LMFDB - Embedded newform 666.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(1,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.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:	$5.31803677462$
Analytic rank:	$1$
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	$\chi$	$=$	666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -3.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{10} -5.00000 q^{11} -3.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} +5.00000 q^{19} -2.00000 q^{20} -5.00000 q^{22} -3.00000 q^{23} -1.00000 q^{25} -3.00000 q^{26} -3.00000 q^{28} +4.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +6.00000 q^{35} +1.00000 q^{37} +5.00000 q^{38} -2.00000 q^{40} -6.00000 q^{41} +4.00000 q^{43} -5.00000 q^{44} -3.00000 q^{46} +4.00000 q^{47} +2.00000 q^{49} -1.00000 q^{50} -3.00000 q^{52} +3.00000 q^{53} +10.0000 q^{55} -3.00000 q^{56} -14.0000 q^{59} -14.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +12.0000 q^{67} -3.00000 q^{68} +6.00000 q^{70} -12.0000 q^{71} +13.0000 q^{73} +1.00000 q^{74} +5.00000 q^{76} +15.0000 q^{77} +6.00000 q^{79} -2.00000 q^{80} -6.00000 q^{82} +7.00000 q^{83} +6.00000 q^{85} +4.00000 q^{86} -5.00000 q^{88} +1.00000 q^{89} +9.00000 q^{91} -3.00000 q^{92} +4.00000 q^{94} -10.0000 q^{95} -12.0000 q^{97} +2.00000 q^{98} +O(q^{100})$

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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	−2.00000	−0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	−5.00000	−1.06600
$23$	−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
$26$	−3.00000	−0.588348
$27$	0	0
$28$	−3.00000	−0.566947
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	6.00000	1.01419
$36$	0	0
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	5.00000	0.811107
$39$	0	0
$40$	−2.00000	−0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	−3.00000	−0.442326
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−3.00000	−0.416025
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	10.0000	1.34840
$56$	−3.00000	−0.400892
$57$	0	0
$58$	0	0
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	6.00000	0.717137
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	5.00000	0.573539
$77$	15.0000	1.70941
$78$	0	0
$79$	6.00000	0.675053	0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000	0.675053	0.337526	+	0.941316i	$0.390410\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	−6.00000	−0.662589
$83$	7.00000	0.768350	0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000	0.768350	0.384175	+	0.923260i	$0.374486\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	4.00000	0.431331
$87$	0	0
$88$	−5.00000	−0.533002
$89$	1.00000	0.106000	0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000	0.106000	0.0529999	+	0.998595i	$0.483122\pi$
$90$	0	0
$91$	9.00000	0.943456
$92$	−3.00000	−0.312772
$93$	0	0
$94$	4.00000	0.412568
$95$	−10.0000	−1.02598
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	2.00000	0.202031
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−2.00000	−0.197066	−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000	−0.197066	−0.0985329	+	0.995134i	$0.531415\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	3.00000	0.291386
$107$	13.0000	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$107$	13.0000	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$108$	0	0
$109$	−13.0000	−1.24517	−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000	−1.24517	−0.622587	+	0.782551i	$0.713918\pi$
$110$	10.0000	0.953463
$111$	0	0
$112$	−3.00000	−0.283473
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	6.00000	0.559503
$116$	0	0
$117$	0	0
$118$	−14.0000	−1.28880
$119$	9.00000	0.825029
$120$	0	0
$121$	14.0000	1.27273
$122$	−14.0000	−1.26750
$123$	0	0
$124$	4.00000	0.359211
$125$	12.0000	1.07331
$126$	0	0
$127$	−17.0000	−1.50851	−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000	−1.50851	−0.754253	+	0.656584i	$0.772001\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	6.00000	0.526235
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	0	0
$133$	−15.0000	−1.30066
$134$	12.0000	1.03664
$135$	0	0
$136$	−3.00000	−0.257248
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	6.00000	0.507093
$141$	0	0
$142$	−12.0000	−1.00702
$143$	15.0000	1.25436
$144$	0	0
$145$	0	0
$146$	13.0000	1.07589
$147$	0	0
$148$	1.00000	0.0821995
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	5.00000	0.405554
$153$	0	0
$154$	15.0000	1.20873
$155$	−8.00000	−0.642575
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	−2.00000	−0.158114
$161$	9.00000	0.709299
$162$	0	0
$163$	7.00000	0.548282	0.274141	−	0.961689i	$-0.411606\pi$
$163$	7.00000	0.548282	0.274141	+	0.961689i	$0.411606\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	7.00000	0.543305
$167$	−13.0000	−1.00597	−0.502985	−	0.864295i	$-0.667765\pi$
$167$	−13.0000	−1.00597	−0.502985	+	0.864295i	$0.667765\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	6.00000	0.460179
$171$	0	0
$172$	4.00000	0.304997
$173$	−19.0000	−1.44454	−0.722272	−	0.691609i	$-0.756902\pi$
$173$	−19.0000	−1.44454	−0.722272	+	0.691609i	$0.756902\pi$
$174$	0	0
$175$	3.00000	0.226779
$176$	−5.00000	−0.376889
$177$	0	0
$178$	1.00000	0.0749532
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	9.00000	0.667124
$183$	0	0
$184$	−3.00000	−0.221163
$185$	−2.00000	−0.147043
$186$	0	0
$187$	15.0000	1.09691
$188$	4.00000	0.291730
$189$	0	0
$190$	−10.0000	−0.725476
$191$	−7.00000	−0.506502	−0.253251	−	0.967401i	$-0.581500\pi$
$191$	−7.00000	−0.506502	−0.253251	+	0.967401i	$0.581500\pi$
$192$	0	0
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	2.00000	0.142857
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−10.0000	−0.703598
$203$	0	0
$204$	0	0
$205$	12.0000	0.838116
$206$	−2.00000	−0.139347
$207$	0	0
$208$	−3.00000	−0.208013
$209$	−25.0000	−1.72929
$210$	0	0
$211$	24.0000	1.65223	0.826114	−	0.563503i	$-0.190547\pi$
$211$	24.0000	1.65223	0.826114	+	0.563503i	$0.190547\pi$
$212$	3.00000	0.206041
$213$	0	0
$214$	13.0000	0.888662
$215$	−8.00000	−0.545595
$216$	0	0
$217$	−12.0000	−0.814613
$218$	−13.0000	−0.880471
$219$	0	0
$220$	10.0000	0.674200
$221$	9.00000	0.605406
$222$	0	0
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	−2.00000	−0.133038
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	0	0
$229$	−20.0000	−1.32164	−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000	−1.32164	−0.660819	+	0.750546i	$0.729791\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	0	0
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	0	0
$235$	−8.00000	−0.521862
$236$	−14.0000	−0.911322
$237$	0	0
$238$	9.00000	0.583383
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	−14.0000	−0.896258
$245$	−4.00000	−0.255551
$246$	0	0
$247$	−15.0000	−0.954427
$248$	4.00000	0.254000
$249$	0	0
$250$	12.0000	0.758947
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	0	0
$253$	15.0000	0.943042
$254$	−17.0000	−1.06667
$255$	0	0
$256$	1.00000	0.0625000
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	0	0
$259$	−3.00000	−0.186411
$260$	6.00000	0.372104
$261$	0	0
$262$	10.0000	0.617802
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−15.0000	−0.919709
$267$	0	0
$268$	12.0000	0.733017
$269$	−23.0000	−1.40233	−0.701167	−	0.712997i	$-0.747337\pi$
$269$	−23.0000	−1.40233	−0.701167	+	0.712997i	$0.747337\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	0	0
$275$	5.00000	0.301511
$276$	0	0
$277$	−21.0000	−1.26177	−0.630884	−	0.775877i	$-0.717308\pi$
$277$	−21.0000	−1.26177	−0.630884	+	0.775877i	$0.717308\pi$
$278$	−16.0000	−0.959616
$279$	0	0
$280$	6.00000	0.358569
$281$	9.00000	0.536895	0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000	0.536895	0.268447	+	0.963294i	$0.413489\pi$
$282$	0	0
$283$	−17.0000	−1.01055	−0.505273	−	0.862960i	$-0.668608\pi$
$283$	−17.0000	−1.01055	−0.505273	+	0.862960i	$0.668608\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	15.0000	0.886969
$287$	18.0000	1.06251
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	13.0000	0.760767
$293$	−25.0000	−1.46052	−0.730258	−	0.683172i	$-0.760600\pi$
$293$	−25.0000	−1.46052	−0.730258	+	0.683172i	$0.760600\pi$
$294$	0	0
$295$	28.0000	1.63022
$296$	1.00000	0.0581238
$297$	0	0
$298$	18.0000	1.04271
$299$	9.00000	0.520483
$300$	0	0
$301$	−12.0000	−0.691669
$302$	−9.00000	−0.517892
$303$	0	0
$304$	5.00000	0.286770
$305$	28.0000	1.60328
$306$	0	0
$307$	14.0000	0.799022	0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000	0.799022	0.399511	+	0.916728i	$0.369180\pi$
$308$	15.0000	0.854704
$309$	0	0
$310$	−8.00000	−0.454369
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	0	0
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	6.00000	0.337526
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	0	0
$319$	0	0
$320$	−2.00000	−0.111803
$321$	0	0
$322$	9.00000	0.501550
$323$	−15.0000	−0.834622
$324$	0	0
$325$	3.00000	0.166410
$326$	7.00000	0.387694
$327$	0	0
$328$	−6.00000	−0.331295
$329$	−12.0000	−0.661581
$330$	0	0
$331$	16.0000	0.879440	0.439720	−	0.898135i	$-0.355078\pi$
$331$	16.0000	0.879440	0.439720	+	0.898135i	$0.355078\pi$
$332$	7.00000	0.384175
$333$	0	0
$334$	−13.0000	−0.711328
$335$	−24.0000	−1.31126
$336$	0	0
$337$	−15.0000	−0.817102	−0.408551	−	0.912735i	$-0.633966\pi$
$337$	−15.0000	−0.817102	−0.408551	+	0.912735i	$0.633966\pi$
$338$	−4.00000	−0.217571
$339$	0	0
$340$	6.00000	0.325396
$341$	−20.0000	−1.08306
$342$	0	0
$343$	15.0000	0.809924
$344$	4.00000	0.215666
$345$	0	0
$346$	−19.0000	−1.02145
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	3.00000	0.160357
$351$	0	0
$352$	−5.00000	−0.266501
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	24.0000	1.27379
$356$	1.00000	0.0529999
$357$	0	0
$358$	18.0000	0.951330
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−10.0000	−0.525588
$363$	0	0
$364$	9.00000	0.471728
$365$	−26.0000	−1.36090
$366$	0	0
$367$	29.0000	1.51379	0.756894	−	0.653538i	$-0.226716\pi$
$367$	29.0000	1.51379	0.756894	+	0.653538i	$0.226716\pi$
$368$	−3.00000	−0.156386
$369$	0	0
$370$	−2.00000	−0.103975
$371$	−9.00000	−0.467257
$372$	0	0
$373$	20.0000	1.03556	0.517780	−	0.855514i	$-0.326758\pi$
$373$	20.0000	1.03556	0.517780	+	0.855514i	$0.326758\pi$
$374$	15.0000	0.775632
$375$	0	0
$376$	4.00000	0.206284
$377$	0	0
$378$	0	0
$379$	−32.0000	−1.64373	−0.821865	−	0.569683i	$-0.807066\pi$
$379$	−32.0000	−1.64373	−0.821865	+	0.569683i	$0.807066\pi$
$380$	−10.0000	−0.512989
$381$	0	0
$382$	−7.00000	−0.358151
$383$	−29.0000	−1.48183	−0.740915	−	0.671598i	$-0.765608\pi$
$383$	−29.0000	−1.48183	−0.740915	+	0.671598i	$0.765608\pi$
$384$	0	0
$385$	−30.0000	−1.52894
$386$	−4.00000	−0.203595
$387$	0	0
$388$	−12.0000	−0.609208
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	9.00000	0.455150
$392$	2.00000	0.101015
$393$	0	0
$394$	21.0000	1.05796
$395$	−12.0000	−0.603786
$396$	0	0
$397$	−10.0000	−0.501886	−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000	−0.501886	−0.250943	+	0.968002i	$0.580741\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	21.0000	1.04869	0.524345	−	0.851506i	$-0.324310\pi$
$401$	21.0000	1.04869	0.524345	+	0.851506i	$0.324310\pi$
$402$	0	0
$403$	−12.0000	−0.597763
$404$	−10.0000	−0.497519
$405$	0	0
$406$	0	0
$407$	−5.00000	−0.247841
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	12.0000	0.592638
$411$	0	0
$412$	−2.00000	−0.0985329
$413$	42.0000	2.06668
$414$	0	0
$415$	−14.0000	−0.687233
$416$	−3.00000	−0.147087
$417$	0	0
$418$	−25.0000	−1.22279
$419$	−35.0000	−1.70986	−0.854931	−	0.518742i	$-0.826401\pi$
$419$	−35.0000	−1.70986	−0.854931	+	0.518742i	$0.826401\pi$
$420$	0	0
$421$	38.0000	1.85201	0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000	1.85201	0.926003	+	0.377515i	$0.123221\pi$
$422$	24.0000	1.16830
$423$	0	0
$424$	3.00000	0.145693
$425$	3.00000	0.145521
$426$	0	0
$427$	42.0000	2.03252
$428$	13.0000	0.628379
$429$	0	0
$430$	−8.00000	−0.385794
$431$	11.0000	0.529851	0.264926	−	0.964269i	$-0.414653\pi$
$431$	11.0000	0.529851	0.264926	+	0.964269i	$0.414653\pi$
$432$	0	0
$433$	27.0000	1.29754	0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000	1.29754	0.648769	+	0.760986i	$0.275284\pi$
$434$	−12.0000	−0.576018
$435$	0	0
$436$	−13.0000	−0.622587
$437$	−15.0000	−0.717547
$438$	0	0
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	10.0000	0.476731
$441$	0	0
$442$	9.00000	0.428086
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	0	0
$445$	−2.00000	−0.0948091
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−3.00000	−0.141737
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	30.0000	1.41264
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	18.0000	0.844782
$455$	−18.0000	−0.843853
$456$	0	0
$457$	−24.0000	−1.12267	−0.561336	−	0.827588i	$-0.689713\pi$
$457$	−24.0000	−1.12267	−0.561336	+	0.827588i	$0.689713\pi$
$458$	−20.0000	−0.934539
$459$	0	0
$460$	6.00000	0.279751
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	0	0
$465$	0	0
$466$	−20.0000	−0.926482
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	0	0
$469$	−36.0000	−1.66233
$470$	−8.00000	−0.369012
$471$	0	0
$472$	−14.0000	−0.644402
$473$	−20.0000	−0.919601
$474$	0	0
$475$	−5.00000	−0.229416
$476$	9.00000	0.412514
$477$	0	0
$478$	8.00000	0.365911
$479$	31.0000	1.41643	0.708213	−	0.705999i	$-0.249502\pi$
$479$	31.0000	1.41643	0.708213	+	0.705999i	$0.249502\pi$
$480$	0	0
$481$	−3.00000	−0.136788
$482$	−10.0000	−0.455488
$483$	0	0
$484$	14.0000	0.636364
$485$	24.0000	1.08978
$486$	0	0
$487$	4.00000	0.181257	0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000	0.181257	0.0906287	+	0.995885i	$0.471112\pi$
$488$	−14.0000	−0.633750
$489$	0	0
$490$	−4.00000	−0.180702
$491$	−33.0000	−1.48927	−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000	−1.48927	−0.744635	+	0.667472i	$0.767376\pi$
$492$	0	0
$493$	0	0
$494$	−15.0000	−0.674882
$495$	0	0
$496$	4.00000	0.179605
$497$	36.0000	1.61482
$498$	0	0
$499$	15.0000	0.671492	0.335746	−	0.941953i	$-0.391012\pi$
$499$	15.0000	0.671492	0.335746	+	0.941953i	$0.391012\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	−2.00000	−0.0892644
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	0	0
$505$	20.0000	0.889988
$506$	15.0000	0.666831
$507$	0	0
$508$	−17.0000	−0.754253
$509$	3.00000	0.132973	0.0664863	−	0.997787i	$-0.478821\pi$
$509$	3.00000	0.132973	0.0664863	+	0.997787i	$0.478821\pi$
$510$	0	0
$511$	−39.0000	−1.72526
$512$	1.00000	0.0441942
$513$	0	0
$514$	−7.00000	−0.308757
$515$	4.00000	0.176261
$516$	0	0
$517$	−20.0000	−0.879599
$518$	−3.00000	−0.131812
$519$	0	0
$520$	6.00000	0.263117
$521$	24.0000	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	12.0000	0.523225
$527$	−12.0000	−0.522728
$528$	0	0
$529$	−14.0000	−0.608696
$530$	−6.00000	−0.260623
$531$	0	0
$532$	−15.0000	−0.650332
$533$	18.0000	0.779667
$534$	0	0
$535$	−26.0000	−1.12408
$536$	12.0000	0.518321
$537$	0	0
$538$	−23.0000	−0.991600
$539$	−10.0000	−0.430730
$540$	0	0
$541$	9.00000	0.386940	0.193470	−	0.981106i	$-0.438026\pi$
$541$	9.00000	0.386940	0.193470	+	0.981106i	$0.438026\pi$
$542$	0	0
$543$	0	0
$544$	−3.00000	−0.128624
$545$	26.0000	1.11372
$546$	0	0
$547$	27.0000	1.15444	0.577218	−	0.816590i	$-0.304138\pi$
$547$	27.0000	1.15444	0.577218	+	0.816590i	$0.304138\pi$
$548$	0	0
$549$	0	0
$550$	5.00000	0.213201
$551$	0	0
$552$	0	0
$553$	−18.0000	−0.765438
$554$	−21.0000	−0.892205
$555$	0	0
$556$	−16.0000	−0.678551
$557$	46.0000	1.94908	0.974541	−	0.224208i	$-0.0719796\pi$
$557$	46.0000	1.94908	0.974541	+	0.224208i	$0.0719796\pi$
$558$	0	0
$559$	−12.0000	−0.507546
$560$	6.00000	0.253546
$561$	0	0
$562$	9.00000	0.379642
$563$	38.0000	1.60151	0.800755	−	0.598993i	$-0.204432\pi$
$563$	38.0000	1.60151	0.800755	+	0.598993i	$0.204432\pi$
$564$	0	0
$565$	4.00000	0.168281
$566$	−17.0000	−0.714563
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−41.0000	−1.71881	−0.859405	−	0.511296i	$-0.829166\pi$
$569$	−41.0000	−1.71881	−0.859405	+	0.511296i	$0.829166\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	15.0000	0.627182
$573$	0	0
$574$	18.0000	0.751305
$575$	3.00000	0.125109
$576$	0	0
$577$	−8.00000	−0.333044	−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000	−0.333044	−0.166522	+	0.986038i	$0.553254\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	0	0
$581$	−21.0000	−0.871227
$582$	0	0
$583$	−15.0000	−0.621237
$584$	13.0000	0.537944
$585$	0	0
$586$	−25.0000	−1.03274
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	20.0000	0.824086
$590$	28.0000	1.15274
$591$	0	0
$592$	1.00000	0.0410997
$593$	−46.0000	−1.88899	−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000	−1.88899	−0.944497	+	0.328521i	$0.893450\pi$
$594$	0	0
$595$	−18.0000	−0.737928
$596$	18.0000	0.737309
$597$	0	0
$598$	9.00000	0.368037
$599$	−40.0000	−1.63436	−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000	−1.63436	−0.817178	+	0.576386i	$0.804463\pi$
$600$	0	0
$601$	19.0000	0.775026	0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000	0.775026	0.387513	+	0.921864i	$0.373334\pi$
$602$	−12.0000	−0.489083
$603$	0	0
$604$	−9.00000	−0.366205
$605$	−28.0000	−1.13836
$606$	0	0
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	5.00000	0.202777
$609$	0	0
$610$	28.0000	1.13369
$611$	−12.0000	−0.485468
$612$	0	0
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	14.0000	0.564994
$615$	0	0
$616$	15.0000	0.604367
$617$	−2.00000	−0.0805170	−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000	−0.0805170	−0.0402585	+	0.999189i	$0.512818\pi$
$618$	0	0
$619$	16.0000	0.643094	0.321547	−	0.946894i	$-0.395797\pi$
$619$	16.0000	0.643094	0.321547	+	0.946894i	$0.395797\pi$
$620$	−8.00000	−0.321288
$621$	0	0
$622$	−12.0000	−0.481156
$623$	−3.00000	−0.120192
$624$	0	0
$625$	−19.0000	−0.760000
$626$	−8.00000	−0.319744
$627$	0	0
$628$	10.0000	0.399043
$629$	−3.00000	−0.119618
$630$	0	0
$631$	22.0000	0.875806	0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000	0.875806	0.437903	+	0.899022i	$0.355721\pi$
$632$	6.00000	0.238667
$633$	0	0
$634$	−22.0000	−0.873732
$635$	34.0000	1.34925
$636$	0	0
$637$	−6.00000	−0.237729
$638$	0	0
$639$	0	0
$640$	−2.00000	−0.0790569
$641$	50.0000	1.97488	0.987441	−	0.157991i	$-0.0505015\pi$
$641$	50.0000	1.97488	0.987441	+	0.157991i	$0.0505015\pi$
$642$	0	0
$643$	5.00000	0.197181	0.0985904	−	0.995128i	$-0.468567\pi$
$643$	5.00000	0.197181	0.0985904	+	0.995128i	$0.468567\pi$
$644$	9.00000	0.354650
$645$	0	0
$646$	−15.0000	−0.590167
$647$	41.0000	1.61188	0.805938	−	0.592000i	$-0.201661\pi$
$647$	41.0000	1.61188	0.805938	+	0.592000i	$0.201661\pi$
$648$	0	0
$649$	70.0000	2.74774
$650$	3.00000	0.117670
$651$	0	0
$652$	7.00000	0.274141
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	0	0
$655$	−20.0000	−0.781465
$656$	−6.00000	−0.234261
$657$	0	0
$658$	−12.0000	−0.467809
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	0	0
$661$	45.0000	1.75030	0.875149	−	0.483854i	$-0.160764\pi$
$661$	45.0000	1.75030	0.875149	+	0.483854i	$0.160764\pi$
$662$	16.0000	0.621858
$663$	0	0
$664$	7.00000	0.271653
$665$	30.0000	1.16335
$666$	0	0
$667$	0	0
$668$	−13.0000	−0.502985
$669$	0	0
$670$	−24.0000	−0.927201
$671$	70.0000	2.70232
$672$	0	0
$673$	37.0000	1.42625	0.713123	−	0.701039i	$-0.247280\pi$
$673$	37.0000	1.42625	0.713123	+	0.701039i	$0.247280\pi$
$674$	−15.0000	−0.577778
$675$	0	0
$676$	−4.00000	−0.153846
$677$	13.0000	0.499631	0.249815	−	0.968294i	$-0.419630\pi$
$677$	13.0000	0.499631	0.249815	+	0.968294i	$0.419630\pi$
$678$	0	0
$679$	36.0000	1.38155
$680$	6.00000	0.230089
$681$	0	0
$682$	−20.0000	−0.765840
$683$	−42.0000	−1.60709	−0.803543	−	0.595247i	$-0.797054\pi$
$683$	−42.0000	−1.60709	−0.803543	+	0.595247i	$0.797054\pi$
$684$	0	0
$685$	0	0
$686$	15.0000	0.572703
$687$	0	0
$688$	4.00000	0.152499
$689$	−9.00000	−0.342873
$690$	0	0
$691$	2.00000	0.0760836	0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000	0.0760836	0.0380418	+	0.999276i	$0.487888\pi$
$692$	−19.0000	−0.722272
$693$	0	0
$694$	18.0000	0.683271
$695$	32.0000	1.21383
$696$	0	0
$697$	18.0000	0.681799
$698$	−26.0000	−0.984115
$699$	0	0
$700$	3.00000	0.113389
$701$	44.0000	1.66186	0.830929	−	0.556379i	$-0.187810\pi$
$701$	44.0000	1.66186	0.830929	+	0.556379i	$0.187810\pi$
$702$	0	0
$703$	5.00000	0.188579
$704$	−5.00000	−0.188445
$705$	0	0
$706$	18.0000	0.677439
$707$	30.0000	1.12827
$708$	0	0
$709$	−3.00000	−0.112667	−0.0563337	−	0.998412i	$-0.517941\pi$
$709$	−3.00000	−0.112667	−0.0563337	+	0.998412i	$0.517941\pi$
$710$	24.0000	0.900704
$711$	0	0
$712$	1.00000	0.0374766
$713$	−12.0000	−0.449404
$714$	0	0
$715$	−30.0000	−1.12194
$716$	18.0000	0.672692
$717$	0	0
$718$	−16.0000	−0.597115
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	6.00000	0.223452
$722$	6.00000	0.223297
$723$	0	0
$724$	−10.0000	−0.371647
$725$	0	0
$726$	0	0
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	9.00000	0.333562
$729$	0	0
$730$	−26.0000	−0.962303
$731$	−12.0000	−0.443836
$732$	0	0
$733$	20.0000	0.738717	0.369358	−	0.929287i	$-0.379577\pi$
$733$	20.0000	0.738717	0.369358	+	0.929287i	$0.379577\pi$
$734$	29.0000	1.07041
$735$	0	0
$736$	−3.00000	−0.110581
$737$	−60.0000	−2.21013
$738$	0	0
$739$	34.0000	1.25071	0.625355	−	0.780340i	$-0.284954\pi$
$739$	34.0000	1.25071	0.625355	+	0.780340i	$0.284954\pi$
$740$	−2.00000	−0.0735215
$741$	0	0
$742$	−9.00000	−0.330400
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	−36.0000	−1.31894
$746$	20.0000	0.732252
$747$	0	0
$748$	15.0000	0.548454
$749$	−39.0000	−1.42503
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	4.00000	0.145865
$753$	0	0
$754$	0	0
$755$	18.0000	0.655087
$756$	0	0
$757$	7.00000	0.254419	0.127210	−	0.991876i	$-0.459398\pi$
$757$	7.00000	0.254419	0.127210	+	0.991876i	$0.459398\pi$
$758$	−32.0000	−1.16229
$759$	0	0
$760$	−10.0000	−0.362738
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	0	0
$763$	39.0000	1.41189
$764$	−7.00000	−0.253251
$765$	0	0
$766$	−29.0000	−1.04781
$767$	42.0000	1.51653
$768$	0	0
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	−30.0000	−1.08112
$771$	0	0
$772$	−4.00000	−0.143963
$773$	−11.0000	−0.395643	−0.197821	−	0.980238i	$-0.563387\pi$
$773$	−11.0000	−0.395643	−0.197821	+	0.980238i	$0.563387\pi$
$774$	0	0
$775$	−4.00000	−0.143684
$776$	−12.0000	−0.430775
$777$	0	0
$778$	−26.0000	−0.932145
$779$	−30.0000	−1.07486
$780$	0	0
$781$	60.0000	2.14697
$782$	9.00000	0.321839
$783$	0	0
$784$	2.00000	0.0714286
$785$	−20.0000	−0.713831
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	21.0000	0.748094
$789$	0	0
$790$	−12.0000	−0.426941
$791$	6.00000	0.213335
$792$	0	0
$793$	42.0000	1.49146
$794$	−10.0000	−0.354887
$795$	0	0
$796$	4.00000	0.141776
$797$	−38.0000	−1.34603	−0.673015	−	0.739629i	$-0.735001\pi$
$797$	−38.0000	−1.34603	−0.673015	+	0.739629i	$0.735001\pi$
$798$	0	0
$799$	−12.0000	−0.424529
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	21.0000	0.741536
$803$	−65.0000	−2.29380
$804$	0	0
$805$	−18.0000	−0.634417
$806$	−12.0000	−0.422682
$807$	0	0
$808$	−10.0000	−0.351799
$809$	−27.0000	−0.949269	−0.474635	−	0.880183i	$-0.657420\pi$
$809$	−27.0000	−0.949269	−0.474635	+	0.880183i	$0.657420\pi$
$810$	0	0
$811$	6.00000	0.210688	0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000	0.210688	0.105344	+	0.994436i	$0.466406\pi$
$812$	0	0
$813$	0	0
$814$	−5.00000	−0.175250
$815$	−14.0000	−0.490399
$816$	0	0
$817$	20.0000	0.699711
$818$	−6.00000	−0.209785
$819$	0	0
$820$	12.0000	0.419058
$821$	7.00000	0.244302	0.122151	−	0.992512i	$-0.461021\pi$
$821$	7.00000	0.244302	0.122151	+	0.992512i	$0.461021\pi$
$822$	0	0
$823$	−45.0000	−1.56860	−0.784301	−	0.620381i	$-0.786978\pi$
$823$	−45.0000	−1.56860	−0.784301	+	0.620381i	$0.786978\pi$
$824$	−2.00000	−0.0696733
$825$	0	0
$826$	42.0000	1.46137
$827$	−32.0000	−1.11275	−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000	−1.11275	−0.556375	+	0.830932i	$0.687808\pi$
$828$	0	0
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	−14.0000	−0.485947
$831$	0	0
$832$	−3.00000	−0.104006
$833$	−6.00000	−0.207888
$834$	0	0
$835$	26.0000	0.899767
$836$	−25.0000	−0.864643
$837$	0	0
$838$	−35.0000	−1.20905
$839$	−34.0000	−1.17381	−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000	−1.17381	−0.586905	+	0.809656i	$0.699654\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	38.0000	1.30957
$843$	0	0
$844$	24.0000	0.826114
$845$	8.00000	0.275208
$846$	0	0
$847$	−42.0000	−1.44314
$848$	3.00000	0.103020
$849$	0	0
$850$	3.00000	0.102899
$851$	−3.00000	−0.102839
$852$	0	0
$853$	−19.0000	−0.650548	−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000	−0.650548	−0.325274	+	0.945620i	$0.605456\pi$
$854$	42.0000	1.43721
$855$	0	0
$856$	13.0000	0.444331
$857$	47.0000	1.60549	0.802745	−	0.596323i	$-0.203372\pi$
$857$	47.0000	1.60549	0.802745	+	0.596323i	$0.203372\pi$
$858$	0	0
$859$	43.0000	1.46714	0.733571	−	0.679613i	$-0.237852\pi$
$859$	43.0000	1.46714	0.733571	+	0.679613i	$0.237852\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	11.0000	0.374661
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	38.0000	1.29204
$866$	27.0000	0.917497
$867$	0	0
$868$	−12.0000	−0.407307
$869$	−30.0000	−1.01768
$870$	0	0
$871$	−36.0000	−1.21981
$872$	−13.0000	−0.440236
$873$	0	0
$874$	−15.0000	−0.507383
$875$	−36.0000	−1.21702
$876$	0	0
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	−26.0000	−0.877457
$879$	0	0
$880$	10.0000	0.337100
$881$	−48.0000	−1.61716	−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000	−1.61716	−0.808581	+	0.588386i	$0.799764\pi$
$882$	0	0
$883$	−5.00000	−0.168263	−0.0841317	−	0.996455i	$-0.526812\pi$
$883$	−5.00000	−0.168263	−0.0841317	+	0.996455i	$0.526812\pi$
$884$	9.00000	0.302703
$885$	0	0
$886$	12.0000	0.403148
$887$	26.0000	0.872995	0.436497	−	0.899706i	$-0.356219\pi$
$887$	26.0000	0.872995	0.436497	+	0.899706i	$0.356219\pi$
$888$	0	0
$889$	51.0000	1.71049
$890$	−2.00000	−0.0670402
$891$	0	0
$892$	−16.0000	−0.535720
$893$	20.0000	0.669274
$894$	0	0
$895$	−36.0000	−1.20335
$896$	−3.00000	−0.100223
$897$	0	0
$898$	22.0000	0.734150
$899$	0	0
$900$	0	0
$901$	−9.00000	−0.299833
$902$	30.0000	0.998891
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	20.0000	0.664822
$906$	0	0
$907$	−25.0000	−0.830111	−0.415056	−	0.909796i	$-0.636238\pi$
$907$	−25.0000	−0.830111	−0.415056	+	0.909796i	$0.636238\pi$
$908$	18.0000	0.597351
$909$	0	0
$910$	−18.0000	−0.596694
$911$	−32.0000	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$912$	0	0
$913$	−35.0000	−1.15833
$914$	−24.0000	−0.793849
$915$	0	0
$916$	−20.0000	−0.660819
$917$	−30.0000	−0.990687
$918$	0	0
$919$	−38.0000	−1.25350	−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000	−1.25350	−0.626752	+	0.779219i	$0.715616\pi$
$920$	6.00000	0.197814
$921$	0	0
$922$	10.0000	0.329332
$923$	36.0000	1.18495
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	−20.0000	−0.657241
$927$	0	0
$928$	0	0
$929$	−8.00000	−0.262471	−0.131236	−	0.991351i	$-0.541894\pi$
$929$	−8.00000	−0.262471	−0.131236	+	0.991351i	$0.541894\pi$
$930$	0	0
$931$	10.0000	0.327737
$932$	−20.0000	−0.655122
$933$	0	0
$934$	−6.00000	−0.196326
$935$	−30.0000	−0.981105
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−36.0000	−1.17544
$939$	0	0
$940$	−8.00000	−0.260931
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	0	0
$943$	18.0000	0.586161
$944$	−14.0000	−0.455661
$945$	0	0
$946$	−20.0000	−0.650256
$947$	54.0000	1.75476	0.877382	−	0.479792i	$-0.159288\pi$
$947$	54.0000	1.75476	0.877382	+	0.479792i	$0.159288\pi$
$948$	0	0
$949$	−39.0000	−1.26599
$950$	−5.00000	−0.162221
$951$	0	0
$952$	9.00000	0.291692
$953$	−46.0000	−1.49009	−0.745043	−	0.667016i	$-0.767571\pi$
$953$	−46.0000	−1.49009	−0.745043	+	0.667016i	$0.767571\pi$
$954$	0	0
$955$	14.0000	0.453029
$956$	8.00000	0.258738
$957$	0	0
$958$	31.0000	1.00156
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−3.00000	−0.0967239
$963$	0	0
$964$	−10.0000	−0.322078
$965$	8.00000	0.257529
$966$	0	0
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	24.0000	0.770594
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	0	0
$973$	48.0000	1.53881
$974$	4.00000	0.128168
$975$	0	0
$976$	−14.0000	−0.448129
$977$	45.0000	1.43968	0.719839	−	0.694141i	$-0.244216\pi$
$977$	45.0000	1.43968	0.719839	+	0.694141i	$0.244216\pi$
$978$	0	0
$979$	−5.00000	−0.159801
$980$	−4.00000	−0.127775
$981$	0	0
$982$	−33.0000	−1.05307
$983$	6.00000	0.191370	0.0956851	−	0.995412i	$-0.469496\pi$
$983$	6.00000	0.191370	0.0956851	+	0.995412i	$0.469496\pi$
$984$	0	0
$985$	−42.0000	−1.33823
$986$	0	0
$987$	0	0
$988$	−15.0000	−0.477214
$989$	−12.0000	−0.381578
$990$	0	0
$991$	−50.0000	−1.58830	−0.794151	−	0.607720i	$-0.792084\pi$
$991$	−50.0000	−1.58830	−0.794151	+	0.607720i	$0.792084\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	36.0000	1.14185
$995$	−8.00000	−0.253617
$996$	0	0
$997$	−9.00000	−0.285033	−0.142516	−	0.989792i	$-0.545519\pi$
$997$	−9.00000	−0.285033	−0.142516	+	0.989792i	$0.545519\pi$
$998$	15.0000	0.474817
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.a.e.1.1	yes	1
3.2	odd	2		666.2.a.c.1.1	✓	1
4.3	odd	2		5328.2.a.f.1.1		1
12.11	even	2		5328.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.a.c.1.1	✓	1	3.2	odd	2
666.2.a.e.1.1	yes	1	1.1	even	1	trivial
5328.2.a.f.1.1		1	4.3	odd	2
5328.2.a.s.1.1		1	12.11	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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