LMFDB - Embedded newform 1575.2.g.e.1574.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(1574,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1575.1574");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.g (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.162447943996702457856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1574.2
Root			$-1.40721 + 0.140577i$ of defining polynomial
Character	$\chi$	$=$	1575.1574
Dual form			1575.2.g.e.1574.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81442 q^{2} +5.92095 q^{4} +2.64575i q^{7} -11.0352 q^{8} +O(q^{10})$	$q-2.81442 q^{2} +5.92095 q^{4} +2.64575i q^{7} -11.0352 q^{8} +4.07592i q^{11} -7.44625i q^{14} +19.2158 q^{16} -11.4714i q^{22} +9.09695 q^{23} +15.6654i q^{28} -0.807232i q^{29} -32.0108 q^{32} +0.0953502i q^{37} +13.0381i q^{43} +24.1333i q^{44} -25.6026 q^{46} -7.00000 q^{49} -0.412247 q^{53} -29.1964i q^{56} +2.27189i q^{58} +51.6603 q^{64} -15.7477i q^{67} +14.0853i q^{71} -0.268355i q^{74} -10.7839 q^{77} -9.74773 q^{79} -36.6945i q^{86} -44.9786i q^{88} +53.8626 q^{92} +19.7009 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} + 72 q^{16} - 88 q^{46} - 112 q^{49} + 144 q^{64} + 64 q^{79}+O(q^{100}) $ 16 * q + 32 * q^4 + 72 * q^16 - 88 * q^46 - 112 * q^49 + 144 * q^64 + 64 * q^79

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−2.81442	−1.99009	−0.995047	−	0.0994033i	$-0.968307\pi$
$2$	−2.81442	−1.99009	−0.995047	+	0.0994033i	$0.968307\pi$
$3$	0	0
$3$	0	0
$4$	5.92095	2.96048
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.64575i	1.00000i
$7$	2.64575i	1.00000i
$8$	−11.0352	−3.90153
$9$	0	0
$10$	0	0
$11$	4.07592i	1.22894i	0.788941	+	0.614468i	$0.210630\pi$
$11$	4.07592i	1.22894i	−0.788941	+	0.614468i	$0.789370\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	− 7.44625i	− 1.99009i
$15$	0	0
$16$	19.2158	4.80394
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	− 11.4714i	− 2.44570i
$23$	9.09695	1.89684	0.948422	−	0.317009i	$-0.102679\pi$
$23$	9.09695	1.89684	0.948422	+	0.317009i	$0.102679\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	15.6654i	2.96048i
$29$	− 0.807232i	− 0.149899i	−0.997187	−	0.0749496i	$-0.976120\pi$
$29$	− 0.807232i	− 0.149899i	0.997187	−	0.0749496i	$-0.0238796\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−32.0108	−5.65877
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0.0953502i	0.0156755i	0.999969	+	0.00783774i	$0.00249486\pi$
$37$	0.0953502i	0.0156755i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	13.0381i	1.98828i	0.108078	+	0.994142i	$0.465531\pi$
$43$	13.0381i	1.98828i	−0.108078	+	0.994142i	$0.534469\pi$
$44$	24.1333i	3.63824i
$45$	0	0
$46$	−25.6026	−3.77490
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−0.412247	−0.0566265	−0.0283132	−	0.999599i	$-0.509014\pi$
$53$	−0.412247	−0.0566265	−0.0283132	+	0.999599i	$0.509014\pi$
$54$	0	0
$55$	0	0
$56$	− 29.1964i	− 3.90153i
$57$	0	0
$58$	2.27189i	0.298313i
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	51.6603	6.45754
$65$	0	0
$66$	0	0
$67$	− 15.7477i	− 1.92389i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	− 15.7477i	− 1.92389i	0.273241	−	0.961946i	$-0.411904\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	14.0853i	1.67161i	0.549023	+	0.835807i	$0.315000\pi$
$71$	14.0853i	1.67161i	−0.549023	+	0.835807i	$0.685000\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	− 0.268355i	− 0.0311957i
$75$	0	0
$76$	0	0
$77$	−10.7839	−1.22894
$78$	0	0
$79$	−9.74773	−1.09670	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	−9.74773	−1.09670	−0.548352	+	0.836247i	$0.684745\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	− 36.6945i	− 3.95687i
$87$	0	0
$88$	− 44.9786i	− 4.79474i
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	53.8626	5.61556
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	19.7009	1.99009
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	1.16024	0.112692
$107$	10.4005	1.00545	0.502726	−	0.864446i	$-0.332330\pi$
$107$	10.4005	1.00545	0.502726	+	0.864446i	$0.332330\pi$
$108$	0	0
$109$	−10.2970	−0.986269	−0.493135	−	0.869953i	$-0.664149\pi$
$109$	−10.2970	−0.986269	−0.493135	+	0.869953i	$0.664149\pi$
$110$	0	0
$111$	0	0
$112$	50.8401i	4.80394i
$113$	7.41002	0.697076	0.348538	−	0.937295i	$-0.386678\pi$
$113$	7.41002	0.697076	0.348538	+	0.937295i	$0.386678\pi$
$114$	0	0
$115$	0	0
$116$	− 4.77958i	− 0.443773i
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−5.61315	−0.510286
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	5.74773i	0.510028i	0.966937	+	0.255014i	$0.0820801\pi$
$127$	5.74773i	0.510028i	−0.966937	+	0.255014i	$0.917920\pi$
$128$	−81.3721	−7.19234
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	44.3207i	3.82872i
$135$	0	0
$136$	0	0
$137$	−22.0377	−1.88281	−0.941404	−	0.337282i	$-0.890493\pi$
$137$	−22.0377	−1.88281	−0.941404	+	0.337282i	$0.890493\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	− 39.6418i	− 3.32667i
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0.564564i	0.0464069i
$149$	15.9164i	1.30392i	0.758252	+	0.651962i	$0.226054\pi$
$149$	15.9164i	1.30392i	−0.758252	+	0.651962i	$0.773946\pi$
$150$	0	0
$151$	−18.1389	−1.47612	−0.738060	−	0.674735i	$-0.764258\pi$
$151$	−18.1389	−1.47612	−0.738060	+	0.674735i	$0.764258\pi$
$152$	0	0
$153$	0	0
$154$	30.3503	2.44570
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	27.4342	2.18255
$159$	0	0
$160$	0	0
$161$	24.0683i	1.89684i
$162$	0	0
$163$	20.0000i	1.56652i	0.621694	+	0.783260i	$0.286445\pi$
$163$	20.0000i	1.56652i	−0.621694	+	0.783260i	$0.713555\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	77.1977i	5.88627i
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	78.3220i	5.90374i
$177$	0	0
$178$	0	0
$179$	− 15.8799i	− 1.18692i	−0.804865	−	0.593458i	$-0.797762\pi$
$179$	− 15.8799i	− 1.18692i	0.804865	−	0.593458i	$-0.202238\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	−100.387	−7.40060
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	24.3651i	1.76300i	0.472184	+	0.881500i	$0.343466\pi$
$191$	24.3651i	1.76300i	−0.472184	+	0.881500i	$0.656534\pi$
$192$	0	0
$193$	26.1715i	1.88386i	0.335805	+	0.941932i	$0.390992\pi$
$193$	26.1715i	1.88386i	−0.335805	+	0.941932i	$0.609008\pi$
$194$	0	0
$195$	0	0
$196$	−41.4467	−2.96048
$197$	−3.49310	−0.248873	−0.124437	−	0.992228i	$-0.539712\pi$
$197$	−3.49310	−0.248873	−0.124437	+	0.992228i	$0.539712\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	2.13573	0.149899
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	26.4575	1.82141	0.910705	−	0.413057i	$-0.135539\pi$
$211$	26.4575	1.82141	0.910705	+	0.413057i	$0.135539\pi$
$212$	−2.44089	−0.167641
$213$	0	0
$214$	−29.2713	−2.00094
$215$	0	0
$216$	0	0
$217$	0	0
$218$	28.9799	1.96277
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	− 84.6926i	− 5.65877i
$225$	0	0
$226$	−20.8549	−1.38725
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	8.90796i	0.584836i
$233$	−14.7508	−0.966356	−0.483178	−	0.875522i	$-0.660518\pi$
$233$	−14.7508	−0.966356	−0.483178	+	0.875522i	$0.660518\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	− 7.39458i	− 0.478316i	−0.970981	−	0.239158i	$-0.923129\pi$
$239$	− 7.39458i	− 0.478316i	0.970981	−	0.239158i	$-0.0768713\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	15.7977	1.01552
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	37.0785i	2.33110i
$254$	− 16.1765i	− 1.01500i
$255$	0	0
$256$	125.694	7.85590
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−0.252273	−0.0156755
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−13.3934	−0.825873	−0.412936	−	0.910760i	$-0.635497\pi$
$263$	−13.3934	−0.825873	−0.412936	+	0.910760i	$0.635497\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	− 93.2415i	− 5.69563i
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	62.0233	3.74696
$275$	0	0
$276$	0	0
$277$	10.0000i	0.600842i	0.953807	+	0.300421i	$0.0971271\pi$
$277$	10.0000i	0.600842i	−0.953807	+	0.300421i	$0.902873\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	− 30.5922i	− 1.82498i	−0.409099	−	0.912490i	$-0.634157\pi$
$281$	− 30.5922i	− 1.82498i	0.409099	−	0.912490i	$-0.365843\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	83.3982i	4.94877i
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	− 1.05221i	− 0.0611584i
$297$	0	0
$298$	− 44.7955i	− 2.59493i
$299$	0	0
$300$	0	0
$301$	−34.4955	−1.98828
$302$	51.0503	2.93762
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	−63.8508	−3.63824
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	0	0
$315$	0	0
$316$	−57.7158	−3.24677
$317$	−19.0222	−1.06840	−0.534198	−	0.845359i	$-0.679386\pi$
$317$	−19.0222	−1.06840	−0.534198	+	0.845359i	$0.679386\pi$
$318$	0	0
$319$	3.29021	0.184217
$320$	0	0
$321$	0	0
$322$	− 67.7382i	− 3.77490i
$323$	0	0
$324$	0	0
$325$	0	0
$326$	− 56.2884i	− 3.11752i
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	33.8227	1.85906	0.929531	−	0.368744i	$-0.120212\pi$
$331$	33.8227	1.85906	0.929531	+	0.368744i	$0.120212\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	21.1660i	1.15299i	0.817102	+	0.576493i	$0.195579\pi$
$337$	21.1660i	1.15299i	−0.817102	+	0.576493i	$0.804421\pi$
$338$	36.5874	1.99009
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 18.5203i	− 1.00000i
$344$	− 143.878i	− 7.75736i
$345$	0	0
$346$	0	0
$347$	−5.72309	−0.307231	−0.153616	−	0.988131i	$-0.549092\pi$
$347$	−5.72309	−0.307231	−0.153616	+	0.988131i	$0.549092\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	− 130.474i	− 6.95427i
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	44.6926i	2.36208i
$359$	17.3142i	0.913808i	0.889516	+	0.456904i	$0.151042\pi$
$359$	17.3142i	0.913808i	−0.889516	+	0.456904i	$0.848958\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	174.805	9.11233
$369$	0	0
$370$	0	0
$371$	− 1.09070i	− 0.0566265i
$372$	0	0
$373$	− 16.4955i	− 0.854102i	−0.904227	−	0.427051i	$-0.859552\pi$
$373$	− 16.4955i	− 0.854102i	0.904227	−	0.427051i	$-0.140448\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−28.9126	−1.48514	−0.742569	−	0.669769i	$-0.766393\pi$
$379$	−28.9126	−1.48514	−0.742569	+	0.669769i	$0.766393\pi$
$380$	0	0
$381$	0	0
$382$	− 68.5737i	− 3.50854i
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	− 73.6575i	− 3.74907i
$387$	0	0
$388$	0	0
$389$	0.387274i	0.0196356i	0.999952	+	0.00981780i	$0.00312515\pi$
$389$	0.387274i	0.0196356i	−0.999952	+	0.00981780i	$0.996875\pi$
$390$	0	0
$391$	0	0
$392$	77.2464	3.90153
$393$	0	0
$394$	9.83105	0.495281
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	27.3633i	1.36646i	0.730204	+	0.683229i	$0.239425\pi$
$401$	27.3633i	1.36646i	−0.730204	+	0.683229i	$0.760575\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	−6.01085	−0.298313
$407$	−0.388640	−0.0192642
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	14.4955	0.706465	0.353233	−	0.935536i	$-0.385082\pi$
$421$	14.4955	0.706465	0.353233	+	0.935536i	$0.385082\pi$
$422$	−74.4625	−3.62478
$423$	0	0
$424$	4.54923	0.220930
$425$	0	0
$426$	0	0
$427$	0	0
$428$	61.5807	2.97662
$429$	0	0
$430$	0	0
$431$	41.3357i	1.99107i	0.0943889	+	0.995535i	$0.469910\pi$
$431$	41.3357i	1.99107i	−0.0943889	+	0.995535i	$0.530090\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	−60.9678	−2.91983
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	12.0495	0.572487	0.286244	−	0.958157i	$-0.407593\pi$
$443$	12.0495	0.572487	0.286244	+	0.958157i	$0.407593\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	136.680i	6.45754i
$449$	40.3720i	1.90527i	0.304116	+	0.952635i	$0.401639\pi$
$449$	40.3720i	1.90527i	−0.304116	+	0.952635i	$0.598361\pi$
$450$	0	0
$451$	0	0
$452$	43.8744	2.06368
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	26.3622i	1.23317i	0.787288	+	0.616585i	$0.211484\pi$
$457$	26.3622i	1.23317i	−0.787288	+	0.616585i	$0.788516\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	− 40.0000i	− 1.85896i	−0.368875	−	0.929479i	$-0.620257\pi$
$463$	− 40.0000i	− 1.85896i	0.368875	−	0.929479i	$-0.379743\pi$
$464$	− 15.5116i	− 0.720107i
$465$	0	0
$466$	41.5149	1.92314
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	41.6646	1.92389
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−53.1421	−2.44348
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	20.8114i	0.951893i
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−33.2352	−1.51069
$485$	0	0
$486$	0	0
$487$	− 39.3049i	− 1.78107i	−0.454911	−	0.890537i	$-0.650329\pi$
$487$	− 39.3049i	− 1.78107i	0.454911	−	0.890537i	$-0.349671\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 43.8703i	− 1.97984i	−0.141635	−	0.989919i	$-0.545236\pi$
$491$	− 43.8703i	− 1.97984i	0.141635	−	0.989919i	$-0.454764\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−37.2661	−1.67161
$498$	0	0
$499$	−26.4575	−1.18440	−0.592200	−	0.805791i	$-0.701741\pi$
$499$	−26.4575	−1.18440	−0.592200	+	0.805791i	$0.701741\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	− 104.354i	− 4.63911i
$507$	0	0
$508$	34.0320i	1.50993i
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	−191.013	−8.44165
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0.710002	0.0311957
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	37.6947	1.64357
$527$	0	0
$528$	0	0
$529$	59.7545	2.59802
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	173.779i	7.50612i
$537$	0	0
$538$	0	0
$539$	− 28.5315i	− 1.22894i
$540$	0	0
$541$	44.4955	1.91301	0.956504	−	0.291718i	$-0.0942267\pi$
$541$	44.4955	1.91301	0.956504	+	0.291718i	$0.0942267\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	35.7477i	1.52846i	0.644942	+	0.764231i	$0.276881\pi$
$547$	35.7477i	1.52846i	−0.644942	+	0.764231i	$0.723119\pi$
$548$	−130.484	−5.57401
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	− 25.7901i	− 1.09670i
$554$	− 28.1442i	− 1.19573i
$555$	0	0
$556$	0	0
$557$	47.1717	1.99873	0.999364	−	0.0356614i	$-0.0113538\pi$
$557$	47.1717	1.99873	0.999364	+	0.0356614i	$0.0113538\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	86.0994i	3.63188i
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	− 155.434i	− 6.52186i
$569$	− 32.2067i	− 1.35018i	−0.737738	−	0.675088i	$-0.764106\pi$
$569$	− 32.2067i	− 1.35018i	0.737738	−	0.675088i	$-0.235894\pi$
$570$	0	0
$571$	−39.2432	−1.64228	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	−39.2432	−1.64228	−0.821138	+	0.570730i	$0.806660\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−47.8451	−1.99009
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	− 1.68029i	− 0.0695904i
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	1.83223i	0.0753041i
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	94.2403i	3.86023i
$597$	0	0
$598$	0	0
$599$	− 44.0606i	− 1.80027i	−0.435614	−	0.900134i	$-0.643469\pi$
$599$	− 44.0606i	− 1.80027i	0.435614	−	0.900134i	$-0.356531\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	97.0846	3.95687
$603$	0	0
$604$	−107.399	−4.37002
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	− 46.4955i	− 1.87793i	−0.344008	−	0.938967i	$-0.611785\pi$
$613$	− 46.4955i	− 1.87793i	0.344008	−	0.938967i	$-0.388215\pi$
$614$	0	0
$615$	0	0
$616$	119.002	4.79474
$617$	−14.1577	−0.569969	−0.284985	−	0.958532i	$-0.591988\pi$
$617$	−14.1577	−0.569969	−0.284985	+	0.958532i	$0.591988\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	49.2432	1.96034	0.980170	−	0.198158i	$-0.0634960\pi$
$631$	49.2432	1.96034	0.980170	+	0.198158i	$0.0634960\pi$
$632$	107.568	4.27883
$633$	0	0
$634$	53.5366	2.12621
$635$	0	0
$636$	0	0
$637$	0	0
$638$	−9.26004	−0.366608
$639$	0	0
$640$	0	0
$641$	8.53912i	0.337275i	0.985678	+	0.168637i	$0.0539367\pi$
$641$	8.53912i	0.337275i	−0.985678	+	0.168637i	$0.946063\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	142.507i	5.61556i
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	118.419i	4.63765i
$653$	−42.8387	−1.67641	−0.838203	−	0.545358i	$-0.816394\pi$
$653$	−42.8387	−1.67641	−0.838203	+	0.545358i	$0.816394\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	− 49.8210i	− 1.94075i	−0.241604	−	0.970375i	$-0.577673\pi$
$659$	− 49.8210i	− 1.94075i	0.241604	−	0.970375i	$-0.422327\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−95.1911	−3.69971
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	− 7.34334i	− 0.284335i
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	42.3320i	1.63178i	0.578208	+	0.815890i	$0.303752\pi$
$673$	42.3320i	1.63178i	−0.578208	+	0.815890i	$0.696248\pi$
$674$	− 59.5700i	− 2.29455i
$675$	0	0
$676$	−76.9724	−2.96048
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−48.8586	−1.86952	−0.934761	−	0.355277i	$-0.884387\pi$
$683$	−48.8586	−1.86952	−0.934761	+	0.355277i	$0.884387\pi$
$684$	0	0
$685$	0	0
$686$	52.1238i	1.99009i
$687$	0	0
$688$	250.536i	9.55161i
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	16.1072	0.611420
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	− 36.0024i	− 1.35979i	−0.733309	−	0.679895i	$-0.762025\pi$
$701$	− 36.0024i	− 1.35979i	0.733309	−	0.679895i	$-0.237975\pi$
$702$	0	0
$703$	0	0
$704$	210.563i	7.93591i
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	52.9150	1.98727	0.993633	−	0.112667i	$-0.0359394\pi$
$709$	52.9150	1.98727	0.993633	+	0.112667i	$0.0359394\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	− 94.0239i	− 3.51384i
$717$	0	0
$718$	− 48.7294i	− 1.81857i
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	−53.4740	−1.99009
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	0	0
$735$	0	0
$736$	−291.201	−10.7338
$737$	64.1865	2.36434
$738$	0	0
$739$	−39.7477	−1.46214	−0.731072	−	0.682300i	$-0.760980\pi$
$739$	−39.7477	−1.46214	−0.731072	+	0.682300i	$0.760980\pi$
$740$	0	0
$741$	0	0
$742$	3.06969i	0.112692i
$743$	54.4759	1.99853	0.999263	−	0.0383863i	$-0.0122217\pi$
$743$	54.4759	1.99853	0.999263	+	0.0383863i	$0.0122217\pi$
$744$	0	0
$745$	0	0
$746$	46.4251i	1.69974i
$747$	0	0
$748$	0	0
$749$	27.5171i	1.00545i
$750$	0	0
$751$	26.4575	0.965448	0.482724	−	0.875772i	$-0.339647\pi$
$751$	26.4575	0.965448	0.482724	+	0.875772i	$0.339647\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	52.0569i	1.89204i	0.324109	+	0.946020i	$0.394935\pi$
$757$	52.0569i	1.89204i	−0.324109	+	0.946020i	$0.605065\pi$
$758$	81.3721	2.95557
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	− 27.2432i	− 0.986269i
$764$	144.265i	5.21932i
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	154.960i	5.57713i
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	− 1.08995i	− 0.0390767i
$779$	0	0
$780$	0	0
$781$	−57.4105	−2.05431
$782$	0	0
$783$	0	0
$784$	−134.510	−4.80394
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	−20.6825	−0.736783
$789$	0	0
$790$	0	0
$791$	19.6051i	0.697076i
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	− 77.0118i	− 2.71938i
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	25.7488i	0.905281i	0.891693	+	0.452641i	$0.149518\pi$
$809$	25.7488i	0.905281i	−0.891693	+	0.452641i	$0.850482\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	12.6456	0.443773
$813$	0	0
$814$	1.09380	0.0383375
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	− 52.9729i	− 1.84877i	−0.381464	−	0.924384i	$-0.624580\pi$
$821$	− 52.9729i	− 1.84877i	0.381464	−	0.924384i	$-0.375420\pi$
$822$	0	0
$823$	− 57.2432i	− 1.99537i	−0.0679910	−	0.997686i	$-0.521659\pi$
$823$	− 57.2432i	− 1.99537i	0.0679910	−	0.997686i	$-0.478341\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	47.1664	1.64014	0.820069	−	0.572265i	$-0.193935\pi$
$827$	47.1664	1.64014	0.820069	+	0.572265i	$0.193935\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	28.3484	0.977530
$842$	−40.7963	−1.40593
$843$	0	0
$844$	156.654	5.39224
$845$	0	0
$846$	0	0
$847$	− 14.8510i	− 0.510286i
$848$	−7.92164	−0.272030
$849$	0	0
$850$	0	0
$851$	0.867396i	0.0297339i
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−114.771	−3.92280
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	− 116.336i	− 3.96242i
$863$	54.1526	1.84338	0.921689	−	0.387931i	$-0.126810\pi$
$863$	54.1526	1.84338	0.921689	+	0.387931i	$0.126810\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	− 39.7310i	− 1.34778i
$870$	0	0
$871$	0	0
$872$	113.629	3.84796
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	− 50.0000i	− 1.68838i	−0.536044	−	0.844190i	$-0.680082\pi$
$877$	− 50.0000i	− 1.68838i	0.536044	−	0.844190i	$-0.319918\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	− 39.4956i	− 1.32913i	−0.747230	−	0.664566i	$-0.768617\pi$
$883$	− 39.4956i	− 1.32913i	0.747230	−	0.664566i	$-0.231383\pi$
$884$	0	0
$885$	0	0
$886$	−33.9122	−1.13930
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	−15.2071	−0.510028
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	− 215.290i	− 7.19234i
$897$	0	0
$898$	− 113.624i	− 3.79167i
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−81.7710	−2.71966
$905$	0	0
$906$	0	0
$907$	5.29150i	0.175701i	0.996134	+	0.0878507i	$0.0279999\pi$
$907$	5.29150i	0.175701i	−0.996134	+	0.0878507i	$0.972000\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	− 60.3643i	− 1.99996i	−0.00645824	−	0.999979i	$-0.502056\pi$
$911$	− 60.3643i	− 1.99996i	0.00645824	−	0.999979i	$-0.497944\pi$
$912$	0	0
$913$	0	0
$914$	− 74.1942i	− 2.45412i
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	23.0490	0.760315	0.380158	−	0.924922i	$-0.375870\pi$
$919$	23.0490	0.760315	0.380158	+	0.924922i	$0.375870\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	112.577i	3.69950i
$927$	0	0
$928$	25.8401i	0.848244i
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	−87.3386	−2.86087
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	−117.262	−3.82872
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	149.564	4.86275
$947$	55.3004	1.79702	0.898510	−	0.438953i	$-0.144650\pi$
$947$	55.3004	1.79702	0.898510	+	0.438953i	$0.144650\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−50.5455	−1.63733	−0.818665	−	0.574271i	$-0.805286\pi$
$953$	−50.5455	−1.63733	−0.818665	+	0.574271i	$0.805286\pi$
$954$	0	0
$955$	0	0
$956$	− 43.7829i	− 1.41604i
$957$	0	0
$958$	0	0
$959$	− 58.3063i	− 1.88281i
$960$	0	0
$961$	31.0000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	40.0000i	1.28631i	0.765735	+	0.643157i	$0.222376\pi$
$967$	40.0000i	1.28631i	−0.765735	+	0.643157i	$0.777624\pi$
$968$	61.9422	1.99090
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	110.620i	3.54450i
$975$	0	0
$976$	0	0
$977$	−52.7953	−1.68907	−0.844535	−	0.535500i	$-0.820123\pi$
$977$	−52.7953	−1.68907	−0.844535	+	0.535500i	$0.820123\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	123.469i	3.94006i
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	118.607i	3.77147i
$990$	0	0
$991$	−8.31865	−0.264251	−0.132125	−	0.991233i	$-0.542180\pi$
$991$	−8.31865	−0.264251	−0.132125	+	0.991233i	$0.542180\pi$
$992$	0	0
$993$	0	0
$994$	104.882	3.32667
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	74.4625	2.35707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.g.e.1574.2		16
3.2	odd	2	inner	1575.2.g.e.1574.16		16
5.2	odd	4		1575.2.b.g.251.1	yes	8
5.3	odd	4		1575.2.b.f.251.8	yes	8
5.4	even	2	inner	1575.2.g.e.1574.15		16
7.6	odd	2	CM	1575.2.g.e.1574.2		16
15.2	even	4		1575.2.b.g.251.8	yes	8
15.8	even	4		1575.2.b.f.251.1	✓	8
15.14	odd	2	inner	1575.2.g.e.1574.1		16
21.20	even	2	inner	1575.2.g.e.1574.16		16
35.13	even	4		1575.2.b.f.251.8	yes	8
35.27	even	4		1575.2.b.g.251.1	yes	8
35.34	odd	2	inner	1575.2.g.e.1574.15		16
105.62	odd	4		1575.2.b.g.251.8	yes	8
105.83	odd	4		1575.2.b.f.251.1	✓	8
105.104	even	2	inner	1575.2.g.e.1574.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1575.2.b.f.251.1	✓	8	15.8	even	4
1575.2.b.f.251.1	✓	8	105.83	odd	4
1575.2.b.f.251.8	yes	8	5.3	odd	4
1575.2.b.f.251.8	yes	8	35.13	even	4
1575.2.b.g.251.1	yes	8	5.2	odd	4
1575.2.b.g.251.1	yes	8	35.27	even	4
1575.2.b.g.251.8	yes	8	15.2	even	4
1575.2.b.g.251.8	yes	8	105.62	odd	4
1575.2.g.e.1574.1		16	15.14	odd	2	inner
1575.2.g.e.1574.1		16	105.104	even	2	inner
1575.2.g.e.1574.2		16	1.1	even	1	trivial
1575.2.g.e.1574.2		16	7.6	odd	2	CM
1575.2.g.e.1574.15		16	5.4	even	2	inner
1575.2.g.e.1574.15		16	35.34	odd	2	inner
1575.2.g.e.1574.16		16	3.2	odd	2	inner
1575.2.g.e.1574.16		16	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.81442 q^{2} +5.92095 q^{4} +2.64575i q^{7} -11.0352 q^{8} +O(q^{10})\)	\(q-2.81442 q^{2} +5.92095 q^{4} +2.64575i q^{7} -11.0352 q^{8} +4.07592i q^{11} -7.44625i q^{14} +19.2158 q^{16} -11.4714i q^{22} +9.09695 q^{23} +15.6654i q^{28} -0.807232i q^{29} -32.0108 q^{32} +0.0953502i q^{37} +13.0381i q^{43} +24.1333i q^{44} -25.6026 q^{46} -7.00000 q^{49} -0.412247 q^{53} -29.1964i q^{56} +2.27189i q^{58} +51.6603 q^{64} -15.7477i q^{67} +14.0853i q^{71} -0.268355i q^{74} -10.7839 q^{77} -9.74773 q^{79} -36.6945i q^{86} -44.9786i q^{88} +53.8626 q^{92} +19.7009 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} + 72 q^{16} - 88 q^{46} - 112 q^{49} + 144 q^{64} + 64 q^{79}+O(q^{100}) \) 16 * q + 32 * q^4 + 72 * q^16 - 88 * q^46 - 112 * q^49 + 144 * q^64 + 64 * q^79

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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