LMFDB - Embedded newform 1170.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(1,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, 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("1170.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.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:	$9.34249703649$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -4.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +6.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} -6.00000 q^{23} +1.00000 q^{25} +1.00000 q^{26} -4.00000 q^{28} -2.00000 q^{29} -6.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} -4.00000 q^{35} -2.00000 q^{37} -6.00000 q^{38} -1.00000 q^{40} -10.0000 q^{41} -10.0000 q^{43} +2.00000 q^{44} +6.00000 q^{46} +12.0000 q^{47} +9.00000 q^{49} -1.00000 q^{50} -1.00000 q^{52} -2.00000 q^{53} +2.00000 q^{55} +4.00000 q^{56} +2.00000 q^{58} -10.0000 q^{59} +2.00000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} -12.0000 q^{67} -2.00000 q^{68} +4.00000 q^{70} -10.0000 q^{71} +10.0000 q^{73} +2.00000 q^{74} +6.00000 q^{76} -8.00000 q^{77} -4.00000 q^{79} +1.00000 q^{80} +10.0000 q^{82} -2.00000 q^{85} +10.0000 q^{86} -2.00000 q^{88} +14.0000 q^{89} +4.00000 q^{91} -6.00000 q^{92} -12.0000 q^{94} +6.00000 q^{95} +14.0000 q^{97} -9.00000 q^{98} +O(q^{100})\)

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
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.00000	1.06904
$15$	0	0
$16$	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	$0.577979\pi$
$18$	0	0
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	0	0
$28$	−4.00000	−0.755929
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	−4.00000	−0.676123
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	6.00000	0.884652
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	2.00000	0.269680
$56$	4.00000	0.534522
$57$	0	0
$58$	2.00000	0.262613
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	6.00000	0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	4.00000	0.478091
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	0	0
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	6.00000	0.688247
$77$	−8.00000	−0.911685
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	10.0000	1.10432
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	10.0000	1.07833
$87$	0	0
$88$	−2.00000	−0.213201
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	4.00000	0.419314
$92$	−6.00000	−0.625543
$93$	0	0
$94$	−12.0000	−1.23771
$95$	6.00000	0.615587
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	−9.00000	−0.909137
$99$	0	0
$100$	1.00000	0.100000
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	0	0
$103$	−18.0000	−1.77359	−0.886796	−	0.462160i	$-0.847074\pi$
$103$	−18.0000	−1.77359	−0.886796	+	0.462160i	$0.847074\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	2.00000	0.194257
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	−4.00000	−0.377964
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	−2.00000	−0.185695
$117$	0	0
$118$	10.0000	0.920575
$119$	8.00000	0.733359
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−6.00000	−0.538816
$125$	1.00000	0.0894427
$126$	0	0
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	1.00000	0.0877058
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	−24.0000	−2.08106
$134$	12.0000	1.03664
$135$	0	0
$136$	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	$0.220793\pi$
$138$	0	0
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	10.0000	0.839181
$143$	−2.00000	−0.167248
$144$	0	0
$145$	−2.00000	−0.166091
$146$	−10.0000	−0.827606
$147$	0	0
$148$	−2.00000	−0.164399
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	8.00000	0.644658
$155$	−6.00000	−0.481932
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	4.00000	0.318223
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	24.0000	1.89146
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	0	0
$167$	−20.0000	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$167$	−20.0000	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.00000	0.153393
$171$	0	0
$172$	−10.0000	−0.762493
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	2.00000	0.150756
$177$	0	0
$178$	−14.0000	−1.04934
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	6.00000	0.442326
$185$	−2.00000	−0.147043
$186$	0	0
$187$	−4.00000	−0.292509
$188$	12.0000	0.875190
$189$	0	0
$190$	−6.00000	−0.435286
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	9.00000	0.642857
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	14.0000	0.985037
$203$	8.00000	0.561490
$204$	0	0
$205$	−10.0000	−0.698430
$206$	18.0000	1.25412
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	12.0000	0.830057
$210$	0	0
$211$	28.0000	1.92760	0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000	1.92760	0.963800	+	0.266627i	$0.0859092\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	6.00000	0.410152
$215$	−10.0000	−0.681994
$216$	0	0
$217$	24.0000	1.62923
$218$	6.00000	0.406371
$219$	0	0
$220$	2.00000	0.134840
$221$	2.00000	0.134535
$222$	0	0
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	2.00000	0.133038
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	2.00000	0.131306
$233$	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
$235$	12.0000	0.782794
$236$	−10.0000	−0.650945
$237$	0	0
$238$	−8.00000	−0.518563
$239$	26.0000	1.68180	0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000	1.68180	0.840900	+	0.541190i	$0.182026\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	2.00000	0.128037
$245$	9.00000	0.574989
$246$	0	0
$247$	−6.00000	−0.381771
$248$	6.00000	0.381000
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	14.0000	0.878438
$255$	0	0
$256$	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	$0.114792\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	−1.00000	−0.0620174
$261$	0	0
$262$	4.00000	0.247121
$263$	−2.00000	−0.123325	−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000	−0.123325	−0.0616626	+	0.998097i	$0.519640\pi$
$264$	0	0
$265$	−2.00000	−0.122859
$266$	24.0000	1.47153
$267$	0	0
$268$	−12.0000	−0.733017
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−18.0000	−1.08742
$275$	2.00000	0.120605
$276$	0	0
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	8.00000	0.479808
$279$	0	0
$280$	4.00000	0.239046
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	2.00000	0.118262
$287$	40.0000	2.36113
$288$	0	0
$289$	−13.0000	−0.764706
$290$	2.00000	0.117444
$291$	0	0
$292$	10.0000	0.585206
$293$	−22.0000	−1.28525	−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000	−1.28525	−0.642627	+	0.766179i	$0.722155\pi$
$294$	0	0
$295$	−10.0000	−0.582223
$296$	2.00000	0.116248
$297$	0	0
$298$	2.00000	0.115857
$299$	6.00000	0.346989
$300$	0	0
$301$	40.0000	2.30556
$302$	−6.00000	−0.345261
$303$	0	0
$304$	6.00000	0.344124
$305$	2.00000	0.114520
$306$	0	0
$307$	24.0000	1.36975	0.684876	−	0.728659i	$-0.259856\pi$
$307$	24.0000	1.36975	0.684876	+	0.728659i	$0.259856\pi$
$308$	−8.00000	−0.455842
$309$	0	0
$310$	6.00000	0.340777
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−4.00000	−0.225018
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	−4.00000	−0.223957
$320$	1.00000	0.0559017
$321$	0	0
$322$	−24.0000	−1.33747
$323$	−12.0000	−0.667698
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	4.00000	0.221540
$327$	0	0
$328$	10.0000	0.552158
$329$	−48.0000	−2.64633
$330$	0	0
$331$	−14.0000	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$332$	0	0
$333$	0	0
$334$	20.0000	1.09435
$335$	−12.0000	−0.655630
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−1.00000	−0.0543928
$339$	0	0
$340$	−2.00000	−0.108465
$341$	−12.0000	−0.649836
$342$	0	0
$343$	−8.00000	−0.431959
$344$	10.0000	0.539164
$345$	0	0
$346$	10.0000	0.537603
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	0	0
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	0	0
$355$	−10.0000	−0.530745
$356$	14.0000	0.741999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−10.0000	−0.525588
$363$	0	0
$364$	4.00000	0.209657
$365$	10.0000	0.523424
$366$	0	0
$367$	30.0000	1.56599	0.782994	−	0.622030i	$-0.213692\pi$
$367$	30.0000	1.56599	0.782994	+	0.622030i	$0.213692\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	2.00000	0.103975
$371$	8.00000	0.415339
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	−12.0000	−0.618853
$377$	2.00000	0.103005
$378$	0	0
$379$	6.00000	0.308199	0.154100	−	0.988055i	$-0.450752\pi$
$379$	6.00000	0.308199	0.154100	+	0.988055i	$0.450752\pi$
$380$	6.00000	0.307794
$381$	0	0
$382$	0	0
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	0	0
$385$	−8.00000	−0.407718
$386$	−14.0000	−0.712581
$387$	0	0
$388$	14.0000	0.710742
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	−9.00000	−0.454569
$393$	0	0
$394$	−6.00000	−0.302276
$395$	−4.00000	−0.201262
$396$	0	0
$397$	38.0000	1.90717	0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000	1.90717	0.953583	+	0.301131i	$0.0973643\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	0.0500000
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	0	0
$403$	6.00000	0.298881
$404$	−14.0000	−0.696526
$405$	0	0
$406$	−8.00000	−0.397033
$407$	−4.00000	−0.198273
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	10.0000	0.493865
$411$	0	0
$412$	−18.0000	−0.886796
$413$	40.0000	1.96827
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	−12.0000	−0.586939
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	−28.0000	−1.36302
$423$	0	0
$424$	2.00000	0.0971286
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	−8.00000	−0.387147
$428$	−6.00000	−0.290021
$429$	0	0
$430$	10.0000	0.482243
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	0	0
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	−24.0000	−1.15204
$435$	0	0
$436$	−6.00000	−0.287348
$437$	−36.0000	−1.72211
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	−2.00000	−0.0951303
$443$	14.0000	0.665160	0.332580	−	0.943075i	$-0.392081\pi$
$443$	14.0000	0.665160	0.332580	+	0.943075i	$0.392081\pi$
$444$	0	0
$445$	14.0000	0.663664
$446$	−4.00000	−0.189405
$447$	0	0
$448$	−4.00000	−0.188982
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	−20.0000	−0.941763
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	−4.00000	−0.187729
$455$	4.00000	0.187523
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	−6.00000	−0.279751
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−10.0000	−0.462745	−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000	−0.462745	−0.231372	+	0.972865i	$0.574322\pi$
$468$	0	0
$469$	48.0000	2.21643
$470$	−12.0000	−0.553519
$471$	0	0
$472$	10.0000	0.460287
$473$	−20.0000	−0.919601
$474$	0	0
$475$	6.00000	0.275299
$476$	8.00000	0.366679
$477$	0	0
$478$	−26.0000	−1.18921
$479$	−2.00000	−0.0913823	−0.0456912	−	0.998956i	$-0.514549\pi$
$479$	−2.00000	−0.0913823	−0.0456912	+	0.998956i	$0.514549\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	22.0000	1.00207
$483$	0	0
$484$	−7.00000	−0.318182
$485$	14.0000	0.635707
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	−9.00000	−0.406579
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	4.00000	0.180151
$494$	6.00000	0.269953
$495$	0	0
$496$	−6.00000	−0.269408
$497$	40.0000	1.79425
$498$	0	0
$499$	38.0000	1.70111	0.850557	−	0.525883i	$-0.176265\pi$
$499$	38.0000	1.70111	0.850557	+	0.525883i	$0.176265\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	0	0
$503$	14.0000	0.624229	0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000	0.624229	0.312115	+	0.950044i	$0.398963\pi$
$504$	0	0
$505$	−14.0000	−0.622992
$506$	12.0000	0.533465
$507$	0	0
$508$	−14.0000	−0.621150
$509$	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
$511$	−40.0000	−1.76950
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−30.0000	−1.32324
$515$	−18.0000	−0.793175
$516$	0	0
$517$	24.0000	1.05552
$518$	−8.00000	−0.351500
$519$	0	0
$520$	1.00000	0.0438529
$521$	26.0000	1.13908	0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000	1.13908	0.569540	+	0.821963i	$0.307121\pi$
$522$	0	0
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	2.00000	0.0872041
$527$	12.0000	0.522728
$528$	0	0
$529$	13.0000	0.565217
$530$	2.00000	0.0868744
$531$	0	0
$532$	−24.0000	−1.04053
$533$	10.0000	0.433148
$534$	0	0
$535$	−6.00000	−0.259403
$536$	12.0000	0.518321
$537$	0	0
$538$	6.00000	0.258678
$539$	18.0000	0.775315
$540$	0	0
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	2.00000	0.0859074
$543$	0	0
$544$	2.00000	0.0857493
$545$	−6.00000	−0.257012
$546$	0	0
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	18.0000	0.768922
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	−12.0000	−0.511217
$552$	0	0
$553$	16.0000	0.680389
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	−8.00000	−0.339276
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	0	0
$559$	10.0000	0.422955
$560$	−4.00000	−0.169031
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	0	0
$565$	−2.00000	−0.0841406
$566$	−14.0000	−0.588464
$567$	0	0
$568$	10.0000	0.419591
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	−2.00000	−0.0836242
$573$	0	0
$574$	−40.0000	−1.66957
$575$	−6.00000	−0.250217
$576$	0	0
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	−2.00000	−0.0830455
$581$	0	0
$582$	0	0
$583$	−4.00000	−0.165663
$584$	−10.0000	−0.413803
$585$	0	0
$586$	22.0000	0.908812
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	−36.0000	−1.48335
$590$	10.0000	0.411693
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	2.00000	0.0821302	0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000	0.0821302	0.0410651	+	0.999156i	$0.486925\pi$
$594$	0	0
$595$	8.00000	0.327968
$596$	−2.00000	−0.0819232
$597$	0	0
$598$	−6.00000	−0.245358
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	−40.0000	−1.63028
$603$	0	0
$604$	6.00000	0.244137
$605$	−7.00000	−0.284590
$606$	0	0
$607$	−34.0000	−1.38002	−0.690009	−	0.723801i	$-0.742393\pi$
$607$	−34.0000	−1.38002	−0.690009	+	0.723801i	$0.742393\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	−12.0000	−0.485468
$612$	0	0
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	−24.0000	−0.968561
$615$	0	0
$616$	8.00000	0.322329
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	−46.0000	−1.84890	−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000	−1.84890	−0.924448	+	0.381308i	$0.875474\pi$
$620$	−6.00000	−0.240966
$621$	0	0
$622$	−12.0000	−0.481156
$623$	−56.0000	−2.24359
$624$	0	0
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	0	0
$628$	10.0000	0.399043
$629$	4.00000	0.159490
$630$	0	0
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	4.00000	0.159111
$633$	0	0
$634$	−18.0000	−0.714871
$635$	−14.0000	−0.555573
$636$	0	0
$637$	−9.00000	−0.356593
$638$	4.00000	0.158362
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	24.0000	0.945732
$645$	0	0
$646$	12.0000	0.472134
$647$	−42.0000	−1.65119	−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000	−1.65119	−0.825595	+	0.564263i	$0.809160\pi$
$648$	0	0
$649$	−20.0000	−0.785069
$650$	1.00000	0.0392232
$651$	0	0
$652$	−4.00000	−0.156652
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	−4.00000	−0.156293
$656$	−10.0000	−0.390434
$657$	0	0
$658$	48.0000	1.87123
$659$	−8.00000	−0.311636	−0.155818	−	0.987786i	$-0.549801\pi$
$659$	−8.00000	−0.311636	−0.155818	+	0.987786i	$0.549801\pi$
$660$	0	0
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	14.0000	0.544125
$663$	0	0
$664$	0	0
$665$	−24.0000	−0.930680
$666$	0	0
$667$	12.0000	0.464642
$668$	−20.0000	−0.773823
$669$	0	0
$670$	12.0000	0.463600
$671$	4.00000	0.154418
$672$	0	0
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	1.00000	0.0384615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	−56.0000	−2.14908
$680$	2.00000	0.0766965
$681$	0	0
$682$	12.0000	0.459504
$683$	44.0000	1.68361	0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000	1.68361	0.841807	+	0.539779i	$0.181492\pi$
$684$	0	0
$685$	18.0000	0.687745
$686$	8.00000	0.305441
$687$	0	0
$688$	−10.0000	−0.381246
$689$	2.00000	0.0761939
$690$	0	0
$691$	−38.0000	−1.44559	−0.722794	−	0.691063i	$-0.757142\pi$
$691$	−38.0000	−1.44559	−0.722794	+	0.691063i	$0.757142\pi$
$692$	−10.0000	−0.380143
$693$	0	0
$694$	6.00000	0.227757
$695$	−8.00000	−0.303457
$696$	0	0
$697$	20.0000	0.757554
$698$	−2.00000	−0.0757011
$699$	0	0
$700$	−4.00000	−0.151186
$701$	−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
$703$	−12.0000	−0.452589
$704$	2.00000	0.0753778
$705$	0	0
$706$	34.0000	1.27961
$707$	56.0000	2.10610
$708$	0	0
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	10.0000	0.375293
$711$	0	0
$712$	−14.0000	−0.524672
$713$	36.0000	1.34821
$714$	0	0
$715$	−2.00000	−0.0747958
$716$	4.00000	0.149487
$717$	0	0
$718$	−6.00000	−0.223918
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	0	0
$721$	72.0000	2.68142
$722$	−17.0000	−0.632674
$723$	0	0
$724$	10.0000	0.371647
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	−4.00000	−0.148250
$729$	0	0
$730$	−10.0000	−0.370117
$731$	20.0000	0.739727
$732$	0	0
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	−30.0000	−1.10732
$735$	0	0
$736$	6.00000	0.221163
$737$	−24.0000	−0.884051
$738$	0	0
$739$	42.0000	1.54499	0.772497	−	0.635018i	$-0.219007\pi$
$739$	42.0000	1.54499	0.772497	+	0.635018i	$0.219007\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	−8.00000	−0.293689
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	0	0
$745$	−2.00000	−0.0732743
$746$	14.0000	0.512576
$747$	0	0
$748$	−4.00000	−0.146254
$749$	24.0000	0.876941
$750$	0	0
$751$	44.0000	1.60558	0.802791	−	0.596260i	$-0.203347\pi$
$751$	44.0000	1.60558	0.802791	+	0.596260i	$0.203347\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	−2.00000	−0.0728357
$755$	6.00000	0.218362
$756$	0	0
$757$	18.0000	0.654221	0.327111	−	0.944986i	$-0.393925\pi$
$757$	18.0000	0.654221	0.327111	+	0.944986i	$0.393925\pi$
$758$	−6.00000	−0.217930
$759$	0	0
$760$	−6.00000	−0.217643
$761$	14.0000	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$762$	0	0
$763$	24.0000	0.868858
$764$	0	0
$765$	0	0
$766$	12.0000	0.433578
$767$	10.0000	0.361079
$768$	0	0
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	8.00000	0.288300
$771$	0	0
$772$	14.0000	0.503871
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	0	0
$775$	−6.00000	−0.215526
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−10.0000	−0.358517
$779$	−60.0000	−2.14972
$780$	0	0
$781$	−20.0000	−0.715656
$782$	−12.0000	−0.429119
$783$	0	0
$784$	9.00000	0.321429
$785$	10.0000	0.356915
$786$	0	0
$787$	−8.00000	−0.285169	−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000	−0.285169	−0.142585	+	0.989783i	$0.545541\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	4.00000	0.142314
$791$	8.00000	0.284447
$792$	0	0
$793$	−2.00000	−0.0710221
$794$	−38.0000	−1.34857
$795$	0	0
$796$	0	0
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	0	0
$799$	−24.0000	−0.849059
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−6.00000	−0.211867
$803$	20.0000	0.705785
$804$	0	0
$805$	24.0000	0.845889
$806$	−6.00000	−0.211341
$807$	0	0
$808$	14.0000	0.492518
$809$	34.0000	1.19538	0.597688	−	0.801729i	$-0.296086\pi$
$809$	34.0000	1.19538	0.597688	+	0.801729i	$0.296086\pi$
$810$	0	0
$811$	−38.0000	−1.33436	−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000	−1.33436	−0.667180	+	0.744896i	$0.732499\pi$
$812$	8.00000	0.280745
$813$	0	0
$814$	4.00000	0.140200
$815$	−4.00000	−0.140114
$816$	0	0
$817$	−60.0000	−2.09913
$818$	−34.0000	−1.18878
$819$	0	0
$820$	−10.0000	−0.349215
$821$	−50.0000	−1.74501	−0.872506	−	0.488603i	$-0.837507\pi$
$821$	−50.0000	−1.74501	−0.872506	+	0.488603i	$0.837507\pi$
$822$	0	0
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	18.0000	0.627060
$825$	0	0
$826$	−40.0000	−1.39178
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	−18.0000	−0.623663
$834$	0	0
$835$	−20.0000	−0.692129
$836$	12.0000	0.415029
$837$	0	0
$838$	16.0000	0.552711
$839$	−26.0000	−0.897620	−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000	−0.897620	−0.448810	+	0.893627i	$0.648152\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−10.0000	−0.344623
$843$	0	0
$844$	28.0000	0.963800
$845$	1.00000	0.0344010
$846$	0	0
$847$	28.0000	0.962091
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	2.00000	0.0685994
$851$	12.0000	0.411355
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	6.00000	0.205076
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	−10.0000	−0.340997
$861$	0	0
$862$	18.0000	0.613082
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	0	0
$865$	−10.0000	−0.340010
$866$	38.0000	1.29129
$867$	0	0
$868$	24.0000	0.814613
$869$	−8.00000	−0.271381
$870$	0	0
$871$	12.0000	0.406604
$872$	6.00000	0.203186
$873$	0	0
$874$	36.0000	1.21772
$875$	−4.00000	−0.135225
$876$	0	0
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	2.00000	0.0674200
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	0	0
$883$	38.0000	1.27880	0.639401	−	0.768874i	$-0.279182\pi$
$883$	38.0000	1.27880	0.639401	+	0.768874i	$0.279182\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	−14.0000	−0.470339
$887$	−22.0000	−0.738688	−0.369344	−	0.929293i	$-0.620418\pi$
$887$	−22.0000	−0.738688	−0.369344	+	0.929293i	$0.620418\pi$
$888$	0	0
$889$	56.0000	1.87818
$890$	−14.0000	−0.469281
$891$	0	0
$892$	4.00000	0.133930
$893$	72.0000	2.40939
$894$	0	0
$895$	4.00000	0.133705
$896$	4.00000	0.133631
$897$	0	0
$898$	−6.00000	−0.200223
$899$	12.0000	0.400222
$900$	0	0
$901$	4.00000	0.133259
$902$	20.0000	0.665927
$903$	0	0
$904$	2.00000	0.0665190
$905$	10.0000	0.332411
$906$	0	0
$907$	−14.0000	−0.464862	−0.232431	−	0.972613i	$-0.574668\pi$
$907$	−14.0000	−0.464862	−0.232431	+	0.972613i	$0.574668\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	−4.00000	−0.132599
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	0	0
$913$	0	0
$914$	10.0000	0.330771
$915$	0	0
$916$	10.0000	0.330409
$917$	16.0000	0.528367
$918$	0	0
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	6.00000	0.197814
$921$	0	0
$922$	−6.00000	−0.197599
$923$	10.0000	0.329154
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	−16.0000	−0.525793
$927$	0	0
$928$	2.00000	0.0656532
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	54.0000	1.76978
$932$	6.00000	0.196537
$933$	0	0
$934$	10.0000	0.327210
$935$	−4.00000	−0.130814
$936$	0	0
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	−48.0000	−1.56726
$939$	0	0
$940$	12.0000	0.391397
$941$	−50.0000	−1.62995	−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000	−1.62995	−0.814977	+	0.579494i	$0.803250\pi$
$942$	0	0
$943$	60.0000	1.95387
$944$	−10.0000	−0.325472
$945$	0	0
$946$	20.0000	0.650256
$947$	8.00000	0.259965	0.129983	−	0.991516i	$-0.458508\pi$
$947$	8.00000	0.259965	0.129983	+	0.991516i	$0.458508\pi$
$948$	0	0
$949$	−10.0000	−0.324614
$950$	−6.00000	−0.194666
$951$	0	0
$952$	−8.00000	−0.259281
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	0	0
$955$	0	0
$956$	26.0000	0.840900
$957$	0	0
$958$	2.00000	0.0646171
$959$	−72.0000	−2.32500
$960$	0	0
$961$	5.00000	0.161290
$962$	−2.00000	−0.0644826
$963$	0	0
$964$	−22.0000	−0.708572
$965$	14.0000	0.450676
$966$	0	0
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	−14.0000	−0.449513
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	32.0000	1.02587
$974$	16.0000	0.512673
$975$	0	0
$976$	2.00000	0.0640184
$977$	30.0000	0.959785	0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000	0.959785	0.479893	+	0.877327i	$0.340676\pi$
$978$	0	0
$979$	28.0000	0.894884
$980$	9.00000	0.287494
$981$	0	0
$982$	0	0
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	−4.00000	−0.127386
$987$	0	0
$988$	−6.00000	−0.190885
$989$	60.0000	1.90789
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	6.00000	0.190500
$993$	0	0
$994$	−40.0000	−1.26872
$995$	0	0
$996$	0	0
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	−38.0000	−1.20287
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.a.d.1.1		1
3.2	odd	2		130.2.a.c.1.1	✓	1
4.3	odd	2		9360.2.a.by.1.1		1
5.2	odd	4		5850.2.e.u.5149.1		2
5.3	odd	4		5850.2.e.u.5149.2		2
5.4	even	2		5850.2.a.cb.1.1		1
12.11	even	2		1040.2.a.b.1.1		1
15.2	even	4		650.2.b.g.599.2		2
15.8	even	4		650.2.b.g.599.1		2
15.14	odd	2		650.2.a.c.1.1		1
21.20	even	2		6370.2.a.l.1.1		1
24.5	odd	2		4160.2.a.c.1.1		1
24.11	even	2		4160.2.a.t.1.1		1
39.2	even	12		1690.2.l.a.1161.2		4
39.5	even	4		1690.2.d.e.1351.1		2
39.8	even	4		1690.2.d.e.1351.2		2
39.11	even	12		1690.2.l.a.1161.1		4
39.17	odd	6		1690.2.e.g.991.1		2
39.20	even	12		1690.2.l.a.361.2		4
39.23	odd	6		1690.2.e.g.191.1		2
39.29	odd	6		1690.2.e.a.191.1		2
39.32	even	12		1690.2.l.a.361.1		4
39.35	odd	6		1690.2.e.a.991.1		2
39.38	odd	2		1690.2.a.e.1.1		1
60.59	even	2		5200.2.a.bd.1.1		1
195.194	odd	2		8450.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.a.c.1.1	✓	1	3.2	odd	2
650.2.a.c.1.1		1	15.14	odd	2
650.2.b.g.599.1		2	15.8	even	4
650.2.b.g.599.2		2	15.2	even	4
1040.2.a.b.1.1		1	12.11	even	2
1170.2.a.d.1.1		1	1.1	even	1	trivial
1690.2.a.e.1.1		1	39.38	odd	2
1690.2.d.e.1351.1		2	39.5	even	4
1690.2.d.e.1351.2		2	39.8	even	4
1690.2.e.a.191.1		2	39.29	odd	6
1690.2.e.a.991.1		2	39.35	odd	6
1690.2.e.g.191.1		2	39.23	odd	6
1690.2.e.g.991.1		2	39.17	odd	6
1690.2.l.a.361.1		4	39.32	even	12
1690.2.l.a.361.2		4	39.20	even	12
1690.2.l.a.1161.1		4	39.11	even	12
1690.2.l.a.1161.2		4	39.2	even	12
4160.2.a.c.1.1		1	24.5	odd	2
4160.2.a.t.1.1		1	24.11	even	2
5200.2.a.bd.1.1		1	60.59	even	2
5850.2.a.cb.1.1		1	5.4	even	2
5850.2.e.u.5149.1		2	5.2	odd	4
5850.2.e.u.5149.2		2	5.3	odd	4
6370.2.a.l.1.1		1	21.20	even	2
8450.2.a.n.1.1		1	195.194	odd	2
9360.2.a.by.1.1		1	4.3	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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