LMFDB - Embedded newform 189.2.v.a.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(22,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("189.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.v (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	189.169
Dual form			189.2.v.a.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.17921 + 0.793168i) q^{2} +(-1.72903 + 0.102202i) q^{3} +(2.58775 - 2.17138i) q^{4} +(0.443161 + 2.51329i) q^{5} +(3.68686 - 1.59413i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-1.59792 + 2.76768i) q^{8} +(2.97911 - 0.353421i) q^{9} +(-2.95920 - 5.12549i) q^{10} +(-0.776717 + 4.40498i) q^{11} +(-4.25239 + 4.01887i) q^{12} +(-3.79638 - 1.38177i) q^{13} +(-2.17921 - 0.793168i) q^{14} +(-1.02310 - 4.30027i) q^{15} +(0.113780 - 0.645277i) q^{16} +(-3.83523 - 6.64281i) q^{17} +(-6.21178 + 3.13311i) q^{18} +(-1.85220 + 3.20810i) q^{19} +(6.60411 + 5.54151i) q^{20} +(-1.39021 - 1.03311i) q^{21} +(-1.80126 - 10.2154i) q^{22} +(-2.63630 + 2.21211i) q^{23} +(2.48000 - 4.94872i) q^{24} +(-1.42178 + 0.517485i) q^{25} +9.36908 q^{26} +(-5.11486 + 0.915548i) q^{27} +3.37807 q^{28} +(-4.86584 + 1.77102i) q^{29} +(5.64039 + 8.55970i) q^{30} +(1.10711 - 0.928979i) q^{31} +(-0.846042 - 4.79814i) q^{32} +(0.892771 - 7.69574i) q^{33} +(13.6266 + 11.4341i) q^{34} +(-1.27603 + 2.21015i) q^{35} +(6.94179 - 7.38336i) q^{36} +(0.0540049 + 0.0935393i) q^{37} +(1.49177 - 8.46023i) q^{38} +(6.70528 + 2.00112i) q^{39} +(-7.66413 - 2.78951i) q^{40} +(-0.384547 - 0.139964i) q^{41} +(3.84899 + 1.14869i) q^{42} +(-1.74698 + 9.90762i) q^{43} +(7.55495 + 13.0856i) q^{44} +(2.20848 + 7.33075i) q^{45} +(3.99046 - 6.91169i) q^{46} +(5.45009 + 4.57317i) q^{47} +(-0.130780 + 1.12733i) q^{48} +(0.173648 + 0.984808i) q^{49} +(2.68790 - 2.25542i) q^{50} +(7.31015 + 11.0937i) q^{51} +(-12.8244 + 4.66771i) q^{52} +0.954837 q^{53} +(10.4202 - 6.05211i) q^{54} -11.4152 q^{55} +(-3.00311 + 1.09304i) q^{56} +(2.87464 - 5.73621i) q^{57} +(9.19898 - 7.71886i) q^{58} +(-1.41087 - 8.00142i) q^{59} +(-11.9851 - 8.90649i) q^{60} +(-7.67594 - 6.44088i) q^{61} +(-1.67580 + 2.90257i) q^{62} +(2.50931 + 1.64420i) q^{63} +(6.30467 + 10.9200i) q^{64} +(1.79038 - 10.1537i) q^{65} +(4.15847 + 17.4787i) q^{66} +(5.16475 + 1.87982i) q^{67} +(-24.3487 - 8.86221i) q^{68} +(4.33216 - 4.09425i) q^{69} +(1.02772 - 5.82849i) q^{70} +(-3.33968 - 5.78450i) q^{71} +(-3.78223 + 8.80997i) q^{72} +(-4.45967 + 7.72438i) q^{73} +(-0.191880 - 0.161007i) q^{74} +(2.40541 - 1.04006i) q^{75} +(2.17298 + 12.3236i) q^{76} +(-3.42647 + 2.87515i) q^{77} +(-16.1994 + 0.957539i) q^{78} +(-1.65874 + 0.603732i) q^{79} +1.67219 q^{80} +(8.75019 - 2.10576i) q^{81} +0.949023 q^{82} +(-2.72698 + 0.992539i) q^{83} +(-5.84080 + 0.345246i) q^{84} +(14.9957 - 12.5829i) q^{85} +(-4.05137 - 22.9764i) q^{86} +(8.23220 - 3.55945i) q^{87} +(-10.9504 - 9.18852i) q^{88} +(0.103017 - 0.178431i) q^{89} +(-10.6272 - 14.2235i) q^{90} +(-2.02001 - 3.49876i) q^{91} +(-2.01874 + 11.4488i) q^{92} +(-1.81929 + 1.71938i) q^{93} +(-15.5042 - 5.64307i) q^{94} +(-8.88371 - 3.23341i) q^{95} +(1.95321 + 8.20968i) q^{96} +(-0.561099 + 3.18215i) q^{97} +(-1.15953 - 2.00837i) q^{98} +(-0.757110 + 13.3974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27}+ \cdots - 117 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.17921	+	0.793168i	−1.54093	+	0.560854i	−0.966269	−	0.257534i	$-0.917090\pi$
$2$	−2.17921	+	0.793168i	−1.54093	+	0.560854i	−0.574665	+	0.818389i	$0.694868\pi$
$3$	−1.72903	+	0.102202i	−0.998258	+	0.0590064i
$3$	−1.72903	+	0.102202i	−0.998258	+	0.0590064i
$4$	2.58775	−	2.17138i	1.29388	−	1.08569i
$5$	0.443161	+	2.51329i	0.198188	+	1.12398i	0.907806	+	0.419391i	$0.137756\pi$
$5$	0.443161	+	2.51329i	0.198188	+	1.12398i	−0.709618	+	0.704587i	$0.751132\pi$
$6$	3.68686	−	1.59413i	1.50516	−	0.650802i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	−1.59792	+	2.76768i	−0.564951	+	0.978523i
$9$	2.97911	−	0.353421i	0.993036	−	0.117807i
$10$	−2.95920	−	5.12549i	−0.935782	−	1.62082i
$11$	−0.776717	+	4.40498i	−0.234189	+	1.32815i	0.610126	+	0.792304i	$0.291119\pi$
$11$	−0.776717	+	4.40498i	−0.234189	+	1.32815i	−0.844315	+	0.535847i	$0.819992\pi$
$12$	−4.25239	+	4.01887i	−1.22756	+	1.16015i
$13$	−3.79638	−	1.38177i	−1.05293	−	0.383233i	−0.243159	−	0.969986i	$-0.578184\pi$
$13$	−3.79638	−	1.38177i	−1.05293	−	0.383233i	−0.809766	+	0.586753i	$0.800406\pi$
$14$	−2.17921	−	0.793168i	−0.582418	−	0.211983i
$15$	−1.02310	−	4.30027i	−0.264164	−	1.11033i
$16$	0.113780	−	0.645277i	0.0284449	−	0.161319i
$17$	−3.83523	−	6.64281i	−0.930180	−	1.61112i	−0.783011	−	0.622008i	$-0.786317\pi$
$17$	−3.83523	−	6.64281i	−0.930180	−	1.61112i	−0.147169	−	0.989111i	$-0.547016\pi$
$18$	−6.21178	+	3.13311i	−1.46413	+	0.738482i
$19$	−1.85220	+	3.20810i	−0.424923	+	0.735989i	−0.996413	−	0.0846203i	$-0.973032\pi$
$19$	−1.85220	+	3.20810i	−0.424923	+	0.735989i	0.571490	+	0.820609i	$0.306366\pi$
$20$	6.60411	+	5.54151i	1.47672	+	1.23912i
$21$	−1.39021	−	1.03311i	−0.303369	−	0.225443i
$22$	−1.80126	−	10.2154i	−0.384030	−	2.17794i
$23$	−2.63630	+	2.21211i	−0.549706	+	0.461258i	−0.874841	−	0.484410i	$-0.839034\pi$
$23$	−2.63630	+	2.21211i	−0.549706	+	0.461258i	0.325136	+	0.945667i	$0.394590\pi$
$24$	2.48000	−	4.94872i	0.506227	−	1.01015i
$25$	−1.42178	+	0.517485i	−0.284356	+	0.103497i
$26$	9.36908			1.83743
$27$	−5.11486	+	0.915548i	−0.984355	+	0.176197i
$28$	3.37807			0.638396
$29$	−4.86584	+	1.77102i	−0.903565	+	0.328871i	−0.751680	−	0.659528i	$-0.770756\pi$
$29$	−4.86584	+	1.77102i	−0.903565	+	0.328871i	−0.151884	+	0.988398i	$0.548534\pi$
$30$	5.64039	+	8.55970i	1.02979	+	1.56278i
$31$	1.10711	−	0.928979i	0.198844	−	0.166850i	−0.537929	−	0.842990i	$-0.680793\pi$
$31$	1.10711	−	0.928979i	0.198844	−	0.166850i	0.736773	+	0.676140i	$0.236349\pi$
$32$	−0.846042	−	4.79814i	−0.149561	−	0.848200i
$33$	0.892771	−	7.69574i	0.155411	−	1.33966i
$34$	13.6266	+	11.4341i	2.33695	+	1.96093i
$35$	−1.27603	+	2.21015i	−0.215689	+	0.373584i
$36$	6.94179	−	7.38336i	1.15696	−	1.23056i
$37$	0.0540049	+	0.0935393i	0.00887836	+	0.0153778i	0.870430	−	0.492291i	$-0.163841\pi$
$37$	0.0540049	+	0.0935393i	0.00887836	+	0.0153778i	−0.861552	+	0.507669i	$0.830507\pi$
$38$	1.49177	−	8.46023i	0.241997	−	1.37243i
$39$	6.70528	+	2.00112i	1.07370	+	0.320436i
$40$	−7.66413	−	2.78951i	−1.21181	−	0.441061i
$41$	−0.384547	−	0.139964i	−0.0600561	−	0.0218586i	0.311817	−	0.950142i	$-0.399062\pi$
$41$	−0.384547	−	0.139964i	−0.0600561	−	0.0218586i	−0.371874	+	0.928283i	$0.621285\pi$
$42$	3.84899	+	1.14869i	0.593912	+	0.177247i
$43$	−1.74698	+	9.90762i	−0.266412	+	1.51090i	0.498571	+	0.866849i	$0.333858\pi$
$43$	−1.74698	+	9.90762i	−0.266412	+	1.51090i	−0.764983	+	0.644050i	$0.777253\pi$
$44$	7.55495	+	13.0856i	1.13895	+	1.97272i
$45$	2.20848	+	7.33075i	0.329220	+	1.09280i
$46$	3.99046	−	6.91169i	0.588362	−	1.01907i
$47$	5.45009	+	4.57317i	0.794978	+	0.667066i	0.946972	−	0.321316i	$-0.104125\pi$
$47$	5.45009	+	4.57317i	0.794978	+	0.667066i	−0.151994	+	0.988381i	$0.548570\pi$
$48$	−0.130780	+	1.12733i	−0.0188765	+	0.162716i
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	2.68790	−	2.25542i	0.380127	−	0.318964i
$51$	7.31015	+	11.0937i	1.02363	+	1.55343i
$52$	−12.8244	+	4.66771i	−1.77843	+	0.647295i
$53$	0.954837			0.131157			0.0655785	−	0.997847i	$-0.479111\pi$
$53$	0.954837			0.131157			0.0655785	+	0.997847i	$0.479111\pi$
$54$	10.4202	−	6.05211i	1.41801	−	0.823588i
$55$	−11.4152			−1.53923
$56$	−3.00311	+	1.09304i	−0.401308	+	0.146064i
$57$	2.87464	−	5.73621i	0.380755	−	0.759780i
$58$	9.19898	−	7.71886i	1.20789	−	1.01354i
$59$	−1.41087	−	8.00142i	−0.183679	−	1.04170i	−0.927641	−	0.373474i	$-0.878167\pi$
$59$	−1.41087	−	8.00142i	−0.183679	−	1.04170i	0.743962	−	0.668222i	$-0.232944\pi$
$60$	−11.9851	−	8.90649i	−1.54727	−	1.14982i
$61$	−7.67594	−	6.44088i	−0.982804	−	0.824670i	0.00170609	−	0.999999i	$-0.499457\pi$
$61$	−7.67594	−	6.44088i	−0.982804	−	0.824670i	−0.984510	+	0.175328i	$0.943901\pi$
$62$	−1.67580	+	2.90257i	−0.212827	+	0.368627i
$63$	2.50931	+	1.64420i	0.316143	+	0.207150i
$64$	6.30467	+	10.9200i	0.788083	+	1.36500i
$65$	1.79038	−	10.1537i	0.222069	−	1.25942i
$66$	4.15847	+	17.4787i	0.511873	+	2.15148i
$67$	5.16475	+	1.87982i	0.630975	+	0.229656i	0.637656	−	0.770322i	$-0.279904\pi$
$67$	5.16475	+	1.87982i	0.630975	+	0.229656i	−0.00668053	+	0.999978i	$0.502126\pi$
$68$	−24.3487	−	8.86221i	−2.95272	−	1.07470i
$69$	4.33216	−	4.09425i	0.521531	−	0.492890i
$70$	1.02772	−	5.82849i	0.122836	−	0.696638i
$71$	−3.33968	−	5.78450i	−0.396347	−	0.686494i	0.596925	−	0.802297i	$-0.296389\pi$
$71$	−3.33968	−	5.78450i	−0.396347	−	0.686494i	−0.993272	+	0.115803i	$0.963056\pi$
$72$	−3.78223	+	8.80997i	−0.445740	+	1.03826i
$73$	−4.45967	+	7.72438i	−0.521965	+	0.904070i	0.477709	+	0.878518i	$0.341467\pi$
$73$	−4.45967	+	7.72438i	−0.521965	+	0.904070i	−0.999674	+	0.0255514i	$0.991866\pi$
$74$	−0.191880	−	0.161007i	−0.0223057	−	0.0187167i
$75$	2.40541	−	1.04006i	0.277753	−	0.120095i
$76$	2.17298	+	12.3236i	0.249258	+	1.41361i
$77$	−3.42647	+	2.87515i	−0.390482	+	0.327653i
$78$	−16.1994	+	0.957539i	−1.83423	+	0.108420i
$79$	−1.65874	+	0.603732i	−0.186623	+	0.0679252i	−0.433641	−	0.901086i	$-0.642771\pi$
$79$	−1.65874	+	0.603732i	−0.186623	+	0.0679252i	0.247018	+	0.969011i	$0.420549\pi$
$80$	1.67219			0.186957
$81$	8.75019	−	2.10576i	0.972243	−	0.233974i
$82$	0.949023			0.104802
$83$	−2.72698	+	0.992539i	−0.299325	+	0.108945i	−0.487317	−	0.873225i	$-0.662024\pi$
$83$	−2.72698	+	0.992539i	−0.299325	+	0.108945i	0.187992	+	0.982171i	$0.439802\pi$
$84$	−5.84080	+	0.345246i	−0.637283	+	0.0376694i
$85$	14.9957	−	12.5829i	1.62651	−	1.36481i
$86$	−4.05137	−	22.9764i	−0.436870	−	2.47761i
$87$	8.23220	−	3.55945i	0.882585	−	0.381614i
$88$	−10.9504	−	9.18852i	−1.16732	−	0.979499i
$89$	0.103017	−	0.178431i	0.0109198	−	0.0189137i	−0.860514	−	0.509427i	$-0.829857\pi$
$89$	0.103017	−	0.178431i	0.0109198	−	0.0189137i	0.871434	+	0.490513i	$0.163191\pi$
$90$	−10.6272	−	14.2235i	−1.12021	−	1.49929i
$91$	−2.02001	−	3.49876i	−0.211755	−	0.366770i
$92$	−2.01874	+	11.4488i	−0.210468	+	1.19362i
$93$	−1.81929	+	1.71938i	−0.188652	+	0.178292i
$94$	−15.5042	−	5.64307i	−1.59914	−	0.582038i
$95$	−8.88371	−	3.23341i	−0.911450	−	0.331741i
$96$	1.95321	+	8.20968i	0.199349	+	0.837897i
$97$	−0.561099	+	3.18215i	−0.0569709	+	0.323098i	−0.999952	−	0.00974674i	$-0.996897\pi$
$97$	−0.561099	+	3.18215i	−0.0569709	+	0.323098i	0.942982	+	0.332845i	$0.108009\pi$
$98$	−1.15953	−	2.00837i	−0.117131	−	0.202876i
$99$	−0.757110	+	13.3974i	−0.0760924	+	1.34649i
$100$	−2.55555	+	4.42635i	−0.255555	+	0.442635i
$101$	8.26959	+	6.93901i	0.822855	+	0.690457i	0.953639	−	0.300953i	$-0.0973049\pi$
$101$	8.26959	+	6.93901i	0.822855	+	0.690457i	−0.130784	+	0.991411i	$0.541749\pi$
$102$	−24.7295	−	18.3773i	−2.44859	−	1.81962i
$103$	1.84847	+	10.4832i	0.182135	+	1.03294i	0.929582	+	0.368617i	$0.120168\pi$
$103$	1.84847	+	10.4832i	0.182135	+	1.03294i	−0.747447	+	0.664322i	$0.768720\pi$
$104$	9.89061	−	8.29920i	0.969854	−	0.813804i
$105$	1.98042	−	3.95184i	0.193269	−	0.385660i
$106$	−2.08079	+	0.757346i	−0.202104	+	0.0735599i
$107$	8.61734			0.833070			0.416535	−	0.909120i	$-0.363244\pi$
$107$	8.61734			0.833070			0.416535	+	0.909120i	$0.363244\pi$
$108$	−11.2480	+	13.4755i	−1.08234	+	1.29668i
$109$	11.3161			1.08389			0.541944	−	0.840415i	$-0.317688\pi$
$109$	11.3161			1.08389			0.541944	+	0.840415i	$0.317688\pi$
$110$	24.8761	−	9.05417i	2.37185	−	0.863282i
$111$	−0.102936	−	0.156213i	−0.00977027	−	0.0148271i
$112$	0.501936	−	0.421174i	0.0474285	−	0.0397972i
$113$	3.38701	+	19.2087i	0.318623	+	1.80700i	0.551146	+	0.834409i	$0.314191\pi$
$113$	3.38701	+	19.2087i	0.318623	+	1.80700i	−0.232523	+	0.972591i	$0.574698\pi$
$114$	−1.71466	+	14.7805i	−0.160593	+	1.38432i
$115$	−6.72799	−	5.64546i	−0.627388	−	0.526441i
$116$	−8.74604	+	15.1486i	−0.812049	+	1.40651i
$117$	−11.7982	−	2.77472i	−1.09074	−	0.256523i
$118$	9.42104	+	16.3177i	0.867277	+	1.50217i
$119$	1.33196	−	7.55393i	0.122101	−	0.692468i
$120$	13.5366	+	4.03987i	1.23572	+	0.368788i
$121$	−8.46393	−	3.08062i	−0.769449	−	0.280056i
$122$	21.8362	+	7.94773i	1.97696	+	0.719553i
$123$	0.679199	+	0.202700i	0.0612413	+	0.0182769i
$124$	0.847769	−	4.80794i	0.0761319	−	0.431766i
$125$	4.44949	+	7.70674i	0.397974	+	0.689312i
$126$	−6.77243	−	1.59275i	−0.603336	−	0.141894i
$127$	1.25303	−	2.17031i	0.111188	−	0.192584i	−0.805061	−	0.593192i	$-0.797868\pi$
$127$	1.25303	−	2.17031i	0.111188	−	0.192584i	0.916250	+	0.400608i	$0.131201\pi$
$128$	−14.9360	−	12.5328i	−1.32017	−	1.10775i
$129$	2.00801	−	17.3092i	0.176795	−	1.52399i
$130$	4.15201	+	23.5472i	0.364155	+	2.06523i
$131$	−14.8692	+	12.4768i	−1.29913	+	1.09010i	−0.308837	+	0.951115i	$0.599940\pi$
$131$	−14.8692	+	12.4768i	−1.29913	+	1.09010i	−0.990294	+	0.138985i	$0.955616\pi$
$132$	−14.4001	−	21.8532i	−1.25337	−	1.90208i
$133$	−3.48099	+	1.26698i	−0.301840	+	0.109861i
$134$	−12.7461			−1.10109
$135$	−4.56775	−	12.4494i	−0.393129	−	1.07147i
$136$	24.5136			2.10202
$137$	17.7488	−	6.46002i	1.51638	−	0.551917i	0.556138	−	0.831090i	$-0.312283\pi$
$137$	17.7488	−	6.46002i	1.51638	−	0.551917i	0.960241	+	0.279173i	$0.0900605\pi$
$138$	−6.19326	+	12.3584i	−0.527205	+	1.05201i
$139$	3.61802	−	3.03588i	0.306876	−	0.257500i	−0.476323	−	0.879270i	$-0.658031\pi$
$139$	3.61802	−	3.03588i	0.306876	−	0.257500i	0.783199	+	0.621771i	$0.213586\pi$
$140$	1.49703	+	8.49008i	0.126522	+	0.717543i
$141$	−9.89078	−	7.35015i	−0.832954	−	0.618995i
$142$	11.8659	+	9.95671i	0.995768	+	0.835549i
$143$	9.03537	−	15.6497i	0.755575	−	1.30869i
$144$	0.110908	−	1.96256i	0.00924230	−	0.163547i
$145$	−6.60745	−	11.4444i	−0.548719	−	0.950409i
$146$	3.59183	−	20.3703i	0.297262	−	1.68586i
$147$	−0.400893	−	1.68502i	−0.0330651	−	0.138978i
$148$	0.342861	+	0.124791i	0.0281830	+	0.0102578i
$149$	20.9033	+	7.60817i	1.71246	+	0.623286i	0.997145	−	0.0755134i	$-0.0240596\pi$
$149$	20.9033	+	7.60817i	1.71246	+	0.623286i	0.715318	+	0.698799i	$0.246282\pi$
$150$	−4.41696	+	4.17440i	−0.360644	+	0.340838i
$151$	−1.28602	+	7.29337i	−0.104655	+	0.593526i	0.886703	+	0.462339i	$0.152990\pi$
$151$	−1.28602	+	7.29337i	−0.104655	+	0.593526i	−0.991358	+	0.131186i	$0.958121\pi$
$152$	−5.91933	−	10.2526i	−0.480121	−	0.831595i
$153$	−13.7733	−	18.4342i	−1.11350	−	1.49032i
$154$	5.18652	−	8.98331i	0.417941	−	0.723896i
$155$	2.82542	+	2.37081i	0.226944	+	0.190428i
$156$	21.6968	−	9.38131i	1.73714	−	0.751106i
$157$	1.01642	+	5.76442i	0.0811193	+	0.460051i	0.998127	+	0.0611804i	$0.0194865\pi$
$157$	1.01642	+	5.76442i	0.0811193	+	0.460051i	−0.917007	+	0.398870i	$0.869402\pi$
$158$	3.13588	−	2.63132i	0.249478	−	0.209337i
$159$	−1.65094	+	0.0975863i	−0.130928	+	0.00773910i
$160$	11.6842	−	4.25270i	0.923717	−	0.336206i
$161$	−3.44144			−0.271223
$162$	−17.3983	+	11.5293i	−1.36694	+	0.905825i
$163$	−18.9586			−1.48495			−0.742477	−	0.669872i	$-0.766349\pi$
$163$	−18.9586			−1.48495			−0.742477	+	0.669872i	$0.766349\pi$
$164$	−1.29903	+	0.472807i	−0.101437	+	0.0369201i
$165$	19.7373	−	1.16666i	1.53654	−	0.0908242i
$166$	5.15541	−	4.32590i	0.400138	−	0.335755i
$167$	0.619706	+	3.51453i	0.0479543	+	0.271962i	0.999352	−	0.0360037i	$-0.0114628\pi$
$167$	0.619706	+	3.51453i	0.0479543	+	0.271962i	−0.951397	+	0.307966i	$0.900352\pi$
$168$	5.08077	−	2.19683i	0.391990	−	0.169489i
$169$	2.54461	+	2.13518i	0.195739	+	0.164245i
$170$	−22.6984	+	39.3149i	−1.74089	+	3.01531i
$171$	−4.38409	+	10.2119i	−0.335260	+	0.780923i
$172$	16.9925	+	29.4319i	1.29567	+	2.24416i
$173$	0.116959	−	0.663309i	0.00889225	−	0.0504304i	−0.980039	−	0.198806i	$-0.936293\pi$
$173$	0.116959	−	0.663309i	0.00889225	−	0.0504304i	0.988931	+	0.148376i	$0.0474046\pi$
$174$	−15.1165	+	14.2863i	−1.14598	+	1.08304i
$175$	−1.42178	−	0.517485i	−0.107476	−	0.0391182i
$176$	2.75406	+	1.00239i	0.207595	+	0.0755583i
$177$	3.25719	+	13.6905i	0.244826	+	1.02904i
$178$	−0.0829705	+	0.470549i	−0.00621890	+	0.0352691i
$179$	1.30268	+	2.25631i	0.0973671	+	0.168645i	0.910594	−	0.413302i	$-0.135625\pi$
$179$	1.30268	+	2.25631i	0.0973671	+	0.168645i	−0.813227	+	0.581947i	$0.802291\pi$
$180$	21.6329	+	14.1747i	1.61242	+	1.05652i
$181$	9.91529	−	17.1738i	0.736998	−	1.27652i	−0.216844	−	0.976206i	$-0.569576\pi$
$181$	9.91529	−	17.1738i	0.736998	−	1.27652i	0.953841	−	0.300311i	$-0.0970905\pi$
$182$	7.17713	+	6.02233i	0.532004	+	0.446404i
$183$	13.9302	+	10.3520i	1.02975	+	0.765242i
$184$	−1.90984	−	10.8312i	−0.140795	−	0.798488i
$185$	−0.211159	+	0.177183i	−0.0155247	+	0.0130268i
$186$	2.60086	−	5.18991i	0.190704	−	0.380542i
$187$	32.2403	−	11.7345i	2.35765	−	0.858113i
$188$	24.0336			1.75283
$189$	−4.50671	−	2.58642i	−0.327815	−	0.188134i
$190$	21.9241			1.59054
$191$	−7.91518	+	2.88089i	−0.572722	+	0.208454i	−0.612113	−	0.790770i	$-0.709680\pi$
$191$	−7.91518	+	2.88089i	−0.572722	+	0.208454i	0.0393910	+	0.999224i	$0.487458\pi$
$192$	−12.0170	−	18.2367i	−0.867254	−	1.31612i
$193$	−2.52070	+	2.11512i	−0.181444	+	0.152249i	−0.728986	−	0.684529i	$-0.760008\pi$
$193$	−2.52070	+	2.11512i	−0.181444	+	0.152249i	0.547542	+	0.836778i	$0.315564\pi$
$194$	−1.30123	−	7.37962i	−0.0934225	−	0.529826i
$195$	−2.05789	+	17.7391i	−0.147369	+	1.27033i
$196$	2.58775	+	2.17138i	0.184840	+	0.155099i
$197$	−1.61451	+	2.79642i	−0.115029	+	0.199236i	−0.917791	−	0.397063i	$-0.870029\pi$
$197$	−1.61451	+	2.79642i	−0.115029	+	0.199236i	0.802762	+	0.596299i	$0.203363\pi$
$198$	−8.97650	−	29.7963i	−0.637932	−	2.11753i
$199$	4.33292	+	7.50484i	0.307153	+	0.532004i	0.977738	−	0.209828i	$-0.0672904\pi$
$199$	4.33292	+	7.50484i	0.307153	+	0.532004i	−0.670586	+	0.741832i	$0.733957\pi$
$200$	0.839657	−	4.76193i	0.0593727	−	0.336719i
$201$	−9.12215	−	2.72242i	−0.643427	−	0.192024i
$202$	−23.5250	−	8.56239i	−1.65521	−	0.602448i
$203$	−4.86584	−	1.77102i	−0.341515	−	0.124301i
$204$	43.0055	+	12.8346i	3.01099	+	0.898599i
$205$	0.181353	−	1.02850i	0.0126663	−	0.0718339i
$206$	−12.3431	−	21.3789i	−0.859986	−	1.48954i
$207$	−7.07200	+	7.52185i	−0.491538	+	0.522805i
$208$	−1.32357	+	2.29250i	−0.0917733	+	0.158956i
$209$	−12.6930	−	10.6507i	−0.877992	−	0.736723i
$210$	−1.18128	+	10.1827i	−0.0815160	+	0.702672i
$211$	−4.40235	−	24.9670i	−0.303070	−	1.71880i	−0.632452	−	0.774599i	$-0.717952\pi$
$211$	−4.40235	−	24.9670i	−0.303070	−	1.71880i	0.329382	−	0.944197i	$-0.393160\pi$
$212$	2.47088	−	2.07332i	0.169701	−	0.142396i
$213$	6.36561	+	9.66027i	0.436164	+	0.661911i
$214$	−18.7790	+	6.83500i	−1.28371	+	0.467231i
$215$	−25.6749			−1.75102
$216$	5.63920	−	15.6193i	0.383699	−	1.06276i
$217$	1.44523			0.0981089
$218$	−24.6602	+	8.97559i	−1.67020	+	0.607903i
$219$	6.92147	−	13.8115i	0.467710	−	0.933294i
$220$	−29.5397	+	24.7868i	−1.99157	+	1.67113i
$221$	5.38115	+	30.5180i	0.361975	+	2.05286i
$222$	0.348223	+	0.258776i	0.0233712	+	0.0173679i
$223$	−8.39665	−	7.04563i	−0.562281	−	0.471810i	0.316793	−	0.948495i	$-0.397394\pi$
$223$	−8.39665	−	7.04563i	−0.562281	−	0.471810i	−0.879074	+	0.476685i	$0.841838\pi$
$224$	2.43608	−	4.21942i	0.162768	−	0.281922i
$225$	−4.05274	+	2.04413i	−0.270183	+	0.136275i
$226$	−22.6167	−	39.1733i	−1.50444	−	2.60577i
$227$	−2.56670	+	14.5565i	−0.170358	+	0.966147i	0.773009	+	0.634395i	$0.218751\pi$
$227$	−2.56670	+	14.5565i	−0.170358	+	0.966147i	−0.943367	+	0.331752i	$0.892360\pi$
$228$	−5.01666	−	21.0858i	−0.332236	−	1.39644i
$229$	−0.935267	−	0.340409i	−0.0618042	−	0.0224949i	0.310933	−	0.950432i	$-0.399359\pi$
$229$	−0.935267	−	0.340409i	−0.0618042	−	0.0224949i	−0.372737	+	0.927937i	$0.621581\pi$
$230$	19.1395	+	6.96621i	1.26202	+	0.459338i
$231$	5.63063	−	5.32141i	0.370468	−	0.350123i
$232$	2.87361	−	16.2971i	0.188662	−	1.06995i
$233$	−9.97465	−	17.2766i	−0.653461	−	1.13183i	−0.982277	−	0.187434i	$-0.939983\pi$
$233$	−9.97465	−	17.2766i	−0.653461	−	1.13183i	0.328816	−	0.944394i	$-0.393350\pi$
$234$	27.9115	−	3.31123i	1.82463	−	0.216462i
$235$	−9.07844	+	15.7243i	−0.592212	+	1.02574i
$236$	−21.0251	−	17.6422i	−1.36862	−	1.14841i
$237$	2.80632	−	1.21340i	0.182290	−	0.0788188i
$238$	3.08891	+	17.5181i	0.200224	+	1.13553i
$239$	16.4915	−	13.8380i	1.06674	−	0.895104i	0.0719903	−	0.997405i	$-0.477065\pi$
$239$	16.4915	−	13.8380i	1.06674	−	0.895104i	0.994753	+	0.102301i	$0.0326205\pi$
$240$	−2.89127	+	0.170901i	−0.186631	+	0.0110316i
$241$	−21.4579	+	7.81004i	−1.38222	+	0.503089i	−0.922852	−	0.385155i	$-0.874148\pi$
$241$	−21.4579	+	7.81004i	−1.38222	+	0.503089i	−0.459373	+	0.888244i	$0.651926\pi$
$242$	20.8881			1.34274
$243$	−14.9141	+	4.53522i	−0.956743	+	0.290934i
$244$	−33.8491			−2.16697
$245$	−2.39815	+	0.872857i	−0.153212	+	0.0557648i
$246$	−1.64089	+	0.0969921i	−0.104619	+	0.00618399i
$247$	11.4645	−	9.61985i	0.729468	−	0.612096i
$248$	0.802037	+	4.54858i	0.0509294	+	0.288835i
$249$	4.61360	−	1.99484i	0.292375	−	0.126418i
$250$	−15.8091	−	13.2654i	−0.999856	−	0.838979i
$251$	−4.59388	+	7.95683i	−0.289963	+	0.502231i	−0.973801	−	0.227403i	$-0.926976\pi$
$251$	−4.59388	+	7.95683i	−0.289963	+	0.502231i	0.683838	+	0.729634i	$0.260310\pi$
$252$	10.0636	−	1.19388i	0.633950	−	0.0752076i
$253$	−7.69666	−	13.3310i	−0.483885	−	0.838114i
$254$	−1.00919	+	5.72342i	−0.0633225	+	0.359120i
$255$	−24.6421	+	23.2888i	−1.54315	+	1.45840i
$256$	18.7915	+	6.83955i	1.17447	+	0.427472i
$257$	14.8450	+	5.40312i	0.926003	+	0.337037i	0.760624	−	0.649193i	$-0.224893\pi$
$257$	14.8450	+	5.40312i	0.926003	+	0.337037i	0.165379	+	0.986230i	$0.447115\pi$
$258$	9.35319	+	39.3130i	0.582304	+	2.44752i
$259$	−0.0187557	+	0.106369i	−0.00116542	+	0.00660945i
$260$	−17.4146	−	30.1630i	−1.08001	−	1.87063i
$261$	−13.8700	+	6.99576i	−0.858529	+	0.433027i
$262$	22.5070	−	38.9833i	1.39049	−	2.40840i
$263$	−8.81529	−	7.39690i	−0.543574	−	0.456113i	0.329184	−	0.944266i	$-0.393226\pi$
$263$	−8.81529	−	7.39690i	−0.543574	−	0.456113i	−0.872758	+	0.488153i	$0.837671\pi$
$264$	19.8728	+	14.7681i	1.22308	+	0.908913i
$265$	0.423147	+	2.39978i	0.0259937	+	0.147418i
$266$	6.58089	−	5.52202i	0.403500	−	0.338577i
$267$	−0.159884	+	0.319042i	−0.00978475	+	0.0195250i
$268$	17.4469	−	6.35016i	1.06574	−	0.387898i
$269$	4.19766			0.255936			0.127968	−	0.991778i	$-0.459155\pi$
$269$	4.19766			0.255936			0.127968	+	0.991778i	$0.459155\pi$
$270$	19.8285	+	23.5069i	1.20673	+	1.43058i
$271$	30.8629			1.87479			0.937394	−	0.348270i	$-0.113231\pi$
$271$	30.8629			1.87479			0.937394	+	0.348270i	$0.113231\pi$
$272$	−4.72282	+	1.71897i	−0.286363	+	0.104228i
$273$	3.85024	+	5.84302i	0.233027	+	0.353636i
$274$	−33.5544	+	28.1555i	−2.02710	+	1.70093i
$275$	−1.17519	−	6.66484i	−0.0708667	−	0.401905i
$276$	2.32037	−	20.0017i	0.139670	−	1.20396i
$277$	−13.7131	−	11.5066i	−0.823938	−	0.691366i	0.129953	−	0.991520i	$-0.458517\pi$
$277$	−13.7131	−	11.5066i	−0.823938	−	0.691366i	−0.953891	+	0.300154i	$0.902962\pi$
$278$	−5.47646	+	9.48551i	−0.328456	+	0.568903i
$279$	2.96989	−	3.15881i	0.177803	−	0.189113i
$280$	−4.07800	−	7.06330i	−0.243707	−	0.422113i
$281$	−4.34306	+	24.6307i	−0.259085	+	1.46934i	0.526280	+	0.850311i	$0.323586\pi$
$281$	−4.34306	+	24.6307i	−0.259085	+	1.46934i	−0.785365	+	0.619033i	$0.787525\pi$
$282$	27.3840	+	8.17249i	1.63069	+	0.486664i
$283$	25.7998	+	9.39035i	1.53364	+	0.558198i	0.964509	−	0.264051i	$-0.0850587\pi$
$283$	25.7998	+	9.39035i	1.53364	+	0.558198i	0.569128	+	0.822249i	$0.307281\pi$
$284$	−21.2026	−	7.71713i	−1.25815	−	0.457928i
$285$	15.6907	+	4.68273i	0.929436	+	0.277381i
$286$	−7.27712	+	41.2706i	−0.430305	+	2.44038i
$287$	−0.204613	−	0.354400i	−0.0120779	−	0.0209196i
$288$	−4.21622	−	13.9952i	−0.248443	−	0.824674i
$289$	−20.9180	+	36.2310i	−1.23047	+	2.13124i
$290$	23.4764	+	19.6990i	1.37858	+	1.15677i
$291$	0.644936	−	5.55938i	0.0378068	−	0.325897i
$292$	5.23205	+	29.6724i	0.306183	+	1.73645i
$293$	3.90322	−	3.27519i	0.228028	−	0.191339i	−0.521614	−	0.853182i	$-0.674670\pi$
$293$	3.90322	−	3.27519i	0.228028	−	0.191339i	0.749642	+	0.661843i	$0.230225\pi$
$294$	2.21013	+	3.35403i	0.128897	+	0.195611i
$295$	19.4847	−	7.09183i	1.13444	−	0.412903i
$296$	−0.345183			−0.0200633
$297$	−0.0601753	−	23.2420i	−0.00349173	−	1.34864i
$298$	−51.5872			−2.98837
$299$	13.0650	−	4.75527i	0.755568	−	0.275004i
$300$	3.96626	−	7.91449i	0.228992	−	0.456943i
$301$	−7.70676	+	6.46674i	−0.444210	+	0.372737i
$302$	−2.98236	−	16.9138i	−0.171616	−	0.973280i
$303$	−15.0076	−	11.1526i	−0.862163	−	0.640701i
$304$	1.85937	+	1.56020i	0.106642	+	0.0894834i
$305$	12.7861	−	22.1462i	0.732132	−	1.26809i
$306$	44.6363	+	29.2475i	2.55169	+	1.67197i
$307$	3.00594	+	5.20644i	0.171558	+	0.297147i	0.938965	−	0.344014i	$-0.111787\pi$
$307$	3.00594	+	5.20644i	0.171558	+	0.297147i	−0.767407	+	0.641161i	$0.778453\pi$
$308$	−2.62381	+	14.8803i	−0.149505	+	0.847886i
$309$	−4.26746	−	17.9368i	−0.242768	−	1.02039i
$310$	−8.03765	−	2.92546i	−0.456508	−	0.166155i
$311$	8.07554	+	2.93926i	0.457922	+	0.166670i	0.560673	−	0.828037i	$-0.310542\pi$
$311$	8.07554	+	2.93926i	0.457922	+	0.166670i	−0.102751	+	0.994707i	$0.532765\pi$
$312$	−16.2530	+	15.3604i	−0.920144	+	0.869613i
$313$	−0.794075	+	4.50343i	−0.0448838	+	0.254549i	−0.998991	−	0.0449176i	$-0.985697\pi$
$313$	−0.794075	+	4.50343i	−0.0448838	+	0.254549i	0.954107	+	0.299466i	$0.0968086\pi$
$314$	−6.78715	−	11.7557i	−0.383021	−	0.663412i
$315$	−3.02032	+	7.03526i	−0.170176	+	0.396392i
$316$	−2.98148	+	5.16407i	−0.167721	+	0.290502i
$317$	−16.7432	−	14.0492i	−0.940391	−	0.789082i	0.0372624	−	0.999306i	$-0.488136\pi$
$317$	−16.7432	−	14.0492i	−0.940391	−	0.789082i	−0.977653	+	0.210224i	$0.932581\pi$
$318$	3.52035	−	1.52214i	0.197412	−	0.0853572i
$319$	−4.02193	−	22.8095i	−0.225185	−	1.27709i
$320$	−24.6512	+	20.6848i	−1.37804	+	1.15631i
$321$	−14.8997	+	0.880710i	−0.831619	+	0.0491564i
$322$	7.49962	−	2.72964i	0.417938	−	0.152117i
$323$	28.4144			1.58102
$324$	18.0709	−	24.4492i	1.00394	−	1.35829i
$325$	6.11265			0.339069
$326$	41.3148	−	15.0374i	2.28822	−	0.832842i
$327$	−19.5660	+	1.15653i	−1.08200	+	0.0639563i
$328$	1.00185	−	0.840653i	0.0553180	−	0.0464173i
$329$	1.23544	+	7.00651i	0.0681118	+	0.386281i
$330$	−42.0863	+	18.1974i	−2.31677	+	1.00173i
$331$	7.34042	+	6.15935i	0.403466	+	0.338548i	0.821832	−	0.569730i	$-0.192952\pi$
$331$	7.34042	+	6.15935i	0.403466	+	0.338548i	−0.418365	+	0.908279i	$0.637397\pi$
$332$	−4.90157	+	8.48977i	−0.269009	+	0.465936i
$333$	0.193945	+	0.259577i	0.0106281	+	0.0142247i
$334$	−4.13808	−	7.16736i	−0.226426	−	0.392181i
$335$	−2.43571	+	13.8136i	−0.133077	+	0.754717i
$336$	−0.824819	+	0.779523i	−0.0449976	+	0.0425265i
$337$	−4.39754	−	1.60058i	−0.239550	−	0.0871889i	0.219456	−	0.975622i	$-0.429572\pi$
$337$	−4.39754	−	1.60058i	−0.239550	−	0.0871889i	−0.459005	+	0.888434i	$0.651794\pi$
$338$	−7.23880	−	2.63471i	−0.393739	−	0.143309i
$339$	−7.81941	−	32.8663i	−0.424692	−	1.78505i
$340$	11.4829	−	65.1228i	0.622748	−	3.53178i
$341$	3.23222	+	5.59837i	0.175034	+	0.303169i
$342$	1.45411	−	25.7312i	0.0786293	−	1.39138i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−24.6296	−	20.6667i	−1.32794	−	1.11427i
$345$	12.2099	+	9.07356i	0.657359	+	0.488504i
$346$	0.271236	+	1.53826i	0.0145818	+	0.0826973i
$347$	4.27014	−	3.58307i	0.229233	−	0.192349i	−0.520935	−	0.853596i	$-0.674417\pi$
$347$	4.27014	−	3.58307i	0.229233	−	0.192349i	0.750169	+	0.661247i	$0.229972\pi$
$348$	13.5740	−	27.0863i	0.727641	−	1.45198i
$349$	−5.14343	+	1.87206i	−0.275321	+	0.100209i	−0.475991	−	0.879450i	$-0.657911\pi$
$349$	−5.14343	+	1.87206i	−0.275321	+	0.100209i	0.200669	+	0.979659i	$0.435688\pi$
$350$	3.50881			0.187554
$351$	20.6830	+	3.59178i	1.10398	+	0.191715i
$352$	21.7929			1.16156
$353$	−5.94574	+	2.16407i	−0.316460	+	0.115182i	−0.495366	−	0.868684i	$-0.664966\pi$
$353$	−5.94574	+	2.16407i	−0.316460	+	0.115182i	0.178907	+	0.983866i	$0.442744\pi$
$354$	−17.9570	−	27.2510i	−0.954403	−	1.44838i
$355$	13.0581	−	10.9571i	0.693053	−	0.581540i
$356$	−0.120859	−	0.685426i	−0.00640552	−	0.0363275i
$357$	−1.53098	+	13.1971i	−0.0810280	+	0.698466i
$358$	−4.62846	−	3.88374i	−0.244621	−	0.205262i
$359$	−5.74065	+	9.94309i	−0.302980	+	0.524776i	−0.976809	−	0.214110i	$-0.931315\pi$
$359$	−5.74065	+	9.94309i	−0.302980	+	0.524776i	0.673830	+	0.738887i	$0.264648\pi$
$360$	−23.8182	−	5.60160i	−1.25533	−	0.295230i
$361$	2.63873	+	4.57041i	0.138880	+	0.240548i
$362$	−7.98581	+	45.2898i	−0.419725	+	2.38038i
$363$	14.9493	+	4.46146i	0.784633	+	0.234166i
$364$	−12.8244	−	4.66771i	−0.672183	−	0.244655i
$365$	−21.3900	−	7.78531i	−1.11960	−	0.407502i
$366$	−38.5678	−	11.5102i	−2.01597	−	0.601647i
$367$	0.0383426	−	0.217452i	0.00200147	−	0.0113509i	−0.983791	−	0.179321i	$-0.942610\pi$
$367$	0.0383426	−	0.217452i	0.00200147	−	0.0113509i	0.985792	+	0.167970i	$0.0537211\pi$
$368$	1.12747	+	1.95283i	0.0587734	+	0.101798i
$369$	−1.19507	−	0.281060i	−0.0622130	−	0.0146314i
$370$	0.319623	−	0.553604i	0.0166164	−	0.0287805i
$371$	0.731448	+	0.613758i	0.0379749	+	0.0318647i
$372$	−0.974440	+	8.39973i	−0.0505224	+	0.435506i
$373$	−0.280325	−	1.58980i	−0.0145147	−	0.0823168i	0.976690	−	0.214655i	$-0.0688627\pi$
$373$	−0.280325	−	1.58980i	−0.0145147	−	0.0823168i	−0.991205	+	0.132338i	$0.957752\pi$
$374$	−60.9510	+	51.1440i	−3.15170	+	2.64459i
$375$	−8.48096	−	12.8705i	−0.437955	−	0.664628i
$376$	−21.3659	+	7.77656i	−1.10186	+	0.401045i
$377$	20.9197			1.07742
$378$	11.8725	+	2.06177i	0.610657	+	0.106046i
$379$	−19.3433			−0.993597			−0.496799	−	0.867866i	$-0.665491\pi$
$379$	−19.3433			−0.993597			−0.496799	+	0.867866i	$0.665491\pi$
$380$	−30.0098	+	10.9227i	−1.53947	+	0.560322i
$381$	−1.94472	+	3.88060i	−0.0996309	+	0.198809i
$382$	14.9638	−	12.5561i	0.765615	−	0.642428i
$383$	2.14661	+	12.1740i	0.109687	+	0.622063i	0.989244	+	0.146271i	$0.0467273\pi$
$383$	2.14661	+	12.1740i	0.109687	+	0.622063i	−0.879558	+	0.475792i	$0.842162\pi$
$384$	27.1057	+	20.1431i	1.38323	+	1.02792i
$385$	−8.74456	−	7.33755i	−0.445664	−	0.373956i
$386$	3.81549	−	6.60862i	0.194203	−	0.336370i
$387$	−1.70288	+	30.1333i	−0.0865624	+	1.53176i
$388$	5.45768	+	9.45298i	0.277072	+	0.479902i
$389$	2.30403	−	13.0668i	0.116819	−	0.662514i	−0.869014	−	0.494787i	$-0.835246\pi$
$389$	2.30403	−	13.0668i	0.116819	−	0.662514i	0.985833	−	0.167727i	$-0.0536427\pi$
$390$	−9.58553	−	40.2896i	−0.485382	−	2.04014i
$391$	24.8055	+	9.02845i	1.25447	+	0.456588i
$392$	−3.00311	−	1.09304i	−0.151680	−	0.0552070i
$393$	24.4342	−	23.0924i	1.23254	−	1.16486i
$394$	1.30033	−	7.37456i	0.0655099	−	0.371525i
$395$	−2.25244	−	3.90135i	−0.113333	−	0.196298i
$396$	27.1317	+	36.3132i	1.36342	+	1.82481i
$397$	−0.821433	+	1.42276i	−0.0412265	+	0.0714065i	−0.885902	−	0.463872i	$-0.846460\pi$
$397$	−0.821433	+	1.42276i	−0.0412265	+	0.0714065i	0.844676	+	0.535278i	$0.179793\pi$
$398$	−15.3950	−	12.9179i	−0.771679	−	0.647516i
$399$	5.88926	−	2.54641i	0.294832	−	0.127480i
$400$	0.172152	+	0.976320i	0.00860758	+	0.0488160i
$401$	21.7787	−	18.2745i	1.08757	−	0.912584i	0.0910473	−	0.995847i	$-0.470979\pi$
$401$	21.7787	−	18.2745i	1.08757	−	0.912584i	0.996528	+	0.0832629i	$0.0265341\pi$
$402$	22.0384	−	1.30268i	1.09918	−	0.0649716i
$403$	−5.48665	+	1.99698i	−0.273310	+	0.0994766i
$404$	36.4669			1.81430
$405$	9.17014	+	21.0586i	0.455668	+	1.04641i
$406$	12.0084			0.595968
$407$	−0.453985	+	0.165237i	−0.0225032	+	0.00819050i
$408$	−42.3848	+	2.50534i	−2.09836	+	0.124033i
$409$	10.9716	−	9.20626i	0.542510	−	0.455220i	−0.329885	−	0.944021i	$-0.607010\pi$
$409$	10.9716	−	9.20626i	0.542510	−	0.455220i	0.872395	+	0.488801i	$0.162566\pi$
$410$	0.420570	+	2.38517i	0.0207705	+	0.117795i
$411$	−30.0280	+	12.9835i	−1.48117	+	0.640431i
$412$	27.5464	+	23.1142i	1.35711	+	1.13875i
$413$	4.06243	−	7.03633i	0.199899	−	0.346235i
$414$	9.44529	−	22.0010i	0.464211	−	1.08129i
$415$	−3.70303	−	6.41384i	−0.181775	−	0.314843i
$416$	−3.41803	+	19.3846i	−0.167583	+	0.950408i
$417$	−5.94540	+	5.61890i	−0.291147	+	0.275159i
$418$	36.1085	+	13.1424i	1.76612	+	0.642816i
$419$	−11.9677	−	4.35589i	−0.584661	−	0.212799i	0.0327188	−	0.999465i	$-0.489583\pi$
$419$	−11.9677	−	4.35589i	−0.584661	−	0.212799i	−0.617379	+	0.786666i	$0.711806\pi$
$420$	−3.45612	−	14.5266i	−0.168641	−	0.708827i
$421$	−2.42609	+	13.7590i	−0.118240	+	0.670573i	0.866855	+	0.498561i	$0.166138\pi$
$421$	−2.42609	+	13.7590i	−0.118240	+	0.670573i	−0.985095	+	0.172012i	$0.944973\pi$
$422$	29.3966	+	50.9164i	1.43101	+	2.47857i
$423$	17.8527	+	11.6978i	0.868027	+	0.568767i
$424$	−1.52576	+	2.64269i	−0.0740972	+	0.128340i
$425$	8.89041	+	7.45994i	0.431248	+	0.361860i
$426$	−21.5342	−	16.0028i	−1.04334	−	0.775336i
$427$	−1.74000	−	9.86800i	−0.0842043	−	0.477546i
$428$	22.2996	−	18.7116i	1.07789	−	0.904457i
$429$	−14.0230	+	27.9823i	−0.677037	+	1.35100i
$430$	55.9511	−	20.3645i	2.69820	−	0.982065i
$431$	−17.6553			−0.850424			−0.425212	−	0.905094i	$-0.639800\pi$
$431$	−17.6553			−0.850424			−0.425212	+	0.905094i	$0.639800\pi$
$432$	0.00881496	+	3.40467i	0.000424110	+	0.163807i
$433$	−6.10505			−0.293390			−0.146695	−	0.989182i	$-0.546864\pi$
$433$	−6.10505			−0.293390			−0.146695	+	0.989182i	$0.546864\pi$
$434$	−3.14947	+	1.14631i	−0.151179	+	0.0550248i
$435$	12.5941	+	19.1125i	0.603843	+	0.916375i
$436$	29.2833	−	24.5716i	1.40242	−	1.17677i
$437$	−2.21375	−	12.5548i	−0.105898	−	0.600576i
$438$	−4.12851	+	35.5880i	−0.197268	+	1.70046i
$439$	−14.9625	−	12.5550i	−0.714122	−	0.599220i	0.211630	−	0.977350i	$-0.432123\pi$
$439$	−14.9625	−	12.5550i	−0.714122	−	0.599220i	−0.925753	+	0.378130i	$0.876567\pi$
$440$	18.2406	−	31.5937i	0.869587	−	1.50617i
$441$	0.865369	+	2.87248i	0.0412080	+	0.136785i
$442$	−35.9326	−	62.2370i	−1.70914	−	2.96031i
$443$	1.87896	−	10.6561i	0.0892723	−	0.506288i	−0.907080	−	0.420957i	$-0.861694\pi$
$443$	1.87896	−	10.6561i	0.0892723	−	0.506288i	0.996353	−	0.0853308i	$-0.0271947\pi$
$444$	−0.605572	−	0.180727i	−0.0287392	−	0.00857693i
$445$	0.494103	+	0.179839i	0.0234227	+	0.00852517i
$446$	23.8864	+	8.69395i	1.13106	+	0.411671i
$447$	−36.9200	−	11.0184i	−1.74626	−	0.521153i
$448$	−2.18959	+	12.4178i	−0.103448	+	0.586685i
$449$	15.3098	+	26.5174i	0.722515	+	1.25143i	0.959989	+	0.280038i	$0.0903472\pi$
$449$	15.3098	+	26.5174i	0.722515	+	1.25143i	−0.237474	+	0.971394i	$0.576319\pi$
$450$	7.21044	−	7.66910i	0.339904	−	0.361525i
$451$	0.915221	−	1.58521i	0.0430961	−	0.0746446i
$452$	50.4741	+	42.3528i	2.37410	+	1.99211i
$453$	1.47817	−	12.7419i	0.0694505	−	0.598667i
$454$	−5.95235	−	33.7574i	−0.279358	−	1.58432i
$455$	7.89821	−	6.62739i	0.370274	−	0.310697i
$456$	11.2826	+	17.1221i	0.528354	+	0.801816i
$457$	31.2165	−	11.3619i	1.46025	−	0.531487i	0.514815	−	0.857301i	$-0.327861\pi$
$457$	31.2165	−	11.3619i	1.46025	−	0.531487i	0.945434	+	0.325815i	$0.105638\pi$
$458$	2.30815			0.107853
$459$	25.6985	+	30.4657i	1.19950	+	1.42202i
$460$	−29.6688			−1.38332
$461$	−16.1518	+	5.87876i	−0.752263	+	0.273801i	−0.689557	−	0.724231i	$-0.742195\pi$
$461$	−16.1518	+	5.87876i	−0.752263	+	0.273801i	−0.0627050	+	0.998032i	$0.519973\pi$
$462$	−8.04954	+	16.0625i	−0.374499	+	0.747296i
$463$	−0.0191481	+	0.0160672i	−0.000889888	+	0.000746705i	−0.643232	−	0.765671i	$-0.722407\pi$
$463$	−0.0191481	+	0.0160672i	−0.000889888	+	0.000746705i	0.642343	+	0.766418i	$0.277963\pi$
$464$	0.589165	+	3.34132i	0.0273513	+	0.155117i
$465$	−5.12755	−	3.81045i	−0.237785	−	0.176705i
$466$	35.4401	+	29.7378i	1.64173	+	1.37758i
$467$	−3.34044	+	5.78582i	−0.154577	+	0.267736i	−0.932905	−	0.360122i	$-0.882735\pi$
$467$	−3.34044	+	5.78582i	−0.154577	+	0.267736i	0.778328	+	0.627858i	$0.216068\pi$
$468$	−36.5557	+	18.4381i	−1.68979	+	0.852299i
$469$	2.74811	+	4.75986i	0.126896	+	0.219790i
$470$	7.31181	−	41.4673i	0.337269	−	1.91275i
$471$	−2.34656	−	9.86299i	−0.108124	−	0.454462i
$472$	24.3998	+	8.88081i	1.12309	+	0.408773i
$473$	−42.2860	−	15.3908i	−1.94431	−	0.707671i
$474$	−5.15312	+	4.87013i	−0.236691	+	0.223693i
$475$	0.973271	−	5.51969i	0.0446567	−	0.253261i
$476$	−12.9557	−	22.4399i	−0.593823	−	1.02853i
$477$	2.84456	−	0.337460i	0.130244	−	0.0154512i
$478$	−24.9625	+	43.2364i	−1.14176	+	1.97758i
$479$	−17.7209	−	14.8696i	−0.809690	−	0.679410i	0.140844	−	0.990032i	$-0.455018\pi$
$479$	−17.7209	−	14.8696i	−0.809690	−	0.679410i	−0.950534	+	0.310621i	$0.899463\pi$
$480$	−19.7677	+	8.54721i	−0.902269	+	0.390125i
$481$	−0.0757735	−	0.429733i	−0.00345497	−	0.0195941i
$482$	40.5666	−	34.0394i	1.84776	−	1.55045i
$483$	5.95036	−	0.351722i	0.270751	−	0.0160039i
$484$	−28.5918	+	10.4066i	−1.29963	+	0.473025i
$485$	−8.24632			−0.374446
$486$	28.9039	−	21.7126i	1.31111	−	0.984904i
$487$	−24.4633			−1.10854			−0.554270	−	0.832337i	$-0.687002\pi$
$487$	−24.4633			−1.10854			−0.554270	+	0.832337i	$0.687002\pi$
$488$	30.0919	−	10.9525i	1.36220	−	0.495798i
$489$	32.7801	−	1.93761i	1.48237	−	0.0876217i
$490$	4.53376	−	3.80428i	0.204814	−	0.171860i
$491$	1.45021	+	8.22453i	0.0654469	+	0.371168i	0.999887	+	0.0150470i	$0.00478980\pi$
$491$	1.45021	+	8.22453i	0.0654469	+	0.371168i	−0.934440	+	0.356121i	$0.884099\pi$
$492$	2.19774	−	0.950263i	0.0990818	−	0.0428412i
$493$	30.4262	+	25.5306i	1.37033	+	1.14984i
$494$	−17.3534	+	30.0569i	−0.780765	+	1.35233i
$495$	−34.0072	+	4.03438i	−1.52851	+	0.181332i
$496$	−0.473481	−	0.820094i	−0.0212599	−	0.0368233i
$497$	1.15986	−	6.57789i	0.0520268	−	0.295059i
$498$	−8.47176	+	8.00652i	−0.379629	+	0.358781i
$499$	27.3506	+	9.95481i	1.22438	+	0.445639i	0.871670	−	0.490093i	$-0.163037\pi$
$499$	27.3506	+	9.95481i	1.22438	+	0.445639i	0.352712	+	0.935732i	$0.385260\pi$
$500$	28.2485	+	10.2816i	1.26331	+	0.459807i
$501$	−1.43068	−	6.01340i	−0.0639182	−	0.268659i
$502$	3.69993	−	20.9833i	0.165136	−	0.936532i
$503$	−14.4215	−	24.9788i	−0.643023	−	1.11375i	−0.984754	−	0.173951i	$-0.944346\pi$
$503$	−14.4215	−	24.9788i	−0.643023	−	1.11375i	0.341731	−	0.939798i	$-0.388987\pi$
$504$	−8.56029	+	4.31766i	−0.381306	+	0.192324i
$505$	−13.7750	+	23.8590i	−0.612979	+	1.06171i
$506$	27.3464	+	22.9463i	1.21569	+	1.02009i
$507$	−4.61793	−	3.43173i	−0.205090	−	0.152409i
$508$	−1.47004	−	8.33703i	−0.0652227	−	0.369896i
$509$	10.5778	−	8.87582i	0.468853	−	0.393414i	−0.377523	−	0.926000i	$-0.623224\pi$
$509$	10.5778	−	8.87582i	0.468853	−	0.393414i	0.846376	+	0.532586i	$0.178780\pi$
$510$	35.2283	−	70.2965i	1.55994	−	3.11278i
$511$	−8.38144	+	3.05059i	−0.370773	+	0.134950i
$512$	−7.38042			−0.326172
$513$	6.53656	−	18.1048i	0.288596	−	0.799344i
$514$	−36.6359			−1.61594
$515$	−25.5281	+	9.29147i	−1.12490	+	0.409431i
$516$	−32.3886	−	49.1520i	−1.42583	−	2.16380i
$517$	−24.3779	+	20.4555i	−1.07214	+	0.899632i
$518$	−0.0434958	−	0.246677i	−0.00191109	−	0.0108384i
$519$	−0.134435	+	1.15884i	−0.00590104	+	0.0508673i
$520$	25.2414	+	21.1801i	1.10691	+	0.928808i
$521$	12.8577	−	22.2703i	0.563308	−	0.975679i	−0.433897	−	0.900963i	$-0.642862\pi$
$521$	12.8577	−	22.2703i	0.563308	−	0.975679i	0.997205	−	0.0747158i	$-0.0238050\pi$
$522$	24.6768	−	26.2464i	1.08007	−	1.14878i
$523$	16.6189	+	28.7848i	0.726695	+	1.25867i	0.958273	+	0.285856i	$0.0922778\pi$
$523$	16.6189	+	28.7848i	0.726695	+	1.25867i	−0.231578	+	0.972816i	$0.574389\pi$
$524$	−11.3861	+	64.5736i	−0.497403	+	2.82091i
$525$	2.51119	+	0.749440i	0.109597	+	0.0327082i
$526$	25.0773	+	9.12741i	1.09342	+	0.397974i
$527$	−10.4171	−	3.79150i	−0.453775	−	0.165161i
$528$	−4.86430	−	1.45170i	−0.211691	−	0.0631772i
$529$	−1.93731	+	10.9870i	−0.0842307	+	0.477696i
$530$	−2.82556	−	4.89401i	−0.122734	−	0.212582i
$531$	−7.03100	−	23.3385i	−0.305119	−	1.01280i
$532$	−6.25686	+	10.8372i	−0.271269	+	0.469852i
$533$	1.26649	+	1.06271i	0.0548577	+	0.0460310i
$534$	0.0953676	−	0.822074i	0.00412696	−	0.0355746i
$535$	3.81887	+	21.6579i	0.165104	+	0.936353i
$536$	−13.4556	+	11.2906i	−0.581194	+	0.487679i
$537$	−2.48298	−	3.76810i	−0.107149	−	0.162606i
$538$	−9.14758	+	3.32945i	−0.394380	+	0.143543i
$539$	−4.47293			−0.192663
$540$	−38.8526	−	22.2976i	−1.67195	−	0.959538i
$541$	−2.71988			−0.116937			−0.0584684	−	0.998289i	$-0.518622\pi$
$541$	−2.71988			−0.116937			−0.0584684	+	0.998289i	$0.518622\pi$
$542$	−67.2568	+	24.4795i	−2.88893	+	1.05148i
$543$	−15.3887	+	30.7074i	−0.660391	+	1.31778i
$544$	−28.6284	+	24.0221i	−1.22743	+	1.02994i
$545$	5.01487	+	28.4407i	0.214813	+	1.21827i
$546$	−13.0250	−	9.67928i	−0.557418	−	0.414235i
$547$	15.1065	+	12.6758i	0.645906	+	0.541979i	0.905826	−	0.423651i	$-0.139252\pi$
$547$	15.1065	+	12.6758i	0.645906	+	0.541979i	−0.259920	+	0.965630i	$0.583696\pi$
$548$	31.9022	−	55.2563i	1.36280	−	2.36043i
$549$	−25.1438	−	16.4753i	−1.07311	−	0.703147i
$550$	7.84733	+	13.5920i	0.334611	+	0.579564i
$551$	3.33089	−	18.8904i	0.141901	−	0.804758i
$552$	4.40914	+	18.5323i	0.187665	+	0.788789i
$553$	−1.65874	−	0.603732i	−0.0705368	−	0.0256733i
$554$	39.0103	+	14.1986i	1.65739	+	0.603241i
$555$	0.346992	−	0.327936i	0.0147290	−	0.0139201i
$556$	2.77049	−	15.7122i	0.117495	−	0.666346i
$557$	−0.308176	−	0.533777i	−0.0130578	−	0.0226168i	0.859423	−	0.511266i	$-0.170823\pi$
$557$	−0.308176	−	0.533777i	−0.0130578	−	0.0226168i	−0.872480	+	0.488649i	$0.837490\pi$
$558$	−3.96656	+	9.23933i	−0.167918	+	0.391132i
$559$	20.3222	−	35.1991i	0.859539	−	1.48877i
$560$	1.28097	+	1.07486i	0.0541310	+	0.0454213i
$561$	−54.5453	+	23.5844i	−2.30291	+	0.995735i
$562$	−10.0718	−	57.1202i	−0.424855	−	2.40947i
$563$	−4.82027	+	4.04469i	−0.203150	+	0.170463i	−0.738687	−	0.674049i	$-0.764554\pi$
$563$	−4.82027	+	4.04469i	−0.203150	+	0.170463i	0.535537	+	0.844512i	$0.320109\pi$
$564$	−41.5549	+	2.45628i	−1.74978	+	0.103428i
$565$	−46.7760	+	17.0251i	−1.96788	+	0.716250i
$566$	−63.6712			−2.67630
$567$	8.05659	+	4.01140i	0.338345	+	0.168463i
$568$	21.3462			0.895667
$569$	−21.0052	+	7.64527i	−0.880585	+	0.320507i	−0.742446	−	0.669906i	$-0.766334\pi$
$569$	−21.0052	+	7.64527i	−0.880585	+	0.320507i	−0.138139	+	0.990413i	$0.544112\pi$
$570$	−37.9075	+	2.24069i	−1.58777	+	0.0938521i
$571$	−32.5855	+	27.3425i	−1.36366	+	1.14425i	−0.388826	+	0.921311i	$0.627119\pi$
$571$	−32.5855	+	27.3425i	−1.36366	+	1.14425i	−0.974833	+	0.222935i	$0.928436\pi$
$572$	−10.6002	−	60.1169i	−0.443218	−	2.51361i
$573$	13.3912	−	5.79010i	0.559424	−	0.241885i
$574$	0.726994	+	0.610020i	0.0303441	+	0.0254618i
$575$	2.60349	−	4.50938i	0.108573	−	0.188054i
$576$	22.6417	+	30.3037i	0.943402	+	1.26265i
$577$	9.42057	+	16.3169i	0.392184	+	0.679282i	0.992737	−	0.120303i	$-0.0383865\pi$
$577$	9.42057	+	16.3169i	0.392184	+	0.679282i	−0.600554	+	0.799584i	$0.705053\pi$
$578$	16.8474	−	95.5465i	0.700760	−	3.97421i
$579$	4.14220	−	3.91472i	0.172144	−	0.162690i
$580$	−41.9487	−	15.2681i	−1.74183	−	0.633973i
$581$	−2.72698	−	0.992539i	−0.113134	−	0.0411775i
$582$	3.00407	+	12.6266i	0.124523	+	0.523390i
$583$	−0.741638	+	4.20604i	−0.0307155	+	0.174196i
$584$	−14.2524	−	24.6859i	−0.589769	−	1.02151i
$585$	1.74519	−	30.8819i	0.0721545	−	1.27681i
$586$	−5.90816	+	10.2332i	−0.244064	+	0.422731i
$587$	3.29450	+	2.76442i	0.135979	+	0.114100i	0.708240	−	0.705971i	$-0.249489\pi$
$587$	3.29450	+	2.76442i	0.135979	+	0.114100i	−0.572262	+	0.820071i	$0.693934\pi$
$588$	−4.69623	−	3.48992i	−0.193669	−	0.143922i
$589$	0.929664	+	5.27239i	0.0383061	+	0.217245i
$590$	−36.8361	+	30.9092i	−1.51652	+	1.27251i
$591$	2.50574	−	5.00010i	0.103073	−	0.205677i
$592$	0.0665034	−	0.0242053i	0.00273327	−	0.000994830i
$593$	15.8693			0.651674			0.325837	−	0.945426i	$-0.394354\pi$
$593$	15.8693			0.651674			0.325837	+	0.945426i	$0.394354\pi$
$594$	18.5659	+	50.6014i	0.761769	+	2.07620i
$595$	19.5755			0.802517
$596$	70.6128	−	25.7010i	2.89241	−	1.05275i
$597$	−8.25878	−	12.5333i	−0.338009	−	0.512953i
$598$	−24.6997	+	20.7255i	−1.01004	+	0.847527i
$599$	−8.17509	−	46.3632i	−0.334025	−	1.89435i	−0.436653	−	0.899630i	$-0.643836\pi$
$599$	−8.17509	−	46.3632i	−0.334025	−	1.89435i	0.102629	−	0.994720i	$-0.467275\pi$
$600$	−0.965116	+	8.31935i	−0.0394007	+	0.339636i
$601$	−19.7117	−	16.5401i	−0.804059	−	0.674685i	0.145123	−	0.989414i	$-0.453642\pi$
$601$	−19.7117	−	16.5401i	−0.804059	−	0.674685i	−0.949182	+	0.314728i	$0.898087\pi$
$602$	11.6654	−	20.2051i	0.475448	−	0.823500i
$603$	16.0507	+	3.77485i	0.653636	+	0.153724i
$604$	12.5088	+	21.6659i	0.508976	+	0.881572i
$605$	3.99161	−	22.6375i	0.162282	−	0.920347i
$606$	41.5506	+	12.4004i	1.68788	+	0.503730i
$607$	−20.2281	−	7.36244i	−0.821035	−	0.298832i	−0.102861	−	0.994696i	$-0.532800\pi$
$607$	−20.2281	−	7.36244i	−0.821035	−	0.298832i	−0.718174	+	0.695864i	$0.755022\pi$
$608$	16.9600	+	6.17292i	0.687817	+	0.250345i
$609$	8.59421	+	2.56486i	0.348255	+	0.103933i
$610$	−10.2980	+	58.4028i	−0.416954	+	2.36466i
$611$	−14.3715	−	24.8922i	−0.581410	−	1.00703i
$612$	−75.6696	−	17.7961i	−3.05876	−	0.719366i
$613$	17.9589	−	31.1057i	0.725352	−	1.25635i	−0.233477	−	0.972362i	$-0.575010\pi$
$613$	17.9589	−	31.1057i	0.725352	−	1.25635i	0.958829	−	0.283984i	$-0.0916562\pi$
$614$	−10.6801	−	8.96171i	−0.431016	−	0.361665i
$615$	−0.208450	+	1.79685i	−0.00840553	+	0.0724561i
$616$	−2.48227	−	14.0776i	−0.100013	−	0.567204i
$617$	−12.6717	+	10.6328i	−0.510142	+	0.428060i	−0.861179	−	0.508301i	$-0.830274\pi$
$617$	−12.6717	+	10.6328i	−0.510142	+	0.428060i	0.351037	+	0.936362i	$0.385829\pi$
$618$	23.5266	+	35.7033i	0.946380	+	1.43620i
$619$	23.9796	−	8.72786i	0.963822	−	0.350802i	0.188292	−	0.982113i	$-0.439705\pi$
$619$	23.9796	−	8.72786i	0.963822	−	0.350802i	0.775530	+	0.631311i	$0.217483\pi$
$620$	12.4594			0.500384
$621$	11.4590	−	13.7283i	0.459833	−	0.550898i
$622$	−19.9296			−0.799105
$623$	0.193609	−	0.0704679i	0.00775678	−	0.00282324i
$624$	2.05420	−	4.09907i	0.0822339	−	0.164094i
$625$	−23.1927	+	19.4610i	−0.927707	+	0.778438i
$626$	−1.84151	−	10.4437i	−0.0736017	−	0.417416i
$627$	23.0351	+	17.1181i	0.919934	+	0.683632i
$628$	15.1470	+	12.7099i	0.604432	+	0.507178i
$629$	0.414243	−	0.717490i	0.0165169	−	0.0286082i
$630$	1.00178	−	17.7269i	0.0399118	−	0.706258i
$631$	−2.50872	−	4.34523i	−0.0998707	−	0.172981i	0.811760	−	0.583991i	$-0.198510\pi$
$631$	−2.50872	−	4.34523i	−0.0998707	−	0.172981i	−0.911631	+	0.411010i	$0.865176\pi$
$632$	0.979600	−	5.55558i	0.0389664	−	0.220989i
$633$	10.1635	+	42.7188i	0.403962	+	1.69792i
$634$	47.6303	+	17.3360i	1.89164	+	0.688501i
$635$	6.00991	+	2.18743i	0.238496	+	0.0868055i
$636$	−4.06034	+	3.83736i	−0.161003	+	0.152161i
$637$	0.701542	−	3.97864i	0.0277961	−	0.157640i
$638$	26.8564	+	46.5167i	1.06326	+	1.84161i
$639$	−11.9936	−	16.0523i	−0.474461	−	0.635021i
$640$	24.8795	−	43.0926i	0.983449	−	1.70338i
$641$	11.6750	+	9.79652i	0.461136	+	0.386939i	0.843549	−	0.537052i	$-0.180462\pi$
$641$	11.6750	+	9.79652i	0.461136	+	0.386939i	−0.382413	+	0.923992i	$0.624907\pi$
$642$	31.7710	−	13.7372i	1.25390	−	0.542164i
$643$	4.21887	+	23.9264i	0.166376	+	0.943564i	0.947635	+	0.319357i	$0.103467\pi$
$643$	4.21887	+	23.9264i	0.166376	+	0.943564i	−0.781259	+	0.624207i	$0.785422\pi$
$644$	−8.90560	+	7.47268i	−0.350930	+	0.294465i
$645$	44.3928	−	2.62403i	1.74797	−	0.103321i
$646$	−61.9210	+	22.5374i	−2.43625	+	0.886722i
$647$	2.80833			0.110407			0.0552035	−	0.998475i	$-0.482419\pi$
$647$	2.80833			0.110407			0.0552035	+	0.998475i	$0.482419\pi$
$648$	−8.15404	+	27.5826i	−0.320321	+	1.08355i
$649$	36.3419			1.42655
$650$	−13.3208	+	4.84836i	−0.522483	+	0.190168i
$651$	−2.49886	+	0.147706i	−0.0979380	+	0.00578905i
$652$	−49.0602	+	41.1664i	−1.92135	+	1.61220i
$653$	2.07701	+	11.7793i	0.0812796	+	0.460959i	0.998098	+	0.0616540i	$0.0196375\pi$
$653$	2.07701	+	11.7793i	0.0812796	+	0.460959i	−0.916818	+	0.399305i	$0.869251\pi$
$654$	41.7210	−	18.0394i	1.63142	−	0.705397i
$655$	−37.9472	−	31.8415i	−1.48272	−	1.24415i
$656$	−0.134069	+	0.232214i	−0.00523451	+	0.00906644i
$657$	−10.5559	+	24.5879i	−0.411824	+	0.959265i
$658$	−8.24961	−	14.2887i	−0.321603	−	0.557033i
$659$	0.597709	−	3.38978i	0.0232834	−	0.132047i	−0.970950	−	0.239281i	$-0.923088\pi$
$659$	0.597709	−	3.38978i	0.0232834	−	0.132047i	0.994234	+	0.107234i	$0.0341994\pi$
$660$	48.5419	−	45.8762i	1.88949	−	1.78573i
$661$	−36.5270	−	13.2947i	−1.42073	−	0.517105i	−0.486474	−	0.873695i	$-0.661717\pi$
$661$	−36.5270	−	13.2947i	−1.42073	−	0.517105i	−0.934261	+	0.356590i	$0.883939\pi$
$662$	−20.8817	−	7.60033i	−0.811591	−	0.295395i
$663$	−12.4232	−	52.2167i	−0.482477	−	2.02793i
$664$	1.61047	−	9.13341i	0.0624982	−	0.354445i
$665$	−4.72692	−	8.18727i	−0.183302	−	0.317489i
$666$	−0.628536	−	0.411842i	−0.0243553	−	0.0159586i
$667$	8.91010	−	15.4327i	0.345000	−	0.597558i
$668$	9.23503	+	7.74911i	0.357314	+	0.299822i
$669$	15.2382	+	11.3240i	0.589142	+	0.437810i
$670$	−5.64857	−	32.0347i	−0.218223	−	1.23761i
$671$	34.3340	−	28.8096i	1.32545	−	1.11218i
$672$	−3.78083	+	7.54448i	−0.145849	+	0.291035i
$673$	30.2329	−	11.0039i	1.16539	−	0.424168i	0.314372	−	0.949300i	$-0.398206\pi$
$673$	30.2329	−	11.0039i	1.16539	−	0.424168i	0.851021	+	0.525132i	$0.175984\pi$
$674$	10.8527			0.418030
$675$	6.79841	−	3.94857i	0.261671	−	0.151981i
$676$	11.2211			0.431582
$677$	−31.8651	+	11.5980i	−1.22468	+	0.445745i	−0.871771	−	0.489914i	$-0.837028\pi$
$677$	−31.8651	+	11.5980i	−1.22468	+	0.445745i	−0.352905	+	0.935659i	$0.614806\pi$
$678$	43.1086	+	65.4204i	1.65558	+	2.51246i
$679$	−2.47527	+	2.07700i	−0.0949922	+	0.0797079i
$680$	10.8635	+	61.6098i	0.416595	+	2.36263i
$681$	2.95021	−	25.4309i	0.113052	−	0.974516i
$682$	−11.4841	−	9.63633i	−0.439750	−	0.368994i
$683$	−1.81643	+	3.14615i	−0.0695038	+	0.120384i	−0.898683	−	0.438599i	$-0.855475\pi$
$683$	−1.81643	+	3.14615i	−0.0695038	+	0.120384i	0.829179	+	0.558983i	$0.188808\pi$
$684$	10.8290	+	35.9454i	0.414057	+	1.37441i
$685$	24.1015	+	41.7450i	0.920870	+	1.59499i
$686$	0.402702	−	2.28384i	0.0153752	−	0.0871972i
$687$	1.65190	+	0.492993i	0.0630238	+	0.0188089i
$688$	6.19439	+	2.25457i	0.236159	+	0.0859548i
$689$	−3.62492	−	1.31936i	−0.138098	−	0.0502637i
$690$	−33.8048	−	10.0887i	−1.28693	−	0.384071i
$691$	3.24911	−	18.4266i	0.123602	−	0.700982i	−0.858526	−	0.512770i	$-0.828619\pi$
$691$	3.24911	−	18.4266i	0.123602	−	0.700982i	0.982128	−	0.188213i	$-0.0602694\pi$
$692$	−1.13764	−	1.97044i	−0.0432464	−	0.0749050i
$693$	−9.19168	+	9.77636i	−0.349163	+	0.371373i
$694$	−6.46356	+	11.1952i	−0.245353	+	0.424964i
$695$	9.23341	+	7.74775i	0.350243	+	0.293889i
$696$	−3.30298	+	28.4718i	−0.125199	+	1.07922i
$697$	0.545074	+	3.09127i	0.0206461	+	0.117090i
$698$	9.72376	−	8.15921i	0.368050	−	0.308830i
$699$	19.0122	+	28.8524i	0.719107	+	1.09130i
$700$	−4.80287	+	1.74810i	−0.181531	+	0.0660721i
$701$	6.33482			0.239263			0.119631	−	0.992818i	$-0.461829\pi$
$701$	6.33482			0.239263			0.119631	+	0.992818i	$0.461829\pi$
$702$	−47.9215	+	8.57784i	−1.80868	+	0.323750i
$703$	−0.400111			−0.0150905
$704$	−52.9993	+	19.2902i	−1.99749	+	0.727026i
$705$	14.0899	−	28.1157i	0.530655	−	1.05890i
$706$	11.2405	−	9.43193i	0.423043	−	0.354976i
$707$	1.87456	+	10.6312i	0.0705002	+	0.399827i
$708$	38.1562	+	28.3551i	1.43400	+	1.06565i
$709$	−20.6505	−	17.3278i	−0.775545	−	0.650760i	0.166577	−	0.986028i	$-0.446728\pi$
$709$	−20.6505	−	17.3278i	−0.775545	−	0.650760i	−0.942123	+	0.335269i	$0.891173\pi$
$710$	−19.7656	+	34.2350i	−0.741790	+	1.28482i
$711$	−4.72820	+	2.38482i	−0.177321	+	0.0894377i
$712$	0.329227	+	0.570238i	0.0123383	+	0.0213706i
$713$	−0.863672	+	4.89813i	−0.0323448	+	0.183436i
$714$	−7.13121	−	29.9736i	−0.266879	−	1.12173i
$715$	43.3364	+	15.7732i	1.62069	+	0.589883i
$716$	8.27035	+	3.01016i	0.309077	+	0.112495i
$717$	−27.1000	+	25.6118i	−1.01207	+	0.956489i
$718$	4.62354	−	26.2214i	0.172549	−	0.978573i
$719$	−0.400043	−	0.692895i	−0.0149191	−	0.0258406i	0.858469	−	0.512865i	$-0.171416\pi$
$719$	−0.400043	−	0.692895i	−0.0149191	−	0.0258406i	−0.873389	+	0.487024i	$0.838082\pi$
$720$	4.98164	−	0.590988i	0.185655	−	0.0220248i
$721$	−5.32245	+	9.21875i	−0.198218	+	0.343324i
$722$	−9.37544	−	7.86693i	−0.348918	−	0.292777i
$723$	36.3032	−	15.6968i	1.35013	−	0.583772i
$724$	−11.6325	−	65.9714i	−0.432320	−	2.45181i
$725$	6.00167	−	5.03600i	0.222897	−	0.187032i
$726$	−36.1163	+	2.13481i	−1.34040	+	0.0792302i
$727$	30.4435	−	11.0805i	1.12909	−	0.410954i	0.291125	−	0.956685i	$-0.405970\pi$
$727$	30.4435	−	11.0805i	1.12909	−	0.410954i	0.837960	+	0.545731i	$0.183748\pi$
$728$	12.9113			0.478523
$729$	25.3235	−	9.36580i	0.937909	−	0.346881i
$730$	52.7883			1.95378
$731$	72.5146	−	26.3931i	2.68205	−	0.976186i
$732$	58.5262	−	3.45944i	2.16319	−	0.127865i
$733$	28.9143	−	24.2619i	1.06797	−	0.896135i	0.0731053	−	0.997324i	$-0.476709\pi$
$733$	28.9143	−	24.2619i	1.06797	−	0.896135i	0.994867	+	0.101189i	$0.0322646\pi$
$734$	0.0889191	+	0.504285i	0.00328206	+	0.0186135i
$735$	4.05728	−	1.75429i	0.149655	−	0.0647081i
$736$	12.8445	+	10.7778i	0.473453	+	0.397274i
$737$	−12.2921	+	21.2905i	−0.452785	+	0.784247i
$738$	2.82724	−	0.335405i	0.104072	−	0.0123464i
$739$	−11.3590	−	19.6744i	−0.417847	−	0.723733i	0.577875	−	0.816125i	$-0.303882\pi$
$739$	−11.3590	−	19.6744i	−0.417847	−	0.723733i	−0.995723	+	0.0923921i	$0.970549\pi$
$740$	−0.161694	+	0.917013i	−0.00594399	+	0.0337101i
$741$	−18.8393	+	17.8047i	−0.692079	+	0.654073i
$742$	−2.08079	−	0.757346i	−0.0763882	−	0.0278030i
$743$	−47.5117	−	17.2928i	−1.74304	−	0.634413i	−0.743620	−	0.668602i	$-0.766893\pi$
$743$	−47.5117	−	17.2928i	−1.74304	−	0.634413i	−0.999415	+	0.0341890i	$0.989115\pi$
$744$	−1.85162	−	7.78267i	−0.0678837	−	0.285326i
$745$	−9.85803	+	55.9077i	−0.361170	+	2.04830i
$746$	1.87187	+	3.24217i	0.0685339	+	0.118704i
$747$	−7.77319	+	3.92066i	−0.284406	+	0.143449i
$748$	57.9499	−	100.372i	2.11886	−	3.66997i
$749$	6.60127	+	5.53912i	0.241205	+	0.202395i
$750$	28.6902	+	21.3206i	1.04762	+	0.778519i
$751$	7.83162	+	44.4153i	0.285780	+	1.62074i	0.702487	+	0.711697i	$0.252073\pi$
$751$	7.83162	+	44.4153i	0.285780	+	1.62074i	−0.416707	+	0.909041i	$0.636816\pi$
$752$	3.57107	−	2.99648i	0.130224	−	0.109271i
$753$	7.12976	−	14.2271i	0.259823	−	0.518465i
$754$	−45.5885	+	16.5928i	−1.66023	+	0.604276i
$755$	−18.9003			−0.687851
$756$	−17.2784	+	3.09279i	−0.628408	+	0.112484i
$757$	−1.81010			−0.0657893			−0.0328946	−	0.999459i	$-0.510473\pi$
$757$	−1.81010			−0.0657893			−0.0328946	+	0.999459i	$0.510473\pi$
$758$	42.1531	−	15.3425i	1.53107	−	0.557263i
$759$	14.6702	+	22.2631i	0.532496	+	0.808101i
$760$	23.1445	−	19.4206i	0.839540	−	0.704458i
$761$	6.55375	+	37.1682i	0.237573	+	1.34734i	0.837126	+	0.547010i	$0.184234\pi$
$761$	6.55375	+	37.1682i	0.237573	+	1.34734i	−0.599553	+	0.800335i	$0.704655\pi$
$762$	1.15998	−	9.99913i	0.0420218	−	0.362230i
$763$	8.66865	+	7.27387i	0.313826	+	0.263332i
$764$	−14.2270	+	24.6419i	−0.514716	+	0.891514i
$765$	40.2268	−	42.7856i	1.45440	−	1.54692i
$766$	−14.3339	−	24.8271i	−0.517907	−	0.897040i
$767$	−5.69992	+	32.3259i	−0.205812	+	1.16722i
$768$	−33.1902	−	9.90528i	−1.19765	−	0.357426i
$769$	−24.1528	−	8.79090i	−0.870972	−	0.317008i	−0.132411	−	0.991195i	$-0.542272\pi$
$769$	−24.1528	−	8.79090i	−0.870972	−	0.317008i	−0.738561	+	0.674187i	$0.764494\pi$
$770$	24.8761	+	9.05417i	0.896474	+	0.326290i
$771$	−26.2196	−	7.82499i	−0.944277	−	0.281810i
$772$	−1.93022	+	10.9468i	−0.0694700	+	0.393984i
$773$	26.4553	+	45.8219i	0.951530	+	1.64810i	0.742117	+	0.670270i	$0.233822\pi$
$773$	26.4553	+	45.8219i	0.951530	+	1.64810i	0.209412	+	0.977827i	$0.432845\pi$
$774$	−20.1898	−	67.0175i	−0.725709	−	2.40889i
$775$	−1.09334	+	1.89372i	−0.0392739	+	0.0680243i
$776$	−7.91058	−	6.63777i	−0.283973	−	0.238282i
$777$	0.0215581	−	0.185832i	0.000773394	−	0.00666670i
$778$	5.34320	+	30.3028i	0.191563	+	1.08641i
$779$	1.16127	−	0.974425i	0.0416070	−	0.0349124i
$780$	33.1932	+	50.3730i	1.18851	+	1.80364i
$781$	28.0746	−	10.2183i	1.00459	−	0.365640i
$782$	−61.2174			−2.18913
$783$	23.2666	−	13.5134i	0.831482	−	0.482931i
$784$	0.655231			0.0234011
$785$	−14.0372	+	5.10913i	−0.501010	+	0.182353i
$786$	−34.9312	+	69.7037i	−1.24595	+	2.48625i
$787$	−3.50781	+	2.94340i	−0.125040	+	0.104921i	−0.703163	−	0.711028i	$-0.748230\pi$
$787$	−3.50781	+	2.94340i	−0.125040	+	0.104921i	0.578123	+	0.815949i	$0.303785\pi$
$788$	1.89413	+	10.7422i	0.0674757	+	0.382674i
$789$	15.9979	+	11.8885i	0.569540	+	0.423244i
$790$	8.00297	+	6.71529i	0.284733	+	0.238919i
$791$	−9.75250	+	16.8918i	−0.346759	+	0.600604i
$792$	−35.8700	−	23.5035i	−1.27459	−	0.835160i
$793$	20.2410	+	35.0584i	0.718778	+	1.24496i
$794$	0.661585	−	3.75204i	0.0234788	−	0.133155i
$795$	−0.976897	−	4.10606i	−0.0346470	−	0.145627i
$796$	27.5084	+	10.0123i	0.975011	+	0.354875i
$797$	35.0935	+	12.7730i	1.24307	+	0.452442i	0.878056	−	0.478558i	$-0.158841\pi$
$797$	35.0935	+	12.7730i	1.24307	+	0.452442i	0.365018	+	0.931000i	$0.381063\pi$
$798$	−10.8142	+	10.2203i	−0.382819	+	0.361796i
$799$	9.47636	−	53.7431i	0.335250	−	1.90130i
$800$	3.68585	+	6.38408i	0.130315	+	0.225711i
$801$	0.243838	−	0.567974i	0.00861560	−	0.0200684i
$802$	−32.9656	+	57.0981i	−1.16406	+	2.01620i
$803$	−30.5618	−	25.6444i	−1.07850	−	0.904971i
$804$	−29.5173	+	12.7627i	−1.04099	+	0.450107i
$805$	−1.52511	−	8.64934i	−0.0537531	−	0.304849i
$806$	10.3726	−	8.70367i	0.365361	−	0.306574i
$807$	−7.25789	+	0.429009i	−0.255490	+	0.0151018i
$808$	−32.4191	+	11.7996i	−1.14050	+	0.415109i
$809$	27.8125			0.977834			0.488917	−	0.872330i	$-0.337392\pi$
$809$	27.8125			0.977834			0.488917	+	0.872330i	$0.337392\pi$
$810$	−36.6866	−	38.6176i	−1.28904	−	1.35688i
$811$	5.53720			0.194438			0.0972188	−	0.995263i	$-0.469005\pi$
$811$	5.53720			0.194438			0.0972188	+	0.995263i	$0.469005\pi$
$812$	−16.4372	+	5.98264i	−0.576832	+	0.209950i
$813$	−53.3630	+	3.15425i	−1.87152	+	0.110624i
$814$	0.858269	−	0.720173i	0.0300823	−	0.0252420i
$815$	−8.40172	−	47.6485i	−0.294299	−	1.66905i
$816$	7.99024	−	3.45483i	0.279714	−	0.120943i
$817$	−28.5489	−	23.9554i	−0.998800	−	0.838092i
$818$	−16.6073	+	28.7647i	−0.580661	+	1.00573i
$819$	−7.25437	−	9.70927i	−0.253488	−	0.339269i
$820$	−1.76398	−	3.05531i	−0.0616009	−	0.106696i
$821$	5.62176	−	31.8826i	0.196201	−	1.11271i	−0.714498	−	0.699638i	$-0.753345\pi$
$821$	5.62176	−	31.8826i	0.196201	−	1.11271i	0.910698	−	0.413072i	$-0.135544\pi$
$822$	55.1391	−	52.1111i	1.92320	−	1.81758i
$823$	8.28465	+	3.01537i	0.288785	+	0.105109i	0.482351	−	0.875978i	$-0.339783\pi$
$823$	8.28465	+	3.01537i	0.288785	+	0.105109i	−0.193566	+	0.981087i	$0.562005\pi$
$824$	−31.9678	−	11.6353i	−1.11365	−	0.405336i
$825$	2.71311	+	11.4036i	0.0944582	+	0.397023i
$826$	−3.27189	+	18.5558i	−0.113844	+	0.645640i
$827$	−12.9449	−	22.4213i	−0.450140	−	0.779665i	0.548254	−	0.836312i	$-0.315293\pi$
$827$	−12.9449	−	22.4213i	−0.450140	−	0.779665i	−0.998394	+	0.0566464i	$0.981959\pi$
$828$	−1.96778	+	34.8207i	−0.0683850	+	1.21010i
$829$	8.46182	−	14.6563i	0.293891	−	0.509034i	−0.680835	−	0.732437i	$-0.738383\pi$
$829$	8.46182	−	14.6563i	0.293891	−	0.509034i	0.974726	+	0.223402i	$0.0717164\pi$
$830$	13.1569	+	11.0400i	0.456684	+	0.383203i
$831$	24.8863	+	18.4938i	0.863297	+	0.641544i
$832$	−8.84598	−	50.1680i	−0.306679	−	1.73926i
$833$	5.87591	−	4.93048i	0.203588	−	0.170831i
$834$	8.49954	−	16.9605i	0.294315	−	0.587293i
$835$	−8.55840	+	3.11500i	−0.296176	+	0.107799i
$836$	−55.9730			−1.93587
$837$	−4.81221	+	5.76521i	−0.166334	+	0.199275i
$838$	29.5351			1.02027
$839$	−2.45064	+	0.891958i	−0.0846053	+	0.0307938i	−0.383976	−	0.923343i	$-0.625445\pi$
$839$	−2.45064	+	0.891958i	−0.0846053	+	0.0307938i	0.299371	+	0.954137i	$0.403223\pi$
$840$	7.77288	+	11.7959i	0.268190	+	0.406997i
$841$	−1.67537	+	1.40580i	−0.0577715	+	0.0484760i
$842$	−5.62625	−	31.9081i	−0.193894	−	1.09962i
$843$	4.99198	−	43.0311i	0.171933	−	1.48207i
$844$	−65.6050	−	55.0492i	−2.25822	−	1.89487i
$845$	−4.23866	+	7.34157i	−0.145814	+	0.252558i
$846$	−48.1831	−	11.3318i	−1.65657	−	0.389595i
$847$	−4.50357	−	7.80040i	−0.154744	−	0.268025i
$848$	0.108641	−	0.616134i	0.00373075	−	0.0211581i
$849$	−45.5684	−	13.5994i	−1.56390	−	0.466731i
$850$	−25.2910	−	9.20519i	−0.867476	−	0.315735i
$851$	−0.349293	−	0.127132i	−0.0119736	−	0.00435803i
$852$	37.4488	+	11.1762i	1.28297	+	0.382891i
$853$	8.03383	−	45.5621i	0.275073	−	1.56002i	−0.463656	−	0.886015i	$-0.653463\pi$
$853$	8.03383	−	45.5621i	0.275073	−	1.56002i	0.738729	−	0.674002i	$-0.235426\pi$
$854$	11.6188	+	20.1243i	0.397587	+	0.688641i
$855$	−27.6083	−	6.49298i	−0.944184	−	0.222055i
$856$	−13.7698	+	23.8501i	−0.470644	+	0.815179i
$857$	−0.712255	−	0.597653i	−0.0243302	−	0.0204154i	0.630541	−	0.776156i	$-0.282833\pi$
$857$	−0.712255	−	0.597653i	−0.0243302	−	0.0204154i	−0.654872	+	0.755740i	$0.727277\pi$
$858$	8.36444	−	72.1019i	0.285557	−	2.46152i
$859$	2.96481	+	16.8143i	0.101158	+	0.573696i	0.992685	+	0.120729i	$0.0385233\pi$
$859$	2.96481	+	16.8143i	0.101158	+	0.573696i	−0.891527	+	0.452967i	$0.850366\pi$
$860$	−66.4404	+	55.7501i	−2.26560	+	1.90106i
$861$	0.390003	+	0.591858i	0.0132913	+	0.0201705i
$862$	38.4745	−	14.0036i	1.31045	−	0.476964i
$863$	13.3183			0.453360			0.226680	−	0.973969i	$-0.427213\pi$
$863$	13.3183			0.453360			0.226680	+	0.973969i	$0.427213\pi$
$864$	8.72032	+	23.7672i	0.296671	+	0.808578i
$865$	1.71892			0.0584450
$866$	13.3042	−	4.84233i	0.452095	−	0.164549i
$867$	32.4650	−	64.7825i	1.10257	−	2.20013i
$868$	3.73991	−	3.13816i	0.126941	−	0.106516i
$869$	−1.37106	−	7.77565i	−0.0465099	−	0.263771i
$870$	−42.6047	−	31.6609i	−1.44443	−	1.07341i
$871$	−17.0099	−	14.2730i	−0.576358	−	0.483622i
$872$	−18.0823	+	31.3194i	−0.612343	+	1.06061i
$873$	−0.546935	+	9.67827i	−0.0185109	+	0.327560i
$874$	14.7823	+	25.6036i	0.500017	+	0.866055i
$875$	−1.54529	+	8.76378i	−0.0522404	+	0.296270i
$876$	−12.0790	−	50.7699i	−0.408111	−	1.71536i
$877$	−2.44725	−	0.890726i	−0.0826378	−	0.0300777i	0.300370	−	0.953823i	$-0.402890\pi$
$877$	−2.44725	−	0.890726i	−0.0826378	−	0.0300777i	−0.383008	+	0.923745i	$0.625112\pi$
$878$	42.5648	+	15.4923i	1.43649	+	0.522840i
$879$	−6.41406	+	6.06183i	−0.216341	+	0.204460i
$880$	−1.29882	+	7.36597i	−0.0437832	+	0.248307i
$881$	5.74125	+	9.94413i	0.193428	+	0.335026i	0.946384	−	0.323044i	$-0.104706\pi$
$881$	5.74125	+	9.94413i	0.193428	+	0.335026i	−0.752956	+	0.658070i	$0.771373\pi$
$882$	−4.16418	−	5.57335i	−0.140215	−	0.187665i
$883$	−7.03560	+	12.1860i	−0.236767	+	0.410092i	−0.959785	−	0.280737i	$-0.909421\pi$
$883$	−7.03560	+	12.1860i	−0.236767	+	0.410092i	0.723018	+	0.690829i	$0.242754\pi$
$884$	80.1914	+	67.2886i	2.69713	+	2.26316i
$885$	−32.9648	+	14.2534i	−1.10810	+	0.479122i
$886$	4.35744	+	24.7123i	0.146391	+	0.830226i
$887$	25.2731	−	21.2066i	0.848587	−	0.712049i	−0.110891	−	0.993833i	$-0.535370\pi$
$887$	25.2731	−	21.2066i	0.848587	−	0.712049i	0.959478	+	0.281784i	$0.0909260\pi$
$888$	0.596832	−	0.0352784i	0.0200284	−	0.00118386i
$889$	2.35492	−	0.857122i	0.0789816	−	0.0287470i
$890$	−1.21940			−0.0408742
$891$	2.47942	+	40.1800i	0.0830637	+	1.34608i
$892$	−37.0272			−1.23976
$893$	−24.7658	+	9.01403i	−0.828757	+	0.301643i
$894$	89.1959	−	5.27232i	2.98316	−	0.176333i
$895$	−5.09347	+	4.27393i	−0.170256	+	0.142862i
$896$	−3.38572	−	19.2014i	−0.113109	−	0.641472i
$897$	−22.1038	+	9.55729i	−0.738025	+	0.319109i
$898$	−54.3960	−	45.6437i	−1.81522	−	1.52315i
$899$	−3.74180	+	6.48099i	−0.124796	+	0.216153i
$900$	−6.04891	+	14.0898i	−0.201630	+	0.469659i
$901$	−3.66202	−	6.34281i	−0.122000	−	0.211309i
$902$	−0.737122	+	4.18043i	−0.0245435	+	0.139193i
$903$	12.6643	−	11.9689i	0.421443	−	0.398299i
$904$	−58.5757	−	21.3198i	−1.94820	−	0.709086i
$905$	47.5568	+	17.3093i	1.58084	+	0.575379i
$906$	6.88523	+	28.9397i	0.228746	+	0.961458i
$907$	−3.32643	+	18.8651i	−0.110452	+	0.626405i	0.878450	+	0.477835i	$0.158578\pi$
$907$	−3.32643	+	18.8651i	−0.110452	+	0.626405i	−0.988902	+	0.148571i	$0.952533\pi$
$908$	24.9657	+	43.2419i	0.828516	+	1.43503i
$909$	27.0884	+	17.7494i	0.898466	+	0.588711i
$910$	−11.9552	+	20.7071i	−0.396312	+	0.686433i
$911$	−15.1191	−	12.6865i	−0.500920	−	0.420321i	0.357001	−	0.934104i	$-0.383799\pi$
$911$	−15.1191	−	12.6865i	−0.500920	−	0.420321i	−0.857920	+	0.513783i	$0.828244\pi$
$912$	−3.37437	−	2.50760i	−0.111736	−	0.0830349i
$913$	−2.25402	−	12.7832i	−0.0745973	−	0.423062i
$914$	−59.0155	+	49.5199i	−1.95206	+	1.63797i
$915$	−19.8443	+	39.5983i	−0.656031	+	1.30908i
$916$	−3.15940	+	1.14993i	−0.104390	+	0.0379947i
$917$	−19.4104			−0.640988
$918$	−80.1668	−	46.0080i	−2.64590	−	1.51849i
$919$	32.8556			1.08381			0.541903	−	0.840441i	$-0.317704\pi$
$919$	32.8556			1.08381			0.541903	+	0.840441i	$0.317704\pi$
$920$	26.3756	−	9.59994i	0.869579	−	0.316501i
$921$	−5.72947	−	8.69489i	−0.188793	−	0.286506i
$922$	30.5352	−	25.6221i	1.00562	−	0.843819i
$923$	4.68585	+	26.5748i	0.154237	+	0.874720i
$924$	3.01585	−	25.9968i	0.0992140	−	0.855231i
$925$	−0.125188	−	0.105045i	−0.00411616	−	0.00345387i
$926$	0.0289838	−	0.0502014i	0.000952467	−	0.00164972i
$927$	9.21177	+	30.5773i	0.302554	+	1.00429i
$928$	12.6143	+	21.8487i	0.414086	+	0.717217i
$929$	2.31537	−	13.1311i	0.0759647	−	0.430817i	−0.922978	−	0.384852i	$-0.874252\pi$
$929$	2.31537	−	13.1311i	0.0759647	−	0.430817i	0.998943	−	0.0459654i	$-0.0146364\pi$
$930$	14.1963	+	4.23676i	0.465517	+	0.138929i
$931$	−3.48099	−	1.26698i	−0.114085	−	0.0415235i
$932$	−63.3261	−	23.0488i	−2.07431	−	0.754989i
$933$	−14.2633	−	4.25673i	−0.466958	−	0.139359i
$934$	2.69041	−	15.2580i	0.0880327	−	0.499259i
$935$	43.7799	+	75.8291i	1.43176	+	2.47988i
$936$	26.5321	−	28.2198i	0.867228	−	0.922393i
$937$	1.84453	−	3.19481i	0.0602580	−	0.104370i	−0.834323	−	0.551276i	$-0.814141\pi$
$937$	1.84453	−	3.19481i	0.0602580	−	0.104370i	0.894581	+	0.446906i	$0.147474\pi$
$938$	−9.76408	−	8.19303i	−0.318808	−	0.267512i
$939$	0.912723	−	7.86773i	0.0297856	−	0.256754i
$940$	10.6508	+	60.4035i	0.347390	+	1.97014i
$941$	4.77158	−	4.00383i	0.155549	−	0.130521i	−0.561692	−	0.827347i	$-0.689849\pi$
$941$	4.77158	−	4.00383i	0.155549	−	0.130521i	0.717241	+	0.696826i	$0.245405\pi$
$942$	12.9367	+	19.6323i	0.421499	+	0.639655i
$943$	1.32340	−	0.481676i	0.0430957	−	0.0156855i
$944$	−5.32366			−0.173270
$945$	4.50322	−	12.4729i	0.146490	−	0.405743i
$946$	104.358			3.39296
$947$	13.1009	−	4.76834i	0.425723	−	0.154950i	−0.120268	−	0.992741i	$-0.538376\pi$
$947$	13.1009	−	4.76834i	0.425723	−	0.154950i	0.545991	+	0.837791i	$0.316153\pi$
$948$	4.62730	−	9.23357i	0.150288	−	0.299892i
$949$	27.6039	−	23.1624i	0.896060	−	0.751883i
$950$	2.25708	+	12.8005i	0.0732294	+	0.415304i
$951$	30.3854	+	22.5803i	0.985313	+	0.732218i
$952$	18.7785	+	15.7570i	0.608615	+	0.510688i
$953$	−0.479532	+	0.830574i	−0.0155336	+	0.0269049i	−0.873688	−	0.486487i	$-0.838278\pi$
$953$	−0.479532	+	0.830574i	−0.0155336	+	0.0269049i	0.858154	+	0.513392i	$0.171611\pi$
$954$	−5.93124	+	2.99161i	−0.192031	+	0.0968570i
$955$	−10.7482	−	18.6165i	−0.347804	−	0.602414i
$956$	12.6283	−	71.6186i	0.408428	−	2.31631i
$957$	9.28524	+	39.0274i	0.300149	+	1.26158i
$958$	50.4117	+	18.3484i	1.62873	+	0.592809i
$959$	17.7488	+	6.46002i	0.573137	+	0.208605i
$960$	40.5087	−	38.2841i	1.30741	−	1.23561i
$961$	−5.02039	+	28.4721i	−0.161948	+	0.918454i
$962$	0.505976	+	0.876377i	0.0163133	+	0.0282555i
$963$	25.6720	−	3.04555i	0.827269	−	0.0981416i
$964$	−38.5692	+	66.8038i	−1.24223	+	2.15160i
$965$	−6.43298	−	5.39791i	−0.207085	−	0.173765i
$966$	−12.6881	+	5.48611i	−0.408233	+	0.176513i
$967$	−9.18842	−	52.1101i	−0.295480	−	1.67575i	−0.665247	−	0.746624i	$-0.731674\pi$
$967$	−9.18842	−	52.1101i	−0.295480	−	1.67575i	0.369767	−	0.929125i	$-0.379438\pi$
$968$	22.0509	−	18.5029i	0.708742	−	0.594705i
$969$	−49.1295	+	2.90401i	−1.57827	+	0.0932903i
$970$	17.9705	−	6.54072i	0.576997	−	0.210010i
$971$	−25.6469			−0.823048			−0.411524	−	0.911399i	$-0.635003\pi$
$971$	−25.6469			−0.823048			−0.411524	+	0.911399i	$0.635003\pi$
$972$	−28.7464	+	44.1204i	−0.922043	+	1.41516i
$973$	4.72298			0.151412
$974$	53.3107	−	19.4035i	1.70819	−	0.621729i
$975$	−10.5690	+	0.624725i	−0.338478	+	0.0200072i
$976$	−5.02952	+	4.22027i	−0.160991	+	0.135087i
$977$	−4.81451	−	27.3045i	−0.154030	−	0.873547i	−0.959667	−	0.281138i	$-0.909288\pi$
$977$	−4.81451	−	27.3045i	−0.154030	−	0.873547i	0.805637	−	0.592409i	$-0.201823\pi$
$978$	−69.8978	+	30.2225i	−2.23509	+	0.966411i
$979$	0.705970	+	0.592379i	0.0225629	+	0.0189325i
$980$	−4.31053	+	7.46605i	−0.137695	+	0.238494i
$981$	33.7120	−	3.99936i	1.07634	−	0.127690i
$982$	−9.68374	−	16.7727i	−0.309021	−	0.535239i
$983$	2.19249	−	12.4342i	0.0699294	−	0.396590i	−0.929673	−	0.368386i	$-0.879910\pi$
$983$	2.19249	−	12.4342i	0.0699294	−	0.396590i	0.999602	−	0.0282032i	$-0.00897854\pi$
$984$	−1.64632	+	1.55591i	−0.0524827	+	0.0496005i
$985$	−7.74370	−	2.81848i	−0.246735	−	0.0898041i
$986$	−86.5552	−	31.5035i	−2.75648	−	1.00328i
$987$	−2.85219	−	11.9882i	−0.0907862	−	0.381589i
$988$	8.77890	−	49.7876i	0.279294	−	1.58395i
$989$	−17.3112	−	29.9839i	−0.550465	−	0.953434i
$990$	70.9088	−	35.7651i	2.25363	−	1.13669i
$991$	0.528761	−	0.915840i	0.0167966	−	0.0290926i	−0.857505	−	0.514476i	$-0.827987\pi$
$991$	0.528761	−	0.915840i	0.0167966	−	0.0290926i	0.874302	+	0.485383i	$0.161320\pi$
$992$	−5.39404	−	4.52614i	−0.171261	−	0.143705i
$993$	−13.3213	−	9.89951i	−0.422740	−	0.314151i
$994$	2.68979	+	15.2546i	0.0853150	+	0.483846i
$995$	−16.9417	+	14.2158i	−0.537087	+	0.450670i
$996$	7.60730	−	15.1800i	0.241047	−	0.480998i
$997$	4.25057	−	1.54708i	0.134617	−	0.0489965i	−0.273833	−	0.961777i	$-0.588292\pi$
$997$	4.25057	−	1.54708i	0.134617	−	0.0489965i	0.408450	+	0.912781i	$0.366069\pi$
$998$	−67.4986			−2.13663
$999$	−0.361867	−	0.428996i	−0.0114490	−	0.0135728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.169.2	yes	54
3.2	odd	2		567.2.v.b.505.8		54
27.2	odd	18		5103.2.a.f.1.5		27
27.4	even	9	inner	189.2.v.a.85.2	✓	54
27.23	odd	18		567.2.v.b.64.8		54
27.25	even	9		5103.2.a.i.1.23		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.85.2	✓	54	27.4	even	9	inner
189.2.v.a.169.2	yes	54	1.1	even	1	trivial
567.2.v.b.64.8		54	27.23	odd	18
567.2.v.b.505.8		54	3.2	odd	2
5103.2.a.f.1.5		27	27.2	odd	18
5103.2.a.i.1.23		27	27.25	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.17921 + 0.793168i) q^{2} +(-1.72903 + 0.102202i) q^{3} +(2.58775 - 2.17138i) q^{4} +(0.443161 + 2.51329i) q^{5} +(3.68686 - 1.59413i) q^{6} +(0.766044 + 0.642788i) q^{7} +(-1.59792 + 2.76768i) q^{8} +(2.97911 - 0.353421i) q^{9} +(-2.95920 - 5.12549i) q^{10} +(-0.776717 + 4.40498i) q^{11} +(-4.25239 + 4.01887i) q^{12} +(-3.79638 - 1.38177i) q^{13} +(-2.17921 - 0.793168i) q^{14} +(-1.02310 - 4.30027i) q^{15} +(0.113780 - 0.645277i) q^{16} +(-3.83523 - 6.64281i) q^{17} +(-6.21178 + 3.13311i) q^{18} +(-1.85220 + 3.20810i) q^{19} +(6.60411 + 5.54151i) q^{20} +(-1.39021 - 1.03311i) q^{21} +(-1.80126 - 10.2154i) q^{22} +(-2.63630 + 2.21211i) q^{23} +(2.48000 - 4.94872i) q^{24} +(-1.42178 + 0.517485i) q^{25} +9.36908 q^{26} +(-5.11486 + 0.915548i) q^{27} +3.37807 q^{28} +(-4.86584 + 1.77102i) q^{29} +(5.64039 + 8.55970i) q^{30} +(1.10711 - 0.928979i) q^{31} +(-0.846042 - 4.79814i) q^{32} +(0.892771 - 7.69574i) q^{33} +(13.6266 + 11.4341i) q^{34} +(-1.27603 + 2.21015i) q^{35} +(6.94179 - 7.38336i) q^{36} +(0.0540049 + 0.0935393i) q^{37} +(1.49177 - 8.46023i) q^{38} +(6.70528 + 2.00112i) q^{39} +(-7.66413 - 2.78951i) q^{40} +(-0.384547 - 0.139964i) q^{41} +(3.84899 + 1.14869i) q^{42} +(-1.74698 + 9.90762i) q^{43} +(7.55495 + 13.0856i) q^{44} +(2.20848 + 7.33075i) q^{45} +(3.99046 - 6.91169i) q^{46} +(5.45009 + 4.57317i) q^{47} +(-0.130780 + 1.12733i) q^{48} +(0.173648 + 0.984808i) q^{49} +(2.68790 - 2.25542i) q^{50} +(7.31015 + 11.0937i) q^{51} +(-12.8244 + 4.66771i) q^{52} +0.954837 q^{53} +(10.4202 - 6.05211i) q^{54} -11.4152 q^{55} +(-3.00311 + 1.09304i) q^{56} +(2.87464 - 5.73621i) q^{57} +(9.19898 - 7.71886i) q^{58} +(-1.41087 - 8.00142i) q^{59} +(-11.9851 - 8.90649i) q^{60} +(-7.67594 - 6.44088i) q^{61} +(-1.67580 + 2.90257i) q^{62} +(2.50931 + 1.64420i) q^{63} +(6.30467 + 10.9200i) q^{64} +(1.79038 - 10.1537i) q^{65} +(4.15847 + 17.4787i) q^{66} +(5.16475 + 1.87982i) q^{67} +(-24.3487 - 8.86221i) q^{68} +(4.33216 - 4.09425i) q^{69} +(1.02772 - 5.82849i) q^{70} +(-3.33968 - 5.78450i) q^{71} +(-3.78223 + 8.80997i) q^{72} +(-4.45967 + 7.72438i) q^{73} +(-0.191880 - 0.161007i) q^{74} +(2.40541 - 1.04006i) q^{75} +(2.17298 + 12.3236i) q^{76} +(-3.42647 + 2.87515i) q^{77} +(-16.1994 + 0.957539i) q^{78} +(-1.65874 + 0.603732i) q^{79} +1.67219 q^{80} +(8.75019 - 2.10576i) q^{81} +0.949023 q^{82} +(-2.72698 + 0.992539i) q^{83} +(-5.84080 + 0.345246i) q^{84} +(14.9957 - 12.5829i) q^{85} +(-4.05137 - 22.9764i) q^{86} +(8.23220 - 3.55945i) q^{87} +(-10.9504 - 9.18852i) q^{88} +(0.103017 - 0.178431i) q^{89} +(-10.6272 - 14.2235i) q^{90} +(-2.02001 - 3.49876i) q^{91} +(-2.01874 + 11.4488i) q^{92} +(-1.81929 + 1.71938i) q^{93} +(-15.5042 - 5.64307i) q^{94} +(-8.88371 - 3.23341i) q^{95} +(1.95321 + 8.20968i) q^{96} +(-0.561099 + 3.18215i) q^{97} +(-1.15953 - 2.00837i) q^{98} +(-0.757110 + 13.3974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27}+ \cdots - 117 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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