LMFDB - Embedded newform 1470.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, 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("1470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +5.00000 q^{19} -1.00000 q^{20} -3.00000 q^{22} -9.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} +1.00000 q^{27} +1.00000 q^{30} -10.0000 q^{31} -1.00000 q^{32} +3.00000 q^{33} +1.00000 q^{36} -1.00000 q^{37} -5.00000 q^{38} +5.00000 q^{39} +1.00000 q^{40} +9.00000 q^{41} +8.00000 q^{43} +3.00000 q^{44} -1.00000 q^{45} +9.00000 q^{46} +3.00000 q^{47} +1.00000 q^{48} -1.00000 q^{50} +5.00000 q^{52} -3.00000 q^{53} -1.00000 q^{54} -3.00000 q^{55} +5.00000 q^{57} +12.0000 q^{59} -1.00000 q^{60} +8.00000 q^{61} +10.0000 q^{62} +1.00000 q^{64} -5.00000 q^{65} -3.00000 q^{66} +8.00000 q^{67} -9.00000 q^{69} -6.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} +1.00000 q^{74} +1.00000 q^{75} +5.00000 q^{76} -5.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.00000 q^{82} -8.00000 q^{86} -3.00000 q^{88} +6.00000 q^{89} +1.00000 q^{90} -9.00000 q^{92} -10.0000 q^{93} -3.00000 q^{94} -5.00000 q^{95} -1.00000 q^{96} +8.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)

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
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	1.00000	0.288675
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−1.00000	−0.235702
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−9.00000	−1.87663	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−9.00000	−1.87663	−0.938315	+	0.345782i	$0.887614\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−5.00000	−0.980581
$27$	1.00000	0.192450
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	1.00000	0.182574
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	−1.00000	−0.176777
$33$	3.00000	0.522233
$34$	0	0
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−5.00000	−0.811107
$39$	5.00000	0.800641
$40$	1.00000	0.158114
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	3.00000	0.452267
$45$	−1.00000	−0.149071
$46$	9.00000	1.32698
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−1.00000	−0.141421
$51$	0	0
$52$	5.00000	0.693375
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−1.00000	−0.136083
$55$	−3.00000	−0.404520
$56$	0	0
$57$	5.00000	0.662266
$58$	0	0
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	−1.00000	−0.129099
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	10.0000	1.27000
$63$	0	0
$64$	1.00000	0.125000
$65$	−5.00000	−0.620174
$66$	−3.00000	−0.369274
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0	0
$69$	−9.00000	−1.08347
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.00000	−0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	1.00000	0.116248
$75$	1.00000	0.115470
$76$	5.00000	0.573539
$77$	0	0
$78$	−5.00000	−0.566139
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−9.00000	−0.993884
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	−8.00000	−0.862662
$87$	0	0
$88$	−3.00000	−0.319801
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−9.00000	−0.938315
$93$	−10.0000	−1.03695
$94$	−3.00000	−0.309426
$95$	−5.00000	−0.512989
$96$	−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	$0.366875\pi$
$98$	0	0
$99$	3.00000	0.301511
$100$	1.00000	0.100000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	3.00000	0.291386
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	1.00000	0.0962250
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	3.00000	0.286039
$111$	−1.00000	−0.0949158
$112$	0	0
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−5.00000	−0.468293
$115$	9.00000	0.839254
$116$	0	0
$117$	5.00000	0.462250
$118$	−12.0000	−1.10469
$119$	0	0
$120$	1.00000	0.0912871
$121$	−2.00000	−0.181818
$122$	−8.00000	−0.724286
$123$	9.00000	0.811503
$124$	−10.0000	−0.898027
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	5.00000	0.438529
$131$	−9.00000	−0.786334	−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000	−0.786334	−0.393167	+	0.919467i	$0.628621\pi$
$132$	3.00000	0.261116
$133$	0	0
$134$	−8.00000	−0.691095
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	9.00000	0.766131
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	6.00000	0.503509
$143$	15.0000	1.25436
$144$	1.00000	0.0833333
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	−1.00000	−0.0816497
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	−5.00000	−0.405554
$153$	0	0
$154$	0	0
$155$	10.0000	0.803219
$156$	5.00000	0.400320
$157$	5.00000	0.399043	0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000	0.399043	0.199522	+	0.979893i	$0.436061\pi$
$158$	−8.00000	−0.636446
$159$	−3.00000	−0.237915
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	9.00000	0.702782
$165$	−3.00000	−0.233550
$166$	0	0
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	5.00000	0.382360
$172$	8.00000	0.609994
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	0	0
$175$	0	0
$176$	3.00000	0.226134
$177$	12.0000	0.901975
$178$	−6.00000	−0.449719
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	−1.00000	−0.0745356
$181$	8.00000	0.594635	0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000	0.594635	0.297318	+	0.954779i	$0.403908\pi$
$182$	0	0
$183$	8.00000	0.591377
$184$	9.00000	0.663489
$185$	1.00000	0.0735215
$186$	10.0000	0.733236
$187$	0	0
$188$	3.00000	0.218797
$189$	0	0
$190$	5.00000	0.362738
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	1.00000	0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−8.00000	−0.574367
$195$	−5.00000	−0.358057
$196$	0	0
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	−3.00000	−0.213201
$199$	−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
$201$	8.00000	0.564276
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−9.00000	−0.628587
$206$	−8.00000	−0.557386
$207$	−9.00000	−0.625543
$208$	5.00000	0.346688
$209$	15.0000	1.03757
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	−3.00000	−0.206041
$213$	−6.00000	−0.411113
$214$	−6.00000	−0.410152
$215$	−8.00000	−0.545595
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−14.0000	−0.948200
$219$	2.00000	0.135147
$220$	−3.00000	−0.202260
$221$	0	0
$222$	1.00000	0.0671156
$223$	−28.0000	−1.87502	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000	−1.87502	−0.937509	+	0.347960i	$0.886874\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	18.0000	1.19734
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	5.00000	0.331133
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	−9.00000	−0.593442
$231$	0	0
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−5.00000	−0.326860
$235$	−3.00000	−0.195698
$236$	12.0000	0.781133
$237$	8.00000	0.519656
$238$	0	0
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	−1.00000	−0.0645497
$241$	−1.00000	−0.0644157	−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000	−0.0644157	−0.0322078	+	0.999481i	$0.510254\pi$
$242$	2.00000	0.128565
$243$	1.00000	0.0641500
$244$	8.00000	0.512148
$245$	0	0
$246$	−9.00000	−0.573819
$247$	25.0000	1.59071
$248$	10.0000	0.635001
$249$	0	0
$250$	1.00000	0.0632456
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	0	0
$253$	−27.0000	−1.69748
$254$	13.0000	0.815693
$255$	0	0
$256$	1.00000	0.0625000
$257$	−12.0000	−0.748539	−0.374270	−	0.927320i	$-0.622107\pi$
$257$	−12.0000	−0.748539	−0.374270	+	0.927320i	$0.622107\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	−5.00000	−0.310087
$261$	0	0
$262$	9.00000	0.556022
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−3.00000	−0.184637
$265$	3.00000	0.184289
$266$	0	0
$267$	6.00000	0.367194
$268$	8.00000	0.488678
$269$	12.0000	0.731653	0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000	0.731653	0.365826	+	0.930683i	$0.380786\pi$
$270$	1.00000	0.0608581
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	0	0
$273$	0	0
$274$	18.0000	1.08742
$275$	3.00000	0.180907
$276$	−9.00000	−0.541736
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	−20.0000	−1.19952
$279$	−10.0000	−0.598684
$280$	0	0
$281$	−21.0000	−1.25275	−0.626377	−	0.779520i	$-0.715463\pi$
$281$	−21.0000	−1.25275	−0.626377	+	0.779520i	$0.715463\pi$
$282$	−3.00000	−0.178647
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	−6.00000	−0.356034
$285$	−5.00000	−0.296174
$286$	−15.0000	−0.886969
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	8.00000	0.468968
$292$	2.00000	0.117041
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	0	0
$295$	−12.0000	−0.698667
$296$	1.00000	0.0581238
$297$	3.00000	0.174078
$298$	0	0
$299$	−45.0000	−2.60242
$300$	1.00000	0.0577350
$301$	0	0
$302$	10.0000	0.575435
$303$	0	0
$304$	5.00000	0.286770
$305$	−8.00000	−0.458079
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	−10.0000	−0.567962
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	−5.00000	−0.283069
$313$	−4.00000	−0.226093	−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000	−0.226093	−0.113047	+	0.993590i	$0.536061\pi$
$314$	−5.00000	−0.282166
$315$	0	0
$316$	8.00000	0.450035
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	3.00000	0.168232
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	6.00000	0.334887
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	5.00000	0.277350
$326$	16.0000	0.886158
$327$	14.0000	0.774202
$328$	−9.00000	−0.496942
$329$	0	0
$330$	3.00000	0.165145
$331$	11.0000	0.604615	0.302307	−	0.953211i	$-0.402243\pi$
$331$	11.0000	0.604615	0.302307	+	0.953211i	$0.402243\pi$
$332$	0	0
$333$	−1.00000	−0.0547997
$334$	3.00000	0.164153
$335$	−8.00000	−0.437087
$336$	0	0
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	−12.0000	−0.652714
$339$	−18.0000	−0.977626
$340$	0	0
$341$	−30.0000	−1.62459
$342$	−5.00000	−0.270369
$343$	0	0
$344$	−8.00000	−0.431331
$345$	9.00000	0.484544
$346$	−9.00000	−0.483843
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	0	0
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	−3.00000	−0.159901
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	−12.0000	−0.637793
$355$	6.00000	0.318447
$356$	6.00000	0.317999
$357$	0	0
$358$	15.0000	0.792775
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	1.00000	0.0527046
$361$	6.00000	0.315789
$362$	−8.00000	−0.420471
$363$	−2.00000	−0.104973
$364$	0	0
$365$	−2.00000	−0.104685
$366$	−8.00000	−0.418167
$367$	−19.0000	−0.991792	−0.495896	−	0.868382i	$-0.665160\pi$
$367$	−19.0000	−0.991792	−0.495896	+	0.868382i	$0.665160\pi$
$368$	−9.00000	−0.469157
$369$	9.00000	0.468521
$370$	−1.00000	−0.0519875
$371$	0	0
$372$	−10.0000	−0.518476
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−3.00000	−0.154713
$377$	0	0
$378$	0	0
$379$	−19.0000	−0.975964	−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000	−0.975964	−0.487982	+	0.872854i	$0.662267\pi$
$380$	−5.00000	−0.256495
$381$	−13.0000	−0.666010
$382$	−18.0000	−0.920960
$383$	27.0000	1.37964	0.689818	−	0.723983i	$-0.257691\pi$
$383$	27.0000	1.37964	0.689818	+	0.723983i	$0.257691\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	8.00000	0.406663
$388$	8.00000	0.406138
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	5.00000	0.253185
$391$	0	0
$392$	0	0
$393$	−9.00000	−0.453990
$394$	−15.0000	−0.755689
$395$	−8.00000	−0.402524
$396$	3.00000	0.150756
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	1.00000	0.0500000
$401$	15.0000	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$402$	−8.00000	−0.399004
$403$	−50.0000	−2.49068
$404$	0	0
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−3.00000	−0.148704
$408$	0	0
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	9.00000	0.444478
$411$	−18.0000	−0.887875
$412$	8.00000	0.394132
$413$	0	0
$414$	9.00000	0.442326
$415$	0	0
$416$	−5.00000	−0.245145
$417$	20.0000	0.979404
$418$	−15.0000	−0.733674
$419$	−9.00000	−0.439679	−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000	−0.439679	−0.219839	+	0.975536i	$0.570553\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	−5.00000	−0.243396
$423$	3.00000	0.145865
$424$	3.00000	0.145693
$425$	0	0
$426$	6.00000	0.290701
$427$	0	0
$428$	6.00000	0.290021
$429$	15.0000	0.724207
$430$	8.00000	0.385794
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	0	0
$435$	0	0
$436$	14.0000	0.670478
$437$	−45.0000	−2.15264
$438$	−2.00000	−0.0955637
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	3.00000	0.143019
$441$	0	0
$442$	0	0
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−1.00000	−0.0474579
$445$	−6.00000	−0.284427
$446$	28.0000	1.32584
$447$	0	0
$448$	0	0
$449$	−33.0000	−1.55737	−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000	−1.55737	−0.778683	+	0.627417i	$0.784112\pi$
$450$	−1.00000	−0.0471405
$451$	27.0000	1.27138
$452$	−18.0000	−0.846649
$453$	−10.0000	−0.469841
$454$	0	0
$455$	0	0
$456$	−5.00000	−0.234146
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−14.0000	−0.654177
$459$	0	0
$460$	9.00000	0.419627
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	0	0
$463$	−1.00000	−0.0464739	−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000	−0.0464739	−0.0232370	+	0.999730i	$0.507397\pi$
$464$	0	0
$465$	10.0000	0.463739
$466$	6.00000	0.277945
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	5.00000	0.231125
$469$	0	0
$470$	3.00000	0.138380
$471$	5.00000	0.230388
$472$	−12.0000	−0.552345
$473$	24.0000	1.10352
$474$	−8.00000	−0.367452
$475$	5.00000	0.229416
$476$	0	0
$477$	−3.00000	−0.137361
$478$	−30.0000	−1.37217
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	1.00000	0.0456435
$481$	−5.00000	−0.227980
$482$	1.00000	0.0455488
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−8.00000	−0.363261
$486$	−1.00000	−0.0453609
$487$	−40.0000	−1.81257	−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000	−1.81257	−0.906287	+	0.422664i	$0.861095\pi$
$488$	−8.00000	−0.362143
$489$	−16.0000	−0.723545
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	9.00000	0.405751
$493$	0	0
$494$	−25.0000	−1.12480
$495$	−3.00000	−0.134840
$496$	−10.0000	−0.449013
$497$	0	0
$498$	0	0
$499$	−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
$501$	−3.00000	−0.134030
$502$	−9.00000	−0.401690
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	0	0
$505$	0	0
$506$	27.0000	1.20030
$507$	12.0000	0.532939
$508$	−13.0000	−0.576782
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	12.0000	0.529297
$515$	−8.00000	−0.352522
$516$	8.00000	0.352180
$517$	9.00000	0.395820
$518$	0	0
$519$	9.00000	0.395056
$520$	5.00000	0.219265
$521$	27.0000	1.18289	0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000	1.18289	0.591446	+	0.806345i	$0.298557\pi$
$522$	0	0
$523$	−22.0000	−0.961993	−0.480996	−	0.876723i	$-0.659725\pi$
$523$	−22.0000	−0.961993	−0.480996	+	0.876723i	$0.659725\pi$
$524$	−9.00000	−0.393167
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	3.00000	0.130558
$529$	58.0000	2.52174
$530$	−3.00000	−0.130312
$531$	12.0000	0.520756
$532$	0	0
$533$	45.0000	1.94917
$534$	−6.00000	−0.259645
$535$	−6.00000	−0.259403
$536$	−8.00000	−0.345547
$537$	−15.0000	−0.647298
$538$	−12.0000	−0.517357
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	16.0000	0.687259
$543$	8.00000	0.343313
$544$	0	0
$545$	−14.0000	−0.599694
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−18.0000	−0.768922
$549$	8.00000	0.341432
$550$	−3.00000	−0.127920
$551$	0	0
$552$	9.00000	0.383065
$553$	0	0
$554$	−26.0000	−1.10463
$555$	1.00000	0.0424476
$556$	20.0000	0.848189
$557$	39.0000	1.65248	0.826242	−	0.563316i	$-0.190475\pi$
$557$	39.0000	1.65248	0.826242	+	0.563316i	$0.190475\pi$
$558$	10.0000	0.423334
$559$	40.0000	1.69182
$560$	0	0
$561$	0	0
$562$	21.0000	0.885832
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	3.00000	0.126323
$565$	18.0000	0.757266
$566$	22.0000	0.924729
$567$	0	0
$568$	6.00000	0.251754
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	5.00000	0.209427
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	15.0000	0.627182
$573$	18.0000	0.751961
$574$	0	0
$575$	−9.00000	−0.375326
$576$	1.00000	0.0416667
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	17.0000	0.707107
$579$	−10.0000	−0.415586
$580$	0	0
$581$	0	0
$582$	−8.00000	−0.331611
$583$	−9.00000	−0.372742
$584$	−2.00000	−0.0827606
$585$	−5.00000	−0.206725
$586$	21.0000	0.867502
$587$	−42.0000	−1.73353	−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000	−1.73353	−0.866763	+	0.498721i	$0.833803\pi$
$588$	0	0
$589$	−50.0000	−2.06021
$590$	12.0000	0.494032
$591$	15.0000	0.617018
$592$	−1.00000	−0.0410997
$593$	24.0000	0.985562	0.492781	−	0.870153i	$-0.335980\pi$
$593$	24.0000	0.985562	0.492781	+	0.870153i	$0.335980\pi$
$594$	−3.00000	−0.123091
$595$	0	0
$596$	0	0
$597$	−16.0000	−0.654836
$598$	45.0000	1.84019
$599$	18.0000	0.735460	0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000	0.735460	0.367730	+	0.929933i	$0.380135\pi$
$600$	−1.00000	−0.0408248
$601$	38.0000	1.55005	0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000	1.55005	0.775026	+	0.631929i	$0.217737\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	−10.0000	−0.406894
$605$	2.00000	0.0813116
$606$	0	0
$607$	−25.0000	−1.01472	−0.507359	−	0.861735i	$-0.669378\pi$
$607$	−25.0000	−1.01472	−0.507359	+	0.861735i	$0.669378\pi$
$608$	−5.00000	−0.202777
$609$	0	0
$610$	8.00000	0.323911
$611$	15.0000	0.606835
$612$	0	0
$613$	11.0000	0.444286	0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000	0.444286	0.222143	+	0.975014i	$0.428695\pi$
$614$	28.0000	1.12999
$615$	−9.00000	−0.362915
$616$	0	0
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	−8.00000	−0.321807
$619$	29.0000	1.16561	0.582804	−	0.812613i	$-0.301955\pi$
$619$	29.0000	1.16561	0.582804	+	0.812613i	$0.301955\pi$
$620$	10.0000	0.401610
$621$	−9.00000	−0.361158
$622$	12.0000	0.481156
$623$	0	0
$624$	5.00000	0.200160
$625$	1.00000	0.0400000
$626$	4.00000	0.159872
$627$	15.0000	0.599042
$628$	5.00000	0.199522
$629$	0	0
$630$	0	0
$631$	−34.0000	−1.35352	−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000	−1.35352	−0.676759	+	0.736204i	$0.736616\pi$
$632$	−8.00000	−0.318223
$633$	5.00000	0.198732
$634$	18.0000	0.714871
$635$	13.0000	0.515889
$636$	−3.00000	−0.118958
$637$	0	0
$638$	0	0
$639$	−6.00000	−0.237356
$640$	1.00000	0.0395285
$641$	33.0000	1.30342	0.651711	−	0.758468i	$-0.274052\pi$
$641$	33.0000	1.30342	0.651711	+	0.758468i	$0.274052\pi$
$642$	−6.00000	−0.236801
$643$	−34.0000	−1.34083	−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000	−1.34083	−0.670415	+	0.741987i	$0.733884\pi$
$644$	0	0
$645$	−8.00000	−0.315000
$646$	0	0
$647$	−9.00000	−0.353827	−0.176913	−	0.984226i	$-0.556611\pi$
$647$	−9.00000	−0.353827	−0.176913	+	0.984226i	$0.556611\pi$
$648$	−1.00000	−0.0392837
$649$	36.0000	1.41312
$650$	−5.00000	−0.196116
$651$	0	0
$652$	−16.0000	−0.626608
$653$	39.0000	1.52619	0.763094	−	0.646288i	$-0.223679\pi$
$653$	39.0000	1.52619	0.763094	+	0.646288i	$0.223679\pi$
$654$	−14.0000	−0.547443
$655$	9.00000	0.351659
$656$	9.00000	0.351391
$657$	2.00000	0.0780274
$658$	0	0
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	−3.00000	−0.116775
$661$	−40.0000	−1.55582	−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000	−1.55582	−0.777910	+	0.628376i	$0.783720\pi$
$662$	−11.0000	−0.427527
$663$	0	0
$664$	0	0
$665$	0	0
$666$	1.00000	0.0387492
$667$	0	0
$668$	−3.00000	−0.116073
$669$	−28.0000	−1.08254
$670$	8.00000	0.309067
$671$	24.0000	0.926510
$672$	0	0
$673$	20.0000	0.770943	0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000	0.770943	0.385472	+	0.922720i	$0.374039\pi$
$674$	−20.0000	−0.770371
$675$	1.00000	0.0384900
$676$	12.0000	0.461538
$677$	3.00000	0.115299	0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000	0.115299	0.0576497	+	0.998337i	$0.481639\pi$
$678$	18.0000	0.691286
$679$	0	0
$680$	0	0
$681$	0	0
$682$	30.0000	1.14876
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	5.00000	0.191180
$685$	18.0000	0.687745
$686$	0	0
$687$	14.0000	0.534133
$688$	8.00000	0.304997
$689$	−15.0000	−0.571454
$690$	−9.00000	−0.342624
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	9.00000	0.342129
$693$	0	0
$694$	−30.0000	−1.13878
$695$	−20.0000	−0.758643
$696$	0	0
$697$	0	0
$698$	28.0000	1.05982
$699$	−6.00000	−0.226941
$700$	0	0
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	−5.00000	−0.188713
$703$	−5.00000	−0.188579
$704$	3.00000	0.113067
$705$	−3.00000	−0.112987
$706$	−24.0000	−0.903252
$707$	0	0
$708$	12.0000	0.450988
$709$	−28.0000	−1.05156	−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000	−1.05156	−0.525781	+	0.850620i	$0.676227\pi$
$710$	−6.00000	−0.225176
$711$	8.00000	0.300023
$712$	−6.00000	−0.224860
$713$	90.0000	3.37053
$714$	0	0
$715$	−15.0000	−0.560968
$716$	−15.0000	−0.560576
$717$	30.0000	1.12037
$718$	−12.0000	−0.447836
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−6.00000	−0.223297
$723$	−1.00000	−0.0371904
$724$	8.00000	0.297318
$725$	0	0
$726$	2.00000	0.0742270
$727$	23.0000	0.853023	0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000	0.853023	0.426511	+	0.904482i	$0.359742\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	0	0
$732$	8.00000	0.295689
$733$	−1.00000	−0.0369358	−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000	−0.0369358	−0.0184679	+	0.999829i	$0.505879\pi$
$734$	19.0000	0.701303
$735$	0	0
$736$	9.00000	0.331744
$737$	24.0000	0.884051
$738$	−9.00000	−0.331295
$739$	5.00000	0.183928	0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000	0.183928	0.0919640	+	0.995762i	$0.470686\pi$
$740$	1.00000	0.0367607
$741$	25.0000	0.918398
$742$	0	0
$743$	−39.0000	−1.43077	−0.715386	−	0.698730i	$-0.753749\pi$
$743$	−39.0000	−1.43077	−0.715386	+	0.698730i	$0.753749\pi$
$744$	10.0000	0.366618
$745$	0	0
$746$	10.0000	0.366126
$747$	0	0
$748$	0	0
$749$	0	0
$750$	1.00000	0.0365148
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	3.00000	0.109399
$753$	9.00000	0.327978
$754$	0	0
$755$	10.0000	0.363937
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	19.0000	0.690111
$759$	−27.0000	−0.980038
$760$	5.00000	0.181369
$761$	−33.0000	−1.19625	−0.598125	−	0.801403i	$-0.704087\pi$
$761$	−33.0000	−1.19625	−0.598125	+	0.801403i	$0.704087\pi$
$762$	13.0000	0.470940
$763$	0	0
$764$	18.0000	0.651217
$765$	0	0
$766$	−27.0000	−0.975550
$767$	60.0000	2.16647
$768$	1.00000	0.0360844
$769$	35.0000	1.26213	0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000	1.26213	0.631066	+	0.775729i	$0.282618\pi$
$770$	0	0
$771$	−12.0000	−0.432169
$772$	−10.0000	−0.359908
$773$	33.0000	1.18693	0.593464	−	0.804861i	$-0.297760\pi$
$773$	33.0000	1.18693	0.593464	+	0.804861i	$0.297760\pi$
$774$	−8.00000	−0.287554
$775$	−10.0000	−0.359211
$776$	−8.00000	−0.287183
$777$	0	0
$778$	6.00000	0.215110
$779$	45.0000	1.61229
$780$	−5.00000	−0.179029
$781$	−18.0000	−0.644091
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−5.00000	−0.178458
$786$	9.00000	0.321019
$787$	14.0000	0.499046	0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000	0.499046	0.249523	+	0.968369i	$0.419726\pi$
$788$	15.0000	0.534353
$789$	−24.0000	−0.854423
$790$	8.00000	0.284627
$791$	0	0
$792$	−3.00000	−0.106600
$793$	40.0000	1.42044
$794$	−14.0000	−0.496841
$795$	3.00000	0.106399
$796$	−16.0000	−0.567105
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	6.00000	0.212000
$802$	−15.0000	−0.529668
$803$	6.00000	0.211735
$804$	8.00000	0.282138
$805$	0	0
$806$	50.0000	1.76117
$807$	12.0000	0.422420
$808$	0	0
$809$	−27.0000	−0.949269	−0.474635	−	0.880183i	$-0.657420\pi$
$809$	−27.0000	−0.949269	−0.474635	+	0.880183i	$0.657420\pi$
$810$	1.00000	0.0351364
$811$	−7.00000	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$812$	0	0
$813$	−16.0000	−0.561144
$814$	3.00000	0.105150
$815$	16.0000	0.560456
$816$	0	0
$817$	40.0000	1.39942
$818$	−2.00000	−0.0699284
$819$	0	0
$820$	−9.00000	−0.314294
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	18.0000	0.627822
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	−8.00000	−0.278693
$825$	3.00000	0.104447
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	−9.00000	−0.312772
$829$	−40.0000	−1.38926	−0.694629	−	0.719368i	$-0.744431\pi$
$829$	−40.0000	−1.38926	−0.694629	+	0.719368i	$0.744431\pi$
$830$	0	0
$831$	26.0000	0.901930
$832$	5.00000	0.173344
$833$	0	0
$834$	−20.0000	−0.692543
$835$	3.00000	0.103819
$836$	15.0000	0.518786
$837$	−10.0000	−0.345651
$838$	9.00000	0.310900
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−14.0000	−0.482472
$843$	−21.0000	−0.723278
$844$	5.00000	0.172107
$845$	−12.0000	−0.412813
$846$	−3.00000	−0.103142
$847$	0	0
$848$	−3.00000	−0.103020
$849$	−22.0000	−0.755038
$850$	0	0
$851$	9.00000	0.308516
$852$	−6.00000	−0.205557
$853$	−37.0000	−1.26686	−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000	−1.26686	−0.633428	+	0.773802i	$0.718353\pi$
$854$	0	0
$855$	−5.00000	−0.170996
$856$	−6.00000	−0.205076
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	−15.0000	−0.512092
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	24.0000	0.817443
$863$	−21.0000	−0.714848	−0.357424	−	0.933942i	$-0.616345\pi$
$863$	−21.0000	−0.714848	−0.357424	+	0.933942i	$0.616345\pi$
$864$	−1.00000	−0.0340207
$865$	−9.00000	−0.306009
$866$	16.0000	0.543702
$867$	−17.0000	−0.577350
$868$	0	0
$869$	24.0000	0.814144
$870$	0	0
$871$	40.0000	1.35535
$872$	−14.0000	−0.474100
$873$	8.00000	0.270759
$874$	45.0000	1.52215
$875$	0	0
$876$	2.00000	0.0675737
$877$	5.00000	0.168838	0.0844190	−	0.996430i	$-0.473097\pi$
$877$	5.00000	0.168838	0.0844190	+	0.996430i	$0.473097\pi$
$878$	−8.00000	−0.269987
$879$	−21.0000	−0.708312
$880$	−3.00000	−0.101130
$881$	−33.0000	−1.11180	−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000	−1.11180	−0.555899	+	0.831250i	$0.687626\pi$
$882$	0	0
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	0	0
$885$	−12.0000	−0.403376
$886$	24.0000	0.806296
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	1.00000	0.0335578
$889$	0	0
$890$	6.00000	0.201120
$891$	3.00000	0.100504
$892$	−28.0000	−0.937509
$893$	15.0000	0.501956
$894$	0	0
$895$	15.0000	0.501395
$896$	0	0
$897$	−45.0000	−1.50251
$898$	33.0000	1.10122
$899$	0	0
$900$	1.00000	0.0333333
$901$	0	0
$902$	−27.0000	−0.899002
$903$	0	0
$904$	18.0000	0.598671
$905$	−8.00000	−0.265929
$906$	10.0000	0.332228
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	5.00000	0.165567
$913$	0	0
$914$	10.0000	0.330771
$915$	−8.00000	−0.264472
$916$	14.0000	0.462573
$917$	0	0
$918$	0	0
$919$	−28.0000	−0.923635	−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000	−0.923635	−0.461817	+	0.886975i	$0.652802\pi$
$920$	−9.00000	−0.296721
$921$	−28.0000	−0.922631
$922$	−12.0000	−0.395199
$923$	−30.0000	−0.987462
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	1.00000	0.0328620
$927$	8.00000	0.262754
$928$	0	0
$929$	39.0000	1.27955	0.639774	−	0.768563i	$-0.279028\pi$
$929$	39.0000	1.27955	0.639774	+	0.768563i	$0.279028\pi$
$930$	−10.0000	−0.327913
$931$	0	0
$932$	−6.00000	−0.196537
$933$	−12.0000	−0.392862
$934$	0	0
$935$	0	0
$936$	−5.00000	−0.163430
$937$	44.0000	1.43742	0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000	1.43742	0.718709	+	0.695311i	$0.244734\pi$
$938$	0	0
$939$	−4.00000	−0.130535
$940$	−3.00000	−0.0978492
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−5.00000	−0.162909
$943$	−81.0000	−2.63772
$944$	12.0000	0.390567
$945$	0	0
$946$	−24.0000	−0.780307
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	8.00000	0.259828
$949$	10.0000	0.324614
$950$	−5.00000	−0.162221
$951$	−18.0000	−0.583690
$952$	0	0
$953$	12.0000	0.388718	0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000	0.388718	0.194359	+	0.980930i	$0.437737\pi$
$954$	3.00000	0.0971286
$955$	−18.0000	−0.582466
$956$	30.0000	0.970269
$957$	0	0
$958$	18.0000	0.581554
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	69.0000	2.22581
$962$	5.00000	0.161206
$963$	6.00000	0.193347
$964$	−1.00000	−0.0322078
$965$	10.0000	0.321911
$966$	0	0
$967$	−28.0000	−0.900419	−0.450210	−	0.892923i	$-0.648651\pi$
$967$	−28.0000	−0.900419	−0.450210	+	0.892923i	$0.648651\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	8.00000	0.256865
$971$	15.0000	0.481373	0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000	0.481373	0.240686	+	0.970603i	$0.422627\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	40.0000	1.28168
$975$	5.00000	0.160128
$976$	8.00000	0.256074
$977$	6.00000	0.191957	0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000	0.191957	0.0959785	+	0.995383i	$0.469402\pi$
$978$	16.0000	0.511624
$979$	18.0000	0.575282
$980$	0	0
$981$	14.0000	0.446986
$982$	−12.0000	−0.382935
$983$	9.00000	0.287055	0.143528	−	0.989646i	$-0.454155\pi$
$983$	9.00000	0.287055	0.143528	+	0.989646i	$0.454155\pi$
$984$	−9.00000	−0.286910
$985$	−15.0000	−0.477940
$986$	0	0
$987$	0	0
$988$	25.0000	0.795356
$989$	−72.0000	−2.28947
$990$	3.00000	0.0953463
$991$	−58.0000	−1.84243	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−58.0000	−1.84243	−0.921215	+	0.389053i	$0.872802\pi$
$992$	10.0000	0.317500
$993$	11.0000	0.349074
$994$	0	0
$995$	16.0000	0.507234
$996$	0	0
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	16.0000	0.506471
$999$	−1.00000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.a.f.1.1		1
3.2	odd	2		4410.2.a.bh.1.1		1
5.4	even	2		7350.2.a.cd.1.1		1
7.2	even	3		210.2.i.c.151.1	yes	2
7.3	odd	6		1470.2.i.p.961.1		2
7.4	even	3		210.2.i.c.121.1	✓	2
7.5	odd	6		1470.2.i.p.361.1		2
7.6	odd	2		1470.2.a.e.1.1		1
21.2	odd	6		630.2.k.a.361.1		2
21.11	odd	6		630.2.k.a.541.1		2
21.20	even	2		4410.2.a.w.1.1		1
28.11	odd	6		1680.2.bg.n.961.1		2
28.23	odd	6		1680.2.bg.n.1201.1		2
35.2	odd	12		1050.2.o.c.949.1		4
35.4	even	6		1050.2.i.i.751.1		2
35.9	even	6		1050.2.i.i.151.1		2
35.18	odd	12		1050.2.o.c.499.1		4
35.23	odd	12		1050.2.o.c.949.2		4
35.32	odd	12		1050.2.o.c.499.2		4
35.34	odd	2		7350.2.a.cx.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.c.121.1	✓	2	7.4	even	3
210.2.i.c.151.1	yes	2	7.2	even	3
630.2.k.a.361.1		2	21.2	odd	6
630.2.k.a.541.1		2	21.11	odd	6
1050.2.i.i.151.1		2	35.9	even	6
1050.2.i.i.751.1		2	35.4	even	6
1050.2.o.c.499.1		4	35.18	odd	12
1050.2.o.c.499.2		4	35.32	odd	12
1050.2.o.c.949.1		4	35.2	odd	12
1050.2.o.c.949.2		4	35.23	odd	12
1470.2.a.e.1.1		1	7.6	odd	2
1470.2.a.f.1.1		1	1.1	even	1	trivial
1470.2.i.p.361.1		2	7.5	odd	6
1470.2.i.p.961.1		2	7.3	odd	6
1680.2.bg.n.961.1		2	28.11	odd	6
1680.2.bg.n.1201.1		2	28.23	odd	6
4410.2.a.w.1.1		1	21.20	even	2
4410.2.a.bh.1.1		1	3.2	odd	2
7350.2.a.cd.1.1		1	5.4	even	2
7350.2.a.cx.1.1		1	35.34	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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