LMFDB - Embedded newform 950.2.h.c.191.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.9
Character	$\chi$	$=$	950.191
Dual form			950.2.h.c.761.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.549973 + 1.69264i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.41010 - 1.73540i) q^{5} +(0.549973 - 1.69264i) q^{6} +4.16162 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.135515 + 0.0984577i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.549973 + 1.69264i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.41010 - 1.73540i) q^{5} +(0.549973 - 1.69264i) q^{6} +4.16162 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.135515 + 0.0984577i) q^{9} +(-2.16084 + 0.575134i) q^{10} +(1.36054 + 0.988491i) q^{11} +(-1.43985 + 1.04611i) q^{12} +(1.73468 - 1.26032i) q^{13} +(-3.36682 - 2.44614i) q^{14} +(3.71293 + 1.43237i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.966804 - 2.97552i) q^{17} +0.167506 q^{18} +(-0.309017 + 0.951057i) q^{19} +(2.08621 + 0.804816i) q^{20} +(2.28878 + 7.04413i) q^{21} +(-0.519680 - 1.59941i) q^{22} +(-5.44570 - 3.95653i) q^{23} +1.77975 q^{24} +(-1.02324 - 4.89418i) q^{25} -2.14418 q^{26} +(4.07836 + 2.96310i) q^{27} +(1.28601 + 3.95793i) q^{28} +(-2.51364 - 7.73618i) q^{29} +(-2.16190 - 3.34122i) q^{30} +(0.869940 - 2.67740i) q^{31} +1.00000 q^{32} +(-0.924900 + 2.84655i) q^{33} +(-2.53112 + 1.83897i) q^{34} +(5.86829 - 7.22208i) q^{35} +(-0.135515 - 0.0984577i) q^{36} +(-8.49759 + 6.17386i) q^{37} +(0.809017 - 0.587785i) q^{38} +(3.08729 + 2.24305i) q^{39} +(-1.21472 - 1.87735i) q^{40} +(-7.55909 + 5.49200i) q^{41} +(2.28878 - 7.04413i) q^{42} -4.38963 q^{43} +(-0.519680 + 1.59941i) q^{44} +(-0.0202265 + 0.374009i) q^{45} +(2.08007 + 6.40180i) q^{46} +(1.76997 + 5.44740i) q^{47} +(-1.43985 - 1.04611i) q^{48} +10.3191 q^{49} +(-2.04891 + 4.56092i) q^{50} +5.56820 q^{51} +(1.73468 + 1.26032i) q^{52} +(-0.525745 - 1.61808i) q^{53} +(-1.55779 - 4.79440i) q^{54} +(3.63393 - 0.967215i) q^{55} +(1.28601 - 3.95793i) q^{56} -1.77975 q^{57} +(-2.51364 + 7.73618i) q^{58} +(8.13004 - 5.90682i) q^{59} +(-0.214906 + 3.97383i) q^{60} +(1.08471 + 0.788088i) q^{61} +(-2.27753 + 1.65472i) q^{62} +(-0.563963 + 0.409743i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.258912 - 4.78754i) q^{65} +(2.42142 - 1.75927i) q^{66} +(-0.182825 + 0.562678i) q^{67} +3.12864 q^{68} +(3.70201 - 11.3936i) q^{69} +(-8.99258 + 2.39349i) q^{70} +(2.65702 + 8.17748i) q^{71} +(0.0517623 + 0.159308i) q^{72} +(2.88521 + 2.09623i) q^{73} +10.5036 q^{74} +(7.72134 - 4.42364i) q^{75} -1.00000 q^{76} +(5.66205 + 4.11372i) q^{77} +(-1.17924 - 3.62933i) q^{78} +(3.54011 + 10.8953i) q^{79} +(-0.120751 + 2.23281i) q^{80} +(-2.92777 + 9.01075i) q^{81} +9.34354 q^{82} +(-2.67494 + 8.23263i) q^{83} +(-5.99209 + 4.35351i) q^{84} +(-3.80043 - 5.87356i) q^{85} +(3.55129 + 2.58016i) q^{86} +(11.7121 - 8.50937i) q^{87} +(1.36054 - 0.988491i) q^{88} +(-4.93495 - 3.58545i) q^{89} +(0.236200 - 0.290691i) q^{90} +(7.21907 - 5.24496i) q^{91} +(2.08007 - 6.40180i) q^{92} +5.01032 q^{93} +(1.76997 - 5.44740i) q^{94} +(1.21472 + 1.87735i) q^{95} +(0.549973 + 1.69264i) q^{96} +(4.53705 + 13.9636i) q^{97} +(-8.34829 - 6.06539i) q^{98} -0.281699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9 + 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + 3 * q^14 - 4 * q^15 - 11 * q^16 + 11 * q^17 + 42 * q^18 + 11 * q^19 - 6 * q^20 + 3 * q^21 - 6 * q^22 - 3 * q^23 + 6 * q^24 - 11 * q^25 + 22 * q^26 - 23 * q^27 - 12 * q^28 + 36 * q^29 - 4 * q^30 + 11 * q^31 + 44 * q^32 + 2 * q^33 - 19 * q^34 + 67 * q^35 - 8 * q^36 + 3 * q^37 + 11 * q^38 + 47 * q^39 + 4 * q^40 + 2 * q^41 + 3 * q^42 + 70 * q^43 - 6 * q^44 - 28 * q^45 - 8 * q^46 - 11 * q^47 - 4 * q^48 + 22 * q^49 + 14 * q^50 + 38 * q^51 + 2 * q^52 - 9 * q^53 + 32 * q^54 + 8 * q^55 - 12 * q^56 - 6 * q^57 + 36 * q^58 - 62 * q^59 + 11 * q^60 - 28 * q^61 - 29 * q^62 + 10 * q^63 - 11 * q^64 - 39 * q^65 - 8 * q^66 + 25 * q^67 + 16 * q^68 - 81 * q^69 - 43 * q^70 - 34 * q^71 - 13 * q^72 + 6 * q^73 + 8 * q^74 - 39 * q^75 - 44 * q^76 - 21 * q^77 - 58 * q^78 + 19 * q^79 - q^80 - 22 * q^81 + 2 * q^82 - 50 * q^83 - 7 * q^84 + 102 * q^85 - 10 * q^86 + 47 * q^87 - q^88 - 4 * q^89 - 38 * q^90 - 8 * q^91 - 8 * q^92 + 60 * q^93 - 11 * q^94 - 4 * q^95 + q^96 + 8 * q^97 + 7 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	0.549973	+	1.69264i	0.317527	+	0.977247i	0.974702	+	0.223509i	$0.0717513\pi$
$3$	0.549973	+	1.69264i	0.317527	+	0.977247i	−0.657175	+	0.753738i	$0.728249\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.41010	−	1.73540i	0.630616	−	0.776095i
$5$	1.41010	−	1.73540i	0.630616	−	0.776095i
$6$	0.549973	−	1.69264i	0.224525	−	0.691018i
$7$	4.16162			1.57294			0.786472	−	0.617626i	$-0.211906\pi$
$7$	4.16162			1.57294			0.786472	+	0.617626i	$0.211906\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.135515	+	0.0984577i	−0.0451718	+	0.0328192i
$10$	−2.16084	+	0.575134i	−0.683317	+	0.181873i
$11$	1.36054	+	0.988491i	0.410218	+	0.298041i	0.773690	−	0.633564i	$-0.218409\pi$
$11$	1.36054	+	0.988491i	0.410218	+	0.298041i	−0.363472	+	0.931605i	$0.618409\pi$
$12$	−1.43985	+	1.04611i	−0.415648	+	0.301986i
$13$	1.73468	−	1.26032i	0.481114	−	0.349549i	−0.320643	−	0.947200i	$-0.603899\pi$
$13$	1.73468	−	1.26032i	0.481114	−	0.349549i	0.801757	+	0.597651i	$0.203899\pi$
$14$	−3.36682	−	2.44614i	−0.899820	−	0.653758i
$15$	3.71293	+	1.43237i	0.958674	+	0.369836i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.966804	−	2.97552i	0.234484	−	0.721668i	−0.762705	−	0.646746i	$-0.776129\pi$
$17$	0.966804	−	2.97552i	0.234484	−	0.721668i	0.997189	−	0.0749220i	$-0.0238708\pi$
$18$	0.167506			0.0394816
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	2.08621	+	0.804816i	0.466491	+	0.179962i
$21$	2.28878	+	7.04413i	0.499452	+	1.53715i
$22$	−0.519680	−	1.59941i	−0.110796	−	0.340996i
$23$	−5.44570	−	3.95653i	−1.13551	−	0.824994i	−0.149020	−	0.988834i	$-0.547612\pi$
$23$	−5.44570	−	3.95653i	−1.13551	−	0.824994i	−0.986487	+	0.163840i	$0.947612\pi$
$24$	1.77975			0.363290
$25$	−1.02324	−	4.89418i	−0.204648	−	0.978836i
$26$	−2.14418			−0.420509
$27$	4.07836	+	2.96310i	0.784880	+	0.570249i
$28$	1.28601	+	3.95793i	0.243033	+	0.747979i
$29$	−2.51364	−	7.73618i	−0.466770	−	1.43657i	−0.856742	−	0.515745i	$-0.827515\pi$
$29$	−2.51364	−	7.73618i	−0.466770	−	1.43657i	0.389972	−	0.920827i	$-0.372485\pi$
$30$	−2.16190	−	3.34122i	−0.394707	−	0.610020i
$31$	0.869940	−	2.67740i	0.156246	−	0.480875i	−0.842039	−	0.539416i	$-0.818645\pi$
$31$	0.869940	−	2.67740i	0.156246	−	0.480875i	0.998285	+	0.0585411i	$0.0186449\pi$
$32$	1.00000			0.176777
$33$	−0.924900	+	2.84655i	−0.161004	+	0.495521i
$34$	−2.53112	+	1.83897i	−0.434084	+	0.315381i
$35$	5.86829	−	7.22208i	0.991923	−	1.22075i
$36$	−0.135515	−	0.0984577i	−0.0225859	−	0.0164096i
$37$	−8.49759	+	6.17386i	−1.39700	+	1.01498i	−0.401938	+	0.915667i	$0.631663\pi$
$37$	−8.49759	+	6.17386i	−1.39700	+	1.01498i	−0.995057	+	0.0993096i	$0.968337\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	3.08729	+	2.24305i	0.494363	+	0.359176i
$40$	−1.21472	−	1.87735i	−0.192064	−	0.296836i
$41$	−7.55909	+	5.49200i	−1.18053	+	0.857706i	−0.992231	−	0.124406i	$-0.960298\pi$
$41$	−7.55909	+	5.49200i	−1.18053	+	0.857706i	−0.188300	+	0.982112i	$0.560298\pi$
$42$	2.28878	−	7.04413i	0.353166	−	1.08693i
$43$	−4.38963			−0.669412			−0.334706	−	0.942323i	$-0.608637\pi$
$43$	−4.38963			−0.669412			−0.334706	+	0.942323i	$0.608637\pi$
$44$	−0.519680	+	1.59941i	−0.0783447	+	0.241120i
$45$	−0.0202265	+	0.374009i	−0.00301519	+	0.0557539i
$46$	2.08007	+	6.40180i	0.306690	+	0.943894i
$47$	1.76997	+	5.44740i	0.258177	+	0.794586i	0.993187	+	0.116530i	$0.0371771\pi$
$47$	1.76997	+	5.44740i	0.258177	+	0.794586i	−0.735011	+	0.678056i	$0.762823\pi$
$48$	−1.43985	−	1.04611i	−0.207824	−	0.150993i
$49$	10.3191			1.47415
$50$	−2.04891	+	4.56092i	−0.289759	+	0.645011i
$51$	5.56820			0.779704
$52$	1.73468	+	1.26032i	0.240557	+	0.174775i
$53$	−0.525745	−	1.61808i	−0.0722166	−	0.222260i	0.908433	−	0.418030i	$-0.137279\pi$
$53$	−0.525745	−	1.61808i	−0.0722166	−	0.222260i	−0.980650	+	0.195770i	$0.937279\pi$
$54$	−1.55779	−	4.79440i	−0.211989	−	0.652435i
$55$	3.63393	−	0.967215i	0.489998	−	0.130419i
$56$	1.28601	−	3.95793i	0.171850	−	0.528901i
$57$	−1.77975			−0.235734
$58$	−2.51364	+	7.73618i	−0.330057	+	1.01581i
$59$	8.13004	−	5.90682i	1.05844	−	0.769002i	0.0846417	−	0.996411i	$-0.473025\pi$
$59$	8.13004	−	5.90682i	1.05844	−	0.769002i	0.973799	+	0.227409i	$0.0730254\pi$
$60$	−0.214906	+	3.97383i	−0.0277442	+	0.513020i
$61$	1.08471	+	0.788088i	0.138883	+	0.100904i	0.655057	−	0.755579i	$-0.272644\pi$
$61$	1.08471	+	0.788088i	0.138883	+	0.100904i	−0.516175	+	0.856483i	$0.672644\pi$
$62$	−2.27753	+	1.65472i	−0.289247	+	0.210150i
$63$	−0.563963	+	0.409743i	−0.0710527	+	0.0516228i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.258912	−	4.78754i	0.0321140	−	0.593821i
$66$	2.42142	−	1.75927i	0.298056	−	0.216551i
$67$	−0.182825	+	0.562678i	−0.0223357	+	0.0687421i	−0.961603	−	0.274444i	$-0.911506\pi$
$67$	−0.182825	+	0.562678i	−0.0223357	+	0.0687421i	0.939267	+	0.343186i	$0.111506\pi$
$68$	3.12864			0.379404
$69$	3.70201	−	11.3936i	0.445669	−	1.37163i
$70$	−8.99258	+	2.39349i	−1.07482	+	0.286076i
$71$	2.65702	+	8.17748i	0.315331	+	0.970488i	0.975618	+	0.219475i	$0.0704344\pi$
$71$	2.65702	+	8.17748i	0.315331	+	0.970488i	−0.660288	+	0.751013i	$0.729566\pi$
$72$	0.0517623	+	0.159308i	0.00610024	+	0.0187746i
$73$	2.88521	+	2.09623i	0.337688	+	0.245345i	0.743686	−	0.668529i	$-0.233076\pi$
$73$	2.88521	+	2.09623i	0.337688	+	0.245345i	−0.405998	+	0.913874i	$0.633076\pi$
$74$	10.5036			1.22102
$75$	7.72134	−	4.42364i	0.891583	−	0.510798i
$76$	−1.00000			−0.114708
$77$	5.66205	+	4.11372i	0.645250	+	0.468802i
$78$	−1.17924	−	3.62933i	−0.133523	−	0.410941i
$79$	3.54011	+	10.8953i	0.398294	+	1.22582i	0.926367	+	0.376623i	$0.122915\pi$
$79$	3.54011	+	10.8953i	0.398294	+	1.22582i	−0.528073	+	0.849199i	$0.677085\pi$
$80$	−0.120751	+	2.23281i	−0.0135003	+	0.249635i
$81$	−2.92777	+	9.01075i	−0.325308	+	1.00119i
$82$	9.34354			1.03182
$83$	−2.67494	+	8.23263i	−0.293613	+	0.903648i	0.690071	+	0.723742i	$0.257579\pi$
$83$	−2.67494	+	8.23263i	−0.293613	+	0.903648i	−0.983684	+	0.179906i	$0.942421\pi$
$84$	−5.99209	+	4.35351i	−0.653791	+	0.475007i
$85$	−3.80043	−	5.87356i	−0.412214	−	0.637078i
$86$	3.55129	+	2.58016i	0.382945	+	0.278226i
$87$	11.7121	−	8.50937i	1.25567	−	0.912300i
$88$	1.36054	−	0.988491i	0.145034	−	0.105373i
$89$	−4.93495	−	3.58545i	−0.523104	−	0.380057i	0.294668	−	0.955600i	$-0.404791\pi$
$89$	−4.93495	−	3.58545i	−0.523104	−	0.380057i	−0.817772	+	0.575543i	$0.804791\pi$
$90$	0.236200	−	0.290691i	0.0248977	−	0.0306415i
$91$	7.21907	−	5.24496i	0.756764	−	0.549821i
$92$	2.08007	−	6.40180i	0.216863	−	0.667434i
$93$	5.01032			0.519546
$94$	1.76997	−	5.44740i	0.182558	−	0.561857i
$95$	1.21472	+	1.87735i	0.124628	+	0.192612i
$96$	0.549973	+	1.69264i	0.0561313	+	0.172755i
$97$	4.53705	+	13.9636i	0.460668	+	1.41779i	0.864350	+	0.502891i	$0.167730\pi$
$97$	4.53705	+	13.9636i	0.460668	+	1.41779i	−0.403682	+	0.914899i	$0.632270\pi$
$98$	−8.34829	−	6.06539i	−0.843304	−	0.612696i
$99$	−0.281699			−0.0283118
$100$	4.33844	−	2.48554i	0.433844	−	0.248554i
$101$	10.0338			0.998401			0.499201	−	0.866486i	$-0.333627\pi$
$101$	10.0338			0.998401			0.499201	+	0.866486i	$0.333627\pi$
$102$	−4.50477	−	3.27290i	−0.446038	−	0.324066i
$103$	5.67191	+	17.4563i	0.558870	+	1.72002i	0.685499	+	0.728073i	$0.259584\pi$
$103$	5.67191	+	17.4563i	0.558870	+	1.72002i	−0.126630	+	0.991950i	$0.540416\pi$
$104$	−0.662589	−	2.03924i	−0.0649722	−	0.199964i
$105$	15.4518	+	5.96097i	1.50794	+	0.581731i
$106$	−0.525745	+	1.61808i	−0.0510649	+	0.157161i
$107$	−13.7240			−1.32675			−0.663374	−	0.748288i	$-0.730876\pi$
$107$	−13.7240			−1.32675			−0.663374	+	0.748288i	$0.730876\pi$
$108$	−1.55779	+	4.79440i	−0.149899	+	0.461341i
$109$	0.960977	−	0.698191i	0.0920449	−	0.0668746i	−0.540811	−	0.841144i	$-0.681883\pi$
$109$	0.960977	−	0.698191i	0.0920449	−	0.0668746i	0.632856	+	0.774270i	$0.281883\pi$
$110$	−3.50842	−	1.35347i	−0.334515	−	0.129049i
$111$	−15.1236	−	10.9879i	−1.43547	−	1.04293i
$112$	−3.36682	+	2.44614i	−0.318134	+	0.231138i
$113$	−12.1709	+	8.84267i	−1.14494	+	0.831848i	−0.987800	−	0.155728i	$-0.950228\pi$
$113$	−12.1709	+	8.84267i	−1.14494	+	0.831848i	−0.157141	+	0.987576i	$0.550228\pi$
$114$	1.43985	+	1.04611i	0.134854	+	0.0979772i
$115$	−14.5452	+	3.87137i	−1.35634	+	0.361007i
$116$	6.58078	−	4.78122i	0.611010	−	0.443925i
$117$	−0.110988	+	0.341585i	−0.0102608	+	0.0315796i
$118$	−10.0493			−0.925111
$119$	4.02347	−	12.3830i	0.368830	−	1.13514i
$120$	2.50962	−	3.08858i	0.229096	−	0.281947i
$121$	−2.52523	−	7.77186i	−0.229566	−	0.706533i
$122$	−0.414322	−	1.27515i	−0.0375110	−	0.115447i
$123$	−13.4533	−	9.77438i	−1.21304	−	0.881326i
$124$	2.81519			0.252811
$125$	−9.93624	−	5.12555i	−0.888724	−	0.458443i
$126$	0.697097			0.0621023
$127$	8.44368	+	6.13469i	0.749255	+	0.544366i	0.895596	−	0.444868i	$-0.146750\pi$
$127$	8.44368	+	6.13469i	0.749255	+	0.544366i	−0.146341	+	0.989234i	$0.546750\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−2.41418	−	7.43007i	−0.212556	−	0.654181i
$130$	−3.02351	+	3.72102i	−0.265179	+	0.326355i
$131$	5.67827	−	17.4759i	0.496113	−	1.52688i	−0.319102	−	0.947720i	$-0.603381\pi$
$131$	5.67827	−	17.4759i	0.496113	−	1.52688i	0.815215	−	0.579158i	$-0.196619\pi$
$132$	−2.99304			−0.260511
$133$	−1.28601	+	3.95793i	−0.111511	+	0.343196i
$134$	0.478643	−	0.347754i	0.0413484	−	0.0300414i
$135$	10.8931	−	2.89932i	0.937525	−	0.249534i
$136$	−2.53112	−	1.83897i	−0.217042	−	0.157690i
$137$	13.2405	−	9.61977i	1.13121	−	0.821872i	0.145340	−	0.989382i	$-0.453572\pi$
$137$	13.2405	−	9.61977i	1.13121	−	0.821872i	0.985870	+	0.167510i	$0.0535725\pi$
$138$	−9.69198	+	7.04163i	−0.825036	+	0.599424i
$139$	−10.7025	−	7.77579i	−0.907771	−	0.659534i	0.0326792	−	0.999466i	$-0.489596\pi$
$139$	−10.7025	−	7.77579i	−0.907771	−	0.659534i	−0.940450	+	0.339932i	$0.889596\pi$
$140$	8.68201	+	3.34933i	0.733763	+	0.283070i
$141$	−8.24707	+	5.99185i	−0.694529	+	0.504605i
$142$	2.65702	−	8.17748i	0.222972	−	0.686238i
$143$	3.60592			0.301542
$144$	0.0517623	−	0.159308i	0.00431352	−	0.0132757i
$145$	−16.9699	−	6.54661i	−1.40927	−	0.543666i
$146$	−1.10205	−	3.39176i	−0.0912064	−	0.280704i
$147$	5.67520	+	17.4665i	0.468082	+	1.44061i
$148$	−8.49759	−	6.17386i	−0.698498	−	0.507488i
$149$	−15.2916			−1.25273			−0.626366	−	0.779529i	$-0.715459\pi$
$149$	−15.2916			−1.25273			−0.626366	+	0.779529i	$0.715459\pi$
$150$	−8.84684	−	0.959686i	−0.722342	−	0.0783581i
$151$	12.2683			0.998377			0.499189	−	0.866493i	$-0.333631\pi$
$151$	12.2683			0.998377			0.499189	+	0.866493i	$0.333631\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	0.161946	+	0.498417i	0.0130925	+	0.0402947i
$154$	−2.16271	−	6.65614i	−0.174276	−	0.536367i
$155$	−3.41966	−	5.28510i	−0.274674	−	0.424509i
$156$	−1.17924	+	3.62933i	−0.0944149	+	0.290579i
$157$	4.21944			0.336748			0.168374	−	0.985723i	$-0.446148\pi$
$157$	4.21944			0.336748			0.168374	+	0.985723i	$0.446148\pi$
$158$	3.54011	−	10.8953i	0.281636	−	0.866787i
$159$	2.44968	−	1.77980i	0.194272	−	0.141147i
$160$	1.41010	−	1.73540i	0.111478	−	0.137196i
$161$	−22.6629	−	16.4656i	−1.78609	−	1.29767i
$162$	7.66500	−	5.56895i	0.602219	−	0.437538i
$163$	−7.80237	+	5.66875i	−0.611129	+	0.444011i	−0.849812	−	0.527087i	$-0.823284\pi$
$163$	−7.80237	+	5.66875i	−0.611129	+	0.444011i	0.238683	+	0.971098i	$0.423284\pi$
$164$	−7.55909	−	5.49200i	−0.590265	−	0.428853i
$165$	3.63571	+	5.61899i	0.283039	+	0.437438i
$166$	7.00309	−	5.08804i	0.543545	−	0.394909i
$167$	−2.88518	+	8.87966i	−0.223262	+	0.687129i	0.775202	+	0.631714i	$0.217648\pi$
$167$	−2.88518	+	8.87966i	−0.223262	+	0.687129i	−0.998463	+	0.0554151i	$0.982352\pi$
$168$	7.40663			0.571434
$169$	−2.59651	+	7.99124i	−0.199732	+	0.614711i
$170$	−0.377786	+	6.98565i	−0.0289748	+	0.535775i
$171$	−0.0517623	−	0.159308i	−0.00395836	−	0.0121826i
$172$	−1.35647	−	4.17479i	−0.103430	−	0.318325i
$173$	5.32710	+	3.87037i	0.405012	+	0.294259i	0.771579	−	0.636133i	$-0.219467\pi$
$173$	5.32710	+	3.87037i	0.405012	+	0.294259i	−0.366567	+	0.930392i	$0.619467\pi$
$174$	−14.4770			−1.09750
$175$	−4.25833	−	20.3677i	−0.321899	−	1.53965i
$176$	−1.68172			−0.126764
$177$	14.4694	+	10.5127i	1.08759	+	0.790180i
$178$	1.88498	+	5.80138i	0.141285	+	0.434832i
$179$	−1.63181	−	5.02218i	−0.121967	−	0.375376i	0.871369	−	0.490628i	$-0.163232\pi$
$179$	−1.63181	−	5.02218i	−0.121967	−	0.375376i	−0.993336	+	0.115252i	$0.963232\pi$
$180$	−0.361954	+	0.0963385i	−0.0269784	+	0.00718065i
$181$	−3.59127	+	11.0528i	−0.266937	+	0.821548i	0.724304	+	0.689481i	$0.242161\pi$
$181$	−3.59127	+	11.0528i	−0.266937	+	0.821548i	−0.991241	+	0.132067i	$0.957839\pi$
$182$	−8.92326			−0.661436
$183$	−0.737390	+	2.26945i	−0.0545094	+	0.167763i
$184$	−5.44570	+	3.95653i	−0.401462	+	0.291679i
$185$	−1.26832	+	23.4525i	−0.0932485	+	1.72426i
$186$	−4.05344	−	2.94499i	−0.297212	−	0.215937i
$187$	4.25664	−	3.09263i	0.311277	−	0.226156i
$188$	−4.63384	+	3.36668i	−0.337957	+	0.245540i
$189$	16.9726	+	12.3313i	1.23457	+	0.896969i
$190$	0.120751	−	2.23281i	0.00876018	−	0.161985i
$191$	5.10261	−	3.70726i	0.369212	−	0.268248i	−0.387672	−	0.921797i	$-0.626721\pi$
$191$	5.10261	−	3.70726i	0.369212	−	0.268248i	0.756884	+	0.653549i	$0.226721\pi$
$192$	0.549973	−	1.69264i	0.0396909	−	0.122156i
$193$	−20.8343			−1.49969			−0.749844	−	0.661615i	$-0.769871\pi$
$193$	−20.8343			−1.49969			−0.749844	+	0.661615i	$0.769871\pi$
$194$	4.53705	−	13.9636i	0.325741	−	1.00253i
$195$	8.24599	−	2.19477i	0.590507	−	0.157171i
$196$	3.18876	+	9.81400i	0.227769	+	0.701000i
$197$	7.92873	+	24.4021i	0.564898	+	1.73858i	0.668253	+	0.743934i	$0.267042\pi$
$197$	7.92873	+	24.4021i	0.564898	+	1.73858i	−0.103354	+	0.994645i	$0.532958\pi$
$198$	0.227899	+	0.165578i	0.0161961	+	0.0117671i
$199$	1.98805			0.140929			0.0704644	−	0.997514i	$-0.477552\pi$
$199$	1.98805			0.140929			0.0704644	+	0.997514i	$0.477552\pi$
$200$	−4.97084	−	0.539226i	−0.351491	−	0.0381290i
$201$	−1.05296			−0.0742702
$202$	−8.11752	−	5.89772i	−0.571147	−	0.414962i
$203$	−10.4608	−	32.1950i	−0.734203	−	2.25965i
$204$	1.72067	+	5.29567i	0.120471	+	0.370771i
$205$	−1.12824	+	20.8623i	−0.0787997	+	1.45709i
$206$	5.67191	−	17.4563i	0.395180	−	1.21624i
$207$	1.12753			0.0783685
$208$	−0.662589	+	2.03924i	−0.0459423	+	0.141396i
$209$	−1.36054	+	0.988491i	−0.0941106	+	0.0683753i
$210$	−8.99699	−	13.9049i	−0.620851	−	0.959527i
$211$	4.82962	+	3.50893i	0.332485	+	0.241565i	0.741484	−	0.670970i	$-0.234122\pi$
$211$	4.82962	+	3.50893i	0.332485	+	0.241565i	−0.408999	+	0.912535i	$0.634122\pi$
$212$	1.37642	−	1.00003i	0.0945328	−	0.0686821i
$213$	−12.3802	+	8.99478i	−0.848281	+	0.616312i
$214$	11.1029	+	8.06676i	0.758982	+	0.551433i
$215$	−6.18982	+	7.61777i	−0.422142	+	0.519528i
$216$	4.07836	−	2.96310i	0.277497	−	0.201613i
$217$	3.62036	−	11.1423i	0.245766	−	0.756389i
$218$	−1.18783			−0.0804502
$219$	−1.96137	+	6.03649i	−0.132537	+	0.407908i
$220$	2.04282	+	3.15718i	0.137727	+	0.212857i
$221$	−2.07300	−	6.38005i	−0.139445	−	0.429168i
$222$	5.77669	+	17.7788i	0.387706	+	1.19324i
$223$	−23.2886	−	16.9202i	−1.55952	−	1.13306i	−0.936400	−	0.350934i	$-0.885864\pi$
$223$	−23.2886	−	16.9202i	−1.55952	−	1.13306i	−0.623122	−	0.782125i	$-0.714136\pi$
$224$	4.16162			0.278060
$225$	0.620534	+	0.562491i	0.0413689	+	0.0374994i
$226$	15.0440			1.00071
$227$	−6.69613	−	4.86503i	−0.444438	−	0.322903i	0.342958	−	0.939351i	$-0.388571\pi$
$227$	−6.69613	−	4.86503i	−0.444438	−	0.322903i	−0.787396	+	0.616448i	$0.788571\pi$
$228$	−0.549973	−	1.69264i	−0.0364228	−	0.112098i
$229$	2.45517	+	7.55625i	0.162242	+	0.499331i	0.998823	−	0.0485138i	$-0.0154485\pi$
$229$	2.45517	+	7.55625i	0.162242	+	0.499331i	−0.836580	+	0.547845i	$0.815448\pi$
$230$	14.0428	+	5.41742i	0.925956	+	0.357214i
$231$	−3.84908	+	11.8463i	−0.253251	+	0.779426i
$232$	−8.13430			−0.534043
$233$	−4.49570	+	13.8363i	−0.294523	+	0.906448i	0.688859	+	0.724896i	$0.258112\pi$
$233$	−4.49570	+	13.8363i	−0.294523	+	0.906448i	−0.983381	+	0.181552i	$0.941888\pi$
$234$	0.290570	−	0.211111i	0.0189951	−	0.0138008i
$235$	11.9493	+	4.60977i	0.779484	+	0.300709i
$236$	8.13004	+	5.90682i	0.529221	+	0.384501i
$237$	−16.4950	+	11.9843i	−1.07146	+	0.778463i
$238$	−10.5336	+	7.65309i	−0.682790	+	0.496076i
$239$	−12.6526	−	9.19269i	−0.818432	−	0.594626i	0.0978311	−	0.995203i	$-0.468810\pi$
$239$	−12.6526	−	9.19269i	−0.818432	−	0.594626i	−0.916263	+	0.400578i	$0.868810\pi$
$240$	−3.84575	+	1.02359i	−0.248242	+	0.0660727i
$241$	−5.96119	+	4.33106i	−0.383994	+	0.278988i	−0.762990	−	0.646410i	$-0.776269\pi$
$241$	−5.96119	+	4.33106i	−0.383994	+	0.278988i	0.378996	+	0.925398i	$0.376269\pi$
$242$	−2.52523	+	7.77186i	−0.162328	+	0.499594i
$243$	−1.73878			−0.111543
$244$	−0.414322	+	1.27515i	−0.0265243	+	0.0816333i
$245$	14.5509	−	17.9077i	0.929622	−	1.14408i
$246$	5.13869	+	15.8153i	0.327631	+	1.00835i
$247$	0.662589	+	2.03924i	0.0421595	+	0.129754i
$248$	−2.27753	−	1.65472i	−0.144623	−	0.105075i
$249$	−15.4060			−0.976318
$250$	5.02586	+	9.98703i	0.317863	+	0.631635i
$251$	18.2530			1.15212			0.576061	−	0.817407i	$-0.304589\pi$
$251$	18.2530			1.15212			0.576061	+	0.817407i	$0.304589\pi$
$252$	−0.563963	−	0.409743i	−0.0355263	−	0.0258114i
$253$	−3.49810	−	10.7660i	−0.219924	−	0.676856i
$254$	−3.22520	−	9.92614i	−0.202367	−	0.622821i
$255$	7.85171	−	9.66306i	0.491693	−	0.605124i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.52595			−0.282321			−0.141160	−	0.989987i	$-0.545083\pi$
$257$	−4.52595			−0.282321			−0.141160	+	0.989987i	$0.545083\pi$
$258$	−2.41418	+	7.43007i	−0.150300	+	0.462576i
$259$	−35.3637	+	25.6932i	−2.19739	+	1.59650i
$260$	4.63323	−	1.23319i	0.287341	−	0.0764793i
$261$	1.10232	+	0.800884i	0.0682320	+	0.0495735i
$262$	−14.8659	+	10.8007i	−0.918419	+	0.667270i
$263$	17.0099	−	12.3584i	1.04887	−	0.762052i	0.0768766	−	0.997041i	$-0.475505\pi$
$263$	17.0099	−	12.3584i	1.04887	−	0.762052i	0.971998	+	0.234989i	$0.0755053\pi$
$264$	2.42142	+	1.75927i	0.149028	+	0.108275i
$265$	−3.54937	−	1.36927i	−0.218036	−	0.0841136i
$266$	3.36682	−	2.44614i	0.206433	−	0.149982i
$267$	3.35480	−	10.3250i	0.205310	−	0.631880i
$268$	−0.591635			−0.0361399
$269$	−0.100375	+	0.308924i	−0.00611999	+	0.0188354i	−0.954070	−	0.299584i	$-0.903152\pi$
$269$	−0.100375	+	0.308924i	−0.00611999	+	0.0188354i	0.947950	+	0.318420i	$0.103152\pi$
$270$	−10.5169	−	4.05718i	−0.640035	−	0.246912i
$271$	2.96393	+	9.12203i	0.180046	+	0.554124i	0.999828	−	0.0185515i	$-0.00590548\pi$
$271$	2.96393	+	9.12203i	0.180046	+	0.554124i	−0.819782	+	0.572676i	$0.805905\pi$
$272$	0.966804	+	2.97552i	0.0586211	+	0.180417i
$273$	12.8481	+	9.33472i	0.777604	+	0.564963i
$274$	−16.3661			−0.988714
$275$	3.44569	−	7.67019i	0.207783	−	0.462530i
$276$	11.9799			0.721108
$277$	−12.0187	−	8.73213i	−0.722137	−	0.524663i	0.164930	−	0.986305i	$-0.447260\pi$
$277$	−12.0187	−	8.73213i	−0.722137	−	0.524663i	−0.887066	+	0.461642i	$0.847260\pi$
$278$	4.08798	+	12.5815i	0.245181	+	0.754588i
$279$	0.145720	+	0.448481i	0.00872405	+	0.0268499i
$280$	−5.05520	−	7.81282i	−0.302106	−	0.466905i
$281$	5.58438	−	17.1870i	0.333136	−	1.02529i	−0.634497	−	0.772926i	$-0.718793\pi$
$281$	5.58438	−	17.1870i	0.333136	−	1.02529i	0.967633	−	0.252362i	$-0.0812075\pi$
$282$	10.1939			0.607040
$283$	−5.00980	+	15.4186i	−0.297802	+	0.916539i	0.684464	+	0.729046i	$0.260036\pi$
$283$	−5.00980	+	15.4186i	−0.297802	+	0.916539i	−0.982266	+	0.187493i	$0.939964\pi$
$284$	−6.95618	+	5.05396i	−0.412773	+	0.299897i
$285$	−2.50962	+	3.08858i	−0.148657	+	0.182952i
$286$	−2.91725	−	2.11950i	−0.172500	−	0.125329i
$287$	−31.4580	+	22.8556i	−1.85691	+	1.34912i
$288$	−0.135515	+	0.0984577i	−0.00798532	+	0.00580167i
$289$	5.83431	+	4.23887i	0.343195	+	0.249345i
$290$	9.88090	+	15.2709i	0.580226	+	0.896741i
$291$	−21.1401	+	15.3592i	−1.23926	+	0.900373i
$292$	−1.10205	+	3.39176i	−0.0644927	+	0.198488i
$293$	25.4014			1.48397			0.741984	−	0.670418i	$-0.233885\pi$
$293$	25.4014			1.48397			0.741984	+	0.670418i	$0.233885\pi$
$294$	5.67520	−	17.4665i	0.330984	−	1.01866i
$295$	1.21346	−	22.4381i	0.0706503	−	1.30640i
$296$	3.24579	+	9.98951i	0.188658	+	0.580629i
$297$	2.61977	+	8.06284i	0.152015	+	0.467853i
$298$	12.3711	+	8.98815i	0.716640	+	0.520670i
$299$	−14.4330			−0.834684
$300$	6.59316	+	5.97645i	0.380656	+	0.345050i
$301$	−18.2680			−1.05295
$302$	−9.92524	−	7.21111i	−0.571133	−	0.414953i
$303$	5.51832	+	16.9836i	0.317019	+	0.975685i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	2.89720	−	0.771125i	0.165893	−	0.0441545i
$306$	0.161946	−	0.498417i	0.00925781	−	0.0284926i
$307$	−15.2592			−0.870889			−0.435445	−	0.900216i	$-0.643409\pi$
$307$	−15.2592			−0.870889			−0.435445	+	0.900216i	$0.643409\pi$
$308$	−2.16271	+	6.65614i	−0.123232	+	0.379269i
$309$	−26.4279	+	19.2010i	−1.50343	+	1.09231i
$310$	−0.339936	+	6.28576i	−0.0193070	+	0.357007i
$311$	2.88541	+	2.09637i	0.163617	+	0.118874i	0.666581	−	0.745433i	$-0.267757\pi$
$311$	2.88541	+	2.09637i	0.163617	+	0.118874i	−0.502964	+	0.864307i	$0.667757\pi$
$312$	3.08729	−	2.24305i	0.174784	−	0.126988i
$313$	18.9069	−	13.7367i	1.06868	−	0.776443i	0.0930071	−	0.995665i	$-0.470352\pi$
$313$	18.9069	−	13.7367i	1.06868	−	0.776443i	0.975675	+	0.219223i	$0.0703521\pi$
$314$	−3.41360	−	2.48013i	−0.192641	−	0.139962i
$315$	−0.0841749	+	1.55648i	−0.00474272	+	0.0876978i
$316$	−9.26814	+	6.73369i	−0.521373	+	0.378800i
$317$	−9.22183	+	28.3819i	−0.517949	+	1.59408i	0.259901	+	0.965635i	$0.416310\pi$
$317$	−9.22183	+	28.3819i	−0.517949	+	1.59408i	−0.777851	+	0.628449i	$0.783690\pi$
$318$	−3.02797			−0.169800
$319$	4.22723	−	13.0101i	0.236680	−	0.728425i
$320$	−2.16084	+	0.575134i	−0.120795	+	0.0321510i
$321$	−7.54782	−	23.2298i	−0.421278	−	1.29656i
$322$	8.65646	+	26.6419i	0.482406	+	1.48469i
$323$	2.53112	+	1.83897i	0.140836	+	0.102323i
$324$	−9.47446			−0.526359
$325$	−7.94322	−	7.20022i	−0.440610	−	0.399397i
$326$	9.64426			0.534146
$327$	1.71030	+	1.24260i	0.0945797	+	0.0687162i
$328$	2.88731	+	8.88624i	0.159425	+	0.490660i
$329$	7.36593	+	22.6700i	0.406097	+	1.24984i
$330$	0.361412	−	6.68288i	0.0198951	−	0.367880i
$331$	6.41175	−	19.7333i	0.352421	−	1.08464i	−0.605068	−	0.796174i	$-0.706854\pi$
$331$	6.41175	−	19.7333i	0.352421	−	1.08464i	0.957490	−	0.288468i	$-0.0931458\pi$
$332$	−8.65630			−0.475076
$333$	0.543690	−	1.67331i	0.0297940	−	0.0916966i
$334$	7.55349	−	5.48793i	0.413309	−	0.300286i
$335$	0.718671	+	1.11071i	0.0392652	+	0.0606844i
$336$	−5.99209	−	4.35351i	−0.326895	−	0.237503i
$337$	15.9551	−	11.5920i	0.869129	−	0.631459i	−0.0612241	−	0.998124i	$-0.519500\pi$
$337$	15.9551	−	11.5920i	0.869129	−	0.631459i	0.930353	+	0.366665i	$0.119500\pi$
$338$	6.79775	−	4.93886i	0.369749	−	0.268638i
$339$	−21.6611	−	15.7377i	−1.17647	−	0.854756i
$340$	4.41170	−	5.42945i	0.239258	−	0.294453i
$341$	3.83017	−	2.78278i	0.207416	−	0.150696i
$342$	−0.0517623	+	0.159308i	−0.00279898	+	0.00861438i
$343$	13.8126			0.745811
$344$	−1.35647	+	4.17479i	−0.0731360	+	0.225089i
$345$	−14.5523	−	22.4906i	−0.783469	−	1.21085i
$346$	−2.03477	−	6.26239i	−0.109390	−	0.336668i
$347$	−6.51476	−	20.0504i	−0.349731	−	1.07636i	−0.959002	−	0.283399i	$-0.908538\pi$
$347$	−6.51476	−	20.0504i	−0.349731	−	1.07636i	0.609272	−	0.792962i	$-0.291462\pi$
$348$	11.7121	+	8.50937i	0.627837	+	0.456150i
$349$	6.82757			0.365472			0.182736	−	0.983162i	$-0.441505\pi$
$349$	6.82757			0.365472			0.182736	+	0.983162i	$0.441505\pi$
$350$	−8.52677	+	18.9808i	−0.455775	+	1.01457i
$351$	10.8091			0.576947
$352$	1.36054	+	0.988491i	0.0725171	+	0.0526867i
$353$	0.160445	+	0.493800i	0.00853965	+	0.0262823i	0.955236	−	0.295846i	$-0.0956016\pi$
$353$	0.160445	+	0.493800i	0.00853965	+	0.0262823i	−0.946696	+	0.322129i	$0.895602\pi$
$354$	−5.52683	−	17.0098i	−0.293748	−	0.904063i
$355$	17.9379	+	6.92005i	0.952043	+	0.367278i
$356$	1.88498	−	5.80138i	0.0999039	−	0.307473i
$357$	23.1727			1.22643
$358$	−1.63181	+	5.02218i	−0.0862436	+	0.265431i
$359$	8.81170	−	6.40208i	0.465064	−	0.337889i	−0.330451	−	0.943823i	$-0.607201\pi$
$359$	8.81170	−	6.40208i	0.465064	−	0.337889i	0.795514	+	0.605935i	$0.207201\pi$
$360$	0.349453	+	0.134812i	0.0184178	+	0.00710520i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	9.40207	−	6.83101i	0.494162	−	0.359030i
$363$	11.7662	−	8.54862i	0.617564	−	0.448686i
$364$	7.21907	+	5.24496i	0.378382	+	0.274911i
$365$	7.70622	−	2.05111i	0.403362	−	0.107360i
$366$	1.93051	−	1.40260i	0.100909	−	0.0733150i
$367$	0.763125	−	2.34866i	0.0398348	−	0.122599i	−0.929162	−	0.369674i	$-0.879469\pi$
$367$	0.763125	−	2.34866i	0.0398348	−	0.122599i	0.968996	+	0.247075i	$0.0794694\pi$
$368$	6.73125			0.350891
$369$	0.483643	−	1.48850i	0.0251775	−	0.0774882i
$370$	14.8111	−	18.2280i	0.769993	−	0.947627i
$371$	−2.18795	−	6.73381i	−0.113593	−	0.349602i
$372$	1.54827	+	4.76510i	0.0802743	+	0.247059i
$373$	−26.0054	−	18.8940i	−1.34651	−	0.978296i	−0.999177	−	0.0405535i	$-0.987088\pi$
$373$	−26.0054	−	18.8940i	−1.34651	−	0.978296i	−0.347331	−	0.937742i	$-0.612912\pi$
$374$	−5.26150			−0.272066
$375$	3.21106	−	19.6374i	0.165818	−	1.01407i
$376$	5.72774			0.295386
$377$	−14.1104	−	10.2518i	−0.726723	−	0.527995i
$378$	−6.48294	−	19.9524i	−0.333447	−	1.02624i
$379$	0.784386	+	2.41409i	0.0402912	+	0.124004i	0.969179	−	0.246358i	$-0.0792338\pi$
$379$	0.784386	+	2.41409i	0.0402912	+	0.124004i	−0.928888	+	0.370361i	$0.879234\pi$
$380$	−1.41010	+	1.73540i	−0.0723366	+	0.0890242i
$381$	−5.74004	+	17.6660i	−0.294071	+	0.905058i
$382$	−6.30717			−0.322703
$383$	−2.48611	+	7.65147i	−0.127035	+	0.390972i	−0.994266	−	0.106933i	$-0.965897\pi$
$383$	−2.48611	+	7.65147i	−0.127035	+	0.390972i	0.867232	+	0.497905i	$0.165897\pi$
$384$	−1.43985	+	1.04611i	−0.0734769	+	0.0533841i
$385$	15.1230	−	4.02518i	0.770740	−	0.205142i
$386$	16.8553	+	12.2461i	0.857913	+	0.623310i
$387$	0.594863	−	0.432193i	0.0302386	−	0.0219696i
$388$	−11.8782	+	8.62999i	−0.603022	+	0.438121i
$389$	−23.4417	−	17.0314i	−1.18854	−	0.863525i	−0.195431	−	0.980717i	$-0.562611\pi$
$389$	−23.4417	−	17.0314i	−1.18854	−	0.863525i	−0.993109	+	0.117192i	$0.962611\pi$
$390$	−7.96120	−	3.07126i	−0.403131	−	0.155519i
$391$	−17.0376	+	12.3786i	−0.861631	+	0.626011i
$392$	3.18876	−	9.81400i	0.161057	−	0.495682i
$393$	32.7034			1.64967
$394$	7.92873	−	24.4021i	0.399444	−	1.22936i
$395$	23.8997	+	9.22000i	1.20253	+	0.463909i
$396$	−0.0870497	−	0.267911i	−0.00437441	−	0.0134631i
$397$	6.82543	+	21.0065i	0.342558	+	1.05429i	0.962878	+	0.269937i	$0.0870029\pi$
$397$	6.82543	+	21.0065i	0.342558	+	1.05429i	−0.620320	+	0.784349i	$0.712997\pi$
$398$	−1.60836	−	1.16854i	−0.0806199	−	0.0585738i
$399$	−7.40663			−0.370795
$400$	3.70454	+	3.35803i	0.185227	+	0.167901i
$401$	11.4709			0.572828			0.286414	−	0.958106i	$-0.407537\pi$
$401$	11.4709			0.572828			0.286414	+	0.958106i	$0.407537\pi$
$402$	0.851864	+	0.618915i	0.0424871	+	0.0308687i
$403$	−1.86531	−	5.74083i	−0.0929177	−	0.285971i
$404$	3.10062	+	9.54272i	0.154261	+	0.474768i
$405$	11.5088	+	17.7869i	0.571878	+	0.883838i
$406$	−10.4608	+	32.1950i	−0.519160	+	1.59781i
$407$	−17.6641			−0.875578
$408$	1.72067	−	5.29567i	0.0851857	−	0.262175i
$409$	16.3858	−	11.9050i	0.810227	−	0.588664i	−0.103669	−	0.994612i	$-0.533058\pi$
$409$	16.3858	−	11.9050i	0.810227	−	0.588664i	0.913896	+	0.405947i	$0.133058\pi$
$410$	13.1753	−	16.2148i	0.650683	−	0.800792i
$411$	23.5647	+	17.1208i	1.16236	+	0.844505i
$412$	−14.8492	+	10.7886i	−0.731570	+	0.531517i
$413$	33.8341	−	24.5819i	1.66487	−	1.20960i
$414$	−0.912189	−	0.662744i	−0.0448316	−	0.0325721i
$415$	10.5150	+	16.2509i	0.516160	+	0.797726i
$416$	1.73468	−	1.26032i	0.0850497	−	0.0617922i
$417$	7.27557	−	22.3919i	0.356286	−	1.09654i
$418$	1.68172			0.0822556
$419$	0.537556	−	1.65443i	0.0262613	−	0.0808240i	−0.937067	−	0.349150i	$-0.886470\pi$
$419$	0.537556	−	1.65443i	0.0262613	−	0.0808240i	0.963328	+	0.268326i	$0.0864704\pi$
$420$	−0.894356	+	16.5376i	−0.0436401	+	0.806951i
$421$	−5.42421	−	16.6940i	−0.264360	−	0.813615i	−0.991840	−	0.127487i	$-0.959309\pi$
$421$	−5.42421	−	16.6940i	−0.264360	−	0.813615i	0.727481	−	0.686128i	$-0.240691\pi$
$422$	−1.84475	−	5.67756i	−0.0898011	−	0.276379i
$423$	−0.776197	−	0.563940i	−0.0377400	−	0.0274197i
$424$	−1.70135			−0.0826247
$425$	−15.5520	−	1.68704i	−0.754382	−	0.0818337i
$426$	15.3028			0.741424
$427$	4.51415	+	3.27972i	0.218455	+	0.158717i
$428$	−4.24095	−	13.0523i	−0.204994	−	0.630907i
$429$	1.98315	+	6.10352i	0.0957476	+	0.294681i
$430$	9.48528	−	2.52463i	0.457421	−	0.121748i
$431$	8.89610	−	27.3794i	0.428510	−	1.31882i	−0.471083	−	0.882089i	$-0.656137\pi$
$431$	8.89610	−	27.3794i	0.428510	−	1.31882i	0.899593	−	0.436730i	$-0.143863\pi$
$432$	−5.04113			−0.242541
$433$	4.35007	−	13.3881i	0.209051	−	0.643393i	−0.790472	−	0.612499i	$-0.790164\pi$
$433$	4.35007	−	13.3881i	0.209051	−	0.643393i	0.999523	−	0.0308943i	$-0.00983552\pi$
$434$	−9.47822	+	6.88633i	−0.454969	+	0.330554i
$435$	1.74811	−	32.3243i	0.0838154	−	1.54983i
$436$	0.960977	+	0.698191i	0.0460225	+	0.0334373i
$437$	5.44570	−	3.95653i	0.260503	−	0.189267i
$438$	5.13494	−	3.73076i	0.245357	−	0.178262i
$439$	2.57534	+	1.87109i	0.122914	+	0.0893024i	0.647544	−	0.762028i	$-0.275796\pi$
$439$	2.57534	+	1.87109i	0.122914	+	0.0893024i	−0.524630	+	0.851331i	$0.675796\pi$
$440$	0.203069	−	3.75495i	0.00968093	−	0.179010i
$441$	−1.39839	+	1.01599i	−0.0665900	+	0.0483805i
$442$	−2.07300	+	6.38005i	−0.0986027	+	0.303468i
$443$	−31.2882			−1.48655			−0.743274	−	0.668987i	$-0.766728\pi$
$443$	−31.2882			−1.48655			−0.743274	+	0.668987i	$0.766728\pi$
$444$	5.77669	−	17.7788i	0.274150	−	0.843746i
$445$	−13.1810	+	3.50828i	−0.624838	+	0.166308i
$446$	8.89546	+	27.3774i	0.421212	+	1.29636i
$447$	−8.40994	−	25.8831i	−0.397776	−	1.22423i
$448$	−3.36682	−	2.44614i	−0.159067	−	0.115569i
$449$	6.42494			0.303212			0.151606	−	0.988441i	$-0.451556\pi$
$449$	6.42494			0.303212			0.151606	+	0.988441i	$0.451556\pi$
$450$	−0.171399	−	0.819805i	−0.00807982	−	0.0386460i
$451$	−15.7132			−0.739907
$452$	−12.1709	−	8.84267i	−0.572470	−	0.415924i
$453$	6.74721	+	20.7658i	0.317012	+	0.975662i
$454$	2.55770	+	7.87178i	0.120039	+	0.369441i
$455$	1.07749	−	19.9239i	0.0505135	−	0.934047i
$456$	−0.549973	+	1.69264i	−0.0257548	+	0.0792652i
$457$	3.55184			0.166148			0.0830741	−	0.996543i	$-0.473526\pi$
$457$	3.55184			0.166148			0.0830741	+	0.996543i	$0.473526\pi$
$458$	2.45517	−	7.55625i	0.114723	−	0.353080i
$459$	12.7597	−	9.27048i	0.595573	−	0.432709i
$460$	−8.17659	−	12.6369i	−0.381236	−	0.589200i
$461$	3.76538	+	2.73571i	0.175371	+	0.127415i	0.672008	−	0.740544i	$-0.265432\pi$
$461$	3.76538	+	2.73571i	0.175371	+	0.127415i	−0.496637	+	0.867958i	$0.665432\pi$
$462$	10.0770	−	7.32139i	0.468826	−	0.340622i
$463$	3.39505	−	2.46665i	0.157781	−	0.114635i	−0.506093	−	0.862479i	$-0.668911\pi$
$463$	3.39505	−	2.46665i	0.157781	−	0.114635i	0.663875	+	0.747844i	$0.268911\pi$
$464$	6.58078	+	4.78122i	0.305505	+	0.221963i
$465$	7.06505	−	8.69492i	0.327634	−	0.403217i
$466$	11.7699	−	8.55132i	0.545229	−	0.396132i
$467$	1.57346	−	4.84261i	0.0728109	−	0.224089i	−0.908028	−	0.418910i	$-0.862412\pi$
$467$	1.57346	−	4.84261i	0.0728109	−	0.224089i	0.980839	+	0.194821i	$0.0624124\pi$
$468$	−0.359164			−0.0166024
$469$	−0.760849	+	2.34165i	−0.0351327	+	0.108127i
$470$	−6.95760	−	10.7530i	−0.320930	−	0.495998i
$471$	2.32058	+	7.14200i	0.106927	+	0.329086i
$472$	−3.10540	−	9.55744i	−0.142938	−	0.439917i
$473$	−5.97227	−	4.33911i	−0.274605	−	0.199512i
$474$	20.3889			0.936493
$475$	4.97084	+	0.539226i	0.228078	+	0.0247414i
$476$	13.0202			0.596780
$477$	0.230559	+	0.167511i	0.0105566	+	0.00766978i
$478$	4.83288	+	14.8741i	0.221051	+	0.680325i
$479$	9.15051	+	28.1624i	0.418098	+	1.28677i	0.909451	+	0.415812i	$0.136503\pi$
$479$	9.15051	+	28.1624i	0.418098	+	1.28677i	−0.491353	+	0.870961i	$0.663497\pi$
$480$	3.71293	+	1.43237i	0.169471	+	0.0653784i
$481$	−6.95956	+	21.4193i	−0.317329	+	0.976638i
$482$	7.36844			0.335623
$483$	15.4063	−	47.4158i	0.701012	−	2.15749i
$484$	6.61114	−	4.80327i	0.300506	−	0.218331i
$485$	30.6302	+	11.8165i	1.39084	+	0.536558i
$486$	1.40670	+	1.02203i	0.0638092	+	0.0463601i
$487$	0.127283	−	0.0924764i	0.00576774	−	0.00419051i	−0.584898	−	0.811107i	$-0.698865\pi$
$487$	0.127283	−	0.0924764i	0.00576774	−	0.00419051i	0.590665	+	0.806917i	$0.298865\pi$
$488$	1.08471	−	0.788088i	0.0491025	−	0.0356751i
$489$	−13.8863	−	10.0890i	−0.627958	−	0.456238i
$490$	−22.2978	+	5.93484i	−1.00731	+	0.268109i
$491$	23.4335	−	17.0254i	1.05754	−	0.768348i	0.0839082	−	0.996473i	$-0.473260\pi$
$491$	23.4335	−	17.0254i	1.05754	−	0.768348i	0.973632	+	0.228126i	$0.0732597\pi$
$492$	5.13869	−	15.8153i	0.231670	−	0.713008i
$493$	−25.4493			−1.14618
$494$	0.662589	−	2.03924i	0.0298113	−	0.0917497i
$495$	−0.397223	+	0.488860i	−0.0178539	+	0.0219726i
$496$	0.869940	+	2.67740i	0.0390615	+	0.120219i
$497$	11.0575	+	34.0315i	0.495997	+	1.52652i
$498$	12.4637	+	9.05544i	0.558514	+	0.405784i
$499$	−26.4971			−1.18617			−0.593086	−	0.805139i	$-0.702091\pi$
$499$	−26.4971			−1.18617			−0.593086	+	0.805139i	$0.702091\pi$
$500$	1.80422	−	11.0338i	0.0806871	−	0.493447i
$501$	−16.6169			−0.742386
$502$	−14.7670	−	10.7289i	−0.659084	−	0.478853i
$503$	−11.5393	−	35.5143i	−0.514512	−	1.58351i	−0.784168	−	0.620549i	$-0.786910\pi$
$503$	−11.5393	−	35.5143i	−0.514512	−	1.58351i	0.269655	−	0.962957i	$-0.413090\pi$
$504$	0.215415	+	0.662978i	0.00959533	+	0.0295314i
$505$	14.1487	−	17.4127i	0.629607	−	0.774854i
$506$	−3.49810	+	10.7660i	−0.155510	+	0.478609i
$507$	−14.9543			−0.664144
$508$	−3.22520	+	9.92614i	−0.143095	+	0.440401i
$509$	−18.3803	+	13.3541i	−0.814691	+	0.591908i	−0.915187	−	0.403030i	$-0.867957\pi$
$509$	−18.3803	+	13.3541i	−0.814691	+	0.591908i	0.100496	+	0.994938i	$0.467957\pi$
$510$	−12.0320	+	3.20246i	−0.532785	+	0.141807i
$511$	12.0071	+	8.72369i	0.531164	+	0.385913i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.07836	+	2.96310i	−0.180064	+	0.130824i
$514$	3.66157	+	2.66028i	0.161505	+	0.117340i
$515$	38.2917	+	14.7721i	1.68733	+	0.650938i
$516$	6.32040	−	4.59204i	0.278240	−	0.202153i
$517$	−2.97659	+	9.16101i	−0.130910	+	0.402901i
$518$	43.7119			1.92059
$519$	−3.62139	+	11.1455i	−0.158961	+	0.489232i
$520$	−4.47321	−	1.72567i	−0.196163	−	0.0756757i
$521$	−4.29124	−	13.2071i	−0.188003	−	0.578613i	0.811984	−	0.583679i	$-0.198387\pi$
$521$	−4.29124	−	13.2071i	−0.188003	−	0.578613i	−0.999987	+	0.00506621i	$0.998387\pi$
$522$	−0.421050	−	1.29586i	−0.0184288	−	0.0567181i
$523$	−28.2769	−	20.5444i	−1.23646	−	0.898343i	−0.239106	−	0.970993i	$-0.576854\pi$
$523$	−28.2769	−	20.5444i	−1.23646	−	0.898343i	−0.997357	+	0.0726501i	$0.976854\pi$
$524$	18.3753			0.802727
$525$	32.1332	−	18.4095i	1.40241	−	0.803457i
$526$	−21.0254			−0.916750
$527$	−7.12558	−	5.17704i	−0.310395	−	0.225515i
$528$	−0.924900	−	2.84655i	−0.0402511	−	0.123880i
$529$	6.89411	+	21.2179i	0.299744	+	0.922516i
$530$	2.06666	+	3.19403i	0.0897700	+	0.138740i
$531$	−0.520174	+	1.60093i	−0.0225736	+	0.0694744i
$532$	−4.16162			−0.180429
$533$	−6.19093	+	19.0537i	−0.268159	+	0.825308i
$534$	−8.78297	+	6.38120i	−0.380076	+	0.276142i
$535$	−19.3522	+	23.8167i	−0.836669	+	1.02968i
$536$	0.478643	+	0.347754i	0.0206742	+	0.0150207i
$537$	7.60331	−	5.52413i	0.328107	−	0.238384i
$538$	0.262786	−	0.190925i	0.0113295	−	0.00823137i
$539$	14.0395	+	10.2003i	0.604724	+	0.439357i
$540$	6.12356	+	9.46398i	0.263516	+	0.407265i
$541$	17.2147	−	12.5072i	0.740118	−	0.537727i	−0.152630	−	0.988283i	$-0.548774\pi$
$541$	17.2147	−	12.5072i	0.740118	−	0.537727i	0.892748	+	0.450556i	$0.148774\pi$
$542$	2.96393	−	9.12203i	0.127312	−	0.391825i
$543$	−20.6835			−0.887615
$544$	0.966804	−	2.97552i	0.0414514	−	0.127574i
$545$	0.143432	−	2.65220i	0.00614394	−	0.113608i
$546$	−4.90755	−	15.1039i	−0.210024	−	0.646387i
$547$	2.82032	+	8.68006i	0.120588	+	0.371133i	0.993072	−	0.117511i	$-0.0374917\pi$
$547$	2.82032	+	8.68006i	0.120588	+	0.371133i	−0.872483	+	0.488644i	$0.837492\pi$
$548$	13.2405	+	9.61977i	0.565605	+	0.410936i
$549$	−0.224588			−0.00958519
$550$	−7.29605	+	4.17999i	−0.311105	+	0.178235i
$551$	8.13430			0.346533
$552$	−9.69198	−	7.04163i	−0.412518	−	0.299712i
$553$	14.7326	+	45.3423i	0.626494	+	1.92815i
$554$	4.59075	+	14.1289i	0.195042	+	0.600279i
$555$	−40.3942	+	10.7514i	−1.71464	+	0.456372i
$556$	4.08798	−	12.5815i	0.173369	−	0.533574i
$557$	15.5467			0.658735			0.329367	−	0.944202i	$-0.393165\pi$
$557$	15.5467			0.658735			0.329367	+	0.944202i	$0.393165\pi$
$558$	0.145720	−	0.448481i	0.00616884	−	0.0189857i
$559$	−7.61460	+	5.53233i	−0.322063	+	0.233993i
$560$	−0.502518	+	9.29208i	−0.0212353	+	0.392662i
$561$	7.57576	+	5.50411i	0.319849	+	0.232384i
$562$	−14.6201	+	10.6221i	−0.616712	+	0.448067i
$563$	27.4469	−	19.9414i	1.15675	−	0.840428i	0.167387	−	0.985891i	$-0.446467\pi$
$563$	27.4469	−	19.9414i	1.15675	−	0.840428i	0.989364	+	0.145463i	$0.0464672\pi$
$564$	−8.24707	−	5.99185i	−0.347264	−	0.252302i
$565$	−1.81658	+	33.5904i	−0.0764241	+	1.41316i
$566$	13.1158	−	9.52920i	0.551299	−	0.400542i
$567$	−12.1843	+	37.4993i	−0.511691	+	1.57482i
$568$	8.59831			0.360777
$569$	−3.99536	+	12.2965i	−0.167494	+	0.515494i	−0.999211	−	0.0397052i	$-0.987358\pi$
$569$	−3.99536	+	12.2965i	−0.167494	+	0.515494i	0.831717	+	0.555200i	$0.187358\pi$
$570$	3.84575	−	1.02359i	0.161081	−	0.0428736i
$571$	5.89348	+	18.1383i	0.246634	+	0.759063i	0.995363	+	0.0961863i	$0.0306645\pi$
$571$	5.89348	+	18.1383i	0.246634	+	0.759063i	−0.748729	+	0.662876i	$0.769336\pi$
$572$	1.11429	+	3.42943i	0.0465908	+	0.143392i
$573$	9.08136	+	6.59800i	0.379379	+	0.275635i
$574$	38.8842			1.62300
$575$	−13.7917	+	30.7007i	−0.575154	+	1.28031i
$576$	0.167506			0.00697943
$577$	−9.34793	−	6.79167i	−0.389159	−	0.282741i	0.375952	−	0.926639i	$-0.377316\pi$
$577$	−9.34793	−	6.79167i	−0.389159	−	0.282741i	−0.765111	+	0.643898i	$0.777316\pi$
$578$	−2.22851	−	6.85864i	−0.0926937	−	0.285282i
$579$	−11.4583	−	35.2650i	−0.476191	−	1.46557i
$580$	0.982222	−	18.1623i	0.0407846	−	0.754148i
$581$	−11.1321	+	34.2610i	−0.461837	+	1.42139i
$582$	26.1306			1.08315
$583$	0.884156	−	2.72115i	0.0366180	−	0.112699i
$584$	2.88521	−	2.09623i	0.119391	−	0.0867424i
$585$	0.436284	+	0.674277i	0.0180381	+	0.0278779i
$586$	−20.5502	−	14.9306i	−0.848921	−	0.616777i
$587$	6.89515	−	5.00962i	0.284593	−	0.206769i	−0.436325	−	0.899789i	$-0.643720\pi$
$587$	6.89515	−	5.00962i	0.284593	−	0.206769i	0.720918	+	0.693020i	$0.243720\pi$
$588$	−14.8579	+	10.7949i	−0.612728	+	0.445173i
$589$	2.27753	+	1.65472i	0.0938441	+	0.0681817i
$590$	−14.1705	+	17.4395i	−0.583390	+	0.717975i
$591$	−36.9435	+	26.8410i	−1.51965	+	1.10409i
$592$	3.24579	−	9.98951i	0.133401	−	0.410567i
$593$	−9.01501			−0.370202			−0.185101	−	0.982720i	$-0.559261\pi$
$593$	−9.01501			−0.370202			−0.185101	+	0.982720i	$0.559261\pi$
$594$	2.61977	−	8.06284i	0.107491	−	0.330822i
$595$	−15.8159	−	24.4435i	−0.648389	−	1.00209i
$596$	−4.72535	−	14.5431i	−0.193558	−	0.595710i
$597$	1.09337	+	3.36505i	0.0447487	+	0.137722i
$598$	11.6766	+	8.48353i	0.477490	+	0.346917i
$599$	−15.5410			−0.634988			−0.317494	−	0.948260i	$-0.602841\pi$
$599$	−15.5410			−0.634988			−0.317494	+	0.948260i	$0.602841\pi$
$600$	−1.82111	−	8.71041i	−0.0743465	−	0.355601i
$601$	1.50248			0.0612874			0.0306437	−	0.999530i	$-0.490244\pi$
$601$	1.50248			0.0612874			0.0306437	+	0.999530i	$0.490244\pi$
$602$	14.7791	+	10.7376i	0.602351	+	0.437633i
$603$	−0.0306244	−	0.0942521i	−0.00124712	−	0.00383824i
$604$	3.79110	+	11.6678i	0.154258	+	0.474757i
$605$	−17.0481	−	6.57680i	−0.693105	−	0.267385i
$606$	5.51832	−	16.9836i	0.224166	−	0.689913i
$607$	43.9592			1.78425			0.892124	−	0.451791i	$-0.149215\pi$
$607$	43.9592			1.78425			0.892124	+	0.451791i	$0.149215\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	48.7414	−	35.4127i	1.97510	−	1.43500i
$610$	−2.79714	−	1.07908i	−0.113253	−	0.0436905i
$611$	9.93579	+	7.21878i	0.401959	+	0.292040i
$612$	−0.423979	+	0.308039i	−0.0171383	+	0.0124517i
$613$	24.6733	−	17.9262i	0.996544	−	0.724031i	0.0351993	−	0.999380i	$-0.488793\pi$
$613$	24.6733	−	17.9262i	0.996544	−	0.724031i	0.961344	+	0.275349i	$0.0887934\pi$
$614$	12.3450	+	8.96914i	0.498202	+	0.361965i
$615$	−35.9329	+	9.56400i	−1.44896	+	0.385658i
$616$	5.66205	−	4.11372i	0.228130	−	0.165746i
$617$	8.69290	−	26.7540i	0.349963	−	1.07708i	−0.608910	−	0.793239i	$-0.708393\pi$
$617$	8.69290	−	26.7540i	0.349963	−	1.07708i	0.958873	−	0.283836i	$-0.0916071\pi$
$618$	32.6667			1.31405
$619$	−0.302839	+	0.932042i	−0.0121721	+	0.0374619i	−0.956958	−	0.290226i	$-0.906269\pi$
$619$	−0.302839	+	0.932042i	−0.0121721	+	0.0374619i	0.944786	+	0.327688i	$0.106269\pi$
$620$	3.96969	−	4.88548i	0.159427	−	0.196206i
$621$	−10.4859	−	32.2723i	−0.420785	−	1.29504i
$622$	−1.10213	−	3.39200i	−0.0441914	−	0.136007i
$623$	−20.5374	−	14.9213i	−0.822812	−	0.597808i
$624$	−3.81611			−0.152766
$625$	−22.9060	+	10.0158i	−0.916238	+	0.400633i
$626$	−23.3702			−0.934062
$627$	−2.42142	−	1.75927i	−0.0967022	−	0.0702583i
$628$	1.30388	+	4.01293i	0.0520304	+	0.160133i
$629$	10.1549	+	31.2536i	0.404903	+	1.24616i
$630$	0.982975	−	1.20974i	0.0391627	−	0.0481973i
$631$	4.91999	−	15.1422i	0.195862	−	0.602800i	−0.804104	−	0.594489i	$-0.797354\pi$
$631$	4.91999	−	15.1422i	0.195862	−	0.602800i	0.999965	−	0.00831132i	$-0.00264561\pi$
$632$	11.4560			0.455697
$633$	−3.28320	+	10.1046i	−0.130495	+	0.401623i
$634$	24.1431	−	17.5410i	0.958843	−	0.696640i
$635$	22.5526	−	6.00265i	0.894972	−	0.238208i
$636$	2.44968	+	1.77980i	0.0971361	+	0.0705735i
$637$	17.9002	−	13.0053i	0.709234	−	0.515288i
$638$	−11.0670	+	8.04068i	−0.438148	+	0.318333i
$639$	−1.16520	−	0.846569i	−0.0460947	−	0.0334898i
$640$	2.08621	+	0.804816i	0.0824647	+	0.0318131i
$641$	19.0142	−	13.8146i	0.751015	−	0.545644i	−0.145126	−	0.989413i	$-0.546359\pi$
$641$	19.0142	−	13.8146i	0.751015	−	0.545644i	0.896141	+	0.443769i	$0.146359\pi$
$642$	−7.54782	+	23.2298i	−0.297889	+	0.916808i
$643$	−27.3851			−1.07996			−0.539982	−	0.841677i	$-0.681569\pi$
$643$	−27.3851			−1.07996			−0.539982	+	0.841677i	$0.681569\pi$
$644$	8.65646	−	26.6419i	0.341112	−	1.04984i
$645$	−16.2984	−	6.28757i	−0.641749	−	0.247573i
$646$	−0.966804	−	2.97552i	−0.0380384	−	0.117070i
$647$	8.33945	+	25.6662i	0.327857	+	1.00904i	0.970134	+	0.242569i	$0.0779900\pi$
$647$	8.33945	+	25.6662i	0.327857	+	1.00904i	−0.642277	+	0.766473i	$0.722010\pi$
$648$	7.66500	+	5.56895i	0.301110	+	0.218769i
$649$	16.9001			0.663386
$650$	2.19401	+	10.4940i	0.0860562	+	0.411609i
$651$	20.8510			0.817217
$652$	−7.80237	−	5.66875i	−0.305564	−	0.222005i
$653$	−7.37425	−	22.6956i	−0.288577	−	0.888148i	−0.985304	−	0.170811i	$-0.945361\pi$
$653$	−7.37425	−	22.6956i	−0.288577	−	0.888148i	0.696727	−	0.717336i	$-0.254639\pi$
$654$	−0.653276	−	2.01058i	−0.0255451	−	0.0786198i
$655$	−22.3208	−	34.4969i	−0.872147	−	1.34790i
$656$	2.88731	−	8.88624i	0.112731	−	0.346949i
$657$	−0.597379			−0.0233060
$658$	7.36593	−	22.6700i	0.287154	−	0.883769i
$659$	−0.613820	+	0.445966i	−0.0239110	+	0.0173724i	−0.599677	−	0.800242i	$-0.704704\pi$
$659$	−0.613820	+	0.445966i	−0.0239110	+	0.0173724i	0.575766	+	0.817615i	$0.304704\pi$
$660$	−4.22048	+	5.19413i	−0.164282	+	0.202181i
$661$	−17.9802	−	13.0634i	−0.699349	−	0.508107i	0.180371	−	0.983599i	$-0.442270\pi$
$661$	−17.9802	−	13.0634i	−0.699349	−	0.508107i	−0.879720	+	0.475492i	$0.842270\pi$
$662$	−16.7862	+	12.1959i	−0.652413	+	0.474006i
$663$	9.65904	−	7.01770i	0.375126	−	0.272545i
$664$	7.00309	+	5.08804i	0.271773	+	0.197454i
$665$	5.05520	+	7.81282i	0.196032	+	0.302968i
$666$	−1.42340	+	1.03416i	−0.0551556	+	0.0400729i
$667$	−16.9199	+	52.0742i	−0.655142	+	2.01632i
$668$	−9.33663			−0.361245
$669$	15.8317	−	48.7249i	0.612089	−	1.88382i
$670$	0.0714404	−	1.32101i	0.00275998	−	0.0510349i
$671$	0.696774	+	2.14445i	0.0268987	+	0.0827856i
$672$	2.28878	+	7.04413i	0.0882914	+	0.271733i
$673$	10.3542	+	7.52274i	0.399123	+	0.289980i	0.769184	−	0.639028i	$-0.220663\pi$
$673$	10.3542	+	7.52274i	0.399123	+	0.289980i	−0.370060	+	0.929008i	$0.620663\pi$
$674$	−19.7216			−0.759647
$675$	10.3288	−	22.9922i	0.397556	−	0.884969i
$676$	−8.40248			−0.323172
$677$	−8.36457	−	6.07721i	−0.321476	−	0.233566i	0.415329	−	0.909671i	$-0.363667\pi$
$677$	−8.36457	−	6.07721i	−0.321476	−	0.233566i	−0.736805	+	0.676105i	$0.763667\pi$
$678$	8.27381	+	25.4642i	0.317754	+	0.977946i
$679$	18.8815	+	58.1112i	0.724604	+	2.23010i
$680$	−6.76049	+	1.79939i	−0.259253	+	0.0690034i
$681$	4.55206	−	14.0098i	0.174435	−	0.536856i
$682$	−4.73436			−0.181288
$683$	−11.3205	+	34.8408i	−0.433166	+	1.33315i	0.461789	+	0.886990i	$0.347208\pi$
$683$	−11.3205	+	34.8408i	−0.433166	+	1.33315i	−0.894955	+	0.446157i	$0.852792\pi$
$684$	0.135515	−	0.0984577i	0.00518156	−	0.00376462i
$685$	1.97622	−	36.5424i	0.0755076	−	1.39621i
$686$	−11.1746	−	8.11885i	−0.426650	−	0.309979i
$687$	−11.4397	+	8.31146i	−0.436453	+	0.317102i
$688$	3.55129	−	2.58016i	0.135392	−	0.0983677i
$689$	−2.95129	−	2.14424i	−0.112435	−	0.0816890i
$690$	−1.44659	+	26.7489i	−0.0550706	+	1.01831i
$691$	20.5958	−	14.9637i	0.783502	−	0.569247i	−0.122526	−	0.992465i	$-0.539100\pi$
$691$	20.5958	−	14.9637i	0.783502	−	0.569247i	0.906028	+	0.423218i	$0.139100\pi$
$692$	−2.03477	+	6.26239i	−0.0773505	+	0.238060i
$693$	−1.17232			−0.0445328
$694$	−6.51476	+	20.0504i	−0.247297	+	0.761102i
$695$	−28.5857	+	7.60843i	−1.08432	+	0.288604i
$696$	−4.47364	−	13.7685i	−0.169573	−	0.521892i
$697$	9.03337	+	27.8019i	0.342163	+	1.05307i
$698$	−5.52362	−	4.01315i	−0.209072	−	0.151900i
$699$	−25.8925			−0.979343
$700$	18.0549	−	10.3439i	0.682412	−	0.390962i
$701$	−33.8585			−1.27882			−0.639409	−	0.768867i	$-0.720821\pi$
$701$	−33.8585			−1.27882			−0.639409	+	0.768867i	$0.720821\pi$
$702$	−8.74474	−	6.35343i	−0.330049	−	0.239795i
$703$	−3.24579	−	9.98951i	−0.122417	−	0.376762i
$704$	−0.519680	−	1.59941i	−0.0195862	−	0.0602801i
$705$	−1.23093	+	22.7611i	−0.0463593	+	0.857232i
$706$	0.160445	−	0.493800i	0.00603844	−	0.0185844i
$707$	41.7569			1.57043
$708$	−5.52683	+	17.0098i	−0.207711	+	0.639269i
$709$	−12.1261	+	8.81015i	−0.455407	+	0.330872i	−0.791727	−	0.610875i	$-0.790818\pi$
$709$	−12.1261	+	8.81015i	−0.455407	+	0.330872i	0.336320	+	0.941748i	$0.390818\pi$
$710$	−10.4445	−	16.1421i	−0.391977	−	0.605801i
$711$	−1.55247	−	1.12794i	−0.0582222	−	0.0423009i
$712$	−4.93495	+	3.58545i	−0.184945	+	0.134370i
$713$	−15.3307	+	11.1384i	−0.574137	+	0.417135i
$714$	−18.7471	−	13.6206i	−0.701593	−	0.509737i
$715$	5.08470	−	6.25771i	0.190157	−	0.234025i
$716$	4.27212	−	3.10388i	0.159657	−	0.115997i
$717$	8.60132	−	26.4721i	0.321222	−	0.988620i
$718$	−10.8919			−0.406481
$719$	−3.28706	+	10.1165i	−0.122587	+	0.377283i	−0.993454	−	0.114236i	$-0.963558\pi$
$719$	−3.28706	+	10.1165i	−0.122587	+	0.377283i	0.870867	+	0.491519i	$0.163558\pi$
$720$	−0.203473	−	0.314468i	−0.00758300	−	0.0117195i
$721$	23.6043	+	72.6466i	0.879070	+	2.70550i
$722$	0.309017	+	0.951057i	0.0115004	+	0.0353947i
$723$	−10.6094	−	7.70820i	−0.394569	−	0.286671i
$724$	−11.6216			−0.431913
$725$	−35.2902	+	20.2181i	−1.31064	+	0.750883i
$726$	−14.5438			−0.539770
$727$	−6.89785	−	5.01158i	−0.255827	−	0.185869i	0.452478	−	0.891775i	$-0.350540\pi$
$727$	−6.89785	−	5.01158i	−0.255827	−	0.185869i	−0.708305	+	0.705906i	$0.750540\pi$
$728$	−2.75744	−	8.48653i	−0.102198	−	0.314532i
$729$	7.82703	+	24.0891i	0.289890	+	0.892189i
$730$	−7.44008	−	2.87022i	−0.275370	−	0.106232i
$731$	−4.24391	+	13.0614i	−0.156967	+	0.483094i
$732$	−2.38624			−0.0881981
$733$	−14.9508	+	46.0137i	−0.552219	+	1.69955i	0.150959	+	0.988540i	$0.451764\pi$
$733$	−14.9508	+	46.0137i	−0.552219	+	1.69955i	−0.703178	+	0.711014i	$0.748236\pi$
$734$	−1.99789	+	1.45155i	−0.0737434	+	0.0535777i
$735$	38.3139	+	14.7807i	1.41323	+	0.545194i
$736$	−5.44570	−	3.95653i	−0.200731	−	0.145840i
$737$	−0.804944	+	0.584826i	−0.0296505	+	0.0215423i
$738$	−1.26619	+	0.919944i	−0.0466092	+	0.0338636i
$739$	32.7325	+	23.7815i	1.20408	+	0.874817i	0.994680	−	0.103012i	$-0.0328480\pi$
$739$	32.7325	+	23.7815i	1.20408	+	0.874817i	0.209403	+	0.977829i	$0.432848\pi$
$740$	−22.6966	+	6.04098i	−0.834343	+	0.222071i
$741$	−3.08729	+	2.24305i	−0.113415	+	0.0824005i
$742$	−2.18795	+	6.73381i	−0.0803221	+	0.247206i
$743$	15.3009			0.561337			0.280669	−	0.959805i	$-0.409444\pi$
$743$	15.3009			0.561337			0.280669	+	0.959805i	$0.409444\pi$
$744$	1.54827	−	4.76510i	0.0567625	−	0.174697i
$745$	−21.5626	+	26.5370i	−0.789993	+	0.972240i
$746$	9.93318	+	30.5712i	0.363680	+	1.11929i
$747$	−0.448070	−	1.37902i	−0.0163940	−	0.0504556i
$748$	4.25664	+	3.09263i	0.155638	+	0.113078i
$749$	−57.1140			−2.08690
$750$	−14.1404	+	13.9996i	−0.516333	+	0.511192i
$751$	−32.2483			−1.17676			−0.588378	−	0.808586i	$-0.700233\pi$
$751$	−32.2483			−1.17676			−0.588378	+	0.808586i	$0.700233\pi$
$752$	−4.63384	−	3.36668i	−0.168979	−	0.122770i
$753$	10.0387	+	30.8959i	0.365830	+	1.12591i
$754$	5.38969	+	16.5878i	0.196281	+	0.604091i
$755$	17.2995	−	21.2904i	0.629592	−	0.774836i
$756$	−6.48294	+	19.9524i	−0.235782	+	0.725663i
$757$	7.69323			0.279615			0.139808	−	0.990179i	$-0.455352\pi$
$757$	7.69323			0.279615			0.139808	+	0.990179i	$0.455352\pi$
$758$	0.784386	−	2.41409i	0.0284902	−	0.0876838i
$759$	16.2992	−	11.8421i	0.591623	−	0.429840i
$760$	2.16084	−	0.575134i	0.0783818	−	0.0208623i
$761$	4.04507	+	2.93892i	0.146634	+	0.106536i	0.658683	−	0.752420i	$-0.271114\pi$
$761$	4.04507	+	2.93892i	0.146634	+	0.106536i	−0.512050	+	0.858956i	$0.671114\pi$
$762$	15.0276	−	10.9182i	0.544394	−	0.395525i
$763$	3.99922	−	2.90560i	0.144781	−	0.105190i
$764$	5.10261	+	3.70726i	0.184606	+	0.134124i
$765$	1.09331	+	0.421777i	0.0395288	+	0.0152494i
$766$	6.50873	−	4.72887i	0.235170	−	0.170861i
$767$	6.65854	−	20.4929i	0.240426	−	0.739955i
$768$	1.77975			0.0642212
$769$	11.2957	−	34.7645i	0.407332	−	1.25364i	−0.511600	−	0.859224i	$-0.670947\pi$
$769$	11.2957	−	34.7645i	0.407332	−	1.25364i	0.918932	−	0.394415i	$-0.129053\pi$
$770$	−14.6007	−	5.63264i	−0.526173	−	0.202986i
$771$	−2.48915	−	7.66081i	−0.0896444	−	0.275897i
$772$	−6.43816	−	19.8146i	−0.231714	−	0.713144i
$773$	−35.0114	−	25.4373i	−1.25927	−	0.914916i	−0.260551	−	0.965460i	$-0.583904\pi$
$773$	−35.0114	−	25.4373i	−1.25927	−	0.914916i	−0.998722	+	0.0505444i	$0.983904\pi$
$774$	−0.735291			−0.0264295
$775$	−13.9938	−	1.51802i	−0.502673	−	0.0545289i
$776$	14.6822			0.527061
$777$	−62.9385	−	45.7275i	−2.25791	−	1.64047i
$778$	8.95393	+	27.5574i	0.321014	+	0.987979i
$779$	−2.88731	−	8.88624i	−0.103449	−	0.318383i
$780$	4.63550	+	7.16418i	0.165978	+	0.256519i
$781$	−4.46837	+	13.7522i	−0.159891	+	0.492093i
$782$	21.0597			0.753093
$783$	12.6716	−	38.9991i	0.452845	−	1.39371i
$784$	−8.34829	+	6.06539i	−0.298153	+	0.216621i
$785$	5.94983	−	7.32243i	0.212359	−	0.261349i
$786$	−26.4576	−	19.2226i	−0.943711	−	0.685646i
$787$	36.2448	−	26.3334i	1.29199	−	0.938684i	0.292144	−	0.956374i	$-0.405631\pi$
$787$	36.2448	−	26.3334i	1.29199	−	0.938684i	0.999844	+	0.0176907i	$0.00563141\pi$
$788$	−20.7577	+	15.0813i	−0.739462	+	0.537250i
$789$	30.2733	+	21.9949i	1.07776	+	0.783038i
$790$	−13.9159	−	21.5070i	−0.495105	−	0.765186i
$791$	−50.6506	+	36.7998i	−1.80093	+	1.30845i
$792$	−0.0870497	+	0.267911i	−0.00309318	+	0.00951982i
$793$	2.87487			0.102089
$794$	6.82543	−	21.0065i	0.242225	−	0.745493i
$795$	0.365629	−	6.76086i	0.0129675	−	0.239783i
$796$	0.614340	+	1.89074i	0.0217747	+	0.0670156i
$797$	−6.64757	−	20.4591i	−0.235469	−	0.724700i	−0.997059	−	0.0766400i	$-0.975581\pi$
$797$	−6.64757	−	20.4591i	−0.235469	−	0.724700i	0.761590	−	0.648060i	$-0.224419\pi$
$798$	5.99209	+	4.35351i	0.212118	+	0.154113i
$799$	17.9200			0.633966
$800$	−1.02324	−	4.89418i	−0.0361770	−	0.173035i
$801$	1.02178			0.0361027
$802$	−9.28012	−	6.74241i	−0.327693	−	0.238083i
$803$	1.85334	+	5.70400i	0.0654030	+	0.201290i
$804$	−0.325383	−	1.00143i	−0.0114754	−	0.0353176i
$805$	−60.5313	+	16.1112i	−2.13345	+	0.567844i
$806$	−1.86531	+	5.74083i	−0.0657027	+	0.202212i
$807$	−0.578101			−0.0203501
$808$	3.10062	−	9.54272i	0.109079	−	0.335712i
$809$	−37.7068	+	27.3956i	−1.32570	+	0.963179i	−0.325860	+	0.945418i	$0.605654\pi$
$809$	−37.7068	+	27.3956i	−1.32570	+	0.963179i	−0.999842	+	0.0177609i	$0.994346\pi$
$810$	1.14405	−	21.1546i	0.0401977	−	0.743298i
$811$	−12.5249	−	9.09989i	−0.439810	−	0.319541i	0.345750	−	0.938327i	$-0.387625\pi$
$811$	−12.5249	−	9.09989i	−0.439810	−	0.319541i	−0.785559	+	0.618786i	$0.787625\pi$
$812$	27.3867	−	19.8976i	0.961085	−	0.698269i
$813$	−13.8103	+	10.0337i	−0.484347	+	0.351899i
$814$	14.2906	+	10.3827i	0.500884	+	0.363914i
$815$	−1.16455	+	21.5337i	−0.0407924	+	0.754294i
$816$	−4.50477	+	3.27290i	−0.157698	+	0.114575i
$817$	1.35647	−	4.17479i	0.0474569	−	0.146057i
$818$	−20.2540			−0.708164
$819$	−0.461888	+	1.42155i	−0.0161397	+	0.0496728i
$820$	−20.1899	+	5.37379i	−0.705061	+	0.187661i
$821$	13.7034	+	42.1747i	0.478252	+	1.47191i	0.841521	+	0.540224i	$0.181661\pi$
$821$	13.7034	+	42.1747i	0.478252	+	1.47191i	−0.363269	+	0.931684i	$0.618339\pi$
$822$	−9.00092	−	27.7020i	−0.313943	−	0.966218i
$823$	35.6066	+	25.8697i	1.24117	+	0.901761i	0.997676	−	0.0681423i	$-0.0217072\pi$
$823$	35.6066	+	25.8697i	1.24117	+	0.901761i	0.243492	+	0.969903i	$0.421707\pi$
$824$	18.3547			0.639415
$825$	14.8779	+	1.61392i	0.517983	+	0.0561896i
$826$	−41.8213			−1.45515
$827$	−32.3636	−	23.5135i	−1.12539	−	0.817646i	−0.140375	−	0.990098i	$-0.544831\pi$
$827$	−32.3636	−	23.5135i	−1.12539	−	0.817646i	−0.985018	+	0.172452i	$0.944831\pi$
$828$	0.348425	+	1.07234i	0.0121086	+	0.0372665i
$829$	−14.1931	−	43.6818i	−0.492946	−	1.51713i	−0.820134	−	0.572172i	$-0.806101\pi$
$829$	−14.1931	−	43.6818i	−0.492946	−	1.51713i	0.327188	−	0.944959i	$-0.393899\pi$
$830$	1.04525	−	19.3278i	0.0362813	−	0.670879i
$831$	8.17039	−	25.1459i	0.283428	−	0.872301i
$832$	−2.14418			−0.0743361
$833$	9.97649	−	30.7045i	0.345665	−	1.06385i
$834$	−19.0477	+	13.8390i	−0.659568	+	0.479204i
$835$	11.3414	+	17.5281i	0.392485	+	0.606587i
$836$	−1.36054	−	0.988491i	−0.0470553	−	0.0341877i
$837$	11.4813	−	8.34168i	0.396853	−	0.288331i
$838$	−1.40734	+	1.02249i	−0.0486157	+	0.0353214i
$839$	45.6904	+	33.1960i	1.57741	+	1.14605i	0.919593	+	0.392872i	$0.128518\pi$
$839$	45.6904	+	33.1960i	1.57741	+	1.14605i	0.657813	+	0.753181i	$0.271482\pi$
$840$	10.4441	−	12.8535i	0.360355	−	0.443487i
$841$	−30.0686	+	21.8461i	−1.03685	+	0.753313i
$842$	−5.42421	+	16.6940i	−0.186930	+	0.575313i
$843$	32.1626			1.10774
$844$	−1.84475	+	5.67756i	−0.0634990	+	0.195430i
$845$	10.2067	+	15.7744i	0.351120	+	0.542657i
$846$	0.296481	+	0.912474i	0.0101932	+	0.0313715i
$847$	−10.5090	−	32.3435i	−0.361095	−	1.11134i
$848$	1.37642	+	1.00003i	0.0472664	+	0.0343410i
$849$	−28.8534			−0.990245
$850$	11.5902	+	10.5061i	0.397540	+	0.360355i
$851$	70.7024			2.42365
$852$	−12.3802	−	8.99478i	−0.424140	−	0.308156i
$853$	3.43890	+	10.5839i	0.117746	+	0.362384i	0.992510	−	0.122165i	$-0.0389837\pi$
$853$	3.43890	+	10.5839i	0.117746	+	0.362384i	−0.874764	+	0.484549i	$0.838984\pi$
$854$	−1.72425	−	5.30670i	−0.0590026	−	0.181591i
$855$	−0.349453	−	0.134812i	−0.0119510	−	0.00461046i
$856$	−4.24095	+	13.0523i	−0.144953	+	0.446118i
$857$	7.53875			0.257519			0.128759	−	0.991676i	$-0.458900\pi$
$857$	7.53875			0.257519			0.128759	+	0.991676i	$0.458900\pi$
$858$	1.98315	−	6.10352i	0.0677038	−	0.208371i
$859$	26.0732	−	18.9433i	0.889606	−	0.646336i	−0.0461696	−	0.998934i	$-0.514701\pi$
$859$	26.0732	−	18.9433i	0.889606	−	0.646336i	0.935775	+	0.352597i	$0.114701\pi$
$860$	−9.15769	−	3.53284i	−0.312275	−	0.120469i
$861$	−55.9874	−	40.6772i	−1.90804	−	1.38628i
$862$	−23.2903	+	16.9214i	−0.793271	+	0.576345i
$863$	10.5212	−	7.64409i	0.358146	−	0.260208i	−0.394133	−	0.919054i	$-0.628955\pi$
$863$	10.5212	−	7.64409i	0.358146	−	0.260208i	0.752278	+	0.658846i	$0.228955\pi$
$864$	4.07836	+	2.96310i	0.138749	+	0.100807i
$865$	14.2284	−	3.78706i	0.483780	−	0.128764i
$866$	−11.3886	+	8.27433i	−0.387001	+	0.281173i
$867$	−3.96618	+	12.2067i	−0.134699	+	0.414560i
$868$	11.7157			0.397657
$869$	−5.95348	+	18.3229i	−0.201958	+	0.621563i
$870$	−20.4140	+	25.1234i	−0.692100	+	0.851764i
$871$	0.392011	+	1.20648i	0.0132828	+	0.0408802i
$872$	−0.367061	−	1.12970i	−0.0124302	−	0.0382564i
$873$	−1.98967	−	1.44558i	−0.0673400	−	0.0489253i
$874$	−6.73125			−0.227688
$875$	−41.3508	−	21.3306i	−1.39791	−	0.721104i
$876$	−6.34714			−0.214450
$877$	8.05219	+	5.85026i	0.271903	+	0.197549i	0.715378	−	0.698738i	$-0.246254\pi$
$877$	8.05219	+	5.85026i	0.271903	+	0.197549i	−0.443475	+	0.896287i	$0.646254\pi$
$878$	−0.983692	−	3.02749i	−0.0331980	−	0.102173i
$879$	13.9701	+	42.9955i	0.471200	+	1.45020i
$880$	−2.37139	+	2.91846i	−0.0799397	+	0.0983813i
$881$	−4.69981	+	14.4645i	−0.158341	+	0.487322i	−0.998484	−	0.0550419i	$-0.982471\pi$
$881$	−4.69981	+	14.4645i	−0.158341	+	0.487322i	0.840143	+	0.542364i	$0.182471\pi$
$882$	1.72851			0.0582018
$883$	1.86102	−	5.72763i	0.0626283	−	0.192750i	−0.914847	−	0.403801i	$-0.867689\pi$
$883$	1.86102	−	5.72763i	0.0626283	−	0.192750i	0.977475	+	0.211051i	$0.0676887\pi$
$884$	5.42719	−	3.94309i	0.182536	−	0.132620i
$885$	38.6470	−	10.2864i	1.29911	−	0.345773i
$886$	25.3127	+	18.3908i	0.850397	+	0.617850i
$887$	−31.1121	+	22.6043i	−1.04464	+	0.758977i	−0.971186	−	0.238322i	$-0.923403\pi$
$887$	−31.1121	+	22.6043i	−1.04464	+	0.758977i	−0.0734557	+	0.997298i	$0.523403\pi$
$888$	−15.1236	+	10.9879i	−0.507514	+	0.368730i
$889$	35.1394	+	25.5302i	1.17854	+	0.856257i
$890$	12.7257	+	4.90932i	0.426568	+	0.164561i
$891$	−12.8904	+	9.36542i	−0.431844	+	0.313753i
$892$	8.89546	−	27.3774i	0.297842	−	0.916664i
$893$	−5.72774			−0.191672
$894$	−8.40994	+	25.8831i	−0.281270	+	0.865661i
$895$	−11.0165	−	4.24994i	−0.368241	−	0.142060i
$896$	1.28601	+	3.95793i	0.0429626	+	0.132225i
$897$	−7.93777	−	24.4300i	−0.265035	−	0.815693i
$898$	−5.19789	−	3.77649i	−0.173456	−	0.126023i
$899$	−22.8996			−0.763743
$900$	−0.343205	+	0.763982i	−0.0114402	+	0.0254661i
$901$	−5.32290			−0.177332
$902$	12.7123	+	9.23601i	0.423272	+	0.307525i
$903$	−10.0469	−	30.9211i	−0.334339	−	1.02899i
$904$	4.64887	+	14.3077i	0.154619	+	0.475868i
$905$	14.1170	+	21.8178i	0.469265	+	0.725250i
$906$	6.74721	−	20.7658i	0.224161	−	0.689897i
$907$	−32.0420			−1.06394			−0.531969	−	0.846764i	$-0.678548\pi$
$907$	−32.0420			−1.06394			−0.531969	+	0.846764i	$0.678548\pi$
$908$	2.55770	−	7.87178i	0.0848801	−	0.261234i
$909$	−1.35974	+	0.987905i	−0.0450996	+	0.0327668i
$910$	−12.5827	+	15.4854i	−0.417112	+	0.513338i
$911$	2.50437	+	1.81953i	0.0829735	+	0.0602838i	0.628499	−	0.777811i	$-0.283670\pi$
$911$	2.50437	+	1.81953i	0.0829735	+	0.0602838i	−0.545525	+	0.838094i	$0.683670\pi$
$912$	1.43985	−	1.04611i	0.0476781	−	0.0346402i
$913$	−11.7772	+	8.55667i	−0.389770	+	0.283184i
$914$	−2.87350	−	2.08772i	−0.0950470	−	0.0690557i
$915$	2.89862	+	4.47982i	0.0958254	+	0.148098i
$916$	−6.42773	+	4.67002i	−0.212378	+	0.154302i
$917$	23.6308	−	72.7281i	0.780357	−	2.40169i
$918$	−15.7719			−0.520550
$919$	−3.83867	+	11.8142i	−0.126626	+	0.389714i	−0.994194	−	0.107604i	$-0.965682\pi$
$919$	−3.83867	+	11.8142i	−0.126626	+	0.389714i	0.867568	+	0.497319i	$0.165682\pi$
$920$	−0.812804	+	15.0296i	−0.0267974	+	0.495511i
$921$	−8.39215	−	25.8284i	−0.276531	−	0.851074i
$922$	−1.43825	−	4.42647i	−0.0473661	−	0.145778i
$923$	14.9153	+	10.8366i	0.490943	+	0.356691i
$924$	−12.4559			−0.409769
$925$	38.9110	+	35.2714i	1.27939	+	1.15972i
$926$	−4.19651			−0.137906
$927$	−2.48734	−	1.80716i	−0.0816950	−	0.0593549i
$928$	−2.51364	−	7.73618i	−0.0825141	−	0.253952i
$929$	−17.2408	−	53.0617i	−0.565652	−	1.74090i	−0.666007	−	0.745945i	$-0.731998\pi$
$929$	−17.2408	−	53.0617i	−0.565652	−	1.74090i	0.100355	−	0.994952i	$-0.468002\pi$
$930$	−10.8265	+	2.88161i	−0.355015	+	0.0944916i
$931$	−3.18876	+	9.81400i	−0.104507	+	0.321641i
$932$	−14.5484			−0.476548
$933$	−1.96151	+	6.03692i	−0.0642171	+	0.197640i
$934$	−4.11937	+	2.99289i	−0.134790	+	0.0979305i
$935$	0.635330	−	11.7479i	0.0207775	−	0.384198i
$936$	0.290570	+	0.211111i	0.00949757	+	0.00690038i
$937$	−11.0140	+	8.00212i	−0.359811	+	0.261418i	−0.752973	−	0.658051i	$-0.771381\pi$
$937$	−11.0140	+	8.00212i	−0.359811	+	0.261418i	0.393162	+	0.919469i	$0.371381\pi$
$938$	1.99193	−	1.44722i	0.0650387	−	0.0472534i
$939$	33.6496	+	24.4478i	1.09811	+	0.797825i
$940$	−0.691629	+	12.7889i	−0.0225584	+	0.417129i
$941$	−0.591279	+	0.429589i	−0.0192751	+	0.0140042i	−0.597381	−	0.801957i	$-0.703792\pi$
$941$	−0.591279	+	0.429589i	−0.0192751	+	0.0140042i	0.578106	+	0.815962i	$0.303792\pi$
$942$	2.32058	−	7.14200i	0.0756085	−	0.232699i
$943$	62.8938			2.04810
$944$	−3.10540	+	9.55744i	−0.101072	+	0.311068i
$945$	45.3327	−	12.0659i	1.47467	−	0.392503i
$946$	2.28120	+	7.02083i	0.0741684	+	0.228267i
$947$	−3.26786	−	10.0574i	−0.106191	−	0.326823i	0.883817	−	0.467833i	$-0.154965\pi$
$947$	−3.26786	−	10.0574i	−0.106191	−	0.326823i	−0.990008	+	0.141010i	$0.954965\pi$
$948$	−16.4950	−	11.9843i	−0.535731	−	0.389232i
$949$	7.64682			0.248226
$950$	−3.70454	−	3.35803i	−0.120191	−	0.108949i
$951$	−53.1121			−1.72228
$952$	−10.5336	−	7.65309i	−0.341395	−	0.248038i
$953$	−9.20865	−	28.3413i	−0.298297	−	0.918065i	−0.982094	−	0.188392i	$-0.939672\pi$
$953$	−9.20865	−	28.3413i	−0.298297	−	0.918065i	0.683796	−	0.729673i	$-0.260328\pi$
$954$	−0.0880655	−	0.271038i	−0.00285123	−	0.00877517i
$955$	0.761595	−	14.0827i	0.0246446	−	0.455705i
$956$	4.83288	−	14.8741i	0.156307	−	0.481062i
$957$	24.3463			0.787003
$958$	9.15051	−	28.1624i	0.295640	−	0.909885i
$959$	55.1018	−	40.0338i	1.77933	−	1.29276i
$960$	−2.16190	−	3.34122i	−0.0697749	−	0.107837i
$961$	18.6679	+	13.5630i	0.602189	+	0.437516i
$962$	18.2204	−	13.2379i	0.587449	−	0.426806i
$963$	1.85981	−	1.35123i	0.0599316	−	0.0435429i
$964$	−5.96119	−	4.33106i	−0.191997	−	0.139494i
$965$	−29.3785	+	36.1559i	−0.945726	+	1.16390i
$966$	−40.3343	+	29.3046i	−1.29773	+	0.942859i
$967$	1.74900	−	5.38287i	0.0562440	−	0.173101i	−0.918988	−	0.394285i	$-0.870992\pi$
$967$	1.74900	−	5.38287i	0.0562440	−	0.173101i	0.975232	+	0.221184i	$0.0709922\pi$
$968$	−8.17182			−0.262652
$969$	−1.72067	+	5.29567i	−0.0552758	+	0.170121i
$970$	−17.8348	−	27.5637i	−0.572640	−	0.885017i
$971$	−15.6862	−	48.2770i	−0.503393	−	1.54928i	−0.803456	−	0.595364i	$-0.797008\pi$
$971$	−15.6862	−	48.2770i	−0.503393	−	1.54928i	0.300063	−	0.953919i	$-0.402992\pi$
$972$	−0.537312	−	1.65368i	−0.0172343	−	0.0530417i
$973$	−44.5395	−	32.3599i	−1.42787	−	1.03741i
$974$	−0.157330			−0.00504119
$975$	7.81885	−	17.4049i	0.250404	−	0.557404i
$976$	−1.34078			−0.0429172
$977$	23.8132	+	17.3013i	0.761851	+	0.553517i	0.899478	−	0.436967i	$-0.143947\pi$
$977$	23.8132	+	17.3013i	0.761851	+	0.553517i	−0.137627	+	0.990484i	$0.543947\pi$
$978$	5.30408	+	16.3243i	0.169606	+	0.521993i
$979$	−3.17002	−	9.75630i	−0.101314	−	0.311813i
$980$	21.5277	+	8.30493i	0.687677	+	0.265291i
$981$	−0.0614849	+	0.189231i	−0.00196306	+	0.00604169i
$982$	−28.9654			−0.924324
$983$	−4.68157	+	14.4084i	−0.149319	+	0.459556i	−0.997541	−	0.0700845i	$-0.977673\pi$
$983$	−4.68157	+	14.4084i	−0.149319	+	0.459556i	0.848222	+	0.529640i	$0.177673\pi$
$984$	−13.4533	+	9.77438i	−0.428875	+	0.311596i
$985$	53.5278	+	20.6499i	1.70554	+	0.657960i
$986$	20.5889	+	14.9587i	0.655685	+	0.476383i
$987$	−34.3211	+	24.9358i	−1.09245	+	0.793714i
$988$	−1.73468	+	1.26032i	−0.0551875	+	0.0400961i
$989$	23.9046	+	17.3677i	0.760122	+	0.552261i
$990$	0.608705	−	0.162014i	0.0193459	−	0.00514916i
$991$	30.9620	−	22.4952i	0.983539	−	0.714583i	0.0250426	−	0.999686i	$-0.492028\pi$
$991$	30.9620	−	22.4952i	0.983539	−	0.714583i	0.958497	+	0.285103i	$0.0920279\pi$
$992$	0.869940	−	2.67740i	0.0276206	−	0.0850075i
$993$	36.9277			1.17187
$994$	11.0575	−	34.0315i	0.350723	−	1.07941i
$995$	2.80334	−	3.45006i	0.0888719	−	0.109374i
$996$	−4.76073	−	14.6520i	−0.150849	−	0.464267i
$997$	−9.79926	−	30.1590i	−0.310346	−	0.955146i	−0.977628	−	0.210341i	$-0.932543\pi$
$997$	−9.79926	−	30.1590i	−0.310346	−	0.955146i	0.667282	−	0.744805i	$-0.267457\pi$
$998$	21.4366	+	15.5746i	0.678564	+	0.493005i
$999$	−52.9500			−1.67526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.c.191.9	✓	44
25.11	even	5	inner	950.2.h.c.761.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.c.191.9	✓	44	1.1	even	1	trivial
950.2.h.c.761.9	yes	44	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.549973 + 1.69264i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.41010 - 1.73540i) q^{5} +(0.549973 - 1.69264i) q^{6} +4.16162 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.135515 + 0.0984577i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.549973 + 1.69264i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.41010 - 1.73540i) q^{5} +(0.549973 - 1.69264i) q^{6} +4.16162 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.135515 + 0.0984577i) q^{9} +(-2.16084 + 0.575134i) q^{10} +(1.36054 + 0.988491i) q^{11} +(-1.43985 + 1.04611i) q^{12} +(1.73468 - 1.26032i) q^{13} +(-3.36682 - 2.44614i) q^{14} +(3.71293 + 1.43237i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.966804 - 2.97552i) q^{17} +0.167506 q^{18} +(-0.309017 + 0.951057i) q^{19} +(2.08621 + 0.804816i) q^{20} +(2.28878 + 7.04413i) q^{21} +(-0.519680 - 1.59941i) q^{22} +(-5.44570 - 3.95653i) q^{23} +1.77975 q^{24} +(-1.02324 - 4.89418i) q^{25} -2.14418 q^{26} +(4.07836 + 2.96310i) q^{27} +(1.28601 + 3.95793i) q^{28} +(-2.51364 - 7.73618i) q^{29} +(-2.16190 - 3.34122i) q^{30} +(0.869940 - 2.67740i) q^{31} +1.00000 q^{32} +(-0.924900 + 2.84655i) q^{33} +(-2.53112 + 1.83897i) q^{34} +(5.86829 - 7.22208i) q^{35} +(-0.135515 - 0.0984577i) q^{36} +(-8.49759 + 6.17386i) q^{37} +(0.809017 - 0.587785i) q^{38} +(3.08729 + 2.24305i) q^{39} +(-1.21472 - 1.87735i) q^{40} +(-7.55909 + 5.49200i) q^{41} +(2.28878 - 7.04413i) q^{42} -4.38963 q^{43} +(-0.519680 + 1.59941i) q^{44} +(-0.0202265 + 0.374009i) q^{45} +(2.08007 + 6.40180i) q^{46} +(1.76997 + 5.44740i) q^{47} +(-1.43985 - 1.04611i) q^{48} +10.3191 q^{49} +(-2.04891 + 4.56092i) q^{50} +5.56820 q^{51} +(1.73468 + 1.26032i) q^{52} +(-0.525745 - 1.61808i) q^{53} +(-1.55779 - 4.79440i) q^{54} +(3.63393 - 0.967215i) q^{55} +(1.28601 - 3.95793i) q^{56} -1.77975 q^{57} +(-2.51364 + 7.73618i) q^{58} +(8.13004 - 5.90682i) q^{59} +(-0.214906 + 3.97383i) q^{60} +(1.08471 + 0.788088i) q^{61} +(-2.27753 + 1.65472i) q^{62} +(-0.563963 + 0.409743i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.258912 - 4.78754i) q^{65} +(2.42142 - 1.75927i) q^{66} +(-0.182825 + 0.562678i) q^{67} +3.12864 q^{68} +(3.70201 - 11.3936i) q^{69} +(-8.99258 + 2.39349i) q^{70} +(2.65702 + 8.17748i) q^{71} +(0.0517623 + 0.159308i) q^{72} +(2.88521 + 2.09623i) q^{73} +10.5036 q^{74} +(7.72134 - 4.42364i) q^{75} -1.00000 q^{76} +(5.66205 + 4.11372i) q^{77} +(-1.17924 - 3.62933i) q^{78} +(3.54011 + 10.8953i) q^{79} +(-0.120751 + 2.23281i) q^{80} +(-2.92777 + 9.01075i) q^{81} +9.34354 q^{82} +(-2.67494 + 8.23263i) q^{83} +(-5.99209 + 4.35351i) q^{84} +(-3.80043 - 5.87356i) q^{85} +(3.55129 + 2.58016i) q^{86} +(11.7121 - 8.50937i) q^{87} +(1.36054 - 0.988491i) q^{88} +(-4.93495 - 3.58545i) q^{89} +(0.236200 - 0.290691i) q^{90} +(7.21907 - 5.24496i) q^{91} +(2.08007 - 6.40180i) q^{92} +5.01032 q^{93} +(1.76997 - 5.44740i) q^{94} +(1.21472 + 1.87735i) q^{95} +(0.549973 + 1.69264i) q^{96} +(4.53705 + 13.9636i) q^{97} +(-8.34829 - 6.06539i) q^{98} -0.281699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9	\( 44 q - 11 q^{2} + q^{3} - 11 q^{4} - q^{5} + q^{6} + 18 q^{7} - 11 q^{8} - 8 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + 3 q^{14} - 4 q^{15} - 11 q^{16} + 11 q^{17} + 42 q^{18} + 11 q^{19} - 6 q^{20} + 3 q^{21} - 6 q^{22} - 3 q^{23} + 6 q^{24} - 11 q^{25} + 22 q^{26} - 23 q^{27} - 12 q^{28} + 36 q^{29} - 4 q^{30} + 11 q^{31} + 44 q^{32} + 2 q^{33} - 19 q^{34} + 67 q^{35} - 8 q^{36} + 3 q^{37} + 11 q^{38} + 47 q^{39} + 4 q^{40} + 2 q^{41} + 3 q^{42} + 70 q^{43} - 6 q^{44} - 28 q^{45} - 8 q^{46} - 11 q^{47} - 4 q^{48} + 22 q^{49} + 14 q^{50} + 38 q^{51} + 2 q^{52} - 9 q^{53} + 32 q^{54} + 8 q^{55} - 12 q^{56} - 6 q^{57} + 36 q^{58} - 62 q^{59} + 11 q^{60} - 28 q^{61} - 29 q^{62} + 10 q^{63} - 11 q^{64} - 39 q^{65} - 8 q^{66} + 25 q^{67} + 16 q^{68} - 81 q^{69} - 43 q^{70} - 34 q^{71} - 13 q^{72} + 6 q^{73} + 8 q^{74} - 39 q^{75} - 44 q^{76} - 21 q^{77} - 58 q^{78} + 19 q^{79} - q^{80} - 22 q^{81} + 2 q^{82} - 50 q^{83} - 7 q^{84} + 102 q^{85} - 10 q^{86} + 47 q^{87} - q^{88} - 4 q^{89} - 38 q^{90} - 8 q^{91} - 8 q^{92} + 60 q^{93} - 11 q^{94} - 4 q^{95} + q^{96} + 8 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 + q^3 - 11 * q^4 - q^5 + q^6 + 18 * q^7 - 11 * q^8 - 8 * q^9 + 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + 3 * q^14 - 4 * q^15 - 11 * q^16 + 11 * q^17 + 42 * q^18 + 11 * q^19 - 6 * q^20 + 3 * q^21 - 6 * q^22 - 3 * q^23 + 6 * q^24 - 11 * q^25 + 22 * q^26 - 23 * q^27 - 12 * q^28 + 36 * q^29 - 4 * q^30 + 11 * q^31 + 44 * q^32 + 2 * q^33 - 19 * q^34 + 67 * q^35 - 8 * q^36 + 3 * q^37 + 11 * q^38 + 47 * q^39 + 4 * q^40 + 2 * q^41 + 3 * q^42 + 70 * q^43 - 6 * q^44 - 28 * q^45 - 8 * q^46 - 11 * q^47 - 4 * q^48 + 22 * q^49 + 14 * q^50 + 38 * q^51 + 2 * q^52 - 9 * q^53 + 32 * q^54 + 8 * q^55 - 12 * q^56 - 6 * q^57 + 36 * q^58 - 62 * q^59 + 11 * q^60 - 28 * q^61 - 29 * q^62 + 10 * q^63 - 11 * q^64 - 39 * q^65 - 8 * q^66 + 25 * q^67 + 16 * q^68 - 81 * q^69 - 43 * q^70 - 34 * q^71 - 13 * q^72 + 6 * q^73 + 8 * q^74 - 39 * q^75 - 44 * q^76 - 21 * q^77 - 58 * q^78 + 19 * q^79 - q^80 - 22 * q^81 + 2 * q^82 - 50 * q^83 - 7 * q^84 + 102 * q^85 - 10 * q^86 + 47 * q^87 - q^88 - 4 * q^89 - 38 * q^90 - 8 * q^91 - 8 * q^92 + 60 * q^93 - 11 * q^94 - 4 * q^95 + q^96 + 8 * q^97 + 7 * q^98 - 12 * q^99

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