LMFDB - Embedded newform 504.2.cj.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.1
Root			$-1.40126 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40126 - 0.190983i) q^{2} +(1.92705 + 0.535233i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 - 1.11803i) q^{8} +O(q^{10})$	\(q+(-1.40126 - 0.190983i) q^{2} +(1.92705 + 0.535233i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(2.92705 - 1.19682i) q^{10} +(1.93649 + 1.11803i) q^{11} +(0.204441 + 3.73607i) q^{14} +(3.42705 + 2.06284i) q^{16} +(-1.73205 + 3.00000i) q^{17} +(-6.70820 + 3.87298i) q^{19} +(-4.33013 + 1.11803i) q^{20} +(-2.50000 - 1.93649i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(0.427051 - 5.27424i) q^{28} -2.23607i q^{29} +(0.500000 - 0.866025i) q^{31} +(-4.40822 - 3.54508i) q^{32} +(3.00000 - 3.87298i) q^{34} +(3.87298 + 4.47214i) q^{35} +(-6.70820 + 3.87298i) q^{37} +(10.1396 - 4.14590i) q^{38} +(6.28115 - 0.739674i) q^{40} -10.3923 q^{41} +(3.13331 + 3.19098i) q^{44} +(3.70820 + 9.06914i) q^{46} +(1.73205 + 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-9.68246 - 5.59017i) q^{53} -5.00000 q^{55} +(-1.60570 + 7.30902i) q^{56} +(-0.427051 + 3.13331i) q^{58} +(1.93649 + 1.11803i) q^{59} +(-6.70820 + 3.87298i) q^{61} +(-0.866025 + 1.11803i) q^{62} +(5.50000 + 5.80948i) q^{64} +(-6.70820 - 3.87298i) q^{67} +(-4.94345 + 4.85410i) q^{68} +(-4.57295 - 7.00629i) q^{70} +10.3923 q^{71} +(5.00000 - 8.66025i) q^{73} +(10.1396 - 4.14590i) q^{74} +(-15.0000 + 3.87298i) q^{76} +(1.93649 - 5.59017i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-8.94278 - 0.163119i) q^{80} +(14.5623 + 1.98475i) q^{82} +11.1803i q^{83} -7.74597i q^{85} +(-3.78115 - 5.06980i) q^{88} +(6.92820 + 12.0000i) q^{89} +(-3.46410 - 13.4164i) q^{92} +(-1.85410 - 4.53457i) q^{94} +(8.66025 - 15.0000i) q^{95} -1.00000 q^{97} +(9.60437 - 2.39919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 4 * q^7	$ 8 q + 2 q^{4} - 4 q^{7} + 10 q^{10} + 14 q^{16} - 20 q^{22} - 10 q^{28} + 4 q^{31} + 24 q^{34} + 10 q^{40} - 24 q^{46} - 52 q^{49} - 40 q^{55} + 10 q^{58} + 44 q^{64} - 50 q^{70} + 40 q^{73} - 120 q^{76} + 52 q^{79} + 36 q^{82} + 10 q^{88} + 12 q^{94} - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 4 * q^7 + 10 * q^10 + 14 * q^16 - 20 * q^22 - 10 * q^28 + 4 * q^31 + 24 * q^34 + 10 * q^40 - 24 * q^46 - 52 * q^49 - 40 * q^55 + 10 * q^58 + 44 * q^64 - 50 * q^70 + 40 * q^73 - 120 * q^76 + 52 * q^79 + 36 * q^82 + 10 * q^88 + 12 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40126	−	0.190983i	−0.990839	−	0.135045i
$2$	−1.40126	−	0.190983i	−0.990839	−	0.135045i
$3$		0			0
$3$		0			0
$4$	1.92705	+	0.535233i	0.963525	+	0.267617i
$5$	−1.93649	+	1.11803i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$5$	−1.93649	+	1.11803i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−2.59808	−	1.11803i	−0.918559	−	0.395285i
$9$		0			0
$10$	2.92705	−	1.19682i	0.925615	−	0.378467i
$11$	1.93649	+	1.11803i	0.583874	+	0.337100i	0.762672	−	0.646786i	$-0.223887\pi$
$11$	1.93649	+	1.11803i	0.583874	+	0.337100i	−0.178797	+	0.983886i	$0.557221\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	0.204441	+	3.73607i	0.0546391	+	0.998506i
$15$		0			0
$16$	3.42705	+	2.06284i	0.856763	+	0.515711i
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	−0.995947	−	0.0899392i	$-0.971333\pi$
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	0.575863	+	0.817546i	$0.304666\pi$
$18$		0			0
$19$	−6.70820	+	3.87298i	−1.53897	+	0.888523i	−0.540068	+	0.841621i	$0.681602\pi$
$19$	−6.70820	+	3.87298i	−1.53897	+	0.888523i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	−4.33013	+	1.11803i	−0.968246	+	0.250000i
$21$		0			0
$22$	−2.50000	−	1.93649i	−0.533002	−	0.412861i
$23$	−3.46410	−	6.00000i	−0.722315	−	1.25109i	−0.960070	−	0.279761i	$-0.909745\pi$
$23$	−3.46410	−	6.00000i	−0.722315	−	1.25109i	0.237754	−	0.971325i	$-0.423589\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	0.427051	−	5.27424i	0.0807050	−	0.996738i
$29$		−	2.23607i		−	0.415227i	−0.978211	−	0.207614i	$-0.933430\pi$
$29$		−	2.23607i		−	0.415227i	0.978211	−	0.207614i	$-0.0665697\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	−4.40822	−	3.54508i	−0.779270	−	0.626688i
$33$		0			0
$34$	3.00000	−	3.87298i	0.514496	−	0.664211i
$35$	3.87298	+	4.47214i	0.654654	+	0.755929i
$36$		0			0
$37$	−6.70820	+	3.87298i	−1.10282	+	0.636715i	−0.936961	−	0.349435i	$-0.886374\pi$
$37$	−6.70820	+	3.87298i	−1.10282	+	0.636715i	−0.165861	+	0.986149i	$0.553040\pi$
$38$	10.1396	−	4.14590i	1.64486	−	0.672553i
$39$		0			0
$40$	6.28115	−	0.739674i	0.993137	−	0.116953i
$41$	−10.3923			−1.62301			−0.811503	−	0.584349i	$-0.801350\pi$
$41$	−10.3923			−1.62301			−0.811503	+	0.584349i	$0.801350\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	3.13331	+	3.19098i	0.472364	+	0.481059i
$45$		0			0
$46$	3.70820	+	9.06914i	0.546745	+	1.33717i
$47$	1.73205	+	3.00000i	0.252646	+	0.437595i	0.964253	−	0.264982i	$-0.0853660\pi$
$47$	1.73205	+	3.00000i	0.252646	+	0.437595i	−0.711608	+	0.702577i	$0.752033\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.68246	−	5.59017i	−1.32999	−	0.767869i	−0.344690	−	0.938716i	$-0.612016\pi$
$53$	−9.68246	−	5.59017i	−1.32999	−	0.767869i	−0.985297	+	0.170848i	$0.945349\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$	−1.60570	+	7.30902i	−0.214571	+	0.976708i
$57$		0			0
$58$	−0.427051	+	3.13331i	−0.0560745	+	0.411424i
$59$	1.93649	+	1.11803i	0.252110	+	0.145556i	0.620730	−	0.784024i	$-0.286836\pi$
$59$	1.93649	+	1.11803i	0.252110	+	0.145556i	−0.368620	+	0.929580i	$0.620170\pi$
$60$		0			0
$61$	−6.70820	+	3.87298i	−0.858898	+	0.495885i	−0.863643	−	0.504104i	$-0.831823\pi$
$61$	−6.70820	+	3.87298i	−0.858898	+	0.495885i	0.00474543	+	0.999989i	$0.498489\pi$
$62$	−0.866025	+	1.11803i	−0.109985	+	0.141990i
$63$		0			0
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$		0			0
$66$		0			0
$67$	−6.70820	−	3.87298i	−0.819538	−	0.473160i	0.0307194	−	0.999528i	$-0.490220\pi$
$67$	−6.70820	−	3.87298i	−0.819538	−	0.473160i	−0.850257	+	0.526368i	$0.823553\pi$
$68$	−4.94345	+	4.85410i	−0.599481	+	0.588646i
$69$		0			0
$70$	−4.57295	−	7.00629i	−0.546572	−	0.837412i
$71$	10.3923			1.23334			0.616670	−	0.787222i	$-0.288481\pi$
$71$	10.3923			1.23334			0.616670	+	0.787222i	$0.288481\pi$
$72$		0			0
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	10.1396	−	4.14590i	1.17870	−	0.481951i
$75$		0			0
$76$	−15.0000	+	3.87298i	−1.72062	+	0.444262i
$77$	1.93649	−	5.59017i	0.220684	−	0.637059i
$78$		0			0
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−8.94278	−	0.163119i	−0.999834	−	0.0182373i
$81$		0			0
$82$	14.5623	+	1.98475i	1.60814	+	0.219179i
$83$			11.1803i			1.22720i	0.789616	+	0.613601i	$0.210280\pi$
$83$			11.1803i			1.22720i	−0.789616	+	0.613601i	$0.789720\pi$
$84$		0			0
$85$		−	7.74597i		−	0.840168i
$86$		0			0
$87$		0			0
$88$	−3.78115	−	5.06980i	−0.403072	−	0.540443i
$89$	6.92820	+	12.0000i	0.734388	+	1.27200i	0.954991	+	0.296634i	$0.0958641\pi$
$89$	6.92820	+	12.0000i	0.734388	+	1.27200i	−0.220603	+	0.975364i	$0.570803\pi$
$90$		0			0
$91$		0			0
$92$	−3.46410	−	13.4164i	−0.361158	−	1.39876i
$93$		0			0
$94$	−1.85410	−	4.53457i	−0.191236	−	0.467705i
$95$	8.66025	−	15.0000i	0.888523	−	1.53897i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	9.60437	−	2.39919i	0.970188	−	0.242354i
$99$		0			0
$100$		0			0
$101$	−3.87298	−	2.23607i	−0.385376	−	0.222497i	0.294779	−	0.955566i	$-0.404754\pi$
$101$	−3.87298	−	2.23607i	−0.385376	−	0.222497i	−0.680155	+	0.733069i	$0.738087\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$		0			0
$106$	12.5000	+	9.68246i	1.21411	+	0.940443i
$107$	9.68246	−	5.59017i	0.936039	−	0.540422i	0.0473223	−	0.998880i	$-0.484931\pi$
$107$	9.68246	−	5.59017i	0.936039	−	0.540422i	0.888716	+	0.458458i	$0.151598\pi$
$108$		0			0
$109$	−6.70820	−	3.87298i	−0.642529	−	0.370965i	0.143059	−	0.989714i	$-0.454306\pi$
$109$	−6.70820	−	3.87298i	−0.642529	−	0.370965i	−0.785588	+	0.618750i	$0.787640\pi$
$110$	7.00629	+	0.954915i	0.668024	+	0.0910476i
$111$		0			0
$112$	3.64590	−	9.93516i	0.344505	−	0.938784i
$113$	10.3923			0.977626			0.488813	−	0.872389i	$-0.337430\pi$
$113$	10.3923			0.977626			0.488813	+	0.872389i	$0.337430\pi$
$114$		0			0
$115$	13.4164	+	7.74597i	1.25109	+	0.722315i
$116$	1.19682	−	4.30902i	0.111122	−	0.400082i
$117$		0			0
$118$	−2.50000	−	1.93649i	−0.230144	−	0.178269i
$119$	8.66025	+	3.00000i	0.793884	+	0.275010i
$120$		0			0
$121$	−3.00000	−	5.19615i	−0.272727	−	0.472377i
$122$	10.1396	−	4.14590i	0.917996	−	0.375352i
$123$		0			0
$124$	1.42705	−	1.40126i	0.128153	−	0.125837i
$125$		−	11.1803i		−	1.00000i
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−6.59741	−	9.19098i	−0.583134	−	0.812376i
$129$		0			0
$130$		0			0
$131$	9.68246	−	5.59017i	0.845960	−	0.488415i	−0.0133255	−	0.999911i	$-0.504242\pi$
$131$	9.68246	−	5.59017i	0.845960	−	0.488415i	0.859286	+	0.511496i	$0.170908\pi$
$132$		0			0
$133$	13.4164	+	15.4919i	1.16335	+	1.34332i
$134$	8.66025	+	6.70820i	0.748132	+	0.579501i
$135$		0			0
$136$	7.85410	−	5.85774i	0.673484	−	0.502297i
$137$	−1.73205	+	3.00000i	−0.147979	+	0.256307i	−0.930480	−	0.366342i	$-0.880610\pi$
$137$	−1.73205	+	3.00000i	−0.147979	+	0.256307i	0.782501	+	0.622649i	$0.213943\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	5.06980	+	10.6910i	0.428476	+	0.903553i
$141$		0			0
$142$	−14.5623	−	1.98475i	−1.22204	−	0.166557i
$143$		0			0
$144$		0			0
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$	−8.66025	+	11.1803i	−0.716728	+	0.925292i
$147$		0			0
$148$	−15.0000	+	3.87298i	−1.23299	+	0.318357i
$149$	−19.3649	+	11.1803i	−1.58644	+	0.915929i	−0.592548	+	0.805535i	$0.701878\pi$
$149$	−19.3649	+	11.1803i	−1.58644	+	0.915929i	−0.993888	+	0.110394i	$0.964789\pi$
$150$		0			0
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	−0.687741	−	0.725956i	$-0.741398\pi$
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	0.972567	+	0.232623i	$0.0747309\pi$
$152$	21.7586	−	2.56231i	1.76485	−	0.207830i
$153$		0			0
$154$	−3.78115	+	7.46344i	−0.304694	+	0.601421i
$155$			2.23607i			0.179605i
$156$		0			0
$157$	13.4164	+	7.74597i	1.07075	+	0.618195i	0.928385	−	0.371619i	$-0.121197\pi$
$157$	13.4164	+	7.74597i	1.07075	+	0.618195i	0.142361	+	0.989815i	$0.454531\pi$
$158$	−6.95803	−	17.0172i	−0.553551	−	1.35382i
$159$		0			0
$160$	12.5000	+	1.93649i	0.988212	+	0.153093i
$161$	−13.8564	+	12.0000i	−1.09204	+	0.945732i
$162$		0			0
$163$	13.4164	−	7.74597i	1.05085	−	0.606711i	0.127966	−	0.991779i	$-0.459155\pi$
$163$	13.4164	−	7.74597i	1.05085	−	0.606711i	0.922888	+	0.385068i	$0.125822\pi$
$164$	−20.0265	−	5.56231i	−1.56381	−	0.434343i
$165$		0			0
$166$	2.13525	−	15.6665i	0.165728	−	1.21596i
$167$	−10.3923			−0.804181			−0.402090	−	0.915600i	$-0.631716\pi$
$167$	−10.3923			−0.804181			−0.402090	+	0.915600i	$0.631716\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$	−1.47935	+	10.8541i	−0.113461	+	0.832472i
$171$		0			0
$172$		0			0
$173$	3.87298	−	2.23607i	0.294457	−	0.170005i	−0.345493	−	0.938421i	$-0.612288\pi$
$173$	3.87298	−	2.23607i	0.294457	−	0.170005i	0.639950	+	0.768416i	$0.278955\pi$
$174$		0			0
$175$		0			0
$176$	4.33013	+	7.82624i	0.326396	+	0.589925i
$177$		0			0
$178$	−7.41641	−	18.1383i	−0.555883	−	1.35952i
$179$	7.74597	+	4.47214i	0.578961	+	0.334263i	0.760720	−	0.649080i	$-0.224846\pi$
$179$	7.74597	+	4.47214i	0.578961	+	0.334263i	−0.181760	+	0.983343i	$0.558179\pi$
$180$		0			0
$181$		−	23.2379i		−	1.72726i	−0.504127	−	0.863630i	$-0.668186\pi$
$181$		−	23.2379i		−	1.72726i	0.504127	−	0.863630i	$-0.331814\pi$
$182$		0			0
$183$		0			0
$184$	2.29180	+	19.4614i	0.168953	+	1.43472i
$185$	8.66025	−	15.0000i	0.636715	−	1.10282i
$186$		0			0
$187$	−6.70820	+	3.87298i	−0.490552	+	0.283221i
$188$	1.73205	+	6.70820i	0.126323	+	0.489246i
$189$		0			0
$190$	−15.0000	+	19.3649i	−1.08821	+	1.40488i
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	0.713052	−	0.701111i	$-0.247312\pi$
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	−0.963706	+	0.266966i	$0.913979\pi$
$192$		0			0
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	0.379086	+	0.925361i	$0.376238\pi$
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	−0.990930	+	0.134382i	$0.957095\pi$
$194$	1.40126	+	0.190983i	0.100605	+	0.0137118i
$195$		0			0
$196$	−13.9164	+	1.52761i	−0.994029	+	0.109115i
$197$			4.47214i			0.318626i	0.987228	+	0.159313i	$0.0509280\pi$
$197$			4.47214i			0.318626i	−0.987228	+	0.159313i	$0.949072\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$		0			0
$201$		0			0
$202$	5.00000	+	3.87298i	0.351799	+	0.272502i
$203$	−5.80948	+	1.11803i	−0.407745	+	0.0784706i
$204$		0			0
$205$	20.1246	−	11.6190i	1.40556	−	0.811503i
$206$	4.28187	+	10.4721i	0.298332	+	0.729628i
$207$		0			0
$208$		0			0
$209$	−17.3205			−1.19808
$210$		0			0
$211$		−	23.2379i		−	1.59976i	−0.600158	−	0.799882i	$-0.704896\pi$
$211$		−	23.2379i		−	1.59976i	0.600158	−	0.799882i	$-0.295104\pi$
$212$	−15.6665	−	15.9549i	−1.07598	−	1.09579i
$213$		0			0
$214$	−14.6353	+	5.98409i	−1.00045	+	0.409064i
$215$		0			0
$216$		0			0
$217$	−2.50000	−	0.866025i	−0.169711	−	0.0587896i
$218$	8.66025	+	6.70820i	0.586546	+	0.454337i
$219$		0			0
$220$	−9.63525	−	2.67617i	−0.649609	−	0.180427i
$221$		0			0
$222$		0			0
$223$	−7.00000			−0.468755			−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000			−0.468755			−0.234377	+	0.972146i	$0.575305\pi$
$224$	−7.00629	+	13.2254i	−0.468128	+	0.883661i
$225$		0			0
$226$	−14.5623	−	1.98475i	−0.968670	−	0.132024i
$227$	−21.3014	−	12.2984i	−1.41382	−	0.816272i	−0.418078	−	0.908411i	$-0.637296\pi$
$227$	−21.3014	−	12.2984i	−1.41382	−	0.816272i	−0.995746	+	0.0921394i	$0.970629\pi$
$228$		0			0
$229$	−6.70820	+	3.87298i	−0.443291	+	0.255934i	−0.704992	−	0.709215i	$-0.749050\pi$
$229$	−6.70820	+	3.87298i	−0.443291	+	0.255934i	0.261702	+	0.965149i	$0.415716\pi$
$230$	−17.3205	−	13.4164i	−1.14208	−	0.884652i
$231$		0			0
$232$	−2.50000	+	5.80948i	−0.164133	+	0.381411i
$233$	1.73205	+	3.00000i	0.113470	+	0.196537i	0.917167	−	0.398502i	$-0.130470\pi$
$233$	1.73205	+	3.00000i	0.113470	+	0.196537i	−0.803697	+	0.595039i	$0.797137\pi$
$234$		0			0
$235$	−6.70820	−	3.87298i	−0.437595	−	0.252646i
$236$	3.13331	+	3.19098i	0.203961	+	0.207715i
$237$		0			0
$238$	−11.5623	−	5.85774i	−0.749473	−	0.379701i
$239$	−20.7846			−1.34444			−0.672222	−	0.740349i	$-0.734660\pi$
$239$	−20.7846			−1.34444			−0.672222	+	0.740349i	$0.734660\pi$
$240$		0			0
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	0.211360	+	0.977408i	$0.432211\pi$
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	−0.952141	+	0.305661i	$0.901123\pi$
$242$	3.21140	+	7.85410i	0.206437	+	0.504881i
$243$		0			0
$244$	−15.0000	+	3.87298i	−0.960277	+	0.247942i
$245$	9.68246	−	12.2984i	0.618590	−	0.785714i
$246$		0			0
$247$		0			0
$248$	−2.26728	+	1.69098i	−0.143973	+	0.107378i
$249$		0			0
$250$	−2.13525	+	15.6665i	−0.135045	+	0.990839i
$251$			24.5967i			1.55253i	0.630405	+	0.776266i	$0.282889\pi$
$251$			24.5967i			1.55253i	−0.630405	+	0.776266i	$0.717111\pi$
$252$		0			0
$253$		−	15.4919i		−	0.973970i
$254$	−7.00629	−	0.954915i	−0.439614	−	0.0599167i
$255$		0			0
$256$	7.48936	+	14.1389i	0.468085	+	0.883684i
$257$	−3.46410	−	6.00000i	−0.216085	−	0.374270i	0.737523	−	0.675322i	$-0.235995\pi$
$257$	−3.46410	−	6.00000i	−0.216085	−	0.374270i	−0.953608	+	0.301052i	$0.902662\pi$
$258$		0			0
$259$	13.4164	+	15.4919i	0.833655	+	0.962622i
$260$		0			0
$261$		0			0
$262$	−14.6353	+	5.98409i	−0.904169	+	0.369698i
$263$	3.46410	−	6.00000i	0.213606	−	0.369976i	−0.739235	−	0.673448i	$-0.764813\pi$
$263$	3.46410	−	6.00000i	0.213606	−	0.369976i	0.952840	+	0.303472i	$0.0981459\pi$
$264$		0			0
$265$	25.0000			1.53574
$266$	−15.8412	−	24.2705i	−0.971284	−	1.48812i
$267$		0			0
$268$	−10.8541	−	11.0539i	−0.663020	−	0.675224i
$269$	25.1744	+	14.5344i	1.53491	+	0.886181i	0.999125	+	0.0418260i	$0.0133175\pi$
$269$	25.1744	+	14.5344i	1.53491	+	0.886181i	0.535785	+	0.844355i	$0.320016\pi$
$270$		0			0
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$	−12.1244	+	6.70820i	−0.735147	+	0.406745i
$273$		0			0
$274$	3.00000	−	3.87298i	0.181237	−	0.233975i
$275$		0			0
$276$		0			0
$277$	13.4164	+	7.74597i	0.806114	+	0.465410i	0.845605	−	0.533810i	$-0.179240\pi$
$277$	13.4164	+	7.74597i	0.806114	+	0.465410i	−0.0394907	+	0.999220i	$0.512574\pi$
$278$		0			0
$279$		0			0
$280$	−5.06231	−	15.9491i	−0.302531	−	0.953140i
$281$	−10.3923			−0.619953			−0.309976	−	0.950744i	$-0.600321\pi$
$281$	−10.3923			−0.619953			−0.309976	+	0.950744i	$0.600321\pi$
$282$		0			0
$283$	13.4164	+	7.74597i	0.797523	+	0.460450i	0.842604	−	0.538533i	$-0.181021\pi$
$283$	13.4164	+	7.74597i	0.797523	+	0.460450i	−0.0450815	+	0.998983i	$0.514355\pi$
$284$	20.0265	+	5.56231i	1.18835	+	0.330062i
$285$		0			0
$286$		0			0
$287$	5.19615	+	27.0000i	0.306719	+	1.59376i
$288$		0			0
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$	−2.67617	−	6.54508i	−0.157150	−	0.384341i
$291$		0			0
$292$	14.2705	−	14.0126i	0.835118	−	0.820025i
$293$			11.1803i			0.653162i	0.945169	+	0.326581i	$0.105897\pi$
$293$			11.1803i			0.653162i	−0.945169	+	0.326581i	$0.894103\pi$
$294$		0			0
$295$	−5.00000			−0.291111
$296$	21.7586	−	2.56231i	1.26469	−	0.148931i
$297$		0			0
$298$	29.2705	−	11.9682i	1.69560	−	0.693298i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−6.06218	+	7.82624i	−0.348839	+	0.450349i
$303$		0			0
$304$	−30.9787	−	0.565061i	−1.77675	−	0.0324085i
$305$	8.66025	−	15.0000i	0.495885	−	0.858898i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	6.72376	−	9.73607i	0.383122	−	0.554764i
$309$		0			0
$310$	0.427051	−	3.13331i	0.0242549	−	0.177960i
$311$	−12.1244	+	21.0000i	−0.687509	+	1.19080i	0.285132	+	0.958488i	$0.407963\pi$
$311$	−12.1244	+	21.0000i	−0.687509	+	1.19080i	−0.972641	+	0.232313i	$0.925371\pi$
$312$		0			0
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	−0.983118	−	0.182973i	$-0.941428\pi$
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	0.333099	−	0.942892i	$-0.391906\pi$
$314$	−17.3205	−	13.4164i	−0.977453	−	0.757132i
$315$		0			0
$316$	6.50000	+	25.1744i	0.365654	+	1.41617i
$317$	−1.93649	+	1.11803i	−0.108764	+	0.0627950i	−0.553395	−	0.832919i	$-0.686668\pi$
$317$	−1.93649	+	1.11803i	−0.108764	+	0.0627950i	0.444631	+	0.895714i	$0.353335\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	−17.1459	−	5.10081i	−0.958485	−	0.285144i
$321$		0			0
$322$	21.7082	−	14.1688i	1.20975	−	0.789594i
$323$		−	26.8328i		−	1.49302i
$324$		0			0
$325$		0			0
$326$	−20.2792	+	8.29180i	−1.12316	+	0.459240i
$327$		0			0
$328$	27.0000	+	11.6190i	1.49083	+	0.641549i
$329$	6.92820	−	6.00000i	0.381964	−	0.330791i
$330$		0			0
$331$	13.4164	−	7.74597i	0.737432	−	0.425757i	−0.0837026	−	0.996491i	$-0.526675\pi$
$331$	13.4164	−	7.74597i	0.737432	−	0.425757i	0.821135	+	0.570734i	$0.193341\pi$
$332$	−5.98409	+	21.5451i	−0.328420	+	1.18244i
$333$		0			0
$334$	14.5623	+	1.98475i	0.796814	+	0.108601i
$335$	17.3205			0.946320
$336$		0			0
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	−18.2164	−	2.48278i	−0.990839	−	0.135045i
$339$		0			0
$340$	4.14590	−	14.9269i	0.224843	−	0.809523i
$341$	1.93649	−	1.11803i	0.104867	−	0.0605449i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$	−5.85410	+	2.39364i	−0.314718	+	0.128683i
$347$	−15.4919	−	8.94427i	−0.831651	−	0.480154i	0.0227669	−	0.999741i	$-0.492752\pi$
$347$	−15.4919	−	8.94427i	−0.831651	−	0.480154i	−0.854417	+	0.519587i	$0.826086\pi$
$348$		0			0
$349$			23.2379i			1.24390i	0.783058	+	0.621948i	$0.213659\pi$
$349$			23.2379i			1.24390i	−0.783058	+	0.621948i	$0.786341\pi$
$350$		0			0
$351$		0			0
$352$	−4.57295	−	11.7936i	−0.243739	−	0.628599i
$353$	13.8564	−	24.0000i	0.737502	−	1.27739i	−0.216115	−	0.976368i	$-0.569339\pi$
$353$	13.8564	−	24.0000i	0.737502	−	1.27739i	0.953617	−	0.301023i	$-0.0973281\pi$
$354$		0			0
$355$	−20.1246	+	11.6190i	−1.06810	+	0.616670i
$356$	6.92820	+	26.8328i	0.367194	+	1.42214i
$357$		0			0
$358$	−10.0000	−	7.74597i	−0.528516	−	0.409387i
$359$	−8.66025	−	15.0000i	−0.457071	−	0.791670i	0.541734	−	0.840550i	$-0.317768\pi$
$359$	−8.66025	−	15.0000i	−0.457071	−	0.791670i	−0.998805	+	0.0488803i	$0.984435\pi$
$360$		0			0
$361$	20.5000	−	35.5070i	1.07895	−	1.86879i
$362$	−4.43804	+	32.5623i	−0.233258	+	1.71144i
$363$		0			0
$364$		0			0
$365$			22.3607i			1.17041i
$366$		0			0
$367$	−2.50000	+	4.33013i	−0.130499	+	0.226031i	−0.923869	−	0.382709i	$-0.874991\pi$
$367$	−2.50000	+	4.33013i	−0.130499	+	0.226031i	0.793370	+	0.608740i	$0.208325\pi$
$368$	0.505406	−	27.7082i	0.0263461	−	1.44439i
$369$		0			0
$370$	−15.0000	+	19.3649i	−0.779813	+	1.00673i
$371$	−9.68246	+	27.9508i	−0.502688	+	1.45114i
$372$		0			0
$373$	−6.70820	+	3.87298i	−0.347338	+	0.200535i	−0.663512	−	0.748166i	$-0.730935\pi$
$373$	−6.70820	+	3.87298i	−0.347338	+	0.200535i	0.316174	+	0.948701i	$0.397602\pi$
$374$	10.1396	−	4.14590i	0.524306	−	0.214379i
$375$		0			0
$376$	−1.14590	−	9.73072i	−0.0590952	−	0.501824i
$377$		0			0
$378$		0			0
$379$		−	23.2379i		−	1.19365i	−0.802371	−	0.596825i	$-0.796429\pi$
$379$		−	23.2379i		−	1.19365i	0.802371	−	0.596825i	$-0.203571\pi$
$380$	24.7172	−	24.2705i	1.26797	−	1.24505i
$381$		0			0
$382$	3.70820	+	9.06914i	0.189728	+	0.464017i
$383$	−3.46410	−	6.00000i	−0.177007	−	0.306586i	0.763847	−	0.645398i	$-0.223308\pi$
$383$	−3.46410	−	6.00000i	−0.177007	−	0.306586i	−0.940854	+	0.338812i	$0.889975\pi$
$384$		0			0
$385$	2.50000	+	12.9904i	0.127412	+	0.662051i
$386$	14.7224	−	19.0066i	0.749352	−	0.967409i
$387$		0			0
$388$	−1.92705	−	0.535233i	−0.0978312	−	0.0271723i
$389$	−3.87298	−	2.23607i	−0.196368	−	0.113373i	0.398592	−	0.917128i	$-0.369499\pi$
$389$	−3.87298	−	2.23607i	−0.196368	−	0.113373i	−0.594960	+	0.803755i	$0.702832\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$	19.7922	+	0.517221i	0.999659	+	0.0261236i
$393$		0			0
$394$	0.854102	−	6.26662i	0.0430290	−	0.315708i
$395$	−25.1744	−	14.5344i	−1.26666	−	0.731307i
$396$		0			0
$397$	−26.8328	+	15.4919i	−1.34670	+	0.777518i	−0.987781	−	0.155851i	$-0.950188\pi$
$397$	−26.8328	+	15.4919i	−1.34670	+	0.777518i	−0.358920	+	0.933368i	$0.616855\pi$
$398$	6.92820	−	8.94427i	0.347279	−	0.448336i
$399$		0			0
$400$		0			0
$401$	17.3205	+	30.0000i	0.864945	+	1.49813i	0.867102	+	0.498131i	$0.165980\pi$
$401$	17.3205	+	30.0000i	0.864945	+	1.49813i	−0.00215698	+	0.999998i	$0.500687\pi$
$402$		0			0
$403$		0			0
$404$	−6.26662	−	6.38197i	−0.311776	−	0.317515i
$405$		0			0
$406$	8.35410	−	0.457144i	0.414607	−	0.0226877i
$407$	−17.3205			−0.858546
$408$		0			0
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	0.939490	+	0.342578i	$0.111300\pi$
$410$	−30.4188	+	12.4377i	−1.50228	+	0.614254i
$411$		0			0
$412$	−4.00000	−	15.4919i	−0.197066	−	0.763233i
$413$	1.93649	−	5.59017i	0.0952885	−	0.275074i
$414$		0			0
$415$	−12.5000	−	21.6506i	−0.613601	−	1.06279i
$416$		0			0
$417$		0			0
$418$	24.2705	+	3.30792i	1.18711	+	0.161796i
$419$		−	35.7771i		−	1.74783i	−0.486083	−	0.873913i	$-0.661575\pi$
$419$		−	35.7771i		−	1.74783i	0.486083	−	0.873913i	$-0.338425\pi$
$420$		0			0
$421$		−	23.2379i		−	1.13255i	−0.824218	−	0.566273i	$-0.808385\pi$
$421$		−	23.2379i		−	1.13255i	0.824218	−	0.566273i	$-0.191615\pi$
$422$	−4.43804	+	32.5623i	−0.216041	+	1.58511i
$423$		0			0
$424$	18.9058	+	25.3490i	0.918145	+	1.23106i
$425$		0			0
$426$		0			0
$427$	13.4164	+	15.4919i	0.649265	+	0.749707i
$428$	21.6506	−	5.59017i	1.04652	−	0.270211i
$429$		0			0
$430$		0			0
$431$	−12.1244	+	21.0000i	−0.584010	+	1.01153i	0.410988	+	0.911641i	$0.365184\pi$
$431$	−12.1244	+	21.0000i	−0.584010	+	1.01153i	−0.994998	+	0.0998939i	$0.968150\pi$
$432$		0			0
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$	3.33775	+	1.69098i	0.160217	+	0.0811698i
$435$		0			0
$436$	−10.8541	−	11.0539i	−0.519817	−	0.529385i
$437$	46.4758	+	26.8328i	2.22324	+	1.28359i
$438$		0			0
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	0.937380	−	0.348309i	$-0.113244\pi$
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	−0.770334	+	0.637641i	$0.779911\pi$
$440$	12.9904	+	5.59017i	0.619292	+	0.266501i
$441$		0			0
$442$		0			0
$443$	21.3014	−	12.2984i	1.01206	−	0.584313i	0.100266	−	0.994961i	$-0.468031\pi$
$443$	21.3014	−	12.2984i	1.01206	−	0.584313i	0.911794	+	0.410647i	$0.134697\pi$
$444$		0			0
$445$	−26.8328	−	15.4919i	−1.27200	−	0.734388i
$446$	9.80881	+	1.33688i	0.464461	+	0.0633032i
$447$		0			0
$448$	12.3435	−	17.1942i	0.583174	−	0.812348i
$449$	20.7846			0.980886			0.490443	−	0.871473i	$-0.336835\pi$
$449$	20.7846			0.980886			0.490443	+	0.871473i	$0.336835\pi$
$450$		0			0
$451$	−20.1246	−	11.6190i	−0.947631	−	0.547115i
$452$	20.0265	+	5.56231i	0.941967	+	0.261629i
$453$		0			0
$454$	27.5000	+	21.3014i	1.29064	+	0.999725i
$455$		0			0
$456$		0			0
$457$	−2.50000	−	4.33013i	−0.116945	−	0.202555i	0.801611	−	0.597847i	$-0.203977\pi$
$457$	−2.50000	−	4.33013i	−0.116945	−	0.202555i	−0.918556	+	0.395292i	$0.870643\pi$
$458$	10.1396	−	4.14590i	0.473792	−	0.193725i
$459$		0			0
$460$	21.7082	+	22.1078i	1.01215	+	1.03078i
$461$		−	22.3607i		−	1.04144i	−0.853727	−	0.520720i	$-0.825663\pi$
$461$		−	22.3607i		−	1.04144i	0.853727	−	0.520720i	$-0.174337\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	4.61266	−	7.66312i	0.214137	−	0.355751i
$465$		0			0
$466$	−1.85410	−	4.53457i	−0.0858896	−	0.210060i
$467$	−7.74597	+	4.47214i	−0.358441	+	0.206946i	−0.668397	−	0.743805i	$-0.733019\pi$
$467$	−7.74597	+	4.47214i	−0.358441	+	0.206946i	0.309956	+	0.950751i	$0.399686\pi$
$468$		0			0
$469$	−6.70820	+	19.3649i	−0.309756	+	0.894189i
$470$	8.66025	+	6.70820i	0.399468	+	0.309426i
$471$		0			0
$472$	−3.78115	−	5.06980i	−0.174042	−	0.233357i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	15.0831	+	10.4164i	0.691331	+	0.477435i
$477$		0			0
$478$	29.1246	+	3.96951i	1.33213	+	0.181561i
$479$	−6.92820	+	12.0000i	−0.316558	+	0.548294i	−0.979767	−	0.200140i	$-0.935860\pi$
$479$	−6.92820	+	12.0000i	−0.316558	+	0.548294i	0.663210	+	0.748434i	$0.269194\pi$
$480$		0			0
$481$		0			0
$482$	19.9186	−	25.7148i	0.907267	−	1.17128i
$483$		0			0
$484$	−3.00000	−	11.6190i	−0.136364	−	0.528134i
$485$	1.93649	−	1.11803i	0.0879316	−	0.0507673i
$486$		0			0
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	−0.854475	−	0.519493i	$-0.826121\pi$
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	0.877132	+	0.480250i	$0.159454\pi$
$488$	21.7586	−	2.56231i	0.984963	−	0.115990i
$489$		0			0
$490$	−15.9164	+	15.3840i	−0.719030	+	0.694979i
$491$		−	29.0689i		−	1.31186i	−0.754822	−	0.655930i	$-0.772277\pi$
$491$		−	29.0689i		−	1.31186i	0.754822	−	0.655930i	$-0.227723\pi$
$492$		0			0
$493$	6.70820	+	3.87298i	0.302122	+	0.174430i
$494$		0			0
$495$		0			0
$496$	3.50000	−	1.93649i	0.157155	−	0.0869510i
$497$	−5.19615	−	27.0000i	−0.233079	−	1.21112i
$498$		0			0
$499$	−26.8328	+	15.4919i	−1.20120	+	0.693514i	−0.960822	−	0.277165i	$-0.910605\pi$
$499$	−26.8328	+	15.4919i	−1.20120	+	0.693514i	−0.240379	+	0.970679i	$0.577272\pi$
$500$	5.98409	−	21.5451i	0.267617	−	0.963525i
$501$		0			0
$502$	4.69756	−	34.4664i	0.209662	−	1.53831i
$503$	31.1769			1.39011			0.695055	−	0.718957i	$-0.255380\pi$
$503$	31.1769			1.39011			0.695055	+	0.718957i	$0.255380\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−2.95870	+	21.7082i	−0.131530	+	0.965047i
$507$		0			0
$508$	9.63525	+	2.67617i	0.427495	+	0.118736i
$509$	−25.1744	+	14.5344i	−1.11584	+	0.644228i	−0.940334	−	0.340251i	$-0.889488\pi$
$509$	−25.1744	+	14.5344i	−1.11584	+	0.644228i	−0.175501	+	0.984479i	$0.556154\pi$
$510$		0			0
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$		0			0
$514$	3.70820	+	9.06914i	0.163562	+	0.400022i
$515$	15.4919	+	8.94427i	0.682656	+	0.394132i
$516$		0			0
$517$			7.74597i			0.340667i
$518$	−15.8412	−	24.2705i	−0.696021	−	1.06638i
$519$		0			0
$520$		0			0
$521$	13.8564	−	24.0000i	0.607060	−	1.05146i	−0.384662	−	0.923057i	$-0.625682\pi$
$521$	13.8564	−	24.0000i	0.607060	−	1.05146i	0.991722	−	0.128402i	$-0.0409847\pi$
$522$		0			0
$523$	−26.8328	+	15.4919i	−1.17332	+	0.677415i	−0.954459	−	0.298342i	$-0.903566\pi$
$523$	−26.8328	+	15.4919i	−1.17332	+	0.677415i	−0.218858	+	0.975757i	$0.570233\pi$
$524$	21.6506	−	5.59017i	0.945812	−	0.244208i
$525$		0			0
$526$	−6.00000	+	7.74597i	−0.261612	+	0.337740i
$527$	1.73205	+	3.00000i	0.0754493	+	0.130682i
$528$		0			0
$529$	−12.5000	+	21.6506i	−0.543478	+	0.941332i
$530$	−35.0315	−	4.77458i	−1.52167	−	0.207394i
$531$		0			0
$532$	17.5623	+	37.0347i	0.761423	+	1.60566i
$533$		0			0
$534$		0			0
$535$	−12.5000	+	21.6506i	−0.540422	+	0.936039i
$536$	13.0983	+	17.5623i	0.565760	+	0.758576i
$537$		0			0
$538$	−32.5000	−	25.1744i	−1.40117	−	1.08535i
$539$	−15.4919	−	2.23607i	−0.667285	−	0.0963143i
$540$		0			0
$541$	13.4164	−	7.74597i	0.576816	−	0.333025i	−0.183051	−	0.983103i	$-0.558597\pi$
$541$	13.4164	−	7.74597i	0.576816	−	0.333025i	0.759867	+	0.650078i	$0.225264\pi$
$542$	−0.535233	−	1.30902i	−0.0229902	−	0.0562271i
$543$		0			0
$544$	18.2705	−	7.08438i	0.783342	−	0.303740i
$545$	17.3205			0.741929
$546$		0			0
$547$			23.2379i			0.993581i	0.867871	+	0.496790i	$0.165488\pi$
$547$			23.2379i			0.993581i	−0.867871	+	0.496790i	$0.834512\pi$
$548$	−4.94345	+	4.85410i	−0.211174	+	0.207357i
$549$		0			0
$550$		0			0
$551$	8.66025	+	15.0000i	0.368939	+	0.639021i
$552$		0			0
$553$	26.0000	−	22.5167i	1.10563	−	0.957506i
$554$	−17.3205	−	13.4164i	−0.735878	−	0.570009i
$555$		0			0
$556$		0			0
$557$	13.5554	+	7.82624i	0.574362	+	0.331608i	0.758890	−	0.651219i	$-0.225742\pi$
$557$	13.5554	+	7.82624i	0.574362	+	0.331608i	−0.184527	+	0.982827i	$0.559075\pi$
$558$		0			0
$559$		0			0
$560$	4.04760	+	23.3156i	0.171042	+	0.985264i
$561$		0			0
$562$	14.5623	+	1.98475i	0.614274	+	0.0837218i
$563$	−32.9204	−	19.0066i	−1.38743	−	0.801032i	−0.394403	−	0.918938i	$-0.629049\pi$
$563$	−32.9204	−	19.0066i	−1.38743	−	0.801032i	−0.993025	+	0.117906i	$0.962382\pi$
$564$		0			0
$565$	−20.1246	+	11.6190i	−0.846649	+	0.488813i
$566$	−17.3205	−	13.4164i	−0.728035	−	0.563934i
$567$		0			0
$568$	−27.0000	−	11.6190i	−1.13289	−	0.487520i
$569$	1.73205	+	3.00000i	0.0726113	+	0.125767i	0.900045	−	0.435797i	$-0.143533\pi$
$569$	1.73205	+	3.00000i	0.0726113	+	0.125767i	−0.827434	+	0.561563i	$0.810200\pi$
$570$		0			0
$571$	−6.70820	−	3.87298i	−0.280730	−	0.162079i	0.353024	−	0.935614i	$-0.385153\pi$
$571$	−6.70820	−	3.87298i	−0.280730	−	0.162079i	−0.633754	+	0.773535i	$0.718487\pi$
$572$		0			0
$573$		0			0
$574$	−2.12461	−	38.8264i	−0.0886796	−	1.62058i
$575$		0			0
$576$		0			0
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	0.228968	+	0.973434i	$0.426465\pi$
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−2.67617	−	6.54508i	−0.111314	−	0.272240i
$579$		0			0
$580$	2.50000	+	9.68246i	0.103807	+	0.402042i
$581$	29.0474	−	5.59017i	1.20509	−	0.231919i
$582$		0			0
$583$	−12.5000	−	21.6506i	−0.517697	−	0.896678i
$584$	−22.6728	+	16.9098i	−0.938209	+	0.699734i
$585$		0			0
$586$	2.13525	−	15.6665i	0.0882066	−	0.647179i
$587$			38.0132i			1.56897i	0.620147	+	0.784485i	$0.287073\pi$
$587$			38.0132i			1.56897i	−0.620147	+	0.784485i	$0.712927\pi$
$588$		0			0
$589$			7.74597i			0.319167i
$590$	7.00629	+	0.954915i	0.288445	+	0.0393132i
$591$		0			0
$592$	−30.9787	−	0.565061i	−1.27322	−	0.0232238i
$593$	−3.46410	−	6.00000i	−0.142254	−	0.246390i	0.786091	−	0.618110i	$-0.212102\pi$
$593$	−3.46410	−	6.00000i	−0.142254	−	0.246390i	−0.928345	+	0.371720i	$0.878768\pi$
$594$		0			0
$595$	−20.1246	+	3.87298i	−0.825029	+	0.158777i
$596$	−43.3013	+	11.1803i	−1.77369	+	0.457965i
$597$		0			0
$598$		0			0
$599$	−1.73205	+	3.00000i	−0.0707697	+	0.122577i	−0.899239	−	0.437458i	$-0.855879\pi$
$599$	−1.73205	+	3.00000i	−0.0707697	+	0.122577i	0.828469	+	0.560035i	$0.189212\pi$
$600$		0			0
$601$	−7.00000			−0.285536			−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000			−0.285536			−0.142768	+	0.989756i	$0.545600\pi$
$602$		0			0
$603$		0			0
$604$	9.98936	−	9.80881i	0.406461	−	0.399115i
$605$	11.6190	+	6.70820i	0.472377	+	0.272727i
$606$		0			0
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	0.405887	−	0.913923i	$-0.366962\pi$
$608$	43.3013	+	6.70820i	1.75610	+	0.272054i
$609$		0			0
$610$	−15.0000	+	19.3649i	−0.607332	+	0.784063i
$611$		0			0
$612$		0			0
$613$	−26.8328	−	15.4919i	−1.08377	−	0.625713i	−0.151857	−	0.988402i	$-0.548525\pi$
$613$	−26.8328	−	15.4919i	−1.08377	−	0.625713i	−0.931910	+	0.362689i	$0.881859\pi$
$614$		0			0
$615$		0			0
$616$	−11.2812	+	12.3586i	−0.454531	+	0.497943i
$617$	31.1769			1.25514			0.627568	−	0.778562i	$-0.284051\pi$
$617$	31.1769			1.25514			0.627568	+	0.778562i	$0.284051\pi$
$618$		0			0
$619$	−6.70820	−	3.87298i	−0.269625	−	0.155668i	0.359092	−	0.933302i	$-0.383086\pi$
$619$	−6.70820	−	3.87298i	−0.269625	−	0.155668i	−0.628717	+	0.777634i	$0.716420\pi$
$620$	−1.19682	+	4.30902i	−0.0480654	+	0.173054i
$621$		0			0
$622$	21.0000	−	27.1109i	0.842023	−	1.08705i
$623$	27.7128	−	24.0000i	1.11029	−	0.961540i
$624$		0			0
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	12.3104	+	30.1074i	0.492021	+	1.20333i
$627$		0			0
$628$	21.7082	+	22.1078i	0.866252	+	0.882196i
$629$		−	26.8328i		−	1.06989i
$630$		0			0
$631$	11.0000			0.437903			0.218952	−	0.975736i	$-0.429736\pi$
$631$	11.0000			0.437903			0.218952	+	0.975736i	$0.429736\pi$
$632$	−4.30030	−	36.5172i	−0.171057	−	1.45258i
$633$		0			0
$634$	2.92705	−	1.19682i	0.116248	−	0.0475317i
$635$	−9.68246	+	5.59017i	−0.384237	+	0.221839i
$636$		0			0
$637$		0			0
$638$	−4.33013	+	5.59017i	−0.171431	+	0.221317i
$639$		0			0
$640$	23.0517	+	10.4221i	0.911197	+	0.411971i
$641$	−22.5167	+	39.0000i	−0.889355	+	1.54041i	−0.0487148	+	0.998813i	$0.515513\pi$
$641$	−22.5167	+	39.0000i	−0.889355	+	1.54041i	−0.840640	+	0.541595i	$0.817821\pi$
$642$		0			0
$643$		−	23.2379i		−	0.916413i	−0.888846	−	0.458207i	$-0.848492\pi$
$643$		−	23.2379i		−	0.916413i	0.888846	−	0.458207i	$-0.151508\pi$
$644$	−33.1248	+	15.7082i	−1.30530	+	0.618990i
$645$		0			0
$646$	−5.12461	+	37.5997i	−0.201625	+	1.47934i
$647$	−22.5167	+	39.0000i	−0.885221	+	1.53325i	−0.0397614	+	0.999209i	$0.512660\pi$
$647$	−22.5167	+	39.0000i	−0.885221	+	1.53325i	−0.845460	+	0.534039i	$0.820674\pi$
$648$		0			0
$649$	2.50000	+	4.33013i	0.0981336	+	0.169972i
$650$		0			0
$651$		0			0
$652$	30.0000	−	7.74597i	1.17489	−	0.303355i
$653$	−36.7933	+	21.2426i	−1.43983	+	0.831289i	−0.997838	−	0.0657275i	$-0.979063\pi$
$653$	−36.7933	+	21.2426i	−1.43983	+	0.831289i	−0.441997	+	0.897016i	$0.645730\pi$
$654$		0			0
$655$	−12.5000	+	21.6506i	−0.488415	+	0.845960i
$656$	−35.6150	−	21.4377i	−1.39053	−	0.837001i
$657$		0			0
$658$	−10.8541	+	7.08438i	−0.423137	+	0.276178i
$659$			17.8885i			0.696839i	0.937339	+	0.348419i	$0.113281\pi$
$659$			17.8885i			0.696839i	−0.937339	+	0.348419i	$0.886719\pi$
$660$		0			0
$661$	13.4164	+	7.74597i	0.521838	+	0.301283i	0.737686	−	0.675144i	$-0.235918\pi$
$661$	13.4164	+	7.74597i	0.521838	+	0.301283i	−0.215848	+	0.976427i	$0.569252\pi$
$662$	−20.2792	+	8.29180i	−0.788174	+	0.322270i
$663$		0			0
$664$	12.5000	−	29.0474i	0.485094	−	1.12726i
$665$	−43.3013	−	15.0000i	−1.67915	−	0.581675i
$666$		0			0
$667$	−13.4164	+	7.74597i	−0.519485	+	0.299925i
$668$	−20.0265	−	5.56231i	−0.774849	−	0.215212i
$669$		0			0
$670$	−24.2705	−	3.30792i	−0.937652	−	0.127796i
$671$	−17.3205			−0.668651
$672$		0			0
$673$	−7.00000			−0.269830			−0.134915	−	0.990857i	$-0.543076\pi$
$673$	−7.00000			−0.269830			−0.134915	+	0.990857i	$0.543076\pi$
$674$	26.6239	+	3.62868i	1.02551	+	0.139771i
$675$		0			0
$676$	25.0517	+	6.95803i	0.963525	+	0.267617i
$677$	21.3014	−	12.2984i	0.818680	−	0.472665i	−0.0312813	−	0.999511i	$-0.509959\pi$
$677$	21.3014	−	12.2984i	0.818680	−	0.472665i	0.849961	+	0.526846i	$0.176625\pi$
$678$		0			0
$679$	0.500000	+	2.59808i	0.0191882	+	0.0997050i
$680$	−8.66025	+	20.1246i	−0.332106	+	0.771744i
$681$		0			0
$682$	−2.92705	+	1.19682i	−0.112083	+	0.0458285i
$683$	−9.68246	−	5.59017i	−0.370489	−	0.213902i	0.303183	−	0.952932i	$-0.401951\pi$
$683$	−9.68246	−	5.59017i	−0.370489	−	0.213902i	−0.673672	+	0.739030i	$0.735284\pi$
$684$		0			0
$685$		−	7.74597i		−	0.295958i
$686$	−11.0355	−	23.7533i	−0.421336	−	0.906905i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	33.5410	−	19.3649i	1.27596	−	0.736676i	0.299857	−	0.953984i	$-0.403061\pi$
$691$	33.5410	−	19.3649i	1.27596	−	0.736676i	0.976103	+	0.217308i	$0.0697276\pi$
$692$	8.66025	−	2.23607i	0.329213	−	0.0850026i
$693$		0			0
$694$	20.0000	+	15.4919i	0.759190	+	0.588066i
$695$		0			0
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$	4.43804	−	32.5623i	0.167982	−	1.23250i
$699$		0			0
$700$		0			0
$701$			24.5967i			0.929006i	0.885571	+	0.464503i	$0.153767\pi$
$701$			24.5967i			0.929006i	−0.885571	+	0.464503i	$0.846233\pi$
$702$		0			0
$703$	30.0000	−	51.9615i	1.13147	−	1.95977i
$704$	4.15551	+	17.3992i	0.156617	+	0.655757i
$705$		0			0
$706$	−24.0000	+	30.9839i	−0.903252	+	1.16609i
$707$	−3.87298	+	11.1803i	−0.145659	+	0.420480i
$708$		0			0
$709$	13.4164	−	7.74597i	0.503864	−	0.290906i	−0.226444	−	0.974024i	$-0.572710\pi$
$709$	13.4164	−	7.74597i	0.503864	−	0.290906i	0.730308	+	0.683118i	$0.239377\pi$
$710$	30.4188	−	12.4377i	1.14160	−	0.466778i
$711$		0			0
$712$	−4.58359	−	38.9229i	−0.171777	−	1.45870i
$713$	−6.92820			−0.259463
$714$		0			0
$715$		0			0
$716$	12.5332	+	12.7639i	0.468389	+	0.477011i
$717$		0			0
$718$	9.27051	+	22.6728i	0.345972	+	0.846143i
$719$	−24.2487	−	42.0000i	−0.904324	−	1.56634i	−0.821822	−	0.569745i	$-0.807042\pi$
$719$	−24.2487	−	42.0000i	−0.904324	−	1.56634i	−0.0825027	−	0.996591i	$-0.526291\pi$
$720$		0			0
$721$	−16.0000	+	13.8564i	−0.595871	+	0.516040i
$722$	−35.5070	+	45.8394i	−1.32144	+	1.70597i
$723$		0			0
$724$	12.4377	−	44.7806i	0.462243	−	1.66426i
$725$		0			0
$726$		0			0
$727$	29.0000			1.07555			0.537775	−	0.843088i	$-0.319265\pi$
$727$	29.0000			1.07555			0.537775	+	0.843088i	$0.319265\pi$
$728$		0			0
$729$		0			0
$730$	4.27051	−	31.3331i	0.158059	−	1.15969i
$731$		0			0
$732$		0			0
$733$	13.4164	−	7.74597i	0.495546	−	0.286104i	−0.231326	−	0.972876i	$-0.574306\pi$
$733$	13.4164	−	7.74597i	0.495546	−	0.286104i	0.726872	+	0.686772i	$0.240973\pi$
$734$	4.33013	−	5.59017i	0.159828	−	0.206337i
$735$		0			0
$736$	−6.00000	+	38.7298i	−0.221163	+	1.42760i
$737$	−8.66025	−	15.0000i	−0.319005	−	0.552532i
$738$		0			0
$739$	13.4164	+	7.74597i	0.493531	+	0.284940i	0.726038	−	0.687655i	$-0.241360\pi$
$739$	13.4164	+	7.74597i	0.493531	+	0.284940i	−0.232507	+	0.972595i	$0.574693\pi$
$740$	24.7172	−	24.2705i	0.908624	−	0.892202i
$741$		0			0
$742$	18.9058	−	37.3172i	0.694052	−	1.36996i
$743$	−10.3923			−0.381257			−0.190628	−	0.981662i	$-0.561053\pi$
$743$	−10.3923			−0.381257			−0.190628	+	0.981662i	$0.561053\pi$
$744$		0			0
$745$	25.0000	−	43.3013i	0.915929	−	1.58644i
$746$	10.1396	−	4.14590i	0.371237	−	0.151792i
$747$		0			0
$748$	−15.0000	+	3.87298i	−0.548454	+	0.141610i
$749$	−19.3649	−	22.3607i	−0.707579	−	0.817041i
$750$		0			0
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	0.929270	+	0.369402i	$0.120437\pi$
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	−0.144724	+	0.989472i	$0.546229\pi$
$752$	−0.252703	+	13.8541i	−0.00921512	+	0.505207i
$753$		0			0
$754$		0			0
$755$			15.6525i			0.569652i
$756$		0			0
$757$			23.2379i			0.844596i	0.906457	+	0.422298i	$0.138776\pi$
$757$			23.2379i			0.844596i	−0.906457	+	0.422298i	$0.861224\pi$
$758$	−4.43804	+	32.5623i	−0.161197	+	1.18272i
$759$		0			0
$760$	−39.2705	+	29.2887i	−1.42449	+	1.06241i
$761$	−3.46410	−	6.00000i	−0.125574	−	0.217500i	0.796383	−	0.604792i	$-0.206744\pi$
$761$	−3.46410	−	6.00000i	−0.125574	−	0.217500i	−0.921957	+	0.387292i	$0.873410\pi$
$762$		0			0
$763$	−6.70820	+	19.3649i	−0.242853	+	0.701057i
$764$	−3.46410	−	13.4164i	−0.125327	−	0.485389i
$765$		0			0
$766$	3.70820	+	9.06914i	0.133983	+	0.327681i
$767$		0			0
$768$		0			0
$769$	−31.0000			−1.11789			−0.558944	−	0.829205i	$-0.688793\pi$
$769$	−31.0000			−1.11789			−0.558944	+	0.829205i	$0.688793\pi$
$770$	−1.02220	−	18.6803i	−0.0368377	−	0.673193i
$771$		0			0
$772$	−24.2599	+	23.8214i	−0.873132	+	0.857351i
$773$	−3.87298	−	2.23607i	−0.139302	−	0.0804258i	0.428730	−	0.903433i	$-0.358961\pi$
$773$	−3.87298	−	2.23607i	−0.139302	−	0.0804258i	−0.568031	+	0.823007i	$0.692295\pi$
$774$		0			0
$775$		0			0
$776$	2.59808	+	1.11803i	0.0932655	+	0.0401351i
$777$		0			0
$778$	5.00000	+	3.87298i	0.179259	+	0.138853i
$779$	69.7137	−	40.2492i	2.49775	−	1.44208i
$780$		0			0
$781$	20.1246	+	11.6190i	0.720115	+	0.415759i
$782$	−33.6302	−	4.58359i	−1.20261	−	0.163909i
$783$		0			0
$784$	−27.6353	−	4.50474i	−0.986973	−	0.160884i
$785$	−34.6410			−1.23639
$786$		0			0
$787$	33.5410	+	19.3649i	1.19561	+	0.690285i	0.959573	−	0.281460i	$-0.0908186\pi$
$787$	33.5410	+	19.3649i	1.19561	+	0.690285i	0.236035	+	0.971745i	$0.424152\pi$
$788$	−2.39364	+	8.61803i	−0.0852697	+	0.307005i
$789$		0			0
$790$	32.5000	+	25.1744i	1.15630	+	0.895665i
$791$	−5.19615	−	27.0000i	−0.184754	−	0.960009i
$792$		0			0
$793$		0			0
$794$	40.5584	−	16.5836i	1.43936	−	0.588530i
$795$		0			0
$796$	−11.4164	+	11.2101i	−0.404644	+	0.397330i
$797$		−	15.6525i		−	0.554439i	−0.960807	−	0.277220i	$-0.910587\pi$
$797$		−	15.6525i		−	0.554439i	0.960807	−	0.277220i	$-0.0894129\pi$
$798$		0			0
$799$	−12.0000			−0.424529
$800$		0			0
$801$		0			0
$802$	−18.5410	−	45.3457i	−0.654706	−	1.60121i
$803$	19.3649	−	11.1803i	0.683373	−	0.394546i
$804$		0			0
$805$	13.4164	−	38.7298i	0.472866	−	1.36505i
$806$		0			0
$807$		0			0
$808$	7.56231	+	10.1396i	0.266041	+	0.356710i
$809$	−17.3205	+	30.0000i	−0.608957	+	1.05474i	0.382456	+	0.923974i	$0.375078\pi$
$809$	−17.3205	+	30.0000i	−0.608957	+	1.05474i	−0.991413	+	0.130770i	$0.958255\pi$
$810$		0			0
$811$		−	23.2379i		−	0.815993i	−0.912983	−	0.407997i	$-0.866228\pi$
$811$		−	23.2379i		−	0.815993i	0.912983	−	0.407997i	$-0.133772\pi$
$812$	−11.7936	−	0.954915i	−0.413873	−	0.0335109i
$813$		0			0
$814$	24.2705	+	3.30792i	0.850681	+	0.115943i
$815$	−17.3205	+	30.0000i	−0.606711	+	1.05085i
$816$		0			0
$817$		0			0
$818$	−6.06218	+	7.82624i	−0.211959	+	0.273638i
$819$		0			0
$820$	45.0000	−	11.6190i	1.57147	−	0.405751i
$821$	−13.5554	+	7.82624i	−0.473088	+	0.273138i	−0.717532	−	0.696526i	$-0.754728\pi$
$821$	−13.5554	+	7.82624i	−0.473088	+	0.273138i	0.244443	+	0.969664i	$0.421395\pi$
$822$		0			0
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	−0.985997	−	0.166762i	$-0.946669\pi$
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	0.637419	+	0.770517i	$0.280002\pi$
$824$	2.64634	+	22.4721i	0.0921896	+	0.782854i
$825$		0			0
$826$	−3.78115	+	7.46344i	−0.131563	+	0.259686i
$827$			24.5967i			0.855313i	0.903941	+	0.427656i	$0.140661\pi$
$827$			24.5967i			0.855313i	−0.903941	+	0.427656i	$0.859339\pi$
$828$		0			0
$829$	−6.70820	−	3.87298i	−0.232986	−	0.134514i	0.378963	−	0.925412i	$-0.376281\pi$
$829$	−6.70820	−	3.87298i	−0.232986	−	0.134514i	−0.611949	+	0.790898i	$0.709614\pi$
$830$	13.3808	+	32.7254i	0.464455	+	1.13592i
$831$		0			0
$832$		0			0
$833$	3.46410	−	24.0000i	0.120024	−	0.831551i
$834$		0			0
$835$	20.1246	−	11.6190i	0.696441	−	0.402090i
$836$	−33.3775	−	9.27051i	−1.15439	−	0.320627i
$837$		0			0
$838$	−6.83282	+	50.1329i	−0.236036	+	1.73181i
$839$	31.1769			1.07635			0.538173	−	0.842834i	$-0.319115\pi$
$839$	31.1769			1.07635			0.538173	+	0.842834i	$0.319115\pi$
$840$		0			0
$841$	24.0000			0.827586
$842$	−4.43804	+	32.5623i	−0.152945	+	1.12217i
$843$		0			0
$844$	12.4377	−	44.7806i	0.428123	−	1.54141i
$845$	−25.1744	+	14.5344i	−0.866025	+	0.500000i
$846$		0			0
$847$	−12.0000	+	10.3923i	−0.412325	+	0.357084i
$848$	−21.6506	−	39.1312i	−0.743486	−	1.34377i
$849$		0			0
$850$		0			0
$851$	46.4758	+	26.8328i	1.59317	+	0.919817i
$852$		0			0
$853$			23.2379i			0.795651i	0.917461	+	0.397825i	$0.130235\pi$
$853$			23.2379i			0.795651i	−0.917461	+	0.397825i	$0.869765\pi$
$854$	−15.8412	−	24.2705i	−0.542073	−	0.830520i
$855$		0			0
$856$	−31.4058	+	3.69837i	−1.07343	+	0.126408i
$857$	−12.1244	+	21.0000i	−0.414160	+	0.717346i	−0.995340	−	0.0964289i	$-0.969258\pi$
$857$	−12.1244	+	21.0000i	−0.414160	+	0.717346i	0.581180	+	0.813775i	$0.302591\pi$
$858$		0			0
$859$	13.4164	−	7.74597i	0.457762	−	0.264289i	−0.253341	−	0.967377i	$-0.581529\pi$
$859$	13.4164	−	7.74597i	0.457762	−	0.264289i	0.711103	+	0.703088i	$0.248196\pi$
$860$		0			0
$861$		0			0
$862$	21.0000	−	27.1109i	0.715263	−	0.923400i
$863$	−13.8564	−	24.0000i	−0.471678	−	0.816970i	0.527797	−	0.849370i	$-0.323018\pi$
$863$	−13.8564	−	24.0000i	−0.471678	−	0.816970i	−0.999475	+	0.0324008i	$0.989685\pi$
$864$		0			0
$865$	−5.00000	+	8.66025i	−0.170005	+	0.294457i
$866$	30.8277	+	4.20163i	1.04757	+	0.142777i
$867$		0			0
$868$	−4.35410	−	3.00696i	−0.147788	−	0.102063i
$869$			29.0689i			0.986094i
$870$		0			0
$871$		0			0
$872$	13.0983	+	17.5623i	0.443564	+	0.594735i
$873$		0			0
$874$	−60.0000	−	46.4758i	−2.02953	−	1.57207i
$875$	−29.0474	+	5.59017i	−0.981981	+	0.188982i
$876$		0			0
$877$	−26.8328	+	15.4919i	−0.906080	+	0.523125i	−0.879168	−	0.476512i	$-0.841901\pi$
$877$	−26.8328	+	15.4919i	−0.906080	+	0.523125i	−0.0269120	+	0.999638i	$0.508567\pi$
$878$	−3.74663	−	9.16312i	−0.126443	−	0.309240i
$879$		0			0
$880$	−17.1353	−	10.3142i	−0.577629	−	0.347692i
$881$	−10.3923			−0.350126			−0.175063	−	0.984557i	$-0.556013\pi$
$881$	−10.3923			−0.350126			−0.175063	+	0.984557i	$0.556013\pi$
$882$		0			0
$883$		−	23.2379i		−	0.782018i	−0.920387	−	0.391009i	$-0.872126\pi$
$883$		−	23.2379i		−	0.782018i	0.920387	−	0.391009i	$-0.127874\pi$
$884$		0			0
$885$		0			0
$886$	−32.1976	+	13.1650i	−1.08170	+	0.442287i
$887$	−13.8564	−	24.0000i	−0.465253	−	0.805841i	0.533960	−	0.845510i	$-0.320703\pi$
$887$	−13.8564	−	24.0000i	−0.465253	−	0.805841i	−0.999213	+	0.0396684i	$0.987370\pi$
$888$		0			0
$889$	−2.50000	−	12.9904i	−0.0838473	−	0.435683i
$890$	34.6410	+	26.8328i	1.16117	+	0.899438i
$891$		0			0
$892$	−13.4894	−	3.74663i	−0.451657	−	0.125447i
$893$	−23.2379	−	13.4164i	−0.777627	−	0.448963i
$894$		0			0
$895$	−20.0000			−0.668526
$896$	−20.5802	+	21.7361i	−0.687535	+	0.726151i
$897$		0			0
$898$	−29.1246	−	3.96951i	−0.971901	−	0.132464i
$899$	−1.93649	−	1.11803i	−0.0645856	−	0.0372885i
$900$		0			0
$901$	33.5410	−	19.3649i	1.11741	−	0.645139i
$902$	25.9808	+	20.1246i	0.865065	+	0.670076i
$903$		0			0
$904$	−27.0000	−	11.6190i	−0.898007	−	0.386441i
$905$	25.9808	+	45.0000i	0.863630	+	1.49585i
$906$		0			0
$907$	13.4164	+	7.74597i	0.445485	+	0.257201i	0.705921	−	0.708290i	$-0.250533\pi$
$907$	13.4164	+	7.74597i	0.445485	+	0.257201i	−0.260437	+	0.965491i	$0.583867\pi$
$908$	−34.4664	−	35.1008i	−1.14381	−	1.16486i
$909$		0			0
$910$		0			0
$911$	10.3923			0.344312			0.172156	−	0.985070i	$-0.444927\pi$
$911$	10.3923			0.344312			0.172156	+	0.985070i	$0.444927\pi$
$912$		0			0
$913$	−12.5000	+	21.6506i	−0.413690	+	0.716531i
$914$	2.67617	+	6.54508i	0.0885197	+	0.216492i
$915$		0			0
$916$	−15.0000	+	3.87298i	−0.495614	+	0.127967i
$917$	−19.3649	−	22.3607i	−0.639486	−	0.738415i
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$	−26.1966	−	35.1246i	−0.863676	−	1.15802i
$921$		0			0
$922$	−4.27051	+	31.3331i	−0.140642	+	1.03190i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−11.2101	−	1.52786i	−0.368386	−	0.0502087i
$927$		0			0
$928$	−7.92705	+	9.85707i	−0.260218	+	0.323574i
$929$	17.3205	+	30.0000i	0.568267	+	0.984268i	0.996737	+	0.0807121i	$0.0257194\pi$
$929$	17.3205	+	30.0000i	0.568267	+	0.984268i	−0.428470	+	0.903556i	$0.640947\pi$
$930$		0			0
$931$	33.5410	−	42.6028i	1.09926	−	1.39625i
$932$	1.73205	+	6.70820i	0.0567352	+	0.219735i
$933$		0			0
$934$	11.7082	−	4.78727i	0.383104	−	0.156644i
$935$	8.66025	−	15.0000i	0.283221	−	0.490552i
$936$		0			0
$937$	5.00000			0.163343			0.0816714	−	0.996659i	$-0.473974\pi$
$937$	5.00000			0.163343			0.0816714	+	0.996659i	$0.473974\pi$
$938$	13.0983	−	25.8541i	0.427675	−	0.844166i
$939$		0			0
$940$	−10.8541	−	11.0539i	−0.354022	−	0.360538i
$941$	−9.68246	−	5.59017i	−0.315639	−	0.182234i	0.333808	−	0.942641i	$-0.391666\pi$
$941$	−9.68246	−	5.59017i	−0.315639	−	0.182234i	−0.649447	+	0.760407i	$0.725000\pi$
$942$		0			0
$943$	36.0000	+	62.3538i	1.17232	+	2.03052i
$944$	4.33013	+	7.82624i	0.140934	+	0.254722i
$945$		0			0
$946$		0			0
$947$	−30.9839	+	17.8885i	−1.00684	+	0.581300i	−0.910265	−	0.414026i	$-0.864122\pi$
$947$	−30.9839	+	17.8885i	−1.00684	+	0.581300i	−0.0965754	+	0.995326i	$0.530789\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−19.1459	−	17.4767i	−0.620522	−	0.566423i
$953$	20.7846			0.673280			0.336640	−	0.941634i	$-0.390710\pi$
$953$	20.7846			0.673280			0.336640	+	0.941634i	$0.390710\pi$
$954$		0			0
$955$	13.4164	+	7.74597i	0.434145	+	0.250654i
$956$	−40.0530	−	11.1246i	−1.29541	−	0.359796i
$957$		0			0
$958$	12.0000	−	15.4919i	0.387702	−	0.500522i
$959$	8.66025	+	3.00000i	0.279654	+	0.0968751i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$		0			0
$964$	−32.8222	+	32.2289i	−1.05713	+	1.03802i
$965$		−	38.0132i		−	1.22369i
$966$		0			0
$967$	−19.0000			−0.610999			−0.305499	−	0.952192i	$-0.598823\pi$
$967$	−19.0000			−0.610999			−0.305499	+	0.952192i	$0.598823\pi$
$968$	1.98475	+	16.8541i	0.0637924	+	0.541711i
$969$		0			0
$970$	−2.92705	+	1.19682i	−0.0939819	+	0.0384275i
$971$	9.68246	−	5.59017i	0.310725	−	0.179397i	−0.336526	−	0.941674i	$-0.609252\pi$
$971$	9.68246	−	5.59017i	0.310725	−	0.179397i	0.647251	+	0.762277i	$0.275919\pi$
$972$		0			0
$973$		0			0
$974$	−0.866025	+	1.11803i	−0.0277492	+	0.0358241i
$975$		0			0
$976$	−30.9787	−	0.565061i	−0.991604	−	0.0180872i
$977$	−6.92820	+	12.0000i	−0.221653	+	0.383914i	−0.955310	−	0.295606i	$-0.904479\pi$
$977$	−6.92820	+	12.0000i	−0.221653	+	0.383914i	0.733657	+	0.679520i	$0.237812\pi$
$978$		0			0
$979$			30.9839i			0.990249i
$980$	25.2411	−	18.5172i	0.806297	−	0.591511i
$981$		0			0
$982$	−5.55166	+	40.7330i	−0.177161	+	1.29984i
$983$	19.0526	−	33.0000i	0.607682	−	1.05254i	−0.383939	−	0.923358i	$-0.625433\pi$
$983$	19.0526	−	33.0000i	0.607682	−	1.05254i	0.991621	−	0.129178i	$-0.0412339\pi$
$984$		0			0
$985$	−5.00000	−	8.66025i	−0.159313	−	0.275939i
$986$	−8.66025	−	6.70820i	−0.275799	−	0.213633i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.500000	−	0.866025i	0.0158830	−	0.0275102i	−0.857975	−	0.513692i	$-0.828277\pi$
$991$	0.500000	−	0.866025i	0.0158830	−	0.0275102i	0.873858	+	0.486182i	$0.161611\pi$
$992$	−5.27424	+	2.04508i	−0.167457	+	0.0649315i
$993$		0			0
$994$	2.12461	+	38.8264i	0.0673886	+	1.23150i
$995$		−	17.8885i		−	0.567105i
$996$		0			0
$997$	−6.70820	−	3.87298i	−0.212451	−	0.122659i	0.389999	−	0.920815i	$-0.372475\pi$
$997$	−6.70820	−	3.87298i	−0.212451	−	0.122659i	−0.602450	+	0.798157i	$0.705809\pi$
$998$	40.5584	−	16.5836i	1.28385	−	0.524944i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.a.109.1	yes	8
3.2	odd	2	inner	504.2.cj.a.109.4	yes	8
4.3	odd	2		2016.2.cr.a.1873.1		8
7.2	even	3	inner	504.2.cj.a.37.3	yes	8
8.3	odd	2		2016.2.cr.a.1873.3		8
8.5	even	2	inner	504.2.cj.a.109.3	yes	8
12.11	even	2		2016.2.cr.a.1873.4		8
21.2	odd	6	inner	504.2.cj.a.37.2	yes	8
24.5	odd	2	inner	504.2.cj.a.109.2	yes	8
24.11	even	2		2016.2.cr.a.1873.2		8
28.23	odd	6		2016.2.cr.a.1297.3		8
56.37	even	6	inner	504.2.cj.a.37.1	✓	8
56.51	odd	6		2016.2.cr.a.1297.1		8
84.23	even	6		2016.2.cr.a.1297.2		8
168.107	even	6		2016.2.cr.a.1297.4		8
168.149	odd	6	inner	504.2.cj.a.37.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cj.a.37.1	✓	8	56.37	even	6	inner
504.2.cj.a.37.2	yes	8	21.2	odd	6	inner
504.2.cj.a.37.3	yes	8	7.2	even	3	inner
504.2.cj.a.37.4	yes	8	168.149	odd	6	inner
504.2.cj.a.109.1	yes	8	1.1	even	1	trivial
504.2.cj.a.109.2	yes	8	24.5	odd	2	inner
504.2.cj.a.109.3	yes	8	8.5	even	2	inner
504.2.cj.a.109.4	yes	8	3.2	odd	2	inner
2016.2.cr.a.1297.1		8	56.51	odd	6
2016.2.cr.a.1297.2		8	84.23	even	6
2016.2.cr.a.1297.3		8	28.23	odd	6
2016.2.cr.a.1297.4		8	168.107	even	6
2016.2.cr.a.1873.1		8	4.3	odd	2
2016.2.cr.a.1873.2		8	24.11	even	2
2016.2.cr.a.1873.3		8	8.3	odd	2
2016.2.cr.a.1873.4		8	12.11	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40126 - 0.190983i) q^{2} +(1.92705 + 0.535233i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 - 1.11803i) q^{8} +O(q^{10})\)	\(q+(-1.40126 - 0.190983i) q^{2} +(1.92705 + 0.535233i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(2.92705 - 1.19682i) q^{10} +(1.93649 + 1.11803i) q^{11} +(0.204441 + 3.73607i) q^{14} +(3.42705 + 2.06284i) q^{16} +(-1.73205 + 3.00000i) q^{17} +(-6.70820 + 3.87298i) q^{19} +(-4.33013 + 1.11803i) q^{20} +(-2.50000 - 1.93649i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(0.427051 - 5.27424i) q^{28} -2.23607i q^{29} +(0.500000 - 0.866025i) q^{31} +(-4.40822 - 3.54508i) q^{32} +(3.00000 - 3.87298i) q^{34} +(3.87298 + 4.47214i) q^{35} +(-6.70820 + 3.87298i) q^{37} +(10.1396 - 4.14590i) q^{38} +(6.28115 - 0.739674i) q^{40} -10.3923 q^{41} +(3.13331 + 3.19098i) q^{44} +(3.70820 + 9.06914i) q^{46} +(1.73205 + 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-9.68246 - 5.59017i) q^{53} -5.00000 q^{55} +(-1.60570 + 7.30902i) q^{56} +(-0.427051 + 3.13331i) q^{58} +(1.93649 + 1.11803i) q^{59} +(-6.70820 + 3.87298i) q^{61} +(-0.866025 + 1.11803i) q^{62} +(5.50000 + 5.80948i) q^{64} +(-6.70820 - 3.87298i) q^{67} +(-4.94345 + 4.85410i) q^{68} +(-4.57295 - 7.00629i) q^{70} +10.3923 q^{71} +(5.00000 - 8.66025i) q^{73} +(10.1396 - 4.14590i) q^{74} +(-15.0000 + 3.87298i) q^{76} +(1.93649 - 5.59017i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-8.94278 - 0.163119i) q^{80} +(14.5623 + 1.98475i) q^{82} +11.1803i q^{83} -7.74597i q^{85} +(-3.78115 - 5.06980i) q^{88} +(6.92820 + 12.0000i) q^{89} +(-3.46410 - 13.4164i) q^{92} +(-1.85410 - 4.53457i) q^{94} +(8.66025 - 15.0000i) q^{95} -1.00000 q^{97} +(9.60437 - 2.39919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 4 * q^7	\( 8 q + 2 q^{4} - 4 q^{7} + 10 q^{10} + 14 q^{16} - 20 q^{22} - 10 q^{28} + 4 q^{31} + 24 q^{34} + 10 q^{40} - 24 q^{46} - 52 q^{49} - 40 q^{55} + 10 q^{58} + 44 q^{64} - 50 q^{70} + 40 q^{73} - 120 q^{76} + 52 q^{79} + 36 q^{82} + 10 q^{88} + 12 q^{94} - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 4 * q^7 + 10 * q^10 + 14 * q^16 - 20 * q^22 - 10 * q^28 + 4 * q^31 + 24 * q^34 + 10 * q^40 - 24 * q^46 - 52 * q^49 - 40 * q^55 + 10 * q^58 + 44 * q^64 - 50 * q^70 + 40 * q^73 - 120 * q^76 + 52 * q^79 + 36 * q^82 + 10 * q^88 + 12 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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