LMFDB - Embedded newform 930.2.n.g.841.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 $ x^16 - x^15 + 31x^14 + 20x^13 + 474x^12 + 463x^11 + 6637x^10 + 13567x^9 + 108596x^8 + 172826x^7 + 917001x^6 + 1583565x^5 + 3229491x^4 - 1732290x^3 + 4672960x^2 - 5544800x + 22848400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			841.4
Root			$3.29488 + 2.39387i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.g.721.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(3.29488 - 2.39387i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(3.29488 - 2.39387i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{10} +(-0.686910 + 0.499069i) q^{11} +(0.309017 + 0.951057i) q^{12} +(1.59548 - 4.91040i) q^{13} +(3.29488 + 2.39387i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.38631 - 1.73375i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.145968 + 0.449244i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(-1.25853 - 3.87337i) q^{21} +(-0.686910 - 0.499069i) q^{22} +(-6.82716 - 4.96022i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +5.16310 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.25853 + 3.87337i) q^{28} +(3.00697 + 9.25451i) q^{29} +1.00000 q^{30} +(5.51248 + 0.782698i) q^{31} +1.00000 q^{32} +(0.262376 + 0.807511i) q^{33} +(0.911489 - 2.80527i) q^{34} +(3.29488 - 2.39387i) q^{35} +1.00000 q^{36} -3.34595 q^{37} +(-0.382150 + 0.277648i) q^{38} +(-4.17703 - 3.03479i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-2.43231 - 7.48589i) q^{41} +(3.29488 - 2.39387i) q^{42} +(0.999109 + 3.07494i) q^{43} +(0.262376 - 0.807511i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(2.60774 - 8.02581i) q^{46} +(2.90870 - 8.95205i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(2.96251 - 9.11767i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-2.38631 + 1.73375i) q^{51} +(1.59548 + 4.91040i) q^{52} +(9.34718 + 6.79112i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-0.686910 + 0.499069i) q^{55} -4.07270 q^{56} +0.472363 q^{57} +(-7.87236 + 5.71960i) q^{58} +(-1.53724 + 4.73114i) q^{59} +(0.309017 + 0.951057i) q^{60} +9.12331 q^{61} +(0.959059 + 5.48454i) q^{62} -4.07270 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.59548 - 4.91040i) q^{65} +(-0.686910 + 0.499069i) q^{66} +5.10872 q^{67} +2.94964 q^{68} +(-6.82716 + 4.96022i) q^{69} +(3.29488 + 2.39387i) q^{70} +(11.2742 + 8.19119i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-6.70649 + 4.87255i) q^{73} +(-1.03395 - 3.18218i) q^{74} +(0.309017 - 0.951057i) q^{75} +(-0.382150 - 0.277648i) q^{76} +(-1.06858 + 3.28875i) q^{77} +(1.59548 - 4.91040i) q^{78} +(1.92968 + 1.40200i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.36788 - 4.62654i) q^{82} +(-3.41587 - 10.5130i) q^{83} +(3.29488 + 2.39387i) q^{84} +(-2.38631 - 1.73375i) q^{85} +(-2.61570 + 1.90042i) q^{86} +9.73077 q^{87} +0.849067 q^{88} +(-12.6306 + 9.17664i) q^{89} +(0.309017 - 0.951057i) q^{90} +(-6.49793 - 19.9986i) q^{91} +8.43883 q^{92} +(2.44784 - 5.00081i) q^{93} +9.41274 q^{94} +(0.145968 + 0.449244i) q^{95} +(0.309017 - 0.951057i) q^{96} +(12.4963 - 9.07908i) q^{97} +9.58688 q^{98} +0.849067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	3.29488	−	2.39387i	1.24535	−	0.904799i	0.247406	−	0.968912i	$-0.420422\pi$
$7$	3.29488	−	2.39387i	1.24535	−	0.904799i	0.997943	+	0.0641130i	$0.0204218\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.309017	+	0.951057i	0.0977198	+	0.300750i
$11$	−0.686910	+	0.499069i	−0.207111	+	0.150475i	−0.686506	−	0.727124i	$-0.740856\pi$
$11$	−0.686910	+	0.499069i	−0.207111	+	0.150475i	0.479395	+	0.877599i	$0.340856\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	1.59548	−	4.91040i	0.442508	−	1.36190i	−0.442686	−	0.896677i	$-0.645974\pi$
$13$	1.59548	−	4.91040i	0.442508	−	1.36190i	0.885194	−	0.465222i	$-0.154026\pi$
$14$	3.29488	+	2.39387i	0.880595	+	0.639789i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.38631	−	1.73375i	−0.578765	−	0.420497i	0.259514	−	0.965739i	$-0.416438\pi$
$17$	−2.38631	−	1.73375i	−0.578765	−	0.420497i	−0.838279	+	0.545242i	$0.816438\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	0.145968	+	0.449244i	0.0334874	+	0.103064i	0.966403	−	0.257031i	$-0.0827443\pi$
$19$	0.145968	+	0.449244i	0.0334874	+	0.103064i	−0.932916	+	0.360095i	$0.882744\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	−1.25853	−	3.87337i	−0.274635	−	0.845238i
$22$	−0.686910	−	0.499069i	−0.146450	−	0.106402i
$23$	−6.82716	−	4.96022i	−1.42356	−	1.03428i	−0.991171	−	0.132591i	$-0.957670\pi$
$23$	−6.82716	−	4.96022i	−1.42356	−	1.03428i	−0.432390	−	0.901687i	$-0.642330\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	5.16310			1.01257
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.25853	+	3.87337i	−0.237840	+	0.731998i
$29$	3.00697	+	9.25451i	0.558381	+	1.71852i	0.686843	+	0.726805i	$0.258996\pi$
$29$	3.00697	+	9.25451i	0.558381	+	1.71852i	−0.128463	+	0.991714i	$0.541004\pi$
$30$	1.00000			0.182574
$31$	5.51248	+	0.782698i	0.990070	+	0.140577i
$31$	5.51248	+	0.782698i	0.990070	+	0.140577i
$32$	1.00000			0.176777
$33$	0.262376	+	0.807511i	0.0456738	+	0.140570i
$34$	0.911489	−	2.80527i	0.156319	−	0.481100i
$35$	3.29488	−	2.39387i	0.556937	−	0.404638i
$36$	1.00000			0.166667
$37$	−3.34595			−0.550070			−0.275035	−	0.961434i	$-0.588689\pi$
$37$	−3.34595			−0.550070			−0.275035	+	0.961434i	$0.588689\pi$
$38$	−0.382150	+	0.277648i	−0.0619929	+	0.0450405i
$39$	−4.17703	−	3.03479i	−0.668861	−	0.485956i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	−2.43231	−	7.48589i	−0.379864	−	1.16910i	−0.940138	−	0.340793i	$-0.889304\pi$
$41$	−2.43231	−	7.48589i	−0.379864	−	1.16910i	0.560275	−	0.828307i	$-0.310696\pi$
$42$	3.29488	−	2.39387i	0.508412	−	0.369383i
$43$	0.999109	+	3.07494i	0.152363	+	0.468924i	0.997884	−	0.0650174i	$-0.0207103\pi$
$43$	0.999109	+	3.07494i	0.152363	+	0.468924i	−0.845521	+	0.533941i	$0.820710\pi$
$44$	0.262376	−	0.807511i	0.0395547	−	0.121737i
$45$	−0.809017	−	0.587785i	−0.120601	−	0.0876219i
$46$	2.60774	−	8.02581i	0.384491	−	1.18334i
$47$	2.90870	−	8.95205i	0.424277	−	1.30579i	−0.479408	−	0.877592i	$-0.659148\pi$
$47$	2.90870	−	8.95205i	0.424277	−	1.30579i	0.903685	−	0.428198i	$-0.140852\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	2.96251	−	9.11767i	0.423216	−	1.30252i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−2.38631	+	1.73375i	−0.334150	+	0.242774i
$52$	1.59548	+	4.91040i	0.221254	+	0.680950i
$53$	9.34718	+	6.79112i	1.28393	+	0.932832i	0.999664	−	0.0259121i	$-0.00824900\pi$
$53$	9.34718	+	6.79112i	1.28393	+	0.932832i	0.284269	+	0.958744i	$0.408249\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−0.686910	+	0.499069i	−0.0926229	+	0.0672945i
$56$	−4.07270			−0.544237
$57$	0.472363			0.0625661
$58$	−7.87236	+	5.71960i	−1.03369	+	0.751021i
$59$	−1.53724	+	4.73114i	−0.200132	+	0.615942i	0.799746	+	0.600338i	$0.204967\pi$
$59$	−1.53724	+	4.73114i	−0.200132	+	0.615942i	−0.999878	+	0.0156043i	$0.995033\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	9.12331			1.16812			0.584060	−	0.811711i	$-0.301463\pi$
$61$	9.12331			1.16812			0.584060	+	0.811711i	$0.301463\pi$
$62$	0.959059	+	5.48454i	0.121801	+	0.696538i
$63$	−4.07270			−0.513112
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.59548	−	4.91040i	0.197896	−	0.609060i
$66$	−0.686910	+	0.499069i	−0.0845527	+	0.0614311i
$67$	5.10872			0.624129			0.312065	−	0.950061i	$-0.398979\pi$
$67$	5.10872			0.624129			0.312065	+	0.950061i	$0.398979\pi$
$68$	2.94964			0.357696
$69$	−6.82716	+	4.96022i	−0.821893	+	0.597141i
$70$	3.29488	+	2.39387i	0.393814	+	0.286123i
$71$	11.2742	+	8.19119i	1.33800	+	0.972115i	0.999515	+	0.0311445i	$0.00991521\pi$
$71$	11.2742	+	8.19119i	1.33800	+	0.972115i	0.338487	+	0.940971i	$0.390085\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−6.70649	+	4.87255i	−0.784936	+	0.570289i	−0.906456	−	0.422300i	$-0.861223\pi$
$73$	−6.70649	+	4.87255i	−0.784936	+	0.570289i	0.121520	+	0.992589i	$0.461223\pi$
$74$	−1.03395	−	3.18218i	−0.120195	−	0.369921i
$75$	0.309017	−	0.951057i	0.0356822	−	0.109819i
$76$	−0.382150	−	0.277648i	−0.0438356	−	0.0318484i
$77$	−1.06858	+	3.28875i	−0.121776	+	0.374788i
$78$	1.59548	−	4.91040i	0.180653	−	0.555993i
$79$	1.92968	+	1.40200i	0.217106	+	0.157737i	0.691023	−	0.722833i	$-0.257160\pi$
$79$	1.92968	+	1.40200i	0.217106	+	0.157737i	−0.473917	+	0.880570i	$0.657160\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	6.36788	−	4.62654i	0.703215	−	0.510915i
$83$	−3.41587	−	10.5130i	−0.374940	−	1.15395i	−0.943519	−	0.331319i	$-0.892506\pi$
$83$	−3.41587	−	10.5130i	−0.374940	−	1.15395i	0.568579	−	0.822629i	$-0.307494\pi$
$84$	3.29488	+	2.39387i	0.359501	+	0.261193i
$85$	−2.38631	−	1.73375i	−0.258831	−	0.188052i
$86$	−2.61570	+	1.90042i	−0.282058	+	0.204927i
$87$	9.73077			1.04325
$88$	0.849067			0.0905108
$89$	−12.6306	+	9.17664i	−1.33884	+	0.972722i	−0.339351	+	0.940660i	$0.610207\pi$
$89$	−12.6306	+	9.17664i	−1.33884	+	0.972722i	−0.999486	+	0.0320616i	$0.989793\pi$
$90$	0.309017	−	0.951057i	0.0325733	−	0.100250i
$91$	−6.49793	−	19.9986i	−0.681168	−	2.09642i
$92$	8.43883			0.879809
$93$	2.44784	−	5.00081i	0.253829	−	0.518560i
$94$	9.41274			0.970850
$95$	0.145968	+	0.449244i	0.0149760	+	0.0460915i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	12.4963	−	9.07908i	1.26880	−	0.921841i	0.269650	−	0.962958i	$-0.413092\pi$
$97$	12.4963	−	9.07908i	1.26880	−	0.921841i	0.999154	+	0.0411178i	$0.0130919\pi$
$98$	9.58688			0.968421
$99$	0.849067			0.0853344
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	−3.18364	−	2.31305i	−0.316784	−	0.230157i	0.418018	−	0.908439i	$-0.362725\pi$
$101$	−3.18364	−	2.31305i	−0.316784	−	0.230157i	−0.734802	+	0.678282i	$0.762725\pi$
$102$	−2.38631	−	1.73375i	−0.236280	−	0.171667i
$103$	1.31139	+	4.03605i	0.129215	+	0.397684i	0.994645	−	0.103346i	$-0.0329548\pi$
$103$	1.31139	+	4.03605i	0.129215	+	0.397684i	−0.865430	+	0.501029i	$0.832955\pi$
$104$	−4.17703	+	3.03479i	−0.409592	+	0.297586i
$105$	−1.25853	−	3.87337i	−0.122820	−	0.378002i
$106$	−3.57030	+	10.9883i	−0.346779	+	1.06727i
$107$	8.21431	+	5.96804i	0.794107	+	0.576953i	0.909179	−	0.416405i	$-0.136710\pi$
$107$	8.21431	+	5.96804i	0.794107	+	0.576953i	−0.115072	+	0.993357i	$0.536710\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−4.05374	+	12.4761i	−0.388278	+	1.19500i	0.545797	+	0.837917i	$0.316227\pi$
$109$	−4.05374	+	12.4761i	−0.388278	+	1.19500i	−0.934075	+	0.357078i	$0.883773\pi$
$110$	−0.686910	−	0.499069i	−0.0654943	−	0.0475844i
$111$	−1.03395	+	3.18218i	−0.0981386	+	0.302040i
$112$	−1.25853	−	3.87337i	−0.118920	−	0.365999i
$113$	−8.18971	+	5.95017i	−0.770423	+	0.559745i	−0.902089	−	0.431549i	$-0.857967\pi$
$113$	−8.18971	+	5.95017i	−0.770423	+	0.559745i	0.131667	+	0.991294i	$0.457967\pi$
$114$	0.145968	+	0.449244i	0.0136712	+	0.0420756i
$115$	−6.82716	−	4.96022i	−0.636636	−	0.462543i
$116$	−7.87236	−	5.71960i	−0.730930	−	0.531052i
$117$	−4.17703	+	3.03479i	−0.386167	+	0.280567i
$118$	−4.97462			−0.457951
$119$	−12.0130			−1.10123
$120$	−0.809017	+	0.587785i	−0.0738528	+	0.0536572i
$121$	−3.17641	+	9.77599i	−0.288765	+	0.888726i
$122$	2.81926	+	8.67678i	0.255243	+	0.785559i
$123$	−7.87113			−0.709716
$124$	−4.91974	+	2.60694i	−0.441806	+	0.234110i
$125$	1.00000			0.0894427
$126$	−1.25853	−	3.87337i	−0.112119	−	0.345067i
$127$	2.07377	−	6.38242i	0.184018	−	0.566348i	−0.815912	−	0.578176i	$-0.803765\pi$
$127$	2.07377	−	6.38242i	0.184018	−	0.566348i	0.999930	+	0.0118272i	$0.00376482\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	3.23318			0.284666
$130$	5.16310			0.452834
$131$	−5.29941	+	3.85025i	−0.463012	+	0.336398i	−0.794712	−	0.606987i	$-0.792378\pi$
$131$	−5.29941	+	3.85025i	−0.463012	+	0.336398i	0.331700	+	0.943385i	$0.392378\pi$
$132$	−0.686910	−	0.499069i	−0.0597878	−	0.0434384i
$133$	1.55638	+	1.13078i	0.134955	+	0.0980509i
$134$	1.57868	+	4.85868i	0.136377	+	0.419726i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	0.911489	+	2.80527i	0.0781595	+	0.240550i
$137$	−6.71951	+	20.6805i	−0.574086	+	1.76686i	0.0651835	+	0.997873i	$0.479237\pi$
$137$	−6.71951	+	20.6805i	−0.574086	+	1.76686i	−0.639270	+	0.768983i	$0.720763\pi$
$138$	−6.82716	−	4.96022i	−0.581166	−	0.422242i
$139$	5.77248	−	17.7659i	0.489615	−	1.50688i	−0.335568	−	0.942016i	$-0.608928\pi$
$139$	5.77248	−	17.7659i	0.489615	−	1.50688i	0.825183	−	0.564865i	$-0.191072\pi$
$140$	−1.25853	+	3.87337i	−0.106365	+	0.327359i
$141$	−7.61507	−	5.53267i	−0.641305	−	0.465935i
$142$	−4.30636	+	13.2536i	−0.361382	+	1.11222i
$143$	1.35467	+	4.16926i	0.113283	+	0.348651i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	3.00697	+	9.25451i	0.249716	+	0.768545i
$146$	−6.70649	−	4.87255i	−0.555033	−	0.403255i
$147$	−7.75595	−	5.63503i	−0.639700	−	0.464769i
$148$	2.70693	−	1.96670i	0.222508	−	0.161662i
$149$	6.82005			0.558720			0.279360	−	0.960186i	$-0.409878\pi$
$149$	6.82005			0.558720			0.279360	+	0.960186i	$0.409878\pi$
$150$	1.00000			0.0816497
$151$	−6.36659	+	4.62560i	−0.518106	+	0.376426i	−0.815890	−	0.578207i	$-0.803752\pi$
$151$	−6.36659	+	4.62560i	−0.518106	+	0.376426i	0.297784	+	0.954633i	$0.403752\pi$
$152$	0.145968	−	0.449244i	0.0118396	−	0.0364385i
$153$	0.911489	+	2.80527i	0.0736895	+	0.226793i
$154$	−3.45799			−0.278653
$155$	5.51248	+	0.782698i	0.442773	+	0.0628678i
$156$	5.16310			0.413379
$157$	−5.14949	−	15.8485i	−0.410974	−	1.26485i	−0.915803	−	0.401629i	$-0.868444\pi$
$157$	−5.14949	−	15.8485i	−0.410974	−	1.26485i	0.504828	−	0.863220i	$-0.331556\pi$
$158$	−0.737073	+	2.26848i	−0.0586384	+	0.180470i
$159$	9.34718	−	6.79112i	0.741279	−	0.538571i
$160$	1.00000			0.0790569
$161$	−34.3688			−2.70864
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−2.03104	−	1.47564i	−0.159083	−	0.115581i	0.505396	−	0.862888i	$-0.331347\pi$
$163$	−2.03104	−	1.47564i	−0.159083	−	0.115581i	−0.664479	+	0.747307i	$0.731347\pi$
$164$	6.36788	+	4.62654i	0.497248	+	0.361272i
$165$	0.262376	+	0.807511i	0.0204260	+	0.0628646i
$166$	8.94286	−	6.49737i	0.694101	−	0.504294i
$167$	6.41051	+	19.7295i	0.496060	+	1.52672i	0.815298	+	0.579042i	$0.196573\pi$
$167$	6.41051	+	19.7295i	0.496060	+	1.52672i	−0.319237	+	0.947675i	$0.603427\pi$
$168$	−1.25853	+	3.87337i	−0.0970980	+	0.298837i
$169$	−11.0492	−	8.02772i	−0.849939	−	0.617517i
$170$	0.911489	−	2.80527i	0.0699080	−	0.215155i
$171$	0.145968	−	0.449244i	0.0111625	−	0.0343546i
$172$	−2.61570	−	1.90042i	−0.199445	−	0.144905i
$173$	−1.34589	+	4.14221i	−0.102326	+	0.314926i	−0.989094	−	0.147289i	$-0.952945\pi$
$173$	−1.34589	+	4.14221i	−0.102326	+	0.314926i	0.886768	+	0.462215i	$0.152945\pi$
$174$	3.00697	+	9.25451i	0.227958	+	0.701583i
$175$	3.29488	−	2.39387i	0.249070	−	0.180960i
$176$	0.262376	+	0.807511i	0.0197773	+	0.0608684i
$177$	4.02455	+	2.92401i	0.302504	+	0.219782i
$178$	−12.6306	−	9.17664i	−0.946700	−	0.687818i
$179$	−11.9531	+	8.68443i	−0.893416	+	0.649105i	−0.936766	−	0.349955i	$-0.886197\pi$
$179$	−11.9531	+	8.68443i	−0.893416	+	0.649105i	0.0433505	+	0.999060i	$0.486197\pi$
$180$	1.00000			0.0745356
$181$	−23.4712			−1.74460			−0.872302	−	0.488968i	$-0.837374\pi$
$181$	−23.4712			−1.74460			−0.872302	+	0.488968i	$0.837374\pi$
$182$	17.0118	−	12.3598i	1.26100	−	0.916169i
$183$	2.81926	−	8.67678i	0.208405	−	0.641406i
$184$	2.60774	+	8.02581i	0.192245	+	0.591670i
$185$	−3.34595			−0.245999
$186$	5.51248	+	0.782698i	0.404194	+	0.0573902i
$187$	2.50444			0.183143
$188$	2.90870	+	8.95205i	0.212139	+	0.652895i
$189$	−1.25853	+	3.87337i	−0.0915448	+	0.281746i
$190$	−0.382150	+	0.277648i	−0.0277241	+	0.0201427i
$191$	18.5643			1.34327			0.671633	−	0.740884i	$-0.265593\pi$
$191$	18.5643			1.34327			0.671633	+	0.740884i	$0.265593\pi$
$192$	1.00000			0.0721688
$193$	−10.1816	+	7.39734i	−0.732885	+	0.532472i	−0.890475	−	0.455032i	$-0.849628\pi$
$193$	−10.1816	+	7.39734i	−0.732885	+	0.532472i	0.157589	+	0.987505i	$0.449628\pi$
$194$	12.4963	+	9.07908i	0.897180	+	0.651840i
$195$	−4.17703	−	3.03479i	−0.299124	−	0.217326i
$196$	2.96251	+	9.11767i	0.211608	+	0.651262i
$197$	9.36035	−	6.80069i	0.666897	−	0.484529i	−0.202088	−	0.979367i	$-0.564773\pi$
$197$	9.36035	−	6.80069i	0.666897	−	0.484529i	0.868985	+	0.494838i	$0.164773\pi$
$198$	0.262376	+	0.807511i	0.0186463	+	0.0573873i
$199$	−3.92460	+	12.0787i	−0.278208	+	0.856236i	0.710145	+	0.704055i	$0.248629\pi$
$199$	−3.92460	+	12.0787i	−0.278208	+	0.856236i	−0.988353	+	0.152180i	$0.951371\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	1.57868	−	4.85868i	0.111352	−	0.342705i
$202$	1.21604	−	3.74259i	0.0855604	−	0.263328i
$203$	32.0618	+	23.2942i	2.25029	+	1.63493i
$204$	0.911489	−	2.80527i	0.0638170	−	0.196408i
$205$	−2.43231	−	7.48589i	−0.169880	−	0.522837i
$206$	−3.43327	+	2.49442i	−0.239207	+	0.173794i
$207$	2.60774	+	8.02581i	0.181251	+	0.557832i
$208$	−4.17703	−	3.03479i	−0.289625	−	0.210425i
$209$	−0.324471	−	0.235742i	−0.0224441	−	0.0163066i
$210$	3.29488	−	2.39387i	0.227369	−	0.165193i
$211$	11.1084			0.764733			0.382366	−	0.924011i	$-0.375109\pi$
$211$	11.1084			0.764733			0.382366	+	0.924011i	$0.375109\pi$
$212$	−11.5537			−0.793515
$213$	11.2742	−	8.19119i	0.772496	−	0.561251i
$214$	−3.13759	+	9.65650i	−0.214481	+	0.660105i
$215$	0.999109	+	3.07494i	0.0681386	+	0.209709i
$216$	1.00000			0.0680414
$217$	20.0366	−	10.6173i	1.36018	−	0.720747i
$218$	−13.1182			−0.888474
$219$	2.56165	+	7.88396i	0.173100	+	0.532748i
$220$	0.262376	−	0.807511i	0.0176894	−	0.0544424i
$221$	−12.3207	+	8.95154i	−0.828783	+	0.602146i
$222$	−3.34595			−0.224565
$223$	−8.59190			−0.575356			−0.287678	−	0.957727i	$-0.592883\pi$
$223$	−8.59190			−0.575356			−0.287678	+	0.957727i	$0.592883\pi$
$224$	3.29488	−	2.39387i	0.220149	−	0.159947i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	−8.18971	−	5.95017i	−0.544771	−	0.395799i
$227$	0.642416	+	1.97715i	0.0426386	+	0.131228i	0.970110	−	0.242667i	$-0.0780221\pi$
$227$	0.642416	+	1.97715i	0.0426386	+	0.131228i	−0.927471	+	0.373895i	$0.878022\pi$
$228$	−0.382150	+	0.277648i	−0.0253085	+	0.0183877i
$229$	−8.31386	−	25.5874i	−0.549396	−	1.69087i	−0.710303	−	0.703896i	$-0.751442\pi$
$229$	−8.31386	−	25.5874i	−0.549396	−	1.69087i	0.160907	−	0.986970i	$-0.448558\pi$
$230$	2.60774	−	8.02581i	0.171949	−	0.529206i
$231$	2.79758	+	2.03256i	0.184067	+	0.133733i
$232$	3.00697	−	9.25451i	0.197417	−	0.607588i
$233$	−0.206257	+	0.634793i	−0.0135123	+	0.0415867i	−0.957585	−	0.288150i	$-0.906960\pi$
$233$	−0.206257	+	0.634793i	−0.0135123	+	0.0415867i	0.944073	+	0.329736i	$0.106960\pi$
$234$	−4.17703	−	3.03479i	−0.273061	−	0.198391i
$235$	2.90870	−	8.95205i	0.189743	−	0.583967i
$236$	−1.53724	−	4.73114i	−0.100066	−	0.307971i
$237$	1.92968	−	1.40200i	0.125346	−	0.0910694i
$238$	−3.71222	−	11.4250i	−0.240627	−	0.740575i
$239$	−10.0026	−	7.26731i	−0.647014	−	0.470083i	0.215238	−	0.976562i	$-0.430947\pi$
$239$	−10.0026	−	7.26731i	−0.647014	−	0.470083i	−0.862253	+	0.506478i	$0.830947\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	−5.20410	+	3.78100i	−0.335226	+	0.243556i	−0.742645	−	0.669686i	$-0.766429\pi$
$241$	−5.20410	+	3.78100i	−0.335226	+	0.243556i	0.407419	+	0.913241i	$0.366429\pi$
$242$	−10.2791			−0.660765
$243$	1.00000			0.0641500
$244$	−7.38091	+	5.36254i	−0.472514	+	0.343302i
$245$	2.96251	−	9.11767i	0.189268	−	0.582506i
$246$	−2.43231	−	7.48589i	−0.155079	−	0.477283i
$247$	2.43886			0.155181
$248$	−3.99963	−	3.87337i	−0.253977	−	0.245959i
$249$	−11.0540			−0.700518
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	2.47239	−	7.60924i	0.156056	−	0.480291i	−0.842210	−	0.539149i	$-0.818746\pi$
$251$	2.47239	−	7.60924i	0.156056	−	0.480291i	0.998266	+	0.0588582i	$0.0187460\pi$
$252$	3.29488	−	2.39387i	0.207558	−	0.150800i
$253$	7.16513			0.450468
$254$	6.71088			0.421078
$255$	−2.38631	+	1.73375i	−0.149436	+	0.108572i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−17.8807	−	12.9911i	−1.11536	−	0.810360i	−0.131865	−	0.991268i	$-0.542096\pi$
$257$	−17.8807	−	12.9911i	−1.11536	−	0.810360i	−0.983500	+	0.180908i	$0.942096\pi$
$258$	0.999109	+	3.07494i	0.0622018	+	0.191437i
$259$	−11.0245	+	8.00977i	−0.685029	+	0.497703i
$260$	1.59548	+	4.91040i	0.0989478	+	0.304530i
$261$	3.00697	−	9.25451i	0.186127	−	0.572840i
$262$	−5.29941	−	3.85025i	−0.327399	−	0.237869i
$263$	1.46857	−	4.51978i	0.0905557	−	0.278702i	−0.895514	−	0.445033i	$-0.853192\pi$
$263$	1.46857	−	4.51978i	0.0905557	−	0.278702i	0.986070	+	0.166331i	$0.0531920\pi$
$264$	0.262376	−	0.807511i	0.0161481	−	0.0496988i
$265$	9.34718	+	6.79112i	0.574193	+	0.417175i
$266$	−0.594485	+	1.82964i	−0.0364502	+	0.112182i
$267$	4.82444	+	14.8481i	0.295251	+	0.908690i
$268$	−4.13304	+	3.00283i	−0.252466	+	0.183427i
$269$	0.719968	+	2.21583i	0.0438972	+	0.135102i	0.970603	−	0.240686i	$-0.0773723\pi$
$269$	0.719968	+	2.21583i	0.0438972	+	0.135102i	−0.926706	+	0.375787i	$0.877372\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	21.3995	+	15.5477i	1.29993	+	0.944453i	0.999955	−	0.00949526i	$-0.00302248\pi$
$271$	21.3995	+	15.5477i	1.29993	+	0.944453i	0.299973	+	0.953948i	$0.403022\pi$
$272$	−2.38631	+	1.73375i	−0.144691	+	0.105124i
$273$	−21.0277			−1.27266
$274$	−21.7448			−1.31365
$275$	−0.686910	+	0.499069i	−0.0414222	+	0.0300950i
$276$	2.60774	−	8.02581i	0.156968	−	0.483097i
$277$	6.47559	+	19.9298i	0.389081	+	1.19747i	0.933476	+	0.358639i	$0.116759\pi$
$277$	6.47559	+	19.9298i	0.389081	+	1.19747i	−0.544396	+	0.838828i	$0.683241\pi$
$278$	18.6801			1.12036
$279$	−3.99963	−	3.87337i	−0.239451	−	0.231892i
$280$	−4.07270			−0.243390
$281$	−1.61408	−	4.96764i	−0.0962881	−	0.296344i	0.891299	−	0.453416i	$-0.149795\pi$
$281$	−1.61408	−	4.96764i	−0.0962881	−	0.296344i	−0.987587	+	0.157071i	$0.949795\pi$
$282$	2.90870	−	8.95205i	0.173210	−	0.533087i
$283$	1.04547	−	0.759580i	0.0621469	−	0.0451524i	−0.556278	−	0.830996i	$-0.687771\pi$
$283$	1.04547	−	0.759580i	0.0621469	−	0.0451524i	0.618425	+	0.785844i	$0.287771\pi$
$284$	−13.9357			−0.826931
$285$	0.472363			0.0279804
$286$	−3.54658	+	2.57674i	−0.209714	+	0.152366i
$287$	−25.9345	−	18.8425i	−1.53086	−	1.11224i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−2.56473	−	7.89342i	−0.150866	−	0.464319i
$290$	−7.87236	+	5.71960i	−0.462281	+	0.335867i
$291$	−4.77315	−	14.6903i	−0.279807	−	0.861158i
$292$	2.56165	−	7.88396i	0.149909	−	0.461374i
$293$	0.379068	+	0.275409i	0.0221454	+	0.0160896i	0.598803	−	0.800896i	$-0.295643\pi$
$293$	0.379068	+	0.275409i	0.0221454	+	0.0160896i	−0.576657	+	0.816986i	$0.695643\pi$
$294$	2.96251	−	9.11767i	0.172777	−	0.531753i
$295$	−1.53724	+	4.73114i	−0.0895016	+	0.275458i
$296$	2.70693	+	1.96670i	0.157337	+	0.114312i
$297$	0.262376	−	0.807511i	0.0152246	−	0.0468565i
$298$	2.10751	+	6.48626i	0.122085	+	0.375739i
$299$	−35.2493	+	25.6101i	−2.03852	+	1.48107i
$300$	0.309017	+	0.951057i	0.0178411	+	0.0549093i
$301$	10.6530	+	7.73983i	0.614027	+	0.446116i
$302$	−6.36659	−	4.62560i	−0.366356	−	0.266173i
$303$	−3.18364	+	2.31305i	−0.182895	+	0.132881i
$304$	0.472363			0.0270919
$305$	9.12331			0.522399
$306$	−2.38631	+	1.73375i	−0.136416	+	0.0991121i
$307$	2.38714	−	7.34685i	0.136241	−	0.419307i	−0.859540	−	0.511069i	$-0.829250\pi$
$307$	2.38714	−	7.34685i	0.136241	−	0.419307i	0.995781	+	0.0917617i	$0.0292498\pi$
$308$	−1.06858	−	3.28875i	−0.0608879	−	0.187394i
$309$	4.24375			0.241419
$310$	0.959059	+	5.48454i	0.0544709	+	0.311501i
$311$	3.26252			0.185000			0.0925001	−	0.995713i	$-0.470514\pi$
$311$	3.26252			0.185000			0.0925001	+	0.995713i	$0.470514\pi$
$312$	1.59548	+	4.91040i	0.0903265	+	0.277996i
$313$	−7.06289	+	21.7373i	−0.399218	+	1.22867i	0.526410	+	0.850231i	$0.323538\pi$
$313$	−7.06289	+	21.7373i	−0.399218	+	1.22867i	−0.925628	+	0.378436i	$0.876462\pi$
$314$	13.4815	−	9.79491i	0.760808	−	0.552759i
$315$	−4.07270			−0.229471
$316$	−2.38522			−0.134179
$317$	4.41434	−	3.20721i	0.247934	−	0.180135i	−0.456877	−	0.889530i	$-0.651032\pi$
$317$	4.41434	−	3.20721i	0.247934	−	0.180135i	0.704811	+	0.709395i	$0.251032\pi$
$318$	9.34718	+	6.79112i	0.524164	+	0.380827i
$319$	−6.68416	−	4.85633i	−0.374241	−	0.271902i
$320$	0.309017	+	0.951057i	0.0172746	+	0.0531657i
$321$	8.21431	−	5.96804i	0.458478	−	0.333104i
$322$	−10.6206	−	32.6867i	−0.591860	−	1.82156i
$323$	0.430554	−	1.32511i	0.0239567	−	0.0737310i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	1.59548	−	4.91040i	0.0885016	−	0.272380i
$326$	0.775788	−	2.38763i	0.0429669	−	0.132239i
$327$	10.6128	+	7.71067i	0.586890	+	0.426401i
$328$	−2.43231	+	7.48589i	−0.134302	+	0.413339i
$329$	−11.8463	−	36.4590i	−0.653105	−	2.01005i
$330$	−0.686910	+	0.499069i	−0.0378131	+	0.0274728i
$331$	9.07883	+	27.9418i	0.499018	+	1.53582i	0.810601	+	0.585599i	$0.199141\pi$
$331$	9.07883	+	27.9418i	0.499018	+	1.53582i	−0.311583	+	0.950219i	$0.600859\pi$
$332$	8.94286	+	6.49737i	0.490803	+	0.356589i
$333$	2.70693	+	1.96670i	0.148339	+	0.107774i
$334$	−16.7829	+	12.1935i	−0.918322	+	0.667200i
$335$	5.10872			0.279119
$336$	−4.07270			−0.222184
$337$	−1.80094	+	1.30846i	−0.0981034	+	0.0712763i	−0.635756	−	0.771890i	$-0.719311\pi$
$337$	−1.80094	+	1.30846i	−0.0981034	+	0.0712763i	0.537652	+	0.843167i	$0.319311\pi$
$338$	4.22042	−	12.9891i	0.229561	−	0.706515i
$339$	3.12819	+	9.62758i	0.169900	+	0.522898i
$340$	2.94964			0.159967
$341$	−4.17719	+	2.21346i	−0.226208	+	0.119866i
$342$	0.472363			0.0255425
$343$	−3.25568	−	10.0199i	−0.175790	−	0.541026i
$344$	0.999109	−	3.07494i	0.0538683	−	0.165790i
$345$	−6.82716	+	4.96022i	−0.367562	+	0.267049i
$346$	−4.35538			−0.234147
$347$	10.4660			0.561844			0.280922	−	0.959731i	$-0.409360\pi$
$347$	10.4660			0.561844			0.280922	+	0.959731i	$0.409360\pi$
$348$	−7.87236	+	5.71960i	−0.422003	+	0.306603i
$349$	−25.2531	−	18.3474i	−1.35177	−	0.982116i	−0.998921	−	0.0464348i	$-0.985214\pi$
$349$	−25.2531	−	18.3474i	−1.35177	−	0.982116i	−0.352846	−	0.935681i	$-0.614786\pi$
$350$	3.29488	+	2.39387i	0.176119	+	0.127958i
$351$	1.59548	+	4.91040i	0.0851607	+	0.262098i
$352$	−0.686910	+	0.499069i	−0.0366124	+	0.0266005i
$353$	5.14433	+	15.8326i	0.273805	+	0.842686i	0.989533	+	0.144307i	$0.0460951\pi$
$353$	5.14433	+	15.8326i	0.273805	+	0.842686i	−0.715728	+	0.698379i	$0.753905\pi$
$354$	−1.53724	+	4.73114i	−0.0817034	+	0.251457i
$355$	11.2742	+	8.19119i	0.598373	+	0.434743i
$356$	4.82444	−	14.8481i	0.255695	−	0.786948i
$357$	−3.71222	+	11.4250i	−0.196471	+	0.604677i
$358$	−11.9531	−	8.68443i	−0.631740	−	0.458986i
$359$	1.71913	−	5.29095i	0.0907324	−	0.279246i	−0.895386	−	0.445292i	$-0.853100\pi$
$359$	1.71913	−	5.29095i	0.0907324	−	0.279246i	0.986118	+	0.166046i	$0.0531000\pi$
$360$	0.309017	+	0.951057i	0.0162866	+	0.0501251i
$361$	15.1908	−	11.0368i	0.799516	−	0.580883i
$362$	−7.25301	−	22.3225i	−0.381210	−	1.17324i
$363$	8.31595	+	6.04189i	0.436474	+	0.317117i
$364$	17.0118	+	12.3598i	0.891661	+	0.647829i
$365$	−6.70649	+	4.87255i	−0.351034	+	0.255041i
$366$	9.12331			0.476883
$367$	−18.5586			−0.968751			−0.484376	−	0.874860i	$-0.660953\pi$
$367$	−18.5586			−0.968751			−0.484376	+	0.874860i	$0.660953\pi$
$368$	−6.82716	+	4.96022i	−0.355890	+	0.258569i
$369$	−2.43231	+	7.48589i	−0.126621	+	0.389700i
$370$	−1.03395	−	3.18218i	−0.0537527	−	0.165434i
$371$	47.0549			2.44297
$372$	0.959059	+	5.48454i	0.0497249	+	0.284360i
$373$	24.2691			1.25661			0.628303	−	0.777969i	$-0.283750\pi$
$373$	24.2691			1.25661			0.628303	+	0.777969i	$0.283750\pi$
$374$	0.773915	+	2.38186i	0.0400182	+	0.123163i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	−7.61507	+	5.53267i	−0.392717	+	0.285326i
$377$	50.2409			2.58754
$378$	−4.07270			−0.209477
$379$	17.8146	−	12.9430i	0.915073	−	0.664840i	−0.0272197	−	0.999629i	$-0.508665\pi$
$379$	17.8146	−	12.9430i	0.915073	−	0.664840i	0.942293	+	0.334790i	$0.108665\pi$
$380$	−0.382150	−	0.277648i	−0.0196039	−	0.0142431i
$381$	−5.42921	−	3.94455i	−0.278147	−	0.202086i
$382$	5.73669	+	17.6557i	0.293515	+	0.903345i
$383$	13.3193	−	9.67706i	0.680586	−	0.494475i	−0.192966	−	0.981205i	$-0.561811\pi$
$383$	13.3193	−	9.67706i	0.680586	−	0.494475i	0.873552	+	0.486731i	$0.161811\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	−1.06858	+	3.28875i	−0.0544598	+	0.167610i
$386$	−10.1816	−	7.39734i	−0.518228	−	0.376515i
$387$	0.999109	−	3.07494i	0.0507875	−	0.156308i
$388$	−4.77315	+	14.6903i	−0.242320	+	0.745785i
$389$	−12.9174	−	9.38505i	−0.654939	−	0.475841i	0.210011	−	0.977699i	$-0.432650\pi$
$389$	−12.9174	−	9.38505i	−0.654939	−	0.475841i	−0.864950	+	0.501858i	$0.832650\pi$
$390$	1.59548	−	4.91040i	0.0807905	−	0.248648i
$391$	7.69190	+	23.6732i	0.388996	+	1.19721i
$392$	−7.75595	+	5.63503i	−0.391735	+	0.284612i
$393$	2.02420	+	6.22984i	0.102107	+	0.314254i
$394$	9.36035	+	6.80069i	0.471567	+	0.342614i
$395$	1.92968	+	1.40200i	0.0970929	+	0.0705421i
$396$	−0.686910	+	0.499069i	−0.0345185	+	0.0250792i
$397$	−14.3123			−0.718313			−0.359156	−	0.933277i	$-0.616936\pi$
$397$	−14.3123			−0.718313			−0.359156	+	0.933277i	$0.616936\pi$
$398$	−12.7003			−0.636608
$399$	1.55638	−	1.13078i	0.0779166	−	0.0566097i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−3.59592	−	11.0671i	−0.179572	−	0.552664i	0.820241	−	0.572018i	$-0.193839\pi$
$401$	−3.59592	−	11.0671i	−0.179572	−	0.552664i	−0.999813	+	0.0193535i	$0.993839\pi$
$402$	5.10872			0.254800
$403$	12.6384	−	25.8197i	0.629565	−	1.28617i
$404$	3.93519			0.195783
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	−12.2465	+	37.6908i	−0.607784	+	1.87057i
$407$	2.29836	−	1.66986i	0.113926	−	0.0827718i
$408$	2.94964			0.146029
$409$	−10.0006			−0.494497			−0.247248	−	0.968952i	$-0.579526\pi$
$409$	−10.0006			−0.494497			−0.247248	+	0.968952i	$0.579526\pi$
$410$	6.36788	−	4.62654i	0.314487	−	0.228488i
$411$	17.5919	+	12.7813i	0.867744	+	0.630453i
$412$	−3.43327	−	2.49442i	−0.169145	−	0.122891i
$413$	6.26072	+	19.2685i	0.308070	+	0.948142i
$414$	−6.82716	+	4.96022i	−0.335537	+	0.243782i
$415$	−3.41587	−	10.5130i	−0.167678	−	0.516061i
$416$	1.59548	−	4.91040i	0.0782251	−	0.240752i
$417$	−15.1125	−	10.9799i	−0.740065	−	0.537688i
$418$	0.123937	−	0.381438i	0.00606195	−	0.0186568i
$419$	6.62769	−	20.3979i	0.323784	−	0.996504i	−0.648203	−	0.761468i	$-0.724479\pi$
$419$	6.62769	−	20.3979i	0.323784	−	0.996504i	0.971987	−	0.235036i	$-0.0755208\pi$
$420$	3.29488	+	2.39387i	0.160774	+	0.116809i
$421$	−10.0805	+	31.0247i	−0.491296	+	1.51205i	0.331355	+	0.943506i	$0.392494\pi$
$421$	−10.0805	+	31.0247i	−0.491296	+	1.51205i	−0.822651	+	0.568547i	$0.807506\pi$
$422$	3.43268	+	10.5647i	0.167100	+	0.514282i
$423$	−7.61507	+	5.53267i	−0.370257	+	0.269008i
$424$	−3.57030	−	10.9883i	−0.173389	−	0.533637i
$425$	−2.38631	−	1.73375i	−0.115753	−	0.0840994i
$426$	11.2742	+	8.19119i	0.546237	+	0.396864i
$427$	30.0602	−	21.8400i	1.45472	−	1.05691i
$428$	−10.1534			−0.490785
$429$	4.38381			0.211653
$430$	−2.61570	+	1.90042i	−0.126140	+	0.0916463i
$431$	−4.53383	+	13.9537i	−0.218387	+	0.672126i	0.780509	+	0.625145i	$0.214960\pi$
$431$	−4.53383	+	13.9537i	−0.218387	+	0.672126i	−0.998896	+	0.0469813i	$0.985040\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	15.0348			0.722528			0.361264	−	0.932464i	$-0.382345\pi$
$433$	15.0348			0.722528			0.361264	+	0.932464i	$0.382345\pi$
$434$	16.2893	+	15.7751i	0.781911	+	0.757227i
$435$	9.73077			0.466555
$436$	−4.05374	−	12.4761i	−0.194139	−	0.597498i
$437$	1.23180	−	3.79110i	0.0589251	−	0.181353i
$438$	−6.70649	+	4.87255i	−0.320449	+	0.232820i
$439$	15.7610			0.752233			0.376117	−	0.926572i	$-0.377259\pi$
$439$	15.7610			0.752233			0.376117	+	0.926572i	$0.377259\pi$
$440$	0.849067			0.0404777
$441$	−7.75595	+	5.63503i	−0.369331	+	0.268335i
$442$	−12.3207	−	8.95154i	−0.586038	−	0.425781i
$443$	5.20477	+	3.78149i	0.247286	+	0.179664i	0.704523	−	0.709681i	$-0.251161\pi$
$443$	5.20477	+	3.78149i	0.247286	+	0.179664i	−0.457237	+	0.889345i	$0.651161\pi$
$444$	−1.03395	−	3.18218i	−0.0490693	−	0.151020i
$445$	−12.6306	+	9.17664i	−0.598746	+	0.435014i
$446$	−2.65504	−	8.17139i	−0.125720	−	0.386926i
$447$	2.10751	−	6.48626i	0.0996819	−	0.306789i
$448$	3.29488	+	2.39387i	0.155669	+	0.113100i
$449$	−7.62291	+	23.4609i	−0.359747	+	1.10719i	0.593458	+	0.804865i	$0.297762\pi$
$449$	−7.62291	+	23.4609i	−0.359747	+	1.10719i	−0.953205	+	0.302323i	$0.902238\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	5.40676	+	3.92824i	0.254594	+	0.184974i
$452$	3.12819	−	9.62758i	0.147138	−	0.452843i
$453$	2.43182	+	7.48438i	0.114257	+	0.351647i
$454$	−1.68187	+	1.22195i	−0.0789339	+	0.0573488i
$455$	−6.49793	−	19.9986i	−0.304628	−	0.937548i
$456$	−0.382150	−	0.277648i	−0.0178958	−	0.0130021i
$457$	0.130617	+	0.0948989i	0.00611001	+	0.00443918i	0.590836	−	0.806792i	$-0.298798\pi$
$457$	0.130617	+	0.0948989i	0.00611001	+	0.00443918i	−0.584726	+	0.811231i	$0.698798\pi$
$458$	21.7660	−	15.8139i	1.01706	−	0.738936i
$459$	2.94964			0.137677
$460$	8.43883			0.393463
$461$	−1.59146	+	1.15626i	−0.0741218	+	0.0538526i	−0.624229	−	0.781241i	$-0.714587\pi$
$461$	−1.59146	+	1.15626i	−0.0741218	+	0.0538526i	0.550107	+	0.835094i	$0.314587\pi$
$462$	−1.06858	+	3.28875i	−0.0497148	+	0.153006i
$463$	−3.40725	−	10.4864i	−0.158348	−	0.487347i	0.840136	−	0.542375i	$-0.182475\pi$
$463$	−3.40725	−	10.4864i	−0.158348	−	0.487347i	−0.998485	+	0.0550288i	$0.982475\pi$
$464$	9.73077			0.451740
$465$	2.44784	−	5.00081i	0.113516	−	0.231907i
$466$	−0.667461			−0.0309195
$467$	1.42479	+	4.38506i	0.0659315	+	0.202916i	0.978595	−	0.205796i	$-0.0659782\pi$
$467$	1.42479	+	4.38506i	0.0659315	+	0.202916i	−0.912664	+	0.408712i	$0.865978\pi$
$468$	1.59548	−	4.91040i	0.0737513	−	0.226983i
$469$	16.8326	−	12.2296i	0.777259	−	0.564712i
$470$	9.41274			0.434177
$471$	−16.6641			−0.767841
$472$	4.02455	−	2.92401i	0.185245	−	0.134588i
$473$	−2.22090	−	1.61358i	−0.102117	−	0.0741926i
$474$	1.92968	+	1.40200i	0.0886332	+	0.0643958i
$475$	0.145968	+	0.449244i	0.00669749	+	0.0206127i
$476$	9.71872	−	7.06106i	0.445457	−	0.323643i
$477$	−3.57030	−	10.9883i	−0.163473	−	0.503118i
$478$	3.82065	−	11.7588i	0.174753	−	0.537833i
$479$	−3.79504	−	2.75726i	−0.173400	−	0.125982i	0.497700	−	0.867349i	$-0.334178\pi$
$479$	−3.79504	−	2.75726i	−0.173400	−	0.125982i	−0.671100	+	0.741367i	$0.734178\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−5.33841	+	16.4299i	−0.243410	+	0.749140i
$482$	−5.20410	−	3.78100i	−0.237040	−	0.172220i
$483$	−10.6206	+	32.6867i	−0.483252	+	1.48730i
$484$	−3.17641	−	9.77599i	−0.144382	−	0.444363i
$485$	12.4963	−	9.07908i	0.567427	−	0.412260i
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−3.82316	−	2.77769i	−0.173244	−	0.125869i	0.497784	−	0.867301i	$-0.334147\pi$
$487$	−3.82316	−	2.77769i	−0.173244	−	0.125869i	−0.671028	+	0.741432i	$0.734147\pi$
$488$	−7.38091	−	5.36254i	−0.334118	−	0.242751i
$489$	−2.03104	+	1.47564i	−0.0918468	+	0.0667306i
$490$	9.58688			0.433091
$491$	14.1040			0.636504			0.318252	−	0.948006i	$-0.396904\pi$
$491$	14.1040			0.636504			0.318252	+	0.948006i	$0.396904\pi$
$492$	6.36788	−	4.62654i	0.287086	−	0.208580i
$493$	8.86949	−	27.2975i	0.399462	−	1.22942i
$494$	0.753649	+	2.31949i	0.0339083	+	0.104359i
$495$	0.849067			0.0381627
$496$	2.44784	−	5.00081i	0.109911	−	0.224543i
$497$	56.7559			2.54585
$498$	−3.41587	−	10.5130i	−0.153069	−	0.471097i
$499$	−3.20627	+	9.86787i	−0.143532	+	0.441747i	−0.996819	−	0.0796947i	$-0.974605\pi$
$499$	−3.20627	+	9.86787i	−0.143532	+	0.441747i	0.853287	+	0.521441i	$0.174605\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	20.7449			0.926812
$502$	8.00082			0.357094
$503$	9.23579	−	6.71020i	0.411804	−	0.299193i	−0.362528	−	0.931973i	$-0.618086\pi$
$503$	9.23579	−	6.71020i	0.411804	−	0.299193i	0.774332	+	0.632780i	$0.218086\pi$
$504$	3.29488	+	2.39387i	0.146766	+	0.106632i
$505$	−3.18364	−	2.31305i	−0.141670	−	0.102929i
$506$	2.21415	+	6.81445i	0.0984309	+	0.302939i
$507$	−11.0492	+	8.02772i	−0.490712	+	0.356523i
$508$	2.07377	+	6.38242i	0.0920089	+	0.283174i
$509$	12.6563	−	38.9522i	0.560982	−	1.72653i	−0.118614	−	0.992940i	$-0.537845\pi$
$509$	12.6563	−	38.9522i	0.560982	−	1.72653i	0.679597	−	0.733586i	$-0.262155\pi$
$510$	−2.38631	−	1.73375i	−0.105667	−	0.0767719i
$511$	−10.4328	+	32.1090i	−0.461522	+	1.42042i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.382150	−	0.277648i	−0.0168723	−	0.0122585i
$514$	6.82980	−	21.0200i	0.301250	−	0.927151i
$515$	1.31139	+	4.03605i	0.0577868	+	0.177850i
$516$	−2.61570	+	1.90042i	−0.115150	+	0.0836612i
$517$	2.46968	+	7.60089i	0.108616	+	0.334287i
$518$	−11.0245	−	8.00977i	−0.484389	−	0.351929i
$519$	3.52357	+	2.56003i	0.154668	+	0.112373i
$520$	−4.17703	+	3.03479i	−0.183175	+	0.133084i
$521$	8.77813			0.384577			0.192289	−	0.981338i	$-0.438409\pi$
$521$	8.77813			0.384577			0.192289	+	0.981338i	$0.438409\pi$
$522$	9.73077			0.425904
$523$	19.9890	−	14.5229i	0.874059	−	0.635041i	−0.0576140	−	0.998339i	$-0.518349\pi$
$523$	19.9890	−	14.5229i	0.874059	−	0.635041i	0.931673	+	0.363298i	$0.118349\pi$
$524$	2.02420	−	6.22984i	0.0884274	−	0.272152i
$525$	−1.25853	−	3.87337i	−0.0549269	−	0.169048i
$526$	4.75238			0.207214
$527$	−11.7975	−	11.4250i	−0.513905	−	0.497682i
$528$	0.849067			0.0369509
$529$	14.8989	+	45.8542i	0.647779	+	1.99366i
$530$	−3.57030	+	10.9883i	−0.155084	+	0.477300i
$531$	4.02455	−	2.92401i	0.174651	−	0.126891i
$532$	−1.92379			−0.0834071
$533$	−40.6394			−1.76029
$534$	−12.6306	+	9.17664i	−0.546578	+	0.397112i
$535$	8.21431	+	5.96804i	0.355135	+	0.258021i
$536$	−4.13304	−	3.00283i	−0.178520	−	0.129702i
$537$	4.56567	+	14.0517i	0.197023	+	0.606376i
$538$	−1.88490	+	1.36946i	−0.0812638	+	0.0590416i
$539$	2.51537	+	7.74151i	0.108345	+	0.333450i
$540$	0.309017	−	0.951057i	0.0132980	−	0.0409270i
$541$	22.0763	+	16.0393i	0.949133	+	0.689585i	0.950602	−	0.310413i	$-0.100468\pi$
$541$	22.0763	+	16.0393i	0.949133	+	0.689585i	−0.00146872	+	0.999999i	$0.500468\pi$
$542$	−8.17388	+	25.1566i	−0.351098	+	1.08057i
$543$	−7.25301	+	22.3225i	−0.311257	+	0.957949i
$544$	−2.38631	−	1.73375i	−0.102312	−	0.0743341i
$545$	−4.05374	+	12.4761i	−0.173643	+	0.534418i
$546$	−6.49793	−	19.9986i	−0.278086	−	0.855860i
$547$	−21.9922	+	15.9782i	−0.940317	+	0.683180i	−0.948497	−	0.316786i	$-0.897396\pi$
$547$	−21.9922	+	15.9782i	−0.940317	+	0.683180i	0.00818017	+	0.999967i	$0.497396\pi$
$548$	−6.71951	−	20.6805i	−0.287043	−	0.883428i
$549$	−7.38091	−	5.36254i	−0.315010	−	0.228868i
$550$	−0.686910	−	0.499069i	−0.0292899	−	0.0212804i
$551$	−3.71861	+	2.70173i	−0.158418	+	0.115098i
$552$	8.43883			0.359181
$553$	9.71428			0.413093
$554$	−16.9533	+	12.3173i	−0.720278	+	0.523312i
$555$	−1.03395	+	3.18218i	−0.0438889	+	0.135076i
$556$	5.77248	+	17.7659i	0.244808	+	0.753441i
$557$	2.91787			0.123634			0.0618171	−	0.998087i	$-0.480310\pi$
$557$	2.91787			0.123634			0.0618171	+	0.998087i	$0.480310\pi$
$558$	2.44784	−	5.00081i	0.103625	−	0.211701i
$559$	16.6932			0.706049
$560$	−1.25853	−	3.87337i	−0.0531827	−	0.163680i
$561$	0.773915	−	2.38186i	0.0326747	−	0.100562i
$562$	4.22573	−	3.07017i	0.178251	−	0.129507i
$563$	4.48991			0.189227			0.0946135	−	0.995514i	$-0.469838\pi$
$563$	4.48991			0.189227			0.0946135	+	0.995514i	$0.469838\pi$
$564$	9.41274			0.396348
$565$	−8.18971	+	5.95017i	−0.344544	+	0.250326i
$566$	1.04547	+	0.759580i	0.0439445	+	0.0319275i
$567$	3.29488	+	2.39387i	0.138372	+	0.100533i
$568$	−4.30636	−	13.2536i	−0.180691	−	0.556110i
$569$	−31.0992	+	22.5949i	−1.30375	+	0.947227i	−0.999985	−	0.00552136i	$-0.998242\pi$
$569$	−31.0992	+	22.5949i	−1.30375	+	0.947227i	−0.303761	+	0.952748i	$0.598242\pi$
$570$	0.145968	+	0.449244i	0.00611394	+	0.0188168i
$571$	9.60870	−	29.5726i	0.402112	−	1.23757i	−0.521171	−	0.853452i	$-0.674505\pi$
$571$	9.60870	−	29.5726i	0.402112	−	1.23757i	0.923283	−	0.384121i	$-0.125495\pi$
$572$	−3.54658	−	2.57674i	−0.148290	−	0.107739i
$573$	5.73669	−	17.6557i	0.239654	−	0.737578i
$574$	9.90608	−	30.4878i	0.413472	−	1.27254i
$575$	−6.82716	−	4.96022i	−0.284712	−	0.206856i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	0.829972	+	2.55439i	0.0345522	+	0.106341i	0.966845	−	0.255363i	$-0.0821951\pi$
$577$	0.829972	+	2.55439i	0.0345522	+	0.106341i	−0.932293	+	0.361704i	$0.882195\pi$
$578$	6.71454	−	4.87840i	0.279288	−	0.202915i
$579$	3.88901	+	11.9692i	0.161622	+	0.497421i
$580$	−7.87236	−	5.71960i	−0.326882	−	0.237494i
$581$	−36.4216	−	26.4618i	−1.51102	−	1.09782i
$582$	12.4963	−	9.07908i	0.517987	−	0.376340i
$583$	−9.80990			−0.406285
$584$	8.28968			0.343030
$585$	−4.17703	+	3.03479i	−0.172699	+	0.125473i
$586$	−0.144791	+	0.445621i	−0.00598127	+	0.0184085i
$587$	−5.62675	−	17.3174i	−0.232241	−	0.714764i	−0.997475	−	0.0710123i	$-0.977377\pi$
$587$	−5.62675	−	17.3174i	−0.232241	−	0.714764i	0.765235	−	0.643751i	$-0.222623\pi$
$588$	9.58688			0.395356
$589$	0.453024	+	2.59070i	0.0186665	+	0.106748i
$590$	−4.97462			−0.204802
$591$	−3.57533	−	11.0037i	−0.147070	−	0.452634i
$592$	−1.03395	+	3.18218i	−0.0424953	+	0.130787i
$593$	30.7825	−	22.3648i	1.26409	−	0.918413i	0.265136	−	0.964211i	$-0.414583\pi$
$593$	30.7825	−	22.3648i	1.26409	−	0.918413i	0.998951	+	0.0457979i	$0.0145830\pi$
$594$	0.849067			0.0348376
$595$	−12.0130			−0.492485
$596$	−5.51754	+	4.00873i	−0.226007	+	0.164204i
$597$	10.2747	+	7.46504i	0.420517	+	0.305524i
$598$	−35.2493	−	25.6101i	−1.44145	−	1.04728i
$599$	10.5270	+	32.3988i	0.430121	+	1.32378i	0.898004	+	0.439987i	$0.145017\pi$
$599$	10.5270	+	32.3988i	0.430121	+	1.32378i	−0.467883	+	0.883790i	$0.654983\pi$
$600$	−0.809017	+	0.587785i	−0.0330280	+	0.0239962i
$601$	4.60918	+	14.1856i	0.188012	+	0.578642i	0.999987	−	0.00504989i	$-0.00160744\pi$
$601$	4.60918	+	14.1856i	0.188012	+	0.578642i	−0.811975	+	0.583692i	$0.801607\pi$
$602$	−4.06907	+	12.5233i	−0.165843	+	0.510412i
$603$	−4.13304	−	3.00283i	−0.168310	−	0.122285i
$604$	2.43182	−	7.48438i	0.0989494	−	0.304535i
$605$	−3.17641	+	9.77599i	−0.129140	+	0.397451i
$606$	−3.18364	−	2.31305i	−0.129326	−	0.0939612i
$607$	0.399152	−	1.22847i	0.0162011	−	0.0498619i	−0.942629	−	0.333842i	$-0.891655\pi$
$607$	0.399152	−	1.22847i	0.0162011	−	0.0498619i	0.958830	+	0.283980i	$0.0916549\pi$
$608$	0.145968	+	0.449244i	0.00591980	+	0.0182193i
$609$	32.0618	−	23.2942i	1.29921	−	0.943930i
$610$	2.81926	+	8.67678i	0.114148	+	0.351313i
$611$	−39.3173	−	28.5657i	−1.59061	−	1.15565i
$612$	−2.38631	−	1.73375i	−0.0964608	−	0.0700829i
$613$	−16.3551	+	11.8826i	−0.660574	+	0.479935i	−0.866857	−	0.498557i	$-0.833863\pi$
$613$	−16.3551	+	11.8826i	−0.660574	+	0.479935i	0.206282	+	0.978492i	$0.433863\pi$
$614$	7.72494			0.311753
$615$	−7.87113			−0.317395
$616$	2.79758	−	2.03256i	0.112718	−	0.0818941i
$617$	−3.92084	+	12.0671i	−0.157847	+	0.485804i	−0.998438	−	0.0558665i	$-0.982208\pi$
$617$	−3.92084	+	12.0671i	−0.157847	+	0.485804i	0.840591	+	0.541670i	$0.182208\pi$
$618$	1.31139	+	4.03605i	0.0527519	+	0.162354i
$619$	35.6032			1.43101			0.715507	−	0.698606i	$-0.246196\pi$
$619$	35.6032			1.43101			0.715507	+	0.698606i	$0.246196\pi$
$620$	−4.91974	+	2.60694i	−0.197582	+	0.104697i
$621$	8.43883			0.338639
$622$	1.00817	+	3.10284i	0.0404240	+	0.124412i
$623$	−19.6485	+	60.4719i	−0.787201	+	2.42276i
$624$	−4.17703	+	3.03479i	−0.167215	+	0.121489i
$625$	1.00000			0.0400000
$626$	−22.8560			−0.913509
$627$	−0.324471	+	0.235742i	−0.0129581	+	0.00941463i
$628$	13.4815	+	9.79491i	0.537972	+	0.390860i
$629$	7.98446	+	5.80105i	0.318361	+	0.231303i
$630$	−1.25853	−	3.87337i	−0.0501412	−	0.154319i
$631$	15.0171	−	10.9106i	0.597821	−	0.434342i	−0.247284	−	0.968943i	$-0.579538\pi$
$631$	15.0171	−	10.9106i	0.597821	−	0.434342i	0.845105	+	0.534601i	$0.179538\pi$
$632$	−0.737073	−	2.26848i	−0.0293192	−	0.0902352i
$633$	3.43268	−	10.5647i	0.136437	−	0.419909i
$634$	4.41434	+	3.20721i	0.175316	+	0.127375i
$635$	2.07377	−	6.38242i	0.0822952	−	0.253279i
$636$	−3.57030	+	10.9883i	−0.141572	+	0.435713i
$637$	−40.0447	−	29.0942i	−1.58663	−	1.15275i
$638$	2.55312	−	7.85770i	0.101079	−	0.311089i
$639$	−4.30636	−	13.2536i	−0.170357	−	0.524305i
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−6.00611	−	18.4849i	−0.237227	−	0.730110i	−0.996818	−	0.0797091i	$-0.974601\pi$
$641$	−6.00611	−	18.4849i	−0.237227	−	0.730110i	0.759591	−	0.650401i	$-0.225399\pi$
$642$	8.21431	+	5.96804i	0.324193	+	0.235540i
$643$	29.8956	+	21.7205i	1.17897	+	0.856571i	0.992055	−	0.125805i	$-0.0401513\pi$
$643$	29.8956	+	21.7205i	1.17897	+	0.856571i	0.186914	+	0.982376i	$0.440151\pi$
$644$	27.8050	−	20.2015i	1.09567	−	0.796050i
$645$	3.23318			0.127306
$646$	1.39330			0.0548187
$647$	−1.26395	+	0.918313i	−0.0496910	+	0.0361026i	−0.612354	−	0.790584i	$-0.709777\pi$
$647$	−1.26395	+	0.918313i	−0.0496910	+	0.0361026i	0.562662	+	0.826687i	$0.309777\pi$
$648$	0.309017	−	0.951057i	0.0121393	−	0.0373610i
$649$	−1.30522	−	4.01706i	−0.0512344	−	0.157683i
$650$	5.16310			0.202513
$651$	−3.90596	−	22.3369i	−0.153087	−	0.875452i
$652$	2.51050			0.0983189
$653$	4.87995	+	15.0189i	0.190967	+	0.587737i	1.00000		2.68109e-5i	$-8.53419e-6\pi$
$653$	4.87995	+	15.0189i	0.190967	+	0.587737i	−0.809033	+	0.587764i	$0.800009\pi$
$654$	−4.05374	+	12.4761i	−0.158514	+	0.487855i
$655$	−5.29941	+	3.85025i	−0.207065	+	0.150442i
$656$	−7.87113			−0.307316
$657$	8.28968			0.323411
$658$	31.0139	−	22.5329i	1.20905	−	0.878424i
$659$	−20.1016	−	14.6047i	−0.783047	−	0.568917i	0.122845	−	0.992426i	$-0.460798\pi$
$659$	−20.1016	−	14.6047i	−0.783047	−	0.568917i	−0.905892	+	0.423509i	$0.860798\pi$
$660$	−0.686910	−	0.499069i	−0.0267379	−	0.0194262i
$661$	−0.783610	−	2.41170i	−0.0304789	−	0.0938044i	0.934660	−	0.355543i	$-0.115704\pi$
$661$	−0.783610	−	2.41170i	−0.0304789	−	0.0938044i	−0.965139	+	0.261739i	$0.915704\pi$
$662$	−23.7687	+	17.2690i	−0.923796	+	0.671177i
$663$	4.70610	+	14.4839i	0.182770	+	0.562508i
$664$	−3.41587	+	10.5130i	−0.132561	+	0.407982i
$665$	1.55638	+	1.13078i	0.0603539	+	0.0438497i
$666$	−1.03395	+	3.18218i	−0.0400649	+	0.123307i
$667$	25.3753	−	78.0973i	0.982537	−	3.02394i
$668$	−16.7829	−	12.1935i	−0.649352	−	0.471781i
$669$	−2.65504	+	8.17139i	−0.102650	+	0.315924i
$670$	1.57868	+	4.85868i	0.0609898	+	0.187707i
$671$	−6.26689	+	4.55316i	−0.241930	+	0.175773i
$672$	−1.25853	−	3.87337i	−0.0485490	−	0.149418i
$673$	−6.45703	−	4.69131i	−0.248900	−	0.180837i	0.456339	−	0.889806i	$-0.349160\pi$
$673$	−6.45703	−	4.69131i	−0.248900	−	0.180837i	−0.705239	+	0.708969i	$0.749160\pi$
$674$	−1.80094	−	1.30846i	−0.0693696	−	0.0503999i
$675$	−0.809017	+	0.587785i	−0.0311391	+	0.0226239i
$676$	13.6576			0.525291
$677$	−10.3232			−0.396751			−0.198376	−	0.980126i	$-0.563567\pi$
$677$	−10.3232			−0.396751			−0.198376	+	0.980126i	$0.563567\pi$
$678$	−8.18971	+	5.95017i	−0.314524	+	0.228515i
$679$	19.4396	−	59.8290i	0.746024	−	2.29603i
$680$	0.911489	+	2.80527i	0.0349540	+	0.107577i
$681$	2.07890			0.0796637
$682$	−3.39595	−	3.28875i	−0.130038	−	0.125933i
$683$	−20.2267			−0.773954			−0.386977	−	0.922089i	$-0.626481\pi$
$683$	−20.2267			−0.773954			−0.386977	+	0.922089i	$0.626481\pi$
$684$	0.145968	+	0.449244i	0.00558124	+	0.0171773i
$685$	−6.71951	+	20.6805i	−0.256739	+	0.790162i
$686$	8.52347	−	6.19267i	0.325428	−	0.236437i
$687$	−26.9042			−1.02646
$688$	3.23318			0.123264
$689$	48.2604	−	35.0632i	1.83857	−	1.33580i
$690$	−6.82716	−	4.96022i	−0.259906	−	0.188832i
$691$	13.7257	+	9.97229i	0.522149	+	0.379364i	0.817413	−	0.576052i	$-0.195408\pi$
$691$	13.7257	+	9.97229i	0.522149	+	0.379364i	−0.295264	+	0.955416i	$0.595408\pi$
$692$	−1.34589	−	4.14221i	−0.0511629	−	0.157463i
$693$	2.79758	−	2.03256i	0.106271	−	0.0772105i
$694$	3.23417	+	9.95375i	0.122767	+	0.377839i
$695$	5.77248	−	17.7659i	0.218963	−	0.673898i
$696$	−7.87236	−	5.71960i	−0.298401	−	0.216801i
$697$	−7.17445	+	22.0807i	−0.271752	+	0.836365i
$698$	9.64582	−	29.6868i	0.365100	−	1.12366i
$699$	0.539987	+	0.392324i	0.0204242	+	0.0148390i
$700$	−1.25853	+	3.87337i	−0.0475681	+	0.146400i
$701$	−12.2269	−	37.6305i	−0.461803	−	1.42128i	−0.862959	−	0.505275i	$-0.831391\pi$
$701$	−12.2269	−	37.6305i	−0.461803	−	1.42128i	0.401155	−	0.916010i	$-0.368609\pi$
$702$	−4.17703	+	3.03479i	−0.157652	+	0.114541i
$703$	−0.488402	−	1.50315i	−0.0184204	−	0.0566923i
$704$	−0.686910	−	0.499069i	−0.0258889	−	0.0188094i
$705$	−7.61507	−	5.53267i	−0.286800	−	0.208372i
$706$	−13.4680	+	9.78510i	−0.506876	+	0.368267i
$707$	−16.0269			−0.602752
$708$	−4.97462			−0.186958
$709$	−20.5031	+	14.8964i	−0.770010	+	0.559445i	−0.901964	−	0.431811i	$-0.857875\pi$
$709$	−20.5031	+	14.8964i	−0.770010	+	0.559445i	0.131955	+	0.991256i	$0.457875\pi$
$710$	−4.30636	+	13.2536i	−0.161615	+	0.497400i
$711$	−0.737073	−	2.26848i	−0.0276424	−	0.0850746i
$712$	15.6122			0.585093
$713$	−33.7522	−	32.6867i	−1.26403	−	1.22413i
$714$	−12.0130			−0.449575
$715$	1.35467	+	4.16926i	0.0506619	+	0.155921i
$716$	4.56567	−	14.0517i	0.170627	−	0.525137i
$717$	−10.0026	+	7.26731i	−0.373554	+	0.271403i
$718$	5.56323			0.207618
$719$	−28.3667			−1.05790			−0.528950	−	0.848653i	$-0.677414\pi$
$719$	−28.3667			−1.05790			−0.528950	+	0.848653i	$0.677414\pi$
$720$	−0.809017	+	0.587785i	−0.0301503	+	0.0219055i
$721$	13.9827	+	10.1590i	0.520742	+	0.378341i
$722$	15.1908	+	11.0368i	0.565343	+	0.410746i
$723$	1.98779	+	6.11779i	0.0739267	+	0.227523i
$724$	18.9886	−	13.7960i	0.705707	−	0.512726i
$725$	3.00697	+	9.25451i	0.111676	+	0.343704i
$726$	−3.17641	+	9.77599i	−0.117888	+	0.362821i
$727$	−33.2150	−	24.1321i	−1.23188	−	0.895010i	−0.234846	−	0.972032i	$-0.575459\pi$
$727$	−33.2150	−	24.1321i	−1.23188	−	0.895010i	−0.997029	+	0.0770223i	$0.975459\pi$
$728$	−6.49793	+	19.9986i	−0.240829	+	0.741196i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−6.70649	−	4.87255i	−0.248218	−	0.180341i
$731$	2.94701	−	9.06996i	0.108999	−	0.335465i
$732$	2.81926	+	8.67678i	0.104203	+	0.320703i
$733$	−25.0876	+	18.2272i	−0.926631	+	0.673237i	−0.945166	−	0.326591i	$-0.894100\pi$
$733$	−25.0876	+	18.2272i	−0.926631	+	0.673237i	0.0185343	+	0.999828i	$0.494100\pi$
$734$	−5.73492	−	17.6503i	−0.211680	−	0.651484i
$735$	−7.75595	−	5.63503i	−0.286083	−	0.207851i
$736$	−6.82716	−	4.96022i	−0.251652	−	0.182836i
$737$	−3.50923	+	2.54960i	−0.129264	+	0.0939158i
$738$	−7.87113			−0.289740
$739$	−5.22254			−0.192114			−0.0960572	−	0.995376i	$-0.530623\pi$
$739$	−5.22254			−0.192114			−0.0960572	+	0.995376i	$0.530623\pi$
$740$	2.70693	−	1.96670i	0.0995086	−	0.0722973i
$741$	0.753649	−	2.31949i	0.0276860	−	0.0852087i
$742$	14.5408	+	44.7519i	0.533809	+	1.64289i
$743$	−4.88591			−0.179246			−0.0896232	−	0.995976i	$-0.528566\pi$
$743$	−4.88591			−0.179246			−0.0896232	+	0.995976i	$0.528566\pi$
$744$	−4.91974	+	2.60694i	−0.180367	+	0.0955749i
$745$	6.82005			0.249867
$746$	7.49956	+	23.0813i	0.274579	+	0.845066i
$747$	−3.41587	+	10.5130i	−0.124980	+	0.384649i
$748$	−2.02614	+	1.47207i	−0.0740828	+	0.0538243i
$749$	41.3519			1.51097
$750$	1.00000			0.0365148
$751$	−18.1614	+	13.1950i	−0.662718	+	0.481493i	−0.867580	−	0.497298i	$-0.834326\pi$
$751$	−18.1614	+	13.1950i	−0.662718	+	0.481493i	0.204861	+	0.978791i	$0.434326\pi$
$752$	−7.61507	−	5.53267i	−0.277693	−	0.201756i
$753$	−6.47280	−	4.70277i	−0.235882	−	0.171378i
$754$	15.5253	+	47.7819i	0.565398	+	1.74012i
$755$	−6.36659	+	4.62560i	−0.231704	+	0.168343i
$756$	−1.25853	−	3.87337i	−0.0457724	−	0.140873i
$757$	−9.04580	+	27.8401i	−0.328775	+	1.01187i	0.640932	+	0.767597i	$0.278548\pi$
$757$	−9.04580	+	27.8401i	−0.328775	+	1.01187i	−0.969708	+	0.244269i	$0.921452\pi$
$758$	17.8146	+	12.9430i	0.647054	+	0.470113i
$759$	2.21415	−	6.81445i	0.0803685	−	0.247349i
$760$	0.145968	−	0.449244i	0.00529483	−	0.0162958i
$761$	12.5290	+	9.10284i	0.454176	+	0.329978i	0.791242	−	0.611503i	$-0.209435\pi$
$761$	12.5290	+	9.10284i	0.454176	+	0.329978i	−0.337067	+	0.941481i	$0.609435\pi$
$762$	2.07377	−	6.38242i	0.0751249	−	0.231211i
$763$	16.5097	+	50.8115i	0.597690	+	1.83950i
$764$	−15.0188	+	10.9118i	−0.543363	+	0.394776i
$765$	0.911489	+	2.80527i	0.0329549	+	0.101425i
$766$	13.3193	+	9.67706i	0.481247	+	0.349646i
$767$	20.7791	+	15.0969i	0.750291	+	0.545118i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	−50.3917			−1.81717			−0.908585	−	0.417699i	$-0.862837\pi$
$769$	−50.3917			−1.81717			−0.908585	+	0.417699i	$0.862837\pi$
$770$	−3.45799			−0.124617
$771$	−17.8807	+	12.9911i	−0.643956	+	0.467861i
$772$	3.88901	−	11.9692i	0.139969	−	0.430779i
$773$	0.203018	+	0.624826i	0.00730206	+	0.0224734i	0.954641	−	0.297759i	$-0.0962391\pi$
$773$	0.203018	+	0.624826i	0.00730206	+	0.0224734i	−0.947339	+	0.320232i	$0.896239\pi$
$774$	3.23318			0.116214
$775$	5.51248	+	0.782698i	0.198014	+	0.0281153i
$776$	−15.4462			−0.554488
$777$	4.21099	+	12.9601i	0.151068	+	0.464940i
$778$	4.93401	−	15.1853i	0.176893	−	0.544421i
$779$	3.00795	−	2.18541i	0.107771	−	0.0783003i
$780$	5.16310			0.184869
$781$	−11.8323			−0.423394
$782$	−20.1377	+	14.6309i	−0.720121	+	0.523199i
$783$	−7.87236	−	5.71960i	−0.281335	−	0.204402i
$784$	−7.75595	−	5.63503i	−0.276998	−	0.201251i
$785$	−5.14949	−	15.8485i	−0.183793	−	0.565657i
$786$	−5.29941	+	3.85025i	−0.189024	+	0.137334i
$787$	−5.26343	−	16.1992i	−0.187621	−	0.577438i	0.812363	−	0.583152i	$-0.198181\pi$
$787$	−5.26343	−	16.1992i	−0.187621	−	0.577438i	−0.999984	+	0.00571475i	$0.998181\pi$
$788$	−3.57533	+	11.0037i	−0.127366	+	0.391992i
$789$	−3.84476	−	2.79338i	−0.136877	−	0.0994469i
$790$	−0.737073	+	2.26848i	−0.0262239	+	0.0807088i
$791$	−12.7402	+	39.2102i	−0.452988	+	1.39416i
$792$	−0.686910	−	0.499069i	−0.0244083	−	0.0177336i
$793$	14.5561	−	44.7991i	0.516902	−	1.59086i
$794$	−4.42274	−	13.6118i	−0.156957	−	0.483064i
$795$	9.34718	−	6.79112i	0.331510	−	0.240856i
$796$	−3.92460	−	12.0787i	−0.139104	−	0.428118i
$797$	−32.6254	−	23.7038i	−1.15565	−	0.839630i	−0.166430	−	0.986053i	$-0.553224\pi$
$797$	−32.6254	−	23.7038i	−1.15565	−	0.839630i	−0.989222	+	0.146423i	$0.953224\pi$
$798$	1.55638	+	1.13078i	0.0550953	+	0.0400291i
$799$	−22.4617	+	16.3194i	−0.794638	+	0.577338i
$800$	1.00000			0.0353553
$801$	15.6122			0.551631
$802$	9.41423	−	6.83984i	0.332428	−	0.241523i
$803$	2.17501	−	6.69401i	0.0767546	−	0.236226i
$804$	1.57868	+	4.85868i	0.0556758	+	0.171352i
$805$	−34.3688			−1.21134
$806$	28.4614	+	4.04114i	1.00251	+	0.142343i
$807$	2.32986			0.0820151
$808$	1.21604	+	3.74259i	0.0427802	+	0.131664i
$809$	15.7599	−	48.5039i	0.554088	−	1.70531i	−0.144253	−	0.989541i	$-0.546078\pi$
$809$	15.7599	−	48.5039i	0.554088	−	1.70531i	0.698341	−	0.715765i	$-0.253922\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	43.7080			1.53479			0.767397	−	0.641172i	$-0.221551\pi$
$811$	43.7080			1.53479			0.767397	+	0.641172i	$0.221551\pi$
$812$	−39.6305			−1.39076
$813$	21.3995	−	15.5477i	0.750513	−	0.545280i
$814$	2.29836	+	1.66986i	0.0805576	+	0.0585285i
$815$	−2.03104	−	1.47564i	−0.0711442	−	0.0516893i
$816$	0.911489	+	2.80527i	0.0319085	+	0.0982042i
$817$	−1.23556	+	0.897688i	−0.0432268	+	0.0314061i
$818$	−3.09035	−	9.51112i	−0.108052	−	0.332548i
$819$	−6.49793	+	19.9986i	−0.227056	+	0.698807i
$820$	6.36788	+	4.62654i	0.222376	+	0.161566i
$821$	3.11239	−	9.57896i	0.108623	−	0.334308i	−0.881940	−	0.471361i	$-0.843763\pi$
$821$	3.11239	−	9.57896i	0.108623	−	0.334308i	0.990564	+	0.137053i	$0.0437630\pi$
$822$	−6.71951	+	20.6805i	−0.234370	+	0.721316i
$823$	−42.0212	−	30.5302i	−1.46477	−	1.06422i	−0.982089	−	0.188418i	$-0.939664\pi$
$823$	−42.0212	−	30.5302i	−1.46477	−	1.06422i	−0.482678	−	0.875798i	$-0.660336\pi$
$824$	1.31139	−	4.03605i	0.0456845	−	0.140602i
$825$	0.262376	+	0.807511i	0.00913476	+	0.0281139i
$826$	−16.3908	+	11.9086i	−0.570308	+	0.414353i
$827$	−13.0691	−	40.2226i	−0.454458	−	1.39868i	−0.871770	−	0.489915i	$-0.837028\pi$
$827$	−13.0691	−	40.2226i	−0.454458	−	1.39868i	0.417312	−	0.908763i	$-0.362972\pi$
$828$	−6.82716	−	4.96022i	−0.237260	−	0.172380i
$829$	11.7944	+	8.56914i	0.409637	+	0.297619i	0.773455	−	0.633852i	$-0.218527\pi$
$829$	11.7944	+	8.56914i	0.409637	+	0.297619i	−0.363818	+	0.931470i	$0.618527\pi$
$830$	8.94286	−	6.49737i	0.310411	−	0.225527i
$831$	20.9555			0.726937
$832$	5.16310			0.178998
$833$	−22.8773	+	16.6213i	−0.792650	+	0.575894i
$834$	5.77248	−	17.7659i	0.199885	−	0.615182i
$835$	6.41051	+	19.7295i	0.221845	+	0.682769i
$836$	0.401068			0.0138712
$837$	−4.91974	+	2.60694i	−0.170051	+	0.0901089i
$838$	21.4476			0.740896
$839$	−7.09427	−	21.8339i	−0.244921	−	0.753790i	−0.995649	−	0.0931790i	$-0.970297\pi$
$839$	−7.09427	−	21.8339i	−0.244921	−	0.753790i	0.750728	−	0.660611i	$-0.229703\pi$
$840$	−1.25853	+	3.87337i	−0.0434235	+	0.133644i
$841$	−53.1426	+	38.6104i	−1.83250	+	1.33139i
$842$	−32.6213			−1.12421
$843$	−5.22328			−0.179899
$844$	−8.98687	+	6.52935i	−0.309341	+	0.224749i
$845$	−11.0492	−	8.02772i	−0.380104	−	0.276162i
$846$	−7.61507	−	5.53267i	−0.261811	−	0.190217i
$847$	12.9366	+	39.8147i	0.444506	+	1.36805i
$848$	9.34718	−	6.79112i	0.320983	−	0.233208i
$849$	−0.399335	−	1.22903i	−0.0137051	−	0.0421801i
$850$	0.911489	−	2.80527i	0.0312638	−	0.0962201i
$851$	22.8433	+	16.5966i	0.783059	+	0.568925i
$852$	−4.30636	+	13.2536i	−0.147534	+	0.454062i
$853$	−10.9039	+	33.5587i	−0.373342	+	1.14903i	0.571249	+	0.820777i	$0.306459\pi$
$853$	−10.9039	+	33.5587i	−0.373342	+	1.14903i	−0.944591	+	0.328251i	$0.893541\pi$
$854$	30.0602	+	21.8400i	1.02864	+	0.747351i
$855$	0.145968	−	0.449244i	0.00499201	−	0.0153638i
$856$	−3.13759	−	9.65650i	−0.107240	−	0.330052i
$857$	24.6938	−	17.9411i	0.843525	−	0.612856i	−0.0798284	−	0.996809i	$-0.525437\pi$
$857$	24.6938	−	17.9411i	0.843525	−	0.612856i	0.923353	+	0.383952i	$0.125437\pi$
$858$	1.35467	+	4.16926i	0.0462478	+	0.142336i
$859$	−23.5248	−	17.0917i	−0.802655	−	0.583163i	0.109037	−	0.994038i	$-0.465223\pi$
$859$	−23.5248	−	17.0917i	−0.802655	−	0.583163i	−0.911692	+	0.410875i	$0.865223\pi$
$860$	−2.61570	−	1.90042i	−0.0891946	−	0.0648037i
$861$	−25.9345	+	18.8425i	−0.883844	+	0.642150i
$862$	−14.6718			−0.499723
$863$	17.6212			0.599831			0.299915	−	0.953966i	$-0.403042\pi$
$863$	17.6212			0.599831			0.299915	+	0.953966i	$0.403042\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−1.34589	+	4.14221i	−0.0457615	+	0.140839i
$866$	4.64602	+	14.2990i	0.157878	+	0.485899i
$867$	−8.29963			−0.281870
$868$	−9.96931	+	20.3668i	−0.338380	+	0.691294i
$869$	−2.02521			−0.0687005
$870$	3.00697	+	9.25451i	0.101946	+	0.313757i
$871$	8.15088	−	25.0858i	0.276182	−	0.850001i
$872$	10.6128	−	7.71067i	0.359395	−	0.261116i
$873$	−15.4462			−0.522776
$874$	3.98620			0.134835
$875$	3.29488	−	2.39387i	0.111387	−	0.0809277i
$876$	−6.70649	−	4.87255i	−0.226591	−	0.164628i
$877$	−8.15698	−	5.92639i	−0.275442	−	0.200120i	0.441485	−	0.897269i	$-0.354452\pi$
$877$	−8.15698	−	5.92639i	−0.275442	−	0.200120i	−0.716927	+	0.697148i	$0.754452\pi$
$878$	4.87043	+	14.9896i	0.164369	+	0.505876i
$879$	0.379068	−	0.275409i	0.0127857	−	0.00928932i
$880$	0.262376	+	0.807511i	0.00884470	+	0.0272212i
$881$	16.5703	−	50.9981i	0.558267	−	1.71817i	−0.128887	−	0.991659i	$-0.541140\pi$
$881$	16.5703	−	50.9981i	0.558267	−	1.71817i	0.687154	−	0.726511i	$-0.258860\pi$
$882$	−7.75595	−	5.63503i	−0.261156	−	0.189741i
$883$	−4.06836	+	12.5211i	−0.136911	+	0.421370i	−0.995882	−	0.0906544i	$-0.971104\pi$
$883$	−4.06836	+	12.5211i	−0.136911	+	0.421370i	0.858971	+	0.512024i	$0.171104\pi$
$884$	4.70610	−	14.4839i	0.158283	−	0.487146i
$885$	4.02455	+	2.92401i	0.135284	+	0.0982894i
$886$	−1.98805	+	6.11857i	−0.0667897	+	0.205558i
$887$	15.3659	+	47.2914i	0.515937	+	1.58789i	0.781570	+	0.623817i	$0.214419\pi$
$887$	15.3659	+	47.2914i	0.515937	+	1.58789i	−0.265633	+	0.964074i	$0.585581\pi$
$888$	2.70693	−	1.96670i	0.0908385	−	0.0659981i
$889$	−8.44586	−	25.9937i	−0.283265	−	0.871800i
$890$	−12.6306	−	9.17664i	−0.423377	−	0.307602i
$891$	−0.686910	−	0.499069i	−0.0230123	−	0.0167194i
$892$	6.95100	−	5.05019i	0.232737	−	0.169093i
$893$	4.44624			0.148788
$894$	6.82005			0.228097
$895$	−11.9531	+	8.68443i	−0.399548	+	0.290288i
$896$	−1.25853	+	3.87337i	−0.0420446	+	0.129400i
$897$	13.4640	+	41.4380i	0.449551	+	1.38358i
$898$	−24.6682			−0.823190
$899$	9.33238	+	53.3688i	0.311252	+	1.77995i
$900$	1.00000			0.0333333
$901$	−10.5311	−	32.4114i	−0.350842	−	1.07978i
$902$	−2.06520	+	6.35602i	−0.0687635	+	0.211632i
$903$	10.6530	−	7.73983i	0.354508	−	0.257565i
$904$	10.1230			0.336687
$905$	−23.4712			−0.780210
$906$	−6.36659	+	4.62560i	−0.211516	+	0.153675i
$907$	−20.1325	−	14.6271i	−0.668487	−	0.485685i	0.201031	−	0.979585i	$-0.435571\pi$
$907$	−20.1325	−	14.6271i	−0.668487	−	0.485685i	−0.869519	+	0.493900i	$0.835571\pi$
$908$	−1.68187	−	1.22195i	−0.0558147	−	0.0405517i
$909$	1.21604	+	3.74259i	0.0403335	+	0.124134i
$910$	17.0118	−	12.3598i	0.563936	−	0.409723i
$911$	−9.23787	−	28.4312i	−0.306064	−	0.941969i	−0.979278	−	0.202521i	$-0.935087\pi$
$911$	−9.23787	−	28.4312i	−0.306064	−	0.941969i	0.673214	−	0.739448i	$-0.264913\pi$
$912$	0.145968	−	0.449244i	0.00483349	−	0.0148760i
$913$	7.59309	+	5.51670i	0.251294	+	0.182576i
$914$	−0.0498913	+	0.153550i	−0.00165026	+	0.00507897i
$915$	2.81926	−	8.67678i	0.0932017	−	0.286845i
$916$	21.7660	+	15.8139i	0.719168	+	0.522506i
$917$	−8.24394	+	25.3722i	−0.272239	+	0.837865i
$918$	0.911489	+	2.80527i	0.0300836	+	0.0925878i
$919$	27.5219	−	19.9958i	0.907862	−	0.659600i	−0.0326111	−	0.999468i	$-0.510382\pi$
$919$	27.5219	−	19.9958i	0.907862	−	0.659600i	0.940473	+	0.339868i	$0.110382\pi$
$920$	2.60774	+	8.02581i	0.0859747	+	0.264603i
$921$	−6.24961	−	4.54060i	−0.205931	−	0.149618i
$922$	−1.59146	−	1.15626i	−0.0524120	−	0.0380795i
$923$	58.2098	−	42.2919i	1.91600	−	1.39206i
$924$	−3.45799			−0.113760
$925$	−3.34595			−0.110014
$926$	8.92031	−	6.48098i	0.293139	−	0.212978i
$927$	1.31139	−	4.03605i	0.0430718	−	0.132561i
$928$	3.00697	+	9.25451i	0.0987087	+	0.303794i
$929$	−40.0303			−1.31335			−0.656676	−	0.754173i	$-0.728038\pi$
$929$	−40.0303			−1.31335			−0.656676	+	0.754173i	$0.728038\pi$
$930$	5.51248	+	0.782698i	0.180761	+	0.0256657i
$931$	4.52849			0.148415
$932$	−0.206257	−	0.634793i	−0.00675617	−	0.0207933i
$933$	1.00817	−	3.10284i	0.0330061	−	0.101582i
$934$	−3.73015	+	2.71011i	−0.122054	+	0.0886776i
$935$	2.50444			0.0819040
$936$	5.16310			0.168761
$937$	−35.6386	+	25.8930i	−1.16426	+	0.845887i	−0.990311	−	0.138867i	$-0.955654\pi$
$937$	−35.6386	+	25.8930i	−1.16426	+	0.845887i	−0.173952	+	0.984754i	$0.555654\pi$
$938$	16.8326	+	12.2296i	0.549605	+	0.399311i
$939$	18.4909	+	13.4344i	0.603427	+	0.438415i
$940$	2.90870	+	8.95205i	0.0948713	+	0.291984i
$941$	−18.2186	+	13.2366i	−0.593910	+	0.431501i	−0.843712	−	0.536796i	$-0.819635\pi$
$941$	−18.2186	+	13.2366i	−0.593910	+	0.431501i	0.249802	+	0.968297i	$0.419635\pi$
$942$	−5.14949	−	15.8485i	−0.167779	−	0.516372i
$943$	−20.5259	+	63.1722i	−0.668415	+	2.05717i
$944$	4.02455	+	2.92401i	0.130988	+	0.0951683i
$945$	−1.25853	+	3.87337i	−0.0409401	+	0.126001i
$946$	0.848310	−	2.61083i	0.0275809	−	0.0848854i
$947$	−27.8851	−	20.2597i	−0.906145	−	0.658353i	0.0338922	−	0.999425i	$-0.489210\pi$
$947$	−27.8851	−	20.2597i	−0.906145	−	0.658353i	−0.940037	+	0.341073i	$0.889210\pi$
$948$	−0.737073	+	2.26848i	−0.0239390	+	0.0736767i
$949$	13.2261	+	40.7056i	0.429336	+	1.32136i
$950$	−0.382150	+	0.277648i	−0.0123986	+	0.00900810i
$951$	−1.68613	−	5.18937i	−0.0546765	−	0.168277i
$952$	9.71872	+	7.06106i	0.314985	+	0.228850i
$953$	7.58051	+	5.50756i	0.245557	+	0.178407i	0.703755	−	0.710442i	$-0.251505\pi$
$953$	7.58051	+	5.50756i	0.245557	+	0.178407i	−0.458199	+	0.888850i	$0.651505\pi$
$954$	9.34718	−	6.79112i	0.302626	−	0.219871i
$955$	18.5643			0.600727
$956$	12.3639			0.399877
$957$	−6.68416	+	4.85633i	−0.216068	+	0.156983i
$958$	1.44958	−	4.46134i	0.0468337	−	0.144139i
$959$	27.3665	+	84.2255i	0.883712	+	2.71978i
$960$	1.00000			0.0322749
$961$	29.7748	+	8.62920i	0.960476	+	0.278361i
$962$	−17.2754			−0.556983
$963$	−3.13759	−	9.65650i	−0.101107	−	0.311176i
$964$	1.98779	−	6.11779i	0.0640224	−	0.197041i
$965$	−10.1816	+	7.39734i	−0.327756	+	0.238129i
$966$	−34.3688			−1.10580
$967$	−10.7440			−0.345505			−0.172753	−	0.984965i	$-0.555266\pi$
$967$	−10.7440			−0.345505			−0.172753	+	0.984965i	$0.555266\pi$
$968$	8.31595	−	6.04189i	0.267285	−	0.194194i
$969$	−1.12720	−	0.818962i	−0.0362110	−	0.0263089i
$970$	12.4963	+	9.07908i	0.401231	+	0.291512i
$971$	12.9037	+	39.7134i	0.414099	+	1.27446i	0.913055	+	0.407837i	$0.133717\pi$
$971$	12.9037	+	39.7134i	0.414099	+	1.27446i	−0.498956	+	0.866627i	$0.666283\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−23.5096	−	72.3550i	−0.753682	−	2.31960i
$974$	1.46032	−	4.49439i	0.0467916	−	0.144010i
$975$	−4.17703	−	3.03479i	−0.133772	−	0.0971911i
$976$	2.81926	−	8.67678i	0.0902422	−	0.277737i
$977$	4.73789	−	14.5817i	0.151578	−	0.466510i	−0.846220	−	0.532834i	$-0.821127\pi$
$977$	4.73789	−	14.5817i	0.151578	−	0.466510i	0.997798	+	0.0663237i	$0.0211270\pi$
$978$	−2.03104	−	1.47564i	−0.0649455	−	0.0471856i
$979$	4.09628	−	12.6070i	0.130918	−	0.402923i
$980$	2.96251	+	9.11767i	0.0946339	+	0.291253i
$981$	10.6128	−	7.71067i	0.338841	−	0.246183i
$982$	4.35837	+	13.4137i	0.139081	+	0.428048i
$983$	2.09963	+	1.52547i	0.0669677	+	0.0486549i	0.620765	−	0.783996i	$-0.286822\pi$
$983$	2.09963	+	1.52547i	0.0669677	+	0.0486549i	−0.553798	+	0.832651i	$0.686822\pi$
$984$	6.36788	+	4.62654i	0.203001	+	0.147489i
$985$	9.36035	−	6.80069i	0.298245	−	0.216688i
$986$	28.7023			0.914066
$987$	−38.3353			−1.22023
$988$	−1.97308	+	1.43352i	−0.0627720	+	0.0456065i
$989$	8.43131	−	25.9489i	0.268100	−	0.825127i
$990$	0.262376	+	0.807511i	0.00833886	+	0.0256644i
$991$	8.75361			0.278068			0.139034	−	0.990288i	$-0.455600\pi$
$991$	8.75361			0.278068			0.139034	+	0.990288i	$0.455600\pi$
$992$	5.51248	+	0.782698i	0.175021	+	0.0248507i
$993$	29.3797			0.932337
$994$	17.5385	+	53.9780i	0.556288	+	1.71208i
$995$	−3.92460	+	12.0787i	−0.124418	+	0.382920i
$996$	8.94286	−	6.49737i	0.283365	−	0.205877i
$997$	22.4286			0.710321			0.355161	−	0.934805i	$-0.384426\pi$
$997$	22.4286			0.710321			0.355161	+	0.934805i	$0.384426\pi$
$998$	−10.3757			−0.328437
$999$	2.70693	−	1.96670i	0.0856434	−	0.0622236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.g.841.4	yes	16
31.8	even	5	inner	930.2.n.g.721.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.g.721.4	✓	16	31.8	even	5	inner
930.2.n.g.841.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(3.29488 - 2.39387i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(3.29488 - 2.39387i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{10} +(-0.686910 + 0.499069i) q^{11} +(0.309017 + 0.951057i) q^{12} +(1.59548 - 4.91040i) q^{13} +(3.29488 + 2.39387i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.38631 - 1.73375i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.145968 + 0.449244i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(-1.25853 - 3.87337i) q^{21} +(-0.686910 - 0.499069i) q^{22} +(-6.82716 - 4.96022i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +5.16310 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.25853 + 3.87337i) q^{28} +(3.00697 + 9.25451i) q^{29} +1.00000 q^{30} +(5.51248 + 0.782698i) q^{31} +1.00000 q^{32} +(0.262376 + 0.807511i) q^{33} +(0.911489 - 2.80527i) q^{34} +(3.29488 - 2.39387i) q^{35} +1.00000 q^{36} -3.34595 q^{37} +(-0.382150 + 0.277648i) q^{38} +(-4.17703 - 3.03479i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-2.43231 - 7.48589i) q^{41} +(3.29488 - 2.39387i) q^{42} +(0.999109 + 3.07494i) q^{43} +(0.262376 - 0.807511i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(2.60774 - 8.02581i) q^{46} +(2.90870 - 8.95205i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(2.96251 - 9.11767i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-2.38631 + 1.73375i) q^{51} +(1.59548 + 4.91040i) q^{52} +(9.34718 + 6.79112i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-0.686910 + 0.499069i) q^{55} -4.07270 q^{56} +0.472363 q^{57} +(-7.87236 + 5.71960i) q^{58} +(-1.53724 + 4.73114i) q^{59} +(0.309017 + 0.951057i) q^{60} +9.12331 q^{61} +(0.959059 + 5.48454i) q^{62} -4.07270 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.59548 - 4.91040i) q^{65} +(-0.686910 + 0.499069i) q^{66} +5.10872 q^{67} +2.94964 q^{68} +(-6.82716 + 4.96022i) q^{69} +(3.29488 + 2.39387i) q^{70} +(11.2742 + 8.19119i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-6.70649 + 4.87255i) q^{73} +(-1.03395 - 3.18218i) q^{74} +(0.309017 - 0.951057i) q^{75} +(-0.382150 - 0.277648i) q^{76} +(-1.06858 + 3.28875i) q^{77} +(1.59548 - 4.91040i) q^{78} +(1.92968 + 1.40200i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(6.36788 - 4.62654i) q^{82} +(-3.41587 - 10.5130i) q^{83} +(3.29488 + 2.39387i) q^{84} +(-2.38631 - 1.73375i) q^{85} +(-2.61570 + 1.90042i) q^{86} +9.73077 q^{87} +0.849067 q^{88} +(-12.6306 + 9.17664i) q^{89} +(0.309017 - 0.951057i) q^{90} +(-6.49793 - 19.9986i) q^{91} +8.43883 q^{92} +(2.44784 - 5.00081i) q^{93} +9.41274 q^{94} +(0.145968 + 0.449244i) q^{95} +(0.309017 - 0.951057i) q^{96} +(12.4963 - 9.07908i) q^{97} +9.58688 q^{98} +0.849067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

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