LMFDB - Embedded newform 8880.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8880,2,Mod(1,8880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8880, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("8880.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8880 = 2^{4} \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8880.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:	$70.9071569949$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1110)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8880.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} -1.00000 q^{5} +5.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{3} -1.00000 q^{5} +5.00000 q^{7} +1.00000 q^{9} +5.00000 q^{11} -1.00000 q^{13} +1.00000 q^{15} -5.00000 q^{17} +3.00000 q^{19} -5.00000 q^{21} -3.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} +6.00000 q^{29} +6.00000 q^{31} -5.00000 q^{33} -5.00000 q^{35} -1.00000 q^{37} +1.00000 q^{39} -4.00000 q^{43} -1.00000 q^{45} +18.0000 q^{49} +5.00000 q^{51} -3.00000 q^{53} -5.00000 q^{55} -3.00000 q^{57} +10.0000 q^{59} +10.0000 q^{61} +5.00000 q^{63} +1.00000 q^{65} +14.0000 q^{67} +3.00000 q^{69} -6.00000 q^{71} -9.00000 q^{73} -1.00000 q^{75} +25.0000 q^{77} +1.00000 q^{81} -5.00000 q^{83} +5.00000 q^{85} -6.00000 q^{87} +13.0000 q^{89} -5.00000 q^{91} -6.00000 q^{93} -3.00000 q^{95} -4.00000 q^{97} +5.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	0	0
$17$	−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
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	0	0
$21$	−5.00000	−1.09109
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0	0
$29$	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
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	0	0
$33$	−5.00000	−0.870388
$34$	0	0
$35$	−5.00000	−0.845154
$36$	0	0
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0	0
$39$	1.00000	0.160128
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	0	0
$51$	5.00000	0.700140
$52$	0	0
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	0	0
$57$	−3.00000	−0.397360
$58$	0	0
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	5.00000	0.629941
$64$	0	0
$65$	1.00000	0.124035
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	0	0
$69$	3.00000	0.361158
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	0	0
$75$	−1.00000	−0.115470
$76$	0	0
$77$	25.0000	2.84901
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−5.00000	−0.548821	−0.274411	−	0.961613i	$-0.588483\pi$
$83$	−5.00000	−0.548821	−0.274411	+	0.961613i	$0.588483\pi$
$84$	0	0
$85$	5.00000	0.542326
$86$	0	0
$87$	−6.00000	−0.643268
$88$	0	0
$89$	13.0000	1.37800	0.688999	−	0.724763i	$-0.258051\pi$
$89$	13.0000	1.37800	0.688999	+	0.724763i	$0.258051\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	0	0
$93$	−6.00000	−0.622171
$94$	0	0
$95$	−3.00000	−0.307794
$96$	0	0
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	0	0
$99$	5.00000	0.502519
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	0	0
$105$	5.00000	0.487950
$106$	0	0
$107$	−15.0000	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$107$	−15.0000	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$108$	0	0
$109$	−5.00000	−0.478913	−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000	−0.478913	−0.239457	+	0.970907i	$0.576969\pi$
$110$	0	0
$111$	1.00000	0.0949158
$112$	0	0
$113$	−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
$115$	3.00000	0.279751
$116$	0	0
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	−25.0000	−2.29175
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	3.00000	0.266207	0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000	0.266207	0.133103	+	0.991102i	$0.457506\pi$
$128$	0	0
$129$	4.00000	0.352180
$130$	0	0
$131$	20.0000	1.74741	0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000	1.74741	0.873704	+	0.486458i	$0.161711\pi$
$132$	0	0
$133$	15.0000	1.30066
$134$	0	0
$135$	1.00000	0.0860663
$136$	0	0
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	−2.00000	−0.169638	−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000	−0.169638	−0.0848189	+	0.996396i	$0.527031\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−5.00000	−0.418121
$144$	0	0
$145$	−6.00000	−0.498273
$146$	0	0
$147$	−18.0000	−1.48461
$148$	0	0
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	0	0
$153$	−5.00000	−0.404226
$154$	0	0
$155$	−6.00000	−0.481932
$156$	0	0
$157$	−20.0000	−1.59617	−0.798087	−	0.602542i	$-0.794154\pi$
$157$	−20.0000	−1.59617	−0.798087	+	0.602542i	$0.794154\pi$
$158$	0	0
$159$	3.00000	0.237915
$160$	0	0
$161$	−15.0000	−1.18217
$162$	0	0
$163$	23.0000	1.80150	0.900750	−	0.434339i	$-0.143018\pi$
$163$	23.0000	1.80150	0.900750	+	0.434339i	$0.143018\pi$
$164$	0	0
$165$	5.00000	0.389249
$166$	0	0
$167$	−5.00000	−0.386912	−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000	−0.386912	−0.193456	+	0.981109i	$0.561970\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	3.00000	0.229416
$172$	0	0
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	0	0
$175$	5.00000	0.377964
$176$	0	0
$177$	−10.0000	−0.751646
$178$	0	0
$179$	−8.00000	−0.597948	−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000	−0.597948	−0.298974	+	0.954261i	$0.596644\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	0	0
$185$	1.00000	0.0735215
$186$	0	0
$187$	−25.0000	−1.82818
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	7.00000	0.506502	0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000	0.506502	0.253251	+	0.967401i	$0.418500\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	23.0000	1.63868	0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000	1.63868	0.819341	+	0.573306i	$0.194340\pi$
$198$	0	0
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	0	0
$201$	−14.0000	−0.987484
$202$	0	0
$203$	30.0000	2.10559
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−3.00000	−0.208514
$208$	0	0
$209$	15.0000	1.03757
$210$	0	0
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	0	0
$213$	6.00000	0.411113
$214$	0	0
$215$	4.00000	0.272798
$216$	0	0
$217$	30.0000	2.03653
$218$	0	0
$219$	9.00000	0.608164
$220$	0	0
$221$	5.00000	0.336336
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	0	0
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0	0
$231$	−25.0000	−1.64488
$232$	0	0
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	−18.0000	−1.14998
$246$	0	0
$247$	−3.00000	−0.190885
$248$	0	0
$249$	5.00000	0.316862
$250$	0	0
$251$	−30.0000	−1.89358	−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000	−1.89358	−0.946792	+	0.321847i	$0.895696\pi$
$252$	0	0
$253$	−15.0000	−0.943042
$254$	0	0
$255$	−5.00000	−0.313112
$256$	0	0
$257$	15.0000	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$258$	0	0
$259$	−5.00000	−0.310685
$260$	0	0
$261$	6.00000	0.371391
$262$	0	0
$263$	−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
$265$	3.00000	0.184289
$266$	0	0
$267$	−13.0000	−0.795587
$268$	0	0
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	0	0
$273$	5.00000	0.302614
$274$	0	0
$275$	5.00000	0.301511
$276$	0	0
$277$	25.0000	1.50210	0.751052	−	0.660243i	$-0.229547\pi$
$277$	25.0000	1.50210	0.751052	+	0.660243i	$0.229547\pi$
$278$	0	0
$279$	6.00000	0.359211
$280$	0	0
$281$	1.00000	0.0596550	0.0298275	−	0.999555i	$-0.490504\pi$
$281$	1.00000	0.0596550	0.0298275	+	0.999555i	$0.490504\pi$
$282$	0	0
$283$	−5.00000	−0.297219	−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000	−0.297219	−0.148610	+	0.988896i	$0.547480\pi$
$284$	0	0
$285$	3.00000	0.177705
$286$	0	0
$287$	0	0
$288$	0	0
$289$	8.00000	0.470588
$290$	0	0
$291$	4.00000	0.234484
$292$	0	0
$293$	−11.0000	−0.642627	−0.321313	−	0.946973i	$-0.604124\pi$
$293$	−11.0000	−0.642627	−0.321313	+	0.946973i	$0.604124\pi$
$294$	0	0
$295$	−10.0000	−0.582223
$296$	0	0
$297$	−5.00000	−0.290129
$298$	0	0
$299$	3.00000	0.173494
$300$	0	0
$301$	−20.0000	−1.15278
$302$	0	0
$303$	6.00000	0.344691
$304$	0	0
$305$	−10.0000	−0.572598
$306$	0	0
$307$	30.0000	1.71219	0.856095	−	0.516818i	$-0.172884\pi$
$307$	30.0000	1.71219	0.856095	+	0.516818i	$0.172884\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	0	0
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	0	0
$313$	24.0000	1.35656	0.678280	−	0.734803i	$-0.262726\pi$
$313$	24.0000	1.35656	0.678280	+	0.734803i	$0.262726\pi$
$314$	0	0
$315$	−5.00000	−0.281718
$316$	0	0
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	0	0
$319$	30.0000	1.67968
$320$	0	0
$321$	15.0000	0.837218
$322$	0	0
$323$	−15.0000	−0.834622
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	0	0
$327$	5.00000	0.276501
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	0	0
$333$	−1.00000	−0.0547997
$334$	0	0
$335$	−14.0000	−0.764902
$336$	0	0
$337$	−9.00000	−0.490261	−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000	−0.490261	−0.245131	+	0.969490i	$0.578831\pi$
$338$	0	0
$339$	10.0000	0.543125
$340$	0	0
$341$	30.0000	1.62459
$342$	0	0
$343$	55.0000	2.96972
$344$	0	0
$345$	−3.00000	−0.161515
$346$	0	0
$347$	36.0000	1.93258	0.966291	−	0.257454i	$-0.0828835\pi$
$347$	36.0000	1.93258	0.966291	+	0.257454i	$0.0828835\pi$
$348$	0	0
$349$	24.0000	1.28469	0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000	1.28469	0.642345	+	0.766415i	$0.277962\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0	0
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	0	0
$355$	6.00000	0.318447
$356$	0	0
$357$	25.0000	1.32314
$358$	0	0
$359$	−36.0000	−1.90001	−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000	−1.90001	−0.950004	+	0.312239i	$0.898921\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	0	0
$363$	−14.0000	−0.734809
$364$	0	0
$365$	9.00000	0.471082
$366$	0	0
$367$	5.00000	0.260998	0.130499	−	0.991448i	$-0.458342\pi$
$367$	5.00000	0.260998	0.130499	+	0.991448i	$0.458342\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	−15.0000	−0.778761
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0	0
$377$	−6.00000	−0.309016
$378$	0	0
$379$	26.0000	1.33553	0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000	1.33553	0.667765	+	0.744372i	$0.267251\pi$
$380$	0	0
$381$	−3.00000	−0.153695
$382$	0	0
$383$	−9.00000	−0.459879	−0.229939	−	0.973205i	$-0.573853\pi$
$383$	−9.00000	−0.459879	−0.229939	+	0.973205i	$0.573853\pi$
$384$	0	0
$385$	−25.0000	−1.27412
$386$	0	0
$387$	−4.00000	−0.203331
$388$	0	0
$389$	34.0000	1.72387	0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000	1.72387	0.861934	+	0.507020i	$0.169253\pi$
$390$	0	0
$391$	15.0000	0.758583
$392$	0	0
$393$	−20.0000	−1.00887
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−36.0000	−1.80679	−0.903394	−	0.428811i	$-0.858933\pi$
$397$	−36.0000	−1.80679	−0.903394	+	0.428811i	$0.858933\pi$
$398$	0	0
$399$	−15.0000	−0.750939
$400$	0	0
$401$	−27.0000	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$402$	0	0
$403$	−6.00000	−0.298881
$404$	0	0
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−5.00000	−0.247841
$408$	0	0
$409$	24.0000	1.18672	0.593362	−	0.804936i	$-0.297800\pi$
$409$	24.0000	1.18672	0.593362	+	0.804936i	$0.297800\pi$
$410$	0	0
$411$	2.00000	0.0986527
$412$	0	0
$413$	50.0000	2.46034
$414$	0	0
$415$	5.00000	0.245440
$416$	0	0
$417$	2.00000	0.0979404
$418$	0	0
$419$	19.0000	0.928211	0.464105	−	0.885780i	$-0.346376\pi$
$419$	19.0000	0.928211	0.464105	+	0.885780i	$0.346376\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−5.00000	−0.242536
$426$	0	0
$427$	50.0000	2.41967
$428$	0	0
$429$	5.00000	0.241402
$430$	0	0
$431$	33.0000	1.58955	0.794777	−	0.606902i	$-0.207588\pi$
$431$	33.0000	1.58955	0.794777	+	0.606902i	$0.207588\pi$
$432$	0	0
$433$	21.0000	1.00920	0.504598	−	0.863355i	$-0.331641\pi$
$433$	21.0000	1.00920	0.504598	+	0.863355i	$0.331641\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	0	0
$437$	−9.00000	−0.430528
$438$	0	0
$439$	−36.0000	−1.71819	−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000	−1.71819	−0.859093	+	0.511819i	$0.828972\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	0	0
$443$	28.0000	1.33032	0.665160	−	0.746701i	$-0.268363\pi$
$443$	28.0000	1.33032	0.665160	+	0.746701i	$0.268363\pi$
$444$	0	0
$445$	−13.0000	−0.616259
$446$	0	0
$447$	−2.00000	−0.0945968
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	15.0000	0.704761
$454$	0	0
$455$	5.00000	0.234404
$456$	0	0
$457$	4.00000	0.187112	0.0935561	−	0.995614i	$-0.470177\pi$
$457$	4.00000	0.187112	0.0935561	+	0.995614i	$0.470177\pi$
$458$	0	0
$459$	5.00000	0.233380
$460$	0	0
$461$	26.0000	1.21094	0.605470	−	0.795868i	$-0.292985\pi$
$461$	26.0000	1.21094	0.605470	+	0.795868i	$0.292985\pi$
$462$	0	0
$463$	28.0000	1.30127	0.650635	−	0.759390i	$-0.274503\pi$
$463$	28.0000	1.30127	0.650635	+	0.759390i	$0.274503\pi$
$464$	0	0
$465$	6.00000	0.278243
$466$	0	0
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	70.0000	3.23230
$470$	0	0
$471$	20.0000	0.921551
$472$	0	0
$473$	−20.0000	−0.919601
$474$	0	0
$475$	3.00000	0.137649
$476$	0	0
$477$	−3.00000	−0.137361
$478$	0	0
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	0	0
$481$	1.00000	0.0455961
$482$	0	0
$483$	15.0000	0.682524
$484$	0	0
$485$	4.00000	0.181631
$486$	0	0
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	0	0
$489$	−23.0000	−1.04010
$490$	0	0
$491$	9.00000	0.406164	0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000	0.406164	0.203082	+	0.979162i	$0.434904\pi$
$492$	0	0
$493$	−30.0000	−1.35113
$494$	0	0
$495$	−5.00000	−0.224733
$496$	0	0
$497$	−30.0000	−1.34568
$498$	0	0
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	0	0
$501$	5.00000	0.223384
$502$	0	0
$503$	20.0000	0.891756	0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000	0.891756	0.445878	+	0.895094i	$0.352892\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	0	0
$507$	12.0000	0.532939
$508$	0	0
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	−45.0000	−1.99068
$512$	0	0
$513$	−3.00000	−0.132453
$514$	0	0
$515$	−16.0000	−0.705044
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−11.0000	−0.482846
$520$	0	0
$521$	12.0000	0.525730	0.262865	−	0.964833i	$-0.415333\pi$
$521$	12.0000	0.525730	0.262865	+	0.964833i	$0.415333\pi$
$522$	0	0
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	0	0
$525$	−5.00000	−0.218218
$526$	0	0
$527$	−30.0000	−1.30682
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	10.0000	0.433963
$532$	0	0
$533$	0	0
$534$	0	0
$535$	15.0000	0.648507
$536$	0	0
$537$	8.00000	0.345225
$538$	0	0
$539$	90.0000	3.87657
$540$	0	0
$541$	5.00000	0.214967	0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000	0.214967	0.107483	+	0.994207i	$0.465721\pi$
$542$	0	0
$543$	10.0000	0.429141
$544$	0	0
$545$	5.00000	0.214176
$546$	0	0
$547$	43.0000	1.83855	0.919274	−	0.393619i	$-0.128777\pi$
$547$	43.0000	1.83855	0.919274	+	0.393619i	$0.128777\pi$
$548$	0	0
$549$	10.0000	0.426790
$550$	0	0
$551$	18.0000	0.766826
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−1.00000	−0.0424476
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	4.00000	0.169182
$560$	0	0
$561$	25.0000	1.05550
$562$	0	0
$563$	−22.0000	−0.927189	−0.463595	−	0.886047i	$-0.653441\pi$
$563$	−22.0000	−0.927189	−0.463595	+	0.886047i	$0.653441\pi$
$564$	0	0
$565$	10.0000	0.420703
$566$	0	0
$567$	5.00000	0.209980
$568$	0	0
$569$	−13.0000	−0.544988	−0.272494	−	0.962157i	$-0.587849\pi$
$569$	−13.0000	−0.544988	−0.272494	+	0.962157i	$0.587849\pi$
$570$	0	0
$571$	10.0000	0.418487	0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000	0.418487	0.209243	+	0.977864i	$0.432900\pi$
$572$	0	0
$573$	−7.00000	−0.292429
$574$	0	0
$575$	−3.00000	−0.125109
$576$	0	0
$577$	26.0000	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$577$	26.0000	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$578$	0	0
$579$	2.00000	0.0831172
$580$	0	0
$581$	−25.0000	−1.03717
$582$	0	0
$583$	−15.0000	−0.621237
$584$	0	0
$585$	1.00000	0.0413449
$586$	0	0
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	0	0
$589$	18.0000	0.741677
$590$	0	0
$591$	−23.0000	−0.946094
$592$	0	0
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	0	0
$595$	25.0000	1.02490
$596$	0	0
$597$	−24.0000	−0.982255
$598$	0	0
$599$	−44.0000	−1.79779	−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000	−1.79779	−0.898896	+	0.438163i	$0.855629\pi$
$600$	0	0
$601$	−13.0000	−0.530281	−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000	−0.530281	−0.265141	+	0.964210i	$0.585418\pi$
$602$	0	0
$603$	14.0000	0.570124
$604$	0	0
$605$	−14.0000	−0.569181
$606$	0	0
$607$	18.0000	0.730597	0.365299	−	0.930890i	$-0.380967\pi$
$607$	18.0000	0.730597	0.365299	+	0.930890i	$0.380967\pi$
$608$	0	0
$609$	−30.0000	−1.21566
$610$	0	0
$611$	0	0
$612$	0	0
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−34.0000	−1.36879	−0.684394	−	0.729112i	$-0.739933\pi$
$617$	−34.0000	−1.36879	−0.684394	+	0.729112i	$0.739933\pi$
$618$	0	0
$619$	32.0000	1.28619	0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000	1.28619	0.643094	+	0.765787i	$0.277650\pi$
$620$	0	0
$621$	3.00000	0.120386
$622$	0	0
$623$	65.0000	2.60417
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−15.0000	−0.599042
$628$	0	0
$629$	5.00000	0.199363
$630$	0	0
$631$	4.00000	0.159237	0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000	0.159237	0.0796187	+	0.996825i	$0.474630\pi$
$632$	0	0
$633$	−2.00000	−0.0794929
$634$	0	0
$635$	−3.00000	−0.119051
$636$	0	0
$637$	−18.0000	−0.713186
$638$	0	0
$639$	−6.00000	−0.237356
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	−23.0000	−0.907031	−0.453516	−	0.891248i	$-0.649830\pi$
$643$	−23.0000	−0.907031	−0.453516	+	0.891248i	$0.649830\pi$
$644$	0	0
$645$	−4.00000	−0.157500
$646$	0	0
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	0	0
$649$	50.0000	1.96267
$650$	0	0
$651$	−30.0000	−1.17579
$652$	0	0
$653$	−48.0000	−1.87839	−0.939193	−	0.343391i	$-0.888424\pi$
$653$	−48.0000	−1.87839	−0.939193	+	0.343391i	$0.888424\pi$
$654$	0	0
$655$	−20.0000	−0.781465
$656$	0	0
$657$	−9.00000	−0.351123
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	−47.0000	−1.82809	−0.914044	−	0.405615i	$-0.867057\pi$
$661$	−47.0000	−1.82809	−0.914044	+	0.405615i	$0.867057\pi$
$662$	0	0
$663$	−5.00000	−0.194184
$664$	0	0
$665$	−15.0000	−0.581675
$666$	0	0
$667$	−18.0000	−0.696963
$668$	0	0
$669$	−8.00000	−0.309298
$670$	0	0
$671$	50.0000	1.93023
$672$	0	0
$673$	19.0000	0.732396	0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000	0.732396	0.366198	+	0.930537i	$0.380659\pi$
$674$	0	0
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	−9.00000	−0.345898	−0.172949	−	0.984931i	$-0.555330\pi$
$677$	−9.00000	−0.345898	−0.172949	+	0.984931i	$0.555330\pi$
$678$	0	0
$679$	−20.0000	−0.767530
$680$	0	0
$681$	8.00000	0.306561
$682$	0	0
$683$	−48.0000	−1.83667	−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000	−1.83667	−0.918334	+	0.395805i	$0.870466\pi$
$684$	0	0
$685$	2.00000	0.0764161
$686$	0	0
$687$	−6.00000	−0.228914
$688$	0	0
$689$	3.00000	0.114291
$690$	0	0
$691$	22.0000	0.836919	0.418460	−	0.908235i	$-0.362570\pi$
$691$	22.0000	0.836919	0.418460	+	0.908235i	$0.362570\pi$
$692$	0	0
$693$	25.0000	0.949671
$694$	0	0
$695$	2.00000	0.0758643
$696$	0	0
$697$	0	0
$698$	0	0
$699$	26.0000	0.983410
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−3.00000	−0.113147
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−30.0000	−1.12827
$708$	0	0
$709$	−35.0000	−1.31445	−0.657226	−	0.753693i	$-0.728270\pi$
$709$	−35.0000	−1.31445	−0.657226	+	0.753693i	$0.728270\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−18.0000	−0.674105
$714$	0	0
$715$	5.00000	0.186989
$716$	0	0
$717$	12.0000	0.448148
$718$	0	0
$719$	26.0000	0.969636	0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000	0.969636	0.484818	+	0.874615i	$0.338886\pi$
$720$	0	0
$721$	80.0000	2.97936
$722$	0	0
$723$	18.0000	0.669427
$724$	0	0
$725$	6.00000	0.222834
$726$	0	0
$727$	30.0000	1.11264	0.556319	−	0.830969i	$-0.312213\pi$
$727$	30.0000	1.11264	0.556319	+	0.830969i	$0.312213\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	20.0000	0.739727
$732$	0	0
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	0	0
$735$	18.0000	0.663940
$736$	0	0
$737$	70.0000	2.57848
$738$	0	0
$739$	−26.0000	−0.956425	−0.478213	−	0.878244i	$-0.658715\pi$
$739$	−26.0000	−0.956425	−0.478213	+	0.878244i	$0.658715\pi$
$740$	0	0
$741$	3.00000	0.110208
$742$	0	0
$743$	−10.0000	−0.366864	−0.183432	−	0.983032i	$-0.558721\pi$
$743$	−10.0000	−0.366864	−0.183432	+	0.983032i	$0.558721\pi$
$744$	0	0
$745$	−2.00000	−0.0732743
$746$	0	0
$747$	−5.00000	−0.182940
$748$	0	0
$749$	−75.0000	−2.74044
$750$	0	0
$751$	−28.0000	−1.02173	−0.510867	−	0.859660i	$-0.670676\pi$
$751$	−28.0000	−1.02173	−0.510867	+	0.859660i	$0.670676\pi$
$752$	0	0
$753$	30.0000	1.09326
$754$	0	0
$755$	15.0000	0.545906
$756$	0	0
$757$	37.0000	1.34479	0.672394	−	0.740193i	$-0.265266\pi$
$757$	37.0000	1.34479	0.672394	+	0.740193i	$0.265266\pi$
$758$	0	0
$759$	15.0000	0.544466
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	0	0
$763$	−25.0000	−0.905061
$764$	0	0
$765$	5.00000	0.180775
$766$	0	0
$767$	−10.0000	−0.361079
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	−15.0000	−0.540212
$772$	0	0
$773$	−21.0000	−0.755318	−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000	−0.755318	−0.377659	+	0.925945i	$0.623271\pi$
$774$	0	0
$775$	6.00000	0.215526
$776$	0	0
$777$	5.00000	0.179374
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−30.0000	−1.07348
$782$	0	0
$783$	−6.00000	−0.214423
$784$	0	0
$785$	20.0000	0.713831
$786$	0	0
$787$	−42.0000	−1.49714	−0.748569	−	0.663057i	$-0.769259\pi$
$787$	−42.0000	−1.49714	−0.748569	+	0.663057i	$0.769259\pi$
$788$	0	0
$789$	12.0000	0.427211
$790$	0	0
$791$	−50.0000	−1.77780
$792$	0	0
$793$	−10.0000	−0.355110
$794$	0	0
$795$	−3.00000	−0.106399
$796$	0	0
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	13.0000	0.459332
$802$	0	0
$803$	−45.0000	−1.58802
$804$	0	0
$805$	15.0000	0.528681
$806$	0	0
$807$	−9.00000	−0.316815
$808$	0	0
$809$	−15.0000	−0.527372	−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000	−0.527372	−0.263686	+	0.964609i	$0.584938\pi$
$810$	0	0
$811$	−40.0000	−1.40459	−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000	−1.40459	−0.702295	+	0.711886i	$0.747841\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	0	0
$815$	−23.0000	−0.805655
$816$	0	0
$817$	−12.0000	−0.419827
$818$	0	0
$819$	−5.00000	−0.174714
$820$	0	0
$821$	39.0000	1.36111	0.680555	−	0.732697i	$-0.261739\pi$
$821$	39.0000	1.36111	0.680555	+	0.732697i	$0.261739\pi$
$822$	0	0
$823$	35.0000	1.22002	0.610012	−	0.792392i	$-0.291165\pi$
$823$	35.0000	1.22002	0.610012	+	0.792392i	$0.291165\pi$
$824$	0	0
$825$	−5.00000	−0.174078
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	7.00000	0.243120	0.121560	−	0.992584i	$-0.461210\pi$
$829$	7.00000	0.243120	0.121560	+	0.992584i	$0.461210\pi$
$830$	0	0
$831$	−25.0000	−0.867240
$832$	0	0
$833$	−90.0000	−3.11832
$834$	0	0
$835$	5.00000	0.173032
$836$	0	0
$837$	−6.00000	−0.207390
$838$	0	0
$839$	42.0000	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−1.00000	−0.0344418
$844$	0	0
$845$	12.0000	0.412813
$846$	0	0
$847$	70.0000	2.40523
$848$	0	0
$849$	5.00000	0.171600
$850$	0	0
$851$	3.00000	0.102839
$852$	0	0
$853$	19.0000	0.650548	0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000	0.650548	0.325274	+	0.945620i	$0.394544\pi$
$854$	0	0
$855$	−3.00000	−0.102598
$856$	0	0
$857$	9.00000	0.307434	0.153717	−	0.988115i	$-0.450876\pi$
$857$	9.00000	0.307434	0.153717	+	0.988115i	$0.450876\pi$
$858$	0	0
$859$	−7.00000	−0.238837	−0.119418	−	0.992844i	$-0.538103\pi$
$859$	−7.00000	−0.238837	−0.119418	+	0.992844i	$0.538103\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	0	0
$865$	−11.0000	−0.374011
$866$	0	0
$867$	−8.00000	−0.271694
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−14.0000	−0.474372
$872$	0	0
$873$	−4.00000	−0.135379
$874$	0	0
$875$	−5.00000	−0.169031
$876$	0	0
$877$	−52.0000	−1.75592	−0.877958	−	0.478738i	$-0.841094\pi$
$877$	−52.0000	−1.75592	−0.877958	+	0.478738i	$0.841094\pi$
$878$	0	0
$879$	11.0000	0.371021
$880$	0	0
$881$	−40.0000	−1.34763	−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000	−1.34763	−0.673817	+	0.738898i	$0.735346\pi$
$882$	0	0
$883$	−21.0000	−0.706706	−0.353353	−	0.935490i	$-0.614959\pi$
$883$	−21.0000	−0.706706	−0.353353	+	0.935490i	$0.614959\pi$
$884$	0	0
$885$	10.0000	0.336146
$886$	0	0
$887$	38.0000	1.27592	0.637958	−	0.770072i	$-0.279780\pi$
$887$	38.0000	1.27592	0.637958	+	0.770072i	$0.279780\pi$
$888$	0	0
$889$	15.0000	0.503084
$890$	0	0
$891$	5.00000	0.167506
$892$	0	0
$893$	0	0
$894$	0	0
$895$	8.00000	0.267411
$896$	0	0
$897$	−3.00000	−0.100167
$898$	0	0
$899$	36.0000	1.20067
$900$	0	0
$901$	15.0000	0.499722
$902$	0	0
$903$	20.0000	0.665558
$904$	0	0
$905$	10.0000	0.332411
$906$	0	0
$907$	−37.0000	−1.22856	−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000	−1.22856	−0.614282	+	0.789086i	$0.710554\pi$
$908$	0	0
$909$	−6.00000	−0.199007
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	0	0
$913$	−25.0000	−0.827379
$914$	0	0
$915$	10.0000	0.330590
$916$	0	0
$917$	100.000	3.30229
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	−30.0000	−0.988534
$922$	0	0
$923$	6.00000	0.197492
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	0	0
$927$	16.0000	0.525509
$928$	0	0
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	0	0
$931$	54.0000	1.76978
$932$	0	0
$933$	8.00000	0.261908
$934$	0	0
$935$	25.0000	0.817587
$936$	0	0
$937$	−34.0000	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$938$	0	0
$939$	−24.0000	−0.783210
$940$	0	0
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	5.00000	0.162650
$946$	0	0
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	0	0
$949$	9.00000	0.292152
$950$	0	0
$951$	10.0000	0.324272
$952$	0	0
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	0	0
$955$	−7.00000	−0.226515
$956$	0	0
$957$	−30.0000	−0.969762
$958$	0	0
$959$	−10.0000	−0.322917
$960$	0	0
$961$	5.00000	0.161290
$962$	0	0
$963$	−15.0000	−0.483368
$964$	0	0
$965$	2.00000	0.0643823
$966$	0	0
$967$	18.0000	0.578841	0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000	0.578841	0.289420	+	0.957202i	$0.406537\pi$
$968$	0	0
$969$	15.0000	0.481869
$970$	0	0
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	0	0
$973$	−10.0000	−0.320585
$974$	0	0
$975$	1.00000	0.0320256
$976$	0	0
$977$	39.0000	1.24772	0.623860	−	0.781536i	$-0.285563\pi$
$977$	39.0000	1.24772	0.623860	+	0.781536i	$0.285563\pi$
$978$	0	0
$979$	65.0000	2.07741
$980$	0	0
$981$	−5.00000	−0.159638
$982$	0	0
$983$	58.0000	1.84991	0.924956	−	0.380073i	$-0.124101\pi$
$983$	58.0000	1.84991	0.924956	+	0.380073i	$0.124101\pi$
$984$	0	0
$985$	−23.0000	−0.732841
$986$	0	0
$987$	0	0
$988$	0	0
$989$	12.0000	0.381578
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	0	0
$993$	4.00000	0.126936
$994$	0	0
$995$	−24.0000	−0.760851
$996$	0	0
$997$	−39.0000	−1.23514	−0.617571	−	0.786515i	$-0.711883\pi$
$997$	−39.0000	−1.23514	−0.617571	+	0.786515i	$0.711883\pi$
$998$	0	0
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8880.2.a.i.1.1		1
4.3	odd	2		1110.2.a.m.1.1	✓	1
12.11	even	2		3330.2.a.f.1.1		1
20.19	odd	2		5550.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.a.m.1.1	✓	1	4.3	odd	2
3330.2.a.f.1.1		1	12.11	even	2
5550.2.a.k.1.1		1	20.19	odd	2
8880.2.a.i.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8880 = 2^{4} \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8880.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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