LMFDB - Embedded newform 117.2.z.b.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(5,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("117.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.2
Character	$\chi$	$=$	117.47
Dual form			117.2.z.b.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.535189 - 1.99735i) q^{2} +(1.67588 - 0.437507i) q^{3} +(-1.97094 + 1.13792i) q^{4} +(-2.39559 - 0.641897i) q^{5} +(-1.77077 - 3.11318i) q^{6} +(-0.185908 - 0.693817i) q^{7} +(0.403326 + 0.403326i) q^{8} +(2.61718 - 1.46642i) q^{9} +O(q^{10})$	\(q+(-0.535189 - 1.99735i) q^{2} +(1.67588 - 0.437507i) q^{3} +(-1.97094 + 1.13792i) q^{4} +(-2.39559 - 0.641897i) q^{5} +(-1.77077 - 3.11318i) q^{6} +(-0.185908 - 0.693817i) q^{7} +(0.403326 + 0.403326i) q^{8} +(2.61718 - 1.46642i) q^{9} +5.12838i q^{10} +(2.71792 - 0.728264i) q^{11} +(-2.80521 + 2.76932i) q^{12} +(2.59667 + 2.50146i) q^{13} +(-1.28630 + 0.742647i) q^{14} +(-4.29557 - 0.0276574i) q^{15} +(-1.68611 + 2.92043i) q^{16} -1.67579 q^{17} +(-4.32964 - 4.44261i) q^{18} +(1.83240 + 1.83240i) q^{19} +(5.45199 - 1.46086i) q^{20} +(-0.615110 - 1.08142i) q^{21} +(-2.90920 - 5.03888i) q^{22} +(4.29628 + 7.44138i) q^{23} +(0.852385 + 0.499470i) q^{24} +(0.996702 + 0.575446i) q^{25} +(3.60658 - 6.52522i) q^{26} +(3.74451 - 3.60258i) q^{27} +(1.15592 + 1.15592i) q^{28} +(-0.554358 - 0.320059i) q^{29} +(2.24370 + 8.59456i) q^{30} +(2.00865 - 7.49638i) q^{31} +(7.83743 + 2.10003i) q^{32} +(4.23629 - 2.40959i) q^{33} +(0.896866 + 3.34715i) q^{34} +1.78144i q^{35} +(-3.48962 + 5.86836i) q^{36} +(-6.11086 + 6.11086i) q^{37} +(2.67927 - 4.64063i) q^{38} +(5.44613 + 3.05609i) q^{39} +(-0.707311 - 1.22510i) q^{40} +(-0.775914 - 0.207905i) q^{41} +(-1.83078 + 1.80736i) q^{42} +(-5.31049 - 3.06601i) q^{43} +(-4.52814 + 4.52814i) q^{44} +(-7.21098 + 1.83299i) q^{45} +(12.5637 - 12.5637i) q^{46} +(-12.4826 + 3.34469i) q^{47} +(-1.54802 + 5.63200i) q^{48} +(5.61536 - 3.24203i) q^{49} +(0.615945 - 2.29874i) q^{50} +(-2.80844 + 0.733171i) q^{51} +(-7.96434 - 1.97541i) q^{52} +2.05637i q^{53} +(-9.19965 - 5.55105i) q^{54} -6.97849 q^{55} +(0.204853 - 0.354816i) q^{56} +(3.87258 + 2.26920i) q^{57} +(-0.342584 + 1.27854i) q^{58} +(0.892842 - 3.33213i) q^{59} +(8.49777 - 4.83351i) q^{60} +(3.19159 - 5.52799i) q^{61} -16.0479 q^{62} +(-1.50398 - 1.54322i) q^{63} -10.0336i q^{64} +(-4.61489 - 7.65927i) q^{65} +(-7.08002 - 7.17178i) q^{66} +(-0.781048 + 2.91491i) q^{67} +(3.30288 - 1.90692i) q^{68} +(10.4557 + 10.5912i) q^{69} +(3.55816 - 0.953405i) q^{70} +(-10.3850 + 10.3850i) q^{71} +(1.64702 + 0.464129i) q^{72} +(-2.15393 + 2.15393i) q^{73} +(15.4760 + 8.93508i) q^{74} +(1.92212 + 0.528317i) q^{75} +(-5.69667 - 1.52642i) q^{76} +(-1.01056 - 1.75035i) q^{77} +(3.18939 - 12.5134i) q^{78} +(-5.01922 + 8.69355i) q^{79} +(5.91386 - 5.91386i) q^{80} +(4.69922 - 7.67576i) q^{81} +1.66104i q^{82} +(1.35972 + 5.07453i) q^{83} +(2.44292 + 1.43147i) q^{84} +(4.01452 + 1.07569i) q^{85} +(-3.28179 + 12.2478i) q^{86} +(-1.06907 - 0.293846i) q^{87} +(1.38993 + 0.802479i) q^{88} +(5.67268 + 5.67268i) q^{89} +(7.52036 + 13.4219i) q^{90} +(1.25281 - 2.26666i) q^{91} +(-16.9354 - 9.77766i) q^{92} +(0.0865468 - 13.4419i) q^{93} +(13.3611 + 23.1420i) q^{94} +(-3.21347 - 5.56589i) q^{95} +(14.0534 + 0.0904842i) q^{96} +(16.2651 - 4.35823i) q^{97} +(-9.48075 - 9.48075i) q^{98} +(6.04533 - 5.89161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9}+O(q^{10}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33} - 12 q^{34} - 16 q^{37} + 16 q^{39} + 36 q^{40} + 36 q^{41} + 20 q^{42} - 56 q^{45} - 12 q^{46} - 18 q^{47} - 8 q^{48} + 120 q^{50} - 8 q^{52} + 52 q^{54} - 64 q^{55} - 8 q^{57} - 40 q^{58} - 24 q^{59} + 8 q^{60} + 2 q^{61} + 64 q^{63} - 42 q^{65} - 4 q^{66} - 36 q^{68} + 20 q^{70} + 18 q^{72} + 48 q^{73} + 216 q^{74} - 26 q^{76} + 22 q^{78} - 22 q^{79} + 10 q^{81} + 30 q^{83} + 94 q^{84} - 18 q^{85} - 120 q^{86} + 68 q^{87} - 72 q^{92} - 62 q^{93} + 32 q^{94} + 16 q^{96} - 4 q^{97} - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.535189	−	1.99735i	−0.378436	−	1.41234i	−0.848259	−	0.529581i	$-0.822349\pi$
$2$	−0.535189	−	1.99735i	−0.378436	−	1.41234i	0.469824	−	0.882760i	$-0.344317\pi$
$3$	1.67588	−	0.437507i	0.967572	−	0.252595i
$3$	1.67588	−	0.437507i	0.967572	−	0.252595i
$4$	−1.97094	+	1.13792i	−0.985468	+	0.568960i
$5$	−2.39559	−	0.641897i	−1.07134	−	0.287065i	−0.320297	−	0.947317i	$-0.603783\pi$
$5$	−2.39559	−	0.641897i	−1.07134	−	0.287065i	−0.751044	+	0.660252i	$0.770449\pi$
$6$	−1.77077	−	3.11318i	−0.722914	−	1.27095i
$7$	−0.185908	−	0.693817i	−0.0702666	−	0.262238i	0.921852	−	0.387543i	$-0.126676\pi$
$7$	−0.185908	−	0.693817i	−0.0702666	−	0.262238i	−0.992118	+	0.125304i	$0.960009\pi$
$8$	0.403326	+	0.403326i	0.142597	+	0.142597i
$9$	2.61718	−	1.46642i	0.872392	−	0.488807i
$10$			5.12838i			1.62173i
$11$	2.71792	−	0.728264i	0.819483	−	0.219580i	0.175363	−	0.984504i	$-0.443890\pi$
$11$	2.71792	−	0.728264i	0.819483	−	0.219580i	0.644120	+	0.764924i	$0.277224\pi$
$12$	−2.80521	+	2.76932i	−0.809796	+	0.799434i
$13$	2.59667	+	2.50146i	0.720187	+	0.693780i
$13$	2.59667	+	2.50146i	0.720187	+	0.693780i
$14$	−1.28630	+	0.742647i	−0.343779	+	0.198481i
$15$	−4.29557	−	0.0276574i	−1.10911	−	0.00714112i
$16$	−1.68611	+	2.92043i	−0.421528	+	0.730109i
$17$	−1.67579			−0.406440			−0.203220	−	0.979133i	$-0.565141\pi$
$17$	−1.67579			−0.406440			−0.203220	+	0.979133i	$0.565141\pi$
$18$	−4.32964	−	4.44261i	−1.02051	−	1.04713i
$19$	1.83240	+	1.83240i	0.420381	+	0.420381i	0.885335	−	0.464954i	$-0.153929\pi$
$19$	1.83240	+	1.83240i	0.420381	+	0.420381i	−0.464954	+	0.885335i	$0.653929\pi$
$20$	5.45199	−	1.46086i	1.21910	−	0.326657i
$21$	−0.615110	−	1.08142i	−0.134228	−	0.235986i
$22$	−2.90920	−	5.03888i	−0.620243	−	1.07429i
$23$	4.29628	+	7.44138i	0.895837	+	1.55163i	0.832766	+	0.553625i	$0.186756\pi$
$23$	4.29628	+	7.44138i	0.895837	+	1.55163i	0.0630707	+	0.998009i	$0.479911\pi$
$24$	0.852385	+	0.499470i	0.173992	+	0.101954i
$25$	0.996702	+	0.575446i	0.199340	+	0.115089i
$26$	3.60658	−	6.52522i	0.707309	−	1.27970i
$27$	3.74451	−	3.60258i	0.720632	−	0.693318i
$28$	1.15592	+	1.15592i	0.218449	+	0.218449i
$29$	−0.554358	−	0.320059i	−0.102942	−	0.0594334i	0.447645	−	0.894211i	$-0.352263\pi$
$29$	−0.554358	−	0.320059i	−0.102942	−	0.0594334i	−0.550587	+	0.834778i	$0.685596\pi$
$30$	2.24370	+	8.59456i	0.409641	+	1.56915i
$31$	2.00865	−	7.49638i	0.360764	−	1.34639i	−0.512309	−	0.858801i	$-0.671210\pi$
$31$	2.00865	−	7.49638i	0.360764	−	1.34639i	0.873073	−	0.487589i	$-0.162124\pi$
$32$	7.83743	+	2.10003i	1.38548	+	0.371237i
$33$	4.23629	−	2.40959i	0.737444	−	0.419456i
$34$	0.896866	+	3.34715i	0.153811	+	0.574031i
$35$			1.78144i			0.301118i
$36$	−3.48962	+	5.86836i	−0.581603	+	0.978060i
$37$	−6.11086	+	6.11086i	−1.00462	+	1.00462i	−0.00463014	+	0.999989i	$0.501474\pi$
$37$	−6.11086	+	6.11086i	−1.00462	+	1.00462i	−0.999989	+	0.00463014i	$0.998526\pi$
$38$	2.67927	−	4.64063i	0.434635	−	0.752809i
$39$	5.44613	+	3.05609i	0.872078	+	0.489367i
$40$	−0.707311	−	1.22510i	−0.111836	−	0.193705i
$41$	−0.775914	−	0.207905i	−0.121177	−	0.0324694i	0.197721	−	0.980258i	$-0.436646\pi$
$41$	−0.775914	−	0.207905i	−0.121177	−	0.0324694i	−0.318898	+	0.947789i	$0.603313\pi$
$42$	−1.83078	+	1.80736i	−0.282495	+	0.278881i
$43$	−5.31049	−	3.06601i	−0.809842	−	0.467563i	0.0370590	−	0.999313i	$-0.488201\pi$
$43$	−5.31049	−	3.06601i	−0.809842	−	0.467563i	−0.846901	+	0.531751i	$0.821534\pi$
$44$	−4.52814	+	4.52814i	−0.682642	+	0.682642i
$45$	−7.21098	+	1.83299i	−1.07495	+	0.273246i
$46$	12.5637	−	12.5637i	1.85242	−	1.85242i
$47$	−12.4826	+	3.34469i	−1.82077	+	0.487874i	−0.996884	−	0.0788833i	$-0.974865\pi$
$47$	−12.4826	+	3.34469i	−1.82077	+	0.487874i	−0.823885	+	0.566757i	$0.808198\pi$
$48$	−1.54802	+	5.63200i	−0.223438	+	0.812909i
$49$	5.61536	−	3.24203i	0.802194	−	0.463147i
$50$	0.615945	−	2.29874i	0.0871077	−	0.325090i
$51$	−2.80844	+	0.733171i	−0.393260	+	0.102664i
$52$	−7.96434	−	1.97541i	−1.10446	−	0.273940i
$53$			2.05637i			0.282464i	0.989977	+	0.141232i	$0.0451064\pi$
$53$			2.05637i			0.282464i	−0.989977	+	0.141232i	$0.954894\pi$
$54$	−9.19965	−	5.55105i	−1.25191	−	0.755402i
$55$	−6.97849			−0.940980
$56$	0.204853	−	0.354816i	0.0273747	−	0.0474143i
$57$	3.87258	+	2.26920i	0.512935	+	0.300563i
$58$	−0.342584	+	1.27854i	−0.0449834	+	0.167880i
$59$	0.892842	−	3.33213i	0.116238	−	0.433807i	−0.883138	−	0.469113i	$-0.844574\pi$
$59$	0.892842	−	3.33213i	0.116238	−	0.433807i	0.999377	+	0.0353058i	$0.0112405\pi$
$60$	8.49777	−	4.83351i	1.09706	−	0.624003i
$61$	3.19159	−	5.52799i	0.408641	−	0.707787i	−0.586097	−	0.810241i	$-0.699336\pi$
$61$	3.19159	−	5.52799i	0.408641	−	0.707787i	0.994738	+	0.102454i	$0.0326695\pi$
$62$	−16.0479			−2.03809
$63$	−1.50398	−	1.54322i	−0.189484	−	0.194428i
$64$		−	10.0336i		−	1.25420i
$65$	−4.61489	−	7.65927i	−0.572406	−	0.950015i
$66$	−7.08002	−	7.17178i	−0.871491	−	0.882786i
$67$	−0.781048	+	2.91491i	−0.0954202	+	0.356113i	−0.997083	−	0.0763272i	$-0.975681\pi$
$67$	−0.781048	+	2.91491i	−0.0954202	+	0.356113i	0.901663	+	0.432440i	$0.142347\pi$
$68$	3.30288	−	1.90692i	0.400533	−	0.231248i
$69$	10.4557	+	10.5912i	1.25872	+	1.27503i
$70$	3.55816	−	0.953405i	0.425281	−	0.113954i
$71$	−10.3850	+	10.3850i	−1.23247	+	1.23247i	−0.269457	+	0.963012i	$0.586844\pi$
$71$	−10.3850	+	10.3850i	−1.23247	+	1.23247i	−0.963012	+	0.269457i	$0.913156\pi$
$72$	1.64702	+	0.464129i	0.194103	+	0.0546982i
$73$	−2.15393	+	2.15393i	−0.252099	+	0.252099i	−0.821831	−	0.569732i	$-0.807047\pi$
$73$	−2.15393	+	2.15393i	−0.252099	+	0.252099i	0.569732	+	0.821831i	$0.307047\pi$
$74$	15.4760	+	8.93508i	1.79905	+	1.03868i
$75$	1.92212	+	0.528317i	0.221947	+	0.0610048i
$76$	−5.69667	−	1.52642i	−0.653453	−	0.175092i
$77$	−1.01056	−	1.75035i	−0.115164	−	0.199471i
$78$	3.18939	−	12.5134i	0.361127	−	1.41687i
$79$	−5.01922	+	8.69355i	−0.564707	+	0.978101i	0.432370	+	0.901696i	$0.357677\pi$
$79$	−5.01922	+	8.69355i	−0.564707	+	0.978101i	−0.997077	+	0.0764047i	$0.975656\pi$
$80$	5.91386	−	5.91386i	0.661189	−	0.661189i
$81$	4.69922	−	7.67576i	0.522135	−	0.852863i
$82$			1.66104i			0.183431i
$83$	1.35972	+	5.07453i	0.149248	+	0.557002i	0.999529	+	0.0306734i	$0.00976517\pi$
$83$	1.35972	+	5.07453i	0.149248	+	0.557002i	−0.850281	+	0.526329i	$0.823568\pi$
$84$	2.44292	+	1.43147i	0.266544	+	0.156186i
$85$	4.01452	+	1.07569i	0.435436	+	0.116675i
$86$	−3.28179	+	12.2478i	−0.353885	+	1.32072i
$87$	−1.06907	−	0.293846i	−0.114616	−	0.0315036i
$88$	1.38993	+	0.802479i	0.148168	+	0.0855445i
$89$	5.67268	+	5.67268i	0.601303	+	0.601303i	0.940658	−	0.339355i	$-0.110209\pi$
$89$	5.67268	+	5.67268i	0.601303	+	0.601303i	−0.339355	+	0.940658i	$0.610209\pi$
$90$	7.52036	+	13.4219i	0.792715	+	1.41479i
$91$	1.25281	−	2.26666i	0.131331	−	0.237610i
$92$	−16.9354	−	9.77766i	−1.76564	−	1.01939i
$93$	0.0865468	−	13.4419i	0.00897448	−	1.39386i
$94$	13.3611	+	23.1420i	1.37809	+	2.38692i
$95$	−3.21347	−	5.56589i	−0.329695	−	0.571049i
$96$	14.0534	+	0.0904842i	1.43432	+	0.00923501i
$97$	16.2651	−	4.35823i	1.65148	−	0.442511i	0.691450	−	0.722425i	$-0.256972\pi$
$97$	16.2651	−	4.35823i	1.65148	−	0.442511i	0.960025	+	0.279913i	$0.0903057\pi$
$98$	−9.48075	−	9.48075i	−0.957700	−	0.957700i
$99$	6.04533	−	5.89161i	0.607578	−	0.592129i
$100$	−2.61925			−0.261925
$101$	5.63656	−	9.76281i	0.560859	−	0.971436i	−0.436563	−	0.899674i	$-0.643804\pi$
$101$	5.63656	−	9.76281i	0.560859	−	0.971436i	0.997422	−	0.0717621i	$-0.0228622\pi$
$102$	2.96744	+	5.21705i	0.293821	+	0.516565i
$103$	−11.2027	+	6.46791i	−1.10384	+	0.637302i	−0.937227	−	0.348720i	$-0.886616\pi$
$103$	−11.2027	+	6.46791i	−1.10384	+	0.637302i	−0.166613	+	0.986022i	$0.553283\pi$
$104$	0.0384021	+	2.05621i	0.00376564	+	0.201628i
$105$	0.779391	+	2.98548i	0.0760607	+	0.291353i
$106$	4.10729	−	1.10055i	0.398936	−	0.106894i
$107$		−	11.7362i		−	1.13458i	−0.823519	−	0.567289i	$-0.807992\pi$
$107$		−	11.7362i		−	1.13458i	0.823519	−	0.567289i	$-0.192008\pi$
$108$	−3.28075	+	11.3614i	−0.315690	+	1.09325i
$109$	−2.82626	−	2.82626i	−0.270706	−	0.270706i	0.558678	−	0.829385i	$-0.311309\pi$
$109$	−2.82626	−	2.82626i	−0.270706	−	0.270706i	−0.829385	+	0.558678i	$0.811309\pi$
$110$	3.73481	+	13.9385i	0.356100	+	1.32898i
$111$	−7.56755	+	12.9146i	−0.718280	+	1.22580i
$112$	2.33971	+	0.626923i	0.221082	+	0.0592387i
$113$	−7.48467	+	4.32128i	−0.704099	+	0.406512i	−0.808872	−	0.587985i	$-0.799922\pi$
$113$	−7.48467	+	4.32128i	−0.704099	+	0.406512i	0.104774	+	0.994496i	$0.466588\pi$
$114$	2.45984	−	8.94935i	0.230385	−	0.838184i
$115$	−5.51554	−	20.5843i	−0.514327	−	1.91949i
$116$	1.45681			0.135261
$117$	10.4641	+	2.73894i	0.967410	+	0.253215i
$118$	−7.13328			−0.656672
$119$	0.311543	+	1.16269i	0.0285591	+	0.106584i
$120$	−1.72136	−	1.74367i	−0.157138	−	0.159175i
$121$	−2.66957	+	1.54128i	−0.242688	+	0.140116i
$122$	−12.7494	−	3.41620i	−1.15428	−	0.309289i
$123$	−1.39130	−	0.00895803i	−0.125449	−	0.000807718i
$124$	4.57137	+	17.0606i	0.410521	+	1.53209i
$125$	6.75016	+	6.75016i	0.603753	+	0.603753i
$126$	−2.27745	+	3.82990i	−0.202891	+	0.341194i
$127$		−	10.5955i		−	0.940201i	−0.882613	−	0.470101i	$-0.844218\pi$
$127$		−	10.5955i		−	0.940201i	0.882613	−	0.470101i	$-0.155782\pi$
$128$	−4.36571	+	1.16979i	−0.385878	+	0.103396i
$129$	−10.2412	−	2.81491i	−0.901684	−	0.247839i
$130$	−12.8284	+	13.3167i	−1.12513	+	1.16795i
$131$	−1.32209	+	0.763310i	−0.115512	+	0.0666907i	−0.556643	−	0.830752i	$-0.687911\pi$
$131$	−1.32209	+	0.763310i	−0.115512	+	0.0666907i	0.441131	+	0.897443i	$0.354577\pi$
$132$	−5.60754	+	9.56972i	−0.488074	+	0.832938i
$133$	0.930694	−	1.61201i	0.0807014	−	0.139779i
$134$	6.24011			0.539063
$135$	−11.2828	+	6.22673i	−0.971070	+	0.535911i
$136$	−0.675891	−	0.675891i	−0.0579572	−	0.0579572i
$137$	6.09224	−	1.63241i	0.520495	−	0.139466i	0.0109995	−	0.999940i	$-0.496499\pi$
$137$	6.09224	−	1.63241i	0.520495	−	0.139466i	0.509496	+	0.860473i	$0.329832\pi$
$138$	15.5586	−	26.5521i	1.32444	−	2.26026i
$139$	−4.73092	−	8.19419i	−0.401271	−	0.695022i	0.592608	−	0.805491i	$-0.298098\pi$
$139$	−4.73092	−	8.19419i	−0.401271	−	0.695022i	−0.993880	+	0.110469i	$0.964765\pi$
$140$	−2.02713	−	3.51110i	−0.171324	−	0.296742i
$141$	−19.4560	+	11.0665i	−1.63849	+	0.931969i
$142$	26.3004	+	15.1845i	2.20708	+	1.27426i
$143$	8.87926	+	4.90770i	0.742521	+	0.410402i
$144$	−0.130269	+	10.1158i	−0.0108558	+	0.842987i
$145$	1.12257	+	1.12257i	0.0932244	+	0.0932244i
$146$	5.45492	+	3.14940i	0.451453	+	0.260646i
$147$	7.99228	−	7.89002i	0.659192	−	0.650758i
$148$	5.09045	−	18.9978i	0.418432	−	1.56161i
$149$	10.6712	+	2.85935i	0.874221	+	0.234247i	0.667912	−	0.744240i	$-0.267188\pi$
$149$	10.6712	+	2.85935i	0.874221	+	0.234247i	0.206309	+	0.978487i	$0.433855\pi$
$150$	0.0265392	−	4.12190i	0.00216692	−	0.336551i
$151$	−2.90110	−	10.8271i	−0.236088	−	0.881094i	−0.977655	−	0.210215i	$-0.932584\pi$
$151$	−2.90110	−	10.8271i	−0.236088	−	0.881094i	0.741567	−	0.670879i	$-0.234083\pi$
$152$			1.47811i			0.119890i
$153$	−4.38585	+	2.45742i	−0.354575	+	0.198671i
$154$	−2.95522	+	2.95522i	−0.238138	+	0.238138i
$155$	−9.62381	+	16.6689i	−0.773003	+	1.33888i
$156$	−14.2116	+	0.173894i	−1.13784	+	0.0139227i
$157$	−2.89323	−	5.01122i	−0.230905	−	0.399939i	0.727170	−	0.686458i	$-0.240835\pi$
$157$	−2.89323	−	5.01122i	−0.230905	−	0.399939i	−0.958075	+	0.286519i	$0.907502\pi$
$158$	20.0503	+	5.37247i	1.59512	+	0.427410i
$159$	0.899675	+	3.44624i	0.0713489	+	0.273304i
$160$	−17.4273	−	10.0616i	−1.37775	−	0.795443i
$161$	4.36425	−	4.36425i	0.343951	−	0.343951i
$162$	−17.8462	−	5.27801i	−1.40213	−	0.414680i
$163$	−8.21885	+	8.21885i	−0.643750	+	0.643750i	−0.951475	−	0.307725i	$-0.900432\pi$
$163$	−8.21885	+	8.21885i	−0.643750	+	0.643750i	0.307725	+	0.951475i	$0.400432\pi$
$164$	1.76586	−	0.473160i	0.137890	−	0.0369476i
$165$	−11.6951	+	3.05314i	−0.910466	+	0.237686i
$166$	9.40792	−	5.43166i	0.730196	−	0.421579i
$167$	1.37227	−	5.12137i	0.106189	−	0.396304i	−0.892288	−	0.451466i	$-0.850901\pi$
$167$	1.37227	−	5.12137i	0.106189	−	0.396304i	0.998477	+	0.0551627i	$0.0175677\pi$
$168$	0.188076	−	0.684255i	0.0145104	−	0.0527914i
$169$	0.485412	+	12.9909i	0.0373394	+	0.999303i
$170$		−	8.59410i		−	0.659137i
$171$	7.48278	+	2.10864i	0.572223	+	0.161252i
$172$	13.9555			1.06410
$173$	11.5412	−	19.9899i	0.877460	−	1.51981i	0.0233410	−	0.999728i	$-0.492570\pi$
$173$	11.5412	−	19.9899i	0.877460	−	1.51981i	0.854119	−	0.520078i	$-0.174097\pi$
$174$	−0.0147609	+	2.29257i	−0.00111902	+	0.173799i
$175$	0.213960	−	0.798509i	0.0161738	−	0.0603616i
$176$	−2.45587	+	9.16544i	−0.185118	+	0.690871i
$177$	0.0384699	−	5.97489i	0.00289158	−	0.449101i
$178$	8.29438	−	14.3663i	0.621690	−	1.07680i
$179$	0.0482995			0.00361007			0.00180504	−	0.999998i	$-0.499425\pi$
$179$	0.0482995			0.00361007			0.00180504	+	0.999998i	$0.499425\pi$
$180$	12.1266	−	11.8182i	0.903862	−	0.880879i
$181$		−	9.19556i		−	0.683501i	−0.939791	−	0.341750i	$-0.888980\pi$
$181$		−	9.19556i		−	0.683501i	0.939791	−	0.341750i	$-0.111020\pi$
$182$	−5.19780	−	1.28922i	−0.385287	−	0.0955634i
$183$	2.93020	−	10.6606i	0.216606	−	0.788055i
$184$	−1.26850	+	4.73410i	−0.0935150	+	0.349003i
$185$	18.5617	−	10.7166i	1.36468	−	0.787899i
$186$	−26.8945	+	7.02107i	−1.97200	+	0.514810i
$187$	−4.55467	+	1.22042i	−0.333070	+	0.0892459i
$188$	20.7963	−	20.7963i	1.51673	−	1.51673i
$189$	−3.19567	−	1.92826i	−0.232451	−	0.140260i
$190$	−9.39724	+	9.39724i	−0.681747	+	0.681747i
$191$	4.52628	+	2.61325i	0.327510	+	0.189088i	0.654735	−	0.755858i	$-0.272780\pi$
$191$	4.52628	+	2.61325i	0.327510	+	0.189088i	−0.327225	+	0.944946i	$0.606113\pi$
$192$	−4.38975	−	16.8151i	−0.316803	−	1.21353i
$193$	7.37927	+	1.97727i	0.531171	+	0.142327i	0.514429	−	0.857533i	$-0.328004\pi$
$193$	7.37927	+	1.97727i	0.531171	+	0.142327i	0.0167422	+	0.999860i	$0.494671\pi$
$194$	−17.4098	−	30.1547i	−1.24995	−	2.16498i
$195$	−11.0850	−	10.8170i	−0.793813	−	0.774622i
$196$	−7.37834	+	12.7797i	−0.527024	+	0.912833i
$197$	−5.73204	+	5.73204i	−0.408391	+	0.408391i	−0.881177	−	0.472786i	$-0.843248\pi$
$197$	−5.73204	+	5.73204i	−0.408391	+	0.408391i	0.472786	+	0.881177i	$0.343248\pi$
$198$	−15.0030	−	8.92152i	−1.06622	−	0.634025i
$199$			12.3928i			0.878502i	0.898364	+	0.439251i	$0.144756\pi$
$199$			12.3928i			0.878502i	−0.898364	+	0.439251i	$0.855244\pi$
$200$	0.169903	+	0.634088i	0.0120140	+	0.0448368i
$201$	−0.0336530	+	5.22677i	−0.00237370	+	0.368668i
$202$	−22.5164	−	6.03325i	−1.58425	−	0.424498i
$203$	−0.119003	+	0.444124i	−0.00835236	+	0.0311714i
$204$	4.70096	−	4.64081i	0.329133	−	0.324922i
$205$	1.72532	+	0.996113i	0.120501	+	0.0695716i
$206$	18.9143	+	18.9143i	1.31782	+	1.31782i
$207$	22.1563	+	13.1752i	1.53997	+	0.915742i
$208$	−11.6836	+	3.36567i	−0.810114	+	0.233367i
$209$	6.31478	+	3.64584i	0.436803	+	0.252188i
$210$	5.54594	−	3.15451i	0.382706	−	0.217682i
$211$	7.98159	+	13.8245i	0.549475	+	0.951719i	0.998311	+	0.0581045i	$0.0185057\pi$
$211$	7.98159	+	13.8245i	0.549475	+	0.951719i	−0.448835	+	0.893614i	$0.648161\pi$
$212$	−2.33999	−	4.05297i	−0.160711	−	0.278359i
$213$	−12.8605	+	21.9475i	−0.881188	+	1.50382i
$214$	−23.4413	+	6.28106i	−1.60241	+	0.429365i
$215$	10.7537	+	10.7537i	0.733396	+	0.733396i
$216$	2.96328	+	0.0572443i	0.201625	+	0.00389498i
$217$	−5.57455			−0.378425
$218$	−4.13245	+	7.15761i	−0.279885	+	0.484775i
$219$	−2.66738	+	4.55210i	−0.180245	+	0.307603i
$220$	13.7542	−	7.94097i	0.927306	−	0.535380i
$221$	−4.35149	−	4.19193i	−0.292713	−	0.281980i
$222$	29.8451	+	8.20330i	2.00308	+	0.550569i
$223$	−14.0156	+	3.75546i	−0.938551	+	0.251484i	−0.695497	−	0.718529i	$-0.744816\pi$
$223$	−14.0156	+	3.75546i	−0.938551	+	0.251484i	−0.243054	+	0.970013i	$0.578149\pi$
$224$		−	5.82816i		−	0.389410i
$225$	3.45239	+	0.0444589i	0.230159	+	0.00296393i
$226$	12.6368	+	12.6368i	0.840589	+	0.840589i
$227$	−2.35795	−	8.79998i	−0.156502	−	0.584075i	−0.998972	−	0.0453312i	$-0.985566\pi$
$227$	−2.35795	−	8.79998i	−0.156502	−	0.584075i	0.842470	−	0.538744i	$-0.181101\pi$
$228$	−10.2148	−	0.0657689i	−0.676490	−	0.00435565i
$229$	−7.12994	−	1.91046i	−0.471160	−	0.126247i	0.0154236	−	0.999881i	$-0.495090\pi$
$229$	−7.12994	−	1.91046i	−0.471160	−	0.126247i	−0.486583	+	0.873634i	$0.661757\pi$
$230$	−38.1622	+	22.0329i	−2.51634	+	1.45281i
$231$	−2.45938	−	2.49125i	−0.161815	−	0.163912i
$232$	−0.0944989	−	0.352675i	−0.00620416	−	0.0231542i
$233$	−22.6764			−1.48558			−0.742790	−	0.669524i	$-0.766498\pi$
$233$	−22.6764			−1.48558			−0.742790	+	0.669524i	$0.766498\pi$
$234$	−0.129660	−	22.3664i	−0.00847612	−	1.46214i
$235$	32.0501			2.09072
$236$	2.03197	+	7.58341i	0.132270	+	0.493638i
$237$	−4.60815	+	16.7653i	−0.299332	+	1.08903i
$238$	2.15558	−	1.24452i	0.139725	−	0.0806704i
$239$	10.0411	+	2.69051i	0.649506	+	0.174035i	0.568506	−	0.822679i	$-0.307522\pi$
$239$	10.0411	+	2.69051i	0.649506	+	0.174035i	0.0810007	+	0.996714i	$0.474188\pi$
$240$	7.32359	−	12.4983i	0.472736	−	0.806761i
$241$	2.80689	+	10.4755i	0.180808	+	0.674784i	0.995489	+	0.0948752i	$0.0302452\pi$
$241$	2.80689	+	10.4755i	0.180808	+	0.674784i	−0.814681	+	0.579909i	$0.803088\pi$
$242$	4.50720	+	4.50720i	0.289734	+	0.289734i
$243$	4.51715	−	14.9196i	0.289775	−	0.957095i
$244$			14.5271i			0.930002i
$245$	−15.5332	+	4.16210i	−0.992377	+	0.265907i
$246$	0.726717	+	2.78371i	0.0463338	+	0.177483i
$247$	0.174470	+	9.34181i	0.0111012	+	0.594405i
$248$	3.83363	−	2.21335i	0.243436	−	0.140548i
$249$	4.49887	+	7.90944i	0.285104	+	0.501240i
$250$	9.86984	−	17.0951i	0.624223	−	1.08119i
$251$	8.85205			0.558737			0.279368	−	0.960184i	$-0.409875\pi$
$251$	8.85205			0.558737			0.279368	+	0.960184i	$0.409875\pi$
$252$	4.72032	+	1.33018i	0.297352	+	0.0837936i
$253$	17.0962	+	17.0962i	1.07483	+	1.07483i
$254$	−21.1630	+	5.67061i	−1.32789	+	0.355806i
$255$	7.19849	+	0.0463482i	0.450787	+	0.00290243i
$256$	−5.36061	−	9.28486i	−0.335038	−	0.580304i
$257$	−2.26603	−	3.92487i	−0.141351	−	0.244827i	0.786655	−	0.617393i	$-0.211811\pi$
$257$	−2.26603	−	3.92487i	−0.141351	−	0.244827i	−0.928006	+	0.372566i	$0.878478\pi$
$258$	−0.141403	+	21.9617i	−0.00880335	+	1.36728i
$259$	5.37588	+	3.10377i	0.334041	+	0.192859i
$260$	17.8113	+	9.84456i	1.10461	+	0.610534i
$261$	−1.92019	−	0.0247277i	−0.118857	−	0.00153061i
$262$	2.23217	+	2.23217i	0.137904	+	0.137904i
$263$	−19.1309	−	11.0452i	−1.17966	−	0.681077i	−0.223724	−	0.974653i	$-0.571821\pi$
$263$	−19.1309	−	11.0452i	−1.17966	−	0.681077i	−0.955936	+	0.293576i	$0.905155\pi$
$264$	2.68046	+	0.736756i	0.164971	+	0.0453442i
$265$	1.31998	−	4.92622i	0.0810855	−	0.302615i
$266$	−3.71785	−	0.996194i	−0.227956	−	0.0610806i
$267$	11.9886	+	7.02492i	0.733690	+	0.429918i
$268$	−1.77754	−	6.63387i	−0.108581	−	0.405228i
$269$		−	15.5727i		−	0.949487i	−0.880124	−	0.474743i	$-0.842541\pi$
$269$		−	15.5727i		−	0.949487i	0.880124	−	0.474743i	$-0.157459\pi$
$270$	18.4754	+	19.2033i	1.12438	+	1.16867i
$271$	13.0889	−	13.0889i	0.795093	−	0.795093i	−0.187224	−	0.982317i	$-0.559949\pi$
$271$	13.0889	−	13.0889i	0.795093	−	0.795093i	0.982317	+	0.187224i	$0.0599490\pi$
$272$	2.82558	−	4.89404i	0.171326	−	0.296745i
$273$	1.10789	−	4.34677i	0.0670528	−	0.263078i
$274$	−6.52100	−	11.2947i	−0.393948	−	0.682338i
$275$	3.12803	+	0.838153i	0.188627	+	0.0505425i
$276$	−32.6596	−	8.97687i	−1.96587	−	0.540344i
$277$	17.9495	+	10.3632i	1.07848	+	0.622663i	0.930487	−	0.366325i	$-0.119384\pi$
$277$	17.9495	+	10.3632i	1.07848	+	0.622663i	0.147996	+	0.988988i	$0.452718\pi$
$278$	−13.8347	+	13.8347i	−0.829753	+	0.829753i
$279$	−5.73587	−	22.5649i	−0.343397	−	1.35092i
$280$	−0.718500	+	0.718500i	−0.0429386	+	0.0429386i
$281$	2.20684	−	0.591321i	0.131649	−	0.0352753i	−0.192393	−	0.981318i	$-0.561625\pi$
$281$	2.20684	−	0.591321i	0.131649	−	0.0352753i	0.324042	+	0.946043i	$0.394958\pi$
$282$	32.5164	+	32.9378i	1.93632	+	1.96142i
$283$	−3.07219	+	1.77373i	−0.182623	+	0.105437i	−0.588524	−	0.808480i	$-0.700291\pi$
$283$	−3.07219	+	1.77373i	−0.182623	+	0.105437i	0.405902	+	0.913917i	$0.366958\pi$
$284$	8.65085	−	32.2854i	0.513333	−	1.91579i
$285$	−7.82052	−	7.92188i	−0.463248	−	0.469252i
$286$	5.05031	−	20.3616i	0.298631	−	1.20400i
$287$			0.576994i			0.0340589i
$288$	23.5915	−	5.99682i	1.39014	−	0.353366i
$289$	−14.1917			−0.834807
$290$	1.64138	−	2.84295i	0.0963852	−	0.166944i
$291$	25.3517	−	14.4200i	1.48615	−	0.845315i
$292$	1.79426	−	6.69627i	0.105001	−	0.391870i
$293$	4.64646	−	17.3408i	0.271449	−	1.01306i	−0.686735	−	0.726908i	$-0.740957\pi$
$293$	4.64646	−	17.3408i	0.271449	−	1.01306i	0.958184	−	0.286154i	$-0.0923768\pi$
$294$	−20.0365	−	11.7407i	−1.16855	−	0.684734i
$295$	−4.27777	+	7.40932i	−0.249062	+	0.431387i
$296$	−4.92934			−0.286512
$297$	7.55365	−	12.5185i	0.438307	−	0.726398i
$298$		−	22.8445i		−	1.32334i
$299$	−7.45826	+	30.0698i	−0.431322	+	1.73898i
$300$	−4.38956	+	1.14594i	−0.253431	+	0.0661608i
$301$	−1.13999	+	4.25451i	−0.0657080	+	0.245226i
$302$	−20.0728	+	11.5890i	−1.15506	+	0.666875i
$303$	5.17493	−	18.8274i	0.297292	−	1.08160i
$304$	−8.44104	+	2.26177i	−0.484127	+	0.129721i
$305$	−11.1941	+	11.1941i	−0.640975	+	0.640975i
$306$	7.25559	+	7.44489i	0.414774	+	0.425596i
$307$	−4.06807	+	4.06807i	−0.232177	+	0.232177i	−0.813601	−	0.581424i	$-0.802496\pi$
$307$	−4.06807	+	4.06807i	−0.232177	+	0.232177i	0.581424	+	0.813601i	$0.302496\pi$
$308$	3.98352	+	2.29988i	0.226982	+	0.131048i
$309$	−15.9448	+	15.7407i	−0.907065	+	0.895460i
$310$	38.4443	+	10.3011i	2.18349	+	0.585064i
$311$	1.38932	+	2.40637i	0.0787811	+	0.136453i	0.902724	−	0.430220i	$-0.141564\pi$
$311$	1.38932	+	2.40637i	0.0787811	+	0.136453i	−0.823943	+	0.566672i	$0.808231\pi$
$312$	0.963962	+	3.42917i	0.0545736	+	0.194138i
$313$	−8.45201	+	14.6393i	−0.477736	+	0.827463i	−0.999674	−	0.0255202i	$-0.991876\pi$
$313$	−8.45201	+	14.6393i	−0.477736	+	0.827463i	0.521938	+	0.852983i	$0.325209\pi$
$314$	−8.46074	+	8.46074i	−0.477467	+	0.477467i
$315$	2.61234	+	4.66233i	0.147189	+	0.262693i
$316$		−	22.8459i		−	1.28518i
$317$	−2.08693	−	7.78853i	−0.117214	−	0.437448i	0.882229	−	0.470820i	$-0.156042\pi$
$317$	−2.08693	−	7.78853i	−0.117214	−	0.437448i	−0.999443	+	0.0333725i	$0.989375\pi$
$318$	6.40185	−	3.64136i	0.358998	−	0.204197i
$319$	−1.73979	−	0.466174i	−0.0974093	−	0.0261007i
$320$	−6.44052	+	24.0363i	−0.360036	+	1.34367i
$321$	−5.13465	−	19.6685i	−0.286588	−	1.09779i
$322$	−11.0526	−	6.38124i	−0.615939	−	0.355613i
$323$	−3.07072	−	3.07072i	−0.170860	−	0.170860i
$324$	−0.527451	+	20.4758i	−0.0293028	+	1.13754i
$325$	1.14865	+	3.98745i	0.0637158	+	0.221184i
$326$	20.8146	+	12.0173i	1.15281	+	0.665577i
$327$	−5.97299	−	3.49997i	−0.330307	−	0.193549i
$328$	−0.229092	−	0.396800i	−0.0126495	−	0.0219096i
$329$	4.64121	+	8.03882i	0.255878	+	0.443194i
$330$	12.3573	+	21.7253i	0.680247	+	1.19594i
$331$	−18.1169	+	4.85441i	−0.995796	+	0.266823i	−0.719683	−	0.694303i	$-0.755713\pi$
$331$	−18.1169	+	4.85441i	−0.995796	+	0.266823i	−0.276113	+	0.961125i	$0.589046\pi$
$332$	−8.45433	−	8.45433i	−0.463992	−	0.463992i
$333$	−7.03210	+	24.9543i	−0.385357	+	1.36749i
$334$	−10.9636			−0.599902
$335$	3.74214	−	6.48158i	0.204455	−	0.354127i
$336$	4.19537	+	0.0270123i	0.228876	+	0.00147364i
$337$	3.68461	−	2.12731i	0.200713	−	0.115882i	−0.396275	−	0.918132i	$-0.629697\pi$
$337$	3.68461	−	2.12731i	0.200713	−	0.115882i	0.596988	+	0.802250i	$0.296364\pi$
$338$	25.6877	−	7.92214i	1.39723	−	0.430908i
$339$	−10.6529	+	10.5166i	−0.578584	+	0.571181i
$340$	−9.13641	+	2.44809i	−0.495491	+	0.132766i
$341$		−	21.8374i		−	1.18256i
$342$	0.207000	−	16.0743i	0.0111933	−	0.869197i
$343$	−6.84868	−	6.84868i	−0.369794	−	0.369794i
$344$	−0.905256	−	3.37846i	−0.0488081	−	0.182154i
$345$	−18.2492	−	32.0838i	−0.982502	−	1.72733i
$346$	−46.1036	−	12.3534i	−2.47855	−	0.664124i
$347$	15.2362	−	8.79662i	0.817921	−	0.472227i	−0.0317778	−	0.999495i	$-0.510117\pi$
$347$	15.2362	−	8.79662i	0.817921	−	0.472227i	0.849699	+	0.527268i	$0.176784\pi$
$348$	2.44144	−	0.637362i	0.130875	−	0.0341662i
$349$	−7.81154	−	29.1531i	−0.418142	−	1.56053i	−0.778457	−	0.627698i	$-0.783997\pi$
$349$	−7.81154	−	29.1531i	−0.418142	−	1.56053i	0.360315	−	0.932831i	$-0.382669\pi$
$350$	−1.70941			−0.0913719
$351$	18.7350	+	0.0120186i	1.00000	+	0.000641506i
$352$	22.8309			1.21689
$353$	2.13655	+	7.97372i	0.113717	+	0.424398i	0.999188	−	0.0402971i	$-0.0128304\pi$
$353$	2.13655	+	7.97372i	0.113717	+	0.424398i	−0.885471	+	0.464696i	$0.846164\pi$
$354$	−11.9546	+	3.12086i	−0.635377	+	0.165872i
$355$	31.5442	−	18.2121i	1.67419	−	0.966597i
$356$	−17.6356	−	4.72543i	−0.934682	−	0.250447i
$357$	1.03080	+	1.81224i	0.0545556	+	0.0959139i
$358$	−0.0258493	−	0.0964710i	−0.00136618	−	0.00509865i
$359$	2.51172	+	2.51172i	0.132563	+	0.132563i	0.770275	−	0.637712i	$-0.220119\pi$
$359$	2.51172	+	2.51172i	0.132563	+	0.132563i	−0.637712	+	0.770275i	$0.720119\pi$
$360$	−3.64767	−	2.16908i	−0.192249	−	0.114321i
$361$		−	12.2846i		−	0.646559i
$362$	−18.3668	+	4.92136i	−0.965337	+	0.258661i
$363$	−3.79957	+	3.75096i	−0.199426	+	0.196874i
$364$	0.110060	+	5.89304i	0.00576869	+	0.308879i
$365$	6.54255	−	3.77734i	0.342453	−	0.197715i
$366$	−22.8612	−	0.147194i	−1.19497	−	0.00769396i
$367$	−13.3528	+	23.1278i	−0.697012	+	1.20726i	0.272486	+	0.962160i	$0.412154\pi$
$367$	−13.3528	+	23.1278i	−0.697012	+	1.20726i	−0.969498	+	0.245100i	$0.921179\pi$
$368$	−28.9761			−1.51048
$369$	−2.33558	+	0.593691i	−0.121585	+	0.0309063i
$370$	−31.3388	−	31.3388i	−1.62923	−	1.62923i
$371$	1.42674	−	0.382295i	0.0740729	−	0.0198478i
$372$	15.1252	+	26.5916i	0.784205	+	1.37871i
$373$	18.6014	+	32.2186i	0.963146	+	1.66822i	0.714517	+	0.699618i	$0.246647\pi$
$373$	18.6014	+	32.2186i	0.963146	+	1.66822i	0.248629	+	0.968599i	$0.420020\pi$
$374$	4.87522	+	8.44412i	0.252091	+	0.436635i
$375$	14.2657	+	8.35925i	0.736679	+	0.431670i
$376$	−6.38354	−	3.68554i	−0.329206	−	0.190067i
$377$	−0.638872	−	2.21779i	−0.0329036	−	0.114222i
$378$	−2.14113	+	7.41486i	−0.110128	+	0.381379i
$379$	−8.49552	−	8.49552i	−0.436386	−	0.436386i	0.454408	−	0.890794i	$-0.349851\pi$
$379$	−8.49552	−	8.49552i	−0.436386	−	0.436386i	−0.890794	+	0.454408i	$0.849851\pi$
$380$	12.6671	+	7.31335i	0.649808	+	0.375167i
$381$	−4.63562	−	17.7569i	−0.237490	−	0.909713i
$382$	2.79716	−	10.4392i	0.143115	−	0.534114i
$383$	−27.4642	−	7.35901i	−1.40336	−	0.376028i	−0.523807	−	0.851837i	$-0.675489\pi$
$383$	−27.4642	−	7.35901i	−1.40336	−	0.376028i	−0.879549	+	0.475809i	$0.842155\pi$
$384$	−6.80463	+	3.87045i	−0.347247	+	0.197513i
$385$	1.29736	+	4.84180i	0.0661194	+	0.246761i
$386$		−	15.7972i		−	0.804057i
$387$	−18.3945	−	0.236880i	−0.935047	−	0.0120413i
$388$	−27.0982	+	27.0982i	−1.37571	+	1.37571i
$389$	−0.183289	+	0.317466i	−0.00929313	+	0.0160962i	−0.870635	−	0.491930i	$-0.836291\pi$
$389$	−0.183289	+	0.317466i	−0.00929313	+	0.0160962i	0.861341	+	0.508026i	$0.169625\pi$
$390$	−15.6728	+	27.9298i	−0.793623	+	1.41428i
$391$	−7.19968	−	12.4702i	−0.364103	−	0.630646i
$392$	3.57241	+	0.957225i	0.180434	+	0.0483472i
$393$	−1.88172	+	1.85764i	−0.0949202	+	0.0937057i
$394$	14.5166	+	8.38118i	0.731337	+	0.422238i
$395$	17.6044	−	17.6044i	0.885772	−	0.885772i
$396$	−5.21078	+	18.4911i	−0.261851	+	0.929212i
$397$	18.2582	−	18.2582i	0.916354	−	0.916354i	−0.0804077	−	0.996762i	$-0.525622\pi$
$397$	18.2582	−	18.2582i	0.916354	−	0.916354i	0.996762	+	0.0804077i	$0.0256222\pi$
$398$	24.7528	−	6.63248i	1.24074	−	0.332456i
$399$	0.854470	−	3.10872i	0.0427770	−	0.155631i
$400$	−3.36111	+	1.94053i	−0.168055	+	0.0970267i
$401$	−3.51653	+	13.1239i	−0.175607	+	0.655374i	0.820840	+	0.571158i	$0.193505\pi$
$401$	−3.51653	+	13.1239i	−0.175607	+	0.655374i	−0.996447	+	0.0842167i	$0.973161\pi$
$402$	10.4577	−	2.73009i	0.521583	−	0.136164i
$403$	23.9677	−	14.4411i	1.19392	−	0.719362i
$404$			25.6558i			1.27643i
$405$	−16.1845	+	15.3716i	−0.804212	+	0.763820i
$406$	0.950762			0.0471855
$407$	−12.1585	+	21.0591i	−0.602674	+	1.04386i
$408$	−1.42842	−	0.837008i	−0.0707174	−	0.0414381i
$409$	1.21223	−	4.52409i	0.0599407	−	0.223702i	−0.929458	−	0.368929i	$-0.879725\pi$
$409$	1.21223	−	4.52409i	0.0599407	−	0.223702i	0.989398	+	0.145227i	$0.0463913\pi$
$410$	1.06622	−	3.97918i	0.0526567	−	0.196518i
$411$	9.49570	−	5.40113i	0.468388	−	0.266418i
$412$	14.7199	−	25.4957i	0.725199	−	1.25608i
$413$	−2.47788			−0.121928
$414$	14.4578	−	51.3052i	0.710561	−	2.52151i
$415$		−	13.0293i		−	0.639583i
$416$	15.0981	+	25.0581i	0.740245	+	1.22857i
$417$	−11.5135	−	11.6627i	−0.563818	−	0.571125i
$418$	3.90243	−	14.5641i	0.190874	−	0.712351i
$419$	8.00346	−	4.62080i	0.390994	−	0.225741i	−0.291596	−	0.956541i	$-0.594186\pi$
$419$	8.00346	−	4.62080i	0.390994	−	0.225741i	0.682591	+	0.730801i	$0.260853\pi$
$420$	−4.93337	−	4.99731i	−0.240724	−	0.243844i
$421$	3.11954	−	0.835879i	0.152037	−	0.0407382i	−0.181998	−	0.983299i	$-0.558256\pi$
$421$	3.11954	−	0.835879i	0.152037	−	0.0407382i	0.334035	+	0.942561i	$0.391590\pi$
$422$	23.3408	−	23.3408i	1.13621	−	1.13621i
$423$	−27.7643	+	27.0583i	−1.34995	+	1.31562i
$424$	−0.829387	+	0.829387i	−0.0402786	+	0.0402786i
$425$	−1.67027	−	0.964329i	−0.0810198	−	0.0467768i
$426$	50.7197	+	13.9409i	2.45738	+	0.675440i
$427$	−4.42876	−	1.18668i	−0.214323	−	0.0574276i
$428$	13.3548	+	23.1312i	0.645530	+	1.11809i
$429$	17.0278	+	4.33999i	0.822108	+	0.209537i
$430$	15.7237	−	27.2342i	0.758262	−	1.31335i
$431$	4.56246	−	4.56246i	0.219766	−	0.219766i	−0.588634	−	0.808400i	$-0.700334\pi$
$431$	4.56246	−	4.56246i	0.219766	−	0.219766i	0.808400	+	0.588634i	$0.200334\pi$
$432$	4.20743	+	17.0100i	0.202430	+	0.818393i
$433$			21.9739i			1.05600i	0.849246	+	0.527998i	$0.177057\pi$
$433$			21.9739i			1.05600i	−0.849246	+	0.527998i	$0.822943\pi$
$434$	2.98343	+	11.1343i	0.143209	+	0.534465i
$435$	2.37243	+	1.39017i	0.113749	+	0.0666533i
$436$	8.78644	+	2.35432i	0.420794	+	0.112751i
$437$	−5.76307	+	21.5081i	−0.275685	+	1.02887i
$438$	10.5197	+	2.89147i	0.502651	+	0.138160i
$439$	26.2789	+	15.1722i	1.25423	+	0.724127i	0.971946	−	0.235205i	$-0.0755761\pi$
$439$	26.2789	+	15.1722i	1.25423	+	0.724127i	0.282280	+	0.959332i	$0.408909\pi$
$440$	−2.81461	−	2.81461i	−0.134181	−	0.134181i
$441$	9.94220	−	16.7194i	0.473438	−	0.796164i
$442$	−6.04389	+	10.9349i	−0.287478	+	0.520121i
$443$	0.263521	+	0.152144i	0.0125203	+	0.00722858i	0.506247	−	0.862388i	$-0.331032\pi$
$443$	0.263521	+	0.152144i	0.0125203	+	0.00722858i	−0.493727	+	0.869617i	$0.664366\pi$
$444$	0.219332	−	34.0652i	0.0104090	−	1.61666i
$445$	−9.94815	−	17.2307i	−0.471588	−	0.816814i
$446$	15.0019	+	25.9841i	0.710362	+	1.23038i
$447$	19.1347	+	0.123201i	0.905041	+	0.00582719i
$448$	−6.96147	+	1.86532i	−0.328898	+	0.0881280i
$449$	−2.84756	−	2.84756i	−0.134384	−	0.134384i	0.636715	−	0.771099i	$-0.280293\pi$
$449$	−2.84756	−	2.84756i	−0.134384	−	0.134384i	−0.771099	+	0.636715i	$0.780293\pi$
$450$	−1.75888	−	6.91943i	−0.0829144	−	0.326185i
$451$	−2.26028			−0.106432
$452$	9.83454	−	17.0339i	0.462578	−	0.801209i
$453$	−9.59882	−	16.8756i	−0.450992	−	0.792887i
$454$	−16.3147	+	9.41930i	−0.765687	+	0.442070i
$455$	−4.45619	+	4.62581i	−0.208909	+	0.216861i
$456$	0.646683	+	2.47714i	0.0302837	+	0.116003i
$457$	−4.45548	+	1.19384i	−0.208419	+	0.0558456i	−0.361518	−	0.932365i	$-0.617741\pi$
$457$	−4.45548	+	1.19384i	−0.208419	+	0.0558456i	0.153099	+	0.988211i	$0.451075\pi$
$458$			15.2635i			0.713215i
$459$	−6.27503	+	6.03719i	−0.292893	+	0.281792i
$460$	34.2941	+	34.2941i	1.59897	+	1.59897i
$461$	−6.74600	−	25.1764i	−0.314192	−	1.17258i	−0.924739	−	0.380602i	$-0.875717\pi$
$461$	−6.74600	−	25.1764i	−0.314192	−	1.17258i	0.610547	−	0.791980i	$-0.290950\pi$
$462$	−3.65968	+	6.24553i	−0.170264	+	0.290569i
$463$	10.2466	+	2.74557i	0.476200	+	0.127597i	0.488933	−	0.872322i	$-0.337386\pi$
$463$	10.2466	+	2.74557i	0.476200	+	0.127597i	−0.0127328	+	0.999919i	$0.504053\pi$
$464$	1.86942	−	1.07931i	0.0867856	−	0.0501057i
$465$	−8.83563	+	32.1457i	−0.409742	+	1.49072i
$466$	12.1362	+	45.2928i	0.562197	+	2.09815i
$467$	16.2595			0.752398			0.376199	−	0.926539i	$-0.377231\pi$
$467$	16.2595			0.752398			0.376199	+	0.926539i	$0.377231\pi$
$468$	−23.7409	+	6.50908i	−1.09742	+	0.300882i
$469$	2.16762			0.100091
$470$	−17.1528	−	64.0153i	−0.791202	−	2.95280i
$471$	−7.04116	−	7.13242i	−0.324439	−	0.328644i
$472$	1.70404	−	0.983829i	0.0784349	−	0.0452844i
$473$	−16.6663	−	4.46573i	−0.766319	−	0.205335i
$474$	35.9525	+	0.231484i	1.65135	+	0.0106324i
$475$	0.771909	+	2.88080i	0.0354176	+	0.132180i
$476$	−1.93709	−	1.93709i	−0.0887862	−	0.0887862i
$477$	3.01550	+	5.38188i	0.138070	+	0.246419i
$478$		−	21.4956i		−	0.983186i
$479$	−21.4454	+	5.74628i	−0.979865	+	0.262554i	−0.712988	−	0.701177i	$-0.752658\pi$
$479$	−21.4454	+	5.74628i	−0.979865	+	0.262554i	−0.266877	+	0.963731i	$0.585992\pi$
$480$	−33.6081	−	9.23760i	−1.53399	−	0.421637i
$481$	−31.1540	+	0.581837i	−1.42050	+	0.0265295i
$482$	19.4210	−	11.2127i	0.884601	−	0.510725i
$483$	5.40458	−	9.22336i	0.245917	−	0.419677i
$484$	3.50770	−	6.07552i	0.159441	−	0.276160i
$485$	−41.7622			−1.89632
$486$	−32.2173	−	1.03751i	−1.46141	−	0.0470626i
$487$	14.0513	+	14.0513i	0.636725	+	0.636725i	0.949746	−	0.313021i	$-0.101341\pi$
$487$	14.0513	+	14.0513i	0.636725	+	0.636725i	−0.313021	+	0.949746i	$0.601341\pi$
$488$	3.51683	−	0.942332i	0.159200	−	0.0426574i
$489$	−10.1780	+	17.3696i	−0.460267	+	0.785482i
$490$	16.6263	+	28.7977i	0.751101	+	1.30095i
$491$	6.14882	+	10.6501i	0.277492	+	0.480631i	0.970761	−	0.240049i	$-0.0771634\pi$
$491$	6.14882	+	10.6501i	0.277492	+	0.480631i	−0.693269	+	0.720679i	$0.743830\pi$
$492$	2.75236	−	1.56554i	0.124086	−	0.0705798i
$493$	0.928989	+	0.536352i	0.0418396	+	0.0241561i
$494$	18.5655	−	5.34811i	0.835302	−	0.240623i
$495$	−18.2639	+	10.2334i	−0.820903	+	0.459957i
$496$	18.5059	+	18.5059i	0.830939	+	0.830939i
$497$	9.13592	+	5.27463i	0.409802	+	0.236599i
$498$	13.3902	−	13.2189i	0.600029	−	0.592352i
$499$	−2.82782	+	10.5536i	−0.126591	+	0.472442i	−0.999891	−	0.0147389i	$-0.995308\pi$
$499$	−2.82782	+	10.5536i	−0.126591	+	0.472442i	0.873301	+	0.487181i	$0.161975\pi$
$500$	−20.9853	−	5.62299i	−0.938491	−	0.251468i
$501$	0.0591270	−	9.18321i	0.00264160	−	0.410275i
$502$	−4.73752	−	17.6807i	−0.211446	−	0.789127i
$503$			14.9431i			0.666280i	0.942877	+	0.333140i	$0.108108\pi$
$503$			14.9431i			0.666280i	−0.942877	+	0.333140i	$0.891892\pi$
$504$	0.0158269	−	1.22902i	0.000704988	−	0.0547448i
$505$	−19.7696	+	19.7696i	−0.879736	+	0.879736i
$506$	24.9975	−	43.2969i	1.11127	−	1.92478i
$507$	6.49711	+	21.5589i	0.288547	+	0.957466i
$508$	12.0569	+	20.8831i	0.534937	+	0.926539i
$509$	0.560573	+	0.150205i	0.0248470	+	0.00665772i	0.271221	−	0.962517i	$-0.412573\pi$
$509$	0.560573	+	0.150205i	0.0248470	+	0.00665772i	−0.246374	+	0.969175i	$0.579239\pi$
$510$	−3.75998	−	14.4027i	−0.166495	−	0.637763i
$511$	1.89487	+	1.09400i	0.0838241	+	0.0483959i
$512$	−22.0680	+	22.0680i	−0.975278	+	0.975278i
$513$	13.4628	+	0.260074i	0.594398	+	0.0114825i
$514$	−6.62660	+	6.62660i	−0.292287	+	0.292287i
$515$	30.9889	−	8.30346i	1.36554	−	0.365894i
$516$	23.3878	−	6.10563i	1.02959	−	0.268786i
$517$	−31.4908	+	18.1812i	−1.38496	+	0.799608i
$518$	3.32220	−	12.3986i	0.145969	−	0.544764i
$519$	10.5960	−	38.5501i	0.465111	−	1.69216i
$520$	1.22788	−	4.95049i	0.0538460	−	0.217093i
$521$			25.9083i			1.13506i	0.823351	+	0.567532i	$0.192102\pi$
$521$			25.9083i			1.13506i	−0.823351	+	0.567532i	$0.807898\pi$
$522$	0.978275	+	3.84853i	0.0428180	+	0.168446i
$523$	−38.2215			−1.67131			−0.835654	−	0.549256i	$-0.814911\pi$
$523$	−38.2215			−1.67131			−0.835654	+	0.549256i	$0.814911\pi$
$524$	1.73717	−	3.00887i	0.0758888	−	0.131443i
$525$	0.00921890	−	1.43182i	0.000402346	−	0.0624896i
$526$	−11.8225	+	44.1223i	−0.515488	+	1.92383i
$527$	−3.36608	+	12.5624i	−0.146629	+	0.547226i
$528$	−0.105816	+	16.4347i	−0.00460506	+	0.715227i
$529$	−25.4161	+	44.0219i	−1.10505	+	1.91400i
$530$	−10.5458			−0.458082
$531$	−2.54958	−	10.0301i	−0.110643	−	0.435268i
$532$			4.23622i			0.183664i
$533$	−1.49473	−	2.48078i	−0.0647438	−	0.107454i
$534$	7.61508	−	27.7051i	0.329537	−	1.19892i
$535$	−7.53341	+	28.1151i	−0.325698	+	1.21552i
$536$	−1.49068	+	0.860642i	−0.0643874	+	0.0371741i
$537$	0.0809443	−	0.0211313i	0.00349301	−	0.000911885i
$538$	−31.1042	+	8.33436i	−1.34100	+	0.359320i
$539$	12.9010	−	12.9010i	0.555687	−	0.555687i
$540$	15.1522	−	25.1114i	0.652047	−	1.08062i
$541$	19.3680	−	19.3680i	0.832697	−	0.832697i	−0.155188	−	0.987885i	$-0.549598\pi$
$541$	19.3680	−	19.3680i	0.832697	−	0.832697i	0.987885	+	0.155188i	$0.0495984\pi$
$542$	−33.1481	−	19.1381i	−1.42383	−	0.822051i
$543$	−4.02312	−	15.4107i	−0.172649	−	0.661337i
$544$	−13.1339	−	3.51922i	−0.563112	−	0.150885i
$545$	4.95639	+	8.58473i	0.212309	+	0.367729i
$546$	−9.27496	+	0.113490i	−0.396932	+	0.00485690i
$547$	16.0080	−	27.7266i	0.684451	−	1.18550i	−0.289158	−	0.957281i	$-0.593375\pi$
$547$	16.0080	−	27.7266i	0.684451	−	1.18550i	0.973609	−	0.228222i	$-0.0732913\pi$
$548$	−10.1499	+	10.1499i	−0.433581	+	0.433581i
$549$	0.246582	−	19.1479i	0.0105239	−	0.817214i
$550$		−	6.69635i		−	0.285533i
$551$	−0.429330	−	1.60228i	−0.0182901	−	0.0682594i
$552$	−0.0546559	+	8.48878i	−0.00232631	+	0.361307i
$553$	6.96485	+	1.86623i	0.296176	+	0.0793600i
$554$	11.0925	−	41.3978i	0.471275	−	1.75882i
$555$	26.4186	−	26.0806i	1.12141	−	1.10706i
$556$	18.6487	+	10.7668i	0.790880	+	0.456615i
$557$	8.80816	+	8.80816i	0.373214	+	0.373214i	0.868646	−	0.495433i	$-0.164990\pi$
$557$	8.80816	+	8.80816i	0.373214	+	0.373214i	−0.495433	+	0.868646i	$0.664990\pi$
$558$	−42.0002	+	23.5330i	−1.77801	+	0.996232i
$559$	−6.12010	−	21.2454i	−0.258853	−	0.898585i
$560$	−5.20257	−	3.00371i	−0.219849	−	0.126930i
$561$	−7.09915	+	4.03798i	−0.299727	+	0.170484i
$562$	−2.36215	−	4.09137i	−0.0996414	−	0.172584i
$563$	−5.20323	−	9.01226i	−0.219290	−	0.379822i	0.735301	−	0.677741i	$-0.237041\pi$
$563$	−5.20323	−	9.01226i	−0.219290	−	0.379822i	−0.954591	+	0.297919i	$0.903707\pi$
$564$	25.7537	−	43.9508i	1.08443	−	1.85066i
$565$	20.7040	−	5.54763i	0.871025	−	0.233390i
$566$	5.18696	+	5.18696i	0.218024	+	0.218024i
$567$	−6.19920	−	1.83342i	−0.260342	−	0.0769962i
$568$	−8.37706			−0.351494
$569$	22.0174	−	38.1353i	0.923018	−	1.59871i	0.128300	−	0.991735i	$-0.459048\pi$
$569$	22.0174	−	38.1353i	0.923018	−	1.59871i	0.794718	−	0.606979i	$-0.207619\pi$
$570$	−11.6373	+	19.8600i	−0.487434	+	0.831845i
$571$	−24.3913	+	14.0823i	−1.02074	+	0.589327i	−0.914320	−	0.404993i	$-0.867274\pi$
$571$	−24.3913	+	14.0823i	−1.02074	+	0.589327i	−0.106425	+	0.994321i	$0.533940\pi$
$572$	−23.0850	+	0.431141i	−0.965234	+	0.0180269i
$573$	8.72884	+	2.39923i	0.364653	+	0.100229i
$574$	1.15246	−	0.308801i	0.0481027	−	0.0128891i
$575$			9.88911i			0.412405i
$576$	−14.7134	−	26.2596i	−0.613060	−	1.09415i
$577$	−11.2232	−	11.2232i	−0.467226	−	0.467226i	0.433788	−	0.901015i	$-0.357177\pi$
$577$	−11.2232	−	11.2232i	−0.467226	−	0.467226i	−0.901015	+	0.433788i	$0.857177\pi$
$578$	7.59525	+	28.3459i	0.315921	+	1.17903i
$579$	13.2319	+	0.0851947i	0.549898	+	0.00354057i
$580$	−3.48991	−	0.935119i	−0.144911	−	0.0388287i
$581$	3.26802	−	1.88679i	0.135580	−	0.0782772i
$582$	−42.3698	−	42.9189i	−1.75628	−	1.77905i
$583$	1.49758	+	5.58904i	0.0620234	+	0.231474i
$584$	−1.73747			−0.0718972
$585$	−23.3097	−	13.2783i	−0.963737	−	0.548990i
$586$	−37.1225			−1.53351
$587$	−2.48413	−	9.27089i	−0.102531	−	0.382650i	0.895522	−	0.445016i	$-0.146802\pi$
$587$	−2.48413	−	9.27089i	−0.102531	−	0.382650i	−0.998053	+	0.0623658i	$0.980135\pi$
$588$	−6.77406	+	24.6453i	−0.279358	+	1.01636i
$589$	17.4170	−	10.0557i	0.717656	−	0.414339i
$590$	17.0884	+	4.57883i	0.703520	+	0.188508i
$591$	−7.09843	+	12.1140i	−0.291990	+	0.498305i
$592$	−7.54276	−	28.1500i	−0.310006	−	1.15696i
$593$	10.2348	+	10.2348i	0.420295	+	0.420295i	0.885305	−	0.465011i	$-0.153949\pi$
$593$	10.2348	+	10.2348i	0.420295	+	0.420295i	−0.465011	+	0.885305i	$0.653949\pi$
$594$	−29.0465	−	8.38753i	−1.19179	−	0.344144i
$595$		−	2.98532i		−	0.122386i
$596$	−24.2860	+	6.50742i	−0.994794	+	0.266554i
$597$	5.42193	+	20.7689i	0.221905	+	0.850014i
$598$	64.0515	−	1.19624i	2.61926	−	0.0489178i
$599$	14.7650	−	8.52460i	0.603283	−	0.348306i	−0.167049	−	0.985949i	$-0.553424\pi$
$599$	14.7650	−	8.52460i	0.603283	−	0.348306i	0.770332	+	0.637643i	$0.220090\pi$
$600$	0.562156	+	0.988324i	0.0229499	+	0.0403482i
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	−0.396398	−	0.918079i	$-0.629740\pi$
$601$	14.6327	−	25.3446i	0.596880	−	1.03383i	0.993279	−	0.115748i	$-0.0369267\pi$
$602$	9.10786			0.371209
$603$	2.23035	+	8.77418i	0.0908267	+	0.357312i
$604$	18.0382	+	18.0382i	0.733965	+	0.733965i
$605$	7.38455	−	1.97868i	0.300224	−	0.0804449i
$606$	−40.3744	−	0.259955i	−1.64010	−	0.0105599i
$607$	−13.8011	−	23.9043i	−0.560171	−	0.970245i	−0.997481	−	0.0709341i	$-0.977402\pi$
$607$	−13.8011	−	23.9043i	−0.560171	−	0.970245i	0.437310	−	0.899311i	$-0.355931\pi$
$608$	10.5132	+	18.2094i	0.426367	+	0.738489i
$609$	−0.00512748	+	0.796366i	−0.000207776	+	0.0322704i
$610$	28.3496	+	16.3677i	1.14784	+	0.662707i
$611$	−40.7797	−	22.5395i	−1.64977	−	0.911852i
$612$	5.84788	−	9.83416i	0.236386	−	0.397522i
$613$	29.6644	+	29.6644i	1.19813	+	1.19813i	0.974724	+	0.223410i	$0.0717190\pi$
$613$	29.6644	+	29.6644i	1.19813	+	1.19813i	0.223410	+	0.974724i	$0.428281\pi$
$614$	10.3026	+	5.94819i	0.415777	+	0.240049i
$615$	3.32724	+	0.914532i	0.134167	+	0.0368775i
$616$	0.298374	−	1.11355i	0.0120218	−	0.0448661i
$617$	−20.7938	−	5.57169i	−0.837129	−	0.224308i	−0.185307	−	0.982681i	$-0.559328\pi$
$617$	−20.7938	−	5.57169i	−0.837129	−	0.224308i	−0.651821	+	0.758373i	$0.725995\pi$
$618$	39.9733	+	23.4230i	1.60796	+	0.942212i
$619$	−8.49836	−	31.7163i	−0.341578	−	1.27479i	−0.896560	−	0.442923i	$-0.853941\pi$
$619$	−8.49836	−	31.7163i	−0.341578	−	1.27479i	0.554982	−	0.831862i	$-0.312725\pi$
$620$		−	43.8045i		−	1.75923i
$621$	42.8957	+	12.3866i	1.72134	+	0.497058i
$622$	4.06283	−	4.06283i	0.162904	−	0.162904i
$623$	2.88121	−	4.99040i	0.115433	−	0.199936i
$624$	−18.1079	+	10.7521i	−0.724896	+	0.430430i
$625$	−14.7150	−	25.4870i	−0.588598	−	1.01948i
$626$	33.7633	+	9.04685i	1.34945	+	0.361585i
$627$	12.1779	+	3.34725i	0.486339	+	0.133676i
$628$	11.4047	+	6.58453i	0.455099	+	0.262751i
$629$	10.2405	−	10.2405i	0.408317	−	0.408317i
$630$	7.91423	−	7.71299i	0.315310	−	0.307293i
$631$	−1.62125	+	1.62125i	−0.0645408	+	0.0645408i	−0.738640	−	0.674100i	$-0.764532\pi$
$631$	−1.62125	+	1.62125i	−0.0645408	+	0.0645408i	0.674100	+	0.738640i	$0.264532\pi$
$632$	−5.53072	+	1.48195i	−0.220000	+	0.0589489i
$633$	19.4245	+	19.6763i	0.772056	+	0.782062i
$634$	−14.4395	+	8.33667i	−0.573467	+	0.331092i
$635$	−6.80124	+	25.3826i	−0.269899	+	1.00728i
$636$	−5.69475	−	5.76856i	−0.225811	−	0.228738i
$637$	22.6910	+	5.62810i	0.899052	+	0.222993i
$638$			3.72446i			0.147453i
$639$	−11.9506	+	42.4080i	−0.472757	+	1.67764i
$640$	11.2093			0.443088
$641$	−16.3798	+	28.3706i	−0.646962	+	1.12057i	0.336883	+	0.941547i	$0.390627\pi$
$641$	−16.3798	+	28.3706i	−0.646962	+	1.12057i	−0.983845	+	0.179024i	$0.942706\pi$
$642$	−36.5368	+	20.7820i	−1.44199	+	0.820202i
$643$	4.76277	−	17.7749i	0.187825	−	0.700974i	−0.806183	−	0.591667i	$-0.798470\pi$
$643$	4.76277	−	17.7749i	0.187825	−	0.700974i	0.994008	−	0.109307i	$-0.0348632\pi$
$644$	−3.63549	+	13.5678i	−0.143258	+	0.534647i
$645$	22.7268	+	13.3171i	0.894866	+	0.524362i
$646$	−4.48990	+	7.77673i	−0.176653	+	0.305971i
$647$	4.78680			0.188189			0.0940943	−	0.995563i	$-0.470004\pi$
$647$	4.78680			0.188189			0.0940943	+	0.995563i	$0.470004\pi$
$648$	4.99115	−	1.20052i	0.196071	−	0.0471608i
$649$		−	9.70669i		−	0.381021i
$650$	7.34960	−	4.42831i	0.288275	−	0.173692i
$651$	−9.34229	+	2.43890i	−0.366153	+	0.0955881i
$652$	6.84643	−	25.5512i	0.268127	−	1.00066i
$653$	19.6024	−	11.3174i	0.767099	−	0.442885i	−0.0647395	−	0.997902i	$-0.520622\pi$
$653$	19.6024	−	11.3174i	0.767099	−	0.442885i	0.831839	+	0.555017i	$0.187288\pi$
$654$	−3.79400	+	13.8033i	−0.148357	+	0.539752i
$655$	3.65716	−	0.979933i	0.142897	−	0.0382891i
$656$	1.91545	−	1.91545i	0.0747859	−	0.0747859i
$657$	−2.47865	+	8.79579i	−0.0967013	+	0.343157i
$658$	13.5724	−	13.5724i	0.529108	−	0.529108i
$659$	26.6129	+	15.3650i	1.03669	+	0.598534i	0.918894	−	0.394504i	$-0.129083\pi$
$659$	26.6129	+	15.3650i	1.03669	+	0.598534i	0.117797	+	0.993038i	$0.462417\pi$
$660$	19.5762	−	19.3257i	0.762001	−	0.752251i
$661$	21.8305	+	5.84945i	0.849106	+	0.227517i	0.657032	−	0.753863i	$-0.271812\pi$
$661$	21.8305	+	5.84945i	0.849106	+	0.227517i	0.192075	+	0.981380i	$0.438478\pi$
$662$	19.3919	+	33.5878i	0.753689	+	1.30543i
$663$	−9.12658	−	5.12138i	−0.354447	−	0.198898i
$664$	−1.49828	+	2.59510i	−0.0581446	+	0.100709i
$665$	−3.26431	+	3.26431i	−0.126584	+	0.126584i
$666$	53.6060	+	0.690324i	2.07719	+	0.0267495i
$667$		−	5.50025i		−	0.212970i
$668$	3.12306	+	11.6554i	0.120835	+	0.450962i
$669$	−21.8454	+	12.4256i	−0.844592	+	0.480402i
$670$	−14.9488	−	4.00551i	−0.577521	−	0.154746i
$671$	4.64863	−	17.3489i	0.179459	−	0.669748i
$672$	−2.54986	−	9.76732i	−0.0983629	−	0.376783i
$673$	−30.7617	−	17.7603i	−1.18577	−	0.684607i	−0.228431	−	0.973560i	$-0.573360\pi$
$673$	−30.7617	−	17.7603i	−1.18577	−	0.684607i	−0.957343	+	0.288953i	$0.906693\pi$
$674$	−6.22095	−	6.22095i	−0.239622	−	0.239622i
$675$	5.80526	−	1.43594i	0.223444	−	0.0552692i
$676$	−15.7394	−	25.0520i	−0.605360	−	0.963537i
$677$	−24.0646	−	13.8937i	−0.924877	−	0.533978i	−0.0396894	−	0.999212i	$-0.512637\pi$
$677$	−24.0646	−	13.8937i	−0.924877	−	0.533978i	−0.885188	+	0.465234i	$0.845970\pi$
$678$	26.7065	+	15.6492i	1.02566	+	0.601002i
$679$	−6.04763	−	10.4748i	−0.232087	−	0.401986i
$680$	1.18531	+	2.05301i	0.0454544	+	0.0787294i
$681$	−7.80170	−	13.7161i	−0.298962	−	0.525603i
$682$	−43.6169	+	11.6871i	−1.67018	+	0.447523i
$683$	9.26458	+	9.26458i	0.354499	+	0.354499i	0.861780	−	0.507281i	$-0.169350\pi$
$683$	9.26458	+	9.26458i	0.354499	+	0.354499i	−0.507281	+	0.861780i	$0.669350\pi$
$684$	−17.1476	+	4.35881i	−0.655653	+	0.166663i
$685$	−15.6424			−0.597664
$686$	−10.0139	+	17.3446i	−0.382332	+	0.662219i
$687$	−12.7848	−	0.0823162i	−0.487770	−	0.00314056i
$688$	17.9082	−	10.3393i	0.682743	−	0.394182i
$689$	−5.14392	+	5.33972i	−0.195968	+	0.203427i
$690$	−54.3158	+	53.6209i	−2.06777	+	2.04131i
$691$	−9.59688	+	2.57148i	−0.365082	+	0.0978235i	−0.436697	−	0.899609i	$-0.643852\pi$
$691$	−9.59688	+	2.57148i	−0.365082	+	0.0978235i	0.0716141	+	0.997432i	$0.477185\pi$
$692$			52.5318i			1.99696i
$693$	−5.21157	−	3.09906i	−0.197971	−	0.117723i
$694$	−25.7242	−	25.7242i	−0.976476	−	0.976476i
$695$	6.07352	+	22.6667i	0.230382	+	0.859797i
$696$	−0.312667	−	0.549698i	−0.0118516	−	0.0208363i
$697$	1.30027	+	0.348407i	0.0492513	+	0.0131968i
$698$	−54.0483	+	31.2048i	−2.04576	+	1.18112i
$699$	−38.0030	+	9.92108i	−1.43741	+	0.375250i
$700$	0.486939	+	1.81728i	0.0184046	+	0.0686867i
$701$	−27.4261			−1.03587			−0.517934	−	0.855420i	$-0.673299\pi$
$701$	−27.4261			−1.03587			−0.517934	+	0.855420i	$0.673299\pi$
$702$	−10.0028	−	37.4268i	−0.377530	−	1.41258i
$703$	−22.3951			−0.844647
$704$	−7.30709	−	27.2704i	−0.275396	−	1.02779i
$705$	53.7122	−	14.0221i	2.02292	−	0.528104i
$706$	14.7829	−	8.53490i	0.556361	−	0.321215i
$707$	−7.82149	−	2.09576i	−0.294157	−	0.0788192i
$708$	6.72314	+	11.8199i	0.252671	+	0.444220i
$709$	−0.967693	−	3.61148i	−0.0363425	−	0.135632i	0.945371	−	0.325996i	$-0.105700\pi$
$709$	−0.967693	−	3.61148i	−0.0363425	−	0.135632i	−0.981713	+	0.190364i	$0.939033\pi$
$710$	−53.2580	−	53.2580i	−1.99874	−	1.99874i
$711$	−0.387785	+	30.1128i	−0.0145431	+	1.12932i
$712$			4.57588i			0.171488i
$713$	64.4131	−	17.2595i	2.41229	−	0.646372i
$714$	3.06801	−	3.02875i	0.114817	−	0.113348i
$715$	−18.1209	−	17.4564i	−0.677682	−	0.652833i
$716$	−0.0951952	+	0.0549610i	−0.00355761	+	0.00205399i
$717$	18.0049	+	0.115926i	0.672405	+	0.00432934i
$718$	3.67254	−	6.36103i	0.137058	−	0.237392i
$719$	6.34901			0.236778			0.118389	−	0.992967i	$-0.462227\pi$
$719$	6.34901			0.236778			0.118389	+	0.992967i	$0.462227\pi$
$720$	6.80540	−	24.1498i	0.253622	−	0.900010i
$721$	6.57023	+	6.57023i	0.244688	+	0.244688i
$722$	−24.5367	+	6.57459i	−0.913162	+	0.244681i
$723$	9.28711	+	16.3276i	0.345391	+	0.607231i
$724$	10.4638	+	18.1239i	0.388885	+	0.673569i
$725$	−0.368353	−	0.638006i	−0.0136803	−	0.0236949i
$726$	9.52547	+	5.58161i	0.353523	+	0.207153i
$727$	0.281315	+	0.162417i	0.0104334	+	0.00602373i	0.505208	−	0.862998i	$-0.331416\pi$
$727$	0.281315	+	0.162417i	0.0104334	+	0.00602373i	−0.494774	+	0.869022i	$0.664749\pi$
$728$	1.41949	−	0.408909i	0.0526099	−	0.0151552i
$729$	1.04278	−	26.9799i	0.0386214	−	0.999254i
$730$	−11.0462	−	11.0462i	−0.408837	−	0.408837i
$731$	8.89928	+	5.13800i	0.329152	+	0.190036i
$732$	6.35570	+	24.3457i	0.234913	+	0.899844i
$733$	−1.07569	+	4.01454i	−0.0397316	+	0.148280i	−0.982942	−	0.183915i	$-0.941123\pi$
$733$	−1.07569	+	4.01454i	−0.0397316	+	0.148280i	0.943211	+	0.332196i	$0.107789\pi$
$734$	53.3406	+	14.2926i	1.96884	+	0.527548i
$735$	−24.2108	+	13.7710i	−0.893029	+	0.507953i
$736$	18.0447	+	67.3436i	0.665135	+	2.48232i
$737$			8.49129i			0.312781i
$738$	2.43579	+	4.34724i	0.0896625	+	0.160024i
$739$	25.4904	−	25.4904i	0.937681	−	0.937681i	−0.0604883	−	0.998169i	$-0.519266\pi$
$739$	25.4904	−	25.4904i	0.937681	−	0.937681i	0.998169	+	0.0604883i	$0.0192658\pi$
$740$	−24.3893	+	42.2434i	−0.896567	+	1.55290i
$741$	4.37950	+	15.5795i	0.160885	+	0.572326i
$742$	−1.52716	−	2.64511i	−0.0560636	−	0.0971051i
$743$	−4.28177	−	1.14730i	−0.157083	−	0.0420902i	0.179421	−	0.983772i	$-0.442578\pi$
$743$	−4.28177	−	1.14730i	−0.157083	−	0.0420902i	−0.336503	+	0.941682i	$0.609244\pi$
$744$	5.45636	−	5.38655i	0.200040	−	0.197480i
$745$	−23.7285	−	13.6996i	−0.869345	−	0.501916i
$746$	54.3967	−	54.3967i	1.99160	−	1.99160i
$747$	11.0000	+	11.2870i	0.402469	+	0.412970i
$748$	7.58822	−	7.58822i	0.277453	−	0.277453i
$749$	−8.14276	+	2.18184i	−0.297530	+	0.0797229i
$750$	9.06150	−	32.9675i	0.330879	−	1.20380i
$751$	6.75231	−	3.89845i	0.246395	−	0.142256i	−0.371717	−	0.928346i	$-0.621231\pi$
$751$	6.75231	−	3.89845i	0.246395	−	0.142256i	0.618113	+	0.786090i	$0.287898\pi$
$752$	11.2791	−	42.0940i	0.411305	−	1.53501i
$753$	14.8350	−	3.87283i	0.540618	−	0.141134i
$754$	−4.08779	+	2.46299i	−0.148869	+	0.0896967i
$755$			27.7994i			1.01172i
$756$	8.49267	+	0.164061i	0.308876	+	0.00596684i
$757$	29.7513			1.08133			0.540664	−	0.841238i	$-0.318173\pi$
$757$	29.7513			1.08133			0.540664	+	0.841238i	$0.318173\pi$
$758$	−12.4218	+	21.5153i	−0.451181	+	0.781469i
$759$	36.1310	+	21.1716i	1.31147	+	0.768480i
$760$	0.948794	−	3.54095i	0.0344164	−	0.128444i
$761$	−2.68682	+	10.0273i	−0.0973970	+	0.363491i	−0.997372	−	0.0724510i	$-0.976918\pi$
$761$	−2.68682	+	10.0273i	−0.0973970	+	0.363491i	0.899975	+	0.435942i	$0.143585\pi$
$762$	−32.9858	+	18.7622i	−1.19495	+	0.679684i
$763$	−1.43548	+	2.48633i	−0.0519680	+	0.0900112i
$764$	−11.8947			−0.430335
$765$	12.0841	−	3.07171i	0.436902	−	0.111058i
$766$			58.7941i			2.12432i
$767$	10.6536	−	6.41905i	0.384680	−	0.231778i
$768$	−13.0460	−	13.2150i	−0.470755	−	0.476857i
$769$	13.3616	−	49.8660i	0.481830	−	1.79822i	−0.112098	−	0.993697i	$-0.535757\pi$
$769$	13.3616	−	49.8660i	0.481830	−	1.79822i	0.593928	−	0.804518i	$-0.297576\pi$
$770$	8.97645	−	5.18255i	0.323489	−	0.186766i
$771$	−5.51476	−	5.58623i	−0.198609	−	0.201183i
$772$	−16.7940	+	4.49995i	−0.604431	+	0.161957i
$773$	18.1418	−	18.1418i	0.652516	−	0.652516i	−0.301082	−	0.953598i	$-0.597348\pi$
$773$	18.1418	−	18.1418i	0.652516	−	0.652516i	0.953598	+	0.301082i	$0.0973478\pi$
$774$	9.37142	+	36.8672i	0.336849	+	1.32516i
$775$	6.31579	−	6.31579i	0.226870	−	0.226870i
$776$	8.31794	+	4.80237i	0.298597	+	0.172395i
$777$	10.3673	+	2.84957i	0.371924	+	0.102228i
$778$	0.732186	+	0.196189i	0.0262501	+	0.00703370i
$779$	−1.04082	−	1.80275i	−0.0372912	−	0.0645902i
$780$	34.1567	+	8.70578i	1.22301	+	0.311717i
$781$	−20.6625	+	35.7885i	−0.739362	+	1.28061i
$782$	−21.0542	+	21.0542i	−0.752897	+	0.752897i
$783$	−3.22884	+	0.798656i	−0.115389	+	0.0285416i
$784$			21.8657i			0.780918i
$785$	3.71431	+	13.8620i	0.132569	+	0.494756i
$786$	4.71744	+	2.76427i	0.168266	+	0.0985981i
$787$	31.1725	+	8.35264i	1.11118	+	0.297740i	0.767309	−	0.641278i	$-0.221595\pi$
$787$	31.1725	+	8.35264i	1.11118	+	0.297740i	0.343870	+	0.939017i	$0.388262\pi$
$788$	4.77488	−	17.8201i	0.170098	−	0.634815i
$789$	−36.8935	−	10.1406i	−1.31344	−	0.361015i
$790$	−44.5838	−	25.7405i	−1.58622	−	0.915805i
$791$	4.38964	+	4.38964i	0.156077	+	0.156077i
$792$	4.81447	+	0.0619995i	0.171075	+	0.00220306i
$793$	22.1155	−	6.37076i	0.785346	−	0.226232i
$794$	−46.2397	−	26.6965i	−1.64099	−	0.947424i
$795$	0.0568739	−	8.83327i	0.00201711	−	0.313284i
$796$	−14.1020	−	24.4254i	−0.499833	−	0.865736i
$797$	12.3872	+	21.4552i	0.438776	+	0.759982i	0.997595	−	0.0693076i	$-0.0220790\pi$
$797$	12.3872	+	21.4552i	0.438776	+	0.759982i	−0.558820	+	0.829289i	$0.688746\pi$
$798$	−6.66652	−	0.0429230i	−0.235992	−	0.00151946i
$799$	20.9182	−	5.60501i	0.740033	−	0.198291i
$800$	6.60313	+	6.60313i	0.233456	+	0.233456i
$801$	23.1649	+	6.52786i	0.818493	+	0.230651i
$802$	28.0950			0.992068
$803$	−4.28558	+	7.42284i	−0.151235	+	0.261946i
$804$	−5.88132	−	10.3399i	−0.207418	−	0.364661i
$805$	−13.2563	+	7.65355i	−0.467225	+	0.269752i
$806$	−41.6712	−	40.1432i	−1.46781	−	1.41398i
$807$	−6.81318	−	26.0981i	−0.239835	−	0.918697i
$808$	6.21096	−	1.66422i	0.218501	−	0.0585472i
$809$			30.3153i			1.06583i	0.846169	+	0.532914i	$0.178903\pi$
$809$			30.3153i			1.06583i	−0.846169	+	0.532914i	$0.821097\pi$
$810$	39.3642	+	24.0994i	1.38312	+	0.846765i
$811$	18.5539	+	18.5539i	0.651515	+	0.651515i	0.953358	−	0.301843i	$-0.0976018\pi$
$811$	18.5539	+	18.5539i	0.651515	+	0.651515i	−0.301843	+	0.953358i	$0.597602\pi$
$812$	−0.270832	−	1.01076i	−0.00950432	−	0.0354706i
$813$	16.2090	−	27.6619i	0.568474	−	0.970146i
$814$	48.5696	+	13.0142i	1.70236	+	0.456147i
$815$	24.9647	−	14.4134i	0.874474	−	0.504878i
$816$	2.59416	−	9.43806i	0.0908139	−	0.330398i
$817$	−4.11278	−	15.3491i	−0.143888	−	0.536997i
$818$	−9.68497			−0.338627
$819$	−0.0450397	−	7.76939i	−0.00157381	−	0.271485i
$820$	−4.53399			−0.158334
$821$	12.4021	+	46.2851i	0.432835	+	1.61536i	0.746195	+	0.665727i	$0.231878\pi$
$821$	12.4021	+	46.2851i	0.432835	+	1.61536i	−0.313361	+	0.949634i	$0.601455\pi$
$822$	−15.8699	−	16.0756i	−0.553528	−	0.560702i
$823$	−37.6019	+	21.7095i	−1.31072	+	0.756744i	−0.982215	−	0.187759i	$-0.939878\pi$
$823$	−37.6019	+	21.7095i	−1.31072	+	0.756744i	−0.328504	+	0.944503i	$0.606544\pi$
$824$	−7.12704	−	1.90968i	−0.248282	−	0.0665270i
$825$	5.60891	+	0.0361135i	0.195277	+	0.00125731i
$826$	1.32613	+	4.94920i	0.0461421	+	0.172205i
$827$	−6.14109	−	6.14109i	−0.213547	−	0.213547i	0.592226	−	0.805772i	$-0.298249\pi$
$827$	−6.14109	−	6.14109i	−0.213547	−	0.213547i	−0.805772	+	0.592226i	$0.798249\pi$
$828$	−58.6611	−	0.755422i	−2.03861	−	0.0262527i
$829$		−	15.6829i		−	0.544690i	−0.962200	−	0.272345i	$-0.912201\pi$
$829$		−	15.6829i		−	0.544690i	0.962200	−	0.272345i	$-0.0877992\pi$
$830$	−26.0241	+	6.97314i	−0.903310	+	0.242041i
$831$	34.6153	+	9.51443i	1.20079	+	0.330052i
$832$	25.0986	−	26.0539i	0.870136	−	0.903256i
$833$	−9.41018	+	5.43297i	−0.326043	+	0.188241i
$834$	−17.1326	+	29.2382i	−0.593255	+	1.01244i
$835$	−6.57479	+	11.3879i	−0.227530	+	0.394093i
$836$	−16.5947			−0.573940
$837$	−19.4849	−	35.3066i	−0.673498	−	1.22038i
$838$	−13.5127	−	13.5127i	−0.466789	−	0.466789i
$839$	15.3834	−	4.12196i	0.531092	−	0.142306i	0.0166997	−	0.999861i	$-0.494684\pi$
$839$	15.3834	−	4.12196i	0.531092	−	0.142306i	0.514393	+	0.857555i	$0.328017\pi$
$840$	−0.889774	+	1.51847i	−0.0307001	+	0.0523922i
$841$	−14.2951	−	24.7599i	−0.492935	−	0.853789i
$842$	−3.33909	−	5.78347i	−0.115073	−	0.199312i
$843$	3.43970	−	1.95649i	0.118470	−	0.0673852i
$844$	−31.4624	−	18.1648i	−1.08298	−	0.625259i
$845$	7.17599	−	31.4326i	0.246862	−	1.08131i
$846$	68.9042	+	40.9738i	2.36898	+	1.40871i
$847$	1.56566	+	1.56566i	0.0537967	+	0.0537967i
$848$	−6.00549	−	3.46727i	−0.206229	−	0.119067i
$849$	−4.37262	+	4.31667i	−0.150068	+	0.148148i
$850$	−1.03220	+	3.85221i	−0.0354040	+	0.132130i
$851$	−71.7272	−	19.2192i	−2.45878	−	0.658827i
$852$	0.372739	−	57.8914i	0.0127698	−	1.98333i
$853$	−5.05120	−	18.8513i	−0.172950	−	0.645457i	−0.996892	−	0.0787829i	$-0.974897\pi$
$853$	−5.05120	−	18.8513i	−0.172950	−	0.645457i	0.823942	−	0.566674i	$-0.191770\pi$
$854$			9.48089i			0.324429i
$855$	−16.5722	−	9.85462i	−0.566756	−	0.337021i
$856$	4.73350	−	4.73350i	0.161788	−	0.161788i
$857$	1.47448	−	2.55388i	0.0503674	−	0.0872388i	−0.839743	−	0.542985i	$-0.817294\pi$
$857$	1.47448	−	2.55388i	0.0503674	−	0.0872388i	0.890110	+	0.455746i	$0.150627\pi$
$858$	−0.444577	−	36.3332i	−0.0151776	−	1.24039i
$859$	1.70873	+	2.95961i	0.0583012	+	0.100981i	0.893703	−	0.448659i	$-0.148098\pi$
$859$	1.70873	+	2.95961i	0.0583012	+	0.100981i	−0.835402	+	0.549640i	$0.814765\pi$
$860$	−33.4317	−	8.95800i	−1.14001	−	0.305465i
$861$	0.252439	+	0.966975i	0.00860308	+	0.0329544i
$862$	−11.5546	−	6.67106i	−0.393552	−	0.227217i
$863$	19.8300	−	19.8300i	0.675023	−	0.675023i	−0.283847	−	0.958870i	$-0.591611\pi$
$863$	19.8300	−	19.8300i	0.675023	−	0.675023i	0.958870	+	0.283847i	$0.0916108\pi$
$864$	36.9129	−	20.3714i	1.25580	−	0.693049i
$865$	−40.4794	+	40.4794i	−1.37634	+	1.37634i
$866$	43.8895	−	11.7602i	1.49143	−	0.399627i
$867$	−23.7837	+	6.20897i	−0.807736	+	0.210868i
$868$	10.9871	−	6.34339i	0.372926	−	0.215309i
$869$	−7.31064	+	27.2837i	−0.247996	+	0.925535i
$870$	1.50695	−	5.48258i	0.0510905	−	0.185877i
$871$	−9.31965	+	5.61531i	−0.315784	+	0.190267i
$872$		−	2.27981i		−	0.0772040i
$873$	36.1777	−	35.2578i	1.22443	−	1.19330i
$874$	46.0435			1.55745
$875$	3.42847	−	5.93829i	0.115903	−	0.200751i
$876$	0.0773094	−	12.0072i	0.00261204	−	0.405685i
$877$	2.56483	−	9.57209i	0.0866082	−	0.323226i	−0.909006	−	0.416784i	$-0.863157\pi$
$877$	2.56483	−	9.57209i	0.0866082	−	0.323226i	0.995614	+	0.0935575i	$0.0298239\pi$
$878$	16.2399	−	60.6083i	0.548071	−	2.04543i
$879$	0.200202	−	31.0941i	0.00675265	−	1.04878i
$880$	11.7665	−	20.3802i	0.396650	−	0.687017i
$881$	−26.6224			−0.896932			−0.448466	−	0.893800i	$-0.648029\pi$
$881$	−26.6224			−0.896932			−0.448466	+	0.893800i	$0.648029\pi$
$882$	−38.7155	−	10.9100i	−1.30362	−	0.367359i
$883$			31.1762i			1.04916i	0.851361	+	0.524581i	$0.175778\pi$
$883$			31.1762i			1.04916i	−0.851361	+	0.524581i	$0.824222\pi$
$884$	13.3466	+	3.31038i	0.448894	+	0.111340i
$885$	−3.92742	+	14.2887i	−0.132019	+	0.480310i
$886$	0.162852	−	0.607770i	0.00547110	−	0.0204184i
$887$	−42.4623	+	24.5156i	−1.42574	+	0.823154i	−0.996781	−	0.0801677i	$-0.974454\pi$
$887$	−42.4623	+	24.5156i	−1.42574	+	0.823154i	−0.428963	+	0.903322i	$0.641121\pi$
$888$	−8.26100	+	2.15662i	−0.277221	+	0.0723714i
$889$	−7.35137	+	1.96979i	−0.246557	+	0.0660647i
$890$	−29.0916	+	29.0916i	−0.975154	+	0.975154i
$891$	7.18211	−	24.2844i	0.240610	−	0.813557i
$892$	23.3504	−	23.3504i	0.781828	−	0.781828i
$893$	−29.0019	−	16.7442i	−0.970510	−	0.560324i
$894$	−9.99461	−	38.2847i	−0.334270	−	1.28043i
$895$	−0.115706	−	0.0310033i	−0.00386762	−	0.00103633i
$896$	1.62324	+	2.81153i	0.0542286	+	0.0939266i
$897$	0.656548	+	53.6565i	0.0219215	+	1.79154i
$898$	−4.16359	+	7.21155i	−0.138941	+	0.240653i
$899$	−3.51279	+	3.51279i	−0.117158	+	0.117158i
$900$	−6.85503	+	3.84092i	−0.228501	+	0.128031i
$901$		−	3.44605i		−	0.114805i
$902$	1.20968	+	4.51457i	0.0402778	+	0.150319i
$903$	−0.0491189	+	7.62881i	−0.00163457	+	0.253871i
$904$	−4.76164	−	1.27588i	−0.158370	−	0.0424351i
$905$	−5.90260	+	22.0288i	−0.196209	+	0.732263i
$906$	−28.5694	+	28.2039i	−0.949156	+	0.937011i
$907$	25.2502	+	14.5782i	0.838421	+	0.484062i	0.856727	−	0.515770i	$-0.172494\pi$
$907$	25.2502	+	14.5782i	0.838421	+	0.484062i	−0.0183065	+	0.999832i	$0.505827\pi$
$908$	14.6610	+	14.6610i	0.486544	+	0.486544i
$909$	0.435480	−	33.8166i	0.0144440	−	1.12162i
$910$	11.6243	+	6.42490i	0.385341	+	0.212983i
$911$	−14.0382	−	8.10498i	−0.465107	−	0.268530i	0.249082	−	0.968482i	$-0.419871\pi$
$911$	−14.0382	−	8.10498i	−0.465107	−	0.268530i	−0.714189	+	0.699953i	$0.753204\pi$
$912$	−13.1567	+	7.48347i	−0.435661	+	0.247803i
$913$	7.39119	+	12.8019i	0.244613	+	0.423682i
$914$	4.76905	+	8.26024i	0.157746	+	0.273224i
$915$	−13.8626	+	23.6576i	−0.458282	+	0.782096i
$916$	16.2266	−	4.34791i	0.536143	−	0.143659i
$917$	0.775385	+	0.775385i	0.0256055	+	0.0256055i
$918$	15.4167	+	9.30241i	0.508827	+	0.307025i
$919$	13.6670			0.450832			0.225416	−	0.974263i	$-0.427626\pi$
$919$	13.6670			0.450832			0.225416	+	0.974263i	$0.427626\pi$
$920$	6.07761	−	10.5267i	0.200373	−	0.347056i
$921$	−5.03781	+	8.59743i	−0.166001	+	0.283295i
$922$	−46.6758	+	26.9483i	−1.53718	+	0.887494i
$923$	−52.9439	+	0.988791i	−1.74267	+	0.0325465i
$924$	7.68213	+	2.11153i	0.252723	+	0.0694641i
$925$	−9.60718	+	2.57424i	−0.315882	+	0.0846403i
$926$		−	21.9355i		−	0.720844i
$927$	−19.8349	+	33.3556i	−0.651463	+	1.09554i
$928$	−3.67261	−	3.67261i	−0.120559	−	0.120559i
$929$	5.23289	+	19.5294i	0.171686	+	0.640739i	0.997092	+	0.0762010i	$0.0242791\pi$
$929$	5.23289	+	19.5294i	0.171686	+	0.640739i	−0.825407	+	0.564538i	$0.809054\pi$
$930$	68.9350	+	0.443845i	2.26047	+	0.0145542i
$931$	16.2303	+	4.34889i	0.531926	+	0.142529i
$932$	44.6938	−	25.8040i	1.46399	−	0.845237i
$933$	3.38114	+	3.42497i	0.110694	+	0.112128i
$934$	−8.70188	−	32.4759i	−0.284734	−	1.06264i
$935$	11.6945			0.382451
$936$	3.11577	+	5.32514i	0.101842	+	0.174058i
$937$	−10.3939			−0.339554			−0.169777	−	0.985483i	$-0.554305\pi$
$937$	−10.3939			−0.339554			−0.169777	+	0.985483i	$0.554305\pi$
$938$	−1.16009	−	4.32950i	−0.0378781	−	0.141363i
$939$	−7.75980	+	28.2316i	−0.253231	+	0.921304i
$940$	−63.1687	+	36.4705i	−2.06034	+	1.18953i
$941$	−41.3297	−	11.0743i	−1.34731	−	0.361011i	−0.488169	−	0.872749i	$-0.662335\pi$
$941$	−41.3297	−	11.0743i	−1.34731	−	0.361011i	−0.859141	+	0.511738i	$0.829002\pi$
$942$	−10.4776	+	17.8809i	−0.341379	+	0.582590i
$943$	−1.78644	−	6.66709i	−0.0581745	−	0.217110i
$944$	8.22584	+	8.22584i	0.267728	+	0.267728i
$945$	6.41778	+	6.67062i	0.208770	+	0.216995i
$946$			35.6786i			1.16001i
$947$	−36.3664	+	9.74435i	−1.18175	+	0.316649i	−0.795620	−	0.605796i	$-0.792855\pi$
$947$	−36.3664	+	9.74435i	−1.18175	+	0.316649i	−0.386129	+	0.922445i	$0.626188\pi$
$948$	−9.99524	−	38.2871i	−0.324630	−	1.24351i
$949$	−10.9810	+	0.205084i	−0.356459	+	0.00665730i
$950$	5.34086	−	3.08355i	0.173280	−	0.100044i
$951$	−6.90499	−	12.1396i	−0.223910	−	0.393655i
$952$	−0.343292	+	0.594598i	−0.0111261	+	0.0192710i
$953$	50.8787			1.64812			0.824062	−	0.566500i	$-0.191703\pi$
$953$	50.8787			1.64812			0.824062	+	0.566500i	$0.191703\pi$
$954$	9.13564	−	8.90334i	0.295777	−	0.288256i
$955$	−9.16569	−	9.16569i	−0.296595	−	0.296595i
$956$	−22.8520	+	6.12318i	−0.739087	+	0.198038i
$957$	−3.11963	−	0.0200861i	−0.100843	−	0.000649290i
$958$	22.9547	+	39.7587i	0.741632	+	1.28454i
$959$	−2.26519	−	3.92342i	−0.0731468	−	0.126694i
$960$	−0.277503	+	43.0999i	−0.00895637	+	1.39104i
$961$	−25.3143	−	14.6152i	−0.816591	−	0.471459i
$962$	17.8354	+	61.9140i	0.575036	+	1.99619i
$963$	−17.2102	−	30.7156i	−0.554590	−	0.989797i
$964$	−17.4525	−	17.4525i	−0.562106	−	0.562106i
$965$	−16.4085	−	9.47346i	−0.528209	−	0.304961i
$966$	−21.3148	−	5.85862i	−0.685791	−	0.188498i
$967$	−5.96423	+	22.2588i	−0.191797	+	0.715795i	0.801276	+	0.598295i	$0.204155\pi$
$967$	−5.96423	+	22.2588i	−0.191797	+	0.715795i	−0.993073	+	0.117500i	$0.962512\pi$
$968$	−1.69834	−	0.455070i	−0.0545869	−	0.0146265i
$969$	−6.48964	−	3.80272i	−0.208477	−	0.122161i
$970$	22.3507	+	83.4138i	0.717636	+	2.67825i
$971$		−	27.2297i		−	0.873844i	−0.899499	−	0.436922i	$-0.856069\pi$
$971$		−	27.2297i		−	0.873844i	0.899499	−	0.436922i	$-0.143931\pi$
$972$	8.07435	+	34.5458i	0.258985	+	1.10806i
$973$	−4.80576	+	4.80576i	−0.154065	+	0.154065i
$974$	20.5453	−	35.5855i	0.658313	−	1.14023i
$975$	3.66955	+	6.17997i	0.117520	+	0.197917i
$976$	10.7628	+	18.6416i	0.344507	+	0.596704i
$977$	48.5116	+	12.9986i	1.55202	+	0.415864i	0.930128	−	0.367236i	$-0.119696\pi$
$977$	48.5116	+	12.9986i	1.55202	+	0.415864i	0.621896	+	0.783100i	$0.286363\pi$
$978$	40.1405	+	11.0331i	1.28355	+	0.352799i
$979$	19.5491	+	11.2867i	0.624791	+	0.360723i
$980$	25.8787	−	25.8787i	0.826666	−	0.826666i
$981$	−11.5413	−	3.25233i	−0.368485	−	0.103839i
$982$	17.9811	−	17.9811i	0.573801	−	0.573801i
$983$	−45.0386	+	12.0681i	−1.43651	+	0.384911i	−0.891310	−	0.453395i	$-0.850213\pi$
$983$	−45.0386	+	12.0681i	−1.43651	+	0.384911i	−0.545199	+	0.838306i	$0.683546\pi$
$984$	−0.557535	−	0.564761i	−0.0177736	−	0.0180039i
$985$	17.4110	−	10.0522i	0.554761	−	0.320291i
$986$	0.574099	−	2.14257i	0.0182830	−	0.0682332i
$987$	11.2952	+	11.4416i	0.359529	+	0.364189i
$988$	−10.9741	−	18.2136i	−0.349133	−	0.579452i
$989$		−	52.6898i		−	1.67544i
$990$	30.2144	+	31.0027i	0.960276	+	0.985331i
$991$	−6.38484			−0.202821			−0.101411	−	0.994845i	$-0.532336\pi$
$991$	−6.38484			−0.202821			−0.101411	+	0.994845i	$0.532336\pi$
$992$	31.4853	−	54.5342i	0.999660	−	1.73146i
$993$	−28.2380	+	16.0617i	−0.896106	+	0.509703i
$994$	5.64584	−	21.0706i	0.179075	−	0.668318i
$995$	7.95489	−	29.6881i	0.252187	−	0.941175i
$996$	−17.8673	−	10.4697i	−0.566147	−	0.331744i
$997$	4.40279	−	7.62585i	0.139438	−	0.241513i	−0.787846	−	0.615872i	$-0.788804\pi$
$997$	4.40279	−	7.62585i	0.139438	−	0.241513i	0.927284	+	0.374359i	$0.122137\pi$
$998$	22.5926			0.715156
$999$	−0.867319	+	44.8971i	−0.0274408	+	1.42048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.47.2	yes	44
3.2	odd	2		351.2.bc.b.8.10		44
9.4	even	3		351.2.bc.b.125.10		44
9.5	odd	6	inner	117.2.z.b.86.2	yes	44
13.5	odd	4	inner	117.2.z.b.83.2	yes	44
39.5	even	4		351.2.bc.b.278.10		44
117.5	even	12	inner	117.2.z.b.5.2	✓	44
117.31	odd	12		351.2.bc.b.44.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.2	✓	44	117.5	even	12	inner
117.2.z.b.47.2	yes	44	1.1	even	1	trivial
117.2.z.b.83.2	yes	44	13.5	odd	4	inner
117.2.z.b.86.2	yes	44	9.5	odd	6	inner
351.2.bc.b.8.10		44	3.2	odd	2
351.2.bc.b.44.10		44	117.31	odd	12
351.2.bc.b.125.10		44	9.4	even	3
351.2.bc.b.278.10		44	39.5	even	4

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.535189 - 1.99735i) q^{2} +(1.67588 - 0.437507i) q^{3} +(-1.97094 + 1.13792i) q^{4} +(-2.39559 - 0.641897i) q^{5} +(-1.77077 - 3.11318i) q^{6} +(-0.185908 - 0.693817i) q^{7} +(0.403326 + 0.403326i) q^{8} +(2.61718 - 1.46642i) q^{9} +O(q^{10})\)	\(q+(-0.535189 - 1.99735i) q^{2} +(1.67588 - 0.437507i) q^{3} +(-1.97094 + 1.13792i) q^{4} +(-2.39559 - 0.641897i) q^{5} +(-1.77077 - 3.11318i) q^{6} +(-0.185908 - 0.693817i) q^{7} +(0.403326 + 0.403326i) q^{8} +(2.61718 - 1.46642i) q^{9} +5.12838i q^{10} +(2.71792 - 0.728264i) q^{11} +(-2.80521 + 2.76932i) q^{12} +(2.59667 + 2.50146i) q^{13} +(-1.28630 + 0.742647i) q^{14} +(-4.29557 - 0.0276574i) q^{15} +(-1.68611 + 2.92043i) q^{16} -1.67579 q^{17} +(-4.32964 - 4.44261i) q^{18} +(1.83240 + 1.83240i) q^{19} +(5.45199 - 1.46086i) q^{20} +(-0.615110 - 1.08142i) q^{21} +(-2.90920 - 5.03888i) q^{22} +(4.29628 + 7.44138i) q^{23} +(0.852385 + 0.499470i) q^{24} +(0.996702 + 0.575446i) q^{25} +(3.60658 - 6.52522i) q^{26} +(3.74451 - 3.60258i) q^{27} +(1.15592 + 1.15592i) q^{28} +(-0.554358 - 0.320059i) q^{29} +(2.24370 + 8.59456i) q^{30} +(2.00865 - 7.49638i) q^{31} +(7.83743 + 2.10003i) q^{32} +(4.23629 - 2.40959i) q^{33} +(0.896866 + 3.34715i) q^{34} +1.78144i q^{35} +(-3.48962 + 5.86836i) q^{36} +(-6.11086 + 6.11086i) q^{37} +(2.67927 - 4.64063i) q^{38} +(5.44613 + 3.05609i) q^{39} +(-0.707311 - 1.22510i) q^{40} +(-0.775914 - 0.207905i) q^{41} +(-1.83078 + 1.80736i) q^{42} +(-5.31049 - 3.06601i) q^{43} +(-4.52814 + 4.52814i) q^{44} +(-7.21098 + 1.83299i) q^{45} +(12.5637 - 12.5637i) q^{46} +(-12.4826 + 3.34469i) q^{47} +(-1.54802 + 5.63200i) q^{48} +(5.61536 - 3.24203i) q^{49} +(0.615945 - 2.29874i) q^{50} +(-2.80844 + 0.733171i) q^{51} +(-7.96434 - 1.97541i) q^{52} +2.05637i q^{53} +(-9.19965 - 5.55105i) q^{54} -6.97849 q^{55} +(0.204853 - 0.354816i) q^{56} +(3.87258 + 2.26920i) q^{57} +(-0.342584 + 1.27854i) q^{58} +(0.892842 - 3.33213i) q^{59} +(8.49777 - 4.83351i) q^{60} +(3.19159 - 5.52799i) q^{61} -16.0479 q^{62} +(-1.50398 - 1.54322i) q^{63} -10.0336i q^{64} +(-4.61489 - 7.65927i) q^{65} +(-7.08002 - 7.17178i) q^{66} +(-0.781048 + 2.91491i) q^{67} +(3.30288 - 1.90692i) q^{68} +(10.4557 + 10.5912i) q^{69} +(3.55816 - 0.953405i) q^{70} +(-10.3850 + 10.3850i) q^{71} +(1.64702 + 0.464129i) q^{72} +(-2.15393 + 2.15393i) q^{73} +(15.4760 + 8.93508i) q^{74} +(1.92212 + 0.528317i) q^{75} +(-5.69667 - 1.52642i) q^{76} +(-1.01056 - 1.75035i) q^{77} +(3.18939 - 12.5134i) q^{78} +(-5.01922 + 8.69355i) q^{79} +(5.91386 - 5.91386i) q^{80} +(4.69922 - 7.67576i) q^{81} +1.66104i q^{82} +(1.35972 + 5.07453i) q^{83} +(2.44292 + 1.43147i) q^{84} +(4.01452 + 1.07569i) q^{85} +(-3.28179 + 12.2478i) q^{86} +(-1.06907 - 0.293846i) q^{87} +(1.38993 + 0.802479i) q^{88} +(5.67268 + 5.67268i) q^{89} +(7.52036 + 13.4219i) q^{90} +(1.25281 - 2.26666i) q^{91} +(-16.9354 - 9.77766i) q^{92} +(0.0865468 - 13.4419i) q^{93} +(13.3611 + 23.1420i) q^{94} +(-3.21347 - 5.56589i) q^{95} +(14.0534 + 0.0904842i) q^{96} +(16.2651 - 4.35823i) q^{97} +(-9.48075 - 9.48075i) q^{98} +(6.04533 - 5.89161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9}+O(q^{10}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33} - 12 q^{34} - 16 q^{37} + 16 q^{39} + 36 q^{40} + 36 q^{41} + 20 q^{42} - 56 q^{45} - 12 q^{46} - 18 q^{47} - 8 q^{48} + 120 q^{50} - 8 q^{52} + 52 q^{54} - 64 q^{55} - 8 q^{57} - 40 q^{58} - 24 q^{59} + 8 q^{60} + 2 q^{61} + 64 q^{63} - 42 q^{65} - 4 q^{66} - 36 q^{68} + 20 q^{70} + 18 q^{72} + 48 q^{73} + 216 q^{74} - 26 q^{76} + 22 q^{78} - 22 q^{79} + 10 q^{81} + 30 q^{83} + 94 q^{84} - 18 q^{85} - 120 q^{86} + 68 q^{87} - 72 q^{92} - 62 q^{93} + 32 q^{94} + 16 q^{96} - 4 q^{97} - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

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