LMFDB - Embedded newform 504.2.cj.a.109.3

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			109.3
Root			$0.535233 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535233 - 1.30902i) q^{2} +(-1.42705 - 1.40126i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 + 1.11803i) q^{8} +O(q^{10})$	\(q+(0.535233 - 1.30902i) q^{2} +(-1.42705 - 1.40126i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(-0.427051 - 3.13331i) q^{10} +(-1.93649 - 1.11803i) q^{11} +(-3.66854 - 0.736068i) q^{14} +(0.0729490 + 3.99933i) q^{16} +(-1.73205 + 3.00000i) q^{17} +(6.70820 - 3.87298i) q^{19} +(-4.33013 - 1.11803i) q^{20} +(-2.50000 + 1.93649i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(-2.92705 + 4.40822i) q^{28} +2.23607i q^{29} +(0.500000 - 0.866025i) q^{31} +(5.27424 + 2.04508i) q^{32} +(3.00000 + 3.87298i) q^{34} +(-3.87298 - 4.47214i) q^{35} +(6.70820 - 3.87298i) q^{37} +(-1.47935 - 10.8541i) q^{38} +(-3.78115 + 5.06980i) q^{40} -10.3923 q^{41} +(1.19682 + 4.30902i) q^{44} +(-9.70820 + 1.32317i) q^{46} +(1.73205 + 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(9.68246 + 5.59017i) q^{53} -5.00000 q^{55} +(4.20378 + 6.19098i) q^{56} +(2.92705 + 1.19682i) q^{58} +(-1.93649 - 1.11803i) q^{59} +(6.70820 - 3.87298i) q^{61} +(-0.866025 - 1.11803i) q^{62} +(5.50000 - 5.80948i) q^{64} +(6.70820 + 3.87298i) q^{67} +(6.67550 - 1.85410i) q^{68} +(-7.92705 + 2.67617i) q^{70} +10.3923 q^{71} +(5.00000 - 8.66025i) q^{73} +(-1.47935 - 10.8541i) q^{74} +(-15.0000 - 3.87298i) q^{76} +(-1.93649 + 5.59017i) q^{77} +(6.50000 + 11.2583i) q^{79} +(4.61266 + 7.66312i) q^{80} +(-5.56231 + 13.6037i) q^{82} -11.1803i q^{83} +7.74597i q^{85} +(6.28115 + 0.739674i) q^{88} +(6.92820 + 12.0000i) q^{89} +(-3.46410 + 13.4164i) q^{92} +(4.85410 - 0.661585i) q^{94} +(8.66025 - 15.0000i) q^{95} -1.00000 q^{97} +(-0.0780895 + 9.89919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.535233	−	1.30902i	0.378467	−	0.925615i
$2$	0.535233	−	1.30902i	0.378467	−	0.925615i
$3$		0			0
$3$		0			0
$4$	−1.42705	−	1.40126i	−0.713525	−	0.700629i
$5$	1.93649	−	1.11803i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$5$	1.93649	−	1.11803i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−2.59808	+	1.11803i	−0.918559	+	0.395285i
$9$		0			0
$10$	−0.427051	−	3.13331i	−0.135045	−	0.990839i
$11$	−1.93649	−	1.11803i	−0.583874	−	0.337100i	0.178797	−	0.983886i	$-0.442779\pi$
$11$	−1.93649	−	1.11803i	−0.583874	−	0.337100i	−0.762672	+	0.646786i	$0.776113\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−3.66854	−	0.736068i	−0.980459	−	0.196722i
$15$		0			0
$16$	0.0729490	+	3.99933i	0.0182373	+	0.999834i
$17$	−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	$-0.318398\pi$
$19$	6.70820	−	3.87298i	1.53897	−	0.888523i	0.998899	−	0.0469020i	$-0.0149348\pi$
$20$	−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
$28$	−2.92705	+	4.40822i	−0.553161	+	0.833075i
$29$			2.23607i			0.415227i	0.978211	+	0.207614i	$0.0665697\pi$
$29$			2.23607i			0.415227i	−0.978211	+	0.207614i	$0.933430\pi$
$30$		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	$0.138043\pi$
$32$	5.27424	+	2.04508i	0.932363	+	0.361523i
$33$		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	0.165861	−	0.986149i	$-0.446960\pi$
$37$	6.70820	−	3.87298i	1.10282	−	0.636715i	0.936961	+	0.349435i	$0.113626\pi$
$38$	−1.47935	−	10.8541i	−0.239982	−	1.76077i
$39$		0			0
$40$	−3.78115	+	5.06980i	−0.597853	+	0.801606i
$41$	−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			$\pi$
$44$	1.19682	+	4.30902i	0.180427	+	0.649609i
$45$		0			0
$46$	−9.70820	+	1.32317i	−1.43140	+	0.195091i
$47$	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	0.985297	−	0.170848i	$-0.0546505\pi$
$53$	9.68246	+	5.59017i	1.32999	+	0.767869i	0.344690	+	0.938716i	$0.387984\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$	4.20378	+	6.19098i	0.561753	+	0.827305i
$57$		0			0
$58$	2.92705	+	1.19682i	0.384341	+	0.157150i
$59$	−1.93649	−	1.11803i	−0.252110	−	0.145556i	0.368620	−	0.929580i	$-0.379830\pi$
$59$	−1.93649	−	1.11803i	−0.252110	−	0.145556i	−0.620730	+	0.784024i	$0.713164\pi$
$60$		0			0
$61$	6.70820	−	3.87298i	0.858898	−	0.495885i	−0.00474543	−	0.999989i	$-0.501511\pi$
$61$	6.70820	−	3.87298i	0.858898	−	0.495885i	0.863643	+	0.504104i	$0.168177\pi$
$62$	−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	0.850257	−	0.526368i	$-0.176447\pi$
$67$	6.70820	+	3.87298i	0.819538	+	0.473160i	−0.0307194	+	0.999528i	$0.509780\pi$
$68$	6.67550	−	1.85410i	0.809523	−	0.224843i
$69$		0			0
$70$	−7.92705	+	2.67617i	−0.947464	+	0.319863i
$71$	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	$-0.0323196\pi$
$74$	−1.47935	−	10.8541i	−0.171971	−	1.26176i
$75$		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	$0.572244\pi$
$80$	4.61266	+	7.66312i	0.515711	+	0.856763i
$81$		0			0
$82$	−5.56231	+	13.6037i	−0.614254	+	1.50228i
$83$		−	11.1803i		−	1.22720i	−0.789616	−	0.613601i	$-0.789720\pi$
$83$		−	11.1803i		−	1.22720i	0.789616	−	0.613601i	$-0.210280\pi$
$84$		0			0
$85$			7.74597i			0.840168i
$86$		0			0
$87$		0			0
$88$	6.28115	+	0.739674i	0.669573	+	0.0788495i
$89$	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
$94$	4.85410	−	0.661585i	0.500662	−	0.0682372i
$95$	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	$0.516167\pi$
$98$	−0.0780895	+	9.89919i	−0.00788823	+	0.999969i
$99$		0			0
$100$		0			0
$101$	3.87298	+	2.23607i	0.385376	+	0.222497i	0.680155	−	0.733069i	$-0.261913\pi$
$101$	3.87298	+	2.23607i	0.385376	+	0.222497i	−0.294779	+	0.955566i	$0.595246\pi$
$102$		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	−0.888716	−	0.458458i	$-0.848402\pi$
$107$	−9.68246	+	5.59017i	−0.936039	+	0.540422i	−0.0473223	+	0.998880i	$0.515069\pi$
$108$		0			0
$109$	6.70820	+	3.87298i	0.642529	+	0.370965i	0.785588	−	0.618750i	$-0.212360\pi$
$109$	6.70820	+	3.87298i	0.642529	+	0.370965i	−0.143059	+	0.989714i	$0.545694\pi$
$110$	−2.67617	+	6.54508i	−0.255162	+	0.624049i
$111$		0			0
$112$	10.3541	−	2.18919i	0.978371	−	0.206859i
$113$	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
$116$	3.13331	−	3.19098i	0.290920	−	0.296275i
$117$		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
$122$	−1.47935	−	10.8541i	−0.133934	−	0.982684i
$123$		0			0
$124$	−1.92705	+	0.535233i	−0.173054	+	0.0480654i
$125$			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	$0.428794\pi$
$128$	−4.66092	−	10.3090i	−0.411971	−	0.911197i
$129$		0			0
$130$		0			0
$131$	−9.68246	+	5.59017i	−0.845960	+	0.488415i	−0.859286	−	0.511496i	$-0.829092\pi$
$131$	−9.68246	+	5.59017i	−0.845960	+	0.488415i	0.0133255	+	0.999911i	$0.495758\pi$
$132$		0			0
$133$	−13.4164	−	15.4919i	−1.16335	−	1.34332i
$134$	8.66025	−	6.70820i	0.748132	−	0.579501i
$135$		0			0
$136$	1.14590	−	9.73072i	0.0982599	−	0.834402i
$137$	−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			$\pi$
$140$	−0.739674	+	11.8090i	−0.0625139	+	0.998044i
$141$		0			0
$142$	5.56231	−	13.6037i	0.466778	−	1.14160i
$143$		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	$-0.298122\pi$
$149$	19.3649	−	11.1803i	1.58644	−	0.915929i	0.993888	−	0.110394i	$-0.0352112\pi$
$150$		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	$0.0747309\pi$
$152$	−13.0983	+	17.5623i	−1.06241	+	1.42449i
$153$		0			0
$154$	6.28115	+	5.52694i	0.506150	+	0.445374i
$155$		−	2.23607i		−	0.179605i
$156$		0			0
$157$	−13.4164	−	7.74597i	−1.07075	−	0.618195i	−0.142361	−	0.989815i	$-0.545469\pi$
$157$	−13.4164	−	7.74597i	−1.07075	−	0.618195i	−0.928385	+	0.371619i	$0.878803\pi$
$158$	18.2164	−	2.48278i	1.44922	−	0.197519i
$159$		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	−0.922888	−	0.385068i	$-0.874178\pi$
$163$	−13.4164	+	7.74597i	−1.05085	+	0.606711i	−0.127966	+	0.991779i	$0.540845\pi$
$164$	14.8303	+	14.5623i	1.15806	+	1.13713i
$165$		0			0
$166$	−14.6353	−	5.98409i	−1.13592	−	0.464455i
$167$	−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
$170$	10.1396	+	4.14590i	0.777672	+	0.317976i
$171$		0			0
$172$		0			0
$173$	−3.87298	+	2.23607i	−0.294457	+	0.170005i	−0.639950	−	0.768416i	$-0.721045\pi$
$173$	−3.87298	+	2.23607i	−0.294457	+	0.170005i	0.345493	+	0.938421i	$0.387712\pi$
$174$		0			0
$175$		0			0
$176$	4.33013	−	7.82624i	0.326396	−	0.589925i
$177$		0			0
$178$	19.4164	−	2.64634i	1.45532	−	0.198351i
$179$	−7.74597	−	4.47214i	−0.578961	−	0.334263i	0.181760	−	0.983343i	$-0.441821\pi$
$179$	−7.74597	−	4.47214i	−0.578961	−	0.334263i	−0.760720	+	0.649080i	$0.775154\pi$
$180$		0			0
$181$			23.2379i			1.72726i	0.504127	+	0.863630i	$0.331814\pi$
$181$			23.2379i			1.72726i	−0.504127	+	0.863630i	$0.668186\pi$
$182$		0			0
$183$		0			0
$184$	15.7082	+	11.7155i	1.15802	+	0.863676i
$185$	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	$0.957095\pi$
$194$	−0.535233	+	1.30902i	−0.0384275	+	0.0939819i
$195$		0			0
$196$	12.9164	+	5.40059i	0.922601	+	0.385757i
$197$		−	4.47214i		−	0.318626i	−0.987228	−	0.159313i	$-0.949072\pi$
$197$		−	4.47214i		−	0.318626i	0.987228	−	0.159313i	$-0.0509280\pi$
$198$		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
$206$	−11.2101	+	1.52786i	−0.781042	+	0.106451i
$207$		0			0
$208$		0			0
$209$	−17.3205			−1.19808
$210$		0			0
$211$			23.2379i			1.59976i	0.600158	+	0.799882i	$0.295104\pi$
$211$			23.2379i			1.59976i	−0.600158	+	0.799882i	$0.704896\pi$
$212$	−5.98409	−	21.5451i	−0.410989	−	1.47972i
$213$		0			0
$214$	2.13525	+	15.6665i	0.145963	+	1.07094i
$215$		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
$220$	7.13525	+	7.00629i	0.481059	+	0.472364i
$221$		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	$0.575305\pi$
$224$	2.67617	−	14.7254i	0.178809	−	0.983884i
$225$		0			0
$226$	5.56231	−	13.6037i	0.369999	−	0.904905i
$227$	21.3014	+	12.2984i	1.41382	+	0.816272i	0.995746	−	0.0921394i	$-0.0293705\pi$
$227$	21.3014	+	12.2984i	1.41382	+	0.816272i	0.418078	+	0.908411i	$0.362704\pi$
$228$		0			0
$229$	6.70820	−	3.87298i	0.443291	−	0.255934i	−0.261702	−	0.965149i	$-0.584284\pi$
$229$	6.70820	−	3.87298i	0.443291	−	0.255934i	0.704992	+	0.709215i	$0.250950\pi$
$230$	−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
$236$	1.19682	+	4.30902i	0.0779062	+	0.280493i
$237$		0			0
$238$	8.56231	−	9.73072i	0.555012	−	0.630749i
$239$	−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	$0.901123\pi$
$242$	−8.40755	+	1.14590i	−0.540458	+	0.0736611i
$243$		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
$248$	−0.330792	+	2.80902i	−0.0210053	+	0.178373i
$249$		0			0
$250$	14.6353	+	5.98409i	0.925615	+	0.378467i
$251$		−	24.5967i		−	1.55253i	−0.630405	−	0.776266i	$-0.717111\pi$
$251$		−	24.5967i		−	1.55253i	0.630405	−	0.776266i	$-0.282889\pi$
$252$		0			0
$253$			15.4919i			0.973970i
$254$	2.67617	−	6.54508i	0.167918	−	0.410675i
$255$		0			0
$256$	−15.9894	+	0.583495i	−0.999335	+	0.0364684i
$257$	−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
$262$	2.13525	+	15.6665i	0.131916	+	0.967882i
$263$	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
$266$	−27.4601	+	9.27051i	−1.68369	+	0.568411i
$267$		0			0
$268$	−4.14590	−	14.9269i	−0.253251	−	0.911804i
$269$	−25.1744	−	14.5344i	−1.53491	−	0.886181i	−0.999125	−	0.0418260i	$-0.986682\pi$
$269$	−25.1744	−	14.5344i	−1.53491	−	0.886181i	−0.535785	−	0.844355i	$-0.679984\pi$
$270$		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	0.0394907	−	0.999220i	$-0.487426\pi$
$277$	−13.4164	−	7.74597i	−0.806114	−	0.465410i	−0.845605	+	0.533810i	$0.820760\pi$
$278$		0			0
$279$		0			0
$280$	15.0623	+	7.28882i	0.900145	+	0.435590i
$281$	−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	0.0450815	−	0.998983i	$-0.485645\pi$
$283$	−13.4164	−	7.74597i	−0.797523	−	0.460450i	−0.842604	+	0.538533i	$0.818979\pi$
$284$	−14.8303	−	14.5623i	−0.880019	−	0.864114i
$285$		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
$290$	7.00629	−	0.954915i	0.411424	−	0.0560745i
$291$		0			0
$292$	−19.2705	+	5.35233i	−1.12772	+	0.313222i
$293$		−	11.1803i		−	0.653162i	−0.945169	−	0.326581i	$-0.894103\pi$
$293$		−	11.1803i		−	0.653162i	0.945169	−	0.326581i	$-0.105897\pi$
$294$		0			0
$295$	−5.00000			−0.291111
$296$	−13.0983	+	17.5623i	−0.761323	+	1.02079i
$297$		0			0
$298$	−4.27051	−	31.3331i	−0.247384	−	1.81508i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−6.06218	−	7.82624i	−0.348839	−	0.450349i
$303$		0			0
$304$	15.9787	+	26.5458i	0.916442	+	1.52251i
$305$	8.66025	−	15.0000i	0.495885	−	0.858898i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	10.5967	−	5.26393i	0.603806	−	0.299940i
$309$		0			0
$310$	−2.92705	−	1.19682i	−0.166245	−	0.0679747i
$311$	−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	−0.444631	−	0.895714i	$-0.646665\pi$
$317$	1.93649	−	1.11803i	0.108764	−	0.0627950i	0.553395	+	0.832919i	$0.313332\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$	4.15551	−	17.3992i	0.232300	−	0.972644i
$321$		0			0
$322$	8.29180	+	24.5611i	0.462084	+	1.36873i
$323$			26.8328i			1.49302i
$324$		0			0
$325$		0			0
$326$	2.95870	+	21.7082i	0.163867	+	1.20231i
$327$		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	−0.821135	−	0.570734i	$-0.806659\pi$
$331$	−13.4164	+	7.74597i	−0.737432	+	0.425757i	0.0837026	+	0.996491i	$0.473325\pi$
$332$	−15.6665	+	15.9549i	−0.859813	+	0.875640i
$333$		0			0
$334$	−5.56231	+	13.6037i	−0.304356	+	0.744362i
$335$	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	$0.673136\pi$
$338$	6.95803	−	17.0172i	0.378467	−	0.925615i
$339$		0			0
$340$	10.8541	−	11.0539i	0.588646	−	0.599481i
$341$	−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
$346$	0.854102	+	6.26662i	0.0459168	+	0.336896i
$347$	15.4919	+	8.94427i	0.831651	+	0.480154i	0.854417	−	0.519587i	$-0.173914\pi$
$347$	15.4919	+	8.94427i	0.831651	+	0.480154i	−0.0227669	+	0.999741i	$0.507248\pi$
$348$		0			0
$349$		−	23.2379i		−	1.24390i	−0.783058	−	0.621948i	$-0.786341\pi$
$349$		−	23.2379i		−	1.24390i	0.783058	−	0.621948i	$-0.213659\pi$
$350$		0			0
$351$		0			0
$352$	−7.92705	−	9.85707i	−0.422513	−	0.525384i
$353$	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
$362$	30.4188	+	12.4377i	1.59878	+	0.653711i
$363$		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	$0.208325\pi$
$368$	23.7433	−	14.2918i	1.23771	−	0.745011i
$369$		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	−0.316174	−	0.948701i	$-0.602398\pi$
$373$	6.70820	−	3.87298i	0.347338	−	0.200535i	0.663512	+	0.748166i	$0.269065\pi$
$374$	−1.47935	−	10.8541i	−0.0764953	−	0.561252i
$375$		0			0
$376$	−7.85410	−	5.85774i	−0.405044	−	0.302090i
$377$		0			0
$378$		0			0
$379$			23.2379i			1.19365i	0.802371	+	0.596825i	$0.203571\pi$
$379$			23.2379i			1.19365i	−0.802371	+	0.596825i	$0.796429\pi$
$380$	−33.3775	+	9.27051i	−1.71223	+	0.475567i
$381$		0			0
$382$	−9.70820	+	1.32317i	−0.496715	+	0.0676992i
$383$	−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
$388$	1.42705	+	1.40126i	0.0724475	+	0.0711381i
$389$	3.87298	+	2.23607i	0.196368	+	0.113373i	0.594960	−	0.803755i	$-0.297168\pi$
$389$	3.87298	+	2.23607i	0.196368	+	0.113373i	−0.398592	+	0.917128i	$0.630501\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$	13.9828	−	14.0172i	0.706236	−	0.707977i
$393$		0			0
$394$	−5.85410	−	2.39364i	−0.294925	−	0.120590i
$395$	25.1744	+	14.5344i	1.26666	+	0.731307i
$396$		0			0
$397$	26.8328	−	15.4919i	1.34670	−	0.777518i	0.358920	−	0.933368i	$-0.383145\pi$
$397$	26.8328	−	15.4919i	1.34670	−	0.777518i	0.987781	+	0.155851i	$0.0498118\pi$
$398$	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
$404$	−2.39364	−	8.61803i	−0.119088	−	0.428763i
$405$		0			0
$406$	1.64590	−	8.20311i	0.0816845	−	0.407114i
$407$	−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	$0.111300\pi$
$410$	4.43804	+	32.5623i	0.219179	+	1.60814i
$411$		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
$418$	−9.27051	+	22.6728i	−0.453435	+	1.10896i
$419$			35.7771i			1.74783i	0.486083	+	0.873913i	$0.338425\pi$
$419$			35.7771i			1.74783i	−0.486083	+	0.873913i	$0.661575\pi$
$420$		0			0
$421$			23.2379i			1.13255i	0.824218	+	0.566273i	$0.191615\pi$
$421$			23.2379i			1.13255i	−0.824218	+	0.566273i	$0.808385\pi$
$422$	30.4188	+	12.4377i	1.48076	+	0.605457i
$423$		0			0
$424$	−31.4058	−	3.69837i	−1.52520	−	0.179609i
$425$		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	$0.677293\pi$
$434$	−2.47172	+	2.80902i	−0.118647	+	0.134837i
$435$		0			0
$436$	−4.14590	−	14.9269i	−0.198553	−	0.714868i
$437$	−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	−0.911794	−	0.410647i	$-0.865303\pi$
$443$	−21.3014	+	12.2984i	−1.01206	+	0.584313i	−0.100266	+	0.994961i	$0.531969\pi$
$444$		0			0
$445$	26.8328	+	15.4919i	1.27200	+	0.734388i
$446$	−3.74663	+	9.16312i	−0.177408	+	0.433886i
$447$		0			0
$448$	−17.8435	−	11.3847i	−0.843024	−	0.537876i
$449$	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
$452$	−14.8303	−	14.5623i	−0.697561	−	0.684953i
$453$		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	$0.870643\pi$
$458$	−1.47935	−	10.8541i	−0.0691254	−	0.507179i
$459$		0			0
$460$	8.29180	+	29.8537i	0.386607	+	1.39194i
$461$			22.3607i			1.04144i	0.853727	+	0.520720i	$0.174337\pi$
$461$			22.3607i			1.04144i	−0.853727	+	0.520720i	$0.825663\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	−8.94278	+	0.163119i	−0.415158	+	0.00757261i
$465$		0			0
$466$	4.85410	−	0.661585i	0.224862	−	0.0306473i
$467$	7.74597	−	4.47214i	0.358441	−	0.206946i	−0.309956	−	0.950751i	$-0.600314\pi$
$467$	7.74597	−	4.47214i	0.358441	−	0.206946i	0.668397	+	0.743805i	$0.266981\pi$
$468$		0			0
$469$	6.70820	−	19.3649i	0.309756	−	0.894189i
$470$	8.66025	−	6.70820i	0.399468	−	0.309426i
$471$		0			0
$472$	6.28115	+	0.739674i	0.289113	+	0.0340463i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−8.15485	−	16.4164i	−0.373777	−	0.752445i
$477$		0			0
$478$	−11.1246	+	27.2074i	−0.508828	+	1.24444i
$479$	−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	$0.159454\pi$
$488$	−13.0983	+	17.5623i	−0.592932	+	0.795008i
$489$		0			0
$490$	10.9164	+	19.2570i	0.493153	+	0.869943i
$491$			29.0689i			1.31186i	0.754822	+	0.655930i	$0.227723\pi$
$491$			29.0689i			1.31186i	−0.754822	+	0.655930i	$0.772277\pi$
$492$		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	0.240379	−	0.970679i	$-0.422728\pi$
$499$	26.8328	−	15.4919i	1.20120	−	0.693514i	0.960822	+	0.277165i	$0.0893948\pi$
$500$	15.6665	−	15.9549i	0.700629	−	0.713525i
$501$		0			0
$502$	−32.1976	−	13.1650i	−1.43705	−	0.587582i
$503$	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
$506$	20.2792	+	8.29180i	0.901521	+	0.368615i
$507$		0			0
$508$	−7.13525	−	7.00629i	−0.316576	−	0.310854i
$509$	25.1744	−	14.5344i	1.11584	−	0.644228i	0.175501	−	0.984479i	$-0.443846\pi$
$509$	25.1744	−	14.5344i	1.11584	−	0.644228i	0.940334	+	0.340251i	$0.110512\pi$
$510$		0			0
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$	−7.79423	+	21.2426i	−0.344459	+	0.938801i
$513$		0			0
$514$	−9.70820	+	1.32317i	−0.428211	+	0.0583625i
$515$	−15.4919	−	8.94427i	−0.682656	−	0.394132i
$516$		0			0
$517$		−	7.74597i		−	0.340667i
$518$	−27.4601	+	9.27051i	−1.20653	+	0.407323i
$519$		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	0.218858	−	0.975757i	$-0.429767\pi$
$523$	26.8328	−	15.4919i	1.17332	−	0.677415i	0.954459	+	0.298342i	$0.0964335\pi$
$524$	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
$530$	13.3808	−	32.7254i	0.581226	−	1.42150i
$531$		0			0
$532$	−2.56231	+	40.9076i	−0.111090	+	1.77357i
$533$		0			0
$534$		0			0
$535$	−12.5000	+	21.6506i	−0.540422	+	0.936039i
$536$	−21.7586	−	2.56231i	−0.939826	−	0.110675i
$537$		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	−0.759867	−	0.650078i	$-0.774736\pi$
$541$	−13.4164	+	7.74597i	−0.576816	+	0.333025i	0.183051	+	0.983103i	$0.441403\pi$
$542$	1.40126	−	0.190983i	0.0601892	−	0.00820342i
$543$		0			0
$544$	−15.2705	+	12.2805i	−0.654718	+	0.526524i
$545$	17.3205			0.741929
$546$		0			0
$547$		−	23.2379i		−	0.993581i	−0.867871	−	0.496790i	$-0.834512\pi$
$547$		−	23.2379i		−	0.993581i	0.867871	−	0.496790i	$-0.165488\pi$
$548$	6.67550	−	1.85410i	0.285163	−	0.0792033i
$549$		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	0.184527	−	0.982827i	$-0.440925\pi$
$557$	−13.5554	−	7.82624i	−0.574362	−	0.331608i	−0.758890	+	0.651219i	$0.774258\pi$
$558$		0			0
$559$		0			0
$560$	17.6030	−	15.8156i	0.743864	−	0.668331i
$561$		0			0
$562$	−5.56231	+	13.6037i	−0.234632	+	0.573838i
$563$	32.9204	+	19.0066i	1.38743	+	0.801032i	0.993025	−	0.117906i	$-0.0376181\pi$
$563$	32.9204	+	19.0066i	1.38743	+	0.801032i	0.394403	+	0.918938i	$0.370951\pi$
$564$		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	0.633754	−	0.773535i	$-0.281513\pi$
$571$	6.70820	+	3.87298i	0.280730	+	0.162079i	−0.353024	+	0.935614i	$0.614847\pi$
$572$		0			0
$573$		0			0
$574$	38.1246	+	7.64944i	1.59129	+	0.319282i
$575$		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	$0.906868\pi$
$578$	7.00629	−	0.954915i	0.291423	−	0.0397192i
$579$		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
$584$	−3.30792	+	28.0902i	−0.136883	+	1.16238i
$585$		0			0
$586$	−14.6353	−	5.98409i	−0.604577	−	0.247200i
$587$		−	38.0132i		−	1.56897i	−0.620147	−	0.784485i	$-0.712927\pi$
$587$		−	38.0132i		−	1.56897i	0.620147	−	0.784485i	$-0.287073\pi$
$588$		0			0
$589$		−	7.74597i		−	0.319167i
$590$	−2.67617	+	6.54508i	−0.110176	+	0.269457i
$591$		0			0
$592$	15.9787	+	26.5458i	0.656721	+	1.09103i
$593$	−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
$604$	−13.4894	+	3.74663i	−0.548874	+	0.152448i
$605$	−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	0.931910	−	0.362689i	$-0.118141\pi$
$613$	26.8328	+	15.4919i	1.08377	+	0.625713i	0.151857	+	0.988402i	$0.451475\pi$
$614$		0			0
$615$		0			0
$616$	−1.21885	−	16.6888i	−0.0491087	−	0.672409i
$617$	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	0.628717	−	0.777634i	$-0.283580\pi$
$619$	6.70820	+	3.87298i	0.269625	+	0.155668i	−0.359092	+	0.933302i	$0.616914\pi$
$620$	−3.13331	+	3.19098i	−0.125837	+	0.128153i
$621$		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
$626$	−32.2289	+	4.39261i	−1.28813	+	0.175564i
$627$		0			0
$628$	8.29180	+	29.8537i	0.330879	+	1.19129i
$629$			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	$0.429736\pi$
$632$	−29.4747	−	21.9828i	−1.17244	−	0.874428i
$633$		0			0
$634$	−0.427051	−	3.13331i	−0.0169604	−	0.124440i
$635$	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
$640$	−20.5517	−	14.7523i	−0.812376	−	0.583134i
$641$	−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	$0.151508\pi$
$643$			23.2379i			0.916413i	−0.888846	+	0.458207i	$0.848492\pi$
$644$	36.5889	+	2.29180i	1.44180	+	0.0903094i
$645$		0			0
$646$	35.1246	+	14.3618i	1.38196	+	0.565058i
$647$	−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	0.441997	−	0.897016i	$-0.354270\pi$
$653$	36.7933	−	21.2426i	1.43983	−	0.831289i	0.997838	+	0.0657275i	$0.0209368\pi$
$654$		0			0
$655$	−12.5000	+	21.6506i	−0.488415	+	0.845960i
$656$	−0.758108	−	41.5623i	−0.0295992	−	1.62274i
$657$		0			0
$658$	−4.14590	−	12.2805i	−0.161624	−	0.478745i
$659$		−	17.8885i		−	0.696839i	−0.937339	−	0.348419i	$-0.886719\pi$
$659$		−	17.8885i		−	0.696839i	0.937339	−	0.348419i	$-0.113281\pi$
$660$		0			0
$661$	−13.4164	−	7.74597i	−0.521838	−	0.301283i	0.215848	−	0.976427i	$-0.430748\pi$
$661$	−13.4164	−	7.74597i	−0.521838	−	0.301283i	−0.737686	+	0.675144i	$0.764082\pi$
$662$	2.95870	+	21.7082i	0.114993	+	0.843713i
$663$		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
$668$	14.8303	+	14.5623i	0.573803	+	0.563433i
$669$		0			0
$670$	9.27051	−	22.6728i	0.358151	−	0.875928i
$671$	−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	$0.543076\pi$
$674$	−10.1694	+	24.8713i	−0.391712	+	0.958008i
$675$		0			0
$676$	−18.5517	−	18.2164i	−0.713525	−	0.700629i
$677$	−21.3014	+	12.2984i	−0.818680	+	0.472665i	−0.849961	−	0.526846i	$-0.823375\pi$
$677$	−21.3014	+	12.2984i	−0.818680	+	0.472665i	0.0312813	+	0.999511i	$0.490041\pi$
$678$		0			0
$679$	0.500000	+	2.59808i	0.0191882	+	0.0997050i
$680$	−8.66025	−	20.1246i	−0.332106	−	0.771744i
$681$		0			0
$682$	0.427051	+	3.13331i	0.0163526	+	0.119981i
$683$	9.68246	+	5.59017i	0.370489	+	0.213902i	0.673672	−	0.739030i	$-0.264716\pi$
$683$	9.68246	+	5.59017i	0.370489	+	0.213902i	−0.303183	+	0.952932i	$0.598049\pi$
$684$		0			0
$685$			7.74597i			0.295958i
$686$	25.7579	−	4.74671i	0.983441	−	0.181230i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−33.5410	+	19.3649i	−1.27596	+	0.736676i	−0.976103	−	0.217308i	$-0.930272\pi$
$691$	−33.5410	+	19.3649i	−1.27596	+	0.736676i	−0.299857	+	0.953984i	$0.596939\pi$
$692$	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
$698$	−30.4188	−	12.4377i	−1.15137	−	0.470774i
$699$		0			0
$700$		0			0
$701$		−	24.5967i		−	0.929006i	−0.885571	−	0.464503i	$-0.846233\pi$
$701$		−	24.5967i		−	0.929006i	0.885571	−	0.464503i	$-0.153767\pi$
$702$		0			0
$703$	30.0000	−	51.9615i	1.13147	−	1.95977i
$704$	−17.1459	+	5.10081i	−0.646210	+	0.192244i
$705$		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	−0.730308	−	0.683118i	$-0.760623\pi$
$709$	−13.4164	+	7.74597i	−0.503864	+	0.290906i	0.226444	+	0.974024i	$0.427290\pi$
$710$	−4.43804	−	32.5623i	−0.166557	−	1.22204i
$711$		0			0
$712$	−31.4164	−	23.4309i	−1.17738	−	0.878112i
$713$	−6.92820			−0.259463
$714$		0			0
$715$		0			0
$716$	4.78727	+	17.2361i	0.178909	+	0.644142i
$717$		0			0
$718$	−24.2705	+	3.30792i	−0.905767	+	0.123451i
$719$	−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
$724$	32.5623	−	33.1617i	1.21017	−	1.23244i
$725$		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
$730$	−29.2705	−	11.9682i	−1.08335	−	0.442962i
$731$		0			0
$732$		0			0
$733$	−13.4164	+	7.74597i	−0.495546	+	0.286104i	−0.726872	−	0.686772i	$-0.759027\pi$
$733$	−13.4164	+	7.74597i	−0.495546	+	0.286104i	0.231326	+	0.972876i	$0.425694\pi$
$734$	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	0.232507	−	0.972595i	$-0.425307\pi$
$739$	−13.4164	−	7.74597i	−0.493531	−	0.284940i	−0.726038	+	0.687655i	$0.758640\pi$
$740$	−33.3775	+	9.27051i	−1.22698	+	0.340791i
$741$		0			0
$742$	−31.4058	−	27.6347i	−1.15294	−	1.01450i
$743$	−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
$746$	−1.47935	−	10.8541i	−0.0541628	−	0.397397i
$747$		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	$0.546229\pi$
$752$	−11.8717	+	7.14590i	−0.432915	+	0.260584i
$753$		0			0
$754$		0			0
$755$		−	15.6525i		−	0.569652i
$756$		0			0
$757$		−	23.2379i		−	0.844596i	−0.906457	−	0.422298i	$-0.861224\pi$
$757$		−	23.2379i		−	0.844596i	0.906457	−	0.422298i	$-0.138776\pi$
$758$	30.4188	+	12.4377i	1.10486	+	0.451757i
$759$		0			0
$760$	−5.72949	+	48.6536i	−0.207830	+	1.76485i
$761$	−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
$766$	−9.70820	+	1.32317i	−0.350772	+	0.0478080i
$767$		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	$0.688793\pi$
$770$	18.3427	+	3.68034i	0.661025	+	0.132630i
$771$		0			0
$772$	32.7599	−	9.09896i	1.17905	−	0.327479i
$773$	3.87298	+	2.23607i	0.139302	+	0.0804258i	0.568031	−	0.823007i	$-0.307705\pi$
$773$	3.87298	+	2.23607i	0.139302	+	0.0804258i	−0.428730	+	0.903433i	$0.641039\pi$
$774$		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
$782$	12.8456	−	31.4164i	0.459358	−	1.12345i
$783$		0			0
$784$	−10.8647	−	25.8061i	−0.388027	−	0.921648i
$785$	−34.6410			−1.23639
$786$		0			0
$787$	−33.5410	−	19.3649i	−1.19561	−	0.690285i	−0.236035	−	0.971745i	$-0.575848\pi$
$787$	−33.5410	−	19.3649i	−1.19561	−	0.690285i	−0.959573	+	0.281460i	$0.909181\pi$
$788$	−6.26662	+	6.38197i	−0.223239	+	0.227348i
$789$		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
$794$	−5.91739	−	43.4164i	−0.210000	−	1.54079i
$795$		0			0
$796$	15.4164	−	4.28187i	0.546420	−	0.151767i
$797$			15.6525i			0.554439i	0.960807	+	0.277220i	$0.0894129\pi$
$797$			15.6525i			0.554439i	−0.960807	+	0.277220i	$0.910587\pi$
$798$		0			0
$799$	−12.0000			−0.424529
$800$		0			0
$801$		0			0
$802$	48.5410	−	6.61585i	1.71404	−	0.233614i
$803$	−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
$808$	−12.5623	−	1.47935i	−0.441940	−	0.0520433i
$809$	−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	$0.133772\pi$
$811$			23.2379i			0.815993i	−0.912983	+	0.407997i	$0.866228\pi$
$812$	−9.85707	−	6.54508i	−0.345915	−	0.229687i
$813$		0			0
$814$	−9.27051	+	22.6728i	−0.324931	+	0.794683i
$815$	−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	−0.244443	−	0.969664i	$-0.578605\pi$
$821$	13.5554	−	7.82624i	0.473088	−	0.273138i	0.717532	+	0.696526i	$0.245272\pi$
$822$		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	$0.280002\pi$
$824$	18.1383	+	13.5279i	0.631877	+	0.471265i
$825$		0			0
$826$	6.28115	+	5.52694i	0.218549	+	0.192307i
$827$		−	24.5967i		−	0.855313i	−0.903941	−	0.427656i	$-0.859339\pi$
$827$		−	24.5967i		−	0.855313i	0.903941	−	0.427656i	$-0.140661\pi$
$828$		0			0
$829$	6.70820	+	3.87298i	0.232986	+	0.134514i	0.611949	−	0.790898i	$-0.290386\pi$
$829$	6.70820	+	3.87298i	0.232986	+	0.134514i	−0.378963	+	0.925412i	$0.623719\pi$
$830$	−35.0315	+	4.77458i	−1.21596	+	0.165728i
$831$		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
$836$	24.7172	+	24.2705i	0.854864	+	0.839413i
$837$		0			0
$838$	46.8328	+	19.1491i	1.61781	+	0.661494i
$839$	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
$842$	30.4188	+	12.4377i	1.04830	+	0.428631i
$843$		0			0
$844$	32.5623	−	33.1617i	1.12084	−	1.14147i
$845$	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	$-0.869765\pi$
$853$		−	23.2379i		−	0.795651i	0.917461	−	0.397825i	$-0.130235\pi$
$854$	−27.4601	+	9.27051i	−0.939666	+	0.317230i
$855$		0			0
$856$	18.9058	−	25.3490i	0.646186	−	0.866411i
$857$	−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	−0.711103	−	0.703088i	$-0.751804\pi$
$859$	−13.4164	+	7.74597i	−0.457762	+	0.264289i	0.253341	+	0.967377i	$0.418471\pi$
$860$		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
$866$	−11.7751	+	28.7984i	−0.400135	+	0.978609i
$867$		0			0
$868$	2.35410	+	4.73901i	0.0799034	+	0.160852i
$869$		−	29.0689i		−	0.986094i
$870$		0			0
$871$		0			0
$872$	−21.7586	−	2.56231i	−0.736838	−	0.0867706i
$873$		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	0.0269120	−	0.999638i	$-0.491433\pi$
$877$	26.8328	−	15.4919i	0.906080	−	0.523125i	0.879168	+	0.476512i	$0.158099\pi$
$878$	9.80881	−	1.33688i	0.331031	−	0.0451175i
$879$		0			0
$880$	−0.364745	−	19.9967i	−0.0122956	−	0.674088i
$881$	−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	$0.127874\pi$
$883$			23.2379i			0.782018i	−0.920387	+	0.391009i	$0.872126\pi$
$884$		0			0
$885$		0			0
$886$	4.69756	+	34.4664i	0.157818	+	1.15792i
$887$	−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
$892$	9.98936	+	9.80881i	0.334468	+	0.328423i
$893$	23.2379	+	13.4164i	0.777627	+	0.448963i
$894$		0			0
$895$	−20.0000			−0.668526
$896$	−24.4532	+	17.2639i	−0.816922	+	0.576747i
$897$		0			0
$898$	11.1246	−	27.2074i	0.371233	−	0.907923i
$899$	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	0.260437	−	0.965491i	$-0.416133\pi$
$907$	−13.4164	−	7.74597i	−0.445485	−	0.257201i	−0.705921	+	0.708290i	$0.749467\pi$
$908$	−13.1650	−	47.3992i	−0.436896	−	1.57300i
$909$		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
$914$	−7.00629	+	0.954915i	−0.231748	+	0.0315858i
$915$		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	$0.875456\pi$
$920$	43.5171	+	5.12461i	1.43472	+	0.168953i
$921$		0			0
$922$	29.2705	+	11.9682i	0.963973	+	0.394151i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	4.28187	−	10.4721i	0.140711	−	0.344136i
$927$		0			0
$928$	−4.57295	+	11.7936i	−0.150114	+	0.387143i
$929$	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
$934$	−1.70820	−	12.5332i	−0.0558941	−	0.410100i
$935$	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	$0.473974\pi$
$938$	−21.7586	−	19.1459i	−0.710442	−	0.625136i
$939$		0			0
$940$	−4.14590	−	14.9269i	−0.135224	−	0.486861i
$941$	9.68246	+	5.59017i	0.315639	+	0.182234i	0.649447	−	0.760407i	$-0.275000\pi$
$941$	9.68246	+	5.59017i	0.315639	+	0.182234i	−0.333808	+	0.942641i	$0.608334\pi$
$942$		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	0.0965754	−	0.995326i	$-0.469211\pi$
$947$	30.9839	−	17.8885i	1.00684	−	0.581300i	0.910265	+	0.414026i	$0.135878\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−25.8541	+	1.88823i	−0.837936	+	0.0611979i
$953$	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
$956$	29.6607	+	29.1246i	0.959296	+	0.941957i
$957$		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
$964$	44.3222	−	12.3104i	1.42752	−	0.396490i
$965$			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	$0.598823\pi$
$968$	13.6037	+	10.1459i	0.437240	+	0.326102i
$969$		0			0
$970$	0.427051	+	3.13331i	0.0137118	+	0.100605i
$971$	−9.68246	+	5.59017i	−0.310725	+	0.179397i	−0.647251	−	0.762277i	$-0.724081\pi$
$971$	−9.68246	+	5.59017i	−0.310725	+	0.179397i	0.336526	+	0.941674i	$0.390748\pi$
$972$		0			0
$973$		0			0
$974$	−0.866025	−	1.11803i	−0.0277492	−	0.0358241i
$975$		0			0
$976$	15.9787	+	26.5458i	0.511466	+	0.849711i
$977$	−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
$980$	31.0506	−	3.98278i	0.991874	−	0.127225i
$981$		0			0
$982$	38.0517	+	15.5586i	1.21428	+	0.496496i
$983$	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	$0.161611\pi$
$992$	4.40822	−	3.54508i	0.139961	−	0.112557i
$993$		0			0
$994$	−38.1246	−	7.64944i	−1.20924	−	0.242626i
$995$			17.8885i			0.567105i
$996$		0			0
$997$	6.70820	+	3.87298i	0.212451	+	0.122659i	0.602450	−	0.798157i	$-0.294191\pi$
$997$	6.70820	+	3.87298i	0.212451	+	0.122659i	−0.389999	+	0.920815i	$0.627525\pi$
$998$	−5.91739	−	43.4164i	−0.187312	−	1.37432i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.535233 - 1.30902i) q^{2} +(-1.42705 - 1.40126i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 + 1.11803i) q^{8} +O(q^{10})\)	\(q+(0.535233 - 1.30902i) q^{2} +(-1.42705 - 1.40126i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(-0.427051 - 3.13331i) q^{10} +(-1.93649 - 1.11803i) q^{11} +(-3.66854 - 0.736068i) q^{14} +(0.0729490 + 3.99933i) q^{16} +(-1.73205 + 3.00000i) q^{17} +(6.70820 - 3.87298i) q^{19} +(-4.33013 - 1.11803i) q^{20} +(-2.50000 + 1.93649i) q^{22} +(-3.46410 - 6.00000i) q^{23} +(-2.92705 + 4.40822i) q^{28} +2.23607i q^{29} +(0.500000 - 0.866025i) q^{31} +(5.27424 + 2.04508i) q^{32} +(3.00000 + 3.87298i) q^{34} +(-3.87298 - 4.47214i) q^{35} +(6.70820 - 3.87298i) q^{37} +(-1.47935 - 10.8541i) q^{38} +(-3.78115 + 5.06980i) q^{40} -10.3923 q^{41} +(1.19682 + 4.30902i) q^{44} +(-9.70820 + 1.32317i) q^{46} +(1.73205 + 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(9.68246 + 5.59017i) q^{53} -5.00000 q^{55} +(4.20378 + 6.19098i) q^{56} +(2.92705 + 1.19682i) q^{58} +(-1.93649 - 1.11803i) q^{59} +(6.70820 - 3.87298i) q^{61} +(-0.866025 - 1.11803i) q^{62} +(5.50000 - 5.80948i) q^{64} +(6.70820 + 3.87298i) q^{67} +(6.67550 - 1.85410i) q^{68} +(-7.92705 + 2.67617i) q^{70} +10.3923 q^{71} +(5.00000 - 8.66025i) q^{73} +(-1.47935 - 10.8541i) q^{74} +(-15.0000 - 3.87298i) q^{76} +(-1.93649 + 5.59017i) q^{77} +(6.50000 + 11.2583i) q^{79} +(4.61266 + 7.66312i) q^{80} +(-5.56231 + 13.6037i) q^{82} -11.1803i q^{83} +7.74597i q^{85} +(6.28115 + 0.739674i) q^{88} +(6.92820 + 12.0000i) q^{89} +(-3.46410 + 13.4164i) q^{92} +(4.85410 - 0.661585i) q^{94} +(8.66025 - 15.0000i) q^{95} -1.00000 q^{97} +(-0.0780895 + 9.89919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 4 q^{7}+O(q^{10}) \) 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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