LMFDB - Embedded newform 9450.2.a.ci.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9450,2,Mod(1,9450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9450, 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("9450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9450.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:	$75.4586299101$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1890)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{11} -5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.00000 q^{17} +7.00000 q^{19} -1.00000 q^{22} -5.00000 q^{26} -1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{32} -4.00000 q^{34} +4.00000 q^{37} +7.00000 q^{38} +3.00000 q^{41} -11.0000 q^{43} -1.00000 q^{44} +1.00000 q^{47} +1.00000 q^{49} -5.00000 q^{52} +1.00000 q^{53} -1.00000 q^{56} +6.00000 q^{58} +2.00000 q^{59} -2.00000 q^{61} +1.00000 q^{64} -15.0000 q^{67} -4.00000 q^{68} -16.0000 q^{71} -11.0000 q^{73} +4.00000 q^{74} +7.00000 q^{76} +1.00000 q^{77} +10.0000 q^{79} +3.00000 q^{82} +7.00000 q^{83} -11.0000 q^{86} -1.00000 q^{88} -1.00000 q^{89} +5.00000 q^{91} +1.00000 q^{94} +14.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	0	0
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	0	0
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	−5.00000	−0.980581
$27$	0	0
$28$	−1.00000	−0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.00000	−0.685994
$35$	0	0
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	7.00000	1.13555
$39$	0	0
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	−11.0000	−1.67748	−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000	−1.67748	−0.838742	+	0.544529i	$0.816708\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	0	0
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−5.00000	−0.693375
$53$	1.00000	0.137361	0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000	0.137361	0.0686803	+	0.997639i	$0.478121\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−15.0000	−1.83254	−0.916271	−	0.400559i	$-0.868816\pi$
$67$	−15.0000	−1.83254	−0.916271	+	0.400559i	$0.868816\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	0	0
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	7.00000	0.802955
$77$	1.00000	0.113961
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	0	0
$82$	3.00000	0.331295
$83$	7.00000	0.768350	0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000	0.768350	0.384175	+	0.923260i	$0.374486\pi$
$84$	0	0
$85$	0	0
$86$	−11.0000	−1.18616
$87$	0	0
$88$	−1.00000	−0.106600
$89$	−1.00000	−0.106000	−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000	−0.106000	−0.0529999	+	0.998595i	$0.516878\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	0	0
$93$	0	0
$94$	1.00000	0.103142
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	0	0
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	1.00000	0.0971286
$107$	−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
$109$	−15.0000	−1.43674	−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000	−1.43674	−0.718370	+	0.695662i	$0.755111\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−15.0000	−1.41108	−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000	−1.41108	−0.705541	+	0.708669i	$0.749296\pi$
$114$	0	0
$115$	0	0
$116$	6.00000	0.557086
$117$	0	0
$118$	2.00000	0.184115
$119$	4.00000	0.366679
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−2.00000	−0.181071
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	9.00000	0.798621	0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000	0.798621	0.399310	+	0.916816i	$0.369250\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−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
$133$	−7.00000	−0.606977
$134$	−15.0000	−1.29580
$135$	0	0
$136$	−4.00000	−0.342997
$137$	−17.0000	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$137$	−17.0000	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	0	0
$142$	−16.0000	−1.34269
$143$	5.00000	0.418121
$144$	0	0
$145$	0	0
$146$	−11.0000	−0.910366
$147$	0	0
$148$	4.00000	0.328798
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	7.00000	0.567775
$153$	0	0
$154$	1.00000	0.0805823
$155$	0	0
$156$	0	0
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	7.00000	0.543305
$167$	−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
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	−11.0000	−0.838742
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−1.00000	−0.0749532
$179$	−7.00000	−0.523205	−0.261602	−	0.965176i	$-0.584251\pi$
$179$	−7.00000	−0.523205	−0.261602	+	0.965176i	$0.584251\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	5.00000	0.370625
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	4.00000	0.292509
$188$	1.00000	0.0729325
$189$	0	0
$190$	0	0
$191$	−11.0000	−0.795932	−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000	−0.795932	−0.397966	+	0.917400i	$0.630284\pi$
$192$	0	0
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	1.00000	0.0714286
$197$	15.0000	1.06871	0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000	1.06871	0.534353	+	0.845262i	$0.320555\pi$
$198$	0	0
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	0	0
$201$	0	0
$202$	−5.00000	−0.351799
$203$	−6.00000	−0.421117
$204$	0	0
$205$	0	0
$206$	6.00000	0.418040
$207$	0	0
$208$	−5.00000	−0.346688
$209$	−7.00000	−0.484200
$210$	0	0
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	1.00000	0.0686803
$213$	0	0
$214$	−6.00000	−0.410152
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−15.0000	−1.01593
$219$	0	0
$220$	0	0
$221$	20.0000	1.34535
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−15.0000	−0.997785
$227$	7.00000	0.464606	0.232303	−	0.972643i	$-0.425374\pi$
$227$	7.00000	0.464606	0.232303	+	0.972643i	$0.425374\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	−3.00000	−0.196537	−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000	−0.196537	−0.0982683	+	0.995160i	$0.531330\pi$
$234$	0	0
$235$	0	0
$236$	2.00000	0.130189
$237$	0	0
$238$	4.00000	0.259281
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−10.0000	−0.642824
$243$	0	0
$244$	−2.00000	−0.128037
$245$	0	0
$246$	0	0
$247$	−35.0000	−2.22700
$248$	0	0
$249$	0	0
$250$	0	0
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	0	0
$253$	0	0
$254$	9.00000	0.564710
$255$	0	0
$256$	1.00000	0.0625000
$257$	28.0000	1.74659	0.873296	−	0.487190i	$-0.161978\pi$
$257$	28.0000	1.74659	0.873296	+	0.487190i	$0.161978\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	0	0
$261$	0	0
$262$	−4.00000	−0.247121
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	0	0
$266$	−7.00000	−0.429198
$267$	0	0
$268$	−15.0000	−0.916271
$269$	−26.0000	−1.58525	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000	−1.58525	−0.792624	+	0.609711i	$0.791286\pi$
$270$	0	0
$271$	5.00000	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	−17.0000	−1.02701
$275$	0	0
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	0	0
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	−16.0000	−0.949425
$285$	0	0
$286$	5.00000	0.295656
$287$	−3.00000	−0.177084
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−11.0000	−0.643726
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	0	0
$295$	0	0
$296$	4.00000	0.232495
$297$	0	0
$298$	−12.0000	−0.695141
$299$	0	0
$300$	0	0
$301$	11.0000	0.634029
$302$	−10.0000	−0.575435
$303$	0	0
$304$	7.00000	0.401478
$305$	0	0
$306$	0	0
$307$	−22.0000	−1.25561	−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000	−1.25561	−0.627803	+	0.778372i	$0.716046\pi$
$308$	1.00000	0.0569803
$309$	0	0
$310$	0	0
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	0	0
$313$	−13.0000	−0.734803	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	−13.0000	−0.734803	−0.367402	+	0.930062i	$0.619753\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	10.0000	0.562544
$317$	25.0000	1.40414	0.702070	−	0.712108i	$-0.252259\pi$
$317$	25.0000	1.40414	0.702070	+	0.712108i	$0.252259\pi$
$318$	0	0
$319$	−6.00000	−0.335936
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−28.0000	−1.55796
$324$	0	0
$325$	0	0
$326$	−12.0000	−0.664619
$327$	0	0
$328$	3.00000	0.165647
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	7.00000	0.384175
$333$	0	0
$334$	−20.0000	−1.09435
$335$	0	0
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−11.0000	−0.593080
$345$	0	0
$346$	14.0000	0.752645
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	0	0
$356$	−1.00000	−0.0529999
$357$	0	0
$358$	−7.00000	−0.369961
$359$	−5.00000	−0.263890	−0.131945	−	0.991257i	$-0.542122\pi$
$359$	−5.00000	−0.263890	−0.131945	+	0.991257i	$0.542122\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−14.0000	−0.735824
$363$	0	0
$364$	5.00000	0.262071
$365$	0	0
$366$	0	0
$367$	2.00000	0.104399	0.0521996	−	0.998637i	$-0.483377\pi$
$367$	2.00000	0.104399	0.0521996	+	0.998637i	$0.483377\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	−1.00000	−0.0519174
$372$	0	0
$373$	−18.0000	−0.932005	−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000	−0.932005	−0.466002	+	0.884783i	$0.654306\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	1.00000	0.0515711
$377$	−30.0000	−1.54508
$378$	0	0
$379$	−10.0000	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$380$	0	0
$381$	0	0
$382$	−11.0000	−0.562809
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	−18.0000	−0.916176
$387$	0	0
$388$	14.0000	0.710742
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	0	0
$392$	1.00000	0.0505076
$393$	0	0
$394$	15.0000	0.755689
$395$	0	0
$396$	0	0
$397$	34.0000	1.70641	0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000	1.70641	0.853206	+	0.521575i	$0.174655\pi$
$398$	7.00000	0.350878
$399$	0	0
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	0	0
$404$	−5.00000	−0.248759
$405$	0	0
$406$	−6.00000	−0.297775
$407$	−4.00000	−0.198273
$408$	0	0
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	0	0
$411$	0	0
$412$	6.00000	0.295599
$413$	−2.00000	−0.0984136
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	−7.00000	−0.342381
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	−11.0000	−0.536107	−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000	−0.536107	−0.268054	+	0.963404i	$0.586380\pi$
$422$	10.0000	0.486792
$423$	0	0
$424$	1.00000	0.0485643
$425$	0	0
$426$	0	0
$427$	2.00000	0.0967868
$428$	−6.00000	−0.290021
$429$	0	0
$430$	0	0
$431$	−3.00000	−0.144505	−0.0722525	−	0.997386i	$-0.523019\pi$
$431$	−3.00000	−0.144505	−0.0722525	+	0.997386i	$0.523019\pi$
$432$	0	0
$433$	−17.0000	−0.816968	−0.408484	−	0.912766i	$-0.633942\pi$
$433$	−17.0000	−0.816968	−0.408484	+	0.912766i	$0.633942\pi$
$434$	0	0
$435$	0	0
$436$	−15.0000	−0.718370
$437$	0	0
$438$	0	0
$439$	−3.00000	−0.143182	−0.0715911	−	0.997434i	$-0.522808\pi$
$439$	−3.00000	−0.143182	−0.0715911	+	0.997434i	$0.522808\pi$
$440$	0	0
$441$	0	0
$442$	20.0000	0.951303
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	0	0
$445$	0	0
$446$	−14.0000	−0.662919
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	0	0
$451$	−3.00000	−0.141264
$452$	−15.0000	−0.705541
$453$	0	0
$454$	7.00000	0.328526
$455$	0	0
$456$	0	0
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	0	0
$461$	15.0000	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$462$	0	0
$463$	−21.0000	−0.975953	−0.487976	−	0.872857i	$-0.662265\pi$
$463$	−21.0000	−0.975953	−0.487976	+	0.872857i	$0.662265\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	−3.00000	−0.138972
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	15.0000	0.692636
$470$	0	0
$471$	0	0
$472$	2.00000	0.0920575
$473$	11.0000	0.505781
$474$	0	0
$475$	0	0
$476$	4.00000	0.183340
$477$	0	0
$478$	4.00000	0.182956
$479$	−14.0000	−0.639676	−0.319838	−	0.947472i	$-0.603629\pi$
$479$	−14.0000	−0.639676	−0.319838	+	0.947472i	$0.603629\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	−10.0000	−0.455488
$483$	0	0
$484$	−10.0000	−0.454545
$485$	0	0
$486$	0	0
$487$	33.0000	1.49537	0.747686	−	0.664052i	$-0.231165\pi$
$487$	33.0000	1.49537	0.747686	+	0.664052i	$0.231165\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	−24.0000	−1.08091
$494$	−35.0000	−1.57472
$495$	0	0
$496$	0	0
$497$	16.0000	0.717698
$498$	0	0
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	0	0
$501$	0	0
$502$	24.0000	1.07117
$503$	39.0000	1.73892	0.869462	−	0.494000i	$-0.164466\pi$
$503$	39.0000	1.73892	0.869462	+	0.494000i	$0.164466\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	9.00000	0.399310
$509$	−38.0000	−1.68432	−0.842160	−	0.539227i	$-0.818716\pi$
$509$	−38.0000	−1.68432	−0.842160	+	0.539227i	$0.818716\pi$
$510$	0	0
$511$	11.0000	0.486611
$512$	1.00000	0.0441942
$513$	0	0
$514$	28.0000	1.23503
$515$	0	0
$516$	0	0
$517$	−1.00000	−0.0439799
$518$	−4.00000	−0.175750
$519$	0	0
$520$	0	0
$521$	−33.0000	−1.44576	−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000	−1.44576	−0.722878	+	0.690976i	$0.757181\pi$
$522$	0	0
$523$	12.0000	0.524723	0.262362	−	0.964970i	$-0.415499\pi$
$523$	12.0000	0.524723	0.262362	+	0.964970i	$0.415499\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	−12.0000	−0.523225
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	−7.00000	−0.303488
$533$	−15.0000	−0.649722
$534$	0	0
$535$	0	0
$536$	−15.0000	−0.647901
$537$	0	0
$538$	−26.0000	−1.12094
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−17.0000	−0.730887	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000	−0.730887	−0.365444	+	0.930834i	$0.619083\pi$
$542$	5.00000	0.214768
$543$	0	0
$544$	−4.00000	−0.171499
$545$	0	0
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	−17.0000	−0.726204
$549$	0	0
$550$	0	0
$551$	42.0000	1.78926
$552$	0	0
$553$	−10.0000	−0.425243
$554$	8.00000	0.339887
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	0	0
$559$	55.0000	2.32625
$560$	0	0
$561$	0	0
$562$	14.0000	0.590554
$563$	−21.0000	−0.885044	−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000	−0.885044	−0.442522	+	0.896758i	$0.645916\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	−16.0000	−0.671345
$569$	42.0000	1.76073	0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000	1.76073	0.880366	+	0.474295i	$0.157297\pi$
$570$	0	0
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	5.00000	0.209061
$573$	0	0
$574$	−3.00000	−0.125218
$575$	0	0
$576$	0	0
$577$	−9.00000	−0.374675	−0.187337	−	0.982296i	$-0.559986\pi$
$577$	−9.00000	−0.374675	−0.187337	+	0.982296i	$0.559986\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	−7.00000	−0.290409
$582$	0	0
$583$	−1.00000	−0.0414158
$584$	−11.0000	−0.455183
$585$	0	0
$586$	26.0000	1.07405
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	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	$0.254026\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	0	0
$598$	0	0
$599$	19.0000	0.776319	0.388159	−	0.921592i	$-0.373111\pi$
$599$	19.0000	0.776319	0.388159	+	0.921592i	$0.373111\pi$
$600$	0	0
$601$	−12.0000	−0.489490	−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000	−0.489490	−0.244745	+	0.969587i	$0.578704\pi$
$602$	11.0000	0.448327
$603$	0	0
$604$	−10.0000	−0.406894
$605$	0	0
$606$	0	0
$607$	−20.0000	−0.811775	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000	−0.811775	−0.405887	+	0.913923i	$0.633038\pi$
$608$	7.00000	0.283887
$609$	0	0
$610$	0	0
$611$	−5.00000	−0.202278
$612$	0	0
$613$	−44.0000	−1.77714	−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000	−1.77714	−0.888572	+	0.458738i	$0.848302\pi$
$614$	−22.0000	−0.887848
$615$	0	0
$616$	1.00000	0.0402911
$617$	−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
$619$	33.0000	1.32638	0.663191	−	0.748450i	$-0.269202\pi$
$619$	33.0000	1.32638	0.663191	+	0.748450i	$0.269202\pi$
$620$	0	0
$621$	0	0
$622$	14.0000	0.561349
$623$	1.00000	0.0400642
$624$	0	0
$625$	0	0
$626$	−13.0000	−0.519584
$627$	0	0
$628$	−14.0000	−0.558661
$629$	−16.0000	−0.637962
$630$	0	0
$631$	−18.0000	−0.716569	−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000	−0.716569	−0.358284	+	0.933613i	$0.616638\pi$
$632$	10.0000	0.397779
$633$	0	0
$634$	25.0000	0.992877
$635$	0	0
$636$	0	0
$637$	−5.00000	−0.198107
$638$	−6.00000	−0.237542
$639$	0	0
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	0	0
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	0	0
$645$	0	0
$646$	−28.0000	−1.10165
$647$	−23.0000	−0.904223	−0.452112	−	0.891961i	$-0.649329\pi$
$647$	−23.0000	−0.904223	−0.452112	+	0.891961i	$0.649329\pi$
$648$	0	0
$649$	−2.00000	−0.0785069
$650$	0	0
$651$	0	0
$652$	−12.0000	−0.469956
$653$	−2.00000	−0.0782660	−0.0391330	−	0.999234i	$-0.512460\pi$
$653$	−2.00000	−0.0782660	−0.0391330	+	0.999234i	$0.512460\pi$
$654$	0	0
$655$	0	0
$656$	3.00000	0.117130
$657$	0	0
$658$	−1.00000	−0.0389841
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	12.0000	0.466393
$663$	0	0
$664$	7.00000	0.271653
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−20.0000	−0.773823
$669$	0	0
$670$	0	0
$671$	2.00000	0.0772091
$672$	0	0
$673$	12.0000	0.462566	0.231283	−	0.972887i	$-0.425708\pi$
$673$	12.0000	0.462566	0.231283	+	0.972887i	$0.425708\pi$
$674$	−2.00000	−0.0770371
$675$	0	0
$676$	12.0000	0.461538
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	−14.0000	−0.537271
$680$	0	0
$681$	0	0
$682$	0	0
$683$	28.0000	1.07139	0.535695	−	0.844411i	$-0.320050\pi$
$683$	28.0000	1.07139	0.535695	+	0.844411i	$0.320050\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−11.0000	−0.419371
$689$	−5.00000	−0.190485
$690$	0	0
$691$	7.00000	0.266293	0.133146	−	0.991096i	$-0.457492\pi$
$691$	7.00000	0.266293	0.133146	+	0.991096i	$0.457492\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	28.0000	1.06287
$695$	0	0
$696$	0	0
$697$	−12.0000	−0.454532
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−48.0000	−1.81293	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000	−1.81293	−0.906467	+	0.422276i	$0.861231\pi$
$702$	0	0
$703$	28.0000	1.05604
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	6.00000	0.225813
$707$	5.00000	0.188044
$708$	0	0
$709$	−17.0000	−0.638448	−0.319224	−	0.947679i	$-0.603422\pi$
$709$	−17.0000	−0.638448	−0.319224	+	0.947679i	$0.603422\pi$
$710$	0	0
$711$	0	0
$712$	−1.00000	−0.0374766
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−7.00000	−0.261602
$717$	0	0
$718$	−5.00000	−0.186598
$719$	50.0000	1.86469	0.932343	−	0.361576i	$-0.117761\pi$
$719$	50.0000	1.86469	0.932343	+	0.361576i	$0.117761\pi$
$720$	0	0
$721$	−6.00000	−0.223452
$722$	30.0000	1.11648
$723$	0	0
$724$	−14.0000	−0.520306
$725$	0	0
$726$	0	0
$727$	−22.0000	−0.815935	−0.407967	−	0.912996i	$-0.633762\pi$
$727$	−22.0000	−0.815935	−0.407967	+	0.912996i	$0.633762\pi$
$728$	5.00000	0.185312
$729$	0	0
$730$	0	0
$731$	44.0000	1.62740
$732$	0	0
$733$	−21.0000	−0.775653	−0.387826	−	0.921732i	$-0.626774\pi$
$733$	−21.0000	−0.775653	−0.387826	+	0.921732i	$0.626774\pi$
$734$	2.00000	0.0738213
$735$	0	0
$736$	0	0
$737$	15.0000	0.552532
$738$	0	0
$739$	−52.0000	−1.91285	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−52.0000	−1.91285	−0.956425	+	0.291977i	$0.905687\pi$
$740$	0	0
$741$	0	0
$742$	−1.00000	−0.0367112
$743$	−26.0000	−0.953847	−0.476924	−	0.878945i	$-0.658248\pi$
$743$	−26.0000	−0.953847	−0.476924	+	0.878945i	$0.658248\pi$
$744$	0	0
$745$	0	0
$746$	−18.0000	−0.659027
$747$	0	0
$748$	4.00000	0.146254
$749$	6.00000	0.219235
$750$	0	0
$751$	−50.0000	−1.82453	−0.912263	−	0.409605i	$-0.865667\pi$
$751$	−50.0000	−1.82453	−0.912263	+	0.409605i	$0.865667\pi$
$752$	1.00000	0.0364662
$753$	0	0
$754$	−30.0000	−1.09254
$755$	0	0
$756$	0	0
$757$	−8.00000	−0.290765	−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000	−0.290765	−0.145382	+	0.989376i	$0.546441\pi$
$758$	−10.0000	−0.363216
$759$	0	0
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	15.0000	0.543036
$764$	−11.0000	−0.397966
$765$	0	0
$766$	0	0
$767$	−10.0000	−0.361079
$768$	0	0
$769$	6.00000	0.216366	0.108183	−	0.994131i	$-0.465497\pi$
$769$	6.00000	0.216366	0.108183	+	0.994131i	$0.465497\pi$
$770$	0	0
$771$	0	0
$772$	−18.0000	−0.647834
$773$	−50.0000	−1.79838	−0.899188	−	0.437564i	$-0.855842\pi$
$773$	−50.0000	−1.79838	−0.899188	+	0.437564i	$0.855842\pi$
$774$	0	0
$775$	0	0
$776$	14.0000	0.502571
$777$	0	0
$778$	6.00000	0.215110
$779$	21.0000	0.752403
$780$	0	0
$781$	16.0000	0.572525
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−22.0000	−0.784215	−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000	−0.784215	−0.392108	+	0.919919i	$0.628254\pi$
$788$	15.0000	0.534353
$789$	0	0
$790$	0	0
$791$	15.0000	0.533339
$792$	0	0
$793$	10.0000	0.355110
$794$	34.0000	1.20661
$795$	0	0
$796$	7.00000	0.248108
$797$	−48.0000	−1.70025	−0.850124	−	0.526583i	$-0.823473\pi$
$797$	−48.0000	−1.70025	−0.850124	+	0.526583i	$0.823473\pi$
$798$	0	0
$799$	−4.00000	−0.141510
$800$	0	0
$801$	0	0
$802$	30.0000	1.05934
$803$	11.0000	0.388182
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−5.00000	−0.175899
$809$	−12.0000	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$810$	0	0
$811$	−37.0000	−1.29925	−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−37.0000	−1.29925	−0.649623	+	0.760257i	$0.725073\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	−4.00000	−0.140200
$815$	0	0
$816$	0	0
$817$	−77.0000	−2.69389
$818$	22.0000	0.769212
$819$	0	0
$820$	0	0
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	0	0
$823$	−17.0000	−0.592583	−0.296291	−	0.955098i	$-0.595750\pi$
$823$	−17.0000	−0.592583	−0.296291	+	0.955098i	$0.595750\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	−2.00000	−0.0695889
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	0	0
$831$	0	0
$832$	−5.00000	−0.173344
$833$	−4.00000	−0.138592
$834$	0	0
$835$	0	0
$836$	−7.00000	−0.242100
$837$	0	0
$838$	−18.0000	−0.621800
$839$	46.0000	1.58810	0.794048	−	0.607855i	$-0.207970\pi$
$839$	46.0000	1.58810	0.794048	+	0.607855i	$0.207970\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−11.0000	−0.379085
$843$	0	0
$844$	10.0000	0.344214
$845$	0	0
$846$	0	0
$847$	10.0000	0.343604
$848$	1.00000	0.0343401
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	−6.00000	−0.205076
$857$	−52.0000	−1.77629	−0.888143	−	0.459567i	$-0.848005\pi$
$857$	−52.0000	−1.77629	−0.888143	+	0.459567i	$0.848005\pi$
$858$	0	0
$859$	15.0000	0.511793	0.255897	−	0.966704i	$-0.417629\pi$
$859$	15.0000	0.511793	0.255897	+	0.966704i	$0.417629\pi$
$860$	0	0
$861$	0	0
$862$	−3.00000	−0.102180
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	0	0
$866$	−17.0000	−0.577684
$867$	0	0
$868$	0	0
$869$	−10.0000	−0.339227
$870$	0	0
$871$	75.0000	2.54128
$872$	−15.0000	−0.507964
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−3.00000	−0.101245
$879$	0	0
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	20.0000	0.672673
$885$	0	0
$886$	−36.0000	−1.20944
$887$	−15.0000	−0.503651	−0.251825	−	0.967773i	$-0.581031\pi$
$887$	−15.0000	−0.503651	−0.251825	+	0.967773i	$0.581031\pi$
$888$	0	0
$889$	−9.00000	−0.301850
$890$	0	0
$891$	0	0
$892$	−14.0000	−0.468755
$893$	7.00000	0.234246
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0000	0.600668
$899$	0	0
$900$	0	0
$901$	−4.00000	−0.133259
$902$	−3.00000	−0.0998891
$903$	0	0
$904$	−15.0000	−0.498893
$905$	0	0
$906$	0	0
$907$	−31.0000	−1.02934	−0.514669	−	0.857389i	$-0.672085\pi$
$907$	−31.0000	−1.02934	−0.514669	+	0.857389i	$0.672085\pi$
$908$	7.00000	0.232303
$909$	0	0
$910$	0	0
$911$	27.0000	0.894550	0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000	0.894550	0.447275	+	0.894397i	$0.352395\pi$
$912$	0	0
$913$	−7.00000	−0.231666
$914$	22.0000	0.727695
$915$	0	0
$916$	14.0000	0.462573
$917$	4.00000	0.132092
$918$	0	0
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	0	0
$921$	0	0
$922$	15.0000	0.493999
$923$	80.0000	2.63323
$924$	0	0
$925$	0	0
$926$	−21.0000	−0.690103
$927$	0	0
$928$	6.00000	0.196960
$929$	45.0000	1.47640	0.738201	−	0.674581i	$-0.235676\pi$
$929$	45.0000	1.47640	0.738201	+	0.674581i	$0.235676\pi$
$930$	0	0
$931$	7.00000	0.229416
$932$	−3.00000	−0.0982683
$933$	0	0
$934$	28.0000	0.916188
$935$	0	0
$936$	0	0
$937$	29.0000	0.947389	0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000	0.947389	0.473694	+	0.880689i	$0.342920\pi$
$938$	15.0000	0.489767
$939$	0	0
$940$	0	0
$941$	33.0000	1.07577	0.537885	−	0.843018i	$-0.319224\pi$
$941$	33.0000	1.07577	0.537885	+	0.843018i	$0.319224\pi$
$942$	0	0
$943$	0	0
$944$	2.00000	0.0650945
$945$	0	0
$946$	11.0000	0.357641
$947$	30.0000	0.974869	0.487435	−	0.873160i	$-0.337933\pi$
$947$	30.0000	0.974869	0.487435	+	0.873160i	$0.337933\pi$
$948$	0	0
$949$	55.0000	1.78538
$950$	0	0
$951$	0	0
$952$	4.00000	0.129641
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	0	0
$956$	4.00000	0.129369
$957$	0	0
$958$	−14.0000	−0.452319
$959$	17.0000	0.548959
$960$	0	0
$961$	−31.0000	−1.00000
$962$	−20.0000	−0.644826
$963$	0	0
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	3.00000	0.0964735	0.0482367	−	0.998836i	$-0.484640\pi$
$967$	3.00000	0.0964735	0.0482367	+	0.998836i	$0.484640\pi$
$968$	−10.0000	−0.321412
$969$	0	0
$970$	0	0
$971$	30.0000	0.962746	0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000	0.962746	0.481373	+	0.876516i	$0.340138\pi$
$972$	0	0
$973$	20.0000	0.641171
$974$	33.0000	1.05739
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	33.0000	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$978$	0	0
$979$	1.00000	0.0319601
$980$	0	0
$981$	0	0
$982$	36.0000	1.14881
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	0	0
$985$	0	0
$986$	−24.0000	−0.764316
$987$	0	0
$988$	−35.0000	−1.11350
$989$	0	0
$990$	0	0
$991$	60.0000	1.90596	0.952981	−	0.303029i	$-0.0979978\pi$
$991$	60.0000	1.90596	0.952981	+	0.303029i	$0.0979978\pi$
$992$	0	0
$993$	0	0
$994$	16.0000	0.507489
$995$	0	0
$996$	0	0
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−40.0000	−1.26618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.ci.1.1		1
3.2	odd	2		9450.2.a.q.1.1		1
5.2	odd	4		1890.2.g.i.379.2	yes	2
5.3	odd	4		1890.2.g.i.379.1	yes	2
5.4	even	2		9450.2.a.bk.1.1		1
15.2	even	4		1890.2.g.d.379.1	✓	2
15.8	even	4		1890.2.g.d.379.2	yes	2
15.14	odd	2		9450.2.a.dq.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.d.379.1	✓	2	15.2	even	4
1890.2.g.d.379.2	yes	2	15.8	even	4
1890.2.g.i.379.1	yes	2	5.3	odd	4
1890.2.g.i.379.2	yes	2	5.2	odd	4
9450.2.a.q.1.1		1	3.2	odd	2
9450.2.a.bk.1.1		1	5.4	even	2
9450.2.a.ci.1.1		1	1.1	even	1	trivial
9450.2.a.dq.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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more