LMFDB - Embedded newform 9450.2.a.r.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:	yes
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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{11} +5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +2.00000 q^{19} -1.00000 q^{22} +5.00000 q^{23} -5.00000 q^{26} -1.00000 q^{28} -6.00000 q^{29} +10.0000 q^{31} -1.00000 q^{32} -4.00000 q^{34} -1.00000 q^{37} -2.00000 q^{38} +2.00000 q^{41} -6.00000 q^{43} +1.00000 q^{44} -5.00000 q^{46} -1.00000 q^{47} +1.00000 q^{49} +5.00000 q^{52} -6.00000 q^{53} +1.00000 q^{56} +6.00000 q^{58} +13.0000 q^{59} +13.0000 q^{61} -10.0000 q^{62} +1.00000 q^{64} +4.00000 q^{68} +11.0000 q^{71} +14.0000 q^{73} +1.00000 q^{74} +2.00000 q^{76} -1.00000 q^{77} -2.00000 q^{82} -12.0000 q^{83} +6.00000 q^{86} -1.00000 q^{88} -4.00000 q^{89} -5.00000 q^{91} +5.00000 q^{92} +1.00000 q^{94} -1.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

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	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	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
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	0	0
$22$	−1.00000	−0.213201
$23$	5.00000	1.04257	0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000	1.04257	0.521286	+	0.853382i	$0.325452\pi$
$24$	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	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−4.00000	−0.685994
$35$	0	0
$36$	0	0
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−2.00000	−0.324443
$39$	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
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−5.00000	−0.737210
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	5.00000	0.693375
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	13.0000	1.69246	0.846228	−	0.532821i	$-0.178868\pi$
$59$	13.0000	1.69246	0.846228	+	0.532821i	$0.178868\pi$
$60$	0	0
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	−10.0000	−1.27000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	11.0000	1.30546	0.652730	−	0.757591i	$-0.273624\pi$
$71$	11.0000	1.30546	0.652730	+	0.757591i	$0.273624\pi$
$72$	0	0
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	2.00000	0.229416
$77$	−1.00000	−0.113961
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	0	0
$82$	−2.00000	−0.220863
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	0	0
$86$	6.00000	0.646997
$87$	0	0
$88$	−1.00000	−0.106600
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	5.00000	0.521286
$93$	0	0
$94$	1.00000	0.103142
$95$	0	0
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	6.00000	0.582772
$107$	−19.0000	−1.83680	−0.918400	−	0.395654i	$-0.870518\pi$
$107$	−19.0000	−1.83680	−0.918400	+	0.395654i	$0.870518\pi$
$108$	0	0
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	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
$116$	−6.00000	−0.557086
$117$	0	0
$118$	−13.0000	−1.19675
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−13.0000	−1.17696
$123$	0	0
$124$	10.0000	0.898027
$125$	0	0
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	9.00000	0.786334	0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000	0.786334	0.393167	+	0.919467i	$0.371379\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	0	0
$135$	0	0
$136$	−4.00000	−0.342997
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	0	0
$142$	−11.0000	−0.923099
$143$	5.00000	0.418121
$144$	0	0
$145$	0	0
$146$	−14.0000	−1.15865
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	−2.00000	−0.162221
$153$	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	$0.688685\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−5.00000	−0.394055
$162$	0	0
$163$	18.0000	1.40987	0.704934	−	0.709273i	$-0.250976\pi$
$163$	18.0000	1.40987	0.704934	+	0.709273i	$0.250976\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	12.0000	0.931381
$167$	−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
$171$	0	0
$172$	−6.00000	−0.457496
$173$	16.0000	1.21646	0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000	1.21646	0.608229	+	0.793762i	$0.291880\pi$
$174$	0	0
$175$	0	0
$176$	1.00000	0.0753778
$177$	0	0
$178$	4.00000	0.299813
$179$	−23.0000	−1.71910	−0.859550	−	0.511051i	$-0.829256\pi$
$179$	−23.0000	−1.71910	−0.859550	+	0.511051i	$0.829256\pi$
$180$	0	0
$181$	11.0000	0.817624	0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000	0.817624	0.408812	+	0.912619i	$0.365943\pi$
$182$	5.00000	0.370625
$183$	0	0
$184$	−5.00000	−0.368605
$185$	0	0
$186$	0	0
$187$	4.00000	0.292509
$188$	−1.00000	−0.0729325
$189$	0	0
$190$	0	0
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	0	0
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	6.00000	0.421117
$204$	0	0
$205$	0	0
$206$	14.0000	0.975426
$207$	0	0
$208$	5.00000	0.346688
$209$	2.00000	0.138343
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	19.0000	1.29881
$215$	0	0
$216$	0	0
$217$	−10.0000	−0.678844
$218$	−10.0000	−0.677285
$219$	0	0
$220$	0	0
$221$	20.0000	1.34535
$222$	0	0
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	10.0000	0.665190
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	0	0
$229$	19.0000	1.25556	0.627778	−	0.778393i	$-0.283965\pi$
$229$	19.0000	1.25556	0.627778	+	0.778393i	$0.283965\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	8.00000	0.524097	0.262049	−	0.965055i	$-0.415602\pi$
$233$	8.00000	0.524097	0.262049	+	0.965055i	$0.415602\pi$
$234$	0	0
$235$	0	0
$236$	13.0000	0.846228
$237$	0	0
$238$	4.00000	0.259281
$239$	−19.0000	−1.22901	−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000	−1.22901	−0.614504	+	0.788914i	$0.710644\pi$
$240$	0	0
$241$	−15.0000	−0.966235	−0.483117	−	0.875556i	$-0.660496\pi$
$241$	−15.0000	−0.966235	−0.483117	+	0.875556i	$0.660496\pi$
$242$	10.0000	0.642824
$243$	0	0
$244$	13.0000	0.832240
$245$	0	0
$246$	0	0
$247$	10.0000	0.636285
$248$	−10.0000	−0.635001
$249$	0	0
$250$	0	0
$251$	1.00000	0.0631194	0.0315597	−	0.999502i	$-0.489953\pi$
$251$	1.00000	0.0631194	0.0315597	+	0.999502i	$0.489953\pi$
$252$	0	0
$253$	5.00000	0.314347
$254$	6.00000	0.376473
$255$	0	0
$256$	1.00000	0.0625000
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	0	0
$259$	1.00000	0.0621370
$260$	0	0
$261$	0	0
$262$	−9.00000	−0.556022
$263$	−3.00000	−0.184988	−0.0924940	−	0.995713i	$-0.529484\pi$
$263$	−3.00000	−0.184988	−0.0924940	+	0.995713i	$0.529484\pi$
$264$	0	0
$265$	0	0
$266$	2.00000	0.122628
$267$	0	0
$268$	0	0
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−2.00000	−0.120824
$275$	0	0
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	0	0
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	11.0000	0.652730
$285$	0	0
$286$	−5.00000	−0.295656
$287$	−2.00000	−0.118056
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	14.0000	0.819288
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	18.0000	1.04271
$299$	25.0000	1.44579
$300$	0	0
$301$	6.00000	0.345834
$302$	10.0000	0.575435
$303$	0	0
$304$	2.00000	0.114708
$305$	0	0
$306$	0	0
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	−1.00000	−0.0569803
$309$	0	0
$310$	0	0
$311$	11.0000	0.623753	0.311876	−	0.950123i	$-0.399043\pi$
$311$	11.0000	0.623753	0.311876	+	0.950123i	$0.399043\pi$
$312$	0	0
$313$	2.00000	0.113047	0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000	0.113047	0.0565233	+	0.998401i	$0.481998\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	0	0
$317$	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
$319$	−6.00000	−0.335936
$320$	0	0
$321$	0	0
$322$	5.00000	0.278639
$323$	8.00000	0.445132
$324$	0	0
$325$	0	0
$326$	−18.0000	−0.996928
$327$	0	0
$328$	−2.00000	−0.110432
$329$	1.00000	0.0551318
$330$	0	0
$331$	22.0000	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$331$	22.0000	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$332$	−12.0000	−0.658586
$333$	0	0
$334$	5.00000	0.273588
$335$	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
$341$	10.0000	0.541530
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	6.00000	0.323498
$345$	0	0
$346$	−16.0000	−0.860165
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	0	0
$356$	−4.00000	−0.212000
$357$	0	0
$358$	23.0000	1.21559
$359$	25.0000	1.31945	0.659725	−	0.751507i	$-0.270673\pi$
$359$	25.0000	1.31945	0.659725	+	0.751507i	$0.270673\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−11.0000	−0.578147
$363$	0	0
$364$	−5.00000	−0.262071
$365$	0	0
$366$	0	0
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	5.00000	0.260643
$369$	0	0
$370$	0	0
$371$	6.00000	0.311504
$372$	0	0
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−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	$-0.417321\pi$
$379$	10.0000	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$380$	0	0
$381$	0	0
$382$	4.00000	0.204658
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	0	0
$385$	0	0
$386$	−2.00000	−0.101797
$387$	0	0
$388$	−1.00000	−0.0507673
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	20.0000	1.01144
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−1.00000	−0.0501886	−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000	−0.0501886	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−2.00000	−0.100251
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	50.0000	2.49068
$404$	0	0
$405$	0	0
$406$	−6.00000	−0.297775
$407$	−1.00000	−0.0495682
$408$	0	0
$409$	37.0000	1.82953	0.914766	−	0.403984i	$-0.132375\pi$
$409$	37.0000	1.82953	0.914766	+	0.403984i	$0.132375\pi$
$410$	0	0
$411$	0	0
$412$	−14.0000	−0.689730
$413$	−13.0000	−0.639688
$414$	0	0
$415$	0	0
$416$	−5.00000	−0.245145
$417$	0	0
$418$	−2.00000	−0.0978232
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	19.0000	0.926003	0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000	0.926003	0.463002	+	0.886357i	$0.346772\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	−13.0000	−0.629114
$428$	−19.0000	−0.918400
$429$	0	0
$430$	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
$433$	33.0000	1.58588	0.792939	−	0.609301i	$-0.208550\pi$
$433$	33.0000	1.58588	0.792939	+	0.609301i	$0.208550\pi$
$434$	10.0000	0.480015
$435$	0	0
$436$	10.0000	0.478913
$437$	10.0000	0.478365
$438$	0	0
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	0	0
$441$	0	0
$442$	−20.0000	−0.951303
$443$	31.0000	1.47285	0.736427	−	0.676517i	$-0.236511\pi$
$443$	31.0000	1.47285	0.736427	+	0.676517i	$0.236511\pi$
$444$	0	0
$445$	0	0
$446$	−6.00000	−0.284108
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−38.0000	−1.79333	−0.896665	−	0.442709i	$-0.854018\pi$
$449$	−38.0000	−1.79333	−0.896665	+	0.442709i	$0.854018\pi$
$450$	0	0
$451$	2.00000	0.0941763
$452$	−10.0000	−0.470360
$453$	0	0
$454$	−3.00000	−0.140797
$455$	0	0
$456$	0	0
$457$	−13.0000	−0.608114	−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000	−0.608114	−0.304057	+	0.952654i	$0.598341\pi$
$458$	−19.0000	−0.887812
$459$	0	0
$460$	0	0
$461$	20.0000	0.931493	0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000	0.931493	0.465746	+	0.884918i	$0.345786\pi$
$462$	0	0
$463$	34.0000	1.58011	0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000	1.58011	0.790057	+	0.613033i	$0.210051\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−8.00000	−0.370593
$467$	−13.0000	−0.601568	−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000	−0.601568	−0.300784	+	0.953692i	$0.597248\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−13.0000	−0.598374
$473$	−6.00000	−0.275880
$474$	0	0
$475$	0	0
$476$	−4.00000	−0.183340
$477$	0	0
$478$	19.0000	0.869040
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	−5.00000	−0.227980
$482$	15.0000	0.683231
$483$	0	0
$484$	−10.0000	−0.454545
$485$	0	0
$486$	0	0
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	−13.0000	−0.588482
$489$	0	0
$490$	0	0
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	0	0
$493$	−24.0000	−1.08091
$494$	−10.0000	−0.449921
$495$	0	0
$496$	10.0000	0.449013
$497$	−11.0000	−0.493417
$498$	0	0
$499$	40.0000	1.79065	0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000	1.79065	0.895323	+	0.445418i	$0.146945\pi$
$500$	0	0
$501$	0	0
$502$	−1.00000	−0.0446322
$503$	−4.00000	−0.178351	−0.0891756	−	0.996016i	$-0.528423\pi$
$503$	−4.00000	−0.178351	−0.0891756	+	0.996016i	$0.528423\pi$
$504$	0	0
$505$	0	0
$506$	−5.00000	−0.222277
$507$	0	0
$508$	−6.00000	−0.266207
$509$	−22.0000	−0.975133	−0.487566	−	0.873086i	$-0.662115\pi$
$509$	−22.0000	−0.975133	−0.487566	+	0.873086i	$0.662115\pi$
$510$	0	0
$511$	−14.0000	−0.619324
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	8.00000	0.352865
$515$	0	0
$516$	0	0
$517$	−1.00000	−0.0439799
$518$	−1.00000	−0.0439375
$519$	0	0
$520$	0	0
$521$	−12.0000	−0.525730	−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000	−0.525730	−0.262865	+	0.964833i	$0.584667\pi$
$522$	0	0
$523$	−8.00000	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$524$	9.00000	0.393167
$525$	0	0
$526$	3.00000	0.130806
$527$	40.0000	1.74243
$528$	0	0
$529$	2.00000	0.0869565
$530$	0	0
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	10.0000	0.433148
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	24.0000	1.03471
$539$	1.00000	0.0430730
$540$	0	0
$541$	−37.0000	−1.59075	−0.795377	−	0.606115i	$-0.792727\pi$
$541$	−37.0000	−1.59075	−0.795377	+	0.606115i	$0.792727\pi$
$542$	0	0
$543$	0	0
$544$	−4.00000	−0.171499
$545$	0	0
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	2.00000	0.0854358
$549$	0	0
$550$	0	0
$551$	−12.0000	−0.511217
$552$	0	0
$553$	0	0
$554$	2.00000	0.0849719
$555$	0	0
$556$	20.0000	0.848189
$557$	−40.0000	−1.69485	−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000	−1.69485	−0.847427	+	0.530912i	$0.821850\pi$
$558$	0	0
$559$	−30.0000	−1.26886
$560$	0	0
$561$	0	0
$562$	14.0000	0.590554
$563$	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
$566$	14.0000	0.588464
$567$	0	0
$568$	−11.0000	−0.461550
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	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
$574$	2.00000	0.0834784
$575$	0	0
$576$	0	0
$577$	1.00000	0.0416305	0.0208153	−	0.999783i	$-0.493374\pi$
$577$	1.00000	0.0416305	0.0208153	+	0.999783i	$0.493374\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	0	0
$581$	12.0000	0.497844
$582$	0	0
$583$	−6.00000	−0.248495
$584$	−14.0000	−0.579324
$585$	0	0
$586$	−24.0000	−0.991431
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	20.0000	0.824086
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	−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
$595$	0	0
$596$	−18.0000	−0.737309
$597$	0	0
$598$	−25.0000	−1.02233
$599$	−4.00000	−0.163436	−0.0817178	−	0.996656i	$-0.526041\pi$
$599$	−4.00000	−0.163436	−0.0817178	+	0.996656i	$0.526041\pi$
$600$	0	0
$601$	23.0000	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$602$	−6.00000	−0.244542
$603$	0	0
$604$	−10.0000	−0.406894
$605$	0	0
$606$	0	0
$607$	−30.0000	−1.21766	−0.608831	−	0.793300i	$-0.708361\pi$
$607$	−30.0000	−1.21766	−0.608831	+	0.793300i	$0.708361\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	0	0
$611$	−5.00000	−0.202278
$612$	0	0
$613$	−29.0000	−1.17130	−0.585649	−	0.810564i	$-0.699160\pi$
$613$	−29.0000	−1.17130	−0.585649	+	0.810564i	$0.699160\pi$
$614$	2.00000	0.0807134
$615$	0	0
$616$	1.00000	0.0402911
$617$	−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
$619$	−2.00000	−0.0803868	−0.0401934	−	0.999192i	$-0.512797\pi$
$619$	−2.00000	−0.0803868	−0.0401934	+	0.999192i	$0.512797\pi$
$620$	0	0
$621$	0	0
$622$	−11.0000	−0.441060
$623$	4.00000	0.160257
$624$	0	0
$625$	0	0
$626$	−2.00000	−0.0799361
$627$	0	0
$628$	−14.0000	−0.558661
$629$	−4.00000	−0.159490
$630$	0	0
$631$	−18.0000	−0.716569	−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000	−0.716569	−0.358284	+	0.933613i	$0.616638\pi$
$632$	0	0
$633$	0	0
$634$	−10.0000	−0.397151
$635$	0	0
$636$	0	0
$637$	5.00000	0.198107
$638$	6.00000	0.237542
$639$	0	0
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	−5.00000	−0.197028
$645$	0	0
$646$	−8.00000	−0.314756
$647$	23.0000	0.904223	0.452112	−	0.891961i	$-0.350671\pi$
$647$	23.0000	0.904223	0.452112	+	0.891961i	$0.350671\pi$
$648$	0	0
$649$	13.0000	0.510295
$650$	0	0
$651$	0	0
$652$	18.0000	0.704934
$653$	−8.00000	−0.313064	−0.156532	−	0.987673i	$-0.550031\pi$
$653$	−8.00000	−0.313064	−0.156532	+	0.987673i	$0.550031\pi$
$654$	0	0
$655$	0	0
$656$	2.00000	0.0780869
$657$	0	0
$658$	−1.00000	−0.0389841
$659$	4.00000	0.155818	0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000	0.155818	0.0779089	+	0.996960i	$0.475176\pi$
$660$	0	0
$661$	5.00000	0.194477	0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000	0.194477	0.0972387	+	0.995261i	$0.468999\pi$
$662$	−22.0000	−0.855054
$663$	0	0
$664$	12.0000	0.465690
$665$	0	0
$666$	0	0
$667$	−30.0000	−1.16160
$668$	−5.00000	−0.193456
$669$	0	0
$670$	0	0
$671$	13.0000	0.501859
$672$	0	0
$673$	−23.0000	−0.886585	−0.443292	−	0.896377i	$-0.646190\pi$
$673$	−23.0000	−0.886585	−0.443292	+	0.896377i	$0.646190\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	12.0000	0.461538
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	0	0
$679$	1.00000	0.0383765
$680$	0	0
$681$	0	0
$682$	−10.0000	−0.382920
$683$	37.0000	1.41577	0.707883	−	0.706330i	$-0.249650\pi$
$683$	37.0000	1.41577	0.707883	+	0.706330i	$0.249650\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−6.00000	−0.228748
$689$	−30.0000	−1.14291
$690$	0	0
$691$	−38.0000	−1.44559	−0.722794	−	0.691063i	$-0.757142\pi$
$691$	−38.0000	−1.44559	−0.722794	+	0.691063i	$0.757142\pi$
$692$	16.0000	0.608229
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	8.00000	0.303022
$698$	10.0000	0.378506
$699$	0	0
$700$	0	0
$701$	48.0000	1.81293	0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000	1.81293	0.906467	+	0.422276i	$0.138769\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	1.00000	0.0376889
$705$	0	0
$706$	6.00000	0.225813
$707$	0	0
$708$	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
$712$	4.00000	0.149906
$713$	50.0000	1.87251
$714$	0	0
$715$	0	0
$716$	−23.0000	−0.859550
$717$	0	0
$718$	−25.0000	−0.932992
$719$	45.0000	1.67822	0.839108	−	0.543964i	$-0.183077\pi$
$719$	45.0000	1.67822	0.839108	+	0.543964i	$0.183077\pi$
$720$	0	0
$721$	14.0000	0.521387
$722$	15.0000	0.558242
$723$	0	0
$724$	11.0000	0.408812
$725$	0	0
$726$	0	0
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	5.00000	0.185312
$729$	0	0
$730$	0	0
$731$	−24.0000	−0.887672
$732$	0	0
$733$	9.00000	0.332423	0.166211	−	0.986090i	$-0.446847\pi$
$733$	9.00000	0.332423	0.166211	+	0.986090i	$0.446847\pi$
$734$	28.0000	1.03350
$735$	0	0
$736$	−5.00000	−0.184302
$737$	0	0
$738$	0	0
$739$	48.0000	1.76571	0.882854	−	0.469647i	$-0.155619\pi$
$739$	48.0000	1.76571	0.882854	+	0.469647i	$0.155619\pi$
$740$	0	0
$741$	0	0
$742$	−6.00000	−0.220267
$743$	−39.0000	−1.43077	−0.715386	−	0.698730i	$-0.753749\pi$
$743$	−39.0000	−1.43077	−0.715386	+	0.698730i	$0.753749\pi$
$744$	0	0
$745$	0	0
$746$	−22.0000	−0.805477
$747$	0	0
$748$	4.00000	0.146254
$749$	19.0000	0.694245
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	−1.00000	−0.0364662
$753$	0	0
$754$	30.0000	1.09254
$755$	0	0
$756$	0	0
$757$	−23.0000	−0.835949	−0.417975	−	0.908459i	$-0.637260\pi$
$757$	−23.0000	−0.835949	−0.417975	+	0.908459i	$0.637260\pi$
$758$	−10.0000	−0.363216
$759$	0	0
$760$	0	0
$761$	50.0000	1.81250	0.906249	−	0.422744i	$-0.138933\pi$
$761$	50.0000	1.81250	0.906249	+	0.422744i	$0.138933\pi$
$762$	0	0
$763$	−10.0000	−0.362024
$764$	−4.00000	−0.144715
$765$	0	0
$766$	−15.0000	−0.541972
$767$	65.0000	2.34701
$768$	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
$771$	0	0
$772$	2.00000	0.0719816
$773$	−10.0000	−0.359675	−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000	−0.359675	−0.179838	+	0.983696i	$0.557557\pi$
$774$	0	0
$775$	0	0
$776$	1.00000	0.0358979
$777$	0	0
$778$	6.00000	0.215110
$779$	4.00000	0.143315
$780$	0	0
$781$	11.0000	0.393611
$782$	−20.0000	−0.715199
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	10.0000	0.355559
$792$	0	0
$793$	65.0000	2.30822
$794$	1.00000	0.0354887
$795$	0	0
$796$	2.00000	0.0708881
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	0	0
$799$	−4.00000	−0.141510
$800$	0	0
$801$	0	0
$802$	0	0
$803$	14.0000	0.494049
$804$	0	0
$805$	0	0
$806$	−50.0000	−1.76117
$807$	0	0
$808$	0	0
$809$	22.0000	0.773479	0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000	0.773479	0.386739	+	0.922189i	$0.373601\pi$
$810$	0	0
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	1.00000	0.0350500
$815$	0	0
$816$	0	0
$817$	−12.0000	−0.419827
$818$	−37.0000	−1.29367
$819$	0	0
$820$	0	0
$821$	−2.00000	−0.0698005	−0.0349002	−	0.999391i	$-0.511111\pi$
$821$	−2.00000	−0.0698005	−0.0349002	+	0.999391i	$0.511111\pi$
$822$	0	0
$823$	−22.0000	−0.766872	−0.383436	−	0.923567i	$-0.625259\pi$
$823$	−22.0000	−0.766872	−0.383436	+	0.923567i	$0.625259\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	13.0000	0.452328
$827$	39.0000	1.35616	0.678081	−	0.734987i	$-0.262812\pi$
$827$	39.0000	1.35616	0.678081	+	0.734987i	$0.262812\pi$
$828$	0	0
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	0	0
$831$	0	0
$832$	5.00000	0.173344
$833$	4.00000	0.138592
$834$	0	0
$835$	0	0
$836$	2.00000	0.0691714
$837$	0	0
$838$	12.0000	0.414533
$839$	9.00000	0.310715	0.155357	−	0.987858i	$-0.450347\pi$
$839$	9.00000	0.310715	0.155357	+	0.987858i	$0.450347\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−19.0000	−0.654783
$843$	0	0
$844$	20.0000	0.688428
$845$	0	0
$846$	0	0
$847$	10.0000	0.343604
$848$	−6.00000	−0.206041
$849$	0	0
$850$	0	0
$851$	−5.00000	−0.171398
$852$	0	0
$853$	11.0000	0.376633	0.188316	−	0.982108i	$-0.439697\pi$
$853$	11.0000	0.376633	0.188316	+	0.982108i	$0.439697\pi$
$854$	13.0000	0.444851
$855$	0	0
$856$	19.0000	0.649407
$857$	52.0000	1.77629	0.888143	−	0.459567i	$-0.151995\pi$
$857$	52.0000	1.77629	0.888143	+	0.459567i	$0.151995\pi$
$858$	0	0
$859$	−10.0000	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$860$	0	0
$861$	0	0
$862$	−33.0000	−1.12398
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	0	0
$866$	−33.0000	−1.12139
$867$	0	0
$868$	−10.0000	−0.339422
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−10.0000	−0.338643
$873$	0	0
$874$	−10.0000	−0.338255
$875$	0	0
$876$	0	0
$877$	43.0000	1.45201	0.726003	−	0.687691i	$-0.241376\pi$
$877$	43.0000	1.45201	0.726003	+	0.687691i	$0.241376\pi$
$878$	−32.0000	−1.07995
$879$	0	0
$880$	0	0
$881$	−12.0000	−0.404290	−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000	−0.404290	−0.202145	+	0.979356i	$0.564791\pi$
$882$	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
$886$	−31.0000	−1.04147
$887$	5.00000	0.167884	0.0839418	−	0.996471i	$-0.473249\pi$
$887$	5.00000	0.167884	0.0839418	+	0.996471i	$0.473249\pi$
$888$	0	0
$889$	6.00000	0.201234
$890$	0	0
$891$	0	0
$892$	6.00000	0.200895
$893$	−2.00000	−0.0669274
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	38.0000	1.26808
$899$	−60.0000	−2.00111
$900$	0	0
$901$	−24.0000	−0.799556
$902$	−2.00000	−0.0665927
$903$	0	0
$904$	10.0000	0.332595
$905$	0	0
$906$	0	0
$907$	54.0000	1.79304	0.896520	−	0.443003i	$-0.146087\pi$
$907$	54.0000	1.79304	0.896520	+	0.443003i	$0.146087\pi$
$908$	3.00000	0.0995585
$909$	0	0
$910$	0	0
$911$	−27.0000	−0.894550	−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000	−0.894550	−0.447275	+	0.894397i	$0.647605\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	13.0000	0.430002
$915$	0	0
$916$	19.0000	0.627778
$917$	−9.00000	−0.297206
$918$	0	0
$919$	−26.0000	−0.857661	−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000	−0.857661	−0.428830	+	0.903385i	$0.641074\pi$
$920$	0	0
$921$	0	0
$922$	−20.0000	−0.658665
$923$	55.0000	1.81035
$924$	0	0
$925$	0	0
$926$	−34.0000	−1.11731
$927$	0	0
$928$	6.00000	0.196960
$929$	10.0000	0.328089	0.164045	−	0.986453i	$-0.447546\pi$
$929$	10.0000	0.328089	0.164045	+	0.986453i	$0.447546\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	8.00000	0.262049
$933$	0	0
$934$	13.0000	0.425373
$935$	0	0
$936$	0	0
$937$	−51.0000	−1.66610	−0.833049	−	0.553200i	$-0.813407\pi$
$937$	−51.0000	−1.66610	−0.833049	+	0.553200i	$0.813407\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−48.0000	−1.56476	−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000	−1.56476	−0.782378	+	0.622804i	$0.785993\pi$
$942$	0	0
$943$	10.0000	0.325645
$944$	13.0000	0.423114
$945$	0	0
$946$	6.00000	0.195077
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	70.0000	2.27230
$950$	0	0
$951$	0	0
$952$	4.00000	0.129641
$953$	36.0000	1.16615	0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000	1.16615	0.583077	+	0.812417i	$0.301849\pi$
$954$	0	0
$955$	0	0
$956$	−19.0000	−0.614504
$957$	0	0
$958$	−24.0000	−0.775405
$959$	−2.00000	−0.0645834
$960$	0	0
$961$	69.0000	2.22581
$962$	5.00000	0.161206
$963$	0	0
$964$	−15.0000	−0.483117
$965$	0	0
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	10.0000	0.321412
$969$	0	0
$970$	0	0
$971$	45.0000	1.44412	0.722059	−	0.691831i	$-0.243196\pi$
$971$	45.0000	1.44412	0.722059	+	0.691831i	$0.243196\pi$
$972$	0	0
$973$	−20.0000	−0.641171
$974$	12.0000	0.384505
$975$	0	0
$976$	13.0000	0.416120
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	0	0
$979$	−4.00000	−0.127841
$980$	0	0
$981$	0	0
$982$	36.0000	1.14881
$983$	31.0000	0.988746	0.494373	−	0.869250i	$-0.335398\pi$
$983$	31.0000	0.988746	0.494373	+	0.869250i	$0.335398\pi$
$984$	0	0
$985$	0	0
$986$	24.0000	0.764316
$987$	0	0
$988$	10.0000	0.318142
$989$	−30.0000	−0.953945
$990$	0	0
$991$	−20.0000	−0.635321	−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000	−0.635321	−0.317660	+	0.948205i	$0.602897\pi$
$992$	−10.0000	−0.317500
$993$	0	0
$994$	11.0000	0.348899
$995$	0	0
$996$	0	0
$997$	7.00000	0.221692	0.110846	−	0.993838i	$-0.464644\pi$
$997$	7.00000	0.221692	0.110846	+	0.993838i	$0.464644\pi$
$998$	−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.r.1.1	✓	1
3.2	odd	2		9450.2.a.cj.1.1	yes	1
5.4	even	2		9450.2.a.dp.1.1	yes	1
15.14	odd	2		9450.2.a.bj.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9450.2.a.r.1.1	✓	1	1.1	even	1	trivial
9450.2.a.bj.1.1	yes	1	15.14	odd	2
9450.2.a.cj.1.1	yes	1	3.2	odd	2
9450.2.a.dp.1.1	yes	1	5.4	even	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

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