LMFDB - Embedded newform 1575.2.g.d.1574.4

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:	$8$
Coefficient field:	8.0.157351936.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{4} + 16 $ x^8 + x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1574.4
Root			$-0.581861 - 1.28897i$ of defining polynomial
Character	$\chi$	$=$	1575.1574
Dual form			1575.2.g.d.1574.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.16372 q^{2} -0.645751 q^{4} +2.64575i q^{7} +3.07892 q^{8} +O(q^{10})$	$q-1.16372 q^{2} -0.645751 q^{4} +2.64575i q^{7} +3.07892 q^{8} +6.57008i q^{11} -3.07892i q^{14} -2.29150 q^{16} -7.64575i q^{22} +1.91520 q^{23} -1.70850i q^{28} +8.89753i q^{29} -3.49117 q^{32} -10.5830i q^{37} -5.29150i q^{43} -4.24264i q^{44} -2.22876 q^{46} -7.00000 q^{49} +0.412247 q^{53} +8.14605i q^{56} -10.3542i q^{58} +8.64575 q^{64} +4.00000i q^{67} +15.0554i q^{71} +12.3157i q^{74} -17.3828 q^{77} -8.00000 q^{79} +6.15784i q^{86} +20.2288i q^{88} -1.23674 q^{92} +8.14605 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4}+O(q^{10}) $ 8 * q + 16 * q^4	$ 8 q + 16 q^{4} + 24 q^{16} + 88 q^{46} - 56 q^{49} + 48 q^{64} - 64 q^{79}+O(q^{100}) $ 8 * q + 16 * q^4 + 24 * q^16 + 88 * q^46 - 56 * q^49 + 48 * 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 $

$2$	−1.16372	−0.822876	−0.411438	−	0.911438i	$-0.634973\pi$
$2$	−1.16372	−0.822876	−0.411438	+	0.911438i	$0.634973\pi$
$3$	0	0
$3$	0	0
$4$	−0.645751	−0.322876
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.64575i	1.00000i
$7$	2.64575i	1.00000i
$8$	3.07892	1.08856
$9$	0	0
$10$	0	0
$11$	6.57008i	1.98096i	0.137675	+	0.990478i	$0.456037\pi$
$11$	6.57008i	1.98096i	−0.137675	+	0.990478i	$0.543963\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	− 3.07892i	− 0.822876i
$15$	0	0
$16$	−2.29150	−0.572876
$17$	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
$22$	− 7.64575i	− 1.63008i
$23$	1.91520	0.399346	0.199673	−	0.979863i	$-0.436012\pi$
$23$	1.91520	0.399346	0.199673	+	0.979863i	$0.436012\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	− 1.70850i	− 0.322876i
$29$	8.89753i	1.65223i	0.563502	+	0.826115i	$0.309454\pi$
$29$	8.89753i	1.65223i	−0.563502	+	0.826115i	$0.690546\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−3.49117	−0.617157
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	− 10.5830i	− 1.73984i	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	− 10.5830i	− 1.73984i	0.493197	−	0.869918i	$-0.335828\pi$
$38$	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
$43$	− 5.29150i	− 0.806947i	−0.914991	−	0.403473i	$-0.867803\pi$
$43$	− 5.29150i	− 0.806947i	0.914991	−	0.403473i	$-0.132197\pi$
$44$	− 4.24264i	− 0.639602i
$45$	0	0
$46$	−2.22876	−0.328612
$47$	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	$-0.490986\pi$
$53$	0.412247	0.0566265	0.0283132	+	0.999599i	$0.490986\pi$
$54$	0	0
$55$	0	0
$56$	8.14605i	1.08856i
$57$	0	0
$58$	− 10.3542i	− 1.35958i
$59$	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
$64$	8.64575	1.08072
$65$	0	0
$66$	0	0
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	15.0554i	1.78674i	0.449319	+	0.893372i	$0.351667\pi$
$71$	15.0554i	1.78674i	−0.449319	+	0.893372i	$0.648333\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	12.3157i	1.43167i
$75$	0	0
$76$	0	0
$77$	−17.3828	−1.98096
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	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
$86$	6.15784i	0.664017i
$87$	0	0
$88$	20.2288i	2.15639i
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	−1.23674	−0.128939
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	8.14605	0.822876
$99$	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
$106$	−0.479741	−0.0465965
$107$	−10.4005	−1.00545	−0.502726	−	0.864446i	$-0.667670\pi$
$107$	−10.4005	−1.00545	−0.502726	+	0.864446i	$0.667670\pi$
$108$	0	0
$109$	−10.5830	−1.01367	−0.506834	−	0.862044i	$-0.669184\pi$
$109$	−10.5830	−1.01367	−0.506834	+	0.862044i	$0.669184\pi$
$110$	0	0
$111$	0	0
$112$	− 6.06275i	− 0.572876i
$113$	−13.5524	−1.27490	−0.637452	−	0.770490i	$-0.720012\pi$
$113$	−13.5524	−1.27490	−0.637452	+	0.770490i	$0.720012\pi$
$114$	0	0
$115$	0	0
$116$	− 5.74559i	− 0.533465i
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−32.1660	−2.92418
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	16.0000i	1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$	16.0000i	1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	−3.07892	−0.272141
$129$	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
$134$	− 4.65489i	− 0.402121i
$135$	0	0
$136$	0	0
$137$	22.0377	1.88281	0.941404	−	0.337282i	$-0.109507\pi$
$137$	22.0377	1.88281	0.941404	+	0.337282i	$0.109507\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	− 17.5203i	− 1.47027i
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	6.83399i	0.561750i
$149$	− 8.07303i	− 0.661369i	−0.943741	−	0.330684i	$-0.892720\pi$
$149$	− 8.07303i	− 0.661369i	0.943741	−	0.330684i	$-0.107280\pi$
$150$	0	0
$151$	−5.29150	−0.430616	−0.215308	−	0.976546i	$-0.569076\pi$
$151$	−5.29150	−0.430616	−0.215308	+	0.976546i	$0.569076\pi$
$152$	0	0
$153$	0	0
$154$	20.2288	1.63008
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	9.30978	0.740646
$159$	0	0
$160$	0	0
$161$	5.06713i	0.399346i
$162$	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
$172$	3.41699i	0.260543i
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	− 15.0554i	− 1.13484i
$177$	0	0
$178$	0	0
$179$	15.8799i	1.18692i	0.804865	+	0.593458i	$0.202238\pi$
$179$	15.8799i	1.18692i	−0.804865	+	0.593458i	$0.797762\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	5.89674	0.434713
$185$	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	$-0.656534\pi$
$191$	− 24.3651i	− 1.76300i	0.472184	−	0.881500i	$-0.343466\pi$
$192$	0	0
$193$	− 21.1660i	− 1.52356i	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	− 21.1660i	− 1.52356i	0.647834	−	0.761781i	$-0.275675\pi$
$194$	0	0
$195$	0	0
$196$	4.52026	0.322876
$197$	−25.8681	−1.84303	−0.921513	−	0.388348i	$-0.873046\pi$
$197$	−25.8681	−1.84303	−0.921513	+	0.388348i	$0.873046\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−23.5406	−1.65223
$204$	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	$0.135539\pi$
$212$	−0.266209	−0.0182833
$213$	0	0
$214$	12.1033	0.827362
$215$	0	0
$216$	0	0
$217$	0	0
$218$	12.3157	0.834123
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	− 9.23676i	− 0.617157i
$225$	0	0
$226$	15.7712	1.04909
$227$	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
$232$	27.3948i	1.79855i
$233$	−30.5230	−1.99963	−0.999813	−	0.0193169i	$-0.993851\pi$
$233$	−30.5230	−1.99963	−0.999813	+	0.0193169i	$0.993851\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	7.39458i	0.478316i	0.970981	+	0.239158i	$0.0768713\pi$
$239$	7.39458i	0.478316i	−0.970981	+	0.239158i	$0.923129\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	37.4323	2.40624
$243$	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
$253$	12.5830i	0.791087i
$254$	− 18.6196i	− 1.16829i
$255$	0	0
$256$	−13.7085	−0.856781
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	28.0000	1.73984
$260$	0	0
$261$	0	0
$262$	0	0
$263$	18.8858	1.16455	0.582273	−	0.812993i	$-0.302164\pi$
$263$	18.8858	1.16455	0.582273	+	0.812993i	$0.302164\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	− 2.58301i	− 0.157782i
$269$	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
$274$	−25.6458	−1.54932
$275$	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
$281$	− 3.41815i	− 0.203910i	−0.994789	−	0.101955i	$-0.967490\pi$
$281$	− 3.41815i	− 0.203910i	0.994789	−	0.101955i	$-0.0325097\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	− 9.72202i	− 0.576896i
$285$	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
$296$	− 32.5842i	− 1.89392i
$297$	0	0
$298$	9.39477i	0.544224i
$299$	0	0
$300$	0	0
$301$	14.0000	0.806947
$302$	6.15784	0.354344
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	11.2250	0.639602
$309$	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
$316$	5.16601	0.290611
$317$	16.5583	0.930008	0.465004	−	0.885309i	$-0.346053\pi$
$317$	16.5583	0.930008	0.465004	+	0.885309i	$0.346053\pi$
$318$	0	0
$319$	−58.4575	−3.27299
$320$	0	0
$321$	0	0
$322$	− 5.89674i	− 0.328612i
$323$	0	0
$324$	0	0
$325$	0	0
$326$	− 23.2744i	− 1.28905i
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−5.29150	−0.290847	−0.145424	−	0.989369i	$-0.546455\pi$
$331$	−5.29150	−0.290847	−0.145424	+	0.989369i	$0.546455\pi$
$332$	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	$0.804421\pi$
$338$	15.1284	0.822876
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 18.5203i	− 1.00000i
$344$	− 16.2921i	− 0.878412i
$345$	0	0
$346$	0	0
$347$	29.0200	1.55788	0.778938	−	0.627100i	$-0.215758\pi$
$347$	29.0200	1.55788	0.778938	+	0.627100i	$0.215758\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	− 22.9373i	− 1.22256i
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	− 18.4797i	− 0.976685i
$359$	− 20.5347i	− 1.08378i	−0.840449	−	0.541891i	$-0.817708\pi$
$359$	− 20.5347i	− 1.08378i	0.840449	−	0.541891i	$-0.182292\pi$
$360$	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	$0.5\pi$
$368$	−4.38868	−0.228776
$369$	0	0
$370$	0	0
$371$	1.09070i	0.0566265i
$372$	0	0
$373$	− 22.0000i	− 1.13912i	−0.821951	−	0.569558i	$-0.807114\pi$
$373$	− 22.0000i	− 1.13912i	0.821951	−	0.569558i	$-0.192886\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	37.0405	1.90264	0.951322	−	0.308199i	$-0.0997264\pi$
$379$	37.0405	1.90264	0.951322	+	0.308199i	$0.0997264\pi$
$380$	0	0
$381$	0	0
$382$	28.3542i	1.45073i
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	24.6314i	1.25370i
$387$	0	0
$388$	0	0
$389$	34.3534i	1.74179i	0.491473	+	0.870893i	$0.336458\pi$
$389$	34.3534i	1.74179i	−0.491473	+	0.870893i	$0.663542\pi$
$390$	0	0
$391$	0	0
$392$	−21.5524	−1.08856
$393$	0	0
$394$	30.1033	1.51658
$395$	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
$401$	39.0083i	1.94798i	0.226592	+	0.973990i	$0.427242\pi$
$401$	39.0083i	1.94798i	−0.226592	+	0.973990i	$0.572758\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	27.3948	1.35958
$407$	69.5312	3.44654
$408$	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
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−30.7892	−1.49879
$423$	0	0
$424$	1.26927	0.0616414
$425$	0	0
$426$	0	0
$427$	0	0
$428$	6.71612	0.324636
$429$	0	0
$430$	0	0
$431$	− 41.3357i	− 1.99107i	−0.0943889	−	0.995535i	$-0.530090\pi$
$431$	− 41.3357i	− 1.99107i	0.0943889	−	0.995535i	$-0.469910\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	6.83399	0.327289
$437$	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	$-0.592407\pi$
$443$	−12.0495	−0.572487	−0.286244	+	0.958157i	$0.592407\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	22.8745i	1.08072i
$449$	31.3475i	1.47938i	0.672948	+	0.739689i	$0.265028\pi$
$449$	31.3475i	1.47938i	−0.672948	+	0.739689i	$0.734972\pi$
$450$	0	0
$451$	0	0
$452$	8.75149	0.411635
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	− 42.3320i	− 1.98021i	−0.140334	−	0.990104i	$-0.544818\pi$
$457$	− 42.3320i	− 1.98021i	0.140334	−	0.990104i	$-0.455182\pi$
$458$	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	$-0.379743\pi$
$464$	− 20.3887i	− 0.946522i
$465$	0	0
$466$	35.5203	1.64544
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	−10.5830	−0.488678
$470$	0	0
$471$	0	0
$472$	0	0
$473$	34.7656	1.59852
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	− 8.60523i	− 0.393594i
$479$	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
$484$	20.7712	0.944147
$485$	0	0
$486$	0	0
$487$	37.0405i	1.67847i	0.543772	+	0.839233i	$0.316996\pi$
$487$	37.0405i	1.67847i	−0.543772	+	0.839233i	$0.683004\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	− 27.3710i	− 1.23524i	−0.786478	−	0.617619i	$-0.788097\pi$
$491$	− 27.3710i	− 1.23524i	0.786478	−	0.617619i	$-0.211903\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−39.8328	−1.78674
$498$	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
$506$	− 14.6431i	− 0.650966i
$507$	0	0
$508$	− 10.3320i	− 0.458409i
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	22.1107	0.977165
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−32.5842	−1.43167
$519$	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
$526$	−21.9778	−0.958276
$527$	0	0
$528$	0	0
$529$	−19.3320	−0.840523
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	12.3157i	0.531956i
$537$	0	0
$538$	0	0
$539$	− 45.9906i	− 1.98096i
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 44.0000i	− 1.88130i	−0.339372	−	0.940652i	$-0.610215\pi$
$547$	− 44.0000i	− 1.88130i	0.339372	−	0.940652i	$-0.389785\pi$
$548$	−14.2309	−0.607913
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	− 21.1660i	− 0.900070i
$554$	− 11.6372i	− 0.494418i
$555$	0	0
$556$	0	0
$557$	25.0436	1.06113	0.530566	−	0.847644i	$-0.321980\pi$
$557$	25.0436	1.06113	0.530566	+	0.847644i	$0.321980\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	3.97777i	0.167792i
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	46.3542i	1.94498i
$569$	14.3769i	0.602711i	0.953512	+	0.301356i	$0.0974392\pi$
$569$	14.3769i	0.602711i	−0.953512	+	0.301356i	$0.902561\pi$
$570$	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
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	−19.7833	−0.822876
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	2.70850i	0.112174i
$584$	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
$592$	24.2510i	0.996709i
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	5.21317i	0.213540i
$597$	0	0
$598$	0	0
$599$	− 3.56418i	− 0.145629i	−0.997346	−	0.0728143i	$-0.976802\pi$
$599$	− 3.56418i	− 0.145629i	0.997346	−	0.0728143i	$-0.0231980\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	−16.2921	−0.664017
$603$	0	0
$604$	3.41699	0.139036
$605$	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
$613$	38.0000i	1.53481i	0.641165	+	0.767403i	$0.278451\pi$
$613$	38.0000i	1.53481i	−0.641165	+	0.767403i	$0.721549\pi$
$614$	0	0
$615$	0	0
$616$	−53.5203	−2.15639
$617$	−48.3180	−1.94521	−0.972605	−	0.232462i	$-0.925322\pi$
$617$	−48.3180	−1.94521	−0.972605	+	0.232462i	$0.925322\pi$
$618$	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
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−24.6314	−0.979783
$633$	0	0
$634$	−19.2693	−0.765281
$635$	0	0
$636$	0	0
$637$	0	0
$638$	68.0283	2.69327
$639$	0	0
$640$	0	0
$641$	47.4935i	1.87588i	0.346795	+	0.937941i	$0.387270\pi$
$641$	47.4935i	1.87588i	−0.346795	+	0.937941i	$0.612730\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	− 3.27211i	− 0.128939i
$645$	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
$652$	− 12.9150i	− 0.505791i
$653$	42.8387	1.67641	0.838203	−	0.545358i	$-0.183606\pi$
$653$	42.8387	1.67641	0.838203	+	0.545358i	$0.183606\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	49.8210i	1.94075i	0.241604	+	0.970375i	$0.422327\pi$
$659$	49.8210i	1.94075i	−0.241604	+	0.970375i	$0.577673\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	6.15784	0.239331
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	17.0405i	0.659812i
$668$	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	$0.696248\pi$
$674$	− 24.6314i	− 0.948764i
$675$	0	0
$676$	8.39477	0.322876
$677$	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
$683$	−40.5112	−1.55012	−0.775059	−	0.631889i	$-0.782280\pi$
$683$	−40.5112	−1.55012	−0.775059	+	0.631889i	$0.782280\pi$
$684$	0	0
$685$	0	0
$686$	21.5524i	0.822876i
$687$	0	0
$688$	12.1255i	0.462280i
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	−33.7712	−1.28194
$695$	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	$0.237975\pi$
$701$	36.0024i	1.35979i	−0.733309	+	0.679895i	$0.762025\pi$
$702$	0	0
$703$	0	0
$704$	56.8033i	2.14086i
$705$	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
$716$	− 10.2544i	− 0.383226i
$717$	0	0
$718$	23.8967i	0.891818i
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	−22.1107	−0.822876
$723$	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
$736$	−6.68627	−0.246459
$737$	−26.2803	−0.968049
$738$	0	0
$739$	52.0000	1.91285	0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000	1.91285	0.956425	+	0.291977i	$0.0943129\pi$
$740$	0	0
$741$	0	0
$742$	− 1.26927i	− 0.0465965i
$743$	−54.4759	−1.99853	−0.999263	−	0.0383863i	$-0.987778\pi$
$743$	−54.4759	−1.99853	−0.999263	+	0.0383863i	$0.987778\pi$
$744$	0	0
$745$	0	0
$746$	25.6019i	0.937352i
$747$	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
$757$	− 10.5830i	− 0.384646i	−0.981332	−	0.192323i	$-0.938398\pi$
$757$	− 10.5830i	− 0.384646i	0.981332	−	0.192323i	$-0.0616021\pi$
$758$	−43.1049	−1.56564
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	− 28.0000i	− 1.01367i
$764$	15.7338i	0.569230i
$765$	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
$772$	13.6680i	0.491921i
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	− 39.9778i	− 1.43327i
$779$	0	0
$780$	0	0
$781$	−98.9150	−3.53946
$782$	0	0
$783$	0	0
$784$	16.0405	0.572876
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	16.7044	0.595068
$789$	0	0
$790$	0	0
$791$	− 35.8563i	− 1.27490i
$792$	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
$802$	− 45.3948i	− 1.60294i
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	56.8033i	1.99710i	0.0538482	+	0.998549i	$0.482851\pi$
$809$	56.8033i	1.99710i	−0.0538482	+	0.998549i	$0.517149\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	15.2014	0.533465
$813$	0	0
$814$	−80.9150	−2.83607
$815$	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	$0.375420\pi$
$821$	52.9729i	1.84877i	−0.381464	+	0.924384i	$0.624580\pi$
$822$	0	0
$823$	32.0000i	1.11545i	0.830026	+	0.557725i	$0.188326\pi$
$823$	32.0000i	1.11545i	−0.830026	+	0.557725i	$0.811674\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−4.92110	−0.171123	−0.0855616	−	0.996333i	$-0.527268\pi$
$827$	−4.92110	−0.171123	−0.0855616	+	0.996333i	$0.527268\pi$
$828$	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
$841$	−50.1660	−1.72986
$842$	−30.2568	−1.04272
$843$	0	0
$844$	−17.0850	−0.588089
$845$	0	0
$846$	0	0
$847$	− 85.1033i	− 2.92418i
$848$	−0.944665	−0.0324399
$849$	0	0
$850$	0	0
$851$	− 20.2685i	− 0.694797i
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	−32.0222	−1.09450
$857$	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
$862$	48.1033i	1.63840i
$863$	46.8151	1.59360	0.796802	−	0.604240i	$-0.206523\pi$
$863$	46.8151	1.59360	0.796802	+	0.604240i	$0.206523\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	− 52.5607i	− 1.78300i
$870$	0	0
$871$	0	0
$872$	−32.5842	−1.10344
$873$	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
$883$	58.2065i	1.95881i	0.201916	+	0.979403i	$0.435283\pi$
$883$	58.2065i	1.95881i	−0.201916	+	0.979403i	$0.564717\pi$
$884$	0	0
$885$	0	0
$886$	14.0222	0.471086
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	−42.3320	−1.41977
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	− 8.14605i	− 0.272141i
$897$	0	0
$898$	− 36.4797i	− 1.21734i
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	−41.7268	−1.38781
$905$	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
$911$	− 29.8445i	− 0.988793i	−0.869236	−	0.494397i	$-0.835389\pi$
$911$	− 29.8445i	− 0.988793i	0.869236	−	0.494397i	$-0.164611\pi$
$912$	0	0
$913$	0	0
$914$	49.2627i	1.62947i
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	37.0405	1.22185	0.610927	−	0.791687i	$-0.290797\pi$
$919$	37.0405	1.22185	0.610927	+	0.791687i	$0.290797\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	46.5489i	1.52969i
$927$	0	0
$928$	− 31.0627i	− 1.01968i
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	19.7103	0.645631
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	12.3157	0.402121
$939$	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
$946$	−40.4575	−1.31539
$947$	−55.3004	−1.79702	−0.898510	−	0.438953i	$-0.855350\pi$
$947$	−55.3004	−1.79702	−0.898510	+	0.438953i	$0.855350\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−55.9788	−1.81333	−0.906666	−	0.421849i	$-0.861381\pi$
$953$	−55.9788	−1.81333	−0.906666	+	0.421849i	$0.861381\pi$
$954$	0	0
$955$	0	0
$956$	− 4.77506i	− 0.154436i
$957$	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	$0.777624\pi$
$968$	−99.0365	−3.18315
$969$	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
$974$	− 43.1049i	− 1.38117i
$975$	0	0
$976$	0	0
$977$	2.59365	0.0829783	0.0414892	−	0.999139i	$-0.486790\pi$
$977$	2.59365	0.0829783	0.0414892	+	0.999139i	$0.486790\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	31.8523i	1.01645i
$983$	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
$989$	− 10.1343i	− 0.322251i
$990$	0	0
$991$	58.2065	1.84899	0.924496	−	0.381193i	$-0.124487\pi$
$991$	58.2065	1.84899	0.924496	+	0.381193i	$0.124487\pi$
$992$	0	0
$993$	0	0
$994$	46.3542	1.47027
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	30.7892	0.974615
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.g.d.1574.4		8
3.2	odd	2	inner	1575.2.g.d.1574.6		8
5.2	odd	4		63.2.c.a.62.2	✓	4
5.3	odd	4		1575.2.b.a.251.3		4
5.4	even	2	inner	1575.2.g.d.1574.5		8
7.6	odd	2	CM	1575.2.g.d.1574.4		8
15.2	even	4		63.2.c.a.62.3	yes	4
15.8	even	4		1575.2.b.a.251.2		4
15.14	odd	2	inner	1575.2.g.d.1574.3		8
20.7	even	4		1008.2.k.a.881.3		4
21.20	even	2	inner	1575.2.g.d.1574.6		8
35.2	odd	12		441.2.p.b.80.2		8
35.12	even	12		441.2.p.b.80.2		8
35.13	even	4		1575.2.b.a.251.3		4
35.17	even	12		441.2.p.b.215.3		8
35.27	even	4		63.2.c.a.62.2	✓	4
35.32	odd	12		441.2.p.b.215.3		8
35.34	odd	2	inner	1575.2.g.d.1574.5		8
40.27	even	4		4032.2.k.b.3905.4		4
40.37	odd	4		4032.2.k.c.3905.1		4
45.2	even	12		567.2.o.f.377.3		8
45.7	odd	12		567.2.o.f.377.2		8
45.22	odd	12		567.2.o.f.188.3		8
45.32	even	12		567.2.o.f.188.2		8
60.47	odd	4		1008.2.k.a.881.4		4
105.2	even	12		441.2.p.b.80.3		8
105.17	odd	12		441.2.p.b.215.2		8
105.32	even	12		441.2.p.b.215.2		8
105.47	odd	12		441.2.p.b.80.3		8
105.62	odd	4		63.2.c.a.62.3	yes	4
105.83	odd	4		1575.2.b.a.251.2		4
105.104	even	2	inner	1575.2.g.d.1574.3		8
120.77	even	4		4032.2.k.c.3905.2		4
120.107	odd	4		4032.2.k.b.3905.3		4
140.27	odd	4		1008.2.k.a.881.3		4
280.27	odd	4		4032.2.k.b.3905.4		4
280.237	even	4		4032.2.k.c.3905.1		4
315.97	even	12		567.2.o.f.377.2		8
315.167	odd	12		567.2.o.f.188.2		8
315.202	even	12		567.2.o.f.188.3		8
315.272	odd	12		567.2.o.f.377.3		8
420.167	even	4		1008.2.k.a.881.4		4
840.587	even	4		4032.2.k.b.3905.3		4
840.797	odd	4		4032.2.k.c.3905.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.c.a.62.2	✓	4	5.2	odd	4
63.2.c.a.62.2	✓	4	35.27	even	4
63.2.c.a.62.3	yes	4	15.2	even	4
63.2.c.a.62.3	yes	4	105.62	odd	4
441.2.p.b.80.2		8	35.2	odd	12
441.2.p.b.80.2		8	35.12	even	12
441.2.p.b.80.3		8	105.2	even	12
441.2.p.b.80.3		8	105.47	odd	12
441.2.p.b.215.2		8	105.17	odd	12
441.2.p.b.215.2		8	105.32	even	12
441.2.p.b.215.3		8	35.17	even	12
441.2.p.b.215.3		8	35.32	odd	12
567.2.o.f.188.2		8	45.32	even	12
567.2.o.f.188.2		8	315.167	odd	12
567.2.o.f.188.3		8	45.22	odd	12
567.2.o.f.188.3		8	315.202	even	12
567.2.o.f.377.2		8	45.7	odd	12
567.2.o.f.377.2		8	315.97	even	12
567.2.o.f.377.3		8	45.2	even	12
567.2.o.f.377.3		8	315.272	odd	12
1008.2.k.a.881.3		4	20.7	even	4
1008.2.k.a.881.3		4	140.27	odd	4
1008.2.k.a.881.4		4	60.47	odd	4
1008.2.k.a.881.4		4	420.167	even	4
1575.2.b.a.251.2		4	15.8	even	4
1575.2.b.a.251.2		4	105.83	odd	4
1575.2.b.a.251.3		4	5.3	odd	4
1575.2.b.a.251.3		4	35.13	even	4
1575.2.g.d.1574.3		8	15.14	odd	2	inner
1575.2.g.d.1574.3		8	105.104	even	2	inner
1575.2.g.d.1574.4		8	1.1	even	1	trivial
1575.2.g.d.1574.4		8	7.6	odd	2	CM
1575.2.g.d.1574.5		8	5.4	even	2	inner
1575.2.g.d.1574.5		8	35.34	odd	2	inner
1575.2.g.d.1574.6		8	3.2	odd	2	inner
1575.2.g.d.1574.6		8	21.20	even	2	inner
4032.2.k.b.3905.3		4	120.107	odd	4
4032.2.k.b.3905.3		4	840.587	even	4
4032.2.k.b.3905.4		4	40.27	even	4
4032.2.k.b.3905.4		4	280.27	odd	4
4032.2.k.c.3905.1		4	40.37	odd	4
4032.2.k.c.3905.1		4	280.237	even	4
4032.2.k.c.3905.2		4	120.77	even	4
4032.2.k.c.3905.2		4	840.797	odd	4

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)

\(f(q)\)	\(=\)	\(q-1.16372 q^{2} -0.645751 q^{4} +2.64575i q^{7} +3.07892 q^{8} +O(q^{10})\)	\(q-1.16372 q^{2} -0.645751 q^{4} +2.64575i q^{7} +3.07892 q^{8} +6.57008i q^{11} -3.07892i q^{14} -2.29150 q^{16} -7.64575i q^{22} +1.91520 q^{23} -1.70850i q^{28} +8.89753i q^{29} -3.49117 q^{32} -10.5830i q^{37} -5.29150i q^{43} -4.24264i q^{44} -2.22876 q^{46} -7.00000 q^{49} +0.412247 q^{53} +8.14605i q^{56} -10.3542i q^{58} +8.64575 q^{64} +4.00000i q^{67} +15.0554i q^{71} +12.3157i q^{74} -17.3828 q^{77} -8.00000 q^{79} +6.15784i q^{86} +20.2288i q^{88} -1.23674 q^{92} +8.14605 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4}+O(q^{10}) \) 8 * q + 16 * q^4	\( 8 q + 16 q^{4} + 24 q^{16} + 88 q^{46} - 56 q^{49} + 48 q^{64} - 64 q^{79}+O(q^{100}) \) 8 * q + 16 * q^4 + 24 * q^16 + 88 * q^46 - 56 * q^49 + 48 * q^64 - 64 * q^79

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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