LMFDB - Embedded newform 7245.2.a.m.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 2415)
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)

$f(q)$

$=$

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

$q+1.00000 q^{2} -1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} -3.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -4.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{20} +2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{25} -4.00000 q^{26} -1.00000 q^{28} +6.00000 q^{29} -2.00000 q^{31} +5.00000 q^{32} +2.00000 q^{34} -1.00000 q^{35} +4.00000 q^{37} +3.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -1.00000 q^{46} +8.00000 q^{47} +1.00000 q^{49} +1.00000 q^{50} +4.00000 q^{52} -2.00000 q^{55} -3.00000 q^{56} +6.00000 q^{58} -2.00000 q^{59} -14.0000 q^{61} -2.00000 q^{62} +7.00000 q^{64} +4.00000 q^{65} -12.0000 q^{67} -2.00000 q^{68} -1.00000 q^{70} +8.00000 q^{73} +4.00000 q^{74} +2.00000 q^{77} +10.0000 q^{79} +1.00000 q^{80} +2.00000 q^{82} -12.0000 q^{83} -2.00000 q^{85} -8.00000 q^{86} -6.00000 q^{88} -6.00000 q^{89} -4.00000 q^{91} +1.00000 q^{92} +8.00000 q^{94} -14.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

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	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	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
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	2.00000	0.342997
$35$	−1.00000	−0.169031
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	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
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0	0
$52$	4.00000	0.554700
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	−3.00000	−0.400892
$57$	0	0
$58$	6.00000	0.787839
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	−1.00000	−0.119523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	0	0
$77$	2.00000	0.227921
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	2.00000	0.220863
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−8.00000	−0.862662
$87$	0	0
$88$	−6.00000	−0.639602
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	1.00000	0.104257
$93$	0	0
$94$	8.00000	0.825137
$95$	0	0
$96$	0	0
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	12.0000	1.17670
$105$	0	0
$106$	0	0
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	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
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	0	0
$115$	1.00000	0.0932505
$116$	−6.00000	−0.557086
$117$	0	0
$118$	−2.00000	−0.184115
$119$	2.00000	0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−14.0000	−1.26750
$123$	0	0
$124$	2.00000	0.179605
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	4.00000	0.350823
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	0	0
$134$	−12.0000	−1.03664
$135$	0	0
$136$	−6.00000	−0.514496
$137$	20.0000	1.70872	0.854358	−	0.519685i	$-0.173951\pi$
$137$	20.0000	1.70872	0.854358	+	0.519685i	$0.173951\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	0	0
$143$	−8.00000	−0.668994
$144$	0	0
$145$	−6.00000	−0.498273
$146$	8.00000	0.662085
$147$	0	0
$148$	−4.00000	−0.328798
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	0	0
$153$	0	0
$154$	2.00000	0.161165
$155$	2.00000	0.160644
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	−5.00000	−0.395285
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−12.0000	−0.931381
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	−2.00000	−0.153393
$171$	0	0
$172$	8.00000	0.609994
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	−2.00000	−0.150756
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	−26.0000	−1.93256	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000	−1.93256	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	3.00000	0.221163
$185$	−4.00000	−0.294086
$186$	0	0
$187$	4.00000	0.292509
$188$	−8.00000	−0.583460
$189$	0	0
$190$	0	0
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	0	0
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	−3.00000	−0.212132
$201$	0	0
$202$	−18.0000	−1.26648
$203$	6.00000	0.421117
$204$	0	0
$205$	−2.00000	−0.139686
$206$	8.00000	0.557386
$207$	0	0
$208$	4.00000	0.277350
$209$	0	0
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	0	0
$213$	0	0
$214$	−4.00000	−0.273434
$215$	8.00000	0.545595
$216$	0	0
$217$	−2.00000	−0.135769
$218$	2.00000	0.135457
$219$	0	0
$220$	2.00000	0.134840
$221$	−8.00000	−0.538138
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	8.00000	0.532152
$227$	−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
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	−18.0000	−1.18176
$233$	−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
$235$	−8.00000	−0.521862
$236$	2.00000	0.130189
$237$	0	0
$238$	2.00000	0.129641
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	14.0000	0.896258
$245$	−1.00000	−0.0638877
$246$	0	0
$247$	0	0
$248$	6.00000	0.381000
$249$	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
$254$	−16.0000	−1.00393
$255$	0	0
$256$	−17.0000	−1.06250
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	−4.00000	−0.248069
$261$	0	0
$262$	6.00000	0.370681
$263$	−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
$265$	0	0
$266$	0	0
$267$	0	0
$268$	12.0000	0.733017
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	−10.0000	−0.607457	−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000	−0.607457	−0.303728	+	0.952759i	$0.598232\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	20.0000	1.20824
$275$	2.00000	0.120605
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	−10.0000	−0.599760
$279$	0	0
$280$	3.00000	0.179284
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	0	0
$285$	0	0
$286$	−8.00000	−0.473050
$287$	2.00000	0.118056
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−6.00000	−0.352332
$291$	0	0
$292$	−8.00000	−0.468165
$293$	10.0000	0.584206	0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000	0.584206	0.292103	+	0.956387i	$0.405645\pi$
$294$	0	0
$295$	2.00000	0.116445
$296$	−12.0000	−0.697486
$297$	0	0
$298$	−2.00000	−0.115857
$299$	4.00000	0.231326
$300$	0	0
$301$	−8.00000	−0.461112
$302$	−20.0000	−1.15087
$303$	0	0
$304$	0	0
$305$	14.0000	0.801638
$306$	0	0
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	2.00000	0.113592
$311$	6.00000	0.340229	0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000	0.340229	0.170114	+	0.985424i	$0.445586\pi$
$312$	0	0
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	−7.00000	−0.391312
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	0	0
$325$	−4.00000	−0.221880
$326$	−20.0000	−1.10770
$327$	0	0
$328$	−6.00000	−0.331295
$329$	8.00000	0.441054
$330$	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
$334$	16.0000	0.875481
$335$	12.0000	0.655630
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	2.00000	0.108465
$341$	−4.00000	−0.216612
$342$	0	0
$343$	1.00000	0.0539949
$344$	24.0000	1.29399
$345$	0	0
$346$	4.00000	0.215041
$347$	−36.0000	−1.93258	−0.966291	−	0.257454i	$-0.917117\pi$
$347$	−36.0000	−1.93258	−0.966291	+	0.257454i	$0.917117\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	10.0000	0.533002
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	0	0
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−26.0000	−1.36653
$363$	0	0
$364$	4.00000	0.209657
$365$	−8.00000	−0.418739
$366$	0	0
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	1.00000	0.0521286
$369$	0	0
$370$	−4.00000	−0.207950
$371$	0	0
$372$	0	0
$373$	28.0000	1.44979	0.724893	−	0.688862i	$-0.241889\pi$
$373$	28.0000	1.44979	0.724893	+	0.688862i	$0.241889\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	−24.0000	−1.23771
$377$	−24.0000	−1.23606
$378$	0	0
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	0	0
$381$	0	0
$382$	18.0000	0.920960
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	−2.00000	−0.101929
$386$	22.0000	1.11977
$387$	0	0
$388$	14.0000	0.710742
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	−2.00000	−0.101144
$392$	−3.00000	−0.151523
$393$	0	0
$394$	−18.0000	−0.906827
$395$	−10.0000	−0.503155
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	−20.0000	−1.00251
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	0	0
$403$	8.00000	0.398508
$404$	18.0000	0.895533
$405$	0	0
$406$	6.00000	0.297775
$407$	8.00000	0.396545
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	−2.00000	−0.0987730
$411$	0	0
$412$	−8.00000	−0.394132
$413$	−2.00000	−0.0984136
$414$	0	0
$415$	12.0000	0.589057
$416$	−20.0000	−0.980581
$417$	0	0
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	8.00000	0.389434
$423$	0	0
$424$	0	0
$425$	2.00000	0.0970143
$426$	0	0
$427$	−14.0000	−0.677507
$428$	4.00000	0.193347
$429$	0	0
$430$	8.00000	0.385794
$431$	−10.0000	−0.481683	−0.240842	−	0.970564i	$-0.577423\pi$
$431$	−10.0000	−0.481683	−0.240842	+	0.970564i	$0.577423\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	0	0
$438$	0	0
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	6.00000	0.286039
$441$	0	0
$442$	−8.00000	−0.380521
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	6.00000	0.284427
$446$	16.0000	0.757622
$447$	0	0
$448$	7.00000	0.330719
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	0	0
$451$	4.00000	0.188353
$452$	−8.00000	−0.376288
$453$	0	0
$454$	−4.00000	−0.187729
$455$	4.00000	0.187523
$456$	0	0
$457$	−20.0000	−0.935561	−0.467780	−	0.883845i	$-0.654946\pi$
$457$	−20.0000	−0.935561	−0.467780	+	0.883845i	$0.654946\pi$
$458$	−14.0000	−0.654177
$459$	0	0
$460$	−1.00000	−0.0466252
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−20.0000	−0.925490	−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000	−0.925490	−0.462745	+	0.886492i	$0.653135\pi$
$468$	0	0
$469$	−12.0000	−0.554109
$470$	−8.00000	−0.369012
$471$	0	0
$472$	6.00000	0.276172
$473$	−16.0000	−0.735681
$474$	0	0
$475$	0	0
$476$	−2.00000	−0.0916698
$477$	0	0
$478$	−8.00000	−0.365911
$479$	−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
$481$	−16.0000	−0.729537
$482$	−6.00000	−0.273293
$483$	0	0
$484$	7.00000	0.318182
$485$	14.0000	0.635707
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	42.0000	1.90125
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	0	0
$495$	0	0
$496$	2.00000	0.0898027
$497$	0	0
$498$	0	0
$499$	−24.0000	−1.07439	−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000	−1.07439	−0.537194	+	0.843459i	$0.680516\pi$
$500$	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
$505$	18.0000	0.800989
$506$	−2.00000	−0.0889108
$507$	0	0
$508$	16.0000	0.709885
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	8.00000	0.353899
$512$	−11.0000	−0.486136
$513$	0	0
$514$	0	0
$515$	−8.00000	−0.352522
$516$	0	0
$517$	16.0000	0.703679
$518$	4.00000	0.175750
$519$	0	0
$520$	−12.0000	−0.526235
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	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
$526$	−20.0000	−0.872041
$527$	−4.00000	−0.174243
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−8.00000	−0.346518
$534$	0	0
$535$	4.00000	0.172935
$536$	36.0000	1.55496
$537$	0	0
$538$	−10.0000	−0.431131
$539$	2.00000	0.0861461
$540$	0	0
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−10.0000	−0.429537
$543$	0	0
$544$	10.0000	0.428746
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	−20.0000	−0.854358
$549$	0	0
$550$	2.00000	0.0852803
$551$	0	0
$552$	0	0
$553$	10.0000	0.425243
$554$	10.0000	0.424859
$555$	0	0
$556$	10.0000	0.424094
$557$	−40.0000	−1.69485	−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000	−1.69485	−0.847427	+	0.530912i	$0.821850\pi$
$558$	0	0
$559$	32.0000	1.35346
$560$	1.00000	0.0422577
$561$	0	0
$562$	18.0000	0.759284
$563$	−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
$565$	−8.00000	−0.336563
$566$	4.00000	0.168133
$567$	0	0
$568$	0	0
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	2.00000	0.0834784
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	−8.00000	−0.333044	−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000	−0.333044	−0.166522	+	0.986038i	$0.553254\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	6.00000	0.249136
$581$	−12.0000	−0.497844
$582$	0	0
$583$	0	0
$584$	−24.0000	−0.993127
$585$	0	0
$586$	10.0000	0.413096
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	0	0
$589$	0	0
$590$	2.00000	0.0823387
$591$	0	0
$592$	−4.00000	−0.164399
$593$	−44.0000	−1.80686	−0.903432	−	0.428732i	$-0.858960\pi$
$593$	−44.0000	−1.80686	−0.903432	+	0.428732i	$0.858960\pi$
$594$	0	0
$595$	−2.00000	−0.0819920
$596$	2.00000	0.0819232
$597$	0	0
$598$	4.00000	0.163572
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	−8.00000	−0.326056
$603$	0	0
$604$	20.0000	0.813788
$605$	7.00000	0.284590
$606$	0	0
$607$	36.0000	1.46119	0.730597	−	0.682808i	$-0.239242\pi$
$607$	36.0000	1.46119	0.730597	+	0.682808i	$0.239242\pi$
$608$	0	0
$609$	0	0
$610$	14.0000	0.566843
$611$	−32.0000	−1.29458
$612$	0	0
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−6.00000	−0.241747
$617$	8.00000	0.322068	0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000	0.322068	0.161034	+	0.986949i	$0.448517\pi$
$618$	0	0
$619$	24.0000	0.964641	0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000	0.964641	0.482321	+	0.875995i	$0.339794\pi$
$620$	−2.00000	−0.0803219
$621$	0	0
$622$	6.00000	0.240578
$623$	−6.00000	−0.240385
$624$	0	0
$625$	1.00000	0.0400000
$626$	−26.0000	−1.03917
$627$	0	0
$628$	−10.0000	−0.399043
$629$	8.00000	0.318981
$630$	0	0
$631$	10.0000	0.398094	0.199047	−	0.979990i	$-0.436215\pi$
$631$	10.0000	0.398094	0.199047	+	0.979990i	$0.436215\pi$
$632$	−30.0000	−1.19334
$633$	0	0
$634$	−10.0000	−0.397151
$635$	16.0000	0.634941
$636$	0	0
$637$	−4.00000	−0.158486
$638$	12.0000	0.475085
$639$	0	0
$640$	3.00000	0.118585
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	12.0000	0.473234	0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000	0.473234	0.236617	+	0.971603i	$0.423961\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	0	0
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	0	0
$649$	−4.00000	−0.157014
$650$	−4.00000	−0.156893
$651$	0	0
$652$	20.0000	0.783260
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	−6.00000	−0.234439
$656$	−2.00000	−0.0780869
$657$	0	0
$658$	8.00000	0.311872
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	0	0
$661$	−26.0000	−1.01128	−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000	−1.01128	−0.505641	+	0.862744i	$0.668744\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	36.0000	1.39707
$665$	0	0
$666$	0	0
$667$	−6.00000	−0.232321
$668$	−16.0000	−0.619059
$669$	0	0
$670$	12.0000	0.463600
$671$	−28.0000	−1.08093
$672$	0	0
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	0	0
$675$	0	0
$676$	−3.00000	−0.115385
$677$	14.0000	0.538064	0.269032	−	0.963131i	$-0.413296\pi$
$677$	14.0000	0.538064	0.269032	+	0.963131i	$0.413296\pi$
$678$	0	0
$679$	−14.0000	−0.537271
$680$	6.00000	0.230089
$681$	0	0
$682$	−4.00000	−0.153168
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	0	0
$685$	−20.0000	−0.764161
$686$	1.00000	0.0381802
$687$	0	0
$688$	8.00000	0.304997
$689$	0	0
$690$	0	0
$691$	14.0000	0.532585	0.266293	−	0.963892i	$-0.414201\pi$
$691$	14.0000	0.532585	0.266293	+	0.963892i	$0.414201\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	−36.0000	−1.36654
$695$	10.0000	0.379322
$696$	0	0
$697$	4.00000	0.151511
$698$	−26.0000	−0.984115
$699$	0	0
$700$	−1.00000	−0.0377964
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	0	0
$703$	0	0
$704$	14.0000	0.527645
$705$	0	0
$706$	4.00000	0.150542
$707$	−18.0000	−0.676960
$708$	0	0
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	0	0
$711$	0	0
$712$	18.0000	0.674579
$713$	2.00000	0.0749006
$714$	0	0
$715$	8.00000	0.299183
$716$	4.00000	0.149487
$717$	0	0
$718$	−10.0000	−0.373197
$719$	−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
$721$	8.00000	0.297936
$722$	−19.0000	−0.707107
$723$	0	0
$724$	26.0000	0.966282
$725$	6.00000	0.222834
$726$	0	0
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	12.0000	0.444750
$729$	0	0
$730$	−8.00000	−0.296093
$731$	−16.0000	−0.591781
$732$	0	0
$733$	−42.0000	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$734$	32.0000	1.18114
$735$	0	0
$736$	−5.00000	−0.184302
$737$	−24.0000	−0.884051
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	0	0
$743$	48.0000	1.76095	0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000	1.76095	0.880475	+	0.474093i	$0.157224\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	28.0000	1.02515
$747$	0	0
$748$	−4.00000	−0.146254
$749$	−4.00000	−0.146157
$750$	0	0
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	−8.00000	−0.291730
$753$	0	0
$754$	−24.0000	−0.874028
$755$	20.0000	0.727875
$756$	0	0
$757$	24.0000	0.872295	0.436147	−	0.899875i	$-0.356343\pi$
$757$	24.0000	0.872295	0.436147	+	0.899875i	$0.356343\pi$
$758$	26.0000	0.944363
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	2.00000	0.0724049
$764$	−18.0000	−0.651217
$765$	0	0
$766$	−24.0000	−0.867155
$767$	8.00000	0.288863
$768$	0	0
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	−2.00000	−0.0720750
$771$	0	0
$772$	−22.0000	−0.791797
$773$	−42.0000	−1.51064	−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000	−1.51064	−0.755318	+	0.655359i	$0.772517\pi$
$774$	0	0
$775$	−2.00000	−0.0718421
$776$	42.0000	1.50771
$777$	0	0
$778$	6.00000	0.215110
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−2.00000	−0.0715199
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	−10.0000	−0.356915
$786$	0	0
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	18.0000	0.641223
$789$	0	0
$790$	−10.0000	−0.355784
$791$	8.00000	0.284447
$792$	0	0
$793$	56.0000	1.98862
$794$	0	0
$795$	0	0
$796$	20.0000	0.708881
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	16.0000	0.566039
$800$	5.00000	0.176777
$801$	0	0
$802$	14.0000	0.494357
$803$	16.0000	0.564628
$804$	0	0
$805$	1.00000	0.0352454
$806$	8.00000	0.281788
$807$	0	0
$808$	54.0000	1.89971
$809$	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
$811$	30.0000	1.05344	0.526721	−	0.850038i	$-0.323421\pi$
$811$	30.0000	1.05344	0.526721	+	0.850038i	$0.323421\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	8.00000	0.280400
$815$	20.0000	0.700569
$816$	0	0
$817$	0	0
$818$	34.0000	1.18878
$819$	0	0
$820$	2.00000	0.0698430
$821$	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
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−24.0000	−0.836080
$825$	0	0
$826$	−2.00000	−0.0695889
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	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
$833$	2.00000	0.0692959
$834$	0	0
$835$	−16.0000	−0.553703
$836$	0	0
$837$	0	0
$838$	12.0000	0.414533
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	0	0
$844$	−8.00000	−0.275371
$845$	−3.00000	−0.103203
$846$	0	0
$847$	−7.00000	−0.240523
$848$	0	0
$849$	0	0
$850$	2.00000	0.0685994
$851$	−4.00000	−0.137118
$852$	0	0
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	−14.0000	−0.479070
$855$	0	0
$856$	12.0000	0.410152
$857$	−20.0000	−0.683187	−0.341593	−	0.939848i	$-0.610967\pi$
$857$	−20.0000	−0.683187	−0.341593	+	0.939848i	$0.610967\pi$
$858$	0	0
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−10.0000	−0.340601
$863$	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
$865$	−4.00000	−0.136004
$866$	2.00000	0.0679628
$867$	0	0
$868$	2.00000	0.0678844
$869$	20.0000	0.678454
$870$	0	0
$871$	48.0000	1.62642
$872$	−6.00000	−0.203186
$873$	0	0
$874$	0	0
$875$	−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	$0.216915\pi$
$878$	−14.0000	−0.472477
$879$	0	0
$880$	2.00000	0.0674200
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	8.00000	0.269069
$885$	0	0
$886$	−4.00000	−0.134383
$887$	28.0000	0.940148	0.470074	−	0.882627i	$-0.344227\pi$
$887$	28.0000	0.940148	0.470074	+	0.882627i	$0.344227\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	6.00000	0.201120
$891$	0	0
$892$	−16.0000	−0.535720
$893$	0	0
$894$	0	0
$895$	4.00000	0.133705
$896$	−3.00000	−0.100223
$897$	0	0
$898$	10.0000	0.333704
$899$	−12.0000	−0.400222
$900$	0	0
$901$	0	0
$902$	4.00000	0.133185
$903$	0	0
$904$	−24.0000	−0.798228
$905$	26.0000	0.864269
$906$	0	0
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	4.00000	0.132599
$911$	38.0000	1.25900	0.629498	−	0.777002i	$-0.283261\pi$
$911$	38.0000	1.25900	0.629498	+	0.777002i	$0.283261\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	−20.0000	−0.661541
$915$	0	0
$916$	14.0000	0.462573
$917$	6.00000	0.198137
$918$	0	0
$919$	38.0000	1.25350	0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000	1.25350	0.626752	+	0.779219i	$0.284384\pi$
$920$	−3.00000	−0.0989071
$921$	0	0
$922$	−18.0000	−0.592798
$923$	0	0
$924$	0	0
$925$	4.00000	0.131519
$926$	−8.00000	−0.262896
$927$	0	0
$928$	30.0000	0.984798
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	0	0
$934$	−20.0000	−0.654420
$935$	−4.00000	−0.130814
$936$	0	0
$937$	−14.0000	−0.457360	−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000	−0.457360	−0.228680	+	0.973502i	$0.573441\pi$
$938$	−12.0000	−0.391814
$939$	0	0
$940$	8.00000	0.260931
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	0	0
$943$	−2.00000	−0.0651290
$944$	2.00000	0.0650945
$945$	0	0
$946$	−16.0000	−0.520205
$947$	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
$949$	−32.0000	−1.03876
$950$	0	0
$951$	0	0
$952$	−6.00000	−0.194461
$953$	44.0000	1.42530	0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000	1.42530	0.712650	+	0.701520i	$0.247495\pi$
$954$	0	0
$955$	−18.0000	−0.582466
$956$	8.00000	0.258738
$957$	0	0
$958$	−28.0000	−0.904639
$959$	20.0000	0.645834
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−16.0000	−0.515861
$963$	0	0
$964$	6.00000	0.193247
$965$	−22.0000	−0.708205
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	21.0000	0.674966
$969$	0	0
$970$	14.0000	0.449513
$971$	−56.0000	−1.79713	−0.898563	−	0.438845i	$-0.855388\pi$
$971$	−56.0000	−1.79713	−0.898563	+	0.438845i	$0.855388\pi$
$972$	0	0
$973$	−10.0000	−0.320585
$974$	−8.00000	−0.256337
$975$	0	0
$976$	14.0000	0.448129
$977$	−48.0000	−1.53566	−0.767828	−	0.640656i	$-0.778662\pi$
$977$	−48.0000	−1.53566	−0.767828	+	0.640656i	$0.778662\pi$
$978$	0	0
$979$	−12.0000	−0.383522
$980$	1.00000	0.0319438
$981$	0	0
$982$	12.0000	0.382935
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	0	0
$985$	18.0000	0.573528
$986$	12.0000	0.382158
$987$	0	0
$988$	0	0
$989$	8.00000	0.254385
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	−10.0000	−0.317500
$993$	0	0
$994$	0	0
$995$	20.0000	0.634043
$996$	0	0
$997$	12.0000	0.380044	0.190022	−	0.981780i	$-0.439144\pi$
$997$	12.0000	0.380044	0.190022	+	0.981780i	$0.439144\pi$
$998$	−24.0000	−0.759707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7245.2.a.m.1.1		1
3.2	odd	2		2415.2.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.d.1.1	✓	1	3.2	odd	2
7245.2.a.m.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

Related objects

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