LMFDB - Embedded newform 594.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [594,2,Mod(1,594)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(594, 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("594.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 594 = 2 \cdot 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	594.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:	$4.74311388006$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	594.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{10} +1.00000 q^{11} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} +2.00000 q^{20} +1.00000 q^{22} +3.00000 q^{23} -1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{28} +1.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} +1.00000 q^{34} +2.00000 q^{35} +1.00000 q^{37} +2.00000 q^{40} +11.0000 q^{41} +1.00000 q^{43} +1.00000 q^{44} +3.00000 q^{46} -5.00000 q^{47} -6.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} +4.00000 q^{53} +2.00000 q^{55} +1.00000 q^{56} +1.00000 q^{58} -3.00000 q^{59} -2.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -12.0000 q^{67} +1.00000 q^{68} +2.00000 q^{70} +8.00000 q^{71} +12.0000 q^{73} +1.00000 q^{74} +1.00000 q^{77} -17.0000 q^{79} +2.00000 q^{80} +11.0000 q^{82} -14.0000 q^{83} +2.00000 q^{85} +1.00000 q^{86} +1.00000 q^{88} -2.00000 q^{89} -2.00000 q^{91} +3.00000 q^{92} -5.00000 q^{94} -5.00000 q^{97} -6.00000 q^{98} +O(q^{100})$

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	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	2.00000	0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	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
$22$	1.00000	0.213201
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	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	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	3.00000	0.442326
$47$	−5.00000	−0.729325	−0.364662	−	0.931140i	$-0.618816\pi$
$47$	−5.00000	−0.729325	−0.364662	+	0.931140i	$0.618816\pi$
$48$	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	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	2.00000	0.269680
$56$	1.00000	0.133631
$57$	0	0
$58$	1.00000	0.131306
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−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	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	0	0
$73$	12.0000	1.40449	0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000	1.40449	0.702247	+	0.711934i	$0.252180\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	0	0
$77$	1.00000	0.113961
$78$	0	0
$79$	−17.0000	−1.91265	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−17.0000	−1.91265	−0.956325	+	0.292306i	$0.905577\pi$
$80$	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
$88$	1.00000	0.106600
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	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	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	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
$115$	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
$121$	1.00000	0.0909091
$122$	−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	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	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	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	0	0
$139$	15.0000	1.27228	0.636142	−	0.771572i	$-0.280529\pi$
$139$	15.0000	1.27228	0.636142	+	0.771572i	$0.280529\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	8.00000	0.671345
$143$	−2.00000	−0.167248
$144$	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	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	0	0
$153$	0	0
$154$	1.00000	0.0805823
$155$	−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
$176$	1.00000	0.0753778
$177$	0	0
$178$	−2.00000	−0.149906
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	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
$187$	1.00000	0.0731272
$188$	−5.00000	−0.364662
$189$	0	0
$190$	0	0
$191$	25.0000	1.80894	0.904468	−	0.426541i	$-0.140268\pi$
$191$	25.0000	1.80894	0.904468	+	0.426541i	$0.140268\pi$
$192$	0	0
$193$	26.0000	1.87152	0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000	1.87152	0.935760	+	0.352636i	$0.114715\pi$
$194$	−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	$-0.532929\pi$
$211$	−3.00000	−0.206529	−0.103264	+	0.994654i	$0.532929\pi$
$212$	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
$220$	2.00000	0.134840
$221$	−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	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	1.00000	0.0642824
$243$	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	$-0.295313\pi$
$251$	19.0000	1.19927	0.599635	+	0.800274i	$0.295313\pi$
$252$	0	0
$253$	3.00000	0.188608
$254$	−4.00000	−0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	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	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	0	0
$271$	1.00000	0.0607457	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	1.00000	0.0607457	0.0303728	+	0.999539i	$0.490331\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−8.00000	−0.483298
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	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	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	−2.00000	−0.118262
$287$	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	$-0.564015\pi$
$307$	−7.00000	−0.399511	−0.199756	+	0.979846i	$0.564015\pi$
$308$	1.00000	0.0569803
$309$	0	0
$310$	−16.0000	−0.908739
$311$	5.00000	0.283524	0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000	0.283524	0.141762	+	0.989901i	$0.454723\pi$
$312$	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	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	0	0
$319$	1.00000	0.0559893
$320$	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	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	2.00000	0.108465
$341$	−8.00000	−0.433224
$342$	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	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	1.00000	0.0533002
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	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	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	1.00000	0.0517088
$375$	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	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	2.00000	0.101929
$386$	26.0000	1.32337
$387$	0	0
$388$	−5.00000	−0.253837
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	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	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	16.0000	0.797017
$404$	−7.00000	−0.348263
$405$	0	0
$406$	1.00000	0.0496292
$407$	1.00000	0.0495682
$408$	0	0
$409$	8.00000	0.395575	0.197787	−	0.980245i	$-0.436624\pi$
$409$	8.00000	0.395575	0.197787	+	0.980245i	$0.436624\pi$
$410$	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	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	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	$-0.814665\pi$
$439$	−35.0000	−1.67046	−0.835229	+	0.549902i	$0.814665\pi$
$440$	2.00000	0.0953463
$441$	0	0
$442$	−2.00000	−0.0951303
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	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	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	11.0000	0.517970
$452$	−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	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−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	$-0.402752\pi$
$467$	13.0000	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$468$	0	0
$469$	−12.0000	−0.554109
$470$	−10.0000	−0.461266
$471$	0	0
$472$	−3.00000	−0.138086
$473$	1.00000	0.0459800
$474$	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
$484$	1.00000	0.0454545
$485$	−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
$506$	3.00000	0.133366
$507$	0	0
$508$	−4.00000	−0.177471
$509$	−26.0000	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$509$	−26.0000	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$510$	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
$517$	−5.00000	−0.219900
$518$	1.00000	0.0439375
$519$	0	0
$520$	−4.00000	−0.175412
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	0	0
$523$	−19.0000	−0.830812	−0.415406	−	0.909636i	$-0.636360\pi$
$523$	−19.0000	−0.830812	−0.415406	+	0.909636i	$0.636360\pi$
$524$	−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
$539$	−6.00000	−0.258438
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	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	$-0.410355\pi$
$547$	13.0000	0.555840	0.277920	+	0.960604i	$0.410355\pi$
$548$	−8.00000	−0.341743
$549$	0	0
$550$	−1.00000	−0.0426401
$551$	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	$-0.238422\pi$
$571$	35.0000	1.46470	0.732352	+	0.680926i	$0.238422\pi$
$572$	−2.00000	−0.0836242
$573$	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
$583$	4.00000	0.165663
$584$	12.0000	0.496564
$585$	0	0
$586$	2.00000	0.0826192
$587$	29.0000	1.19696	0.598479	−	0.801138i	$-0.295772\pi$
$587$	29.0000	1.19696	0.598479	+	0.801138i	$0.295772\pi$
$588$	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	$-0.793448\pi$
$599$	−39.0000	−1.59350	−0.796748	+	0.604311i	$0.793448\pi$
$600$	0	0
$601$	−12.0000	−0.489490	−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000	−0.489490	−0.244745	+	0.969587i	$0.578704\pi$
$602$	1.00000	0.0407570
$603$	0	0
$604$	8.00000	0.325515
$605$	2.00000	0.0813116
$606$	0	0
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	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	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	−7.00000	−0.282497
$615$	0	0
$616$	1.00000	0.0402911
$617$	20.0000	0.805170	0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000	0.805170	0.402585	+	0.915383i	$0.368112\pi$
$618$	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
$638$	1.00000	0.0395904
$639$	0	0
$640$	2.00000	0.0790569
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	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	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	0	0
$649$	−3.00000	−0.117760
$650$	2.00000	0.0784465
$651$	0	0
$652$	−2.00000	−0.0783260
$653$	−12.0000	−0.469596	−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000	−0.469596	−0.234798	+	0.972044i	$0.575443\pi$
$654$	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
$671$	−2.00000	−0.0772091
$672$	0	0
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	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
$682$	−8.00000	−0.306336
$683$	47.0000	1.79841	0.899203	−	0.437533i	$-0.144148\pi$
$683$	47.0000	1.79841	0.899203	+	0.437533i	$0.144148\pi$
$684$	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
$704$	1.00000	0.0376889
$705$	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
$715$	−4.00000	−0.149592
$716$	9.00000	0.336346
$717$	0	0
$718$	34.0000	1.26887
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	0	0
$721$	−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	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	3.00000	0.110581
$737$	−12.0000	−0.442026
$738$	0	0
$739$	29.0000	1.06678	0.533391	−	0.845869i	$-0.320917\pi$
$739$	29.0000	1.06678	0.533391	+	0.845869i	$0.320917\pi$
$740$	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
$748$	1.00000	0.0365636
$749$	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	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	2.00000	0.0720750
$771$	0	0
$772$	26.0000	0.935760
$773$	−32.0000	−1.15096	−0.575480	−	0.817816i	$-0.695185\pi$
$773$	−32.0000	−1.15096	−0.575480	+	0.817816i	$0.695185\pi$
$774$	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
$781$	8.00000	0.286263
$782$	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	$-0.383983\pi$
$787$	20.0000	0.712923	0.356462	+	0.934310i	$0.383983\pi$
$788$	−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	$-0.334836\pi$
$797$	28.0000	0.991811	0.495905	+	0.868377i	$0.334836\pi$
$798$	0	0
$799$	−5.00000	−0.176887
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	30.0000	1.05934
$803$	12.0000	0.423471
$804$	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	$-0.303290\pi$
$811$	33.0000	1.15879	0.579393	+	0.815048i	$0.303290\pi$
$812$	1.00000	0.0350931
$813$	0	0
$814$	1.00000	0.0350500
$815$	−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	$-0.654331\pi$
$839$	−27.0000	−0.932144	−0.466072	+	0.884747i	$0.654331\pi$
$840$	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
$847$	1.00000	0.0343604
$848$	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	$-0.365224\pi$
$853$	24.0000	0.821744	0.410872	+	0.911693i	$0.365224\pi$
$854$	−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	$-0.310160\pi$
$863$	33.0000	1.12333	0.561667	+	0.827364i	$0.310160\pi$
$864$	0	0
$865$	12.0000	0.408012
$866$	−3.00000	−0.101944
$867$	0	0
$868$	−8.00000	−0.271538
$869$	−17.0000	−0.576686
$870$	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	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−35.0000	−1.18119
$879$	0	0
$880$	2.00000	0.0674200
$881$	−2.00000	−0.0673817	−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000	−0.0673817	−0.0336909	+	0.999432i	$0.510726\pi$
$882$	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
$902$	11.0000	0.366260
$903$	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	$-0.303130\pi$
$911$	35.0000	1.15960	0.579801	+	0.814758i	$0.303130\pi$
$912$	0	0
$913$	−14.0000	−0.463332
$914$	−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	$-0.376148\pi$
$919$	23.0000	0.758700	0.379350	+	0.925253i	$0.376148\pi$
$920$	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	$-0.788581\pi$
$929$	−48.0000	−1.57483	−0.787414	+	0.616424i	$0.788581\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	0	0
$934$	13.0000	0.425373
$935$	2.00000	0.0654070
$936$	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
$940$	−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
$946$	1.00000	0.0325128
$947$	40.0000	1.29983	0.649913	−	0.760009i	$-0.274805\pi$
$947$	40.0000	1.29983	0.649913	+	0.760009i	$0.274805\pi$
$948$	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	$-0.443403\pi$
$967$	11.0000	0.353736	0.176868	+	0.984235i	$0.443403\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−10.0000	−0.321081
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	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	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	0	0
$979$	−2.00000	−0.0639203
$980$	−12.0000	−0.383326
$981$	0	0
$982$	6.00000	0.191468
$983$	32.0000	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$984$	0	0
$985$	−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	$-0.718344\pi$
$997$	−40.0000	−1.26681	−0.633406	+	0.773819i	$0.718344\pi$
$998$	−14.0000	−0.443162
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	594.2.a.g.1.1	yes	1
3.2	odd	2		594.2.a.c.1.1	✓	1
4.3	odd	2		4752.2.a.n.1.1		1
9.2	odd	6		1782.2.e.t.595.1		2
9.4	even	3		1782.2.e.c.1189.1		2
9.5	odd	6		1782.2.e.t.1189.1		2
9.7	even	3		1782.2.e.c.595.1		2
11.10	odd	2		6534.2.a.k.1.1		1
12.11	even	2		4752.2.a.d.1.1		1
33.32	even	2		6534.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.a.c.1.1	✓	1	3.2	odd	2
594.2.a.g.1.1	yes	1	1.1	even	1	trivial
1782.2.e.c.595.1		2	9.7	even	3
1782.2.e.c.1189.1		2	9.4	even	3
1782.2.e.t.595.1		2	9.2	odd	6
1782.2.e.t.1189.1		2	9.5	odd	6
4752.2.a.d.1.1		1	12.11	even	2
4752.2.a.n.1.1		1	4.3	odd	2
6534.2.a.k.1.1		1	11.10	odd	2
6534.2.a.t.1.1		1	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 594 = 2 \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	594.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more