LMFDB - Embedded newform 100.5.d.a.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,5,Mod(99,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("100.99");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	100.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:	$10.3369963084$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			99.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	100.99
Dual form			100.5.d.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000i q^{2} -16.0000 q^{4} -64.0000i q^{8} -81.0000 q^{9} -238.000i q^{13} +256.000 q^{16} -322.000i q^{17} -324.000i q^{18} +952.000 q^{26} -82.0000 q^{29} +1024.00i q^{32} +1288.00 q^{34} +1296.00 q^{36} -2162.00i q^{37} -3038.00 q^{41} -2401.00 q^{49} +3808.00i q^{52} +2482.00i q^{53} -328.000i q^{58} -6958.00 q^{61} -4096.00 q^{64} +5152.00i q^{68} +5184.00i q^{72} +1442.00i q^{73} +8648.00 q^{74} +6561.00 q^{81} -12152.0i q^{82} +9758.00 q^{89} +1918.00i q^{97} -9604.00i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 162 q^{9} + 512 q^{16} + 1904 q^{26} - 164 q^{29} + 2576 q^{34} + 2592 q^{36} - 6076 q^{41} - 4802 q^{49} - 13916 q^{61} - 8192 q^{64} + 17296 q^{74} + 13122 q^{81} + 19516 q^{89}+O(q^{100}) $ 2 * q - 32 * q^4 - 162 * q^9 + 512 * q^16 + 1904 * q^26 - 164 * q^29 + 2576 * q^34 + 2592 * q^36 - 6076 * q^41 - 4802 * q^49 - 13916 * q^61 - 8192 * q^64 + 17296 * q^74 + 13122 * q^81 + 19516 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	4.00000i	1.00000i
$2$	4.00000i	1.00000i
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−16.0000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	− 64.0000i	− 1.00000i
$9$	−81.0000	−1.00000
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0	0
$13$	− 238.000i	− 1.40828i	−0.710059	−	0.704142i	$-0.751332\pi$
$13$	− 238.000i	− 1.40828i	0.710059	−	0.704142i	$-0.248668\pi$
$14$	0	0
$15$	0	0
$16$	256.000	1.00000
$17$	− 322.000i	− 1.11419i	−0.830450	−	0.557093i	$-0.811917\pi$
$17$	− 322.000i	− 1.11419i	0.830450	−	0.557093i	$-0.188083\pi$
$18$	− 324.000i	− 1.00000i
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	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
$26$	952.000	1.40828
$27$	0	0
$28$	0	0
$29$	−82.0000	−0.0975030	−0.0487515	−	0.998811i	$-0.515524\pi$
$29$	−82.0000	−0.0975030	−0.0487515	+	0.998811i	$0.515524\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	1024.00i	1.00000i
$33$	0	0
$34$	1288.00	1.11419
$35$	0	0
$36$	1296.00	1.00000
$37$	− 2162.00i	− 1.57925i	−0.613587	−	0.789627i	$-0.710274\pi$
$37$	− 2162.00i	− 1.57925i	0.613587	−	0.789627i	$-0.289726\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−3038.00	−1.80726	−0.903629	−	0.428316i	$-0.859107\pi$
$41$	−3038.00	−1.80726	−0.903629	+	0.428316i	$0.859107\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	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
$49$	−2401.00	−1.00000
$50$	0	0
$51$	0	0
$52$	3808.00i	1.40828i
$53$	2482.00i	0.883588i	0.897116	+	0.441794i	$0.145658\pi$
$53$	2482.00i	0.883588i	−0.897116	+	0.441794i	$0.854342\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	− 328.000i	− 0.0975030i
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	−6958.00	−1.86993	−0.934964	−	0.354743i	$-0.884568\pi$
$61$	−6958.00	−1.86993	−0.934964	+	0.354743i	$0.884568\pi$
$62$	0	0
$63$	0	0
$64$	−4096.00	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	5152.00i	1.11419i
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	5184.00i	1.00000i
$73$	1442.00i	0.270595i	0.990805	+	0.135297i	$0.0431990\pi$
$73$	1442.00i	0.270595i	−0.990805	+	0.135297i	$0.956801\pi$
$74$	8648.00	1.57925
$75$	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
$81$	6561.00	1.00000
$82$	− 12152.0i	− 1.80726i
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	9758.00	1.23192	0.615958	−	0.787779i	$-0.288769\pi$
$89$	9758.00	1.23192	0.615958	+	0.787779i	$0.288769\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1918.00i	0.203847i	0.994792	+	0.101924i	$0.0324998\pi$
$97$	1918.00i	0.203847i	−0.994792	+	0.101924i	$0.967500\pi$
$98$	− 9604.00i	− 1.00000i
$99$	0	0
$100$	0	0
$101$	18802.0	1.84315	0.921576	−	0.388197i	$-0.126902\pi$
$101$	18802.0	1.84315	0.921576	+	0.388197i	$0.126902\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−15232.0	−1.40828
$105$	0	0
$106$	−9928.00	−0.883588
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−9362.00	−0.787981	−0.393990	−	0.919115i	$-0.628906\pi$
$109$	−9362.00	−0.787981	−0.393990	+	0.919115i	$0.628906\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	− 24638.0i	− 1.92952i	−0.263137	−	0.964758i	$-0.584757\pi$
$113$	− 24638.0i	− 1.92952i	0.263137	−	0.964758i	$-0.415243\pi$
$114$	0	0
$115$	0	0
$116$	1312.00	0.0975030
$117$	19278.0i	1.40828i
$118$	0	0
$119$	0	0
$120$	0	0
$121$	14641.0	1.00000
$122$	− 27832.0i	− 1.86993i
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	− 16384.0i	− 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
$134$	0	0
$135$	0	0
$136$	−20608.0	−1.11419
$137$	− 6562.00i	− 0.349619i	−0.984602	−	0.174810i	$-0.944069\pi$
$137$	− 6562.00i	− 0.349619i	0.984602	−	0.174810i	$-0.0559310\pi$
$138$	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
$144$	−20736.0	−1.00000
$145$	0	0
$146$	−5768.00	−0.270595
$147$	0	0
$148$	34592.0i	1.57925i
$149$	33998.0	1.53137	0.765686	−	0.643214i	$-0.222400\pi$
$149$	33998.0	1.53137	0.765686	+	0.643214i	$0.222400\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	26082.0i	1.11419i
$154$	0	0
$155$	0	0
$156$	0	0
$157$	20398.0i	0.827539i	0.910382	+	0.413769i	$0.135788\pi$
$157$	20398.0i	0.827539i	−0.910382	+	0.413769i	$0.864212\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	26244.0i	1.00000i
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	48608.0	1.80726
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−28083.0	−0.983264
$170$	0	0
$171$	0	0
$172$	0	0
$173$	49042.0i	1.63861i	0.573357	+	0.819306i	$0.305641\pi$
$173$	49042.0i	1.63861i	−0.573357	+	0.819306i	$0.694359\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	39032.0i	1.23192i
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−64078.0	−1.95592	−0.977962	−	0.208785i	$-0.933049\pi$
$181$	−64078.0	−1.95592	−0.977962	+	0.208785i	$0.933049\pi$
$182$	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	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	− 38398.0i	− 1.03085i	−0.856936	−	0.515423i	$-0.827635\pi$
$193$	− 38398.0i	− 1.03085i	0.856936	−	0.515423i	$-0.172365\pi$
$194$	−7672.00	−0.203847
$195$	0	0
$196$	38416.0	1.00000
$197$	− 74482.0i	− 1.91919i	−0.281378	−	0.959597i	$-0.590791\pi$
$197$	− 74482.0i	− 1.91919i	0.281378	−	0.959597i	$-0.409209\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	75208.0i	1.84315i
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	− 60928.0i	− 1.40828i
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	− 39712.0i	− 0.883588i
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	− 37448.0i	− 0.787981i
$219$	0	0
$220$	0	0
$221$	−76636.0	−1.56909
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	98552.0	1.92952
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	−90482.0	−1.72541	−0.862703	−	0.505711i	$-0.831230\pi$
$229$	−90482.0	−1.72541	−0.862703	+	0.505711i	$0.831230\pi$
$230$	0	0
$231$	0	0
$232$	5248.00i	0.0975030i
$233$	− 64478.0i	− 1.18768i	−0.804583	−	0.593840i	$-0.797611\pi$
$233$	− 64478.0i	− 1.18768i	0.804583	−	0.593840i	$-0.202389\pi$
$234$	−77112.0	−1.40828
$235$	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
$241$	58562.0	1.00828	0.504141	−	0.863621i	$-0.331809\pi$
$241$	58562.0	1.00828	0.504141	+	0.863621i	$0.331809\pi$
$242$	58564.0i	1.00000i
$243$	0	0
$244$	111328.	1.86993
$245$	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
$254$	0	0
$255$	0	0
$256$	65536.0	1.00000
$257$	− 128002.i	− 1.93799i	−0.247089	−	0.968993i	$-0.579474\pi$
$257$	− 128002.i	− 1.93799i	0.247089	−	0.968993i	$-0.420526\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	6642.00	0.0975030
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	125678.	1.73682	0.868410	−	0.495847i	$-0.165142\pi$
$269$	125678.	1.73682	0.868410	+	0.495847i	$0.165142\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	− 82432.0i	− 1.11419i
$273$	0	0
$274$	26248.0	0.349619
$275$	0	0
$276$	0	0
$277$	100558.i	1.31056i	0.755386	+	0.655280i	$0.227449\pi$
$277$	100558.i	1.31056i	−0.755386	+	0.655280i	$0.772551\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	55522.0	0.703157	0.351579	−	0.936158i	$-0.385645\pi$
$281$	55522.0	0.703157	0.351579	+	0.936158i	$0.385645\pi$
$282$	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
$288$	− 82944.0i	− 1.00000i
$289$	−20163.0	−0.241412
$290$	0	0
$291$	0	0
$292$	− 23072.0i	− 0.270595i
$293$	153202.i	1.78455i	0.451490	+	0.892276i	$0.350893\pi$
$293$	153202.i	1.78455i	−0.451490	+	0.892276i	$0.649107\pi$
$294$	0	0
$295$	0	0
$296$	−138368.	−1.57925
$297$	0	0
$298$	135992.i	1.53137i
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	−104328.	−1.11419
$307$	0	0		−	1.00000i	$-0.5\pi$
$307$	0	0			1.00000i	$0.5\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	− 193438.i	− 1.97448i	−0.159234	−	0.987241i	$-0.550902\pi$
$313$	− 193438.i	− 1.97448i	0.159234	−	0.987241i	$-0.449098\pi$
$314$	−81592.0	−0.827539
$315$	0	0
$316$	0	0
$317$	178478.i	1.77609i	0.459752	+	0.888047i	$0.347938\pi$
$317$	178478.i	1.77609i	−0.459752	+	0.888047i	$0.652062\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−104976.	−1.00000
$325$	0	0
$326$	0	0
$327$	0	0
$328$	194432.i	1.80726i
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	175122.i	1.57925i
$334$	0	0
$335$	0	0
$336$	0	0
$337$	104638.i	0.921361i	0.887566	+	0.460680i	$0.152395\pi$
$337$	104638.i	0.921361i	−0.887566	+	0.460680i	$0.847605\pi$
$338$	− 112332.i	− 0.983264i
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	−196168.	−1.63861
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	−114002.	−0.935969	−0.467985	−	0.883737i	$-0.655020\pi$
$349$	−114002.	−0.935969	−0.467985	+	0.883737i	$0.655020\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 46718.0i	− 0.374917i	−0.982273	−	0.187458i	$-0.939975\pi$
$353$	− 46718.0i	− 0.374917i	0.982273	−	0.187458i	$-0.0600250\pi$
$354$	0	0
$355$	0	0
$356$	−156128.	−1.23192
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	130321.	1.00000
$362$	− 256312.i	− 1.95592i
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	246078.	1.80726
$370$	0	0
$371$	0	0
$372$	0	0
$373$	24242.0i	0.174241i	0.996198	+	0.0871206i	$0.0277665\pi$
$373$	24242.0i	0.174241i	−0.996198	+	0.0871206i	$0.972233\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	19516.0i	0.137312i
$378$	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		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	153592.	1.03085
$387$	0	0
$388$	− 30688.0i	− 0.203847i
$389$	159758.	1.05576	0.527878	−	0.849320i	$-0.322988\pi$
$389$	159758.	1.05576	0.527878	+	0.849320i	$0.322988\pi$
$390$	0	0
$391$	0	0
$392$	153664.i	1.00000i
$393$	0	0
$394$	297928.	1.91919
$395$	0	0
$396$	0	0
$397$	− 107282.i	− 0.680684i	−0.940302	−	0.340342i	$-0.889457\pi$
$397$	− 107282.i	− 0.680684i	0.940302	−	0.340342i	$-0.110543\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	315202.	1.96020	0.980100	−	0.198506i	$-0.0636090\pi$
$401$	315202.	1.96020	0.980100	+	0.198506i	$0.0636090\pi$
$402$	0	0
$403$	0	0
$404$	−300832.	−1.84315
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−276962.	−1.65567	−0.827835	−	0.560972i	$-0.810427\pi$
$409$	−276962.	−1.65567	−0.827835	+	0.560972i	$0.810427\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	243712.	1.40828
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	−351118.	−1.98102	−0.990510	−	0.137440i	$-0.956113\pi$
$421$	−351118.	−1.98102	−0.990510	+	0.137440i	$0.956113\pi$
$422$	0	0
$423$	0	0
$424$	158848.	0.883588
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	− 290878.i	− 1.55144i	−0.631077	−	0.775720i	$-0.717387\pi$
$433$	− 290878.i	− 1.55144i	0.631077	−	0.775720i	$-0.282613\pi$
$434$	0	0
$435$	0	0
$436$	149792.	0.787981
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	194481.	1.00000
$442$	− 306544.i	− 1.56909i
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−89602.0	−0.444452	−0.222226	−	0.974995i	$-0.571332\pi$
$449$	−89602.0	−0.444452	−0.222226	+	0.974995i	$0.571332\pi$
$450$	0	0
$451$	0	0
$452$	394208.i	1.92952i
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	− 304802.i	− 1.45944i	−0.683748	−	0.729719i	$-0.739651\pi$
$457$	− 304802.i	− 1.45944i	0.683748	−	0.729719i	$-0.260349\pi$
$458$	− 361928.i	− 1.72541i
$459$	0	0
$460$	0	0
$461$	−152558.	−0.717849	−0.358925	−	0.933367i	$-0.616856\pi$
$461$	−152558.	−0.717849	−0.358925	+	0.933367i	$0.616856\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	−20992.0	−0.0975030
$465$	0	0
$466$	257912.	1.18768
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	− 308448.i	− 1.40828i
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	− 201042.i	− 0.883588i
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	−514556.	−2.22404
$482$	234248.i	1.00828i
$483$	0	0
$484$	−234256.	−1.00000
$485$	0	0
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	445312.i	1.86993i
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	26404.0i	0.108637i
$494$	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
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	−324562.	−1.25274	−0.626372	−	0.779525i	$-0.715461\pi$
$509$	−324562.	−1.25274	−0.626372	+	0.779525i	$0.715461\pi$
$510$	0	0
$511$	0	0
$512$	262144.i	1.00000i
$513$	0	0
$514$	512008.	1.93799
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−231518.	−0.852922	−0.426461	−	0.904506i	$-0.640240\pi$
$521$	−231518.	−0.852922	−0.426461	+	0.904506i	$0.640240\pi$
$522$	26568.0i	0.0975030i
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−279841.	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	723044.i	2.54513i
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	502712.i	1.73682i
$539$	0	0
$540$	0	0
$541$	−120238.	−0.410816	−0.205408	−	0.978676i	$-0.565852\pi$
$541$	−120238.	−0.410816	−0.205408	+	0.978676i	$0.565852\pi$
$542$	0	0
$543$	0	0
$544$	329728.	1.11419
$545$	0	0
$546$	0	0
$547$	0	0		−	1.00000i	$-0.5\pi$
$547$	0	0			1.00000i	$0.5\pi$
$548$	104992.i	0.349619i
$549$	563598.	1.86993
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−402232.	−1.31056
$555$	0	0
$556$	0	0
$557$	511598.i	1.64899i	0.565868	+	0.824496i	$0.308541\pi$
$557$	511598.i	1.64899i	−0.565868	+	0.824496i	$0.691459\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	222088.i	0.703157i
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	434078.	1.34074	0.670368	−	0.742029i	$-0.266136\pi$
$569$	434078.	1.34074	0.670368	+	0.742029i	$0.266136\pi$
$570$	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
$576$	331776.	1.00000
$577$	− 656642.i	− 1.97232i	−0.165801	−	0.986159i	$-0.553021\pi$
$577$	− 656642.i	− 1.97232i	0.165801	−	0.986159i	$-0.446979\pi$
$578$	− 80652.0i	− 0.241412i
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	92288.0	0.270595
$585$	0	0
$586$	−612808.	−1.78455
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	− 553472.i	− 1.57925i
$593$	161602.i	0.459555i	0.973243	+	0.229777i	$0.0737998\pi$
$593$	161602.i	0.459555i	−0.973243	+	0.229777i	$0.926200\pi$
$594$	0	0
$595$	0	0
$596$	−543968.	−1.53137
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	492002.	1.36213	0.681064	−	0.732224i	$-0.261518\pi$
$601$	492002.	1.36213	0.681064	+	0.732224i	$0.261518\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	− 417312.i	− 1.11419i
$613$	− 746638.i	− 1.98696i	−0.114006	−	0.993480i	$-0.536368\pi$
$613$	− 746638.i	− 1.98696i	0.114006	−	0.993480i	$-0.463632\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	717278.i	1.88416i	0.335392	+	0.942079i	$0.391131\pi$
$617$	717278.i	1.88416i	−0.335392	+	0.942079i	$0.608869\pi$
$618$	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
$626$	773752.	1.97448
$627$	0	0
$628$	− 326368.i	− 0.827539i
$629$	−696164.	−1.75959
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	−713912.	−1.77609
$635$	0	0
$636$	0	0
$637$	571438.i	1.40828i
$638$	0	0
$639$	0	0
$640$	0	0
$641$	661762.	1.61059	0.805296	−	0.592872i	$-0.202006\pi$
$641$	661762.	1.61059	0.805296	+	0.592872i	$0.202006\pi$
$642$	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		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	− 419904.i	− 1.00000i
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	− 455918.i	− 1.06920i	−0.845104	−	0.534602i	$-0.820462\pi$
$653$	− 455918.i	− 1.06920i	0.845104	−	0.534602i	$-0.179538\pi$
$654$	0	0
$655$	0	0
$656$	−777728.	−1.80726
$657$	− 116802.i	− 0.270595i
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	513842.	1.17605	0.588026	−	0.808842i	$-0.299905\pi$
$661$	513842.	1.17605	0.588026	+	0.808842i	$0.299905\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−700488.	−1.57925
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	− 312958.i	− 0.690965i	−0.938425	−	0.345482i	$-0.887715\pi$
$673$	− 312958.i	− 0.690965i	0.938425	−	0.345482i	$-0.112285\pi$
$674$	−418552.	−0.921361
$675$	0	0
$676$	449328.	0.983264
$677$	− 905842.i	− 1.97640i	−0.153165	−	0.988201i	$-0.548947\pi$
$677$	− 905842.i	− 1.97640i	0.153165	−	0.988201i	$-0.451053\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	590716.	1.24434
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	− 784672.i	− 1.63861i
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	978236.i	2.01362i
$698$	− 456008.i	− 0.935969i
$699$	0	0
$700$	0	0
$701$	712402.	1.44974	0.724868	−	0.688887i	$-0.241901\pi$
$701$	712402.	1.44974	0.724868	+	0.688887i	$0.241901\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	186872.	0.374917
$707$	0	0
$708$	0	0
$709$	737038.	1.46621	0.733107	−	0.680113i	$-0.238069\pi$
$709$	737038.	1.46621	0.733107	+	0.680113i	$0.238069\pi$
$710$	0	0
$711$	0	0
$712$	− 624512.i	− 1.23192i
$713$	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
$721$	0	0
$722$	521284.i	1.00000i
$723$	0	0
$724$	1.02525e6	1.95592
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−531441.	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	1.02792e6i	1.91316i	0.291463	+	0.956582i	$0.405858\pi$
$733$	1.02792e6i	1.91316i	−0.291463	+	0.956582i	$0.594142\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	984312.i	1.80726i
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	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
$746$	−96968.0	−0.174241
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	−78064.0	−0.137312
$755$	0	0
$756$	0	0
$757$	− 270002.i	− 0.471167i	−0.971854	−	0.235584i	$-0.924300\pi$
$757$	− 270002.i	− 0.471167i	0.971854	−	0.235584i	$-0.0757002\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−1.15216e6	−1.98949	−0.994747	−	0.102362i	$-0.967360\pi$
$761$	−1.15216e6	−1.98949	−0.994747	+	0.102362i	$0.967360\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	257278.	0.435061	0.217530	−	0.976054i	$-0.430200\pi$
$769$	257278.	0.435061	0.217530	+	0.976054i	$0.430200\pi$
$770$	0	0
$771$	0	0
$772$	614368.i	1.03085i
$773$	− 1.04296e6i	− 1.74545i	−0.488211	−	0.872726i	$-0.662350\pi$
$773$	− 1.04296e6i	− 1.74545i	0.488211	−	0.872726i	$-0.337650\pi$
$774$	0	0
$775$	0	0
$776$	122752.	0.203847
$777$	0	0
$778$	639032.i	1.05576i
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−614656.	−1.00000
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	1.19171e6i	1.91919i
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	1.65600e6i	2.63339i
$794$	429128.	0.680684
$795$	0	0
$796$	0	0
$797$	38318.0i	0.0603235i	0.999545	+	0.0301617i	$0.00960223\pi$
$797$	38318.0i	0.0603235i	−0.999545	+	0.0301617i	$0.990398\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−790398.	−1.23192
$802$	1.26081e6i	1.96020i
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	− 1.20333e6i	− 1.84315i
$809$	−995362.	−1.52084	−0.760421	−	0.649431i	$-0.775007\pi$
$809$	−995362.	−1.52084	−0.760421	+	0.649431i	$0.775007\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	− 1.10785e6i	− 1.65567i
$819$	0	0
$820$	0	0
$821$	−611918.	−0.907835	−0.453917	−	0.891044i	$-0.649974\pi$
$821$	−611918.	−0.907835	−0.453917	+	0.891044i	$0.649974\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	−208082.	−0.302779	−0.151389	−	0.988474i	$-0.548375\pi$
$829$	−208082.	−0.302779	−0.151389	+	0.988474i	$0.548375\pi$
$830$	0	0
$831$	0	0
$832$	974848.i	1.40828i
$833$	773122.i	1.11419i
$834$	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
$841$	−700557.	−0.990493
$842$	− 1.40447e6i	− 1.98102i
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	635392.i	0.883588i
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 1.28712e6i	− 1.76897i	−0.466569	−	0.884485i	$-0.654510\pi$
$853$	− 1.28712e6i	− 1.76897i	0.466569	−	0.884485i	$-0.345490\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 1.25360e6i	− 1.70686i	−0.521207	−	0.853430i	$-0.674518\pi$
$857$	− 1.25360e6i	− 1.70686i	0.521207	−	0.853430i	$-0.325482\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	1.16351e6	1.55144
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	599168.i	0.787981i
$873$	− 155358.i	− 0.203847i
$874$	0	0
$875$	0	0
$876$	0	0
$877$	− 1.05384e6i	− 1.37018i	−0.728460	−	0.685088i	$-0.759764\pi$
$877$	− 1.05384e6i	− 1.37018i	0.728460	−	0.685088i	$-0.240236\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−1.00768e6	−1.29828	−0.649142	−	0.760667i	$-0.724872\pi$
$881$	−1.00768e6	−1.29828	−0.649142	+	0.760667i	$0.724872\pi$
$882$	777924.i	1.00000i
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	1.22618e6	1.56909
$885$	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
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	− 358408.i	− 0.444452i
$899$	0	0
$900$	0	0
$901$	799204.	0.984483
$902$	0	0
$903$	0	0
$904$	−1.57683e6	−1.92952
$905$	0	0
$906$	0	0
$907$	0	0		−	1.00000i	$-0.5\pi$
$907$	0	0			1.00000i	$0.5\pi$
$908$	0	0
$909$	−1.52296e6	−1.84315
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	0	0
$914$	1.21921e6	1.45944
$915$	0	0
$916$	1.44771e6	1.72541
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	− 610232.i	− 0.717849i
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	− 83968.0i	− 0.0975030i
$929$	1.65952e6	1.92287	0.961436	−	0.275027i	$-0.0886870\pi$
$929$	1.65952e6	1.92287	0.961436	+	0.275027i	$0.0886870\pi$
$930$	0	0
$931$	0	0
$932$	1.03165e6i	1.18768i
$933$	0	0
$934$	0	0
$935$	0	0
$936$	1.23379e6	1.40828
$937$	1.57104e6i	1.78940i	0.446667	+	0.894700i	$0.352611\pi$
$937$	1.57104e6i	1.78940i	−0.446667	+	0.894700i	$0.647389\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	425362.	0.480374	0.240187	−	0.970727i	$-0.422791\pi$
$941$	425362.	0.480374	0.240187	+	0.970727i	$0.422791\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	343196.	0.381074
$950$	0	0
$951$	0	0
$952$	0	0
$953$	− 303518.i	− 0.334194i	−0.985940	−	0.167097i	$-0.946561\pi$
$953$	− 303518.i	− 0.334194i	0.985940	−	0.167097i	$-0.0534393\pi$
$954$	804168.	0.883588
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	923521.	1.00000
$962$	− 2.05822e6i	− 2.22404i
$963$	0	0
$964$	−936992.	−1.00828
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	− 937024.i	− 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
$974$	0	0
$975$	0	0
$976$	−1.78125e6	−1.86993
$977$	− 1.66304e6i	− 1.74226i	−0.491048	−	0.871132i	$-0.663386\pi$
$977$	− 1.66304e6i	− 1.74226i	0.491048	−	0.871132i	$-0.336614\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	758322.	0.787981
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	−105616.	−0.108637
$987$	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
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	− 1.43448e6i	− 1.44313i	−0.692348	−	0.721564i	$-0.743424\pi$
$997$	− 1.43448e6i	− 1.44313i	0.692348	−	0.721564i	$-0.256576\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.5.d.a.99.2		2
4.3	odd	2	CM	100.5.d.a.99.2		2
5.2	odd	4		4.5.b.a.3.1	✓	1
5.3	odd	4		100.5.b.a.51.1		1
5.4	even	2	inner	100.5.d.a.99.1		2
15.2	even	4		36.5.d.a.19.1		1
20.3	even	4		100.5.b.a.51.1		1
20.7	even	4		4.5.b.a.3.1	✓	1
20.19	odd	2	inner	100.5.d.a.99.1		2
35.27	even	4		196.5.c.a.99.1		1
40.27	even	4		64.5.c.a.63.1		1
40.37	odd	4		64.5.c.a.63.1		1
60.47	odd	4		36.5.d.a.19.1		1
80.27	even	4		256.5.d.c.127.1		2
80.37	odd	4		256.5.d.c.127.1		2
80.67	even	4		256.5.d.c.127.2		2
80.77	odd	4		256.5.d.c.127.2		2
120.77	even	4		576.5.g.b.127.1		1
120.107	odd	4		576.5.g.b.127.1		1
140.27	odd	4		196.5.c.a.99.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.5.b.a.3.1	✓	1	5.2	odd	4
4.5.b.a.3.1	✓	1	20.7	even	4
36.5.d.a.19.1		1	15.2	even	4
36.5.d.a.19.1		1	60.47	odd	4
64.5.c.a.63.1		1	40.27	even	4
64.5.c.a.63.1		1	40.37	odd	4
100.5.b.a.51.1		1	5.3	odd	4
100.5.b.a.51.1		1	20.3	even	4
100.5.d.a.99.1		2	5.4	even	2	inner
100.5.d.a.99.1		2	20.19	odd	2	inner
100.5.d.a.99.2		2	1.1	even	1	trivial
100.5.d.a.99.2		2	4.3	odd	2	CM
196.5.c.a.99.1		1	35.27	even	4
196.5.c.a.99.1		1	140.27	odd	4
256.5.d.c.127.1		2	80.27	even	4
256.5.d.c.127.1		2	80.37	odd	4
256.5.d.c.127.2		2	80.67	even	4
256.5.d.c.127.2		2	80.77	odd	4
576.5.g.b.127.1		1	120.77	even	4
576.5.g.b.127.1		1	120.107	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} -16.0000 q^{4} -64.0000i q^{8} -81.0000 q^{9} -238.000i q^{13} +256.000 q^{16} -322.000i q^{17} -324.000i q^{18} +952.000 q^{26} -82.0000 q^{29} +1024.00i q^{32} +1288.00 q^{34} +1296.00 q^{36} -2162.00i q^{37} -3038.00 q^{41} -2401.00 q^{49} +3808.00i q^{52} +2482.00i q^{53} -328.000i q^{58} -6958.00 q^{61} -4096.00 q^{64} +5152.00i q^{68} +5184.00i q^{72} +1442.00i q^{73} +8648.00 q^{74} +6561.00 q^{81} -12152.0i q^{82} +9758.00 q^{89} +1918.00i q^{97} -9604.00i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 162 q^{9} + 512 q^{16} + 1904 q^{26} - 164 q^{29} + 2576 q^{34} + 2592 q^{36} - 6076 q^{41} - 4802 q^{49} - 13916 q^{61} - 8192 q^{64} + 17296 q^{74} + 13122 q^{81} + 19516 q^{89}+O(q^{100}) \) 2 * q - 32 * q^4 - 162 * q^9 + 512 * q^16 + 1904 * q^26 - 164 * q^29 + 2576 * q^34 + 2592 * q^36 - 6076 * q^41 - 4802 * q^49 - 13916 * q^61 - 8192 * q^64 + 17296 * q^74 + 13122 * q^81 + 19516 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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