LMFDB - Embedded newform 2.42.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,42,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 42, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	2.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:	$21.2943340913$
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	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.04858e6 q^{2} +5.04352e9 q^{3} +1.09951e12 q^{4} -4.85042e13 q^{5} -5.28851e15 q^{6} -1.19392e17 q^{7} -1.15292e18 q^{8} -1.10359e19 q^{9} +O(q^{10})$

\(q-1.04858e6 q^{2} +5.04352e9 q^{3} +1.09951e12 q^{4} -4.85042e13 q^{5} -5.28851e15 q^{6} -1.19392e17 q^{7} -1.15292e18 q^{8} -1.10359e19 q^{9} +5.08603e19 q^{10} +3.15381e21 q^{11} +5.54541e21 q^{12} -1.14103e22 q^{13} +1.25192e23 q^{14} -2.44632e23 q^{15} +1.20893e24 q^{16} -2.67238e25 q^{17} +1.15720e25 q^{18} +6.79752e25 q^{19} -5.33309e25 q^{20} -6.02158e26 q^{21} -3.30701e27 q^{22} -1.35051e28 q^{23} -5.81478e27 q^{24} -4.31221e28 q^{25} +1.19646e28 q^{26} -2.39612e29 q^{27} -1.31273e29 q^{28} +1.36715e29 q^{29} +2.56515e29 q^{30} +3.06142e30 q^{31} -1.26765e30 q^{32} +1.59063e31 q^{33} +2.80219e31 q^{34} +5.79103e30 q^{35} -1.21341e31 q^{36} -2.21949e32 q^{37} -7.12772e31 q^{38} -5.75480e31 q^{39} +5.59215e31 q^{40} -5.01985e32 q^{41} +6.31408e32 q^{42} -3.11848e33 q^{43} +3.46765e33 q^{44} +5.35289e32 q^{45} +1.41611e34 q^{46} +1.31555e34 q^{47} +6.09724e33 q^{48} -3.03131e34 q^{49} +4.52168e34 q^{50} -1.34782e35 q^{51} -1.25458e34 q^{52} -3.23999e35 q^{53} +2.51251e35 q^{54} -1.52973e35 q^{55} +1.37650e35 q^{56} +3.42834e35 q^{57} -1.43357e35 q^{58} +3.45957e36 q^{59} -2.68975e35 q^{60} -9.78043e35 q^{61} -3.21013e36 q^{62} +1.31761e36 q^{63} +1.32923e36 q^{64} +5.53447e35 q^{65} -1.66790e37 q^{66} +1.66275e37 q^{67} -2.93831e37 q^{68} -6.81131e37 q^{69} -6.07234e36 q^{70} +1.16969e38 q^{71} +1.27236e37 q^{72} +1.90709e38 q^{73} +2.32731e38 q^{74} -2.17487e38 q^{75} +7.47395e37 q^{76} -3.76541e38 q^{77} +6.03435e37 q^{78} -5.61362e38 q^{79} -5.86380e37 q^{80} -8.05974e38 q^{81} +5.26369e38 q^{82} -6.05771e38 q^{83} -6.62079e38 q^{84} +1.29621e39 q^{85} +3.26996e39 q^{86} +6.89527e38 q^{87} -3.63609e39 q^{88} +1.19154e40 q^{89} -5.61291e38 q^{90} +1.36230e39 q^{91} -1.48490e40 q^{92} +1.54403e40 q^{93} -1.37946e40 q^{94} -3.29708e39 q^{95} -6.39342e39 q^{96} -6.35760e40 q^{97} +3.17856e40 q^{98} -3.48052e40 q^{99} +O(q^{100})\)

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 $

$2$	−1.04858e6	−0.707107
$2$	−1.04858e6	−0.707107
$3$	5.04352e9	0.835118	0.417559	−	0.908650i	$-0.362886\pi$
$3$	5.04352e9	0.835118	0.417559	+	0.908650i	$0.362886\pi$
$4$	1.09951e12	0.500000
$5$	−4.85042e13	−0.227454	−0.113727	−	0.993512i	$-0.536279\pi$
$5$	−4.85042e13	−0.227454	−0.113727	+	0.993512i	$0.536279\pi$
$6$	−5.28851e15	−0.590517
$7$	−1.19392e17	−0.565545	−0.282772	−	0.959187i	$-0.591254\pi$
$7$	−1.19392e17	−0.565545	−0.282772	+	0.959187i	$0.591254\pi$
$8$	−1.15292e18	−0.353553
$9$	−1.10359e19	−0.302578
$10$	5.08603e19	0.160835
$11$	3.15381e21	1.41347	0.706733	−	0.707480i	$-0.250168\pi$
$11$	3.15381e21	1.41347	0.706733	+	0.707480i	$0.250168\pi$
$12$	5.54541e21	0.417559
$13$	−1.14103e22	−0.166517	−0.0832585	−	0.996528i	$-0.526533\pi$
$13$	−1.14103e22	−0.166517	−0.0832585	+	0.996528i	$0.526533\pi$
$14$	1.25192e23	0.399901
$15$	−2.44632e23	−0.189951
$16$	1.20893e24	0.250000
$17$	−2.67238e25	−1.59476	−0.797379	−	0.603479i	$-0.793781\pi$
$17$	−2.67238e25	−1.59476	−0.797379	+	0.603479i	$0.793781\pi$
$18$	1.15720e25	0.213955
$19$	6.79752e25	0.414860	0.207430	−	0.978250i	$-0.433490\pi$
$19$	6.79752e25	0.414860	0.207430	+	0.978250i	$0.433490\pi$
$20$	−5.33309e25	−0.113727
$21$	−6.02158e26	−0.472297
$22$	−3.30701e27	−0.999471
$23$	−1.35051e28	−1.64088	−0.820439	−	0.571734i	$-0.806271\pi$
$23$	−1.35051e28	−1.64088	−0.820439	+	0.571734i	$0.806271\pi$
$24$	−5.81478e27	−0.295259
$25$	−4.31221e28	−0.948265
$26$	1.19646e28	0.117745
$27$	−2.39612e29	−1.08781
$28$	−1.31273e29	−0.282772
$29$	1.36715e29	0.143436	0.0717181	−	0.997425i	$-0.477152\pi$
$29$	1.36715e29	0.143436	0.0717181	+	0.997425i	$0.477152\pi$
$30$	2.56515e29	0.134316
$31$	3.06142e30	0.818481	0.409241	−	0.912427i	$-0.365794\pi$
$31$	3.06142e30	0.818481	0.409241	+	0.912427i	$0.365794\pi$
$32$	−1.26765e30	−0.176777
$33$	1.59063e31	1.18041
$34$	2.80219e31	1.12766
$35$	5.79103e30	0.128636
$36$	−1.21341e31	−0.151289
$37$	−2.21949e32	−1.57804	−0.789021	−	0.614366i	$-0.789412\pi$
$37$	−2.21949e32	−1.57804	−0.789021	+	0.614366i	$0.789412\pi$
$38$	−7.12772e31	−0.293350
$39$	−5.75480e31	−0.139061
$40$	5.59215e31	0.0804173
$41$	−5.01985e32	−0.435133	−0.217566	−	0.976046i	$-0.569812\pi$
$41$	−5.01985e32	−0.435133	−0.217566	+	0.976046i	$0.569812\pi$
$42$	6.31408e32	0.333964
$43$	−3.11848e33	−1.01821	−0.509107	−	0.860703i	$-0.670024\pi$
$43$	−3.11848e33	−1.01821	−0.509107	+	0.860703i	$0.670024\pi$
$44$	3.46765e33	0.706733
$45$	5.35289e32	0.0688227
$46$	1.41611e34	1.16028
$47$	1.31555e34	0.693588	0.346794	−	0.937941i	$-0.387270\pi$
$47$	1.31555e34	0.693588	0.346794	+	0.937941i	$0.387270\pi$
$48$	6.09724e33	0.208779
$49$	−3.03131e34	−0.680159
$50$	4.52168e34	0.670524
$51$	−1.34782e35	−1.33181
$52$	−1.25458e34	−0.0832585
$53$	−3.23999e35	−1.45508	−0.727542	−	0.686064i	$-0.759337\pi$
$53$	−3.23999e35	−1.45508	−0.727542	+	0.686064i	$0.759337\pi$
$54$	2.51251e35	0.769195
$55$	−1.52973e35	−0.321499
$56$	1.37650e35	0.199950
$57$	3.42834e35	0.346457
$58$	−1.43357e35	−0.101425
$59$	3.45957e36	1.72408	0.862038	−	0.506844i	$-0.169188\pi$
$59$	3.45957e36	1.72408	0.862038	+	0.506844i	$0.169188\pi$
$60$	−2.68975e35	−0.0949756
$61$	−9.78043e35	−0.246091	−0.123046	−	0.992401i	$-0.539266\pi$
$61$	−9.78043e35	−0.246091	−0.123046	+	0.992401i	$0.539266\pi$
$62$	−3.21013e36	−0.578753
$63$	1.31761e36	0.171122
$64$	1.32923e36	0.125000
$65$	5.53447e35	0.0378750
$66$	−1.66790e37	−0.834676
$67$	1.66275e37	0.611357	0.305678	−	0.952135i	$-0.401117\pi$
$67$	1.66275e37	0.611357	0.305678	+	0.952135i	$0.401117\pi$
$68$	−2.93831e37	−0.797379
$69$	−6.81131e37	−1.37033
$70$	−6.07234e36	−0.0909591
$71$	1.16969e38	1.31001	0.655004	−	0.755625i	$-0.272667\pi$
$71$	1.16969e38	1.31001	0.655004	+	0.755625i	$0.272667\pi$
$72$	1.27236e37	0.106978
$73$	1.90709e38	1.20851	0.604257	−	0.796790i	$-0.293470\pi$
$73$	1.90709e38	1.20851	0.604257	+	0.796790i	$0.293470\pi$
$74$	2.32731e38	1.11584
$75$	−2.17487e38	−0.791913
$76$	7.47395e37	0.207430
$77$	−3.76541e38	−0.799378
$78$	6.03435e37	0.0983311
$79$	−5.61362e38	−0.704511	−0.352256	−	0.935904i	$-0.614585\pi$
$79$	−5.61362e38	−0.704511	−0.352256	+	0.935904i	$0.614585\pi$
$80$	−5.86380e37	−0.0568636
$81$	−8.05974e38	−0.605868
$82$	5.26369e38	0.307685
$83$	−6.05771e38	−0.276190	−0.138095	−	0.990419i	$-0.544098\pi$
$83$	−6.05771e38	−0.276190	−0.138095	+	0.990419i	$0.544098\pi$
$84$	−6.62079e38	−0.236148
$85$	1.29621e39	0.362735
$86$	3.26996e39	0.719987
$87$	6.89527e38	0.119786
$88$	−3.63609e39	−0.499736
$89$	1.19154e40	1.29902	0.649508	−	0.760355i	$-0.274975\pi$
$89$	1.19154e40	1.29902	0.649508	+	0.760355i	$0.274975\pi$
$90$	−5.61291e38	−0.0486650
$91$	1.36230e39	0.0941728
$92$	−1.48490e40	−0.820439
$93$	1.54403e40	0.683528
$94$	−1.37946e40	−0.490441
$95$	−3.29708e39	−0.0943618
$96$	−6.39342e39	−0.147629
$97$	−6.35760e40	−1.18706	−0.593530	−	0.804812i	$-0.702266\pi$
$97$	−6.35760e40	−1.18706	−0.593530	+	0.804812i	$0.702266\pi$
$98$	3.17856e40	0.480945
$99$	−3.48052e40	−0.427684
$100$	−4.74132e40	−0.474132
$101$	6.20987e39	0.0506401	0.0253200	−	0.999679i	$-0.491940\pi$
$101$	6.20987e39	0.0506401	0.0253200	+	0.999679i	$0.491940\pi$
$102$	1.41329e41	0.941732
$103$	1.73412e41	0.946056	0.473028	−	0.881047i	$-0.343161\pi$
$103$	1.73412e41	0.946056	0.473028	+	0.881047i	$0.343161\pi$
$104$	1.31552e40	0.0588726
$105$	2.92072e40	0.107426
$106$	3.39737e41	1.02890
$107$	1.77847e41	0.444304	0.222152	−	0.975012i	$-0.428692\pi$
$107$	1.77847e41	0.444304	0.222152	+	0.975012i	$0.428692\pi$
$108$	−2.63456e41	−0.543903
$109$	−1.02737e42	−1.75583	−0.877916	−	0.478815i	$-0.841066\pi$
$109$	−1.02737e42	−1.75583	−0.877916	+	0.478815i	$0.841066\pi$
$110$	1.60404e41	0.227334
$111$	−1.11941e42	−1.31785
$112$	−1.44337e41	−0.141386
$113$	1.36076e42	1.11089	0.555447	−	0.831552i	$-0.312547\pi$
$113$	1.36076e42	1.11089	0.555447	+	0.831552i	$0.312547\pi$
$114$	−3.59488e41	−0.244982
$115$	6.55053e41	0.373225
$116$	1.50320e41	0.0717181
$117$	1.25923e41	0.0503844
$118$	−3.62763e42	−1.21911
$119$	3.19062e42	0.901907
$120$	2.82041e41	0.0671579
$121$	4.96799e42	0.997886
$122$	1.02555e42	0.174013
$123$	−2.53177e42	−0.363387
$124$	3.36607e42	0.409241
$125$	4.29732e42	0.443141
$126$	−1.38161e42	−0.121001
$127$	−1.25701e43	−0.936185	−0.468092	−	0.883679i	$-0.655059\pi$
$127$	−1.25701e43	−0.936185	−0.468092	+	0.883679i	$0.655059\pi$
$128$	−1.39380e42	−0.0883883
$129$	−1.57281e43	−0.850329
$130$	−5.80332e41	−0.0267817
$131$	−1.14997e43	−0.453551	−0.226776	−	0.973947i	$-0.572818\pi$
$131$	−1.14997e43	−0.453551	−0.226776	+	0.973947i	$0.572818\pi$
$132$	1.74891e43	0.590205
$133$	−8.11573e42	−0.234622
$134$	−1.74352e43	−0.432295
$135$	1.16222e43	0.247426
$136$	3.08104e43	0.563832
$137$	−1.99120e43	−0.313577	−0.156788	−	0.987632i	$-0.550114\pi$
$137$	−1.99120e43	−0.313577	−0.156788	+	0.987632i	$0.550114\pi$
$138$	7.14217e43	0.968967
$139$	8.57436e43	1.00322	0.501612	−	0.865093i	$-0.332740\pi$
$139$	8.57436e43	1.00322	0.501612	+	0.865093i	$0.332740\pi$
$140$	6.36731e42	0.0643178
$141$	6.63501e43	0.579228
$142$	−1.22651e44	−0.926316
$143$	−3.59859e43	−0.235366
$144$	−1.33416e43	−0.0756446
$145$	−6.63127e42	−0.0326252
$146$	−1.99972e44	−0.854548
$147$	−1.52885e44	−0.568013
$148$	−2.44036e44	−0.789021
$149$	2.85509e43	0.0804083	0.0402041	−	0.999191i	$-0.487199\pi$
$149$	2.85509e43	0.0804083	0.0402041	+	0.999191i	$0.487199\pi$
$150$	2.28052e44	0.559967
$151$	1.89816e44	0.406729	0.203365	−	0.979103i	$-0.434812\pi$
$151$	1.89816e44	0.406729	0.203365	+	0.979103i	$0.434812\pi$
$152$	−7.83701e43	−0.146675
$153$	2.94922e44	0.482539
$154$	3.94832e44	0.565246
$155$	−1.48492e44	−0.186167
$156$	−6.32747e43	−0.0695306
$157$	3.84758e44	0.370890	0.185445	−	0.982655i	$-0.440627\pi$
$157$	3.84758e44	0.370890	0.185445	+	0.982655i	$0.440627\pi$
$158$	5.88631e44	0.498165
$159$	−1.63409e45	−1.21517
$160$	6.14864e43	0.0402086
$161$	1.61240e45	0.927990
$162$	8.45125e44	0.428413
$163$	−4.75006e44	−0.212253	−0.106126	−	0.994353i	$-0.533845\pi$
$163$	−4.75006e44	−0.212253	−0.106126	+	0.994353i	$0.533845\pi$
$164$	−5.51938e44	−0.217566
$165$	−7.71522e44	−0.268489
$166$	6.35197e44	0.195296
$167$	−4.32345e45	−1.17528	−0.587642	−	0.809121i	$-0.699944\pi$
$167$	−4.32345e45	−1.17528	−0.587642	+	0.809121i	$0.699944\pi$
$168$	6.94241e44	0.166982
$169$	−4.56526e45	−0.972272
$170$	−1.35918e45	−0.256492
$171$	−7.50170e44	−0.125528
$172$	−3.42880e45	−0.509107
$173$	1.44924e46	1.91072	0.955358	−	0.295452i	$-0.0954703\pi$
$173$	1.44924e46	1.91072	0.955358	+	0.295452i	$0.0954703\pi$
$174$	−7.23021e44	−0.0847016
$175$	5.14845e45	0.536286
$176$	3.81272e45	0.353366
$177$	1.74484e46	1.43981
$178$	−1.24942e46	−0.918543
$179$	5.67669e45	0.372056	0.186028	−	0.982544i	$-0.440439\pi$
$179$	5.67669e45	0.372056	0.186028	+	0.982544i	$0.440439\pi$
$180$	5.88557e44	0.0344114
$181$	−2.20895e46	−1.15286	−0.576429	−	0.817147i	$-0.695554\pi$
$181$	−2.20895e46	−1.15286	−0.576429	+	0.817147i	$0.695554\pi$
$182$	−1.42848e45	−0.0665902
$183$	−4.93278e45	−0.205515
$184$	1.55703e46	0.580138
$185$	1.07655e46	0.358932
$186$	−1.61904e46	−0.483327
$187$	−8.42816e46	−2.25414
$188$	1.44646e46	0.346794
$189$	2.86079e46	0.615203
$190$	3.45724e45	0.0667238
$191$	−6.23395e46	−1.08039	−0.540194	−	0.841541i	$-0.681649\pi$
$191$	−6.23395e46	−1.08039	−0.540194	+	0.841541i	$0.681649\pi$
$192$	6.70398e45	0.104390
$193$	1.06448e47	1.49009	0.745043	−	0.667017i	$-0.232429\pi$
$193$	1.06448e47	1.49009	0.745043	+	0.667017i	$0.232429\pi$
$194$	6.66643e46	0.839378
$195$	2.79132e45	0.0316301
$196$	−3.33296e46	−0.340080
$197$	8.49296e46	0.780731	0.390365	−	0.920660i	$-0.372349\pi$
$197$	8.49296e46	0.780731	0.390365	+	0.920660i	$0.372349\pi$
$198$	3.64959e46	0.302418
$199$	−1.82716e47	−1.36549	−0.682746	−	0.730656i	$-0.739214\pi$
$199$	−1.82716e47	−1.36549	−0.682746	+	0.730656i	$0.739214\pi$
$200$	4.97164e46	0.335262
$201$	8.38613e46	0.510555
$202$	−6.51152e45	−0.0358079
$203$	−1.63228e46	−0.0811196
$204$	−1.48194e47	−0.665905
$205$	2.43484e46	0.0989728
$206$	−1.81836e47	−0.668963
$207$	1.49041e47	0.496494
$208$	−1.37942e46	−0.0416292
$209$	2.14381e47	0.586391
$210$	−3.06259e46	−0.0759616
$211$	−7.87226e47	−1.77137	−0.885684	−	0.464288i	$-0.846310\pi$
$211$	−7.87226e47	−1.77137	−0.885684	+	0.464288i	$0.846310\pi$
$212$	−3.56240e47	−0.727542
$213$	5.89934e47	1.09401
$214$	−1.86487e47	−0.314170
$215$	1.51259e47	0.231597
$216$	2.76254e47	0.384598
$217$	−3.65511e47	−0.462888
$218$	1.07727e48	1.24156
$219$	9.61842e47	1.00925
$220$	−1.68196e47	−0.160749
$221$	3.04926e47	0.265554
$222$	1.17378e48	0.931861
$223$	−1.32160e48	−0.956862	−0.478431	−	0.878125i	$-0.658794\pi$
$223$	−1.32160e48	−0.956862	−0.478431	+	0.878125i	$0.658794\pi$
$224$	1.51348e47	0.0999751
$225$	4.75893e47	0.286924
$226$	−1.42686e48	−0.785521
$227$	−1.43456e48	−0.721419	−0.360710	−	0.932678i	$-0.617465\pi$
$227$	−1.43456e48	−0.721419	−0.360710	+	0.932678i	$0.617465\pi$
$228$	3.76950e47	0.173229
$229$	−3.68923e48	−1.54991	−0.774957	−	0.632014i	$-0.782229\pi$
$229$	−3.68923e48	−1.54991	−0.774957	+	0.632014i	$0.782229\pi$
$230$	−6.86873e47	−0.263910
$231$	−1.89909e48	−0.667575
$232$	−1.57622e47	−0.0507123
$233$	6.32561e48	1.86340	0.931700	−	0.363228i	$-0.118325\pi$
$233$	6.32561e48	1.86340	0.931700	+	0.363228i	$0.118325\pi$
$234$	−1.32040e47	−0.0356272
$235$	−6.38098e47	−0.157760
$236$	3.80384e48	0.862038
$237$	−2.83124e48	−0.588350
$238$	−3.34560e48	−0.637744
$239$	8.39385e48	1.46826	0.734132	−	0.679006i	$-0.237589\pi$
$239$	8.39385e48	1.46826	0.734132	+	0.679006i	$0.237589\pi$
$240$	−2.95742e47	−0.0474878
$241$	2.76168e48	0.407215	0.203608	−	0.979053i	$-0.434733\pi$
$241$	2.76168e48	0.407215	0.203608	+	0.979053i	$0.434733\pi$
$242$	−5.20932e48	−0.705612
$243$	4.67443e48	0.581835
$244$	−1.07537e48	−0.123046
$245$	1.47031e48	0.154705
$246$	2.65475e48	0.256953
$247$	−7.75618e47	−0.0690812
$248$	−3.52958e48	−0.289377
$249$	−3.05522e48	−0.230651
$250$	−4.50606e48	−0.313348
$251$	5.47506e48	0.350814	0.175407	−	0.984496i	$-0.443876\pi$
$251$	5.47506e48	0.350814	0.175407	+	0.984496i	$0.443876\pi$
$252$	1.44872e48	0.0855608
$253$	−4.25924e49	−2.31933
$254$	1.31807e49	0.661983
$255$	6.53748e48	0.302926
$256$	1.46150e48	0.0625000
$257$	−2.41403e49	−0.953045	−0.476522	−	0.879162i	$-0.658103\pi$
$257$	−2.41403e49	−0.953045	−0.476522	+	0.879162i	$0.658103\pi$
$258$	1.64921e49	0.601274
$259$	2.64991e49	0.892453
$260$	6.08522e47	0.0189375
$261$	−1.50878e48	−0.0434007
$262$	1.20583e49	0.320709
$263$	−1.00767e49	−0.247871	−0.123936	−	0.992290i	$-0.539552\pi$
$263$	−1.00767e49	−0.247871	−0.123936	+	0.992290i	$0.539552\pi$
$264$	−1.83387e49	−0.417338
$265$	1.57153e49	0.330965
$266$	8.50996e48	0.165903
$267$	6.00957e49	1.08483
$268$	1.82822e49	0.305678
$269$	−3.47580e49	−0.538435	−0.269217	−	0.963079i	$-0.586765\pi$
$269$	−3.47580e49	−0.538435	−0.269217	+	0.963079i	$0.586765\pi$
$270$	−1.21868e49	−0.174957
$271$	9.20219e49	1.22468	0.612338	−	0.790596i	$-0.290229\pi$
$271$	9.20219e49	1.22468	0.612338	+	0.790596i	$0.290229\pi$
$272$	−3.23070e49	−0.398689
$273$	6.87080e48	0.0786454
$274$	2.08793e49	0.221732
$275$	−1.35999e50	−1.34034
$276$	−7.48911e49	−0.685163
$277$	−1.12019e50	−0.951605	−0.475803	−	0.879552i	$-0.657842\pi$
$277$	−1.12019e50	−0.951605	−0.475803	+	0.879552i	$0.657842\pi$
$278$	−8.99087e49	−0.709387
$279$	−3.37857e49	−0.247655
$280$	−6.67661e48	−0.0454796
$281$	1.13941e50	0.721441	0.360720	−	0.932674i	$-0.382531\pi$
$281$	1.13941e50	0.721441	0.360720	+	0.932674i	$0.382531\pi$
$282$	−6.95731e49	−0.409576
$283$	2.06091e50	1.12833	0.564167	−	0.825661i	$-0.309197\pi$
$283$	2.06091e50	1.12833	0.564167	+	0.825661i	$0.309197\pi$
$284$	1.28609e50	0.655004
$285$	−1.66289e49	−0.0788032
$286$	3.77340e49	0.166429
$287$	5.99332e49	0.246087
$288$	1.39897e49	0.0534888
$289$	4.33354e50	1.54325
$290$	6.95339e48	0.0230695
$291$	−3.20647e50	−0.991335
$292$	2.09686e50	0.604257
$293$	−3.36281e50	−0.903475	−0.451738	−	0.892151i	$-0.649196\pi$
$293$	−3.36281e50	−0.903475	−0.451738	+	0.892151i	$0.649196\pi$
$294$	1.60311e50	0.401646
$295$	−1.67804e50	−0.392149
$296$	2.55890e50	0.557922
$297$	−7.55691e50	−1.53758
$298$	−2.99378e49	−0.0568573
$299$	1.54097e50	0.273234
$300$	−2.39129e50	−0.395956
$301$	3.72323e50	0.575846
$302$	−1.99037e50	−0.287601
$303$	3.13196e49	0.0422904
$304$	8.21770e49	0.103715
$305$	4.74392e49	0.0559746
$306$	−3.09248e50	−0.341207
$307$	−6.52252e50	−0.673099	−0.336550	−	0.941666i	$-0.609260\pi$
$307$	−6.52252e50	−0.673099	−0.336550	+	0.941666i	$0.609260\pi$
$308$	−4.14011e50	−0.399689
$309$	8.74608e50	0.790068
$310$	1.55705e50	0.131640
$311$	−7.73007e50	−0.611781	−0.305890	−	0.952067i	$-0.598954\pi$
$311$	−7.73007e50	−0.611781	−0.305890	+	0.952067i	$0.598954\pi$
$312$	6.63484e49	0.0491656
$313$	2.76877e51	1.92144	0.960722	−	0.277511i	$-0.0895095\pi$
$313$	2.76877e51	1.92144	0.960722	+	0.277511i	$0.0895095\pi$
$314$	−4.03448e50	−0.262259
$315$	−6.39095e49	−0.0389223
$316$	−6.17225e50	−0.352256
$317$	7.05058e50	0.377146	0.188573	−	0.982059i	$-0.439614\pi$
$317$	7.05058e50	0.377146	0.188573	+	0.982059i	$0.439614\pi$
$318$	1.71347e51	0.859252
$319$	4.31174e50	0.202742
$320$	−6.44731e49	−0.0284318
$321$	8.96976e50	0.371046
$322$	−1.69073e51	−0.656188
$323$	−1.81655e51	−0.661601
$324$	−8.86178e50	−0.302934
$325$	4.92036e50	0.157902
$326$	4.98079e50	0.150085
$327$	−5.18155e51	−1.46633
$328$	5.78749e50	0.153843
$329$	−1.57067e51	−0.392255
$330$	8.08999e50	0.189851
$331$	−2.05137e51	−0.452449	−0.226224	−	0.974075i	$-0.572638\pi$
$331$	−2.05137e51	−0.452449	−0.226224	+	0.974075i	$0.572638\pi$
$332$	−6.66052e50	−0.138095
$333$	2.44942e51	0.477481
$334$	4.53347e51	0.831052
$335$	−8.06506e50	−0.139056
$336$	−7.27964e50	−0.118074
$337$	−1.03725e52	−1.58296	−0.791479	−	0.611196i	$-0.790689\pi$
$337$	−1.03725e52	−1.58296	−0.791479	+	0.611196i	$0.790689\pi$
$338$	4.78702e51	0.687500
$339$	6.86301e51	0.927728
$340$	1.42520e51	0.181367
$341$	9.65514e51	1.15689
$342$	7.86611e50	0.0887615
$343$	8.94019e51	0.950205
$344$	3.59536e51	0.359993
$345$	3.30377e51	0.311687
$346$	−1.51964e52	−1.35108
$347$	2.85107e50	0.0238921	0.0119461	−	0.999929i	$-0.496197\pi$
$347$	2.85107e50	0.0238921	0.0119461	+	0.999929i	$0.496197\pi$
$348$	7.58143e50	0.0598931
$349$	−9.31673e51	−0.693973	−0.346986	−	0.937870i	$-0.612795\pi$
$349$	−9.31673e51	−0.693973	−0.346986	+	0.937870i	$0.612795\pi$
$350$	−5.39854e51	−0.379212
$351$	2.73405e51	0.181138
$352$	−3.99793e51	−0.249868
$353$	−1.81721e52	−1.07158	−0.535788	−	0.844353i	$-0.679985\pi$
$353$	−1.81721e52	−1.07158	−0.535788	+	0.844353i	$0.679985\pi$
$354$	−1.82960e52	−1.01810
$355$	−5.67348e51	−0.297967
$356$	1.31012e52	0.649508
$357$	1.60919e52	0.753198
$358$	−5.95244e51	−0.263083
$359$	1.90791e52	0.796384	0.398192	−	0.917302i	$-0.369638\pi$
$359$	1.90791e52	0.796384	0.398192	+	0.917302i	$0.369638\pi$
$360$	−6.17147e50	−0.0243325
$361$	−2.22265e52	−0.827891
$362$	2.31626e52	0.815193
$363$	2.50562e52	0.833352
$364$	1.49787e51	0.0470864
$365$	−9.25016e51	−0.274882
$366$	5.17239e51	0.145321
$367$	−2.11760e52	−0.562586	−0.281293	−	0.959622i	$-0.590763\pi$
$367$	−2.11760e52	−0.562586	−0.281293	+	0.959622i	$0.590763\pi$
$368$	−1.63266e52	−0.410220
$369$	5.53988e51	0.131662
$370$	−1.12884e52	−0.253804
$371$	3.86830e52	0.822915
$372$	1.69768e52	0.341764
$373$	−2.64566e52	−0.504083	−0.252042	−	0.967716i	$-0.581102\pi$
$373$	−2.64566e52	−0.504083	−0.252042	+	0.967716i	$0.581102\pi$
$374$	8.83757e52	1.59391
$375$	2.16736e52	0.370075
$376$	−1.51673e52	−0.245221
$377$	−1.55996e51	−0.0238845
$378$	−2.99975e52	−0.435014
$379$	−6.28388e52	−0.863225	−0.431613	−	0.902059i	$-0.642055\pi$
$379$	−6.28388e52	−0.863225	−0.431613	+	0.902059i	$0.642055\pi$
$380$	−3.62518e51	−0.0471809
$381$	−6.33974e52	−0.781825
$382$	6.53677e52	0.763949
$383$	−7.96221e52	−0.881980	−0.440990	−	0.897512i	$-0.645373\pi$
$383$	−7.96221e52	−0.881980	−0.440990	+	0.897512i	$0.645373\pi$
$384$	−7.02964e51	−0.0738147
$385$	1.82638e52	0.181822
$386$	−1.11618e53	−1.05365
$387$	3.44153e52	0.308090
$388$	−6.99026e52	−0.593530
$389$	−1.09705e53	−0.883607	−0.441803	−	0.897112i	$-0.645661\pi$
$389$	−1.09705e53	−0.883607	−0.441803	+	0.897112i	$0.645661\pi$
$390$	−2.92691e51	−0.0223658
$391$	3.60906e53	2.61680
$392$	3.49486e52	0.240473
$393$	−5.79991e52	−0.378769
$394$	−8.90551e52	−0.552060
$395$	2.72284e52	0.160244
$396$	−3.82688e52	−0.213842
$397$	3.48161e53	1.84746	0.923729	−	0.383046i	$-0.125125\pi$
$397$	3.48161e53	1.84746	0.923729	+	0.383046i	$0.125125\pi$
$398$	1.91592e53	0.965548
$399$	−4.09318e52	−0.195937
$400$	−5.21314e52	−0.237066
$401$	2.78180e52	0.120190	0.0600948	−	0.998193i	$-0.480860\pi$
$401$	2.78180e52	0.120190	0.0600948	+	0.998193i	$0.480860\pi$
$402$	−8.79350e52	−0.361017
$403$	−3.49318e52	−0.136291
$404$	6.82782e51	0.0253200
$405$	3.90931e52	0.137807
$406$	1.71157e52	0.0573602
$407$	−6.99986e53	−2.23051
$408$	1.55393e53	0.470866
$409$	4.34541e52	0.125228	0.0626141	−	0.998038i	$-0.480056\pi$
$409$	4.34541e52	0.125228	0.0626141	+	0.998038i	$0.480056\pi$
$410$	−2.55311e52	−0.0699843
$411$	−1.00427e53	−0.261873
$412$	1.90669e53	0.473028
$413$	−4.13047e53	−0.975042
$414$	−1.56281e53	−0.351074
$415$	2.93824e52	0.0628206
$416$	1.44643e52	0.0294363
$417$	4.32449e53	0.837811
$418$	−2.24795e53	−0.414641
$419$	−5.48344e53	−0.963087	−0.481544	−	0.876422i	$-0.659924\pi$
$419$	−5.48344e53	−0.963087	−0.481544	+	0.876422i	$0.659924\pi$
$420$	3.21136e52	0.0537129
$421$	3.35909e53	0.535105	0.267552	−	0.963543i	$-0.413785\pi$
$421$	3.35909e53	0.535105	0.267552	+	0.963543i	$0.413785\pi$
$422$	8.25466e53	1.25255
$423$	−1.45183e53	−0.209865
$424$	3.73545e53	0.514450
$425$	1.15238e54	1.51225
$426$	−6.18591e53	−0.773583
$427$	1.16771e53	0.139176
$428$	1.95545e53	0.222152
$429$	−1.81496e53	−0.196558
$430$	−1.58607e53	−0.163764
$431$	−7.52113e53	−0.740456	−0.370228	−	0.928941i	$-0.620720\pi$
$431$	−7.52113e53	−0.740456	−0.370228	+	0.928941i	$0.620720\pi$
$432$	−2.89673e53	−0.271952
$433$	1.01171e54	0.905848	0.452924	−	0.891549i	$-0.350381\pi$
$433$	1.01171e54	0.905848	0.452924	+	0.891549i	$0.350381\pi$
$434$	3.83266e53	0.327311
$435$	−3.34449e52	−0.0272459
$436$	−1.12960e54	−0.877916
$437$	−9.18010e53	−0.680735
$438$	−1.00856e54	−0.713648
$439$	1.17795e54	0.795436	0.397718	−	0.917508i	$-0.369802\pi$
$439$	1.17795e54	0.795436	0.397718	+	0.917508i	$0.369802\pi$
$440$	1.76366e53	0.113667
$441$	3.34533e53	0.205801
$442$	−3.19738e53	−0.187775
$443$	5.72043e53	0.320739	0.160370	−	0.987057i	$-0.448731\pi$
$443$	5.72043e53	0.320739	0.160370	+	0.987057i	$0.448731\pi$
$444$	−1.23080e54	−0.658925
$445$	−5.77948e53	−0.295467
$446$	1.38579e54	0.676604
$447$	1.43997e53	0.0671504
$448$	−1.58700e53	−0.0706931
$449$	−2.89270e54	−1.23099	−0.615493	−	0.788142i	$-0.711043\pi$
$449$	−2.89270e54	−1.23099	−0.615493	+	0.788142i	$0.711043\pi$
$450$	−4.99010e53	−0.202886
$451$	−1.58316e54	−0.615045
$452$	1.49617e54	0.555447
$453$	9.57340e53	0.339667
$454$	1.50424e54	0.510121
$455$	−6.60774e52	−0.0214200
$456$	−3.95261e53	−0.122491
$457$	−3.35307e53	−0.0993483	−0.0496742	−	0.998765i	$-0.515818\pi$
$457$	−3.35307e53	−0.0993483	−0.0496742	+	0.998765i	$0.515818\pi$
$458$	3.86843e54	1.09596
$459$	6.40334e54	1.73479
$460$	7.20238e53	0.186612
$461$	6.94064e53	0.172001	0.0860004	−	0.996295i	$-0.472591\pi$
$461$	6.94064e53	0.172001	0.0860004	+	0.996295i	$0.472591\pi$
$462$	1.99134e54	0.472047
$463$	−8.64109e53	−0.195956	−0.0979779	−	0.995189i	$-0.531237\pi$
$463$	−8.64109e53	−0.195956	−0.0979779	+	0.995189i	$0.531237\pi$
$464$	1.65279e53	0.0358590
$465$	−7.48921e53	−0.155471
$466$	−6.63289e54	−1.31762
$467$	−5.75866e54	−1.09478	−0.547388	−	0.836879i	$-0.684378\pi$
$467$	−5.75866e54	−1.09478	−0.547388	+	0.836879i	$0.684378\pi$
$468$	1.38454e53	0.0251922
$469$	−1.98520e54	−0.345750
$470$	6.69094e53	0.111553
$471$	1.94053e54	0.309737
$472$	−3.98862e54	−0.609553
$473$	−9.83508e54	−1.43921
$474$	2.96877e54	0.416026
$475$	−2.93123e54	−0.393397
$476$	3.50812e54	0.450953
$477$	3.57563e54	0.440277
$478$	−8.80159e54	−1.03822
$479$	1.06241e55	1.20065	0.600323	−	0.799757i	$-0.295039\pi$
$479$	1.06241e55	1.20065	0.600323	+	0.799757i	$0.295039\pi$
$480$	3.10108e53	0.0335789
$481$	2.53251e54	0.262771
$482$	−2.89583e54	−0.287945
$483$	8.13219e54	0.774981
$484$	5.46237e54	0.498943
$485$	3.08370e54	0.270002
$486$	−4.90149e54	−0.411420
$487$	2.53731e54	0.204188	0.102094	−	0.994775i	$-0.467446\pi$
$487$	2.53731e54	0.204188	0.102094	+	0.994775i	$0.467446\pi$
$488$	1.12761e54	0.0870065
$489$	−2.39570e54	−0.177256
$490$	−1.54173e54	−0.109393
$491$	1.74013e55	1.18416	0.592080	−	0.805880i	$-0.298307\pi$
$491$	1.74013e55	1.18416	0.592080	+	0.805880i	$0.298307\pi$
$492$	−2.78371e54	−0.181694
$493$	−3.65355e54	−0.228746
$494$	8.13294e53	0.0488478
$495$	1.68820e54	0.0972786
$496$	3.70103e54	0.204620
$497$	−1.39652e55	−0.740868
$498$	3.20363e54	0.163095
$499$	1.71532e54	0.0838079	0.0419039	−	0.999122i	$-0.486658\pi$
$499$	1.71532e54	0.0838079	0.0419039	+	0.999122i	$0.486658\pi$
$500$	4.72495e54	0.221571
$501$	−2.18054e55	−0.981501
$502$	−5.74101e54	−0.248063
$503$	−3.16291e55	−1.31203	−0.656014	−	0.754749i	$-0.727759\pi$
$503$	−3.16291e55	−1.31203	−0.656014	+	0.754749i	$0.727759\pi$
$504$	−1.51910e54	−0.0605006
$505$	−3.01205e53	−0.0115183
$506$	4.46614e55	1.64001
$507$	−2.30250e55	−0.811962
$508$	−1.38209e55	−0.468092
$509$	3.59116e55	1.16821	0.584104	−	0.811679i	$-0.301446\pi$
$509$	3.59116e55	1.16821	0.584104	+	0.811679i	$0.301446\pi$
$510$	−6.85504e54	−0.214201
$511$	−2.27692e55	−0.683469
$512$	−1.53250e54	−0.0441942
$513$	−1.62877e55	−0.451288
$514$	2.53129e55	0.673904
$515$	−8.41122e54	−0.215185
$516$	−1.72932e55	−0.425165
$517$	4.14900e55	0.980364
$518$	−2.77863e55	−0.631060
$519$	7.30928e55	1.59567
$520$	−6.38081e53	−0.0133908
$521$	1.03534e55	0.208885	0.104443	−	0.994531i	$-0.466694\pi$
$521$	1.03534e55	0.208885	0.104443	+	0.994531i	$0.466694\pi$
$522$	1.58207e54	0.0306889
$523$	1.16796e54	0.0217843	0.0108922	−	0.999941i	$-0.496533\pi$
$523$	1.16796e54	0.0217843	0.0108922	+	0.999941i	$0.496533\pi$
$524$	−1.26441e55	−0.226776
$525$	2.59663e55	0.447862
$526$	1.05662e55	0.175272
$527$	−8.18127e55	−1.30528
$528$	1.92295e55	0.295103
$529$	1.14648e56	1.69248
$530$	−1.64787e55	−0.234028
$531$	−3.81796e55	−0.521668
$532$	−8.92334e54	−0.117311
$533$	5.72780e54	0.0724569
$534$	−6.30149e55	−0.767092
$535$	−8.62635e54	−0.101059
$536$	−1.91703e55	−0.216147
$537$	2.86305e55	0.310710
$538$	3.64464e55	0.380731
$539$	−9.56017e55	−0.961382
$540$	1.27787e55	0.123713
$541$	−1.27601e56	−1.18935	−0.594677	−	0.803964i	$-0.702720\pi$
$541$	−1.27601e56	−1.18935	−0.594677	+	0.803964i	$0.702720\pi$
$542$	−9.64920e55	−0.865976
$543$	−1.11409e56	−0.962772
$544$	3.38764e55	0.281916
$545$	4.98317e55	0.399372
$546$	−7.20456e54	−0.0556107
$547$	1.90287e56	1.41472	0.707359	−	0.706854i	$-0.249886\pi$
$547$	1.90287e56	1.41472	0.707359	+	0.706854i	$0.249886\pi$
$548$	−2.18935e55	−0.156788
$549$	1.07936e55	0.0744619
$550$	1.42605e56	0.947763
$551$	9.29326e54	0.0595060
$552$	7.85290e55	0.484484
$553$	6.70224e55	0.398433
$554$	1.17461e56	0.672887
$555$	5.42958e55	0.299751
$556$	9.42761e55	0.501612
$557$	1.52473e55	0.0781921	0.0390960	−	0.999235i	$-0.487552\pi$
$557$	1.52473e55	0.0781921	0.0390960	+	0.999235i	$0.487552\pi$
$558$	3.54268e55	0.175118
$559$	3.55828e55	0.169550
$560$	7.00093e54	0.0321589
$561$	−4.25076e56	−1.88247
$562$	−1.19476e56	−0.510136
$563$	−8.99832e55	−0.370458	−0.185229	−	0.982695i	$-0.559303\pi$
$563$	−8.99832e55	−0.370458	−0.185229	+	0.982695i	$0.559303\pi$
$564$	7.29527e55	0.289614
$565$	−6.60025e55	−0.252678
$566$	−2.16102e56	−0.797853
$567$	9.62272e55	0.342646
$568$	−1.34856e56	−0.463158
$569$	3.81740e56	1.26464	0.632319	−	0.774708i	$-0.282103\pi$
$569$	3.81740e56	1.26464	0.632319	+	0.774708i	$0.282103\pi$
$570$	1.74367e55	0.0557223
$571$	−2.86684e56	−0.883819	−0.441910	−	0.897060i	$-0.645699\pi$
$571$	−2.86684e56	−0.883819	−0.441910	+	0.897060i	$0.645699\pi$
$572$	−3.95669e55	−0.117683
$573$	−3.14410e56	−0.902251
$574$	−6.28445e55	−0.174010
$575$	5.82367e56	1.55599
$576$	−1.46693e55	−0.0378223
$577$	−2.66238e55	−0.0662469	−0.0331235	−	0.999451i	$-0.510545\pi$
$577$	−2.66238e55	−0.0662469	−0.0331235	+	0.999451i	$0.510545\pi$
$578$	−4.54404e56	−1.09124
$579$	5.36870e56	1.24440
$580$	−7.29116e54	−0.0163126
$581$	7.23245e55	0.156198
$582$	3.36222e56	0.700980
$583$	−1.02183e57	−2.05671
$584$	−2.19872e56	−0.427274
$585$	−6.10781e54	−0.0114602
$586$	3.52616e56	0.638853
$587$	7.89073e56	1.38050	0.690250	−	0.723571i	$-0.257501\pi$
$587$	7.89073e56	1.38050	0.690250	+	0.723571i	$0.257501\pi$
$588$	−1.68098e56	−0.284006
$589$	2.08101e56	0.339555
$590$	1.75955e56	0.277291
$591$	4.28344e56	0.652002
$592$	−2.68320e56	−0.394510
$593$	2.06394e56	0.293141	0.146570	−	0.989200i	$-0.453177\pi$
$593$	2.06394e56	0.293141	0.146570	+	0.989200i	$0.453177\pi$
$594$	7.92399e56	1.08723
$595$	−1.54758e56	−0.205143
$596$	3.13920e55	0.0402041
$597$	−9.21532e56	−1.14035
$598$	−1.61582e56	−0.193206
$599$	2.76254e56	0.319196	0.159598	−	0.987182i	$-0.448980\pi$
$599$	2.76254e56	0.319196	0.159598	+	0.987182i	$0.448980\pi$
$600$	2.50745e56	0.279983
$601$	−8.31600e56	−0.897404	−0.448702	−	0.893681i	$-0.648113\pi$
$601$	−8.31600e56	−0.897404	−0.448702	+	0.893681i	$0.648113\pi$
$602$	−3.90409e56	−0.407185
$603$	−1.83501e56	−0.184983
$604$	2.08705e56	0.203365
$605$	−2.40968e56	−0.226973
$606$	−3.28410e55	−0.0299039
$607$	−2.29755e56	−0.202254	−0.101127	−	0.994874i	$-0.532245\pi$
$607$	−2.29755e56	−0.202254	−0.101127	+	0.994874i	$0.532245\pi$
$608$	−8.61688e55	−0.0733376
$609$	−8.23243e55	−0.0677444
$610$	−4.97436e55	−0.0395800
$611$	−1.50108e56	−0.115494
$612$	3.24270e56	0.241270
$613$	−2.25026e57	−1.61917	−0.809585	−	0.587002i	$-0.800308\pi$
$613$	−2.25026e57	−1.61917	−0.809585	+	0.587002i	$0.800308\pi$
$614$	6.83936e56	0.475953
$615$	1.22801e56	0.0826540
$616$	4.34122e56	0.282623
$617$	−3.86090e56	−0.243132	−0.121566	−	0.992583i	$-0.538792\pi$
$617$	−3.86090e56	−0.243132	−0.121566	+	0.992583i	$0.538792\pi$
$618$	−9.17093e56	−0.558663
$619$	1.66300e57	0.980017	0.490008	−	0.871718i	$-0.336994\pi$
$619$	1.66300e57	0.980017	0.490008	+	0.871718i	$0.336994\pi$
$620$	−1.63269e56	−0.0930835
$621$	3.23598e57	1.78496
$622$	8.10557e56	0.432594
$623$	−1.42261e57	−0.734652
$624$	−6.95713e55	−0.0347653
$625$	1.75253e57	0.847470
$626$	−2.90327e57	−1.35867
$627$	1.08123e57	0.489705
$628$	4.23046e56	0.185445
$629$	5.93132e57	2.51659
$630$	6.70140e55	0.0275223
$631$	−1.11322e57	−0.442569	−0.221285	−	0.975209i	$-0.571025\pi$
$631$	−1.11322e57	−0.442569	−0.221285	+	0.975209i	$0.571025\pi$
$632$	6.47207e56	0.249082
$633$	−3.97039e57	−1.47930
$634$	−7.39307e56	−0.266683
$635$	6.09701e56	0.212939
$636$	−1.79670e57	−0.607583
$637$	3.45881e56	0.113258
$638$	−4.52119e56	−0.143360
$639$	−1.29086e57	−0.396380
$640$	6.76050e55	0.0201043
$641$	−4.23006e57	−1.21831	−0.609153	−	0.793053i	$-0.708491\pi$
$641$	−4.23006e57	−1.21831	−0.609153	+	0.793053i	$0.708491\pi$
$642$	−9.40548e56	−0.262369
$643$	−3.65416e57	−0.987330	−0.493665	−	0.869652i	$-0.664343\pi$
$643$	−3.65416e57	−0.987330	−0.493665	+	0.869652i	$0.664343\pi$
$644$	1.77286e57	0.463995
$645$	7.62879e56	0.193411
$646$	1.90479e57	0.467823
$647$	−8.11040e57	−1.92976	−0.964882	−	0.262682i	$-0.915393\pi$
$647$	−8.11040e57	−1.92976	−0.964882	+	0.262682i	$0.915393\pi$
$648$	9.29225e56	0.214207
$649$	1.09108e58	2.43692
$650$	−5.15937e56	−0.111654
$651$	−1.84346e57	−0.386566
$652$	−5.22274e56	−0.106126
$653$	1.52356e57	0.300013	0.150006	−	0.988685i	$-0.452071\pi$
$653$	1.52356e57	0.300013	0.150006	+	0.988685i	$0.452071\pi$
$654$	5.43325e57	1.03685
$655$	5.57786e56	0.103162
$656$	−6.06863e56	−0.108783
$657$	−2.10465e57	−0.365670
$658$	1.64697e57	0.277366
$659$	4.79803e57	0.783271	0.391635	−	0.920120i	$-0.371909\pi$
$659$	4.79803e57	0.783271	0.391635	+	0.920120i	$0.371909\pi$
$660$	−8.48297e56	−0.134245
$661$	−7.23138e56	−0.110941	−0.0554704	−	0.998460i	$-0.517666\pi$
$661$	−7.23138e56	−0.110941	−0.0554704	+	0.998460i	$0.517666\pi$
$662$	2.15101e57	0.319930
$663$	1.53790e57	0.221769
$664$	6.98406e56	0.0976478
$665$	3.93647e56	0.0533658
$666$	−2.56840e57	−0.337630
$667$	−1.84635e57	−0.235361
$668$	−4.75369e57	−0.587642
$669$	−6.66549e57	−0.799092
$670$	8.45683e56	0.0983273
$671$	−3.08456e57	−0.347842
$672$	7.63326e56	0.0834910
$673$	4.08444e57	0.433334	0.216667	−	0.976246i	$-0.430481\pi$
$673$	4.08444e57	0.433334	0.216667	+	0.976246i	$0.430481\pi$
$674$	1.08763e58	1.11932
$675$	1.03326e58	1.03153
$676$	−5.01955e57	−0.486136
$677$	−5.75968e57	−0.541166	−0.270583	−	0.962697i	$-0.587217\pi$
$677$	−5.75968e57	−0.541166	−0.270583	+	0.962697i	$0.587217\pi$
$678$	−7.19638e57	−0.656003
$679$	7.59050e57	0.671336
$680$	−1.49443e57	−0.128246
$681$	−7.23521e57	−0.602470
$682$	−1.01242e58	−0.818048
$683$	−4.27246e56	−0.0335007	−0.0167503	−	0.999860i	$-0.505332\pi$
$683$	−4.27246e56	−0.0335007	−0.0167503	+	0.999860i	$0.505332\pi$
$684$	−8.24821e56	−0.0627639
$685$	9.65817e56	0.0713244
$686$	−9.37447e57	−0.671897
$687$	−1.86067e58	−1.29436
$688$	−3.77001e57	−0.254554
$689$	3.69692e57	0.242296
$690$	−3.46425e57	−0.220396
$691$	2.15615e58	1.33161	0.665807	−	0.746124i	$-0.268088\pi$
$691$	2.15615e58	1.33161	0.665807	+	0.746124i	$0.268088\pi$
$692$	1.59346e58	0.955358
$693$	4.15548e57	0.241875
$694$	−2.98957e56	−0.0168943
$695$	−4.15892e57	−0.228188
$696$	−7.94970e56	−0.0423508
$697$	1.34149e58	0.693931
$698$	9.76930e57	0.490713
$699$	3.19033e58	1.55616
$700$	5.66078e57	0.268143
$701$	−1.34583e58	−0.619113	−0.309557	−	0.950881i	$-0.600181\pi$
$701$	−1.34583e58	−0.619113	−0.309557	+	0.950881i	$0.600181\pi$
$702$	−2.86685e57	−0.128084
$703$	−1.50871e58	−0.654667
$704$	4.19213e57	0.176683
$705$	−3.21826e57	−0.131748
$706$	1.90548e58	0.757719
$707$	−7.41412e56	−0.0286392
$708$	1.91847e58	0.719903
$709$	−4.49893e58	−1.64006	−0.820032	−	0.572317i	$-0.806045\pi$
$709$	−4.49893e58	−1.64006	−0.820032	+	0.572317i	$0.806045\pi$
$710$	5.94908e57	0.210695
$711$	6.19516e57	0.213170
$712$	−1.37376e58	−0.459271
$713$	−4.13447e58	−1.34303
$714$	−1.68736e58	−0.532592
$715$	1.74547e57	0.0535350
$716$	6.24158e57	0.186028
$717$	4.23345e58	1.22617
$718$	−2.00059e58	−0.563128
$719$	−3.60264e58	−0.985550	−0.492775	−	0.870157i	$-0.664017\pi$
$719$	−3.60264e58	−0.985550	−0.492775	+	0.870157i	$0.664017\pi$
$720$	6.47125e56	0.0172057
$721$	−2.07041e58	−0.535037
$722$	2.33062e58	0.585407
$723$	1.39286e58	0.340073
$724$	−2.42877e58	−0.576429
$725$	−5.89546e57	−0.136015
$726$	−2.62733e58	−0.589269
$727$	−1.21072e58	−0.263991	−0.131995	−	0.991250i	$-0.542138\pi$
$727$	−1.21072e58	−0.263991	−0.131995	+	0.991250i	$0.542138\pi$
$728$	−1.57063e57	−0.0332951
$729$	5.29718e58	1.09177
$730$	9.69950e57	0.194371
$731$	8.33375e58	1.62381
$732$	−5.42365e57	−0.102758
$733$	−4.56071e58	−0.840234	−0.420117	−	0.907470i	$-0.638011\pi$
$733$	−4.56071e58	−0.840234	−0.420117	+	0.907470i	$0.638011\pi$
$734$	2.22046e58	0.397808
$735$	7.41554e57	0.129197
$736$	1.71197e58	0.290069
$737$	5.24401e58	0.864132
$738$	−5.80898e57	−0.0930989
$739$	5.98997e58	0.933713	0.466857	−	0.884333i	$-0.345386\pi$
$739$	5.98997e58	0.933713	0.466857	+	0.884333i	$0.345386\pi$
$740$	1.18368e58	0.179466
$741$	−3.91184e57	−0.0576910
$742$	−4.05620e58	−0.581889
$743$	−1.60800e58	−0.224395	−0.112198	−	0.993686i	$-0.535789\pi$
$743$	−1.60800e58	−0.224395	−0.112198	+	0.993686i	$0.535789\pi$
$744$	−1.78015e58	−0.241664
$745$	−1.38484e57	−0.0182892
$746$	2.77417e58	0.356441
$747$	6.68525e57	0.0835690
$748$	−9.26686e58	−1.12707
$749$	−2.12336e58	−0.251274
$750$	−2.27264e58	−0.261683
$751$	−1.29410e59	−1.44994	−0.724970	−	0.688781i	$-0.758146\pi$
$751$	−1.29410e59	−1.44994	−0.724970	+	0.688781i	$0.758146\pi$
$752$	1.59040e58	0.173397
$753$	2.76135e58	0.292971
$754$	1.63574e57	0.0168889
$755$	−9.20687e57	−0.0925123
$756$	3.14547e58	0.307602
$757$	1.04679e59	0.996312	0.498156	−	0.867088i	$-0.334011\pi$
$757$	1.04679e59	0.996312	0.498156	+	0.867088i	$0.334011\pi$
$758$	6.58913e58	0.610392
$759$	−2.14816e59	−1.93691
$760$	3.80128e57	0.0333619
$761$	−5.22023e58	−0.445969	−0.222984	−	0.974822i	$-0.571580\pi$
$761$	−5.22023e58	−0.445969	−0.222984	+	0.974822i	$0.571580\pi$
$762$	6.64770e58	0.552834
$763$	1.22660e59	0.993002
$764$	−6.85430e58	−0.540194
$765$	−1.43049e58	−0.109756
$766$	8.34899e58	0.623654
$767$	−3.94748e58	−0.287088
$768$	7.37111e57	0.0521949
$769$	−1.14958e59	−0.792592	−0.396296	−	0.918123i	$-0.629705\pi$
$769$	−1.14958e59	−0.792592	−0.396296	+	0.918123i	$0.629705\pi$
$770$	−1.91510e58	−0.128568
$771$	−1.21752e59	−0.795904
$772$	1.17040e59	0.745043
$773$	2.16390e59	1.34140	0.670699	−	0.741729i	$-0.265994\pi$
$773$	2.16390e59	1.34140	0.670699	+	0.741729i	$0.265994\pi$
$774$	−3.60871e58	−0.217852
$775$	−1.32015e59	−0.776137
$776$	7.32981e58	0.419689
$777$	1.33649e59	0.745304
$778$	1.15034e59	0.624804
$779$	−3.41225e58	−0.180519
$780$	3.06909e57	0.0158150
$781$	3.68897e59	1.85165
$782$	−3.78438e59	−1.85036
$783$	−3.27587e58	−0.156031
$784$	−3.66463e58	−0.170040
$785$	−1.86624e58	−0.0843605
$786$	6.08165e58	0.267830
$787$	3.26265e59	1.39987	0.699937	−	0.714204i	$-0.253211\pi$
$787$	3.26265e59	1.39987	0.699937	+	0.714204i	$0.253211\pi$
$788$	9.33811e58	0.390365
$789$	−5.08221e58	−0.207002
$790$	−2.85511e58	−0.113310
$791$	−1.62464e59	−0.628261
$792$	4.01277e58	0.151209
$793$	1.11598e58	0.0409784
$794$	−3.65073e59	−1.30635
$795$	7.92603e58	0.276395
$796$	−2.00899e59	−0.682746
$797$	−5.37864e59	−1.78146	−0.890731	−	0.454530i	$-0.849807\pi$
$797$	−5.37864e59	−1.78146	−0.890731	+	0.454530i	$0.849807\pi$
$798$	4.29201e58	0.138548
$799$	−3.51565e59	−1.10611
$800$	5.46637e58	0.167631
$801$	−1.31498e59	−0.393054
$802$	−2.91693e58	−0.0849868
$803$	6.01458e59	1.70819
$804$	9.22065e58	0.255277
$805$	−7.82083e58	−0.211075
$806$	3.66286e58	0.0963722
$807$	−1.75303e59	−0.449657
$808$	−7.15949e57	−0.0179040
$809$	−7.04425e58	−0.171747	−0.0858737	−	0.996306i	$-0.527368\pi$
$809$	−7.04425e58	−0.171747	−0.0858737	+	0.996306i	$0.527368\pi$
$810$	−4.09921e58	−0.0974445
$811$	6.75289e59	1.56517	0.782586	−	0.622543i	$-0.213900\pi$
$811$	6.75289e59	1.56517	0.782586	+	0.622543i	$0.213900\pi$
$812$	−1.79471e58	−0.0405598
$813$	4.64114e59	1.02275
$814$	7.33988e59	1.57721
$815$	2.30398e58	0.0482778
$816$	−1.62941e59	−0.332953
$817$	−2.11979e59	−0.422417
$818$	−4.55649e58	−0.0885498
$819$	−1.50343e58	−0.0284946
$820$	2.67713e58	0.0494864
$821$	1.04795e59	0.188932	0.0944659	−	0.995528i	$-0.469886\pi$
$821$	1.04795e59	0.188932	0.0944659	+	0.995528i	$0.469886\pi$
$822$	1.05305e59	0.185172
$823$	2.14107e57	0.00367227	0.00183614	−	0.999998i	$-0.499416\pi$
$823$	2.14107e57	0.00367227	0.00183614	+	0.999998i	$0.499416\pi$
$824$	−1.99931e59	−0.334481
$825$	−6.85912e59	−1.11934
$826$	4.33111e59	0.689459
$827$	−3.28295e58	−0.0509802	−0.0254901	−	0.999675i	$-0.508115\pi$
$827$	−3.28295e58	−0.0509802	−0.0254901	+	0.999675i	$0.508115\pi$
$828$	1.63872e59	0.248247
$829$	−7.20495e59	−1.06479	−0.532394	−	0.846497i	$-0.678707\pi$
$829$	−7.20495e59	−1.06479	−0.532394	+	0.846497i	$0.678707\pi$
$830$	−3.08097e58	−0.0444208
$831$	−5.64970e59	−0.794703
$832$	−1.51669e58	−0.0208146
$833$	8.10080e59	1.08469
$834$	−4.53456e59	−0.592422
$835$	2.09706e59	0.267324
$836$	2.35714e59	0.293195
$837$	−7.33554e59	−0.890349
$838$	5.74980e59	0.681006
$839$	−2.37196e59	−0.274149	−0.137074	−	0.990561i	$-0.543770\pi$
$839$	−2.37196e59	−0.274149	−0.137074	+	0.990561i	$0.543770\pi$
$840$	−3.36736e58	−0.0379808
$841$	−8.89794e59	−0.979426
$842$	−3.52226e59	−0.378376
$843$	5.74664e59	0.602488
$844$	−8.65564e59	−0.885684
$845$	2.21434e59	0.221148
$846$	1.52236e59	0.148397
$847$	−5.93141e59	−0.564349
$848$	−3.91690e59	−0.363771
$849$	1.03942e60	0.942292
$850$	−1.20836e60	−1.06932
$851$	2.99744e60	2.58937
$852$	6.48640e59	0.547006
$853$	1.03258e59	0.0850096	0.0425048	−	0.999096i	$-0.486466\pi$
$853$	1.03258e59	0.0850096	0.0425048	+	0.999096i	$0.486466\pi$
$854$	−1.22443e59	−0.0984121
$855$	3.63864e58	0.0285518
$856$	−2.05044e59	−0.157085
$857$	1.28058e60	0.957852	0.478926	−	0.877855i	$-0.341026\pi$
$857$	1.28058e60	0.957852	0.478926	+	0.877855i	$0.341026\pi$
$858$	1.90312e59	0.138988
$859$	−1.16067e60	−0.827657	−0.413828	−	0.910355i	$-0.635809\pi$
$859$	−1.16067e60	−0.827657	−0.413828	+	0.910355i	$0.635809\pi$
$860$	1.66311e59	0.115799
$861$	3.02274e59	0.205512
$862$	7.88648e59	0.523581
$863$	−1.19897e60	−0.777296	−0.388648	−	0.921386i	$-0.627058\pi$
$863$	−1.19897e60	−0.777296	−0.388648	+	0.921386i	$0.627058\pi$
$864$	3.03744e59	0.192299
$865$	−7.02943e59	−0.434600
$866$	−1.06086e60	−0.640531
$867$	2.18563e60	1.28880
$868$	−4.01883e59	−0.231444
$869$	−1.77043e60	−0.995803
$870$	3.50696e58	0.0192657
$871$	−1.89725e59	−0.101801
$872$	1.18447e60	0.620780
$873$	7.01621e59	0.359179
$874$	9.62604e59	0.481352
$875$	−5.13067e59	−0.250616
$876$	1.05756e60	0.504626
$877$	−1.62618e60	−0.758014	−0.379007	−	0.925394i	$-0.623734\pi$
$877$	−1.62618e60	−0.758014	−0.379007	+	0.925394i	$0.623734\pi$
$878$	−1.23517e60	−0.562459
$879$	−1.69604e60	−0.754508
$880$	−1.84933e59	−0.0803747
$881$	5.20975e59	0.221213	0.110607	−	0.993864i	$-0.464721\pi$
$881$	5.20975e59	0.221213	0.110607	+	0.993864i	$0.464721\pi$
$882$	−3.50784e59	−0.145524
$883$	−1.27377e60	−0.516292	−0.258146	−	0.966106i	$-0.583112\pi$
$883$	−1.27377e60	−0.516292	−0.258146	+	0.966106i	$0.583112\pi$
$884$	3.35270e59	0.132777
$885$	−8.46322e59	−0.327490
$886$	−5.99831e59	−0.226797
$887$	−1.40271e60	−0.518243	−0.259122	−	0.965845i	$-0.583433\pi$
$887$	−1.40271e60	−0.518243	−0.259122	+	0.965845i	$0.583433\pi$
$888$	1.29059e60	0.465931
$889$	1.50077e60	0.529455
$890$	6.06023e59	0.208927
$891$	−2.54189e60	−0.856374
$892$	−1.45311e60	−0.478431
$893$	8.94249e59	0.287742
$894$	−1.50992e59	−0.0474825
$895$	−2.75343e59	−0.0846256
$896$	1.66409e59	0.0499876
$897$	7.77190e59	0.228183
$898$	3.03321e60	0.870439
$899$	4.18544e59	0.117400
$900$	5.23249e59	0.143462
$901$	8.65846e60	2.32050
$902$	1.66007e60	0.434903
$903$	1.87782e60	0.480899
$904$	−1.56885e60	−0.392761
$905$	1.07143e60	0.262222
$906$	−1.00384e60	−0.240181
$907$	1.32324e60	0.309519	0.154760	−	0.987952i	$-0.450540\pi$
$907$	1.32324e60	0.309519	0.154760	+	0.987952i	$0.450540\pi$
$908$	−1.57731e60	−0.360710
$909$	−6.85317e58	−0.0153226
$910$	6.92872e58	0.0151462
$911$	−4.51973e60	−0.966019	−0.483009	−	0.875615i	$-0.660456\pi$
$911$	−4.51973e60	−0.966019	−0.483009	+	0.875615i	$0.660456\pi$
$912$	4.14461e59	0.0866143
$913$	−1.91049e60	−0.390385
$914$	3.51595e59	0.0702499
$915$	2.39260e59	0.0467454
$916$	−4.05635e60	−0.774957
$917$	1.37298e60	0.256504
$918$	−6.71438e60	−1.22668
$919$	−3.08144e60	−0.550536	−0.275268	−	0.961368i	$-0.588767\pi$
$919$	−3.08144e60	−0.550536	−0.275268	+	0.961368i	$0.588767\pi$
$920$	−7.55224e59	−0.131955
$921$	−3.28965e60	−0.562117
$922$	−7.27779e59	−0.121623
$923$	−1.33465e60	−0.218139
$924$	−2.08807e60	−0.333788
$925$	9.57092e60	1.49640
$926$	9.06084e59	0.138562
$927$	−1.91377e60	−0.286256
$928$	−1.73307e59	−0.0253562
$929$	−3.19320e60	−0.456987	−0.228494	−	0.973545i	$-0.573380\pi$
$929$	−3.19320e60	−0.456987	−0.228494	+	0.973545i	$0.573380\pi$
$930$	7.85301e59	0.109935
$931$	−2.06054e60	−0.282171
$932$	6.95509e60	0.931700
$933$	−3.89868e60	−0.510909
$934$	6.03839e60	0.774124
$935$	4.08801e60	0.512713
$936$	−1.45180e59	−0.0178136
$937$	−1.07427e60	−0.128959	−0.0644794	−	0.997919i	$-0.520539\pi$
$937$	−1.07427e60	−0.128959	−0.0644794	+	0.997919i	$0.520539\pi$
$938$	2.08164e60	0.244482
$939$	1.39643e61	1.60463
$940$	−7.01596e59	−0.0788799
$941$	−1.47841e61	−1.62633	−0.813164	−	0.582035i	$-0.802257\pi$
$941$	−1.47841e61	−1.62633	−0.813164	+	0.582035i	$0.802257\pi$
$942$	−2.03480e60	−0.219017
$943$	6.77934e60	0.714000
$944$	4.18237e60	0.431019
$945$	−1.38760e60	−0.139931
$946$	1.03128e61	1.01768
$947$	−8.72067e60	−0.842122	−0.421061	−	0.907032i	$-0.638342\pi$
$947$	−8.72067e60	−0.842122	−0.421061	+	0.907032i	$0.638342\pi$
$948$	−3.11298e60	−0.294175
$949$	−2.17604e60	−0.201238
$950$	3.07362e60	0.278174
$951$	3.55597e60	0.314962
$952$	−3.67853e60	−0.318872
$953$	6.02037e59	0.0510762	0.0255381	−	0.999674i	$-0.491870\pi$
$953$	6.02037e59	0.0510762	0.0255381	+	0.999674i	$0.491870\pi$
$954$	−3.74932e60	−0.311323
$955$	3.02373e60	0.245739
$956$	9.22914e60	0.734132
$957$	2.17464e60	0.169314
$958$	−1.11402e61	−0.848986
$959$	2.37735e60	0.177342
$960$	−3.25171e59	−0.0237439
$961$	−4.61807e60	−0.330089
$962$	−2.65553e60	−0.185807
$963$	−1.96271e60	−0.134437
$964$	3.03650e60	0.203608
$965$	−5.16316e60	−0.338926
$966$	−8.52721e60	−0.547994
$967$	1.85730e61	1.16853	0.584266	−	0.811562i	$-0.301383\pi$
$967$	1.85730e61	1.16853	0.584266	+	0.811562i	$0.301383\pi$
$968$	−5.72771e60	−0.352806
$969$	−9.16182e60	−0.552515
$970$	−3.23350e60	−0.190920
$971$	−2.80101e61	−1.61928	−0.809638	−	0.586929i	$-0.800337\pi$
$971$	−2.80101e61	−1.61928	−0.809638	+	0.586929i	$0.800337\pi$
$972$	5.13959e60	0.290918
$973$	−1.02371e61	−0.567369
$974$	−2.66057e60	−0.144383
$975$	2.48159e60	0.131867
$976$	−1.18238e60	−0.0615229
$977$	2.94713e60	0.150162	0.0750812	−	0.997177i	$-0.476078\pi$
$977$	2.94713e60	0.150162	0.0750812	+	0.997177i	$0.476078\pi$
$978$	2.51207e60	0.125339
$979$	3.75790e61	1.83611
$980$	1.61662e60	0.0773526
$981$	1.13380e61	0.531277
$982$	−1.82465e61	−0.837327
$983$	1.11718e61	0.502084	0.251042	−	0.967976i	$-0.419227\pi$
$983$	1.11718e61	0.502084	0.251042	+	0.967976i	$0.419227\pi$
$984$	2.91893e60	0.128477
$985$	−4.11944e60	−0.177581
$986$	3.83103e60	0.161748
$987$	−7.92170e60	−0.327579
$988$	−8.52801e59	−0.0345406
$989$	4.21153e61	1.67077
$990$	−1.77021e60	−0.0687864
$991$	−9.78682e60	−0.372505	−0.186252	−	0.982502i	$-0.559634\pi$
$991$	−9.78682e60	−0.372505	−0.186252	+	0.982502i	$0.559634\pi$
$992$	−3.88081e60	−0.144688
$993$	−1.03461e61	−0.377848
$994$	1.46436e61	0.523873
$995$	8.86250e60	0.310587
$996$	−3.35925e60	−0.115325
$997$	−1.62230e61	−0.545609	−0.272805	−	0.962069i	$-0.587951\pi$
$997$	−1.62230e61	−0.545609	−0.272805	+	0.962069i	$0.587951\pi$
$998$	−1.79865e60	−0.0592611
$999$	5.31817e61	1.71660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.42.a.a.1.1	✓	1
3.2	odd	2		18.42.a.b.1.1		1
4.3	odd	2		16.42.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.42.a.a.1.1	✓	1	1.1	even	1	trivial
16.42.a.a.1.1		1	4.3	odd	2
18.42.a.b.1.1		1	3.2	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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