LMFDB - Embedded newform 6534.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6534,2,Mod(1,6534)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6534, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6534.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6534 = 2 \cdot 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6534.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:	$52.1742526807$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 594)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6534.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{10} +2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -2.00000 q^{20} -3.00000 q^{23} -1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{28} +1.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} +1.00000 q^{34} +2.00000 q^{35} +1.00000 q^{37} -2.00000 q^{40} +11.0000 q^{41} -1.00000 q^{43} -3.00000 q^{46} +5.00000 q^{47} -6.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} -4.00000 q^{53} -1.00000 q^{56} +1.00000 q^{58} +3.00000 q^{59} +2.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -12.0000 q^{67} +1.00000 q^{68} +2.00000 q^{70} -8.00000 q^{71} -12.0000 q^{73} +1.00000 q^{74} +17.0000 q^{79} -2.00000 q^{80} +11.0000 q^{82} -14.0000 q^{83} -2.00000 q^{85} -1.00000 q^{86} +2.00000 q^{89} -2.00000 q^{91} -3.00000 q^{92} +5.00000 q^{94} -5.00000 q^{97} -6.00000 q^{98} +O(q^{100})$

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
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−2.00000	−0.632456
$11$	0	0
$11$	0	0
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	−1.00000	−0.188982
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	2.00000	0.338062
$36$	0	0
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	0	0
$39$	0	0
$40$	−2.00000	−0.316228
$41$	11.0000	1.71791	0.858956	−	0.512050i	$-0.171114\pi$
$41$	11.0000	1.71791	0.858956	+	0.512050i	$0.171114\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	0	0
$45$	0	0
$46$	−3.00000	−0.442326
$47$	5.00000	0.729325	0.364662	−	0.931140i	$-0.381184\pi$
$47$	5.00000	0.729325	0.364662	+	0.931140i	$0.381184\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−1.00000	−0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	1.00000	0.131306
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	−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	$0.761888\pi$
$68$	1.00000	0.121268
$69$	0	0
$70$	2.00000	0.239046
$71$	−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
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	17.0000	1.91265	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	17.0000	1.91265	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	11.0000	1.21475
$83$	−14.0000	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−1.00000	−0.107833
$87$	0	0
$88$	0	0
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	−3.00000	−0.312772
$93$	0	0
$94$	5.00000	0.515711
$95$	0	0
$96$	0	0
$97$	−5.00000	−0.507673	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000	−0.507673	−0.253837	+	0.967247i	$0.581693\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−7.00000	−0.696526	−0.348263	−	0.937397i	$-0.613228\pi$
$101$	−7.00000	−0.696526	−0.348263	+	0.937397i	$0.613228\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−4.00000	−0.388514
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	0	0
$115$	6.00000	0.559503
$116$	1.00000	0.0928477
$117$	0	0
$118$	3.00000	0.276172
$119$	−1.00000	−0.0916698
$120$	0	0
$121$	0	0
$122$	2.00000	0.181071
$123$	0	0
$124$	−8.00000	−0.718421
$125$	12.0000	1.07331
$126$	0	0
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−4.00000	−0.350823
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	0	0
$134$	−12.0000	−1.03664
$135$	0	0
$136$	1.00000	0.0857493
$137$	8.00000	0.683486	0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000	0.683486	0.341743	+	0.939793i	$0.388983\pi$
$138$	0	0
$139$	−15.0000	−1.27228	−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000	−1.27228	−0.636142	+	0.771572i	$0.719471\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	−8.00000	−0.671345
$143$	0	0
$144$	0	0
$145$	−2.00000	−0.166091
$146$	−12.0000	−0.993127
$147$	0	0
$148$	1.00000	0.0821995
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	16.0000	1.28515
$156$	0	0
$157$	15.0000	1.19713	0.598565	−	0.801074i	$-0.295738\pi$
$157$	15.0000	1.19713	0.598565	+	0.801074i	$0.295738\pi$
$158$	17.0000	1.35245
$159$	0	0
$160$	−2.00000	−0.158114
$161$	3.00000	0.236433
$162$	0	0
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	11.0000	0.858956
$165$	0	0
$166$	−14.0000	−1.08661
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	0	0
$172$	−1.00000	−0.0762493
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	0	0
$177$	0	0
$178$	2.00000	0.149906
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	0	0
$181$	23.0000	1.70958	0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000	1.70958	0.854788	+	0.518977i	$0.173687\pi$
$182$	−2.00000	−0.148250
$183$	0	0
$184$	−3.00000	−0.221163
$185$	−2.00000	−0.147043
$186$	0	0
$187$	0	0
$188$	5.00000	0.364662
$189$	0	0
$190$	0	0
$191$	−25.0000	−1.80894	−0.904468	−	0.426541i	$-0.859732\pi$
$191$	−25.0000	−1.80894	−0.904468	+	0.426541i	$0.859732\pi$
$192$	0	0
$193$	−26.0000	−1.87152	−0.935760	−	0.352636i	$-0.885285\pi$
$193$	−26.0000	−1.87152	−0.935760	+	0.352636i	$0.885285\pi$
$194$	−5.00000	−0.358979
$195$	0	0
$196$	−6.00000	−0.428571
$197$	−15.0000	−1.06871	−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000	−1.06871	−0.534353	+	0.845262i	$0.679445\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−7.00000	−0.492518
$203$	−1.00000	−0.0701862
$204$	0	0
$205$	−22.0000	−1.53655
$206$	−14.0000	−0.975426
$207$	0	0
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	3.00000	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$212$	−4.00000	−0.274721
$213$	0	0
$214$	6.00000	0.410152
$215$	2.00000	0.136399
$216$	0	0
$217$	8.00000	0.543075
$218$	−14.0000	−0.948200
$219$	0	0
$220$	0	0
$221$	2.00000	0.134535
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	12.0000	0.798228
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	0	0
$229$	−29.0000	−1.91637	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−29.0000	−1.91637	−0.958187	+	0.286143i	$0.907627\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	1.00000	0.0656532
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	−10.0000	−0.652328
$236$	3.00000	0.195283
$237$	0	0
$238$	−1.00000	−0.0648204
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	0	0
$243$	0	0
$244$	2.00000	0.128037
$245$	12.0000	0.766652
$246$	0	0
$247$	0	0
$248$	−8.00000	−0.508001
$249$	0	0
$250$	12.0000	0.758947
$251$	−19.0000	−1.19927	−0.599635	−	0.800274i	$-0.704687\pi$
$251$	−19.0000	−1.19927	−0.599635	+	0.800274i	$0.704687\pi$
$252$	0	0
$253$	0	0
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	0	0
$259$	−1.00000	−0.0621370
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−18.0000	−1.11204
$263$	2.00000	0.123325	0.0616626	−	0.998097i	$-0.480360\pi$
$263$	2.00000	0.123325	0.0616626	+	0.998097i	$0.480360\pi$
$264$	0	0
$265$	8.00000	0.491436
$266$	0	0
$267$	0	0
$268$	−12.0000	−0.733017
$269$	−16.0000	−0.975537	−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000	−0.975537	−0.487769	+	0.872973i	$0.662189\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	8.00000	0.483298
$275$	0	0
$276$	0	0
$277$	16.0000	0.961347	0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000	0.961347	0.480673	+	0.876900i	$0.340392\pi$
$278$	−15.0000	−0.899640
$279$	0	0
$280$	2.00000	0.119523
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	0	0
$287$	−11.0000	−0.649309
$288$	0	0
$289$	−16.0000	−0.941176
$290$	−2.00000	−0.117444
$291$	0	0
$292$	−12.0000	−0.702247
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	0	0
$295$	−6.00000	−0.349334
$296$	1.00000	0.0581238
$297$	0	0
$298$	2.00000	0.115857
$299$	−6.00000	−0.346989
$300$	0	0
$301$	1.00000	0.0576390
$302$	−8.00000	−0.460348
$303$	0	0
$304$	0	0
$305$	−4.00000	−0.229039
$306$	0	0
$307$	7.00000	0.399511	0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000	0.399511	0.199756	+	0.979846i	$0.435985\pi$
$308$	0	0
$309$	0	0
$310$	16.0000	0.908739
$311$	−5.00000	−0.283524	−0.141762	−	0.989901i	$-0.545277\pi$
$311$	−5.00000	−0.283524	−0.141762	+	0.989901i	$0.545277\pi$
$312$	0	0
$313$	30.0000	1.69570	0.847850	−	0.530236i	$-0.177897\pi$
$313$	30.0000	1.69570	0.847850	+	0.530236i	$0.177897\pi$
$314$	15.0000	0.846499
$315$	0	0
$316$	17.0000	0.956325
$317$	−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
$319$	0	0
$320$	−2.00000	−0.111803
$321$	0	0
$322$	3.00000	0.167183
$323$	0	0
$324$	0	0
$325$	−2.00000	−0.110940
$326$	−2.00000	−0.110770
$327$	0	0
$328$	11.0000	0.607373
$329$	−5.00000	−0.275659
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−14.0000	−0.768350
$333$	0	0
$334$	−6.00000	−0.328305
$335$	24.0000	1.31126
$336$	0	0
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	−2.00000	−0.108465
$341$	0	0
$342$	0	0
$343$	13.0000	0.701934
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	6.00000	0.322562
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	0	0
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	0	0
$355$	16.0000	0.849192
$356$	2.00000	0.106000
$357$	0	0
$358$	−9.00000	−0.475665
$359$	34.0000	1.79445	0.897226	−	0.441572i	$-0.145579\pi$
$359$	34.0000	1.79445	0.897226	+	0.441572i	$0.145579\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	23.0000	1.20885
$363$	0	0
$364$	−2.00000	−0.104828
$365$	24.0000	1.25622
$366$	0	0
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−3.00000	−0.156386
$369$	0	0
$370$	−2.00000	−0.103975
$371$	4.00000	0.207670
$372$	0	0
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	0	0
$375$	0	0
$376$	5.00000	0.257855
$377$	2.00000	0.103005
$378$	0	0
$379$	34.0000	1.74646	0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000	1.74646	0.873231	+	0.487306i	$0.162020\pi$
$380$	0	0
$381$	0	0
$382$	−25.0000	−1.27911
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−26.0000	−1.32337
$387$	0	0
$388$	−5.00000	−0.253837
$389$	−22.0000	−1.11544	−0.557722	−	0.830028i	$-0.688325\pi$
$389$	−22.0000	−1.11544	−0.557722	+	0.830028i	$0.688325\pi$
$390$	0	0
$391$	−3.00000	−0.151717
$392$	−6.00000	−0.303046
$393$	0	0
$394$	−15.0000	−0.755689
$395$	−34.0000	−1.71073
$396$	0	0
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−30.0000	−1.49813	−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000	−1.49813	−0.749064	+	0.662497i	$0.769497\pi$
$402$	0	0
$403$	−16.0000	−0.797017
$404$	−7.00000	−0.348263
$405$	0	0
$406$	−1.00000	−0.0496292
$407$	0	0
$408$	0	0
$409$	−8.00000	−0.395575	−0.197787	−	0.980245i	$-0.563376\pi$
$409$	−8.00000	−0.395575	−0.197787	+	0.980245i	$0.563376\pi$
$410$	−22.0000	−1.08650
$411$	0	0
$412$	−14.0000	−0.689730
$413$	−3.00000	−0.147620
$414$	0	0
$415$	28.0000	1.37447
$416$	2.00000	0.0980581
$417$	0	0
$418$	0	0
$419$	−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
$421$	21.0000	1.02348	0.511739	−	0.859141i	$-0.329002\pi$
$421$	21.0000	1.02348	0.511739	+	0.859141i	$0.329002\pi$
$422$	3.00000	0.146038
$423$	0	0
$424$	−4.00000	−0.194257
$425$	−1.00000	−0.0485071
$426$	0	0
$427$	−2.00000	−0.0967868
$428$	6.00000	0.290021
$429$	0	0
$430$	2.00000	0.0964486
$431$	26.0000	1.25238	0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000	1.25238	0.626188	+	0.779672i	$0.284614\pi$
$432$	0	0
$433$	−3.00000	−0.144171	−0.0720854	−	0.997398i	$-0.522965\pi$
$433$	−3.00000	−0.144171	−0.0720854	+	0.997398i	$0.522965\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	−14.0000	−0.670478
$437$	0	0
$438$	0	0
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	0	0
$441$	0	0
$442$	2.00000	0.0951303
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	−4.00000	−0.189618
$446$	−4.00000	−0.189405
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	24.0000	1.13263	0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000	1.13263	0.566315	+	0.824189i	$0.308369\pi$
$450$	0	0
$451$	0	0
$452$	12.0000	0.564433
$453$	0	0
$454$	18.0000	0.844782
$455$	4.00000	0.187523
$456$	0	0
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	−29.0000	−1.35508
$459$	0	0
$460$	6.00000	0.279751
$461$	42.0000	1.95614	0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000	1.95614	0.978068	+	0.208288i	$0.0667892\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	6.00000	0.277945
$467$	−13.0000	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$468$	0	0
$469$	12.0000	0.554109
$470$	−10.0000	−0.461266
$471$	0	0
$472$	3.00000	0.138086
$473$	0	0
$474$	0	0
$475$	0	0
$476$	−1.00000	−0.0458349
$477$	0	0
$478$	4.00000	0.182956
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	−18.0000	−0.819878
$483$	0	0
$484$	0	0
$485$	10.0000	0.454077
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	2.00000	0.0905357
$489$	0	0
$490$	12.0000	0.542105
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	0	0
$493$	1.00000	0.0450377
$494$	0	0
$495$	0	0
$496$	−8.00000	−0.359211
$497$	8.00000	0.358849
$498$	0	0
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	−19.0000	−0.848012
$503$	−26.0000	−1.15928	−0.579641	−	0.814872i	$-0.696807\pi$
$503$	−26.0000	−1.15928	−0.579641	+	0.814872i	$0.696807\pi$
$504$	0	0
$505$	14.0000	0.622992
$506$	0	0
$507$	0	0
$508$	4.00000	0.177471
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	1.00000	0.0441942
$513$	0	0
$514$	−18.0000	−0.793946
$515$	28.0000	1.23383
$516$	0	0
$517$	0	0
$518$	−1.00000	−0.0439375
$519$	0	0
$520$	−4.00000	−0.175412
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	0	0
$523$	19.0000	0.830812	0.415406	−	0.909636i	$-0.363640\pi$
$523$	19.0000	0.830812	0.415406	+	0.909636i	$0.363640\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	2.00000	0.0872041
$527$	−8.00000	−0.348485
$528$	0	0
$529$	−14.0000	−0.608696
$530$	8.00000	0.347498
$531$	0	0
$532$	0	0
$533$	22.0000	0.952926
$534$	0	0
$535$	−12.0000	−0.518805
$536$	−12.0000	−0.518321
$537$	0	0
$538$	−16.0000	−0.689809
$539$	0	0
$540$	0	0
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	−1.00000	−0.0429537
$543$	0	0
$544$	1.00000	0.0428746
$545$	28.0000	1.19939
$546$	0	0
$547$	−13.0000	−0.555840	−0.277920	−	0.960604i	$-0.589645\pi$
$547$	−13.0000	−0.555840	−0.277920	+	0.960604i	$0.589645\pi$
$548$	8.00000	0.341743
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−17.0000	−0.722914
$554$	16.0000	0.679775
$555$	0	0
$556$	−15.0000	−0.636142
$557$	−13.0000	−0.550828	−0.275414	−	0.961326i	$-0.588815\pi$
$557$	−13.0000	−0.550828	−0.275414	+	0.961326i	$0.588815\pi$
$558$	0	0
$559$	−2.00000	−0.0845910
$560$	2.00000	0.0845154
$561$	0	0
$562$	7.00000	0.295277
$563$	−18.0000	−0.758610	−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000	−0.758610	−0.379305	+	0.925272i	$0.623837\pi$
$564$	0	0
$565$	−24.0000	−1.00969
$566$	−4.00000	−0.168133
$567$	0	0
$568$	−8.00000	−0.335673
$569$	38.0000	1.59304	0.796521	−	0.604610i	$-0.206671\pi$
$569$	38.0000	1.59304	0.796521	+	0.604610i	$0.206671\pi$
$570$	0	0
$571$	−35.0000	−1.46470	−0.732352	−	0.680926i	$-0.761578\pi$
$571$	−35.0000	−1.46470	−0.732352	+	0.680926i	$0.761578\pi$
$572$	0	0
$573$	0	0
$574$	−11.0000	−0.459131
$575$	3.00000	0.125109
$576$	0	0
$577$	1.00000	0.0416305	0.0208153	−	0.999783i	$-0.493374\pi$
$577$	1.00000	0.0416305	0.0208153	+	0.999783i	$0.493374\pi$
$578$	−16.0000	−0.665512
$579$	0	0
$580$	−2.00000	−0.0830455
$581$	14.0000	0.580818
$582$	0	0
$583$	0	0
$584$	−12.0000	−0.496564
$585$	0	0
$586$	2.00000	0.0826192
$587$	−29.0000	−1.19696	−0.598479	−	0.801138i	$-0.704228\pi$
$587$	−29.0000	−1.19696	−0.598479	+	0.801138i	$0.704228\pi$
$588$	0	0
$589$	0	0
$590$	−6.00000	−0.247016
$591$	0	0
$592$	1.00000	0.0410997
$593$	−37.0000	−1.51941	−0.759704	−	0.650269i	$-0.774656\pi$
$593$	−37.0000	−1.51941	−0.759704	+	0.650269i	$0.774656\pi$
$594$	0	0
$595$	2.00000	0.0819920
$596$	2.00000	0.0819232
$597$	0	0
$598$	−6.00000	−0.245358
$599$	39.0000	1.59350	0.796748	−	0.604311i	$-0.206552\pi$
$599$	39.0000	1.59350	0.796748	+	0.604311i	$0.206552\pi$
$600$	0	0
$601$	12.0000	0.489490	0.244745	−	0.969587i	$-0.421296\pi$
$601$	12.0000	0.489490	0.244745	+	0.969587i	$0.421296\pi$
$602$	1.00000	0.0407570
$603$	0	0
$604$	−8.00000	−0.325515
$605$	0	0
$606$	0	0
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	0	0
$609$	0	0
$610$	−4.00000	−0.161955
$611$	10.0000	0.404557
$612$	0	0
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	7.00000	0.282497
$615$	0	0
$616$	0	0
$617$	−20.0000	−0.805170	−0.402585	−	0.915383i	$-0.631888\pi$
$617$	−20.0000	−0.805170	−0.402585	+	0.915383i	$0.631888\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	16.0000	0.642575
$621$	0	0
$622$	−5.00000	−0.200482
$623$	−2.00000	−0.0801283
$624$	0	0
$625$	−19.0000	−0.760000
$626$	30.0000	1.19904
$627$	0	0
$628$	15.0000	0.598565
$629$	1.00000	0.0398726
$630$	0	0
$631$	6.00000	0.238856	0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000	0.238856	0.119428	+	0.992843i	$0.461894\pi$
$632$	17.0000	0.676224
$633$	0	0
$634$	−10.0000	−0.397151
$635$	−8.00000	−0.317470
$636$	0	0
$637$	−12.0000	−0.475457
$638$	0	0
$639$	0	0
$640$	−2.00000	−0.0790569
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	0	0
$643$	2.00000	0.0788723	0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000	0.0788723	0.0394362	+	0.999222i	$0.487444\pi$
$644$	3.00000	0.118217
$645$	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
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−2.00000	−0.0783260
$653$	12.0000	0.469596	0.234798	−	0.972044i	$-0.424557\pi$
$653$	12.0000	0.469596	0.234798	+	0.972044i	$0.424557\pi$
$654$	0	0
$655$	36.0000	1.40664
$656$	11.0000	0.429478
$657$	0	0
$658$	−5.00000	−0.194920
$659$	28.0000	1.09073	0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000	1.09073	0.545363	+	0.838200i	$0.316392\pi$
$660$	0	0
$661$	3.00000	0.116686	0.0583432	−	0.998297i	$-0.481418\pi$
$661$	3.00000	0.116686	0.0583432	+	0.998297i	$0.481418\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	−14.0000	−0.543305
$665$	0	0
$666$	0	0
$667$	−3.00000	−0.116160
$668$	−6.00000	−0.232147
$669$	0	0
$670$	24.0000	0.927201
$671$	0	0
$672$	0	0
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−7.00000	−0.269032	−0.134516	−	0.990911i	$-0.542948\pi$
$677$	−7.00000	−0.269032	−0.134516	+	0.990911i	$0.542948\pi$
$678$	0	0
$679$	5.00000	0.191882
$680$	−2.00000	−0.0766965
$681$	0	0
$682$	0	0
$683$	−47.0000	−1.79841	−0.899203	−	0.437533i	$-0.855852\pi$
$683$	−47.0000	−1.79841	−0.899203	+	0.437533i	$0.855852\pi$
$684$	0	0
$685$	−16.0000	−0.611329
$686$	13.0000	0.496342
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	−8.00000	−0.304776
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	0	0
$695$	30.0000	1.13796
$696$	0	0
$697$	11.0000	0.416655
$698$	2.00000	0.0757011
$699$	0	0
$700$	1.00000	0.0377964
$701$	15.0000	0.566542	0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000	0.566542	0.283271	+	0.959040i	$0.408580\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	30.0000	1.12906
$707$	7.00000	0.263262
$708$	0	0
$709$	−41.0000	−1.53979	−0.769894	−	0.638172i	$-0.779691\pi$
$709$	−41.0000	−1.53979	−0.769894	+	0.638172i	$0.779691\pi$
$710$	16.0000	0.600469
$711$	0	0
$712$	2.00000	0.0749532
$713$	24.0000	0.898807
$714$	0	0
$715$	0	0
$716$	−9.00000	−0.336346
$717$	0	0
$718$	34.0000	1.26887
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	0	0
$721$	14.0000	0.521387
$722$	−19.0000	−0.707107
$723$	0	0
$724$	23.0000	0.854788
$725$	−1.00000	−0.0371391
$726$	0	0
$727$	−44.0000	−1.63187	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000	−1.63187	−0.815935	+	0.578144i	$0.803777\pi$
$728$	−2.00000	−0.0741249
$729$	0	0
$730$	24.0000	0.888280
$731$	−1.00000	−0.0369863
$732$	0	0
$733$	32.0000	1.18195	0.590973	−	0.806691i	$-0.298744\pi$
$733$	32.0000	1.18195	0.590973	+	0.806691i	$0.298744\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	−3.00000	−0.110581
$737$	0	0
$738$	0	0
$739$	−29.0000	−1.06678	−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000	−1.06678	−0.533391	+	0.845869i	$0.679083\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	4.00000	0.146845
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	0	0
$745$	−4.00000	−0.146549
$746$	−16.0000	−0.585802
$747$	0	0
$748$	0	0
$749$	−6.00000	−0.219235
$750$	0	0
$751$	−26.0000	−0.948753	−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000	−0.948753	−0.474377	+	0.880322i	$0.657327\pi$
$752$	5.00000	0.182331
$753$	0	0
$754$	2.00000	0.0728357
$755$	16.0000	0.582300
$756$	0	0
$757$	9.00000	0.327111	0.163555	−	0.986534i	$-0.447704\pi$
$757$	9.00000	0.327111	0.163555	+	0.986534i	$0.447704\pi$
$758$	34.0000	1.23494
$759$	0	0
$760$	0	0
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	0	0
$763$	14.0000	0.506834
$764$	−25.0000	−0.904468
$765$	0	0
$766$	24.0000	0.867155
$767$	6.00000	0.216647
$768$	0	0
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	0	0
$772$	−26.0000	−0.935760
$773$	32.0000	1.15096	0.575480	−	0.817816i	$-0.304815\pi$
$773$	32.0000	1.15096	0.575480	+	0.817816i	$0.304815\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	−5.00000	−0.179490
$777$	0	0
$778$	−22.0000	−0.788738
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−3.00000	−0.107280
$783$	0	0
$784$	−6.00000	−0.214286
$785$	−30.0000	−1.07075
$786$	0	0
$787$	−20.0000	−0.712923	−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000	−0.712923	−0.356462	+	0.934310i	$0.616017\pi$
$788$	−15.0000	−0.534353
$789$	0	0
$790$	−34.0000	−1.20967
$791$	−12.0000	−0.426671
$792$	0	0
$793$	4.00000	0.142044
$794$	−6.00000	−0.212932
$795$	0	0
$796$	−16.0000	−0.567105
$797$	−28.0000	−0.991811	−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000	−0.991811	−0.495905	+	0.868377i	$0.665164\pi$
$798$	0	0
$799$	5.00000	0.176887
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−30.0000	−1.05934
$803$	0	0
$804$	0	0
$805$	−6.00000	−0.211472
$806$	−16.0000	−0.563576
$807$	0	0
$808$	−7.00000	−0.246259
$809$	37.0000	1.30085	0.650425	−	0.759570i	$-0.274591\pi$
$809$	37.0000	1.30085	0.650425	+	0.759570i	$0.274591\pi$
$810$	0	0
$811$	−33.0000	−1.15879	−0.579393	−	0.815048i	$-0.696710\pi$
$811$	−33.0000	−1.15879	−0.579393	+	0.815048i	$0.696710\pi$
$812$	−1.00000	−0.0350931
$813$	0	0
$814$	0	0
$815$	4.00000	0.140114
$816$	0	0
$817$	0	0
$818$	−8.00000	−0.279713
$819$	0	0
$820$	−22.0000	−0.768273
$821$	37.0000	1.29131	0.645654	−	0.763630i	$-0.276585\pi$
$821$	37.0000	1.29131	0.645654	+	0.763630i	$0.276585\pi$
$822$	0	0
$823$	−24.0000	−0.836587	−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000	−0.836587	−0.418294	+	0.908312i	$0.637372\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	−3.00000	−0.104383
$827$	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
$829$	21.0000	0.729360	0.364680	−	0.931133i	$-0.381178\pi$
$829$	21.0000	0.729360	0.364680	+	0.931133i	$0.381178\pi$
$830$	28.0000	0.971894
$831$	0	0
$832$	2.00000	0.0693375
$833$	−6.00000	−0.207888
$834$	0	0
$835$	12.0000	0.415277
$836$	0	0
$837$	0	0
$838$	−12.0000	−0.414533
$839$	27.0000	0.932144	0.466072	−	0.884747i	$-0.345669\pi$
$839$	27.0000	0.932144	0.466072	+	0.884747i	$0.345669\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	21.0000	0.723708
$843$	0	0
$844$	3.00000	0.103264
$845$	18.0000	0.619219
$846$	0	0
$847$	0	0
$848$	−4.00000	−0.137361
$849$	0	0
$850$	−1.00000	−0.0342997
$851$	−3.00000	−0.102839
$852$	0	0
$853$	−24.0000	−0.821744	−0.410872	−	0.911693i	$-0.634776\pi$
$853$	−24.0000	−0.821744	−0.410872	+	0.911693i	$0.634776\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	6.00000	0.205076
$857$	53.0000	1.81045	0.905223	−	0.424937i	$-0.139704\pi$
$857$	53.0000	1.81045	0.905223	+	0.424937i	$0.139704\pi$
$858$	0	0
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	2.00000	0.0681994
$861$	0	0
$862$	26.0000	0.885564
$863$	−33.0000	−1.12333	−0.561667	−	0.827364i	$-0.689840\pi$
$863$	−33.0000	−1.12333	−0.561667	+	0.827364i	$0.689840\pi$
$864$	0	0
$865$	−12.0000	−0.408012
$866$	−3.00000	−0.101944
$867$	0	0
$868$	8.00000	0.271538
$869$	0	0
$870$	0	0
$871$	−24.0000	−0.813209
$872$	−14.0000	−0.474100
$873$	0	0
$874$	0	0
$875$	−12.0000	−0.405674
$876$	0	0
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	35.0000	1.18119
$879$	0	0
$880$	0	0
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	0	0
$883$	50.0000	1.68263	0.841317	−	0.540542i	$-0.181781\pi$
$883$	50.0000	1.68263	0.841317	+	0.540542i	$0.181781\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	24.0000	0.806296
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	0	0
$889$	−4.00000	−0.134156
$890$	−4.00000	−0.134080
$891$	0	0
$892$	−4.00000	−0.133930
$893$	0	0
$894$	0	0
$895$	18.0000	0.601674
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	24.0000	0.800890
$899$	−8.00000	−0.266815
$900$	0	0
$901$	−4.00000	−0.133259
$902$	0	0
$903$	0	0
$904$	12.0000	0.399114
$905$	−46.0000	−1.52909
$906$	0	0
$907$	−6.00000	−0.199227	−0.0996134	−	0.995026i	$-0.531761\pi$
$907$	−6.00000	−0.199227	−0.0996134	+	0.995026i	$0.531761\pi$
$908$	18.0000	0.597351
$909$	0	0
$910$	4.00000	0.132599
$911$	−35.0000	−1.15960	−0.579801	−	0.814758i	$-0.696870\pi$
$911$	−35.0000	−1.15960	−0.579801	+	0.814758i	$0.696870\pi$
$912$	0	0
$913$	0	0
$914$	2.00000	0.0661541
$915$	0	0
$916$	−29.0000	−0.958187
$917$	18.0000	0.594412
$918$	0	0
$919$	−23.0000	−0.758700	−0.379350	−	0.925253i	$-0.623852\pi$
$919$	−23.0000	−0.758700	−0.379350	+	0.925253i	$0.623852\pi$
$920$	6.00000	0.197814
$921$	0	0
$922$	42.0000	1.38320
$923$	−16.0000	−0.526646
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	4.00000	0.131448
$927$	0	0
$928$	1.00000	0.0328266
$929$	48.0000	1.57483	0.787414	−	0.616424i	$-0.211419\pi$
$929$	48.0000	1.57483	0.787414	+	0.616424i	$0.211419\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	0	0
$934$	−13.0000	−0.425373
$935$	0	0
$936$	0	0
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	12.0000	0.391814
$939$	0	0
$940$	−10.0000	−0.326164
$941$	−3.00000	−0.0977972	−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000	−0.0977972	−0.0488986	+	0.998804i	$0.515571\pi$
$942$	0	0
$943$	−33.0000	−1.07463
$944$	3.00000	0.0976417
$945$	0	0
$946$	0	0
$947$	−40.0000	−1.29983	−0.649913	−	0.760009i	$-0.725195\pi$
$947$	−40.0000	−1.29983	−0.649913	+	0.760009i	$0.725195\pi$
$948$	0	0
$949$	−24.0000	−0.779073
$950$	0	0
$951$	0	0
$952$	−1.00000	−0.0324102
$953$	−39.0000	−1.26333	−0.631667	−	0.775240i	$-0.717629\pi$
$953$	−39.0000	−1.26333	−0.631667	+	0.775240i	$0.717629\pi$
$954$	0	0
$955$	50.0000	1.61796
$956$	4.00000	0.129369
$957$	0	0
$958$	−20.0000	−0.646171
$959$	−8.00000	−0.258333
$960$	0	0
$961$	33.0000	1.06452
$962$	2.00000	0.0644826
$963$	0	0
$964$	−18.0000	−0.579741
$965$	52.0000	1.67394
$966$	0	0
$967$	−11.0000	−0.353736	−0.176868	−	0.984235i	$-0.556597\pi$
$967$	−11.0000	−0.353736	−0.176868	+	0.984235i	$0.556597\pi$
$968$	0	0
$969$	0	0
$970$	10.0000	0.321081
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	15.0000	0.480878
$974$	−8.00000	−0.256337
$975$	0	0
$976$	2.00000	0.0640184
$977$	−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
$979$	0	0
$980$	12.0000	0.383326
$981$	0	0
$982$	6.00000	0.191468
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	0	0
$985$	30.0000	0.955879
$986$	1.00000	0.0318465
$987$	0	0
$988$	0	0
$989$	3.00000	0.0953945
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	8.00000	0.253745
$995$	32.0000	1.01447
$996$	0	0
$997$	40.0000	1.26681	0.633406	−	0.773819i	$-0.281656\pi$
$997$	40.0000	1.26681	0.633406	+	0.773819i	$0.281656\pi$
$998$	−14.0000	−0.443162
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6534.2.a.t.1.1		1
3.2	odd	2		6534.2.a.k.1.1		1
11.10	odd	2		594.2.a.c.1.1	✓	1
33.32	even	2		594.2.a.g.1.1	yes	1
44.43	even	2		4752.2.a.d.1.1		1
99.32	even	6		1782.2.e.c.1189.1		2
99.43	odd	6		1782.2.e.t.595.1		2
99.65	even	6		1782.2.e.c.595.1		2
99.76	odd	6		1782.2.e.t.1189.1		2
132.131	odd	2		4752.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.a.c.1.1	✓	1	11.10	odd	2
594.2.a.g.1.1	yes	1	33.32	even	2
1782.2.e.c.595.1		2	99.65	even	6
1782.2.e.c.1189.1		2	99.32	even	6
1782.2.e.t.595.1		2	99.43	odd	6
1782.2.e.t.1189.1		2	99.76	odd	6
4752.2.a.d.1.1		1	44.43	even	2
4752.2.a.n.1.1		1	132.131	odd	2
6534.2.a.k.1.1		1	3.2	odd	2
6534.2.a.t.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:	\( N \)	\(=\)	\( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6534.a (trivial)

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