LMFDB - Embedded newform 9450.2.a.j.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:	$0$
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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{11} +5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -5.00000 q^{17} +8.00000 q^{19} +2.00000 q^{22} -1.00000 q^{23} -5.00000 q^{26} -1.00000 q^{28} +9.00000 q^{29} +1.00000 q^{31} -1.00000 q^{32} +5.00000 q^{34} +8.00000 q^{37} -8.00000 q^{38} +2.00000 q^{41} -9.00000 q^{43} -2.00000 q^{44} +1.00000 q^{46} +2.00000 q^{47} +1.00000 q^{49} +5.00000 q^{52} -9.00000 q^{53} +1.00000 q^{56} -9.00000 q^{58} +1.00000 q^{59} -2.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +3.00000 q^{67} -5.00000 q^{68} +5.00000 q^{71} +2.00000 q^{73} -8.00000 q^{74} +8.00000 q^{76} +2.00000 q^{77} -12.0000 q^{79} -2.00000 q^{82} +12.0000 q^{83} +9.00000 q^{86} +2.00000 q^{88} -1.00000 q^{89} -5.00000 q^{91} -1.00000 q^{92} -2.00000 q^{94} -10.0000 q^{97} -1.00000 q^{98} +O(q^{100})$

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
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	0	0
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	0	0
$26$	−5.00000	−0.980581
$27$	0	0
$28$	−1.00000	−0.188982
$29$	9.00000	1.67126	0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000	1.67126	0.835629	+	0.549294i	$0.185103\pi$
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	5.00000	0.857493
$35$	0	0
$36$	0	0
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	−8.00000	−1.29777
$39$	0	0
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	1.00000	0.147442
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	5.00000	0.693375
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−9.00000	−1.18176
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−5.00000	−0.606339
$69$	0	0
$70$	0	0
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	8.00000	0.917663
$77$	2.00000	0.227921
$78$	0	0
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	0	0
$81$	0	0
$82$	−2.00000	−0.220863
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	0	0
$86$	9.00000	0.970495
$87$	0	0
$88$	2.00000	0.213201
$89$	−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
$92$	−1.00000	−0.104257
$93$	0	0
$94$	−2.00000	−0.206284
$95$	0	0
$96$	0	0
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	19.0000	1.87213	0.936063	−	0.351833i	$-0.114441\pi$
$103$	19.0000	1.87213	0.936063	+	0.351833i	$0.114441\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	9.00000	0.874157
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	0	0
$115$	0	0
$116$	9.00000	0.835629
$117$	0	0
$118$	−1.00000	−0.0920575
$119$	5.00000	0.458349
$120$	0	0
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	0	0
$124$	1.00000	0.0898027
$125$	0	0
$126$	0	0
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	0	0
$133$	−8.00000	−0.693688
$134$	−3.00000	−0.259161
$135$	0	0
$136$	5.00000	0.428746
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	−5.00000	−0.419591
$143$	−10.0000	−0.836242
$144$	0	0
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	8.00000	0.657596
$149$	21.0000	1.72039	0.860194	−	0.509968i	$-0.170343\pi$
$149$	21.0000	1.72039	0.860194	+	0.509968i	$0.170343\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	−8.00000	−0.648886
$153$	0	0
$154$	−2.00000	−0.161165
$155$	0	0
$156$	0	0
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	12.0000	0.954669
$159$	0	0
$160$	0	0
$161$	1.00000	0.0788110
$162$	0	0
$163$	−9.00000	−0.704934	−0.352467	−	0.935824i	$-0.614657\pi$
$163$	−9.00000	−0.704934	−0.352467	+	0.935824i	$0.614657\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−12.0000	−0.931381
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	−9.00000	−0.686244
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	0	0
$176$	−2.00000	−0.150756
$177$	0	0
$178$	1.00000	0.0749532
$179$	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
$181$	17.0000	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$182$	5.00000	0.370625
$183$	0	0
$184$	1.00000	0.0737210
$185$	0	0
$186$	0	0
$187$	10.0000	0.731272
$188$	2.00000	0.145865
$189$	0	0
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	17.0000	1.22369	0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000	1.22369	0.611843	+	0.790979i	$0.290428\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	−25.0000	−1.77220	−0.886102	−	0.463491i	$-0.846597\pi$
$199$	−25.0000	−1.77220	−0.886102	+	0.463491i	$0.846597\pi$
$200$	0	0
$201$	0	0
$202$	12.0000	0.844317
$203$	−9.00000	−0.631676
$204$	0	0
$205$	0	0
$206$	−19.0000	−1.32379
$207$	0	0
$208$	5.00000	0.346688
$209$	−16.0000	−1.10674
$210$	0	0
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	−9.00000	−0.618123
$213$	0	0
$214$	10.0000	0.683586
$215$	0	0
$216$	0	0
$217$	−1.00000	−0.0678844
$218$	14.0000	0.948200
$219$	0	0
$220$	0	0
$221$	−25.0000	−1.68168
$222$	0	0
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	10.0000	0.665190
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	0	0
$232$	−9.00000	−0.590879
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	0	0
$235$	0	0
$236$	1.00000	0.0650945
$237$	0	0
$238$	−5.00000	−0.324102
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	−2.00000	−0.128037
$245$	0	0
$246$	0	0
$247$	40.0000	2.54514
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	−12.0000	−0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.0000	1.37232	0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000	1.37232	0.686161	+	0.727450i	$0.259294\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	0	0
$261$	0	0
$262$	−3.00000	−0.185341
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	0	0
$266$	8.00000	0.490511
$267$	0	0
$268$	3.00000	0.183254
$269$	12.0000	0.731653	0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000	0.731653	0.365826	+	0.930683i	$0.380786\pi$
$270$	0	0
$271$	9.00000	0.546711	0.273356	−	0.961913i	$-0.411866\pi$
$271$	9.00000	0.546711	0.273356	+	0.961913i	$0.411866\pi$
$272$	−5.00000	−0.303170
$273$	0	0
$274$	10.0000	0.604122
$275$	0	0
$276$	0	0
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	0	0
$281$	4.00000	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$282$	0	0
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	5.00000	0.296695
$285$	0	0
$286$	10.0000	0.591312
$287$	−2.00000	−0.118056
$288$	0	0
$289$	8.00000	0.470588
$290$	0	0
$291$	0	0
$292$	2.00000	0.117041
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	0	0
$295$	0	0
$296$	−8.00000	−0.464991
$297$	0	0
$298$	−21.0000	−1.21650
$299$	−5.00000	−0.289157
$300$	0	0
$301$	9.00000	0.518751
$302$	−20.0000	−1.15087
$303$	0	0
$304$	8.00000	0.458831
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	0	0
$311$	−10.0000	−0.567048	−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000	−0.567048	−0.283524	+	0.958965i	$0.591504\pi$
$312$	0	0
$313$	−4.00000	−0.226093	−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000	−0.226093	−0.113047	+	0.993590i	$0.536061\pi$
$314$	−7.00000	−0.395033
$315$	0	0
$316$	−12.0000	−0.675053
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	0	0
$319$	−18.0000	−1.00781
$320$	0	0
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	−40.0000	−2.22566
$324$	0	0
$325$	0	0
$326$	9.00000	0.498464
$327$	0	0
$328$	−2.00000	−0.110432
$329$	−2.00000	−0.110264
$330$	0	0
$331$	25.0000	1.37412	0.687062	−	0.726599i	$-0.258900\pi$
$331$	25.0000	1.37412	0.687062	+	0.726599i	$0.258900\pi$
$332$	12.0000	0.658586
$333$	0	0
$334$	−22.0000	−1.20379
$335$	0	0
$336$	0	0
$337$	19.0000	1.03500	0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000	1.03500	0.517498	+	0.855684i	$0.326864\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	−2.00000	−0.108306
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	9.00000	0.485247
$345$	0	0
$346$	14.0000	0.752645
$347$	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
$349$	35.0000	1.87351	0.936754	−	0.349990i	$-0.113815\pi$
$349$	35.0000	1.87351	0.936754	+	0.349990i	$0.113815\pi$
$350$	0	0
$351$	0	0
$352$	2.00000	0.106600
$353$	33.0000	1.75641	0.878206	−	0.478282i	$-0.158740\pi$
$353$	33.0000	1.75641	0.878206	+	0.478282i	$0.158740\pi$
$354$	0	0
$355$	0	0
$356$	−1.00000	−0.0529999
$357$	0	0
$358$	−4.00000	−0.211407
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	−17.0000	−0.893500
$363$	0	0
$364$	−5.00000	−0.262071
$365$	0	0
$366$	0	0
$367$	5.00000	0.260998	0.130499	−	0.991448i	$-0.458342\pi$
$367$	5.00000	0.260998	0.130499	+	0.991448i	$0.458342\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	0	0
$371$	9.00000	0.467257
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	−10.0000	−0.517088
$375$	0	0
$376$	−2.00000	−0.103142
$377$	45.0000	2.31762
$378$	0	0
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	0	0
$381$	0	0
$382$	−8.00000	−0.409316
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	0	0
$385$	0	0
$386$	−17.0000	−0.865277
$387$	0	0
$388$	−10.0000	−0.507673
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	5.00000	0.252861
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−18.0000	−0.906827
$395$	0	0
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	25.0000	1.25314
$399$	0	0
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	5.00000	0.249068
$404$	−12.0000	−0.597022
$405$	0	0
$406$	9.00000	0.446663
$407$	−16.0000	−0.793091
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	0	0
$412$	19.0000	0.936063
$413$	−1.00000	−0.0492068
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	16.0000	0.782586
$419$	−15.0000	−0.732798	−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000	−0.732798	−0.366399	+	0.930458i	$0.619409\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	1.00000	0.0486792
$423$	0	0
$424$	9.00000	0.437079
$425$	0	0
$426$	0	0
$427$	2.00000	0.0967868
$428$	−10.0000	−0.483368
$429$	0	0
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	−36.0000	−1.73005	−0.865025	−	0.501729i	$-0.832697\pi$
$433$	−36.0000	−1.73005	−0.865025	+	0.501729i	$0.832697\pi$
$434$	1.00000	0.0480015
$435$	0	0
$436$	−14.0000	−0.670478
$437$	−8.00000	−0.382692
$438$	0	0
$439$	11.0000	0.525001	0.262501	−	0.964932i	$-0.415453\pi$
$439$	11.0000	0.525001	0.262501	+	0.964932i	$0.415453\pi$
$440$	0	0
$441$	0	0
$442$	25.0000	1.18913
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	0	0
$445$	0	0
$446$	−24.0000	−1.13643
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	40.0000	1.88772	0.943858	−	0.330350i	$-0.107167\pi$
$449$	40.0000	1.88772	0.943858	+	0.330350i	$0.107167\pi$
$450$	0	0
$451$	−4.00000	−0.188353
$452$	−10.0000	−0.470360
$453$	0	0
$454$	3.00000	0.140797
$455$	0	0
$456$	0	0
$457$	23.0000	1.07589	0.537947	−	0.842978i	$-0.319200\pi$
$457$	23.0000	1.07589	0.537947	+	0.842978i	$0.319200\pi$
$458$	2.00000	0.0934539
$459$	0	0
$460$	0	0
$461$	−22.0000	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	9.00000	0.417815
$465$	0	0
$466$	22.0000	1.01913
$467$	−4.00000	−0.185098	−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000	−0.185098	−0.0925490	+	0.995708i	$0.529501\pi$
$468$	0	0
$469$	−3.00000	−0.138527
$470$	0	0
$471$	0	0
$472$	−1.00000	−0.0460287
$473$	18.0000	0.827641
$474$	0	0
$475$	0	0
$476$	5.00000	0.229175
$477$	0	0
$478$	16.0000	0.731823
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	0	0
$481$	40.0000	1.82384
$482$	12.0000	0.546585
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−18.0000	−0.815658	−0.407829	−	0.913058i	$-0.633714\pi$
$487$	−18.0000	−0.815658	−0.407829	+	0.913058i	$0.633714\pi$
$488$	2.00000	0.0905357
$489$	0	0
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	0	0
$493$	−45.0000	−2.02670
$494$	−40.0000	−1.79969
$495$	0	0
$496$	1.00000	0.0449013
$497$	−5.00000	−0.224281
$498$	0	0
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	0	0
$502$	8.00000	0.357057
$503$	26.0000	1.15928	0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000	1.15928	0.579641	+	0.814872i	$0.303193\pi$
$504$	0	0
$505$	0	0
$506$	−2.00000	−0.0889108
$507$	0	0
$508$	12.0000	0.532414
$509$	20.0000	0.886484	0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000	0.886484	0.443242	+	0.896402i	$0.353828\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−22.0000	−0.970378
$515$	0	0
$516$	0	0
$517$	−4.00000	−0.175920
$518$	8.00000	0.351500
$519$	0	0
$520$	0	0
$521$	3.00000	0.131432	0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000	0.131432	0.0657162	+	0.997838i	$0.479067\pi$
$522$	0	0
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	3.00000	0.131056
$525$	0	0
$526$	−9.00000	−0.392419
$527$	−5.00000	−0.217803
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	0	0
$532$	−8.00000	−0.346844
$533$	10.0000	0.433148
$534$	0	0
$535$	0	0
$536$	−3.00000	−0.129580
$537$	0	0
$538$	−12.0000	−0.517357
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−9.00000	−0.386583
$543$	0	0
$544$	5.00000	0.214373
$545$	0	0
$546$	0	0
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−10.0000	−0.427179
$549$	0	0
$550$	0	0
$551$	72.0000	3.06730
$552$	0	0
$553$	12.0000	0.510292
$554$	−4.00000	−0.169944
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−7.00000	−0.296600	−0.148300	−	0.988942i	$-0.547380\pi$
$557$	−7.00000	−0.296600	−0.148300	+	0.988942i	$0.547380\pi$
$558$	0	0
$559$	−45.0000	−1.90330
$560$	0	0
$561$	0	0
$562$	−4.00000	−0.168730
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	0	0
$565$	0	0
$566$	−22.0000	−0.924729
$567$	0	0
$568$	−5.00000	−0.209795
$569$	−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
$571$	−23.0000	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$572$	−10.0000	−0.418121
$573$	0	0
$574$	2.00000	0.0834784
$575$	0	0
$576$	0	0
$577$	4.00000	0.166522	0.0832611	−	0.996528i	$-0.473466\pi$
$577$	4.00000	0.166522	0.0832611	+	0.996528i	$0.473466\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	0	0
$581$	−12.0000	−0.497844
$582$	0	0
$583$	18.0000	0.745484
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	30.0000	1.23929
$587$	33.0000	1.36206	0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000	1.36206	0.681028	+	0.732257i	$0.261533\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	0	0
$591$	0	0
$592$	8.00000	0.328798
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	0	0
$596$	21.0000	0.860194
$597$	0	0
$598$	5.00000	0.204465
$599$	41.0000	1.67521	0.837607	−	0.546273i	$-0.183954\pi$
$599$	41.0000	1.67521	0.837607	+	0.546273i	$0.183954\pi$
$600$	0	0
$601$	−16.0000	−0.652654	−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000	−0.652654	−0.326327	+	0.945257i	$0.605811\pi$
$602$	−9.00000	−0.366813
$603$	0	0
$604$	20.0000	0.813788
$605$	0	0
$606$	0	0
$607$	−3.00000	−0.121766	−0.0608831	−	0.998145i	$-0.519392\pi$
$607$	−3.00000	−0.121766	−0.0608831	+	0.998145i	$0.519392\pi$
$608$	−8.00000	−0.324443
$609$	0	0
$610$	0	0
$611$	10.0000	0.404557
$612$	0	0
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	−46.0000	−1.85189	−0.925945	−	0.377658i	$-0.876729\pi$
$617$	−46.0000	−1.85189	−0.925945	+	0.377658i	$0.876729\pi$
$618$	0	0
$619$	−26.0000	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$620$	0	0
$621$	0	0
$622$	10.0000	0.400963
$623$	1.00000	0.0400642
$624$	0	0
$625$	0	0
$626$	4.00000	0.159872
$627$	0	0
$628$	7.00000	0.279330
$629$	−40.0000	−1.59490
$630$	0	0
$631$	36.0000	1.43314	0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000	1.43314	0.716569	+	0.697517i	$0.245712\pi$
$632$	12.0000	0.477334
$633$	0	0
$634$	−10.0000	−0.397151
$635$	0	0
$636$	0	0
$637$	5.00000	0.198107
$638$	18.0000	0.712627
$639$	0	0
$640$	0	0
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	0	0
$643$	−46.0000	−1.81406	−0.907031	−	0.421063i	$-0.861657\pi$
$643$	−46.0000	−1.81406	−0.907031	+	0.421063i	$0.861657\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	40.0000	1.57378
$647$	38.0000	1.49393	0.746967	−	0.664861i	$-0.231509\pi$
$647$	38.0000	1.49393	0.746967	+	0.664861i	$0.231509\pi$
$648$	0	0
$649$	−2.00000	−0.0785069
$650$	0	0
$651$	0	0
$652$	−9.00000	−0.352467
$653$	−17.0000	−0.665261	−0.332631	−	0.943057i	$-0.607936\pi$
$653$	−17.0000	−0.665261	−0.332631	+	0.943057i	$0.607936\pi$
$654$	0	0
$655$	0	0
$656$	2.00000	0.0780869
$657$	0	0
$658$	2.00000	0.0779681
$659$	−2.00000	−0.0779089	−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000	−0.0779089	−0.0389545	+	0.999241i	$0.512403\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−25.0000	−0.971653
$663$	0	0
$664$	−12.0000	−0.465690
$665$	0	0
$666$	0	0
$667$	−9.00000	−0.348481
$668$	22.0000	0.851206
$669$	0	0
$670$	0	0
$671$	4.00000	0.154418
$672$	0	0
$673$	7.00000	0.269830	0.134915	−	0.990857i	$-0.456924\pi$
$673$	7.00000	0.269830	0.134915	+	0.990857i	$0.456924\pi$
$674$	−19.0000	−0.731853
$675$	0	0
$676$	12.0000	0.461538
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	10.0000	0.383765
$680$	0	0
$681$	0	0
$682$	2.00000	0.0765840
$683$	−2.00000	−0.0765279	−0.0382639	−	0.999268i	$-0.512183\pi$
$683$	−2.00000	−0.0765279	−0.0382639	+	0.999268i	$0.512183\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−9.00000	−0.343122
$689$	−45.0000	−1.71436
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	−30.0000	−1.13878
$695$	0	0
$696$	0	0
$697$	−10.0000	−0.378777
$698$	−35.0000	−1.32477
$699$	0	0
$700$	0	0
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	64.0000	2.41381
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−33.0000	−1.24197
$707$	12.0000	0.451306
$708$	0	0
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	0	0
$711$	0	0
$712$	1.00000	0.0374766
$713$	−1.00000	−0.0374503
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	11.0000	0.410516
$719$	6.00000	0.223762	0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000	0.223762	0.111881	+	0.993722i	$0.464312\pi$
$720$	0	0
$721$	−19.0000	−0.707597
$722$	−45.0000	−1.67473
$723$	0	0
$724$	17.0000	0.631800
$725$	0	0
$726$	0	0
$727$	33.0000	1.22390	0.611951	−	0.790896i	$-0.290385\pi$
$727$	33.0000	1.22390	0.611951	+	0.790896i	$0.290385\pi$
$728$	5.00000	0.185312
$729$	0	0
$730$	0	0
$731$	45.0000	1.66439
$732$	0	0
$733$	15.0000	0.554038	0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000	0.554038	0.277019	+	0.960864i	$0.410654\pi$
$734$	−5.00000	−0.184553
$735$	0	0
$736$	1.00000	0.0368605
$737$	−6.00000	−0.221013
$738$	0	0
$739$	24.0000	0.882854	0.441427	−	0.897297i	$-0.354472\pi$
$739$	24.0000	0.882854	0.441427	+	0.897297i	$0.354472\pi$
$740$	0	0
$741$	0	0
$742$	−9.00000	−0.330400
$743$	−21.0000	−0.770415	−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000	−0.770415	−0.385208	+	0.922830i	$0.625870\pi$
$744$	0	0
$745$	0	0
$746$	−4.00000	−0.146450
$747$	0	0
$748$	10.0000	0.365636
$749$	10.0000	0.365392
$750$	0	0
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	2.00000	0.0729325
$753$	0	0
$754$	−45.0000	−1.63880
$755$	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	$0.546441\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	0	0
$761$	41.0000	1.48625	0.743124	−	0.669153i	$-0.233343\pi$
$761$	41.0000	1.48625	0.743124	+	0.669153i	$0.233343\pi$
$762$	0	0
$763$	14.0000	0.506834
$764$	8.00000	0.289430
$765$	0	0
$766$	−36.0000	−1.30073
$767$	5.00000	0.180540
$768$	0	0
$769$	22.0000	0.793340	0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000	0.793340	0.396670	+	0.917961i	$0.370166\pi$
$770$	0	0
$771$	0	0
$772$	17.0000	0.611843
$773$	−28.0000	−1.00709	−0.503545	−	0.863969i	$-0.667971\pi$
$773$	−28.0000	−1.00709	−0.503545	+	0.863969i	$0.667971\pi$
$774$	0	0
$775$	0	0
$776$	10.0000	0.358979
$777$	0	0
$778$	30.0000	1.07555
$779$	16.0000	0.573259
$780$	0	0
$781$	−10.0000	−0.357828
$782$	−5.00000	−0.178800
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−2.00000	−0.0712923	−0.0356462	−	0.999364i	$-0.511349\pi$
$787$	−2.00000	−0.0712923	−0.0356462	+	0.999364i	$0.511349\pi$
$788$	18.0000	0.641223
$789$	0	0
$790$	0	0
$791$	10.0000	0.355559
$792$	0	0
$793$	−10.0000	−0.355110
$794$	−2.00000	−0.0709773
$795$	0	0
$796$	−25.0000	−0.886102
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	−10.0000	−0.353775
$800$	0	0
$801$	0	0
$802$	6.00000	0.211867
$803$	−4.00000	−0.141157
$804$	0	0
$805$	0	0
$806$	−5.00000	−0.176117
$807$	0	0
$808$	12.0000	0.422159
$809$	28.0000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$809$	28.0000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$810$	0	0
$811$	−42.0000	−1.47482	−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000	−1.47482	−0.737410	+	0.675446i	$0.763951\pi$
$812$	−9.00000	−0.315838
$813$	0	0
$814$	16.0000	0.560800
$815$	0	0
$816$	0	0
$817$	−72.0000	−2.51896
$818$	26.0000	0.909069
$819$	0	0
$820$	0	0
$821$	55.0000	1.91951	0.959757	−	0.280833i	$-0.0906107\pi$
$821$	55.0000	1.91951	0.959757	+	0.280833i	$0.0906107\pi$
$822$	0	0
$823$	44.0000	1.53374	0.766872	−	0.641800i	$-0.221812\pi$
$823$	44.0000	1.53374	0.766872	+	0.641800i	$0.221812\pi$
$824$	−19.0000	−0.661896
$825$	0	0
$826$	1.00000	0.0347945
$827$	−6.00000	−0.208640	−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000	−0.208640	−0.104320	+	0.994544i	$0.533267\pi$
$828$	0	0
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	0	0
$831$	0	0
$832$	5.00000	0.173344
$833$	−5.00000	−0.173240
$834$	0	0
$835$	0	0
$836$	−16.0000	−0.553372
$837$	0	0
$838$	15.0000	0.518166
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	−10.0000	−0.344623
$843$	0	0
$844$	−1.00000	−0.0344214
$845$	0	0
$846$	0	0
$847$	7.00000	0.240523
$848$	−9.00000	−0.309061
$849$	0	0
$850$	0	0
$851$	−8.00000	−0.274236
$852$	0	0
$853$	−25.0000	−0.855984	−0.427992	−	0.903783i	$-0.640779\pi$
$853$	−25.0000	−0.855984	−0.427992	+	0.903783i	$0.640779\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	10.0000	0.341793
$857$	1.00000	0.0341593	0.0170797	−	0.999854i	$-0.494563\pi$
$857$	1.00000	0.0341593	0.0170797	+	0.999854i	$0.494563\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	0	0
$862$	24.0000	0.817443
$863$	−3.00000	−0.102121	−0.0510606	−	0.998696i	$-0.516260\pi$
$863$	−3.00000	−0.102121	−0.0510606	+	0.998696i	$0.516260\pi$
$864$	0	0
$865$	0	0
$866$	36.0000	1.22333
$867$	0	0
$868$	−1.00000	−0.0339422
$869$	24.0000	0.814144
$870$	0	0
$871$	15.0000	0.508256
$872$	14.0000	0.474100
$873$	0	0
$874$	8.00000	0.270604
$875$	0	0
$876$	0	0
$877$	40.0000	1.35070	0.675352	−	0.737496i	$-0.263992\pi$
$877$	40.0000	1.35070	0.675352	+	0.737496i	$0.263992\pi$
$878$	−11.0000	−0.371232
$879$	0	0
$880$	0	0
$881$	−3.00000	−0.101073	−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000	−0.101073	−0.0505363	+	0.998722i	$0.516093\pi$
$882$	0	0
$883$	5.00000	0.168263	0.0841317	−	0.996455i	$-0.473188\pi$
$883$	5.00000	0.168263	0.0841317	+	0.996455i	$0.473188\pi$
$884$	−25.0000	−0.840841
$885$	0	0
$886$	−4.00000	−0.134383
$887$	20.0000	0.671534	0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000	0.671534	0.335767	+	0.941945i	$0.391004\pi$
$888$	0	0
$889$	−12.0000	−0.402467
$890$	0	0
$891$	0	0
$892$	24.0000	0.803579
$893$	16.0000	0.535420
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−40.0000	−1.33482
$899$	9.00000	0.300167
$900$	0	0
$901$	45.0000	1.49917
$902$	4.00000	0.133185
$903$	0	0
$904$	10.0000	0.332595
$905$	0	0
$906$	0	0
$907$	36.0000	1.19536	0.597680	−	0.801735i	$-0.296089\pi$
$907$	36.0000	1.19536	0.597680	+	0.801735i	$0.296089\pi$
$908$	−3.00000	−0.0995585
$909$	0	0
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	−23.0000	−0.760772
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	−3.00000	−0.0990687
$918$	0	0
$919$	−14.0000	−0.461817	−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000	−0.461817	−0.230909	+	0.972975i	$0.574170\pi$
$920$	0	0
$921$	0	0
$922$	22.0000	0.724531
$923$	25.0000	0.822885
$924$	0	0
$925$	0	0
$926$	32.0000	1.05159
$927$	0	0
$928$	−9.00000	−0.295439
$929$	58.0000	1.90292	0.951459	−	0.307775i	$-0.0995844\pi$
$929$	58.0000	1.90292	0.951459	+	0.307775i	$0.0995844\pi$
$930$	0	0
$931$	8.00000	0.262189
$932$	−22.0000	−0.720634
$933$	0	0
$934$	4.00000	0.130884
$935$	0	0
$936$	0	0
$937$	42.0000	1.37208	0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000	1.37208	0.686040	+	0.727564i	$0.259347\pi$
$938$	3.00000	0.0979535
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	−2.00000	−0.0651290
$944$	1.00000	0.0325472
$945$	0	0
$946$	−18.0000	−0.585230
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	0	0
$949$	10.0000	0.324614
$950$	0	0
$951$	0	0
$952$	−5.00000	−0.162051
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	0	0
$955$	0	0
$956$	−16.0000	−0.517477
$957$	0	0
$958$	−36.0000	−1.16311
$959$	10.0000	0.322917
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−40.0000	−1.28965
$963$	0	0
$964$	−12.0000	−0.386494
$965$	0	0
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	0	0
$971$	−9.00000	−0.288824	−0.144412	−	0.989518i	$-0.546129\pi$
$971$	−9.00000	−0.288824	−0.144412	+	0.989518i	$0.546129\pi$
$972$	0	0
$973$	4.00000	0.128234
$974$	18.0000	0.576757
$975$	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
$979$	2.00000	0.0639203
$980$	0	0
$981$	0	0
$982$	12.0000	0.382935
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	0	0
$986$	45.0000	1.43309
$987$	0	0
$988$	40.0000	1.27257
$989$	9.00000	0.286183
$990$	0	0
$991$	−50.0000	−1.58830	−0.794151	−	0.607720i	$-0.792084\pi$
$991$	−50.0000	−1.58830	−0.794151	+	0.607720i	$0.792084\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	5.00000	0.158590
$995$	0	0
$996$	0	0
$997$	−11.0000	−0.348373	−0.174187	−	0.984713i	$-0.555730\pi$
$997$	−11.0000	−0.348373	−0.174187	+	0.984713i	$0.555730\pi$
$998$	−4.00000	−0.126618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.j.1.1		1
3.2	odd	2		9450.2.a.cq.1.1		1
5.4	even	2		1890.2.a.w.1.1	yes	1
15.14	odd	2		1890.2.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.d.1.1	✓	1	15.14	odd	2
1890.2.a.w.1.1	yes	1	5.4	even	2
9450.2.a.j.1.1		1	1.1	even	1	trivial
9450.2.a.cq.1.1		1	3.2	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)

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