LMFDB - Embedded newform 570.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("570.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
Analytic rank:	$1$
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	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} -1.00000 q^{12} +2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.00000 q^{20} +2.00000 q^{21} +2.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} -2.00000 q^{28} +1.00000 q^{30} -1.00000 q^{32} +2.00000 q^{33} +2.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +4.00000 q^{37} -1.00000 q^{38} -1.00000 q^{40} -8.00000 q^{41} -2.00000 q^{42} -6.00000 q^{43} -2.00000 q^{44} +1.00000 q^{45} +8.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} -10.0000 q^{53} +1.00000 q^{54} -2.00000 q^{55} +2.00000 q^{56} -1.00000 q^{57} -8.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} -2.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -2.00000 q^{68} +8.00000 q^{69} +2.00000 q^{70} +8.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -4.00000 q^{74} -1.00000 q^{75} +1.00000 q^{76} +4.00000 q^{77} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.00000 q^{82} -16.0000 q^{83} +2.00000 q^{84} -2.00000 q^{85} +6.00000 q^{86} +2.00000 q^{88} +16.0000 q^{89} -1.00000 q^{90} -8.00000 q^{92} +8.00000 q^{94} +1.00000 q^{95} +1.00000 q^{96} +8.00000 q^{97} +3.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−1.00000	−0.288675
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	2.00000	0.534522
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.00000	0.223607
$21$	2.00000	0.436436
$22$	2.00000	0.426401
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−2.00000	−0.377964
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	1.00000	0.182574
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	2.00000	0.342997
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−2.00000	−0.308607
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−2.00000	−0.301511
$45$	1.00000	0.149071
$46$	8.00000	1.17954
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	−1.00000	−0.141421
$51$	2.00000	0.280056
$52$	0	0
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	1.00000	0.136083
$55$	−2.00000	−0.269680
$56$	2.00000	0.267261
$57$	−1.00000	−0.132453
$58$	0	0
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	−1.00000	−0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−2.00000	−0.242536
$69$	8.00000	0.963087
$70$	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	$0.342552\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−4.00000	−0.464991
$75$	−1.00000	−0.115470
$76$	1.00000	0.114708
$77$	4.00000	0.455842
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	2.00000	0.218218
$85$	−2.00000	−0.216930
$86$	6.00000	0.646997
$87$	0	0
$88$	2.00000	0.213201
$89$	16.0000	1.69600	0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000	1.69600	0.847998	+	0.529999i	$0.177808\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−8.00000	−0.834058
$93$	0	0
$94$	8.00000	0.825137
$95$	1.00000	0.102598
$96$	1.00000	0.102062
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	3.00000	0.303046
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	−2.00000	−0.198030
$103$	12.0000	1.18240	0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000	1.18240	0.591198	+	0.806527i	$0.298655\pi$
$104$	0	0
$105$	2.00000	0.195180
$106$	10.0000	0.971286
$107$	20.0000	1.93347	0.966736	−	0.255774i	$-0.0823304\pi$
$107$	20.0000	1.93347	0.966736	+	0.255774i	$0.0823304\pi$
$108$	−1.00000	−0.0962250
$109$	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
$111$	−4.00000	−0.379663
$112$	−2.00000	−0.188982
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	1.00000	0.0936586
$115$	−8.00000	−0.746004
$116$	0	0
$117$	0	0
$118$	8.00000	0.736460
$119$	4.00000	0.366679
$120$	1.00000	0.0912871
$121$	−7.00000	−0.636364
$122$	−2.00000	−0.181071
$123$	8.00000	0.721336
$124$	0	0
$125$	1.00000	0.0894427
$126$	2.00000	0.178174
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	6.00000	0.528271
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	2.00000	0.174078
$133$	−2.00000	−0.173422
$134$	0	0
$135$	−1.00000	−0.0860663
$136$	2.00000	0.171499
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	−8.00000	−0.681005
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	−2.00000	−0.169031
$141$	8.00000	0.673722
$142$	−8.00000	−0.671345
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	3.00000	0.247436
$148$	4.00000	0.328798
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	1.00000	0.0816497
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.00000	−0.0811107
$153$	−2.00000	−0.161690
$154$	−4.00000	−0.322329
$155$	0	0
$156$	0	0
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	8.00000	0.636446
$159$	10.0000	0.793052
$160$	−1.00000	−0.0790569
$161$	16.0000	1.26098
$162$	−1.00000	−0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	−8.00000	−0.624695
$165$	2.00000	0.155700
$166$	16.0000	1.24184
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−2.00000	−0.154303
$169$	−13.0000	−1.00000
$170$	2.00000	0.153393
$171$	1.00000	0.0764719
$172$	−6.00000	−0.457496
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	−2.00000	−0.151186
$176$	−2.00000	−0.150756
$177$	8.00000	0.601317
$178$	−16.0000	−1.19925
$179$	−8.00000	−0.597948	−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000	−0.597948	−0.298974	+	0.954261i	$0.596644\pi$
$180$	1.00000	0.0745356
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	8.00000	0.589768
$185$	4.00000	0.294086
$186$	0	0
$187$	4.00000	0.292509
$188$	−8.00000	−0.583460
$189$	2.00000	0.145479
$190$	−1.00000	−0.0725476
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	−1.00000	−0.0721688
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−8.00000	−0.574367
$195$	0	0
$196$	−3.00000	−0.214286
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	2.00000	0.142134
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−2.00000	−0.140720
$203$	0	0
$204$	2.00000	0.140028
$205$	−8.00000	−0.558744
$206$	−12.0000	−0.836080
$207$	−8.00000	−0.556038
$208$	0	0
$209$	−2.00000	−0.138343
$210$	−2.00000	−0.138013
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	−10.0000	−0.686803
$213$	−8.00000	−0.548151
$214$	−20.0000	−1.36717
$215$	−6.00000	−0.409197
$216$	1.00000	0.0680414
$217$	0	0
$218$	−2.00000	−0.135457
$219$	2.00000	0.135147
$220$	−2.00000	−0.134840
$221$	0	0
$222$	4.00000	0.268462
$223$	12.0000	0.803579	0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000	0.803579	0.401790	+	0.915732i	$0.368388\pi$
$224$	2.00000	0.133631
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	−1.00000	−0.0662266
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	8.00000	0.527504
$231$	−4.00000	−0.263181
$232$	0	0
$233$	−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
$236$	−8.00000	−0.520756
$237$	8.00000	0.519656
$238$	−4.00000	−0.259281
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	−1.00000	−0.0645497
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	7.00000	0.449977
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	−3.00000	−0.191663
$246$	−8.00000	−0.510061
$247$	0	0
$248$	0	0
$249$	16.0000	1.01396
$250$	−1.00000	−0.0632456
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	−2.00000	−0.125988
$253$	16.0000	1.00591
$254$	−16.0000	−1.00393
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	30.0000	1.87135	0.935674	−	0.352865i	$-0.114792\pi$
$257$	30.0000	1.87135	0.935674	+	0.352865i	$0.114792\pi$
$258$	−6.00000	−0.373544
$259$	−8.00000	−0.497096
$260$	0	0
$261$	0	0
$262$	6.00000	0.370681
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−2.00000	−0.123091
$265$	−10.0000	−0.614295
$266$	2.00000	0.122628
$267$	−16.0000	−0.979184
$268$	0	0
$269$	8.00000	0.487769	0.243884	−	0.969804i	$-0.421578\pi$
$269$	8.00000	0.487769	0.243884	+	0.969804i	$0.421578\pi$
$270$	1.00000	0.0608581
$271$	−4.00000	−0.242983	−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000	−0.242983	−0.121491	+	0.992592i	$0.538768\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−18.0000	−1.08742
$275$	−2.00000	−0.120605
$276$	8.00000	0.481543
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	−8.00000	−0.479808
$279$	0	0
$280$	2.00000	0.119523
$281$	−20.0000	−1.19310	−0.596550	−	0.802576i	$-0.703462\pi$
$281$	−20.0000	−1.19310	−0.596550	+	0.802576i	$0.703462\pi$
$282$	−8.00000	−0.476393
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	8.00000	0.474713
$285$	−1.00000	−0.0592349
$286$	0	0
$287$	16.0000	0.944450
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−8.00000	−0.468968
$292$	−2.00000	−0.117041
$293$	−22.0000	−1.28525	−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000	−1.28525	−0.642627	+	0.766179i	$0.722155\pi$
$294$	−3.00000	−0.174964
$295$	−8.00000	−0.465778
$296$	−4.00000	−0.232495
$297$	2.00000	0.116052
$298$	−2.00000	−0.115857
$299$	0	0
$300$	−1.00000	−0.0577350
$301$	12.0000	0.691669
$302$	8.00000	0.460348
$303$	−2.00000	−0.114897
$304$	1.00000	0.0573539
$305$	2.00000	0.114520
$306$	2.00000	0.114332
$307$	−24.0000	−1.36975	−0.684876	−	0.728659i	$-0.740144\pi$
$307$	−24.0000	−1.36975	−0.684876	+	0.728659i	$0.740144\pi$
$308$	4.00000	0.227921
$309$	−12.0000	−0.682656
$310$	0	0
$311$	−14.0000	−0.793867	−0.396934	−	0.917847i	$-0.629926\pi$
$311$	−14.0000	−0.793867	−0.396934	+	0.917847i	$0.629926\pi$
$312$	0	0
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	6.00000	0.338600
$315$	−2.00000	−0.112687
$316$	−8.00000	−0.450035
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−10.0000	−0.560772
$319$	0	0
$320$	1.00000	0.0559017
$321$	−20.0000	−1.11629
$322$	−16.0000	−0.891645
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	0	0
$326$	10.0000	0.553849
$327$	−2.00000	−0.110600
$328$	8.00000	0.441726
$329$	16.0000	0.882109
$330$	−2.00000	−0.110096
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	−16.0000	−0.878114
$333$	4.00000	0.219199
$334$	0	0
$335$	0	0
$336$	2.00000	0.109109
$337$	−16.0000	−0.871576	−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000	−0.871576	−0.435788	+	0.900049i	$0.643530\pi$
$338$	13.0000	0.707107
$339$	2.00000	0.108625
$340$	−2.00000	−0.108465
$341$	0	0
$342$	−1.00000	−0.0540738
$343$	20.0000	1.07990
$344$	6.00000	0.323498
$345$	8.00000	0.430706
$346$	6.00000	0.322562
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	2.00000	0.106904
$351$	0	0
$352$	2.00000	0.106600
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	−8.00000	−0.425195
$355$	8.00000	0.424596
$356$	16.0000	0.847998
$357$	−4.00000	−0.211702
$358$	8.00000	0.422813
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	−1.00000	−0.0527046
$361$	1.00000	0.0526316
$362$	6.00000	0.315353
$363$	7.00000	0.367405
$364$	0	0
$365$	−2.00000	−0.104685
$366$	2.00000	0.104542
$367$	26.0000	1.35719	0.678594	−	0.734513i	$-0.262589\pi$
$367$	26.0000	1.35719	0.678594	+	0.734513i	$0.262589\pi$
$368$	−8.00000	−0.417029
$369$	−8.00000	−0.416463
$370$	−4.00000	−0.207950
$371$	20.0000	1.03835
$372$	0	0
$373$	32.0000	1.65690	0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000	1.65690	0.828449	+	0.560065i	$0.189224\pi$
$374$	−4.00000	−0.206835
$375$	−1.00000	−0.0516398
$376$	8.00000	0.412568
$377$	0	0
$378$	−2.00000	−0.102869
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	1.00000	0.0512989
$381$	−16.0000	−0.819705
$382$	−10.0000	−0.511645
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	1.00000	0.0510310
$385$	4.00000	0.203859
$386$	4.00000	0.203595
$387$	−6.00000	−0.304997
$388$	8.00000	0.406138
$389$	14.0000	0.709828	0.354914	−	0.934899i	$-0.384510\pi$
$389$	14.0000	0.709828	0.354914	+	0.934899i	$0.384510\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	3.00000	0.151523
$393$	6.00000	0.302660
$394$	−10.0000	−0.503793
$395$	−8.00000	−0.402524
$396$	−2.00000	−0.100504
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	4.00000	0.200502
$399$	2.00000	0.100125
$400$	1.00000	0.0500000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	0	0
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	0	0
$407$	−8.00000	−0.396545
$408$	−2.00000	−0.0990148
$409$	−18.0000	−0.890043	−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000	−0.890043	−0.445021	+	0.895520i	$0.646804\pi$
$410$	8.00000	0.395092
$411$	−18.0000	−0.887875
$412$	12.0000	0.591198
$413$	16.0000	0.787309
$414$	8.00000	0.393179
$415$	−16.0000	−0.785409
$416$	0	0
$417$	−8.00000	−0.391762
$418$	2.00000	0.0978232
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	2.00000	0.0975900
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	−4.00000	−0.194717
$423$	−8.00000	−0.388973
$424$	10.0000	0.485643
$425$	−2.00000	−0.0970143
$426$	8.00000	0.387601
$427$	−4.00000	−0.193574
$428$	20.0000	0.966736
$429$	0	0
$430$	6.00000	0.289346
$431$	20.0000	0.963366	0.481683	−	0.876346i	$-0.340026\pi$
$431$	20.0000	0.963366	0.481683	+	0.876346i	$0.340026\pi$
$432$	−1.00000	−0.0481125
$433$	−12.0000	−0.576683	−0.288342	−	0.957528i	$-0.593104\pi$
$433$	−12.0000	−0.576683	−0.288342	+	0.957528i	$0.593104\pi$
$434$	0	0
$435$	0	0
$436$	2.00000	0.0957826
$437$	−8.00000	−0.382692
$438$	−2.00000	−0.0955637
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	2.00000	0.0953463
$441$	−3.00000	−0.142857
$442$	0	0
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−4.00000	−0.189832
$445$	16.0000	0.758473
$446$	−12.0000	−0.568216
$447$	−2.00000	−0.0945968
$448$	−2.00000	−0.0944911
$449$	24.0000	1.13263	0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000	1.13263	0.566315	+	0.824189i	$0.308369\pi$
$450$	−1.00000	−0.0471405
$451$	16.0000	0.753411
$452$	−2.00000	−0.0940721
$453$	8.00000	0.375873
$454$	4.00000	0.187729
$455$	0	0
$456$	1.00000	0.0468293
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	−10.0000	−0.467269
$459$	2.00000	0.0933520
$460$	−8.00000	−0.373002
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	4.00000	0.186097
$463$	18.0000	0.836531	0.418265	−	0.908325i	$-0.362638\pi$
$463$	18.0000	0.836531	0.418265	+	0.908325i	$0.362638\pi$
$464$	0	0
$465$	0	0
$466$	6.00000	0.277945
$467$	20.0000	0.925490	0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000	0.925490	0.462745	+	0.886492i	$0.346865\pi$
$468$	0	0
$469$	0	0
$470$	8.00000	0.369012
$471$	6.00000	0.276465
$472$	8.00000	0.368230
$473$	12.0000	0.551761
$474$	−8.00000	−0.367452
$475$	1.00000	0.0458831
$476$	4.00000	0.183340
$477$	−10.0000	−0.457869
$478$	−6.00000	−0.274434
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	1.00000	0.0456435
$481$	0	0
$482$	−10.0000	−0.455488
$483$	−16.0000	−0.728025
$484$	−7.00000	−0.318182
$485$	8.00000	0.363261
$486$	1.00000	0.0453609
$487$	20.0000	0.906287	0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000	0.906287	0.453143	+	0.891438i	$0.350303\pi$
$488$	−2.00000	−0.0905357
$489$	10.0000	0.452216
$490$	3.00000	0.135526
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	8.00000	0.360668
$493$	0	0
$494$	0	0
$495$	−2.00000	−0.0898933
$496$	0	0
$497$	−16.0000	−0.717698
$498$	−16.0000	−0.716977
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−6.00000	−0.267793
$503$	28.0000	1.24846	0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000	1.24846	0.624229	+	0.781241i	$0.285413\pi$
$504$	2.00000	0.0890871
$505$	2.00000	0.0889988
$506$	−16.0000	−0.711287
$507$	13.0000	0.577350
$508$	16.0000	0.709885
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	−2.00000	−0.0885615
$511$	4.00000	0.176950
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−30.0000	−1.32324
$515$	12.0000	0.528783
$516$	6.00000	0.264135
$517$	16.0000	0.703679
$518$	8.00000	0.351500
$519$	6.00000	0.263371
$520$	0	0
$521$	−20.0000	−0.876216	−0.438108	−	0.898922i	$-0.644351\pi$
$521$	−20.0000	−0.876216	−0.438108	+	0.898922i	$0.644351\pi$
$522$	0	0
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	−6.00000	−0.262111
$525$	2.00000	0.0872872
$526$	12.0000	0.523225
$527$	0	0
$528$	2.00000	0.0870388
$529$	41.0000	1.78261
$530$	10.0000	0.434372
$531$	−8.00000	−0.347170
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	16.0000	0.692388
$535$	20.0000	0.864675
$536$	0	0
$537$	8.00000	0.345225
$538$	−8.00000	−0.344904
$539$	6.00000	0.258438
$540$	−1.00000	−0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	4.00000	0.171815
$543$	6.00000	0.257485
$544$	2.00000	0.0857493
$545$	2.00000	0.0856706
$546$	0	0
$547$	−40.0000	−1.71028	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000	−1.71028	−0.855138	+	0.518400i	$0.826528\pi$
$548$	18.0000	0.768922
$549$	2.00000	0.0853579
$550$	2.00000	0.0852803
$551$	0	0
$552$	−8.00000	−0.340503
$553$	16.0000	0.680389
$554$	14.0000	0.594803
$555$	−4.00000	−0.169791
$556$	8.00000	0.339276
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	0	0
$560$	−2.00000	−0.0845154
$561$	−4.00000	−0.168880
$562$	20.0000	0.843649
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	8.00000	0.336861
$565$	−2.00000	−0.0841406
$566$	2.00000	0.0840663
$567$	−2.00000	−0.0839921
$568$	−8.00000	−0.335673
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	1.00000	0.0418854
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	0	0
$573$	−10.0000	−0.417756
$574$	−16.0000	−0.667827
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	13.0000	0.540729
$579$	4.00000	0.166234
$580$	0	0
$581$	32.0000	1.32758
$582$	8.00000	0.331611
$583$	20.0000	0.828315
$584$	2.00000	0.0827606
$585$	0	0
$586$	22.0000	0.908812
$587$	−44.0000	−1.81607	−0.908037	−	0.418890i	$-0.862419\pi$
$587$	−44.0000	−1.81607	−0.908037	+	0.418890i	$0.862419\pi$
$588$	3.00000	0.123718
$589$	0	0
$590$	8.00000	0.329355
$591$	−10.0000	−0.411345
$592$	4.00000	0.164399
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	−2.00000	−0.0820610
$595$	4.00000	0.163984
$596$	2.00000	0.0819232
$597$	4.00000	0.163709
$598$	0	0
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	1.00000	0.0408248
$601$	−42.0000	−1.71322	−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000	−1.71322	−0.856608	+	0.515968i	$0.827432\pi$
$602$	−12.0000	−0.489083
$603$	0	0
$604$	−8.00000	−0.325515
$605$	−7.00000	−0.284590
$606$	2.00000	0.0812444
$607$	44.0000	1.78590	0.892952	−	0.450151i	$-0.148630\pi$
$607$	44.0000	1.78590	0.892952	+	0.450151i	$0.148630\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	0	0
$612$	−2.00000	−0.0808452
$613$	−46.0000	−1.85792	−0.928961	−	0.370177i	$-0.879297\pi$
$613$	−46.0000	−1.85792	−0.928961	+	0.370177i	$0.879297\pi$
$614$	24.0000	0.968561
$615$	8.00000	0.322591
$616$	−4.00000	−0.161165
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	12.0000	0.482711
$619$	−32.0000	−1.28619	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000	−1.28619	−0.643094	+	0.765787i	$0.722350\pi$
$620$	0	0
$621$	8.00000	0.321029
$622$	14.0000	0.561349
$623$	−32.0000	−1.28205
$624$	0	0
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	2.00000	0.0798723
$628$	−6.00000	−0.239426
$629$	−8.00000	−0.318981
$630$	2.00000	0.0796819
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	8.00000	0.318223
$633$	−4.00000	−0.158986
$634$	−6.00000	−0.238290
$635$	16.0000	0.634941
$636$	10.0000	0.396526
$637$	0	0
$638$	0	0
$639$	8.00000	0.316475
$640$	−1.00000	−0.0395285
$641$	16.0000	0.631962	0.315981	−	0.948766i	$-0.397666\pi$
$641$	16.0000	0.631962	0.315981	+	0.948766i	$0.397666\pi$
$642$	20.0000	0.789337
$643$	46.0000	1.81406	0.907031	−	0.421063i	$-0.138343\pi$
$643$	46.0000	1.81406	0.907031	+	0.421063i	$0.138343\pi$
$644$	16.0000	0.630488
$645$	6.00000	0.236250
$646$	2.00000	0.0786889
$647$	36.0000	1.41531	0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000	1.41531	0.707653	+	0.706560i	$0.249754\pi$
$648$	−1.00000	−0.0392837
$649$	16.0000	0.628055
$650$	0	0
$651$	0	0
$652$	−10.0000	−0.391630
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	2.00000	0.0782062
$655$	−6.00000	−0.234439
$656$	−8.00000	−0.312348
$657$	−2.00000	−0.0780274
$658$	−16.0000	−0.623745
$659$	−44.0000	−1.71400	−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000	−1.71400	−0.856998	+	0.515319i	$0.827673\pi$
$660$	2.00000	0.0778499
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	12.0000	0.466393
$663$	0	0
$664$	16.0000	0.620920
$665$	−2.00000	−0.0775567
$666$	−4.00000	−0.154997
$667$	0	0
$668$	0	0
$669$	−12.0000	−0.463947
$670$	0	0
$671$	−4.00000	−0.154418
$672$	−2.00000	−0.0771517
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	16.0000	0.616297
$675$	−1.00000	−0.0384900
$676$	−13.0000	−0.500000
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	−2.00000	−0.0768095
$679$	−16.0000	−0.614024
$680$	2.00000	0.0766965
$681$	4.00000	0.153280
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	1.00000	0.0382360
$685$	18.0000	0.687745
$686$	−20.0000	−0.763604
$687$	−10.0000	−0.381524
$688$	−6.00000	−0.228748
$689$	0	0
$690$	−8.00000	−0.304555
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	−6.00000	−0.228086
$693$	4.00000	0.151947
$694$	8.00000	0.303676
$695$	8.00000	0.303457
$696$	0	0
$697$	16.0000	0.606043
$698$	26.0000	0.984115
$699$	6.00000	0.226941
$700$	−2.00000	−0.0755929
$701$	−38.0000	−1.43524	−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000	−1.43524	−0.717620	+	0.696435i	$0.754769\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	−2.00000	−0.0753778
$705$	8.00000	0.301297
$706$	−18.0000	−0.677439
$707$	−4.00000	−0.150435
$708$	8.00000	0.300658
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	−8.00000	−0.300235
$711$	−8.00000	−0.300023
$712$	−16.0000	−0.599625
$713$	0	0
$714$	4.00000	0.149696
$715$	0	0
$716$	−8.00000	−0.298974
$717$	−6.00000	−0.224074
$718$	30.0000	1.11959
$719$	22.0000	0.820462	0.410231	−	0.911982i	$-0.365448\pi$
$719$	22.0000	0.820462	0.410231	+	0.911982i	$0.365448\pi$
$720$	1.00000	0.0372678
$721$	−24.0000	−0.893807
$722$	−1.00000	−0.0372161
$723$	−10.0000	−0.371904
$724$	−6.00000	−0.222988
$725$	0	0
$726$	−7.00000	−0.259794
$727$	−22.0000	−0.815935	−0.407967	−	0.912996i	$-0.633762\pi$
$727$	−22.0000	−0.815935	−0.407967	+	0.912996i	$0.633762\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	12.0000	0.443836
$732$	−2.00000	−0.0739221
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	−26.0000	−0.959678
$735$	3.00000	0.110657
$736$	8.00000	0.294884
$737$	0	0
$738$	8.00000	0.294484
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	−20.0000	−0.734223
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	−32.0000	−1.17160
$747$	−16.0000	−0.585409
$748$	4.00000	0.146254
$749$	−40.0000	−1.46157
$750$	1.00000	0.0365148
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	−8.00000	−0.291730
$753$	−6.00000	−0.218652
$754$	0	0
$755$	−8.00000	−0.291150
$756$	2.00000	0.0727393
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	28.0000	1.01701
$759$	−16.0000	−0.580763
$760$	−1.00000	−0.0362738
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	16.0000	0.579619
$763$	−4.00000	−0.144810
$764$	10.0000	0.361787
$765$	−2.00000	−0.0723102
$766$	−8.00000	−0.289052
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	18.0000	0.649097	0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000	0.649097	0.324548	+	0.945869i	$0.394788\pi$
$770$	−4.00000	−0.144150
$771$	−30.0000	−1.08042
$772$	−4.00000	−0.143963
$773$	−42.0000	−1.51064	−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000	−1.51064	−0.755318	+	0.655359i	$0.772517\pi$
$774$	6.00000	0.215666
$775$	0	0
$776$	−8.00000	−0.287183
$777$	8.00000	0.286998
$778$	−14.0000	−0.501924
$779$	−8.00000	−0.286630
$780$	0	0
$781$	−16.0000	−0.572525
$782$	−16.0000	−0.572159
$783$	0	0
$784$	−3.00000	−0.107143
$785$	−6.00000	−0.214149
$786$	−6.00000	−0.214013
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	10.0000	0.356235
$789$	12.0000	0.427211
$790$	8.00000	0.284627
$791$	4.00000	0.142224
$792$	2.00000	0.0710669
$793$	0	0
$794$	6.00000	0.212932
$795$	10.0000	0.354663
$796$	−4.00000	−0.141776
$797$	−22.0000	−0.779280	−0.389640	−	0.920967i	$-0.627401\pi$
$797$	−22.0000	−0.779280	−0.389640	+	0.920967i	$0.627401\pi$
$798$	−2.00000	−0.0707992
$799$	16.0000	0.566039
$800$	−1.00000	−0.0353553
$801$	16.0000	0.565332
$802$	12.0000	0.423735
$803$	4.00000	0.141157
$804$	0	0
$805$	16.0000	0.563926
$806$	0	0
$807$	−8.00000	−0.281613
$808$	−2.00000	−0.0703598
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	−1.00000	−0.0351364
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	0	0
$813$	4.00000	0.140286
$814$	8.00000	0.280400
$815$	−10.0000	−0.350285
$816$	2.00000	0.0700140
$817$	−6.00000	−0.209913
$818$	18.0000	0.629355
$819$	0	0
$820$	−8.00000	−0.279372
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	18.0000	0.627822
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	−12.0000	−0.418040
$825$	2.00000	0.0696311
$826$	−16.0000	−0.556711
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	−8.00000	−0.278019
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	16.0000	0.555368
$831$	14.0000	0.485655
$832$	0	0
$833$	6.00000	0.207888
$834$	8.00000	0.277017
$835$	0	0
$836$	−2.00000	−0.0691714
$837$	0	0
$838$	−30.0000	−1.03633
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	−2.00000	−0.0690066
$841$	−29.0000	−1.00000
$842$	26.0000	0.896019
$843$	20.0000	0.688837
$844$	4.00000	0.137686
$845$	−13.0000	−0.447214
$846$	8.00000	0.275046
$847$	14.0000	0.481046
$848$	−10.0000	−0.343401
$849$	2.00000	0.0686398
$850$	2.00000	0.0685994
$851$	−32.0000	−1.09695
$852$	−8.00000	−0.274075
$853$	6.00000	0.205436	0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000	0.205436	0.102718	+	0.994711i	$0.467246\pi$
$854$	4.00000	0.136877
$855$	1.00000	0.0341993
$856$	−20.0000	−0.683586
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	−6.00000	−0.204598
$861$	−16.0000	−0.545279
$862$	−20.0000	−0.681203
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	1.00000	0.0340207
$865$	−6.00000	−0.204006
$866$	12.0000	0.407777
$867$	13.0000	0.441503
$868$	0	0
$869$	16.0000	0.542763
$870$	0	0
$871$	0	0
$872$	−2.00000	−0.0677285
$873$	8.00000	0.270759
$874$	8.00000	0.270604
$875$	−2.00000	−0.0676123
$876$	2.00000	0.0675737
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	−16.0000	−0.539974
$879$	22.0000	0.742042
$880$	−2.00000	−0.0674200
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	3.00000	0.101015
$883$	−18.0000	−0.605748	−0.302874	−	0.953031i	$-0.597946\pi$
$883$	−18.0000	−0.605748	−0.302874	+	0.953031i	$0.597946\pi$
$884$	0	0
$885$	8.00000	0.268917
$886$	−12.0000	−0.403148
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	4.00000	0.134231
$889$	−32.0000	−1.07325
$890$	−16.0000	−0.536321
$891$	−2.00000	−0.0670025
$892$	12.0000	0.401790
$893$	−8.00000	−0.267710
$894$	2.00000	0.0668900
$895$	−8.00000	−0.267411
$896$	2.00000	0.0668153
$897$	0	0
$898$	−24.0000	−0.800890
$899$	0	0
$900$	1.00000	0.0333333
$901$	20.0000	0.666297
$902$	−16.0000	−0.532742
$903$	−12.0000	−0.399335
$904$	2.00000	0.0665190
$905$	−6.00000	−0.199447
$906$	−8.00000	−0.265782
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	−4.00000	−0.132745
$909$	2.00000	0.0663358
$910$	0	0
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	−1.00000	−0.0331133
$913$	32.0000	1.05905
$914$	22.0000	0.727695
$915$	−2.00000	−0.0661180
$916$	10.0000	0.330409
$917$	12.0000	0.396275
$918$	−2.00000	−0.0660098
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	8.00000	0.263752
$921$	24.0000	0.790827
$922$	6.00000	0.197599
$923$	0	0
$924$	−4.00000	−0.131590
$925$	4.00000	0.131519
$926$	−18.0000	−0.591517
$927$	12.0000	0.394132
$928$	0	0
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−3.00000	−0.0983210
$932$	−6.00000	−0.196537
$933$	14.0000	0.458339
$934$	−20.0000	−0.654420
$935$	4.00000	0.130814
$936$	0	0
$937$	−58.0000	−1.89478	−0.947389	−	0.320085i	$-0.896288\pi$
$937$	−58.0000	−1.89478	−0.947389	+	0.320085i	$0.896288\pi$
$938$	0	0
$939$	−18.0000	−0.587408
$940$	−8.00000	−0.260931
$941$	16.0000	0.521585	0.260793	−	0.965395i	$-0.416016\pi$
$941$	16.0000	0.521585	0.260793	+	0.965395i	$0.416016\pi$
$942$	−6.00000	−0.195491
$943$	64.0000	2.08413
$944$	−8.00000	−0.260378
$945$	2.00000	0.0650600
$946$	−12.0000	−0.390154
$947$	−32.0000	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$948$	8.00000	0.259828
$949$	0	0
$950$	−1.00000	−0.0324443
$951$	−6.00000	−0.194563
$952$	−4.00000	−0.129641
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	10.0000	0.323762
$955$	10.0000	0.323592
$956$	6.00000	0.194054
$957$	0	0
$958$	30.0000	0.969256
$959$	−36.0000	−1.16250
$960$	−1.00000	−0.0322749
$961$	−31.0000	−1.00000
$962$	0	0
$963$	20.0000	0.644491
$964$	10.0000	0.322078
$965$	−4.00000	−0.128765
$966$	16.0000	0.514792
$967$	−6.00000	−0.192947	−0.0964735	−	0.995336i	$-0.530756\pi$
$967$	−6.00000	−0.192947	−0.0964735	+	0.995336i	$0.530756\pi$
$968$	7.00000	0.224989
$969$	2.00000	0.0642493
$970$	−8.00000	−0.256865
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−1.00000	−0.0320750
$973$	−16.0000	−0.512936
$974$	−20.0000	−0.640841
$975$	0	0
$976$	2.00000	0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−10.0000	−0.319765
$979$	−32.0000	−1.02272
$980$	−3.00000	−0.0958315
$981$	2.00000	0.0638551
$982$	30.0000	0.957338
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−8.00000	−0.255031
$985$	10.0000	0.318626
$986$	0	0
$987$	−16.0000	−0.509286
$988$	0	0
$989$	48.0000	1.52631
$990$	2.00000	0.0635642
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	0	0
$993$	12.0000	0.380808
$994$	16.0000	0.507489
$995$	−4.00000	−0.126809
$996$	16.0000	0.506979
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	16.0000	0.506471
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.a.c.1.1	✓	1
3.2	odd	2		1710.2.a.n.1.1		1
4.3	odd	2		4560.2.a.bd.1.1		1
5.2	odd	4		2850.2.d.n.799.1		2
5.3	odd	4		2850.2.d.n.799.2		2
5.4	even	2		2850.2.a.ba.1.1		1
15.14	odd	2		8550.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.c.1.1	✓	1	1.1	even	1	trivial
1710.2.a.n.1.1		1	3.2	odd	2
2850.2.a.ba.1.1		1	5.4	even	2
2850.2.d.n.799.1		2	5.2	odd	4
2850.2.d.n.799.2		2	5.3	odd	4
4560.2.a.bd.1.1		1	4.3	odd	2
8550.2.a.o.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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