LMFDB - Embedded newform 3640.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3640,2,Mod(1,3640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3640, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3640.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3640.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:	$29.0655463357$
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	$\chi$	$=$	3640.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{3} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} -3.00000 q^{11} -1.00000 q^{13} -1.00000 q^{15} -6.00000 q^{17} -6.00000 q^{19} +1.00000 q^{21} +5.00000 q^{23} +1.00000 q^{25} +5.00000 q^{27} -6.00000 q^{29} +7.00000 q^{31} +3.00000 q^{33} -1.00000 q^{35} -3.00000 q^{37} +1.00000 q^{39} +3.00000 q^{41} +2.00000 q^{43} -2.00000 q^{45} +13.0000 q^{47} +1.00000 q^{49} +6.00000 q^{51} +4.00000 q^{53} -3.00000 q^{55} +6.00000 q^{57} +5.00000 q^{61} +2.00000 q^{63} -1.00000 q^{65} +7.00000 q^{67} -5.00000 q^{69} -11.0000 q^{73} -1.00000 q^{75} +3.00000 q^{77} +17.0000 q^{79} +1.00000 q^{81} +2.00000 q^{83} -6.00000 q^{85} +6.00000 q^{87} +6.00000 q^{89} +1.00000 q^{91} -7.00000 q^{93} -6.00000 q^{95} -13.0000 q^{97} +6.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	−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	$0.649385\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	0	0
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	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
$21$	1.00000	0.218218
$22$	0	0
$23$	5.00000	1.04257	0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000	1.04257	0.521286	+	0.853382i	$0.325452\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	5.00000	0.962250
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	0	0
$33$	3.00000	0.522233
$34$	0	0
$35$	−1.00000	−0.169031
$36$	0	0
$37$	−3.00000	−0.493197	−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000	−0.493197	−0.246598	+	0.969118i	$0.579313\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	0	0
$47$	13.0000	1.89624	0.948122	−	0.317905i	$-0.102979\pi$
$47$	13.0000	1.89624	0.948122	+	0.317905i	$0.102979\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	6.00000	0.840168
$52$	0	0
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	−3.00000	−0.404520
$56$	0	0
$57$	6.00000	0.794719
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	0	0
$65$	−1.00000	−0.124035
$66$	0	0
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	0	0
$69$	−5.00000	−0.601929
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	0	0
$75$	−1.00000	−0.115470
$76$	0	0
$77$	3.00000	0.341882
$78$	0	0
$79$	17.0000	1.91265	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	17.0000	1.91265	0.956325	+	0.292306i	$0.0944227\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	0	0
$87$	6.00000	0.643268
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	0	0
$93$	−7.00000	−0.725866
$94$	0	0
$95$	−6.00000	−0.615587
$96$	0	0
$97$	−13.0000	−1.31995	−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000	−1.31995	−0.659975	+	0.751288i	$0.729433\pi$
$98$	0	0
$99$	6.00000	0.603023
$100$	0	0
$101$	15.0000	1.49256	0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000	1.49256	0.746278	+	0.665635i	$0.231839\pi$
$102$	0	0
$103$	2.00000	0.197066	0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000	0.197066	0.0985329	+	0.995134i	$0.468585\pi$
$104$	0	0
$105$	1.00000	0.0975900
$106$	0	0
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	0	0
$109$	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
$111$	3.00000	0.284747
$112$	0	0
$113$	−1.00000	−0.0940721	−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000	−0.0940721	−0.0470360	+	0.998893i	$0.514978\pi$
$114$	0	0
$115$	5.00000	0.466252
$116$	0	0
$117$	2.00000	0.184900
$118$	0	0
$119$	6.00000	0.550019
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	−3.00000	−0.270501
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−11.0000	−0.976092	−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000	−0.976092	−0.488046	+	0.872818i	$0.662290\pi$
$128$	0	0
$129$	−2.00000	−0.176090
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	0	0
$135$	5.00000	0.430331
$136$	0	0
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	−13.0000	−1.09480
$142$	0	0
$143$	3.00000	0.250873
$144$	0	0
$145$	−6.00000	−0.498273
$146$	0	0
$147$	−1.00000	−0.0824786
$148$	0	0
$149$	11.0000	0.901155	0.450578	−	0.892737i	$-0.351218\pi$
$149$	11.0000	0.901155	0.450578	+	0.892737i	$0.351218\pi$
$150$	0	0
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	0	0
$153$	12.0000	0.970143
$154$	0	0
$155$	7.00000	0.562254
$156$	0	0
$157$	−5.00000	−0.399043	−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000	−0.399043	−0.199522	+	0.979893i	$0.563939\pi$
$158$	0	0
$159$	−4.00000	−0.317221
$160$	0	0
$161$	−5.00000	−0.394055
$162$	0	0
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	0	0
$165$	3.00000	0.233550
$166$	0	0
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	12.0000	0.917663
$172$	0	0
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	0	0
$183$	−5.00000	−0.369611
$184$	0	0
$185$	−3.00000	−0.220564
$186$	0	0
$187$	18.0000	1.31629
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	0	0
$195$	1.00000	0.0716115
$196$	0	0
$197$	−3.00000	−0.213741	−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000	−0.213741	−0.106871	+	0.994273i	$0.534083\pi$
$198$	0	0
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	0	0
$203$	6.00000	0.421117
$204$	0	0
$205$	3.00000	0.209529
$206$	0	0
$207$	−10.0000	−0.695048
$208$	0	0
$209$	18.0000	1.24509
$210$	0	0
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	2.00000	0.136399
$216$	0	0
$217$	−7.00000	−0.475191
$218$	0	0
$219$	11.0000	0.743311
$220$	0	0
$221$	6.00000	0.403604
$222$	0	0
$223$	19.0000	1.27233	0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000	1.27233	0.636167	+	0.771551i	$0.280519\pi$
$224$	0	0
$225$	−2.00000	−0.133333
$226$	0	0
$227$	10.0000	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	0	0
$233$	21.0000	1.37576	0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000	1.37576	0.687878	+	0.725826i	$0.258542\pi$
$234$	0	0
$235$	13.0000	0.848026
$236$	0	0
$237$	−17.0000	−1.10427
$238$	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
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	0	0
$245$	1.00000	0.0638877
$246$	0	0
$247$	6.00000	0.381771
$248$	0	0
$249$	−2.00000	−0.126745
$250$	0	0
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	0	0
$253$	−15.0000	−0.943042
$254$	0	0
$255$	6.00000	0.375735
$256$	0	0
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	0	0
$259$	3.00000	0.186411
$260$	0	0
$261$	12.0000	0.742781
$262$	0	0
$263$	−20.0000	−1.23325	−0.616626	−	0.787256i	$-0.711501\pi$
$263$	−20.0000	−1.23325	−0.616626	+	0.787256i	$0.711501\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	0	0
$267$	−6.00000	−0.367194
$268$	0	0
$269$	−19.0000	−1.15845	−0.579225	−	0.815168i	$-0.696645\pi$
$269$	−19.0000	−1.15845	−0.579225	+	0.815168i	$0.696645\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	0	0
$273$	−1.00000	−0.0605228
$274$	0	0
$275$	−3.00000	−0.180907
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	0	0
$279$	−14.0000	−0.838158
$280$	0	0
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	0	0
$283$	−5.00000	−0.297219	−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000	−0.297219	−0.148610	+	0.988896i	$0.547480\pi$
$284$	0	0
$285$	6.00000	0.355409
$286$	0	0
$287$	−3.00000	−0.177084
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	13.0000	0.762073
$292$	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
$295$	0	0
$296$	0	0
$297$	−15.0000	−0.870388
$298$	0	0
$299$	−5.00000	−0.289157
$300$	0	0
$301$	−2.00000	−0.115278
$302$	0	0
$303$	−15.0000	−0.861727
$304$	0	0
$305$	5.00000	0.286299
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	−2.00000	−0.113776
$310$	0	0
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	0	0
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	0	0
$315$	2.00000	0.112687
$316$	0	0
$317$	−7.00000	−0.393159	−0.196580	−	0.980488i	$-0.562983\pi$
$317$	−7.00000	−0.393159	−0.196580	+	0.980488i	$0.562983\pi$
$318$	0	0
$319$	18.0000	1.00781
$320$	0	0
$321$	10.0000	0.558146
$322$	0	0
$323$	36.0000	2.00309
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	0	0
$327$	−10.0000	−0.553001
$328$	0	0
$329$	−13.0000	−0.716713
$330$	0	0
$331$	25.0000	1.37412	0.687062	−	0.726599i	$-0.258900\pi$
$331$	25.0000	1.37412	0.687062	+	0.726599i	$0.258900\pi$
$332$	0	0
$333$	6.00000	0.328798
$334$	0	0
$335$	7.00000	0.382451
$336$	0	0
$337$	27.0000	1.47078	0.735392	−	0.677642i	$-0.236998\pi$
$337$	27.0000	1.47078	0.735392	+	0.677642i	$0.236998\pi$
$338$	0	0
$339$	1.00000	0.0543125
$340$	0	0
$341$	−21.0000	−1.13721
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	−5.00000	−0.269191
$346$	0	0
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	−18.0000	−0.963518	−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000	−0.963518	−0.481759	+	0.876304i	$0.660002\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	0	0
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−6.00000	−0.317554
$358$	0	0
$359$	22.0000	1.16112	0.580558	−	0.814219i	$-0.302835\pi$
$359$	22.0000	1.16112	0.580558	+	0.814219i	$0.302835\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	0	0
$363$	2.00000	0.104973
$364$	0	0
$365$	−11.0000	−0.575766
$366$	0	0
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	−4.00000	−0.207670
$372$	0	0
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	11.0000	0.563547
$382$	0	0
$383$	−9.00000	−0.459879	−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000	−0.459879	−0.229939	+	0.973205i	$0.573853\pi$
$384$	0	0
$385$	3.00000	0.152894
$386$	0	0
$387$	−4.00000	−0.203331
$388$	0	0
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	0	0
$391$	−30.0000	−1.51717
$392$	0	0
$393$	12.0000	0.605320
$394$	0	0
$395$	17.0000	0.855363
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	−6.00000	−0.300376
$400$	0	0
$401$	16.0000	0.799002	0.399501	−	0.916733i	$-0.369183\pi$
$401$	16.0000	0.799002	0.399501	+	0.916733i	$0.369183\pi$
$402$	0	0
$403$	−7.00000	−0.348695
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	9.00000	0.446113
$408$	0	0
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	0	0
$411$	14.0000	0.690569
$412$	0	0
$413$	0	0
$414$	0	0
$415$	2.00000	0.0981761
$416$	0	0
$417$	4.00000	0.195881
$418$	0	0
$419$	5.00000	0.244266	0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000	0.244266	0.122133	+	0.992514i	$0.461027\pi$
$420$	0	0
$421$	−3.00000	−0.146211	−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000	−0.146211	−0.0731055	+	0.997324i	$0.523291\pi$
$422$	0	0
$423$	−26.0000	−1.26416
$424$	0	0
$425$	−6.00000	−0.291043
$426$	0	0
$427$	−5.00000	−0.241967
$428$	0	0
$429$	−3.00000	−0.144841
$430$	0	0
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	0	0
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	0	0
$437$	−30.0000	−1.43509
$438$	0	0
$439$	38.0000	1.81364	0.906821	−	0.421517i	$-0.138502\pi$
$439$	38.0000	1.81364	0.906821	+	0.421517i	$0.138502\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	0	0
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	0	0
$445$	6.00000	0.284427
$446$	0	0
$447$	−11.0000	−0.520282
$448$	0	0
$449$	8.00000	0.377543	0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000	0.377543	0.188772	+	0.982021i	$0.439549\pi$
$450$	0	0
$451$	−9.00000	−0.423793
$452$	0	0
$453$	2.00000	0.0939682
$454$	0	0
$455$	1.00000	0.0468807
$456$	0	0
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	0	0
$459$	−30.0000	−1.40028
$460$	0	0
$461$	36.0000	1.67669	0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000	1.67669	0.838344	+	0.545142i	$0.183524\pi$
$462$	0	0
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	0	0
$465$	−7.00000	−0.324617
$466$	0	0
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	−7.00000	−0.323230
$470$	0	0
$471$	5.00000	0.230388
$472$	0	0
$473$	−6.00000	−0.275880
$474$	0	0
$475$	−6.00000	−0.275299
$476$	0	0
$477$	−8.00000	−0.366295
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	3.00000	0.136788
$482$	0	0
$483$	5.00000	0.227508
$484$	0	0
$485$	−13.0000	−0.590300
$486$	0	0
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	0	0
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−4.00000	−0.180517	−0.0902587	−	0.995918i	$-0.528769\pi$
$491$	−4.00000	−0.180517	−0.0902587	+	0.995918i	$0.528769\pi$
$492$	0	0
$493$	36.0000	1.62136
$494$	0	0
$495$	6.00000	0.269680
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−29.0000	−1.29822	−0.649109	−	0.760695i	$-0.724858\pi$
$499$	−29.0000	−1.29822	−0.649109	+	0.760695i	$0.724858\pi$
$500$	0	0
$501$	−8.00000	−0.357414
$502$	0	0
$503$	−4.00000	−0.178351	−0.0891756	−	0.996016i	$-0.528423\pi$
$503$	−4.00000	−0.178351	−0.0891756	+	0.996016i	$0.528423\pi$
$504$	0	0
$505$	15.0000	0.667491
$506$	0	0
$507$	−1.00000	−0.0444116
$508$	0	0
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	0	0
$511$	11.0000	0.486611
$512$	0	0
$513$	−30.0000	−1.32453
$514$	0	0
$515$	2.00000	0.0881305
$516$	0	0
$517$	−39.0000	−1.71522
$518$	0	0
$519$	−14.0000	−0.614532
$520$	0	0
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	0	0
$523$	31.0000	1.35554	0.677768	−	0.735276i	$-0.262948\pi$
$523$	31.0000	1.35554	0.677768	+	0.735276i	$0.262948\pi$
$524$	0	0
$525$	1.00000	0.0436436
$526$	0	0
$527$	−42.0000	−1.82955
$528$	0	0
$529$	2.00000	0.0869565
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−3.00000	−0.129944
$534$	0	0
$535$	−10.0000	−0.432338
$536$	0	0
$537$	12.0000	0.517838
$538$	0	0
$539$	−3.00000	−0.129219
$540$	0	0
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	0	0
$543$	5.00000	0.214571
$544$	0	0
$545$	10.0000	0.428353
$546$	0	0
$547$	−24.0000	−1.02617	−0.513083	−	0.858339i	$-0.671497\pi$
$547$	−24.0000	−1.02617	−0.513083	+	0.858339i	$0.671497\pi$
$548$	0	0
$549$	−10.0000	−0.426790
$550$	0	0
$551$	36.0000	1.53365
$552$	0	0
$553$	−17.0000	−0.722914
$554$	0	0
$555$	3.00000	0.127343
$556$	0	0
$557$	−27.0000	−1.14403	−0.572013	−	0.820244i	$-0.693837\pi$
$557$	−27.0000	−1.14403	−0.572013	+	0.820244i	$0.693837\pi$
$558$	0	0
$559$	−2.00000	−0.0845910
$560$	0	0
$561$	−18.0000	−0.759961
$562$	0	0
$563$	−45.0000	−1.89652	−0.948262	−	0.317489i	$-0.897160\pi$
$563$	−45.0000	−1.89652	−0.948262	+	0.317489i	$0.897160\pi$
$564$	0	0
$565$	−1.00000	−0.0420703
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	9.00000	0.377300	0.188650	−	0.982044i	$-0.439589\pi$
$569$	9.00000	0.377300	0.188650	+	0.982044i	$0.439589\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	0	0
$573$	−24.0000	−1.00261
$574$	0	0
$575$	5.00000	0.208514
$576$	0	0
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	0	0
$579$	14.0000	0.581820
$580$	0	0
$581$	−2.00000	−0.0829740
$582$	0	0
$583$	−12.0000	−0.496989
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	26.0000	1.07313	0.536567	−	0.843857i	$-0.319721\pi$
$587$	26.0000	1.07313	0.536567	+	0.843857i	$0.319721\pi$
$588$	0	0
$589$	−42.0000	−1.73058
$590$	0	0
$591$	3.00000	0.123404
$592$	0	0
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	6.00000	0.245976
$596$	0	0
$597$	−10.0000	−0.409273
$598$	0	0
$599$	13.0000	0.531166	0.265583	−	0.964088i	$-0.414436\pi$
$599$	13.0000	0.531166	0.265583	+	0.964088i	$0.414436\pi$
$600$	0	0
$601$	4.00000	0.163163	0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000	0.163163	0.0815817	+	0.996667i	$0.474003\pi$
$602$	0	0
$603$	−14.0000	−0.570124
$604$	0	0
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	20.0000	0.811775	0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000	0.811775	0.405887	+	0.913923i	$0.366962\pi$
$608$	0	0
$609$	−6.00000	−0.243132
$610$	0	0
$611$	−13.0000	−0.525924
$612$	0	0
$613$	−45.0000	−1.81753	−0.908766	−	0.417305i	$-0.862975\pi$
$613$	−45.0000	−1.81753	−0.908766	+	0.417305i	$0.862975\pi$
$614$	0	0
$615$	−3.00000	−0.120972
$616$	0	0
$617$	−44.0000	−1.77137	−0.885687	−	0.464283i	$-0.846312\pi$
$617$	−44.0000	−1.77137	−0.885687	+	0.464283i	$0.846312\pi$
$618$	0	0
$619$	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
$621$	25.0000	1.00322
$622$	0	0
$623$	−6.00000	−0.240385
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−18.0000	−0.718851
$628$	0	0
$629$	18.0000	0.717707
$630$	0	0
$631$	−38.0000	−1.51276	−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000	−1.51276	−0.756378	+	0.654135i	$0.773033\pi$
$632$	0	0
$633$	−10.0000	−0.397464
$634$	0	0
$635$	−11.0000	−0.436522
$636$	0	0
$637$	−1.00000	−0.0396214
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−9.00000	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$642$	0	0
$643$	−30.0000	−1.18308	−0.591542	−	0.806274i	$-0.701481\pi$
$643$	−30.0000	−1.18308	−0.591542	+	0.806274i	$0.701481\pi$
$644$	0	0
$645$	−2.00000	−0.0787499
$646$	0	0
$647$	22.0000	0.864909	0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000	0.864909	0.432455	+	0.901656i	$0.357648\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	7.00000	0.274352
$652$	0	0
$653$	50.0000	1.95665	0.978326	−	0.207072i	$-0.0663936\pi$
$653$	50.0000	1.95665	0.978326	+	0.207072i	$0.0663936\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	0	0
$657$	22.0000	0.858302
$658$	0	0
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	−24.0000	−0.933492	−0.466746	−	0.884391i	$-0.654574\pi$
$661$	−24.0000	−0.933492	−0.466746	+	0.884391i	$0.654574\pi$
$662$	0	0
$663$	−6.00000	−0.233021
$664$	0	0
$665$	6.00000	0.232670
$666$	0	0
$667$	−30.0000	−1.16160
$668$	0	0
$669$	−19.0000	−0.734582
$670$	0	0
$671$	−15.0000	−0.579069
$672$	0	0
$673$	−43.0000	−1.65753	−0.828764	−	0.559598i	$-0.810955\pi$
$673$	−43.0000	−1.65753	−0.828764	+	0.559598i	$0.810955\pi$
$674$	0	0
$675$	5.00000	0.192450
$676$	0	0
$677$	−35.0000	−1.34516	−0.672580	−	0.740025i	$-0.734814\pi$
$677$	−35.0000	−1.34516	−0.672580	+	0.740025i	$0.734814\pi$
$678$	0	0
$679$	13.0000	0.498894
$680$	0	0
$681$	−10.0000	−0.383201
$682$	0	0
$683$	7.00000	0.267848	0.133924	−	0.990992i	$-0.457242\pi$
$683$	7.00000	0.267848	0.133924	+	0.990992i	$0.457242\pi$
$684$	0	0
$685$	−14.0000	−0.534913
$686$	0	0
$687$	−14.0000	−0.534133
$688$	0	0
$689$	−4.00000	−0.152388
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	−6.00000	−0.227921
$694$	0	0
$695$	−4.00000	−0.151729
$696$	0	0
$697$	−18.0000	−0.681799
$698$	0	0
$699$	−21.0000	−0.794293
$700$	0	0
$701$	28.0000	1.05755	0.528773	−	0.848763i	$-0.322652\pi$
$701$	28.0000	1.05755	0.528773	+	0.848763i	$0.322652\pi$
$702$	0	0
$703$	18.0000	0.678883
$704$	0	0
$705$	−13.0000	−0.489608
$706$	0	0
$707$	−15.0000	−0.564133
$708$	0	0
$709$	21.0000	0.788672	0.394336	−	0.918966i	$-0.370975\pi$
$709$	21.0000	0.788672	0.394336	+	0.918966i	$0.370975\pi$
$710$	0	0
$711$	−34.0000	−1.27510
$712$	0	0
$713$	35.0000	1.31076
$714$	0	0
$715$	3.00000	0.112194
$716$	0	0
$717$	6.00000	0.224074
$718$	0	0
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	0	0
$721$	−2.00000	−0.0744839
$722$	0	0
$723$	−18.0000	−0.669427
$724$	0	0
$725$	−6.00000	−0.222834
$726$	0	0
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−12.0000	−0.443836
$732$	0	0
$733$	4.00000	0.147743	0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000	0.147743	0.0738717	+	0.997268i	$0.476464\pi$
$734$	0	0
$735$	−1.00000	−0.0368856
$736$	0	0
$737$	−21.0000	−0.773545
$738$	0	0
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	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
$745$	11.0000	0.403009
$746$	0	0
$747$	−4.00000	−0.146352
$748$	0	0
$749$	10.0000	0.365392
$750$	0	0
$751$	43.0000	1.56909	0.784546	−	0.620070i	$-0.212896\pi$
$751$	43.0000	1.56909	0.784546	+	0.620070i	$0.212896\pi$
$752$	0	0
$753$	−9.00000	−0.327978
$754$	0	0
$755$	−2.00000	−0.0727875
$756$	0	0
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	0	0
$759$	15.0000	0.544466
$760$	0	0
$761$	47.0000	1.70375	0.851874	−	0.523746i	$-0.175466\pi$
$761$	47.0000	1.70375	0.851874	+	0.523746i	$0.175466\pi$
$762$	0	0
$763$	−10.0000	−0.362024
$764$	0	0
$765$	12.0000	0.433861
$766$	0	0
$767$	0	0
$768$	0	0
$769$	23.0000	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$770$	0	0
$771$	8.00000	0.288113
$772$	0	0
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	0	0
$775$	7.00000	0.251447
$776$	0	0
$777$	−3.00000	−0.107624
$778$	0	0
$779$	−18.0000	−0.644917
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−30.0000	−1.07211
$784$	0	0
$785$	−5.00000	−0.178458
$786$	0	0
$787$	38.0000	1.35455	0.677277	−	0.735728i	$-0.263160\pi$
$787$	38.0000	1.35455	0.677277	+	0.735728i	$0.263160\pi$
$788$	0	0
$789$	20.0000	0.712019
$790$	0	0
$791$	1.00000	0.0355559
$792$	0	0
$793$	−5.00000	−0.177555
$794$	0	0
$795$	−4.00000	−0.141865
$796$	0	0
$797$	−11.0000	−0.389640	−0.194820	−	0.980839i	$-0.562412\pi$
$797$	−11.0000	−0.389640	−0.194820	+	0.980839i	$0.562412\pi$
$798$	0	0
$799$	−78.0000	−2.75944
$800$	0	0
$801$	−12.0000	−0.423999
$802$	0	0
$803$	33.0000	1.16454
$804$	0	0
$805$	−5.00000	−0.176227
$806$	0	0
$807$	19.0000	0.668832
$808$	0	0
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	−5.00000	−0.175358
$814$	0	0
$815$	8.00000	0.280228
$816$	0	0
$817$	−12.0000	−0.419827
$818$	0	0
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	0	0
$823$	−3.00000	−0.104573	−0.0522867	−	0.998632i	$-0.516651\pi$
$823$	−3.00000	−0.104573	−0.0522867	+	0.998632i	$0.516651\pi$
$824$	0	0
$825$	3.00000	0.104447
$826$	0	0
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	0	0
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	0	0
$833$	−6.00000	−0.207888
$834$	0	0
$835$	8.00000	0.276851
$836$	0	0
$837$	35.0000	1.20978
$838$	0	0
$839$	57.0000	1.96786	0.983929	−	0.178559i	$-0.0571434\pi$
$839$	57.0000	1.96786	0.983929	+	0.178559i	$0.0571434\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	14.0000	0.482186
$844$	0	0
$845$	1.00000	0.0344010
$846$	0	0
$847$	2.00000	0.0687208
$848$	0	0
$849$	5.00000	0.171600
$850$	0	0
$851$	−15.0000	−0.514193
$852$	0	0
$853$	−8.00000	−0.273915	−0.136957	−	0.990577i	$-0.543732\pi$
$853$	−8.00000	−0.273915	−0.136957	+	0.990577i	$0.543732\pi$
$854$	0	0
$855$	12.0000	0.410391
$856$	0	0
$857$	24.0000	0.819824	0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000	0.819824	0.409912	+	0.912125i	$0.365559\pi$
$858$	0	0
$859$	−5.00000	−0.170598	−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000	−0.170598	−0.0852989	+	0.996355i	$0.527185\pi$
$860$	0	0
$861$	3.00000	0.102240
$862$	0	0
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	0	0
$865$	14.0000	0.476014
$866$	0	0
$867$	−19.0000	−0.645274
$868$	0	0
$869$	−51.0000	−1.73006
$870$	0	0
$871$	−7.00000	−0.237186
$872$	0	0
$873$	26.0000	0.879967
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−25.0000	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$878$	0	0
$879$	−24.0000	−0.809500
$880$	0	0
$881$	−34.0000	−1.14549	−0.572745	−	0.819734i	$-0.694121\pi$
$881$	−34.0000	−1.14549	−0.572745	+	0.819734i	$0.694121\pi$
$882$	0	0
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	2.00000	0.0671534	0.0335767	−	0.999436i	$-0.489310\pi$
$887$	2.00000	0.0671534	0.0335767	+	0.999436i	$0.489310\pi$
$888$	0	0
$889$	11.0000	0.368928
$890$	0	0
$891$	−3.00000	−0.100504
$892$	0	0
$893$	−78.0000	−2.61017
$894$	0	0
$895$	−12.0000	−0.401116
$896$	0	0
$897$	5.00000	0.166945
$898$	0	0
$899$	−42.0000	−1.40078
$900$	0	0
$901$	−24.0000	−0.799556
$902$	0	0
$903$	2.00000	0.0665558
$904$	0	0
$905$	−5.00000	−0.166206
$906$	0	0
$907$	−36.0000	−1.19536	−0.597680	−	0.801735i	$-0.703911\pi$
$907$	−36.0000	−1.19536	−0.597680	+	0.801735i	$0.703911\pi$
$908$	0	0
$909$	−30.0000	−0.995037
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	−6.00000	−0.198571
$914$	0	0
$915$	−5.00000	−0.165295
$916$	0	0
$917$	12.0000	0.396275
$918$	0	0
$919$	−3.00000	−0.0989609	−0.0494804	−	0.998775i	$-0.515757\pi$
$919$	−3.00000	−0.0989609	−0.0494804	+	0.998775i	$0.515757\pi$
$920$	0	0
$921$	28.0000	0.922631
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−3.00000	−0.0986394
$926$	0	0
$927$	−4.00000	−0.131377
$928$	0	0
$929$	−1.00000	−0.0328089	−0.0164045	−	0.999865i	$-0.505222\pi$
$929$	−1.00000	−0.0328089	−0.0164045	+	0.999865i	$0.505222\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	0	0
$933$	−16.0000	−0.523816
$934$	0	0
$935$	18.0000	0.588663
$936$	0	0
$937$	−28.0000	−0.914720	−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000	−0.914720	−0.457360	+	0.889282i	$0.651205\pi$
$938$	0	0
$939$	18.0000	0.587408
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	0	0
$943$	15.0000	0.488467
$944$	0	0
$945$	−5.00000	−0.162650
$946$	0	0
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	0	0
$949$	11.0000	0.357075
$950$	0	0
$951$	7.00000	0.226991
$952$	0	0
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	0	0
$955$	24.0000	0.776622
$956$	0	0
$957$	−18.0000	−0.581857
$958$	0	0
$959$	14.0000	0.452084
$960$	0	0
$961$	18.0000	0.580645
$962$	0	0
$963$	20.0000	0.644491
$964$	0	0
$965$	−14.0000	−0.450676
$966$	0	0
$967$	12.0000	0.385894	0.192947	−	0.981209i	$-0.438195\pi$
$967$	12.0000	0.385894	0.192947	+	0.981209i	$0.438195\pi$
$968$	0	0
$969$	−36.0000	−1.15649
$970$	0	0
$971$	35.0000	1.12320	0.561602	−	0.827408i	$-0.310185\pi$
$971$	35.0000	1.12320	0.561602	+	0.827408i	$0.310185\pi$
$972$	0	0
$973$	4.00000	0.128234
$974$	0	0
$975$	1.00000	0.0320256
$976$	0	0
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	0	0
$979$	−18.0000	−0.575282
$980$	0	0
$981$	−20.0000	−0.638551
$982$	0	0
$983$	32.0000	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$984$	0	0
$985$	−3.00000	−0.0955879
$986$	0	0
$987$	13.0000	0.413795
$988$	0	0
$989$	10.0000	0.317982
$990$	0	0
$991$	−59.0000	−1.87420	−0.937098	−	0.349065i	$-0.886499\pi$
$991$	−59.0000	−1.87420	−0.937098	+	0.349065i	$0.886499\pi$
$992$	0	0
$993$	−25.0000	−0.793351
$994$	0	0
$995$	10.0000	0.317021
$996$	0	0
$997$	−53.0000	−1.67853	−0.839263	−	0.543725i	$-0.817013\pi$
$997$	−53.0000	−1.67853	−0.839263	+	0.543725i	$0.817013\pi$
$998$	0	0
$999$	−15.0000	−0.474579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3640.2.a.c.1.1	✓	1
4.3	odd	2		7280.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3640.2.a.c.1.1	✓	1	1.1	even	1	trivial
7280.2.a.r.1.1		1	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3640.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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