LMFDB - Embedded newform 21.30.c.a.20.13

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			20.13
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42628.6i q^{2} +(-4.19005e6 + 7.14660e6i) q^{3} -1.28033e9 q^{4} -1.62384e10 q^{5} +(3.04650e11 + 1.78616e11i) q^{6} +(1.66265e12 + 6.74901e11i) q^{7} +3.16925e13i q^{8} +(-3.35174e13 - 5.98892e13i) q^{9} +O(q^{10})$	\(q-42628.6i q^{2} +(-4.19005e6 + 7.14660e6i) q^{3} -1.28033e9 q^{4} -1.62384e10 q^{5} +(3.04650e11 + 1.78616e11i) q^{6} +(1.66265e12 + 6.74901e11i) q^{7} +3.16925e13i q^{8} +(-3.35174e13 - 5.98892e13i) q^{9} +6.92219e14i q^{10} +1.89246e15i q^{11} +(5.36463e15 - 9.14999e15i) q^{12} -1.67013e16i q^{13} +(2.87701e16 - 7.08766e16i) q^{14} +(6.80395e16 - 1.16049e17i) q^{15} +6.63637e17 q^{16} +1.70898e17 q^{17} +(-2.55299e18 + 1.42880e18i) q^{18} -2.87863e18i q^{19} +2.07904e19 q^{20} +(-1.17898e19 + 9.05445e18i) q^{21} +8.06728e19 q^{22} -8.58865e18i q^{23} +(-2.26494e20 - 1.32793e20i) q^{24} +7.74198e19 q^{25} -7.11953e20 q^{26} +(5.68443e20 + 1.14028e19i) q^{27} +(-2.12874e21 - 8.64094e20i) q^{28} +1.33896e21i q^{29} +(-4.94701e21 - 2.90043e21i) q^{30} -8.21487e21i q^{31} -1.12751e22i q^{32} +(-1.35246e22 - 7.92948e21i) q^{33} -7.28513e21i q^{34} +(-2.69988e22 - 1.09593e22i) q^{35} +(4.29133e22 + 7.66777e22i) q^{36} -6.15011e22 q^{37} -1.22712e23 q^{38} +(1.19358e23 + 6.99792e22i) q^{39} -5.14634e23i q^{40} -2.49794e21 q^{41} +(3.85979e23 + 5.02584e23i) q^{42} +8.52749e23 q^{43} -2.42296e24i q^{44} +(5.44268e23 + 9.72502e23i) q^{45} -3.66122e23 q^{46} -2.18694e24 q^{47} +(-2.78067e24 + 4.74275e24i) q^{48} +(2.30892e24 + 2.24425e24i) q^{49} -3.30030e24i q^{50} +(-7.16069e23 + 1.22134e24i) q^{51} +2.13831e25i q^{52} -1.34081e25i q^{53} +(4.86084e23 - 2.42320e25i) q^{54} -3.07304e25i q^{55} +(-2.13893e25 + 5.26936e25i) q^{56} +(2.05724e25 + 1.20616e25i) q^{57} +5.70780e25 q^{58} -2.12081e25 q^{59} +(-8.71128e25 + 1.48581e26i) q^{60} +5.23975e25i q^{61} -3.50188e26 q^{62} +(-1.53086e25 - 1.22196e26i) q^{63} -1.24356e26 q^{64} +2.71202e26i q^{65} +(-3.38023e26 + 5.76536e26i) q^{66} +1.73869e26 q^{67} -2.18805e26 q^{68} +(6.13796e25 + 3.59868e25i) q^{69} +(-4.67179e26 + 1.15092e27i) q^{70} -1.36215e26i q^{71} +(1.89804e27 - 1.06225e27i) q^{72} -1.03806e27i q^{73} +2.62171e27i q^{74} +(-3.24393e26 + 5.53288e26i) q^{75} +3.68558e27i q^{76} +(-1.27722e27 + 3.14650e27i) q^{77} +(2.98312e27 - 5.08804e27i) q^{78} +1.92827e27 q^{79} -1.07764e28 q^{80} +(-2.46329e27 + 4.01466e27i) q^{81} +1.06484e26i q^{82} +5.55458e27 q^{83} +(1.50949e28 - 1.15927e28i) q^{84} -2.77510e27 q^{85} -3.63515e28i q^{86} +(-9.56902e27 - 5.61031e27i) q^{87} -5.99767e28 q^{88} -3.90521e26 q^{89} +(4.14564e28 - 2.32014e28i) q^{90} +(1.12717e28 - 2.77685e28i) q^{91} +1.09963e28i q^{92} +(5.87084e28 + 3.44207e28i) q^{93} +9.32264e28i q^{94} +4.67442e28i q^{95} +(8.05790e28 + 4.72434e28i) q^{96} -2.98614e28i q^{97} +(9.56693e28 - 9.84262e28i) q^{98} +(1.13338e29 - 6.34302e28i) 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 $

$2$		−	42628.6i		−	1.83978i	−0.392175	−	0.919891i	$-0.628277\pi$
$2$		−	42628.6i		−	1.83978i	0.392175	−	0.919891i	$-0.371723\pi$
$3$	−4.19005e6	+	7.14660e6i	−0.505779	+	0.862663i
$3$	−4.19005e6	+	7.14660e6i	−0.505779	+	0.862663i
$4$	−1.28033e9			−2.38480
$5$	−1.62384e10			−1.18981			−0.594904	−	0.803797i	$-0.702810\pi$
$5$	−1.62384e10			−1.18981			−0.594904	+	0.803797i	$0.702810\pi$
$6$	3.04650e11	+	1.78616e11i	1.58711	+	0.930522i
$7$	1.66265e12	+	6.74901e11i	0.926574	+	0.376113i
$7$	1.66265e12	+	6.74901e11i	0.926574	+	0.376113i
$8$			3.16925e13i			2.54772i
$9$	−3.35174e13	−	5.98892e13i	−0.488376	−	0.872633i
$10$			6.92219e14i			2.18899i
$11$			1.89246e15i			1.50256i	0.659984	+	0.751280i	$0.270563\pi$
$11$			1.89246e15i			1.50256i	−0.659984	+	0.751280i	$0.729437\pi$
$12$	5.36463e15	−	9.14999e15i	1.20618	−	2.05728i
$13$		−	1.67013e16i		−	1.17644i	−0.808699	−	0.588222i	$-0.799828\pi$
$13$		−	1.67013e16i		−	1.17644i	0.808699	−	0.588222i	$-0.200172\pi$
$14$	2.87701e16	−	7.08766e16i	0.691966	−	1.70469i
$15$	6.80395e16	−	1.16049e17i	0.601780	−	1.02640i
$16$	6.63637e17			2.30245
$17$	1.70898e17			0.246165			0.123083	−	0.992396i	$-0.460722\pi$
$17$	1.70898e17			0.246165			0.123083	+	0.992396i	$0.460722\pi$
$18$	−2.55299e18	+	1.42880e18i	−1.60545	+	0.898505i
$19$		−	2.87863e18i		−	0.826529i	−0.910611	−	0.413265i	$-0.864388\pi$
$19$		−	2.87863e18i		−	0.826529i	0.910611	−	0.413265i	$-0.135612\pi$
$20$	2.07904e19			2.83745
$21$	−1.17898e19	+	9.05445e18i	−0.793100	+	0.609091i
$22$	8.06728e19			2.76438
$23$		−	8.58865e18i		−	0.154480i	−0.997013	−	0.0772398i	$-0.975389\pi$
$23$		−	8.58865e18i		−	0.154480i	0.997013	−	0.0772398i	$-0.0246107\pi$
$24$	−2.26494e20	−	1.32793e20i	−2.19783	−	1.28858i
$25$	7.74198e19			0.415644
$26$	−7.11953e20			−2.16440
$27$	5.68443e20	+	1.14028e19i	0.999799	+	0.0200556i
$28$	−2.12874e21	−	8.64094e20i	−2.20969	−	0.896953i
$29$			1.33896e21i			0.835597i	0.908540	+	0.417799i	$0.137198\pi$
$29$			1.33896e21i			0.835597i	−0.908540	+	0.417799i	$0.862802\pi$
$30$	−4.94701e21	−	2.90043e21i	−1.88836	−	1.10714i
$31$		−	8.21487e21i		−	1.94920i	−0.223955	−	0.974599i	$-0.571897\pi$
$31$		−	8.21487e21i		−	1.94920i	0.223955	−	0.974599i	$-0.428103\pi$
$32$		−	1.12751e22i		−	1.68829i
$33$	−1.35246e22	−	7.92948e21i	−1.29620	−	0.759963i
$34$		−	7.28513e21i		−	0.452890i
$35$	−2.69988e22	−	1.09593e22i	−1.10245	−	0.447503i
$36$	4.29133e22	+	7.66777e22i	1.16468	+	2.08105i
$37$	−6.15011e22			−1.12191			−0.560955	−	0.827846i	$-0.689566\pi$
$37$	−6.15011e22			−1.12191			−0.560955	+	0.827846i	$0.689566\pi$
$38$	−1.22712e23			−1.52063
$39$	1.19358e23	+	6.99792e22i	1.01488	+	0.595021i
$40$		−	5.14634e23i		−	3.03130i
$41$	−2.49794e21			−0.0102853			−0.00514264	−	0.999987i	$-0.501637\pi$
$41$	−2.49794e21			−0.0102853			−0.00514264	+	0.999987i	$0.501637\pi$
$42$	3.85979e23	+	5.02584e23i	1.12059	+	1.45913i
$43$	8.52749e23			1.76006			0.880032	−	0.474914i	$-0.157521\pi$
$43$	8.52749e23			1.76006			0.880032	+	0.474914i	$0.157521\pi$
$44$		−	2.42296e24i		−	3.58330i
$45$	5.44268e23	+	9.72502e23i	0.581074	+	1.03827i
$46$	−3.66122e23			−0.284209
$47$	−2.18694e24			−1.24285			−0.621425	−	0.783474i	$-0.713446\pi$
$47$	−2.18694e24			−1.24285			−0.621425	+	0.783474i	$0.713446\pi$
$48$	−2.78067e24	+	4.74275e24i	−1.16453	+	1.98624i
$49$	2.30892e24	+	2.24425e24i	0.717078	+	0.696993i
$50$		−	3.30030e24i		−	0.764695i
$51$	−7.16069e23	+	1.22134e24i	−0.124505	+	0.212358i
$52$			2.13831e25i			2.80558i
$53$		−	1.34081e25i		−	1.33465i	−0.744768	−	0.667323i	$-0.767440\pi$
$53$		−	1.34081e25i		−	1.33465i	0.744768	−	0.667323i	$-0.232560\pi$
$54$	4.86084e23	−	2.42320e25i	0.0368979	−	1.83941i
$55$		−	3.07304e25i		−	1.78776i
$56$	−2.13893e25	+	5.26936e25i	−0.958231	+	2.36065i
$57$	2.05724e25	+	1.20616e25i	0.713016	+	0.418041i
$58$	5.70780e25			1.53732
$59$	−2.12081e25			−0.445807			−0.222904	−	0.974840i	$-0.571554\pi$
$59$	−2.12081e25			−0.445807			−0.222904	+	0.974840i	$0.571554\pi$
$60$	−8.71128e25	+	1.48581e26i	−1.43512	+	2.44776i
$61$			5.23975e25i			0.679247i	0.940561	+	0.339623i	$0.110300\pi$
$61$			5.23975e25i			0.679247i	−0.940561	+	0.339623i	$0.889700\pi$
$62$	−3.50188e26			−3.58610
$63$	−1.53086e25	−	1.22196e26i	−0.124307	−	0.992244i
$64$	−1.24356e26			−0.803633
$65$			2.71202e26i			1.39974i
$66$	−3.38023e26	+	5.76536e26i	−1.39817	+	2.38473i
$67$	1.73869e26			0.578279			0.289140	−	0.957287i	$-0.406631\pi$
$67$	1.73869e26			0.578279			0.289140	+	0.957287i	$0.406631\pi$
$68$	−2.18805e26			−0.587053
$69$	6.13796e25	+	3.59868e25i	0.133264	+	0.0781325i
$70$	−4.67179e26	+	1.15092e27i	−0.823307	+	2.02826i
$71$		−	1.36215e26i		−	0.195424i	−0.995215	−	0.0977121i	$-0.968848\pi$
$71$		−	1.36215e26i		−	0.195424i	0.995215	−	0.0977121i	$-0.0311524\pi$
$72$	1.89804e27	−	1.06225e27i	2.22323	−	1.24425i
$73$		−	1.03806e27i		−	0.995504i	−0.867320	−	0.497752i	$-0.834159\pi$
$73$		−	1.03806e27i		−	0.995504i	0.867320	−	0.497752i	$-0.165841\pi$
$74$			2.62171e27i			2.06407i
$75$	−3.24393e26	+	5.53288e26i	−0.210224	+	0.358561i
$76$			3.68558e27i			1.97110i
$77$	−1.27722e27	+	3.14650e27i	−0.565133	+	1.39223i
$78$	2.98312e27	−	5.08804e27i	1.09471	−	1.86715i
$79$	1.92827e27			0.588267			0.294133	−	0.955764i	$-0.404969\pi$
$79$	1.92827e27			0.588267			0.294133	+	0.955764i	$0.404969\pi$
$80$	−1.07764e28			−2.73948
$81$	−2.46329e27	+	4.01466e27i	−0.522978	+	0.852346i
$82$			1.06484e26i			0.0189227i
$83$	5.55458e27			0.827978			0.413989	−	0.910282i	$-0.364135\pi$
$83$	5.55458e27			0.827978			0.413989	+	0.910282i	$0.364135\pi$
$84$	1.50949e28	−	1.15927e28i	1.89138	−	1.45256i
$85$	−2.77510e27			−0.292889
$86$		−	3.63515e28i		−	3.23813i
$87$	−9.56902e27	−	5.61031e27i	−0.720839	−	0.422627i
$88$	−5.99767e28			−3.82810
$89$	−3.90521e26			−0.0211587			−0.0105794	−	0.999944i	$-0.503368\pi$
$89$	−3.90521e26			−0.0211587			−0.0105794	+	0.999944i	$0.503368\pi$
$90$	4.14564e28	−	2.32014e28i	1.91018	−	1.06905i
$91$	1.12717e28	−	2.77685e28i	0.442476	−	1.09006i
$92$			1.09963e28i			0.368402i
$93$	5.87084e28	+	3.44207e28i	1.68150	+	0.985863i
$94$			9.32264e28i			2.28657i
$95$			4.67442e28i			0.983411i
$96$	8.05790e28	+	4.72434e28i	1.45643	+	0.853902i
$97$		−	2.98614e28i		−	0.464429i	−0.972665	−	0.232215i	$-0.925403\pi$
$97$		−	2.98614e28i		−	0.464429i	0.972665	−	0.232215i	$-0.0745972\pi$
$98$	9.56693e28	−	9.84262e28i	1.28231	−	1.31927i
$99$	1.13338e29	−	6.34302e28i	1.31118	−	0.733814i
$100$	−9.91227e28			−0.991227
$101$	1.65441e29			1.43213			0.716066	−	0.698032i	$-0.245941\pi$
$101$	1.65441e29			1.43213			0.716066	+	0.698032i	$0.245941\pi$
$102$	5.20639e28	+	3.05250e28i	0.390692	+	0.229062i
$103$			4.45488e28i			0.290199i	0.989417	+	0.145099i	$0.0463502\pi$
$103$			4.45488e28i			0.290199i	−0.989417	+	0.145099i	$0.953650\pi$
$104$	5.29306e29			2.99725
$105$	1.91448e29	−	1.47029e29i	0.943637	−	0.724702i
$106$	−5.71567e29			−2.45546
$107$			1.85090e29i			0.693933i	0.937878	+	0.346966i	$0.112788\pi$
$107$			1.85090e29i			0.693933i	−0.937878	+	0.346966i	$0.887212\pi$
$108$	−7.27794e29	−	1.45993e28i	−2.38432	−	0.0478285i
$109$	−1.95150e29			−0.559350			−0.279675	−	0.960095i	$-0.590227\pi$
$109$	−1.95150e29			−0.559350			−0.279675	+	0.960095i	$0.590227\pi$
$110$	−1.30999e30			−3.28909
$111$	2.57693e29	−	4.39524e29i	0.567438	−	0.967831i
$112$	1.10340e30	+	4.47889e29i	2.13339	+	0.865983i
$113$			8.95088e29i			1.52135i	0.649135	+	0.760673i	$0.275131\pi$
$113$			8.95088e29i			1.52135i	−0.649135	+	0.760673i	$0.724869\pi$
$114$	5.14168e29	−	8.76973e29i	0.769104	−	1.31179i
$115$			1.39466e29i			0.183801i
$116$		−	1.71431e30i		−	1.99273i
$117$	−1.00023e30	+	5.59784e29i	−1.02661	+	0.574547i
$118$			9.04071e29i			0.820188i
$119$	2.84143e29	+	1.15339e29i	0.228090	+	0.0925859i
$120$	3.67789e30	+	2.15634e30i	2.61499	+	1.53317i
$121$	−1.99508e30			−1.25769
$122$	2.23363e30			1.24967
$123$	1.04665e28	−	1.78518e28i	0.00520208	−	0.00887274i
$124$			1.05177e31i			4.64844i
$125$	1.76746e30			0.695271
$126$	−5.20904e30	+	6.52583e29i	−1.82551	+	0.228698i
$127$	7.73525e29			0.241724			0.120862	−	0.992669i	$-0.461434\pi$
$127$	7.73525e29			0.241724			0.120862	+	0.992669i	$0.461434\pi$
$128$		−	7.52166e29i		−	0.209782i
$129$	−3.57306e30	+	6.09426e30i	−0.890203	+	1.51834i
$130$	1.15610e31			2.57522
$131$	−7.88995e30			−1.57268			−0.786340	−	0.617794i	$-0.788027\pi$
$131$	−7.88995e30			−1.57268			−0.786340	+	0.617794i	$0.788027\pi$
$132$	1.73159e31	+	1.01523e31i	3.09118	+	1.81236i
$133$	1.94279e30	−	4.78616e30i	0.310868	−	0.765840i
$134$		−	7.41180e30i		−	1.06391i
$135$	−9.23059e30	−	1.85162e29i	−1.18957	−	0.0238623i
$136$			5.41617e30i			0.627160i
$137$			7.65395e30i			0.796962i	0.917177	+	0.398481i	$0.130463\pi$
$137$			7.65395e30i			0.796962i	−0.917177	+	0.398481i	$0.869537\pi$
$138$	1.53407e30	−	2.61653e30i	0.143747	−	0.245176i
$139$		−	1.56074e31i		−	1.31709i	−0.752540	−	0.658547i	$-0.771172\pi$
$139$		−	1.56074e31i		−	1.31709i	0.752540	−	0.658547i	$-0.228828\pi$
$140$	3.45672e31	+	1.40315e31i	2.62911	+	1.06720i
$141$	9.16339e30	−	1.56292e31i	0.628607	−	1.07216i
$142$	−5.80665e30			−0.359538
$143$	3.16065e31			1.76768
$144$	−2.22434e31	−	3.97447e31i	−1.12446	−	2.00920i
$145$		−	2.17425e31i		−	0.994201i
$146$	−4.42512e31			−1.83151
$147$	−2.57133e31	+	7.09743e30i	−0.963953	+	0.266072i
$148$	7.87416e31			2.67553
$149$		−	3.20467e31i		−	0.987603i	−0.869575	−	0.493801i	$-0.835607\pi$
$149$		−	3.20467e31i		−	0.987603i	0.869575	−	0.493801i	$-0.164393\pi$
$150$	2.35859e31	+	1.38284e31i	0.659674	+	0.386766i
$151$	−4.16619e31			−1.05821			−0.529107	−	0.848555i	$-0.677473\pi$
$151$	−4.16619e31			−1.05821			−0.529107	+	0.848555i	$0.677473\pi$
$152$	9.12309e31			2.10577
$153$	−5.72804e30	−	1.02349e31i	−0.120221	−	0.214812i
$154$	1.34131e32	+	5.44461e31i	2.56140	+	1.03972i
$155$			1.33396e32i			2.31917i
$156$	−1.52817e32	−	8.95963e31i	−2.42027	−	1.41900i
$157$			5.28389e31i			0.762797i	0.924411	+	0.381399i	$0.124557\pi$
$157$			5.28389e31i			0.762797i	−0.924411	+	0.381399i	$0.875443\pi$
$158$		−	8.21993e31i		−	1.08228i
$159$	9.58221e31	+	5.61804e31i	1.15135	+	0.675035i
$160$			1.83090e32i			2.00874i
$161$	5.79649e30	−	1.42799e31i	0.0581018	−	0.143137i
$162$	1.71139e32	+	1.05007e32i	1.56813	+	0.962166i
$163$	−2.67602e31			−0.224269			−0.112134	−	0.993693i	$-0.535769\pi$
$163$	−2.67602e31			−0.224269			−0.112134	+	0.993693i	$0.535769\pi$
$164$	3.19818e30			0.0245283
$165$	2.19618e32	+	1.28762e32i	1.54223	+	0.904210i
$166$		−	2.36784e32i		−	1.52330i
$167$	−2.65867e32			−1.56774			−0.783872	−	0.620923i	$-0.786758\pi$
$167$	−2.65867e32			−1.56774			−0.783872	+	0.620923i	$0.786758\pi$
$168$	−2.86958e32	−	3.73650e32i	−1.55179	−	2.02060i
$169$	−7.73952e31			−0.384023
$170$			1.18298e32i			0.538852i
$171$	−1.72399e32	+	9.64841e31i	−0.721257	+	0.403657i
$172$	−1.09180e33			−4.19739
$173$	8.39332e31			0.296664			0.148332	−	0.988938i	$-0.452610\pi$
$173$	8.39332e31			0.296664			0.148332	+	0.988938i	$0.452610\pi$
$174$	−2.39160e32	+	4.07914e32i	−0.777542	+	1.32619i
$175$	1.28722e32	+	5.22507e31i	0.385125	+	0.156329i
$176$			1.25590e33i			3.45958i
$177$	8.88629e31	−	1.51566e32i	0.225480	−	0.384582i
$178$			1.66474e31i			0.0389274i
$179$			2.95712e32i			0.637529i	0.947834	+	0.318764i	$0.103268\pi$
$179$			2.95712e32i			0.637529i	−0.947834	+	0.318764i	$0.896732\pi$
$180$	−6.96841e32	−	1.24512e33i	−1.38574	−	2.47605i
$181$		−	4.15225e32i		−	0.761981i	−0.924579	−	0.380991i	$-0.875583\pi$
$181$		−	4.15225e32i		−	0.761981i	0.924579	−	0.380991i	$-0.124417\pi$
$182$	−1.18373e33	−	4.80498e32i	−2.00548	−	0.814060i
$183$	−3.74464e32	−	2.19548e32i	−0.585961	−	0.343549i
$184$	2.72196e32			0.393571
$185$	9.98678e32			1.33486
$186$	1.46731e33	−	2.50266e33i	1.81377	−	3.09360i
$187$			3.23416e32i			0.369878i
$188$	2.80000e33			2.96394
$189$	9.37428e32	+	4.02602e32i	0.918844	+	0.394620i
$190$	1.99264e33			1.80926
$191$			1.57626e33i			1.32631i	0.748483	+	0.663154i	$0.230782\pi$
$191$			1.57626e33i			1.32631i	−0.748483	+	0.663154i	$0.769218\pi$
$192$	5.21058e32	−	8.88724e32i	0.406460	−	0.693265i
$193$	−2.12406e33			−1.53669			−0.768343	−	0.640038i	$-0.778919\pi$
$193$	−2.12406e33			−1.53669			−0.768343	+	0.640038i	$0.778919\pi$
$194$	−1.27295e33			−0.854448
$195$	−1.93817e33	−	1.13635e33i	−1.20751	−	0.707961i
$196$	−2.95618e33	−	2.87338e33i	−1.71008	−	1.66219i
$197$		−	3.51020e31i		−	0.0188613i	−0.999956	−	0.00943065i	$-0.996998\pi$
$197$		−	3.51020e31i		−	0.0188613i	0.999956	−	0.00943065i	$-0.00300191\pi$
$198$	−2.70394e33	−	4.83142e33i	−1.35006	−	2.41229i
$199$			4.24135e33i			1.96849i	0.176799	+	0.984247i	$0.443426\pi$
$199$			4.24135e33i			1.96849i	−0.176799	+	0.984247i	$0.556574\pi$
$200$			2.45363e33i			1.05895i
$201$	−7.28519e32	+	1.24257e33i	−0.292481	+	0.498860i
$202$		−	7.05252e33i		−	2.63481i
$203$	−9.03666e32	+	2.22623e33i	−0.314279	+	0.774242i
$204$	9.16802e32	−	1.56371e33i	0.296919	−	0.506429i
$205$	4.05625e31			0.0122375
$206$	1.89905e33			0.533903
$207$	−5.14367e32	+	2.87869e32i	−0.134804	+	0.0754441i
$208$		−	1.10836e34i		−	2.70871i
$209$	5.44767e33			1.24191
$210$	−6.26766e33	−	8.16115e33i	−1.33329	−	1.73609i
$211$	−9.91975e32			−0.196972			−0.0984861	−	0.995138i	$-0.531400\pi$
$211$	−9.91975e32			−0.196972			−0.0984861	+	0.995138i	$0.531400\pi$
$212$			1.71667e34i			3.18286i
$213$	9.73473e32	+	5.70746e32i	0.168585	+	0.0988414i
$214$	7.89011e33			1.27668
$215$	−1.38472e34			−2.09414
$216$	−3.61382e32	+	1.80154e34i	−0.0510961	+	2.54721i
$217$	5.54422e33	−	1.36585e34i	0.733119	−	1.80608i
$218$			8.31897e33i			1.02908i
$219$	7.41863e33	+	4.34954e33i	0.858784	+	0.503505i
$220$			3.93449e34i			4.26344i
$221$		−	2.85421e33i		−	0.289600i
$222$	−1.87363e34	−	1.09851e34i	−1.78060	−	1.04396i
$223$			1.85405e34i			1.65083i	0.564528	+	0.825414i	$0.309058\pi$
$223$			1.85405e34i			1.65083i	−0.564528	+	0.825414i	$0.690942\pi$
$224$	7.60961e33	−	1.87467e34i	0.634989	−	1.56433i
$225$	−2.59491e33	−	4.63661e33i	−0.202991	−	0.362705i
$226$	3.81563e34			2.79895
$227$	−1.20656e33			−0.0830186			−0.0415093	−	0.999138i	$-0.513217\pi$
$227$	−1.20656e33			−0.0830186			−0.0415093	+	0.999138i	$0.513217\pi$
$228$	−2.63394e34	−	1.54428e34i	−1.70040	−	0.996942i
$229$			1.39988e34i			0.848159i	0.905625	+	0.424079i	$0.139402\pi$
$229$			1.39988e34i			0.848159i	−0.905625	+	0.424079i	$0.860598\pi$
$230$	5.94522e33			0.338154
$231$	−1.71351e34	−	2.23117e34i	−0.915196	−	1.19168i
$232$	−4.24350e34			−2.12887
$233$			5.02379e33i			0.236794i	0.992966	+	0.118397i	$0.0377756\pi$
$233$			5.02379e33i			0.236794i	−0.992966	+	0.118397i	$0.962224\pi$
$234$	2.38628e34	+	4.26383e34i	1.05704	+	1.88873i
$235$	3.55124e34			1.47875
$236$	2.71533e34			1.06316
$237$	−8.07953e33	+	1.37806e34i	−0.297533	+	0.507476i
$238$	4.91674e33	−	1.21126e34i	0.170338	−	0.419636i
$239$			2.45052e34i			0.798894i	0.916756	+	0.399447i	$0.130798\pi$
$239$			2.45052e34i			0.798894i	−0.916756	+	0.399447i	$0.869202\pi$
$240$	4.51535e34	−	7.70145e34i	1.38557	−	2.36325i
$241$			4.09826e34i			1.18400i	0.805938	+	0.592000i	$0.201662\pi$
$241$			4.09826e34i			1.18400i	−0.805938	+	0.592000i	$0.798338\pi$
$242$			8.50475e34i			2.31387i
$243$	−1.83698e34	−	3.44258e34i	−0.470776	−	0.882253i
$244$		−	6.70859e34i		−	1.61986i
$245$	−3.74931e34	−	3.64430e34i	−0.853185	−	0.829288i
$246$	−7.60997e32	−	4.46172e32i	−0.0163239	−	0.00957069i
$247$	−4.80768e34			−0.972366
$248$	2.60350e35			4.96602
$249$	−2.32739e34	+	3.96963e34i	−0.418774	+	0.714266i
$250$		−	7.53443e34i		−	1.27915i
$251$	−9.77945e34			−1.56691			−0.783457	−	0.621446i	$-0.786546\pi$
$251$	−9.77945e34			−1.56691			−0.783457	+	0.621446i	$0.786546\pi$
$252$	1.96000e34	+	1.56451e35i	0.296447	+	2.36630i
$253$	1.62536e34			0.232115
$254$		−	3.29743e34i		−	0.444720i
$255$	1.16278e34	−	1.98325e34i	0.148137	−	0.252665i
$256$	−9.88270e34			−1.18959
$257$	3.16712e34			0.360275			0.180137	−	0.983641i	$-0.442346\pi$
$257$	3.16712e34			0.360275			0.180137	+	0.983641i	$0.442346\pi$
$258$	2.59790e35	+	1.52314e35i	2.79342	+	1.63778i
$259$	−1.02255e35	−	4.15072e34i	−1.03953	−	0.421965i
$260$		−	3.47227e35i		−	3.33810i
$261$	8.01893e34	−	4.48785e34i	0.729170	−	0.408085i
$262$			3.36338e35i			2.89339i
$263$		−	8.13052e34i		−	0.661851i	−0.943657	−	0.330925i	$-0.892639\pi$
$263$		−	8.13052e34i		−	0.661851i	0.943657	−	0.330925i	$-0.107361\pi$
$264$	2.51305e35	−	4.28629e35i	1.93617	−	3.30236i
$265$			2.17725e35i			1.58797i
$266$	−2.04027e35	−	8.28183e34i	−1.40898	−	0.571930i
$267$	1.63630e33	−	2.79090e33i	0.0107016	−	0.0182528i
$268$	−2.22609e35			−1.37908
$269$	−2.19676e35			−1.28936			−0.644679	−	0.764453i	$-0.723009\pi$
$269$	−2.19676e35			−1.28936			−0.644679	+	0.764453i	$0.723009\pi$
$270$	−7.89321e33	+	3.93487e35i	−0.0439015	+	2.18855i
$271$			7.81113e34i			0.411774i	0.978576	+	0.205887i	$0.0660080\pi$
$271$			7.81113e34i			0.411774i	−0.978576	+	0.205887i	$0.933992\pi$
$272$	1.13414e35			0.566784
$273$	1.51221e35	+	1.96906e35i	0.716562	+	0.933039i
$274$	3.26277e35			1.46624
$275$			1.46514e35i			0.624531i
$276$	−7.85860e34	−	4.60749e34i	−0.317807	−	0.186330i
$277$	3.47632e35			1.33402			0.667011	−	0.745048i	$-0.267573\pi$
$277$	3.47632e35			1.33402			0.667011	+	0.745048i	$0.267573\pi$
$278$	−6.65323e35			−2.42316
$279$	−4.91982e35	+	2.75341e35i	−1.70094	+	0.951941i
$280$	3.47327e35	−	8.55658e35i	1.14011	−	2.80872i
$281$			3.03762e35i			0.946872i	0.880828	+	0.473436i	$0.156986\pi$
$281$			3.03762e35i			0.946872i	−0.880828	+	0.473436i	$0.843014\pi$
$282$	−6.66252e35	−	3.90623e35i	−1.97254	−	1.15650i
$283$		−	2.26273e35i		−	0.636400i	−0.948024	−	0.318200i	$-0.896922\pi$
$283$		−	2.26273e35i		−	0.636400i	0.948024	−	0.318200i	$-0.103078\pi$
$284$			1.74400e35i			0.466047i
$285$	−3.34062e35	−	1.95860e35i	−0.848353	−	0.497389i
$286$		−	1.34734e36i		−	3.25214i
$287$	−4.15321e33	−	1.68586e33i	−0.00953008	−	0.00386843i
$288$	−6.75259e35	+	3.77914e35i	−1.47326	+	0.824521i
$289$	−4.52763e35			−0.939403
$290$	−9.26854e35			−1.82911
$291$	2.13407e35	+	1.25120e35i	0.400646	+	0.234898i
$292$			1.32906e36i			2.37407i
$293$	1.20746e35			0.205254			0.102627	−	0.994720i	$-0.467275\pi$
$293$	1.20746e35			0.205254			0.102627	+	0.994720i	$0.467275\pi$
$294$	3.02554e35	+	1.09612e36i	0.489515	+	1.77346i
$295$	3.44385e35			0.530426
$296$		−	1.94913e36i		−	2.85832i
$297$	−2.15792e34	+	1.07575e36i	−0.0301348	+	1.50226i
$298$	−1.36611e36			−1.81697
$299$	−1.43442e35			−0.181737
$300$	4.15329e35	−	7.08390e35i	0.501342	−	0.855095i
$301$	1.41783e36	+	5.75521e35i	1.63083	+	0.661983i
$302$			1.77599e36i			1.94688i
$303$	−6.93205e35	+	1.18234e36i	−0.724342	+	1.23545i
$304$		−	1.91036e36i		−	1.90305i
$305$		−	8.50849e35i		−	0.808174i
$306$	−4.36300e35	+	2.44179e35i	−0.395207	+	0.221181i
$307$		−	4.19561e35i		−	0.362484i	−0.983439	−	0.181242i	$-0.941988\pi$
$307$		−	4.19561e35i		−	0.362484i	0.983439	−	0.181242i	$-0.0580117\pi$
$308$	1.63526e36	−	4.02855e36i	1.34773	−	3.32019i
$309$	−3.18372e35	−	1.86661e35i	−0.250344	−	0.146776i
$310$	5.68649e36			4.26677
$311$	1.38364e34			0.00990823			0.00495411	−	0.999988i	$-0.498423\pi$
$311$	1.38364e34			0.00990823			0.00495411	+	0.999988i	$0.498423\pi$
$312$	−2.21782e36	+	3.78274e36i	−1.51595	+	2.58562i
$313$		−	4.32475e35i		−	0.282207i	−0.989995	−	0.141104i	$-0.954935\pi$
$313$		−	4.32475e35i		−	0.282207i	0.989995	−	0.141104i	$-0.0450651\pi$
$314$	2.25245e36			1.40338
$315$	2.48586e35	+	1.98426e36i	0.147902	+	1.18058i
$316$	−2.46881e36			−1.40290
$317$			1.15872e36i			0.628954i	0.949265	+	0.314477i	$0.101829\pi$
$317$			1.15872e36i			0.628954i	−0.949265	+	0.314477i	$0.898171\pi$
$318$	2.39489e36	−	4.08476e36i	1.24192	−	2.11823i
$319$	−2.53392e36			−1.25553
$320$	2.01934e36			0.956169
$321$	−1.32276e36	−	7.75534e35i	−0.598630	−	0.350976i
$322$	−6.08734e35	−	2.47096e35i	−0.263340	−	0.106895i
$323$		−	4.91950e35i		−	0.203463i
$324$	3.15382e36	−	5.14008e36i	1.24720	−	2.03267i
$325$		−	1.29301e36i		−	0.488983i
$326$			1.14075e36i			0.412606i
$327$	8.17687e35	−	1.39466e36i	0.282908	−	0.482531i
$328$		−	7.91661e34i		−	0.0262041i
$329$	−3.63613e36	−	1.47597e36i	−1.15159	−	0.467452i
$330$	5.48893e36	−	9.36200e36i	1.66355	−	2.83737i
$331$	−3.22513e36			−0.935494			−0.467747	−	0.883863i	$-0.654934\pi$
$331$	−3.22513e36			−0.935494			−0.467747	+	0.883863i	$0.654934\pi$
$332$	−7.11168e36			−1.97456
$333$	2.06136e36	+	3.68325e36i	0.547914	+	0.979017i
$334$			1.13335e37i			2.88430i
$335$	−2.82335e36			−0.688042
$336$	−7.82418e36	+	6.00887e36i	−1.82608	+	1.40240i
$337$	−1.45896e36			−0.326144			−0.163072	−	0.986614i	$-0.552140\pi$
$337$	−1.45896e36			−0.326144			−0.163072	+	0.986614i	$0.552140\pi$
$338$			3.29925e36i			0.706518i
$339$	−6.39683e36	−	3.75046e36i	−1.31241	−	0.769465i
$340$	3.55303e36			0.698481
$341$	1.55463e37			2.92879
$342$	4.11298e36	+	7.34911e36i	0.742640	+	1.32695i
$343$	2.32429e36	+	5.28971e36i	0.402277	+	0.915518i
$344$			2.70258e37i			4.48415i
$345$	−9.96705e35	−	5.84367e35i	−0.158559	−	0.0929627i
$346$		−	3.57796e36i		−	0.545798i
$347$		−	3.82608e36i		−	0.559727i	−0.960040	−	0.279864i	$-0.909711\pi$
$347$		−	3.82608e36i		−	0.559727i	0.960040	−	0.279864i	$-0.0902893\pi$
$348$	1.22515e37	+	7.18303e36i	1.71905	+	1.00788i
$349$			2.85704e36i			0.384545i	0.981342	+	0.192272i	$0.0615857\pi$
$349$			2.85704e36i			0.384545i	−0.981342	+	0.192272i	$0.938414\pi$
$350$	2.22737e36	−	5.48725e36i	0.287612	−	0.708546i
$351$	1.90441e35	−	9.49374e36i	0.0235943	−	1.17621i
$352$	2.13377e37			2.53676
$353$	1.00942e36			0.115170			0.0575850	−	0.998341i	$-0.481660\pi$
$353$	1.00942e36			0.115170			0.0575850	+	0.998341i	$0.481660\pi$
$354$	−6.46104e36	−	3.78810e36i	−0.707546	−	0.414834i
$355$			2.21191e36i			0.232517i
$356$	4.99994e35			0.0504592
$357$	−2.01485e36	+	1.54738e36i	−0.195234	+	0.149937i
$358$	1.26058e37			1.17291
$359$			9.97546e36i			0.891381i	0.895187	+	0.445691i	$0.147042\pi$
$359$			9.97546e36i			0.891381i	−0.895187	+	0.445691i	$0.852958\pi$
$360$	−3.08210e37	+	1.72492e37i	−2.64521	+	1.48041i
$361$	3.84333e36			0.316850
$362$	−1.77005e37			−1.40188
$363$	8.35947e36	−	1.42580e37i	0.636111	−	1.08496i
$364$	−1.44315e37	+	3.55527e37i	−1.05522	+	2.59958i
$365$			1.68565e37i			1.18446i
$366$	−9.35901e36	+	1.59629e37i	−0.632054	+	1.07804i
$367$		−	1.83505e37i		−	1.19122i	−0.803275	−	0.595608i	$-0.796911\pi$
$367$		−	1.83505e37i		−	1.19122i	0.803275	−	0.595608i	$-0.203089\pi$
$368$		−	5.69975e36i		−	0.355682i
$369$	8.37246e34	+	1.49600e35i	0.00502309	+	0.00897529i
$370$		−	4.25722e37i		−	2.45585i
$371$	9.04912e36	−	2.22930e37i	0.501978	−	1.23665i
$372$	−7.51660e37	−	4.40697e37i	−4.01004	−	2.35108i
$373$	−1.43895e37			−0.738360			−0.369180	−	0.929358i	$-0.620361\pi$
$373$	−1.43895e37			−0.738360			−0.369180	+	0.929358i	$0.620361\pi$
$374$	1.37868e37			0.680494
$375$	−7.40574e36	+	1.26313e37i	−0.351653	+	0.599785i
$376$		−	6.93097e37i		−	3.16643i
$377$	2.23624e37			0.983034
$378$	1.71624e37	−	3.99613e37i	0.726015	−	1.69047i
$379$	3.90053e37			1.58802			0.794008	−	0.607907i	$-0.207991\pi$
$379$	3.90053e37			1.58802			0.794008	+	0.607907i	$0.207991\pi$
$380$		−	5.98478e37i		−	2.34523i
$381$	−3.24110e36	+	5.52807e36i	−0.122259	+	0.208527i
$382$	6.71938e37			2.44012
$383$	5.07083e37			1.77295			0.886476	−	0.462775i	$-0.153146\pi$
$383$	5.07083e37			1.77295			0.886476	+	0.462775i	$0.153146\pi$
$384$	5.37543e36	+	3.15161e36i	0.180972	+	0.106104i
$385$	2.07400e37	−	5.10939e37i	0.672399	−	1.65649i
$386$			9.05456e37i			2.82717i
$387$	−2.85819e37	−	5.10704e37i	−0.859573	−	1.53589i
$388$			3.82323e37i			1.10757i
$389$		−	2.09477e37i		−	0.584612i	−0.956325	−	0.292306i	$-0.905578\pi$
$389$		−	2.09477e37i		−	0.584612i	0.956325	−	0.292306i	$-0.0944225\pi$
$390$	−4.84409e37	+	8.26215e37i	−1.30249	+	2.22155i
$391$		−	1.46778e36i		−	0.0380275i
$392$	−7.11260e37	+	7.31756e37i	−1.77574	+	1.82691i
$393$	3.30592e37	−	5.63863e37i	0.795428	−	1.35669i
$394$	−1.49635e36			−0.0347007
$395$	−3.13119e37			−0.699925
$396$	−1.45109e38	+	8.12114e37i	−3.12691	+	1.75000i
$397$		−	3.28408e37i		−	0.682262i	−0.940016	−	0.341131i	$-0.889190\pi$
$397$		−	3.28408e37i		−	0.682262i	0.940016	−	0.341131i	$-0.110810\pi$
$398$	1.80803e38			3.62160
$399$	2.60644e37	+	3.39385e37i	0.503431	+	0.655520i
$400$	5.13787e37			0.957002
$401$			5.91548e37i			1.06267i	0.847163	+	0.531333i	$0.178309\pi$
$401$			5.91548e37i			1.06267i	−0.847163	+	0.531333i	$0.821691\pi$
$402$	5.29691e37	+	3.10558e37i	0.917794	+	0.538102i
$403$	−1.37199e38			−2.29313
$404$	−2.11819e38			−3.41534
$405$	3.99999e37	−	6.51915e37i	0.622244	−	1.01413i
$406$	9.49010e37	+	3.85220e37i	1.42444	+	0.578205i
$407$		−	1.16388e38i		−	1.68574i
$408$	−3.87072e37	−	2.26940e37i	−0.541028	−	0.317204i
$409$			4.47203e37i			0.603277i	0.953422	+	0.301638i	$0.0975336\pi$
$409$			4.47203e37i			0.603277i	−0.953422	+	0.301638i	$0.902466\pi$
$410$		−	1.72912e36i		−	0.0225144i
$411$	−5.46997e37	−	3.20704e37i	−0.687510	−	0.403086i
$412$		−	5.70370e37i		−	0.692065i
$413$	−3.52617e37	−	1.43134e37i	−0.413074	−	0.167674i
$414$	1.22715e37	+	2.19267e37i	0.138801	+	0.248010i
$415$	−9.01972e37			−0.985135
$416$	−1.88310e38			−1.98618
$417$	1.11540e38	+	6.53958e37i	1.13621	+	0.666158i
$418$		−	2.32227e38i		−	2.28484i
$419$	−1.08659e38			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$419$	−1.08659e38			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$420$	−2.45116e38	+	1.88246e38i	−2.25038	+	1.72827i
$421$	−1.13162e38			−1.00372			−0.501858	−	0.864950i	$-0.667350\pi$
$421$	−1.13162e38			−1.00372			−0.501858	+	0.864950i	$0.667350\pi$
$422$			4.22865e37i			0.362386i
$423$	7.33007e37	+	1.30974e38i	0.606978	+	1.08455i
$424$	4.24935e38			3.40031
$425$	1.32309e37			0.102317
$426$	2.43301e37	−	4.14978e37i	0.181847	−	0.310160i
$427$	−3.53631e37	+	8.71188e37i	−0.255474	+	0.629372i
$428$		−	2.36975e38i		−	1.65489i
$429$	−1.32433e38	+	2.25879e38i	−0.894054	+	1.52491i
$430$			5.90289e38i			3.85276i
$431$		−	1.11081e38i		−	0.701002i	−0.936562	−	0.350501i	$-0.886011\pi$
$431$		−	1.11081e38i		−	0.701002i	0.936562	−	0.350501i	$-0.113989\pi$
$432$	3.77240e38	+	7.56730e36i	2.30199	+	0.0461771i
$433$		−	5.00180e37i		−	0.295156i	−0.989050	−	0.147578i	$-0.952852\pi$
$433$		−	5.00180e37i		−	0.295156i	0.989050	−	0.147578i	$-0.0471478\pi$
$434$	−5.82242e38	−	2.36343e38i	−3.32279	−	1.34878i
$435$	1.55385e38	+	9.11022e37i	0.857660	+	0.502846i
$436$	2.49856e38			1.33394
$437$	−2.47235e37			−0.127682
$438$	1.85415e38	−	3.16246e38i	0.926338	−	1.57998i
$439$		−	2.71259e38i		−	1.31114i	−0.755135	−	0.655569i	$-0.772429\pi$
$439$		−	2.71259e38i		−	1.31114i	0.755135	−	0.655569i	$-0.227571\pi$
$440$	9.73923e38			4.55471
$441$	5.70172e37	−	2.13501e38i	0.258016	−	0.966141i
$442$	−1.21671e38			−0.532800
$443$		−	1.09543e38i		−	0.464228i	−0.972689	−	0.232114i	$-0.925436\pi$
$443$		−	1.09543e38i		−	0.464228i	0.972689	−	0.232114i	$-0.0745643\pi$
$444$	−3.29931e38	+	5.62735e38i	−1.35322	+	2.30808i
$445$	6.34142e36			0.0251748
$446$	7.90357e38			3.03716
$447$	2.29025e38	+	1.34277e38i	0.851969	+	0.499508i
$448$	−2.06761e38	−	8.39281e37i	−0.744625	−	0.302257i
$449$			2.09076e38i			0.729008i	0.931202	+	0.364504i	$0.118762\pi$
$449$			2.09076e38i			0.729008i	−0.931202	+	0.364504i	$0.881238\pi$
$450$	−1.97652e38	+	1.10617e38i	−0.667298	+	0.373458i
$451$		−	4.72725e36i		−	0.0154543i
$452$		−	1.14601e39i		−	3.62810i
$453$	1.74565e38	−	2.97741e38i	0.535222	−	0.912882i
$454$			5.14342e37i			0.152736i
$455$	−1.83034e38	+	4.50914e38i	−0.526462	+	1.29697i
$456$	−3.82262e38	+	6.51991e38i	−1.06505	+	1.81657i
$457$	5.95107e38			1.60624			0.803119	−	0.595818i	$-0.203172\pi$
$457$	5.95107e38			1.60624			0.803119	+	0.595818i	$0.203172\pi$
$458$	5.96750e38			1.56043
$459$	9.71456e37	+	1.94871e36i	0.246116	+	0.00493699i
$460$		−	1.78562e38i		−	0.438328i
$461$	−2.80849e38			−0.668051			−0.334025	−	0.942564i	$-0.608407\pi$
$461$	−2.80849e38			−0.668051			−0.334025	+	0.942564i	$0.608407\pi$
$462$	−9.51119e38	+	7.30447e38i	−2.19243	+	1.68376i
$463$	3.33521e37			0.0745074			0.0372537	−	0.999306i	$-0.488139\pi$
$463$	3.33521e37			0.0745074			0.0372537	+	0.999306i	$0.488139\pi$
$464$			8.88584e38i			1.92392i
$465$	−9.53328e38	−	5.58935e38i	−2.00067	−	1.17299i
$466$	2.14157e38			0.435649
$467$	−4.61986e38			−0.911034			−0.455517	−	0.890227i	$-0.650545\pi$
$467$	−4.61986e38			−0.911034			−0.455517	+	0.890227i	$0.650545\pi$
$468$	1.28062e39	−	7.16707e38i	2.44824	−	1.37018i
$469$	2.89084e38	+	1.17344e38i	0.535819	+	0.217498i
$470$		−	1.51384e39i		−	2.72058i
$471$	−3.77619e38	−	2.21398e38i	−0.658037	−	0.385807i
$472$		−	6.72138e38i		−	1.13579i
$473$			1.61379e39i			2.64460i
$474$	5.87446e38	+	3.44419e38i	0.933645	+	0.547395i
$475$		−	2.22863e38i		−	0.343542i
$476$	−3.63796e38	−	1.47672e38i	−0.543948	−	0.220799i
$477$	−8.02998e38	+	4.49404e38i	−1.16466	+	0.651809i
$478$	1.04462e39			1.46979
$479$	−1.28353e39			−1.75203			−0.876014	−	0.482287i	$-0.839806\pi$
$479$	−1.28353e39			−1.75203			−0.876014	+	0.482287i	$0.839806\pi$
$480$	−1.30847e39	−	7.67155e38i	−1.73287	−	1.01598i
$481$			1.02715e39i			1.31987i
$482$	1.74703e39			2.17830
$483$	7.77655e37	+	1.01259e38i	0.0940922	+	0.122518i
$484$	2.55436e39			2.99933
$485$			4.84900e38i			0.552582i
$486$	−1.46752e39	+	7.83081e38i	−1.62315	+	0.866126i
$487$	−7.13633e38			−0.766135			−0.383067	−	0.923720i	$-0.625132\pi$
$487$	−7.13633e38			−0.766135			−0.383067	+	0.923720i	$0.625132\pi$
$488$	−1.66061e39			−1.73053
$489$	1.12126e38	−	1.91244e38i	0.113430	−	0.193469i
$490$	−1.55351e39	+	1.59828e39i	−1.52571	+	1.56967i
$491$		−	7.76737e38i		−	0.740615i	−0.928909	−	0.370307i	$-0.879252\pi$
$491$		−	7.76737e38i		−	0.740615i	0.928909	−	0.370307i	$-0.120748\pi$
$492$	−1.34005e37	+	2.28561e37i	−0.0124059	+	0.0211597i
$493$			2.28825e38i			0.205695i
$494$			2.04945e39i			1.78894i
$495$	−1.84042e39	+	1.03000e39i	−1.56006	+	0.873098i
$496$		−	5.45169e39i		−	4.48794i
$497$	9.19315e37	−	2.26478e38i	0.0735016	−	0.181075i
$498$	1.69220e39	+	9.92135e38i	1.31409	+	0.770452i
$499$	9.62333e37			0.0725884			0.0362942	−	0.999341i	$-0.488445\pi$
$499$	9.62333e37			0.0725884			0.0362942	+	0.999341i	$0.488445\pi$
$500$	−2.26293e39			−1.65808
$501$	1.11399e39	−	1.90004e39i	0.792931	−	1.35243i
$502$			4.16884e39i			2.88278i
$503$	6.01385e38			0.404033			0.202017	−	0.979382i	$-0.435251\pi$
$503$	6.01385e38			0.404033			0.202017	+	0.979382i	$0.435251\pi$
$504$	3.87269e39	−	4.85167e38i	2.52796	−	0.316700i
$505$	−2.68649e39			−1.70396
$506$		−	6.92870e38i		−	0.427041i
$507$	3.24290e38	−	5.53113e38i	0.194231	−	0.331282i
$508$	−9.90365e38			−0.576463
$509$	4.89063e38			0.276667			0.138333	−	0.990386i	$-0.455825\pi$
$509$	4.89063e38			0.276667			0.138333	+	0.990386i	$0.455825\pi$
$510$	−8.45432e38	−	4.95676e38i	−0.464848	−	0.272540i
$511$	7.00591e38	−	1.72594e39i	0.374422	−	0.922407i
$512$			3.80904e39i			1.97880i
$513$	3.28243e37	−	1.63634e39i	0.0165765	−	0.826363i
$514$		−	1.35010e39i		−	0.662826i
$515$		−	7.23399e38i		−	0.345281i
$516$	4.57468e39	−	7.80264e39i	2.12295	−	3.62094i
$517$		−	4.13869e39i		−	1.86746i
$518$	−1.76939e39	+	4.35899e39i	−0.776324	+	1.91251i
$519$	−3.51684e38	+	5.99837e38i	−0.150047	+	0.255921i
$520$	−8.59506e39			−3.56616
$521$	−4.65997e39			−1.88034			−0.940170	−	0.340707i	$-0.889334\pi$
$521$	−4.65997e39			−1.88034			−0.940170	+	0.340707i	$0.889334\pi$
$522$	−1.91311e39	−	3.41836e39i	−0.750788	−	1.34151i
$523$			6.05568e38i			0.231147i	0.993299	+	0.115573i	$0.0368706\pi$
$523$			6.05568e38i			0.231147i	−0.993299	+	0.115573i	$0.963129\pi$
$524$	1.01017e40			3.75052
$525$	−9.12767e38	+	7.00994e38i	−0.329648	+	0.253165i
$526$	−3.46593e39			−1.21766
$527$		−	1.40390e39i		−	0.479825i
$528$	−8.97545e39	−	5.26230e39i	−2.98445	−	1.74978i
$529$	3.01729e39			0.976136
$530$	9.28131e39			2.92152
$531$	7.10840e38	+	1.27013e39i	0.217722	+	0.389027i
$532$	−2.48740e39	+	6.12785e39i	−0.741358	+	1.82637i
$533$			4.17189e37i			0.0121001i
$534$	−1.18972e38	−	6.97532e37i	−0.0335812	−	0.0196886i
$535$		−	3.00555e39i		−	0.825647i
$536$			5.51035e39i			1.47329i
$537$	−2.11333e39	−	1.23905e39i	−0.549973	−	0.322449i
$538$			9.36446e39i			2.37214i
$539$	−4.24715e39	+	4.36953e39i	−1.04727	+	1.07745i
$540$	1.18182e40	+	2.37068e38i	2.83688	+	0.0569068i
$541$	3.55979e39			0.831886			0.415943	−	0.909391i	$-0.363452\pi$
$541$	3.55979e39			0.831886			0.415943	+	0.909391i	$0.363452\pi$
$542$	3.32978e39			0.757575
$543$	2.96745e39	+	1.73981e39i	0.657333	+	0.385394i
$544$		−	1.92689e39i		−	0.415598i
$545$	3.16891e39			0.665520
$546$	8.39381e39	−	6.44634e39i	1.71659	−	1.31832i
$547$	−8.86194e39			−1.76487			−0.882434	−	0.470436i	$-0.844097\pi$
$547$	−8.86194e39			−1.76487			−0.882434	+	0.470436i	$0.844097\pi$
$548$		−	9.79957e39i		−	1.90059i
$549$	3.13804e39	−	1.75623e39i	0.592733	−	0.331728i
$550$	6.24567e39			1.14900
$551$	3.85437e39			0.690645
$552$	−1.14051e39	+	1.94528e39i	−0.199060	+	0.339519i
$553$	3.20604e39	+	1.30139e39i	0.545073	+	0.221255i
$554$		−	1.48191e40i		−	2.45431i
$555$	−4.18451e39	+	7.13715e39i	−0.675143	+	1.15153i
$556$			1.99826e40i			3.14100i
$557$		−	1.32679e39i		−	0.203189i	−0.994826	−	0.101595i	$-0.967606\pi$
$557$		−	1.32679e39i		−	0.203189i	0.994826	−	0.101595i	$-0.0323945\pi$
$558$	1.17374e40	+	2.09725e40i	1.75136	+	3.12935i
$559$		−	1.42420e40i		−	2.07062i
$560$	−1.79174e40	−	7.27299e39i	−2.53833	−	1.03035i
$561$	−2.31133e39	−	1.35513e39i	−0.319080	−	0.187076i
$562$	1.29489e40			1.74204
$563$	8.43743e39			1.10621			0.553106	−	0.833111i	$-0.313443\pi$
$563$	8.43743e39			1.10621			0.553106	+	0.833111i	$0.313443\pi$
$564$	−1.17321e40	+	2.00105e40i	−1.49910	+	2.55688i
$565$		−	1.45348e40i		−	1.81011i
$566$	−9.64572e39			−1.17084
$567$	−6.80510e39	+	5.01250e39i	−0.805156	+	0.593063i
$568$	4.31699e39			0.497886
$569$		−	5.26041e39i		−	0.591414i	−0.955279	−	0.295707i	$-0.904445\pi$
$569$		−	5.26041e39i		−	0.591414i	0.955279	−	0.295707i	$-0.0955553\pi$
$570$	−8.34925e39	+	1.42406e40i	−0.915086	+	1.56078i
$571$	−1.34038e40			−1.43220			−0.716099	−	0.697999i	$-0.754074\pi$
$571$	−1.34038e40			−1.43220			−0.716099	+	0.697999i	$0.754074\pi$
$572$	−4.04666e40			−4.21555
$573$	−1.12649e40	−	6.60460e39i	−1.14416	−	0.670818i
$574$	−7.18660e37	+	1.77046e38i	−0.00711707	+	0.0175333i
$575$		−	6.64932e38i		−	0.0642086i
$576$	4.16810e39	+	7.44759e39i	0.392475	+	0.701277i
$577$			1.01243e40i			0.929643i	0.885404	+	0.464822i	$0.153882\pi$
$577$			1.01243e40i			0.929643i	−0.885404	+	0.464822i	$0.846118\pi$
$578$			1.93006e40i			1.72830i
$579$	8.89990e39	−	1.51798e40i	0.777223	−	1.32564i
$580$			2.78376e40i			2.37097i
$581$	9.23533e39	+	3.74879e39i	0.767182	+	0.311413i
$582$	5.33371e39	−	9.09725e39i	0.432162	−	0.737101i
$583$	2.53742e40			2.00539
$584$	3.28989e40			2.53627
$585$	1.62420e40	−	9.08998e39i	1.22146	−	0.683601i
$586$		−	5.14723e39i		−	0.377623i
$587$	6.26225e39			0.448206			0.224103	−	0.974565i	$-0.428055\pi$
$587$	6.26225e39			0.448206			0.224103	+	0.974565i	$0.428055\pi$
$588$	3.29214e40	−	9.08704e39i	2.29883	−	0.634528i
$589$	−2.36475e40			−1.61107
$590$		−	1.46806e40i		−	0.975867i
$591$	2.50860e38	+	1.47079e38i	0.0162710	+	0.00953965i
$592$	−4.08145e40			−2.58315
$593$	−1.54878e40			−0.956527			−0.478264	−	0.878216i	$-0.658734\pi$
$593$	−1.54878e40			−0.956527			−0.478264	+	0.878216i	$0.658734\pi$
$594$	4.58579e40	+	9.19893e38i	2.76383	+	0.0554414i
$595$	−4.61402e39	−	1.87292e39i	−0.271384	−	0.110160i
$596$			4.10303e40i			2.35523i
$597$	−3.03112e40	−	1.77714e40i	−1.69815	−	0.995622i
$598$			6.11472e39i			0.334356i
$599$			1.20812e39i			0.0644795i	0.999480	+	0.0322398i	$0.0102640\pi$
$599$			1.20812e39i			0.0644795i	−0.999480	+	0.0322398i	$0.989736\pi$
$600$	−1.75351e40	−	1.02808e40i	−0.913514	−	0.535592i
$601$			2.22116e40i			1.12953i	0.825250	+	0.564767i	$0.191034\pi$
$601$			2.22116e40i			1.12953i	−0.825250	+	0.564767i	$0.808966\pi$
$602$	2.45337e40	−	6.04399e40i	1.21790	−	3.00037i
$603$	−5.82764e39	−	1.04129e40i	−0.282418	−	0.504626i
$604$	5.33408e40			2.52362
$605$	3.23968e40			1.49641
$606$	5.04015e40	+	2.95504e40i	2.27295	+	1.33263i
$607$			5.52437e39i			0.243247i	0.992576	+	0.121623i	$0.0388100\pi$
$607$			5.52437e39i			0.243247i	−0.992576	+	0.121623i	$0.961190\pi$
$608$	−3.24569e40			−1.39542
$609$	−1.21236e40	−	1.57861e40i	−0.508955	−	0.662712i
$610$	−3.62705e40			−1.48686
$611$			3.65248e40i			1.46214i
$612$	7.33377e39	+	1.31040e40i	0.286703	+	0.512282i
$613$	3.71583e39			0.141866			0.0709332	−	0.997481i	$-0.477402\pi$
$613$	3.71583e39			0.141866			0.0709332	+	0.997481i	$0.477402\pi$
$614$	−1.78853e40			−0.666891
$615$	−1.69959e38	+	2.89884e38i	−0.00618948	+	0.0105569i
$616$	−9.97204e40	−	4.04783e40i	−3.54702	−	1.43980i
$617$		−	2.67277e40i		−	0.928595i	−0.885679	−	0.464297i	$-0.846307\pi$
$617$		−	2.67277e40i		−	0.928595i	0.885679	−	0.464297i	$-0.153693\pi$
$618$	−7.95711e39	+	1.35718e40i	−0.270037	+	0.460578i
$619$		−	4.32119e40i		−	1.43248i	−0.697853	−	0.716241i	$-0.745861\pi$
$619$		−	4.32119e40i		−	1.43248i	0.697853	−	0.716241i	$-0.254139\pi$
$620$		−	1.70791e41i		−	5.53075i
$621$	9.79344e37	−	4.88216e39i	0.00309818	−	0.154449i
$622$		−	5.89825e38i		−	0.0182290i
$623$	−6.49301e38	−	2.63563e38i	−0.0196051	−	0.00795807i
$624$	7.92101e40	+	4.64408e40i	2.33671	+	1.37001i
$625$	−4.31212e40			−1.24288
$626$	−1.84358e40			−0.519200
$627$	−2.28260e40	+	3.89323e40i	−0.628131	+	1.07135i
$628$		−	6.76512e40i		−	1.81912i
$629$	−1.05104e40			−0.276175
$630$	8.45862e40	−	1.05969e40i	2.17201	−	0.272107i
$631$	−3.99053e40			−1.00139			−0.500696	−	0.865623i	$-0.666923\pi$
$631$	−3.99053e40			−1.00139			−0.500696	+	0.865623i	$0.666923\pi$
$632$			6.11116e40i			1.49874i
$633$	4.15642e39	−	7.08925e39i	0.0996244	−	0.169921i
$634$	4.93946e40			1.15714
$635$	−1.25608e40			−0.287606
$636$	−1.22684e41	−	7.19293e40i	−2.74573	−	1.60982i
$637$	3.74819e40	−	3.85620e40i	0.819974	−	0.843603i
$638$			1.08018e41i			2.30991i
$639$	−8.15779e39	+	4.56557e39i	−0.170534	+	0.0954404i
$640$			1.22139e40i			0.249601i
$641$			4.28272e40i			0.855614i	0.903870	+	0.427807i	$0.140714\pi$
$641$			4.28272e40i			0.855614i	−0.903870	+	0.427807i	$0.859286\pi$
$642$	−3.30599e40	+	5.63875e40i	−0.645720	+	1.10135i
$643$			9.04997e40i			1.72818i	0.503340	+	0.864088i	$0.332104\pi$
$643$			9.04997e40i			1.72818i	−0.503340	+	0.864088i	$0.667896\pi$
$644$	−7.42140e39	+	1.82830e40i	−0.138561	+	0.341352i
$645$	5.80206e40	−	9.89607e40i	1.05917	−	1.80654i
$646$	−2.09712e40			−0.374327
$647$	−3.67746e38			−0.00641853			−0.00320926	−	0.999995i	$-0.501022\pi$
$647$	−3.67746e38			−0.00641853			−0.00320926	+	0.999995i	$0.501022\pi$
$648$	−1.27235e41	−	7.80680e40i	−2.17154	−	1.33240i
$649$		−	4.01354e40i		−	0.669852i
$650$	−5.51193e40			−0.899621
$651$	7.43811e40	+	9.68520e40i	1.18724	+	1.54591i
$652$	3.42618e40			0.534836
$653$		−	5.73825e39i		−	0.0876069i	−0.999040	−	0.0438035i	$-0.986052\pi$
$653$		−	5.73825e39i		−	0.0876069i	0.999040	−	0.0438035i	$-0.0139475\pi$
$654$	−5.94523e40	−	3.48568e40i	−0.887752	−	0.520488i
$655$	1.28120e41			1.87119
$656$	−1.65773e39			−0.0236814
$657$	−6.21688e40	+	3.47932e40i	−0.868710	+	0.486180i
$658$	−6.29186e40	+	1.55003e41i	−0.860010	+	2.11868i
$659$			8.55947e40i			1.14448i	0.820086	+	0.572241i	$0.193926\pi$
$659$			8.55947e40i			1.14448i	−0.820086	+	0.572241i	$0.806074\pi$
$660$	−2.81183e41	−	1.64857e41i	−3.67791	−	2.15636i
$661$		−	3.55669e40i		−	0.455119i	−0.973764	−	0.227560i	$-0.926925\pi$
$661$		−	3.55669e40i		−	0.455119i	0.973764	−	0.227560i	$-0.0730747\pi$
$662$			1.37483e41i			1.72110i
$663$	2.03979e40	+	1.19593e40i	0.249827	+	0.146473i
$664$			1.76039e41i			2.10946i
$665$	−3.15477e40	+	7.77193e40i	−0.369874	+	0.911203i
$666$	1.57012e41	−	8.78729e40i	1.80118	−	1.00804i
$667$	1.14999e40			0.129083
$668$	3.40396e41			3.73875
$669$	−1.32502e41	−	7.76857e40i	−1.42411	−	0.834954i
$670$			1.20355e41i			1.26585i
$671$	−9.91599e40			−1.02061
$672$	1.02090e41	+	1.32932e41i	1.02832	+	1.33898i
$673$	3.87780e40			0.382268			0.191134	−	0.981564i	$-0.438784\pi$
$673$	3.87780e40			0.382268			0.191134	+	0.981564i	$0.438784\pi$
$674$			6.21933e40i			0.600033i
$675$	4.40088e40	+	8.82800e38i	0.415561	+	0.00833600i
$676$	9.90912e40			0.915816
$677$	8.03411e39			0.0726779			0.0363389	−	0.999340i	$-0.488430\pi$
$677$	8.03411e39			0.0726779			0.0363389	+	0.999340i	$0.488430\pi$
$678$	−1.59877e41	+	2.72688e41i	−1.41565	+	2.41455i
$679$	2.01535e40	−	4.96491e40i	0.174678	−	0.430328i
$680$		−	8.79498e40i		−	0.746200i
$681$	5.05556e39	−	8.62283e39i	0.0419890	−	0.0716171i
$682$		−	6.62716e41i		−	5.38833i
$683$		−	6.79765e40i		−	0.541077i	−0.962709	−	0.270538i	$-0.912798\pi$
$683$		−	6.79765e40i		−	0.541077i	0.962709	−	0.270538i	$-0.0872017\pi$
$684$	2.20727e41	−	1.23531e41i	1.72005	−	0.962639i
$685$		−	1.24288e41i		−	0.948232i
$686$	2.25493e41	−	9.90812e40i	1.68435	−	0.740102i
$687$	−1.00044e41	−	5.86557e40i	−0.731675	−	0.428981i
$688$	5.65916e41			4.05247
$689$	−2.23932e41			−1.57014
$690$	−2.49108e40	+	4.24881e40i	−0.171031	+	0.291713i
$691$			2.70551e41i			1.81893i	0.415775	+	0.909467i	$0.363510\pi$
$691$			2.70551e41i			1.81893i	−0.415775	+	0.909467i	$0.636490\pi$
$692$	−1.07462e41			−0.707484
$693$	2.31250e41	−	2.89708e40i	1.49091	−	0.186779i
$694$	−1.63100e41			−1.02978
$695$			2.53439e41i			1.56709i
$696$	1.77805e41	−	3.03266e41i	1.07674	−	1.83650i
$697$	−4.26892e38			−0.00253188
$698$	1.21791e41			0.707479
$699$	−3.59030e40	−	2.10499e40i	−0.204274	−	0.119765i
$700$	−1.64807e41	−	6.68980e40i	−0.918445	−	0.372813i
$701$		−	2.10589e41i		−	1.14954i	−0.818314	−	0.574771i	$-0.805091\pi$
$701$		−	2.10589e41i		−	1.14954i	0.818314	−	0.574771i	$-0.194909\pi$
$702$	−4.04705e41	−	8.11824e39i	−2.16397	−	0.0434084i
$703$			1.77039e41i			0.927292i
$704$		−	2.35339e41i		−	1.20751i
$705$	−1.48798e41	+	2.53793e41i	−0.747922	+	1.27567i
$706$		−	4.30302e40i		−	0.211888i
$707$	2.75071e41	+	1.11656e41i	1.32698	+	0.538644i
$708$	−1.13774e41	+	1.94054e41i	−0.537724	+	0.917149i
$709$	1.75830e41			0.814183			0.407091	−	0.913387i	$-0.366543\pi$
$709$	1.75830e41			0.814183			0.407091	+	0.913387i	$0.366543\pi$
$710$	9.42905e40			0.427781
$711$	−6.46305e40	−	1.15482e41i	−0.287295	−	0.513341i
$712$		−	1.23766e40i		−	0.0539065i
$713$	−7.05546e40			−0.301112
$714$	6.59628e40	+	8.58905e40i	0.275851	+	0.359187i
$715$	−5.13237e41			−2.10320
$716$		−	3.78608e41i		−	1.52038i
$717$	−1.75129e41	−	1.02678e41i	−0.689176	−	0.404063i
$718$	4.25240e41			1.63995
$719$	6.69236e40			0.252936			0.126468	−	0.991971i	$-0.459636\pi$
$719$	6.69236e40			0.252936			0.126468	+	0.991971i	$0.459636\pi$
$720$	3.61196e41	+	6.45388e41i	1.33790	+	2.39056i
$721$	−3.00660e40	+	7.40691e40i	−0.109148	+	0.268891i
$722$		−	1.63836e41i		−	0.582934i
$723$	−2.92886e41	−	1.71719e41i	−1.02139	−	0.598842i
$724$			5.31624e41i			1.81717i
$725$			1.03662e41i			0.347311i
$726$	−6.07800e41	−	3.56353e41i	−1.99609	−	1.17031i
$727$		−	9.31430e40i		−	0.299848i	−0.988698	−	0.149924i	$-0.952097\pi$
$727$		−	9.31430e40i		−	0.299848i	0.988698	−	0.149924i	$-0.0479029\pi$
$728$	8.80052e41	+	3.57229e41i	2.77718	+	1.12731i
$729$	3.22998e41	+	1.29637e40i	0.999196	+	0.0401031i
$730$	7.18568e41			2.17914
$731$	1.45733e41			0.433266
$732$	4.79436e41	+	2.81093e41i	1.39740	+	0.819293i
$733$			2.83486e41i			0.810072i	0.914301	+	0.405036i	$0.132741\pi$
$733$			2.83486e41i			0.810072i	−0.914301	+	0.405036i	$0.867259\pi$
$734$	−7.82258e41			−2.19158
$735$	4.17541e41	−	1.15251e41i	1.14692	−	0.316575i
$736$	−9.68383e40			−0.260807
$737$			3.29040e41i			0.868899i
$738$	6.37723e39	−	3.56906e39i	0.0165126	−	0.00924138i
$739$	3.16897e41			0.804590			0.402295	−	0.915510i	$-0.368213\pi$
$739$	3.16897e41			0.804590			0.402295	+	0.915510i	$0.368213\pi$
$740$	−1.27863e42			−3.18337
$741$	2.01444e41	−	3.43586e41i	0.491802	−	0.838824i
$742$	−9.50318e41	−	3.85751e41i	−2.27516	−	0.923529i
$743$			2.03599e41i			0.478012i	0.971018	+	0.239006i	$0.0768216\pi$
$743$			2.03599e41i			0.478012i	−0.971018	+	0.239006i	$0.923178\pi$
$744$	−1.09088e42	+	1.86062e42i	−2.51170	+	4.28400i
$745$			5.20386e41i			1.17506i
$746$			6.13405e41i			1.35842i
$747$	−1.86175e41	−	3.32659e41i	−0.404364	−	0.722521i
$748$		−	4.14078e41i		−	0.882083i
$749$	−1.24917e41	+	3.07740e41i	−0.260997	+	0.642980i
$750$	5.38456e41	+	3.15696e41i	1.10347	+	0.646965i
$751$	1.13321e41			0.227789			0.113894	−	0.993493i	$-0.463667\pi$
$751$	1.13321e41			0.227789			0.113894	+	0.993493i	$0.463667\pi$
$752$	−1.45134e42			−2.86160
$753$	4.09763e41	−	6.98898e41i	0.792512	−	1.35172i
$754$		−	9.53277e41i		−	1.80857i
$755$	6.76521e41			1.25907
$756$	−1.20022e42	−	5.15462e41i	−2.19126	−	0.941089i
$757$	−3.74734e40			−0.0671171			−0.0335585	−	0.999437i	$-0.510684\pi$
$757$	−3.74734e40			−0.0671171			−0.0335585	+	0.999437i	$0.510684\pi$
$758$		−	1.66274e42i		−	2.92160i
$759$	−6.81035e40	+	1.16158e41i	−0.117399	+	0.200237i
$760$	−1.48144e42			−2.50546
$761$	4.12750e41			0.684872			0.342436	−	0.939541i	$-0.388748\pi$
$761$	4.12750e41			0.684872			0.342436	+	0.939541i	$0.388748\pi$
$762$	2.35654e41	+	1.38164e41i	0.383643	+	0.224930i
$763$	−3.24466e41	−	1.31707e41i	−0.518279	−	0.210379i
$764$		−	2.01813e42i		−	3.16297i
$765$	9.30140e40	+	1.66198e41i	0.143040	+	0.255585i
$766$		−	2.16162e42i		−	3.26184i
$767$			3.54203e41i			0.524468i
$768$	4.14090e41	−	7.06277e41i	0.601668	−	1.02621i
$769$			7.44193e41i			1.06109i	0.847656	+	0.530546i	$0.178013\pi$
$769$			7.44193e41i			1.06109i	−0.847656	+	0.530546i	$0.821987\pi$
$770$	−2.17806e42	−	8.84116e41i	−3.04758	−	1.23707i
$771$	−1.32704e41	+	2.26341e41i	−0.182219	+	0.310796i
$772$	2.71949e42			3.66468
$773$	1.18820e42			1.57141			0.785703	−	0.618604i	$-0.212301\pi$
$773$	1.18820e42			1.57141			0.785703	+	0.618604i	$0.212301\pi$
$774$	−2.17706e42	+	1.21841e42i	−2.82570	+	1.58143i
$775$		−	6.35994e41i		−	0.810174i
$776$	9.46382e41			1.18324
$777$	7.25089e41	−	5.56859e41i	0.889787	−	0.683346i
$778$	−8.92972e41			−1.07556
$779$			7.19064e39i			0.00850109i
$780$	2.48149e42	+	1.45490e42i	2.87966	+	1.68834i
$781$	2.57781e41			0.293637
$782$	−6.25694e40			−0.0699623
$783$	−1.52679e40	+	7.61124e41i	−0.0167584	+	0.835429i
$784$	1.53229e42	+	1.48937e42i	1.65104	+	1.60479i
$785$		−	8.58018e41i		−	0.907583i
$786$	−2.40367e42	−	1.40927e42i	−2.49602	−	1.46341i
$787$			5.53722e41i			0.564493i	0.959342	+	0.282246i	$0.0910796\pi$
$787$			5.53722e41i			0.564493i	−0.959342	+	0.282246i	$0.908920\pi$
$788$			4.49421e40i			0.0449804i
$789$	5.81056e41	+	3.40673e41i	0.570954	+	0.334750i
$790$			1.33478e42i			1.28771i
$791$	−6.04096e41	+	1.48822e42i	−0.572198	+	1.40964i
$792$	2.01026e42	+	3.59195e42i	1.86955	+	3.34053i
$793$	8.75106e41			0.799097
$794$	−1.39996e42			−1.25521
$795$	−1.55599e42	−	9.12278e41i	−1.36989	−	0.803163i
$796$		−	5.43031e42i		−	4.69446i
$797$	1.82944e42			1.55300			0.776502	−	0.630114i	$-0.216992\pi$
$797$	1.82944e42			1.55300			0.776502	+	0.630114i	$0.216992\pi$
$798$	1.44675e42	−	1.11109e42i	1.20601	−	0.926204i
$799$	−3.73743e41			−0.305946
$800$		−	8.72920e41i		−	0.701729i
$801$	1.30892e40	+	2.33880e40i	0.0103334	+	0.0184638i
$802$	2.52169e42			1.95507
$803$	1.96449e42			1.49580
$804$	9.32743e41	−	1.59090e42i	0.697508	−	1.18968i
$805$	−9.41254e40	+	2.31883e41i	−0.0691300	+	0.170305i
$806$			5.84860e42i			4.21885i
$807$	9.20450e41	−	1.56993e42i	0.652130	−	1.11228i
$808$			5.24324e42i			3.64868i
$809$		−	1.31136e42i		−	0.896333i	−0.893950	−	0.448167i	$-0.852077\pi$
$809$		−	1.31136e42i		−	0.896333i	0.893950	−	0.448167i	$-0.147923\pi$
$810$	−2.77902e42	−	1.70514e42i	−1.86577	−	1.14479i
$811$			1.64058e41i			0.108192i	0.998536	+	0.0540959i	$0.0172277\pi$
$811$			1.64058e41i			0.108192i	−0.998536	+	0.0540959i	$0.982772\pi$
$812$	1.15699e42	−	2.85030e42i	0.749491	−	1.84641i
$813$	−5.58231e41	−	3.27290e41i	−0.355223	−	0.208267i
$814$	−4.96147e42			−3.10139
$815$	4.34542e41			0.266837
$816$	−4.75210e41	+	8.10524e41i	−0.286667	+	0.488944i
$817$		−	2.45475e42i		−	1.45474i
$818$	1.90636e42			1.10990
$819$	−2.04083e42	+	2.55673e41i	−1.16732	+	0.146241i
$820$	−5.19333e40			−0.0291840
$821$		−	4.86041e41i		−	0.268347i	−0.990958	−	0.134174i	$-0.957162\pi$
$821$		−	4.86041e41i		−	0.268347i	0.990958	−	0.134174i	$-0.0428380\pi$
$822$	−1.36712e42	+	2.33177e42i	−0.741591	+	1.26487i
$823$	−2.32959e42			−1.24160			−0.620800	−	0.783969i	$-0.713192\pi$
$823$	−2.32959e42			−1.24160			−0.620800	+	0.783969i	$0.713192\pi$
$824$	−1.41186e42			−0.739346
$825$	−1.04707e42	−	6.13899e41i	−0.538760	−	0.315874i
$826$	−6.10159e41	+	1.50316e42i	−0.308484	+	0.759965i
$827$			1.76908e42i			0.878857i	0.898278	+	0.439428i	$0.144819\pi$
$827$			1.76908e42i			0.878857i	−0.898278	+	0.439428i	$0.855181\pi$
$828$	6.58558e41	−	3.68567e41i	0.321480	−	0.179919i
$829$		−	1.36122e40i		−	0.00652960i	−0.999995	−	0.00326480i	$-0.998961\pi$
$829$		−	1.36122e40i		−	0.00652960i	0.999995	−	0.00326480i	$-0.00103922\pi$
$830$			3.84498e42i			1.81243i
$831$	−1.45659e42	+	2.48439e42i	−0.674720	+	1.15081i
$832$			2.07691e42i			0.945430i
$833$	3.94589e41	+	3.83537e41i	0.176520	+	0.171575i
$834$	2.78773e42	−	4.75479e42i	1.22558	−	2.09037i
$835$	4.31724e42			1.86531
$836$	−6.97481e42			−2.96170
$837$	9.36723e40	−	4.66969e42i	0.0390924	−	1.94881i
$838$			4.63200e42i			1.89990i
$839$	−5.08775e41			−0.205105			−0.102553	−	0.994728i	$-0.532701\pi$
$839$	−5.08775e41			−0.205105			−0.102553	+	0.994728i	$0.532701\pi$
$840$	4.65973e42	+	6.06746e42i	1.84634	+	2.40413i
$841$	7.74870e41			0.301777
$842$			4.82394e42i			1.84662i
$843$	−2.17086e42	−	1.27277e42i	−0.816832	−	0.478908i
$844$	1.27005e42			0.469739
$845$	1.25677e42			0.456914
$846$	5.58325e42	−	3.12471e42i	1.99534	−	1.11671i
$847$	−3.31712e42	−	1.34648e42i	−1.16534	−	0.473032i
$848$		−	8.89809e42i		−	3.07296i
$849$	1.61708e42	+	9.48095e41i	0.548999	+	0.321877i
$850$		−	5.64013e41i		−	0.188241i
$851$			5.28212e41i			0.173312i
$852$	−1.24636e42	−	7.30742e41i	−0.402041	−	0.235717i
$853$			1.46159e42i			0.463517i	0.972773	+	0.231758i	$0.0744479\pi$
$853$			1.46159e42i			0.463517i	−0.972773	+	0.231758i	$0.925552\pi$
$854$	3.71375e42	+	1.50748e42i	1.15791	+	0.470016i
$855$	2.79947e42	−	1.56674e42i	0.858158	−	0.480274i
$856$	−5.86596e42			−1.76795
$857$	−2.78902e42			−0.826474			−0.413237	−	0.910624i	$-0.635602\pi$
$857$	−2.78902e42			−0.826474			−0.413237	+	0.910624i	$0.635602\pi$
$858$	9.62890e42	+	5.64542e42i	2.80550	+	1.64486i
$859$			4.60345e42i			1.31881i	0.751787	+	0.659406i	$0.229192\pi$
$859$			4.60345e42i			1.31881i	−0.751787	+	0.659406i	$0.770808\pi$
$860$	1.77290e43			4.99409
$861$	2.94503e40	−	2.26175e40i	0.00815727	−	0.00626468i
$862$	−4.73522e42			−1.28969
$863$			3.11363e42i			0.833893i	0.908931	+	0.416946i	$0.136900\pi$
$863$			3.11363e42i			0.833893i	−0.908931	+	0.416946i	$0.863100\pi$
$864$	1.28568e41	−	6.40928e42i	0.0338597	−	1.68795i
$865$	−1.36294e42			−0.352974
$866$	−2.13220e42			−0.543023
$867$	1.89710e42	−	3.23571e42i	0.475130	−	0.810388i
$868$	−7.09842e42	+	1.74873e43i	−1.74834	+	4.30712i
$869$			3.64916e42i			0.883906i
$870$	3.88356e42	−	6.62385e42i	0.925126	−	1.57791i
$871$		−	2.90384e42i		−	0.680314i
$872$		−	6.18479e42i		−	1.42507i
$873$	−1.78837e42	+	1.00088e42i	−0.405276	+	0.226816i
$874$			1.05393e42i			0.234907i
$875$	2.93867e42	+	1.19286e42i	0.644220	+	0.261501i
$876$	−9.49828e42	−	5.56883e42i	−2.04803	−	1.20076i
$877$	−2.16367e42			−0.458877			−0.229438	−	0.973323i	$-0.573689\pi$
$877$	−2.16367e42			−0.458877			−0.229438	+	0.973323i	$0.573689\pi$
$878$	−1.15634e43			−2.41221
$879$	−5.05931e41	+	8.62923e41i	−0.103813	+	0.177065i
$880$		−	2.03938e43i		−	4.11623i
$881$	−6.51135e42			−1.29277			−0.646384	−	0.763012i	$-0.723720\pi$
$881$	−6.51135e42			−1.29277			−0.646384	+	0.763012i	$0.723720\pi$
$882$	−9.10125e42	−	2.43057e42i	−1.77749	−	0.474693i
$883$	9.76807e42			1.87663			0.938314	−	0.345783i	$-0.112387\pi$
$883$	9.76807e42			1.87663			0.938314	+	0.345783i	$0.112387\pi$
$884$			3.65432e42i			0.690636i
$885$	−1.44299e42	+	2.46118e42i	−0.268278	+	0.457579i
$886$	−4.66968e42			−0.854079
$887$	−2.22619e42			−0.400561			−0.200281	−	0.979739i	$-0.564185\pi$
$887$	−2.22619e42			−0.400561			−0.200281	+	0.979739i	$0.564185\pi$
$888$	1.39296e43	+	8.16693e42i	2.46576	+	1.44567i
$889$	1.28610e42	+	5.22053e41i	0.223975	+	0.0909157i
$890$		−	2.70326e41i		−	0.0463161i
$891$	−7.59757e42	−	4.66168e42i	−1.28070	−	0.785806i
$892$		−	2.37380e43i		−	3.93689i
$893$			6.29539e42i			1.02725i
$894$	5.72405e42	−	9.76301e42i	0.918986	−	1.56744i
$895$		−	4.80188e42i		−	0.758537i
$896$	5.07638e41	−	1.25059e42i	0.0789019	−	0.194379i
$897$	6.01027e41	−	1.02512e42i	0.0919186	−	0.156778i
$898$	8.91262e42			1.34122
$899$	1.09994e43			1.62875
$900$	3.32234e42	+	5.93638e42i	0.484091	+	0.864978i
$901$		−	2.29141e42i		−	0.328543i
$902$	−2.01516e41			−0.0284325
$903$	−1.00538e43	+	7.72117e42i	−1.39591	+	1.07204i
$904$	−2.83676e43			−3.87597
$905$			6.74257e42i			0.906612i
$906$	−1.26923e43	−	7.44147e42i	−1.67950	−	0.984691i
$907$	−5.32245e42			−0.693116			−0.346558	−	0.938028i	$-0.612650\pi$
$907$	−5.32245e42			−0.693116			−0.346558	+	0.938028i	$0.612650\pi$
$908$	1.54480e42			0.197982
$909$	−5.54516e42	−	9.90812e42i	−0.699419	−	1.24973i
$910$	1.92218e43	+	7.80250e42i	2.38613	+	0.968575i
$911$			1.18310e43i			1.44546i	0.691130	+	0.722730i	$0.257113\pi$
$911$			1.18310e43i			1.44546i	−0.691130	+	0.722730i	$0.742887\pi$
$912$	1.36526e43	+	8.00451e42i	1.64169	+	0.962520i
$913$			1.05118e43i			1.24409i
$914$		−	2.53686e43i		−	2.95513i
$915$	6.08068e42	+	3.56510e42i	0.697182	+	0.408757i
$916$		−	1.79231e43i		−	2.02268i
$917$	−1.31182e43	−	5.32493e42i	−1.45720	−	0.591506i
$918$	8.30706e40	−	4.14118e42i	0.00908298	−	0.452799i
$919$	1.41281e43			1.52058			0.760290	−	0.649583i	$-0.225057\pi$
$919$	1.41281e43			1.52058			0.760290	+	0.649583i	$0.225057\pi$
$920$	−4.42001e42			−0.468274
$921$	2.99844e42	+	1.75798e42i	0.312702	+	0.183337i
$922$			1.19722e43i			1.22907i
$923$	−2.27496e42			−0.229906
$924$	2.19386e43	+	2.85663e43i	2.18256	+	2.84191i
$925$	−4.76141e42			−0.466316
$926$		−	1.42176e42i		−	0.137077i
$927$	2.66799e42	−	1.49316e42i	0.253237	−	0.141726i
$928$	1.50970e43			1.41073
$929$	−4.38245e42			−0.403171			−0.201586	−	0.979471i	$-0.564609\pi$
$929$	−4.38245e42			−0.403171			−0.201586	+	0.979471i	$0.564609\pi$
$930$	−2.38266e43	+	4.06390e43i	−2.15804	+	3.68079i
$931$	6.46036e42	−	6.64653e42i	0.576085	−	0.592686i
$932$		−	6.43210e42i		−	0.564705i
$933$	−5.79750e40	+	9.88829e40i	−0.00501137	+	0.00854747i
$934$			1.96938e43i			1.67610i
$935$		−	5.25175e42i		−	0.440084i
$936$	−1.77410e43	−	3.16997e43i	−1.46379	−	2.61550i
$937$			1.84887e43i			1.50204i	0.660277	+	0.751022i	$0.270439\pi$
$937$			1.84887e43i			1.50204i	−0.660277	+	0.751022i	$0.729561\pi$
$938$	5.00223e42	−	1.23232e43i	0.400150	−	0.985789i
$939$	3.09073e42	+	1.81209e42i	0.243450	+	0.142735i
$940$	−4.54675e43			−3.52652
$941$	−2.02949e43			−1.55002			−0.775009	−	0.631950i	$-0.782255\pi$
$941$	−2.02949e43			−1.55002			−0.775009	+	0.631950i	$0.782255\pi$
$942$	−9.43787e42	+	1.60974e43i	−0.709800	+	1.21064i
$943$			2.14540e40i			0.00158887i
$944$	−1.40745e43			−1.02645
$945$	−1.52223e43	−	6.53759e42i	−1.09325	−	0.469523i
$946$	6.87936e43			4.86549
$947$			5.73675e42i			0.399569i	0.979840	+	0.199784i	$0.0640242\pi$
$947$			5.73675e42i			0.399569i	−0.979840	+	0.199784i	$0.935976\pi$
$948$	1.03444e43	−	1.76436e43i	0.709555	−	1.21023i
$949$	−1.73370e43			−1.17116
$950$	−9.50033e42			−0.632043
$951$	−8.28091e42	−	4.85509e42i	−0.542576	−	0.318112i
$952$	−3.65538e42	+	9.00522e42i	−0.235883	+	0.581110i
$953$			3.42786e42i			0.217859i	0.994049	+	0.108929i	$0.0347423\pi$
$953$			3.42786e42i			0.217859i	−0.994049	+	0.108929i	$0.965258\pi$
$954$	1.91575e43	+	3.42307e43i	1.19919	+	2.14271i
$955$		−	2.55959e43i		−	1.57805i
$956$		−	3.13747e43i		−	1.90520i
$957$	1.06173e43	−	1.81089e43i	0.635023	−	1.08310i
$958$			5.47151e43i			3.22335i
$959$	−5.16566e42	+	1.27259e43i	−0.299748	+	0.738444i
$960$	−8.46113e42	+	1.44314e43i	−0.483610	+	0.824852i
$961$	−4.97222e43			−2.79938
$962$	4.37859e43			2.42826
$963$	1.10849e43	−	6.20373e42i	0.605549	−	0.338900i
$964$		−	5.24711e43i		−	2.82360i
$965$	3.44912e43			1.82836
$966$	4.31652e42	−	3.31503e42i	0.225406	−	0.173109i
$967$	−7.51156e42			−0.386408			−0.193204	−	0.981159i	$-0.561888\pi$
$967$	−7.51156e42			−0.386408			−0.193204	+	0.981159i	$0.561888\pi$
$968$		−	6.32291e43i		−	3.20423i
$969$	3.51577e42	+	2.06129e42i	0.175520	+	0.102907i
$970$	2.06706e43			1.01663
$971$	−2.84958e43			−1.38071			−0.690354	−	0.723472i	$-0.742545\pi$
$971$	−2.84958e43			−1.38071			−0.690354	+	0.723472i	$0.742545\pi$
$972$	2.35194e43	+	4.40763e43i	1.12271	+	2.10399i
$973$	1.05335e43	−	2.59497e43i	0.495376	−	1.22038i
$974$			3.04212e43i			1.40952i
$975$	9.24064e42	+	5.41778e42i	0.421828	+	0.247317i
$976$			3.47729e43i			1.56393i
$977$			8.83529e41i			0.0391516i	0.999808	+	0.0195758i	$0.00623157\pi$
$977$			8.83529e41i			0.0391516i	−0.999808	+	0.0195758i	$0.993768\pi$
$978$	−8.15249e42	−	4.77980e42i	−0.355940	−	0.208687i
$979$		−	7.39043e41i		−	0.0317922i
$980$	4.80035e43	+	4.66589e43i	2.03467	+	1.97768i
$981$	6.54092e42	+	1.16874e43i	0.273173	+	0.488108i
$982$	−3.31112e43			−1.36257
$983$	1.12350e43			0.455560			0.227780	−	0.973713i	$-0.426853\pi$
$983$	1.12350e43			0.455560			0.227780	+	0.973713i	$0.426853\pi$
$984$	5.65768e41	+	3.31710e41i	0.0226053	+	0.0132535i
$985$			5.69999e41i			0.0224413i
$986$	9.75450e42			0.378434
$987$	2.57837e43	−	1.98016e43i	0.985704	−	0.757009i
$988$	6.15540e43			2.31889
$989$		−	7.32396e42i		−	0.271894i
$990$	4.39076e43	+	7.84544e43i	1.60631	+	2.87017i
$991$	−1.88068e43			−0.678027			−0.339014	−	0.940781i	$-0.610093\pi$
$991$	−1.88068e43			−0.678027			−0.339014	+	0.940781i	$0.610093\pi$
$992$	−9.26239e43			−3.29082
$993$	1.35134e43	−	2.30487e43i	0.473153	−	0.807016i
$994$	−9.65444e42	−	3.91891e42i	−0.333138	−	0.135227i
$995$		−	6.88725e43i		−	2.34213i
$996$	2.97983e43	−	5.08243e43i	0.998689	−	1.70338i
$997$		−	3.63727e42i		−	0.120142i	−0.998194	−	0.0600711i	$-0.980867\pi$
$997$		−	3.63727e42i		−	0.120142i	0.998194	−	0.0600711i	$-0.0191327\pi$
$998$		−	4.10229e42i		−	0.133547i
$999$	−3.49599e43	−	7.01283e41i	−1.12168	−	0.0225006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.13	✓	76
3.2	odd	2	inner	21.30.c.a.20.64	yes	76
7.6	odd	2	inner	21.30.c.a.20.63	yes	76
21.20	even	2	inner	21.30.c.a.20.14	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.13	✓	76	1.1	even	1	trivial
21.30.c.a.20.14	yes	76	21.20	even	2	inner
21.30.c.a.20.63	yes	76	7.6	odd	2	inner
21.30.c.a.20.64	yes	76	3.2	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)

\(f(q)\)	\(=\)	\(q-42628.6i q^{2} +(-4.19005e6 + 7.14660e6i) q^{3} -1.28033e9 q^{4} -1.62384e10 q^{5} +(3.04650e11 + 1.78616e11i) q^{6} +(1.66265e12 + 6.74901e11i) q^{7} +3.16925e13i q^{8} +(-3.35174e13 - 5.98892e13i) q^{9} +O(q^{10})\)	\(q-42628.6i q^{2} +(-4.19005e6 + 7.14660e6i) q^{3} -1.28033e9 q^{4} -1.62384e10 q^{5} +(3.04650e11 + 1.78616e11i) q^{6} +(1.66265e12 + 6.74901e11i) q^{7} +3.16925e13i q^{8} +(-3.35174e13 - 5.98892e13i) q^{9} +6.92219e14i q^{10} +1.89246e15i q^{11} +(5.36463e15 - 9.14999e15i) q^{12} -1.67013e16i q^{13} +(2.87701e16 - 7.08766e16i) q^{14} +(6.80395e16 - 1.16049e17i) q^{15} +6.63637e17 q^{16} +1.70898e17 q^{17} +(-2.55299e18 + 1.42880e18i) q^{18} -2.87863e18i q^{19} +2.07904e19 q^{20} +(-1.17898e19 + 9.05445e18i) q^{21} +8.06728e19 q^{22} -8.58865e18i q^{23} +(-2.26494e20 - 1.32793e20i) q^{24} +7.74198e19 q^{25} -7.11953e20 q^{26} +(5.68443e20 + 1.14028e19i) q^{27} +(-2.12874e21 - 8.64094e20i) q^{28} +1.33896e21i q^{29} +(-4.94701e21 - 2.90043e21i) q^{30} -8.21487e21i q^{31} -1.12751e22i q^{32} +(-1.35246e22 - 7.92948e21i) q^{33} -7.28513e21i q^{34} +(-2.69988e22 - 1.09593e22i) q^{35} +(4.29133e22 + 7.66777e22i) q^{36} -6.15011e22 q^{37} -1.22712e23 q^{38} +(1.19358e23 + 6.99792e22i) q^{39} -5.14634e23i q^{40} -2.49794e21 q^{41} +(3.85979e23 + 5.02584e23i) q^{42} +8.52749e23 q^{43} -2.42296e24i q^{44} +(5.44268e23 + 9.72502e23i) q^{45} -3.66122e23 q^{46} -2.18694e24 q^{47} +(-2.78067e24 + 4.74275e24i) q^{48} +(2.30892e24 + 2.24425e24i) q^{49} -3.30030e24i q^{50} +(-7.16069e23 + 1.22134e24i) q^{51} +2.13831e25i q^{52} -1.34081e25i q^{53} +(4.86084e23 - 2.42320e25i) q^{54} -3.07304e25i q^{55} +(-2.13893e25 + 5.26936e25i) q^{56} +(2.05724e25 + 1.20616e25i) q^{57} +5.70780e25 q^{58} -2.12081e25 q^{59} +(-8.71128e25 + 1.48581e26i) q^{60} +5.23975e25i q^{61} -3.50188e26 q^{62} +(-1.53086e25 - 1.22196e26i) q^{63} -1.24356e26 q^{64} +2.71202e26i q^{65} +(-3.38023e26 + 5.76536e26i) q^{66} +1.73869e26 q^{67} -2.18805e26 q^{68} +(6.13796e25 + 3.59868e25i) q^{69} +(-4.67179e26 + 1.15092e27i) q^{70} -1.36215e26i q^{71} +(1.89804e27 - 1.06225e27i) q^{72} -1.03806e27i q^{73} +2.62171e27i q^{74} +(-3.24393e26 + 5.53288e26i) q^{75} +3.68558e27i q^{76} +(-1.27722e27 + 3.14650e27i) q^{77} +(2.98312e27 - 5.08804e27i) q^{78} +1.92827e27 q^{79} -1.07764e28 q^{80} +(-2.46329e27 + 4.01466e27i) q^{81} +1.06484e26i q^{82} +5.55458e27 q^{83} +(1.50949e28 - 1.15927e28i) q^{84} -2.77510e27 q^{85} -3.63515e28i q^{86} +(-9.56902e27 - 5.61031e27i) q^{87} -5.99767e28 q^{88} -3.90521e26 q^{89} +(4.14564e28 - 2.32014e28i) q^{90} +(1.12717e28 - 2.77685e28i) q^{91} +1.09963e28i q^{92} +(5.87084e28 + 3.44207e28i) q^{93} +9.32264e28i q^{94} +4.67442e28i q^{95} +(8.05790e28 + 4.72434e28i) q^{96} -2.98614e28i q^{97} +(9.56693e28 - 9.84262e28i) q^{98} +(1.13338e29 - 6.34302e28i) 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

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