LMFDB - Embedded newform 2646.2.h.j.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (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:	$21.1284163748$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.j.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -3.00000 q^{23} -4.00000 q^{25} +(-1.00000 + 1.73205i) q^{26} +(-4.00000 + 6.92820i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{37} -7.00000 q^{38} -1.00000 q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-2.00000 - 3.46410i) q^{50} -2.00000 q^{52} +(2.00000 + 3.46410i) q^{53} +2.00000 q^{55} -8.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +5.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +6.00000 q^{74} +(-3.50000 - 6.06218i) q^{76} +(5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.00000 + 10.3923i) q^{82} +(-6.00000 + 10.3923i) q^{83} +8.00000 q^{86} -2.00000 q^{88} +(-7.00000 + 12.1244i) q^{89} +(1.50000 - 2.59808i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(-3.50000 + 6.06218i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 2 * q^5 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} - q^{16} - 7 q^{19} - q^{20} + 2 q^{22} - 6 q^{23} - 8 q^{25} - 2 q^{26} - 8 q^{29} + 4 q^{31} + q^{32} + 6 q^{37} - 14 q^{38} - 2 q^{40} + 12 q^{41} + 8 q^{43} - 2 q^{44} - 3 q^{46} + 8 q^{47} - 4 q^{50} - 4 q^{52} + 4 q^{53} + 4 q^{55} - 16 q^{58} - 4 q^{59} + 13 q^{61} + 8 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 10 q^{71} - 14 q^{73} + 12 q^{74} - 7 q^{76} + 11 q^{79} - q^{80} - 12 q^{82} - 12 q^{83} + 16 q^{86} - 4 q^{88} - 14 q^{89} + 3 q^{92} - 8 q^{94} - 7 q^{95} - 2 q^{97}+O(q^{100}) $ 2 * q + q^2 - q^4 + 2 * q^5 - 2 * q^8 + q^10 + 4 * q^11 + 2 * q^13 - q^16 - 7 * q^19 - q^20 + 2 * q^22 - 6 * q^23 - 8 * q^25 - 2 * q^26 - 8 * q^29 + 4 * q^31 + q^32 + 6 * q^37 - 14 * q^38 - 2 * q^40 + 12 * q^41 + 8 * q^43 - 2 * q^44 - 3 * q^46 + 8 * q^47 - 4 * q^50 - 4 * q^52 + 4 * q^53 + 4 * q^55 - 16 * q^58 - 4 * q^59 + 13 * q^61 + 8 * q^62 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 10 * q^71 - 14 * q^73 + 12 * q^74 - 7 * q^76 + 11 * q^79 - q^80 - 12 * q^82 - 12 * q^83 + 16 * q^86 - 4 * q^88 - 14 * q^89 + 3 * q^92 - 8 * q^94 - 7 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$		0			0
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	0.208443	+	0.978035i	$0.433160\pi$
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	−0.951224	+	0.308500i	$0.900173\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	−7.00000			−1.13555
$39$		0			0
$40$	−1.00000			−0.158114
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.770950	+	0.636895i	$0.219782\pi$
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.166092	+	0.986110i	$0.446885\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−2.00000			−0.277350
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$	−8.00000			−1.05045
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		0			0
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$		0			0
$78$		0			0
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$		0			0
$86$	8.00000			0.862662
$87$		0			0
$88$	−2.00000			−0.213201
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$		0			0
$91$		0			0
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$		0			0
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$	−3.50000	+	6.06218i	−0.359092	+	0.621966i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$		0			0
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−11.0000			−1.09454			−0.547270	−	0.836956i	$-0.684333\pi$
$101$	−11.0000			−1.09454			−0.547270	+	0.836956i	$0.684333\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	−0.605308	−	0.795991i	$-0.706950\pi$
$107$	4.00000	−	6.92820i	0.386695	−	0.669775i	0.992003	+	0.126217i	$0.0402834\pi$
$108$		0			0
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$		0			0
$112$		0			0
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	0.841549	−	0.540181i	$-0.181644\pi$
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	−0.888585	+	0.458712i	$0.848311\pi$
$114$		0			0
$115$	−3.00000			−0.279751
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−6.50000	+	11.2583i	−0.588482	+	1.01928i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.00000	+	1.73205i	−0.0877058	+	0.151911i
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$		0			0
$133$		0			0
$134$	2.00000			0.172774
$135$		0			0
$136$		0			0
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$		0			0
$142$	2.50000	+	4.33013i	0.209795	+	0.363376i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$		0			0
$145$	−4.00000	+	6.92820i	−0.332182	+	0.575356i
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$		0			0
$148$	3.00000	+	5.19615i	0.246598	+	0.427121i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$		0			0
$151$	19.0000			1.54620			0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000			1.54620			0.773099	+	0.634285i	$0.218706\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$		0			0
$154$		0			0
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		0			0
$157$	5.50000	−	9.52628i	0.438948	−	0.760280i	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	5.50000	−	9.52628i	0.438948	−	0.760280i	0.997609	+	0.0691164i	$0.0220180\pi$
$158$	−5.50000	+	9.52628i	−0.437557	+	0.757870i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$		0			0
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	−12.0000			−0.937043
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	0.824737	−	0.565516i	$-0.191323\pi$
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	−0.902120	+	0.431486i	$0.857990\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	0.892956	+	0.450145i	$0.148628\pi$
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	−0.0566411	+	0.998395i	$0.518039\pi$
$174$		0			0
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	−14.0000			−1.04934
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		0			0
$184$	3.00000			0.221163
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−7.00000			−0.507833
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	4.00000			0.282843
$201$		0			0
$202$	−5.50000	−	9.52628i	−0.386979	−	0.670267i
$203$		0			0
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	−7.00000	+	12.1244i	−0.484200	+	0.838659i
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	−4.00000			−0.274721
$213$		0			0
$214$	8.00000			0.546869
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$		0			0
$217$		0			0
$218$	2.00000	−	3.46410i	0.135457	−	0.234619i
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$		0			0
$222$		0			0
$223$	−1.00000	+	1.73205i	−0.0669650	+	0.115987i	−0.897564	−	0.440884i	$-0.854665\pi$
$223$	−1.00000	+	1.73205i	−0.0669650	+	0.115987i	0.830599	+	0.556871i	$0.187998\pi$
$224$		0			0
$225$		0			0
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	17.0000			1.12833			0.564165	−	0.825662i	$-0.309198\pi$
$227$	17.0000			1.12833			0.564165	+	0.825662i	$0.309198\pi$
$228$		0			0
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$	−1.50000	−	2.59808i	−0.0989071	−	0.171312i
$231$		0			0
$232$	4.00000	−	6.92820i	0.262613	−	0.454859i
$233$	0.500000	−	0.866025i	0.0327561	−	0.0567352i	−0.849183	−	0.528099i	$-0.822905\pi$
$233$	0.500000	−	0.866025i	0.0327561	−	0.0567352i	0.881939	+	0.471364i	$0.156238\pi$
$234$		0			0
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$		0			0
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−13.0000			−0.832240
$245$		0			0
$246$		0			0
$247$	−14.0000			−0.890799
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	7.00000			0.441836			0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000			0.441836			0.220918	+	0.975292i	$0.429095\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−9.50000	−	16.4545i	−0.596083	−	1.03245i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.00000			0.499026			0.249513	−	0.968371i	$-0.419729\pi$
$257$	8.00000			0.499026			0.249513	+	0.968371i	$0.419729\pi$
$258$		0			0
$259$		0			0
$260$	−2.00000			−0.124035
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	−19.0000			−1.17159			−0.585795	−	0.810459i	$-0.699218\pi$
$263$	−19.0000			−1.17159			−0.585795	+	0.810459i	$0.699218\pi$
$264$		0			0
$265$	2.00000	+	3.46410i	0.122859	+	0.212798i
$266$		0			0
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−3.50000	−	6.06218i	−0.213399	−	0.369618i	0.739377	−	0.673291i	$-0.235120\pi$
$269$	−3.50000	−	6.06218i	−0.213399	−	0.369618i	−0.952776	+	0.303674i	$0.901787\pi$
$270$		0			0
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	−0.571221	−	0.820796i	$-0.693530\pi$
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	0.996441	+	0.0842940i	$0.0268635\pi$
$272$		0			0
$273$		0			0
$274$	1.00000	+	1.73205i	0.0604122	+	0.104637i
$275$	−8.00000			−0.482418
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−4.50000	+	7.79423i	−0.269892	+	0.467467i
$279$		0			0
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$		0			0
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$	−2.50000	+	4.33013i	−0.148348	+	0.256946i
$285$		0			0
$286$	−2.00000	+	3.46410i	−0.118262	+	0.204837i
$287$		0			0
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−8.00000			−0.469776
$291$		0			0
$292$	14.0000			0.819288
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$		0			0
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$		0			0
$302$	9.50000	+	16.4545i	0.546664	+	0.946849i
$303$		0			0
$304$	7.00000			0.401478
$305$	6.50000	+	11.2583i	0.372189	+	0.644650i
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$		0			0
$310$	4.00000			0.227185
$311$	5.00000	−	8.66025i	0.283524	−	0.491078i	−0.688726	−	0.725022i	$-0.741830\pi$
$311$	5.00000	−	8.66025i	0.283524	−	0.491078i	0.972250	+	0.233944i	$0.0751631\pi$
$312$		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	$0.779095\pi$
$314$	11.0000			0.620766
$315$		0			0
$316$	−11.0000			−0.618798
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$		0			0
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$	1.00000			0.0559017
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	6.00000			0.332309
$327$		0			0
$328$	−6.00000	−	10.3923i	−0.331295	−	0.573819i
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$		0			0
$334$	1.00000	−	1.73205i	0.0547176	−	0.0947736i
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	9.00000			0.489535
$339$		0			0
$340$		0			0
$341$	4.00000	−	6.92820i	0.216612	−	0.375183i
$342$		0			0
$343$		0			0
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	−11.0000	+	19.0526i	−0.591364	+	1.02427i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	0.114747	+	0.993395i	$0.463394\pi$
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	−0.917679	+	0.397324i	$0.869939\pi$
$350$		0			0
$351$		0			0
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	24.0000			1.27739			0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$		0			0
$355$	5.00000			0.265372
$356$	−7.00000	−	12.1244i	−0.370999	−	0.642590i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	14.5000	−	25.1147i	0.765281	−	1.32551i	−0.174817	−	0.984601i	$-0.555933\pi$
$359$	14.5000	−	25.1147i	0.765281	−	1.32551i	0.940098	−	0.340904i	$-0.110733\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$		0			0
$364$		0			0
$365$	−7.00000	−	12.1244i	−0.366397	−	0.634618i
$366$		0			0
$367$	32.0000			1.67039			0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000			1.67039			0.835193	+	0.549957i	$0.185356\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$		0			0
$370$	6.00000			0.311925
$371$		0			0
$372$		0			0
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$		0			0
$375$		0			0
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$	−16.0000			−0.824042
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	−3.50000	−	6.06218i	−0.179546	−	0.310983i
$381$		0			0
$382$	−1.50000	+	2.59808i	−0.0767467	+	0.132929i
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$		0			0
$385$		0			0
$386$	−5.00000			−0.254493
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	5.50000	+	9.52628i	0.276735	+	0.479319i
$396$		0			0
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−3.00000			−0.149813			−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000			−0.149813			−0.0749064	+	0.997191i	$0.523866\pi$
$402$		0			0
$403$	8.00000			0.398508
$404$	5.50000	−	9.52628i	0.273635	−	0.473950i
$405$		0			0
$406$		0			0
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$		0			0
$409$	−12.0000	+	20.7846i	−0.593362	+	1.02773i	0.400414	+	0.916334i	$0.368866\pi$
$409$	−12.0000	+	20.7846i	−0.593362	+	1.02773i	−0.993776	+	0.111398i	$0.964467\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$		0			0
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	2.00000			0.0980581
$417$		0			0
$418$	−14.0000			−0.684762
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	0.920609	−	0.390487i	$-0.127693\pi$
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	−0.798476	+	0.602027i	$0.794360\pi$
$420$		0			0
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.0229375	−	0.999737i	$-0.492698\pi$
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.854329	−	0.519733i	$-0.173969\pi$
$422$	−11.0000	+	19.0526i	−0.535472	+	0.927464i
$423$		0			0
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.00000	+	6.92820i	0.193347	+	0.334887i
$429$		0			0
$430$	8.00000			0.385794
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$		0			0
$435$		0			0
$436$	4.00000			0.191565
$437$	10.5000	−	18.1865i	0.502283	−	0.869980i
$438$		0			0
$439$	−18.0000	−	31.1769i	−0.859093	−	1.48799i	−0.872795	−	0.488087i	$-0.837695\pi$
$439$	−18.0000	−	31.1769i	−0.859093	−	1.48799i	0.0137020	−	0.999906i	$-0.495638\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	0.996551	+	0.0829786i	$0.0264433\pi$
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	−0.426414	+	0.904528i	$0.640223\pi$
$444$		0			0
$445$	−7.00000	+	12.1244i	−0.331832	+	0.574750i
$446$	−2.00000			−0.0947027
$447$		0			0
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	12.0000	+	20.7846i	0.565058	+	0.978709i
$452$	1.00000			0.0470360
$453$		0			0
$454$	8.50000	+	14.7224i	0.398925	+	0.690958i
$455$		0			0
$456$		0			0
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	0.595818	−	0.803120i	$-0.296828\pi$
$457$	−8.50000	−	14.7224i	−0.397613	−	0.688686i	−0.993431	+	0.114433i	$0.963495\pi$
$458$	6.50000	+	11.2583i	0.303725	+	0.526067i
$459$		0			0
$460$	1.50000	−	2.59808i	0.0699379	−	0.121136i
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	0.877410	−	0.479741i	$-0.159269\pi$
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	−0.854173	+	0.519989i	$0.825936\pi$
$464$	8.00000			0.371391
$465$		0			0
$466$	1.00000			0.0463241
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	−0.335794	−	0.941935i	$-0.609005\pi$
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	0.983637	−	0.180161i	$-0.0576619\pi$
$468$		0			0
$469$		0			0
$470$	−4.00000	+	6.92820i	−0.184506	+	0.319574i
$471$		0			0
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$		0			0
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$		0			0
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$	12.0000			0.547153
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$		0			0
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−12.5000	−	21.6506i	−0.566429	−	0.981084i	0.430486	−	0.902597i	$-0.358342\pi$
$488$	−6.50000	−	11.2583i	−0.294241	−	0.509641i
$489$		0			0
$490$		0			0
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$		0			0
$493$		0			0
$494$	−7.00000	−	12.1244i	−0.314945	−	0.545501i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$		0			0
$502$	3.50000	+	6.06218i	0.156213	+	0.270568i
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$		0			0
$505$	−11.0000			−0.489494
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$		0			0
$508$	9.50000	−	16.4545i	0.421494	−	0.730050i
$509$	−34.0000			−1.50702			−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000			−1.50702			−0.753512	+	0.657434i	$0.771642\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.00000	+	6.92820i	0.176432	+	0.305590i
$515$	−8.00000			−0.352522
$516$		0			0
$517$	8.00000	+	13.8564i	0.351840	+	0.609404i
$518$		0			0
$519$		0			0
$520$	−1.00000	−	1.73205i	−0.0438529	−	0.0759555i
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$		0			0
$523$	17.5000	−	30.3109i	0.765222	−	1.32540i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	17.5000	−	30.3109i	0.765222	−	1.32540i	0.940129	−	0.340818i	$-0.110704\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−9.50000	−	16.4545i	−0.414220	−	0.717450i
$527$		0			0
$528$		0			0
$529$	−14.0000			−0.608696
$530$	−2.00000	+	3.46410i	−0.0868744	+	0.150471i
$531$		0			0
$532$		0			0
$533$	−12.0000	+	20.7846i	−0.519778	+	0.900281i
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$		0			0
$538$	3.50000	−	6.06218i	0.150896	−	0.261359i
$539$		0			0
$540$		0			0
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	−0.566933	−	0.823764i	$-0.691870\pi$
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	0.996867	+	0.0790969i	$0.0252036\pi$
$542$	14.0000			0.601351
$543$		0			0
$544$		0			0
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$		0			0
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$548$	−1.00000	+	1.73205i	−0.0427179	+	0.0739895i
$549$		0			0
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$	−28.0000	−	48.4974i	−1.19284	−	2.06606i
$552$		0			0
$553$		0			0
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	−9.00000			−0.381685
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	−15.0000			−0.632737
$563$	−5.50000	+	9.52628i	−0.231797	+	0.401485i	−0.958337	−	0.285640i	$-0.907794\pi$
$563$	−5.50000	+	9.52628i	−0.231797	+	0.401485i	0.726540	+	0.687124i	$0.241127\pi$
$564$		0			0
$565$	−0.500000	−	0.866025i	−0.0210352	−	0.0364340i
$566$	25.0000			1.05083
$567$		0			0
$568$	−5.00000			−0.209795
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	−4.00000			−0.167248
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	14.0000	+	24.2487i	0.582828	+	1.00949i	0.995142	+	0.0984456i	$0.0313871\pi$
$577$	14.0000	+	24.2487i	0.582828	+	1.00949i	−0.412315	+	0.911041i	$0.635280\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	−4.00000	−	6.92820i	−0.166091	−	0.287678i
$581$		0			0
$582$		0			0
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$		0			0
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	11.5000	−	19.9186i	0.474656	−	0.822128i	−0.524923	−	0.851150i	$-0.675906\pi$
$587$	11.5000	−	19.9186i	0.474656	−	0.822128i	0.999579	+	0.0290218i	$0.00923921\pi$
$588$		0			0
$589$	14.0000	+	24.2487i	0.576860	+	0.999151i
$590$	−4.00000			−0.164677
$591$		0			0
$592$	−6.00000			−0.246598
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$		0			0
$595$		0			0
$596$	5.00000	−	8.66025i	0.204808	−	0.354738i
$597$		0			0
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$		0			0
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	−7.00000			−0.284590
$606$		0			0
$607$	6.00000			0.243532			0.121766	−	0.992559i	$-0.461144\pi$
$607$	6.00000			0.243532			0.121766	+	0.992559i	$0.461144\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	−6.50000	+	11.2583i	−0.263177	+	0.455836i
$611$	−8.00000	+	13.8564i	−0.323645	+	0.560570i
$612$		0			0
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$		0			0
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	0.555056	−	0.831813i	$-0.312697\pi$
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	−0.997899	+	0.0647859i	$0.979364\pi$
$618$		0			0
$619$	11.0000			0.442127			0.221064	−	0.975259i	$-0.429047\pi$
$619$	11.0000			0.442127			0.221064	+	0.975259i	$0.429047\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	10.0000			0.400963
$623$		0			0
$624$		0			0
$625$	11.0000			0.440000
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	5.50000	+	9.52628i	0.219474	+	0.380140i
$629$		0			0
$630$		0			0
$631$	9.00000			0.358284			0.179142	−	0.983823i	$-0.442668\pi$
$631$	9.00000			0.358284			0.179142	+	0.983823i	$0.442668\pi$
$632$	−5.50000	−	9.52628i	−0.218778	−	0.378935i
$633$		0			0
$634$	−12.0000	+	20.7846i	−0.476581	+	0.825462i
$635$	−19.0000			−0.753992
$636$		0			0
$637$		0			0
$638$	−16.0000			−0.633446
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−47.0000			−1.85639			−0.928194	−	0.372096i	$-0.878639\pi$
$641$	−47.0000			−1.85639			−0.928194	+	0.372096i	$0.878639\pi$
$642$		0			0
$643$	−6.00000	−	10.3923i	−0.236617	−	0.409832i	0.723124	−	0.690718i	$-0.242705\pi$
$643$	−6.00000	−	10.3923i	−0.236617	−	0.409832i	−0.959741	+	0.280885i	$0.909372\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	0.901464	+	0.432855i	$0.142494\pi$
$647$	21.0000	+	36.3731i	0.825595	+	1.42997i	−0.0758684	+	0.997118i	$0.524173\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	3.00000	+	5.19615i	0.117489	+	0.203497i
$653$	32.0000			1.25226			0.626128	−	0.779720i	$-0.284639\pi$
$653$	32.0000			1.25226			0.626128	+	0.779720i	$0.284639\pi$
$654$		0			0
$655$	15.0000			0.586098
$656$	6.00000	−	10.3923i	0.234261	−	0.405751i
$657$		0			0
$658$		0			0
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	−0.602844	−	0.797859i	$-0.705966\pi$
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	0.992388	+	0.123148i	$0.0392990\pi$
$660$		0			0
$661$	−15.5000	+	26.8468i	−0.602880	+	1.04422i	0.389503	+	0.921025i	$0.372647\pi$
$661$	−15.5000	+	26.8468i	−0.602880	+	1.04422i	−0.992383	+	0.123194i	$0.960686\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$		0			0
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$	2.00000			0.0773823
$669$		0			0
$670$	2.00000			0.0772667
$671$	13.0000	+	22.5167i	0.501859	+	0.869246i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	−11.0000	+	19.0526i	−0.423704	+	0.733877i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	8.00000			0.306336
$683$	−5.00000	−	8.66025i	−0.191320	−	0.331375i	0.754368	−	0.656452i	$-0.227943\pi$
$683$	−5.00000	−	8.66025i	−0.191320	−	0.331375i	−0.945688	+	0.325076i	$0.894610\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$		0			0
$687$		0			0
$688$	−8.00000			−0.304997
$689$	−4.00000	+	6.92820i	−0.152388	+	0.263944i
$690$		0			0
$691$	−14.5000	−	25.1147i	−0.551606	−	0.955410i	−0.998159	−	0.0606524i	$-0.980682\pi$
$691$	−14.5000	−	25.1147i	−0.551606	−	0.955410i	0.446553	−	0.894757i	$-0.352651\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	4.50000	+	7.79423i	0.170695	+	0.295652i
$696$		0			0
$697$		0			0
$698$	−30.0000			−1.13552
$699$		0			0
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	21.0000	+	36.3731i	0.792030	+	1.37184i
$704$	2.00000			0.0753778
$705$		0			0
$706$	12.0000	+	20.7846i	0.451626	+	0.782239i
$707$		0			0
$708$		0			0
$709$	16.0000	+	27.7128i	0.600893	+	1.04078i	0.992686	+	0.120723i	$0.0385214\pi$
$709$	16.0000	+	27.7128i	0.600893	+	1.04078i	−0.391794	+	0.920053i	$0.628145\pi$
$710$	2.50000	+	4.33013i	0.0938233	+	0.162507i
$711$		0			0
$712$	7.00000	−	12.1244i	0.262336	−	0.454379i
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	2.00000	+	3.46410i	0.0747958	+	0.129550i
$716$	24.0000			0.896922
$717$		0			0
$718$	29.0000			1.08227
$719$		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
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$		0			0
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$	16.0000	−	27.7128i	0.594225	−	1.02923i
$726$		0			0
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	−0.517647	−	0.855595i	$-0.673192\pi$
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	0.999790	+	0.0204978i	$0.00652512\pi$
$728$		0			0
$729$		0			0
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$		0			0
$732$		0			0
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$		0			0
$736$	−1.50000	+	2.59808i	−0.0552907	+	0.0957664i
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$		0			0
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	0.968839	+	0.247691i	$0.0796718\pi$
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	−0.269913	+	0.962885i	$0.586995\pi$
$740$	3.00000	+	5.19615i	0.110282	+	0.191014i
$741$		0			0
$742$		0			0
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.850814	+	0.525467i	$0.176109\pi$
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.0296605	+	0.999560i	$0.490557\pi$
$744$		0			0
$745$	−10.0000			−0.366372
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−39.0000			−1.42313			−0.711565	−	0.702620i	$-0.752013\pi$
$751$	−39.0000			−1.42313			−0.711565	+	0.702620i	$0.752013\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$	−8.00000	−	13.8564i	−0.291343	−	0.504621i
$755$	19.0000			0.691481
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−6.00000	−	10.3923i	−0.217930	−	0.377466i
$759$		0			0
$760$	3.50000	−	6.06218i	0.126958	−	0.219898i
$761$	−20.0000			−0.724999			−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000			−0.724999			−0.362500	+	0.931984i	$0.618077\pi$
$762$		0			0
$763$		0			0
$764$	−3.00000			−0.108536
$765$		0			0
$766$	−3.00000	−	5.19615i	−0.108394	−	0.187745i
$767$	−8.00000			−0.288863
$768$		0			0
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	0.883493	−	0.468445i	$-0.155186\pi$
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	−0.847432	+	0.530904i	$0.821852\pi$
$770$		0			0
$771$		0			0
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$		0			0
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$	−84.0000			−3.00961
$780$		0			0
$781$	10.0000			0.357828
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.50000	−	9.52628i	0.196303	−	0.340007i
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$		0			0
$790$	−5.50000	+	9.52628i	−0.195681	+	0.338930i
$791$		0			0
$792$		0			0
$793$	−13.0000	+	22.5167i	−0.461644	+	0.799590i
$794$	14.0000			0.496841
$795$		0			0
$796$	14.0000			0.496217
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.823241	−	0.567692i	$-0.807836\pi$
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.0800155	−	0.996794i	$-0.525497\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$	−14.0000	−	24.2487i	−0.494049	−	0.855718i
$804$		0			0
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$		0			0
$808$	11.0000			0.386979
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$		0			0
$814$	12.0000			0.420600
$815$	3.00000	−	5.19615i	0.105085	−	0.182013i
$816$		0			0
$817$	28.0000	+	48.4974i	0.979596	+	1.69671i
$818$	−24.0000			−0.839140
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−16.0000	−	27.7128i	−0.558404	−	0.967184i	−0.997630	−	0.0688073i	$-0.978081\pi$
$821$	−16.0000	−	27.7128i	−0.558404	−	0.967184i	0.439226	−	0.898377i	$-0.355253\pi$
$822$		0			0
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	−0.172379	−	0.985031i	$-0.555146\pi$
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	0.939251	−	0.343230i	$-0.111521\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$	−12.0000			−0.416526
$831$		0			0
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$		0			0
$834$		0			0
$835$	−1.00000	−	1.73205i	−0.0346064	−	0.0599401i
$836$	−7.00000	−	12.1244i	−0.242100	−	0.419330i
$837$		0			0
$838$	−2.50000	+	4.33013i	−0.0863611	+	0.149582i
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	36.0000			1.24064
$843$		0			0
$844$	−22.0000			−0.757271
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$	2.00000	−	3.46410i	0.0686803	−	0.118958i
$849$		0			0
$850$		0			0
$851$	−9.00000	+	15.5885i	−0.308516	+	0.534365i
$852$		0			0
$853$	−18.5000	+	32.0429i	−0.633428	+	1.09713i	0.353418	+	0.935466i	$0.385019\pi$
$853$	−18.5000	+	32.0429i	−0.633428	+	1.09713i	−0.986846	+	0.161664i	$0.948314\pi$
$854$		0			0
$855$		0			0
$856$	−4.00000	+	6.92820i	−0.136717	+	0.236801i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	−36.0000			−1.22830			−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000			−1.22830			−0.614152	+	0.789188i	$0.710502\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$		0			0
$862$	−16.0000	+	27.7128i	−0.544962	+	0.943902i
$863$	28.5000	−	49.3634i	0.970151	−	1.68035i	0.275064	−	0.961426i	$-0.411301\pi$
$863$	28.5000	−	49.3634i	0.970151	−	1.68035i	0.695087	−	0.718925i	$-0.255366\pi$
$864$		0			0
$865$	11.0000	+	19.0526i	0.374011	+	0.647806i
$866$	14.0000	+	24.2487i	0.475739	+	0.824005i
$867$		0			0
$868$		0			0
$869$	11.0000	+	19.0526i	0.373149	+	0.646314i
$870$		0			0
$871$	4.00000			0.135535
$872$	2.00000	+	3.46410i	0.0677285	+	0.117309i
$873$		0			0
$874$	21.0000			0.710336
$875$		0			0
$876$		0			0
$877$	24.0000			0.810422			0.405211	−	0.914223i	$-0.367198\pi$
$877$	24.0000			0.810422			0.405211	+	0.914223i	$0.367198\pi$
$878$	18.0000	−	31.1769i	0.607471	−	1.05217i
$879$		0			0
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	28.0000			0.943344			0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000			0.943344			0.471672	+	0.881774i	$0.343651\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	36.0000			1.20876			0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000			1.20876			0.604381	+	0.796696i	$0.293421\pi$
$888$		0			0
$889$		0			0
$890$	−14.0000			−0.469281
$891$		0			0
$892$	−1.00000	−	1.73205i	−0.0334825	−	0.0579934i
$893$	−56.0000			−1.87397
$894$		0			0
$895$	−12.0000	−	20.7846i	−0.401116	−	0.694753i
$896$		0			0
$897$		0			0
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	16.0000	+	27.7128i	0.533630	+	0.924274i
$900$		0			0
$901$		0			0
$902$	−12.0000	+	20.7846i	−0.399556	+	0.692052i
$903$		0			0
$904$	0.500000	+	0.866025i	0.0166298	+	0.0288036i
$905$	−7.00000			−0.232688
$906$		0			0
$907$	−2.00000			−0.0664089			−0.0332045	−	0.999449i	$-0.510571\pi$
$907$	−2.00000			−0.0664089			−0.0332045	+	0.999449i	$0.510571\pi$
$908$	−8.50000	+	14.7224i	−0.282082	+	0.488581i
$909$		0			0
$910$		0			0
$911$	−0.500000	+	0.866025i	−0.0165657	+	0.0286927i	−0.874189	−	0.485585i	$-0.838607\pi$
$911$	−0.500000	+	0.866025i	−0.0165657	+	0.0286927i	0.857624	+	0.514278i	$0.171940\pi$
$912$		0			0
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$	8.50000	−	14.7224i	0.281155	−	0.486975i
$915$		0			0
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$		0			0
$918$		0			0
$919$	−7.50000	+	12.9904i	−0.247402	+	0.428513i	−0.962804	−	0.270200i	$-0.912910\pi$
$919$	−7.50000	+	12.9904i	−0.247402	+	0.428513i	0.715402	+	0.698713i	$0.246244\pi$
$920$	3.00000			0.0989071
$921$		0			0
$922$	9.00000			0.296399
$923$	5.00000	+	8.66025i	0.164577	+	0.285056i
$924$		0			0
$925$	−12.0000	+	20.7846i	−0.394558	+	0.683394i
$926$	−0.500000	+	0.866025i	−0.0164310	+	0.0284594i
$927$		0			0
$928$	4.00000	+	6.92820i	0.131306	+	0.227429i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$		0			0
$932$	0.500000	+	0.866025i	0.0163780	+	0.0283676i
$933$		0			0
$934$	28.0000			0.916188
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$	−8.00000			−0.260931
$941$	1.50000	−	2.59808i	0.0488986	−	0.0846949i	−0.840540	−	0.541749i	$-0.817762\pi$
$941$	1.50000	−	2.59808i	0.0488986	−	0.0846949i	0.889439	+	0.457054i	$0.151096\pi$
$942$		0			0
$943$	−18.0000	−	31.1769i	−0.586161	−	1.01526i
$944$	4.00000			0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	0.935757	−	0.352646i	$-0.114718\pi$
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	−0.773279	+	0.634066i	$0.781385\pi$
$948$		0			0
$949$	14.0000	−	24.2487i	0.454459	−	0.787146i
$950$	28.0000			0.908440
$951$		0			0
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	1.50000	+	2.59808i	0.0485389	+	0.0840718i
$956$	15.0000			0.485135
$957$		0			0
$958$	12.0000	+	20.7846i	0.387702	+	0.671520i
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	6.00000	+	10.3923i	0.193448	+	0.335061i
$963$		0			0
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	−2.50000	+	4.33013i	−0.0804778	+	0.139392i
$966$		0			0
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	0.742382	−	0.669977i	$-0.233696\pi$
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	−0.951408	+	0.307933i	$0.900363\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	−2.00000			−0.0642161
$971$	17.5000	−	30.3109i	0.561602	−	0.972723i	−0.435755	−	0.900065i	$-0.643519\pi$
$971$	17.5000	−	30.3109i	0.561602	−	0.972723i	0.997357	−	0.0726575i	$-0.0231480\pi$
$972$		0			0
$973$		0			0
$974$	12.5000	−	21.6506i	0.400526	−	0.693731i
$975$		0			0
$976$	6.50000	−	11.2583i	0.208060	−	0.360370i
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$		0			0
$979$	−14.0000	+	24.2487i	−0.447442	+	0.774992i
$980$		0			0
$981$		0			0
$982$	−3.00000	+	5.19615i	−0.0957338	+	0.165816i
$983$	−32.0000			−1.02064			−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000			−1.02064			−0.510321	+	0.859984i	$0.670473\pi$
$984$		0			0
$985$	12.0000			0.382352
$986$		0			0
$987$		0			0
$988$	7.00000	−	12.1244i	0.222700	−	0.385727i
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$		0			0
$995$	−7.00000	−	12.1244i	−0.221915	−	0.384368i
$996$		0			0
$997$	−17.0000			−0.538395			−0.269198	−	0.963085i	$-0.586759\pi$
$997$	−17.0000			−0.538395			−0.269198	+	0.963085i	$0.586759\pi$
$998$	12.0000	+	20.7846i	0.379853	+	0.657925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.j.667.1		2
3.2	odd	2		882.2.h.a.79.1		2
7.2	even	3		2646.2.f.f.883.1		2
7.3	odd	6		2646.2.e.d.2125.1		2
7.4	even	3		2646.2.e.a.2125.1		2
7.5	odd	6		2646.2.f.h.883.1		2
7.6	odd	2		2646.2.h.g.667.1		2
9.4	even	3		2646.2.e.a.1549.1		2
9.5	odd	6		882.2.e.j.373.1		2
21.2	odd	6		882.2.f.c.295.1	yes	2
21.5	even	6		882.2.f.b.295.1	✓	2
21.11	odd	6		882.2.e.j.655.1		2
21.17	even	6		882.2.e.f.655.1		2
21.20	even	2		882.2.h.d.79.1		2
63.2	odd	6		7938.2.a.v.1.1		1
63.4	even	3	inner	2646.2.h.j.361.1		2
63.5	even	6		882.2.f.b.589.1	yes	2
63.13	odd	6		2646.2.e.d.1549.1		2
63.16	even	3		7938.2.a.k.1.1		1
63.23	odd	6		882.2.f.c.589.1	yes	2
63.31	odd	6		2646.2.h.g.361.1		2
63.32	odd	6		882.2.h.a.67.1		2
63.40	odd	6		2646.2.f.h.1765.1		2
63.41	even	6		882.2.e.f.373.1		2
63.47	even	6		7938.2.a.ba.1.1		1
63.58	even	3		2646.2.f.f.1765.1		2
63.59	even	6		882.2.h.d.67.1		2
63.61	odd	6		7938.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.f.373.1		2	63.41	even	6
882.2.e.f.655.1		2	21.17	even	6
882.2.e.j.373.1		2	9.5	odd	6
882.2.e.j.655.1		2	21.11	odd	6
882.2.f.b.295.1	✓	2	21.5	even	6
882.2.f.b.589.1	yes	2	63.5	even	6
882.2.f.c.295.1	yes	2	21.2	odd	6
882.2.f.c.589.1	yes	2	63.23	odd	6
882.2.h.a.67.1		2	63.32	odd	6
882.2.h.a.79.1		2	3.2	odd	2
882.2.h.d.67.1		2	63.59	even	6
882.2.h.d.79.1		2	21.20	even	2
2646.2.e.a.1549.1		2	9.4	even	3
2646.2.e.a.2125.1		2	7.4	even	3
2646.2.e.d.1549.1		2	63.13	odd	6
2646.2.e.d.2125.1		2	7.3	odd	6
2646.2.f.f.883.1		2	7.2	even	3
2646.2.f.f.1765.1		2	63.58	even	3
2646.2.f.h.883.1		2	7.5	odd	6
2646.2.f.h.1765.1		2	63.40	odd	6
2646.2.h.g.361.1		2	63.31	odd	6
2646.2.h.g.667.1		2	7.6	odd	2
2646.2.h.j.361.1		2	63.4	even	3	inner
2646.2.h.j.667.1		2	1.1	even	1	trivial
7938.2.a.f.1.1		1	63.61	odd	6
7938.2.a.k.1.1		1	63.16	even	3
7938.2.a.v.1.1		1	63.2	odd	6
7938.2.a.ba.1.1		1	63.47	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -3.00000 q^{23} -4.00000 q^{25} +(-1.00000 + 1.73205i) q^{26} +(-4.00000 + 6.92820i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{37} -7.00000 q^{38} -1.00000 q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-2.00000 - 3.46410i) q^{50} -2.00000 q^{52} +(2.00000 + 3.46410i) q^{53} +2.00000 q^{55} -8.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +5.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +6.00000 q^{74} +(-3.50000 - 6.06218i) q^{76} +(5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.00000 + 10.3923i) q^{82} +(-6.00000 + 10.3923i) q^{83} +8.00000 q^{86} -2.00000 q^{88} +(-7.00000 + 12.1244i) q^{89} +(1.50000 - 2.59808i) q^{92} +(-4.00000 + 6.92820i) q^{94} +(-3.50000 + 6.06218i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 2 * q^5 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} - q^{16} - 7 q^{19} - q^{20} + 2 q^{22} - 6 q^{23} - 8 q^{25} - 2 q^{26} - 8 q^{29} + 4 q^{31} + q^{32} + 6 q^{37} - 14 q^{38} - 2 q^{40} + 12 q^{41} + 8 q^{43} - 2 q^{44} - 3 q^{46} + 8 q^{47} - 4 q^{50} - 4 q^{52} + 4 q^{53} + 4 q^{55} - 16 q^{58} - 4 q^{59} + 13 q^{61} + 8 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 10 q^{71} - 14 q^{73} + 12 q^{74} - 7 q^{76} + 11 q^{79} - q^{80} - 12 q^{82} - 12 q^{83} + 16 q^{86} - 4 q^{88} - 14 q^{89} + 3 q^{92} - 8 q^{94} - 7 q^{95} - 2 q^{97}+O(q^{100}) \) 2 * q + q^2 - q^4 + 2 * q^5 - 2 * q^8 + q^10 + 4 * q^11 + 2 * q^13 - q^16 - 7 * q^19 - q^20 + 2 * q^22 - 6 * q^23 - 8 * q^25 - 2 * q^26 - 8 * q^29 + 4 * q^31 + q^32 + 6 * q^37 - 14 * q^38 - 2 * q^40 + 12 * q^41 + 8 * q^43 - 2 * q^44 - 3 * q^46 + 8 * q^47 - 4 * q^50 - 4 * q^52 + 4 * q^53 + 4 * q^55 - 16 * q^58 - 4 * q^59 + 13 * q^61 + 8 * q^62 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 10 * q^71 - 14 * q^73 + 12 * q^74 - 7 * q^76 + 11 * q^79 - q^80 - 12 * q^82 - 12 * q^83 + 16 * q^86 - 4 * q^88 - 14 * q^89 + 3 * q^92 - 8 * q^94 - 7 * q^95 - 2 * q^97

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