LMFDB - Embedded newform 585.2.i.h.196.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.10
Character	$\chi$	$=$	585.196
Dual form			585.2.i.h.391.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.562020 - 0.973448i) q^{2} +(-0.0186726 - 1.73195i) q^{3} +(0.368266 + 0.637856i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.69646 - 0.955214i) q^{6} +(1.91433 - 3.31571i) q^{7} +3.07597 q^{8} +(-2.99930 + 0.0646801i) q^{9} +O(q^{10})$	\(q+(0.562020 - 0.973448i) q^{2} +(-0.0186726 - 1.73195i) q^{3} +(0.368266 + 0.637856i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.69646 - 0.955214i) q^{6} +(1.91433 - 3.31571i) q^{7} +3.07597 q^{8} +(-2.99930 + 0.0646801i) q^{9} +1.12404 q^{10} +(-0.975625 + 1.68983i) q^{11} +(1.09786 - 0.649730i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.15178 - 3.72700i) q^{14} +(1.49058 - 0.882146i) q^{15} +(0.992227 - 1.71859i) q^{16} +6.58579 q^{17} +(-1.62271 + 2.95602i) q^{18} +0.304113 q^{19} +(-0.368266 + 0.637856i) q^{20} +(-5.77840 - 3.25361i) q^{21} +(1.09664 + 1.89944i) q^{22} +(-3.00958 - 5.21275i) q^{23} +(-0.0574365 - 5.32743i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.12404 q^{26} +(0.168028 + 5.19343i) q^{27} +2.81993 q^{28} +(-0.378122 + 0.654926i) q^{29} +(-0.0209888 - 1.94678i) q^{30} +(-3.95628 - 6.85248i) q^{31} +(1.96067 + 3.39598i) q^{32} +(2.94492 + 1.65818i) q^{33} +(3.70135 - 6.41093i) q^{34} +3.82866 q^{35} +(-1.14580 - 1.88930i) q^{36} -8.54464 q^{37} +(0.170918 - 0.296038i) q^{38} +(-1.49058 + 0.882146i) q^{39} +(1.53799 + 2.66387i) q^{40} +(5.74126 + 9.94416i) q^{41} +(-6.41479 + 3.79637i) q^{42} +(-3.06293 + 5.30515i) q^{43} -1.43716 q^{44} +(-1.55567 - 2.56513i) q^{45} -6.76579 q^{46} +(4.90423 - 8.49437i) q^{47} +(-2.99504 - 1.68640i) q^{48} +(-3.82930 - 6.63255i) q^{49} +(0.562020 + 0.973448i) q^{50} +(-0.122974 - 11.4063i) q^{51} +(0.368266 - 0.637856i) q^{52} +0.480958 q^{53} +(5.14997 + 2.75525i) q^{54} -1.95125 q^{55} +(5.88842 - 10.1990i) q^{56} +(-0.00567859 - 0.526709i) q^{57} +(0.425024 + 0.736164i) q^{58} +(4.91277 + 8.50916i) q^{59} +(1.11161 + 0.625909i) q^{60} +(-4.93916 + 8.55488i) q^{61} -8.89404 q^{62} +(-5.52719 + 10.0686i) q^{63} +8.37665 q^{64} +(0.500000 - 0.866025i) q^{65} +(3.26926 - 1.93480i) q^{66} +(0.805583 + 1.39531i) q^{67} +(2.42533 + 4.20079i) q^{68} +(-8.97203 + 5.30979i) q^{69} +(2.15178 - 3.72700i) q^{70} -10.6648 q^{71} +(-9.22578 + 0.198954i) q^{72} -10.2640 q^{73} +(-4.80226 + 8.31776i) q^{74} +(1.50925 + 0.849804i) q^{75} +(0.111995 + 0.193980i) q^{76} +(3.73533 + 6.46979i) q^{77} +(0.0209888 + 1.94678i) q^{78} +(3.35755 - 5.81544i) q^{79} +1.98445 q^{80} +(8.99163 - 0.387991i) q^{81} +12.9068 q^{82} +(-4.46272 + 7.72966i) q^{83} +(-0.0526555 - 4.88398i) q^{84} +(3.29290 + 5.70346i) q^{85} +(3.44286 + 5.96320i) q^{86} +(1.14136 + 0.642659i) q^{87} +(-3.00100 + 5.19788i) q^{88} +6.53502 q^{89} +(-3.37134 + 0.0727031i) q^{90} -3.82866 q^{91} +(2.21666 - 3.83936i) q^{92} +(-11.7943 + 6.98003i) q^{93} +(-5.51255 - 9.54802i) q^{94} +(0.152057 + 0.263370i) q^{95} +(5.84506 - 3.45920i) q^{96} +(0.256330 - 0.443977i) q^{97} -8.60859 q^{98} +(2.81690 - 5.13142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.562020	−	0.973448i	0.397408	−	0.688331i	−0.595997	−	0.802987i	$-0.703243\pi$
$2$	0.562020	−	0.973448i	0.397408	−	0.688331i	0.993405	+	0.114655i	$0.0365763\pi$
$3$	−0.0186726	−	1.73195i	−0.0107807	−	0.999942i
$3$	−0.0186726	−	1.73195i	−0.0107807	−	0.999942i
$4$	0.368266	+	0.637856i	0.184133	+	0.318928i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.69646	−	0.955214i	−0.692576	−	0.389965i
$7$	1.91433	−	3.31571i	0.723548	−	1.25322i	−0.236021	−	0.971748i	$-0.575843\pi$
$7$	1.91433	−	3.31571i	0.723548	−	1.25322i	0.959569	−	0.281474i	$-0.0908233\pi$
$8$	3.07597			1.08752
$9$	−2.99930	+	0.0646801i	−0.999768	+	0.0215600i
$10$	1.12404			0.355453
$11$	−0.975625	+	1.68983i	−0.294162	+	0.509504i	−0.974790	−	0.223126i	$-0.928374\pi$
$11$	−0.975625	+	1.68983i	−0.294162	+	0.509504i	0.680627	+	0.732630i	$0.261707\pi$
$12$	1.09786	−	0.649730i	0.316924	−	0.187561i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−2.15178	−	3.72700i	−0.575088	−	0.996082i
$15$	1.49058	−	0.882146i	0.384865	−	0.227769i
$16$	0.992227	−	1.71859i	0.248057	−	0.429647i
$17$	6.58579			1.59729			0.798645	−	0.601803i	$-0.205551\pi$
$17$	6.58579			1.59729			0.798645	+	0.601803i	$0.205551\pi$
$18$	−1.62271	+	2.95602i	−0.382476	+	0.696740i
$19$	0.304113			0.0697684			0.0348842	−	0.999391i	$-0.488894\pi$
$19$	0.304113			0.0697684			0.0348842	+	0.999391i	$0.488894\pi$
$20$	−0.368266	+	0.637856i	−0.0823469	+	0.142629i
$21$	−5.77840	−	3.25361i	−1.26095	−	0.709995i
$22$	1.09664	+	1.89944i	0.233805	+	0.404962i
$23$	−3.00958	−	5.21275i	−0.627542	−	1.08693i	−0.988043	−	0.154176i	$-0.950728\pi$
$23$	−3.00958	−	5.21275i	−0.627542	−	1.08693i	0.360502	−	0.932759i	$-0.382605\pi$
$24$	−0.0574365	−	5.32743i	−0.0117242	−	1.08746i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.12404			−0.220442
$27$	0.168028	+	5.19343i	0.0323369	+	0.999477i
$28$	2.81993			0.532917
$29$	−0.378122	+	0.654926i	−0.0702155	+	0.121617i	−0.898996	−	0.437958i	$-0.855702\pi$
$29$	−0.378122	+	0.654926i	−0.0702155	+	0.121617i	0.828780	+	0.559574i	$0.189035\pi$
$30$	−0.0209888	−	1.94678i	−0.00383201	−	0.355432i
$31$	−3.95628	−	6.85248i	−0.710569	−	1.23074i	−0.964644	−	0.263557i	$-0.915104\pi$
$31$	−3.95628	−	6.85248i	−0.710569	−	1.23074i	0.254075	−	0.967185i	$-0.418229\pi$
$32$	1.96067	+	3.39598i	0.346601	+	0.600330i
$33$	2.94492	+	1.65818i	0.512645	+	0.288652i
$34$	3.70135	−	6.41093i	0.634776	−	1.09946i
$35$	3.82866			0.647161
$36$	−1.14580	−	1.88930i	−0.190967	−	0.314884i
$37$	−8.54464			−1.40473			−0.702365	−	0.711817i	$-0.747872\pi$
$37$	−8.54464			−1.40473			−0.702365	+	0.711817i	$0.747872\pi$
$38$	0.170918	−	0.296038i	0.0277265	−	0.0480238i
$39$	−1.49058	+	0.882146i	−0.238683	+	0.141256i
$40$	1.53799	+	2.66387i	0.243177	+	0.421195i
$41$	5.74126	+	9.94416i	0.896635	+	1.55302i	0.831769	+	0.555123i	$0.187329\pi$
$41$	5.74126	+	9.94416i	0.896635	+	1.55302i	0.0648660	+	0.997894i	$0.479338\pi$
$42$	−6.41479	+	3.79637i	−0.989824	+	0.585793i
$43$	−3.06293	+	5.30515i	−0.467092	+	0.809027i	−0.999293	−	0.0375907i	$-0.988032\pi$
$43$	−3.06293	+	5.30515i	−0.467092	+	0.809027i	0.532201	+	0.846618i	$0.321365\pi$
$44$	−1.43716			−0.216660
$45$	−1.55567	−	2.56513i	−0.231905	−	0.382387i
$46$	−6.76579			−0.997561
$47$	4.90423	−	8.49437i	0.715355	−	1.23903i	−0.247467	−	0.968896i	$-0.579598\pi$
$47$	4.90423	−	8.49437i	0.715355	−	1.23903i	0.962822	−	0.270135i	$-0.0870684\pi$
$48$	−2.99504	−	1.68640i	−0.432296	−	0.243410i
$49$	−3.82930	−	6.63255i	−0.547043	−	0.947507i
$50$	0.562020	+	0.973448i	0.0794817	+	0.137666i
$51$	−0.122974	−	11.4063i	−0.0172198	−	1.59720i
$52$	0.368266	−	0.637856i	0.0510694	−	0.0884547i
$53$	0.480958			0.0660646			0.0330323	−	0.999454i	$-0.489484\pi$
$53$	0.480958			0.0660646			0.0330323	+	0.999454i	$0.489484\pi$
$54$	5.14997	+	2.75525i	0.700822	+	0.374942i
$55$	−1.95125			−0.263107
$56$	5.88842	−	10.1990i	0.786874	−	1.36291i
$57$	−0.00567859	−	0.526709i	−0.000752148	−	0.0697643i
$58$	0.425024	+	0.736164i	0.0558084	+	0.0966630i
$59$	4.91277	+	8.50916i	0.639588	+	1.10780i	0.985523	+	0.169540i	$0.0542283\pi$
$59$	4.91277	+	8.50916i	0.639588	+	1.10780i	−0.345935	+	0.938258i	$0.612438\pi$
$60$	1.11161	+	0.625909i	0.143508	+	0.0808045i
$61$	−4.93916	+	8.55488i	−0.632395	+	1.09534i	0.354666	+	0.934993i	$0.384595\pi$
$61$	−4.93916	+	8.55488i	−0.632395	+	1.09534i	−0.987061	+	0.160347i	$0.948739\pi$
$62$	−8.89404			−1.12954
$63$	−5.52719	+	10.0686i	−0.696360	+	1.26853i
$64$	8.37665			1.04708
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	3.26926	−	1.93480i	0.402418	−	0.238157i
$67$	0.805583	+	1.39531i	0.0984176	+	0.170464i	0.911030	−	0.412340i	$-0.135289\pi$
$67$	0.805583	+	1.39531i	0.0984176	+	0.170464i	−0.812612	+	0.582805i	$0.801955\pi$
$68$	2.42533	+	4.20079i	0.294114	+	0.509420i
$69$	−8.97203	+	5.30979i	−1.08011	+	0.639223i
$70$	2.15178	−	3.72700i	0.257187	−	0.445461i
$71$	−10.6648			−1.26567			−0.632837	−	0.774285i	$-0.718110\pi$
$71$	−10.6648			−1.26567			−0.632837	+	0.774285i	$0.718110\pi$
$72$	−9.22578	+	0.198954i	−1.08727	+	0.0234470i
$73$	−10.2640			−1.20131			−0.600654	−	0.799509i	$-0.705093\pi$
$73$	−10.2640			−1.20131			−0.600654	+	0.799509i	$0.705093\pi$
$74$	−4.80226	+	8.31776i	−0.558251	+	0.966920i
$75$	1.50925	+	0.849804i	0.174273	+	0.0981269i
$76$	0.111995	+	0.193980i	0.0128467	+	0.0222511i
$77$	3.73533	+	6.46979i	0.425681	+	0.737301i
$78$	0.0209888	+	1.94678i	0.00237651	+	0.220430i
$79$	3.35755	−	5.81544i	0.377754	−	0.654289i	−0.612981	−	0.790097i	$-0.710030\pi$
$79$	3.35755	−	5.81544i	0.377754	−	0.654289i	0.990735	+	0.135809i	$0.0433633\pi$
$80$	1.98445			0.221869
$81$	8.99163	−	0.387991i	0.999070	−	0.0431101i
$82$	12.9068			1.42532
$83$	−4.46272	+	7.72966i	−0.489848	+	0.848441i	−0.999932	−	0.0116836i	$-0.996281\pi$
$83$	−4.46272	+	7.72966i	−0.489848	+	0.848441i	0.510084	+	0.860124i	$0.329614\pi$
$84$	−0.0526555	−	4.88398i	−0.00574519	−	0.532886i
$85$	3.29290	+	5.70346i	0.357165	+	0.618628i
$86$	3.44286	+	5.96320i	0.371253	+	0.643028i
$87$	1.14136	+	0.642659i	0.122367	+	0.0689003i
$88$	−3.00100	+	5.19788i	−0.319908	+	0.554096i
$89$	6.53502			0.692711			0.346356	−	0.938103i	$-0.387419\pi$
$89$	6.53502			0.692711			0.346356	+	0.938103i	$0.387419\pi$
$90$	−3.37134	+	0.0727031i	−0.355370	+	0.00766358i
$91$	−3.82866			−0.401352
$92$	2.21666	−	3.83936i	0.231103	−	0.400281i
$93$	−11.7943	+	6.98003i	−1.22301	+	0.723796i
$94$	−5.51255	−	9.54802i	−0.568576	−	0.984803i
$95$	0.152057	+	0.263370i	0.0156007	+	0.0270212i
$96$	5.84506	−	3.45920i	0.596559	−	0.353053i
$97$	0.256330	−	0.443977i	0.0260264	−	0.0450790i	−0.852719	−	0.522370i	$-0.825048\pi$
$97$	0.256330	−	0.443977i	0.0260264	−	0.0450790i	0.878745	+	0.477291i	$0.158381\pi$
$98$	−8.60859			−0.869598
$99$	2.81690	−	5.13142i	0.283109	−	0.515727i
$100$	−0.736533			−0.0736533
$101$	−4.40630	+	7.63193i	−0.438443	+	0.759405i	−0.997570	−	0.0696769i	$-0.977803\pi$
$101$	−4.40630	+	7.63193i	−0.438443	+	0.759405i	0.559127	+	0.829082i	$0.311137\pi$
$102$	−11.1725	−	6.29084i	−1.10624	−	0.622886i
$103$	−1.50238	−	2.60219i	−0.148034	−	0.256402i	0.782467	−	0.622692i	$-0.213961\pi$
$103$	−1.50238	−	2.60219i	−0.148034	−	0.256402i	−0.930501	+	0.366290i	$0.880628\pi$
$104$	−1.53799	−	2.66387i	−0.150812	−	0.261214i
$105$	−0.0714911	−	6.63104i	−0.00697682	−	0.647123i
$106$	0.270308	−	0.468187i	0.0262546	−	0.0454743i
$107$	14.3585			1.38809			0.694045	−	0.719932i	$-0.255827\pi$
$107$	14.3585			1.38809			0.694045	+	0.719932i	$0.255827\pi$
$108$	−3.25079	+	2.01975i	−0.312807	+	0.194350i
$109$	16.0914			1.54127			0.770637	−	0.637275i	$-0.219938\pi$
$109$	16.0914			1.54127			0.770637	+	0.637275i	$0.219938\pi$
$110$	−1.09664	+	1.89944i	−0.104561	+	0.181105i
$111$	0.159551	+	14.7989i	0.0151439	+	1.40465i
$112$	−3.79890	−	6.57988i	−0.358962	−	0.621740i
$113$	6.46260	+	11.1935i	0.607950	+	1.05300i	0.991578	+	0.129512i	$0.0413412\pi$
$113$	6.46260	+	11.1935i	0.607950	+	1.05300i	−0.383628	+	0.923488i	$0.625326\pi$
$114$	−0.515915	−	0.290493i	−0.0483199	−	0.0272072i
$115$	3.00958	−	5.21275i	0.280645	−	0.486092i
$116$	−0.556998			−0.0517160
$117$	1.55567	+	2.56513i	0.143821	+	0.237147i
$118$	11.0443			1.01671
$119$	12.6074	−	21.8366i	1.15572	−	2.00176i
$120$	4.58497	−	2.71346i	0.418549	−	0.247704i
$121$	3.59631	+	6.22899i	0.326937	+	0.566272i
$122$	5.55182	+	9.61603i	0.502638	+	0.870594i
$123$	17.1156	−	10.1293i	1.54326	−	0.913325i
$124$	2.91393	−	5.04708i	0.261679	−	0.453241i
$125$	−1.00000			−0.0894427
$126$	6.69491	+	11.0392i	0.596430	+	0.983451i
$127$	9.34826			0.829524			0.414762	−	0.909930i	$-0.363865\pi$
$127$	9.34826			0.829524			0.414762	+	0.909930i	$0.363865\pi$
$128$	0.786508	−	1.36227i	0.0695182	−	0.120409i
$129$	9.24544	+	5.20578i	0.814016	+	0.458343i
$130$	−0.562020	−	0.973448i	−0.0492924	−	0.0853770i
$131$	−0.354061	−	0.613252i	−0.0309345	−	0.0535801i	0.850144	−	0.526551i	$-0.176515\pi$
$131$	−0.354061	−	0.613252i	−0.0309345	−	0.0535801i	−0.881078	+	0.472971i	$0.843182\pi$
$132$	0.0268356	+	2.48909i	0.00233574	+	0.216647i
$133$	0.582172	−	1.00835i	0.0504808	−	0.0874352i
$134$	1.81102			0.156448
$135$	−4.41363	+	2.74223i	−0.379865	+	0.236014i
$136$	20.2577			1.73709
$137$	−2.20907	+	3.82622i	−0.188733	+	0.326896i	−0.944828	−	0.327566i	$-0.893772\pi$
$137$	−2.20907	+	3.82622i	−0.188733	+	0.326896i	0.756095	+	0.654462i	$0.227105\pi$
$138$	0.126335	+	11.7180i	0.0107544	+	0.997503i
$139$	2.67228	+	4.62852i	0.226660	+	0.392586i	0.956816	−	0.290694i	$-0.0938862\pi$
$139$	2.67228	+	4.62852i	0.226660	+	0.392586i	−0.730156	+	0.683280i	$0.760553\pi$
$140$	1.40997	+	2.44213i	0.119164	+	0.206398i
$141$	−14.8034	−	8.33526i	−1.24667	−	0.701956i
$142$	−5.99381	+	10.3816i	−0.502989	+	0.871203i
$143$	1.95125			0.163172
$144$	−2.86483	+	5.21874i	−0.238736	+	0.434895i
$145$	−0.756244			−0.0628026
$146$	−5.76857	+	9.99145i	−0.477410	+	0.826898i
$147$	−11.4157	+	6.75601i	−0.941554	+	0.557226i
$148$	−3.14670	−	5.45025i	−0.258657	−	0.448008i
$149$	−0.997275	−	1.72733i	−0.0817000	−	0.141508i	0.822280	−	0.569083i	$-0.192702\pi$
$149$	−0.997275	−	1.72733i	−0.0817000	−	0.141508i	−0.903980	+	0.427574i	$0.859368\pi$
$150$	1.67547	−	0.991568i	0.136801	−	0.0809612i
$151$	−3.61446	+	6.26042i	−0.294140	+	0.509466i	−0.974785	−	0.223148i	$-0.928367\pi$
$151$	−3.61446	+	6.26042i	−0.294140	+	0.509466i	0.680644	+	0.732614i	$0.261700\pi$
$152$	0.935444			0.0758746
$153$	−19.7528	+	0.425970i	−1.59692	+	0.0344376i
$154$	8.39733			0.676677
$155$	3.95628	−	6.85248i	0.317776	−	0.550404i
$156$	−1.11161	−	0.625909i	−0.0890002	−	0.0501128i
$157$	−2.32550	−	4.02788i	−0.185595	−	0.321460i	0.758182	−	0.652043i	$-0.226088\pi$
$157$	−2.32550	−	4.02788i	−0.185595	−	0.321460i	−0.943777	+	0.330583i	$0.892755\pi$
$158$	−3.77402	−	6.53680i	−0.300245	−	0.520040i
$159$	−0.00898075	−	0.832995i	−0.000712219	−	0.0660608i
$160$	−1.96067	+	3.39598i	−0.155005	+	0.268476i
$161$	−23.0453			−1.81623
$162$	4.67579	−	8.97094i	0.367365	−	0.704824i
$163$	17.1340			1.34204			0.671018	−	0.741441i	$-0.265857\pi$
$163$	17.1340			1.34204			0.671018	+	0.741441i	$0.265857\pi$
$164$	−4.22863	+	7.32420i	−0.330200	+	0.571924i
$165$	0.0364350	+	3.37947i	0.00283646	+	0.263091i
$166$	5.01628	+	8.68846i	0.389339	+	0.674355i
$167$	−2.09230	−	3.62397i	−0.161907	−	0.280431i	0.773646	−	0.633619i	$-0.218431\pi$
$167$	−2.09230	−	3.62397i	−0.161907	−	0.280431i	−0.935553	+	0.353188i	$0.885098\pi$
$168$	−17.7742	−	10.0080i	−1.37131	−	0.772135i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	7.40270			0.567761
$171$	−0.912128	+	0.0196701i	−0.0697521	+	0.00150421i
$172$	−4.51189			−0.344029
$173$	−11.2563	+	19.4965i	−0.855799	+	1.48229i	0.0201020	+	0.999798i	$0.493601\pi$
$173$	−11.2563	+	19.4965i	−0.855799	+	1.48229i	−0.875901	+	0.482490i	$0.839732\pi$
$174$	1.26706	−	0.749867i	0.0960558	−	0.0568473i
$175$	1.91433	+	3.31571i	0.144710	+	0.250644i
$176$	1.93608	+	3.35340i	0.145938	+	0.252772i
$177$	14.6457	−	8.66756i	1.10084	−	0.651493i
$178$	3.67282	−	6.36150i	0.275289	−	0.476815i
$179$	−18.7924			−1.40461			−0.702306	−	0.711875i	$-0.747846\pi$
$179$	−18.7924			−1.40461			−0.702306	+	0.711875i	$0.747846\pi$
$180$	1.06329	−	1.93694i	0.0792526	−	0.144371i
$181$	−11.5003			−0.854814			−0.427407	−	0.904059i	$-0.640573\pi$
$181$	−11.5003			−0.854814			−0.427407	+	0.904059i	$0.640573\pi$
$182$	−2.15178	+	3.72700i	−0.159501	+	0.276263i
$183$	14.9088	+	8.39464i	1.10209	+	0.620549i
$184$	−9.25740	−	16.0343i	−0.682465	−	1.18206i
$185$	−4.27232	−	7.39987i	−0.314107	−	0.544049i
$186$	0.166075	+	15.4040i	0.0121772	+	1.12948i
$187$	−6.42527	+	11.1289i	−0.469862	+	0.813825i
$188$	7.22425			0.526882
$189$	17.5416	+	9.38481i	1.27596	+	0.682644i
$190$	0.341836			0.0247994
$191$	1.51376	−	2.62191i	0.109532	−	0.189715i	−0.806049	−	0.591849i	$-0.798398\pi$
$191$	1.51376	−	2.62191i	0.109532	−	0.189715i	0.915581	+	0.402134i	$0.131731\pi$
$192$	−0.156414	−	14.5079i	−0.0112882	−	1.04702i
$193$	−11.8241	−	20.4799i	−0.851115	−	1.47417i	−0.880203	−	0.474597i	$-0.842594\pi$
$193$	−11.8241	−	20.4799i	−0.851115	−	1.47417i	0.0290881	−	0.999577i	$-0.490740\pi$
$194$	−0.288126	−	0.499048i	−0.0206862	−	0.0358296i
$195$	−1.50925	−	0.849804i	−0.108080	−	0.0608557i
$196$	2.82041	−	4.88509i	0.201458	−	0.348935i
$197$	9.10668			0.648824			0.324412	−	0.945916i	$-0.394834\pi$
$197$	9.10668			0.648824			0.324412	+	0.945916i	$0.394834\pi$
$198$	−3.41202	−	5.62607i	−0.242482	−	0.399827i
$199$	−20.5423			−1.45621			−0.728103	−	0.685468i	$-0.759598\pi$
$199$	−20.5423			−1.45621			−0.728103	+	0.685468i	$0.759598\pi$
$200$	−1.53799	+	2.66387i	−0.108752	+	0.188364i
$201$	2.40157	−	1.42128i	0.169393	−	0.100250i
$202$	4.95286	+	8.57860i	0.348482	+	0.603588i
$203$	1.44770	+	2.50749i	0.101609	+	0.175991i
$204$	7.23027	−	4.27898i	0.506220	−	0.299589i
$205$	−5.74126	+	9.94416i	−0.400987	+	0.694530i
$206$	−3.37747			−0.235319
$207$	9.36382	+	15.4400i	0.650830	+	1.07315i
$208$	−1.98445			−0.137597
$209$	−0.296701	+	0.513900i	−0.0205232	+	0.0355472i
$210$	−6.49515	−	3.65719i	−0.448208	−	0.252370i
$211$	−6.01318	−	10.4151i	−0.413964	−	0.717007i	0.581355	−	0.813650i	$-0.302523\pi$
$211$	−6.01318	−	10.4151i	−0.413964	−	0.717007i	−0.995319	+	0.0966431i	$0.969189\pi$
$212$	0.177121	+	0.306782i	0.0121647	+	0.0210699i
$213$	0.199139	+	18.4708i	0.0136448	+	1.26560i
$214$	8.06977	−	13.9773i	0.551638	−	0.955466i
$215$	−6.12586			−0.417780
$216$	0.516849	+	15.9749i	0.0351671	+	1.08695i
$217$	−30.2945			−2.05652
$218$	9.04367	−	15.6641i	0.612515	−	1.06091i
$219$	0.191656	+	17.7767i	0.0129509	+	1.20124i
$220$	−0.718580	−	1.24462i	−0.0484467	−	0.0839121i
$221$	−3.29290	−	5.70346i	−0.221504	−	0.383657i
$222$	14.4956	+	8.16196i	0.972882	+	0.547795i
$223$	−1.53935	+	2.66624i	−0.103083	+	0.178544i	−0.912953	−	0.408064i	$-0.866204\pi$
$223$	−1.53935	+	2.66624i	−0.103083	+	0.178544i	0.809871	+	0.586609i	$0.199537\pi$
$224$	15.0135			1.00313
$225$	1.44364	−	2.62981i	0.0962424	−	0.175321i
$226$	14.5284			0.966417
$227$	1.67941	−	2.90882i	0.111466	−	0.193065i	−0.804895	−	0.593417i	$-0.797779\pi$
$227$	1.67941	−	2.90882i	0.111466	−	0.193065i	0.916362	+	0.400352i	$0.131112\pi$
$228$	0.333873	−	0.197591i	0.0221113	−	0.0130858i
$229$	−14.2299	−	24.6469i	−0.940336	−	1.62871i	−0.764830	−	0.644232i	$-0.777177\pi$
$229$	−14.2299	−	24.6469i	−0.940336	−	1.62871i	−0.175506	−	0.984478i	$-0.556156\pi$
$230$	−3.38290	−	5.85935i	−0.223061	−	0.386354i
$231$	11.1356	−	6.59022i	0.732669	−	0.433605i
$232$	−1.16309	+	2.01454i	−0.0763608	+	0.132261i
$233$	−27.8026			−1.82141			−0.910703	−	0.413061i	$-0.864460\pi$
$233$	−27.8026			−1.82141			−0.910703	+	0.413061i	$0.864460\pi$
$234$	3.37134	−	0.0727031i	0.220391	−	0.00475275i
$235$	9.80845			0.639833
$236$	−3.61841	+	6.26728i	−0.235539	+	0.407965i
$237$	−10.1348	−	5.70652i	−0.658323	−	0.370678i
$238$	−14.1712	−	24.5452i	−0.918582	−	1.59103i
$239$	0.219452	+	0.380102i	0.0141952	+	0.0245868i	0.873036	−	0.487656i	$-0.162148\pi$
$239$	0.219452	+	0.380102i	0.0141952	+	0.0245868i	−0.858841	+	0.512243i	$0.828815\pi$
$240$	−0.0370550	−	3.43698i	−0.00239189	−	0.221856i
$241$	0.473845	−	0.820723i	0.0305230	−	0.0528674i	−0.850360	−	0.526201i	$-0.823616\pi$
$241$	0.473845	−	0.820723i	0.0305230	−	0.0528674i	0.880883	+	0.473333i	$0.156949\pi$
$242$	8.08480			0.519710
$243$	−0.839878	−	15.5658i	−0.0538782	−	0.998548i
$244$	−7.27571			−0.465779
$245$	3.82930	−	6.63255i	0.244645	−	0.423738i
$246$	−0.241004	−	22.3540i	−0.0153659	−	1.42524i
$247$	−0.152057	−	0.263370i	−0.00967513	−	0.0167578i
$248$	−12.1694	−	21.0780i	−0.772759	−	1.33846i
$249$	13.4707	+	7.58488i	0.853672	+	0.480672i
$250$	−0.562020	+	0.973448i	−0.0355453	+	0.0615662i
$251$	−11.1351			−0.702843			−0.351421	−	0.936217i	$-0.614302\pi$
$251$	−11.1351			−0.702843			−0.351421	+	0.936217i	$0.614302\pi$
$252$	−8.45783	+	0.182394i	−0.532793	+	0.0114897i
$253$	11.7449			0.738396
$254$	5.25391	−	9.10004i	0.329660	−	0.570988i
$255$	9.81663	−	5.80963i	0.614741	−	0.363813i
$256$	7.49259	+	12.9775i	0.468287	+	0.811096i
$257$	−1.12637	−	1.95094i	−0.0702612	−	0.121696i	0.828755	−	0.559612i	$-0.189050\pi$
$257$	−1.12637	−	1.95094i	−0.0702612	−	0.121696i	−0.899016	+	0.437916i	$0.855717\pi$
$258$	10.2637	−	6.07420i	0.638989	−	0.378163i
$259$	−16.3572	+	28.3316i	−1.01639	+	1.76044i
$260$	0.736533			0.0456778
$261$	1.09174	−	1.98878i	0.0675771	−	0.123102i
$262$	−0.795958			−0.0491745
$263$	−8.59225	+	14.8822i	−0.529821	+	0.917677i	0.469574	+	0.882893i	$0.344408\pi$
$263$	−8.59225	+	14.8822i	−0.529821	+	0.917677i	−0.999395	+	0.0347835i	$0.988926\pi$
$264$	9.05851	+	5.10052i	0.557513	+	0.313915i
$265$	0.240479	+	0.416522i	0.0147725	+	0.0255867i
$266$	−0.654385	−	1.13343i	−0.0401229	−	0.0694950i
$267$	−0.122026	−	11.3183i	−0.00746788	−	0.692671i
$268$	−0.593338	+	1.02769i	−0.0362439	+	0.0627763i
$269$	−4.35353			−0.265439			−0.132720	−	0.991154i	$-0.542371\pi$
$269$	−4.35353			−0.265439			−0.132720	+	0.991154i	$0.542371\pi$
$270$	0.188870	+	5.83763i	0.0114943	+	0.355267i
$271$	27.0019			1.64025			0.820126	−	0.572184i	$-0.193904\pi$
$271$	27.0019			1.64025			0.820126	+	0.572184i	$0.193904\pi$
$272$	6.53460	−	11.3183i	0.396218	−	0.686270i
$273$	0.0714911	+	6.63104i	0.00432684	+	0.401329i
$274$	2.48308	+	4.30082i	0.150008	+	0.259822i
$275$	−0.975625	−	1.68983i	−0.0588324	−	0.101901i
$276$	−6.69098	−	3.76745i	−0.402750	−	0.226774i
$277$	1.57986	−	2.73641i	0.0949249	−	0.164415i	−0.814652	−	0.579950i	$-0.803072\pi$
$277$	1.57986	−	2.73641i	0.0949249	−	0.164415i	0.909577	+	0.415535i	$0.136406\pi$
$278$	6.00750			0.360306
$279$	12.3093	+	20.2968i	0.736939	+	1.21514i
$280$	11.7768			0.703801
$281$	6.20464	−	10.7468i	0.370138	−	0.641098i	−0.619448	−	0.785037i	$-0.712644\pi$
$281$	6.20464	−	10.7468i	0.370138	−	0.641098i	0.989587	+	0.143939i	$0.0459770\pi$
$282$	−16.4338	+	9.72575i	−0.978616	+	0.579160i
$283$	−4.11524	−	7.12780i	−0.244625	−	0.423704i	0.717401	−	0.696661i	$-0.245332\pi$
$283$	−4.11524	−	7.12780i	−0.244625	−	0.423704i	−0.962026	+	0.272957i	$0.911998\pi$
$284$	−3.92747	−	6.80258i	−0.233053	−	0.403659i
$285$	0.453304	−	0.268272i	0.0268514	−	0.0158911i
$286$	1.09664	−	1.89944i	0.0648458	−	0.112316i
$287$	43.9626			2.59503
$288$	−6.10030	−	10.0588i	−0.359463	−	0.592718i
$289$	26.3727			1.55133
$290$	−0.425024	+	0.736164i	−0.0249583	+	0.0432290i
$291$	−0.773732	−	0.435661i	−0.0453570	−	0.0255389i
$292$	−3.77988	−	6.54695i	−0.221201	−	0.383131i
$293$	−8.73941	−	15.1371i	−0.510562	−	0.884319i	−0.999925	−	0.0122387i	$-0.996104\pi$
$293$	−8.73941	−	15.1371i	−0.510562	−	0.884319i	0.489364	−	0.872080i	$-0.337229\pi$
$294$	0.160745	+	14.9096i	0.00937484	+	0.869548i
$295$	−4.91277	+	8.50916i	−0.286032	+	0.495423i
$296$	−26.2831			−1.52767
$297$	−8.93997	−	4.78291i	−0.518750	−	0.277533i
$298$	−2.24196			−0.129873
$299$	−3.00958	+	5.21275i	−0.174049	+	0.301461i
$300$	0.0137530	+	1.27564i	0.000794030	+	0.0736490i
$301$	11.7269	+	20.3116i	0.675927	+	1.17074i
$302$	4.06279	+	7.03697i	0.233788	+	0.404932i
$303$	13.3004	+	7.48898i	0.764088	+	0.430231i
$304$	0.301749	−	0.522645i	0.0173065	−	0.0299758i
$305$	−9.87832			−0.565631
$306$	−10.6868	+	19.4677i	−0.610924	+	1.11289i
$307$	−19.8767			−1.13442			−0.567211	−	0.823573i	$-0.691978\pi$
$307$	−19.8767			−1.13442			−0.567211	+	0.823573i	$0.691978\pi$
$308$	−2.75120	+	4.76521i	−0.156764	+	0.271523i
$309$	−4.47882	+	2.65063i	−0.254791	+	0.150789i
$310$	−4.44702	−	7.70246i	−0.252574	−	0.437471i
$311$	4.25073	+	7.36249i	0.241037	+	0.417488i	0.961010	−	0.276514i	$-0.0891792\pi$
$311$	4.25073	+	7.36249i	0.241037	+	0.417488i	−0.719973	+	0.694002i	$0.755846\pi$
$312$	−4.58497	+	2.71346i	−0.259573	+	0.153619i
$313$	−12.1968	+	21.1255i	−0.689406	+	1.19409i	0.282624	+	0.959231i	$0.408795\pi$
$313$	−12.1968	+	21.1255i	−0.689406	+	1.19409i	−0.972030	+	0.234856i	$0.924538\pi$
$314$	−5.22791			−0.295028
$315$	−11.4833	+	0.247638i	−0.647011	+	0.0139528i
$316$	4.94589			0.278228
$317$	8.74202	−	15.1416i	0.491001	−	0.850438i	−0.508946	−	0.860799i	$-0.669965\pi$
$317$	8.74202	−	15.1416i	0.491001	−	0.850438i	0.999946	+	0.0103606i	$0.00329795\pi$
$318$	−0.815924	−	0.459418i	−0.0457547	−	0.0257629i
$319$	−0.737811	−	1.27793i	−0.0413095	−	0.0715501i
$320$	4.18833	+	7.25440i	0.234135	+	0.405533i
$321$	−0.268111	−	24.8682i	−0.0149645	−	1.38801i
$322$	−12.9519	+	22.4334i	−0.721784	+	1.25017i
$323$	2.00283			0.111440
$324$	3.55880	+	5.59248i	0.197711	+	0.310694i
$325$	1.00000			0.0554700
$326$	9.62964	−	16.6790i	0.533337	−	0.923766i
$327$	−0.300468	−	27.8694i	−0.0166159	−	1.54118i
$328$	17.6600	+	30.5880i	0.975109	+	1.68894i
$329$	−18.7766	−	32.5220i	−1.03519	−	1.79300i
$330$	3.31021	+	1.86386i	0.182221	+	0.102602i
$331$	10.7092	−	18.5489i	0.588632	−	1.01954i	−0.405780	−	0.913971i	$-0.633000\pi$
$331$	10.7092	−	18.5489i	0.588632	−	1.01954i	0.994412	−	0.105570i	$-0.0336667\pi$
$332$	−6.57389			−0.360789
$333$	25.6279	−	0.552668i	1.40440	−	0.0302860i
$334$	−4.70366			−0.257373
$335$	−0.805583	+	1.39531i	−0.0440137	+	0.0762340i
$336$	−11.3251	+	6.70236i	−0.617834	+	0.365644i
$337$	−3.94760	−	6.83744i	−0.215039	−	0.372459i	0.738245	−	0.674532i	$-0.235655\pi$
$337$	−3.94760	−	6.83744i	−0.215039	−	0.372459i	−0.953285	+	0.302073i	$0.902321\pi$
$338$	0.562020	+	0.973448i	0.0305699	+	0.0529486i
$339$	19.2660	−	11.4019i	1.04638	−	0.619267i
$340$	−2.42533	+	4.20079i	−0.131532	+	0.227820i
$341$	15.4394			0.836090
$342$	−0.493486	+	0.898963i	−0.0266847	+	0.0486104i
$343$	−2.52158			−0.136153
$344$	−9.42149	+	16.3185i	−0.507972	+	0.879834i
$345$	−9.08443	−	5.11511i	−0.489089	−	0.275389i
$346$	12.6525	+	21.9148i	0.680204	+	1.17815i
$347$	0.881063	+	1.52605i	0.0472979	+	0.0819224i	0.888705	−	0.458479i	$-0.151606\pi$
$347$	0.881063	+	1.52605i	0.0472979	+	0.0819224i	−0.841407	+	0.540402i	$0.818272\pi$
$348$	0.0104006	+	0.964693i	0.000557532	+	0.0517130i
$349$	10.3864	−	17.9898i	0.555972	−	0.962973i	−0.441855	−	0.897087i	$-0.645679\pi$
$349$	10.3864	−	17.9898i	0.555972	−	0.962973i	0.997827	−	0.0658859i	$-0.0209873\pi$
$350$	4.30356			0.230035
$351$	4.41363	−	2.74223i	0.235582	−	0.146370i
$352$	−7.65152			−0.407827
$353$	6.50407	−	11.2654i	0.346177	−	0.599595i	−0.639390	−	0.768882i	$-0.720813\pi$
$353$	6.50407	−	11.2654i	0.346177	−	0.599595i	0.985567	+	0.169287i	$0.0541465\pi$
$354$	−0.206226	−	19.1282i	−0.0109608	−	1.01665i
$355$	−5.33238	−	9.23595i	−0.283013	−	0.490193i
$356$	2.40663	+	4.16841i	0.127551	+	0.220925i
$357$	−38.0553	−	21.4276i	−2.01410	−	1.13407i
$358$	−10.5617	+	18.2934i	−0.558205	+	0.966839i
$359$	17.8285			0.940953			0.470476	−	0.882413i	$-0.344082\pi$
$359$	17.8285			0.940953			0.470476	+	0.882413i	$0.344082\pi$
$360$	−4.78519	−	7.89028i	−0.252202	−	0.415854i
$361$	−18.9075			−0.995132
$362$	−6.46342	+	11.1950i	−0.339710	+	0.588395i
$363$	10.7212	−	6.34494i	0.562714	−	0.333023i
$364$	−1.40997	−	2.44213i	−0.0739023	−	0.128002i
$365$	−5.13199	−	8.88887i	−0.268621	−	0.465265i
$366$	16.5508	−	9.79503i	0.865125	−	0.511994i
$367$	−15.5309	+	26.9002i	−0.810705	+	1.40418i	0.101667	+	0.994818i	$0.467582\pi$
$367$	−15.5309	+	26.9002i	−0.810705	+	1.40418i	−0.912372	+	0.409363i	$0.865751\pi$
$368$	−11.9448			−0.622664
$369$	−17.8630	−	29.4542i	−0.929909	−	1.53332i
$370$	−9.60452			−0.499315
$371$	0.920711	−	1.59472i	0.0478009	−	0.0827936i
$372$	−8.79569	−	4.95254i	−0.456035	−	0.256777i
$373$	8.04771	+	13.9390i	0.416695	+	0.721736i	0.995605	−	0.0936553i	$-0.0298551\pi$
$373$	8.04771	+	13.9390i	0.416695	+	0.721736i	−0.578910	+	0.815391i	$0.696522\pi$
$374$	7.22226	+	12.5093i	0.373454	+	0.646842i
$375$	0.0186726	+	1.73195i	0.000964251	+	0.0894375i
$376$	15.0853	−	26.1285i	0.777964	−	1.34747i
$377$	0.756244			0.0389485
$378$	18.9944	−	11.8014i	0.976964	−	0.606998i
$379$	0.329371			0.0169186			0.00845931	−	0.999964i	$-0.497307\pi$
$379$	0.329371			0.0169186			0.00845931	+	0.999964i	$0.497307\pi$
$380$	−0.111995	+	0.193980i	−0.00574521	+	0.00995099i
$381$	−0.174557	−	16.1907i	−0.00894281	−	0.829476i
$382$	−1.70153	−	2.94713i	−0.0870578	−	0.150788i
$383$	0.225667	+	0.390866i	0.0115310	+	0.0199723i	0.871733	−	0.489981i	$-0.162996\pi$
$383$	0.225667	+	0.390866i	0.0115310	+	0.0199723i	−0.860202	+	0.509953i	$0.829663\pi$
$384$	−2.37407	−	1.33676i	−0.121151	−	0.0682160i
$385$	−3.73533	+	6.46979i	−0.190370	+	0.329731i
$386$	−26.5815			−1.35296
$387$	8.84351	−	16.1099i	0.449541	−	0.818910i
$388$	0.377591			0.0191693
$389$	−3.49719	+	6.05730i	−0.177314	+	0.307117i	−0.940960	−	0.338518i	$-0.890074\pi$
$389$	−3.49719	+	6.05730i	−0.177314	+	0.307117i	0.763645	+	0.645636i	$0.223408\pi$
$390$	−1.67547	+	0.991568i	−0.0848406	+	0.0502100i
$391$	−19.8205	−	34.3301i	−1.00237	−	1.73615i
$392$	−11.7788	−	20.4015i	−0.594921	−	1.03043i
$393$	−1.05551	+	0.624667i	−0.0532435	+	0.0315103i
$394$	5.11814	−	8.86488i	0.257848	−	0.446606i
$395$	6.71510			0.337873
$396$	4.31048	−	0.0929557i	0.216610	−	0.00467120i
$397$	−22.5639			−1.13245			−0.566224	−	0.824251i	$-0.691596\pi$
$397$	−22.5639			−1.13245			−0.566224	+	0.824251i	$0.691596\pi$
$398$	−11.5452	+	19.9969i	−0.578708	+	1.00235i
$399$	−1.75729	−	0.989465i	−0.0879744	−	0.0495352i
$400$	0.992227	+	1.71859i	0.0496113	+	0.0859294i
$401$	−15.0330	−	26.0379i	−0.750711	−	1.30027i	−0.947478	−	0.319820i	$-0.896378\pi$
$401$	−15.0330	−	26.0379i	−0.750711	−	1.30027i	0.196767	−	0.980450i	$-0.436956\pi$
$402$	−0.0338164	−	3.13659i	−0.00168661	−	0.156439i
$403$	−3.95628	+	6.85248i	−0.197076	+	0.341346i
$404$	−6.49076			−0.322928
$405$	4.83183	+	7.59299i	0.240095	+	0.377299i
$406$	3.25454			0.161520
$407$	8.33636	−	14.4390i	0.413218	−	0.715715i
$408$	−0.378265	−	35.0854i	−0.0187269	−	1.73699i
$409$	18.0148	+	31.2025i	0.890773	+	1.54286i	0.838950	+	0.544208i	$0.183170\pi$
$409$	18.0148	+	31.2025i	0.890773	+	1.54286i	0.0518226	+	0.998656i	$0.483497\pi$
$410$	6.45341	+	11.1776i	0.318711	+	0.552024i
$411$	6.66806	+	3.75455i	0.328911	+	0.185198i
$412$	1.10655	−	1.91660i	0.0545158	−	0.0944242i
$413$	37.6186			1.85109
$414$	20.2927	−	0.437612i	0.997329	−	0.0215075i
$415$	−8.92545			−0.438133
$416$	1.96067	−	3.39598i	0.0961298	−	0.166502i
$417$	7.96647	−	4.71468i	0.390120	−	0.230879i
$418$	0.333503	+	0.577645i	0.0163122	+	0.0282535i
$419$	1.15719	+	2.00431i	0.0565325	+	0.0979172i	0.892907	−	0.450242i	$-0.148662\pi$
$419$	1.15719	+	2.00431i	0.0565325	+	0.0979172i	−0.836374	+	0.548159i	$0.815329\pi$
$420$	4.20332	−	2.48759i	0.205101	−	0.121382i
$421$	−2.08544	+	3.61209i	−0.101638	+	0.176042i	−0.912360	−	0.409389i	$-0.865742\pi$
$421$	−2.08544	+	3.61209i	−0.101638	+	0.176042i	0.810722	+	0.585432i	$0.199075\pi$
$422$	−13.5181			−0.658051
$423$	−14.1598	+	25.7944i	−0.688475	+	1.25417i
$424$	1.47941			0.0718466
$425$	−3.29290	+	5.70346i	−0.159729	+	0.276659i
$426$	18.0923	+	10.1871i	0.876575	+	0.493568i
$427$	18.9103	+	32.7537i	0.915136	+	1.58506i
$428$	5.28776	+	9.15866i	0.255593	+	0.442701i
$429$	−0.0364350	−	3.37947i	−0.00175910	−	0.163162i
$430$	−3.44286	+	5.96320i	−0.166029	+	0.287571i
$431$	−9.57882			−0.461396			−0.230698	−	0.973025i	$-0.574101\pi$
$431$	−9.57882			−0.461396			−0.230698	+	0.973025i	$0.574101\pi$
$432$	9.09209	+	4.86430i	0.437444	+	0.234034i
$433$	24.5710			1.18081			0.590403	−	0.807109i	$-0.298969\pi$
$433$	24.5710			1.18081			0.590403	+	0.807109i	$0.298969\pi$
$434$	−17.0261	+	29.4901i	−0.817279	+	1.41557i
$435$	0.0141211	+	1.30978i	0.000677053	+	0.0627990i
$436$	5.92591	+	10.2640i	0.283800	+	0.491555i
$437$	−0.915254	−	1.58527i	−0.0437826	−	0.0758336i
$438$	17.4124	+	9.80430i	0.831997	+	0.468468i
$439$	−5.90780	+	10.2326i	−0.281964	+	0.488376i	−0.971868	−	0.235525i	$-0.924319\pi$
$439$	−5.90780	+	10.2326i	−0.281964	+	0.488376i	0.689905	+	0.723900i	$0.257652\pi$
$440$	−6.00200			−0.286134
$441$	11.9142	+	19.6453i	0.567345	+	0.935492i
$442$	−7.40270			−0.352111
$443$	18.1834	−	31.4945i	0.863918	−	1.49635i	−0.00419998	−	0.999991i	$-0.501337\pi$
$443$	18.1834	−	31.4945i	0.863918	−	1.49635i	0.868118	−	0.496358i	$-0.165330\pi$
$444$	−9.38080	+	5.55170i	−0.445193	+	0.263472i
$445$	3.26751	+	5.65950i	0.154895	+	0.268286i
$446$	1.73029	+	2.99696i	0.0819318	+	0.141910i
$447$	−2.97303	+	1.75948i	−0.140619	+	0.0832208i
$448$	16.0357	−	27.7746i	0.757614	−	1.31223i
$449$	−6.02318			−0.284251			−0.142126	−	0.989849i	$-0.545394\pi$
$449$	−6.02318			−0.284251			−0.142126	+	0.989849i	$0.545394\pi$
$450$	−1.74863	−	2.88331i	−0.0824313	−	0.135921i
$451$	−22.4053			−1.05502
$452$	−4.75991	+	8.24441i	−0.223888	+	0.387785i
$453$	10.9102	+	6.14316i	0.512607	+	0.288631i
$454$	−1.88772	−	3.26963i	−0.0885951	−	0.153451i
$455$	−1.91433	−	3.31571i	−0.0897451	−	0.155443i
$456$	−0.0174672	−	1.62014i	−0.000817977	−	0.0758701i
$457$	15.5330	−	26.9040i	0.726605	−	1.25852i	−0.231705	−	0.972786i	$-0.574430\pi$
$457$	15.5330	−	26.9040i	0.726605	−	1.25852i	0.958310	−	0.285730i	$-0.0922362\pi$
$458$	−31.9899			−1.49479
$459$	1.10660	+	34.2029i	0.0516515	+	1.59645i
$460$	4.43332			0.206704
$461$	18.6546	−	32.3108i	0.868833	−	1.50486i	0.00564260	−	0.999984i	$-0.498204\pi$
$461$	18.6546	−	32.3108i	0.868833	−	1.50486i	0.863190	−	0.504879i	$-0.168463\pi$
$462$	−0.156800	−	14.5438i	−0.00729501	−	0.676637i
$463$	−16.8901	−	29.2545i	−0.784950	−	1.35957i	−0.929029	−	0.370007i	$-0.879355\pi$
$463$	−16.8901	−	29.2545i	−0.784950	−	1.35957i	0.144079	−	0.989566i	$-0.453978\pi$
$464$	0.750365	+	1.29967i	0.0348348	+	0.0603357i
$465$	−11.9420	−	6.72413i	−0.553798	−	0.311824i
$466$	−15.6256	+	27.0643i	−0.723842	+	1.25373i
$467$	23.2695			1.07678			0.538391	−	0.842695i	$-0.319032\pi$
$467$	23.2695			1.07678			0.538391	+	0.842695i	$0.319032\pi$
$468$	−1.06329	+	1.93694i	−0.0491504	+	0.0895352i
$469$	6.16860			0.284839
$470$	5.51255	−	9.54802i	0.254275	−	0.440417i
$471$	−6.93267	+	4.10286i	−0.319440	+	0.189050i
$472$	15.1115	+	26.1740i	0.695565	+	1.20475i
$473$	−5.97654	−	10.3517i	−0.274802	−	0.475970i
$474$	−11.2509	+	6.65847i	−0.516772	+	0.305834i
$475$	−0.152057	+	0.263370i	−0.00697684	+	0.0120842i
$476$	18.5715			0.851223
$477$	−1.44254	+	0.0311084i	−0.0660493	+	0.00142436i
$478$	0.493346			0.0225651
$479$	−7.81727	+	13.5399i	−0.357180	+	0.618654i	−0.987489	−	0.157691i	$-0.949595\pi$
$479$	−7.81727	+	13.5399i	−0.357180	+	0.618654i	0.630308	+	0.776345i	$0.282928\pi$
$480$	5.91828	+	3.33237i	0.270131	+	0.152101i
$481$	4.27232	+	7.39987i	0.194801	+	0.337405i
$482$	−0.532621	−	0.922526i	−0.0242602	−	0.0420199i
$483$	0.430317	+	39.9134i	0.0195801	+	1.81612i
$484$	−2.64880	+	4.58786i	−0.120400	+	0.208539i
$485$	0.512660			0.0232787
$486$	−15.6245	−	7.93073i	−0.708743	−	0.359745i
$487$	20.7305			0.939388			0.469694	−	0.882829i	$-0.344364\pi$
$487$	20.7305			0.939388			0.469694	+	0.882829i	$0.344364\pi$
$488$	−15.1927	+	26.3146i	−0.687742	+	1.19120i
$489$	−0.319936	−	29.6752i	−0.0144680	−	1.34196i
$490$	−4.30429	−	7.45525i	−0.194448	−	0.336794i
$491$	2.17786	+	3.77216i	0.0982854	+	0.170235i	0.910975	−	0.412461i	$-0.135331\pi$
$491$	2.17786	+	3.77216i	0.0982854	+	0.170235i	−0.812690	+	0.582697i	$0.801998\pi$
$492$	12.7641	+	7.18701i	0.575450	+	0.324015i
$493$	−2.49023	+	4.31321i	−0.112154	+	0.194257i
$494$	−0.341836			−0.0153799
$495$	5.85239	−	0.126207i	0.263045	−	0.00567259i
$496$	−15.7021			−0.705046
$497$	−20.4158	+	35.3613i	−0.915776	+	1.58617i
$498$	14.9543	−	8.85019i	0.670118	−	0.396586i
$499$	−6.15484	−	10.6605i	−0.275529	−	0.477229i	0.694740	−	0.719261i	$-0.255520\pi$
$499$	−6.15484	−	10.6605i	−0.275529	−	0.477229i	−0.970268	+	0.242032i	$0.922186\pi$
$500$	−0.368266	−	0.637856i	−0.0164694	−	0.0285258i
$501$	−6.23746	+	3.69143i	−0.278669	+	0.164921i
$502$	−6.25816	+	10.8395i	−0.279316	+	0.483789i
$503$	5.53638			0.246855			0.123428	−	0.992354i	$-0.460611\pi$
$503$	5.53638			0.246855			0.123428	+	0.992354i	$0.460611\pi$
$504$	−17.0015	+	30.9709i	−0.757306	+	1.37955i
$505$	−8.81259			−0.392155
$506$	6.60088	−	11.4331i	0.293445	−	0.508261i
$507$	1.50925	+	0.849804i	0.0670281	+	0.0377411i
$508$	3.44265	+	5.96285i	0.152743	+	0.264559i
$509$	−16.8782	−	29.2339i	−0.748112	−	1.29577i	−0.948726	−	0.316098i	$-0.897627\pi$
$509$	−16.8782	−	29.2339i	−0.748112	−	1.29577i	0.200614	−	0.979670i	$-0.435706\pi$
$510$	−0.138228	−	12.8211i	−0.00612083	−	0.567728i
$511$	−19.6486	+	34.0324i	−0.869204	+	1.50551i
$512$	19.9900			0.883440
$513$	0.0510994	+	1.57939i	0.00225610	+	0.0697319i
$514$	−2.53218			−0.111690
$515$	1.50238	−	2.60219i	0.0662027	−	0.114666i
$516$	0.0842489	+	7.81438i	0.00370885	+	0.344009i
$517$	9.56938	+	16.5746i	0.420861	+	0.728952i
$518$	18.3862	+	31.8458i	0.807843	+	1.39923i
$519$	33.9771	+	19.1313i	1.49143	+	0.839770i
$520$	1.53799	−	2.66387i	0.0674452	−	0.116818i
$521$	2.51785			0.110309			0.0551544	−	0.998478i	$-0.482435\pi$
$521$	2.51785			0.110309			0.0551544	+	0.998478i	$0.482435\pi$
$522$	−1.32239	−	2.18049i	−0.0578795	−	0.0954373i
$523$	30.1042			1.31637			0.658183	−	0.752858i	$-0.271325\pi$
$523$	30.1042			1.31637			0.658183	+	0.752858i	$0.271325\pi$
$524$	0.260778	−	0.451680i	0.0113921	−	0.0197317i
$525$	5.70690	−	3.37743i	0.249070	−	0.147403i
$526$	9.65804	+	16.7282i	0.421110	+	0.729385i
$527$	−26.0552	−	45.1290i	−1.13498	−	1.96585i
$528$	5.77176	−	3.41582i	0.251184	−	0.148654i
$529$	−6.61520	+	11.4579i	−0.287617	+	0.498168i
$530$	0.540616			0.0234829
$531$	−15.2853	−	25.2038i	−0.663323	−	1.09375i
$532$	0.857578			0.0371807
$533$	5.74126	−	9.94416i	0.248682	−	0.430729i
$534$	−11.0864	−	6.24235i	−0.479755	−	0.270133i
$535$	7.17925	+	12.4348i	0.310386	+	0.537605i
$536$	2.47795	+	4.29194i	0.107031	+	0.185384i
$537$	0.350904	+	32.5476i	0.0151426	+	1.40453i
$538$	−2.44677	+	4.23793i	−0.105488	+	0.182710i
$539$	14.9439			0.643678
$540$	−3.37454	−	1.80539i	−0.145217	−	0.0776916i
$541$	−27.6914			−1.19054			−0.595272	−	0.803524i	$-0.702956\pi$
$541$	−27.6914			−1.19054			−0.595272	+	0.803524i	$0.702956\pi$
$542$	15.1756	−	26.2850i	0.651849	−	1.12904i
$543$	0.214742	+	19.9180i	0.00921545	+	0.854764i
$544$	12.9126	+	22.3652i	0.553622	+	0.958901i
$545$	8.04568	+	13.9355i	0.344639	+	0.596933i
$546$	6.49515	+	3.65719i	0.277967	+	0.156513i
$547$	−1.77794	+	3.07948i	−0.0760191	+	0.131669i	−0.901529	−	0.432719i	$-0.857554\pi$
$547$	−1.77794	+	3.07948i	−0.0760191	+	0.131669i	0.825510	+	0.564388i	$0.190888\pi$
$548$	−3.25410			−0.139008
$549$	14.2607	−	25.9781i	0.608632	−	1.10872i
$550$	−2.19329			−0.0935220
$551$	−0.114992	+	0.199172i	−0.00489882	+	0.00848500i
$552$	−27.5977	+	16.3328i	−1.17464	+	0.695169i
$553$	−12.8549	−	22.2653i	−0.546646	−	0.946818i
$554$	−1.77583	−	3.07583i	−0.0754479	−	0.130680i
$555$	−12.7364	+	7.53762i	−0.540632	+	0.319954i
$556$	−1.96822	+	3.40906i	−0.0834711	+	0.144576i
$557$	18.6002			0.788114			0.394057	−	0.919086i	$-0.371071\pi$
$557$	18.6002			0.788114			0.394057	+	0.919086i	$0.371071\pi$
$558$	26.6759	−	0.575268i	1.12928	−	0.0243530i
$559$	6.12586			0.259096
$560$	3.79890	−	6.57988i	0.160533	−	0.278051i
$561$	19.3947	+	10.9204i	0.818843	+	0.461061i
$562$	−6.97427	−	12.0798i	−0.294192	−	0.509555i
$563$	1.88299	+	3.26143i	0.0793584	+	0.137453i	0.902973	−	0.429697i	$-0.141380\pi$
$563$	1.88299	+	3.26143i	0.0793584	+	0.137453i	−0.823615	+	0.567149i	$0.808046\pi$
$564$	−0.134896	−	12.5120i	−0.00568014	−	0.526852i
$565$	−6.46260	+	11.1935i	−0.271883	+	0.470916i
$566$	−9.25138			−0.388865
$567$	15.9265	−	30.5564i	0.668849	−	1.28325i
$568$	−32.8045			−1.37645
$569$	−4.90097	+	8.48873i	−0.205459	+	0.355866i	−0.950279	−	0.311400i	$-0.899202\pi$
$569$	−4.90097	+	8.48873i	−0.205459	+	0.355866i	0.744820	+	0.667266i	$0.232536\pi$
$570$	−0.00638297	−	0.592042i	−0.000267353	−	0.0247979i
$571$	−15.6655	−	27.1334i	−0.655579	−	1.13550i	−0.981748	−	0.190185i	$-0.939091\pi$
$571$	−15.6655	−	27.1334i	−0.655579	−	1.13550i	0.326169	−	0.945311i	$-0.394242\pi$
$572$	0.718580	+	1.24462i	0.0300453	+	0.0520401i
$573$	−4.56928	−	2.57280i	−0.190885	−	0.107480i
$574$	24.7079	−	42.7953i	1.03129	−	1.78624i
$575$	6.01917			0.251017
$576$	−25.1241	+	0.541803i	−1.04684	+	0.0225751i
$577$	19.2387			0.800919			0.400459	−	0.916315i	$-0.368851\pi$
$577$	19.2387			0.800919			0.400459	+	0.916315i	$0.368851\pi$
$578$	14.8220	−	25.6724i	0.616513	−	1.06783i
$579$	−35.2493	+	20.8611i	−1.46491	+	0.866958i
$580$	−0.278499	−	0.482375i	−0.0115641	−	0.0200295i
$581$	17.0862	+	29.5942i	0.708856	+	1.22778i
$582$	−0.858946	+	0.508338i	−0.0356045	+	0.0210713i
$583$	−0.469234	+	0.812738i	−0.0194337	+	0.0336602i
$584$	−31.5717			−1.30645
$585$	−1.44364	+	2.62981i	−0.0596870	+	0.108729i
$586$	−19.6469			−0.811606
$587$	−8.13403	+	14.0886i	−0.335727	+	0.581497i	−0.983624	−	0.180231i	$-0.942315\pi$
$587$	−8.13403	+	14.0886i	−0.335727	+	0.581497i	0.647897	+	0.761728i	$0.275649\pi$
$588$	−8.51340	−	4.79359i	−0.351087	−	0.197684i
$589$	−1.20316	−	2.08393i	−0.0495752	−	0.0858668i
$590$	5.52215	+	9.56464i	0.227343	+	0.393770i
$591$	−0.170046	−	15.7723i	−0.00699474	−	0.648786i
$592$	−8.47822	+	14.6847i	−0.348453	+	0.603538i
$593$	8.99873			0.369534			0.184767	−	0.982782i	$-0.440847\pi$
$593$	8.99873			0.369534			0.184767	+	0.982782i	$0.440847\pi$
$594$	−9.68036	+	6.01450i	−0.397190	+	0.246778i
$595$	25.2147			1.03370
$596$	0.734526	−	1.27224i	0.0300874	−	0.0521128i
$597$	0.383579	+	35.5783i	0.0156988	+	1.45612i
$598$	3.38290	+	5.85935i	0.138337	+	0.239606i
$599$	1.67069	+	2.89371i	0.0682624	+	0.118234i	0.898136	−	0.439717i	$-0.144921\pi$
$599$	1.67069	+	2.89371i	0.0682624	+	0.118234i	−0.829874	+	0.557951i	$0.811588\pi$
$600$	4.64241	+	2.61398i	0.189526	+	0.106715i
$601$	2.08140	−	3.60509i	0.0849020	−	0.147055i	−0.820447	−	0.571722i	$-0.806276\pi$
$601$	2.08140	−	3.60509i	0.0849020	−	0.147055i	0.905349	+	0.424667i	$0.139609\pi$
$602$	26.3630			1.07448
$603$	−2.50644	−	4.13285i	−0.102070	−	0.168303i
$604$	−5.32433			−0.216644
$605$	−3.59631	+	6.22899i	−0.146211	+	0.253245i
$606$	14.7652	−	8.73828i	0.599796	−	0.354969i
$607$	−15.1943	−	26.3173i	−0.616717	−	1.06819i	−0.990081	−	0.140501i	$-0.955129\pi$
$607$	−15.1943	−	26.3173i	−0.616717	−	1.06819i	0.373363	−	0.927685i	$-0.378205\pi$
$608$	0.596266	+	1.03276i	0.0241818	+	0.0418841i
$609$	4.31581	−	2.55416i	0.174886	−	0.103500i
$610$	−5.55182	+	9.61603i	−0.224786	+	0.389342i
$611$	−9.80845			−0.396808
$612$	−7.54600	−	12.4426i	−0.305029	−	0.502961i
$613$	37.1560			1.50072			0.750358	−	0.661031i	$-0.229881\pi$
$613$	37.1560			1.50072			0.750358	+	0.661031i	$0.229881\pi$
$614$	−11.1711	+	19.3489i	−0.450829	+	0.780858i
$615$	17.3300	+	9.75790i	0.698813	+	0.393476i
$616$	11.4898	+	19.9009i	0.462937	+	0.801830i
$617$	3.12464	+	5.41204i	0.125793	+	0.217880i	0.922043	−	0.387088i	$-0.126519\pi$
$617$	3.12464	+	5.41204i	0.125793	+	0.217880i	−0.796249	+	0.604968i	$0.793186\pi$
$618$	0.0630662	+	5.84960i	0.00253689	+	0.235306i
$619$	−16.1132	+	27.9088i	−0.647642	+	1.12175i	0.336042	+	0.941847i	$0.390911\pi$
$619$	−16.1132	+	27.9088i	−0.647642	+	1.12175i	−0.983684	+	0.179902i	$0.942422\pi$
$620$	5.82786			0.234053
$621$	26.5664	−	16.5060i	1.06607	−	0.662362i
$622$	9.55599			0.383160
$623$	12.5102	−	21.6683i	0.501210	−	0.868121i
$624$	0.0370550	+	3.43698i	0.00148339	+	0.137589i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.7097	+	23.7460i	0.547951	+	0.949080i
$627$	0.895590	+	0.504275i	0.0357664	+	0.0201388i
$628$	1.71281	−	2.96667i	0.0683484	−	0.118383i
$629$	−56.2732			−2.24376
$630$	−6.21278	+	11.3176i	−0.247523	+	0.450903i
$631$	15.5600			0.619435			0.309717	−	0.950829i	$-0.399766\pi$
$631$	15.5600			0.619435			0.309717	+	0.950829i	$0.399766\pi$
$632$	10.3277	−	17.8882i	0.410815	−	0.711553i
$633$	−17.9262	+	10.6090i	−0.712503	+	0.421670i
$634$	−9.82638	−	17.0198i	−0.390255	−	0.675942i
$635$	4.67413	+	8.09583i	0.185487	+	0.321273i
$636$	0.528023	−	0.312492i	0.0209375	−	0.0123911i
$637$	−3.82930	+	6.63255i	−0.151723	+	0.262791i
$638$	−1.65866			−0.0656669
$639$	31.9868	−	0.689798i	1.26538	−	0.0272880i
$640$	1.57302			0.0621789
$641$	8.86882	−	15.3612i	0.350297	−	0.606733i	−0.636004	−	0.771686i	$-0.719414\pi$
$641$	8.86882	−	15.3612i	0.350297	−	0.606733i	0.986301	+	0.164953i	$0.0527472\pi$
$642$	−24.3586	−	13.7155i	−0.961357	−	0.541306i
$643$	−2.81241	−	4.87124i	−0.110911	−	0.192103i	0.805227	−	0.592967i	$-0.202043\pi$
$643$	−2.81241	−	4.87124i	−0.110911	−	0.192103i	−0.916138	+	0.400864i	$0.868710\pi$
$644$	−8.48682	−	14.6996i	−0.334428	−	0.579246i
$645$	0.114386	+	10.6097i	0.00450394	+	0.417756i
$646$	1.12563	−	1.94965i	0.0442873	−	0.0767078i
$647$	28.5003			1.12046			0.560231	−	0.828337i	$-0.310713\pi$
$647$	28.5003			1.12046			0.560231	+	0.828337i	$0.310713\pi$
$648$	27.6580	−	1.19345i	1.08651	−	0.0468831i
$649$	−19.1721			−0.752570
$650$	0.562020	−	0.973448i	0.0220442	−	0.0381818i
$651$	0.565678	+	52.4685i	0.0221707	+	2.05640i
$652$	6.30987	+	10.9290i	0.247113	+	0.428013i
$653$	11.4654	+	19.8587i	0.448677	+	0.777131i	0.998300	−	0.0582816i	$-0.0185621\pi$
$653$	11.4654	+	19.8587i	0.448677	+	0.777131i	−0.549623	+	0.835413i	$0.685229\pi$
$654$	−27.2983	−	15.3707i	−1.06745	−	0.601042i
$655$	0.354061	−	0.613252i	0.0138343	−	0.0239617i
$656$	22.7865			0.889665
$657$	30.7848	−	0.663876i	1.20103	−	0.0259003i
$658$	−42.2113			−1.64557
$659$	−13.7179	+	23.7601i	−0.534373	+	0.925561i	0.464820	+	0.885405i	$0.346119\pi$
$659$	−13.7179	+	23.7601i	−0.534373	+	0.925561i	−0.999193	+	0.0401563i	$0.987214\pi$
$660$	−2.14220	+	1.26779i	−0.0833849	+	0.0493485i
$661$	−6.08409	−	10.5379i	−0.236643	−	0.409879i	0.723106	−	0.690738i	$-0.242714\pi$
$661$	−6.08409	−	10.5379i	−0.236643	−	0.409879i	−0.959749	+	0.280859i	$0.909381\pi$
$662$	−12.0376	−	20.8497i	−0.467855	−	0.810348i
$663$	−9.81663	+	5.80963i	−0.381246	+	0.225627i
$664$	−13.7272	+	23.7762i	−0.532720	+	0.922697i
$665$	1.16434			0.0451514
$666$	13.8654	−	25.2581i	0.537275	−	0.978731i
$667$	4.55196			0.176253
$668$	1.54105	−	2.66917i	0.0596249	−	0.103273i
$669$	4.64653	+	2.61630i	0.179645	+	0.101152i
$670$	0.905508	+	1.56839i	0.0349828	+	0.0605920i
$671$	−9.63754	−	16.6927i	−0.372053	−	0.644415i
$672$	−0.280341	−	26.0026i	−0.0108144	−	1.00307i
$673$	16.7910	−	29.0828i	0.647244	−	1.12106i	−0.336534	−	0.941671i	$-0.609255\pi$
$673$	16.7910	−	29.0828i	0.647244	−	1.12106i	0.983778	−	0.179388i	$-0.0574118\pi$
$674$	−8.87452			−0.341834
$675$	−4.58166	−	2.45120i	−0.176348	−	0.0943468i
$676$	−0.736533			−0.0283282
$677$	−11.0078	+	19.0660i	−0.423063	+	0.732766i	−0.996237	−	0.0866673i	$-0.972378\pi$
$677$	−11.0078	+	19.0660i	−0.423063	+	0.732766i	0.573175	+	0.819433i	$0.305712\pi$
$678$	−0.271284	−	25.1625i	−0.0104186	−	0.966361i
$679$	−0.981400	−	1.69984i	−0.0376627	−	0.0652337i
$680$	10.1289	+	17.5437i	0.388424	+	0.672771i
$681$	−5.06929	−	2.85433i	−0.194255	−	0.109378i
$682$	8.67725	−	15.0294i	0.332269	−	0.575507i
$683$	33.7088			1.28983			0.644915	−	0.764254i	$-0.276893\pi$
$683$	33.7088			1.28983			0.644915	+	0.764254i	$0.276893\pi$
$684$	−0.348453	−	0.574562i	−0.0133234	−	0.0219689i
$685$	−4.41813			−0.168808
$686$	−1.41718	+	2.45463i	−0.0541082	+	0.0937182i
$687$	−42.4214	+	25.1056i	−1.61848	+	0.957840i
$688$	6.07824	+	10.5278i	0.231731	+	0.401369i
$689$	−0.240479	−	0.416522i	−0.00916151	−	0.0158682i
$690$	−10.0849	+	5.96842i	−0.383927	+	0.227214i
$691$	11.2006	−	19.4000i	0.426091	−	0.738012i	−0.570430	−	0.821346i	$-0.693224\pi$
$691$	11.2006	−	19.4000i	0.426091	−	0.738012i	0.996522	+	0.0833343i	$0.0265569\pi$
$692$	−16.5812			−0.630324
$693$	−11.6219	−	19.1633i	−0.441478	−	0.727952i
$694$	1.98070			0.0751863
$695$	−2.67228	+	4.62852i	−0.101365	+	0.175570i
$696$	3.51079	+	1.97680i	0.133076	+	0.0749305i
$697$	37.8108	+	65.4902i	1.43219	+	2.48062i
$698$	−11.6748	−	20.2213i	−0.441896	−	0.765387i
$699$	0.519147	+	48.1527i	0.0196359	+	1.82130i
$700$	−1.40997	+	2.44213i	−0.0532917	+	0.0923039i
$701$	19.7517			0.746010			0.373005	−	0.927829i	$-0.378327\pi$
$701$	19.7517			0.746010			0.373005	+	0.927829i	$0.378327\pi$
$702$	−0.188870	−	5.83763i	−0.00712844	−	0.220327i
$703$	−2.59854			−0.0980057
$704$	−8.17248	+	14.1551i	−0.308012	+	0.533492i
$705$	−0.183150	−	16.9878i	−0.00689782	−	0.639796i
$706$	−7.31083	−	12.6627i	−0.275147	−	0.476568i
$707$	16.8702	+	29.2200i	0.634469	+	1.09893i
$708$	10.9222	+	6.14989i	0.410481	+	0.231127i
$709$	0.664817	−	1.15150i	0.0249677	−	0.0432454i	−0.853272	−	0.521467i	$-0.825385\pi$
$709$	0.664817	−	1.15150i	0.0249677	−	0.0432454i	0.878239	+	0.478221i	$0.158718\pi$
$710$	−11.9876			−0.449887
$711$	−9.69416	+	17.6594i	−0.363559	+	0.662281i
$712$	20.1016			0.753338
$713$	−23.8135	+	41.2462i	−0.891823	+	1.54468i
$714$	−42.2465	+	25.0021i	−1.58104	+	0.935681i
$715$	0.975625	+	1.68983i	0.0364863	+	0.0631962i
$716$	−6.92062	−	11.9869i	−0.258636	−	0.447970i
$717$	0.654221	−	0.387178i	0.0244323	−	0.0144594i
$718$	10.0200	−	17.3551i	0.373943	−	0.647687i
$719$	−17.8818			−0.666878			−0.333439	−	0.942772i	$-0.608209\pi$
$719$	−17.8818			−0.666878			−0.333439	+	0.942772i	$0.608209\pi$
$720$	−5.95198	+	0.128355i	−0.221817	+	0.00478350i
$721$	−11.5042			−0.428438
$722$	−10.6264	+	18.4055i	−0.395474	+	0.684981i
$723$	−1.43030	−	0.805351i	−0.0531934	−	0.0299513i
$724$	−4.23519	−	7.33556i	−0.157400	−	0.272624i
$725$	−0.378122	−	0.654926i	−0.0140431	−	0.0243234i
$726$	−0.150964	−	14.0025i	−0.00560282	−	0.519680i
$727$	−8.00408	+	13.8635i	−0.296855	+	0.514168i	−0.975415	−	0.220377i	$-0.929271\pi$
$727$	−8.00408	+	13.8635i	−0.296855	+	0.514168i	0.678560	+	0.734545i	$0.262604\pi$
$728$	−11.7768			−0.436479
$729$	−26.9435	+	1.74528i	−0.997909	+	0.0646401i
$730$	−11.5371			−0.427009
$731$	−20.1718	+	34.9386i	−0.746081	+	1.29225i
$732$	0.135857	+	12.6012i	0.00502140	+	0.465752i
$733$	1.12473	+	1.94809i	0.0415428	+	0.0719542i	0.886049	−	0.463591i	$-0.153439\pi$
$733$	1.12473	+	1.94809i	0.0415428	+	0.0719542i	−0.844506	+	0.535545i	$0.820106\pi$
$734$	17.4573	+	30.2370i	0.644362	+	1.11607i
$735$	−11.5587	−	6.50832i	−0.426351	−	0.240063i
$736$	11.8016	−	20.4410i	0.435013	−	0.753465i
$737$	−3.14379			−0.115803
$738$	−38.7115	+	0.834815i	−1.42499	+	0.0307300i
$739$	7.65597			0.281629			0.140815	−	0.990036i	$-0.455028\pi$
$739$	7.65597			0.281629			0.140815	+	0.990036i	$0.455028\pi$
$740$	3.14670	−	5.45025i	0.115675	−	0.200355i
$741$	−0.453304	+	0.268272i	−0.0166525	+	0.00985523i
$742$	−1.03492	−	1.79253i	−0.0379930	−	0.0658057i
$743$	−8.10475	−	14.0378i	−0.297334	−	0.514998i	0.678191	−	0.734886i	$-0.262764\pi$
$743$	−8.10475	−	14.0378i	−0.297334	−	0.514998i	−0.975525	+	0.219888i	$0.929431\pi$
$744$	−36.2789	+	21.4704i	−1.33005	+	0.787143i
$745$	0.997275	−	1.72733i	0.0365373	−	0.0632845i
$746$	18.0919			0.662392
$747$	12.8851	−	23.4723i	0.471441	−	0.858805i
$748$	−9.46484			−0.346069
$749$	27.4869	−	47.6087i	1.00435	−	1.73958i
$750$	1.69646	+	0.955214i	0.0619459	+	0.0348795i
$751$	−22.7237	−	39.3586i	−0.829199	−	1.43621i	−0.898668	−	0.438630i	$-0.855464\pi$
$751$	−22.7237	−	39.3586i	−0.829199	−	1.43621i	0.0694692	−	0.997584i	$-0.477869\pi$
$752$	−9.73221	−	16.8567i	−0.354897	−	0.614700i
$753$	0.207922	+	19.2855i	0.00757710	+	0.702802i
$754$	0.425024	−	0.736164i	0.0154785	−	0.0268095i
$755$	−7.22891			−0.263087
$756$	0.473826	+	14.6451i	0.0172329	+	0.532638i
$757$	44.1058			1.60305			0.801527	−	0.597959i	$-0.204021\pi$
$757$	44.1058			1.60305			0.801527	+	0.597959i	$0.204021\pi$
$758$	0.185113	−	0.320625i	0.00672360	−	0.0116456i
$759$	−0.219308	−	20.3416i	−0.00796039	−	0.738353i
$760$	0.467722	+	0.810119i	0.0169661	+	0.0293861i
$761$	−8.95332	−	15.5076i	−0.324558	−	0.562150i	0.656865	−	0.754008i	$-0.271882\pi$
$761$	−8.95332	−	15.5076i	−0.324558	−	0.562150i	−0.981423	+	0.191858i	$0.938549\pi$
$762$	−15.8589	−	8.92959i	−0.574508	−	0.323485i
$763$	30.8042	−	53.3544i	1.11519	−	1.93156i
$764$	2.22987			0.0806738
$765$	−10.2453	−	16.8934i	−0.370419	−	0.610783i
$766$	0.507317			0.0183301
$767$	4.91277	−	8.50916i	0.177390	−	0.307248i
$768$	22.3365	−	13.2191i	0.806001	−	0.477004i
$769$	5.79221	+	10.0324i	0.208873	+	0.361778i	0.951360	−	0.308083i	$-0.0996873\pi$
$769$	5.79221	+	10.0324i	0.208873	+	0.361778i	−0.742487	+	0.669860i	$0.766354\pi$
$770$	4.19867	+	7.27231i	0.151309	+	0.262076i
$771$	−3.35789	+	1.98725i	−0.120932	+	0.0715691i
$772$	8.70881	−	15.0841i	0.313437	−	0.542889i
$773$	−52.7091			−1.89582			−0.947908	−	0.318544i	$-0.896806\pi$
$773$	−52.7091			−1.89582			−0.947908	+	0.318544i	$0.896806\pi$
$774$	−10.7119	−	17.6628i	−0.385030	−	0.634875i
$775$	7.91256			0.284228
$776$	0.788465	−	1.36566i	0.0283042	−	0.0490244i
$777$	49.3743	+	27.8009i	1.77129	+	0.997351i
$778$	3.93098	+	6.80866i	0.140932	+	0.244102i
$779$	1.74599	+	3.02415i	0.0625567	+	0.108351i
$780$	−0.0137530	−	1.27564i	−0.000492437	−	0.0456752i
$781$	10.4048	−	18.0217i	0.372313	−	0.644865i
$782$	−44.5581			−1.59339
$783$	−3.46485	−	1.85371i	−0.123824	−	0.0662460i
$784$	−15.1982			−0.542791
$785$	2.32550	−	4.02788i	0.0830006	−	0.143761i
$786$	0.0148626	+	1.37856i	0.000530133	+	0.0491716i
$787$	−3.83611	−	6.64433i	−0.136742	−	0.236845i	0.789519	−	0.613726i	$-0.210330\pi$
$787$	−3.83611	−	6.64433i	−0.136742	−	0.236845i	−0.926262	+	0.376881i	$0.876997\pi$
$788$	3.35368	+	5.80875i	0.119470	+	0.206928i
$789$	25.9357	+	14.6035i	0.923335	+	0.519897i
$790$	3.77402	−	6.53680i	0.134274	−	0.232569i
$791$	49.4861			1.75952
$792$	8.66470	−	15.7841i	0.307887	−	0.560864i
$793$	9.87832			0.350789
$794$	−12.6814	+	21.9648i	−0.450044	+	0.779500i
$795$	0.716904	−	0.424275i	0.0254260	−	0.0150475i
$796$	−7.56504	−	13.1030i	−0.268136	−	0.464425i
$797$	−9.00026	−	15.5889i	−0.318806	−	0.552187i	0.661434	−	0.750004i	$-0.269948\pi$
$797$	−9.00026	−	15.5889i	−0.318806	−	0.552187i	−0.980239	+	0.197816i	$0.936615\pi$
$798$	−1.95082	+	1.15453i	−0.0690584	+	0.0408698i
$799$	32.2982	−	55.9422i	1.14263	−	1.97909i
$800$	−3.92134			−0.138640
$801$	−19.6005	+	0.422686i	−0.692550	+	0.0149349i
$802$	−33.7954			−1.19336
$803$	10.0138	−	17.3444i	0.353379	−	0.612071i
$804$	1.79099	+	1.00844i	0.0631634	+	0.0355650i
$805$	−11.5227	−	19.9578i	−0.406121	−	0.703421i
$806$	4.44702	+	7.70246i	0.156640	+	0.271308i
$807$	0.0812918	+	7.54009i	0.00286161	+	0.265424i
$808$	−13.5537	+	23.4756i	−0.476816	+	0.825869i
$809$	−26.6115			−0.935609			−0.467805	−	0.883832i	$-0.654955\pi$
$809$	−26.6115			−0.935609			−0.467805	+	0.883832i	$0.654955\pi$
$810$	10.1070	−	0.436117i	0.355122	−	0.0153236i
$811$	32.3751			1.13684			0.568422	−	0.822737i	$-0.307554\pi$
$811$	32.3751			1.13684			0.568422	+	0.822737i	$0.307554\pi$
$812$	−1.06628	+	1.84685i	−0.0374190	+	0.0648116i
$813$	−0.504197	−	46.7660i	−0.0176830	−	1.64016i
$814$	−9.37041	−	16.2300i	−0.328433	−	0.568862i
$815$	8.56699	+	14.8385i	0.300088	+	0.519768i
$816$	−19.7247	−	11.1063i	−0.690502	−	0.388797i
$817$	−0.931477	+	1.61337i	−0.0325882	+	0.0564445i
$818$	40.4987			1.41600
$819$	11.4833	−	0.247638i	0.401259	−	0.00865317i
$820$	−8.45726			−0.295340
$821$	−25.1137	+	43.4982i	−0.876474	+	1.51810i	−0.0212898	+	0.999773i	$0.506777\pi$
$821$	−25.1137	+	43.4982i	−0.876474	+	1.51810i	−0.855184	+	0.518324i	$0.826556\pi$
$822$	7.40244	−	4.38088i	0.258190	−	0.152801i
$823$	−22.6114	−	39.1641i	−0.788184	−	1.36518i	−0.927078	−	0.374868i	$-0.877688\pi$
$823$	−22.6114	−	39.1641i	−0.788184	−	1.36518i	0.138894	−	0.990307i	$-0.455645\pi$
$824$	−4.62127	−	8.00428i	−0.160990	−	0.278842i
$825$	−2.90849	+	1.72129i	−0.101261	+	0.0599276i
$826$	21.1424	−	36.6197i	0.735639	−	1.27416i
$827$	−15.3452			−0.533605			−0.266803	−	0.963751i	$-0.585967\pi$
$827$	−15.3452			−0.533605			−0.266803	+	0.963751i	$0.585967\pi$
$828$	−6.40010	+	11.6588i	−0.222419	+	0.405171i
$829$	−30.8233			−1.07054			−0.535269	−	0.844681i	$-0.679790\pi$
$829$	−30.8233			−1.07054			−0.535269	+	0.844681i	$0.679790\pi$
$830$	−5.01628	+	8.68846i	−0.174118	+	0.301581i
$831$	−4.76882	−	2.68515i	−0.165429	−	0.0931469i
$832$	−4.18833	−	7.25440i	−0.145204	−	0.251501i
$833$	−25.2190	−	43.6806i	−0.873787	−	1.51344i
$834$	−0.112176	−	10.4047i	−0.00388433	−	0.360285i
$835$	2.09230	−	3.62397i	0.0724070	−	0.125413i
$836$	−0.437059			−0.0151160
$837$	34.9231	−	21.6981i	1.20712	−	0.749996i
$838$	2.60146			0.0898659
$839$	2.73319	−	4.73403i	0.0943604	−	0.163437i	−0.814981	−	0.579488i	$-0.803253\pi$
$839$	2.73319	−	4.73403i	0.0943604	−	0.163437i	0.909341	+	0.416051i	$0.136586\pi$
$840$	−0.219905	−	20.3969i	−0.00758743	−	0.703760i
$841$	14.2140	+	24.6195i	0.490140	+	0.848947i
$842$	2.34412	+	4.06013i	0.0807837	+	0.139921i
$843$	−18.7287	−	10.5455i	−0.645051	−	0.363205i
$844$	4.42890	−	7.67108i	0.152449	−	0.264050i
$845$	−1.00000			−0.0344010
$846$	17.1514	+	28.2808i	0.589676	+	0.972315i
$847$	27.5381			0.946219
$848$	0.477219	−	0.826568i	0.0163878	−	0.0283845i
$849$	−12.2681	+	7.26048i	−0.421042	+	0.249179i
$850$	3.70135	+	6.41093i	0.126955	+	0.219893i
$851$	25.7158	+	44.5411i	0.881526	+	1.52685i
$852$	−11.7084	+	6.92921i	−0.401123	+	0.237391i
$853$	−19.5309	+	33.8286i	−0.668726	+	1.15827i	0.309534	+	0.950888i	$0.399827\pi$
$853$	−19.5309	+	33.8286i	−0.668726	+	1.15827i	−0.978261	+	0.207380i	$0.933506\pi$
$854$	42.5120			1.45473
$855$	−0.473099	−	0.780091i	−0.0161796	−	0.0266785i
$856$	44.1664			1.50958
$857$	6.24701	−	10.8201i	0.213394	−	0.369609i	−0.739381	−	0.673288i	$-0.764882\pi$
$857$	6.24701	−	10.8201i	0.213394	−	0.369609i	0.952774	+	0.303679i	$0.0982150\pi$
$858$	−3.31021	−	1.86386i	−0.113009	−	0.0636312i
$859$	−12.2680	−	21.2487i	−0.418577	−	0.724997i	0.577219	−	0.816589i	$-0.304138\pi$
$859$	−12.2680	−	21.2487i	−0.418577	−	0.724997i	−0.995797	+	0.0915921i	$0.970804\pi$
$860$	−2.25595	−	3.90741i	−0.0769271	−	0.133242i
$861$	−0.820898	−	76.1411i	−0.0279761	−	2.59488i
$862$	−5.38349	+	9.32448i	−0.183362	+	0.317593i
$863$	−14.5106			−0.493945			−0.246973	−	0.969022i	$-0.579436\pi$
$863$	−14.5106			−0.493945			−0.246973	+	0.969022i	$0.579436\pi$
$864$	−17.3074	+	10.7532i	−0.588808	+	0.365832i
$865$	−22.5126			−0.765450
$866$	13.8094	−	23.9186i	0.469262	−	0.812786i
$867$	−0.492447	−	45.6762i	−0.0167244	−	1.55124i
$868$	−11.1564	−	19.3235i	−0.378674	−	0.655883i
$869$	6.55142	+	11.3474i	0.222242	+	0.384934i
$870$	1.28294	+	0.722375i	0.0434956	+	0.0244908i
$871$	0.805583	−	1.39531i	0.0272961	−	0.0472783i
$872$	49.4966			1.67617
$873$	−0.740095	+	1.34820i	−0.0250484	+	0.0456297i
$874$	−2.05757			−0.0695982
$875$	−1.91433	+	3.31571i	−0.0647161	+	0.112092i
$876$	−11.2684	+	6.66881i	−0.380724	+	0.225318i
$877$	−19.8686	−	34.4134i	−0.670915	−	1.16206i	−0.977645	−	0.210262i	$-0.932568\pi$
$877$	−19.8686	−	34.4134i	−0.670915	−	1.16206i	0.306730	−	0.951796i	$-0.400765\pi$
$878$	6.64060	+	11.5019i	0.224110	+	0.388169i
$879$	−26.0535	+	15.4189i	−0.878763	+	0.520065i
$880$	−1.93608	+	3.35340i	−0.0652654	+	0.113043i
$881$	18.5089			0.623580			0.311790	−	0.950151i	$-0.399072\pi$
$881$	18.5089			0.623580			0.311790	+	0.950151i	$0.399072\pi$
$882$	25.8198	−	0.556805i	0.869396	−	0.0187486i
$883$	22.2042			0.747230			0.373615	−	0.927584i	$-0.378118\pi$
$883$	22.2042			0.747230			0.373615	+	0.927584i	$0.378118\pi$
$884$	2.42533	−	4.20079i	0.0815726	−	0.141288i
$885$	14.8292	+	8.34978i	0.498477	+	0.280675i
$886$	−20.4388	−	35.4011i	−0.686656	−	1.18932i
$887$	18.5994	+	32.2152i	0.624508	+	1.08168i	0.988636	+	0.150331i	$0.0480340\pi$
$887$	18.5994	+	32.2152i	0.624508	+	1.08168i	−0.364127	+	0.931349i	$0.618633\pi$
$888$	0.490774	+	45.5210i	0.0164693	+	1.52758i
$889$	17.8956	−	30.9962i	0.600201	−	1.03958i
$890$	7.34563			0.246226
$891$	−8.11683	+	15.5729i	−0.271924	+	0.521711i
$892$	−2.26757			−0.0759237
$893$	1.49144	−	2.58325i	0.0499091	−	0.0864452i
$894$	0.0418632	+	3.88295i	0.00140012	+	0.129865i
$895$	−9.39622	−	16.2747i	−0.314081	−	0.544004i
$896$	−3.01127	−	5.21567i	−0.100599	−	0.174243i
$897$	9.08443	+	5.11511i	0.303320	+	0.170789i
$898$	−3.38515	+	5.86325i	−0.112964	+	0.195659i
$899$	5.98383			0.199572
$900$	2.20908	−	0.0476390i	0.0736362	−	0.00158797i
$901$	3.16749			0.105524
$902$	−12.5922	+	21.8104i	−0.419275	+	0.726206i
$903$	34.9597	−	20.6897i	1.16339	−	0.688509i
$904$	19.8788	+	34.4310i	0.661158	+	1.14516i
$905$	−5.75017	−	9.95959i	−0.191142	−	0.331068i
$906$	12.1118	−	7.16796i	0.402388	−	0.238139i
$907$	−8.20165	+	14.2057i	−0.272331	+	0.471692i	−0.969458	−	0.245256i	$-0.921128\pi$
$907$	−8.20165	+	14.2057i	−0.272331	+	0.471692i	0.697127	+	0.716948i	$0.254461\pi$
$908$	2.47388			0.0820984
$909$	12.7222	−	23.1755i	0.421968	−	0.768682i
$910$	−4.30356			−0.142662
$911$	−2.63596	+	4.56561i	−0.0873332	+	0.151265i	−0.906383	−	0.422457i	$-0.861168\pi$
$911$	−2.63596	+	4.56561i	−0.0873332	+	0.151265i	0.819050	+	0.573722i	$0.194501\pi$
$912$	−0.910830	−	0.512856i	−0.0301606	−	0.0169823i
$913$	−8.70789	−	15.0825i	−0.288189	−	0.499158i
$914$	−17.4598	−	30.2412i	−0.577518	−	1.00029i
$915$	0.184454	+	17.1088i	0.00609787	+	0.565598i
$916$	10.4808	−	18.1532i	0.346294	−	0.599799i
$917$	−2.71116			−0.0895303
$918$	33.9167	+	18.1455i	1.11942	+	0.598891i
$919$	3.85840			0.127277			0.0636384	−	0.997973i	$-0.479730\pi$
$919$	3.85840			0.127277			0.0636384	+	0.997973i	$0.479730\pi$
$920$	9.25740	−	16.0343i	0.305208	−	0.528635i
$921$	0.371150	+	34.4254i	0.0122298	+	1.13436i
$922$	−20.9686	−	36.3186i	−0.690563	−	1.19609i
$923$	5.33238	+	9.23595i	0.175517	+	0.304005i
$924$	8.30448	+	4.67596i	0.273197	+	0.153828i
$925$	4.27232	−	7.39987i	0.140473	−	0.243306i
$926$	−37.9703			−1.24778
$927$	4.67439	+	7.70759i	0.153527	+	0.253151i
$928$	−2.96549			−0.0973470
$929$	−21.1302	+	36.5986i	−0.693261	+	1.20076i	0.277503	+	0.960725i	$0.410493\pi$
$929$	−21.1302	+	36.5986i	−0.693261	+	1.20076i	−0.970764	+	0.240038i	$0.922840\pi$
$930$	−13.2572	+	7.84584i	−0.434722	+	0.257275i
$931$	−1.16454	−	2.01705i	−0.0381663	−	0.0661060i
$932$	−10.2387	−	17.7340i	−0.335381	−	0.580898i
$933$	12.6721	−	7.49953i	0.414865	−	0.245524i
$934$	13.0779	−	22.6516i	0.427922	−	0.741183i
$935$	−12.8505			−0.420257
$936$	4.78519	+	7.89028i	0.156409	+	0.257902i
$937$	−30.1222			−0.984048			−0.492024	−	0.870582i	$-0.663743\pi$
$937$	−30.1222			−0.984048			−0.492024	+	0.870582i	$0.663743\pi$
$938$	3.46688	−	6.00481i	0.113198	−	0.196064i
$939$	36.8161	+	20.7298i	1.20145	+	0.676493i
$940$	3.61212	+	6.25638i	0.117815	+	0.204061i
$941$	22.5998	+	39.1440i	0.736732	+	1.27606i	0.953959	+	0.299936i	$0.0969653\pi$
$941$	22.5998	+	39.1440i	0.736732	+	1.27606i	−0.217228	+	0.976121i	$0.569701\pi$
$942$	0.0976188	+	9.05448i	0.00318059	+	0.295011i
$943$	34.5576	−	59.8556i	1.12535	−	1.94917i
$944$	19.4983			0.634616
$945$	0.643320	+	19.8839i	0.0209272	+	0.646823i
$946$	−13.4357			−0.436834
$947$	−10.4455	+	18.0921i	−0.339433	+	0.587915i	−0.984326	−	0.176358i	$-0.943568\pi$
$947$	−10.4455	+	18.0921i	−0.339433	+	0.587915i	0.644893	+	0.764273i	$0.276902\pi$
$948$	−0.0923528	−	8.56603i	−0.00299948	−	0.278212i
$949$	5.13199	+	8.88887i	0.166592	+	0.288545i
$950$	0.170918	+	0.296038i	0.00554531	+	0.00960475i
$951$	−26.3878	−	14.8580i	−0.855682	−	0.481804i
$952$	38.7799	−	67.1688i	1.25687	−	2.17695i
$953$	−49.9066			−1.61663			−0.808317	−	0.588747i	$-0.799621\pi$
$953$	−49.9066			−1.61663			−0.808317	+	0.588747i	$0.799621\pi$
$954$	−0.780453	+	1.42172i	−0.0252681	+	0.0460298i
$955$	3.02752			0.0979683
$956$	−0.161634	+	0.279958i	−0.00522761	+	0.00905448i
$957$	−2.19953	+	1.30171i	−0.0711006	+	0.0420784i
$958$	8.78693	+	15.2194i	0.283893	+	0.491717i
$959$	8.45776	+	14.6493i	0.273115	+	0.473049i
$960$	12.4860	−	7.38943i	0.402985	−	0.238493i
$961$	−15.8043	+	27.3739i	−0.509816	+	0.883028i
$962$	9.60452			0.309662
$963$	−43.0655	+	0.928710i	−1.38777	+	0.0299273i
$964$	0.698005			0.0224812
$965$	11.8241	−	20.4799i	0.380630	−	0.659271i
$966$	39.0954	+	22.0132i	1.25787	+	0.708264i
$967$	7.50567	+	13.0002i	0.241366	+	0.418058i	0.961104	−	0.276188i	$-0.0890712\pi$
$967$	7.50567	+	13.0002i	0.241366	+	0.418058i	−0.719738	+	0.694246i	$0.755738\pi$
$968$	11.0622	+	19.1602i	0.355551	+	0.615833i
$969$	−0.0373981	−	3.46880i	−0.00120140	−	0.111434i
$970$	0.288126	−	0.499048i	0.00925115	−	0.0160235i
$971$	22.1581			0.711088			0.355544	−	0.934660i	$-0.384296\pi$
$971$	22.1581			0.711088			0.355544	+	0.934660i	$0.384296\pi$
$972$	9.61945	−	6.26809i	0.308544	−	0.201049i
$973$	20.4625			0.655996
$974$	11.6510	−	20.1801i	0.373321	−	0.646611i
$975$	−0.0186726	−	1.73195i	−0.000598003	−	0.0554668i
$976$	9.80153	+	16.9768i	0.313739	+	0.543413i
$977$	−21.0888	−	36.5268i	−0.674690	−	1.16860i	−0.976559	−	0.215248i	$-0.930944\pi$
$977$	−21.0888	−	36.5268i	−0.674690	−	1.16860i	0.301870	−	0.953349i	$-0.402389\pi$
$978$	−29.0671	−	16.3666i	−0.929462	−	0.523347i
$979$	−6.37574	+	11.0431i	−0.203769	+	0.352939i
$980$	5.64082			0.180189
$981$	−48.2629	+	1.04079i	−1.54091	+	0.0332299i
$982$	4.89600			0.156238
$983$	12.7219	−	22.0349i	0.405765	−	0.702805i	−0.588645	−	0.808391i	$-0.700339\pi$
$983$	12.7219	−	22.0349i	0.405765	−	0.702805i	0.994410	+	0.105586i	$0.0336719\pi$
$984$	52.6471	−	31.1574i	1.67833	−	0.993260i
$985$	4.55334	+	7.88662i	0.145081	+	0.251288i
$986$	2.79912	+	4.84822i	0.0891422	+	0.154399i
$987$	−55.9759	+	33.1274i	−1.78173	+	1.05446i
$988$	0.111995	−	0.193980i	0.00356303	−	0.00617134i
$989$	36.8726			1.17248
$990$	3.16631	−	5.76793i	0.100632	−	0.183317i
$991$	−39.3269			−1.24926			−0.624630	−	0.780920i	$-0.714750\pi$
$991$	−39.3269			−1.24926			−0.624630	+	0.780920i	$0.714750\pi$
$992$	15.5139	−	26.8709i	0.492568	−	0.853152i
$993$	−32.3258	−	18.2015i	−1.02583	−	0.577607i
$994$	22.9482	+	39.7475i	0.727874	+	1.26071i
$995$	−10.2712	−	17.7902i	−0.325618	−	0.563986i
$996$	0.122752	+	11.3856i	0.00388954	+	0.360768i
$997$	6.25348	−	10.8313i	0.198050	−	0.343032i	−0.749846	−	0.661612i	$-0.769873\pi$
$997$	6.25348	−	10.8313i	0.198050	−	0.343032i	0.947896	+	0.318580i	$0.103206\pi$
$998$	−13.8366			−0.437989
$999$	−1.43574	−	44.3760i	−0.0454247	−	1.40399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.196.10	✓	30
3.2	odd	2		1755.2.i.h.586.6		30
9.2	odd	6		5265.2.a.bl.1.10		15
9.4	even	3	inner	585.2.i.h.391.10	yes	30
9.5	odd	6		1755.2.i.h.1171.6		30
9.7	even	3		5265.2.a.bk.1.6		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.10	✓	30	1.1	even	1	trivial
585.2.i.h.391.10	yes	30	9.4	even	3	inner
1755.2.i.h.586.6		30	3.2	odd	2
1755.2.i.h.1171.6		30	9.5	odd	6
5265.2.a.bk.1.6		15	9.7	even	3
5265.2.a.bl.1.10		15	9.2	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.562020 - 0.973448i) q^{2} +(-0.0186726 - 1.73195i) q^{3} +(0.368266 + 0.637856i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.69646 - 0.955214i) q^{6} +(1.91433 - 3.31571i) q^{7} +3.07597 q^{8} +(-2.99930 + 0.0646801i) q^{9} +O(q^{10})\)	\(q+(0.562020 - 0.973448i) q^{2} +(-0.0186726 - 1.73195i) q^{3} +(0.368266 + 0.637856i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.69646 - 0.955214i) q^{6} +(1.91433 - 3.31571i) q^{7} +3.07597 q^{8} +(-2.99930 + 0.0646801i) q^{9} +1.12404 q^{10} +(-0.975625 + 1.68983i) q^{11} +(1.09786 - 0.649730i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.15178 - 3.72700i) q^{14} +(1.49058 - 0.882146i) q^{15} +(0.992227 - 1.71859i) q^{16} +6.58579 q^{17} +(-1.62271 + 2.95602i) q^{18} +0.304113 q^{19} +(-0.368266 + 0.637856i) q^{20} +(-5.77840 - 3.25361i) q^{21} +(1.09664 + 1.89944i) q^{22} +(-3.00958 - 5.21275i) q^{23} +(-0.0574365 - 5.32743i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.12404 q^{26} +(0.168028 + 5.19343i) q^{27} +2.81993 q^{28} +(-0.378122 + 0.654926i) q^{29} +(-0.0209888 - 1.94678i) q^{30} +(-3.95628 - 6.85248i) q^{31} +(1.96067 + 3.39598i) q^{32} +(2.94492 + 1.65818i) q^{33} +(3.70135 - 6.41093i) q^{34} +3.82866 q^{35} +(-1.14580 - 1.88930i) q^{36} -8.54464 q^{37} +(0.170918 - 0.296038i) q^{38} +(-1.49058 + 0.882146i) q^{39} +(1.53799 + 2.66387i) q^{40} +(5.74126 + 9.94416i) q^{41} +(-6.41479 + 3.79637i) q^{42} +(-3.06293 + 5.30515i) q^{43} -1.43716 q^{44} +(-1.55567 - 2.56513i) q^{45} -6.76579 q^{46} +(4.90423 - 8.49437i) q^{47} +(-2.99504 - 1.68640i) q^{48} +(-3.82930 - 6.63255i) q^{49} +(0.562020 + 0.973448i) q^{50} +(-0.122974 - 11.4063i) q^{51} +(0.368266 - 0.637856i) q^{52} +0.480958 q^{53} +(5.14997 + 2.75525i) q^{54} -1.95125 q^{55} +(5.88842 - 10.1990i) q^{56} +(-0.00567859 - 0.526709i) q^{57} +(0.425024 + 0.736164i) q^{58} +(4.91277 + 8.50916i) q^{59} +(1.11161 + 0.625909i) q^{60} +(-4.93916 + 8.55488i) q^{61} -8.89404 q^{62} +(-5.52719 + 10.0686i) q^{63} +8.37665 q^{64} +(0.500000 - 0.866025i) q^{65} +(3.26926 - 1.93480i) q^{66} +(0.805583 + 1.39531i) q^{67} +(2.42533 + 4.20079i) q^{68} +(-8.97203 + 5.30979i) q^{69} +(2.15178 - 3.72700i) q^{70} -10.6648 q^{71} +(-9.22578 + 0.198954i) q^{72} -10.2640 q^{73} +(-4.80226 + 8.31776i) q^{74} +(1.50925 + 0.849804i) q^{75} +(0.111995 + 0.193980i) q^{76} +(3.73533 + 6.46979i) q^{77} +(0.0209888 + 1.94678i) q^{78} +(3.35755 - 5.81544i) q^{79} +1.98445 q^{80} +(8.99163 - 0.387991i) q^{81} +12.9068 q^{82} +(-4.46272 + 7.72966i) q^{83} +(-0.0526555 - 4.88398i) q^{84} +(3.29290 + 5.70346i) q^{85} +(3.44286 + 5.96320i) q^{86} +(1.14136 + 0.642659i) q^{87} +(-3.00100 + 5.19788i) q^{88} +6.53502 q^{89} +(-3.37134 + 0.0727031i) q^{90} -3.82866 q^{91} +(2.21666 - 3.83936i) q^{92} +(-11.7943 + 6.98003i) q^{93} +(-5.51255 - 9.54802i) q^{94} +(0.152057 + 0.263370i) q^{95} +(5.84506 - 3.45920i) q^{96} +(0.256330 - 0.443977i) q^{97} -8.60859 q^{98} +(2.81690 - 5.13142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

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