LMFDB - Embedded newform 1232.2.q.d.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (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:	$9.83756952902$
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 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.d.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(3.00000 + 5.19615i) q^{17} +(1.00000 - 1.73205i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +5.00000 q^{27} +9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(-0.500000 - 0.866025i) q^{39} -6.00000 q^{41} +4.00000 q^{43} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-3.00000 + 5.19615i) q^{51} +2.00000 q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(5.00000 + 1.73205i) q^{63} +(5.50000 + 9.52628i) q^{67} -6.00000 q^{69} +(-1.00000 - 1.73205i) q^{73} +(-2.50000 + 4.33013i) q^{75} +(2.00000 - 1.73205i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +6.00000 q^{83} +(4.50000 + 7.79423i) q^{87} +(9.00000 - 15.5885i) q^{89} +(-0.500000 - 2.59808i) q^{91} +(2.00000 - 3.46410i) q^{93} -13.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + q^7 + 2 * q^9	$ 2 q + q^{3} + q^{7} + 2 q^{9} - q^{11} - 2 q^{13} + 6 q^{17} + 2 q^{19} - 4 q^{21} - 6 q^{23} + 5 q^{25} + 10 q^{27} + 18 q^{29} - 4 q^{31} + q^{33} - 2 q^{37} - q^{39} - 12 q^{41} + 8 q^{43} - 6 q^{47} - 13 q^{49} - 6 q^{51} + 4 q^{57} - 3 q^{59} - 11 q^{61} + 10 q^{63} + 11 q^{67} - 12 q^{69} - 2 q^{73} - 5 q^{75} + 4 q^{77} + 5 q^{79} - q^{81} + 12 q^{83} + 9 q^{87} + 18 q^{89} - q^{91} + 4 q^{93} - 26 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q + q^3 + q^7 + 2 * q^9 - q^11 - 2 * q^13 + 6 * q^17 + 2 * q^19 - 4 * q^21 - 6 * q^23 + 5 * q^25 + 10 * q^27 + 18 * q^29 - 4 * q^31 + q^33 - 2 * q^37 - q^39 - 12 * q^41 + 8 * q^43 - 6 * q^47 - 13 * q^49 - 6 * q^51 + 4 * q^57 - 3 * q^59 - 11 * q^61 + 10 * q^63 + 11 * q^67 - 12 * q^69 - 2 * q^73 - 5 * q^75 + 4 * q^77 + 5 * q^79 - q^81 + 12 * q^83 + 9 * q^87 + 18 * q^89 - q^91 + 4 * q^93 - 26 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		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
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	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
$27$	5.00000			0.962250
$28$		0			0
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$		0			0
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$		0			0
$63$	5.00000	+	1.73205i	0.629941	+	0.218218i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	0.977356	+	0.211604i	$0.0678686\pi$
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	−0.305424	+	0.952217i	$0.598798\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	−2.50000	+	4.33013i	−0.288675	+	0.500000i
$76$		0			0
$77$	2.00000	−	1.73205i	0.227921	−	0.197386i
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$		0			0
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.217354	−	0.976093i	$-0.430258\pi$
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.736644	−	0.676280i	$-0.236409\pi$
$90$		0			0
$91$	−0.500000	−	2.59808i	−0.0524142	−	0.272352i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$		0			0
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$		0			0
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$		0			0
$119$	−12.0000	+	10.3923i	−1.10004	+	0.952661i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	7.00000			0.621150			0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000			0.621150			0.310575	+	0.950549i	$0.399478\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		0			0
$133$	5.00000	+	1.73205i	0.433555	+	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.50000	−	4.33013i	−0.453632	−	0.357143i
$148$		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
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−15.0000	−	5.19615i	−1.18217	−	0.409514i
$162$		0			0
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127601\pi$
$174$		0			0
$175$	−10.0000	+	8.66025i	−0.755929	+	0.654654i
$176$		0			0
$177$	1.50000	−	2.59808i	0.112747	−	0.195283i
$178$		0			0
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	−11.0000			−0.813143
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$		0			0
$189$	2.50000	+	12.9904i	0.181848	+	0.944911i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$		0			0
$201$	−5.50000	+	9.52628i	−0.387940	+	0.671932i
$202$		0			0
$203$	4.50000	+	23.3827i	0.315838	+	1.64114i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$		0			0
$209$	−2.00000			−0.138343
$210$		0			0
$211$	10.0000			0.688428			0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000			0.688428			0.344214	+	0.938891i	$0.388145\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$		0			0
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$		0			0
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$		0			0
$223$	−26.0000			−1.74109			−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000			−1.74109			−0.870544	+	0.492090i	$0.836233\pi$
$224$		0			0
$225$	10.0000			0.666667
$226$		0			0
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	−0.470787	−	0.882247i	$-0.656030\pi$
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	0.999442	−	0.0334101i	$-0.0106368\pi$
$230$		0			0
$231$	2.50000	+	0.866025i	0.164488	+	0.0569803i
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.00000			0.324785
$238$		0			0
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.00000	+	1.73205i	−0.0636285	+	0.110208i
$248$		0			0
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	−5.00000	−	1.73205i	−0.310685	−	0.107624i
$260$		0			0
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$		0			0
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.0000			1.10158
$268$		0			0
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		0			0
$271$	14.5000	−	25.1147i	0.880812	−	1.52561i	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	14.5000	−	25.1147i	0.880812	−	1.52561i	0.850439	−	0.526073i	$-0.176336\pi$
$272$		0			0
$273$	2.00000	−	1.73205i	0.121046	−	0.104828i
$274$		0			0
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	−14.5000	−	25.1147i	−0.871221	−	1.50900i	−0.860735	−	0.509053i	$-0.829996\pi$
$277$	−14.5000	−	25.1147i	−0.871221	−	1.50900i	−0.0104855	−	0.999945i	$-0.503338\pi$
$278$		0			0
$279$	−8.00000			−0.478947
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−6.50000	−	11.2583i	−0.381037	−	0.659975i
$292$		0			0
$293$	−30.0000			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.50000	−	4.33013i	−0.145065	−	0.251259i
$298$		0			0
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	2.00000	+	10.3923i	0.115278	+	0.599002i
$302$		0			0
$303$	−7.50000	+	12.9904i	−0.430864	+	0.746278i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	−0.999748	−	0.0224310i	$-0.992859\pi$
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	0.519300	+	0.854592i	$0.326193\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	−2.50000	−	4.33013i	−0.138675	−	0.240192i
$326$		0			0
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$	−15.0000	−	5.19615i	−0.826977	−	0.286473i
$330$		0			0
$331$	17.5000	−	30.3109i	0.961887	−	1.66604i	0.244131	−	0.969742i	$-0.421497\pi$
$331$	17.5000	−	30.3109i	0.961887	−	1.66604i	0.717756	−	0.696295i	$-0.245169\pi$
$332$		0			0
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	4.50000	+	7.79423i	0.244406	+	0.423324i
$340$		0			0
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$		0			0
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−15.0000	−	5.19615i	−0.793884	−	0.275010i
$358$		0			0
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	−0.902891	−	0.429870i	$-0.858559\pi$
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	0.823724	+	0.566991i	$0.191893\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−1.00000			−0.0524864
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$		0			0
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−23.0000			−1.18143			−0.590715	−	0.806880i	$-0.701154\pi$
$379$	−23.0000			−1.18143			−0.590715	+	0.806880i	$0.701154\pi$
$380$		0			0
$381$	3.50000	+	6.06218i	0.179310	+	0.310575i
$382$		0			0
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$		0			0
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	0.672874	−	0.739758i	$-0.265060\pi$
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931726\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$		0			0
$393$	18.0000			0.907980
$394$		0			0
$395$		0			0
$396$		0			0
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$		0			0
$399$	1.00000	+	5.19615i	0.0500626	+	0.260133i
$400$		0			0
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$		0			0
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.00000			0.0991363
$408$		0			0
$409$	2.00000	+	3.46410i	0.0988936	+	0.171289i	0.911227	−	0.411905i	$-0.135136\pi$
$409$	2.00000	+	3.46410i	0.0988936	+	0.171289i	−0.812333	+	0.583193i	$0.801803\pi$
$410$		0			0
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$		0			0
$413$	6.00000	−	5.19615i	0.295241	−	0.255686i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$		0			0
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$		0			0
$425$	−15.0000	+	25.9808i	−0.727607	+	1.26025i
$426$		0			0
$427$	−27.5000	−	9.52628i	−1.33082	−	0.461009i
$428$		0			0
$429$	−0.500000	+	0.866025i	−0.0241402	+	0.0418121i
$430$		0			0
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$		0			0
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	−0.877711	−	0.479191i	$-0.840930\pi$
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	0.853847	+	0.520524i	$0.174263\pi$
$440$		0			0
$441$	−2.00000	+	13.8564i	−0.0952381	+	0.659829i
$442$		0			0
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$		0			0
$453$	9.50000	−	16.4545i	0.446349	−	0.773099i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	−0.485299	−	0.874348i	$-0.661289\pi$
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	0.999857	−	0.0168929i	$-0.00537742\pi$
$458$		0			0
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$		0			0
$461$	21.0000			0.978068			0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000			0.978068			0.489034	+	0.872265i	$0.337349\pi$
$462$		0			0
$463$	22.0000			1.02243			0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000			1.02243			0.511213	+	0.859454i	$0.329196\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$		0			0
$469$	−22.0000	+	19.0526i	−1.01587	+	0.879765i
$470$		0			0
$471$	−2.00000	+	3.46410i	−0.0921551	+	0.159617i
$472$		0			0
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$		0			0
$475$	10.0000			0.458831
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	0.984930	−	0.172953i	$-0.0553307\pi$
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	−0.642246	+	0.766498i	$0.721997\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$		0			0
$483$	−3.00000	−	15.5885i	−0.136505	−	0.709299i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	0.998579	−	0.0532853i	$-0.0169693\pi$
$487$	10.0000	+	17.3205i	0.453143	+	0.784867i	−0.545436	+	0.838152i	$0.683636\pi$
$488$		0			0
$489$	17.0000			0.768767
$490$		0			0
$491$	−42.0000			−1.89543			−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000			−1.89543			−0.947717	+	0.319113i	$0.896615\pi$
$492$		0			0
$493$	27.0000	+	46.7654i	1.21602	+	2.10621i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−20.0000	+	34.6410i	−0.895323	+	1.55074i	−0.0619186	+	0.998081i	$0.519722\pi$
$499$	−20.0000	+	34.6410i	−0.895323	+	1.55074i	−0.833404	+	0.552664i	$0.813611\pi$
$500$		0			0
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$		0			0
$503$	33.0000			1.47140			0.735699	−	0.677309i	$-0.236854\pi$
$503$	33.0000			1.47140			0.735699	+	0.677309i	$0.236854\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$	4.00000	−	3.46410i	0.176950	−	0.153243i
$512$		0			0
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.00000			0.263880
$518$		0			0
$519$	21.0000			0.921798
$520$		0			0
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$		0			0
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$		0			0
$525$	−12.5000	−	4.33013i	−0.545545	−	0.188982i
$526$		0			0
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	6.00000			0.259889
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.50000	−	12.9904i	0.323649	−	0.560576i
$538$		0			0
$539$	5.50000	+	4.33013i	0.236902	+	0.186512i
$540$		0			0
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$		0			0
$543$	1.00000	+	1.73205i	0.0429141	+	0.0743294i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	11.0000	+	19.0526i	0.469469	+	0.813143i
$550$		0			0
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$		0			0
$553$	12.5000	+	4.33013i	0.531554	+	0.184136i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$	6.00000			0.253320
$562$		0			0
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.00000	−	1.73205i	0.0839921	−	0.0727393i
$568$		0			0
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	−0.190974	−	0.981595i	$-0.561165\pi$
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	0.945573	−	0.325409i	$-0.105502\pi$
$570$		0			0
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$	6.00000			0.250654
$574$		0			0
$575$	−30.0000			−1.25109
$576$		0			0
$577$	3.50000	+	6.06218i	0.145707	+	0.252372i	0.929636	−	0.368478i	$-0.120121\pi$
$577$	3.50000	+	6.06218i	0.145707	+	0.252372i	−0.783930	+	0.620850i	$0.786788\pi$
$578$		0			0
$579$	7.00000	−	12.1244i	0.290910	−	0.503871i
$580$		0			0
$581$	3.00000	+	15.5885i	0.124461	+	0.646718i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.00000			−0.371470			−0.185735	−	0.982600i	$-0.559467\pi$
$587$	−9.00000			−0.371470			−0.185735	+	0.982600i	$0.559467\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$		0			0
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.00000	+	12.1244i	−0.286491	+	0.496217i
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$	22.0000			0.895909
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$		0			0
$609$	−18.0000	+	15.5885i	−0.729397	+	0.631676i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.0000			0.845428			0.422714	−	0.906263i	$-0.361077\pi$
$617$	21.0000			0.845428			0.422714	+	0.906263i	$0.361077\pi$
$618$		0			0
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$		0			0
$623$	45.0000	+	15.5885i	1.80289	+	0.624538i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$		0			0
$627$	−1.00000	−	1.73205i	−0.0399362	−	0.0691714i
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		0			0
$633$	5.00000	+	8.66025i	0.198732	+	0.344214i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	6.50000	−	2.59808i	0.257539	−	0.102940i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$		0			0
$643$	−5.00000			−0.197181			−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000			−0.197181			−0.0985904	+	0.995128i	$0.531433\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$		0			0
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$		0			0
$651$	10.0000	+	3.46410i	0.391931	+	0.135769i
$652$		0			0
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$		0			0
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$		0			0
$669$	−13.0000	−	22.5167i	−0.502609	−	0.870544i
$670$		0			0
$671$	11.0000			0.424650
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$		0			0
$675$	12.5000	+	21.6506i	0.481125	+	0.833333i
$676$		0			0
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$		0			0
$679$	−6.50000	−	33.7750i	−0.249447	−	1.29617i
$680$		0			0
$681$	−9.00000	+	15.5885i	−0.344881	+	0.597351i
$682$		0			0
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	16.0000			0.610438
$688$		0			0
$689$		0			0
$690$		0			0
$691$	5.50000	−	9.52628i	0.209230	−	0.362397i	−0.742242	−	0.670132i	$-0.766238\pi$
$691$	5.50000	−	9.52628i	0.209230	−	0.362397i	0.951472	+	0.307735i	$0.0995710\pi$
$692$		0			0
$693$	−1.00000	−	5.19615i	−0.0379869	−	0.197386i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$		0			0
$699$	6.00000			0.226941
$700$		0			0
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$		0			0
$703$	2.00000	+	3.46410i	0.0754314	+	0.130651i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.0000	+	25.9808i	−1.12827	+	0.977107i
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$	−5.00000	−	8.66025i	−0.187515	−	0.324785i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.50000	+	7.79423i	0.168056	+	0.291081i
$718$		0			0
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	0.146920	+	0.989148i	$0.453064\pi$
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	−0.930087	+	0.367338i	$0.880269\pi$
$720$		0			0
$721$	−40.0000	−	13.8564i	−1.48968	−	0.516040i
$722$		0			0
$723$	13.0000	−	22.5167i	0.483475	−	0.837404i
$724$		0			0
$725$	22.5000	+	38.9711i	0.835629	+	1.44735i
$726$		0			0
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	12.5000	−	21.6506i	0.461698	−	0.799684i	−0.537348	−	0.843361i	$-0.680574\pi$
$733$	12.5000	−	21.6506i	0.461698	−	0.799684i	0.999046	+	0.0436764i	$0.0139070\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.50000	−	9.52628i	0.202595	−	0.350905i
$738$		0			0
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.799962	+	0.600050i	$0.204853\pi$
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.119677	+	0.992813i	$0.461814\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$	30.0000	+	10.3923i	1.09618	+	0.379727i
$750$		0			0
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$		0			0
$753$	6.00000	+	10.3923i	0.218652	+	0.378717i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$		0			0
$759$	3.00000	+	5.19615i	0.108893	+	0.188608i
$760$		0			0
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	−0.655515	−	0.755182i	$-0.727548\pi$
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	0.981764	+	0.190101i	$0.0608816\pi$
$762$		0			0
$763$	4.00000	−	3.46410i	0.144810	−	0.125409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.50000	+	2.59808i	0.0541619	+	0.0938111i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$		0			0
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	0.565402	−	0.824815i	$-0.308721\pi$
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	−0.997012	+	0.0772449i	$0.975388\pi$
$774$		0			0
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$		0			0
$777$	−1.00000	−	5.19615i	−0.0358748	−	0.186411i
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	45.0000			1.60817
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	0.963394	−	0.268091i	$-0.0863928\pi$
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	−0.713871	+	0.700278i	$0.753059\pi$
$788$		0			0
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$	4.50000	+	23.3827i	0.160002	+	0.831393i
$792$		0			0
$793$	5.50000	−	9.52628i	0.195311	−	0.338288i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$		0			0
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$		0			0
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.00000	−	10.3923i	0.211210	−	0.365826i
$808$		0			0
$809$	24.0000	+	41.5692i	0.843795	+	1.46150i	0.886664	+	0.462415i	$0.153017\pi$
$809$	24.0000	+	41.5692i	0.843795	+	1.46150i	−0.0428684	+	0.999081i	$0.513650\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	29.0000			1.01707
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$		0			0
$819$	−5.00000	−	1.73205i	−0.174714	−	0.0605228i
$820$		0			0
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		0			0
$823$	−5.00000	−	8.66025i	−0.174289	−	0.301877i	0.765626	−	0.643286i	$-0.222429\pi$
$823$	−5.00000	−	8.66025i	−0.174289	−	0.301877i	−0.939915	+	0.341409i	$0.889096\pi$
$824$		0			0
$825$	5.00000			0.174078
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.823557	+	0.567234i	$0.191986\pi$
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.0794606	+	0.996838i	$0.474680\pi$
$830$		0			0
$831$	14.5000	−	25.1147i	0.502999	−	0.871221i
$832$		0			0
$833$	−33.0000	−	25.9808i	−1.14338	−	0.900180i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−10.0000	−	17.3205i	−0.345651	−	0.598684i
$838$		0			0
$839$	−6.00000			−0.207143			−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000			−0.207143			−0.103572	+	0.994622i	$0.533027\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.50000	−	0.866025i	−0.0859010	−	0.0297570i
$848$		0			0
$849$	5.00000	−	8.66025i	0.171600	−	0.297219i
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	−0.990408	−	0.138177i	$-0.955876\pi$
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	0.375539	−	0.926806i	$-0.377458\pi$
$858$		0			0
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	0.356092	+	0.934451i	$0.384109\pi$
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	−0.987304	+	0.158840i	$0.949225\pi$
$860$		0			0
$861$	12.0000	−	10.3923i	0.408959	−	0.354169i
$862$		0			0
$863$	15.0000	−	25.9808i	0.510606	−	0.884395i	−0.489319	−	0.872105i	$-0.662754\pi$
$863$	15.0000	−	25.9808i	0.510606	−	0.884395i	0.999924	−	0.0122903i	$-0.00391222\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−19.0000			−0.645274
$868$		0			0
$869$	−5.00000			−0.169613
$870$		0			0
$871$	−5.50000	−	9.52628i	−0.186360	−	0.322786i
$872$		0			0
$873$	−13.0000	+	22.5167i	−0.439983	+	0.762073i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$		0			0
$879$	−15.0000	−	25.9808i	−0.505937	−	0.876309i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	−0.839744	−	0.542983i	$-0.817295\pi$
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	0.890109	+	0.455748i	$0.150628\pi$
$888$		0			0
$889$	3.50000	+	18.1865i	0.117386	+	0.609957i
$890$		0			0
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$		0			0
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.00000			0.200334
$898$		0			0
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−8.00000	+	6.92820i	−0.266223	+	0.230556i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$		0			0
$909$	30.0000			0.995037
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	−3.00000	−	5.19615i	−0.0992855	−	0.171968i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	45.0000	+	15.5885i	1.48603	+	0.514776i
$918$		0			0
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$		0			0
$927$	16.0000	+	27.7128i	0.525509	+	0.910208i
$928$		0			0
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$930$		0			0
$931$	−2.00000	+	13.8564i	−0.0655474	+	0.454125i
$932$		0			0
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$		0			0
$939$	−17.0000			−0.554774
$940$		0			0
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	0.717496	−	0.696563i	$-0.245288\pi$
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	−0.961989	+	0.273088i	$0.911955\pi$
$942$		0			0
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	−0.602494	−	0.798123i	$-0.705826\pi$
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	0.992442	+	0.122714i	$0.0391598\pi$
$948$		0			0
$949$	1.00000	+	1.73205i	0.0324614	+	0.0562247i
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	4.50000	−	7.79423i	0.145464	−	0.251952i
$958$		0			0
$959$	−18.0000	+	15.5885i	−0.581250	+	0.503378i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−12.0000	−	20.7846i	−0.386695	−	0.669775i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$		0			0
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	−4.00000	−	20.7846i	−0.128234	−	0.666324i
$974$		0			0
$975$	2.50000	−	4.33013i	0.0800641	−	0.138675i
$976$		0			0
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$		0			0
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	−0.909894	+	0.414840i	$0.863838\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.00000	−	15.5885i	−0.0954911	−	0.496186i
$988$		0			0
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	−20.0000	−	34.6410i	−0.635321	−	1.10041i	−0.986447	−	0.164080i	$-0.947534\pi$
$991$	−20.0000	−	34.6410i	−0.635321	−	1.10041i	0.351126	−	0.936328i	$-0.385799\pi$
$992$		0			0
$993$	35.0000			1.11069
$994$		0			0
$995$		0			0
$996$		0			0
$997$	17.0000	+	29.4449i	0.538395	+	0.932528i	0.998991	+	0.0449179i	$0.0143026\pi$
$997$	17.0000	+	29.4449i	0.538395	+	0.932528i	−0.460595	+	0.887610i	$0.652364\pi$
$998$		0			0
$999$	−5.00000	+	8.66025i	−0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.d.177.1		2
4.3	odd	2		154.2.e.c.23.1	✓	2
7.2	even	3		8624.2.a.k.1.1		1
7.4	even	3	inner	1232.2.q.d.529.1		2
7.5	odd	6		8624.2.a.u.1.1		1
12.11	even	2		1386.2.k.e.793.1		2
28.3	even	6		1078.2.e.k.67.1		2
28.11	odd	6		154.2.e.c.67.1	yes	2
28.19	even	6		1078.2.a.c.1.1		1
28.23	odd	6		1078.2.a.e.1.1		1
28.27	even	2		1078.2.e.k.177.1		2
84.11	even	6		1386.2.k.e.991.1		2
84.23	even	6		9702.2.a.br.1.1		1
84.47	odd	6		9702.2.a.bs.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.c.23.1	✓	2	4.3	odd	2
154.2.e.c.67.1	yes	2	28.11	odd	6
1078.2.a.c.1.1		1	28.19	even	6
1078.2.a.e.1.1		1	28.23	odd	6
1078.2.e.k.67.1		2	28.3	even	6
1078.2.e.k.177.1		2	28.27	even	2
1232.2.q.d.177.1		2	1.1	even	1	trivial
1232.2.q.d.529.1		2	7.4	even	3	inner
1386.2.k.e.793.1		2	12.11	even	2
1386.2.k.e.991.1		2	84.11	even	6
8624.2.a.k.1.1		1	7.2	even	3
8624.2.a.u.1.1		1	7.5	odd	6
9702.2.a.br.1.1		1	84.23	even	6
9702.2.a.bs.1.1		1	84.47	odd	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(3.00000 + 5.19615i) q^{17} +(1.00000 - 1.73205i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} +5.00000 q^{27} +9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(-0.500000 - 0.866025i) q^{39} -6.00000 q^{41} +4.00000 q^{43} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-3.00000 + 5.19615i) q^{51} +2.00000 q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(5.00000 + 1.73205i) q^{63} +(5.50000 + 9.52628i) q^{67} -6.00000 q^{69} +(-1.00000 - 1.73205i) q^{73} +(-2.50000 + 4.33013i) q^{75} +(2.00000 - 1.73205i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +6.00000 q^{83} +(4.50000 + 7.79423i) q^{87} +(9.00000 - 15.5885i) q^{89} +(-0.500000 - 2.59808i) q^{91} +(2.00000 - 3.46410i) q^{93} -13.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + q^7 + 2 * q^9	\( 2 q + q^{3} + q^{7} + 2 q^{9} - q^{11} - 2 q^{13} + 6 q^{17} + 2 q^{19} - 4 q^{21} - 6 q^{23} + 5 q^{25} + 10 q^{27} + 18 q^{29} - 4 q^{31} + q^{33} - 2 q^{37} - q^{39} - 12 q^{41} + 8 q^{43} - 6 q^{47} - 13 q^{49} - 6 q^{51} + 4 q^{57} - 3 q^{59} - 11 q^{61} + 10 q^{63} + 11 q^{67} - 12 q^{69} - 2 q^{73} - 5 q^{75} + 4 q^{77} + 5 q^{79} - q^{81} + 12 q^{83} + 9 q^{87} + 18 q^{89} - q^{91} + 4 q^{93} - 26 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q + q^3 + q^7 + 2 * q^9 - q^11 - 2 * q^13 + 6 * q^17 + 2 * q^19 - 4 * q^21 - 6 * q^23 + 5 * q^25 + 10 * q^27 + 18 * q^29 - 4 * q^31 + q^33 - 2 * q^37 - q^39 - 12 * q^41 + 8 * q^43 - 6 * q^47 - 13 * q^49 - 6 * q^51 + 4 * q^57 - 3 * q^59 - 11 * q^61 + 10 * q^63 + 11 * q^67 - 12 * q^69 - 2 * q^73 - 5 * q^75 + 4 * q^77 + 5 * q^79 - q^81 + 12 * q^83 + 9 * q^87 + 18 * q^89 - q^91 + 4 * q^93 - 26 * q^97 - 4 * q^99

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