LMFDB - Embedded newform 2352.2.q.l.1537.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(961,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("2352.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.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:	$18.7808145554$
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 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2352.1537
Dual form			2352.2.q.l.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -2.00000 q^{13} -2.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +6.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-3.00000 - 5.19615i) q^{37} +(1.00000 - 1.73205i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(1.00000 - 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +8.00000 q^{55} +4.00000 q^{57} +(2.00000 - 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{69} -8.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} -4.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{95} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 2 q^{5} - q^{9}+O(q^{10}) $ 2 * q - q^3 + 2 * q^5 - q^9	$ 2 q - q^{3} + 2 q^{5} - q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} - 8 q^{23} + q^{25} + 2 q^{27} + 12 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{37} + 2 q^{39} - 12 q^{41} - 8 q^{43} + 2 q^{45} - 2 q^{51} + 2 q^{53} + 16 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} - 4 q^{65} - 4 q^{67} + 16 q^{69} - 16 q^{71} - 10 q^{73} + q^{75} - 8 q^{79} - q^{81} + 8 q^{83} - 8 q^{85} - 6 q^{87} + 6 q^{89} + 8 q^{93} + 8 q^{95} + 4 q^{97} - 8 q^{99}+O(q^{100}) $ 2 * q - q^3 + 2 * q^5 - q^9 + 4 * q^11 - 4 * q^13 - 4 * q^15 - 2 * q^17 - 4 * q^19 - 8 * q^23 + q^25 + 2 * q^27 + 12 * q^29 + 8 * q^31 + 4 * q^33 - 6 * q^37 + 2 * q^39 - 12 * q^41 - 8 * q^43 + 2 * q^45 - 2 * q^51 + 2 * q^53 + 16 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 - 4 * q^65 - 4 * q^67 + 16 * q^69 - 16 * q^71 - 10 * q^73 + q^75 - 8 * q^79 - q^81 + 8 * q^83 - 8 * q^85 - 6 * q^87 + 6 * q^89 + 8 * q^93 + 8 * q^95 + 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$		0			0
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$		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	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$		0			0
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$	4.00000			0.529813
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$		0			0
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$		0			0
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	8.00000	−	13.8564i	0.746004	−	1.29212i
$116$		0			0
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.00000	+	1.73205i	0.0860663	+	0.149071i
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.00000	+	6.92820i	−0.334497	+	0.579365i
$144$		0			0
$145$	6.00000	+	10.3923i	0.498273	+	0.863034i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$		0			0
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	0.331842	+	0.943335i	$0.392330\pi$
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	−0.982873	+	0.184284i	$0.941004\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$	16.0000			1.28515
$156$		0			0
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	−0.823359	−	0.567521i	$-0.807902\pi$
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	0.903167	+	0.429289i	$0.141236\pi$
$158$		0			0
$159$	1.00000	+	1.73205i	0.0793052	+	0.137361i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	0.999410	−	0.0343508i	$-0.0109363\pi$
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	−0.529454	+	0.848339i	$0.677603\pi$
$164$		0			0
$165$	−4.00000	+	6.92820i	−0.311400	+	0.539360i
$166$		0			0
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$		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
$175$		0			0
$176$		0			0
$177$	2.00000	+	3.46410i	0.150329	+	0.260378i
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$		0			0
$185$	6.00000	−	10.3923i	0.441129	−	0.764057i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$		0			0
$201$	−2.00000	−	3.46410i	−0.141069	−	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$		0			0
$207$	−4.00000	+	6.92820i	−0.278019	+	0.481543i
$208$		0			0
$209$	−16.0000			−1.10674
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$		0			0
$213$	4.00000	−	6.92820i	0.274075	−	0.474713i
$214$		0			0
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$		0			0
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.00000	−	8.66025i	−0.327561	−	0.567352i	0.654466	−	0.756091i	$-0.272893\pi$
$233$	−5.00000	−	8.66025i	−0.327561	−	0.567352i	−0.982027	+	0.188739i	$0.939560\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.00000			0.519656
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$		0			0
$249$	−2.00000	+	3.46410i	−0.126745	+	0.219529i
$250$		0			0
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		0			0
$253$	−32.0000			−2.01182
$254$		0			0
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$		0			0
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	0.833150	−	0.553047i	$-0.186535\pi$
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	−0.895528	+	0.445005i	$0.853202\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	−4.00000	+	6.92820i	−0.246651	+	0.427211i	−0.962594	−	0.270947i	$-0.912663\pi$
$263$	−4.00000	+	6.92820i	−0.246651	+	0.427211i	0.715944	+	0.698158i	$0.245997\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	−6.00000			−0.367194
$268$		0			0
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	13.0000	−	22.5167i	0.781094	−	1.35290i	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	13.0000	−	22.5167i	0.781094	−	1.35290i	0.931305	−	0.364241i	$-0.118672\pi$
$278$		0			0
$279$	−8.00000			−0.478947
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$		0			0
$285$	4.00000	+	6.92820i	0.236940	+	0.410391i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$		0			0
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$		0			0
$299$	8.00000	+	13.8564i	0.462652	+	0.801337i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	9.00000	+	15.5885i	0.517036	+	0.895533i
$304$		0			0
$305$	−2.00000	+	3.46410i	−0.114520	+	0.198354i
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	8.00000			0.445132
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$		0			0
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$		0			0
$335$	−8.00000			−0.437087
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$		0			0
$341$	−16.0000	−	27.7128i	−0.866449	−	1.50073i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	8.00000	+	13.8564i	0.430706	+	0.746004i
$346$		0			0
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	−0.891410	−	0.453197i	$-0.850283\pi$
$353$	−1.00000	+	1.73205i	−0.0532246	+	0.0921878i	0.838186	+	0.545385i	$0.183617\pi$
$354$		0			0
$355$	−8.00000	−	13.8564i	−0.424596	−	0.735422i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$	5.00000			0.262432
$364$		0			0
$365$	−20.0000			−1.04685
$366$		0			0
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$		0			0
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$		0			0
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	−0.839561	−	0.543266i	$-0.817187\pi$
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	0.890263	+	0.455448i	$0.150521\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$	4.00000			0.201773
$394$		0			0
$395$	8.00000	−	13.8564i	0.402524	−	0.697191i
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$		0			0
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$		0			0
$405$	−2.00000			−0.0993808
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	3.00000	−	5.19615i	0.148340	−	0.256933i	−0.782274	−	0.622935i	$-0.785940\pi$
$409$	3.00000	−	5.19615i	0.148340	−	0.256933i	0.930614	+	0.366002i	$0.119274\pi$
$410$		0			0
$411$	3.00000	+	5.19615i	0.147979	+	0.256307i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.00000	+	6.92820i	0.196352	+	0.340092i
$416$		0			0
$417$	−6.00000	+	10.3923i	−0.293821	+	0.508913i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$		0			0
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	−0.166491	−	0.986043i	$-0.553244\pi$
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	0.937184	−	0.348836i	$-0.113423\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$		0			0
$437$	−16.0000	+	27.7128i	−0.765384	+	1.32568i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.0000	+	17.3205i	0.475114	+	0.822922i	0.999594	−	0.0285009i	$-0.00907336\pi$
$443$	10.0000	+	17.3205i	0.475114	+	0.822922i	−0.524479	+	0.851423i	$0.675740\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$		0			0
$447$	14.0000			0.662177
$448$		0			0
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$		0			0
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$		0			0
$453$	−8.00000	−	13.8564i	−0.375873	−	0.651031i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$		0			0
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$		0			0
$461$	−26.0000			−1.21094			−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000			−1.21094			−0.605470	+	0.795868i	$0.707015\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$		0			0
$465$	−8.00000	+	13.8564i	−0.370991	+	0.642575i
$466$		0			0
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$		0			0
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−2.00000			−0.0915737
$478$		0			0
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$		0			0
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$		0			0
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	0.233933	+	0.972253i	$0.424840\pi$
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	−0.958962	+	0.283535i	$0.908493\pi$
$488$		0			0
$489$	−12.0000			−0.542659
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$		0			0
$495$	−4.00000	−	6.92820i	−0.179787	−	0.311400i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	0.968500	−	0.249015i	$-0.0801067\pi$
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	−0.699903	+	0.714238i	$0.746773\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	36.0000			1.60198
$506$		0			0
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$		0			0
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$		0			0
$515$	−16.0000	+	27.7128i	−0.705044	+	1.22117i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	−13.0000	+	22.5167i	−0.569540	+	0.986473i	0.427071	+	0.904218i	$0.359545\pi$
$521$	−13.0000	+	22.5167i	−0.569540	+	0.986473i	−0.996611	+	0.0822547i	$0.973788\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$	12.0000	−	20.7846i	0.518805	−	0.898597i
$536$		0			0
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$		0			0
$543$	−3.00000	+	5.19615i	−0.128742	+	0.222988i
$544$		0			0
$545$	4.00000			0.171341
$546$		0			0
$547$	−44.0000			−1.88130			−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000			−1.88130			−0.940652	+	0.339372i	$0.889785\pi$
$548$		0			0
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.00000	+	10.3923i	0.254686	+	0.441129i
$556$		0			0
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	−0.447387	−	0.894340i	$-0.647645\pi$
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	0.998215	−	0.0597213i	$-0.0190212\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	−0.404198	−	0.914671i	$-0.632449\pi$
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	0.994228	−	0.107290i	$-0.0342173\pi$
$564$		0			0
$565$	18.0000	+	31.1769i	0.757266	+	1.31162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$		0			0
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	−0.192950	−	0.981209i	$-0.561806\pi$
$571$	18.0000	−	31.1769i	0.753277	−	1.30471i	0.946227	−	0.323505i	$-0.104861\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−8.00000			−0.333623
$576$		0			0
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$		0			0
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$		0			0
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$		0			0
$587$	44.0000			1.81607			0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000			1.81607			0.908037	+	0.418890i	$0.137581\pi$
$588$		0			0
$589$	−32.0000			−1.31854
$590$		0			0
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$		0			0
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	0.973202	−	0.229953i	$-0.0738573\pi$
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	−0.685746	+	0.727841i	$0.740524\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.00000	+	13.8564i	0.327418	+	0.567105i
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	5.00000	−	8.66025i	0.203279	−	0.352089i
$606$		0			0
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	−0.911621	−	0.411033i	$-0.865168\pi$
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	0.0998457	−	0.995003i	$-0.468165\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	0.171564	+	0.985173i	$0.445118\pi$
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	−0.938967	+	0.344008i	$0.888215\pi$
$614$		0			0
$615$	12.0000			0.483887
$616$		0			0
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$		0			0
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$		0			0
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$	8.00000	−	13.8564i	0.319489	−	0.553372i
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$		0			0
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.00000	+	6.92820i	0.158238	+	0.274075i
$640$		0			0
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	−0.694025	−	0.719951i	$-0.744164\pi$
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	0.970508	+	0.241068i	$0.0774976\pi$
$642$		0			0
$643$	−12.0000			−0.473234			−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000			−0.473234			−0.236617	+	0.971603i	$0.576039\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	4.00000	−	6.92820i	0.157256	−	0.272376i	−0.776622	−	0.629967i	$-0.783068\pi$
$647$	4.00000	−	6.92820i	0.157256	−	0.272376i	0.933878	+	0.357591i	$0.116402\pi$
$648$		0			0
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$		0			0
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$		0			0
$657$	10.0000			0.390137
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$		0			0
$663$	2.00000	+	3.46410i	0.0776736	+	0.134535i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.0000	−	41.5692i	−0.929284	−	1.60957i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	8.00000			0.308837
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	0.884602	−	0.466347i	$-0.154430\pi$
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	−0.846169	+	0.532915i	$0.821097\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	22.0000			0.839352
$688$		0			0
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	0.825473	−	0.564441i	$-0.190908\pi$
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	−0.901557	+	0.432660i	$0.857575\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$		0			0
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$		0			0
$699$	10.0000			0.378235
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	−12.0000	+	20.7846i	−0.452589	+	0.783906i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$		0			0
$713$	−64.0000			−2.39682
$714$		0			0
$715$	−16.0000			−0.598366
$716$		0			0
$717$	−8.00000	+	13.8564i	−0.298765	+	0.517477i
$718$		0			0
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	−0.993305	−	0.115524i	$-0.963145\pi$
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	0.396605	−	0.917989i	$-0.370188\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−9.00000	−	15.5885i	−0.334714	−	0.579741i
$724$		0			0
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	−48.0000			−1.78022			−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000			−1.78022			−0.890111	+	0.455744i	$0.849373\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.00000	+	13.8564i	0.294684	+	0.510407i
$738$		0			0
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	−0.900464	−	0.434930i	$-0.856773\pi$
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	0.826893	+	0.562360i	$0.190106\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$		0			0
$743$	8.00000			0.293492			0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000			0.293492			0.146746	+	0.989174i	$0.453120\pi$
$744$		0			0
$745$	14.0000	−	24.2487i	0.512920	−	0.888404i
$746$		0			0
$747$	−2.00000	−	3.46410i	−0.0731762	−	0.126745i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$		0			0
$753$	10.0000	−	17.3205i	0.364420	−	0.631194i
$754$		0			0
$755$	−32.0000			−1.16460
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		0			0
$759$	16.0000	−	27.7128i	0.580763	−	1.00591i
$760$		0			0
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	0.993572	−	0.113203i	$-0.0361109\pi$
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	−0.594822	+	0.803857i	$0.702778\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$		0			0
$767$	−4.00000	+	6.92820i	−0.144432	+	0.250163i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$		0			0
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$	−16.0000	+	27.7128i	−0.572525	+	0.991642i
$782$		0			0
$783$	6.00000			0.214423
$784$		0			0
$785$	4.00000			0.142766
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$		0			0
$789$	−4.00000	−	6.92820i	−0.142404	−	0.246651i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.00000	−	3.46410i	−0.0710221	−	0.123014i
$794$		0			0
$795$	−2.00000	+	3.46410i	−0.0709327	+	0.122859i
$796$		0			0
$797$	22.0000			0.779280			0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000			0.779280			0.389640	+	0.920967i	$0.372599\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$		0			0
$803$	20.0000	+	34.6410i	0.705785	+	1.22245i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.00000	+	8.66025i	0.176008	+	0.304855i
$808$		0			0
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	−0.998804	−	0.0488972i	$-0.984429\pi$
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	0.541748	+	0.840541i	$0.317763\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	−8.00000			−0.280572
$814$		0			0
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$		0			0
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		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
$825$	4.00000			0.139262
$826$		0			0
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$		0			0
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.00453881	−	0.999990i	$-0.498555\pi$
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.863747	−	0.503926i	$-0.168111\pi$
$830$		0			0
$831$	13.0000	+	22.5167i	0.450965	+	0.781094i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−24.0000	−	41.5692i	−0.830554	−	1.43856i
$836$		0			0
$837$	4.00000	−	6.92820i	0.138260	−	0.239474i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−13.0000	+	22.5167i	−0.447744	+	0.775515i
$844$		0			0
$845$	−9.00000	−	15.5885i	−0.309609	−	0.536259i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$	−24.0000	+	41.5692i	−0.822709	+	1.42497i
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		0			0
$855$	−8.00000			−0.273594
$856$		0			0
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	−6.00000	−	10.3923i	−0.204717	−	0.354581i	0.745325	−	0.666701i	$-0.232294\pi$
$859$	−6.00000	−	10.3923i	−0.204717	−	0.354581i	−0.950043	+	0.312120i	$0.898961\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.0000	−	27.7128i	−0.544646	−	0.943355i	−0.998629	−	0.0523446i	$-0.983331\pi$
$863$	−16.0000	−	27.7128i	−0.544646	−	0.943355i	0.453983	−	0.891010i	$-0.350003\pi$
$864$		0			0
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$		0			0
$867$	−13.0000			−0.441503
$868$		0			0
$869$	−32.0000			−1.08553
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$		0			0
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	0.977018	−	0.213158i	$-0.0683750\pi$
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	−0.673109	+	0.739543i	$0.735042\pi$
$878$		0			0
$879$	9.00000	−	15.5885i	0.303562	−	0.525786i
$880$		0			0
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$	−4.00000	+	6.92820i	−0.134459	+	0.232889i
$886$		0			0
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	24.0000			0.802232
$896$		0			0
$897$	−16.0000			−0.534224
$898$		0			0
$899$	24.0000	−	41.5692i	0.800445	−	1.38641i
$900$		0			0
$901$	2.00000	+	3.46410i	0.0666297	+	0.115406i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.00000	+	10.3923i	0.199447	+	0.345452i
$906$		0			0
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	−0.830909	−	0.556408i	$-0.812179\pi$
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	0.897318	+	0.441384i	$0.145512\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$	8.00000	−	13.8564i	0.264761	−	0.458580i
$914$		0			0
$915$	−2.00000	−	3.46410i	−0.0661180	−	0.114520i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	6.00000	−	10.3923i	0.197707	−	0.342438i
$922$		0			0
$923$	16.0000			0.526646
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$	8.00000	−	13.8564i	0.262754	−	0.455104i
$928$		0			0
$929$	−25.0000	−	43.3013i	−0.820223	−	1.42067i	−0.905516	−	0.424313i	$-0.860516\pi$
$929$	−25.0000	−	43.3013i	−0.820223	−	1.42067i	0.0852924	−	0.996356i	$-0.472818\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$		0			0
$935$	−8.00000	+	13.8564i	−0.261628	+	0.453153i
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$	−6.00000			−0.195803
$940$		0			0
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$		0			0
$943$	24.0000	+	41.5692i	0.781548	+	1.35368i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$		0			0
$951$	6.00000			0.194563
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	12.0000	+	20.7846i	0.387905	+	0.671871i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$		0			0
$965$	−4.00000			−0.128765
$966$		0			0
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$		0			0
$969$	−4.00000	+	6.92820i	−0.128499	+	0.222566i
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	24.0000			0.767043
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	−18.0000	−	31.1769i	−0.573528	−	0.993379i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$		0			0
$993$	−20.0000			−0.634681
$994$		0			0
$995$	32.0000			1.01447
$996$		0			0
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$		0			0
$999$	−3.00000	−	5.19615i	−0.0949158	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.q.l.1537.1		2
4.3	odd	2		1176.2.q.i.361.1		2
7.2	even	3	inner	2352.2.q.l.961.1		2
7.3	odd	6		2352.2.a.i.1.1		1
7.4	even	3		48.2.a.a.1.1		1
7.5	odd	6		2352.2.q.r.961.1		2
7.6	odd	2		2352.2.q.r.1537.1		2
12.11	even	2		3528.2.s.j.361.1		2
21.11	odd	6		144.2.a.b.1.1		1
21.17	even	6		7056.2.a.q.1.1		1
28.3	even	6		1176.2.a.i.1.1		1
28.11	odd	6		24.2.a.a.1.1	✓	1
28.19	even	6		1176.2.q.a.961.1		2
28.23	odd	6		1176.2.q.i.961.1		2
28.27	even	2		1176.2.q.a.361.1		2
35.4	even	6		1200.2.a.d.1.1		1
35.18	odd	12		1200.2.f.b.49.2		2
35.32	odd	12		1200.2.f.b.49.1		2
56.3	even	6		9408.2.a.h.1.1		1
56.11	odd	6		192.2.a.d.1.1		1
56.45	odd	6		9408.2.a.cc.1.1		1
56.53	even	6		192.2.a.b.1.1		1
63.4	even	3		1296.2.i.m.865.1		2
63.11	odd	6		1296.2.i.e.433.1		2
63.25	even	3		1296.2.i.m.433.1		2
63.32	odd	6		1296.2.i.e.865.1		2
77.32	odd	6		5808.2.a.s.1.1		1
84.11	even	6		72.2.a.a.1.1		1
84.23	even	6		3528.2.s.j.3313.1		2
84.47	odd	6		3528.2.s.y.3313.1		2
84.59	odd	6		3528.2.a.d.1.1		1
84.83	odd	2		3528.2.s.y.361.1		2
91.25	even	6		8112.2.a.be.1.1		1
105.32	even	12		3600.2.f.r.2449.2		2
105.53	even	12		3600.2.f.r.2449.1		2
105.74	odd	6		3600.2.a.v.1.1		1
112.11	odd	12		768.2.d.e.385.2		2
112.53	even	12		768.2.d.d.385.1		2
112.67	odd	12		768.2.d.e.385.1		2
112.109	even	12		768.2.d.d.385.2		2
140.39	odd	6		600.2.a.h.1.1		1
140.67	even	12		600.2.f.e.49.2		2
140.123	even	12		600.2.f.e.49.1		2
168.11	even	6		576.2.a.d.1.1		1
168.53	odd	6		576.2.a.b.1.1		1
252.11	even	6		648.2.i.b.433.1		2
252.67	odd	6		648.2.i.g.217.1		2
252.95	even	6		648.2.i.b.217.1		2
252.151	odd	6		648.2.i.g.433.1		2
280.53	odd	12		4800.2.f.bg.3649.1		2
280.67	even	12		4800.2.f.d.3649.1		2
280.109	even	6		4800.2.a.cc.1.1		1
280.123	even	12		4800.2.f.d.3649.2		2
280.179	odd	6		4800.2.a.q.1.1		1
280.277	odd	12		4800.2.f.bg.3649.2		2
308.263	even	6		2904.2.a.c.1.1		1
336.11	even	12		2304.2.d.i.1153.2		2
336.53	odd	12		2304.2.d.k.1153.2		2
336.179	even	12		2304.2.d.i.1153.1		2
336.221	odd	12		2304.2.d.k.1153.1		2
364.151	even	12		4056.2.c.e.337.1		2
364.207	odd	6		4056.2.a.i.1.1		1
364.291	even	12		4056.2.c.e.337.2		2
420.179	even	6		1800.2.a.m.1.1		1
420.263	odd	12		1800.2.f.c.649.1		2
420.347	odd	12		1800.2.f.c.649.2		2
476.67	odd	6		6936.2.a.p.1.1		1
532.151	even	6		8664.2.a.j.1.1		1
924.263	odd	6		8712.2.a.u.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.2.a.a.1.1	✓	1	28.11	odd	6
48.2.a.a.1.1		1	7.4	even	3
72.2.a.a.1.1		1	84.11	even	6
144.2.a.b.1.1		1	21.11	odd	6
192.2.a.b.1.1		1	56.53	even	6
192.2.a.d.1.1		1	56.11	odd	6
576.2.a.b.1.1		1	168.53	odd	6
576.2.a.d.1.1		1	168.11	even	6
600.2.a.h.1.1		1	140.39	odd	6
600.2.f.e.49.1		2	140.123	even	12
600.2.f.e.49.2		2	140.67	even	12
648.2.i.b.217.1		2	252.95	even	6
648.2.i.b.433.1		2	252.11	even	6
648.2.i.g.217.1		2	252.67	odd	6
648.2.i.g.433.1		2	252.151	odd	6
768.2.d.d.385.1		2	112.53	even	12
768.2.d.d.385.2		2	112.109	even	12
768.2.d.e.385.1		2	112.67	odd	12
768.2.d.e.385.2		2	112.11	odd	12
1176.2.a.i.1.1		1	28.3	even	6
1176.2.q.a.361.1		2	28.27	even	2
1176.2.q.a.961.1		2	28.19	even	6
1176.2.q.i.361.1		2	4.3	odd	2
1176.2.q.i.961.1		2	28.23	odd	6
1200.2.a.d.1.1		1	35.4	even	6
1200.2.f.b.49.1		2	35.32	odd	12
1200.2.f.b.49.2		2	35.18	odd	12
1296.2.i.e.433.1		2	63.11	odd	6
1296.2.i.e.865.1		2	63.32	odd	6
1296.2.i.m.433.1		2	63.25	even	3
1296.2.i.m.865.1		2	63.4	even	3
1800.2.a.m.1.1		1	420.179	even	6
1800.2.f.c.649.1		2	420.263	odd	12
1800.2.f.c.649.2		2	420.347	odd	12
2304.2.d.i.1153.1		2	336.179	even	12
2304.2.d.i.1153.2		2	336.11	even	12
2304.2.d.k.1153.1		2	336.221	odd	12
2304.2.d.k.1153.2		2	336.53	odd	12
2352.2.a.i.1.1		1	7.3	odd	6
2352.2.q.l.961.1		2	7.2	even	3	inner
2352.2.q.l.1537.1		2	1.1	even	1	trivial
2352.2.q.r.961.1		2	7.5	odd	6
2352.2.q.r.1537.1		2	7.6	odd	2
2904.2.a.c.1.1		1	308.263	even	6
3528.2.a.d.1.1		1	84.59	odd	6
3528.2.s.j.361.1		2	12.11	even	2
3528.2.s.j.3313.1		2	84.23	even	6
3528.2.s.y.361.1		2	84.83	odd	2
3528.2.s.y.3313.1		2	84.47	odd	6
3600.2.a.v.1.1		1	105.74	odd	6
3600.2.f.r.2449.1		2	105.53	even	12
3600.2.f.r.2449.2		2	105.32	even	12
4056.2.a.i.1.1		1	364.207	odd	6
4056.2.c.e.337.1		2	364.151	even	12
4056.2.c.e.337.2		2	364.291	even	12
4800.2.a.q.1.1		1	280.179	odd	6
4800.2.a.cc.1.1		1	280.109	even	6
4800.2.f.d.3649.1		2	280.67	even	12
4800.2.f.d.3649.2		2	280.123	even	12
4800.2.f.bg.3649.1		2	280.53	odd	12
4800.2.f.bg.3649.2		2	280.277	odd	12
5808.2.a.s.1.1		1	77.32	odd	6
6936.2.a.p.1.1		1	476.67	odd	6
7056.2.a.q.1.1		1	21.17	even	6
8112.2.a.be.1.1		1	91.25	even	6
8664.2.a.j.1.1		1	532.151	even	6
8712.2.a.u.1.1		1	924.263	odd	6
9408.2.a.h.1.1		1	56.3	even	6
9408.2.a.cc.1.1		1	56.45	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:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -2.00000 q^{13} -2.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +6.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-3.00000 - 5.19615i) q^{37} +(1.00000 - 1.73205i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(1.00000 - 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +8.00000 q^{55} +4.00000 q^{57} +(2.00000 - 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{69} -8.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} -4.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{95} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 2 q^{5} - q^{9}+O(q^{10}) \) 2 * q - q^3 + 2 * q^5 - q^9	\( 2 q - q^{3} + 2 q^{5} - q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} - 8 q^{23} + q^{25} + 2 q^{27} + 12 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{37} + 2 q^{39} - 12 q^{41} - 8 q^{43} + 2 q^{45} - 2 q^{51} + 2 q^{53} + 16 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} - 4 q^{65} - 4 q^{67} + 16 q^{69} - 16 q^{71} - 10 q^{73} + q^{75} - 8 q^{79} - q^{81} + 8 q^{83} - 8 q^{85} - 6 q^{87} + 6 q^{89} + 8 q^{93} + 8 q^{95} + 4 q^{97} - 8 q^{99}+O(q^{100}) \) 2 * q - q^3 + 2 * q^5 - q^9 + 4 * q^11 - 4 * q^13 - 4 * q^15 - 2 * q^17 - 4 * q^19 - 8 * q^23 + q^25 + 2 * q^27 + 12 * q^29 + 8 * q^31 + 4 * q^33 - 6 * q^37 + 2 * q^39 - 12 * q^41 - 8 * q^43 + 2 * q^45 - 2 * q^51 + 2 * q^53 + 16 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 - 4 * q^65 - 4 * q^67 + 16 * q^69 - 16 * q^71 - 10 * q^73 + q^75 - 8 * q^79 - q^81 + 8 * q^83 - 8 * q^85 - 6 * q^87 + 6 * q^89 + 8 * q^93 + 8 * q^95 + 4 * q^97 - 8 * q^99

Introduction

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