LMFDB - Embedded newform 462.2.u.b.13.6

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			13.6
Character	$\chi$	$=$	462.13
Dual form			462.2.u.b.391.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.169394 + 0.0550394i) q^{5} +(0.309017 + 0.951057i) q^{6} +(2.60497 - 0.462752i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(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} +(2.60497 - 0.462752i) 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} +(2.62047 + 0.364877i) 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} +(2.37946 + 1.15679i) 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} +(-0.415796 + 0.221763i) 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} +(1.24508 + 2.33447i) 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} +(6.57172 - 2.41091i) 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} +(-0.364877 + 2.62047i) 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} +(-0.463974 + 0.0824213i) 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} +(3.61255 - 7.99684i) 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} +(0.462752 + 2.60497i) 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} +(-1.10600 + 7.94304i) 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} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 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} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 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} - 20 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 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * 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 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * 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 - 20 * 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	−0.346649	−	0.937995i	$-0.612681\pi$
$5$	−0.169394	+	0.0550394i	−0.0757552	+	0.0246144i	0.270894	+	0.962609i	$0.412681\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	2.60497	−	0.462752i	0.984586	−	0.174904i
$7$	2.60497	−	0.462752i	0.984586	−	0.174904i
$8$	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	$0.238091\pi$
$13$	−0.936678	+	2.88280i	−0.259788	+	0.799544i	−0.992849	+	0.119381i	$0.961909\pi$
$14$	2.62047	+	0.364877i	0.700350	+	0.0975174i
$15$	−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	0.865746	−	0.500484i	$-0.166845\pi$
$17$	−0.531198	−	1.63486i	−0.128835	−	0.396512i	−0.994580	+	0.103972i	$0.966845\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−2.99491	+	2.17593i	−0.687080	+	0.499193i	−0.875699	−	0.482857i	$-0.839599\pi$
$19$	−2.99491	+	2.17593i	−0.687080	+	0.499193i	0.188619	+	0.982050i	$0.439599\pi$
$20$	−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
$28$	2.37946	+	1.15679i	0.449676	+	0.218612i
$29$	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	0.321706	−	0.946840i	$-0.395744\pi$
$31$	0.141605	+	0.0460103i	0.0254330	+	0.00826369i	−0.296273	+	0.955103i	$0.595744\pi$
$32$			1.00000i			0.176777i
$33$	3.31531	−	0.0935330i	0.577121	−	0.0162820i
$34$		−	1.71899i		−	0.294805i
$35$	−0.415796	+	0.221763i	−0.0702824	+	0.0374848i
$36$	−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	−0.555288	−	0.831658i	$-0.687392\pi$
$41$	0.410258	−	0.298070i	0.0640716	−	0.0465507i	0.619360	+	0.785107i	$0.287392\pi$
$42$	1.24508	+	2.33447i	0.192120	+	0.360217i
$43$			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	$-0.947409\pi$
$47$	−5.74499	−	7.90729i	−0.837992	−	1.15340i	0.148390	−	0.988929i	$-0.452591\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	6.57172	−	2.41091i	0.938817	−	0.344415i
$50$	−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	−0.790794	−	0.612082i	$-0.790332\pi$
$59$	0.274208	−	0.377415i	0.0356988	−	0.0491352i	0.826493	+	0.562947i	$0.190332\pi$
$60$	−0.0550394	−	0.169394i	−0.00710556	−	0.0218687i
$61$	−4.45516	−	13.7116i	−0.570425	−	1.75559i	−0.651255	−	0.758859i	$-0.725757\pi$
$61$	−4.45516	−	13.7116i	−0.570425	−	1.75559i	0.0808303	−	0.996728i	$-0.474243\pi$
$62$	0.120456	+	0.0875167i	0.0152980	+	0.0111146i
$63$	−0.364877	+	2.62047i	−0.0459701	+	0.330148i
$64$	−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
$70$	−0.463974	+	0.0824213i	−0.0554555	+	0.00985123i
$71$	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	0.938833	−	0.344372i	$-0.111908\pi$
$73$	7.70183	+	5.59571i	0.901431	+	0.654928i	−0.0374021	+	0.999300i	$0.511908\pi$
$74$	−2.74089	−	3.77251i	−0.318622	−	0.438546i
$75$	−4.72511	−	1.53528i	−0.545609	−	0.177279i
$76$	−3.70192			−0.424639
$77$	3.61255	−	7.99684i	0.411688	−	0.911325i
$78$	−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	$-0.982352\pi$
$83$	−2.03400	−	6.26002i	−0.223261	−	0.687126i	0.775203	−	0.631713i	$-0.217648\pi$
$84$	0.462752	+	2.60497i	0.0504903	+	0.284225i
$85$	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	$-0.633681\pi$
$89$		−	17.2283i		−	1.82620i	0.407735	−	0.913100i	$-0.366319\pi$
$90$	0.0550394	−	0.169394i	0.00580166	−	0.0178557i
$91$	−1.10600	+	7.94304i	−0.115940	+	0.832657i
$92$	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	0.523074	−	0.852287i	$-0.324785\pi$
$97$	4.38558	+	1.42496i	0.445288	+	0.144683i	−0.0777862	+	0.996970i	$0.524785\pi$
$98$	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	−0.940381	−	0.340122i	$-0.889532\pi$
$101$	0.204230	−	0.628555i	0.0203216	−	0.0625435i	0.960703	+	0.277578i	$0.0895317\pi$
$102$	1.39070	−	1.01040i	0.137699	−	0.100044i
$103$	−4.85382	+	6.68071i	−0.478261	+	0.658270i	−0.978170	−	0.207808i	$-0.933367\pi$
$103$	−4.85382	+	6.68071i	−0.478261	+	0.658270i	0.499909	+	0.866078i	$0.333367\pi$
$104$	−2.88280	+	0.936678i	−0.282682	+	0.0918488i
$105$	−0.423809	−	0.206037i	−0.0413595	−	0.0201072i
$106$	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
$112$	1.24508	+	2.33447i	0.117649	+	0.220587i
$113$	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
$119$	−2.14029	−	4.01295i	−0.196200	−	0.367866i
$120$		−	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
$126$	−1.15679	+	2.37946i	−0.103055	+	0.211979i
$127$	−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	$-0.800623\pi$
$131$	−18.5456			−1.62033			−0.810166	+	0.586200i	$0.800623\pi$
$132$	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	0.912719	−	0.408587i	$-0.133978\pi$
$139$	9.50467	+	6.90555i	0.806176	+	0.585721i	−0.106544	+	0.994308i	$0.533978\pi$
$140$	−0.466735	−	0.0649886i	−0.0394463	−	0.00549254i
$141$	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
$147$	5.81323	+	3.89954i	0.479467	+	0.321629i
$148$	−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
$154$	5.90690	−	6.48911i	0.475991	−	0.522907i
$155$	−0.0265194			−0.00213009
$156$	−2.88280	−	0.936678i	−0.230808	−	0.0749942i
$157$	1.63711	+	2.25329i	0.130656	+	0.179832i	0.869333	−	0.494227i	$-0.164549\pi$
$157$	1.63711	+	2.25329i	0.130656	+	0.179832i	−0.738677	+	0.674060i	$0.764549\pi$
$158$	−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
$161$	8.78341	−	1.56030i	0.692229	−	0.122969i
$162$	−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	$0.251442\pi$
$167$	−3.65812	+	11.2585i	−0.283074	+	0.871211i	−0.986969	+	0.160908i	$0.948558\pi$
$168$	−0.364877	+	2.62047i	−0.0281508	+	0.202174i
$169$	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	−0.922454	−	0.386107i	$-0.873819\pi$
$173$	−11.0524	+	8.03003i	−0.840298	+	0.610512i	0.0821560	+	0.996619i	$0.473819\pi$
$174$	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	−0.0838556	−	0.996478i	$-0.526723\pi$
$181$	5.83913	−	1.89725i	0.434019	−	0.141021i	0.517874	+	0.855457i	$0.326723\pi$
$182$	−3.50640	+	7.21251i	−0.259912	+	0.534627i
$183$	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
$189$	−2.33447	+	1.24508i	−0.169808	+	0.0905664i
$190$	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
$196$	6.73373	+	1.91230i	0.480981	+	0.136593i
$197$			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	$0.184387\pi$
$199$			15.4444i			1.09482i	−0.836863	+	0.547412i	$0.815613\pi$
$200$	−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
$203$	2.26803	−	4.66524i	0.159184	−	0.327435i
$204$	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
$217$	0.390168	+	0.0543273i	0.0264863	+	0.00368798i
$218$	−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	$0.0634713\pi$
$223$	12.9273	+	17.7930i	0.865679	+	1.19150i	−0.114506	+	0.993423i	$0.536529\pi$
$224$	0.462752	+	2.60497i	0.0309189	+	0.174052i
$225$	−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	0.585262	−	0.810844i	$-0.300992\pi$
$227$	−0.0759450	−	0.0551772i	−0.00504064	−	0.00366224i	−0.590303	+	0.807182i	$0.700992\pi$
$228$	−2.17593	−	2.99491i	−0.144105	−	0.198343i
$229$	−26.5120	−	8.61426i	−1.75196	−	0.569246i	−0.755643	−	0.654984i	$-0.772675\pi$
$229$	−26.5120	−	8.61426i	−1.75196	−	0.569246i	−0.996318	+	0.0857375i	$0.972675\pi$
$230$	−0.600554			−0.0395993
$231$	8.59298	−	1.77781i	0.565377	−	0.116972i
$232$	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
$238$	−0.795468	−	4.47793i	−0.0515625	−	0.290261i
$239$	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	$-0.345183\pi$
$241$	14.5127			0.934843			0.467421	+	0.884035i	$0.345183\pi$
$242$	−0.620181	−	10.9825i	−0.0398667	−	0.705982i
$243$		−	1.00000i		−	0.0641500i
$244$	4.45516	−	13.7116i	0.285212	−	0.877793i
$245$	−0.980515	+	0.770097i	−0.0626428	+	0.0491997i
$246$	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	0.796801	−	0.604242i	$-0.206524\pi$
$251$	17.2096	+	5.59175i	1.08626	+	0.352948i	0.289461	+	0.957190i	$0.406524\pi$
$252$	−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	−0.549110	−	0.835750i	$-0.685033\pi$
$257$	6.65969	−	9.16627i	0.415420	−	0.571776i	0.964530	+	0.263974i	$0.0850332\pi$
$258$	−1.39842	+	0.454375i	−0.0870621	+	0.0282882i
$259$	−11.0956	−	5.39420i	−0.689449	−	0.335179i
$260$	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
$266$	−8.64203	+	4.60919i	−0.529877	+	0.282608i
$267$	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	−0.195563	−	0.980691i	$-0.562653\pi$
$269$	3.65188	−	1.18657i	0.222659	−	0.0723463i	0.418222	+	0.908345i	$0.362653\pi$
$270$	0.169394	−	0.0550394i	0.0103090	−	0.00334959i
$271$	−0.849788	−	0.617407i	−0.0516209	−	0.0375048i	0.561676	−	0.827358i	$-0.310157\pi$
$271$	−0.849788	−	0.617407i	−0.0516209	−	0.0375048i	−0.613297	+	0.789853i	$0.710157\pi$
$272$	1.39070	−	1.01040i	0.0843233	−	0.0612645i
$273$	−7.07615	+	3.77403i	−0.428268	+	0.228415i
$274$		−	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
$280$	−0.423809	−	0.206037i	−0.0253274	−	0.0123131i
$281$	−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	$0.733372\pi$
$283$	−26.6254	+	19.3445i	−1.58272	+	1.14991i	−0.913496	+	0.406848i	$0.866628\pi$
$284$	−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	$0.0221404\pi$
$293$	23.4840	+	17.0621i	1.37195	+	0.996780i	0.374368	+	0.927280i	$0.377860\pi$
$294$	4.32368	+	5.50507i	0.252162	+	0.321062i
$295$	−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
$301$	0.680425	+	3.83032i	0.0392191	+	0.220776i
$302$	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	$-0.727596\pi$
$307$	−22.9750			−1.31125			−0.655627	+	0.755085i	$0.727596\pi$
$308$	7.62304	−	4.34618i	0.434363	−	0.247647i
$309$	−8.25781			−0.469770
$310$	−0.0252215	−	0.00819495i	−0.00143248	−	0.000465442i
$311$	4.63947	+	6.38568i	0.263080	+	0.362099i	0.920038	−	0.391828i	$-0.128157\pi$
$311$	4.63947	+	6.38568i	0.263080	+	0.362099i	−0.656958	+	0.753927i	$0.728157\pi$
$312$	−2.45225	−	1.78167i	−0.138832	−	0.100867i
$313$	26.5726	−	8.63397i	1.50197	−	0.488021i	0.561380	−	0.827558i	$-0.310270\pi$
$313$	26.5726	−	8.63397i	1.50197	−	0.488021i	0.940593	+	0.339537i	$0.110270\pi$
$314$	0.860681	+	2.64891i	0.0485711	+	0.149486i
$315$	−0.0824213	−	0.463974i	−0.00464391	−	0.0261420i
$316$	−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
$322$	8.83568	+	1.23029i	0.492393	+	0.0685612i
$323$	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
$336$	−1.15679	+	2.37946i	−0.0631080	+	0.129810i
$337$	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
$343$	16.0035	−	9.32141i	0.864107	−	0.503309i
$344$	−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	−0.458517	−	0.888686i	$-0.651619\pi$
$349$	4.57667	−	3.32514i	0.244983	−	0.177991i	0.703501	+	0.710695i	$0.251619\pi$
$350$	−11.5983	+	6.18591i	−0.619956	+	0.330651i
$351$		−	3.03115i		−	0.161791i
$352$	2.73712	+	1.87302i	0.145889	+	0.0998322i
$353$			25.0557i			1.33358i	0.745245	+	0.666791i	$0.232333\pi$
$353$			25.0557i			1.33358i	−0.745245	+	0.666791i	$0.767667\pi$
$354$	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
$357$	1.98851	−	4.09028i	0.105243	−	0.216481i
$358$	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	−0.693831	−	0.720138i	$-0.744078\pi$
$367$	3.93618	−	5.41769i	0.205467	−	0.282801i	0.899298	+	0.437337i	$0.144078\pi$
$368$	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
$371$	0.293403	−	2.10716i	0.0152327	−	0.109398i
$372$	−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
$378$	−2.60497	+	0.462752i	−0.133985	+	0.0238014i
$379$	−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	0.800955	−	0.598725i	$-0.204326\pi$
$383$	21.4691	+	6.97573i	1.09702	+	0.356443i	0.296064	+	0.955168i	$0.404326\pi$
$384$	−1.00000			−0.0510310
$385$	−0.171802	+	1.55345i	−0.00875584	+	0.0791711i
$386$	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
$392$	5.81323	+	3.89954i	0.293612	+	0.196956i
$393$	−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	$-0.759638\pi$
$397$		−	27.3120i		−	1.37075i	0.728189	−	0.685376i	$-0.240362\pi$
$398$	−4.77258	+	14.6885i	−0.239228	+	0.736268i
$399$	−9.70076	−	1.35074i	−0.485645	−	0.0676217i
$400$	−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	$-0.664249\pi$
$409$	8.43375	−	25.9564i	0.417022	−	1.28346i	0.910430	−	0.413664i	$-0.135751\pi$
$410$	−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
$413$	0.539654	−	1.11004i	0.0265546	−	0.0546217i
$414$	−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	$-0.711783\pi$
$419$		−	32.2071i		−	1.57342i	0.617324	−	0.786709i	$-0.288217\pi$
$420$	−0.221763	−	0.415796i	−0.0108209	−	0.0202888i
$421$	−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
$427$	−17.9506	−	33.6566i	−0.868691	−	1.62876i
$428$			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	−0.495021	−	0.868881i	$-0.664840\pi$
$433$	10.0777	−	13.8708i	0.484304	−	0.666587i	0.979325	+	0.202294i	$0.0648396\pi$
$434$	0.354284	+	0.172237i	0.0170062	+	0.00826764i
$435$	−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	$-0.510294\pi$
$439$	−1.35499			−0.0646703			−0.0323352	+	0.999477i	$0.510294\pi$
$440$	−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
$448$	−0.364877	+	2.62047i	−0.0172388	+	0.123806i
$449$	−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
$455$	−0.249831	−	1.40638i	−0.0117123	−	0.0659319i
$456$	−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	$-0.664896\pi$
$461$	−21.2637			−0.990349			−0.495174	+	0.868794i	$0.664896\pi$
$462$	8.72179	+	0.964577i	0.405774	+	0.0448762i
$463$	−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	0.0321506	−	0.999483i	$-0.489764\pi$
$467$	13.9524	−	4.53343i	0.645642	−	0.209782i	0.613492	+	0.789701i	$0.289764\pi$
$468$	−0.936678	−	2.88280i	−0.0432979	−	0.133257i
$469$	−29.3592	+	5.21543i	−1.35568	+	0.240826i
$470$	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
$476$	0.627221	−	4.50457i	0.0287486	−	0.206467i
$477$	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	$-0.856325\pi$
$479$	−9.37264	−	28.8460i	−0.428247	−	1.31801i	0.471604	−	0.881810i	$-0.343675\pi$
$480$	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
$490$	−1.17050	+	0.429410i	−0.0528777	+	0.0193988i
$491$	−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
$497$	3.18469	+	5.97115i	0.142853	+	0.267842i
$498$	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	−0.439200	−	0.898390i	$-0.644738\pi$
$503$	6.26852	−	4.55435i	0.279500	−	0.203068i	0.718699	+	0.695321i	$0.244738\pi$
$504$	−2.33447	+	1.24508i	−0.103986	+	0.0554604i
$505$			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	$-0.884963\pi$
$509$	−22.1690	−	30.5130i	−0.982625	−	1.35247i	−0.0472214	−	0.998884i	$-0.515037\pi$
$510$	−0.179964	+	0.247699i	−0.00796892	+	0.0109683i
$511$	22.6524	+	11.0126i	1.00209	+	0.487169i
$512$	−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	−0.658079	−	0.752949i	$-0.728631\pi$
$521$	5.96600	−	8.21149i	0.261375	−	0.359752i	0.919454	+	0.393197i	$0.128631\pi$
$522$	0.605867	+	1.86467i	0.0265181	+	0.0816142i
$523$	12.8903	+	39.6724i	0.563655	+	1.73475i	0.671915	+	0.740628i	$0.265472\pi$
$523$	12.8903	+	39.6724i	0.563655	+	1.73475i	−0.108260	+	0.994123i	$0.534528\pi$
$524$	−15.0037	−	10.9008i	−0.655438	−	0.476204i
$525$	−13.0192	−	1.81281i	−0.568205	−	0.0791174i
$526$	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
$532$	−9.64337	+	1.71307i	−0.418093	+	0.0742709i
$533$	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
$539$	5.71002	−	22.5032i	0.245948	−	0.969283i
$540$	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
$546$	−7.89606	+	1.40267i	−0.337920	+	0.0600288i
$547$	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
$553$	−0.710007	−	0.0988620i	−0.0301926	−	0.00420404i
$554$	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	$0.275770\pi$
$563$	−7.69239	+	23.6747i	−0.324195	+	0.997771i	−0.971802	+	0.235796i	$0.924230\pi$
$564$	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
$567$	−2.37946	−	1.15679i	−0.0999280	−	0.0485805i
$568$	−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
$574$	1.18383	−	0.631390i	0.0494121	−	0.0263537i
$575$	−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	−0.139004	−	0.990292i	$-0.544390\pi$
$577$	7.94172	−	2.58042i	0.330618	−	0.107424i	0.469622	+	0.882868i	$0.344390\pi$
$578$	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
$581$	−8.19535	−	15.3659i	−0.340000	−	0.637486i
$582$			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	−0.664832	−	0.746993i	$-0.731497\pi$
$587$	6.08235	−	8.37163i	0.251045	−	0.345534i	0.915877	+	0.401459i	$0.131497\pi$
$588$	2.41091	+	6.57172i	0.0994241	+	0.271013i
$589$	−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	$-0.350324\pi$
$593$	22.0666			0.906165			0.453083	+	0.891469i	$0.350324\pi$
$594$	−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	0.853202	−	0.521581i	$-0.174658\pi$
$601$	15.2192	+	11.0574i	0.620803	+	0.451040i	−0.232399	+	0.972621i	$0.574658\pi$
$602$	−0.536511	+	3.85311i	−0.0218665	+	0.157041i
$603$	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	−0.999866	−	0.0163736i	$-0.994788\pi$
$607$	−4.46757	+	13.7498i	−0.181333	+	0.558086i	0.818533	+	0.574460i	$0.194788\pi$
$608$	−2.17593	−	2.99491i	−0.0882457	−	0.121460i
$609$	5.10737	−	0.907283i	0.206961	−	0.0367650i
$610$	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
$616$	8.59298	−	1.77781i	0.346221	−	0.0716302i
$617$	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	$0.0274797\pi$
$619$	19.1676	+	26.3820i	0.770413	+	1.06038i	−0.225863	+	0.974159i	$0.572520\pi$
$620$	−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
$623$	−7.97244	−	44.8793i	−0.319409	−	1.79805i
$624$	−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
$630$	0.0649886	−	0.466735i	0.00258921	−	0.0185952i
$631$	−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	−0.601646	−	0.798763i	$-0.705488\pi$
$643$	−15.6934	+	5.09909i	−0.618886	+	0.201088i	−0.0172405	+	0.999851i	$0.505488\pi$
$644$	8.02305	+	3.90045i	0.316152	+	0.153699i
$645$	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	0.942336	−	0.334670i	$-0.108625\pi$
$647$	38.3575	+	12.4631i	1.50799	+	0.489975i	0.565652	+	0.824644i	$0.308625\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−0.519432	−	1.45744i	−0.0203895	−	0.0572097i
$650$		−	15.0596i		−	0.590686i
$651$	0.185383	+	0.347585i	0.00726574	+	0.0136229i
$652$	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
$658$	−12.1694	−	22.8170i	−0.474412	−	0.889501i
$659$		−	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	$0.281522\pi$
$661$			39.7760i			1.54711i	−0.633732	+	0.773553i	$0.718478\pi$
$662$	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
$665$	0.762732	−	1.56891i	0.0295775	−	0.0608395i
$666$	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	$0.0244302\pi$
$677$	6.12724	+	18.8577i	0.235489	+	0.724760i	−0.761567	+	0.648086i	$0.775570\pi$
$678$	5.21790	+	3.79102i	0.200392	+	0.145593i
$679$	12.0837	+	1.68254i	0.463729	+	0.0645701i
$680$	−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
$686$	18.1007	−	3.91984i	0.691087	−	0.149660i
$687$	−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	0.731934	−	0.681376i	$-0.238618\pi$
$691$	24.2780	+	7.88839i	0.923578	+	0.300089i	0.191644	+	0.981464i	$0.438618\pi$
$692$	−13.6615			−0.519333
$693$	6.48911	+	5.90690i	0.246501	+	0.224384i
$694$	−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
$700$	−12.9422	+	2.29908i	−0.489169	+	0.0868970i
$701$	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
$707$	0.241148	−	1.73187i	0.00906929	−	0.0651338i
$708$	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	$0.464850\pi$
$719$	−23.3046	+	32.0760i	−0.869114	+	1.19623i	−0.979319	+	0.202324i	$0.935150\pi$
$720$	0.169394	−	0.0550394i	0.00631294	−	0.00205120i
$721$	−9.55254	+	19.6492i	−0.355755	+	0.731773i
$722$	−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	$-0.810787\pi$
$727$		−	30.2005i		−	1.12007i	0.828468	−	0.560036i	$-0.189213\pi$
$728$	−7.07615	+	3.77403i	−0.262259	+	0.139875i
$729$	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	0.668342	−	0.743854i	$-0.267004\pi$
$733$	4.53282	+	3.29328i	0.167423	+	0.121640i	−0.500918	+	0.865494i	$0.667004\pi$
$734$	5.41769	−	3.93618i	0.199971	−	0.145287i
$735$	−1.19935	−	0.340602i	−0.0442388	−	0.0125633i
$736$			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
$742$	0.930192	−	1.91336i	0.0341484	−	0.0702418i
$743$	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
$756$	−2.62047	−	0.364877i	−0.0953056	−	0.0132704i
$757$	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	$0.236690\pi$
$761$	−7.09840	+	21.8466i	−0.257317	+	0.791940i	−0.993364	+	0.115010i	$0.963310\pi$
$762$	−8.05721	−	11.0898i	−0.291882	−	0.401741i
$763$	4.52482	+	25.4716i	0.163809	+	0.922133i
$764$	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	$-0.719089\pi$
$769$	−35.2302			−1.27043			−0.635217	+	0.772334i	$0.719089\pi$
$770$	−0.643435	+	1.42433i	−0.0231878	+	0.0513292i
$771$	11.3301			0.408045
$772$	5.16230	+	1.67733i	0.185795	+	0.0603686i
$773$	−14.0693	−	19.3647i	−0.506037	−	0.696501i	0.477207	−	0.878791i	$-0.341649\pi$
$773$	−14.0693	−	19.3647i	−0.506037	−	0.696501i	−0.983245	+	0.182290i	$0.941649\pi$
$774$	−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
$777$	−2.15785	−	12.1472i	−0.0774124	−	0.435778i
$778$	−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
$784$	4.32368	+	5.50507i	0.154417	+	0.196610i
$785$	−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	0.905110	−	0.425177i	$-0.139788\pi$
$787$	−2.16159	−	6.65269i	−0.0770524	−	0.237143i	−0.982162	+	0.188035i	$0.939788\pi$
$788$	−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	−0.992958	−	0.118467i	$-0.962202\pi$
$797$	−48.7452	+	15.8383i	−1.72665	+	0.561021i	−0.733687	+	0.679488i	$0.762202\pi$
$798$	−8.80857	−	4.28233i	−0.311820	−	0.151593i
$799$	−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
$805$	−1.40198	+	0.747739i	−0.0494132	+	0.0263543i
$806$	−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	−0.0873749	−	0.996176i	$-0.527848\pi$
$811$	23.7235	−	17.2361i	0.833044	−	0.605242i	0.920419	+	0.390934i	$0.127848\pi$
$812$	4.57703	−	2.44114i	0.160622	−	0.0856673i
$813$		−	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
$819$	−7.21251	−	3.50640i	−0.252026	−	0.122524i
$820$	−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	−0.864132	−	0.503266i	$-0.832132\pi$
$829$	−3.41091	+	4.69472i	−0.118466	+	0.163054i	0.745666	+	0.666320i	$0.232132\pi$
$830$	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
$833$	−7.43239	−	9.46318i	−0.257517	−	0.327880i
$834$	−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	0.361323	−	0.932441i	$-0.382325\pi$
$839$	−18.4549	−	25.4011i	−0.637135	−	0.876942i	−0.998459	+	0.0554989i	$0.982325\pi$
$840$	−0.0824213	−	0.463974i	−0.00284380	−	0.0160086i
$841$	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
$847$	−15.1219	−	24.8662i	−0.519595	−	0.854413i
$848$	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	0.995483	−	0.0949358i	$-0.0302646\pi$
$853$	3.92293	+	12.0735i	0.134319	+	0.413390i	−0.861165	+	0.508326i	$0.830265\pi$
$854$	−6.67158	−	37.5564i	−0.228297	−	1.28515i
$855$	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	$-0.191121\pi$
$857$	48.3086			1.65019			0.825095	+	0.564993i	$0.191121\pi$
$858$	−5.67740	+	8.29662i	−0.193823	+	0.283242i
$859$			34.8875i			1.19035i	0.803597	+	0.595173i	$0.202917\pi$
$859$			34.8875i			1.19035i	−0.803597	+	0.595173i	$0.797083\pi$
$860$	0.0809294	−	0.249075i	0.00275967	−	0.00849339i
$861$	1.32886	+	0.185032i	0.0452874	+	0.00630586i
$862$	−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
$875$	2.05383	−	4.22465i	0.0694322	−	0.142819i
$876$	−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	$-0.856809\pi$
$881$		−	25.8129i		−	0.869660i	0.900513	−	0.434830i	$-0.143191\pi$
$882$	−1.91230	+	6.73373i	−0.0643904	+	0.226736i
$883$	−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	0.829846	−	0.557993i	$-0.188428\pi$
$887$	16.5472	+	12.0222i	0.555599	+	0.403667i	−0.274246	+	0.961659i	$0.588428\pi$
$888$	3.77251	−	2.74089i	0.126597	−	0.0919783i
$889$	−32.0004	+	17.0673i	−1.07326	+	0.572418i
$890$			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
$896$	−1.15679	+	2.37946i	−0.0386456	+	0.0794923i
$897$	−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
$910$	0.196990	−	1.41475i	0.00653017	−	0.0468984i
$911$	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
$917$	−48.3106	+	8.58199i	−1.59536	+	0.283402i
$918$	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
$924$	7.99684	+	3.61255i	0.263077	+	0.118844i
$925$	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	−0.564787	−	0.825237i	$-0.691042\pi$
$929$	−16.3568	+	5.31463i	−0.536648	+	0.174367i	0.0281395	+	0.999604i	$0.491042\pi$
$930$	−0.00819495	−	0.0252215i	−0.000268723	−	0.000827044i
$931$	−14.4358	+	21.5201i	−0.473113	+	0.705292i
$932$	−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	−0.999756	−	0.0220808i	$-0.992971\pi$
$937$	−5.44737	+	16.7653i	−0.177958	+	0.547697i	0.821799	+	0.569778i	$0.192971\pi$
$938$	−29.5340	−	4.11233i	−0.964318	−	0.134272i
$939$	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	$-0.909632\pi$
$941$	−10.6744	−	32.8526i	−0.347977	−	1.07096i	0.611994	−	0.790863i	$-0.290368\pi$
$942$	−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
$952$	1.98851	−	4.09028i	0.0644481	−	0.132567i
$953$	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
$959$	−23.4666	−	43.9989i	−0.757777	−	1.42080i
$960$	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
$966$	4.19816	+	7.87136i	0.135073	+	0.253257i
$967$		−	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	0.932377	−	0.361486i	$-0.117731\pi$
$971$	9.36270	+	12.8866i	0.300463	+	0.413552i	−0.631914	+	0.775038i	$0.717731\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	27.9549	+	13.5904i	0.896194	+	0.435689i
$974$	−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	−0.988510	−	0.151155i	$-0.951701\pi$
$983$	−16.9082	+	23.2721i	−0.539287	+	0.742265i	0.449223	+	0.893420i	$0.351701\pi$
$984$	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
$987$	3.56629	−	25.6124i	0.113516	−	0.815250i
$988$	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
$994$	1.18363	+	6.66302i	0.0375425	+	0.211338i
$995$	−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	0.123039	−	0.992402i	$-0.460736\pi$
$997$	−24.7162	−	17.9574i	−0.782771	−	0.568716i	−0.905809	+	0.423686i	$0.860736\pi$
$998$	−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.b.13.6	yes	32
7.6	odd	2		462.2.u.a.13.7	✓	32
11.6	odd	10		462.2.u.a.391.7	yes	32
77.6	even	10	inner	462.2.u.b.391.6	yes	32

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

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)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.169394 + 0.0550394i) q^{5} +(0.309017 + 0.951057i) q^{6} +(2.60497 - 0.462752i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(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} +(2.60497 - 0.462752i) 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} +(2.62047 + 0.364877i) 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} +(2.37946 + 1.15679i) 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} +(-0.415796 + 0.221763i) 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} +(1.24508 + 2.33447i) 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} +(6.57172 - 2.41091i) 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} +(-0.364877 + 2.62047i) 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} +(-0.463974 + 0.0824213i) 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} +(3.61255 - 7.99684i) 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} +(0.462752 + 2.60497i) 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} +(-1.10600 + 7.94304i) 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	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 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 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * 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 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * 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 - 20 * 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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