LMFDB - Embedded newform 1911.1.h.d.1520.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,1,Mod(1520,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("1911.1520");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1911.h (of order $2$, degree $1$, 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:	yes
Analytic conductor:	$0.953713239142$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{16})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 2 $ x^4 - 4*x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{8}$
Projective field:	Galois closure of 8.2.90724673403.2

Embedding invariants

Embedding label			1520.4
Root			$-1.84776$ of defining polynomial
Character	$\chi$	$=$	1911.1520

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84776 q^{2} -1.00000 q^{3} +2.41421 q^{4} +0.765367 q^{5} -1.84776 q^{6} +2.61313 q^{8} +1.00000 q^{9} +O(q^{10})$	$q+1.84776 q^{2} -1.00000 q^{3} +2.41421 q^{4} +0.765367 q^{5} -1.84776 q^{6} +2.61313 q^{8} +1.00000 q^{9} +1.41421 q^{10} -1.84776 q^{11} -2.41421 q^{12} +1.00000 q^{13} -0.765367 q^{15} +2.41421 q^{16} +1.84776 q^{18} +1.84776 q^{20} -3.41421 q^{22} -2.61313 q^{24} -0.414214 q^{25} +1.84776 q^{26} -1.00000 q^{27} -1.41421 q^{30} +1.84776 q^{32} +1.84776 q^{33} +2.41421 q^{36} -1.00000 q^{39} +2.00000 q^{40} -0.765367 q^{41} -4.46088 q^{44} +0.765367 q^{45} -0.765367 q^{47} -2.41421 q^{48} -0.765367 q^{50} +2.41421 q^{52} -1.84776 q^{54} -1.41421 q^{55} +1.84776 q^{59} -1.84776 q^{60} +1.00000 q^{64} +0.765367 q^{65} +3.41421 q^{66} +0.765367 q^{71} +2.61313 q^{72} +0.414214 q^{75} -1.84776 q^{78} -1.41421 q^{79} +1.84776 q^{80} +1.00000 q^{81} -1.41421 q^{82} -1.84776 q^{83} -4.82843 q^{88} -1.84776 q^{89} +1.41421 q^{90} -1.41421 q^{94} -1.84776 q^{96} -1.84776 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^9	$ 4 q - 4 q^{3} + 4 q^{4} + 4 q^{9} - 4 q^{12} + 4 q^{13} + 4 q^{16} - 8 q^{22} + 4 q^{25} - 4 q^{27} + 4 q^{36} - 4 q^{39} + 8 q^{40} - 4 q^{48} + 4 q^{52} + 4 q^{64} + 8 q^{66} - 4 q^{75} + 4 q^{81} - 8 q^{88}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^9 - 4 * q^12 + 4 * q^13 + 4 * q^16 - 8 * q^22 + 4 * q^25 - 4 * q^27 + 4 * q^36 - 4 * q^39 + 8 * q^40 - 4 * q^48 + 4 * q^52 + 4 * q^64 + 8 * q^66 - 4 * q^75 + 4 * q^81 - 8 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times$.

$n$	$638$	$1471$	$1522$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$2$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$3$	−1.00000	−1.00000
$3$	−1.00000	−1.00000
$4$	2.41421	2.41421
$5$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$5$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$6$	−1.84776	−1.84776
$7$	0	0
$7$	0	0
$8$	2.61313	2.61313
$9$	1.00000	1.00000
$10$	1.41421	1.41421
$11$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$11$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$12$	−2.41421	−2.41421
$13$	1.00000	1.00000
$13$	1.00000	1.00000
$14$	0	0
$15$	−0.765367	−0.765367
$16$	2.41421	2.41421
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	1.84776	1.84776
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	1.84776	1.84776
$21$	0	0
$22$	−3.41421	−3.41421
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	−2.61313	−2.61313
$25$	−0.414214	−0.414214
$26$	1.84776	1.84776
$27$	−1.00000	−1.00000
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	−1.41421	−1.41421
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	1.84776	1.84776
$33$	1.84776	1.84776
$34$	0	0
$35$	0	0
$36$	2.41421	2.41421
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−1.00000	−1.00000
$40$	2.00000	2.00000
$41$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$41$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−4.46088	−4.46088
$45$	0.765367	0.765367
$46$	0	0
$47$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$47$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$48$	−2.41421	−2.41421
$49$	0	0
$50$	−0.765367	−0.765367
$51$	0	0
$52$	2.41421	2.41421
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	−1.84776	−1.84776
$55$	−1.41421	−1.41421
$56$	0	0
$57$	0	0
$58$	0	0
$59$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$59$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$60$	−1.84776	−1.84776
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	1.00000
$65$	0.765367	0.765367
$66$	3.41421	3.41421
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$71$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$72$	2.61313	2.61313
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0.414214	0.414214
$76$	0	0
$77$	0	0
$78$	−1.84776	−1.84776
$79$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$79$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$80$	1.84776	1.84776
$81$	1.00000	1.00000
$82$	−1.41421	−1.41421
$83$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$83$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	−4.82843	−4.82843
$89$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$89$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$90$	1.41421	1.41421
$91$	0	0
$92$	0	0
$93$	0	0
$94$	−1.41421	−1.41421
$95$	0	0
$96$	−1.84776	−1.84776
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	−1.84776	−1.84776
$100$	−1.00000	−1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$103$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$104$	2.61313	2.61313
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−2.41421	−2.41421
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	−2.61313	−2.61313
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	1.00000	1.00000
$118$	3.41421	3.41421
$119$	0	0
$120$	−2.00000	−2.00000
$121$	2.41421	2.41421
$122$	0	0
$123$	0.765367	0.765367
$124$	0	0
$125$	−1.08239	−1.08239
$126$	0	0
$127$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$127$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$128$	0	0
$129$	0	0
$130$	1.41421	1.41421
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	4.46088	4.46088
$133$	0	0
$134$	0	0
$135$	−0.765367	−0.765367
$136$	0	0
$137$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$137$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$138$	0	0
$139$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$139$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$140$	0	0
$141$	0.765367	0.765367
$142$	1.41421	1.41421
$143$	−1.84776	−1.84776
$144$	2.41421	2.41421
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$149$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$150$	0.765367	0.765367
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	−2.41421	−2.41421
$157$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$157$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$158$	−2.61313	−2.61313
$159$	0	0
$160$	1.41421	1.41421
$161$	0	0
$162$	1.84776	1.84776
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	−1.84776	−1.84776
$165$	1.41421	1.41421
$166$	−3.41421	−3.41421
$167$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$167$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$168$	0	0
$169$	1.00000	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−4.46088	−4.46088
$177$	−1.84776	−1.84776
$178$	−3.41421	−3.41421
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	1.84776	1.84776
$181$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$181$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−1.84776	−1.84776
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−1.00000	−1.00000
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	−0.765367	−0.765367
$196$	0	0
$197$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$197$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$198$	−3.41421	−3.41421
$199$	2.00000	2.00000	1.00000			$0$
$199$	2.00000	2.00000	1.00000			$0$
$200$	−1.08239	−1.08239
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−0.585786	−0.585786
$206$	2.61313	2.61313
$207$	0	0
$208$	2.41421	2.41421
$209$	0	0
$210$	0	0
$211$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$211$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$212$	0	0
$213$	−0.765367	−0.765367
$214$	0	0
$215$	0	0
$216$	−2.61313	−2.61313
$217$	0	0
$218$	0	0
$219$	0	0
$220$	−3.41421	−3.41421
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	−0.414214	−0.414214
$226$	0	0
$227$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$227$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	1.84776	1.84776
$235$	−0.585786	−0.585786
$236$	4.46088	4.46088
$237$	1.41421	1.41421
$238$	0	0
$239$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$239$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$240$	−1.84776	−1.84776
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	4.46088	4.46088
$243$	−1.00000	−1.00000
$244$	0	0
$245$	0	0
$246$	1.41421	1.41421
$247$	0	0
$248$	0	0
$249$	1.84776	1.84776
$250$	−2.00000	−2.00000
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	2.61313	2.61313
$255$	0	0
$256$	−1.00000	−1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	1.84776	1.84776
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	4.82843	4.82843
$265$	0	0
$266$	0	0
$267$	1.84776	1.84776
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	−1.41421	−1.41421
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	−1.41421	−1.41421
$275$	0.765367	0.765367
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	−2.61313	−2.61313
$279$	0	0
$280$	0	0
$281$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$281$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$282$	1.41421	1.41421
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	1.84776	1.84776
$285$	0	0
$286$	−3.41421	−3.41421
$287$	0	0
$288$	1.84776	1.84776
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$293$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$294$	0	0
$295$	1.41421	1.41421
$296$	0	0
$297$	1.84776	1.84776
$298$	−1.41421	−1.41421
$299$	0	0
$300$	1.00000	1.00000
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	−1.41421	−1.41421
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	−2.61313	−2.61313
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	−2.61313	−2.61313
$315$	0	0
$316$	−3.41421	−3.41421
$317$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$317$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$318$	0	0
$319$	0	0
$320$	0.765367	0.765367
$321$	0	0
$322$	0	0
$323$	0	0
$324$	2.41421	2.41421
$325$	−0.414214	−0.414214
$326$	0	0
$327$	0	0
$328$	−2.00000	−2.00000
$329$	0	0
$330$	2.61313	2.61313
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	−4.46088	−4.46088
$333$	0	0
$334$	3.41421	3.41421
$335$	0	0
$336$	0	0
$337$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$337$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$338$	1.84776	1.84776
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	−1.00000	−1.00000
$352$	−3.41421	−3.41421
$353$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$353$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$354$	−3.41421	−3.41421
$355$	0.585786	0.585786
$356$	−4.46088	−4.46088
$357$	0	0
$358$	0	0
$359$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$359$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$360$	2.00000	2.00000
$361$	1.00000	1.00000
$362$	2.61313	2.61313
$363$	−2.41421	−2.41421
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$367$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$368$	0	0
$369$	−0.765367	−0.765367
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$373$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$374$	0	0
$375$	1.08239	1.08239
$376$	−2.00000	−2.00000
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	−1.41421	−1.41421
$382$	0	0
$383$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$383$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	−1.41421	−1.41421
$391$	0	0
$392$	0	0
$393$	0	0
$394$	−3.41421	−3.41421
$395$	−1.08239	−1.08239
$396$	−4.46088	−4.46088
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	3.69552	3.69552
$399$	0	0
$400$	−1.00000	−1.00000
$401$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$401$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0.765367	0.765367
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	−1.08239	−1.08239
$411$	0.765367	0.765367
$412$	3.41421	3.41421
$413$	0	0
$414$	0	0
$415$	−1.41421	−1.41421
$416$	1.84776	1.84776
$417$	1.41421	1.41421
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	−2.61313	−2.61313
$423$	−0.765367	−0.765367
$424$	0	0
$425$	0	0
$426$	−1.41421	−1.41421
$427$	0	0
$428$	0	0
$429$	1.84776	1.84776
$430$	0	0
$431$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$431$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$432$	−2.41421	−2.41421
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$439$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$440$	−3.69552	−3.69552
$441$	0	0
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	−1.41421	−1.41421
$446$	0	0
$447$	0.765367	0.765367
$448$	0	0
$449$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$449$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$450$	−0.765367	−0.765367
$451$	1.41421	1.41421
$452$	0	0
$453$	0	0
$454$	−1.41421	−1.41421
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$461$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	2.41421	2.41421
$469$	0	0
$470$	−1.08239	−1.08239
$471$	1.41421	1.41421
$472$	4.82843	4.82843
$473$	0	0
$474$	2.61313	2.61313
$475$	0	0
$476$	0	0
$477$	0	0
$478$	3.41421	3.41421
$479$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$479$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$480$	−1.41421	−1.41421
$481$	0	0
$482$	0	0
$483$	0	0
$484$	5.82843	5.82843
$485$	0	0
$486$	−1.84776	−1.84776
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	1.84776	1.84776
$493$	0	0
$494$	0	0
$495$	−1.41421	−1.41421
$496$	0	0
$497$	0	0
$498$	3.41421	3.41421
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−2.61313	−2.61313
$501$	−1.84776	−1.84776
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−1.00000	−1.00000
$508$	3.41421	3.41421
$509$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$509$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$510$	0	0
$511$	0	0
$512$	−1.84776	−1.84776
$513$	0	0
$514$	0	0
$515$	1.08239	1.08239
$516$	0	0
$517$	1.41421	1.41421
$518$	0	0
$519$	0	0
$520$	2.00000	2.00000
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$523$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	4.46088	4.46088
$529$	1.00000	1.00000
$530$	0	0
$531$	1.84776	1.84776
$532$	0	0
$533$	−0.765367	−0.765367
$534$	3.41421	3.41421
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	−1.84776	−1.84776
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	−1.41421	−1.41421
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−2.00000	−2.00000	−1.00000			$\pi$
$547$	−2.00000	−2.00000	−1.00000			$\pi$
$548$	−1.84776	−1.84776
$549$	0	0
$550$	1.41421	1.41421
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	−3.41421	−3.41421
$557$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$557$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−1.41421	−1.41421
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	1.84776	1.84776
$565$	0	0
$566$	0	0
$567$	0	0
$568$	2.00000	2.00000
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$571$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$572$	−4.46088	−4.46088
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.00000	1.00000
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	1.84776	1.84776
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0.765367	0.765367
$586$	3.41421	3.41421
$587$	0.765367	0.765367	0.382683	−	0.923880i	$-0.375000\pi$
$587$	0.765367	0.765367	0.382683	+	0.923880i	$0.375000\pi$
$588$	0	0
$589$	0	0
$590$	2.61313	2.61313
$591$	1.84776	1.84776
$592$	0	0
$593$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$593$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$594$	3.41421	3.41421
$595$	0	0
$596$	−1.84776	−1.84776
$597$	−2.00000	−2.00000
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	1.08239	1.08239
$601$	2.00000	2.00000	1.00000			$0$
$601$	2.00000	2.00000	1.00000			$0$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	1.84776	1.84776
$606$	0	0
$607$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$607$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−0.765367	−0.765367
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0.585786	0.585786
$616$	0	0
$617$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$617$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$618$	−2.61313	−2.61313
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	−2.41421	−2.41421
$625$	−0.414214	−0.414214
$626$	0	0
$627$	0	0
$628$	−3.41421	−3.41421
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	−3.69552	−3.69552
$633$	1.41421	1.41421
$634$	3.41421	3.41421
$635$	1.08239	1.08239
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0.765367	0.765367
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	2.61313	2.61313
$649$	−3.41421	−3.41421
$650$	−0.765367	−0.765367
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	−1.84776	−1.84776
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	3.41421	3.41421
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	−4.82843	−4.82843
$665$	0	0
$666$	0	0
$667$	0	0
$668$	4.46088	4.46088
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−2.00000	−2.00000	−1.00000			$\pi$
$673$	−2.00000	−2.00000	−1.00000			$\pi$
$674$	2.61313	2.61313
$675$	0.414214	0.414214
$676$	2.41421	2.41421
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0.765367	0.765367
$682$	0	0
$683$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$683$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$684$	0	0
$685$	−0.585786	−0.585786
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−1.08239	−1.08239
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	−1.84776	−1.84776
$703$	0	0
$704$	−1.84776	−1.84776
$705$	0.585786	0.585786
$706$	−3.41421	−3.41421
$707$	0	0
$708$	−4.46088	−4.46088
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	1.08239	1.08239
$711$	−1.41421	−1.41421
$712$	−4.82843	−4.82843
$713$	0	0
$714$	0	0
$715$	−1.41421	−1.41421
$716$	0	0
$717$	−1.84776	−1.84776
$718$	3.41421	3.41421
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	1.84776	1.84776
$721$	0	0
$722$	1.84776	1.84776
$723$	0	0
$724$	3.41421	3.41421
$725$	0	0
$726$	−4.46088	−4.46088
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	1.00000	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	2.61313	2.61313
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−1.41421	−1.41421
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$743$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$744$	0	0
$745$	−0.585786	−0.585786
$746$	−2.61313	−2.61313
$747$	−1.84776	−1.84776
$748$	0	0
$749$	0	0
$750$	2.00000	2.00000
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	−1.84776	−1.84776
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	1.41421	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$757$	1.41421	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$761$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$762$	−2.61313	−2.61313
$763$	0	0
$764$	0	0
$765$	0	0
$766$	1.41421	1.41421
$767$	1.84776	1.84776
$768$	1.00000	1.00000
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$773$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	−1.84776	−1.84776
$781$	−1.41421	−1.41421
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−1.08239	−1.08239
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−4.46088	−4.46088
$789$	0	0
$790$	−2.00000	−2.00000
$791$	0	0
$792$	−4.82843	−4.82843
$793$	0	0
$794$	0	0
$795$	0	0
$796$	4.82843	4.82843
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	−0.765367	−0.765367
$801$	−1.84776	−1.84776
$802$	−3.41421	−3.41421
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	1.41421	1.41421
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	−1.41421	−1.41421
$821$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$821$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$822$	1.41421	1.41421
$823$	−2.00000	−2.00000	−1.00000			$\pi$
$823$	−2.00000	−2.00000	−1.00000			$\pi$
$824$	3.69552	3.69552
$825$	−0.765367	−0.765367
$826$	0	0
$827$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$827$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$828$	0	0
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$829$	−2.00000	−2.00000	−1.00000			$\pi$
$830$	−2.61313	−2.61313
$831$	0	0
$832$	1.00000	1.00000
$833$	0	0
$834$	2.61313	2.61313
$835$	1.41421	1.41421
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$839$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	0.765367	0.765367
$844$	−3.41421	−3.41421
$845$	0.765367	0.765367
$846$	−1.41421	−1.41421
$847$	0	0
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	−1.84776	−1.84776
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	3.41421	3.41421
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	0	0
$862$	1.41421	1.41421
$863$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$863$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$864$	−1.84776	−1.84776
$865$	0	0
$866$	0	0
$867$	−1.00000	−1.00000
$868$	0	0
$869$	2.61313	2.61313
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	2.61313	2.61313
$879$	−1.84776	−1.84776
$880$	−3.41421	−3.41421
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$883$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$884$	0	0
$885$	−1.41421	−1.41421
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	−2.61313	−2.61313
$891$	−1.84776	−1.84776
$892$	0	0
$893$	0	0
$894$	1.41421	1.41421
$895$	0	0
$896$	0	0
$897$	0	0
$898$	3.41421	3.41421
$899$	0	0
$900$	−1.00000	−1.00000
$901$	0	0
$902$	2.61313	2.61313
$903$	0	0
$904$	0	0
$905$	1.08239	1.08239
$906$	0	0
$907$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$907$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$908$	−1.84776	−1.84776
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	3.41421	3.41421
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$919$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$920$	0	0
$921$	0	0
$922$	3.41421	3.41421
$923$	0.765367	0.765367
$924$	0	0
$925$	0	0
$926$	0	0
$927$	1.41421	1.41421
$928$	0	0
$929$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$929$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	2.61313	2.61313
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$937$	−2.00000	−2.00000	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	−1.41421	−1.41421
$941$	1.84776	1.84776	0.923880	−	0.382683i	$-0.125000\pi$
$941$	1.84776	1.84776	0.923880	+	0.382683i	$0.125000\pi$
$942$	2.61313	2.61313
$943$	0	0
$944$	4.46088	4.46088
$945$	0	0
$946$	0	0
$947$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$947$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$948$	3.41421	3.41421
$949$	0	0
$950$	0	0
$951$	−1.84776	−1.84776
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	4.46088	4.46088
$957$	0	0
$958$	1.41421	1.41421
$959$	0	0
$960$	−0.765367	−0.765367
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	6.30864	6.30864
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	−2.41421	−2.41421
$973$	0	0
$974$	0	0
$975$	0.414214	0.414214
$976$	0	0
$977$	−1.84776	−1.84776	−0.923880	−	0.382683i	$-0.875000\pi$
$977$	−1.84776	−1.84776	−0.923880	+	0.382683i	$0.875000\pi$
$978$	0	0
$979$	3.41421	3.41421
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−0.765367	−0.765367	−0.382683	−	0.923880i	$-0.625000\pi$
$983$	−0.765367	−0.765367	−0.382683	+	0.923880i	$0.625000\pi$
$984$	2.00000	2.00000
$985$	−1.41421	−1.41421
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	−2.61313	−2.61313
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	1.53073	1.53073
$996$	4.46088	4.46088
$997$	−1.41421	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$997$	−1.41421	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.1.h.d.1520.4	yes	4
3.2	odd	2	inner	1911.1.h.d.1520.1	✓	4
7.2	even	3		1911.1.w.f.116.1		8
7.3	odd	6		1911.1.w.e.1598.1		8
7.4	even	3		1911.1.w.f.1598.1		8
7.5	odd	6		1911.1.w.e.116.1		8
7.6	odd	2		1911.1.h.e.1520.4	yes	4
13.12	even	2	inner	1911.1.h.d.1520.1	✓	4
21.2	odd	6		1911.1.w.f.116.4		8
21.5	even	6		1911.1.w.e.116.4		8
21.11	odd	6		1911.1.w.f.1598.4		8
21.17	even	6		1911.1.w.e.1598.4		8
21.20	even	2		1911.1.h.e.1520.1	yes	4
39.38	odd	2	CM	1911.1.h.d.1520.4	yes	4
91.12	odd	6		1911.1.w.e.116.4		8
91.25	even	6		1911.1.w.f.1598.4		8
91.38	odd	6		1911.1.w.e.1598.4		8
91.51	even	6		1911.1.w.f.116.4		8
91.90	odd	2		1911.1.h.e.1520.1	yes	4
273.38	even	6		1911.1.w.e.1598.1		8
273.116	odd	6		1911.1.w.f.1598.1		8
273.194	even	6		1911.1.w.e.116.1		8
273.233	odd	6		1911.1.w.f.116.1		8
273.272	even	2		1911.1.h.e.1520.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.1.h.d.1520.1	✓	4	3.2	odd	2	inner
1911.1.h.d.1520.1	✓	4	13.12	even	2	inner
1911.1.h.d.1520.4	yes	4	1.1	even	1	trivial
1911.1.h.d.1520.4	yes	4	39.38	odd	2	CM
1911.1.h.e.1520.1	yes	4	21.20	even	2
1911.1.h.e.1520.1	yes	4	91.90	odd	2
1911.1.h.e.1520.4	yes	4	7.6	odd	2
1911.1.h.e.1520.4	yes	4	273.272	even	2
1911.1.w.e.116.1		8	7.5	odd	6
1911.1.w.e.116.1		8	273.194	even	6
1911.1.w.e.116.4		8	21.5	even	6
1911.1.w.e.116.4		8	91.12	odd	6
1911.1.w.e.1598.1		8	7.3	odd	6
1911.1.w.e.1598.1		8	273.38	even	6
1911.1.w.e.1598.4		8	21.17	even	6
1911.1.w.e.1598.4		8	91.38	odd	6
1911.1.w.f.116.1		8	7.2	even	3
1911.1.w.f.116.1		8	273.233	odd	6
1911.1.w.f.116.4		8	21.2	odd	6
1911.1.w.f.116.4		8	91.51	even	6
1911.1.w.f.1598.1		8	7.4	even	3
1911.1.w.f.1598.1		8	273.116	odd	6
1911.1.w.f.1598.4		8	21.11	odd	6
1911.1.w.f.1598.4		8	91.25	even	6

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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1911.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.84776 q^{2} -1.00000 q^{3} +2.41421 q^{4} +0.765367 q^{5} -1.84776 q^{6} +2.61313 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.84776 q^{2} -1.00000 q^{3} +2.41421 q^{4} +0.765367 q^{5} -1.84776 q^{6} +2.61313 q^{8} +1.00000 q^{9} +1.41421 q^{10} -1.84776 q^{11} -2.41421 q^{12} +1.00000 q^{13} -0.765367 q^{15} +2.41421 q^{16} +1.84776 q^{18} +1.84776 q^{20} -3.41421 q^{22} -2.61313 q^{24} -0.414214 q^{25} +1.84776 q^{26} -1.00000 q^{27} -1.41421 q^{30} +1.84776 q^{32} +1.84776 q^{33} +2.41421 q^{36} -1.00000 q^{39} +2.00000 q^{40} -0.765367 q^{41} -4.46088 q^{44} +0.765367 q^{45} -0.765367 q^{47} -2.41421 q^{48} -0.765367 q^{50} +2.41421 q^{52} -1.84776 q^{54} -1.41421 q^{55} +1.84776 q^{59} -1.84776 q^{60} +1.00000 q^{64} +0.765367 q^{65} +3.41421 q^{66} +0.765367 q^{71} +2.61313 q^{72} +0.414214 q^{75} -1.84776 q^{78} -1.41421 q^{79} +1.84776 q^{80} +1.00000 q^{81} -1.41421 q^{82} -1.84776 q^{83} -4.82843 q^{88} -1.84776 q^{89} +1.41421 q^{90} -1.41421 q^{94} -1.84776 q^{96} -1.84776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^9	\( 4 q - 4 q^{3} + 4 q^{4} + 4 q^{9} - 4 q^{12} + 4 q^{13} + 4 q^{16} - 8 q^{22} + 4 q^{25} - 4 q^{27} + 4 q^{36} - 4 q^{39} + 8 q^{40} - 4 q^{48} + 4 q^{52} + 4 q^{64} + 8 q^{66} - 4 q^{75} + 4 q^{81} - 8 q^{88}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^9 - 4 * q^12 + 4 * q^13 + 4 * q^16 - 8 * q^22 + 4 * q^25 - 4 * q^27 + 4 * q^36 - 4 * q^39 + 8 * q^40 - 4 * q^48 + 4 * q^52 + 4 * q^64 + 8 * q^66 - 4 * q^75 + 4 * q^81 - 8 * q^88

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