LMFDB - Embedded newform 576.2.i.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(193,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("576.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.i (of order $3$, degree $2$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	576.193
Dual form			576.2.i.a.385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 1.73205i) q^{13} -3.00000 q^{17} -1.00000 q^{19} +(-3.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +5.19615i q^{27} +(3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-4.50000 - 2.59808i) q^{33} +4.00000 q^{37} +3.46410i q^{39} +(-4.50000 + 7.79423i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} +(4.50000 - 2.59808i) q^{51} -12.0000 q^{53} +(1.50000 - 0.866025i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(4.00000 + 6.92820i) q^{61} +6.00000 q^{63} +(-2.50000 + 4.33013i) q^{67} -10.3923i q^{69} +12.0000 q^{71} +11.0000 q^{73} +(-7.50000 - 4.33013i) q^{75} +(-3.00000 + 5.19615i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{83} +(-9.00000 - 5.19615i) q^{87} +6.00000 q^{89} +4.00000 q^{91} -6.92820i q^{93} +(-2.50000 - 4.33013i) q^{97} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 2 q^{7} + 3 q^{9} + 3 q^{11} + 2 q^{13} - 6 q^{17} - 2 q^{19} - 6 q^{21} - 6 q^{23} + 5 q^{25} + 6 q^{29} - 4 q^{31} - 9 q^{33} + 8 q^{37} - 9 q^{41} + q^{43} - 6 q^{47} + 3 q^{49} + 9 q^{51}+ \cdots + 18 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 2 * q^7 + 3 * q^9 + 3 * q^11 + 2 * q^13 - 6 * q^17 - 2 * q^19 - 6 * q^21 - 6 * q^23 + 5 * q^25 + 6 * q^29 - 4 * q^31 - 9 * q^33 + 8 * q^37 - 9 * q^41 + q^43 - 6 * q^47 + 3 * q^49 + 9 * q^51 - 24 * q^53 + 3 * q^57 - 3 * q^59 + 8 * q^61 + 12 * q^63 - 5 * q^67 + 24 * q^71 + 22 * q^73 - 15 * q^75 - 6 * q^77 - 4 * q^79 - 9 * q^81 - 12 * q^83 - 18 * q^87 + 12 * q^89 + 8 * q^91 - 5 * q^97 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$		0			0
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$		0			0
$21$	−3.00000	−	1.73205i	−0.654654	−	0.377964i
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	−4.50000	−	2.59808i	−0.783349	−	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$		0			0
$39$			3.46410i			0.554700i
$40$		0			0
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	4.50000	−	2.59808i	0.630126	−	0.363803i
$52$		0			0
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.50000	−	0.866025i	0.198680	−	0.114708i
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$	6.00000			0.755929
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		−	10.3923i		−	1.25109i
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$		0			0
$75$	−7.50000	−	4.33013i	−0.866025	−	0.500000i
$76$		0			0
$77$	−3.00000	+	5.19615i	−0.341882	+	0.592157i
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.00000	−	5.19615i	−0.964901	−	0.557086i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$		0			0
$93$		−	6.92820i		−	0.718421i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	0.710742	−	0.703452i	$-0.248359\pi$
$97$	−2.50000	−	4.33013i	−0.253837	−	0.439658i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$	9.00000			0.904534
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$		0			0
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$		0			0
$111$	−6.00000	+	3.46410i	−0.569495	+	0.328798i
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$		0			0
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		−	15.5885i		−	1.40556i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$		0			0
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	−0.109984	−	0.993933i	$-0.535080\pi$
$139$	9.50000	−	16.4545i	0.805779	−	1.39565i	0.915764	−	0.401718i	$-0.131587\pi$
$140$		0			0
$141$	9.00000	+	5.19615i	0.757937	+	0.437595i
$142$		0			0
$143$	6.00000			0.501745
$144$		0			0
$145$		0			0
$146$		0			0
$147$			5.19615i			0.428571i
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$		0			0
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$		0			0
$159$	18.0000	−	10.3923i	1.42749	−	0.824163i
$160$		0			0
$161$	−12.0000			−0.945732
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−5.00000	+	8.66025i	−0.377964	+	0.654654i
$176$		0			0
$177$		−	5.19615i		−	0.390567i
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$	−12.0000	−	6.92820i	−0.887066	−	0.512148i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$		0			0
$189$	−9.00000	+	5.19615i	−0.654654	+	0.377964i
$190$		0			0
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$		−	8.66025i		−	0.610847i
$202$		0			0
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	9.00000	+	15.5885i	0.625543	+	1.08347i
$208$		0			0
$209$	−1.50000	−	2.59808i	−0.103757	−	0.179713i
$210$		0			0
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$		0			0
$213$	−18.0000	+	10.3923i	−1.23334	+	0.712069i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.00000			−0.543075
$218$		0			0
$219$	−16.5000	+	9.52628i	−1.11497	+	0.643726i
$220$		0			0
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.861435	+	0.507869i	$0.169566\pi$
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.00910984	+	0.999959i	$0.497100\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$		0			0
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		−	10.3923i		−	0.683763i
$232$		0			0
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.00000	+	3.46410i	0.389742	+	0.225018i
$238$		0			0
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.00000	+	1.73205i	−0.0636285	+	0.110208i
$248$		0			0
$249$	18.0000	+	10.3923i	1.14070	+	0.658586i
$250$		0			0
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$		0			0
$259$	4.00000	+	6.92820i	0.248548	+	0.430498i
$260$		0			0
$261$	18.0000			1.11417
$262$		0			0
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$		0			0
$269$	24.0000			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$270$		0			0
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$		0			0
$273$	−6.00000	+	3.46410i	−0.363137	+	0.209657i
$274$		0			0
$275$	−7.50000	+	12.9904i	−0.452267	+	0.783349i
$276$		0			0
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$		0			0
$279$	6.00000	+	10.3923i	0.359211	+	0.622171i
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.0000			−1.06251
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$	7.50000	+	4.33013i	0.439658	+	0.253837i
$292$		0			0
$293$	15.0000	−	25.9808i	0.876309	−	1.51781i	0.0209480	−	0.999781i	$-0.493332\pi$
$293$	15.0000	−	25.9808i	0.876309	−	1.51781i	0.855361	−	0.518032i	$-0.173335\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−13.5000	+	7.79423i	−0.783349	+	0.452267i
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	−1.00000	+	1.73205i	−0.0576390	+	0.0998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$			24.2487i			1.37946i
$310$		0			0
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	−14.5000	−	25.1147i	−0.819588	−	1.41957i	−0.905986	−	0.423308i	$-0.860869\pi$
$313$	−14.5000	−	25.1147i	−0.819588	−	1.41957i	0.0863973	−	0.996261i	$-0.472465\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$	3.00000			0.166924
$324$		0			0
$325$	10.0000			0.554700
$326$		0			0
$327$	−24.0000	+	13.8564i	−1.32720	+	0.766261i
$328$		0			0
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$		0			0
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.500000	−	0.866025i	0.0272367	−	0.0471754i	−0.852086	−	0.523402i	$-0.824663\pi$
$337$	0.500000	−	0.866025i	0.0272367	−	0.0471754i	0.879322	+	0.476227i	$0.157996\pi$
$338$		0			0
$339$		−	10.3923i		−	0.564433i
$340$		0			0
$341$	−12.0000			−0.649836
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.0409337	+	0.999162i	$0.513033\pi$
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.844833	+	0.535031i	$0.820300\pi$
$348$		0			0
$349$	−8.00000	−	13.8564i	−0.428230	−	0.741716i	0.568486	−	0.822693i	$-0.307529\pi$
$349$	−8.00000	−	13.8564i	−0.428230	−	0.741716i	−0.996716	+	0.0809766i	$0.974196\pi$
$350$		0			0
$351$	9.00000	+	5.19615i	0.480384	+	0.277350i
$352$		0			0
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	9.00000	+	5.19615i	0.476331	+	0.275010i
$358$		0			0
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$		0			0
$363$			3.46410i			0.181818i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$		0			0
$369$	13.5000	+	23.3827i	0.702782	+	1.21725i
$370$		0			0
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.0291379	+	0.999575i	$0.509276\pi$
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.851089	+	0.525022i	$0.824057\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$		0			0
$381$	3.00000	−	1.73205i	0.153695	−	0.0887357i
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.00000			0.152499
$388$		0			0
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−20.0000			−1.00377			−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000			−1.00377			−0.501886	+	0.864934i	$0.667360\pi$
$398$		0			0
$399$	3.00000	+	1.73205i	0.150188	+	0.0867110i
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.00000	+	10.3923i	0.297409	+	0.515127i
$408$		0			0
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$		0			0
$411$	−4.50000	−	2.59808i	−0.221969	−	0.128154i
$412$		0			0
$413$	−6.00000			−0.295241
$414$		0			0
$415$		0			0
$416$		0			0
$417$			32.9090i			1.61156i
$418$		0			0
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	10.0000	+	17.3205i	0.487370	+	0.844150i	0.999895	−	0.0145228i	$-0.00462290\pi$
$421$	10.0000	+	17.3205i	0.487370	+	0.844150i	−0.512524	+	0.858673i	$0.671290\pi$
$422$		0			0
$423$	−18.0000			−0.875190
$424$		0			0
$425$	−7.50000	−	12.9904i	−0.363803	−	0.630126i
$426$		0			0
$427$	−8.00000	+	13.8564i	−0.387147	+	0.670559i
$428$		0			0
$429$	−9.00000	+	5.19615i	−0.434524	+	0.250873i
$430$		0			0
$431$	30.0000			1.44505			0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000			1.44505			0.722525	+	0.691345i	$0.242982\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	0.828190	−	0.560448i	$-0.189371\pi$
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	−0.899457	+	0.437009i	$0.856038\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	10.3923i		−	0.491539i
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	−27.0000			−1.27138
$452$		0			0
$453$	15.0000	+	8.66025i	0.704761	+	0.406894i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	0.595818	−	0.803120i	$-0.296828\pi$
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	−0.993431	+	0.114433i	$0.963495\pi$
$458$		0			0
$459$		−	15.5885i		−	0.727607i
$460$		0			0
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	−0.968945	−	0.247276i	$-0.920465\pi$
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	0.270326	−	0.962769i	$-0.412869\pi$
$462$		0			0
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	−0.534450	−	0.845200i	$-0.679481\pi$
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	0.999190	+	0.0402476i	$0.0128147\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$		0			0
$469$	−10.0000			−0.461757
$470$		0			0
$471$		−	6.92820i		−	0.319235i
$472$		0			0
$473$	−1.50000	+	2.59808i	−0.0689701	+	0.119460i
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$		0			0
$477$	−18.0000	+	31.1769i	−0.824163	+	1.42749i
$478$		0			0
$479$	−21.0000	−	36.3731i	−0.959514	−	1.66193i	−0.723681	−	0.690134i	$-0.757551\pi$
$479$	−21.0000	−	36.3731i	−0.959514	−	1.66193i	−0.235833	−	0.971794i	$-0.575782\pi$
$480$		0			0
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$		0			0
$483$	18.0000	−	10.3923i	0.819028	−	0.472866i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−26.0000			−1.17817			−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000			−1.17817			−0.589086	+	0.808070i	$0.700512\pi$
$488$		0			0
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$		0			0
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		0			0
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$		0			0
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	−0.683062	−	0.730361i	$-0.739352\pi$
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	0.974042	+	0.226369i	$0.0726854\pi$
$500$		0			0
$501$		−	20.7846i		−	0.928588i
$502$		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
$507$	−13.5000	−	7.79423i	−0.599556	−	0.346154i
$508$		0			0
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	11.0000	+	19.0526i	0.486611	+	0.842836i
$512$		0			0
$513$		−	5.19615i		−	0.229416i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	9.00000	−	15.5885i	0.395820	−	0.685580i
$518$		0			0
$519$	9.00000	+	5.19615i	0.395056	+	0.228086i
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$		0			0
$525$		−	17.3205i		−	0.755929i
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	4.50000	+	7.79423i	0.195283	+	0.338241i
$532$		0			0
$533$	9.00000	+	15.5885i	0.389833	+	0.675211i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−18.0000	+	10.3923i	−0.776757	+	0.448461i
$538$		0			0
$539$	9.00000			0.387657
$540$		0			0
$541$	4.00000			0.171973			0.0859867	−	0.996296i	$-0.472596\pi$
$541$	4.00000			0.171973			0.0859867	+	0.996296i	$0.472596\pi$
$542$		0			0
$543$	21.0000	−	12.1244i	0.901196	−	0.520306i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$	24.0000			1.02430
$550$		0			0
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$		0			0
$561$	13.5000	+	7.79423i	0.569970	+	0.329073i
$562$		0			0
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	−0.0824933	−	0.996592i	$-0.526288\pi$
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	0.904320	−	0.426855i	$-0.140378\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	9.00000	−	15.5885i	0.377964	−	0.654654i
$568$		0			0
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.759220	−	0.650835i	$-0.774419\pi$
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.184030	−	0.982921i	$-0.558914\pi$
$570$		0			0
$571$	18.5000	−	32.0429i	0.774201	−	1.34096i	−0.161042	−	0.986948i	$-0.551485\pi$
$571$	18.5000	−	32.0429i	0.774201	−	1.34096i	0.935243	−	0.354008i	$-0.115181\pi$
$572$		0			0
$573$	27.0000	+	15.5885i	1.12794	+	0.651217i
$574$		0			0
$575$	−30.0000			−1.25109
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$		−	8.66025i		−	0.359908i
$580$		0			0
$581$	12.0000	−	20.7846i	0.497844	−	0.862291i
$582$		0			0
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	0.943824	−	0.330449i	$-0.107200\pi$
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	−0.758089	+	0.652151i	$0.773867\pi$
$588$		0			0
$589$	2.00000	−	3.46410i	0.0824086	−	0.142736i
$590$		0			0
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−15.0000	+	8.66025i	−0.613909	+	0.354441i
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$		0			0
$603$	7.50000	+	12.9904i	0.305424	+	0.529009i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−14.0000	+	24.2487i	−0.568242	+	0.984225i	0.428497	+	0.903543i	$0.359043\pi$
$607$	−14.0000	+	24.2487i	−0.568242	+	0.984225i	−0.996740	+	0.0806818i	$0.974290\pi$
$608$		0			0
$609$		−	20.7846i		−	0.842235i
$610$		0			0
$611$	−12.0000			−0.485468
$612$		0			0
$613$	16.0000			0.646234			0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000			0.646234			0.323117	+	0.946359i	$0.395269\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$		0			0
$621$	−27.0000	−	15.5885i	−1.08347	−	0.625543i
$622$		0			0
$623$	6.00000	+	10.3923i	0.240385	+	0.416359i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$		0			0
$627$	4.50000	+	2.59808i	0.179713	+	0.103757i
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$		−	34.6410i		−	1.37686i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$		0			0
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$		0			0
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$		0			0
$643$	−11.5000	+	19.9186i	−0.453516	+	0.785512i	−0.998602	−	0.0528680i	$-0.983164\pi$
$643$	−11.5000	+	19.9186i	−0.453516	+	0.785512i	0.545086	+	0.838380i	$0.316497\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$	12.0000	−	6.92820i	0.470317	−	0.271538i
$652$		0			0
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	16.5000	−	28.5788i	0.643726	−	1.11497i
$658$		0			0
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	−0.902297	−	0.431116i	$-0.858120\pi$
$661$	−2.00000	+	3.46410i	−0.0777910	+	0.134738i	0.824506	+	0.565854i	$0.191453\pi$
$662$		0			0
$663$		−	10.3923i		−	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−36.0000			−1.39393
$668$		0			0
$669$	−39.0000	−	22.5167i	−1.50783	−	0.870544i
$670$		0			0
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		0			0
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	0.996328	−	0.0856156i	$-0.0272857\pi$
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	−0.572309	+	0.820038i	$0.693952\pi$
$674$		0			0
$675$	−22.5000	+	12.9904i	−0.866025	+	0.500000i
$676$		0			0
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	0.971249	+	0.238067i	$0.0765137\pi$
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	−0.279453	+	0.960159i	$0.590153\pi$
$678$		0			0
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$		0			0
$681$	31.5000	+	18.1865i	1.20708	+	0.696909i
$682$		0			0
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			24.2487i			0.925146i
$688$		0			0
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		0			0
$693$	9.00000	+	15.5885i	0.341882	+	0.592157i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$		0			0
$699$	−4.50000	+	2.59808i	−0.170206	+	0.0982683i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−4.00000			−0.150863
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	0.826023	−	0.563636i	$-0.190598\pi$
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	−0.901135	+	0.433539i	$0.857265\pi$
$710$		0			0
$711$	−12.0000			−0.450035
$712$		0			0
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$		0			0
$716$		0			0
$717$			10.3923i			0.388108i
$718$		0			0
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	28.0000			1.04277
$722$		0			0
$723$	−10.5000	−	6.06218i	−0.390499	−	0.225455i
$724$		0			0
$725$	−15.0000	+	25.9808i	−0.557086	+	0.964901i
$726$		0			0
$727$	13.0000	+	22.5167i	0.482143	+	0.835097i	0.999790	−	0.0204978i	$-0.00652512\pi$
$727$	13.0000	+	22.5167i	0.482143	+	0.835097i	−0.517647	+	0.855595i	$0.673192\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.0000			−0.552532
$738$		0			0
$739$	47.0000			1.72892			0.864461	−	0.502699i	$-0.167660\pi$
$739$	47.0000			1.72892			0.864461	+	0.502699i	$0.167660\pi$
$740$		0			0
$741$		−	3.46410i		−	0.127257i
$742$		0			0
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−36.0000			−1.31717
$748$		0			0
$749$	3.00000	+	5.19615i	0.109618	+	0.189863i
$750$		0			0
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	−0.783769	−	0.621052i	$-0.786706\pi$
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	0.929731	+	0.368238i	$0.120039\pi$
$752$		0			0
$753$	−31.5000	+	18.1865i	−1.14792	+	0.662754i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		0			0
$759$	27.0000	−	15.5885i	0.980038	−	0.565825i
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$	16.0000	+	27.7128i	0.579239	+	1.00327i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.00000	+	5.19615i	0.108324	+	0.187622i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$			36.3731i			1.30994i
$772$		0			0
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$	−20.0000			−0.718421
$776$		0			0
$777$	−12.0000	−	6.92820i	−0.430498	−	0.248548i
$778$		0			0
$779$	4.50000	−	7.79423i	0.161229	−	0.279257i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$	−27.0000	+	15.5885i	−0.964901	+	0.557086i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$		0			0
$789$	−27.0000	−	15.5885i	−0.961225	−	0.554964i
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$	16.0000			0.568177
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$		0			0
$801$	9.00000	−	15.5885i	0.317999	−	0.550791i
$802$		0			0
$803$	16.5000	+	28.5788i	0.582272	+	1.00853i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−36.0000	+	20.7846i	−1.26726	+	0.731653i
$808$		0			0
$809$	33.0000			1.16022			0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000			1.16022			0.580109	+	0.814539i	$0.303010\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$		0			0
$813$	30.0000	−	17.3205i	1.05215	−	0.607457i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.500000	−	0.866025i	−0.0174928	−	0.0302984i
$818$		0			0
$819$	6.00000	−	10.3923i	0.209657	−	0.363137i
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$		−	25.9808i		−	0.904534i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$		0			0
$831$	15.0000	+	8.66025i	0.520344	+	0.300421i
$832$		0			0
$833$	−4.50000	+	7.79423i	−0.155916	+	0.270054i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−18.0000	−	10.3923i	−0.622171	−	0.359211i
$838$		0			0
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	0.950813	−	0.309764i	$-0.100250\pi$
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	−0.743670	+	0.668546i	$0.766917\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	9.00000	+	5.19615i	0.309976	+	0.178965i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	4.00000			0.137442
$848$		0			0
$849$			6.92820i			0.237775i
$850$		0			0
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$	13.0000	+	22.5167i	0.445112	+	0.770956i	0.998060	−	0.0622597i	$-0.0198307\pi$
$853$	13.0000	+	22.5167i	0.445112	+	0.770956i	−0.552948	+	0.833215i	$0.686497\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	−17.5000	+	30.3109i	−0.597092	+	1.03419i	0.396156	+	0.918183i	$0.370344\pi$
$859$	−17.5000	+	30.3109i	−0.597092	+	1.03419i	−0.993248	+	0.116011i	$0.962989\pi$
$860$		0			0
$861$	27.0000	−	15.5885i	0.920158	−	0.531253i
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$		0			0
$869$	6.00000	−	10.3923i	0.203536	−	0.352535i
$870$		0			0
$871$	5.00000	+	8.66025i	0.169419	+	0.293442i
$872$		0			0
$873$	−15.0000			−0.507673
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	−0.790554	−	0.612392i	$-0.790207\pi$
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	0.925624	+	0.378444i	$0.123541\pi$
$878$		0			0
$879$			51.9615i			1.75262i
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	−2.00000	−	3.46410i	−0.0670778	−	0.116182i
$890$		0			0
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$		0			0
$893$	3.00000	+	5.19615i	0.100391	+	0.173883i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−18.0000	−	10.3923i	−0.601003	−	0.346989i
$898$		0			0
$899$	−24.0000			−0.800445
$900$		0			0
$901$	36.0000			1.19933
$902$		0			0
$903$		−	3.46410i		−	0.115278i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	0.999855	+	0.0170220i	$0.00541854\pi$
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	−0.485186	+	0.874411i	$0.661248\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	0.922740	+	0.385422i	$0.125944\pi$
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	−0.127585	+	0.991828i	$0.540723\pi$
$912$		0			0
$913$	18.0000	−	31.1769i	0.595713	−	1.03181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$		0			0
$921$	10.5000	−	6.06218i	0.345987	−	0.199756i
$922$		0			0
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	10.0000	+	17.3205i	0.328798	+	0.569495i
$926$		0			0
$927$	−21.0000	−	36.3731i	−0.689730	−	1.19465i
$928$		0			0
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	−1.50000	+	2.59808i	−0.0491605	+	0.0851485i
$932$		0			0
$933$		−	31.1769i		−	1.02069i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$		0			0
$939$	43.5000	+	25.1147i	1.41957	+	0.819588i
$940$		0			0
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.308215	+	0.951317i	$0.599732\pi$
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.669757	+	0.742581i	$0.733602\pi$
$942$		0			0
$943$	−27.0000	−	46.7654i	−0.879241	−	1.52289i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$		0			0
$949$	11.0000	−	19.0526i	0.357075	−	0.618472i
$950$		0			0
$951$	27.0000	+	15.5885i	0.875535	+	0.505490i
$952$		0			0
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	31.1769i		−	1.00781i
$958$		0			0
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.0000	+	19.0526i	−0.353736	+	0.612689i	−0.986901	−	0.161328i	$-0.948422\pi$
$967$	−11.0000	+	19.0526i	−0.353736	+	0.612689i	0.633165	+	0.774017i	$0.281756\pi$
$968$		0			0
$969$	−4.50000	+	2.59808i	−0.144561	+	0.0834622i
$970$		0			0
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		0			0
$973$	38.0000			1.21822
$974$		0			0
$975$	−15.0000	+	8.66025i	−0.480384	+	0.277350i
$976$		0			0
$977$	25.5000	−	44.1673i	0.815817	−	1.41304i	−0.0929223	−	0.995673i	$-0.529621\pi$
$977$	25.5000	−	44.1673i	0.815817	−	1.41304i	0.908740	−	0.417364i	$-0.137046\pi$
$978$		0			0
$979$	9.00000	+	15.5885i	0.287641	+	0.498209i
$980$		0			0
$981$	24.0000	−	41.5692i	0.766261	−	1.32720i
$982$		0			0
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			20.7846i			0.661581i
$988$		0			0
$989$	−6.00000			−0.190789
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	−6.00000	−	3.46410i	−0.190404	−	0.109930i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	0.554554	−	0.832148i	$-0.312889\pi$
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	−0.997938	+	0.0641836i	$0.979556\pi$
$998$		0			0
$999$			20.7846i			0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.i.a.193.1		2
3.2	odd	2		1728.2.i.f.577.1		2
4.3	odd	2		576.2.i.g.193.1		2
8.3	odd	2		18.2.c.a.13.1	yes	2
8.5	even	2		144.2.i.c.49.1		2
9.2	odd	6		1728.2.i.f.1153.1		2
9.4	even	3		5184.2.a.o.1.1		1
9.5	odd	6		5184.2.a.p.1.1		1
9.7	even	3	inner	576.2.i.a.385.1		2
12.11	even	2		1728.2.i.e.577.1		2
24.5	odd	2		432.2.i.b.145.1		2
24.11	even	2		54.2.c.a.37.1		2
36.7	odd	6		576.2.i.g.385.1		2
36.11	even	6		1728.2.i.e.1153.1		2
36.23	even	6		5184.2.a.q.1.1		1
36.31	odd	6		5184.2.a.r.1.1		1
40.3	even	4		450.2.j.e.49.1		4
40.19	odd	2		450.2.e.i.301.1		2
40.27	even	4		450.2.j.e.49.2		4
56.3	even	6		882.2.e.g.373.1		2
56.11	odd	6		882.2.e.i.373.1		2
56.19	even	6		882.2.h.b.67.1		2
56.27	even	2		882.2.f.d.589.1		2
56.51	odd	6		882.2.h.c.67.1		2
72.5	odd	6		1296.2.a.f.1.1		1
72.11	even	6		54.2.c.a.19.1		2
72.13	even	6		1296.2.a.g.1.1		1
72.29	odd	6		432.2.i.b.289.1		2
72.43	odd	6		18.2.c.a.7.1	✓	2
72.59	even	6		162.2.a.b.1.1		1
72.61	even	6		144.2.i.c.97.1		2
72.67	odd	6		162.2.a.c.1.1		1
120.59	even	2		1350.2.e.c.901.1		2
120.83	odd	4		1350.2.j.a.199.2		4
120.107	odd	4		1350.2.j.a.199.1		4
168.11	even	6		2646.2.e.b.1549.1		2
168.59	odd	6		2646.2.e.c.1549.1		2
168.83	odd	2		2646.2.f.g.1765.1		2
168.107	even	6		2646.2.h.h.361.1		2
168.131	odd	6		2646.2.h.i.361.1		2
360.43	even	12		450.2.j.e.349.2		4
360.59	even	6		4050.2.a.v.1.1		1
360.67	even	12		4050.2.c.c.649.2		2
360.83	odd	12		1350.2.j.a.1099.1		4
360.139	odd	6		4050.2.a.c.1.1		1
360.187	even	12		450.2.j.e.349.1		4
360.203	odd	12		4050.2.c.r.649.2		2
360.227	odd	12		1350.2.j.a.1099.2		4
360.259	odd	6		450.2.e.i.151.1		2
360.283	even	12		4050.2.c.c.649.1		2
360.299	even	6		1350.2.e.c.451.1		2
360.347	odd	12		4050.2.c.r.649.1		2
504.11	even	6		2646.2.h.h.667.1		2
504.83	odd	6		2646.2.f.g.883.1		2
504.115	even	6		882.2.h.b.79.1		2
504.139	even	6		7938.2.a.x.1.1		1
504.187	even	6		882.2.e.g.655.1		2
504.227	odd	6		2646.2.h.i.667.1		2
504.299	odd	6		2646.2.e.c.2125.1		2
504.331	odd	6		882.2.e.i.655.1		2
504.403	odd	6		882.2.h.c.79.1		2
504.419	odd	6		7938.2.a.i.1.1		1
504.443	even	6		2646.2.e.b.2125.1		2
504.475	even	6		882.2.f.d.295.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.2.c.a.7.1	✓	2	72.43	odd	6
18.2.c.a.13.1	yes	2	8.3	odd	2
54.2.c.a.19.1		2	72.11	even	6
54.2.c.a.37.1		2	24.11	even	2
144.2.i.c.49.1		2	8.5	even	2
144.2.i.c.97.1		2	72.61	even	6
162.2.a.b.1.1		1	72.59	even	6
162.2.a.c.1.1		1	72.67	odd	6
432.2.i.b.145.1		2	24.5	odd	2
432.2.i.b.289.1		2	72.29	odd	6
450.2.e.i.151.1		2	360.259	odd	6
450.2.e.i.301.1		2	40.19	odd	2
450.2.j.e.49.1		4	40.3	even	4
450.2.j.e.49.2		4	40.27	even	4
450.2.j.e.349.1		4	360.187	even	12
450.2.j.e.349.2		4	360.43	even	12
576.2.i.a.193.1		2	1.1	even	1	trivial
576.2.i.a.385.1		2	9.7	even	3	inner
576.2.i.g.193.1		2	4.3	odd	2
576.2.i.g.385.1		2	36.7	odd	6
882.2.e.g.373.1		2	56.3	even	6
882.2.e.g.655.1		2	504.187	even	6
882.2.e.i.373.1		2	56.11	odd	6
882.2.e.i.655.1		2	504.331	odd	6
882.2.f.d.295.1		2	504.475	even	6
882.2.f.d.589.1		2	56.27	even	2
882.2.h.b.67.1		2	56.19	even	6
882.2.h.b.79.1		2	504.115	even	6
882.2.h.c.67.1		2	56.51	odd	6
882.2.h.c.79.1		2	504.403	odd	6
1296.2.a.f.1.1		1	72.5	odd	6
1296.2.a.g.1.1		1	72.13	even	6
1350.2.e.c.451.1		2	360.299	even	6
1350.2.e.c.901.1		2	120.59	even	2
1350.2.j.a.199.1		4	120.107	odd	4
1350.2.j.a.199.2		4	120.83	odd	4
1350.2.j.a.1099.1		4	360.83	odd	12
1350.2.j.a.1099.2		4	360.227	odd	12
1728.2.i.e.577.1		2	12.11	even	2
1728.2.i.e.1153.1		2	36.11	even	6
1728.2.i.f.577.1		2	3.2	odd	2
1728.2.i.f.1153.1		2	9.2	odd	6
2646.2.e.b.1549.1		2	168.11	even	6
2646.2.e.b.2125.1		2	504.443	even	6
2646.2.e.c.1549.1		2	168.59	odd	6
2646.2.e.c.2125.1		2	504.299	odd	6
2646.2.f.g.883.1		2	504.83	odd	6
2646.2.f.g.1765.1		2	168.83	odd	2
2646.2.h.h.361.1		2	168.107	even	6
2646.2.h.h.667.1		2	504.11	even	6
2646.2.h.i.361.1		2	168.131	odd	6
2646.2.h.i.667.1		2	504.227	odd	6
4050.2.a.c.1.1		1	360.139	odd	6
4050.2.a.v.1.1		1	360.59	even	6
4050.2.c.c.649.1		2	360.283	even	12
4050.2.c.c.649.2		2	360.67	even	12
4050.2.c.r.649.1		2	360.347	odd	12
4050.2.c.r.649.2		2	360.203	odd	12
5184.2.a.o.1.1		1	9.4	even	3
5184.2.a.p.1.1		1	9.5	odd	6
5184.2.a.q.1.1		1	36.23	even	6
5184.2.a.r.1.1		1	36.31	odd	6
7938.2.a.i.1.1		1	504.419	odd	6
7938.2.a.x.1.1		1	504.139	even	6

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 1.73205i) q^{13} -3.00000 q^{17} -1.00000 q^{19} +(-3.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +5.19615i q^{27} +(3.00000 + 5.19615i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-4.50000 - 2.59808i) q^{33} +4.00000 q^{37} +3.46410i q^{39} +(-4.50000 + 7.79423i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} +(4.50000 - 2.59808i) q^{51} -12.0000 q^{53} +(1.50000 - 0.866025i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(4.00000 + 6.92820i) q^{61} +6.00000 q^{63} +(-2.50000 + 4.33013i) q^{67} -10.3923i q^{69} +12.0000 q^{71} +11.0000 q^{73} +(-7.50000 - 4.33013i) q^{75} +(-3.00000 + 5.19615i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{83} +(-9.00000 - 5.19615i) q^{87} +6.00000 q^{89} +4.00000 q^{91} -6.92820i q^{93} +(-2.50000 - 4.33013i) q^{97} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 2 q^{7} + 3 q^{9} + 3 q^{11} + 2 q^{13} - 6 q^{17} - 2 q^{19} - 6 q^{21} - 6 q^{23} + 5 q^{25} + 6 q^{29} - 4 q^{31} - 9 q^{33} + 8 q^{37} - 9 q^{41} + q^{43} - 6 q^{47} + 3 q^{49} + 9 q^{51}+ \cdots + 18 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 2 * q^7 + 3 * q^9 + 3 * q^11 + 2 * q^13 - 6 * q^17 - 2 * q^19 - 6 * q^21 - 6 * q^23 + 5 * q^25 + 6 * q^29 - 4 * q^31 - 9 * q^33 + 8 * q^37 - 9 * q^41 + q^43 - 6 * q^47 + 3 * q^49 + 9 * q^51 - 24 * q^53 + 3 * q^57 - 3 * q^59 + 8 * q^61 + 12 * q^63 - 5 * q^67 + 24 * q^71 + 22 * q^73 - 15 * q^75 - 6 * q^77 - 4 * q^79 - 9 * q^81 - 12 * q^83 - 18 * q^87 + 12 * q^89 + 8 * q^91 - 5 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more