LMFDB - Embedded newform 462.2.u.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	462.13
Dual form			462.2.u.a.391.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.169394 - 0.0550394i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.364877 - 2.62047i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.169394 - 0.0550394i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.364877 - 2.62047i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +0.178111 q^{10} +(1.87302 - 2.73712i) q^{11} -1.00000i q^{12} +(0.936678 - 2.88280i) q^{13} +(0.462752 - 2.60497i) q^{14} +(-0.144095 - 0.104691i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.531198 + 1.63486i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(2.99491 - 2.17593i) q^{19} +(0.169394 + 0.0550394i) q^{20} +(-1.90554 + 1.83547i) q^{21} +(2.62716 - 2.02436i) q^{22} +3.37179 q^{23} +(0.309017 - 0.951057i) q^{24} +(-4.01942 + 2.92028i) q^{25} +(1.78167 - 2.45225i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.24508 - 2.33447i) q^{28} +(1.15243 - 1.58618i) q^{29} +(-0.104691 - 0.144095i) q^{30} +(-0.141605 - 0.0460103i) q^{31} +1.00000i q^{32} +(-3.31531 + 0.0935330i) q^{33} +1.71899i q^{34} +(-0.206037 - 0.423809i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-3.77251 - 2.74089i) q^{37} +(3.52073 - 1.14395i) q^{38} +(-2.88280 + 0.936678i) q^{39} +(0.144095 + 0.104691i) q^{40} +(-0.410258 + 0.298070i) q^{41} +(-2.37946 + 1.15679i) q^{42} +1.47039i q^{43} +(3.12414 - 1.11344i) q^{44} +0.178111i q^{45} +(3.20676 + 1.04194i) q^{46} +(5.74499 + 7.90729i) q^{47} +(0.587785 - 0.809017i) q^{48} +(-6.73373 + 1.91230i) q^{49} +(-4.72511 + 1.53528i) q^{50} +(1.01040 - 1.39070i) q^{51} +(2.45225 - 1.78167i) q^{52} +(0.248485 - 0.764760i) q^{53} +1.00000 q^{54} +(0.166629 - 0.566740i) q^{55} +(1.90554 - 1.83547i) q^{56} +(-3.52073 - 1.14395i) q^{57} +(1.58618 - 1.15243i) q^{58} +(-0.274208 + 0.377415i) q^{59} +(-0.0550394 - 0.169394i) q^{60} +(4.45516 + 13.7116i) q^{61} +(-0.120456 - 0.0875167i) q^{62} +(2.60497 + 0.462752i) q^{63} +(-0.309017 + 0.951057i) q^{64} -0.539882i q^{65} +(-3.18195 - 0.935531i) q^{66} -11.2705 q^{67} +(-0.531198 + 1.63486i) q^{68} +(-1.98189 - 2.72784i) q^{69} +(-0.0649886 - 0.466735i) q^{70} +(0.790407 + 2.43262i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-7.70183 - 5.59571i) q^{73} +(-2.74089 - 3.77251i) q^{74} +(4.72511 + 1.53528i) q^{75} +3.70192 q^{76} +(-7.85595 - 3.90948i) q^{77} -3.03115 q^{78} +(-0.257685 - 0.0837271i) q^{79} +(0.104691 + 0.144095i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.482288 + 0.156705i) q^{82} +(2.03400 + 6.26002i) q^{83} +(-2.62047 + 0.364877i) q^{84} +(0.179964 + 0.247699i) q^{85} +(-0.454375 + 1.39842i) q^{86} -1.96063 q^{87} +(3.31531 - 0.0935330i) q^{88} +17.2283i q^{89} +(-0.0550394 + 0.169394i) q^{90} +(-7.89606 - 1.40267i) q^{91} +(2.72784 + 1.98189i) q^{92} +(0.0460103 + 0.141605i) q^{93} +(3.02032 + 9.29558i) q^{94} +(0.387558 - 0.533428i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.38558 - 1.42496i) q^{97} +(-6.99509 - 0.262135i) q^{98} +(2.02436 + 2.62716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.169394	−	0.0550394i	0.0757552	−	0.0246144i	−0.270894	−	0.962609i	$-0.587319\pi$
$5$	0.169394	−	0.0550394i	0.0757552	−	0.0246144i	0.346649	+	0.937995i	$0.387319\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−0.364877	−	2.62047i	−0.137910	−	0.990445i
$7$	−0.364877	−	2.62047i	−0.137910	−	0.990445i
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	0.178111			0.0563237
$11$	1.87302	−	2.73712i	0.564736	−	0.825272i
$11$	1.87302	−	2.73712i	0.564736	−	0.825272i
$12$		−	1.00000i		−	0.288675i
$13$	0.936678	−	2.88280i	0.259788	−	0.799544i	−0.733061	−	0.680163i	$-0.761909\pi$
$13$	0.936678	−	2.88280i	0.259788	−	0.799544i	0.992849	−	0.119381i	$-0.0380910\pi$
$14$	0.462752	−	2.60497i	0.123676	−	0.696207i
$15$	−0.144095	−	0.104691i	−0.0372052	−	0.0270311i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.531198	+	1.63486i	0.128835	+	0.396512i	0.994580	−	0.103972i	$-0.0331553\pi$
$17$	0.531198	+	1.63486i	0.128835	+	0.396512i	−0.865746	+	0.500484i	$0.833155\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	2.99491	−	2.17593i	0.687080	−	0.499193i	−0.188619	−	0.982050i	$-0.560401\pi$
$19$	2.99491	−	2.17593i	0.687080	−	0.499193i	0.875699	+	0.482857i	$0.160401\pi$
$20$	0.169394	+	0.0550394i	0.0378776	+	0.0123072i
$21$	−1.90554	+	1.83547i	−0.415822	+	0.400531i
$22$	2.62716	−	2.02436i	0.560113	−	0.431594i
$23$	3.37179			0.703067			0.351533	−	0.936175i	$-0.385660\pi$
$23$	3.37179			0.703067			0.351533	+	0.936175i	$0.385660\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	−4.01942	+	2.92028i	−0.803884	+	0.584056i
$26$	1.78167	−	2.45225i	0.349414	−	0.480927i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	1.24508	−	2.33447i	0.235298	−	0.441174i
$29$	1.15243	−	1.58618i	0.214000	−	0.294546i	−0.688499	−	0.725237i	$-0.741730\pi$
$29$	1.15243	−	1.58618i	0.214000	−	0.294546i	0.902499	+	0.430691i	$0.141730\pi$
$30$	−0.104691	−	0.144095i	−0.0191139	−	0.0263080i
$31$	−0.141605	−	0.0460103i	−0.0254330	−	0.00826369i	0.296273	−	0.955103i	$-0.404256\pi$
$31$	−0.141605	−	0.0460103i	−0.0254330	−	0.00826369i	−0.321706	+	0.946840i	$0.604256\pi$
$32$			1.00000i			0.176777i
$33$	−3.31531	+	0.0935330i	−0.577121	+	0.0162820i
$34$			1.71899i			0.294805i
$35$	−0.206037	−	0.423809i	−0.0348266	−	0.0716368i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−3.77251	−	2.74089i	−0.620197	−	0.450600i	0.232793	−	0.972526i	$-0.425213\pi$
$37$	−3.77251	−	2.74089i	−0.620197	−	0.450600i	−0.852990	+	0.521927i	$0.825213\pi$
$38$	3.52073	−	1.14395i	0.571138	−	0.185574i
$39$	−2.88280	+	0.936678i	−0.461617	+	0.149988i
$40$	0.144095	+	0.104691i	0.0227834	+	0.0165531i
$41$	−0.410258	+	0.298070i	−0.0640716	+	0.0465507i	−0.619360	−	0.785107i	$-0.712608\pi$
$41$	−0.410258	+	0.298070i	−0.0640716	+	0.0465507i	0.555288	+	0.831658i	$0.312608\pi$
$42$	−2.37946	+	1.15679i	−0.367159	+	0.178496i
$43$			1.47039i			0.224232i	0.993695	+	0.112116i	$0.0357629\pi$
$43$			1.47039i			0.224232i	−0.993695	+	0.112116i	$0.964237\pi$
$44$	3.12414	−	1.11344i	0.470982	−	0.167858i
$45$			0.178111i			0.0265513i
$46$	3.20676	+	1.04194i	0.472811	+	0.153626i
$47$	5.74499	+	7.90729i	0.837992	+	1.15340i	0.986382	+	0.164468i	$0.0525909\pi$
$47$	5.74499	+	7.90729i	0.837992	+	1.15340i	−0.148390	+	0.988929i	$0.547409\pi$
$48$	0.587785	−	0.809017i	0.0848395	−	0.116772i
$49$	−6.73373	+	1.91230i	−0.961961	+	0.273185i
$50$	−4.72511	+	1.53528i	−0.668232	+	0.217122i
$51$	1.01040	−	1.39070i	0.141484	−	0.194736i
$52$	2.45225	−	1.78167i	0.340066	−	0.247073i
$53$	0.248485	−	0.764760i	0.0341321	−	0.105048i	−0.932539	−	0.361069i	$-0.882412\pi$
$53$	0.248485	−	0.764760i	0.0341321	−	0.105048i	0.966671	+	0.256021i	$0.0824118\pi$
$54$	1.00000			0.136083
$55$	0.166629	−	0.566740i	0.0224682	−	0.0764193i
$56$	1.90554	−	1.83547i	0.254638	−	0.245274i
$57$	−3.52073	−	1.14395i	−0.466332	−	0.151521i
$58$	1.58618	−	1.15243i	0.208276	−	0.151321i
$59$	−0.274208	+	0.377415i	−0.0356988	+	0.0491352i	−0.826493	−	0.562947i	$-0.809668\pi$
$59$	−0.274208	+	0.377415i	−0.0356988	+	0.0491352i	0.790794	+	0.612082i	$0.209668\pi$
$60$	−0.0550394	−	0.169394i	−0.00710556	−	0.0218687i
$61$	4.45516	+	13.7116i	0.570425	+	1.75559i	0.651255	+	0.758859i	$0.274243\pi$
$61$	4.45516	+	13.7116i	0.570425	+	1.75559i	−0.0808303	+	0.996728i	$0.525757\pi$
$62$	−0.120456	−	0.0875167i	−0.0152980	−	0.0111146i
$63$	2.60497	+	0.462752i	0.328195	+	0.0583012i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		−	0.539882i		−	0.0669642i
$66$	−3.18195	−	0.935531i	−0.391671	−	0.115156i
$67$	−11.2705			−1.37691			−0.688454	−	0.725280i	$-0.741710\pi$
$67$	−11.2705			−1.37691			−0.688454	+	0.725280i	$0.741710\pi$
$68$	−0.531198	+	1.63486i	−0.0644173	+	0.198256i
$69$	−1.98189	−	2.72784i	−0.238591	−	0.328393i
$70$	−0.0649886	−	0.466735i	−0.00776763	−	0.0557855i
$71$	0.790407	+	2.43262i	0.0938041	+	0.288699i	0.986940	−	0.161087i	$-0.0515001\pi$
$71$	0.790407	+	2.43262i	0.0938041	+	0.288699i	−0.893136	+	0.449787i	$0.851500\pi$
$72$	−0.951057	+	0.309017i	−0.112083	+	0.0364180i
$73$	−7.70183	−	5.59571i	−0.901431	−	0.654928i	0.0374021	−	0.999300i	$-0.488092\pi$
$73$	−7.70183	−	5.59571i	−0.901431	−	0.654928i	−0.938833	+	0.344372i	$0.888092\pi$
$74$	−2.74089	−	3.77251i	−0.318622	−	0.438546i
$75$	4.72511	+	1.53528i	0.545609	+	0.177279i
$76$	3.70192			0.424639
$77$	−7.85595	−	3.90948i	−0.895269	−	0.445526i
$78$	−3.03115			−0.343210
$79$	−0.257685	−	0.0837271i	−0.0289919	−	0.00942003i	0.294485	−	0.955656i	$-0.404852\pi$
$79$	−0.257685	−	0.0837271i	−0.0289919	−	0.00942003i	−0.323477	+	0.946236i	$0.604852\pi$
$80$	0.104691	+	0.144095i	0.0117048	+	0.0161103i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.482288	+	0.156705i	−0.0532598	+	0.0173051i
$83$	2.03400	+	6.26002i	0.223261	+	0.687126i	0.998463	+	0.0554137i	$0.0176478\pi$
$83$	2.03400	+	6.26002i	0.223261	+	0.687126i	−0.775203	+	0.631713i	$0.782352\pi$
$84$	−2.62047	+	0.364877i	−0.285917	+	0.0398113i
$85$	0.179964	+	0.247699i	0.0195198	+	0.0268667i
$86$	−0.454375	+	1.39842i	−0.0489966	+	0.150796i
$87$	−1.96063			−0.210201
$88$	3.31531	−	0.0935330i	0.353413	−	0.00997065i
$89$			17.2283i			1.82620i	0.407735	+	0.913100i	$0.366319\pi$
$89$			17.2283i			1.82620i	−0.407735	+	0.913100i	$0.633681\pi$
$90$	−0.0550394	+	0.169394i	−0.00580166	+	0.0178557i
$91$	−7.89606	−	1.40267i	−0.827732	−	0.147040i
$92$	2.72784	+	1.98189i	0.284397	+	0.206626i
$93$	0.0460103	+	0.141605i	0.00477104	+	0.0146838i
$94$	3.02032	+	9.29558i	0.311522	+	0.958766i
$95$	0.387558	−	0.533428i	0.0397626	−	0.0547285i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−4.38558	−	1.42496i	−0.445288	−	0.144683i	0.0777862	−	0.996970i	$-0.475215\pi$
$97$	−4.38558	−	1.42496i	−0.445288	−	0.144683i	−0.523074	+	0.852287i	$0.675215\pi$
$98$	−6.99509	−	0.262135i	−0.706611	−	0.0264796i
$99$	2.02436	+	2.62716i	0.203456	+	0.264040i
$100$	−4.96828			−0.496828
$101$	−0.204230	+	0.628555i	−0.0203216	+	0.0625435i	−0.960703	−	0.277578i	$-0.910468\pi$
$101$	−0.204230	+	0.628555i	−0.0203216	+	0.0625435i	0.940381	+	0.340122i	$0.110468\pi$
$102$	1.39070	−	1.01040i	0.137699	−	0.100044i
$103$	4.85382	−	6.68071i	0.478261	−	0.658270i	−0.499909	−	0.866078i	$-0.666633\pi$
$103$	4.85382	−	6.68071i	0.478261	−	0.658270i	0.978170	+	0.207808i	$0.0666330\pi$
$104$	2.88280	−	0.936678i	0.282682	−	0.0918488i
$105$	−0.221763	+	0.415796i	−0.0216419	+	0.0405775i
$106$	0.472647	−	0.650543i	0.0459076	−	0.0631864i
$107$	8.59835	+	11.8346i	0.831234	+	1.14410i	0.987692	+	0.156411i	$0.0499923\pi$
$107$	8.59835	+	11.8346i	0.831234	+	1.14410i	−0.156458	+	0.987685i	$0.550008\pi$
$108$	0.951057	+	0.309017i	0.0915155	+	0.0297352i
$109$			9.77807i			0.936570i	0.883578	+	0.468285i	$0.155128\pi$
$109$			9.77807i			0.936570i	−0.883578	+	0.468285i	$0.844872\pi$
$110$	0.333606	−	0.487511i	0.0318080	−	0.0464824i
$111$			4.66308i			0.442600i
$112$	2.37946	−	1.15679i	0.224838	−	0.109306i
$113$	5.21790	−	3.79102i	0.490858	−	0.356630i	−0.314656	−	0.949206i	$-0.601889\pi$
$113$	5.21790	−	3.79102i	0.490858	−	0.356630i	0.805514	+	0.592576i	$0.201889\pi$
$114$	−2.99491	−	2.17593i	−0.280499	−	0.203795i
$115$	0.571161	−	0.185581i	0.0532610	−	0.0173055i
$116$	1.86467	−	0.605867i	0.173130	−	0.0562533i
$117$	2.45225	+	1.78167i	0.226711	+	0.164715i
$118$	−0.377415	+	0.274208i	−0.0347439	+	0.0252429i
$119$	4.09028	−	1.98851i	0.374956	−	0.182287i
$120$		−	0.178111i		−	0.0162593i
$121$	−3.98361	−	10.2533i	−0.362146	−	0.932121i
$122$			14.4172i			1.30527i
$123$	0.482288	+	0.156705i	0.0434864	+	0.0141296i
$124$	−0.0875167	−	0.120456i	−0.00785924	−	0.0108173i
$125$	−1.04359	+	1.43638i	−0.0933416	+	0.128474i
$126$	2.33447	+	1.24508i	0.207971	+	0.110921i
$127$	−13.0368	+	4.23593i	−1.15683	+	0.375878i	−0.823713	−	0.567007i	$-0.808101\pi$
$127$	−13.0368	+	4.23593i	−1.15683	+	0.375878i	−0.333120	+	0.942885i	$0.608101\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	1.18957	−	0.864273i	0.104736	−	0.0760950i
$130$	0.166833	−	0.513459i	0.0146322	−	0.0450333i
$131$	18.5456			1.62033			0.810166	−	0.586200i	$-0.199377\pi$
$131$	18.5456			1.62033			0.810166	+	0.586200i	$0.199377\pi$
$132$	−2.73712	−	1.87302i	−0.238235	−	0.163025i
$133$	−6.79474	−	7.05413i	−0.589178	−	0.611671i
$134$	−10.7189	−	3.48277i	−0.925969	−	0.300865i
$135$	0.144095	−	0.104691i	0.0124017	−	0.00901038i
$136$	−1.01040	+	1.39070i	−0.0866410	+	0.119251i
$137$	−5.82418	−	17.9250i	−0.497593	−	1.53144i	−0.812876	−	0.582437i	$-0.802099\pi$
$137$	−5.82418	−	17.9250i	−0.497593	−	1.53144i	0.315282	−	0.948998i	$-0.397901\pi$
$138$	−1.04194	−	3.20676i	−0.0886959	−	0.272978i
$139$	−9.50467	−	6.90555i	−0.806176	−	0.585721i	0.106544	−	0.994308i	$-0.466022\pi$
$139$	−9.50467	−	6.90555i	−0.806176	−	0.585721i	−0.912719	+	0.408587i	$0.866022\pi$
$140$	0.0824213	−	0.463974i	0.00696587	−	0.0392130i
$141$	3.02032	−	9.29558i	0.254357	−	0.782829i
$142$			2.55781i			0.214647i
$143$	−6.13614	−	7.96333i	−0.513129	−	0.665927i
$144$	−1.00000			−0.0833333
$145$	0.107912	−	0.332118i	0.00896158	−	0.0275809i
$146$	−5.59571	−	7.70183i	−0.463104	−	0.637408i
$147$	5.50507	+	4.32368i	0.454050	+	0.356611i
$148$	−1.44097	−	4.43485i	−0.118447	−	0.364543i
$149$	−7.17801	+	2.33228i	−0.588046	+	0.191068i	−0.587902	−	0.808932i	$-0.700046\pi$
$149$	−7.17801	+	2.33228i	−0.588046	+	0.191068i	−0.000143915		1.00000i	$0.500046\pi$
$150$	4.01942	+	2.92028i	0.328184	+	0.238440i
$151$	10.7702	+	14.8238i	0.876462	+	1.20635i	0.977388	+	0.211453i	$0.0678195\pi$
$151$	10.7702	+	14.8238i	0.876462	+	1.20635i	−0.100926	+	0.994894i	$0.532180\pi$
$152$	3.52073	+	1.14395i	0.285569	+	0.0927870i
$153$	−1.71899			−0.138972
$154$	−6.26336	−	6.14576i	−0.504716	−	0.495239i
$155$	−0.0265194			−0.00213009
$156$	−2.88280	−	0.936678i	−0.230808	−	0.0749942i
$157$	−1.63711	−	2.25329i	−0.130656	−	0.179832i	0.738677	−	0.674060i	$-0.235451\pi$
$157$	−1.63711	−	2.25329i	−0.130656	−	0.179832i	−0.869333	+	0.494227i	$0.835451\pi$
$158$	−0.219200	−	0.159258i	−0.0174386	−	0.0126699i
$159$	−0.764760	+	0.248485i	−0.0606494	+	0.0197062i
$160$	0.0550394	+	0.169394i	0.00435125	+	0.0133918i
$161$	−1.23029	−	8.83568i	−0.0969602	−	0.696349i
$162$	−0.587785	−	0.809017i	−0.0461808	−	0.0635624i
$163$	3.20376	−	9.86015i	0.250938	−	0.772306i	−0.743665	−	0.668552i	$-0.766914\pi$
$163$	3.20376	−	9.86015i	0.250938	−	0.772306i	0.994603	−	0.103754i	$-0.0330856\pi$
$164$	−0.507107			−0.0395984
$165$	−0.556444	+	0.198316i	−0.0433191	+	0.0154389i
$166$			6.58217i			0.510876i
$167$	3.65812	−	11.2585i	0.283074	−	0.871211i	−0.703896	−	0.710303i	$-0.748558\pi$
$167$	3.65812	−	11.2585i	0.283074	−	0.871211i	0.986969	−	0.160908i	$-0.0514421\pi$
$168$	−2.60497	−	0.462752i	−0.200978	−	0.0357021i
$169$	3.08407	+	2.24071i	0.237236	+	0.172362i
$170$	0.0946124	+	0.291187i	0.00725644	+	0.0223330i
$171$	1.14395	+	3.52073i	0.0874804	+	0.269237i
$172$	−0.864273	+	1.18957i	−0.0659002	+	0.0907039i
$173$	11.0524	−	8.03003i	0.840298	−	0.610512i	−0.0821560	−	0.996619i	$-0.526181\pi$
$173$	11.0524	−	8.03003i	0.840298	−	0.610512i	0.922454	+	0.386107i	$0.126181\pi$
$174$	−1.86467	−	0.605867i	−0.141360	−	0.0459307i
$175$	9.11910	+	9.46723i	0.689339	+	0.715655i
$176$	3.18195	+	0.935531i	0.239848	+	0.0705183i
$177$	0.466511			0.0350651
$178$	−5.32385	+	16.3851i	−0.399039	+	1.22812i
$179$	9.78375	−	7.10831i	0.731272	−	0.531300i	−0.158694	−	0.987328i	$-0.550728\pi$
$179$	9.78375	−	7.10831i	0.731272	−	0.531300i	0.889965	+	0.456028i	$0.150728\pi$
$180$	−0.104691	+	0.144095i	−0.00780322	+	0.0107402i
$181$	−5.83913	+	1.89725i	−0.434019	+	0.141021i	−0.517874	−	0.855457i	$-0.673277\pi$
$181$	−5.83913	+	1.89725i	−0.434019	+	0.141021i	0.0838556	+	0.996478i	$0.473277\pi$
$182$	−7.07615	−	3.77403i	−0.524519	−	0.279750i
$183$	8.47422	−	11.6638i	0.626432	−	0.862210i
$184$	1.98189	+	2.72784i	0.146107	+	0.201099i
$185$	−0.789898	−	0.256653i	−0.0580744	−	0.0188695i
$186$			0.148892i			0.0109173i
$187$	5.46975	+	1.60817i	0.399988	+	0.117601i
$188$			9.77395i			0.712839i
$189$	−1.15679	−	2.37946i	−0.0841440	−	0.173080i
$190$	0.533428	−	0.387558i	0.0386989	−	0.0281164i
$191$	5.31138	+	3.85894i	0.384318	+	0.279223i	0.763123	−	0.646253i	$-0.223665\pi$
$191$	5.31138	+	3.85894i	0.384318	+	0.279223i	−0.378805	+	0.925476i	$0.623665\pi$
$192$	0.951057	−	0.309017i	0.0686366	−	0.0223014i
$193$	5.16230	−	1.67733i	0.371591	−	0.120737i	−0.117268	−	0.993100i	$-0.537413\pi$
$193$	5.16230	−	1.67733i	0.371591	−	0.120737i	0.488858	+	0.872363i	$0.337413\pi$
$194$	−3.73059	−	2.71044i	−0.267841	−	0.194598i
$195$	−0.436774	+	0.317335i	−0.0312780	+	0.0227248i
$196$	−6.57172	−	2.41091i	−0.469409	−	0.172208i
$197$			22.6835i			1.61613i	0.589090	+	0.808067i	$0.299486\pi$
$197$			22.6835i			1.61613i	−0.589090	+	0.808067i	$0.700514\pi$
$198$	1.11344	+	3.12414i	0.0791288	+	0.222023i
$199$		−	15.4444i		−	1.09482i	−0.836863	−	0.547412i	$-0.815613\pi$
$199$		−	15.4444i		−	1.09482i	0.836863	−	0.547412i	$-0.184387\pi$
$200$	−4.72511	−	1.53528i	−0.334116	−	0.108561i
$201$	6.62462	+	9.11801i	0.467265	+	0.643135i
$202$	−0.388468	+	0.534681i	−0.0273325	+	0.0376200i
$203$	−4.57703	−	2.44114i	−0.321245	−	0.171335i
$204$	1.63486	−	0.531198i	0.114463	−	0.0371913i
$205$	−0.0530897	+	0.0730716i	−0.00370794	+	0.00510354i
$206$	6.68071	−	4.85382i	0.465467	−	0.338182i
$207$	−1.04194	+	3.20676i	−0.0724199	+	0.222885i
$208$	3.03115			0.210173
$209$	−0.346251	−	12.2730i	−0.0239507	−	0.848940i
$210$	−0.339397	+	0.326917i	−0.0234206	+	0.0225594i
$211$	4.59087	+	1.49166i	0.316048	+	0.102690i	0.462746	−	0.886491i	$-0.346864\pi$
$211$	4.59087	+	1.49166i	0.316048	+	0.102690i	−0.146697	+	0.989181i	$0.546864\pi$
$212$	0.650543	−	0.472647i	0.0446795	−	0.0324616i
$213$	1.50344	−	2.06931i	0.103014	−	0.141787i
$214$	4.52042	+	13.9124i	0.309010	+	0.951034i
$215$	0.0809294	+	0.249075i	0.00551934	+	0.0169868i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−0.0689002	+	0.387860i	−0.00467725	+	0.0263296i
$218$	−3.02159	+	9.29950i	−0.204648	+	0.629842i
$219$			9.51999i			0.643301i
$220$	0.467927	−	0.360561i	0.0315476	−	0.0243090i
$221$	5.21053			0.350498
$222$	−1.44097	+	4.43485i	−0.0967117	+	0.297648i
$223$	−12.9273	−	17.7930i	−0.865679	−	1.19150i	−0.980185	−	0.198082i	$-0.936529\pi$
$223$	−12.9273	−	17.7930i	−0.865679	−	1.19150i	0.114506	−	0.993423i	$-0.463471\pi$
$224$	2.62047	−	0.364877i	0.175088	−	0.0243793i
$225$	−1.53528	−	4.72511i	−0.102352	−	0.315007i
$226$	6.13401	−	1.99306i	0.408028	−	0.132576i
$227$	0.0759450	+	0.0551772i	0.00504064	+	0.00366224i	0.590303	−	0.807182i	$-0.299008\pi$
$227$	0.0759450	+	0.0551772i	0.00504064	+	0.00366224i	−0.585262	+	0.810844i	$0.699008\pi$
$228$	−2.17593	−	2.99491i	−0.144105	−	0.198343i
$229$	26.5120	+	8.61426i	1.75196	+	0.569246i	0.996318	−	0.0857375i	$-0.0273246\pi$
$229$	26.5120	+	8.61426i	1.75196	+	0.569246i	0.755643	+	0.654984i	$0.227325\pi$
$230$	0.600554			0.0395993
$231$	1.45478	+	8.65353i	0.0957173	+	0.569361i
$232$	1.96063			0.128721
$233$	−3.26529	−	1.06096i	−0.213916	−	0.0695055i	0.200099	−	0.979776i	$-0.435874\pi$
$233$	−3.26529	−	1.06096i	−0.213916	−	0.0695055i	−0.414015	+	0.910270i	$0.635874\pi$
$234$	1.78167	+	2.45225i	0.116471	+	0.160309i
$235$	1.40838	+	1.02325i	0.0918725	+	0.0667492i
$236$	−0.443678	+	0.144160i	−0.0288810	+	0.00938400i
$237$	0.0837271	+	0.257685i	0.00543866	+	0.0167385i
$238$	4.50457	−	0.627221i	0.291988	−	0.0406567i
$239$	9.86650	+	13.5801i	0.638211	+	0.878422i	0.998519	−	0.0544114i	$-0.0173282\pi$
$239$	9.86650	+	13.5801i	0.638211	+	0.878422i	−0.360308	+	0.932834i	$0.617328\pi$
$240$	0.0550394	−	0.169394i	0.00355278	−	0.0109343i
$241$	−14.5127			−0.934843			−0.467421	−	0.884035i	$-0.654817\pi$
$241$	−14.5127			−0.934843			−0.467421	+	0.884035i	$0.654817\pi$
$242$	−0.620181	−	10.9825i	−0.0398667	−	0.705982i
$243$			1.00000i			0.0641500i
$244$	−4.45516	+	13.7116i	−0.285212	+	0.877793i
$245$	−1.03540	+	0.694552i	−0.0661493	+	0.0443733i
$246$	0.410258	+	0.298070i	0.0261571	+	0.0190043i
$247$	−3.46750	−	10.6719i	−0.220632	−	0.679035i
$248$	−0.0460103	−	0.141605i	−0.00292166	−	0.00899193i
$249$	3.86891	−	5.32509i	0.245182	−	0.337464i
$250$	−1.43638	+	1.04359i	−0.0908446	+	0.0660025i
$251$	−17.2096	−	5.59175i	−1.08626	−	0.352948i	−0.289461	−	0.957190i	$-0.593476\pi$
$251$	−17.2096	−	5.59175i	−1.08626	−	0.352948i	−0.796801	+	0.604242i	$0.793476\pi$
$252$	1.83547	+	1.90554i	0.115623	+	0.120037i
$253$	6.31542	−	9.22898i	0.397047	−	0.580221i
$254$	−13.7077			−0.860100
$255$	0.0946124	−	0.291187i	0.00592486	−	0.0182348i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−6.65969	+	9.16627i	−0.415420	+	0.571776i	−0.964530	−	0.263974i	$-0.914967\pi$
$257$	−6.65969	+	9.16627i	−0.415420	+	0.571776i	0.549110	+	0.835750i	$0.314967\pi$
$258$	1.39842	−	0.454375i	0.0870621	−	0.0282882i
$259$	−5.80592	+	10.8858i	−0.360762	+	0.676413i
$260$	0.317335	−	0.436774i	0.0196803	−	0.0270876i
$261$	1.15243	+	1.58618i	0.0713335	+	0.0981821i
$262$	17.6379	+	5.73089i	1.08967	+	0.354056i
$263$		−	10.9182i		−	0.673243i	−0.941640	−	0.336621i	$-0.890716\pi$
$263$		−	10.9182i		−	0.673243i	0.941640	−	0.336621i	$-0.109284\pi$
$264$	−2.02436	−	2.62716i	−0.124591	−	0.161691i
$265$		−	0.143222i		−	0.00879806i
$266$	−4.28233	−	8.80857i	−0.262567	−	0.540088i
$267$	13.9380	−	10.1266i	0.852993	−	0.619736i
$268$	−9.11801	−	6.62462i	−0.556971	−	0.404663i
$269$	−3.65188	+	1.18657i	−0.222659	+	0.0723463i	−0.418222	−	0.908345i	$-0.637347\pi$
$269$	−3.65188	+	1.18657i	−0.222659	+	0.0723463i	0.195563	+	0.980691i	$0.437347\pi$
$270$	0.169394	−	0.0550394i	0.0103090	−	0.00334959i
$271$	0.849788	+	0.617407i	0.0516209	+	0.0375048i	0.613297	−	0.789853i	$-0.289843\pi$
$271$	0.849788	+	0.617407i	0.0516209	+	0.0375048i	−0.561676	+	0.827358i	$0.689843\pi$
$272$	−1.39070	+	1.01040i	−0.0843233	+	0.0612645i
$273$	3.50640	+	7.21251i	0.212217	+	0.436521i
$274$		−	18.8475i		−	1.13862i
$275$	0.464698	+	16.4714i	0.0280223	+	0.993260i
$276$		−	3.37179i		−	0.202958i
$277$	27.3555	+	8.88834i	1.64363	+	0.534049i	0.977346	−	0.211646i	$-0.0678825\pi$
$277$	27.3555	+	8.88834i	1.64363	+	0.534049i	0.666287	+	0.745695i	$0.267883\pi$
$278$	−6.90555	−	9.50467i	−0.414167	−	0.570052i
$279$	0.0875167	−	0.120456i	0.00523949	−	0.00721154i
$280$	0.221763	−	0.415796i	0.0132529	−	0.0248486i
$281$	−15.9152	+	5.17117i	−0.949422	+	0.308486i	−0.742481	−	0.669867i	$-0.766351\pi$
$281$	−15.9152	+	5.17117i	−0.949422	+	0.308486i	−0.206941	+	0.978353i	$0.566351\pi$
$282$	5.74499	−	7.90729i	0.342109	−	0.470873i
$283$	26.6254	−	19.3445i	1.58272	−	1.14991i	0.669221	−	0.743063i	$-0.266628\pi$
$283$	26.6254	−	19.3445i	1.58272	−	1.14991i	0.913496	−	0.406848i	$-0.133372\pi$
$284$	−0.790407	+	2.43262i	−0.0469020	+	0.144350i
$285$	−0.659353			−0.0390567
$286$	−3.37501	−	9.46974i	−0.199568	−	0.559958i
$287$	0.930778	+	0.966311i	0.0549421	+	0.0570395i
$288$	−0.951057	−	0.309017i	−0.0560415	−	0.0182090i
$289$	11.3627	−	8.25548i	0.668394	−	0.485616i
$290$	0.205260	−	0.282517i	0.0120533	−	0.0165899i
$291$	1.42496	+	4.38558i	0.0835326	+	0.257087i
$292$	−2.94184	−	9.05405i	−0.172158	−	0.529848i
$293$	−23.4840	−	17.0621i	−1.37195	−	0.996780i	−0.997582	−	0.0695001i	$-0.977860\pi$
$293$	−23.4840	−	17.0621i	−1.37195	−	0.996780i	−0.374368	−	0.927280i	$-0.622140\pi$
$294$	3.89954	+	5.81323i	0.227426	+	0.339034i
$295$	−0.0256765	+	0.0790240i	−0.00149494	+	0.00460096i
$296$		−	4.66308i		−	0.271036i
$297$	0.935531	−	3.18195i	0.0542850	−	0.184635i
$298$	−7.54741			−0.437210
$299$	3.15828	−	9.72019i	0.182648	−	0.562133i
$300$	2.92028	+	4.01942i	0.168602	+	0.232061i
$301$	3.85311	−	0.536511i	0.222090	−	0.0309240i
$302$	5.66220	+	17.4265i	0.325823	+	1.00278i
$303$	0.628555	−	0.204230i	0.0361095	−	0.0117327i
$304$	2.99491	+	2.17593i	0.171770	+	0.124798i
$305$	1.50935	+	2.07745i	0.0864253	+	0.118954i
$306$	−1.63486	−	0.531198i	−0.0934588	−	0.0303666i
$307$	22.9750			1.31125			0.655627	−	0.755085i	$-0.272404\pi$
$307$	22.9750			1.31125			0.655627	+	0.755085i	$0.272404\pi$
$308$	−4.05766	−	7.78045i	−0.231207	−	0.443332i
$309$	−8.25781			−0.469770
$310$	−0.0252215	−	0.00819495i	−0.00143248	−	0.000465442i
$311$	−4.63947	−	6.38568i	−0.263080	−	0.362099i	0.656958	−	0.753927i	$-0.271843\pi$
$311$	−4.63947	−	6.38568i	−0.263080	−	0.362099i	−0.920038	+	0.391828i	$0.871843\pi$
$312$	−2.45225	−	1.78167i	−0.138832	−	0.100867i
$313$	−26.5726	+	8.63397i	−1.50197	+	0.488021i	−0.940593	−	0.339537i	$-0.889730\pi$
$313$	−26.5726	+	8.63397i	−1.50197	+	0.488021i	−0.561380	+	0.827558i	$0.689730\pi$
$314$	−0.860681	−	2.64891i	−0.0485711	−	0.149486i
$315$	0.466735	−	0.0649886i	0.0262976	−	0.00366169i
$316$	−0.159258	−	0.219200i	−0.00895898	−	0.0123310i
$317$	−9.84302	+	30.2937i	−0.552839	+	1.70146i	0.148743	+	0.988876i	$0.452477\pi$
$317$	−9.84302	+	30.2937i	−0.552839	+	1.70146i	−0.701582	+	0.712588i	$0.747523\pi$
$318$	−0.804116			−0.0450926
$319$	−2.18304	−	6.12527i	−0.122227	−	0.342949i
$320$			0.178111i			0.00995672i
$321$	4.52042	−	13.9124i	0.252305	−	0.776516i
$322$	1.56030	−	8.78341i	0.0869522	−	0.489480i
$323$	5.14824	+	3.74041i	0.286456	+	0.208122i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	4.65367	+	14.3225i	0.258139	+	0.794471i
$326$	6.09391	−	8.38754i	0.337510	−	0.464543i
$327$	7.91063	−	5.74741i	0.437459	−	0.317832i
$328$	−0.482288	−	0.156705i	−0.0266299	−	0.00865257i
$329$	18.6246	−	17.9398i	1.02681	−	0.989050i
$330$	−0.590493	+	0.0166593i	−0.0325056	+	0.000917063i
$331$	0.204427			0.0112363			0.00561817	−	0.999984i	$-0.498212\pi$
$331$	0.204427			0.0112363			0.00561817	+	0.999984i	$0.498212\pi$
$332$	−2.03400	+	6.26002i	−0.111630	+	0.343563i
$333$	3.77251	−	2.74089i	0.206732	−	0.150200i
$334$	6.95815	−	9.57707i	0.380733	−	0.524034i
$335$	−1.90915	+	0.620320i	−0.104308	+	0.0338917i
$336$	−2.33447	−	1.24508i	−0.127356	−	0.0679248i
$337$	11.2196	−	15.4425i	0.611171	−	0.841204i	−0.385503	−	0.922707i	$-0.625972\pi$
$337$	11.2196	−	15.4425i	0.611171	−	0.841204i	0.996673	+	0.0815026i	$0.0259719\pi$
$338$	2.24071	+	3.08407i	0.121878	+	0.167751i
$339$	−6.13401	−	1.99306i	−0.333153	−	0.108248i
$340$			0.306172i			0.0166045i
$341$	−0.391164	+	0.301411i	−0.0211827	+	0.0163223i
$342$			3.70192i			0.200177i
$343$	7.46810	+	16.9478i	0.403239	+	0.915095i
$344$	−1.18957	+	0.864273i	−0.0641373	+	0.0465985i
$345$	−0.485858	−	0.352997i	−0.0261577	−	0.0190047i
$346$	12.9929	−	4.22164i	0.698501	−	0.226957i
$347$	−15.3178	+	4.97707i	−0.822305	+	0.267183i	−0.689801	−	0.723999i	$-0.742302\pi$
$347$	−15.3178	+	4.97707i	−0.822305	+	0.267183i	−0.132504	+	0.991182i	$0.542302\pi$
$348$	−1.58618	−	1.15243i	−0.0850282	−	0.0617766i
$349$	−4.57667	+	3.32514i	−0.244983	+	0.177991i	−0.703501	−	0.710695i	$-0.748381\pi$
$349$	−4.57667	+	3.32514i	−0.244983	+	0.177991i	0.458517	+	0.888686i	$0.348381\pi$
$350$	5.74724	+	11.8218i	0.307203	+	0.631903i
$351$		−	3.03115i		−	0.161791i
$352$	2.73712	+	1.87302i	0.145889	+	0.0998322i
$353$		−	25.0557i		−	1.33358i	−0.745245	−	0.666791i	$-0.767667\pi$
$353$		−	25.0557i		−	1.33358i	0.745245	−	0.666791i	$-0.232333\pi$
$354$	0.443678	+	0.144160i	0.0235812	+	0.00766200i
$355$	0.267780	+	0.368568i	0.0142123	+	0.0195616i
$356$	−10.1266	+	13.9380i	−0.536707	+	0.738714i
$357$	−4.01295	−	2.14029i	−0.212388	−	0.113276i
$358$	11.5015	−	3.73706i	0.607872	−	0.197510i
$359$	−12.7267	+	17.5169i	−0.671692	+	0.924504i	−0.999797	−	0.0201369i	$-0.993590\pi$
$359$	−12.7267	+	17.5169i	−0.671692	+	0.924504i	0.328106	+	0.944641i	$0.393590\pi$
$360$	−0.144095	+	0.104691i	−0.00759448	+	0.00551771i
$361$	−1.63650	+	5.03662i	−0.0861315	+	0.265085i
$362$	−6.13962			−0.322691
$363$	−5.95362	+	9.24956i	−0.312484	+	0.485476i
$364$	−5.56357	−	5.77597i	−0.291611	−	0.302743i
$365$	−1.61263	−	0.523974i	−0.0844088	−	0.0274261i
$366$	11.6638	−	8.47422i	0.609674	−	0.442954i
$367$	−3.93618	+	5.41769i	−0.205467	+	0.282801i	−0.899298	−	0.437337i	$-0.855922\pi$
$367$	−3.93618	+	5.41769i	−0.205467	+	0.282801i	0.693831	+	0.720138i	$0.255922\pi$
$368$	1.04194	+	3.20676i	0.0543149	+	0.167164i
$369$	−0.156705	−	0.482288i	−0.00815772	−	0.0251069i
$370$	−0.671927	−	0.488184i	−0.0349318	−	0.0253795i
$371$	−2.09470	−	0.372106i	−0.108751	−	0.0193188i
$372$	−0.0460103	+	0.141605i	−0.00238552	+	0.00734188i
$373$		−	18.8387i		−	0.975432i	−0.873002	−	0.487716i	$-0.837830\pi$
$373$		−	18.8387i		−	0.975432i	0.873002	−	0.487716i	$-0.162170\pi$
$374$	4.70509	+	3.21971i	0.243294	+	0.166487i
$375$	1.77546			0.0916845
$376$	−3.02032	+	9.29558i	−0.155761	+	0.479383i
$377$	−3.49318	−	4.80795i	−0.179908	−	0.247622i
$378$	−0.364877	−	2.62047i	−0.0187672	−	0.134782i
$379$	−3.95681	−	12.1778i	−0.203248	−	0.625532i	−0.999781	−	0.0209371i	$-0.993335\pi$
$379$	−3.95681	−	12.1778i	−0.203248	−	0.625532i	0.796533	−	0.604595i	$-0.206665\pi$
$380$	0.627082	−	0.203751i	0.0321686	−	0.0104522i
$381$	11.0898	+	8.05721i	0.568148	+	0.412783i
$382$	3.85894	+	5.31138i	0.197441	+	0.271754i
$383$	−21.4691	−	6.97573i	−1.09702	−	0.356443i	−0.296064	−	0.955168i	$-0.595674\pi$
$383$	−21.4691	−	6.97573i	−1.09702	−	0.356443i	−0.800955	+	0.598725i	$0.795674\pi$
$384$	1.00000			0.0510310
$385$	−1.54593	−	0.229855i	−0.0787877	−	0.0117145i
$386$	5.42797			0.276276
$387$	−1.39842	−	0.454375i	−0.0710859	−	0.0230972i
$388$	−2.71044	−	3.73059i	−0.137601	−	0.189392i
$389$	−22.7681	−	16.5420i	−1.15439	−	0.838713i	−0.165331	−	0.986238i	$-0.552869\pi$
$389$	−22.7681	−	16.5420i	−1.15439	−	0.838713i	−0.989058	+	0.147526i	$0.952869\pi$
$390$	−0.513459	+	0.166833i	−0.0260000	+	0.00844791i
$391$	1.79109	+	5.51241i	0.0905793	+	0.278774i
$392$	−5.50507	−	4.32368i	−0.278048	−	0.218379i
$393$	−10.9008	−	15.0037i	−0.549873	−	0.756835i
$394$	−7.00960	+	21.5733i	−0.353138	+	1.08685i
$395$	−0.0482586			−0.00242815
$396$	0.0935330	+	3.31531i	0.00470021	+	0.166600i
$397$			27.3120i			1.37075i	0.728189	+	0.685376i	$0.240362\pi$
$397$			27.3120i			1.37075i	−0.728189	+	0.685376i	$0.759638\pi$
$398$	4.77258	−	14.6885i	0.239228	−	0.736268i
$399$	−1.71307	+	9.64337i	−0.0857607	+	0.482773i
$400$	−4.01942	−	2.92028i	−0.200971	−	0.146014i
$401$	−11.5083	−	35.4189i	−0.574697	−	1.76874i	−0.637207	−	0.770693i	$-0.719910\pi$
$401$	−11.5083	−	35.4189i	−0.574697	−	1.76874i	0.0625096	−	0.998044i	$-0.480090\pi$
$402$	3.48277	+	10.7189i	0.173705	+	0.534608i
$403$	−0.265277	+	0.365122i	−0.0132144	+	0.0181880i
$404$	−0.534681	+	0.388468i	−0.0266014	+	0.0193270i
$405$	−0.169394	−	0.0550394i	−0.00841725	−	0.00273493i
$406$	−3.59866	−	3.73604i	−0.178599	−	0.185417i
$407$	−14.5681	+	5.19207i	−0.722115	+	0.257361i
$408$	1.71899			0.0851029
$409$	−8.43375	+	25.9564i	−0.417022	+	1.28346i	0.493407	+	0.869798i	$0.335751\pi$
$409$	−8.43375	+	25.9564i	−0.417022	+	1.28346i	−0.910430	+	0.413664i	$0.864249\pi$
$410$	−0.0730716	+	0.0530897i	−0.00360875	+	0.00262191i
$411$	−11.0783	+	15.2479i	−0.546450	+	0.752124i
$412$	7.85365	−	2.55180i	0.386921	−	0.125718i
$413$	1.08906	+	0.580844i	0.0535890	+	0.0285815i
$414$	−1.98189	+	2.72784i	−0.0974045	+	0.134066i
$415$	0.689096	+	0.948459i	0.0338264	+	0.0465580i
$416$	2.88280	+	0.936678i	0.141341	+	0.0459244i
$417$			11.7484i			0.575323i
$418$	3.46326	−	11.7793i	0.169393	−	0.576144i
$419$			32.2071i			1.57342i	0.617324	+	0.786709i	$0.288217\pi$
$419$			32.2071i			1.57342i	−0.617324	+	0.786709i	$0.711783\pi$
$420$	−0.423809	+	0.206037i	−0.0206798	+	0.0100536i
$421$	−16.6362	+	12.0869i	−0.810799	+	0.589080i	−0.914062	−	0.405574i	$-0.867072\pi$
$421$	−16.6362	+	12.0869i	−0.810799	+	0.589080i	0.103263	+	0.994654i	$0.467072\pi$
$422$	3.90523	+	2.83731i	0.190103	+	0.138118i
$423$	−9.29558	+	3.02032i	−0.451967	+	0.146853i
$424$	0.764760	−	0.248485i	0.0371400	−	0.0120675i
$425$	−6.90936	−	5.01994i	−0.335153	−	0.243503i
$426$	2.06931	−	1.50344i	0.100259	−	0.0728421i
$427$	34.3052	−	16.6776i	1.66014	−	0.807088i
$428$			14.6284i			0.707090i
$429$	−2.83574	+	9.64496i	−0.136911	+	0.465663i
$430$			0.261893i			0.0126296i
$431$	−16.3386	−	5.30874i	−0.787003	−	0.255713i	−0.112176	−	0.993688i	$-0.535782\pi$
$431$	−16.3386	−	5.30874i	−0.787003	−	0.255713i	−0.674827	+	0.737976i	$0.735782\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$	−10.0777	+	13.8708i	−0.484304	+	0.666587i	−0.979325	−	0.202294i	$-0.935160\pi$
$433$	−10.0777	+	13.8708i	−0.484304	+	0.666587i	0.495021	+	0.868881i	$0.335160\pi$
$434$	−0.185383	+	0.347585i	−0.00889868	+	0.0166846i
$435$	−0.332118	+	0.107912i	−0.0159238	+	0.00517397i
$436$	−5.74741	+	7.91063i	−0.275251	+	0.378850i
$437$	10.0982	−	7.33678i	0.483063	−	0.350966i
$438$	−2.94184	+	9.05405i	−0.140566	+	0.432619i
$439$	1.35499			0.0646703			0.0323352	−	0.999477i	$-0.489706\pi$
$439$	1.35499			0.0646703			0.0323352	+	0.999477i	$0.489706\pi$
$440$	0.556444	−	0.198316i	0.0265274	−	0.00945436i
$441$	0.262135	−	6.99509i	0.0124826	−	0.333100i
$442$	4.95551	+	1.61014i	0.235710	+	0.0765867i
$443$	12.2131	−	8.87331i	0.580260	−	0.421584i	−0.258558	−	0.965996i	$-0.583247\pi$
$443$	12.2131	−	8.87331i	0.580260	−	0.421584i	0.838818	+	0.544412i	$0.183247\pi$
$444$	−2.74089	+	3.77251i	−0.130077	+	0.179036i
$445$	0.948238	+	2.91838i	0.0449508	+	0.138344i
$446$	−6.79631	−	20.9169i	−0.321814	−	0.990443i
$447$	6.10598	+	4.43625i	0.288803	+	0.209828i
$448$	2.60497	+	0.462752i	0.123073	+	0.0218630i
$449$	−9.49441	+	29.2208i	−0.448069	+	1.37901i	0.431014	+	0.902345i	$0.358156\pi$
$449$	−9.49441	+	29.2208i	−0.448069	+	1.37901i	−0.879083	+	0.476669i	$0.841844\pi$
$450$		−	4.96828i		−	0.234207i
$451$	0.0474313	+	1.68122i	0.00223345	+	0.0791653i
$452$	6.44968			0.303367
$453$	5.66220	−	17.4265i	0.266034	−	0.818767i
$454$	0.0551772	+	0.0759450i	0.00258960	+	0.00356427i
$455$	−1.41475	+	0.196990i	−0.0663243	+	0.00923505i
$456$	−1.14395	−	3.52073i	−0.0535706	−	0.164873i
$457$	1.22963	−	0.399530i	0.0575196	−	0.0186892i	−0.280116	−	0.959966i	$-0.590373\pi$
$457$	1.22963	−	0.399530i	0.0575196	−	0.0186892i	0.337635	+	0.941277i	$0.390373\pi$
$458$	22.5524	+	16.3853i	1.05381	+	0.765635i
$459$	1.01040	+	1.39070i	0.0471614	+	0.0649121i
$460$	0.571161	+	0.185581i	0.0266305	+	0.00865277i
$461$	21.2637			0.990349			0.495174	−	0.868794i	$-0.335104\pi$
$461$	21.2637			0.990349			0.495174	+	0.868794i	$0.335104\pi$
$462$	−1.29051	+	8.67955i	−0.0600401	+	0.403809i
$463$	−15.7750			−0.733127			−0.366564	−	0.930393i	$-0.619466\pi$
$463$	−15.7750			−0.733127			−0.366564	+	0.930393i	$0.619466\pi$
$464$	1.86467	+	0.605867i	0.0865650	+	0.0281267i
$465$	0.0155877	+	0.0214547i	0.000722863	+	0.000994936i
$466$	−2.77762	−	2.01806i	−0.128671	−	0.0934847i
$467$	−13.9524	+	4.53343i	−0.645642	+	0.209782i	−0.613492	−	0.789701i	$-0.710236\pi$
$467$	−13.9524	+	4.53343i	−0.645642	+	0.209782i	−0.0321506	+	0.999483i	$0.510236\pi$
$468$	0.936678	+	2.88280i	0.0432979	+	0.133257i
$469$	4.11233	+	29.5340i	0.189890	+	1.36375i
$470$	1.02325	+	1.40838i	0.0471988	+	0.0649636i
$471$	−0.860681	+	2.64891i	−0.0396581	+	0.122055i
$472$	−0.466511			−0.0214729
$473$	4.02463	+	2.75407i	0.185053	+	0.126632i
$474$			0.270947i			0.0124450i
$475$	−5.68348	+	17.4920i	−0.260776	+	0.802586i
$476$	4.47793	+	0.795468i	0.205245	+	0.0364602i
$477$	0.650543	+	0.472647i	0.0297863	+	0.0216410i
$478$	5.18713	+	15.9643i	0.237254	+	0.730192i
$479$	9.37264	+	28.8460i	0.428247	+	1.31801i	0.899851	+	0.436198i	$0.143675\pi$
$479$	9.37264	+	28.8460i	0.428247	+	1.31801i	−0.471604	+	0.881810i	$0.656325\pi$
$480$	0.104691	−	0.144095i	0.00477848	−	0.00657701i
$481$	−11.4351	+	8.30806i	−0.521394	+	0.378815i
$482$	−13.8024	−	4.48466i	−0.628680	−	0.204271i
$483$	−6.42507	+	6.18880i	−0.292351	+	0.281600i
$484$	2.80395	−	10.6366i	0.127452	−	0.483483i
$485$	−0.821319			−0.0372942
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−16.1863	+	11.7601i	−0.733472	+	0.532899i	−0.890660	−	0.454670i	$-0.849757\pi$
$487$	−16.1863	+	11.7601i	−0.733472	+	0.532899i	0.157188	+	0.987569i	$0.449757\pi$
$488$	−8.47422	+	11.6638i	−0.383610	+	0.527994i
$489$	−9.86015	+	3.20376i	−0.445891	+	0.144879i
$490$	−1.19935	+	0.340602i	−0.0541813	+	0.0153868i
$491$	−5.64071	+	7.76377i	−0.254562	+	0.350374i	−0.917102	−	0.398652i	$-0.869478\pi$
$491$	−5.64071	+	7.76377i	−0.254562	+	0.350374i	0.662541	+	0.749026i	$0.269478\pi$
$492$	0.298070	+	0.410258i	0.0134380	+	0.0184959i
$493$	3.20535	+	1.04148i	0.144362	+	0.0469060i
$494$		−	11.2211i		−	0.504860i
$495$	0.487511	+	0.333606i	0.0219120	+	0.0149945i
$496$		−	0.148892i		−	0.00668546i
$497$	6.08622	−	2.95885i	0.273004	−	0.132722i
$498$	5.32509	−	3.86891i	0.238623	−	0.173370i
$499$	−31.8273	−	23.1239i	−1.42478	−	1.03517i	−0.990958	−	0.134170i	$-0.957163\pi$
$499$	−31.8273	−	23.1239i	−1.42478	−	1.03517i	−0.433827	−	0.900996i	$-0.642837\pi$
$500$	−1.68856	+	0.548648i	−0.0755149	+	0.0245363i
$501$	−11.2585	+	3.65812i	−0.502994	+	0.163433i
$502$	−14.6394	−	10.6361i	−0.653388	−	0.474714i
$503$	−6.26852	+	4.55435i	−0.279500	+	0.203068i	−0.718699	−	0.695321i	$-0.755262\pi$
$503$	−6.26852	+	4.55435i	−0.279500	+	0.203068i	0.439200	+	0.898390i	$0.355262\pi$
$504$	1.15679	+	2.37946i	0.0515274	+	0.105990i
$505$			0.117714i			0.00523821i
$506$	8.85824	−	6.82571i	0.393797	−	0.303440i
$507$		−	3.81212i		−	0.169302i
$508$	−13.0368	−	4.23593i	−0.578416	−	0.187939i
$509$	22.1690	+	30.5130i	0.982625	+	1.35247i	0.935403	+	0.353582i	$0.115037\pi$
$509$	22.1690	+	30.5130i	0.982625	+	1.35247i	0.0472214	+	0.998884i	$0.484963\pi$
$510$	0.179964	−	0.247699i	0.00796892	−	0.0109683i
$511$	−11.8532	+	22.2242i	−0.524353	+	0.983139i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	2.17593	−	2.99491i	0.0960697	−	0.132229i
$514$	−9.16627	+	6.65969i	−0.404307	+	0.293746i
$515$	0.454505	−	1.39882i	0.0200279	−	0.0616395i
$516$	1.47039			0.0647303
$517$	32.4036	−	0.914187i	1.42511	−	0.0402059i
$518$	−8.88567	+	8.55892i	−0.390414	+	0.376058i
$519$	−12.9929	−	4.22164i	−0.570324	−	0.185309i
$520$	0.436774	−	0.317335i	0.0191538	−	0.0139161i
$521$	−5.96600	+	8.21149i	−0.261375	+	0.359752i	−0.919454	−	0.393197i	$-0.871369\pi$
$521$	−5.96600	+	8.21149i	−0.261375	+	0.359752i	0.658079	+	0.752949i	$0.271369\pi$
$522$	0.605867	+	1.86467i	0.0265181	+	0.0816142i
$523$	−12.8903	−	39.6724i	−0.563655	−	1.73475i	−0.671915	−	0.740628i	$-0.734528\pi$
$523$	−12.8903	−	39.6724i	−0.563655	−	1.73475i	0.108260	−	0.994123i	$-0.465472\pi$
$524$	15.0037	+	10.9008i	0.655438	+	0.476204i
$525$	2.29908	−	12.9422i	0.100340	−	0.564844i
$526$	3.37390	−	10.3838i	0.147109	−	0.452755i
$527$		−	0.255945i		−	0.0111491i
$528$	−1.11344	−	3.12414i	−0.0484563	−	0.135961i
$529$	−11.6310			−0.505697
$530$	0.0442581	−	0.136212i	0.00192245	−	0.00591668i
$531$	−0.274208	−	0.377415i	−0.0118996	−	0.0163784i
$532$	−1.35074	−	9.70076i	−0.0585621	−	0.420581i
$533$	0.474996	+	1.46189i	0.0205744	+	0.0633214i
$534$	16.3851	−	5.32385i	0.709054	−	0.230386i
$535$	2.10788	+	1.53146i	0.0911315	+	0.0662109i
$536$	−6.62462	−	9.11801i	−0.286140	−	0.393838i
$537$	−11.5015	−	3.73706i	−0.496326	−	0.161266i
$538$	−3.83981			−0.165546
$539$	−7.37822	+	22.0128i	−0.317802	+	0.948157i
$540$	0.178111			0.00766469
$541$	41.5249	+	13.4923i	1.78530	+	0.580078i	0.999273	−	0.0381210i	$-0.0121372\pi$
$541$	41.5249	+	13.4923i	1.78530	+	0.580078i	0.786022	+	0.618199i	$0.212137\pi$
$542$	0.617407	+	0.849788i	0.0265199	+	0.0365015i
$543$	4.96706	+	3.60878i	0.213157	+	0.154868i
$544$	−1.63486	+	0.531198i	−0.0700941	+	0.0227749i
$545$	0.538179	+	1.65635i	0.0230531	+	0.0709501i
$546$	1.10600	+	7.94304i	0.0473323	+	0.339931i
$547$	1.07543	+	1.48020i	0.0459821	+	0.0632890i	0.831389	−	0.555691i	$-0.187546\pi$
$547$	1.07543	+	1.48020i	0.0459821	+	0.0632890i	−0.785407	+	0.618980i	$0.787546\pi$
$548$	5.82418	−	17.9250i	0.248797	−	0.765718i
$549$	−14.4172			−0.615311
$550$	−4.64797	+	15.8088i	−0.198190	+	0.674089i
$551$		−	7.25807i		−	0.309204i
$552$	1.04194	−	3.20676i	0.0443479	−	0.136489i
$553$	−0.125381	+	0.705807i	−0.00533174	+	0.0300140i
$554$	23.2700	+	16.9066i	0.988647	+	0.718294i
$555$	0.256653	+	0.789898i	0.0108943	+	0.0335293i
$556$	−3.63046	−	11.1734i	−0.153966	−	0.473858i
$557$	0.896529	−	1.23397i	0.0379872	−	0.0522848i	−0.789601	−	0.613621i	$-0.789712\pi$
$557$	0.896529	−	1.23397i	0.0379872	−	0.0522848i	0.827588	+	0.561336i	$0.189712\pi$
$558$	0.120456	−	0.0875167i	0.00509933	−	0.00370488i
$559$	4.23884	+	1.37728i	0.179284	+	0.0582528i
$560$	0.339397	−	0.326917i	0.0143422	−	0.0138148i
$561$	−1.91400	−	5.37038i	−0.0808091	−	0.226738i
$562$	−16.7342			−0.705892
$563$	7.69239	−	23.6747i	0.324195	−	0.997771i	−0.647607	−	0.761974i	$-0.724230\pi$
$563$	7.69239	−	23.6747i	0.324195	−	0.997771i	0.971802	−	0.235796i	$-0.0757698\pi$
$564$	7.90729	−	5.74499i	0.332957	−	0.241908i
$565$	0.675224	−	0.929366i	0.0284069	−	0.0390987i
$566$	31.3001	−	10.1700i	1.31564	−	0.427477i
$567$	−1.24508	+	2.33447i	−0.0522886	+	0.0980387i
$568$	−1.50344	+	2.06931i	−0.0630831	+	0.0868265i
$569$	−4.84490	−	6.66843i	−0.203109	−	0.279555i	0.695296	−	0.718723i	$-0.255273\pi$
$569$	−4.84490	−	6.66843i	−0.203109	−	0.279555i	−0.898405	+	0.439168i	$0.855273\pi$
$570$	−0.627082	−	0.203751i	−0.0262656	−	0.00853420i
$571$		−	23.2889i		−	0.974610i	−0.873232	−	0.487305i	$-0.837980\pi$
$571$		−	23.2889i		−	0.974610i	0.873232	−	0.487305i	$-0.162020\pi$
$572$	−0.283513	−	10.0492i	−0.0118543	−	0.420178i
$573$		−	6.56523i		−	0.274266i
$574$	0.586616	+	1.20664i	0.0244849	+	0.0503643i
$575$	−13.5526	+	9.84657i	−0.565184	+	0.410630i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−7.94172	+	2.58042i	−0.330618	+	0.107424i	−0.469622	−	0.882868i	$-0.655610\pi$
$577$	−7.94172	+	2.58042i	−0.330618	+	0.107424i	0.139004	+	0.990292i	$0.455610\pi$
$578$	13.3576	−	4.34016i	0.555605	−	0.180527i
$579$	−4.39132	−	3.19048i	−0.182497	−	0.132592i
$580$	0.282517	−	0.205260i	0.0117309	−	0.00852297i
$581$	15.6620	−	7.61418i	0.649771	−	0.315889i
$582$			4.61127i			0.191143i
$583$	−1.62782	−	2.11254i	−0.0674173	−	0.0874925i
$584$		−	9.51999i		−	0.393940i
$585$	0.513459	+	0.166833i	0.0212289	+	0.00689769i
$586$	−17.0621	−	23.4840i	−0.704830	−	0.970115i
$587$	−6.08235	+	8.37163i	−0.251045	+	0.345534i	−0.915877	−	0.401459i	$-0.868503\pi$
$587$	−6.08235	+	8.37163i	−0.251045	+	0.345534i	0.664832	+	0.746993i	$0.268503\pi$
$588$	1.91230	+	6.73373i	0.0788618	+	0.277694i
$589$	−0.524210	+	0.170326i	−0.0215997	+	0.00701817i
$590$	−0.0488395	+	0.0672219i	−0.00201069	+	0.00276748i
$591$	18.3514	−	13.3330i	0.754874	−	0.548448i
$592$	1.44097	−	4.43485i	0.0592236	−	0.182271i
$593$	−22.0666			−0.906165			−0.453083	−	0.891469i	$-0.649676\pi$
$593$	−22.0666			−0.906165			−0.453083	+	0.891469i	$0.649676\pi$
$594$	1.87302	−	2.73712i	0.0768509	−	0.112305i
$595$	0.583422	−	0.561968i	0.0239180	−	0.0230385i
$596$	−7.17801	−	2.33228i	−0.294023	−	0.0955338i
$597$	−12.4948	+	9.07799i	−0.511377	+	0.371537i
$598$	6.00741	−	8.26848i	0.245661	−	0.338123i
$599$	−6.32125	−	19.4548i	−0.258279	−	0.794902i	−0.993166	−	0.116712i	$-0.962765\pi$
$599$	−6.32125	−	19.4548i	−0.258279	−	0.794902i	0.734886	−	0.678190i	$-0.237235\pi$
$600$	1.53528	+	4.72511i	0.0626776	+	0.192902i
$601$	−15.2192	−	11.0574i	−0.620803	−	0.451040i	0.232399	−	0.972621i	$-0.425342\pi$
$601$	−15.2192	−	11.0574i	−0.620803	−	0.451040i	−0.853202	+	0.521581i	$0.825342\pi$
$602$	3.83032	+	0.680425i	0.156112	+	0.0277321i
$603$	3.48277	−	10.7189i	0.141829	−	0.436506i
$604$			18.3233i			0.745563i
$605$	−1.23914	−	1.51760i	−0.0503780	−	0.0616991i
$606$	0.660902			0.0268473
$607$	4.46757	−	13.7498i	0.181333	−	0.558086i	−0.818533	−	0.574460i	$-0.805212\pi$
$607$	4.46757	−	13.7498i	0.181333	−	0.558086i	0.999866	+	0.0163736i	$0.00521211\pi$
$608$	2.17593	+	2.99491i	0.0882457	+	0.121460i
$609$	0.715387	+	5.13776i	0.0289889	+	0.208193i
$610$	0.793514	+	2.44219i	0.0321284	+	0.0988812i
$611$	28.1763	−	9.15504i	1.13989	−	0.370373i
$612$	−1.39070	−	1.01040i	−0.0562155	−	0.0408430i
$613$	18.4014	+	25.3273i	0.743224	+	1.02296i	0.998427	+	0.0560730i	$0.0178580\pi$
$613$	18.4014	+	25.3273i	0.743224	+	1.02296i	−0.255202	+	0.966888i	$0.582142\pi$
$614$	21.8506	+	7.09968i	0.881817	+	0.286520i
$615$	0.0903215			0.00364211
$616$	−1.45478	−	8.65353i	−0.0586147	−	0.348661i
$617$	15.0315			0.605146			0.302573	−	0.953126i	$-0.402154\pi$
$617$	15.0315			0.605146			0.302573	+	0.953126i	$0.402154\pi$
$618$	−7.85365	−	2.55180i	−0.315920	−	0.102649i
$619$	−19.1676	−	26.3820i	−0.770413	−	1.06038i	−0.996276	−	0.0862229i	$-0.972520\pi$
$619$	−19.1676	−	26.3820i	−0.770413	−	1.06038i	0.225863	−	0.974159i	$-0.427480\pi$
$620$	−0.0214547	−	0.0155877i	−0.000861640	−	0.000626018i
$621$	3.20676	−	1.04194i	0.128683	−	0.0418116i
$622$	−2.43911	−	7.50682i	−0.0977996	−	0.300996i
$623$	45.1464	−	6.28622i	1.80875	−	0.251852i
$624$	−1.78167	−	2.45225i	−0.0713237	−	0.0981687i
$625$	7.57869	−	23.3248i	0.303148	−	0.932992i
$626$	−27.9401			−1.11671
$627$	−9.72553	+	7.49400i	−0.388400	+	0.299282i
$628$		−	2.78522i		−	0.111143i
$629$	2.47702	−	7.62349i	0.0987653	−	0.303968i
$630$	0.463974	+	0.0824213i	0.0184852	+	0.00328374i
$631$	−9.84315	−	7.15147i	−0.391850	−	0.284696i	0.374363	−	0.927282i	$-0.377861\pi$
$631$	−9.84315	−	7.15147i	−0.391850	−	0.284696i	−0.766213	+	0.642587i	$0.777861\pi$
$632$	−0.0837271	−	0.257685i	−0.00333048	−	0.0102502i
$633$	−1.49166	−	4.59087i	−0.0592883	−	0.182471i
$634$	−18.7225	+	25.7694i	−0.743567	+	1.02343i
$635$	−1.97522	+	1.43508i	−0.0783841	+	0.0569494i
$636$	−0.764760	−	0.248485i	−0.0303247	−	0.00985309i
$637$	−0.794571	+	21.2032i	−0.0314821	+	0.840101i
$638$	−0.183383	−	6.50008i	−0.00726021	−	0.257340i
$639$	−2.55781			−0.101185
$640$	−0.0550394	+	0.169394i	−0.00217562	+	0.00669588i
$641$	26.9365	−	19.5705i	1.06393	−	0.772989i	0.0891166	−	0.996021i	$-0.471596\pi$
$641$	26.9365	−	19.5705i	1.06393	−	0.772989i	0.974811	+	0.223033i	$0.0715956\pi$
$642$	8.59835	−	11.8346i	0.339350	−	0.467075i
$643$	15.6934	−	5.09909i	0.618886	−	0.201088i	0.0172405	−	0.999851i	$-0.494512\pi$
$643$	15.6934	−	5.09909i	0.618886	−	0.201088i	0.601646	+	0.798763i	$0.294512\pi$
$644$	4.19816	−	7.87136i	0.165431	−	0.310175i
$645$	0.153937	−	0.211876i	0.00606126	−	0.00834260i
$646$	3.74041	+	5.14824i	0.147165	+	0.202555i
$647$	−38.3575	−	12.4631i	−1.50799	−	0.489975i	−0.565652	−	0.824644i	$-0.691375\pi$
$647$	−38.3575	−	12.4631i	−1.50799	−	0.489975i	−0.942336	+	0.334670i	$0.891375\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	0.519432	+	1.45744i	0.0203895	+	0.0572097i
$650$			15.0596i			0.590686i
$651$	0.354284	−	0.172237i	0.0138855	−	0.00675050i
$652$	8.38754	−	6.09391i	0.328482	−	0.238656i
$653$	5.66777	+	4.11787i	0.221797	+	0.161145i	0.693135	−	0.720808i	$-0.256229\pi$
$653$	5.66777	+	4.11787i	0.221797	+	0.161145i	−0.471338	+	0.881953i	$0.656229\pi$
$654$	9.29950	−	3.02159i	0.363639	−	0.118154i
$655$	3.14150	−	1.02074i	0.122749	−	0.0398835i
$656$	−0.410258	−	0.298070i	−0.0160179	−	0.0116377i
$657$	7.70183	−	5.59571i	0.300477	−	0.218309i
$658$	23.2568	−	11.3064i	0.906643	−	0.440769i
$659$		−	2.23103i		−	0.0869085i	−0.999055	−	0.0434543i	$-0.986164\pi$
$659$		−	2.23103i		−	0.0869085i	0.999055	−	0.0434543i	$-0.0138363\pi$
$660$	−0.566740	−	0.166629i	−0.0220603	−	0.00648601i
$661$		−	39.7760i		−	1.54711i	−0.633732	−	0.773553i	$-0.718478\pi$
$661$		−	39.7760i		−	1.54711i	0.633732	−	0.773553i	$-0.281522\pi$
$662$	0.194422	+	0.0631716i	0.00755643	+	0.00245523i
$663$	−3.06267	−	4.21541i	−0.118944	−	0.163713i
$664$	−3.86891	+	5.32509i	−0.150143	+	0.206654i
$665$	−1.53924	−	0.820949i	−0.0596893	−	0.0318350i
$666$	4.43485	−	1.44097i	0.171847	−	0.0558365i
$667$	3.88574	−	5.34827i	0.150457	−	0.207086i
$668$	9.57707	−	6.95815i	0.370548	−	0.269219i
$669$	−6.79631	+	20.9169i	−0.262760	+	0.808693i
$670$	−2.00740			−0.0775526
$671$	45.8748	+	13.4877i	1.77098	+	0.520688i
$672$	−1.83547	−	1.90554i	−0.0708046	−	0.0735076i
$673$	32.8313	+	10.6675i	1.26555	+	0.411204i	0.863471	−	0.504399i	$-0.168286\pi$
$673$	32.8313	+	10.6675i	1.26555	+	0.411204i	0.402084	+	0.915603i	$0.368286\pi$
$674$	15.4425	−	11.2196i	0.594821	−	0.432163i
$675$	−2.92028	+	4.01942i	−0.112402	+	0.154708i
$676$	1.17801	+	3.62554i	0.0453080	+	0.139444i
$677$	−6.12724	−	18.8577i	−0.235489	−	0.724760i	−0.997056	−	0.0766745i	$-0.975570\pi$
$677$	−6.12724	−	18.8577i	−0.235489	−	0.724760i	0.761567	−	0.648086i	$-0.224430\pi$
$678$	−5.21790	−	3.79102i	−0.200392	−	0.145593i
$679$	−2.13387	+	12.0122i	−0.0818905	+	0.460986i
$680$	−0.0946124	+	0.291187i	−0.00362822	+	0.0111665i
$681$		−	0.0938731i		−	0.00359723i
$682$	−0.465161	+	0.165783i	−0.0178119	+	0.00634815i
$683$	21.9573			0.840174			0.420087	−	0.907484i	$-0.362000\pi$
$683$	21.9573			0.840174			0.420087	+	0.907484i	$0.362000\pi$
$684$	−1.14395	+	3.52073i	−0.0437402	+	0.134619i
$685$	−1.97316	−	2.71582i	−0.0753906	−	0.103766i
$686$	1.86543	+	18.4261i	0.0712223	+	0.703511i
$687$	−8.61426	−	26.5120i	−0.328655	−	1.01149i
$688$	−1.39842	+	0.454375i	−0.0533144	+	0.0173229i
$689$	−1.97190	−	1.43267i	−0.0751232	−	0.0545802i
$690$	−0.352997	−	0.485858i	−0.0134384	−	0.0184963i
$691$	−24.2780	−	7.88839i	−0.923578	−	0.300089i	−0.191644	−	0.981464i	$-0.561382\pi$
$691$	−24.2780	−	7.88839i	−0.923578	−	0.300089i	−0.731934	+	0.681376i	$0.761382\pi$
$692$	13.6615			0.519333
$693$	6.14576	−	6.26336i	0.233458	−	0.237925i
$694$	−16.1061			−0.611381
$695$	−1.99011	−	0.646626i	−0.0754892	−	0.0245279i
$696$	−1.15243	−	1.58618i	−0.0436826	−	0.0601240i
$697$	−0.705232	−	0.512381i	−0.0267126	−	0.0194078i
$698$	−5.38019	+	1.74813i	−0.203643	+	0.0661677i
$699$	1.06096	+	3.26529i	0.0401290	+	0.123504i
$700$	1.81281	+	13.0192i	0.0685177	+	0.492080i
$701$	9.50709	+	13.0854i	0.359078	+	0.494228i	0.949892	−	0.312580i	$-0.101193\pi$
$701$	9.50709	+	13.0854i	0.359078	+	0.494228i	−0.590814	+	0.806808i	$0.701193\pi$
$702$	0.936678	−	2.88280i	0.0353526	−	0.108804i
$703$	−17.2623			−0.651061
$704$	2.02436	+	2.62716i	0.0762958	+	0.0990149i
$705$		−	1.74085i		−	0.0655642i
$706$	7.74265	−	23.8294i	0.291398	−	0.896832i
$707$	1.72163	+	0.305833i	0.0647485	+	0.0115020i
$708$	0.377415	+	0.274208i	0.0141841	+	0.0103054i
$709$	9.09430	+	27.9894i	0.341544	+	1.05116i	0.963408	+	0.268039i	$0.0863755\pi$
$709$	9.09430	+	27.9894i	0.341544	+	1.05116i	−0.621864	+	0.783125i	$0.713625\pi$
$710$	0.140780	+	0.433278i	0.00528340	+	0.0162606i
$711$	0.159258	−	0.219200i	0.00597266	−	0.00822065i
$712$	−13.9380	+	10.1266i	−0.522349	+	0.379509i
$713$	−0.477463	−	0.155137i	−0.0178811	−	0.00580993i
$714$	−3.15515	−	3.27561i	−0.118079	−	0.122586i
$715$	−1.47772	−	1.01121i	−0.0552636	−	0.0378171i
$716$	12.0934			0.451951
$717$	5.18713	−	15.9643i	0.193717	−	0.596199i
$718$	−17.5169	+	12.7267i	−0.653723	+	0.474958i
$719$	23.3046	−	32.0760i	0.869114	−	1.19623i	−0.110204	−	0.993909i	$-0.535150\pi$
$719$	23.3046	−	32.0760i	0.869114	−	1.19623i	0.979319	−	0.202324i	$-0.0648495\pi$
$720$	−0.169394	+	0.0550394i	−0.00631294	+	0.00205120i
$721$	−19.2776	−	10.2817i	−0.717937	−	0.382909i
$722$	−3.11280	+	4.28441i	−0.115847	+	0.159449i
$723$	8.53033	+	11.7410i	0.317246	+	0.436652i
$724$	−5.83913	−	1.89725i	−0.217009	−	0.0705106i
$725$			9.74094i			0.361769i
$726$	−8.52050	+	6.95709i	−0.316225	+	0.258202i
$727$			30.2005i			1.12007i	0.828468	+	0.560036i	$0.189213\pi$
$727$			30.2005i			1.12007i	−0.828468	+	0.560036i	$0.810787\pi$
$728$	−3.50640	−	7.21251i	−0.129956	−	0.267314i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−1.37178	−	0.996658i	−0.0507720	−	0.0368880i
$731$	−2.40388	+	0.781069i	−0.0889108	+	0.0288889i
$732$	13.7116	−	4.45516i	0.506794	−	0.164667i
$733$	−4.53282	−	3.29328i	−0.167423	−	0.121640i	0.500918	−	0.865494i	$-0.332996\pi$
$733$	−4.53282	−	3.29328i	−0.167423	−	0.121640i	−0.668342	+	0.743854i	$0.732996\pi$
$734$	−5.41769	+	3.93618i	−0.199971	+	0.145287i
$735$	1.17050	+	0.429410i	0.0431745	+	0.0158390i
$736$			3.37179i			0.124286i
$737$	−21.1098	+	30.8486i	−0.777590	+	1.13632i
$738$		−	0.507107i		−	0.0186669i
$739$	−8.67158	−	2.81757i	−0.318989	−	0.103646i	0.145146	−	0.989410i	$-0.453635\pi$
$739$	−8.67158	−	2.81757i	−0.318989	−	0.103646i	−0.464135	+	0.885764i	$0.653635\pi$
$740$	−0.488184	−	0.671927i	−0.0179460	−	0.0247005i
$741$	−6.59558	+	9.07804i	−0.242295	+	0.333490i
$742$	−1.87719	−	1.00119i	−0.0689137	−	0.0367549i
$743$	49.8178	−	16.1868i	1.82764	−	0.593835i	0.828195	−	0.560440i	$-0.189368\pi$
$743$	49.8178	−	16.1868i	1.82764	−	0.593835i	0.999442	−	0.0333956i	$-0.0106321\pi$
$744$	−0.0875167	+	0.120456i	−0.00320852	+	0.00441615i
$745$	−1.08754	+	0.790147i	−0.0398445	+	0.0289487i
$746$	5.82148	−	17.9167i	0.213140	−	0.655976i
$747$	−6.58217			−0.240829
$748$	3.47986	+	4.51608i	0.127236	+	0.165124i
$749$	27.8749	−	26.8499i	1.01853	−	0.981074i
$750$	1.68856	+	0.548648i	0.0616577	+	0.0200338i
$751$	−9.21964	+	6.69846i	−0.336429	+	0.244430i	−0.743154	−	0.669121i	$-0.766671\pi$
$751$	−9.21964	+	6.69846i	−0.336429	+	0.244430i	0.406724	+	0.913551i	$0.366671\pi$
$752$	−5.74499	+	7.90729i	−0.209498	+	0.288349i
$753$	5.59175	+	17.2096i	0.203775	+	0.627154i
$754$	−1.83647	−	5.65209i	−0.0668805	−	0.205837i
$755$	2.64029	+	1.91828i	0.0960901	+	0.0698135i
$756$	0.462752	−	2.60497i	0.0168301	−	0.0947418i
$757$	5.13233	−	15.7957i	0.186538	−	0.574104i	−0.813434	−	0.581657i	$-0.802404\pi$
$757$	5.13233	−	15.7957i	0.186538	−	0.574104i	0.999971	+	0.00755359i	$0.00240441\pi$
$758$		−	12.8045i		−	0.465081i
$759$	−11.1785	+	0.315374i	−0.405754	+	0.0114473i
$760$	0.659353			0.0239172
$761$	7.09840	−	21.8466i	0.257317	−	0.791940i	−0.736048	−	0.676930i	$-0.763310\pi$
$761$	7.09840	−	21.8466i	0.257317	−	0.791940i	0.993364	−	0.115010i	$-0.0366899\pi$
$762$	8.05721	+	11.0898i	0.291882	+	0.401741i
$763$	25.6232	−	3.56779i	0.927621	−	0.129163i
$764$	2.02877	+	6.24390i	0.0733982	+	0.225896i
$765$	−0.291187	+	0.0946124i	−0.0105279	+	0.00342072i
$766$	−18.2627	−	13.2686i	−0.659858	−	0.479415i
$767$	0.831166	+	1.14400i	0.0300117	+	0.0413075i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	35.2302			1.27043			0.635217	−	0.772334i	$-0.280911\pi$
$769$	35.2302			1.27043			0.635217	+	0.772334i	$0.280911\pi$
$770$	−1.39923	−	0.696322i	−0.0504249	−	0.0250937i
$771$	11.3301			0.408045
$772$	5.16230	+	1.67733i	0.185795	+	0.0603686i
$773$	14.0693	+	19.3647i	0.506037	+	0.696501i	0.983245	−	0.182290i	$-0.0583510\pi$
$773$	14.0693	+	19.3647i	0.506037	+	0.696501i	−0.477207	+	0.878791i	$0.658351\pi$
$774$	−1.18957	−	0.864273i	−0.0427582	−	0.0310657i
$775$	0.703533	−	0.228592i	0.0252717	−	0.00821126i
$776$	−1.42496	−	4.38558i	−0.0511531	−	0.157433i
$777$	12.2195	−	1.70145i	0.438371	−	0.0610392i
$778$	−16.5420	−	22.7681i	−0.593059	−	0.816276i
$779$	−0.580108	+	1.78539i	−0.0207845	+	0.0639682i
$780$	−0.539882			−0.0193309
$781$	8.13882	+	2.39291i	0.291230	+	0.0856251i
$782$			5.79609i			0.207268i
$783$	0.605867	−	1.86467i	0.0216519	−	0.0666378i
$784$	−3.89954	−	5.81323i	−0.139269	−	0.207615i
$785$	−0.401337	−	0.291588i	−0.0143243	−	0.0104072i
$786$	−5.73089	−	17.6379i	−0.204414	−	0.629122i
$787$	2.16159	+	6.65269i	0.0770524	+	0.237143i	0.982162	−	0.188035i	$-0.0602117\pi$
$787$	2.16159	+	6.65269i	0.0770524	+	0.237143i	−0.905110	+	0.425177i	$0.860212\pi$
$788$	−13.3330	+	18.3514i	−0.474970	+	0.653740i
$789$	−8.83298	+	6.41754i	−0.314462	+	0.228470i
$790$	−0.0458967	−	0.0149127i	−0.00163293	−	0.000530571i
$791$	−11.8382	−	12.2901i	−0.420916	−	0.436985i
$792$	−0.935531	+	3.18195i	−0.0332426	+	0.113066i
$793$	43.7007			1.55186
$794$	−8.43988	+	25.9753i	−0.299520	+	0.921829i
$795$	−0.115869	+	0.0841838i	−0.00410945	+	0.00298569i
$796$	9.07799	−	12.4948i	0.321761	−	0.442866i
$797$	48.7452	−	15.8383i	1.72665	−	0.561021i	0.733687	−	0.679488i	$-0.237798\pi$
$797$	48.7452	−	15.8383i	1.72665	−	0.561021i	0.992958	+	0.118467i	$0.0377978\pi$
$798$	−4.60919	+	8.64203i	−0.163164	+	0.305924i
$799$	−9.87560	+	13.5926i	−0.349374	+	0.480871i
$800$	−2.92028	−	4.01942i	−0.103247	−	0.142108i
$801$	−16.3851	−	5.32385i	−0.578940	−	0.188109i
$802$		−	37.2417i		−	1.31505i
$803$	−29.7418	+	10.5999i	−1.04956	+	0.374064i
$804$			11.2705i			0.397479i
$805$	−0.694713	−	1.42900i	−0.0244854	−	0.0503655i
$806$	−0.365122	+	0.265277i	−0.0128609	+	0.00934397i
$807$	3.10647	+	2.25698i	0.109353	+	0.0794496i
$808$	−0.628555	+	0.204230i	−0.0221125	+	0.00718478i
$809$	3.85064	−	1.25115i	0.135381	−	0.0439880i	−0.240543	−	0.970639i	$-0.577325\pi$
$809$	3.85064	−	1.25115i	0.135381	−	0.0439880i	0.375924	+	0.926651i	$0.377325\pi$
$810$	−0.144095	−	0.104691i	−0.00506298	−	0.00367847i
$811$	−23.7235	+	17.2361i	−0.833044	+	0.605242i	−0.920419	−	0.390934i	$-0.872152\pi$
$811$	−23.7235	+	17.2361i	−0.833044	+	0.605242i	0.0873749	+	0.996176i	$0.472152\pi$
$812$	−2.26803	−	4.66524i	−0.0795922	−	0.163718i
$813$		−	1.05040i		−	0.0368390i
$814$	−15.4595	+	0.436152i	−0.541857	+	0.0152871i
$815$		−	1.84658i		−	0.0646829i
$816$	1.63486	+	0.531198i	0.0572316	+	0.0185957i
$817$	3.19947	+	4.40369i	0.111935	+	0.154066i
$818$	−16.0420	+	22.0799i	−0.560894	+	0.772004i
$819$	3.77403	−	7.07615i	0.131875	−	0.247261i
$820$	−0.0859009	+	0.0279109i	−0.00299979	+	0.000974690i
$821$	−14.2572	+	19.6233i	−0.497578	+	0.684857i	−0.981763	−	0.190108i	$-0.939116\pi$
$821$	−14.2572	+	19.6233i	−0.497578	+	0.684857i	0.484185	+	0.874966i	$0.339116\pi$
$822$	−15.2479	+	11.0783i	−0.531832	+	0.386398i
$823$	13.1466	−	40.4611i	0.458262	−	1.41038i	−0.409001	−	0.912534i	$-0.634123\pi$
$823$	13.1466	−	40.4611i	0.458262	−	1.41038i	0.867263	−	0.497850i	$-0.165877\pi$
$824$	8.25781			0.287674
$825$	13.0525	−	10.0576i	0.454428	−	0.350160i
$826$	0.856264	+	0.888953i	0.0297932	+	0.0309306i
$827$	−2.23130	−	0.724993i	−0.0775899	−	0.0252105i	0.269965	−	0.962870i	$-0.412988\pi$
$827$	−2.23130	−	0.724993i	−0.0775899	−	0.0252105i	−0.347555	+	0.937660i	$0.612988\pi$
$828$	−2.72784	+	1.98189i	−0.0947988	+	0.0688754i
$829$	3.41091	−	4.69472i	0.118466	−	0.163054i	−0.745666	−	0.666320i	$-0.767868\pi$
$829$	3.41091	−	4.69472i	0.118466	−	0.163054i	0.864132	+	0.503266i	$0.167868\pi$
$830$	0.362279	+	1.11498i	0.0125749	+	0.0387015i
$831$	−8.88834	−	27.3555i	−0.308333	−	0.948952i
$832$	2.45225	+	1.78167i	0.0850166	+	0.0617682i
$833$	−6.70329	−	9.99290i	−0.232255	−	0.346234i
$834$	−3.63046	+	11.1734i	−0.125713	+	0.386904i
$835$		−	2.10847i		−	0.0729665i
$836$	6.93375	−	10.1326i	0.239809	−	0.350442i
$837$	−0.148892			−0.00514647
$838$	−9.95253	+	30.6307i	−0.343804	+	1.05812i
$839$	18.4549	+	25.4011i	0.637135	+	0.876942i	0.998459	−	0.0554989i	$-0.0176749\pi$
$839$	18.4549	+	25.4011i	0.637135	+	0.876942i	−0.361323	+	0.932441i	$0.617675\pi$
$840$	−0.466735	+	0.0649886i	−0.0161039	+	0.00224232i
$841$	7.77361	+	23.9247i	0.268056	+	0.824990i
$842$	−19.5570	+	6.35447i	−0.673980	+	0.218989i
$843$	13.5383	+	9.83614i	0.466283	+	0.338775i
$844$	2.83731	+	3.90523i	0.0976643	+	0.134423i
$845$	0.645749	+	0.209817i	0.0222144	+	0.00721791i
$846$	−9.77395			−0.336035
$847$	−25.4150	+	14.1801i	−0.873271	+	0.487235i
$848$	0.804116			0.0276134
$849$	−31.3001	−	10.1700i	−1.07422	−	0.349034i
$850$	−5.01994	−	6.90936i	−0.172183	−	0.236989i
$851$	−12.7201	−	9.24171i	−0.436040	−	0.316802i
$852$	2.43262	−	0.790407i	0.0833403	−	0.0270789i
$853$	−3.92293	−	12.0735i	−0.134319	−	0.413390i	0.861165	−	0.508326i	$-0.169735\pi$
$853$	−3.92293	−	12.0735i	−0.134319	−	0.413390i	−0.995483	+	0.0949358i	$0.969735\pi$
$854$	37.7798	−	5.26050i	1.29280	−	0.180011i
$855$	0.387558	+	0.533428i	0.0132542	+	0.0182428i
$856$	−4.52042	+	13.9124i	−0.154505	+	0.475517i
$857$	−48.3086			−1.65019			−0.825095	−	0.564993i	$-0.808879\pi$
$857$	−48.3086			−1.65019			−0.825095	+	0.564993i	$0.808879\pi$
$858$	−5.67740	+	8.29662i	−0.193823	+	0.283242i
$859$		−	34.8875i		−	1.19035i	−0.803597	−	0.595173i	$-0.797083\pi$
$859$		−	34.8875i		−	1.19035i	0.803597	−	0.595173i	$-0.202917\pi$
$860$	−0.0809294	+	0.249075i	−0.00275967	+	0.00849339i
$861$	0.234665	−	1.32100i	0.00799735	−	0.0450195i
$862$	−13.8985	−	10.0978i	−0.473383	−	0.343933i
$863$	−0.809597	−	2.49168i	−0.0275590	−	0.0848179i	0.936331	−	0.351119i	$-0.114199\pi$
$863$	−0.809597	−	2.49168i	−0.0275590	−	0.0848179i	−0.963890	+	0.266301i	$0.914199\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	1.43024	−	1.96856i	0.0486296	−	0.0669329i
$866$	−13.8708	+	10.0777i	−0.471348	+	0.342455i
$867$	−13.3576	−	4.34016i	−0.453649	−	0.147400i
$868$	−0.283720	+	0.273287i	−0.00963008	+	0.00927596i
$869$	−0.711820	+	0.548493i	−0.0241468	+	0.0186063i
$870$	−0.349210			−0.0118393
$871$	−10.5568	+	32.4905i	−0.357704	+	1.10090i
$872$	−7.91063	+	5.74741i	−0.267888	+	0.194632i
$873$	2.71044	−	3.73059i	0.0917343	−	0.126261i
$874$	11.8712	−	3.85718i	0.401548	−	0.130471i
$875$	4.14477	+	2.21060i	0.140119	+	0.0747318i
$876$	−5.59571	+	7.70183i	−0.189061	+	0.260221i
$877$	−11.2531	−	15.4885i	−0.379990	−	0.523011i	0.575592	−	0.817737i	$-0.304772\pi$
$877$	−11.2531	−	15.4885i	−0.379990	−	0.523011i	−0.955582	+	0.294726i	$0.904772\pi$
$878$	1.28868	+	0.418716i	0.0434907	+	0.0141310i
$879$			29.0278i			0.979084i
$880$	0.590493	−	0.0166593i	0.0199055	−	0.000561584i
$881$			25.8129i			0.869660i	0.900513	+	0.434830i	$0.143191\pi$
$881$			25.8129i			0.869660i	−0.900513	+	0.434830i	$0.856809\pi$
$882$	2.41091	−	6.57172i	0.0811795	−	0.221281i
$883$	−33.3178	+	24.2068i	−1.12123	+	0.814622i	−0.984395	−	0.175971i	$-0.943693\pi$
$883$	−33.3178	+	24.2068i	−1.12123	+	0.814622i	−0.136836	+	0.990594i	$0.543693\pi$
$884$	4.21541	+	3.06267i	0.141780	+	0.103009i
$885$	0.0790240	−	0.0256765i	0.00265636	−	0.000863105i
$886$	14.3573	−	4.66498i	0.482344	−	0.156723i
$887$	−16.5472	−	12.0222i	−0.555599	−	0.403667i	0.274246	−	0.961659i	$-0.411572\pi$
$887$	−16.5472	−	12.0222i	−0.555599	−	0.403667i	−0.829846	+	0.557993i	$0.811572\pi$
$888$	−3.77251	+	2.74089i	−0.126597	+	0.0919783i
$889$	15.8570	+	32.6171i	0.531825	+	1.09394i
$890$			3.06856i			0.102858i
$891$	−3.12414	+	1.11344i	−0.104663	+	0.0373017i
$892$		−	21.9933i		−	0.736390i
$893$	34.4115	+	11.1810i	1.15154	+	0.374157i
$894$	4.43625	+	6.10598i	0.148371	+	0.204215i
$895$	1.26607	−	1.74260i	0.0423200	−	0.0582485i
$896$	2.33447	+	1.24508i	0.0779893	+	0.0415953i
$897$	−9.72019	+	3.15828i	−0.324548	+	0.105452i
$898$	−18.0594	+	24.8567i	−0.602651	+	0.829478i
$899$	−0.236170	+	0.171588i	−0.00787672	+	0.00572277i
$900$	1.53528	−	4.72511i	0.0511761	−	0.157504i
$901$	1.38227			0.0460501
$902$	−0.474414	+	1.61359i	−0.0157963	+	0.0537266i
$903$	−2.69885	−	2.80188i	−0.0898121	−	0.0932408i
$904$	6.13401	+	1.99306i	0.204014	+	0.0662882i
$905$	−0.884689	+	0.642764i	−0.0294081	+	0.0213662i
$906$	10.7702	−	14.8238i	0.357814	−	0.492489i
$907$	−12.4835	−	38.4204i	−0.414509	−	1.27573i	−0.912690	−	0.408654i	$-0.865998\pi$
$907$	−12.4835	−	38.4204i	−0.414509	−	1.27573i	0.498181	−	0.867073i	$-0.334002\pi$
$908$	0.0290084	+	0.0892787i	0.000962677	+	0.00296282i
$909$	−0.534681	−	0.388468i	−0.0177342	−	0.0128847i
$910$	−1.40638	−	0.249831i	−0.0466209	−	0.00828183i
$911$	0.0760361	−	0.234015i	0.00251919	−	0.00775326i	−0.949789	−	0.312891i	$-0.898703\pi$
$911$	0.0760361	−	0.234015i	0.00251919	−	0.00775326i	0.952308	+	0.305138i	$0.0987025\pi$
$912$		−	3.70192i		−	0.122583i
$913$	20.9441	+	6.15783i	0.693149	+	0.203794i
$914$	1.29291			0.0427656
$915$	0.793514	−	2.44219i	0.0262328	−	0.0807362i
$916$	16.3853	+	22.5524i	0.541386	+	0.745153i
$917$	−6.76684	−	48.5981i	−0.223461	−	1.60485i
$918$	0.531198	+	1.63486i	0.0175322	+	0.0539584i
$919$	27.6321	−	8.97822i	0.911500	−	0.296164i	0.184525	−	0.982828i	$-0.440925\pi$
$919$	27.6321	−	8.97822i	0.911500	−	0.296164i	0.726975	+	0.686664i	$0.240925\pi$
$920$	0.485858	+	0.352997i	0.0160183	+	0.0116380i
$921$	−13.5044	−	18.5872i	−0.444985	−	0.612469i
$922$	20.2230	+	6.57084i	0.666008	+	0.216399i
$923$	7.75312			0.255197
$924$	−3.90948	+	7.85595i	−0.128612	+	0.258442i
$925$	23.1675			0.761742
$926$	−15.0029	−	4.87475i	−0.493027	−	0.160194i
$927$	4.85382	+	6.68071i	0.159420	+	0.219423i
$928$	1.58618	+	1.15243i	0.0520689	+	0.0378303i
$929$	16.3568	−	5.31463i	0.536648	−	0.174367i	−0.0281395	−	0.999604i	$-0.508958\pi$
$929$	16.3568	−	5.31463i	0.536648	−	0.174367i	0.564787	+	0.825237i	$0.308958\pi$
$930$	0.00819495	+	0.0252215i	0.000268723	+	0.000827044i
$931$	−16.0059	+	20.3793i	−0.524572	+	0.667904i
$932$	−2.01806	−	2.77762i	−0.0661037	−	0.0909839i
$933$	−2.43911	+	7.50682i	−0.0798530	+	0.245762i
$934$	−14.6705			−0.480033
$935$	1.01505	−	0.0286372i	0.0331958	−	0.000936537i
$936$			3.03115i			0.0990763i
$937$	5.44737	−	16.7653i	0.177958	−	0.547697i	−0.821799	−	0.569778i	$-0.807029\pi$
$937$	5.44737	−	16.7653i	0.177958	−	0.547697i	0.999756	+	0.0220808i	$0.00702910\pi$
$938$	−5.21543	+	29.3592i	−0.170290	+	0.958613i
$939$	22.6040	+	16.4228i	0.737654	+	0.535937i
$940$	0.537953	+	1.65565i	0.0175461	+	0.0540013i
$941$	10.6744	+	32.8526i	0.347977	+	1.07096i	0.959971	+	0.280101i	$0.0903678\pi$
$941$	10.6744	+	32.8526i	0.347977	+	1.07096i	−0.611994	+	0.790863i	$0.709632\pi$
$942$	−1.63711	+	2.25329i	−0.0533400	+	0.0734163i
$943$	−1.38331	+	1.00503i	−0.0450466	+	0.0327283i
$944$	−0.443678	−	0.144160i	−0.0144405	−	0.00469200i
$945$	−0.326917	−	0.339397i	−0.0106346	−	0.0110406i
$946$	2.97659	+	3.86295i	0.0967774	+	0.125595i
$947$	−18.7366			−0.608859			−0.304429	−	0.952535i	$-0.598466\pi$
$947$	−18.7366			−0.608859			−0.304429	+	0.952535i	$0.598466\pi$
$948$	−0.0837271	+	0.257685i	−0.00271933	+	0.00836923i
$949$	−23.3454	+	16.9614i	−0.757824	+	0.550592i
$950$	−10.8106	+	14.8796i	−0.350743	+	0.482756i
$951$	30.2937	−	9.84302i	0.982341	−	0.319182i
$952$	4.01295	+	2.14029i	0.130060	+	0.0693672i
$953$	15.6030	−	21.4757i	0.505431	−	0.695666i	−0.477710	−	0.878518i	$-0.658533\pi$
$953$	15.6030	−	21.4757i	0.505431	−	0.695666i	0.983140	+	0.182852i	$0.0585329\pi$
$954$	0.472647	+	0.650543i	0.0153025	+	0.0210621i
$955$	1.11211	+	0.361346i	0.0359870	+	0.0116929i
$956$			16.7859i			0.542895i
$957$	−3.67229	+	5.36646i	−0.118708	+	0.173473i
$958$			30.3305i			0.979934i
$959$	−44.8468	+	21.8025i	−1.44818	+	0.704040i
$960$	0.144095	−	0.104691i	0.00465065	−	0.00337889i
$961$	−25.0616	−	18.2083i	−0.808438	−	0.587365i
$962$	−13.4427	+	4.36780i	−0.433411	+	0.140824i
$963$	−13.9124	+	4.52042i	−0.448322	+	0.145669i
$964$	−11.7410	−	8.53033i	−0.378152	−	0.274743i
$965$	0.782143	−	0.568260i	0.0251781	−	0.0182929i
$966$	−8.02305	+	3.90045i	−0.258137	+	0.125495i
$967$		−	8.11531i		−	0.260971i	−0.991450	−	0.130485i	$-0.958346\pi$
$967$		−	8.11531i		−	0.260971i	0.991450	−	0.130485i	$-0.0416536\pi$
$968$	5.95362	−	9.24956i	0.191356	−	0.297292i
$969$		−	6.36357i		−	0.204427i
$970$	−0.781120	−	0.253801i	−0.0250803	−	0.00814907i
$971$	−9.36270	−	12.8866i	−0.300463	−	0.413552i	0.631914	−	0.775038i	$-0.282269\pi$
$971$	−9.36270	−	12.8866i	−0.300463	−	0.413552i	−0.932377	+	0.361486i	$0.882269\pi$
$972$	−0.587785	+	0.809017i	−0.0188532	+	0.0259492i
$973$	−14.6278	+	27.4264i	−0.468944	+	0.879249i
$974$	−19.0282	+	6.18263i	−0.609702	+	0.198104i
$975$	8.85181	−	12.1835i	0.283485	−	0.390183i
$976$	−11.6638	+	8.47422i	−0.373348	+	0.271253i
$977$	−2.90277	+	8.93381i	−0.0928679	+	0.285818i	−0.986692	−	0.162599i	$-0.948012\pi$
$977$	−2.90277	+	8.93381i	−0.0928679	+	0.285818i	0.893824	+	0.448417i	$0.148012\pi$
$978$	−10.3676			−0.331518
$979$	47.1560	+	32.2690i	1.50711	+	1.03132i
$980$	−1.24590	−	0.0466892i	−0.0397990	−	0.00149143i
$981$	−9.29950	−	3.02159i	−0.296910	−	0.0964720i
$982$	−7.76377	+	5.64071i	−0.247752	+	0.180002i
$983$	16.9082	−	23.2721i	0.539287	−	0.742265i	−0.449223	−	0.893420i	$-0.648299\pi$
$983$	16.9082	−	23.2721i	0.539287	−	0.742265i	0.988510	+	0.151155i	$0.0482991\pi$
$984$	0.156705	+	0.482288i	0.00499557	+	0.0153748i
$985$	1.24849	+	3.84245i	0.0397801	+	0.122431i
$986$	2.72663	+	1.98102i	0.0868337	+	0.0630884i
$987$	−25.4608	−	4.52291i	−0.810427	−	0.143966i
$988$	3.46750	−	10.6719i	0.110316	−	0.339517i
$989$			4.95785i			0.157650i
$990$	0.360561	+	0.467927i	0.0114594	+	0.0148717i
$991$	5.20646			0.165389			0.0826943	−	0.996575i	$-0.473648\pi$
$991$	5.20646			0.165389			0.0826943	+	0.996575i	$0.473648\pi$
$992$	0.0460103	−	0.141605i	0.00146083	−	0.00449597i
$993$	−0.120159	−	0.165385i	−0.00381314	−	0.00524834i
$994$	6.70267	−	0.933286i	0.212596	−	0.0296020i
$995$	−0.850051	−	2.61619i	−0.0269484	−	0.0829387i
$996$	6.26002	−	2.03400i	0.198356	−	0.0644499i
$997$	24.7162	+	17.9574i	0.782771	+	0.568716i	0.905809	−	0.423686i	$-0.139264\pi$
$997$	24.7162	+	17.9574i	0.782771	+	0.568716i	−0.123039	+	0.992402i	$0.539264\pi$
$998$	−23.1239	−	31.8273i	−0.731973	−	1.00748i
$999$	−4.43485	−	1.44097i	−0.140313	−	0.0455903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.13.7	✓	32
7.6	odd	2		462.2.u.b.13.6	yes	32
11.6	odd	10		462.2.u.b.391.6	yes	32
77.6	even	10	inner	462.2.u.a.391.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.13.7	✓	32	1.1	even	1	trivial
462.2.u.a.391.7	yes	32	77.6	even	10	inner
462.2.u.b.13.6	yes	32	7.6	odd	2
462.2.u.b.391.6	yes	32	11.6	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.169394 - 0.0550394i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.364877 - 2.62047i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.169394 - 0.0550394i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.364877 - 2.62047i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +0.178111 q^{10} +(1.87302 - 2.73712i) q^{11} -1.00000i q^{12} +(0.936678 - 2.88280i) q^{13} +(0.462752 - 2.60497i) q^{14} +(-0.144095 - 0.104691i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.531198 + 1.63486i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(2.99491 - 2.17593i) q^{19} +(0.169394 + 0.0550394i) q^{20} +(-1.90554 + 1.83547i) q^{21} +(2.62716 - 2.02436i) q^{22} +3.37179 q^{23} +(0.309017 - 0.951057i) q^{24} +(-4.01942 + 2.92028i) q^{25} +(1.78167 - 2.45225i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.24508 - 2.33447i) q^{28} +(1.15243 - 1.58618i) q^{29} +(-0.104691 - 0.144095i) q^{30} +(-0.141605 - 0.0460103i) q^{31} +1.00000i q^{32} +(-3.31531 + 0.0935330i) q^{33} +1.71899i q^{34} +(-0.206037 - 0.423809i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-3.77251 - 2.74089i) q^{37} +(3.52073 - 1.14395i) q^{38} +(-2.88280 + 0.936678i) q^{39} +(0.144095 + 0.104691i) q^{40} +(-0.410258 + 0.298070i) q^{41} +(-2.37946 + 1.15679i) q^{42} +1.47039i q^{43} +(3.12414 - 1.11344i) q^{44} +0.178111i q^{45} +(3.20676 + 1.04194i) q^{46} +(5.74499 + 7.90729i) q^{47} +(0.587785 - 0.809017i) q^{48} +(-6.73373 + 1.91230i) q^{49} +(-4.72511 + 1.53528i) q^{50} +(1.01040 - 1.39070i) q^{51} +(2.45225 - 1.78167i) q^{52} +(0.248485 - 0.764760i) q^{53} +1.00000 q^{54} +(0.166629 - 0.566740i) q^{55} +(1.90554 - 1.83547i) q^{56} +(-3.52073 - 1.14395i) q^{57} +(1.58618 - 1.15243i) q^{58} +(-0.274208 + 0.377415i) q^{59} +(-0.0550394 - 0.169394i) q^{60} +(4.45516 + 13.7116i) q^{61} +(-0.120456 - 0.0875167i) q^{62} +(2.60497 + 0.462752i) q^{63} +(-0.309017 + 0.951057i) q^{64} -0.539882i q^{65} +(-3.18195 - 0.935531i) q^{66} -11.2705 q^{67} +(-0.531198 + 1.63486i) q^{68} +(-1.98189 - 2.72784i) q^{69} +(-0.0649886 - 0.466735i) q^{70} +(0.790407 + 2.43262i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-7.70183 - 5.59571i) q^{73} +(-2.74089 - 3.77251i) q^{74} +(4.72511 + 1.53528i) q^{75} +3.70192 q^{76} +(-7.85595 - 3.90948i) q^{77} -3.03115 q^{78} +(-0.257685 - 0.0837271i) q^{79} +(0.104691 + 0.144095i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.482288 + 0.156705i) q^{82} +(2.03400 + 6.26002i) q^{83} +(-2.62047 + 0.364877i) q^{84} +(0.179964 + 0.247699i) q^{85} +(-0.454375 + 1.39842i) q^{86} -1.96063 q^{87} +(3.31531 - 0.0935330i) q^{88} +17.2283i q^{89} +(-0.0550394 + 0.169394i) q^{90} +(-7.89606 - 1.40267i) q^{91} +(2.72784 + 1.98189i) q^{92} +(0.0460103 + 0.141605i) q^{93} +(3.02032 + 9.29558i) q^{94} +(0.387558 - 0.533428i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.38558 - 1.42496i) q^{97} +(-6.99509 - 0.262135i) q^{98} +(2.02436 + 2.62716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

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