LMFDB - Embedded newform 62.2.d.b.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(33,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("62.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.d (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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1903140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 6x^{6} + x^{5} + 29x^{4} + 43x^{3} + 194x^{2} + 209x + 361 $ x^8 - 3x^7 + 6x^6 + x^5 + 29x^4 + 43x^3 + 194x^2 + 209x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.2
Root			$-0.480762 - 1.47963i$ of defining polynomial
Character	$\chi$	$=$	62.33
Dual form			62.2.d.b.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(1.25865 - 0.914463i) q^{3} +(0.309017 + 0.951057i) q^{4} -4.13533 q^{5} +1.55578 q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.179093 + 0.551192i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(1.25865 - 0.914463i) q^{3} +(0.309017 + 0.951057i) q^{4} -4.13533 q^{5} +1.55578 q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.179093 + 0.551192i) q^{9} +(-3.34556 - 2.43069i) q^{10} +(1.14062 + 3.51046i) q^{11} +(1.25865 + 0.914463i) q^{12} +(3.20494 - 2.32852i) q^{13} +(0.500000 - 1.53884i) q^{14} +(-5.20494 + 3.78161i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.27789 - 3.93294i) q^{17} +(-0.468872 + 0.340655i) q^{18} +(-3.62344 - 2.63259i) q^{19} +(-1.27789 - 3.93294i) q^{20} +(-2.03654 - 1.47963i) q^{21} +(-1.14062 + 3.51046i) q^{22} +(-0.306950 + 0.944696i) q^{23} +(0.480762 + 1.47963i) q^{24} +12.1010 q^{25} +3.96152 q^{26} +(1.72091 + 5.29643i) q^{27} +(1.30902 - 0.951057i) q^{28} +(-3.00855 - 2.18584i) q^{29} -6.43366 q^{30} +(2.85204 + 4.78183i) q^{31} -1.00000 q^{32} +(4.64582 + 3.37538i) q^{33} +(3.34556 - 2.43069i) q^{34} +(2.06767 + 6.36363i) q^{35} -0.579557 q^{36} -6.89927 q^{37} +(-1.38403 - 4.25961i) q^{38} +(1.90455 - 5.86160i) q^{39} +(1.27789 - 3.93294i) q^{40} +(1.84556 + 1.34087i) q^{41} +(-0.777889 - 2.39409i) q^{42} +(-0.399266 - 0.290084i) q^{43} +(-2.98617 + 2.16958i) q^{44} +(0.740610 - 2.27936i) q^{45} +(-0.803607 + 0.583854i) q^{46} +(-1.50000 + 1.08981i) q^{47} +(-0.480762 + 1.47963i) q^{48} +(3.54508 - 2.57565i) q^{49} +(9.78991 + 7.11278i) q^{50} +(-1.98811 - 6.11877i) q^{51} +(3.20494 + 2.32852i) q^{52} +(-0.0524334 + 0.161373i) q^{53} +(-1.72091 + 5.29643i) q^{54} +(-4.71683 - 14.5169i) q^{55} +1.61803 q^{56} -6.96805 q^{57} +(-1.14916 - 3.53676i) q^{58} +(-10.1301 + 7.35991i) q^{59} +(-5.20494 - 3.78161i) q^{60} -3.34762 q^{61} +(-0.503344 + 5.54497i) q^{62} +0.937743 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-13.2535 + 9.62923i) q^{65} +(1.77454 + 5.46149i) q^{66} +1.47882 q^{67} +4.13533 q^{68} +(0.477546 + 1.46974i) q^{69} +(-2.06767 + 6.36363i) q^{70} +(2.55904 - 7.87592i) q^{71} +(-0.468872 - 0.340655i) q^{72} +(-0.547152 - 1.68396i) q^{73} +(-5.58162 - 4.05529i) q^{74} +(15.2309 - 11.0659i) q^{75} +(1.38403 - 4.25961i) q^{76} +(4.83173 - 3.51046i) q^{77} +(4.98617 - 3.62267i) q^{78} +(-1.87668 + 5.77584i) q^{79} +(3.34556 - 2.43069i) q^{80} +(5.60280 + 4.07067i) q^{81} +(0.704940 + 2.16958i) q^{82} +(6.35410 + 4.61653i) q^{83} +(0.777889 - 2.39409i) q^{84} +(-5.28450 + 16.2640i) q^{85} +(-0.152506 - 0.469366i) q^{86} -5.78557 q^{87} -3.69111 q^{88} +(-5.81649 - 17.9013i) q^{89} +(1.93894 - 1.40872i) q^{90} +(-5.18570 - 3.76763i) q^{91} -0.993312 q^{92} +(7.96252 + 3.41057i) q^{93} -1.85410 q^{94} +(14.9842 + 10.8866i) q^{95} +(-1.25865 + 0.914463i) q^{96} +(-0.291845 - 0.898207i) q^{97} +4.38197 q^{98} -2.13921 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9} - 5 q^{10} + 6 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} - 23 q^{15} - 2 q^{16} + 5 q^{17} - 3 q^{18} - 2 q^{19} - 5 q^{20} + q^{21} - 6 q^{22} - 15 q^{23} - 3 q^{24} + 16 q^{25} + 18 q^{26} + 37 q^{27} + 6 q^{28} - 19 q^{29} - 2 q^{30} + 13 q^{31} - 8 q^{32} + 30 q^{33} + 5 q^{34} + 18 q^{36} - 40 q^{37} - 3 q^{38} + 30 q^{39} + 5 q^{40} - 7 q^{41} - q^{42} + 12 q^{43} + q^{44} - 31 q^{45} - 20 q^{46} - 12 q^{47} + 3 q^{48} + 6 q^{49} + 19 q^{50} - 22 q^{51} + 7 q^{52} + 9 q^{53} - 37 q^{54} - 13 q^{55} + 4 q^{56} + 28 q^{57} - q^{58} - 18 q^{59} - 23 q^{60} + 12 q^{61} - 3 q^{62} + 6 q^{63} - 2 q^{64} - 16 q^{65} + 10 q^{66} - 26 q^{67} - 50 q^{69} - 25 q^{71} - 3 q^{72} + 35 q^{73} - 5 q^{74} + 26 q^{75} + 3 q^{76} - 8 q^{77} + 15 q^{78} + 6 q^{79} + 5 q^{80} + 43 q^{81} - 13 q^{82} + 24 q^{83} + q^{84} - q^{85} + 8 q^{86} + 8 q^{87} + 14 q^{88} - 7 q^{89} - 4 q^{90} - 16 q^{91} - 10 q^{92} + 3 q^{93} + 12 q^{94} + 30 q^{95} + 2 q^{96} + 26 q^{97} + 44 q^{98} - 46 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9 - 5 * q^10 + 6 * q^11 - 2 * q^12 + 7 * q^13 + 4 * q^14 - 23 * q^15 - 2 * q^16 + 5 * q^17 - 3 * q^18 - 2 * q^19 - 5 * q^20 + q^21 - 6 * q^22 - 15 * q^23 - 3 * q^24 + 16 * q^25 + 18 * q^26 + 37 * q^27 + 6 * q^28 - 19 * q^29 - 2 * q^30 + 13 * q^31 - 8 * q^32 + 30 * q^33 + 5 * q^34 + 18 * q^36 - 40 * q^37 - 3 * q^38 + 30 * q^39 + 5 * q^40 - 7 * q^41 - q^42 + 12 * q^43 + q^44 - 31 * q^45 - 20 * q^46 - 12 * q^47 + 3 * q^48 + 6 * q^49 + 19 * q^50 - 22 * q^51 + 7 * q^52 + 9 * q^53 - 37 * q^54 - 13 * q^55 + 4 * q^56 + 28 * q^57 - q^58 - 18 * q^59 - 23 * q^60 + 12 * q^61 - 3 * q^62 + 6 * q^63 - 2 * q^64 - 16 * q^65 + 10 * q^66 - 26 * q^67 - 50 * q^69 - 25 * q^71 - 3 * q^72 + 35 * q^73 - 5 * q^74 + 26 * q^75 + 3 * q^76 - 8 * q^77 + 15 * q^78 + 6 * q^79 + 5 * q^80 + 43 * q^81 - 13 * q^82 + 24 * q^83 + q^84 - q^85 + 8 * q^86 + 8 * q^87 + 14 * q^88 - 7 * q^89 - 4 * q^90 - 16 * q^91 - 10 * q^92 + 3 * q^93 + 12 * q^94 + 30 * q^95 + 2 * q^96 + 26 * q^97 + 44 * q^98 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	1.25865	−	0.914463i	0.726682	−	0.527965i	−0.161830	−	0.986819i	$-0.551740\pi$
$3$	1.25865	−	0.914463i	0.726682	−	0.527965i	0.888512	+	0.458853i	$0.151740\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−4.13533			−1.84938			−0.924689	−	0.380724i	$-0.875675\pi$
$5$	−4.13533			−1.84938			−0.924689	+	0.380724i	$0.875675\pi$
$6$	1.55578			0.635143
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	0.811012	−	0.585030i	$-0.198917\pi$
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	−0.999994	+	0.00340203i	$0.998917\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.179093	+	0.551192i	−0.0596977	+	0.183731i
$10$	−3.34556	−	2.43069i	−1.05796	−	0.768651i
$11$	1.14062	+	3.51046i	0.343909	+	1.05844i	0.962165	+	0.272466i	$0.0878392\pi$
$11$	1.14062	+	3.51046i	0.343909	+	1.05844i	−0.618257	+	0.785976i	$0.712161\pi$
$12$	1.25865	+	0.914463i	0.363341	+	0.263983i
$13$	3.20494	−	2.32852i	0.888890	−	0.645817i	−0.0466981	−	0.998909i	$-0.514870\pi$
$13$	3.20494	−	2.32852i	0.888890	−	0.645817i	0.935588	+	0.353092i	$0.114870\pi$
$14$	0.500000	−	1.53884i	0.133631	−	0.411273i
$15$	−5.20494	+	3.78161i	−1.34391	+	0.976407i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.27789	−	3.93294i	0.309934	−	0.953877i	−0.667856	−	0.744290i	$-0.732788\pi$
$17$	1.27789	−	3.93294i	0.309934	−	0.953877i	0.977790	−	0.209587i	$-0.0672120\pi$
$18$	−0.468872	+	0.340655i	−0.110514	+	0.0802932i
$19$	−3.62344	−	2.63259i	−0.831275	−	0.603957i	0.0886446	−	0.996063i	$-0.471746\pi$
$19$	−3.62344	−	2.63259i	−0.831275	−	0.603957i	−0.919920	+	0.392107i	$0.871746\pi$
$20$	−1.27789	−	3.93294i	−0.285745	−	0.879431i
$21$	−2.03654	−	1.47963i	−0.444409	−	0.322882i
$22$	−1.14062	+	3.51046i	−0.243180	+	0.748432i
$23$	−0.306950	+	0.944696i	−0.0640036	+	0.196983i	−0.977945	−	0.208864i	$-0.933023\pi$
$23$	−0.306950	+	0.944696i	−0.0640036	+	0.196983i	0.913941	+	0.405847i	$0.133023\pi$
$24$	0.480762	+	1.47963i	0.0981351	+	0.302029i
$25$	12.1010			2.42020
$26$	3.96152			0.776919
$27$	1.72091	+	5.29643i	0.331190	+	1.01930i
$28$	1.30902	−	0.951057i	0.247381	−	0.179733i
$29$	−3.00855	−	2.18584i	−0.558673	−	0.405900i	0.272300	−	0.962212i	$-0.412216\pi$
$29$	−3.00855	−	2.18584i	−0.558673	−	0.405900i	−0.830973	+	0.556313i	$0.812216\pi$
$30$	−6.43366			−1.17462
$31$	2.85204	+	4.78183i	0.512241	+	0.858842i
$31$	2.85204	+	4.78183i	0.512241	+	0.858842i
$32$	−1.00000			−0.176777
$33$	4.64582	+	3.37538i	0.808733	+	0.587579i
$34$	3.34556	−	2.43069i	0.573758	−	0.416860i
$35$	2.06767	+	6.36363i	0.349500	+	1.07565i
$36$	−0.579557			−0.0965929
$37$	−6.89927			−1.13423			−0.567116	−	0.823638i	$-0.691941\pi$
$37$	−6.89927			−1.13423			−0.567116	+	0.823638i	$0.691941\pi$
$38$	−1.38403	−	4.25961i	−0.224520	−	0.691001i
$39$	1.90455	−	5.86160i	0.304972	−	0.938607i
$40$	1.27789	−	3.93294i	0.202052	−	0.621852i
$41$	1.84556	+	1.34087i	0.288227	+	0.209409i	0.722498	−	0.691373i	$-0.242994\pi$
$41$	1.84556	+	1.34087i	0.288227	+	0.209409i	−0.434271	+	0.900782i	$0.642994\pi$
$42$	−0.777889	−	2.39409i	−0.120031	−	0.369417i
$43$	−0.399266	−	0.290084i	−0.0608876	−	0.0442374i	0.556925	−	0.830563i	$-0.311981\pi$
$43$	−0.399266	−	0.290084i	−0.0608876	−	0.0442374i	−0.617813	+	0.786325i	$0.711981\pi$
$44$	−2.98617	+	2.16958i	−0.450182	+	0.327077i
$45$	0.740610	−	2.27936i	0.110404	−	0.339787i
$46$	−0.803607	+	0.583854i	−0.118485	+	0.0860846i
$47$	−1.50000	+	1.08981i	−0.218797	+	0.158966i	−0.691785	−	0.722103i	$-0.743175\pi$
$47$	−1.50000	+	1.08981i	−0.218797	+	0.158966i	0.472988	+	0.881069i	$0.343175\pi$
$48$	−0.480762	+	1.47963i	−0.0693920	+	0.213566i
$49$	3.54508	−	2.57565i	0.506441	−	0.367951i
$50$	9.78991	+	7.11278i	1.38450	+	1.00590i
$51$	−1.98811	−	6.11877i	−0.278391	−	0.856800i
$52$	3.20494	+	2.32852i	0.444445	+	0.322908i
$53$	−0.0524334	+	0.161373i	−0.00720228	+	0.0221663i	−0.954593	−	0.297913i	$-0.903710\pi$
$53$	−0.0524334	+	0.161373i	−0.00720228	+	0.0221663i	0.947391	+	0.320079i	$0.103710\pi$
$54$	−1.72091	+	5.29643i	−0.234187	+	0.720753i
$55$	−4.71683	−	14.5169i	−0.636017	−	1.95746i
$56$	1.61803			0.216219
$57$	−6.96805			−0.922941
$58$	−1.14916	−	3.53676i	−0.150892	−	0.464399i
$59$	−10.1301	+	7.35991i	−1.31882	+	0.958179i	−0.318874	+	0.947797i	$0.603305\pi$
$59$	−10.1301	+	7.35991i	−1.31882	+	0.958179i	−0.999946	+	0.0103822i	$0.996695\pi$
$60$	−5.20494	−	3.78161i	−0.671955	−	0.488204i
$61$	−3.34762			−0.428619			−0.214310	−	0.976766i	$-0.568750\pi$
$61$	−3.34762			−0.428619			−0.214310	+	0.976766i	$0.568750\pi$
$62$	−0.503344	+	5.54497i	−0.0639247	+	0.704211i
$63$	0.937743			0.118145
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−13.2535	+	9.62923i	−1.64389	+	1.19436i
$66$	1.77454	+	5.46149i	0.218431	+	0.672263i
$67$	1.47882			0.180667			0.0903335	−	0.995912i	$-0.471207\pi$
$67$	1.47882			0.180667			0.0903335	+	0.995912i	$0.471207\pi$
$68$	4.13533			0.501483
$69$	0.477546	+	1.46974i	0.0574898	+	0.176936i
$70$	−2.06767	+	6.36363i	−0.247134	+	0.760599i
$71$	2.55904	−	7.87592i	0.303702	−	0.934700i	−0.676456	−	0.736483i	$-0.736485\pi$
$71$	2.55904	−	7.87592i	0.303702	−	0.934700i	0.980158	−	0.198217i	$-0.0635149\pi$
$72$	−0.468872	−	0.340655i	−0.0552571	−	0.0401466i
$73$	−0.547152	−	1.68396i	−0.0640392	−	0.197093i	0.913918	−	0.405900i	$-0.133042\pi$
$73$	−0.547152	−	1.68396i	−0.0640392	−	0.197093i	−0.977957	+	0.208807i	$0.933042\pi$
$74$	−5.58162	−	4.05529i	−0.648851	−	0.471418i
$75$	15.2309	−	11.0659i	1.75871	−	1.27778i
$76$	1.38403	−	4.25961i	0.158759	−	0.488611i
$77$	4.83173	−	3.51046i	0.550626	−	0.400054i
$78$	4.98617	−	3.62267i	0.564573	−	0.410186i
$79$	−1.87668	+	5.77584i	−0.211143	+	0.649833i	0.788261	+	0.615340i	$0.210981\pi$
$79$	−1.87668	+	5.77584i	−0.211143	+	0.649833i	−0.999405	+	0.0344924i	$0.989019\pi$
$80$	3.34556	−	2.43069i	0.374045	−	0.271759i
$81$	5.60280	+	4.07067i	0.622533	+	0.452297i
$82$	0.704940	+	2.16958i	0.0778476	+	0.239590i
$83$	6.35410	+	4.61653i	0.697453	+	0.506729i	0.879102	−	0.476634i	$-0.158143\pi$
$83$	6.35410	+	4.61653i	0.697453	+	0.506729i	−0.181649	+	0.983364i	$0.558143\pi$
$84$	0.777889	−	2.39409i	0.0848746	−	0.261217i
$85$	−5.28450	+	16.2640i	−0.573184	+	1.76408i
$86$	−0.152506	−	0.469366i	−0.0164452	−	0.0506130i
$87$	−5.78557			−0.620279
$88$	−3.69111			−0.393474
$89$	−5.81649	−	17.9013i	−0.616547	−	1.89754i	−0.374204	−	0.927346i	$-0.622084\pi$
$89$	−5.81649	−	17.9013i	−0.616547	−	1.89754i	−0.242343	−	0.970191i	$-0.577916\pi$
$90$	1.93894	−	1.40872i	0.204382	−	0.148492i
$91$	−5.18570	−	3.76763i	−0.543609	−	0.394955i
$92$	−0.993312			−0.103560
$93$	7.96252	+	3.41057i	0.825675	+	0.353660i
$94$	−1.85410			−0.191236
$95$	14.9842	+	10.8866i	1.53734	+	1.11694i
$96$	−1.25865	+	0.914463i	−0.128460	+	0.0933320i
$97$	−0.291845	−	0.898207i	−0.0296324	−	0.0911991i	0.935147	−	0.354261i	$-0.115268\pi$
$97$	−0.291845	−	0.898207i	−0.0296324	−	0.0911991i	−0.964779	+	0.263062i	$0.915268\pi$
$98$	4.38197			0.442645
$99$	−2.13921			−0.214999
$100$	3.73941	+	11.5087i	0.373941	+	1.15087i
$101$	3.35612	−	10.3291i	0.333946	−	1.02778i	−0.633292	−	0.773913i	$-0.718297\pi$
$101$	3.35612	−	10.3291i	0.333946	−	1.02778i	0.967239	−	0.253869i	$-0.0817031\pi$
$102$	1.98811	−	6.11877i	0.196852	−	0.605849i
$103$	11.9134	+	8.65556i	1.17386	+	0.852857i	0.991466	−	0.130369i	$-0.0416161\pi$
$103$	11.9134	+	8.65556i	1.17386	+	0.852857i	0.182392	+	0.983226i	$0.441616\pi$
$104$	1.22418	+	3.76763i	0.120041	+	0.369447i
$105$	8.42177	+	6.11877i	0.821881	+	0.597131i
$106$	−0.137272	+	0.0997342i	−0.0133331	+	0.00968704i
$107$	2.96759	−	9.13332i	0.286888	−	0.882951i	−0.698938	−	0.715182i	$-0.746344\pi$
$107$	2.96759	−	9.13332i	0.286888	−	0.882951i	0.985826	−	0.167769i	$-0.0536562\pi$
$108$	−4.50541	+	3.27337i	−0.433533	+	0.314980i
$109$	−3.97548	+	2.88836i	−0.380782	+	0.276654i	−0.761668	−	0.647968i	$-0.775619\pi$
$109$	−3.97548	+	2.88836i	−0.380782	+	0.276654i	0.380886	+	0.924622i	$0.375619\pi$
$110$	4.71683	−	14.5169i	0.449732	−	1.38413i
$111$	−8.68376	+	6.30912i	−0.824226	+	0.598835i
$112$	1.30902	+	0.951057i	0.123690	+	0.0898664i
$113$	3.80126	+	11.6991i	0.357592	+	1.10056i	0.954491	+	0.298240i	$0.0963995\pi$
$113$	3.80126	+	11.6991i	0.357592	+	1.10056i	−0.596899	+	0.802317i	$0.703601\pi$
$114$	−5.63727	−	4.09572i	−0.527979	−	0.383599i
$115$	1.26934	−	3.90663i	0.118367	−	0.364296i
$116$	1.14916	−	3.53676i	0.106697	−	0.328380i
$117$	0.709481	+	2.18356i	0.0655916	+	0.201870i
$118$	−12.5214			−1.15269
$119$	−6.69111			−0.613373
$120$	−1.98811	−	6.11877i	−0.181489	−	0.558565i
$121$	−2.12311	+	1.54253i	−0.193010	+	0.140230i
$122$	−2.70828	−	1.96768i	−0.245196	−	0.178146i
$123$	3.54909			0.320011
$124$	−3.66646	+	4.19011i	−0.329258	+	0.376283i
$125$	−29.3650			−2.62648
$126$	0.758650	+	0.551192i	0.0675859	+	0.0491041i
$127$	8.26733	−	6.00656i	0.733606	−	0.532996i	−0.157096	−	0.987583i	$-0.550213\pi$
$127$	8.26733	−	6.00656i	0.733606	−	0.532996i	0.890702	+	0.454587i	$0.150213\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−0.767808			−0.0676017
$130$	−16.3822			−1.43682
$131$	−4.29647	−	13.2232i	−0.375384	−	1.15531i	−0.943219	−	0.332171i	$-0.892219\pi$
$131$	−4.29647	−	13.2232i	−0.375384	−	1.15531i	0.567835	−	0.823142i	$-0.307781\pi$
$132$	−1.77454	+	5.46149i	−0.154454	+	0.475361i
$133$	−2.23941	+	6.89220i	−0.194182	+	0.597630i
$134$	1.19639	+	0.869231i	0.103353	+	0.0750901i
$135$	−7.11655	−	21.9025i	−0.612495	−	1.88507i
$136$	3.34556	+	2.43069i	0.286879	+	0.208430i
$137$	0.329324	−	0.239268i	0.0281361	−	0.0204421i	−0.573628	−	0.819116i	$-0.694465\pi$
$137$	0.329324	−	0.239268i	0.0281361	−	0.0204421i	0.601764	+	0.798674i	$0.294465\pi$
$138$	−0.477546	+	1.46974i	−0.0406515	+	0.125112i
$139$	−14.9307	+	10.8478i	−1.26640	+	0.920094i	−0.999053	−	0.0435055i	$-0.986147\pi$
$139$	−14.9307	+	10.8478i	−1.26640	+	0.920094i	−0.267348	+	0.963600i	$0.586147\pi$
$140$	−5.41322	+	3.93294i	−0.457501	+	0.332394i
$141$	−0.891381	+	2.74339i	−0.0750678	+	0.231035i
$142$	6.69966	−	4.86759i	0.562223	−	0.408479i
$143$	11.8298	+	8.59485i	0.989257	+	0.718737i
$144$	−0.179093	−	0.551192i	−0.0149244	−	0.0459326i
$145$	12.4413	+	9.03917i	1.03320	+	0.750662i
$146$	0.547152	−	1.68396i	0.0452826	−	0.139365i
$147$	2.10668	−	6.48370i	0.173756	−	0.534766i
$148$	−2.13199	−	6.56159i	−0.175249	−	0.539360i
$149$	14.3755			1.17769			0.588845	−	0.808246i	$-0.299583\pi$
$149$	14.3755			1.17769			0.588845	+	0.808246i	$0.299583\pi$
$150$	18.8264			1.53717
$151$	4.54236	+	13.9799i	0.369652	+	1.13767i	0.947016	+	0.321185i	$0.104081\pi$
$151$	4.54236	+	13.9799i	0.369652	+	1.13767i	−0.577365	+	0.816486i	$0.695919\pi$
$152$	3.62344	−	2.63259i	0.293900	−	0.213531i
$153$	1.93894	+	1.40872i	0.156754	+	0.113889i
$154$	5.97234			0.481265
$155$	−11.7941	−	19.7745i	−0.947327	−	1.58832i
$156$	6.16325			0.493455
$157$	−0.996656	−	0.724113i	−0.0795418	−	0.0577905i	0.547304	−	0.836934i	$-0.315654\pi$
$157$	−0.996656	−	0.724113i	−0.0795418	−	0.0577905i	−0.626845	+	0.779144i	$0.715654\pi$
$158$	−4.91322	+	3.56967i	−0.390875	+	0.283987i
$159$	0.0815747	+	0.251061i	0.00646929	+	0.0199104i
$160$	4.13533			0.326927
$161$	1.60721			0.126666
$162$	2.14008	+	6.58649i	0.168141	+	0.517483i
$163$	−2.07101	+	6.37392i	−0.162214	+	0.499244i	−0.998820	−	0.0485612i	$-0.984536\pi$
$163$	−2.07101	+	6.37392i	−0.162214	+	0.499244i	0.836606	+	0.547805i	$0.184536\pi$
$164$	−0.704940	+	2.16958i	−0.0550465	+	0.169416i
$165$	−19.2120	−	13.9583i	−1.49565	−	1.08666i
$166$	2.42705	+	7.46969i	0.188376	+	0.579761i
$167$	7.61816	+	5.53492i	0.589511	+	0.428305i	0.842140	−	0.539258i	$-0.181295\pi$
$167$	7.61816	+	5.53492i	0.589511	+	0.428305i	−0.252629	+	0.967563i	$0.581295\pi$
$168$	2.03654	−	1.47963i	0.157122	−	0.114156i
$169$	0.832389	−	2.56183i	0.0640299	−	0.197064i
$170$	−13.8350	+	10.0517i	−1.06110	+	0.770931i
$171$	2.09999	−	1.52573i	0.160591	−	0.116676i
$172$	0.152506	−	0.469366i	0.0116285	−	0.0357888i
$173$	7.56573	−	5.49682i	0.575212	−	0.417916i	−0.261783	−	0.965127i	$-0.584310\pi$
$173$	7.56573	−	5.49682i	0.575212	−	0.417916i	0.836995	+	0.547211i	$0.184310\pi$
$174$	−4.68063	−	3.40067i	−0.354837	−	0.257805i
$175$	−6.05050	−	18.6215i	−0.457374	−	1.40765i
$176$	−2.98617	−	2.16958i	−0.225091	−	0.163538i
$177$	−6.01982	+	18.5271i	−0.452478	+	1.39258i
$178$	5.81649	−	17.9013i	0.435965	−	1.34176i
$179$	3.75411	+	11.5540i	0.280595	+	0.863583i	0.987684	+	0.156459i	$0.0500079\pi$
$179$	3.75411	+	11.5540i	0.280595	+	0.863583i	−0.707089	+	0.707124i	$0.749992\pi$
$180$	2.39666			0.178637
$181$	−8.50648			−0.632282			−0.316141	−	0.948712i	$-0.602387\pi$
$181$	−8.50648			−0.632282			−0.316141	+	0.948712i	$0.602387\pi$
$182$	−1.98076	−	6.09616i	−0.146824	−	0.451877i
$183$	−4.21349	+	3.06128i	−0.311470	+	0.226296i
$184$	−0.803607	−	0.583854i	−0.0592427	−	0.0430423i
$185$	28.5308			2.09762
$186$	4.43713	+	7.43946i	0.325346	+	0.545488i
$187$	15.2640			1.11621
$188$	−1.50000	−	1.08981i	−0.109399	−	0.0794828i
$189$	7.28991	−	5.29643i	0.530263	−	0.385258i
$190$	5.72344	+	17.6149i	0.415222	+	1.27792i
$191$	−2.75964			−0.199681			−0.0998403	−	0.995003i	$-0.531833\pi$
$191$	−2.75964			−0.199681			−0.0998403	+	0.995003i	$0.531833\pi$
$192$	−1.55578			−0.112279
$193$	−7.77802	−	23.9383i	−0.559874	−	1.72311i	−0.682712	−	0.730688i	$-0.739199\pi$
$193$	−7.77802	−	23.9383i	−0.559874	−	1.72311i	0.122838	−	0.992427i	$-0.460801\pi$
$194$	0.291845	−	0.898207i	0.0209533	−	0.0644875i
$195$	−7.87594	+	24.2397i	−0.564008	+	1.73584i
$196$	3.54508	+	2.57565i	0.253220	+	0.183975i
$197$	1.60668	+	4.94486i	0.114471	+	0.352306i	0.991836	−	0.127517i	$-0.0407007\pi$
$197$	1.60668	+	4.94486i	0.114471	+	0.352306i	−0.877365	+	0.479823i	$0.840701\pi$
$198$	−1.73066	−	1.25740i	−0.122992	−	0.0893593i
$199$	−5.94122	+	4.31655i	−0.421162	+	0.305992i	−0.778105	−	0.628134i	$-0.783819\pi$
$199$	−5.94122	+	4.31655i	−0.421162	+	0.305992i	0.356943	+	0.934126i	$0.383819\pi$
$200$	−3.73941	+	11.5087i	−0.264416	+	0.813790i
$201$	1.86132	−	1.35233i	0.131288	−	0.0953860i
$202$	8.78643	−	6.38372i	0.618211	−	0.449157i
$203$	−1.85938	+	5.72259i	−0.130503	+	0.401647i
$204$	5.20494	−	3.78161i	0.364419	−	0.264766i
$205$	−7.63199	−	5.54497i	−0.533041	−	0.387277i
$206$	4.55050	+	14.0050i	0.317048	+	0.975774i
$207$	−0.465736	−	0.338377i	−0.0323709	−	0.0235188i
$208$	−1.22418	+	3.76763i	−0.0848815	+	0.261238i
$209$	5.10862	−	15.7227i	0.353371	−	1.08756i
$210$	3.21683	+	9.90038i	0.221982	+	0.683191i
$211$	−7.72943			−0.532116			−0.266058	−	0.963957i	$-0.585721\pi$
$211$	−7.72943			−0.532116			−0.266058	+	0.963957i	$0.585721\pi$
$212$	−0.169678			−0.0116535
$213$	−3.98130	−	12.2532i	−0.272794	−	0.839574i
$214$	7.76926	−	5.64470i	0.531096	−	0.385864i
$215$	1.65110	+	1.19959i	0.112604	+	0.0818117i
$216$	−5.56899			−0.378922
$217$	5.93246	−	6.77975i	0.402722	−	0.460239i
$218$	−4.91396			−0.332816
$219$	−2.22859	−	1.61917i	−0.150594	−	0.109413i
$220$	12.3488	−	8.97194i	0.832557	−	0.604888i
$221$	−5.06239	−	15.5804i	−0.340533	−	1.04805i
$222$	−10.7337			−0.720400
$223$	−9.81950			−0.657562			−0.328781	−	0.944406i	$-0.606638\pi$
$223$	−9.81950			−0.657562			−0.328781	+	0.944406i	$0.606638\pi$
$224$	0.500000	+	1.53884i	0.0334077	+	0.102818i
$225$	−2.16720	+	6.66997i	−0.144480	+	0.444664i
$226$	−3.80126	+	11.6991i	−0.252856	+	0.778211i
$227$	0.0762929	+	0.0554300i	0.00506374	+	0.00367902i	0.590314	−	0.807174i	$-0.299004\pi$
$227$	0.0762929	+	0.0554300i	0.00506374	+	0.00367902i	−0.585251	+	0.810853i	$0.699004\pi$
$228$	−2.15325	−	6.62701i	−0.142602	−	0.438885i
$229$	13.6643	+	9.92771i	0.902963	+	0.656041i	0.939225	−	0.343301i	$-0.111545\pi$
$229$	13.6643	+	9.92771i	0.902963	+	0.656041i	−0.0362620	+	0.999342i	$0.511545\pi$
$230$	3.32318	−	2.41443i	0.219124	−	0.159203i
$231$	2.87127	−	8.83687i	0.188916	−	0.581423i
$232$	3.00855	−	2.18584i	0.197521	−	0.143507i
$233$	−11.8436	+	8.60489i	−0.775901	+	0.563725i	−0.903746	−	0.428069i	$-0.859194\pi$
$233$	−11.8436	+	8.60489i	−0.775901	+	0.563725i	0.127845	+	0.991794i	$0.459194\pi$
$234$	−0.709481	+	2.18356i	−0.0463802	+	0.142744i
$235$	6.20300	−	4.50674i	0.404639	−	0.293988i
$236$	−10.1301	−	7.35991i	−0.659410	−	0.479090i
$237$	2.91970	+	8.98592i	0.189655	+	0.583698i
$238$	−5.41322	−	3.93294i	−0.350887	−	0.254934i
$239$	−4.27789	+	13.1660i	−0.276714	+	0.851637i	0.712047	+	0.702132i	$0.247768\pi$
$239$	−4.27789	+	13.1660i	−0.276714	+	0.851637i	−0.988761	+	0.149505i	$0.952232\pi$
$240$	1.98811	−	6.11877i	0.128332	−	0.394965i
$241$	−0.0786883	−	0.242178i	−0.00506876	−	0.0156000i	0.948490	−	0.316807i	$-0.102611\pi$
$241$	−0.0786883	−	0.242178i	−0.00506876	−	0.0156000i	−0.953559	+	0.301207i	$0.902611\pi$
$242$	−2.62431			−0.168697
$243$	−5.93254			−0.380572
$244$	−1.03447	−	3.18378i	−0.0662253	−	0.203821i
$245$	−14.6601	+	10.6512i	−0.936600	+	0.680480i
$246$	2.87127	+	2.08610i	0.183066	+	0.133005i
$247$	−17.7430			−1.12896
$248$	−5.42912	+	1.23478i	−0.344749	+	0.0784086i
$249$	12.2192			0.774362
$250$	−23.7568	−	17.2603i	−1.50251	−	1.09164i
$251$	20.2869	−	14.7393i	1.28050	−	0.930336i	0.280930	−	0.959728i	$-0.409357\pi$
$251$	20.2869	−	14.7393i	1.28050	−	0.930336i	0.999568	+	0.0293922i	$0.00935718\pi$
$252$	0.289779	+	0.891847i	0.0182543	+	0.0561811i
$253$	−3.66643			−0.230506
$254$	10.2190			0.641196
$255$	8.22150	+	25.3032i	0.514850	+	1.58455i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.86934	−	11.9086i	0.241363	−	0.742838i	−0.754851	−	0.655896i	$-0.772291\pi$
$257$	3.86934	−	11.9086i	0.241363	−	0.742838i	0.996213	−	0.0869411i	$-0.0277092\pi$
$258$	−0.621170	−	0.451306i	−0.0386723	−	0.0280971i
$259$	3.44963	+	10.6169i	0.214350	+	0.659701i
$260$	−13.2535	−	9.62923i	−0.821947	−	0.597179i
$261$	1.74362	−	1.26682i	0.107928	−	0.0784140i
$262$	4.29647	−	13.2232i	0.265437	−	0.816930i
$263$	11.8245	−	8.59101i	0.729130	−	0.529744i	−0.160158	−	0.987091i	$-0.551200\pi$
$263$	11.8245	−	8.59101i	0.729130	−	0.529744i	0.889288	+	0.457347i	$0.151200\pi$
$264$	−4.64582	+	3.37538i	−0.285930	+	0.207741i
$265$	0.216830	−	0.667333i	0.0133197	−	0.0409939i
$266$	−5.86286	+	4.25961i	−0.359475	+	0.261174i
$267$	−23.6910	−	17.2125i	−1.44987	−	1.05339i
$268$	0.456982	+	1.40644i	0.0279146	+	0.0859123i
$269$	−7.21489	−	5.24193i	−0.439900	−	0.319606i	0.345695	−	0.938347i	$-0.387643\pi$
$269$	−7.21489	−	5.24193i	−0.439900	−	0.319606i	−0.785595	+	0.618741i	$0.787643\pi$
$270$	7.11655	−	21.9025i	0.433100	−	1.33294i
$271$	−8.28582	+	25.5011i	−0.503328	+	1.54908i	0.300236	+	0.953865i	$0.402935\pi$
$271$	−8.28582	+	25.5011i	−0.503328	+	1.54908i	−0.803564	+	0.595219i	$0.797065\pi$
$272$	1.27789	+	3.93294i	0.0774834	+	0.238469i
$273$	−9.97234			−0.603554
$274$	0.407067			0.0245918
$275$	13.8026	+	42.4800i	0.832327	+	2.56164i
$276$	−1.25023	+	0.908347i	−0.0752552	+	0.0546761i
$277$	5.17501	+	3.75986i	0.310936	+	0.225908i	0.732298	−	0.680984i	$-0.238448\pi$
$277$	5.17501	+	3.75986i	0.310936	+	0.225908i	−0.421362	+	0.906893i	$0.638448\pi$
$278$	−18.4553			−1.10688
$279$	−3.14648	+	0.715626i	−0.188375	+	0.0428434i
$280$	−6.69111			−0.399870
$281$	−7.87033	−	5.71813i	−0.469505	−	0.341115i	0.327744	−	0.944767i	$-0.393712\pi$
$281$	−7.87033	−	5.71813i	−0.469505	−	0.341115i	−0.797248	+	0.603652i	$0.793712\pi$
$282$	−2.33367	+	1.69551i	−0.138968	+	0.100966i
$283$	−2.50702	−	7.71580i	−0.149027	−	0.458657i	0.848480	−	0.529227i	$-0.177518\pi$
$283$	−2.50702	−	7.71580i	−0.149027	−	0.458657i	−0.997507	+	0.0705703i	$0.977518\pi$
$284$	8.28123			0.491401
$285$	28.8152			1.70687
$286$	4.51858	+	13.9068i	0.267189	+	0.822323i
$287$	1.14062	−	3.51046i	0.0673284	−	0.207216i
$288$	0.179093	−	0.551192i	0.0105532	−	0.0324793i
$289$	−0.0817033	−	0.0593609i	−0.00480608	−	0.00349182i
$290$	4.75217	+	14.6257i	0.279057	+	0.858849i
$291$	−1.18871	−	0.863647i	−0.0696833	−	0.0506279i
$292$	1.43246	−	1.04074i	0.0838285	−	0.0609049i
$293$	−3.33024	+	10.2494i	−0.194555	+	0.598778i	0.805427	+	0.592695i	$0.201936\pi$
$293$	−3.33024	+	10.2494i	−0.194555	+	0.598778i	−0.999981	+	0.00608278i	$0.998064\pi$
$294$	5.51536	−	4.00715i	0.321662	−	0.233701i
$295$	41.8912	−	30.4357i	2.43900	−	1.77204i
$296$	2.13199	−	6.56159i	0.123919	−	0.381385i
$297$	−16.6300	+	12.0824i	−0.964969	+	0.701091i
$298$	11.6301	+	8.44973i	0.673711	+	0.489480i
$299$	1.21599	+	3.74244i	0.0703226	+	0.216431i
$300$	15.2309	+	11.0659i	0.879357	+	0.638890i
$301$	−0.246760	+	0.759450i	−0.0142230	+	0.0437740i
$302$	−4.54236	+	13.9799i	−0.261383	+	0.804455i
$303$	−5.22137	−	16.0697i	−0.299960	−	0.923182i
$304$	4.47882			0.256878
$305$	13.8435			0.792679
$306$	0.740610	+	2.27936i	0.0423378	+	0.130302i
$307$	18.3455	−	13.3288i	1.04703	−	0.760713i	0.0753859	−	0.997154i	$-0.475981\pi$
$307$	18.3455	−	13.3288i	1.04703	−	0.760713i	0.971646	+	0.236441i	$0.0759811\pi$
$308$	4.83173	+	3.51046i	0.275313	+	0.200027i
$309$	22.9099			1.30330
$310$	2.08150	−	22.9303i	0.118221	−	1.30235i
$311$	−11.8398			−0.671375			−0.335687	−	0.941973i	$-0.608969\pi$
$311$	−11.8398			−0.671375			−0.335687	+	0.941973i	$0.608969\pi$
$312$	4.98617	+	3.62267i	0.282286	+	0.205093i
$313$	−21.7119	+	15.7746i	−1.22723	+	0.891634i	−0.996679	−	0.0814272i	$-0.974052\pi$
$313$	−21.7119	+	15.7746i	−1.22723	+	0.891634i	−0.230549	+	0.973061i	$0.574052\pi$
$314$	−0.380689	−	1.17164i	−0.0214835	−	0.0661194i
$315$	−3.87788			−0.218494
$316$	−6.07308			−0.341637
$317$	6.70147	+	20.6250i	0.376392	+	1.15842i	0.942535	+	0.334109i	$0.108435\pi$
$317$	6.70147	+	20.6250i	0.376392	+	1.15842i	−0.566142	+	0.824307i	$0.691565\pi$
$318$	−0.0815747	+	0.251061i	−0.00457448	+	0.0140788i
$319$	4.24169	−	13.0546i	0.237489	−	0.730916i
$320$	3.34556	+	2.43069i	0.187022	+	0.135880i
$321$	−4.61692	−	14.2094i	−0.257691	−	0.793092i
$322$	1.30026	+	0.944696i	0.0724608	+	0.0526459i
$323$	−14.9842	+	10.8866i	−0.833741	+	0.605748i
$324$	−2.14008	+	6.58649i	−0.118893	+	0.365916i
$325$	38.7829	−	28.1775i	2.15129	−	1.56300i
$326$	−5.42198	+	3.93930i	−0.300296	+	0.218177i
$327$	−2.36244	+	7.27086i	−0.130643	+	0.402079i
$328$	−1.84556	+	1.34087i	−0.101904	+	0.0740374i
$329$	2.42705	+	1.76336i	0.133808	+	0.0972169i
$330$	−7.33834	−	22.5851i	−0.403962	−	1.24327i
$331$	−14.9811	−	10.8844i	−0.823438	−	0.598263i	0.0942570	−	0.995548i	$-0.469952\pi$
$331$	−14.9811	−	10.8844i	−0.823438	−	0.598263i	−0.917695	+	0.397285i	$0.869952\pi$
$332$	−2.42705	+	7.46969i	−0.133202	+	0.409953i
$333$	1.23561	−	3.80282i	0.0677110	−	0.208393i
$334$	2.90988	+	8.95569i	0.159222	+	0.490033i
$335$	−6.11543			−0.334122
$336$	2.51730			0.137330
$337$	−1.53641	−	4.72858i	−0.0836936	−	0.257582i	0.900449	−	0.434962i	$-0.143238\pi$
$337$	−1.53641	−	4.72858i	−0.0836936	−	0.257582i	−0.984143	+	0.177379i	$0.943238\pi$
$338$	2.17922	−	1.58330i	0.118534	−	0.0861200i
$339$	15.4828	+	11.2489i	0.840912	+	0.610958i
$340$	−17.1010			−0.927431
$341$	−13.5333	+	15.4662i	−0.732871	+	0.837540i
$342$	2.59573			0.140361
$343$	−14.8992	−	10.8249i	−0.804480	−	0.584489i
$344$	0.399266	−	0.290084i	0.0215270	−	0.0156403i
$345$	−1.97481	−	6.07785i	−0.106320	−	0.327221i
$346$	9.35176			0.502753
$347$	3.74642			0.201119			0.100559	−	0.994931i	$-0.467937\pi$
$347$	3.74642			0.201119			0.100559	+	0.994931i	$0.467937\pi$
$348$	−1.78784	−	5.50241i	−0.0958383	−	0.294960i
$349$	8.04848	−	24.7707i	0.430825	−	1.32594i	−0.466480	−	0.884532i	$-0.654478\pi$
$349$	8.04848	−	24.7707i	0.430825	−	1.32594i	0.897305	−	0.441412i	$-0.145522\pi$
$350$	6.05050	−	18.6215i	0.323413	−	0.995362i
$351$	17.8483	+	12.9675i	0.952671	+	0.692156i
$352$	−1.14062	−	3.51046i	−0.0607950	−	0.187108i
$353$	−25.3145	−	18.3920i	−1.34735	−	0.978910i	−0.999139	−	0.0414950i	$-0.986788\pi$
$353$	−25.3145	−	18.3920i	−1.34735	−	0.978910i	−0.348215	−	0.937415i	$-0.613212\pi$
$354$	−15.7601	+	11.4504i	−0.837640	+	0.608581i
$355$	−10.5825	+	32.5696i	−0.561660	+	1.72861i
$356$	15.2278	−	11.0636i	0.807071	−	0.586371i
$357$	−8.42177	+	6.11877i	−0.445727	+	0.323840i
$358$	−3.75411	+	11.5540i	−0.198411	+	0.610646i
$359$	−2.19111	+	1.59194i	−0.115642	+	0.0840192i	−0.644103	−	0.764939i	$-0.722769\pi$
$359$	−2.19111	+	1.59194i	−0.115642	+	0.0840192i	0.528461	+	0.848958i	$0.322769\pi$
$360$	1.93894	+	1.40872i	0.102191	+	0.0742462i
$361$	0.327515	+	1.00799i	0.0172376	+	0.0530520i
$362$	−6.88189	−	4.99998i	−0.361704	−	0.262793i
$363$	−1.26167	+	3.88301i	−0.0662203	+	0.203805i
$364$	1.98076	−	6.09616i	0.103820	−	0.319525i
$365$	2.26265	+	6.96374i	0.118433	+	0.364499i
$366$	−5.20815			−0.272235
$367$	−23.1077			−1.20621			−0.603106	−	0.797661i	$-0.706070\pi$
$367$	−23.1077			−1.20621			−0.603106	+	0.797661i	$0.706070\pi$
$368$	−0.306950	−	0.944696i	−0.0160009	−	0.0492457i
$369$	−1.06961	+	0.777114i	−0.0556814	+	0.0404549i
$370$	23.0819	+	16.7700i	1.19997	+	0.871829i
$371$	0.274545			0.0142537
$372$	−0.783091	+	8.62673i	−0.0406014	+	0.447275i
$373$	29.7285			1.53928			0.769642	−	0.638475i	$-0.220435\pi$
$373$	29.7285			1.53928			0.769642	+	0.638475i	$0.220435\pi$
$374$	12.3488	+	8.97194i	0.638542	+	0.463928i
$375$	−36.9602	+	26.8532i	−1.90862	+	1.38669i
$376$	−0.572949	−	1.76336i	−0.0295476	−	0.0909381i
$377$	−14.7320			−0.758736
$378$	9.01082			0.463467
$379$	−3.92376	−	12.0761i	−0.201550	−	0.620307i	−0.999837	−	0.0180302i	$-0.994261\pi$
$379$	−3.92376	−	12.0761i	−0.201550	−	0.620307i	0.798288	−	0.602276i	$-0.205739\pi$
$380$	−5.72344	+	17.6149i	−0.293606	+	0.903627i
$381$	4.91289	−	15.1203i	0.251695	−	0.774638i
$382$	−2.23260	−	1.62208i	−0.114230	−	0.0829926i
$383$	−7.27789	−	22.3990i	−0.371883	−	1.14454i	−0.945558	−	0.325454i	$-0.894483\pi$
$383$	−7.27789	−	22.3990i	−0.371883	−	1.14454i	0.573675	−	0.819083i	$-0.305517\pi$
$384$	−1.25865	−	0.914463i	−0.0642302	−	0.0466660i
$385$	−19.9808	+	14.5169i	−1.01832	+	0.739850i
$386$	7.77802	−	23.9383i	0.395891	−	1.21843i
$387$	0.231398	−	0.168120i	0.0117626	−	0.00854604i
$388$	0.764061	−	0.555123i	0.0387893	−	0.0281821i
$389$	1.29792	−	3.99458i	0.0658070	−	0.202533i	−0.912746	−	0.408527i	$-0.866043\pi$
$389$	1.29792	−	3.99458i	0.0658070	−	0.202533i	0.978553	+	0.205994i	$0.0660427\pi$
$390$	−20.6195	+	14.9809i	−1.04411	+	0.758589i
$391$	3.32318	+	2.41443i	0.168061	+	0.122103i
$392$	1.35410	+	4.16750i	0.0683925	+	0.210490i
$393$	−17.4998	−	12.7144i	−0.882750	−	0.641356i
$394$	−1.60668	+	4.94486i	−0.0809434	+	0.249118i
$395$	7.76072	−	23.8850i	0.390484	−	1.20179i
$396$	−0.661052	−	2.03451i	−0.0332191	−	0.102238i
$397$	−2.48096			−0.124516			−0.0622580	−	0.998060i	$-0.519830\pi$
$397$	−2.48096			−0.124516			−0.0622580	+	0.998060i	$0.519830\pi$
$398$	−7.34375			−0.368109
$399$	3.48403	+	10.7227i	0.174419	+	0.536808i
$400$	−9.78991	+	7.11278i	−0.489495	+	0.355639i
$401$	3.35938	+	2.44074i	0.167760	+	0.121884i	0.668497	−	0.743715i	$-0.266938\pi$
$401$	3.35938	+	2.44074i	0.167760	+	0.121884i	−0.500738	+	0.865599i	$0.666938\pi$
$402$	2.30072			0.114749
$403$	20.2752	+	8.68444i	1.00998	+	0.432603i
$404$	10.8606			0.540337
$405$	−23.1695	−	16.8336i	−1.15130	−	0.836468i
$406$	−4.86793	+	3.53676i	−0.241591	+	0.175526i
$407$	−7.86942	−	24.2196i	−0.390072	−	1.20052i
$408$	6.43366			0.318514
$409$	−8.88004			−0.439090			−0.219545	−	0.975602i	$-0.570457\pi$
$409$	−8.88004			−0.439090			−0.219545	+	0.975602i	$0.570457\pi$
$410$	−2.91516	−	8.97194i	−0.143970	−	0.443093i
$411$	0.195702	−	0.602310i	0.00965329	−	0.0297098i
$412$	−4.55050	+	14.0050i	−0.224187	+	0.689976i
$413$	16.3908	+	11.9086i	0.806537	+	0.585983i
$414$	−0.177895	−	0.547505i	−0.00874308	−	0.0269084i
$415$	−26.2763	−	19.0909i	−1.28985	−	0.937134i
$416$	−3.20494	+	2.32852i	−0.157135	+	0.114165i
$417$	−8.87260	+	27.3071i	−0.434493	+	1.33723i
$418$	13.3745	−	9.71717i	0.654170	−	0.475282i
$419$	−7.17154	+	5.21043i	−0.350352	+	0.254546i	−0.749017	−	0.662551i	$-0.769474\pi$
$419$	−7.17154	+	5.21043i	−0.350352	+	0.254546i	0.398664	+	0.917097i	$0.369474\pi$
$420$	−3.21683	+	9.90038i	−0.156965	+	0.483089i
$421$	−9.36686	+	6.80542i	−0.456513	+	0.331676i	−0.792162	−	0.610311i	$-0.791044\pi$
$421$	−9.36686	+	6.80542i	−0.456513	+	0.331676i	0.335649	+	0.941987i	$0.391044\pi$
$422$	−6.25324	−	4.54324i	−0.304403	−	0.221162i
$423$	−0.332057	−	1.02197i	−0.0161452	−	0.0496897i
$424$	−0.137272	−	0.0997342i	−0.00666654	−	0.00484352i
$425$	15.4637	−	47.5924i	0.750101	−	2.30857i
$426$	3.98130	−	12.2532i	0.192895	−	0.593668i
$427$	1.67381	+	5.15146i	0.0810014	+	0.249297i
$428$	9.60334			0.464195
$429$	22.7492			1.09834
$430$	0.630664	+	1.94098i	0.0304133	+	0.0936026i
$431$	21.1076	−	15.3356i	1.01672	−	0.738688i	0.0511099	−	0.998693i	$-0.483724\pi$
$431$	21.1076	−	15.3356i	1.01672	−	0.738688i	0.965607	+	0.260005i	$0.0837241\pi$
$432$	−4.50541	−	3.27337i	−0.216767	−	0.157490i
$433$	6.62901			0.318570			0.159285	−	0.987233i	$-0.449081\pi$
$433$	6.62901			0.318570			0.159285	+	0.987233i	$0.449081\pi$
$434$	8.78450	−	1.99792i	0.421669	−	0.0959031i
$435$	23.9253			1.14713
$436$	−3.97548	−	2.88836i	−0.190391	−	0.138327i
$437$	3.59921	−	2.61498i	0.172174	−	0.125091i
$438$	−0.851246	−	2.61987i	−0.0406741	−	0.125182i
$439$	21.1272			1.00834			0.504172	−	0.863603i	$-0.331798\pi$
$439$	21.1272			1.00834			0.504172	+	0.863603i	$0.331798\pi$
$440$	15.2640			0.727682
$441$	0.784780	+	2.41530i	0.0373705	+	0.115014i
$442$	5.06239	−	15.5804i	0.240793	−	0.741085i
$443$	1.96953	−	6.06160i	0.0935753	−	0.287995i	−0.893304	−	0.449452i	$-0.851619\pi$
$443$	1.96953	−	6.06160i	0.0935753	−	0.287995i	0.986880	+	0.161457i	$0.0516193\pi$
$444$	−8.68376	−	6.30912i	−0.412113	−	0.299418i
$445$	24.0531	+	74.0280i	1.14023	+	3.50926i
$446$	−7.94414	−	5.77176i	−0.376166	−	0.273301i
$447$	18.0938	−	13.1459i	0.855806	−	0.621779i
$448$	−0.500000	+	1.53884i	−0.0236228	+	0.0727034i
$449$	−2.61296	+	1.89843i	−0.123313	+	0.0895923i	−0.647732	−	0.761868i	$-0.724283\pi$
$449$	−2.61296	+	1.89843i	−0.123313	+	0.0895923i	0.524419	+	0.851460i	$0.324283\pi$
$450$	−5.67381	+	4.12227i	−0.267466	+	0.194325i
$451$	−2.60201	+	8.00817i	−0.122524	+	0.377090i
$452$	−9.95183	+	7.23043i	−0.468095	+	0.340091i
$453$	18.5014	+	13.4420i	0.869270	+	0.631562i
$454$	0.0291413	+	0.0896876i	0.00136767	+	0.00420925i
$455$	21.4446	+	15.5804i	1.00534	+	0.730421i
$456$	2.15325	−	6.62701i	0.100835	−	0.310338i
$457$	−7.33565	+	22.5768i	−0.343147	+	1.05610i	0.619421	+	0.785059i	$0.287368\pi$
$457$	−7.33565	+	22.5768i	−0.343147	+	1.05610i	−0.962568	+	0.271040i	$0.912632\pi$
$458$	5.21930	+	16.0634i	0.243882	+	0.750592i
$459$	23.0297			1.07493
$460$	4.10768			0.191522
$461$	4.54187	+	13.9784i	0.211536	+	0.651041i	0.999381	+	0.0351678i	$0.0111966\pi$
$461$	4.54187	+	13.9784i	0.211536	+	0.651041i	−0.787845	+	0.615873i	$0.788803\pi$
$462$	7.51709	−	5.46149i	0.349727	−	0.254091i
$463$	10.5701	+	7.67961i	0.491233	+	0.356902i	0.805658	−	0.592381i	$-0.201812\pi$
$463$	10.5701	+	7.67961i	0.491233	+	0.356902i	−0.314425	+	0.949282i	$0.601812\pi$
$464$	3.71877			0.172639
$465$	−32.9277	−	14.1038i	−1.52698	−	0.654050i
$466$	−14.6395			−0.678163
$467$	7.91657	+	5.75172i	0.366335	+	0.266158i	0.755690	−	0.654930i	$-0.227302\pi$
$467$	7.91657	+	5.75172i	0.366335	+	0.266158i	−0.389355	+	0.921088i	$0.627302\pi$
$468$	−1.85745	+	1.34951i	−0.0858605	+	0.0623813i
$469$	−0.739412	−	2.27568i	−0.0341429	−	0.105081i
$470$	7.66733			0.353668
$471$	−1.91662			−0.0883130
$472$	−3.86934	−	11.9086i	−0.178101	−	0.548137i
$473$	0.562917	−	1.73248i	0.0258830	−	0.0796596i
$474$	−2.91970	+	8.98592i	−0.134106	+	0.412737i
$475$	−43.8473	−	31.8569i	−2.01185	−	1.46170i
$476$	−2.06767	−	6.36363i	−0.0947714	−	0.291676i
$477$	−0.0795572	−	0.0578017i	−0.00364267	−	0.00264656i
$478$	−11.1997	+	8.13703i	−0.512260	+	0.372179i
$479$	−3.35084	+	10.3128i	−0.153104	+	0.471205i	−0.997964	−	0.0637826i	$-0.979684\pi$
$479$	−3.35084	+	10.3128i	−0.153104	+	0.471205i	0.844860	+	0.534987i	$0.179684\pi$
$480$	5.20494	−	3.78161i	0.237572	−	0.172606i
$481$	−22.1117	+	16.0651i	−1.00821	+	0.732506i
$482$	0.0786883	−	0.242178i	0.00358415	−	0.0110309i
$483$	2.02292	−	1.46974i	0.0920460	−	0.0668753i
$484$	−2.12311	−	1.54253i	−0.0965049	−	0.0701149i
$485$	1.20688	+	3.71439i	0.0548015	+	0.168662i
$486$	−4.79952	−	3.48706i	−0.217711	−	0.158176i
$487$	11.2158	−	34.5187i	0.508237	−	1.56419i	−0.287023	−	0.957924i	$-0.592666\pi$
$487$	11.2158	−	34.5187i	0.508237	−	1.56419i	0.795260	−	0.606269i	$-0.207334\pi$
$488$	1.03447	−	3.18378i	0.0468284	−	0.144123i
$489$	3.22203	+	9.91639i	0.145705	+	0.448435i
$490$	−18.1209			−0.818619
$491$	21.3211			0.962209			0.481105	−	0.876663i	$-0.340236\pi$
$491$	21.3211			0.962209			0.481105	+	0.876663i	$0.340236\pi$
$492$	1.09673	+	3.37538i	0.0494444	+	0.152174i
$493$	−12.4413	+	9.03917i	−0.560330	+	0.407104i
$494$	−14.3544	−	10.4291i	−0.645833	−	0.469225i
$495$	8.84635			0.397614
$496$	−5.11803	−	2.19220i	−0.229807	−	0.0984326i
$497$	−13.3993			−0.601041
$498$	9.88557	+	7.18228i	0.442983	+	0.321846i
$499$	30.1562	−	21.9097i	1.34997	−	0.980814i	0.350962	−	0.936390i	$-0.385855\pi$
$499$	30.1562	−	21.9097i	1.34997	−	0.980814i	0.999013	−	0.0444246i	$-0.0141454\pi$
$500$	−9.07428	−	27.9277i	−0.405814	−	1.24897i
$501$	14.6501			0.654517
$502$	25.0760			1.11920
$503$	9.37087	+	28.8406i	0.417826	+	1.28594i	0.909698	+	0.415270i	$0.136313\pi$
$503$	9.37087	+	28.8406i	0.417826	+	1.28594i	−0.491872	+	0.870667i	$0.663687\pi$
$504$	−0.289779	+	0.891847i	−0.0129078	+	0.0397260i
$505$	−13.8787	+	42.7142i	−0.617593	+	1.90076i
$506$	−2.96620	−	2.15507i	−0.131864	−	0.0958046i
$507$	−1.29501	−	3.98563i	−0.0575135	−	0.177008i
$508$	8.26733	+	6.00656i	0.366803	+	0.266498i
$509$	−21.3468	+	15.5094i	−0.946180	+	0.687440i	−0.949900	−	0.312553i	$-0.898816\pi$
$509$	−21.3468	+	15.5094i	−0.946180	+	0.687440i	0.00372000	+	0.999993i	$0.498816\pi$
$510$	−8.22150	+	25.3032i	−0.364054	+	1.12044i
$511$	−2.31777	+	1.68396i	−0.102532	+	0.0744940i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	7.70767	−	23.7218i	0.340302	−	1.04734i
$514$	10.1301	−	7.35991i	0.446817	−	0.324632i
$515$	−49.2657	−	35.7936i	−2.17091	−	1.57726i
$516$	−0.237266	−	0.730229i	−0.0104450	−	0.0321465i
$517$	−5.53667	−	4.02262i	−0.243502	−	0.176915i
$518$	−3.44963	+	10.6169i	−0.151568	+	0.466479i
$519$	4.49597	−	13.8372i	0.197351	−	0.607384i
$520$	−5.06239	−	15.5804i	−0.222000	−	0.683247i
$521$	−27.4596			−1.20303			−0.601513	−	0.798863i	$-0.705435\pi$
$521$	−27.4596			−1.20303			−0.601513	+	0.798863i	$0.705435\pi$
$522$	2.15524			0.0943322
$523$	−5.32116	−	16.3769i	−0.232678	−	0.716110i	−0.997421	−	0.0717742i	$-0.977134\pi$
$523$	−5.32116	−	16.3769i	−0.232678	−	0.716110i	0.764743	−	0.644336i	$-0.222866\pi$
$524$	11.2483	−	8.17236i	0.491384	−	0.357011i
$525$	−24.6441	−	17.9050i	−1.07556	−	0.781439i
$526$	14.6159			0.637283
$527$	22.4512	−	5.10623i	0.977990	−	0.222431i
$528$	−5.74255			−0.249912
$529$	17.8092	+	12.9391i	0.774311	+	0.562570i
$530$	0.567667	−	0.412434i	0.0246579	−	0.0179150i
$531$	−2.24250	−	6.90171i	−0.0973163	−	0.299509i
$532$	−7.24689			−0.314192
$533$	9.03716			0.391443
$534$	−9.04917	−	27.8505i	−0.391596	−	1.20521i
$535$	−12.2720	+	37.7693i	−0.530565	+	1.63291i
$536$	−0.456982	+	1.40644i	−0.0197386	+	0.0607492i
$537$	15.2908	+	11.1094i	0.659846	+	0.479406i
$538$	−2.75584	−	8.48161i	−0.118813	−	0.365668i
$539$	13.0853	+	9.50703i	0.563624	+	0.409497i
$540$	18.6314	−	13.5365i	0.801767	−	0.582518i
$541$	−0.966725	+	2.97528i	−0.0415628	+	0.127917i	−0.969685	−	0.244359i	$-0.921423\pi$
$541$	−0.966725	+	2.97528i	−0.0415628	+	0.127917i	0.928122	+	0.372276i	$0.121423\pi$
$542$	−21.6926	+	15.7606i	−0.931776	+	0.676975i
$543$	−10.7067	+	7.77886i	−0.459468	+	0.333823i
$544$	−1.27789	+	3.93294i	−0.0547890	+	0.168623i
$545$	16.4399	−	11.9443i	0.704210	−	0.511638i
$546$	−8.06780	−	5.86160i	−0.345270	−	0.250853i
$547$	9.92070	+	30.5328i	0.424179	+	1.30549i	0.903779	+	0.428000i	$0.140782\pi$
$547$	9.92070	+	30.5328i	0.424179	+	1.30549i	−0.479600	+	0.877487i	$0.659218\pi$
$548$	0.329324	+	0.239268i	0.0140680	+	0.0102210i
$549$	0.599536	−	1.84518i	0.0255876	−	0.0787504i
$550$	−13.8026	+	42.4800i	−0.588544	+	1.81135i
$551$	5.14690	+	15.8405i	0.219265	+	0.674829i
$552$	−1.54537			−0.0657754
$553$	9.82645			0.417863
$554$	1.97668	+	6.08359i	0.0839810	+	0.258467i
$555$	35.9103	−	26.0903i	1.52431	−	1.10747i
$556$	−14.9307	−	10.8478i	−0.633201	−	0.460047i
$557$	−39.3743			−1.66834			−0.834172	−	0.551505i	$-0.814054\pi$
$557$	−39.3743			−1.66834			−0.834172	+	0.551505i	$0.814054\pi$
$558$	−2.96619	−	1.27050i	−0.125569	−	0.0537847i
$559$	−1.95509			−0.0826916
$560$	−5.41322	−	3.93294i	−0.228750	−	0.166197i
$561$	19.2120	−	13.9583i	0.811132	−	0.589322i
$562$	−3.00620	−	9.25213i	−0.126809	−	0.390278i
$563$	−43.9055			−1.85040			−0.925198	−	0.379485i	$-0.876101\pi$
$563$	−43.9055			−1.85040			−0.925198	+	0.379485i	$0.876101\pi$
$564$	−2.88457			−0.121462
$565$	−15.7195	−	48.3796i	−0.661324	−	2.03534i
$566$	2.50702	−	7.71580i	0.105378	−	0.324319i
$567$	3.46272	−	10.6572i	0.145421	−	0.447559i
$568$	6.69966	+	4.86759i	0.281111	+	0.204239i
$569$	0.626832	+	1.92919i	0.0262782	+	0.0808759i	0.963336	−	0.268300i	$-0.0864617\pi$
$569$	0.626832	+	1.92919i	0.0262782	+	0.0808759i	−0.937057	+	0.349176i	$0.886462\pi$
$570$	23.3120	+	16.9372i	0.976433	+	0.709420i
$571$	−29.3872	+	21.3511i	−1.22982	+	0.893514i	−0.996876	−	0.0789768i	$-0.974835\pi$
$571$	−29.3872	+	21.3511i	−1.22982	+	0.893514i	−0.232940	+	0.972491i	$0.574835\pi$
$572$	−4.51858	+	13.9068i	−0.188931	+	0.581471i
$573$	−3.47342	+	2.52359i	−0.145104	+	0.105424i
$574$	2.98617	−	2.16958i	0.124640	−	0.0905566i
$575$	−3.71440	+	11.4318i	−0.154901	+	0.476737i
$576$	0.468872	−	0.340655i	0.0195363	−	0.0141940i
$577$	−9.45645	−	6.87051i	−0.393677	−	0.286023i	0.373284	−	0.927717i	$-0.378232\pi$
$577$	−9.45645	−	6.87051i	−0.393677	−	0.286023i	−0.766961	+	0.641694i	$0.778232\pi$
$578$	−0.0312079	−	0.0960480i	−0.00129808	−	0.00399507i
$579$	−31.6805	−	23.0172i	−1.31660	−	0.956563i
$580$	−4.75217	+	14.6257i	−0.197323	+	0.607298i
$581$	3.92705	−	12.0862i	0.162922	−	0.501421i
$582$	−0.454046	−	1.39741i	−0.0188208	−	0.0579245i
$583$	−0.626300			−0.0259387
$584$	1.77062			0.0732688
$585$	−2.93394	−	9.02974i	−0.121304	−	0.373334i
$586$	−8.71869	+	6.33450i	−0.360166	+	0.261676i
$587$	26.4283	+	19.2013i	1.09081	+	0.792522i	0.979536	−	0.201268i	$-0.0645061\pi$
$587$	26.4283	+	19.2013i	1.09081	+	0.792522i	0.111276	+	0.993790i	$0.464506\pi$
$588$	6.81736			0.281143
$589$	2.25439	−	24.8349i	0.0928905	−	1.02331i
$590$	51.7803			2.13176
$591$	6.54414	+	4.75459i	0.269190	+	0.195578i
$592$	5.58162	−	4.05529i	0.229403	−	0.166671i
$593$	1.72831	+	5.31919i	0.0709732	+	0.218433i	0.980251	−	0.197756i	$-0.0633654\pi$
$593$	1.72831	+	5.31919i	0.0709732	+	0.218433i	−0.909278	+	0.416189i	$0.863365\pi$
$594$	−20.5558			−0.843414
$595$	27.6700			1.13436
$596$	4.44228	+	13.6719i	0.181963	+	0.560025i
$597$	−3.53059	+	10.8660i	−0.144497	+	0.444718i
$598$	−1.21599	+	3.74244i	−0.0497256	+	0.153040i
$599$	−28.9455	−	21.0301i	−1.18268	−	0.859267i	−0.190208	−	0.981744i	$-0.560916\pi$
$599$	−28.9455	−	21.0301i	−1.18268	−	0.859267i	−0.992471	+	0.122477i	$0.960916\pi$
$600$	5.81769	+	17.9050i	0.237506	+	0.730969i
$601$	25.2107	+	18.3167i	1.02837	+	0.747153i	0.967981	−	0.251022i	$-0.0807668\pi$
$601$	25.2107	+	18.3167i	1.02837	+	0.747153i	0.0603861	+	0.998175i	$0.480767\pi$
$602$	−0.646027	+	0.469366i	−0.0263301	+	0.0191299i
$603$	−0.264847	+	0.815115i	−0.0107854	+	0.0331941i
$604$	−11.8920	+	8.64008i	−0.483881	+	0.351560i
$605$	8.77976	−	6.37887i	0.356948	−	0.259338i
$606$	5.22137	−	16.0697i	0.212104	−	0.652788i
$607$	6.53192	−	4.74572i	0.265122	−	0.192623i	−0.447280	−	0.894394i	$-0.647607\pi$
$607$	6.53192	−	4.74572i	0.265122	−	0.192623i	0.712402	+	0.701771i	$0.247607\pi$
$608$	3.62344	+	2.63259i	0.146950	+	0.106765i
$609$	2.89279	+	8.90308i	0.117222	+	0.360771i
$610$	11.1997	+	8.13703i	0.453461	+	0.329459i
$611$	−2.26975	+	6.98557i	−0.0918243	+	0.282606i
$612$	−0.740610	+	2.27936i	−0.0299374	+	0.0921377i
$613$	−14.4099	−	44.3492i	−0.582012	−	1.79125i	−0.610954	−	0.791666i	$-0.709214\pi$
$613$	−14.4099	−	44.3492i	−0.582012	−	1.79125i	0.0289423	−	0.999581i	$-0.490786\pi$
$614$	22.6763			0.915139
$615$	−14.6767			−0.591821
$616$	1.84556	+	5.68004i	0.0743596	+	0.228855i
$617$	15.2449	−	11.0760i	0.613735	−	0.445905i	−0.236992	−	0.971512i	$-0.576162\pi$
$617$	15.2449	−	11.0760i	0.613735	−	0.445905i	0.850728	+	0.525607i	$0.176162\pi$
$618$	18.5345	+	13.4661i	0.745568	+	0.541687i
$619$	−24.0731			−0.967579			−0.483789	−	0.875184i	$-0.660740\pi$
$619$	−24.0731			−0.967579			−0.483789	+	0.875184i	$0.660740\pi$
$620$	15.1620	−	17.3275i	0.608923	−	0.695890i
$621$	−5.53175			−0.221981
$622$	−9.57862	−	6.95927i	−0.384068	−	0.279041i
$623$	−24.6391	+	17.9013i	−0.987143	+	0.717202i
$624$	1.90455	+	5.86160i	0.0762429	+	0.234652i
$625$	60.9290			2.43716
$626$	−26.8374			−1.07264
$627$	−7.94787	−	24.4610i	−0.317407	−	0.976880i
$628$	0.380689	−	1.17164i	0.0151911	−	0.0467535i
$629$	−8.81649	+	27.1344i	−0.351537	+	1.08192i
$630$	−3.13727	−	2.27936i	−0.124992	−	0.0908119i
$631$	−2.28120	−	7.02082i	−0.0908132	−	0.279494i	0.895327	−	0.445410i	$-0.146942\pi$
$631$	−2.28120	−	7.02082i	−0.0908132	−	0.279494i	−0.986140	+	0.165916i	$0.946942\pi$
$632$	−4.91322	−	3.56967i	−0.195438	−	0.141994i
$633$	−9.72865	+	7.06828i	−0.386679	+	0.280939i
$634$	−6.70147	+	20.6250i	−0.266149	+	0.819124i
$635$	−34.1882	+	24.8391i	−1.35672	+	0.985712i
$636$	−0.213565	+	0.155164i	−0.00846841	+	0.00615266i
$637$	5.36431	−	16.5096i	0.212542	−	0.654136i
$638$	11.1049	−	8.06817i	0.439646	−	0.319422i
$639$	3.88283	+	2.82104i	0.153603	+	0.111599i
$640$	1.27789	+	3.93294i	0.0505130	+	0.155463i
$641$	22.0208	+	15.9991i	0.869770	+	0.631925i	0.930525	−	0.366228i	$-0.119351\pi$
$641$	22.0208	+	15.9991i	0.869770	+	0.631925i	−0.0607551	+	0.998153i	$0.519351\pi$
$642$	4.61692	−	14.2094i	0.182215	−	0.560801i
$643$	3.13620	−	9.65224i	0.123680	−	0.380647i	−0.869978	−	0.493090i	$-0.835867\pi$
$643$	3.13620	−	9.65224i	0.123680	−	0.380647i	0.993658	+	0.112443i	$0.0358674\pi$
$644$	0.496656	+	1.52855i	0.0195710	+	0.0602333i
$645$	3.17514			0.125021
$646$	−18.5214			−0.728716
$647$	−6.54146	−	20.1325i	−0.257171	−	0.791492i	−0.993394	−	0.114753i	$-0.963392\pi$
$647$	−6.54146	−	20.1325i	−0.257171	−	0.791492i	0.736223	−	0.676739i	$-0.236608\pi$
$648$	−5.60280	+	4.07067i	−0.220099	+	0.159911i
$649$	−37.3912	−	27.1663i	−1.46773	−	1.06637i
$650$	47.9384			1.88030
$651$	1.26707	−	13.9583i	0.0496603	−	0.547071i
$652$	−6.70193			−0.262468
$653$	12.5300	+	9.10356i	0.490336	+	0.356250i	0.805314	−	0.592849i	$-0.201997\pi$
$653$	12.5300	+	9.10356i	0.490336	+	0.356250i	−0.314978	+	0.949099i	$0.601997\pi$
$654$	−6.18496	+	4.49364i	−0.241851	+	0.175715i
$655$	17.7673	+	54.6822i	0.694227	+	2.13661i
$656$	−2.28123			−0.0890672
$657$	1.02618			0.0400349
$658$	0.927051	+	2.85317i	0.0361402	+	0.111228i
$659$	−10.3489	+	31.8506i	−0.403136	+	1.24072i	0.519306	+	0.854588i	$0.326191\pi$
$659$	−10.3489	+	31.8506i	−0.403136	+	1.24072i	−0.922442	+	0.386136i	$0.873809\pi$
$660$	7.33834	−	22.5851i	0.285644	−	0.879123i
$661$	32.1373	+	23.3491i	1.24999	+	0.908174i	0.998222	−	0.0596123i	$-0.0189865\pi$
$661$	32.1373	+	23.3491i	1.24999	+	0.908174i	0.251773	+	0.967786i	$0.418986\pi$
$662$	−5.72229	−	17.6114i	−0.222403	−	0.684486i
$663$	−20.6195	−	14.9809i	−0.800795	−	0.581811i
$664$	−6.35410	+	4.61653i	−0.246587	+	0.179156i
$665$	9.26072	−	28.5016i	0.359115	−	1.10524i
$666$	3.23487	−	2.35027i	0.125349	−	0.0910711i
$667$	2.98843	−	2.17122i	0.115712	−	0.0840699i
$668$	−2.90988	+	8.95569i	−0.112587	+	0.346506i
$669$	−12.3593	+	8.97957i	−0.477839	+	0.347170i
$670$	−4.94749	−	3.59456i	−0.191138	−	0.138870i
$671$	−3.81835	−	11.7517i	−0.147406	−	0.453669i
$672$	2.03654	+	1.47963i	0.0785612	+	0.0570780i
$673$	4.17567	−	12.8514i	0.160960	−	0.495385i	−0.837756	−	0.546046i	$-0.816133\pi$
$673$	4.17567	−	12.8514i	0.160960	−	0.495385i	0.998716	+	0.0506602i	$0.0161326\pi$
$674$	1.53641	−	4.72858i	0.0591803	−	0.182138i
$675$	20.8248	+	64.0920i	0.801545	+	2.46690i
$676$	2.69367			0.103603
$677$	31.6226			1.21535			0.607677	−	0.794184i	$-0.292101\pi$
$677$	31.6226			1.21535			0.607677	+	0.794184i	$0.292101\pi$
$678$	5.91391	+	18.2012i	0.227123	+	0.699011i
$679$	−1.23628	+	0.898207i	−0.0474439	+	0.0344700i
$680$	−13.8350	−	10.0517i	−0.530548	−	0.385465i
$681$	0.146715			0.00562212
$682$	−20.0395	+	4.55771i	−0.767351	+	0.174524i
$683$	45.1151			1.72628			0.863141	−	0.504962i	$-0.168494\pi$
$683$	45.1151			1.72628			0.863141	+	0.504962i	$0.168494\pi$
$684$	2.09999	+	1.52573i	0.0802953	+	0.0583379i
$685$	−1.36187	+	0.989454i	−0.0520343	+	0.0378051i
$686$	−5.69098	−	17.5150i	−0.217283	−	0.668728i
$687$	26.2771			1.00253
$688$	0.493520			0.0188153
$689$	0.207716	+	0.639284i	0.00791335	+	0.0243548i
$690$	1.97481	−	6.07785i	0.0751799	−	0.231380i
$691$	−7.63071	+	23.4849i	−0.290286	+	0.893408i	0.694478	+	0.719514i	$0.255635\pi$
$691$	−7.63071	+	23.4849i	−0.290286	+	0.893408i	−0.984764	+	0.173895i	$0.944365\pi$
$692$	7.56573	+	5.49682i	0.287606	+	0.208958i
$693$	1.06961	+	3.29191i	0.0406309	+	0.125049i
$694$	3.03092	+	2.20209i	0.115052	+	0.0835903i
$695$	61.7432	−	44.8591i	2.34205	−	1.70160i
$696$	1.78784	−	5.50241i	0.0677679	−	0.208568i
$697$	7.63199	−	5.54497i	0.289082	−	0.210031i
$698$	21.0712	−	15.3091i	0.797556	−	0.579459i
$699$	−7.03812	+	21.6611i	−0.266206	+	0.819298i
$700$	15.8404	−	11.5087i	0.598711	−	0.434989i
$701$	20.6833	+	15.0273i	0.781199	+	0.567574i	0.905339	−	0.424690i	$-0.139617\pi$
$701$	20.6833	+	15.0273i	0.781199	+	0.567574i	−0.124139	+	0.992265i	$0.539617\pi$
$702$	6.81744	+	20.9819i	0.257308	+	0.791912i
$703$	24.9991	+	18.1629i	0.942859	+	0.685027i
$704$	1.14062	−	3.51046i	0.0429886	−	0.132305i
$705$	3.68616	−	11.3448i	0.138829	−	0.427271i
$706$	−9.66927	−	29.7590i	−0.363908	−	1.11999i
$707$	−17.5729			−0.660896
$708$	−19.4806			−0.732124
$709$	−2.03021	−	6.24834i	−0.0762461	−	0.234662i	0.905668	−	0.423987i	$-0.139370\pi$
$709$	−2.03021	−	6.24834i	−0.0762461	−	0.234662i	−0.981914	+	0.189326i	$0.939370\pi$
$710$	−27.7053	+	20.1291i	−1.03976	+	0.755432i
$711$	−2.84749	−	2.06883i	−0.106789	−	0.0775870i
$712$	18.8226			0.705406
$713$	−5.39281	+	1.22652i	−0.201962	+	0.0459336i
$714$	−10.4099			−0.389580
$715$	−48.9201	−	35.5426i	−1.82951	−	1.32922i
$716$	−9.82838	+	7.14074i	−0.367304	+	0.266862i
$717$	6.65544	+	20.4833i	0.248552	+	0.764964i
$718$	−2.70836			−0.101075
$719$	−52.8053			−1.96931			−0.984653	−	0.174523i	$-0.944162\pi$
$719$	−52.8053			−1.96931			−0.984653	+	0.174523i	$0.944162\pi$
$720$	0.740610	+	2.27936i	0.0276009	+	0.0849468i
$721$	7.36286	−	22.6605i	0.274207	−	0.843923i
$722$	−0.327515	+	1.00799i	−0.0121889	+	0.0375134i
$723$	−0.320504	−	0.232859i	−0.0119197	−	0.00866014i
$724$	−2.62865	−	8.09014i	−0.0976929	−	0.300668i
$725$	−36.4064	−	26.4508i	−1.35210	−	0.982358i
$726$	−3.30308	+	2.39983i	−0.122589	+	0.0890660i
$727$	15.7990	−	48.6243i	0.585952	−	1.80338i	−0.00946067	−	0.999955i	$-0.503011\pi$
$727$	15.7990	−	48.6243i	0.585952	−	1.80338i	0.595413	−	0.803420i	$-0.296989\pi$
$728$	5.18570	−	3.76763i	0.192195	−	0.139638i
$729$	−24.2754	+	17.6371i	−0.899088	+	0.653226i
$730$	−2.26265	+	6.96374i	−0.0837446	+	0.257739i
$731$	−1.65110	+	1.19959i	−0.0610682	+	0.0443686i
$732$	−4.21349	−	3.06128i	−0.155735	−	0.113148i
$733$	−15.2390	−	46.9007i	−0.562864	−	1.73232i	−0.674215	−	0.738535i	$-0.735518\pi$
$733$	−15.2390	−	46.9007i	−0.562864	−	1.73232i	0.111351	−	0.993781i	$-0.464482\pi$
$734$	−18.6945	−	13.5824i	−0.690027	−	0.501334i
$735$	−8.71183	+	26.8123i	−0.321341	+	0.988985i
$736$	0.306950	−	0.944696i	0.0113143	−	0.0348220i
$737$	1.68677	+	5.19135i	0.0621330	+	0.191226i
$738$	−1.32210			−0.0486673
$739$	21.3614			0.785790			0.392895	−	0.919583i	$-0.371474\pi$
$739$	21.3614			0.785790			0.392895	+	0.919583i	$0.371474\pi$
$740$	8.81649	+	27.1344i	0.324101	+	0.997480i
$741$	−22.3322	+	16.2253i	−0.820393	+	0.596051i
$742$	0.222111	+	0.161373i	0.00815397	+	0.00592420i
$743$	−39.9128			−1.46426			−0.732130	−	0.681165i	$-0.761474\pi$
$743$	−39.9128			−1.46426			−0.732130	+	0.681165i	$0.761474\pi$
$744$	−5.70420	+	6.51888i	−0.209126	+	0.238994i
$745$	−59.4476			−2.17799
$746$	24.0509	+	17.4740i	0.880565	+	0.639768i
$747$	−3.68257	+	2.67554i	−0.134738	+	0.0978929i
$748$	4.71683	+	14.5169i	0.172464	+	0.530791i
$749$	−15.5385			−0.567765
$750$	−45.6854			−1.66819
$751$	10.9531	+	33.7102i	0.399685	+	1.23010i	0.925253	+	0.379351i	$0.123853\pi$
$751$	10.9531	+	33.7102i	0.399685	+	1.23010i	−0.525568	+	0.850751i	$0.676147\pi$
$752$	0.572949	−	1.76336i	0.0208933	−	0.0643030i
$753$	12.0556	−	37.1032i	0.439329	−	1.35212i
$754$	−11.9184	−	8.65924i	−0.434043	−	0.315351i
$755$	−18.7842	−	57.8117i	−0.683626	−	2.10398i
$756$	7.28991	+	5.29643i	0.265131	+	0.192629i
$757$	−11.1591	+	8.10757i	−0.405585	+	0.294675i	−0.771812	−	0.635851i	$-0.780649\pi$
$757$	−11.1591	+	8.10757i	−0.405585	+	0.294675i	0.366227	+	0.930526i	$0.380649\pi$
$758$	3.92376	−	12.0761i	0.142517	−	0.438623i
$759$	−4.61475	+	3.35281i	−0.167505	+	0.121699i
$760$	−14.9842	+	10.8866i	−0.543532	+	0.394899i
$761$	−9.08229	+	27.9524i	−0.329233	+	1.01327i	0.640261	+	0.768158i	$0.278826\pi$
$761$	−9.08229	+	27.9524i	−0.329233	+	1.01327i	−0.969494	+	0.245117i	$0.921174\pi$
$762$	12.8621	−	9.34487i	0.465945	−	0.338529i
$763$	6.43246	+	4.67346i	0.232871	+	0.169190i
$764$	−0.852776	−	2.62457i	−0.0308523	−	0.0949537i
$765$	−8.01817	−	5.82554i	−0.289898	−	0.210623i
$766$	7.27789	−	22.3990i	0.262961	−	0.809310i
$767$	−15.3285	+	47.1762i	−0.553479	+	1.70343i
$768$	−0.480762	−	1.47963i	−0.0173480	−	0.0533916i
$769$	−15.1984			−0.548067			−0.274033	−	0.961720i	$-0.588358\pi$
$769$	−15.1984			−0.548067			−0.274033	+	0.961720i	$0.588358\pi$
$770$	−24.6976			−0.890041
$771$	−6.01982	−	18.5271i	−0.216799	−	0.667238i
$772$	20.3631	−	14.7947i	0.732884	−	0.532472i
$773$	42.9850	+	31.2304i	1.54606	+	1.12328i	0.946386	+	0.323039i	$0.104704\pi$
$773$	42.9850	+	31.2304i	1.54606	+	1.12328i	0.599678	+	0.800242i	$0.295296\pi$
$774$	0.286023			0.0102809
$775$	34.5125	+	57.8649i	1.23972	+	2.07857i
$776$	0.944431			0.0339031
$777$	14.0506	+	10.2084i	0.504063	+	0.366223i
$778$	3.39799	−	2.46878i	0.121824	−	0.0885102i
$779$	−3.15730	−	9.71717i	−0.113122	−	0.348154i
$780$	−25.4871			−0.912584
$781$	30.5670			1.09377
$782$	1.26934	+	3.90663i	0.0453916	+	0.139701i
$783$	6.39968	−	19.6962i	0.228706	−	0.703884i
$784$	−1.35410	+	4.16750i	−0.0483608	+	0.148839i
$785$	4.12151	+	2.99445i	0.147103	+	0.106876i
$786$	−6.68434	−	20.5723i	−0.238423	−	0.733790i
$787$	23.3312	+	16.9511i	0.831669	+	0.604243i	0.920031	−	0.391845i	$-0.128163\pi$
$787$	23.3312	+	16.9511i	0.831669	+	0.604243i	−0.0883620	+	0.996088i	$0.528163\pi$
$788$	−4.20635	+	3.05609i	−0.149845	+	0.108869i
$789$	7.02676	−	21.6261i	0.250159	−	0.769911i
$790$	20.3178	−	14.7618i	0.722876	−	0.525200i
$791$	16.1024	−	11.6991i	0.572535	−	0.415971i
$792$	0.661052	−	2.03451i	0.0234895	−	0.0722932i
$793$	−10.7289	+	7.79502i	−0.380995	+	0.276809i
$794$	−2.00714	−	1.45827i	−0.0712307	−	0.0517522i
$795$	−0.337339	−	1.03822i	−0.0119642	−	0.0368219i
$796$	−5.94122	−	4.31655i	−0.210581	−	0.152996i
$797$	−6.34446	+	19.5262i	−0.224732	+	0.691655i	0.773587	+	0.633691i	$0.218461\pi$
$797$	−6.34446	+	19.5262i	−0.224732	+	0.691655i	−0.998319	+	0.0579638i	$0.981539\pi$
$798$	−3.48403	+	10.7227i	−0.123333	+	0.379581i
$799$	2.36934	+	7.29207i	0.0838211	+	0.257975i
$800$	−12.1010			−0.427835
$801$	10.9088			0.385442
$802$	1.28317	+	3.94919i	0.0453103	+	0.139451i
$803$	5.28738	−	3.84150i	0.186587	−	0.135564i
$804$	1.86132	+	1.35233i	0.0656438	+	0.0476930i
$805$	−6.64636			−0.234254
$806$	11.2984	+	18.9433i	0.397969	+	0.667250i
$807$	−13.8746			−0.488408
$808$	8.78643	+	6.38372i	0.309106	+	0.224578i
$809$	16.6458	−	12.0939i	0.585236	−	0.425199i	−0.255372	−	0.966843i	$-0.582198\pi$
$809$	16.6458	−	12.0939i	0.585236	−	0.425199i	0.840608	+	0.541644i	$0.182198\pi$
$810$	−8.84994	−	27.2373i	−0.310955	−	0.957022i
$811$	34.9206			1.22623			0.613114	−	0.789995i	$-0.289917\pi$
$811$	34.9206			1.22623			0.613114	+	0.789995i	$0.289917\pi$
$812$	−6.01709			−0.211159
$813$	12.8909	+	39.6741i	0.452103	+	1.39143i
$814$	7.86942	−	24.2196i	0.275823	−	0.848895i
$815$	8.56432	−	26.3583i	0.299995	−	0.923290i
$816$	5.20494	+	3.78161i	0.182209	+	0.132383i
$817$	0.683048	+	2.10221i	0.0238968	+	0.0735469i
$818$	−7.18410	−	5.21955i	−0.251186	−	0.182497i
$819$	3.00541	−	2.18356i	0.105018	−	0.0762997i
$820$	2.91516	−	8.97194i	0.101802	−	0.313314i
$821$	−14.9403	+	10.8547i	−0.521419	+	0.378833i	−0.817138	−	0.576442i	$-0.804441\pi$
$821$	−14.9403	+	10.8547i	−0.521419	+	0.378833i	0.295719	+	0.955275i	$0.404441\pi$
$822$	0.512355	−	0.372248i	0.0178704	−	0.0129836i
$823$	−2.83770	+	8.73354i	−0.0989160	+	0.304432i	−0.988254	−	0.152817i	$-0.951165\pi$
$823$	−2.83770	+	8.73354i	−0.0989160	+	0.304432i	0.889338	+	0.457250i	$0.151165\pi$
$824$	−11.9134	+	8.65556i	−0.415021	+	0.301531i
$825$	56.2190	+	40.8455i	1.95729	+	1.42206i
$826$	6.26072	+	19.2685i	0.217838	+	0.670437i
$827$	19.4603	+	14.1387i	0.676701	+	0.491652i	0.872262	−	0.489040i	$-0.162653\pi$
$827$	19.4603	+	14.1387i	0.676701	+	0.491652i	−0.195561	+	0.980692i	$0.562653\pi$
$828$	0.177895	−	0.547505i	0.00618229	−	0.0190271i
$829$	14.8682	−	45.7596i	0.516393	−	1.58930i	−0.264339	−	0.964430i	$-0.585154\pi$
$829$	14.8682	−	45.7596i	0.516393	−	1.58930i	0.780732	−	0.624866i	$-0.214846\pi$
$830$	−10.0367	−	30.8897i	−0.348378	−	1.07220i
$831$	9.95178			0.345224
$832$	−3.96152			−0.137341
$833$	−5.59966	−	17.2340i	−0.194017	−	0.597123i
$834$	−23.2288	+	16.8767i	−0.804346	+	0.584392i
$835$	−31.5037	−	22.8887i	−1.09023	−	0.792098i
$836$	16.5318			0.571766
$837$	−20.4185	+	23.3347i	−0.705767	+	0.806566i
$838$	−8.86451			−0.306219
$839$	−3.42132	−	2.48573i	−0.118117	−	0.0858170i	0.527159	−	0.849767i	$-0.323257\pi$
$839$	−3.42132	−	2.48573i	−0.118117	−	0.0858170i	−0.645275	+	0.763950i	$0.723257\pi$
$840$	−8.42177	+	6.11877i	−0.290579	+	0.211118i
$841$	−4.68803	−	14.4283i	−0.161656	−	0.497526i
$842$	−11.5781			−0.399007
$843$	−15.1350			−0.521278
$844$	−2.38853	−	7.35112i	−0.0822164	−	0.253036i
$845$	−3.44221	+	10.5940i	−0.118415	+	0.364445i
$846$	0.332057	−	1.02197i	0.0114163	−	0.0351359i
$847$	3.43526	+	2.49586i	0.118037	+	0.0857589i
$848$	−0.0524334	−	0.161373i	−0.00180057	−	0.00554158i
$849$	−10.2113	−	7.41892i	−0.350450	−	0.254617i
$850$	40.4845	−	29.4137i	1.38861	−	1.00888i
$851$	2.11773	−	6.51771i	0.0725949	−	0.223424i
$852$	10.4232	−	7.57288i	0.357092	−	0.259443i
$853$	35.1668	−	25.5502i	1.20409	−	0.874823i	0.209409	−	0.977828i	$-0.432846\pi$
$853$	35.1668	−	25.5502i	1.20409	−	0.874823i	0.994681	+	0.103006i	$0.0328459\pi$
$854$	−1.67381	+	5.15146i	−0.0572766	+	0.176279i
$855$	−8.68417	+	6.30942i	−0.296993	+	0.215778i
$856$	7.76926	+	5.64470i	0.265548	+	0.192932i
$857$	−0.577699	−	1.77797i	−0.0197338	−	0.0607344i	0.940705	−	0.339227i	$-0.110165\pi$
$857$	−0.577699	−	1.77797i	−0.0197338	−	0.0607344i	−0.960438	+	0.278492i	$0.910165\pi$
$858$	18.4045	+	13.3717i	0.628320	+	0.456501i
$859$	−14.4239	+	44.3921i	−0.492136	+	1.51464i	0.329237	+	0.944247i	$0.393208\pi$
$859$	−14.4239	+	44.3921i	−0.492136	+	1.51464i	−0.821373	+	0.570391i	$0.806792\pi$
$860$	−0.630664	+	1.94098i	−0.0215055	+	0.0661870i
$861$	−1.77454	−	5.46149i	−0.0604763	−	0.186127i
$862$	26.0904			0.888643
$863$	−34.4041			−1.17113			−0.585565	−	0.810625i	$-0.699127\pi$
$863$	−34.4041			−1.17113			−0.585565	+	0.810625i	$0.699127\pi$
$864$	−1.72091	−	5.29643i	−0.0585467	−	0.180188i
$865$	−31.2868	+	22.7312i	−1.06378	+	0.772884i
$866$	5.36298	+	3.89644i	0.182242	+	0.132406i
$867$	−0.157119			−0.00533605
$868$	8.28115	+	3.54705i	0.281081	+	0.120395i
$869$	−22.4164			−0.760425
$870$	19.3560	+	14.0629i	0.656229	+	0.476778i
$871$	4.73954	−	3.44348i	0.160593	−	0.116678i
$872$	−1.51850	−	4.67346i	−0.0514228	−	0.158263i
$873$	0.547352			0.0185251
$874$	4.44887			0.150485
$875$	14.6825	+	45.1880i	0.496359	+	1.52763i
$876$	0.851246	−	2.61987i	0.0287609	−	0.0885171i
$877$	15.7513	−	48.4775i	0.531884	−	1.63697i	−0.218404	−	0.975859i	$-0.570085\pi$
$877$	15.7513	−	48.4775i	0.531884	−	1.63697i	0.750288	−	0.661112i	$-0.229915\pi$
$878$	17.0922	+	12.4182i	0.576835	+	0.419095i
$879$	5.18112	+	15.9458i	0.174755	+	0.537840i
$880$	12.3488	+	8.97194i	0.416279	+	0.302444i
$881$	32.1915	−	23.3885i	1.08456	−	0.787978i	0.106087	−	0.994357i	$-0.466168\pi$
$881$	32.1915	−	23.3885i	1.08456	−	0.787978i	0.978472	+	0.206379i	$0.0661678\pi$
$882$	−0.784780	+	2.41530i	−0.0264249	+	0.0813275i
$883$	29.6091	−	21.5123i	0.996427	−	0.723946i	0.0351076	−	0.999384i	$-0.488823\pi$
$883$	29.6091	−	21.5123i	0.996427	−	0.723946i	0.961319	+	0.275437i	$0.0888226\pi$
$884$	13.2535	−	9.62923i	0.445763	−	0.323866i
$885$	24.8940	−	76.6158i	0.836802	−	2.57541i
$886$	5.15630	−	3.74627i	0.173229	−	0.125859i
$887$	21.2916	+	15.4693i	0.714903	+	0.519408i	0.884752	−	0.466063i	$-0.154328\pi$
$887$	21.2916	+	15.4693i	0.714903	+	0.519408i	−0.169849	+	0.985470i	$0.554328\pi$
$888$	−3.31690	−	10.2084i	−0.111308	−	0.342571i
$889$	−13.3768	−	9.71882i	−0.448644	−	0.325959i
$890$	−24.0531	+	74.0280i	−0.806263	+	2.48142i
$891$	−7.89927	+	24.3115i	−0.264636	+	0.814464i
$892$	−3.03439	−	9.33890i	−0.101599	−	0.312690i
$893$	8.30420			0.277889
$894$	22.3651			0.748002
$895$	−15.5245	−	47.7795i	−0.518927	−	1.59709i
$896$	−1.30902	+	0.951057i	−0.0437312	+	0.0317726i
$897$	4.95283	+	3.59844i	0.165370	+	0.120148i
$898$	−3.22980			−0.107780
$899$	1.87182	−	20.6204i	0.0624287	−	0.687730i
$900$	−7.01322			−0.233774
$901$	0.567667	+	0.412434i	0.0189117	+	0.0137402i
$902$	−6.81215	+	4.94932i	−0.226820	+	0.164794i
$903$	0.383904	+	1.18153i	0.0127755	+	0.0393190i
$904$	−12.3011			−0.409130
$905$	35.1771			1.16933
$906$	7.06690	+	21.7497i	0.234782	+	0.722584i
$907$	−4.47780	+	13.7812i	−0.148683	+	0.457599i	−0.997466	−	0.0711420i	$-0.977336\pi$
$907$	−4.47780	+	13.7812i	−0.148683	+	0.457599i	0.848783	+	0.528741i	$0.177336\pi$
$908$	−0.0291413	+	0.0896876i	−0.000967087	+	0.00297639i
$909$	5.09224	+	3.69973i	0.168899	+	0.122712i
$910$	8.19111	+	25.2096i	0.271533	+	0.835692i
$911$	−10.4176	−	7.56880i	−0.345149	−	0.250766i	0.401682	−	0.915779i	$-0.368426\pi$
$911$	−10.4176	−	7.56880i	−0.345149	−	0.250766i	−0.746831	+	0.665014i	$0.768426\pi$
$912$	5.63727	−	4.09572i	0.186669	−	0.135623i
$913$	−8.95852	+	27.5715i	−0.296484	+	0.912483i
$914$	−19.2050	+	13.9532i	−0.635245	+	0.461532i
$915$	17.4242	−	12.6594i	0.576025	−	0.418507i
$916$	−5.21930	+	16.0634i	−0.172451	+	0.530749i
$917$	−18.2001	+	13.2232i	−0.601021	+	0.436667i
$918$	18.6314	+	13.5365i	0.614927	+	0.446771i
$919$	−0.781055	−	2.40384i	−0.0257646	−	0.0792953i	0.937347	−	0.348396i	$-0.113274\pi$
$919$	−0.781055	−	2.40384i	−0.0257646	−	0.0792953i	−0.963112	+	0.269101i	$0.913274\pi$
$920$	3.32318	+	2.41443i	0.109562	+	0.0796015i
$921$	10.9019	−	33.5525i	0.359229	−	1.10559i
$922$	−4.54187	+	13.9784i	−0.149579	+	0.460355i
$923$	−10.1377	−	31.2006i	−0.333687	−	1.02698i
$924$	9.29164			0.305672
$925$	−83.4880			−2.74507
$926$	4.03741	+	12.4259i	0.132677	+	0.408339i
$927$	−6.90447	+	5.01639i	−0.226773	+	0.164760i
$928$	3.00855	+	2.18584i	0.0987604	+	0.0717536i
$929$	−2.72439			−0.0893844			−0.0446922	−	0.999001i	$-0.514231\pi$
$929$	−2.72439			−0.0893844			−0.0446922	+	0.999001i	$0.514231\pi$
$930$	−18.3490	−	30.7647i	−0.601688	−	1.00881i
$931$	−19.6261			−0.643218
$932$	−11.8436	−	8.60489i	−0.387951	−	0.281863i
$933$	−14.9022	+	10.8271i	−0.487876	+	0.354463i
$934$	3.02386	+	9.30648i	0.0989437	+	0.304517i
$935$	−63.1217			−2.06430
$936$	−2.29593			−0.0750448
$937$	8.08785	+	24.8919i	0.264219	+	0.813181i	0.991872	+	0.127237i	$0.0406108\pi$
$937$	8.08785	+	24.8919i	0.264219	+	0.813181i	−0.727654	+	0.685945i	$0.759389\pi$
$938$	0.739412	−	2.27568i	0.0241427	−	0.0743034i
$939$	−12.9024	+	39.7094i	−0.421053	+	1.29587i
$940$	6.20300	+	4.50674i	0.202320	+	0.146994i
$941$	−6.39199	−	19.6725i	−0.208373	−	0.641306i	−0.999558	−	0.0297293i	$-0.990535\pi$
$941$	−6.39199	−	19.6725i	−0.208373	−	0.641306i	0.791185	−	0.611577i	$-0.209465\pi$
$942$	−1.55057	−	1.12656i	−0.0505205	−	0.0367053i
$943$	−1.83321	+	1.33191i	−0.0596976	+	0.0433729i
$944$	3.86934	−	11.9086i	0.125936	−	0.387592i
$945$	−30.1462	+	21.9025i	−0.980656	+	0.712488i
$946$	1.47374	−	1.07073i	0.0479153	−	0.0348125i
$947$	12.2321	−	37.6467i	0.397491	−	1.22335i	−0.529513	−	0.848302i	$-0.677625\pi$
$947$	12.2321	−	37.6467i	0.397491	−	1.22335i	0.927004	−	0.375051i	$-0.122375\pi$
$948$	−7.64388	+	5.55360i	−0.248262	+	0.180373i
$949$	−5.67473	−	4.12293i	−0.184210	−	0.133836i
$950$	−16.7482	−	51.5456i	−0.543382	−	1.67236i
$951$	27.2956	+	19.8314i	0.885121	+	0.643078i
$952$	2.06767	−	6.36363i	0.0670135	−	0.206246i
$953$	9.07721	−	27.9368i	0.294040	−	0.904961i	−0.689503	−	0.724283i	$-0.742171\pi$
$953$	9.07721	−	27.9368i	0.294040	−	0.904961i	0.983542	−	0.180678i	$-0.0578292\pi$
$954$	−0.0303881	−	0.0935251i	−0.000983853	−	0.00302799i
$955$	11.4120			0.369285
$956$	−13.8435			−0.447732
$957$	−6.59912	−	20.3100i	−0.213319	−	0.656529i
$958$	−8.77261	+	6.37367i	−0.283430	+	0.205924i
$959$	−0.532858	−	0.387144i	−0.0172069	−	0.0125015i
$960$	6.43366			0.207645
$961$	−14.7318	+	27.2759i	−0.475219	+	0.879868i
$962$	−27.3316			−0.881206
$963$	4.50273	+	3.27143i	0.145099	+	0.105420i
$964$	0.206009	−	0.149674i	0.00663509	−	0.00482068i
$965$	32.1647	+	98.9928i	1.03542	+	3.18669i
$966$	2.50047			0.0804512
$967$	−42.0811			−1.35324			−0.676618	−	0.736334i	$-0.736555\pi$
$967$	−42.0811			−1.35324			−0.676618	+	0.736334i	$0.736555\pi$
$968$	−0.810955	−	2.49586i	−0.0260651	−	0.0802201i
$969$	−8.90439	+	27.4049i	−0.286050	+	0.880372i
$970$	−1.20688	+	3.71439i	−0.0387505	+	0.119262i
$971$	−17.7644	−	12.9066i	−0.570088	−	0.414193i	0.265049	−	0.964235i	$-0.414612\pi$
$971$	−17.7644	−	12.9066i	−0.570088	−	0.414193i	−0.835137	+	0.550042i	$0.814612\pi$
$972$	−1.83325	−	5.64218i	−0.0588017	−	0.180973i
$973$	24.1583	+	17.5520i	0.774480	+	0.562692i
$974$	29.3634	−	21.3337i	0.940863	−	0.683577i
$975$	23.0469	−	70.9311i	0.738092	−	2.27161i
$976$	2.70828	−	1.96768i	0.0866900	−	0.0629840i
$977$	−5.29357	+	3.84601i	−0.169356	+	0.123045i	−0.669235	−	0.743051i	$-0.733378\pi$
$977$	−5.29357	+	3.84601i	−0.169356	+	0.123045i	0.499878	+	0.866096i	$0.333378\pi$
$978$	−3.22203	+	9.91639i	−0.103029	+	0.317091i
$979$	56.2074	−	40.8371i	1.79640	−	1.30516i
$980$	−14.6601	−	10.6512i	−0.468300	−	0.340240i
$981$	−0.880057	−	2.70854i	−0.0280980	−	0.0864769i
$982$	17.2492	+	12.5322i	0.550443	+	0.399920i
$983$	−2.73290	+	8.41101i	−0.0871660	+	0.268269i	−0.985133	−	0.171793i	$-0.945044\pi$
$983$	−2.73290	+	8.41101i	−0.0871660	+	0.268269i	0.897967	+	0.440063i	$0.145044\pi$
$984$	−1.09673	+	3.37538i	−0.0349624	+	0.107603i
$985$	−6.64416	−	20.4486i	−0.211701	−	0.651548i
$986$	−15.3783			−0.489746
$987$	4.66733			0.148563
$988$	−5.48288	−	16.8746i	−0.174434	−	0.536851i
$989$	0.396596	−	0.288144i	0.0126110	−	0.00916245i
$990$	7.15685	+	5.19975i	0.227460	+	0.165259i
$991$	−38.6991			−1.22932			−0.614658	−	0.788794i	$-0.710706\pi$
$991$	−38.6991			−1.22932			−0.614658	+	0.788794i	$0.710706\pi$
$992$	−2.85204	−	4.78183i	−0.0905522	−	0.151823i
$993$	−28.8094			−0.914240
$994$	−10.8403	−	7.87592i	−0.343833	−	0.249809i
$995$	24.5689	−	17.8504i	0.778887	−	0.565894i
$996$	3.77595	+	11.6212i	0.119646	+	0.368231i
$997$	−14.2268			−0.450568			−0.225284	−	0.974293i	$-0.572331\pi$
$997$	−14.2268			−0.450568			−0.225284	+	0.974293i	$0.572331\pi$
$998$	37.2751			1.17992
$999$	−11.8730	−	36.5415i	−0.375646	−	1.15612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.d.b.33.2	✓	8
3.2	odd	2		558.2.i.g.343.2		8
4.3	odd	2		496.2.n.d.33.1		8
31.4	even	5		1922.2.a.i.1.2		4
31.16	even	5	inner	62.2.d.b.47.2	yes	8
31.27	odd	10		1922.2.a.l.1.3		4
93.47	odd	10		558.2.i.g.109.2		8
124.47	odd	10		496.2.n.d.481.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.b.33.2	✓	8	1.1	even	1	trivial
62.2.d.b.47.2	yes	8	31.16	even	5	inner
496.2.n.d.33.1		8	4.3	odd	2
496.2.n.d.481.1		8	124.47	odd	10
558.2.i.g.109.2		8	93.47	odd	10
558.2.i.g.343.2		8	3.2	odd	2
1922.2.a.i.1.2		4	31.4	even	5
1922.2.a.l.1.3		4	31.27	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(1.25865 - 0.914463i) q^{3} +(0.309017 + 0.951057i) q^{4} -4.13533 q^{5} +1.55578 q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.179093 + 0.551192i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(1.25865 - 0.914463i) q^{3} +(0.309017 + 0.951057i) q^{4} -4.13533 q^{5} +1.55578 q^{6} +(-0.500000 - 1.53884i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.179093 + 0.551192i) q^{9} +(-3.34556 - 2.43069i) q^{10} +(1.14062 + 3.51046i) q^{11} +(1.25865 + 0.914463i) q^{12} +(3.20494 - 2.32852i) q^{13} +(0.500000 - 1.53884i) q^{14} +(-5.20494 + 3.78161i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.27789 - 3.93294i) q^{17} +(-0.468872 + 0.340655i) q^{18} +(-3.62344 - 2.63259i) q^{19} +(-1.27789 - 3.93294i) q^{20} +(-2.03654 - 1.47963i) q^{21} +(-1.14062 + 3.51046i) q^{22} +(-0.306950 + 0.944696i) q^{23} +(0.480762 + 1.47963i) q^{24} +12.1010 q^{25} +3.96152 q^{26} +(1.72091 + 5.29643i) q^{27} +(1.30902 - 0.951057i) q^{28} +(-3.00855 - 2.18584i) q^{29} -6.43366 q^{30} +(2.85204 + 4.78183i) q^{31} -1.00000 q^{32} +(4.64582 + 3.37538i) q^{33} +(3.34556 - 2.43069i) q^{34} +(2.06767 + 6.36363i) q^{35} -0.579557 q^{36} -6.89927 q^{37} +(-1.38403 - 4.25961i) q^{38} +(1.90455 - 5.86160i) q^{39} +(1.27789 - 3.93294i) q^{40} +(1.84556 + 1.34087i) q^{41} +(-0.777889 - 2.39409i) q^{42} +(-0.399266 - 0.290084i) q^{43} +(-2.98617 + 2.16958i) q^{44} +(0.740610 - 2.27936i) q^{45} +(-0.803607 + 0.583854i) q^{46} +(-1.50000 + 1.08981i) q^{47} +(-0.480762 + 1.47963i) q^{48} +(3.54508 - 2.57565i) q^{49} +(9.78991 + 7.11278i) q^{50} +(-1.98811 - 6.11877i) q^{51} +(3.20494 + 2.32852i) q^{52} +(-0.0524334 + 0.161373i) q^{53} +(-1.72091 + 5.29643i) q^{54} +(-4.71683 - 14.5169i) q^{55} +1.61803 q^{56} -6.96805 q^{57} +(-1.14916 - 3.53676i) q^{58} +(-10.1301 + 7.35991i) q^{59} +(-5.20494 - 3.78161i) q^{60} -3.34762 q^{61} +(-0.503344 + 5.54497i) q^{62} +0.937743 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-13.2535 + 9.62923i) q^{65} +(1.77454 + 5.46149i) q^{66} +1.47882 q^{67} +4.13533 q^{68} +(0.477546 + 1.46974i) q^{69} +(-2.06767 + 6.36363i) q^{70} +(2.55904 - 7.87592i) q^{71} +(-0.468872 - 0.340655i) q^{72} +(-0.547152 - 1.68396i) q^{73} +(-5.58162 - 4.05529i) q^{74} +(15.2309 - 11.0659i) q^{75} +(1.38403 - 4.25961i) q^{76} +(4.83173 - 3.51046i) q^{77} +(4.98617 - 3.62267i) q^{78} +(-1.87668 + 5.77584i) q^{79} +(3.34556 - 2.43069i) q^{80} +(5.60280 + 4.07067i) q^{81} +(0.704940 + 2.16958i) q^{82} +(6.35410 + 4.61653i) q^{83} +(0.777889 - 2.39409i) q^{84} +(-5.28450 + 16.2640i) q^{85} +(-0.152506 - 0.469366i) q^{86} -5.78557 q^{87} -3.69111 q^{88} +(-5.81649 - 17.9013i) q^{89} +(1.93894 - 1.40872i) q^{90} +(-5.18570 - 3.76763i) q^{91} -0.993312 q^{92} +(7.96252 + 3.41057i) q^{93} -1.85410 q^{94} +(14.9842 + 10.8866i) q^{95} +(-1.25865 + 0.914463i) q^{96} +(-0.291845 - 0.898207i) q^{97} +4.38197 q^{98} -2.13921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9} - 5 q^{10} + 6 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} - 23 q^{15} - 2 q^{16} + 5 q^{17} - 3 q^{18} - 2 q^{19} - 5 q^{20} + q^{21} - 6 q^{22} - 15 q^{23} - 3 q^{24} + 16 q^{25} + 18 q^{26} + 37 q^{27} + 6 q^{28} - 19 q^{29} - 2 q^{30} + 13 q^{31} - 8 q^{32} + 30 q^{33} + 5 q^{34} + 18 q^{36} - 40 q^{37} - 3 q^{38} + 30 q^{39} + 5 q^{40} - 7 q^{41} - q^{42} + 12 q^{43} + q^{44} - 31 q^{45} - 20 q^{46} - 12 q^{47} + 3 q^{48} + 6 q^{49} + 19 q^{50} - 22 q^{51} + 7 q^{52} + 9 q^{53} - 37 q^{54} - 13 q^{55} + 4 q^{56} + 28 q^{57} - q^{58} - 18 q^{59} - 23 q^{60} + 12 q^{61} - 3 q^{62} + 6 q^{63} - 2 q^{64} - 16 q^{65} + 10 q^{66} - 26 q^{67} - 50 q^{69} - 25 q^{71} - 3 q^{72} + 35 q^{73} - 5 q^{74} + 26 q^{75} + 3 q^{76} - 8 q^{77} + 15 q^{78} + 6 q^{79} + 5 q^{80} + 43 q^{81} - 13 q^{82} + 24 q^{83} + q^{84} - q^{85} + 8 q^{86} + 8 q^{87} + 14 q^{88} - 7 q^{89} - 4 q^{90} - 16 q^{91} - 10 q^{92} + 3 q^{93} + 12 q^{94} + 30 q^{95} + 2 q^{96} + 26 q^{97} + 44 q^{98} - 46 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 4 * q^7 + 2 * q^8 - 12 * q^9 - 5 * q^10 + 6 * q^11 - 2 * q^12 + 7 * q^13 + 4 * q^14 - 23 * q^15 - 2 * q^16 + 5 * q^17 - 3 * q^18 - 2 * q^19 - 5 * q^20 + q^21 - 6 * q^22 - 15 * q^23 - 3 * q^24 + 16 * q^25 + 18 * q^26 + 37 * q^27 + 6 * q^28 - 19 * q^29 - 2 * q^30 + 13 * q^31 - 8 * q^32 + 30 * q^33 + 5 * q^34 + 18 * q^36 - 40 * q^37 - 3 * q^38 + 30 * q^39 + 5 * q^40 - 7 * q^41 - q^42 + 12 * q^43 + q^44 - 31 * q^45 - 20 * q^46 - 12 * q^47 + 3 * q^48 + 6 * q^49 + 19 * q^50 - 22 * q^51 + 7 * q^52 + 9 * q^53 - 37 * q^54 - 13 * q^55 + 4 * q^56 + 28 * q^57 - q^58 - 18 * q^59 - 23 * q^60 + 12 * q^61 - 3 * q^62 + 6 * q^63 - 2 * q^64 - 16 * q^65 + 10 * q^66 - 26 * q^67 - 50 * q^69 - 25 * q^71 - 3 * q^72 + 35 * q^73 - 5 * q^74 + 26 * q^75 + 3 * q^76 - 8 * q^77 + 15 * q^78 + 6 * q^79 + 5 * q^80 + 43 * q^81 - 13 * q^82 + 24 * q^83 + q^84 - q^85 + 8 * q^86 + 8 * q^87 + 14 * q^88 - 7 * q^89 - 4 * q^90 - 16 * q^91 - 10 * q^92 + 3 * q^93 + 12 * q^94 + 30 * q^95 + 2 * q^96 + 26 * q^97 + 44 * q^98 - 46 * q^99

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