LMFDB - Embedded newform 320.6.c.h.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,6,Mod(129,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("320.129");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	320.c (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:	$51.3228223402$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			129.2
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	320.129
Dual form			320.6.c.h.129.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.81966i q^{3} -55.9017 q^{5} +171.820i q^{7} +181.853 q^{9} +O(q^{10})$	$q-7.81966i q^{3} -55.9017 q^{5} +171.820i q^{7} +181.853 q^{9} +437.132i q^{15} +1343.57 q^{21} -230.741i q^{23} +3125.00 q^{25} -3322.21i q^{27} -1686.00 q^{29} -9605.01i q^{35} -21041.4 q^{41} -22019.5i q^{43} -10165.9 q^{45} +30116.9i q^{47} -12715.0 q^{49} -52256.9 q^{61} +31245.9i q^{63} +36856.5i q^{67} -1804.31 q^{69} -24436.4i q^{75} +18211.7 q^{81} -46781.9i q^{83} +13183.9i q^{87} -149286. q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 972 q^{9}+O(q^{10}) $ 4 * q - 972 * q^9	$ 4 q - 972 q^{9} + 14408 q^{21} + 12500 q^{25} - 6744 q^{29} - 95000 q^{45} - 67228 q^{49} + 302344 q^{69} + 485804 q^{81} - 597144 q^{89}+O(q^{100}) $ 4 * q - 972 * q^9 + 14408 * q^21 + 12500 * q^25 - 6744 * q^29 - 95000 * q^45 - 67228 * q^49 + 302344 * q^69 + 485804 * q^81 - 597144 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	− 7.81966i	− 0.501631i	−0.968035	−	0.250816i	$-0.919301\pi$
$3$	− 7.81966i	− 0.501631i	0.968035	−	0.250816i	$-0.0806988\pi$
$4$	0	0
$5$	−55.9017	−1.00000
$5$	−55.9017	−1.00000
$6$	0	0
$7$	171.820i	1.32534i	0.748911	+	0.662671i	$0.230577\pi$
$7$	171.820i	1.32534i	−0.748911	+	0.662671i	$0.769423\pi$
$8$	0	0
$9$	181.853	0.748366
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	437.132i	0.501631i
$16$	0	0
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	1343.57	0.664833
$22$	0	0
$23$	− 230.741i	− 0.0909503i	−0.998965	−	0.0454752i	$-0.985520\pi$
$23$	− 230.741i	− 0.0909503i	0.998965	−	0.0454752i	$-0.0144802\pi$
$24$	0	0
$25$	3125.00	1.00000
$26$	0	0
$27$	− 3322.21i	− 0.877035i
$28$	0	0
$29$	−1686.00	−0.372274	−0.186137	−	0.982524i	$-0.559597\pi$
$29$	−1686.00	−0.372274	−0.186137	+	0.982524i	$0.559597\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	− 9605.01i	− 1.32534i
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−21041.4	−1.95486	−0.977428	−	0.211267i	$-0.932241\pi$
$41$	−21041.4	−1.95486	−0.977428	+	0.211267i	$0.932241\pi$
$42$	0	0
$43$	− 22019.5i	− 1.81609i	−0.418877	−	0.908043i	$-0.637576\pi$
$43$	− 22019.5i	− 1.81609i	0.418877	−	0.908043i	$-0.362424\pi$
$44$	0	0
$45$	−10165.9	−0.748366
$46$	0	0
$47$	30116.9i	1.98869i	0.106214	+	0.994343i	$0.466127\pi$
$47$	30116.9i	1.98869i	−0.106214	+	0.994343i	$0.533873\pi$
$48$	0	0
$49$	−12715.0	−0.756530
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−52256.9	−1.79812	−0.899061	−	0.437824i	$-0.855749\pi$
$61$	−52256.9	−1.79812	−0.899061	+	0.437824i	$0.855749\pi$
$62$	0	0
$63$	31245.9i	0.991840i
$64$	0	0
$65$	0	0
$66$	0	0
$67$	36856.5i	1.00306i	0.865140	+	0.501530i	$0.167229\pi$
$67$	36856.5i	1.00306i	−0.865140	+	0.501530i	$0.832771\pi$
$68$	0	0
$69$	−1804.31	−0.0456236
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	− 24436.4i	− 0.501631i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	18211.7	0.308417
$82$	0	0
$83$	− 46781.9i	− 0.745388i	−0.927954	−	0.372694i	$-0.878434\pi$
$83$	− 46781.9i	− 0.745388i	0.927954	−	0.372694i	$-0.121566\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	13183.9i	0.186744i
$88$	0	0
$89$	−149286.	−1.99776	−0.998882	−	0.0472789i	$-0.984945\pi$
$89$	−149286.	−1.99776	−0.998882	+	0.0472789i	$0.984945\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−137502.	−1.34124	−0.670619	−	0.741802i	$-0.733971\pi$
$101$	−137502.	−1.34124	−0.670619	+	0.741802i	$0.733971\pi$
$102$	0	0
$103$	− 184905.i	− 1.71734i	−0.512528	−	0.858670i	$-0.671291\pi$
$103$	− 184905.i	− 1.71734i	0.512528	−	0.858670i	$-0.328709\pi$
$104$	0	0
$105$	−75107.9	−0.664833
$106$	0	0
$107$	236781.i	1.99934i	0.0256922	+	0.999670i	$0.491821\pi$
$107$	236781.i	1.99934i	−0.0256922	+	0.999670i	$0.508179\pi$
$108$	0	0
$109$	−84456.3	−0.680872	−0.340436	−	0.940268i	$-0.610575\pi$
$109$	−84456.3	−0.680872	−0.340436	+	0.940268i	$0.610575\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	12898.8i	0.0909503i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−161051.	−1.00000
$122$	0	0
$123$	164537.i	0.980618i
$124$	0	0
$125$	−174693.	−1.00000
$126$	0	0
$127$	− 358803.i	− 1.97400i	−0.160734	−	0.986998i	$-0.551386\pi$
$127$	− 358803.i	− 1.97400i	0.160734	−	0.986998i	$-0.448614\pi$
$128$	0	0
$129$	−172185.	−0.911006
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	185717.i	0.877035i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	235504.	0.997588
$142$	0	0
$143$	0	0
$144$	0	0
$145$	94250.3	0.372274
$146$	0	0
$147$	99426.9i	0.379499i
$148$	0	0
$149$	−431583.	−1.59257	−0.796286	−	0.604920i	$-0.793205\pi$
$149$	−431583.	−1.59257	−0.796286	+	0.604920i	$0.793205\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	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
$161$	39645.8	0.120540
$162$	0	0
$163$	− 656835.i	− 1.93636i	−0.250247	−	0.968182i	$-0.580512\pi$
$163$	− 656835.i	− 1.93636i	0.250247	−	0.968182i	$-0.419488\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	− 640357.i	− 1.77677i	−0.459099	−	0.888385i	$-0.651828\pi$
$167$	− 640357.i	− 1.77677i	0.459099	−	0.888385i	$-0.348172\pi$
$168$	0	0
$169$	371293.	1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	536936.i	1.32534i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	320402.	0.726940	0.363470	−	0.931606i	$-0.381592\pi$
$181$	320402.	0.726940	0.363470	+	0.931606i	$0.381592\pi$
$182$	0	0
$183$	408631.i	0.901994i
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	570820.	1.16237
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	288205.	0.503167
$202$	0	0
$203$	− 289688.i	− 0.493390i
$204$	0	0
$205$	1.17625e6	1.95486
$206$	0	0
$207$	− 41960.8i	− 0.0680641i
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	1.23093e6i	1.81609i
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	1.43720e6i	1.93533i	0.252245	+	0.967663i	$0.418831\pi$
$223$	1.43720e6i	1.93533i	−0.252245	+	0.967663i	$0.581169\pi$
$224$	0	0
$225$	568290.	0.748366
$226$	0	0
$227$	1.20493e6i	1.55202i	0.630720	+	0.776011i	$0.282760\pi$
$227$	1.20493e6i	1.55202i	−0.630720	+	0.776011i	$0.717240\pi$
$228$	0	0
$229$	−1.06681e6	−1.34431	−0.672156	−	0.740410i	$-0.734632\pi$
$229$	−1.06681e6	−1.34431	−0.672156	+	0.740410i	$0.734632\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	− 1.68359e6i	− 1.98869i
$236$	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
$241$	1.42086e6	1.57583	0.787916	−	0.615782i	$-0.211160\pi$
$241$	1.42086e6	1.57583	0.787916	+	0.615782i	$0.211160\pi$
$242$	0	0
$243$	− 949706.i	− 1.03175i
$244$	0	0
$245$	710790.	0.756530
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−365818.	−0.373910
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−306604.	−0.278597
$262$	0	0
$263$	− 2.21995e6i	− 1.97903i	−0.144423	−	0.989516i	$-0.546132\pi$
$263$	− 2.21995e6i	− 1.97903i	0.144423	−	0.989516i	$-0.453868\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	1.16737e6i	1.00214i
$268$	0	0
$269$	1.35718e6	1.14356	0.571778	−	0.820409i	$-0.306254\pi$
$269$	1.35718e6	1.14356	0.571778	+	0.820409i	$0.306254\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	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
$281$	−679161.	−0.513106	−0.256553	−	0.966530i	$-0.582587\pi$
$281$	−679161.	−0.513106	−0.256553	+	0.966530i	$0.582587\pi$
$282$	0	0
$283$	242044.i	0.179650i	0.995958	+	0.0898251i	$0.0286308\pi$
$283$	242044.i	0.179650i	−0.995958	+	0.0898251i	$0.971369\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	− 3.61533e6i	− 2.59085i
$288$	0	0
$289$	1.41986e6	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	3.78338e6	2.40693
$302$	0	0
$303$	1.07522e6i	0.672807i
$304$	0	0
$305$	2.92125e6	1.79812
$306$	0	0
$307$	3.25024e6i	1.96820i	0.177611	+	0.984101i	$0.443163\pi$
$307$	3.25024e6i	1.96820i	−0.177611	+	0.984101i	$0.556837\pi$
$308$	0	0
$309$	−1.44590e6	−0.861472
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	− 1.74670e6i	− 0.991840i
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	1.85154e6	1.00293
$322$	0	0
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	660419.i	0.341547i
$328$	0	0
$329$	−5.17468e6	−2.63569
$330$	0	0
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	− 2.06034e6i	− 1.00306i
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	703087.i	0.322681i
$344$	0	0
$345$	100864.	0.0456236
$346$	0	0
$347$	4.09636e6i	1.82631i	0.407613	+	0.913155i	$0.366361\pi$
$347$	4.09636e6i	1.82631i	−0.407613	+	0.913155i	$0.633639\pi$
$348$	0	0
$349$	−2.95461e6	−1.29849	−0.649243	−	0.760581i	$-0.724914\pi$
$349$	−2.95461e6	−1.29849	−0.649243	+	0.760581i	$0.724914\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−2.47610e6	−1.00000
$362$	0	0
$363$	1.25936e6i	0.501631i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	− 1.87697e6i	− 0.727433i	−0.931510	−	0.363716i	$-0.881508\pi$
$367$	− 1.87697e6i	− 0.727433i	0.931510	−	0.363716i	$-0.118492\pi$
$368$	0	0
$369$	−3.82644e6	−1.46295
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	1.36604e6i	0.501631i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	−2.80571e6	−0.990218
$382$	0	0
$383$	− 822119.i	− 0.286377i	−0.989695	−	0.143188i	$-0.954265\pi$
$383$	− 822119.i	− 0.286377i	0.989695	−	0.143188i	$-0.0457355\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	− 4.00431e6i	− 1.35910i
$388$	0	0
$389$	−5.91961e6	−1.98344	−0.991720	−	0.128419i	$-0.959010\pi$
$389$	−5.91961e6	−1.98344	−0.991720	+	0.128419i	$0.959010\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	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
$401$	4.66850e6	1.44983	0.724914	−	0.688840i	$-0.241880\pi$
$401$	4.66850e6	1.44983	0.724914	+	0.688840i	$0.241880\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−1.01807e6	−0.308417
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−5.95306e6	−1.75967	−0.879837	−	0.475276i	$-0.842348\pi$
$409$	−5.95306e6	−1.75967	−0.879837	+	0.475276i	$0.842348\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	2.61519e6i	0.745388i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−4.04525e6	−1.11235	−0.556173	−	0.831067i	$-0.687731\pi$
$421$	−4.04525e6	−1.11235	−0.556173	+	0.831067i	$0.687731\pi$
$422$	0	0
$423$	5.47685e6i	1.48827i
$424$	0	0
$425$	0	0
$426$	0	0
$427$	− 8.97876e6i	− 2.38313i
$428$	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
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	− 737005.i	− 0.186744i
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−2.31226e6	−0.566161
$442$	0	0
$443$	2.84202e6i	0.688046i	0.938961	+	0.344023i	$0.111790\pi$
$443$	2.84202e6i	0.688046i	−0.938961	+	0.344023i	$0.888210\pi$
$444$	0	0
$445$	8.34534e6	1.99776
$446$	0	0
$447$	3.37484e6i	0.798884i
$448$	0	0
$449$	−3.02998e6	−0.709291	−0.354646	−	0.935001i	$-0.615398\pi$
$449$	−3.02998e6	−0.709291	−0.354646	+	0.935001i	$0.615398\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	4.54780e6	0.996665	0.498333	−	0.866986i	$-0.333946\pi$
$461$	4.54780e6	0.996665	0.498333	+	0.866986i	$0.333946\pi$
$462$	0	0
$463$	6.96086e6i	1.50907i	0.656258	+	0.754537i	$0.272138\pi$
$463$	6.96086e6i	1.50907i	−0.656258	+	0.754537i	$0.727862\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 3.08014e6i	− 0.653549i	−0.945102	−	0.326774i	$-0.894038\pi$
$467$	− 3.08014e6i	− 0.653549i	0.945102	−	0.326774i	$-0.105962\pi$
$468$	0	0
$469$	−6.33267e6	−1.32940
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	− 310016.i	− 0.0604668i
$484$	0	0
$485$	0	0
$486$	0	0
$487$	2.79895e6i	0.534777i	0.963589	+	0.267388i	$0.0861607\pi$
$487$	2.79895e6i	0.534777i	−0.963589	+	0.267388i	$0.913839\pi$
$488$	0	0
$489$	−5.13622e6	−0.971341
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	−5.00738e6	−0.891284
$502$	0	0
$503$	− 1.09064e7i	− 1.92203i	−0.276491	−	0.961016i	$-0.589172\pi$
$503$	− 1.09064e7i	− 1.92203i	0.276491	−	0.961016i	$-0.410828\pi$
$504$	0	0
$505$	7.68660e6	1.34124
$506$	0	0
$507$	− 2.90339e6i	− 0.501631i
$508$	0	0
$509$	−7.23049e6	−1.23701	−0.618505	−	0.785781i	$-0.712261\pi$
$509$	−7.23049e6	−1.23701	−0.618505	+	0.785781i	$0.712261\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	1.03365e7i	1.71734i
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−5.30540e6	−0.856295	−0.428148	−	0.903709i	$-0.640834\pi$
$521$	−5.30540e6	−0.856295	−0.428148	+	0.903709i	$0.640834\pi$
$522$	0	0
$523$	− 4.79800e6i	− 0.767019i	−0.923537	−	0.383509i	$-0.874715\pi$
$523$	− 4.79800e6i	− 0.767019i	0.923537	−	0.383509i	$-0.125285\pi$
$524$	0	0
$525$	4.19866e6	0.664833
$526$	0	0
$527$	0	0
$528$	0	0
$529$	6.38310e6	0.991728
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	− 1.32364e7i	− 1.99934i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	1.35842e7	1.99545	0.997725	−	0.0674113i	$-0.0214740\pi$
$541$	1.35842e7	1.99545	0.997725	+	0.0674113i	$0.0214740\pi$
$542$	0	0
$543$	− 2.50543e6i	− 0.364656i
$544$	0	0
$545$	4.72125e6	0.680872
$546$	0	0
$547$	− 1.26200e7i	− 1.80339i	−0.432368	−	0.901697i	$-0.642322\pi$
$547$	− 1.26200e7i	− 1.80339i	0.432368	−	0.901697i	$-0.357678\pi$
$548$	0	0
$549$	−9.50307e6	−1.34565
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	8.93908e6i	1.18856i	0.804258	+	0.594281i	$0.202563\pi$
$563$	8.93908e6i	1.18856i	−0.804258	+	0.594281i	$0.797437\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	3.12914e6i	0.408758i
$568$	0	0
$569$	−6.53945e6	−0.846760	−0.423380	−	0.905952i	$-0.639157\pi$
$569$	−6.53945e6	−0.846760	−0.423380	+	0.905952i	$0.639157\pi$
$570$	0	0
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	− 721064.i	− 0.0909503i
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	8.03805e6	0.987894
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1.62046e7i	1.94108i	0.240940	+	0.970540i	$0.422544\pi$
$587$	1.62046e7i	1.94108i	−0.240940	+	0.970540i	$0.577456\pi$
$588$	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
$596$	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
$601$	1.76169e7	1.98950	0.994748	−	0.102358i	$-0.0326387\pi$
$601$	1.76169e7	1.98950	0.994748	+	0.102358i	$0.0326387\pi$
$602$	0	0
$603$	6.70246e6i	0.750656i
$604$	0	0
$605$	9.00302e6	1.00000
$606$	0	0
$607$	1.20107e7i	1.32311i	0.749897	+	0.661555i	$0.230103\pi$
$607$	1.20107e7i	1.32311i	−0.749897	+	0.661555i	$0.769897\pi$
$608$	0	0
$609$	−2.26526e6	−0.247500
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	− 9.19788e6i	− 0.980618i
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0		−	1.00000i	$-0.5\pi$
$619$	0	0			1.00000i	$0.5\pi$
$620$	0	0
$621$	−766568.	−0.0797667
$622$	0	0
$623$	− 2.56503e7i	− 2.64772i
$624$	0	0
$625$	9.76562e6	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	2.00577e7i	1.97400i
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	7.61048e6	0.731589	0.365794	−	0.930696i	$-0.380797\pi$
$641$	7.61048e6	0.731589	0.365794	+	0.930696i	$0.380797\pi$
$642$	0	0
$643$	1.46250e7i	1.39498i	0.716596	+	0.697489i	$0.245699\pi$
$643$	1.46250e7i	1.39498i	−0.716596	+	0.697489i	$0.754301\pi$
$644$	0	0
$645$	9.62544e6	0.911006
$646$	0	0
$647$	1.86126e7i	1.74802i	0.485909	+	0.874009i	$0.338489\pi$
$647$	1.86126e7i	1.74802i	−0.485909	+	0.874009i	$0.661511\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	2.19397e7	1.95311	0.976554	−	0.215275i	$-0.0690647\pi$
$661$	2.19397e7	1.95311	0.976554	+	0.215275i	$0.0690647\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	389029.i	0.0338584i
$668$	0	0
$669$	1.12384e7	0.970821
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	− 1.03819e7i	− 0.877035i
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	9.42215e6	0.778543
$682$	0	0
$683$	− 2.11257e7i	− 1.73285i	−0.499310	−	0.866424i	$-0.666413\pi$
$683$	− 2.11257e7i	− 1.73285i	0.499310	−	0.866424i	$-0.333587\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	8.34212e6i	0.674349i
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0		−	1.00000i	$-0.5\pi$
$691$	0	0			1.00000i	$0.5\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−2.13434e7	−1.64047	−0.820235	−	0.572027i	$-0.806157\pi$
$701$	−2.13434e7	−1.64047	−0.820235	+	0.572027i	$0.806157\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	−1.31651e7	−0.997588
$706$	0	0
$707$	− 2.36255e7i	− 1.77760i
$708$	0	0
$709$	2.34765e7	1.75395	0.876977	−	0.480533i	$-0.159557\pi$
$709$	2.34765e7	1.75395	0.876977	+	0.480533i	$0.159557\pi$
$710$	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
$721$	3.17704e7	2.27606
$722$	0	0
$723$	− 1.11107e7i	− 0.790487i
$724$	0	0
$725$	−5.26875e6	−0.372274
$726$	0	0
$727$	1.08784e7i	0.763362i	0.924294	+	0.381681i	$0.124655\pi$
$727$	1.08784e7i	0.763362i	−0.924294	+	0.381681i	$0.875345\pi$
$728$	0	0
$729$	−3.00092e6	−0.209139
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	− 5.55814e6i	− 0.379499i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	6.59147e6i	0.438037i	0.975721	+	0.219018i	$0.0702855\pi$
$743$	6.59147e6i	0.438037i	−0.975721	+	0.219018i	$0.929715\pi$
$744$	0	0
$745$	2.41262e7	1.59257
$746$	0	0
$747$	− 8.50742e6i	− 0.557823i
$748$	0	0
$749$	−4.06836e7	−2.64981
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	0	0
$754$	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
$761$	−2.95982e7	−1.85269	−0.926347	−	0.376672i	$-0.877069\pi$
$761$	−2.95982e7	−1.85269	−0.926347	+	0.376672i	$0.877069\pi$
$762$	0	0
$763$	− 1.45113e7i	− 0.902388i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−3.13824e7	−1.91369	−0.956843	−	0.290607i	$-0.906143\pi$
$769$	−3.13824e7	−1.91369	−0.956843	+	0.290607i	$0.906143\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	5.60124e6i	0.326497i
$784$	0	0
$785$	0	0
$786$	0	0
$787$	6.37220e6i	0.366735i	0.983044	+	0.183368i	$0.0586999\pi$
$787$	6.37220e6i	0.366735i	−0.983044	+	0.183368i	$0.941300\pi$
$788$	0	0
$789$	−1.73592e7	−0.992745
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−2.71481e7	−1.49506
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−2.21627e6	−0.120540
$806$	0	0
$807$	− 1.06127e7i	− 0.573643i
$808$	0	0
$809$	1.06699e6	0.0573175	0.0286588	−	0.999589i	$-0.490876\pi$
$809$	1.06699e6	0.0573175	0.0286588	+	0.999589i	$0.490876\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	3.67182e7i	1.93636i
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	9.63269e6	0.498758	0.249379	−	0.968406i	$-0.419774\pi$
$821$	9.63269e6	0.498758	0.249379	+	0.968406i	$0.419774\pi$
$822$	0	0
$823$	2.22803e7i	1.14662i	0.819338	+	0.573311i	$0.194341\pi$
$823$	2.22803e7i	1.14662i	−0.819338	+	0.573311i	$0.805659\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	− 2.37814e7i	− 1.20913i	−0.796556	−	0.604565i	$-0.793347\pi$
$827$	− 2.37814e7i	− 1.20913i	0.796556	−	0.604565i	$-0.206653\pi$
$828$	0	0
$829$	3.65262e7	1.84594	0.922972	−	0.384867i	$-0.125753\pi$
$829$	3.65262e7	1.84594	0.922972	+	0.384867i	$0.125753\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	3.57971e7i	1.77677i
$836$	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
$841$	−1.76686e7	−0.861412
$842$	0	0
$843$	5.31081e6i	0.257390i
$844$	0	0
$845$	−2.07559e7	−1.00000
$846$	0	0
$847$	− 2.76717e7i	− 1.32534i
$848$	0	0
$849$	1.89270e6	0.0901182
$850$	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
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	−2.82706e7	−1.29965
$862$	0	0
$863$	− 1.11530e6i	− 0.0509758i	−0.999675	−	0.0254879i	$-0.991886\pi$
$863$	− 1.11530e6i	− 0.0509758i	0.999675	−	0.0254879i	$-0.00811393\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 1.11028e7i	− 0.501631i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	− 3.00157e7i	− 1.32534i
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−2.42030e7	−1.05058	−0.525291	−	0.850922i	$-0.676044\pi$
$881$	−2.42030e7	−1.05058	−0.525291	+	0.850922i	$0.676044\pi$
$882$	0	0
$883$	2.00661e7i	0.866085i	0.901373	+	0.433043i	$0.142560\pi$
$883$	2.00661e7i	0.866085i	−0.901373	+	0.433043i	$0.857440\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	− 6.28780e6i	− 0.268343i	−0.990958	−	0.134171i	$-0.957163\pi$
$887$	− 6.28780e6i	− 0.268343i	0.990958	−	0.134171i	$-0.0428373\pi$
$888$	0	0
$889$	6.16493e7	2.61622
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	− 2.95848e7i	− 1.20739i
$904$	0	0
$905$	−1.79110e7	−0.726940
$906$	0	0
$907$	4.49792e7i	1.81549i	0.419523	+	0.907745i	$0.362197\pi$
$907$	4.49792e7i	1.81549i	−0.419523	+	0.907745i	$0.637803\pi$
$908$	0	0
$909$	−2.50051e7	−1.00374
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	− 2.28432e7i	− 0.901994i
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	2.54158e7	0.987312
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	− 3.36256e7i	− 1.28520i
$928$	0	0
$929$	−5.26024e7	−1.99971	−0.999853	−	0.0171747i	$-0.994533\pi$
$929$	−5.26024e7	−1.99971	−0.999853	+	0.0171747i	$0.994533\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−3.19418e7	−1.17594	−0.587970	−	0.808883i	$-0.700073\pi$
$941$	−3.19418e7	−1.17594	−0.587970	+	0.808883i	$0.700073\pi$
$942$	0	0
$943$	4.85510e6i	0.177795i
$944$	0	0
$945$	−3.19098e7	−1.16237
$946$	0	0
$947$	5.51919e7i	1.99987i	0.0116113	+	0.999933i	$0.496304\pi$
$947$	5.51919e7i	1.99987i	−0.0116113	+	0.999933i	$0.503696\pi$
$948$	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
$961$	−2.86292e7	−1.00000
$962$	0	0
$963$	4.30592e7i	1.49624i
$964$	0	0
$965$	0	0
$966$	0	0
$967$	− 5.52721e7i	− 1.90082i	−0.311006	−	0.950408i	$-0.600666\pi$
$967$	− 5.52721e7i	− 1.90082i	0.311006	−	0.950408i	$-0.399334\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	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
$981$	−1.53586e7	−0.509542
$982$	0	0
$983$	2.14814e7i	0.709052i	0.935046	+	0.354526i	$0.115358\pi$
$983$	2.14814e7i	0.709052i	−0.935046	+	0.354526i	$0.884642\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	4.04643e7i	1.32214i
$988$	0	0
$989$	−5.08079e6	−0.165174
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	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	320.6.c.h.129.2		4
4.3	odd	2	inner	320.6.c.h.129.3		4
5.4	even	2	inner	320.6.c.h.129.3		4
8.3	odd	2		160.6.c.b.129.2	✓	4
8.5	even	2		160.6.c.b.129.3	yes	4
20.19	odd	2	CM	320.6.c.h.129.2		4
40.3	even	4		800.6.a.m.1.1		2
40.13	odd	4		800.6.a.f.1.2		2
40.19	odd	2		160.6.c.b.129.3	yes	4
40.27	even	4		800.6.a.f.1.2		2
40.29	even	2		160.6.c.b.129.2	✓	4
40.37	odd	4		800.6.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.c.b.129.2	✓	4	8.3	odd	2
160.6.c.b.129.2	✓	4	40.29	even	2
160.6.c.b.129.3	yes	4	8.5	even	2
160.6.c.b.129.3	yes	4	40.19	odd	2
320.6.c.h.129.2		4	1.1	even	1	trivial
320.6.c.h.129.2		4	20.19	odd	2	CM
320.6.c.h.129.3		4	4.3	odd	2	inner
320.6.c.h.129.3		4	5.4	even	2	inner
800.6.a.f.1.2		2	40.13	odd	4
800.6.a.f.1.2		2	40.27	even	4
800.6.a.m.1.1		2	40.3	even	4
800.6.a.m.1.1		2	40.37	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-7.81966i q^{3} -55.9017 q^{5} +171.820i q^{7} +181.853 q^{9} +O(q^{10})\)	\(q-7.81966i q^{3} -55.9017 q^{5} +171.820i q^{7} +181.853 q^{9} +437.132i q^{15} +1343.57 q^{21} -230.741i q^{23} +3125.00 q^{25} -3322.21i q^{27} -1686.00 q^{29} -9605.01i q^{35} -21041.4 q^{41} -22019.5i q^{43} -10165.9 q^{45} +30116.9i q^{47} -12715.0 q^{49} -52256.9 q^{61} +31245.9i q^{63} +36856.5i q^{67} -1804.31 q^{69} -24436.4i q^{75} +18211.7 q^{81} -46781.9i q^{83} +13183.9i q^{87} -149286. q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 972 q^{9}+O(q^{10}) \) 4 * q - 972 * q^9	\( 4 q - 972 q^{9} + 14408 q^{21} + 12500 q^{25} - 6744 q^{29} - 95000 q^{45} - 67228 q^{49} + 302344 q^{69} + 485804 q^{81} - 597144 q^{89}+O(q^{100}) \) 4 * q - 972 * q^9 + 14408 * q^21 + 12500 * q^25 - 6744 * q^29 - 95000 * q^45 - 67228 * q^49 + 302344 * q^69 + 485804 * q^81 - 597144 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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