LMFDB - Embedded newform 7245.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7245,2,Mod(1,7245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7245.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7245.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:	$57.8516162644$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{10} -2.00000 q^{11} +4.00000 q^{13} -1.00000 q^{14} -1.00000 q^{16} +6.00000 q^{17} -8.00000 q^{19} -1.00000 q^{20} -2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{28} -10.0000 q^{29} +10.0000 q^{31} +5.00000 q^{32} +6.00000 q^{34} -1.00000 q^{35} +8.00000 q^{37} -8.00000 q^{38} -3.00000 q^{40} +2.00000 q^{41} +2.00000 q^{44} -1.00000 q^{46} -12.0000 q^{47} +1.00000 q^{49} +1.00000 q^{50} -4.00000 q^{52} +4.00000 q^{53} -2.00000 q^{55} +3.00000 q^{56} -10.0000 q^{58} -14.0000 q^{59} -2.00000 q^{61} +10.0000 q^{62} +7.00000 q^{64} +4.00000 q^{65} -4.00000 q^{67} -6.00000 q^{68} -1.00000 q^{70} -8.00000 q^{71} +8.00000 q^{74} +8.00000 q^{76} +2.00000 q^{77} +6.00000 q^{79} -1.00000 q^{80} +2.00000 q^{82} +12.0000 q^{83} +6.00000 q^{85} +6.00000 q^{88} -10.0000 q^{89} -4.00000 q^{91} +1.00000 q^{92} -12.0000 q^{94} -8.00000 q^{95} -2.00000 q^{97} +1.00000 q^{98} +O(q^{100})$

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.00000	−1.06066
$9$	0	0
$10$	1.00000	0.316228
$11$	−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
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	0	0
$28$	1.00000	0.188982
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	6.00000	1.02899
$35$	−1.00000	−0.169031
$36$	0	0
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−8.00000	−1.29777
$39$	0	0
$40$	−3.00000	−0.474342
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0	0
$52$	−4.00000	−0.554700
$53$	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
$55$	−2.00000	−0.269680
$56$	3.00000	0.400892
$57$	0	0
$58$	−10.0000	−1.31306
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	10.0000	1.27000
$63$	0	0
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	−1.00000	−0.119523
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	8.00000	0.917663
$77$	2.00000	0.227921
$78$	0	0
$79$	6.00000	0.675053	0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000	0.675053	0.337526	+	0.941316i	$0.390410\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	2.00000	0.220863
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	0	0
$87$	0	0
$88$	6.00000	0.639602
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	1.00000	0.104257
$93$	0	0
$94$	−12.0000	−1.23771
$95$	−8.00000	−0.820783
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−12.0000	−1.17670
$105$	0	0
$106$	4.00000	0.388514
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	1.00000	0.0944911
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	10.0000	0.928477
$117$	0	0
$118$	−14.0000	−1.28880
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−10.0000	−0.898027
$125$	1.00000	0.0894427
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	4.00000	0.350823
$131$	−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
$133$	8.00000	0.693688
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−18.0000	−1.54349
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	−8.00000	−0.671345
$143$	−8.00000	−0.668994
$144$	0	0
$145$	−10.0000	−0.830455
$146$	0	0
$147$	0	0
$148$	−8.00000	−0.657596
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	24.0000	1.94666
$153$	0	0
$154$	2.00000	0.161165
$155$	10.0000	0.803219
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	5.00000	0.395285
$161$	1.00000	0.0788110
$162$	0	0
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	12.0000	0.931381
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	6.00000	0.460179
$171$	0	0
$172$	0	0
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	2.00000	0.150756
$177$	0	0
$178$	−10.0000	−0.749532
$179$	−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
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	3.00000	0.221163
$185$	8.00000	0.588172
$186$	0	0
$187$	−12.0000	−0.877527
$188$	12.0000	0.875190
$189$	0	0
$190$	−8.00000	−0.580381
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	14.0000	0.997459	0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000	0.997459	0.498729	+	0.866758i	$0.333800\pi$
$198$	0	0
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−3.00000	−0.212132
$201$	0	0
$202$	−10.0000	−0.703598
$203$	10.0000	0.701862
$204$	0	0
$205$	2.00000	0.139686
$206$	−8.00000	−0.557386
$207$	0	0
$208$	−4.00000	−0.277350
$209$	16.0000	1.10674
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	12.0000	0.820303
$215$	0	0
$216$	0	0
$217$	−10.0000	−0.678844
$218$	2.00000	0.135457
$219$	0	0
$220$	2.00000	0.134840
$221$	24.0000	1.61441
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	−5.00000	−0.334077
$225$	0	0
$226$	−12.0000	−0.798228
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	30.0000	1.96960
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	0	0
$235$	−12.0000	−0.782794
$236$	14.0000	0.911322
$237$	0	0
$238$	−6.00000	−0.388922
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	2.00000	0.128037
$245$	1.00000	0.0638877
$246$	0	0
$247$	−32.0000	−2.03611
$248$	−30.0000	−1.90500
$249$	0	0
$250$	1.00000	0.0632456
$251$	−16.0000	−1.00991	−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000	−1.00991	−0.504956	+	0.863145i	$0.668491\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	8.00000	0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	8.00000	0.499026	0.249513	−	0.968371i	$-0.419729\pi$
$257$	8.00000	0.499026	0.249513	+	0.968371i	$0.419729\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−6.00000	−0.370681
$263$	−4.00000	−0.246651	−0.123325	−	0.992366i	$-0.539356\pi$
$263$	−4.00000	−0.246651	−0.123325	+	0.992366i	$0.539356\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	8.00000	0.490511
$267$	0	0
$268$	4.00000	0.244339
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	10.0000	0.607457	0.303728	−	0.952759i	$-0.401768\pi$
$271$	10.0000	0.607457	0.303728	+	0.952759i	$0.401768\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	0	0
$275$	−2.00000	−0.120605
$276$	0	0
$277$	−6.00000	−0.360505	−0.180253	−	0.983620i	$-0.557691\pi$
$277$	−6.00000	−0.360505	−0.180253	+	0.983620i	$0.557691\pi$
$278$	−22.0000	−1.31947
$279$	0	0
$280$	3.00000	0.179284
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	−8.00000	−0.473050
$287$	−2.00000	−0.118056
$288$	0	0
$289$	19.0000	1.11765
$290$	−10.0000	−0.587220
$291$	0	0
$292$	0	0
$293$	−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
$295$	−14.0000	−0.815112
$296$	−24.0000	−1.39497
$297$	0	0
$298$	−10.0000	−0.579284
$299$	−4.00000	−0.231326
$300$	0	0
$301$	0	0
$302$	−12.0000	−0.690522
$303$	0	0
$304$	8.00000	0.458831
$305$	−2.00000	−0.114520
$306$	0	0
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	10.0000	0.567962
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−6.00000	−0.337526
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	20.0000	1.11979
$320$	7.00000	0.391312
$321$	0	0
$322$	1.00000	0.0557278
$323$	−48.0000	−2.67079
$324$	0	0
$325$	4.00000	0.221880
$326$	12.0000	0.664619
$327$	0	0
$328$	−6.00000	−0.331295
$329$	12.0000	0.661581
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−12.0000	−0.658586
$333$	0	0
$334$	−12.0000	−0.656611
$335$	−4.00000	−0.218543
$336$	0	0
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	−6.00000	−0.325396
$341$	−20.0000	−1.08306
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	12.0000	0.645124
$347$	−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
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	−10.0000	−0.533002
$353$	20.0000	1.06449	0.532246	−	0.846590i	$-0.321348\pi$
$353$	20.0000	1.06449	0.532246	+	0.846590i	$0.321348\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	10.0000	0.529999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	10.0000	0.525588
$363$	0	0
$364$	4.00000	0.209657
$365$	0	0
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	1.00000	0.0521286
$369$	0	0
$370$	8.00000	0.415900
$371$	−4.00000	−0.207670
$372$	0	0
$373$	8.00000	0.414224	0.207112	−	0.978317i	$-0.433593\pi$
$373$	8.00000	0.414224	0.207112	+	0.978317i	$0.433593\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	36.0000	1.85656
$377$	−40.0000	−2.06010
$378$	0	0
$379$	30.0000	1.54100	0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000	1.54100	0.770498	+	0.637442i	$0.220007\pi$
$380$	8.00000	0.410391
$381$	0	0
$382$	−18.0000	−0.920960
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	0	0
$385$	2.00000	0.101929
$386$	−2.00000	−0.101797
$387$	0	0
$388$	2.00000	0.101535
$389$	−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
$391$	−6.00000	−0.303433
$392$	−3.00000	−0.151523
$393$	0	0
$394$	14.0000	0.705310
$395$	6.00000	0.301893
$396$	0	0
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	0	0
$403$	40.0000	1.99254
$404$	10.0000	0.497519
$405$	0	0
$406$	10.0000	0.496292
$407$	−16.0000	−0.793091
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	2.00000	0.0987730
$411$	0	0
$412$	8.00000	0.394132
$413$	14.0000	0.688895
$414$	0	0
$415$	12.0000	0.589057
$416$	20.0000	0.980581
$417$	0	0
$418$	16.0000	0.782586
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	0	0
$423$	0	0
$424$	−12.0000	−0.582772
$425$	6.00000	0.291043
$426$	0	0
$427$	2.00000	0.0967868
$428$	−12.0000	−0.580042
$429$	0	0
$430$	0	0
$431$	−22.0000	−1.05970	−0.529851	−	0.848091i	$-0.677752\pi$
$431$	−22.0000	−1.05970	−0.529851	+	0.848091i	$0.677752\pi$
$432$	0	0
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	−10.0000	−0.480015
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	8.00000	0.382692
$438$	0	0
$439$	−34.0000	−1.62273	−0.811366	−	0.584539i	$-0.801275\pi$
$439$	−34.0000	−1.62273	−0.811366	+	0.584539i	$0.801275\pi$
$440$	6.00000	0.286039
$441$	0	0
$442$	24.0000	1.14156
$443$	−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
$445$	−10.0000	−0.474045
$446$	−4.00000	−0.189405
$447$	0	0
$448$	−7.00000	−0.330719
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	−4.00000	−0.188353
$452$	12.0000	0.564433
$453$	0	0
$454$	−4.00000	−0.187729
$455$	−4.00000	−0.187523
$456$	0	0
$457$	16.0000	0.748448	0.374224	−	0.927338i	$-0.377909\pi$
$457$	16.0000	0.748448	0.374224	+	0.927338i	$0.377909\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	1.00000	0.0466252
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	10.0000	0.464238
$465$	0	0
$466$	26.0000	1.20443
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	0	0
$469$	4.00000	0.184703
$470$	−12.0000	−0.553519
$471$	0	0
$472$	42.0000	1.93321
$473$	0	0
$474$	0	0
$475$	−8.00000	−0.367065
$476$	6.00000	0.275010
$477$	0	0
$478$	−16.0000	−0.731823
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	32.0000	1.45907
$482$	−18.0000	−0.819878
$483$	0	0
$484$	7.00000	0.318182
$485$	−2.00000	−0.0908153
$486$	0	0
$487$	32.0000	1.45006	0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000	1.45006	0.725029	+	0.688718i	$0.241826\pi$
$488$	6.00000	0.271607
$489$	0	0
$490$	1.00000	0.0451754
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	−60.0000	−2.70226
$494$	−32.0000	−1.43975
$495$	0	0
$496$	−10.0000	−0.449013
$497$	8.00000	0.358849
$498$	0	0
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−16.0000	−0.714115
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−10.0000	−0.444994
$506$	2.00000	0.0889108
$507$	0	0
$508$	−8.00000	−0.354943
$509$	42.0000	1.86162	0.930809	−	0.365507i	$-0.119104\pi$
$509$	42.0000	1.86162	0.930809	+	0.365507i	$0.119104\pi$
$510$	0	0
$511$	0	0
$512$	−11.0000	−0.486136
$513$	0	0
$514$	8.00000	0.352865
$515$	−8.00000	−0.352522
$516$	0	0
$517$	24.0000	1.05552
$518$	−8.00000	−0.351500
$519$	0	0
$520$	−12.0000	−0.526235
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	−4.00000	−0.174408
$527$	60.0000	2.61364
$528$	0	0
$529$	1.00000	0.0434783
$530$	4.00000	0.173749
$531$	0	0
$532$	−8.00000	−0.346844
$533$	8.00000	0.346518
$534$	0	0
$535$	12.0000	0.518805
$536$	12.0000	0.518321
$537$	0	0
$538$	6.00000	0.258678
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	34.0000	1.46177	0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000	1.46177	0.730887	+	0.682498i	$0.239107\pi$
$542$	10.0000	0.429537
$543$	0	0
$544$	30.0000	1.28624
$545$	2.00000	0.0856706
$546$	0	0
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	0	0
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	80.0000	3.40811
$552$	0	0
$553$	−6.00000	−0.255146
$554$	−6.00000	−0.254916
$555$	0	0
$556$	22.0000	0.933008
$557$	−20.0000	−0.847427	−0.423714	−	0.905796i	$-0.639274\pi$
$557$	−20.0000	−0.847427	−0.423714	+	0.905796i	$0.639274\pi$
$558$	0	0
$559$	0	0
$560$	1.00000	0.0422577
$561$	0	0
$562$	−30.0000	−1.26547
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	−12.0000	−0.504844
$566$	20.0000	0.840663
$567$	0	0
$568$	24.0000	1.00702
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−10.0000	−0.418487	−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000	−0.418487	−0.209243	+	0.977864i	$0.567100\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	−2.00000	−0.0834784
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	10.0000	0.415227
$581$	−12.0000	−0.497844
$582$	0	0
$583$	−8.00000	−0.331326
$584$	0	0
$585$	0	0
$586$	−18.0000	−0.743573
$587$	−8.00000	−0.330195	−0.165098	−	0.986277i	$-0.552794\pi$
$587$	−8.00000	−0.330195	−0.165098	+	0.986277i	$0.552794\pi$
$588$	0	0
$589$	−80.0000	−3.29634
$590$	−14.0000	−0.576371
$591$	0	0
$592$	−8.00000	−0.328798
$593$	−20.0000	−0.821302	−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000	−0.821302	−0.410651	+	0.911793i	$0.634698\pi$
$594$	0	0
$595$	−6.00000	−0.245976
$596$	10.0000	0.409616
$597$	0	0
$598$	−4.00000	−0.163572
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	0	0
$603$	0	0
$604$	12.0000	0.488273
$605$	−7.00000	−0.284590
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−40.0000	−1.62221
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	−48.0000	−1.94187
$612$	0	0
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	−8.00000	−0.322854
$615$	0	0
$616$	−6.00000	−0.241747
$617$	44.0000	1.77137	0.885687	−	0.464283i	$-0.153688\pi$
$617$	44.0000	1.77137	0.885687	+	0.464283i	$0.153688\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	−10.0000	−0.401610
$621$	0	0
$622$	2.00000	0.0801927
$623$	10.0000	0.400642
$624$	0	0
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	10.0000	0.399043
$629$	48.0000	1.91389
$630$	0	0
$631$	22.0000	0.875806	0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000	0.875806	0.437903	+	0.899022i	$0.355721\pi$
$632$	−18.0000	−0.716002
$633$	0	0
$634$	−18.0000	−0.714871
$635$	8.00000	0.317470
$636$	0	0
$637$	4.00000	0.158486
$638$	20.0000	0.791808
$639$	0	0
$640$	−3.00000	−0.118585
$641$	34.0000	1.34292	0.671460	−	0.741041i	$-0.265668\pi$
$641$	34.0000	1.34292	0.671460	+	0.741041i	$0.265668\pi$
$642$	0	0
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	−48.0000	−1.88853
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	0	0
$649$	28.0000	1.09910
$650$	4.00000	0.156893
$651$	0	0
$652$	−12.0000	−0.469956
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	−6.00000	−0.234439
$656$	−2.00000	−0.0780869
$657$	0	0
$658$	12.0000	0.467809
$659$	−6.00000	−0.233727	−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000	−0.233727	−0.116863	+	0.993148i	$0.537284\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	−36.0000	−1.39707
$665$	8.00000	0.310227
$666$	0	0
$667$	10.0000	0.387202
$668$	12.0000	0.464294
$669$	0	0
$670$	−4.00000	−0.154533
$671$	4.00000	0.154418
$672$	0	0
$673$	−50.0000	−1.92736	−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−50.0000	−1.92736	−0.963679	+	0.267063i	$0.913947\pi$
$674$	4.00000	0.154074
$675$	0	0
$676$	−3.00000	−0.115385
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	−18.0000	−0.690268
$681$	0	0
$682$	−20.0000	−0.765840
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	0	0
$689$	16.0000	0.609551
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	−12.0000	−0.455514
$695$	−22.0000	−0.834508
$696$	0	0
$697$	12.0000	0.454532
$698$	−10.0000	−0.378506
$699$	0	0
$700$	1.00000	0.0377964
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	−64.0000	−2.41381
$704$	−14.0000	−0.527645
$705$	0	0
$706$	20.0000	0.752710
$707$	10.0000	0.376089
$708$	0	0
$709$	30.0000	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$710$	−8.00000	−0.300235
$711$	0	0
$712$	30.0000	1.12430
$713$	−10.0000	−0.374503
$714$	0	0
$715$	−8.00000	−0.299183
$716$	12.0000	0.448461
$717$	0	0
$718$	−30.0000	−1.11959
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	45.0000	1.67473
$723$	0	0
$724$	−10.0000	−0.371647
$725$	−10.0000	−0.371391
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	12.0000	0.444750
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	50.0000	1.84679	0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000	1.84679	0.923396	+	0.383849i	$0.125402\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−5.00000	−0.184302
$737$	8.00000	0.294684
$738$	0	0
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	−4.00000	−0.146845
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	8.00000	0.292901
$747$	0	0
$748$	12.0000	0.438763
$749$	−12.0000	−0.438470
$750$	0	0
$751$	14.0000	0.510867	0.255434	−	0.966827i	$-0.417782\pi$
$751$	14.0000	0.510867	0.255434	+	0.966827i	$0.417782\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	−40.0000	−1.45671
$755$	−12.0000	−0.436725
$756$	0	0
$757$	4.00000	0.145382	0.0726912	−	0.997354i	$-0.476841\pi$
$757$	4.00000	0.145382	0.0726912	+	0.997354i	$0.476841\pi$
$758$	30.0000	1.08965
$759$	0	0
$760$	24.0000	0.870572
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	0	0
$763$	−2.00000	−0.0724049
$764$	18.0000	0.651217
$765$	0	0
$766$	16.0000	0.578103
$767$	−56.0000	−2.02204
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	2.00000	0.0720750
$771$	0	0
$772$	2.00000	0.0719816
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	0	0
$775$	10.0000	0.359211
$776$	6.00000	0.215387
$777$	0	0
$778$	−10.0000	−0.358517
$779$	−16.0000	−0.573259
$780$	0	0
$781$	16.0000	0.572525
$782$	−6.00000	−0.214560
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	−10.0000	−0.356915
$786$	0	0
$787$	20.0000	0.712923	0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000	0.712923	0.356462	+	0.934310i	$0.383983\pi$
$788$	−14.0000	−0.498729
$789$	0	0
$790$	6.00000	0.213470
$791$	12.0000	0.426671
$792$	0	0
$793$	−8.00000	−0.284088
$794$	−8.00000	−0.283909
$795$	0	0
$796$	4.00000	0.141776
$797$	−26.0000	−0.920967	−0.460484	−	0.887668i	$-0.652324\pi$
$797$	−26.0000	−0.920967	−0.460484	+	0.887668i	$0.652324\pi$
$798$	0	0
$799$	−72.0000	−2.54718
$800$	5.00000	0.176777
$801$	0	0
$802$	22.0000	0.776847
$803$	0	0
$804$	0	0
$805$	1.00000	0.0352454
$806$	40.0000	1.40894
$807$	0	0
$808$	30.0000	1.05540
$809$	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
$811$	18.0000	0.632065	0.316033	−	0.948748i	$-0.397649\pi$
$811$	18.0000	0.632065	0.316033	+	0.948748i	$0.397649\pi$
$812$	−10.0000	−0.350931
$813$	0	0
$814$	−16.0000	−0.560800
$815$	12.0000	0.420342
$816$	0	0
$817$	0	0
$818$	10.0000	0.349642
$819$	0	0
$820$	−2.00000	−0.0698430
$821$	−22.0000	−0.767805	−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000	−0.767805	−0.383903	+	0.923374i	$0.625420\pi$
$822$	0	0
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	24.0000	0.836080
$825$	0	0
$826$	14.0000	0.487122
$827$	20.0000	0.695468	0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000	0.695468	0.347734	+	0.937593i	$0.386951\pi$
$828$	0	0
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	12.0000	0.416526
$831$	0	0
$832$	28.0000	0.970725
$833$	6.00000	0.207888
$834$	0	0
$835$	−12.0000	−0.415277
$836$	−16.0000	−0.553372
$837$	0	0
$838$	−12.0000	−0.414533
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	−26.0000	−0.896019
$843$	0	0
$844$	0	0
$845$	3.00000	0.103203
$846$	0	0
$847$	7.00000	0.240523
$848$	−4.00000	−0.137361
$849$	0	0
$850$	6.00000	0.205798
$851$	−8.00000	−0.274236
$852$	0	0
$853$	−56.0000	−1.91740	−0.958702	−	0.284413i	$-0.908201\pi$
$853$	−56.0000	−1.91740	−0.958702	+	0.284413i	$0.908201\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	−36.0000	−1.23045
$857$	20.0000	0.683187	0.341593	−	0.939848i	$-0.389033\pi$
$857$	20.0000	0.683187	0.341593	+	0.939848i	$0.389033\pi$
$858$	0	0
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	0	0
$861$	0	0
$862$	−22.0000	−0.749323
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	0	0
$865$	12.0000	0.408012
$866$	−34.0000	−1.15537
$867$	0	0
$868$	10.0000	0.339422
$869$	−12.0000	−0.407072
$870$	0	0
$871$	−16.0000	−0.542139
$872$	−6.00000	−0.203186
$873$	0	0
$874$	8.00000	0.270604
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	−34.0000	−1.14744
$879$	0	0
$880$	2.00000	0.0674200
$881$	50.0000	1.68454	0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000	1.68454	0.842271	+	0.539054i	$0.181218\pi$
$882$	0	0
$883$	4.00000	0.134611	0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000	0.134611	0.0673054	+	0.997732i	$0.478560\pi$
$884$	−24.0000	−0.807207
$885$	0	0
$886$	−28.0000	−0.940678
$887$	32.0000	1.07445	0.537227	−	0.843437i	$-0.319472\pi$
$887$	32.0000	1.07445	0.537227	+	0.843437i	$0.319472\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	−10.0000	−0.335201
$891$	0	0
$892$	4.00000	0.133930
$893$	96.0000	3.21252
$894$	0	0
$895$	−12.0000	−0.401116
$896$	3.00000	0.100223
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−100.000	−3.33519
$900$	0	0
$901$	24.0000	0.799556
$902$	−4.00000	−0.133185
$903$	0	0
$904$	36.0000	1.19734
$905$	10.0000	0.332411
$906$	0	0
$907$	−16.0000	−0.531271	−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000	−0.531271	−0.265636	+	0.964073i	$0.585582\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	−4.00000	−0.132599
$911$	−14.0000	−0.463841	−0.231920	−	0.972735i	$-0.574501\pi$
$911$	−14.0000	−0.463841	−0.231920	+	0.972735i	$0.574501\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	16.0000	0.529233
$915$	0	0
$916$	10.0000	0.330409
$917$	6.00000	0.198137
$918$	0	0
$919$	26.0000	0.857661	0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000	0.857661	0.428830	+	0.903385i	$0.358926\pi$
$920$	3.00000	0.0989071
$921$	0	0
$922$	14.0000	0.461065
$923$	−32.0000	−1.05329
$924$	0	0
$925$	8.00000	0.263038
$926$	8.00000	0.262896
$927$	0	0
$928$	−50.0000	−1.64133
$929$	54.0000	1.77168	0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000	1.77168	0.885841	+	0.463988i	$0.153582\pi$
$930$	0	0
$931$	−8.00000	−0.262189
$932$	−26.0000	−0.851658
$933$	0	0
$934$	−36.0000	−1.17796
$935$	−12.0000	−0.392442
$936$	0	0
$937$	−58.0000	−1.89478	−0.947389	−	0.320085i	$-0.896288\pi$
$937$	−58.0000	−1.89478	−0.947389	+	0.320085i	$0.896288\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	12.0000	0.391397
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	0	0
$943$	−2.00000	−0.0651290
$944$	14.0000	0.455661
$945$	0	0
$946$	0	0
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	0	0
$949$	0	0
$950$	−8.00000	−0.259554
$951$	0	0
$952$	18.0000	0.583383
$953$	−32.0000	−1.03658	−0.518291	−	0.855204i	$-0.673432\pi$
$953$	−32.0000	−1.03658	−0.518291	+	0.855204i	$0.673432\pi$
$954$	0	0
$955$	−18.0000	−0.582466
$956$	16.0000	0.517477
$957$	0	0
$958$	12.0000	0.387702
$959$	0	0
$960$	0	0
$961$	69.0000	2.22581
$962$	32.0000	1.03172
$963$	0	0
$964$	18.0000	0.579741
$965$	−2.00000	−0.0643823
$966$	0	0
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	21.0000	0.674966
$969$	0	0
$970$	−2.00000	−0.0642161
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	0	0
$973$	22.0000	0.705288
$974$	32.0000	1.02535
$975$	0	0
$976$	2.00000	0.0640184
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	0	0
$979$	20.0000	0.639203
$980$	−1.00000	−0.0319438
$981$	0	0
$982$	36.0000	1.14881
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	0	0
$985$	14.0000	0.446077
$986$	−60.0000	−1.91079
$987$	0	0
$988$	32.0000	1.01806
$989$	0	0
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	50.0000	1.58750
$993$	0	0
$994$	8.00000	0.253745
$995$	−4.00000	−0.126809
$996$	0	0
$997$	44.0000	1.39349	0.696747	−	0.717317i	$-0.254630\pi$
$997$	44.0000	1.39349	0.696747	+	0.717317i	$0.254630\pi$
$998$	16.0000	0.506471
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7245.2.a.p.1.1		1
3.2	odd	2		805.2.a.b.1.1	✓	1
15.14	odd	2		4025.2.a.g.1.1		1
21.20	even	2		5635.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.b.1.1	✓	1	3.2	odd	2
4025.2.a.g.1.1		1	15.14	odd	2
5635.2.a.c.1.1		1	21.20	even	2
7245.2.a.p.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7245.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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