LMFDB - Embedded newform 462.2.j.c.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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, 0, 2]))

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			295.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	462.295
Dual form			462.2.j.c.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.427051 - 1.31433i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.427051 - 1.31433i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.38197 q^{10} +(-0.309017 + 3.30220i) q^{11} +1.00000 q^{12} +(-0.381966 + 1.17557i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(1.11803 + 0.812299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.35410 + 7.24518i) q^{17} +(0.809017 + 0.587785i) q^{18} +(-3.30902 + 2.40414i) q^{19} +(-0.427051 + 1.31433i) q^{20} -1.00000 q^{21} +(-3.04508 - 1.31433i) q^{22} -9.32624 q^{23} +(-0.309017 + 0.951057i) q^{24} +(2.50000 - 1.81636i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(1.00000 + 0.726543i) q^{29} +(-1.11803 + 0.812299i) q^{30} +(0.336881 - 1.03681i) q^{31} -1.00000 q^{32} +(-1.69098 - 2.85317i) q^{33} -7.61803 q^{34} +(0.427051 - 1.31433i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(6.97214 + 5.06555i) q^{37} +(-1.26393 - 3.88998i) q^{38} +(-0.381966 - 1.17557i) q^{39} +(-1.11803 - 0.812299i) q^{40} +(-9.59017 + 6.96767i) q^{41} +(0.309017 - 0.951057i) q^{42} +5.23607 q^{43} +(2.19098 - 2.48990i) q^{44} -1.38197 q^{45} +(2.88197 - 8.86978i) q^{46} +(-8.23607 + 5.98385i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.954915 + 2.93893i) q^{50} +(-6.16312 - 4.47777i) q^{51} +(1.00000 - 0.726543i) q^{52} +(2.76393 - 8.50651i) q^{53} -1.00000 q^{54} +(4.47214 - 1.00406i) q^{55} +1.00000 q^{56} +(1.26393 - 3.88998i) q^{57} +(-1.00000 + 0.726543i) q^{58} +(7.23607 + 5.25731i) q^{59} +(-0.427051 - 1.31433i) q^{60} +(-2.85410 - 8.78402i) q^{61} +(0.881966 + 0.640786i) q^{62} +(0.809017 - 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.70820 q^{65} +(3.23607 - 0.726543i) q^{66} -1.23607 q^{67} +(2.35410 - 7.24518i) q^{68} +(7.54508 - 5.48183i) q^{69} +(1.11803 + 0.812299i) q^{70} +(0.472136 + 1.45309i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(6.47214 + 4.70228i) q^{73} +(-6.97214 + 5.06555i) q^{74} +(-0.954915 + 2.93893i) q^{75} +4.09017 q^{76} +(-2.19098 + 2.48990i) q^{77} +1.23607 q^{78} +(-2.38197 + 7.33094i) q^{79} +(1.11803 - 0.812299i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.66312 - 11.2739i) q^{82} +(4.70820 + 14.4904i) q^{83} +(0.809017 + 0.587785i) q^{84} +(8.51722 - 6.18812i) q^{85} +(-1.61803 + 4.97980i) q^{86} -1.23607 q^{87} +(1.69098 + 2.85317i) q^{88} -5.14590 q^{89} +(0.427051 - 1.31433i) q^{90} +(-1.00000 + 0.726543i) q^{91} +(7.54508 + 5.48183i) q^{92} +(0.336881 + 1.03681i) q^{93} +(-3.14590 - 9.68208i) q^{94} +(4.57295 + 3.32244i) q^{95} +(0.809017 - 0.587785i) q^{96} +(3.47214 - 10.6861i) q^{97} -1.00000 q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9	$ 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9} + 10 q^{10} + q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} + q^{18} - 11 q^{19} + 5 q^{20} - 4 q^{21} - q^{22} - 6 q^{23} + q^{24} + 10 q^{25} - 4 q^{26} - q^{27} + q^{28} + 4 q^{29} + 17 q^{31} - 4 q^{32} - 9 q^{33} - 26 q^{34} - 5 q^{35} - q^{36} + 10 q^{37} - 14 q^{38} - 6 q^{39} - 16 q^{41} - q^{42} + 12 q^{43} + 11 q^{44} - 10 q^{45} + 16 q^{46} - 24 q^{47} - q^{48} - q^{49} + 15 q^{50} - 9 q^{51} + 4 q^{52} + 20 q^{53} - 4 q^{54} + 4 q^{56} + 14 q^{57} - 4 q^{58} + 20 q^{59} + 5 q^{60} + 2 q^{61} + 8 q^{62} + q^{63} - q^{64} - 20 q^{65} + 4 q^{66} + 4 q^{67} - 4 q^{68} + 19 q^{69} - 16 q^{71} + q^{72} + 8 q^{73} - 10 q^{74} - 15 q^{75} - 6 q^{76} - 11 q^{77} - 4 q^{78} - 14 q^{79} - q^{81} + q^{82} - 8 q^{83} + q^{84} + 5 q^{85} - 2 q^{86} + 4 q^{87} + 9 q^{88} - 34 q^{89} - 5 q^{90} - 4 q^{91} + 19 q^{92} + 17 q^{93} - 26 q^{94} + 25 q^{95} + q^{96} - 4 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9 + 10 * q^10 + q^11 + 4 * q^12 - 6 * q^13 - q^14 - q^16 - 4 * q^17 + q^18 - 11 * q^19 + 5 * q^20 - 4 * q^21 - q^22 - 6 * q^23 + q^24 + 10 * q^25 - 4 * q^26 - q^27 + q^28 + 4 * q^29 + 17 * q^31 - 4 * q^32 - 9 * q^33 - 26 * q^34 - 5 * q^35 - q^36 + 10 * q^37 - 14 * q^38 - 6 * q^39 - 16 * q^41 - q^42 + 12 * q^43 + 11 * q^44 - 10 * q^45 + 16 * q^46 - 24 * q^47 - q^48 - q^49 + 15 * q^50 - 9 * q^51 + 4 * q^52 + 20 * q^53 - 4 * q^54 + 4 * q^56 + 14 * q^57 - 4 * q^58 + 20 * q^59 + 5 * q^60 + 2 * q^61 + 8 * q^62 + q^63 - q^64 - 20 * q^65 + 4 * q^66 + 4 * q^67 - 4 * q^68 + 19 * q^69 - 16 * q^71 + q^72 + 8 * q^73 - 10 * q^74 - 15 * q^75 - 6 * q^76 - 11 * q^77 - 4 * q^78 - 14 * q^79 - q^81 + q^82 - 8 * q^83 + q^84 + 5 * q^85 - 2 * q^86 + 4 * q^87 + 9 * q^88 - 34 * q^89 - 5 * q^90 - 4 * q^91 + 19 * q^92 + 17 * q^93 - 26 * q^94 + 25 * q^95 + q^96 - 4 * q^97 - 4 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.427051	−	1.31433i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$5$	−0.427051	−	1.31433i	−0.190983	−	0.587785i	−1.00000			$\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.38197			0.437016
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$12$	1.00000			0.288675
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	−0.989950	−	0.141421i	$-0.954833\pi$
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	0.884011	+	0.467466i	$0.154833\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	1.11803	+	0.812299i	0.288675	+	0.209735i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.35410	+	7.24518i	0.570954	+	1.75721i	0.649562	+	0.760309i	$0.274952\pi$
$17$	2.35410	+	7.24518i	0.570954	+	1.75721i	−0.0786081	+	0.996906i	$0.525048\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	−3.30902	+	2.40414i	−0.759141	+	0.551548i	−0.898647	−	0.438673i	$-0.855449\pi$
$19$	−3.30902	+	2.40414i	−0.759141	+	0.551548i	0.139506	+	0.990221i	$0.455449\pi$
$20$	−0.427051	+	1.31433i	−0.0954915	+	0.293893i
$21$	−1.00000			−0.218218
$22$	−3.04508	−	1.31433i	−0.649214	−	0.280216i
$23$	−9.32624			−1.94466			−0.972328	−	0.233622i	$-0.924942\pi$
$23$	−9.32624			−1.94466			−0.972328	+	0.233622i	$0.924942\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	2.50000	−	1.81636i	0.500000	−	0.363271i
$26$	−1.00000	−	0.726543i	−0.196116	−	0.142487i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	1.00000	+	0.726543i	0.185695	+	0.134916i	0.676749	−	0.736214i	$-0.263388\pi$
$29$	1.00000	+	0.726543i	0.185695	+	0.134916i	−0.491054	+	0.871129i	$0.663388\pi$
$30$	−1.11803	+	0.812299i	−0.204124	+	0.148305i
$31$	0.336881	−	1.03681i	0.0605056	−	0.186217i	−0.916235	−	0.400641i	$-0.868787\pi$
$31$	0.336881	−	1.03681i	0.0605056	−	0.186217i	0.976741	+	0.214424i	$0.0687874\pi$
$32$	−1.00000			−0.176777
$33$	−1.69098	−	2.85317i	−0.294362	−	0.496673i
$34$	−7.61803			−1.30648
$35$	0.427051	−	1.31433i	0.0721848	−	0.222162i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	6.97214	+	5.06555i	1.14621	+	0.832772i	0.987973	−	0.154629i	$-0.0494182\pi$
$37$	6.97214	+	5.06555i	1.14621	+	0.832772i	0.158239	+	0.987401i	$0.449418\pi$
$38$	−1.26393	−	3.88998i	−0.205037	−	0.631039i
$39$	−0.381966	−	1.17557i	−0.0611635	−	0.188242i
$40$	−1.11803	−	0.812299i	−0.176777	−	0.128436i
$41$	−9.59017	+	6.96767i	−1.49773	+	1.08817i	−0.526460	+	0.850200i	$0.676481\pi$
$41$	−9.59017	+	6.96767i	−1.49773	+	1.08817i	−0.971273	+	0.237966i	$0.923519\pi$
$42$	0.309017	−	0.951057i	0.0476824	−	0.146751i
$43$	5.23607			0.798493			0.399246	−	0.916844i	$-0.369272\pi$
$43$	5.23607			0.798493			0.399246	+	0.916844i	$0.369272\pi$
$44$	2.19098	−	2.48990i	0.330303	−	0.375366i
$45$	−1.38197			−0.206011
$46$	2.88197	−	8.86978i	0.424923	−	1.30778i
$47$	−8.23607	+	5.98385i	−1.20135	+	0.872835i	−0.994417	−	0.105520i	$-0.966349\pi$
$47$	−8.23607	+	5.98385i	−1.20135	+	0.872835i	−0.206937	+	0.978354i	$0.566349\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.954915	+	2.93893i	0.135045	+	0.415627i
$51$	−6.16312	−	4.47777i	−0.863009	−	0.627013i
$52$	1.00000	−	0.726543i	0.138675	−	0.100753i
$53$	2.76393	−	8.50651i	0.379655	−	1.16846i	−0.560629	−	0.828067i	$-0.689440\pi$
$53$	2.76393	−	8.50651i	0.379655	−	1.16846i	0.940284	−	0.340391i	$-0.110560\pi$
$54$	−1.00000			−0.136083
$55$	4.47214	−	1.00406i	0.603023	−	0.135387i
$56$	1.00000			0.133631
$57$	1.26393	−	3.88998i	0.167412	−	0.515241i
$58$	−1.00000	+	0.726543i	−0.131306	+	0.0953997i
$59$	7.23607	+	5.25731i	0.942056	+	0.684444i	0.948915	−	0.315533i	$-0.102183\pi$
$59$	7.23607	+	5.25731i	0.942056	+	0.684444i	−0.00685884	+	0.999976i	$0.502183\pi$
$60$	−0.427051	−	1.31433i	−0.0551320	−	0.169679i
$61$	−2.85410	−	8.78402i	−0.365430	−	1.12468i	−0.949711	−	0.313127i	$-0.898623\pi$
$61$	−2.85410	−	8.78402i	−0.365430	−	1.12468i	0.584281	−	0.811552i	$-0.301377\pi$
$62$	0.881966	+	0.640786i	0.112010	+	0.0813799i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.70820			0.211877
$66$	3.23607	−	0.726543i	0.398332	−	0.0894312i
$67$	−1.23607			−0.151010			−0.0755049	−	0.997145i	$-0.524057\pi$
$67$	−1.23607			−0.151010			−0.0755049	+	0.997145i	$0.524057\pi$
$68$	2.35410	−	7.24518i	0.285477	−	0.878607i
$69$	7.54508	−	5.48183i	0.908321	−	0.659934i
$70$	1.11803	+	0.812299i	0.133631	+	0.0970883i
$71$	0.472136	+	1.45309i	0.0560322	+	0.172449i	0.975156	−	0.221520i	$-0.0711017\pi$
$71$	0.472136	+	1.45309i	0.0560322	+	0.172449i	−0.919124	+	0.393969i	$0.871102\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	6.47214	+	4.70228i	0.757506	+	0.550360i	0.898144	−	0.439701i	$-0.144915\pi$
$73$	6.47214	+	4.70228i	0.757506	+	0.550360i	−0.140638	+	0.990061i	$0.544915\pi$
$74$	−6.97214	+	5.06555i	−0.810494	+	0.588859i
$75$	−0.954915	+	2.93893i	−0.110264	+	0.339358i
$76$	4.09017			0.469175
$77$	−2.19098	+	2.48990i	−0.249686	+	0.283750i
$78$	1.23607			0.139957
$79$	−2.38197	+	7.33094i	−0.267992	+	0.824795i	0.722997	+	0.690851i	$0.242764\pi$
$79$	−2.38197	+	7.33094i	−0.267992	+	0.824795i	−0.990989	+	0.133944i	$0.957236\pi$
$80$	1.11803	−	0.812299i	0.125000	−	0.0908178i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.66312	−	11.2739i	−0.404524	−	1.24500i
$83$	4.70820	+	14.4904i	0.516793	+	1.59052i	0.779997	+	0.625784i	$0.215221\pi$
$83$	4.70820	+	14.4904i	0.516793	+	1.59052i	−0.263204	+	0.964740i	$0.584779\pi$
$84$	0.809017	+	0.587785i	0.0882710	+	0.0641326i
$85$	8.51722	−	6.18812i	0.923822	−	0.671196i
$86$	−1.61803	+	4.97980i	−0.174477	+	0.536985i
$87$	−1.23607			−0.132520
$88$	1.69098	+	2.85317i	0.180259	+	0.304149i
$89$	−5.14590			−0.545464			−0.272732	−	0.962090i	$-0.587927\pi$
$89$	−5.14590			−0.545464			−0.272732	+	0.962090i	$0.587927\pi$
$90$	0.427051	−	1.31433i	0.0450151	−	0.138542i
$91$	−1.00000	+	0.726543i	−0.104828	+	0.0761624i
$92$	7.54508	+	5.48183i	0.786629	+	0.571520i
$93$	0.336881	+	1.03681i	0.0349329	+	0.107513i
$94$	−3.14590	−	9.68208i	−0.324475	−	0.998630i
$95$	4.57295	+	3.32244i	0.469175	+	0.340875i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	3.47214	−	10.6861i	0.352542	−	1.08501i	−0.604879	−	0.796317i	$-0.706779\pi$
$97$	3.47214	−	10.6861i	0.352542	−	1.08501i	0.957421	−	0.288695i	$-0.0932215\pi$
$98$	−1.00000			−0.101015
$99$	3.04508	+	1.31433i	0.306043	+	0.132095i
$100$	−3.09017			−0.309017
$101$	3.66312	−	11.2739i	0.364494	−	1.12180i	−0.585803	−	0.810453i	$-0.699221\pi$
$101$	3.66312	−	11.2739i	0.364494	−	1.12180i	0.950297	−	0.311344i	$-0.100779\pi$
$102$	6.16312	−	4.47777i	0.610240	−	0.443365i
$103$	−4.69098	−	3.40820i	−0.462216	−	0.335820i	0.332184	−	0.943215i	$-0.392215\pi$
$103$	−4.69098	−	3.40820i	−0.462216	−	0.335820i	−0.794400	+	0.607395i	$0.792215\pi$
$104$	0.381966	+	1.17557i	0.0374548	+	0.115274i
$105$	0.427051	+	1.31433i	0.0416759	+	0.128265i
$106$	7.23607	+	5.25731i	0.702829	+	0.510635i
$107$	15.3992	−	11.1882i	1.48870	−	1.08160i	0.514073	−	0.857746i	$-0.328136\pi$
$107$	15.3992	−	11.1882i	1.48870	−	1.08160i	0.974623	−	0.223854i	$-0.0718639\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	4.61803			0.442327			0.221164	−	0.975237i	$-0.429014\pi$
$109$	4.61803			0.442327			0.221164	+	0.975237i	$0.429014\pi$
$110$	−0.427051	+	4.56352i	−0.0407177	+	0.435115i
$111$	−8.61803			−0.817988
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	5.23607	−	3.80423i	0.492568	−	0.357871i	−0.313603	−	0.949554i	$-0.601536\pi$
$113$	5.23607	−	3.80423i	0.492568	−	0.357871i	0.806171	+	0.591683i	$0.201536\pi$
$114$	3.30902	+	2.40414i	0.309918	+	0.225168i
$115$	3.98278	+	12.2577i	0.371396	+	1.14304i
$116$	−0.381966	−	1.17557i	−0.0354647	−	0.109149i
$117$	1.00000	+	0.726543i	0.0924500	+	0.0671689i
$118$	−7.23607	+	5.25731i	−0.666134	+	0.483975i
$119$	−2.35410	+	7.24518i	−0.215800	+	0.664165i
$120$	1.38197			0.126156
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	9.23607			0.836194
$123$	3.66312	−	11.2739i	0.330292	−	1.01654i
$124$	−0.881966	+	0.640786i	−0.0792029	+	0.0575443i
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$	0.309017	+	0.951057i	0.0275294	+	0.0847268i
$127$	3.47214	+	10.6861i	0.308102	+	0.948241i	0.978501	+	0.206240i	$0.0661229\pi$
$127$	3.47214	+	10.6861i	0.308102	+	0.948241i	−0.670399	+	0.742001i	$0.733877\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−4.23607	+	3.07768i	−0.372965	+	0.270975i
$130$	−0.527864	+	1.62460i	−0.0462967	+	0.142487i
$131$	15.2361			1.33118			0.665591	−	0.746317i	$-0.268180\pi$
$131$	15.2361			1.33118			0.665591	+	0.746317i	$0.268180\pi$
$132$	−0.309017	+	3.30220i	−0.0268965	+	0.287419i
$133$	−4.09017			−0.354663
$134$	0.381966	−	1.17557i	0.0329968	−	0.101554i
$135$	1.11803	−	0.812299i	0.0962250	−	0.0699116i
$136$	6.16312	+	4.47777i	0.528483	+	0.383965i
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	0.999421	−	0.0340275i	$-0.0108334\pi$
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	−0.828549	+	0.559916i	$0.810833\pi$
$138$	2.88197	+	8.86978i	0.245329	+	0.755046i
$139$	−13.6353	−	9.90659i	−1.15653	−	0.840266i	−0.167192	−	0.985924i	$-0.553470\pi$
$139$	−13.6353	−	9.90659i	−1.15653	−	0.840266i	−0.989335	+	0.145658i	$0.953470\pi$
$140$	−1.11803	+	0.812299i	−0.0944911	+	0.0686518i
$141$	3.14590	−	9.68208i	0.264932	−	0.815378i
$142$	−1.52786			−0.128216
$143$	−3.76393	−	1.62460i	−0.314756	−	0.135856i
$144$	1.00000			0.0833333
$145$	0.527864	−	1.62460i	0.0438367	−	0.134916i
$146$	−6.47214	+	4.70228i	−0.535638	+	0.389164i
$147$	−0.809017	−	0.587785i	−0.0667266	−	0.0484797i
$148$	−2.66312	−	8.19624i	−0.218907	−	0.673727i
$149$	−6.00000	−	18.4661i	−0.491539	−	1.51280i	−0.822282	−	0.569081i	$-0.807299\pi$
$149$	−6.00000	−	18.4661i	−0.491539	−	1.51280i	0.330742	−	0.943721i	$-0.392701\pi$
$150$	−2.50000	−	1.81636i	−0.204124	−	0.148305i
$151$	7.23607	−	5.25731i	0.588863	−	0.427834i	−0.253046	−	0.967454i	$-0.581432\pi$
$151$	7.23607	−	5.25731i	0.588863	−	0.427834i	0.841908	+	0.539620i	$0.181432\pi$
$152$	−1.26393	+	3.88998i	−0.102518	+	0.315519i
$153$	7.61803			0.615882
$154$	−1.69098	−	2.85317i	−0.136263	−	0.229915i
$155$	−1.50658			−0.121011
$156$	−0.381966	+	1.17557i	−0.0305818	+	0.0941210i
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	−0.701028	−	0.713134i	$-0.747275\pi$
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	0.461601	+	0.887087i	$0.347275\pi$
$158$	−6.23607	−	4.53077i	−0.496115	−	0.360449i
$159$	2.76393	+	8.50651i	0.219194	+	0.674610i
$160$	0.427051	+	1.31433i	0.0337613	+	0.103907i
$161$	−7.54508	−	5.48183i	−0.594636	−	0.432028i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	6.32624	−	19.4702i	0.495509	−	1.52502i	−0.320652	−	0.947197i	$-0.603902\pi$
$163$	6.32624	−	19.4702i	0.495509	−	1.52502i	0.816162	−	0.577824i	$-0.196098\pi$
$164$	11.8541			0.925650
$165$	−3.02786	+	3.44095i	−0.235719	+	0.267878i
$166$	−15.2361			−1.18255
$167$	2.32624	−	7.15942i	0.180010	−	0.554013i	−0.819817	−	0.572625i	$-0.805925\pi$
$167$	2.32624	−	7.15942i	0.180010	−	0.554013i	0.999827	+	0.0186126i	$0.00592492\pi$
$168$	−0.809017	+	0.587785i	−0.0624170	+	0.0453486i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	3.25329	+	10.0126i	0.249516	+	0.767931i
$171$	1.26393	+	3.88998i	0.0966553	+	0.297474i
$172$	−4.23607	−	3.07768i	−0.322997	−	0.234671i
$173$	−5.54508	+	4.02874i	−0.421585	+	0.306299i	−0.778275	−	0.627923i	$-0.783905\pi$
$173$	−5.54508	+	4.02874i	−0.421585	+	0.306299i	0.356690	+	0.934223i	$0.383905\pi$
$174$	0.381966	−	1.17557i	0.0289568	−	0.0891198i
$175$	3.09017			0.233595
$176$	−3.23607	+	0.726543i	−0.243928	+	0.0547652i
$177$	−8.94427			−0.672293
$178$	1.59017	−	4.89404i	0.119188	−	0.366824i
$179$	−17.4443	+	12.6740i	−1.30385	+	0.947300i	−0.999985	−	0.00541681i	$-0.998276\pi$
$179$	−17.4443	+	12.6740i	−1.30385	+	0.947300i	−0.303861	+	0.952716i	$0.598276\pi$
$180$	1.11803	+	0.812299i	0.0833333	+	0.0605452i
$181$	2.47214	+	7.60845i	0.183752	+	0.565532i	0.999925	−	0.0122769i	$-0.00390796\pi$
$181$	2.47214	+	7.60845i	0.183752	+	0.565532i	−0.816172	+	0.577809i	$0.803908\pi$
$182$	−0.381966	−	1.17557i	−0.0283132	−	0.0871391i
$183$	7.47214	+	5.42882i	0.552356	+	0.401310i
$184$	−7.54508	+	5.48183i	−0.556231	+	0.404126i
$185$	3.68034	−	11.3269i	0.270584	−	0.832772i
$186$	−1.09017			−0.0799351
$187$	−24.6525	+	5.53483i	−1.80277	+	0.404747i
$188$	10.1803			0.742478
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$	−4.57295	+	3.32244i	−0.331757	+	0.241035i
$191$	−8.97214	−	6.51864i	−0.649201	−	0.471672i	0.213798	−	0.976878i	$-0.431417\pi$
$191$	−8.97214	−	6.51864i	−0.649201	−	0.471672i	−0.862999	+	0.505206i	$0.831417\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	−0.572949	−	1.76336i	−0.0412418	−	0.126929i	0.928316	−	0.371793i	$-0.121257\pi$
$193$	−0.572949	−	1.76336i	−0.0412418	−	0.126929i	−0.969558	+	0.244864i	$0.921257\pi$
$194$	9.09017	+	6.60440i	0.652636	+	0.474168i
$195$	−1.38197	+	1.00406i	−0.0989646	+	0.0719020i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	18.7639			1.33687			0.668437	−	0.743768i	$-0.266963\pi$
$197$	18.7639			1.33687			0.668437	+	0.743768i	$0.266963\pi$
$198$	−2.19098	+	2.48990i	−0.155706	+	0.176949i
$199$	−8.27051			−0.586281			−0.293140	−	0.956069i	$-0.594700\pi$
$199$	−8.27051			−0.586281			−0.293140	+	0.956069i	$0.594700\pi$
$200$	0.954915	−	2.93893i	0.0675227	−	0.207813i
$201$	1.00000	−	0.726543i	0.0705346	−	0.0512464i
$202$	9.59017	+	6.96767i	0.674762	+	0.490243i
$203$	0.381966	+	1.17557i	0.0268088	+	0.0825089i
$204$	2.35410	+	7.24518i	0.164820	+	0.507264i
$205$	13.2533	+	9.62908i	0.925650	+	0.672524i
$206$	4.69098	−	3.40820i	0.326836	−	0.237460i
$207$	−2.88197	+	8.86978i	−0.200310	+	0.616492i
$208$	−1.23607			−0.0857059
$209$	−6.91641	−	11.6699i	−0.478418	−	0.807227i
$210$	−1.38197			−0.0953647
$211$	0.236068	−	0.726543i	0.0162516	−	0.0500173i	−0.942602	−	0.333919i	$-0.891629\pi$
$211$	0.236068	−	0.726543i	0.0162516	−	0.0500173i	0.958853	+	0.283902i	$0.0916289\pi$
$212$	−7.23607	+	5.25731i	−0.496975	+	0.361074i
$213$	−1.23607	−	0.898056i	−0.0846940	−	0.0615338i
$214$	5.88197	+	18.1028i	0.402083	+	1.23748i
$215$	−2.23607	−	6.88191i	−0.152499	−	0.469342i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	0.881966	−	0.640786i	0.0598718	−	0.0434994i
$218$	−1.42705	+	4.39201i	−0.0966521	+	0.297465i
$219$	−8.00000			−0.540590
$220$	−4.20820	−	1.81636i	−0.283717	−	0.122459i
$221$	−9.41641			−0.633416
$222$	2.66312	−	8.19624i	0.178737	−	0.550095i
$223$	−2.54508	+	1.84911i	−0.170431	+	0.123826i	−0.669731	−	0.742604i	$-0.733591\pi$
$223$	−2.54508	+	1.84911i	−0.170431	+	0.123826i	0.499300	+	0.866429i	$0.333591\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	−0.954915	−	2.93893i	−0.0636610	−	0.195928i
$226$	2.00000	+	6.15537i	0.133038	+	0.409449i
$227$	−10.9443	−	7.95148i	−0.726397	−	0.527758i	0.162025	−	0.986787i	$-0.448198\pi$
$227$	−10.9443	−	7.95148i	−0.726397	−	0.527758i	−0.888422	+	0.459029i	$0.848198\pi$
$228$	−3.30902	+	2.40414i	−0.219145	+	0.159218i
$229$	−8.90983	+	27.4216i	−0.588778	+	1.81207i	−0.00524111	+	0.999986i	$0.501668\pi$
$229$	−8.90983	+	27.4216i	−0.588778	+	1.81207i	−0.583537	+	0.812087i	$0.698332\pi$
$230$	−12.8885			−0.849845
$231$	0.309017	−	3.30220i	0.0203318	−	0.217269i
$232$	1.23607			0.0811518
$233$	6.14590	−	18.9151i	0.402631	−	1.23917i	−0.520226	−	0.854029i	$-0.674152\pi$
$233$	6.14590	−	18.9151i	0.402631	−	1.23917i	0.922857	−	0.385143i	$-0.125848\pi$
$234$	−1.00000	+	0.726543i	−0.0653720	+	0.0474956i
$235$	11.3820	+	8.26948i	0.742478	+	0.539442i
$236$	−2.76393	−	8.50651i	−0.179917	−	0.553727i
$237$	−2.38197	−	7.33094i	−0.154725	−	0.476196i
$238$	−6.16312	−	4.47777i	−0.399496	−	0.290251i
$239$	−9.39919	+	6.82891i	−0.607983	+	0.441725i	−0.848703	−	0.528869i	$-0.822616\pi$
$239$	−9.39919	+	6.82891i	−0.607983	+	0.441725i	0.240721	+	0.970594i	$0.422616\pi$
$240$	−0.427051	+	1.31433i	−0.0275660	+	0.0848395i
$241$	−6.18034			−0.398111			−0.199055	−	0.979988i	$-0.563787\pi$
$241$	−6.18034			−0.398111			−0.199055	+	0.979988i	$0.563787\pi$
$242$	5.28115	−	9.64932i	0.339485	−	0.620282i
$243$	1.00000			0.0641500
$244$	−2.85410	+	8.78402i	−0.182715	+	0.562339i
$245$	1.11803	−	0.812299i	0.0714286	−	0.0518959i
$246$	9.59017	+	6.96767i	0.611447	+	0.444242i
$247$	−1.56231	−	4.80828i	−0.0994071	−	0.305944i
$248$	−0.336881	−	1.03681i	−0.0213920	−	0.0658377i
$249$	−12.3262	−	8.95554i	−0.781144	−	0.567534i
$250$	9.04508	−	6.57164i	0.572061	−	0.415627i
$251$	−2.76393	+	8.50651i	−0.174458	+	0.536926i	−0.999608	−	0.0279870i	$-0.991090\pi$
$251$	−2.76393	+	8.50651i	−0.174458	+	0.536926i	0.825150	+	0.564913i	$0.191090\pi$
$252$	−1.00000			−0.0629941
$253$	2.88197	−	30.7971i	0.181188	−	1.93620i
$254$	−11.2361			−0.705014
$255$	−3.25329	+	10.0126i	−0.203729	+	0.627013i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	7.39919	+	5.37582i	0.461549	+	0.335335i	0.794138	−	0.607737i	$-0.207922\pi$
$257$	7.39919	+	5.37582i	0.461549	+	0.335335i	−0.332590	+	0.943072i	$0.607922\pi$
$258$	−1.61803	−	4.97980i	−0.100734	−	0.310029i
$259$	2.66312	+	8.19624i	0.165478	+	0.509289i
$260$	−1.38197	−	1.00406i	−0.0857059	−	0.0622690i
$261$	1.00000	−	0.726543i	0.0618984	−	0.0449719i
$262$	−4.70820	+	14.4904i	−0.290874	+	0.895218i
$263$	7.03444			0.433762			0.216881	−	0.976198i	$-0.430412\pi$
$263$	7.03444			0.433762			0.216881	+	0.976198i	$0.430412\pi$
$264$	−3.04508	−	1.31433i	−0.187412	−	0.0808913i
$265$	−12.3607			−0.759311
$266$	1.26393	−	3.88998i	0.0774966	−	0.238510i
$267$	4.16312	−	3.02468i	0.254779	−	0.185108i
$268$	1.00000	+	0.726543i	0.0610847	+	0.0443806i
$269$	1.85410	+	5.70634i	0.113047	+	0.347922i	0.991535	−	0.129843i	$-0.0414473\pi$
$269$	1.85410	+	5.70634i	0.113047	+	0.347922i	−0.878488	+	0.477764i	$0.841447\pi$
$270$	0.427051	+	1.31433i	0.0259895	+	0.0799874i
$271$	−4.11803	−	2.99193i	−0.250153	−	0.181747i	0.455642	−	0.890163i	$-0.349410\pi$
$271$	−4.11803	−	2.99193i	−0.250153	−	0.181747i	−0.705795	+	0.708417i	$0.749410\pi$
$272$	−6.16312	+	4.47777i	−0.373694	+	0.271505i
$273$	0.381966	−	1.17557i	0.0231176	−	0.0711488i
$274$	−6.47214			−0.390996
$275$	5.22542	+	8.81678i	0.315105	+	0.531672i
$276$	−9.32624			−0.561374
$277$	0.972136	−	2.99193i	0.0584100	−	0.179767i	−0.917595	−	0.397518i	$-0.869872\pi$
$277$	0.972136	−	2.99193i	0.0584100	−	0.179767i	0.976005	+	0.217750i	$0.0698718\pi$
$278$	13.6353	−	9.90659i	0.817788	−	0.594158i
$279$	−0.881966	−	0.640786i	−0.0528019	−	0.0383628i
$280$	−0.427051	−	1.31433i	−0.0255212	−	0.0785461i
$281$	4.52786	+	13.9353i	0.270110	+	0.831312i	0.990472	+	0.137714i	$0.0439756\pi$
$281$	4.52786	+	13.9353i	0.270110	+	0.831312i	−0.720362	+	0.693598i	$0.756024\pi$
$282$	8.23607	+	5.98385i	0.490451	+	0.356333i
$283$	−0.881966	+	0.640786i	−0.0524274	+	0.0380908i	−0.613690	−	0.789547i	$-0.710316\pi$
$283$	−0.881966	+	0.640786i	−0.0524274	+	0.0380908i	0.561263	+	0.827638i	$0.310316\pi$
$284$	0.472136	−	1.45309i	0.0280161	−	0.0862247i
$285$	−5.65248			−0.334824
$286$	2.70820	−	3.07768i	0.160139	−	0.181987i
$287$	−11.8541			−0.699726
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−33.1976	+	24.1194i	−1.95280	+	1.41879i
$290$	1.38197	+	1.00406i	0.0811518	+	0.0589603i
$291$	3.47214	+	10.6861i	0.203540	+	0.626432i
$292$	−2.47214	−	7.60845i	−0.144671	−	0.445251i
$293$	−7.11803	−	5.17155i	−0.415840	−	0.302125i	0.360122	−	0.932905i	$-0.382735\pi$
$293$	−7.11803	−	5.17155i	−0.415840	−	0.302125i	−0.775962	+	0.630780i	$0.782735\pi$
$294$	0.809017	−	0.587785i	0.0471828	−	0.0342803i
$295$	3.81966	−	11.7557i	0.222389	−	0.684444i
$296$	8.61803			0.500913
$297$	−3.23607	+	0.726543i	−0.187776	+	0.0421583i
$298$	19.4164			1.12476
$299$	3.56231	−	10.9637i	0.206013	−	0.634044i
$300$	2.50000	−	1.81636i	0.144338	−	0.104867i
$301$	4.23607	+	3.07768i	0.244163	+	0.177395i
$302$	2.76393	+	8.50651i	0.159046	+	0.489495i
$303$	3.66312	+	11.2739i	0.210441	+	0.647670i
$304$	−3.30902	−	2.40414i	−0.189785	−	0.137887i
$305$	−10.3262	+	7.50245i	−0.591279	+	0.429589i
$306$	−2.35410	+	7.24518i	−0.134575	+	0.414179i
$307$	15.8541			0.904841			0.452421	−	0.891805i	$-0.350561\pi$
$307$	15.8541			0.904841			0.452421	+	0.891805i	$0.350561\pi$
$308$	3.23607	−	0.726543i	0.184392	−	0.0413986i
$309$	5.79837			0.329858
$310$	0.465558	−	1.43284i	0.0264419	−	0.0813799i
$311$	10.9443	−	7.95148i	0.620593	−	0.450887i	−0.232536	−	0.972588i	$-0.574702\pi$
$311$	10.9443	−	7.95148i	0.620593	−	0.450887i	0.853128	+	0.521701i	$0.174702\pi$
$312$	−1.00000	−	0.726543i	−0.0566139	−	0.0411324i
$313$	4.41641	+	13.5923i	0.249630	+	0.768283i	0.994840	+	0.101453i	$0.0323491\pi$
$313$	4.41641	+	13.5923i	0.249630	+	0.768283i	−0.745210	+	0.666830i	$0.767651\pi$
$314$	−1.14590	−	3.52671i	−0.0646668	−	0.199024i
$315$	−1.11803	−	0.812299i	−0.0629941	−	0.0457679i
$316$	6.23607	−	4.53077i	0.350806	−	0.254876i
$317$	3.70820	−	11.4127i	0.208273	−	0.641000i	−0.791290	−	0.611442i	$-0.790590\pi$
$317$	3.70820	−	11.4127i	0.208273	−	0.641000i	0.999563	−	0.0295583i	$-0.00941007\pi$
$318$	−8.94427			−0.501570
$319$	−2.70820	+	3.07768i	−0.151630	+	0.172317i
$320$	−1.38197			−0.0772542
$321$	−5.88197	+	18.1028i	−0.328299	+	1.01040i
$322$	7.54508	−	5.48183i	0.420471	−	0.305490i
$323$	−25.2082	−	18.3148i	−1.40262	−	1.01906i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	1.18034	+	3.63271i	0.0654735	+	0.201507i
$326$	16.5623	+	12.0332i	0.917301	+	0.666458i
$327$	−3.73607	+	2.71441i	−0.206605	+	0.150107i
$328$	−3.66312	+	11.2739i	−0.202262	+	0.622498i
$329$	−10.1803			−0.561260
$330$	−2.33688	−	3.94298i	−0.128641	−	0.217054i
$331$	−0.180340			−0.00991238			−0.00495619	−	0.999988i	$-0.501578\pi$
$331$	−0.180340			−0.00991238			−0.00495619	+	0.999988i	$0.501578\pi$
$332$	4.70820	−	14.4904i	0.258396	−	0.795262i
$333$	6.97214	−	5.06555i	0.382071	−	0.277591i
$334$	6.09017	+	4.42477i	0.333239	+	0.242113i
$335$	0.527864	+	1.62460i	0.0288403	+	0.0887613i
$336$	−0.309017	−	0.951057i	−0.0168583	−	0.0518844i
$337$	6.73607	+	4.89404i	0.366937	+	0.266595i	0.755940	−	0.654641i	$-0.227180\pi$
$337$	6.73607	+	4.89404i	0.366937	+	0.266595i	−0.389003	+	0.921237i	$0.627180\pi$
$338$	−9.28115	+	6.74315i	−0.504828	+	0.366779i
$339$	−2.00000	+	6.15537i	−0.108625	+	0.334314i
$340$	−10.5279			−0.570954
$341$	3.31966	+	1.43284i	0.179770	+	0.0775927i
$342$	−4.09017			−0.221171
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	4.23607	−	3.07768i	0.228393	−	0.165938i
$345$	−10.4271	−	7.57570i	−0.561374	−	0.407862i
$346$	−2.11803	−	6.51864i	−0.113866	−	0.350444i
$347$	3.33688	+	10.2699i	0.179133	+	0.551315i	0.999798	−	0.0200946i	$-0.00639673\pi$
$347$	3.33688	+	10.2699i	0.179133	+	0.551315i	−0.820665	+	0.571410i	$0.806397\pi$
$348$	1.00000	+	0.726543i	0.0536056	+	0.0389468i
$349$	7.70820	−	5.60034i	0.412611	−	0.299779i	−0.362047	−	0.932160i	$-0.617922\pi$
$349$	7.70820	−	5.60034i	0.412611	−	0.299779i	0.774658	+	0.632381i	$0.217922\pi$
$350$	−0.954915	+	2.93893i	−0.0510424	+	0.157092i
$351$	−1.23607			−0.0659764
$352$	0.309017	−	3.30220i	0.0164707	−	0.176008i
$353$	22.9443			1.22120			0.610600	−	0.791939i	$-0.290928\pi$
$353$	22.9443			1.22120			0.610600	+	0.791939i	$0.290928\pi$
$354$	2.76393	−	8.50651i	0.146901	−	0.452116i
$355$	1.70820	−	1.24108i	0.0906621	−	0.0658698i
$356$	4.16312	+	3.02468i	0.220645	+	0.160308i
$357$	−2.35410	−	7.24518i	−0.124592	−	0.383456i
$358$	−6.66312	−	20.5070i	−0.352157	−	1.08383i
$359$	24.4443	+	17.7598i	1.29012	+	0.937327i	0.999808	−	0.0196056i	$-0.00624107\pi$
$359$	24.4443	+	17.7598i	1.29012	+	0.937327i	0.290312	+	0.956932i	$0.406241\pi$
$360$	−1.11803	+	0.812299i	−0.0589256	+	0.0428119i
$361$	−0.701626	+	2.15938i	−0.0369277	+	0.113652i
$362$	−8.00000			−0.420471
$363$	9.94427	−	4.70228i	0.521939	−	0.246806i
$364$	1.23607			0.0647876
$365$	3.41641	−	10.5146i	0.178823	−	0.550360i
$366$	−7.47214	+	5.42882i	−0.390575	+	0.283769i
$367$	15.8262	+	11.4984i	0.826123	+	0.600213i	0.918460	−	0.395514i	$-0.129434\pi$
$367$	15.8262	+	11.4984i	0.826123	+	0.600213i	−0.0923369	+	0.995728i	$0.529434\pi$
$368$	−2.88197	−	8.86978i	−0.150233	−	0.462369i
$369$	3.66312	+	11.2739i	0.190694	+	0.586897i
$370$	9.63525	+	7.00042i	0.500913	+	0.363935i
$371$	7.23607	−	5.25731i	0.375678	−	0.272946i
$372$	0.336881	−	1.03681i	0.0174665	−	0.0537563i
$373$	26.5066			1.37246			0.686229	−	0.727385i	$-0.259265\pi$
$373$	26.5066			1.37246			0.686229	+	0.727385i	$0.259265\pi$
$374$	2.35410	−	25.1563i	0.121728	−	1.30080i
$375$	11.1803			0.577350
$376$	−3.14590	+	9.68208i	−0.162237	+	0.499315i
$377$	−1.23607	+	0.898056i	−0.0636607	+	0.0462522i
$378$	−0.809017	−	0.587785i	−0.0416113	−	0.0302324i
$379$	6.70820	+	20.6457i	0.344577	+	1.06050i	0.961810	+	0.273719i	$0.0882538\pi$
$379$	6.70820	+	20.6457i	0.344577	+	1.06050i	−0.617232	+	0.786781i	$0.711746\pi$
$380$	−1.74671	−	5.37582i	−0.0896044	−	0.275774i
$381$	−9.09017	−	6.60440i	−0.465704	−	0.338353i
$382$	8.97214	−	6.51864i	0.459054	−	0.333523i
$383$	1.85410	−	5.70634i	0.0947402	−	0.291580i	−0.892446	−	0.451155i	$-0.851012\pi$
$383$	1.85410	−	5.70634i	0.0947402	−	0.291580i	0.987186	+	0.159575i	$0.0510122\pi$
$384$	−1.00000			−0.0510310
$385$	4.20820	+	1.81636i	0.214470	+	0.0925701i
$386$	1.85410			0.0943713
$387$	1.61803	−	4.97980i	0.0822493	−	0.253137i
$388$	−9.09017	+	6.60440i	−0.461483	+	0.335287i
$389$	−21.1803	−	15.3884i	−1.07389	−	0.780224i	−0.0972792	−	0.995257i	$-0.531014\pi$
$389$	−21.1803	−	15.3884i	−1.07389	−	0.780224i	−0.976607	+	0.215033i	$0.931014\pi$
$390$	−0.527864	−	1.62460i	−0.0267294	−	0.0822647i
$391$	−21.9549	−	67.5703i	−1.11031	−	3.41718i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$	−12.3262	+	8.95554i	−0.621776	+	0.451747i
$394$	−5.79837	+	17.8456i	−0.292118	+	0.899046i
$395$	10.6525			0.535984
$396$	−1.69098	−	2.85317i	−0.0849751	−	0.143377i
$397$	16.0000			0.803017			0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000			0.803017			0.401508	+	0.915855i	$0.368486\pi$
$398$	2.55573	−	7.86572i	0.128107	−	0.394273i
$399$	3.30902	−	2.40414i	0.165658	−	0.120358i
$400$	2.50000	+	1.81636i	0.125000	+	0.0908178i
$401$	−3.61803	−	11.1352i	−0.180676	−	0.556064i	0.819171	−	0.573549i	$-0.194434\pi$
$401$	−3.61803	−	11.1352i	−0.180676	−	0.556064i	−0.999847	+	0.0174857i	$0.994434\pi$
$402$	0.381966	+	1.17557i	0.0190507	+	0.0586321i
$403$	1.09017	+	0.792055i	0.0543052	+	0.0394551i
$404$	−9.59017	+	6.96767i	−0.477129	+	0.346654i
$405$	−0.427051	+	1.31433i	−0.0212203	+	0.0653095i
$406$	−1.23607			−0.0613450
$407$	−18.8820	+	21.4580i	−0.935944	+	1.06363i
$408$	−7.61803			−0.377149
$409$	−11.0344	+	33.9605i	−0.545618	+	1.67924i	0.173898	+	0.984764i	$0.444364\pi$
$409$	−11.0344	+	33.9605i	−0.545618	+	1.67924i	−0.719516	+	0.694476i	$0.755636\pi$
$410$	−13.2533	+	9.62908i	−0.654533	+	0.475546i
$411$	−5.23607	−	3.80423i	−0.258276	−	0.187649i
$412$	1.79180	+	5.51458i	0.0882755	+	0.271684i
$413$	2.76393	+	8.50651i	0.136004	+	0.418578i
$414$	−7.54508	−	5.48183i	−0.370821	−	0.269417i
$415$	17.0344	−	12.3762i	0.836188	−	0.607526i
$416$	0.381966	−	1.17557i	0.0187274	−	0.0576371i
$417$	16.8541			0.825349
$418$	13.2361	−	2.97168i	0.647397	−	0.145350i
$419$	2.94427			0.143837			0.0719185	−	0.997411i	$-0.477088\pi$
$419$	2.94427			0.143837			0.0719185	+	0.997411i	$0.477088\pi$
$420$	0.427051	−	1.31433i	0.0208380	−	0.0641326i
$421$	12.3992	−	9.00854i	0.604299	−	0.439049i	−0.243103	−	0.970000i	$-0.578165\pi$
$421$	12.3992	−	9.00854i	0.604299	−	0.439049i	0.847402	+	0.530951i	$0.178165\pi$
$422$	0.618034	+	0.449028i	0.0300854	+	0.0218583i
$423$	3.14590	+	9.68208i	0.152959	+	0.470759i
$424$	−2.76393	−	8.50651i	−0.134228	−	0.413113i
$425$	19.0451	+	13.8371i	0.923822	+	0.671196i
$426$	1.23607	−	0.898056i	0.0598877	−	0.0435110i
$427$	2.85410	−	8.78402i	0.138120	−	0.425089i
$428$	−19.0344			−0.920064
$429$	4.00000	−	0.898056i	0.193122	−	0.0433585i
$430$	7.23607			0.348954
$431$	2.86475	−	8.81678i	0.137990	−	0.424689i	−0.858053	−	0.513561i	$-0.828326\pi$
$431$	2.86475	−	8.81678i	0.137990	−	0.424689i	0.996043	+	0.0888716i	$0.0283261\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	2.70820	+	1.96763i	0.130148	+	0.0945580i	0.650955	−	0.759117i	$-0.274369\pi$
$433$	2.70820	+	1.96763i	0.130148	+	0.0945580i	−0.520807	+	0.853675i	$0.674369\pi$
$434$	0.336881	+	1.03681i	0.0161708	+	0.0497686i
$435$	0.527864	+	1.62460i	0.0253091	+	0.0778935i
$436$	−3.73607	−	2.71441i	−0.178925	−	0.129997i
$437$	30.8607	−	22.4216i	1.47627	−	1.07257i
$438$	2.47214	−	7.60845i	0.118123	−	0.363546i
$439$	22.0344			1.05165			0.525823	−	0.850594i	$-0.323757\pi$
$439$	22.0344			1.05165			0.525823	+	0.850594i	$0.323757\pi$
$440$	3.02786	−	3.44095i	0.144348	−	0.164041i
$441$	1.00000			0.0476190
$442$	2.90983	−	8.95554i	0.138407	−	0.425971i
$443$	16.1631	−	11.7432i	0.767933	−	0.557936i	−0.133400	−	0.991062i	$-0.542590\pi$
$443$	16.1631	−	11.7432i	0.767933	−	0.557936i	0.901333	+	0.433126i	$0.142590\pi$
$444$	6.97214	+	5.06555i	0.330883	+	0.240401i
$445$	2.19756	+	6.76340i	0.104174	+	0.320616i
$446$	−0.972136	−	2.99193i	−0.0460320	−	0.141672i
$447$	15.7082	+	11.4127i	0.742973	+	0.539801i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	3.76393	−	11.5842i	0.177631	−	0.546692i	−0.822113	−	0.569324i	$-0.807205\pi$
$449$	3.76393	−	11.5842i	0.177631	−	0.546692i	0.999744	+	0.0226327i	$0.00720482\pi$
$450$	3.09017			0.145672
$451$	−20.0451	−	33.8218i	−0.943886	−	1.59260i
$452$	−6.47214			−0.304424
$453$	−2.76393	+	8.50651i	−0.129861	+	0.399671i
$454$	10.9443	−	7.95148i	0.513640	−	0.373181i
$455$	1.38197	+	1.00406i	0.0647876	+	0.0470709i
$456$	−1.26393	−	3.88998i	−0.0591890	−	0.182165i
$457$	−2.03444	−	6.26137i	−0.0951672	−	0.292894i	0.892130	−	0.451779i	$-0.149210\pi$
$457$	−2.03444	−	6.26137i	−0.0951672	−	0.292894i	−0.987297	+	0.158884i	$0.949210\pi$
$458$	−23.3262	−	16.9475i	−1.08996	−	0.791905i
$459$	−6.16312	+	4.47777i	−0.287670	+	0.209004i
$460$	3.98278	−	12.2577i	0.185698	−	0.571520i
$461$	19.8885			0.926302			0.463151	−	0.886279i	$-0.346719\pi$
$461$	19.8885			0.926302			0.463151	+	0.886279i	$0.346719\pi$
$462$	3.04508	+	1.31433i	0.141670	+	0.0611481i
$463$	−37.4164			−1.73889			−0.869444	−	0.494032i	$-0.835523\pi$
$463$	−37.4164			−1.73889			−0.869444	+	0.494032i	$0.835523\pi$
$464$	−0.381966	+	1.17557i	−0.0177323	+	0.0545745i
$465$	1.21885	−	0.885544i	0.0565227	−	0.0410661i
$466$	16.0902	+	11.6902i	0.745363	+	0.541538i
$467$	2.47214	+	7.60845i	0.114397	+	0.352077i	0.991821	−	0.127639i	$-0.0407398\pi$
$467$	2.47214	+	7.60845i	0.114397	+	0.352077i	−0.877424	+	0.479716i	$0.840740\pi$
$468$	−0.381966	−	1.17557i	−0.0176564	−	0.0543408i
$469$	−1.00000	−	0.726543i	−0.0461757	−	0.0335486i
$470$	−11.3820	+	8.26948i	−0.525011	+	0.381443i
$471$	1.14590	−	3.52671i	0.0528002	−	0.162502i
$472$	8.94427			0.411693
$473$	−1.61803	+	17.2905i	−0.0743973	+	0.795019i
$474$	7.70820			0.354050
$475$	−3.90576	+	12.0207i	−0.179209	+	0.551548i
$476$	6.16312	−	4.47777i	0.282486	−	0.205238i
$477$	−7.23607	−	5.25731i	−0.331317	−	0.240716i
$478$	−3.59017	−	11.0494i	−0.164211	−	0.505388i
$479$	1.52786	+	4.70228i	0.0698099	+	0.214853i	0.979875	−	0.199613i	$-0.0639685\pi$
$479$	1.52786	+	4.70228i	0.0698099	+	0.214853i	−0.910065	+	0.414466i	$0.863968\pi$
$480$	−1.11803	−	0.812299i	−0.0510310	−	0.0370762i
$481$	−8.61803	+	6.26137i	−0.392949	+	0.285494i
$482$	1.90983	−	5.87785i	0.0869904	−	0.267729i
$483$	9.32624			0.424359
$484$	7.54508	+	8.00448i	0.342958	+	0.363840i
$485$	−15.5279			−0.705084
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−26.1803	+	19.0211i	−1.18634	+	0.861930i	−0.992873	−	0.119176i	$-0.961975\pi$
$487$	−26.1803	+	19.0211i	−1.18634	+	0.861930i	−0.193471	+	0.981106i	$0.561975\pi$
$488$	−7.47214	−	5.42882i	−0.338248	−	0.245751i
$489$	6.32624	+	19.4702i	0.286082	+	0.880471i
$490$	0.427051	+	1.31433i	0.0192922	+	0.0593753i
$491$	9.07295	+	6.59188i	0.409456	+	0.297488i	0.773382	−	0.633941i	$-0.218564\pi$
$491$	9.07295	+	6.59188i	0.409456	+	0.297488i	−0.363925	+	0.931428i	$0.618564\pi$
$492$	−9.59017	+	6.96767i	−0.432358	+	0.314127i
$493$	−2.90983	+	8.95554i	−0.131052	+	0.403337i
$494$	5.05573			0.227468
$495$	0.427051	−	4.56352i	0.0191945	−	0.205115i
$496$	1.09017			0.0489501
$497$	−0.472136	+	1.45309i	−0.0211782	+	0.0651798i
$498$	12.3262	−	8.95554i	0.552352	−	0.401307i
$499$	−10.7082	−	7.77997i	−0.479365	−	0.348279i	0.321715	−	0.946837i	$-0.395741\pi$
$499$	−10.7082	−	7.77997i	−0.479365	−	0.348279i	−0.801080	+	0.598558i	$0.795741\pi$
$500$	3.45492	+	10.6331i	0.154508	+	0.475528i
$501$	2.32624	+	7.15942i	0.103929	+	0.319859i
$502$	−7.23607	−	5.25731i	−0.322962	−	0.234645i
$503$	2.52786	−	1.83660i	0.112712	−	0.0818900i	−0.530001	−	0.847997i	$-0.677809\pi$
$503$	2.52786	−	1.83660i	0.112712	−	0.0818900i	0.642713	+	0.766107i	$0.277809\pi$
$504$	0.309017	−	0.951057i	0.0137647	−	0.0423634i
$505$	−16.3820			−0.728988
$506$	28.3992	+	12.2577i	1.26250	+	0.544923i
$507$	−11.4721			−0.509495
$508$	3.47214	−	10.6861i	0.154051	−	0.474121i
$509$	14.0623	−	10.2169i	0.623301	−	0.452855i	−0.230772	−	0.973008i	$-0.574125\pi$
$509$	14.0623	−	10.2169i	0.623301	−	0.452855i	0.854073	+	0.520153i	$0.174125\pi$
$510$	−8.51722	−	6.18812i	−0.377149	−	0.274015i
$511$	2.47214	+	7.60845i	0.109361	+	0.336578i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−3.30902	−	2.40414i	−0.146097	−	0.106145i
$514$	−7.39919	+	5.37582i	−0.326364	+	0.237117i
$515$	−2.47620	+	7.62096i	−0.109114	+	0.335820i
$516$	5.23607			0.230505
$517$	−17.2148	−	29.0462i	−0.757105	−	1.27745i
$518$	−8.61803			−0.378655
$519$	2.11803	−	6.51864i	0.0929714	−	0.286136i
$520$	1.38197	−	1.00406i	0.0606032	−	0.0440308i
$521$	−23.0623	−	16.7557i	−1.01038	−	0.734083i	−0.0460896	−	0.998937i	$-0.514676\pi$
$521$	−23.0623	−	16.7557i	−1.01038	−	0.734083i	−0.964288	+	0.264855i	$0.914676\pi$
$522$	0.381966	+	1.17557i	0.0167182	+	0.0514533i
$523$	−1.26393	−	3.88998i	−0.0552679	−	0.170097i	0.919612	−	0.392827i	$-0.128503\pi$
$523$	−1.26393	−	3.88998i	−0.0552679	−	0.170097i	−0.974880	+	0.222730i	$0.928503\pi$
$524$	−12.3262	−	8.95554i	−0.538474	−	0.391224i
$525$	−2.50000	+	1.81636i	−0.109109	+	0.0792723i
$526$	−2.17376	+	6.69015i	−0.0947805	+	0.291704i
$527$	8.30495			0.361769
$528$	2.19098	−	2.48990i	0.0953503	−	0.108359i
$529$	63.9787			2.78168
$530$	3.81966	−	11.7557i	0.165915	−	0.510635i
$531$	7.23607	−	5.25731i	0.314019	−	0.228148i
$532$	3.30902	+	2.40414i	0.143464	+	0.104233i
$533$	−4.52786	−	13.9353i	−0.196124	−	0.603606i
$534$	1.59017	+	4.89404i	0.0688134	+	0.211786i
$535$	−21.2812	−	15.4617i	−0.920064	−	0.668466i
$536$	−1.00000	+	0.726543i	−0.0431934	+	0.0313819i
$537$	6.66312	−	20.5070i	0.287535	−	0.884941i
$538$	−6.00000			−0.258678
$539$	−3.23607	+	0.726543i	−0.139387	+	0.0312944i
$540$	−1.38197			−0.0594703
$541$	−3.71885	+	11.4454i	−0.159886	+	0.492078i	−0.998623	−	0.0524585i	$-0.983294\pi$
$541$	−3.71885	+	11.4454i	−0.159886	+	0.492078i	0.838737	+	0.544536i	$0.183294\pi$
$542$	4.11803	−	2.99193i	0.176885	−	0.128514i
$543$	−6.47214	−	4.70228i	−0.277746	−	0.201794i
$544$	−2.35410	−	7.24518i	−0.100931	−	0.310635i
$545$	−1.97214	−	6.06961i	−0.0844770	−	0.259994i
$546$	1.00000	+	0.726543i	0.0427960	+	0.0310931i
$547$	−14.1803	+	10.3026i	−0.606308	+	0.440508i	−0.848112	−	0.529817i	$-0.822261\pi$
$547$	−14.1803	+	10.3026i	−0.606308	+	0.440508i	0.241805	+	0.970325i	$0.422261\pi$
$548$	2.00000	−	6.15537i	0.0854358	−	0.262944i
$549$	−9.23607			−0.394186
$550$	−10.0000	+	2.24514i	−0.426401	+	0.0957331i
$551$	−5.05573			−0.215381
$552$	2.88197	−	8.86978i	0.122665	−	0.377523i
$553$	−6.23607	+	4.53077i	−0.265185	+	0.192668i
$554$	2.54508	+	1.84911i	0.108130	+	0.0785613i
$555$	3.68034	+	11.3269i	0.156222	+	0.480801i
$556$	5.20820	+	16.0292i	0.220877	+	0.679790i
$557$	23.3262	+	16.9475i	0.988364	+	0.718089i	0.959562	−	0.281496i	$-0.0908307\pi$
$557$	23.3262	+	16.9475i	0.988364	+	0.718089i	0.0288021	+	0.999585i	$0.490831\pi$
$558$	0.881966	−	0.640786i	0.0373366	−	0.0271266i
$559$	−2.00000	+	6.15537i	−0.0845910	+	0.260344i
$560$	1.38197			0.0583987
$561$	16.6910	−	18.9681i	0.704694	−	0.800835i
$562$	−14.6525			−0.618077
$563$	3.85410	−	11.8617i	0.162431	−	0.499911i	−0.836407	−	0.548109i	$-0.815348\pi$
$563$	3.85410	−	11.8617i	0.162431	−	0.499911i	0.998838	+	0.0481979i	$0.0153478\pi$
$564$	−8.23607	+	5.98385i	−0.346801	+	0.251966i
$565$	−7.23607	−	5.25731i	−0.304424	−	0.221177i
$566$	−0.336881	−	1.03681i	−0.0141602	−	0.0435805i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	1.23607	+	0.898056i	0.0518643	+	0.0376816i
$569$	−18.7082	+	13.5923i	−0.784289	+	0.569819i	−0.906263	−	0.422714i	$-0.861077\pi$
$569$	−18.7082	+	13.5923i	−0.784289	+	0.569819i	0.121974	+	0.992533i	$0.461077\pi$
$570$	1.74671	−	5.37582i	0.0731617	−	0.225168i
$571$	−19.7082			−0.824763			−0.412381	−	0.911011i	$-0.635303\pi$
$571$	−19.7082			−0.824763			−0.412381	+	0.911011i	$0.635303\pi$
$572$	2.09017	+	3.52671i	0.0873944	+	0.147459i
$573$	11.0902			0.463298
$574$	3.66312	−	11.2739i	0.152896	−	0.470564i
$575$	−23.3156	+	16.9398i	−0.972328	+	0.706437i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	0.472136	+	1.45309i	0.0196553	+	0.0604927i	0.960403	−	0.278614i	$-0.0898751\pi$
$577$	0.472136	+	1.45309i	0.0196553	+	0.0604927i	−0.940748	+	0.339107i	$0.889875\pi$
$578$	−12.6803	−	39.0261i	−0.527433	−	1.62327i
$579$	1.50000	+	1.08981i	0.0623379	+	0.0452911i
$580$	−1.38197	+	1.00406i	−0.0573830	+	0.0416912i
$581$	−4.70820	+	14.4904i	−0.195329	+	0.601162i
$582$	−11.2361			−0.465750
$583$	27.2361	+	11.7557i	1.12800	+	0.486872i
$584$	8.00000			0.331042
$585$	0.527864	−	1.62460i	0.0218245	−	0.0671689i
$586$	7.11803	−	5.17155i	0.294043	−	0.213635i
$587$	19.3262	+	14.0413i	0.797679	+	0.579548i	0.910232	−	0.414098i	$-0.135903\pi$
$587$	19.3262	+	14.0413i	0.797679	+	0.579548i	−0.112553	+	0.993646i	$0.535903\pi$
$588$	0.309017	+	0.951057i	0.0127436	+	0.0392209i
$589$	1.37790	+	4.24074i	0.0567754	+	0.174737i
$590$	10.0000	+	7.26543i	0.411693	+	0.299113i
$591$	−15.1803	+	11.0292i	−0.624436	+	0.453679i
$592$	−2.66312	+	8.19624i	−0.109454	+	0.336863i
$593$	−13.7426			−0.564343			−0.282171	−	0.959364i	$-0.591055\pi$
$593$	−13.7426			−0.564343			−0.282171	+	0.959364i	$0.591055\pi$
$594$	0.309017	−	3.30220i	0.0126791	−	0.135491i
$595$	10.5279			0.431600
$596$	−6.00000	+	18.4661i	−0.245770	+	0.756401i
$597$	6.69098	−	4.86128i	0.273844	−	0.198959i
$598$	9.32624	+	6.77591i	0.381378	+	0.277088i
$599$	2.82624	+	8.69827i	0.115477	+	0.355402i	0.992046	−	0.125874i	$-0.0401736\pi$
$599$	2.82624	+	8.69827i	0.115477	+	0.355402i	−0.876569	+	0.481276i	$0.840174\pi$
$600$	0.954915	+	2.93893i	0.0389842	+	0.119981i
$601$	6.09017	+	4.42477i	0.248423	+	0.180490i	0.705028	−	0.709180i	$-0.250935\pi$
$601$	6.09017	+	4.42477i	0.248423	+	0.180490i	−0.456604	+	0.889670i	$0.650935\pi$
$602$	−4.23607	+	3.07768i	−0.172649	+	0.125437i
$603$	−0.381966	+	1.17557i	−0.0155549	+	0.0478729i
$604$	−8.94427			−0.363937
$605$	1.93363	+	15.0781i	0.0786132	+	0.613014i
$606$	−11.8541			−0.481540
$607$	9.38854	−	28.8950i	0.381069	−	1.17281i	−0.558223	−	0.829691i	$-0.688516\pi$
$607$	9.38854	−	28.8950i	0.381069	−	1.17281i	0.939292	−	0.343119i	$-0.111484\pi$
$608$	3.30902	−	2.40414i	0.134198	−	0.0975008i
$609$	−1.00000	−	0.726543i	−0.0405220	−	0.0294410i
$610$	−3.94427	−	12.1392i	−0.159699	−	0.491503i
$611$	−3.88854	−	11.9677i	−0.157314	−	0.484162i
$612$	−6.16312	−	4.47777i	−0.249129	−	0.181003i
$613$	−7.01722	+	5.09831i	−0.283423	+	0.205919i	−0.720409	−	0.693549i	$-0.756046\pi$
$613$	−7.01722	+	5.09831i	−0.283423	+	0.205919i	0.436986	+	0.899468i	$0.356046\pi$
$614$	−4.89919	+	15.0781i	−0.197715	+	0.608504i
$615$	−16.3820			−0.660585
$616$	−0.309017	+	3.30220i	−0.0124506	+	0.133049i
$617$	−33.4164			−1.34529			−0.672647	−	0.739964i	$-0.734843\pi$
$617$	−33.4164			−1.34529			−0.672647	+	0.739964i	$0.734843\pi$
$618$	−1.79180	+	5.51458i	−0.0720766	+	0.221829i
$619$	7.88197	−	5.72658i	0.316803	−	0.230171i	−0.418007	−	0.908444i	$-0.637271\pi$
$619$	7.88197	−	5.72658i	0.316803	−	0.230171i	0.734810	+	0.678273i	$0.237271\pi$
$620$	1.21885	+	0.885544i	0.0489501	+	0.0355643i
$621$	−2.88197	−	8.86978i	−0.115649	−	0.355932i
$622$	4.18034	+	12.8658i	0.167616	+	0.515870i
$623$	−4.16312	−	3.02468i	−0.166792	−	0.121181i
$624$	1.00000	−	0.726543i	0.0400320	−	0.0290850i
$625$		0			0
$626$	−14.2918			−0.571215
$627$	12.4549	+	5.37582i	0.497401	+	0.214690i
$628$	3.70820			0.147973
$629$	−20.2877	+	62.4392i	−0.808925	+	2.48961i
$630$	1.11803	−	0.812299i	0.0445435	−	0.0323628i
$631$	7.94427	+	5.77185i	0.316256	+	0.229774i	0.734576	−	0.678526i	$-0.237381\pi$
$631$	7.94427	+	5.77185i	0.316256	+	0.229774i	−0.418320	+	0.908300i	$0.637381\pi$
$632$	2.38197	+	7.33094i	0.0947495	+	0.291609i
$633$	0.236068	+	0.726543i	0.00938286	+	0.0288775i
$634$	9.70820	+	7.05342i	0.385562	+	0.280127i
$635$	12.5623	−	9.12705i	0.498520	−	0.362196i
$636$	2.76393	−	8.50651i	0.109597	−	0.337305i
$637$	−1.23607			−0.0489748
$638$	−2.09017	−	3.52671i	−0.0827506	−	0.139624i
$639$	1.52786			0.0604414
$640$	0.427051	−	1.31433i	0.0168807	−	0.0519534i
$641$	−31.8885	+	23.1684i	−1.25952	+	0.915096i	−0.998734	−	0.0503001i	$-0.983982\pi$
$641$	−31.8885	+	23.1684i	−1.25952	+	0.915096i	−0.260788	+	0.965396i	$0.583982\pi$
$642$	−15.3992	−	11.1882i	−0.607757	−	0.441562i
$643$	−2.15248	−	6.62464i	−0.0848854	−	0.261250i	0.899601	−	0.436714i	$-0.143858\pi$
$643$	−2.15248	−	6.62464i	−0.0848854	−	0.261250i	−0.984486	+	0.175463i	$0.943858\pi$
$644$	2.88197	+	8.86978i	0.113565	+	0.349518i
$645$	5.85410	+	4.25325i	0.230505	+	0.167472i
$646$	25.2082	−	18.3148i	0.991804	−	0.720587i
$647$	−0.381966	+	1.17557i	−0.0150166	+	0.0462164i	−0.958284	−	0.285818i	$-0.907735\pi$
$647$	−0.381966	+	1.17557i	−0.0150166	+	0.0462164i	0.943267	+	0.332034i	$0.107735\pi$
$648$	−1.00000			−0.0392837
$649$	−19.5967	+	22.2703i	−0.769240	+	0.874187i
$650$	−3.81966			−0.149819
$651$	−0.336881	+	1.03681i	−0.0132034	+	0.0406359i
$652$	−16.5623	+	12.0332i	−0.648630	+	0.471257i
$653$	22.0902	+	16.0494i	0.864455	+	0.628063i	0.929093	−	0.369845i	$-0.120589\pi$
$653$	22.0902	+	16.0494i	0.864455	+	0.628063i	−0.0646382	+	0.997909i	$0.520589\pi$
$654$	−1.42705	−	4.39201i	−0.0558021	−	0.171741i
$655$	−6.50658	−	20.0252i	−0.254233	−	0.782449i
$656$	−9.59017	−	6.96767i	−0.374433	−	0.272042i
$657$	6.47214	−	4.70228i	0.252502	−	0.183453i
$658$	3.14590	−	9.68208i	0.122640	−	0.377447i
$659$	−31.1591			−1.21378			−0.606892	−	0.794784i	$-0.707584\pi$
$659$	−31.1591			−1.21378			−0.606892	+	0.794784i	$0.707584\pi$
$660$	4.47214	−	1.00406i	0.174078	−	0.0390829i
$661$	15.8885			0.617993			0.308996	−	0.951063i	$-0.400007\pi$
$661$	15.8885			0.617993			0.308996	+	0.951063i	$0.400007\pi$
$662$	0.0557281	−	0.171513i	0.00216593	−	0.00666606i
$663$	7.61803	−	5.53483i	0.295860	−	0.214955i
$664$	12.3262	+	8.95554i	0.478351	+	0.347542i
$665$	1.74671	+	5.37582i	0.0677346	+	0.208466i
$666$	2.66312	+	8.19624i	0.103194	+	0.317598i
$667$	−9.32624	−	6.77591i	−0.361113	−	0.262364i
$668$	−6.09017	+	4.42477i	−0.235636	+	0.171199i
$669$	0.972136	−	2.99193i	0.0375849	−	0.115675i
$670$	−1.70820			−0.0659937
$671$	29.8885	−	6.71040i	1.15383	−	0.259052i
$672$	1.00000			0.0385758
$673$	−8.43769	+	25.9686i	−0.325249	+	1.00101i	0.646079	+	0.763271i	$0.276408\pi$
$673$	−8.43769	+	25.9686i	−0.325249	+	1.00101i	−0.971328	+	0.237743i	$0.923592\pi$
$674$	−6.73607	+	4.89404i	−0.259464	+	0.188511i
$675$	2.50000	+	1.81636i	0.0962250	+	0.0699116i
$676$	−3.54508	−	10.9106i	−0.136349	−	0.419640i
$677$	4.14590	+	12.7598i	0.159340	+	0.490397i	0.998575	−	0.0533715i	$-0.0169968\pi$
$677$	4.14590	+	12.7598i	0.159340	+	0.490397i	−0.839235	+	0.543769i	$0.816997\pi$
$678$	−5.23607	−	3.80423i	−0.201090	−	0.146100i
$679$	9.09017	−	6.60440i	0.348849	−	0.253453i
$680$	3.25329	−	10.0126i	0.124758	−	0.383965i
$681$	13.5279			0.518389
$682$	−2.38854	+	2.71441i	−0.0914621	+	0.103940i
$683$	18.4377			0.705499			0.352749	−	0.935718i	$-0.385247\pi$
$683$	18.4377			0.705499			0.352749	+	0.935718i	$0.385247\pi$
$684$	1.26393	−	3.88998i	0.0483276	−	0.148737i
$685$	7.23607	−	5.25731i	0.276476	−	0.200872i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	−8.90983	−	27.4216i	−0.339931	−	1.04620i
$688$	1.61803	+	4.97980i	0.0616870	+	0.189853i
$689$	8.94427	+	6.49839i	0.340750	+	0.247569i
$690$	10.4271	−	7.57570i	0.396951	−	0.288402i
$691$	−7.50000	+	23.0826i	−0.285313	+	0.878104i	0.700991	+	0.713170i	$0.252741\pi$
$691$	−7.50000	+	23.0826i	−0.285313	+	0.878104i	−0.986305	+	0.164934i	$0.947259\pi$
$692$	6.85410			0.260554
$693$	1.69098	+	2.85317i	0.0642351	+	0.108383i
$694$	−10.7984			−0.409901
$695$	−7.19756	+	22.1518i	−0.273019	+	0.840266i
$696$	−1.00000	+	0.726543i	−0.0379049	+	0.0275395i
$697$	−73.0582	−	53.0799i	−2.76728	−	2.01055i
$698$	2.94427	+	9.06154i	0.111442	+	0.342984i
$699$	6.14590	+	18.9151i	0.232459	+	0.715436i
$700$	−2.50000	−	1.81636i	−0.0944911	−	0.0686518i
$701$	−24.0902	+	17.5025i	−0.909873	+	0.661062i	−0.940983	−	0.338454i	$-0.890096\pi$
$701$	−24.0902	+	17.5025i	−0.909873	+	0.661062i	0.0311096	+	0.999516i	$0.490096\pi$
$702$	0.381966	−	1.17557i	0.0144164	−	0.0443690i
$703$	−35.2492			−1.32945
$704$	3.04508	+	1.31433i	0.114766	+	0.0495356i
$705$	−14.0689			−0.529865
$706$	−7.09017	+	21.8213i	−0.266842	+	0.821255i
$707$	9.59017	−	6.96767i	0.360675	−	0.262046i
$708$	7.23607	+	5.25731i	0.271948	+	0.197582i
$709$	−4.10081	−	12.6210i	−0.154009	−	0.473992i	0.844050	−	0.536265i	$-0.180165\pi$
$709$	−4.10081	−	12.6210i	−0.154009	−	0.473992i	−0.998059	+	0.0622729i	$0.980165\pi$
$710$	0.652476	+	2.00811i	0.0244870	+	0.0753632i
$711$	6.23607	+	4.53077i	0.233871	+	0.169917i
$712$	−4.16312	+	3.02468i	−0.156019	+	0.113355i
$713$	−3.14183	+	9.66957i	−0.117663	+	0.362128i
$714$	7.61803			0.285098
$715$	−0.527864	+	5.64083i	−0.0197410	+	0.210955i
$716$	21.5623			0.805821
$717$	3.59017	−	11.0494i	0.134077	−	0.412648i
$718$	−24.4443	+	17.7598i	−0.912252	+	0.662790i
$719$	1.90983	+	1.38757i	0.0712246	+	0.0517477i	0.622828	−	0.782359i	$-0.285984\pi$
$719$	1.90983	+	1.38757i	0.0712246	+	0.0517477i	−0.551603	+	0.834107i	$0.685984\pi$
$720$	−0.427051	−	1.31433i	−0.0159153	−	0.0489821i
$721$	−1.79180	−	5.51458i	−0.0667300	−	0.205374i
$722$	−1.83688	−	1.33457i	−0.0683616	−	0.0496676i
$723$	5.00000	−	3.63271i	0.185952	−	0.135102i
$724$	2.47214	−	7.60845i	0.0918762	−	0.282766i
$725$	3.81966			0.141859
$726$	1.39919	+	10.9106i	0.0519287	+	0.404932i
$727$	23.5066			0.871811			0.435905	−	0.899993i	$-0.356428\pi$
$727$	23.5066			0.871811			0.435905	+	0.899993i	$0.356428\pi$
$728$	−0.381966	+	1.17557i	−0.0141566	+	0.0435695i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	8.94427	+	6.49839i	0.331042	+	0.240516i
$731$	12.3262	+	37.9363i	0.455902	+	1.40312i
$732$	−2.85410	−	8.78402i	−0.105491	−	0.324667i
$733$	1.52786	+	1.11006i	0.0564329	+	0.0410009i	0.615644	−	0.788024i	$-0.288896\pi$
$733$	1.52786	+	1.11006i	0.0564329	+	0.0410009i	−0.559211	+	0.829025i	$0.688896\pi$
$734$	−15.8262	+	11.4984i	−0.584157	+	0.424415i
$735$	−0.427051	+	1.31433i	−0.0157520	+	0.0484797i
$736$	9.32624			0.343770
$737$	0.381966	−	4.08174i	0.0140699	−	0.150353i
$738$	−11.8541			−0.436356
$739$	0.236068	−	0.726543i	0.00868390	−	0.0267263i	−0.946621	−	0.322350i	$-0.895527\pi$
$739$	0.236068	−	0.726543i	0.00868390	−	0.0267263i	0.955305	+	0.295623i	$0.0955273\pi$
$740$	−9.63525	+	7.00042i	−0.354199	+	0.257341i
$741$	4.09017	+	2.97168i	0.150256	+	0.109167i
$742$	2.76393	+	8.50651i	0.101467	+	0.312284i
$743$	11.6287	+	35.7894i	0.426615	+	1.31299i	0.901440	+	0.432905i	$0.142511\pi$
$743$	11.6287	+	35.7894i	0.426615	+	1.31299i	−0.474825	+	0.880080i	$0.657489\pi$
$744$	0.881966	+	0.640786i	0.0323344	+	0.0234923i
$745$	−21.7082	+	15.7719i	−0.795327	+	0.577839i
$746$	−8.19098	+	25.2093i	−0.299893	+	0.922976i
$747$	15.2361			0.557459
$748$	23.1976	+	10.0126i	0.848187	+	0.366097i
$749$	19.0344			0.695503
$750$	−3.45492	+	10.6331i	−0.126156	+	0.388267i
$751$	13.3262	−	9.68208i	0.486281	−	0.353304i	−0.317471	−	0.948268i	$-0.602834\pi$
$751$	13.3262	−	9.68208i	0.486281	−	0.353304i	0.803752	+	0.594964i	$0.202834\pi$
$752$	−8.23607	−	5.98385i	−0.300338	−	0.218209i
$753$	−2.76393	−	8.50651i	−0.100723	−	0.309994i
$754$	−0.472136	−	1.45309i	−0.0171942	−	0.0529182i
$755$	−10.0000	−	7.26543i	−0.363937	−	0.264416i
$756$	0.809017	−	0.587785i	0.0294237	−	0.0213775i
$757$	−2.02786	+	6.24112i	−0.0737040	+	0.226838i	−0.981121	−	0.193393i	$-0.938051\pi$
$757$	−2.02786	+	6.24112i	−0.0737040	+	0.226838i	0.907417	+	0.420230i	$0.138051\pi$
$758$	−21.7082			−0.788477
$759$	15.7705	+	26.6093i	0.572433	+	0.965858i
$760$	5.65248			0.205037
$761$	7.67376	−	23.6174i	0.278174	−	0.856130i	−0.710189	−	0.704012i	$-0.751390\pi$
$761$	7.67376	−	23.6174i	0.278174	−	0.856130i	0.988362	−	0.152119i	$-0.0486097\pi$
$762$	9.09017	−	6.60440i	0.329302	−	0.239252i
$763$	3.73607	+	2.71441i	0.135255	+	0.0982683i
$764$	3.42705	+	10.5474i	0.123986	+	0.381591i
$765$	−3.25329	−	10.0126i	−0.117623	−	0.362006i
$766$	4.85410	+	3.52671i	0.175386	+	0.127425i
$767$	−8.94427	+	6.49839i	−0.322959	+	0.234643i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	10.4721			0.377635			0.188817	−	0.982012i	$-0.439535\pi$
$769$	10.4721			0.377635			0.188817	+	0.982012i	$0.439535\pi$
$770$	−3.02786	+	3.44095i	−0.109117	+	0.124003i
$771$	−9.14590			−0.329381
$772$	−0.572949	+	1.76336i	−0.0206209	+	0.0634646i
$773$	32.5623	−	23.6579i	1.17118	−	0.850916i	0.180034	−	0.983660i	$-0.442379\pi$
$773$	32.5623	−	23.6579i	1.17118	−	0.850916i	0.991150	+	0.132745i	$0.0423791\pi$
$774$	4.23607	+	3.07768i	0.152262	+	0.110625i
$775$	−1.04102	−	3.20393i	−0.0373945	−	0.115089i
$776$	−3.47214	−	10.6861i	−0.124642	−	0.383610i
$777$	−6.97214	−	5.06555i	−0.250124	−	0.181726i
$778$	21.1803	−	15.3884i	0.759352	−	0.551702i
$779$	14.9828	−	46.1123i	0.536814	−	1.65214i
$780$	1.70820			0.0611635
$781$	−4.94427	+	1.11006i	−0.176920	+	0.0397210i
$782$	71.0476			2.54066
$783$	−0.381966	+	1.17557i	−0.0136504	+	0.0420115i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	4.14590	+	3.01217i	0.147973	+	0.107509i
$786$	−4.70820	−	14.4904i	−0.167936	−	0.516854i
$787$	−4.60739	−	14.1801i	−0.164236	−	0.505466i	0.834743	−	0.550639i	$-0.185616\pi$
$787$	−4.60739	−	14.1801i	−0.164236	−	0.505466i	−0.998979	+	0.0451735i	$0.985616\pi$
$788$	−15.1803	−	11.0292i	−0.540777	−	0.392898i
$789$	−5.69098	+	4.13474i	−0.202604	+	0.147201i
$790$	−3.29180	+	10.1311i	−0.117117	+	0.360449i
$791$	6.47214			0.230123
$792$	3.23607	−	0.726543i	0.114989	−	0.0258166i
$793$	11.4164			0.405409
$794$	−4.94427	+	15.2169i	−0.175466	+	0.540028i
$795$	10.0000	−	7.26543i	0.354663	−	0.257678i
$796$	6.69098	+	4.86128i	0.237156	+	0.172304i
$797$	1.07953	+	3.32244i	0.0382388	+	0.117687i	0.968354	−	0.249581i	$-0.0802930\pi$
$797$	1.07953	+	3.32244i	0.0382388	+	0.117687i	−0.930115	+	0.367268i	$0.880293\pi$
$798$	1.26393	+	3.88998i	0.0447427	+	0.137704i
$799$	−62.7426	−	45.5852i	−2.21968	−	1.61269i
$800$	−2.50000	+	1.81636i	−0.0883883	+	0.0642179i
$801$	−1.59017	+	4.89404i	−0.0561859	+	0.172922i
$802$	11.7082			0.413431
$803$	−17.5279	+	19.9192i	−0.618545	+	0.702933i
$804$	−1.23607			−0.0435928
$805$	−3.98278	+	12.2577i	−0.140375	+	0.432028i
$806$	−1.09017	+	0.792055i	−0.0383996	+	0.0278989i
$807$	−4.85410	−	3.52671i	−0.170872	−	0.124146i
$808$	−3.66312	−	11.2739i	−0.128868	−	0.396615i
$809$	7.14590	+	21.9928i	0.251236	+	0.773226i	0.994548	+	0.104281i	$0.0332540\pi$
$809$	7.14590	+	21.9928i	0.251236	+	0.773226i	−0.743312	+	0.668945i	$0.766746\pi$
$810$	−1.11803	−	0.812299i	−0.0392837	−	0.0285413i
$811$	11.4164	−	8.29451i	0.400884	−	0.291259i	−0.369017	−	0.929423i	$-0.620306\pi$
$811$	11.4164	−	8.29451i	0.400884	−	0.291259i	0.769901	+	0.638163i	$0.220306\pi$
$812$	0.381966	−	1.17557i	0.0134044	−	0.0412544i
$813$	5.09017			0.178520
$814$	−14.5729	−	24.5887i	−0.510782	−	0.861834i
$815$	−28.2918			−0.991018
$816$	2.35410	−	7.24518i	0.0824101	−	0.253632i
$817$	−17.3262	+	12.5882i	−0.606168	+	0.440407i
$818$	−28.8885	−	20.9888i	−1.01006	−	0.733855i
$819$	0.381966	+	1.17557i	0.0133470	+	0.0410778i
$820$	−5.06231	−	15.5802i	−0.176783	−	0.544083i
$821$	15.9443	+	11.5842i	0.556459	+	0.404291i	0.830161	−	0.557523i	$-0.188248\pi$
$821$	15.9443	+	11.5842i	0.556459	+	0.404291i	−0.273702	+	0.961814i	$0.588248\pi$
$822$	5.23607	−	3.80423i	0.182629	−	0.132688i
$823$	14.5836	−	44.8837i	0.508352	−	1.56455i	−0.286709	−	0.958018i	$-0.592561\pi$
$823$	14.5836	−	44.8837i	0.508352	−	1.56455i	0.795061	−	0.606529i	$-0.207439\pi$
$824$	−5.79837			−0.201996
$825$	−9.40983	−	4.06150i	−0.327608	−	0.141403i
$826$	−8.94427			−0.311211
$827$	−14.7016	+	45.2470i	−0.511226	+	1.57339i	0.278820	+	0.960343i	$0.410057\pi$
$827$	−14.7016	+	45.2470i	−0.511226	+	1.57339i	−0.790046	+	0.613047i	$0.789943\pi$
$828$	7.54508	−	5.48183i	0.262210	−	0.190507i
$829$	2.61803	+	1.90211i	0.0909281	+	0.0660631i	0.632320	−	0.774707i	$-0.282103\pi$
$829$	2.61803	+	1.90211i	0.0909281	+	0.0660631i	−0.541392	+	0.840770i	$0.682103\pi$
$830$	6.50658	+	20.0252i	0.225847	+	0.695084i
$831$	0.972136	+	2.99193i	0.0337230	+	0.103789i
$832$	1.00000	+	0.726543i	0.0346688	+	0.0251883i
$833$	−6.16312	+	4.47777i	−0.213539	+	0.155145i
$834$	−5.20820	+	16.0292i	−0.180345	+	0.555046i
$835$	−10.4033			−0.360019
$836$	−1.26393	+	13.5065i	−0.0437140	+	0.467134i
$837$	1.09017			0.0376818
$838$	−0.909830	+	2.80017i	−0.0314296	+	0.0967302i
$839$	25.8885	−	18.8091i	0.893772	−	0.649363i	−0.0430869	−	0.999071i	$-0.513719\pi$
$839$	25.8885	−	18.8091i	0.893772	−	0.649363i	0.936859	+	0.349708i	$0.113719\pi$
$840$	1.11803	+	0.812299i	0.0385758	+	0.0280270i
$841$	−8.48936	−	26.1276i	−0.292736	−	0.900950i
$842$	4.73607	+	14.5761i	0.163216	+	0.502326i
$843$	−11.8541	−	8.61251i	−0.408277	−	0.296631i
$844$	−0.618034	+	0.449028i	−0.0212736	+	0.0154562i
$845$	4.89919	−	15.0781i	0.168537	−	0.518704i
$846$	−10.1803			−0.350007
$847$	−7.54508	−	8.00448i	−0.259252	−	0.275037i
$848$	8.94427			0.307148
$849$	0.336881	−	1.03681i	0.0115617	−	0.0355833i
$850$	−19.0451	+	13.8371i	−0.653241	+	0.474607i
$851$	−65.0238	−	47.2426i	−2.22899	−	1.61945i
$852$	0.472136	+	1.45309i	0.0161751	+	0.0497819i
$853$	6.81966	+	20.9888i	0.233501	+	0.718641i	0.997317	+	0.0732073i	$0.0233235\pi$
$853$	6.81966	+	20.9888i	0.233501	+	0.718641i	−0.763816	+	0.645434i	$0.776677\pi$
$854$	7.47214	+	5.42882i	0.255691	+	0.185771i
$855$	4.57295	−	3.32244i	0.156392	−	0.113625i
$856$	5.88197	−	18.1028i	0.201041	−	0.618742i
$857$	−7.30495			−0.249532			−0.124766	−	0.992186i	$-0.539818\pi$
$857$	−7.30495			−0.249532			−0.124766	+	0.992186i	$0.539818\pi$
$858$	−0.381966	+	4.08174i	−0.0130401	+	0.139348i
$859$	25.5279			0.870999			0.435500	−	0.900189i	$-0.356572\pi$
$859$	25.5279			0.870999			0.435500	+	0.900189i	$0.356572\pi$
$860$	−2.23607	+	6.88191i	−0.0762493	+	0.234671i
$861$	9.59017	−	6.96767i	0.326832	−	0.237457i
$862$	7.50000	+	5.44907i	0.255451	+	0.185596i
$863$	−3.42705	−	10.5474i	−0.116658	−	0.359037i	0.875631	−	0.482981i	$-0.160446\pi$
$863$	−3.42705	−	10.5474i	−0.116658	−	0.359037i	−0.992289	+	0.123944i	$0.960446\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	7.66312	+	5.56758i	0.260554	+	0.189303i
$866$	−2.70820	+	1.96763i	−0.0920285	+	0.0668626i
$867$	12.6803	−	39.0261i	0.430647	−	1.32539i
$868$	−1.09017			−0.0370028
$869$	−23.4721	−	10.1311i	−0.796238	−	0.343674i
$870$	−1.70820			−0.0579135
$871$	0.472136	−	1.45309i	0.0159977	−	0.0492359i
$872$	3.73607	−	2.71441i	0.126519	−	0.0919216i
$873$	−9.09017	−	6.60440i	−0.307656	−	0.223525i
$874$	11.7877	+	36.2789i	0.398726	+	1.22715i
$875$	−3.45492	−	10.6331i	−0.116797	−	0.359466i
$876$	6.47214	+	4.70228i	0.218673	+	0.158875i
$877$	−31.7984	+	23.1029i	−1.07375	+	0.780129i	−0.976583	−	0.215139i	$-0.930979\pi$
$877$	−31.7984	+	23.1029i	−1.07375	+	0.780129i	−0.0971714	+	0.995268i	$0.530979\pi$
$878$	−6.80902	+	20.9560i	−0.229793	+	0.707231i
$879$	8.79837			0.296762
$880$	2.33688	+	3.94298i	0.0787762	+	0.132918i
$881$	−23.2148			−0.782126			−0.391063	−	0.920364i	$-0.627893\pi$
$881$	−23.2148			−0.782126			−0.391063	+	0.920364i	$0.627893\pi$
$882$	−0.309017	+	0.951057i	−0.0104051	+	0.0320237i
$883$	−1.61803	+	1.17557i	−0.0544512	+	0.0395611i	−0.614678	−	0.788778i	$-0.710714\pi$
$883$	−1.61803	+	1.17557i	−0.0544512	+	0.0395611i	0.560227	+	0.828339i	$0.310714\pi$
$884$	7.61803	+	5.53483i	0.256222	+	0.186156i
$885$	3.81966	+	11.7557i	0.128396	+	0.395164i
$886$	6.17376	+	19.0009i	0.207412	+	0.638347i
$887$	−6.00000	−	4.35926i	−0.201460	−	0.146369i	0.482481	−	0.875906i	$-0.339736\pi$
$887$	−6.00000	−	4.35926i	−0.201460	−	0.146369i	−0.683942	+	0.729537i	$0.739736\pi$
$888$	−6.97214	+	5.06555i	−0.233970	+	0.169989i
$889$	−3.47214	+	10.6861i	−0.116452	+	0.358401i
$890$	−7.11146			−0.238377
$891$	2.19098	−	2.48990i	0.0734007	−	0.0834147i
$892$	3.14590			0.105332
$893$	12.8673	−	39.6013i	0.430586	−	1.32521i
$894$	−15.7082	+	11.4127i	−0.525361	+	0.381697i
$895$	24.1074	+	17.5150i	0.805821	+	0.585463i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	3.56231	+	10.9637i	0.118942	+	0.366066i
$898$	9.85410	+	7.15942i	0.328836	+	0.238913i
$899$	1.09017	−	0.792055i	0.0363592	−	0.0264165i
$900$	−0.954915	+	2.93893i	−0.0318305	+	0.0979642i
$901$	68.1378			2.27000
$902$	38.3607	−	8.61251i	1.27727	−	0.286765i
$903$	−5.23607			−0.174245
$904$	2.00000	−	6.15537i	0.0665190	−	0.204724i
$905$	8.94427	−	6.49839i	0.297318	−	0.216014i
$906$	−7.23607	−	5.25731i	−0.240402	−	0.174662i
$907$	−13.6180	−	41.9120i	−0.452179	−	1.39167i	−0.874415	−	0.485179i	$-0.838754\pi$
$907$	−13.6180	−	41.9120i	−0.452179	−	1.39167i	0.422236	−	0.906486i	$-0.361246\pi$
$908$	4.18034	+	12.8658i	0.138729	+	0.426965i
$909$	−9.59017	−	6.96767i	−0.318086	−	0.231103i
$910$	−1.38197	+	1.00406i	−0.0458117	+	0.0332842i
$911$	17.5967	−	54.1572i	0.583006	−	1.79431i	−0.0241272	−	0.999709i	$-0.507681\pi$
$911$	17.5967	−	54.1572i	0.583006	−	1.79431i	0.607133	−	0.794600i	$-0.292319\pi$
$912$	4.09017			0.135439
$913$	−49.3050	+	11.0697i	−1.63176	+	0.366352i
$914$	6.58359			0.217766
$915$	3.94427	−	12.1392i	0.130394	−	0.401310i
$916$	23.3262	−	16.9475i	0.770721	−	0.559961i
$917$	12.3262	+	8.95554i	0.407048	+	0.295738i
$918$	−2.35410	−	7.24518i	−0.0776969	−	0.239127i
$919$	−12.6738	−	39.0058i	−0.418069	−	1.28668i	−0.909477	−	0.415754i	$-0.863518\pi$
$919$	−12.6738	−	39.0058i	−0.418069	−	1.28668i	0.491408	−	0.870929i	$-0.336482\pi$
$920$	10.4271	+	7.57570i	0.343770	+	0.249763i
$921$	−12.8262	+	9.31881i	−0.422639	+	0.307065i
$922$	−6.14590	+	18.9151i	−0.202404	+	0.622937i
$923$	−1.88854			−0.0621622
$924$	−2.19098	+	2.48990i	−0.0720780	+	0.0819116i
$925$	26.6312			0.875628
$926$	11.5623	−	35.5851i	0.379961	−	1.16940i
$927$	−4.69098	+	3.40820i	−0.154072	+	0.111940i
$928$	−1.00000	−	0.726543i	−0.0328266	−	0.0238499i
$929$	−15.1869	−	46.7405i	−0.498267	−	1.53351i	−0.811803	−	0.583931i	$-0.801514\pi$
$929$	−15.1869	−	46.7405i	−0.498267	−	1.53351i	0.313537	−	0.949576i	$-0.398486\pi$
$930$	0.465558	+	1.43284i	0.0152663	+	0.0469847i
$931$	−3.30902	−	2.40414i	−0.108449	−	0.0787926i
$932$	−16.0902	+	11.6902i	−0.527051	+	0.382925i
$933$	−4.18034	+	12.8658i	−0.136858	+	0.421206i
$934$	−8.00000			−0.261768
$935$	17.8024	+	30.0378i	0.582202	+	0.982340i
$936$	1.23607			0.0404021
$937$	−5.81966	+	17.9111i	−0.190120	+	0.585129i	−0.999999	−	0.00146787i	$-0.999533\pi$
$937$	−5.81966	+	17.9111i	−0.190120	+	0.585129i	0.809879	+	0.586597i	$0.199533\pi$
$938$	1.00000	−	0.726543i	0.0326512	−	0.0237225i
$939$	−11.5623	−	8.40051i	−0.377322	−	0.274140i
$940$	−4.34752	−	13.3803i	−0.141801	−	0.436417i
$941$	0.354102	+	1.08981i	0.0115434	+	0.0355269i	0.956662	−	0.291200i	$-0.0940544\pi$
$941$	0.354102	+	1.08981i	0.0115434	+	0.0355269i	−0.945119	+	0.326727i	$0.894054\pi$
$942$	3.00000	+	2.17963i	0.0977453	+	0.0710161i
$943$	89.4402	−	64.9821i	2.91257	−	2.11611i
$944$	−2.76393	+	8.50651i	−0.0899583	+	0.276863i
$945$	1.38197			0.0449554
$946$	−15.9443	−	6.88191i	−0.518393	−	0.223750i
$947$	3.38197			0.109899			0.0549496	−	0.998489i	$-0.482500\pi$
$947$	3.38197			0.109899			0.0549496	+	0.998489i	$0.482500\pi$
$948$	−2.38197	+	7.33094i	−0.0773627	+	0.238098i
$949$	−8.00000	+	5.81234i	−0.259691	+	0.188677i
$950$	−10.2254	−	7.42921i	−0.331757	−	0.241035i
$951$	3.70820	+	11.4127i	0.120247	+	0.370081i
$952$	2.35410	+	7.24518i	0.0762969	+	0.234818i
$953$	−1.47214	−	1.06957i	−0.0476872	−	0.0346468i	0.563686	−	0.825989i	$-0.309383\pi$
$953$	−1.47214	−	1.06957i	−0.0476872	−	0.0346468i	−0.611373	+	0.791342i	$0.709383\pi$
$954$	7.23607	−	5.25731i	0.234276	−	0.170212i
$955$	−4.73607	+	14.5761i	−0.153256	+	0.471672i
$956$	11.6180			0.375754
$957$	0.381966	−	4.08174i	0.0123472	−	0.131944i
$958$	−4.94427			−0.159742
$959$	−2.00000	+	6.15537i	−0.0645834	+	0.198767i
$960$	1.11803	−	0.812299i	0.0360844	−	0.0262168i
$961$	24.1180	+	17.5228i	0.778001	+	0.565251i
$962$	−3.29180	−	10.1311i	−0.106132	−	0.326640i
$963$	−5.88197	−	18.1028i	−0.189544	−	0.583356i
$964$	5.00000	+	3.63271i	0.161039	+	0.117002i
$965$	−2.07295	+	1.50609i	−0.0667306	+	0.0484826i
$966$	−2.88197	+	8.86978i	−0.0927257	+	0.285380i
$967$	20.1803			0.648956			0.324478	−	0.945893i	$-0.394811\pi$
$967$	20.1803			0.648956			0.324478	+	0.945893i	$0.394811\pi$
$968$	−9.94427	+	4.70228i	−0.319621	+	0.151137i
$969$	31.1591			1.00097
$970$	4.79837	−	14.7679i	0.154067	−	0.474168i
$971$	−32.5623	+	23.6579i	−1.04497	+	0.759218i	−0.971250	−	0.238061i	$-0.923488\pi$
$971$	−32.5623	+	23.6579i	−1.04497	+	0.759218i	−0.0737238	+	0.997279i	$0.523488\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−5.20820	−	16.0292i	−0.166967	−	0.513873i
$974$	−10.0000	−	30.7768i	−0.320421	−	0.986153i
$975$	−3.09017	−	2.24514i	−0.0989646	−	0.0719020i
$976$	7.47214	−	5.42882i	0.239177	−	0.173772i
$977$	−15.1459	+	46.6143i	−0.484560	+	1.49132i	0.348057	+	0.937474i	$0.386842\pi$
$977$	−15.1459	+	46.6143i	−0.484560	+	1.49132i	−0.832617	+	0.553849i	$0.813158\pi$
$978$	−20.4721			−0.654627
$979$	1.59017	−	16.9928i	0.0508221	−	0.543091i
$980$	−1.38197			−0.0441453
$981$	1.42705	−	4.39201i	0.0455622	−	0.140226i
$982$	−9.07295	+	6.59188i	−0.289529	+	0.210355i
$983$	−12.5623	−	9.12705i	−0.400675	−	0.291108i	0.369141	−	0.929374i	$-0.379652\pi$
$983$	−12.5623	−	9.12705i	−0.400675	−	0.291108i	−0.769816	+	0.638266i	$0.779652\pi$
$984$	−3.66312	−	11.2739i	−0.116776	−	0.359399i
$985$	−8.01316	−	24.6620i	−0.255320	−	0.785795i
$986$	−7.61803	−	5.53483i	−0.242608	−	0.176265i
$987$	8.23607	−	5.98385i	0.262157	−	0.190468i
$988$	−1.56231	+	4.80828i	−0.0497036	+	0.152972i
$989$	−48.8328			−1.55279
$990$	4.20820	+	1.81636i	0.133746	+	0.0577276i
$991$	4.29180			0.136333			0.0681667	−	0.997674i	$-0.478285\pi$
$991$	4.29180			0.136333			0.0681667	+	0.997674i	$0.478285\pi$
$992$	−0.336881	+	1.03681i	−0.0106960	+	0.0329189i
$993$	0.145898	−	0.106001i	0.00462993	−	0.00336384i
$994$	−1.23607	−	0.898056i	−0.0392057	−	0.0284846i
$995$	3.53193	+	10.8702i	0.111970	+	0.344607i
$996$	4.70820	+	14.4904i	0.149185	+	0.459145i
$997$	−21.3262	−	15.4944i	−0.675409	−	0.490713i	0.196423	−	0.980519i	$-0.437068\pi$
$997$	−21.3262	−	15.4944i	−0.675409	−	0.490713i	−0.871831	+	0.489806i	$0.837068\pi$
$998$	10.7082	−	7.77997i	0.338962	−	0.246271i
$999$	−2.66312	+	8.19624i	−0.0842574	+	0.259317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.c.295.1	✓	4
11.4	even	5		5082.2.a.bh.1.2		2
11.5	even	5	inner	462.2.j.c.379.1	yes	4
11.7	odd	10		5082.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.c.295.1	✓	4	1.1	even	1	trivial
462.2.j.c.379.1	yes	4	11.5	even	5	inner
5082.2.a.bh.1.2		2	11.4	even	5
5082.2.a.br.1.2		2	11.7	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.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.427051 - 1.31433i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.427051 - 1.31433i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.38197 q^{10} +(-0.309017 + 3.30220i) q^{11} +1.00000 q^{12} +(-0.381966 + 1.17557i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(1.11803 + 0.812299i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.35410 + 7.24518i) q^{17} +(0.809017 + 0.587785i) q^{18} +(-3.30902 + 2.40414i) q^{19} +(-0.427051 + 1.31433i) q^{20} -1.00000 q^{21} +(-3.04508 - 1.31433i) q^{22} -9.32624 q^{23} +(-0.309017 + 0.951057i) q^{24} +(2.50000 - 1.81636i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(1.00000 + 0.726543i) q^{29} +(-1.11803 + 0.812299i) q^{30} +(0.336881 - 1.03681i) q^{31} -1.00000 q^{32} +(-1.69098 - 2.85317i) q^{33} -7.61803 q^{34} +(0.427051 - 1.31433i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(6.97214 + 5.06555i) q^{37} +(-1.26393 - 3.88998i) q^{38} +(-0.381966 - 1.17557i) q^{39} +(-1.11803 - 0.812299i) q^{40} +(-9.59017 + 6.96767i) q^{41} +(0.309017 - 0.951057i) q^{42} +5.23607 q^{43} +(2.19098 - 2.48990i) q^{44} -1.38197 q^{45} +(2.88197 - 8.86978i) q^{46} +(-8.23607 + 5.98385i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.954915 + 2.93893i) q^{50} +(-6.16312 - 4.47777i) q^{51} +(1.00000 - 0.726543i) q^{52} +(2.76393 - 8.50651i) q^{53} -1.00000 q^{54} +(4.47214 - 1.00406i) q^{55} +1.00000 q^{56} +(1.26393 - 3.88998i) q^{57} +(-1.00000 + 0.726543i) q^{58} +(7.23607 + 5.25731i) q^{59} +(-0.427051 - 1.31433i) q^{60} +(-2.85410 - 8.78402i) q^{61} +(0.881966 + 0.640786i) q^{62} +(0.809017 - 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.70820 q^{65} +(3.23607 - 0.726543i) q^{66} -1.23607 q^{67} +(2.35410 - 7.24518i) q^{68} +(7.54508 - 5.48183i) q^{69} +(1.11803 + 0.812299i) q^{70} +(0.472136 + 1.45309i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(6.47214 + 4.70228i) q^{73} +(-6.97214 + 5.06555i) q^{74} +(-0.954915 + 2.93893i) q^{75} +4.09017 q^{76} +(-2.19098 + 2.48990i) q^{77} +1.23607 q^{78} +(-2.38197 + 7.33094i) q^{79} +(1.11803 - 0.812299i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.66312 - 11.2739i) q^{82} +(4.70820 + 14.4904i) q^{83} +(0.809017 + 0.587785i) q^{84} +(8.51722 - 6.18812i) q^{85} +(-1.61803 + 4.97980i) q^{86} -1.23607 q^{87} +(1.69098 + 2.85317i) q^{88} -5.14590 q^{89} +(0.427051 - 1.31433i) q^{90} +(-1.00000 + 0.726543i) q^{91} +(7.54508 + 5.48183i) q^{92} +(0.336881 + 1.03681i) q^{93} +(-3.14590 - 9.68208i) q^{94} +(4.57295 + 3.32244i) q^{95} +(0.809017 - 0.587785i) q^{96} +(3.47214 - 10.6861i) q^{97} -1.00000 q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} + q^{7} + q^{8} - q^{9} + 10 q^{10} + q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} + q^{18} - 11 q^{19} + 5 q^{20} - 4 q^{21} - q^{22} - 6 q^{23} + q^{24} + 10 q^{25} - 4 q^{26} - q^{27} + q^{28} + 4 q^{29} + 17 q^{31} - 4 q^{32} - 9 q^{33} - 26 q^{34} - 5 q^{35} - q^{36} + 10 q^{37} - 14 q^{38} - 6 q^{39} - 16 q^{41} - q^{42} + 12 q^{43} + 11 q^{44} - 10 q^{45} + 16 q^{46} - 24 q^{47} - q^{48} - q^{49} + 15 q^{50} - 9 q^{51} + 4 q^{52} + 20 q^{53} - 4 q^{54} + 4 q^{56} + 14 q^{57} - 4 q^{58} + 20 q^{59} + 5 q^{60} + 2 q^{61} + 8 q^{62} + q^{63} - q^{64} - 20 q^{65} + 4 q^{66} + 4 q^{67} - 4 q^{68} + 19 q^{69} - 16 q^{71} + q^{72} + 8 q^{73} - 10 q^{74} - 15 q^{75} - 6 q^{76} - 11 q^{77} - 4 q^{78} - 14 q^{79} - q^{81} + q^{82} - 8 q^{83} + q^{84} + 5 q^{85} - 2 q^{86} + 4 q^{87} + 9 q^{88} - 34 q^{89} - 5 q^{90} - 4 q^{91} + 19 q^{92} + 17 q^{93} - 26 q^{94} + 25 q^{95} + q^{96} - 4 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 + q^7 + q^8 - q^9 + 10 * q^10 + q^11 + 4 * q^12 - 6 * q^13 - q^14 - q^16 - 4 * q^17 + q^18 - 11 * q^19 + 5 * q^20 - 4 * q^21 - q^22 - 6 * q^23 + q^24 + 10 * q^25 - 4 * q^26 - q^27 + q^28 + 4 * q^29 + 17 * q^31 - 4 * q^32 - 9 * q^33 - 26 * q^34 - 5 * q^35 - q^36 + 10 * q^37 - 14 * q^38 - 6 * q^39 - 16 * q^41 - q^42 + 12 * q^43 + 11 * q^44 - 10 * q^45 + 16 * q^46 - 24 * q^47 - q^48 - q^49 + 15 * q^50 - 9 * q^51 + 4 * q^52 + 20 * q^53 - 4 * q^54 + 4 * q^56 + 14 * q^57 - 4 * q^58 + 20 * q^59 + 5 * q^60 + 2 * q^61 + 8 * q^62 + q^63 - q^64 - 20 * q^65 + 4 * q^66 + 4 * q^67 - 4 * q^68 + 19 * q^69 - 16 * q^71 + q^72 + 8 * q^73 - 10 * q^74 - 15 * q^75 - 6 * q^76 - 11 * q^77 - 4 * q^78 - 14 * q^79 - q^81 + q^82 - 8 * q^83 + q^84 + 5 * q^85 - 2 * q^86 + 4 * q^87 + 9 * q^88 - 34 * q^89 - 5 * q^90 - 4 * q^91 + 19 * q^92 + 17 * q^93 - 26 * q^94 + 25 * q^95 + q^96 - 4 * q^97 - 4 * q^98 + q^99

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