LMFDB - Embedded newform 900.3.c.h.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.c (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			451.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.h.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -4.00000 q^{4} +4.00000i q^{7} +8.00000i q^{8} +O(q^{10})$	$q-2.00000i q^{2} -4.00000 q^{4} +4.00000i q^{7} +8.00000i q^{8} +8.00000 q^{14} +16.0000 q^{16} -44.0000i q^{23} -16.0000i q^{28} -22.0000 q^{29} -32.0000i q^{32} -62.0000 q^{41} -76.0000i q^{43} -88.0000 q^{46} -4.00000i q^{47} +33.0000 q^{49} -32.0000 q^{56} +44.0000i q^{58} -58.0000 q^{61} -64.0000 q^{64} -116.000i q^{67} +124.000i q^{82} +76.0000i q^{83} -152.000 q^{86} -142.000 q^{89} +176.000i q^{92} -8.00000 q^{94} -66.0000i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4}+O(q^{10}) $ 2 * q - 8 * q^4	$ 2 q - 8 q^{4} + 16 q^{14} + 32 q^{16} - 44 q^{29} - 124 q^{41} - 176 q^{46} + 66 q^{49} - 64 q^{56} - 116 q^{61} - 128 q^{64} - 304 q^{86} - 284 q^{89} - 16 q^{94}+O(q^{100}) $ 2 * q - 8 * q^4 + 16 * q^14 + 32 * q^16 - 44 * q^29 - 124 * q^41 - 176 * q^46 + 66 * q^49 - 64 * q^56 - 116 * q^61 - 128 * q^64 - 304 * q^86 - 284 * q^89 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	− 2.00000i	− 1.00000i
$2$	− 2.00000i	− 1.00000i
$3$	0	0
$3$	0	0
$4$	−4.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	4.00000i	0.571429i	0.958315	+	0.285714i	$0.0922308\pi$
$7$	4.00000i	0.571429i	−0.958315	+	0.285714i	$0.907769\pi$
$8$	8.00000i	1.00000i
$9$	0	0
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	8.00000	0.571429
$15$	0	0
$16$	16.0000	1.00000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	− 44.0000i	− 1.91304i	−0.291661	−	0.956522i	$-0.594208\pi$
$23$	− 44.0000i	− 1.91304i	0.291661	−	0.956522i	$-0.405792\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	− 16.0000i	− 0.571429i
$29$	−22.0000	−0.758621	−0.379310	−	0.925270i	$-0.623839\pi$
$29$	−22.0000	−0.758621	−0.379310	+	0.925270i	$0.623839\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	− 32.0000i	− 1.00000i
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−62.0000	−1.51220	−0.756098	−	0.654459i	$-0.772896\pi$
$41$	−62.0000	−1.51220	−0.756098	+	0.654459i	$0.772896\pi$
$42$	0	0
$43$	− 76.0000i	− 1.76744i	−0.468014	−	0.883721i	$-0.655030\pi$
$43$	− 76.0000i	− 1.76744i	0.468014	−	0.883721i	$-0.344970\pi$
$44$	0	0
$45$	0	0
$46$	−88.0000	−1.91304
$47$	− 4.00000i	− 0.0851064i	−0.999094	−	0.0425532i	$-0.986451\pi$
$47$	− 4.00000i	− 0.0851064i	0.999094	−	0.0425532i	$-0.0135492\pi$
$48$	0	0
$49$	33.0000	0.673469
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	−32.0000	−0.571429
$57$	0	0
$58$	44.0000i	0.758621i
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	−58.0000	−0.950820	−0.475410	−	0.879764i	$-0.657700\pi$
$61$	−58.0000	−0.950820	−0.475410	+	0.879764i	$0.657700\pi$
$62$	0	0
$63$	0	0
$64$	−64.0000	−1.00000
$65$	0	0
$66$	0	0
$67$	− 116.000i	− 1.73134i	−0.500612	−	0.865672i	$-0.666892\pi$
$67$	− 116.000i	− 1.73134i	0.500612	−	0.865672i	$-0.333108\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	0	0
$82$	124.000i	1.51220i
$83$	76.0000i	0.915663i	0.889039	+	0.457831i	$0.151374\pi$
$83$	76.0000i	0.915663i	−0.889039	+	0.457831i	$0.848626\pi$
$84$	0	0
$85$	0	0
$86$	−152.000	−1.76744
$87$	0	0
$88$	0	0
$89$	−142.000	−1.59551	−0.797753	−	0.602985i	$-0.793978\pi$
$89$	−142.000	−1.59551	−0.797753	+	0.602985i	$0.793978\pi$
$90$	0	0
$91$	0	0
$92$	176.000i	1.91304i
$93$	0	0
$94$	−8.00000	−0.0851064
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	− 66.0000i	− 0.673469i
$99$	0	0
$100$	0	0
$101$	−122.000	−1.20792	−0.603960	−	0.797014i	$-0.706411\pi$
$101$	−122.000	−1.20792	−0.603960	+	0.797014i	$0.706411\pi$
$102$	0	0
$103$	44.0000i	0.427184i	0.976923	+	0.213592i	$0.0685164\pi$
$103$	44.0000i	0.427184i	−0.976923	+	0.213592i	$0.931484\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 124.000i	− 1.15888i	−0.815015	−	0.579439i	$-0.803272\pi$
$107$	− 124.000i	− 1.15888i	0.815015	−	0.579439i	$-0.196728\pi$
$108$	0	0
$109$	−38.0000	−0.348624	−0.174312	−	0.984690i	$-0.555770\pi$
$109$	−38.0000	−0.348624	−0.174312	+	0.984690i	$0.555770\pi$
$110$	0	0
$111$	0	0
$112$	64.0000i	0.571429i
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	88.0000	0.758621
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	121.000	1.00000
$122$	116.000i	0.950820i
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	− 236.000i	− 1.85827i	−0.369744	−	0.929134i	$-0.620554\pi$
$127$	− 236.000i	− 1.85827i	0.369744	−	0.929134i	$-0.379446\pi$
$128$	128.000i	1.00000i
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−232.000	−1.73134
$135$	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	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	278.000	1.86577	0.932886	−	0.360172i	$-0.117282\pi$
$149$	278.000	1.86577	0.932886	+	0.360172i	$0.117282\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	176.000	1.09317
$162$	0	0
$163$	164.000i	1.00613i	0.864247	+	0.503067i	$0.167795\pi$
$163$	164.000i	1.00613i	−0.864247	+	0.503067i	$0.832205\pi$
$164$	248.000	1.51220
$165$	0	0
$166$	152.000	0.915663
$167$	− 244.000i	− 1.46108i	−0.682871	−	0.730539i	$-0.739269\pi$
$167$	− 244.000i	− 1.46108i	0.682871	−	0.730539i	$-0.260731\pi$
$168$	0	0
$169$	−169.000	−1.00000
$170$	0	0
$171$	0	0
$172$	304.000i	1.76744i
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	284.000i	1.59551i
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−358.000	−1.97790	−0.988950	−	0.148248i	$-0.952637\pi$
$181$	−358.000	−1.97790	−0.988950	+	0.148248i	$0.952637\pi$
$182$	0	0
$183$	0	0
$184$	352.000	1.91304
$185$	0	0
$186$	0	0
$187$	0	0
$188$	16.0000i	0.0851064i
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	0	0
$195$	0	0
$196$	−132.000	−0.673469
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	244.000i	1.20792i
$203$	− 88.0000i	− 0.433498i
$204$	0	0
$205$	0	0
$206$	88.0000	0.427184
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	−248.000	−1.15888
$215$	0	0
$216$	0	0
$217$	0	0
$218$	76.0000i	0.348624i
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 436.000i	− 1.95516i	−0.210571	−	0.977578i	$-0.567532\pi$
$223$	− 436.000i	− 1.95516i	0.210571	−	0.977578i	$-0.432468\pi$
$224$	128.000	0.571429
$225$	0	0
$226$	0	0
$227$	356.000i	1.56828i	0.620583	+	0.784141i	$0.286896\pi$
$227$	356.000i	1.56828i	−0.620583	+	0.784141i	$0.713104\pi$
$228$	0	0
$229$	262.000	1.14410	0.572052	−	0.820217i	$-0.306147\pi$
$229$	262.000	1.14410	0.572052	+	0.820217i	$0.306147\pi$
$230$	0	0
$231$	0	0
$232$	− 176.000i	− 0.758621i
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	302.000	1.25311	0.626556	−	0.779376i	$-0.284464\pi$
$241$	302.000	1.25311	0.626556	+	0.779376i	$0.284464\pi$
$242$	− 242.000i	− 1.00000i
$243$	0	0
$244$	232.000	0.950820
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	−472.000	−1.85827
$255$	0	0
$256$	256.000	1.00000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 284.000i	− 1.07985i	−0.841714	−	0.539924i	$-0.818453\pi$
$263$	− 284.000i	− 1.07985i	0.841714	−	0.539924i	$-0.181547\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	464.000i	1.73134i
$269$	38.0000	0.141264	0.0706320	−	0.997502i	$-0.477498\pi$
$269$	38.0000	0.141264	0.0706320	+	0.997502i	$0.477498\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	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
$281$	418.000	1.48754	0.743772	−	0.668433i	$-0.233035\pi$
$281$	418.000	1.48754	0.743772	+	0.668433i	$0.233035\pi$
$282$	0	0
$283$	− 316.000i	− 1.11661i	−0.829637	−	0.558304i	$-0.811452\pi$
$283$	− 316.000i	− 1.11661i	0.829637	−	0.558304i	$-0.188548\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	− 248.000i	− 0.864111i
$288$	0	0
$289$	−289.000	−1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	− 556.000i	− 1.86577i
$299$	0	0
$300$	0	0
$301$	304.000	1.00997
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	− 596.000i	− 1.94137i	−0.240359	−	0.970684i	$-0.577265\pi$
$307$	− 596.000i	− 1.94137i	0.240359	−	0.970684i	$-0.422735\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	− 352.000i	− 1.09317i
$323$	0	0
$324$	0	0
$325$	0	0
$326$	328.000	1.00613
$327$	0	0
$328$	− 496.000i	− 1.51220i
$329$	16.0000	0.0486322
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	− 304.000i	− 0.915663i
$333$	0	0
$334$	−488.000	−1.46108
$335$	0	0
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	338.000i	1.00000i
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	328.000i	0.956268i
$344$	608.000	1.76744
$345$	0	0
$346$	0	0
$347$	116.000i	0.334294i	0.985932	+	0.167147i	$0.0534554\pi$
$347$	116.000i	0.334294i	−0.985932	+	0.167147i	$0.946545\pi$
$348$	0	0
$349$	22.0000	0.0630372	0.0315186	−	0.999503i	$-0.489966\pi$
$349$	22.0000	0.0630372	0.0315186	+	0.999503i	$0.489966\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	568.000	1.59551
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	361.000	1.00000
$362$	716.000i	1.97790i
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	724.000i	1.97275i	0.164506	+	0.986376i	$0.447397\pi$
$367$	724.000i	1.97275i	−0.164506	+	0.986376i	$0.552603\pi$
$368$	− 704.000i	− 1.91304i
$369$	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
$376$	32.0000	0.0851064
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	− 44.0000i	− 0.114883i	−0.998349	−	0.0574413i	$-0.981706\pi$
$383$	− 44.0000i	− 0.114883i	0.998349	−	0.0574413i	$-0.0182942\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−202.000	−0.519280	−0.259640	−	0.965705i	$-0.583604\pi$
$389$	−202.000	−0.519280	−0.259640	+	0.965705i	$0.583604\pi$
$390$	0	0
$391$	0	0
$392$	264.000i	0.673469i
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	478.000	1.19202	0.596010	−	0.802977i	$-0.296752\pi$
$401$	478.000	1.19202	0.596010	+	0.802977i	$0.296752\pi$
$402$	0	0
$403$	0	0
$404$	488.000	1.20792
$405$	0	0
$406$	−176.000	−0.433498
$407$	0	0
$408$	0	0
$409$	802.000	1.96088	0.980440	−	0.196818i	$-0.0630607\pi$
$409$	802.000	1.96088	0.980440	+	0.196818i	$0.0630607\pi$
$410$	0	0
$411$	0	0
$412$	− 176.000i	− 0.427184i
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	−778.000	−1.84798	−0.923990	−	0.382415i	$-0.875092\pi$
$421$	−778.000	−1.84798	−0.923990	+	0.382415i	$0.875092\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	− 232.000i	− 0.543326i
$428$	496.000i	1.15888i
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	0	0
$436$	152.000	0.348624
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	796.000i	1.79684i	0.439138	+	0.898420i	$0.355284\pi$
$443$	796.000i	1.79684i	−0.439138	+	0.898420i	$0.644716\pi$
$444$	0	0
$445$	0	0
$446$	−872.000	−1.95516
$447$	0	0
$448$	− 256.000i	− 0.571429i
$449$	398.000	0.886414	0.443207	−	0.896419i	$-0.353841\pi$
$449$	398.000	0.886414	0.443207	+	0.896419i	$0.353841\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	712.000	1.56828
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	− 524.000i	− 1.14410i
$459$	0	0
$460$	0	0
$461$	−842.000	−1.82646	−0.913232	−	0.407440i	$-0.866422\pi$
$461$	−842.000	−1.82646	−0.913232	+	0.407440i	$0.866422\pi$
$462$	0	0
$463$	764.000i	1.65011i	0.565054	+	0.825054i	$0.308855\pi$
$463$	764.000i	1.65011i	−0.565054	+	0.825054i	$0.691145\pi$
$464$	−352.000	−0.758621
$465$	0	0
$466$	0	0
$467$	− 124.000i	− 0.265525i	−0.991148	−	0.132762i	$-0.957615\pi$
$467$	− 124.000i	− 0.265525i	0.991148	−	0.132762i	$-0.0423847\pi$
$468$	0	0
$469$	464.000	0.989339
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	− 604.000i	− 1.25311i
$483$	0	0
$484$	−484.000	−1.00000
$485$	0	0
$486$	0	0
$487$	484.000i	0.993840i	0.867796	+	0.496920i	$0.165536\pi$
$487$	484.000i	0.993840i	−0.867796	+	0.496920i	$0.834464\pi$
$488$	− 464.000i	− 0.950820i
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	916.000i	1.82107i	0.413428	+	0.910537i	$0.364331\pi$
$503$	916.000i	1.82107i	−0.413428	+	0.910537i	$0.635669\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	944.000i	1.85827i
$509$	−982.000	−1.92927	−0.964637	−	0.263584i	$-0.915095\pi$
$509$	−982.000	−1.92927	−0.964637	+	0.263584i	$0.915095\pi$
$510$	0	0
$511$	0	0
$512$	− 512.000i	− 1.00000i
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−722.000	−1.38580	−0.692898	−	0.721035i	$-0.743667\pi$
$521$	−722.000	−1.38580	−0.692898	+	0.721035i	$0.743667\pi$
$522$	0	0
$523$	164.000i	0.313576i	0.987632	+	0.156788i	$0.0501139\pi$
$523$	164.000i	0.313576i	−0.987632	+	0.156788i	$0.949886\pi$
$524$	0	0
$525$	0	0
$526$	−568.000	−1.07985
$527$	0	0
$528$	0	0
$529$	−1407.00	−2.65974
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	928.000	1.73134
$537$	0	0
$538$	− 76.0000i	− 0.141264i
$539$	0	0
$540$	0	0
$541$	362.000	0.669131	0.334566	−	0.942372i	$-0.391410\pi$
$541$	362.000	0.669131	0.334566	+	0.942372i	$0.391410\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	1084.00i	1.98172i	0.134900	+	0.990859i	$0.456929\pi$
$547$	1084.00i	1.98172i	−0.134900	+	0.990859i	$0.543071\pi$
$548$	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
$561$	0	0
$562$	− 836.000i	− 1.48754i
$563$	− 1124.00i	− 1.99645i	−0.0595755	−	0.998224i	$-0.518975\pi$
$563$	− 1124.00i	− 1.99645i	0.0595755	−	0.998224i	$-0.481025\pi$
$564$	0	0
$565$	0	0
$566$	−632.000	−1.11661
$567$	0	0
$568$	0	0
$569$	158.000	0.277680	0.138840	−	0.990315i	$-0.455663\pi$
$569$	158.000	0.277680	0.138840	+	0.990315i	$0.455663\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	−496.000	−0.864111
$575$	0	0
$576$	0	0
$577$	0	0		−	1.00000i	$-0.5\pi$
$577$	0	0			1.00000i	$0.5\pi$
$578$	578.000i	1.00000i
$579$	0	0
$580$	0	0
$581$	−304.000	−0.523236
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1076.00i	1.83305i	0.399978	+	0.916525i	$0.369018\pi$
$587$	1076.00i	1.83305i	−0.399978	+	0.916525i	$0.630982\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−1112.00	−1.86577
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	−418.000	−0.695507	−0.347754	−	0.937586i	$-0.613055\pi$
$601$	−418.000	−0.695507	−0.347754	+	0.937586i	$0.613055\pi$
$602$	− 608.000i	− 1.00997i
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	964.000i	1.58814i	0.607827	+	0.794069i	$0.292041\pi$
$607$	964.000i	1.58814i	−0.607827	+	0.794069i	$0.707959\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	−1192.00	−1.94137
$615$	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	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	− 568.000i	− 0.911717i
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	1138.00	1.77535	0.887676	−	0.460470i	$-0.152319\pi$
$641$	1138.00	1.77535	0.887676	+	0.460470i	$0.152319\pi$
$642$	0	0
$643$	404.000i	0.628305i	0.949373	+	0.314152i	$0.101720\pi$
$643$	404.000i	0.628305i	−0.949373	+	0.314152i	$0.898280\pi$
$644$	−704.000	−1.09317
$645$	0	0
$646$	0	0
$647$	956.000i	1.47759i	0.673931	+	0.738794i	$0.264605\pi$
$647$	956.000i	1.47759i	−0.673931	+	0.738794i	$0.735395\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	− 656.000i	− 1.00613i
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	−992.000	−1.51220
$657$	0	0
$658$	− 32.0000i	− 0.0486322i
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	−298.000	−0.450832	−0.225416	−	0.974263i	$-0.572374\pi$
$661$	−298.000	−0.450832	−0.225416	+	0.974263i	$0.572374\pi$
$662$	0	0
$663$	0	0
$664$	−608.000	−0.915663
$665$	0	0
$666$	0	0
$667$	968.000i	1.45127i
$668$	976.000i	1.46108i
$669$	0	0
$670$	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
$676$	676.000	1.00000
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	556.000i	0.814056i	0.913416	+	0.407028i	$0.133435\pi$
$683$	556.000i	0.814056i	−0.913416	+	0.407028i	$0.866565\pi$
$684$	0	0
$685$	0	0
$686$	656.000	0.956268
$687$	0	0
$688$	− 1216.00i	− 1.76744i
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	232.000	0.334294
$695$	0	0
$696$	0	0
$697$	0	0
$698$	− 44.0000i	− 0.0630372i
$699$	0	0
$700$	0	0
$701$	−902.000	−1.28673	−0.643367	−	0.765558i	$-0.722463\pi$
$701$	−902.000	−1.28673	−0.643367	+	0.765558i	$0.722463\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	− 488.000i	− 0.690240i
$708$	0	0
$709$	−698.000	−0.984485	−0.492243	−	0.870458i	$-0.663823\pi$
$709$	−698.000	−0.984485	−0.492243	+	0.870458i	$0.663823\pi$
$710$	0	0
$711$	0	0
$712$	− 1136.00i	− 1.59551i
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	−176.000	−0.244105
$722$	− 722.000i	− 1.00000i
$723$	0	0
$724$	1432.00	1.97790
$725$	0	0
$726$	0	0
$727$	− 1436.00i	− 1.97524i	−0.156863	−	0.987620i	$-0.550138\pi$
$727$	− 1436.00i	− 1.97524i	0.156863	−	0.987620i	$-0.449862\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	1448.00	1.97275
$735$	0	0
$736$	−1408.00	−1.91304
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	− 764.000i	− 1.02826i	−0.857711	−	0.514132i	$-0.828114\pi$
$743$	− 764.000i	− 1.02826i	0.857711	−	0.514132i	$-0.171886\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	496.000	0.662216
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	− 64.0000i	− 0.0851064i
$753$	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
$761$	−242.000	−0.318003	−0.159001	−	0.987278i	$-0.550827\pi$
$761$	−242.000	−0.318003	−0.159001	+	0.987278i	$0.550827\pi$
$762$	0	0
$763$	− 152.000i	− 0.199214i
$764$	0	0
$765$	0	0
$766$	−88.0000	−0.114883
$767$	0	0
$768$	0	0
$769$	1342.00	1.74512	0.872562	−	0.488504i	$-0.162457\pi$
$769$	1342.00	1.74512	0.872562	+	0.488504i	$0.162457\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	404.000i	0.519280i
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	528.000	0.673469
$785$	0	0
$786$	0	0
$787$	− 116.000i	− 0.147395i	−0.997281	−	0.0736976i	$-0.976520\pi$
$787$	− 116.000i	− 0.147395i	0.997281	−	0.0736976i	$-0.0234800\pi$
$788$	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
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	− 956.000i	− 1.19202i
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	− 976.000i	− 1.20792i
$809$	1298.00	1.60445	0.802225	−	0.597022i	$-0.203649\pi$
$809$	1298.00	1.60445	0.802225	+	0.597022i	$0.203649\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	352.000i	0.433498i
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	− 1604.00i	− 1.96088i
$819$	0	0
$820$	0	0
$821$	−662.000	−0.806334	−0.403167	−	0.915126i	$-0.632091\pi$
$821$	−662.000	−0.806334	−0.403167	+	0.915126i	$0.632091\pi$
$822$	0	0
$823$	− 1396.00i	− 1.69623i	−0.529810	−	0.848117i	$-0.677737\pi$
$823$	− 1396.00i	− 1.69623i	0.529810	−	0.848117i	$-0.322263\pi$
$824$	−352.000	−0.427184
$825$	0	0
$826$	0	0
$827$	596.000i	0.720677i	0.932822	+	0.360339i	$0.117339\pi$
$827$	596.000i	0.720677i	−0.932822	+	0.360339i	$0.882661\pi$
$828$	0	0
$829$	−1478.00	−1.78287	−0.891435	−	0.453148i	$-0.850301\pi$
$829$	−1478.00	−1.78287	−0.891435	+	0.453148i	$0.850301\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−357.000	−0.424495
$842$	1556.00i	1.84798i
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	484.000i	0.571429i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	−464.000	−0.543326
$855$	0	0
$856$	992.000	1.15888
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	1636.00i	1.89571i	0.318698	+	0.947856i	$0.396754\pi$
$863$	1636.00i	1.89571i	−0.318698	+	0.947856i	$0.603246\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	− 304.000i	− 0.348624i
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	1618.00	1.83655	0.918275	−	0.395944i	$-0.129583\pi$
$881$	1618.00	1.83655	0.918275	+	0.395944i	$0.129583\pi$
$882$	0	0
$883$	− 1276.00i	− 1.44507i	−0.691332	−	0.722537i	$-0.742976\pi$
$883$	− 1276.00i	− 1.44507i	0.691332	−	0.722537i	$-0.257024\pi$
$884$	0	0
$885$	0	0
$886$	1592.00	1.79684
$887$	− 964.000i	− 1.08681i	−0.839471	−	0.543405i	$-0.817135\pi$
$887$	− 964.000i	− 1.08681i	0.839471	−	0.543405i	$-0.182865\pi$
$888$	0	0
$889$	944.000	1.06187
$890$	0	0
$891$	0	0
$892$	1744.00i	1.95516i
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−512.000	−0.571429
$897$	0	0
$898$	− 796.000i	− 0.886414i
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	− 1796.00i	− 1.98015i	−0.140525	−	0.990077i	$-0.544879\pi$
$907$	− 1796.00i	− 1.98015i	0.140525	−	0.990077i	$-0.455121\pi$
$908$	− 1424.00i	− 1.56828i
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−1048.00	−1.14410
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	1684.00i	1.82646i
$923$	0	0
$924$	0	0
$925$	0	0
$926$	1528.00	1.65011
$927$	0	0
$928$	704.000i	0.758621i
$929$	−562.000	−0.604952	−0.302476	−	0.953157i	$-0.597813\pi$
$929$	−562.000	−0.604952	−0.302476	+	0.953157i	$0.597813\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	−248.000	−0.265525
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	− 928.000i	− 0.989339i
$939$	0	0
$940$	0	0
$941$	118.000	0.125399	0.0626993	−	0.998032i	$-0.480029\pi$
$941$	118.000	0.125399	0.0626993	+	0.998032i	$0.480029\pi$
$942$	0	0
$943$	2728.00i	2.89290i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	− 1804.00i	− 1.90496i	−0.304596	−	0.952482i	$-0.598522\pi$
$947$	− 1804.00i	− 1.90496i	0.304596	−	0.952482i	$-0.401478\pi$
$948$	0	0
$949$	0	0
$950$	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
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	0	0
$963$	0	0
$964$	−1208.00	−1.25311
$965$	0	0
$966$	0	0
$967$	244.000i	0.252327i	0.992009	+	0.126163i	$0.0402664\pi$
$967$	244.000i	0.252327i	−0.992009	+	0.126163i	$0.959734\pi$
$968$	968.000i	1.00000i
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	968.000	0.993840
$975$	0	0
$976$	−928.000	−0.950820
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	− 284.000i	− 0.288911i	−0.989511	−	0.144456i	$-0.953857\pi$
$983$	− 284.000i	− 0.288911i	0.989511	−	0.144456i	$-0.0461431\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−3344.00	−3.38119
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.h.451.1		2
3.2	odd	2		100.3.b.c.51.2		2
4.3	odd	2	inner	900.3.c.h.451.2		2
5.2	odd	4		180.3.f.b.19.1		1
5.3	odd	4		180.3.f.a.19.1		1
5.4	even	2	inner	900.3.c.h.451.2		2
12.11	even	2		100.3.b.c.51.1		2
15.2	even	4		20.3.d.a.19.1	✓	1
15.8	even	4		20.3.d.b.19.1	yes	1
15.14	odd	2		100.3.b.c.51.1		2
20.3	even	4		180.3.f.b.19.1		1
20.7	even	4		180.3.f.a.19.1		1
20.19	odd	2	CM	900.3.c.h.451.1		2
24.5	odd	2		1600.3.b.f.1151.1		2
24.11	even	2		1600.3.b.f.1151.2		2
60.23	odd	4		20.3.d.a.19.1	✓	1
60.47	odd	4		20.3.d.b.19.1	yes	1
60.59	even	2		100.3.b.c.51.2		2
120.29	odd	2		1600.3.b.f.1151.2		2
120.53	even	4		320.3.h.b.319.1		1
120.59	even	2		1600.3.b.f.1151.1		2
120.77	even	4		320.3.h.a.319.1		1
120.83	odd	4		320.3.h.a.319.1		1
120.107	odd	4		320.3.h.b.319.1		1
240.53	even	4		1280.3.e.b.639.2		2
240.77	even	4		1280.3.e.c.639.2		2
240.83	odd	4		1280.3.e.c.639.2		2
240.107	odd	4		1280.3.e.b.639.2		2
240.173	even	4		1280.3.e.b.639.1		2
240.197	even	4		1280.3.e.c.639.1		2
240.203	odd	4		1280.3.e.c.639.1		2
240.227	odd	4		1280.3.e.b.639.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.d.a.19.1	✓	1	15.2	even	4
20.3.d.a.19.1	✓	1	60.23	odd	4
20.3.d.b.19.1	yes	1	15.8	even	4
20.3.d.b.19.1	yes	1	60.47	odd	4
100.3.b.c.51.1		2	12.11	even	2
100.3.b.c.51.1		2	15.14	odd	2
100.3.b.c.51.2		2	3.2	odd	2
100.3.b.c.51.2		2	60.59	even	2
180.3.f.a.19.1		1	5.3	odd	4
180.3.f.a.19.1		1	20.7	even	4
180.3.f.b.19.1		1	5.2	odd	4
180.3.f.b.19.1		1	20.3	even	4
320.3.h.a.319.1		1	120.77	even	4
320.3.h.a.319.1		1	120.83	odd	4
320.3.h.b.319.1		1	120.53	even	4
320.3.h.b.319.1		1	120.107	odd	4
900.3.c.h.451.1		2	1.1	even	1	trivial
900.3.c.h.451.1		2	20.19	odd	2	CM
900.3.c.h.451.2		2	4.3	odd	2	inner
900.3.c.h.451.2		2	5.4	even	2	inner
1280.3.e.b.639.1		2	240.173	even	4
1280.3.e.b.639.1		2	240.227	odd	4
1280.3.e.b.639.2		2	240.53	even	4
1280.3.e.b.639.2		2	240.107	odd	4
1280.3.e.c.639.1		2	240.197	even	4
1280.3.e.c.639.1		2	240.203	odd	4
1280.3.e.c.639.2		2	240.77	even	4
1280.3.e.c.639.2		2	240.83	odd	4
1600.3.b.f.1151.1		2	24.5	odd	2
1600.3.b.f.1151.1		2	120.59	even	2
1600.3.b.f.1151.2		2	24.11	even	2
1600.3.b.f.1151.2		2	120.29	odd	2

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -4.00000 q^{4} +4.00000i q^{7} +8.00000i q^{8} +O(q^{10})\)	\(q-2.00000i q^{2} -4.00000 q^{4} +4.00000i q^{7} +8.00000i q^{8} +8.00000 q^{14} +16.0000 q^{16} -44.0000i q^{23} -16.0000i q^{28} -22.0000 q^{29} -32.0000i q^{32} -62.0000 q^{41} -76.0000i q^{43} -88.0000 q^{46} -4.00000i q^{47} +33.0000 q^{49} -32.0000 q^{56} +44.0000i q^{58} -58.0000 q^{61} -64.0000 q^{64} -116.000i q^{67} +124.000i q^{82} +76.0000i q^{83} -152.000 q^{86} -142.000 q^{89} +176.000i q^{92} -8.00000 q^{94} -66.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4}+O(q^{10}) \) 2 * q - 8 * q^4	\( 2 q - 8 q^{4} + 16 q^{14} + 32 q^{16} - 44 q^{29} - 124 q^{41} - 176 q^{46} + 66 q^{49} - 64 q^{56} - 116 q^{61} - 128 q^{64} - 304 q^{86} - 284 q^{89} - 16 q^{94}+O(q^{100}) \) 2 * q - 8 * q^4 + 16 * q^14 + 32 * q^16 - 44 * q^29 - 124 * q^41 - 176 * q^46 + 66 * q^49 - 64 * q^56 - 116 * q^61 - 128 * q^64 - 304 * q^86 - 284 * q^89 - 16 * q^94

Introduction

L-functions

Modular forms

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Database

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