LMFDB - Embedded newform 64.14.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,14,Mod(1,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	64.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:	$68.6277945292$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1236.00 q^{3} +57450.0 q^{5} -64232.0 q^{7} -66627.0 q^{9} +O(q^{10})$

$q+1236.00 q^{3} +57450.0 q^{5} -64232.0 q^{7} -66627.0 q^{9} +2.46457e6 q^{11} -8.03277e6 q^{13} +7.10082e7 q^{15} +7.11124e7 q^{17} +1.36337e8 q^{19} -7.93908e7 q^{21} +1.18656e9 q^{23} +2.07980e9 q^{25} -2.05293e9 q^{27} +8.90583e8 q^{29} -4.59555e9 q^{31} +3.04621e9 q^{33} -3.69013e9 q^{35} +1.95851e10 q^{37} -9.92850e9 q^{39} -2.72417e9 q^{41} +5.17623e10 q^{43} -3.82772e9 q^{45} +5.35728e10 q^{47} -9.27633e10 q^{49} +8.78949e10 q^{51} -8.26334e10 q^{53} +1.41590e11 q^{55} +1.68513e11 q^{57} -3.94266e11 q^{59} -6.71062e11 q^{61} +4.27959e9 q^{63} -4.61482e11 q^{65} +3.88156e11 q^{67} +1.46659e12 q^{69} +3.88772e11 q^{71} +1.54097e12 q^{73} +2.57063e12 q^{75} -1.58304e11 q^{77} +3.30651e12 q^{79} -2.43120e12 q^{81} +4.93176e12 q^{83} +4.08541e12 q^{85} +1.10076e12 q^{87} +3.50295e12 q^{89} +5.15961e11 q^{91} -5.68010e12 q^{93} +7.83256e12 q^{95} -3.88933e11 q^{97} -1.64207e11 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	1236.00	0.978882	0.489441	−	0.872036i	$-0.337201\pi$
$3$	1236.00	0.978882	0.489441	+	0.872036i	$0.337201\pi$
$4$	0	0
$5$	57450.0	1.64431	0.822157	−	0.569260i	$-0.192770\pi$
$5$	57450.0	1.64431	0.822157	+	0.569260i	$0.192770\pi$
$6$	0	0
$7$	−64232.0	−0.206355	−0.103177	−	0.994663i	$-0.532901\pi$
$7$	−64232.0	−0.206355	−0.103177	+	0.994663i	$0.532901\pi$
$8$	0	0
$9$	−66627.0	−0.0417902
$10$	0	0
$11$	2.46457e6	0.419459	0.209729	−	0.977759i	$-0.432742\pi$
$11$	2.46457e6	0.419459	0.209729	+	0.977759i	$0.432742\pi$
$12$	0	0
$13$	−8.03277e6	−0.461565	−0.230783	−	0.973005i	$-0.574129\pi$
$13$	−8.03277e6	−0.461565	−0.230783	+	0.973005i	$0.574129\pi$
$14$	0	0
$15$	7.10082e7	1.60959
$16$	0	0
$17$	7.11124e7	0.714541	0.357271	−	0.934001i	$-0.383707\pi$
$17$	7.11124e7	0.714541	0.357271	+	0.934001i	$0.383707\pi$
$18$	0	0
$19$	1.36337e8	0.664838	0.332419	−	0.943132i	$-0.392135\pi$
$19$	1.36337e8	0.664838	0.332419	+	0.943132i	$0.392135\pi$
$20$	0	0
$21$	−7.93908e7	−0.201997
$22$	0	0
$23$	1.18656e9	1.67132	0.835661	−	0.549246i	$-0.185085\pi$
$23$	1.18656e9	1.67132	0.835661	+	0.549246i	$0.185085\pi$
$24$	0	0
$25$	2.07980e9	1.70377
$26$	0	0
$27$	−2.05293e9	−1.01979
$28$	0	0
$29$	8.90583e8	0.278027	0.139014	−	0.990290i	$-0.455607\pi$
$29$	8.90583e8	0.278027	0.139014	+	0.990290i	$0.455607\pi$
$30$	0	0
$31$	−4.59555e9	−0.930008	−0.465004	−	0.885309i	$-0.653947\pi$
$31$	−4.59555e9	−0.930008	−0.465004	+	0.885309i	$0.653947\pi$
$32$	0	0
$33$	3.04621e9	0.410600
$34$	0	0
$35$	−3.69013e9	−0.339312
$36$	0	0
$37$	1.95851e10	1.25491	0.627456	−	0.778652i	$-0.284096\pi$
$37$	1.95851e10	1.25491	0.627456	+	0.778652i	$0.284096\pi$
$38$	0	0
$39$	−9.92850e9	−0.451818
$40$	0	0
$41$	−2.72417e9	−0.0895652	−0.0447826	−	0.998997i	$-0.514260\pi$
$41$	−2.72417e9	−0.0895652	−0.0447826	+	0.998997i	$0.514260\pi$
$42$	0	0
$43$	5.17623e10	1.24873	0.624365	−	0.781132i	$-0.285358\pi$
$43$	5.17623e10	1.24873	0.624365	+	0.781132i	$0.285358\pi$
$44$	0	0
$45$	−3.82772e9	−0.0687162
$46$	0	0
$47$	5.35728e10	0.724951	0.362475	−	0.931993i	$-0.381932\pi$
$47$	5.35728e10	0.724951	0.362475	+	0.931993i	$0.381932\pi$
$48$	0	0
$49$	−9.27633e10	−0.957418
$50$	0	0
$51$	8.78949e10	0.699452
$52$	0	0
$53$	−8.26334e10	−0.512109	−0.256055	−	0.966662i	$-0.582423\pi$
$53$	−8.26334e10	−0.512109	−0.256055	+	0.966662i	$0.582423\pi$
$54$	0	0
$55$	1.41590e11	0.689722
$56$	0	0
$57$	1.68513e11	0.650797
$58$	0	0
$59$	−3.94266e11	−1.21689	−0.608445	−	0.793596i	$-0.708207\pi$
$59$	−3.94266e11	−1.21689	−0.608445	+	0.793596i	$0.708207\pi$
$60$	0	0
$61$	−6.71062e11	−1.66770	−0.833851	−	0.551989i	$-0.813869\pi$
$61$	−6.71062e11	−1.66770	−0.833851	+	0.551989i	$0.813869\pi$
$62$	0	0
$63$	4.27959e9	0.00862359
$64$	0	0
$65$	−4.61482e11	−0.758959
$66$	0	0
$67$	3.88156e11	0.524228	0.262114	−	0.965037i	$-0.415580\pi$
$67$	3.88156e11	0.524228	0.262114	+	0.965037i	$0.415580\pi$
$68$	0	0
$69$	1.46659e12	1.63603
$70$	0	0
$71$	3.88772e11	0.360177	0.180089	−	0.983650i	$-0.442362\pi$
$71$	3.88772e11	0.360177	0.180089	+	0.983650i	$0.442362\pi$
$72$	0	0
$73$	1.54097e12	1.19178	0.595890	−	0.803066i	$-0.296799\pi$
$73$	1.54097e12	1.19178	0.595890	+	0.803066i	$0.296799\pi$
$74$	0	0
$75$	2.57063e12	1.66779
$76$	0	0
$77$	−1.58304e11	−0.0865572
$78$	0	0
$79$	3.30651e12	1.53036	0.765180	−	0.643816i	$-0.222650\pi$
$79$	3.30651e12	1.53036	0.765180	+	0.643816i	$0.222650\pi$
$80$	0	0
$81$	−2.43120e12	−0.956463
$82$	0	0
$83$	4.93176e12	1.65575	0.827874	−	0.560915i	$-0.189550\pi$
$83$	4.93176e12	1.65575	0.827874	+	0.560915i	$0.189550\pi$
$84$	0	0
$85$	4.08541e12	1.17493
$86$	0	0
$87$	1.10076e12	0.272156
$88$	0	0
$89$	3.50295e12	0.747135	0.373567	−	0.927603i	$-0.378134\pi$
$89$	3.50295e12	0.747135	0.373567	+	0.927603i	$0.378134\pi$
$90$	0	0
$91$	5.15961e11	0.0952462
$92$	0	0
$93$	−5.68010e12	−0.910368
$94$	0	0
$95$	7.83256e12	1.09320
$96$	0	0
$97$	−3.88933e11	−0.0474087	−0.0237044	−	0.999719i	$-0.507546\pi$
$97$	−3.88933e11	−0.0474087	−0.0237044	+	0.999719i	$0.507546\pi$
$98$	0	0
$99$	−1.64207e11	−0.0175292
$100$	0	0
$101$	−1.05696e13	−0.990764	−0.495382	−	0.868675i	$-0.664972\pi$
$101$	−1.05696e13	−0.990764	−0.495382	+	0.868675i	$0.664972\pi$
$102$	0	0
$103$	5.68637e12	0.469238	0.234619	−	0.972087i	$-0.424616\pi$
$103$	5.68637e12	0.469238	0.234619	+	0.972087i	$0.424616\pi$
$104$	0	0
$105$	−4.56100e12	−0.332146
$106$	0	0
$107$	−1.67196e12	−0.107704	−0.0538520	−	0.998549i	$-0.517150\pi$
$107$	−1.67196e12	−0.107704	−0.0538520	+	0.998549i	$0.517150\pi$
$108$	0	0
$109$	8.36468e11	0.0477724	0.0238862	−	0.999715i	$-0.492396\pi$
$109$	8.36468e11	0.0477724	0.0238862	+	0.999715i	$0.492396\pi$
$110$	0	0
$111$	2.42071e13	1.22841
$112$	0	0
$113$	−3.63881e12	−0.164418	−0.0822089	−	0.996615i	$-0.526197\pi$
$113$	−3.63881e12	−0.164418	−0.0822089	+	0.996615i	$0.526197\pi$
$114$	0	0
$115$	6.81681e13	2.74818
$116$	0	0
$117$	5.35199e11	0.0192889
$118$	0	0
$119$	−4.56769e12	−0.147449
$120$	0	0
$121$	−2.84486e13	−0.824055
$122$	0	0
$123$	−3.36707e12	−0.0876737
$124$	0	0
$125$	4.93551e13	1.15722
$126$	0	0
$127$	3.59301e13	0.759860	0.379930	−	0.925015i	$-0.375948\pi$
$127$	3.59301e13	0.759860	0.379930	+	0.925015i	$0.375948\pi$
$128$	0	0
$129$	6.39782e13	1.22236
$130$	0	0
$131$	−2.05411e13	−0.355108	−0.177554	−	0.984111i	$-0.556818\pi$
$131$	−2.05411e13	−0.355108	−0.177554	+	0.984111i	$0.556818\pi$
$132$	0	0
$133$	−8.75720e12	−0.137192
$134$	0	0
$135$	−1.17941e14	−1.67686
$136$	0	0
$137$	−4.24002e12	−0.0547879	−0.0273939	−	0.999625i	$-0.508721\pi$
$137$	−4.24002e12	−0.0547879	−0.0273939	+	0.999625i	$0.508721\pi$
$138$	0	0
$139$	−6.70911e13	−0.788985	−0.394492	−	0.918899i	$-0.629080\pi$
$139$	−6.70911e13	−0.788985	−0.394492	+	0.918899i	$0.629080\pi$
$140$	0	0
$141$	6.62160e13	0.709641
$142$	0	0
$143$	−1.97973e13	−0.193608
$144$	0	0
$145$	5.11640e13	0.457164
$146$	0	0
$147$	−1.14655e14	−0.937199
$148$	0	0
$149$	−1.97426e14	−1.47807	−0.739033	−	0.673669i	$-0.764717\pi$
$149$	−1.97426e14	−1.47807	−0.739033	+	0.673669i	$0.764717\pi$
$150$	0	0
$151$	5.70163e13	0.391425	0.195713	−	0.980661i	$-0.437298\pi$
$151$	5.70163e13	0.391425	0.195713	+	0.980661i	$0.437298\pi$
$152$	0	0
$153$	−4.73801e12	−0.0298608
$154$	0	0
$155$	−2.64015e14	−1.52923
$156$	0	0
$157$	−5.89786e13	−0.314302	−0.157151	−	0.987575i	$-0.550231\pi$
$157$	−5.89786e13	−0.314302	−0.157151	+	0.987575i	$0.550231\pi$
$158$	0	0
$159$	−1.02135e14	−0.501295
$160$	0	0
$161$	−7.62153e13	−0.344885
$162$	0	0
$163$	3.63206e14	1.51682	0.758410	−	0.651778i	$-0.225977\pi$
$163$	3.63206e14	1.51682	0.758410	+	0.651778i	$0.225977\pi$
$164$	0	0
$165$	1.75005e14	0.675156
$166$	0	0
$167$	−2.29455e14	−0.818542	−0.409271	−	0.912413i	$-0.634217\pi$
$167$	−2.29455e14	−0.818542	−0.409271	+	0.912413i	$0.634217\pi$
$168$	0	0
$169$	−2.38350e14	−0.786957
$170$	0	0
$171$	−9.08373e12	−0.0277837
$172$	0	0
$173$	−2.62985e14	−0.745817	−0.372908	−	0.927868i	$-0.621639\pi$
$173$	−2.62985e14	−0.745817	−0.372908	+	0.927868i	$0.621639\pi$
$174$	0	0
$175$	−1.33590e14	−0.351581
$176$	0	0
$177$	−4.87313e14	−1.19119
$178$	0	0
$179$	−8.66397e14	−1.96867	−0.984334	−	0.176315i	$-0.943582\pi$
$179$	−8.66397e14	−1.96867	−0.984334	+	0.176315i	$0.943582\pi$
$180$	0	0
$181$	4.81127e14	1.01707	0.508533	−	0.861043i	$-0.330188\pi$
$181$	4.81127e14	1.01707	0.508533	+	0.861043i	$0.330188\pi$
$182$	0	0
$183$	−8.29432e14	−1.63248
$184$	0	0
$185$	1.12516e15	2.06347
$186$	0	0
$187$	1.75262e14	0.299720
$188$	0	0
$189$	1.31864e14	0.210438
$190$	0	0
$191$	−2.23030e14	−0.332389	−0.166195	−	0.986093i	$-0.553148\pi$
$191$	−2.23030e14	−0.332389	−0.166195	+	0.986093i	$0.553148\pi$
$192$	0	0
$193$	−2.87173e14	−0.399964	−0.199982	−	0.979800i	$-0.564088\pi$
$193$	−2.87173e14	−0.399964	−0.199982	+	0.979800i	$0.564088\pi$
$194$	0	0
$195$	−5.70392e14	−0.742931
$196$	0	0
$197$	−2.70793e14	−0.330071	−0.165035	−	0.986288i	$-0.552774\pi$
$197$	−2.70793e14	−0.330071	−0.165035	+	0.986288i	$0.552774\pi$
$198$	0	0
$199$	1.16045e15	1.32459	0.662293	−	0.749245i	$-0.269583\pi$
$199$	1.16045e15	1.32459	0.662293	+	0.749245i	$0.269583\pi$
$200$	0	0
$201$	4.79761e14	0.513158
$202$	0	0
$203$	−5.72039e13	−0.0573722
$204$	0	0
$205$	−1.56504e14	−0.147273
$206$	0	0
$207$	−7.90571e13	−0.0698448
$208$	0	0
$209$	3.36013e14	0.278872
$210$	0	0
$211$	1.30749e15	1.02000	0.510002	−	0.860173i	$-0.329645\pi$
$211$	1.30749e15	1.02000	0.510002	+	0.860173i	$0.329645\pi$
$212$	0	0
$213$	4.80522e14	0.352571
$214$	0	0
$215$	2.97375e15	2.05331
$216$	0	0
$217$	2.95182e14	0.191911
$218$	0	0
$219$	1.90464e15	1.16661
$220$	0	0
$221$	−5.71229e14	−0.329808
$222$	0	0
$223$	−4.26599e14	−0.232294	−0.116147	−	0.993232i	$-0.537054\pi$
$223$	−4.26599e14	−0.232294	−0.116147	+	0.993232i	$0.537054\pi$
$224$	0	0
$225$	−1.38571e14	−0.0712009
$226$	0	0
$227$	−2.07409e14	−0.100614	−0.0503072	−	0.998734i	$-0.516020\pi$
$227$	−2.07409e14	−0.100614	−0.0503072	+	0.998734i	$0.516020\pi$
$228$	0	0
$229$	−1.58866e15	−0.727950	−0.363975	−	0.931409i	$-0.618581\pi$
$229$	−1.58866e15	−0.727950	−0.363975	+	0.931409i	$0.618581\pi$
$230$	0	0
$231$	−1.95664e14	−0.0847293
$232$	0	0
$233$	−4.47010e15	−1.83022	−0.915110	−	0.403204i	$-0.867896\pi$
$233$	−4.47010e15	−1.83022	−0.915110	+	0.403204i	$0.867896\pi$
$234$	0	0
$235$	3.07776e15	1.19205
$236$	0	0
$237$	4.08685e15	1.49804
$238$	0	0
$239$	−5.89754e14	−0.204684	−0.102342	−	0.994749i	$-0.532634\pi$
$239$	−5.89754e14	−0.204684	−0.102342	+	0.994749i	$0.532634\pi$
$240$	0	0
$241$	−3.51183e15	−1.15458	−0.577288	−	0.816541i	$-0.695889\pi$
$241$	−3.51183e15	−1.15458	−0.577288	+	0.816541i	$0.695889\pi$
$242$	0	0
$243$	2.68075e14	0.0835248
$244$	0	0
$245$	−5.32925e15	−1.57430
$246$	0	0
$247$	−1.09516e15	−0.306866
$248$	0	0
$249$	6.09565e15	1.62078
$250$	0	0
$251$	−5.95213e14	−0.150243	−0.0751213	−	0.997174i	$-0.523934\pi$
$251$	−5.95213e14	−0.150243	−0.0751213	+	0.997174i	$0.523934\pi$
$252$	0	0
$253$	2.92437e15	0.701050
$254$	0	0
$255$	5.04956e15	1.15012
$256$	0	0
$257$	5.84357e15	1.26507	0.632533	−	0.774534i	$-0.282015\pi$
$257$	5.84357e15	1.26507	0.632533	+	0.774534i	$0.282015\pi$
$258$	0	0
$259$	−1.25799e15	−0.258957
$260$	0	0
$261$	−5.93369e13	−0.0116188
$262$	0	0
$263$	6.77703e15	1.26278	0.631389	−	0.775466i	$-0.282485\pi$
$263$	6.77703e15	1.26278	0.631389	+	0.775466i	$0.282485\pi$
$264$	0	0
$265$	−4.74729e15	−0.842069
$266$	0	0
$267$	4.32965e15	0.731357
$268$	0	0
$269$	1.56021e15	0.251070	0.125535	−	0.992089i	$-0.459935\pi$
$269$	1.56021e15	0.251070	0.125535	+	0.992089i	$0.459935\pi$
$270$	0	0
$271$	−7.13286e14	−0.109386	−0.0546932	−	0.998503i	$-0.517418\pi$
$271$	−7.13286e14	−0.109386	−0.0546932	+	0.998503i	$0.517418\pi$
$272$	0	0
$273$	6.37727e14	0.0932348
$274$	0	0
$275$	5.12582e15	0.714662
$276$	0	0
$277$	−3.72867e15	−0.495947	−0.247973	−	0.968767i	$-0.579765\pi$
$277$	−3.72867e15	−0.495947	−0.247973	+	0.968767i	$0.579765\pi$
$278$	0	0
$279$	3.06188e14	0.0388652
$280$	0	0
$281$	1.29294e16	1.56671	0.783354	−	0.621575i	$-0.213507\pi$
$281$	1.29294e16	1.56671	0.783354	+	0.621575i	$0.213507\pi$
$282$	0	0
$283$	−1.14247e16	−1.32200	−0.661001	−	0.750385i	$-0.729868\pi$
$283$	−1.14247e16	−1.32200	−0.661001	+	0.750385i	$0.729868\pi$
$284$	0	0
$285$	9.68105e15	1.07012
$286$	0	0
$287$	1.74979e14	0.0184822
$288$	0	0
$289$	−4.84760e15	−0.489431
$290$	0	0
$291$	−4.80721e14	−0.0464075
$292$	0	0
$293$	−5.38943e15	−0.497626	−0.248813	−	0.968551i	$-0.580041\pi$
$293$	−5.38943e15	−0.497626	−0.248813	+	0.968551i	$0.580041\pi$
$294$	0	0
$295$	−2.26506e16	−2.00095
$296$	0	0
$297$	−5.05960e15	−0.427759
$298$	0	0
$299$	−9.53138e15	−0.771424
$300$	0	0
$301$	−3.32480e15	−0.257681
$302$	0	0
$303$	−1.30640e16	−0.969841
$304$	0	0
$305$	−3.85525e16	−2.74223
$306$	0	0
$307$	−1.31900e16	−0.899176	−0.449588	−	0.893236i	$-0.648429\pi$
$307$	−1.31900e16	−0.899176	−0.449588	+	0.893236i	$0.648429\pi$
$308$	0	0
$309$	7.02835e15	0.459329
$310$	0	0
$311$	−1.63560e16	−1.02503	−0.512514	−	0.858679i	$-0.671286\pi$
$311$	−1.63560e16	−1.02503	−0.512514	+	0.858679i	$0.671286\pi$
$312$	0	0
$313$	3.03621e16	1.82513	0.912566	−	0.408930i	$-0.134098\pi$
$313$	3.03621e16	1.82513	0.912566	+	0.408930i	$0.134098\pi$
$314$	0	0
$315$	2.45862e14	0.0141799
$316$	0	0
$317$	−2.97252e15	−0.164528	−0.0822641	−	0.996611i	$-0.526215\pi$
$317$	−2.97252e15	−0.164528	−0.0822641	+	0.996611i	$0.526215\pi$
$318$	0	0
$319$	2.19491e15	0.116621
$320$	0	0
$321$	−2.06655e15	−0.105430
$322$	0	0
$323$	9.69526e15	0.475054
$324$	0	0
$325$	−1.67065e16	−0.786402
$326$	0	0
$327$	1.03387e15	0.0467635
$328$	0	0
$329$	−3.44109e15	−0.149597
$330$	0	0
$331$	−3.37419e16	−1.41022	−0.705111	−	0.709097i	$-0.749103\pi$
$331$	−3.37419e16	−1.41022	−0.705111	+	0.709097i	$0.749103\pi$
$332$	0	0
$333$	−1.30489e15	−0.0524430
$334$	0	0
$335$	2.22996e16	0.861997
$336$	0	0
$337$	−2.25069e16	−0.836991	−0.418496	−	0.908219i	$-0.637443\pi$
$337$	−2.25069e16	−0.836991	−0.418496	+	0.908219i	$0.637443\pi$
$338$	0	0
$339$	−4.49756e15	−0.160946
$340$	0	0
$341$	−1.13261e16	−0.390100
$342$	0	0
$343$	1.21817e16	0.403922
$344$	0	0
$345$	8.42557e16	2.69014
$346$	0	0
$347$	1.51473e16	0.465794	0.232897	−	0.972501i	$-0.425180\pi$
$347$	1.51473e16	0.465794	0.232897	+	0.972501i	$0.425180\pi$
$348$	0	0
$349$	2.27836e16	0.674928	0.337464	−	0.941338i	$-0.390431\pi$
$349$	2.27836e16	0.674928	0.337464	+	0.941338i	$0.390431\pi$
$350$	0	0
$351$	1.64907e16	0.470700
$352$	0	0
$353$	−1.34392e16	−0.369690	−0.184845	−	0.982768i	$-0.559178\pi$
$353$	−1.34392e16	−0.369690	−0.184845	+	0.982768i	$0.559178\pi$
$354$	0	0
$355$	2.23350e16	0.592244
$356$	0	0
$357$	−5.64567e15	−0.144335
$358$	0	0
$359$	−4.79199e16	−1.18141	−0.590707	−	0.806886i	$-0.701151\pi$
$359$	−4.79199e16	−1.18141	−0.590707	+	0.806886i	$0.701151\pi$
$360$	0	0
$361$	−2.34652e16	−0.557991
$362$	0	0
$363$	−3.51625e16	−0.806652
$364$	0	0
$365$	8.85289e16	1.95966
$366$	0	0
$367$	−5.26047e16	−1.12382	−0.561908	−	0.827200i	$-0.689932\pi$
$367$	−5.26047e16	−1.12382	−0.561908	+	0.827200i	$0.689932\pi$
$368$	0	0
$369$	1.81503e14	0.00374294
$370$	0	0
$371$	5.30771e15	0.105676
$372$	0	0
$373$	−7.05110e16	−1.35566	−0.677828	−	0.735221i	$-0.737079\pi$
$373$	−7.05110e16	−1.35566	−0.677828	+	0.735221i	$0.737079\pi$
$374$	0	0
$375$	6.10029e16	1.13278
$376$	0	0
$377$	−7.15385e15	−0.128328
$378$	0	0
$379$	4.40814e16	0.764012	0.382006	−	0.924160i	$-0.375233\pi$
$379$	4.40814e16	0.764012	0.382006	+	0.924160i	$0.375233\pi$
$380$	0	0
$381$	4.44096e16	0.743814
$382$	0	0
$383$	4.57018e15	0.0739846	0.0369923	−	0.999316i	$-0.488222\pi$
$383$	4.57018e15	0.0739846	0.0369923	+	0.999316i	$0.488222\pi$
$384$	0	0
$385$	−9.09459e15	−0.142327
$386$	0	0
$387$	−3.44877e15	−0.0521846
$388$	0	0
$389$	−5.52721e16	−0.808786	−0.404393	−	0.914585i	$-0.632517\pi$
$389$	−5.52721e16	−0.808786	−0.404393	+	0.914585i	$0.632517\pi$
$390$	0	0
$391$	8.43794e16	1.19423
$392$	0	0
$393$	−2.53888e16	−0.347608
$394$	0	0
$395$	1.89959e17	2.51639
$396$	0	0
$397$	7.34209e16	0.941199	0.470599	−	0.882347i	$-0.344038\pi$
$397$	7.34209e16	0.941199	0.470599	+	0.882347i	$0.344038\pi$
$398$	0	0
$399$	−1.08239e16	−0.134295
$400$	0	0
$401$	−6.73973e16	−0.809476	−0.404738	−	0.914433i	$-0.632637\pi$
$401$	−6.73973e16	−0.809476	−0.404738	+	0.914433i	$0.632637\pi$
$402$	0	0
$403$	3.69150e16	0.429260
$404$	0	0
$405$	−1.39673e17	−1.57273
$406$	0	0
$407$	4.82688e16	0.526384
$408$	0	0
$409$	6.51487e16	0.688184	0.344092	−	0.938936i	$-0.388187\pi$
$409$	6.51487e16	0.688184	0.344092	+	0.938936i	$0.388187\pi$
$410$	0	0
$411$	−5.24067e15	−0.0536309
$412$	0	0
$413$	2.53245e16	0.251111
$414$	0	0
$415$	2.83329e17	2.72257
$416$	0	0
$417$	−8.29246e16	−0.772323
$418$	0	0
$419$	−1.35401e17	−1.22245	−0.611224	−	0.791458i	$-0.709323\pi$
$419$	−1.35401e17	−1.22245	−0.611224	+	0.791458i	$0.709323\pi$
$420$	0	0
$421$	−1.42084e17	−1.24369	−0.621846	−	0.783139i	$-0.713617\pi$
$421$	−1.42084e17	−1.24369	−0.621846	+	0.783139i	$0.713617\pi$
$422$	0	0
$423$	−3.56940e15	−0.0302958
$424$	0	0
$425$	1.47900e17	1.21742
$426$	0	0
$427$	4.31036e16	0.344138
$428$	0	0
$429$	−2.44695e16	−0.189519
$430$	0	0
$431$	−2.16583e17	−1.62750	−0.813750	−	0.581215i	$-0.802578\pi$
$431$	−2.16583e17	−1.62750	−0.813750	+	0.581215i	$0.802578\pi$
$432$	0	0
$433$	6.10685e16	0.445293	0.222647	−	0.974899i	$-0.428530\pi$
$433$	6.10685e16	0.445293	0.222647	+	0.974899i	$0.428530\pi$
$434$	0	0
$435$	6.32387e16	0.447510
$436$	0	0
$437$	1.61773e17	1.11116
$438$	0	0
$439$	5.60005e16	0.373398	0.186699	−	0.982417i	$-0.440221\pi$
$439$	5.60005e16	0.373398	0.186699	+	0.982417i	$0.440221\pi$
$440$	0	0
$441$	6.18054e15	0.0400106
$442$	0	0
$443$	−1.30777e17	−0.822064	−0.411032	−	0.911621i	$-0.634832\pi$
$443$	−1.30777e17	−0.822064	−0.411032	+	0.911621i	$0.634832\pi$
$444$	0	0
$445$	2.01244e17	1.22852
$446$	0	0
$447$	−2.44019e17	−1.44685
$448$	0	0
$449$	−8.96832e16	−0.516547	−0.258274	−	0.966072i	$-0.583154\pi$
$449$	−8.96832e16	−0.516547	−0.258274	+	0.966072i	$0.583154\pi$
$450$	0	0
$451$	−6.71391e15	−0.0375689
$452$	0	0
$453$	7.04722e16	0.383159
$454$	0	0
$455$	2.96419e16	0.156615
$456$	0	0
$457$	1.70088e17	0.873411	0.436706	−	0.899605i	$-0.356145\pi$
$457$	1.70088e17	0.873411	0.436706	+	0.899605i	$0.356145\pi$
$458$	0	0
$459$	−1.45989e17	−0.728682
$460$	0	0
$461$	−5.74786e16	−0.278901	−0.139450	−	0.990229i	$-0.544534\pi$
$461$	−5.74786e16	−0.278901	−0.139450	+	0.990229i	$0.544534\pi$
$462$	0	0
$463$	−2.63593e17	−1.24353	−0.621767	−	0.783202i	$-0.713585\pi$
$463$	−2.63593e17	−1.24353	−0.621767	+	0.783202i	$0.713585\pi$
$464$	0	0
$465$	−3.26322e17	−1.49693
$466$	0	0
$467$	1.30250e16	0.0581055	0.0290528	−	0.999578i	$-0.490751\pi$
$467$	1.30250e16	0.0581055	0.0290528	+	0.999578i	$0.490751\pi$
$468$	0	0
$469$	−2.49321e16	−0.108177
$470$	0	0
$471$	−7.28976e16	−0.307664
$472$	0	0
$473$	1.27572e17	0.523791
$474$	0	0
$475$	2.83554e17	1.13273
$476$	0	0
$477$	5.50562e15	0.0214011
$478$	0	0
$479$	4.73314e17	1.79047	0.895237	−	0.445589i	$-0.147006\pi$
$479$	4.73314e17	1.79047	0.895237	+	0.445589i	$0.147006\pi$
$480$	0	0
$481$	−1.57322e17	−0.579224
$482$	0	0
$483$	−9.42021e16	−0.337602
$484$	0	0
$485$	−2.23442e16	−0.0779548
$486$	0	0
$487$	−4.45244e17	−1.51238	−0.756188	−	0.654355i	$-0.772940\pi$
$487$	−4.45244e17	−1.51238	−0.756188	+	0.654355i	$0.772940\pi$
$488$	0	0
$489$	4.48923e17	1.48479
$490$	0	0
$491$	−1.88599e17	−0.607450	−0.303725	−	0.952760i	$-0.598230\pi$
$491$	−1.88599e17	−0.607450	−0.303725	+	0.952760i	$0.598230\pi$
$492$	0	0
$493$	6.33315e16	0.198662
$494$	0	0
$495$	−9.43369e15	−0.0288236
$496$	0	0
$497$	−2.49716e16	−0.0743242
$498$	0	0
$499$	−5.11071e17	−1.48193	−0.740965	−	0.671544i	$-0.765632\pi$
$499$	−5.11071e17	−1.48193	−0.740965	+	0.671544i	$0.765632\pi$
$500$	0	0
$501$	−2.83607e17	−0.801256
$502$	0	0
$503$	3.38952e16	0.0933138	0.0466569	−	0.998911i	$-0.485143\pi$
$503$	3.38952e16	0.0933138	0.0466569	+	0.998911i	$0.485143\pi$
$504$	0	0
$505$	−6.07224e17	−1.62913
$506$	0	0
$507$	−2.94600e17	−0.770338
$508$	0	0
$509$	−5.25773e17	−1.34009	−0.670043	−	0.742323i	$-0.733724\pi$
$509$	−5.25773e17	−1.34009	−0.670043	+	0.742323i	$0.733724\pi$
$510$	0	0
$511$	−9.89798e16	−0.245929
$512$	0	0
$513$	−2.79891e17	−0.677994
$514$	0	0
$515$	3.26682e17	0.771575
$516$	0	0
$517$	1.32034e17	0.304087
$518$	0	0
$519$	−3.25050e17	−0.730066
$520$	0	0
$521$	5.85720e17	1.28305	0.641527	−	0.767100i	$-0.278301\pi$
$521$	5.85720e17	1.28305	0.641527	+	0.767100i	$0.278301\pi$
$522$	0	0
$523$	−7.95921e17	−1.70063	−0.850313	−	0.526277i	$-0.823587\pi$
$523$	−7.95921e17	−1.70063	−0.850313	+	0.526277i	$0.823587\pi$
$524$	0	0
$525$	−1.65117e17	−0.344156
$526$	0	0
$527$	−3.26801e17	−0.664529
$528$	0	0
$529$	9.03896e17	1.79331
$530$	0	0
$531$	2.62688e16	0.0508541
$532$	0	0
$533$	2.18826e16	0.0413402
$534$	0	0
$535$	−9.60543e16	−0.177099
$536$	0	0
$537$	−1.07087e18	−1.92709
$538$	0	0
$539$	−2.28622e17	−0.401597
$540$	0	0
$541$	8.51256e17	1.45975	0.729874	−	0.683582i	$-0.239579\pi$
$541$	8.51256e17	1.45975	0.729874	+	0.683582i	$0.239579\pi$
$542$	0	0
$543$	5.94673e17	0.995587
$544$	0	0
$545$	4.80551e16	0.0785528
$546$	0	0
$547$	8.54108e17	1.36331	0.681656	−	0.731673i	$-0.261260\pi$
$547$	8.54108e17	1.36331	0.681656	+	0.731673i	$0.261260\pi$
$548$	0	0
$549$	4.47108e16	0.0696935
$550$	0	0
$551$	1.21419e17	0.184843
$552$	0	0
$553$	−2.12384e17	−0.315797
$554$	0	0
$555$	1.39070e18	2.01990
$556$	0	0
$557$	9.37087e17	1.32960	0.664800	−	0.747021i	$-0.268517\pi$
$557$	9.37087e17	1.32960	0.664800	+	0.747021i	$0.268517\pi$
$558$	0	0
$559$	−4.15795e17	−0.576371
$560$	0	0
$561$	2.16623e17	0.293391
$562$	0	0
$563$	7.64389e17	1.01160	0.505801	−	0.862650i	$-0.331197\pi$
$563$	7.64389e17	1.01160	0.505801	+	0.862650i	$0.331197\pi$
$564$	0	0
$565$	−2.09049e17	−0.270355
$566$	0	0
$567$	1.56161e17	0.197371
$568$	0	0
$569$	2.80724e16	0.0346777	0.0173388	−	0.999850i	$-0.494481\pi$
$569$	2.80724e16	0.0346777	0.0173388	+	0.999850i	$0.494481\pi$
$570$	0	0
$571$	−2.19382e17	−0.264891	−0.132446	−	0.991190i	$-0.542283\pi$
$571$	−2.19382e17	−0.264891	−0.132446	+	0.991190i	$0.542283\pi$
$572$	0	0
$573$	−2.75666e17	−0.325370
$574$	0	0
$575$	2.46781e18	2.84755
$576$	0	0
$577$	7.93868e17	0.895582	0.447791	−	0.894138i	$-0.352211\pi$
$577$	7.93868e17	0.895582	0.447791	+	0.894138i	$0.352211\pi$
$578$	0	0
$579$	−3.54945e17	−0.391517
$580$	0	0
$581$	−3.16777e17	−0.341671
$582$	0	0
$583$	−2.03656e17	−0.214809
$584$	0	0
$585$	3.07472e16	0.0317170
$586$	0	0
$587$	7.65857e17	0.772681	0.386340	−	0.922356i	$-0.373739\pi$
$587$	7.65857e17	0.772681	0.386340	+	0.922356i	$0.373739\pi$
$588$	0	0
$589$	−6.26544e17	−0.618304
$590$	0	0
$591$	−3.34700e17	−0.323100
$592$	0	0
$593$	8.88052e17	0.838654	0.419327	−	0.907835i	$-0.362266\pi$
$593$	8.88052e17	0.838654	0.419327	+	0.907835i	$0.362266\pi$
$594$	0	0
$595$	−2.62414e17	−0.242452
$596$	0	0
$597$	1.43431e18	1.29661
$598$	0	0
$599$	1.62392e18	1.43645	0.718225	−	0.695811i	$-0.244955\pi$
$599$	1.62392e18	1.43645	0.718225	+	0.695811i	$0.244955\pi$
$600$	0	0
$601$	−1.97791e18	−1.71207	−0.856035	−	0.516917i	$-0.827080\pi$
$601$	−1.97791e18	−1.71207	−0.856035	+	0.516917i	$0.827080\pi$
$602$	0	0
$603$	−2.58617e16	−0.0219076
$604$	0	0
$605$	−1.63437e18	−1.35501
$606$	0	0
$607$	−1.28369e18	−1.04168	−0.520840	−	0.853655i	$-0.674381\pi$
$607$	−1.28369e18	−1.04168	−0.520840	+	0.853655i	$0.674381\pi$
$608$	0	0
$609$	−7.07041e16	−0.0561606
$610$	0	0
$611$	−4.30338e17	−0.334612
$612$	0	0
$613$	−6.80248e17	−0.517814	−0.258907	−	0.965902i	$-0.583362\pi$
$613$	−6.80248e17	−0.517814	−0.258907	+	0.965902i	$0.583362\pi$
$614$	0	0
$615$	−1.93438e17	−0.144163
$616$	0	0
$617$	−3.13363e17	−0.228662	−0.114331	−	0.993443i	$-0.536473\pi$
$617$	−3.13363e17	−0.228662	−0.114331	+	0.993443i	$0.536473\pi$
$618$	0	0
$619$	−9.14817e17	−0.653649	−0.326825	−	0.945085i	$-0.605979\pi$
$619$	−9.14817e17	−0.653649	−0.326825	+	0.945085i	$0.605979\pi$
$620$	0	0
$621$	−2.43594e18	−1.70440
$622$	0	0
$623$	−2.25001e17	−0.154175
$624$	0	0
$625$	2.96632e17	0.199066
$626$	0	0
$627$	4.15311e17	0.272983
$628$	0	0
$629$	1.39274e18	0.896687
$630$	0	0
$631$	1.45935e18	0.920385	0.460193	−	0.887819i	$-0.347780\pi$
$631$	1.45935e18	0.920385	0.460193	+	0.887819i	$0.347780\pi$
$632$	0	0
$633$	1.61606e18	0.998463
$634$	0	0
$635$	2.06418e18	1.24945
$636$	0	0
$637$	7.45146e17	0.441911
$638$	0	0
$639$	−2.59027e16	−0.0150519
$640$	0	0
$641$	−1.94853e18	−1.10951	−0.554753	−	0.832015i	$-0.687187\pi$
$641$	−1.94853e18	−1.10951	−0.554753	+	0.832015i	$0.687187\pi$
$642$	0	0
$643$	−5.48334e17	−0.305966	−0.152983	−	0.988229i	$-0.548888\pi$
$643$	−5.48334e17	−0.305966	−0.152983	+	0.988229i	$0.548888\pi$
$644$	0	0
$645$	3.67555e18	2.00994
$646$	0	0
$647$	2.47157e17	0.132463	0.0662316	−	0.997804i	$-0.478902\pi$
$647$	2.47157e17	0.132463	0.0662316	+	0.997804i	$0.478902\pi$
$648$	0	0
$649$	−9.71698e17	−0.510435
$650$	0	0
$651$	3.64844e17	0.187859
$652$	0	0
$653$	−1.66810e18	−0.841951	−0.420975	−	0.907072i	$-0.638312\pi$
$653$	−1.66810e18	−0.841951	−0.420975	+	0.907072i	$0.638312\pi$
$654$	0	0
$655$	−1.18009e18	−0.583909
$656$	0	0
$657$	−1.02670e17	−0.0498047
$658$	0	0
$659$	2.10117e18	0.999324	0.499662	−	0.866221i	$-0.333458\pi$
$659$	2.10117e18	0.999324	0.499662	+	0.866221i	$0.333458\pi$
$660$	0	0
$661$	−6.36982e17	−0.297042	−0.148521	−	0.988909i	$-0.547451\pi$
$661$	−6.36982e17	−0.297042	−0.148521	+	0.988909i	$0.547451\pi$
$662$	0	0
$663$	−7.06039e17	−0.322843
$664$	0	0
$665$	−5.03101e17	−0.225587
$666$	0	0
$667$	1.05673e18	0.464673
$668$	0	0
$669$	−5.27277e17	−0.227389
$670$	0	0
$671$	−1.65388e18	−0.699532
$672$	0	0
$673$	3.87100e18	1.60593	0.802963	−	0.596029i	$-0.203256\pi$
$673$	3.87100e18	1.60593	0.802963	+	0.596029i	$0.203256\pi$
$674$	0	0
$675$	−4.26969e18	−1.73749
$676$	0	0
$677$	4.97460e18	1.98578	0.992892	−	0.119020i	$-0.0379752\pi$
$677$	4.97460e18	1.98578	0.992892	+	0.119020i	$0.0379752\pi$
$678$	0	0
$679$	2.49819e16	0.00978300
$680$	0	0
$681$	−2.56358e17	−0.0984896
$682$	0	0
$683$	−6.35114e17	−0.239396	−0.119698	−	0.992810i	$-0.538193\pi$
$683$	−6.35114e17	−0.239396	−0.119698	+	0.992810i	$0.538193\pi$
$684$	0	0
$685$	−2.43589e17	−0.0900885
$686$	0	0
$687$	−1.96359e18	−0.712577
$688$	0	0
$689$	6.63775e17	0.236372
$690$	0	0
$691$	−3.98112e18	−1.39123	−0.695614	−	0.718416i	$-0.744868\pi$
$691$	−3.98112e18	−1.39123	−0.695614	+	0.718416i	$0.744868\pi$
$692$	0	0
$693$	1.05473e16	0.00361724
$694$	0	0
$695$	−3.85438e18	−1.29734
$696$	0	0
$697$	−1.93722e17	−0.0639980
$698$	0	0
$699$	−5.52504e18	−1.79157
$700$	0	0
$701$	−4.12225e18	−1.31210	−0.656050	−	0.754717i	$-0.727774\pi$
$701$	−4.12225e18	−1.31210	−0.656050	+	0.754717i	$0.727774\pi$
$702$	0	0
$703$	2.67017e18	0.834313
$704$	0	0
$705$	3.80411e18	1.16687
$706$	0	0
$707$	6.78907e17	0.204449
$708$	0	0
$709$	−3.84948e18	−1.13816	−0.569078	−	0.822283i	$-0.692700\pi$
$709$	−3.84948e18	−1.13816	−0.569078	+	0.822283i	$0.692700\pi$
$710$	0	0
$711$	−2.20303e17	−0.0639540
$712$	0	0
$713$	−5.45291e18	−1.55434
$714$	0	0
$715$	−1.13736e18	−0.318352
$716$	0	0
$717$	−7.28936e17	−0.200362
$718$	0	0
$719$	−2.83787e17	−0.0766045	−0.0383022	−	0.999266i	$-0.512195\pi$
$719$	−2.83787e17	−0.0766045	−0.0383022	+	0.999266i	$0.512195\pi$
$720$	0	0
$721$	−3.65247e17	−0.0968294
$722$	0	0
$723$	−4.34062e18	−1.13019
$724$	0	0
$725$	1.85223e18	0.473695
$726$	0	0
$727$	−2.79417e18	−0.701907	−0.350954	−	0.936393i	$-0.614143\pi$
$727$	−2.79417e18	−0.701907	−0.350954	+	0.936393i	$0.614143\pi$
$728$	0	0
$729$	4.20746e18	1.03822
$730$	0	0
$731$	3.68094e18	0.892270
$732$	0	0
$733$	3.41031e18	0.812115	0.406058	−	0.913848i	$-0.366903\pi$
$733$	3.41031e18	0.812115	0.406058	+	0.913848i	$0.366903\pi$
$734$	0	0
$735$	−6.58695e18	−1.54105
$736$	0	0
$737$	9.56640e17	0.219892
$738$	0	0
$739$	5.41674e18	1.22335	0.611673	−	0.791111i	$-0.290497\pi$
$739$	5.41674e18	1.22335	0.611673	+	0.791111i	$0.290497\pi$
$740$	0	0
$741$	−1.35362e18	−0.300386
$742$	0	0
$743$	5.36910e18	1.17078	0.585388	−	0.810753i	$-0.300942\pi$
$743$	5.36910e18	1.17078	0.585388	+	0.810753i	$0.300942\pi$
$744$	0	0
$745$	−1.13421e19	−2.43041
$746$	0	0
$747$	−3.28588e17	−0.0691939
$748$	0	0
$749$	1.07394e17	0.0222252
$750$	0	0
$751$	5.99551e18	1.21946	0.609728	−	0.792610i	$-0.291279\pi$
$751$	5.99551e18	1.21946	0.609728	+	0.792610i	$0.291279\pi$
$752$	0	0
$753$	−7.35683e17	−0.147070
$754$	0	0
$755$	3.27559e18	0.643627
$756$	0	0
$757$	−2.96483e18	−0.572632	−0.286316	−	0.958135i	$-0.592431\pi$
$757$	−2.96483e18	−0.572632	−0.286316	+	0.958135i	$0.592431\pi$
$758$	0	0
$759$	3.61452e18	0.686245
$760$	0	0
$761$	−1.76419e18	−0.329264	−0.164632	−	0.986355i	$-0.552644\pi$
$761$	−1.76419e18	−0.329264	−0.164632	+	0.986355i	$0.552644\pi$
$762$	0	0
$763$	−5.37280e16	−0.00985805
$764$	0	0
$765$	−2.72198e17	−0.0491005
$766$	0	0
$767$	3.16705e18	0.561675
$768$	0	0
$769$	7.24260e18	1.26291	0.631456	−	0.775412i	$-0.282458\pi$
$769$	7.24260e18	1.26291	0.631456	+	0.775412i	$0.282458\pi$
$770$	0	0
$771$	7.22265e18	1.23835
$772$	0	0
$773$	2.72675e17	0.0459705	0.0229852	−	0.999736i	$-0.492683\pi$
$773$	2.72675e17	0.0459705	0.0229852	+	0.999736i	$0.492683\pi$
$774$	0	0
$775$	−9.55783e18	−1.58452
$776$	0	0
$777$	−1.55487e18	−0.253488
$778$	0	0
$779$	−3.71405e17	−0.0595463
$780$	0	0
$781$	9.58157e17	0.151079
$782$	0	0
$783$	−1.82831e18	−0.283529
$784$	0	0
$785$	−3.38832e18	−0.516811
$786$	0	0
$787$	1.51655e18	0.227521	0.113761	−	0.993508i	$-0.463710\pi$
$787$	1.51655e18	0.227521	0.113761	+	0.993508i	$0.463710\pi$
$788$	0	0
$789$	8.37641e18	1.23611
$790$	0	0
$791$	2.33728e17	0.0339284
$792$	0	0
$793$	5.39048e18	0.769754
$794$	0	0
$795$	−5.86765e18	−0.824286
$796$	0	0
$797$	6.36258e18	0.879335	0.439667	−	0.898161i	$-0.355096\pi$
$797$	6.36258e18	0.879335	0.439667	+	0.898161i	$0.355096\pi$
$798$	0	0
$799$	3.80969e18	0.518007
$800$	0	0
$801$	−2.33391e17	−0.0312229
$802$	0	0
$803$	3.79784e18	0.499903
$804$	0	0
$805$	−4.37857e18	−0.567099
$806$	0	0
$807$	1.92842e18	0.245768
$808$	0	0
$809$	8.69050e18	1.08988	0.544941	−	0.838475i	$-0.316552\pi$
$809$	8.69050e18	1.08988	0.544941	+	0.838475i	$0.316552\pi$
$810$	0	0
$811$	−7.15112e18	−0.882549	−0.441274	−	0.897372i	$-0.645473\pi$
$811$	−7.15112e18	−0.882549	−0.441274	+	0.897372i	$0.645473\pi$
$812$	0	0
$813$	−8.81621e17	−0.107076
$814$	0	0
$815$	2.08662e19	2.49413
$816$	0	0
$817$	7.05712e18	0.830203
$818$	0	0
$819$	−3.43769e16	−0.00398035
$820$	0	0
$821$	−1.09070e19	−1.24301	−0.621505	−	0.783410i	$-0.713479\pi$
$821$	−1.09070e19	−1.24301	−0.621505	+	0.783410i	$0.713479\pi$
$822$	0	0
$823$	−3.37291e18	−0.378360	−0.189180	−	0.981942i	$-0.560583\pi$
$823$	−3.37291e18	−0.378360	−0.189180	+	0.981942i	$0.560583\pi$
$824$	0	0
$825$	6.33551e18	0.699569
$826$	0	0
$827$	1.42936e19	1.55366	0.776829	−	0.629712i	$-0.216827\pi$
$827$	1.42936e19	1.55366	0.776829	+	0.629712i	$0.216827\pi$
$828$	0	0
$829$	−2.16429e18	−0.231585	−0.115792	−	0.993273i	$-0.536941\pi$
$829$	−2.16429e18	−0.231585	−0.115792	+	0.993273i	$0.536941\pi$
$830$	0	0
$831$	−4.60863e18	−0.485474
$832$	0	0
$833$	−6.59662e18	−0.684115
$834$	0	0
$835$	−1.31822e19	−1.34594
$836$	0	0
$837$	9.43437e18	0.948413
$838$	0	0
$839$	1.41500e19	1.40056	0.700282	−	0.713866i	$-0.253058\pi$
$839$	1.41500e19	1.40056	0.700282	+	0.713866i	$0.253058\pi$
$840$	0	0
$841$	−9.46749e18	−0.922701
$842$	0	0
$843$	1.59808e19	1.53362
$844$	0	0
$845$	−1.36932e19	−1.29401
$846$	0	0
$847$	1.82731e18	0.170047
$848$	0	0
$849$	−1.41209e19	−1.29408
$850$	0	0
$851$	2.32389e19	2.09736
$852$	0	0
$853$	7.95957e18	0.707491	0.353746	−	0.935342i	$-0.384908\pi$
$853$	7.95957e18	0.707491	0.353746	+	0.935342i	$0.384908\pi$
$854$	0	0
$855$	−5.21860e17	−0.0456851
$856$	0	0
$857$	1.91543e19	1.65155	0.825776	−	0.563999i	$-0.190738\pi$
$857$	1.91543e19	1.65155	0.825776	+	0.563999i	$0.190738\pi$
$858$	0	0
$859$	−5.82602e18	−0.494785	−0.247392	−	0.968915i	$-0.579574\pi$
$859$	−5.82602e18	−0.494785	−0.247392	+	0.968915i	$0.579574\pi$
$860$	0	0
$861$	2.16274e17	0.0180919
$862$	0	0
$863$	2.49725e17	0.0205775	0.0102887	−	0.999947i	$-0.496725\pi$
$863$	2.49725e17	0.0205775	0.0102887	+	0.999947i	$0.496725\pi$
$864$	0	0
$865$	−1.51085e19	−1.22636
$866$	0	0
$867$	−5.99164e18	−0.479095
$868$	0	0
$869$	8.14913e18	0.641923
$870$	0	0
$871$	−3.11797e18	−0.241966
$872$	0	0
$873$	2.59134e16	0.00198122
$874$	0	0
$875$	−3.17018e18	−0.238798
$876$	0	0
$877$	8.11300e18	0.602122	0.301061	−	0.953605i	$-0.402659\pi$
$877$	8.11300e18	0.602122	0.301061	+	0.953605i	$0.402659\pi$
$878$	0	0
$879$	−6.66134e18	−0.487118
$880$	0	0
$881$	−1.51802e19	−1.09379	−0.546895	−	0.837201i	$-0.684190\pi$
$881$	−1.51802e19	−1.09379	−0.546895	+	0.837201i	$0.684190\pi$
$882$	0	0
$883$	6.81904e18	0.484148	0.242074	−	0.970258i	$-0.422172\pi$
$883$	6.81904e18	0.484148	0.242074	+	0.970258i	$0.422172\pi$
$884$	0	0
$885$	−2.79961e19	−1.95870
$886$	0	0
$887$	9.14117e18	0.630229	0.315114	−	0.949054i	$-0.397957\pi$
$887$	9.14117e18	0.630229	0.315114	+	0.949054i	$0.397957\pi$
$888$	0	0
$889$	−2.30786e18	−0.156801
$890$	0	0
$891$	−5.99187e18	−0.401197
$892$	0	0
$893$	7.30396e18	0.481974
$894$	0	0
$895$	−4.97745e19	−3.23711
$896$	0	0
$897$	−1.17808e19	−0.755133
$898$	0	0
$899$	−4.09272e18	−0.258568
$900$	0	0
$901$	−5.87626e18	−0.365923
$902$	0	0
$903$	−4.10945e18	−0.252240
$904$	0	0
$905$	2.76407e19	1.67238
$906$	0	0
$907$	−1.16589e19	−0.695361	−0.347680	−	0.937613i	$-0.613031\pi$
$907$	−1.16589e19	−0.695361	−0.347680	+	0.937613i	$0.613031\pi$
$908$	0	0
$909$	7.04222e17	0.0414042
$910$	0	0
$911$	2.31264e19	1.34041	0.670207	−	0.742174i	$-0.266205\pi$
$911$	2.31264e19	1.34041	0.670207	+	0.742174i	$0.266205\pi$
$912$	0	0
$913$	1.21547e19	0.694517
$914$	0	0
$915$	−4.76509e19	−2.68432
$916$	0	0
$917$	1.31940e18	0.0732781
$918$	0	0
$919$	−2.72587e19	−1.49264	−0.746320	−	0.665588i	$-0.768181\pi$
$919$	−2.72587e19	−1.49264	−0.746320	+	0.665588i	$0.768181\pi$
$920$	0	0
$921$	−1.63028e19	−0.880187
$922$	0	0
$923$	−3.12292e18	−0.166245
$924$	0	0
$925$	4.07330e19	2.13808
$926$	0	0
$927$	−3.78866e17	−0.0196095
$928$	0	0
$929$	1.13327e19	0.578406	0.289203	−	0.957268i	$-0.406610\pi$
$929$	1.13327e19	0.578406	0.289203	+	0.957268i	$0.406610\pi$
$930$	0	0
$931$	−1.26471e19	−0.636527
$932$	0	0
$933$	−2.02161e19	−1.00338
$934$	0	0
$935$	1.00688e19	0.492835
$936$	0	0
$937$	2.96694e19	1.43219	0.716097	−	0.698001i	$-0.245927\pi$
$937$	2.96694e19	1.43219	0.716097	+	0.698001i	$0.245927\pi$
$938$	0	0
$939$	3.75276e19	1.78659
$940$	0	0
$941$	−6.14808e17	−0.0288673	−0.0144337	−	0.999896i	$-0.504595\pi$
$941$	−6.14808e17	−0.0288673	−0.0144337	+	0.999896i	$0.504595\pi$
$942$	0	0
$943$	−3.23240e18	−0.149692
$944$	0	0
$945$	7.57559e18	0.346027
$946$	0	0
$947$	−1.12631e19	−0.507439	−0.253720	−	0.967278i	$-0.581654\pi$
$947$	−1.12631e19	−0.507439	−0.253720	+	0.967278i	$0.581654\pi$
$948$	0	0
$949$	−1.23783e19	−0.550085
$950$	0	0
$951$	−3.67404e18	−0.161054
$952$	0	0
$953$	−2.02437e19	−0.875358	−0.437679	−	0.899131i	$-0.644199\pi$
$953$	−2.02437e19	−0.875358	−0.437679	+	0.899131i	$0.644199\pi$
$954$	0	0
$955$	−1.28131e19	−0.546553
$956$	0	0
$957$	2.71290e18	0.114158
$958$	0	0
$959$	2.72345e17	0.0113057
$960$	0	0
$961$	−3.29844e18	−0.135085
$962$	0	0
$963$	1.11398e17	0.00450097
$964$	0	0
$965$	−1.64981e19	−0.657666
$966$	0	0
$967$	3.10102e19	1.21964	0.609821	−	0.792539i	$-0.291241\pi$
$967$	3.10102e19	1.21964	0.609821	+	0.792539i	$0.291241\pi$
$968$	0	0
$969$	1.19833e19	0.465022
$970$	0	0
$971$	−1.40646e19	−0.538520	−0.269260	−	0.963068i	$-0.586779\pi$
$971$	−1.40646e19	−0.538520	−0.269260	+	0.963068i	$0.586779\pi$
$972$	0	0
$973$	4.30940e18	0.162811
$974$	0	0
$975$	−2.06493e19	−0.769795
$976$	0	0
$977$	2.00060e19	0.735945	0.367972	−	0.929837i	$-0.380052\pi$
$977$	2.00060e19	0.735945	0.367972	+	0.929837i	$0.380052\pi$
$978$	0	0
$979$	8.63327e18	0.313392
$980$	0	0
$981$	−5.57313e16	−0.00199641
$982$	0	0
$983$	9.33086e18	0.329856	0.164928	−	0.986306i	$-0.447261\pi$
$983$	9.33086e18	0.329856	0.164928	+	0.986306i	$0.447261\pi$
$984$	0	0
$985$	−1.55571e19	−0.542740
$986$	0	0
$987$	−4.25319e18	−0.146438
$988$	0	0
$989$	6.14193e19	2.08703
$990$	0	0
$991$	−1.96605e19	−0.659351	−0.329675	−	0.944094i	$-0.606939\pi$
$991$	−1.96605e19	−0.659351	−0.329675	+	0.944094i	$0.606939\pi$
$992$	0	0
$993$	−4.17050e19	−1.38044
$994$	0	0
$995$	6.66677e19	2.17804
$996$	0	0
$997$	−2.59924e19	−0.838161	−0.419080	−	0.907949i	$-0.637647\pi$
$997$	−2.59924e19	−0.838161	−0.419080	+	0.907949i	$0.637647\pi$
$998$	0	0
$999$	−4.02068e19	−1.27975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.14.a.h.1.1		1
4.3	odd	2		64.14.a.b.1.1		1
8.3	odd	2		2.14.a.b.1.1	✓	1
8.5	even	2		16.14.a.a.1.1		1
24.5	odd	2		144.14.a.l.1.1		1
24.11	even	2		18.14.a.c.1.1		1
40.3	even	4		50.14.b.d.49.1		2
40.19	odd	2		50.14.a.a.1.1		1
40.27	even	4		50.14.b.d.49.2		2
56.3	even	6		98.14.c.d.79.1		2
56.11	odd	6		98.14.c.a.79.1		2
56.19	even	6		98.14.c.d.67.1		2
56.27	even	2		98.14.a.c.1.1		1
56.51	odd	6		98.14.c.a.67.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.14.a.b.1.1	✓	1	8.3	odd	2
16.14.a.a.1.1		1	8.5	even	2
18.14.a.c.1.1		1	24.11	even	2
50.14.a.a.1.1		1	40.19	odd	2
50.14.b.d.49.1		2	40.3	even	4
50.14.b.d.49.2		2	40.27	even	4
64.14.a.b.1.1		1	4.3	odd	2
64.14.a.h.1.1		1	1.1	even	1	trivial
98.14.a.c.1.1		1	56.27	even	2
98.14.c.a.67.1		2	56.51	odd	6
98.14.c.a.79.1		2	56.11	odd	6
98.14.c.d.67.1		2	56.19	even	6
98.14.c.d.79.1		2	56.3	even	6
144.14.a.l.1.1		1	24.5	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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