LMFDB - Embedded newform 9282.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$0$
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	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.00000 q^{19} -1.00000 q^{21} -2.00000 q^{22} -2.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -10.0000 q^{29} +1.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +5.00000 q^{38} +1.00000 q^{39} +5.00000 q^{41} +1.00000 q^{42} -5.00000 q^{43} +2.00000 q^{44} +2.00000 q^{46} -7.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +5.00000 q^{50} +1.00000 q^{51} -1.00000 q^{52} +3.00000 q^{53} +1.00000 q^{54} -1.00000 q^{56} +5.00000 q^{57} +10.0000 q^{58} +8.00000 q^{59} -8.00000 q^{61} -1.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} +4.00000 q^{67} -1.00000 q^{68} +2.00000 q^{69} +7.00000 q^{71} -1.00000 q^{72} +14.0000 q^{73} +5.00000 q^{75} -5.00000 q^{76} +2.00000 q^{77} -1.00000 q^{78} -3.00000 q^{79} +1.00000 q^{81} -5.00000 q^{82} -10.0000 q^{83} -1.00000 q^{84} +5.00000 q^{86} +10.0000 q^{87} -2.00000 q^{88} +14.0000 q^{89} -1.00000 q^{91} -2.00000 q^{92} -1.00000 q^{93} +7.00000 q^{94} +1.00000 q^{96} -2.00000 q^{97} -1.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−2.00000	−0.426401
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	1.00000	0.204124
$25$	−5.00000	−1.00000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	5.00000	0.811107
$39$	1.00000	0.160128
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	1.00000	0.154303
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	2.00000	0.294884
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	5.00000	0.707107
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	5.00000	0.662266
$58$	10.0000	1.31306
$59$	8.00000	1.04151	0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000	1.04151	0.520756	+	0.853706i	$0.325650\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	−1.00000	−0.127000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−1.00000	−0.121268
$69$	2.00000	0.240772
$70$	0	0
$71$	7.00000	0.830747	0.415374	−	0.909651i	$-0.363651\pi$
$71$	7.00000	0.830747	0.415374	+	0.909651i	$0.363651\pi$
$72$	−1.00000	−0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	0	0
$75$	5.00000	0.577350
$76$	−5.00000	−0.573539
$77$	2.00000	0.227921
$78$	−1.00000	−0.113228
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.00000	−0.552158
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	5.00000	0.539164
$87$	10.0000	1.07211
$88$	−2.00000	−0.213201
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	−2.00000	−0.208514
$93$	−1.00000	−0.103695
$94$	7.00000	0.721995
$95$	0	0
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.00000	−0.101015
$99$	2.00000	0.201008
$100$	−5.00000	−0.500000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−1.00000	−0.0990148
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−3.00000	−0.291386
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	−1.00000	−0.0962250
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	15.0000	1.41108	0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000	1.41108	0.705541	+	0.708669i	$0.250704\pi$
$114$	−5.00000	−0.468293
$115$	0	0
$116$	−10.0000	−0.928477
$117$	−1.00000	−0.0924500
$118$	−8.00000	−0.736460
$119$	−1.00000	−0.0916698
$120$	0	0
$121$	−7.00000	−0.636364
$122$	8.00000	0.724286
$123$	−5.00000	−0.450835
$124$	1.00000	0.0898027
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	−1.00000	−0.0883883
$129$	5.00000	0.440225
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−2.00000	−0.174078
$133$	−5.00000	−0.433555
$134$	−4.00000	−0.345547
$135$	0	0
$136$	1.00000	0.0857493
$137$	−3.00000	−0.256307	−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000	−0.256307	−0.128154	+	0.991754i	$0.540905\pi$
$138$	−2.00000	−0.170251
$139$	−3.00000	−0.254457	−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000	−0.254457	−0.127228	+	0.991873i	$0.540608\pi$
$140$	0	0
$141$	7.00000	0.589506
$142$	−7.00000	−0.587427
$143$	−2.00000	−0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	−14.0000	−1.15865
$147$	−1.00000	−0.0824786
$148$	0	0
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	−5.00000	−0.408248
$151$	−5.00000	−0.406894	−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000	−0.406894	−0.203447	+	0.979086i	$0.565214\pi$
$152$	5.00000	0.405554
$153$	−1.00000	−0.0808452
$154$	−2.00000	−0.161165
$155$	0	0
$156$	1.00000	0.0800641
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	3.00000	0.238667
$159$	−3.00000	−0.237915
$160$	0	0
$161$	−2.00000	−0.157622
$162$	−1.00000	−0.0785674
$163$	−3.00000	−0.234978	−0.117489	−	0.993074i	$-0.537485\pi$
$163$	−3.00000	−0.234978	−0.117489	+	0.993074i	$0.537485\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	10.0000	0.776151
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	1.00000	0.0771517
$169$	1.00000	0.0769231
$170$	0	0
$171$	−5.00000	−0.382360
$172$	−5.00000	−0.381246
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	−10.0000	−0.758098
$175$	−5.00000	−0.377964
$176$	2.00000	0.150756
$177$	−8.00000	−0.601317
$178$	−14.0000	−1.04934
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	1.00000	0.0741249
$183$	8.00000	0.591377
$184$	2.00000	0.147442
$185$	0	0
$186$	1.00000	0.0733236
$187$	−2.00000	−0.146254
$188$	−7.00000	−0.510527
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	5.00000	0.361787	0.180894	−	0.983503i	$-0.442101\pi$
$191$	5.00000	0.361787	0.180894	+	0.983503i	$0.442101\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	−2.00000	−0.142134
$199$	−6.00000	−0.425329	−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000	−0.425329	−0.212664	+	0.977125i	$0.568214\pi$
$200$	5.00000	0.353553
$201$	−4.00000	−0.282138
$202$	6.00000	0.422159
$203$	−10.0000	−0.701862
$204$	1.00000	0.0700140
$205$	0	0
$206$	−13.0000	−0.905753
$207$	−2.00000	−0.139010
$208$	−1.00000	−0.0693375
$209$	−10.0000	−0.691714
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	3.00000	0.206041
$213$	−7.00000	−0.479632
$214$	−13.0000	−0.888662
$215$	0	0
$216$	1.00000	0.0680414
$217$	1.00000	0.0678844
$218$	−10.0000	−0.677285
$219$	−14.0000	−0.946032
$220$	0	0
$221$	1.00000	0.0672673
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	−1.00000	−0.0668153
$225$	−5.00000	−0.333333
$226$	−15.0000	−0.997785
$227$	9.00000	0.597351	0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000	0.597351	0.298675	+	0.954355i	$0.403455\pi$
$228$	5.00000	0.331133
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	10.0000	0.656532
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	8.00000	0.520756
$237$	3.00000	0.194871
$238$	1.00000	0.0648204
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	7.00000	0.449977
$243$	−1.00000	−0.0641500
$244$	−8.00000	−0.512148
$245$	0	0
$246$	5.00000	0.318788
$247$	5.00000	0.318142
$248$	−1.00000	−0.0635001
$249$	10.0000	0.633724
$250$	0	0
$251$	15.0000	0.946792	0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000	0.946792	0.473396	+	0.880850i	$0.343028\pi$
$252$	1.00000	0.0629941
$253$	−4.00000	−0.251478
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	−21.0000	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$258$	−5.00000	−0.311286
$259$	0	0
$260$	0	0
$261$	−10.0000	−0.618984
$262$	6.00000	0.370681
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	5.00000	0.306570
$267$	−14.0000	−0.856786
$268$	4.00000	0.244339
$269$	−15.0000	−0.914566	−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000	−0.914566	−0.457283	+	0.889321i	$0.651177\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.00000	−0.0606339
$273$	1.00000	0.0605228
$274$	3.00000	0.181237
$275$	−10.0000	−0.603023
$276$	2.00000	0.120386
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	3.00000	0.179928
$279$	1.00000	0.0598684
$280$	0	0
$281$	−9.00000	−0.536895	−0.268447	−	0.963294i	$-0.586511\pi$
$281$	−9.00000	−0.536895	−0.268447	+	0.963294i	$0.586511\pi$
$282$	−7.00000	−0.416844
$283$	−11.0000	−0.653882	−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000	−0.653882	−0.326941	+	0.945045i	$0.606018\pi$
$284$	7.00000	0.415374
$285$	0	0
$286$	2.00000	0.118262
$287$	5.00000	0.295141
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	2.00000	0.117242
$292$	14.0000	0.819288
$293$	29.0000	1.69420	0.847099	−	0.531435i	$-0.178347\pi$
$293$	29.0000	1.69420	0.847099	+	0.531435i	$0.178347\pi$
$294$	1.00000	0.0583212
$295$	0	0
$296$	0	0
$297$	−2.00000	−0.116052
$298$	−14.0000	−0.810998
$299$	2.00000	0.115663
$300$	5.00000	0.288675
$301$	−5.00000	−0.288195
$302$	5.00000	0.287718
$303$	6.00000	0.344691
$304$	−5.00000	−0.286770
$305$	0	0
$306$	1.00000	0.0571662
$307$	4.00000	0.228292	0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000	0.228292	0.114146	+	0.993464i	$0.463587\pi$
$308$	2.00000	0.113961
$309$	−13.0000	−0.739544
$310$	0	0
$311$	33.0000	1.87126	0.935629	−	0.352985i	$-0.114833\pi$
$311$	33.0000	1.87126	0.935629	+	0.352985i	$0.114833\pi$
$312$	−1.00000	−0.0566139
$313$	19.0000	1.07394	0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000	1.07394	0.536972	+	0.843600i	$0.319568\pi$
$314$	−1.00000	−0.0564333
$315$	0	0
$316$	−3.00000	−0.168763
$317$	−17.0000	−0.954815	−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000	−0.954815	−0.477408	+	0.878682i	$0.658423\pi$
$318$	3.00000	0.168232
$319$	−20.0000	−1.11979
$320$	0	0
$321$	−13.0000	−0.725589
$322$	2.00000	0.111456
$323$	5.00000	0.278207
$324$	1.00000	0.0555556
$325$	5.00000	0.277350
$326$	3.00000	0.166155
$327$	−10.0000	−0.553001
$328$	−5.00000	−0.276079
$329$	−7.00000	−0.385922
$330$	0	0
$331$	10.0000	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$332$	−10.0000	−0.548821
$333$	0	0
$334$	−22.0000	−1.20379
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−1.00000	−0.0543928
$339$	−15.0000	−0.814688
$340$	0	0
$341$	2.00000	0.108306
$342$	5.00000	0.270369
$343$	1.00000	0.0539949
$344$	5.00000	0.269582
$345$	0	0
$346$	−11.0000	−0.591364
$347$	23.0000	1.23470	0.617352	−	0.786687i	$-0.288205\pi$
$347$	23.0000	1.23470	0.617352	+	0.786687i	$0.288205\pi$
$348$	10.0000	0.536056
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	5.00000	0.267261
$351$	1.00000	0.0533761
$352$	−2.00000	−0.106600
$353$	−4.00000	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$354$	8.00000	0.425195
$355$	0	0
$356$	14.0000	0.741999
$357$	1.00000	0.0529256
$358$	16.0000	0.845626
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−2.00000	−0.105118
$363$	7.00000	0.367405
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	−8.00000	−0.418167
$367$	−6.00000	−0.313197	−0.156599	−	0.987662i	$-0.550053\pi$
$367$	−6.00000	−0.313197	−0.156599	+	0.987662i	$0.550053\pi$
$368$	−2.00000	−0.104257
$369$	5.00000	0.260290
$370$	0	0
$371$	3.00000	0.155752
$372$	−1.00000	−0.0518476
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	7.00000	0.360997
$377$	10.0000	0.515026
$378$	1.00000	0.0514344
$379$	−37.0000	−1.90056	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−37.0000	−1.90056	−0.950281	+	0.311393i	$0.899204\pi$
$380$	0	0
$381$	−2.00000	−0.102463
$382$	−5.00000	−0.255822
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	−5.00000	−0.254164
$388$	−2.00000	−0.101535
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	−1.00000	−0.0505076
$393$	6.00000	0.302660
$394$	−6.00000	−0.302276
$395$	0	0
$396$	2.00000	0.100504
$397$	35.0000	1.75660	0.878300	−	0.478110i	$-0.158678\pi$
$397$	35.0000	1.75660	0.878300	+	0.478110i	$0.158678\pi$
$398$	6.00000	0.300753
$399$	5.00000	0.250313
$400$	−5.00000	−0.250000
$401$	28.0000	1.39825	0.699127	−	0.714998i	$-0.253572\pi$
$401$	28.0000	1.39825	0.699127	+	0.714998i	$0.253572\pi$
$402$	4.00000	0.199502
$403$	−1.00000	−0.0498135
$404$	−6.00000	−0.298511
$405$	0	0
$406$	10.0000	0.496292
$407$	0	0
$408$	−1.00000	−0.0495074
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	0	0
$411$	3.00000	0.147979
$412$	13.0000	0.640464
$413$	8.00000	0.393654
$414$	2.00000	0.0982946
$415$	0	0
$416$	1.00000	0.0490290
$417$	3.00000	0.146911
$418$	10.0000	0.489116
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	0	0
$421$	7.00000	0.341159	0.170580	−	0.985344i	$-0.445436\pi$
$421$	7.00000	0.341159	0.170580	+	0.985344i	$0.445436\pi$
$422$	0	0
$423$	−7.00000	−0.340352
$424$	−3.00000	−0.145693
$425$	5.00000	0.242536
$426$	7.00000	0.339151
$427$	−8.00000	−0.387147
$428$	13.0000	0.628379
$429$	2.00000	0.0965609
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	−1.00000	−0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	−1.00000	−0.0480015
$435$	0	0
$436$	10.0000	0.478913
$437$	10.0000	0.478365
$438$	14.0000	0.668946
$439$	12.0000	0.572729	0.286364	−	0.958121i	$-0.407553\pi$
$439$	12.0000	0.572729	0.286364	+	0.958121i	$0.407553\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	0	0
$445$	0	0
$446$	4.00000	0.189405
$447$	−14.0000	−0.662177
$448$	1.00000	0.0472456
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	5.00000	0.235702
$451$	10.0000	0.470882
$452$	15.0000	0.705541
$453$	5.00000	0.234920
$454$	−9.00000	−0.422391
$455$	0	0
$456$	−5.00000	−0.234146
$457$	−38.0000	−1.77757	−0.888783	−	0.458329i	$-0.848448\pi$
$457$	−38.0000	−1.77757	−0.888783	+	0.458329i	$0.848448\pi$
$458$	−2.00000	−0.0934539
$459$	1.00000	0.0466760
$460$	0	0
$461$	26.0000	1.21094	0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000	1.21094	0.605470	+	0.795868i	$0.292985\pi$
$462$	2.00000	0.0930484
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−10.0000	−0.464238
$465$	0	0
$466$	−14.0000	−0.648537
$467$	27.0000	1.24941	0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000	1.24941	0.624705	+	0.780860i	$0.285219\pi$
$468$	−1.00000	−0.0462250
$469$	4.00000	0.184703
$470$	0	0
$471$	−1.00000	−0.0460776
$472$	−8.00000	−0.368230
$473$	−10.0000	−0.459800
$474$	−3.00000	−0.137795
$475$	25.0000	1.14708
$476$	−1.00000	−0.0458349
$477$	3.00000	0.137361
$478$	6.00000	0.274434
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	0	0
$482$	2.00000	0.0910975
$483$	2.00000	0.0910032
$484$	−7.00000	−0.318182
$485$	0	0
$486$	1.00000	0.0453609
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	8.00000	0.362143
$489$	3.00000	0.135665
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	−5.00000	−0.225417
$493$	10.0000	0.450377
$494$	−5.00000	−0.224961
$495$	0	0
$496$	1.00000	0.0449013
$497$	7.00000	0.313993
$498$	−10.0000	−0.448111
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	−22.0000	−0.982888
$502$	−15.0000	−0.669483
$503$	37.0000	1.64975	0.824874	−	0.565316i	$-0.191246\pi$
$503$	37.0000	1.64975	0.824874	+	0.565316i	$0.191246\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	4.00000	0.177822
$507$	−1.00000	−0.0444116
$508$	2.00000	0.0887357
$509$	−15.0000	−0.664863	−0.332432	−	0.943127i	$-0.607869\pi$
$509$	−15.0000	−0.664863	−0.332432	+	0.943127i	$0.607869\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	21.0000	0.926270
$515$	0	0
$516$	5.00000	0.220113
$517$	−14.0000	−0.615719
$518$	0	0
$519$	−11.0000	−0.482846
$520$	0	0
$521$	−28.0000	−1.22670	−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000	−1.22670	−0.613351	+	0.789810i	$0.710179\pi$
$522$	10.0000	0.437688
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	−6.00000	−0.262111
$525$	5.00000	0.218218
$526$	−28.0000	−1.22086
$527$	−1.00000	−0.0435607
$528$	−2.00000	−0.0870388
$529$	−19.0000	−0.826087
$530$	0	0
$531$	8.00000	0.347170
$532$	−5.00000	−0.216777
$533$	−5.00000	−0.216574
$534$	14.0000	0.605839
$535$	0	0
$536$	−4.00000	−0.172774
$537$	16.0000	0.690451
$538$	15.0000	0.646696
$539$	2.00000	0.0861461
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−20.0000	−0.859074
$543$	−2.00000	−0.0858282
$544$	1.00000	0.0428746
$545$	0	0
$546$	−1.00000	−0.0427960
$547$	−18.0000	−0.769624	−0.384812	−	0.922995i	$-0.625734\pi$
$547$	−18.0000	−0.769624	−0.384812	+	0.922995i	$0.625734\pi$
$548$	−3.00000	−0.128154
$549$	−8.00000	−0.341432
$550$	10.0000	0.426401
$551$	50.0000	2.13007
$552$	−2.00000	−0.0851257
$553$	−3.00000	−0.127573
$554$	10.0000	0.424859
$555$	0	0
$556$	−3.00000	−0.127228
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−1.00000	−0.0423334
$559$	5.00000	0.211477
$560$	0	0
$561$	2.00000	0.0844401
$562$	9.00000	0.379642
$563$	28.0000	1.18006	0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000	1.18006	0.590030	+	0.807382i	$0.299116\pi$
$564$	7.00000	0.294753
$565$	0	0
$566$	11.0000	0.462364
$567$	1.00000	0.0419961
$568$	−7.00000	−0.293713
$569$	28.0000	1.17382	0.586911	−	0.809652i	$-0.300344\pi$
$569$	28.0000	1.17382	0.586911	+	0.809652i	$0.300344\pi$
$570$	0	0
$571$	−6.00000	−0.251092	−0.125546	−	0.992088i	$-0.540068\pi$
$571$	−6.00000	−0.251092	−0.125546	+	0.992088i	$0.540068\pi$
$572$	−2.00000	−0.0836242
$573$	−5.00000	−0.208878
$574$	−5.00000	−0.208696
$575$	10.0000	0.417029
$576$	1.00000	0.0416667
$577$	−5.00000	−0.208153	−0.104076	−	0.994569i	$-0.533189\pi$
$577$	−5.00000	−0.208153	−0.104076	+	0.994569i	$0.533189\pi$
$578$	−1.00000	−0.0415945
$579$	10.0000	0.415586
$580$	0	0
$581$	−10.0000	−0.414870
$582$	−2.00000	−0.0829027
$583$	6.00000	0.248495
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−29.0000	−1.19798
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	−1.00000	−0.0412393
$589$	−5.00000	−0.206021
$590$	0	0
$591$	−6.00000	−0.246807
$592$	0	0
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	14.0000	0.573462
$597$	6.00000	0.245564
$598$	−2.00000	−0.0817861
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	−5.00000	−0.204124
$601$	−9.00000	−0.367118	−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000	−0.367118	−0.183559	+	0.983009i	$0.558762\pi$
$602$	5.00000	0.203785
$603$	4.00000	0.162893
$604$	−5.00000	−0.203447
$605$	0	0
$606$	−6.00000	−0.243733
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	5.00000	0.202777
$609$	10.0000	0.405220
$610$	0	0
$611$	7.00000	0.283190
$612$	−1.00000	−0.0404226
$613$	−9.00000	−0.363507	−0.181753	−	0.983344i	$-0.558177\pi$
$613$	−9.00000	−0.363507	−0.181753	+	0.983344i	$0.558177\pi$
$614$	−4.00000	−0.161427
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	13.0000	0.522937
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	2.00000	0.0802572
$622$	−33.0000	−1.32318
$623$	14.0000	0.560898
$624$	1.00000	0.0400320
$625$	25.0000	1.00000
$626$	−19.0000	−0.759393
$627$	10.0000	0.399362
$628$	1.00000	0.0399043
$629$	0	0
$630$	0	0
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	3.00000	0.119334
$633$	0	0
$634$	17.0000	0.675156
$635$	0	0
$636$	−3.00000	−0.118958
$637$	−1.00000	−0.0396214
$638$	20.0000	0.791808
$639$	7.00000	0.276916
$640$	0	0
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	13.0000	0.513069
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	−2.00000	−0.0788110
$645$	0	0
$646$	−5.00000	−0.196722
$647$	30.0000	1.17942	0.589711	−	0.807614i	$-0.299242\pi$
$647$	30.0000	1.17942	0.589711	+	0.807614i	$0.299242\pi$
$648$	−1.00000	−0.0392837
$649$	16.0000	0.628055
$650$	−5.00000	−0.196116
$651$	−1.00000	−0.0391931
$652$	−3.00000	−0.117489
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	10.0000	0.391031
$655$	0	0
$656$	5.00000	0.195217
$657$	14.0000	0.546192
$658$	7.00000	0.272888
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	0	0
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	−10.0000	−0.388661
$663$	−1.00000	−0.0388368
$664$	10.0000	0.388075
$665$	0	0
$666$	0	0
$667$	20.0000	0.774403
$668$	22.0000	0.851206
$669$	4.00000	0.154649
$670$	0	0
$671$	−16.0000	−0.617673
$672$	1.00000	0.0385758
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	−2.00000	−0.0770371
$675$	5.00000	0.192450
$676$	1.00000	0.0384615
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	15.0000	0.576072
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	−9.00000	−0.344881
$682$	−2.00000	−0.0765840
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	−5.00000	−0.191180
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−2.00000	−0.0763048
$688$	−5.00000	−0.190623
$689$	−3.00000	−0.114291
$690$	0	0
$691$	34.0000	1.29342	0.646710	−	0.762736i	$-0.276144\pi$
$691$	34.0000	1.29342	0.646710	+	0.762736i	$0.276144\pi$
$692$	11.0000	0.418157
$693$	2.00000	0.0759737
$694$	−23.0000	−0.873068
$695$	0	0
$696$	−10.0000	−0.379049
$697$	−5.00000	−0.189389
$698$	26.0000	0.984115
$699$	−14.0000	−0.529529
$700$	−5.00000	−0.188982
$701$	9.00000	0.339925	0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000	0.339925	0.169963	+	0.985451i	$0.445635\pi$
$702$	−1.00000	−0.0377426
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	4.00000	0.150542
$707$	−6.00000	−0.225653
$708$	−8.00000	−0.300658
$709$	8.00000	0.300446	0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000	0.300446	0.150223	+	0.988652i	$0.452001\pi$
$710$	0	0
$711$	−3.00000	−0.112509
$712$	−14.0000	−0.524672
$713$	−2.00000	−0.0749006
$714$	−1.00000	−0.0374241
$715$	0	0
$716$	−16.0000	−0.597948
$717$	6.00000	0.224074
$718$	4.00000	0.149279
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	13.0000	0.484145
$722$	−6.00000	−0.223297
$723$	2.00000	0.0743808
$724$	2.00000	0.0743294
$725$	50.0000	1.85695
$726$	−7.00000	−0.259794
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	0	0
$731$	5.00000	0.184932
$732$	8.00000	0.295689
$733$	20.0000	0.738717	0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000	0.738717	0.369358	+	0.929287i	$0.379577\pi$
$734$	6.00000	0.221464
$735$	0	0
$736$	2.00000	0.0737210
$737$	8.00000	0.294684
$738$	−5.00000	−0.184053
$739$	26.0000	0.956425	0.478213	−	0.878244i	$-0.341285\pi$
$739$	26.0000	0.956425	0.478213	+	0.878244i	$0.341285\pi$
$740$	0	0
$741$	−5.00000	−0.183680
$742$	−3.00000	−0.110133
$743$	−1.00000	−0.0366864	−0.0183432	−	0.999832i	$-0.505839\pi$
$743$	−1.00000	−0.0366864	−0.0183432	+	0.999832i	$0.505839\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	−4.00000	−0.146450
$747$	−10.0000	−0.365881
$748$	−2.00000	−0.0731272
$749$	13.0000	0.475010
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	−7.00000	−0.255264
$753$	−15.0000	−0.546630
$754$	−10.0000	−0.364179
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	−32.0000	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$758$	37.0000	1.34390
$759$	4.00000	0.145191
$760$	0	0
$761$	2.00000	0.0724999	0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000	0.0724999	0.0362500	+	0.999343i	$0.488459\pi$
$762$	2.00000	0.0724524
$763$	10.0000	0.362024
$764$	5.00000	0.180894
$765$	0	0
$766$	16.0000	0.578103
$767$	−8.00000	−0.288863
$768$	−1.00000	−0.0360844
$769$	−1.00000	−0.0360609	−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000	−0.0360609	−0.0180305	+	0.999837i	$0.505740\pi$
$770$	0	0
$771$	21.0000	0.756297
$772$	−10.0000	−0.359908
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	5.00000	0.179721
$775$	−5.00000	−0.179605
$776$	2.00000	0.0717958
$777$	0	0
$778$	−22.0000	−0.788738
$779$	−25.0000	−0.895718
$780$	0	0
$781$	14.0000	0.500959
$782$	−2.00000	−0.0715199
$783$	10.0000	0.357371
$784$	1.00000	0.0357143
$785$	0	0
$786$	−6.00000	−0.214013
$787$	36.0000	1.28326	0.641631	−	0.767014i	$-0.278258\pi$
$787$	36.0000	1.28326	0.641631	+	0.767014i	$0.278258\pi$
$788$	6.00000	0.213741
$789$	−28.0000	−0.996826
$790$	0	0
$791$	15.0000	0.533339
$792$	−2.00000	−0.0710669
$793$	8.00000	0.284088
$794$	−35.0000	−1.24210
$795$	0	0
$796$	−6.00000	−0.212664
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	−5.00000	−0.176998
$799$	7.00000	0.247642
$800$	5.00000	0.176777
$801$	14.0000	0.494666
$802$	−28.0000	−0.988714
$803$	28.0000	0.988099
$804$	−4.00000	−0.141069
$805$	0	0
$806$	1.00000	0.0352235
$807$	15.0000	0.528025
$808$	6.00000	0.211079
$809$	−29.0000	−1.01959	−0.509793	−	0.860297i	$-0.670278\pi$
$809$	−29.0000	−1.01959	−0.509793	+	0.860297i	$0.670278\pi$
$810$	0	0
$811$	24.0000	0.842754	0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000	0.842754	0.421377	+	0.906886i	$0.361547\pi$
$812$	−10.0000	−0.350931
$813$	−20.0000	−0.701431
$814$	0	0
$815$	0	0
$816$	1.00000	0.0350070
$817$	25.0000	0.874639
$818$	−22.0000	−0.769212
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	−3.00000	−0.104637
$823$	27.0000	0.941161	0.470580	−	0.882357i	$-0.344045\pi$
$823$	27.0000	0.941161	0.470580	+	0.882357i	$0.344045\pi$
$824$	−13.0000	−0.452876
$825$	10.0000	0.348155
$826$	−8.00000	−0.278356
$827$	20.0000	0.695468	0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000	0.695468	0.347734	+	0.937593i	$0.386951\pi$
$828$	−2.00000	−0.0695048
$829$	−19.0000	−0.659897	−0.329949	−	0.943999i	$-0.607031\pi$
$829$	−19.0000	−0.659897	−0.329949	+	0.943999i	$0.607031\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	−1.00000	−0.0346688
$833$	−1.00000	−0.0346479
$834$	−3.00000	−0.103882
$835$	0	0
$836$	−10.0000	−0.345857
$837$	−1.00000	−0.0345651
$838$	30.0000	1.03633
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	−7.00000	−0.241236
$843$	9.00000	0.309976
$844$	0	0
$845$	0	0
$846$	7.00000	0.240665
$847$	−7.00000	−0.240523
$848$	3.00000	0.103020
$849$	11.0000	0.377519
$850$	−5.00000	−0.171499
$851$	0	0
$852$	−7.00000	−0.239816
$853$	19.0000	0.650548	0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000	0.650548	0.325274	+	0.945620i	$0.394544\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	−13.0000	−0.444331
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	−2.00000	−0.0682789
$859$	50.0000	1.70598	0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000	1.70598	0.852989	+	0.521929i	$0.174787\pi$
$860$	0	0
$861$	−5.00000	−0.170400
$862$	−36.0000	−1.22616
$863$	−10.0000	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	16.0000	0.543702
$867$	−1.00000	−0.0339618
$868$	1.00000	0.0339422
$869$	−6.00000	−0.203536
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−10.0000	−0.338643
$873$	−2.00000	−0.0676897
$874$	−10.0000	−0.338255
$875$	0	0
$876$	−14.0000	−0.473016
$877$	−8.00000	−0.270141	−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000	−0.270141	−0.135070	+	0.990836i	$0.543126\pi$
$878$	−12.0000	−0.404980
$879$	−29.0000	−0.978146
$880$	0	0
$881$	−8.00000	−0.269527	−0.134763	−	0.990878i	$-0.543027\pi$
$881$	−8.00000	−0.269527	−0.134763	+	0.990878i	$0.543027\pi$
$882$	−1.00000	−0.0336718
$883$	51.0000	1.71629	0.858143	−	0.513410i	$-0.171618\pi$
$883$	51.0000	1.71629	0.858143	+	0.513410i	$0.171618\pi$
$884$	1.00000	0.0336336
$885$	0	0
$886$	12.0000	0.403148
$887$	40.0000	1.34307	0.671534	−	0.740973i	$-0.265636\pi$
$887$	40.0000	1.34307	0.671534	+	0.740973i	$0.265636\pi$
$888$	0	0
$889$	2.00000	0.0670778
$890$	0	0
$891$	2.00000	0.0670025
$892$	−4.00000	−0.133930
$893$	35.0000	1.17123
$894$	14.0000	0.468230
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	24.0000	0.800890
$899$	−10.0000	−0.333519
$900$	−5.00000	−0.166667
$901$	−3.00000	−0.0999445
$902$	−10.0000	−0.332964
$903$	5.00000	0.166390
$904$	−15.0000	−0.498893
$905$	0	0
$906$	−5.00000	−0.166114
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	9.00000	0.298675
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−42.0000	−1.39152	−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000	−1.39152	−0.695761	+	0.718273i	$0.744933\pi$
$912$	5.00000	0.165567
$913$	−20.0000	−0.661903
$914$	38.0000	1.25693
$915$	0	0
$916$	2.00000	0.0660819
$917$	−6.00000	−0.198137
$918$	−1.00000	−0.0330049
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	−26.0000	−0.856264
$923$	−7.00000	−0.230408
$924$	−2.00000	−0.0657952
$925$	0	0
$926$	16.0000	0.525793
$927$	13.0000	0.426976
$928$	10.0000	0.328266
$929$	−57.0000	−1.87011	−0.935055	−	0.354504i	$-0.884650\pi$
$929$	−57.0000	−1.87011	−0.935055	+	0.354504i	$0.884650\pi$
$930$	0	0
$931$	−5.00000	−0.163868
$932$	14.0000	0.458585
$933$	−33.0000	−1.08037
$934$	−27.0000	−0.883467
$935$	0	0
$936$	1.00000	0.0326860
$937$	−36.0000	−1.17607	−0.588034	−	0.808836i	$-0.700098\pi$
$937$	−36.0000	−1.17607	−0.588034	+	0.808836i	$0.700098\pi$
$938$	−4.00000	−0.130605
$939$	−19.0000	−0.620042
$940$	0	0
$941$	−50.0000	−1.62995	−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000	−1.62995	−0.814977	+	0.579494i	$0.803250\pi$
$942$	1.00000	0.0325818
$943$	−10.0000	−0.325645
$944$	8.00000	0.260378
$945$	0	0
$946$	10.0000	0.325128
$947$	26.0000	0.844886	0.422443	−	0.906389i	$-0.361173\pi$
$947$	26.0000	0.844886	0.422443	+	0.906389i	$0.361173\pi$
$948$	3.00000	0.0974355
$949$	−14.0000	−0.454459
$950$	−25.0000	−0.811107
$951$	17.0000	0.551263
$952$	1.00000	0.0324102
$953$	34.0000	1.10137	0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000	1.10137	0.550684	+	0.834714i	$0.314367\pi$
$954$	−3.00000	−0.0971286
$955$	0	0
$956$	−6.00000	−0.194054
$957$	20.0000	0.646508
$958$	−12.0000	−0.387702
$959$	−3.00000	−0.0968751
$960$	0	0
$961$	−30.0000	−0.967742
$962$	0	0
$963$	13.0000	0.418919
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	−2.00000	−0.0643489
$967$	−12.0000	−0.385894	−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000	−0.385894	−0.192947	+	0.981209i	$0.561805\pi$
$968$	7.00000	0.224989
$969$	−5.00000	−0.160623
$970$	0	0
$971$	44.0000	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$971$	44.0000	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$972$	−1.00000	−0.0320750
$973$	−3.00000	−0.0961756
$974$	12.0000	0.384505
$975$	−5.00000	−0.160128
$976$	−8.00000	−0.256074
$977$	−5.00000	−0.159964	−0.0799821	−	0.996796i	$-0.525486\pi$
$977$	−5.00000	−0.159964	−0.0799821	+	0.996796i	$0.525486\pi$
$978$	−3.00000	−0.0959294
$979$	28.0000	0.894884
$980$	0	0
$981$	10.0000	0.319275
$982$	0	0
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	5.00000	0.159394
$985$	0	0
$986$	−10.0000	−0.318465
$987$	7.00000	0.222812
$988$	5.00000	0.159071
$989$	10.0000	0.317982
$990$	0	0
$991$	24.0000	0.762385	0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000	0.762385	0.381193	+	0.924496i	$0.375513\pi$
$992$	−1.00000	−0.0317500
$993$	−10.0000	−0.317340
$994$	−7.00000	−0.222027
$995$	0	0
$996$	10.0000	0.316862
$997$	12.0000	0.380044	0.190022	−	0.981780i	$-0.439144\pi$
$997$	12.0000	0.380044	0.190022	+	0.981780i	$0.439144\pi$
$998$	20.0000	0.633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.e.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.e.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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