LMFDB - Embedded newform 262.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [262,2,Mod(1,262)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(262, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("262.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 262 = 2 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	262.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:	$2.09208053296$
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	$\chi$	$=$	262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -5.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -5.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +2.00000 q^{11} -2.00000 q^{13} +5.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} +3.00000 q^{18} +7.00000 q^{19} -2.00000 q^{22} -6.00000 q^{23} -5.00000 q^{25} +2.00000 q^{26} -5.00000 q^{28} -3.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} +6.00000 q^{34} -3.00000 q^{36} -1.00000 q^{37} -7.00000 q^{38} -9.00000 q^{41} +12.0000 q^{43} +2.00000 q^{44} +6.00000 q^{46} +18.0000 q^{49} +5.00000 q^{50} -2.00000 q^{52} +10.0000 q^{53} +5.00000 q^{56} +3.00000 q^{58} -4.00000 q^{59} -8.00000 q^{61} -2.00000 q^{62} +15.0000 q^{63} +1.00000 q^{64} +7.00000 q^{67} -6.00000 q^{68} -10.0000 q^{71} +3.00000 q^{72} +6.00000 q^{73} +1.00000 q^{74} +7.00000 q^{76} -10.0000 q^{77} -4.00000 q^{79} +9.00000 q^{81} +9.00000 q^{82} -11.0000 q^{83} -12.0000 q^{86} -2.00000 q^{88} +13.0000 q^{89} +10.0000 q^{91} -6.00000 q^{92} -8.00000 q^{97} -18.0000 q^{98} -6.00000 q^{99} +O(q^{100})$

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−5.00000	−1.88982	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000	−1.88982	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	5.00000	1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	3.00000	0.707107
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	2.00000	0.392232
$27$	0	0
$28$	−5.00000	−0.944911
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	0	0
$36$	−3.00000	−0.500000
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−7.00000	−1.13555
$39$	0	0
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	6.00000	0.884652
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	5.00000	0.707107
$51$	0	0
$52$	−2.00000	−0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	0	0
$55$	0	0
$56$	5.00000	0.668153
$57$	0	0
$58$	3.00000	0.393919
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	−2.00000	−0.254000
$63$	15.0000	1.88982
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	3.00000	0.353553
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	7.00000	0.802955
$77$	−10.0000	−1.13961
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	9.00000	0.993884
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	0	0
$85$	0	0
$86$	−12.0000	−1.29399
$87$	0	0
$88$	−2.00000	−0.213201
$89$	13.0000	1.37800	0.688999	−	0.724763i	$-0.258051\pi$
$89$	13.0000	1.37800	0.688999	+	0.724763i	$0.258051\pi$
$90$	0	0
$91$	10.0000	1.04828
$92$	−6.00000	−0.625543
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−18.0000	−1.81827
$99$	−6.00000	−0.603023
$100$	−5.00000	−0.500000
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−10.0000	−0.971286
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	0	0
$111$	0	0
$112$	−5.00000	−0.472456
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	6.00000	0.554700
$118$	4.00000	0.368230
$119$	30.0000	2.75010
$120$	0	0
$121$	−7.00000	−0.636364
$122$	8.00000	0.724286
$123$	0	0
$124$	2.00000	0.179605
$125$	0	0
$126$	−15.0000	−1.33631
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0	0
$133$	−35.0000	−3.03488
$134$	−7.00000	−0.604708
$135$	0	0
$136$	6.00000	0.514496
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	0	0
$142$	10.0000	0.839181
$143$	−4.00000	−0.334497
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−6.00000	−0.496564
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	−7.00000	−0.569652	−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000	−0.569652	−0.284826	+	0.958579i	$0.591936\pi$
$152$	−7.00000	−0.567775
$153$	18.0000	1.45521
$154$	10.0000	0.805823
$155$	0	0
$156$	0	0
$157$	−1.00000	−0.0798087	−0.0399043	−	0.999204i	$-0.512705\pi$
$157$	−1.00000	−0.0798087	−0.0399043	+	0.999204i	$0.512705\pi$
$158$	4.00000	0.318223
$159$	0	0
$160$	0	0
$161$	30.0000	2.36433
$162$	−9.00000	−0.707107
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	11.0000	0.853766
$167$	−11.0000	−0.851206	−0.425603	−	0.904910i	$-0.639938\pi$
$167$	−11.0000	−0.851206	−0.425603	+	0.904910i	$0.639938\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−21.0000	−1.60591
$172$	12.0000	0.914991
$173$	−13.0000	−0.988372	−0.494186	−	0.869356i	$-0.664534\pi$
$173$	−13.0000	−0.988372	−0.494186	+	0.869356i	$0.664534\pi$
$174$	0	0
$175$	25.0000	1.88982
$176$	2.00000	0.150756
$177$	0	0
$178$	−13.0000	−0.974391
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−10.0000	−0.741249
$183$	0	0
$184$	6.00000	0.442326
$185$	0	0
$186$	0	0
$187$	−12.0000	−0.877527
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	0	0
$193$	−15.0000	−1.07972	−0.539862	−	0.841754i	$-0.681524\pi$
$193$	−15.0000	−1.07972	−0.539862	+	0.841754i	$0.681524\pi$
$194$	8.00000	0.574367
$195$	0	0
$196$	18.0000	1.28571
$197$	−5.00000	−0.356235	−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000	−0.356235	−0.178118	+	0.984009i	$0.557001\pi$
$198$	6.00000	0.426401
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	5.00000	0.353553
$201$	0	0
$202$	−12.0000	−0.844317
$203$	15.0000	1.05279
$204$	0	0
$205$	0	0
$206$	−8.00000	−0.557386
$207$	18.0000	1.25109
$208$	−2.00000	−0.138675
$209$	14.0000	0.968400
$210$	0	0
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	−8.00000	−0.546869
$215$	0	0
$216$	0	0
$217$	−10.0000	−0.678844
$218$	16.0000	1.08366
$219$	0	0
$220$	0	0
$221$	12.0000	0.807207
$222$	0	0
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	5.00000	0.334077
$225$	15.0000	1.00000
$226$	15.0000	0.997785
$227$	−23.0000	−1.52656	−0.763282	−	0.646066i	$-0.776413\pi$
$227$	−23.0000	−1.52656	−0.763282	+	0.646066i	$0.776413\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	0	0
$232$	3.00000	0.196960
$233$	−1.00000	−0.0655122	−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000	−0.0655122	−0.0327561	+	0.999463i	$0.510428\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	−30.0000	−1.94461
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	−8.00000	−0.512148
$245$	0	0
$246$	0	0
$247$	−14.0000	−0.890799
$248$	−2.00000	−0.127000
$249$	0	0
$250$	0	0
$251$	−1.00000	−0.0631194	−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000	−0.0631194	−0.0315597	+	0.999502i	$0.510047\pi$
$252$	15.0000	0.944911
$253$	−12.0000	−0.754434
$254$	12.0000	0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	0	0
$259$	5.00000	0.310685
$260$	0	0
$261$	9.00000	0.557086
$262$	1.00000	0.0617802
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	0	0
$266$	35.0000	2.14599
$267$	0	0
$268$	7.00000	0.427593
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	−24.0000	−1.45790	−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000	−1.45790	−0.728948	+	0.684569i	$0.759990\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	12.0000	0.724947
$275$	−10.0000	−0.603023
$276$	0	0
$277$	12.0000	0.721010	0.360505	−	0.932757i	$-0.382604\pi$
$277$	12.0000	0.721010	0.360505	+	0.932757i	$0.382604\pi$
$278$	8.00000	0.479808
$279$	−6.00000	−0.359211
$280$	0	0
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	4.00000	0.236525
$287$	45.0000	2.65627
$288$	3.00000	0.176777
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	6.00000	0.351123
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	0	0
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	6.00000	0.347571
$299$	12.0000	0.693978
$300$	0	0
$301$	−60.0000	−3.45834
$302$	7.00000	0.402805
$303$	0	0
$304$	7.00000	0.401478
$305$	0	0
$306$	−18.0000	−1.02899
$307$	−14.0000	−0.799022	−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000	−0.799022	−0.399511	+	0.916728i	$0.630820\pi$
$308$	−10.0000	−0.569803
$309$	0	0
$310$	0	0
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	0	0
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	1.00000	0.0564333
$315$	0	0
$316$	−4.00000	−0.225018
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	0	0
$319$	−6.00000	−0.335936
$320$	0	0
$321$	0	0
$322$	−30.0000	−1.67183
$323$	−42.0000	−2.33694
$324$	9.00000	0.500000
$325$	10.0000	0.554700
$326$	−24.0000	−1.32924
$327$	0	0
$328$	9.00000	0.496942
$329$	0	0
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−11.0000	−0.603703
$333$	3.00000	0.164399
$334$	11.0000	0.601893
$335$	0	0
$336$	0	0
$337$	19.0000	1.03500	0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000	1.03500	0.517498	+	0.855684i	$0.326864\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	0	0
$341$	4.00000	0.216612
$342$	21.0000	1.13555
$343$	−55.0000	−2.96972
$344$	−12.0000	−0.646997
$345$	0	0
$346$	13.0000	0.698884
$347$	13.0000	0.697877	0.348938	−	0.937146i	$-0.386542\pi$
$347$	13.0000	0.697877	0.348938	+	0.937146i	$0.386542\pi$
$348$	0	0
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	−25.0000	−1.33631
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−25.0000	−1.33062	−0.665308	−	0.746569i	$-0.731700\pi$
$353$	−25.0000	−1.33062	−0.665308	+	0.746569i	$0.731700\pi$
$354$	0	0
$355$	0	0
$356$	13.0000	0.688999
$357$	0	0
$358$	−10.0000	−0.528516
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	2.00000	0.105118
$363$	0	0
$364$	10.0000	0.524142
$365$	0	0
$366$	0	0
$367$	3.00000	0.156599	0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000	0.156599	0.0782994	+	0.996930i	$0.475051\pi$
$368$	−6.00000	−0.312772
$369$	27.0000	1.40556
$370$	0	0
$371$	−50.0000	−2.59587
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	12.0000	0.620505
$375$	0	0
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	0	0
$382$	9.00000	0.460480
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	0	0
$385$	0	0
$386$	15.0000	0.763480
$387$	−36.0000	−1.82998
$388$	−8.00000	−0.406138
$389$	−19.0000	−0.963338	−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000	−0.963338	−0.481669	+	0.876353i	$0.659969\pi$
$390$	0	0
$391$	36.0000	1.82060
$392$	−18.0000	−0.909137
$393$	0	0
$394$	5.00000	0.251896
$395$	0	0
$396$	−6.00000	−0.301511
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	−24.0000	−1.20301
$399$	0	0
$400$	−5.00000	−0.250000
$401$	4.00000	0.199750	0.0998752	−	0.995000i	$-0.468156\pi$
$401$	4.00000	0.199750	0.0998752	+	0.995000i	$0.468156\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	12.0000	0.597022
$405$	0	0
$406$	−15.0000	−0.744438
$407$	−2.00000	−0.0991363
$408$	0	0
$409$	−13.0000	−0.642809	−0.321404	−	0.946942i	$-0.604155\pi$
$409$	−13.0000	−0.642809	−0.321404	+	0.946942i	$0.604155\pi$
$410$	0	0
$411$	0	0
$412$	8.00000	0.394132
$413$	20.0000	0.984136
$414$	−18.0000	−0.884652
$415$	0	0
$416$	2.00000	0.0980581
$417$	0	0
$418$	−14.0000	−0.684762
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	0	0
$421$	−38.0000	−1.85201	−0.926003	−	0.377515i	$-0.876779\pi$
$421$	−38.0000	−1.85201	−0.926003	+	0.377515i	$0.876779\pi$
$422$	2.00000	0.0973585
$423$	0	0
$424$	−10.0000	−0.485643
$425$	30.0000	1.45521
$426$	0	0
$427$	40.0000	1.93574
$428$	8.00000	0.386695
$429$	0	0
$430$	0	0
$431$	20.0000	0.963366	0.481683	−	0.876346i	$-0.340026\pi$
$431$	20.0000	0.963366	0.481683	+	0.876346i	$0.340026\pi$
$432$	0	0
$433$	6.00000	0.288342	0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000	0.288342	0.144171	+	0.989553i	$0.453949\pi$
$434$	10.0000	0.480015
$435$	0	0
$436$	−16.0000	−0.766261
$437$	−42.0000	−2.00913
$438$	0	0
$439$	−5.00000	−0.238637	−0.119318	−	0.992856i	$-0.538071\pi$
$439$	−5.00000	−0.238637	−0.119318	+	0.992856i	$0.538071\pi$
$440$	0	0
$441$	−54.0000	−2.57143
$442$	−12.0000	−0.570782
$443$	9.00000	0.427603	0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000	0.427603	0.213801	+	0.976877i	$0.431415\pi$
$444$	0	0
$445$	0	0
$446$	−10.0000	−0.473514
$447$	0	0
$448$	−5.00000	−0.236228
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	−15.0000	−0.707107
$451$	−18.0000	−0.847587
$452$	−15.0000	−0.705541
$453$	0	0
$454$	23.0000	1.07944
$455$	0	0
$456$	0	0
$457$	−5.00000	−0.233890	−0.116945	−	0.993138i	$-0.537310\pi$
$457$	−5.00000	−0.233890	−0.116945	+	0.993138i	$0.537310\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	0	0
$461$	21.0000	0.978068	0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000	0.978068	0.489034	+	0.872265i	$0.337349\pi$
$462$	0	0
$463$	−18.0000	−0.836531	−0.418265	−	0.908325i	$-0.637362\pi$
$463$	−18.0000	−0.836531	−0.418265	+	0.908325i	$0.637362\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	1.00000	0.0463241
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	6.00000	0.277350
$469$	−35.0000	−1.61615
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	24.0000	1.10352
$474$	0	0
$475$	−35.0000	−1.60591
$476$	30.0000	1.37505
$477$	−30.0000	−1.37361
$478$	15.0000	0.686084
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	0	0
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	8.00000	0.362143
$489$	0	0
$490$	0	0
$491$	5.00000	0.225647	0.112823	−	0.993615i	$-0.464011\pi$
$491$	5.00000	0.225647	0.112823	+	0.993615i	$0.464011\pi$
$492$	0	0
$493$	18.0000	0.810679
$494$	14.0000	0.629890
$495$	0	0
$496$	2.00000	0.0898027
$497$	50.0000	2.24281
$498$	0	0
$499$	11.0000	0.492428	0.246214	−	0.969216i	$-0.420813\pi$
$499$	11.0000	0.492428	0.246214	+	0.969216i	$0.420813\pi$
$500$	0	0
$501$	0	0
$502$	1.00000	0.0446322
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	−15.0000	−0.668153
$505$	0	0
$506$	12.0000	0.533465
$507$	0	0
$508$	−12.0000	−0.532414
$509$	11.0000	0.487566	0.243783	−	0.969830i	$-0.421611\pi$
$509$	11.0000	0.487566	0.243783	+	0.969830i	$0.421611\pi$
$510$	0	0
$511$	−30.0000	−1.32712
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−22.0000	−0.970378
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−5.00000	−0.219687
$519$	0	0
$520$	0	0
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	−9.00000	−0.393919
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−1.00000	−0.0436852
$525$	0	0
$526$	12.0000	0.523225
$527$	−12.0000	−0.522728
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	12.0000	0.520756
$532$	−35.0000	−1.51744
$533$	18.0000	0.779667
$534$	0	0
$535$	0	0
$536$	−7.00000	−0.302354
$537$	0	0
$538$	10.0000	0.431131
$539$	36.0000	1.55063
$540$	0	0
$541$	41.0000	1.76273	0.881364	−	0.472438i	$-0.156626\pi$
$541$	41.0000	1.76273	0.881364	+	0.472438i	$0.156626\pi$
$542$	24.0000	1.03089
$543$	0	0
$544$	6.00000	0.257248
$545$	0	0
$546$	0	0
$547$	13.0000	0.555840	0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000	0.555840	0.277920	+	0.960604i	$0.410355\pi$
$548$	−12.0000	−0.512615
$549$	24.0000	1.02430
$550$	10.0000	0.426401
$551$	−21.0000	−0.894630
$552$	0	0
$553$	20.0000	0.850487
$554$	−12.0000	−0.509831
$555$	0	0
$556$	−8.00000	−0.339276
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	6.00000	0.254000
$559$	−24.0000	−1.01509
$560$	0	0
$561$	0	0
$562$	−2.00000	−0.0843649
$563$	38.0000	1.60151	0.800755	−	0.598993i	$-0.204432\pi$
$563$	38.0000	1.60151	0.800755	+	0.598993i	$0.204432\pi$
$564$	0	0
$565$	0	0
$566$	−6.00000	−0.252199
$567$	−45.0000	−1.88982
$568$	10.0000	0.419591
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	0	0
$571$	13.0000	0.544033	0.272017	−	0.962293i	$-0.412309\pi$
$571$	13.0000	0.544033	0.272017	+	0.962293i	$0.412309\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	−45.0000	−1.87826
$575$	30.0000	1.25109
$576$	−3.00000	−0.125000
$577$	−15.0000	−0.624458	−0.312229	−	0.950007i	$-0.601076\pi$
$577$	−15.0000	−0.624458	−0.312229	+	0.950007i	$0.601076\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	0	0
$581$	55.0000	2.28178
$582$	0	0
$583$	20.0000	0.828315
$584$	−6.00000	−0.248282
$585$	0	0
$586$	2.00000	0.0826192
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	14.0000	0.576860
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	16.0000	0.657041	0.328521	−	0.944497i	$-0.393450\pi$
$593$	16.0000	0.657041	0.328521	+	0.944497i	$0.393450\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	−12.0000	−0.490716
$599$	−27.0000	−1.10319	−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000	−1.10319	−0.551595	+	0.834112i	$0.685981\pi$
$600$	0	0
$601$	13.0000	0.530281	0.265141	−	0.964210i	$-0.414582\pi$
$601$	13.0000	0.530281	0.265141	+	0.964210i	$0.414582\pi$
$602$	60.0000	2.44542
$603$	−21.0000	−0.855186
$604$	−7.00000	−0.284826
$605$	0	0
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	−7.00000	−0.283887
$609$	0	0
$610$	0	0
$611$	0	0
$612$	18.0000	0.727607
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	14.0000	0.564994
$615$	0	0
$616$	10.0000	0.402911
$617$	−40.0000	−1.61034	−0.805170	−	0.593045i	$-0.797926\pi$
$617$	−40.0000	−1.61034	−0.805170	+	0.593045i	$0.797926\pi$
$618$	0	0
$619$	17.0000	0.683288	0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000	0.683288	0.341644	+	0.939829i	$0.389016\pi$
$620$	0	0
$621$	0	0
$622$	16.0000	0.641542
$623$	−65.0000	−2.60417
$624$	0	0
$625$	25.0000	1.00000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	−1.00000	−0.0399043
$629$	6.00000	0.239236
$630$	0	0
$631$	−25.0000	−0.995234	−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000	−0.995234	−0.497617	+	0.867397i	$0.665792\pi$
$632$	4.00000	0.159111
$633$	0	0
$634$	−10.0000	−0.397151
$635$	0	0
$636$	0	0
$637$	−36.0000	−1.42637
$638$	6.00000	0.237542
$639$	30.0000	1.18678
$640$	0	0
$641$	−9.00000	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$642$	0	0
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	30.0000	1.18217
$645$	0	0
$646$	42.0000	1.65247
$647$	17.0000	0.668339	0.334169	−	0.942513i	$-0.391544\pi$
$647$	17.0000	0.668339	0.334169	+	0.942513i	$0.391544\pi$
$648$	−9.00000	−0.353553
$649$	−8.00000	−0.314027
$650$	−10.0000	−0.392232
$651$	0	0
$652$	24.0000	0.939913
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	0	0
$656$	−9.00000	−0.351391
$657$	−18.0000	−0.702247
$658$	0	0
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	0	0
$661$	9.00000	0.350059	0.175030	−	0.984563i	$-0.443998\pi$
$661$	9.00000	0.350059	0.175030	+	0.984563i	$0.443998\pi$
$662$	28.0000	1.08825
$663$	0	0
$664$	11.0000	0.426883
$665$	0	0
$666$	−3.00000	−0.116248
$667$	18.0000	0.696963
$668$	−11.0000	−0.425603
$669$	0	0
$670$	0	0
$671$	−16.0000	−0.617673
$672$	0	0
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	−19.0000	−0.731853
$675$	0	0
$676$	−9.00000	−0.346154
$677$	11.0000	0.422764	0.211382	−	0.977403i	$-0.432204\pi$
$677$	11.0000	0.422764	0.211382	+	0.977403i	$0.432204\pi$
$678$	0	0
$679$	40.0000	1.53506
$680$	0	0
$681$	0	0
$682$	−4.00000	−0.153168
$683$	2.00000	0.0765279	0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000	0.0765279	0.0382639	+	0.999268i	$0.487817\pi$
$684$	−21.0000	−0.802955
$685$	0	0
$686$	55.0000	2.09991
$687$	0	0
$688$	12.0000	0.457496
$689$	−20.0000	−0.761939
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	−13.0000	−0.494186
$693$	30.0000	1.13961
$694$	−13.0000	−0.493473
$695$	0	0
$696$	0	0
$697$	54.0000	2.04540
$698$	−23.0000	−0.870563
$699$	0	0
$700$	25.0000	0.944911
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	0	0
$703$	−7.00000	−0.264010
$704$	2.00000	0.0753778
$705$	0	0
$706$	25.0000	0.940887
$707$	−60.0000	−2.25653
$708$	0	0
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	−13.0000	−0.487196
$713$	−12.0000	−0.449404
$714$	0	0
$715$	0	0
$716$	10.0000	0.373718
$717$	0	0
$718$	0	0
$719$	−7.00000	−0.261056	−0.130528	−	0.991445i	$-0.541667\pi$
$719$	−7.00000	−0.261056	−0.130528	+	0.991445i	$0.541667\pi$
$720$	0	0
$721$	−40.0000	−1.48968
$722$	−30.0000	−1.11648
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	15.0000	0.557086
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−10.0000	−0.370625
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−72.0000	−2.66302
$732$	0	0
$733$	−49.0000	−1.80986	−0.904928	−	0.425564i	$-0.860076\pi$
$733$	−49.0000	−1.80986	−0.904928	+	0.425564i	$0.860076\pi$
$734$	−3.00000	−0.110732
$735$	0	0
$736$	6.00000	0.221163
$737$	14.0000	0.515697
$738$	−27.0000	−0.993884
$739$	−44.0000	−1.61857	−0.809283	−	0.587419i	$-0.800144\pi$
$739$	−44.0000	−1.61857	−0.809283	+	0.587419i	$0.800144\pi$
$740$	0	0
$741$	0	0
$742$	50.0000	1.83556
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	0	0
$745$	0	0
$746$	6.00000	0.219676
$747$	33.0000	1.20741
$748$	−12.0000	−0.438763
$749$	−40.0000	−1.46157
$750$	0	0
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	0	0
$753$	0	0
$754$	−6.00000	−0.218507
$755$	0	0
$756$	0	0
$757$	−52.0000	−1.88997	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000	−1.88997	−0.944986	+	0.327111i	$0.893925\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	80.0000	2.89619
$764$	−9.00000	−0.325609
$765$	0	0
$766$	−36.0000	−1.30073
$767$	8.00000	0.288863
$768$	0	0
$769$	−23.0000	−0.829401	−0.414701	−	0.909958i	$-0.636114\pi$
$769$	−23.0000	−0.829401	−0.414701	+	0.909958i	$0.636114\pi$
$770$	0	0
$771$	0	0
$772$	−15.0000	−0.539862
$773$	7.00000	0.251773	0.125886	−	0.992045i	$-0.459823\pi$
$773$	7.00000	0.251773	0.125886	+	0.992045i	$0.459823\pi$
$774$	36.0000	1.29399
$775$	−10.0000	−0.359211
$776$	8.00000	0.287183
$777$	0	0
$778$	19.0000	0.681183
$779$	−63.0000	−2.25721
$780$	0	0
$781$	−20.0000	−0.715656
$782$	−36.0000	−1.28736
$783$	0	0
$784$	18.0000	0.642857
$785$	0	0
$786$	0	0
$787$	48.0000	1.71102	0.855508	−	0.517790i	$-0.173245\pi$
$787$	48.0000	1.71102	0.855508	+	0.517790i	$0.173245\pi$
$788$	−5.00000	−0.178118
$789$	0	0
$790$	0	0
$791$	75.0000	2.66669
$792$	6.00000	0.213201
$793$	16.0000	0.568177
$794$	−22.0000	−0.780751
$795$	0	0
$796$	24.0000	0.850657
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	0	0
$799$	0	0
$800$	5.00000	0.176777
$801$	−39.0000	−1.37800
$802$	−4.00000	−0.141245
$803$	12.0000	0.423471
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	−12.0000	−0.422159
$809$	−16.0000	−0.562530	−0.281265	−	0.959630i	$-0.590754\pi$
$809$	−16.0000	−0.562530	−0.281265	+	0.959630i	$0.590754\pi$
$810$	0	0
$811$	−36.0000	−1.26413	−0.632065	−	0.774915i	$-0.717793\pi$
$811$	−36.0000	−1.26413	−0.632065	+	0.774915i	$0.717793\pi$
$812$	15.0000	0.526397
$813$	0	0
$814$	2.00000	0.0701000
$815$	0	0
$816$	0	0
$817$	84.0000	2.93879
$818$	13.0000	0.454534
$819$	−30.0000	−1.04828
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	0	0
$823$	−12.0000	−0.418294	−0.209147	−	0.977884i	$-0.567069\pi$
$823$	−12.0000	−0.418294	−0.209147	+	0.977884i	$0.567069\pi$
$824$	−8.00000	−0.278693
$825$	0	0
$826$	−20.0000	−0.695889
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	18.0000	0.625543
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	0	0
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	−108.000	−3.74198
$834$	0	0
$835$	0	0
$836$	14.0000	0.484200
$837$	0	0
$838$	−36.0000	−1.24360
$839$	9.00000	0.310715	0.155357	−	0.987858i	$-0.450347\pi$
$839$	9.00000	0.310715	0.155357	+	0.987858i	$0.450347\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	38.0000	1.30957
$843$	0	0
$844$	−2.00000	−0.0688428
$845$	0	0
$846$	0	0
$847$	35.0000	1.20261
$848$	10.0000	0.343401
$849$	0	0
$850$	−30.0000	−1.02899
$851$	6.00000	0.205677
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	−40.0000	−1.36877
$855$	0	0
$856$	−8.00000	−0.273434
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	0	0
$859$	−37.0000	−1.26242	−0.631212	−	0.775610i	$-0.717442\pi$
$859$	−37.0000	−1.26242	−0.631212	+	0.775610i	$0.717442\pi$
$860$	0	0
$861$	0	0
$862$	−20.0000	−0.681203
$863$	1.00000	0.0340404	0.0170202	−	0.999855i	$-0.494582\pi$
$863$	1.00000	0.0340404	0.0170202	+	0.999855i	$0.494582\pi$
$864$	0	0
$865$	0	0
$866$	−6.00000	−0.203888
$867$	0	0
$868$	−10.0000	−0.339422
$869$	−8.00000	−0.271381
$870$	0	0
$871$	−14.0000	−0.474372
$872$	16.0000	0.541828
$873$	24.0000	0.812277
$874$	42.0000	1.42067
$875$	0	0
$876$	0	0
$877$	−8.00000	−0.270141	−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000	−0.270141	−0.135070	+	0.990836i	$0.543126\pi$
$878$	5.00000	0.168742
$879$	0	0
$880$	0	0
$881$	8.00000	0.269527	0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000	0.269527	0.134763	+	0.990878i	$0.456973\pi$
$882$	54.0000	1.81827
$883$	5.00000	0.168263	0.0841317	−	0.996455i	$-0.473188\pi$
$883$	5.00000	0.168263	0.0841317	+	0.996455i	$0.473188\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	−9.00000	−0.302361
$887$	−32.0000	−1.07445	−0.537227	−	0.843437i	$-0.680528\pi$
$887$	−32.0000	−1.07445	−0.537227	+	0.843437i	$0.680528\pi$
$888$	0	0
$889$	60.0000	2.01234
$890$	0	0
$891$	18.0000	0.603023
$892$	10.0000	0.334825
$893$	0	0
$894$	0	0
$895$	0	0
$896$	5.00000	0.167038
$897$	0	0
$898$	24.0000	0.800890
$899$	−6.00000	−0.200111
$900$	15.0000	0.500000
$901$	−60.0000	−1.99889
$902$	18.0000	0.599334
$903$	0	0
$904$	15.0000	0.498893
$905$	0	0
$906$	0	0
$907$	−40.0000	−1.32818	−0.664089	−	0.747653i	$-0.731180\pi$
$907$	−40.0000	−1.32818	−0.664089	+	0.747653i	$0.731180\pi$
$908$	−23.0000	−0.763282
$909$	−36.0000	−1.19404
$910$	0	0
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	0	0
$913$	−22.0000	−0.728094
$914$	5.00000	0.165385
$915$	0	0
$916$	10.0000	0.330409
$917$	5.00000	0.165115
$918$	0	0
$919$	−26.0000	−0.857661	−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000	−0.857661	−0.428830	+	0.903385i	$0.641074\pi$
$920$	0	0
$921$	0	0
$922$	−21.0000	−0.691598
$923$	20.0000	0.658308
$924$	0	0
$925$	5.00000	0.164399
$926$	18.0000	0.591517
$927$	−24.0000	−0.788263
$928$	3.00000	0.0984798
$929$	−23.0000	−0.754606	−0.377303	−	0.926090i	$-0.623148\pi$
$929$	−23.0000	−0.754606	−0.377303	+	0.926090i	$0.623148\pi$
$930$	0	0
$931$	126.000	4.12948
$932$	−1.00000	−0.0327561
$933$	0	0
$934$	−6.00000	−0.196326
$935$	0	0
$936$	−6.00000	−0.196116
$937$	1.00000	0.0326686	0.0163343	−	0.999867i	$-0.494800\pi$
$937$	1.00000	0.0326686	0.0163343	+	0.999867i	$0.494800\pi$
$938$	35.0000	1.14279
$939$	0	0
$940$	0	0
$941$	1.00000	0.0325991	0.0162995	−	0.999867i	$-0.494811\pi$
$941$	1.00000	0.0325991	0.0162995	+	0.999867i	$0.494811\pi$
$942$	0	0
$943$	54.0000	1.75848
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−24.0000	−0.780307
$947$	−35.0000	−1.13735	−0.568674	−	0.822563i	$-0.692543\pi$
$947$	−35.0000	−1.13735	−0.568674	+	0.822563i	$0.692543\pi$
$948$	0	0
$949$	−12.0000	−0.389536
$950$	35.0000	1.13555
$951$	0	0
$952$	−30.0000	−0.972306
$953$	−57.0000	−1.84641	−0.923206	−	0.384307i	$-0.874441\pi$
$953$	−57.0000	−1.84641	−0.923206	+	0.384307i	$0.874441\pi$
$954$	30.0000	0.971286
$955$	0	0
$956$	−15.0000	−0.485135
$957$	0	0
$958$	−24.0000	−0.775405
$959$	60.0000	1.93750
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−2.00000	−0.0644826
$963$	−24.0000	−0.773389
$964$	0	0
$965$	0	0
$966$	0	0
$967$	46.0000	1.47926	0.739630	−	0.673014i	$-0.235000\pi$
$967$	46.0000	1.47926	0.739630	+	0.673014i	$0.235000\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	0	0
$971$	45.0000	1.44412	0.722059	−	0.691831i	$-0.243196\pi$
$971$	45.0000	1.44412	0.722059	+	0.691831i	$0.243196\pi$
$972$	0	0
$973$	40.0000	1.28234
$974$	4.00000	0.128168
$975$	0	0
$976$	−8.00000	−0.256074
$977$	−19.0000	−0.607864	−0.303932	−	0.952694i	$-0.598300\pi$
$977$	−19.0000	−0.607864	−0.303932	+	0.952694i	$0.598300\pi$
$978$	0	0
$979$	26.0000	0.830964
$980$	0	0
$981$	48.0000	1.53252
$982$	−5.00000	−0.159556
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	0	0
$985$	0	0
$986$	−18.0000	−0.573237
$987$	0	0
$988$	−14.0000	−0.445399
$989$	−72.0000	−2.28947
$990$	0	0
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	−2.00000	−0.0635001
$993$	0	0
$994$	−50.0000	−1.58590
$995$	0	0
$996$	0	0
$997$	−16.0000	−0.506725	−0.253363	−	0.967371i	$-0.581537\pi$
$997$	−16.0000	−0.506725	−0.253363	+	0.967371i	$0.581537\pi$
$998$	−11.0000	−0.348199
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	262.2.a.a.1.1	✓	1
3.2	odd	2		2358.2.a.q.1.1		1
4.3	odd	2		2096.2.a.c.1.1		1
5.4	even	2		6550.2.a.o.1.1		1
8.3	odd	2		8384.2.a.j.1.1		1
8.5	even	2		8384.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
262.2.a.a.1.1	✓	1	1.1	even	1	trivial
2096.2.a.c.1.1		1	4.3	odd	2
2358.2.a.q.1.1		1	3.2	odd	2
6550.2.a.o.1.1		1	5.4	even	2
8384.2.a.i.1.1		1	8.5	even	2
8384.2.a.j.1.1		1	8.3	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:	\( N \)	\(=\)	\( 262 = 2 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	262.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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