LMFDB - Embedded newform 959.2.e.b.275.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [959,2,Mod(275,959)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(959, base_ring=CyclotomicField(6))

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("959.275");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 959 = 7 \cdot 137 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	959.e (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:	$7.65765355384$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			275.15
Character	$\chi$	$=$	959.275
Dual form			959.2.e.b.823.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.588727 + 1.01971i) q^{2} +(1.53187 + 2.65327i) q^{3} +(0.306801 + 0.531394i) q^{4} +(1.41809 - 2.45621i) q^{5} -3.60741 q^{6} +(-2.64142 - 0.151251i) q^{7} -3.07740 q^{8} +(-3.19323 + 5.53084i) q^{9} +O(q^{10})$	\(q+(-0.588727 + 1.01971i) q^{2} +(1.53187 + 2.65327i) q^{3} +(0.306801 + 0.531394i) q^{4} +(1.41809 - 2.45621i) q^{5} -3.60741 q^{6} +(-2.64142 - 0.151251i) q^{7} -3.07740 q^{8} +(-3.19323 + 5.53084i) q^{9} +(1.66974 + 2.89207i) q^{10} +(-0.242607 - 0.420207i) q^{11} +(-0.939956 + 1.62805i) q^{12} -3.60414 q^{13} +(1.70931 - 2.60443i) q^{14} +8.68932 q^{15} +(1.19815 - 2.07525i) q^{16} +(3.86529 + 6.69488i) q^{17} +(-3.75989 - 6.51232i) q^{18} +(-1.76823 + 3.06267i) q^{19} +1.74029 q^{20} +(-3.64500 - 7.24011i) q^{21} +0.571317 q^{22} +(-1.78547 + 3.09252i) q^{23} +(-4.71416 - 8.16517i) q^{24} +(-1.52197 - 2.63614i) q^{25} +(2.12185 - 3.67516i) q^{26} -10.3752 q^{27} +(-0.730017 - 1.45004i) q^{28} -6.92372 q^{29} +(-5.11564 + 8.86055i) q^{30} +(-2.67104 - 4.62637i) q^{31} +(-1.66663 - 2.88670i) q^{32} +(0.743283 - 1.28740i) q^{33} -9.10241 q^{34} +(-4.11729 + 6.27340i) q^{35} -3.91874 q^{36} +(0.501163 - 0.868041i) q^{37} +(-2.08201 - 3.60616i) q^{38} +(-5.52106 - 9.56276i) q^{39} +(-4.36403 + 7.55873i) q^{40} +2.10674 q^{41} +(9.52869 + 0.545624i) q^{42} +11.9335 q^{43} +(0.148864 - 0.257840i) q^{44} +(9.05661 + 15.6865i) q^{45} +(-2.10231 - 3.64130i) q^{46} +(-0.654942 + 1.13439i) q^{47} +7.34160 q^{48} +(6.95425 + 0.799036i) q^{49} +3.58411 q^{50} +(-11.8422 + 20.5113i) q^{51} +(-1.10575 - 1.91522i) q^{52} +(4.42485 + 7.66406i) q^{53} +(6.10819 - 10.5797i) q^{54} -1.37616 q^{55} +(8.12871 + 0.465459i) q^{56} -10.8348 q^{57} +(4.07618 - 7.06015i) q^{58} +(-4.60065 - 7.96856i) q^{59} +(2.66589 + 4.61745i) q^{60} +(-3.38907 + 5.87004i) q^{61} +6.29005 q^{62} +(9.27123 - 14.1263i) q^{63} +8.71735 q^{64} +(-5.11100 + 8.85251i) q^{65} +(0.875182 + 1.51586i) q^{66} +(0.183996 + 0.318690i) q^{67} +(-2.37175 + 4.10799i) q^{68} -10.9404 q^{69} +(-3.97306 - 7.89174i) q^{70} +11.2367 q^{71} +(9.82685 - 17.0206i) q^{72} +(2.99960 + 5.19545i) q^{73} +(0.590097 + 1.02208i) q^{74} +(4.66293 - 8.07642i) q^{75} -2.16998 q^{76} +(0.577271 + 1.14664i) q^{77} +13.0016 q^{78} +(-1.08159 + 1.87336i) q^{79} +(-3.39816 - 5.88579i) q^{80} +(-6.31379 - 10.9358i) q^{81} +(-1.24029 + 2.14825i) q^{82} +10.4557 q^{83} +(2.72907 - 4.15820i) q^{84} +21.9254 q^{85} +(-7.02558 + 12.1687i) q^{86} +(-10.6062 - 18.3705i) q^{87} +(0.746597 + 1.29314i) q^{88} +(-2.30947 + 4.00012i) q^{89} -21.3275 q^{90} +(9.52006 + 0.545129i) q^{91} -2.19113 q^{92} +(8.18335 - 14.1740i) q^{93} +(-0.771165 - 1.33570i) q^{94} +(5.01504 + 8.68630i) q^{95} +(5.10612 - 8.84407i) q^{96} -7.76811 q^{97} +(-4.90894 + 6.62087i) q^{98} +3.09880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) $ 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9	\( 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9} + 25 q^{10} + 33 q^{12} - 72 q^{13} - 38 q^{16} + 18 q^{17} + 5 q^{18} + 43 q^{19} - 20 q^{20} + 8 q^{21} + q^{23} + 20 q^{24} - 43 q^{25} + 2 q^{26} - 106 q^{27} + 7 q^{28} - 8 q^{29} + 12 q^{30} + 59 q^{31} + 11 q^{32} + 37 q^{33} - 96 q^{34} + 2 q^{35} + 28 q^{36} + 39 q^{38} - 16 q^{39} + 56 q^{40} - 30 q^{41} + 26 q^{42} - 2 q^{43} + 2 q^{44} + 28 q^{45} - 31 q^{46} + 58 q^{47} - 24 q^{48} + 15 q^{49} - 148 q^{50} + 5 q^{51} + 115 q^{52} - 10 q^{53} + 39 q^{54} - 162 q^{55} + 63 q^{56} - 36 q^{57} + 11 q^{58} + 41 q^{59} - 90 q^{60} + 40 q^{61} + 58 q^{62} + 53 q^{63} + 30 q^{64} + 9 q^{65} + 42 q^{66} + 56 q^{68} - 10 q^{69} + 84 q^{70} - 84 q^{71} + 11 q^{72} + 67 q^{73} - 39 q^{74} + 40 q^{75} - 136 q^{76} + 21 q^{77} - 156 q^{78} + 9 q^{79} + 14 q^{80} - 73 q^{81} + 34 q^{82} - 96 q^{83} + 28 q^{84} + 12 q^{85} + 13 q^{86} + 135 q^{87} - 47 q^{88} + 17 q^{89} + 88 q^{90} + 26 q^{91} - 122 q^{92} + q^{93} + 28 q^{94} - 47 q^{95} + 50 q^{96} - 162 q^{97} + 128 q^{98} - 70 q^{99}+O(q^{100}) \) 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9 + 25 * q^10 + 33 * q^12 - 72 * q^13 - 38 * q^16 + 18 * q^17 + 5 * q^18 + 43 * q^19 - 20 * q^20 + 8 * q^21 + q^23 + 20 * q^24 - 43 * q^25 + 2 * q^26 - 106 * q^27 + 7 * q^28 - 8 * q^29 + 12 * q^30 + 59 * q^31 + 11 * q^32 + 37 * q^33 - 96 * q^34 + 2 * q^35 + 28 * q^36 + 39 * q^38 - 16 * q^39 + 56 * q^40 - 30 * q^41 + 26 * q^42 - 2 * q^43 + 2 * q^44 + 28 * q^45 - 31 * q^46 + 58 * q^47 - 24 * q^48 + 15 * q^49 - 148 * q^50 + 5 * q^51 + 115 * q^52 - 10 * q^53 + 39 * q^54 - 162 * q^55 + 63 * q^56 - 36 * q^57 + 11 * q^58 + 41 * q^59 - 90 * q^60 + 40 * q^61 + 58 * q^62 + 53 * q^63 + 30 * q^64 + 9 * q^65 + 42 * q^66 + 56 * q^68 - 10 * q^69 + 84 * q^70 - 84 * q^71 + 11 * q^72 + 67 * q^73 - 39 * q^74 + 40 * q^75 - 136 * q^76 + 21 * q^77 - 156 * q^78 + 9 * q^79 + 14 * q^80 - 73 * q^81 + 34 * q^82 - 96 * q^83 + 28 * q^84 + 12 * q^85 + 13 * q^86 + 135 * q^87 - 47 * q^88 + 17 * q^89 + 88 * q^90 + 26 * q^91 - 122 * q^92 + q^93 + 28 * q^94 - 47 * q^95 + 50 * q^96 - 162 * q^97 + 128 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/959\mathbb{Z}\right)^\times$.

$n$	$414$	$549$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.588727	+	1.01971i	−0.416293	+	0.721041i	−0.995563	−	0.0940950i	$-0.970004\pi$
$2$	−0.588727	+	1.01971i	−0.416293	+	0.721041i	0.579270	+	0.815136i	$0.303338\pi$
$3$	1.53187	+	2.65327i	0.884424	+	1.53187i	0.846372	+	0.532591i	$0.178782\pi$
$3$	1.53187	+	2.65327i	0.884424	+	1.53187i	0.0380515	+	0.999276i	$0.487885\pi$
$4$	0.306801	+	0.531394i	0.153400	+	0.265697i
$5$	1.41809	−	2.45621i	0.634190	−	1.09845i	−0.352496	−	0.935813i	$-0.614667\pi$
$5$	1.41809	−	2.45621i	0.634190	−	1.09845i	0.986686	−	0.162637i	$-0.0519998\pi$
$6$	−3.60741			−1.47272
$7$	−2.64142	−	0.151251i	−0.998365	−	0.0571675i
$7$	−2.64142	−	0.151251i	−0.998365	−	0.0571675i
$8$	−3.07740			−1.08802
$9$	−3.19323	+	5.53084i	−1.06441	+	1.84361i
$10$	1.66974	+	2.89207i	0.528018	+	0.914554i
$11$	−0.242607	−	0.420207i	−0.0731487	−	0.126697i	0.827131	−	0.562009i	$-0.189971\pi$
$11$	−0.242607	−	0.420207i	−0.0731487	−	0.126697i	−0.900280	+	0.435312i	$0.856638\pi$
$12$	−0.939956	+	1.62805i	−0.271342	+	0.469978i
$13$	−3.60414			−0.999608			−0.499804	−	0.866139i	$-0.666595\pi$
$13$	−3.60414			−0.999608			−0.499804	+	0.866139i	$0.666595\pi$
$14$	1.70931	−	2.60443i	0.456832	−	0.696063i
$15$	8.68932			2.24357
$16$	1.19815	−	2.07525i	0.299536	−	0.518812i
$17$	3.86529	+	6.69488i	0.937471	+	1.62375i	0.770167	+	0.637842i	$0.220173\pi$
$17$	3.86529	+	6.69488i	0.937471	+	1.62375i	0.167304	+	0.985905i	$0.446494\pi$
$18$	−3.75989	−	6.51232i	−0.886214	−	1.53497i
$19$	−1.76823	+	3.06267i	−0.405661	+	0.702625i	−0.994398	−	0.105699i	$-0.966292\pi$
$19$	−1.76823	+	3.06267i	−0.405661	+	0.702625i	0.588737	+	0.808324i	$0.299625\pi$
$20$	1.74029			0.389140
$21$	−3.64500	−	7.24011i	−0.795405	−	1.57992i
$22$	0.571317			0.121805
$23$	−1.78547	+	3.09252i	−0.372295	+	0.644835i	−0.989918	−	0.141640i	$-0.954763\pi$
$23$	−1.78547	+	3.09252i	−0.372295	+	0.644835i	0.617623	+	0.786474i	$0.288096\pi$
$24$	−4.71416	−	8.16517i	−0.962274	−	1.66671i
$25$	−1.52197	−	2.63614i	−0.304395	−	0.527227i
$26$	2.12185	−	3.67516i	0.416130	−	0.720758i
$27$	−10.3752			−1.99672
$28$	−0.730017	−	1.45004i	−0.137960	−	0.274032i
$29$	−6.92372			−1.28570			−0.642851	−	0.765991i	$-0.722249\pi$
$29$	−6.92372			−1.28570			−0.642851	+	0.765991i	$0.722249\pi$
$30$	−5.11564	+	8.86055i	−0.933984	+	1.61771i
$31$	−2.67104	−	4.62637i	−0.479733	−	0.830921i	0.519997	−	0.854168i	$-0.325933\pi$
$31$	−2.67104	−	4.62637i	−0.479733	−	0.830921i	−0.999730	+	0.0232468i	$0.992600\pi$
$32$	−1.66663	−	2.88670i	−0.294622	−	0.510300i
$33$	0.743283	−	1.28740i	0.129389	−	0.224108i
$34$	−9.10241			−1.56105
$35$	−4.11729	+	6.27340i	−0.695949	+	1.06040i
$36$	−3.91874			−0.653124
$37$	0.501163	−	0.868041i	0.0823908	−	0.142705i	−0.821886	−	0.569653i	$-0.807078\pi$
$37$	0.501163	−	0.868041i	0.0823908	−	0.142705i	0.904276	+	0.426948i	$0.140411\pi$
$38$	−2.08201	−	3.60616i	−0.337747	−	0.584996i
$39$	−5.52106	−	9.56276i	−0.884077	−	1.53127i
$40$	−4.36403	+	7.55873i	−0.690014	+	1.19514i
$41$	2.10674			0.329017			0.164509	−	0.986376i	$-0.447396\pi$
$41$	2.10674			0.329017			0.164509	+	0.986376i	$0.447396\pi$
$42$	9.52869	+	0.545624i	1.47031	+	0.0841916i
$43$	11.9335			1.81984			0.909921	−	0.414782i	$-0.136142\pi$
$43$	11.9335			1.81984			0.909921	+	0.414782i	$0.136142\pi$
$44$	0.148864	−	0.257840i	0.0224421	−	0.0388708i
$45$	9.05661	+	15.6865i	1.35008	+	2.33841i
$46$	−2.10231	−	3.64130i	−0.309968	−	0.536880i
$47$	−0.654942	+	1.13439i	−0.0955332	+	0.165468i	−0.909831	−	0.414979i	$-0.863789\pi$
$47$	−0.654942	+	1.13439i	−0.0955332	+	0.165468i	0.814298	+	0.580447i	$0.197122\pi$
$48$	7.34160			1.05967
$49$	6.95425	+	0.799036i	0.993464	+	0.114148i
$50$	3.58411			0.506870
$51$	−11.8422	+	20.5113i	−1.65824	+	2.87216i
$52$	−1.10575	−	1.91522i	−0.153340	−	0.265593i
$53$	4.42485	+	7.66406i	0.607799	+	1.05274i	0.991602	+	0.129325i	$0.0412809\pi$
$53$	4.42485	+	7.66406i	0.607799	+	1.05274i	−0.383803	+	0.923415i	$0.625386\pi$
$54$	6.10819	−	10.5797i	0.831219	−	1.43971i
$55$	−1.37616			−0.185561
$56$	8.12871	+	0.465459i	1.08624	+	0.0621996i
$57$	−10.8348			−1.43510
$58$	4.07618	−	7.06015i	0.535229	−	0.927044i
$59$	−4.60065	−	7.96856i	−0.598954	−	1.03742i	−0.992976	−	0.118317i	$-0.962250\pi$
$59$	−4.60065	−	7.96856i	−0.598954	−	1.03742i	0.394022	−	0.919101i	$-0.371083\pi$
$60$	2.66589	+	4.61745i	0.344165	+	0.596111i
$61$	−3.38907	+	5.87004i	−0.433926	+	0.751581i	−0.997207	−	0.0746839i	$-0.976205\pi$
$61$	−3.38907	+	5.87004i	−0.433926	+	0.751581i	0.563282	+	0.826265i	$0.309539\pi$
$62$	6.29005			0.798837
$63$	9.27123	−	14.1263i	1.16807	−	1.77975i
$64$	8.71735			1.08967
$65$	−5.11100	+	8.85251i	−0.633942	+	1.09802i
$66$	0.875182	+	1.51586i	0.107727	+	0.186589i
$67$	0.183996	+	0.318690i	0.0224787	+	0.0389342i	0.877046	−	0.480407i	$-0.159511\pi$
$67$	0.183996	+	0.318690i	0.0224787	+	0.0389342i	−0.854567	+	0.519341i	$0.826178\pi$
$68$	−2.37175	+	4.10799i	−0.287617	+	0.498167i
$69$	−10.9404			−1.31707
$70$	−3.97306	−	7.89174i	−0.474872	−	0.943244i
$71$	11.2367			1.33355			0.666775	−	0.745259i	$-0.267674\pi$
$71$	11.2367			1.33355			0.666775	+	0.745259i	$0.267674\pi$
$72$	9.82685	−	17.0206i	1.15811	−	2.00590i
$73$	2.99960	+	5.19545i	0.351076	+	0.608082i	0.986438	−	0.164132i	$-0.0524825\pi$
$73$	2.99960	+	5.19545i	0.351076	+	0.608082i	−0.635362	+	0.772214i	$0.719149\pi$
$74$	0.590097	+	1.02208i	0.0685974	+	0.118814i
$75$	4.66293	−	8.07642i	0.538428	−	0.932585i
$76$	−2.16998			−0.248914
$77$	0.577271	+	1.14664i	0.0657861	+	0.130672i
$78$	13.0016			1.47214
$79$	−1.08159	+	1.87336i	−0.121688	+	0.210770i	−0.920433	−	0.390899i	$-0.872164\pi$
$79$	−1.08159	+	1.87336i	−0.121688	+	0.210770i	0.798745	+	0.601669i	$0.205497\pi$
$80$	−3.39816	−	5.88579i	−0.379926	−	0.658052i
$81$	−6.31379	−	10.9358i	−0.701532	−	1.21509i
$82$	−1.24029	+	2.14825i	−0.136967	+	0.237235i
$83$	10.4557			1.14766			0.573832	−	0.818973i	$-0.305456\pi$
$83$	10.4557			1.14766			0.573832	+	0.818973i	$0.305456\pi$
$84$	2.72907	−	4.15820i	0.297765	−	0.453697i
$85$	21.9254			2.37814
$86$	−7.02558	+	12.1687i	−0.757587	+	1.31218i
$87$	−10.6062	−	18.3705i	−1.13711	−	1.96953i
$88$	0.746597	+	1.29314i	0.0795875	+	0.137850i
$89$	−2.30947	+	4.00012i	−0.244803	+	0.424012i	−0.962076	−	0.272781i	$-0.912057\pi$
$89$	−2.30947	+	4.00012i	−0.244803	+	0.424012i	0.717273	+	0.696792i	$0.245390\pi$
$90$	−21.3275			−2.24811
$91$	9.52006	+	0.545129i	0.997973	+	0.0571451i
$92$	−2.19113			−0.228441
$93$	8.18335	−	14.1740i	0.848574	−	1.46977i
$94$	−0.771165	−	1.33570i	−0.0795396	−	0.137767i
$95$	5.01504	+	8.68630i	0.514532	+	0.891196i
$96$	5.10612	−	8.84407i	0.521142	−	0.902644i
$97$	−7.76811			−0.788732			−0.394366	−	0.918953i	$-0.629036\pi$
$97$	−7.76811			−0.788732			−0.394366	+	0.918953i	$0.629036\pi$
$98$	−4.90894	+	6.62087i	−0.495877	+	0.668809i
$99$	3.09880			0.311441
$100$	0.933885	−	1.61754i	0.0933885	−	0.161754i
$101$	−1.63523	−	2.83230i	−0.162711	−	0.281824i	0.773129	−	0.634249i	$-0.218691\pi$
$101$	−1.63523	−	2.83230i	−0.162711	−	0.281824i	−0.935840	+	0.352425i	$0.885357\pi$
$102$	−13.9437	−	24.1512i	−1.38063	−	2.39132i
$103$	6.96216	−	12.0588i	0.686002	−	1.18819i	−0.287119	−	0.957895i	$-0.592698\pi$
$103$	6.96216	−	12.0588i	0.686002	−	1.18819i	0.973121	−	0.230295i	$-0.0739691\pi$
$104$	11.0914			1.08760
$105$	−22.9522	−	1.31427i	−2.23990	−	0.128259i
$106$	−10.4201			−1.01209
$107$	−5.99158	+	10.3777i	−0.579227	+	1.00325i	0.416341	+	0.909209i	$0.363312\pi$
$107$	−5.99158	+	10.3777i	−0.579227	+	1.00325i	−0.995568	+	0.0940427i	$0.970021\pi$
$108$	−3.18313	−	5.51334i	−0.306297	−	0.530522i
$109$	3.32998	+	5.76770i	0.318955	+	0.552446i	0.980270	−	0.197662i	$-0.0633349\pi$
$109$	3.32998	+	5.76770i	0.318955	+	0.552446i	−0.661316	+	0.750108i	$0.730002\pi$
$110$	0.810180	−	1.40327i	0.0772477	−	0.133797i
$111$	3.07086			0.291473
$112$	−3.47869	+	5.30039i	−0.328706	+	0.500840i
$113$	1.07435			0.101066			0.0505331	−	0.998722i	$-0.483908\pi$
$113$	1.07435			0.101066			0.0505331	+	0.998722i	$0.483908\pi$
$114$	6.37874	−	11.0483i	0.597424	−	1.03477i
$115$	5.06391	+	8.77096i	0.472212	+	0.817896i
$116$	−2.12420	−	3.67922i	−0.197227	−	0.341607i
$117$	11.5089	−	19.9339i	1.06399	−	1.84289i
$118$	10.8341			0.997361
$119$	−9.19727	−	18.2687i	−0.843112	−	1.67468i
$120$	−26.7405			−2.44106
$121$	5.38228	−	9.32239i	0.489299	−	0.847490i
$122$	−3.99047	−	6.91170i	−0.361280	−	0.625756i
$123$	3.22724	+	5.58975i	0.290991	+	0.504010i
$124$	1.63895	−	2.83875i	0.147182	−	0.254927i
$125$	5.54772			0.496203
$126$	8.94647	+	17.7705i	0.797014	+	1.58312i
$127$	−2.12464			−0.188531			−0.0942657	−	0.995547i	$-0.530050\pi$
$127$	−2.12464			−0.188531			−0.0942657	+	0.995547i	$0.530050\pi$
$128$	−1.79887	+	3.11574i	−0.159000	+	0.275395i
$129$	18.2805	+	31.6628i	1.60951	+	2.78776i
$130$	−6.01797	−	10.4234i	−0.527811	−	0.914195i
$131$	−4.63300	+	8.02458i	−0.404787	+	0.701111i	−0.994297	−	0.106650i	$-0.965988\pi$
$131$	−4.63300	+	8.02458i	−0.404787	+	0.701111i	0.589510	+	0.807761i	$0.299321\pi$
$132$	0.912158			0.0793932
$133$	5.13389	−	7.82237i	0.445165	−	0.678285i
$134$	−0.433294			−0.0374309
$135$	−14.7131	+	25.4838i	−1.26630	+	2.19329i
$136$	−11.8950	−	20.6028i	−1.01999	−	1.76668i
$137$	0.500000	+	0.866025i	0.0427179	+	0.0739895i
$137$	0.500000	+	0.866025i	0.0427179	+	0.0739895i
$138$	6.44091	−	11.1560i	0.548286	−	0.949660i
$139$	14.9668			1.26947			0.634733	−	0.772732i	$-0.281110\pi$
$139$	14.9668			1.26947			0.634733	+	0.772732i	$0.281110\pi$
$140$	−4.59684	−	0.263220i	−0.388504	−	0.0222462i
$141$	−4.01314			−0.337967
$142$	−6.61534	+	11.4581i	−0.555147	+	0.961543i
$143$	0.874388	+	1.51448i	0.0731200	+	0.126648i
$144$	7.65192	+	13.2535i	0.637660	+	1.10446i
$145$	−9.81848	+	17.0061i	−0.815380	+	1.41228i
$146$	−7.06378			−0.584602
$147$	8.53292	+	19.6755i	0.703784	+	1.62281i
$148$	0.615029			0.0505551
$149$	−9.34346	+	16.1834i	−0.765446	+	1.32579i	0.174564	+	0.984646i	$0.444148\pi$
$149$	−9.34346	+	16.1834i	−0.765446	+	1.32579i	−0.940010	+	0.341146i	$0.889185\pi$
$150$	5.49038	+	9.50962i	0.448288	+	0.776457i
$151$	4.24339	+	7.34976i	0.345322	+	0.598115i	0.985412	−	0.170185i	$-0.0544364\pi$
$151$	4.24339	+	7.34976i	0.345322	+	0.598115i	−0.640090	+	0.768300i	$0.721103\pi$
$152$	5.44156	−	9.42505i	0.441368	−	0.764473i
$153$	−49.3711			−3.99142
$154$	−1.50909	−	0.0864122i	−0.121606	−	0.00696329i
$155$	−15.1511			−1.21697
$156$	3.38773	−	5.86772i	0.271235	−	0.469793i
$157$	6.50664	+	11.2698i	0.519287	+	0.899431i	0.999749	+	0.0224153i	$0.00713562\pi$
$157$	6.50664	+	11.2698i	0.519287	+	0.899431i	−0.480462	+	0.877015i	$0.659531\pi$
$158$	−1.27352	−	2.20580i	−0.101316	−	0.175484i
$159$	−13.5566	+	23.4806i	−1.07510	+	1.86214i
$160$	−9.45377			−0.747386
$161$	5.18392	−	7.89860i	0.408550	−	0.622497i
$162$	14.8684			1.16817
$163$	8.37496	−	14.5059i	0.655977	−	1.13619i	−0.325670	−	0.945483i	$-0.605590\pi$
$163$	8.37496	−	14.5059i	0.655977	−	1.13619i	0.981648	−	0.190703i	$-0.0610767\pi$
$164$	0.646348	+	1.11951i	0.0504713	+	0.0874189i
$165$	−2.10809	−	3.65132i	−0.164114	−	0.284255i
$166$	−6.15556	+	10.6617i	−0.477764	+	0.827512i
$167$	−16.1671			−1.25105			−0.625526	−	0.780204i	$-0.715115\pi$
$167$	−16.1671			−1.25105			−0.625526	+	0.780204i	$0.715115\pi$
$168$	11.2171	+	22.2807i	0.865419	+	1.71899i
$169$	−0.0101922			−0.000784015
$170$	−12.9081	+	22.3574i	−0.990003	+	1.71474i
$171$	−11.2928	−	19.5597i	−0.863580	−	1.49576i
$172$	3.66121	+	6.34139i	0.279164	+	0.483527i
$173$	−1.36712	+	2.36793i	−0.103940	+	0.180030i	−0.913305	−	0.407277i	$-0.866478\pi$
$173$	−1.36712	+	2.36793i	−0.103940	+	0.180030i	0.809364	+	0.587307i	$0.199812\pi$
$174$	24.9767			1.89348
$175$	3.62146	+	7.19336i	0.273757	+	0.543767i
$176$	−1.16271			−0.0876428
$177$	14.0952	−	24.4136i	1.05946	−	1.83504i
$178$	−2.71929	−	4.70996i	−0.203820	−	0.353026i
$179$	−10.8507	−	18.7940i	−0.811021	−	1.40473i	−0.912150	−	0.409856i	$-0.865579\pi$
$179$	−10.8507	−	18.7940i	−0.811021	−	1.40473i	0.101129	−	0.994873i	$-0.467754\pi$
$180$	−5.55714	+	9.62525i	−0.414205	+	0.717424i
$181$	18.7544			1.39400			0.697000	−	0.717071i	$-0.254518\pi$
$181$	18.7544			1.39400			0.697000	+	0.717071i	$0.254518\pi$
$182$	−6.16059	+	9.38672i	−0.456653	+	0.695790i
$183$	−20.7664			−1.53510
$184$	5.49459	−	9.51691i	0.405066	−	0.701596i
$185$	−1.42139	−	2.46192i	−0.104503	−	0.181004i
$186$	9.63552	+	16.6892i	0.706511	+	1.22371i
$187$	1.87549	−	3.24845i	0.137150	−	0.237550i
$188$	−0.803747			−0.0586193
$189$	27.4054	+	1.56926i	1.99345	+	0.114147i
$190$	−11.8100			−0.856785
$191$	5.98554	−	10.3673i	0.433099	−	0.750149i	−0.564040	−	0.825748i	$-0.690753\pi$
$191$	5.98554	−	10.3673i	0.433099	−	0.750149i	0.997138	+	0.0755987i	$0.0240868\pi$
$192$	13.3538	+	23.1295i	0.963730	+	1.66923i
$193$	7.67468	+	13.2929i	0.552436	+	0.956846i	0.998098	+	0.0616454i	$0.0196348\pi$
$193$	7.67468	+	13.2929i	0.552436	+	0.956846i	−0.445663	+	0.895201i	$0.647032\pi$
$194$	4.57330	−	7.92118i	0.328344	−	0.568708i
$195$	−31.3175			−2.24269
$196$	1.70896	+	3.94059i	0.122069	+	0.281471i
$197$	22.8565			1.62846			0.814228	−	0.580545i	$-0.197161\pi$
$197$	22.8565			1.62846			0.814228	+	0.580545i	$0.197161\pi$
$198$	−1.82435	+	3.15986i	−0.129651	+	0.224562i
$199$	12.4389	+	21.5448i	0.881770	+	1.52727i	0.849372	+	0.527795i	$0.176981\pi$
$199$	12.4389	+	21.5448i	0.881770	+	1.52727i	0.0323977	+	0.999475i	$0.489686\pi$
$200$	4.68372	+	8.11244i	0.331189	+	0.573636i
$201$	−0.563715	+	0.976383i	−0.0397614	+	0.0688687i
$202$	3.85081			0.270942
$203$	18.2885	+	1.04722i	1.28360	+	0.0735004i
$204$	−14.5328			−1.01750
$205$	2.98755	−	5.17459i	0.208659	−	0.361409i
$206$	8.19762	+	14.1987i	0.571155	+	0.989270i
$207$	−11.4028	−	19.7503i	−0.792551	−	1.37274i
$208$	−4.31828	+	7.47948i	−0.299419	+	0.518609i
$209$	1.71594			0.118694
$210$	14.8527	−	22.6307i	1.02494	−	1.56167i
$211$	−22.6700			−1.56067			−0.780333	−	0.625364i	$-0.784950\pi$
$211$	−22.6700			−1.56067			−0.780333	+	0.625364i	$0.784950\pi$
$212$	−2.71509	+	4.70268i	−0.186473	+	0.322981i
$213$	17.2131	+	29.8140i	1.17942	+	2.04282i
$214$	−7.05481	−	12.2193i	−0.482257	−	0.835293i
$215$	16.9228	−	29.3112i	1.15413	−	1.99901i
$216$	31.9287			2.17247
$217$	6.35560	+	12.6242i	0.431446	+	0.856987i
$218$	−7.84181			−0.531114
$219$	−9.18997	+	15.9175i	−0.621000	+	1.07560i
$220$	−0.422205	−	0.731281i	−0.0284651	−	0.0493030i
$221$	−13.9310	−	24.1293i	−0.937104	−	1.62311i
$222$	−1.80790	+	3.13138i	−0.121338	+	0.210164i
$223$	−10.0151			−0.670661			−0.335330	−	0.942101i	$-0.608848\pi$
$223$	−10.0151			−0.670661			−0.335330	+	0.942101i	$0.608848\pi$
$224$	3.96567	+	7.87707i	0.264968	+	0.526309i
$225$	19.4401			1.29601
$226$	−0.632498	+	1.09552i	−0.0420732	+	0.0728728i
$227$	−2.17931	−	3.77467i	−0.144646	−	0.250534i	0.784595	−	0.620009i	$-0.212871\pi$
$227$	−2.17931	−	3.77467i	−0.144646	−	0.250534i	−0.929241	+	0.369475i	$0.879538\pi$
$228$	−3.32412	−	5.75755i	−0.220145	−	0.381303i
$229$	13.8022	−	23.9061i	0.912075	−	1.57976i	0.100947	−	0.994892i	$-0.467813\pi$
$229$	13.8022	−	23.9061i	0.912075	−	1.57976i	0.811128	−	0.584868i	$-0.198854\pi$
$230$	−11.9251			−0.786315
$231$	−2.15805	+	3.28816i	−0.141989	+	0.216345i
$232$	21.3070			1.39888
$233$	1.43372	−	2.48328i	0.0939262	−	0.162685i	−0.815234	−	0.579132i	$-0.803392\pi$
$233$	1.43372	−	2.48328i	0.0939262	−	0.162685i	0.909160	+	0.416447i	$0.136725\pi$
$234$	13.5512	+	23.4713i	0.885867	+	1.53437i
$235$	1.85754	+	3.21735i	0.121172	+	0.209877i
$236$	2.82296	−	4.88952i	0.183759	−	0.318281i
$237$	−6.62739			−0.430495
$238$	24.0433	+	1.37675i	1.55850	+	0.0892413i
$239$	−26.1761			−1.69319			−0.846597	−	0.532235i	$-0.821352\pi$
$239$	−26.1761			−1.69319			−0.846597	+	0.532235i	$0.821352\pi$
$240$	10.4111	−	18.0325i	0.672032	−	1.16399i
$241$	10.2782	+	17.8024i	0.662079	+	1.14676i	0.980068	+	0.198661i	$0.0636592\pi$
$241$	10.2782	+	17.8024i	0.662079	+	1.14676i	−0.317989	+	0.948094i	$0.603007\pi$
$242$	6.33739	+	10.9767i	0.407383	+	0.705608i
$243$	3.78091	−	6.54872i	0.242545	−	0.420101i
$244$	−4.15907			−0.266257
$245$	11.8244	−	15.9480i	0.755431	−	1.01888i
$246$	−7.59986			−0.484549
$247$	6.37296	−	11.0383i	0.405502	−	0.702349i
$248$	8.21984	+	14.2372i	0.521961	+	0.904062i
$249$	16.0168	+	27.7419i	1.01502	+	1.75807i
$250$	−3.26610	+	5.65704i	−0.206566	+	0.357783i
$251$	2.73193			0.172438			0.0862191	−	0.996276i	$-0.472522\pi$
$251$	2.73193			0.172438			0.0862191	+	0.996276i	$0.472522\pi$
$252$	10.3511	+	0.592714i	0.652056	+	0.0373375i
$253$	1.73267			0.108932
$254$	1.25083	−	2.16651i	0.0784843	−	0.135939i
$255$	33.5868	+	58.1740i	2.10328	+	3.64300i
$256$	6.59926	+	11.4303i	0.412454	+	0.714391i
$257$	−5.84872	+	10.1303i	−0.364833	+	0.631909i	−0.988749	−	0.149582i	$-0.952207\pi$
$257$	−5.84872	+	10.1303i	−0.364833	+	0.631909i	0.623916	+	0.781491i	$0.285541\pi$
$258$	−43.0490			−2.68011
$259$	−1.45508	+	2.21706i	−0.0904141	+	0.137762i
$260$	−6.27223			−0.388987
$261$	22.1091	−	38.2940i	1.36852	−	2.37034i
$262$	−5.45514	−	9.44858i	−0.337020	−	0.583735i
$263$	−15.1965	−	26.3210i	−0.937054	−	1.62303i	−0.770930	−	0.636920i	$-0.780208\pi$
$263$	−15.1965	−	26.3210i	−0.937054	−	1.62303i	−0.166124	−	0.986105i	$-0.553125\pi$
$264$	−2.28738	+	3.96185i	−0.140778	+	0.243835i
$265$	25.0994			1.54184
$266$	4.95405	+	9.84029i	0.303752	+	0.603347i
$267$	−14.1512			−0.866039
$268$	−0.112900	+	0.195549i	−0.00689647	+	0.0119450i
$269$	−10.0107	−	17.3390i	−0.610361	−	1.05718i	−0.991179	−	0.132527i	$-0.957691\pi$
$269$	−10.0107	−	17.3390i	−0.610361	−	1.05718i	0.380818	−	0.924650i	$-0.375642\pi$
$270$	−17.3239	−	30.0060i	−1.05430	−	1.82610i
$271$	8.06861	−	13.9752i	0.490133	−	0.848936i	−0.509802	−	0.860292i	$-0.670281\pi$
$271$	8.06861	−	13.9752i	0.490133	−	0.848936i	0.999936	+	0.0113559i	$0.00361477\pi$
$272$	18.5247			1.12323
$273$	13.1371	+	26.0944i	0.795093	+	1.57930i
$274$	−1.17745			−0.0711326
$275$	−0.738483	+	1.27909i	−0.0445322	+	0.0771320i
$276$	−3.35652	−	5.81366i	−0.202039	−	0.349941i
$277$	−1.36703	−	2.36776i	−0.0821367	−	0.142265i	0.822031	−	0.569443i	$-0.192841\pi$
$277$	−1.36703	−	2.36776i	−0.0821367	−	0.142265i	−0.904168	+	0.427178i	$0.859508\pi$
$278$	−8.81135	+	15.2617i	−0.528470	+	0.915336i
$279$	34.1170			2.04253
$280$	12.6705	−	19.3057i	0.757209	−	1.15374i
$281$	−27.6584			−1.64996			−0.824980	−	0.565163i	$-0.808813\pi$
$281$	−27.6584			−1.64996			−0.824980	+	0.565163i	$0.808813\pi$
$282$	2.36264	−	4.09222i	0.140693	−	0.243688i
$283$	−3.38622	−	5.86510i	−0.201290	−	0.348644i	0.747654	−	0.664088i	$-0.231180\pi$
$283$	−3.38622	−	5.86510i	−0.201290	−	0.348644i	−0.948944	+	0.315444i	$0.897847\pi$
$284$	3.44742	+	5.97111i	0.204567	+	0.354320i
$285$	−15.3647	+	26.6125i	−0.910129	+	1.57639i
$286$	−2.05910			−0.121757
$287$	−5.56479	−	0.318646i	−0.328479	−	0.0188091i
$288$	21.2878			1.25440
$289$	−21.3810	+	37.0329i	−1.25770	+	2.17841i
$290$	−11.5608	−	20.0239i	−0.678874	−	1.17584i
$291$	−11.8997	−	20.6109i	−0.697573	−	1.20823i
$292$	−1.84056	+	3.18794i	−0.107710	+	0.186560i
$293$	−0.397955			−0.0232488			−0.0116244	−	0.999932i	$-0.503700\pi$
$293$	−0.397955			−0.0232488			−0.0116244	+	0.999932i	$0.503700\pi$
$294$	−25.0868	−	2.88245i	−1.46309	−	0.168108i
$295$	−26.0966			−1.51940
$296$	−1.54228	+	2.67130i	−0.0896431	+	0.155266i
$297$	2.51710	+	4.35975i	0.146057	+	0.252978i
$298$	−11.0015	−	19.0552i	−0.637300	−	1.10384i
$299$	6.43507	−	11.1459i	0.372150	−	0.644582i
$300$	5.72235			0.330380
$301$	−31.5214	−	1.80495i	−1.81687	−	0.104036i
$302$	−9.99279			−0.575020
$303$	5.00990	−	8.67740i	0.287811	−	0.498504i
$304$	4.23720	+	7.33905i	0.243020	+	0.420923i
$305$	9.61202	+	16.6485i	0.550383	+	0.953291i
$306$	29.0661	−	50.3440i	1.66160	−	2.87798i
$307$	9.43628			0.538557			0.269279	−	0.963062i	$-0.413215\pi$
$307$	9.43628			0.538557			0.269279	+	0.963062i	$0.413215\pi$
$308$	−0.432211	+	0.658548i	−0.0246275	+	0.0375243i
$309$	42.6604			2.42687
$310$	8.91988	−	15.4497i	0.506615	−	0.877483i
$311$	−6.04325	−	10.4672i	−0.342681	−	0.593542i	0.642248	−	0.766497i	$-0.278002\pi$
$311$	−6.04325	−	10.4672i	−0.342681	−	0.593542i	−0.984930	+	0.172955i	$0.944668\pi$
$312$	16.9905	+	29.4284i	0.961897	+	1.66605i
$313$	−2.66160	+	4.61002i	−0.150442	+	0.260574i	−0.931390	−	0.364023i	$-0.881403\pi$
$313$	−2.66160	+	4.61002i	−0.150442	+	0.260574i	0.780948	+	0.624596i	$0.214736\pi$
$314$	−15.3225			−0.864702
$315$	−21.5497	−	42.8045i	−1.21419	−	2.41176i
$316$	−1.32733			−0.0746679
$317$	−4.09296	+	7.08921i	−0.229883	+	0.398170i	−0.957773	−	0.287524i	$-0.907168\pi$
$317$	−4.09296	+	7.08921i	−0.229883	+	0.398170i	0.727890	+	0.685694i	$0.240501\pi$
$318$	−15.9622	−	27.6474i	−0.895117	−	1.55039i
$319$	1.67974	+	2.90940i	0.0940475	+	0.162895i
$320$	12.3620	−	21.4116i	0.691058	−	1.19695i
$321$	−36.7132			−2.04913
$322$	5.00233	+	9.93619i	0.278769	+	0.553722i
$323$	−27.3390			−1.52118
$324$	3.87415	−	6.71022i	0.215230	−	0.372790i
$325$	5.48541	+	9.50100i	0.304276	+	0.527021i
$326$	9.86113	+	17.0800i	0.546158	+	0.945973i
$327$	−10.2022	+	17.6707i	−0.564182	+	0.977192i
$328$	−6.48326			−0.357978
$329$	1.90156	−	2.89735i	0.104836	−	0.159736i
$330$	4.96435			0.273279
$331$	−13.4673	+	23.3260i	−0.740228	+	1.28211i	0.212164	+	0.977234i	$0.431949\pi$
$331$	−13.4673	+	23.3260i	−0.740228	+	1.28211i	−0.952391	+	0.304878i	$0.901384\pi$
$332$	3.20782	+	5.55611i	0.176052	+	0.304931i
$333$	3.20066	+	5.54371i	0.175395	+	0.303794i
$334$	9.51804	−	16.4857i	0.520804	−	0.902059i
$335$	1.04369			0.0570231
$336$	−19.3923	−	1.11042i	−1.05794	−	0.0605786i
$337$	5.85289			0.318827			0.159414	−	0.987212i	$-0.449040\pi$
$337$	5.85289			0.318827			0.159414	+	0.987212i	$0.449040\pi$
$338$	0.00600042	−	0.0103930i	0.000326380	−	0.000565306i
$339$	1.64576	+	2.85054i	0.0893854	+	0.154820i
$340$	6.72672	+	11.6510i	0.364807	+	0.631865i
$341$	−1.29602	+	2.24478i	−0.0701836	+	0.121562i
$342$	26.5934			1.43801
$343$	−18.2483	−	3.16243i	−0.985313	−	0.170755i
$344$	−36.7241			−1.98003
$345$	−15.5145	+	26.8719i	−0.835272	+	1.44673i
$346$	−1.60972	−	2.78812i	−0.0865393	−	0.149890i
$347$	14.7211	+	25.4978i	0.790272	+	1.36879i	0.925798	+	0.378018i	$0.123394\pi$
$347$	14.7211	+	25.4978i	0.790272	+	1.36879i	−0.135526	+	0.990774i	$0.543272\pi$
$348$	6.50799	−	11.2722i	0.348865	−	0.604252i
$349$	10.0948			0.540362			0.270181	−	0.962810i	$-0.412916\pi$
$349$	10.0948			0.540362			0.270181	+	0.962810i	$0.412916\pi$
$350$	−9.46716	−	0.542100i	−0.506041	−	0.0289765i
$351$	37.3938			1.99593
$352$	−0.808674	+	1.40066i	−0.0431024	+	0.0746556i
$353$	2.84472	+	4.92720i	0.151409	+	0.262248i	0.931746	−	0.363111i	$-0.118286\pi$
$353$	2.84472	+	4.92720i	0.151409	+	0.262248i	−0.780337	+	0.625360i	$0.784952\pi$
$354$	16.5964	+	28.7458i	0.882090	+	1.52782i
$355$	15.9347	−	27.5996i	0.845724	−	1.46484i
$356$	−2.83419			−0.150212
$357$	34.3827	−	52.3880i	1.81973	−	2.77267i
$358$	25.5525			1.35049
$359$	−10.2054	+	17.6763i	−0.538621	+	0.932920i	0.460357	+	0.887734i	$0.347721\pi$
$359$	−10.2054	+	17.6763i	−0.538621	+	0.932920i	−0.998979	+	0.0451859i	$0.985612\pi$
$360$	−27.8708	−	48.2736i	−1.46892	−	2.54424i
$361$	3.24670	+	5.62345i	0.170879	+	0.295971i
$362$	−11.0412	+	19.1239i	−0.580312	+	1.00513i
$363$	32.9798			1.73099
$364$	2.63108	+	5.22615i	0.137906	+	0.273925i
$365$	17.0148			0.890597
$366$	12.2257	−	21.1756i	0.639050	−	1.10687i
$367$	−9.60270	−	16.6324i	−0.501257	−	0.868202i	−0.999999	−	0.00145192i	$-0.999538\pi$
$367$	−9.60270	−	16.6324i	−0.501257	−	0.868202i	0.498742	−	0.866750i	$-0.333795\pi$
$368$	4.27850	+	7.41058i	0.223032	+	0.386303i
$369$	−6.72730	+	11.6520i	−0.350209	+	0.606581i
$370$	3.34725			0.174015
$371$	−10.5287	−	20.9133i	−0.546623	−	1.08576i
$372$	10.0426			0.520686
$373$	13.4027	−	23.2141i	0.693964	−	1.20198i	−0.276565	−	0.960995i	$-0.589196\pi$
$373$	13.4027	−	23.2141i	0.693964	−	1.20198i	0.970529	−	0.240985i	$-0.0774705\pi$
$374$	2.20831	+	3.82490i	0.114189	+	0.197781i
$375$	8.49838	+	14.7196i	0.438854	+	0.760118i
$376$	2.01552	−	3.49098i	0.103942	−	0.180033i
$377$	24.9540			1.28520
$378$	−17.7345	+	27.0216i	−0.912164	+	1.38984i
$379$	6.63406			0.340769			0.170384	−	0.985378i	$-0.445499\pi$
$379$	6.63406			0.340769			0.170384	+	0.985378i	$0.445499\pi$
$380$	−3.07723	+	5.32993i	−0.157859	+	0.273419i
$381$	−3.25467	−	5.63725i	−0.166742	−	0.288805i
$382$	7.04770	+	12.2070i	0.360592	+	0.624564i
$383$	14.7450	−	25.5391i	0.753435	−	1.30499i	−0.192714	−	0.981255i	$-0.561729\pi$
$383$	14.7450	−	25.5391i	0.753435	−	1.30499i	0.946149	−	0.323732i	$-0.104938\pi$
$384$	−11.0225			−0.562492
$385$	3.63501	+	0.208145i	0.185257	+	0.0106080i
$386$	−18.0732			−0.919900
$387$	−38.1065	+	66.0023i	−1.93706	+	3.35509i
$388$	−2.38326	−	4.12793i	−0.120992	−	0.209564i
$389$	8.68349	+	15.0402i	0.440270	+	0.762570i	0.997709	−	0.0676475i	$-0.0215493\pi$
$389$	8.68349	+	15.0402i	0.440270	+	0.762570i	−0.557439	+	0.830218i	$0.688216\pi$
$390$	18.4375	−	31.9346i	0.933617	−	1.61707i
$391$	−27.6054			−1.39607
$392$	−21.4010	−	2.45895i	−1.08091	−	0.124196i
$393$	−28.3885			−1.43201
$394$	−13.4562	+	23.3069i	−0.677915	+	1.17418i
$395$	3.06758	+	5.31321i	0.154347	+	0.267337i
$396$	0.950714	+	1.64668i	0.0477752	+	0.0827490i
$397$	3.19957	−	5.54182i	0.160582	−	0.278136i	−0.774496	−	0.632579i	$-0.781996\pi$
$397$	3.19957	−	5.54182i	0.160582	−	0.278136i	0.935078	+	0.354443i	$0.115330\pi$
$398$	−29.2925			−1.46830
$399$	28.6193	+	1.63877i	1.43276	+	0.0820413i
$400$	−7.29419			−0.364709
$401$	−1.29530	+	2.24353i	−0.0646844	+	0.112037i	−0.896554	−	0.442935i	$-0.853937\pi$
$401$	−1.29530	+	2.24353i	−0.0646844	+	0.112037i	0.831870	+	0.554971i	$0.187271\pi$
$402$	−0.663748	−	1.14965i	−0.0331048	−	0.0573391i
$403$	9.62679	+	16.6741i	0.479544	+	0.830595i
$404$	1.00338	−	1.73790i	0.0499199	−	0.0864638i
$405$	−35.8141			−1.77962
$406$	−11.8348	+	18.0323i	−0.587350	+	0.894930i
$407$	−0.486343			−0.0241071
$408$	36.4432	−	63.1215i	1.80421	−	3.12498i
$409$	−14.2708	−	24.7177i	−0.705643	−	1.22221i	−0.966459	−	0.256821i	$-0.917325\pi$
$409$	−14.2708	−	24.7177i	−0.705643	−	1.22221i	0.260816	−	0.965389i	$-0.416009\pi$
$410$	3.51770	+	6.09284i	0.173727	+	0.300904i
$411$	−1.53187	+	2.65327i	−0.0755614	+	0.130876i
$412$	8.54398			0.420931
$413$	10.9470	+	21.7442i	0.538668	+	1.06996i
$414$	26.8526			1.31973
$415$	14.8272	−	25.6814i	0.727837	−	1.26065i
$416$	6.00678	+	10.4040i	0.294507	+	0.510100i
$417$	22.9271	+	39.7109i	1.12275	+	1.94465i
$418$	−1.01022	+	1.74976i	−0.0494116	+	0.0855833i
$419$	−7.96923			−0.389322			−0.194661	−	0.980871i	$-0.562361\pi$
$419$	−7.96923			−0.389322			−0.194661	+	0.980871i	$0.562361\pi$
$420$	−6.34335	−	12.5999i	−0.309524	−	0.614811i
$421$	−26.5671			−1.29480			−0.647400	−	0.762151i	$-0.724144\pi$
$421$	−26.5671			−1.29480			−0.647400	+	0.762151i	$0.724144\pi$
$422$	13.3464	−	23.1167i	0.649694	−	1.12530i
$423$	−4.18277	−	7.24477i	−0.203373	−	0.352253i
$424$	−13.6170	−	23.5853i	−0.661300	−	1.14541i
$425$	11.7658	−	20.3789i	0.570723	−	0.988521i
$426$	−40.5353			−1.96394
$427$	9.83981	−	14.9927i	0.476182	−	0.725545i
$428$	−7.35287			−0.355415
$429$	−2.67889	+	4.63998i	−0.129338	+	0.224020i
$430$	19.9258	+	34.5126i	0.960909	+	1.66434i
$431$	−13.4205	−	23.2449i	−0.646441	−	1.11967i	−0.983967	−	0.178353i	$-0.942923\pi$
$431$	−13.4205	−	23.2449i	−0.646441	−	1.11967i	0.337525	−	0.941316i	$-0.390410\pi$
$432$	−12.4310	+	21.5312i	−0.598089	+	1.03592i
$433$	25.3421			1.21786			0.608931	−	0.793223i	$-0.291599\pi$
$433$	25.3421			1.21786			0.608931	+	0.793223i	$0.291599\pi$
$434$	−16.6147	−	0.951376i	−0.797531	−	0.0456675i
$435$	−60.1624			−2.88457
$436$	−2.04328	+	3.53907i	−0.0978555	+	0.169491i
$437$	−6.31424	−	10.9366i	−0.302051	−	0.523168i
$438$	−10.8208	−	18.7421i	−0.517036	−	0.895533i
$439$	1.42261	−	2.46404i	0.0678975	−	0.117602i	−0.830078	−	0.557647i	$-0.811704\pi$
$439$	1.42261	−	2.46404i	0.0678975	−	0.117602i	0.897976	+	0.440045i	$0.145038\pi$
$440$	4.23498			0.201895
$441$	−26.6259	+	35.9113i	−1.26790	+	1.71006i
$442$	32.8063			1.56044
$443$	3.99005	−	6.91098i	0.189573	−	0.328350i	−0.755535	−	0.655109i	$-0.772623\pi$
$443$	3.99005	−	6.91098i	0.189573	−	0.328350i	0.945108	+	0.326758i	$0.105956\pi$
$444$	0.942143	+	1.63184i	0.0447121	+	0.0774437i
$445$	6.55008	+	11.3451i	0.310504	+	0.537808i
$446$	5.89616	−	10.2125i	0.279191	−	0.483574i
$447$	−57.2518			−2.70792
$448$	−23.0262	−	1.31851i	−1.08789	−	0.0622936i
$449$	−1.08341			−0.0511294			−0.0255647	−	0.999673i	$-0.508138\pi$
$449$	−1.08341			−0.0511294			−0.0255647	+	0.999673i	$0.508138\pi$
$450$	−11.4449	+	19.8232i	−0.539518	+	0.934473i
$451$	−0.511109	−	0.885266i	−0.0240672	−	0.0416856i
$452$	0.329611	+	0.570903i	0.0155036	+	0.0268530i
$453$	−13.0006	+	22.5177i	−0.610822	+	1.05797i
$454$	5.13207			0.240860
$455$	14.8393	−	22.6102i	0.695676	−	1.05998i
$456$	33.3430			1.56143
$457$	6.26761	−	10.8558i	0.293187	−	0.507814i	−0.681375	−	0.731935i	$-0.738618\pi$
$457$	6.26761	−	10.8558i	0.293187	−	0.507814i	0.974561	+	0.224121i	$0.0719510\pi$
$458$	16.2515	+	28.1484i	0.759381	+	1.31529i
$459$	−40.1033	−	69.4610i	−1.87186	−	3.24216i
$460$	−3.10722	+	5.38187i	−0.144875	+	0.250931i
$461$	5.89923			0.274755			0.137377	−	0.990519i	$-0.456133\pi$
$461$	5.89923			0.274755			0.137377	+	0.990519i	$0.456133\pi$
$462$	−2.08245	−	4.13640i	−0.0968844	−	0.192443i
$463$	4.17449			0.194005			0.0970026	−	0.995284i	$-0.469074\pi$
$463$	4.17449			0.194005			0.0970026	+	0.995284i	$0.469074\pi$
$464$	−8.29563	+	14.3684i	−0.385115	+	0.667038i
$465$	−23.2095	−	40.2000i	−1.07631	−	1.86423i
$466$	1.68814	+	2.92395i	0.0782017	+	0.135449i
$467$	−20.1090	+	34.8298i	−0.930533	+	1.61173i	−0.148122	+	0.988969i	$0.547323\pi$
$467$	−20.1090	+	34.8298i	−0.930533	+	1.61173i	−0.782412	+	0.622762i	$0.786011\pi$
$468$	14.1237			0.652868
$469$	−0.437809	−	0.869626i	−0.0202161	−	0.0401556i
$470$	−4.37433			−0.201773
$471$	−19.9346	+	34.5278i	−0.918539	+	1.59096i
$472$	14.1580	+	24.5224i	0.651676	+	1.12874i
$473$	−2.89515	−	5.01454i	−0.133119	−	0.230569i
$474$	3.90173	−	6.75799i	0.179212	−	0.310405i
$475$	10.7648			0.493924
$476$	6.88613	−	10.4922i	0.315625	−	0.480910i
$477$	−56.5183			−2.58779
$478$	15.4106	−	26.6919i	0.704864	−	1.22086i
$479$	−0.210876	−	0.365248i	−0.00963518	−	0.0166886i	0.861168	−	0.508321i	$-0.169734\pi$
$479$	−0.210876	−	0.365248i	−0.00963518	−	0.0166886i	−0.870803	+	0.491632i	$0.836400\pi$
$480$	−14.4819	−	25.0834i	−0.661006	−	1.14490i
$481$	−1.80626	+	3.12854i	−0.0823585	+	0.142649i
$482$	−24.2043			−1.10248
$483$	28.8982	+	1.65474i	1.31491	+	0.0752935i
$484$	6.60515			0.300234
$485$	−11.0159	+	19.0801i	−0.500206	+	0.866383i
$486$	4.45185	+	7.71082i	0.201940	+	0.349770i
$487$	8.91682	+	15.4444i	0.404060	+	0.699852i	0.994212	−	0.107440i	$-0.0342655\pi$
$487$	8.91682	+	15.4444i	0.404060	+	0.699852i	−0.590152	+	0.807292i	$0.700932\pi$
$488$	10.4295	−	18.0644i	0.472121	−	0.817738i
$489$	51.3173			2.32065
$490$	9.30091	+	21.4464i	0.420172	+	0.968849i
$491$	−29.4561			−1.32933			−0.664667	−	0.747140i	$-0.731427\pi$
$491$	−29.4561			−1.32933			−0.664667	+	0.747140i	$0.731427\pi$
$492$	−1.98024	+	3.42987i	−0.0892761	+	0.154631i
$493$	−26.7622	−	46.3535i	−1.20531	−	2.08766i
$494$	7.50387	+	12.9971i	0.337615	+	0.584766i
$495$	4.39439	−	7.61130i	0.197513	−	0.342103i
$496$	−12.8012			−0.574790
$497$	−29.6809	−	1.69956i	−1.33137	−	0.0762357i
$498$	−37.7180			−1.69019
$499$	−0.266242	+	0.461144i	−0.0119186	+	0.0206437i	−0.871923	−	0.489643i	$-0.837127\pi$
$499$	−0.266242	+	0.461144i	−0.0119186	+	0.0206437i	0.860005	+	0.510286i	$0.170461\pi$
$500$	1.70204	+	2.94803i	0.0761178	+	0.131840i
$501$	−24.7659	−	42.8958i	−1.10646	−	1.91644i
$502$	−1.60836	+	2.78577i	−0.0717848	+	0.124335i
$503$	15.4728			0.689897			0.344948	−	0.938622i	$-0.387896\pi$
$503$	15.4728			0.689897			0.344948	+	0.938622i	$0.387896\pi$
$504$	−28.5313	+	43.4723i	−1.27088	+	1.93641i
$505$	−9.27561			−0.412759
$506$	−1.02007	+	1.76681i	−0.0453475	+	0.0785442i
$507$	−0.0156131	−	0.0270427i	−0.000693401	−	0.00120101i
$508$	−0.651841	−	1.12902i	−0.0289208	−	0.0500922i
$509$	−10.2966	+	17.8343i	−0.456390	+	0.790491i	−0.998767	−	0.0496442i	$-0.984191\pi$
$509$	−10.2966	+	17.8343i	−0.456390	+	0.790491i	0.542377	+	0.840135i	$0.317525\pi$
$510$	−79.0938			−3.50233
$511$	−7.13739	−	14.1771i	−0.315740	−	0.627158i
$512$	−22.7362			−1.00481
$513$	18.3459	−	31.7759i	0.809989	−	1.40294i
$514$	−6.88660	−	11.9279i	−0.303755	−	0.526119i
$515$	−19.7460	−	34.2010i	−0.870111	−	1.50708i
$516$	−11.2170	+	19.4283i	−0.493799	+	0.855285i
$517$	0.635574			0.0279525
$518$	−1.40411	−	2.78900i	−0.0616929	−	0.122541i
$519$	−8.37700			−0.367709
$520$	15.7286	−	27.2427i	0.689744	−	1.19467i
$521$	12.9130	+	22.3660i	0.565730	+	0.979873i	0.996981	+	0.0776412i	$0.0247389\pi$
$521$	12.9130	+	22.3660i	0.565730	+	0.979873i	−0.431251	+	0.902232i	$0.641928\pi$
$522$	26.0324	+	45.0895i	1.13941	+	1.97351i
$523$	10.8016	−	18.7089i	0.472320	−	0.818083i	−0.527178	−	0.849755i	$-0.676750\pi$
$523$	10.8016	−	18.7089i	0.472320	−	0.818083i	0.999498	+	0.0316722i	$0.0100833\pi$
$524$	−5.68562			−0.248378
$525$	−13.5383	+	20.6280i	−0.590861	+	0.900279i
$526$	35.7863			1.56036
$527$	20.6487	−	35.7646i	0.899471	−	1.55793i
$528$	−1.78112	−	3.08499i	−0.0775134	−	0.134257i
$529$	5.12422	+	8.87541i	0.222792	+	0.385887i
$530$	−14.7767	+	25.5940i	−0.641858	+	1.11173i
$531$	58.7638			2.55013
$532$	5.73184	+	0.328212i	0.248507	+	0.0142298i
$533$	−7.59297			−0.328888
$534$	8.33120	−	14.4301i	0.360526	−	0.624450i
$535$	16.9932	+	29.4331i	0.734681	+	1.27250i
$536$	−0.566228	−	0.980736i	−0.0244573	−	0.0423614i
$537$	33.2437	−	57.5798i	1.43457	−	2.48475i
$538$	23.5742			1.01636
$539$	−1.35139	−	3.11608i	−0.0582083	−	0.134219i
$540$	−18.0559			−0.777002
$541$	5.55932	−	9.62903i	0.239014	−	0.413984i	−0.721418	−	0.692500i	$-0.756509\pi$
$541$	5.55932	−	9.62903i	0.239014	−	0.413984i	0.960432	+	0.278516i	$0.0898425\pi$
$542$	9.50042	+	16.4552i	0.408078	+	0.706812i
$543$	28.7292	+	49.7604i	1.23289	+	2.13542i
$544$	12.8841	−	22.3158i	0.552399	−	0.956784i
$545$	18.8889			0.809112
$546$	−34.3427	−	1.96650i	−1.46973	−	0.0841586i
$547$	9.85090			0.421194			0.210597	−	0.977573i	$-0.432459\pi$
$547$	9.85090			0.421194			0.210597	+	0.977573i	$0.432459\pi$
$548$	−0.306801	+	0.531394i	−0.0131059	+	0.0227000i
$549$	−21.6442	−	37.4888i	−0.923751	−	1.59998i
$550$	−0.869530	−	1.50607i	−0.0370769	−	0.0642190i
$551$	12.2428	−	21.2051i	0.521559	−	0.903367i
$552$	33.6679			1.43300
$553$	3.14028	−	4.78476i	0.133538	−	0.203469i
$554$	3.21923			0.136772
$555$	4.35477	−	7.54268i	0.184850	−	0.320169i
$556$	4.59182	+	7.95326i	0.194736	+	0.337293i
$557$	19.1426	+	33.1559i	0.811097	+	1.40486i	0.912097	+	0.409975i	$0.134463\pi$
$557$	19.1426	+	33.1559i	0.811097	+	1.40486i	−0.100999	+	0.994887i	$0.532204\pi$
$558$	−20.0856	+	34.7893i	−0.850292	+	1.47275i
$559$	−43.0100			−1.81913
$560$	8.08576	+	16.0608i	0.341686	+	0.678695i
$561$	11.4920			0.485193
$562$	16.2832	−	28.2034i	0.686866	−	1.18969i
$563$	12.9471	+	22.4250i	0.545654	+	0.945101i	0.998565	+	0.0535453i	$0.0170522\pi$
$563$	12.9471	+	22.4250i	0.545654	+	0.945101i	−0.452911	+	0.891556i	$0.649615\pi$
$564$	−1.23123	−	2.13256i	−0.0518443	−	0.0897969i
$565$	1.52353	−	2.63882i	0.0640952	−	0.111016i
$566$	7.97424			0.335182
$567$	15.0233	+	29.8411i	0.630921	+	1.25321i
$568$	−34.5797			−1.45093
$569$	−14.9801	+	25.9463i	−0.627999	+	1.08773i	0.359954	+	0.932970i	$0.382792\pi$
$569$	−14.9801	+	25.9463i	−0.627999	+	1.08773i	−0.987953	+	0.154756i	$0.950541\pi$
$570$	−18.0913	−	31.3350i	−0.757761	−	1.31248i
$571$	−15.3665	−	26.6156i	−0.643069	−	1.11383i	−0.984744	−	0.174010i	$-0.944327\pi$
$571$	−15.3665	−	26.6156i	−0.643069	−	1.11383i	0.341674	−	0.939818i	$-0.389006\pi$
$572$	−0.536526	+	0.929290i	−0.0224333	+	0.0388556i
$573$	36.6762			1.53217
$574$	3.60107	−	5.48685i	0.150306	−	0.229017i
$575$	10.8697			0.453299
$576$	−27.8366	+	48.2143i	−1.15986	+	2.00893i
$577$	−11.4718	−	19.8697i	−0.477577	−	0.827188i	0.522092	−	0.852889i	$-0.325152\pi$
$577$	−11.4718	−	19.8697i	−0.477577	−	0.827188i	−0.999670	+	0.0257008i	$0.991818\pi$
$578$	−25.1751	−	43.6046i	−1.04715	−	1.81371i
$579$	−23.5132	+	40.7260i	−0.977174	+	1.69252i
$580$	−12.0493			−0.500318
$581$	−27.6180	−	1.58144i	−1.14579	−	0.0656090i
$582$	28.0227			1.16158
$583$	2.14700	−	3.71871i	0.0889195	−	0.154013i
$584$	−9.23095	−	15.9885i	−0.381979	−	0.661608i
$585$	−32.6413	−	56.5363i	−1.34955	−	2.33749i
$586$	0.234287	−	0.405797i	0.00967830	−	0.0167633i
$587$	37.8267			1.56127			0.780636	−	0.624985i	$-0.214895\pi$
$587$	37.8267			1.56127			0.780636	+	0.624985i	$0.214895\pi$
$588$	−7.83755	+	10.5708i	−0.323215	+	0.435933i
$589$	18.8921			0.778435
$590$	15.3638	−	26.6108i	0.632517	−	1.09555i
$591$	35.0131	+	60.6444i	1.44025	+	2.49458i
$592$	−1.20093	−	2.08008i	−0.0493581	−	0.0854907i
$593$	9.47197	−	16.4059i	0.388967	−	0.673711i	−0.603344	−	0.797481i	$-0.706165\pi$
$593$	9.47197	−	16.4059i	0.388967	−	0.673711i	0.992311	+	0.123770i	$0.0394986\pi$
$594$	−5.92755			−0.243210
$595$	−57.9142	−	3.31623i	−2.37425	−	0.135952i
$596$	−11.4663			−0.469679
$597$	−38.1095	+	66.0075i	−1.55972	+	2.70151i
$598$	7.57700	+	13.1237i	0.309846	+	0.536670i
$599$	2.71458	+	4.70180i	0.110915	+	0.192110i	0.916139	−	0.400860i	$-0.131289\pi$
$599$	2.71458	+	4.70180i	0.110915	+	0.192110i	−0.805225	+	0.592970i	$0.797955\pi$
$600$	−14.3497	+	24.8544i	−0.585823	+	1.01467i
$601$	24.9297			1.01690			0.508452	−	0.861090i	$-0.330218\pi$
$601$	24.9297			1.01690			0.508452	+	0.861090i	$0.330218\pi$
$602$	20.3981	−	31.0800i	0.831362	−	1.26672i
$603$	−2.35017			−0.0957063
$604$	−2.60375	+	4.50982i	−0.105945	+	0.183502i
$605$	−15.2652	−	26.4400i	−0.620617	−	1.07494i
$606$	5.89893	+	10.2172i	0.239628	+	0.415047i
$607$	18.6341	−	32.2752i	0.756334	−	1.31001i	−0.188374	−	0.982097i	$-0.560322\pi$
$607$	18.6341	−	32.2752i	0.756334	−	1.31001i	0.944708	−	0.327912i	$-0.106345\pi$
$608$	11.7880			0.478066
$609$	25.2370	+	50.1285i	1.02265	+	2.03131i
$610$	−22.6354			−0.916482
$611$	2.36050	−	4.08851i	0.0954957	−	0.165403i
$612$	−15.1471	−	26.2355i	−0.612285	−	1.06051i
$613$	−9.77403	−	16.9291i	−0.394769	−	0.683761i	0.598302	−	0.801270i	$-0.295842\pi$
$613$	−9.77403	−	16.9291i	−0.394769	−	0.683761i	−0.993072	+	0.117510i	$0.962509\pi$
$614$	−5.55540	+	9.62223i	−0.224198	+	0.388322i
$615$	18.3061			0.738174
$616$	−1.77649	−	3.52867i	−0.0715769	−	0.142174i
$617$	6.28443			0.253002			0.126501	−	0.991967i	$-0.459625\pi$
$617$	6.28443			0.253002			0.126501	+	0.991967i	$0.459625\pi$
$618$	−25.1153	+	43.5010i	−1.01029	+	1.74987i
$619$	−14.0726	−	24.3744i	−0.565624	−	0.979689i	−0.996991	−	0.0775131i	$-0.975302\pi$
$619$	−14.0726	−	24.3744i	−0.565624	−	0.979689i	0.431367	−	0.902176i	$-0.358031\pi$
$620$	−4.64837	−	8.05122i	−0.186683	−	0.323345i
$621$	18.5246	−	32.0856i	0.743368	−	1.28755i
$622$	14.2313			0.570624
$623$	6.70531	−	10.2167i	0.268643	−	0.409323i
$624$	−26.4601			−1.05925
$625$	15.4771	−	26.8071i	0.619082	−	1.07228i
$626$	−3.13391	−	5.42809i	−0.125256	−	0.216950i
$627$	2.62860	+	4.55286i	0.104976	+	0.181824i
$628$	−3.99248	+	6.91518i	−0.159317	+	0.275946i
$629$	7.74857			0.308956
$630$	56.3349	+	3.22580i	2.24444	+	0.128519i
$631$	−15.9599			−0.635352			−0.317676	−	0.948199i	$-0.602902\pi$
$631$	−15.9599			−0.635352			−0.317676	+	0.948199i	$0.602902\pi$
$632$	3.32847	−	5.76508i	0.132400	−	0.229323i
$633$	−34.7274	−	60.1496i	−1.38029	−	2.39073i
$634$	−4.81927	−	8.34722i	−0.191398	−	0.331510i
$635$	−3.01294	+	5.21856i	−0.119565	+	0.207092i
$636$	−16.6366			−0.659686
$637$	−25.0641	−	2.87984i	−0.993074	−	0.114103i
$638$	−3.95564			−0.156605
$639$	−35.8814	+	62.1484i	−1.41945	+	2.45855i
$640$	5.10194	+	8.83682i	0.201672	+	0.349306i
$641$	−5.24253	−	9.08033i	−0.207067	−	0.358651i	0.743722	−	0.668489i	$-0.233059\pi$
$641$	−5.24253	−	9.08033i	−0.207067	−	0.358651i	−0.950789	+	0.309838i	$0.899725\pi$
$642$	21.6141	−	37.4366i	0.853039	−	1.47751i
$643$	18.7581			0.739746			0.369873	−	0.929082i	$-0.379401\pi$
$643$	18.7581			0.739746			0.369873	+	0.929082i	$0.379401\pi$
$644$	5.78770	+	0.331410i	0.228067	+	0.0130594i
$645$	103.694			4.08295
$646$	16.0952	−	27.8777i	0.633257	−	1.09683i
$647$	0.196059	+	0.339585i	0.00770789	+	0.0133505i	0.869854	−	0.493310i	$-0.164213\pi$
$647$	0.196059	+	0.339585i	0.00770789	+	0.0133505i	−0.862146	+	0.506660i	$0.830880\pi$
$648$	19.4300	+	33.6538i	0.763283	+	1.32205i
$649$	−2.23230	+	3.86645i	−0.0876254	+	0.151772i
$650$	−12.9176			−0.506671
$651$	−23.7595	+	36.2018i	−0.931209	+	1.41886i
$652$	10.2778			0.402508
$653$	3.43834	−	5.95539i	0.134553	−	0.233052i	−0.790874	−	0.611979i	$-0.790374\pi$
$653$	3.43834	−	5.95539i	0.134553	−	0.233052i	0.925427	+	0.378927i	$0.123707\pi$
$654$	−12.0126	−	20.8065i	−0.469730	−	0.813597i
$655$	13.1400	+	22.7592i	0.513424	+	0.889276i
$656$	2.52418	−	4.37200i	0.0985526	−	0.170698i
$657$	−38.3137			−1.49476
$658$	1.83495	+	3.64478i	0.0715337	+	0.142088i
$659$	17.6160			0.686223			0.343111	−	0.939295i	$-0.388519\pi$
$659$	17.6160			0.686223			0.343111	+	0.939295i	$0.388519\pi$
$660$	1.29353	−	2.24045i	0.0503504	−	0.0872095i
$661$	3.29186	+	5.70166i	0.128038	+	0.221769i	0.922917	−	0.385000i	$-0.125799\pi$
$661$	3.29186	+	5.70166i	0.128038	+	0.221769i	−0.794878	+	0.606769i	$0.792465\pi$
$662$	−15.8571	−	27.4653i	−0.616303	−	1.06747i
$663$	42.6810	−	73.9257i	1.65759	−	2.87104i
$664$	−32.1764			−1.24869
$665$	−11.9330	−	23.7027i	−0.462743	−	0.919153i
$666$	−7.53727			−0.292063
$667$	12.3621	−	21.4117i	0.478661	−	0.829066i
$668$	−4.96009	−	8.59113i	−0.191912	−	0.332401i
$669$	−15.3418	−	26.5728i	−0.593148	−	1.02736i
$670$	−0.614451	+	1.06426i	−0.0237383	+	0.0411159i
$671$	3.28884			0.126964
$672$	−14.8251	+	22.5886i	−0.571891	+	0.871375i
$673$	−8.51552			−0.328249			−0.164125	−	0.986440i	$-0.552480\pi$
$673$	−8.51552			−0.328249			−0.164125	+	0.986440i	$0.552480\pi$
$674$	−3.44576	+	5.96823i	−0.132726	+	0.229888i
$675$	15.7909	+	27.3506i	0.607790	+	1.05272i
$676$	−0.00312697	−	0.00541607i	−0.000120268	−	0.000208310i
$677$	4.19382	−	7.26391i	0.161182	−	0.279175i	−0.774111	−	0.633050i	$-0.781803\pi$
$677$	4.19382	−	7.26391i	0.161182	−	0.279175i	0.935293	+	0.353875i	$0.115136\pi$
$678$	−3.87561			−0.148842
$679$	20.5189	+	1.17493i	0.787442	+	0.0450898i
$680$	−67.4731			−2.58747
$681$	6.67682	−	11.5646i	0.255856	−	0.443156i
$682$	−1.52601	−	2.64313i	−0.0584339	−	0.101210i
$683$	−16.9826	−	29.4148i	−0.649822	−	1.12552i	−0.983165	−	0.182719i	$-0.941510\pi$
$683$	−16.9826	−	29.4148i	−0.649822	−	1.12552i	0.333343	−	0.942806i	$-0.391823\pi$
$684$	6.92926	−	12.0018i	0.264947	−	0.458901i
$685$	2.83619			0.108365
$686$	13.9680	−	16.7460i	0.533300	−	0.639367i
$687$	84.5725			3.22664
$688$	14.2981	−	24.7650i	0.545109	−	0.944156i
$689$	−15.9478	−	27.6223i	−0.607561	−	1.05233i
$690$	−18.2676	−	31.6404i	−0.695436	−	1.20453i
$691$	11.7116	−	20.2851i	0.445531	−	0.771683i	−0.552558	−	0.833475i	$-0.686348\pi$
$691$	11.7116	−	20.2851i	0.445531	−	0.771683i	0.998089	+	0.0617917i	$0.0196815\pi$
$692$	−1.67774			−0.0637779
$693$	−8.18525	−	0.468697i	−0.310932	−	0.0178043i
$694$	−34.6670			−1.31594
$695$	21.2243	−	36.7615i	0.805083	−	1.39444i
$696$	32.6395	+	56.5333i	1.23720	+	2.14289i
$697$	8.14315	+	14.1044i	0.308444	+	0.534241i
$698$	−5.94308	+	10.2937i	−0.224949	+	0.389623i
$699$	8.78509			0.332282
$700$	−2.71144	+	4.13135i	−0.102483	+	0.156150i
$701$	−11.2818			−0.426107			−0.213053	−	0.977041i	$-0.568341\pi$
$701$	−11.2818			−0.426107			−0.213053	+	0.977041i	$0.568341\pi$
$702$	−22.0147	+	38.1307i	−0.830893	+	1.43915i
$703$	1.77235	+	3.06980i	0.0668454	+	0.115780i
$704$	−2.11489	−	3.66310i	−0.0797079	−	0.138058i
$705$	−5.69100	+	9.85711i	−0.214336	+	0.371240i
$706$	−6.69906			−0.252122
$707$	3.89094	+	7.72863i	0.146334	+	0.290665i
$708$	17.2976			0.650085
$709$	−19.4140	+	33.6260i	−0.729107	+	1.26285i	0.228154	+	0.973625i	$0.426731\pi$
$709$	−19.4140	+	33.6260i	−0.729107	+	1.26285i	−0.957261	+	0.289225i	$0.906602\pi$
$710$	18.7623	+	32.4973i	0.704138	+	1.21960i
$711$	−6.90752	−	11.9642i	−0.259052	−	0.448692i
$712$	7.10715	−	12.3099i	0.266352	−	0.461335i
$713$	19.0762			0.714409
$714$	33.1783	+	65.9025i	1.24167	+	2.46634i
$715$	4.95985			0.185488
$716$	6.65802	−	11.5320i	0.248822	−	0.430972i
$717$	−40.0984	−	69.4524i	−1.49750	−	2.59375i
$718$	−12.0164	−	20.8130i	−0.448449	−	0.776736i
$719$	−7.67328	+	13.2905i	−0.286165	+	0.495653i	−0.972891	−	0.231264i	$-0.925714\pi$
$719$	−7.67328	+	13.2905i	−0.286165	+	0.495653i	0.686726	+	0.726916i	$0.259047\pi$
$720$	43.4045			1.61759
$721$	−20.2139	+	30.7994i	−0.752806	+	1.14703i
$722$	−7.64568			−0.284543
$723$	−31.4898	+	54.5419i	−1.17112	+	2.02844i
$724$	5.75385	+	9.96595i	0.213840	+	0.370382i
$725$	10.5377	+	18.2519i	0.391361	+	0.677858i
$726$	−19.4161	+	33.6297i	−0.720599	+	1.24811i
$727$	42.7963			1.58723			0.793613	−	0.608423i	$-0.208197\pi$
$727$	42.7963			1.58723			0.793613	+	0.608423i	$0.208197\pi$
$728$	−29.2970	−	1.67758i	−1.08582	−	0.0621752i
$729$	−14.7153			−0.545012
$730$	−10.0171	+	17.3501i	−0.370749	+	0.642156i
$731$	46.1265	+	79.8934i	1.70605	+	2.95496i
$732$	−6.37114	−	11.0351i	−0.235484	−	0.407871i
$733$	−7.37931	+	12.7813i	−0.272561	+	0.472090i	−0.969517	−	0.245024i	$-0.921204\pi$
$733$	−7.37931	+	12.7813i	−0.272561	+	0.472090i	0.696956	+	0.717114i	$0.254537\pi$
$734$	22.6135			0.834679
$735$	60.4277	+	6.94308i	2.22891	+	0.256099i
$736$	11.9029			0.438746
$737$	0.0892773	−	0.154633i	0.00328857	−	0.00569598i
$738$	−7.92109	−	13.7197i	−0.291580	−	0.505031i
$739$	−12.8578	−	22.2704i	−0.472983	−	0.819231i	0.526539	−	0.850151i	$-0.323489\pi$
$739$	−12.8578	−	22.2704i	−0.472983	−	0.819231i	−0.999522	+	0.0309205i	$0.990156\pi$
$740$	0.872168	−	1.51064i	0.0320615	−	0.0555322i
$741$	39.0501			1.43454
$742$	27.5239	+	1.57605i	1.01044	+	0.0578587i
$743$	49.9690			1.83318			0.916592	−	0.399825i	$-0.130929\pi$
$743$	49.9690			1.83318			0.916592	+	0.399825i	$0.130929\pi$
$744$	−25.1834	+	43.6190i	−0.923269	+	1.59915i
$745$	26.4998	+	45.8990i	0.970878	+	1.68161i
$746$	15.7810	+	27.3335i	0.577784	+	1.00075i
$747$	−33.3875	+	57.8289i	−1.22159	+	2.11585i
$748$	2.30161			0.0841551
$749$	17.3959	−	26.5057i	0.635634	−	0.968498i
$750$	−20.0129			−0.730768
$751$	17.2195	−	29.8251i	0.628349	−	1.08833i	−0.359535	−	0.933132i	$-0.617065\pi$
$751$	17.2195	−	29.8251i	0.628349	−	1.08833i	0.987883	−	0.155200i	$-0.0496021\pi$
$752$	1.56943	+	2.71834i	0.0572313	+	0.0991276i
$753$	4.18496	+	7.24856i	0.152508	+	0.264152i
$754$	−14.6911	+	25.4458i	−0.535019	+	0.926680i
$755$	24.0701			0.875999
$756$	7.57410	+	15.0445i	0.275467	+	0.547164i
$757$	−17.7011			−0.643359			−0.321679	−	0.946849i	$-0.604247\pi$
$757$	−17.7011			−0.643359			−0.321679	+	0.946849i	$0.604247\pi$
$758$	−3.90565	+	6.76479i	−0.141860	+	0.245708i
$759$	2.65421	+	4.59723i	0.0963418	+	0.166869i
$760$	−15.4333	−	26.7312i	−0.559823	−	0.969642i
$761$	1.59080	−	2.75534i	0.0576664	−	0.0998811i	−0.835751	−	0.549109i	$-0.814967\pi$
$761$	1.59080	−	2.75534i	0.0576664	−	0.0998811i	0.893417	+	0.449227i	$0.148301\pi$
$762$	7.66445			0.277654
$763$	−7.92353	−	15.7386i	−0.286851	−	0.569776i
$764$	7.34547			0.265750
$765$	−70.0129	+	121.266i	−2.53132	+	4.38438i
$766$	17.3616	+	30.0711i	0.627299	+	1.08651i
$767$	16.5814	+	28.7198i	0.598719	+	1.03701i
$768$	−20.2184	+	35.0193i	−0.729568	+	1.26365i
$769$	6.40234			0.230874			0.115437	−	0.993315i	$-0.463173\pi$
$769$	6.40234			0.230874			0.115437	+	0.993315i	$0.463173\pi$
$770$	−2.35228	+	3.58410i	−0.0847702	+	0.129162i
$771$	−35.8378			−1.29067
$772$	−4.70919	+	8.15656i	−0.169488	+	0.293561i
$773$	12.6655	+	21.9373i	0.455547	+	0.789031i	0.998719	−	0.0505903i	$-0.0161103\pi$
$773$	12.6655	+	21.9373i	0.455547	+	0.789031i	−0.543172	+	0.839621i	$0.682777\pi$
$774$	−44.8686	−	77.7147i	−1.61277	−	2.79340i
$775$	−8.13050	+	14.0824i	−0.292056	+	0.505856i
$776$	23.9055			0.858159
$777$	−8.11145	−	0.464471i	−0.290997	−	0.0166628i
$778$	−20.4488			−0.733126
$779$	−3.72520	+	6.45224i	−0.133469	+	0.231176i
$780$	−9.60823	−	16.6419i	−0.344030	−	0.595877i
$781$	−2.72610	−	4.72174i	−0.0975474	−	0.168957i
$782$	16.2520	−	28.1494i	0.581172	−	1.00662i
$783$	71.8353			2.56718
$784$	9.99040	−	13.4744i	0.356800	−	0.481230i
$785$	36.9081			1.31731
$786$	16.7131	−	28.9479i	0.596137	−	1.03254i
$787$	7.57166	+	13.1145i	0.269901	+	0.467482i	0.968836	−	0.247703i	$-0.0796758\pi$
$787$	7.57166	+	13.1145i	0.269901	+	0.467482i	−0.698935	+	0.715185i	$0.746342\pi$
$788$	7.01238	+	12.1458i	0.249806	+	0.432676i
$789$	46.5579	−	80.6407i	1.65751	−	2.87088i
$790$	−7.22388			−0.257014
$791$	−2.83781	−	0.162496i	−0.100901	−	0.00577770i
$792$	−9.53624			−0.338855
$793$	12.2147	−	21.1564i	0.433755	−	0.751286i
$794$	3.76735	+	6.52524i	0.133698	+	0.231572i
$795$	38.4489	+	66.5955i	1.36364	+	2.36190i
$796$	−7.63252	+	13.2199i	−0.270527	+	0.468567i
$797$	16.0618			0.568938			0.284469	−	0.958685i	$-0.408183\pi$
$797$	16.0618			0.568938			0.284469	+	0.958685i	$0.408183\pi$
$798$	−18.5200	+	28.2185i	−0.655602	+	0.998923i
$799$	−10.1262			−0.358238
$800$	−5.07315	+	8.78695i	−0.179363	+	0.310666i
$801$	−14.7494	−	25.5466i	−0.521143	−	0.902646i
$802$	−1.52516	−	2.64166i	−0.0538553	−	0.0932802i
$803$	1.45545	−	2.52090i	0.0513615	−	0.0889608i
$804$	−0.691792			−0.0243976
$805$	−12.0493	−	23.9337i	−0.424683	−	0.843554i
$806$	−22.6702			−0.798524
$807$	30.6700	−	53.1221i	1.07964	−	1.86999i
$808$	5.03224	+	8.71610i	0.177034	+	0.306631i
$809$	−15.0278	−	26.0288i	−0.528348	−	0.915125i	−0.999454	−	0.0330484i	$-0.989478\pi$
$809$	−15.0278	−	26.0288i	−0.528348	−	0.915125i	0.471106	−	0.882077i	$-0.343855\pi$
$810$	21.0848	−	36.5199i	0.740843	−	1.28318i
$811$	6.48625			0.227763			0.113882	−	0.993494i	$-0.463672\pi$
$811$	6.48625			0.227763			0.113882	+	0.993494i	$0.463672\pi$
$812$	5.05443	+	10.0397i	0.177376	+	0.352324i
$813$	49.4402			1.73394
$814$	0.286323	−	0.495926i	0.0100356	−	0.0173822i
$815$	−23.7529	−	41.1413i	−0.832029	−	1.44112i
$816$	28.3774	+	49.1512i	0.993409	+	1.72063i
$817$	−21.1012	+	36.5484i	−0.738238	+	1.27867i
$818$	33.6063			1.17502
$819$	−33.4148	+	50.9132i	−1.16761	+	1.77905i
$820$	3.66633			0.128034
$821$	20.7610	−	35.9591i	0.724564	−	1.25498i	−0.234590	−	0.972094i	$-0.575375\pi$
$821$	20.7610	−	35.9591i	0.724564	−	1.25498i	0.959153	−	0.282886i	$-0.0912920\pi$
$822$	−1.80370	−	3.12411i	−0.0629114	−	0.108966i
$823$	28.3517	+	49.1066i	0.988278	+	1.71175i	0.626351	+	0.779541i	$0.284548\pi$
$823$	28.3517	+	49.1066i	0.988278	+	1.71175i	0.361927	+	0.932206i	$0.382119\pi$
$824$	−21.4253	+	37.1097i	−0.746386	+	1.29278i
$825$	−4.52503			−0.157541
$826$	−28.6175	−	1.63867i	−0.995730	−	0.0570166i
$827$	−38.3263			−1.33274			−0.666368	−	0.745623i	$-0.732152\pi$
$827$	−38.3263			−1.33274			−0.666368	+	0.745623i	$0.732152\pi$
$828$	6.99679	−	12.1188i	0.243155	−	0.421157i
$829$	7.03101	+	12.1781i	0.244197	+	0.422962i	0.961906	−	0.273382i	$-0.0881423\pi$
$829$	7.03101	+	12.1781i	0.244197	+	0.422962i	−0.717709	+	0.696344i	$0.754809\pi$
$830$	17.4583	+	30.2387i	0.605987	+	1.04960i
$831$	4.18821	−	7.25419i	0.145287	−	0.251645i
$832$	−31.4185			−1.08924
$833$	21.5307	+	49.6464i	0.745996	+	1.72014i
$834$	−53.9913			−1.86956
$835$	−22.9265	+	39.7099i	−0.793405	+	1.37422i
$836$	0.526452	+	0.911842i	0.0182077	+	0.0315367i
$837$	27.7127	+	47.9997i	0.957890	+	1.65911i
$838$	4.69170	−	8.12626i	0.162072	−	0.280717i
$839$	16.6332			0.574243			0.287122	−	0.957894i	$-0.407302\pi$
$839$	16.6332			0.574243			0.287122	+	0.957894i	$0.407302\pi$
$840$	70.6330	+	4.04452i	2.43707	+	0.139549i
$841$	18.9379			0.653031
$842$	15.6408	−	27.0906i	0.539016	−	0.933603i
$843$	−42.3689	−	73.3851i	−1.45926	−	2.52752i
$844$	−6.95516	−	12.0467i	−0.239407	−	0.414664i
$845$	−0.0144535	+	0.0250342i	−0.000497215	+	0.000861201i
$846$	9.85004			0.338651
$847$	−15.6269	+	23.8103i	−0.536947	+	0.818132i
$848$	21.2064			0.728232
$849$	10.3745	−	17.9691i	0.356051	−	0.616699i
$850$	13.8536	+	23.9952i	0.475176	+	0.823029i
$851$	1.78962	+	3.09971i	0.0613474	+	0.106257i
$852$	−10.5620	+	18.2939i	−0.361848	+	0.626739i
$853$	−5.86698			−0.200882			−0.100441	−	0.994943i	$-0.532025\pi$
$853$	−5.86698			−0.200882			−0.100441	+	0.994943i	$0.532025\pi$
$854$	9.49513	+	18.8603i	0.324917	+	0.645386i
$855$	−64.0568			−2.19070
$856$	18.4384	−	31.9363i	0.630213	−	1.09156i
$857$	−4.52709	−	7.84116i	−0.154643	−	0.267849i	0.778286	−	0.627910i	$-0.216089\pi$
$857$	−4.52709	−	7.84116i	−0.154643	−	0.267849i	−0.932929	+	0.360061i	$0.882756\pi$
$858$	−3.15427	−	5.46336i	−0.107685	−	0.186516i
$859$	−0.196897	+	0.341035i	−0.00671802	+	0.0116360i	−0.869365	−	0.494171i	$-0.835472\pi$
$859$	−0.196897	+	0.341035i	−0.00671802	+	0.0116360i	0.862647	+	0.505807i	$0.168805\pi$
$860$	20.7677			0.708173
$861$	−7.67906	−	15.2530i	−0.261702	−	0.519821i
$862$	31.6040			1.07644
$863$	−21.8631	+	37.8679i	−0.744227	+	1.28904i	0.206328	+	0.978483i	$0.433849\pi$
$863$	−21.8631	+	37.8679i	−0.744227	+	1.28904i	−0.950555	+	0.310556i	$0.899485\pi$
$864$	17.2917	+	29.9502i	0.588277	+	1.01893i
$865$	3.87741	+	6.71588i	0.131836	+	0.228347i
$866$	−14.9196	+	25.8414i	−0.506987	+	0.878128i
$867$	−131.011			−4.44937
$868$	−4.75853	+	7.25045i	−0.161515	+	0.246096i
$869$	1.04960			0.0356053
$870$	35.4193	−	61.3479i	1.20083	−	2.07989i
$871$	−0.663147	−	1.14860i	−0.0224699	−	0.0389190i
$872$	−10.2477	−	17.7495i	−0.347030	−	0.601074i
$873$	24.8054	−	42.9642i	0.839535	−	1.45412i
$874$	14.8695			0.502967
$875$	−14.6539	−	0.839098i	−0.495392	−	0.0283667i
$876$	−11.2780			−0.381047
$877$	−2.19021	+	3.79355i	−0.0739581	+	0.128099i	−0.900633	−	0.434581i	$-0.856896\pi$
$877$	−2.19021	+	3.79355i	−0.0739581	+	0.128099i	0.826675	+	0.562680i	$0.190230\pi$
$878$	1.67506	+	2.90129i	0.0565305	+	0.0979138i
$879$	−0.609614	−	1.05588i	−0.0205618	−	0.0356140i
$880$	−1.64884	+	2.85587i	−0.0555822	+	0.0962712i
$881$	−20.5199			−0.691332			−0.345666	−	0.938358i	$-0.612347\pi$
$881$	−20.5199			−0.691332			−0.345666	+	0.938358i	$0.612347\pi$
$882$	−20.9436	−	48.2925i	−0.705208	−	1.62609i
$883$	−29.2367			−0.983894			−0.491947	−	0.870625i	$-0.663715\pi$
$883$	−29.2367			−0.983894			−0.491947	+	0.870625i	$0.663715\pi$
$884$	8.54811	−	14.8058i	0.287504	−	0.497971i
$885$	−39.9765	−	69.2414i	−1.34380	−	2.32752i
$886$	4.69811	+	8.13736i	0.157836	+	0.273380i
$887$	7.26435	−	12.5822i	0.243913	−	0.422470i	−0.717912	−	0.696134i	$-0.754902\pi$
$887$	7.26435	−	12.5822i	0.243913	−	0.422470i	0.961825	+	0.273664i	$0.0882355\pi$
$888$	−9.45026			−0.317130
$889$	5.61208	+	0.321354i	0.188223	+	0.0107779i
$890$	−15.4248			−0.517042
$891$	−3.06354	+	5.30620i	−0.102632	+	0.177764i
$892$	−3.07264	−	5.32197i	−0.102880	−	0.178193i
$893$	−2.31618	−	4.01175i	−0.0775081	−	0.134248i
$894$	33.7057	−	58.3800i	1.12729	−	1.95252i
$895$	−61.5493			−2.05737
$896$	5.22285	−	7.95792i	0.174483	−	0.265855i
$897$	39.4307			1.31655
$898$	0.637835	−	1.10476i	0.0212848	−	0.0368664i
$899$	18.4935	+	32.0317i	0.616793	+	1.06832i
$900$	5.96423	+	10.3303i	0.198808	+	0.344345i
$901$	−34.2067	+	59.2477i	−1.13959	+	1.97383i
$902$	1.20361			0.0400760
$903$	−43.4976	−	86.3999i	−1.44751	−	2.87521i
$904$	−3.30620			−0.109962
$905$	26.5954	−	46.0646i	0.884061	−	1.53124i
$906$	−15.3076	−	26.5136i	−0.508562	−	0.880855i
$907$	−6.05058	−	10.4799i	−0.200906	−	0.347980i	0.747914	−	0.663795i	$-0.231055\pi$
$907$	−6.05058	−	10.4799i	−0.200906	−	0.347980i	−0.948821	+	0.315815i	$0.897722\pi$
$908$	1.33723	−	2.31614i	0.0443774	−	0.0768639i
$909$	20.8867			0.692766
$910$	14.3195	+	28.4429i	0.474686	+	0.942874i
$911$	48.0518			1.59203			0.796013	−	0.605279i	$-0.206939\pi$
$911$	48.0518			1.59203			0.796013	+	0.605279i	$0.206939\pi$
$912$	−12.9817	+	22.4849i	−0.429866	+	0.744550i
$913$	−2.53663	−	4.39357i	−0.0839501	−	0.145406i
$914$	7.37983	+	12.7822i	0.244103	+	0.422799i
$915$	−29.4487	+	51.0066i	−0.973543	+	1.68623i
$916$	16.9381			0.559650
$917$	13.4514	−	20.4956i	0.444206	−	0.676824i
$918$	94.4397			3.11697
$919$	−11.9077	+	20.6248i	−0.392799	+	0.680349i	−0.992818	−	0.119638i	$-0.961827\pi$
$919$	−11.9077	+	20.6248i	−0.392799	+	0.680349i	0.600018	+	0.799986i	$0.295160\pi$
$920$	−15.5837	−	26.9917i	−0.513778	−	0.889890i
$921$	14.4551	+	25.0370i	0.476313	+	0.824998i
$922$	−3.47304	+	6.01548i	−0.114378	+	0.198109i
$923$	−40.4986			−1.33303
$924$	−2.40940	−	0.137965i	−0.0792634	−	0.00453871i
$925$	−3.05103			−0.100317
$926$	−2.45764	+	4.25675i	−0.0807630	+	0.139886i
$927$	44.4636	+	77.0132i	1.46038	+	2.52945i
$928$	11.5393	+	19.9867i	0.378796	+	0.656095i
$929$	18.5878	−	32.1950i	0.609846	−	1.05628i	−0.381420	−	0.924402i	$-0.624565\pi$
$929$	18.5878	−	32.1950i	0.609846	−	1.05628i	0.991265	−	0.131882i	$-0.0421019\pi$
$930$	54.6563			1.79225
$931$	−14.7439	+	19.8857i	−0.483212	+	0.651727i
$932$	1.75947			0.0576333
$933$	18.5149	−	32.0688i	0.606151	−	1.04989i
$934$	−23.6774	−	41.0105i	−0.774749	−	1.34190i
$935$	−5.31924	−	9.21320i	−0.173958	−	0.301304i
$936$	−35.4173	+	61.3446i	−1.15765	+	2.00511i
$937$	52.2777			1.70784			0.853920	−	0.520405i	$-0.174219\pi$
$937$	52.2777			1.70784			0.853920	+	0.520405i	$0.174219\pi$
$938$	1.14451	+	0.0655361i	0.0373697	+	0.00213983i
$939$	−16.3088			−0.532219
$940$	−1.13979	+	1.97417i	−0.0371758	+	0.0643903i
$941$	−9.82570	−	17.0186i	−0.320309	−	0.554791i	0.660243	−	0.751052i	$-0.270453\pi$
$941$	−9.82570	−	17.0186i	−0.320309	−	0.554791i	−0.980552	+	0.196261i	$0.937120\pi$
$942$	−23.4721	−	40.6549i	−0.764763	−	1.32461i
$943$	−3.76151	+	6.51512i	−0.122492	+	0.212162i
$944$	−22.0490			−0.717634
$945$	42.7179	−	65.0881i	1.38961	−	2.11731i
$946$	6.81781			0.221666
$947$	−26.0922	+	45.1929i	−0.847881	+	1.46857i	0.0352143	+	0.999380i	$0.488789\pi$
$947$	−26.0922	+	45.1929i	−0.847881	+	1.46857i	−0.883095	+	0.469193i	$0.844545\pi$
$948$	−2.03329	−	3.52176i	−0.0660381	−	0.114381i
$949$	−10.8110	−	18.7251i	−0.350939	−	0.607843i
$950$	−6.33755	+	10.9770i	−0.205617	+	0.356139i
$951$	−25.0795			−0.813257
$952$	28.3036	+	56.2199i	0.917326	+	1.82210i
$953$	−11.4631			−0.371325			−0.185663	−	0.982614i	$-0.559443\pi$
$953$	−11.4631			−0.371325			−0.185663	+	0.982614i	$0.559443\pi$
$954$	33.2739	−	57.6320i	1.07728	−	1.86591i
$955$	−16.9761	−	29.4035i	−0.549334	−	0.951475i
$956$	−8.03085	−	13.9098i	−0.259736	−	0.449877i
$957$	−5.14628	+	8.91362i	−0.166356	+	0.288136i
$958$	0.496594			0.0160442
$959$	−1.18973	−	2.36317i	−0.0384182	−	0.0763106i
$960$	75.7479			2.44475
$961$	1.23111	−	2.13235i	0.0397133	−	0.0687854i
$962$	−2.12679	−	3.68371i	−0.0685705	−	0.118768i
$963$	−38.2650	−	66.2769i	−1.23307	−	2.13574i
$964$	−6.30674	+	10.9236i	−0.203126	+	0.351825i
$965$	43.5336			1.40140
$966$	−18.7005	+	28.4935i	−0.601679	+	0.916762i
$967$	−28.6772			−0.922198			−0.461099	−	0.887349i	$-0.652545\pi$
$967$	−28.6772			−0.922198			−0.461099	+	0.887349i	$0.652545\pi$
$968$	−16.5634	+	28.6887i	−0.532368	+	0.922089i
$969$	−41.8797	−	72.5377i	−1.34537	−	2.33025i
$970$	−12.9707	−	22.4659i	−0.416465	−	0.721338i
$971$	4.04865	−	7.01246i	0.129927	−	0.225041i	−0.793721	−	0.608282i	$-0.791859\pi$
$971$	4.04865	−	7.01246i	0.129927	−	0.225041i	0.923648	+	0.383241i	$0.125192\pi$
$972$	4.63994			0.148826
$973$	−39.5336	−	2.26374i	−1.26739	−	0.0725721i
$974$	−20.9983			−0.672829
$975$	−16.8058	+	29.1085i	−0.538217	+	0.932220i
$976$	8.12119	+	14.0663i	0.259953	+	0.450252i
$977$	20.4077	+	35.3471i	0.652899	+	1.13085i	0.982416	+	0.186705i	$0.0597807\pi$
$977$	20.4077	+	35.3471i	0.652899	+	1.13085i	−0.329517	+	0.944150i	$0.606886\pi$
$978$	−30.2119	+	52.3285i	−0.966070	+	1.67328i
$979$	2.24117			0.0716282
$980$	12.1024	+	1.39055i	0.386596	+	0.0444195i
$981$	−42.5337			−1.35800
$982$	17.3416	−	30.0365i	0.553393	−	0.958504i
$983$	23.1191	+	40.0434i	0.737384	+	1.27719i	0.953669	+	0.300856i	$0.0972725\pi$
$983$	23.1191	+	40.0434i	0.737384	+	1.27719i	−0.216285	+	0.976330i	$0.569394\pi$
$984$	−9.93150	−	17.2019i	−0.316605	−	0.548375i
$985$	32.4126	−	56.1403i	1.03275	−	1.78878i
$986$	63.0225			2.00705
$987$	10.6004	+	0.606991i	0.337415	+	0.0193207i
$988$	7.82091			0.248816
$989$	−21.3069	+	36.9046i	−0.677519	+	1.17350i
$990$	5.17419	+	8.96196i	0.164447	+	0.284830i
$991$	−19.6861	−	34.0973i	−0.625348	−	1.08313i	−0.988473	−	0.151395i	$-0.951624\pi$
$991$	−19.6861	−	34.0973i	−0.625348	−	1.08313i	0.363125	−	0.931740i	$-0.381710\pi$
$992$	−8.90329	+	15.4209i	−0.282680	+	0.489616i
$993$	−82.5202			−2.61870
$994$	19.2070	−	29.2652i	0.609208	−	0.928234i
$995$	70.5580			2.23684
$996$	−9.82791	+	17.0224i	−0.311409	+	0.539376i
$997$	9.30020	+	16.1084i	0.294540	+	0.510159i	0.974878	−	0.222740i	$-0.0715001\pi$
$997$	9.30020	+	16.1084i	0.294540	+	0.510159i	−0.680338	+	0.732899i	$0.738167\pi$
$998$	−0.313488	−	0.542977i	−0.00992328	−	0.0171876i
$999$	−5.19969	+	9.00613i	−0.164511	+	0.284941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.2.e.b.275.15	✓	90
7.2	even	3		6713.2.a.k.1.31		45
7.4	even	3	inner	959.2.e.b.823.15	yes	90
7.5	odd	6		6713.2.a.l.1.31		45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.2.e.b.275.15	✓	90	1.1	even	1	trivial
959.2.e.b.823.15	yes	90	7.4	even	3	inner
6713.2.a.k.1.31		45	7.2	even	3
6713.2.a.l.1.31		45	7.5	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:	\( N \)	\(=\)	\( 959 = 7 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	959.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.588727 + 1.01971i) q^{2} +(1.53187 + 2.65327i) q^{3} +(0.306801 + 0.531394i) q^{4} +(1.41809 - 2.45621i) q^{5} -3.60741 q^{6} +(-2.64142 - 0.151251i) q^{7} -3.07740 q^{8} +(-3.19323 + 5.53084i) q^{9} +O(q^{10})\)	\(q+(-0.588727 + 1.01971i) q^{2} +(1.53187 + 2.65327i) q^{3} +(0.306801 + 0.531394i) q^{4} +(1.41809 - 2.45621i) q^{5} -3.60741 q^{6} +(-2.64142 - 0.151251i) q^{7} -3.07740 q^{8} +(-3.19323 + 5.53084i) q^{9} +(1.66974 + 2.89207i) q^{10} +(-0.242607 - 0.420207i) q^{11} +(-0.939956 + 1.62805i) q^{12} -3.60414 q^{13} +(1.70931 - 2.60443i) q^{14} +8.68932 q^{15} +(1.19815 - 2.07525i) q^{16} +(3.86529 + 6.69488i) q^{17} +(-3.75989 - 6.51232i) q^{18} +(-1.76823 + 3.06267i) q^{19} +1.74029 q^{20} +(-3.64500 - 7.24011i) q^{21} +0.571317 q^{22} +(-1.78547 + 3.09252i) q^{23} +(-4.71416 - 8.16517i) q^{24} +(-1.52197 - 2.63614i) q^{25} +(2.12185 - 3.67516i) q^{26} -10.3752 q^{27} +(-0.730017 - 1.45004i) q^{28} -6.92372 q^{29} +(-5.11564 + 8.86055i) q^{30} +(-2.67104 - 4.62637i) q^{31} +(-1.66663 - 2.88670i) q^{32} +(0.743283 - 1.28740i) q^{33} -9.10241 q^{34} +(-4.11729 + 6.27340i) q^{35} -3.91874 q^{36} +(0.501163 - 0.868041i) q^{37} +(-2.08201 - 3.60616i) q^{38} +(-5.52106 - 9.56276i) q^{39} +(-4.36403 + 7.55873i) q^{40} +2.10674 q^{41} +(9.52869 + 0.545624i) q^{42} +11.9335 q^{43} +(0.148864 - 0.257840i) q^{44} +(9.05661 + 15.6865i) q^{45} +(-2.10231 - 3.64130i) q^{46} +(-0.654942 + 1.13439i) q^{47} +7.34160 q^{48} +(6.95425 + 0.799036i) q^{49} +3.58411 q^{50} +(-11.8422 + 20.5113i) q^{51} +(-1.10575 - 1.91522i) q^{52} +(4.42485 + 7.66406i) q^{53} +(6.10819 - 10.5797i) q^{54} -1.37616 q^{55} +(8.12871 + 0.465459i) q^{56} -10.8348 q^{57} +(4.07618 - 7.06015i) q^{58} +(-4.60065 - 7.96856i) q^{59} +(2.66589 + 4.61745i) q^{60} +(-3.38907 + 5.87004i) q^{61} +6.29005 q^{62} +(9.27123 - 14.1263i) q^{63} +8.71735 q^{64} +(-5.11100 + 8.85251i) q^{65} +(0.875182 + 1.51586i) q^{66} +(0.183996 + 0.318690i) q^{67} +(-2.37175 + 4.10799i) q^{68} -10.9404 q^{69} +(-3.97306 - 7.89174i) q^{70} +11.2367 q^{71} +(9.82685 - 17.0206i) q^{72} +(2.99960 + 5.19545i) q^{73} +(0.590097 + 1.02208i) q^{74} +(4.66293 - 8.07642i) q^{75} -2.16998 q^{76} +(0.577271 + 1.14664i) q^{77} +13.0016 q^{78} +(-1.08159 + 1.87336i) q^{79} +(-3.39816 - 5.88579i) q^{80} +(-6.31379 - 10.9358i) q^{81} +(-1.24029 + 2.14825i) q^{82} +10.4557 q^{83} +(2.72907 - 4.15820i) q^{84} +21.9254 q^{85} +(-7.02558 + 12.1687i) q^{86} +(-10.6062 - 18.3705i) q^{87} +(0.746597 + 1.29314i) q^{88} +(-2.30947 + 4.00012i) q^{89} -21.3275 q^{90} +(9.52006 + 0.545129i) q^{91} -2.19113 q^{92} +(8.18335 - 14.1740i) q^{93} +(-0.771165 - 1.33570i) q^{94} +(5.01504 + 8.68630i) q^{95} +(5.10612 - 8.84407i) q^{96} -7.76811 q^{97} +(-4.90894 + 6.62087i) q^{98} +3.09880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) \) 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9	\( 90 q + 11 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} - q^{7} - 6 q^{8} - 44 q^{9} + 25 q^{10} + 33 q^{12} - 72 q^{13} - 38 q^{16} + 18 q^{17} + 5 q^{18} + 43 q^{19} - 20 q^{20} + 8 q^{21} + q^{23} + 20 q^{24} - 43 q^{25} + 2 q^{26} - 106 q^{27} + 7 q^{28} - 8 q^{29} + 12 q^{30} + 59 q^{31} + 11 q^{32} + 37 q^{33} - 96 q^{34} + 2 q^{35} + 28 q^{36} + 39 q^{38} - 16 q^{39} + 56 q^{40} - 30 q^{41} + 26 q^{42} - 2 q^{43} + 2 q^{44} + 28 q^{45} - 31 q^{46} + 58 q^{47} - 24 q^{48} + 15 q^{49} - 148 q^{50} + 5 q^{51} + 115 q^{52} - 10 q^{53} + 39 q^{54} - 162 q^{55} + 63 q^{56} - 36 q^{57} + 11 q^{58} + 41 q^{59} - 90 q^{60} + 40 q^{61} + 58 q^{62} + 53 q^{63} + 30 q^{64} + 9 q^{65} + 42 q^{66} + 56 q^{68} - 10 q^{69} + 84 q^{70} - 84 q^{71} + 11 q^{72} + 67 q^{73} - 39 q^{74} + 40 q^{75} - 136 q^{76} + 21 q^{77} - 156 q^{78} + 9 q^{79} + 14 q^{80} - 73 q^{81} + 34 q^{82} - 96 q^{83} + 28 q^{84} + 12 q^{85} + 13 q^{86} + 135 q^{87} - 47 q^{88} + 17 q^{89} + 88 q^{90} + 26 q^{91} - 122 q^{92} + q^{93} + 28 q^{94} - 47 q^{95} + 50 q^{96} - 162 q^{97} + 128 q^{98} - 70 q^{99}+O(q^{100}) \) 90 * q + 11 * q^3 - 44 * q^4 + 4 * q^5 - 20 * q^6 - q^7 - 6 * q^8 - 44 * q^9 + 25 * q^10 + 33 * q^12 - 72 * q^13 - 38 * q^16 + 18 * q^17 + 5 * q^18 + 43 * q^19 - 20 * q^20 + 8 * q^21 + q^23 + 20 * q^24 - 43 * q^25 + 2 * q^26 - 106 * q^27 + 7 * q^28 - 8 * q^29 + 12 * q^30 + 59 * q^31 + 11 * q^32 + 37 * q^33 - 96 * q^34 + 2 * q^35 + 28 * q^36 + 39 * q^38 - 16 * q^39 + 56 * q^40 - 30 * q^41 + 26 * q^42 - 2 * q^43 + 2 * q^44 + 28 * q^45 - 31 * q^46 + 58 * q^47 - 24 * q^48 + 15 * q^49 - 148 * q^50 + 5 * q^51 + 115 * q^52 - 10 * q^53 + 39 * q^54 - 162 * q^55 + 63 * q^56 - 36 * q^57 + 11 * q^58 + 41 * q^59 - 90 * q^60 + 40 * q^61 + 58 * q^62 + 53 * q^63 + 30 * q^64 + 9 * q^65 + 42 * q^66 + 56 * q^68 - 10 * q^69 + 84 * q^70 - 84 * q^71 + 11 * q^72 + 67 * q^73 - 39 * q^74 + 40 * q^75 - 136 * q^76 + 21 * q^77 - 156 * q^78 + 9 * q^79 + 14 * q^80 - 73 * q^81 + 34 * q^82 - 96 * q^83 + 28 * q^84 + 12 * q^85 + 13 * q^86 + 135 * q^87 - 47 * q^88 + 17 * q^89 + 88 * q^90 + 26 * q^91 - 122 * q^92 + q^93 + 28 * q^94 - 47 * q^95 + 50 * q^96 - 162 * q^97 + 128 * q^98 - 70 * q^99

Introduction

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