LMFDB - Embedded newform 750.2.l.a.293.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			293.7
Character	$\chi$	$=$	750.293
Dual form			750.2.l.a.407.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(-0.876876 + 1.49368i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.61247 - 0.632416i) q^{6} +(1.43195 - 1.43195i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-1.46218 - 2.61955i) q^{9} +O(q^{10})$	\(q+(0.156434 + 0.987688i) q^{2} +(-0.876876 + 1.49368i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.61247 - 0.632416i) q^{6} +(1.43195 - 1.43195i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-1.46218 - 2.61955i) q^{9} +(3.22713 - 4.44177i) q^{11} +(0.372385 - 1.69155i) q^{12} +(6.34051 + 1.00424i) q^{13} +(1.63832 + 1.19031i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-0.199309 + 0.101553i) q^{17} +(2.35856 - 1.85396i) q^{18} +(-2.05900 - 0.669009i) q^{19} +(0.883235 + 3.39451i) q^{21} +(4.89192 + 2.49256i) q^{22} +(2.14504 - 0.339741i) q^{23} +(1.72897 + 0.103184i) q^{24} +6.41955i q^{26} +(5.19492 + 0.112987i) q^{27} +(-0.919366 + 1.80436i) q^{28} +(-2.33841 - 7.19688i) q^{29} +(-0.944961 + 2.90829i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.80480 + 8.71519i) q^{33} +(-0.131482 - 0.180969i) q^{34} +(2.20010 + 2.03950i) q^{36} +(-1.02386 + 6.46438i) q^{37} +(0.338674 - 2.13830i) q^{38} +(-7.05986 + 8.59013i) q^{39} +(-0.896615 - 1.23409i) q^{41} +(-3.21455 + 1.40338i) q^{42} +(2.14384 + 2.14384i) q^{43} +(-1.69660 + 5.22161i) q^{44} +(0.671116 + 2.06548i) q^{46} +(2.37459 - 4.66039i) q^{47} +(0.168558 + 1.72383i) q^{48} +2.89906i q^{49} +(0.0230812 - 0.386754i) q^{51} +(-6.34051 + 1.00424i) q^{52} +(-10.9216 - 5.56485i) q^{53} +(0.701069 + 5.14864i) q^{54} +(-1.92596 - 0.625783i) q^{56} +(2.80477 - 2.48885i) q^{57} +(6.74246 - 3.43546i) q^{58} +(4.61185 - 3.35071i) q^{59} +(2.55529 + 1.85653i) q^{61} +(-3.02031 - 0.478370i) q^{62} +(-5.84481 - 1.65729i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-8.01269 + 5.12131i) q^{66} +(1.13368 + 2.22498i) q^{67} +(0.158173 - 0.158173i) q^{68} +(-1.37347 + 3.50192i) q^{69} +(5.77333 - 1.87587i) q^{71} +(-1.67022 + 2.49206i) q^{72} +(0.478324 + 3.02002i) q^{73} -6.54496 q^{74} +2.16496 q^{76} +(-1.73929 - 10.9815i) q^{77} +(-9.58877 - 5.62915i) q^{78} +(11.0020 - 3.57478i) q^{79} +(-4.72407 + 7.66049i) q^{81} +(1.07863 - 1.07863i) q^{82} +(4.74686 + 9.31624i) q^{83} +(-1.88897 - 2.95544i) q^{84} +(-1.78208 + 2.45282i) q^{86} +(12.8003 + 2.81793i) q^{87} +(-5.42273 - 0.858876i) q^{88} +(7.34358 + 5.33542i) q^{89} +(10.5173 - 7.64126i) q^{91} +(-1.93507 + 0.985966i) q^{92} +(-3.51545 - 3.96168i) q^{93} +(4.97448 + 1.61631i) q^{94} +(-1.67624 + 0.436149i) q^{96} +(2.14637 + 1.09363i) q^{97} +(-2.86337 + 0.453513i) q^{98} +(-16.3541 - 1.95898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

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 $

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	−0.876876	+	1.49368i	−0.506264	+	0.862378i
$3$	−0.876876	+	1.49368i	−0.506264	+	0.862378i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$		0			0
$5$		0			0
$6$	−1.61247	−	0.632416i	−0.658287	−	0.258183i
$7$	1.43195	−	1.43195i	0.541225	−	0.541225i	−0.382663	−	0.923888i	$-0.624993\pi$
$7$	1.43195	−	1.43195i	0.541225	−	0.541225i	0.923888	+	0.382663i	$0.124993\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−1.46218	−	2.61955i	−0.487393	−	0.873183i
$10$		0			0
$11$	3.22713	−	4.44177i	0.973017	−	1.33924i	0.0325093	−	0.999471i	$-0.489650\pi$
$11$	3.22713	−	4.44177i	0.973017	−	1.33924i	0.940508	−	0.339772i	$-0.110350\pi$
$12$	0.372385	−	1.69155i	0.107498	−	0.488307i
$13$	6.34051	+	1.00424i	1.75854	+	0.278526i	0.950528	−	0.310638i	$-0.100543\pi$
$13$	6.34051	+	1.00424i	1.75854	+	0.278526i	0.808014	+	0.589164i	$0.200543\pi$
$14$	1.63832	+	1.19031i	0.437860	+	0.318124i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.199309	+	0.101553i	−0.0483396	+	0.0246303i	−0.477993	−	0.878364i	$-0.658636\pi$
$17$	−0.199309	+	0.101553i	−0.0483396	+	0.0246303i	0.429654	+	0.902994i	$0.358636\pi$
$18$	2.35856	−	1.85396i	0.555919	−	0.436984i
$19$	−2.05900	−	0.669009i	−0.472366	−	0.153481i	0.0631534	−	0.998004i	$-0.479884\pi$
$19$	−2.05900	−	0.669009i	−0.472366	−	0.153481i	−0.535520	+	0.844523i	$0.679884\pi$
$20$		0			0
$21$	0.883235	+	3.39451i	0.192738	+	0.740743i
$22$	4.89192	+	2.49256i	1.04296	+	0.531415i
$23$	2.14504	−	0.339741i	0.447271	−	0.0708408i	0.0712640	−	0.997457i	$-0.477297\pi$
$23$	2.14504	−	0.339741i	0.447271	−	0.0708408i	0.376007	+	0.926617i	$0.377297\pi$
$24$	1.72897	+	0.103184i	0.352925	+	0.0210623i
$25$		0			0
$26$			6.41955i			1.25898i
$27$	5.19492	+	0.112987i	0.999764	+	0.0217444i
$28$	−0.919366	+	1.80436i	−0.173744	+	0.340992i
$29$	−2.33841	−	7.19688i	−0.434231	−	1.33643i	−0.893872	−	0.448322i	$-0.852022\pi$
$29$	−2.33841	−	7.19688i	−0.434231	−	1.33643i	0.459641	−	0.888105i	$-0.347978\pi$
$30$		0			0
$31$	−0.944961	+	2.90829i	−0.169720	+	0.522344i	−0.999353	−	0.0359646i	$-0.988550\pi$
$31$	−0.944961	+	2.90829i	−0.169720	+	0.522344i	0.829633	+	0.558309i	$0.188550\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.80480	+	8.71519i	0.662330	+	1.51712i
$34$	−0.131482	−	0.180969i	−0.0225489	−	0.0310359i
$35$		0			0
$36$	2.20010	+	2.03950i	0.366683	+	0.339917i
$37$	−1.02386	+	6.46438i	−0.168321	+	1.06274i	0.748411	+	0.663235i	$0.230817\pi$
$37$	−1.02386	+	6.46438i	−0.168321	+	1.06274i	−0.916732	+	0.399502i	$0.869183\pi$
$38$	0.338674	−	2.13830i	0.0549402	−	0.346879i
$39$	−7.05986	+	8.59013i	−1.13048	+	1.37552i
$40$		0			0
$41$	−0.896615	−	1.23409i	−0.140028	−	0.192732i	0.733243	−	0.679966i	$-0.238006\pi$
$41$	−0.896615	−	1.23409i	−0.140028	−	0.192732i	−0.873271	+	0.487235i	$0.838006\pi$
$42$	−3.21455	+	1.40338i	−0.496016	+	0.216546i
$43$	2.14384	+	2.14384i	0.326933	+	0.326933i	0.851419	−	0.524486i	$-0.175742\pi$
$43$	2.14384	+	2.14384i	0.326933	+	0.326933i	−0.524486	+	0.851419i	$0.675742\pi$
$44$	−1.69660	+	5.22161i	−0.255773	+	0.787187i
$45$		0			0
$46$	0.671116	+	2.06548i	0.0989506	+	0.304539i
$47$	2.37459	−	4.66039i	0.346369	−	0.679788i	−0.650444	−	0.759554i	$-0.725417\pi$
$47$	2.37459	−	4.66039i	0.346369	−	0.679788i	0.996814	+	0.0797657i	$0.0254172\pi$
$48$	0.168558	+	1.72383i	0.0243292	+	0.248813i
$49$			2.89906i			0.414151i
$50$		0			0
$51$	0.0230812	−	0.386754i	0.00323202	−	0.0541564i
$52$	−6.34051	+	1.00424i	−0.879271	+	0.139263i
$53$	−10.9216	−	5.56485i	−1.50020	−	0.764390i	−0.505082	−	0.863072i	$-0.668538\pi$
$53$	−10.9216	−	5.56485i	−1.50020	−	0.764390i	−0.995119	+	0.0986812i	$0.968538\pi$
$54$	0.701069	+	5.14864i	0.0954034	+	0.700641i
$55$		0			0
$56$	−1.92596	−	0.625783i	−0.257368	−	0.0836238i
$57$	2.80477	−	2.48885i	0.371501	−	0.329657i
$58$	6.74246	−	3.43546i	0.885329	−	0.451098i
$59$	4.61185	−	3.35071i	0.600412	−	0.436225i	−0.245613	−	0.969368i	$-0.578989\pi$
$59$	4.61185	−	3.35071i	0.600412	−	0.436225i	0.846025	+	0.533143i	$0.178989\pi$
$60$		0			0
$61$	2.55529	+	1.85653i	0.327171	+	0.237704i	0.739229	−	0.673454i	$-0.235190\pi$
$61$	2.55529	+	1.85653i	0.327171	+	0.237704i	−0.412058	+	0.911158i	$0.635190\pi$
$62$	−3.02031	−	0.478370i	−0.383580	−	0.0607530i
$63$	−5.84481	−	1.65729i	−0.736377	−	0.208799i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$		0			0
$66$	−8.01269	+	5.12131i	−0.986294	+	0.630390i
$67$	1.13368	+	2.22498i	0.138501	+	0.271824i	0.949830	−	0.312766i	$-0.101255\pi$
$67$	1.13368	+	2.22498i	0.138501	+	0.271824i	−0.811329	+	0.584590i	$0.801255\pi$
$68$	0.158173	−	0.158173i	0.0191813	−	0.0191813i
$69$	−1.37347	+	3.50192i	−0.165346	+	0.421581i
$70$		0			0
$71$	5.77333	−	1.87587i	0.685168	−	0.222625i	0.0543113	−	0.998524i	$-0.482704\pi$
$71$	5.77333	−	1.87587i	0.685168	−	0.222625i	0.630856	+	0.775900i	$0.282704\pi$
$72$	−1.67022	+	2.49206i	−0.196837	+	0.293692i
$73$	0.478324	+	3.02002i	0.0559836	+	0.353467i	0.999740	+	0.0228237i	$0.00726563\pi$
$73$	0.478324	+	3.02002i	0.0559836	+	0.353467i	−0.943756	+	0.330643i	$0.892734\pi$
$74$	−6.54496			−0.760836
$75$		0			0
$76$	2.16496			0.248338
$77$	−1.73929	−	10.9815i	−0.198211	−	1.25145i
$78$	−9.58877	−	5.62915i	−1.08571	−	0.637375i
$79$	11.0020	−	3.57478i	1.23783	−	0.402194i	0.384282	−	0.923216i	$-0.374449\pi$
$79$	11.0020	−	3.57478i	1.23783	−	0.402194i	0.853543	+	0.521022i	$0.174449\pi$
$80$		0			0
$81$	−4.72407	+	7.66049i	−0.524897	+	0.851166i
$82$	1.07863	−	1.07863i	0.119115	−	0.119115i
$83$	4.74686	+	9.31624i	0.521036	+	1.02259i	0.990223	+	0.139492i	$0.0445469\pi$
$83$	4.74686	+	9.31624i	0.521036	+	1.02259i	−0.469187	+	0.883099i	$0.655453\pi$
$84$	−1.88897	−	2.95544i	−0.206103	−	0.322465i
$85$		0			0
$86$	−1.78208	+	2.45282i	−0.192166	+	0.264494i
$87$	12.8003	+	2.81793i	1.37234	+	0.302113i
$88$	−5.42273	−	0.858876i	−0.578065	−	0.0915565i
$89$	7.34358	+	5.33542i	0.778418	+	0.565554i	0.904504	−	0.426466i	$-0.140241\pi$
$89$	7.34358	+	5.33542i	0.778418	+	0.565554i	−0.126086	+	0.992019i	$0.540241\pi$
$90$		0			0
$91$	10.5173	−	7.64126i	1.10251	−	0.801022i
$92$	−1.93507	+	0.985966i	−0.201745	+	0.102794i
$93$	−3.51545	−	3.96168i	−0.364535	−	0.410807i
$94$	4.97448	+	1.61631i	0.513079	+	0.166709i
$95$		0			0
$96$	−1.67624	+	0.436149i	−0.171080	+	0.0445142i
$97$	2.14637	+	1.09363i	0.217931	+	0.111041i	0.559548	−	0.828798i	$-0.310975\pi$
$97$	2.14637	+	1.09363i	0.217931	+	0.111041i	−0.341617	+	0.939839i	$0.610975\pi$
$98$	−2.86337	+	0.453513i	−0.289244	+	0.0458117i
$99$	−16.3541	−	1.95898i	−1.64365	−	0.196884i
$100$		0			0
$101$			7.60118i			0.756346i	0.925735	+	0.378173i	$0.123448\pi$
$101$			7.60118i			0.756346i	−0.925735	+	0.378173i	$0.876552\pi$
$102$	0.385604	−	0.0377047i	0.0381804	−	0.00373332i
$103$	3.87657	−	7.60819i	0.381970	−	0.749657i	−0.617344	−	0.786693i	$-0.711791\pi$
$103$	3.87657	−	7.60819i	0.381970	−	0.749657i	0.999314	+	0.0370356i	$0.0117915\pi$
$104$	−1.98375	−	6.10535i	−0.194523	−	0.598679i
$105$		0			0
$106$	3.78781	−	11.6577i	0.367905	−	1.13230i
$107$	3.60945	+	3.60945i	0.348939	+	0.348939i	0.859714	−	0.510775i	$-0.170642\pi$
$107$	3.60945	+	3.60945i	0.348939	+	0.348939i	−0.510775	+	0.859714i	$0.670642\pi$
$108$	−4.97558	+	1.49786i	−0.478776	+	0.144132i
$109$	−5.74999	−	7.91418i	−0.550749	−	0.758041i	0.439365	−	0.898309i	$-0.355204\pi$
$109$	−5.74999	−	7.91418i	−0.550749	−	0.758041i	−0.990114	+	0.140268i	$0.955204\pi$
$110$		0			0
$111$	−8.75794	−	7.19777i	−0.831266	−	0.683182i
$112$	0.316792	−	2.00015i	0.0299340	−	0.188996i
$113$	−2.06024	+	13.0078i	−0.193811	+	1.22367i	0.678454	+	0.734642i	$0.262650\pi$
$113$	−2.06024	+	13.0078i	−0.193811	+	1.22367i	−0.872266	+	0.489033i	$0.837350\pi$
$114$	2.89697	+	2.38090i	0.271326	+	0.222992i
$115$		0			0
$116$	4.44791	+	6.12203i	0.412978	+	0.568416i
$117$	−6.64031	−	18.0777i	−0.613897	−	1.67128i
$118$	4.03091	+	4.03091i	0.371075	+	0.371075i
$119$	−0.139982	+	0.430819i	−0.0128321	+	0.0394931i
$120$		0			0
$121$	−5.91572	−	18.2067i	−0.537793	−	1.65516i
$122$	−1.43393	+	2.81426i	−0.129822	+	0.254791i
$123$	2.62955	−	0.257120i	0.237099	−	0.0231837i
$124$		−	3.05796i		−	0.274613i
$125$		0			0
$126$	0.722558	−	6.03211i	0.0643706	−	0.537383i
$127$	−11.3429	+	1.79653i	−1.00652	+	0.159417i	−0.637863	−	0.770150i	$-0.720181\pi$
$127$	−11.3429	+	1.79653i	−1.00652	+	0.159417i	−0.368654	+	0.929567i	$0.620181\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	−5.08211	+	1.32234i	−0.447455	+	0.116425i
$130$		0			0
$131$	−9.82350	−	3.19185i	−0.858284	−	0.278873i	−0.153372	−	0.988169i	$-0.549013\pi$
$131$	−9.82350	−	3.19185i	−0.858284	−	0.278873i	−0.704911	+	0.709295i	$0.749013\pi$
$132$	−6.31172	−	7.11289i	−0.549365	−	0.619098i
$133$	−3.90636	+	1.99039i	−0.338724	+	0.172589i
$134$	−2.02024	+	1.46779i	−0.174522	+	0.126797i
$135$		0			0
$136$	0.180969	+	0.131482i	0.0155180	+	0.0112745i
$137$	−13.3238	−	2.11029i	−1.13833	−	0.180294i	−0.441317	−	0.897351i	$-0.645489\pi$
$137$	−13.3238	−	2.11029i	−1.13833	−	0.180294i	−0.697014	+	0.717057i	$0.745489\pi$
$138$	−3.67366	−	0.808736i	−0.312723	−	0.0688442i
$139$	6.69452	−	9.21421i	0.567822	−	0.781539i	−0.424473	−	0.905441i	$-0.639541\pi$
$139$	6.69452	−	9.21421i	0.567822	−	0.781539i	0.992295	+	0.123901i	$0.0395406\pi$
$140$		0			0
$141$	4.87893	+	7.63347i	0.410880	+	0.642854i
$142$	2.75592	+	5.40880i	0.231272	+	0.453896i
$143$	24.9223	−	24.9223i	2.08411	−	2.08411i
$144$	−2.72266	−	1.25981i	−0.226888	−	0.104984i
$145$		0			0
$146$	−2.90801	+	0.944871i	−0.240669	+	0.0781981i
$147$	−4.33028	−	2.54211i	−0.357155	−	0.209670i
$148$	−1.02386	−	6.46438i	−0.0841605	−	0.531369i
$149$	5.97158			0.489211			0.244606	−	0.969623i	$-0.421342\pi$
$149$	5.97158			0.489211			0.244606	+	0.969623i	$0.421342\pi$
$150$		0			0
$151$	−3.02183			−0.245913			−0.122956	−	0.992412i	$-0.539238\pi$
$151$	−3.02183			−0.245913			−0.122956	+	0.992412i	$0.539238\pi$
$152$	0.338674	+	2.13830i	0.0274701	+	0.173439i
$153$	0.557449	+	0.373612i	0.0450671	+	0.0302047i
$154$	10.5742	−	3.43576i	0.852091	−	0.276861i
$155$		0			0
$156$	4.05983	−	10.3513i	0.325046	−	0.828768i
$157$	−4.40896	+	4.40896i	−0.351873	+	0.351873i	−0.860806	−	0.508933i	$-0.830040\pi$
$157$	−4.40896	+	4.40896i	−0.351873	+	0.351873i	0.508933	+	0.860806i	$0.330040\pi$
$158$	5.25186	+	10.3074i	0.417816	+	0.820010i
$159$	17.8890	−	11.4338i	1.41869	−	0.906757i
$160$		0			0
$161$	2.58509	−	3.55807i	0.203734	−	0.280415i
$162$	−8.30519	−	3.46754i	−0.652517	−	0.272436i
$163$	5.66023	+	0.896493i	0.443344	+	0.0702187i	0.374116	−	0.927382i	$-0.377946\pi$
$163$	5.66023	+	0.896493i	0.443344	+	0.0702187i	0.0692282	+	0.997601i	$0.477946\pi$
$164$	1.23409	+	0.896615i	0.0963659	+	0.0700139i
$165$		0			0
$166$	−8.45897	+	6.14580i	−0.656544	+	0.477007i
$167$	8.68941	−	4.42748i	0.672407	−	0.342608i	−0.0842276	−	0.996447i	$-0.526842\pi$
$167$	8.68941	−	4.42748i	0.672407	−	0.342608i	0.756634	+	0.653838i	$0.226842\pi$
$168$	2.62355	−	2.32804i	0.202411	−	0.179613i
$169$	26.8299	+	8.71756i	2.06384	+	0.670581i
$170$		0			0
$171$	1.25812	+	6.37185i	0.0962109	+	0.487268i
$172$	−2.70140	−	1.37643i	−0.205980	−	0.104952i
$173$	−17.3254	+	2.74408i	−1.31723	+	0.208629i	−0.775192	−	0.631726i	$-0.782347\pi$
$173$	−17.3254	+	2.74408i	−1.31723	+	0.208629i	−0.542037	+	0.840354i	$0.682347\pi$
$174$	−0.780818	+	13.0836i	−0.0591937	+	0.991863i
$175$		0			0
$176$		−	5.49033i		−	0.413849i
$177$	0.960873	+	9.82680i	0.0722237	+	0.738627i
$178$	−4.12095	+	8.08781i	−0.308878	+	0.606207i
$179$	−3.59155	−	11.0537i	−0.268445	−	0.826190i	−0.990880	−	0.134750i	$-0.956977\pi$
$179$	−3.59155	−	11.0537i	−0.268445	−	0.826190i	0.722434	−	0.691440i	$-0.243023\pi$
$180$		0			0
$181$	−1.22208	+	3.76116i	−0.0908362	+	0.279565i	−0.986146	−	0.165879i	$-0.946954\pi$
$181$	−1.22208	+	3.76116i	−0.0908362	+	0.279565i	0.895310	+	0.445444i	$0.146954\pi$
$182$	9.19245	+	9.19245i	0.681390	+	0.681390i
$183$	−5.01373	+	2.18885i	−0.370626	+	0.161804i
$184$	−1.27654	−	1.75700i	−0.0941076	−	0.129528i
$185$		0			0
$186$	3.36297	−	4.09191i	0.246585	−	0.300034i
$187$	−0.192122	+	1.21301i	−0.0140494	+	0.0887042i
$188$	−0.818228	+	5.16609i	−0.0596754	+	0.376776i
$189$	7.60064	−	7.27706i	0.552865	−	0.529328i
$190$		0			0
$191$	−9.89270	−	13.6161i	−0.715810	−	0.985228i	−0.999653	−	0.0263574i	$-0.991609\pi$
$191$	−9.89270	−	13.6161i	−0.715810	−	0.985228i	0.283842	−	0.958871i	$-0.408391\pi$
$192$	−0.693000	−	1.58737i	−0.0500130	−	0.114559i
$193$	−11.0921	−	11.0921i	−0.798428	−	0.798428i	0.184419	−	0.982848i	$-0.440960\pi$
$193$	−11.0921	−	11.0921i	−0.798428	−	0.798428i	−0.982848	+	0.184419i	$0.940960\pi$
$194$	−0.744401	+	2.29103i	−0.0534449	+	0.164486i
$195$		0			0
$196$	−0.895859	−	2.75717i	−0.0639899	−	0.196941i
$197$	−8.05955	+	15.8178i	−0.574219	+	1.12697i	0.403091	+	0.915160i	$0.367936\pi$
$197$	−8.05955	+	15.8178i	−0.574219	+	1.12697i	−0.977311	+	0.211809i	$0.932064\pi$
$198$	−0.623483	−	16.4592i	−0.0443090	−	1.16970i
$199$			2.78155i			0.197179i	0.995128	+	0.0985894i	$0.0314330\pi$
$199$			2.78155i			0.197179i	−0.995128	+	0.0985894i	$0.968567\pi$
$200$		0			0
$201$	−4.31751	−	0.257666i	−0.304533	−	0.0181743i
$202$	−7.50760	+	1.18909i	−0.528233	+	0.0836639i
$203$	−13.6540	−	6.95707i	−0.958324	−	0.488290i
$204$	0.0975621	+	0.374958i	0.00683072	+	0.0262523i
$205$		0			0
$206$	8.12095	+	2.63866i	0.565813	+	0.183844i
$207$	−4.02640	−	5.12227i	−0.279854	−	0.356022i
$208$	5.71986	−	2.91441i	0.396601	−	0.202078i
$209$	−9.61624	+	6.98661i	−0.665169	+	0.483274i
$210$		0			0
$211$	−11.4724	−	8.33520i	−0.789794	−	0.573819i	0.118108	−	0.993001i	$-0.462317\pi$
$211$	−11.4724	−	8.33520i	−0.789794	−	0.573819i	−0.907902	+	0.419182i	$0.862317\pi$
$212$	12.1067	+	1.91752i	0.831493	+	0.131695i
$213$	−2.26054	+	10.2684i	−0.154889	+	0.703581i
$214$	−3.00037	+	4.12966i	−0.205101	+	0.282298i
$215$		0			0
$216$	−2.25777	−	4.68001i	−0.153622	−	0.318434i
$217$	2.81138	+	5.51765i	0.190849	+	0.374562i
$218$	6.91725	−	6.91725i	0.468495	−	0.468495i
$219$	−4.93039	−	1.93372i	−0.333165	−	0.130669i
$220$		0			0
$221$	−1.36571	+	0.443745i	−0.0918674	+	0.0298495i
$222$	5.73911	−	9.77609i	0.385184	−	0.656128i
$223$	−0.849459	−	5.36327i	−0.0568840	−	0.359151i	−0.999668	−	0.0257485i	$-0.991803\pi$
$223$	−0.849459	−	5.36327i	−0.0568840	−	0.359151i	0.942784	−	0.333403i	$-0.108197\pi$
$224$	2.02508			0.135306
$225$		0			0
$226$	−13.1700			−0.876055
$227$	3.12180	+	19.7103i	0.207201	+	1.30822i	0.843649	+	0.536896i	$0.180403\pi$
$227$	3.12180	+	19.7103i	0.207201	+	1.30822i	−0.636448	+	0.771320i	$0.719597\pi$
$228$	−1.89840	+	3.23376i	−0.125725	+	0.214161i
$229$	−10.9433	+	3.55568i	−0.723151	+	0.234966i	−0.647389	−	0.762160i	$-0.724139\pi$
$229$	−10.9433	+	3.55568i	−0.723151	+	0.234966i	−0.0757621	+	0.997126i	$0.524139\pi$
$230$		0			0
$231$	17.9280	+	7.03142i	1.17957	+	0.462633i
$232$	−5.35085	+	5.35085i	−0.351300	+	0.351300i
$233$	2.20854	+	4.33449i	0.144686	+	0.283962i	0.951964	−	0.306208i	$-0.0990605\pi$
$233$	2.20854	+	4.33449i	0.144686	+	0.283962i	−0.807279	+	0.590171i	$0.799060\pi$
$234$	16.8163	−	9.38652i	1.09932	−	0.613616i
$235$		0			0
$236$	−3.35071	+	4.61185i	−0.218112	+	0.300206i
$237$	−4.30783	+	19.5682i	−0.279824	+	1.27109i
$238$	−0.447413	−	0.0708632i	−0.0290015	−	0.00459338i
$239$	13.5737	+	9.86185i	0.878008	+	0.637910i	0.932724	−	0.360592i	$-0.117425\pi$
$239$	13.5737	+	9.86185i	0.878008	+	0.637910i	−0.0547159	+	0.998502i	$0.517425\pi$
$240$		0			0
$241$	13.7609	−	9.99786i	0.886416	−	0.644019i	−0.0485253	−	0.998822i	$-0.515452\pi$
$241$	13.7609	−	9.99786i	0.886416	−	0.644019i	0.934941	+	0.354803i	$0.115452\pi$
$242$	17.0571	−	8.69105i	1.09648	−	0.558682i
$243$	−7.29993	−	13.7736i	−0.468291	−	0.883574i
$244$	−3.00392	−	0.976034i	−0.192307	−	0.0624842i
$245$		0			0
$246$	0.665307	+	2.55696i	0.0424184	+	0.163026i
$247$	−12.3833	−	6.30958i	−0.787928	−	0.401469i
$248$	3.02031	−	0.478370i	0.191790	−	0.0303765i
$249$	−18.0779	−	1.07888i	−1.14564	−	0.0683711i
$250$		0			0
$251$		−	27.1027i		−	1.71071i	−0.518046	−	0.855353i	$-0.673340\pi$
$251$		−	27.1027i		−	1.71071i	0.518046	−	0.855353i	$-0.326660\pi$
$252$	6.07088	−	0.229968i	0.382429	−	0.0144866i
$253$	5.41327	−	10.6241i	0.340330	−	0.667934i
$254$	−3.54883	−	10.9222i	−0.222673	−	0.685318i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−11.8188	−	11.8188i	−0.737238	−	0.737238i	0.234805	−	0.972043i	$-0.424555\pi$
$257$	−11.8188	−	11.8188i	−0.737238	−	0.737238i	−0.972043	+	0.234805i	$0.924555\pi$
$258$	−2.10108	−	4.81268i	−0.130807	−	0.299624i
$259$	7.79053	+	10.7227i	0.484080	+	0.666279i
$260$		0			0
$261$	−15.4334	+	16.6487i	−0.955303	+	1.03053i
$262$	1.61582	−	10.2019i	0.0998256	−	0.630274i
$263$	1.14180	−	7.20902i	0.0704062	−	0.444527i	−0.927152	−	0.374686i	$-0.877751\pi$
$263$	1.14180	−	7.20902i	0.0704062	−	0.444527i	0.997558	−	0.0698415i	$-0.0222493\pi$
$264$	6.03795	−	7.34671i	0.371610	−	0.452159i
$265$		0			0
$266$	−2.57697	−	3.54690i	−0.158004	−	0.217474i
$267$	−14.4088	+	6.29048i	−0.881807	+	0.384971i
$268$	−1.76575	−	1.76575i	−0.107860	−	0.107860i
$269$	−9.50784	+	29.2621i	−0.579703	+	1.78414i	0.0398701	+	0.999205i	$0.487306\pi$
$269$	−9.50784	+	29.2621i	−0.579703	+	1.78414i	−0.619573	+	0.784939i	$0.712694\pi$
$270$		0			0
$271$	4.91027	+	15.1123i	0.298278	+	0.918004i	0.982101	+	0.188356i	$0.0603160\pi$
$271$	4.91027	+	15.1123i	0.298278	+	0.918004i	−0.683823	+	0.729648i	$0.739684\pi$
$272$	−0.101553	+	0.199309i	−0.00615756	+	0.0120849i
$273$	2.19126	+	22.4099i	0.132621	+	1.35631i
$274$		−	13.4899i		−	0.814956i
$275$		0			0
$276$	0.224092	−	3.75495i	0.0134888	−	0.226021i
$277$	9.49399	−	1.50370i	0.570438	−	0.0903486i	0.135449	−	0.990784i	$-0.456752\pi$
$277$	9.49399	−	1.50370i	0.570438	−	0.0903486i	0.434989	+	0.900436i	$0.356752\pi$
$278$	10.1480	+	5.17068i	0.608638	+	0.310117i
$279$	9.00011	−	1.77707i	0.538822	−	0.106390i
$280$		0			0
$281$	19.6851	+	6.39607i	1.17431	+	0.381558i	0.830251	−	0.557389i	$-0.188197\pi$
$281$	19.6851	+	6.39607i	1.17431	+	0.381558i	0.344062	+	0.938947i	$0.388197\pi$
$282$	−6.77626	+	6.01300i	−0.403520	+	0.358069i
$283$	−10.8711	+	5.53912i	−0.646222	+	0.329267i	−0.746199	−	0.665723i	$-0.768123\pi$
$283$	−10.8711	+	5.53912i	−0.646222	+	0.329267i	0.0999766	+	0.994990i	$0.468123\pi$
$284$	−4.91108	+	3.56811i	−0.291419	+	0.211728i
$285$		0			0
$286$	28.5141	+	20.7167i	1.68608	+	1.22501i
$287$	−3.05105	−	0.483239i	−0.180098	−	0.0285247i
$288$	0.818384	−	2.88622i	0.0482238	−	0.170072i
$289$	−9.96294	+	13.7128i	−0.586055	+	0.806636i
$290$		0			0
$291$	−3.51564	+	2.24702i	−0.206091	+	0.131723i
$292$	−1.38815	−	2.72440i	−0.0812354	−	0.159433i
$293$	−0.153372	+	0.153372i	−0.00896009	+	0.00896009i	−0.711573	−	0.702613i	$-0.752017\pi$
$293$	−0.153372	+	0.153372i	−0.00896009	+	0.00896009i	0.702613	+	0.711573i	$0.252017\pi$
$294$	1.83341	−	4.67464i	0.106927	−	0.272630i
$295$		0			0
$296$	6.22462	−	2.02250i	0.361799	−	0.117556i
$297$	17.2666	−	22.7100i	1.00191	−	1.31777i
$298$	0.934161	+	5.89806i	0.0541145	+	0.341666i
$299$	13.9418			0.806276
$300$		0			0
$301$	6.13974			0.353889
$302$	−0.472718	−	2.98463i	−0.0272019	−	0.171746i
$303$	−11.3538	−	6.66529i	−0.652256	−	0.382911i
$304$	−2.05900	+	0.669009i	−0.118092	+	0.0383703i
$305$		0			0
$306$	−0.281808	+	0.609032i	−0.0161099	+	0.0348160i
$307$	4.76351	−	4.76351i	0.271868	−	0.271868i	−0.557984	−	0.829852i	$-0.688425\pi$
$307$	4.76351	−	4.76351i	0.271868	−	0.271868i	0.829852	+	0.557984i	$0.188425\pi$
$308$	5.04762	+	9.90651i	0.287615	+	0.564476i
$309$	7.96496	+	12.4618i	0.453111	+	0.708927i
$310$		0			0
$311$	−17.8640	+	24.5877i	−1.01298	+	1.39424i	−0.0959647	+	0.995385i	$0.530594\pi$
$311$	−17.8640	+	24.5877i	−1.01298	+	1.39424i	−0.917012	+	0.398859i	$0.869406\pi$
$312$	10.8590	+	2.39054i	0.614768	+	0.135338i
$313$	−8.62568	−	1.36617i	−0.487552	−	0.0772206i	−0.0921812	−	0.995742i	$-0.529384\pi$
$313$	−8.62568	−	1.36617i	−0.487552	−	0.0772206i	−0.395371	+	0.918522i	$0.629384\pi$
$314$	−5.04439	−	3.66496i	−0.284671	−	0.206826i
$315$		0			0
$316$	−9.35889	+	6.79963i	−0.526479	+	0.382509i
$317$	−8.99167	+	4.58149i	−0.505023	+	0.257322i	−0.687889	−	0.725816i	$-0.741462\pi$
$317$	−8.99167	+	4.58149i	−0.505023	+	0.257322i	0.182866	+	0.983138i	$0.441462\pi$
$318$	14.0915	+	15.8801i	0.790210	+	0.890514i
$319$	−39.5132	−	12.8386i	−2.21231	−	0.718825i
$320$		0			0
$321$	−8.55642	+	2.22634i	−0.477573	+	0.124262i
$322$	3.91866	+	1.99666i	0.218378	+	0.111269i
$323$	0.478317	−	0.0757580i	0.0266143	−	0.00421529i
$324$	2.12563	−	8.74538i	0.118091	−	0.485854i
$325$		0			0
$326$			5.73079i			0.317399i
$327$	16.8633	−	1.64891i	0.932543	−	0.0911849i
$328$	−0.692523	+	1.35915i	−0.0382382	+	0.0750467i
$329$	−3.27315	−	10.0737i	−0.180455	−	0.555382i
$330$		0			0
$331$	−7.78449	+	23.9582i	−0.427874	+	1.31686i	0.472341	+	0.881416i	$0.343409\pi$
$331$	−7.78449	+	23.9582i	−0.427874	+	1.31686i	−0.900215	+	0.435445i	$0.856591\pi$
$332$	−7.39341	−	7.39341i	−0.405766	−	0.405766i
$333$	18.4308	−	6.77003i	1.01000	−	0.370995i
$334$	5.73229	+	7.88982i	0.313657	+	0.431712i
$335$		0			0
$336$	2.70980	+	2.22707i	0.147832	+	0.121496i
$337$	4.74900	−	29.9840i	0.258694	−	1.63333i	−0.426157	−	0.904649i	$-0.640133\pi$
$337$	4.74900	−	29.9840i	0.258694	−	1.63333i	0.684852	−	0.728683i	$-0.259867\pi$
$338$	−4.41311	+	27.8633i	−0.240042	+	1.51556i
$339$	−17.6230	−	14.4836i	−0.957151	−	0.786642i
$340$		0			0
$341$	9.86844	+	13.5827i	0.534406	+	0.735546i
$342$	−6.09659	+	2.23941i	−0.329666	+	0.121093i
$343$	14.1749	+	14.1749i	0.765374	+	0.765374i
$344$	0.936894	−	2.88346i	0.0505139	−	0.155466i
$345$		0			0
$346$	−5.42059	−	16.6829i	−0.291413	−	0.896877i
$347$	−11.2852	+	22.1485i	−0.605823	+	1.18899i	0.360765	+	0.932657i	$0.382516\pi$
$347$	−11.2852	+	22.1485i	−0.605823	+	1.18899i	−0.966587	+	0.256337i	$0.917484\pi$
$348$	−13.0446	+	1.27552i	−0.699266	+	0.0683749i
$349$		−	7.66380i		−	0.410234i	−0.978737	−	0.205117i	$-0.934243\pi$
$349$		−	7.66380i		−	0.410234i	0.978737	−	0.205117i	$-0.0657575\pi$
$350$		0			0
$351$	32.8250	+	5.93334i	1.75207	+	0.316698i
$352$	5.42273	−	0.858876i	0.289033	−	0.0457783i
$353$	−2.41473	−	1.23037i	−0.128523	−	0.0654859i	0.388547	−	0.921429i	$-0.372977\pi$
$353$	−2.41473	−	1.23037i	−0.128523	−	0.0654859i	−0.517070	+	0.855943i	$0.672977\pi$
$354$	−9.55550	+	2.48629i	−0.507869	+	0.132145i
$355$		0			0
$356$	−8.63290	−	2.80500i	−0.457543	−	0.148665i
$357$	−0.520760	−	0.586863i	−0.0275616	−	0.0310601i
$358$	10.3557	−	5.27651i	0.547317	−	0.278872i
$359$	−3.19128	+	2.31860i	−0.168429	+	0.122371i	−0.668807	−	0.743436i	$-0.733195\pi$
$359$	−3.19128	+	2.31860i	−0.168429	+	0.122371i	0.500377	+	0.865807i	$0.333195\pi$
$360$		0			0
$361$	−11.5794	−	8.41294i	−0.609443	−	0.442787i
$362$	−3.90603	−	0.618655i	−0.205297	−	0.0325158i
$363$	32.3824	+	7.12882i	1.69964	+	0.374166i
$364$	−7.64126	+	10.5173i	−0.400511	+	0.551256i
$365$		0			0
$366$	−2.94622	−	4.60960i	−0.154002	−	0.240947i
$367$	12.7890	+	25.0999i	0.667581	+	1.31020i	0.937724	+	0.347381i	$0.112929\pi$
$367$	12.7890	+	25.0999i	0.667581	+	1.31020i	−0.270143	+	0.962820i	$0.587071\pi$
$368$	1.53568	−	1.53568i	0.0800527	−	0.0800527i
$369$	−1.92173	+	4.15318i	−0.100042	+	0.216206i
$370$		0			0
$371$	−23.6077	+	7.67062i	−1.22565	+	0.398239i
$372$	4.56762	+	2.68145i	0.236820	+	0.139027i
$373$	4.08750	+	25.8075i	0.211643	+	1.33626i	0.833235	+	0.552919i	$0.186486\pi$
$373$	4.08750	+	25.8075i	0.211643	+	1.33626i	−0.621592	+	0.783341i	$0.713514\pi$
$374$	−1.22813			−0.0635052
$375$		0			0
$376$	−5.23048			−0.269742
$377$	−7.59932	−	47.9802i	−0.391385	−	2.47111i
$378$	8.37647	+	6.36868i	0.430839	+	0.327570i
$379$	−20.6572	+	6.71194i	−1.06109	+	0.344769i	−0.787012	−	0.616938i	$-0.788373\pi$
$379$	−20.6572	+	6.71194i	−1.06109	+	0.344769i	−0.274079	+	0.961707i	$0.588373\pi$
$380$		0			0
$381$	7.26283	−	18.5180i	0.372086	−	0.948705i
$382$	11.9009	−	11.9009i	0.608905	−	0.608905i
$383$	−10.8440	−	21.2826i	−0.554104	−	1.08749i	−0.982909	−	0.184093i	$-0.941065\pi$
$383$	−10.8440	−	21.2826i	−0.554104	−	1.08749i	0.428805	−	0.903397i	$-0.358935\pi$
$384$	1.45942	−	0.932788i	0.0744757	−	0.0476011i
$385$		0			0
$386$	9.22037	−	12.6908i	0.469304	−	0.645942i
$387$	2.48122	−	8.75058i	0.126128	−	0.444817i
$388$	−2.37927	−	0.376840i	−0.120789	−	0.0191311i
$389$	14.6439	+	10.6394i	0.742476	+	0.539440i	0.893486	−	0.449092i	$-0.148252\pi$
$389$	14.6439	+	10.6394i	0.742476	+	0.539440i	−0.151010	+	0.988532i	$0.548252\pi$
$390$		0			0
$391$	−0.393024	+	0.285549i	−0.0198761	+	0.0144408i
$392$	2.58308	−	1.31615i	0.130465	−	0.0664754i
$393$	13.3816	−	11.8743i	0.675013	−	0.598982i
$394$	−16.8838	−	5.48588i	−0.850594	−	0.276375i
$395$		0			0
$396$	16.1590	−	3.19059i	0.812020	−	0.160333i
$397$	12.5321	+	6.38543i	0.628969	+	0.320476i	0.739257	−	0.673424i	$-0.235177\pi$
$397$	12.5321	+	6.38543i	0.628969	+	0.320476i	−0.110287	+	0.993900i	$0.535177\pi$
$398$	−2.74730	+	0.435130i	−0.137710	+	0.0218111i
$399$	0.452380	−	7.58019i	0.0226473	−	0.379484i
$400$		0			0
$401$			0.841787i			0.0420368i	0.999779	+	0.0210184i	$0.00669086\pi$
$401$			0.841787i			0.0420368i	−0.999779	+	0.0210184i	$0.993309\pi$
$402$	−0.420913	−	4.30466i	−0.0209933	−	0.214697i
$403$	−8.91216	+	17.4911i	−0.443946	+	0.871293i
$404$	−2.34889	−	7.22915i	−0.116862	−	0.359664i
$405$		0			0
$406$	4.73546	−	14.5742i	0.235017	−	0.723307i
$407$	25.4091	+	25.4091i	1.25948	+	1.25948i
$408$	−0.355079	+	0.155017i	−0.0175790	+	0.00767450i
$409$	−8.95042	−	12.3192i	−0.442570	−	0.609145i	0.528211	−	0.849113i	$-0.322863\pi$
$409$	−8.95042	−	12.3192i	−0.442570	−	0.609145i	−0.970781	+	0.239968i	$0.922863\pi$
$410$		0			0
$411$	14.8354	−	18.0511i	0.731779	−	0.890396i
$412$	−1.33577	+	8.43375i	−0.0658089	+	0.415501i
$413$	1.80589	−	11.4020i	0.0888622	−	0.561054i
$414$	4.42934	−	4.77812i	0.217690	−	0.234832i
$415$		0			0
$416$	3.77332	+	5.19352i	0.185002	+	0.254633i
$417$	7.89285	+	18.0792i	0.386515	+	0.885343i
$418$	−8.40490	−	8.40490i	−0.411097	−	0.411097i
$419$	0.0964938	−	0.296977i	0.00471403	−	0.0145083i	−0.948672	−	0.316262i	$-0.897572\pi$
$419$	0.0964938	−	0.296977i	0.00471403	−	0.0145083i	0.953386	+	0.301754i	$0.0975721\pi$
$420$		0			0
$421$	11.7686	+	36.2199i	0.573565	+	1.76525i	0.641015	+	0.767528i	$0.278514\pi$
$421$	11.7686	+	36.2199i	0.573565	+	1.76525i	−0.0674500	+	0.997723i	$0.521486\pi$
$422$	6.43790	−	12.6351i	0.313392	−	0.615067i
$423$	−15.6802	+	0.593975i	−0.762398	+	0.0288800i
$424$			12.2576i			0.595283i
$425$		0			0
$426$	−10.4956	−	0.626372i	−0.508515	−	0.0303478i
$427$	6.31749	−	1.00059i	0.305725	−	0.0484220i
$428$	−4.54817	−	2.31741i	−0.219844	−	0.112016i
$429$	15.3722	+	59.0797i	0.742179	+	2.85240i
$430$		0			0
$431$	−23.0434	−	7.48726i	−1.10996	−	0.360648i	−0.304033	−	0.952661i	$-0.598333\pi$
$431$	−23.0434	−	7.48726i	−1.10996	−	0.360648i	−0.805928	+	0.592013i	$0.798333\pi$
$432$	4.26919	−	2.96209i	0.205402	−	0.142514i
$433$	−4.82804	+	2.46001i	−0.232021	+	0.118220i	−0.566136	−	0.824312i	$-0.691562\pi$
$433$	−4.82804	+	2.46001i	−0.232021	+	0.118220i	0.334116	+	0.942532i	$0.391562\pi$
$434$	−5.00992	+	3.63992i	−0.240484	+	0.174722i
$435$		0			0
$436$	7.91418	+	5.74999i	0.379021	+	0.275375i
$437$	−4.64392	−	0.735524i	−0.222149	−	0.0351849i
$438$	1.13863	−	5.17219i	0.0544058	−	0.247137i
$439$	15.7160	−	21.6312i	0.750083	−	1.03240i	−0.247892	−	0.968788i	$-0.579738\pi$
$439$	15.7160	−	21.6312i	0.750083	−	1.03240i	0.997975	−	0.0636130i	$-0.0202623\pi$
$440$		0			0
$441$	7.59423	−	4.23894i	0.361630	−	0.201854i
$442$	−0.651925	−	1.27948i	−0.0310089	−	0.0608585i
$443$	−16.9801	+	16.9801i	−0.806749	+	0.806749i	−0.984140	−	0.177391i	$-0.943234\pi$
$443$	−16.9801	+	16.9801i	−0.806749	+	0.806749i	0.177391	+	0.984140i	$0.443234\pi$
$444$	10.5535	+	4.13914i	0.500848	+	0.196435i
$445$		0			0
$446$	5.16436	−	1.67800i	0.244539	−	0.0794557i
$447$	−5.23633	+	8.91965i	−0.247670	+	0.421885i
$448$	0.316792	+	2.00015i	0.0149670	+	0.0944980i
$449$	−6.98488			−0.329637			−0.164818	−	0.986324i	$-0.552704\pi$
$449$	−6.98488			−0.329637			−0.164818	+	0.986324i	$0.552704\pi$
$450$		0			0
$451$	−8.37502			−0.394364
$452$	−2.06024	−	13.0078i	−0.0969055	−	0.611837i
$453$	2.64977	−	4.51366i	0.124497	−	0.212070i
$454$	−18.9792	+	6.16673i	−0.890739	+	0.289419i
$455$		0			0
$456$	−3.49092	−	1.36915i	−0.163477	−	0.0641165i
$457$	4.53549	−	4.53549i	0.212161	−	0.212161i	−0.593024	−	0.805185i	$-0.702066\pi$
$457$	4.53549	−	4.53549i	0.212161	−	0.212161i	0.805185	+	0.593024i	$0.202066\pi$
$458$	−5.22381	−	10.2523i	−0.244092	−	0.479058i
$459$	−1.04687	+	0.505042i	−0.0488637	+	0.0235733i
$460$		0			0
$461$	1.73628	−	2.38979i	0.0808667	−	0.111303i	−0.766667	−	0.642045i	$-0.778086\pi$
$461$	1.73628	−	2.38979i	0.0808667	−	0.111303i	0.847534	+	0.530741i	$0.178086\pi$
$462$	−4.14030	+	18.8072i	−0.192624	+	0.874990i
$463$	28.2610	+	4.47610i	1.31340	+	0.208022i	0.773547	−	0.633739i	$-0.218481\pi$
$463$	28.2610	+	4.47610i	1.31340	+	0.208022i	0.539851	+	0.841761i	$0.318481\pi$
$464$	−6.12203	−	4.44791i	−0.284208	−	0.206489i
$465$		0			0
$466$	−3.93564	+	2.85941i	−0.182315	+	0.132460i
$467$	4.07796	−	2.07783i	0.188706	−	0.0961504i	−0.357085	−	0.934072i	$-0.616229\pi$
$467$	4.07796	−	2.07783i	0.188706	−	0.0961504i	0.545791	+	0.837922i	$0.316229\pi$
$468$	11.9016	+	15.1409i	0.550152	+	0.699889i
$469$	4.80942	+	1.56267i	0.222078	+	0.0721576i
$470$		0			0
$471$	−2.71948	−	10.4517i	−0.125307	−	0.481588i
$472$	−5.07924	−	2.58800i	−0.233791	−	0.119122i
$473$	16.4409	−	2.60399i	0.755955	−	0.119731i
$474$	−20.0012	−	1.19365i	−0.918684	−	0.0548264i
$475$		0			0
$476$		−	0.452990i		−	0.0207628i
$477$	1.39198	+	36.7465i	0.0637343	+	1.68251i
$478$	−7.61704	+	14.9493i	−0.348395	+	0.683765i
$479$	−8.54601	−	26.3019i	−0.390477	−	1.20176i	−0.932428	−	0.361355i	$-0.882314\pi$
$479$	−8.54601	−	26.3019i	−0.390477	−	1.20176i	0.541951	−	0.840410i	$-0.317686\pi$
$480$		0			0
$481$	−12.9836	+	39.9593i	−0.591999	+	1.82199i
$482$	12.0274	+	12.0274i	0.547835	+	0.547835i
$483$	3.04783	+	6.98129i	0.138681	+	0.317660i
$484$	11.2524	+	15.4876i	0.511472	+	0.703980i
$485$		0			0
$486$	12.4620	−	9.36471i	0.565289	−	0.424792i
$487$	4.73443	−	29.8920i	0.214538	−	1.35454i	−0.611644	−	0.791133i	$-0.709491\pi$
$487$	4.73443	−	29.8920i	0.214538	−	1.35454i	0.826182	−	0.563404i	$-0.190509\pi$
$488$	0.494100	−	3.11963i	0.0223669	−	0.141219i
$489$	−6.30240	+	7.66848i	−0.285004	+	0.346781i
$490$		0			0
$491$	4.84555	+	6.66933i	0.218677	+	0.300982i	0.904235	−	0.427035i	$-0.140442\pi$
$491$	4.84555	+	6.66933i	0.218677	+	0.300982i	−0.685558	+	0.728018i	$0.740442\pi$
$492$	−2.42140	+	1.05711i	−0.109165	+	0.0476583i
$493$	1.19693	+	1.19693i	0.0539071	+	0.0539071i
$494$	4.29473	−	13.2178i	0.193229	−	0.594698i
$495$		0			0
$496$	0.944961	+	2.90829i	0.0424300	+	0.130586i
$497$	5.58095	−	10.9532i	0.250340	−	0.491320i
$498$	−1.76242	−	18.0241i	−0.0789757	−	0.807680i
$499$			38.0463i			1.70318i	0.524205	+	0.851592i	$0.324363\pi$
$499$			38.0463i			1.70318i	−0.524205	+	0.851592i	$0.675637\pi$
$500$		0			0
$501$	−1.00629	+	16.8616i	−0.0449576	+	0.753320i
$502$	26.7690	−	4.23979i	1.19476	−	0.189231i
$503$	33.9723	+	17.3097i	1.51475	+	0.771804i	0.996513	−	0.0834338i	$-0.0265887\pi$
$503$	33.9723	+	17.3097i	1.51475	+	0.771804i	0.518236	+	0.855237i	$0.326589\pi$
$504$	1.17683	+	5.96016i	0.0524203	+	0.265487i
$505$		0			0
$506$	11.3402	+	3.68464i	0.504132	+	0.163802i
$507$	−36.5477	+	32.4311i	−1.62314	+	1.44032i
$508$	10.2325	−	5.21374i	0.453996	−	0.231322i
$509$	−5.62616	+	4.08765i	−0.249375	+	0.181182i	−0.705450	−	0.708760i	$-0.749255\pi$
$509$	−5.62616	+	4.08765i	−0.249375	+	0.181182i	0.456075	+	0.889942i	$0.349255\pi$
$510$		0			0
$511$	5.00944	+	3.63957i	0.221605	+	0.161005i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	−10.6207	−	3.70809i	−0.468917	−	0.163716i
$514$	9.82444	−	13.5222i	0.433337	−	0.596438i
$515$		0			0
$516$	4.42475	−	2.82808i	0.194789	−	0.124499i
$517$	−13.0373	−	25.5871i	−0.573379	−	1.12532i
$518$	−9.37203	+	9.37203i	−0.411783	+	0.411783i
$519$	11.0935	−	28.2849i	0.486950	−	1.24157i
$520$		0			0
$521$	20.6631	−	6.71385i	0.905267	−	0.294139i	0.180858	−	0.983509i	$-0.442113\pi$
$521$	20.6631	−	6.71385i	0.905267	−	0.294139i	0.724409	+	0.689370i	$0.242113\pi$
$522$	−18.8580	−	12.6390i	−0.825394	−	0.553192i
$523$	−6.72718	−	42.4737i	−0.294159	−	1.85725i	−0.483513	−	0.875337i	$-0.660639\pi$
$523$	−6.72718	−	42.4737i	−0.294159	−	1.85725i	0.189354	−	0.981909i	$-0.439361\pi$
$524$	10.3290			0.451226
$525$		0			0
$526$	7.29888			0.318246
$527$	−0.107007	−	0.675613i	−0.00466128	−	0.0294302i
$528$	8.20081	+	4.81433i	0.356894	+	0.209517i
$529$	−17.3885	+	5.64988i	−0.756023	+	0.245647i
$530$		0			0
$531$	−15.5207	−	7.18164i	−0.673541	−	0.311657i
$532$	3.10010	−	3.10010i	0.134407	−	0.134407i
$533$	−4.44569	−	8.72515i	−0.192564	−	0.377928i
$534$	−8.46707	−	13.2474i	−0.366406	−	0.573271i
$535$		0			0
$536$	1.46779	−	2.02024i	0.0633987	−	0.0872609i
$537$	19.6600	+	4.32805i	0.848392	+	0.186769i
$538$	−30.3892	−	4.81318i	−1.31017	−	0.207511i
$539$	12.8769	+	9.35565i	0.554649	+	0.402976i
$540$		0			0
$541$	−8.60979	+	6.25538i	−0.370164	+	0.268940i	−0.757279	−	0.653092i	$-0.773472\pi$
$541$	−8.60979	+	6.25538i	−0.370164	+	0.268940i	0.387115	+	0.922031i	$0.373472\pi$
$542$	−14.1581	+	7.21390i	−0.608141	+	0.309863i
$543$	−4.54638	−	5.12347i	−0.195104	−	0.219869i
$544$	−0.212742	−	0.0691240i	−0.00912123	−	0.00296367i
$545$		0			0
$546$	−21.7912	+	5.66997i	−0.932579	+	0.242652i
$547$	12.7347	+	6.48863i	0.544495	+	0.277434i	0.704526	−	0.709678i	$-0.251160\pi$
$547$	12.7347	+	6.48863i	0.544495	+	0.277434i	−0.160031	+	0.987112i	$0.551160\pi$
$548$	13.3238	−	2.11029i	0.569166	−	0.0901470i
$549$	1.12697	−	9.40828i	0.0480980	−	0.401536i
$550$		0			0
$551$			16.3828i			0.697929i
$552$	3.74377	−	0.366069i	0.159346	−	0.0155809i
$553$	10.6354	−	20.8732i	0.452265	−	0.887619i
$554$	2.97037	+	9.14187i	0.126199	+	0.388401i
$555$		0			0
$556$	−3.51952	+	10.8320i	−0.149261	+	0.459377i
$557$	−3.60663	−	3.60663i	−0.152818	−	0.152818i	0.626557	−	0.779375i	$-0.284463\pi$
$557$	−3.60663	−	3.60663i	−0.152818	−	0.152818i	−0.779375	+	0.626557i	$0.784463\pi$
$558$	3.16312	+	8.61131i	0.133905	+	0.364546i
$559$	11.4401	+	15.7460i	0.483866	+	0.665985i
$560$		0			0
$561$	−1.64339	−	1.35063i	−0.0693839	−	0.0570236i
$562$	−3.23790	+	20.4433i	−0.136583	+	0.862349i
$563$	3.98324	−	25.1492i	0.167874	−	1.05991i	−0.749534	−	0.661965i	$-0.769723\pi$
$563$	3.98324	−	25.1492i	0.167874	−	1.05991i	0.917408	−	0.397948i	$-0.130277\pi$
$564$	−6.99901	−	5.75219i	−0.294712	−	0.242211i
$565$		0			0
$566$	−7.17155	−	9.87079i	−0.301443	−	0.414900i
$567$	4.20480	+	17.7340i	0.176585	+	0.744759i
$568$	−4.29245	−	4.29245i	−0.180107	−	0.180107i
$569$	9.49637	−	29.2268i	0.398108	−	1.22525i	−0.528406	−	0.848992i	$-0.677210\pi$
$569$	9.49637	−	29.2268i	0.398108	−	1.22525i	0.926514	−	0.376260i	$-0.122790\pi$
$570$		0			0
$571$	−6.95564	−	21.4073i	−0.291085	−	0.895866i	−0.984509	−	0.175336i	$-0.943899\pi$
$571$	−6.95564	−	21.4073i	−0.291085	−	0.895866i	0.693424	−	0.720530i	$-0.256101\pi$
$572$	−16.0011	+	31.4039i	−0.669039	+	1.31306i
$573$	29.0128	−	2.83690i	1.21203	−	0.118513i
$574$		−	3.08908i		−	0.128936i
$575$		0			0
$576$	2.97871	+	0.356805i	0.124113	+	0.0148669i
$577$	−41.1545	+	6.51823i	−1.71328	+	0.271358i	−0.934508	−	0.355943i	$-0.884160\pi$
$577$	−41.1545	+	6.51823i	−1.71328	+	0.271358i	−0.778777	+	0.627301i	$0.784160\pi$
$578$	−15.1025	−	7.69512i	−0.628182	−	0.320075i
$579$	26.2945	−	6.84170i	1.09276	−	0.284332i
$580$		0			0
$581$	20.1376	+	6.54311i	0.835449	+	0.271454i
$582$	−2.76933	−	3.12085i	−0.114792	−	0.129363i
$583$	−59.9633	+	30.5528i	−2.48343	+	1.26537i
$584$	2.47370	−	1.79725i	0.102363	−	0.0743708i
$585$		0			0
$586$	−0.175477	−	0.127491i	−0.00724887	−	0.00526661i
$587$	−24.5435	−	3.88731i	−1.01302	−	0.160447i	−0.372212	−	0.928148i	$-0.621400\pi$
$587$	−24.5435	−	3.88731i	−1.01302	−	0.160447i	−0.640808	+	0.767701i	$0.721400\pi$
$588$	4.90389	+	1.07957i	0.202233	+	0.0445205i
$589$	3.89134	−	5.35598i	0.160340	−	0.220689i
$590$		0			0
$591$	−16.5595	−	25.9086i	−0.681167	−	1.06574i
$592$	2.97135	+	5.83160i	0.122122	+	0.239677i
$593$	−25.7915	+	25.7915i	−1.05913	+	1.05913i	−0.0609902	+	0.998138i	$0.519426\pi$
$593$	−25.7915	+	25.7915i	−1.05913	+	1.05913i	−0.998138	+	0.0609902i	$0.980574\pi$
$594$	25.1315	+	13.5014i	1.03116	+	0.553968i
$595$		0			0
$596$	−5.67931	+	1.84532i	−0.232634	+	0.0755873i
$597$	−4.15475	−	2.43907i	−0.170043	−	0.0998246i
$598$	2.18098	+	13.7702i	0.0891870	+	0.563104i
$599$	36.9040			1.50786			0.753929	−	0.656956i	$-0.228156\pi$
$599$	36.9040			1.50786			0.753929	+	0.656956i	$0.228156\pi$
$600$		0			0
$601$	20.4696			0.834972			0.417486	−	0.908683i	$-0.362911\pi$
$601$	20.4696			0.834972			0.417486	+	0.908683i	$0.362911\pi$
$602$	0.960467	+	6.06415i	0.0391457	+	0.247156i
$603$	4.17079	−	6.22305i	0.169848	−	0.253422i
$604$	2.87393	−	0.933797i	0.116939	−	0.0379956i
$605$		0			0
$606$	4.80711	−	12.2567i	0.195276	−	0.497893i
$607$	4.57545	−	4.57545i	0.185712	−	0.185712i	−0.608128	−	0.793839i	$-0.708079\pi$
$607$	4.57545	−	4.57545i	0.185712	−	0.185712i	0.793839	+	0.608128i	$0.208079\pi$
$608$	−0.982870	−	1.92899i	−0.0398607	−	0.0782309i
$609$	22.3645	−	14.2943i	0.906256	−	0.579234i
$610$		0			0
$611$	19.7363	−	27.1646i	0.798444	−	1.09896i
$612$	−0.645618	−	0.183064i	−0.0260976	−	0.00739994i
$613$	−29.0842	−	4.60648i	−1.17470	−	0.186054i	−0.461581	−	0.887098i	$-0.652718\pi$
$613$	−29.0842	−	4.60648i	−1.17470	−	0.186054i	−0.713118	+	0.701044i	$0.752718\pi$
$614$	5.45004	+	3.95968i	0.219946	+	0.159800i
$615$		0			0
$616$	−8.99493	+	6.53520i	−0.362416	+	0.263311i
$617$	22.4860	−	11.4572i	0.905254	−	0.461250i	0.0615777	−	0.998102i	$-0.480387\pi$
$617$	22.4860	−	11.4572i	0.905254	−	0.461250i	0.843676	+	0.536852i	$0.180387\pi$
$618$	−11.0624	+	9.81635i	−0.444994	+	0.394872i
$619$	2.83846	+	0.922271i	0.114087	+	0.0370692i	0.365504	−	0.930810i	$-0.380897\pi$
$619$	2.83846	+	0.922271i	0.114087	+	0.0370692i	−0.251417	+	0.967879i	$0.580897\pi$
$620$		0			0
$621$	11.1817	−	1.52256i	0.448706	−	0.0610984i
$622$	−27.0796	−	13.7977i	−1.08579	−	0.553239i
$623$	18.1557	−	2.87557i	0.727391	−	0.115207i
$624$	−0.662395	+	11.0992i	−0.0265170	+	0.444325i
$625$		0			0
$626$		−	8.73320i		−	0.349049i
$627$	−2.00353	−	20.4900i	−0.0800133	−	0.818292i
$628$	2.83072	−	5.55561i	0.112958	−	0.221693i
$629$	−0.452414	−	1.39239i	−0.0180389	−	0.0555181i
$630$		0			0
$631$	9.27752	−	28.5533i	0.369332	−	1.13669i	−0.577891	−	0.816114i	$-0.696124\pi$
$631$	9.27752	−	28.5533i	0.369332	−	1.13669i	0.947223	−	0.320574i	$-0.103876\pi$
$632$	−8.17997	−	8.17997i	−0.325382	−	0.325382i
$633$	22.5100	−	9.82723i	0.894694	−	0.390597i
$634$	−5.93169	−	8.16427i	−0.235577	−	0.324245i
$635$		0			0
$636$	−13.4802	+	16.4022i	−0.534526	+	0.650388i
$637$	−2.91135	+	18.3815i	−0.115352	+	0.728303i
$638$	6.49933	−	41.0351i	0.257311	−	1.62460i
$639$	−13.3556	−	12.3807i	−0.528338	−	0.489771i
$640$		0			0
$641$	−10.4719	−	14.4133i	−0.413614	−	0.569291i	0.550481	−	0.834847i	$-0.314444\pi$
$641$	−10.4719	−	14.4133i	−0.413614	−	0.569291i	−0.964095	+	0.265557i	$0.914444\pi$
$642$	−3.53745	−	8.10280i	−0.139612	−	0.319792i
$643$	−10.8997	−	10.8997i	−0.429840	−	0.429840i	0.458734	−	0.888574i	$-0.348303\pi$
$643$	−10.8997	−	10.8997i	−0.429840	−	0.429840i	−0.888574	+	0.458734i	$0.848303\pi$
$644$	−1.35906	+	4.18276i	−0.0535545	+	0.164824i
$645$		0			0
$646$	0.149651	+	0.460577i	0.00588792	+	0.0181212i
$647$	0.982107	−	1.92749i	0.0386106	−	0.0757776i	−0.870895	−	0.491469i	$-0.836460\pi$
$647$	0.982107	−	1.92749i	0.0386106	−	0.0757776i	0.909506	+	0.415691i	$0.136460\pi$
$648$	8.97023	+	0.731385i	0.352384	+	0.0287315i
$649$		−	31.2980i		−	1.22855i
$650$		0			0
$651$	−10.7069	−	0.638977i	−0.419635	−	0.0250435i
$652$	−5.66023	+	0.896493i	−0.221672	+	0.0351094i
$653$	−5.67905	−	2.89362i	−0.222238	−	0.113236i	0.339327	−	0.940668i	$-0.389801\pi$
$653$	−5.67905	−	2.89362i	−0.222238	−	0.113236i	−0.561565	+	0.827432i	$0.689801\pi$
$654$	4.26661	+	16.3977i	0.166838	+	0.641202i
$655$		0			0
$656$	−1.45075	−	0.471379i	−0.0566424	−	0.0184042i
$657$	7.21170	−	5.66880i	0.281355	−	0.221161i
$658$	9.43766	−	4.80873i	0.367918	−	0.187464i
$659$	−27.9601	+	20.3142i	−1.08917	+	0.791330i	−0.979259	−	0.202611i	$-0.935057\pi$
$659$	−27.9601	+	20.3142i	−1.08917	+	0.791330i	−0.109913	+	0.993941i	$0.535057\pi$
$660$		0			0
$661$	−33.8226	−	24.5736i	−1.31555	−	0.955801i	−0.999976	−	0.00689972i	$-0.997804\pi$
$661$	−33.8226	−	24.5736i	−1.31555	−	0.955801i	−0.315572	−	0.948902i	$-0.602196\pi$
$662$	−24.8810	−	3.94076i	−0.967027	−	0.153162i
$663$	0.534741	−	2.42904i	0.0207676	−	0.0943362i
$664$	6.14580	−	8.45897i	0.238503	−	0.328272i
$665$		0			0
$666$	9.56989	+	17.1448i	0.370826	+	0.664349i
$667$	−7.46104	−	14.6431i	−0.288893	−	0.566984i
$668$	−6.89596	+	6.89596i	−0.266813	+	0.266813i
$669$	8.75590	+	3.43410i	0.338523	+	0.132770i
$670$		0			0
$671$	16.4925	−	5.35875i	0.636687	−	0.206872i
$672$	−1.77574	+	3.02482i	−0.0685007	+	0.116685i
$673$	0.934113	+	5.89775i	0.0360074	+	0.227342i	0.999129	−	0.0417241i	$-0.0132851\pi$
$673$	0.934113	+	5.89775i	0.0360074	+	0.227342i	−0.963122	+	0.269066i	$0.913285\pi$
$674$	30.3577			1.16934
$675$		0			0
$676$	−28.2106			−1.08502
$677$	3.42993	+	21.6557i	0.131823	+	0.832297i	0.961651	+	0.274277i	$0.0884386\pi$
$677$	3.42993	+	21.6557i	0.131823	+	0.832297i	−0.829828	+	0.558020i	$0.811561\pi$
$678$	11.5484	−	19.6718i	0.443515	−	0.755490i
$679$	4.63951	−	1.50747i	0.178048	−	0.0578514i
$680$		0			0
$681$	−32.1783	−	12.6205i	−1.23308	−	0.483617i
$682$	−11.8717	+	11.8717i	−0.454593	+	0.454593i
$683$	5.64753	+	11.0839i	0.216097	+	0.424114i	0.973453	−	0.228888i	$-0.0735091\pi$
$683$	5.64753	+	11.0839i	0.216097	+	0.424114i	−0.757356	+	0.653002i	$0.773509\pi$
$684$	−3.16555	−	5.67121i	−0.121038	−	0.216844i
$685$		0			0
$686$	−11.7830	+	16.2179i	−0.449875	+	0.619200i
$687$	4.28482	−	19.4637i	0.163476	−	0.742585i
$688$	2.99453	+	0.474286i	0.114165	+	0.0180820i
$689$	−63.6603	−	46.2519i	−2.42526	−	1.76206i
$690$		0			0
$691$	6.87945	−	4.99821i	0.261706	−	0.190141i	−0.449193	−	0.893435i	$-0.648288\pi$
$691$	6.87945	−	4.99821i	0.261706	−	0.190141i	0.710899	+	0.703294i	$0.248288\pi$
$692$	15.6295	−	7.96363i	0.594145	−	0.302732i
$693$	−26.2233	+	20.6130i	−0.996141	+	0.783023i
$694$	−23.6412	−	7.68150i	−0.897408	−	0.291586i
$695$		0			0
$696$	−3.30044	−	12.6845i	−0.125103	−	0.480805i
$697$	0.304029	+	0.154911i	0.0115159	+	0.00586765i
$698$	7.56945	−	1.19888i	0.286508	−	0.0453784i
$699$	−8.41097	−	0.501961i	−0.318132	−	0.0189859i
$700$		0			0
$701$			19.8483i			0.749660i	0.927093	+	0.374830i	$0.122299\pi$
$701$			19.8483i			0.749660i	−0.927093	+	0.374830i	$0.877701\pi$
$702$	−0.725327	+	33.3491i	−0.0273757	+	1.25868i
$703$	6.43284	−	12.6252i	0.242619	−	0.476167i
$704$	1.69660	+	5.22161i	0.0639432	+	0.196797i
$705$		0			0
$706$	0.837472	−	2.57747i	0.0315187	−	0.0970045i
$707$	10.8845	+	10.8845i	0.409353	+	0.409353i
$708$	−3.95049	−	9.04891i	−0.148469	−	0.340079i
$709$	−2.74291	−	3.77529i	−0.103012	−	0.141784i	0.754399	−	0.656416i	$-0.227928\pi$
$709$	−2.74291	−	3.77529i	−0.103012	−	0.141784i	−0.857411	+	0.514632i	$0.827928\pi$
$710$		0			0
$711$	−25.4512	−	23.5934i	−0.954496	−	0.884821i
$712$	1.41998	−	8.96541i	0.0532160	−	0.335993i
$713$	−1.03891	+	6.55944i	−0.0389076	+	0.245653i
$714$	0.498173	−	0.606155i	0.0186436	−	0.0226848i
$715$		0			0
$716$	6.83154	+	9.40281i	0.255307	+	0.351399i
$717$	−26.6329	+	11.6271i	−0.994624	+	0.434224i
$718$	−2.78928	−	2.78928i	−0.104095	−	0.104095i
$719$	−5.35309	+	16.4751i	−0.199637	+	0.614418i	0.800255	+	0.599660i	$0.204698\pi$
$719$	−5.35309	+	16.4751i	−0.199637	+	0.614418i	−0.999891	+	0.0147577i	$0.995302\pi$
$720$		0			0
$721$	−5.34349	−	16.4456i	−0.199002	−	0.612465i
$722$	6.49795	−	12.7529i	0.241829	−	0.474615i
$723$	2.86706	+	29.3213i	0.106627	+	1.09047i
$724$		−	3.95472i		−	0.146976i
$725$		0			0
$726$	−1.97532	+	33.0989i	−0.0733111	+	1.22842i
$727$	5.26211	−	0.833437i	0.195161	−	0.0309105i	−0.0580887	−	0.998311i	$-0.518501\pi$
$727$	5.26211	−	0.833437i	0.195161	−	0.0309105i	0.253250	+	0.967401i	$0.418501\pi$
$728$	−11.5832	−	5.90192i	−0.429301	−	0.218740i
$729$	26.9745	+	1.17392i	0.999054	+	0.0434785i
$730$		0			0
$731$	−0.645002	−	0.209574i	−0.0238563	−	0.00775137i
$732$	4.09195	−	3.63105i	0.151243	−	0.134207i
$733$	14.8502	−	7.56657i	0.548506	−	0.279478i	−0.157697	−	0.987488i	$-0.550407\pi$
$733$	14.8502	−	7.56657i	0.548506	−	0.279478i	0.706202	+	0.708010i	$0.250407\pi$
$734$	−22.7902	+	16.5580i	−0.841201	+	0.611168i
$735$		0			0
$736$	1.75700	+	1.27654i	0.0647640	+	0.0470538i
$737$	13.5414	+	2.14474i	0.498803	+	0.0790026i
$738$	−4.40267	−	1.24837i	−0.162065	−	0.0459533i
$739$	−4.33206	+	5.96257i	−0.159357	+	0.219337i	−0.881228	−	0.472691i	$-0.843283\pi$
$739$	−4.33206	+	5.96257i	−0.159357	+	0.219337i	0.721871	+	0.692028i	$0.243283\pi$
$740$		0			0
$741$	20.2831	−	12.9639i	0.745118	−	0.476242i
$742$	−11.2692	−	22.1171i	−0.413707	−	0.811946i
$743$	−24.6348	+	24.6348i	−0.903763	+	0.903763i	−0.995759	−	0.0919959i	$-0.970675\pi$
$743$	−24.6348	+	24.6348i	−0.903763	+	0.903763i	0.0919959	+	0.995759i	$0.470675\pi$
$744$	−1.93390	+	4.93086i	−0.0709003	+	0.180774i
$745$		0			0
$746$	−24.8503	+	8.07436i	−0.909835	+	0.295623i
$747$	17.4636	−	26.0566i	0.638959	−	0.953363i
$748$	−0.192122	−	1.21301i	−0.00702468	−	0.0443521i
$749$	10.3371			0.377709
$750$		0			0
$751$	−16.0915			−0.587188			−0.293594	−	0.955930i	$-0.594851\pi$
$751$	−16.0915			−0.587188			−0.293594	+	0.955930i	$0.594851\pi$
$752$	−0.818228	−	5.16609i	−0.0298377	−	0.188388i
$753$	40.4828	+	23.7657i	1.47528	+	0.866069i
$754$	46.2007	−	15.0115i	1.68253	−	0.546687i
$755$		0			0
$756$	−4.97991	+	9.26962i	−0.181117	+	0.337133i
$757$	5.11239	−	5.11239i	0.185813	−	0.185813i	−0.608070	−	0.793883i	$-0.708056\pi$
$757$	5.11239	−	5.11239i	0.185813	−	0.185813i	0.793883	+	0.608070i	$0.208056\pi$
$758$	−9.86081	−	19.3529i	−0.358161	−	0.702930i
$759$	11.1223	+	17.4018i	0.403715	+	0.631644i
$760$		0			0
$761$	17.3299	−	23.8525i	0.628208	−	0.864654i	−0.369711	−	0.929147i	$-0.620543\pi$
$761$	17.3299	−	23.8525i	0.628208	−	0.864654i	0.997918	+	0.0644935i	$0.0205432\pi$
$762$	19.4261	+	4.27656i	0.703735	+	0.154923i
$763$	−19.5664	−	3.09901i	−0.708350	−	0.112192i
$764$	13.6161	+	9.89270i	0.492614	+	0.357905i
$765$		0			0
$766$	19.3242	−	14.0399i	0.698212	−	0.507281i
$767$	32.6064	−	16.6138i	1.17735	−	0.599890i
$768$	1.14961	+	1.29553i	0.0414829	+	0.0467485i
$769$	44.5425	+	14.4727i	1.60624	+	0.521900i	0.968641	−	0.248466i	$-0.0799264\pi$
$769$	44.5425	+	14.4727i	1.60624	+	0.521900i	0.637602	+	0.770366i	$0.279926\pi$
$770$		0			0
$771$	28.0172	−	7.28994i	1.00901	−	0.262541i
$772$	13.9769	+	7.12158i	0.503039	+	0.256311i
$773$	−37.2215	+	5.89531i	−1.33876	+	0.212039i	−0.784411	−	0.620242i	$-0.787034\pi$
$773$	−37.2215	+	5.89531i	−1.33876	+	0.212039i	−0.554353	+	0.832281i	$0.687034\pi$
$774$	9.03100	+	1.08178i	0.324613	+	0.0388838i
$775$		0			0
$776$		−	2.40893i		−	0.0864756i
$777$	−22.8477	+	2.23407i	−0.819657	+	0.0801468i
$778$	−8.21763	+	16.1280i	−0.294616	+	0.578217i
$779$	1.02051	+	3.14082i	0.0365637	+	0.112532i
$780$		0			0
$781$	10.2991	−	31.6974i	0.368532	−	1.13422i
$782$	−0.343516	−	0.343516i	−0.0122841	−	0.0122841i
$783$	−11.3347	−	37.6514i	−0.405069	−	1.34555i
$784$	1.70402	+	2.34539i	0.0608580	+	0.0837639i
$785$		0			0
$786$	13.8215	+	11.3593i	0.492997	+	0.405173i
$787$	−0.968005	+	6.11175i	−0.0345057	+	0.217860i	−0.998916	−	0.0465501i	$-0.985177\pi$
$787$	−0.968005	+	6.11175i	−0.0345057	+	0.217860i	0.964410	+	0.264410i	$0.0851773\pi$
$788$	2.77713	−	17.5341i	0.0989313	−	0.624627i
$789$	9.76677	+	8.02689i	0.347706	+	0.285765i
$790$		0			0
$791$	15.6764	+	21.5767i	0.557388	+	0.767179i
$792$	5.67913	+	15.4609i	0.201799	+	0.549381i
$793$	14.3375	+	14.3375i	0.509138	+	0.509138i
$794$	−4.34636	+	13.3767i	−0.154247	+	0.474722i
$795$		0			0
$796$	−0.859546	−	2.64541i	−0.0304658	−	0.0937641i
$797$	5.46214	−	10.7200i	0.193479	−	0.379724i	−0.773804	−	0.633426i	$-0.781648\pi$
$797$	5.46214	−	10.7200i	0.193479	−	0.379724i	0.967282	+	0.253702i	$0.0816483\pi$
$798$	7.55763	−	0.738992i	0.267537	−	0.0261600i
$799$			1.17001i			0.0413919i
$800$		0			0
$801$	3.23878	−	27.0382i	0.114437	−	0.955348i
$802$	−0.831423	+	0.131684i	−0.0293586	+	0.00464994i
$803$	14.9579	+	7.62141i	0.527851	+	0.268954i
$804$	4.18582	−	1.08913i	0.147622	−	0.0384106i
$805$		0			0
$806$	−18.6699	−	6.06622i	−0.657620	−	0.213674i
$807$	−35.3712	−	39.8610i	−1.24512	−	1.40317i
$808$	6.77270	−	3.45086i	0.238263	−	0.121401i
$809$	−31.1568	+	22.6367i	−1.09542	+	0.795866i	−0.980305	−	0.197487i	$-0.936722\pi$
$809$	−31.1568	+	22.6367i	−1.09542	+	0.795866i	−0.115110	+	0.993353i	$0.536722\pi$
$810$		0			0
$811$	12.9742	+	9.42631i	0.455586	+	0.331002i	0.791797	−	0.610784i	$-0.209146\pi$
$811$	12.9742	+	9.42631i	0.455586	+	0.331002i	−0.336211	+	0.941787i	$0.609146\pi$
$812$	15.1356	+	2.39724i	0.531155	+	0.0841267i
$813$	−26.8786	−	5.91718i	−0.942674	−	0.207525i
$814$	−21.1214	+	29.0712i	−0.740306	+	1.01894i
$815$		0			0
$816$	−0.208655	−	0.326458i	−0.00730440	−	0.0114283i
$817$	−2.97992	−	5.84842i	−0.104254	−	0.204610i
$818$	10.7674	−	10.7674i	0.376472	−	0.376472i
$819$	−35.3948	−	16.3777i	−1.23679	−	0.572282i
$820$		0			0
$821$	−5.82793	+	1.89361i	−0.203396	+	0.0660875i	−0.408943	−	0.912560i	$-0.634103\pi$
$821$	−5.82793	+	1.89361i	−0.203396	+	0.0660875i	0.205547	+	0.978647i	$0.434103\pi$
$822$	20.1497	+	11.8290i	0.702800	+	0.412583i
$823$	−3.12202	−	19.7116i	−0.108827	−	0.687105i	−0.980426	−	0.196886i	$-0.936917\pi$
$823$	−3.12202	−	19.7116i	−0.108827	−	0.687105i	0.871600	−	0.490218i	$-0.163083\pi$
$824$	−8.53887			−0.297466
$825$		0			0
$826$	11.5441			0.401670
$827$	−2.58216	−	16.3031i	−0.0897904	−	0.566914i	−0.991035	−	0.133603i	$-0.957345\pi$
$827$	−2.58216	−	16.3031i	−0.0897904	−	0.566914i	0.901244	−	0.433311i	$-0.142655\pi$
$828$	5.41220	+	3.62734i	0.188087	+	0.126059i
$829$	−6.29526	+	2.04545i	−0.218643	+	0.0710415i	−0.416290	−	0.909232i	$-0.636670\pi$
$829$	−6.29526	+	2.04545i	−0.218643	+	0.0710415i	0.197647	+	0.980273i	$0.436670\pi$
$830$		0			0
$831$	−6.07900	+	15.4996i	−0.210878	+	0.537674i
$832$	−4.53931	+	4.53931i	−0.157372	+	0.157372i
$833$	−0.294409	−	0.577809i	−0.0102007	−	0.0200199i
$834$	−16.6219	+	10.6239i	−0.575570	+	0.367875i
$835$		0			0
$836$	6.98661	−	9.61624i	0.241637	−	0.332585i
$837$	−5.23760	+	15.0016i	−0.181038	+	0.518530i
$838$	0.308416	+	0.0488483i	0.0106541	+	0.00168744i
$839$	−7.33822	−	5.33153i	−0.253343	−	0.184065i	0.453864	−	0.891071i	$-0.350045\pi$
$839$	−7.33822	−	5.33153i	−0.253343	−	0.184065i	−0.707207	+	0.707006i	$0.750045\pi$
$840$		0			0
$841$	−22.8654	+	16.6127i	−0.788462	+	0.572851i
$842$	−33.9330	+	17.2897i	−1.16941	+	0.595843i
$843$	−26.8151	+	23.7947i	−0.923560	+	0.819534i
$844$	13.4866	+	4.38208i	0.464229	+	0.150837i
$845$		0			0
$846$	−3.03959	−	15.3942i	−0.104503	−	0.529265i
$847$	−34.5421	−	17.6001i	−1.18688	−	0.604745i
$848$	−12.1067	+	1.91752i	−0.415746	+	0.0658477i
$849$	1.25894	−	21.0952i	0.0432069	−	0.723984i
$850$		0			0
$851$			14.2142i			0.487256i
$852$	−1.02322	−	10.4644i	−0.0350549	−	0.358504i
$853$	−5.41209	+	10.6218i	−0.185306	+	0.363684i	−0.964907	−	0.262593i	$-0.915422\pi$
$853$	−5.41209	+	10.6218i	−0.185306	+	0.363684i	0.779600	+	0.626277i	$0.215422\pi$
$854$	1.97655	+	6.08318i	0.0676360	+	0.208162i
$855$		0			0
$856$	1.57739	−	4.85470i	0.0539140	−	0.165930i
$857$	−7.62449	−	7.62449i	−0.260448	−	0.260448i	0.564788	−	0.825236i	$-0.308958\pi$
$857$	−7.62449	−	7.62449i	−0.260448	−	0.260448i	−0.825236	+	0.564788i	$0.808958\pi$
$858$	−55.9476	+	24.4251i	−1.91002	+	0.833859i
$859$	−19.5703	−	26.9362i	−0.667730	−	0.919051i	0.331976	−	0.943288i	$-0.392285\pi$
$859$	−19.5703	−	26.9362i	−0.667730	−	0.919051i	−0.999706	+	0.0242364i	$0.992285\pi$
$860$		0			0
$861$	3.39720	−	4.13356i	0.115776	−	0.140871i
$862$	3.79029	−	23.9310i	0.129098	−	0.815092i
$863$	−3.76211	+	23.7530i	−0.128064	+	0.808562i	0.837126	+	0.547010i	$0.184234\pi$
$863$	−3.76211	+	23.7530i	−0.128064	+	0.808562i	−0.965189	+	0.261552i	$0.915766\pi$
$864$	3.59347	+	3.75326i	0.122252	+	0.127688i
$865$		0			0
$866$	−3.18499	−	4.38377i	−0.108230	−	0.148966i
$867$	−11.7463	−	26.9059i	−0.398926	−	0.913772i
$868$	−4.37883	−	4.37883i	−0.148627	−	0.148627i
$869$	19.6267	−	60.4048i	0.665790	−	2.04909i
$870$		0			0
$871$	4.95372	+	15.2460i	0.167850	+	0.516590i
$872$	−4.44115	+	8.71624i	−0.150396	+	0.295169i
$873$	−0.273559	−	7.22161i	−0.00925856	−	0.244415i
$874$		−	4.70180i		−	0.159041i
$875$		0			0
$876$	5.28663	+	0.315502i	0.178619	+	0.0106598i
$877$	−13.7146	+	2.17218i	−0.463110	+	0.0733494i	−0.383630	−	0.923487i	$-0.625326\pi$
$877$	−13.7146	+	2.17218i	−0.463110	+	0.0733494i	−0.0794802	+	0.996836i	$0.525326\pi$
$878$	23.8234	+	12.1386i	0.804001	+	0.409659i
$879$	−0.0946011	−	0.363578i	−0.00319081	−	0.0122632i
$880$		0			0
$881$	−27.0334	−	8.78367i	−0.910777	−	0.295930i	−0.184099	−	0.982908i	$-0.558937\pi$
$881$	−27.0334	−	8.78367i	−0.910777	−	0.295930i	−0.726678	+	0.686978i	$0.758937\pi$
$882$	5.37475	+	6.83761i	0.180977	+	0.230234i
$883$	15.6986	−	7.99886i	0.528301	−	0.269183i	−0.169430	−	0.985542i	$-0.554193\pi$
$883$	15.6986	−	7.99886i	0.528301	−	0.269183i	0.697732	+	0.716359i	$0.254193\pi$
$884$	1.16174	−	0.844053i	0.0390735	−	0.0283886i
$885$		0			0
$886$	−19.4273	−	14.1148i	−0.652674	−	0.474195i
$887$	9.80527	+	1.55300i	0.329229	+	0.0521447i	0.318861	−	0.947802i	$-0.396700\pi$
$887$	9.80527	+	1.55300i	0.329229	+	0.0521447i	0.0103679	+	0.999946i	$0.496700\pi$
$888$	−2.43724	+	11.0711i	−0.0817885	+	0.371522i
$889$	−13.6698	+	18.8149i	−0.458471	+	0.631032i
$890$		0			0
$891$	18.7809	+	45.7047i	0.629185	+	1.53116i
$892$	2.46523	+	4.83828i	0.0825419	+	0.161998i
$893$	−8.00712	+	8.00712i	−0.267948	+	0.267948i
$894$	−9.62898	−	3.77653i	−0.322041	−	0.126306i
$895$		0			0
$896$	−1.92596	+	0.625783i	−0.0643419	+	0.0209060i
$897$	−12.2252	+	20.8247i	−0.408189	+	0.695315i
$898$	−1.09268	−	6.89889i	−0.0364631	−	0.230219i
$899$	23.1403			0.771773
$900$		0			0
$901$	2.74191			0.0913462
$902$	−1.31014	−	8.27191i	−0.0436229	−	0.275424i
$903$	−5.38379	+	9.17082i	−0.179161	+	0.305186i
$904$	12.5254	−	4.06975i	0.416589	−	0.135358i
$905$		0			0
$906$	4.87260	+	1.91105i	0.161881	+	0.0634905i
$907$	−16.5638	+	16.5638i	−0.549992	+	0.549992i	−0.926438	−	0.376446i	$-0.877146\pi$
$907$	−16.5638	+	16.5638i	−0.549992	+	0.549992i	0.376446	+	0.926438i	$0.377146\pi$
$908$	−9.05981	−	17.7809i	−0.300660	−	0.590079i
$909$	19.9117	−	11.1143i	0.660428	−	0.368638i
$910$		0			0
$911$	−25.0445	+	34.4709i	−0.829763	+	1.14207i	0.158205	+	0.987406i	$0.449429\pi$
$911$	−25.0445	+	34.4709i	−0.829763	+	1.14207i	−0.987967	+	0.154664i	$0.950571\pi$
$912$	0.806197	−	3.66213i	0.0266959	−	0.121265i
$913$	56.6993	+	8.98029i	1.87647	+	0.297204i
$914$	5.18916	+	3.77014i	0.171642	+	0.124705i
$915$		0			0
$916$	9.30889	−	6.76331i	0.307574	−	0.223466i
$917$	−18.6373	+	9.49617i	−0.615458	+	0.313591i
$918$	−0.662590	−	0.954976i	−0.0218687	−	0.0315189i
$919$	−6.21323	−	2.01880i	−0.204955	−	0.0665940i	0.204740	−	0.978816i	$-0.434365\pi$
$919$	−6.21323	−	2.01880i	−0.204955	−	0.0665940i	−0.409696	+	0.912222i	$0.634365\pi$
$920$		0			0
$921$	2.93817	+	11.2922i	0.0968159	+	0.372090i
$922$	2.63198	+	1.34106i	0.0866796	+	0.0441655i
$923$	38.4897	−	6.09617i	1.26690	−	0.200658i
$924$	−19.2233	−	1.14723i	−0.632401	−	0.0377412i
$925$		0			0
$926$			28.6132i			0.940289i
$927$	−25.5983	+	0.969677i	−0.840757	+	0.0318484i
$928$	3.43546	−	6.74246i	0.112774	−	0.221332i
$929$	−8.15479	−	25.0979i	−0.267550	−	0.823434i	−0.991095	−	0.133157i	$-0.957489\pi$
$929$	−8.15479	−	25.0979i	−0.267550	−	0.823434i	0.723545	−	0.690277i	$-0.242511\pi$
$930$		0			0
$931$	1.93950	−	5.96916i	0.0635644	−	0.195631i
$932$	−3.43987	−	3.43987i	−0.112677	−	0.112677i
$933$	−21.0618	−	48.2436i	−0.689531	−	1.57943i
$934$	2.69018	+	3.70271i	0.0880254	+	0.121157i
$935$		0			0
$936$	−13.0927	+	14.1236i	−0.427947	+	0.461646i
$937$	−6.92001	+	43.6912i	−0.226067	+	1.42733i	0.569763	+	0.821809i	$0.307035\pi$
$937$	−6.92001	+	43.6912i	−0.226067	+	1.42733i	−0.795829	+	0.605521i	$0.792965\pi$
$938$	−0.791077	+	4.99466i	−0.0258296	+	0.163081i
$939$	9.60427	−	11.6861i	0.313424	−	0.381360i
$940$		0			0
$941$	3.24570	+	4.46733i	0.105807	+	0.145631i	0.858637	−	0.512584i	$-0.171312\pi$
$941$	3.24570	+	4.46733i	0.105807	+	0.145631i	−0.752830	+	0.658215i	$0.771312\pi$
$942$	9.89759	−	4.32100i	0.322481	−	0.140786i
$943$	−2.34254	−	2.34254i	−0.0762837	−	0.0762837i
$944$	1.76157	−	5.42156i	0.0573342	−	0.176457i
$945$		0			0
$946$	5.14385	+	15.8312i	0.167241	+	0.514715i
$947$	−1.68564	+	3.30825i	−0.0547759	+	0.107504i	−0.916772	−	0.399412i	$-0.869214\pi$
$947$	−1.68564	+	3.30825i	−0.0547759	+	0.107504i	0.861996	+	0.506916i	$0.169214\pi$
$948$	−1.94991	−	19.9416i	−0.0633302	−	0.647674i
$949$			19.6288i			0.637179i
$950$		0			0
$951$	1.04129	−	17.4481i	0.0337662	−	0.565794i
$952$	0.447413	−	0.0708632i	0.0145007	−	0.00229669i
$953$	38.9868	+	19.8647i	1.26290	+	0.643482i	0.951749	−	0.306877i	$-0.0992840\pi$
$953$	38.9868	+	19.8647i	1.26290	+	0.643482i	0.311156	+	0.950359i	$0.399284\pi$
$954$	−36.0764	+	7.12326i	−1.16802	+	0.230624i
$955$		0			0
$956$	−15.9568	−	5.18468i	−0.516080	−	0.167685i
$957$	53.8250	−	47.7623i	1.73991	−	1.54394i
$958$	24.6412	−	12.5553i	0.796121	−	0.405644i
$959$	−22.1008	+	16.0572i	−0.713673	+	0.518514i
$960$		0			0
$961$	17.5143	+	12.7249i	0.564978	+	0.410481i
$962$	−41.4984	−	6.57270i	−1.33796	−	0.211912i
$963$	4.17747	−	14.7328i	0.134617	−	0.474758i
$964$	−9.99786	+	13.7609i	−0.322009	+	0.443208i
$965$		0			0
$966$	−6.41855	+	4.10242i	−0.206514	+	0.131993i
$967$	11.3768	+	22.3283i	0.365854	+	0.718028i	0.998403	−	0.0564917i	$-0.0179914\pi$
$967$	11.3768	+	22.3283i	0.365854	+	0.718028i	−0.632549	+	0.774520i	$0.717991\pi$
$968$	−13.5366	+	13.5366i	−0.435084	+	0.435084i
$969$	−0.306266	+	0.780885i	−0.00983869	+	0.0250856i
$970$		0			0
$971$	−26.2601	+	8.53244i	−0.842728	+	0.273819i	−0.698397	−	0.715711i	$-0.746103\pi$
$971$	−26.2601	+	8.53244i	−0.842728	+	0.273819i	−0.144331	+	0.989529i	$0.546103\pi$
$972$	11.1989	+	10.8436i	0.359205	+	0.347810i
$973$	−3.60807	−	22.7804i	−0.115669	−	0.730308i
$974$	30.2646			0.969741
$975$		0			0
$976$	3.15851			0.101102
$977$	1.45735	+	9.20136i	0.0466248	+	0.294378i	0.999972	−	0.00749885i	$-0.00238698\pi$
$977$	1.45735	+	9.20136i	0.0466248	+	0.294378i	−0.953347	+	0.301876i	$0.902387\pi$
$978$	−8.55998	−	5.02519i	−0.273718	−	0.160688i
$979$	47.3974	−	15.4004i	1.51483	−	0.492197i
$980$		0			0
$981$	−12.3241	+	26.6343i	−0.393477	+	0.850368i
$982$	−5.82921	+	5.82921i	−0.186017	+	0.186017i
$983$	21.0084	+	41.2314i	0.670065	+	1.31508i	0.936311	+	0.351172i	$0.114217\pi$
$983$	21.0084	+	41.2314i	0.670065	+	1.31508i	−0.266245	+	0.963905i	$0.585783\pi$
$984$	−1.42289	−	2.22622i	−0.0453600	−	0.0709692i
$985$		0			0
$986$	−0.994954	+	1.36944i	−0.0316858	+	0.0436118i
$987$	17.9171	+	3.94435i	0.570307	+	0.125550i
$988$	13.7269	+	2.17413i	0.436712	+	0.0691684i
$989$	5.32698	+	3.87028i	0.169388	+	0.123068i
$990$		0			0
$991$	−18.5452	+	13.4739i	−0.589107	+	0.428011i	−0.841996	−	0.539484i	$-0.818619\pi$
$991$	−18.5452	+	13.4739i	−0.589107	+	0.428011i	0.252889	+	0.967495i	$0.418619\pi$
$992$	−2.72466	+	1.38828i	−0.0865081	+	0.0440781i
$993$	−28.9599	−	32.6359i	−0.919015	−	1.03567i
$994$	11.6914	+	3.79878i	0.370830	+	0.120490i
$995$		0			0
$996$	17.5265	−	4.56031i	0.555349	−	0.144499i
$997$	42.9560	+	21.8872i	1.36043	+	0.693173i	0.973447	−	0.228914i	$-0.0735173\pi$
$997$	42.9560	+	21.8872i	1.36043	+	0.693173i	0.386983	+	0.922087i	$0.373517\pi$
$998$	−37.5779	+	5.95175i	−1.18951	+	0.188399i
$999$	−6.04925	+	33.4663i	−0.191390	+	1.05883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.a.293.7		80
3.2	odd	2	inner	750.2.l.a.293.2		80
5.2	odd	4		750.2.l.b.707.5		80
5.3	odd	4		150.2.l.a.137.6	yes	80
5.4	even	2		750.2.l.c.293.4		80
15.2	even	4		750.2.l.b.707.10		80
15.8	even	4		150.2.l.a.137.1	yes	80
15.14	odd	2		750.2.l.c.293.9		80
25.2	odd	20	inner	750.2.l.a.407.2		80
25.11	even	5		750.2.l.b.593.10		80
25.14	even	10		150.2.l.a.23.1	✓	80
25.23	odd	20		750.2.l.c.407.9		80
75.2	even	20	inner	750.2.l.a.407.7		80
75.11	odd	10		750.2.l.b.593.5		80
75.14	odd	10		150.2.l.a.23.6	yes	80
75.23	even	20		750.2.l.c.407.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.1	✓	80	25.14	even	10
150.2.l.a.23.6	yes	80	75.14	odd	10
150.2.l.a.137.1	yes	80	15.8	even	4
150.2.l.a.137.6	yes	80	5.3	odd	4
750.2.l.a.293.2		80	3.2	odd	2	inner
750.2.l.a.293.7		80	1.1	even	1	trivial
750.2.l.a.407.2		80	25.2	odd	20	inner
750.2.l.a.407.7		80	75.2	even	20	inner
750.2.l.b.593.5		80	75.11	odd	10
750.2.l.b.593.10		80	25.11	even	5
750.2.l.b.707.5		80	5.2	odd	4
750.2.l.b.707.10		80	15.2	even	4
750.2.l.c.293.4		80	5.4	even	2
750.2.l.c.293.9		80	15.14	odd	2
750.2.l.c.407.4		80	75.23	even	20
750.2.l.c.407.9		80	25.23	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(-0.876876 + 1.49368i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.61247 - 0.632416i) q^{6} +(1.43195 - 1.43195i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-1.46218 - 2.61955i) q^{9} +O(q^{10})\)	\(q+(0.156434 + 0.987688i) q^{2} +(-0.876876 + 1.49368i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.61247 - 0.632416i) q^{6} +(1.43195 - 1.43195i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-1.46218 - 2.61955i) q^{9} +(3.22713 - 4.44177i) q^{11} +(0.372385 - 1.69155i) q^{12} +(6.34051 + 1.00424i) q^{13} +(1.63832 + 1.19031i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-0.199309 + 0.101553i) q^{17} +(2.35856 - 1.85396i) q^{18} +(-2.05900 - 0.669009i) q^{19} +(0.883235 + 3.39451i) q^{21} +(4.89192 + 2.49256i) q^{22} +(2.14504 - 0.339741i) q^{23} +(1.72897 + 0.103184i) q^{24} +6.41955i q^{26} +(5.19492 + 0.112987i) q^{27} +(-0.919366 + 1.80436i) q^{28} +(-2.33841 - 7.19688i) q^{29} +(-0.944961 + 2.90829i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.80480 + 8.71519i) q^{33} +(-0.131482 - 0.180969i) q^{34} +(2.20010 + 2.03950i) q^{36} +(-1.02386 + 6.46438i) q^{37} +(0.338674 - 2.13830i) q^{38} +(-7.05986 + 8.59013i) q^{39} +(-0.896615 - 1.23409i) q^{41} +(-3.21455 + 1.40338i) q^{42} +(2.14384 + 2.14384i) q^{43} +(-1.69660 + 5.22161i) q^{44} +(0.671116 + 2.06548i) q^{46} +(2.37459 - 4.66039i) q^{47} +(0.168558 + 1.72383i) q^{48} +2.89906i q^{49} +(0.0230812 - 0.386754i) q^{51} +(-6.34051 + 1.00424i) q^{52} +(-10.9216 - 5.56485i) q^{53} +(0.701069 + 5.14864i) q^{54} +(-1.92596 - 0.625783i) q^{56} +(2.80477 - 2.48885i) q^{57} +(6.74246 - 3.43546i) q^{58} +(4.61185 - 3.35071i) q^{59} +(2.55529 + 1.85653i) q^{61} +(-3.02031 - 0.478370i) q^{62} +(-5.84481 - 1.65729i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-8.01269 + 5.12131i) q^{66} +(1.13368 + 2.22498i) q^{67} +(0.158173 - 0.158173i) q^{68} +(-1.37347 + 3.50192i) q^{69} +(5.77333 - 1.87587i) q^{71} +(-1.67022 + 2.49206i) q^{72} +(0.478324 + 3.02002i) q^{73} -6.54496 q^{74} +2.16496 q^{76} +(-1.73929 - 10.9815i) q^{77} +(-9.58877 - 5.62915i) q^{78} +(11.0020 - 3.57478i) q^{79} +(-4.72407 + 7.66049i) q^{81} +(1.07863 - 1.07863i) q^{82} +(4.74686 + 9.31624i) q^{83} +(-1.88897 - 2.95544i) q^{84} +(-1.78208 + 2.45282i) q^{86} +(12.8003 + 2.81793i) q^{87} +(-5.42273 - 0.858876i) q^{88} +(7.34358 + 5.33542i) q^{89} +(10.5173 - 7.64126i) q^{91} +(-1.93507 + 0.985966i) q^{92} +(-3.51545 - 3.96168i) q^{93} +(4.97448 + 1.61631i) q^{94} +(-1.67624 + 0.436149i) q^{96} +(2.14637 + 1.09363i) q^{97} +(-2.86337 + 0.453513i) q^{98} +(-16.3541 - 1.95898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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