LMFDB - Embedded newform 30.14.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,14,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, 14, names="a")

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

chi := DirichletCharacter("30.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 14 $
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:	$32.1692786856$
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)

$f(q)$

$=$

\(q+64.0000 q^{2} +729.000 q^{3} +4096.00 q^{4} -15625.0 q^{5} +46656.0 q^{6} -246868. q^{7} +262144. q^{8} +531441. q^{9} -1.00000e6 q^{10} -5.81381e6 q^{11} +2.98598e6 q^{12} -1.39141e7 q^{13} -1.57996e7 q^{14} -1.13906e7 q^{15} +1.67772e7 q^{16} -8.12644e7 q^{17} +3.40122e7 q^{18} -4.40567e7 q^{19} -6.40000e7 q^{20} -1.79967e8 q^{21} -3.72084e8 q^{22} +6.88232e7 q^{23} +1.91103e8 q^{24} +2.44141e8 q^{25} -8.90502e8 q^{26} +3.87420e8 q^{27} -1.01117e9 q^{28} +1.04621e9 q^{29} -7.29000e8 q^{30} -9.19646e9 q^{31} +1.07374e9 q^{32} -4.23827e9 q^{33} -5.20092e9 q^{34} +3.85731e9 q^{35} +2.17678e9 q^{36} +1.72290e10 q^{37} -2.81963e9 q^{38} -1.01434e10 q^{39} -4.09600e9 q^{40} -1.71231e10 q^{41} -1.15179e10 q^{42} -1.23539e10 q^{43} -2.38134e10 q^{44} -8.30377e9 q^{45} +4.40469e9 q^{46} -1.18627e11 q^{47} +1.22306e10 q^{48} -3.59452e10 q^{49} +1.56250e10 q^{50} -5.92417e10 q^{51} -5.69921e10 q^{52} -7.89259e10 q^{53} +2.47949e10 q^{54} +9.08408e10 q^{55} -6.47150e10 q^{56} -3.21173e10 q^{57} +6.69577e10 q^{58} +7.50161e10 q^{59} -4.66560e10 q^{60} -2.07562e11 q^{61} -5.88574e11 q^{62} -1.31196e11 q^{63} +6.87195e10 q^{64} +2.17408e11 q^{65} -2.71249e11 q^{66} +6.17859e11 q^{67} -3.32859e11 q^{68} +5.01721e10 q^{69} +2.46868e11 q^{70} +1.84925e12 q^{71} +1.39314e11 q^{72} +1.44938e12 q^{73} +1.10266e12 q^{74} +1.77979e11 q^{75} -1.80456e11 q^{76} +1.43524e12 q^{77} -6.49176e11 q^{78} +3.27888e12 q^{79} -2.62144e11 q^{80} +2.82430e11 q^{81} -1.09588e12 q^{82} +5.76024e11 q^{83} -7.37144e11 q^{84} +1.26976e12 q^{85} -7.90650e11 q^{86} +7.62690e11 q^{87} -1.52405e12 q^{88} +1.44139e12 q^{89} -5.31441e11 q^{90} +3.43494e12 q^{91} +2.81900e11 q^{92} -6.70422e12 q^{93} -7.59211e12 q^{94} +6.88385e11 q^{95} +7.82758e11 q^{96} -9.16164e12 q^{97} -2.30049e12 q^{98} -3.08970e12 q^{99} +O(q^{100})\)

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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	4096.00	0.500000
$5$	−15625.0	−0.447214
$5$	−15625.0	−0.447214
$6$	46656.0	0.408248
$7$	−246868.	−0.793099	−0.396550	−	0.918013i	$-0.629793\pi$
$7$	−246868.	−0.793099	−0.396550	+	0.918013i	$0.629793\pi$
$8$	262144.	0.353553
$9$	531441.	0.333333
$10$	−1.00000e6	−0.316228
$11$	−5.81381e6	−0.989483	−0.494741	−	0.869040i	$-0.664737\pi$
$11$	−5.81381e6	−0.989483	−0.494741	+	0.869040i	$0.664737\pi$
$12$	2.98598e6	0.288675
$13$	−1.39141e7	−0.799509	−0.399754	−	0.916622i	$-0.630905\pi$
$13$	−1.39141e7	−0.799509	−0.399754	+	0.916622i	$0.630905\pi$
$14$	−1.57996e7	−0.560806
$15$	−1.13906e7	−0.258199
$16$	1.67772e7	0.250000
$17$	−8.12644e7	−0.816549	−0.408274	−	0.912859i	$-0.633869\pi$
$17$	−8.12644e7	−0.816549	−0.408274	+	0.912859i	$0.633869\pi$
$18$	3.40122e7	0.235702
$19$	−4.40567e7	−0.214839	−0.107420	−	0.994214i	$-0.534259\pi$
$19$	−4.40567e7	−0.214839	−0.107420	+	0.994214i	$0.534259\pi$
$20$	−6.40000e7	−0.223607
$21$	−1.79967e8	−0.457896
$22$	−3.72084e8	−0.699670
$23$	6.88232e7	0.0969402	0.0484701	−	0.998825i	$-0.484565\pi$
$23$	6.88232e7	0.0969402	0.0484701	+	0.998825i	$0.484565\pi$
$24$	1.91103e8	0.204124
$25$	2.44141e8	0.200000
$26$	−8.90502e8	−0.565338
$27$	3.87420e8	0.192450
$28$	−1.01117e9	−0.396550
$29$	1.04621e9	0.326613	0.163306	−	0.986575i	$-0.447784\pi$
$29$	1.04621e9	0.326613	0.163306	+	0.986575i	$0.447784\pi$
$30$	−7.29000e8	−0.182574
$31$	−9.19646e9	−1.86110	−0.930550	−	0.366164i	$-0.880671\pi$
$31$	−9.19646e9	−1.86110	−0.930550	+	0.366164i	$0.880671\pi$
$32$	1.07374e9	0.176777
$33$	−4.23827e9	−0.571278
$34$	−5.20092e9	−0.577387
$35$	3.85731e9	0.354685
$36$	2.17678e9	0.166667
$37$	1.72290e10	1.10395	0.551975	−	0.833860i	$-0.313874\pi$
$37$	1.72290e10	1.10395	0.551975	+	0.833860i	$0.313874\pi$
$38$	−2.81963e9	−0.151914
$39$	−1.01434e10	−0.461597
$40$	−4.09600e9	−0.158114
$41$	−1.71231e10	−0.562973	−0.281487	−	0.959565i	$-0.590827\pi$
$41$	−1.71231e10	−0.562973	−0.281487	+	0.959565i	$0.590827\pi$
$42$	−1.15179e10	−0.323781
$43$	−1.23539e10	−0.298029	−0.149015	−	0.988835i	$-0.547610\pi$
$43$	−1.23539e10	−0.298029	−0.149015	+	0.988835i	$0.547610\pi$
$44$	−2.38134e10	−0.494741
$45$	−8.30377e9	−0.149071
$46$	4.40469e9	0.0685471
$47$	−1.18627e11	−1.60526	−0.802632	−	0.596474i	$-0.796568\pi$
$47$	−1.18627e11	−1.60526	−0.802632	+	0.596474i	$0.796568\pi$
$48$	1.22306e10	0.144338
$49$	−3.59452e10	−0.370994
$50$	1.56250e10	0.141421
$51$	−5.92417e10	−0.471435
$52$	−5.69921e10	−0.399754
$53$	−7.89259e10	−0.489132	−0.244566	−	0.969633i	$-0.578645\pi$
$53$	−7.89259e10	−0.489132	−0.244566	+	0.969633i	$0.578645\pi$
$54$	2.47949e10	0.136083
$55$	9.08408e10	0.442510
$56$	−6.47150e10	−0.280403
$57$	−3.21173e10	−0.124037
$58$	6.69577e10	0.230950
$59$	7.50161e10	0.231535	0.115767	−	0.993276i	$-0.463067\pi$
$59$	7.50161e10	0.231535	0.115767	+	0.993276i	$0.463067\pi$
$60$	−4.66560e10	−0.129099
$61$	−2.07562e11	−0.515828	−0.257914	−	0.966168i	$-0.583035\pi$
$61$	−2.07562e11	−0.515828	−0.257914	+	0.966168i	$0.583035\pi$
$62$	−5.88574e11	−1.31600
$63$	−1.31196e11	−0.264366
$64$	6.87195e10	0.125000
$65$	2.17408e11	0.357551
$66$	−2.71249e11	−0.403955
$67$	6.17859e11	0.834455	0.417228	−	0.908802i	$-0.363002\pi$
$67$	6.17859e11	0.834455	0.417228	+	0.908802i	$0.363002\pi$
$68$	−3.32859e11	−0.408274
$69$	5.01721e10	0.0559685
$70$	2.46868e11	0.250800
$71$	1.84925e12	1.71323	0.856614	−	0.515957i	$-0.172564\pi$
$71$	1.84925e12	1.71323	0.856614	+	0.515957i	$0.172564\pi$
$72$	1.39314e11	0.117851
$73$	1.44938e12	1.12094	0.560471	−	0.828174i	$-0.310620\pi$
$73$	1.44938e12	1.12094	0.560471	+	0.828174i	$0.310620\pi$
$74$	1.10266e12	0.780611
$75$	1.77979e11	0.115470
$76$	−1.80456e11	−0.107420
$77$	1.43524e12	0.784758
$78$	−6.49176e11	−0.326398
$79$	3.27888e12	1.51757	0.758785	−	0.651341i	$-0.225793\pi$
$79$	3.27888e12	1.51757	0.758785	+	0.651341i	$0.225793\pi$
$80$	−2.62144e11	−0.111803
$81$	2.82430e11	0.111111
$82$	−1.09588e12	−0.398082
$83$	5.76024e11	0.193389	0.0966947	−	0.995314i	$-0.469173\pi$
$83$	5.76024e11	0.193389	0.0966947	+	0.995314i	$0.469173\pi$
$84$	−7.37144e11	−0.228948
$85$	1.26976e12	0.365172
$86$	−7.90650e11	−0.210739
$87$	7.62690e11	0.188570
$88$	−1.52405e12	−0.349835
$89$	1.44139e12	0.307431	0.153715	−	0.988115i	$-0.450876\pi$
$89$	1.44139e12	0.307431	0.153715	+	0.988115i	$0.450876\pi$
$90$	−5.31441e11	−0.105409
$91$	3.43494e12	0.634090
$92$	2.81900e11	0.0484701
$93$	−6.70422e12	−1.07451
$94$	−7.59211e12	−1.13509
$95$	6.88385e11	0.0960789
$96$	7.82758e11	0.102062
$97$	−9.16164e12	−1.11675	−0.558376	−	0.829588i	$-0.688575\pi$
$97$	−9.16164e12	−1.11675	−0.558376	+	0.829588i	$0.688575\pi$
$98$	−2.30049e12	−0.262332
$99$	−3.08970e12	−0.329828
$100$	1.00000e12	0.100000
$101$	1.34740e13	1.26301	0.631506	−	0.775371i	$-0.282437\pi$
$101$	1.34740e13	1.26301	0.631506	+	0.775371i	$0.282437\pi$
$102$	−3.79147e12	−0.333355
$103$	−5.90313e12	−0.487125	−0.243563	−	0.969885i	$-0.578316\pi$
$103$	−5.90313e12	−0.487125	−0.243563	+	0.969885i	$0.578316\pi$
$104$	−3.64750e12	−0.282669
$105$	2.81198e12	0.204777
$106$	−5.05125e12	−0.345869
$107$	4.49397e12	0.289491	0.144746	−	0.989469i	$-0.453764\pi$
$107$	4.49397e12	0.289491	0.144746	+	0.989469i	$0.453764\pi$
$108$	1.58687e12	0.0962250
$109$	−2.18610e13	−1.24853	−0.624264	−	0.781213i	$-0.714601\pi$
$109$	−2.18610e13	−1.24853	−0.624264	+	0.781213i	$0.714601\pi$
$110$	5.81381e12	0.312902
$111$	1.25600e13	0.637366
$112$	−4.14176e12	−0.198275
$113$	3.02283e12	0.136585	0.0682927	−	0.997665i	$-0.478245\pi$
$113$	3.02283e12	0.136585	0.0682927	+	0.997665i	$0.478245\pi$
$114$	−2.05551e12	−0.0877077
$115$	−1.07536e12	−0.0433530
$116$	4.28529e12	0.163306
$117$	−7.39452e12	−0.266503
$118$	4.80103e12	0.163720
$119$	2.00616e13	0.647604
$120$	−2.98598e12	−0.0912871
$121$	−7.22349e11	−0.0209239
$122$	−1.32840e13	−0.364745
$123$	−1.24827e13	−0.325033
$124$	−3.76687e13	−0.930550
$125$	−3.81470e12	−0.0894427
$126$	−8.39653e12	−0.186935
$127$	−6.76719e13	−1.43115	−0.715573	−	0.698538i	$-0.753834\pi$
$127$	−6.76719e13	−1.43115	−0.715573	+	0.698538i	$0.753834\pi$
$128$	4.39805e12	0.0883883
$129$	−9.00599e12	−0.172067
$130$	1.39141e13	0.252827
$131$	6.24818e13	1.08017	0.540083	−	0.841612i	$-0.318393\pi$
$131$	6.24818e13	1.08017	0.540083	+	0.841612i	$0.318393\pi$
$132$	−1.73599e13	−0.285639
$133$	1.08762e13	0.170389
$134$	3.95430e13	0.590049
$135$	−6.05345e12	−0.0860663
$136$	−2.13030e13	−0.288694
$137$	1.47888e14	1.91095	0.955476	−	0.295069i	$-0.0953426\pi$
$137$	1.47888e14	1.91095	0.955476	+	0.295069i	$0.0953426\pi$
$138$	3.21102e12	0.0395757
$139$	−1.23994e14	−1.45816	−0.729079	−	0.684430i	$-0.760051\pi$
$139$	−1.23994e14	−1.45816	−0.729079	+	0.684430i	$0.760051\pi$
$140$	1.57996e13	0.177342
$141$	−8.64789e13	−0.926800
$142$	1.18352e14	1.21144
$143$	8.08939e13	0.791100
$144$	8.91610e12	0.0833333
$145$	−1.63471e13	−0.146066
$146$	9.27602e13	0.792626
$147$	−2.62041e13	−0.214193
$148$	7.05701e13	0.551975
$149$	−1.19266e14	−0.892905	−0.446452	−	0.894807i	$-0.647313\pi$
$149$	−1.19266e14	−0.892905	−0.446452	+	0.894807i	$0.647313\pi$
$150$	1.13906e13	0.0816497
$151$	8.94919e13	0.614375	0.307188	−	0.951649i	$-0.400612\pi$
$151$	8.94919e13	0.614375	0.307188	+	0.951649i	$0.400612\pi$
$152$	−1.15492e13	−0.0759571
$153$	−4.31872e13	−0.272183
$154$	9.18556e13	0.554908
$155$	1.43695e14	0.832310
$156$	−4.15473e13	−0.230798
$157$	1.97486e14	1.05242	0.526209	−	0.850355i	$-0.323613\pi$
$157$	1.97486e14	1.05242	0.526209	+	0.850355i	$0.323613\pi$
$158$	2.09848e14	1.07308
$159$	−5.75369e13	−0.282401
$160$	−1.67772e13	−0.0790569
$161$	−1.69902e13	−0.0768832
$162$	1.80755e13	0.0785674
$163$	−2.94421e14	−1.22956	−0.614780	−	0.788699i	$-0.710755\pi$
$163$	−2.94421e14	−1.22956	−0.614780	+	0.788699i	$0.710755\pi$
$164$	−7.01363e13	−0.281487
$165$	6.62229e13	0.255483
$166$	3.68655e13	0.136747
$167$	1.61334e14	0.575532	0.287766	−	0.957701i	$-0.407087\pi$
$167$	1.61334e14	0.575532	0.287766	+	0.957701i	$0.407087\pi$
$168$	−4.71772e13	−0.161891
$169$	−1.09273e14	−0.360786
$170$	8.12644e13	0.258215
$171$	−2.34135e13	−0.0716130
$172$	−5.06016e13	−0.149015
$173$	−6.43190e14	−1.82406	−0.912030	−	0.410123i	$-0.865486\pi$
$173$	−6.43190e14	−1.82406	−0.912030	+	0.410123i	$0.865486\pi$
$174$	4.88121e13	0.133339
$175$	−6.02705e13	−0.158620
$176$	−9.75395e13	−0.247371
$177$	5.46867e13	0.133677
$178$	9.22491e13	0.217386
$179$	3.03082e14	0.688678	0.344339	−	0.938845i	$-0.388103\pi$
$179$	3.03082e14	0.688678	0.344339	+	0.938845i	$0.388103\pi$
$180$	−3.40122e13	−0.0745356
$181$	−1.51647e14	−0.320569	−0.160285	−	0.987071i	$-0.551241\pi$
$181$	−1.51647e14	−0.320569	−0.160285	+	0.987071i	$0.551241\pi$
$182$	2.19836e14	0.448369
$183$	−1.51313e14	−0.297813
$184$	1.80416e13	0.0342735
$185$	−2.69204e14	−0.493702
$186$	−4.29070e14	−0.759791
$187$	4.72455e14	0.807961
$188$	−4.85895e14	−0.802632
$189$	−9.56417e13	−0.152632
$190$	4.40567e13	0.0679381
$191$	−1.11118e15	−1.65603	−0.828014	−	0.560707i	$-0.810529\pi$
$191$	−1.11118e15	−1.65603	−0.828014	+	0.560707i	$0.810529\pi$
$192$	5.00965e13	0.0721688
$193$	−2.78088e14	−0.387311	−0.193656	−	0.981070i	$-0.562034\pi$
$193$	−2.78088e14	−0.387311	−0.193656	+	0.981070i	$0.562034\pi$
$194$	−5.86345e14	−0.789663
$195$	1.58490e14	0.206432
$196$	−1.47232e14	−0.185497
$197$	1.35041e15	1.64602	0.823012	−	0.568024i	$-0.192292\pi$
$197$	1.35041e15	1.64602	0.823012	+	0.568024i	$0.192292\pi$
$198$	−1.97741e14	−0.233223
$199$	−1.66096e15	−1.89589	−0.947947	−	0.318428i	$-0.896845\pi$
$199$	−1.66096e15	−1.89589	−0.947947	+	0.318428i	$0.896845\pi$
$200$	6.40000e13	0.0707107
$201$	4.50419e14	0.481773
$202$	8.62336e14	0.893085
$203$	−2.58277e14	−0.259036
$204$	−2.42654e14	−0.235717
$205$	2.67549e14	0.251769
$206$	−3.77801e14	−0.344450
$207$	3.65755e13	0.0323134
$208$	−2.33440e14	−0.199877
$209$	2.56137e14	0.212580
$210$	1.79967e14	0.144799
$211$	−1.24740e15	−0.973128	−0.486564	−	0.873645i	$-0.661750\pi$
$211$	−1.24740e15	−0.973128	−0.486564	+	0.873645i	$0.661750\pi$
$212$	−3.23280e14	−0.244566
$213$	1.34810e15	0.989133
$214$	2.87614e14	0.204701
$215$	1.93030e14	0.133283
$216$	1.01560e14	0.0680414
$217$	2.27031e15	1.47604
$218$	−1.39911e15	−0.882843
$219$	1.05660e15	0.647176
$220$	3.72084e14	0.221255
$221$	1.13072e15	0.652838
$222$	8.03838e14	0.450686
$223$	1.46101e15	0.795556	0.397778	−	0.917482i	$-0.369781\pi$
$223$	1.46101e15	0.795556	0.397778	+	0.917482i	$0.369781\pi$
$224$	−2.65072e14	−0.140201
$225$	1.29746e14	0.0666667
$226$	1.93461e14	0.0965805
$227$	2.21289e15	1.07347	0.536736	−	0.843750i	$-0.319657\pi$
$227$	2.21289e15	1.07347	0.536736	+	0.843750i	$0.319657\pi$
$228$	−1.31552e14	−0.0620187
$229$	−1.38494e15	−0.634602	−0.317301	−	0.948325i	$-0.602777\pi$
$229$	−1.38494e15	−0.634602	−0.317301	+	0.948325i	$0.602777\pi$
$230$	−6.88232e13	−0.0306552
$231$	1.04629e15	0.453080
$232$	2.74259e14	0.115475
$233$	6.33581e14	0.259411	0.129706	−	0.991553i	$-0.458597\pi$
$233$	6.33581e14	0.259411	0.129706	+	0.991553i	$0.458597\pi$
$234$	−4.73249e14	−0.188446
$235$	1.85354e15	0.717896
$236$	3.07266e14	0.115767
$237$	2.39030e15	0.876170
$238$	1.28394e15	0.457925
$239$	−5.18618e15	−1.79995	−0.899976	−	0.435939i	$-0.856416\pi$
$239$	−5.18618e15	−1.79995	−0.899976	+	0.435939i	$0.856416\pi$
$240$	−1.91103e14	−0.0645497
$241$	7.14380e14	0.234865	0.117433	−	0.993081i	$-0.462534\pi$
$241$	7.14380e14	0.234865	0.117433	+	0.993081i	$0.462534\pi$
$242$	−4.62303e13	−0.0147954
$243$	2.05891e14	0.0641500
$244$	−8.50175e14	−0.257914
$245$	5.61644e14	0.165913
$246$	−7.98896e14	−0.229833
$247$	6.13009e14	0.171766
$248$	−2.41080e15	−0.657998
$249$	4.19921e14	0.111653
$250$	−2.44141e14	−0.0632456
$251$	7.71773e14	0.194810	0.0974048	−	0.995245i	$-0.468946\pi$
$251$	7.71773e14	0.194810	0.0974048	+	0.995245i	$0.468946\pi$
$252$	−5.37378e14	−0.132183
$253$	−4.00125e14	−0.0959207
$254$	−4.33100e15	−1.01197
$255$	9.25652e14	0.210832
$256$	2.81475e14	0.0625000
$257$	4.22506e14	0.0914677	0.0457339	−	0.998954i	$-0.485437\pi$
$257$	4.22506e14	0.0914677	0.0457339	+	0.998954i	$0.485437\pi$
$258$	−5.76384e14	−0.121670
$259$	−4.25330e15	−0.875542
$260$	8.90502e14	0.178776
$261$	5.56001e14	0.108871
$262$	3.99884e15	0.763792
$263$	−5.49790e15	−1.02443	−0.512217	−	0.858856i	$-0.671176\pi$
$263$	−5.49790e15	−1.02443	−0.512217	+	0.858856i	$0.671176\pi$
$264$	−1.11104e15	−0.201977
$265$	1.23322e15	0.218747
$266$	6.96075e14	0.120483
$267$	1.05077e15	0.177495
$268$	2.53075e15	0.417228
$269$	−9.14876e15	−1.47222	−0.736109	−	0.676863i	$-0.763339\pi$
$269$	−9.14876e15	−1.47222	−0.736109	+	0.676863i	$0.763339\pi$
$270$	−3.87420e14	−0.0608581
$271$	−7.68380e15	−1.17835	−0.589177	−	0.808004i	$-0.700548\pi$
$271$	−7.68380e15	−1.17835	−0.589177	+	0.808004i	$0.700548\pi$
$272$	−1.36339e15	−0.204137
$273$	2.50407e15	0.366092
$274$	9.46484e15	1.35125
$275$	−1.41939e15	−0.197897
$276$	2.05505e14	0.0279842
$277$	−5.04745e15	−0.671357	−0.335679	−	0.941977i	$-0.608966\pi$
$277$	−5.04745e15	−0.671357	−0.335679	+	0.941977i	$0.608966\pi$
$278$	−7.93562e15	−1.03107
$279$	−4.88738e15	−0.620367
$280$	1.01117e15	0.125400
$281$	9.13541e15	1.10697	0.553486	−	0.832858i	$-0.313297\pi$
$281$	9.13541e15	1.10697	0.553486	+	0.832858i	$0.313297\pi$
$282$	−5.53465e15	−0.655347
$283$	−1.11914e15	−0.129501	−0.0647506	−	0.997901i	$-0.520625\pi$
$283$	−1.11914e15	−0.129501	−0.0647506	+	0.997901i	$0.520625\pi$
$284$	7.57451e15	0.856614
$285$	5.01833e14	0.0554712
$286$	5.17721e15	0.559392
$287$	4.22715e15	0.446494
$288$	5.70630e14	0.0589256
$289$	−3.30068e15	−0.333248
$290$	−1.04621e15	−0.103284
$291$	−6.67883e15	−0.644757
$292$	5.93665e15	0.560471
$293$	−4.71945e15	−0.435764	−0.217882	−	0.975975i	$-0.569915\pi$
$293$	−4.71945e15	−0.435764	−0.217882	+	0.975975i	$0.569915\pi$
$294$	−1.67706e15	−0.151457
$295$	−1.17213e15	−0.103546
$296$	4.51649e15	0.390305
$297$	−2.25239e15	−0.190426
$298$	−7.63301e15	−0.631379
$299$	−9.57613e14	−0.0775045
$300$	7.29000e14	0.0577350
$301$	3.04978e15	0.236367
$302$	5.72748e15	0.434429
$303$	9.82255e15	0.729201
$304$	−7.39148e14	−0.0537098
$305$	3.24316e15	0.230685
$306$	−2.76398e15	−0.192462
$307$	−1.60000e16	−1.09074	−0.545370	−	0.838196i	$-0.683611\pi$
$307$	−1.60000e16	−1.09074	−0.545370	+	0.838196i	$0.683611\pi$
$308$	5.87876e15	0.392379
$309$	−4.30339e15	−0.281242
$310$	9.19646e15	0.588532
$311$	8.71351e15	0.546073	0.273036	−	0.962004i	$-0.411972\pi$
$311$	8.71351e15	0.546073	0.273036	+	0.962004i	$0.411972\pi$
$312$	−2.65902e15	−0.163199
$313$	−1.69623e16	−1.01964	−0.509819	−	0.860281i	$-0.670288\pi$
$313$	−1.69623e16	−1.01964	−0.509819	+	0.860281i	$0.670288\pi$
$314$	1.26391e16	0.744172
$315$	2.04993e15	0.118228
$316$	1.34303e16	0.758785
$317$	1.06703e16	0.590596	0.295298	−	0.955405i	$-0.404581\pi$
$317$	1.06703e16	0.590596	0.295298	+	0.955405i	$0.404581\pi$
$318$	−3.68236e15	−0.199687
$319$	−6.08249e15	−0.323178
$320$	−1.07374e15	−0.0559017
$321$	3.27610e15	0.167138
$322$	−1.08738e15	−0.0543646
$323$	3.58024e15	0.175427
$324$	1.15683e15	0.0555556
$325$	−3.39700e15	−0.159902
$326$	−1.88430e16	−0.869430
$327$	−1.59367e16	−0.720838
$328$	−4.48872e15	−0.199041
$329$	2.92852e16	1.27313
$330$	4.23827e15	0.180654
$331$	−2.33878e16	−0.977477	−0.488739	−	0.872430i	$-0.662543\pi$
$331$	−2.33878e16	−0.977477	−0.488739	+	0.872430i	$0.662543\pi$
$332$	2.35939e15	0.0966947
$333$	9.15621e15	0.367984
$334$	1.03254e16	0.406963
$335$	−9.65405e15	−0.373180
$336$	−3.01934e15	−0.114474
$337$	2.43894e16	0.906998	0.453499	−	0.891257i	$-0.350175\pi$
$337$	2.43894e16	0.906998	0.453499	+	0.891257i	$0.350175\pi$
$338$	−6.99348e15	−0.255114
$339$	2.20365e15	0.0788576
$340$	5.20092e15	0.182586
$341$	5.34665e16	1.84153
$342$	−1.49846e15	−0.0506380
$343$	3.27925e16	1.08733
$344$	−3.23850e15	−0.105369
$345$	−7.83939e14	−0.0250299
$346$	−4.11641e16	−1.28981
$347$	−8.83452e15	−0.271670	−0.135835	−	0.990731i	$-0.543372\pi$
$347$	−8.83452e15	−0.271670	−0.135835	+	0.990731i	$0.543372\pi$
$348$	3.12398e15	0.0942850
$349$	3.53103e16	1.04601	0.523005	−	0.852330i	$-0.324811\pi$
$349$	3.53103e16	1.04601	0.523005	+	0.852330i	$0.324811\pi$
$350$	−3.85731e15	−0.112161
$351$	−5.39061e15	−0.153866
$352$	−6.24253e15	−0.174917
$353$	6.10369e16	1.67902	0.839512	−	0.543342i	$-0.182841\pi$
$353$	6.10369e16	1.67902	0.839512	+	0.543342i	$0.182841\pi$
$354$	3.49995e15	0.0945237
$355$	−2.88945e16	−0.766179
$356$	5.90394e15	0.153715
$357$	1.46249e16	0.373895
$358$	1.93973e16	0.486969
$359$	3.44407e16	0.849099	0.424550	−	0.905405i	$-0.360432\pi$
$359$	3.44407e16	0.849099	0.424550	+	0.905405i	$0.360432\pi$
$360$	−2.17678e15	−0.0527046
$361$	−4.01120e16	−0.953844
$362$	−9.70538e15	−0.226677
$363$	−5.26592e14	−0.0120804
$364$	1.40695e16	0.317045
$365$	−2.26465e16	−0.501300
$366$	−9.68403e15	−0.210586
$367$	−6.95086e16	−1.48494	−0.742470	−	0.669879i	$-0.766346\pi$
$367$	−6.95086e16	−1.48494	−0.742470	+	0.669879i	$0.766346\pi$
$368$	1.15466e15	0.0242351
$369$	−9.09992e15	−0.187658
$370$	−1.72290e16	−0.349100
$371$	1.94843e16	0.387930
$372$	−2.74605e16	−0.537254
$373$	4.63874e16	0.891852	0.445926	−	0.895070i	$-0.352874\pi$
$373$	4.63874e16	0.891852	0.445926	+	0.895070i	$0.352874\pi$
$374$	3.02372e16	0.571315
$375$	−2.78091e15	−0.0516398
$376$	−3.10973e16	−0.567547
$377$	−1.45571e16	−0.261130
$378$	−6.12107e15	−0.107927
$379$	−8.60587e16	−1.49156	−0.745779	−	0.666194i	$-0.767922\pi$
$379$	−8.60587e16	−1.49156	−0.745779	+	0.666194i	$0.767922\pi$
$380$	2.81963e15	0.0480395
$381$	−4.93328e16	−0.826273
$382$	−7.11156e16	−1.17099
$383$	−9.10638e16	−1.47419	−0.737095	−	0.675789i	$-0.763803\pi$
$383$	−9.10638e16	−1.47419	−0.737095	+	0.675789i	$0.763803\pi$
$384$	3.20618e15	0.0510310
$385$	−2.24257e16	−0.350954
$386$	−1.77977e16	−0.273871
$387$	−6.56537e15	−0.0993432
$388$	−3.75261e16	−0.558376
$389$	−5.31668e16	−0.777979	−0.388989	−	0.921242i	$-0.627176\pi$
$389$	−5.31668e16	−0.777979	−0.388989	+	0.921242i	$0.627176\pi$
$390$	1.01434e16	0.145970
$391$	−5.59288e15	−0.0791564
$392$	−9.42282e15	−0.131166
$393$	4.55493e16	0.623634
$394$	8.64265e16	1.16391
$395$	−5.12324e16	−0.678678
$396$	−1.26554e16	−0.164914
$397$	8.67494e16	1.11206	0.556030	−	0.831162i	$-0.312324\pi$
$397$	8.67494e16	1.11206	0.556030	+	0.831162i	$0.312324\pi$
$398$	−1.06301e17	−1.34060
$399$	7.92873e15	0.0983739
$400$	4.09600e15	0.0500000
$401$	1.02886e17	1.23571	0.617856	−	0.786291i	$-0.288002\pi$
$401$	1.02886e17	1.23571	0.617856	+	0.786291i	$0.288002\pi$
$402$	2.88268e16	0.340665
$403$	1.27960e17	1.48797
$404$	5.51895e16	0.631506
$405$	−4.41296e15	−0.0496904
$406$	−1.65297e16	−0.183166
$407$	−1.00166e17	−1.09234
$408$	−1.55299e16	−0.166677
$409$	8.39573e16	0.886864	0.443432	−	0.896308i	$-0.353761\pi$
$409$	8.39573e16	0.886864	0.443432	+	0.896308i	$0.353761\pi$
$410$	1.71231e16	0.178028
$411$	1.07810e17	1.10329
$412$	−2.41792e16	−0.243563
$413$	−1.85191e16	−0.183630
$414$	2.34083e15	0.0228490
$415$	−9.00037e15	−0.0864864
$416$	−1.49401e16	−0.141334
$417$	−9.03917e16	−0.841868
$418$	1.63928e16	0.150316
$419$	−7.15458e16	−0.645942	−0.322971	−	0.946409i	$-0.604682\pi$
$419$	−7.15458e16	−0.645942	−0.322971	+	0.946409i	$0.604682\pi$
$420$	1.15179e16	0.102389
$421$	1.18480e17	1.03708	0.518540	−	0.855054i	$-0.326476\pi$
$421$	1.18480e17	1.03708	0.518540	+	0.855054i	$0.326476\pi$
$422$	−7.98337e16	−0.688106
$423$	−6.30431e16	−0.535088
$424$	−2.06899e16	−0.172934
$425$	−1.98399e16	−0.163310
$426$	8.62784e16	0.699423
$427$	5.12405e16	0.409103
$428$	1.84073e16	0.144746
$429$	5.89716e16	0.456742
$430$	1.23539e16	0.0942452
$431$	−8.18970e16	−0.615412	−0.307706	−	0.951481i	$-0.599561\pi$
$431$	−8.18970e16	−0.615412	−0.307706	+	0.951481i	$0.599561\pi$
$432$	6.49984e15	0.0481125
$433$	2.61320e17	1.90546	0.952732	−	0.303812i	$-0.0982595\pi$
$433$	2.61320e17	1.90546	0.952732	+	0.303812i	$0.0982595\pi$
$434$	1.45300e17	1.04372
$435$	−1.19170e16	−0.0843311
$436$	−8.95428e16	−0.624264
$437$	−3.03212e15	−0.0208265
$438$	6.76222e16	0.457623
$439$	6.04446e16	0.403031	0.201515	−	0.979485i	$-0.435413\pi$
$439$	6.04446e16	0.403031	0.201515	+	0.979485i	$0.435413\pi$
$440$	2.38134e16	0.156451
$441$	−1.91028e16	−0.123665
$442$	7.23661e16	0.461626
$443$	1.30237e16	0.0818675	0.0409338	−	0.999162i	$-0.486967\pi$
$443$	1.30237e16	0.0818675	0.0409338	+	0.999162i	$0.486967\pi$
$444$	5.14456e16	0.318683
$445$	−2.25218e16	−0.137487
$446$	9.35045e16	0.562543
$447$	−8.69447e16	−0.515519
$448$	−1.69646e16	−0.0991374
$449$	−3.34728e16	−0.192793	−0.0963964	−	0.995343i	$-0.530732\pi$
$449$	−3.34728e16	−0.192793	−0.0963964	+	0.995343i	$0.530732\pi$
$450$	8.30377e15	0.0471405
$451$	9.95505e16	0.557052
$452$	1.23815e16	0.0682927
$453$	6.52396e16	0.354710
$454$	1.41625e17	0.759060
$455$	−5.36710e16	−0.283574
$456$	−8.41936e15	−0.0438538
$457$	−1.84021e16	−0.0944956	−0.0472478	−	0.998883i	$-0.515045\pi$
$457$	−1.84021e16	−0.0944956	−0.0472478	+	0.998883i	$0.515045\pi$
$458$	−8.86364e16	−0.448732
$459$	−3.14835e16	−0.157145
$460$	−4.40469e15	−0.0216765
$461$	−1.94324e17	−0.942912	−0.471456	−	0.881890i	$-0.656271\pi$
$461$	−1.94324e17	−0.942912	−0.471456	+	0.881890i	$0.656271\pi$
$462$	6.69627e16	0.320376
$463$	−1.61147e17	−0.760232	−0.380116	−	0.924939i	$-0.624116\pi$
$463$	−1.61147e17	−0.760232	−0.380116	+	0.924939i	$0.624116\pi$
$464$	1.75526e16	0.0816532
$465$	1.04753e17	0.480534
$466$	4.05492e16	0.183431
$467$	−1.84358e17	−0.822438	−0.411219	−	0.911537i	$-0.634897\pi$
$467$	−1.84358e17	−0.822438	−0.411219	+	0.911537i	$0.634897\pi$
$468$	−3.02880e16	−0.133251
$469$	−1.52530e17	−0.661806
$470$	1.18627e17	0.507629
$471$	1.43967e17	0.607614
$472$	1.96650e16	0.0818599
$473$	7.18232e16	0.294895
$474$	1.52979e17	0.619546
$475$	−1.07560e16	−0.0429678
$476$	8.21722e16	0.323802
$477$	−4.19444e16	−0.163044
$478$	−3.31915e17	−1.27276
$479$	−2.29206e17	−0.867052	−0.433526	−	0.901141i	$-0.642731\pi$
$479$	−2.29206e17	−0.867052	−0.433526	+	0.901141i	$0.642731\pi$
$480$	−1.22306e16	−0.0456435
$481$	−2.39726e17	−0.882618
$482$	4.57203e16	0.166075
$483$	−1.23859e16	−0.0443885
$484$	−2.95874e15	−0.0104619
$485$	1.43151e17	0.499427
$486$	1.31770e16	0.0453609
$487$	−5.58396e16	−0.189672	−0.0948362	−	0.995493i	$-0.530233\pi$
$487$	−5.58396e16	−0.189672	−0.0948362	+	0.995493i	$0.530233\pi$
$488$	−5.44112e16	−0.182373
$489$	−2.14633e17	−0.709887
$490$	3.59452e16	0.117318
$491$	2.32354e17	0.748376	0.374188	−	0.927353i	$-0.377922\pi$
$491$	2.32354e17	0.748376	0.374188	+	0.927353i	$0.377922\pi$
$492$	−5.11293e16	−0.162516
$493$	−8.50199e16	−0.266695
$494$	3.92325e16	0.121457
$495$	4.82765e16	0.147503
$496$	−1.54291e17	−0.465275
$497$	−4.56520e17	−1.35876
$498$	2.68750e16	0.0789509
$499$	1.26866e17	0.367867	0.183933	−	0.982939i	$-0.441117\pi$
$499$	1.26866e17	0.367867	0.183933	+	0.982939i	$0.441117\pi$
$500$	−1.56250e16	−0.0447214
$501$	1.17613e17	0.332284
$502$	4.93935e16	0.137751
$503$	2.52062e17	0.693930	0.346965	−	0.937878i	$-0.387212\pi$
$503$	2.52062e17	0.693930	0.346965	+	0.937878i	$0.387212\pi$
$504$	−3.43922e16	−0.0934676
$505$	−2.10531e17	−0.564836
$506$	−2.56080e16	−0.0678262
$507$	−7.96601e16	−0.208300
$508$	−2.77184e17	−0.715573
$509$	−7.58416e17	−1.93304	−0.966522	−	0.256583i	$-0.917403\pi$
$509$	−7.58416e17	−1.93304	−0.966522	+	0.256583i	$0.917403\pi$
$510$	5.92417e16	0.149081
$511$	−3.57805e17	−0.889018
$512$	1.80144e16	0.0441942
$513$	−1.70685e16	−0.0413458
$514$	2.70404e16	0.0646775
$515$	9.22365e16	0.217849
$516$	−3.68886e16	−0.0860337
$517$	6.89673e17	1.58838
$518$	−2.72211e17	−0.619102
$519$	−4.68885e17	−1.05312
$520$	5.69921e16	0.126413
$521$	2.57270e17	0.563565	0.281782	−	0.959478i	$-0.409074\pi$
$521$	2.57270e17	0.563565	0.281782	+	0.959478i	$0.409074\pi$
$522$	3.55841e16	0.0769834
$523$	6.17878e17	1.32021	0.660103	−	0.751175i	$-0.270513\pi$
$523$	6.17878e17	1.32021	0.660103	+	0.751175i	$0.270513\pi$
$524$	2.55926e17	0.540083
$525$	−4.39372e16	−0.0915792
$526$	−3.51865e17	−0.724385
$527$	7.47345e17	1.51968
$528$	−7.11063e16	−0.142820
$529$	−4.99300e17	−0.990603
$530$	7.89259e16	0.154677
$531$	3.98666e16	0.0771783
$532$	4.45488e16	0.0851943
$533$	2.38253e17	0.450102
$534$	6.72496e16	0.125508
$535$	−7.02183e16	−0.129464
$536$	1.61968e17	0.295025
$537$	2.20947e17	0.397608
$538$	−5.85521e17	−1.04102
$539$	2.08978e17	0.367092
$540$	−2.47949e16	−0.0430331
$541$	4.98664e17	0.855117	0.427559	−	0.903988i	$-0.359374\pi$
$541$	4.98664e17	0.855117	0.427559	+	0.903988i	$0.359374\pi$
$542$	−4.91763e17	−0.833222
$543$	−1.10550e17	−0.185081
$544$	−8.72570e16	−0.144347
$545$	3.41579e17	0.558359
$546$	1.60261e17	0.258866
$547$	1.17958e18	1.88282	0.941409	−	0.337267i	$-0.109503\pi$
$547$	1.17958e18	1.88282	0.941409	+	0.337267i	$0.109503\pi$
$548$	6.05750e17	0.955476
$549$	−1.10307e17	−0.171943
$550$	−9.08408e16	−0.139934
$551$	−4.60927e16	−0.0701692
$552$	1.31523e16	0.0197878
$553$	−8.09449e17	−1.20358
$554$	−3.23037e17	−0.474721
$555$	−1.96249e17	−0.285039
$556$	−5.07880e17	−0.729079
$557$	1.20922e18	1.71572	0.857862	−	0.513880i	$-0.171792\pi$
$557$	1.20922e18	1.71572	0.857862	+	0.513880i	$0.171792\pi$
$558$	−3.12792e17	−0.438666
$559$	1.71893e17	0.238277
$560$	6.47150e16	0.0886712
$561$	3.44420e17	0.466477
$562$	5.84666e17	0.782748
$563$	3.34970e17	0.443303	0.221652	−	0.975126i	$-0.428855\pi$
$563$	3.34970e17	0.443303	0.221652	+	0.975126i	$0.428855\pi$
$564$	−3.54218e17	−0.463400
$565$	−4.72318e16	−0.0610829
$566$	−7.16251e16	−0.0915711
$567$	−6.97228e16	−0.0881221
$568$	4.84769e17	0.605718
$569$	−9.93914e17	−1.22778	−0.613888	−	0.789393i	$-0.710395\pi$
$569$	−9.93914e17	−1.22778	−0.613888	+	0.789393i	$0.710395\pi$
$570$	3.21173e16	0.0392241
$571$	−1.31297e18	−1.58533	−0.792666	−	0.609656i	$-0.791308\pi$
$571$	−1.31297e18	−1.58533	−0.792666	+	0.609656i	$0.791308\pi$
$572$	3.31341e17	0.395550
$573$	−8.10051e17	−0.956108
$574$	2.70538e17	0.315719
$575$	1.68025e16	0.0193880
$576$	3.65203e16	0.0416667
$577$	1.71430e18	1.93394	0.966972	−	0.254883i	$-0.0820369\pi$
$577$	1.71430e18	1.93394	0.966972	+	0.254883i	$0.0820369\pi$
$578$	−2.11243e17	−0.235642
$579$	−2.02726e17	−0.223614
$580$	−6.69577e16	−0.0730329
$581$	−1.42202e17	−0.153377
$582$	−4.27445e17	−0.455912
$583$	4.58860e17	0.483988
$584$	3.79946e17	0.396313
$585$	1.15539e17	0.119184
$586$	−3.02045e17	−0.308132
$587$	9.06698e16	0.0914777	0.0457388	−	0.998953i	$-0.485436\pi$
$587$	9.06698e16	0.0914777	0.0457388	+	0.998953i	$0.485436\pi$
$588$	−1.07332e17	−0.107097
$589$	4.05166e17	0.399837
$590$	−7.50161e16	−0.0732177
$591$	9.84451e17	0.950333
$592$	2.89055e17	0.275988
$593$	1.28956e18	1.21783	0.608913	−	0.793237i	$-0.291606\pi$
$593$	1.28956e18	1.21783	0.608913	+	0.793237i	$0.291606\pi$
$594$	−1.44153e17	−0.134652
$595$	−3.13462e17	−0.289617
$596$	−4.88513e17	−0.446452
$597$	−1.21084e18	−1.09459
$598$	−6.12872e16	−0.0548040
$599$	1.38078e18	1.22138	0.610691	−	0.791869i	$-0.290892\pi$
$599$	1.38078e18	1.22138	0.610691	+	0.791869i	$0.290892\pi$
$600$	4.66560e16	0.0408248
$601$	−1.72898e18	−1.49660	−0.748300	−	0.663360i	$-0.769130\pi$
$601$	−1.72898e18	−1.49660	−0.748300	+	0.663360i	$0.769130\pi$
$602$	1.95186e17	0.167137
$603$	3.28356e17	0.278152
$604$	3.66559e17	0.307188
$605$	1.12867e16	0.00935744
$606$	6.28643e17	0.515623
$607$	−4.22893e17	−0.343166	−0.171583	−	0.985170i	$-0.554888\pi$
$607$	−4.22893e17	−0.343166	−0.171583	+	0.985170i	$0.554888\pi$
$608$	−4.73055e16	−0.0379785
$609$	−1.88284e17	−0.149555
$610$	2.07562e17	0.163119
$611$	1.65058e18	1.28342
$612$	−1.76895e17	−0.136091
$613$	−1.47848e18	−1.12544	−0.562719	−	0.826648i	$-0.690245\pi$
$613$	−1.47848e18	−1.12544	−0.562719	+	0.826648i	$0.690245\pi$
$614$	−1.02400e18	−0.771269
$615$	1.95043e17	0.145359
$616$	3.76240e17	0.277454
$617$	−8.73995e17	−0.637757	−0.318879	−	0.947796i	$-0.603306\pi$
$617$	−8.73995e17	−0.637757	−0.318879	+	0.947796i	$0.603306\pi$
$618$	−2.75417e17	−0.198868
$619$	−1.94778e17	−0.139171	−0.0695857	−	0.997576i	$-0.522168\pi$
$619$	−1.94778e17	−0.139171	−0.0695857	+	0.997576i	$0.522168\pi$
$620$	5.88574e17	0.416155
$621$	2.66635e16	0.0186562
$622$	5.57665e17	0.386132
$623$	−3.55834e17	−0.243823
$624$	−1.70178e17	−0.115399
$625$	5.96046e16	0.0400000
$626$	−1.08559e18	−0.720994
$627$	1.86724e17	0.122733
$628$	8.08902e17	0.526209
$629$	−1.40011e18	−0.901430
$630$	1.31196e17	0.0836000
$631$	−1.41467e18	−0.892201	−0.446101	−	0.894983i	$-0.647188\pi$
$631$	−1.41467e18	−0.892201	−0.446101	+	0.894983i	$0.647188\pi$
$632$	8.59538e17	0.536542
$633$	−9.09355e17	−0.561836
$634$	6.82898e17	0.417615
$635$	1.05737e18	0.640028
$636$	−2.35671e17	−0.141200
$637$	5.00145e17	0.296613
$638$	−3.89279e17	−0.228521
$639$	9.82765e17	0.571076
$640$	−6.87195e16	−0.0395285
$641$	−8.47052e17	−0.482318	−0.241159	−	0.970486i	$-0.577527\pi$
$641$	−8.47052e17	−0.482318	−0.241159	+	0.970486i	$0.577527\pi$
$642$	2.09671e17	0.118184
$643$	−3.73889e17	−0.208628	−0.104314	−	0.994544i	$-0.533265\pi$
$643$	−3.73889e17	−0.208628	−0.104314	+	0.994544i	$0.533265\pi$
$644$	−6.95921e16	−0.0384416
$645$	1.40719e17	0.0769509
$646$	2.29135e17	0.124045
$647$	−3.11882e18	−1.67153	−0.835763	−	0.549091i	$-0.814974\pi$
$647$	−3.11882e18	−1.67153	−0.835763	+	0.549091i	$0.814974\pi$
$648$	7.40372e16	0.0392837
$649$	−4.36129e17	−0.229100
$650$	−2.17408e17	−0.113068
$651$	1.65506e18	0.852191
$652$	−1.20595e18	−0.614780
$653$	−3.00682e18	−1.51765	−0.758825	−	0.651294i	$-0.774226\pi$
$653$	−3.00682e18	−1.51765	−0.758825	+	0.651294i	$0.774226\pi$
$654$	−1.01995e18	−0.509710
$655$	−9.76279e17	−0.483065
$656$	−2.87278e17	−0.140743
$657$	7.70259e17	0.373647
$658$	1.87425e18	0.900242
$659$	−2.44266e18	−1.16174	−0.580868	−	0.813998i	$-0.697287\pi$
$659$	−2.44266e18	−1.16174	−0.580868	+	0.813998i	$0.697287\pi$
$660$	2.71249e17	0.127742
$661$	−2.85085e18	−1.32943	−0.664715	−	0.747097i	$-0.731447\pi$
$661$	−2.85085e18	−1.32943	−0.664715	+	0.747097i	$0.731447\pi$
$662$	−1.49682e18	−0.691181
$663$	8.24295e17	0.376916
$664$	1.51001e17	0.0683735
$665$	−1.69940e17	−0.0762001
$666$	5.85998e17	0.260204
$667$	7.20038e16	0.0316619
$668$	6.60825e17	0.287766
$669$	1.06507e18	0.459314
$670$	−6.17859e17	−0.263878
$671$	1.20673e18	0.510403
$672$	−1.93238e17	−0.0809454
$673$	−6.70156e17	−0.278021	−0.139011	−	0.990291i	$-0.544392\pi$
$673$	−6.70156e17	−0.278021	−0.139011	+	0.990291i	$0.544392\pi$
$674$	1.56092e18	0.641345
$675$	9.45851e16	0.0384900
$676$	−4.47583e17	−0.180393
$677$	−1.89487e18	−0.756404	−0.378202	−	0.925723i	$-0.623457\pi$
$677$	−1.89487e18	−0.756404	−0.378202	+	0.925723i	$0.623457\pi$
$678$	1.41033e17	0.0557608
$679$	2.26172e18	0.885695
$680$	3.32859e17	0.129108
$681$	1.61319e18	0.619770
$682$	3.42185e18	1.30216
$683$	1.10368e18	0.416016	0.208008	−	0.978127i	$-0.433302\pi$
$683$	1.10368e18	0.416016	0.208008	+	0.978127i	$0.433302\pi$
$684$	−9.59018e16	−0.0358065
$685$	−2.31075e18	−0.854604
$686$	2.09872e18	0.768861
$687$	−1.00962e18	−0.366388
$688$	−2.07264e17	−0.0745074
$689$	1.09818e18	0.391065
$690$	−5.01721e16	−0.0176988
$691$	−6.91657e16	−0.0241704	−0.0120852	−	0.999927i	$-0.503847\pi$
$691$	−6.91657e16	−0.0241704	−0.0120852	+	0.999927i	$0.503847\pi$
$692$	−2.63450e18	−0.912030
$693$	7.62747e17	0.261586
$694$	−5.65409e17	−0.192099
$695$	1.93741e18	0.652108
$696$	1.99935e17	0.0666696
$697$	1.39150e18	0.459695
$698$	2.25986e18	0.739641
$699$	4.61880e17	0.149771
$700$	−2.46868e17	−0.0793099
$701$	2.17439e18	0.692104	0.346052	−	0.938215i	$-0.387522\pi$
$701$	2.17439e18	0.692104	0.346052	+	0.938215i	$0.387522\pi$
$702$	−3.44999e17	−0.108799
$703$	−7.59054e17	−0.237172
$704$	−3.99522e17	−0.123685
$705$	1.35123e18	0.414478
$706$	3.90636e18	1.18725
$707$	−3.32630e18	−1.00169
$708$	2.23997e17	0.0668383
$709$	5.52547e18	1.63369	0.816844	−	0.576859i	$-0.195722\pi$
$709$	5.52547e18	1.63369	0.816844	+	0.576859i	$0.195722\pi$
$710$	−1.84925e18	−0.541770
$711$	1.74253e18	0.505857
$712$	3.77852e17	0.108693
$713$	−6.32930e17	−0.180416
$714$	9.35993e17	0.264383
$715$	−1.26397e18	−0.353791
$716$	1.24143e18	0.344339
$717$	−3.78072e18	−1.03920
$718$	2.20421e18	0.600404
$719$	7.09858e18	1.91617	0.958085	−	0.286485i	$-0.0924868\pi$
$719$	7.09858e18	1.91617	0.958085	+	0.286485i	$0.0924868\pi$
$720$	−1.39314e17	−0.0372678
$721$	1.45730e18	0.386339
$722$	−2.56717e18	−0.674470
$723$	5.20783e17	0.135599
$724$	−6.21144e17	−0.160285
$725$	2.55423e17	0.0653226
$726$	−3.37019e16	−0.00854213
$727$	2.05702e18	0.516732	0.258366	−	0.966047i	$-0.416816\pi$
$727$	2.05702e18	0.516732	0.258366	+	0.966047i	$0.416816\pi$
$728$	9.00450e17	0.224185
$729$	1.50095e17	0.0370370
$730$	−1.44938e18	−0.354473
$731$	1.00393e18	0.243356
$732$	−6.19778e17	−0.148907
$733$	3.63415e18	0.865420	0.432710	−	0.901533i	$-0.357557\pi$
$733$	3.63415e18	0.865420	0.432710	+	0.901533i	$0.357557\pi$
$734$	−4.44855e18	−1.05001
$735$	4.09438e17	0.0957901
$736$	7.38984e16	0.0171368
$737$	−3.59211e18	−0.825679
$738$	−5.82395e17	−0.132694
$739$	2.50725e17	0.0566251	0.0283125	−	0.999599i	$-0.490987\pi$
$739$	2.50725e17	0.0566251	0.0283125	+	0.999599i	$0.490987\pi$
$740$	−1.10266e18	−0.246851
$741$	4.46883e17	0.0991689
$742$	1.24699e18	0.274308
$743$	6.04321e16	0.0131777	0.00658886	−	0.999978i	$-0.497903\pi$
$743$	6.04321e16	0.0131777	0.00658886	+	0.999978i	$0.497903\pi$
$744$	−1.75747e18	−0.379896
$745$	1.86353e18	0.399319
$746$	2.96879e18	0.630635
$747$	3.06123e17	0.0644631
$748$	1.93518e18	0.403981
$749$	−1.10942e18	−0.229595
$750$	−1.77979e17	−0.0365148
$751$	−3.11331e18	−0.633231	−0.316616	−	0.948554i	$-0.602547\pi$
$751$	−3.11331e18	−0.633231	−0.316616	+	0.948554i	$0.602547\pi$
$752$	−1.99023e18	−0.401316
$753$	5.62622e17	0.112473
$754$	−9.31655e17	−0.184647
$755$	−1.39831e18	−0.274757
$756$	−3.91748e17	−0.0763160
$757$	−2.83534e18	−0.547623	−0.273812	−	0.961783i	$-0.588284\pi$
$757$	−2.83534e18	−0.547623	−0.273812	+	0.961783i	$0.588284\pi$
$758$	−5.50776e18	−1.05469
$759$	−2.91691e17	−0.0553798
$760$	1.80456e17	0.0339690
$761$	7.02743e17	0.131158	0.0655792	−	0.997847i	$-0.479110\pi$
$761$	7.02743e17	0.131158	0.0655792	+	0.997847i	$0.479110\pi$
$762$	−3.15730e18	−0.584263
$763$	5.39679e18	0.990207
$764$	−4.55140e18	−0.828014
$765$	6.74800e17	0.121724
$766$	−5.82808e18	−1.04241
$767$	−1.04378e18	−0.185114
$768$	2.05195e17	0.0360844
$769$	2.41682e18	0.421428	0.210714	−	0.977548i	$-0.432421\pi$
$769$	2.41682e18	0.421428	0.210714	+	0.977548i	$0.432421\pi$
$770$	−1.43524e18	−0.248162
$771$	3.08007e17	0.0528089
$772$	−1.13905e18	−0.193656
$773$	−2.17379e18	−0.366481	−0.183240	−	0.983068i	$-0.558659\pi$
$773$	−2.17379e18	−0.366481	−0.183240	+	0.983068i	$0.558659\pi$
$774$	−4.20184e17	−0.0702462
$775$	−2.24523e18	−0.372220
$776$	−2.40167e18	−0.394832
$777$	−3.10065e18	−0.505495
$778$	−3.40267e18	−0.550114
$779$	7.54387e17	0.120949
$780$	6.49176e17	0.103216
$781$	−1.07512e19	−1.69521
$782$	−3.57944e17	−0.0559721
$783$	4.05325e17	0.0628567
$784$	−6.03060e17	−0.0927484
$785$	−3.08572e18	−0.470656
$786$	2.91515e18	0.440976
$787$	−5.18814e18	−0.778352	−0.389176	−	0.921163i	$-0.627240\pi$
$787$	−5.18814e18	−0.778352	−0.389176	+	0.921163i	$0.627240\pi$
$788$	5.53129e18	0.823012
$789$	−4.00797e18	−0.591458
$790$	−3.27888e18	−0.479898
$791$	−7.46241e17	−0.108326
$792$	−8.09945e17	−0.116612
$793$	2.88804e18	0.412409
$794$	5.55196e18	0.786346
$795$	8.99015e17	0.126293
$796$	−6.80329e18	−0.947947
$797$	1.10148e19	1.52229	0.761144	−	0.648583i	$-0.224638\pi$
$797$	1.10148e19	1.52229	0.761144	+	0.648583i	$0.224638\pi$
$798$	5.07439e17	0.0695609
$799$	9.64013e18	1.31078
$800$	2.62144e17	0.0353553
$801$	7.66015e17	0.102477
$802$	6.58469e18	0.873780
$803$	−8.42641e18	−1.10915
$804$	1.84492e18	0.240887
$805$	2.65473e17	0.0343832
$806$	8.18947e18	1.05215
$807$	−6.66944e18	−0.849986
$808$	3.53213e18	0.446542
$809$	7.14073e18	0.895524	0.447762	−	0.894153i	$-0.352221\pi$
$809$	7.14073e18	0.895524	0.447762	+	0.894153i	$0.352221\pi$
$810$	−2.82430e17	−0.0351364
$811$	−8.16933e18	−1.00821	−0.504105	−	0.863643i	$-0.668177\pi$
$811$	−8.16933e18	−1.00821	−0.504105	+	0.863643i	$0.668177\pi$
$812$	−1.05790e18	−0.129518
$813$	−5.60149e18	−0.680323
$814$	−6.41064e18	−0.772401
$815$	4.60033e18	0.549876
$816$	−9.93911e17	−0.117859
$817$	5.44272e17	0.0640284
$818$	5.37327e18	0.627107
$819$	1.82547e18	0.211363
$820$	1.09588e18	0.125885
$821$	−7.76919e16	−0.00885412	−0.00442706	−	0.999990i	$-0.501409\pi$
$821$	−7.76919e16	−0.00885412	−0.00442706	+	0.999990i	$0.501409\pi$
$822$	6.89987e18	0.780143
$823$	−8.01213e18	−0.898771	−0.449386	−	0.893338i	$-0.648357\pi$
$823$	−8.01213e18	−0.898771	−0.449386	+	0.893338i	$0.648357\pi$
$824$	−1.54747e18	−0.172225
$825$	−1.03473e18	−0.114256
$826$	−1.18522e18	−0.129846
$827$	4.37194e18	0.475214	0.237607	−	0.971361i	$-0.423637\pi$
$827$	4.37194e18	0.475214	0.237607	+	0.971361i	$0.423637\pi$
$828$	1.49813e17	0.0161567
$829$	1.70519e19	1.82461	0.912303	−	0.409517i	$-0.134303\pi$
$829$	1.70519e19	1.82461	0.912303	+	0.409517i	$0.134303\pi$
$830$	−5.76024e17	−0.0611551
$831$	−3.67959e18	−0.387608
$832$	−9.56169e17	−0.0999386
$833$	2.92106e18	0.302934
$834$	−5.78507e18	−0.595291
$835$	−2.52085e18	−0.257386
$836$	1.04914e18	0.106290
$837$	−3.56290e18	−0.358169
$838$	−4.57893e18	−0.456750
$839$	1.16401e19	1.15213	0.576067	−	0.817402i	$-0.304587\pi$
$839$	1.16401e19	1.15213	0.576067	+	0.817402i	$0.304587\pi$
$840$	7.37144e17	0.0723997
$841$	−9.16607e18	−0.893324
$842$	7.58273e18	0.733326
$843$	6.65971e18	0.639111
$844$	−5.10935e18	−0.486564
$845$	1.70739e18	0.161348
$846$	−4.03476e18	−0.378365
$847$	1.78325e17	0.0165947
$848$	−1.32416e18	−0.122283
$849$	−8.15855e17	−0.0747675
$850$	−1.26976e18	−0.115477
$851$	1.18576e18	0.107017
$852$	5.52182e18	0.494567
$853$	1.00864e19	0.896539	0.448270	−	0.893898i	$-0.352040\pi$
$853$	1.00864e19	0.896539	0.448270	+	0.893898i	$0.352040\pi$
$854$	3.27939e18	0.289279
$855$	3.65836e17	0.0320263
$856$	1.17807e18	0.102351
$857$	8.84171e18	0.762361	0.381181	−	0.924501i	$-0.375518\pi$
$857$	8.84171e18	0.762361	0.381181	+	0.924501i	$0.375518\pi$
$858$	3.77418e18	0.322965
$859$	−1.44967e19	−1.23116	−0.615579	−	0.788075i	$-0.711078\pi$
$859$	−1.44967e19	−1.23116	−0.615579	+	0.788075i	$0.711078\pi$
$860$	7.90650e17	0.0666414
$861$	3.08159e18	0.257783
$862$	−5.24141e18	−0.435162
$863$	−1.63841e19	−1.35005	−0.675027	−	0.737793i	$-0.735868\pi$
$863$	−1.63841e19	−1.35005	−0.675027	+	0.737793i	$0.735868\pi$
$864$	4.15990e17	0.0340207
$865$	1.00498e19	0.815745
$866$	1.67245e19	1.34737
$867$	−2.40619e18	−0.192401
$868$	9.29920e18	0.738019
$869$	−1.90628e19	−1.50161
$870$	−7.62690e17	−0.0596311
$871$	−8.59695e18	−0.667154
$872$	−5.73074e18	−0.441421
$873$	−4.86887e18	−0.372251
$874$	−1.94056e17	−0.0147266
$875$	9.41727e17	0.0709370
$876$	4.32782e18	0.323588
$877$	1.76436e19	1.30945	0.654727	−	0.755865i	$-0.272783\pi$
$877$	1.76436e19	1.30945	0.654727	+	0.755865i	$0.272783\pi$
$878$	3.86845e18	0.284986
$879$	−3.44048e18	−0.251589
$880$	1.52405e18	0.110628
$881$	1.98036e19	1.42693	0.713463	−	0.700693i	$-0.247126\pi$
$881$	1.98036e19	1.42693	0.713463	+	0.700693i	$0.247126\pi$
$882$	−1.22258e18	−0.0874440
$883$	−2.48109e19	−1.76156	−0.880782	−	0.473522i	$-0.842983\pi$
$883$	−2.48109e19	−1.76156	−0.880782	+	0.473522i	$0.842983\pi$
$884$	4.63143e18	0.326419
$885$	−8.54480e17	−0.0597820
$886$	8.33520e17	0.0578891
$887$	3.12970e18	0.215774	0.107887	−	0.994163i	$-0.465592\pi$
$887$	3.12970e18	0.215774	0.107887	+	0.994163i	$0.465592\pi$
$888$	3.29252e18	0.225343
$889$	1.67060e19	1.13504
$890$	−1.44139e18	−0.0972181
$891$	−1.64199e18	−0.109943
$892$	5.98429e18	0.397778
$893$	5.22630e18	0.344874
$894$	−5.56446e18	−0.364527
$895$	−4.73566e18	−0.307986
$896$	−1.08574e18	−0.0701007
$897$	−6.98100e17	−0.0447473
$898$	−2.14226e18	−0.136325
$899$	−9.62147e18	−0.607860
$900$	5.31441e17	0.0333333
$901$	6.41386e18	0.399400
$902$	6.37123e18	0.393895
$903$	2.22329e18	0.136467
$904$	7.92418e17	0.0482902
$905$	2.36948e18	0.143363
$906$	4.17533e18	0.250818
$907$	1.67393e19	0.998368	0.499184	−	0.866496i	$-0.333633\pi$
$907$	1.67393e19	0.998368	0.499184	+	0.866496i	$0.333633\pi$
$908$	9.06398e18	0.536736
$909$	7.16064e18	0.421004
$910$	−3.43494e18	−0.200517
$911$	1.36209e19	0.789470	0.394735	−	0.918795i	$-0.370836\pi$
$911$	1.36209e19	0.789470	0.394735	+	0.918795i	$0.370836\pi$
$912$	−5.38839e17	−0.0310093
$913$	−3.34889e18	−0.191356
$914$	−1.17773e18	−0.0668185
$915$	2.36426e18	0.133186
$916$	−5.67273e18	−0.317301
$917$	−1.54248e19	−0.856678
$918$	−2.01494e18	−0.111118
$919$	−2.39335e19	−1.31055	−0.655277	−	0.755388i	$-0.727448\pi$
$919$	−2.39335e19	−1.31055	−0.655277	+	0.755388i	$0.727448\pi$
$920$	−2.81900e17	−0.0153276
$921$	−1.16640e19	−0.629739
$922$	−1.24368e19	−0.666740
$923$	−2.57306e19	−1.36974
$924$	4.28561e18	0.226540
$925$	4.20631e18	0.220790
$926$	−1.03134e19	−0.537565
$927$	−3.13717e18	−0.162375
$928$	1.12336e18	0.0577376
$929$	−2.62102e19	−1.33773	−0.668866	−	0.743383i	$-0.733220\pi$
$929$	−2.62102e19	−1.33773	−0.668866	+	0.743383i	$0.733220\pi$
$930$	6.70422e18	0.339789
$931$	1.58363e18	0.0797039
$932$	2.59515e18	0.129706
$933$	6.35215e18	0.315275
$934$	−1.17989e19	−0.581551
$935$	−7.38212e18	−0.361331
$936$	−1.93843e18	−0.0942230
$937$	2.81835e19	1.36046	0.680232	−	0.732997i	$-0.261879\pi$
$937$	2.81835e19	1.36046	0.680232	+	0.732997i	$0.261879\pi$
$938$	−9.76190e18	−0.467968
$939$	−1.23655e19	−0.588689
$940$	7.59211e18	0.358948
$941$	−2.54613e19	−1.19549	−0.597747	−	0.801685i	$-0.703937\pi$
$941$	−2.54613e19	−1.19549	−0.597747	+	0.801685i	$0.703937\pi$
$942$	9.21390e18	0.429648
$943$	−1.17847e18	−0.0545747
$944$	1.25856e18	0.0578837
$945$	1.49440e18	0.0682591
$946$	4.59669e18	0.208522
$947$	2.53093e19	1.14026	0.570131	−	0.821554i	$-0.306892\pi$
$947$	2.53093e19	1.14026	0.570131	+	0.821554i	$0.306892\pi$
$948$	9.79067e18	0.438085
$949$	−2.01668e19	−0.896203
$950$	−6.88385e17	−0.0303828
$951$	7.77864e18	0.340981
$952$	5.25902e18	0.228963
$953$	−1.35627e19	−0.586464	−0.293232	−	0.956041i	$-0.594731\pi$
$953$	−1.35627e19	−0.586464	−0.293232	+	0.956041i	$0.594731\pi$
$954$	−2.68444e18	−0.115290
$955$	1.73622e19	0.740598
$956$	−2.12426e19	−0.899976
$957$	−4.43413e18	−0.186587
$958$	−1.46692e19	−0.613098
$959$	−3.65089e19	−1.51557
$960$	−7.82758e17	−0.0322749
$961$	6.01574e19	2.46370
$962$	−1.53425e19	−0.624105
$963$	2.38828e18	0.0964971
$964$	2.92610e18	0.117433
$965$	4.34513e18	0.173211
$966$	−7.92697e17	−0.0313874
$967$	−3.16626e19	−1.24530	−0.622650	−	0.782500i	$-0.713944\pi$
$967$	−3.16626e19	−1.24530	−0.622650	+	0.782500i	$0.713944\pi$
$968$	−1.89359e17	−0.00739770
$969$	2.60999e18	0.101283
$970$	9.16164e18	0.353148
$971$	−2.69476e19	−1.03180	−0.515900	−	0.856649i	$-0.672543\pi$
$971$	−2.69476e19	−1.03180	−0.515900	+	0.856649i	$0.672543\pi$
$972$	8.43330e17	0.0320750
$973$	3.06102e19	1.15646
$974$	−3.57374e18	−0.134119
$975$	−2.47641e18	−0.0923193
$976$	−3.48232e18	−0.128957
$977$	7.53679e18	0.277250	0.138625	−	0.990345i	$-0.455732\pi$
$977$	7.53679e18	0.277250	0.138625	+	0.990345i	$0.455732\pi$
$978$	−1.37365e19	−0.501966
$979$	−8.37998e18	−0.304197
$980$	2.30049e18	0.0829567
$981$	−1.16178e19	−0.416176
$982$	1.48706e19	0.529182
$983$	3.65300e19	1.29137	0.645687	−	0.763602i	$-0.276571\pi$
$983$	3.65300e19	1.29137	0.645687	+	0.763602i	$0.276571\pi$
$984$	−3.27228e18	−0.114916
$985$	−2.11002e19	−0.736124
$986$	−5.44127e18	−0.188582
$987$	2.13489e19	0.735044
$988$	2.51088e18	0.0858828
$989$	−8.50235e17	−0.0288910
$990$	3.08970e18	0.104301
$991$	2.98763e19	1.00195	0.500977	−	0.865460i	$-0.332974\pi$
$991$	2.98763e19	1.00195	0.500977	+	0.865460i	$0.332974\pi$
$992$	−9.87463e18	−0.328999
$993$	−1.70497e19	−0.564347
$994$	−2.92173e19	−0.960789
$995$	2.59525e19	0.847870
$996$	1.72000e18	0.0558267
$997$	−6.62600e18	−0.213665	−0.106832	−	0.994277i	$-0.534071\pi$
$997$	−6.62600e18	−0.213665	−0.106832	+	0.994277i	$0.534071\pi$
$998$	8.11941e18	0.260121
$999$	6.67488e18	0.212455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.14.a.f.1.1	✓	1
3.2	odd	2		90.14.a.c.1.1		1
5.2	odd	4		150.14.c.e.49.2		2
5.3	odd	4		150.14.c.e.49.1		2
5.4	even	2		150.14.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.14.a.f.1.1	✓	1	1.1	even	1	trivial
90.14.a.c.1.1		1	3.2	odd	2
150.14.a.a.1.1		1	5.4	even	2
150.14.c.e.49.1		2	5.3	odd	4
150.14.c.e.49.2		2	5.2	odd	4

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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	30.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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