LMFDB - Embedded newform 2275.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2275,2,Mod(1,2275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2275, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2275 = 5^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2275.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:	$18.1659664598$
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	$\chi$	$=$	2275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +1.00000 q^{3} +2.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} -2.00000 q^{9} +4.00000 q^{11} +2.00000 q^{12} -1.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} -2.00000 q^{17} +4.00000 q^{18} +2.00000 q^{19} -1.00000 q^{21} -8.00000 q^{22} -3.00000 q^{23} +2.00000 q^{26} -5.00000 q^{27} -2.00000 q^{28} +1.00000 q^{29} +2.00000 q^{31} +8.00000 q^{32} +4.00000 q^{33} +4.00000 q^{34} -4.00000 q^{36} -10.0000 q^{37} -4.00000 q^{38} -1.00000 q^{39} +2.00000 q^{42} +7.00000 q^{43} +8.00000 q^{44} +6.00000 q^{46} -12.0000 q^{47} -4.00000 q^{48} +1.00000 q^{49} -2.00000 q^{51} -2.00000 q^{52} +5.00000 q^{53} +10.0000 q^{54} +2.00000 q^{57} -2.00000 q^{58} +6.00000 q^{59} +5.00000 q^{61} -4.00000 q^{62} +2.00000 q^{63} -8.00000 q^{64} -8.00000 q^{66} -10.0000 q^{67} -4.00000 q^{68} -3.00000 q^{69} -6.00000 q^{71} -4.00000 q^{73} +20.0000 q^{74} +4.00000 q^{76} -4.00000 q^{77} +2.00000 q^{78} -9.00000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -2.00000 q^{84} -14.0000 q^{86} +1.00000 q^{87} +1.00000 q^{91} -6.00000 q^{92} +2.00000 q^{93} +24.0000 q^{94} +8.00000 q^{96} +14.0000 q^{97} -2.00000 q^{98} -8.00000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.816497
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	2.00000	0.577350
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.00000	0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	4.00000	0.942809
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−8.00000	−1.70561
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	0	0
$26$	2.00000	0.392232
$27$	−5.00000	−0.962250
$28$	−2.00000	−0.377964
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	8.00000	1.41421
$33$	4.00000	0.696311
$34$	4.00000	0.685994
$35$	0	0
$36$	−4.00000	−0.666667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−4.00000	−0.648886
$39$	−1.00000	−0.160128
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	2.00000	0.308607
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	8.00000	1.20605
$45$	0	0
$46$	6.00000	0.884652
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	−4.00000	−0.577350
$49$	1.00000	0.142857
$50$	0	0
$51$	−2.00000	−0.280056
$52$	−2.00000	−0.277350
$53$	5.00000	0.686803	0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000	0.686803	0.343401	+	0.939189i	$0.388421\pi$
$54$	10.0000	1.36083
$55$	0	0
$56$	0	0
$57$	2.00000	0.264906
$58$	−2.00000	−0.262613
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	−4.00000	−0.508001
$63$	2.00000	0.251976
$64$	−8.00000	−1.00000
$65$	0	0
$66$	−8.00000	−0.984732
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−4.00000	−0.485071
$69$	−3.00000	−0.361158
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	20.0000	2.32495
$75$	0	0
$76$	4.00000	0.458831
$77$	−4.00000	−0.455842
$78$	2.00000	0.226455
$79$	−9.00000	−1.01258	−0.506290	−	0.862364i	$-0.668983\pi$
$79$	−9.00000	−1.01258	−0.506290	+	0.862364i	$0.668983\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−14.0000	−1.50966
$87$	1.00000	0.107211
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−6.00000	−0.625543
$93$	2.00000	0.207390
$94$	24.0000	2.47541
$95$	0	0
$96$	8.00000	0.816497
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−2.00000	−0.202031
$99$	−8.00000	−0.804030
$100$	0	0
$101$	−13.0000	−1.29355	−0.646774	−	0.762682i	$-0.723882\pi$
$101$	−13.0000	−1.29355	−0.646774	+	0.762682i	$0.723882\pi$
$102$	4.00000	0.396059
$103$	−13.0000	−1.28093	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000	−1.28093	−0.640464	+	0.767988i	$0.721258\pi$
$104$	0	0
$105$	0	0
$106$	−10.0000	−0.971286
$107$	17.0000	1.64345	0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000	1.64345	0.821726	+	0.569883i	$0.193011\pi$
$108$	−10.0000	−0.962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	−10.0000	−0.949158
$112$	4.00000	0.377964
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	2.00000	0.185695
$117$	2.00000	0.184900
$118$	−12.0000	−1.10469
$119$	2.00000	0.183340
$120$	0	0
$121$	5.00000	0.454545
$122$	−10.0000	−0.905357
$123$	0	0
$124$	4.00000	0.359211
$125$	0	0
$126$	−4.00000	−0.356348
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	0	0
$129$	7.00000	0.616316
$130$	0	0
$131$	−1.00000	−0.0873704	−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000	−0.0873704	−0.0436852	+	0.999045i	$0.513910\pi$
$132$	8.00000	0.696311
$133$	−2.00000	−0.173422
$134$	20.0000	1.72774
$135$	0	0
$136$	0	0
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	6.00000	0.510754
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	12.0000	1.00702
$143$	−4.00000	−0.334497
$144$	8.00000	0.666667
$145$	0	0
$146$	8.00000	0.662085
$147$	1.00000	0.0824786
$148$	−20.0000	−1.64399
$149$	−16.0000	−1.31077	−0.655386	−	0.755295i	$-0.727494\pi$
$149$	−16.0000	−1.31077	−0.655386	+	0.755295i	$0.727494\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	4.00000	0.323381
$154$	8.00000	0.644658
$155$	0	0
$156$	−2.00000	−0.160128
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	18.0000	1.43200
$159$	5.00000	0.396526
$160$	0	0
$161$	3.00000	0.236433
$162$	−2.00000	−0.157135
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	0	0
$165$	0	0
$166$	24.0000	1.86276
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−4.00000	−0.305888
$172$	14.0000	1.06749
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−2.00000	−0.151620
$175$	0	0
$176$	−16.0000	−1.20605
$177$	6.00000	0.450988
$178$	0	0
$179$	−25.0000	−1.86859	−0.934294	−	0.356504i	$-0.883969\pi$
$179$	−25.0000	−1.86859	−0.934294	+	0.356504i	$0.883969\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	−2.00000	−0.148250
$183$	5.00000	0.369611
$184$	0	0
$185$	0	0
$186$	−4.00000	−0.293294
$187$	−8.00000	−0.585018
$188$	−24.0000	−1.75038
$189$	5.00000	0.363696
$190$	0	0
$191$	−7.00000	−0.506502	−0.253251	−	0.967401i	$-0.581500\pi$
$191$	−7.00000	−0.506502	−0.253251	+	0.967401i	$0.581500\pi$
$192$	−8.00000	−0.577350
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	−28.0000	−2.01028
$195$	0	0
$196$	2.00000	0.142857
$197$	−14.0000	−0.997459	−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000	−0.997459	−0.498729	+	0.866758i	$0.666200\pi$
$198$	16.0000	1.13707
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	0	0
$201$	−10.0000	−0.705346
$202$	26.0000	1.82935
$203$	−1.00000	−0.0701862
$204$	−4.00000	−0.280056
$205$	0	0
$206$	26.0000	1.81151
$207$	6.00000	0.417029
$208$	4.00000	0.277350
$209$	8.00000	0.553372
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	10.0000	0.686803
$213$	−6.00000	−0.411113
$214$	−34.0000	−2.32419
$215$	0	0
$216$	0	0
$217$	−2.00000	−0.135769
$218$	−4.00000	−0.270914
$219$	−4.00000	−0.270295
$220$	0	0
$221$	2.00000	0.134535
$222$	20.0000	1.34231
$223$	−22.0000	−1.47323	−0.736614	−	0.676313i	$-0.763577\pi$
$223$	−22.0000	−1.47323	−0.736614	+	0.676313i	$0.763577\pi$
$224$	−8.00000	−0.534522
$225$	0	0
$226$	18.0000	1.19734
$227$	−14.0000	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$227$	−14.0000	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$228$	4.00000	0.264906
$229$	−20.0000	−1.32164	−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000	−1.32164	−0.660819	+	0.750546i	$0.729791\pi$
$230$	0	0
$231$	−4.00000	−0.263181
$232$	0	0
$233$	−21.0000	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$234$	−4.00000	−0.261488
$235$	0	0
$236$	12.0000	0.781133
$237$	−9.00000	−0.584613
$238$	−4.00000	−0.259281
$239$	−22.0000	−1.42306	−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000	−1.42306	−0.711531	+	0.702655i	$0.751998\pi$
$240$	0	0
$241$	−16.0000	−1.03065	−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000	−1.03065	−0.515325	+	0.856995i	$0.672329\pi$
$242$	−10.0000	−0.642824
$243$	16.0000	1.02640
$244$	10.0000	0.640184
$245$	0	0
$246$	0	0
$247$	−2.00000	−0.127257
$248$	0	0
$249$	−12.0000	−0.760469
$250$	0	0
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	4.00000	0.251976
$253$	−12.0000	−0.754434
$254$	14.0000	0.878438
$255$	0	0
$256$	16.0000	1.00000
$257$	−19.0000	−1.18519	−0.592594	−	0.805502i	$-0.701896\pi$
$257$	−19.0000	−1.18519	−0.592594	+	0.805502i	$0.701896\pi$
$258$	−14.0000	−0.871602
$259$	10.0000	0.621370
$260$	0	0
$261$	−2.00000	−0.123797
$262$	2.00000	0.123560
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	4.00000	0.245256
$267$	0	0
$268$	−20.0000	−1.22169
$269$	3.00000	0.182913	0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000	0.182913	0.0914566	+	0.995809i	$0.470848\pi$
$270$	0	0
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	8.00000	0.485071
$273$	1.00000	0.0605228
$274$	12.0000	0.724947
$275$	0	0
$276$	−6.00000	−0.361158
$277$	31.0000	1.86261	0.931305	−	0.364241i	$-0.118672\pi$
$277$	31.0000	1.86261	0.931305	+	0.364241i	$0.118672\pi$
$278$	−26.0000	−1.55938
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−8.00000	−0.477240	−0.238620	−	0.971113i	$-0.576695\pi$
$281$	−8.00000	−0.477240	−0.238620	+	0.971113i	$0.576695\pi$
$282$	24.0000	1.42918
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	8.00000	0.473050
$287$	0	0
$288$	−16.0000	−0.942809
$289$	−13.0000	−0.764706
$290$	0	0
$291$	14.0000	0.820695
$292$	−8.00000	−0.468165
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	0	0
$297$	−20.0000	−1.16052
$298$	32.0000	1.85371
$299$	3.00000	0.173494
$300$	0	0
$301$	−7.00000	−0.403473
$302$	0	0
$303$	−13.0000	−0.746830
$304$	−8.00000	−0.458831
$305$	0	0
$306$	−8.00000	−0.457330
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	−8.00000	−0.455842
$309$	−13.0000	−0.739544
$310$	0	0
$311$	−7.00000	−0.396934	−0.198467	−	0.980108i	$-0.563596\pi$
$311$	−7.00000	−0.396934	−0.198467	+	0.980108i	$0.563596\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	−28.0000	−1.58013
$315$	0	0
$316$	−18.0000	−1.01258
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	−10.0000	−0.560772
$319$	4.00000	0.223957
$320$	0	0
$321$	17.0000	0.948847
$322$	−6.00000	−0.334367
$323$	−4.00000	−0.222566
$324$	2.00000	0.111111
$325$	0	0
$326$	−16.0000	−0.886158
$327$	2.00000	0.110600
$328$	0	0
$329$	12.0000	0.661581
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−24.0000	−1.31717
$333$	20.0000	1.09599
$334$	20.0000	1.09435
$335$	0	0
$336$	4.00000	0.218218
$337$	5.00000	0.272367	0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000	0.272367	0.136184	+	0.990684i	$0.456516\pi$
$338$	−2.00000	−0.108786
$339$	−9.00000	−0.488813
$340$	0	0
$341$	8.00000	0.433224
$342$	8.00000	0.432590
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	−36.0000	−1.93537
$347$	−17.0000	−0.912608	−0.456304	−	0.889824i	$-0.650827\pi$
$347$	−17.0000	−0.912608	−0.456304	+	0.889824i	$0.650827\pi$
$348$	2.00000	0.107211
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	32.0000	1.70561
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	0	0
$357$	2.00000	0.105851
$358$	50.0000	2.64258
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−20.0000	−1.05118
$363$	5.00000	0.262432
$364$	2.00000	0.104828
$365$	0	0
$366$	−10.0000	−0.522708
$367$	13.0000	0.678594	0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000	0.678594	0.339297	+	0.940679i	$0.389811\pi$
$368$	12.0000	0.625543
$369$	0	0
$370$	0	0
$371$	−5.00000	−0.259587
$372$	4.00000	0.207390
$373$	−13.0000	−0.673114	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000	−0.673114	−0.336557	+	0.941663i	$0.609263\pi$
$374$	16.0000	0.827340
$375$	0	0
$376$	0	0
$377$	−1.00000	−0.0515026
$378$	−10.0000	−0.514344
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	−7.00000	−0.358621
$382$	14.0000	0.716302
$383$	14.0000	0.715367	0.357683	−	0.933843i	$-0.383567\pi$
$383$	14.0000	0.715367	0.357683	+	0.933843i	$0.383567\pi$
$384$	0	0
$385$	0	0
$386$	−12.0000	−0.610784
$387$	−14.0000	−0.711660
$388$	28.0000	1.42148
$389$	−1.00000	−0.0507020	−0.0253510	−	0.999679i	$-0.508070\pi$
$389$	−1.00000	−0.0507020	−0.0253510	+	0.999679i	$0.508070\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	0	0
$393$	−1.00000	−0.0504433
$394$	28.0000	1.41062
$395$	0	0
$396$	−16.0000	−0.804030
$397$	20.0000	1.00377	0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000	1.00377	0.501886	+	0.864934i	$0.332640\pi$
$398$	14.0000	0.701757
$399$	−2.00000	−0.100125
$400$	0	0
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	20.0000	0.997509
$403$	−2.00000	−0.0996271
$404$	−26.0000	−1.29355
$405$	0	0
$406$	2.00000	0.0992583
$407$	−40.0000	−1.98273
$408$	0	0
$409$	4.00000	0.197787	0.0988936	−	0.995098i	$-0.468470\pi$
$409$	4.00000	0.197787	0.0988936	+	0.995098i	$0.468470\pi$
$410$	0	0
$411$	−6.00000	−0.295958
$412$	−26.0000	−1.28093
$413$	−6.00000	−0.295241
$414$	−12.0000	−0.589768
$415$	0	0
$416$	−8.00000	−0.392232
$417$	13.0000	0.636613
$418$	−16.0000	−0.782586
$419$	21.0000	1.02592	0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000	1.02592	0.512959	+	0.858413i	$0.328549\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	16.0000	0.778868
$423$	24.0000	1.16692
$424$	0	0
$425$	0	0
$426$	12.0000	0.581402
$427$	−5.00000	−0.241967
$428$	34.0000	1.64345
$429$	−4.00000	−0.193122
$430$	0	0
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	20.0000	0.962250
$433$	1.00000	0.0480569	0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000	0.0480569	0.0240285	+	0.999711i	$0.492351\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	4.00000	0.191565
$437$	−6.00000	−0.287019
$438$	8.00000	0.382255
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	−4.00000	−0.190261
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	−20.0000	−0.949158
$445$	0	0
$446$	44.0000	2.08346
$447$	−16.0000	−0.756774
$448$	8.00000	0.377964
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	0	0
$452$	−18.0000	−0.846649
$453$	0	0
$454$	28.0000	1.31411
$455$	0	0
$456$	0	0
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	40.0000	1.86908
$459$	10.0000	0.466760
$460$	0	0
$461$	24.0000	1.11779	0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000	1.11779	0.558896	+	0.829238i	$0.311225\pi$
$462$	8.00000	0.372194
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	42.0000	1.94561
$467$	41.0000	1.89725	0.948627	−	0.316397i	$-0.102473\pi$
$467$	41.0000	1.89725	0.948627	+	0.316397i	$0.102473\pi$
$468$	4.00000	0.184900
$469$	10.0000	0.461757
$470$	0	0
$471$	14.0000	0.645086
$472$	0	0
$473$	28.0000	1.28744
$474$	18.0000	0.826767
$475$	0	0
$476$	4.00000	0.183340
$477$	−10.0000	−0.457869
$478$	44.0000	2.01251
$479$	−14.0000	−0.639676	−0.319838	−	0.947472i	$-0.603629\pi$
$479$	−14.0000	−0.639676	−0.319838	+	0.947472i	$0.603629\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	32.0000	1.45756
$483$	3.00000	0.136505
$484$	10.0000	0.454545
$485$	0	0
$486$	−32.0000	−1.45155
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	0	0
$489$	8.00000	0.361773
$490$	0	0
$491$	11.0000	0.496423	0.248212	−	0.968706i	$-0.420157\pi$
$491$	11.0000	0.496423	0.248212	+	0.968706i	$0.420157\pi$
$492$	0	0
$493$	−2.00000	−0.0900755
$494$	4.00000	0.179969
$495$	0	0
$496$	−8.00000	−0.359211
$497$	6.00000	0.269137
$498$	24.0000	1.07547
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	0	0
$501$	−10.0000	−0.446767
$502$	40.0000	1.78529
$503$	17.0000	0.757993	0.378996	−	0.925398i	$-0.376269\pi$
$503$	17.0000	0.757993	0.378996	+	0.925398i	$0.376269\pi$
$504$	0	0
$505$	0	0
$506$	24.0000	1.06693
$507$	1.00000	0.0444116
$508$	−14.0000	−0.621150
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	0	0
$511$	4.00000	0.176950
$512$	−32.0000	−1.41421
$513$	−10.0000	−0.441511
$514$	38.0000	1.67611
$515$	0	0
$516$	14.0000	0.616316
$517$	−48.0000	−2.11104
$518$	−20.0000	−0.878750
$519$	18.0000	0.790112
$520$	0	0
$521$	−9.00000	−0.394297	−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000	−0.394297	−0.197149	+	0.980374i	$0.563168\pi$
$522$	4.00000	0.175075
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−2.00000	−0.0873704
$525$	0	0
$526$	−32.0000	−1.39527
$527$	−4.00000	−0.174243
$528$	−16.0000	−0.696311
$529$	−14.0000	−0.608696
$530$	0	0
$531$	−12.0000	−0.520756
$532$	−4.00000	−0.173422
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−25.0000	−1.07883
$538$	−6.00000	−0.258678
$539$	4.00000	0.172292
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	−24.0000	−1.03089
$543$	10.0000	0.429141
$544$	−16.0000	−0.685994
$545$	0	0
$546$	−2.00000	−0.0855921
$547$	20.0000	0.855138	0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000	0.855138	0.427569	+	0.903983i	$0.359370\pi$
$548$	−12.0000	−0.512615
$549$	−10.0000	−0.426790
$550$	0	0
$551$	2.00000	0.0852029
$552$	0	0
$553$	9.00000	0.382719
$554$	−62.0000	−2.63413
$555$	0	0
$556$	26.0000	1.10265
$557$	−26.0000	−1.10166	−0.550828	−	0.834619i	$-0.685688\pi$
$557$	−26.0000	−1.10166	−0.550828	+	0.834619i	$0.685688\pi$
$558$	8.00000	0.338667
$559$	−7.00000	−0.296068
$560$	0	0
$561$	−8.00000	−0.337760
$562$	16.0000	0.674919
$563$	−17.0000	−0.716465	−0.358232	−	0.933632i	$-0.616620\pi$
$563$	−17.0000	−0.716465	−0.358232	+	0.933632i	$0.616620\pi$
$564$	−24.0000	−1.01058
$565$	0	0
$566$	−56.0000	−2.35386
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	25.0000	1.04805	0.524027	−	0.851701i	$-0.324429\pi$
$569$	25.0000	1.04805	0.524027	+	0.851701i	$0.324429\pi$
$570$	0	0
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	−8.00000	−0.334497
$573$	−7.00000	−0.292429
$574$	0	0
$575$	0	0
$576$	16.0000	0.666667
$577$	22.0000	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$578$	26.0000	1.08146
$579$	6.00000	0.249351
$580$	0	0
$581$	12.0000	0.497844
$582$	−28.0000	−1.16064
$583$	20.0000	0.828315
$584$	0	0
$585$	0	0
$586$	60.0000	2.47858
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	2.00000	0.0824786
$589$	4.00000	0.164817
$590$	0	0
$591$	−14.0000	−0.575883
$592$	40.0000	1.64399
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	40.0000	1.64122
$595$	0	0
$596$	−32.0000	−1.31077
$597$	−7.00000	−0.286491
$598$	−6.00000	−0.245358
$599$	−3.00000	−0.122577	−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000	−0.122577	−0.0612883	+	0.998120i	$0.519521\pi$
$600$	0	0
$601$	−37.0000	−1.50926	−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000	−1.50926	−0.754631	+	0.656150i	$0.772184\pi$
$602$	14.0000	0.570597
$603$	20.0000	0.814463
$604$	0	0
$605$	0	0
$606$	26.0000	1.05618
$607$	48.0000	1.94826	0.974130	−	0.225989i	$-0.0725612\pi$
$607$	48.0000	1.94826	0.974130	+	0.225989i	$0.0725612\pi$
$608$	16.0000	0.648886
$609$	−1.00000	−0.0405220
$610$	0	0
$611$	12.0000	0.485468
$612$	8.00000	0.323381
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	32.0000	1.29141
$615$	0	0
$616$	0	0
$617$	−12.0000	−0.483102	−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000	−0.483102	−0.241551	+	0.970388i	$0.577656\pi$
$618$	26.0000	1.04587
$619$	36.0000	1.44696	0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000	1.44696	0.723481	+	0.690344i	$0.242541\pi$
$620$	0	0
$621$	15.0000	0.601929
$622$	14.0000	0.561349
$623$	0	0
$624$	4.00000	0.160128
$625$	0	0
$626$	−2.00000	−0.0799361
$627$	8.00000	0.319489
$628$	28.0000	1.11732
$629$	20.0000	0.797452
$630$	0	0
$631$	12.0000	0.477712	0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000	0.477712	0.238856	+	0.971055i	$0.423228\pi$
$632$	0	0
$633$	−8.00000	−0.317971
$634$	0	0
$635$	0	0
$636$	10.0000	0.396526
$637$	−1.00000	−0.0396214
$638$	−8.00000	−0.316723
$639$	12.0000	0.474713
$640$	0	0
$641$	−21.0000	−0.829450	−0.414725	−	0.909947i	$-0.636122\pi$
$641$	−21.0000	−0.829450	−0.414725	+	0.909947i	$0.636122\pi$
$642$	−34.0000	−1.34187
$643$	18.0000	0.709851	0.354925	−	0.934895i	$-0.384506\pi$
$643$	18.0000	0.709851	0.354925	+	0.934895i	$0.384506\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	8.00000	0.314756
$647$	−48.0000	−1.88707	−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000	−1.88707	−0.943537	+	0.331266i	$0.892524\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	16.0000	0.626608
$653$	10.0000	0.391330	0.195665	−	0.980671i	$-0.437313\pi$
$653$	10.0000	0.391330	0.195665	+	0.980671i	$0.437313\pi$
$654$	−4.00000	−0.156412
$655$	0	0
$656$	0	0
$657$	8.00000	0.312110
$658$	−24.0000	−0.935617
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	−40.0000	−1.55464
$663$	2.00000	0.0776736
$664$	0	0
$665$	0	0
$666$	−40.0000	−1.54997
$667$	−3.00000	−0.116160
$668$	−20.0000	−0.773823
$669$	−22.0000	−0.850569
$670$	0	0
$671$	20.0000	0.772091
$672$	−8.00000	−0.308607
$673$	−22.0000	−0.848038	−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000	−0.848038	−0.424019	+	0.905653i	$0.639381\pi$
$674$	−10.0000	−0.385186
$675$	0	0
$676$	2.00000	0.0769231
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	18.0000	0.691286
$679$	−14.0000	−0.537271
$680$	0	0
$681$	−14.0000	−0.536481
$682$	−16.0000	−0.612672
$683$	42.0000	1.60709	0.803543	−	0.595247i	$-0.202946\pi$
$683$	42.0000	1.60709	0.803543	+	0.595247i	$0.202946\pi$
$684$	−8.00000	−0.305888
$685$	0	0
$686$	2.00000	0.0763604
$687$	−20.0000	−0.763048
$688$	−28.0000	−1.06749
$689$	−5.00000	−0.190485
$690$	0	0
$691$	18.0000	0.684752	0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000	0.684752	0.342376	+	0.939563i	$0.388768\pi$
$692$	36.0000	1.36851
$693$	8.00000	0.303895
$694$	34.0000	1.29062
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−4.00000	−0.151402
$699$	−21.0000	−0.794293
$700$	0	0
$701$	35.0000	1.32193	0.660966	−	0.750416i	$-0.270147\pi$
$701$	35.0000	1.32193	0.660966	+	0.750416i	$0.270147\pi$
$702$	−10.0000	−0.377426
$703$	−20.0000	−0.754314
$704$	−32.0000	−1.20605
$705$	0	0
$706$	52.0000	1.95705
$707$	13.0000	0.488915
$708$	12.0000	0.450988
$709$	28.0000	1.05156	0.525781	−	0.850620i	$-0.323773\pi$
$709$	28.0000	1.05156	0.525781	+	0.850620i	$0.323773\pi$
$710$	0	0
$711$	18.0000	0.675053
$712$	0	0
$713$	−6.00000	−0.224702
$714$	−4.00000	−0.149696
$715$	0	0
$716$	−50.0000	−1.86859
$717$	−22.0000	−0.821605
$718$	60.0000	2.23918
$719$	−31.0000	−1.15610	−0.578052	−	0.816000i	$-0.696187\pi$
$719$	−31.0000	−1.15610	−0.578052	+	0.816000i	$0.696187\pi$
$720$	0	0
$721$	13.0000	0.484145
$722$	30.0000	1.11648
$723$	−16.0000	−0.595046
$724$	20.0000	0.743294
$725$	0	0
$726$	−10.0000	−0.371135
$727$	−27.0000	−1.00137	−0.500687	−	0.865628i	$-0.666919\pi$
$727$	−27.0000	−1.00137	−0.500687	+	0.865628i	$0.666919\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−14.0000	−0.517809
$732$	10.0000	0.369611
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	−26.0000	−0.959678
$735$	0	0
$736$	−24.0000	−0.884652
$737$	−40.0000	−1.47342
$738$	0	0
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	0	0
$741$	−2.00000	−0.0734718
$742$	10.0000	0.367112
$743$	2.00000	0.0733729	0.0366864	−	0.999327i	$-0.488320\pi$
$743$	2.00000	0.0733729	0.0366864	+	0.999327i	$0.488320\pi$
$744$	0	0
$745$	0	0
$746$	26.0000	0.951928
$747$	24.0000	0.878114
$748$	−16.0000	−0.585018
$749$	−17.0000	−0.621166
$750$	0	0
$751$	27.0000	0.985244	0.492622	−	0.870243i	$-0.336039\pi$
$751$	27.0000	0.985244	0.492622	+	0.870243i	$0.336039\pi$
$752$	48.0000	1.75038
$753$	−20.0000	−0.728841
$754$	2.00000	0.0728357
$755$	0	0
$756$	10.0000	0.363696
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	40.0000	1.45287
$759$	−12.0000	−0.435572
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	14.0000	0.507166
$763$	−2.00000	−0.0724049
$764$	−14.0000	−0.506502
$765$	0	0
$766$	−28.0000	−1.01168
$767$	−6.00000	−0.216647
$768$	16.0000	0.577350
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	−19.0000	−0.684268
$772$	12.0000	0.431889
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	28.0000	1.00644
$775$	0	0
$776$	0	0
$777$	10.0000	0.358748
$778$	2.00000	0.0717035
$779$	0	0
$780$	0	0
$781$	−24.0000	−0.858788
$782$	−12.0000	−0.429119
$783$	−5.00000	−0.178685
$784$	−4.00000	−0.142857
$785$	0	0
$786$	2.00000	0.0713376
$787$	2.00000	0.0712923	0.0356462	−	0.999364i	$-0.488651\pi$
$787$	2.00000	0.0712923	0.0356462	+	0.999364i	$0.488651\pi$
$788$	−28.0000	−0.997459
$789$	16.0000	0.569615
$790$	0	0
$791$	9.00000	0.320003
$792$	0	0
$793$	−5.00000	−0.177555
$794$	−40.0000	−1.41955
$795$	0	0
$796$	−14.0000	−0.496217
$797$	−9.00000	−0.318796	−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000	−0.318796	−0.159398	+	0.987214i	$0.550955\pi$
$798$	4.00000	0.141598
$799$	24.0000	0.849059
$800$	0	0
$801$	0	0
$802$	−48.0000	−1.69494
$803$	−16.0000	−0.564628
$804$	−20.0000	−0.705346
$805$	0	0
$806$	4.00000	0.140894
$807$	3.00000	0.105605
$808$	0	0
$809$	38.0000	1.33601	0.668004	−	0.744157i	$-0.267149\pi$
$809$	38.0000	1.33601	0.668004	+	0.744157i	$0.267149\pi$
$810$	0	0
$811$	46.0000	1.61528	0.807639	−	0.589677i	$-0.200745\pi$
$811$	46.0000	1.61528	0.807639	+	0.589677i	$0.200745\pi$
$812$	−2.00000	−0.0701862
$813$	12.0000	0.420858
$814$	80.0000	2.80400
$815$	0	0
$816$	8.00000	0.280056
$817$	14.0000	0.489798
$818$	−8.00000	−0.279713
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	12.0000	0.418548
$823$	−17.0000	−0.592583	−0.296291	−	0.955098i	$-0.595750\pi$
$823$	−17.0000	−0.592583	−0.296291	+	0.955098i	$0.595750\pi$
$824$	0	0
$825$	0	0
$826$	12.0000	0.417533
$827$	−18.0000	−0.625921	−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000	−0.625921	−0.312961	+	0.949766i	$0.601321\pi$
$828$	12.0000	0.417029
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	0	0
$831$	31.0000	1.07538
$832$	8.00000	0.277350
$833$	−2.00000	−0.0692959
$834$	−26.0000	−0.900306
$835$	0	0
$836$	16.0000	0.553372
$837$	−10.0000	−0.345651
$838$	−42.0000	−1.45087
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−28.0000	−0.964944
$843$	−8.00000	−0.275535
$844$	−16.0000	−0.550743
$845$	0	0
$846$	−48.0000	−1.65027
$847$	−5.00000	−0.171802
$848$	−20.0000	−0.686803
$849$	28.0000	0.960958
$850$	0	0
$851$	30.0000	1.02839
$852$	−12.0000	−0.411113
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	10.0000	0.342193
$855$	0	0
$856$	0	0
$857$	−7.00000	−0.239115	−0.119558	−	0.992827i	$-0.538148\pi$
$857$	−7.00000	−0.239115	−0.119558	+	0.992827i	$0.538148\pi$
$858$	8.00000	0.273115
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	0	0
$861$	0	0
$862$	4.00000	0.136241
$863$	8.00000	0.272323	0.136162	−	0.990687i	$-0.456523\pi$
$863$	8.00000	0.272323	0.136162	+	0.990687i	$0.456523\pi$
$864$	−40.0000	−1.36083
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	−13.0000	−0.441503
$868$	−4.00000	−0.135769
$869$	−36.0000	−1.22122
$870$	0	0
$871$	10.0000	0.338837
$872$	0	0
$873$	−28.0000	−0.947656
$874$	12.0000	0.405906
$875$	0	0
$876$	−8.00000	−0.270295
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	32.0000	1.07995
$879$	−30.0000	−1.01187
$880$	0	0
$881$	51.0000	1.71823	0.859117	−	0.511780i	$-0.171014\pi$
$881$	51.0000	1.71823	0.859117	+	0.511780i	$0.171014\pi$
$882$	4.00000	0.134687
$883$	51.0000	1.71629	0.858143	−	0.513410i	$-0.171618\pi$
$883$	51.0000	1.71629	0.858143	+	0.513410i	$0.171618\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	−48.0000	−1.61259
$887$	32.0000	1.07445	0.537227	−	0.843437i	$-0.319472\pi$
$887$	32.0000	1.07445	0.537227	+	0.843437i	$0.319472\pi$
$888$	0	0
$889$	7.00000	0.234772
$890$	0	0
$891$	4.00000	0.134005
$892$	−44.0000	−1.47323
$893$	−24.0000	−0.803129
$894$	32.0000	1.07024
$895$	0	0
$896$	0	0
$897$	3.00000	0.100167
$898$	−44.0000	−1.46830
$899$	2.00000	0.0667037
$900$	0	0
$901$	−10.0000	−0.333148
$902$	0	0
$903$	−7.00000	−0.232945
$904$	0	0
$905$	0	0
$906$	0	0
$907$	47.0000	1.56061	0.780305	−	0.625400i	$-0.215064\pi$
$907$	47.0000	1.56061	0.780305	+	0.625400i	$0.215064\pi$
$908$	−28.0000	−0.929213
$909$	26.0000	0.862366
$910$	0	0
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	−8.00000	−0.264906
$913$	−48.0000	−1.58857
$914$	32.0000	1.05847
$915$	0	0
$916$	−40.0000	−1.32164
$917$	1.00000	0.0330229
$918$	−20.0000	−0.660098
$919$	−48.0000	−1.58337	−0.791687	−	0.610927i	$-0.790797\pi$
$919$	−48.0000	−1.58337	−0.791687	+	0.610927i	$0.790797\pi$
$920$	0	0
$921$	−16.0000	−0.527218
$922$	−48.0000	−1.58080
$923$	6.00000	0.197492
$924$	−8.00000	−0.263181
$925$	0	0
$926$	−8.00000	−0.262896
$927$	26.0000	0.853952
$928$	8.00000	0.262613
$929$	−32.0000	−1.04989	−0.524943	−	0.851137i	$-0.675913\pi$
$929$	−32.0000	−1.04989	−0.524943	+	0.851137i	$0.675913\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	−42.0000	−1.37576
$933$	−7.00000	−0.229170
$934$	−82.0000	−2.68312
$935$	0	0
$936$	0	0
$937$	11.0000	0.359354	0.179677	−	0.983726i	$-0.442495\pi$
$937$	11.0000	0.359354	0.179677	+	0.983726i	$0.442495\pi$
$938$	−20.0000	−0.653023
$939$	1.00000	0.0326338
$940$	0	0
$941$	−8.00000	−0.260793	−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000	−0.260793	−0.130396	+	0.991462i	$0.541625\pi$
$942$	−28.0000	−0.912289
$943$	0	0
$944$	−24.0000	−0.781133
$945$	0	0
$946$	−56.0000	−1.82072
$947$	−14.0000	−0.454939	−0.227469	−	0.973785i	$-0.573045\pi$
$947$	−14.0000	−0.454939	−0.227469	+	0.973785i	$0.573045\pi$
$948$	−18.0000	−0.584613
$949$	4.00000	0.129845
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	20.0000	0.647524
$955$	0	0
$956$	−44.0000	−1.42306
$957$	4.00000	0.129302
$958$	28.0000	0.904639
$959$	6.00000	0.193750
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−20.0000	−0.644826
$963$	−34.0000	−1.09563
$964$	−32.0000	−1.03065
$965$	0	0
$966$	−6.00000	−0.193047
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	0	0
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	32.0000	1.02640
$973$	−13.0000	−0.416761
$974$	−64.0000	−2.05069
$975$	0	0
$976$	−20.0000	−0.640184
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	−16.0000	−0.511624
$979$	0	0
$980$	0	0
$981$	−4.00000	−0.127710
$982$	−22.0000	−0.702048
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	0	0
$986$	4.00000	0.127386
$987$	12.0000	0.381964
$988$	−4.00000	−0.127257
$989$	−21.0000	−0.667761
$990$	0	0
$991$	−13.0000	−0.412959	−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000	−0.412959	−0.206479	+	0.978451i	$0.566201\pi$
$992$	16.0000	0.508001
$993$	20.0000	0.634681
$994$	−12.0000	−0.380617
$995$	0	0
$996$	−24.0000	−0.760469
$997$	51.0000	1.61519	0.807593	−	0.589740i	$-0.200770\pi$
$997$	51.0000	1.61519	0.807593	+	0.589740i	$0.200770\pi$
$998$	8.00000	0.253236
$999$	50.0000	1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2275.2.a.a.1.1	✓	1
5.4	even	2		2275.2.a.g.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2275.2.a.a.1.1	✓	1	1.1	even	1	trivial
2275.2.a.g.1.1	yes	1	5.4	even	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:	\( N \)	\(=\)	\( 2275 = 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2275.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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