LMFDB - Embedded newform 15.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,10,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	15.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:	$7.72553754246$
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	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+22.0000 q^{2} -81.0000 q^{3} -28.0000 q^{4} -625.000 q^{5} -1782.00 q^{6} -5988.00 q^{7} -11880.0 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q+22.0000 q^{2} -81.0000 q^{3} -28.0000 q^{4} -625.000 q^{5} -1782.00 q^{6} -5988.00 q^{7} -11880.0 q^{8} +6561.00 q^{9} -13750.0 q^{10} -14648.0 q^{11} +2268.00 q^{12} +37906.0 q^{13} -131736. q^{14} +50625.0 q^{15} -247024. q^{16} -441098. q^{17} +144342. q^{18} +441820. q^{19} +17500.0 q^{20} +485028. q^{21} -322256. q^{22} +2.26414e6 q^{23} +962280. q^{24} +390625. q^{25} +833932. q^{26} -531441. q^{27} +167664. q^{28} -1.04935e6 q^{29} +1.11375e6 q^{30} -7.91057e6 q^{31} +648032. q^{32} +1.18649e6 q^{33} -9.70416e6 q^{34} +3.74250e6 q^{35} -183708. q^{36} -2.09926e7 q^{37} +9.72004e6 q^{38} -3.07039e6 q^{39} +7.42500e6 q^{40} +1.32856e7 q^{41} +1.06706e7 q^{42} -2.31308e7 q^{43} +410144. q^{44} -4.10062e6 q^{45} +4.98110e7 q^{46} -1.38737e7 q^{47} +2.00089e7 q^{48} -4.49746e6 q^{49} +8.59375e6 q^{50} +3.57289e7 q^{51} -1.06137e6 q^{52} -5.76352e7 q^{53} -1.16917e7 q^{54} +9.15500e6 q^{55} +7.11374e7 q^{56} -3.57874e7 q^{57} -2.30857e7 q^{58} -3.20421e7 q^{59} -1.41750e6 q^{60} +1.10664e8 q^{61} -1.74032e8 q^{62} -3.92873e7 q^{63} +1.40733e8 q^{64} -2.36912e7 q^{65} +2.61027e7 q^{66} -1.18568e8 q^{67} +1.23507e7 q^{68} -1.83395e8 q^{69} +8.23350e7 q^{70} +2.76680e8 q^{71} -7.79447e7 q^{72} -2.64023e8 q^{73} -4.61836e8 q^{74} -3.16406e7 q^{75} -1.23710e7 q^{76} +8.77122e7 q^{77} -6.75485e7 q^{78} +4.48203e8 q^{79} +1.54390e8 q^{80} +4.30467e7 q^{81} +2.92282e8 q^{82} +8.51016e8 q^{83} -1.35808e7 q^{84} +2.75686e8 q^{85} -5.08877e8 q^{86} +8.49974e7 q^{87} +1.74018e8 q^{88} +1.89895e8 q^{89} -9.02138e7 q^{90} -2.26981e8 q^{91} -6.33958e7 q^{92} +6.40756e8 q^{93} -3.05221e8 q^{94} -2.76138e8 q^{95} -5.24906e7 q^{96} -1.01415e9 q^{97} -9.89442e7 q^{98} -9.61055e7 q^{99} +O(q^{100})\)

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 $

$2$	22.0000	0.972272	0.486136	−	0.873883i	$-0.338406\pi$
$2$	22.0000	0.972272	0.486136	+	0.873883i	$0.338406\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−28.0000	−0.0546875
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−1782.00	−0.561341
$7$	−5988.00	−0.942629	−0.471314	−	0.881965i	$-0.656220\pi$
$7$	−5988.00	−0.942629	−0.471314	+	0.881965i	$0.656220\pi$
$8$	−11880.0	−1.02544
$9$	6561.00	0.333333
$10$	−13750.0	−0.434813
$11$	−14648.0	−0.301655	−0.150828	−	0.988560i	$-0.548194\pi$
$11$	−14648.0	−0.301655	−0.150828	+	0.988560i	$0.548194\pi$
$12$	2268.00	0.0315738
$13$	37906.0	0.368098	0.184049	−	0.982917i	$-0.441080\pi$
$13$	37906.0	0.368098	0.184049	+	0.982917i	$0.441080\pi$
$14$	−131736.	−0.916491
$15$	50625.0	0.258199
$16$	−247024.	−0.942322
$17$	−441098.	−1.28090	−0.640450	−	0.768000i	$-0.721252\pi$
$17$	−441098.	−1.28090	−0.640450	+	0.768000i	$0.721252\pi$
$18$	144342.	0.324091
$19$	441820.	0.777775	0.388888	−	0.921285i	$-0.372859\pi$
$19$	441820.	0.777775	0.388888	+	0.921285i	$0.372859\pi$
$20$	17500.0	0.0244570
$21$	485028.	0.544227
$22$	−322256.	−0.293291
$23$	2.26414e6	1.68705	0.843524	−	0.537092i	$-0.180477\pi$
$23$	2.26414e6	1.68705	0.843524	+	0.537092i	$0.180477\pi$
$24$	962280.	0.592040
$25$	390625.	0.200000
$26$	833932.	0.357891
$27$	−531441.	−0.192450
$28$	167664.	0.0515500
$29$	−1.04935e6	−0.275505	−0.137752	−	0.990467i	$-0.543988\pi$
$29$	−1.04935e6	−0.275505	−0.137752	+	0.990467i	$0.543988\pi$
$30$	1.11375e6	0.251040
$31$	−7.91057e6	−1.53844	−0.769219	−	0.638985i	$-0.779355\pi$
$31$	−7.91057e6	−1.53844	−0.769219	+	0.638985i	$0.779355\pi$
$32$	648032.	0.109250
$33$	1.18649e6	0.174161
$34$	−9.70416e6	−1.24538
$35$	3.74250e6	0.421556
$36$	−183708.	−0.0182292
$37$	−2.09926e7	−1.84144	−0.920720	−	0.390224i	$-0.872398\pi$
$37$	−2.09926e7	−1.84144	−0.920720	+	0.390224i	$0.872398\pi$
$38$	9.72004e6	0.756209
$39$	−3.07039e6	−0.212521
$40$	7.42500e6	0.458592
$41$	1.32856e7	0.734265	0.367132	−	0.930169i	$-0.380340\pi$
$41$	1.32856e7	0.734265	0.367132	+	0.930169i	$0.380340\pi$
$42$	1.06706e7	0.529136
$43$	−2.31308e7	−1.03177	−0.515884	−	0.856659i	$-0.672536\pi$
$43$	−2.31308e7	−1.03177	−0.515884	+	0.856659i	$0.672536\pi$
$44$	410144.	0.0164968
$45$	−4.10062e6	−0.149071
$46$	4.98110e7	1.64027
$47$	−1.38737e7	−0.414717	−0.207358	−	0.978265i	$-0.566487\pi$
$47$	−1.38737e7	−0.414717	−0.207358	+	0.978265i	$0.566487\pi$
$48$	2.00089e7	0.544050
$49$	−4.49746e6	−0.111451
$50$	8.59375e6	0.194454
$51$	3.57289e7	0.739527
$52$	−1.06137e6	−0.0201303
$53$	−5.76352e7	−1.00334	−0.501668	−	0.865060i	$-0.667280\pi$
$53$	−5.76352e7	−1.00334	−0.501668	+	0.865060i	$0.667280\pi$
$54$	−1.16917e7	−0.187114
$55$	9.15500e6	0.134904
$56$	7.11374e7	0.966612
$57$	−3.57874e7	−0.449049
$58$	−2.30857e7	−0.267866
$59$	−3.20421e7	−0.344260	−0.172130	−	0.985074i	$-0.555065\pi$
$59$	−3.20421e7	−0.344260	−0.172130	+	0.985074i	$0.555065\pi$
$60$	−1.41750e6	−0.0141203
$61$	1.10664e8	1.02335	0.511673	−	0.859180i	$-0.329026\pi$
$61$	1.10664e8	1.02335	0.511673	+	0.859180i	$0.329026\pi$
$62$	−1.74032e8	−1.49578
$63$	−3.92873e7	−0.314210
$64$	1.40733e8	1.04854
$65$	−2.36912e7	−0.164618
$66$	2.61027e7	0.169332
$67$	−1.18568e8	−0.718839	−0.359420	−	0.933176i	$-0.617025\pi$
$67$	−1.18568e8	−0.718839	−0.359420	+	0.933176i	$0.617025\pi$
$68$	1.23507e7	0.0700492
$69$	−1.83395e8	−0.974017
$70$	8.23350e7	0.409867
$71$	2.76680e8	1.29216	0.646078	−	0.763272i	$-0.276408\pi$
$71$	2.76680e8	1.29216	0.646078	+	0.763272i	$0.276408\pi$
$72$	−7.79447e7	−0.341814
$73$	−2.64023e8	−1.08815	−0.544076	−	0.839036i	$-0.683120\pi$
$73$	−2.64023e8	−1.08815	−0.544076	+	0.839036i	$0.683120\pi$
$74$	−4.61836e8	−1.79038
$75$	−3.16406e7	−0.115470
$76$	−1.23710e7	−0.0425346
$77$	8.77122e7	0.284349
$78$	−6.75485e7	−0.206628
$79$	4.48203e8	1.29465	0.647325	−	0.762214i	$-0.275888\pi$
$79$	4.48203e8	1.29465	0.647325	+	0.762214i	$0.275888\pi$
$80$	1.54390e8	0.421419
$81$	4.30467e7	0.111111
$82$	2.92282e8	0.713905
$83$	8.51016e8	1.96828	0.984138	−	0.177402i	$-0.0567693\pi$
$83$	8.51016e8	1.96828	0.984138	+	0.177402i	$0.0567693\pi$
$84$	−1.35808e7	−0.0297624
$85$	2.75686e8	0.572836
$86$	−5.08877e8	−1.00316
$87$	8.49974e7	0.159063
$88$	1.74018e8	0.309331
$89$	1.89895e8	0.320818	0.160409	−	0.987051i	$-0.448719\pi$
$89$	1.89895e8	0.320818	0.160409	+	0.987051i	$0.448719\pi$
$90$	−9.02138e7	−0.144938
$91$	−2.26981e8	−0.346979
$92$	−6.33958e7	−0.0922604
$93$	6.40756e8	0.888218
$94$	−3.05221e8	−0.403217
$95$	−2.76138e8	−0.347832
$96$	−5.24906e7	−0.0630755
$97$	−1.01415e9	−1.16313	−0.581566	−	0.813499i	$-0.697560\pi$
$97$	−1.01415e9	−1.16313	−0.581566	+	0.813499i	$0.697560\pi$
$98$	−9.89442e7	−0.108361
$99$	−9.61055e7	−0.100552
$100$	−1.09375e7	−0.0109375
$101$	−1.31537e9	−1.25777	−0.628885	−	0.777498i	$-0.716488\pi$
$101$	−1.31537e9	−1.25777	−0.628885	+	0.777498i	$0.716488\pi$
$102$	7.86037e8	0.719022
$103$	−1.82797e9	−1.60030	−0.800151	−	0.599798i	$-0.795248\pi$
$103$	−1.82797e9	−1.60030	−0.800151	+	0.599798i	$0.795248\pi$
$104$	−4.50323e8	−0.377463
$105$	−3.03142e8	−0.243386
$106$	−1.26797e9	−0.975515
$107$	1.85367e8	0.136712	0.0683559	−	0.997661i	$-0.478225\pi$
$107$	1.85367e8	0.136712	0.0683559	+	0.997661i	$0.478225\pi$
$108$	1.48803e7	0.0105246
$109$	1.97869e9	1.34264	0.671318	−	0.741169i	$-0.265728\pi$
$109$	1.97869e9	1.34264	0.671318	+	0.741169i	$0.265728\pi$
$110$	2.01410e8	0.131164
$111$	1.70040e9	1.06316
$112$	1.47918e9	0.888259
$113$	1.57875e9	0.910876	0.455438	−	0.890267i	$-0.349483\pi$
$113$	1.57875e9	0.910876	0.455438	+	0.890267i	$0.349483\pi$
$114$	−7.87323e8	−0.436597
$115$	−1.41508e9	−0.754470
$116$	2.93818e7	0.0150667
$117$	2.48701e8	0.122699
$118$	−7.04927e8	−0.334715
$119$	2.64129e9	1.20741
$120$	−6.01425e8	−0.264768
$121$	−2.14338e9	−0.909004
$122$	2.43461e9	0.994970
$123$	−1.07613e9	−0.423928
$124$	2.21496e8	0.0841333
$125$	−2.44141e8	−0.0894427
$126$	−8.64320e8	−0.305497
$127$	2.40001e9	0.818645	0.409322	−	0.912390i	$-0.365765\pi$
$127$	2.40001e9	0.818645	0.409322	+	0.912390i	$0.365765\pi$
$128$	2.76433e9	0.910218
$129$	1.87359e9	0.595691
$130$	−5.21208e8	−0.160054
$131$	−1.96840e9	−0.583971	−0.291986	−	0.956423i	$-0.594316\pi$
$131$	−1.96840e9	−0.583971	−0.291986	+	0.956423i	$0.594316\pi$
$132$	−3.32217e7	−0.00952442
$133$	−2.64562e9	−0.733153
$134$	−2.60850e9	−0.698907
$135$	3.32151e8	0.0860663
$136$	5.24024e9	1.31349
$137$	−2.02909e9	−0.492107	−0.246054	−	0.969256i	$-0.579134\pi$
$137$	−2.02909e9	−0.492107	−0.246054	+	0.969256i	$0.579134\pi$
$138$	−4.03469e9	−0.947009
$139$	−1.13673e9	−0.258280	−0.129140	−	0.991626i	$-0.541222\pi$
$139$	−1.13673e9	−0.258280	−0.129140	+	0.991626i	$0.541222\pi$
$140$	−1.04790e8	−0.0230539
$141$	1.12377e9	0.239437
$142$	6.08695e9	1.25633
$143$	−5.55247e8	−0.111039
$144$	−1.62072e9	−0.314107
$145$	6.55844e8	0.123210
$146$	−5.80851e9	−1.05798
$147$	3.64295e8	0.0643465
$148$	5.87792e8	0.100704
$149$	−4.73854e9	−0.787601	−0.393800	−	0.919196i	$-0.628840\pi$
$149$	−4.73854e9	−0.787601	−0.393800	+	0.919196i	$0.628840\pi$
$150$	−6.96094e8	−0.112268
$151$	2.26216e9	0.354101	0.177051	−	0.984202i	$-0.443344\pi$
$151$	2.26216e9	0.354101	0.177051	+	0.984202i	$0.443344\pi$
$152$	−5.24882e9	−0.797564
$153$	−2.89404e9	−0.426966
$154$	1.92967e9	0.276465
$155$	4.94410e9	0.688010
$156$	8.59708e7	0.0116223
$157$	−1.17889e10	−1.54854	−0.774272	−	0.632853i	$-0.781884\pi$
$157$	−1.17889e10	−1.54854	−0.774272	+	0.632853i	$0.781884\pi$
$158$	9.86046e9	1.25875
$159$	4.66845e9	0.579276
$160$	−4.05020e8	−0.0488581
$161$	−1.35576e10	−1.59026
$162$	9.47028e8	0.108030
$163$	1.14608e10	1.27166	0.635829	−	0.771830i	$-0.280658\pi$
$163$	1.14608e10	1.27166	0.635829	+	0.771830i	$0.280658\pi$
$164$	−3.71996e8	−0.0401551
$165$	−7.41555e8	−0.0778871
$166$	1.87223e10	1.91370
$167$	−1.33707e10	−1.33024	−0.665118	−	0.746738i	$-0.731619\pi$
$167$	−1.33707e10	−1.33024	−0.665118	+	0.746738i	$0.731619\pi$
$168$	−5.76213e9	−0.558074
$169$	−9.16763e9	−0.864504
$170$	6.06510e9	0.556952
$171$	2.89878e9	0.259258
$172$	6.47661e8	0.0564248
$173$	1.06264e10	0.901939	0.450970	−	0.892539i	$-0.351078\pi$
$173$	1.06264e10	0.901939	0.450970	+	0.892539i	$0.351078\pi$
$174$	1.86994e9	0.154652
$175$	−2.33906e9	−0.188526
$176$	3.61841e9	0.284257
$177$	2.59541e9	0.198759
$178$	4.17769e9	0.311922
$179$	2.61254e10	1.90206	0.951031	−	0.309094i	$-0.100026\pi$
$179$	2.61254e10	1.90206	0.951031	+	0.309094i	$0.100026\pi$
$180$	1.14818e8	0.00815233
$181$	2.34689e9	0.162532	0.0812660	−	0.996692i	$-0.474104\pi$
$181$	2.34689e9	0.162532	0.0812660	+	0.996692i	$0.474104\pi$
$182$	−4.99358e9	−0.337358
$183$	−8.96379e9	−0.590829
$184$	−2.68979e10	−1.72997
$185$	1.31203e10	0.823517
$186$	1.40966e10	0.863589
$187$	6.46120e9	0.386390
$188$	3.88463e8	0.0226798
$189$	3.18227e9	0.181409
$190$	−6.07502e9	−0.338187
$191$	2.24064e10	1.21821	0.609105	−	0.793089i	$-0.291529\pi$
$191$	2.24064e10	1.21821	0.609105	+	0.793089i	$0.291529\pi$
$192$	−1.13994e10	−0.605376
$193$	−3.65959e10	−1.89856	−0.949282	−	0.314427i	$-0.898188\pi$
$193$	−3.65959e10	−1.89856	−0.949282	+	0.314427i	$0.898188\pi$
$194$	−2.23113e10	−1.13088
$195$	1.91899e9	0.0950424
$196$	1.25929e8	0.00609499
$197$	−5.41546e9	−0.256175	−0.128088	−	0.991763i	$-0.540884\pi$
$197$	−5.41546e9	−0.256175	−0.128088	+	0.991763i	$0.540884\pi$
$198$	−2.11432e9	−0.0977637
$199$	2.62714e8	0.0118753	0.00593764	−	0.999982i	$-0.498110\pi$
$199$	2.62714e8	0.0118753	0.00593764	+	0.999982i	$0.498110\pi$
$200$	−4.64062e9	−0.205089
$201$	9.60403e9	0.415022
$202$	−2.89381e10	−1.22289
$203$	6.28351e9	0.259699
$204$	−1.00041e9	−0.0404429
$205$	−8.30348e9	−0.328373
$206$	−4.02154e10	−1.55593
$207$	1.48550e10	0.562349
$208$	−9.36369e9	−0.346866
$209$	−6.47178e9	−0.234620
$210$	−6.66914e9	−0.236637
$211$	1.34493e10	0.467121	0.233560	−	0.972342i	$-0.424962\pi$
$211$	1.34493e10	0.467121	0.233560	+	0.972342i	$0.424962\pi$
$212$	1.61378e9	0.0548699
$213$	−2.24111e10	−0.746026
$214$	4.07808e9	0.132921
$215$	1.44567e10	0.461421
$216$	6.31352e9	0.197347
$217$	4.73685e10	1.45018
$218$	4.35312e10	1.30541
$219$	2.13859e10	0.628245
$220$	−2.56340e8	−0.00737759
$221$	−1.67203e10	−0.471496
$222$	3.74087e10	1.03368
$223$	−2.66463e10	−0.721547	−0.360773	−	0.932654i	$-0.617487\pi$
$223$	−2.66463e10	−0.721547	−0.360773	+	0.932654i	$0.617487\pi$
$224$	−3.88042e9	−0.102982
$225$	2.56289e9	0.0666667
$226$	3.47324e10	0.885619
$227$	3.36318e10	0.840686	0.420343	−	0.907365i	$-0.361910\pi$
$227$	3.36318e10	0.840686	0.420343	+	0.907365i	$0.361910\pi$
$228$	1.00205e9	0.0245574
$229$	5.00453e10	1.20255	0.601276	−	0.799042i	$-0.294659\pi$
$229$	5.00453e10	1.20255	0.601276	+	0.799042i	$0.294659\pi$
$230$	−3.11319e10	−0.733550
$231$	−7.10469e9	−0.164169
$232$	1.24663e10	0.282515
$233$	−3.29626e10	−0.732688	−0.366344	−	0.930479i	$-0.619391\pi$
$233$	−3.29626e10	−0.732688	−0.366344	+	0.930479i	$0.619391\pi$
$234$	5.47143e9	0.119297
$235$	8.67106e9	0.185467
$236$	8.97179e8	0.0188267
$237$	−3.63044e10	−0.747467
$238$	5.81085e10	1.17393
$239$	−7.95422e9	−0.157691	−0.0788455	−	0.996887i	$-0.525123\pi$
$239$	−7.95422e9	−0.157691	−0.0788455	+	0.996887i	$0.525123\pi$
$240$	−1.25056e10	−0.243306
$241$	−7.52477e10	−1.43687	−0.718434	−	0.695595i	$-0.755141\pi$
$241$	−7.52477e10	−1.43687	−0.718434	+	0.695595i	$0.755141\pi$
$242$	−4.71544e10	−0.883799
$243$	−3.48678e9	−0.0641500
$244$	−3.09859e9	−0.0559642
$245$	2.81091e9	0.0498425
$246$	−2.36749e10	−0.412173
$247$	1.67476e10	0.286297
$248$	9.39775e10	1.57758
$249$	−6.89323e10	−1.13639
$250$	−5.37109e9	−0.0869626
$251$	−9.84631e10	−1.56582	−0.782910	−	0.622135i	$-0.786266\pi$
$251$	−9.84631e10	−1.56582	−0.782910	+	0.622135i	$0.786266\pi$
$252$	1.10004e9	0.0171833
$253$	−3.31651e10	−0.508907
$254$	5.28001e10	0.795945
$255$	−2.23306e10	−0.330727
$256$	−1.12400e10	−0.163563
$257$	8.52399e9	0.121883	0.0609416	−	0.998141i	$-0.480590\pi$
$257$	8.52399e9	0.121883	0.0609416	+	0.998141i	$0.480590\pi$
$258$	4.12190e10	0.579174
$259$	1.25703e11	1.73579
$260$	6.63355e8	0.00900256
$261$	−6.88479e9	−0.0918350
$262$	−4.33047e10	−0.567779
$263$	5.90654e9	0.0761259	0.0380630	−	0.999275i	$-0.487881\pi$
$263$	5.90654e9	0.0761259	0.0380630	+	0.999275i	$0.487881\pi$
$264$	−1.40955e10	−0.178592
$265$	3.60220e10	0.448705
$266$	−5.82036e10	−0.712824
$267$	−1.53815e10	−0.185224
$268$	3.31991e9	0.0393115
$269$	−7.15961e10	−0.833689	−0.416845	−	0.908978i	$-0.636864\pi$
$269$	−7.15961e10	−0.833689	−0.416845	+	0.908978i	$0.636864\pi$
$270$	7.30731e9	0.0836798
$271$	−1.24755e11	−1.40506	−0.702530	−	0.711654i	$-0.747946\pi$
$271$	−1.24755e11	−1.40506	−0.702530	+	0.711654i	$0.747946\pi$
$272$	1.08962e11	1.20702
$273$	1.83855e10	0.200329
$274$	−4.46401e10	−0.478462
$275$	−5.72187e9	−0.0603311
$276$	5.13506e9	0.0532666
$277$	1.12824e11	1.15145	0.575723	−	0.817645i	$-0.304721\pi$
$277$	1.12824e11	1.15145	0.575723	+	0.817645i	$0.304721\pi$
$278$	−2.50080e10	−0.251118
$279$	−5.19012e10	−0.512813
$280$	−4.44609e10	−0.432282
$281$	8.70208e10	0.832616	0.416308	−	0.909224i	$-0.363324\pi$
$281$	8.70208e10	0.832616	0.416308	+	0.909224i	$0.363324\pi$
$282$	2.47229e10	0.232798
$283$	3.27696e9	0.0303692	0.0151846	−	0.999885i	$-0.495166\pi$
$283$	3.27696e9	0.0303692	0.0151846	+	0.999885i	$0.495166\pi$
$284$	−7.74703e9	−0.0706647
$285$	2.23671e10	0.200821
$286$	−1.22154e10	−0.107960
$287$	−7.95539e10	−0.692139
$288$	4.25174e9	0.0364167
$289$	7.59796e10	0.640703
$290$	1.44286e10	0.119793
$291$	8.21461e10	0.671535
$292$	7.39265e9	0.0595083
$293$	−1.49860e11	−1.18791	−0.593953	−	0.804500i	$-0.702433\pi$
$293$	−1.49860e11	−1.18791	−0.593953	+	0.804500i	$0.702433\pi$
$294$	8.01448e9	0.0625622
$295$	2.00263e10	0.153958
$296$	2.49392e11	1.88829
$297$	7.78455e9	0.0580536
$298$	−1.04248e11	−0.765762
$299$	8.58243e10	0.620998
$300$	8.85938e8	0.00631477
$301$	1.38507e11	0.972574
$302$	4.97676e10	0.344283
$303$	1.06545e11	0.726174
$304$	−1.09140e11	−0.732915
$305$	−6.91650e10	−0.457654
$306$	−6.36690e10	−0.415127
$307$	−1.84570e11	−1.18587	−0.592937	−	0.805249i	$-0.702032\pi$
$307$	−1.84570e11	−1.18587	−0.592937	+	0.805249i	$0.702032\pi$
$308$	−2.45594e9	−0.0155503
$309$	1.48066e11	0.923935
$310$	1.08770e11	0.668933
$311$	9.04650e10	0.548351	0.274176	−	0.961680i	$-0.411595\pi$
$311$	9.04650e10	0.548351	0.274176	+	0.961680i	$0.411595\pi$
$312$	3.64762e10	0.217928
$313$	1.07930e10	0.0635615	0.0317808	−	0.999495i	$-0.489882\pi$
$313$	1.07930e10	0.0635615	0.0317808	+	0.999495i	$0.489882\pi$
$314$	−2.59355e11	−1.50560
$315$	2.45545e10	0.140519
$316$	−1.25497e10	−0.0708012
$317$	4.18319e10	0.232670	0.116335	−	0.993210i	$-0.462885\pi$
$317$	4.18319e10	0.232670	0.116335	+	0.993210i	$0.462885\pi$
$318$	1.02706e11	0.563214
$319$	1.53709e10	0.0831076
$320$	−8.79581e10	−0.468922
$321$	−1.50148e10	−0.0789306
$322$	−2.98268e11	−1.54616
$323$	−1.94886e11	−0.996252
$324$	−1.20531e9	−0.00607639
$325$	1.48070e10	0.0736195
$326$	2.52137e11	1.23640
$327$	−1.60274e11	−0.775172
$328$	−1.57832e11	−0.752946
$329$	8.30756e10	0.390924
$330$	−1.63142e10	−0.0757274
$331$	−1.23310e10	−0.0564640	−0.0282320	−	0.999601i	$-0.508988\pi$
$331$	−1.23310e10	−0.0564640	−0.0282320	+	0.999601i	$0.508988\pi$
$332$	−2.38284e10	−0.107640
$333$	−1.37732e11	−0.613813
$334$	−2.94154e11	−1.29335
$335$	7.41052e10	0.321475
$336$	−1.19814e11	−0.512837
$337$	−2.17976e10	−0.0920606	−0.0460303	−	0.998940i	$-0.514657\pi$
$337$	−2.17976e10	−0.0920606	−0.0460303	+	0.998940i	$0.514657\pi$
$338$	−2.01688e11	−0.840533
$339$	−1.27878e11	−0.525895
$340$	−7.71922e9	−0.0313269
$341$	1.15874e11	0.464078
$342$	6.37732e10	0.252070
$343$	2.68568e11	1.04769
$344$	2.74793e11	1.05802
$345$	1.14622e11	0.435594
$346$	2.33780e11	0.876930
$347$	−8.43613e10	−0.312364	−0.156182	−	0.987728i	$-0.549919\pi$
$347$	−8.43613e10	−0.312364	−0.156182	+	0.987728i	$0.549919\pi$
$348$	−2.37993e9	−0.00869875
$349$	−1.23295e9	−0.00444867	−0.00222434	−	0.999998i	$-0.500708\pi$
$349$	−1.23295e9	−0.00444867	−0.00222434	+	0.999998i	$0.500708\pi$
$350$	−5.14594e10	−0.183298
$351$	−2.01448e10	−0.0708404
$352$	−9.49237e9	−0.0329559
$353$	1.73388e11	0.594336	0.297168	−	0.954825i	$-0.403958\pi$
$353$	1.73388e11	0.594336	0.297168	+	0.954825i	$0.403958\pi$
$354$	5.70991e10	0.193248
$355$	−1.72925e11	−0.577869
$356$	−5.31706e9	−0.0175447
$357$	−2.13945e11	−0.697100
$358$	5.74760e11	1.84932
$359$	6.38159e10	0.202770	0.101385	−	0.994847i	$-0.467673\pi$
$359$	6.38159e10	0.202770	0.101385	+	0.994847i	$0.467673\pi$
$360$	4.87154e10	0.152864
$361$	−1.27483e11	−0.395066
$362$	5.16316e10	0.158025
$363$	1.73614e11	0.524814
$364$	6.35547e9	0.0189754
$365$	1.65015e11	0.486636
$366$	−1.97203e11	−0.574446
$367$	1.12242e11	0.322966	0.161483	−	0.986876i	$-0.448372\pi$
$367$	1.12242e11	0.322966	0.161483	+	0.986876i	$0.448372\pi$
$368$	−5.59296e11	−1.58974
$369$	8.71666e10	0.244755
$370$	2.88648e11	0.800682
$371$	3.45119e11	0.945773
$372$	−1.79412e10	−0.0485744
$373$	7.21004e11	1.92863	0.964313	−	0.264766i	$-0.0852948\pi$
$373$	7.21004e11	1.92863	0.964313	+	0.264766i	$0.0852948\pi$
$374$	1.42146e11	0.375676
$375$	1.97754e10	0.0516398
$376$	1.64819e11	0.425268
$377$	−3.97767e10	−0.101413
$378$	7.00099e10	0.176379
$379$	−2.04331e11	−0.508695	−0.254348	−	0.967113i	$-0.581861\pi$
$379$	−2.04331e11	−0.508695	−0.254348	+	0.967113i	$0.581861\pi$
$380$	7.73185e9	0.0190220
$381$	−1.94400e11	−0.472645
$382$	4.92941e11	1.18443
$383$	−5.47180e11	−1.29938	−0.649689	−	0.760200i	$-0.725101\pi$
$383$	−5.47180e11	−1.29938	−0.649689	+	0.760200i	$0.725101\pi$
$384$	−2.23911e11	−0.525515
$385$	−5.48201e10	−0.127165
$386$	−8.05111e11	−1.84592
$387$	−1.51761e11	−0.343923
$388$	2.83962e10	0.0636088
$389$	−3.46262e11	−0.766711	−0.383356	−	0.923601i	$-0.625232\pi$
$389$	−3.46262e11	−0.766711	−0.383356	+	0.923601i	$0.625232\pi$
$390$	4.22178e10	0.0924070
$391$	−9.98706e11	−2.16094
$392$	5.34299e10	0.114287
$393$	1.59440e11	0.337156
$394$	−1.19140e11	−0.249072
$395$	−2.80127e11	−0.578985
$396$	2.69095e9	0.00549893
$397$	2.56758e11	0.518760	0.259380	−	0.965775i	$-0.416482\pi$
$397$	2.56758e11	0.518760	0.259380	+	0.965775i	$0.416482\pi$
$398$	5.77971e9	0.0115460
$399$	2.14295e11	0.423286
$400$	−9.64938e10	−0.188464
$401$	2.01679e10	0.0389504	0.0194752	−	0.999810i	$-0.493800\pi$
$401$	2.01679e10	0.0389504	0.0194752	+	0.999810i	$0.493800\pi$
$402$	2.11289e11	0.403514
$403$	−2.99858e11	−0.566295
$404$	3.68303e10	0.0687843
$405$	−2.69042e10	−0.0496904
$406$	1.38237e11	0.252498
$407$	3.07499e11	0.555481
$408$	−4.24460e11	−0.758343
$409$	−4.33405e10	−0.0765842	−0.0382921	−	0.999267i	$-0.512192\pi$
$409$	−4.33405e10	−0.0765842	−0.0382921	+	0.999267i	$0.512192\pi$
$410$	−1.82676e11	−0.319268
$411$	1.64357e11	0.284118
$412$	5.11832e10	0.0875166
$413$	1.91868e11	0.324510
$414$	3.26810e11	0.546756
$415$	−5.31885e11	−0.880240
$416$	2.45643e10	0.0402147
$417$	9.20751e10	0.149118
$418$	−1.42379e11	−0.228115
$419$	5.10680e11	0.809443	0.404721	−	0.914440i	$-0.367369\pi$
$419$	5.10680e11	0.809443	0.404721	+	0.914440i	$0.367369\pi$
$420$	8.48799e9	0.0133102
$421$	3.21228e11	0.498361	0.249181	−	0.968457i	$-0.419839\pi$
$421$	3.21228e11	0.498361	0.249181	+	0.968457i	$0.419839\pi$
$422$	2.95885e11	0.454168
$423$	−9.10253e10	−0.138239
$424$	6.84706e11	1.02886
$425$	−1.72304e11	−0.256180
$426$	−4.93043e11	−0.725340
$427$	−6.62656e11	−0.964635
$428$	−5.19029e9	−0.00747643
$429$	4.49750e10	0.0641082
$430$	3.18048e11	0.448626
$431$	4.47617e11	0.624826	0.312413	−	0.949946i	$-0.398863\pi$
$431$	4.47617e11	0.624826	0.312413	+	0.949946i	$0.398863\pi$
$432$	1.31279e11	0.181350
$433$	−1.41186e11	−0.193017	−0.0965085	−	0.995332i	$-0.530767\pi$
$433$	−1.41186e11	−0.193017	−0.0965085	+	0.995332i	$0.530767\pi$
$434$	1.04211e12	1.40997
$435$	−5.31233e10	−0.0711351
$436$	−5.54033e10	−0.0734254
$437$	1.00034e12	1.31214
$438$	4.70490e11	0.610824
$439$	−8.50498e11	−1.09291	−0.546453	−	0.837490i	$-0.684022\pi$
$439$	−8.50498e11	−1.09291	−0.546453	+	0.837490i	$0.684022\pi$
$440$	−1.08761e11	−0.138337
$441$	−2.95079e10	−0.0371504
$442$	−3.67846e11	−0.458422
$443$	3.03188e11	0.374020	0.187010	−	0.982358i	$-0.440120\pi$
$443$	3.03188e11	0.374020	0.187010	+	0.982358i	$0.440120\pi$
$444$	−4.76111e10	−0.0581413
$445$	−1.18684e11	−0.143474
$446$	−5.86218e11	−0.701540
$447$	3.83822e11	0.454721
$448$	−8.42709e11	−0.988386
$449$	−1.40328e12	−1.62943	−0.814714	−	0.579863i	$-0.803106\pi$
$449$	−1.40328e12	−1.62943	−0.814714	+	0.579863i	$0.803106\pi$
$450$	5.63836e10	0.0648181
$451$	−1.94607e11	−0.221495
$452$	−4.42049e10	−0.0498136
$453$	−1.83235e11	−0.204440
$454$	7.39899e11	0.817375
$455$	1.41863e11	0.155174
$456$	4.25155e11	0.460474
$457$	3.35354e11	0.359650	0.179825	−	0.983699i	$-0.442447\pi$
$457$	3.35354e11	0.359650	0.179825	+	0.983699i	$0.442447\pi$
$458$	1.10100e12	1.16921
$459$	2.34418e11	0.246509
$460$	3.96224e10	0.0412601
$461$	1.04275e12	1.07529	0.537645	−	0.843171i	$-0.319314\pi$
$461$	1.04275e12	1.07529	0.537645	+	0.843171i	$0.319314\pi$
$462$	−1.56303e11	−0.159617
$463$	−9.74084e11	−0.985103	−0.492552	−	0.870283i	$-0.663936\pi$
$463$	−9.74084e11	−0.985103	−0.492552	+	0.870283i	$0.663936\pi$
$464$	2.59215e11	0.259614
$465$	−4.00473e11	−0.397223
$466$	−7.25176e11	−0.712372
$467$	−1.97851e11	−0.192492	−0.0962458	−	0.995358i	$-0.530683\pi$
$467$	−1.97851e11	−0.192492	−0.0962458	+	0.995358i	$0.530683\pi$
$468$	−6.96364e9	−0.00671011
$469$	7.09987e11	0.677599
$470$	1.90763e11	0.180324
$471$	9.54898e11	0.894052
$472$	3.80660e11	0.353019
$473$	3.38819e11	0.311238
$474$	−7.98697e11	−0.726741
$475$	1.72586e11	0.155555
$476$	−7.39563e10	−0.0660304
$477$	−3.78144e11	−0.334445
$478$	−1.74993e11	−0.153319
$479$	−9.08731e11	−0.788725	−0.394362	−	0.918955i	$-0.629035\pi$
$479$	−9.08731e11	−0.788725	−0.394362	+	0.918955i	$0.629035\pi$
$480$	3.28066e10	0.0282082
$481$	−7.95744e11	−0.677830
$482$	−1.65545e12	−1.39703
$483$	1.09817e12	0.918136
$484$	6.00147e10	0.0497112
$485$	6.33843e11	0.520169
$486$	−7.67093e10	−0.0623713
$487$	1.16963e12	0.942254	0.471127	−	0.882065i	$-0.343847\pi$
$487$	1.16963e12	0.942254	0.471127	+	0.882065i	$0.343847\pi$
$488$	−1.31469e12	−1.04938
$489$	−9.28324e11	−0.734192
$490$	6.18401e10	0.0484605
$491$	−2.49149e12	−1.93460	−0.967301	−	0.253630i	$-0.918375\pi$
$491$	−2.49149e12	−1.93460	−0.967301	+	0.253630i	$0.918375\pi$
$492$	3.01317e10	0.0231836
$493$	4.62866e11	0.352894
$494$	3.68448e11	0.278359
$495$	6.00660e10	0.0449681
$496$	1.95410e12	1.44970
$497$	−1.65676e12	−1.21802
$498$	−1.51651e12	−1.10488
$499$	−5.57571e11	−0.402576	−0.201288	−	0.979532i	$-0.564513\pi$
$499$	−5.57571e11	−0.402576	−0.201288	+	0.979532i	$0.564513\pi$
$500$	6.83594e9	0.00489140
$501$	1.08302e12	0.768012
$502$	−2.16619e12	−1.52240
$503$	1.80137e12	1.25472	0.627359	−	0.778730i	$-0.284136\pi$
$503$	1.80137e12	1.25472	0.627359	+	0.778730i	$0.284136\pi$
$504$	4.66733e11	0.322204
$505$	8.22105e11	0.562492
$506$	−7.29631e11	−0.494796
$507$	7.42578e11	0.499122
$508$	−6.72001e10	−0.0447696
$509$	−2.40110e12	−1.58555	−0.792774	−	0.609515i	$-0.791364\pi$
$509$	−2.40110e12	−1.58555	−0.792774	+	0.609515i	$0.791364\pi$
$510$	−4.91273e11	−0.321556
$511$	1.58097e12	1.02572
$512$	−1.66262e12	−1.06925
$513$	−2.34801e11	−0.149683
$514$	1.87528e11	0.118504
$515$	1.14248e12	0.715677
$516$	−5.24606e10	−0.0325769
$517$	2.03222e11	0.125102
$518$	2.76548e12	1.68766
$519$	−8.60735e11	−0.520735
$520$	2.81452e11	0.168807
$521$	1.03008e12	0.612491	0.306246	−	0.951953i	$-0.400927\pi$
$521$	1.03008e12	0.612491	0.306246	+	0.951953i	$0.400927\pi$
$522$	−1.51465e11	−0.0892886
$523$	1.06637e12	0.623232	0.311616	−	0.950208i	$-0.399130\pi$
$523$	1.06637e12	0.623232	0.311616	+	0.950208i	$0.399130\pi$
$524$	5.51151e10	0.0319359
$525$	1.89464e11	0.108845
$526$	1.29944e11	0.0740151
$527$	3.48934e12	1.97058
$528$	−2.93091e11	−0.164116
$529$	3.32516e12	1.84613
$530$	7.92484e11	0.436264
$531$	−2.10228e11	−0.114753
$532$	7.40773e10	0.0400943
$533$	5.03603e11	0.270281
$534$	−3.38393e11	−0.180088
$535$	−1.15855e11	−0.0611394
$536$	1.40859e12	0.737129
$537$	−2.11616e12	−1.09816
$538$	−1.57511e12	−0.810572
$539$	6.58788e10	0.0336199
$540$	−9.30022e9	−0.00470675
$541$	2.51749e12	1.26351	0.631756	−	0.775167i	$-0.282334\pi$
$541$	2.51749e12	1.26351	0.631756	+	0.775167i	$0.282334\pi$
$542$	−2.74460e12	−1.36610
$543$	−1.90098e11	−0.0938379
$544$	−2.85846e11	−0.139938
$545$	−1.23668e12	−0.600445
$546$	4.04480e11	0.194774
$547$	−1.10353e12	−0.527037	−0.263518	−	0.964654i	$-0.584883\pi$
$547$	−1.10353e12	−0.527037	−0.263518	+	0.964654i	$0.584883\pi$
$548$	5.68146e10	0.0269121
$549$	7.26067e11	0.341115
$550$	−1.25881e11	−0.0586582
$551$	−4.63624e11	−0.214281
$552$	2.17873e12	0.998799
$553$	−2.68384e12	−1.22037
$554$	2.48213e12	1.11952
$555$	−1.06275e12	−0.475458
$556$	3.18284e10	0.0141247
$557$	−1.09072e12	−0.480137	−0.240068	−	0.970756i	$-0.577170\pi$
$557$	−1.09072e12	−0.480137	−0.240068	+	0.970756i	$0.577170\pi$
$558$	−1.14183e12	−0.498593
$559$	−8.76795e11	−0.379791
$560$	−9.24487e11	−0.397242
$561$	−5.23357e11	−0.223083
$562$	1.91446e12	0.809529
$563$	1.03081e12	0.432403	0.216202	−	0.976349i	$-0.430633\pi$
$563$	1.03081e12	0.432403	0.216202	+	0.976349i	$0.430633\pi$
$564$	−3.14655e10	−0.0130942
$565$	−9.86717e11	−0.407356
$566$	7.20932e10	0.0295271
$567$	−2.57764e11	−0.104737
$568$	−3.28695e12	−1.32503
$569$	−4.06618e12	−1.62623	−0.813113	−	0.582106i	$-0.802229\pi$
$569$	−4.06618e12	−1.62623	−0.813113	+	0.582106i	$0.802229\pi$
$570$	4.92077e11	0.195252
$571$	9.86144e11	0.388220	0.194110	−	0.980980i	$-0.437818\pi$
$571$	9.86144e11	0.388220	0.194110	+	0.980980i	$0.437818\pi$
$572$	1.55469e10	0.00607243
$573$	−1.81492e12	−0.703334
$574$	−1.75019e12	−0.672947
$575$	8.84428e11	0.337409
$576$	9.23349e11	0.349514
$577$	−2.86947e12	−1.07773	−0.538866	−	0.842391i	$-0.681147\pi$
$577$	−2.86947e12	−1.07773	−0.538866	+	0.842391i	$0.681147\pi$
$578$	1.67155e12	0.622937
$579$	2.96427e12	1.09614
$580$	−1.83636e10	−0.00673802
$581$	−5.09588e12	−1.85535
$582$	1.80721e12	0.652914
$583$	8.44240e11	0.302662
$584$	3.13660e12	1.11584
$585$	−1.55438e11	−0.0548727
$586$	−3.29692e12	−1.15497
$587$	1.14169e12	0.396898	0.198449	−	0.980111i	$-0.436410\pi$
$587$	1.14169e12	0.396898	0.198449	+	0.980111i	$0.436410\pi$
$588$	−1.02002e10	−0.00351895
$589$	−3.49505e12	−1.19656
$590$	4.40579e11	0.149689
$591$	4.38652e11	0.147903
$592$	5.18567e12	1.73523
$593$	−2.97176e12	−0.986888	−0.493444	−	0.869777i	$-0.664262\pi$
$593$	−2.97176e12	−0.986888	−0.493444	+	0.869777i	$0.664262\pi$
$594$	1.71260e11	0.0564439
$595$	−1.65081e12	−0.539971
$596$	1.32679e11	0.0430719
$597$	−2.12798e10	−0.00685620
$598$	1.88814e12	0.603779
$599$	1.77262e12	0.562593	0.281297	−	0.959621i	$-0.409236\pi$
$599$	1.77262e12	0.562593	0.281297	+	0.959621i	$0.409236\pi$
$600$	3.75891e11	0.118408
$601$	1.25838e12	0.393439	0.196719	−	0.980460i	$-0.436971\pi$
$601$	1.25838e12	0.393439	0.196719	+	0.980460i	$0.436971\pi$
$602$	3.04715e12	0.945606
$603$	−7.77926e11	−0.239613
$604$	−6.33405e10	−0.0193649
$605$	1.33961e12	0.406519
$606$	2.34399e12	0.706038
$607$	1.74535e11	0.0521834	0.0260917	−	0.999660i	$-0.491694\pi$
$607$	1.74535e11	0.0521834	0.0260917	+	0.999660i	$0.491694\pi$
$608$	2.86313e11	0.0849720
$609$	−5.08964e11	−0.149937
$610$	−1.52163e12	−0.444964
$611$	−5.25896e11	−0.152656
$612$	8.10332e10	0.0233497
$613$	4.63037e12	1.32447	0.662237	−	0.749294i	$-0.269607\pi$
$613$	4.63037e12	1.32447	0.662237	+	0.749294i	$0.269607\pi$
$614$	−4.06054e12	−1.15299
$615$	6.72582e11	0.189586
$616$	−1.04202e12	−0.291584
$617$	2.50518e12	0.695914	0.347957	−	0.937511i	$-0.386876\pi$
$617$	2.50518e12	0.695914	0.347957	+	0.937511i	$0.386876\pi$
$618$	3.25745e12	0.898316
$619$	5.44228e11	0.148995	0.0744977	−	0.997221i	$-0.476265\pi$
$619$	5.44228e11	0.148995	0.0744977	+	0.997221i	$0.476265\pi$
$620$	−1.38435e11	−0.0376256
$621$	−1.20325e12	−0.324672
$622$	1.99023e12	0.533146
$623$	−1.13709e12	−0.302412
$624$	7.58459e11	0.200263
$625$	1.52588e11	0.0400000
$626$	2.37447e11	0.0617991
$627$	5.24214e11	0.135458
$628$	3.30088e11	0.0846860
$629$	9.25978e12	2.35870
$630$	5.40200e11	0.136622
$631$	−6.51975e12	−1.63719	−0.818594	−	0.574372i	$-0.805246\pi$
$631$	−6.51975e12	−1.63719	−0.818594	+	0.574372i	$0.805246\pi$
$632$	−5.32465e12	−1.32759
$633$	−1.08939e12	−0.269692
$634$	9.20303e11	0.226219
$635$	−1.50000e12	−0.366109
$636$	−1.30717e11	−0.0316792
$637$	−1.70481e11	−0.0410250
$638$	3.38159e11	0.0808032
$639$	1.81530e12	0.430718
$640$	−1.72771e12	−0.407062
$641$	−3.36297e12	−0.786794	−0.393397	−	0.919369i	$-0.628700\pi$
$641$	−3.36297e12	−0.786794	−0.393397	+	0.919369i	$0.628700\pi$
$642$	−3.30325e11	−0.0767420
$643$	1.18082e12	0.272417	0.136208	−	0.990680i	$-0.456508\pi$
$643$	1.18082e12	0.272417	0.136208	+	0.990680i	$0.456508\pi$
$644$	3.79614e11	0.0869673
$645$	−1.17099e12	−0.266401
$646$	−4.28749e12	−0.968628
$647$	6.63176e12	1.48785	0.743926	−	0.668262i	$-0.232962\pi$
$647$	6.63176e12	1.48785	0.743926	+	0.668262i	$0.232962\pi$
$648$	−5.11395e11	−0.113938
$649$	4.69353e11	0.103848
$650$	3.25755e11	0.0715782
$651$	−3.83685e12	−0.837259
$652$	−3.20902e11	−0.0695438
$653$	8.25189e11	0.177601	0.0888003	−	0.996049i	$-0.471697\pi$
$653$	8.25189e11	0.177601	0.0888003	+	0.996049i	$0.471697\pi$
$654$	−3.52602e12	−0.753677
$655$	1.23025e12	0.261160
$656$	−3.28185e12	−0.691913
$657$	−1.73226e12	−0.362717
$658$	1.82766e12	0.380084
$659$	−4.40214e11	−0.0909242	−0.0454621	−	0.998966i	$-0.514476\pi$
$659$	−4.40214e11	−0.0909242	−0.0454621	+	0.998966i	$0.514476\pi$
$660$	2.07635e10	0.00425945
$661$	9.77788e12	1.99222	0.996112	−	0.0880914i	$-0.0280767\pi$
$661$	9.77788e12	1.99222	0.996112	+	0.0880914i	$0.0280767\pi$
$662$	−2.71281e11	−0.0548983
$663$	1.35434e12	0.272218
$664$	−1.01101e13	−2.01836
$665$	1.65351e12	0.327876
$666$	−3.03011e12	−0.596793
$667$	−2.37587e12	−0.464790
$668$	3.74378e11	0.0727473
$669$	2.15835e12	0.416585
$670$	1.63031e12	0.312561
$671$	−1.62101e12	−0.308698
$672$	3.14314e11	0.0594568
$673$	4.22591e12	0.794058	0.397029	−	0.917806i	$-0.370041\pi$
$673$	4.22591e12	0.794058	0.397029	+	0.917806i	$0.370041\pi$
$674$	−4.79547e11	−0.0895079
$675$	−2.07594e11	−0.0384900
$676$	2.56694e11	0.0472776
$677$	−7.56977e12	−1.38495	−0.692474	−	0.721442i	$-0.743479\pi$
$677$	−7.56977e12	−1.38495	−0.692474	+	0.721442i	$0.743479\pi$
$678$	−2.81333e12	−0.511313
$679$	6.07273e12	1.09640
$680$	−3.27515e12	−0.587410
$681$	−2.72418e12	−0.485370
$682$	2.54923e12	0.451210
$683$	−1.92029e12	−0.337655	−0.168827	−	0.985646i	$-0.553998\pi$
$683$	−1.92029e12	−0.337655	−0.168827	+	0.985646i	$0.553998\pi$
$684$	−8.11659e10	−0.0141782
$685$	1.26818e12	0.220077
$686$	5.90850e12	1.01864
$687$	−4.05367e12	−0.694293
$688$	5.71385e12	0.972257
$689$	−2.18472e12	−0.369325
$690$	2.52168e12	0.423516
$691$	−3.99839e12	−0.667166	−0.333583	−	0.942721i	$-0.608258\pi$
$691$	−3.99839e12	−0.667166	−0.333583	+	0.942721i	$0.608258\pi$
$692$	−2.97538e11	−0.0493248
$693$	5.75480e11	0.0947830
$694$	−1.85595e12	−0.303702
$695$	7.10456e11	0.115506
$696$	−1.00977e12	−0.163110
$697$	−5.86023e12	−0.940519
$698$	−2.71249e10	−0.00432532
$699$	2.66997e12	0.423018
$700$	6.54938e10	0.0103100
$701$	1.12736e13	1.76332	0.881662	−	0.471881i	$-0.156425\pi$
$701$	1.12736e13	1.76332	0.881662	+	0.471881i	$0.156425\pi$
$702$	−4.43186e11	−0.0688761
$703$	−9.27493e12	−1.43223
$704$	−2.06146e12	−0.316299
$705$	−7.02355e11	−0.107079
$706$	3.81453e12	0.577856
$707$	7.87643e12	1.18561
$708$	−7.26715e10	−0.0108696
$709$	1.12679e13	1.67469	0.837346	−	0.546673i	$-0.184106\pi$
$709$	1.12679e13	1.67469	0.837346	+	0.546673i	$0.184106\pi$
$710$	−3.80435e12	−0.561846
$711$	2.94066e12	0.431550
$712$	−2.25595e12	−0.328980
$713$	−1.79106e13	−2.59542
$714$	−4.70679e12	−0.677770
$715$	3.47029e11	0.0496580
$716$	−7.31512e11	−0.104019
$717$	6.44292e11	0.0910429
$718$	1.40395e12	0.197148
$719$	−9.05247e12	−1.26324	−0.631622	−	0.775277i	$-0.717610\pi$
$719$	−9.05247e12	−1.26324	−0.631622	+	0.775277i	$0.717610\pi$
$720$	1.01295e12	0.140473
$721$	1.09459e13	1.50849
$722$	−2.80462e12	−0.384111
$723$	6.09507e12	0.829576
$724$	−6.57129e10	−0.00888847
$725$	−4.09902e11	−0.0551010
$726$	3.81951e12	0.510262
$727$	1.34408e12	0.178452	0.0892260	−	0.996011i	$-0.471561\pi$
$727$	1.34408e12	0.178452	0.0892260	+	0.996011i	$0.471561\pi$
$728$	2.69654e12	0.355807
$729$	2.82430e11	0.0370370
$730$	3.63032e12	0.473143
$731$	1.02029e13	1.32159
$732$	2.50986e11	0.0323109
$733$	6.57401e11	0.0841129	0.0420564	−	0.999115i	$-0.486609\pi$
$733$	6.57401e11	0.0841129	0.0420564	+	0.999115i	$0.486609\pi$
$734$	2.46932e12	0.314011
$735$	−2.27684e11	−0.0287766
$736$	1.46723e12	0.184310
$737$	1.73679e12	0.216842
$738$	1.91766e12	0.237968
$739$	2.15587e12	0.265903	0.132951	−	0.991123i	$-0.457555\pi$
$739$	2.15587e12	0.265903	0.132951	+	0.991123i	$0.457555\pi$
$740$	−3.67370e11	−0.0450361
$741$	−1.35656e12	−0.165294
$742$	7.59263e12	0.919548
$743$	−7.73594e12	−0.931244	−0.465622	−	0.884984i	$-0.654169\pi$
$743$	−7.73594e12	−0.931244	−0.465622	+	0.884984i	$0.654169\pi$
$744$	−7.61218e12	−0.910817
$745$	2.96159e12	0.352226
$746$	1.58621e13	1.87515
$747$	5.58351e12	0.656092
$748$	−1.80914e11	−0.0211307
$749$	−1.10998e12	−0.128869
$750$	4.35059e11	0.0502079
$751$	−1.12448e13	−1.28995	−0.644974	−	0.764205i	$-0.723132\pi$
$751$	−1.12448e13	−1.28995	−0.644974	+	0.764205i	$0.723132\pi$
$752$	3.42713e12	0.390797
$753$	7.97551e12	0.904027
$754$	−8.75087e11	−0.0986007
$755$	−1.41385e12	−0.158359
$756$	−8.91035e10	−0.00992080
$757$	−1.18544e13	−1.31205	−0.656024	−	0.754740i	$-0.727763\pi$
$757$	−1.18544e13	−1.31205	−0.656024	+	0.754740i	$0.727763\pi$
$758$	−4.49528e12	−0.494590
$759$	2.68637e12	0.293818
$760$	3.28051e12	0.356682
$761$	−2.24765e12	−0.242939	−0.121470	−	0.992595i	$-0.538761\pi$
$761$	−2.24765e12	−0.242939	−0.121470	+	0.992595i	$0.538761\pi$
$762$	−4.27681e12	−0.459539
$763$	−1.18484e13	−1.26561
$764$	−6.27380e11	−0.0666209
$765$	1.80878e12	0.190945
$766$	−1.20380e13	−1.26335
$767$	−1.21459e12	−0.126721
$768$	9.10436e11	0.0944331
$769$	−1.44505e13	−1.49010	−0.745049	−	0.667009i	$-0.767574\pi$
$769$	−1.44505e13	−1.49010	−0.745049	+	0.667009i	$0.767574\pi$
$770$	−1.20604e12	−0.123639
$771$	−6.90443e11	−0.0703693
$772$	1.02469e12	0.103828
$773$	5.19022e12	0.522852	0.261426	−	0.965224i	$-0.415807\pi$
$773$	5.19022e12	0.522852	0.261426	+	0.965224i	$0.415807\pi$
$774$	−3.33874e12	−0.334386
$775$	−3.09007e12	−0.307688
$776$	1.20481e13	1.19273
$777$	−1.01820e13	−1.00216
$778$	−7.61777e12	−0.745452
$779$	5.86983e12	0.571093
$780$	−5.37318e10	−0.00519763
$781$	−4.05280e12	−0.389786
$782$	−2.19715e13	−2.10102
$783$	5.57668e11	0.0530209
$784$	1.11098e12	0.105023
$785$	7.36804e12	0.692530
$786$	3.50768e12	0.327807
$787$	−1.39938e13	−1.30032	−0.650161	−	0.759797i	$-0.725299\pi$
$787$	−1.39938e13	−1.30032	−0.650161	+	0.759797i	$0.725299\pi$
$788$	1.51633e11	0.0140096
$789$	−4.78430e11	−0.0439513
$790$	−6.16279e12	−0.562931
$791$	−9.45354e12	−0.858618
$792$	1.14173e12	0.103110
$793$	4.19483e12	0.376691
$794$	5.64867e12	0.504375
$795$	−2.91778e12	−0.259060
$796$	−7.35599e9	−0.000649430 0
$797$	2.01269e13	1.76691	0.883454	−	0.468518i	$-0.155212\pi$
$797$	2.01269e13	1.76691	0.883454	+	0.468518i	$0.155212\pi$
$798$	4.71449e12	0.411549
$799$	6.11966e12	0.531210
$800$	2.53138e11	0.0218500
$801$	1.24590e12	0.106939
$802$	4.43695e11	0.0378704
$803$	3.86741e12	0.328247
$804$	−2.68913e11	−0.0226965
$805$	8.47353e12	0.711185
$806$	−6.59688e12	−0.550593
$807$	5.79928e12	0.481331
$808$	1.56266e13	1.28977
$809$	−8.95775e12	−0.735242	−0.367621	−	0.929976i	$-0.619828\pi$
$809$	−8.95775e12	−0.735242	−0.367621	+	0.929976i	$0.619828\pi$
$810$	−5.91892e11	−0.0483126
$811$	−1.76446e12	−0.143225	−0.0716123	−	0.997433i	$-0.522814\pi$
$811$	−1.76446e12	−0.143225	−0.0716123	+	0.997433i	$0.522814\pi$
$812$	−1.75938e11	−0.0142023
$813$	1.01051e13	0.811212
$814$	6.76498e12	0.540078
$815$	−7.16300e12	−0.568703
$816$	−8.82591e12	−0.696873
$817$	−1.02196e13	−0.802483
$818$	−9.53491e11	−0.0744607
$819$	−1.48922e12	−0.115660
$820$	2.32497e11	0.0179579
$821$	1.48082e13	1.13752	0.568758	−	0.822505i	$-0.307424\pi$
$821$	1.48082e13	1.13752	0.568758	+	0.822505i	$0.307424\pi$
$822$	3.61585e12	0.276240
$823$	−3.39651e12	−0.258067	−0.129034	−	0.991640i	$-0.541188\pi$
$823$	−3.39651e12	−0.258067	−0.129034	+	0.991640i	$0.541188\pi$
$824$	2.17163e13	1.64102
$825$	4.63472e11	0.0348322
$826$	4.22110e12	0.315512
$827$	1.88344e13	1.40016	0.700080	−	0.714065i	$-0.253148\pi$
$827$	1.88344e13	1.40016	0.700080	+	0.714065i	$0.253148\pi$
$828$	−4.15940e11	−0.0307535
$829$	1.18947e13	0.874695	0.437348	−	0.899292i	$-0.355918\pi$
$829$	1.18947e13	0.874695	0.437348	+	0.899292i	$0.355918\pi$
$830$	−1.17015e13	−0.855833
$831$	−9.13876e12	−0.664787
$832$	5.33462e12	0.385966
$833$	1.98382e12	0.142758
$834$	2.02565e12	0.144983
$835$	8.35666e12	0.594899
$836$	1.81210e11	0.0128308
$837$	4.20400e12	0.296073
$838$	1.12350e13	0.786998
$839$	−1.22881e13	−0.856165	−0.428083	−	0.903740i	$-0.640811\pi$
$839$	−1.22881e13	−0.856165	−0.428083	+	0.903740i	$0.640811\pi$
$840$	3.60133e12	0.249578
$841$	−1.34060e13	−0.924097
$842$	7.06702e12	0.484543
$843$	−7.04869e12	−0.480711
$844$	−3.76581e11	−0.0255457
$845$	5.72977e12	0.386618
$846$	−2.00256e12	−0.134406
$847$	1.28346e13	0.856853
$848$	1.42373e13	0.945465
$849$	−2.65434e11	−0.0175336
$850$	−3.79069e12	−0.249076
$851$	−4.75300e13	−3.10660
$852$	6.27510e11	0.0407983
$853$	−4.61355e12	−0.298376	−0.149188	−	0.988809i	$-0.547666\pi$
$853$	−4.61355e12	−0.298376	−0.149188	+	0.988809i	$0.547666\pi$
$854$	−1.45784e13	−0.937887
$855$	−1.81174e12	−0.115944
$856$	−2.20216e12	−0.140190
$857$	−4.29363e12	−0.271901	−0.135950	−	0.990716i	$-0.543409\pi$
$857$	−4.29363e12	−0.271901	−0.135950	+	0.990716i	$0.543409\pi$
$858$	9.89450e11	0.0623306
$859$	−6.40428e12	−0.401330	−0.200665	−	0.979660i	$-0.564310\pi$
$859$	−6.40428e12	−0.401330	−0.200665	+	0.979660i	$0.564310\pi$
$860$	−4.04788e11	−0.0252339
$861$	6.44387e12	0.399607
$862$	9.84758e12	0.607501
$863$	−3.24421e12	−0.199095	−0.0995474	−	0.995033i	$-0.531740\pi$
$863$	−3.24421e12	−0.199095	−0.0995474	+	0.995033i	$0.531740\pi$
$864$	−3.44391e11	−0.0210252
$865$	−6.64148e12	−0.403359
$866$	−3.10609e12	−0.187665
$867$	−6.15435e12	−0.369910
$868$	−1.32632e12	−0.0793065
$869$	−6.56527e12	−0.390539
$870$	−1.16871e12	−0.0691626
$871$	−4.49445e12	−0.264603
$872$	−2.35068e13	−1.37680
$873$	−6.65383e12	−0.387711
$874$	2.20075e13	1.27576
$875$	1.46191e12	0.0843113
$876$	−5.98805e11	−0.0343571
$877$	2.89711e13	1.65374	0.826871	−	0.562392i	$-0.190119\pi$
$877$	2.89711e13	1.65374	0.826871	+	0.562392i	$0.190119\pi$
$878$	−1.87109e13	−1.06260
$879$	1.21387e13	0.685838
$880$	−2.26150e12	−0.127123
$881$	7.50447e12	0.419690	0.209845	−	0.977735i	$-0.432704\pi$
$881$	7.50447e12	0.419690	0.209845	+	0.977735i	$0.432704\pi$
$882$	−6.49173e11	−0.0361203
$883$	2.87141e13	1.58954	0.794772	−	0.606908i	$-0.207590\pi$
$883$	2.87141e13	1.58954	0.794772	+	0.606908i	$0.207590\pi$
$884$	4.68167e11	0.0257849
$885$	−1.62213e12	−0.0888877
$886$	6.67013e12	0.363649
$887$	9.99825e12	0.542335	0.271168	−	0.962532i	$-0.412590\pi$
$887$	9.99825e12	0.542335	0.271168	+	0.962532i	$0.412590\pi$
$888$	−2.02007e13	−1.09021
$889$	−1.43712e13	−0.771678
$890$	−2.61106e12	−0.139496
$891$	−6.30548e11	−0.0335173
$892$	7.46095e11	0.0394596
$893$	−6.12967e12	−0.322556
$894$	8.44407e12	0.442113
$895$	−1.63284e13	−0.850628
$896$	−1.65528e13	−0.857998
$897$	−6.95177e12	−0.358533
$898$	−3.08721e13	−1.58425
$899$	8.30095e12	0.423847
$900$	−7.17609e10	−0.00364583
$901$	2.54228e13	1.28517
$902$	−4.28135e12	−0.215353
$903$	−1.12191e13	−0.561516
$904$	−1.87555e13	−0.934052
$905$	−1.46681e12	−0.0726865
$906$	−4.03117e12	−0.198772
$907$	4.70846e12	0.231018	0.115509	−	0.993306i	$-0.463150\pi$
$907$	4.70846e12	0.231018	0.115509	+	0.993306i	$0.463150\pi$
$908$	−9.41690e11	−0.0459750
$909$	−8.63013e12	−0.419257
$910$	3.12099e12	0.150871
$911$	2.69663e13	1.29714	0.648572	−	0.761154i	$-0.275367\pi$
$911$	2.69663e13	1.29714	0.648572	+	0.761154i	$0.275367\pi$
$912$	8.84035e12	0.423148
$913$	−1.24657e13	−0.593742
$914$	7.37778e12	0.349678
$915$	5.60237e12	0.264227
$916$	−1.40127e12	−0.0657645
$917$	1.17868e13	0.550468
$918$	5.15719e12	0.239674
$919$	−3.96618e12	−0.183422	−0.0917112	−	0.995786i	$-0.529234\pi$
$919$	−3.96618e12	−0.183422	−0.0917112	+	0.995786i	$0.529234\pi$
$920$	1.68112e13	0.773666
$921$	1.49502e13	0.684664
$922$	2.29405e13	1.04547
$923$	1.04878e13	0.475639
$924$	1.98931e11	0.00897799
$925$	−8.20022e12	−0.368288
$926$	−2.14298e13	−0.957788
$927$	−1.19933e13	−0.533434
$928$	−6.80012e11	−0.0300989
$929$	1.96912e13	0.867365	0.433683	−	0.901066i	$-0.357214\pi$
$929$	1.96912e13	0.867365	0.433683	+	0.901066i	$0.357214\pi$
$930$	−8.81040e12	−0.386209
$931$	−1.98707e12	−0.0866841
$932$	9.22952e11	0.0400689
$933$	−7.32766e12	−0.316591
$934$	−4.35271e12	−0.187154
$935$	−4.03825e12	−0.172799
$936$	−2.95457e12	−0.125821
$937$	−2.11305e13	−0.895532	−0.447766	−	0.894151i	$-0.647780\pi$
$937$	−2.11305e13	−0.895532	−0.447766	+	0.894151i	$0.647780\pi$
$938$	1.56197e13	0.658810
$939$	−8.74236e11	−0.0366973
$940$	−2.42790e11	−0.0101427
$941$	5.41072e12	0.224958	0.112479	−	0.993654i	$-0.464121\pi$
$941$	5.41072e12	0.224958	0.112479	+	0.993654i	$0.464121\pi$
$942$	2.10077e13	0.869261
$943$	3.00803e13	1.23874
$944$	7.91517e12	0.324404
$945$	−1.98892e12	−0.0811286
$946$	7.45403e12	0.302608
$947$	3.44259e12	0.139095	0.0695473	−	0.997579i	$-0.477845\pi$
$947$	3.44259e12	0.139095	0.0695473	+	0.997579i	$0.477845\pi$
$948$	1.01652e12	0.0408771
$949$	−1.00081e13	−0.400546
$950$	3.79689e12	0.151242
$951$	−3.38839e12	−0.134332
$952$	−3.13786e13	−1.23813
$953$	−4.18440e12	−0.164329	−0.0821647	−	0.996619i	$-0.526183\pi$
$953$	−4.18440e12	−0.164329	−0.0821647	+	0.996619i	$0.526183\pi$
$954$	−8.31918e12	−0.325172
$955$	−1.40040e13	−0.544800
$956$	2.22718e11	0.00862373
$957$	−1.24504e12	−0.0479822
$958$	−1.99921e13	−0.766855
$959$	1.21502e13	0.463874
$960$	7.12461e12	0.270733
$961$	3.61375e13	1.36679
$962$	−1.75064e13	−0.659035
$963$	1.21620e12	0.0455706
$964$	2.10694e12	0.0785787
$965$	2.28725e13	0.849063
$966$	2.41597e13	0.892678
$967$	1.49800e13	0.550926	0.275463	−	0.961312i	$-0.411169\pi$
$967$	1.49800e13	0.550926	0.275463	+	0.961312i	$0.411169\pi$
$968$	2.54634e13	0.932132
$969$	1.57858e13	0.575186
$970$	1.39446e13	0.505745
$971$	−2.82460e13	−1.01970	−0.509848	−	0.860264i	$-0.670299\pi$
$971$	−2.82460e13	−1.01970	−0.509848	+	0.860264i	$0.670299\pi$
$972$	9.76300e10	0.00350820
$973$	6.80673e12	0.243462
$974$	2.57318e13	0.916127
$975$	−1.19937e12	−0.0425042
$976$	−2.73367e13	−0.964321
$977$	−4.62242e13	−1.62309	−0.811547	−	0.584287i	$-0.801374\pi$
$977$	−4.62242e13	−1.62309	−0.811547	+	0.584287i	$0.801374\pi$
$978$	−2.04231e13	−0.713835
$979$	−2.78158e12	−0.0967764
$980$	−7.87056e10	−0.00272576
$981$	1.29822e13	0.447545
$982$	−5.48127e13	−1.88096
$983$	4.80363e13	1.64089	0.820443	−	0.571728i	$-0.193727\pi$
$983$	4.80363e13	1.64089	0.820443	+	0.571728i	$0.193727\pi$
$984$	1.27844e13	0.434714
$985$	3.38466e12	0.114565
$986$	1.01831e13	0.343109
$987$	−6.72913e12	−0.225700
$988$	−4.68934e11	−0.0156569
$989$	−5.23712e13	−1.74064
$990$	1.32145e12	0.0437213
$991$	2.31211e13	0.761512	0.380756	−	0.924675i	$-0.375664\pi$
$991$	2.31211e13	0.761512	0.380756	+	0.924675i	$0.375664\pi$
$992$	−5.12630e12	−0.168074
$993$	9.98809e11	0.0325995
$994$	−3.64487e13	−1.18425
$995$	−1.64196e11	−0.00531079
$996$	1.93010e12	0.0621461
$997$	−1.35362e13	−0.433878	−0.216939	−	0.976185i	$-0.569607\pi$
$997$	−1.35362e13	−0.433878	−0.216939	+	0.976185i	$0.569607\pi$
$998$	−1.22666e13	−0.391413
$999$	1.11563e13	0.354385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.10.a.b.1.1	✓	1
3.2	odd	2		45.10.a.a.1.1		1
4.3	odd	2		240.10.a.g.1.1		1
5.2	odd	4		75.10.b.b.49.2		2
5.3	odd	4		75.10.b.b.49.1		2
5.4	even	2		75.10.a.a.1.1		1
15.2	even	4		225.10.b.b.199.1		2
15.8	even	4		225.10.b.b.199.2		2
15.14	odd	2		225.10.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.b.1.1	✓	1	1.1	even	1	trivial
45.10.a.a.1.1		1	3.2	odd	2
75.10.a.a.1.1		1	5.4	even	2
75.10.b.b.49.1		2	5.3	odd	4
75.10.b.b.49.2		2	5.2	odd	4
225.10.a.f.1.1		1	15.14	odd	2
225.10.b.b.199.1		2	15.2	even	4
225.10.b.b.199.2		2	15.8	even	4
240.10.a.g.1.1		1	4.3	odd	2

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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