LMFDB - Embedded newform 5915.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5915,2,Mod(1,5915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5915, 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("5915.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5915 = 5 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5915.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:	$47.2315127956$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5915.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -2.00000 q^{9} +3.00000 q^{11} -2.00000 q^{12} +1.00000 q^{15} +4.00000 q^{16} +3.00000 q^{17} -2.00000 q^{19} -2.00000 q^{20} -1.00000 q^{21} -6.00000 q^{23} +1.00000 q^{25} -5.00000 q^{27} +2.00000 q^{28} +3.00000 q^{29} +4.00000 q^{31} +3.00000 q^{33} -1.00000 q^{35} +4.00000 q^{36} -2.00000 q^{37} +12.0000 q^{41} -10.0000 q^{43} -6.00000 q^{44} -2.00000 q^{45} -9.00000 q^{47} +4.00000 q^{48} +1.00000 q^{49} +3.00000 q^{51} +12.0000 q^{53} +3.00000 q^{55} -2.00000 q^{57} -2.00000 q^{60} +8.00000 q^{61} +2.00000 q^{63} -8.00000 q^{64} +4.00000 q^{67} -6.00000 q^{68} -6.00000 q^{69} -2.00000 q^{73} +1.00000 q^{75} +4.00000 q^{76} -3.00000 q^{77} -1.00000 q^{79} +4.00000 q^{80} +1.00000 q^{81} -12.0000 q^{83} +2.00000 q^{84} +3.00000 q^{85} +3.00000 q^{87} +12.0000 q^{89} +12.0000 q^{92} +4.00000 q^{93} -2.00000 q^{95} +1.00000 q^{97} -6.00000 q^{99} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	−2.00000	−1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	−2.00000	−0.577350
$13$	0	0
$13$	0	0
$14$	0	0
$15$	1.00000	0.258199
$16$	4.00000	1.00000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−0.447214
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.00000	−0.962250
$28$	2.00000	0.377964
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	0	0
$33$	3.00000	0.522233
$34$	0	0
$35$	−1.00000	−0.169031
$36$	4.00000	0.666667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	12.0000	1.87409	0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000	1.87409	0.937043	+	0.349215i	$0.113552\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−6.00000	−0.904534
$45$	−2.00000	−0.298142
$46$	0	0
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	4.00000	0.577350
$49$	1.00000	0.142857
$50$	0	0
$51$	3.00000	0.420084
$52$	0	0
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	3.00000	0.404520
$56$	0	0
$57$	−2.00000	−0.264906
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−2.00000	−0.258199
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−6.00000	−0.727607
$69$	−6.00000	−0.722315
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	0	0
$75$	1.00000	0.115470
$76$	4.00000	0.458831
$77$	−3.00000	−0.341882
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	4.00000	0.447214
$81$	1.00000	0.111111
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	2.00000	0.218218
$85$	3.00000	0.325396
$86$	0	0
$87$	3.00000	0.321634
$88$	0	0
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	0	0
$91$	0	0
$92$	12.0000	1.25109
$93$	4.00000	0.414781
$94$	0	0
$95$	−2.00000	−0.205196
$96$	0	0
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	0	0
$99$	−6.00000	−0.603023
$100$	−2.00000	−0.200000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	0	0
$105$	−1.00000	−0.0975900
$106$	0	0
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	10.0000	0.962250
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	−4.00000	−0.377964
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	−6.00000	−0.557086
$117$	0	0
$118$	0	0
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	12.0000	1.08200
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	0	0
$129$	−10.0000	−0.880451
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−6.00000	−0.522233
$133$	2.00000	0.173422
$134$	0	0
$135$	−5.00000	−0.430331
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	2.00000	0.169031
$141$	−9.00000	−0.757937
$142$	0	0
$143$	0	0
$144$	−8.00000	−0.666667
$145$	3.00000	0.249136
$146$	0	0
$147$	1.00000	0.0824786
$148$	4.00000	0.328798
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	1.00000	0.0813788	0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000	0.0813788	0.0406894	+	0.999172i	$0.487045\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	4.00000	0.321288
$156$	0	0
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	0	0
$159$	12.0000	0.951662
$160$	0	0
$161$	6.00000	0.472866
$162$	0	0
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	−24.0000	−1.87409
$165$	3.00000	0.233550
$166$	0	0
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	4.00000	0.305888
$172$	20.0000	1.52499
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	12.0000	0.904534
$177$	0	0
$178$	0	0
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	4.00000	0.298142
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	0	0
$183$	8.00000	0.591377
$184$	0	0
$185$	−2.00000	−0.147043
$186$	0	0
$187$	9.00000	0.658145
$188$	18.0000	1.31278
$189$	5.00000	0.363696
$190$	0	0
$191$	9.00000	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$192$	−8.00000	−0.577350
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	0	0
$195$	0	0
$196$	−2.00000	−0.142857
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	0	0
$203$	−3.00000	−0.210559
$204$	−6.00000	−0.420084
$205$	12.0000	0.838116
$206$	0	0
$207$	12.0000	0.834058
$208$	0	0
$209$	−6.00000	−0.415029
$210$	0	0
$211$	−13.0000	−0.894957	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000	−0.894957	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−24.0000	−1.64833
$213$	0	0
$214$	0	0
$215$	−10.0000	−0.681994
$216$	0	0
$217$	−4.00000	−0.271538
$218$	0	0
$219$	−2.00000	−0.135147
$220$	−6.00000	−0.404520
$221$	0	0
$222$	0	0
$223$	19.0000	1.27233	0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000	1.27233	0.636167	+	0.771551i	$0.280519\pi$
$224$	0	0
$225$	−2.00000	−0.133333
$226$	0	0
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	4.00000	0.264906
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	0	0
$233$	24.0000	1.57229	0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000	1.57229	0.786146	+	0.618041i	$0.212073\pi$
$234$	0	0
$235$	−9.00000	−0.587095
$236$	0	0
$237$	−1.00000	−0.0649570
$238$	0	0
$239$	21.0000	1.35838	0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000	1.35838	0.679189	+	0.733964i	$0.262332\pi$
$240$	4.00000	0.258199
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	0	0
$243$	16.0000	1.02640
$244$	−16.0000	−1.02430
$245$	1.00000	0.0638877
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−12.0000	−0.760469
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	−4.00000	−0.251976
$253$	−18.0000	−1.13165
$254$	0	0
$255$	3.00000	0.187867
$256$	16.0000	1.00000
$257$	30.0000	1.87135	0.935674	−	0.352865i	$-0.114792\pi$
$257$	30.0000	1.87135	0.935674	+	0.352865i	$0.114792\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	0	0
$261$	−6.00000	−0.371391
$262$	0	0
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	0	0
$267$	12.0000	0.734388
$268$	−8.00000	−0.488678
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	12.0000	0.727607
$273$	0	0
$274$	0	0
$275$	3.00000	0.180907
$276$	12.0000	0.722315
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	0	0
$279$	−8.00000	−0.478947
$280$	0	0
$281$	−3.00000	−0.178965	−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000	−0.178965	−0.0894825	+	0.995988i	$0.528521\pi$
$282$	0	0
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	0	0
$285$	−2.00000	−0.118470
$286$	0	0
$287$	−12.0000	−0.708338
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	1.00000	0.0586210
$292$	4.00000	0.234082
$293$	21.0000	1.22683	0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000	1.22683	0.613417	+	0.789760i	$0.289795\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−15.0000	−0.870388
$298$	0	0
$299$	0	0
$300$	−2.00000	−0.115470
$301$	10.0000	0.576390
$302$	0	0
$303$	6.00000	0.344691
$304$	−8.00000	−0.458831
$305$	8.00000	0.458079
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	6.00000	0.341882
$309$	5.00000	0.284440
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	−19.0000	−1.07394	−0.536972	−	0.843600i	$-0.680432\pi$
$313$	−19.0000	−1.07394	−0.536972	+	0.843600i	$0.680432\pi$
$314$	0	0
$315$	2.00000	0.112687
$316$	2.00000	0.112509
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	9.00000	0.503903
$320$	−8.00000	−0.447214
$321$	6.00000	0.334887
$322$	0	0
$323$	−6.00000	−0.333849
$324$	−2.00000	−0.111111
$325$	0	0
$326$	0	0
$327$	7.00000	0.387101
$328$	0	0
$329$	9.00000	0.496186
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	24.0000	1.31717
$333$	4.00000	0.219199
$334$	0	0
$335$	4.00000	0.218543
$336$	−4.00000	−0.218218
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	0	0
$339$	6.00000	0.325875
$340$	−6.00000	−0.325396
$341$	12.0000	0.649836
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	−6.00000	−0.323029
$346$	0	0
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	−6.00000	−0.321634
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−15.0000	−0.798369	−0.399185	−	0.916871i	$-0.630707\pi$
$353$	−15.0000	−0.798369	−0.399185	+	0.916871i	$0.630707\pi$
$354$	0	0
$355$	0	0
$356$	−24.0000	−1.27200
$357$	−3.00000	−0.158777
$358$	0	0
$359$	−24.0000	−1.26667	−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000	−1.26667	−0.633336	+	0.773877i	$0.718315\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	0	0
$363$	−2.00000	−0.104973
$364$	0	0
$365$	−2.00000	−0.104685
$366$	0	0
$367$	17.0000	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$368$	−24.0000	−1.25109
$369$	−24.0000	−1.24939
$370$	0	0
$371$	−12.0000	−0.623009
$372$	−8.00000	−0.414781
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	4.00000	0.205196
$381$	−16.0000	−0.819705
$382$	0	0
$383$	−12.0000	−0.613171	−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000	−0.613171	−0.306586	+	0.951843i	$0.599187\pi$
$384$	0	0
$385$	−3.00000	−0.152894
$386$	0	0
$387$	20.0000	1.01666
$388$	−2.00000	−0.101535
$389$	−3.00000	−0.152106	−0.0760530	−	0.997104i	$-0.524232\pi$
$389$	−3.00000	−0.152106	−0.0760530	+	0.997104i	$0.524232\pi$
$390$	0	0
$391$	−18.0000	−0.910299
$392$	0	0
$393$	−6.00000	−0.302660
$394$	0	0
$395$	−1.00000	−0.0503155
$396$	12.0000	0.603023
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	0	0
$399$	2.00000	0.100125
$400$	4.00000	0.200000
$401$	15.0000	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$402$	0	0
$403$	0	0
$404$	−12.0000	−0.597022
$405$	1.00000	0.0496904
$406$	0	0
$407$	−6.00000	−0.297409
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	−10.0000	−0.492665
$413$	0	0
$414$	0	0
$415$	−12.0000	−0.589057
$416$	0	0
$417$	14.0000	0.685583
$418$	0	0
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	2.00000	0.0975900
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	0	0
$423$	18.0000	0.875190
$424$	0	0
$425$	3.00000	0.145521
$426$	0	0
$427$	−8.00000	−0.387147
$428$	−12.0000	−0.580042
$429$	0	0
$430$	0	0
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	−20.0000	−0.962250
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	3.00000	0.143839
$436$	−14.0000	−0.670478
$437$	12.0000	0.574038
$438$	0	0
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	0	0
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	4.00000	0.189832
$445$	12.0000	0.568855
$446$	0	0
$447$	6.00000	0.283790
$448$	8.00000	0.377964
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	0	0
$451$	36.0000	1.69517
$452$	−12.0000	−0.564433
$453$	1.00000	0.0469841
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	0	0
$459$	−15.0000	−0.700140
$460$	12.0000	0.559503
$461$	24.0000	1.11779	0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000	1.11779	0.558896	+	0.829238i	$0.311225\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	12.0000	0.557086
$465$	4.00000	0.185496
$466$	0	0
$467$	15.0000	0.694117	0.347059	−	0.937843i	$-0.387180\pi$
$467$	15.0000	0.694117	0.347059	+	0.937843i	$0.387180\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	14.0000	0.645086
$472$	0	0
$473$	−30.0000	−1.37940
$474$	0	0
$475$	−2.00000	−0.0917663
$476$	6.00000	0.275010
$477$	−24.0000	−1.09888
$478$	0	0
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	6.00000	0.273009
$484$	4.00000	0.181818
$485$	1.00000	0.0454077
$486$	0	0
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	0	0
$489$	−2.00000	−0.0904431
$490$	0	0
$491$	15.0000	0.676941	0.338470	−	0.940977i	$-0.390091\pi$
$491$	15.0000	0.676941	0.338470	+	0.940977i	$0.390091\pi$
$492$	−24.0000	−1.08200
$493$	9.00000	0.405340
$494$	0	0
$495$	−6.00000	−0.269680
$496$	16.0000	0.718421
$497$	0	0
$498$	0	0
$499$	31.0000	1.38775	0.693875	−	0.720095i	$-0.255902\pi$
$499$	31.0000	1.38775	0.693875	+	0.720095i	$0.255902\pi$
$500$	−2.00000	−0.0894427
$501$	3.00000	0.134030
$502$	0	0
$503$	27.0000	1.20387	0.601935	−	0.798545i	$-0.294397\pi$
$503$	27.0000	1.20387	0.601935	+	0.798545i	$0.294397\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	0	0
$507$	0	0
$508$	32.0000	1.41977
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	0	0
$513$	10.0000	0.441511
$514$	0	0
$515$	5.00000	0.220326
$516$	20.0000	0.880451
$517$	−27.0000	−1.18746
$518$	0	0
$519$	−9.00000	−0.395056
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	12.0000	0.524222
$525$	−1.00000	−0.0436436
$526$	0	0
$527$	12.0000	0.522728
$528$	12.0000	0.522233
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	−4.00000	−0.173422
$533$	0	0
$534$	0	0
$535$	6.00000	0.259403
$536$	0	0
$537$	12.0000	0.517838
$538$	0	0
$539$	3.00000	0.129219
$540$	10.0000	0.430331
$541$	−11.0000	−0.472927	−0.236463	−	0.971640i	$-0.575988\pi$
$541$	−11.0000	−0.472927	−0.236463	+	0.971640i	$0.575988\pi$
$542$	0	0
$543$	20.0000	0.858282
$544$	0	0
$545$	7.00000	0.299847
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−24.0000	−1.02523
$549$	−16.0000	−0.682863
$550$	0	0
$551$	−6.00000	−0.255609
$552$	0	0
$553$	1.00000	0.0425243
$554$	0	0
$555$	−2.00000	−0.0848953
$556$	−28.0000	−1.18746
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	0	0
$559$	0	0
$560$	−4.00000	−0.169031
$561$	9.00000	0.379980
$562$	0	0
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	18.0000	0.757937
$565$	6.00000	0.252422
$566$	0	0
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	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
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0	0
$573$	9.00000	0.375980
$574$	0	0
$575$	−6.00000	−0.250217
$576$	16.0000	0.666667
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	0	0
$579$	4.00000	0.166234
$580$	−6.00000	−0.249136
$581$	12.0000	0.497844
$582$	0	0
$583$	36.0000	1.49097
$584$	0	0
$585$	0	0
$586$	0	0
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	−2.00000	−0.0824786
$589$	−8.00000	−0.329634
$590$	0	0
$591$	0	0
$592$	−8.00000	−0.328798
$593$	39.0000	1.60154	0.800769	−	0.598973i	$-0.204424\pi$
$593$	39.0000	1.60154	0.800769	+	0.598973i	$0.204424\pi$
$594$	0	0
$595$	−3.00000	−0.122988
$596$	−12.0000	−0.491539
$597$	−16.0000	−0.654836
$598$	0	0
$599$	45.0000	1.83865	0.919325	−	0.393499i	$-0.128735\pi$
$599$	45.0000	1.83865	0.919325	+	0.393499i	$0.128735\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	−2.00000	−0.0813788
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	−13.0000	−0.527654	−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000	−0.527654	−0.263827	+	0.964570i	$0.584985\pi$
$608$	0	0
$609$	−3.00000	−0.121566
$610$	0	0
$611$	0	0
$612$	12.0000	0.485071
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	0	0
$615$	12.0000	0.483887
$616$	0	0
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	0	0
$619$	−26.0000	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$620$	−8.00000	−0.321288
$621$	30.0000	1.20386
$622$	0	0
$623$	−12.0000	−0.480770
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−6.00000	−0.239617
$628$	−28.0000	−1.11732
$629$	−6.00000	−0.239236
$630$	0	0
$631$	−29.0000	−1.15447	−0.577236	−	0.816577i	$-0.695869\pi$
$631$	−29.0000	−1.15447	−0.577236	+	0.816577i	$0.695869\pi$
$632$	0	0
$633$	−13.0000	−0.516704
$634$	0	0
$635$	−16.0000	−0.634941
$636$	−24.0000	−0.951662
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	−41.0000	−1.61688	−0.808441	−	0.588577i	$-0.799688\pi$
$643$	−41.0000	−1.61688	−0.808441	+	0.588577i	$0.799688\pi$
$644$	−12.0000	−0.472866
$645$	−10.0000	−0.393750
$646$	0	0
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−4.00000	−0.156772
$652$	4.00000	0.156652
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	−6.00000	−0.234439
$656$	48.0000	1.87409
$657$	4.00000	0.156055
$658$	0	0
$659$	−15.0000	−0.584317	−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000	−0.584317	−0.292159	+	0.956370i	$0.594373\pi$
$660$	−6.00000	−0.233550
$661$	−32.0000	−1.24466	−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000	−1.24466	−0.622328	+	0.782757i	$0.713813\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	2.00000	0.0775567
$666$	0	0
$667$	−18.0000	−0.696963
$668$	−6.00000	−0.232147
$669$	19.0000	0.734582
$670$	0	0
$671$	24.0000	0.926510
$672$	0	0
$673$	−28.0000	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$674$	0	0
$675$	−5.00000	−0.192450
$676$	0	0
$677$	45.0000	1.72949	0.864745	−	0.502211i	$-0.167480\pi$
$677$	45.0000	1.72949	0.864745	+	0.502211i	$0.167480\pi$
$678$	0	0
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	3.00000	0.114960
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	−8.00000	−0.305888
$685$	12.0000	0.458496
$686$	0	0
$687$	4.00000	0.152610
$688$	−40.0000	−1.52499
$689$	0	0
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	18.0000	0.684257
$693$	6.00000	0.227921
$694$	0	0
$695$	14.0000	0.531050
$696$	0	0
$697$	36.0000	1.36360
$698$	0	0
$699$	24.0000	0.907763
$700$	2.00000	0.0755929
$701$	−9.00000	−0.339925	−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000	−0.339925	−0.169963	+	0.985451i	$0.554365\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	−24.0000	−0.904534
$705$	−9.00000	−0.338960
$706$	0	0
$707$	−6.00000	−0.225653
$708$	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
$711$	2.00000	0.0750059
$712$	0	0
$713$	−24.0000	−0.898807
$714$	0	0
$715$	0	0
$716$	−24.0000	−0.896922
$717$	21.0000	0.784259
$718$	0	0
$719$	−30.0000	−1.11881	−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000	−1.11881	−0.559406	+	0.828894i	$0.688971\pi$
$720$	−8.00000	−0.298142
$721$	−5.00000	−0.186210
$722$	0	0
$723$	10.0000	0.371904
$724$	−40.0000	−1.48659
$725$	3.00000	0.111417
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−30.0000	−1.10959
$732$	−16.0000	−0.591377
$733$	31.0000	1.14501	0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000	1.14501	0.572506	+	0.819901i	$0.305971\pi$
$734$	0	0
$735$	1.00000	0.0368856
$736$	0	0
$737$	12.0000	0.442026
$738$	0	0
$739$	43.0000	1.58178	0.790890	−	0.611958i	$-0.209618\pi$
$739$	43.0000	1.58178	0.790890	+	0.611958i	$0.209618\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	0	0
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	0	0
$747$	24.0000	0.878114
$748$	−18.0000	−0.658145
$749$	−6.00000	−0.219235
$750$	0	0
$751$	23.0000	0.839282	0.419641	−	0.907690i	$-0.362156\pi$
$751$	23.0000	0.839282	0.419641	+	0.907690i	$0.362156\pi$
$752$	−36.0000	−1.31278
$753$	18.0000	0.655956
$754$	0	0
$755$	1.00000	0.0363937
$756$	−10.0000	−0.363696
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	0	0
$759$	−18.0000	−0.653359
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	−7.00000	−0.253417
$764$	−18.0000	−0.651217
$765$	−6.00000	−0.216930
$766$	0	0
$767$	0	0
$768$	16.0000	0.577350
$769$	−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
$771$	30.0000	1.08042
$772$	−8.00000	−0.287926
$773$	−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
$775$	4.00000	0.143684
$776$	0	0
$777$	2.00000	0.0717496
$778$	0	0
$779$	−24.0000	−0.859889
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−15.0000	−0.536056
$784$	4.00000	0.142857
$785$	14.0000	0.499681
$786$	0	0
$787$	−5.00000	−0.178231	−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000	−0.178231	−0.0891154	+	0.996021i	$0.528404\pi$
$788$	0	0
$789$	6.00000	0.213606
$790$	0	0
$791$	−6.00000	−0.213335
$792$	0	0
$793$	0	0
$794$	0	0
$795$	12.0000	0.425596
$796$	32.0000	1.13421
$797$	15.0000	0.531327	0.265664	−	0.964066i	$-0.414409\pi$
$797$	15.0000	0.531327	0.265664	+	0.964066i	$0.414409\pi$
$798$	0	0
$799$	−27.0000	−0.955191
$800$	0	0
$801$	−24.0000	−0.847998
$802$	0	0
$803$	−6.00000	−0.211735
$804$	−8.00000	−0.282138
$805$	6.00000	0.211472
$806$	0	0
$807$	−6.00000	−0.211210
$808$	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
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	6.00000	0.210559
$813$	16.0000	0.561144
$814$	0	0
$815$	−2.00000	−0.0700569
$816$	12.0000	0.420084
$817$	20.0000	0.699711
$818$	0	0
$819$	0	0
$820$	−24.0000	−0.838116
$821$	27.0000	0.942306	0.471153	−	0.882051i	$-0.343838\pi$
$821$	27.0000	0.942306	0.471153	+	0.882051i	$0.343838\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	3.00000	0.104447
$826$	0	0
$827$	−54.0000	−1.87776	−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000	−1.87776	−0.938882	+	0.344239i	$0.888137\pi$
$828$	−24.0000	−0.834058
$829$	−52.0000	−1.80603	−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000	−1.80603	−0.903017	+	0.429604i	$0.858653\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	0	0
$833$	3.00000	0.103944
$834$	0	0
$835$	3.00000	0.103819
$836$	12.0000	0.415029
$837$	−20.0000	−0.691301
$838$	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
$841$	−20.0000	−0.689655
$842$	0	0
$843$	−3.00000	−0.103325
$844$	26.0000	0.894957
$845$	0	0
$846$	0	0
$847$	2.00000	0.0687208
$848$	48.0000	1.64833
$849$	−13.0000	−0.446159
$850$	0	0
$851$	12.0000	0.411355
$852$	0	0
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	4.00000	0.136797
$856$	0	0
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	20.0000	0.681994
$861$	−12.0000	−0.408959
$862$	0	0
$863$	−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
$865$	−9.00000	−0.306009
$866$	0	0
$867$	−8.00000	−0.271694
$868$	8.00000	0.271538
$869$	−3.00000	−0.101768
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	4.00000	0.135147
$877$	−50.0000	−1.68838	−0.844190	−	0.536044i	$-0.819918\pi$
$877$	−50.0000	−1.68838	−0.844190	+	0.536044i	$0.819918\pi$
$878$	0	0
$879$	21.0000	0.708312
$880$	12.0000	0.404520
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	16.0000	0.536623
$890$	0	0
$891$	3.00000	0.100504
$892$	−38.0000	−1.27233
$893$	18.0000	0.602347
$894$	0	0
$895$	12.0000	0.401116
$896$	0	0
$897$	0	0
$898$	0	0
$899$	12.0000	0.400222
$900$	4.00000	0.133333
$901$	36.0000	1.19933
$902$	0	0
$903$	10.0000	0.332779
$904$	0	0
$905$	20.0000	0.664822
$906$	0	0
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	−6.00000	−0.199117
$909$	−12.0000	−0.398015
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	−8.00000	−0.264906
$913$	−36.0000	−1.19143
$914$	0	0
$915$	8.00000	0.264472
$916$	−8.00000	−0.264327
$917$	6.00000	0.198137
$918$	0	0
$919$	11.0000	0.362857	0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000	0.362857	0.181428	+	0.983404i	$0.441928\pi$
$920$	0	0
$921$	−11.0000	−0.362462
$922$	0	0
$923$	0	0
$924$	6.00000	0.197386
$925$	−2.00000	−0.0657596
$926$	0	0
$927$	−10.0000	−0.328443
$928$	0	0
$929$	−36.0000	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	−48.0000	−1.57229
$933$	18.0000	0.589294
$934$	0	0
$935$	9.00000	0.294331
$936$	0	0
$937$	47.0000	1.53542	0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000	1.53542	0.767712	+	0.640796i	$0.221395\pi$
$938$	0	0
$939$	−19.0000	−0.620042
$940$	18.0000	0.587095
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−72.0000	−2.34464
$944$	0	0
$945$	5.00000	0.162650
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	2.00000	0.0649570
$949$	0	0
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	9.00000	0.291233
$956$	−42.0000	−1.35838
$957$	9.00000	0.290929
$958$	0	0
$959$	−12.0000	−0.387500
$960$	−8.00000	−0.258199
$961$	−15.0000	−0.483871
$962$	0	0
$963$	−12.0000	−0.386695
$964$	−20.0000	−0.644157
$965$	4.00000	0.128765
$966$	0	0
$967$	22.0000	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$968$	0	0
$969$	−6.00000	−0.192748
$970$	0	0
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	−32.0000	−1.02640
$973$	−14.0000	−0.448819
$974$	0	0
$975$	0	0
$976$	32.0000	1.02430
$977$	−54.0000	−1.72761	−0.863807	−	0.503824i	$-0.831926\pi$
$977$	−54.0000	−1.72761	−0.863807	+	0.503824i	$0.831926\pi$
$978$	0	0
$979$	36.0000	1.15056
$980$	−2.00000	−0.0638877
$981$	−14.0000	−0.446986
$982$	0	0
$983$	21.0000	0.669796	0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000	0.669796	0.334898	+	0.942254i	$0.391298\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	9.00000	0.286473
$988$	0	0
$989$	60.0000	1.90789
$990$	0	0
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	0	0
$993$	28.0000	0.888553
$994$	0	0
$995$	−16.0000	−0.507234
$996$	24.0000	0.760469
$997$	−37.0000	−1.17180	−0.585901	−	0.810383i	$-0.699259\pi$
$997$	−37.0000	−1.17180	−0.585901	+	0.810383i	$0.699259\pi$
$998$	0	0
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5915.2.a.f.1.1		1
13.12	even	2		35.2.a.a.1.1	✓	1
39.38	odd	2		315.2.a.b.1.1		1
52.51	odd	2		560.2.a.b.1.1		1
65.12	odd	4		175.2.b.a.99.1		2
65.38	odd	4		175.2.b.a.99.2		2
65.64	even	2		175.2.a.b.1.1		1
91.12	odd	6		245.2.e.b.116.1		2
91.25	even	6		245.2.e.a.226.1		2
91.38	odd	6		245.2.e.b.226.1		2
91.51	even	6		245.2.e.a.116.1		2
91.90	odd	2		245.2.a.c.1.1		1
104.51	odd	2		2240.2.a.u.1.1		1
104.77	even	2		2240.2.a.k.1.1		1
143.142	odd	2		4235.2.a.c.1.1		1
156.155	even	2		5040.2.a.v.1.1		1
195.38	even	4		1575.2.d.c.1324.1		2
195.77	even	4		1575.2.d.c.1324.2		2
195.194	odd	2		1575.2.a.f.1.1		1
260.103	even	4		2800.2.g.l.449.1		2
260.207	even	4		2800.2.g.l.449.2		2
260.259	odd	2		2800.2.a.z.1.1		1
273.272	even	2		2205.2.a.e.1.1		1
364.363	even	2		3920.2.a.ba.1.1		1
455.272	even	4		1225.2.b.d.99.2		2
455.363	even	4		1225.2.b.d.99.1		2
455.454	odd	2		1225.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.a.a.1.1	✓	1	13.12	even	2
175.2.a.b.1.1		1	65.64	even	2
175.2.b.a.99.1		2	65.12	odd	4
175.2.b.a.99.2		2	65.38	odd	4
245.2.a.c.1.1		1	91.90	odd	2
245.2.e.a.116.1		2	91.51	even	6
245.2.e.a.226.1		2	91.25	even	6
245.2.e.b.116.1		2	91.12	odd	6
245.2.e.b.226.1		2	91.38	odd	6
315.2.a.b.1.1		1	39.38	odd	2
560.2.a.b.1.1		1	52.51	odd	2
1225.2.a.e.1.1		1	455.454	odd	2
1225.2.b.d.99.1		2	455.363	even	4
1225.2.b.d.99.2		2	455.272	even	4
1575.2.a.f.1.1		1	195.194	odd	2
1575.2.d.c.1324.1		2	195.38	even	4
1575.2.d.c.1324.2		2	195.77	even	4
2205.2.a.e.1.1		1	273.272	even	2
2240.2.a.k.1.1		1	104.77	even	2
2240.2.a.u.1.1		1	104.51	odd	2
2800.2.a.z.1.1		1	260.259	odd	2
2800.2.g.l.449.1		2	260.103	even	4
2800.2.g.l.449.2		2	260.207	even	4
3920.2.a.ba.1.1		1	364.363	even	2
4235.2.a.c.1.1		1	143.142	odd	2
5040.2.a.v.1.1		1	156.155	even	2
5915.2.a.f.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:	\( N \)	\(=\)	\( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5915.a (trivial)

Introduction

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