LMFDB - Embedded newform 30.16.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,16,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, 16, names="a")

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

chi := DirichletCharacter("30.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
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:	$42.8080515300$
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)

$f(q)$

$=$

\(q+128.000 q^{2} +2187.00 q^{3} +16384.0 q^{4} +78125.0 q^{5} +279936. q^{6} -3.06746e6 q^{7} +2.09715e6 q^{8} +4.78297e6 q^{9} +1.00000e7 q^{10} -4.13607e7 q^{11} +3.58318e7 q^{12} -3.95659e8 q^{13} -3.92634e8 q^{14} +1.70859e8 q^{15} +2.68435e8 q^{16} -1.61057e9 q^{17} +6.12220e8 q^{18} +2.28502e9 q^{19} +1.28000e9 q^{20} -6.70853e9 q^{21} -5.29418e9 q^{22} -1.13005e10 q^{23} +4.58647e9 q^{24} +6.10352e9 q^{25} -5.06443e10 q^{26} +1.04604e10 q^{27} -5.02572e10 q^{28} -7.39546e10 q^{29} +2.18700e10 q^{30} +2.68626e11 q^{31} +3.43597e10 q^{32} -9.04560e10 q^{33} -2.06153e11 q^{34} -2.39645e11 q^{35} +7.83642e10 q^{36} -1.01233e12 q^{37} +2.92483e11 q^{38} -8.65305e11 q^{39} +1.63840e11 q^{40} +2.15804e12 q^{41} -8.58691e11 q^{42} -3.74268e11 q^{43} -6.77654e11 q^{44} +3.73669e11 q^{45} -1.44647e12 q^{46} -3.23165e12 q^{47} +5.87068e11 q^{48} +4.66172e12 q^{49} +7.81250e11 q^{50} -3.52232e12 q^{51} -6.48247e12 q^{52} -7.59435e12 q^{53} +1.33893e12 q^{54} -3.23131e12 q^{55} -6.43292e12 q^{56} +4.99734e12 q^{57} -9.46619e12 q^{58} -2.72206e13 q^{59} +2.79936e12 q^{60} +5.26942e12 q^{61} +3.43842e13 q^{62} -1.46715e13 q^{63} +4.39805e12 q^{64} -3.09108e13 q^{65} -1.15784e13 q^{66} -6.82764e13 q^{67} -2.63876e13 q^{68} -2.47143e13 q^{69} -3.06746e13 q^{70} -8.17197e13 q^{71} +1.00306e13 q^{72} +4.95616e13 q^{73} -1.29579e14 q^{74} +1.33484e13 q^{75} +3.74378e13 q^{76} +1.26872e14 q^{77} -1.10759e14 q^{78} +1.93169e14 q^{79} +2.09715e13 q^{80} +2.28768e13 q^{81} +2.76229e14 q^{82} +1.87748e14 q^{83} -1.09912e14 q^{84} -1.25826e14 q^{85} -4.79063e13 q^{86} -1.61739e14 q^{87} -8.67398e13 q^{88} +3.64870e14 q^{89} +4.78297e13 q^{90} +1.21367e15 q^{91} -1.85148e14 q^{92} +5.87486e14 q^{93} -4.13652e14 q^{94} +1.78517e14 q^{95} +7.51447e13 q^{96} +8.98382e14 q^{97} +5.96701e14 q^{98} -1.97827e14 q^{99} +O(q^{100})\)

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 $

$2$	128.000	0.707107
$2$	128.000	0.707107
$3$	2187.00	0.577350
$3$	2187.00	0.577350
$4$	16384.0	0.500000
$5$	78125.0	0.447214
$5$	78125.0	0.447214
$6$	279936.	0.408248
$7$	−3.06746e6	−1.40781	−0.703903	−	0.710296i	$-0.748561\pi$
$7$	−3.06746e6	−1.40781	−0.703903	+	0.710296i	$0.748561\pi$
$8$	2.09715e6	0.353553
$9$	4.78297e6	0.333333
$10$	1.00000e7	0.316228
$11$	−4.13607e7	−0.639946	−0.319973	−	0.947427i	$-0.603674\pi$
$11$	−4.13607e7	−0.639946	−0.319973	+	0.947427i	$0.603674\pi$
$12$	3.58318e7	0.288675
$13$	−3.95659e8	−1.74882	−0.874411	−	0.485187i	$-0.838752\pi$
$13$	−3.95659e8	−1.74882	−0.874411	+	0.485187i	$0.838752\pi$
$14$	−3.92634e8	−0.995470
$15$	1.70859e8	0.258199
$16$	2.68435e8	0.250000
$17$	−1.61057e9	−0.951947	−0.475974	−	0.879460i	$-0.657904\pi$
$17$	−1.61057e9	−0.951947	−0.475974	+	0.879460i	$0.657904\pi$
$18$	6.12220e8	0.235702
$19$	2.28502e9	0.586460	0.293230	−	0.956042i	$-0.405270\pi$
$19$	2.28502e9	0.586460	0.293230	+	0.956042i	$0.405270\pi$
$20$	1.28000e9	0.223607
$21$	−6.70853e9	−0.812798
$22$	−5.29418e9	−0.452510
$23$	−1.13005e10	−0.692054	−0.346027	−	0.938225i	$-0.612469\pi$
$23$	−1.13005e10	−0.692054	−0.346027	+	0.938225i	$0.612469\pi$
$24$	4.58647e9	0.204124
$25$	6.10352e9	0.200000
$26$	−5.06443e10	−1.23660
$27$	1.04604e10	0.192450
$28$	−5.02572e10	−0.703903
$29$	−7.39546e10	−0.796123	−0.398062	−	0.917359i	$-0.630317\pi$
$29$	−7.39546e10	−0.796123	−0.398062	+	0.917359i	$0.630317\pi$
$30$	2.18700e10	0.182574
$31$	2.68626e11	1.75362	0.876811	−	0.480835i	$-0.159666\pi$
$31$	2.68626e11	1.75362	0.876811	+	0.480835i	$0.159666\pi$
$32$	3.43597e10	0.176777
$33$	−9.04560e10	−0.369473
$34$	−2.06153e11	−0.673128
$35$	−2.39645e11	−0.629590
$36$	7.83642e10	0.166667
$37$	−1.01233e12	−1.75311	−0.876557	−	0.481297i	$-0.840166\pi$
$37$	−1.01233e12	−1.75311	−0.876557	+	0.481297i	$0.840166\pi$
$38$	2.92483e11	0.414690
$39$	−8.65305e11	−1.00968
$40$	1.63840e11	0.158114
$41$	2.15804e12	1.73053	0.865266	−	0.501312i	$-0.167149\pi$
$41$	2.15804e12	1.73053	0.865266	+	0.501312i	$0.167149\pi$
$42$	−8.58691e11	−0.574735
$43$	−3.74268e11	−0.209976	−0.104988	−	0.994474i	$-0.533480\pi$
$43$	−3.74268e11	−0.209976	−0.104988	+	0.994474i	$0.533480\pi$
$44$	−6.77654e11	−0.319973
$45$	3.73669e11	0.149071
$46$	−1.44647e12	−0.489356
$47$	−3.23165e12	−0.930445	−0.465223	−	0.885194i	$-0.654026\pi$
$47$	−3.23165e12	−0.930445	−0.465223	+	0.885194i	$0.654026\pi$
$48$	5.87068e11	0.144338
$49$	4.66172e12	0.981920
$50$	7.81250e11	0.141421
$51$	−3.52232e12	−0.549607
$52$	−6.48247e12	−0.874411
$53$	−7.59435e12	−0.888017	−0.444009	−	0.896022i	$-0.646444\pi$
$53$	−7.59435e12	−0.888017	−0.444009	+	0.896022i	$0.646444\pi$
$54$	1.33893e12	0.136083
$55$	−3.23131e12	−0.286192
$56$	−6.43292e12	−0.497735
$57$	4.99734e12	0.338593
$58$	−9.46619e12	−0.562944
$59$	−2.72206e13	−1.42399	−0.711996	−	0.702184i	$-0.752209\pi$
$59$	−2.72206e13	−1.42399	−0.711996	+	0.702184i	$0.752209\pi$
$60$	2.79936e12	0.129099
$61$	5.26942e12	0.214679	0.107339	−	0.994222i	$-0.465767\pi$
$61$	5.26942e12	0.214679	0.107339	+	0.994222i	$0.465767\pi$
$62$	3.43842e13	1.24000
$63$	−1.46715e13	−0.469269
$64$	4.39805e12	0.125000
$65$	−3.09108e13	−0.782097
$66$	−1.15784e13	−0.261257
$67$	−6.82764e13	−1.37629	−0.688144	−	0.725574i	$-0.741574\pi$
$67$	−6.82764e13	−1.37629	−0.688144	+	0.725574i	$0.741574\pi$
$68$	−2.63876e13	−0.475974
$69$	−2.47143e13	−0.399558
$70$	−3.06746e13	−0.445188
$71$	−8.17197e13	−1.06632	−0.533162	−	0.846013i	$-0.678996\pi$
$71$	−8.17197e13	−1.06632	−0.533162	+	0.846013i	$0.678996\pi$
$72$	1.00306e13	0.117851
$73$	4.95616e13	0.525078	0.262539	−	0.964921i	$-0.415440\pi$
$73$	4.95616e13	0.525078	0.262539	+	0.964921i	$0.415440\pi$
$74$	−1.29579e14	−1.23964
$75$	1.33484e13	0.115470
$76$	3.74378e13	0.293230
$77$	1.26872e14	0.900920
$78$	−1.10759e14	−0.713953
$79$	1.93169e14	1.13171	0.565853	−	0.824506i	$-0.308547\pi$
$79$	1.93169e14	1.13171	0.565853	+	0.824506i	$0.308547\pi$
$80$	2.09715e13	0.111803
$81$	2.28768e13	0.111111
$82$	2.76229e14	1.22367
$83$	1.87748e14	0.759434	0.379717	−	0.925103i	$-0.376021\pi$
$83$	1.87748e14	0.759434	0.379717	+	0.925103i	$0.376021\pi$
$84$	−1.09912e14	−0.406399
$85$	−1.25826e14	−0.425724
$86$	−4.79063e13	−0.148475
$87$	−1.61739e14	−0.459642
$88$	−8.67398e13	−0.226255
$89$	3.64870e14	0.874406	0.437203	−	0.899363i	$-0.355969\pi$
$89$	3.64870e14	0.874406	0.437203	+	0.899363i	$0.355969\pi$
$90$	4.78297e13	0.105409
$91$	1.21367e15	2.46200
$92$	−1.85148e14	−0.346027
$93$	5.87486e14	1.01245
$94$	−4.13652e14	−0.657924
$95$	1.78517e14	0.262273
$96$	7.51447e13	0.102062
$97$	8.98382e14	1.12895	0.564473	−	0.825452i	$-0.309080\pi$
$97$	8.98382e14	1.12895	0.564473	+	0.825452i	$0.309080\pi$
$98$	5.96701e14	0.694322
$99$	−1.97827e14	−0.213315
$100$	1.00000e14	0.100000
$101$	2.83904e14	0.263488	0.131744	−	0.991284i	$-0.457942\pi$
$101$	2.83904e14	0.263488	0.131744	+	0.991284i	$0.457942\pi$
$102$	−4.50857e14	−0.388631
$103$	2.98486e14	0.239136	0.119568	−	0.992826i	$-0.461849\pi$
$103$	2.98486e14	0.239136	0.119568	+	0.992826i	$0.461849\pi$
$104$	−8.29756e14	−0.618302
$105$	−5.24104e14	−0.363494
$106$	−9.72077e14	−0.627923
$107$	9.17434e14	0.552328	0.276164	−	0.961111i	$-0.410937\pi$
$107$	9.17434e14	0.552328	0.276164	+	0.961111i	$0.410937\pi$
$108$	1.71382e14	0.0962250
$109$	−8.23884e14	−0.431685	−0.215843	−	0.976428i	$-0.569250\pi$
$109$	−8.23884e14	−0.431685	−0.215843	+	0.976428i	$0.569250\pi$
$110$	−4.13607e14	−0.202369
$111$	−2.21397e15	−1.01216
$112$	−8.23414e14	−0.351952
$113$	2.16477e15	0.865613	0.432807	−	0.901487i	$-0.357523\pi$
$113$	2.16477e15	0.865613	0.432807	+	0.901487i	$0.357523\pi$
$114$	6.39660e14	0.239421
$115$	−8.82854e14	−0.309496
$116$	−1.21167e15	−0.398062
$117$	−1.89242e15	−0.582940
$118$	−3.48424e15	−1.00691
$119$	4.94036e15	1.34016
$120$	3.58318e14	0.0912871
$121$	−2.46654e15	−0.590469
$122$	6.74485e14	0.151801
$123$	4.71963e15	0.999124
$124$	4.40118e15	0.876811
$125$	4.76837e14	0.0894427
$126$	−1.87796e15	−0.331823
$127$	8.80670e15	1.46651	0.733256	−	0.679953i	$-0.238000\pi$
$127$	8.80670e15	1.46651	0.733256	+	0.679953i	$0.238000\pi$
$128$	5.62950e14	0.0883883
$129$	−8.18524e14	−0.121230
$130$	−3.95659e15	−0.553026
$131$	−9.36793e15	−1.23626	−0.618129	−	0.786077i	$-0.712109\pi$
$131$	−9.36793e15	−1.23626	−0.618129	+	0.786077i	$0.712109\pi$
$132$	−1.48203e15	−0.184736
$133$	−7.00920e15	−0.825622
$134$	−8.73938e15	−0.973183
$135$	8.17215e14	0.0860663
$136$	−3.37761e15	−0.336564
$137$	5.82827e15	0.549713	0.274856	−	0.961485i	$-0.411370\pi$
$137$	5.82827e15	0.549713	0.274856	+	0.961485i	$0.411370\pi$
$138$	−3.16343e15	−0.282530
$139$	−1.09694e16	−0.928052	−0.464026	−	0.885822i	$-0.653596\pi$
$139$	−1.09694e16	−0.928052	−0.464026	+	0.885822i	$0.653596\pi$
$140$	−3.92634e15	−0.314795
$141$	−7.06763e15	−0.537193
$142$	−1.04601e16	−0.754005
$143$	1.63647e16	1.11915
$144$	1.28392e15	0.0833333
$145$	−5.77771e15	−0.356037
$146$	6.34388e15	0.371286
$147$	1.01952e16	0.566912
$148$	−1.65861e16	−0.876557
$149$	1.33354e16	0.670053	0.335026	−	0.942209i	$-0.391255\pi$
$149$	1.33354e16	0.670053	0.335026	+	0.942209i	$0.391255\pi$
$150$	1.70859e15	0.0816497
$151$	−1.85052e16	−0.841330	−0.420665	−	0.907216i	$-0.638203\pi$
$151$	−1.85052e16	−0.841330	−0.420665	+	0.907216i	$0.638203\pi$
$152$	4.79204e15	0.207345
$153$	−7.70331e15	−0.317316
$154$	1.62397e16	0.637047
$155$	2.09864e16	0.784244
$156$	−1.41772e16	−0.504841
$157$	−3.14502e16	−1.06752	−0.533760	−	0.845636i	$-0.679221\pi$
$157$	−3.14502e16	−1.06752	−0.533760	+	0.845636i	$0.679221\pi$
$158$	2.47256e16	0.800237
$159$	−1.66088e16	−0.512697
$160$	2.68435e15	0.0790569
$161$	3.46639e16	0.974279
$162$	2.92823e15	0.0785674
$163$	−5.92873e16	−1.51899	−0.759495	−	0.650513i	$-0.774554\pi$
$163$	−5.92873e16	−1.51899	−0.759495	+	0.650513i	$0.774554\pi$
$164$	3.53573e16	0.865266
$165$	−7.06687e15	−0.165233
$166$	2.40318e16	0.537001
$167$	3.64336e16	0.778268	0.389134	−	0.921181i	$-0.372774\pi$
$167$	3.64336e16	0.778268	0.389134	+	0.921181i	$0.372774\pi$
$168$	−1.40688e16	−0.287367
$169$	1.05360e17	2.05838
$170$	−1.61057e16	−0.301032
$171$	1.09292e16	0.195487
$172$	−6.13200e15	−0.104988
$173$	1.70672e16	0.279780	0.139890	−	0.990167i	$-0.455325\pi$
$173$	1.70672e16	0.279780	0.139890	+	0.990167i	$0.455325\pi$
$174$	−2.07026e16	−0.325016
$175$	−1.87223e16	−0.281561
$176$	−1.11027e16	−0.159986
$177$	−5.95314e16	−0.822142
$178$	4.67034e16	0.618299
$179$	1.32549e17	1.68260	0.841299	−	0.540570i	$-0.181792\pi$
$179$	1.32549e17	1.68260	0.841299	+	0.540570i	$0.181792\pi$
$180$	6.12220e15	0.0745356
$181$	−1.22459e17	−1.43022	−0.715109	−	0.699013i	$-0.753623\pi$
$181$	−1.22459e17	−1.43022	−0.715109	+	0.699013i	$0.753623\pi$
$182$	1.55349e17	1.74090
$183$	1.15242e16	0.123945
$184$	−2.36989e16	−0.244678
$185$	−7.90885e16	−0.784017
$186$	7.51982e16	0.715913
$187$	6.66144e16	0.609195
$188$	−5.29474e16	−0.465223
$189$	−3.20867e16	−0.270933
$190$	2.28502e16	0.185455
$191$	2.00681e16	0.156587	0.0782934	−	0.996930i	$-0.475053\pi$
$191$	2.00681e16	0.156587	0.0782934	+	0.996930i	$0.475053\pi$
$192$	9.61853e15	0.0721688
$193$	2.39484e17	1.72821	0.864106	−	0.503311i	$-0.167885\pi$
$193$	2.39484e17	1.72821	0.864106	+	0.503311i	$0.167885\pi$
$194$	1.14993e17	0.798285
$195$	−6.76020e16	−0.451544
$196$	7.63777e16	0.490960
$197$	−2.86905e17	−1.77518	−0.887588	−	0.460637i	$-0.847621\pi$
$197$	−2.86905e17	−1.77518	−0.887588	+	0.460637i	$0.847621\pi$
$198$	−2.53219e16	−0.150837
$199$	−2.14194e17	−1.22860	−0.614299	−	0.789073i	$-0.710561\pi$
$199$	−2.14194e17	−1.22860	−0.614299	+	0.789073i	$0.710561\pi$
$200$	1.28000e16	0.0707107
$201$	−1.49320e17	−0.794601
$202$	3.63397e16	0.186314
$203$	2.26853e17	1.12079
$204$	−5.77097e16	−0.274804
$205$	1.68597e17	0.773918
$206$	3.82063e16	0.169095
$207$	−5.40501e16	−0.230685
$208$	−1.06209e17	−0.437205
$209$	−9.45102e16	−0.375303
$210$	−6.70853e16	−0.257029
$211$	−3.49385e17	−1.29177	−0.645887	−	0.763433i	$-0.723512\pi$
$211$	−3.49385e17	−1.29177	−0.645887	+	0.763433i	$0.723512\pi$
$212$	−1.24426e17	−0.444009
$213$	−1.78721e17	−0.615642
$214$	1.17432e17	0.390555
$215$	−2.92397e16	−0.0939040
$216$	2.19370e16	0.0680414
$217$	−8.24000e17	−2.46876
$218$	−1.05457e17	−0.305248
$219$	1.08391e17	0.303154
$220$	−5.29418e16	−0.143096
$221$	6.37236e17	1.66479
$222$	−2.83388e17	−0.715706
$223$	−3.01392e17	−0.735945	−0.367973	−	0.929837i	$-0.619948\pi$
$223$	−3.01392e17	−0.735945	−0.367973	+	0.929837i	$0.619948\pi$
$224$	−1.05397e17	−0.248867
$225$	2.91929e16	0.0666667
$226$	2.77091e17	0.612081
$227$	−4.80145e17	−1.02607	−0.513036	−	0.858367i	$-0.671479\pi$
$227$	−4.80145e17	−1.02607	−0.513036	+	0.858367i	$0.671479\pi$
$228$	8.18765e16	0.169296
$229$	4.14103e17	0.828595	0.414298	−	0.910141i	$-0.364027\pi$
$229$	4.14103e17	0.828595	0.414298	+	0.910141i	$0.364027\pi$
$230$	−1.13005e17	−0.218847
$231$	2.77470e17	0.520146
$232$	−1.55094e17	−0.281472
$233$	5.46836e17	0.960922	0.480461	−	0.877016i	$-0.340469\pi$
$233$	5.46836e17	0.960922	0.480461	+	0.877016i	$0.340469\pi$
$234$	−2.42230e17	−0.412201
$235$	−2.52473e17	−0.416108
$236$	−4.45982e17	−0.711996
$237$	4.22460e17	0.653391
$238$	6.32365e17	0.947635
$239$	−1.14592e18	−1.66406	−0.832029	−	0.554733i	$-0.812821\pi$
$239$	−1.14592e18	−1.66406	−0.832029	+	0.554733i	$0.812821\pi$
$240$	4.58647e16	0.0645497
$241$	2.61779e17	0.357114	0.178557	−	0.983930i	$-0.442857\pi$
$241$	2.61779e17	0.357114	0.178557	+	0.983930i	$0.442857\pi$
$242$	−3.15717e17	−0.417525
$243$	5.00315e16	0.0641500
$244$	8.63341e16	0.107339
$245$	3.64197e17	0.439128
$246$	6.04112e17	0.706487
$247$	−9.04088e17	−1.02561
$248$	5.63351e17	0.619999
$249$	4.10605e17	0.438460
$250$	6.10352e16	0.0632456
$251$	1.24850e18	1.25555	0.627775	−	0.778395i	$-0.283966\pi$
$251$	1.24850e18	1.25555	0.627775	+	0.778395i	$0.283966\pi$
$252$	−2.40379e17	−0.234634
$253$	4.67398e17	0.442877
$254$	1.12726e18	1.03698
$255$	−2.75181e17	−0.245792
$256$	7.20576e16	0.0625000
$257$	−2.39248e17	−0.201534	−0.100767	−	0.994910i	$-0.532130\pi$
$257$	−2.39248e17	−0.201534	−0.100767	+	0.994910i	$0.532130\pi$
$258$	−1.04771e17	−0.0857222
$259$	3.10529e18	2.46805
$260$	−5.06443e17	−0.391048
$261$	−3.53723e17	−0.265374
$262$	−1.19909e18	−0.874166
$263$	−6.78661e16	−0.0480823	−0.0240411	−	0.999711i	$-0.507653\pi$
$263$	−6.78661e16	−0.0480823	−0.0240411	+	0.999711i	$0.507653\pi$
$264$	−1.89700e17	−0.130628
$265$	−5.93308e17	−0.397133
$266$	−8.97178e17	−0.583803
$267$	7.97971e17	0.504839
$268$	−1.11864e18	−0.688144
$269$	2.43188e18	1.45479	0.727395	−	0.686219i	$-0.240731\pi$
$269$	2.43188e18	1.45479	0.727395	+	0.686219i	$0.240731\pi$
$270$	1.04604e17	0.0608581
$271$	1.76910e18	1.00111	0.500557	−	0.865703i	$-0.333128\pi$
$271$	1.76910e18	1.00111	0.500557	+	0.865703i	$0.333128\pi$
$272$	−4.32334e17	−0.237987
$273$	2.65429e18	1.42144
$274$	7.46019e17	0.388706
$275$	−2.52446e17	−0.127989
$276$	−4.04919e17	−0.199779
$277$	1.19686e16	0.00574707	0.00287353	−	0.999996i	$-0.499085\pi$
$277$	1.19686e16	0.00574707	0.00287353	+	0.999996i	$0.499085\pi$
$278$	−1.40408e18	−0.656232
$279$	1.28483e18	0.584541
$280$	−5.02572e17	−0.222594
$281$	−2.30835e18	−0.995414	−0.497707	−	0.867345i	$-0.665824\pi$
$281$	−2.30835e18	−0.995414	−0.497707	+	0.867345i	$0.665824\pi$
$282$	−9.04656e17	−0.379853
$283$	−2.12642e18	−0.869460	−0.434730	−	0.900561i	$-0.643156\pi$
$283$	−2.12642e18	−0.869460	−0.434730	+	0.900561i	$0.643156\pi$
$284$	−1.33890e18	−0.533162
$285$	3.90417e17	0.151423
$286$	2.09469e18	0.791359
$287$	−6.61968e18	−2.43626
$288$	1.64342e17	0.0589256
$289$	−2.68484e17	−0.0937962
$290$	−7.39546e17	−0.251756
$291$	1.96476e18	0.651797
$292$	8.12017e17	0.262539
$293$	1.60780e18	0.506669	0.253335	−	0.967379i	$-0.418473\pi$
$293$	1.60780e18	0.506669	0.253335	+	0.967379i	$0.418473\pi$
$294$	1.30498e18	0.400867
$295$	−2.12661e18	−0.636829
$296$	−2.12302e18	−0.619820
$297$	−4.32648e17	−0.123158
$298$	1.70693e18	0.473799
$299$	4.47115e18	1.21028
$300$	2.18700e17	0.0577350
$301$	1.14805e18	0.295605
$302$	−2.36866e18	−0.594910
$303$	6.20897e17	0.152125
$304$	6.13381e17	0.146615
$305$	4.11673e17	0.0960072
$306$	−9.86024e17	−0.224376
$307$	−1.90872e18	−0.423842	−0.211921	−	0.977287i	$-0.567972\pi$
$307$	−1.90872e18	−0.423842	−0.211921	+	0.977287i	$0.567972\pi$
$308$	2.07868e18	0.450460
$309$	6.52790e17	0.138065
$310$	2.68626e18	0.554544
$311$	−2.59682e18	−0.523286	−0.261643	−	0.965165i	$-0.584264\pi$
$311$	−2.59682e18	−0.523286	−0.261643	+	0.965165i	$0.584264\pi$
$312$	−1.81468e18	−0.356977
$313$	−2.45229e18	−0.470965	−0.235483	−	0.971879i	$-0.575667\pi$
$313$	−2.45229e18	−0.470965	−0.235483	+	0.971879i	$0.575667\pi$
$314$	−4.02563e18	−0.754851
$315$	−1.14621e18	−0.209863
$316$	3.16488e18	0.565853
$317$	−7.19181e18	−1.25572	−0.627861	−	0.778325i	$-0.716070\pi$
$317$	−7.19181e18	−1.25572	−0.627861	+	0.778325i	$0.716070\pi$
$318$	−2.12593e18	−0.362532
$319$	3.05882e18	0.509476
$320$	3.43597e17	0.0559017
$321$	2.00643e18	0.318886
$322$	4.43698e18	0.688919
$323$	−3.68019e18	−0.558279
$324$	3.74813e17	0.0555556
$325$	−2.41491e18	−0.349764
$326$	−7.58878e18	−1.07409
$327$	−1.80183e18	−0.249234
$328$	4.52573e18	0.611836
$329$	9.91296e18	1.30989
$330$	−9.04560e17	−0.116838
$331$	−7.48745e18	−0.945418	−0.472709	−	0.881219i	$-0.656724\pi$
$331$	−7.48745e18	−0.945418	−0.472709	+	0.881219i	$0.656724\pi$
$332$	3.07607e18	0.379717
$333$	−4.84196e18	−0.584372
$334$	4.66351e18	0.550318
$335$	−5.33409e18	−0.615495
$336$	−1.80081e18	−0.203199
$337$	−7.00605e18	−0.773123	−0.386562	−	0.922264i	$-0.626337\pi$
$337$	−7.00605e18	−0.773123	−0.386562	+	0.922264i	$0.626337\pi$
$338$	1.34861e19	1.45549
$339$	4.73436e18	0.499762
$340$	−2.06153e18	−0.212862
$341$	−1.11106e19	−1.12222
$342$	1.39894e18	0.138230
$343$	2.63300e17	0.0254534
$344$	−7.84896e17	−0.0742376
$345$	−1.93080e18	−0.178688
$346$	2.18460e18	0.197834
$347$	−1.08705e18	−0.0963341	−0.0481671	−	0.998839i	$-0.515338\pi$
$347$	−1.08705e18	−0.0963341	−0.0481671	+	0.998839i	$0.515338\pi$
$348$	−2.64993e18	−0.229821
$349$	−2.86789e18	−0.243429	−0.121714	−	0.992565i	$-0.538839\pi$
$349$	−2.86789e18	−0.243429	−0.121714	+	0.992565i	$0.538839\pi$
$350$	−2.39645e18	−0.199094
$351$	−4.13873e18	−0.336561
$352$	−1.42114e18	−0.113128
$353$	1.73775e19	1.35418	0.677092	−	0.735899i	$-0.263240\pi$
$353$	1.73775e19	1.35418	0.677092	+	0.735899i	$0.263240\pi$
$354$	−7.62002e18	−0.581342
$355$	−6.38435e18	−0.476875
$356$	5.97803e18	0.437203
$357$	1.08046e19	0.773741
$358$	1.69663e19	1.18978
$359$	−1.19231e19	−0.818802	−0.409401	−	0.912354i	$-0.634262\pi$
$359$	−1.19231e19	−0.818802	−0.409401	+	0.912354i	$0.634262\pi$
$360$	7.83642e17	0.0527046
$361$	−9.95980e18	−0.656065
$362$	−1.56748e19	−1.01132
$363$	−5.39432e18	−0.340908
$364$	1.98847e19	1.23100
$365$	3.87200e18	0.234822
$366$	1.47510e18	0.0876422
$367$	−4.94881e18	−0.288075	−0.144037	−	0.989572i	$-0.546009\pi$
$367$	−4.94881e18	−0.288075	−0.144037	+	0.989572i	$0.546009\pi$
$368$	−3.03346e18	−0.173014
$369$	1.03218e19	0.576844
$370$	−1.01233e19	−0.554384
$371$	2.32953e19	1.25016
$372$	9.62537e18	0.506227
$373$	2.81093e19	1.44889	0.724444	−	0.689334i	$-0.242097\pi$
$373$	2.81093e19	1.44889	0.724444	+	0.689334i	$0.242097\pi$
$374$	8.52665e18	0.430766
$375$	1.04284e18	0.0516398
$376$	−6.77727e18	−0.328962
$377$	2.92608e19	1.39228
$378$	−4.10709e18	−0.191578
$379$	−1.07279e19	−0.490593	−0.245296	−	0.969448i	$-0.578885\pi$
$379$	−1.07279e19	−0.490593	−0.245296	+	0.969448i	$0.578885\pi$
$380$	2.92483e18	0.131136
$381$	1.92603e19	0.846691
$382$	2.56871e18	0.110724
$383$	−8.51605e18	−0.359954	−0.179977	−	0.983671i	$-0.557602\pi$
$383$	−8.51605e18	−0.359954	−0.179977	+	0.983671i	$0.557602\pi$
$384$	1.23117e18	0.0510310
$385$	9.91190e18	0.402904
$386$	3.06540e19	1.22203
$387$	−1.79011e18	−0.0699919
$388$	1.47191e19	0.564473
$389$	4.54565e19	1.70991	0.854956	−	0.518700i	$-0.173584\pi$
$389$	4.54565e19	1.70991	0.854956	+	0.518700i	$0.173584\pi$
$390$	−8.65305e18	−0.319290
$391$	1.82003e19	0.658799
$392$	9.77635e18	0.347161
$393$	−2.04877e19	−0.713753
$394$	−3.67239e19	−1.25524
$395$	1.50913e19	0.506114
$396$	−3.24120e18	−0.106658
$397$	−3.52266e19	−1.13748	−0.568738	−	0.822519i	$-0.692568\pi$
$397$	−3.52266e19	−1.13748	−0.568738	+	0.822519i	$0.692568\pi$
$398$	−2.74169e19	−0.868750
$399$	−1.53291e19	−0.476673
$400$	1.63840e18	0.0500000
$401$	−3.67077e19	−1.09945	−0.549724	−	0.835347i	$-0.685267\pi$
$401$	−3.67077e19	−1.09945	−0.549724	+	0.835347i	$0.685267\pi$
$402$	−1.91130e19	−0.561868
$403$	−1.06284e20	−3.06677
$404$	4.65148e18	0.131744
$405$	1.78725e18	0.0496904
$406$	2.90371e19	0.792517
$407$	4.18708e19	1.12190
$408$	−7.38684e18	−0.194315
$409$	−5.90647e19	−1.52547	−0.762735	−	0.646712i	$-0.776144\pi$
$409$	−5.90647e19	−1.52547	−0.762735	+	0.646712i	$0.776144\pi$
$410$	2.15804e19	0.547243
$411$	1.27464e19	0.317377
$412$	4.89040e18	0.119568
$413$	8.34980e19	2.00471
$414$	−6.91841e18	−0.163119
$415$	1.46678e19	0.339629
$416$	−1.35947e19	−0.309151
$417$	−2.39901e19	−0.535811
$418$	−1.20973e19	−0.265379
$419$	−1.14506e19	−0.246731	−0.123366	−	0.992361i	$-0.539369\pi$
$419$	−1.14506e19	−0.246731	−0.123366	+	0.992361i	$0.539369\pi$
$420$	−8.58691e18	−0.181747
$421$	2.08148e19	0.432769	0.216385	−	0.976308i	$-0.430573\pi$
$421$	2.08148e19	0.432769	0.216385	+	0.976308i	$0.430573\pi$
$422$	−4.47213e19	−0.913421
$423$	−1.54569e19	−0.310148
$424$	−1.59265e19	−0.313962
$425$	−9.83014e18	−0.190389
$426$	−2.28763e19	−0.435325
$427$	−1.61637e19	−0.302226
$428$	1.50312e19	0.276164
$429$	3.57897e19	0.646142
$430$	−3.74268e18	−0.0664001
$431$	−3.60393e19	−0.628344	−0.314172	−	0.949366i	$-0.601727\pi$
$431$	−3.60393e19	−0.628344	−0.314172	+	0.949366i	$0.601727\pi$
$432$	2.80793e18	0.0481125
$433$	−4.47025e19	−0.752788	−0.376394	−	0.926460i	$-0.622836\pi$
$433$	−4.47025e19	−0.752788	−0.376394	+	0.926460i	$0.622836\pi$
$434$	−1.05472e20	−1.74568
$435$	−1.26358e19	−0.205558
$436$	−1.34985e19	−0.215843
$437$	−2.58220e19	−0.405862
$438$	1.38741e19	0.214362
$439$	1.97921e19	0.300614	0.150307	−	0.988639i	$-0.451974\pi$
$439$	1.97921e19	0.300614	0.150307	+	0.988639i	$0.451974\pi$
$440$	−6.77654e18	−0.101184
$441$	2.22969e19	0.327307
$442$	8.15662e19	1.17718
$443$	2.03806e19	0.289194	0.144597	−	0.989491i	$-0.453811\pi$
$443$	2.03806e19	0.289194	0.144597	+	0.989491i	$0.453811\pi$
$444$	−3.62737e19	−0.506081
$445$	2.85055e19	0.391046
$446$	−3.85782e19	−0.520392
$447$	2.91645e19	0.386855
$448$	−1.34908e19	−0.175976
$449$	3.40190e19	0.436389	0.218194	−	0.975905i	$-0.429983\pi$
$449$	3.40190e19	0.436389	0.218194	+	0.975905i	$0.429983\pi$
$450$	3.73669e18	0.0471405
$451$	−8.92580e19	−1.10745
$452$	3.54676e19	0.432807
$453$	−4.04708e19	−0.485742
$454$	−6.14585e19	−0.725543
$455$	9.48176e19	1.10104
$456$	1.04802e19	0.119711
$457$	1.58344e20	1.77922	0.889611	−	0.456719i	$-0.150975\pi$
$457$	1.58344e20	1.77922	0.889611	+	0.456719i	$0.150975\pi$
$458$	5.30052e19	0.585905
$459$	−1.68471e19	−0.183202
$460$	−1.44647e19	−0.154748
$461$	−4.91040e19	−0.516845	−0.258423	−	0.966032i	$-0.583203\pi$
$461$	−4.91040e19	−0.516845	−0.258423	+	0.966032i	$0.583203\pi$
$462$	3.55161e19	0.367799
$463$	−9.86911e19	−1.00559	−0.502794	−	0.864406i	$-0.667695\pi$
$463$	−9.86911e19	−1.00559	−0.502794	+	0.864406i	$0.667695\pi$
$464$	−1.98520e19	−0.199031
$465$	4.58973e19	0.452783
$466$	6.99950e19	0.679474
$467$	−3.01926e19	−0.288419	−0.144209	−	0.989547i	$-0.546064\pi$
$467$	−3.01926e19	−0.288419	−0.144209	+	0.989547i	$0.546064\pi$
$468$	−3.10055e19	−0.291470
$469$	2.09435e20	1.93755
$470$	−3.23165e19	−0.294233
$471$	−6.87816e19	−0.616333
$472$	−5.70857e19	−0.503457
$473$	1.54800e19	0.134373
$474$	5.40749e19	0.462017
$475$	1.39467e19	0.117292
$476$	8.09428e19	0.670079
$477$	−3.63235e19	−0.296006
$478$	−1.46677e20	−1.17667
$479$	−1.11196e20	−0.878157	−0.439078	−	0.898449i	$-0.644695\pi$
$479$	−1.11196e20	−0.878157	−0.439078	+	0.898449i	$0.644695\pi$
$480$	5.87068e18	0.0456435
$481$	4.00538e20	3.06588
$482$	3.35077e19	0.252518
$483$	7.58099e19	0.562500
$484$	−4.04117e19	−0.295235
$485$	7.01861e19	0.504880
$486$	6.40404e18	0.0453609
$487$	−5.32893e19	−0.371683	−0.185841	−	0.982580i	$-0.559501\pi$
$487$	−5.32893e19	−0.371683	−0.185841	+	0.982580i	$0.559501\pi$
$488$	1.10508e19	0.0759003
$489$	−1.29661e20	−0.876989
$490$	4.66172e19	0.310510
$491$	−2.71447e20	−1.78063	−0.890314	−	0.455347i	$-0.849515\pi$
$491$	−2.71447e20	−1.78063	−0.890314	+	0.455347i	$0.849515\pi$
$492$	7.73264e19	0.499562
$493$	1.19109e20	0.757868
$494$	−1.15723e20	−0.725218
$495$	−1.54552e19	−0.0953975
$496$	7.21089e19	0.438406
$497$	2.50672e20	1.50118
$498$	5.25575e19	0.310038
$499$	−8.94331e19	−0.519690	−0.259845	−	0.965650i	$-0.583671\pi$
$499$	−8.94331e19	−0.519690	−0.259845	+	0.965650i	$0.583671\pi$
$500$	7.81250e18	0.0447214
$501$	7.96804e19	0.449333
$502$	1.59807e20	0.887808
$503$	−1.01357e20	−0.554745	−0.277372	−	0.960762i	$-0.589464\pi$
$503$	−1.01357e20	−0.554745	−0.277372	+	0.960762i	$0.589464\pi$
$504$	−3.07685e19	−0.165912
$505$	2.21800e19	0.117835
$506$	5.98270e19	0.313162
$507$	2.30422e20	1.18840
$508$	1.44289e20	0.733256
$509$	−8.88667e19	−0.444995	−0.222498	−	0.974933i	$-0.571421\pi$
$509$	−8.88667e19	−0.444995	−0.222498	+	0.974933i	$0.571421\pi$
$510$	−3.52232e19	−0.173801
$511$	−1.52028e20	−0.739208
$512$	9.22337e18	0.0441942
$513$	2.39021e19	0.112864
$514$	−3.06237e19	−0.142506
$515$	2.33193e19	0.106945
$516$	−1.34107e19	−0.0606148
$517$	1.33664e20	0.595435
$518$	3.97477e20	1.74517
$519$	3.73259e19	0.161531
$520$	−6.48247e19	−0.276513
$521$	−7.89026e19	−0.331748	−0.165874	−	0.986147i	$-0.553044\pi$
$521$	−7.89026e19	−0.331748	−0.165874	+	0.986147i	$0.553044\pi$
$522$	−4.52765e19	−0.187648
$523$	−1.91914e20	−0.784049	−0.392024	−	0.919955i	$-0.628225\pi$
$523$	−1.91914e20	−0.784049	−0.392024	+	0.919955i	$0.628225\pi$
$524$	−1.53484e20	−0.618129
$525$	−4.09456e19	−0.162560
$526$	−8.68686e18	−0.0339993
$527$	−4.32642e20	−1.66936
$528$	−2.42816e19	−0.0923682
$529$	−1.38933e20	−0.521061
$530$	−7.59435e19	−0.280816
$531$	−1.30195e20	−0.474664
$532$	−1.14839e20	−0.412811
$533$	−8.53846e20	−3.02639
$534$	1.02140e20	0.356975
$535$	7.16746e19	0.247008
$536$	−1.43186e20	−0.486592
$537$	2.89886e20	0.971448
$538$	3.11281e20	1.02869
$539$	−1.92812e20	−0.628376
$540$	1.33893e19	0.0430331
$541$	−3.44055e20	−1.09056	−0.545279	−	0.838255i	$-0.683576\pi$
$541$	−3.44055e20	−1.09056	−0.545279	+	0.838255i	$0.683576\pi$
$542$	2.26445e20	0.707895
$543$	−2.67818e20	−0.825737
$544$	−5.53388e19	−0.168282
$545$	−6.43659e19	−0.193056
$546$	3.39749e20	1.00511
$547$	6.22453e20	1.81636	0.908179	−	0.418582i	$-0.137473\pi$
$547$	6.22453e20	1.81636	0.908179	+	0.418582i	$0.137473\pi$
$548$	9.54905e19	0.274856
$549$	2.52034e19	0.0715595
$550$	−3.23131e19	−0.0905020
$551$	−1.68988e20	−0.466895
$552$	−5.18296e19	−0.141265
$553$	−5.92536e20	−1.59322
$554$	1.53199e18	0.00406379
$555$	−1.72967e20	−0.452652
$556$	−1.79723e20	−0.464026
$557$	5.49947e20	1.40090	0.700450	−	0.713701i	$-0.252983\pi$
$557$	5.49947e20	1.40090	0.700450	+	0.713701i	$0.252983\pi$
$558$	1.64458e20	0.413333
$559$	1.48082e20	0.367210
$560$	−6.43292e19	−0.157398
$561$	1.45686e20	0.351719
$562$	−2.95468e20	−0.703864
$563$	6.60749e20	1.55319	0.776593	−	0.630002i	$-0.216946\pi$
$563$	6.60749e20	1.55319	0.776593	+	0.630002i	$0.216946\pi$
$564$	−1.15796e20	−0.268596
$565$	1.69123e20	0.387114
$566$	−2.72181e20	−0.614801
$567$	−7.01736e19	−0.156423
$568$	−1.71379e20	−0.377002
$569$	6.41939e20	1.39364	0.696822	−	0.717244i	$-0.254597\pi$
$569$	6.41939e20	1.39364	0.696822	+	0.717244i	$0.254597\pi$
$570$	4.99734e19	0.107072
$571$	3.98576e18	0.00842832	0.00421416	−	0.999991i	$-0.498659\pi$
$571$	3.98576e18	0.00842832	0.00421416	+	0.999991i	$0.498659\pi$
$572$	2.68120e20	0.559575
$573$	4.38888e19	0.0904054
$574$	−8.47319e20	−1.72269
$575$	−6.89730e19	−0.138411
$576$	2.10357e19	0.0416667
$577$	−5.34283e20	−1.04461	−0.522303	−	0.852760i	$-0.674927\pi$
$577$	−5.34283e20	−1.04461	−0.522303	+	0.852760i	$0.674927\pi$
$578$	−3.43660e19	−0.0663239
$579$	5.23752e20	0.997783
$580$	−9.46619e19	−0.178019
$581$	−5.75910e20	−1.06914
$582$	2.51489e20	0.460890
$583$	3.14108e20	0.568283
$584$	1.03938e20	0.185643
$585$	−1.47846e20	−0.260699
$586$	2.05798e20	0.358269
$587$	−8.47583e20	−1.45679	−0.728395	−	0.685158i	$-0.759733\pi$
$587$	−8.47583e20	−1.45679	−0.728395	+	0.685158i	$0.759733\pi$
$588$	1.67038e20	0.283456
$589$	6.13817e20	1.02843
$590$	−2.72206e20	−0.450306
$591$	−6.27462e20	−1.02490
$592$	−2.71746e20	−0.438279
$593$	−3.01600e20	−0.480310	−0.240155	−	0.970735i	$-0.577198\pi$
$593$	−3.01600e20	−0.480310	−0.240155	+	0.970735i	$0.577198\pi$
$594$	−5.53789e19	−0.0870856
$595$	3.85965e20	0.599337
$596$	2.18487e20	0.335026
$597$	−4.68443e20	−0.709331
$598$	5.72308e20	0.855797
$599$	−1.60540e20	−0.237073	−0.118536	−	0.992950i	$-0.537820\pi$
$599$	−1.60540e20	−0.237073	−0.118536	+	0.992950i	$0.537820\pi$
$600$	2.79936e19	0.0408248
$601$	4.08865e20	0.588872	0.294436	−	0.955671i	$-0.404868\pi$
$601$	4.08865e20	0.588872	0.294436	+	0.955671i	$0.404868\pi$
$602$	1.46950e20	0.209024
$603$	−3.26564e20	−0.458763
$604$	−3.03189e20	−0.420665
$605$	−1.92698e20	−0.264066
$606$	7.94748e19	0.107568
$607$	−7.91780e20	−1.05850	−0.529248	−	0.848467i	$-0.677526\pi$
$607$	−7.91780e20	−1.05850	−0.529248	+	0.848467i	$0.677526\pi$
$608$	7.85128e19	0.103672
$609$	4.96127e20	0.647087
$610$	5.26942e19	0.0678873
$611$	1.27863e21	1.62718
$612$	−1.26211e20	−0.158658
$613$	1.15590e21	1.43537	0.717687	−	0.696366i	$-0.245201\pi$
$613$	1.15590e21	1.43537	0.717687	+	0.696366i	$0.245201\pi$
$614$	−2.44316e20	−0.299702
$615$	3.68721e20	0.446822
$616$	2.66070e20	0.318523
$617$	−4.13431e19	−0.0488949	−0.0244475	−	0.999701i	$-0.507783\pi$
$617$	−4.13431e19	−0.0488949	−0.0244475	+	0.999701i	$0.507783\pi$
$618$	8.35571e19	0.0976270
$619$	1.42683e21	1.64700	0.823500	−	0.567316i	$-0.192018\pi$
$619$	1.42683e21	1.64700	0.823500	+	0.567316i	$0.192018\pi$
$620$	3.43842e20	0.392122
$621$	−1.18208e20	−0.133186
$622$	−3.32393e20	−0.370019
$623$	−1.11922e21	−1.23100
$624$	−2.32279e20	−0.252421
$625$	3.72529e19	0.0400000
$626$	−3.13893e20	−0.333023
$627$	−2.06694e20	−0.216681
$628$	−5.15280e20	−0.533760
$629$	1.63043e21	1.66887
$630$	−1.46715e20	−0.148396
$631$	1.24140e21	1.24077	0.620387	−	0.784296i	$-0.286976\pi$
$631$	1.24140e21	1.24077	0.620387	+	0.784296i	$0.286976\pi$
$632$	4.05104e20	0.400118
$633$	−7.64106e20	−0.745805
$634$	−9.20552e20	−0.887930
$635$	6.88024e20	0.655844
$636$	−2.72119e20	−0.256349
$637$	−1.84445e21	−1.71720
$638$	3.91529e20	0.360254
$639$	−3.90863e20	−0.355441
$640$	4.39805e19	0.0395285
$641$	9.44072e20	0.838629	0.419315	−	0.907841i	$-0.362270\pi$
$641$	9.44072e20	0.838629	0.419315	+	0.907841i	$0.362270\pi$
$642$	2.56823e20	0.225487
$643$	−3.24966e20	−0.282004	−0.141002	−	0.990009i	$-0.545032\pi$
$643$	−3.24966e20	−0.282004	−0.141002	+	0.990009i	$0.545032\pi$
$644$	5.67933e20	0.487139
$645$	−6.39472e19	−0.0542155
$646$	−4.71064e20	−0.394763
$647$	1.59578e21	1.32188	0.660940	−	0.750439i	$-0.270158\pi$
$647$	1.59578e21	1.32188	0.660940	+	0.750439i	$0.270158\pi$
$648$	4.79761e19	0.0392837
$649$	1.12586e21	0.911278
$650$	−3.09108e20	−0.247321
$651$	−1.80209e21	−1.42534
$652$	−9.71364e20	−0.759495
$653$	2.21448e21	1.71168	0.855841	−	0.517238i	$-0.173040\pi$
$653$	2.21448e21	1.71168	0.855841	+	0.517238i	$0.173040\pi$
$654$	−2.30635e20	−0.176235
$655$	−7.31869e20	−0.552871
$656$	5.79294e20	0.432633
$657$	2.37052e20	0.175026
$658$	1.26886e21	0.926230
$659$	1.41582e21	1.02180	0.510902	−	0.859639i	$-0.329312\pi$
$659$	1.41582e21	1.02180	0.510902	+	0.859639i	$0.329312\pi$
$660$	−1.15784e20	−0.0826167
$661$	1.49880e21	1.05738	0.528692	−	0.848814i	$-0.322683\pi$
$661$	1.49880e21	1.05738	0.528692	+	0.848814i	$0.322683\pi$
$662$	−9.58393e20	−0.668511
$663$	1.39364e21	0.961165
$664$	3.93737e20	0.268501
$665$	−5.47594e20	−0.369229
$666$	−6.19770e20	−0.413213
$667$	8.35727e20	0.550961
$668$	5.96929e20	0.389134
$669$	−6.59145e20	−0.424898
$670$	−6.82764e20	−0.435221
$671$	−2.17947e20	−0.137383
$672$	−2.30503e20	−0.143684
$673$	−1.44986e21	−0.893743	−0.446872	−	0.894598i	$-0.647462\pi$
$673$	−1.44986e21	−0.893743	−0.446872	+	0.894598i	$0.647462\pi$
$674$	−8.96774e20	−0.546681
$675$	6.38449e19	0.0384900
$676$	1.72622e21	1.02919
$677$	−2.97847e21	−1.75622	−0.878108	−	0.478462i	$-0.841194\pi$
$677$	−2.97847e21	−1.75622	−0.878108	+	0.478462i	$0.841194\pi$
$678$	6.05998e20	0.353385
$679$	−2.75575e21	−1.58934
$680$	−2.63876e20	−0.150516
$681$	−1.05008e21	−0.592403
$682$	−1.42216e21	−0.793532
$683$	−1.67668e21	−0.925325	−0.462663	−	0.886534i	$-0.653106\pi$
$683$	−1.67668e21	−0.925325	−0.462663	+	0.886534i	$0.653106\pi$
$684$	1.79064e20	0.0977433
$685$	4.55334e20	0.245839
$686$	3.37024e19	0.0179983
$687$	9.05644e20	0.478390
$688$	−1.00467e20	−0.0524939
$689$	3.00477e21	1.55298
$690$	−2.47143e20	−0.126351
$691$	1.06753e21	0.539879	0.269940	−	0.962877i	$-0.412996\pi$
$691$	1.06753e21	0.539879	0.269940	+	0.962877i	$0.412996\pi$
$692$	2.79629e20	0.139890
$693$	6.06826e20	0.300307
$694$	−1.39143e20	−0.0681185
$695$	−8.56985e20	−0.415037
$696$	−3.39191e20	−0.162508
$697$	−3.47567e21	−1.64738
$698$	−3.67090e20	−0.172130
$699$	1.19593e21	0.554788
$700$	−3.06746e20	−0.140781
$701$	−3.13817e21	−1.42492	−0.712461	−	0.701712i	$-0.752419\pi$
$701$	−3.13817e21	−1.42492	−0.712461	+	0.701712i	$0.752419\pi$
$702$	−5.29757e20	−0.237984
$703$	−2.31320e21	−1.02813
$704$	−1.81906e20	−0.0799932
$705$	−5.52158e20	−0.240240
$706$	2.22432e21	0.957552
$707$	−8.70862e20	−0.370940
$708$	−9.75363e20	−0.411071
$709$	−1.00699e21	−0.419933	−0.209967	−	0.977709i	$-0.567336\pi$
$709$	−1.00699e21	−0.419933	−0.209967	+	0.977709i	$0.567336\pi$
$710$	−8.17197e20	−0.337201
$711$	9.23920e20	0.377235
$712$	7.65188e20	0.309149
$713$	−3.03562e21	−1.21360
$714$	1.38298e21	0.547117
$715$	1.27849e21	0.500500
$716$	2.17169e21	0.841299
$717$	−2.50612e21	−0.960744
$718$	−1.52615e21	−0.578981
$719$	7.62891e20	0.286415	0.143208	−	0.989693i	$-0.454258\pi$
$719$	7.62891e20	0.286415	0.143208	+	0.989693i	$0.454258\pi$
$720$	1.00306e20	0.0372678
$721$	−9.15594e20	−0.336658
$722$	−1.27485e21	−0.463908
$723$	5.72510e20	0.206180
$724$	−2.00637e21	−0.715109
$725$	−4.51383e20	−0.159225
$726$	−6.90472e20	−0.241058
$727$	−4.41755e21	−1.52642	−0.763208	−	0.646153i	$-0.776377\pi$
$727$	−4.41755e21	−1.52642	−0.763208	+	0.646153i	$0.776377\pi$
$728$	2.54524e21	0.870449
$729$	1.09419e20	0.0370370
$730$	4.95616e20	0.166044
$731$	6.02785e20	0.199886
$732$	1.88813e20	0.0619724
$733$	4.39662e21	1.42837	0.714183	−	0.699959i	$-0.246798\pi$
$733$	4.39662e21	1.42837	0.714183	+	0.699959i	$0.246798\pi$
$734$	−6.33448e20	−0.203700
$735$	7.96499e20	0.253531
$736$	−3.88283e20	−0.122339
$737$	2.82396e21	0.880750
$738$	1.32119e21	0.407891
$739$	−9.77741e20	−0.298807	−0.149403	−	0.988776i	$-0.547735\pi$
$739$	−9.77741e20	−0.298807	−0.149403	+	0.988776i	$0.547735\pi$
$740$	−1.29579e21	−0.392008
$741$	−1.97724e21	−0.592138
$742$	2.98180e21	0.883994
$743$	2.77204e21	0.813548	0.406774	−	0.913529i	$-0.366654\pi$
$743$	2.77204e21	0.813548	0.406774	+	0.913529i	$0.366654\pi$
$744$	1.23205e21	0.357957
$745$	1.04183e21	0.299657
$746$	3.59800e21	1.02452
$747$	8.97994e20	0.253145
$748$	1.09141e21	0.304597
$749$	−2.81419e21	−0.777570
$750$	1.33484e20	0.0365148
$751$	2.06741e21	0.559922	0.279961	−	0.960011i	$-0.409678\pi$
$751$	2.06741e21	0.559922	0.279961	+	0.960011i	$0.409678\pi$
$752$	−8.67491e20	−0.232611
$753$	2.73046e21	0.724892
$754$	3.74538e21	0.984489
$755$	−1.44572e21	−0.376254
$756$	−5.25708e20	−0.135466
$757$	−5.23990e21	−1.33691	−0.668457	−	0.743751i	$-0.733045\pi$
$757$	−5.23990e21	−1.33691	−0.668457	+	0.743751i	$0.733045\pi$
$758$	−1.37317e21	−0.346902
$759$	1.02220e21	0.255695
$760$	3.74378e20	0.0927275
$761$	−2.45142e21	−0.601219	−0.300610	−	0.953747i	$-0.597190\pi$
$761$	−2.45142e21	−0.601219	−0.300610	+	0.953747i	$0.597190\pi$
$762$	2.46531e21	0.598701
$763$	2.52723e21	0.607729
$764$	3.28795e20	0.0782934
$765$	−6.01821e20	−0.141908
$766$	−1.09005e21	−0.254526
$767$	1.07701e22	2.49031
$768$	1.57590e20	0.0360844
$769$	−3.17813e21	−0.720650	−0.360325	−	0.932827i	$-0.617334\pi$
$769$	−3.17813e21	−0.720650	−0.360325	+	0.932827i	$0.617334\pi$
$770$	1.26872e21	0.284896
$771$	−5.23235e20	−0.116356
$772$	3.92371e21	0.864106
$773$	−2.81548e21	−0.614054	−0.307027	−	0.951701i	$-0.599334\pi$
$773$	−2.81548e21	−0.614054	−0.307027	+	0.951701i	$0.599334\pi$
$774$	−2.29134e20	−0.0494917
$775$	1.63957e21	0.350724
$776$	1.88404e21	0.399142
$777$	6.79126e21	1.42493
$778$	5.81843e21	1.20909
$779$	4.93116e21	1.01489
$780$	−1.10759e21	−0.225772
$781$	3.37999e21	0.682390
$782$	2.32964e21	0.465841
$783$	−7.73592e20	−0.153214
$784$	1.25137e21	0.245480
$785$	−2.45705e21	−0.477410
$786$	−2.62242e21	−0.504700
$787$	−3.49874e21	−0.666961	−0.333481	−	0.942757i	$-0.608223\pi$
$787$	−3.49874e21	−0.666961	−0.333481	+	0.942757i	$0.608223\pi$
$788$	−4.70065e21	−0.887588
$789$	−1.48423e20	−0.0277603
$790$	1.93169e21	0.357877
$791$	−6.64034e21	−1.21862
$792$	−4.14874e20	−0.0754183
$793$	−2.08489e21	−0.375434
$794$	−4.50901e21	−0.804317
$795$	−1.29757e21	−0.229285
$796$	−3.50936e21	−0.614299
$797$	−7.13892e20	−0.123793	−0.0618964	−	0.998083i	$-0.519715\pi$
$797$	−7.13892e20	−0.123793	−0.0618964	+	0.998083i	$0.519715\pi$
$798$	−1.96213e21	−0.337059
$799$	5.20481e21	0.885735
$800$	2.09715e20	0.0353553
$801$	1.74516e21	0.291469
$802$	−4.69859e21	−0.777427
$803$	−2.04990e21	−0.336021
$804$	−2.44647e21	−0.397300
$805$	2.70812e21	0.435711
$806$	−1.36044e22	−2.16854
$807$	5.31852e21	0.839923
$808$	5.95389e20	0.0931570
$809$	2.23280e21	0.346128	0.173064	−	0.984911i	$-0.444633\pi$
$809$	2.23280e21	0.346128	0.173064	+	0.984911i	$0.444633\pi$
$810$	2.28768e20	0.0351364
$811$	−7.62184e20	−0.115985	−0.0579927	−	0.998317i	$-0.518470\pi$
$811$	−7.62184e20	−0.115985	−0.0579927	+	0.998317i	$0.518470\pi$
$812$	3.71675e21	0.560394
$813$	3.86903e21	0.577994
$814$	5.35947e21	0.793302
$815$	−4.63182e21	−0.679313
$816$	−9.45515e20	−0.137402
$817$	−8.55210e20	−0.123142
$818$	−7.56029e21	−1.07867
$819$	5.80492e21	0.820667
$820$	2.76229e21	0.386959
$821$	−9.57602e21	−1.32926	−0.664632	−	0.747171i	$-0.731412\pi$
$821$	−9.57602e21	−1.32926	−0.664632	+	0.747171i	$0.731412\pi$
$822$	1.63154e21	0.224419
$823$	−3.94115e21	−0.537186	−0.268593	−	0.963254i	$-0.586559\pi$
$823$	−3.94115e21	−0.537186	−0.268593	+	0.963254i	$0.586559\pi$
$824$	6.25971e20	0.0845474
$825$	−5.52099e20	−0.0738946
$826$	1.06877e22	1.41754
$827$	9.68795e21	1.27333	0.636664	−	0.771141i	$-0.280314\pi$
$827$	9.68795e21	1.27333	0.636664	+	0.771141i	$0.280314\pi$
$828$	−8.85557e20	−0.115342
$829$	−2.44796e21	−0.315969	−0.157985	−	0.987442i	$-0.550500\pi$
$829$	−2.44796e21	−0.315969	−0.157985	+	0.987442i	$0.550500\pi$
$830$	1.87748e21	0.240154
$831$	2.61754e19	0.00331807
$832$	−1.74012e21	−0.218603
$833$	−7.50804e21	−0.934736
$834$	−3.07073e21	−0.378876
$835$	2.84638e21	0.348052
$836$	−1.54846e21	−0.187651
$837$	2.80993e21	0.337485
$838$	−1.46568e21	−0.174465
$839$	−1.40532e22	−1.65791	−0.828954	−	0.559318i	$-0.811063\pi$
$839$	−1.40532e22	−1.65791	−0.828954	+	0.559318i	$0.811063\pi$
$840$	−1.09912e21	−0.128515
$841$	−3.15990e21	−0.366187
$842$	2.66429e21	0.306014
$843$	−5.04835e21	−0.574702
$844$	−5.72433e21	−0.645887
$845$	8.23123e21	0.920534
$846$	−1.97848e21	−0.219308
$847$	7.56599e21	0.831267
$848$	−2.03859e21	−0.222004
$849$	−4.65047e21	−0.501983
$850$	−1.25826e21	−0.134626
$851$	1.14399e22	1.21325
$852$	−2.92816e21	−0.307821
$853$	5.24040e21	0.546068	0.273034	−	0.962004i	$-0.411973\pi$
$853$	5.24040e21	0.546068	0.273034	+	0.962004i	$0.411973\pi$
$854$	−2.06895e21	−0.213706
$855$	8.53843e20	0.0874243
$856$	1.92400e21	0.195277
$857$	−1.62073e22	−1.63063	−0.815313	−	0.579020i	$-0.803435\pi$
$857$	−1.62073e22	−1.63063	−0.815313	+	0.579020i	$0.803435\pi$
$858$	4.58108e21	0.456891
$859$	−9.40358e21	−0.929703	−0.464852	−	0.885389i	$-0.653892\pi$
$859$	−9.40358e21	−0.929703	−0.464852	+	0.885389i	$0.653892\pi$
$860$	−4.79063e20	−0.0469520
$861$	−1.44772e22	−1.40657
$862$	−4.61303e21	−0.444306
$863$	1.45952e22	1.39357	0.696786	−	0.717279i	$-0.254613\pi$
$863$	1.45952e22	1.39357	0.696786	+	0.717279i	$0.254613\pi$
$864$	3.59415e20	0.0340207
$865$	1.33337e21	0.125121
$866$	−5.72192e21	−0.532301
$867$	−5.87176e20	−0.0541533
$868$	−1.35004e22	−1.23438
$869$	−7.98960e21	−0.724230
$870$	−1.61739e21	−0.145352
$871$	2.70141e22	2.40688
$872$	−1.72781e21	−0.152624
$873$	4.29693e21	0.376315
$874$	−3.30521e21	−0.286988
$875$	−1.46268e21	−0.125918
$876$	1.77588e21	0.151577
$877$	6.38272e21	0.540143	0.270071	−	0.962840i	$-0.412953\pi$
$877$	6.38272e21	0.540143	0.270071	+	0.962840i	$0.412953\pi$
$878$	2.53339e21	0.212566
$879$	3.51626e21	0.292526
$880$	−8.67398e20	−0.0715481
$881$	1.76031e22	1.43969	0.719845	−	0.694135i	$-0.244213\pi$
$881$	1.76031e22	1.43969	0.719845	+	0.694135i	$0.244213\pi$
$882$	2.85400e21	0.231441
$883$	−2.08324e22	−1.67508	−0.837539	−	0.546378i	$-0.816006\pi$
$883$	−2.08324e22	−1.67508	−0.837539	+	0.546378i	$0.816006\pi$
$884$	1.04405e22	0.832393
$885$	−4.65089e21	−0.367673
$886$	2.60872e21	0.204491
$887$	2.12463e22	1.65141	0.825706	−	0.564101i	$-0.190777\pi$
$887$	2.12463e22	1.65141	0.825706	+	0.564101i	$0.190777\pi$
$888$	−4.64303e21	−0.357853
$889$	−2.70142e22	−2.06456
$890$	3.64870e21	0.276512
$891$	−9.46201e20	−0.0711051
$892$	−4.93801e21	−0.367973
$893$	−7.38440e21	−0.545669
$894$	3.73306e21	0.273548
$895$	1.03554e22	0.752481
$896$	−1.72682e21	−0.124434
$897$	9.77841e21	0.698755
$898$	4.35443e21	0.308573
$899$	−1.98662e22	−1.39610
$900$	4.78297e20	0.0333333
$901$	1.22312e22	0.845346
$902$	−1.14250e22	−0.783084
$903$	2.51079e21	0.170668
$904$	4.53986e21	0.306040
$905$	−9.56713e21	−0.639613
$906$	−5.18027e21	−0.343471
$907$	−5.60947e21	−0.368865	−0.184432	−	0.982845i	$-0.559045\pi$
$907$	−5.60947e21	−0.368865	−0.184432	+	0.982845i	$0.559045\pi$
$908$	−7.86669e21	−0.513036
$909$	1.35790e21	0.0878293
$910$	1.21367e22	0.778554
$911$	−1.72156e22	−1.09530	−0.547651	−	0.836707i	$-0.684478\pi$
$911$	−1.72156e22	−1.09530	−0.547651	+	0.836707i	$0.684478\pi$
$912$	1.34146e21	0.0846482
$913$	−7.76541e21	−0.485997
$914$	2.02680e22	1.25810
$915$	9.00329e20	0.0554298
$916$	6.78467e21	0.414298
$917$	2.87357e22	1.74041
$918$	−2.15643e21	−0.129544
$919$	−2.17178e22	−1.29404	−0.647021	−	0.762472i	$-0.723986\pi$
$919$	−2.17178e22	−1.29404	−0.647021	+	0.762472i	$0.723986\pi$
$920$	−1.85148e21	−0.109423
$921$	−4.17437e21	−0.244705
$922$	−6.28532e21	−0.365465
$923$	3.23331e22	1.86481
$924$	4.54606e21	0.260073
$925$	−6.17879e21	−0.350623
$926$	−1.26325e22	−0.711059
$927$	1.42765e21	0.0797121
$928$	−2.54106e21	−0.140736
$929$	3.18113e22	1.74769	0.873844	−	0.486206i	$-0.161619\pi$
$929$	3.18113e22	1.74769	0.873844	+	0.486206i	$0.161619\pi$
$930$	5.87486e21	0.320166
$931$	1.06521e22	0.575857
$932$	8.95937e21	0.480461
$933$	−5.67925e21	−0.302119
$934$	−3.86465e21	−0.203943
$935$	5.20425e21	0.272440
$936$	−3.96870e21	−0.206101
$937$	3.20402e21	0.165063	0.0825313	−	0.996588i	$-0.473700\pi$
$937$	3.20402e21	0.165063	0.0825313	+	0.996588i	$0.473700\pi$
$938$	2.68077e22	1.37005
$939$	−5.36315e21	−0.271912
$940$	−4.13652e21	−0.208054
$941$	2.01668e22	1.00627	0.503134	−	0.864208i	$-0.332180\pi$
$941$	2.01668e22	1.00627	0.503134	+	0.864208i	$0.332180\pi$
$942$	−8.80404e21	−0.435813
$943$	−2.43870e22	−1.19762
$944$	−7.30697e21	−0.355998
$945$	−2.50677e21	−0.121165
$946$	1.98144e21	0.0950161
$947$	3.06292e21	0.145717	0.0728586	−	0.997342i	$-0.476788\pi$
$947$	3.06292e21	0.145717	0.0728586	+	0.997342i	$0.476788\pi$
$948$	6.92158e21	0.326695
$949$	−1.96095e22	−0.918267
$950$	1.78517e21	0.0829380
$951$	−1.57285e22	−0.724992
$952$	1.03607e22	0.473817
$953$	3.11794e22	1.41472	0.707360	−	0.706853i	$-0.249886\pi$
$953$	3.11794e22	1.41472	0.707360	+	0.706853i	$0.249886\pi$
$954$	−4.64941e21	−0.209308
$955$	1.56782e21	0.0700277
$956$	−1.87747e22	−0.832029
$957$	6.68964e21	0.294146
$958$	−1.42331e22	−0.620950
$959$	−1.78780e22	−0.773889
$960$	7.51447e20	0.0322749
$961$	4.86949e22	2.07519
$962$	5.12689e22	2.16791
$963$	4.38806e21	0.184109
$964$	4.28898e21	0.178557
$965$	1.87097e22	0.772880
$966$	9.70367e21	0.397748
$967$	−2.87477e22	−1.16924	−0.584620	−	0.811307i	$-0.698756\pi$
$967$	−2.87477e22	−1.16924	−0.584620	+	0.811307i	$0.698756\pi$
$968$	−5.17270e21	−0.208762
$969$	−8.04857e21	−0.322323
$970$	8.98382e21	0.357004
$971$	−2.32350e22	−0.916216	−0.458108	−	0.888897i	$-0.651473\pi$
$971$	−2.32350e22	−0.916216	−0.458108	+	0.888897i	$0.651473\pi$
$972$	8.19717e20	0.0320750
$973$	3.36482e22	1.30652
$974$	−6.82103e21	−0.262819
$975$	−5.28140e21	−0.201936
$976$	1.41450e21	0.0536696
$977$	−5.23387e22	−1.97067	−0.985334	−	0.170637i	$-0.945417\pi$
$977$	−5.23387e22	−1.97067	−0.985334	+	0.170637i	$0.945417\pi$
$978$	−1.65967e22	−0.620125
$979$	−1.50913e22	−0.559573
$980$	5.96701e21	0.219564
$981$	−3.94061e21	−0.143895
$982$	−3.47452e22	−1.25909
$983$	2.71260e22	0.975515	0.487757	−	0.872979i	$-0.337815\pi$
$983$	2.71260e22	0.975515	0.487757	+	0.872979i	$0.337815\pi$
$984$	9.89777e21	0.353244
$985$	−2.24145e22	−0.793883
$986$	1.52460e22	0.535893
$987$	2.16796e22	0.756264
$988$	−1.48126e22	−0.512807
$989$	4.22943e21	0.145315
$990$	−1.97827e21	−0.0674562
$991$	−4.42394e21	−0.149712	−0.0748560	−	0.997194i	$-0.523850\pi$
$991$	−4.42394e21	−0.149712	−0.0748560	+	0.997194i	$0.523850\pi$
$992$	9.22993e21	0.310000
$993$	−1.63750e22	−0.545837
$994$	3.20860e22	1.06149
$995$	−1.67339e22	−0.549446
$996$	6.72736e21	0.219230
$997$	−3.88665e22	−1.25708	−0.628538	−	0.777779i	$-0.716347\pi$
$997$	−3.88665e22	−1.25708	−0.628538	+	0.777779i	$0.716347\pi$
$998$	−1.14474e22	−0.367476
$999$	−1.05894e22	−0.337387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.16.a.f.1.1	✓	1
3.2	odd	2		90.16.a.a.1.1		1
5.2	odd	4		150.16.c.f.49.2		2
5.3	odd	4		150.16.c.f.49.1		2
5.4	even	2		150.16.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.16.a.f.1.1	✓	1	1.1	even	1	trivial
90.16.a.a.1.1		1	3.2	odd	2
150.16.a.c.1.1		1	5.4	even	2
150.16.c.f.49.1		2	5.3	odd	4
150.16.c.f.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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	30.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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