LMFDB - Embedded newform 1176.2.q.f.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(361,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1176.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.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:	$9.39040727770$
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 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1176.961
Dual form			1176.2.q.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +6.00000 q^{13} -2.00000 q^{15} +(1.00000 + 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -10.0000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-3.00000 + 5.19615i) q^{37} +(3.00000 + 5.19615i) q^{39} -2.00000 q^{41} -4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(-1.00000 + 1.73205i) q^{51} +(5.00000 + 8.66025i) q^{53} -4.00000 q^{57} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-6.00000 + 10.3923i) q^{65} +(-6.00000 - 10.3923i) q^{67} +4.00000 q^{69} -12.0000 q^{71} +(7.00000 + 12.1244i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -4.00000 q^{85} +(-5.00000 - 8.66025i) q^{87} +(1.00000 - 1.73205i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-4.00000 - 6.92820i) q^{95} +10.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 q^{13} - 4 q^{15} + 2 q^{17} - 4 q^{19} + 4 q^{23} + q^{25} - 2 q^{27} - 20 q^{29} + 8 q^{31} - 6 q^{37} + 6 q^{39} - 4 q^{41} - 8 q^{43} - 2 q^{45} - 8 q^{47} - 2 q^{51} + 10 q^{53} - 8 q^{57} - 12 q^{59} + 2 q^{61} - 12 q^{65} - 12 q^{67} + 8 q^{69} - 24 q^{71} + 14 q^{73} - q^{75} + 8 q^{79} - q^{81} + 24 q^{83} - 8 q^{85} - 10 q^{87} + 2 q^{89} - 8 q^{93} - 8 q^{95} + 20 q^{97}+O(q^{100}) $ 2 * q + q^3 - 2 * q^5 - q^9 + 12 * q^13 - 4 * q^15 + 2 * q^17 - 4 * q^19 + 4 * q^23 + q^25 - 2 * q^27 - 20 * q^29 + 8 * q^31 - 6 * q^37 + 6 * q^39 - 4 * q^41 - 8 * q^43 - 2 * q^45 - 8 * q^47 - 2 * q^51 + 10 * q^53 - 8 * q^57 - 12 * q^59 + 2 * q^61 - 12 * q^65 - 12 * q^67 + 8 * q^69 - 24 * q^71 + 14 * q^73 - q^75 + 8 * q^79 - q^81 + 24 * q^83 - 8 * q^85 - 10 * q^87 + 2 * q^89 - 8 * q^93 - 8 * q^95 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−10.0000			−1.85695			−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000			−1.85695			−0.928477	+	0.371391i	$0.878881\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$		0			0
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		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
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$		0			0
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$		0			0
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$		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	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$		0			0
$87$	−5.00000	−	8.66025i	−0.536056	−	0.928477i
$88$		0			0
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	−0.808146	−	0.588982i	$-0.799529\pi$
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	0.914146	+	0.405385i	$0.132862\pi$
$90$		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
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		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
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$		0			0
$117$	−3.00000	+	5.19615i	−0.277350	+	0.480384i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$		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	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.00000	−	1.73205i	0.0860663	−	0.149071i
$136$		0			0
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	0.820141	−	0.572161i	$-0.193895\pi$
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	−0.905577	+	0.424182i	$0.860562\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$	−8.00000			−0.673722
$142$		0			0
$143$		0			0
$144$		0			0
$145$	10.0000	−	17.3205i	0.830455	−	1.43839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.0000	+	19.0526i	−0.901155	+	1.56085i	−0.0751583	+	0.997172i	$0.523946\pi$
$149$	−11.0000	+	19.0526i	−0.901155	+	1.56085i	−0.825997	+	0.563675i	$0.809387\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	0.961681	+	0.274169i	$0.0884028\pi$
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	−0.243403	+	0.969925i	$0.578264\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	−0.901533	−	0.432710i	$-0.857557\pi$
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	0.825505	+	0.564396i	$0.190891\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.00000	−	10.3923i	0.450988	−	0.781133i
$178$		0			0
$179$	8.00000	+	13.8564i	0.597948	+	1.03568i	0.993124	+	0.117071i	$0.0373504\pi$
$179$	8.00000	+	13.8564i	0.597948	+	1.03568i	−0.395175	+	0.918606i	$0.629316\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	−6.00000	−	10.3923i	−0.441129	−	0.764057i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$		0			0
$193$	−9.00000	−	15.5885i	−0.647834	−	1.12208i	−0.983639	−	0.180150i	$-0.942342\pi$
$193$	−9.00000	−	15.5885i	−0.647834	−	1.12208i	0.335805	−	0.941932i	$-0.390992\pi$
$194$		0			0
$195$	−12.0000			−0.859338
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$		0			0
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$		0			0
$209$		0			0
$210$		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
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$		0			0
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	−0.896921	−	0.442191i	$-0.854201\pi$
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	0.831409	+	0.555661i	$0.187535\pi$
$234$		0			0
$235$	−8.00000	−	13.8564i	−0.521862	−	0.903892i
$236$		0			0
$237$	8.00000			0.519656
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.0000	+	20.7846i	−0.763542	+	1.32249i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		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
$253$		0			0
$254$		0			0
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$		0			0
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.00000	−	8.66025i	0.309492	−	0.536056i
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	−20.0000			−1.22859
$266$		0			0
$267$	2.00000			0.122398
$268$		0			0
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$		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
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$		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
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	2.00000	+	3.46410i	0.114520	+	0.198354i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.00000			−0.445132
$324$		0			0
$325$	3.00000	+	5.19615i	0.166410	+	0.288231i
$326$		0			0
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$		0			0
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$		0			0
$335$	24.0000			1.31126
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4.00000	+	6.92820i	−0.215353	+	0.373002i
$346$		0			0
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	−6.00000			−0.320256
$352$		0			0
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$		0			0
$355$	12.0000	−	20.7846i	0.636894	−	1.10313i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$	11.0000			0.577350
$364$		0			0
$365$	−28.0000			−1.46559
$366$		0			0
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$		0			0
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$		0			0
$377$	−60.0000			−3.09016
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$	4.00000	+	6.92820i	0.204926	+	0.354943i
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$		0			0
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	0.890263	−	0.455448i	$-0.150521\pi$
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	−0.839561	+	0.543266i	$0.817187\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$		0			0
$393$	4.00000			0.201773
$394$		0			0
$395$	8.00000	+	13.8564i	0.402524	+	0.697191i
$396$		0			0
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$	24.0000	+	41.5692i	1.19553	+	2.07071i
$404$		0			0
$405$	2.00000			0.0993808
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−9.00000	−	15.5885i	−0.445021	−	0.770800i	0.553032	−	0.833160i	$-0.313471\pi$
$409$	−9.00000	−	15.5885i	−0.445021	−	0.770800i	−0.998054	+	0.0623602i	$0.980137\pi$
$410$		0			0
$411$	1.00000	−	1.73205i	0.0493264	−	0.0854358i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$		0			0
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$		0			0
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$		0			0
$423$	−4.00000	−	6.92820i	−0.194487	−	0.336861i
$424$		0			0
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		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
$435$	20.0000			0.958927
$436$		0			0
$437$	8.00000	+	13.8564i	0.382692	+	0.662842i
$438$		0			0
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	−0.423556	−	0.905870i	$-0.639218\pi$
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	0.996284	−	0.0861252i	$-0.0274485\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.00000	+	6.92820i	−0.190046	+	0.329169i	−0.945265	−	0.326303i	$-0.894197\pi$
$443$	−4.00000	+	6.92820i	−0.190046	+	0.329169i	0.755219	+	0.655472i	$0.227530\pi$
$444$		0			0
$445$	2.00000	+	3.46410i	0.0948091	+	0.164214i
$446$		0			0
$447$	−22.0000			−1.04056
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$		0			0
$465$	−8.00000	−	13.8564i	−0.370991	−	0.642575i
$466$		0			0
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	0.0627555	+	0.998029i	$0.480011\pi$
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	−0.895696	+	0.444667i	$0.853322\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−9.00000	+	15.5885i	−0.414698	+	0.718278i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−10.0000			−0.457869
$478$		0			0
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	0.942821	−	0.333300i	$-0.108162\pi$
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	−0.760056	+	0.649857i	$0.774829\pi$
$480$		0			0
$481$	−18.0000	+	31.1769i	−0.820729	+	1.42154i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−10.0000	+	17.3205i	−0.454077	+	0.786484i
$486$		0			0
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$		0			0
$489$	20.0000			0.904431
$490$		0			0
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$		0			0
$493$	−10.0000	−	17.3205i	−0.450377	−	0.780076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$		0			0
$507$	11.5000	+	19.9186i	0.510733	+	0.884615i
$508$		0			0
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.148866	+	0.988857i	$0.547562\pi$
$509$	−21.0000	+	36.3731i	−0.930809	+	1.61221i	−0.781943	+	0.623350i	$0.785771\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−2.00000			−0.0877903
$520$		0			0
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.00000	+	13.8564i	−0.345225	+	0.597948i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	−0.843728	−	0.536771i	$-0.819644\pi$
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	0.886721	+	0.462304i	$0.152977\pi$
$542$		0			0
$543$	7.00000	+	12.1244i	0.300399	+	0.520306i
$544$		0			0
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$		0			0
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	20.0000	−	34.6410i	0.852029	−	1.47576i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.00000	−	10.3923i	0.254686	−	0.441129i
$556$		0			0
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	−18.0000	+	31.1769i	−0.757266	+	1.31162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$		0			0
$573$	20.0000			0.835512
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	−9.00000	−	15.5885i	−0.374675	−	0.648956i	0.615603	−	0.788056i	$-0.288912\pi$
$577$	−9.00000	−	15.5885i	−0.374675	−	0.648956i	−0.990278	+	0.139100i	$0.955579\pi$
$578$		0			0
$579$	9.00000	−	15.5885i	0.374027	−	0.647834i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−6.00000	−	10.3923i	−0.248069	−	0.429669i
$586$		0			0
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$	−32.0000			−1.31854
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$		0			0
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	−0.619915	−	0.784669i	$-0.712833\pi$
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	0.989501	+	0.144528i	$0.0461663\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.00000	−	6.92820i	0.163709	−	0.283552i
$598$		0			0
$599$	22.0000	+	38.1051i	0.898896	+	1.55693i	0.828908	+	0.559385i	$0.188963\pi$
$599$	22.0000	+	38.1051i	0.898896	+	1.55693i	0.0699877	+	0.997548i	$0.477704\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$		0			0
$605$	11.0000	+	19.0526i	0.447214	+	0.774597i
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−24.0000	+	41.5692i	−0.970936	+	1.68171i
$612$		0			0
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	0.999574	+	0.0291886i	$0.00929235\pi$
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	−0.474509	+	0.880251i	$0.657374\pi$
$614$		0			0
$615$	4.00000			0.161296
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	6.00000	+	10.3923i	0.241160	+	0.417702i	0.961045	−	0.276392i	$-0.0891387\pi$
$619$	6.00000	+	10.3923i	0.241160	+	0.417702i	−0.719885	+	0.694094i	$0.755805\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		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
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	0.750225	−	0.661182i	$-0.229945\pi$
$641$	−5.00000	−	8.66025i	−0.197488	−	0.342059i	−0.947713	+	0.319123i	$0.896612\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.758654	+	0.651494i	$0.225858\pi$
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.184884	+	0.982760i	$0.440809\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.00000	−	8.66025i	0.195665	−	0.338902i	−0.751453	−	0.659786i	$-0.770647\pi$
$653$	5.00000	−	8.66025i	0.195665	−	0.338902i	0.947118	+	0.320884i	$0.103980\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$		0			0
$657$	−14.0000			−0.546192
$658$		0			0
$659$	8.00000			0.311636			0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000			0.311636			0.155818	+	0.987786i	$0.450199\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$		0			0
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−20.0000	+	34.6410i	−0.774403	+	1.34131i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$		0			0
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	−14.0000			−0.534133
$688$		0			0
$689$	30.0000	+	51.9615i	1.14291	+	1.97958i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.0000	−	20.7846i	0.455186	−	0.788405i
$696$		0			0
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$		0			0
$699$	−2.00000			−0.0756469
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$		0			0
$703$	−12.0000	−	20.7846i	−0.452589	−	0.783906i
$704$		0			0
$705$	8.00000	−	13.8564i	0.301297	−	0.521862i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−11.0000	+	19.0526i	−0.413114	+	0.715534i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−11.0000	+	19.0526i	−0.413114	+	0.715534i	0.582115	+	0.813107i	$0.302225\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$		0			0
$713$	32.0000			1.19841
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.0000	+	17.3205i	0.373457	+	0.646846i
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$		0			0
$725$	−5.00000	−	8.66025i	−0.185695	−	0.321634i
$726$		0			0
$727$	−16.0000			−0.593407			−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000			−0.593407			−0.296704	+	0.954970i	$0.595887\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$		0			0
$733$	13.0000	−	22.5167i	0.480166	−	0.831672i	−0.519575	−	0.854425i	$-0.673910\pi$
$733$	13.0000	−	22.5167i	0.480166	−	0.831672i	0.999741	+	0.0227529i	$0.00724310\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	0.989230	−	0.146369i	$-0.0467586\pi$
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	−0.621374	+	0.783514i	$0.713425\pi$
$740$		0			0
$741$	−24.0000			−0.881662
$742$		0			0
$743$	20.0000			0.733729			0.366864	−	0.930274i	$-0.380431\pi$
$743$	20.0000			0.733729			0.366864	+	0.930274i	$0.380431\pi$
$744$		0			0
$745$	−22.0000	−	38.1051i	−0.806018	−	1.39606i
$746$		0			0
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$		0			0
$753$	−10.0000	−	17.3205i	−0.364420	−	0.631194i
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$		0			0
$759$		0			0
$760$		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
$763$		0			0
$764$		0			0
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$		0			0
$767$	−36.0000	−	62.3538i	−1.29988	−	2.25147i
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	0.761987	−	0.647592i	$-0.224224\pi$
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	−0.941825	+	0.336104i	$0.890891\pi$
$774$		0			0
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.00000	−	6.92820i	0.143315	−	0.248229i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	10.0000			0.357371
$784$		0			0
$785$	−36.0000			−1.28490
$786$		0			0
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$		0			0
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.00000	−	10.3923i	0.213066	−	0.369042i
$794$		0			0
$795$	−10.0000	−	17.3205i	−0.354663	−	0.614295i
$796$		0			0
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$		0			0
$801$	1.00000	+	1.73205i	0.0353333	+	0.0611990i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$		0			0
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$		0			0
$811$	36.0000			1.26413			0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000			1.26413			0.632065	+	0.774915i	$0.282207\pi$
$812$		0			0
$813$	−8.00000			−0.280572
$814$		0			0
$815$	20.0000	+	34.6410i	0.700569	+	1.21342i
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$		0			0
$831$	11.0000	−	19.0526i	0.381586	−	0.660926i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.00000	−	6.92820i	−0.138260	−	0.239474i
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$		0			0
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$		0			0
$845$	−23.0000	+	39.8372i	−0.791224	+	1.37044i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$		0			0
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$		0			0
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	−0.643459	−	0.765480i	$-0.722501\pi$
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	0.984655	+	0.174512i	$0.0558348\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.0000	+	17.3205i	−0.340404	+	0.589597i	−0.984508	−	0.175341i	$-0.943897\pi$
$863$	−10.0000	+	17.3205i	−0.340404	+	0.589597i	0.644104	+	0.764938i	$0.277230\pi$
$864$		0			0
$865$	−2.00000	−	3.46410i	−0.0680020	−	0.117783i
$866$		0			0
$867$	13.0000			0.441503
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−36.0000	−	62.3538i	−1.21981	−	2.11278i
$872$		0			0
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$		0			0
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		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
$885$	12.0000	+	20.7846i	0.403376	+	0.698667i
$886$		0			0
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	−0.109881	−	0.993945i	$-0.535047\pi$
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	0.915722	−	0.401813i	$-0.131620\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−16.0000	−	27.7128i	−0.535420	−	0.927374i
$894$		0			0
$895$	−32.0000			−1.06964
$896$		0			0
$897$	24.0000			0.801337
$898$		0			0
$899$	−40.0000	−	69.2820i	−1.33407	−	2.31069i
$900$		0			0
$901$	−10.0000	+	17.3205i	−0.333148	+	0.577030i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.0000	+	24.2487i	−0.465376	+	0.806054i
$906$		0			0
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−2.00000	+	3.46410i	−0.0661180	+	0.114520i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	−0.792480	−	0.609898i	$-0.791210\pi$
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	0.924427	+	0.381358i	$0.124544\pi$
$920$		0			0
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$		0			0
$923$	−72.0000			−2.36991
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.0000	−	22.5167i	0.426516	−	0.738748i	−0.570045	−	0.821614i	$-0.693074\pi$
$929$	13.0000	−	22.5167i	0.426516	−	0.738748i	0.996561	+	0.0828661i	$0.0264074\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−54.0000			−1.76410			−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000			−1.76410			−0.882052	+	0.471153i	$0.843838\pi$
$938$		0			0
$939$	22.0000			0.717943
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$		0			0
$943$	−4.00000	+	6.92820i	−0.130258	+	0.225613i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.0000	−	48.4974i	0.909878	−	1.57595i	0.0956453	−	0.995415i	$-0.469509\pi$
$947$	28.0000	−	48.4974i	0.909878	−	1.57595i	0.814232	−	0.580539i	$-0.197158\pi$
$948$		0			0
$949$	42.0000	+	72.7461i	1.36338	+	2.36144i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$	58.0000			1.87880			0.939402	−	0.342817i	$-0.111381\pi$
$953$	58.0000			1.87880			0.939402	+	0.342817i	$0.111381\pi$
$954$		0			0
$955$	20.0000	+	34.6410i	0.647185	+	1.12096i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	36.0000			1.15888
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$		0			0
$969$	−4.00000	−	6.92820i	−0.128499	−	0.222566i
$970$		0			0
$971$	−2.00000	+	3.46410i	−0.0641831	+	0.111168i	−0.896331	−	0.443385i	$-0.853777\pi$
$971$	−2.00000	+	3.46410i	−0.0641831	+	0.111168i	0.832148	+	0.554553i	$0.187111\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.00000	+	5.19615i	−0.0960769	+	0.166410i
$976$		0			0
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.00000	+	13.8564i	−0.254385	+	0.440608i
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$	4.00000			0.126936
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	0.995077	−	0.0991016i	$-0.0315969\pi$
$997$	13.0000	+	22.5167i	0.411714	+	0.713110i	−0.583363	+	0.812211i	$0.698264\pi$
$998$		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	1176.2.q.f.961.1		2
3.2	odd	2		3528.2.s.w.3313.1		2
4.3	odd	2		2352.2.q.d.961.1		2
7.2	even	3		168.2.a.a.1.1	✓	1
7.3	odd	6		1176.2.q.d.361.1		2
7.4	even	3	inner	1176.2.q.f.361.1		2
7.5	odd	6		1176.2.a.f.1.1		1
7.6	odd	2		1176.2.q.d.961.1		2
21.2	odd	6		504.2.a.e.1.1		1
21.5	even	6		3528.2.a.v.1.1		1
21.11	odd	6		3528.2.s.w.361.1		2
21.17	even	6		3528.2.s.g.361.1		2
21.20	even	2		3528.2.s.g.3313.1		2
28.3	even	6		2352.2.q.w.1537.1		2
28.11	odd	6		2352.2.q.d.1537.1		2
28.19	even	6		2352.2.a.c.1.1		1
28.23	odd	6		336.2.a.e.1.1		1
28.27	even	2		2352.2.q.w.961.1		2
35.2	odd	12		4200.2.t.j.1849.2		2
35.9	even	6		4200.2.a.t.1.1		1
35.23	odd	12		4200.2.t.j.1849.1		2
56.5	odd	6		9408.2.a.be.1.1		1
56.19	even	6		9408.2.a.da.1.1		1
56.37	even	6		1344.2.a.m.1.1		1
56.51	odd	6		1344.2.a.b.1.1		1
84.23	even	6		1008.2.a.b.1.1		1
84.47	odd	6		7056.2.a.bq.1.1		1
112.37	even	12		5376.2.c.d.2689.2		2
112.51	odd	12		5376.2.c.bb.2689.2		2
112.93	even	12		5376.2.c.d.2689.1		2
112.107	odd	12		5376.2.c.bb.2689.1		2
140.79	odd	6		8400.2.a.y.1.1		1
168.107	even	6		4032.2.a.bc.1.1		1
168.149	odd	6		4032.2.a.bh.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.a.a.1.1	✓	1	7.2	even	3
336.2.a.e.1.1		1	28.23	odd	6
504.2.a.e.1.1		1	21.2	odd	6
1008.2.a.b.1.1		1	84.23	even	6
1176.2.a.f.1.1		1	7.5	odd	6
1176.2.q.d.361.1		2	7.3	odd	6
1176.2.q.d.961.1		2	7.6	odd	2
1176.2.q.f.361.1		2	7.4	even	3	inner
1176.2.q.f.961.1		2	1.1	even	1	trivial
1344.2.a.b.1.1		1	56.51	odd	6
1344.2.a.m.1.1		1	56.37	even	6
2352.2.a.c.1.1		1	28.19	even	6
2352.2.q.d.961.1		2	4.3	odd	2
2352.2.q.d.1537.1		2	28.11	odd	6
2352.2.q.w.961.1		2	28.27	even	2
2352.2.q.w.1537.1		2	28.3	even	6
3528.2.a.v.1.1		1	21.5	even	6
3528.2.s.g.361.1		2	21.17	even	6
3528.2.s.g.3313.1		2	21.20	even	2
3528.2.s.w.361.1		2	21.11	odd	6
3528.2.s.w.3313.1		2	3.2	odd	2
4032.2.a.bc.1.1		1	168.107	even	6
4032.2.a.bh.1.1		1	168.149	odd	6
4200.2.a.t.1.1		1	35.9	even	6
4200.2.t.j.1849.1		2	35.23	odd	12
4200.2.t.j.1849.2		2	35.2	odd	12
5376.2.c.d.2689.1		2	112.93	even	12
5376.2.c.d.2689.2		2	112.37	even	12
5376.2.c.bb.2689.1		2	112.107	odd	12
5376.2.c.bb.2689.2		2	112.51	odd	12
7056.2.a.bq.1.1		1	84.47	odd	6
8400.2.a.y.1.1		1	140.79	odd	6
9408.2.a.be.1.1		1	56.5	odd	6
9408.2.a.da.1.1		1	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +6.00000 q^{13} -2.00000 q^{15} +(1.00000 + 1.73205i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -10.0000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-3.00000 + 5.19615i) q^{37} +(3.00000 + 5.19615i) q^{39} -2.00000 q^{41} -4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(-1.00000 + 1.73205i) q^{51} +(5.00000 + 8.66025i) q^{53} -4.00000 q^{57} +(-6.00000 - 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-6.00000 + 10.3923i) q^{65} +(-6.00000 - 10.3923i) q^{67} +4.00000 q^{69} -12.0000 q^{71} +(7.00000 + 12.1244i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -4.00000 q^{85} +(-5.00000 - 8.66025i) q^{87} +(1.00000 - 1.73205i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-4.00000 - 6.92820i) q^{95} +10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - 2 q^{5} - q^{9}+O(q^{10}) \) 2 * q + q^3 - 2 * q^5 - q^9	\( 2 q + q^{3} - 2 q^{5} - q^{9} + 12 q^{13} - 4 q^{15} + 2 q^{17} - 4 q^{19} + 4 q^{23} + q^{25} - 2 q^{27} - 20 q^{29} + 8 q^{31} - 6 q^{37} + 6 q^{39} - 4 q^{41} - 8 q^{43} - 2 q^{45} - 8 q^{47} - 2 q^{51} + 10 q^{53} - 8 q^{57} - 12 q^{59} + 2 q^{61} - 12 q^{65} - 12 q^{67} + 8 q^{69} - 24 q^{71} + 14 q^{73} - q^{75} + 8 q^{79} - q^{81} + 24 q^{83} - 8 q^{85} - 10 q^{87} + 2 q^{89} - 8 q^{93} - 8 q^{95} + 20 q^{97}+O(q^{100}) \) 2 * q + q^3 - 2 * q^5 - q^9 + 12 * q^13 - 4 * q^15 + 2 * q^17 - 4 * q^19 + 4 * q^23 + q^25 - 2 * q^27 - 20 * q^29 + 8 * q^31 - 6 * q^37 + 6 * q^39 - 4 * q^41 - 8 * q^43 - 2 * q^45 - 8 * q^47 - 2 * q^51 + 10 * q^53 - 8 * q^57 - 12 * q^59 + 2 * q^61 - 12 * q^65 - 12 * q^67 + 8 * q^69 - 24 * q^71 + 14 * q^73 - q^75 + 8 * q^79 - q^81 + 24 * q^83 - 8 * q^85 - 10 * q^87 + 2 * q^89 - 8 * q^93 - 8 * q^95 + 20 * q^97

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