LMFDB - Embedded newform 1225.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1225,2,Mod(1,1225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1225, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1225 = 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1225.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.78167424761$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 245)
Fricke sign:	$+1$
Sato-Tate group:	$N(\mathrm{U}(1))$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{3} -2.00000 q^{4} +2.00000 q^{9} -3.00000 q^{11} +4.47214 q^{12} +6.70820 q^{13} +4.00000 q^{16} +2.23607 q^{17} +2.23607 q^{27} -9.00000 q^{29} +6.70820 q^{33} -4.00000 q^{36} -15.0000 q^{39} +6.00000 q^{44} -11.1803 q^{47} -8.94427 q^{48} -5.00000 q^{51} -13.4164 q^{52} -8.00000 q^{64} -4.47214 q^{68} -12.0000 q^{71} +13.4164 q^{73} -1.00000 q^{79} -11.0000 q^{81} -8.94427 q^{83} +20.1246 q^{87} -6.70820 q^{97} -6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{4} + 4 q^{9} - 6 q^{11} + 8 q^{16} - 18 q^{29} - 8 q^{36} - 30 q^{39} + 12 q^{44} - 10 q^{51} - 16 q^{64} - 24 q^{71} - 2 q^{79} - 22 q^{81} - 12 q^{99}+O(q^{100}) $ 2 * q - 4 * q^4 + 4 * q^9 - 6 * q^11 + 8 * q^16 - 18 * q^29 - 8 * q^36 - 30 * q^39 + 12 * q^44 - 10 * q^51 - 16 * q^64 - 24 * q^71 - 2 * q^79 - 22 * q^81 - 12 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	−2.23607	−1.29099	−0.645497	−	0.763763i	$-0.723350\pi$
$3$	−2.23607	−1.29099	−0.645497	+	0.763763i	$0.723350\pi$
$4$	−2.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	2.00000	0.666667
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	4.47214	1.29099
$13$	6.70820	1.86052	0.930261	−	0.366900i	$-0.119581\pi$
$13$	6.70820	1.86052	0.930261	+	0.366900i	$0.119581\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	2.23607	0.542326	0.271163	−	0.962533i	$-0.412592\pi$
$17$	2.23607	0.542326	0.271163	+	0.962533i	$0.412592\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	2.23607	0.430331
$28$	0	0
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	6.70820	1.16775
$34$	0	0
$35$	0	0
$36$	−4.00000	−0.666667
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	−15.0000	−2.40192
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	0	0
$47$	−11.1803	−1.63082	−0.815410	−	0.578884i	$-0.803489\pi$
$47$	−11.1803	−1.63082	−0.815410	+	0.578884i	$0.803489\pi$
$48$	−8.94427	−1.29099
$49$	0	0
$50$	0	0
$51$	−5.00000	−0.700140
$52$	−13.4164	−1.86052
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−4.47214	−0.542326
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	13.4164	1.57027	0.785136	−	0.619324i	$-0.212593\pi$
$73$	13.4164	1.57027	0.785136	+	0.619324i	$0.212593\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−8.94427	−0.981761	−0.490881	−	0.871227i	$-0.663325\pi$
$83$	−8.94427	−0.981761	−0.490881	+	0.871227i	$0.663325\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	20.1246	2.15758
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−6.70820	−0.681115	−0.340557	−	0.940224i	$-0.610616\pi$
$97$	−6.70820	−0.681115	−0.340557	+	0.940224i	$0.610616\pi$
$98$	0	0
$99$	−6.00000	−0.603023
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−20.1246	−1.98294	−0.991468	−	0.130347i	$-0.958391\pi$
$103$	−20.1246	−1.98294	−0.991468	+	0.130347i	$0.958391\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	−4.47214	−0.430331
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	18.0000	1.67126
$117$	13.4164	1.24035
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	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		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−13.4164	−1.16775
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	25.0000	2.10538
$142$	0	0
$143$	−20.1246	−1.68290
$144$	8.00000	0.666667
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	−17.0000	−1.38344	−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000	−1.38344	−0.691720	+	0.722166i	$0.743147\pi$
$152$	0	0
$153$	4.47214	0.361551
$154$	0	0
$155$	0	0
$156$	30.0000	2.40192
$157$	−13.4164	−1.07075	−0.535373	−	0.844616i	$-0.679829\pi$
$157$	−13.4164	−1.07075	−0.535373	+	0.844616i	$0.679829\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	24.5967	1.90335	0.951677	−	0.307102i	$-0.0993591\pi$
$167$	24.5967	1.90335	0.951677	+	0.307102i	$0.0993591\pi$
$168$	0	0
$169$	32.0000	2.46154
$170$	0	0
$171$	0	0
$172$	0	0
$173$	11.1803	0.850026	0.425013	−	0.905187i	$-0.360270\pi$
$173$	11.1803	0.850026	0.425013	+	0.905187i	$0.360270\pi$
$174$	0	0
$175$	0	0
$176$	−12.0000	−0.904534
$177$	0	0
$178$	0	0
$179$	24.0000	1.79384	0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000	1.79384	0.896922	+	0.442189i	$0.145798\pi$
$180$	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
$187$	−6.70820	−0.490552
$188$	22.3607	1.63082
$189$	0	0
$190$	0	0
$191$	−27.0000	−1.95365	−0.976826	−	0.214036i	$-0.931339\pi$
$191$	−27.0000	−1.95365	−0.976826	+	0.214036i	$0.931339\pi$
$192$	17.8885	1.29099
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	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
$203$	0	0
$204$	10.0000	0.700140
$205$	0	0
$206$	0	0
$207$	0	0
$208$	26.8328	1.86052
$209$	0	0
$210$	0	0
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	0	0
$213$	26.8328	1.83855
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−30.0000	−2.02721
$220$	0	0
$221$	15.0000	1.00901
$222$	0	0
$223$	6.70820	0.449215	0.224607	−	0.974449i	$-0.427890\pi$
$223$	6.70820	0.449215	0.224607	+	0.974449i	$0.427890\pi$
$224$	0	0
$225$	0	0
$226$	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
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	2.23607	0.145248
$238$	0	0
$239$	−9.00000	−0.582162	−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000	−0.582162	−0.291081	+	0.956698i	$0.594015\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	0	0
$243$	17.8885	1.14755
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	20.0000	1.26745
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	4.47214	0.278964	0.139482	−	0.990225i	$-0.455456\pi$
$257$	4.47214	0.278964	0.139482	+	0.990225i	$0.455456\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−18.0000	−1.11417
$262$	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	$0.5\pi$
$272$	8.94427	0.542326
$273$	0	0
$274$	0	0
$275$	0	0
$276$	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	$0.974943\pi$
$284$	24.0000	1.42414
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−12.0000	−0.705882
$290$	0	0
$291$	15.0000	0.879316
$292$	−26.8328	−1.57027
$293$	−24.5967	−1.43696	−0.718479	−	0.695549i	$-0.755161\pi$
$293$	−24.5967	−1.43696	−0.718479	+	0.695549i	$0.755161\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−6.70820	−0.389249
$298$	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	$-0.561312\pi$
$307$	−6.70820	−0.382857	−0.191429	+	0.981507i	$0.561312\pi$
$308$	0	0
$309$	45.0000	2.55996
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−20.1246	−1.13751	−0.568755	−	0.822507i	$-0.692575\pi$
$313$	−20.1246	−1.13751	−0.568755	+	0.822507i	$0.692575\pi$
$314$	0	0
$315$	0	0
$316$	2.00000	0.112509
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	27.0000	1.51171
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	22.0000	1.22222
$325$	0	0
$326$	0	0
$327$	24.5967	1.36020
$328$	0	0
$329$	0	0
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	17.8885	0.981761
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	0	0
$339$	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		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−40.2492	−2.15758
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	15.0000	0.800641
$352$	0	0
$353$	29.0689	1.54718	0.773590	−	0.633686i	$-0.218459\pi$
$353$	29.0689	1.54718	0.773590	+	0.633686i	$0.218459\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−36.0000	−1.90001	−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000	−1.90001	−0.950004	+	0.312239i	$0.898921\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	0	0
$363$	4.47214	0.234726
$364$	0	0
$365$	0	0
$366$	0	0
$367$	33.5410	1.75083	0.875413	−	0.483375i	$-0.160589\pi$
$367$	33.5410	1.75083	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
$375$	0	0
$376$	0	0
$377$	−60.3738	−3.10941
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−35.7771	−1.82812	−0.914062	−	0.405575i	$-0.867071\pi$
$383$	−35.7771	−1.82812	−0.914062	+	0.405575i	$0.867071\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	13.4164	0.681115
$389$	−39.0000	−1.97738	−0.988689	−	0.149979i	$-0.952080\pi$
$389$	−39.0000	−1.97738	−0.988689	+	0.149979i	$0.952080\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	12.0000	0.603023
$397$	20.1246	1.01003	0.505013	−	0.863112i	$-0.331488\pi$
$397$	20.1246	1.01003	0.505013	+	0.863112i	$0.331488\pi$
$398$	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
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	40.2492	1.98294
$413$	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
$421$	37.0000	1.80327	0.901635	−	0.432498i	$-0.142368\pi$
$421$	37.0000	1.80327	0.901635	+	0.432498i	$0.142368\pi$
$422$	0	0
$423$	−22.3607	−1.08721
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	45.0000	2.17262
$430$	0	0
$431$	−3.00000	−0.144505	−0.0722525	−	0.997386i	$-0.523019\pi$
$431$	−3.00000	−0.144505	−0.0722525	+	0.997386i	$0.523019\pi$
$432$	8.94427	0.430331
$433$	−40.2492	−1.93425	−0.967127	−	0.254293i	$-0.918157\pi$
$433$	−40.2492	−1.93425	−0.967127	+	0.254293i	$0.918157\pi$
$434$	0	0
$435$	0	0
$436$	22.0000	1.05361
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−13.4164	−0.634574
$448$	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
$453$	38.0132	1.78601
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	0	0
$459$	5.00000	0.233380
$460$	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	$0.5\pi$
$464$	−36.0000	−1.67126
$465$	0	0
$466$	0	0
$467$	−42.4853	−1.96598	−0.982992	−	0.183646i	$-0.941210\pi$
$467$	−42.4853	−1.96598	−0.982992	+	0.183646i	$0.941210\pi$
$468$	−26.8328	−1.24035
$469$	0	0
$470$	0	0
$471$	30.0000	1.38233
$472$	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
$484$	4.00000	0.181818
$485$	0	0
$486$	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
$491$	−33.0000	−1.48927	−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000	−1.48927	−0.744635	+	0.667472i	$0.767376\pi$
$492$	0	0
$493$	−20.1246	−0.906367
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	41.0000	1.83541	0.917706	−	0.397260i	$-0.130039\pi$
$499$	41.0000	1.83541	0.917706	+	0.397260i	$0.130039\pi$
$500$	0	0
$501$	−55.0000	−2.45722
$502$	0	0
$503$	38.0132	1.69492	0.847461	−	0.530857i	$-0.178130\pi$
$503$	38.0132	1.69492	0.847461	+	0.530857i	$0.178130\pi$
$504$	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
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	33.5410	1.47513
$518$	0	0
$519$	−25.0000	−1.09738
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	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
$525$	0	0
$526$	0	0
$527$	0	0
$528$	26.8328	1.16775
$529$	−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
$537$	−53.6656	−2.31584
$538$	0	0
$539$	0	0
$540$	0	0
$541$	43.0000	1.84871	0.924357	−	0.381528i	$-0.124602\pi$
$541$	43.0000	1.84871	0.924357	+	0.381528i	$0.124602\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	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
$561$	15.0000	0.633300
$562$	0	0
$563$	44.7214	1.88478	0.942390	−	0.334515i	$-0.108573\pi$
$563$	44.7214	1.88478	0.942390	+	0.334515i	$0.108573\pi$
$564$	−50.0000	−2.10538
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	40.2492	1.68290
$573$	60.3738	2.52215
$574$	0	0
$575$	0	0
$576$	−16.0000	−0.666667
$577$	33.5410	1.39633	0.698165	−	0.715936i	$-0.254000\pi$
$577$	33.5410	1.39633	0.698165	+	0.715936i	$0.254000\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	8.94427	0.369170	0.184585	−	0.982817i	$-0.440906\pi$
$587$	8.94427	0.369170	0.184585	+	0.982817i	$0.440906\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	42.4853	1.74466	0.872331	−	0.488916i	$-0.162608\pi$
$593$	42.4853	1.74466	0.872331	+	0.488916i	$0.162608\pi$
$594$	0	0
$595$	0	0
$596$	−12.0000	−0.491539
$597$	0	0
$598$	0	0
$599$	−39.0000	−1.59350	−0.796748	−	0.604311i	$-0.793448\pi$
$599$	−39.0000	−1.59350	−0.796748	+	0.604311i	$0.793448\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	0	0
$604$	34.0000	1.38344
$605$	0	0
$606$	0	0
$607$	20.1246	0.816833	0.408416	−	0.912796i	$-0.366081\pi$
$607$	20.1246	0.816833	0.408416	+	0.912796i	$0.366081\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−75.0000	−3.03418
$612$	−8.94427	−0.361551
$613$	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		−	1.00000i	$-0.5\pi$
$617$	0	0			1.00000i	$0.5\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	−60.0000	−2.40192
$625$	0	0
$626$	0	0
$627$	0	0
$628$	26.8328	1.07075
$629$	0	0
$630$	0	0
$631$	−47.0000	−1.87104	−0.935520	−	0.353273i	$-0.885069\pi$
$631$	−47.0000	−1.87104	−0.935520	+	0.353273i	$0.885069\pi$
$632$	0	0
$633$	−51.4296	−2.04414
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−24.0000	−0.949425
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	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
$647$	17.8885	0.703271	0.351636	−	0.936137i	$-0.385626\pi$
$647$	17.8885	0.703271	0.351636	+	0.936137i	$0.385626\pi$
$648$	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
$657$	26.8328	1.04685
$658$	0	0
$659$	−51.0000	−1.98668	−0.993339	−	0.115229i	$-0.963240\pi$
$659$	−51.0000	−1.98668	−0.993339	+	0.115229i	$0.963240\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	−33.5410	−1.30263
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−49.1935	−1.90335
$669$	−15.0000	−0.579934
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	0	0
$675$	0	0
$676$	−64.0000	−2.46154
$677$	51.4296	1.97660	0.988299	−	0.152527i	$-0.0487410\pi$
$677$	51.4296	1.97660	0.988299	+	0.152527i	$0.0487410\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	65.0000	2.49081
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	−22.3607	−0.850026
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−33.0000	−1.24639	−0.623196	−	0.782065i	$-0.714166\pi$
$701$	−33.0000	−1.24639	−0.623196	+	0.782065i	$0.714166\pi$
$702$	0	0
$703$	0	0
$704$	24.0000	0.904534
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−1.00000	−0.0375558	−0.0187779	−	0.999824i	$-0.505978\pi$
$709$	−1.00000	−0.0375558	−0.0187779	+	0.999824i	$0.505978\pi$
$710$	0	0
$711$	−2.00000	−0.0750059
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−48.0000	−1.79384
$717$	20.1246	0.751567
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−53.6656	−1.99035	−0.995174	−	0.0981255i	$-0.968715\pi$
$727$	−53.6656	−1.99035	−0.995174	+	0.0981255i	$0.968715\pi$
$728$	0	0
$729$	−7.00000	−0.259259
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−20.1246	−0.743319	−0.371660	−	0.928369i	$-0.621211\pi$
$733$	−20.1246	−0.743319	−0.371660	+	0.928369i	$0.621211\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−11.0000	−0.404642	−0.202321	−	0.979319i	$-0.564848\pi$
$739$	−11.0000	−0.404642	−0.202321	+	0.979319i	$0.564848\pi$
$740$	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
$745$	0	0
$746$	0	0
$747$	−17.8885	−0.654508
$748$	13.4164	0.490552
$749$	0	0
$750$	0	0
$751$	−13.0000	−0.474377	−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000	−0.474377	−0.237188	+	0.971464i	$0.576226\pi$
$752$	−44.7214	−1.63082
$753$	0	0
$754$	0	0
$755$	0	0
$756$	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		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	0	0
$764$	54.0000	1.95365
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−35.7771	−1.29099
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	−10.0000	−0.360141
$772$	0	0
$773$	−2.23607	−0.0804258	−0.0402129	−	0.999191i	$-0.512804\pi$
$773$	−2.23607	−0.0804258	−0.0402129	+	0.999191i	$0.512804\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	36.0000	1.28818
$782$	0	0
$783$	−20.1246	−0.719195
$784$	0	0
$785$	0	0
$786$	0	0
$787$	33.5410	1.19561	0.597804	−	0.801642i	$-0.296040\pi$
$787$	33.5410	1.19561	0.597804	+	0.801642i	$0.296040\pi$
$788$	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
$797$	55.9017	1.98014	0.990070	−	0.140576i	$-0.0448954\pi$
$797$	55.9017	1.98014	0.990070	+	0.140576i	$0.0448954\pi$
$798$	0	0
$799$	−25.0000	−0.884436
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−40.2492	−1.42036
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−39.0000	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	−20.0000	−0.700140
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	57.0000	1.98931	0.994657	−	0.103236i	$-0.0329198\pi$
$821$	57.0000	1.98931	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
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	−53.6656	−1.86052
$833$	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
$841$	52.0000	1.79310
$842$	0	0
$843$	73.7902	2.54147
$844$	−46.0000	−1.58339
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	75.0000	2.57399
$850$	0	0
$851$	0	0
$852$	−53.6656	−1.83855
$853$	−40.2492	−1.37811	−0.689054	−	0.724710i	$-0.741974\pi$
$853$	−40.2492	−1.37811	−0.689054	+	0.724710i	$0.741974\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	49.1935	1.68042	0.840209	−	0.542263i	$-0.182432\pi$
$857$	49.1935	1.68042	0.840209	+	0.542263i	$0.182432\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	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
$865$	0	0
$866$	0	0
$867$	26.8328	0.911290
$868$	0	0
$869$	3.00000	0.101768
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−13.4164	−0.454077
$874$	0	0
$875$	0	0
$876$	60.0000	2.02721
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	55.0000	1.85510
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	−30.0000	−1.00901
$885$	0	0
$886$	0	0
$887$	35.7771	1.20128	0.600639	−	0.799521i	$-0.294913\pi$
$887$	35.7771	1.20128	0.600639	+	0.799521i	$0.294913\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	33.0000	1.10554
$892$	−13.4164	−0.449215
$893$	0	0
$894$	0	0
$895$	0	0
$896$	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		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	58.1378	1.92937
$909$	0	0
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	26.8328	0.888037
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−29.0000	−0.956622	−0.478311	−	0.878191i	$-0.658751\pi$
$919$	−29.0000	−0.956622	−0.478311	+	0.878191i	$0.658751\pi$
$920$	0	0
$921$	15.0000	0.494267
$922$	0	0
$923$	−80.4984	−2.64964
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−40.2492	−1.32196
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−6.70820	−0.219147	−0.109574	−	0.993979i	$-0.534949\pi$
$937$	−6.70820	−0.219147	−0.109574	+	0.993979i	$0.534949\pi$
$938$	0	0
$939$	45.0000	1.46852
$940$	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
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	−4.47214	−0.145248
$949$	90.0000	2.92152
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0		−	1.00000i	$-0.5\pi$
$953$	0	0			1.00000i	$0.5\pi$
$954$	0	0
$955$	0	0
$956$	18.0000	0.582162
$957$	−60.3738	−1.95161
$958$	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		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	−35.7771	−1.14755
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−22.0000	−0.702406
$982$	0	0
$983$	29.0689	0.927153	0.463577	−	0.886057i	$-0.346566\pi$
$983$	29.0689	0.927153	0.463577	+	0.886057i	$0.346566\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−52.0000	−1.65183	−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000	−1.65183	−0.825917	+	0.563791i	$0.809342\pi$
$992$	0	0
$993$	−17.8885	−0.567676
$994$	0	0
$995$	0	0
$996$	−40.0000	−1.26745
$997$	−60.3738	−1.91206	−0.956029	−	0.293271i	$-0.905256\pi$
$997$	−60.3738	−1.91206	−0.956029	+	0.293271i	$0.905256\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1225.2.a.q.1.1		2
5.2	odd	4		245.2.b.d.99.2	yes	2
5.3	odd	4		245.2.b.d.99.1	✓	2
5.4	even	2	inner	1225.2.a.q.1.2		2
7.6	odd	2	inner	1225.2.a.q.1.2		2
15.2	even	4		2205.2.d.h.1324.1		2
15.8	even	4		2205.2.d.h.1324.2		2
35.2	odd	12		245.2.j.b.214.1		4
35.3	even	12		245.2.j.b.79.2		4
35.12	even	12		245.2.j.b.214.2		4
35.13	even	4		245.2.b.d.99.2	yes	2
35.17	even	12		245.2.j.b.79.1		4
35.18	odd	12		245.2.j.b.79.1		4
35.23	odd	12		245.2.j.b.214.2		4
35.27	even	4		245.2.b.d.99.1	✓	2
35.32	odd	12		245.2.j.b.79.2		4
35.33	even	12		245.2.j.b.214.1		4
35.34	odd	2	CM	1225.2.a.q.1.1		2
105.62	odd	4		2205.2.d.h.1324.2		2
105.83	odd	4		2205.2.d.h.1324.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.b.d.99.1	✓	2	5.3	odd	4
245.2.b.d.99.1	✓	2	35.27	even	4
245.2.b.d.99.2	yes	2	5.2	odd	4
245.2.b.d.99.2	yes	2	35.13	even	4
245.2.j.b.79.1		4	35.17	even	12
245.2.j.b.79.1		4	35.18	odd	12
245.2.j.b.79.2		4	35.3	even	12
245.2.j.b.79.2		4	35.32	odd	12
245.2.j.b.214.1		4	35.2	odd	12
245.2.j.b.214.1		4	35.33	even	12
245.2.j.b.214.2		4	35.12	even	12
245.2.j.b.214.2		4	35.23	odd	12
1225.2.a.q.1.1		2	1.1	even	1	trivial
1225.2.a.q.1.1		2	35.34	odd	2	CM
1225.2.a.q.1.2		2	5.4	even	2	inner
1225.2.a.q.1.2		2	7.6	odd	2	inner
2205.2.d.h.1324.1		2	15.2	even	4
2205.2.d.h.1324.1		2	105.83	odd	4
2205.2.d.h.1324.2		2	15.8	even	4
2205.2.d.h.1324.2		2	105.62	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:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1225.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23607 q^{3} -2.00000 q^{4} +2.00000 q^{9} -3.00000 q^{11} +4.47214 q^{12} +6.70820 q^{13} +4.00000 q^{16} +2.23607 q^{17} +2.23607 q^{27} -9.00000 q^{29} +6.70820 q^{33} -4.00000 q^{36} -15.0000 q^{39} +6.00000 q^{44} -11.1803 q^{47} -8.94427 q^{48} -5.00000 q^{51} -13.4164 q^{52} -8.00000 q^{64} -4.47214 q^{68} -12.0000 q^{71} +13.4164 q^{73} -1.00000 q^{79} -11.0000 q^{81} -8.94427 q^{83} +20.1246 q^{87} -6.70820 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{4} + 4 q^{9} - 6 q^{11} + 8 q^{16} - 18 q^{29} - 8 q^{36} - 30 q^{39} + 12 q^{44} - 10 q^{51} - 16 q^{64} - 24 q^{71} - 2 q^{79} - 22 q^{81} - 12 q^{99}+O(q^{100}) \) 2 * q - 4 * q^4 + 4 * q^9 - 6 * q^11 + 8 * q^16 - 18 * q^29 - 8 * q^36 - 30 * q^39 + 12 * q^44 - 10 * q^51 - 16 * q^64 - 24 * q^71 - 2 * q^79 - 22 * q^81 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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