LMFDB - Embedded newform 2240.2.n.f.1119.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(1119,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("2240.1119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.n (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:	no
Analytic conductor:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.384160000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 37x^{4} - 36x^{2} + 16 $ x^8 - 9x^6 + 37x^4 - 36*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1119.5
Root			$-2.14046 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	2240.1119
Dual form			2240.2.n.f.1119.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23607 q^{3} -2.23607i q^{5} -2.64575i q^{7} +2.00000 q^{9} +O(q^{10})$	$q+2.23607 q^{3} -2.23607i q^{5} -2.64575i q^{7} +2.00000 q^{9} +5.91608 q^{11} +6.70820i q^{13} -5.00000i q^{15} +7.93725 q^{17} -5.91608i q^{21} -5.00000 q^{25} -2.23607 q^{27} -5.91608i q^{29} +13.2288 q^{33} -5.91608 q^{35} +15.0000i q^{39} -4.47214i q^{45} +7.93725i q^{47} -7.00000 q^{49} +17.7482 q^{51} -13.2288i q^{55} -5.29150i q^{63} +15.0000 q^{65} -12.0000i q^{71} -10.5830 q^{73} -11.1803 q^{75} -15.6525i q^{77} +1.00000i q^{79} -11.0000 q^{81} +8.94427 q^{83} -17.7482i q^{85} -13.2288i q^{87} +17.7482 q^{91} -18.5203 q^{97} +11.8322 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{9}+O(q^{10}) $ 8 * q + 16 * q^9	$ 8 q + 16 q^{9} - 40 q^{25} - 56 q^{49} + 120 q^{65} - 88 q^{81}+O(q^{100}) $ 8 * q + 16 * q^9 - 40 * q^25 - 56 * q^49 + 120 * q^65 - 88 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0	0
$2$	0	0
$3$	2.23607	1.29099	0.645497	−	0.763763i	$-0.276650\pi$
$3$	2.23607	1.29099	0.645497	+	0.763763i	$0.276650\pi$
$4$	0	0
$5$	− 2.23607i	− 1.00000i
$5$	− 2.23607i	− 1.00000i
$6$	0	0
$7$	− 2.64575i	− 1.00000i
$7$	− 2.64575i	− 1.00000i
$8$	0	0
$9$	2.00000	0.666667
$10$	0	0
$11$	5.91608	1.78377	0.891883	−	0.452267i	$-0.149385\pi$
$11$	5.91608	1.78377	0.891883	+	0.452267i	$0.149385\pi$
$12$	0	0
$13$	6.70820i	1.86052i	0.366900	+	0.930261i	$0.380419\pi$
$13$	6.70820i	1.86052i	−0.366900	+	0.930261i	$0.619581\pi$
$14$	0	0
$15$	− 5.00000i	− 1.29099i
$16$	0	0
$17$	7.93725	1.92507	0.962533	−	0.271163i	$-0.0874083\pi$
$17$	7.93725	1.92507	0.962533	+	0.271163i	$0.0874083\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	− 5.91608i	− 1.29099i
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	−2.23607	−0.430331
$28$	0	0
$29$	− 5.91608i	− 1.09859i	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	− 5.91608i	− 1.09859i	0.835629	−	0.549294i	$-0.185103\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	13.2288	2.30283
$34$	0	0
$35$	−5.91608	−1.00000
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	15.0000i	2.40192i
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	− 4.47214i	− 0.666667i
$46$	0	0
$47$	7.93725i	1.15777i	0.815410	+	0.578884i	$0.196511\pi$
$47$	7.93725i	1.15777i	−0.815410	+	0.578884i	$0.803489\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	17.7482	2.48525
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	− 13.2288i	− 1.78377i
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	− 5.29150i	− 0.666667i
$64$	0	0
$65$	15.0000	1.86052
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	− 12.0000i	− 1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$	− 12.0000i	− 1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$	0	0
$73$	−10.5830	−1.23865	−0.619324	−	0.785136i	$-0.712593\pi$
$73$	−10.5830	−1.23865	−0.619324	+	0.785136i	$0.712593\pi$
$74$	0	0
$75$	−11.1803	−1.29099
$76$	0	0
$77$	− 15.6525i	− 1.78377i
$78$	0	0
$79$	1.00000i	0.112509i	0.998416	+	0.0562544i	$0.0179158\pi$
$79$	1.00000i	0.112509i	−0.998416	+	0.0562544i	$0.982084\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	8.94427	0.981761	0.490881	−	0.871227i	$-0.336675\pi$
$83$	8.94427	0.981761	0.490881	+	0.871227i	$0.336675\pi$
$84$	0	0
$85$	− 17.7482i	− 1.92507i
$86$	0	0
$87$	− 13.2288i	− 1.41827i
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	17.7482	1.86052
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−18.5203	−1.88045	−0.940224	−	0.340557i	$-0.889384\pi$
$97$	−18.5203	−1.88045	−0.940224	+	0.340557i	$0.889384\pi$
$98$	0	0
$99$	11.8322	1.18918
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	2.64575i	0.260694i	0.991468	+	0.130347i	$0.0416091\pi$
$103$	2.64575i	0.260694i	−0.991468	+	0.130347i	$0.958391\pi$
$104$	0	0
$105$	−13.2288	−1.29099
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	− 17.7482i	− 1.69997i	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	− 17.7482i	− 1.69997i	0.526804	−	0.849987i	$-0.323390\pi$
$110$	0	0
$111$	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
$117$	13.4164i	1.24035i
$118$	0	0
$119$	− 21.0000i	− 1.92507i
$120$	0	0
$121$	24.0000	2.18182
$122$	0	0
$123$	0	0
$124$	0	0
$125$	11.1803i	1.00000i
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	5.00000i	0.430331i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	17.7482i	1.49467i
$142$	0	0
$143$	39.6863i	3.31873i
$144$	0	0
$145$	−13.2288	−1.09859
$146$	0	0
$147$	−15.6525	−1.29099
$148$	0	0
$149$	− 23.6643i	− 1.93866i	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	− 23.6643i	− 1.93866i	0.245770	−	0.969328i	$-0.420959\pi$
$150$	0	0
$151$	17.0000i	1.38344i	0.722166	+	0.691720i	$0.243147\pi$
$151$	17.0000i	1.38344i	−0.722166	+	0.691720i	$0.756853\pi$
$152$	0	0
$153$	15.8745	1.28338
$154$	0	0
$155$	0	0
$156$	0	0
$157$	13.4164i	1.07075i	0.844616	+	0.535373i	$0.179829\pi$
$157$	13.4164i	1.07075i	−0.844616	+	0.535373i	$0.820171\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	− 29.5804i	− 2.30283i
$166$	0	0
$167$	7.93725i	0.614203i	0.951677	+	0.307102i	$0.0993591\pi$
$167$	7.93725i	0.614203i	−0.951677	+	0.307102i	$0.900641\pi$
$168$	0	0
$169$	−32.0000	−2.46154
$170$	0	0
$171$	0	0
$172$	0	0
$173$	− 11.1803i	− 0.850026i	−0.905187	−	0.425013i	$-0.860270\pi$
$173$	− 11.1803i	− 0.850026i	0.905187	−	0.425013i	$-0.139730\pi$
$174$	0	0
$175$	13.2288i	1.00000i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	11.8322	0.884377	0.442189	−	0.896922i	$-0.354202\pi$
$179$	11.8322	0.884377	0.442189	+	0.896922i	$0.354202\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	46.9574	3.43387
$188$	0	0
$189$	5.91608i	0.430331i
$190$	0	0
$191$	27.0000i	1.95365i	0.214036	+	0.976826i	$0.431339\pi$
$191$	27.0000i	1.95365i	−0.214036	+	0.976826i	$0.568661\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	33.5410	2.40192
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−15.6525	−1.09859
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	17.7482	1.22184	0.610920	−	0.791693i	$-0.290800\pi$
$211$	17.7482	1.22184	0.610920	+	0.791693i	$0.290800\pi$
$212$	0	0
$213$	− 26.8328i	− 1.83855i
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−23.6643	−1.59909
$220$	0	0
$221$	53.2447i	3.58163i
$222$	0	0
$223$	29.1033i	1.94890i	0.224607	+	0.974449i	$0.427890\pi$
$223$	29.1033i	1.94890i	−0.224607	+	0.974449i	$0.572110\pi$
$224$	0	0
$225$	−10.0000	−0.666667
$226$	0	0
$227$	−29.0689	−1.92937	−0.964685	−	0.263407i	$-0.915154\pi$
$227$	−29.0689	−1.92937	−0.964685	+	0.263407i	$0.915154\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	− 35.0000i	− 2.30283i
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	17.7482	1.15777
$236$	0	0
$237$	2.23607i	0.145248i
$238$	0	0
$239$	9.00000i	0.582162i	0.956698	+	0.291081i	$0.0940149\pi$
$239$	9.00000i	0.582162i	−0.956698	+	0.291081i	$0.905985\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−17.8885	−1.14755
$244$	0	0
$245$	15.6525i	1.00000i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	20.0000	1.26745
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	− 39.6863i	− 2.48525i
$256$	0	0
$257$	−31.7490	−1.98045	−0.990225	−	0.139482i	$-0.955456\pi$
$257$	−31.7490	−1.98045	−0.990225	+	0.139482i	$0.955456\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	− 11.8322i	− 0.732392i
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	39.6863	2.40192
$274$	0	0
$275$	−29.5804	−1.78377
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−33.0000	−1.96861	−0.984307	−	0.176462i	$-0.943535\pi$
$281$	−33.0000	−1.96861	−0.984307	+	0.176462i	$0.943535\pi$
$282$	0	0
$283$	−33.5410	−1.99381	−0.996903	−	0.0786368i	$-0.974943\pi$
$283$	−33.5410	−1.99381	−0.996903	+	0.0786368i	$0.974943\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	46.0000	2.70588
$290$	0	0
$291$	−41.4126	−2.42765
$292$	0	0
$293$	24.5967i	1.43696i	0.695549	+	0.718479i	$0.255161\pi$
$293$	24.5967i	1.43696i	−0.695549	+	0.718479i	$0.744839\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−13.2288	−0.767610
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	6.70820	0.382857	0.191429	−	0.981507i	$-0.438688\pi$
$307$	6.70820	0.382857	0.191429	+	0.981507i	$0.438688\pi$
$308$	0	0
$309$	5.91608i	0.336554i
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	29.1033	1.64501	0.822507	−	0.568755i	$-0.192575\pi$
$313$	29.1033	1.64501	0.822507	+	0.568755i	$0.192575\pi$
$314$	0	0
$315$	−11.8322	−0.666667
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	− 35.0000i	− 1.95962i
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	− 33.5410i	− 1.86052i
$326$	0	0
$327$	− 39.6863i	− 2.19466i
$328$	0	0
$329$	21.0000	1.15777
$330$	0	0
$331$	35.4965	1.95106	0.975531	−	0.219860i	$-0.0705600\pi$
$331$	35.4965	1.95106	0.975531	+	0.219860i	$0.0705600\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	18.5203i	1.00000i
$344$	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		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	− 15.0000i	− 0.800641i
$352$	0	0
$353$	23.8118	1.26737	0.633686	−	0.773590i	$-0.281541\pi$
$353$	23.8118	1.26737	0.633686	+	0.773590i	$0.281541\pi$
$354$	0	0
$355$	−26.8328	−1.42414
$356$	0	0
$357$	− 46.9574i	− 2.48525i
$358$	0	0
$359$	36.0000i	1.90001i	0.312239	+	0.950004i	$0.398921\pi$
$359$	36.0000i	1.90001i	−0.312239	+	0.950004i	$0.601079\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	53.6656	2.81672
$364$	0	0
$365$	23.6643i	1.23865i
$366$	0	0
$367$	− 18.5203i	− 0.966750i	−0.875413	−	0.483375i	$-0.839411\pi$
$367$	− 18.5203i	− 0.966750i	0.875413	−	0.483375i	$-0.160589\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	25.0000i	1.29099i
$376$	0	0
$377$	39.6863	2.04395
$378$	0	0
$379$	−35.4965	−1.82333	−0.911666	−	0.410932i	$-0.865203\pi$
$379$	−35.4965	−1.82333	−0.911666	+	0.410932i	$0.865203\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	− 15.8745i	− 0.811149i	−0.914062	−	0.405575i	$-0.867071\pi$
$383$	− 15.8745i	− 0.811149i	0.914062	−	0.405575i	$-0.132929\pi$
$384$	0	0
$385$	−35.0000	−1.78377
$386$	0	0
$387$	0	0
$388$	0	0
$389$	− 5.91608i	− 0.299957i	−0.988689	−	0.149979i	$-0.952080\pi$
$389$	− 5.91608i	− 0.299957i	0.988689	−	0.149979i	$-0.0479205\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	2.23607	0.112509
$396$	0	0
$397$	20.1246i	1.01003i	0.863112	+	0.505013i	$0.168512\pi$
$397$	20.1246i	1.01003i	−0.863112	+	0.505013i	$0.831488\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−27.0000	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	24.5967i	1.22222i
$406$	0	0
$407$	0	0
$408$	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
$415$	− 20.0000i	− 0.981761i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	− 17.7482i	− 0.864996i	−0.901635	−	0.432498i	$-0.857632\pi$
$421$	− 17.7482i	− 0.864996i	0.901635	−	0.432498i	$-0.142368\pi$
$422$	0	0
$423$	15.8745i	0.771845i
$424$	0	0
$425$	−39.6863	−1.92507
$426$	0	0
$427$	0	0
$428$	0	0
$429$	88.7412i	4.28447i
$430$	0	0
$431$	3.00000i	0.144505i	0.997386	+	0.0722525i	$0.0230187\pi$
$431$	3.00000i	0.144505i	−0.997386	+	0.0722525i	$0.976981\pi$
$432$	0	0
$433$	10.5830	0.508587	0.254293	−	0.967127i	$-0.418157\pi$
$433$	10.5830	0.508587	0.254293	+	0.967127i	$0.418157\pi$
$434$	0	0
$435$	−29.5804	−1.41827
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−14.0000	−0.666667
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	− 52.9150i	− 2.50279i
$448$	0	0
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	38.0132i	1.78601i
$454$	0	0
$455$	− 39.6863i	− 1.86052i
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	−17.7482	−0.828417
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	42.4853	1.96598	0.982992	−	0.183646i	$-0.0587901\pi$
$467$	42.4853	1.96598	0.982992	+	0.183646i	$0.0587901\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	30.0000i	1.38233i
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	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
$484$	0	0
$485$	41.4126i	1.88045i
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−29.5804	−1.33494	−0.667472	−	0.744635i	$-0.732624\pi$
$491$	−29.5804	−1.33494	−0.667472	+	0.744635i	$0.732624\pi$
$492$	0	0
$493$	− 46.9574i	− 2.11486i
$494$	0	0
$495$	− 26.4575i	− 1.18918i
$496$	0	0
$497$	−31.7490	−1.42414
$498$	0	0
$499$	17.7482	0.794520	0.397260	−	0.917706i	$-0.369961\pi$
$499$	17.7482	0.794520	0.397260	+	0.917706i	$0.369961\pi$
$500$	0	0
$501$	17.7482i	0.792933i
$502$	0	0
$503$	23.8118i	1.06171i	0.847461	+	0.530857i	$0.178130\pi$
$503$	23.8118i	1.06171i	−0.847461	+	0.530857i	$0.821870\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−71.5542	−3.17783
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	28.0000i	1.23865i
$512$	0	0
$513$	0	0
$514$	0	0
$515$	5.91608	0.260694
$516$	0	0
$517$	46.9574i	2.06519i
$518$	0	0
$519$	− 25.0000i	− 1.09738i
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	26.8328	1.17332	0.586659	−	0.809834i	$-0.300443\pi$
$523$	26.8328	1.17332	0.586659	+	0.809834i	$0.300443\pi$
$524$	0	0
$525$	29.5804i	1.29099i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	26.4575	1.14173
$538$	0	0
$539$	−41.4126	−1.78377
$540$	0	0
$541$	− 17.7482i	− 0.763056i	−0.924357	−	0.381528i	$-0.875398\pi$
$541$	− 17.7482i	− 0.763056i	0.924357	−	0.381528i	$-0.124602\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−39.6863	−1.69997
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	2.64575	0.112509
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	105.000	4.43310
$562$	0	0
$563$	44.7214	1.88478	0.942390	−	0.334515i	$-0.108573\pi$
$563$	44.7214	1.88478	0.942390	+	0.334515i	$0.108573\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	29.1033i	1.22222i
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−35.4965	−1.48548	−0.742741	−	0.669579i	$-0.766474\pi$
$571$	−35.4965	−1.48548	−0.742741	+	0.669579i	$0.766474\pi$
$572$	0	0
$573$	60.3738i	2.52215i
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−34.3948	−1.43187	−0.715936	−	0.698165i	$-0.754000\pi$
$577$	−34.3948	−1.43187	−0.715936	+	0.698165i	$0.754000\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 23.6643i	− 0.981761i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	30.0000	1.24035
$586$	0	0
$587$	−8.94427	−0.369170	−0.184585	−	0.982817i	$-0.559094\pi$
$587$	−8.94427	−0.369170	−0.184585	+	0.982817i	$0.559094\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	23.8118	0.977832	0.488916	−	0.872331i	$-0.337392\pi$
$593$	23.8118	0.977832	0.488916	+	0.872331i	$0.337392\pi$
$594$	0	0
$595$	−46.9574	−1.92507
$596$	0	0
$597$	0	0
$598$	0	0
$599$	− 39.0000i	− 1.59350i	−0.604311	−	0.796748i	$-0.706552\pi$
$599$	− 39.0000i	− 1.59350i	0.604311	−	0.796748i	$-0.293448\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 53.6656i	− 2.18182i
$606$	0	0
$607$	44.9778i	1.82559i	0.408416	+	0.912796i	$0.366081\pi$
$607$	44.9778i	1.82559i	−0.408416	+	0.912796i	$0.633919\pi$
$608$	0	0
$609$	−35.0000	−1.41827
$610$	0	0
$611$	−53.2447	−2.15405
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	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
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	− 47.0000i	− 1.87104i	−0.353273	−	0.935520i	$-0.614931\pi$
$631$	− 47.0000i	− 1.87104i	0.353273	−	0.935520i	$-0.385069\pi$
$632$	0	0
$633$	39.6863	1.57739
$634$	0	0
$635$	0	0
$636$	0	0
$637$	− 46.9574i	− 1.86052i
$638$	0	0
$639$	− 24.0000i	− 0.949425i
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	0	0
$643$	6.70820	0.264546	0.132273	−	0.991213i	$-0.457772\pi$
$643$	6.70820	0.264546	0.132273	+	0.991213i	$0.457772\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	47.6235i	1.87227i	0.351636	+	0.936137i	$0.385626\pi$
$647$	47.6235i	1.87227i	−0.351636	+	0.936137i	$0.614374\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−21.1660	−0.825765
$658$	0	0
$659$	5.91608	0.230458	0.115229	−	0.993339i	$-0.463240\pi$
$659$	5.91608	0.230458	0.115229	+	0.993339i	$0.463240\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	119.059i	4.62386i
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	65.0769i	2.51602i
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	11.1803	0.430331
$676$	0	0
$677$	− 51.4296i	− 1.97660i	−0.152527	−	0.988299i	$-0.548741\pi$
$677$	− 51.4296i	− 1.97660i	0.152527	−	0.988299i	$-0.451259\pi$
$678$	0	0
$679$	49.0000i	1.88045i
$680$	0	0
$681$	−65.0000	−2.49081
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	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
$693$	− 31.3050i	− 1.18918i
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	41.4126i	1.56413i	0.623196	+	0.782065i	$0.285834\pi$
$701$	41.4126i	1.56413i	−0.623196	+	0.782065i	$0.714166\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	39.6863	1.49467
$706$	0	0
$707$	0	0
$708$	0	0
$709$	− 53.2447i	− 1.99965i	−0.0187779	−	0.999824i	$-0.505978\pi$
$709$	− 53.2447i	− 1.99965i	0.0187779	−	0.999824i	$-0.494022\pi$
$710$	0	0
$711$	2.00000i	0.0750059i
$712$	0	0
$713$	0	0
$714$	0	0
$715$	88.7412	3.31873
$716$	0	0
$717$	20.1246i	0.751567i
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	7.00000	0.260694
$722$	0	0
$723$	0	0
$724$	0	0
$725$	29.5804i	1.09859i
$726$	0	0
$727$	5.29150i	0.196251i	0.995174	+	0.0981255i	$0.0312847\pi$
$727$	5.29150i	0.196251i	−0.995174	+	0.0981255i	$0.968715\pi$
$728$	0	0
$729$	−7.00000	−0.259259
$730$	0	0
$731$	0	0
$732$	0	0
$733$	20.1246i	0.743319i	0.928369	+	0.371660i	$0.121211\pi$
$733$	20.1246i	0.743319i	−0.928369	+	0.371660i	$0.878789\pi$
$734$	0	0
$735$	35.0000i	1.29099i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	53.2447	1.95864	0.979319	−	0.202321i	$-0.0648484\pi$
$739$	53.2447	1.95864	0.979319	+	0.202321i	$0.0648484\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	−52.9150	−1.93866
$746$	0	0
$747$	17.8885	0.654508
$748$	0	0
$749$	0	0
$750$	0	0
$751$	− 13.0000i	− 0.474377i	−0.971464	−	0.237188i	$-0.923774\pi$
$751$	− 13.0000i	− 0.474377i	0.971464	−	0.237188i	$-0.0762259\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	38.0132	1.38344
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	−46.9574	−1.69997
$764$	0	0
$765$	− 35.4965i	− 1.28338i
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	−70.9930	−2.55675
$772$	0	0
$773$	2.23607i	0.0804258i	0.999191	+	0.0402129i	$0.0128036\pi$
$773$	2.23607i	0.0804258i	−0.999191	+	0.0402129i	$0.987196\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	− 70.9930i	− 2.54033i
$782$	0	0
$783$	13.2288i	0.472757i
$784$	0	0
$785$	30.0000	1.07075
$786$	0	0
$787$	−33.5410	−1.19561	−0.597804	−	0.801642i	$-0.703960\pi$
$787$	−33.5410	−1.19561	−0.597804	+	0.801642i	$0.703960\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	55.9017i	1.98014i	0.140576	+	0.990070i	$0.455105\pi$
$797$	55.9017i	1.98014i	−0.140576	+	0.990070i	$0.544895\pi$
$798$	0	0
$799$	63.0000i	2.22878i
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−62.6099	−2.20946
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	39.0000	1.37117	0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000	1.37117	0.685583	+	0.727994i	$0.259547\pi$
$810$	0	0
$811$	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
$819$	35.4965	1.24035
$820$	0	0
$821$	− 5.91608i	− 0.206473i	−0.994657	−	0.103236i	$-0.967080\pi$
$821$	− 5.91608i	− 0.206473i	0.994657	−	0.103236i	$-0.0329198\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	−66.1438	−2.30283
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−55.5608	−1.92507
$834$	0	0
$835$	17.7482	0.614203
$836$	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
$841$	−6.00000	−0.206897
$842$	0	0
$843$	−73.7902	−2.54147
$844$	0	0
$845$	71.5542i	2.46154i
$846$	0	0
$847$	− 63.4980i	− 2.18182i
$848$	0	0
$849$	−75.0000	−2.57399
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 40.2492i	− 1.37811i	−0.724710	−	0.689054i	$-0.758026\pi$
$853$	− 40.2492i	− 1.37811i	0.724710	−	0.689054i	$-0.241974\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	31.7490	1.08453	0.542263	−	0.840209i	$-0.317568\pi$
$857$	31.7490	1.08453	0.542263	+	0.840209i	$0.317568\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	−25.0000	−0.850026
$866$	0	0
$867$	102.859	3.49328
$868$	0	0
$869$	5.91608i	0.200689i
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−37.0405	−1.25363
$874$	0	0
$875$	29.5804	1.00000
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	55.0000i	1.85510i
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	− 47.6235i	− 1.59904i	−0.600639	−	0.799521i	$-0.705087\pi$
$887$	− 47.6235i	− 1.59904i	0.600639	−	0.799521i	$-0.294913\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−65.0769	−2.18016
$892$	0	0
$893$	0	0
$894$	0	0
$895$	− 26.4575i	− 0.884377i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	12.0000i	0.397578i	0.980042	+	0.198789i	$0.0637008\pi$
$911$	12.0000i	0.397578i	−0.980042	+	0.198789i	$0.936299\pi$
$912$	0	0
$913$	52.9150	1.75123
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	− 29.0000i	− 0.956622i	−0.878191	−	0.478311i	$-0.841249\pi$
$919$	− 29.0000i	− 0.956622i	0.878191	−	0.478311i	$-0.158751\pi$
$920$	0	0
$921$	15.0000	0.494267
$922$	0	0
$923$	80.4984	2.64964
$924$	0	0
$925$	0	0
$926$	0	0
$927$	5.29150i	0.173796i
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	− 105.000i	− 3.43387i
$936$	0	0
$937$	−60.8523	−1.98796	−0.993979	−	0.109574i	$-0.965051\pi$
$937$	−60.8523	−1.98796	−0.993979	+	0.109574i	$0.965051\pi$
$938$	0	0
$939$	65.0769	2.12370
$940$	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
$945$	13.2288	0.430331
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	− 70.9930i	− 2.30453i
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	60.3738	1.95365
$956$	0	0
$957$	− 78.2624i	− 2.52986i
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	− 75.0000i	− 2.40192i
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	− 35.4965i	− 1.13332i
$982$	0	0
$983$	− 55.5608i	− 1.77211i	−0.463577	−	0.886057i	$-0.653434\pi$
$983$	− 55.5608i	− 1.77211i	0.463577	−	0.886057i	$-0.346566\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	46.9574	1.49467
$988$	0	0
$989$	0	0
$990$	0	0
$991$	− 52.0000i	− 1.65183i	−0.563791	−	0.825917i	$-0.690658\pi$
$991$	− 52.0000i	− 1.65183i	0.563791	−	0.825917i	$-0.309342\pi$
$992$	0	0
$993$	79.3725	2.51881
$994$	0	0
$995$	0	0
$996$	0	0
$997$	60.3738i	1.91206i	0.293271	+	0.956029i	$0.405256\pi$
$997$	60.3738i	1.91206i	−0.293271	+	0.956029i	$0.594744\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.n.f.1119.5	yes	8
4.3	odd	2	inner	2240.2.n.f.1119.2	yes	8
5.4	even	2	inner	2240.2.n.f.1119.4	yes	8
7.6	odd	2	inner	2240.2.n.f.1119.4	yes	8
8.3	odd	2	inner	2240.2.n.f.1119.8	yes	8
8.5	even	2	inner	2240.2.n.f.1119.3	yes	8
20.19	odd	2	inner	2240.2.n.f.1119.7	yes	8
28.27	even	2	inner	2240.2.n.f.1119.7	yes	8
35.34	odd	2	CM	2240.2.n.f.1119.5	yes	8
40.19	odd	2	inner	2240.2.n.f.1119.1	✓	8
40.29	even	2	inner	2240.2.n.f.1119.6	yes	8
56.13	odd	2	inner	2240.2.n.f.1119.6	yes	8
56.27	even	2	inner	2240.2.n.f.1119.1	✓	8
140.139	even	2	inner	2240.2.n.f.1119.2	yes	8
280.69	odd	2	inner	2240.2.n.f.1119.3	yes	8
280.139	even	2	inner	2240.2.n.f.1119.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2240.2.n.f.1119.1	✓	8	40.19	odd	2	inner
2240.2.n.f.1119.1	✓	8	56.27	even	2	inner
2240.2.n.f.1119.2	yes	8	4.3	odd	2	inner
2240.2.n.f.1119.2	yes	8	140.139	even	2	inner
2240.2.n.f.1119.3	yes	8	8.5	even	2	inner
2240.2.n.f.1119.3	yes	8	280.69	odd	2	inner
2240.2.n.f.1119.4	yes	8	5.4	even	2	inner
2240.2.n.f.1119.4	yes	8	7.6	odd	2	inner
2240.2.n.f.1119.5	yes	8	1.1	even	1	trivial
2240.2.n.f.1119.5	yes	8	35.34	odd	2	CM
2240.2.n.f.1119.6	yes	8	40.29	even	2	inner
2240.2.n.f.1119.6	yes	8	56.13	odd	2	inner
2240.2.n.f.1119.7	yes	8	20.19	odd	2	inner
2240.2.n.f.1119.7	yes	8	28.27	even	2	inner
2240.2.n.f.1119.8	yes	8	8.3	odd	2	inner
2240.2.n.f.1119.8	yes	8	280.139	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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.23607 q^{3} -2.23607i q^{5} -2.64575i q^{7} +2.00000 q^{9} +O(q^{10})\)	\(q+2.23607 q^{3} -2.23607i q^{5} -2.64575i q^{7} +2.00000 q^{9} +5.91608 q^{11} +6.70820i q^{13} -5.00000i q^{15} +7.93725 q^{17} -5.91608i q^{21} -5.00000 q^{25} -2.23607 q^{27} -5.91608i q^{29} +13.2288 q^{33} -5.91608 q^{35} +15.0000i q^{39} -4.47214i q^{45} +7.93725i q^{47} -7.00000 q^{49} +17.7482 q^{51} -13.2288i q^{55} -5.29150i q^{63} +15.0000 q^{65} -12.0000i q^{71} -10.5830 q^{73} -11.1803 q^{75} -15.6525i q^{77} +1.00000i q^{79} -11.0000 q^{81} +8.94427 q^{83} -17.7482i q^{85} -13.2288i q^{87} +17.7482 q^{91} -18.5203 q^{97} +11.8322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{9}+O(q^{10}) \) 8 * q + 16 * q^9	\( 8 q + 16 q^{9} - 40 q^{25} - 56 q^{49} + 120 q^{65} - 88 q^{81}+O(q^{100}) \) 8 * q + 16 * q^9 - 40 * q^25 - 56 * q^49 + 120 * q^65 - 88 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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