LMFDB - Embedded newform 2400.2.b.d.2351.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2400,2,Mod(2351,2400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2400, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2400.2351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2400 = 2^{5} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2400.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.1640964851$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 600)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			2351.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2400.2351
Dual form			2400.2.b.d.2351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.724745 + 1.57313i) q^{3} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})$	$q+(-0.724745 + 1.57313i) q^{3} +(-1.94949 - 2.28024i) q^{9} +6.61037i q^{11} +2.36773i q^{17} +8.34847 q^{19} +(5.00000 - 1.41421i) q^{27} +(-10.3990 - 4.79083i) q^{33} -0.460702i q^{41} -10.0000 q^{43} +7.00000 q^{49} +(-3.72474 - 1.71600i) q^{51} +(-6.05051 + 13.1332i) q^{57} +14.1421i q^{59} -14.3485 q^{67} -13.6969 q^{73} +(-1.39898 + 8.89060i) q^{81} +14.1742i q^{83} -12.7600i q^{89} +10.0000 q^{97} +(15.0732 - 12.8868i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{9} + 4 q^{19} + 20 q^{27} - 22 q^{33} - 40 q^{43} + 28 q^{49} - 10 q^{51} - 34 q^{57} - 28 q^{67} + 4 q^{73} + 14 q^{81} + 40 q^{97} + 26 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^9 + 4 * q^19 + 20 * q^27 - 22 * q^33 - 40 * q^43 + 28 * q^49 - 10 * q^51 - 34 * q^57 - 28 * q^67 + 4 * q^73 + 14 * q^81 + 40 * q^97 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1601$	$1951$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$		0			0
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$		0			0
$11$			6.61037i			1.99310i	0.0829925	+	0.996550i	$0.473552\pi$
$11$			6.61037i			1.99310i	−0.0829925	+	0.996550i	$0.526448\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			2.36773i			0.574258i	0.957892	+	0.287129i	$0.0927008\pi$
$17$			2.36773i			0.574258i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	8.34847			1.91527			0.957635	−	0.287984i	$-0.0929851\pi$
$19$	8.34847			1.91527			0.957635	+	0.287984i	$0.0929851\pi$
$20$		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
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		0			0
$33$	−10.3990	−	4.79083i	−1.81023	−	0.833976i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	0.460702i		−	0.0719495i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$		−	0.460702i		−	0.0719495i	0.999353	−	0.0359748i	$-0.0114536\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	7.00000			1.00000
$50$		0			0
$51$	−3.72474	−	1.71600i	−0.521569	−	0.240288i
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.05051	+	13.1332i	−0.801410	+	1.73954i
$58$		0			0
$59$			14.1421i			1.84115i	0.390567	+	0.920575i	$0.372279\pi$
$59$			14.1421i			1.84115i	−0.390567	+	0.920575i	$0.627721\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−14.3485			−1.75294			−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−14.3485			−1.75294			−0.876472	+	0.481452i	$0.840109\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−13.6969			−1.60311			−0.801553	−	0.597924i	$-0.795992\pi$
$73$	−13.6969			−1.60311			−0.801553	+	0.597924i	$0.795992\pi$
$74$		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
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$		0			0
$83$			14.1742i			1.55583i	0.628372	+	0.777913i	$0.283721\pi$
$83$			14.1742i			1.55583i	−0.628372	+	0.777913i	$0.716279\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	12.7600i		−	1.35256i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$		−	12.7600i		−	1.35256i	0.736644	−	0.676280i	$-0.236409\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$	15.0732	−	12.8868i	1.51492	−	1.29518i
$100$		0			0
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.70334i		−	0.454689i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$		−	4.70334i		−	0.454689i	0.973814	−	0.227345i	$-0.0730044\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			21.2453i			1.99859i	0.0375328	+	0.999295i	$0.488050\pi$
$113$			21.2453i			1.99859i	−0.0375328	+	0.999295i	$0.511950\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−32.6969			−2.97245
$122$		0			0
$123$	0.724745	+	0.333891i	0.0653480	+	0.0301060i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		0			0
$129$	7.24745	−	15.7313i	0.638102	−	1.38507i
$130$		0			0
$131$			14.1421i			1.23560i	0.786334	+	0.617802i	$0.211977\pi$
$131$			14.1421i			1.23560i	−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	16.5099i		−	1.41053i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$		−	16.5099i		−	1.41053i	0.708942	−	0.705266i	$-0.249173\pi$
$138$		0			0
$139$	−18.3485			−1.55630			−0.778148	−	0.628080i	$-0.783841\pi$
$139$	−18.3485			−1.55630			−0.778148	+	0.628080i	$0.783841\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.07321	+	11.0119i	−0.418432	+	0.908248i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	5.39898	−	4.61586i	0.436482	−	0.373170i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−23.0454			−1.80506			−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−23.0454			−1.80506			−0.902528	+	0.430632i	$0.858291\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	−16.2753	−	19.0365i	−1.24460	−	1.45576i
$172$		0			0
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−22.2474	−	10.2494i	−1.67222	−	0.770395i
$178$		0			0
$179$		−	5.68896i		−	0.425213i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$		−	5.68896i		−	0.425213i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−15.6515			−1.14455
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	3.69694			0.266111			0.133056	−	0.991109i	$-0.457521\pi$
$193$	3.69694			0.266111			0.133056	+	0.991109i	$0.457521\pi$
$194$		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		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$	10.3990	−	22.5720i	0.733487	−	1.59211i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$			55.1864i			3.81733i
$210$		0			0
$211$	−15.0454			−1.03577			−0.517884	−	0.855451i	$-0.673280\pi$
$211$	−15.0454			−1.03577			−0.517884	+	0.855451i	$0.673280\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.92679	−	21.5471i	0.670790	−	1.45602i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			2.82843i			0.187729i	0.995585	+	0.0938647i	$0.0299221\pi$
$227$			2.82843i			0.187729i	−0.995585	+	0.0938647i	$0.970078\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			5.65685i			0.370593i	0.982683	+	0.185296i	$0.0593245\pi$
$233$			5.65685i			0.370593i	−0.982683	+	0.185296i	$0.940675\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	1.69694			0.109309			0.0546547	−	0.998505i	$-0.482594\pi$
$241$	1.69694			0.109309			0.0546547	+	0.998505i	$0.482594\pi$
$242$		0			0
$243$	−12.9722	−	8.64420i	−0.832167	−	0.554526i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−22.2980	−	10.2727i	−1.41308	−	0.651007i
$250$		0			0
$251$		−	20.7525i		−	1.30989i	−0.755678	−	0.654943i	$-0.772693\pi$
$251$		−	20.7525i		−	1.30989i	0.755678	−	0.654943i	$-0.227307\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	11.3137i		−	0.705730i	−0.935674	−	0.352865i	$-0.885208\pi$
$257$		−	11.3137i		−	0.705730i	0.935674	−	0.352865i	$-0.114792\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		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
$267$	20.0732	+	9.24777i	1.22846	+	0.565954i
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			28.2843i			1.68730i	0.536895	+	0.843649i	$0.319597\pi$
$281$			28.2843i			1.68730i	−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	33.0454			1.96435			0.982173	−	0.187980i	$-0.0601941\pi$
$283$	33.0454			1.96435			0.982173	+	0.187980i	$0.0601941\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	11.3939			0.670228
$290$		0			0
$291$	−7.24745	+	15.7313i	−0.424853	+	0.922186i
$292$		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
$297$	9.34847	+	33.0518i	0.542453	+	1.91786i
$298$		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
$307$	24.3485			1.38964			0.694820	−	0.719183i	$-0.255484\pi$
$307$	24.3485			1.38964			0.694820	+	0.719183i	$0.255484\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$		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
$321$	7.39898	+	3.40872i	0.412971	+	0.190256i
$322$		0			0
$323$			19.7669i			1.09986i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	35.0454			1.92627			0.963135	−	0.269019i	$-0.0866994\pi$
$331$	35.0454			1.92627			0.963135	+	0.269019i	$0.0866994\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−22.3939			−1.21987			−0.609936	−	0.792451i	$-0.708805\pi$
$337$	−22.3939			−1.21987			−0.609936	+	0.792451i	$0.708805\pi$
$338$		0			0
$339$	−33.4217	−	15.3974i	−1.81522	−	0.836274i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	23.5809i		−	1.26589i	−0.774197	−	0.632945i	$-0.781846\pi$
$347$		−	23.5809i		−	1.26589i	0.774197	−	0.632945i	$-0.218154\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			22.6274i			1.20434i	0.798369	+	0.602168i	$0.205696\pi$
$353$			22.6274i			1.20434i	−0.798369	+	0.602168i	$0.794304\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	50.6969			2.66826
$362$		0			0
$363$	23.6969	−	51.4366i	1.24377	−	2.69972i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$	−1.05051	+	0.898133i	−0.0546874	+	0.0467550i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	11.6515			0.598499			0.299249	−	0.954175i	$-0.403264\pi$
$379$	11.6515			0.598499			0.299249	+	0.954175i	$0.403264\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	19.4949	+	22.8024i	0.990981	+	1.15911i
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−22.2474	−	10.2494i	−1.12224	−	0.517016i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			14.6028i			0.729231i	0.931158	+	0.364615i	$0.118800\pi$
$401$			14.6028i			0.729231i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−18.3939			−0.909519			−0.454759	−	0.890614i	$-0.650275\pi$
$409$	−18.3939			−0.909519			−0.454759	+	0.890614i	$0.650275\pi$
$410$		0			0
$411$	25.9722	+	11.9654i	1.28111	+	0.590211i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	13.2980	−	28.8646i	0.651204	−	1.41350i
$418$		0			0
$419$			33.9732i			1.65970i	0.557986	+	0.829851i	$0.311574\pi$
$419$			33.9732i			1.65970i	−0.557986	+	0.829851i	$0.688426\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	33.6969			1.61937			0.809686	−	0.586864i	$-0.199638\pi$
$433$	33.6969			1.61937			0.809686	+	0.586864i	$0.199638\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	−13.6464	−	15.9617i	−0.649830	−	0.760080i
$442$		0			0
$443$		−	37.7873i		−	1.79533i	−0.440681	−	0.897664i	$-0.645263\pi$
$443$		−	37.7873i		−	1.79533i	0.440681	−	0.897664i	$-0.354737\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$			39.2015i			1.85003i	0.379927	+	0.925016i	$0.375949\pi$
$449$			39.2015i			1.85003i	−0.379927	+	0.925016i	$0.624051\pi$
$450$		0			0
$451$	3.04541			0.143403
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	42.3939			1.98310			0.991551	−	0.129718i	$-0.0414071\pi$
$457$	42.3939			1.98310			0.991551	+	0.129718i	$0.0414071\pi$
$458$		0			0
$459$	3.34847	+	11.8386i	0.156293	+	0.552580i
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	31.1127i		−	1.43972i	−0.694117	−	0.719862i	$-0.744205\pi$
$467$		−	31.1127i		−	1.43972i	0.694117	−	0.719862i	$-0.255795\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	66.1037i		−	3.03945i
$474$		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
$485$		0			0
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	16.7020	−	36.2535i	0.755292	−	1.63944i
$490$		0			0
$491$			14.1421i			0.638226i	0.947717	+	0.319113i	$0.103385\pi$
$491$			14.1421i			0.638226i	−0.947717	+	0.319113i	$0.896615\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.42168	+	20.4507i	−0.418432	+	0.908248i
$508$		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
$513$	41.7423	−	11.8065i	1.84297	−	0.521271i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	27.8236i		−	1.21897i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$		−	27.8236i		−	1.21897i	0.792797	−	0.609486i	$-0.208624\pi$
$522$		0			0
$523$	3.04541			0.133166			0.0665832	−	0.997781i	$-0.478790\pi$
$523$	3.04541			0.133166			0.0665832	+	0.997781i	$0.478790\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$	32.2474	−	27.5699i	1.39942	−	1.19643i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	8.94949	+	4.12305i	0.386199	+	0.177923i
$538$		0			0
$539$			46.2726i			1.99310i
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	15.6515			0.669211			0.334606	−	0.942358i	$-0.391397\pi$
$547$	15.6515			0.669211			0.334606	+	0.942358i	$0.391397\pi$
$548$		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
$561$	11.3434	−	24.6219i	0.478917	−	1.03954i
$562$		0			0
$563$			36.7696i			1.54965i	0.632175	+	0.774826i	$0.282163\pi$
$563$			36.7696i			1.54965i	−0.632175	+	0.774826i	$0.717837\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	25.0594i		−	1.05054i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$		−	25.0594i		−	1.05054i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		0			0
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.3939			0.515964			0.257982	−	0.966150i	$-0.416942\pi$
$577$	12.3939			0.515964			0.257982	+	0.966150i	$0.416942\pi$
$578$		0			0
$579$	−2.67934	+	5.81577i	−0.111349	+	0.241695i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$			18.8455i			0.777836i	0.921272	+	0.388918i	$0.127151\pi$
$587$			18.8455i			0.777836i	−0.921272	+	0.388918i	$0.872849\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			7.03896i			0.289055i	0.989501	+	0.144528i	$0.0461663\pi$
$593$			7.03896i			0.289055i	−0.989501	+	0.144528i	$0.953834\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	8.30306			0.338689			0.169344	−	0.985557i	$-0.445835\pi$
$601$	8.30306			0.338689			0.169344	+	0.985557i	$0.445835\pi$
$602$		0			0
$603$	27.9722	+	32.7179i	1.13912	+	1.33238i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			39.5980i			1.59415i	0.603877	+	0.797077i	$0.293622\pi$
$617$			39.5980i			1.59415i	−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−86.8156	−	39.9961i	−3.46708	−	1.59729i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	10.9041	−	23.6684i	0.433398	−	0.940735i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$			28.2843i			1.11716i	0.829450	+	0.558581i	$0.188654\pi$
$641$			28.2843i			1.11716i	−0.829450	+	0.558581i	$0.811346\pi$
$642$		0			0
$643$	50.0000			1.97181			0.985904	−	0.167313i	$-0.0535092\pi$
$643$	50.0000			1.97181			0.985904	+	0.167313i	$0.0535092\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$	−93.4847			−3.66960
$650$		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
$657$	26.7020	+	31.2323i	1.04175	+	1.21849i
$658$		0			0
$659$		−	8.45317i		−	0.329289i	−0.986353	−	0.164644i	$-0.947352\pi$
$659$		−	8.45317i		−	0.329289i	0.986353	−	0.164644i	$-0.0526477\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	10.0000			0.385472			0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000			0.385472			0.192736	+	0.981251i	$0.438264\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−4.44949	−	2.04989i	−0.170505	−	0.0785519i
$682$		0			0
$683$			51.9294i			1.98702i	0.113728	+	0.993512i	$0.463721\pi$
$683$			51.9294i			1.98702i	−0.113728	+	0.993512i	$0.536279\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−45.0454			−1.71361			−0.856804	−	0.515642i	$-0.827553\pi$
$691$	−45.0454			−1.71361			−0.856804	+	0.515642i	$0.827553\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.09082			0.0413176
$698$		0			0
$699$	−8.89898	−	4.09978i	−0.336590	−	0.155068i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		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
$723$	−1.22985	+	2.66951i	−0.0457385	+	0.0992801i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$		−	23.6773i		−	0.875735i
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	94.8486i		−	3.49379i
$738$		0			0
$739$	34.0000			1.25071			0.625355	−	0.780340i	$-0.284954\pi$
$739$	34.0000			1.25071			0.625355	+	0.780340i	$0.284954\pi$
$740$		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
$747$	32.3207	−	27.6325i	1.18255	−	1.01102i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$	32.6464	+	15.0403i	1.18970	+	0.548098i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	52.4222i		−	1.90030i	−0.311787	−	0.950152i	$-0.600927\pi$
$761$		−	52.4222i		−	1.90030i	0.311787	−	0.950152i	$-0.399073\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	55.0908			1.98663			0.993313	−	0.115454i	$-0.0368323\pi$
$769$	55.0908			1.98663			0.993313	+	0.115454i	$0.0368323\pi$
$770$		0			0
$771$	17.7980	+	8.19955i	0.640978	+	0.295300i
$772$		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
$778$		0			0
$779$		−	3.84616i		−	0.137803i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	50.0000			1.78231			0.891154	−	0.453701i	$-0.149897\pi$
$787$	50.0000			1.78231			0.891154	+	0.453701i	$0.149897\pi$
$788$		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
$801$	−29.0959	+	24.8755i	−1.02805	+	0.878934i
$802$		0			0
$803$		−	90.5418i		−	3.19515i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	56.5685i		−	1.98884i	−0.105474	−	0.994422i	$-0.533636\pi$
$809$		−	56.5685i		−	1.98884i	0.105474	−	0.994422i	$-0.466364\pi$
$810$		0			0
$811$	−38.0000			−1.33436			−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000			−1.33436			−0.667180	+	0.744896i	$0.732499\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−83.4847			−2.92076
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0			−	1.00000i	$-0.5\pi$
$821$		0			0				1.00000i	$0.5\pi$
$822$		0			0
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	56.6649i		−	1.97043i	−0.171321	−	0.985215i	$-0.554804\pi$
$827$		−	56.6649i		−	1.97043i	0.171321	−	0.985215i	$-0.445196\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			16.5741i			0.574258i
$834$		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
$841$	−29.0000			−1.00000
$842$		0			0
$843$	−44.4949	−	20.4989i	−1.53249	−	0.706019i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−23.9495	+	51.9848i	−0.821944	+	1.78411i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			35.4517i			1.21101i	0.795843	+	0.605503i	$0.207028\pi$
$857$			35.4517i			1.21101i	−0.795843	+	0.605503i	$0.792972\pi$
$858$		0			0
$859$	−21.6515			−0.738741			−0.369370	−	0.929282i	$-0.620427\pi$
$859$	−21.6515			−0.738741			−0.369370	+	0.929282i	$0.620427\pi$
$860$		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
$867$	−8.25765	+	17.9241i	−0.280445	+	0.608733i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−19.4949	−	22.8024i	−0.659802	−	0.771744i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	56.5685i		−	1.90584i	−0.303218	−	0.952921i	$-0.598061\pi$
$881$		−	56.5685i		−	1.90584i	0.303218	−	0.952921i	$-0.401939\pi$
$882$		0			0
$883$	50.4393			1.69742			0.848709	−	0.528861i	$-0.177381\pi$
$883$	50.4393			1.69742			0.848709	+	0.528861i	$0.177381\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−58.7702	−	9.24777i	−1.96887	−	0.309812i
$892$		0			0
$893$		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
$907$	−10.0000			−0.332045			−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000			−0.332045			−0.166022	+	0.986122i	$0.553092\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−93.6969			−3.10092
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−17.6464	+	38.3034i	−0.581470	+	1.26214i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$			28.2843i			0.927977i	0.885841	+	0.463988i	$0.153582\pi$
$929$			28.2843i			0.927977i	−0.885841	+	0.463988i	$0.846418\pi$
$930$		0			0
$931$	58.4393			1.91527
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−61.0908			−1.99575			−0.997875	−	0.0651578i	$-0.979245\pi$
$937$	−61.0908			−1.99575			−0.997875	+	0.0651578i	$0.979245\pi$
$938$		0			0
$939$	−7.24745	+	15.7313i	−0.236512	+	0.513372i
$940$		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
$947$			53.7401i			1.74632i	0.487435	+	0.873160i	$0.337933\pi$
$947$			53.7401i			1.74632i	−0.487435	+	0.873160i	$0.662067\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$			59.0005i			1.91121i	0.294646	+	0.955607i	$0.404798\pi$
$953$			59.0005i			1.91121i	−0.294646	+	0.955607i	$0.595202\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	31.0000			1.00000
$962$		0			0
$963$	−10.7247	+	9.16912i	−0.345600	+	0.295471i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$		0			0
$969$	−31.0959	−	14.3259i	−0.998945	−	0.460216i
$970$		0			0
$971$			31.2090i			1.00155i	0.865579	+	0.500773i	$0.166951\pi$
$971$			31.2090i			1.00155i	−0.865579	+	0.500773i	$0.833049\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$			25.9165i			0.829144i	0.910017	+	0.414572i	$0.136069\pi$
$977$			25.9165i			0.829144i	−0.910017	+	0.414572i	$0.863931\pi$
$978$		0			0
$979$	84.3485			2.69579
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	−25.3990	+	55.1311i	−0.806012	+	1.74953i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2400.2.b.d.2351.2		4
3.2	odd	2	inner	2400.2.b.d.2351.1		4
4.3	odd	2		600.2.b.b.251.2	✓	4
5.2	odd	4		2400.2.m.b.1199.8		8
5.3	odd	4		2400.2.m.b.1199.1		8
5.4	even	2		2400.2.b.b.2351.3		4
8.3	odd	2	CM	2400.2.b.d.2351.2		4
8.5	even	2		600.2.b.b.251.2	✓	4
12.11	even	2		600.2.b.b.251.4	yes	4
15.2	even	4		2400.2.m.b.1199.2		8
15.8	even	4		2400.2.m.b.1199.7		8
15.14	odd	2		2400.2.b.b.2351.4		4
20.3	even	4		600.2.m.b.299.4		8
20.7	even	4		600.2.m.b.299.5		8
20.19	odd	2		600.2.b.d.251.3	yes	4
24.5	odd	2		600.2.b.b.251.4	yes	4
24.11	even	2	inner	2400.2.b.d.2351.1		4
40.3	even	4		2400.2.m.b.1199.1		8
40.13	odd	4		600.2.m.b.299.4		8
40.19	odd	2		2400.2.b.b.2351.3		4
40.27	even	4		2400.2.m.b.1199.8		8
40.29	even	2		600.2.b.d.251.3	yes	4
40.37	odd	4		600.2.m.b.299.5		8
60.23	odd	4		600.2.m.b.299.6		8
60.47	odd	4		600.2.m.b.299.3		8
60.59	even	2		600.2.b.d.251.1	yes	4
120.29	odd	2		600.2.b.d.251.1	yes	4
120.53	even	4		600.2.m.b.299.6		8
120.59	even	2		2400.2.b.b.2351.4		4
120.77	even	4		600.2.m.b.299.3		8
120.83	odd	4		2400.2.m.b.1199.7		8
120.107	odd	4		2400.2.m.b.1199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.b.251.2	✓	4	4.3	odd	2
600.2.b.b.251.2	✓	4	8.5	even	2
600.2.b.b.251.4	yes	4	12.11	even	2
600.2.b.b.251.4	yes	4	24.5	odd	2
600.2.b.d.251.1	yes	4	60.59	even	2
600.2.b.d.251.1	yes	4	120.29	odd	2
600.2.b.d.251.3	yes	4	20.19	odd	2
600.2.b.d.251.3	yes	4	40.29	even	2
600.2.m.b.299.3		8	60.47	odd	4
600.2.m.b.299.3		8	120.77	even	4
600.2.m.b.299.4		8	20.3	even	4
600.2.m.b.299.4		8	40.13	odd	4
600.2.m.b.299.5		8	20.7	even	4
600.2.m.b.299.5		8	40.37	odd	4
600.2.m.b.299.6		8	60.23	odd	4
600.2.m.b.299.6		8	120.53	even	4
2400.2.b.b.2351.3		4	5.4	even	2
2400.2.b.b.2351.3		4	40.19	odd	2
2400.2.b.b.2351.4		4	15.14	odd	2
2400.2.b.b.2351.4		4	120.59	even	2
2400.2.b.d.2351.1		4	3.2	odd	2	inner
2400.2.b.d.2351.1		4	24.11	even	2	inner
2400.2.b.d.2351.2		4	1.1	even	1	trivial
2400.2.b.d.2351.2		4	8.3	odd	2	CM
2400.2.m.b.1199.1		8	5.3	odd	4
2400.2.m.b.1199.1		8	40.3	even	4
2400.2.m.b.1199.2		8	15.2	even	4
2400.2.m.b.1199.2		8	120.107	odd	4
2400.2.m.b.1199.7		8	15.8	even	4
2400.2.m.b.1199.7		8	120.83	odd	4
2400.2.m.b.1199.8		8	5.2	odd	4
2400.2.m.b.1199.8		8	40.27	even	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:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.724745 + 1.57313i) q^{3} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(-0.724745 + 1.57313i) q^{3} +(-1.94949 - 2.28024i) q^{9} +6.61037i q^{11} +2.36773i q^{17} +8.34847 q^{19} +(5.00000 - 1.41421i) q^{27} +(-10.3990 - 4.79083i) q^{33} -0.460702i q^{41} -10.0000 q^{43} +7.00000 q^{49} +(-3.72474 - 1.71600i) q^{51} +(-6.05051 + 13.1332i) q^{57} +14.1421i q^{59} -14.3485 q^{67} -13.6969 q^{73} +(-1.39898 + 8.89060i) q^{81} +14.1742i q^{83} -12.7600i q^{89} +10.0000 q^{97} +(15.0732 - 12.8868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{9} + 4 q^{19} + 20 q^{27} - 22 q^{33} - 40 q^{43} + 28 q^{49} - 10 q^{51} - 34 q^{57} - 28 q^{67} + 4 q^{73} + 14 q^{81} + 40 q^{97} + 26 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^9 + 4 * q^19 + 20 * q^27 - 22 * q^33 - 40 * q^43 + 28 * q^49 - 10 * q^51 - 34 * q^57 - 28 * q^67 + 4 * q^73 + 14 * q^81 + 40 * q^97 + 26 * q^99

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