LMFDB - Embedded newform 35.23.c.a.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,23,Mod(34,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 23, names="a")

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

chi := DirichletCharacter("35.34");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 23 $
Character orbit:	$[\chi]$	$=$	35.c (of order $2$, degree $1$, minimal)

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:	$107.347602195$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			34.1
Character	$\chi$	$=$	35.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-341351. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} +1.97733e9 q^{7} +8.51394e10 q^{9} +3.54730e11 q^{11} -1.43173e12 q^{12} +1.43153e12 q^{13} +1.66675e13 q^{15} +1.75922e13 q^{16} +6.65471e13 q^{17} -2.04800e14 q^{20} -6.74962e14 q^{21} +2.38419e15 q^{25} -1.83505e16 q^{27} +8.29351e15 q^{28} +2.37747e16 q^{29} -1.21088e17 q^{33} -9.65492e16 q^{35} +3.57101e17 q^{36} -4.88655e17 q^{39} +1.48785e18 q^{44} -4.15720e18 q^{45} -2.60650e18 q^{47} -6.00511e18 q^{48} +3.90982e18 q^{49} -2.27159e19 q^{51} +6.00428e18 q^{52} -1.73208e19 q^{55} +6.99087e19 q^{60} +1.68349e20 q^{63} +7.37870e19 q^{64} -6.98990e19 q^{65} +2.79119e20 q^{68} -7.13315e19 q^{71} +3.31278e20 q^{73} -8.13844e20 q^{75} +7.01418e20 q^{77} -4.88366e20 q^{79} -8.58993e20 q^{80} +3.59219e21 q^{81} +7.43013e20 q^{83} -2.83100e21 q^{84} -3.24937e21 q^{85} -8.11553e21 q^{87} +2.83061e21 q^{91} +2.96499e21 q^{97} +3.02015e22 q^{99} +O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

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	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	−341351.	−1.92694	−0.963468	−	0.267823i	$-0.913696\pi$
$3$	−341351.	−1.92694	−0.963468	+	0.267823i	$0.913696\pi$
$4$	4.19430e6	1.00000
$5$	−4.88281e7	−1.00000
$5$	−4.88281e7	−1.00000
$6$	0	0
$7$	1.97733e9	1.00000
$7$	1.97733e9	1.00000
$8$	0	0
$9$	8.51394e10	2.71308
$10$	0	0
$11$	3.54730e11	1.24331	0.621654	−	0.783292i	$-0.286461\pi$
$11$	3.54730e11	1.24331	0.621654	+	0.783292i	$0.286461\pi$
$12$	−1.43173e12	−1.92694
$13$	1.43153e12	0.798774	0.399387	−	0.916782i	$-0.369223\pi$
$13$	1.43153e12	0.798774	0.399387	+	0.916782i	$0.369223\pi$
$14$	0	0
$15$	1.66675e13	1.92694
$16$	1.75922e13	1.00000
$17$	6.65471e13	1.94174	0.970870	−	0.239606i	$-0.0770181\pi$
$17$	6.65471e13	1.94174	0.970870	+	0.239606i	$0.0770181\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−2.04800e14	−1.00000
$21$	−6.74962e14	−1.92694
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	2.38419e15	1.00000
$26$	0	0
$27$	−1.83505e16	−3.30100
$28$	8.29351e15	1.00000
$29$	2.37747e16	1.94867	0.974333	−	0.225110i	$-0.0722742\pi$
$29$	2.37747e16	1.94867	0.974333	+	0.225110i	$0.0722742\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	−1.21088e17	−2.39578
$34$	0	0
$35$	−9.65492e16	−1.00000
$36$	3.57101e17	2.71308
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−4.88655e17	−1.53919
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	1.48785e18	1.24331
$45$	−4.15720e18	−2.71308
$46$	0	0
$47$	−2.60650e18	−1.05434	−0.527171	−	0.849759i	$-0.676747\pi$
$47$	−2.60650e18	−1.05434	−0.527171	+	0.849759i	$0.676747\pi$
$48$	−6.00511e18	−1.92694
$49$	3.90982e18	1.00000
$50$	0	0
$51$	−2.27159e19	−3.74161
$52$	6.00428e18	0.798774
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	−1.73208e19	−1.24331
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	6.99087e19	1.92694
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	1.68349e20	2.71308
$64$	7.37870e19	1.00000
$65$	−6.98990e19	−0.798774
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	2.79119e20	1.94174
$69$	0	0
$70$	0	0
$71$	−7.13315e19	−0.308631	−0.154316	−	0.988022i	$-0.549317\pi$
$71$	−7.13315e19	−0.308631	−0.154316	+	0.988022i	$0.549317\pi$
$72$	0	0
$73$	3.31278e20	1.05594	0.527972	−	0.849262i	$-0.322952\pi$
$73$	3.31278e20	1.05594	0.527972	+	0.849262i	$0.322952\pi$
$74$	0	0
$75$	−8.13844e20	−1.92694
$76$	0	0
$77$	7.01418e20	1.24331
$78$	0	0
$79$	−4.88366e20	−0.652901	−0.326451	−	0.945214i	$-0.605853\pi$
$79$	−4.88366e20	−0.652901	−0.326451	+	0.945214i	$0.605853\pi$
$80$	−8.58993e20	−1.00000
$81$	3.59219e21	3.64774
$82$	0	0
$83$	7.43013e20	0.576949	0.288474	−	0.957488i	$-0.406852\pi$
$83$	7.43013e20	0.576949	0.288474	+	0.957488i	$0.406852\pi$
$84$	−2.83100e21	−1.92694
$85$	−3.24937e21	−1.94174
$86$	0	0
$87$	−8.11553e21	−3.75496
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	2.83061e21	0.798774
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	2.96499e21	0.414509	0.207254	−	0.978287i	$-0.433547\pi$
$97$	2.96499e21	0.414509	0.207254	+	0.978287i	$0.433547\pi$
$98$	0	0
$99$	3.02015e22	3.37320
$100$	1.00000e22	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	2.67126e22	1.92978	0.964888	−	0.262662i	$-0.0846003\pi$
$103$	2.67126e22	1.92978	0.964888	+	0.262662i	$0.0846003\pi$
$104$	0	0
$105$	3.29572e22	1.92694
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−7.69675e22	−3.30100
$109$	−4.83009e22	−1.87182	−0.935909	−	0.352241i	$-0.885420\pi$
$109$	−4.83009e22	−1.87182	−0.935909	+	0.352241i	$0.885420\pi$
$110$	0	0
$111$	0	0
$112$	3.47855e22	1.00000
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	9.97184e22	1.94867
$117$	1.21880e23	2.16714
$118$	0	0
$119$	1.31585e23	1.94174
$120$	0	0
$121$	4.44308e22	0.545814
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−1.16415e23	−1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	−5.07878e23	−2.39578
$133$	0	0
$134$	0	0
$135$	8.96019e23	3.30100
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	−4.04957e23	−1.00000
$141$	8.89731e23	2.03165
$142$	0	0
$143$	5.07808e23	0.993123
$144$	1.49779e24	2.71308
$145$	−1.16088e24	−1.94867
$146$	0	0
$147$	−1.33462e24	−1.92694
$148$	0	0
$149$	−1.09615e24	−1.36402	−0.682011	−	0.731342i	$-0.738894\pi$
$149$	−1.09615e24	−1.36402	−0.682011	+	0.731342i	$0.738894\pi$
$150$	0	0
$151$	8.48941e23	0.912286	0.456143	−	0.889906i	$-0.349231\pi$
$151$	8.48941e23	0.912286	0.456143	+	0.889906i	$0.349231\pi$
$152$	0	0
$153$	5.66579e24	5.26811
$154$	0	0
$155$	0	0
$156$	−2.04957e24	−1.53919
$157$	2.83014e24	1.98113	0.990564	−	0.137054i	$-0.0437635\pi$
$157$	2.83014e24	1.98113	0.990564	+	0.137054i	$0.0437635\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	5.91248e24	2.39578
$166$	0	0
$167$	−4.70119e24	−1.66850	−0.834250	−	0.551386i	$-0.814099\pi$
$167$	−4.70119e24	−1.66850	−0.834250	+	0.551386i	$0.814099\pi$
$168$	0	0
$169$	−1.16255e24	−0.361959
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−8.08485e24	−1.94610	−0.973049	−	0.230599i	$-0.925931\pi$
$173$	−8.08485e24	−1.94610	−0.973049	+	0.230599i	$0.925931\pi$
$174$	0	0
$175$	4.71431e24	1.00000
$176$	6.24048e24	1.24331
$177$	0	0
$178$	0	0
$179$	−9.60940e24	−1.58969	−0.794846	−	0.606811i	$-0.792448\pi$
$179$	−9.60940e24	−1.58969	−0.794846	+	0.606811i	$0.792448\pi$
$180$	−1.74366e25	−2.71308
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	2.36063e25	2.41418
$188$	−1.09325e25	−1.05434
$189$	−3.62849e25	−3.30100
$190$	0	0
$191$	8.17437e23	0.0662349	0.0331175	−	0.999451i	$-0.489456\pi$
$191$	8.17437e23	0.0662349	0.0331175	+	0.999451i	$0.489456\pi$
$192$	−2.51873e25	−1.92694
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	2.38601e25	1.53919
$196$	1.63990e25	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	4.70104e25	1.94867
$204$	−9.52775e25	−3.74161
$205$	0	0
$206$	0	0
$207$	0	0
$208$	2.51838e25	0.798774
$209$	0	0
$210$	0	0
$211$	−2.33390e25	−0.632376	−0.316188	−	0.948697i	$-0.602403\pi$
$211$	−2.33390e25	−0.632376	−0.316188	+	0.948697i	$0.602403\pi$
$212$	0	0
$213$	2.43491e25	0.594713
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−1.13082e26	−2.03474
$220$	−7.26488e25	−1.24331
$221$	9.52644e25	1.55101
$222$	0	0
$223$	3.63740e25	0.536336	0.268168	−	0.963372i	$-0.413582\pi$
$223$	3.63740e25	0.536336	0.268168	+	0.963372i	$0.413582\pi$
$224$	0	0
$225$	2.02988e26	2.71308
$226$	0	0
$227$	−1.50666e26	−1.82696	−0.913482	−	0.406880i	$-0.866617\pi$
$227$	−1.50666e26	−1.82696	−0.913482	+	0.406880i	$0.866617\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−2.39430e26	−2.39578
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	1.27270e26	1.05434
$236$	0	0
$237$	1.66704e26	1.25810
$238$	0	0
$239$	−2.84004e26	−1.95410	−0.977050	−	0.213010i	$-0.931673\pi$
$239$	−2.84004e26	−1.95410	−0.977050	+	0.213010i	$0.931673\pi$
$240$	2.93218e26	1.92694
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−6.50340e26	−3.72796
$244$	0	0
$245$	−1.90909e26	−1.00000
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−2.53628e26	−1.11174
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	7.06105e26	2.71308
$253$	0	0
$254$	0	0
$255$	1.10918e27	3.74161
$256$	3.09485e26	1.00000
$257$	−6.44812e26	−1.99604	−0.998019	−	0.0629069i	$-0.979963\pi$
$257$	−6.44812e26	−1.99604	−0.998019	+	0.0629069i	$0.979963\pi$
$258$	0	0
$259$	0	0
$260$	−2.93178e26	−0.798774
$261$	2.02417e27	5.28690
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	1.17071e27	1.94174
$273$	−9.66230e26	−1.53919
$274$	0	0
$275$	8.45743e26	1.24331
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−1.24918e27	−1.44829	−0.724144	−	0.689649i	$-0.757765\pi$
$281$	−1.24918e27	−1.44829	−0.724144	+	0.689649i	$0.757765\pi$
$282$	0	0
$283$	2.98973e26	0.320613	0.160306	−	0.987067i	$-0.448752\pi$
$283$	2.98973e26	0.320613	0.160306	+	0.987067i	$0.448752\pi$
$284$	−2.99186e26	−0.308631
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	3.25396e27	2.77036
$290$	0	0
$291$	−1.01210e27	−0.798732
$292$	1.38948e27	1.05594
$293$	9.54220e26	0.698401	0.349201	−	0.937048i	$-0.386453\pi$
$293$	9.54220e26	0.698401	0.349201	+	0.937048i	$0.386453\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−6.50947e27	−4.10416
$298$	0	0
$299$	0	0
$300$	−3.41351e27	−1.92694
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−2.08748e27	−0.914325	−0.457163	−	0.889383i	$-0.651134\pi$
$307$	−2.08748e27	−0.914325	−0.457163	+	0.889383i	$0.651134\pi$
$308$	2.94196e27	1.24331
$309$	−9.11838e27	−3.71856
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	4.15891e27	1.47228	0.736142	−	0.676827i	$-0.236646\pi$
$313$	4.15891e27	1.47228	0.736142	+	0.676827i	$0.236646\pi$
$314$	0	0
$315$	−8.22014e27	−2.71308
$316$	−2.04836e27	−0.652901
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	8.43361e27	2.42279
$320$	−3.60288e27	−1.00000
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.50667e28	3.64774
$325$	3.41304e27	0.798774
$326$	0	0
$327$	1.64876e28	3.60688
$328$	0	0
$329$	−5.15390e27	−1.05434
$330$	0	0
$331$	−1.71002e27	−0.327261	−0.163630	−	0.986522i	$-0.552320\pi$
$331$	−1.71002e27	−0.327261	−0.163630	+	0.986522i	$0.552320\pi$
$332$	3.11642e27	0.576949
$333$	0	0
$334$	0	0
$335$	0	0
$336$	−1.18741e28	−1.92694
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	−1.36289e28	−1.94174
$341$	0	0
$342$	0	0
$343$	7.73099e27	1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	−3.40390e28	−3.75496
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	−2.62693e28	−2.63676
$352$	0	0
$353$	1.73953e28	1.64025	0.820125	−	0.572185i	$-0.193904\pi$
$353$	1.73953e28	1.64025	0.820125	+	0.572185i	$0.193904\pi$
$354$	0	0
$355$	3.48299e27	0.308631
$356$	0	0
$357$	−4.49168e28	−3.74161
$358$	0	0
$359$	1.94797e28	1.52596	0.762980	−	0.646422i	$-0.223736\pi$
$359$	1.94797e28	1.52596	0.762980	+	0.646422i	$0.223736\pi$
$360$	0	0
$361$	1.35700e28	1.00000
$362$	0	0
$363$	−1.51665e28	−1.05175
$364$	1.18724e28	0.798774
$365$	−1.61757e28	−1.05594
$366$	0	0
$367$	−3.36310e27	−0.206735	−0.103367	−	0.994643i	$-0.532962\pi$
$367$	−3.36310e27	−0.206735	−0.103367	+	0.994643i	$0.532962\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	3.97385e28	1.92694
$376$	0	0
$377$	3.40343e28	1.55655
$378$	0	0
$379$	4.60797e28	1.98828	0.994142	−	0.108082i	$-0.0344709\pi$
$379$	4.60797e28	1.98828	0.994142	+	0.108082i	$0.0344709\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	5.05662e28	1.94390	0.971950	−	0.235189i	$-0.0755708\pi$
$383$	5.05662e28	1.94390	0.971950	+	0.235189i	$0.0755708\pi$
$384$	0	0
$385$	−3.42489e28	−1.24331
$386$	0	0
$387$	0	0
$388$	1.24361e28	0.414509
$389$	−6.08327e28	−1.97102	−0.985511	−	0.169609i	$-0.945750\pi$
$389$	−6.08327e28	−1.97102	−0.985511	+	0.169609i	$0.945750\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	2.38460e28	0.652901
$396$	1.26674e29	3.37320
$397$	4.68028e28	1.21221	0.606103	−	0.795386i	$-0.292732\pi$
$397$	4.68028e28	1.21221	0.606103	+	0.795386i	$0.292732\pi$
$398$	0	0
$399$	0	0
$400$	4.19430e28	1.00000
$401$	7.26758e28	1.68578	0.842892	−	0.538083i	$-0.180851\pi$
$401$	7.26758e28	1.68578	0.842892	+	0.538083i	$0.180851\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−1.75400e29	−3.64774
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	1.12041e29	1.92978
$413$	0	0
$414$	0	0
$415$	−3.62799e28	−0.576949
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	1.38232e29	1.92694
$421$	−1.34776e29	−1.83025	−0.915125	−	0.403169i	$-0.867909\pi$
$421$	−1.34776e29	−1.83025	−0.915125	+	0.403169i	$0.867909\pi$
$422$	0	0
$423$	−2.21916e29	−2.86052
$424$	0	0
$425$	1.58661e29	1.94174
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−1.73341e29	−1.91368
$430$	0	0
$431$	3.84058e27	0.0402853	0.0201427	−	0.999797i	$-0.493588\pi$
$431$	3.84058e27	0.0402853	0.0201427	+	0.999797i	$0.493588\pi$
$432$	−3.22825e29	−3.30100
$433$	−1.62515e29	−1.62004	−0.810019	−	0.586403i	$-0.800543\pi$
$433$	−1.62515e29	−1.62004	−0.810019	+	0.586403i	$0.800543\pi$
$434$	0	0
$435$	3.96266e29	3.75496
$436$	−2.02589e29	−1.87182
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	3.32880e29	2.71308
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	3.74172e29	2.62838
$448$	1.45901e29	1.00000
$449$	1.32742e27	0.00887768	0.00443884	−	0.999990i	$-0.498587\pi$
$449$	1.32742e27	0.00887768	0.00443884	+	0.999990i	$0.498587\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−2.89787e29	−1.75792
$454$	0	0
$455$	−1.38213e29	−0.798774
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	−1.22117e30	−6.40969
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	4.18249e29	1.94867
$465$	0	0
$466$	0	0
$467$	2.78546e29	1.20896	0.604479	−	0.796621i	$-0.293381\pi$
$467$	2.78546e29	1.20896	0.604479	+	0.796621i	$0.293381\pi$
$468$	5.11201e29	2.16714
$469$	0	0
$470$	0	0
$471$	−9.66072e29	−3.81751
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	5.51909e29	1.94174
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	1.86356e29	0.545814
$485$	−1.44775e29	−0.414509
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−7.45628e29	−1.86477	−0.932386	−	0.361464i	$-0.882277\pi$
$491$	−7.45628e29	−1.86477	−0.932386	+	0.361464i	$0.882277\pi$
$492$	0	0
$493$	1.58214e30	3.78381
$494$	0	0
$495$	−1.47468e30	−3.37320
$496$	0	0
$497$	−1.41046e29	−0.308631
$498$	0	0
$499$	−8.65465e29	−1.81194	−0.905970	−	0.423343i	$-0.860857\pi$
$499$	−8.65465e29	−1.81194	−0.905970	+	0.423343i	$0.860857\pi$
$500$	−4.88281e29	−1.00000
$501$	1.60475e30	3.21509
$502$	0	0
$503$	−1.00928e30	−1.93537	−0.967684	−	0.252166i	$-0.918857\pi$
$503$	−1.00928e30	−1.93537	−0.967684	+	0.252166i	$0.918857\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	3.96839e29	0.697473
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	6.55045e29	1.05594
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−1.30433e30	−1.92978
$516$	0	0
$517$	−9.24604e29	−1.31087
$518$	0	0
$519$	2.75977e30	3.75001
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	5.41321e29	0.675984	0.337992	−	0.941149i	$-0.390252\pi$
$523$	5.41321e29	0.675984	0.337992	+	0.941149i	$0.390252\pi$
$524$	0	0
$525$	−1.60924e30	−1.92694
$526$	0	0
$527$	0	0
$528$	−2.13019e30	−2.39578
$529$	9.07846e29	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	3.28018e30	3.06324
$538$	0	0
$539$	1.38693e30	1.24331
$540$	3.75818e30	3.30100
$541$	−1.59737e30	−1.37479	−0.687395	−	0.726284i	$-0.741246\pi$
$541$	−1.59737e30	−1.37479	−0.687395	+	0.726284i	$0.741246\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	2.35844e30	1.87182
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−9.65659e29	−0.652901
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	−1.69851e30	−1.00000
$561$	−8.05803e30	−4.65197
$562$	0	0
$563$	−1.23528e30	−0.685760	−0.342880	−	0.939379i	$-0.611402\pi$
$563$	−1.23528e30	−0.685760	−0.342880	+	0.939379i	$0.611402\pi$
$564$	3.73180e30	2.03165
$565$	0	0
$566$	0	0
$567$	7.10293e30	3.64774
$568$	0	0
$569$	3.77809e30	1.86654	0.933271	−	0.359174i	$-0.116941\pi$
$569$	3.77809e30	1.86654	0.933271	+	0.359174i	$0.116941\pi$
$570$	0	0
$571$	3.82070e30	1.81613	0.908063	−	0.418835i	$-0.137561\pi$
$571$	3.82070e30	1.81613	0.908063	+	0.418835i	$0.137561\pi$
$572$	2.12990e30	0.993123
$573$	−2.79033e29	−0.127630
$574$	0	0
$575$	0	0
$576$	6.28218e30	2.71308
$577$	−1.28839e30	−0.545901	−0.272951	−	0.962028i	$-0.588000\pi$
$577$	−1.28839e30	−0.545901	−0.272951	+	0.962028i	$0.588000\pi$
$578$	0	0
$579$	0	0
$580$	−4.86906e30	−1.94867
$581$	1.46918e30	0.576949
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−5.95116e30	−2.16714
$586$	0	0
$587$	−3.35072e30	−1.17522	−0.587610	−	0.809144i	$-0.699931\pi$
$587$	−3.35072e30	−1.17522	−0.587610	+	0.809144i	$0.699931\pi$
$588$	−5.59781e30	−1.92694
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−1.53477e30	−0.481330	−0.240665	−	0.970608i	$-0.577365\pi$
$593$	−1.53477e30	−0.481330	−0.240665	+	0.970608i	$0.577365\pi$
$594$	0	0
$595$	−6.42507e30	−1.94174
$596$	−4.59759e30	−1.36402
$597$	0	0
$598$	0	0
$599$	−9.84624e29	−0.276424	−0.138212	−	0.990403i	$-0.544135\pi$
$599$	−9.84624e29	−0.276424	−0.138212	+	0.990403i	$0.544135\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	3.56072e30	0.912286
$605$	−2.16947e30	−0.545814
$606$	0	0
$607$	−8.12599e30	−1.97152	−0.985758	−	0.168168i	$-0.946215\pi$
$607$	−8.12599e30	−1.97152	−0.985758	+	0.168168i	$0.946215\pi$
$608$	0	0
$609$	−1.60470e31	−3.75496
$610$	0	0
$611$	−3.73129e30	−0.842181
$612$	2.37640e31	5.26811
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	−8.59651e30	−1.53919
$625$	5.68434e30	1.00000
$626$	0	0
$627$	0	0
$628$	1.18705e31	1.98113
$629$	0	0
$630$	0	0
$631$	−1.12879e30	−0.178769	−0.0893845	−	0.995997i	$-0.528490\pi$
$631$	−1.12879e30	−0.178769	−0.0893845	+	0.995997i	$0.528490\pi$
$632$	0	0
$633$	7.96680e30	1.21855
$634$	0	0
$635$	0	0
$636$	0	0
$637$	5.59703e30	0.798774
$638$	0	0
$639$	−6.07313e30	−0.837342
$640$	0	0
$641$	2.11566e30	0.281843	0.140922	−	0.990021i	$-0.454993\pi$
$641$	2.11566e30	0.281843	0.140922	+	0.990021i	$0.454993\pi$
$642$	0	0
$643$	−1.51516e31	−1.95046	−0.975230	−	0.221192i	$-0.929005\pi$
$643$	−1.51516e31	−1.95046	−0.975230	+	0.221192i	$0.929005\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−8.48066e29	−0.101972	−0.0509862	−	0.998699i	$-0.516236\pi$
$647$	−8.48066e29	−0.101972	−0.0509862	+	0.998699i	$0.516236\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	2.82048e31	2.86487
$658$	0	0
$659$	−1.67930e31	−1.64964	−0.824819	−	0.565396i	$-0.808723\pi$
$659$	−1.67930e31	−1.64964	−0.824819	+	0.565396i	$0.808723\pi$
$660$	2.47987e31	2.39578
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	−3.25186e31	−2.98870
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−1.97182e31	−1.66850
$669$	−1.24163e31	−1.03349
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−4.37510e31	−3.30100
$676$	−4.87611e30	−0.361959
$677$	2.66811e31	1.94863	0.974313	−	0.225196i	$-0.0723023\pi$
$677$	2.66811e31	1.94863	0.974313	+	0.225196i	$0.0723023\pi$
$678$	0	0
$679$	5.86275e30	0.414509
$680$	0	0
$681$	5.14299e31	3.52044
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	−3.39103e31	−1.94610
$693$	5.97183e31	3.37320
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	1.97733e31	1.00000
$701$	2.47870e31	1.23403	0.617015	−	0.786952i	$-0.288342\pi$
$701$	2.47870e31	1.23403	0.617015	+	0.786952i	$0.288342\pi$
$702$	0	0
$703$	0	0
$704$	2.61745e31	1.24331
$705$	−4.34439e31	−2.03165
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−4.16841e31	−1.83173	−0.915865	−	0.401485i	$-0.868494\pi$
$709$	−4.16841e31	−1.83173	−0.915865	+	0.401485i	$0.868494\pi$
$710$	0	0
$711$	−4.15792e31	−1.77138
$712$	0	0
$713$	0	0
$714$	0	0
$715$	−2.47953e31	−0.993123
$716$	−4.03048e31	−1.58969
$717$	9.69449e31	3.76543
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−7.31342e31	−2.71308
$721$	5.28196e31	1.92978
$722$	0	0
$723$	0	0
$724$	0	0
$725$	5.66834e31	1.94867
$726$	0	0
$727$	3.34349e31	1.11512	0.557560	−	0.830137i	$-0.311738\pi$
$727$	3.34349e31	1.11512	0.557560	+	0.830137i	$0.311738\pi$
$728$	0	0
$729$	1.09267e32	3.53580
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−3.28167e31	−0.999889	−0.499944	−	0.866057i	$-0.666646\pi$
$733$	−3.28167e31	−0.999889	−0.499944	+	0.866057i	$0.666646\pi$
$734$	0	0
$735$	6.51671e31	1.92694
$736$	0	0
$737$	0	0
$738$	0	0
$739$	1.63960e31	0.456719	0.228359	−	0.973577i	$-0.426664\pi$
$739$	1.63960e31	0.456719	0.228359	+	0.973577i	$0.426664\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	5.35230e31	1.36402
$746$	0	0
$747$	6.32597e31	1.56531
$748$	9.90119e31	2.41418
$749$	0	0
$750$	0	0
$751$	−4.52385e31	−1.05553	−0.527763	−	0.849392i	$-0.676969\pi$
$751$	−4.52385e31	−1.05553	−0.527763	+	0.849392i	$0.676969\pi$
$752$	−4.58540e31	−1.05434
$753$	0	0
$754$	0	0
$755$	−4.14522e31	−0.912286
$756$	−1.52190e32	−3.30100
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	−9.55067e31	−1.87182
$764$	3.42858e30	0.0662349
$765$	−2.76650e32	−5.26811
$766$	0	0
$767$	0	0
$768$	−1.05643e32	−1.92694
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	2.20107e32	3.84624
$772$	0	0
$773$	7.45844e31	1.26670	0.633350	−	0.773866i	$-0.281679\pi$
$773$	7.45844e31	1.26670	0.633350	+	0.773866i	$0.281679\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	1.00077e32	1.53919
$781$	−2.53035e31	−0.383724
$782$	0	0
$783$	−4.36278e32	−6.43256
$784$	6.87823e31	1.00000
$785$	−1.38191e32	−1.98113
$786$	0	0
$787$	5.80416e30	0.0809128	0.0404564	−	0.999181i	$-0.487119\pi$
$787$	5.80416e30	0.0809128	0.0404564	+	0.999181i	$0.487119\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	1.64720e32	1.99851	0.999253	−	0.0386338i	$-0.0123006\pi$
$797$	1.64720e32	1.99851	0.999253	+	0.0386338i	$0.0123006\pi$
$798$	0	0
$799$	−1.73455e32	−2.04726
$800$	0	0
$801$	0	0
$802$	0	0
$803$	1.17514e32	1.31286
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	1.19103e32	1.22600	0.613000	−	0.790083i	$-0.289963\pi$
$809$	1.19103e32	1.22600	0.613000	+	0.790083i	$0.289963\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	1.97176e32	1.94867
$813$	0	0
$814$	0	0
$815$	0	0
$816$	−3.99623e32	−3.74161
$817$	0	0
$818$	0	0
$819$	2.40996e32	2.16714
$820$	0	0
$821$	−1.47953e32	−1.29524	−0.647620	−	0.761964i	$-0.724235\pi$
$821$	−1.47953e32	−1.29524	−0.647620	+	0.761964i	$0.724235\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−2.88695e32	−2.39578
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	1.05628e32	0.798774
$833$	2.60187e32	1.94174
$834$	0	0
$835$	2.29550e32	1.66850
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	4.16385e32	2.79730
$842$	0	0
$843$	4.26408e32	2.79076
$844$	−9.78909e31	−0.632376
$845$	5.67654e31	0.361959
$846$	0	0
$847$	8.78542e31	0.545814
$848$	0	0
$849$	−1.02055e32	−0.617801
$850$	0	0
$851$	0	0
$852$	1.02127e32	0.594713
$853$	−1.83256e32	−1.05346	−0.526730	−	0.850033i	$-0.676582\pi$
$853$	−1.83256e32	−1.05346	−0.526730	+	0.850033i	$0.676582\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−3.65955e32	−1.99820	−0.999099	−	0.0424323i	$-0.986489\pi$
$857$	−3.65955e32	−1.99820	−0.999099	+	0.0424323i	$0.986489\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	3.94768e32	1.94610
$866$	0	0
$867$	−1.11074e33	−5.33830
$868$	0	0
$869$	−1.73238e32	−0.811757
$870$	0	0
$871$	0	0
$872$	0	0
$873$	2.52437e32	1.12460
$874$	0	0
$875$	−2.30191e32	−1.00000
$876$	−4.74301e32	−2.03474
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	−3.25724e32	−1.34577
$880$	−3.04711e32	−1.24331
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	3.99568e32	1.55101
$885$	0	0
$886$	0	0
$887$	−2.00085e31	−0.0748264	−0.0374132	−	0.999300i	$-0.511912\pi$
$887$	−2.00085e31	−0.0748264	−0.0374132	+	0.999300i	$0.511912\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	1.27426e33	4.53526
$892$	1.52563e32	0.536336
$893$	0	0
$894$	0	0
$895$	4.69209e32	1.58969
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	8.51394e32	2.71308
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	−6.31938e32	−1.82696
$909$	0	0
$910$	0	0
$911$	2.18633e32	0.609557	0.304778	−	0.952423i	$-0.401418\pi$
$911$	2.18633e32	0.609557	0.304778	+	0.952423i	$0.401418\pi$
$912$	0	0
$913$	2.63569e32	0.717325
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	1.85644e31	0.0470121	0.0235060	−	0.999724i	$-0.492517\pi$
$919$	1.85644e31	0.0470121	0.0235060	+	0.999724i	$0.492517\pi$
$920$	0	0
$921$	7.12564e32	1.76185
$922$	0	0
$923$	−1.02113e32	−0.246527
$924$	−1.00424e33	−2.39578
$925$	0	0
$926$	0	0
$927$	2.27430e33	5.23564
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−1.15265e33	−2.41418
$936$	0	0
$937$	−7.31013e32	−1.49551	−0.747756	−	0.663974i	$-0.768869\pi$
$937$	−7.31013e32	−1.49551	−0.747756	+	0.663974i	$0.768869\pi$
$938$	0	0
$939$	−1.41965e33	−2.83700
$940$	5.33811e32	1.05434
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	1.77172e33	3.30100
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	6.99208e32	1.25810
$949$	4.74235e32	0.843462
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	−3.99139e31	−0.0662349
$956$	−1.19120e33	−1.95410
$957$	−2.87882e33	−4.66857
$958$	0	0
$959$	0	0
$960$	1.22985e33	1.92694
$961$	6.45591e32	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−2.72772e33	−3.72796
$973$	0	0
$974$	0	0
$975$	−1.16504e33	−1.53919
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	−8.00731e32	−1.00000
$981$	−4.11231e33	−5.07840
$982$	0	0
$983$	−6.31158e32	−0.762165	−0.381083	−	0.924541i	$-0.624449\pi$
$983$	−6.31158e32	−0.762165	−0.381083	+	0.924541i	$0.624449\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	1.75929e33	2.03165
$988$	0	0
$989$	0	0
$990$	0	0
$991$	1.48313e33	1.63821	0.819103	−	0.573647i	$-0.194472\pi$
$991$	1.48313e33	1.63821	0.819103	+	0.573647i	$0.194472\pi$
$992$	0	0
$993$	5.83718e32	0.630610
$994$	0	0
$995$	0	0
$996$	−1.06379e33	−1.11174
$997$	−1.86741e33	−1.93016	−0.965081	−	0.261951i	$-0.915634\pi$
$997$	−1.86741e33	−1.93016	−0.965081	+	0.261951i	$0.915634\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.23.c.a.34.1	✓	1
5.4	even	2		35.23.c.b.34.1	yes	1
7.6	odd	2		35.23.c.b.34.1	yes	1
35.34	odd	2	CM	35.23.c.a.34.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.23.c.a.34.1	✓	1	1.1	even	1	trivial
35.23.c.a.34.1	✓	1	35.34	odd	2	CM
35.23.c.b.34.1	yes	1	5.4	even	2
35.23.c.b.34.1	yes	1	7.6	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(n\)	\(22\)	\(31\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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