	−	0.292365i	$-0.905558\pi$
$751$		−	1.21768e27i		−	0.584729i	0.956307	−	0.292365i	$-0.0944421\pi$
$752$	−1.40136e26	−	8.09516e26i	−0.0664477	−	0.383845i
$753$	−9.00447e26	−	9.00447e26i	−0.421605	−	0.421605i
$754$	4.55803e26	+	7.05189e25i	0.210741	+	0.0326045i
$755$	−1.90357e27	−	1.55608e27i	−0.869107	−	0.710456i
$756$	2.77247e27	+	8.78914e26i	1.25000	+	0.396268i
$757$	−5.81747e26	+	5.81747e26i	−0.259014	+	0.259014i	−0.824653	−	0.565639i	$-0.808630\pi$
$757$	−5.81747e26	+	5.81747e26i	−0.259014	+	0.259014i	0.565639	+	0.824653i	$0.308630\pi$
$758$	−7.72284e26	−	1.05499e27i	−0.339562	−	0.463863i
$759$	1.47722e27			0.641428
$760$	−8.87356e26	+	2.35471e27i	−0.380512	+	1.00974i
$761$	−1.16026e27			−0.491363			−0.245682	−	0.969351i	$-0.579012\pi$
$761$	−1.16026e27			−0.491363			−0.245682	+	0.969351i	$0.579012\pi$
$762$	2.07330e27	+	2.83226e27i	0.867141	+	1.18457i
$763$	4.59349e26	−	4.59349e26i	0.189740	−	0.189740i
$764$	3.22314e27	+	1.02178e27i	1.31490	+	0.416842i
$765$	7.62584e27	−	7.65941e26i	3.07259	−	0.308611i
$766$	3.86499e26	+	5.97966e25i	0.153807	+	0.0237960i
$767$	−9.10573e26	−	9.10573e26i	−0.357897	−	0.357897i
$768$	−4.43979e27	−	2.10415e27i	−1.72358	−	0.816854i
$769$			9.46553e26i			0.362948i	0.983396	+	0.181474i	$0.0580868\pi$
$769$			9.46553e26i			0.362948i	−0.983396	+	0.181474i	$0.941913\pi$
$770$	−1.27857e27	+	1.14884e27i	−0.484243	+	0.435110i
$771$			4.49548e27i			1.68174i
$772$	−2.07186e27	+	1.07443e27i	−0.765588	+	0.397023i
$773$	−3.02914e27	−	3.02914e27i	−1.10564	−	1.10564i	−0.993717	−	0.111926i	$-0.964298\pi$
$773$	−3.02914e27	−	3.02914e27i	−1.10564	−	1.10564i	−0.111926	−	0.993717i	$-0.535702\pi$
$774$	9.34279e26	−	6.03877e27i	0.336851	−	2.17726i
$775$	−1.67722e27	+	3.40354e26i	−0.597342	+	0.121217i
$776$	−1.85867e27	+	3.74688e27i	−0.653907	+	1.31821i
$777$	−1.35302e27	+	1.35302e27i	−0.470225	+	0.470225i
$778$	−6.97157e26	+	5.10341e26i	−0.239345	+	0.175208i
$779$	3.23561e26			0.109736
$780$	−1.52344e27	−	2.33284e27i	−0.510417	−	0.781601i
$781$	9.07704e27			3.00441
$782$	−6.26322e26	+	4.58488e26i	−0.204802	+	0.149921i
$783$	−2.97961e27	+	2.97961e27i	−0.962549	+	0.962549i
$784$	−1.48717e27	+	2.10985e27i	−0.474633	+	0.673364i
$785$	−8.21377e25	−	8.17777e26i	−0.0258989	−	0.257854i
$786$	1.21119e27	−	7.82860e27i	0.377310	−	2.43877i
$787$	−1.25122e27	−	1.25122e27i	−0.385100	−	0.385100i	0.487835	−	0.872936i	$-0.337787\pi$
$787$	−1.25122e27	−	1.25122e27i	−0.385100	−	0.385100i	−0.872936	+	0.487835i	$0.837787\pi$
$788$	−1.66362e25	−	3.20800e25i	−0.00505890	−	0.00975519i
$789$			3.60581e26i			0.108336i
$790$	−1.82372e27	−	9.74645e25i	−0.541377	−	0.0289327i
$791$			9.83035e26i			0.288332i
$792$	1.33796e28	−	4.50685e27i	3.87751	−	1.30612i
$793$	1.65445e27	+	1.65445e27i	0.473760	+	0.473760i
$794$	−5.55759e27	−	8.59834e26i	−1.57250	−	0.243287i
$795$	−4.81894e27	+	5.89506e27i	−1.34730	+	1.64816i
$796$	4.09607e26	−	1.29207e27i	0.113160	−	0.356955i
$797$	1.51762e27	−	1.51762e27i	0.414293	−	0.414293i	−0.468938	−	0.883231i	$-0.655363\pi$
$797$	1.51762e27	−	1.51762e27i	0.414293	−	0.414293i	0.883231	+	0.468938i	$0.155363\pi$
$798$	1.89156e27	+	2.58399e27i	0.510262	+	0.697049i
$799$	−1.71070e27			−0.456016
$800$	3.70630e27	−	8.21505e26i	0.976305	−	0.216399i
$801$	−9.73488e27			−2.53409
$802$	−3.00406e27	−	4.10373e27i	−0.772773	−	1.05566i
$803$	1.33310e27	−	1.33310e27i	0.338894	−	0.338894i
$804$	−6.19377e26	+	1.95378e27i	−0.155605	+	0.490843i
$805$	2.31986e26	−	2.83790e26i	0.0575970	−	0.0704590i
$806$	−1.20148e27	−	1.85886e26i	−0.294805	−	0.0456103i
$807$	−1.04407e25	−	1.04407e25i	−0.00253182	−	0.00253182i
$808$	6.61591e27	−	2.22854e27i	1.58556	−	0.534089i
$809$		−	5.45987e27i		−	1.29322i	−0.762822	−	0.646609i	$-0.776187\pi$
$809$		−	5.45987e27i		−	1.29322i	0.762822	−	0.646609i	$-0.223813\pi$
$810$	1.41661e28	+	7.57074e26i	3.31621	+	0.177227i
$811$			7.98050e27i			1.84643i	0.384287	+	0.923214i	$0.374447\pi$
$811$			7.98050e27i			1.84643i	−0.384287	+	0.923214i	$0.625553\pi$
$812$	3.68172e26	+	7.09954e26i	0.0841915	+	0.162348i
$813$	−5.85088e27	−	5.85088e27i	−1.32239	−	1.32239i
$814$	−8.81796e26	+	5.69954e27i	−0.196986	+	1.27323i
$815$	−8.95030e26	−	8.91107e27i	−0.197624	−	1.96758i
$816$	−5.89413e27	+	8.36203e27i	−1.28636	+	1.82497i
$817$	2.95402e27	−	2.95402e27i	0.637241	−	0.637241i
$818$	3.51054e27	−	2.56983e27i	0.748545	−	0.547958i
$819$	−2.57111e27			−0.541905
$820$	−2.66899e26	−	4.08702e26i	−0.0556052	−	0.0851482i
$821$	−7.84199e27			−1.61498			−0.807488	−	0.589884i	$-0.799174\pi$
$821$	−7.84199e27			−1.61498			−0.807488	+	0.589884i	$0.799174\pi$
$822$	3.00248e27	−	2.19791e27i	0.611219	−	0.447432i
$823$	3.54356e27	−	3.54356e27i	0.713085	−	0.713085i	−0.254094	−	0.967179i	$-0.581777\pi$
$823$	3.54356e27	−	3.54356e27i	0.713085	−	0.713085i	0.967179	+	0.254094i	$0.0817773\pi$
$824$	2.85625e27	−	5.75788e27i	0.568181	−	1.14539i
$825$	−8.30965e27	+	1.25408e28i	−1.63407	+	2.46611i
$826$	3.41395e26	−	2.20663e27i	0.0663661	−	0.428961i
$827$	−5.85794e27	−	5.85794e27i	−1.12575	−	1.12575i	−0.990860	−	0.134891i	$-0.956932\pi$
$827$	−5.85794e27	−	5.85794e27i	−1.12575	−	1.12575i	−0.134891	−	0.990860i	$-0.543068\pi$
$828$	−2.67263e27	+	1.38598e27i	−0.507750	+	0.263312i
$829$			7.49353e27i			1.40740i	0.710496	+	0.703702i	$0.248471\pi$
$829$			7.49353e27i			1.40740i	−0.710496	+	0.703702i	$0.751529\pi$
$830$	−4.48001e26	+	4.02545e26i	−0.0831835	+	0.0747434i
$831$		−	5.86784e27i		−	1.07713i
$832$	2.67210e27	+	3.64522e26i	0.484933	+	0.0661534i
$833$	3.80069e27	+	3.80069e27i	0.681923	+	0.681923i
$834$	−1.13950e28	−	1.76296e27i	−2.02132	−	0.312726i
$835$	−1.48327e26	+	1.48980e25i	−0.0260135	+	0.00261281i
$836$	9.20087e27	+	2.91682e27i	1.59540	+	0.505766i
$837$	7.85417e27	−	7.85417e27i	1.34651	−	1.34651i
$838$	4.91422e26	+	6.71313e26i	0.0832984	+	0.113791i
$839$	6.17700e27			1.03523			0.517617	−	0.855612i	$-0.326819\pi$
$839$	6.17700e27			1.03523			0.517617	+	0.855612i	$0.326819\pi$
$840$	1.70363e27	−	4.52079e27i	0.282307	−	0.749137i
$841$	4.94458e27			0.810154
$842$	3.87972e27	+	5.29994e27i	0.628544	+	0.858629i
$843$	−6.45229e27	+	6.45229e27i	−1.03360	+	1.03360i
$844$	5.65942e27	+	1.79412e27i	0.896434	+	0.284183i
$845$	−3.75915e27	−	3.07293e27i	−0.588776	−	0.481298i
$846$	−6.55723e27	−	1.01449e27i	−1.01555	−	0.157119i
$847$	2.72417e27	+	2.72417e27i	0.417198	+	0.417198i
$848$	−1.25711e27	−	7.26185e27i	−0.190376	−	1.09973i
$849$		−	4.27937e27i		−	0.640851i
$850$	−3.69121e26	−	7.89621e27i	−0.0546624	−	1.16933i
$851$		−	1.22985e27i		−	0.180103i
$852$	−2.26478e28	+	1.17448e28i	−3.27982	+	1.70087i
$853$	1.40635e27	+	1.40635e27i	0.201409	+	0.201409i	0.800603	−	0.599195i	$-0.204512\pi$
$853$	1.40635e27	+	1.40635e27i	0.201409	+	0.201409i	−0.599195	+	0.800603i	$0.704512\pi$
$854$	−6.20292e26	+	4.00930e27i	−0.0878510	+	0.567830i
$855$	1.57349e28	+	1.28626e28i	2.20387	+	1.80157i
$856$	−2.74945e27	−	1.36389e27i	−0.380842	−	0.188920i
$857$	−4.99466e27	+	4.99466e27i	−0.684208	+	0.684208i	−0.960945	−	0.276738i	$-0.910747\pi$
$857$	−4.99466e27	+	4.99466e27i	−0.684208	+	0.684208i	0.276738	+	0.960945i	$0.410747\pi$
$858$	−8.62358e27	+	6.31273e27i	−1.16831	+	0.855240i
$859$	−5.62959e27			−0.754296			−0.377148	−	0.926153i	$-0.623095\pi$
$859$	−5.62959e27			−0.754296			−0.377148	+	0.926153i	$0.623095\pi$
$860$	−6.16806e27	−	1.29462e27i	−0.817360	−	0.171557i
$861$	−6.21201e26			−0.0814146
$862$	9.29392e27	−	6.80344e27i	1.20470	−	0.881880i
$863$	4.52254e27	−	4.52254e27i	0.579803	−	0.579803i	−0.355046	−	0.934849i	$-0.615535\pi$
$863$	4.52254e27	−	4.52254e27i	0.579803	−	0.579803i	0.934849	+	0.355046i	$0.115535\pi$
$864$	−1.71073e28	+	1.77315e28i	−2.16921	+	2.24836i
$865$	3.84627e27	−	3.86320e26i	0.482377	−	0.0484501i
$866$	−1.78147e27	+	1.15146e28i	−0.220982	+	1.42833i
$867$	4.07087e27	+	4.07087e27i	0.499466	+	0.499466i
$868$	−9.70490e26	−	1.87142e27i	−0.117775	−	0.227109i
$869$			7.00531e27i			0.840891i
$870$	4.67817e27	+	5.20643e27i	0.555447	+	0.618169i
$871$		−	1.12503e27i		−	0.132127i
$872$	1.75674e27	+	5.21527e27i	0.204081	+	0.605857i
$873$	2.38861e28	+	2.38861e28i	2.74480	+	2.74480i
$874$	−2.03406e27	−	3.14697e26i	−0.231209	−	0.0357712i
$875$	1.10426e27	+	3.56580e27i	0.124163	+	0.400941i
$876$	−1.60126e27	+	5.05106e27i	−0.178104	+	0.561815i
$877$	−3.14303e27	+	3.14303e27i	−0.345822	+	0.345822i	−0.858551	−	0.512729i	$-0.828635\pi$
$877$	−3.14303e27	+	3.14303e27i	−0.345822	+	0.345822i	0.512729	+	0.858551i	$0.328635\pi$
$878$	−8.07691e27	−	1.10336e28i	−0.879118	−	1.20093i
$879$	1.53209e28			1.64965
$880$	−3.90529e27	−	1.40280e28i	−0.415975	−	1.49421i
$881$	7.83609e27			0.825711			0.412856	−	0.910797i	$-0.364531\pi$
$881$	7.83609e27			0.825711			0.412856	+	0.910797i	$0.364531\pi$
$882$	1.23144e28	+	1.68222e28i	1.28369	+	1.75360i
$883$	−5.91925e27	+	5.91925e27i	−0.610436	+	0.610436i	−0.943060	−	0.332624i	$-0.892066\pi$
$883$	−5.91925e27	+	5.91925e27i	−0.610436	+	0.610436i	0.332624	+	0.943060i	$0.392066\pi$
$884$	1.69699e27	−	5.35304e27i	0.173135	−	0.546140i
$885$	−1.95302e27	−	1.94446e28i	−0.197127	−	1.96263i
$886$	1.58870e28	+	2.45793e27i	1.58643	+	0.245442i
$887$	−1.30645e27	−	1.30645e27i	−0.129068	−	0.129068i	0.639622	−	0.768690i	$-0.279091\pi$
$887$	−1.30645e27	−	1.30645e27i	−0.129068	−	0.129068i	−0.768690	+	0.639622i	$0.779091\pi$
$888$	−5.17452e27	−	1.53617e28i	−0.505763	−	1.50147i
$889$		−	3.34073e27i		−	0.323053i
$890$	−5.35828e26	+	1.00262e28i	−0.0512649	+	0.959249i
$891$		−	5.44151e28i		−	5.15088i
$892$	1.20974e27	+	2.33277e27i	0.113299	+	0.218477i
$893$	−3.20764e27	−	3.20764e27i	−0.297233	−	0.297233i
$894$	−1.69103e27	+	1.09301e28i	−0.155041	+	1.00212i
$895$	8.41728e26	−	1.02969e27i	0.0763577	−	0.0934092i
$896$	2.22677e27	+	4.11197e27i	0.199871	+	0.369083i
$897$	1.61149e27	−	1.61149e27i	0.143119	−	0.143119i
$898$	−9.91195e27	+	7.25585e27i	−0.871031	+	0.637622i
$899$	3.05424e27			0.265574
$900$	3.26780e27	−	3.04855e28i	0.281158	−	2.62295i
$901$	−1.53461e28			−1.30651
$902$	−1.51081e27	+	1.10596e27i	−0.127277	+	0.0931705i
$903$	−5.67140e27	+	5.67140e27i	−0.472777	+	0.472777i
$904$	−7.46026e27	−	3.70072e27i	−0.615395	−	0.305272i
$905$	−1.17427e28	+	1.43649e28i	−0.958530	+	1.17258i
$906$	4.05267e27	−	2.61947e28i	0.327358	−	2.11590i
$907$	7.54339e27	+	7.54339e27i	0.602972	+	0.602972i	0.941100	−	0.338128i	$-0.109794\pi$
$907$	7.54339e27	+	7.54339e27i	0.602972	+	0.602972i	−0.338128	+	0.941100i	$0.609794\pi$
$908$	−7.22088e26	+	3.74464e26i	−0.0571182	+	0.0296207i
$909$		−	5.63830e28i		−	4.41358i
$910$	−1.41519e26	+	2.64805e27i	−0.0109628	+	0.205132i
$911$		−	3.12688e26i		−	0.0239710i	−0.999928	−	0.0119855i	$-0.996185\pi$
$911$		−	3.12688e26i		−	0.0239710i	0.999928	−	0.0119855i	$-0.00381519\pi$
$912$	−2.67309e28	+	4.62741e27i	−2.02797	+	0.351064i
$913$	1.63357e27	+	1.63357e27i	0.122649	+	0.122649i
$914$	1.93318e28	+	2.99089e27i	1.43643	+	0.222235i
$915$	3.54852e27	+	3.53296e28i	0.260943	+	2.59800i
$916$	1.47554e28	+	4.67769e27i	1.07385	+	0.340427i
$917$	−5.33135e27	+	5.33135e27i	−0.383997	+	0.383997i
$918$	3.03046e28	+	4.13979e28i	2.16024	+	2.95103i
$919$	2.17942e28			1.53760			0.768801	−	0.639489i	$-0.220854\pi$
$919$	2.17942e28			1.53760			0.768801	+	0.639489i	$0.220854\pi$
$920$	1.28035e27	+	2.82889e27i	0.0894017	+	0.197530i
$921$	−2.23869e28			−1.54714
$922$	−9.11375e27	−	1.24499e28i	−0.623381	−	0.851576i
$923$	9.90207e27	−	9.90207e27i	0.670362	−	0.670362i
$924$	−1.76647e28	−	5.59997e27i	−1.18365	−	0.375234i
$925$	1.04408e28	+	6.91816e27i	0.692446	+	0.458822i
$926$	4.68894e26	+	7.25443e25i	0.0307801	+	0.00476210i
$927$	−3.67062e28	−	3.67062e28i	−2.38496	−	2.38496i
$928$	−6.77386e27	+	1.21371e26i	−0.435643	+	0.00780567i
$929$			1.27181e27i			0.0809607i	0.999180	+	0.0404804i	$0.0128888\pi$
$929$			1.27181e27i			0.0809607i	−0.999180	+	0.0404804i	$0.987111\pi$
$930$	−1.23315e28	−	1.37240e28i	−0.777013	−	0.864754i
$931$			1.42529e28i			0.888958i
$932$	5.04461e27	−	2.61606e27i	0.311442	−	0.161509i
$933$	5.92756e27	+	5.92756e27i	0.362244	+	0.362244i
$934$	2.05550e27	−	1.32859e28i	0.124343	−	0.803700i
$935$	−3.01692e28	+	3.03020e27i	−1.80656	+	0.181452i
$936$	9.67917e27	−	1.95121e28i	0.573743	−	1.15660i
$937$	−9.84153e27	+	9.84153e27i	−0.577480	+	0.577480i	−0.934208	−	0.356728i	$-0.883892\pi$
$937$	−9.84153e27	+	9.84153e27i	−0.577480	+	0.577480i	0.356728	+	0.934208i	$0.383892\pi$
$938$	1.57407e27	−	1.15227e27i	0.0914317	−	0.0669309i
$939$	3.15748e28			1.81559
$940$	−1.40577e27	+	6.69762e27i	−0.0800205	+	0.381246i
$941$	2.23824e28			1.26126			0.630631	−	0.776083i	$-0.282796\pi$
$941$	2.23824e28			1.26126			0.630631	+	0.776083i	$0.282796\pi$
$942$	7.14972e27	−	5.23382e27i	0.398846	−	0.291968i
$943$	2.82325e26	−	2.82325e26i	0.0155915	−	0.0155915i
$944$	1.54609e28	+	1.08979e28i	0.845280	+	0.595811i
$945$	−1.87576e28	−	1.53335e28i	−1.01526	−	0.829926i
$946$	−3.69618e27	+	2.38905e28i	−0.198056	+	1.28014i
$947$	−8.12425e27	−	8.12425e27i	−0.430981	−	0.430981i	0.457981	−	0.888962i	$-0.348573\pi$
$947$	−8.12425e27	−	8.12425e27i	−0.430981	−	0.430981i	−0.888962	+	0.457981i	$0.848573\pi$
$948$	−9.06421e27	−	1.74787e28i	−0.476048	−	0.917974i
$949$		−	2.90852e27i		−	0.151232i
$950$	1.41136e28	−	1.54978e28i	0.726546	−	0.797805i
$951$			2.92558e28i			1.49107i
$952$	9.22767e27	−	3.10831e27i	0.465630	−	0.156846i
$953$	−1.73846e28	−	1.73846e28i	−0.868522	−	0.868522i	0.123786	−	0.992309i	$-0.460496\pi$
$953$	−1.73846e28	−	1.73846e28i	−0.868522	−	0.868522i	−0.992309	+	0.123786i	$0.960496\pi$
$954$	−5.88224e28	−	9.10062e27i	−2.90960	−	0.450154i
$955$	−2.18067e28	−	1.78260e28i	−1.06797	−	0.873016i
$956$	−4.44826e27	+	1.40317e28i	−0.215695	+	0.680393i
$957$	1.89845e28	−	1.89845e28i	0.911456	−	0.911456i
$958$	−8.86883e27	−	1.21154e28i	−0.421594	−	0.575923i
$959$	−3.54151e27			−0.166691
$960$	2.78949e28	+	2.99478e28i	1.30001	+	1.39569i
$961$	1.36198e28			0.628489
$962$	5.25564e27	+	7.17952e27i	0.240139	+	0.328044i
$963$	−1.75276e28	+	1.75276e28i	−0.792999	+	0.792999i
$964$	−4.35614e27	+	1.37411e28i	−0.195151	+	0.615588i
$965$	1.93439e28	−	1.94291e27i	0.858094	−	0.0861871i
$966$	3.90518e27	+	6.04184e26i	0.171537	+	0.0265391i
$967$	1.10505e28	+	1.10505e28i	0.480652	+	0.480652i	0.905340	−	0.424688i	$-0.139616\pi$
$967$	1.10505e28	+	1.10505e28i	0.480652	+	0.480652i	−0.424688	+	0.905340i	$0.639616\pi$
$968$	−3.09292e28	+	1.04184e28i	−1.33215	+	0.448729i
$969$			5.64888e28i			2.40928i
$970$	2.59157e28	−	2.32862e28i	1.09454	−	0.983485i
$971$		−	1.97511e28i		−	0.826055i	−0.910718	−	0.413028i	$-0.864471\pi$
$971$		−	1.97511e28i		−	0.826055i	0.910718	−	0.413028i	$-0.135529\pi$
$972$	3.56809e28	+	6.88043e28i	1.47777	+	2.84961i
$973$	7.76008e27	+	7.76008e27i	0.318269	+	0.318269i
$974$	4.77529e27	−	3.08653e28i	0.193950	−	1.25361i
$975$	4.61570e27	+	2.27455e28i	0.185650	+	0.914856i
$976$	−2.80914e28	−	1.98008e28i	−1.11892	−	0.788695i
$977$	−3.20519e28	+	3.20519e28i	−1.26431	+	1.26431i	−0.315333	+	0.948981i	$0.602116\pi$
$977$	−3.20519e28	+	3.20519e28i	−1.26431	+	1.26431i	−0.948981	+	0.315333i	$0.897884\pi$
$978$	7.79083e28	−	5.70313e28i	3.04344	−	2.22789i
$979$	3.85129e28			1.48995
$980$	1.80034e28	−	1.17570e28i	0.689775	−	0.450451i
$981$	4.44462e28			1.68647
$982$	−2.29448e28	+	1.67963e28i	−0.862232	+	0.631181i
$983$	−4.99354e26	+	4.99354e26i	−0.0185845	+	0.0185845i	−0.716338	−	0.697753i	$-0.754183\pi$
$983$	−4.99354e26	+	4.99354e26i	−0.0185845	+	0.0185845i	0.697753	+	0.716338i	$0.254183\pi$
$984$	2.33857e27	−	4.71430e27i	0.0861979	−	0.173766i
$985$	3.00834e25	+	2.99516e26i	0.00109820	+	0.0109339i
$986$	−2.15693e27	+	1.39414e28i	−0.0779839	+	0.504054i
$987$	6.15832e27	+	6.15832e27i	0.220520	+	0.220520i
$988$	1.32191e28	−	6.85523e27i	0.468825	−	0.243126i
$989$		−	5.15511e27i		−	0.181081i
$990$	−1.17437e29	−	6.27617e27i	−4.08575	−	0.218354i
$991$			2.40501e28i			0.828737i	0.910109	+	0.414368i	$0.135997\pi$
$991$			2.40501e28i			0.828737i	−0.910109	+	0.414368i	$0.864003\pi$
$992$	1.78557e28	−	3.19931e26i	0.609419	−	0.0109193i
$993$	−4.49662e27	−	4.49662e27i	−0.152009	−	0.152009i
$994$	2.39961e28	+	3.71251e27i	0.803469	+	0.124308i
$995$	−7.14599e27	+	8.74176e27i	−0.236997	+	0.289921i
$996$	−6.18955e27	−	1.96218e27i	−0.203327	−	0.0644578i
$997$	1.19897e28	−	1.19897e28i	0.390126	−	0.390126i	−0.484606	−	0.874732i	$-0.661037\pi$
$997$	1.19897e28	−	1.19897e28i	0.390126	−	0.390126i	0.874732	+	0.484606i	$0.161037\pi$
$998$	3.46152e28	+	4.72865e28i	1.11565	+	1.52404i
$999$	−8.12893e28			−2.59514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.20.e.b.3.16	✓	108
4.3	odd	2	inner	20.20.e.b.3.43	yes	108
5.2	odd	4	inner	20.20.e.b.7.43	yes	108
20.7	even	4	inner	20.20.e.b.7.16	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.20.e.b.3.16	✓	108	1.1	even	1	trivial
20.20.e.b.3.43	yes	108	4.3	odd	2	inner
20.20.e.b.7.16	yes	108	20.7	even	4	inner
20.20.e.b.7.43	yes	108	5.2	odd	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+(-427.698 - 584.262i) q^{2} +(-45979.8 + 45979.8i) q^{3} +(-158436. + 499776. i) q^{4} +(2.76408e6 - 3.38132e6i) q^{5} +(4.65297e7 + 7.19877e6i) q^{6} +(-3.16871e7 - 3.16871e7i) q^{7} +(3.59763e8 - 1.21185e8i) q^{8} -3.06602e9i q^{9} +(-3.15777e9 - 1.68760e8i) q^{10} +1.21297e10i q^{11} +(-1.56947e10 - 3.02644e10i) q^{12} +(1.32322e10 + 1.32322e10i) q^{13} +(-4.96106e9 + 3.20661e10i) q^{14} +(2.83808e10 + 2.82564e11i) q^{15} +(-2.24674e11 - 1.58365e11i) q^{16} +(-4.04727e11 + 4.04727e11i) q^{17} +(-1.79136e12 + 1.31133e12i) q^{18} -1.51776e12 q^{19} +(1.25197e12 + 1.91714e12i) q^{20} +2.91393e12 q^{21} +(7.08694e12 - 5.18786e12i) q^{22} +(-1.32433e12 + 1.32433e12i) q^{23} +(-1.09698e13 + 2.21139e13i) q^{24} +(-3.79322e12 - 1.86925e13i) q^{25} +(2.07169e12 - 1.33905e13i) q^{26} +(8.75343e13 + 8.75343e13i) q^{27} +(2.08569e13 - 1.08161e13i) q^{28} +3.40394e13i q^{29} +(1.52953e14 - 1.37434e14i) q^{30} -8.97267e13i q^{31} +(3.56561e12 + 1.99001e14i) q^{32} +(-5.57722e14 - 5.57722e14i) q^{33} +(4.09568e14 + 6.33657e13i) q^{34} +(-1.94730e14 + 1.95588e13i) q^{35} +(1.53232e15 + 4.85769e14i) q^{36} +(-4.64329e14 + 4.64329e14i) q^{37} +(6.49143e14 + 8.86770e14i) q^{38} -1.21683e15 q^{39} +(5.84648e14 - 1.55144e15i) q^{40} -2.13183e14 q^{41} +(-1.24628e15 - 1.70250e15i) q^{42} +(-1.94630e15 + 1.94630e15i) q^{43} +(-6.06214e15 - 1.92179e15i) q^{44} +(-1.03672e16 - 8.47471e15i) q^{45} +(1.34017e15 + 2.07343e14i) q^{46} +(2.11340e15 + 2.11340e15i) q^{47} +(1.76121e16 - 3.04884e15i) q^{48} -9.39075e15i q^{49} +(-9.29896e15 + 1.02110e16i) q^{50} -3.72186e16i q^{51} +(-8.70960e15 + 4.51667e15i) q^{52} +(1.89585e16 + 1.89585e16i) q^{53} +(1.37047e16 - 8.85812e16i) q^{54} +(4.10145e16 + 3.35275e16i) q^{55} +(-1.52399e16 - 7.55986e15i) q^{56} +(6.97863e16 - 6.97863e16i) q^{57} +(1.98879e16 - 1.45586e16i) q^{58} -6.88149e16 q^{59} +(-1.45715e17 - 3.05844e16i) q^{60} +1.25032e17 q^{61} +(-5.24239e16 + 3.83760e16i) q^{62} +(-9.71533e16 + 9.71533e16i) q^{63} +(1.14744e17 - 8.71956e16i) q^{64} +(8.13173e16 - 8.16753e15i) q^{65} +(-8.73191e16 + 5.64392e17i) q^{66} +(-4.25112e16 - 4.25112e16i) q^{67} +(-1.38149e17 - 2.66397e17i) q^{68} -1.21785e17i q^{69} +(9.47132e16 + 1.05408e17i) q^{70} -7.48331e17i q^{71} +(-3.71555e17 - 1.10304e18i) q^{72} +(-1.09903e17 - 1.09903e17i) q^{73} +(4.69882e17 + 7.26971e16i) q^{74} +(1.03389e18 + 6.85065e17i) q^{75} +(2.40469e17 - 7.58540e17i) q^{76} +(3.84356e17 - 3.84356e17i) q^{77} +(5.20435e17 + 7.10946e17i) q^{78} +5.77533e17 q^{79} +(-1.15650e18 + 3.21960e17i) q^{80} -4.48610e18 q^{81} +(9.11780e16 + 1.24555e17i) q^{82} +(1.34675e17 - 1.34675e17i) q^{83} +(-4.61674e17 + 1.45631e18i) q^{84} +(2.49816e17 + 2.48721e18i) q^{85} +(1.96958e18 + 3.04721e17i) q^{86} +(-1.56512e18 - 1.56512e18i) q^{87} +(1.46994e18 + 4.36382e18i) q^{88} -3.17509e18i q^{89} +(-5.17421e17 + 9.68178e18i) q^{90} -8.38582e17i q^{91} +(-4.52047e17 - 8.71693e17i) q^{92} +(4.12562e18 + 4.12562e18i) q^{93} +(3.30882e17 - 2.13868e18i) q^{94} +(-4.19521e18 + 5.13204e18i) q^{95} +(-9.31396e18 - 8.98607e18i) q^{96} +(-7.79061e18 + 7.79061e18i) q^{97} +(-5.48666e18 + 4.01641e18i) q^{98} +3.71899e19 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

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Fields

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Database

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