LMFDB - Embedded newform 1274.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(1,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1274.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.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:	$10.1729412175$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} -2.00000 q^{18} -2.00000 q^{19} -3.00000 q^{22} -3.00000 q^{23} -1.00000 q^{24} -5.00000 q^{25} -1.00000 q^{26} +5.00000 q^{27} -5.00000 q^{31} +1.00000 q^{32} +3.00000 q^{33} -2.00000 q^{36} -7.00000 q^{37} -2.00000 q^{38} +1.00000 q^{39} -3.00000 q^{41} +8.00000 q^{43} -3.00000 q^{44} -3.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} -5.00000 q^{50} -1.00000 q^{52} -12.0000 q^{53} +5.00000 q^{54} +2.00000 q^{57} -6.00000 q^{59} +1.00000 q^{61} -5.00000 q^{62} +1.00000 q^{64} +3.00000 q^{66} +5.00000 q^{67} +3.00000 q^{69} +12.0000 q^{71} -2.00000 q^{72} -11.0000 q^{73} -7.00000 q^{74} +5.00000 q^{75} -2.00000 q^{76} +1.00000 q^{78} -1.00000 q^{79} +1.00000 q^{81} -3.00000 q^{82} -12.0000 q^{83} +8.00000 q^{86} -3.00000 q^{88} +18.0000 q^{89} -3.00000 q^{92} +5.00000 q^{93} +3.00000 q^{94} -1.00000 q^{96} -17.0000 q^{97} +6.00000 q^{99} +O(q^{100})$

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
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	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
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−2.00000	−0.471405
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	−1.00000	−0.204124
$25$	−5.00000	−1.00000
$26$	−1.00000	−0.196116
$27$	5.00000	0.962250
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	1.00000	0.176777
$33$	3.00000	0.522233
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	−2.00000	−0.324443
$39$	1.00000	0.160128
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	−3.00000	−0.442326
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−5.00000	−0.707107
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	0	0
$57$	2.00000	0.264906
$58$	0	0
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−5.00000	−0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	5.00000	0.610847	0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000	0.610847	0.305424	+	0.952217i	$0.401202\pi$
$68$	0	0
$69$	3.00000	0.361158
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	−2.00000	−0.235702
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−7.00000	−0.813733
$75$	5.00000	0.577350
$76$	−2.00000	−0.229416
$77$	0	0
$78$	1.00000	0.113228
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.00000	−0.331295
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	0	0
$86$	8.00000	0.862662
$87$	0	0
$88$	−3.00000	−0.319801
$89$	18.0000	1.90800	0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000	1.90800	0.953998	+	0.299813i	$0.0969242\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	5.00000	0.518476
$94$	3.00000	0.309426
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	0	0
$99$	6.00000	0.603023
$100$	−5.00000	−0.500000
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−12.0000	−1.16554
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	5.00000	0.481125
$109$	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
$111$	7.00000	0.664411
$112$	0	0
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	2.00000	0.187317
$115$	0	0
$116$	0	0
$117$	2.00000	0.184900
$118$	−6.00000	−0.552345
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	1.00000	0.0905357
$123$	3.00000	0.270501
$124$	−5.00000	−0.449013
$125$	0	0
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	3.00000	0.261116
$133$	0	0
$134$	5.00000	0.431934
$135$	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	$0.582506\pi$
$138$	3.00000	0.255377
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−3.00000	−0.252646
$142$	12.0000	1.00702
$143$	3.00000	0.250873
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−11.0000	−0.910366
$147$	0	0
$148$	−7.00000	−0.575396
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	5.00000	0.408248
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.00000	−0.162221
$153$	0	0
$154$	0	0
$155$	0	0
$156$	1.00000	0.0800641
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	−1.00000	−0.0795557
$159$	12.0000	0.951662
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	−3.00000	−0.234261
$165$	0	0
$166$	−12.0000	−0.931381
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	4.00000	0.305888
$172$	8.00000	0.609994
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	0	0
$176$	−3.00000	−0.226134
$177$	6.00000	0.450988
$178$	18.0000	1.34916
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	0	0
$183$	−1.00000	−0.0739221
$184$	−3.00000	−0.221163
$185$	0	0
$186$	5.00000	0.366618
$187$	0	0
$188$	3.00000	0.218797
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−17.0000	−1.22053
$195$	0	0
$196$	0	0
$197$	−3.00000	−0.213741	−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000	−0.213741	−0.106871	+	0.994273i	$0.534083\pi$
$198$	6.00000	0.426401
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−5.00000	−0.353553
$201$	−5.00000	−0.352673
$202$	3.00000	0.211079
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−14.0000	−0.975426
$207$	6.00000	0.417029
$208$	−1.00000	−0.0693375
$209$	6.00000	0.415029
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	−12.0000	−0.824163
$213$	−12.0000	−0.822226
$214$	0	0
$215$	0	0
$216$	5.00000	0.340207
$217$	0	0
$218$	2.00000	0.135457
$219$	11.0000	0.743311
$220$	0	0
$221$	0	0
$222$	7.00000	0.469809
$223$	1.00000	0.0669650	0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000	0.0669650	0.0334825	+	0.999439i	$0.489340\pi$
$224$	0	0
$225$	10.0000	0.666667
$226$	9.00000	0.598671
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	2.00000	0.132453
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	3.00000	0.196537	0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000	0.196537	0.0982683	+	0.995160i	$0.468670\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−6.00000	−0.390567
$237$	1.00000	0.0649570
$238$	0	0
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	−2.00000	−0.128565
$243$	−16.0000	−1.02640
$244$	1.00000	0.0640184
$245$	0	0
$246$	3.00000	0.191273
$247$	2.00000	0.127257
$248$	−5.00000	−0.317500
$249$	12.0000	0.760469
$250$	0	0
$251$	15.0000	0.946792	0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000	0.946792	0.473396	+	0.880850i	$0.343028\pi$
$252$	0	0
$253$	9.00000	0.565825
$254$	−7.00000	−0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	0	0
$267$	−18.0000	−1.10158
$268$	5.00000	0.305424
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	0	0
$271$	−11.0000	−0.668202	−0.334101	−	0.942537i	$-0.608433\pi$
$271$	−11.0000	−0.668202	−0.334101	+	0.942537i	$0.608433\pi$
$272$	0	0
$273$	0	0
$274$	−6.00000	−0.362473
$275$	15.0000	0.904534
$276$	3.00000	0.180579
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	4.00000	0.239904
$279$	10.0000	0.598684
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	−3.00000	−0.178647
$283$	31.0000	1.84276	0.921379	−	0.388664i	$-0.127063\pi$
$283$	31.0000	1.84276	0.921379	+	0.388664i	$0.127063\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	3.00000	0.177394
$287$	0	0
$288$	−2.00000	−0.117851
$289$	−17.0000	−1.00000
$290$	0	0
$291$	17.0000	0.996558
$292$	−11.0000	−0.643726
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	0	0
$296$	−7.00000	−0.406867
$297$	−15.0000	−0.870388
$298$	−15.0000	−0.868927
$299$	3.00000	0.173494
$300$	5.00000	0.288675
$301$	0	0
$302$	8.00000	0.460348
$303$	−3.00000	−0.172345
$304$	−2.00000	−0.114708
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	0	0
$309$	14.0000	0.796432
$310$	0	0
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	1.00000	0.0566139
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	13.0000	0.733632
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	−3.00000	−0.168497	−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000	−0.168497	−0.0842484	+	0.996445i	$0.526849\pi$
$318$	12.0000	0.672927
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	5.00000	0.277350
$326$	20.0000	1.10770
$327$	−2.00000	−0.110600
$328$	−3.00000	−0.165647
$329$	0	0
$330$	0	0
$331$	−19.0000	−1.04433	−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000	−1.04433	−0.522167	+	0.852843i	$0.674876\pi$
$332$	−12.0000	−0.658586
$333$	14.0000	0.767195
$334$	24.0000	1.31322
$335$	0	0
$336$	0	0
$337$	−31.0000	−1.68868	−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000	−1.68868	−0.844339	+	0.535810i	$0.820006\pi$
$338$	1.00000	0.0543928
$339$	−9.00000	−0.488813
$340$	0	0
$341$	15.0000	0.812296
$342$	4.00000	0.216295
$343$	0	0
$344$	8.00000	0.431331
$345$	0	0
$346$	18.0000	0.967686
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	−3.00000	−0.159901
$353$	−15.0000	−0.798369	−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000	−0.798369	−0.399185	+	0.916871i	$0.630707\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	18.0000	0.953998
$357$	0	0
$358$	−6.00000	−0.317110
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	7.00000	0.367912
$363$	2.00000	0.104973
$364$	0	0
$365$	0	0
$366$	−1.00000	−0.0522708
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	−3.00000	−0.156386
$369$	6.00000	0.312348
$370$	0	0
$371$	0	0
$372$	5.00000	0.259238
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	0	0
$375$	0	0
$376$	3.00000	0.154713
$377$	0	0
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	7.00000	0.358621
$382$	0	0
$383$	−3.00000	−0.153293	−0.0766464	−	0.997058i	$-0.524421\pi$
$383$	−3.00000	−0.153293	−0.0766464	+	0.997058i	$0.524421\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−4.00000	−0.203595
$387$	−16.0000	−0.813326
$388$	−17.0000	−0.863044
$389$	−36.0000	−1.82527	−0.912636	−	0.408773i	$-0.865957\pi$
$389$	−36.0000	−1.82527	−0.912636	+	0.408773i	$0.865957\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−3.00000	−0.151138
$395$	0	0
$396$	6.00000	0.301511
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−5.00000	−0.250000
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	−5.00000	−0.249377
$403$	5.00000	0.249068
$404$	3.00000	0.149256
$405$	0	0
$406$	0	0
$407$	21.0000	1.04093
$408$	0	0
$409$	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
$411$	6.00000	0.295958
$412$	−14.0000	−0.689730
$413$	0	0
$414$	6.00000	0.294884
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	−4.00000	−0.195881
$418$	6.00000	0.293470
$419$	−21.0000	−1.02592	−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000	−1.02592	−0.512959	+	0.858413i	$0.671451\pi$
$420$	0	0
$421$	−37.0000	−1.80327	−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000	−1.80327	−0.901635	+	0.432498i	$0.857632\pi$
$422$	−22.0000	−1.07094
$423$	−6.00000	−0.291730
$424$	−12.0000	−0.582772
$425$	0	0
$426$	−12.0000	−0.581402
$427$	0	0
$428$	0	0
$429$	−3.00000	−0.144841
$430$	0	0
$431$	−6.00000	−0.289010	−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000	−0.289010	−0.144505	+	0.989504i	$0.546159\pi$
$432$	5.00000	0.240563
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	0	0
$435$	0	0
$436$	2.00000	0.0957826
$437$	6.00000	0.287019
$438$	11.0000	0.525600
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	7.00000	0.332205
$445$	0	0
$446$	1.00000	0.0473514
$447$	15.0000	0.709476
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	10.0000	0.471405
$451$	9.00000	0.423793
$452$	9.00000	0.423324
$453$	−8.00000	−0.375873
$454$	24.0000	1.12638
$455$	0	0
$456$	2.00000	0.0936586
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	4.00000	0.186908
$459$	0	0
$460$	0	0
$461$	−24.0000	−1.11779	−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000	−1.11779	−0.558896	+	0.829238i	$0.688775\pi$
$462$	0	0
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	0	0
$465$	0	0
$466$	3.00000	0.138972
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	0	0
$471$	−13.0000	−0.599008
$472$	−6.00000	−0.276172
$473$	−24.0000	−1.10352
$474$	1.00000	0.0459315
$475$	10.0000	0.458831
$476$	0	0
$477$	24.0000	1.09888
$478$	6.00000	0.274434
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	7.00000	0.319173
$482$	−26.0000	−1.18427
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	−16.0000	−0.725775
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	1.00000	0.0452679
$489$	−20.0000	−0.904431
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	3.00000	0.135250
$493$	0	0
$494$	2.00000	0.0899843
$495$	0	0
$496$	−5.00000	−0.224507
$497$	0	0
$498$	12.0000	0.537733
$499$	23.0000	1.02962	0.514811	−	0.857304i	$-0.327862\pi$
$499$	23.0000	1.02962	0.514811	+	0.857304i	$0.327862\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	15.0000	0.669483
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	0	0
$505$	0	0
$506$	9.00000	0.400099
$507$	−1.00000	−0.0444116
$508$	−7.00000	−0.310575
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	−10.0000	−0.441511
$514$	−24.0000	−1.05859
$515$	0	0
$516$	−8.00000	−0.352180
$517$	−9.00000	−0.395820
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	0	0
$523$	7.00000	0.306089	0.153044	−	0.988219i	$-0.451092\pi$
$523$	7.00000	0.306089	0.153044	+	0.988219i	$0.451092\pi$
$524$	0	0
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	3.00000	0.130558
$529$	−14.0000	−0.608696
$530$	0	0
$531$	12.0000	0.520756
$532$	0	0
$533$	3.00000	0.129944
$534$	−18.0000	−0.778936
$535$	0	0
$536$	5.00000	0.215967
$537$	6.00000	0.258919
$538$	9.00000	0.388018
$539$	0	0
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	−11.0000	−0.472490
$543$	−7.00000	−0.300399
$544$	0	0
$545$	0	0
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−6.00000	−0.256307
$549$	−2.00000	−0.0853579
$550$	15.0000	0.639602
$551$	0	0
$552$	3.00000	0.127688
$553$	0	0
$554$	26.0000	1.10463
$555$	0	0
$556$	4.00000	0.169638
$557$	−15.0000	−0.635570	−0.317785	−	0.948163i	$-0.602939\pi$
$557$	−15.0000	−0.635570	−0.317785	+	0.948163i	$0.602939\pi$
$558$	10.0000	0.423334
$559$	−8.00000	−0.338364
$560$	0	0
$561$	0	0
$562$	12.0000	0.506189
$563$	39.0000	1.64365	0.821827	−	0.569737i	$-0.192955\pi$
$563$	39.0000	1.64365	0.821827	+	0.569737i	$0.192955\pi$
$564$	−3.00000	−0.126323
$565$	0	0
$566$	31.0000	1.30303
$567$	0	0
$568$	12.0000	0.503509
$569$	21.0000	0.880366	0.440183	−	0.897908i	$-0.354914\pi$
$569$	21.0000	0.880366	0.440183	+	0.897908i	$0.354914\pi$
$570$	0	0
$571$	−22.0000	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$572$	3.00000	0.125436
$573$	0	0
$574$	0	0
$575$	15.0000	0.625543
$576$	−2.00000	−0.0833333
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−17.0000	−0.707107
$579$	4.00000	0.166234
$580$	0	0
$581$	0	0
$582$	17.0000	0.704673
$583$	36.0000	1.49097
$584$	−11.0000	−0.455183
$585$	0	0
$586$	−18.0000	−0.743573
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	0	0
$589$	10.0000	0.412043
$590$	0	0
$591$	3.00000	0.123404
$592$	−7.00000	−0.287698
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	−15.0000	−0.615457
$595$	0	0
$596$	−15.0000	−0.614424
$597$	−16.0000	−0.654836
$598$	3.00000	0.122679
$599$	39.0000	1.59350	0.796748	−	0.604311i	$-0.206552\pi$
$599$	39.0000	1.59350	0.796748	+	0.604311i	$0.206552\pi$
$600$	5.00000	0.204124
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	−10.0000	−0.407231
$604$	8.00000	0.325515
$605$	0	0
$606$	−3.00000	−0.121867
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	0	0
$611$	−3.00000	−0.121367
$612$	0	0
$613$	−25.0000	−1.00974	−0.504870	−	0.863195i	$-0.668460\pi$
$613$	−25.0000	−1.00974	−0.504870	+	0.863195i	$0.668460\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	0	0
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	14.0000	0.563163
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	0	0
$621$	−15.0000	−0.601929
$622$	−30.0000	−1.20289
$623$	0	0
$624$	1.00000	0.0400320
$625$	25.0000	1.00000
$626$	−26.0000	−1.03917
$627$	−6.00000	−0.239617
$628$	13.0000	0.518756
$629$	0	0
$630$	0	0
$631$	−34.0000	−1.35352	−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000	−1.35352	−0.676759	+	0.736204i	$0.736616\pi$
$632$	−1.00000	−0.0397779
$633$	22.0000	0.874421
$634$	−3.00000	−0.119145
$635$	0	0
$636$	12.0000	0.475831
$637$	0	0
$638$	0	0
$639$	−24.0000	−0.949425
$640$	0	0
$641$	−33.0000	−1.30342	−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000	−1.30342	−0.651711	+	0.758468i	$0.725948\pi$
$642$	0	0
$643$	−32.0000	−1.26196	−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000	−1.26196	−0.630978	+	0.775800i	$0.717346\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	1.00000	0.0392837
$649$	18.0000	0.706562
$650$	5.00000	0.196116
$651$	0	0
$652$	20.0000	0.783260
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	−2.00000	−0.0782062
$655$	0	0
$656$	−3.00000	−0.117130
$657$	22.0000	0.858302
$658$	0	0
$659$	42.0000	1.63609	0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000	1.63609	0.818044	+	0.575156i	$0.195059\pi$
$660$	0	0
$661$	−32.0000	−1.24466	−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000	−1.24466	−0.622328	+	0.782757i	$0.713813\pi$
$662$	−19.0000	−0.738456
$663$	0	0
$664$	−12.0000	−0.465690
$665$	0	0
$666$	14.0000	0.542489
$667$	0	0
$668$	24.0000	0.928588
$669$	−1.00000	−0.0386622
$670$	0	0
$671$	−3.00000	−0.115814
$672$	0	0
$673$	−1.00000	−0.0385472	−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000	−0.0385472	−0.0192736	+	0.999814i	$0.506135\pi$
$674$	−31.0000	−1.19408
$675$	−25.0000	−0.962250
$676$	1.00000	0.0384615
$677$	39.0000	1.49889	0.749446	−	0.662066i	$-0.230320\pi$
$677$	39.0000	1.49889	0.749446	+	0.662066i	$0.230320\pi$
$678$	−9.00000	−0.345643
$679$	0	0
$680$	0	0
$681$	−24.0000	−0.919682
$682$	15.0000	0.574380
$683$	−27.0000	−1.03313	−0.516563	−	0.856249i	$-0.672789\pi$
$683$	−27.0000	−1.03313	−0.516563	+	0.856249i	$0.672789\pi$
$684$	4.00000	0.152944
$685$	0	0
$686$	0	0
$687$	−4.00000	−0.152610
$688$	8.00000	0.304997
$689$	12.0000	0.457164
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	24.0000	0.911028
$695$	0	0
$696$	0	0
$697$	0	0
$698$	10.0000	0.378506
$699$	−3.00000	−0.113470
$700$	0	0
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	−5.00000	−0.188713
$703$	14.0000	0.528020
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−15.0000	−0.564532
$707$	0	0
$708$	6.00000	0.225494
$709$	35.0000	1.31445	0.657226	−	0.753693i	$-0.271730\pi$
$709$	35.0000	1.31445	0.657226	+	0.753693i	$0.271730\pi$
$710$	0	0
$711$	2.00000	0.0750059
$712$	18.0000	0.674579
$713$	15.0000	0.561754
$714$	0	0
$715$	0	0
$716$	−6.00000	−0.224231
$717$	−6.00000	−0.224074
$718$	−24.0000	−0.895672
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	0	0
$722$	−15.0000	−0.558242
$723$	26.0000	0.966950
$724$	7.00000	0.260153
$725$	0	0
$726$	2.00000	0.0742270
$727$	−26.0000	−0.964287	−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000	−0.964287	−0.482143	+	0.876092i	$0.660142\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	−1.00000	−0.0369611
$733$	4.00000	0.147743	0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000	0.147743	0.0738717	+	0.997268i	$0.476464\pi$
$734$	28.0000	1.03350
$735$	0	0
$736$	−3.00000	−0.110581
$737$	−15.0000	−0.552532
$738$	6.00000	0.220863
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	0	0
$741$	−2.00000	−0.0734718
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	5.00000	0.183309
$745$	0	0
$746$	−4.00000	−0.146450
$747$	24.0000	0.878114
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	3.00000	0.109399
$753$	−15.0000	−0.546630
$754$	0	0
$755$	0	0
$756$	0	0
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	−16.0000	−0.581146
$759$	−9.00000	−0.326679
$760$	0	0
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	7.00000	0.253583
$763$	0	0
$764$	0	0
$765$	0	0
$766$	−3.00000	−0.108394
$767$	6.00000	0.216647
$768$	−1.00000	−0.0360844
$769$	13.0000	0.468792	0.234396	−	0.972141i	$-0.424689\pi$
$769$	13.0000	0.468792	0.234396	+	0.972141i	$0.424689\pi$
$770$	0	0
$771$	24.0000	0.864339
$772$	−4.00000	−0.143963
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	−16.0000	−0.575108
$775$	25.0000	0.898027
$776$	−17.0000	−0.610264
$777$	0	0
$778$	−36.0000	−1.29066
$779$	6.00000	0.214972
$780$	0	0
$781$	−36.0000	−1.28818
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	−3.00000	−0.106871
$789$	−24.0000	−0.854423
$790$	0	0
$791$	0	0
$792$	6.00000	0.213201
$793$	−1.00000	−0.0355110
$794$	−20.0000	−0.709773
$795$	0	0
$796$	16.0000	0.567105
$797$	−9.00000	−0.318796	−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000	−0.318796	−0.159398	+	0.987214i	$0.550955\pi$
$798$	0	0
$799$	0	0
$800$	−5.00000	−0.176777
$801$	−36.0000	−1.27200
$802$	24.0000	0.847469
$803$	33.0000	1.16454
$804$	−5.00000	−0.176336
$805$	0	0
$806$	5.00000	0.176117
$807$	−9.00000	−0.316815
$808$	3.00000	0.105540
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	11.0000	0.385787
$814$	21.0000	0.736050
$815$	0	0
$816$	0	0
$817$	−16.0000	−0.559769
$818$	22.0000	0.769212
$819$	0	0
$820$	0	0
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	6.00000	0.209274
$823$	41.0000	1.42917	0.714585	−	0.699549i	$-0.246616\pi$
$823$	41.0000	1.42917	0.714585	+	0.699549i	$0.246616\pi$
$824$	−14.0000	−0.487713
$825$	−15.0000	−0.522233
$826$	0	0
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	6.00000	0.208514
$829$	−38.0000	−1.31979	−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000	−1.31979	−0.659897	+	0.751356i	$0.729400\pi$
$830$	0	0
$831$	−26.0000	−0.901930
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	−4.00000	−0.138509
$835$	0	0
$836$	6.00000	0.207514
$837$	−25.0000	−0.864126
$838$	−21.0000	−0.725433
$839$	21.0000	0.725001	0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000	0.725001	0.362500	+	0.931984i	$0.381923\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−37.0000	−1.27510
$843$	−12.0000	−0.413302
$844$	−22.0000	−0.757271
$845$	0	0
$846$	−6.00000	−0.206284
$847$	0	0
$848$	−12.0000	−0.412082
$849$	−31.0000	−1.06392
$850$	0	0
$851$	21.0000	0.719871
$852$	−12.0000	−0.411113
$853$	−44.0000	−1.50653	−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000	−1.50653	−0.753266	+	0.657716i	$0.771523\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−54.0000	−1.84460	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000	−1.84460	−0.922302	+	0.386469i	$0.873695\pi$
$858$	−3.00000	−0.102418
$859$	−23.0000	−0.784750	−0.392375	−	0.919805i	$-0.628346\pi$
$859$	−23.0000	−0.784750	−0.392375	+	0.919805i	$0.628346\pi$
$860$	0	0
$861$	0	0
$862$	−6.00000	−0.204361
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	5.00000	0.170103
$865$	0	0
$866$	−38.0000	−1.29129
$867$	17.0000	0.577350
$868$	0	0
$869$	3.00000	0.101768
$870$	0	0
$871$	−5.00000	−0.169419
$872$	2.00000	0.0677285
$873$	34.0000	1.15073
$874$	6.00000	0.202953
$875$	0	0
$876$	11.0000	0.371656
$877$	−13.0000	−0.438979	−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000	−0.438979	−0.219489	+	0.975615i	$0.570439\pi$
$878$	−26.0000	−0.877457
$879$	18.0000	0.607125
$880$	0	0
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	0	0
$885$	0	0
$886$	24.0000	0.806296
$887$	−42.0000	−1.41022	−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000	−1.41022	−0.705111	+	0.709097i	$0.749103\pi$
$888$	7.00000	0.234905
$889$	0	0
$890$	0	0
$891$	−3.00000	−0.100504
$892$	1.00000	0.0334825
$893$	−6.00000	−0.200782
$894$	15.0000	0.501675
$895$	0	0
$896$	0	0
$897$	−3.00000	−0.100167
$898$	−6.00000	−0.200223
$899$	0	0
$900$	10.0000	0.333333
$901$	0	0
$902$	9.00000	0.299667
$903$	0	0
$904$	9.00000	0.299336
$905$	0	0
$906$	−8.00000	−0.265782
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	24.0000	0.796468
$909$	−6.00000	−0.199007
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	2.00000	0.0662266
$913$	36.0000	1.19143
$914$	26.0000	0.860004
$915$	0	0
$916$	4.00000	0.132164
$917$	0	0
$918$	0	0
$919$	−25.0000	−0.824674	−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000	−0.824674	−0.412337	+	0.911031i	$0.635287\pi$
$920$	0	0
$921$	−16.0000	−0.527218
$922$	−24.0000	−0.790398
$923$	−12.0000	−0.394985
$924$	0	0
$925$	35.0000	1.15079
$926$	−40.0000	−1.31448
$927$	28.0000	0.919641
$928$	0	0
$929$	9.00000	0.295280	0.147640	−	0.989041i	$-0.452832\pi$
$929$	9.00000	0.295280	0.147640	+	0.989041i	$0.452832\pi$
$930$	0	0
$931$	0	0
$932$	3.00000	0.0982683
$933$	30.0000	0.982156
$934$	−12.0000	−0.392652
$935$	0	0
$936$	2.00000	0.0653720
$937$	52.0000	1.69877	0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000	1.69877	0.849383	+	0.527777i	$0.176974\pi$
$938$	0	0
$939$	26.0000	0.848478
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	−13.0000	−0.423563
$943$	9.00000	0.293080
$944$	−6.00000	−0.195283
$945$	0	0
$946$	−24.0000	−0.780307
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	1.00000	0.0324785
$949$	11.0000	0.357075
$950$	10.0000	0.324443
$951$	3.00000	0.0972817
$952$	0	0
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	24.0000	0.777029
$955$	0	0
$956$	6.00000	0.194054
$957$	0	0
$958$	−24.0000	−0.775405
$959$	0	0
$960$	0	0
$961$	−6.00000	−0.193548
$962$	7.00000	0.225689
$963$	0	0
$964$	−26.0000	−0.837404
$965$	0	0
$966$	0	0
$967$	−22.0000	−0.707472	−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000	−0.707472	−0.353736	+	0.935345i	$0.615089\pi$
$968$	−2.00000	−0.0642824
$969$	0	0
$970$	0	0
$971$	21.0000	0.673922	0.336961	−	0.941519i	$-0.390601\pi$
$971$	21.0000	0.673922	0.336961	+	0.941519i	$0.390601\pi$
$972$	−16.0000	−0.513200
$973$	0	0
$974$	2.00000	0.0640841
$975$	−5.00000	−0.160128
$976$	1.00000	0.0320092
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−20.0000	−0.639529
$979$	−54.0000	−1.72585
$980$	0	0
$981$	−4.00000	−0.127710
$982$	12.0000	0.382935
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	3.00000	0.0956365
$985$	0	0
$986$	0	0
$987$	0	0
$988$	2.00000	0.0636285
$989$	−24.0000	−0.763156
$990$	0	0
$991$	11.0000	0.349427	0.174713	−	0.984619i	$-0.444100\pi$
$991$	11.0000	0.349427	0.174713	+	0.984619i	$0.444100\pi$
$992$	−5.00000	−0.158750
$993$	19.0000	0.602947
$994$	0	0
$995$	0	0
$996$	12.0000	0.380235
$997$	37.0000	1.17180	0.585901	−	0.810383i	$-0.300741\pi$
$997$	37.0000	1.17180	0.585901	+	0.810383i	$0.300741\pi$
$998$	23.0000	0.728052
$999$	−35.0000	−1.10735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.a.j.1.1		1
7.2	even	3		1274.2.f.i.1145.1		2
7.3	odd	6		1274.2.f.d.79.1		2
7.4	even	3		1274.2.f.i.79.1		2
7.5	odd	6		1274.2.f.d.1145.1		2
7.6	odd	2		182.2.a.d.1.1	✓	1
21.20	even	2		1638.2.a.f.1.1		1
28.27	even	2		1456.2.a.d.1.1		1
35.34	odd	2		4550.2.a.c.1.1		1
56.13	odd	2		5824.2.a.k.1.1		1
56.27	even	2		5824.2.a.x.1.1		1
91.34	even	4		2366.2.d.e.337.2		2
91.83	even	4		2366.2.d.e.337.1		2
91.90	odd	2		2366.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.d.1.1	✓	1	7.6	odd	2
1274.2.a.j.1.1		1	1.1	even	1	trivial
1274.2.f.d.79.1		2	7.3	odd	6
1274.2.f.d.1145.1		2	7.5	odd	6
1274.2.f.i.79.1		2	7.4	even	3
1274.2.f.i.1145.1		2	7.2	even	3
1456.2.a.d.1.1		1	28.27	even	2
1638.2.a.f.1.1		1	21.20	even	2
2366.2.a.e.1.1		1	91.90	odd	2
2366.2.d.e.337.1		2	91.83	even	4
2366.2.d.e.337.2		2	91.34	even	4
4550.2.a.c.1.1		1	35.34	odd	2
5824.2.a.k.1.1		1	56.13	odd	2
5824.2.a.x.1.1		1	56.27	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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