LMFDB - Embedded newform 1264.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1264,2,Mod(1,1264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1264, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1264.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1264 = 2^{4} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1264.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:	$10.0930908155$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 316)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1264.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} +1.00000 q^{5} -3.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} +1.00000 q^{5} -3.00000 q^{7} -2.00000 q^{9} -2.00000 q^{11} -1.00000 q^{13} +1.00000 q^{15} +4.00000 q^{17} -6.00000 q^{19} -3.00000 q^{21} -6.00000 q^{23} -4.00000 q^{25} -5.00000 q^{27} +8.00000 q^{29} +4.00000 q^{31} -2.00000 q^{33} -3.00000 q^{35} -8.00000 q^{37} -1.00000 q^{39} -10.0000 q^{41} -4.00000 q^{43} -2.00000 q^{45} +9.00000 q^{47} +2.00000 q^{49} +4.00000 q^{51} -2.00000 q^{53} -2.00000 q^{55} -6.00000 q^{57} -5.00000 q^{59} -6.00000 q^{61} +6.00000 q^{63} -1.00000 q^{65} +10.0000 q^{67} -6.00000 q^{69} +1.00000 q^{71} +6.00000 q^{73} -4.00000 q^{75} +6.00000 q^{77} +1.00000 q^{79} +1.00000 q^{81} +4.00000 q^{85} +8.00000 q^{87} +9.00000 q^{89} +3.00000 q^{91} +4.00000 q^{93} -6.00000 q^{95} -11.0000 q^{97} +4.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	0	0
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	0	0
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	0	0
$23$	−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
$25$	−4.00000	−0.800000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	0	0
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	0	0
$33$	−2.00000	−0.348155
$34$	0	0
$35$	−3.00000	−0.507093
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	0	0
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	4.00000	0.560112
$52$	0	0
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	−6.00000	−0.794719
$58$	0	0
$59$	−5.00000	−0.650945	−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000	−0.650945	−0.325472	+	0.945552i	$0.605523\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	0	0
$63$	6.00000	0.755929
$64$	0	0
$65$	−1.00000	−0.124035
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	0	0
$69$	−6.00000	−0.722315
$70$	0	0
$71$	1.00000	0.118678	0.0593391	−	0.998238i	$-0.481101\pi$
$71$	1.00000	0.118678	0.0593391	+	0.998238i	$0.481101\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	0	0
$77$	6.00000	0.683763
$78$	0	0
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	0	0
$87$	8.00000	0.857690
$88$	0	0
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	3.00000	0.314485
$92$	0	0
$93$	4.00000	0.414781
$94$	0	0
$95$	−6.00000	−0.615587
$96$	0	0
$97$	−11.0000	−1.11688	−0.558440	−	0.829545i	$-0.688600\pi$
$97$	−11.0000	−1.11688	−0.558440	+	0.829545i	$0.688600\pi$
$98$	0	0
$99$	4.00000	0.402015
$100$	0	0
$101$	7.00000	0.696526	0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000	0.696526	0.348263	+	0.937397i	$0.386772\pi$
$102$	0	0
$103$	17.0000	1.67506	0.837530	−	0.546392i	$-0.183999\pi$
$103$	17.0000	1.67506	0.837530	+	0.546392i	$0.183999\pi$
$104$	0	0
$105$	−3.00000	−0.292770
$106$	0	0
$107$	−1.00000	−0.0966736	−0.0483368	−	0.998831i	$-0.515392\pi$
$107$	−1.00000	−0.0966736	−0.0483368	+	0.998831i	$0.515392\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	0	0
$113$	−8.00000	−0.752577	−0.376288	−	0.926503i	$-0.622800\pi$
$113$	−8.00000	−0.752577	−0.376288	+	0.926503i	$0.622800\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	−12.0000	−1.10004
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	−10.0000	−0.901670
$124$	0	0
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−17.0000	−1.50851	−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000	−1.50851	−0.754253	+	0.656584i	$0.772001\pi$
$128$	0	0
$129$	−4.00000	−0.352180
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	0	0
$133$	18.0000	1.56080
$134$	0	0
$135$	−5.00000	−0.430331
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−7.00000	−0.593732	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000	−0.593732	−0.296866	+	0.954919i	$0.595942\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	0	0
$143$	2.00000	0.167248
$144$	0	0
$145$	8.00000	0.664364
$146$	0	0
$147$	2.00000	0.164957
$148$	0	0
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	0	0
$153$	−8.00000	−0.646762
$154$	0	0
$155$	4.00000	0.321288
$156$	0	0
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	0	0
$159$	−2.00000	−0.158610
$160$	0	0
$161$	18.0000	1.41860
$162$	0	0
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	0	0
$165$	−2.00000	−0.155700
$166$	0	0
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	12.0000	0.917663
$172$	0	0
$173$	16.0000	1.21646	0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000	1.21646	0.608229	+	0.793762i	$0.291880\pi$
$174$	0	0
$175$	12.0000	0.907115
$176$	0	0
$177$	−5.00000	−0.375823
$178$	0	0
$179$	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
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	0	0
$185$	−8.00000	−0.588172
$186$	0	0
$187$	−8.00000	−0.585018
$188$	0	0
$189$	15.0000	1.09109
$190$	0	0
$191$	−21.0000	−1.51951	−0.759753	−	0.650211i	$-0.774680\pi$
$191$	−21.0000	−1.51951	−0.759753	+	0.650211i	$0.774680\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	0	0
$201$	10.0000	0.705346
$202$	0	0
$203$	−24.0000	−1.68447
$204$	0	0
$205$	−10.0000	−0.698430
$206$	0	0
$207$	12.0000	0.834058
$208$	0	0
$209$	12.0000	0.830057
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	0	0
$213$	1.00000	0.0685189
$214$	0	0
$215$	−4.00000	−0.272798
$216$	0	0
$217$	−12.0000	−0.814613
$218$	0	0
$219$	6.00000	0.405442
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	0	0
$225$	8.00000	0.533333
$226$	0	0
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	9.00000	0.587095
$236$	0	0
$237$	1.00000	0.0649570
$238$	0	0
$239$	−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
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	0	0
$245$	2.00000	0.127775
$246$	0	0
$247$	6.00000	0.381771
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−15.0000	−0.946792	−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000	−0.946792	−0.473396	+	0.880850i	$0.656972\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	0	0
$255$	4.00000	0.250490
$256$	0	0
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	24.0000	1.49129
$260$	0	0
$261$	−16.0000	−0.990375
$262$	0	0
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	0	0
$265$	−2.00000	−0.122859
$266$	0	0
$267$	9.00000	0.550791
$268$	0	0
$269$	−23.0000	−1.40233	−0.701167	−	0.712997i	$-0.747337\pi$
$269$	−23.0000	−1.40233	−0.701167	+	0.712997i	$0.747337\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	0	0
$273$	3.00000	0.181568
$274$	0	0
$275$	8.00000	0.482418
$276$	0	0
$277$	−29.0000	−1.74244	−0.871221	−	0.490892i	$-0.836671\pi$
$277$	−29.0000	−1.74244	−0.871221	+	0.490892i	$0.836671\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	0	0
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	0	0
$285$	−6.00000	−0.355409
$286$	0	0
$287$	30.0000	1.77084
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−11.0000	−0.644831
$292$	0	0
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	−5.00000	−0.291111
$296$	0	0
$297$	10.0000	0.580259
$298$	0	0
$299$	6.00000	0.346989
$300$	0	0
$301$	12.0000	0.691669
$302$	0	0
$303$	7.00000	0.402139
$304$	0	0
$305$	−6.00000	−0.343559
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	17.0000	0.967096
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	0	0
$315$	6.00000	0.338062
$316$	0	0
$317$	−21.0000	−1.17948	−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000	−1.17948	−0.589739	+	0.807594i	$0.700769\pi$
$318$	0	0
$319$	−16.0000	−0.895828
$320$	0	0
$321$	−1.00000	−0.0558146
$322$	0	0
$323$	−24.0000	−1.33540
$324$	0	0
$325$	4.00000	0.221880
$326$	0	0
$327$	−2.00000	−0.110600
$328$	0	0
$329$	−27.0000	−1.48856
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	0	0
$333$	16.0000	0.876795
$334$	0	0
$335$	10.0000	0.546358
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	0	0
$339$	−8.00000	−0.434500
$340$	0	0
$341$	−8.00000	−0.433224
$342$	0	0
$343$	15.0000	0.809924
$344$	0	0
$345$	−6.00000	−0.323029
$346$	0	0
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	16.0000	0.856460	0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000	0.856460	0.428230	+	0.903670i	$0.359137\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	1.00000	0.0530745
$356$	0	0
$357$	−12.0000	−0.635107
$358$	0	0
$359$	−25.0000	−1.31945	−0.659725	−	0.751507i	$-0.729327\pi$
$359$	−25.0000	−1.31945	−0.659725	+	0.751507i	$0.729327\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	0	0
$363$	−7.00000	−0.367405
$364$	0	0
$365$	6.00000	0.314054
$366$	0	0
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	0	0
$369$	20.0000	1.04116
$370$	0	0
$371$	6.00000	0.311504
$372$	0	0
$373$	8.00000	0.414224	0.207112	−	0.978317i	$-0.433593\pi$
$373$	8.00000	0.414224	0.207112	+	0.978317i	$0.433593\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	0	0
$377$	−8.00000	−0.412021
$378$	0	0
$379$	−21.0000	−1.07870	−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000	−1.07870	−0.539349	+	0.842082i	$0.681330\pi$
$380$	0	0
$381$	−17.0000	−0.870936
$382$	0	0
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	6.00000	0.305788
$386$	0	0
$387$	8.00000	0.406663
$388$	0	0
$389$	7.00000	0.354914	0.177457	−	0.984129i	$-0.443213\pi$
$389$	7.00000	0.354914	0.177457	+	0.984129i	$0.443213\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	0	0
$393$	−6.00000	−0.302660
$394$	0	0
$395$	1.00000	0.0503155
$396$	0	0
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	0	0
$399$	18.0000	0.901127
$400$	0	0
$401$	−4.00000	−0.199750	−0.0998752	−	0.995000i	$-0.531844\pi$
$401$	−4.00000	−0.199750	−0.0998752	+	0.995000i	$0.531844\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	16.0000	0.793091
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	−18.0000	−0.887875
$412$	0	0
$413$	15.0000	0.738102
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−7.00000	−0.342791
$418$	0	0
$419$	−25.0000	−1.22133	−0.610665	−	0.791889i	$-0.709098\pi$
$419$	−25.0000	−1.22133	−0.610665	+	0.791889i	$0.709098\pi$
$420$	0	0
$421$	19.0000	0.926003	0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000	0.926003	0.463002	+	0.886357i	$0.346772\pi$
$422$	0	0
$423$	−18.0000	−0.875190
$424$	0	0
$425$	−16.0000	−0.776114
$426$	0	0
$427$	18.0000	0.871081
$428$	0	0
$429$	2.00000	0.0965609
$430$	0	0
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	0	0
$433$	25.0000	1.20142	0.600712	−	0.799466i	$-0.294884\pi$
$433$	25.0000	1.20142	0.600712	+	0.799466i	$0.294884\pi$
$434$	0	0
$435$	8.00000	0.383571
$436$	0	0
$437$	36.0000	1.72211
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	−4.00000	−0.190476
$442$	0	0
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	0	0
$445$	9.00000	0.426641
$446$	0	0
$447$	14.0000	0.662177
$448$	0	0
$449$	−40.0000	−1.88772	−0.943858	−	0.330350i	$-0.892833\pi$
$449$	−40.0000	−1.88772	−0.943858	+	0.330350i	$0.892833\pi$
$450$	0	0
$451$	20.0000	0.941763
$452$	0	0
$453$	10.0000	0.469841
$454$	0	0
$455$	3.00000	0.140642
$456$	0	0
$457$	35.0000	1.63723	0.818615	−	0.574342i	$-0.194742\pi$
$457$	35.0000	1.63723	0.818615	+	0.574342i	$0.194742\pi$
$458$	0	0
$459$	−20.0000	−0.933520
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−17.0000	−0.790057	−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000	−0.790057	−0.395029	+	0.918669i	$0.629265\pi$
$464$	0	0
$465$	4.00000	0.185496
$466$	0	0
$467$	−24.0000	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$468$	0	0
$469$	−30.0000	−1.38527
$470$	0	0
$471$	6.00000	0.276465
$472$	0	0
$473$	8.00000	0.367840
$474$	0	0
$475$	24.0000	1.10120
$476$	0	0
$477$	4.00000	0.183147
$478$	0	0
$479$	−28.0000	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$479$	−28.0000	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$480$	0	0
$481$	8.00000	0.364769
$482$	0	0
$483$	18.0000	0.819028
$484$	0	0
$485$	−11.0000	−0.499484
$486$	0	0
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	0	0
$489$	20.0000	0.904431
$490$	0	0
$491$	−9.00000	−0.406164	−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000	−0.406164	−0.203082	+	0.979162i	$0.565096\pi$
$492$	0	0
$493$	32.0000	1.44121
$494$	0	0
$495$	4.00000	0.179787
$496$	0	0
$497$	−3.00000	−0.134568
$498$	0	0
$499$	40.0000	1.79065	0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000	1.79065	0.895323	+	0.445418i	$0.146945\pi$
$500$	0	0
$501$	−10.0000	−0.446767
$502$	0	0
$503$	9.00000	0.401290	0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000	0.401290	0.200645	+	0.979664i	$0.435696\pi$
$504$	0	0
$505$	7.00000	0.311496
$506$	0	0
$507$	−12.0000	−0.532939
$508$	0	0
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	0	0
$513$	30.0000	1.32453
$514$	0	0
$515$	17.0000	0.749110
$516$	0	0
$517$	−18.0000	−0.791639
$518$	0	0
$519$	16.0000	0.702322
$520$	0	0
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	0	0
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	0	0
$525$	12.0000	0.523723
$526$	0	0
$527$	16.0000	0.696971
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	10.0000	0.433963
$532$	0	0
$533$	10.0000	0.433148
$534$	0	0
$535$	−1.00000	−0.0432338
$536$	0	0
$537$	10.0000	0.431532
$538$	0	0
$539$	−4.00000	−0.172292
$540$	0	0
$541$	−29.0000	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$541$	−29.0000	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$542$	0	0
$543$	6.00000	0.257485
$544$	0	0
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	−34.0000	−1.45374	−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000	−1.45374	−0.726868	+	0.686778i	$0.759025\pi$
$548$	0	0
$549$	12.0000	0.512148
$550$	0	0
$551$	−48.0000	−2.04487
$552$	0	0
$553$	−3.00000	−0.127573
$554$	0	0
$555$	−8.00000	−0.339581
$556$	0	0
$557$	−31.0000	−1.31351	−0.656756	−	0.754103i	$-0.728072\pi$
$557$	−31.0000	−1.31351	−0.656756	+	0.754103i	$0.728072\pi$
$558$	0	0
$559$	4.00000	0.169182
$560$	0	0
$561$	−8.00000	−0.337760
$562$	0	0
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	−8.00000	−0.336563
$566$	0	0
$567$	−3.00000	−0.125988
$568$	0	0
$569$	−42.0000	−1.76073	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000	−1.76073	−0.880366	+	0.474295i	$0.842703\pi$
$570$	0	0
$571$	38.0000	1.59025	0.795125	−	0.606445i	$-0.207405\pi$
$571$	38.0000	1.59025	0.795125	+	0.606445i	$0.207405\pi$
$572$	0	0
$573$	−21.0000	−0.877288
$574$	0	0
$575$	24.0000	1.00087
$576$	0	0
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	0	0
$579$	−16.0000	−0.664937
$580$	0	0
$581$	0	0
$582$	0	0
$583$	4.00000	0.165663
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	7.00000	0.288921	0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000	0.288921	0.144460	+	0.989511i	$0.453855\pi$
$588$	0	0
$589$	−24.0000	−0.988903
$590$	0	0
$591$	6.00000	0.246807
$592$	0	0
$593$	−9.00000	−0.369586	−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000	−0.369586	−0.184793	+	0.982777i	$0.559161\pi$
$594$	0	0
$595$	−12.0000	−0.491952
$596$	0	0
$597$	−15.0000	−0.613909
$598$	0	0
$599$	−10.0000	−0.408589	−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000	−0.408589	−0.204294	+	0.978909i	$0.565490\pi$
$600$	0	0
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	0	0
$603$	−20.0000	−0.814463
$604$	0	0
$605$	−7.00000	−0.284590
$606$	0	0
$607$	3.00000	0.121766	0.0608831	−	0.998145i	$-0.480608\pi$
$607$	3.00000	0.121766	0.0608831	+	0.998145i	$0.480608\pi$
$608$	0	0
$609$	−24.0000	−0.972529
$610$	0	0
$611$	−9.00000	−0.364101
$612$	0	0
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	0	0
$615$	−10.0000	−0.403239
$616$	0	0
$617$	33.0000	1.32853	0.664265	−	0.747497i	$-0.268745\pi$
$617$	33.0000	1.32853	0.664265	+	0.747497i	$0.268745\pi$
$618$	0	0
$619$	−37.0000	−1.48716	−0.743578	−	0.668649i	$-0.766873\pi$
$619$	−37.0000	−1.48716	−0.743578	+	0.668649i	$0.766873\pi$
$620$	0	0
$621$	30.0000	1.20386
$622$	0	0
$623$	−27.0000	−1.08173
$624$	0	0
$625$	11.0000	0.440000
$626$	0	0
$627$	12.0000	0.479234
$628$	0	0
$629$	−32.0000	−1.27592
$630$	0	0
$631$	−13.0000	−0.517522	−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000	−0.517522	−0.258761	+	0.965941i	$0.583314\pi$
$632$	0	0
$633$	4.00000	0.158986
$634$	0	0
$635$	−17.0000	−0.674624
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	−2.00000	−0.0791188
$640$	0	0
$641$	−45.0000	−1.77739	−0.888697	−	0.458496i	$-0.848388\pi$
$641$	−45.0000	−1.77739	−0.888697	+	0.458496i	$0.848388\pi$
$642$	0	0
$643$	44.0000	1.73519	0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000	1.73519	0.867595	+	0.497271i	$0.165665\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	0	0
$647$	−16.0000	−0.629025	−0.314512	−	0.949253i	$-0.601841\pi$
$647$	−16.0000	−0.629025	−0.314512	+	0.949253i	$0.601841\pi$
$648$	0	0
$649$	10.0000	0.392534
$650$	0	0
$651$	−12.0000	−0.470317
$652$	0	0
$653$	−23.0000	−0.900060	−0.450030	−	0.893014i	$-0.648587\pi$
$653$	−23.0000	−0.900060	−0.450030	+	0.893014i	$0.648587\pi$
$654$	0	0
$655$	−6.00000	−0.234439
$656$	0	0
$657$	−12.0000	−0.468165
$658$	0	0
$659$	45.0000	1.75295	0.876476	−	0.481446i	$-0.159888\pi$
$659$	45.0000	1.75295	0.876476	+	0.481446i	$0.159888\pi$
$660$	0	0
$661$	−46.0000	−1.78919	−0.894596	−	0.446875i	$-0.852537\pi$
$661$	−46.0000	−1.78919	−0.894596	+	0.446875i	$0.852537\pi$
$662$	0	0
$663$	−4.00000	−0.155347
$664$	0	0
$665$	18.0000	0.698010
$666$	0	0
$667$	−48.0000	−1.85857
$668$	0	0
$669$	4.00000	0.154649
$670$	0	0
$671$	12.0000	0.463255
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	0	0
$675$	20.0000	0.769800
$676$	0	0
$677$	33.0000	1.26829	0.634147	−	0.773213i	$-0.281352\pi$
$677$	33.0000	1.26829	0.634147	+	0.773213i	$0.281352\pi$
$678$	0	0
$679$	33.0000	1.26642
$680$	0	0
$681$	4.00000	0.153280
$682$	0	0
$683$	14.0000	0.535695	0.267848	−	0.963461i	$-0.413688\pi$
$683$	14.0000	0.535695	0.267848	+	0.963461i	$0.413688\pi$
$684$	0	0
$685$	−18.0000	−0.687745
$686$	0	0
$687$	26.0000	0.991962
$688$	0	0
$689$	2.00000	0.0761939
$690$	0	0
$691$	−5.00000	−0.190209	−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000	−0.190209	−0.0951045	+	0.995467i	$0.530319\pi$
$692$	0	0
$693$	−12.0000	−0.455842
$694$	0	0
$695$	−7.00000	−0.265525
$696$	0	0
$697$	−40.0000	−1.51511
$698$	0	0
$699$	−6.00000	−0.226941
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	48.0000	1.81035
$704$	0	0
$705$	9.00000	0.338960
$706$	0	0
$707$	−21.0000	−0.789786
$708$	0	0
$709$	40.0000	1.50223	0.751116	−	0.660171i	$-0.229516\pi$
$709$	40.0000	1.50223	0.751116	+	0.660171i	$0.229516\pi$
$710$	0	0
$711$	−2.00000	−0.0750059
$712$	0	0
$713$	−24.0000	−0.898807
$714$	0	0
$715$	2.00000	0.0747958
$716$	0	0
$717$	−6.00000	−0.224074
$718$	0	0
$719$	−30.0000	−1.11881	−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000	−1.11881	−0.559406	+	0.828894i	$0.688971\pi$
$720$	0	0
$721$	−51.0000	−1.89934
$722$	0	0
$723$	17.0000	0.632237
$724$	0	0
$725$	−32.0000	−1.18845
$726$	0	0
$727$	−30.0000	−1.11264	−0.556319	−	0.830969i	$-0.687787\pi$
$727$	−30.0000	−1.11264	−0.556319	+	0.830969i	$0.687787\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−16.0000	−0.591781
$732$	0	0
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	0	0
$735$	2.00000	0.0737711
$736$	0	0
$737$	−20.0000	−0.736709
$738$	0	0
$739$	−43.0000	−1.58178	−0.790890	−	0.611958i	$-0.790382\pi$
$739$	−43.0000	−1.58178	−0.790890	+	0.611958i	$0.790382\pi$
$740$	0	0
$741$	6.00000	0.220416
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	14.0000	0.512920
$746$	0	0
$747$	0	0
$748$	0	0
$749$	3.00000	0.109618
$750$	0	0
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	0	0
$753$	−15.0000	−0.546630
$754$	0	0
$755$	10.0000	0.363937
$756$	0	0
$757$	−49.0000	−1.78094	−0.890468	−	0.455047i	$-0.849623\pi$
$757$	−49.0000	−1.78094	−0.890468	+	0.455047i	$0.849623\pi$
$758$	0	0
$759$	12.0000	0.435572
$760$	0	0
$761$	−50.0000	−1.81250	−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000	−1.81250	−0.906249	+	0.422744i	$0.861067\pi$
$762$	0	0
$763$	6.00000	0.217215
$764$	0	0
$765$	−8.00000	−0.289241
$766$	0	0
$767$	5.00000	0.180540
$768$	0	0
$769$	38.0000	1.37032	0.685158	−	0.728395i	$-0.259733\pi$
$769$	38.0000	1.37032	0.685158	+	0.728395i	$0.259733\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	0	0
$773$	−14.0000	−0.503545	−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000	−0.503545	−0.251773	+	0.967786i	$0.581013\pi$
$774$	0	0
$775$	−16.0000	−0.574737
$776$	0	0
$777$	24.0000	0.860995
$778$	0	0
$779$	60.0000	2.14972
$780$	0	0
$781$	−2.00000	−0.0715656
$782$	0	0
$783$	−40.0000	−1.42948
$784$	0	0
$785$	6.00000	0.214149
$786$	0	0
$787$	30.0000	1.06938	0.534692	−	0.845047i	$-0.320428\pi$
$787$	30.0000	1.06938	0.534692	+	0.845047i	$0.320428\pi$
$788$	0	0
$789$	18.0000	0.640817
$790$	0	0
$791$	24.0000	0.853342
$792$	0	0
$793$	6.00000	0.213066
$794$	0	0
$795$	−2.00000	−0.0709327
$796$	0	0
$797$	−6.00000	−0.212531	−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000	−0.212531	−0.106265	+	0.994338i	$0.533889\pi$
$798$	0	0
$799$	36.0000	1.27359
$800$	0	0
$801$	−18.0000	−0.635999
$802$	0	0
$803$	−12.0000	−0.423471
$804$	0	0
$805$	18.0000	0.634417
$806$	0	0
$807$	−23.0000	−0.809638
$808$	0	0
$809$	−33.0000	−1.16022	−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000	−1.16022	−0.580109	+	0.814539i	$0.696990\pi$
$810$	0	0
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	0	0
$815$	20.0000	0.700569
$816$	0	0
$817$	24.0000	0.839654
$818$	0	0
$819$	−6.00000	−0.209657
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	0	0
$825$	8.00000	0.278524
$826$	0	0
$827$	−23.0000	−0.799788	−0.399894	−	0.916561i	$-0.630953\pi$
$827$	−23.0000	−0.799788	−0.399894	+	0.916561i	$0.630953\pi$
$828$	0	0
$829$	−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
$831$	−29.0000	−1.00600
$832$	0	0
$833$	8.00000	0.277184
$834$	0	0
$835$	−10.0000	−0.346064
$836$	0	0
$837$	−20.0000	−0.691301
$838$	0	0
$839$	−44.0000	−1.51905	−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000	−1.51905	−0.759524	+	0.650479i	$0.774568\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	0	0
$843$	15.0000	0.516627
$844$	0	0
$845$	−12.0000	−0.412813
$846$	0	0
$847$	21.0000	0.721569
$848$	0	0
$849$	14.0000	0.480479
$850$	0	0
$851$	48.0000	1.64542
$852$	0	0
$853$	32.0000	1.09566	0.547830	−	0.836590i	$-0.315454\pi$
$853$	32.0000	1.09566	0.547830	+	0.836590i	$0.315454\pi$
$854$	0	0
$855$	12.0000	0.410391
$856$	0	0
$857$	45.0000	1.53717	0.768585	−	0.639747i	$-0.220961\pi$
$857$	45.0000	1.53717	0.768585	+	0.639747i	$0.220961\pi$
$858$	0	0
$859$	−13.0000	−0.443554	−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000	−0.443554	−0.221777	+	0.975097i	$0.571186\pi$
$860$	0	0
$861$	30.0000	1.02240
$862$	0	0
$863$	4.00000	0.136162	0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000	0.136162	0.0680808	+	0.997680i	$0.478312\pi$
$864$	0	0
$865$	16.0000	0.544016
$866$	0	0
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−2.00000	−0.0678454
$870$	0	0
$871$	−10.0000	−0.338837
$872$	0	0
$873$	22.0000	0.744587
$874$	0	0
$875$	27.0000	0.912767
$876$	0	0
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	0	0
$879$	24.0000	0.809500
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	0	0
$883$	−35.0000	−1.17784	−0.588922	−	0.808190i	$-0.700447\pi$
$883$	−35.0000	−1.17784	−0.588922	+	0.808190i	$0.700447\pi$
$884$	0	0
$885$	−5.00000	−0.168073
$886$	0	0
$887$	−2.00000	−0.0671534	−0.0335767	−	0.999436i	$-0.510690\pi$
$887$	−2.00000	−0.0671534	−0.0335767	+	0.999436i	$0.510690\pi$
$888$	0	0
$889$	51.0000	1.71049
$890$	0	0
$891$	−2.00000	−0.0670025
$892$	0	0
$893$	−54.0000	−1.80704
$894$	0	0
$895$	10.0000	0.334263
$896$	0	0
$897$	6.00000	0.200334
$898$	0	0
$899$	32.0000	1.06726
$900$	0	0
$901$	−8.00000	−0.266519
$902$	0	0
$903$	12.0000	0.399335
$904$	0	0
$905$	6.00000	0.199447
$906$	0	0
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	0	0
$909$	−14.0000	−0.464351
$910$	0	0
$911$	−18.0000	−0.596367	−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000	−0.596367	−0.298183	+	0.954509i	$0.596381\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−6.00000	−0.198354
$916$	0	0
$917$	18.0000	0.594412
$918$	0	0
$919$	6.00000	0.197922	0.0989609	−	0.995091i	$-0.468448\pi$
$919$	6.00000	0.197922	0.0989609	+	0.995091i	$0.468448\pi$
$920$	0	0
$921$	−12.0000	−0.395413
$922$	0	0
$923$	−1.00000	−0.0329154
$924$	0	0
$925$	32.0000	1.05215
$926$	0	0
$927$	−34.0000	−1.11671
$928$	0	0
$929$	60.0000	1.96854	0.984268	−	0.176682i	$-0.0565363\pi$
$929$	60.0000	1.96854	0.984268	+	0.176682i	$0.0565363\pi$
$930$	0	0
$931$	−12.0000	−0.393284
$932$	0	0
$933$	24.0000	0.785725
$934$	0	0
$935$	−8.00000	−0.261628
$936$	0	0
$937$	6.00000	0.196011	0.0980057	−	0.995186i	$-0.468754\pi$
$937$	6.00000	0.196011	0.0980057	+	0.995186i	$0.468754\pi$
$938$	0	0
$939$	14.0000	0.456873
$940$	0	0
$941$	46.0000	1.49956	0.749779	−	0.661689i	$-0.230160\pi$
$941$	46.0000	1.49956	0.749779	+	0.661689i	$0.230160\pi$
$942$	0	0
$943$	60.0000	1.95387
$944$	0	0
$945$	15.0000	0.487950
$946$	0	0
$947$	8.00000	0.259965	0.129983	−	0.991516i	$-0.458508\pi$
$947$	8.00000	0.259965	0.129983	+	0.991516i	$0.458508\pi$
$948$	0	0
$949$	−6.00000	−0.194768
$950$	0	0
$951$	−21.0000	−0.680972
$952$	0	0
$953$	17.0000	0.550684	0.275342	−	0.961346i	$-0.411209\pi$
$953$	17.0000	0.550684	0.275342	+	0.961346i	$0.411209\pi$
$954$	0	0
$955$	−21.0000	−0.679544
$956$	0	0
$957$	−16.0000	−0.517207
$958$	0	0
$959$	54.0000	1.74375
$960$	0	0
$961$	−15.0000	−0.483871
$962$	0	0
$963$	2.00000	0.0644491
$964$	0	0
$965$	−16.0000	−0.515058
$966$	0	0
$967$	22.0000	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$968$	0	0
$969$	−24.0000	−0.770991
$970$	0	0
$971$	−40.0000	−1.28366	−0.641831	−	0.766846i	$-0.721825\pi$
$971$	−40.0000	−1.28366	−0.641831	+	0.766846i	$0.721825\pi$
$972$	0	0
$973$	21.0000	0.673229
$974$	0	0
$975$	4.00000	0.128103
$976$	0	0
$977$	4.00000	0.127971	0.0639857	−	0.997951i	$-0.479619\pi$
$977$	4.00000	0.127971	0.0639857	+	0.997951i	$0.479619\pi$
$978$	0	0
$979$	−18.0000	−0.575282
$980$	0	0
$981$	4.00000	0.127710
$982$	0	0
$983$	48.0000	1.53096	0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000	1.53096	0.765481	+	0.643458i	$0.222501\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	0	0
$987$	−27.0000	−0.859419
$988$	0	0
$989$	24.0000	0.763156
$990$	0	0
$991$	−23.0000	−0.730619	−0.365310	−	0.930886i	$-0.619037\pi$
$991$	−23.0000	−0.730619	−0.365310	+	0.930886i	$0.619037\pi$
$992$	0	0
$993$	28.0000	0.888553
$994$	0	0
$995$	−15.0000	−0.475532
$996$	0	0
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	0	0
$999$	40.0000	1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1264.2.a.g.1.1		1
4.3	odd	2		316.2.a.b.1.1	✓	1
8.3	odd	2		5056.2.a.n.1.1		1
8.5	even	2		5056.2.a.f.1.1		1
12.11	even	2		2844.2.a.d.1.1		1
20.19	odd	2		7900.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
316.2.a.b.1.1	✓	1	4.3	odd	2
1264.2.a.g.1.1		1	1.1	even	1	trivial
2844.2.a.d.1.1		1	12.11	even	2
5056.2.a.f.1.1		1	8.5	even	2
5056.2.a.n.1.1		1	8.3	odd	2
7900.2.a.c.1.1		1	20.19	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:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.a (trivial)

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L-functions

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