LMFDB - Embedded newform 21.30.c.a.20.7

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			20.7
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21897.4i q^{2} +(-3.41396e6 + 7.54819e6i) q^{3} +5.73727e7 q^{4} -2.19660e10 q^{5} +(1.65286e11 + 7.47571e10i) q^{6} +(7.76630e11 - 1.61764e12i) q^{7} -1.30124e13i q^{8} +(-4.53201e13 - 5.15385e13i) q^{9} +O(q^{10})$	\(q-21897.4i q^{2} +(-3.41396e6 + 7.54819e6i) q^{3} +5.73727e7 q^{4} -2.19660e10 q^{5} +(1.65286e11 + 7.47571e10i) q^{6} +(7.76630e11 - 1.61764e12i) q^{7} -1.30124e13i q^{8} +(-4.53201e13 - 5.15385e13i) q^{9} +4.81000e14i q^{10} -2.40340e15i q^{11} +(-1.95868e14 + 4.33060e14i) q^{12} +1.13407e16i q^{13} +(-3.54221e16 - 1.70062e16i) q^{14} +(7.49912e16 - 1.65804e17i) q^{15} -2.54137e17 q^{16} -2.64385e17 q^{17} +(-1.12856e18 + 9.92395e17i) q^{18} -3.62583e18i q^{19} -1.26025e18 q^{20} +(9.55886e18 + 1.13847e19i) q^{21} -5.26284e19 q^{22} -1.89636e19i q^{23} +(9.82203e19 + 4.44239e19i) q^{24} +2.96242e20 q^{25} +2.48332e20 q^{26} +(5.43744e20 - 1.66134e20i) q^{27} +(4.45574e19 - 9.28082e19i) q^{28} -1.75722e21i q^{29} +(-3.63068e21 - 1.64212e21i) q^{30} -5.25929e21i q^{31} -1.42104e21i q^{32} +(1.81414e22 + 8.20513e21i) q^{33} +5.78936e21i q^{34} +(-1.70595e22 + 3.55331e22i) q^{35} +(-2.60014e21 - 2.95690e21i) q^{36} +7.21764e22 q^{37} -7.93963e22 q^{38} +(-8.56016e22 - 3.87166e22i) q^{39} +2.85831e23i q^{40} -6.20335e22 q^{41} +(2.49296e23 - 2.09315e23i) q^{42} +4.32096e23 q^{43} -1.37890e23i q^{44} +(9.95503e23 + 1.13210e24i) q^{45} -4.15254e23 q^{46} +2.59257e24 q^{47} +(8.67614e23 - 1.91828e24i) q^{48} +(-2.01360e24 - 2.51261e24i) q^{49} -6.48695e24i q^{50} +(9.02602e23 - 1.99563e24i) q^{51} +6.50645e23i q^{52} +2.18705e24i q^{53} +(-3.63792e24 - 1.19066e25i) q^{54} +5.27933e25i q^{55} +(-2.10494e25 - 1.01058e25i) q^{56} +(2.73684e25 + 1.23784e25i) q^{57} -3.84786e25 q^{58} -3.87703e25 q^{59} +(4.30245e24 - 9.51262e24i) q^{60} -1.06739e26i q^{61} -1.15165e26 q^{62} +(-1.18568e26 + 3.32852e25i) q^{63} -1.67556e26 q^{64} -2.49110e26i q^{65} +(1.79671e26 - 3.97249e26i) q^{66} -3.98782e26 q^{67} -1.51685e25 q^{68} +(1.43141e26 + 6.47410e25i) q^{69} +(7.78084e26 + 3.73559e26i) q^{70} -9.94824e26i q^{71} +(-6.70640e26 + 5.89724e26i) q^{72} -8.49053e25i q^{73} -1.58048e27i q^{74} +(-1.01136e27 + 2.23610e27i) q^{75} -2.08023e26i q^{76} +(-3.88784e27 - 1.86656e27i) q^{77} +(-8.47796e26 + 1.87446e27i) q^{78} +1.57874e27 q^{79} +5.58238e27 q^{80} +(-6.02305e26 + 4.67146e27i) q^{81} +1.35838e27i q^{82} +3.67441e27 q^{83} +(5.48417e26 + 6.53171e26i) q^{84} +5.80750e27 q^{85} -9.46180e27i q^{86} +(1.32638e28 + 5.99908e27i) q^{87} -3.12741e28 q^{88} -2.12846e28 q^{89} +(2.47900e28 - 2.17990e28i) q^{90} +(1.83451e28 + 8.80751e27i) q^{91} -1.08799e27i q^{92} +(3.96981e28 + 1.79550e28i) q^{93} -5.67706e28i q^{94} +7.96450e28i q^{95} +(1.07263e28 + 4.85136e27i) q^{96} +7.01706e28i q^{97} +(-5.50198e28 + 4.40926e28i) q^{98} +(-1.23868e29 + 1.08923e29i) 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 $

$2$		−	21897.4i		−	0.945058i	−0.881315	−	0.472529i	$-0.843341\pi$
$2$		−	21897.4i		−	0.945058i	0.881315	−	0.472529i	$-0.156659\pi$
$3$	−3.41396e6	+	7.54819e6i	−0.412098	+	0.911140i
$3$	−3.41396e6	+	7.54819e6i	−0.412098	+	0.911140i
$4$	5.73727e7			0.106865
$5$	−2.19660e10			−1.60948			−0.804742	−	0.593625i	$-0.797696\pi$
$5$	−2.19660e10			−1.60948			−0.804742	+	0.593625i	$0.797696\pi$
$6$	1.65286e11	+	7.47571e10i	0.861080	+	0.389457i
$7$	7.76630e11	−	1.61764e12i	0.432805	−	0.901487i
$7$	7.76630e11	−	1.61764e12i	0.432805	−	0.901487i
$8$		−	1.30124e13i		−	1.04605i
$9$	−4.53201e13	−	5.15385e13i	−0.660351	−	0.750958i
$10$			4.81000e14i			1.52106i
$11$		−	2.40340e15i		−	1.90824i	−0.299426	−	0.954120i	$-0.596795\pi$
$11$		−	2.40340e15i		−	1.90824i	0.299426	−	0.954120i	$-0.403205\pi$
$12$	−1.95868e14	+	4.33060e14i	−0.0440388	+	0.0973689i
$13$			1.13407e16i			0.798841i	0.916768	+	0.399421i	$0.130789\pi$
$13$			1.13407e16i			0.798841i	−0.916768	+	0.399421i	$0.869211\pi$
$14$	−3.54221e16	−	1.70062e16i	−0.851958	−	0.409026i
$15$	7.49912e16	−	1.65804e17i	0.663265	−	1.46646i
$16$	−2.54137e17			−0.881715
$17$	−2.64385e17			−0.380827			−0.190414	−	0.981704i	$-0.560983\pi$
$17$	−2.64385e17			−0.380827			−0.190414	+	0.981704i	$0.560983\pi$
$18$	−1.12856e18	+	9.92395e17i	−0.709699	+	0.624070i
$19$		−	3.62583e18i		−	1.04107i	−0.853840	−	0.520535i	$-0.825733\pi$
$19$		−	3.62583e18i		−	1.04107i	0.853840	−	0.520535i	$-0.174267\pi$
$20$	−1.26025e18			−0.171997
$21$	9.55886e18	+	1.13847e19i	0.643023	+	0.765847i
$22$	−5.26284e19			−1.80340
$23$		−	1.89636e19i		−	0.341089i	−0.985350	−	0.170544i	$-0.945447\pi$
$23$		−	1.89636e19i		−	0.341089i	0.985350	−	0.170544i	$-0.0545526\pi$
$24$	9.82203e19	+	4.44239e19i	0.953099	+	0.431076i
$25$	2.96242e20			1.59044
$26$	2.48332e20			0.754951
$27$	5.43744e20	−	1.66134e20i	0.956356	−	0.292203i
$28$	4.45574e19	−	9.28082e19i	0.0462517	−	0.0963374i
$29$		−	1.75722e21i		−	1.09662i	−0.836276	−	0.548309i	$-0.815272\pi$
$29$		−	1.75722e21i		−	1.09662i	0.836276	−	0.548309i	$-0.184728\pi$
$30$	−3.63068e21	−	1.64212e21i	−1.38589	−	0.626824i
$31$		−	5.25929e21i		−	1.24791i	−0.781462	−	0.623953i	$-0.785525\pi$
$31$		−	5.25929e21i		−	1.24791i	0.781462	−	0.623953i	$-0.214475\pi$
$32$		−	1.42104e21i		−	0.212780i
$33$	1.81414e22	+	8.20513e21i	1.73867	+	0.786381i
$34$			5.78936e21i			0.359904i
$35$	−1.70595e22	+	3.55331e22i	−0.696593	+	1.45093i
$36$	−2.60014e21	−	2.95690e21i	−0.0705683	−	0.0802510i
$37$	7.21764e22			1.31665			0.658325	−	0.752734i	$-0.271265\pi$
$37$	7.21764e22			1.31665			0.658325	+	0.752734i	$0.271265\pi$
$38$	−7.93963e22			−0.983871
$39$	−8.56016e22	−	3.87166e22i	−0.727856	−	0.329201i
$40$			2.85831e23i			1.68360i
$41$	−6.20335e22			−0.255423			−0.127712	−	0.991811i	$-0.540763\pi$
$41$	−6.20335e22			−0.255423			−0.127712	+	0.991811i	$0.540763\pi$
$42$	2.49296e23	−	2.09315e23i	0.723770	−	0.607694i
$43$	4.32096e23			0.891841			0.445921	−	0.895072i	$-0.352876\pi$
$43$	4.32096e23			0.891841			0.445921	+	0.895072i	$0.352876\pi$
$44$		−	1.37890e23i		−	0.203924i
$45$	9.95503e23	+	1.13210e24i	1.06282	+	1.20865i
$46$	−4.15254e23			−0.322349
$47$	2.59257e24			1.47337			0.736684	−	0.676237i	$-0.236391\pi$
$47$	2.59257e24			1.47337			0.736684	+	0.676237i	$0.236391\pi$
$48$	8.67614e23	−	1.91828e24i	0.363353	−	0.803365i
$49$	−2.01360e24	−	2.51261e24i	−0.625359	−	0.780337i
$50$		−	6.48695e24i		−	1.50306i
$51$	9.02602e23	−	1.99563e24i	0.156938	−	0.346987i
$52$			6.50645e23i			0.0853681i
$53$			2.18705e24i			0.217700i	0.994058	+	0.108850i	$0.0347168\pi$
$53$			2.18705e24i			0.217700i	−0.994058	+	0.108850i	$0.965283\pi$
$54$	−3.63792e24	−	1.19066e25i	−0.276149	−	0.903812i
$55$			5.27933e25i			3.07128i
$56$	−2.10494e25	−	1.01058e25i	−0.943003	−	0.452737i
$57$	2.73684e25	+	1.23784e25i	0.948560	+	0.429023i
$58$	−3.84786e25			−1.03637
$59$	−3.87703e25			−0.814975			−0.407488	−	0.913211i	$-0.633595\pi$
$59$	−3.87703e25			−0.814975			−0.407488	+	0.913211i	$0.633595\pi$
$60$	4.30245e24	−	9.51262e24i	0.0708798	−	0.156714i
$61$		−	1.06739e26i		−	1.38369i	−0.722044	−	0.691847i	$-0.756797\pi$
$61$		−	1.06739e26i		−	1.38369i	0.722044	−	0.691847i	$-0.243203\pi$
$62$	−1.15165e26			−1.17934
$63$	−1.18568e26	+	3.32852e25i	−0.962782	+	0.270279i
$64$	−1.67556e26			−1.08280
$65$		−	2.49110e26i		−	1.28572i
$66$	1.79671e26	−	3.97249e26i	0.743176	−	1.64315i
$67$	−3.98782e26			−1.32633			−0.663164	−	0.748474i	$-0.730787\pi$
$67$	−3.98782e26			−1.32633			−0.663164	+	0.748474i	$0.730787\pi$
$68$	−1.51685e25			−0.0406971
$69$	1.43141e26	+	6.47410e25i	0.310779	+	0.140562i
$70$	7.78084e26	+	3.73559e26i	1.37121	+	0.658321i
$71$		−	9.94824e26i		−	1.42725i	−0.700527	−	0.713625i	$-0.747052\pi$
$71$		−	9.94824e26i		−	1.42725i	0.700527	−	0.713625i	$-0.252948\pi$
$72$	−6.70640e26	+	5.89724e26i	−0.785540	+	0.690761i
$73$		−	8.49053e25i		−	0.0814242i	−0.999171	−	0.0407121i	$-0.987037\pi$
$73$		−	8.49053e25i		−	0.0814242i	0.999171	−	0.0407121i	$-0.0129626\pi$
$74$		−	1.58048e27i		−	1.24431i
$75$	−1.01136e27	+	2.23610e27i	−0.655417	+	1.44911i
$76$		−	2.08023e26i		−	0.111254i
$77$	−3.88784e27	−	1.86656e27i	−1.72025	−	0.825896i
$78$	−8.47796e26	+	1.87446e27i	−0.311114	+	0.687866i
$79$	1.57874e27			0.481635			0.240817	−	0.970570i	$-0.422585\pi$
$79$	1.57874e27			0.481635			0.240817	+	0.970570i	$0.422585\pi$
$80$	5.58238e27			1.41911
$81$	−6.02305e26	+	4.67146e27i	−0.127874	+	0.991790i
$82$			1.35838e27i			0.241390i
$83$	3.67441e27			0.547715			0.273858	−	0.961770i	$-0.411700\pi$
$83$	3.67441e27			0.547715			0.273858	+	0.961770i	$0.411700\pi$
$84$	5.48417e26	+	6.53171e26i	0.0687166	+	0.0818422i
$85$	5.80750e27			0.612935
$86$		−	9.46180e27i		−	0.842842i
$87$	1.32638e28	+	5.99908e27i	0.999172	+	0.451914i
$88$	−3.12741e28			−1.99612
$89$	−2.12846e28			−1.15321			−0.576607	−	0.817022i	$-0.695623\pi$
$89$	−2.12846e28			−1.15321			−0.576607	+	0.817022i	$0.695623\pi$
$90$	2.47900e28	−	2.17990e28i	1.14225	−	1.00443i
$91$	1.83451e28	+	8.80751e27i	0.720145	+	0.345743i
$92$		−	1.08799e27i		−	0.0364504i
$93$	3.96981e28	+	1.79550e28i	1.13702	+	0.514260i
$94$		−	5.67706e28i		−	1.39242i
$95$			7.96450e28i			1.67558i
$96$	1.07263e28	+	4.85136e27i	0.193872	+	0.0876862i
$97$			7.01706e28i			1.09135i	0.837996	+	0.545676i	$0.183727\pi$
$97$			7.01706e28i			1.09135i	−0.837996	+	0.545676i	$0.816273\pi$
$98$	−5.50198e28	+	4.40926e28i	−0.737464	+	0.591001i
$99$	−1.23868e29	+	1.08923e29i	−1.43301	+	1.26011i
$100$	1.69962e28			0.169962
$101$	−5.37882e28			−0.465615			−0.232808	−	0.972523i	$-0.574791\pi$
$101$	−5.37882e28			−0.465615			−0.232808	+	0.972523i	$0.574791\pi$
$102$	−4.36993e28	−	1.97647e28i	−0.327923	−	0.148316i
$103$		−	1.26950e27i		−	0.00826978i	−0.999991	−	0.00413489i	$-0.998684\pi$
$103$		−	1.26950e27i		−	0.00826978i	0.999991	−	0.00413489i	$-0.00131618\pi$
$104$	1.47570e29			0.835629
$105$	−2.09970e29	−	2.50077e29i	−1.03493	−	1.23262i
$106$	4.78908e28			0.205739
$107$			3.07470e28i			0.115276i	0.998338	+	0.0576379i	$0.0183569\pi$
$107$			3.07470e28i			0.115276i	−0.998338	+	0.0576379i	$0.981643\pi$
$108$	3.11960e28	−	9.53158e27i	0.102201	−	0.0312263i
$109$	−4.56998e29			−1.30988			−0.654938	−	0.755683i	$-0.727305\pi$
$109$	−4.56998e29			−1.30988			−0.654938	+	0.755683i	$0.727305\pi$
$110$	1.15604e30			2.90254
$111$	−2.46407e29	+	5.44801e29i	−0.542589	+	1.19965i
$112$	−1.97370e29	+	4.11102e29i	−0.381611	+	0.794855i
$113$			3.63848e29i			0.618418i	0.950994	+	0.309209i	$0.100064\pi$
$113$			3.63848e29i			0.618418i	−0.950994	+	0.309209i	$0.899936\pi$
$114$	2.71056e29	−	5.99299e29i	0.405451	−	0.896444i
$115$			4.16555e29i			0.548977i
$116$		−	1.00816e29i		−	0.117190i
$117$	5.84482e29	−	5.13961e29i	0.599896	−	0.527515i
$118$			8.48970e29i			0.770199i
$119$	−2.05330e29	+	4.27680e29i	−0.164824	+	0.343311i
$120$	−2.15751e30	−	9.75817e29i	−1.53400	−	0.693810i
$121$	−4.19004e30			−2.64138
$122$	−2.33731e30			−1.30767
$123$	2.11780e29	−	4.68241e29i	0.105259	−	0.232726i
$124$		−	3.01739e29i		−	0.133358i
$125$	−2.41578e30			−0.950302
$126$	7.28860e29	+	2.59633e30i	0.255430	+	0.909885i
$127$	4.56878e30			1.42773			0.713865	−	0.700283i	$-0.246943\pi$
$127$	4.56878e30			1.42773			0.713865	+	0.700283i	$0.246943\pi$
$128$			2.90613e30i			0.810533i
$129$	−1.47516e30	+	3.26154e30i	−0.367526	+	0.812592i
$130$	−5.45487e30			−1.21508
$131$	3.50396e30			0.698433			0.349217	−	0.937042i	$-0.386448\pi$
$131$	3.50396e30			0.698433			0.349217	+	0.937042i	$0.386448\pi$
$132$	1.04082e30	+	4.70750e29i	0.185803	+	0.0840366i
$133$	−5.86527e30	−	2.81593e30i	−0.938511	−	0.450580i
$134$			8.73231e30i			1.25346i
$135$	−1.19439e31	+	3.64932e30i	−1.53924	+	0.470297i
$136$			3.44029e30i			0.398365i
$137$		−	7.58548e30i		−	0.789832i	−0.918717	−	0.394916i	$-0.870774\pi$
$137$		−	7.58548e30i		−	0.789832i	0.918717	−	0.394916i	$-0.129226\pi$
$138$	1.41766e30	−	3.13442e30i	0.132839	−	0.293705i
$139$		−	2.33968e30i		−	0.197443i	−0.995115	−	0.0987214i	$-0.968525\pi$
$139$		−	2.33968e30i		−	0.197443i	0.995115	−	0.0987214i	$-0.0314753\pi$
$140$	−9.78749e29	+	2.03863e30i	−0.0744414	+	0.155054i
$141$	−8.85093e30	+	1.95692e31i	−0.607172	+	1.34244i
$142$	−2.17841e31			−1.34884
$143$	2.72562e31			1.52438
$144$	1.15175e31	+	1.30978e31i	0.582241	+	0.662130i
$145$			3.85992e31i			1.76499i
$146$	−1.85921e30			−0.0769506
$147$	2.58400e31	−	6.62106e30i	0.968705	−	0.248214i
$148$	4.14095e30			0.140704
$149$		−	1.50710e31i		−	0.464452i	−0.972662	−	0.232226i	$-0.925399\pi$
$149$		−	1.50710e31i		−	0.464452i	0.972662	−	0.232226i	$-0.0746009\pi$
$150$	4.89648e31	+	2.21462e31i	1.36950	+	0.619407i
$151$	−2.61445e31			−0.664070			−0.332035	−	0.943267i	$-0.607735\pi$
$151$	−2.61445e31			−0.664070			−0.332035	+	0.943267i	$0.607735\pi$
$152$	−4.71808e31			−1.08901
$153$	1.19820e31	+	1.36260e31i	0.251479	+	0.285985i
$154$	−4.08728e31	+	8.51337e31i	−0.780520	+	1.62574i
$155$			1.15526e32i			2.00849i
$156$	−4.91120e30	−	2.22128e30i	−0.0777823	−	0.0351800i
$157$		−	1.20234e32i		−	1.73573i	−0.496796	−	0.867867i	$-0.665490\pi$
$157$		−	1.20234e32i		−	1.73573i	0.496796	−	0.867867i	$-0.334510\pi$
$158$		−	3.45704e31i		−	0.455173i
$159$	−1.65083e31	−	7.46650e30i	−0.198355	−	0.0897137i
$160$			3.12145e31i			0.342466i
$161$	−3.06762e31	−	1.47277e31i	−0.307487	−	0.147625i
$162$	1.02293e32	+	1.31889e31i	0.937300	+	0.120849i
$163$	2.51953e31			0.211154			0.105577	−	0.994411i	$-0.466331\pi$
$163$	2.51953e31			0.211154			0.105577	+	0.994411i	$0.466331\pi$
$164$	−3.55903e30			−0.0272958
$165$	−3.98494e32	−	1.80234e32i	−2.79837	−	1.26567i
$166$		−	8.04602e31i		−	0.517623i
$167$	−4.27606e31			−0.252148			−0.126074	−	0.992021i	$-0.540238\pi$
$167$	−4.27606e31			−0.252148			−0.126074	+	0.992021i	$0.540238\pi$
$168$	1.48143e32	−	1.24384e32i	0.801116	−	0.672635i
$169$	7.29271e31			0.361853
$170$		−	1.27169e32i		−	0.579260i
$171$	−1.86870e32	+	1.64323e32i	−0.781799	+	0.687471i
$172$	2.47905e31			0.0953066
$173$	−2.31530e32			−0.818350			−0.409175	−	0.912456i	$-0.634183\pi$
$173$	−2.31530e32			−0.818350			−0.409175	+	0.912456i	$0.634183\pi$
$174$	1.31365e32	−	2.90444e32i	0.427085	−	0.944275i
$175$	2.30071e32	−	4.79213e32i	0.688351	−	1.43376i
$176$			6.10794e32i			1.68252i
$177$	1.32360e32	−	2.92645e32i	0.335850	−	0.742556i
$178$			4.66078e32i			1.08985i
$179$		−	1.69293e32i		−	0.364982i	−0.983208	−	0.182491i	$-0.941584\pi$
$179$		−	1.69293e32i		−	0.364982i	0.983208	−	0.182491i	$-0.0584160\pi$
$180$	5.71147e31	+	6.49514e31i	0.113579	+	0.129163i
$181$		−	2.15005e32i		−	0.394557i	−0.980347	−	0.197279i	$-0.936790\pi$
$181$		−	2.15005e32i		−	0.394557i	0.980347	−	0.197279i	$-0.0632104\pi$
$182$	1.92862e32	−	4.01711e32i	0.326747	−	0.680579i
$183$	8.05685e32	+	3.64402e32i	1.26074	+	0.570217i
$184$	−2.46762e32			−0.356796
$185$	−1.58543e33			−2.11913
$186$	3.93169e32	−	8.69287e32i	0.486006	−	1.07455i
$187$			6.35425e32i			0.726709i
$188$	1.48743e32			0.157451
$189$	1.53542e32	−	1.00861e33i	0.150498	−	0.988610i
$190$	1.74402e33			1.58353
$191$			2.23371e32i			0.187950i	0.995575	+	0.0939750i	$0.0299574\pi$
$191$			2.23371e32i			0.187950i	−0.995575	+	0.0939750i	$0.970043\pi$
$192$	5.72029e32	−	1.26474e33i	0.446221	−	0.986586i
$193$	1.36259e33			0.985793			0.492897	−	0.870088i	$-0.335938\pi$
$193$	1.36259e33			0.985793			0.492897	+	0.870088i	$0.335938\pi$
$194$	1.53656e33			1.03139
$195$	1.88033e33	+	8.50451e32i	1.17147	+	0.529844i
$196$	−1.15525e32	−	1.44155e32i	−0.0668290	−	0.0833907i
$197$			3.00287e33i			1.61353i	0.590875	+	0.806763i	$0.298783\pi$
$197$			3.00287e33i			1.61353i	−0.590875	+	0.806763i	$0.701217\pi$
$198$	2.38512e33	+	2.71239e33i	1.19087	+	1.35427i
$199$		−	2.91566e33i		−	1.35322i	−0.736343	−	0.676608i	$-0.763449\pi$
$199$		−	2.91566e33i		−	1.35322i	0.736343	−	0.676608i	$-0.236551\pi$
$200$		−	3.85483e33i		−	1.66368i
$201$	1.36143e33	−	3.01008e33i	0.546577	−	1.20847i
$202$			1.17782e33i			0.440033i
$203$	−2.84255e33	−	1.36471e33i	−0.988587	−	0.474622i
$204$	5.17847e31	−	1.14495e32i	0.0167712	−	0.0370807i
$205$	1.36263e33			0.411100
$206$	−2.77989e31			−0.00781543
$207$	−9.77356e32	+	8.59432e32i	−0.256143	+	0.225238i
$208$		−	2.88209e33i		−	0.704350i
$209$	−8.71432e33			−1.98661
$210$	−5.47605e33	+	4.59781e33i	−1.16490	+	0.978074i
$211$	3.24786e33			0.644913			0.322457	−	0.946584i	$-0.395491\pi$
$211$	3.24786e33			0.644913			0.322457	+	0.946584i	$0.395491\pi$
$212$			1.25477e32i			0.0232645i
$213$	7.50913e33	+	3.39629e33i	1.30042	+	0.588167i
$214$	6.73281e32			0.108942
$215$	−9.49144e33			−1.43540
$216$	−2.16181e33	−	7.07542e33i	−0.305660	−	1.00040i
$217$	−8.50762e33	−	4.08452e33i	−1.12497	−	0.540101i
$218$			1.00071e34i			1.23791i
$219$	6.40882e32	+	2.89864e32i	0.0741888	+	0.0335547i
$220$			3.02889e33i			0.328212i
$221$		−	2.99831e33i		−	0.304221i
$222$	1.19298e34	+	5.39569e33i	1.13374	+	0.512778i
$223$			3.14572e33i			0.280091i	0.990145	+	0.140045i	$0.0447249\pi$
$223$			3.14572e33i			0.280091i	−0.990145	+	0.140045i	$0.955275\pi$
$224$	−2.29872e33	−	1.10362e33i	−0.191818	−	0.0920923i
$225$	−1.34257e34	−	1.52679e34i	−1.05025	−	1.19435i
$226$	7.96734e33			0.584441
$227$	1.49046e34			1.02552			0.512761	−	0.858531i	$-0.328623\pi$
$227$	1.49046e34			1.02552			0.512761	+	0.858531i	$0.328623\pi$
$228$	1.57020e33	+	7.10184e32i	0.101368	+	0.0458475i
$229$			1.96703e34i			1.19178i	0.803065	+	0.595891i	$0.203201\pi$
$229$			1.96703e34i			1.19178i	−0.803065	+	0.595891i	$0.796799\pi$
$230$	9.12150e33			0.518815
$231$	2.73620e34	−	2.29738e34i	1.46142	−	1.22704i
$232$	−2.28657e34			−1.14712
$233$		−	1.34458e34i		−	0.633763i	−0.948465	−	0.316882i	$-0.897364\pi$
$233$		−	1.34458e34i		−	0.633763i	0.948465	−	0.316882i	$-0.102636\pi$
$234$	−1.12544e34	−	1.27987e34i	−0.498533	−	0.566936i
$235$	−5.69484e34			−2.37136
$236$	−2.22435e33			−0.0870923
$237$	−5.38976e33	+	1.19166e34i	−0.198481	+	0.438836i
$238$	9.36509e33	+	4.49619e33i	0.324449	+	0.155768i
$239$		−	5.26810e31i		−	0.00171745i	−1.00000		0.000858726i	$-0.999727\pi$
$239$		−	5.26810e31i		−	0.00171745i	1.00000		0.000858726i	$-0.000273341\pi$
$240$	−1.90580e34	+	4.21369e34i	−0.584811	+	1.29300i
$241$			2.27777e34i			0.658057i	0.944320	+	0.329028i	$0.106721\pi$
$241$			2.27777e34i			0.658057i	−0.944320	+	0.329028i	$0.893279\pi$
$242$			9.17512e34i			2.49625i
$243$	−3.32048e34	−	2.04945e34i	−0.850963	−	0.525226i
$244$		−	6.12389e33i		−	0.147868i
$245$	4.42308e34	+	5.51921e34i	1.00651	+	1.25594i
$246$	−1.02533e34	−	4.63744e33i	−0.219940	−	0.0994763i
$247$	4.11193e34			0.831649
$248$	−6.84360e34			−1.30538
$249$	−1.25443e34	+	2.77351e34i	−0.225712	+	0.499045i
$250$			5.28994e34i			0.898091i
$251$	3.42737e34			0.549151			0.274575	−	0.961566i	$-0.411463\pi$
$251$	3.42737e34			0.549151			0.274575	+	0.961566i	$0.411463\pi$
$252$	−6.80254e33	+	1.90966e33i	−0.102888	+	0.0288834i
$253$	−4.55772e34			−0.650879
$254$		−	1.00045e35i		−	1.34929i
$255$	−1.98266e34	+	4.38361e34i	−0.252589	+	0.558470i
$256$	−2.63190e34			−0.316803
$257$	5.24054e34			0.596137			0.298068	−	0.954545i	$-0.403658\pi$
$257$	5.24054e34			0.596137			0.298068	+	0.954545i	$0.403658\pi$
$258$	7.14195e34	+	3.23022e34i	0.767947	+	0.347333i
$259$	5.60544e34	−	1.16755e35i	0.569853	−	1.18694i
$260$		−	1.42921e34i		−	0.137399i
$261$	−9.05645e34	+	7.96374e34i	−0.823513	+	0.724152i
$262$		−	7.67277e34i		−	0.660060i
$263$			3.50044e34i			0.284947i	0.989799	+	0.142474i	$0.0455056\pi$
$263$			3.50044e34i			0.284947i	−0.989799	+	0.142474i	$0.954494\pi$
$264$	1.06769e35	−	2.36063e35i	0.822596	−	1.81874i
$265$		−	4.80408e34i		−	0.350385i
$266$	−6.16616e34	+	1.28434e35i	−0.425825	+	0.886948i
$267$	7.26647e34	−	1.60660e35i	0.475237	−	1.05074i
$268$	−2.28792e34			−0.141738
$269$	−3.67604e34			−0.215761			−0.107880	−	0.994164i	$-0.534406\pi$
$269$	−3.67604e34			−0.215761			−0.107880	+	0.994164i	$0.534406\pi$
$270$	7.99107e34	+	2.61541e35i	0.444458	+	1.45467i
$271$			3.33205e35i			1.75653i	0.478171	+	0.878267i	$0.341300\pi$
$271$			3.33205e35i			1.75653i	−0.478171	+	0.878267i	$0.658700\pi$
$272$	6.71901e34			0.335781
$273$	−1.29110e35	+	1.08404e35i	−0.611790	+	0.513673i
$274$	−1.66103e35			−0.746437
$275$		−	7.11990e35i		−	3.03494i
$276$	8.21238e33	+	3.71437e33i	0.0332114	+	0.0150211i
$277$	3.53976e35			1.35837			0.679183	−	0.733969i	$-0.262334\pi$
$277$	3.53976e35			1.35837			0.679183	+	0.733969i	$0.262334\pi$
$278$	−5.12330e34			−0.186595
$279$	−2.71056e35	+	2.38351e35i	−0.937125	+	0.824056i
$280$	4.62371e35	+	2.21985e35i	1.51775	+	0.728673i
$281$		−	3.54541e35i		−	1.10516i	−0.833460	−	0.552579i	$-0.813644\pi$
$281$		−	3.54541e35i		−	1.10516i	0.833460	−	0.552579i	$-0.186356\pi$
$282$	4.28516e35	+	1.93813e35i	1.26869	+	0.573813i
$283$			4.63712e34i			0.130420i	0.997872	+	0.0652101i	$0.0207717\pi$
$283$			4.63712e34i			0.130420i	−0.997872	+	0.0652101i	$0.979228\pi$
$284$		−	5.70757e34i		−	0.152523i
$285$	−6.01176e35	−	2.71905e35i	−1.52669	−	0.690505i
$286$		−	5.96842e35i		−	1.44063i
$287$	−4.81771e34	+	1.00348e35i	−0.110549	+	0.230261i
$288$	−7.32381e34	+	6.44015e34i	−0.159789	+	0.140509i
$289$	−4.12069e35			−0.854971
$290$	8.45223e35			1.66802
$291$	−5.29662e35	−	2.39560e35i	−0.994375	−	0.449744i
$292$		−	4.87125e33i		−	0.00870139i
$293$	3.34930e35			0.569342			0.284671	−	0.958625i	$-0.408116\pi$
$293$	3.34930e35			0.569342			0.284671	+	0.958625i	$0.408116\pi$
$294$	−1.44984e35	−	5.65831e35i	−0.234577	−	0.915483i
$295$	8.51629e35			1.31169
$296$		−	9.39189e35i		−	1.37728i
$297$	−3.99288e35	−	1.30684e36i	−0.557594	−	1.82496i
$298$	−3.30016e35			−0.438934
$299$	2.15060e35			0.272476
$300$	−5.80244e34	+	1.28291e35i	−0.0700411	+	0.154859i
$301$	3.35579e35	−	6.98975e35i	0.385994	−	0.803984i
$302$			5.72497e35i			0.627585i
$303$	1.83631e35	−	4.06004e35i	0.191879	−	0.424240i
$304$			9.21457e35i			0.917927i
$305$			2.34463e36i			2.22703i
$306$	2.98375e35	−	2.62375e35i	0.270273	−	0.237663i
$307$		−	8.52543e34i		−	0.0736563i	−0.999322	−	0.0368281i	$-0.988275\pi$
$307$		−	8.52543e34i		−	0.0736563i	0.999322	−	0.0368281i	$-0.0117254\pi$
$308$	−2.23056e35	−	1.07089e35i	−0.183835	−	0.0882593i
$309$	9.58246e33	+	4.33404e33i	0.00753493	+	0.00340796i
$310$	2.52972e36			1.89814
$311$	−8.00785e35			−0.573443			−0.286722	−	0.958014i	$-0.592565\pi$
$311$	−8.00785e35			−0.573443			−0.286722	+	0.958014i	$0.592565\pi$
$312$	−5.03797e35	+	1.11388e36i	−0.344361	+	0.761375i
$313$			3.66167e35i			0.238938i	0.992838	+	0.119469i	$0.0381193\pi$
$313$			3.66167e35i			0.238938i	−0.992838	+	0.119469i	$0.961881\pi$
$314$	−2.63282e36			−1.64037
$315$	2.60446e36	−	7.31143e35i	1.54958	−	0.435010i
$316$	9.05765e34			0.0514699
$317$			1.30822e36i			0.710102i	0.934847	+	0.355051i	$0.115537\pi$
$317$			1.30822e36i			0.710102i	−0.934847	+	0.355051i	$0.884463\pi$
$318$	−1.63497e35	+	3.61489e35i	−0.0847847	+	0.187457i
$319$	−4.22331e36			−2.09261
$320$	3.68054e36			1.74276
$321$	−2.32084e35	−	1.04969e35i	−0.105032	−	0.0475049i
$322$	−3.22499e35	+	6.71731e35i	−0.139514	+	0.290593i
$323$			9.58615e35i			0.396468i
$324$	−3.45559e34	+	2.68014e35i	−0.0136653	+	0.105988i
$325$			3.35959e36i			1.27051i
$326$		−	5.51712e35i		−	0.199553i
$327$	1.56017e36	−	3.44951e36i	0.539797	−	1.19348i
$328$			8.07206e35i			0.267186i
$329$	2.01347e36	−	4.19383e36i	0.637681	−	1.32822i
$330$	−3.94667e36	+	8.72600e36i	−1.19613	+	2.64462i
$331$	4.26098e36			1.23596			0.617978	−	0.786195i	$-0.287952\pi$
$331$	4.26098e36			1.23596			0.617978	+	0.786195i	$0.287952\pi$
$332$	2.10811e35			0.0585316
$333$	−3.27104e36	−	3.71986e36i	−0.869450	−	0.988748i
$334$			9.36348e35i			0.238294i
$335$	8.75966e36			2.13470
$336$	−2.42926e36	−	2.89328e36i	−0.566963	−	0.675259i
$337$	−1.86913e36			−0.417835			−0.208918	−	0.977933i	$-0.566994\pi$
$337$	−1.86913e36			−0.417835			−0.208918	+	0.977933i	$0.566994\pi$
$338$		−	1.59692e36i		−	0.341972i
$339$	−2.74639e36	−	1.24216e36i	−0.563466	−	0.254849i
$340$	3.33192e35			0.0655013
$341$	−1.26402e37			−2.38130
$342$	3.59825e36	+	4.09197e36i	0.649700	+	0.738846i
$343$	−5.62832e36	+	1.30590e36i	−0.974123	+	0.226019i
$344$		−	5.62261e36i		−	0.932912i
$345$	−3.14424e36	−	1.42210e36i	−0.500194	−	0.226232i
$346$			5.06992e36i			0.773388i
$347$			9.08226e36i			1.32867i	0.747436	+	0.664334i	$0.231285\pi$
$347$			9.08226e36i			1.32867i	−0.747436	+	0.664334i	$0.768715\pi$
$348$	7.60982e35	+	3.44183e35i	0.106776	+	0.0482938i
$349$		−	3.64732e36i		−	0.490914i	−0.969407	−	0.245457i	$-0.921062\pi$
$349$		−	3.64732e36i		−	0.490914i	0.969407	−	0.245457i	$-0.0789381\pi$
$350$	−1.04935e37	−	5.03796e36i	−1.35499	−	0.650531i
$351$	1.88408e36	+	6.16642e36i	0.233424	+	0.763977i
$352$	−3.41532e36			−0.406035
$353$	−1.22050e37			−1.39253			−0.696263	−	0.717787i	$-0.745155\pi$
$353$	−1.22050e37			−1.39253			−0.696263	+	0.717787i	$0.745155\pi$
$354$	−6.40819e36	−	2.89835e36i	−0.701759	−	0.317398i
$355$			2.18523e37i			2.29714i
$356$	−1.22115e36			−0.123238
$357$	−2.52722e36	−	3.00995e36i	−0.244881	−	0.291655i
$358$	−3.70709e36			−0.344929
$359$			1.78777e37i			1.59751i	0.601657	+	0.798754i	$0.294507\pi$
$359$			1.78777e37i			1.59751i	−0.601657	+	0.798754i	$0.705493\pi$
$360$	1.47313e37	−	1.29539e37i	1.26431	−	1.11177i
$361$	−1.01679e36			−0.0838257
$362$	−4.70807e36			−0.372880
$363$	1.43046e37	−	3.16272e37i	1.08851	−	2.40666i
$364$	1.05251e36	+	5.05311e35i	0.0769583	+	0.0369478i
$365$			1.86503e36i			0.131051i
$366$	7.97948e36	−	1.76425e37i	0.538888	−	1.19147i
$367$		−	5.42324e36i		−	0.352047i	−0.984386	−	0.176024i	$-0.943676\pi$
$367$		−	5.42324e36i		−	0.352047i	0.984386	−	0.176024i	$-0.0563235\pi$
$368$			4.81935e36i			0.300743i
$369$	2.81137e36	+	3.19712e36i	0.168669	+	0.191812i
$370$			3.47169e37i			2.00270i
$371$	3.53785e36	+	1.69853e36i	0.196254	+	0.0942217i
$372$	2.27759e36	+	1.03013e36i	0.121507	+	0.0549564i
$373$	−3.01156e36			−0.154530			−0.0772651	−	0.997011i	$-0.524619\pi$
$373$	−3.01156e36			−0.154530			−0.0772651	+	0.997011i	$0.524619\pi$
$374$	1.39142e37			0.686783
$375$	8.24737e36	−	1.82348e37i	0.391618	−	0.865858i
$376$		−	3.37356e37i		−	1.54122i
$377$	1.99281e37			0.876023
$378$	−2.20859e37	−	3.36219e36i	−0.934294	−	0.142230i
$379$	4.09990e37			1.66919			0.834594	−	0.550866i	$-0.185702\pi$
$379$	4.09990e37			1.66919			0.834594	+	0.550866i	$0.185702\pi$
$380$			4.56945e36i			0.179061i
$381$	−1.55976e37	+	3.44860e37i	−0.588365	+	1.30086i
$382$	4.89125e36			0.177624
$383$	3.77532e37			1.31999			0.659996	−	0.751269i	$-0.270558\pi$
$383$	3.77532e37			1.31999			0.659996	+	0.751269i	$0.270558\pi$
$384$	−2.19361e37	−	9.92143e36i	−0.738509	−	0.334019i
$385$	8.54004e37	+	4.10008e37i	2.76872	+	1.32927i
$386$		−	2.98374e37i		−	0.931632i
$387$	−1.95826e37	−	2.22696e37i	−0.588928	−	0.669735i
$388$			4.02588e36i			0.116627i
$389$			5.53900e37i			1.54583i	0.634509	+	0.772915i	$0.281202\pi$
$389$			5.53900e37i			1.54583i	−0.634509	+	0.772915i	$0.718798\pi$
$390$	1.86227e37	−	4.11744e37i	0.500733	−	1.10711i
$391$			5.01370e36i			0.129896i
$392$	−3.26952e37	+	2.62018e37i	−0.816273	+	0.654158i
$393$	−1.19624e37	+	2.64485e37i	−0.287823	+	0.636370i
$394$	6.57552e37			1.52488
$395$	−3.46787e37			−0.775183
$396$	−7.10663e36	+	6.24918e36i	−0.153138	+	0.134661i
$397$		−	5.20498e37i		−	1.08133i	−0.841239	−	0.540663i	$-0.818173\pi$
$397$		−	5.20498e37i		−	1.08133i	0.841239	−	0.540663i	$-0.181827\pi$
$398$	−6.38455e37			−1.27887
$399$	4.12790e37	−	3.46588e37i	0.797300	−	0.669431i
$400$	−7.52862e37			−1.40231
$401$		−	6.29881e37i		−	1.13153i	−0.824567	−	0.565764i	$-0.808581\pi$
$401$		−	6.29881e37i		−	1.13153i	0.824567	−	0.565764i	$-0.191419\pi$
$402$	−6.59131e37	−	2.98118e37i	−1.14207	−	0.516547i
$403$	5.96439e37			0.996879
$404$	−3.08597e36			−0.0497579
$405$	1.32303e37	−	1.02613e38i	0.205812	−	1.59627i
$406$	−2.98837e37	+	6.22445e37i	−0.448545	+	0.934272i
$407$		−	1.73469e38i		−	2.51248i
$408$	−2.59680e37	−	1.17450e37i	−0.362966	−	0.164165i
$409$			3.88534e37i			0.524133i	0.965050	+	0.262066i	$0.0844040\pi$
$409$			3.88534e37i			0.524133i	−0.965050	+	0.262066i	$0.915596\pi$
$410$		−	2.98381e37i		−	0.388513i
$411$	5.72566e37	+	2.58965e37i	0.719647	+	0.325488i
$412$		−	7.28348e34i		−	0.000883750i
$413$	−3.01101e37	+	6.27162e37i	−0.352726	+	0.734690i
$414$	1.88194e37	+	2.14016e37i	0.212863	+	0.242070i
$415$	−8.07122e37			−0.881539
$416$	1.61155e37			0.169977
$417$	1.76603e37	+	7.98757e36i	0.179898	+	0.0813658i
$418$			1.90821e38i			1.87746i
$419$	1.74807e38			1.66133			0.830664	−	0.556774i	$-0.187961\pi$
$419$	1.74807e38			1.66133			0.830664	+	0.556774i	$0.187961\pi$
$420$	−1.20466e37	−	1.43476e37i	−0.110598	−	0.131724i
$421$	1.75218e38			1.55413			0.777067	−	0.629418i	$-0.216706\pi$
$421$	1.75218e38			1.55413			0.777067	+	0.629418i	$0.216706\pi$
$422$		−	7.11198e37i		−	0.609480i
$423$	−1.17495e38	−	1.33617e38i	−0.972939	−	1.10644i
$424$	2.84588e37			0.227726
$425$	−7.83221e37			−0.605683
$426$	7.43701e37	−	1.64431e38i	0.555852	−	1.22898i
$427$	−1.72665e38	−	8.28966e37i	−1.24738	−	0.598870i
$428$			1.76404e36i			0.0123189i
$429$	−9.30517e37	+	2.05735e38i	−0.628194	+	1.38892i
$430$			2.07838e38i			1.35654i
$431$		−	2.27636e38i		−	1.43655i	−0.695759	−	0.718275i	$-0.744932\pi$
$431$		−	2.27636e38i		−	1.43655i	0.695759	−	0.718275i	$-0.255068\pi$
$432$	−1.38185e38	+	4.22209e37i	−0.843234	+	0.257640i
$433$			2.67289e38i			1.57727i	0.614861	+	0.788636i	$0.289212\pi$
$433$			2.67289e38i			1.57727i	−0.614861	+	0.788636i	$0.710788\pi$
$434$	−8.94405e37	+	1.86295e38i	−0.510427	+	1.06316i
$435$	−2.91354e38	−	1.31776e38i	−1.60815	−	0.727348i
$436$	−2.62192e37			−0.139980
$437$	−6.87587e37			−0.355097
$438$	6.34727e36	−	1.40337e37i	0.0317112	−	0.0701127i
$439$		−	1.23795e38i		−	0.598368i	−0.954195	−	0.299184i	$-0.903286\pi$
$439$		−	1.23795e38i		−	0.598368i	0.954195	−	0.299184i	$-0.0967144\pi$
$440$	6.86968e38			3.21272
$441$	−3.82398e37	+	2.17650e38i	−0.173044	+	0.984914i
$442$	−6.56553e37			−0.287506
$443$			2.63871e38i			1.11825i	0.829084	+	0.559124i	$0.188862\pi$
$443$			2.63871e38i			1.11825i	−0.829084	+	0.559124i	$0.811138\pi$
$444$	−1.41371e37	+	3.12567e37i	−0.0579837	+	0.128201i
$445$	4.67537e38			1.85608
$446$	6.88832e37			0.264702
$447$	1.13759e38	+	5.14518e37i	0.423180	+	0.191400i
$448$	−1.30129e38	+	2.71045e38i	−0.468644	+	0.976134i
$449$			3.98673e38i			1.39010i	0.718963	+	0.695048i	$0.244617\pi$
$449$			3.98673e38i			1.39010i	−0.718963	+	0.695048i	$0.755383\pi$
$450$	−3.34328e38	+	2.93989e38i	−1.12873	+	0.992545i
$451$			1.49092e38i			0.487409i
$452$			2.08749e37i			0.0660873i
$453$	8.92562e37	−	1.97344e38i	0.273662	−	0.605061i
$454$		−	3.26372e38i		−	0.969178i
$455$	−4.02969e38	−	1.93466e38i	−1.15906	−	0.556467i
$456$	1.61073e38	−	3.56130e38i	0.448780	−	0.992242i
$457$	−2.56102e38			−0.691239			−0.345620	−	0.938375i	$-0.612331\pi$
$457$	−2.56102e38			−0.691239			−0.345620	+	0.938375i	$0.612331\pi$
$458$	4.30730e38			1.12630
$459$	−1.43758e38	+	4.39235e37i	−0.364207	+	0.111279i
$460$			2.38989e37i			0.0586664i
$461$	−4.38167e37			−0.104226			−0.0521130	−	0.998641i	$-0.516596\pi$
$461$	−4.38167e37			−0.104226			−0.0521130	+	0.998641i	$0.516596\pi$
$462$	−5.03067e38	−	5.99159e38i	−1.15963	−	1.38113i
$463$	1.24196e38			0.277448			0.138724	−	0.990331i	$-0.455700\pi$
$463$	1.24196e38			0.277448			0.138724	+	0.990331i	$0.455700\pi$
$464$			4.46575e38i			0.966904i
$465$	−8.72010e38	−	3.94400e38i	−1.83001	−	0.827693i
$466$	−2.94430e38			−0.598943
$467$	4.25993e38			0.840054			0.420027	−	0.907512i	$-0.362021\pi$
$467$	4.25993e38			0.840054			0.420027	+	0.907512i	$0.362021\pi$
$468$	3.35333e37	−	2.94873e37i	0.0641078	−	0.0563729i
$469$	−3.09706e38	+	6.45085e38i	−0.574042	+	1.19567i
$470$			1.24703e39i			2.24108i
$471$	9.07551e38	+	4.10475e38i	1.58150	+	0.715293i
$472$			5.04495e38i			0.852506i
$473$		−	1.03850e39i		−	1.70185i
$474$	2.60944e38	+	1.18022e38i	0.414726	+	0.187576i
$475$		−	1.07412e39i		−	1.65576i
$476$	−1.17803e37	+	2.45371e37i	−0.0176139	+	0.0366879i
$477$	1.12717e38	−	9.91173e37i	0.163483	−	0.143758i
$478$	−1.15358e36			−0.00162309
$479$	−9.45275e38			−1.29031			−0.645153	−	0.764053i	$-0.723207\pi$
$479$	−9.45275e38			−1.29031			−0.645153	+	0.764053i	$0.723207\pi$
$480$	−2.35613e38	−	1.06565e38i	−0.312034	−	0.141129i
$481$			8.18529e38i			1.05179i
$482$	4.98774e38			0.621902
$483$	2.15895e38	−	1.81270e38i	0.261222	−	0.219328i
$484$	−2.40394e38			−0.282271
$485$		−	1.54137e39i		−	1.75652i
$486$	−4.48777e38	+	7.27101e38i	−0.496369	+	0.804209i
$487$	−2.50491e38			−0.268920			−0.134460	−	0.990919i	$-0.542930\pi$
$487$	−2.50491e38			−0.268920			−0.134460	+	0.990919i	$0.542930\pi$
$488$	−1.38893e39			−1.44741
$489$	−8.60157e37	+	1.90179e38i	−0.0870161	+	0.192391i
$490$	1.20857e39	−	9.68541e38i	1.18694	−	0.951206i
$491$		−	7.94407e38i		−	0.757463i	−0.925507	−	0.378732i	$-0.876360\pi$
$491$		−	7.94407e38i		−	0.757463i	0.925507	−	0.378732i	$-0.123640\pi$
$492$	1.21504e37	−	2.68643e37i	0.0112485	−	0.0248703i
$493$			4.64583e38i			0.417622i
$494$		−	9.00408e38i		−	0.785957i
$495$	2.72089e39	−	2.39260e39i	2.30640	−	2.02812i
$496$			1.33658e39i			1.10030i
$497$	−1.60927e39	−	7.72610e38i	−1.28665	−	0.617722i
$498$	6.07329e38	+	2.74688e38i	0.471627	+	0.213311i
$499$	1.96619e39			1.48309			0.741546	−	0.670902i	$-0.234093\pi$
$499$	1.96619e39			1.48309			0.741546	+	0.670902i	$0.234093\pi$
$500$	−1.38600e38			−0.101554
$501$	1.45983e38	−	3.22765e38i	0.103910	−	0.229742i
$502$		−	7.50506e38i		−	0.518980i
$503$	1.11150e39			0.746748			0.373374	−	0.927681i	$-0.378201\pi$
$503$	1.11150e39			0.746748			0.373374	+	0.927681i	$0.378201\pi$
$504$	4.33120e38	+	1.54285e39i	0.282726	+	1.00712i
$505$	1.18151e39			0.749400
$506$			9.98024e38i			0.615118i
$507$	−2.48970e38	+	5.50468e38i	−0.149119	+	0.329698i
$508$	2.62123e38			0.152574
$509$	−8.58590e38			−0.485711			−0.242856	−	0.970062i	$-0.578084\pi$
$509$	−8.58590e38			−0.485711			−0.242856	+	0.970062i	$0.578084\pi$
$510$	9.59899e38	+	4.34152e38i	0.527786	+	0.238712i
$511$	−1.37346e38	−	6.59400e37i	−0.0734029	−	0.0352408i
$512$			2.13654e39i			1.10993i
$513$	−6.02375e38	−	1.97152e39i	−0.304204	−	0.995633i
$514$		−	1.14754e39i		−	0.563384i
$515$			2.78860e37i			0.0133101i
$516$	−8.46338e37	+	1.87124e38i	−0.0392756	+	0.0868376i
$517$		−	6.23099e39i		−	2.81154i
$518$	−2.55664e39	−	1.22745e39i	−1.12173	−	0.538544i
$519$	7.90435e38	−	1.74763e39i	0.337240	−	0.745631i
$520$	−3.24152e39			−1.34493
$521$	1.57313e39			0.634773			0.317386	−	0.948296i	$-0.397195\pi$
$521$	1.57313e39			0.634773			0.317386	+	0.948296i	$0.397195\pi$
$522$	1.74386e39	+	1.98313e39i	0.684366	+	0.778268i
$523$			6.19575e38i			0.236494i	0.992984	+	0.118247i	$0.0377274\pi$
$523$			6.19575e38i			0.236494i	−0.992984	+	0.118247i	$0.962273\pi$
$524$	2.01031e38			0.0746380
$525$	2.83174e39	+	3.37263e39i	1.02269	+	1.21803i
$526$	7.66507e38			0.269292
$527$			1.39048e39i			0.475237i
$528$	−4.61039e39	−	2.08523e39i	−1.53301	−	0.693364i
$529$	2.73144e39			0.883659
$530$	−1.05197e39			−0.331134
$531$	1.75707e39	+	1.99816e39i	0.538169	+	0.612012i
$532$	−3.36506e38	−	1.61557e38i	−0.100294	−	0.0481513i
$533$		−	7.03502e38i		−	0.204043i
$534$	−3.51804e39	−	1.59117e39i	−0.993009	−	0.449126i
$535$		−	6.75390e38i		−	0.185535i
$536$			5.18912e39i			1.38741i
$537$	1.27786e39	+	5.77961e38i	0.332549	+	0.150408i
$538$			8.04959e38i			0.203906i
$539$	−6.03882e39	+	4.83949e39i	−1.48907	+	1.19333i
$540$	−6.85253e38	+	2.09371e38i	−0.164491	+	0.0502582i
$541$	3.88333e39			0.907495			0.453748	−	0.891130i	$-0.350087\pi$
$541$	3.88333e39			0.907495			0.453748	+	0.891130i	$0.350087\pi$
$542$	7.29633e39			1.66003
$543$	1.62290e39	+	7.34020e38i	0.359497	+	0.162596i
$544$			3.75701e38i			0.0810324i
$545$	1.00384e40			2.10822
$546$	2.37377e39	+	2.82719e39i	0.485451	+	0.578177i
$547$	−2.41811e39			−0.481570			−0.240785	−	0.970578i	$-0.577405\pi$
$547$	−2.41811e39			−0.481570			−0.240785	+	0.970578i	$0.577405\pi$
$548$		−	4.35199e38i		−	0.0844053i
$549$	−5.50116e39	+	4.83741e39i	−1.03909	+	0.913723i
$550$	−1.55908e40			−2.86819
$551$	−6.37137e39			−1.14166
$552$	8.42437e38	−	1.86261e39i	0.147035	−	0.325091i
$553$	1.22610e39	−	2.55383e39i	0.208454	−	0.434188i
$554$		−	7.75117e39i		−	1.28374i
$555$	5.41260e39	−	1.19671e40i	0.873288	−	1.93082i
$556$		−	1.34234e38i		−	0.0210997i
$557$			7.29364e39i			1.11698i	0.829513	+	0.558488i	$0.188618\pi$
$557$			7.29364e39i			1.11698i	−0.829513	+	0.558488i	$0.811382\pi$
$558$	5.21929e39	+	5.93543e39i	0.778781	+	0.885638i
$559$			4.90026e39i			0.712440i
$560$	4.33545e39	−	9.03027e39i	0.614197	−	1.27931i
$561$	−4.79631e39	−	2.16932e39i	−0.662134	−	0.299475i
$562$	−7.76354e39			−1.04444
$563$	−4.96577e39			−0.651051			−0.325525	−	0.945533i	$-0.605541\pi$
$563$	−4.96577e39			−0.651051			−0.325525	+	0.945533i	$0.605541\pi$
$564$	−5.07801e38	+	1.12274e39i	−0.0648854	+	0.143460i
$565$		−	7.99230e39i		−	0.995335i
$566$	1.01541e39			0.123255
$567$	7.08896e39	+	4.60231e39i	0.838742	+	0.544529i
$568$	−1.29451e40			−1.49298
$569$			3.34448e39i			0.376011i	0.982168	+	0.188006i	$0.0602023\pi$
$569$			3.34448e39i			0.376011i	−0.982168	+	0.188006i	$0.939798\pi$
$570$	−5.95403e39	+	1.31642e40i	−0.652568	+	1.44281i
$571$	4.89459e39			0.522989			0.261494	−	0.965205i	$-0.415785\pi$
$571$	4.89459e39			0.522989			0.261494	+	0.965205i	$0.415785\pi$
$572$	1.56376e39			0.162903
$573$	−1.68605e39	−	7.62579e38i	−0.171249	−	0.0774538i
$574$	2.19736e39	+	1.05496e39i	0.217610	+	0.104475i
$575$		−	5.61782e39i		−	0.542481i
$576$	7.59365e39	+	8.63558e39i	0.715030	+	0.813140i
$577$		−	3.45684e39i		−	0.317417i	−0.987326	−	0.158708i	$-0.949267\pi$
$577$		−	3.45684e39i		−	0.317417i	0.987326	−	0.158708i	$-0.0507329\pi$
$578$			9.02326e39i			0.807997i
$579$	−4.65185e39	+	1.02851e40i	−0.406243	+	0.898195i
$580$			2.21454e39i			0.188615i
$581$	2.85366e39	−	5.94386e39i	0.237054	−	0.493759i
$582$	−5.24575e39	+	1.15982e40i	−0.425035	+	0.939742i
$583$	5.25636e39			0.415424
$584$	−1.10482e39			−0.0851739
$585$	−1.28387e40	+	1.12897e40i	−0.965523	+	0.849027i
$586$		−	7.33410e39i		−	0.538061i
$587$	−6.89040e39			−0.493165			−0.246583	−	0.969122i	$-0.579308\pi$
$587$	−6.89040e39			−0.493165			−0.246583	+	0.969122i	$0.579308\pi$
$588$	1.48251e39	−	3.79868e38i	0.103521	−	0.0265254i
$589$	−1.90693e40			−1.29916
$590$		−	1.86485e40i		−	1.23962i
$591$	−2.26662e40	−	1.02517e40i	−1.47015	−	0.664931i
$592$	−1.83427e40			−1.16091
$593$	−3.60617e39			−0.222717			−0.111358	−	0.993780i	$-0.535520\pi$
$593$	−3.60617e39			−0.222717			−0.111358	+	0.993780i	$0.535520\pi$
$594$	−2.86164e40	+	8.74339e39i	−1.72469	+	0.526959i
$595$	4.51028e39	−	9.39443e39i	0.265282	−	0.552554i
$596$		−	8.64663e38i		−	0.0496336i
$597$	2.20080e40	+	9.95395e39i	1.23297	+	0.557658i
$598$		−	4.70927e39i		−	0.257505i
$599$		−	6.74977e39i		−	0.360247i	−0.983644	−	0.180123i	$-0.942350\pi$
$599$		−	6.74977e39i		−	0.360247i	0.983644	−	0.180123i	$-0.0576497\pi$
$600$	2.90970e40	+	1.31602e40i	1.51585	+	0.685600i
$601$		−	1.72976e40i		−	0.879642i	−0.898086	−	0.439821i	$-0.855042\pi$
$601$		−	1.72976e40i		−	0.879642i	0.898086	−	0.439821i	$-0.144958\pi$
$602$	−1.53058e40	−	7.34832e39i	−0.759811	−	0.364787i
$603$	1.80728e40	+	2.05526e40i	0.875841	+	0.996016i
$604$	−1.49998e39			−0.0709658
$605$	9.20386e40			4.25125
$606$	−8.89045e39	−	4.02105e39i	−0.400932	−	0.181337i
$607$		−	4.03223e40i		−	1.77545i	−0.460371	−	0.887726i	$-0.652284\pi$
$607$		−	4.03223e40i		−	1.77545i	0.460371	−	0.887726i	$-0.347716\pi$
$608$	−5.15243e39			−0.221519
$609$	2.00054e40	−	1.67970e40i	0.839842	−	0.705150i
$610$	5.13414e40			2.10468
$611$			2.94015e40i			1.17699i
$612$	6.87438e38	+	7.81762e38i	0.0268743	+	0.0305618i
$613$	3.64404e40			1.39125			0.695627	−	0.718403i	$-0.255127\pi$
$613$	3.64404e40			1.39125			0.695627	+	0.718403i	$0.255127\pi$
$614$	−1.86685e39			−0.0696095
$615$	−4.65197e39	+	1.02854e40i	−0.169413	+	0.374569i
$616$	−2.42884e40	+	5.05901e40i	−0.863930	+	1.79947i
$617$		−	1.67933e40i		−	0.583445i	−0.956503	−	0.291723i	$-0.905772\pi$
$617$		−	1.67933e40i		−	0.583445i	0.956503	−	0.291723i	$-0.0942284\pi$
$618$	9.49043e37	−	2.09831e38i	0.00322072	−	0.00712094i
$619$		−	3.40129e40i		−	1.12753i	−0.825935	−	0.563766i	$-0.809352\pi$
$619$		−	3.40129e40i		−	1.12753i	0.825935	−	0.563766i	$-0.190648\pi$
$620$			6.62802e39i			0.214637i
$621$	−3.15051e39	−	1.03113e40i	−0.0996672	−	0.326202i
$622$			1.75352e40i			0.541937i
$623$	−1.65302e40	+	3.44307e40i	−0.499117	+	1.03961i
$624$	2.17545e40	+	9.83933e39i	0.641761	+	0.290261i
$625$	−2.11437e39			−0.0609425
$626$	8.01811e39			0.225811
$627$	2.97504e40	−	6.57774e40i	0.818678	−	1.81008i
$628$		−	6.89816e39i		−	0.185489i
$629$	−1.90824e40			−0.501416
$630$	−1.60102e40	−	5.70310e40i	−0.411110	−	1.46445i
$631$	2.25030e39			0.0564695			0.0282348	−	0.999601i	$-0.491011\pi$
$631$	2.25030e39			0.0564695			0.0282348	+	0.999601i	$0.491011\pi$
$632$		−	2.05432e40i		−	0.503815i
$633$	−1.10881e40	+	2.45155e40i	−0.265767	+	0.587606i
$634$	2.86466e40			0.671088
$635$	−1.00358e41			−2.29791
$636$	−9.47124e38	−	4.28373e38i	−0.0211972	−	0.00958725i
$637$	2.84947e40	−	2.28356e40i	0.623365	−	0.499563i
$638$			9.24797e40i			1.97764i
$639$	−5.12717e40	+	4.50855e40i	−1.07180	+	0.942486i
$640$		−	6.38362e40i		−	1.30454i
$641$		−	7.96830e40i		−	1.59193i	−0.605342	−	0.795965i	$-0.706964\pi$
$641$		−	7.96830e40i		−	1.59193i	0.605342	−	0.795965i	$-0.293036\pi$
$642$	−2.29856e39	+	5.08206e39i	−0.0448949	+	0.0992617i
$643$			5.54592e40i			1.05905i	0.848296	+	0.529523i	$0.177629\pi$
$643$			5.54592e40i			1.05905i	−0.848296	+	0.529523i	$0.822371\pi$
$644$	−1.75998e39	−	8.44968e38i	−0.0328596	−	0.0157759i
$645$	3.24034e40	−	7.16432e40i	0.591527	−	1.30785i
$646$	2.09912e40			0.374685
$647$	−1.94441e40			−0.339372			−0.169686	−	0.985498i	$-0.554275\pi$
$647$	−1.94441e40			−0.339372			−0.169686	+	0.985498i	$0.554275\pi$
$648$	6.07870e40	+	7.83744e39i	1.03746	+	0.133763i
$649$			9.31806e40i			1.55517i
$650$	7.35664e40			1.20070
$651$	5.98754e40	−	5.02728e40i	0.955706	−	0.802432i
$652$	1.44552e39			0.0225649
$653$		−	8.42089e40i		−	1.28563i	−0.766020	−	0.642816i	$-0.777766\pi$
$653$		−	8.42089e40i		−	1.28563i	0.766020	−	0.642816i	$-0.222234\pi$
$654$	−7.55355e40	−	3.41638e40i	−1.12791	−	0.510140i
$655$	−7.69680e40			−1.12412
$656$	1.57650e40			0.225211
$657$	−4.37589e39	+	3.84792e39i	−0.0611461	+	0.0537685i
$658$	−9.18343e40	−	4.40898e40i	−1.25525	−	0.602646i
$659$			2.47918e40i			0.331489i	0.986169	+	0.165745i	$0.0530027\pi$
$659$			2.47918e40i			0.331489i	−0.986169	+	0.165745i	$0.946997\pi$
$660$	−2.28627e40	−	1.03405e40i	−0.299047	−	0.135256i
$661$			4.90162e40i			0.627218i	0.949552	+	0.313609i	$0.101538\pi$
$661$			4.90162e40i			0.627218i	−0.949552	+	0.313609i	$0.898462\pi$
$662$		−	9.33045e40i		−	1.16805i
$663$	2.26318e40	+	1.02361e40i	0.277187	+	0.125369i
$664$		−	4.78129e40i		−	0.572939i
$665$	1.28837e41	+	6.18547e40i	1.51052	+	0.725202i
$666$	−8.14555e40	+	7.16275e40i	−0.934424	+	0.821681i
$667$	−3.33232e40			−0.374044
$668$	−2.45329e39			−0.0269458
$669$	−2.37445e40	−	1.07394e40i	−0.255202	−	0.115425i
$670$		−	1.91814e41i		−	2.01742i
$671$	−2.56536e41			−2.64042
$672$	1.61781e40	−	1.35835e40i	0.162957	−	0.136822i
$673$	3.96130e40			0.390499			0.195249	−	0.980754i	$-0.437448\pi$
$673$	3.96130e40			0.390499			0.195249	+	0.980754i	$0.437448\pi$
$674$			4.09291e40i			0.394879i
$675$	1.61080e41	−	4.92161e40i	1.52103	−	0.464732i
$676$	4.18403e39			0.0386694
$677$	−7.59452e40			−0.687012			−0.343506	−	0.939150i	$-0.611615\pi$
$677$	−7.59452e40			−0.687012			−0.343506	+	0.939150i	$0.611615\pi$
$678$	−2.72002e40	+	6.01390e40i	−0.240847	+	0.532508i
$679$	1.13511e41	+	5.44966e40i	0.983841	+	0.472343i
$680$		−	7.55696e40i		−	0.641162i
$681$	−5.08837e40	+	1.12503e41i	−0.422616	+	0.934394i
$682$			2.76788e41i			2.25047i
$683$			1.13829e41i			0.906054i	0.891497	+	0.453027i	$0.149656\pi$
$683$			1.13829e41i			0.906054i	−0.891497	+	0.453027i	$0.850344\pi$
$684$	−1.07212e40	+	9.42764e39i	−0.0835469	+	0.0734665i
$685$			1.66623e41i			1.27122i
$686$	2.85959e40	+	1.23246e41i	0.213601	+	0.920603i
$687$	−1.48475e41	−	6.71537e40i	−1.08588	−	0.491131i
$688$	−1.09812e41			−0.786350
$689$	−2.48026e40			−0.173908
$690$	−3.11404e40	+	6.88508e40i	−0.213803	+	0.472713i
$691$			1.08632e41i			0.730338i	0.930941	+	0.365169i	$0.118989\pi$
$691$			1.08632e41i			0.730338i	−0.930941	+	0.365169i	$0.881011\pi$
$692$	−1.32835e40			−0.0874529
$693$	7.99977e40	+	2.84966e41i	0.515757	+	1.83722i
$694$	1.98878e41			1.25567
$695$			5.13935e40i			0.317781i
$696$	7.80626e40	−	1.72595e41i	0.472725	−	1.04519i
$697$	1.64008e40			0.0972722
$698$	−7.98671e40			−0.463943
$699$	1.01492e41	+	4.59036e40i	0.577447	+	0.261173i
$700$	1.31998e40	−	2.74937e40i	0.0735605	−	0.153219i
$701$		−	2.18266e41i		−	1.19145i	−0.803189	−	0.595725i	$-0.796865\pi$
$701$		−	2.18266e41i		−	1.19145i	0.803189	−	0.595725i	$-0.203135\pi$
$702$	1.35029e41	−	4.12565e40i	0.722002	−	0.220599i
$703$		−	2.61699e41i		−	1.37072i
$704$			4.02704e41i			2.06625i
$705$	1.94420e41	−	4.29858e41i	0.977233	−	2.16064i
$706$			2.67258e41i			1.31602i
$707$	−4.17735e40	+	8.70098e40i	−0.201521	+	0.419746i
$708$	7.59386e39	−	1.67899e40i	0.0358906	−	0.0793532i
$709$	−1.65763e41			−0.767568			−0.383784	−	0.923423i	$-0.625379\pi$
$709$	−1.65763e41			−0.767568			−0.383784	+	0.923423i	$0.625379\pi$
$710$	4.78511e41			2.17093
$711$	−7.15486e40	−	8.13659e40i	−0.318048	−	0.361687i
$712$			2.76964e41i			1.20632i
$713$	−9.97350e40			−0.425647
$714$	−6.59102e40	+	5.53397e40i	−0.275631	+	0.231426i
$715$	−5.98711e41			−2.45347
$716$		−	9.71282e39i		−	0.0390038i
$717$	3.97647e38	+	1.79851e38i	0.00156484	+	0.000707758i
$718$	3.91477e41			1.50974
$719$	1.69268e41			0.639745			0.319873	−	0.947461i	$-0.396360\pi$
$719$	1.69268e41			0.639745			0.319873	+	0.947461i	$0.396360\pi$
$720$	−2.52994e41	−	2.87708e41i	−0.937107	−	1.06569i
$721$	−2.05360e39	−	9.85934e38i	−0.00745510	−	0.00357921i
$722$			2.22651e40i			0.0792201i
$723$	−1.71931e41	−	7.77623e40i	−0.599581	−	0.271184i
$724$		−	1.23354e40i		−	0.0421643i
$725$		−	5.20563e41i		−	1.74410i
$726$	−6.92556e41	−	3.13235e41i	−2.27444	−	1.02870i
$727$			8.07078e40i			0.259816i	0.991526	+	0.129908i	$0.0414682\pi$
$727$			8.07078e40i			0.259816i	−0.991526	+	0.129908i	$0.958532\pi$
$728$	1.14607e41	−	2.38714e41i	0.361665	−	0.753309i
$729$	2.68057e41	−	1.80669e41i	0.829234	−	0.558901i
$730$	4.08395e40			0.123851
$731$	−1.14240e41			−0.339637
$732$	4.62243e40	+	2.09067e40i	0.134729	+	0.0609362i
$733$			2.55511e41i			0.730134i	0.930981	+	0.365067i	$0.118954\pi$
$733$			2.55511e41i			0.730134i	−0.930981	+	0.365067i	$0.881046\pi$
$734$	−1.18755e41			−0.332705
$735$	−5.67603e41	+	1.45438e41i	−1.55912	+	0.399496i
$736$	−2.69480e40			−0.0725768
$737$			9.58434e41i			2.53095i
$738$	7.00087e40	−	6.15617e40i	0.181274	−	0.159402i
$739$	9.41730e40			0.239101			0.119551	−	0.992828i	$-0.461855\pi$
$739$	9.41730e40			0.239101			0.119551	+	0.992828i	$0.461855\pi$
$740$	−9.09603e40			−0.226460
$741$	−1.40380e41	+	3.10377e41i	−0.342721	+	0.757748i
$742$	3.71934e40	−	7.74700e40i	0.0890450	−	0.185471i
$743$		−	4.06339e41i		−	0.954005i	−0.878902	−	0.477003i	$-0.841723\pi$
$743$		−	4.06339e41i		−	0.954005i	0.878902	−	0.477003i	$-0.158277\pi$
$744$	2.33638e41	−	5.16568e41i	0.537943	−	1.18938i
$745$			3.31050e41i			0.747528i
$746$			6.59455e40i			0.146040i
$747$	−1.66525e41	−	1.89373e41i	−0.361684	−	0.411311i
$748$			3.64560e40i			0.0776598i
$749$	4.97375e40	+	2.38791e40i	0.103920	+	0.0498920i
$750$	−3.99295e41	−	1.80596e41i	−0.818286	−	0.370102i
$751$	8.78253e41			1.76539			0.882695	−	0.469947i	$-0.155727\pi$
$751$	8.78253e41			1.76539			0.882695	+	0.469947i	$0.155727\pi$
$752$	−6.58867e41			−1.29909
$753$	−1.17009e41	+	2.58704e41i	−0.226304	+	0.500353i
$754$		−	4.36374e41i		−	0.827893i
$755$	5.74290e41			1.06881
$756$	8.80914e39	−	5.78664e40i	0.0160830	−	0.105648i
$757$	5.89345e41			1.05555			0.527775	−	0.849384i	$-0.323026\pi$
$757$	5.89345e41			1.05555			0.527775	+	0.849384i	$0.323026\pi$
$758$		−	8.97774e41i		−	1.57748i
$759$	1.55599e41	−	3.44025e41i	0.268226	−	0.593041i
$760$	1.03637e42			1.75275
$761$	5.21591e41			0.865471			0.432736	−	0.901521i	$-0.357548\pi$
$761$	5.21591e41			0.865471			0.432736	+	0.901521i	$0.357548\pi$
$762$	7.55156e41	+	3.41548e41i	1.22939	+	0.556039i
$763$	−3.54919e41	+	7.39257e41i	−0.566921	+	1.18084i
$764$			1.28154e40i			0.0200853i
$765$	−2.63196e41	−	2.99310e41i	−0.404752	−	0.460288i
$766$		−	8.26698e41i		−	1.24747i
$767$		−	4.39681e41i		−	0.651036i
$768$	8.98520e40	−	1.98661e41i	0.130554	−	0.288652i
$769$			3.60602e41i			0.514157i	0.966390	+	0.257079i	$0.0827600\pi$
$769$			3.60602e41i			0.514157i	−0.966390	+	0.257079i	$0.917240\pi$
$770$	8.97814e41	−	1.87005e42i	1.25623	−	2.61660i
$771$	−1.78910e41	+	3.95566e41i	−0.245667	+	0.543164i
$772$	7.81757e40			0.105347
$773$	−1.32815e42			−1.75648			−0.878242	−	0.478216i	$-0.841284\pi$
$773$	−1.32815e42			−1.75648			−0.878242	+	0.478216i	$0.841284\pi$
$774$	−4.87647e41	+	4.28810e41i	−0.632939	+	0.556571i
$775$		−	1.55802e42i		−	1.98472i
$776$	9.13090e41			1.14161
$777$	6.89924e41	+	8.21707e41i	0.846635	+	1.00835i
$778$	1.21290e42			1.46090
$779$			2.24923e41i			0.265913i
$780$	1.07880e41	+	4.87927e40i	0.125189	+	0.0566217i
$781$	−2.39096e42			−2.72354
$782$	1.09787e41			0.122759
$783$	−2.91935e41	−	9.55477e41i	−0.320435	−	1.04876i
$784$	5.11730e41	+	6.38548e41i	0.551388	+	0.688035i
$785$			2.64107e42i			2.79364i
$786$	5.79156e41	+	2.61945e41i	0.601407	+	0.272009i
$787$			3.23407e41i			0.329697i	0.986319	+	0.164849i	$0.0527136\pi$
$787$			3.23407e41i			0.329697i	−0.986319	+	0.164849i	$0.947286\pi$
$788$			1.72283e41i			0.172429i
$789$	−2.64220e41	−	1.19504e41i	−0.259627	−	0.117426i
$790$			7.59374e41i			0.732593i
$791$	5.88574e41	+	2.82575e41i	0.557496	+	0.267655i
$792$	1.41735e42	+	1.61182e42i	1.31814	+	1.49900i
$793$	1.21049e42			1.10535
$794$	−1.13976e42			−1.02192
$795$	3.62621e41	+	1.64010e41i	0.319249	+	0.144393i
$796$		−	1.67279e41i		−	0.144611i
$797$	−4.16632e41			−0.353677			−0.176839	−	0.984240i	$-0.556587\pi$
$797$	−4.16632e41			−0.353677			−0.176839	+	0.984240i	$0.556587\pi$
$798$	−7.58938e41	−	9.03904e41i	−0.632651	−	0.753495i
$799$	−6.85437e41			−0.561099
$800$		−	4.20971e41i		−	0.338413i
$801$	9.64618e41	+	1.09697e42i	0.761525	+	0.866014i
$802$	−1.37928e42			−1.06936
$803$	−2.04062e41			−0.155377
$804$	7.81087e40	−	1.72697e41i	0.0584099	−	0.129143i
$805$	6.73835e41	+	3.23509e41i	0.494896	+	0.237600i
$806$		−	1.30605e42i		−	0.942109i
$807$	1.25499e41	−	2.77475e41i	0.0889145	−	0.196588i
$808$			6.99915e41i			0.487058i
$809$			1.03543e41i			0.0707730i	0.999374	+	0.0353865i	$0.0112662\pi$
$809$			1.03543e41i			0.0707730i	−0.999374	+	0.0353865i	$0.988734\pi$
$810$	−2.24697e42	−	2.89709e41i	−1.50857	−	0.194504i
$811$			1.51069e41i			0.0996263i	0.998759	+	0.0498131i	$0.0158626\pi$
$811$			1.51069e41i			0.0996263i	−0.998759	+	0.0498131i	$0.984137\pi$
$812$	−1.63084e41	−	7.82971e40i	−0.105645	−	0.0507205i
$813$	−2.51509e42	−	1.13755e42i	−1.60045	−	0.723864i
$814$	−3.79853e42			−2.37444
$815$	−5.53441e41			−0.339849
$816$	−2.29384e41	+	5.07164e41i	−0.138375	+	0.305943i
$817$		−	1.56670e42i		−	0.928469i
$818$	8.50791e41			0.495336
$819$	−3.77476e41	−	1.34464e42i	−0.215910	−	0.769110i
$820$	7.81778e40			0.0439322
$821$			2.56278e41i			0.141493i	0.997494	+	0.0707466i	$0.0225382\pi$
$821$			2.56278e41i			0.141493i	−0.997494	+	0.0707466i	$0.977462\pi$
$822$	5.67068e41	−	1.25377e42i	0.307605	−	0.680108i
$823$	−1.96772e42			−1.04873			−0.524367	−	0.851492i	$-0.675698\pi$
$823$	−1.96772e42			−1.04873			−0.524367	+	0.851492i	$0.675698\pi$
$824$	−1.65193e40			−0.00865062
$825$	5.37424e42	+	2.43071e42i	2.76525	+	1.25069i
$826$	1.37333e42	+	6.59335e41i	0.694325	+	0.333346i
$827$			3.29125e42i			1.63505i	0.575892	+	0.817526i	$0.304655\pi$
$827$			3.29125e42i			1.63505i	−0.575892	+	0.817526i	$0.695345\pi$
$828$	−5.60735e40	+	4.93079e40i	−0.0273727	+	0.0240701i
$829$		−	1.78654e42i		−	0.856982i	−0.903546	−	0.428491i	$-0.859045\pi$
$829$		−	1.78654e42i		−	0.856982i	0.903546	−	0.428491i	$-0.140955\pi$
$830$			1.76739e42i			0.833106i
$831$	−1.20846e42	+	2.67188e42i	−0.559780	+	1.23766i
$832$		−	1.90020e42i		−	0.864989i
$833$	5.32366e41	+	6.64298e41i	0.238154	+	0.297174i
$834$	1.74907e41	−	3.86716e41i	0.0768954	−	0.170014i
$835$	9.39281e41			0.405828
$836$	−4.99964e41			−0.212299
$837$	−8.73749e41	−	2.85970e42i	−0.364643	−	1.19344i
$838$		−	3.82783e42i		−	1.57005i
$839$	2.75094e42			1.10900			0.554502	−	0.832182i	$-0.312909\pi$
$839$	2.75094e42			1.10900			0.554502	+	0.832182i	$0.312909\pi$
$840$	−3.25411e42	+	2.73222e42i	−1.28938	+	1.08260i
$841$	−5.20136e41			−0.202570
$842$		−	3.83683e42i		−	1.46875i
$843$	2.67614e42	+	1.21039e42i	1.00695	+	0.455434i
$844$	1.86338e41			0.0689186
$845$	−1.60192e42			−0.582396
$846$	−2.92587e42	+	2.57285e42i	−1.04565	+	0.919484i
$847$	−3.25411e42	+	6.77797e42i	−1.14320	+	2.38117i
$848$		−	5.55810e41i		−	0.191949i
$849$	−3.50019e41	−	1.58309e41i	−0.118831	−	0.0537459i
$850$			1.71506e42i			0.572405i
$851$		−	1.36872e42i		−	0.449094i
$852$	4.30819e41	+	1.94854e41i	0.138970	+	0.0628545i
$853$			4.01860e42i			1.27442i	0.770689	+	0.637212i	$0.219912\pi$
$853$			4.01860e42i			1.27442i	−0.770689	+	0.637212i	$0.780088\pi$
$854$	−1.81522e42	+	3.78092e42i	−0.565967	+	1.17885i
$855$	4.10479e42	−	3.60952e42i	1.25829	−	1.10647i
$856$	4.00093e41			0.120584
$857$	−5.84887e42			−1.73321			−0.866603	−	0.498998i	$-0.833701\pi$
$857$	−5.84887e42			−1.73321			−0.866603	+	0.498998i	$0.833701\pi$
$858$	4.50508e42	+	2.03760e42i	1.31261	+	0.593680i
$859$		−	6.36561e42i		−	1.82364i	−0.410589	−	0.911820i	$-0.634677\pi$
$859$		−	6.36561e42i		−	1.82364i	0.410589	−	0.911820i	$-0.365323\pi$
$860$	−5.44549e41			−0.153394
$861$	−5.92970e41	−	7.06234e41i	−0.164243	−	0.195615i
$862$	−4.98465e42			−1.35762
$863$			1.37045e42i			0.367035i	0.983016	+	0.183517i	$0.0587483\pi$
$863$			1.37045e42i			0.367035i	−0.983016	+	0.183517i	$0.941252\pi$
$864$	−2.36083e41	−	7.72680e41i	−0.0621750	−	0.203493i
$865$	5.08580e42			1.31712
$866$	5.85295e42			1.49061
$867$	1.40679e42	−	3.11038e42i	0.352332	−	0.778998i
$868$	−4.88105e41	−	2.34340e41i	−0.120220	−	0.0577178i
$869$		−	3.79435e42i		−	0.919074i
$870$	−2.88556e42	+	6.37991e42i	−0.687386	+	1.51980i
$871$		−	4.52246e42i		−	1.05952i
$872$			5.94665e42i			1.37020i
$873$	3.61649e42	−	3.18014e42i	0.819560	−	0.720675i
$874$			1.50564e42i			0.335587i
$875$	−1.87617e42	+	3.90785e42i	−0.411296	+	0.856686i
$876$	3.67691e40	+	1.66302e40i	0.00792818	+	0.00358583i
$877$	−3.50696e42			−0.743766			−0.371883	−	0.928280i	$-0.621288\pi$
$877$	−3.50696e42			−0.743766			−0.371883	+	0.928280i	$0.621288\pi$
$878$	−2.71080e42			−0.565492
$879$	−1.14344e42	+	2.52811e42i	−0.234625	+	0.518750i
$880$		−	1.34167e43i		−	2.70799i
$881$	3.81213e42			0.756864			0.378432	−	0.925629i	$-0.376463\pi$
$881$	3.81213e42			0.756864			0.378432	+	0.925629i	$0.376463\pi$
$882$	4.76597e42	+	8.37354e41i	0.930801	+	0.163537i
$883$	−5.57603e42			−1.07126			−0.535630	−	0.844453i	$-0.679926\pi$
$883$	−5.57603e42			−1.07126			−0.535630	+	0.844453i	$0.679926\pi$
$884$		−	1.72021e41i		−	0.0325105i
$885$	−2.90743e42	+	6.42826e42i	−0.540545	+	1.19513i
$886$	5.77811e42			1.05681
$887$	−7.14514e42			−1.28564			−0.642819	−	0.766018i	$-0.722235\pi$
$887$	−7.14514e42			−1.28564			−0.642819	+	0.766018i	$0.722235\pi$
$888$	7.08918e42	+	3.20636e42i	1.25490	+	0.567576i
$889$	3.54825e42	−	7.39063e42i	0.617929	−	1.28708i
$890$		−	1.02379e43i		−	1.75410i
$891$	1.12274e43	+	1.44758e42i	1.89257	+	0.244015i
$892$			1.80478e41i			0.0299319i
$893$		−	9.40020e42i		−	1.53388i
$894$	1.12666e42	−	2.49102e42i	0.180884	−	0.399930i
$895$			3.71871e42i			0.587432i
$896$	4.70107e42	+	2.25699e42i	0.730686	+	0.350803i
$897$	−7.34207e41	+	1.62332e42i	−0.112287	+	0.248263i
$898$	8.72993e42			1.31372
$899$	−9.24172e42			−1.36848
$900$	−7.70270e41	−	8.75960e41i	−0.112235	−	0.127634i
$901$		−	5.78224e41i		−	0.0829061i
$902$	3.26473e42			0.460630
$903$	4.13034e42	+	4.91929e42i	0.573474	+	0.683014i
$904$	4.73454e42			0.646898
$905$			4.72282e42i			0.635034i
$906$	−4.32132e42	−	1.95448e42i	−0.571818	−	0.258627i
$907$	1.64542e42			0.214275			0.107137	−	0.994244i	$-0.465832\pi$
$907$	1.64542e42			0.214275			0.107137	+	0.994244i	$0.465832\pi$
$908$	8.55116e41			0.109592
$909$	2.43769e42	+	2.77216e42i	0.307469	+	0.349657i
$910$	−4.23642e42	+	8.82400e42i	−0.525894	+	1.09538i
$911$		−	4.57291e42i		−	0.558696i	−0.960190	−	0.279348i	$-0.909882\pi$
$911$		−	4.57291e42i		−	0.558696i	0.960190	−	0.279348i	$-0.0901184\pi$
$912$	−6.95533e42	−	3.14582e42i	−0.836359	−	0.378276i
$913$		−	8.83108e42i		−	1.04517i
$914$			5.60798e42i			0.653261i
$915$	−1.76977e43	−	8.00448e42i	−2.02914	−	0.917756i
$916$			1.12854e42i			0.127360i
$917$	2.72128e42	−	5.66813e42i	0.302286	−	0.629629i
$918$	9.61813e41	+	3.14793e42i	0.105165	+	0.344196i
$919$	−5.81514e42			−0.625872			−0.312936	−	0.949774i	$-0.601313\pi$
$919$	−5.81514e42			−0.625872			−0.312936	+	0.949774i	$0.601313\pi$
$920$	5.42039e42			0.574258
$921$	6.43516e41	+	2.91055e41i	0.0671112	+	0.0303536i
$922$			9.59474e41i			0.0984996i
$923$	1.12820e43			1.14015
$924$	1.56983e42	−	1.31807e42i	0.156175	−	0.131128i
$925$	2.13817e43			2.09405
$926$		−	2.71957e42i		−	0.262205i
$927$	−6.54283e40	+	5.75340e40i	−0.00621026	+	0.00546096i
$928$	−2.49707e42			−0.233338
$929$	−1.50298e43			−1.38269			−0.691345	−	0.722525i	$-0.742981\pi$
$929$	−1.50298e43			−1.38269			−0.691345	+	0.722525i	$0.742981\pi$
$930$	−8.63636e42	+	1.90948e43i	−0.782218	+	1.72947i
$931$	−9.11029e42	+	7.30095e42i	−0.812385	+	0.651042i
$932$		−	7.71424e41i		−	0.0677271i
$933$	2.73385e42	−	6.04448e42i	0.236315	−	0.522487i
$934$		−	9.32815e42i		−	0.793900i
$935$		−	1.39578e43i		−	1.16963i
$936$	−6.68787e42	−	7.60552e42i	−0.551808	−	0.627522i
$937$		−	9.35203e42i		−	0.759770i	−0.925034	−	0.379885i	$-0.875964\pi$
$937$		−	9.35203e42i		−	0.759770i	0.925034	−	0.379885i	$-0.124036\pi$
$938$	1.41257e43	+	6.78177e42i	1.12998	+	0.542503i
$939$	−2.76390e42	−	1.25008e42i	−0.217706	−	0.0984660i
$940$	−3.26728e42			−0.253415
$941$	2.56054e43			1.95561			0.977805	−	0.209517i	$-0.0671891\pi$
$941$	2.56054e43			1.95561			0.977805	+	0.209517i	$0.0671891\pi$
$942$	8.98836e42	−	1.98731e43i	0.675993	−	1.49461i
$943$			1.17638e42i			0.0871220i
$944$	9.85296e42			0.718576
$945$	−3.37272e42	+	2.21551e43i	−0.242225	+	1.59115i
$946$	−2.27405e43			−1.60834
$947$		−	3.74201e42i		−	0.260634i	−0.991472	−	0.130317i	$-0.958401\pi$
$947$		−	3.74201e42i		−	0.260634i	0.991472	−	0.130317i	$-0.0415995\pi$
$948$	−3.09225e41	+	6.83689e41i	−0.0212106	+	0.0468962i
$949$	9.62884e41			0.0650450
$950$	−2.35206e43			−1.56479
$951$	−9.87468e42	−	4.46621e42i	−0.647002	−	0.292632i
$952$	5.56515e42	+	2.67183e42i	0.359121	+	0.172415i
$953$			5.66163e42i			0.359827i	0.983682	+	0.179914i	$0.0575818\pi$
$953$			5.66163e42i			0.359827i	−0.983682	+	0.179914i	$0.942418\pi$
$954$	−2.17042e42	−	2.46822e42i	−0.135860	−	0.154501i
$955$		−	4.90657e42i		−	0.302503i
$956$		−	3.02245e39i		−	0.000183535i
$957$	1.44182e43	−	3.18784e43i	0.862360	−	1.90666i
$958$			2.06991e43i			1.21942i
$959$	−1.22706e43	−	5.89111e42i	−0.712023	−	0.341843i
$960$	−1.25652e43	+	2.77814e43i	−0.718186	+	1.58789i
$961$	−9.89819e42			−0.557272
$962$	1.79237e43			0.994006
$963$	1.58465e42	−	1.39346e42i	0.0865672	−	0.0761224i
$964$			1.30682e42i			0.0703232i
$965$	−2.99308e43			−1.58662
$966$	−3.96936e42	−	4.72755e42i	−0.207277	−	0.246870i
$967$	2.89678e43			1.49016			0.745079	−	0.666976i	$-0.232412\pi$
$967$	2.89678e43			1.49016			0.745079	+	0.666976i	$0.232412\pi$
$968$			5.45225e43i			2.76302i
$969$	−7.23581e42	−	3.27268e42i	−0.361237	−	0.163384i
$970$	−3.37521e43			−1.66001
$971$	3.22888e41			0.0156449			0.00782245	−	0.999969i	$-0.497510\pi$
$971$	3.22888e41			0.0156449			0.00782245	+	0.999969i	$0.497510\pi$
$972$	−1.90505e42	−	1.17582e42i	−0.0909381	−	0.0561283i
$973$	−3.78475e42	−	1.81706e42i	−0.177992	−	0.0854543i
$974$			5.48512e42i			0.254145i
$975$	−2.53588e43	−	1.14695e43i	−1.15761	−	0.523574i
$976$			2.71263e43i			1.22002i
$977$		−	2.36187e42i		−	0.104661i	−0.998630	−	0.0523305i	$-0.983335\pi$
$977$		−	2.36187e42i		−	0.104661i	0.998630	−	0.0523305i	$-0.0166649\pi$
$978$	4.16443e42	+	1.88352e42i	0.181820	+	0.0822352i
$979$			5.11554e43i			2.20061i
$980$	2.53764e42	+	3.16652e42i	0.107560	+	0.134216i
$981$	2.07112e43	+	2.35530e43i	0.864977	+	0.983661i
$982$	−1.73955e43			−0.715847
$983$	2.18701e43			0.886799			0.443399	−	0.896324i	$-0.353772\pi$
$983$	2.18701e43			0.886799			0.443399	+	0.896324i	$0.353772\pi$
$984$	−6.09295e42	−	2.75577e42i	−0.243444	−	0.110107i
$985$		−	6.59612e43i		−	2.59695i
$986$	1.01732e43			0.394677
$987$	2.47820e43	+	2.95156e43i	0.947409	+	1.12837i
$988$	2.35913e42			0.0888741
$989$		−	8.19410e42i		−	0.304197i
$990$	−5.23917e43	−	5.95804e43i	−1.91669	−	2.17968i
$991$	4.77081e43			1.71998			0.859991	−	0.510310i	$-0.170469\pi$
$991$	4.77081e43			1.71998			0.859991	+	0.510310i	$0.170469\pi$
$992$	−7.47364e42			−0.265529
$993$	−1.45468e43	+	3.21627e43i	−0.509335	+	1.12613i
$994$	−1.69182e43	+	3.52388e43i	−0.583783	+	1.21596i
$995$			6.40455e43i			2.17798i
$996$	−7.19699e41	+	1.59124e42i	−0.0241207	+	0.0533304i
$997$			5.29465e42i			0.174887i	0.996169	+	0.0874434i	$0.0278697\pi$
$997$			5.29465e42i			0.174887i	−0.996169	+	0.0874434i	$0.972130\pi$
$998$		−	4.30546e43i		−	1.40161i
$999$	3.92455e43	−	1.19910e43i	1.25919	−	0.384729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.7	✓	76
3.2	odd	2	inner	21.30.c.a.20.70	yes	76
7.6	odd	2	inner	21.30.c.a.20.69	yes	76
21.20	even	2	inner	21.30.c.a.20.8	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.7	✓	76	1.1	even	1	trivial
21.30.c.a.20.8	yes	76	21.20	even	2	inner
21.30.c.a.20.69	yes	76	7.6	odd	2	inner
21.30.c.a.20.70	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)

\(f(q)\)	\(=\)	\(q-21897.4i q^{2} +(-3.41396e6 + 7.54819e6i) q^{3} +5.73727e7 q^{4} -2.19660e10 q^{5} +(1.65286e11 + 7.47571e10i) q^{6} +(7.76630e11 - 1.61764e12i) q^{7} -1.30124e13i q^{8} +(-4.53201e13 - 5.15385e13i) q^{9} +O(q^{10})\)	\(q-21897.4i q^{2} +(-3.41396e6 + 7.54819e6i) q^{3} +5.73727e7 q^{4} -2.19660e10 q^{5} +(1.65286e11 + 7.47571e10i) q^{6} +(7.76630e11 - 1.61764e12i) q^{7} -1.30124e13i q^{8} +(-4.53201e13 - 5.15385e13i) q^{9} +4.81000e14i q^{10} -2.40340e15i q^{11} +(-1.95868e14 + 4.33060e14i) q^{12} +1.13407e16i q^{13} +(-3.54221e16 - 1.70062e16i) q^{14} +(7.49912e16 - 1.65804e17i) q^{15} -2.54137e17 q^{16} -2.64385e17 q^{17} +(-1.12856e18 + 9.92395e17i) q^{18} -3.62583e18i q^{19} -1.26025e18 q^{20} +(9.55886e18 + 1.13847e19i) q^{21} -5.26284e19 q^{22} -1.89636e19i q^{23} +(9.82203e19 + 4.44239e19i) q^{24} +2.96242e20 q^{25} +2.48332e20 q^{26} +(5.43744e20 - 1.66134e20i) q^{27} +(4.45574e19 - 9.28082e19i) q^{28} -1.75722e21i q^{29} +(-3.63068e21 - 1.64212e21i) q^{30} -5.25929e21i q^{31} -1.42104e21i q^{32} +(1.81414e22 + 8.20513e21i) q^{33} +5.78936e21i q^{34} +(-1.70595e22 + 3.55331e22i) q^{35} +(-2.60014e21 - 2.95690e21i) q^{36} +7.21764e22 q^{37} -7.93963e22 q^{38} +(-8.56016e22 - 3.87166e22i) q^{39} +2.85831e23i q^{40} -6.20335e22 q^{41} +(2.49296e23 - 2.09315e23i) q^{42} +4.32096e23 q^{43} -1.37890e23i q^{44} +(9.95503e23 + 1.13210e24i) q^{45} -4.15254e23 q^{46} +2.59257e24 q^{47} +(8.67614e23 - 1.91828e24i) q^{48} +(-2.01360e24 - 2.51261e24i) q^{49} -6.48695e24i q^{50} +(9.02602e23 - 1.99563e24i) q^{51} +6.50645e23i q^{52} +2.18705e24i q^{53} +(-3.63792e24 - 1.19066e25i) q^{54} +5.27933e25i q^{55} +(-2.10494e25 - 1.01058e25i) q^{56} +(2.73684e25 + 1.23784e25i) q^{57} -3.84786e25 q^{58} -3.87703e25 q^{59} +(4.30245e24 - 9.51262e24i) q^{60} -1.06739e26i q^{61} -1.15165e26 q^{62} +(-1.18568e26 + 3.32852e25i) q^{63} -1.67556e26 q^{64} -2.49110e26i q^{65} +(1.79671e26 - 3.97249e26i) q^{66} -3.98782e26 q^{67} -1.51685e25 q^{68} +(1.43141e26 + 6.47410e25i) q^{69} +(7.78084e26 + 3.73559e26i) q^{70} -9.94824e26i q^{71} +(-6.70640e26 + 5.89724e26i) q^{72} -8.49053e25i q^{73} -1.58048e27i q^{74} +(-1.01136e27 + 2.23610e27i) q^{75} -2.08023e26i q^{76} +(-3.88784e27 - 1.86656e27i) q^{77} +(-8.47796e26 + 1.87446e27i) q^{78} +1.57874e27 q^{79} +5.58238e27 q^{80} +(-6.02305e26 + 4.67146e27i) q^{81} +1.35838e27i q^{82} +3.67441e27 q^{83} +(5.48417e26 + 6.53171e26i) q^{84} +5.80750e27 q^{85} -9.46180e27i q^{86} +(1.32638e28 + 5.99908e27i) q^{87} -3.12741e28 q^{88} -2.12846e28 q^{89} +(2.47900e28 - 2.17990e28i) q^{90} +(1.83451e28 + 8.80751e27i) q^{91} -1.08799e27i q^{92} +(3.96981e28 + 1.79550e28i) q^{93} -5.67706e28i q^{94} +7.96450e28i q^{95} +(1.07263e28 + 4.85136e27i) q^{96} +7.01706e28i q^{97} +(-5.50198e28 + 4.40926e28i) q^{98} +(-1.23868e29 + 1.08923e29i) 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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