LMFDB - Embedded newform 1800.2.d.n.1549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(1549,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.d (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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1549.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1800.1549
Dual form			1800.2.d.n.1549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.00000 q^{4} -2.00000i q^{7} -2.82843 q^{8} +O(q^{10})$	$q-1.41421 q^{2} +2.00000 q^{4} -2.00000i q^{7} -2.82843 q^{8} +5.65685i q^{11} +2.82843i q^{14} +4.00000 q^{16} -8.00000i q^{22} -4.00000i q^{28} +2.82843i q^{29} -10.0000 q^{31} -5.65685 q^{32} +11.3137i q^{44} +3.00000 q^{49} -14.1421 q^{53} +5.65685i q^{56} -4.00000i q^{58} +11.3137i q^{59} +14.1421 q^{62} +8.00000 q^{64} +14.0000i q^{73} +11.3137 q^{77} +10.0000 q^{79} -5.65685 q^{83} -16.0000i q^{88} -2.00000i q^{97} -4.24264 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4}+O(q^{10}) $ 4 * q + 8 * q^4	$ 4 q + 8 q^{4} + 16 q^{16} - 40 q^{31} + 12 q^{49} + 32 q^{64} + 40 q^{79}+O(q^{100}) $ 4 * q + 8 * q^4 + 16 * q^16 - 40 * q^31 + 12 * q^49 + 32 * q^64 + 40 * q^79

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−1.41421	−1.00000
$2$	−1.41421	−1.00000
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	− 2.00000i	− 0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$	− 2.00000i	− 0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−2.82843	−1.00000
$9$	0	0
$10$	0	0
$11$	5.65685i	1.70561i	0.522233	+	0.852803i	$0.325099\pi$
$11$	5.65685i	1.70561i	−0.522233	+	0.852803i	$0.674901\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	2.82843i	0.755929i
$15$	0	0
$16$	4.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	− 8.00000i	− 1.70561i
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	− 4.00000i	− 0.755929i
$29$	2.82843i	0.525226i	0.964901	+	0.262613i	$0.0845842\pi$
$29$	2.82843i	0.525226i	−0.964901	+	0.262613i	$0.915416\pi$
$30$	0	0
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	−5.65685	−1.00000
$33$	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
$41$	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	$0.5\pi$
$44$	11.3137i	1.70561i
$45$	0	0
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	3.00000	0.428571
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−14.1421	−1.94257	−0.971286	−	0.237915i	$-0.923536\pi$
$53$	−14.1421	−1.94257	−0.971286	+	0.237915i	$0.923536\pi$
$54$	0	0
$55$	0	0
$56$	5.65685i	0.755929i
$57$	0	0
$58$	− 4.00000i	− 0.525226i
$59$	11.3137i	1.47292i	0.676481	+	0.736460i	$0.263504\pi$
$59$	11.3137i	1.47292i	−0.676481	+	0.736460i	$0.736496\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	14.1421	1.79605
$63$	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	$0.5\pi$
$68$	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
$73$	14.0000i	1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$	14.0000i	1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	11.3137	1.28932
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	−5.65685	−0.620920	−0.310460	−	0.950586i	$-0.600483\pi$
$83$	−5.65685	−0.620920	−0.310460	+	0.950586i	$0.600483\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	− 16.0000i	− 1.70561i
$89$	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
$97$	− 2.00000i	− 0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$	− 2.00000i	− 0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$	−4.24264	−0.428571
$99$	0	0
$100$	0	0
$101$	− 19.7990i	− 1.97007i	−0.172345	−	0.985037i	$-0.555135\pi$
$101$	− 19.7990i	− 1.97007i	0.172345	−	0.985037i	$-0.444865\pi$
$102$	0	0
$103$	14.0000i	1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$	14.0000i	1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	0	0
$105$	0	0
$106$	20.0000	1.94257
$107$	−11.3137	−1.09374	−0.546869	−	0.837218i	$-0.684180\pi$
$107$	−11.3137	−1.09374	−0.546869	+	0.837218i	$0.684180\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	− 8.00000i	− 0.755929i
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	5.65685i	0.525226i
$117$	0	0
$118$	− 16.0000i	− 1.47292i
$119$	0	0
$120$	0	0
$121$	−21.0000	−1.90909
$122$	0	0
$123$	0	0
$124$	−20.0000	−1.79605
$125$	0	0
$126$	0	0
$127$	22.0000i	1.95218i	0.217357	+	0.976092i	$0.430256\pi$
$127$	22.0000i	1.95218i	−0.217357	+	0.976092i	$0.569744\pi$
$128$	−11.3137	−1.00000
$129$	0	0
$130$	0	0
$131$	22.6274i	1.97697i	0.151330	+	0.988483i	$0.451644\pi$
$131$	22.6274i	1.97697i	−0.151330	+	0.988483i	$0.548356\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	− 19.7990i	− 1.63858i
$147$	0	0
$148$	0	0
$149$	2.82843i	0.231714i	0.993266	+	0.115857i	$0.0369614\pi$
$149$	2.82843i	0.231714i	−0.993266	+	0.115857i	$0.963039\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	0	0
$153$	0	0
$154$	−16.0000	−1.28932
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	−14.1421	−1.12509
$159$	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
$166$	8.00000	0.620920
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	19.7990	1.50529	0.752645	−	0.658427i	$-0.228778\pi$
$173$	19.7990	1.50529	0.752645	+	0.658427i	$0.228778\pi$
$174$	0	0
$175$	0	0
$176$	22.6274i	1.70561i
$177$	0	0
$178$	0	0
$179$	11.3137i	0.845626i	0.906217	+	0.422813i	$0.138957\pi$
$179$	11.3137i	0.845626i	−0.906217	+	0.422813i	$0.861043\pi$
$180$	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
$187$	0	0
$188$	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
$193$	26.0000i	1.87152i	0.352636	+	0.935760i	$0.385285\pi$
$193$	26.0000i	1.87152i	−0.352636	+	0.935760i	$0.614715\pi$
$194$	2.82843i	0.203069i
$195$	0	0
$196$	6.00000	0.428571
$197$	14.1421	1.00759	0.503793	−	0.863825i	$-0.331938\pi$
$197$	14.1421	1.00759	0.503793	+	0.863825i	$0.331938\pi$
$198$	0	0
$199$	−14.0000	−0.992434	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000	−0.992434	−0.496217	+	0.868199i	$0.665278\pi$
$200$	0	0
$201$	0	0
$202$	28.0000i	1.97007i
$203$	5.65685	0.397033
$204$	0	0
$205$	0	0
$206$	− 19.7990i	− 1.37946i
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	−28.2843	−1.94257
$213$	0	0
$214$	16.0000	1.09374
$215$	0	0
$216$	0	0
$217$	20.0000i	1.35769i
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	26.0000i	1.74109i	0.492090	+	0.870544i	$0.336233\pi$
$223$	26.0000i	1.74109i	−0.492090	+	0.870544i	$0.663767\pi$
$224$	11.3137i	0.755929i
$225$	0	0
$226$	0	0
$227$	−28.2843	−1.87729	−0.938647	−	0.344881i	$-0.887919\pi$
$227$	−28.2843	−1.87729	−0.938647	+	0.344881i	$0.887919\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	− 8.00000i	− 0.525226i
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	22.6274i	1.47292i
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	29.6985	1.90909
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	28.2843	1.79605
$249$	0	0
$250$	0	0
$251$	5.65685i	0.357057i	0.983935	+	0.178529i	$0.0571337\pi$
$251$	5.65685i	0.357057i	−0.983935	+	0.178529i	$0.942866\pi$
$252$	0	0
$253$	0	0
$254$	− 31.1127i	− 1.95218i
$255$	0	0
$256$	16.0000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	− 32.0000i	− 1.97697i
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	− 31.1127i	− 1.89697i	−0.316815	−	0.948487i	$-0.602613\pi$
$269$	− 31.1127i	− 1.89697i	0.316815	−	0.948487i	$-0.397387\pi$
$270$	0	0
$271$	−22.0000	−1.33640	−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000	−1.33640	−0.668202	+	0.743980i	$0.732936\pi$
$272$	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
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.0000	1.00000
$290$	0	0
$291$	0	0
$292$	28.0000i	1.63858i
$293$	−14.1421	−0.826192	−0.413096	−	0.910687i	$-0.635553\pi$
$293$	−14.1421	−0.826192	−0.413096	+	0.910687i	$0.635553\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	− 4.00000i	− 0.231714i
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−2.82843	−0.162758
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	22.6274	1.28932
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	− 34.0000i	− 1.92179i	−0.276907	−	0.960897i	$-0.589309\pi$
$313$	− 34.0000i	− 1.92179i	0.276907	−	0.960897i	$-0.410691\pi$
$314$	0	0
$315$	0	0
$316$	20.0000	1.12509
$317$	31.1127	1.74746	0.873732	−	0.486408i	$-0.161693\pi$
$317$	31.1127	1.74746	0.873732	+	0.486408i	$0.161693\pi$
$318$	0	0
$319$	−16.0000	−0.895828
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	−11.3137	−0.620920
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	22.0000i	1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$	22.0000i	1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$	18.3848	1.00000
$339$	0	0
$340$	0	0
$341$	− 56.5685i	− 3.06336i
$342$	0	0
$343$	− 20.0000i	− 1.07990i
$344$	0	0
$345$	0	0
$346$	−28.0000	−1.50529
$347$	−28.2843	−1.51838	−0.759190	−	0.650870i	$-0.774404\pi$
$347$	−28.2843	−1.51838	−0.759190	+	0.650870i	$0.774404\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	− 32.0000i	− 1.70561i
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	− 16.0000i	− 0.845626i
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	− 38.0000i	− 1.98358i	−0.127862	−	0.991792i	$-0.540812\pi$
$367$	− 38.0000i	− 1.98358i	0.127862	−	0.991792i	$-0.459188\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	28.2843i	1.46845i
$372$	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
$377$	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
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	− 36.7696i	− 1.87152i
$387$	0	0
$388$	− 4.00000i	− 0.203069i
$389$	− 31.1127i	− 1.57748i	−0.614729	−	0.788738i	$-0.710735\pi$
$389$	− 31.1127i	− 1.57748i	0.614729	−	0.788738i	$-0.289265\pi$
$390$	0	0
$391$	0	0
$392$	−8.48528	−0.428571
$393$	0	0
$394$	−20.0000	−1.00759
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	19.7990	0.992434
$399$	0	0
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	− 39.5980i	− 1.97007i
$405$	0	0
$406$	−8.00000	−0.397033
$407$	0	0
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	0	0
$411$	0	0
$412$	28.0000i	1.37946i
$413$	22.6274	1.11342
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	− 39.5980i	− 1.93449i	−0.253849	−	0.967244i	$-0.581697\pi$
$419$	− 39.5980i	− 1.93449i	0.253849	−	0.967244i	$-0.418303\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	40.0000	1.94257
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−22.6274	−1.09374
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	14.0000i	0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$	14.0000i	0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	− 28.2843i	− 1.35769i
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	34.0000	1.62273	0.811366	−	0.584539i	$-0.198725\pi$
$439$	34.0000	1.62273	0.811366	+	0.584539i	$0.198725\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	28.2843	1.34383	0.671913	−	0.740630i	$-0.265473\pi$
$443$	28.2843	1.34383	0.671913	+	0.740630i	$0.265473\pi$
$444$	0	0
$445$	0	0
$446$	− 36.7696i	− 1.74109i
$447$	0	0
$448$	− 16.0000i	− 0.755929i
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	40.0000	1.87729
$455$	0	0
$456$	0	0
$457$	− 38.0000i	− 1.77757i	−0.458329	−	0.888783i	$-0.651552\pi$
$457$	− 38.0000i	− 1.77757i	0.458329	−	0.888783i	$-0.348448\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	− 19.7990i	− 0.922131i	−0.887366	−	0.461065i	$-0.847467\pi$
$461$	− 19.7990i	− 0.922131i	0.887366	−	0.461065i	$-0.152533\pi$
$462$	0	0
$463$	26.0000i	1.20832i	0.796862	+	0.604161i	$0.206492\pi$
$463$	26.0000i	1.20832i	−0.796862	+	0.604161i	$0.793508\pi$
$464$	11.3137i	0.525226i
$465$	0	0
$466$	0	0
$467$	39.5980	1.83238	0.916188	−	0.400749i	$-0.131250\pi$
$467$	39.5980	1.83238	0.916188	+	0.400749i	$0.131250\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	− 32.0000i	− 1.47292i
$473$	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
$482$	14.1421	0.644157
$483$	0	0
$484$	−42.0000	−1.90909
$485$	0	0
$486$	0	0
$487$	− 2.00000i	− 0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$	− 2.00000i	− 0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	22.6274i	1.02116i	0.859830	+	0.510581i	$0.170569\pi$
$491$	22.6274i	1.02116i	−0.859830	+	0.510581i	$0.829431\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−40.0000	−1.79605
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	0	0
$502$	− 8.00000i	− 0.357057i
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	44.0000i	1.95218i
$509$	2.82843i	0.125368i	0.998033	+	0.0626839i	$0.0199660\pi$
$509$	2.82843i	0.125368i	−0.998033	+	0.0626839i	$0.980034\pi$
$510$	0	0
$511$	28.0000	1.23865
$512$	−22.6274	−1.00000
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	45.2548i	1.97697i
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	23.0000	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	44.0000i	1.89697i
$539$	16.9706i	0.730974i
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	31.1127	1.33640
$543$	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
$553$	− 20.0000i	− 0.850487i
$554$	0	0
$555$	0	0
$556$	0	0
$557$	14.1421	0.599222	0.299611	−	0.954062i	$-0.403143\pi$
$557$	14.1421	0.599222	0.299611	+	0.954062i	$0.403143\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	28.2843	1.19204	0.596020	−	0.802970i	$-0.296748\pi$
$563$	28.2843	1.19204	0.596020	+	0.802970i	$0.296748\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	− 38.0000i	− 1.58196i	−0.611842	−	0.790980i	$-0.709571\pi$
$577$	− 38.0000i	− 1.58196i	0.611842	−	0.790980i	$-0.290429\pi$
$578$	−24.0416	−1.00000
$579$	0	0
$580$	0	0
$581$	11.3137i	0.469372i
$582$	0	0
$583$	− 80.0000i	− 3.31326i
$584$	− 39.5980i	− 1.63858i
$585$	0	0
$586$	20.0000	0.826192
$587$	−45.2548	−1.86787	−0.933933	−	0.357447i	$-0.883647\pi$
$587$	−45.2548	−1.86787	−0.933933	+	0.357447i	$0.883647\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	5.65685i	0.231714i
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	0	0
$603$	0	0
$604$	4.00000	0.162758
$605$	0	0
$606$	0	0
$607$	22.0000i	0.892952i	0.894795	+	0.446476i	$0.147321\pi$
$607$	22.0000i	0.892952i	−0.894795	+	0.446476i	$0.852679\pi$
$608$	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	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	−32.0000	−1.28932
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	48.0833i	1.92179i
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	50.0000	1.99047	0.995234	−	0.0975126i	$-0.0310886\pi$
$631$	50.0000	1.99047	0.995234	+	0.0975126i	$0.0310886\pi$
$632$	−28.2843	−1.12509
$633$	0	0
$634$	−44.0000	−1.74746
$635$	0	0
$636$	0	0
$637$	0	0
$638$	22.6274	0.895828
$639$	0	0
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	0	0		−	1.00000i	$-0.5\pi$
$643$	0	0			1.00000i	$0.5\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	0	0
$649$	−64.0000	−2.51222
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−48.0833	−1.88164	−0.940822	−	0.338902i	$-0.889945\pi$
$653$	−48.0833	−1.88164	−0.940822	+	0.338902i	$0.889945\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	45.2548i	1.76288i	0.472298	+	0.881439i	$0.343425\pi$
$659$	45.2548i	1.76288i	−0.472298	+	0.881439i	$0.656575\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	16.0000	0.620920
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	− 34.0000i	− 1.31060i	−0.755367	−	0.655302i	$-0.772541\pi$
$673$	− 34.0000i	− 1.31060i	0.755367	−	0.655302i	$-0.227459\pi$
$674$	− 31.1127i	− 1.19842i
$675$	0	0
$676$	−26.0000	−1.00000
$677$	−2.82843	−0.108705	−0.0543526	−	0.998522i	$-0.517310\pi$
$677$	−2.82843	−0.108705	−0.0543526	+	0.998522i	$0.517310\pi$
$678$	0	0
$679$	−4.00000	−0.153506
$680$	0	0
$681$	0	0
$682$	80.0000i	3.06336i
$683$	−5.65685	−0.216454	−0.108227	−	0.994126i	$-0.534517\pi$
$683$	−5.65685	−0.216454	−0.108227	+	0.994126i	$0.534517\pi$
$684$	0	0
$685$	0	0
$686$	28.2843i	1.07990i
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	39.5980	1.50529
$693$	0	0
$694$	40.0000	1.51838
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	− 36.7696i	− 1.38877i	−0.719605	−	0.694383i	$-0.755677\pi$
$701$	− 36.7696i	− 1.38877i	0.719605	−	0.694383i	$-0.244323\pi$
$702$	0	0
$703$	0	0
$704$	45.2548i	1.70561i
$705$	0	0
$706$	0	0
$707$	−39.5980	−1.48924
$708$	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
$716$	22.6274i	0.845626i
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	28.0000	1.04277
$722$	−26.8701	−1.00000
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	− 2.00000i	− 0.0741759i	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$	− 2.00000i	− 0.0741759i	0.999312	−	0.0370879i	$-0.0118082\pi$
$728$	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	$0.5\pi$
$734$	53.7401i	1.98358i
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	− 40.0000i	− 1.46845i
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	22.6274i	0.826788i
$750$	0	0
$751$	−10.0000	−0.364905	−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000	−0.364905	−0.182453	+	0.983215i	$0.558404\pi$
$752$	0	0
$753$	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
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	0	0
$772$	52.0000i	1.87152i
$773$	19.7990	0.712120	0.356060	−	0.934463i	$-0.384120\pi$
$773$	19.7990	0.712120	0.356060	+	0.934463i	$0.384120\pi$
$774$	0	0
$775$	0	0
$776$	5.65685i	0.203069i
$777$	0	0
$778$	44.0000i	1.57748i
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	12.0000	0.428571
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	28.2843	1.00759
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	−28.0000	−0.992434
$797$	−53.7401	−1.90357	−0.951786	−	0.306762i	$-0.900754\pi$
$797$	−53.7401	−1.90357	−0.951786	+	0.306762i	$0.900754\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−79.1960	−2.79476
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	56.0000i	1.97007i
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	11.3137	0.397033
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	−14.1421	−0.494468
$819$	0	0
$820$	0	0
$821$	48.0833i	1.67812i	0.544041	+	0.839059i	$0.316894\pi$
$821$	48.0833i	1.67812i	−0.544041	+	0.839059i	$0.683106\pi$
$822$	0	0
$823$	− 46.0000i	− 1.60346i	−0.597687	−	0.801730i	$-0.703913\pi$
$823$	− 46.0000i	− 1.60346i	0.597687	−	0.801730i	$-0.296087\pi$
$824$	− 39.5980i	− 1.37946i
$825$	0	0
$826$	−32.0000	−1.11342
$827$	56.5685	1.96708	0.983540	−	0.180688i	$-0.0578324\pi$
$827$	56.5685	1.96708	0.983540	+	0.180688i	$0.0578324\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	56.0000i	1.93449i
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	21.0000	0.724138
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	42.0000i	1.44314i
$848$	−56.5685	−1.94257
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	32.0000	1.09374
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	− 19.7990i	− 0.672797i
$867$	0	0
$868$	40.0000i	1.35769i
$869$	56.5685i	1.91896i
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	−48.0833	−1.62273
$879$	0	0
$880$	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	$0.5\pi$
$884$	0	0
$885$	0	0
$886$	−40.0000	−1.34383
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	44.0000	1.47571
$890$	0	0
$891$	0	0
$892$	52.0000i	1.74109i
$893$	0	0
$894$	0	0
$895$	0	0
$896$	22.6274i	0.755929i
$897$	0	0
$898$	0	0
$899$	− 28.2843i	− 0.943333i
$900$	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	$0.5\pi$
$908$	−56.5685	−1.87729
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	− 32.0000i	− 1.05905i
$914$	53.7401i	1.77757i
$915$	0	0
$916$	0	0
$917$	45.2548	1.49445
$918$	0	0
$919$	−50.0000	−1.64935	−0.824674	−	0.565608i	$-0.808641\pi$
$919$	−50.0000	−1.64935	−0.824674	+	0.565608i	$0.808641\pi$
$920$	0	0
$921$	0	0
$922$	28.0000i	0.922131i
$923$	0	0
$924$	0	0
$925$	0	0
$926$	− 36.7696i	− 1.20832i
$927$	0	0
$928$	− 16.0000i	− 0.525226i
$929$	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
$934$	−56.0000	−1.83238
$935$	0	0
$936$	0	0
$937$	58.0000i	1.89478i	0.320085	+	0.947389i	$0.396288\pi$
$937$	58.0000i	1.89478i	−0.320085	+	0.947389i	$0.603712\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	48.0833i	1.56747i	0.621096	+	0.783735i	$0.286688\pi$
$941$	48.0833i	1.56747i	−0.621096	+	0.783735i	$0.713312\pi$
$942$	0	0
$943$	0	0
$944$	45.2548i	1.47292i
$945$	0	0
$946$	0	0
$947$	56.5685	1.83823	0.919115	−	0.393989i	$-0.128905\pi$
$947$	56.5685	1.83823	0.919115	+	0.393989i	$0.128905\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	69.0000	2.22581
$962$	0	0
$963$	0	0
$964$	−20.0000	−0.644157
$965$	0	0
$966$	0	0
$967$	− 62.0000i	− 1.99379i	−0.0787703	−	0.996893i	$-0.525099\pi$
$967$	− 62.0000i	− 1.99379i	0.0787703	−	0.996893i	$-0.474901\pi$
$968$	59.3970	1.90909
$969$	0	0
$970$	0	0
$971$	− 62.2254i	− 1.99691i	−0.0555842	−	0.998454i	$-0.517702\pi$
$971$	− 62.2254i	− 1.99691i	0.0555842	−	0.998454i	$-0.482298\pi$
$972$	0	0
$973$	0	0
$974$	2.82843i	0.0906287i
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	− 32.0000i	− 1.02116i
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−58.0000	−1.84243	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−58.0000	−1.84243	−0.921215	+	0.389053i	$0.872802\pi$
$992$	56.5685	1.79605
$993$	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	1800.2.d.n.1549.1		4
3.2	odd	2	inner	1800.2.d.n.1549.3		4
4.3	odd	2		7200.2.d.p.2449.3		4
5.2	odd	4		72.2.d.a.37.1	✓	2
5.3	odd	4		1800.2.k.e.901.2		2
5.4	even	2	inner	1800.2.d.n.1549.4		4
8.3	odd	2		7200.2.d.p.2449.4		4
8.5	even	2	inner	1800.2.d.n.1549.3		4
12.11	even	2		7200.2.d.p.2449.4		4
15.2	even	4		72.2.d.a.37.2	yes	2
15.8	even	4		1800.2.k.e.901.1		2
15.14	odd	2	inner	1800.2.d.n.1549.2		4
20.3	even	4		7200.2.k.h.3601.1		2
20.7	even	4		288.2.d.a.145.1		2
20.19	odd	2		7200.2.d.p.2449.1		4
24.5	odd	2	CM	1800.2.d.n.1549.1		4
24.11	even	2		7200.2.d.p.2449.3		4
40.3	even	4		7200.2.k.h.3601.2		2
40.13	odd	4		1800.2.k.e.901.1		2
40.19	odd	2		7200.2.d.p.2449.2		4
40.27	even	4		288.2.d.a.145.2		2
40.29	even	2	inner	1800.2.d.n.1549.2		4
40.37	odd	4		72.2.d.a.37.2	yes	2
45.2	even	12		648.2.n.h.109.2		4
45.7	odd	12		648.2.n.h.109.1		4
45.22	odd	12		648.2.n.h.541.2		4
45.32	even	12		648.2.n.h.541.1		4
60.23	odd	4		7200.2.k.h.3601.2		2
60.47	odd	4		288.2.d.a.145.2		2
60.59	even	2		7200.2.d.p.2449.2		4
80.27	even	4		2304.2.a.y.1.2		2
80.37	odd	4		2304.2.a.q.1.2		2
80.67	even	4		2304.2.a.y.1.1		2
80.77	odd	4		2304.2.a.q.1.1		2
120.29	odd	2	inner	1800.2.d.n.1549.4		4
120.53	even	4		1800.2.k.e.901.2		2
120.59	even	2		7200.2.d.p.2449.1		4
120.77	even	4		72.2.d.a.37.1	✓	2
120.83	odd	4		7200.2.k.h.3601.1		2
120.107	odd	4		288.2.d.a.145.1		2
180.7	even	12		2592.2.r.i.433.2		4
180.47	odd	12		2592.2.r.i.433.1		4
180.67	even	12		2592.2.r.i.2161.1		4
180.167	odd	12		2592.2.r.i.2161.2		4
240.77	even	4		2304.2.a.q.1.2		2
240.107	odd	4		2304.2.a.y.1.1		2
240.197	even	4		2304.2.a.q.1.1		2
240.227	odd	4		2304.2.a.y.1.2		2
360.67	even	12		2592.2.r.i.2161.2		4
360.77	even	12		648.2.n.h.541.2		4
360.157	odd	12		648.2.n.h.541.1		4
360.187	even	12		2592.2.r.i.433.1		4
360.227	odd	12		2592.2.r.i.433.2		4
360.277	odd	12		648.2.n.h.109.2		4
360.317	even	12		648.2.n.h.109.1		4
360.347	odd	12		2592.2.r.i.2161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.d.a.37.1	✓	2	5.2	odd	4
72.2.d.a.37.1	✓	2	120.77	even	4
72.2.d.a.37.2	yes	2	15.2	even	4
72.2.d.a.37.2	yes	2	40.37	odd	4
288.2.d.a.145.1		2	20.7	even	4
288.2.d.a.145.1		2	120.107	odd	4
288.2.d.a.145.2		2	40.27	even	4
288.2.d.a.145.2		2	60.47	odd	4
648.2.n.h.109.1		4	45.7	odd	12
648.2.n.h.109.1		4	360.317	even	12
648.2.n.h.109.2		4	45.2	even	12
648.2.n.h.109.2		4	360.277	odd	12
648.2.n.h.541.1		4	45.32	even	12
648.2.n.h.541.1		4	360.157	odd	12
648.2.n.h.541.2		4	45.22	odd	12
648.2.n.h.541.2		4	360.77	even	12
1800.2.d.n.1549.1		4	1.1	even	1	trivial
1800.2.d.n.1549.1		4	24.5	odd	2	CM
1800.2.d.n.1549.2		4	15.14	odd	2	inner
1800.2.d.n.1549.2		4	40.29	even	2	inner
1800.2.d.n.1549.3		4	3.2	odd	2	inner
1800.2.d.n.1549.3		4	8.5	even	2	inner
1800.2.d.n.1549.4		4	5.4	even	2	inner
1800.2.d.n.1549.4		4	120.29	odd	2	inner
1800.2.k.e.901.1		2	15.8	even	4
1800.2.k.e.901.1		2	40.13	odd	4
1800.2.k.e.901.2		2	5.3	odd	4
1800.2.k.e.901.2		2	120.53	even	4
2304.2.a.q.1.1		2	80.77	odd	4
2304.2.a.q.1.1		2	240.197	even	4
2304.2.a.q.1.2		2	80.37	odd	4
2304.2.a.q.1.2		2	240.77	even	4
2304.2.a.y.1.1		2	80.67	even	4
2304.2.a.y.1.1		2	240.107	odd	4
2304.2.a.y.1.2		2	80.27	even	4
2304.2.a.y.1.2		2	240.227	odd	4
2592.2.r.i.433.1		4	180.47	odd	12
2592.2.r.i.433.1		4	360.187	even	12
2592.2.r.i.433.2		4	180.7	even	12
2592.2.r.i.433.2		4	360.227	odd	12
2592.2.r.i.2161.1		4	180.67	even	12
2592.2.r.i.2161.1		4	360.347	odd	12
2592.2.r.i.2161.2		4	180.167	odd	12
2592.2.r.i.2161.2		4	360.67	even	12
7200.2.d.p.2449.1		4	20.19	odd	2
7200.2.d.p.2449.1		4	120.59	even	2
7200.2.d.p.2449.2		4	40.19	odd	2
7200.2.d.p.2449.2		4	60.59	even	2
7200.2.d.p.2449.3		4	4.3	odd	2
7200.2.d.p.2449.3		4	24.11	even	2
7200.2.d.p.2449.4		4	8.3	odd	2
7200.2.d.p.2449.4		4	12.11	even	2
7200.2.k.h.3601.1		2	20.3	even	4
7200.2.k.h.3601.1		2	120.83	odd	4
7200.2.k.h.3601.2		2	40.3	even	4
7200.2.k.h.3601.2		2	60.23	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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.00000 q^{4} -2.00000i q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q-1.41421 q^{2} +2.00000 q^{4} -2.00000i q^{7} -2.82843 q^{8} +5.65685i q^{11} +2.82843i q^{14} +4.00000 q^{16} -8.00000i q^{22} -4.00000i q^{28} +2.82843i q^{29} -10.0000 q^{31} -5.65685 q^{32} +11.3137i q^{44} +3.00000 q^{49} -14.1421 q^{53} +5.65685i q^{56} -4.00000i q^{58} +11.3137i q^{59} +14.1421 q^{62} +8.00000 q^{64} +14.0000i q^{73} +11.3137 q^{77} +10.0000 q^{79} -5.65685 q^{83} -16.0000i q^{88} -2.00000i q^{97} -4.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4}+O(q^{10}) \) 4 * q + 8 * q^4	\( 4 q + 8 q^{4} + 16 q^{16} - 40 q^{31} + 12 q^{49} + 32 q^{64} + 40 q^{79}+O(q^{100}) \) 4 * q + 8 * q^4 + 16 * q^16 - 40 * q^31 + 12 * q^49 + 32 * q^64 + 40 * q^79

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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