LMFDB - Embedded newform 21.30.c.a.20.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, 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:	$111.883889004$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.4
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+40537.3i q^{2} +(-896293. - 8.23572e6i) q^{3} -1.10640e9 q^{4} +2.53522e10 q^{5} +(3.33854e11 - 3.63333e10i) q^{6} +(3.38830e11 + 1.76213e12i) q^{7} -2.30873e13i q^{8} +(-6.70237e13 + 1.47632e13i) q^{9} +O(q^{10})$	\(q+40537.3i q^{2} +(-896293. - 8.23572e6i) q^{3} -1.10640e9 q^{4} +2.53522e10 q^{5} +(3.33854e11 - 3.63333e10i) q^{6} +(3.38830e11 + 1.76213e12i) q^{7} -2.30873e13i q^{8} +(-6.70237e13 + 1.47632e13i) q^{9} +1.02771e15i q^{10} +1.41931e15i q^{11} +(9.91662e14 + 9.11203e15i) q^{12} +2.20140e16i q^{13} +(-7.14320e16 + 1.37353e16i) q^{14} +(-2.27230e16 - 2.08794e17i) q^{15} +3.41903e17 q^{16} +9.03848e17 q^{17} +(-5.98462e17 - 2.71696e18i) q^{18} -2.84158e17i q^{19} -2.80498e19 q^{20} +(1.42087e19 - 4.36989e18i) q^{21} -5.75350e19 q^{22} +3.67708e19i q^{23} +(-1.90141e20 + 2.06930e19i) q^{24} +4.56470e20 q^{25} -8.92390e20 q^{26} +(1.81659e20 + 5.38756e20i) q^{27} +(-3.74882e20 - 1.94963e21i) q^{28} -1.16157e21i q^{29} +(8.46394e21 - 9.21130e20i) q^{30} -1.18888e21i q^{31} +1.46491e21i q^{32} +(1.16890e22 - 1.27212e21i) q^{33} +3.66396e22i q^{34} +(8.59008e21 + 4.46739e22i) q^{35} +(7.41553e22 - 1.63341e22i) q^{36} -1.35607e21 q^{37} +1.15190e22 q^{38} +(1.81301e23 - 1.97310e22i) q^{39} -5.85315e23i q^{40} +1.70731e23 q^{41} +(1.77144e23 + 5.75983e23i) q^{42} -6.75136e23 q^{43} -1.57033e24i q^{44} +(-1.69920e24 + 3.74280e23i) q^{45} -1.49059e24 q^{46} +1.96537e24 q^{47} +(-3.06445e23 - 2.81582e24i) q^{48} +(-2.99029e24 + 1.19412e24i) q^{49} +1.85041e25i q^{50} +(-8.10112e23 - 7.44384e24i) q^{51} -2.43564e25i q^{52} -1.77266e24i q^{53} +(-2.18397e25 + 7.36395e24i) q^{54} +3.59826e25i q^{55} +(4.06829e25 - 7.82268e24i) q^{56} +(-2.34025e24 + 2.54689e23i) q^{57} +4.70870e25 q^{58} -4.83190e25 q^{59} +(2.51408e25 + 2.31010e26i) q^{60} +7.56453e25i q^{61} +4.81939e25 q^{62} +(-4.87243e25 - 1.13102e26i) q^{63} +1.24174e26 q^{64} +5.58105e26i q^{65} +(5.15682e25 + 4.73842e26i) q^{66} -1.04824e26 q^{67} -1.00002e27 q^{68} +(3.02834e26 - 3.29574e25i) q^{69} +(-1.81096e27 + 3.48219e26i) q^{70} -2.52140e26i q^{71} +(3.40844e26 + 1.54740e27i) q^{72} -9.99284e26i q^{73} -5.49714e25i q^{74} +(-4.09131e26 - 3.75936e27i) q^{75} +3.14394e26i q^{76} +(-2.50101e27 + 4.80904e26i) q^{77} +(7.99843e26 + 7.34948e27i) q^{78} -2.17559e27 q^{79} +8.66800e27 q^{80} +(4.27422e27 - 1.97897e27i) q^{81} +6.92096e27i q^{82} +6.73274e27 q^{83} +(-1.57206e28 + 4.83486e27i) q^{84} +2.29145e28 q^{85} -2.73682e28i q^{86} +(-9.56638e27 + 1.04111e27i) q^{87} +3.27681e28 q^{88} -8.13678e27 q^{89} +(-1.51723e28 - 6.88810e28i) q^{90} +(-3.87916e28 + 7.45901e27i) q^{91} -4.06833e28i q^{92} +(-9.79126e27 + 1.06558e27i) q^{93} +7.96709e28i q^{94} -7.20404e27i q^{95} +(1.20646e28 - 1.31299e27i) q^{96} +1.01638e29i q^{97} +(-4.84066e28 - 1.21219e29i) q^{98} +(-2.09536e28 - 9.51273e28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			40537.3i			1.74952i	0.484552	+	0.874762i	$0.338983\pi$
$2$			40537.3i			1.74952i	−0.484552	+	0.874762i	$0.661017\pi$
$3$	−896293.	−	8.23572e6i	−0.108191	−	0.994130i
$3$	−896293.	−	8.23572e6i	−0.108191	−	0.994130i
$4$	−1.10640e9			−2.06084
$5$	2.53522e10			1.85759			0.928797	−	0.370589i	$-0.120844\pi$
$5$	2.53522e10			1.85759			0.928797	+	0.370589i	$0.120844\pi$
$6$	3.33854e11	−	3.63333e10i	1.73926	−	0.189283i
$7$	3.38830e11	+	1.76213e12i	0.188825	+	0.982011i
$7$	3.38830e11	+	1.76213e12i	0.188825	+	0.982011i
$8$		−	2.30873e13i		−	1.85596i
$9$	−6.70237e13	+	1.47632e13i	−0.976589	+	0.215112i
$10$			1.02771e15i			3.24991i
$11$			1.41931e15i			1.12689i	0.826152	+	0.563447i	$0.190525\pi$
$11$			1.41931e15i			1.12689i	−0.826152	+	0.563447i	$0.809475\pi$
$12$	9.91662e14	+	9.11203e15i	0.222964	+	2.04874i
$13$			2.20140e16i			1.55068i	0.631546	+	0.775338i	$0.282421\pi$
$13$			2.20140e16i			1.55068i	−0.631546	+	0.775338i	$0.717579\pi$
$14$	−7.14320e16	+	1.37353e16i	−1.71805	+	0.330354i
$15$	−2.27230e16	−	2.08794e17i	−0.200975	−	1.84669i
$16$	3.41903e17			1.18621
$17$	9.03848e17			1.30193			0.650963	−	0.759110i	$-0.274365\pi$
$17$	9.03848e17			1.30193			0.650963	+	0.759110i	$0.274365\pi$
$18$	−5.98462e17	−	2.71696e18i	−0.376344	−	1.70857i
$19$		−	2.84158e17i		−	0.0815893i	−0.999168	−	0.0407947i	$-0.987011\pi$
$19$		−	2.84158e17i		−	0.0815893i	0.999168	−	0.0407947i	$-0.0129889\pi$
$20$	−2.80498e19			−3.82820
$21$	1.42087e19	−	4.36989e18i	0.955817	−	0.293962i
$22$	−5.75350e19			−1.97153
$23$			3.67708e19i			0.661377i	0.943740	+	0.330689i	$0.107281\pi$
$23$			3.67708e19i			0.661377i	−0.943740	+	0.330689i	$0.892719\pi$
$24$	−1.90141e20	+	2.06930e19i	−1.84507	+	0.200799i
$25$	4.56470e20			2.45066
$26$	−8.92390e20			−2.71295
$27$	1.81659e20	+	5.38756e20i	0.319508	+	0.947584i
$28$	−3.74882e20	−	1.94963e21i	−0.389138	−	2.02376i
$29$		−	1.16157e21i		−	0.724895i	−0.932004	−	0.362448i	$-0.881941\pi$
$29$		−	1.16157e21i		−	0.724895i	0.932004	−	0.362448i	$-0.118059\pi$
$30$	8.46394e21	−	9.21130e20i	3.23083	−	0.351611i
$31$		−	1.18888e21i		−	0.282093i	−0.990003	−	0.141047i	$-0.954953\pi$
$31$		−	1.18888e21i		−	0.282093i	0.990003	−	0.141047i	$-0.0450468\pi$
$32$			1.46491e21i			0.219350i
$33$	1.16890e22	−	1.27212e21i	1.12028	−	0.121920i
$34$			3.66396e22i			2.27775i
$35$	8.59008e21	+	4.46739e22i	0.350761	+	1.82418i
$36$	7.41553e22	−	1.63341e22i	2.01259	−	0.443311i
$37$	−1.35607e21			−0.0247375			−0.0123688	−	0.999924i	$-0.503937\pi$
$37$	−1.35607e21			−0.0247375			−0.0123688	+	0.999924i	$0.503937\pi$
$38$	1.15190e22			0.142743
$39$	1.81301e23	−	1.97310e22i	1.54157	−	0.167769i
$40$		−	5.85315e23i		−	3.44762i
$41$	1.70731e23			0.702984			0.351492	−	0.936191i	$-0.385674\pi$
$41$	1.70731e23			0.702984			0.351492	+	0.936191i	$0.385674\pi$
$42$	1.77144e23	+	5.75983e23i	0.514293	+	1.67223i
$43$	−6.75136e23			−1.39347			−0.696737	−	0.717327i	$-0.745365\pi$
$43$	−6.75136e23			−1.39347			−0.696737	+	0.717327i	$0.745365\pi$
$44$		−	1.57033e24i		−	2.32235i
$45$	−1.69920e24	+	3.74280e23i	−1.81411	+	0.399591i
$46$	−1.49059e24			−1.15710
$47$	1.96537e24			1.11693			0.558464	−	0.829528i	$-0.311391\pi$
$47$	1.96537e24			1.11693			0.558464	+	0.829528i	$0.311391\pi$
$48$	−3.06445e23	−	2.81582e24i	−0.128338	−	1.17925i
$49$	−2.99029e24	+	1.19412e24i	−0.928690	+	0.370857i
$50$			1.85041e25i			4.28748i
$51$	−8.10112e23	−	7.44384e24i	−0.140857	−	1.29428i
$52$		−	2.43564e25i		−	3.19569i
$53$		−	1.77266e24i		−	0.176451i	−0.996101	−	0.0882257i	$-0.971880\pi$
$53$		−	1.77266e24i		−	0.176451i	0.996101	−	0.0882257i	$-0.0281197\pi$
$54$	−2.18397e25	+	7.36395e24i	−1.65782	+	0.558987i
$55$			3.59826e25i			2.09331i
$56$	4.06829e25	−	7.82268e24i	1.82257	−	0.350452i
$57$	−2.34025e24	+	2.54689e23i	−0.0811104	+	0.00882724i
$58$	4.70870e25			1.26822
$59$	−4.83190e25			−1.01570			−0.507848	−	0.861447i	$-0.669559\pi$
$59$	−4.83190e25			−1.01570			−0.507848	+	0.861447i	$0.669559\pi$
$60$	2.51408e25	+	2.31010e26i	0.414177	+	3.80573i
$61$			7.56453e25i			0.980617i	0.871549	+	0.490309i	$0.163116\pi$
$61$			7.56453e25i			0.980617i	−0.871549	+	0.490309i	$0.836884\pi$
$62$	4.81939e25			0.493529
$63$	−4.87243e25	−	1.13102e26i	−0.395647	−	0.918403i
$64$	1.24174e26			0.802457
$65$			5.58105e26i			2.88053i
$66$	5.15682e25	+	4.73842e26i	0.213302	+	1.95996i
$67$	−1.04824e26			−0.348639			−0.174319	−	0.984689i	$-0.555773\pi$
$67$	−1.04824e26			−0.348639			−0.174319	+	0.984689i	$0.555773\pi$
$68$	−1.00002e27			−2.68306
$69$	3.02834e26	−	3.29574e25i	0.657495	−	0.0715552i
$70$	−1.81096e27	+	3.48219e26i	−3.19144	+	0.613664i
$71$		−	2.52140e26i		−	0.361739i	−0.983507	−	0.180869i	$-0.942109\pi$
$71$		−	2.52140e26i		−	0.361739i	0.983507	−	0.180869i	$-0.0578911\pi$
$72$	3.40844e26	+	1.54740e27i	0.399240	+	1.81251i
$73$		−	9.99284e26i		−	0.958313i	−0.877729	−	0.479157i	$-0.840943\pi$
$73$		−	9.99284e26i		−	0.958313i	0.877729	−	0.479157i	$-0.159057\pi$
$74$		−	5.49714e25i		−	0.0432789i
$75$	−4.09131e26	−	3.75936e27i	−0.265139	−	2.43627i
$76$			3.14394e26i			0.168142i
$77$	−2.50101e27	+	4.80904e26i	−1.10662	+	0.212786i
$78$	7.99843e26	+	7.34948e27i	0.293517	+	2.69702i
$79$	−2.17559e27			−0.663720			−0.331860	−	0.943329i	$-0.607676\pi$
$79$	−2.17559e27			−0.663720			−0.331860	+	0.943329i	$0.607676\pi$
$80$	8.66800e27			2.20350
$81$	4.27422e27	−	1.97897e27i	0.907454	−	0.420152i
$82$			6.92096e27i			1.22989i
$83$	6.73274e27			1.00360			0.501798	−	0.864985i	$-0.332672\pi$
$83$	6.73274e27			1.00360			0.501798	+	0.864985i	$0.332672\pi$
$84$	−1.57206e28	+	4.83486e27i	−1.96978	+	0.605807i
$85$	2.29145e28			2.41845
$86$		−	2.73682e28i		−	2.43792i
$87$	−9.56638e27	+	1.04111e27i	−0.720640	+	0.0784273i
$88$	3.27681e28			2.09147
$89$	−8.13678e27			−0.440857			−0.220428	−	0.975403i	$-0.570746\pi$
$89$	−8.13678e27			−0.440857			−0.220428	+	0.975403i	$0.570746\pi$
$90$	−1.51723e28	−	6.88810e28i	−0.699094	−	3.17382i
$91$	−3.87916e28	+	7.45901e27i	−1.52278	+	0.292807i
$92$		−	4.06833e28i		−	1.36299i
$93$	−9.79126e27	+	1.06558e27i	−0.280437	+	0.0305200i
$94$			7.96709e28i			1.95409i
$95$		−	7.20404e27i		−	0.151560i
$96$	1.20646e28	−	1.31299e27i	0.218062	−	0.0237317i
$97$			1.01638e29i			1.58075i	0.612621	+	0.790377i	$0.290115\pi$
$97$			1.01638e29i			1.58075i	−0.612621	+	0.790377i	$0.709885\pi$
$98$	−4.84066e28	−	1.21219e29i	−0.648823	−	1.62477i
$99$	−2.09536e28	−	9.51273e28i	−0.242409	−	1.10051i
$100$	−5.05040e29			−5.05040
$101$	2.70459e28			0.234121			0.117061	−	0.993125i	$-0.462653\pi$
$101$	2.70459e28			0.234121			0.117061	+	0.993125i	$0.462653\pi$
$102$	3.01753e29	−	3.28398e28i	2.26438	−	0.246432i
$103$		−	7.33945e28i		−	0.478106i	−0.971007	−	0.239053i	$-0.923163\pi$
$103$		−	7.33945e28i		−	0.478106i	0.971007	−	0.239053i	$-0.0768369\pi$
$104$	5.08246e29			2.87800
$105$	3.60222e29	−	1.10786e29i	1.77552	−	0.546061i
$106$	7.18589e28			0.308706
$107$			2.13042e29i			0.798732i	0.916792	+	0.399366i	$0.130770\pi$
$107$			2.13042e29i			0.798732i	−0.916792	+	0.399366i	$0.869230\pi$
$108$	−2.00988e29	−	5.96082e29i	−0.658454	−	1.95282i
$109$	7.01375e28			0.201033			0.100516	−	0.994935i	$-0.467951\pi$
$109$	7.01375e28			0.201033			0.100516	+	0.994935i	$0.467951\pi$
$110$	−1.45864e30			−3.66230
$111$	1.21543e27	+	1.11682e28i	0.00267638	+	0.0245923i
$112$	1.15847e29	+	6.02477e29i	0.223987	+	1.16488i
$113$			3.32301e29i			0.564800i	0.959297	+	0.282400i	$0.0911305\pi$
$113$			3.32301e29i			0.564800i	−0.959297	+	0.282400i	$0.908869\pi$
$114$	−1.03244e28	−	9.48674e28i	−0.0154435	−	0.141905i
$115$			9.32221e29i			1.22857i
$116$			1.28517e30i			1.49389i
$117$	−3.24998e29	−	1.47546e30i	−0.333569	−	1.51437i
$118$		−	1.95872e30i		−	1.77699i
$119$	3.06251e29	+	1.59270e30i	0.245836	+	1.27850i
$120$	−4.82049e30	+	5.24614e29i	−3.42739	+	0.373002i
$121$	−4.28128e29			−0.269890
$122$	−3.06646e30			−1.71561
$123$	−1.53025e29	−	1.40609e30i	−0.0760566	−	0.698857i
$124$			1.31538e30i			0.581348i
$125$	6.85031e30			2.69473
$126$	4.58486e30	−	1.97515e30i	1.60677	−	0.692194i
$127$	−1.74410e28			−0.00545026			−0.00272513	−	0.999996i	$-0.500867\pi$
$127$	−1.74410e28			−0.00545026			−0.00272513	+	0.999996i	$0.500867\pi$
$128$			5.82016e30i			1.62327i
$129$	6.05120e29	+	5.56023e30i	0.150761	+	1.38529i
$130$	−2.26241e31			−5.03955
$131$	−6.50358e29			−0.129634			−0.0648170	−	0.997897i	$-0.520646\pi$
$131$	−6.50358e29			−0.129634			−0.0648170	+	0.997897i	$0.520646\pi$
$132$	−1.29328e31	+	1.40747e30i	−2.30871	+	0.251257i
$133$	5.00724e29	−	9.62813e28i	0.0801216	−	0.0154061i
$134$		−	4.24928e30i		−	0.609952i
$135$	4.60545e30	+	1.36587e31i	0.593516	+	1.76023i
$136$		−	2.08674e31i		−	2.41632i
$137$		−	1.06805e31i		−	1.11209i	−0.831151	−	0.556047i	$-0.812317\pi$
$137$		−	1.06805e31i		−	1.11209i	0.831151	−	0.556047i	$-0.187683\pi$
$138$	1.33600e30	+	1.22761e31i	0.125188	+	1.15030i
$139$			6.22380e30i			0.525220i	0.964902	+	0.262610i	$0.0845832\pi$
$139$			6.22380e30i			0.525220i	−0.964902	+	0.262610i	$0.915417\pi$
$140$	−9.50410e30	−	4.94273e31i	−0.722860	−	3.75933i
$141$	−1.76155e30	−	1.61862e31i	−0.120842	−	1.11037i
$142$	1.02211e31			0.632871
$143$	−3.12447e31			−1.74745
$144$	−2.29156e31	+	5.04759e30i	−1.15844	+	0.255169i
$145$		−	2.94484e31i		−	1.34656i
$146$	4.05083e31			1.67659
$147$	1.25146e31	+	2.35569e31i	0.469156	+	0.883115i
$148$	1.50036e30			0.0509800
$149$			7.49140e30i			0.230867i	0.993315	+	0.115434i	$0.0368257\pi$
$149$			7.49140e30i			0.230867i	−0.993315	+	0.115434i	$0.963174\pi$
$150$	1.52394e32	−	1.65851e31i	4.26232	−	0.463868i
$151$	−3.37654e31			−0.857643			−0.428821	−	0.903389i	$-0.641071\pi$
$151$	−3.37654e31			−0.857643			−0.428821	+	0.903389i	$0.641071\pi$
$152$	−6.56046e30			−0.151427
$153$	−6.05792e31	+	1.33437e31i	−1.27145	+	0.280060i
$154$	−1.94946e31	−	1.01384e32i	−0.372274	−	1.93606i
$155$		−	3.01407e31i		−	0.524015i
$156$	−2.00593e32	+	2.18305e31i	−3.17693	+	0.345746i
$157$		−	2.00568e31i		−	0.289545i	−0.989465	−	0.144772i	$-0.953755\pi$
$157$		−	2.00568e31i		−	0.289545i	0.989465	−	0.144772i	$-0.0462450\pi$
$158$		−	8.81927e31i		−	1.16119i
$159$	−1.45991e31	+	1.58882e30i	−0.175416	+	0.0190905i
$160$			3.71387e31i			0.407462i
$161$	−6.47949e31	+	1.24590e31i	−0.649480	+	0.124885i
$162$	8.02222e31	+	1.73266e32i	0.735067	+	1.58761i
$163$	−1.57676e32			−1.32144			−0.660719	−	0.750634i	$-0.729748\pi$
$163$	−1.57676e32			−1.32144			−0.660719	+	0.750634i	$0.729748\pi$
$164$	−1.88897e32			−1.44874
$165$	2.96343e32	−	3.22510e31i	2.08102	−	0.226478i
$166$			2.72927e32i			1.75582i
$167$	−1.17503e32			−0.692885			−0.346443	−	0.938071i	$-0.612611\pi$
$167$	−1.17503e32			−0.692885			−0.346443	+	0.938071i	$0.612611\pi$
$168$	−1.00889e32	−	3.28041e32i	−0.545582	−	1.77396i
$169$	−2.83080e32			−1.40460
$170$			9.28894e32i			4.23114i
$171$	4.19510e30	+	1.90453e31i	0.0175509	+	0.0796793i
$172$	7.46973e32			2.87172
$173$	4.13553e31			0.146171			0.0730857	−	0.997326i	$-0.476715\pi$
$173$	4.13553e31			0.146171			0.0730857	+	0.997326i	$0.476715\pi$
$174$	−4.22038e31	−	3.87796e32i	−0.137210	−	1.26078i
$175$	1.54666e32	+	8.04359e32i	0.462745	+	2.40657i
$176$			4.85266e32i			1.33674i
$177$	4.33080e31	+	3.97942e32i	0.109889	+	1.00973i
$178$		−	3.29843e32i		−	0.771290i
$179$			4.08045e32i			0.879709i	0.898069	+	0.439855i	$0.144970\pi$
$179$			4.08045e32i			0.879709i	−0.898069	+	0.439855i	$0.855030\pi$
$180$	1.88000e33	−	4.14105e32i	3.73858	−	0.823492i
$181$		−	2.24904e32i		−	0.412723i	−0.978476	−	0.206361i	$-0.933838\pi$
$181$		−	2.24904e32i		−	0.412723i	0.978476	−	0.206361i	$-0.0661622\pi$
$182$	−3.02368e32	−	1.57251e33i	−0.512273	−	2.66414i
$183$	6.22994e32	−	6.78004e31i	0.974861	−	0.106094i
$184$	8.48940e32			1.22749
$185$	−3.43793e31			−0.0459523
$186$	−4.31959e31	−	3.96912e32i	−0.0533955	−	0.490632i
$187$			1.28284e33i			1.46713i
$188$	−2.17449e33			−2.30181
$189$	−8.87807e32	+	5.02653e32i	−0.870206	+	0.492688i
$190$	2.92033e32			0.265158
$191$		−	1.73131e33i		−	1.45677i	−0.685167	−	0.728386i	$-0.740271\pi$
$191$		−	1.73131e33i		−	1.45677i	0.685167	−	0.728386i	$-0.259729\pi$
$192$	−1.11296e32	−	1.02266e33i	−0.0868187	−	0.797747i
$193$	−2.27621e33			−1.64676			−0.823382	−	0.567488i	$-0.807915\pi$
$193$	−2.27621e33			−1.64676			−0.823382	+	0.567488i	$0.807915\pi$
$194$	−4.12012e33			−2.76557
$195$	4.59639e33	−	5.00225e32i	2.86362	−	0.311648i
$196$	3.30847e33	−	1.32118e33i	1.91388	−	0.764275i
$197$			3.08387e33i			1.65705i	0.559953	+	0.828524i	$0.310819\pi$
$197$			3.08387e33i			1.65705i	−0.559953	+	0.828524i	$0.689181\pi$
$198$	3.85621e33	−	8.49402e32i	1.92537	−	0.424100i
$199$		−	2.22436e33i		−	1.03237i	−0.856477	−	0.516185i	$-0.827352\pi$
$199$		−	2.22436e33i		−	1.03237i	0.856477	−	0.516185i	$-0.172648\pi$
$200$		−	1.05387e34i		−	4.54832i
$201$	9.39529e31	+	8.63300e32i	0.0377196	+	0.346592i
$202$			1.09637e33i			0.409601i
$203$	2.04684e33	−	3.93575e32i	0.711855	−	0.136879i
$204$	8.96311e32	+	8.23589e33i	0.290283	+	2.66731i
$205$	4.32840e33			1.30586
$206$	2.97522e33			0.836458
$207$	−5.42856e32	−	2.46451e33i	−0.142270	−	0.645894i
$208$			7.52667e33i			1.83943i
$209$	4.03309e32			0.0919425
$210$	4.49098e33	+	1.46024e34i	0.955348	+	3.10632i
$211$	5.33777e33			1.05990			0.529949	−	0.848029i	$-0.322211\pi$
$211$	5.33777e33			1.05990			0.529949	+	0.848029i	$0.322211\pi$
$212$			1.96128e33i			0.363638i
$213$	−2.07655e33	+	2.25991e32i	−0.359615	+	0.0391369i
$214$	−8.63617e33			−1.39740
$215$	−1.71162e34			−2.58851
$216$	1.24384e34	−	4.19401e33i	1.75868	−	0.592994i
$217$	2.09496e33	−	4.02827e32i	0.277019	−	0.0532663i
$218$			2.84319e33i			0.351711i
$219$	−8.22982e33	+	8.95651e32i	−0.952688	+	0.103681i
$220$		−	3.98113e34i		−	4.31397i
$221$			1.98973e34i			2.01886i
$222$	−4.52729e32	+	4.92704e31i	−0.0430249	+	0.00468240i
$223$		−	1.01051e33i		−	0.0899746i	−0.998988	−	0.0449873i	$-0.985675\pi$
$223$		−	1.01051e33i		−	0.0899746i	0.998988	−	0.0449873i	$-0.0143247\pi$
$224$	−2.58136e33	+	4.96356e32i	−0.215404	+	0.0414187i
$225$	−3.05943e34	+	6.73897e33i	−2.39328	+	0.527166i
$226$	−1.34706e34			−0.988132
$227$	−2.00462e34			−1.37930			−0.689649	−	0.724144i	$-0.742235\pi$
$227$	−2.00462e34			−1.37930			−0.689649	+	0.724144i	$0.742235\pi$
$228$	2.58926e33	−	2.81789e32i	0.167155	−	0.0181915i
$229$			2.74288e34i			1.66185i	0.556382	+	0.830927i	$0.312189\pi$
$229$			2.74288e34i			1.66185i	−0.556382	+	0.830927i	$0.687811\pi$
$230$	−3.77897e34			−2.14942
$231$	6.20222e33	+	2.01665e34i	0.331264	+	1.07710i
$232$	−2.68176e34			−1.34538
$233$		−	1.74777e34i		−	0.823804i	−0.911228	−	0.411902i	$-0.864865\pi$
$233$		−	1.74777e34i		−	0.823804i	0.911228	−	0.411902i	$-0.135135\pi$
$234$	5.98113e34	−	1.31746e34i	2.64944	−	0.583588i
$235$	4.98265e34			2.07480
$236$	5.34603e34			2.09319
$237$	1.94997e33	+	1.79176e34i	0.0718086	+	0.659824i
$238$	−6.45637e34	+	1.24146e34i	−2.23678	+	0.430097i
$239$			3.55379e34i			1.15857i	0.815125	+	0.579285i	$0.196668\pi$
$239$			3.55379e34i			1.15857i	−0.815125	+	0.579285i	$0.803332\pi$
$240$	−7.76906e33	−	7.13872e34i	−0.238400	−	2.19057i
$241$		−	5.61592e34i		−	1.62246i	−0.584728	−	0.811229i	$-0.698799\pi$
$241$		−	5.61592e34i		−	1.62246i	0.584728	−	0.811229i	$-0.301201\pi$
$242$		−	1.73552e34i		−	0.472179i
$243$	−2.01292e34	−	3.34276e34i	−0.515865	−	0.856670i
$244$		−	8.36943e34i		−	2.02089i
$245$	−7.58106e34	+	3.02737e34i	−1.72513	+	0.688901i
$246$	5.69991e34	−	6.20321e33i	1.22267	−	0.133063i
$247$	6.25548e33			0.126519
$248$	−2.74480e34			−0.523554
$249$	−6.03450e33	−	5.54489e34i	−0.108580	−	0.997706i
$250$			2.77693e35i			4.71449i
$251$	1.02385e35			1.64047			0.820237	−	0.572024i	$-0.193842\pi$
$251$	1.02385e35			1.64047			0.820237	+	0.572024i	$0.193842\pi$
$252$	5.39088e34	+	1.25137e35i	0.815364	+	1.89268i
$253$	−5.21891e34			−0.745302
$254$		−	7.07011e32i		−	0.00953537i
$255$	−2.05381e34	−	1.88718e35i	−0.261655	−	2.40425i
$256$	−1.69268e35			−2.03749
$257$	1.38355e35			1.57385			0.786927	−	0.617046i	$-0.211671\pi$
$257$	1.38355e35			1.57385			0.786927	+	0.617046i	$0.211671\pi$
$258$	−2.25397e35	+	2.45299e34i	−2.42361	+	0.263761i
$259$	−4.59476e32	−	2.38957e33i	−0.00467107	−	0.0242925i
$260$		−	6.17489e35i		−	5.93630i
$261$	1.71486e34	+	7.78529e34i	0.155934	+	0.707925i
$262$		−	2.63638e34i		−	0.226798i
$263$			1.90296e35i			1.54907i	0.632531	+	0.774535i	$0.282016\pi$
$263$			1.90296e35i			1.54907i	−0.632531	+	0.774535i	$0.717984\pi$
$264$	−2.93698e34	−	2.69869e35i	−0.226279	−	2.07920i
$265$		−	4.49408e34i		−	0.327775i
$266$	3.90299e33	+	2.02980e34i	0.0269534	+	0.140175i
$267$	7.29294e33	+	6.70122e34i	0.0476968	+	0.438269i
$268$	1.15978e35			0.718488
$269$	8.92185e34			0.523657			0.261828	−	0.965114i	$-0.415675\pi$
$269$	8.92185e34			0.523657			0.261828	+	0.965114i	$0.415675\pi$
$270$	−5.53685e35	+	1.86693e35i	−3.07956	+	1.03837i
$271$			1.16122e35i			0.612152i	0.952007	+	0.306076i	$0.0990162\pi$
$271$			1.16122e35i			0.612152i	−0.952007	+	0.306076i	$0.900984\pi$
$272$	3.09028e35			1.54436
$273$	9.61989e34	+	3.12791e35i	0.455839	+	1.48216i
$274$	4.32957e35			1.94564
$275$			6.47872e35i			2.76163i
$276$	−3.35057e35	+	3.64642e34i	−1.35499	+	0.147464i
$277$	−2.67170e35			−1.02525			−0.512626	−	0.858612i	$-0.671327\pi$
$277$	−2.67170e35			−1.02525			−0.512626	+	0.858612i	$0.671327\pi$
$278$	−2.52296e35			−0.918885
$279$	1.75517e34	+	7.96830e34i	0.0606817	+	0.275489i
$280$	1.03140e36	−	1.98322e35i	3.38560	−	0.650998i
$281$			8.53294e34i			0.265985i	0.991117	+	0.132993i	$0.0424586\pi$
$281$			8.53294e34i			0.265985i	−0.991117	+	0.132993i	$0.957541\pi$
$282$	6.56147e35	−	7.14084e34i	1.94262	−	0.211416i
$283$			4.51797e34i			0.127069i	0.997980	+	0.0635345i	$0.0202373\pi$
$283$			4.51797e34i			0.127069i	−0.997980	+	0.0635345i	$0.979763\pi$
$284$			2.78968e35i			0.745485i
$285$	−5.93305e34	+	6.45693e33i	−0.150670	+	0.0163974i
$286$		−	1.26658e36i		−	3.05720i
$287$	5.78486e34	+	3.00849e35i	0.132741	+	0.690338i
$288$	−2.16268e34	−	9.81838e34i	−0.0471847	−	0.214214i
$289$	3.34973e35			0.695009
$290$	1.19376e36			2.35584
$291$	8.37059e35	−	9.10971e34i	1.57148	−	0.171024i
$292$			1.10561e36i			1.97493i
$293$	−6.15925e34			−0.104700			−0.0523501	−	0.998629i	$-0.516671\pi$
$293$	−6.15925e34			−0.104700			−0.0523501	+	0.998629i	$0.516671\pi$
$294$	−9.54935e35	+	5.07310e35i	−1.54503	+	0.820800i
$295$	−1.22499e36			−1.88675
$296$			3.13080e34i			0.0459119i
$297$	−7.64661e35	+	2.57830e35i	−1.06783	+	0.360051i
$298$	−3.03681e35			−0.403908
$299$	−8.09474e35			−1.02558
$300$	4.52664e35	+	4.15937e36i	0.546409	+	5.02076i
$301$	−2.28756e35	−	1.18968e36i	−0.263123	−	1.36841i
$302$		−	1.36876e36i		−	1.50047i
$303$	−2.42410e34	−	2.22742e35i	−0.0253299	−	0.232747i
$304$		−	9.71546e34i		−	0.0967824i
$305$			1.91778e36i			1.82159i
$306$	−5.40918e35	−	2.45572e36i	−0.489972	−	2.22443i
$307$		−	4.68306e35i		−	0.404598i	−0.979324	−	0.202299i	$-0.935159\pi$
$307$		−	4.68306e35i		−	0.404598i	0.979324	−	0.202299i	$-0.0648412\pi$
$308$	2.76712e36	−	5.32074e35i	2.28057	−	0.438517i
$309$	−6.04457e35	+	6.57830e34i	−0.475299	+	0.0517268i
$310$	1.22182e36			0.916777
$311$	−1.53662e36			−1.10037			−0.550186	−	0.835042i	$-0.685443\pi$
$311$	−1.53662e36			−1.10037			−0.550186	+	0.835042i	$0.685443\pi$
$312$	−4.55537e35	−	4.18577e36i	−0.311374	−	2.86110i
$313$		−	1.19248e36i		−	0.778141i	−0.921208	−	0.389071i	$-0.872796\pi$
$313$		−	1.19248e36i		−	0.778141i	0.921208	−	0.389071i	$-0.127204\pi$
$314$	8.13048e35			0.506566
$315$	−1.23527e36	−	2.86739e36i	−0.734952	−	1.70602i
$316$	2.40708e36			1.36782
$317$			6.75081e34i			0.0366435i	0.999832	+	0.0183217i	$0.00583231\pi$
$317$			6.75081e34i			0.0366435i	−0.999832	+	0.0183217i	$0.994168\pi$
$318$	−6.44066e34	−	5.91809e35i	−0.0333993	−	0.306894i
$319$	1.64863e36			0.816880
$320$	3.14809e36			1.49064
$321$	1.75456e36	−	1.90948e35i	0.794044	−	0.0864157i
$322$	−5.05056e35	−	2.62661e36i	−0.218489	−	1.13628i
$323$		−	2.56836e35i		−	0.106223i
$324$	−4.72902e36	+	2.18954e36i	−1.87011	+	0.865866i
$325$			1.00488e37i			3.80017i
$326$		−	6.39178e36i		−	2.31189i
$327$	−6.28638e34	−	5.77633e35i	−0.0217499	−	0.199853i
$328$		−	3.94171e36i		−	1.30471i
$329$	6.65926e35	+	3.46324e36i	0.210904	+	1.09684i
$330$	1.30737e36	+	1.20129e37i	0.396228	+	3.64080i
$331$	4.49145e36			1.30281			0.651405	−	0.758730i	$-0.274180\pi$
$331$	4.49145e36			1.30281			0.651405	+	0.758730i	$0.274180\pi$
$332$	−7.44912e36			−2.06825
$333$	9.08887e34	−	2.00199e34i	0.0241584	−	0.00532134i
$334$		−	4.76327e36i		−	1.21222i
$335$	−2.65752e36			−0.647629
$336$	4.85800e36	−	1.49408e36i	1.13380	−	0.348702i
$337$	−4.28477e36			−0.957842			−0.478921	−	0.877858i	$-0.658972\pi$
$337$	−4.28477e36			−0.957842			−0.478921	+	0.877858i	$0.658972\pi$
$338$		−	1.14753e37i		−	2.45738i
$339$	2.73674e36	−	2.97839e35i	0.561485	−	0.0611064i
$340$	−2.53527e37			−4.98403
$341$	1.68739e36			0.317889
$342$	−7.72047e35	+	1.70058e35i	−0.139401	+	0.0307057i
$343$	−3.11740e36	−	4.86468e36i	−0.539545	−	0.841957i
$344$			1.55871e37i			2.58623i
$345$	7.67751e36	−	8.35543e35i	1.22136	−	0.132920i
$346$			1.67643e36i			0.255731i
$347$		−	1.36597e36i		−	0.199831i	−0.994996	−	0.0999157i	$-0.968143\pi$
$347$		−	1.36597e36i		−	0.199831i	0.994996	−	0.0999157i	$-0.0318573\pi$
$348$	1.05843e37	−	1.15189e36i	1.48512	−	0.161626i
$349$			6.00688e36i			0.808500i	0.914648	+	0.404250i	$0.132467\pi$
$349$			6.00688e36i			0.808500i	−0.914648	+	0.404250i	$0.867533\pi$
$350$	−3.26066e37	+	6.26973e36i	−4.21035	+	0.809585i
$351$	−1.18602e37	+	3.99904e36i	−1.46940	+	0.495453i
$352$	−2.07916e36			−0.247184
$353$	4.96737e36			0.566752			0.283376	−	0.959009i	$-0.408546\pi$
$353$	4.96737e36			0.566752			0.283376	+	0.959009i	$0.408546\pi$
$354$	−1.61315e37	+	1.75559e36i	−1.76656	+	0.192254i
$355$		−	6.39230e36i		−	0.671964i
$356$	9.00256e36			0.908534
$357$	1.28425e37	−	3.94972e36i	1.24440	−	0.382716i
$358$	−1.65411e37			−1.53907
$359$			2.42934e36i			0.217080i	0.994092	+	0.108540i	$0.0346175\pi$
$359$			2.42934e36i			0.217080i	−0.994092	+	0.108540i	$0.965382\pi$
$360$	8.64114e36	+	3.92300e37i	0.741626	+	3.36691i
$361$	1.20491e37			0.993343
$362$	9.11702e36			0.722069
$363$	3.83728e35	+	3.52594e36i	0.0291997	+	0.268305i
$364$	4.29192e37	−	8.25268e36i	3.13820	−	0.603427i
$365$		−	2.53341e37i		−	1.78016i
$366$	2.74845e36	+	2.52545e37i	0.185614	+	1.70554i
$367$		−	1.82108e37i		−	1.18214i	−0.806618	−	0.591072i	$-0.798705\pi$
$367$		−	1.82108e37i		−	1.18214i	0.806618	−	0.591072i	$-0.201295\pi$
$368$			1.25720e37i			0.784535i
$369$	−1.14430e37	+	2.52053e36i	−0.686526	+	0.151220i
$370$		−	1.39365e36i		−	0.0803947i
$371$	3.12366e36	−	6.00630e35i	0.173277	−	0.0333185i
$372$	1.08331e37	−	1.17896e36i	0.577936	−	0.0628968i
$373$	2.96683e37			1.52235			0.761175	−	0.648547i	$-0.224623\pi$
$373$	2.96683e37			1.52235			0.761175	+	0.648547i	$0.224623\pi$
$374$	−5.20029e37			−2.56678
$375$	−6.13988e36	−	5.64172e37i	−0.291546	−	2.67891i
$376$		−	4.53752e37i		−	2.07298i
$377$	2.55709e37			1.12408
$378$	−2.03762e37	−	3.59893e37i	−0.861969	−	1.52245i
$379$	7.48995e36			0.304937			0.152469	−	0.988308i	$-0.451278\pi$
$379$	7.48995e36			0.304937			0.152469	+	0.988308i	$0.451278\pi$
$380$			7.97058e36i			0.312340i
$381$	1.56322e34	+	1.43639e35i	0.000589670	+	0.00541827i
$382$	7.01827e37			2.54866
$383$	−3.26768e37			−1.14250			−0.571251	−	0.820776i	$-0.693542\pi$
$383$	−3.26768e37			−1.14250			−0.571251	+	0.820776i	$0.693542\pi$
$384$	4.79332e37	−	5.21657e36i	1.61374	−	0.175623i
$385$	−6.34060e37	+	1.21920e37i	−2.05565	+	0.395270i
$386$		−	9.22714e37i		−	2.88105i
$387$	4.52501e37	−	9.96719e36i	1.36085	−	0.299753i
$388$		−	1.12452e38i		−	3.25768i
$389$			2.80009e37i			0.781452i	0.920507	+	0.390726i	$0.127776\pi$
$389$			2.80009e37i			0.781452i	−0.920507	+	0.390726i	$0.872224\pi$
$390$	2.02778e37	+	1.86325e38i	0.545235	+	5.00997i
$391$			3.32352e37i			0.861064i
$392$	2.75691e37	+	6.90379e37i	0.688296	+	1.72361i
$393$	5.82911e35	+	5.35616e36i	0.0140252	+	0.128873i
$394$	−1.25012e38			−2.89905
$395$	−5.51561e37			−1.23292
$396$	2.31831e37	+	1.05249e38i	0.499565	+	2.26798i
$397$		−	7.23184e37i		−	1.50240i	−0.660073	−	0.751201i	$-0.729475\pi$
$397$		−	7.23184e37i		−	1.50240i	0.660073	−	0.751201i	$-0.270525\pi$
$398$	9.01696e37			1.80616
$399$	−1.24174e36	−	4.03752e36i	−0.0239841	−	0.0779845i
$400$	1.56068e38			2.90700
$401$		−	6.54810e37i		−	1.17631i	−0.808748	−	0.588155i	$-0.799855\pi$
$401$		−	6.54810e37i		−	1.17631i	0.808748	−	0.588155i	$-0.200145\pi$
$402$	−3.49959e37	+	3.80860e36i	−0.606372	+	0.0659914i
$403$	2.61720e37			0.437435
$404$	−2.99237e37			−0.482486
$405$	1.08361e38	−	5.01713e37i	1.68568	−	0.780473i
$406$	1.59545e37	+	8.29735e37i	0.239472	+	1.24541i
$407$		−	1.92468e36i		−	0.0278766i
$408$	−1.71858e38	+	1.87033e37i	−2.40214	+	0.261425i
$409$			9.85984e36i			0.133009i	0.997786	+	0.0665046i	$0.0211847\pi$
$409$			9.85984e36i			0.133009i	−0.997786	+	0.0665046i	$0.978815\pi$
$410$			1.75462e38i			2.28463i
$411$	−8.79612e37	+	9.57282e36i	−1.10557	+	0.120319i
$412$			8.12040e37i			0.985298i
$413$	−1.63719e37	−	8.51444e37i	−0.191789	−	0.997425i
$414$	9.99048e37	−	2.20059e37i	1.13001	−	0.248905i
$415$	1.70690e38			1.86428
$416$	−3.22486e37			−0.340140
$417$	5.12575e37	−	5.57835e36i	0.522137	−	0.0568241i
$418$			1.63491e37i			0.160856i
$419$	−5.25615e37			−0.499533			−0.249767	−	0.968306i	$-0.580354\pi$
$419$	−5.25615e37			−0.499533			−0.249767	+	0.968306i	$0.580354\pi$
$420$	−3.98551e38	+	1.22574e38i	−3.65906	+	1.12534i
$421$	3.20373e37			0.284162			0.142081	−	0.989855i	$-0.454621\pi$
$421$	3.20373e37			0.284162			0.142081	+	0.989855i	$0.454621\pi$
$422$			2.16379e38i			1.85432i
$423$	−1.31726e38	+	2.90152e37i	−1.09078	+	0.240265i
$424$	−4.09260e37			−0.327487
$425$	4.12580e38			3.19057
$426$	−9.16106e36	−	8.41778e37i	−0.0684710	−	0.629156i
$427$	−1.33297e38	+	2.56309e37i	−0.962977	+	0.185165i
$428$		−	2.35711e38i		−	1.64606i
$429$	2.80044e37	+	2.57323e38i	0.189058	+	1.73719i
$430$		−	6.93845e38i		−	4.52866i
$431$			2.30202e37i			0.145274i	0.997358	+	0.0726371i	$0.0231415\pi$
$431$			2.30202e37i			0.145274i	−0.997358	+	0.0726371i	$0.976859\pi$
$432$	6.21096e37	+	1.84202e38i	0.379005	+	1.12404i
$433$		−	3.08651e37i		−	0.182135i	−0.995845	−	0.0910676i	$-0.970972\pi$
$433$		−	3.08651e37i		−	0.182135i	0.995845	−	0.0910676i	$-0.0290279\pi$
$434$	1.63295e37	+	8.49240e37i	0.0931908	+	0.484651i
$435$	−2.42529e38	+	2.63944e37i	−1.33866	+	0.145686i
$436$	−7.76005e37			−0.414295
$437$	1.04487e37			0.0539613
$438$	−3.63073e37	−	3.33615e38i	−0.181393	−	1.66675i
$439$			3.14943e38i			1.52229i	0.648585	+	0.761143i	$0.275361\pi$
$439$			3.14943e38i			1.52229i	−0.648585	+	0.761143i	$0.724639\pi$
$440$	8.30743e38			3.88511
$441$	1.82791e38	−	1.24181e38i	0.827173	−	0.561947i
$442$	−8.06585e38			−3.53205
$443$		−	3.05724e38i		−	1.29561i	−0.761805	−	0.647807i	$-0.775686\pi$
$443$		−	3.05724e38i		−	1.29561i	0.761805	−	0.647807i	$-0.224314\pi$
$444$	−1.34476e36	−	1.23565e37i	−0.00551559	−	0.0506808i
$445$	−2.06285e38			−0.818933
$446$	4.09634e37			0.157413
$447$	6.16970e37	−	6.71449e36i	0.229512	−	0.0249778i
$448$	4.20739e37	+	2.18811e38i	0.151524	+	0.788021i
$449$			2.65621e38i			0.926170i	0.886314	+	0.463085i	$0.153258\pi$
$449$			2.65621e38i			0.926170i	−0.886314	+	0.463085i	$0.846742\pi$
$450$	−2.73180e38	−	1.24021e39i	−0.922290	−	4.18711i
$451$			2.42319e38i			0.792188i
$452$		−	3.67659e38i		−	1.16396i
$453$	3.02637e37	+	2.78082e38i	0.0927893	+	0.852608i
$454$		−	8.12621e38i		−	2.41311i
$455$	−9.83453e38	+	1.89102e38i	−2.82871	+	0.543916i
$456$	5.88009e36	+	5.40301e37i	0.0163830	+	0.150538i
$457$	3.78952e38			1.02282			0.511410	−	0.859337i	$-0.329123\pi$
$457$	3.78952e38			1.02282			0.511410	+	0.859337i	$0.329123\pi$
$458$	−1.11189e39			−2.90745
$459$	1.64192e38	+	4.86954e38i	0.415975	+	1.23368i
$460$		−	1.03141e39i		−	2.53188i
$461$	6.92235e38			1.64661			0.823304	−	0.567600i	$-0.192128\pi$
$461$	6.92235e38			1.64661			0.823304	+	0.567600i	$0.192128\pi$
$462$	−8.17498e38	+	2.51422e38i	−1.88442	+	0.579554i
$463$	7.45245e38			1.66485			0.832424	−	0.554139i	$-0.186952\pi$
$463$	7.45245e38			1.66485			0.832424	+	0.554139i	$0.186952\pi$
$464$		−	3.97145e38i		−	0.859881i
$465$	−2.48230e38	+	2.70149e37i	−0.520939	+	0.0566938i
$466$	7.08500e38			1.44127
$467$	4.66425e38			0.919787			0.459893	−	0.887974i	$-0.347888\pi$
$467$	4.66425e38			0.919787			0.459893	+	0.887974i	$0.347888\pi$
$468$	3.59579e38	+	1.63246e39i	0.687432	+	3.12088i
$469$	−3.55174e37	−	1.84713e38i	−0.0658318	−	0.342367i
$470$			2.01983e39i			3.62991i
$471$	−1.65182e38	+	1.79767e37i	−0.287845	+	0.0313262i
$472$			1.11556e39i			1.88509i
$473$		−	9.58227e38i		−	1.57030i
$474$	−7.26330e38	+	7.90465e37i	−1.15438	+	0.125631i
$475$		−	1.29710e38i		−	0.199947i
$476$	−3.38837e38	−	1.76217e39i	−0.506629	−	2.63479i
$477$	2.61702e37	+	1.18810e38i	0.0379568	+	0.172321i
$478$	−1.44061e39			−2.02695
$479$	−8.86151e38			−1.20960			−0.604802	−	0.796376i	$-0.706748\pi$
$479$	−8.86151e38			−1.20960			−0.604802	+	0.796376i	$0.706748\pi$
$480$	3.05864e38	−	3.32872e37i	0.405071	−	0.0440838i
$481$		−	2.98525e37i		−	0.0383599i
$482$	2.27654e39			2.83853
$483$	1.60684e38	+	5.22466e38i	0.194420	+	0.632156i
$484$	4.73683e38			0.556199
$485$			2.57674e39i			2.93640i
$486$	1.35506e39	−	8.15984e38i	1.49877	−	0.902518i
$487$	1.52650e39			1.63880			0.819399	−	0.573223i	$-0.194307\pi$
$487$	1.52650e39			1.63880			0.819399	+	0.573223i	$0.194307\pi$
$488$	1.74645e39			1.81999
$489$	1.41324e38	+	1.29858e39i	0.142968	+	1.31368i
$490$	−1.22721e39	−	3.07316e39i	−1.20525	−	3.01816i
$491$			9.61324e38i			0.916617i	0.888793	+	0.458309i	$0.151545\pi$
$491$			9.61324e38i			0.916617i	−0.888793	+	0.458309i	$0.848455\pi$
$492$	1.69307e38	+	1.55570e39i	0.156740	+	1.44023i
$493$		−	1.04988e39i		−	0.943760i
$494$			2.53580e38i			0.221348i
$495$	−5.31220e38	−	2.41169e39i	−0.450297	−	2.04431i
$496$		−	4.06481e38i		−	0.334623i
$497$	4.44303e38	−	8.54324e37i	0.355231	−	0.0683054i
$498$	2.24775e39	−	2.44623e38i	1.74551	−	0.189964i
$499$	−2.19901e39			−1.65871			−0.829354	−	0.558723i	$-0.811291\pi$
$499$	−2.19901e39			−1.65871			−0.829354	+	0.558723i	$0.811291\pi$
$500$	−7.57921e39			−5.55340
$501$	1.05317e38	+	9.67724e38i	0.0749641	+	0.688818i
$502$			4.15043e39i			2.87005i
$503$	−1.09841e39			−0.737954			−0.368977	−	0.929438i	$-0.620292\pi$
$503$	−1.09841e39			−0.737954			−0.368977	+	0.929438i	$0.620292\pi$
$504$	−2.61123e39	+	1.12492e39i	−1.70452	+	0.734306i
$505$	6.85673e38			0.434902
$506$		−	2.11561e39i		−	1.30392i
$507$	2.53723e38	+	2.33137e39i	0.151965	+	1.39635i
$508$	1.92968e37			0.0112321
$509$	−6.04238e38			−0.341822			−0.170911	−	0.985286i	$-0.554671\pi$
$509$	−6.04238e38			−0.341822			−0.170911	+	0.985286i	$0.554671\pi$
$510$	7.65011e39	−	8.32561e38i	4.20630	−	0.457771i
$511$	1.76087e39	−	3.38587e38i	0.941074	−	0.180954i
$512$		−	3.73700e39i		−	1.94137i
$513$	1.53092e38	−	5.16198e37i	0.0773127	−	0.0260684i
$514$			5.60854e39i			2.75350i
$515$		−	1.86071e39i		−	0.888126i
$516$	−6.69507e38	−	6.15186e39i	−0.310695	−	2.85487i
$517$			2.78947e39i			1.25866i
$518$	9.68666e37	−	1.86259e37i	0.0425004	−	0.00817215i
$519$	−3.70665e37	−	3.40591e38i	−0.0158145	−	0.145313i
$520$	1.28852e40			5.34615
$521$	−2.48661e38			−0.100337			−0.0501684	−	0.998741i	$-0.515976\pi$
$521$	−2.48661e38			−0.100337			−0.0501684	+	0.998741i	$0.515976\pi$
$522$	−3.15595e39	+	6.95157e38i	−1.23853	+	0.272810i
$523$		−	1.18620e39i		−	0.452777i	−0.974037	−	0.226389i	$-0.927308\pi$
$523$		−	1.18620e39i		−	0.452777i	0.974037	−	0.226389i	$-0.0726919\pi$
$524$	7.19559e38			0.267154
$525$	6.48585e39	−	1.99472e39i	2.34238	−	0.720399i
$526$	−7.71408e39			−2.71014
$527$		−	1.07456e39i		−	0.367264i
$528$	3.99651e39	−	4.34940e38i	1.32889	−	0.144623i
$529$	1.73897e39			0.562580
$530$	1.82178e39			0.573451
$531$	3.23852e39	−	7.13345e38i	0.991918	−	0.218489i
$532$	−5.54003e38	+	1.06526e38i	−0.165118	+	0.0317495i
$533$			3.75847e39i			1.09010i
$534$	−2.71650e39	+	2.95636e38i	−0.766762	+	0.0834467i
$535$			5.40109e39i			1.48372i
$536$			2.42010e39i			0.647060i
$537$	3.36054e39	−	3.65728e38i	0.874545	−	0.0951767i
$538$			3.61668e39i			0.916151i
$539$	−1.69483e39	−	4.24415e39i	−0.417916	−	1.04654i
$540$	−5.09548e39	−	1.51120e40i	−1.22314	−	3.62754i
$541$	−1.96022e39			−0.458084			−0.229042	−	0.973417i	$-0.573559\pi$
$541$	−1.96022e39			−0.458084			−0.229042	+	0.973417i	$0.573559\pi$
$542$	−4.70727e39			−1.07098
$543$	−1.85225e39	+	2.01580e38i	−0.410300	+	0.0446529i
$544$			1.32406e39i			0.285577i
$545$	1.77814e39			0.373437
$546$	−1.26797e40	+	3.89965e39i	−2.59308	+	0.797503i
$547$	5.39261e39			1.07395			0.536973	−	0.843599i	$-0.319568\pi$
$547$	5.39261e39			1.07395			0.536973	+	0.843599i	$0.319568\pi$
$548$			1.18169e40i			2.29185i
$549$	−1.11677e39	−	5.07003e39i	−0.210943	−	0.957661i
$550$	−2.62630e40			−4.83154
$551$	−3.30071e38			−0.0591437
$552$	−7.60899e38	−	6.99163e39i	−0.132804	−	1.22029i
$553$	−7.37155e38	−	3.83368e39i	−0.125327	−	0.651780i
$554$		−	1.08304e40i		−	1.79370i
$555$	3.08139e37	+	2.83138e38i	0.00497163	+	0.0456826i
$556$		−	6.88604e39i		−	1.08239i
$557$		−	1.86146e39i		−	0.285071i	−0.989790	−	0.142536i	$-0.954474\pi$
$557$		−	1.86146e39i		−	0.285071i	0.989790	−	0.142536i	$-0.0455256\pi$
$558$	−3.23014e39	+	7.11498e38i	−0.481975	+	0.106164i
$559$		−	1.48625e40i		−	2.16083i
$560$	2.93698e39	+	1.52741e40i	0.416077	+	2.16387i
$561$	1.05651e40	−	1.14980e39i	1.45852	−	0.158731i
$562$	−3.45903e39			−0.465348
$563$	−9.81277e38			−0.128653			−0.0643265	−	0.997929i	$-0.520490\pi$
$563$	−9.81277e38			−0.128653			−0.0643265	+	0.997929i	$0.520490\pi$
$564$	1.94898e39	+	1.79085e40i	0.249035	+	2.28830i
$565$			8.42457e39i			1.04917i
$566$	−1.83146e39			−0.222310
$567$	4.93544e39	+	6.86120e39i	0.583944	+	0.811794i
$568$	−5.82123e39			−0.671373
$569$		−	1.20996e40i		−	1.36033i	−0.733061	−	0.680163i	$-0.761909\pi$
$569$		−	1.20996e40i		−	1.36033i	0.733061	−	0.680163i	$-0.238091\pi$
$570$	−2.61747e38	−	2.40510e39i	−0.0286877	−	0.263601i
$571$	1.66810e40			1.78238			0.891189	−	0.453633i	$-0.149872\pi$
$571$	1.66810e40			1.78238			0.891189	+	0.453633i	$0.149872\pi$
$572$	3.45693e40			3.60121
$573$	−1.42586e40	+	1.55176e39i	−1.44822	+	0.157610i
$574$	−1.21956e40	+	2.34503e39i	−1.20776	+	0.232234i
$575$			1.67848e40i			1.62081i
$576$	−8.32261e39	+	1.83321e39i	−0.783671	+	0.172618i
$577$		−	1.46760e40i		−	1.34760i	−0.738916	−	0.673798i	$-0.764662\pi$
$577$		−	1.46760e40i		−	1.34760i	0.738916	−	0.673798i	$-0.235338\pi$
$578$			1.35789e40i			1.21594i
$579$	2.04015e39	+	1.87462e40i	0.178165	+	1.63710i
$580$			3.25819e40i			2.77504i
$581$	2.28125e39	+	1.18640e40i	0.189504	+	0.985543i
$582$	3.69283e39	+	3.39321e40i	0.299210	+	2.74934i
$583$	2.51595e39			0.198842
$584$	−2.30708e40			−1.77859
$585$	−8.23943e39	−	3.74062e40i	−0.619636	−	2.81309i
$586$		−	2.49680e39i		−	0.183176i
$587$	1.75156e40			1.25364			0.626819	−	0.779165i	$-0.284356\pi$
$587$	1.75156e40			1.25364			0.626819	+	0.779165i	$0.284356\pi$
$588$	−1.38462e40	−	2.60635e40i	−0.966854	−	1.81996i
$589$	−3.37830e38			−0.0230158
$590$		−	4.96580e40i		−	3.30092i
$591$	2.53978e40	−	2.76405e39i	1.64732	−	0.179278i
$592$	−4.63644e38			−0.0293440
$593$	−2.04282e40			−1.26164			−0.630822	−	0.775928i	$-0.717282\pi$
$593$	−2.04282e40			−1.26164			−0.630822	+	0.775928i	$0.717282\pi$
$594$	−1.04517e40	−	3.09973e40i	−0.629919	−	1.86819i
$595$	7.76413e39	+	4.03784e40i	0.456664	+	2.37494i
$596$		−	8.28851e39i		−	0.475780i
$597$	−1.83192e40	+	1.99368e39i	−1.02631	+	0.111693i
$598$		−	3.28139e40i		−	1.79428i
$599$		−	3.07821e40i		−	1.64289i	−0.570287	−	0.821445i	$-0.693168\pi$
$599$		−	3.07821e40i		−	1.64289i	0.570287	−	0.821445i	$-0.306832\pi$
$600$	−8.67936e40	+	9.44574e39i	−4.52162	+	0.492088i
$601$			2.87869e40i			1.46391i	0.681351	+	0.731957i	$0.261393\pi$
$601$			2.87869e40i			1.46391i	−0.681351	+	0.731957i	$0.738607\pi$
$602$	4.82263e40	−	9.27316e39i	2.39406	−	0.460340i
$603$	7.02568e39	−	1.54754e39i	0.340477	−	0.0749964i
$604$	3.73582e40			1.76746
$605$	−1.08540e40			−0.501345
$606$	9.02937e39	−	9.82666e38i	0.407197	−	0.0443152i
$607$			6.50759e39i			0.286539i	0.989684	+	0.143270i	$0.0457616\pi$
$607$			6.50759e39i			0.286539i	−0.989684	+	0.143270i	$0.954238\pi$
$608$	4.16267e38			0.0178966
$609$	−5.07594e39	−	1.65044e40i	−0.213091	−	0.692867i
$610$	−7.77415e40			−3.18692
$611$			4.32658e40i			1.73200i
$612$	6.70251e40	−	1.47635e40i	2.62024	−	0.577158i
$613$	2.10947e40			0.805370			0.402685	−	0.915339i	$-0.368077\pi$
$613$	2.10947e40			0.805370			0.402685	+	0.915339i	$0.368077\pi$
$614$	1.89839e40			0.707854
$615$	−3.87951e39	−	3.56474e40i	−0.141282	−	1.29819i
$616$	1.11028e40	+	5.77416e40i	0.394923	+	2.05385i
$617$		−	2.77271e40i		−	0.963317i	−0.876359	−	0.481659i	$-0.840035\pi$
$617$		−	2.77271e40i		−	0.963317i	0.876359	−	0.481659i	$-0.159965\pi$
$618$	−2.66667e39	−	2.45031e40i	−0.0904973	−	0.831548i
$619$			3.62054e39i			0.120021i	0.998198	+	0.0600107i	$0.0191135\pi$
$619$			3.62054e39i			0.120021i	−0.998198	+	0.0600107i	$0.980887\pi$
$620$			3.33478e40i			1.07991i
$621$	−1.98105e40	+	6.67973e39i	−0.626710	+	0.211315i
$622$		−	6.22903e40i		−	1.92513i
$623$	−2.75698e39	−	1.43381e40i	−0.0832448	−	0.432926i
$624$	6.19875e40	−	6.74610e39i	1.82864	−	0.199011i
$625$	8.86463e40			2.55506
$626$	4.83400e40			1.36138
$627$	−3.61483e38	−	3.32154e39i	−0.00994736	−	0.0914028i
$628$			2.21909e40i			0.596705i
$629$	−1.22568e39			−0.0322064
$630$	1.16236e41	−	5.00745e40i	2.98472	−	1.28582i
$631$	−3.16287e40			−0.793699			−0.396849	−	0.917884i	$-0.629896\pi$
$631$	−3.16287e40			−0.793699			−0.396849	+	0.917884i	$0.629896\pi$
$632$			5.02286e40i			1.23184i
$633$	−4.78421e39	−	4.39604e40i	−0.114672	−	1.05368i
$634$	−2.73660e39			−0.0641086
$635$	−4.42168e38			−0.0101244
$636$	1.61525e40	−	1.75788e39i	0.361503	−	0.0393424i
$637$	−2.62875e40	−	6.58285e40i	−0.575079	−	1.44010i
$638$			6.68311e40i			1.42915i
$639$	3.72239e39	+	1.68993e40i	0.0778144	+	0.353270i
$640$			1.47554e41i			3.01537i
$641$		−	3.32279e40i		−	0.663838i	−0.943308	−	0.331919i	$-0.892304\pi$
$641$		−	3.32279e40i		−	0.663838i	0.943308	−	0.331919i	$-0.107696\pi$
$642$	7.74053e39	+	7.11250e40i	0.151187	+	1.38920i
$643$			6.25407e40i			1.19427i	0.802140	+	0.597136i	$0.203695\pi$
$643$			6.25407e40i			1.19427i	−0.802140	+	0.597136i	$0.796305\pi$
$644$	7.16893e40	−	1.37847e40i	1.33847	−	0.257367i
$645$	1.53411e40	+	1.40964e41i	0.280054	+	2.57331i
$646$	1.04114e40			0.185840
$647$	−2.46712e40			−0.430604			−0.215302	−	0.976547i	$-0.569074\pi$
$647$	−2.46712e40			−0.430604			−0.215302	+	0.976547i	$0.569074\pi$
$648$	−4.56892e40	−	9.86804e40i	−0.779787	−	1.68420i
$649$		−	6.85796e40i		−	1.14458i
$650$	−4.07350e41			−6.64850
$651$	−5.19527e39	−	1.68924e40i	−0.0829246	−	0.269630i
$652$	1.74454e41			2.72327
$653$			8.56660e40i			1.30788i	0.756547	+	0.653939i	$0.226885\pi$
$653$			8.56660e40i			1.30788i	−0.756547	+	0.653939i	$0.773115\pi$
$654$	2.34157e40	−	2.54833e39i	0.349647	−	0.0380521i
$655$	−1.64880e40			−0.240807
$656$	5.83733e40			0.833889
$657$	1.47527e40	+	6.69757e40i	0.206145	+	0.935879i
$658$	−1.40390e41	+	2.69949e40i	−1.91894	+	0.368982i
$659$			2.34042e39i			0.0312935i	0.999878	+	0.0156468i	$0.00498073\pi$
$659$			2.34042e39i			0.0312935i	−0.999878	+	0.0156468i	$0.995019\pi$
$660$	−3.27875e41	+	3.56826e40i	−4.28865	+	0.466734i
$661$		−	4.64889e40i		−	0.594878i	−0.954741	−	0.297439i	$-0.903868\pi$
$661$		−	4.64889e40i		−	0.594878i	0.954741	−	0.297439i	$-0.0961325\pi$
$662$			1.82072e41i			2.27930i
$663$	1.63869e41	−	1.78338e40i	2.00701	−	0.218423i
$664$		−	1.55441e41i		−	1.86264i
$665$	1.26945e40	−	2.44094e39i	0.148833	−	0.0286183i
$666$	8.11555e38	+	3.68438e39i	0.00930982	+	0.0422657i
$667$	4.27119e40			0.479429
$668$	1.30006e41			1.42792
$669$	−8.32227e39	+	9.05713e38i	−0.0894465	+	0.00973446i
$670$		−	1.07729e41i		−	1.13304i
$671$	−1.07364e41			−1.10505
$672$	6.40150e39	+	2.08145e40i	0.0644803	+	0.209658i
$673$	−1.84928e41			−1.82299			−0.911497	−	0.411307i	$-0.865072\pi$
$673$	−1.84928e41			−1.82299			−0.911497	+	0.411307i	$0.865072\pi$
$674$		−	1.73693e41i		−	1.67577i
$675$	8.29217e40	+	2.45926e41i	0.783003	+	2.32220i
$676$	3.13201e41			2.89465
$677$	−1.58660e41			−1.43527			−0.717633	−	0.696422i	$-0.754774\pi$
$677$	−1.58660e41			−1.43527			−0.717633	+	0.696422i	$0.754774\pi$
$678$	1.20736e40	+	1.10940e41i	0.106907	+	0.982332i
$679$	−1.79099e41	+	3.44378e40i	−1.55232	+	0.298486i
$680$		−	5.29036e41i		−	4.48855i
$681$	1.79673e40	+	1.65095e41i	0.149228	+	1.37120i
$682$			6.84021e40i			0.556155i
$683$		−	1.21940e41i		−	0.970609i	−0.874345	−	0.485304i	$-0.838709\pi$
$683$		−	1.21940e41i		−	0.970609i	0.874345	−	0.485304i	$-0.161291\pi$
$684$	−4.64147e39	−	2.10718e40i	−0.0361695	−	0.164206i
$685$		−	2.70773e41i		−	2.06582i
$686$	1.97201e41	−	1.26371e41i	1.47302	−	0.943948i
$687$	2.25896e41	−	2.45843e40i	1.65210	−	0.179798i
$688$	−2.30831e41			−1.65296
$689$	3.90234e40			0.273619
$690$	3.38707e40	+	3.11226e41i	0.232548	+	2.13680i
$691$			1.29754e41i			0.872348i	0.899862	+	0.436174i	$0.143667\pi$
$691$			1.29754e41i			0.872348i	−0.899862	+	0.436174i	$0.856333\pi$
$692$	−4.57557e40			−0.301236
$693$	1.60527e41	−	6.91549e40i	1.03494	−	0.445852i
$694$	5.53727e40			0.349610
$695$			1.57787e41i			0.975645i
$696$	2.40364e40	+	2.20862e41i	0.145558	+	1.33748i
$697$	1.54314e41			0.915232
$698$	−2.43503e41			−1.41449
$699$	−1.43942e41	+	1.56652e40i	−0.818969	+	0.0891283i
$700$	−1.71123e41	−	8.89946e41i	−0.953643	−	4.95955i
$701$			1.30986e41i			0.715013i	0.933911	+	0.357507i	$0.116373\pi$
$701$			1.30986e41i			0.715013i	−0.933911	+	0.357507i	$0.883627\pi$
$702$	−1.62110e41	−	4.80781e41i	−0.866808	−	2.57074i
$703$			3.85338e38i			0.00201832i
$704$			1.76242e41i			0.904284i
$705$	−4.46591e40	−	4.10357e41i	−0.224475	−	2.06262i
$706$			2.01364e41i			0.991547i
$707$	9.16394e39	+	4.76583e40i	0.0442080	+	0.229910i
$708$	−4.79161e40	−	4.40284e41i	−0.226464	−	2.08090i
$709$	2.32302e41			1.07568			0.537840	−	0.843047i	$-0.319241\pi$
$709$	2.32302e41			1.07568			0.537840	+	0.843047i	$0.319241\pi$
$710$	2.59127e41			1.17562
$711$	1.45816e41	−	3.21188e40i	0.648182	−	0.142774i
$712$			1.87857e41i			0.818213i
$713$	4.37160e40			0.186570
$714$	1.60111e41	+	5.20601e41i	0.669571	+	2.17711i
$715$	−7.92123e41			−3.24605
$716$		−	4.51463e41i		−	1.81294i
$717$	2.92680e41	−	3.18524e40i	1.15177	−	0.125347i
$718$	−9.84790e40			−0.379786
$719$	−9.86131e40			−0.372705			−0.186353	−	0.982483i	$-0.559667\pi$
$719$	−9.86131e40			−0.372705			−0.186353	+	0.982483i	$0.559667\pi$
$720$	−5.80961e41	+	1.27968e41i	−2.15192	+	0.474001i
$721$	1.29331e41	−	2.48682e40i	0.469505	−	0.0902784i
$722$			4.88437e41i			1.73788i
$723$	−4.62511e41	+	5.03351e40i	−1.61293	+	0.175536i
$724$			2.48835e41i			0.850555i
$725$		−	5.30223e41i		−	1.77647i
$726$	−1.42932e41	+	1.55553e40i	−0.469407	+	0.0510855i
$727$			9.34355e40i			0.300790i	0.988626	+	0.150395i	$0.0480545\pi$
$727$			9.34355e40i			0.300790i	−0.988626	+	0.150395i	$0.951946\pi$
$728$	1.72209e41	+	8.95595e41i	0.543438	+	2.82622i
$729$	−2.57258e41	+	1.95739e41i	−0.795830	+	0.605521i
$730$	1.02698e42			3.11443
$731$	−6.10220e41			−1.81420
$732$	−6.89283e41	+	7.50146e40i	−2.00903	+	0.218643i
$733$			3.34929e41i			0.957072i	0.878068	+	0.478536i	$0.158832\pi$
$733$			3.34929e41i			0.957072i	−0.878068	+	0.478536i	$0.841168\pi$
$734$	7.38217e41			2.06819
$735$	3.17274e41	+	5.97220e41i	0.871501	+	1.64047i
$736$	−5.38660e40			−0.145073
$737$		−	1.48777e41i		−	0.392879i
$738$	−1.02176e41	−	4.63868e41i	−0.264564	−	1.20110i
$739$	−3.87117e41			−0.982875			−0.491437	−	0.870913i	$-0.663528\pi$
$739$	−3.87117e41			−0.982875			−0.491437	+	0.870913i	$0.663528\pi$
$740$	3.80374e40			0.0947002
$741$	−5.60674e39	−	5.15183e40i	−0.0136882	−	0.125776i
$742$	2.43479e40	+	1.26625e41i	0.0582915	+	0.303153i
$743$			7.69793e40i			0.180733i	0.995909	+	0.0903663i	$0.0288038\pi$
$743$			7.69793e40i			0.180733i	−0.995909	+	0.0903663i	$0.971196\pi$
$744$	2.46015e40	+	2.26054e41i	0.0566439	+	0.520481i
$745$			1.89924e41i			0.428857i
$746$			1.20267e42i			2.66339i
$747$	−4.51253e41	+	9.93969e40i	−0.980102	+	0.215886i
$748$		−	1.41934e42i		−	3.02352i
$749$	−3.75408e41	+	7.21851e40i	−0.784364	+	0.150821i
$750$	2.28700e42	−	2.48894e41i	4.68682	−	0.510067i
$751$	6.59473e41			1.32562			0.662809	−	0.748789i	$-0.269364\pi$
$751$	6.59473e41			1.32562			0.662809	+	0.748789i	$0.269364\pi$
$752$	6.71966e41			1.32492
$753$	−9.17673e40	−	8.43217e41i	−0.177485	−	1.63084i
$754$			1.03658e42i			1.96660i
$755$	−8.56028e41			−1.59315
$756$	9.82273e41	−	5.56137e41i	1.79335	−	1.01535i
$757$	2.53641e41			0.454286			0.227143	−	0.973861i	$-0.427062\pi$
$757$	2.53641e41			0.454286			0.227143	+	0.973861i	$0.427062\pi$
$758$			3.03622e41i			0.533495i
$759$	4.67767e40	+	4.29815e41i	0.0806351	+	0.740927i
$760$	−1.66322e41			−0.281289
$761$	7.53557e41			1.25037			0.625185	−	0.780477i	$-0.285024\pi$
$761$	7.53557e41			1.25037			0.625185	+	0.780477i	$0.285024\pi$
$762$	−5.82274e39	+	6.33689e38i	−0.00947939	+	0.00103164i
$763$	2.37647e40	+	1.23591e41i	0.0379600	+	0.197416i
$764$			1.91553e42i			3.00217i
$765$	−1.53582e42	+	3.38293e41i	−2.36183	+	0.520238i
$766$		−	1.32463e42i		−	1.99884i
$767$		−	1.06370e42i		−	1.57502i
$768$	1.51714e41	+	1.39404e42i	0.220438	+	2.02553i
$769$			6.57063e40i			0.0936862i	0.998902	+	0.0468431i	$0.0149161\pi$
$769$			6.57063e40i			0.0936862i	−0.998902	+	0.0468431i	$0.985084\pi$
$770$	−4.94230e41	−	2.57031e42i	−0.691534	−	3.59642i
$771$	−1.24007e41	−	1.13945e42i	−0.170277	−	1.56462i
$772$	2.51841e42			3.39371
$773$	1.43189e42			1.89369			0.946844	−	0.321694i	$-0.104252\pi$
$773$	1.43189e42			1.89369			0.946844	+	0.321694i	$0.104252\pi$
$774$	4.04043e41	+	1.83432e42i	0.524426	+	2.38084i
$775$		−	5.42687e41i		−	0.691313i
$776$	2.34654e42			2.93382
$777$	−1.92680e40	+	5.92587e39i	−0.0236446	+	0.00727189i
$778$	−1.13508e42			−1.36717
$779$		−	4.85145e40i		−	0.0573560i
$780$	−5.08547e42	+	5.53451e41i	−5.90145	+	0.642255i
$781$	3.57864e41			0.407641
$782$	−1.34727e42			−1.50645
$783$	6.25804e41	−	2.11010e41i	0.686899	−	0.231610i
$784$	−1.02239e42	+	4.08274e41i	−1.10163	+	0.439916i
$785$		−	5.08483e41i		−	0.537857i
$786$	−2.17125e41	+	2.36297e40i	−0.225467	+	0.0245375i
$787$		−	1.17907e42i		−	1.20201i	−0.799246	−	0.601004i	$-0.794767\pi$
$787$		−	1.17907e42i		−	1.20201i	0.799246	−	0.601004i	$-0.205233\pi$
$788$		−	3.41200e42i		−	3.41491i
$789$	1.56722e42	−	1.70561e41i	1.53998	−	0.167596i
$790$		−	2.23588e42i		−	2.15703i
$791$	−5.85558e41	+	1.12594e41i	−0.554640	+	0.106648i
$792$	−2.19624e42	+	4.83762e41i	−2.04251	+	0.449901i
$793$	−1.66526e42			−1.52062
$794$	2.93159e42			2.62849
$795$	−3.70120e41	+	4.02801e40i	−0.325851	+	0.0354624i
$796$			2.46104e42i			2.12755i
$797$	−7.12284e41			−0.604655			−0.302328	−	0.953204i	$-0.597764\pi$
$797$	−7.12284e41			−0.604655			−0.302328	+	0.953204i	$0.597764\pi$
$798$	1.63670e41	−	5.03369e40i	0.136436	−	0.0419608i
$799$	1.77640e42			1.45416
$800$			6.68688e41i			0.537550i
$801$	5.45357e41	−	1.20125e41i	0.430536	−	0.0948336i
$802$	2.65442e42			2.05798
$803$	1.41829e42			1.07992
$804$	−1.03950e41	−	9.55158e41i	−0.0777340	−	0.714270i
$805$	−1.64269e42	+	3.15864e41i	−1.20647	+	0.231985i
$806$			1.06094e42i			0.765304i
$807$	−7.99659e40	−	7.34778e41i	−0.0566550	−	0.520583i
$808$		−	6.24417e41i		−	0.434520i
$809$		−	2.10855e41i		−	0.144122i	−0.997400	−	0.0720609i	$-0.977042\pi$
$809$		−	2.10855e41i		−	0.144122i	0.997400	−	0.0720609i	$-0.0229576\pi$
$810$	2.03381e42	+	4.39267e42i	1.36546	+	2.94914i
$811$			2.50434e42i			1.65154i	0.564004	+	0.825772i	$0.309260\pi$
$811$			2.50434e42i			1.65154i	−0.564004	+	0.825772i	$0.690740\pi$
$812$	−2.26463e42	+	4.35453e41i	−1.46702	+	0.282084i
$813$	9.56347e41	−	1.04079e41i	0.608559	−	0.0662295i
$814$	7.80213e40			0.0487708
$815$	−3.99745e42			−2.45469
$816$	−2.76980e41	−	2.54507e42i	−0.167086	−	1.53530i
$817$			1.91846e41i			0.113693i
$818$	−3.99691e41			−0.232703
$819$	2.48984e42	−	1.07262e42i	1.42415	−	0.613521i
$820$	−4.78895e42			−2.69116
$821$			2.58842e42i			1.42909i	0.699590	+	0.714544i	$0.253366\pi$
$821$			2.58842e42i			1.42909i	−0.699590	+	0.714544i	$0.746634\pi$
$822$	−3.88056e41	−	3.56571e42i	−0.210501	−	1.93422i
$823$	−3.55304e42			−1.89366			−0.946832	−	0.321729i	$-0.895736\pi$
$823$	−3.55304e42			−1.89366			−0.946832	+	0.321729i	$0.895736\pi$
$824$	−1.69448e42			−0.887346
$825$	5.33569e42	−	5.80683e41i	2.74542	−	0.298784i
$826$	3.45152e42	−	6.63674e41i	1.74502	−	0.335540i
$827$		−	3.04056e42i		−	1.51051i	−0.655431	−	0.755255i	$-0.727513\pi$
$827$		−	3.04056e42i		−	1.51051i	0.655431	−	0.755255i	$-0.272487\pi$
$828$	6.00618e41	+	2.72675e42i	0.293196	+	1.33108i
$829$		−	2.58916e42i		−	1.24199i	−0.783814	−	0.620995i	$-0.786729\pi$
$829$		−	2.58916e42i		−	1.24199i	0.783814	−	0.620995i	$-0.213271\pi$
$830$			6.91931e42i			3.26160i
$831$	2.39462e41	+	2.20034e42i	0.110923	+	1.01923i
$832$			2.73358e42i			1.24435i
$833$	−2.70277e42	+	1.07931e42i	−1.20908	+	0.482828i
$834$	2.26131e41	+	2.07784e42i	0.0994152	+	0.913491i
$835$	−2.97897e42			−1.28710
$836$	−4.46222e41			−0.189479
$837$	6.40515e41	−	2.15970e41i	0.267307	−	0.0901310i
$838$		−	2.13070e42i		−	0.873946i
$839$	2.13343e42			0.860062			0.430031	−	0.902814i	$-0.358503\pi$
$839$	2.13343e42			0.860062			0.430031	+	0.902814i	$0.358503\pi$
$840$	−2.55776e42	−	8.31657e42i	−1.01347	−	3.29530i
$841$	1.21844e42			0.474527
$842$			1.29871e42i			0.497149i
$843$	7.02749e41	−	7.64802e40i	0.264424	−	0.0287772i
$844$	−5.90573e42			−2.18428
$845$	−7.17670e42			−2.60917
$846$	−1.17620e42	−	5.33984e42i	−0.420350	−	1.90835i
$847$	−1.45063e41	−	7.54418e41i	−0.0509620	−	0.265034i
$848$		−	6.06077e41i		−	0.209309i
$849$	3.72087e41	−	4.04942e40i	0.126323	−	0.0137477i
$850$			1.67249e43i			5.58198i
$851$		−	4.98637e40i		−	0.0163608i
$852$	2.29750e42	−	2.50037e41i	0.741109	−	0.0806548i
$853$		−	5.00613e42i		−	1.58760i	−0.608178	−	0.793801i	$-0.708099\pi$
$853$		−	5.00613e42i		−	1.58760i	0.608178	−	0.793801i	$-0.291901\pi$
$854$	−1.03901e42	−	5.40350e42i	−0.323951	−	1.68475i
$855$	1.06355e41	+	4.82842e41i	0.0326024	+	0.148012i
$856$	4.91858e42			1.48242
$857$	−4.67549e42			−1.38550			−0.692748	−	0.721179i	$-0.743600\pi$
$857$	−4.67549e42			−1.38550			−0.692748	+	0.721179i	$0.743600\pi$
$858$	−1.04312e43	+	1.13522e42i	−3.03926	+	0.330762i
$859$			2.01030e42i			0.575918i	0.957643	+	0.287959i	$0.0929767\pi$
$859$			2.01030e42i			0.575918i	−0.957643	+	0.287959i	$0.907023\pi$
$860$	1.89374e43			5.33449
$861$	2.42586e42	−	7.46074e41i	0.671924	−	0.206650i
$862$	−9.33177e41			−0.254161
$863$			8.04899e41i			0.215568i	0.994174	+	0.107784i	$0.0343755\pi$
$863$			8.04899e41i			0.215568i	−0.994174	+	0.107784i	$0.965624\pi$
$864$	−7.89230e41	+	2.66114e41i	−0.207852	+	0.0700839i
$865$	1.04845e42			0.271527
$866$	1.25119e42			0.318650
$867$	−3.00233e41	−	2.75874e42i	−0.0751938	−	0.690929i
$868$	−2.31787e42	+	4.45690e41i	−0.570890	+	0.109773i
$869$		−	3.08784e42i		−	0.747942i
$870$	−1.06996e42	−	9.83147e42i	−0.254881	−	2.34201i
$871$		−	2.30760e42i		−	0.540626i
$872$		−	1.61929e42i		−	0.373109i
$873$	−1.50050e42	−	6.81213e42i	−0.340039	−	1.54375i
$874$			4.23564e41i			0.0944067i
$875$	2.32109e42	+	1.20711e43i	0.508833	+	2.64625i
$876$	9.10551e42	−	9.90952e41i	1.96334	−	0.213670i
$877$	4.94014e42			1.04772			0.523860	−	0.851804i	$-0.324491\pi$
$877$	4.94014e42			1.04772			0.523860	+	0.851804i	$0.324491\pi$
$878$	−1.27669e43			−2.66328
$879$	5.52049e40	+	5.07259e41i	0.0113276	+	0.104086i
$880$			1.23026e43i			2.48312i
$881$	1.13033e42			0.224417			0.112208	−	0.993685i	$-0.464208\pi$
$881$	1.13033e42			0.224417			0.112208	+	0.993685i	$0.464208\pi$
$882$	5.03396e42	+	7.40988e42i	0.983141	+	1.44716i
$883$	−6.29335e41			−0.120907			−0.0604535	−	0.998171i	$-0.519255\pi$
$883$	−6.29335e41			−0.120907			−0.0604535	+	0.998171i	$0.519255\pi$
$884$		−	2.20145e43i		−	4.16055i
$885$	1.09795e42	+	1.00887e43i	0.204130	+	1.87568i
$886$	1.23932e43			2.26671
$887$	−2.75262e42			−0.495283			−0.247641	−	0.968852i	$-0.579655\pi$
$887$	−2.75262e42			−0.495283			−0.247641	+	0.968852i	$0.579655\pi$
$888$	2.57844e41	−	2.80611e40i	0.0456424	−	0.00496726i
$889$	−5.90953e39	−	3.07333e40i	−0.00102915	−	0.00535221i
$890$		−	8.36226e42i		−	1.43274i
$891$	2.80877e42	+	6.06644e42i	0.473467	+	1.02260i
$892$			1.11803e42i			0.185423i
$893$		−	5.58477e41i		−	0.0911295i
$894$	2.72187e41	+	2.50103e42i	0.0436992	+	0.401537i
$895$			1.03448e43i			1.63414i
$896$	−1.02559e43	+	1.97204e42i	−1.59407	+	0.306514i
$897$	7.25526e41	+	6.66660e42i	0.110959	+	1.01956i
$898$	−1.07676e43			−1.62036
$899$	−1.38097e42			−0.204488
$900$	3.38497e43	−	7.45602e42i	4.93217	−	1.08640i
$901$		−	1.60221e42i		−	0.229727i
$902$	−9.82298e42			−1.38595
$903$	−9.59281e42	+	2.95027e42i	−1.33191	+	0.409628i
$904$	7.67195e42			1.04825
$905$		−	5.70182e42i		−	0.766671i
$906$	−1.12727e43	+	1.22681e42i	−1.49166	+	0.162337i
$907$	5.70163e42			0.742495			0.371247	−	0.928534i	$-0.378930\pi$
$907$	5.70163e42			0.742495			0.371247	+	0.928534i	$0.378930\pi$
$908$	2.21792e43			2.84251
$909$	−1.81271e42	+	3.99284e41i	−0.228640	+	0.0503623i
$910$	−7.66571e42	−	3.98665e43i	−0.951595	−	4.94890i
$911$		−	9.54791e42i		−	1.16652i	−0.812286	−	0.583260i	$-0.801777\pi$
$911$		−	9.54791e42i		−	1.16652i	0.812286	−	0.583260i	$-0.198223\pi$
$912$	−8.00138e41	+	8.70790e40i	−0.0962143	+	0.0104710i
$913$			9.55583e42i			1.13095i
$914$			1.53617e43i			1.78945i
$915$	1.57943e43	−	1.71889e42i	1.81090	−	0.197080i
$916$		−	3.03474e43i		−	3.42481i
$917$	−2.20361e41	−	1.14601e42i	−0.0244781	−	0.127302i
$918$	−1.97398e43	+	6.65590e42i	−2.15836	+	0.727759i
$919$	7.31122e42			0.786892			0.393446	−	0.919348i	$-0.371283\pi$
$919$	7.31122e42			0.786892			0.393446	+	0.919348i	$0.371283\pi$
$920$	2.15225e43			2.28018
$921$	−3.85684e42	+	4.19739e41i	−0.402223	+	0.0437739i
$922$			2.80614e43i			2.88078i
$923$	5.55061e42			0.560940
$924$	−6.86216e42	−	2.23123e43i	−0.682680	−	2.21974i
$925$	−6.19004e41			−0.0606232
$926$			3.02102e43i			2.91269i
$927$	1.08354e42	+	4.91917e42i	0.102846	+	0.466913i
$928$	1.70160e42			0.159005
$929$	−5.29124e42			−0.486776			−0.243388	−	0.969929i	$-0.578259\pi$
$929$	−5.29124e42			−0.486776			−0.243388	+	0.969929i	$0.578259\pi$
$930$	−1.09511e42	−	1.00626e43i	−0.0991871	−	0.911396i
$931$	3.39320e41	+	8.49717e41i	0.0302579	+	0.0757712i
$932$			1.93374e43i			1.69773i
$933$	1.37726e42	+	1.26551e43i	0.119050	+	1.09391i
$934$			1.89076e43i			1.60919i
$935$			3.25228e43i			2.72533i
$936$	−3.40645e43	+	7.50335e42i	−2.81062	+	0.619092i
$937$			8.95227e42i			0.727293i	0.931537	+	0.363646i	$0.118468\pi$
$937$			8.95227e42i			0.727293i	−0.931537	+	0.363646i	$0.881532\pi$
$938$	7.48778e42	−	1.43978e42i	0.598980	−	0.115174i
$939$	−9.82094e42	+	1.06881e42i	−0.773574	+	0.0841880i
$940$	−5.51282e43			−4.27583
$941$	2.40860e43			1.83956			0.919782	−	0.392430i	$-0.128365\pi$
$941$	2.40860e43			1.83956			0.919782	+	0.392430i	$0.128365\pi$
$942$	−7.28729e41	−	6.69603e42i	−0.0548060	−	0.503593i
$943$			6.27790e42i			0.464938i
$944$	−1.65204e43			−1.20483
$945$	−2.25079e43	+	1.27434e43i	−1.61649	+	0.915214i
$946$	3.88439e43			2.74727
$947$		−	1.12201e43i		−	0.781488i	−0.920499	−	0.390744i	$-0.872218\pi$
$947$		−	1.12201e43i		−	0.781488i	0.920499	−	0.390744i	$-0.127782\pi$
$948$	−2.15745e42	−	1.98241e43i	−0.147986	−	1.35979i
$949$	2.19983e43			1.48603
$950$	5.25809e42			0.349813
$951$	5.55977e41	−	6.05070e40i	0.0364284	−	0.00396450i
$952$	3.67711e43	−	7.07051e42i	2.37286	−	0.456263i
$953$			1.19102e42i			0.0756957i	0.999284	+	0.0378478i	$0.0120502\pi$
$953$			1.19102e42i			0.0756957i	−0.999284	+	0.0378478i	$0.987950\pi$
$954$	−4.81625e42	+	1.06087e42i	−0.301479	+	0.0664064i
$955$		−	4.38926e43i		−	2.70609i
$956$		−	3.93193e43i		−	2.38762i
$957$	−1.47766e42	−	1.35777e43i	−0.0883792	−	0.812085i
$958$		−	3.59222e43i		−	2.11623i
$959$	1.88203e43	−	3.61886e42i	1.09209	−	0.209991i
$960$	−2.82161e42	−	2.59268e43i	−0.161274	−	1.48189i
$961$	1.63485e43			0.920423
$962$	1.21014e42			0.0671116
$963$	−3.14519e42	−	1.42789e43i	−0.171817	−	0.780033i
$964$			6.21347e43i			3.34362i
$965$	−5.77069e43			−3.05902
$966$	−2.11794e43	+	6.51371e42i	−1.10597	+	0.340142i
$967$	−3.71332e42			−0.191020			−0.0955099	−	0.995428i	$-0.530448\pi$
$967$	−3.71332e42			−0.191020			−0.0955099	+	0.995428i	$0.530448\pi$
$968$			9.88435e42i			0.500905i
$969$	−2.11523e42	+	2.30200e41i	−0.105600	+	0.0114924i
$970$	−1.04454e44			−5.13730
$971$	−7.89413e42			−0.382495			−0.191247	−	0.981542i	$-0.561253\pi$
$971$	−7.89413e42			−0.382495			−0.191247	+	0.981542i	$0.561253\pi$
$972$	2.22710e43	+	3.69844e43i	1.06311	+	1.76546i
$973$	−1.09671e43	+	2.10881e42i	−0.515772	+	0.0991747i
$974$			6.18800e43i			2.86712i
$975$	8.27587e43	−	9.00662e42i	3.77787	−	0.411145i
$976$			2.58634e43i			1.16322i
$977$		−	5.83677e42i		−	0.258644i	−0.991603	−	0.129322i	$-0.958720\pi$
$977$		−	5.83677e42i		−	0.258644i	0.991603	−	0.129322i	$-0.0412800\pi$
$978$	−5.26409e43	+	5.72891e42i	−2.29832	+	0.250126i
$979$		−	1.15486e43i		−	0.496799i
$980$	8.38771e43	−	3.34949e43i	3.55521	−	1.41971i
$981$	−4.70088e42	+	1.03546e42i	−0.196326	+	0.0432445i
$982$	−3.89695e43			−1.60364
$983$	−1.53736e43			−0.623375			−0.311687	−	0.950185i	$-0.600894\pi$
$983$	−1.53736e43			−0.623375			−0.311687	+	0.950185i	$0.600894\pi$
$984$	−3.24628e43	+	3.53293e42i	−1.29705	+	0.141158i
$985$			7.81828e43i			3.07812i
$986$	4.25595e43			1.65113
$987$	2.79254e43	−	8.58845e42i	1.06758	−	0.328334i
$988$	−6.92108e42			−0.260734
$989$		−	2.48253e43i		−	0.921612i
$990$	9.77634e43	−	2.15342e43i	3.57656	−	0.787805i
$991$	9.62473e42			0.346993			0.173497	−	0.984834i	$-0.444493\pi$
$991$	9.62473e42			0.346993			0.173497	+	0.984834i	$0.444493\pi$
$992$	1.74160e42			0.0618770
$993$	−4.02566e42	−	3.69904e43i	−0.140953	−	1.29516i
$994$	3.46320e42	+	1.80108e43i	0.119502	+	0.621486i
$995$		−	5.63925e43i		−	1.91772i
$996$	6.67660e42	+	6.13489e43i	0.223766	+	2.05611i
$997$		−	3.99552e43i		−	1.31976i	−0.751373	−	0.659878i	$-0.770608\pi$
$997$		−	3.99552e43i		−	1.31976i	0.751373	−	0.659878i	$-0.229392\pi$
$998$		−	8.91421e43i		−	2.90195i
$999$	−2.46341e41	−	7.30590e41i	−0.00790383	−	0.0234409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.4	yes	76
3.2	odd	2	inner	21.30.c.a.20.73	yes	76
7.6	odd	2	inner	21.30.c.a.20.74	yes	76
21.20	even	2	inner	21.30.c.a.20.3	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.3	✓	76	21.20	even	2	inner
21.30.c.a.20.4	yes	76	1.1	even	1	trivial
21.30.c.a.20.73	yes	76	3.2	odd	2	inner
21.30.c.a.20.74	yes	76	7.6	odd	2	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+40537.3i q^{2} +(-896293. - 8.23572e6i) q^{3} -1.10640e9 q^{4} +2.53522e10 q^{5} +(3.33854e11 - 3.63333e10i) q^{6} +(3.38830e11 + 1.76213e12i) q^{7} -2.30873e13i q^{8} +(-6.70237e13 + 1.47632e13i) q^{9} +O(q^{10})\)	\(q+40537.3i q^{2} +(-896293. - 8.23572e6i) q^{3} -1.10640e9 q^{4} +2.53522e10 q^{5} +(3.33854e11 - 3.63333e10i) q^{6} +(3.38830e11 + 1.76213e12i) q^{7} -2.30873e13i q^{8} +(-6.70237e13 + 1.47632e13i) q^{9} +1.02771e15i q^{10} +1.41931e15i q^{11} +(9.91662e14 + 9.11203e15i) q^{12} +2.20140e16i q^{13} +(-7.14320e16 + 1.37353e16i) q^{14} +(-2.27230e16 - 2.08794e17i) q^{15} +3.41903e17 q^{16} +9.03848e17 q^{17} +(-5.98462e17 - 2.71696e18i) q^{18} -2.84158e17i q^{19} -2.80498e19 q^{20} +(1.42087e19 - 4.36989e18i) q^{21} -5.75350e19 q^{22} +3.67708e19i q^{23} +(-1.90141e20 + 2.06930e19i) q^{24} +4.56470e20 q^{25} -8.92390e20 q^{26} +(1.81659e20 + 5.38756e20i) q^{27} +(-3.74882e20 - 1.94963e21i) q^{28} -1.16157e21i q^{29} +(8.46394e21 - 9.21130e20i) q^{30} -1.18888e21i q^{31} +1.46491e21i q^{32} +(1.16890e22 - 1.27212e21i) q^{33} +3.66396e22i q^{34} +(8.59008e21 + 4.46739e22i) q^{35} +(7.41553e22 - 1.63341e22i) q^{36} -1.35607e21 q^{37} +1.15190e22 q^{38} +(1.81301e23 - 1.97310e22i) q^{39} -5.85315e23i q^{40} +1.70731e23 q^{41} +(1.77144e23 + 5.75983e23i) q^{42} -6.75136e23 q^{43} -1.57033e24i q^{44} +(-1.69920e24 + 3.74280e23i) q^{45} -1.49059e24 q^{46} +1.96537e24 q^{47} +(-3.06445e23 - 2.81582e24i) q^{48} +(-2.99029e24 + 1.19412e24i) q^{49} +1.85041e25i q^{50} +(-8.10112e23 - 7.44384e24i) q^{51} -2.43564e25i q^{52} -1.77266e24i q^{53} +(-2.18397e25 + 7.36395e24i) q^{54} +3.59826e25i q^{55} +(4.06829e25 - 7.82268e24i) q^{56} +(-2.34025e24 + 2.54689e23i) q^{57} +4.70870e25 q^{58} -4.83190e25 q^{59} +(2.51408e25 + 2.31010e26i) q^{60} +7.56453e25i q^{61} +4.81939e25 q^{62} +(-4.87243e25 - 1.13102e26i) q^{63} +1.24174e26 q^{64} +5.58105e26i q^{65} +(5.15682e25 + 4.73842e26i) q^{66} -1.04824e26 q^{67} -1.00002e27 q^{68} +(3.02834e26 - 3.29574e25i) q^{69} +(-1.81096e27 + 3.48219e26i) q^{70} -2.52140e26i q^{71} +(3.40844e26 + 1.54740e27i) q^{72} -9.99284e26i q^{73} -5.49714e25i q^{74} +(-4.09131e26 - 3.75936e27i) q^{75} +3.14394e26i q^{76} +(-2.50101e27 + 4.80904e26i) q^{77} +(7.99843e26 + 7.34948e27i) q^{78} -2.17559e27 q^{79} +8.66800e27 q^{80} +(4.27422e27 - 1.97897e27i) q^{81} +6.92096e27i q^{82} +6.73274e27 q^{83} +(-1.57206e28 + 4.83486e27i) q^{84} +2.29145e28 q^{85} -2.73682e28i q^{86} +(-9.56638e27 + 1.04111e27i) q^{87} +3.27681e28 q^{88} -8.13678e27 q^{89} +(-1.51723e28 - 6.88810e28i) q^{90} +(-3.87916e28 + 7.45901e27i) q^{91} -4.06833e28i q^{92} +(-9.79126e27 + 1.06558e27i) q^{93} +7.96709e28i q^{94} -7.20404e27i q^{95} +(1.20646e28 - 1.31299e27i) q^{96} +1.01638e29i q^{97} +(-4.84066e28 - 1.21219e29i) q^{98} +(-2.09536e28 - 9.51273e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more