LMFDB - Embedded newform 30.24.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,24,Mod(1,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("30.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	30.a (trivial)

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:	yes
Analytic conductor:	$100.561211204$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2048.00 q^{2} +177147. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} +3.62797e8 q^{6} -8.22923e9 q^{7} +8.58993e9 q^{8} +3.13811e10 q^{9} +O(q^{10})$

\(q+2048.00 q^{2} +177147. q^{3} +4.19430e6 q^{4} +4.88281e7 q^{5} +3.62797e8 q^{6} -8.22923e9 q^{7} +8.58993e9 q^{8} +3.13811e10 q^{9} +1.00000e11 q^{10} +4.90369e11 q^{11} +7.43008e11 q^{12} -8.53522e12 q^{13} -1.68535e13 q^{14} +8.64976e12 q^{15} +1.75922e13 q^{16} +2.41968e14 q^{17} +6.42684e13 q^{18} +1.38950e14 q^{19} +2.04800e14 q^{20} -1.45778e15 q^{21} +1.00428e15 q^{22} -8.33866e15 q^{23} +1.52168e15 q^{24} +2.38419e15 q^{25} -1.74801e16 q^{26} +5.55906e15 q^{27} -3.45159e16 q^{28} -2.05223e16 q^{29} +1.77147e16 q^{30} -2.17380e17 q^{31} +3.60288e16 q^{32} +8.68675e16 q^{33} +4.95551e17 q^{34} -4.01818e17 q^{35} +1.31622e17 q^{36} +4.61524e17 q^{37} +2.84570e17 q^{38} -1.51199e18 q^{39} +4.19430e17 q^{40} -5.80127e18 q^{41} -2.98554e18 q^{42} +4.58623e17 q^{43} +2.05676e18 q^{44} +1.53228e18 q^{45} -1.70776e19 q^{46} -1.47518e19 q^{47} +3.11640e18 q^{48} +4.03514e19 q^{49} +4.88281e18 q^{50} +4.28639e19 q^{51} -3.57993e19 q^{52} -7.71992e19 q^{53} +1.13850e19 q^{54} +2.39438e19 q^{55} -7.06885e19 q^{56} +2.46146e19 q^{57} -4.20296e19 q^{58} -2.56753e20 q^{59} +3.62797e19 q^{60} +2.15560e20 q^{61} -4.45194e20 q^{62} -2.58242e20 q^{63} +7.37870e19 q^{64} -4.16759e20 q^{65} +1.77905e20 q^{66} +1.98509e20 q^{67} +1.01489e21 q^{68} -1.47717e21 q^{69} -8.22923e20 q^{70} +2.44686e21 q^{71} +2.69561e20 q^{72} -1.39210e21 q^{73} +9.45201e20 q^{74} +4.22351e20 q^{75} +5.82799e20 q^{76} -4.03536e21 q^{77} -3.09655e21 q^{78} -7.92537e21 q^{79} +8.58993e20 q^{80} +9.84771e20 q^{81} -1.18810e22 q^{82} +6.38214e21 q^{83} -6.11439e21 q^{84} +1.18148e22 q^{85} +9.39259e20 q^{86} -3.63546e21 q^{87} +4.21224e21 q^{88} +1.08621e22 q^{89} +3.13811e21 q^{90} +7.02383e22 q^{91} -3.49749e22 q^{92} -3.85082e22 q^{93} -3.02117e22 q^{94} +6.78467e21 q^{95} +6.38239e21 q^{96} -5.59553e22 q^{97} +8.26398e22 q^{98} +1.53883e22 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	2048.00	0.707107
$2$	2048.00	0.707107
$3$	177147.	0.577350
$3$	177147.	0.577350
$4$	4.19430e6	0.500000
$5$	4.88281e7	0.447214
$5$	4.88281e7	0.447214
$6$	3.62797e8	0.408248
$7$	−8.22923e9	−1.57301	−0.786505	−	0.617584i	$-0.788112\pi$
$7$	−8.22923e9	−1.57301	−0.786505	+	0.617584i	$0.788112\pi$
$8$	8.58993e9	0.353553
$9$	3.13811e10	0.333333
$10$	1.00000e11	0.316228
$11$	4.90369e11	0.518212	0.259106	−	0.965849i	$-0.416572\pi$
$11$	4.90369e11	0.518212	0.259106	+	0.965849i	$0.416572\pi$
$12$	7.43008e11	0.288675
$13$	−8.53522e12	−1.32089	−0.660445	−	0.750875i	$-0.729632\pi$
$13$	−8.53522e12	−1.32089	−0.660445	+	0.750875i	$0.729632\pi$
$14$	−1.68535e13	−1.11229
$15$	8.64976e12	0.258199
$16$	1.75922e13	0.250000
$17$	2.41968e14	1.71236	0.856181	−	0.516677i	$-0.172831\pi$
$17$	2.41968e14	1.71236	0.856181	+	0.516677i	$0.172831\pi$
$18$	6.42684e13	0.235702
$19$	1.38950e14	0.273648	0.136824	−	0.990595i	$-0.456311\pi$
$19$	1.38950e14	0.273648	0.136824	+	0.990595i	$0.456311\pi$
$20$	2.04800e14	0.223607
$21$	−1.45778e15	−0.908178
$22$	1.00428e15	0.366431
$23$	−8.33866e15	−1.82485	−0.912423	−	0.409248i	$-0.865791\pi$
$23$	−8.33866e15	−1.82485	−0.912423	+	0.409248i	$0.865791\pi$
$24$	1.52168e15	0.204124
$25$	2.38419e15	0.200000
$26$	−1.74801e16	−0.934010
$27$	5.55906e15	0.192450
$28$	−3.45159e16	−0.786505
$29$	−2.05223e16	−0.312355	−0.156178	−	0.987729i	$-0.549917\pi$
$29$	−2.05223e16	−0.312355	−0.156178	+	0.987729i	$0.549917\pi$
$30$	1.77147e16	0.182574
$31$	−2.17380e17	−1.53660	−0.768298	−	0.640092i	$-0.778896\pi$
$31$	−2.17380e17	−1.53660	−0.768298	+	0.640092i	$0.778896\pi$
$32$	3.60288e16	0.176777
$33$	8.68675e16	0.299190
$34$	4.95551e17	1.21082
$35$	−4.01818e17	−0.703472
$36$	1.31622e17	0.166667
$37$	4.61524e17	0.426456	0.213228	−	0.977002i	$-0.431602\pi$
$37$	4.61524e17	0.426456	0.213228	+	0.977002i	$0.431602\pi$
$38$	2.84570e17	0.193498
$39$	−1.51199e18	−0.762616
$40$	4.19430e17	0.158114
$41$	−5.80127e18	−1.64630	−0.823150	−	0.567825i	$-0.807785\pi$
$41$	−5.80127e18	−1.64630	−0.823150	+	0.567825i	$0.807785\pi$
$42$	−2.98554e18	−0.642179
$43$	4.58623e17	0.0752607	0.0376304	−	0.999292i	$-0.488019\pi$
$43$	4.58623e17	0.0752607	0.0376304	+	0.999292i	$0.488019\pi$
$44$	2.05676e18	0.259106
$45$	1.53228e18	0.149071
$46$	−1.70776e19	−1.29036
$47$	−1.47518e19	−0.870401	−0.435200	−	0.900334i	$-0.643322\pi$
$47$	−1.47518e19	−0.870401	−0.435200	+	0.900334i	$0.643322\pi$
$48$	3.11640e18	0.144338
$49$	4.03514e19	1.47436
$50$	4.88281e18	0.141421
$51$	4.28639e19	0.988632
$52$	−3.57993e19	−0.660445
$53$	−7.71992e19	−1.14404	−0.572019	−	0.820241i	$-0.693840\pi$
$53$	−7.71992e19	−1.14404	−0.572019	+	0.820241i	$0.693840\pi$
$54$	1.13850e19	0.136083
$55$	2.39438e19	0.231751
$56$	−7.06885e19	−0.556143
$57$	2.46146e19	0.157991
$58$	−4.20296e19	−0.220868
$59$	−2.56753e20	−1.10845	−0.554227	−	0.832365i	$-0.686986\pi$
$59$	−2.56753e20	−1.10845	−0.554227	+	0.832365i	$0.686986\pi$
$60$	3.62797e19	0.129099
$61$	2.15560e20	0.634272	0.317136	−	0.948380i	$-0.397279\pi$
$61$	2.15560e20	0.634272	0.317136	+	0.948380i	$0.397279\pi$
$62$	−4.45194e20	−1.08654
$63$	−2.58242e20	−0.524337
$64$	7.37870e19	0.125000
$65$	−4.16759e20	−0.590720
$66$	1.77905e20	0.211559
$67$	1.98509e20	0.198573	0.0992866	−	0.995059i	$-0.468344\pi$
$67$	1.98509e20	0.198573	0.0992866	+	0.995059i	$0.468344\pi$
$68$	1.01489e21	0.856181
$69$	−1.47717e21	−1.05358
$70$	−8.22923e20	−0.497430
$71$	2.44686e21	1.25643	0.628215	−	0.778040i	$-0.283786\pi$
$71$	2.44686e21	1.25643	0.628215	+	0.778040i	$0.283786\pi$
$72$	2.69561e20	0.117851
$73$	−1.39210e21	−0.519346	−0.259673	−	0.965697i	$-0.583615\pi$
$73$	−1.39210e21	−0.519346	−0.259673	+	0.965697i	$0.583615\pi$
$74$	9.45201e20	0.301550
$75$	4.22351e20	0.115470
$76$	5.82799e20	0.136824
$77$	−4.03536e21	−0.815153
$78$	−3.09655e21	−0.539251
$79$	−7.92537e21	−1.19209	−0.596043	−	0.802952i	$-0.703261\pi$
$79$	−7.92537e21	−1.19209	−0.596043	+	0.802952i	$0.703261\pi$
$80$	8.58993e20	0.111803
$81$	9.84771e20	0.111111
$82$	−1.18810e22	−1.16411
$83$	6.38214e21	0.543962	0.271981	−	0.962303i	$-0.412321\pi$
$83$	6.38214e21	0.543962	0.271981	+	0.962303i	$0.412321\pi$
$84$	−6.11439e21	−0.454089
$85$	1.18148e22	0.765791
$86$	9.39259e20	0.0532174
$87$	−3.63546e21	−0.180338
$88$	4.21224e21	0.183216
$89$	1.08621e22	0.414886	0.207443	−	0.978247i	$-0.433486\pi$
$89$	1.08621e22	0.414886	0.207443	+	0.978247i	$0.433486\pi$
$90$	3.13811e21	0.105409
$91$	7.02383e22	2.07777
$92$	−3.49749e22	−0.912423
$93$	−3.85082e22	−0.887154
$94$	−3.02117e22	−0.615466
$95$	6.78467e21	0.122379
$96$	6.38239e21	0.102062
$97$	−5.59553e22	−0.794267	−0.397133	−	0.917761i	$-0.629995\pi$
$97$	−5.59553e22	−0.794267	−0.397133	+	0.917761i	$0.629995\pi$
$98$	8.26398e22	1.04253
$99$	1.53883e22	0.172737
$100$	1.00000e22	0.100000
$101$	−5.24380e21	−0.0467681	−0.0233841	−	0.999727i	$-0.507444\pi$
$101$	−5.24380e21	−0.0467681	−0.0233841	+	0.999727i	$0.507444\pi$
$102$	8.77853e22	0.699069
$103$	−1.92030e23	−1.36691	−0.683455	−	0.729993i	$-0.739523\pi$
$103$	−1.92030e23	−1.36691	−0.683455	+	0.729993i	$0.739523\pi$
$104$	−7.33170e22	−0.467005
$105$	−7.11808e22	−0.406150
$106$	−1.58104e23	−0.808957
$107$	−3.04987e23	−1.40078	−0.700388	−	0.713763i	$-0.746989\pi$
$107$	−3.04987e23	−1.40078	−0.700388	+	0.713763i	$0.746989\pi$
$108$	2.33164e22	0.0962250
$109$	4.58905e23	1.70340	0.851702	−	0.524026i	$-0.175571\pi$
$109$	4.58905e23	1.70340	0.851702	+	0.524026i	$0.175571\pi$
$110$	4.90369e22	0.163873
$111$	8.17576e22	0.246215
$112$	−1.44770e23	−0.393253
$113$	8.45822e22	0.207432	0.103716	−	0.994607i	$-0.466927\pi$
$113$	8.45822e22	0.207432	0.103716	+	0.994607i	$0.466927\pi$
$114$	5.04107e22	0.111716
$115$	−4.07161e23	−0.816096
$116$	−8.60767e22	−0.156178
$117$	−2.67844e23	−0.440296
$118$	−5.25831e23	−0.783796
$119$	−1.99121e24	−2.69356
$120$	7.43008e22	0.0912871
$121$	−6.54968e23	−0.731456
$122$	4.41468e23	0.448498
$123$	−1.02768e24	−0.950491
$124$	−9.11757e23	−0.768298
$125$	1.16415e23	0.0894427
$126$	−5.28879e23	−0.370762
$127$	−2.68215e24	−1.71688	−0.858439	−	0.512915i	$-0.828565\pi$
$127$	−2.68215e24	−1.71688	−0.858439	+	0.512915i	$0.828565\pi$
$128$	1.51116e23	0.0883883
$129$	8.12437e22	0.0434518
$130$	−8.53522e23	−0.417702
$131$	−3.87063e24	−1.73445	−0.867224	−	0.497918i	$-0.834098\pi$
$131$	−3.87063e24	−1.73445	−0.867224	+	0.497918i	$0.834098\pi$
$132$	3.64349e23	0.149595
$133$	−1.14345e24	−0.430451
$134$	4.06547e23	0.140412
$135$	2.71439e23	0.0860663
$136$	2.07849e24	0.605411
$137$	4.04295e24	1.08246	0.541231	−	0.840874i	$-0.317959\pi$
$137$	4.04295e24	1.08246	0.541231	+	0.840874i	$0.317959\pi$
$138$	−3.02524e24	−0.744990
$139$	8.19907e24	1.85821	0.929105	−	0.369817i	$-0.120580\pi$
$139$	8.19907e24	1.85821	0.929105	+	0.369817i	$0.120580\pi$
$140$	−1.68535e24	−0.351736
$141$	−2.61324e24	−0.502526
$142$	5.01117e24	0.888430
$143$	−4.18541e24	−0.684501
$144$	5.52061e23	0.0833333
$145$	−1.00206e24	−0.139689
$146$	−2.85102e24	−0.367233
$147$	7.14814e24	0.851223
$148$	1.93577e24	0.213228
$149$	−1.36109e25	−1.38753	−0.693767	−	0.720200i	$-0.744050\pi$
$149$	−1.36109e25	−1.38753	−0.693767	+	0.720200i	$0.744050\pi$
$150$	8.64976e23	0.0816497
$151$	5.88991e23	0.0515079	0.0257540	−	0.999668i	$-0.491801\pi$
$151$	5.88991e23	0.0515079	0.0257540	+	0.999668i	$0.491801\pi$
$152$	1.19357e24	0.0967492
$153$	7.59321e24	0.570787
$154$	−8.26442e24	−0.576400
$155$	−1.06142e25	−0.687187
$156$	−6.34174e24	−0.381308
$157$	−1.10971e24	−0.0619961	−0.0309981	−	0.999519i	$-0.509869\pi$
$157$	−1.10971e24	−0.0619961	−0.0309981	+	0.999519i	$0.509869\pi$
$158$	−1.62312e25	−0.842933
$159$	−1.36756e25	−0.660510
$160$	1.75922e24	0.0790569
$161$	6.86208e25	2.87050
$162$	2.01681e24	0.0785674
$163$	2.08283e25	0.755957	0.377979	−	0.925814i	$-0.376619\pi$
$163$	2.08283e25	0.755957	0.377979	+	0.925814i	$0.376619\pi$
$164$	−2.43323e25	−0.823150
$165$	4.24158e24	0.133802
$166$	1.30706e25	0.384639
$167$	−6.25491e25	−1.71784	−0.858918	−	0.512113i	$-0.828863\pi$
$167$	−6.25491e25	−1.71784	−0.858918	+	0.512113i	$0.828863\pi$
$168$	−1.25223e25	−0.321089
$169$	3.10962e25	0.744748
$170$	2.41968e25	0.541496
$171$	4.36040e24	0.0912160
$172$	1.92360e24	0.0376304
$173$	2.78562e25	0.509791	0.254895	−	0.966969i	$-0.417959\pi$
$173$	2.78562e25	0.509791	0.254895	+	0.966969i	$0.417959\pi$
$174$	−7.44542e24	−0.127518
$175$	−1.96200e25	−0.314602
$176$	8.62667e24	0.129553
$177$	−4.54831e25	−0.639966
$178$	2.22456e25	0.293369
$179$	6.76947e25	0.837037	0.418518	−	0.908208i	$-0.362550\pi$
$179$	6.76947e25	0.837037	0.418518	+	0.908208i	$0.362550\pi$
$180$	6.42684e24	0.0745356
$181$	6.20254e25	0.674942	0.337471	−	0.941336i	$-0.390429\pi$
$181$	6.20254e25	0.674942	0.337471	+	0.941336i	$0.390429\pi$
$182$	1.43848e26	1.46921
$183$	3.81859e25	0.366197
$184$	−7.16286e25	−0.645181
$185$	2.25354e25	0.190717
$186$	−7.88648e25	−0.627313
$187$	1.18654e26	0.887366
$188$	−6.18735e25	−0.435200
$189$	−4.57468e25	−0.302726
$190$	1.38950e25	0.0865351
$191$	1.01320e26	0.594034	0.297017	−	0.954872i	$-0.404008\pi$
$191$	1.01320e26	0.594034	0.297017	+	0.954872i	$0.404008\pi$
$192$	1.30711e25	0.0721688
$193$	5.58166e25	0.290305	0.145152	−	0.989409i	$-0.453633\pi$
$193$	5.58166e25	0.290305	0.145152	+	0.989409i	$0.453633\pi$
$194$	−1.14596e26	−0.561631
$195$	−7.38276e25	−0.341052
$196$	1.69246e26	0.737181
$197$	1.11056e26	0.456225	0.228113	−	0.973635i	$-0.426745\pi$
$197$	1.11056e26	0.456225	0.228113	+	0.973635i	$0.426745\pi$
$198$	3.15153e25	0.122144
$199$	4.47556e26	1.63696	0.818478	−	0.574538i	$-0.194818\pi$
$199$	4.47556e26	1.63696	0.818478	+	0.574538i	$0.194818\pi$
$200$	2.04800e25	0.0707107
$201$	3.51653e25	0.114646
$202$	−1.07393e25	−0.0330701
$203$	1.68882e26	0.491338
$204$	1.79784e26	0.494316
$205$	−2.83265e26	−0.736247
$206$	−3.93276e26	−0.966551
$207$	−2.61676e26	−0.608282
$208$	−1.50153e26	−0.330222
$209$	6.81368e25	0.141808
$210$	−1.45778e26	−0.287191
$211$	5.51988e26	1.02963	0.514815	−	0.857301i	$-0.327861\pi$
$211$	5.51988e26	1.02963	0.514815	+	0.857301i	$0.327861\pi$
$212$	−3.23797e26	−0.572019
$213$	4.33454e26	0.725400
$214$	−6.24614e26	−0.990498
$215$	2.23937e25	0.0336576
$216$	4.77520e25	0.0680414
$217$	1.78887e27	2.41708
$218$	9.39837e26	1.20449
$219$	−2.46606e26	−0.299845
$220$	1.00428e26	0.115876
$221$	−2.06525e27	−2.26184
$222$	1.67440e26	0.174100
$223$	8.90256e26	0.879040	0.439520	−	0.898233i	$-0.355149\pi$
$223$	8.90256e26	0.879040	0.439520	+	0.898233i	$0.355149\pi$
$224$	−2.96489e26	−0.278072
$225$	7.48183e25	0.0666667
$226$	1.73224e26	0.146677
$227$	−4.59681e26	−0.369964	−0.184982	−	0.982742i	$-0.559223\pi$
$227$	−4.59681e26	−0.369964	−0.184982	+	0.982742i	$0.559223\pi$
$228$	1.03241e26	0.0789954
$229$	−1.57123e27	−1.14323	−0.571614	−	0.820523i	$-0.693683\pi$
$229$	−1.57123e27	−1.14323	−0.571614	+	0.820523i	$0.693683\pi$
$230$	−8.33866e26	−0.577067
$231$	−7.14852e26	−0.470629
$232$	−1.76285e26	−0.110434
$233$	2.52051e27	1.50278	0.751389	−	0.659859i	$-0.229384\pi$
$233$	2.52051e27	1.50278	0.751389	+	0.659859i	$0.229384\pi$
$234$	−5.48545e26	−0.311337
$235$	−7.20302e26	−0.389255
$236$	−1.07690e27	−0.554227
$237$	−1.40396e27	−0.688252
$238$	−4.07800e27	−1.90464
$239$	5.28927e26	0.235407	0.117704	−	0.993049i	$-0.462447\pi$
$239$	5.28927e26	0.235407	0.117704	+	0.993049i	$0.462447\pi$
$240$	1.52168e26	0.0645497
$241$	−2.42041e27	−0.978797	−0.489399	−	0.872060i	$-0.662784\pi$
$241$	−2.42041e27	−0.978797	−0.489399	+	0.872060i	$0.662784\pi$
$242$	−1.34137e27	−0.517218
$243$	1.74449e26	0.0641500
$244$	9.04126e26	0.317136
$245$	1.97029e27	0.659355
$246$	−2.10468e27	−0.672099
$247$	−1.18597e27	−0.361459
$248$	−1.86728e27	−0.543269
$249$	1.13058e27	0.314057
$250$	2.38419e26	0.0632456
$251$	5.00383e27	1.26781	0.633905	−	0.773411i	$-0.281451\pi$
$251$	5.00383e27	1.26781	0.633905	+	0.773411i	$0.281451\pi$
$252$	−1.08314e27	−0.262168
$253$	−4.08903e27	−0.945657
$254$	−5.49303e27	−1.21402
$255$	2.09296e27	0.442130
$256$	3.09485e26	0.0625000
$257$	6.51244e27	1.25751	0.628757	−	0.777602i	$-0.283564\pi$
$257$	6.51244e27	1.25751	0.628757	+	0.777602i	$0.283564\pi$
$258$	1.66387e26	0.0307251
$259$	−3.79799e27	−0.670820
$260$	−1.74801e27	−0.295360
$261$	−6.44011e26	−0.104118
$262$	−7.92705e27	−1.22644
$263$	−3.47579e27	−0.514710	−0.257355	−	0.966317i	$-0.582851\pi$
$263$	−3.47579e27	−0.514710	−0.257355	+	0.966317i	$0.582851\pi$
$264$	7.46186e26	0.105780
$265$	−3.76949e27	−0.511629
$266$	−2.34179e27	−0.304375
$267$	1.92419e27	0.239534
$268$	8.32608e26	0.0992866
$269$	−3.74875e27	−0.428287	−0.214144	−	0.976802i	$-0.568696\pi$
$269$	−3.74875e27	−0.428287	−0.214144	+	0.976802i	$0.568696\pi$
$270$	5.55906e26	0.0608581
$271$	1.07804e28	1.13106	0.565531	−	0.824727i	$-0.308671\pi$
$271$	1.07804e28	1.13106	0.565531	+	0.824727i	$0.308671\pi$
$272$	4.25675e27	0.428090
$273$	1.24425e28	1.19960
$274$	8.27997e27	0.765416
$275$	1.16913e27	0.103642
$276$	−6.19570e27	−0.526788
$277$	5.52964e27	0.451003	0.225502	−	0.974243i	$-0.427598\pi$
$277$	5.52964e27	0.451003	0.225502	+	0.974243i	$0.427598\pi$
$278$	1.67917e28	1.31395
$279$	−6.82161e27	−0.512199
$280$	−3.45159e27	−0.248715
$281$	−1.51341e28	−1.04673	−0.523363	−	0.852110i	$-0.675323\pi$
$281$	−1.51341e28	−1.04673	−0.523363	+	0.852110i	$0.675323\pi$
$282$	−5.35191e27	−0.355340
$283$	−2.20581e28	−1.40612	−0.703062	−	0.711128i	$-0.748185\pi$
$283$	−2.20581e28	−1.40612	−0.703062	+	0.711128i	$0.748185\pi$
$284$	1.02629e28	0.628215
$285$	1.20188e27	0.0706556
$286$	−8.57173e27	−0.484015
$287$	4.77400e28	2.58965
$288$	1.13062e27	0.0589256
$289$	3.85810e28	1.93218
$290$	−2.05223e27	−0.0987753
$291$	−9.91231e27	−0.458570
$292$	−5.83888e27	−0.259673
$293$	3.07219e28	1.31362	0.656811	−	0.754055i	$-0.271905\pi$
$293$	3.07219e28	1.31362	0.656811	+	0.754055i	$0.271905\pi$
$294$	1.46394e28	0.601906
$295$	−1.25368e28	−0.495716
$296$	3.96446e27	0.150775
$297$	2.72599e27	0.0997299
$298$	−2.78750e28	−0.981134
$299$	7.11724e28	2.41042
$300$	1.77147e27	0.0577350
$301$	−3.77411e27	−0.118386
$302$	1.20625e27	0.0364216
$303$	−9.28923e26	−0.0270016
$304$	2.44444e27	0.0684120
$305$	1.05254e28	0.283655
$306$	1.55509e28	0.403607
$307$	5.17050e28	1.29253	0.646266	−	0.763112i	$-0.276329\pi$
$307$	5.17050e28	1.29253	0.646266	+	0.763112i	$0.276329\pi$
$308$	−1.69255e28	−0.407576
$309$	−3.40175e28	−0.789186
$310$	−2.17380e28	−0.485914
$311$	−2.93836e28	−0.632938	−0.316469	−	0.948603i	$-0.602497\pi$
$311$	−2.93836e28	−0.632938	−0.316469	+	0.948603i	$0.602497\pi$
$312$	−1.29879e28	−0.269625
$313$	−6.23254e27	−0.124711	−0.0623555	−	0.998054i	$-0.519861\pi$
$313$	−6.23254e27	−0.124711	−0.0623555	+	0.998054i	$0.519861\pi$
$314$	−2.27269e27	−0.0438379
$315$	−1.26095e28	−0.234491
$316$	−3.32414e28	−0.596043
$317$	−7.86366e28	−1.35970	−0.679850	−	0.733351i	$-0.737955\pi$
$317$	−7.86366e28	−1.35970	−0.679850	+	0.733351i	$0.737955\pi$
$318$	−2.80076e28	−0.467051
$319$	−1.00635e28	−0.161866
$320$	3.60288e27	0.0559017
$321$	−5.40276e28	−0.808738
$322$	1.40535e29	2.02975
$323$	3.36215e28	0.468584
$324$	4.13043e27	0.0555556
$325$	−2.03496e28	−0.264178
$326$	4.26565e28	0.534543
$327$	8.12936e28	0.983461
$328$	−4.98325e28	−0.582055
$329$	1.21396e29	1.36915
$330$	8.68675e27	0.0946121
$331$	−5.75248e28	−0.605108	−0.302554	−	0.953132i	$-0.597839\pi$
$331$	−5.75248e28	−0.605108	−0.302554	+	0.953132i	$0.597839\pi$
$332$	2.67687e28	0.271981
$333$	1.44831e28	0.142152
$334$	−1.28101e29	−1.21469
$335$	9.69283e27	0.0888046
$336$	−2.56456e28	−0.227045
$337$	−1.75049e29	−1.49767	−0.748834	−	0.662758i	$-0.769386\pi$
$337$	−1.75049e29	−1.49767	−0.748834	+	0.662758i	$0.769386\pi$
$338$	6.36849e28	0.526617
$339$	1.49835e28	0.119761
$340$	4.95551e28	0.382896
$341$	−1.06596e29	−0.796283
$342$	8.93010e27	0.0644995
$343$	−1.06838e29	−0.746176
$344$	3.93954e27	0.0266087
$345$	−7.21274e28	−0.471173
$346$	5.70495e28	0.360476
$347$	8.38188e28	0.512333	0.256166	−	0.966633i	$-0.417540\pi$
$347$	8.38188e28	0.512333	0.256166	+	0.966633i	$0.417540\pi$
$348$	−1.52482e28	−0.0901691
$349$	7.31601e28	0.418583	0.209292	−	0.977853i	$-0.432884\pi$
$349$	7.31601e28	0.418583	0.209292	+	0.977853i	$0.432884\pi$
$350$	−4.01818e28	−0.222457
$351$	−4.74478e28	−0.254205
$352$	1.76674e28	0.0916078
$353$	3.11109e28	0.156136	0.0780680	−	0.996948i	$-0.475125\pi$
$353$	3.11109e28	0.156136	0.0780680	+	0.996948i	$0.475125\pi$
$354$	−9.31493e28	−0.452525
$355$	1.19476e29	0.561892
$356$	4.55589e28	0.207443
$357$	−3.52737e29	−1.55513
$358$	1.38639e29	0.591874
$359$	−5.23487e28	−0.216431	−0.108216	−	0.994127i	$-0.534514\pi$
$359$	−5.23487e28	−0.216431	−0.108216	+	0.994127i	$0.534514\pi$
$360$	1.31622e28	0.0527046
$361$	−2.38523e29	−0.925117
$362$	1.27028e29	0.477256
$363$	−1.16026e29	−0.422307
$364$	2.94601e29	1.03889
$365$	−6.79735e28	−0.232259
$366$	7.82047e28	0.258941
$367$	−2.19593e29	−0.704625	−0.352312	−	0.935882i	$-0.614605\pi$
$367$	−2.19593e29	−0.704625	−0.352312	+	0.935882i	$0.614605\pi$
$368$	−1.46695e29	−0.456212
$369$	−1.82050e29	−0.548766
$370$	4.61524e28	0.134857
$371$	6.35290e29	1.79958
$372$	−1.61515e29	−0.443577
$373$	2.06340e29	0.549455	0.274727	−	0.961522i	$-0.411412\pi$
$373$	2.06340e29	0.549455	0.274727	+	0.961522i	$0.411412\pi$
$374$	2.43003e29	0.627463
$375$	2.06226e28	0.0516398
$376$	−1.26717e29	−0.307733
$377$	1.75162e29	0.412586
$378$	−9.36894e28	−0.214060
$379$	−7.80972e29	−1.73095	−0.865475	−	0.500953i	$-0.832983\pi$
$379$	−7.80972e29	−1.73095	−0.865475	+	0.500953i	$0.832983\pi$
$380$	2.84570e28	0.0611896
$381$	−4.75134e29	−0.991240
$382$	2.07503e29	0.420046
$383$	6.21663e28	0.122115	0.0610575	−	0.998134i	$-0.480553\pi$
$383$	6.21663e28	0.122115	0.0610575	+	0.998134i	$0.480553\pi$
$384$	2.67697e28	0.0510310
$385$	−1.97039e29	−0.364547
$386$	1.14312e29	0.205276
$387$	1.43921e28	0.0250869
$388$	−2.34694e29	−0.397133
$389$	−1.16984e29	−0.192179	−0.0960897	−	0.995373i	$-0.530634\pi$
$389$	−1.16984e29	−0.192179	−0.0960897	+	0.995373i	$0.530634\pi$
$390$	−1.51199e29	−0.241160
$391$	−2.01769e30	−3.12480
$392$	3.46616e29	0.521266
$393$	−6.85670e29	−1.00138
$394$	2.27442e29	0.322600
$395$	−3.86981e29	−0.533117
$396$	6.45433e28	0.0863687
$397$	−3.66094e29	−0.475884	−0.237942	−	0.971279i	$-0.576473\pi$
$397$	−3.66094e29	−0.475884	−0.237942	+	0.971279i	$0.576473\pi$
$398$	9.16595e29	1.15750
$399$	−2.02559e29	−0.248521
$400$	4.19430e28	0.0500000
$401$	−8.36010e28	−0.0968392	−0.0484196	−	0.998827i	$-0.515418\pi$
$401$	−8.36010e28	−0.0968392	−0.0484196	+	0.998827i	$0.515418\pi$
$402$	7.20186e28	0.0810671
$403$	1.85539e30	2.02967
$404$	−2.19941e28	−0.0233841
$405$	4.80845e28	0.0496904
$406$	3.45871e29	0.347428
$407$	2.26317e29	0.220995
$408$	3.68198e29	0.349534
$409$	1.66287e30	1.53476	0.767379	−	0.641194i	$-0.221560\pi$
$409$	1.66287e30	1.53476	0.767379	+	0.641194i	$0.221560\pi$
$410$	−5.80127e29	−0.520605
$411$	7.16197e29	0.624959
$412$	−8.05430e29	−0.683455
$413$	2.11288e30	1.74361
$414$	−5.35913e29	−0.430120
$415$	3.11628e29	0.243267
$416$	−3.07514e29	−0.233502
$417$	1.45244e30	1.07284
$418$	1.39544e29	0.100273
$419$	−6.55850e29	−0.458504	−0.229252	−	0.973367i	$-0.573628\pi$
$419$	−6.55850e29	−0.458504	−0.229252	+	0.973367i	$0.573628\pi$
$420$	−2.98554e29	−0.203075
$421$	1.67732e30	1.11013	0.555063	−	0.831808i	$-0.312694\pi$
$421$	1.67732e30	1.11013	0.555063	+	0.831808i	$0.312694\pi$
$422$	1.13047e30	0.728058
$423$	−4.62927e29	−0.290134
$424$	−6.63136e29	−0.404478
$425$	5.76897e29	0.342472
$426$	8.87713e29	0.512935
$427$	−1.77390e30	−0.997717
$428$	−1.27921e30	−0.700388
$429$	−7.41433e29	−0.395197
$430$	4.58623e28	0.0237995
$431$	3.85396e30	1.94724	0.973619	−	0.228179i	$-0.0732773\pi$
$431$	3.85396e30	1.94724	0.973619	+	0.228179i	$0.0732773\pi$
$432$	9.77960e28	0.0481125
$433$	−1.20261e30	−0.576122	−0.288061	−	0.957612i	$-0.593011\pi$
$433$	−1.20261e30	−0.576122	−0.288061	+	0.957612i	$0.593011\pi$
$434$	3.66360e30	1.70914
$435$	−1.77513e29	−0.0806497
$436$	1.92479e30	0.851702
$437$	−1.15866e30	−0.499366
$438$	−5.05049e29	−0.212022
$439$	1.15759e30	0.473382	0.236691	−	0.971585i	$-0.423937\pi$
$439$	1.15759e30	0.473382	0.236691	+	0.971585i	$0.423937\pi$
$440$	2.05676e29	0.0819365
$441$	1.26627e30	0.491454
$442$	−4.22964e30	−1.59936
$443$	1.49627e30	0.551275	0.275637	−	0.961262i	$-0.411111\pi$
$443$	1.49627e30	0.551275	0.275637	+	0.961262i	$0.411111\pi$
$444$	3.42916e29	0.123107
$445$	5.30376e29	0.185543
$446$	1.82324e30	0.621575
$447$	−2.41112e30	−0.801093
$448$	−6.07210e29	−0.196626
$449$	1.06527e30	0.336222	0.168111	−	0.985768i	$-0.446233\pi$
$449$	1.06527e30	0.336222	0.168111	+	0.985768i	$0.446233\pi$
$450$	1.53228e29	0.0471405
$451$	−2.84477e30	−0.853132
$452$	3.54763e29	0.103716
$453$	1.04338e29	0.0297381
$454$	−9.41427e29	−0.261604
$455$	3.42960e30	0.929208
$456$	2.11438e29	0.0558582
$457$	8.53337e29	0.219829	0.109914	−	0.993941i	$-0.464942\pi$
$457$	8.53337e29	0.219829	0.109914	+	0.993941i	$0.464942\pi$
$458$	−3.21789e30	−0.808384
$459$	1.34512e30	0.329544
$460$	−1.70776e30	−0.408048
$461$	3.81056e30	0.888031	0.444015	−	0.896019i	$-0.353554\pi$
$461$	3.81056e30	0.888031	0.444015	+	0.896019i	$0.353554\pi$
$462$	−1.46402e30	−0.332785
$463$	−5.71527e30	−1.26723	−0.633615	−	0.773649i	$-0.718429\pi$
$463$	−5.71527e30	−1.26723	−0.633615	+	0.773649i	$0.718429\pi$
$464$	−3.61032e29	−0.0780888
$465$	−1.88028e30	−0.396747
$466$	5.16200e30	1.06263
$467$	−2.80083e29	−0.0562526	−0.0281263	−	0.999604i	$-0.508954\pi$
$467$	−2.80083e29	−0.0562526	−0.0281263	+	0.999604i	$0.508954\pi$
$468$	−1.12342e30	−0.220148
$469$	−1.63358e30	−0.312358
$470$	−1.47518e30	−0.275245
$471$	−1.96582e29	−0.0357935
$472$	−2.20549e30	−0.391898
$473$	2.24895e29	0.0390010
$474$	−2.87530e30	−0.486667
$475$	3.31283e29	0.0547296
$476$	−8.35174e30	−1.34678
$477$	−2.42259e30	−0.381346
$478$	1.08324e30	0.166458
$479$	−7.25380e30	−1.08820	−0.544098	−	0.839022i	$-0.683128\pi$
$479$	−7.25380e30	−1.08820	−0.544098	+	0.839022i	$0.683128\pi$
$480$	3.11640e29	0.0456435
$481$	−3.93921e30	−0.563302
$482$	−4.95700e30	−0.692114
$483$	1.21560e31	1.65729
$484$	−2.74714e30	−0.365728
$485$	−2.73219e30	−0.355207
$486$	3.57272e29	0.0453609
$487$	−6.01205e30	−0.745487	−0.372743	−	0.927934i	$-0.621583\pi$
$487$	−6.01205e30	−0.745487	−0.372743	+	0.927934i	$0.621583\pi$
$488$	1.85165e30	0.224249
$489$	3.68968e30	0.436452
$490$	4.03514e30	0.466234
$491$	1.11238e31	1.25550	0.627750	−	0.778415i	$-0.283976\pi$
$491$	1.11238e31	1.25550	0.627750	+	0.778415i	$0.283976\pi$
$492$	−4.31039e30	−0.475246
$493$	−4.96573e30	−0.534865
$494$	−2.42887e30	−0.255590
$495$	7.51382e29	0.0772505
$496$	−3.82419e30	−0.384149
$497$	−2.01358e31	−1.97638
$498$	2.31542e30	0.222072
$499$	1.31926e31	1.23644	0.618221	−	0.786004i	$-0.287854\pi$
$499$	1.31926e31	1.23644	0.618221	+	0.786004i	$0.287854\pi$
$500$	4.88281e29	0.0447214
$501$	−1.10804e31	−0.991793
$502$	1.02478e31	0.896477
$503$	−2.47554e30	−0.211660	−0.105830	−	0.994384i	$-0.533750\pi$
$503$	−2.47554e30	−0.211660	−0.105830	+	0.994384i	$0.533750\pi$
$504$	−2.21828e30	−0.185381
$505$	−2.56045e29	−0.0209153
$506$	−8.37432e30	−0.668681
$507$	5.50859e30	0.429981
$508$	−1.12497e31	−0.858439
$509$	1.75363e31	1.30823	0.654115	−	0.756395i	$-0.273041\pi$
$509$	1.75363e31	1.30823	0.654115	+	0.756395i	$0.273041\pi$
$510$	4.28639e30	0.312633
$511$	1.14559e31	0.816937
$512$	6.33825e29	0.0441942
$513$	7.72432e29	0.0526636
$514$	1.33375e31	0.889197
$515$	−9.37644e30	−0.611301
$516$	3.40761e29	0.0217259
$517$	−7.23383e30	−0.451052
$518$	−7.77828e30	−0.474342
$519$	4.93464e30	0.294328
$520$	−3.57993e30	−0.208851
$521$	−1.71273e31	−0.977359	−0.488679	−	0.872463i	$-0.662521\pi$
$521$	−1.71273e31	−0.977359	−0.488679	+	0.872463i	$0.662521\pi$
$522$	−1.31893e30	−0.0736228
$523$	−9.03843e30	−0.493541	−0.246771	−	0.969074i	$-0.579369\pi$
$523$	−9.03843e30	−0.493541	−0.246771	+	0.969074i	$0.579369\pi$
$524$	−1.62346e31	−0.867224
$525$	−3.47563e30	−0.181636
$526$	−7.11842e30	−0.363955
$527$	−5.25990e31	−2.63121
$528$	1.52819e30	0.0747975
$529$	4.86528e31	2.33007
$530$	−7.71992e30	−0.361776
$531$	−8.05719e30	−0.369485
$532$	−4.79598e30	−0.215226
$533$	4.95151e31	2.17458
$534$	3.94074e30	0.169376
$535$	−1.48920e31	−0.626446
$536$	1.70518e30	0.0702062
$537$	1.19919e31	0.483263
$538$	−7.67744e30	−0.302845
$539$	1.97871e31	0.764032
$540$	1.13850e30	0.0430331
$541$	3.08009e31	1.13971	0.569856	−	0.821745i	$-0.306999\pi$
$541$	3.08009e31	1.13971	0.569856	+	0.821745i	$0.306999\pi$
$542$	2.20782e31	0.799782
$543$	1.09876e31	0.389678
$544$	8.71782e30	0.302706
$545$	2.24075e31	0.761786
$546$	2.54823e31	0.848247
$547$	1.64679e31	0.536763	0.268382	−	0.963313i	$-0.413511\pi$
$547$	1.64679e31	0.536763	0.268382	+	0.963313i	$0.413511\pi$
$548$	1.69574e31	0.541231
$549$	6.76451e30	0.211424
$550$	2.39438e30	0.0732862
$551$	−2.85157e30	−0.0854753
$552$	−1.26888e31	−0.372495
$553$	6.52197e31	1.87516
$554$	1.13247e31	0.318907
$555$	3.99207e30	0.110111
$556$	3.43894e31	0.929105
$557$	−2.96279e31	−0.784090	−0.392045	−	0.919946i	$-0.628232\pi$
$557$	−2.96279e31	−0.784090	−0.392045	+	0.919946i	$0.628232\pi$
$558$	−1.39707e31	−0.362179
$559$	−3.91445e30	−0.0994111
$560$	−7.06885e30	−0.175868
$561$	2.10192e31	0.512321
$562$	−3.09945e31	−0.740146
$563$	−4.70736e31	−1.10136	−0.550682	−	0.834715i	$-0.685632\pi$
$563$	−4.70736e31	−1.10136	−0.550682	+	0.834715i	$0.685632\pi$
$564$	−1.09607e31	−0.251263
$565$	4.12999e30	0.0927666
$566$	−4.51750e31	−0.994280
$567$	−8.10390e30	−0.174779
$568$	2.10184e31	0.444215
$569$	−5.37447e31	−1.11313	−0.556563	−	0.830805i	$-0.687880\pi$
$569$	−5.37447e31	−1.11313	−0.556563	+	0.830805i	$0.687880\pi$
$570$	2.46146e30	0.0499611
$571$	3.50119e31	0.696466	0.348233	−	0.937408i	$-0.386782\pi$
$571$	3.50119e31	0.696466	0.348233	+	0.937408i	$0.386782\pi$
$572$	−1.75549e31	−0.342250
$573$	1.79485e31	0.342966
$574$	9.77715e31	1.83116
$575$	−1.98809e31	−0.364969
$576$	2.31551e30	0.0416667
$577$	−5.54935e31	−0.978859	−0.489429	−	0.872043i	$-0.662795\pi$
$577$	−5.54935e31	−0.978859	−0.489429	+	0.872043i	$0.662795\pi$
$578$	7.90138e31	1.36626
$579$	9.88774e30	0.167608
$580$	−4.20296e30	−0.0698447
$581$	−5.25201e31	−0.855658
$582$	−2.03004e31	−0.324258
$583$	−3.78561e31	−0.592854
$584$	−1.19580e31	−0.183617
$585$	−1.30783e31	−0.196907
$586$	6.29185e31	0.928872
$587$	−6.58773e31	−0.953668	−0.476834	−	0.878993i	$-0.658216\pi$
$587$	−6.58773e31	−0.953668	−0.476834	+	0.878993i	$0.658216\pi$
$588$	2.99815e31	0.425612
$589$	−3.02049e31	−0.420486
$590$	−2.56753e31	−0.350524
$591$	1.96732e31	0.263402
$592$	8.11922e30	0.106614
$593$	−7.68700e31	−0.989983	−0.494992	−	0.868898i	$-0.664829\pi$
$593$	−7.68700e31	−0.989983	−0.494992	+	0.868898i	$0.664829\pi$
$594$	5.58283e30	0.0705197
$595$	−9.72271e31	−1.20460
$596$	−5.70881e31	−0.693767
$597$	7.92832e31	0.945097
$598$	1.45761e32	1.70442
$599$	9.69343e31	1.11191	0.555954	−	0.831213i	$-0.312353\pi$
$599$	9.69343e31	1.11191	0.555954	+	0.831213i	$0.312353\pi$
$600$	3.62797e30	0.0408248
$601$	−1.35858e32	−1.49978	−0.749890	−	0.661563i	$-0.769894\pi$
$601$	−1.35858e32	−1.49978	−0.749890	+	0.661563i	$0.769894\pi$
$602$	−7.72938e30	−0.0837115
$603$	6.22943e30	0.0661910
$604$	2.47041e30	0.0257540
$605$	−3.19809e31	−0.327117
$606$	−1.90243e30	−0.0190930
$607$	2.47698e31	0.243923	0.121962	−	0.992535i	$-0.461082\pi$
$607$	2.47698e31	0.243923	0.121962	+	0.992535i	$0.461082\pi$
$608$	5.00620e30	0.0483746
$609$	2.99170e31	0.283674
$610$	2.15560e31	0.200575
$611$	1.25910e32	1.14970
$612$	3.18482e31	0.285394
$613$	−7.81274e31	−0.687081	−0.343541	−	0.939138i	$-0.611626\pi$
$613$	−7.81274e31	−0.687081	−0.343541	+	0.939138i	$0.611626\pi$
$614$	1.05892e32	0.913959
$615$	−5.01796e31	−0.425073
$616$	−3.46635e31	−0.288200
$617$	6.30553e31	0.514567	0.257284	−	0.966336i	$-0.417173\pi$
$617$	6.30553e31	0.514567	0.257284	+	0.966336i	$0.417173\pi$
$618$	−6.96677e31	−0.558039
$619$	1.14983e32	0.904051	0.452025	−	0.892005i	$-0.350702\pi$
$619$	1.14983e32	0.904051	0.452025	+	0.892005i	$0.350702\pi$
$620$	−4.45194e31	−0.343593
$621$	−4.63551e31	−0.351192
$622$	−6.01777e31	−0.447555
$623$	−8.93867e31	−0.652620
$624$	−2.65992e31	−0.190654
$625$	5.68434e30	0.0400000
$626$	−1.27642e31	−0.0881841
$627$	1.20702e31	0.0818727
$628$	−4.65447e30	−0.0309981
$629$	1.11674e32	0.730247
$630$	−2.58242e31	−0.165810
$631$	−2.94021e32	−1.85371	−0.926853	−	0.375425i	$-0.877497\pi$
$631$	−2.94021e32	−1.85371	−0.926853	+	0.375425i	$0.877497\pi$
$632$	−6.80784e31	−0.421466
$633$	9.77830e31	0.594457
$634$	−1.61048e32	−0.961453
$635$	−1.30964e32	−0.767811
$636$	−5.73596e31	−0.330255
$637$	−3.44409e32	−1.94747
$638$	−2.06100e31	−0.114457
$639$	7.67850e31	0.418810
$640$	7.37870e30	0.0395285
$641$	6.63302e31	0.349015	0.174508	−	0.984656i	$-0.444167\pi$
$641$	6.63302e31	0.349015	0.174508	+	0.984656i	$0.444167\pi$
$642$	−1.10649e32	−0.571864
$643$	3.49930e32	1.77646	0.888229	−	0.459400i	$-0.151936\pi$
$643$	3.49930e32	1.77646	0.888229	+	0.459400i	$0.151936\pi$
$644$	2.87816e32	1.43525
$645$	3.96698e30	0.0194322
$646$	6.88568e31	0.331339
$647$	−3.21831e32	−1.52135	−0.760674	−	0.649134i	$-0.775132\pi$
$647$	−3.21831e32	−1.52135	−0.760674	+	0.649134i	$0.775132\pi$
$648$	8.45912e30	0.0392837
$649$	−1.25904e32	−0.574414
$650$	−4.16759e31	−0.186802
$651$	3.16893e32	1.39550
$652$	8.73604e31	0.377979
$653$	3.63439e32	1.54501	0.772503	−	0.635011i	$-0.219004\pi$
$653$	3.63439e32	1.54501	0.772503	+	0.635011i	$0.219004\pi$
$654$	1.66489e32	0.695412
$655$	−1.88995e32	−0.775669
$656$	−1.02057e32	−0.411575
$657$	−4.36855e31	−0.173115
$658$	2.48619e32	0.968135
$659$	−8.88429e31	−0.339970	−0.169985	−	0.985447i	$-0.554372\pi$
$659$	−8.88429e31	−0.339970	−0.169985	+	0.985447i	$0.554372\pi$
$660$	1.77905e31	0.0669009
$661$	−3.90957e32	−1.44481	−0.722407	−	0.691468i	$-0.756964\pi$
$661$	−3.90957e32	−1.44481	−0.722407	+	0.691468i	$0.756964\pi$
$662$	−1.17811e32	−0.427876
$663$	−3.65853e32	−1.30587
$664$	5.48222e31	0.192320
$665$	−5.58326e31	−0.192504
$666$	2.96614e31	0.100517
$667$	1.71128e32	0.570000
$668$	−2.62350e32	−0.858918
$669$	1.57706e32	0.507514
$670$	1.98509e31	0.0627943
$671$	1.05704e32	0.328688
$672$	−5.25222e31	−0.160545
$673$	−3.47820e32	−1.04516	−0.522578	−	0.852591i	$-0.675030\pi$
$673$	−3.47820e32	−1.04516	−0.522578	+	0.852591i	$0.675030\pi$
$674$	−3.58500e32	−1.05901
$675$	1.32538e31	0.0384900
$676$	1.30427e32	0.372374
$677$	−2.04150e32	−0.573034	−0.286517	−	0.958075i	$-0.592497\pi$
$677$	−2.04150e32	−0.573034	−0.286517	+	0.958075i	$0.592497\pi$
$678$	3.06862e31	0.0846839
$679$	4.60469e32	1.24939
$680$	1.01489e32	0.270748
$681$	−8.14312e31	−0.213599
$682$	−2.18309e32	−0.563057
$683$	3.07053e31	0.0778709	0.0389355	−	0.999242i	$-0.487603\pi$
$683$	3.07053e31	0.0778709	0.0389355	+	0.999242i	$0.487603\pi$
$684$	1.82888e31	0.0456080
$685$	1.97410e32	0.484091
$686$	−2.18803e32	−0.527626
$687$	−2.78339e32	−0.660043
$688$	8.06818e30	0.0188152
$689$	6.58912e32	1.51115
$690$	−1.47717e32	−0.333170
$691$	4.88431e32	1.08344	0.541721	−	0.840559i	$-0.317773\pi$
$691$	4.88431e32	1.08344	0.541721	+	0.840559i	$0.317773\pi$
$692$	1.16837e32	0.254895
$693$	−1.26634e32	−0.271718
$694$	1.71661e32	0.362274
$695$	4.00345e32	0.831016
$696$	−3.12284e31	−0.0637592
$697$	−1.40372e33	−2.81906
$698$	1.49832e32	0.295983
$699$	4.46500e32	0.867630
$700$	−8.22923e31	−0.157301
$701$	5.32721e32	1.00171	0.500856	−	0.865531i	$-0.333019\pi$
$701$	5.32721e32	1.00171	0.500856	+	0.865531i	$0.333019\pi$
$702$	−9.71732e31	−0.179750
$703$	6.41288e31	0.116699
$704$	3.61829e31	0.0647765
$705$	−1.27599e32	−0.224737
$706$	6.37151e31	0.110405
$707$	4.31524e31	0.0735667
$708$	−1.90770e32	−0.319983
$709$	6.59065e32	1.08767	0.543834	−	0.839193i	$-0.316972\pi$
$709$	6.59065e32	1.08767	0.543834	+	0.839193i	$0.316972\pi$
$710$	2.44686e32	0.397318
$711$	−2.48706e32	−0.397362
$712$	9.33047e31	0.146684
$713$	1.81266e33	2.80405
$714$	−7.22405e32	−1.09964
$715$	−2.04366e32	−0.306118
$716$	2.83932e32	0.418518
$717$	9.36978e31	0.135912
$718$	−1.07210e32	−0.153040
$719$	7.58159e32	1.06507	0.532535	−	0.846408i	$-0.321239\pi$
$719$	7.58159e32	1.06507	0.532535	+	0.846408i	$0.321239\pi$
$720$	2.69561e31	0.0372678
$721$	1.58025e33	2.15016
$722$	−4.88494e32	−0.654156
$723$	−4.28768e32	−0.565109
$724$	2.60154e32	0.337471
$725$	−4.89289e31	−0.0624710
$726$	−2.37621e32	−0.298616
$727$	−7.99688e32	−0.989179	−0.494589	−	0.869127i	$-0.664682\pi$
$727$	−7.99688e32	−0.989179	−0.494589	+	0.869127i	$0.664682\pi$
$728$	6.03342e32	0.734604
$729$	3.09032e31	0.0370370
$730$	−1.39210e32	−0.164232
$731$	1.10972e32	0.128874
$732$	1.60163e32	0.183099
$733$	1.11656e33	1.25657	0.628286	−	0.777983i	$-0.283757\pi$
$733$	1.11656e33	1.25657	0.628286	+	0.777983i	$0.283757\pi$
$734$	−4.49726e32	−0.498245
$735$	3.49030e32	0.380679
$736$	−3.00432e32	−0.322590
$737$	9.73429e31	0.102903
$738$	−3.72838e32	−0.388036
$739$	−1.38537e33	−1.41956	−0.709779	−	0.704424i	$-0.751205\pi$
$739$	−1.38537e33	−1.41956	−0.709779	+	0.704424i	$0.751205\pi$
$740$	9.45201e31	0.0953585
$741$	−2.10091e32	−0.208688
$742$	1.30107e33	1.27250
$743$	2.57754e32	0.248219	0.124109	−	0.992269i	$-0.460393\pi$
$743$	2.57754e32	0.248219	0.124109	+	0.992269i	$0.460393\pi$
$744$	−3.30783e32	−0.313656
$745$	−6.64593e32	−0.620524
$746$	4.22584e32	0.388523
$747$	2.00278e32	0.181321
$748$	4.97670e32	0.443683
$749$	2.50981e33	2.20343
$750$	4.22351e31	0.0365148
$751$	−1.86892e32	−0.159122	−0.0795611	−	0.996830i	$-0.525352\pi$
$751$	−1.86892e32	−0.159122	−0.0795611	+	0.996830i	$0.525352\pi$
$752$	−2.59516e32	−0.217600
$753$	8.86413e32	0.731971
$754$	3.58732e32	0.291743
$755$	2.87593e31	0.0230350
$756$	−1.91876e32	−0.151363
$757$	3.67745e32	0.285722	0.142861	−	0.989743i	$-0.454370\pi$
$757$	3.67745e32	0.285722	0.142861	+	0.989743i	$0.454370\pi$
$758$	−1.59943e33	−1.22397
$759$	−7.24359e32	−0.545976
$760$	5.82799e31	0.0432675
$761$	−2.38785e33	−1.74616	−0.873079	−	0.487578i	$-0.837880\pi$
$761$	−2.38785e33	−1.74616	−0.873079	+	0.487578i	$0.837880\pi$
$762$	−9.73075e32	−0.700913
$763$	−3.77643e33	−2.67947
$764$	4.24967e32	0.297017
$765$	3.70762e32	0.255264
$766$	1.27317e32	0.0863483
$767$	2.19145e33	1.46415
$768$	5.48243e31	0.0360844
$769$	−2.36127e32	−0.153106	−0.0765532	−	0.997065i	$-0.524392\pi$
$769$	−2.36127e32	−0.153106	−0.0765532	+	0.997065i	$0.524392\pi$
$770$	−4.03536e32	−0.257774
$771$	1.15366e33	0.726026
$772$	2.34112e32	0.145152
$773$	−3.92768e32	−0.239923	−0.119962	−	0.992779i	$-0.538277\pi$
$773$	−3.92768e32	−0.239923	−0.119962	+	0.992779i	$0.538277\pi$
$774$	2.94750e31	0.0177391
$775$	−5.18274e32	−0.307319
$776$	−4.80652e32	−0.280816
$777$	−6.72802e32	−0.387298
$778$	−2.39584e32	−0.135891
$779$	−8.06087e32	−0.450506
$780$	−3.09655e32	−0.170526
$781$	1.19986e33	0.651097
$782$	−4.13223e33	−2.20957
$783$	−1.14085e32	−0.0601128
$784$	7.09870e32	0.368591
$785$	−5.41852e31	−0.0277255
$786$	−1.40425e33	−0.708086
$787$	−1.70895e33	−0.849220	−0.424610	−	0.905376i	$-0.639589\pi$
$787$	−1.70895e33	−0.849220	−0.424610	+	0.905376i	$0.639589\pi$
$788$	4.65801e32	0.228113
$789$	−6.15726e32	−0.297168
$790$	−7.92537e32	−0.376971
$791$	−6.96046e32	−0.326293
$792$	1.32185e32	0.0610719
$793$	−1.83986e33	−0.837804
$794$	−7.49760e32	−0.336501
$795$	−6.67754e32	−0.295389
$796$	1.87719e33	0.818478
$797$	−1.85542e33	−0.797392	−0.398696	−	0.917083i	$-0.630537\pi$
$797$	−1.85542e33	−0.797392	−0.398696	+	0.917083i	$0.630537\pi$
$798$	−4.14841e32	−0.175731
$799$	−3.56946e33	−1.49044
$800$	8.58993e31	0.0353553
$801$	3.40864e32	0.138295
$802$	−1.71215e32	−0.0684757
$803$	−6.82642e32	−0.269131
$804$	1.47494e32	0.0573231
$805$	3.35062e33	1.28373
$806$	3.79983e33	1.43520
$807$	−6.64079e32	−0.247272
$808$	−4.50439e31	−0.0165350
$809$	−3.52136e33	−1.27439	−0.637194	−	0.770703i	$-0.719905\pi$
$809$	−3.52136e33	−1.27439	−0.637194	+	0.770703i	$0.719905\pi$
$810$	9.84771e31	0.0351364
$811$	−7.40479e31	−0.0260479	−0.0130239	−	0.999915i	$-0.504146\pi$
$811$	−7.40479e31	−0.0260479	−0.0130239	+	0.999915i	$0.504146\pi$
$812$	7.08344e32	0.245669
$813$	1.90971e33	0.653019
$814$	4.63498e32	0.156267
$815$	1.01701e33	0.338074
$816$	7.54070e32	0.247158
$817$	6.37257e31	0.0205949
$818$	3.40556e33	1.08524
$819$	2.20415e33	0.692591
$820$	−1.18810e33	−0.368124
$821$	−1.51285e33	−0.462221	−0.231110	−	0.972928i	$-0.574236\pi$
$821$	−1.51285e33	−0.462221	−0.231110	+	0.972928i	$0.574236\pi$
$822$	1.46677e33	0.441913
$823$	−2.03735e33	−0.605296	−0.302648	−	0.953102i	$-0.597871\pi$
$823$	−2.03735e33	−0.605296	−0.302648	+	0.953102i	$0.597871\pi$
$824$	−1.64952e33	−0.483276
$825$	2.07108e32	0.0598380
$826$	4.32718e33	1.23292
$827$	−1.56184e33	−0.438856	−0.219428	−	0.975629i	$-0.570419\pi$
$827$	−1.56184e33	−0.438856	−0.219428	+	0.975629i	$0.570419\pi$
$828$	−1.09755e33	−0.304141
$829$	−3.03574e33	−0.829634	−0.414817	−	0.909905i	$-0.636154\pi$
$829$	−3.03574e33	−0.829634	−0.414817	+	0.909905i	$0.636154\pi$
$830$	6.38214e32	0.172016
$831$	9.79559e32	0.260387
$832$	−6.29788e32	−0.165111
$833$	9.76376e33	2.52464
$834$	2.97460e33	0.758611
$835$	−3.05416e33	−0.768240
$836$	2.85787e32	0.0709038
$837$	−1.20843e33	−0.295718
$838$	−1.34318e33	−0.324211
$839$	1.73921e33	0.414085	0.207043	−	0.978332i	$-0.433616\pi$
$839$	1.73921e33	0.414085	0.207043	+	0.978332i	$0.433616\pi$
$840$	−6.11439e32	−0.143596
$841$	−3.89556e33	−0.902434
$842$	3.43516e33	0.784978
$843$	−2.68095e33	−0.604327
$844$	2.31520e33	0.514815
$845$	1.51837e33	0.333062
$846$	−9.48074e32	−0.205155
$847$	5.38988e33	1.15059
$848$	−1.35810e33	−0.286009
$849$	−3.90752e33	−0.811826
$850$	1.18148e33	0.242164
$851$	−3.84849e33	−0.778217
$852$	1.81804e33	0.362700
$853$	1.35246e33	0.266201	0.133101	−	0.991103i	$-0.457507\pi$
$853$	1.35246e33	0.266201	0.133101	+	0.991103i	$0.457507\pi$
$854$	−3.63294e33	−0.705493
$855$	2.12910e32	0.0407930
$856$	−2.61982e33	−0.495249
$857$	3.88101e33	0.723878	0.361939	−	0.932202i	$-0.382115\pi$
$857$	3.88101e33	0.723878	0.361939	+	0.932202i	$0.382115\pi$
$858$	−1.51846e33	−0.279446
$859$	−4.47048e33	−0.811769	−0.405885	−	0.913924i	$-0.633037\pi$
$859$	−4.47048e33	−0.811769	−0.405885	+	0.913924i	$0.633037\pi$
$860$	9.39259e31	0.0168288
$861$	8.45699e33	1.49513
$862$	7.89292e33	1.37691
$863$	−9.90128e32	−0.170438	−0.0852191	−	0.996362i	$-0.527159\pi$
$863$	−9.90128e32	−0.170438	−0.0852191	+	0.996362i	$0.527159\pi$
$864$	2.00286e32	0.0340207
$865$	1.36017e33	0.227985
$866$	−2.46295e33	−0.407380
$867$	6.83450e33	1.11555
$868$	7.50306e33	1.20854
$869$	−3.88636e33	−0.617754
$870$	−3.63546e32	−0.0570280
$871$	−1.69432e33	−0.262293
$872$	3.94196e33	0.602244
$873$	−1.75594e33	−0.264756
$874$	−2.37293e33	−0.353105
$875$	−9.58008e32	−0.140694
$876$	−1.03434e33	−0.149922
$877$	1.03415e34	1.47942	0.739708	−	0.672928i	$-0.234964\pi$
$877$	1.03415e34	1.47942	0.739708	+	0.672928i	$0.234964\pi$
$878$	2.37074e33	0.334731
$879$	5.44230e33	0.758420
$880$	4.21224e32	0.0579379
$881$	−7.78259e33	−1.05658	−0.528289	−	0.849065i	$-0.677166\pi$
$881$	−7.78259e33	−1.05658	−0.528289	+	0.849065i	$0.677166\pi$
$882$	2.59332e33	0.347510
$883$	−1.36376e34	−1.80380	−0.901902	−	0.431940i	$-0.857829\pi$
$883$	−1.36376e34	−1.80380	−0.901902	+	0.431940i	$0.857829\pi$
$884$	−8.66229e33	−1.13092
$885$	−2.22085e33	−0.286202
$886$	3.06437e33	0.389810
$887$	−7.57523e33	−0.951205	−0.475603	−	0.879660i	$-0.657770\pi$
$887$	−7.57523e33	−0.951205	−0.475603	+	0.879660i	$0.657770\pi$
$888$	7.02293e32	0.0870500
$889$	2.20720e34	2.70067
$890$	1.08621e33	0.131198
$891$	4.82902e32	0.0575791
$892$	3.73400e33	0.439520
$893$	−2.04976e33	−0.238183
$894$	−4.93798e33	−0.566458
$895$	3.30540e33	0.374334
$896$	−1.24357e33	−0.139036
$897$	1.26080e34	1.39166
$898$	2.18167e33	0.237745
$899$	4.46113e33	0.479964
$900$	3.13811e32	0.0333333
$901$	−1.86797e34	−1.95901
$902$	−5.82608e33	−0.603255
$903$	−6.68573e32	−0.0683501
$904$	7.26555e32	0.0733385
$905$	3.02859e33	0.301843
$906$	2.13684e32	0.0210280
$907$	−1.11690e34	−1.08525	−0.542626	−	0.839975i	$-0.682570\pi$
$907$	−1.11690e34	−1.08525	−0.542626	+	0.839975i	$0.682570\pi$
$908$	−1.92804e33	−0.184982
$909$	−1.64556e32	−0.0155894
$910$	7.02383e33	0.657049
$911$	−9.12878e33	−0.843240	−0.421620	−	0.906773i	$-0.638538\pi$
$911$	−9.12878e33	−0.843240	−0.421620	+	0.906773i	$0.638538\pi$
$912$	4.33024e32	0.0394977
$913$	3.12961e33	0.281888
$914$	1.74764e33	0.155442
$915$	1.86454e33	0.163768
$916$	−6.59023e33	−0.571614
$917$	3.18523e34	2.72831
$918$	2.75480e33	0.233023
$919$	−1.07173e34	−0.895276	−0.447638	−	0.894215i	$-0.647735\pi$
$919$	−1.07173e34	−0.895276	−0.447638	+	0.894215i	$0.647735\pi$
$920$	−3.49749e33	−0.288534
$921$	9.15939e33	0.746244
$922$	7.80402e33	0.627932
$923$	−2.08845e34	−1.65960
$924$	−2.99831e33	−0.235314
$925$	1.10036e33	0.0852913
$926$	−1.17049e34	−0.896066
$927$	−6.02609e33	−0.455637
$928$	−7.39393e32	−0.0552171
$929$	−8.93267e33	−0.658871	−0.329436	−	0.944178i	$-0.606858\pi$
$929$	−8.93267e33	−0.658871	−0.329436	+	0.944178i	$0.606858\pi$
$930$	−3.85082e33	−0.280543
$931$	5.60683e33	0.403456
$932$	1.05718e34	0.751389
$933$	−5.20523e33	−0.365427
$934$	−5.73610e32	−0.0397766
$935$	5.79364e33	0.396842
$936$	−2.30077e33	−0.155668
$937$	8.31694e33	0.555851	0.277925	−	0.960603i	$-0.410353\pi$
$937$	8.31694e33	0.555851	0.277925	+	0.960603i	$0.410353\pi$
$938$	−3.34557e33	−0.220870
$939$	−1.10408e33	−0.0720020
$940$	−3.02117e33	−0.194628
$941$	−1.85332e34	−1.17942	−0.589712	−	0.807614i	$-0.700759\pi$
$941$	−1.85332e34	−1.17942	−0.589712	+	0.807614i	$0.700759\pi$
$942$	−4.02600e32	−0.0253098
$943$	4.83748e34	3.00424
$944$	−4.51685e33	−0.277114
$945$	−2.23373e33	−0.135383
$946$	4.60584e32	0.0275779
$947$	5.68849e33	0.336490	0.168245	−	0.985745i	$-0.446190\pi$
$947$	5.68849e33	0.336490	0.168245	+	0.985745i	$0.446190\pi$
$948$	−5.88861e33	−0.344126
$949$	1.18819e34	0.685999
$950$	6.78467e32	0.0386997
$951$	−1.39302e34	−0.785023
$952$	−1.71044e34	−0.952318
$953$	−5.69520e33	−0.313286	−0.156643	−	0.987655i	$-0.550067\pi$
$953$	−5.69520e33	−0.313286	−0.156643	+	0.987655i	$0.550067\pi$
$954$	−4.96147e33	−0.269652
$955$	4.94727e33	0.265660
$956$	2.21848e33	0.117704
$957$	−1.78272e33	−0.0934535
$958$	−1.48558e34	−0.769470
$959$	−3.32704e34	−1.70272
$960$	6.38239e32	0.0322749
$961$	2.72407e34	1.36113
$962$	−8.06751e33	−0.398314
$963$	−9.57083e33	−0.466925
$964$	−1.01519e34	−0.489399
$965$	2.72542e33	0.129828
$966$	2.48954e34	1.17188
$967$	1.68474e33	0.0783660	0.0391830	−	0.999232i	$-0.487524\pi$
$967$	1.68474e33	0.0783660	0.0391830	+	0.999232i	$0.487524\pi$
$968$	−5.62613e33	−0.258609
$969$	5.95594e33	0.270537
$970$	−5.59553e33	−0.251169
$971$	−2.40818e33	−0.106824	−0.0534118	−	0.998573i	$-0.517010\pi$
$971$	−2.40818e33	−0.106824	−0.0534118	+	0.998573i	$0.517010\pi$
$972$	7.31693e32	0.0320750
$973$	−6.74720e34	−2.92298
$974$	−1.23127e34	−0.527139
$975$	−3.60486e33	−0.152523
$976$	3.79218e33	0.158568
$977$	−3.21272e34	−1.32766	−0.663828	−	0.747886i	$-0.731069\pi$
$977$	−3.21272e34	−1.32766	−0.663828	+	0.747886i	$0.731069\pi$
$978$	7.55646e33	0.308618
$979$	5.32644e33	0.214999
$980$	8.26398e33	0.329677
$981$	1.44009e34	0.567801
$982$	2.27816e34	0.887773
$983$	−9.75871e33	−0.375861	−0.187930	−	0.982182i	$-0.560178\pi$
$983$	−9.75871e33	−0.375861	−0.187930	+	0.982182i	$0.560178\pi$
$984$	−8.82768e33	−0.336049
$985$	5.42264e33	0.204030
$986$	−1.01698e34	−0.378206
$987$	2.15049e34	0.790479
$988$	−4.97432e33	−0.180729
$989$	−3.82430e33	−0.137339
$990$	1.53883e33	0.0546243
$991$	4.31932e33	0.151554	0.0757772	−	0.997125i	$-0.475856\pi$
$991$	4.31932e33	0.151554	0.0757772	+	0.997125i	$0.475856\pi$
$992$	−7.83193e33	−0.271634
$993$	−1.01903e34	−0.349359
$994$	−4.12380e34	−1.39751
$995$	2.18533e34	0.732069
$996$	4.74199e33	0.157028
$997$	5.73019e34	1.87575	0.937874	−	0.346975i	$-0.112791\pi$
$997$	5.73019e34	1.87575	0.937874	+	0.346975i	$0.112791\pi$
$998$	2.70184e34	0.874296
$999$	2.56564e33	0.0820716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.24.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.24.a.b.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	30.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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