LMFDB - Embedded newform 165.2.s.a.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(4,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("165.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.s (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	165.4
Dual form			165.2.s.a.124.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38939 - 1.91233i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(-1.97379 - 1.05079i) q^{5} +(-1.91233 + 1.38939i) q^{6} +(1.63033 - 0.529727i) q^{7} +(-3.56862 - 1.15951i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.38939 - 1.91233i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(-1.97379 - 1.05079i) q^{5} +(-1.91233 + 1.38939i) q^{6} +(1.63033 - 0.529727i) q^{7} +(-3.56862 - 1.15951i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-4.75182 + 2.31457i) q^{10} +(-0.406668 + 3.29160i) q^{11} +3.58741i q^{12} +(2.07687 - 2.85857i) q^{13} +(1.25215 - 3.85373i) q^{14} +(1.55247 + 1.60930i) q^{15} +(-1.37103 + 0.996109i) q^{16} +(0.219423 + 0.302010i) q^{17} +(2.24808 - 0.730445i) q^{18} +(1.78239 - 5.48564i) q^{19} +(-1.39705 + 7.89910i) q^{20} -1.71423 q^{21} +(5.72960 + 5.35099i) q^{22} +3.80745i q^{23} +(3.03565 + 2.20553i) q^{24} +(2.79166 + 4.14809i) q^{25} +(-2.58094 - 7.94332i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-3.61467 - 4.97517i) q^{28} +(1.08672 + 3.34458i) q^{29} +(5.23449 - 0.732891i) q^{30} +(8.16928 + 5.93533i) q^{31} -3.49870i q^{32} +(1.40392 - 3.00483i) q^{33} +0.882407 q^{34} +(-3.77456 - 0.667576i) q^{35} +(1.10857 - 3.41183i) q^{36} +(-10.9770 + 3.56666i) q^{37} +(-8.01391 - 11.0302i) q^{38} +(-2.85857 + 2.07687i) q^{39} +(5.82528 + 6.03852i) q^{40} +(-0.747505 + 2.30059i) q^{41} +(-2.38174 + 3.27818i) q^{42} +0.224486i q^{43} +(11.6812 - 2.26149i) q^{44} +(-0.979185 - 2.01027i) q^{45} +(7.28109 + 5.29002i) q^{46} +(-4.44749 - 1.44508i) q^{47} +(1.61174 - 0.523685i) q^{48} +(-3.28575 + 2.38724i) q^{49} +(11.8112 + 0.424728i) q^{50} +(-0.115358 - 0.355034i) q^{51} +(-12.0553 - 3.91700i) q^{52} +(1.43665 - 1.97737i) q^{53} -2.36377 q^{54} +(4.26147 - 6.06959i) q^{55} -6.43226 q^{56} +(-3.39031 + 4.66636i) q^{57} +(7.90582 + 2.56876i) q^{58} +(-1.65630 - 5.09757i) q^{59} +(3.76963 - 7.08078i) q^{60} +(2.75575 - 2.00217i) q^{61} +(22.7006 - 7.37587i) q^{62} +(1.63033 + 0.529727i) q^{63} +(-9.43272 - 6.85327i) q^{64} +(-7.10307 + 3.45984i) q^{65} +(-3.79563 - 6.85964i) q^{66} +9.08988i q^{67} +(0.787161 - 1.08343i) q^{68} +(1.17657 - 3.62110i) q^{69} +(-6.52096 + 6.29068i) q^{70} +(7.09964 - 5.15819i) q^{71} +(-2.20553 - 3.03565i) q^{72} +(-14.2299 + 4.62358i) q^{73} +(-8.43076 + 25.9472i) q^{74} +(-1.37320 - 4.80774i) q^{75} -20.6919 q^{76} +(1.08064 + 5.58182i) q^{77} +8.35211i q^{78} +(7.11291 + 5.16783i) q^{79} +(3.75282 - 0.525439i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.36090 + 4.62589i) q^{82} +(4.37438 + 6.02082i) q^{83} +(1.90035 + 5.84866i) q^{84} +(-0.115744 - 0.826672i) q^{85} +(0.429291 + 0.311898i) q^{86} -3.51670i q^{87} +(5.26790 - 11.2749i) q^{88} -15.5058 q^{89} +(-5.20477 - 0.920527i) q^{90} +(1.87173 - 5.76059i) q^{91} +(12.9903 - 4.22082i) q^{92} +(-5.93533 - 8.16928i) q^{93} +(-8.94275 + 6.49729i) q^{94} +(-9.28233 + 8.95454i) q^{95} +(-1.08116 + 3.32746i) q^{96} +(8.61910 - 11.8632i) q^{97} +9.60024i q^{98} +(-2.26375 + 2.42393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.38939	−	1.91233i	0.982446	−	1.35222i	0.0469455	−	0.998897i	$-0.485051\pi$
$2$	1.38939	−	1.91233i	0.982446	−	1.35222i	0.935501	−	0.353324i	$-0.114949\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−1.10857	−	3.41183i	−0.554285	−	1.70591i
$5$	−1.97379	−	1.05079i	−0.882704	−	0.469930i
$5$	−1.97379	−	1.05079i	−0.882704	−	0.469930i
$6$	−1.91233	+	1.38939i	−0.780705	+	0.567216i
$7$	1.63033	−	0.529727i	0.616207	−	0.200218i	0.0157517	−	0.999876i	$-0.494986\pi$
$7$	1.63033	−	0.529727i	0.616207	−	0.200218i	0.600456	+	0.799658i	$0.294986\pi$
$8$	−3.56862	−	1.15951i	−1.26170	−	0.409950i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−4.75182	+	2.31457i	−1.50266	+	0.731931i
$11$	−0.406668	+	3.29160i	−0.122615	+	0.992454i
$11$	−0.406668	+	3.29160i	−0.122615	+	0.992454i
$12$			3.58741i			1.03560i
$13$	2.07687	−	2.85857i	0.576020	−	0.792824i	−0.417232	−	0.908800i	$-0.637000\pi$
$13$	2.07687	−	2.85857i	0.576020	−	0.792824i	0.993252	+	0.115976i	$0.0369996\pi$
$14$	1.25215	−	3.85373i	0.334652	−	1.02995i
$15$	1.55247	+	1.60930i	0.400846	+	0.415519i
$16$	−1.37103	+	0.996109i	−0.342757	+	0.249027i
$17$	0.219423	+	0.302010i	0.0532180	+	0.0732482i	0.834797	−	0.550559i	$-0.185585\pi$
$17$	0.219423	+	0.302010i	0.0532180	+	0.0732482i	−0.781579	+	0.623807i	$0.785585\pi$
$18$	2.24808	−	0.730445i	0.529877	−	0.172168i
$19$	1.78239	−	5.48564i	0.408909	−	1.25849i	−0.508679	−	0.860956i	$-0.669866\pi$
$19$	1.78239	−	5.48564i	0.408909	−	1.25849i	0.917587	−	0.397535i	$-0.130134\pi$
$20$	−1.39705	+	7.89910i	−0.312390	+	1.76629i
$21$	−1.71423			−0.374076
$22$	5.72960	+	5.35099i	1.22156	+	1.14084i
$23$			3.80745i			0.793907i	0.917839	+	0.396954i	$0.129933\pi$
$23$			3.80745i			0.793907i	−0.917839	+	0.396954i	$0.870067\pi$
$24$	3.03565	+	2.20553i	0.619649	+	0.450201i
$25$	2.79166	+	4.14809i	0.558332	+	0.829617i
$26$	−2.58094	−	7.94332i	−0.506165	−	1.55781i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−3.61467	−	4.97517i	−0.683109	−	0.940219i
$29$	1.08672	+	3.34458i	0.201799	+	0.621073i	0.999830	+	0.0184562i	$0.00587514\pi$
$29$	1.08672	+	3.34458i	0.201799	+	0.621073i	−0.798031	+	0.602617i	$0.794125\pi$
$30$	5.23449	−	0.732891i	0.955683	−	0.133807i
$31$	8.16928	+	5.93533i	1.46725	+	1.06602i	0.981401	+	0.191971i	$0.0614880\pi$
$31$	8.16928	+	5.93533i	1.46725	+	1.06602i	0.485845	+	0.874045i	$0.338512\pi$
$32$		−	3.49870i		−	0.618488i
$33$	1.40392	−	3.00483i	0.244392	−	0.523074i
$34$	0.882407			0.151332
$35$	−3.77456	−	0.667576i	−0.638017	−	0.112841i
$36$	1.10857	−	3.41183i	0.184762	−	0.568638i
$37$	−10.9770	+	3.56666i	−1.80462	+	0.586355i	−0.999973	−	0.00740399i	$-0.997643\pi$
$37$	−10.9770	+	3.56666i	−1.80462	+	0.586355i	−0.804643	+	0.593759i	$0.797643\pi$
$38$	−8.01391	−	11.0302i	−1.30003	−	1.78933i
$39$	−2.85857	+	2.07687i	−0.457737	+	0.332565i
$40$	5.82528	+	6.03852i	0.921057	+	0.954774i
$41$	−0.747505	+	2.30059i	−0.116741	+	0.359291i	−0.992306	−	0.123809i	$-0.960489\pi$
$41$	−0.747505	+	2.30059i	−0.116741	+	0.359291i	0.875565	+	0.483100i	$0.160489\pi$
$42$	−2.38174	+	3.27818i	−0.367510	+	0.505834i
$43$			0.224486i			0.0342338i	0.999853	+	0.0171169i	$0.00544874\pi$
$43$			0.224486i			0.0342338i	−0.999853	+	0.0171169i	$0.994551\pi$
$44$	11.6812	−	2.26149i	1.76101	−	0.340932i
$45$	−0.979185	−	2.01027i	−0.145968	−	0.299674i
$46$	7.28109	+	5.29002i	1.07354	+	0.779971i
$47$	−4.44749	−	1.44508i	−0.648733	−	0.210786i	−0.0338775	−	0.999426i	$-0.510786\pi$
$47$	−4.44749	−	1.44508i	−0.648733	−	0.210786i	−0.614855	+	0.788640i	$0.710786\pi$
$48$	1.61174	−	0.523685i	0.232634	−	0.0755875i
$49$	−3.28575	+	2.38724i	−0.469393	+	0.341034i
$50$	11.8112	+	0.424728i	1.67036	+	0.0600656i
$51$	−0.115358	−	0.355034i	−0.0161533	−	0.0497147i
$52$	−12.0553	−	3.91700i	−1.67177	−	0.543191i
$53$	1.43665	−	1.97737i	0.197339	−	0.271613i	−0.698868	−	0.715251i	$-0.746312\pi$
$53$	1.43665	−	1.97737i	0.197339	−	0.271613i	0.896206	+	0.443638i	$0.146312\pi$
$54$	−2.36377			−0.321668
$55$	4.26147	−	6.06959i	0.574616	−	0.818423i
$56$	−6.43226			−0.859547
$57$	−3.39031	+	4.66636i	−0.449057	+	0.618074i
$58$	7.90582	+	2.56876i	1.03808	+	0.337294i
$59$	−1.65630	−	5.09757i	−0.215632	−	0.663648i	−0.999108	−	0.0422255i	$-0.986555\pi$
$59$	−1.65630	−	5.09757i	−0.215632	−	0.663648i	0.783476	−	0.621422i	$-0.213445\pi$
$60$	3.76963	−	7.08078i	0.486657	−	0.914124i
$61$	2.75575	−	2.00217i	0.352838	−	0.256352i	−0.397221	−	0.917723i	$-0.630025\pi$
$61$	2.75575	−	2.00217i	0.352838	−	0.256352i	0.750058	+	0.661371i	$0.230025\pi$
$62$	22.7006	−	7.37587i	2.88298	−	0.936737i
$63$	1.63033	+	0.529727i	0.205402	+	0.0667393i
$64$	−9.43272	−	6.85327i	−1.17909	−	0.856659i
$65$	−7.10307	+	3.45984i	−0.881027	+	0.429140i
$66$	−3.79563	−	6.85964i	−0.467210	−	0.844364i
$67$			9.08988i			1.11051i	0.831682	+	0.555253i	$0.187379\pi$
$67$			9.08988i			1.11051i	−0.831682	+	0.555253i	$0.812621\pi$
$68$	0.787161	−	1.08343i	0.0954573	−	0.131386i
$69$	1.17657	−	3.62110i	0.141642	−	0.435929i
$70$	−6.52096	+	6.29068i	−0.779403	+	0.751880i
$71$	7.09964	−	5.15819i	0.842572	−	0.612165i	−0.0805158	−	0.996753i	$-0.525657\pi$
$71$	7.09964	−	5.15819i	0.842572	−	0.612165i	0.923088	+	0.384589i	$0.125657\pi$
$72$	−2.20553	−	3.03565i	−0.259924	−	0.357755i
$73$	−14.2299	+	4.62358i	−1.66549	+	0.541150i	−0.982011	−	0.188823i	$-0.939533\pi$
$73$	−14.2299	+	4.62358i	−1.66549	+	0.541150i	−0.683476	+	0.729973i	$0.739533\pi$
$74$	−8.43076	+	25.9472i	−0.980056	+	3.01630i
$75$	−1.37320	−	4.80774i	−0.158563	−	0.555150i
$76$	−20.6919			−2.37353
$77$	1.08064	+	5.58182i	0.123151	+	0.636107i
$78$			8.35211i			0.945690i
$79$	7.11291	+	5.16783i	0.800265	+	0.581426i	0.910992	−	0.412425i	$-0.135318\pi$
$79$	7.11291	+	5.16783i	0.800265	+	0.581426i	−0.110727	+	0.993851i	$0.535318\pi$
$80$	3.75282	−	0.525439i	0.419578	−	0.0587458i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	3.36090	+	4.62589i	0.371150	+	0.510844i
$83$	4.37438	+	6.02082i	0.480151	+	0.660871i	0.978534	−	0.206086i	$-0.0660726\pi$
$83$	4.37438	+	6.02082i	0.480151	+	0.660871i	−0.498383	+	0.866957i	$0.666073\pi$
$84$	1.90035	+	5.84866i	0.207345	+	0.638142i
$85$	−0.115744	−	0.826672i	−0.0125542	−	0.0896652i
$86$	0.429291	+	0.311898i	0.0462916	+	0.0336328i
$87$		−	3.51670i		−	0.377030i
$88$	5.26790	−	11.2749i	0.561560	−	1.20191i
$89$	−15.5058			−1.64361			−0.821806	−	0.569767i	$-0.807034\pi$
$89$	−15.5058			−1.64361			−0.821806	+	0.569767i	$0.807034\pi$
$90$	−5.20477	−	0.920527i	−0.548631	−	0.0970320i
$91$	1.87173	−	5.76059i	0.196210	−	0.603874i
$92$	12.9903	−	4.22082i	1.35434	−	0.440051i
$93$	−5.93533	−	8.16928i	−0.615465	−	0.847115i
$94$	−8.94275	+	6.49729i	−0.922375	+	0.670144i
$95$	−9.28233	+	8.95454i	−0.952347	+	0.918717i
$96$	−1.08116	+	3.32746i	−0.110345	+	0.339607i
$97$	8.61910	−	11.8632i	0.875137	−	1.20452i	−0.102608	−	0.994722i	$-0.532719\pi$
$97$	8.61910	−	11.8632i	0.875137	−	1.20452i	0.977744	−	0.209800i	$-0.0672814\pi$
$98$			9.60024i			0.969770i
$99$	−2.26375	+	2.42393i	−0.227516	+	0.243614i
$100$	11.0578	−	14.1231i	1.10578	−	1.41231i
$101$	−4.96307	−	3.60588i	−0.493844	−	0.358798i	0.312817	−	0.949813i	$-0.398727\pi$
$101$	−4.96307	−	3.60588i	−0.493844	−	0.358798i	−0.806661	+	0.591015i	$0.798727\pi$
$102$	−0.839219	−	0.272679i	−0.0830951	−	0.0269992i
$103$	7.48471	−	2.43193i	0.737490	−	0.239625i	0.0839005	−	0.996474i	$-0.473262\pi$
$103$	7.48471	−	2.43193i	0.737490	−	0.239625i	0.653590	+	0.756849i	$0.273262\pi$
$104$	−10.7261	+	7.79298i	−1.05178	+	0.764164i
$105$	3.38353	+	1.80131i	0.330198	+	0.175789i
$106$	−1.78533	−	5.49468i	−0.173407	−	0.533691i
$107$	−4.71361	−	1.53155i	−0.455682	−	0.148060i	0.0721774	−	0.997392i	$-0.477005\pi$
$107$	−4.71361	−	1.53155i	−0.455682	−	0.148060i	−0.527859	+	0.849332i	$0.677005\pi$
$108$	−2.10863	+	2.90227i	−0.202903	+	0.279271i
$109$	2.61667			0.250632			0.125316	−	0.992117i	$-0.460006\pi$
$109$	2.61667			0.250632			0.125316	+	0.992117i	$0.460006\pi$
$110$	−5.68621	−	16.5824i	−0.542159	−	1.58107i
$111$	11.5420			1.09551
$112$	−1.70756	+	2.35026i	−0.161349	+	0.222078i
$113$	2.01298	+	0.654058i	0.189366	+	0.0615286i	0.402165	−	0.915567i	$-0.368258\pi$
$113$	2.01298	+	0.654058i	0.189366	+	0.0615286i	−0.212799	+	0.977096i	$0.568258\pi$
$114$	4.21316	+	12.9668i	0.394599	+	1.21445i
$115$	4.00084	−	7.51508i	0.373081	−	0.700785i
$116$	10.2064	−	7.41540i	0.947643	−	0.688503i
$117$	3.36045	−	1.09188i	0.310673	−	0.100944i
$118$	−12.0495	−	3.91512i	−1.10925	−	0.360416i
$119$	0.517715	+	0.376142i	0.0474589	+	0.0344809i
$120$	−3.67416	−	7.54308i	−0.335404	−	0.688586i
$121$	−10.6692	−	2.67717i	−0.969931	−	0.243379i
$122$		−	8.05170i		−	0.728966i
$123$	1.42184	−	1.95699i	0.128203	−	0.176456i
$124$	11.1941	−	34.4519i	1.00526	−	3.09387i
$125$	−1.15136	−	11.1209i	−0.102980	−	0.994683i
$126$	3.27818	−	2.38174i	0.292043	−	0.212182i
$127$	7.02266	+	9.66586i	0.623160	+	0.857707i	0.997578	−	0.0695535i	$-0.0221575\pi$
$127$	7.02266	+	9.66586i	0.623160	+	0.857707i	−0.374418	+	0.927260i	$0.622157\pi$
$128$	−19.5565	+	6.35430i	−1.72857	+	0.561646i
$129$	0.0693699	−	0.213499i	0.00610768	−	0.0187975i
$130$	−3.25257	+	18.3905i	−0.285270	+	1.61295i
$131$	20.3359			1.77676			0.888380	−	0.459110i	$-0.151831\pi$
$131$	20.3359			1.77676			0.888380	+	0.459110i	$0.151831\pi$
$132$	−11.8083	−	1.45888i	−1.02778	−	0.126980i
$133$		−	9.88758i		−	0.857362i
$134$	17.3829	+	12.6294i	1.50165	+	1.09101i
$135$	0.310052	+	2.21447i	0.0266850	+	0.190591i
$136$	−0.432853	−	1.33218i	−0.0371168	−	0.114234i
$137$	3.12316	+	4.29866i	0.266829	+	0.367259i	0.921316	−	0.388814i	$-0.127115\pi$
$137$	3.12316	+	4.29866i	0.266829	+	0.367259i	−0.654487	+	0.756073i	$0.727115\pi$
$138$	−5.29002	−	7.28109i	−0.450317	−	0.619808i
$139$	−4.08383	−	12.5688i	−0.346386	−	1.06607i	−0.960837	−	0.277113i	$-0.910622\pi$
$139$	−4.08383	−	12.5688i	−0.346386	−	1.06607i	0.614451	−	0.788955i	$-0.289378\pi$
$140$	1.90671	+	13.6182i	0.161146	+	1.15095i
$141$	3.78326	+	2.74870i	0.318608	+	0.231482i
$142$		−	20.7436i		−	1.74076i
$143$	8.56466	+	7.99871i	0.716213	+	0.668886i
$144$	−1.69468			−0.141223
$145$	1.36951	−	7.74340i	0.113732	−	0.643055i
$146$	−10.9291	+	33.6363i	−0.904498	+	2.78376i
$147$	3.86263	−	1.25504i	0.318584	−	0.103514i
$148$	24.3377	+	33.4979i	2.00054	+	2.75351i
$149$	−4.90495	+	3.56366i	−0.401830	+	0.291946i	−0.770286	−	0.637699i	$-0.779886\pi$
$149$	−4.90495	+	3.56366i	−0.401830	+	0.291946i	0.368456	+	0.929645i	$0.379886\pi$
$150$	−11.1019	−	4.05381i	−0.906465	−	0.330992i
$151$	−2.26661	+	6.97591i	−0.184454	+	0.567692i	−0.999939	−	0.0110874i	$-0.996471\pi$
$151$	−2.26661	+	6.97591i	−0.184454	+	0.567692i	0.815484	+	0.578779i	$0.196471\pi$
$152$	−12.7213	+	17.5094i	−1.03184	+	1.42020i
$153$			0.373305i			0.0301799i
$154$	12.1757	+	5.68877i	0.981147	+	0.458414i
$155$	−9.88759	−	20.2993i	−0.794191	−	1.63048i
$156$	10.2548	+	7.45058i	0.821045	+	0.596524i
$157$	−10.0392	−	3.26192i	−0.801212	−	0.260329i	−0.120340	−	0.992733i	$-0.538399\pi$
$157$	−10.0392	−	3.26192i	−0.801212	−	0.260329i	−0.680871	+	0.732403i	$0.738399\pi$
$158$	19.7652	−	6.42210i	1.57243	−	0.510915i
$159$	−1.97737	+	1.43665i	−0.156816	+	0.113933i
$160$	−3.67641	+	6.90568i	−0.290646	+	0.545942i
$161$	2.01691	+	6.20740i	0.158954	+	0.489211i
$162$	2.24808	+	0.730445i	0.176626	+	0.0573892i
$163$	5.94077	−	8.17677i	0.465317	−	0.640454i	−0.510284	−	0.860006i	$-0.670460\pi$
$163$	5.94077	−	8.17677i	0.465317	−	0.640454i	0.975601	+	0.219552i	$0.0704596\pi$
$164$	8.67786			0.677627
$165$	−5.92850	+	4.45565i	−0.461533	+	0.346872i
$166$	17.5915			1.36537
$167$	−7.84529	+	10.7981i	−0.607087	+	0.835583i	−0.996334	−	0.0855502i	$-0.972735\pi$
$167$	−7.84529	+	10.7981i	−0.607087	+	0.835583i	0.389247	+	0.921133i	$0.372735\pi$
$168$	6.11744	+	1.98768i	0.471971	+	0.153353i
$169$	0.159206	+	0.489985i	0.0122466	+	0.0376911i
$170$	−1.74168	−	0.927229i	−0.133581	−	0.0711152i
$171$	4.66636	−	3.39031i	0.356845	−	0.259263i
$172$	0.765907	−	0.248858i	0.0583999	−	0.0189753i
$173$	16.9862	+	5.51914i	1.29144	+	0.419613i	0.872594	−	0.488447i	$-0.162436\pi$
$173$	16.9862	+	5.51914i	1.29144	+	0.419613i	0.418841	+	0.908059i	$0.362436\pi$
$174$	−6.72509	−	4.88606i	−0.509828	−	0.370411i
$175$	6.74869	+	5.28394i	0.510153	+	0.399428i
$176$	−2.72124	−	4.91795i	−0.205121	−	0.370705i
$177$			5.35991i			0.402875i
$178$	−21.5436	+	29.6522i	−1.61476	+	2.22253i
$179$	3.93601	−	12.1138i	0.294192	−	0.905428i	−0.689300	−	0.724476i	$-0.742082\pi$
$179$	3.93601	−	12.1138i	0.294192	−	0.905428i	0.983492	−	0.180953i	$-0.0579181\pi$
$180$	−5.77321	+	5.56934i	−0.430310	+	0.415114i
$181$	−16.7562	+	12.1741i	−1.24548	+	0.904891i	−0.997950	−	0.0639909i	$-0.979617\pi$
$181$	−16.7562	+	12.1741i	−1.24548	+	0.904891i	−0.247525	+	0.968882i	$0.579617\pi$
$182$	−8.41558	−	11.5831i	−0.623805	−	0.858593i
$183$	−3.23958	+	1.05260i	−0.239477	+	0.0778106i
$184$	4.41479	−	13.5873i	0.325463	−	1.00167i
$185$	25.4142	+	4.49480i	1.86849	+	0.330464i
$186$	−23.8688			−1.75015
$187$	−1.08333	+	0.599435i	−0.0792208	+	0.0438351i
$188$			16.7760i			1.22352i
$189$	−1.38684	−	1.00760i	−0.100878	−	0.0732921i
$190$	4.22727	+	30.1922i	0.306678	+	2.19037i
$191$	−1.91577	−	5.89614i	−0.138620	−	0.426630i	0.857515	−	0.514459i	$-0.172007\pi$
$191$	−1.91577	−	5.89614i	−0.138620	−	0.426630i	−0.996136	+	0.0878289i	$0.972007\pi$
$192$	6.85327	+	9.43272i	0.494592	+	0.680748i
$193$	−3.24670	−	4.46870i	−0.233703	−	0.321664i	0.676018	−	0.736885i	$-0.263704\pi$
$193$	−3.24670	−	4.46870i	−0.233703	−	0.321664i	−0.909721	+	0.415221i	$0.863704\pi$
$194$	−10.7110	−	32.9651i	−0.769006	−	2.36676i
$195$	7.82456	−	1.09553i	0.560329	−	0.0784526i
$196$	11.7873	+	8.56399i	0.841952	+	0.611714i
$197$		−	12.8524i		−	0.915693i	−0.889031	−	0.457846i	$-0.848621\pi$
$197$		−	12.8524i		−	0.915693i	0.889031	−	0.457846i	$-0.151379\pi$
$198$	1.49011	+	7.69682i	0.105898	+	0.546989i
$199$	−3.42830			−0.243026			−0.121513	−	0.992590i	$-0.538775\pi$
$199$	−3.42830			−0.243026			−0.121513	+	0.992590i	$0.538775\pi$
$200$	−5.15261	−	18.0399i	−0.364345	−	1.27561i
$201$	2.80893	−	8.64499i	0.198126	−	0.609771i
$202$	−13.7913	+	4.48105i	−0.970350	+	0.315286i
$203$	3.54343	+	4.87711i	0.248700	+	0.342306i
$204$	−1.08343	+	0.787161i	−0.0758555	+	0.0551123i
$205$	3.89286	−	3.75539i	0.271889	−	0.262288i
$206$	5.74852	−	17.6921i	0.400518	−	1.23267i
$207$	−2.23796	+	3.08029i	−0.155549	+	0.214095i
$208$			5.98796i			0.415190i
$209$	17.3317	+	8.09775i	1.19886	+	0.560133i
$210$	8.14573	−	3.96771i	0.562108	−	0.273798i
$211$	−14.4241	−	10.4797i	−0.992996	−	0.721454i	−0.0324211	−	0.999474i	$-0.510322\pi$
$211$	−14.4241	−	10.4797i	−0.992996	−	0.721454i	−0.960575	+	0.278020i	$0.910322\pi$
$212$	−8.33908	−	2.70953i	−0.572731	−	0.186091i
$213$	−8.34613	+	2.71182i	−0.571867	+	0.185811i
$214$	−9.47786	+	6.88607i	−0.647893	+	0.470722i
$215$	0.235888	−	0.443087i	0.0160875	−	0.0302183i
$216$	1.15951	+	3.56862i	0.0788950	+	0.242814i
$217$	16.4627	+	5.34907i	1.11756	+	0.363118i
$218$	3.63558	−	5.00395i	0.246232	−	0.338910i
$219$	14.9622			1.01105
$220$	−25.4325	−	7.81084i	−1.71466	−	0.526607i
$221$	1.31903			0.0887276
$222$	16.0363	−	22.0720i	1.07628	−	1.48138i
$223$	−4.10580	−	1.33405i	−0.274944	−	0.0893349i	0.168299	−	0.985736i	$-0.446172\pi$
$223$	−4.10580	−	1.33405i	−0.274944	−	0.0893349i	−0.443244	+	0.896401i	$0.646172\pi$
$224$	−1.85335	−	5.70404i	−0.123832	−	0.381117i
$225$	−0.179682	+	4.99677i	−0.0119788	+	0.333118i
$226$	4.04759	−	2.94075i	0.269242	−	0.195616i
$227$	−24.1914	+	7.86025i	−1.60564	+	0.521703i	−0.968493	−	0.249041i	$-0.919885\pi$
$227$	−24.1914	+	7.86025i	−1.60564	+	0.521703i	−0.637145	+	0.770744i	$0.719885\pi$
$228$	19.6792	+	6.39416i	1.30329	+	0.423464i
$229$	11.6445	+	8.46020i	0.769488	+	0.559066i	0.901806	−	0.432142i	$-0.142242\pi$
$229$	11.6445	+	8.46020i	0.769488	+	0.559066i	−0.132318	+	0.991207i	$0.542242\pi$
$230$	−8.81259	−	18.0923i	−0.581085	−	1.19297i
$231$	0.697123	−	5.64256i	0.0458673	−	0.371253i
$232$		−	13.1956i		−	0.866333i
$233$	7.01317	−	9.65280i	0.459448	−	0.632376i	−0.514946	−	0.857223i	$-0.672188\pi$
$233$	7.01317	−	9.65280i	0.459448	−	0.632376i	0.974394	+	0.224847i	$0.0721881\pi$
$234$	2.58094	−	7.94332i	0.168722	−	0.519271i
$235$	7.25991	+	7.52567i	0.473584	+	0.490920i
$236$	−15.5559	+	11.3020i	−1.01260	+	0.735700i
$237$	−5.16783	−	7.11291i	−0.335687	−	0.462033i
$238$	1.43862	−	0.467435i	0.0932517	−	0.0302993i
$239$	2.55170	−	7.85333i	0.165056	−	0.507990i	−0.833985	−	0.551788i	$-0.813946\pi$
$239$	2.55170	−	7.85333i	0.165056	−	0.507990i	0.999040	+	0.0437981i	$0.0139458\pi$
$240$	−3.73151	−	0.659963i	−0.240868	−	0.0426004i
$241$	−11.1487			−0.718154			−0.359077	−	0.933308i	$-0.616908\pi$
$241$	−11.1487			−0.718154			−0.359077	+	0.933308i	$0.616908\pi$
$242$	−19.9434	+	16.6835i	−1.28201	+	1.07245i
$243$		−	1.00000i		−	0.0641500i
$244$	−9.88600	−	7.18260i	−0.632886	−	0.459819i
$245$	8.99386	−	1.25925i	0.574597	−	0.0804503i
$246$	−1.76693	−	5.43805i	−0.112655	−	0.346718i
$247$	−11.9793	−	16.4880i	−0.762222	−	1.04911i
$248$	−22.2709	−	30.6533i	−1.41421	−	1.94649i
$249$	−2.29975	−	7.07790i	−0.145741	−	0.448544i
$250$	−22.8665	−	13.2495i	−1.44621	−	0.837971i
$251$	−23.1886	−	16.8475i	−1.46365	−	1.06341i	−0.982392	−	0.186831i	$-0.940178\pi$
$251$	−23.1886	−	16.8475i	−1.46365	−	1.06341i	−0.481262	−	0.876577i	$-0.659822\pi$
$252$		−	6.14965i		−	0.387392i
$253$	−12.5326	−	1.54837i	−0.787917	−	0.0973449i
$254$	28.2415			1.77203
$255$	−0.145377	+	0.821979i	−0.00910385	+	0.0514743i
$256$	−7.81414	+	24.0494i	−0.488384	+	1.50309i
$257$	−2.20649	+	0.716932i	−0.137637	+	0.0447210i	−0.377025	−	0.926203i	$-0.623053\pi$
$257$	−2.20649	+	0.716932i	−0.137637	+	0.0447210i	0.239388	+	0.970924i	$0.423053\pi$
$258$	−0.311898	−	0.429291i	−0.0194179	−	0.0267265i
$259$	−16.0069	+	11.6297i	−0.994619	+	0.722633i
$260$	19.6786	+	20.3990i	1.22042	+	1.26509i
$261$	−1.08672	+	3.34458i	−0.0672663	+	0.207024i
$262$	28.2545	−	38.8890i	1.74557	−	2.40257i
$263$			2.92970i			0.180653i	0.995912	+	0.0903265i	$0.0287910\pi$
$263$			2.92970i			0.180653i	−0.995912	+	0.0903265i	$0.971209\pi$
$264$	−8.49421	+	9.09522i	−0.522783	+	0.559772i
$265$	−4.91345	+	2.39329i	−0.301831	+	0.147019i
$266$	−18.9083	−	13.7377i	−1.15934	−	0.842312i
$267$	14.7469	+	4.79156i	0.902496	+	0.293239i
$268$	31.0131	−	10.0768i	1.89443	−	0.615537i
$269$	−3.66649	+	2.66386i	−0.223550	+	0.162418i	−0.693923	−	0.720049i	$-0.744119\pi$
$269$	−3.66649	+	2.66386i	−0.223550	+	0.162418i	0.470373	+	0.882468i	$0.344119\pi$
$270$	4.66558	+	2.48384i	0.283938	+	0.151161i
$271$	8.37796	+	25.7847i	0.508925	+	1.56631i	0.794071	+	0.607825i	$0.207958\pi$
$271$	8.37796	+	25.7847i	0.508925	+	1.56631i	−0.285146	+	0.958484i	$0.592042\pi$
$272$	−0.601670	−	0.195494i	−0.0364816	−	0.0118536i
$273$	−3.56024	+	4.90025i	−0.215475	+	0.296576i
$274$	12.5597			0.758761
$275$	−14.7891	+	7.50214i	−0.891817	+	0.452396i
$276$	−13.6589			−0.822167
$277$	−7.78897	+	10.7206i	−0.467994	+	0.644139i	−0.976142	−	0.217131i	$-0.930330\pi$
$277$	−7.78897	+	10.7206i	−0.467994	+	0.644139i	0.508148	+	0.861270i	$0.330330\pi$
$278$	−29.7096	−	9.65325i	−1.78187	−	0.578963i
$279$	3.12039	+	9.60356i	0.186813	+	0.574950i
$280$	12.6959	+	6.75898i	0.758725	+	0.403926i
$281$	8.95715	−	6.50775i	0.534339	−	0.388220i	−0.287640	−	0.957739i	$-0.592871\pi$
$281$	8.95715	−	6.50775i	0.534339	−	0.388220i	0.821978	+	0.569519i	$0.192871\pi$
$282$	10.5128	−	3.41583i	0.626030	−	0.203410i
$283$	9.58356	+	3.11389i	0.569683	+	0.185101i	0.579674	−	0.814849i	$-0.303180\pi$
$283$	9.58356	+	3.11389i	0.569683	+	0.185101i	−0.00999031	+	0.999950i	$0.503180\pi$
$284$	−25.4693	−	18.5045i	−1.51133	−	1.09804i
$285$	11.5951	−	5.64788i	0.686836	−	0.334551i
$286$	27.1958	−	5.26513i	1.60812	−	0.311334i
$287$			4.14669i			0.244771i
$288$	2.05648	−	2.83051i	0.121179	−	0.166789i
$289$	5.21023	−	16.0354i	0.306484	−	0.943260i
$290$	−12.9052	−	13.3776i	−0.757817	−	0.785557i
$291$	−11.8632	+	8.61910i	−0.695431	+	0.505260i
$292$	31.5498	+	43.4245i	1.84631	+	2.54123i
$293$	−7.46255	+	2.42473i	−0.435967	+	0.141654i	−0.518774	−	0.854911i	$-0.673611\pi$
$293$	−7.46255	+	2.42473i	−0.435967	+	0.141654i	0.0828074	+	0.996566i	$0.473611\pi$
$294$	2.96664	−	9.13037i	0.173018	−	0.532494i
$295$	−2.08732	+	11.8020i	−0.121528	+	0.687136i
$296$	43.3085			2.51725
$297$	2.90199	−	1.60575i	0.168391	−	0.0931752i
$298$			14.3312i			0.830184i
$299$	10.8838	+	7.90757i	0.629429	+	0.457307i
$300$	−14.8809	+	10.0148i	−0.859148	+	0.578207i
$301$	0.118916	+	0.365986i	0.00685421	+	0.0210951i
$302$	10.1910	+	14.0268i	0.586429	+	0.807150i
$303$	3.60588	+	4.96307i	0.207152	+	0.285121i
$304$	3.02059	+	9.29641i	0.173242	+	0.533185i
$305$	−7.54313	+	1.05613i	−0.431918	+	0.0604737i
$306$	0.713883	+	0.518666i	0.0408099	+	0.0296502i
$307$			2.64692i			0.151068i	0.997143	+	0.0755339i	$0.0240661\pi$
$307$			2.64692i			0.151068i	−0.997143	+	0.0755339i	$0.975934\pi$
$308$	17.8462	−	9.87481i	1.01688	−	0.562670i
$309$	−7.86989			−0.447702
$310$	−52.5567	−	9.29528i	−2.98502	−	0.527936i
$311$	−1.39311	+	4.28755i	−0.0789959	+	0.243125i	−0.982754	−	0.184920i	$-0.940797\pi$
$311$	−1.39311	+	4.28755i	−0.0789959	+	0.243125i	0.903758	+	0.428045i	$0.140797\pi$
$312$	12.6093	−	4.09701i	0.713861	−	0.231948i
$313$	−5.70694	−	7.85494i	−0.322576	−	0.443987i	0.616676	−	0.787217i	$-0.288479\pi$
$313$	−5.70694	−	7.85494i	−0.322576	−	0.443987i	−0.939251	+	0.343230i	$0.888479\pi$
$314$	−20.1862	+	14.6661i	−1.13917	+	0.827656i
$315$	−2.66129	−	2.75871i	−0.149947	−	0.155436i
$316$	9.74659	−	29.9969i	0.548288	−	1.68746i
$317$	−10.0368	+	13.8145i	−0.563725	+	0.775901i	−0.991794	−	0.127845i	$-0.959194\pi$
$317$	−10.0368	+	13.8145i	−0.563725	+	0.775901i	0.428069	+	0.903746i	$0.359194\pi$
$318$			5.77745i			0.323984i
$319$	−11.4509	+	2.21691i	−0.641130	+	0.124123i
$320$	11.4168	+	23.4387i	0.638218	+	1.31027i
$321$	4.00964	+	2.91317i	0.223796	+	0.162597i
$322$	14.6729	+	4.76750i	0.817687	+	0.265682i
$323$	2.04782	−	0.665376i	0.113944	−	0.0370225i
$324$	2.90227	−	2.10863i	0.161237	−	0.117146i
$325$	17.6555	+	0.634887i	0.979351	+	0.0352172i
$326$	−7.38264	−	22.7214i	−0.408887	−	1.25842i
$327$	−2.48861	−	0.808597i	−0.137620	−	0.0447155i
$328$	5.33512	−	7.34317i	0.294583	−	0.405459i
$329$	−8.01638			−0.441957
$330$	0.283682	+	17.5279i	0.0156162	+	0.964879i
$331$	−2.79769			−0.153775			−0.0768874	−	0.997040i	$-0.524498\pi$
$331$	−2.79769			−0.153775			−0.0768874	+	0.997040i	$0.524498\pi$
$332$	15.6927	−	21.5992i	0.861249	−	1.18541i
$333$	−10.9770	−	3.56666i	−0.601538	−	0.195452i
$334$	9.74940	+	30.0056i	0.533463	+	1.64183i
$335$	9.55160	−	17.9415i	0.521859	−	0.980248i
$336$	2.35026	−	1.70756i	0.128217	−	0.0931551i
$337$	−8.83320	+	2.87008i	−0.481175	+	0.156343i	−0.539554	−	0.841951i	$-0.681407\pi$
$337$	−8.83320	+	2.87008i	−0.481175	+	0.156343i	0.0583785	+	0.998295i	$0.481407\pi$
$338$	1.15821	+	0.376325i	0.0629984	+	0.0204694i
$339$	−1.71235	−	1.24409i	−0.0930019	−	0.0675698i
$340$	−2.69215	+	1.31132i	−0.146002	+	0.0711164i
$341$	−22.8589	+	24.4763i	−1.23788	+	1.32546i
$342$		−	13.6341i		−	0.737247i
$343$	−11.1455	+	15.3404i	−0.601799	+	0.828306i
$344$	0.260295	−	0.801104i	0.0140341	−	0.0431926i
$345$	−6.12732	+	5.91094i	−0.329884	+	0.318234i
$346$	34.1548	−	24.8149i	1.83618	−	1.33406i
$347$	−5.49888	−	7.56856i	−0.295195	−	0.406301i	0.635498	−	0.772103i	$-0.280795\pi$
$347$	−5.49888	−	7.56856i	−0.295195	−	0.406301i	−0.930693	+	0.365801i	$0.880795\pi$
$348$	−11.9984	+	3.89851i	−0.643180	+	0.208982i
$349$	0.521608	−	1.60534i	0.0279210	−	0.0859321i	−0.936125	−	0.351668i	$-0.885615\pi$
$349$	0.521608	−	1.60534i	0.0279210	−	0.0859321i	0.964046	+	0.265735i	$0.0856148\pi$
$350$	19.4812	−	5.56427i	1.04131	−	0.297423i
$351$	−3.53338			−0.188598
$352$	11.5163	+	1.42281i	0.613821	+	0.0758359i
$353$		−	9.60028i		−	0.510971i	−0.966813	−	0.255486i	$-0.917765\pi$
$353$		−	9.60028i		−	0.510971i	0.966813	−	0.255486i	$-0.0822353\pi$
$354$	10.2499	+	7.44700i	0.544777	+	0.395803i
$355$	−19.4334	+	2.72090i	−1.03142	+	0.144410i
$356$	17.1893	+	52.9032i	0.911030	+	2.80386i
$357$	−0.376142	−	0.517715i	−0.0199076	−	0.0274004i
$358$	−17.6969	−	24.3577i	−0.935312	−	1.28735i
$359$	8.40104	+	25.8557i	0.443390	+	1.36461i	0.884240	+	0.467033i	$0.154677\pi$
$359$	8.40104	+	25.8557i	0.443390	+	1.36461i	−0.440850	+	0.897581i	$0.645323\pi$
$360$	1.16340	+	8.30928i	0.0613164	+	0.437937i
$361$	−11.5440	−	8.38717i	−0.607576	−	0.441430i
$362$			48.9578i			2.57317i
$363$	9.31976	+	5.84312i	0.489161	+	0.306684i
$364$	−21.7291			−1.13891
$365$	32.9453	+	5.82677i	1.72443	+	0.304987i
$366$	−2.48811	+	7.65762i	−0.130056	+	0.400270i
$367$	−7.33892	+	2.38456i	−0.383088	+	0.124473i	−0.494229	−	0.869332i	$-0.664550\pi$
$367$	−7.33892	+	2.38456i	−0.383088	+	0.124473i	0.111141	+	0.993805i	$0.464550\pi$
$368$	−3.79263	−	5.22011i	−0.197705	−	0.272117i
$369$	−1.95699	+	1.42184i	−0.101877	+	0.0740180i
$370$	43.9057	−	42.3552i	2.28255	−	2.20194i
$371$	1.29474	−	3.98481i	0.0672196	−	0.206881i
$372$	−21.2924	+	29.3065i	−1.10396	+	1.51947i
$373$			20.0037i			1.03575i	0.855456	+	0.517876i	$0.173277\pi$
$373$			20.0037i			1.03575i	−0.855456	+	0.517876i	$0.826723\pi$
$374$	−0.358847	+	2.90453i	−0.0185555	+	0.150190i
$375$	−2.34154	+	10.9324i	−0.120917	+	0.564546i
$376$	14.1958	+	10.3139i	0.732093	+	0.531896i
$377$	11.8177	+	3.83980i	0.608642	+	0.197760i
$378$	−3.85373	+	1.25215i	−0.198214	+	0.0644038i
$379$	−5.43469	+	3.94854i	−0.279161	+	0.202823i	−0.718552	−	0.695474i	$-0.755195\pi$
$379$	−5.43469	+	3.94854i	−0.279161	+	0.202823i	0.439390	+	0.898296i	$0.355195\pi$
$380$	40.8415	+	21.7430i	2.09512	+	1.11539i
$381$	−3.69203	−	11.3629i	−0.189148	−	0.582139i
$382$	−13.9371	−	4.52845i	−0.713085	−	0.231695i
$383$	6.67102	−	9.18187i	0.340873	−	0.469171i	−0.603823	−	0.797118i	$-0.706357\pi$
$383$	6.67102	−	9.18187i	0.340873	−	0.469171i	0.944696	+	0.327947i	$0.106357\pi$
$384$	20.5629			1.04935
$385$	3.73238	−	12.1529i	0.190220	−	0.619367i
$386$	−13.0566			−0.664562
$387$	−0.131949	+	0.181613i	−0.00670737	+	0.00923190i
$388$	−50.0300	−	16.2557i	−2.53989	−	0.825259i
$389$	1.59639	+	4.91317i	0.0809399	+	0.249108i	0.983335	−	0.181802i	$-0.0581929\pi$
$389$	1.59639	+	4.91317i	0.0809399	+	0.249108i	−0.902395	+	0.430909i	$0.858193\pi$
$390$	8.77635	−	16.4853i	0.444408	−	0.834764i
$391$	−1.14989	+	0.835442i	−0.0581523	+	0.0422501i
$392$	14.4936	−	4.70926i	0.732038	−	0.237854i
$393$	−19.3406	−	6.28415i	−0.975606	−	0.316993i
$394$	−24.5780	−	17.8569i	−1.23822	−	0.899619i
$395$	−8.60903	−	17.6744i	−0.433167	−	0.889295i
$396$	10.7795	+	5.03645i	0.541693	+	0.253091i
$397$		−	7.40026i		−	0.371408i	−0.982606	−	0.185704i	$-0.940543\pi$
$397$		−	7.40026i		−	0.371408i	0.982606	−	0.185704i	$-0.0594566\pi$
$398$	−4.76324	+	6.55604i	−0.238760	+	0.328625i
$399$	−3.05543	+	9.40365i	−0.152963	+	0.470771i
$400$	−7.95939	−	2.90634i	−0.397969	−	0.145317i
$401$	25.7212	−	18.6876i	1.28446	−	0.933213i	0.284780	−	0.958593i	$-0.408079\pi$
$401$	25.7212	−	18.6876i	1.28446	−	0.933213i	0.999678	+	0.0253797i	$0.00807948\pi$
$402$	−12.6294	−	17.3829i	−0.629896	−	0.866978i
$403$	33.9331	−	11.0255i	1.69033	−	0.549220i
$404$	−6.80073	+	20.9305i	−0.338349	+	1.04133i
$405$	0.389432	−	2.20190i	0.0193510	−	0.109413i
$406$	14.2498			0.707208
$407$	−7.27600	−	37.5825i	−0.360658	−	1.86289i
$408$			1.40074i			0.0693470i
$409$	9.62734	+	6.99467i	0.476041	+	0.345864i	0.799791	−	0.600279i	$-0.204944\pi$
$409$	9.62734	+	6.99467i	0.476041	+	0.345864i	−0.323750	+	0.946143i	$0.604944\pi$
$410$	−1.77285	−	12.6621i	−0.0875547	−	0.625338i
$411$	−1.64194	−	5.05338i	−0.0809910	−	0.249265i
$412$	−16.5946	−	22.8406i	−0.817560	−	1.12527i
$413$	−5.40064	−	7.43335i	−0.265748	−	0.365771i
$414$	2.78113	+	8.55944i	0.136685	+	0.420673i
$415$	−2.30745	−	16.4804i	−0.113268	−	0.808991i
$416$	−10.0013	−	7.26634i	−0.490352	−	0.356262i
$417$			13.2156i			0.647169i
$418$	39.5660	−	21.8929i	1.93524	−	1.07082i
$419$	−6.57012			−0.320971			−0.160486	−	0.987038i	$-0.551306\pi$
$419$	−6.57012			−0.320971			−0.160486	+	0.987038i	$0.551306\pi$
$420$	2.39487	−	13.5409i	0.116858	−	0.660728i
$421$	9.68283	−	29.8007i	0.471912	−	1.45240i	−0.378165	−	0.925738i	$-0.623445\pi$
$421$	9.68283	−	29.8007i	0.471912	−	1.45240i	0.850077	−	0.526658i	$-0.176555\pi$
$422$	−40.0814	+	13.0232i	−1.95113	+	0.633961i
$423$	−2.74870	−	3.78326i	−0.133646	−	0.183948i
$424$	−7.41964	+	5.39068i	−0.360330	+	0.261795i
$425$	−0.640209	+	1.75330i	−0.0310547	+	0.0850474i
$426$	−6.41012	+	19.7283i	−0.310571	+	0.955840i
$427$	3.43218	−	4.72399i	0.166095	−	0.228610i
$428$			17.7799i			0.859422i
$429$	−5.67374	−	10.2539i	−0.273931	−	0.495061i
$430$	−0.519588	−	1.06672i	−0.0250567	−	0.0514416i
$431$	−10.1465	−	7.37184i	−0.488738	−	0.355089i	0.315961	−	0.948772i	$-0.397673\pi$
$431$	−10.1465	−	7.37184i	−0.488738	−	0.355089i	−0.804699	+	0.593683i	$0.797673\pi$
$432$	1.61174	+	0.523685i	0.0775448	+	0.0251958i
$433$	−24.7497	+	8.04167i	−1.18939	+	0.386458i	−0.835849	−	0.548959i	$-0.815024\pi$
$433$	−24.7497	+	8.04167i	−1.18939	+	0.386458i	−0.353546	+	0.935417i	$0.615024\pi$
$434$	33.1023	−	24.0502i	1.58896	−	1.15445i
$435$	−3.69533	+	6.94121i	−0.177177	+	0.332806i
$436$	−2.90077	−	8.92764i	−0.138922	−	0.427557i
$437$	20.8863	+	6.78636i	0.999125	+	0.324635i
$438$	20.7884	−	28.6127i	0.993307	−	1.36717i
$439$	35.0511			1.67290			0.836450	−	0.548044i	$-0.184627\pi$
$439$	35.0511			1.67290			0.836450	+	0.548044i	$0.184627\pi$
$440$	−22.2453	+	16.7188i	−1.06050	+	0.797038i
$441$	−4.06141			−0.193400
$442$	1.83265	−	2.52242i	0.0871701	−	0.119979i
$443$	24.8003	+	8.05811i	1.17830	+	0.382852i	0.831734	−	0.555174i	$-0.187348\pi$
$443$	24.8003	+	8.05811i	1.17830	+	0.382852i	0.346564	+	0.938026i	$0.387348\pi$
$444$	−12.7951	−	39.3792i	−0.607227	−	1.86885i
$445$	30.6052	+	16.2934i	1.45082	+	0.772382i
$446$	−8.25570	+	5.99812i	−0.390919	+	0.284019i
$447$	5.76612	−	1.87353i	0.272728	−	0.0886147i
$448$	−19.0088	−	6.17634i	−0.898082	−	0.291805i
$449$	−0.577580	−	0.419636i	−0.0272577	−	0.0198039i	0.574073	−	0.818804i	$-0.305363\pi$
$449$	−0.577580	−	0.419636i	−0.0272577	−	0.0198039i	−0.601331	+	0.799000i	$0.705363\pi$
$450$	9.30583	+	7.28607i	0.438681	+	0.343469i
$451$	−7.26862	−	3.39606i	−0.342266	−	0.159914i
$452$		−	7.59303i		−	0.357146i
$453$	4.31135	−	5.93407i	0.202565	−	0.278807i
$454$	−18.5798	+	57.1828i	−0.871995	+	2.68372i
$455$	−9.74758	+	9.40336i	−0.456974	+	0.440836i
$456$	17.5094	−	12.7213i	0.819954	−	0.595732i
$457$	17.6323	+	24.2688i	0.824805	+	1.13525i	0.988868	+	0.148796i	$0.0475399\pi$
$457$	17.6323	+	24.2688i	0.824805	+	1.13525i	−0.164063	+	0.986450i	$0.552460\pi$
$458$	32.3574	−	10.5136i	1.51196	−	0.491266i
$459$	0.115358	−	0.355034i	0.00538443	−	0.0165716i
$460$	−30.0754	−	5.31919i	−1.40227	−	0.248009i
$461$	0.0359281			0.00167334			0.000836670	−	1.00000i	$-0.499734\pi$
$461$	0.0359281			0.00167334			0.000836670		1.00000i	$0.499734\pi$
$462$	−9.82187	−	9.17285i	−0.456955	−	0.426759i
$463$			3.65474i			0.169850i	0.996387	+	0.0849251i	$0.0270651\pi$
$463$			3.65474i			0.169850i	−0.996387	+	0.0849251i	$0.972935\pi$
$464$	−4.82149	−	3.50302i	−0.223832	−	0.162623i
$465$	3.13083	+	22.3612i	0.145189	+	1.03698i
$466$	−8.71532	−	26.8230i	−0.403729	−	1.24255i
$467$	−8.95659	−	12.3277i	−0.414462	−	0.570457i	0.549838	−	0.835271i	$-0.314689\pi$
$467$	−8.95659	−	12.3277i	−0.414462	−	0.570457i	−0.964300	+	0.264814i	$0.914689\pi$
$468$	−7.45058	−	10.2548i	−0.344403	−	0.474031i
$469$	4.81515	+	14.8195i	0.222343	+	0.684302i
$470$	24.4784	−	3.42727i	1.12910	−	0.158088i
$471$	8.53981	+	6.20454i	0.393494	+	0.285890i
$472$			20.1118i			0.925721i
$473$	−0.738917	−	0.0912911i	−0.0339754	−	0.00419757i
$474$	−20.7824			−0.954565
$475$	27.7307	−	7.92053i	1.27237	−	0.363419i
$476$	0.709409	−	2.18334i	0.0325157	−	0.100073i
$477$	2.32454	−	0.755290i	0.106434	−	0.0345823i
$478$	−11.4729	−	15.7910i	−0.524756	−	0.722265i
$479$	−10.1619	+	7.38305i	−0.464309	+	0.337340i	−0.795219	−	0.606322i	$-0.792644\pi$
$479$	−10.1619	+	7.38305i	−0.464309	+	0.337340i	0.330910	+	0.943662i	$0.392644\pi$
$480$	5.63045	−	5.43162i	0.256994	−	0.247918i
$481$	−12.6024	+	38.7861i	−0.574619	+	1.76849i
$482$	−15.4899	+	21.3201i	−0.705548	+	0.971103i
$483$		−	6.52684i		−	0.296982i
$484$	2.69355	+	39.3695i	0.122434	+	1.78952i
$485$	−29.4780	+	14.3585i	−1.33853	+	0.651984i
$486$	−1.91233	−	1.38939i	−0.0867451	−	0.0630240i
$487$	1.63805	+	0.532235i	0.0742271	+	0.0241179i	0.345895	−	0.938273i	$-0.387575\pi$
$487$	1.63805	+	0.532235i	0.0742271	+	0.0241179i	−0.271668	+	0.962391i	$0.587575\pi$
$488$	−12.1558	+	3.94965i	−0.550266	+	0.178792i
$489$	−8.17677	+	5.94077i	−0.369766	+	0.268651i
$490$	10.0879	−	18.9488i	0.455724	−	0.856020i
$491$	6.21824	+	19.1378i	0.280625	+	0.863675i	0.987676	+	0.156513i	$0.0500252\pi$
$491$	6.21824	+	19.1378i	0.280625	+	0.863675i	−0.707051	+	0.707163i	$0.749975\pi$
$492$	−8.25314	−	2.68161i	−0.372080	−	0.120896i
$493$	−0.771645	+	1.06208i	−0.0347532	+	0.0478336i
$494$	−48.1744			−2.16747
$495$	7.01521	−	2.40557i	0.315310	−	0.108122i
$496$	−17.1125			−0.768375
$497$	8.84233	−	12.1704i	0.396633	−	0.545918i
$498$	−16.7305	−	5.43608i	−0.749713	−	0.243597i
$499$	−5.52718	−	17.0109i	−0.247430	−	0.761513i	−0.995227	−	0.0975849i	$-0.968888\pi$
$499$	−5.52718	−	17.0109i	−0.247430	−	0.761513i	0.747797	−	0.663928i	$-0.231112\pi$
$500$	−36.6662	+	16.2565i	−1.63976	+	0.727014i
$501$	10.7981	−	7.84529i	0.482424	−	0.350502i
$502$	−64.4361	+	20.9366i	−2.87592	+	0.934444i
$503$	−15.5816	−	5.06278i	−0.694750	−	0.225738i	−0.0597085	−	0.998216i	$-0.519017\pi$
$503$	−15.5816	−	5.06278i	−0.694750	−	0.225738i	−0.635042	+	0.772478i	$0.719017\pi$
$504$	−5.20381	−	3.78079i	−0.231796	−	0.168410i
$505$	6.00699	+	12.3324i	0.267308	+	0.548784i
$506$	−20.3736	+	21.8152i	−0.905718	+	0.969802i
$507$		−	0.515200i		−	0.0228808i
$508$	25.1931	−	34.6754i	1.11777	−	1.53847i
$509$	−0.0434607	+	0.133758i	−0.00192636	+	0.00592873i	−0.952015	−	0.306051i	$-0.900992\pi$
$509$	−0.0434607	+	0.133758i	−0.00192636	+	0.00592873i	0.950089	+	0.311980i	$0.100992\pi$
$510$	1.36991	+	1.42006i	0.0606606	+	0.0628812i
$511$	−20.7503	+	15.0760i	−0.917938	+	0.666921i
$512$	10.9604	+	15.0857i	0.484387	+	0.666701i
$513$	−5.48564	+	1.78239i	−0.242197	+	0.0786945i
$514$	−1.69466	+	5.21564i	−0.0747484	+	0.230052i
$515$	−17.3287	−	3.06478i	−0.763592	−	0.135050i
$516$	−0.805322			−0.0354523
$517$	6.56526	−	14.0517i	0.288740	−	0.617992i
$518$			46.7686i			2.05489i
$519$	−14.4493	−	10.4980i	−0.634254	−	0.460813i
$520$	29.3599	−	4.11073i	1.28752	−	0.180267i
$521$	1.82811	+	5.62634i	0.0800909	+	0.246495i	0.983082	−	0.183164i	$-0.0586339\pi$
$521$	1.82811	+	5.62634i	0.0800909	+	0.246495i	−0.902991	+	0.429659i	$0.858634\pi$
$522$	4.88606	+	6.72509i	0.213857	+	0.294349i
$523$	−11.1538	−	15.3518i	−0.487720	−	0.671289i	0.492246	−	0.870456i	$-0.336176\pi$
$523$	−11.1538	−	15.3518i	−0.487720	−	0.671289i	−0.979965	+	0.199168i	$0.936176\pi$
$524$	−22.5438	−	69.3827i	−0.984831	−	3.03100i
$525$	−4.78556	−	7.11078i	−0.208859	−	0.310340i
$526$	5.60255	+	4.07049i	0.244283	+	0.177482i
$527$			3.76955i			0.164204i
$528$	1.06832	+	5.51816i	0.0464927	+	0.240147i
$529$	8.50336			0.369711
$530$	−2.24992	+	12.7213i	−0.0977304	+	0.552580i
$531$	1.65630	−	5.09757i	0.0718774	−	0.221216i
$532$	−33.7347	+	10.9611i	−1.46259	+	0.475223i
$533$	5.02391	+	6.91481i	0.217610	+	0.299514i
$534$	29.6522	−	21.5436i	1.28318	−	0.932283i
$535$	7.69432	+	7.97598i	0.332655	+	0.344832i
$536$	10.5398	−	32.4383i	0.455252	−	1.40112i
$537$	−7.48674	+	10.3046i	−0.323077	+	0.444677i
$538$			10.7127i			0.461856i
$539$	−6.52162	−	11.7862i	−0.280906	−	0.507667i
$540$	7.21167	−	3.51274i	0.310341	−	0.151164i
$541$	−14.8245	−	10.7706i	−0.637354	−	0.463065i	0.221586	−	0.975141i	$-0.428877\pi$
$541$	−14.8245	−	10.7706i	−0.637354	−	0.463065i	−0.858940	+	0.512076i	$0.828877\pi$
$542$	60.9491	+	19.8036i	2.61799	+	0.850636i
$543$	19.6980	−	6.40028i	0.845324	−	0.274662i
$544$	1.05664	−	0.767696i	0.0453032	−	0.0329147i
$545$	−5.16476	−	2.74959i	−0.221234	−	0.117779i
$546$	4.42433	+	13.6167i	0.189344	+	0.582741i
$547$	29.3476	+	9.53561i	1.25481	+	0.407713i	0.859643	−	0.510895i	$-0.170686\pi$
$547$	29.3476	+	9.53561i	1.25481	+	0.407713i	0.395169	+	0.918608i	$0.370686\pi$
$548$	11.2040	−	15.4210i	0.478613	−	0.658754i
$549$	3.40629			0.145377
$550$	−6.20128	+	38.7051i	−0.264423	+	1.65039i
$551$	20.2841			0.864132
$552$	−8.39743	+	11.5581i	−0.357418	+	0.491944i
$553$	14.3339	+	4.65738i	0.609541	+	0.198052i
$554$	9.67942	+	29.7902i	0.411239	+	1.26566i
$555$	−22.7813	−	12.1282i	−0.967014	−	0.514814i
$556$	−38.3552	+	27.8667i	−1.62662	+	1.18181i
$557$	35.4614	−	11.5221i	1.50255	−	0.488207i	0.561787	−	0.827282i	$-0.310114\pi$
$557$	35.4614	−	11.5221i	1.50255	−	0.488207i	0.940759	+	0.339075i	$0.110114\pi$
$558$	22.7006	+	7.37587i	0.960993	+	0.312246i
$559$	0.641708	+	0.466228i	0.0271413	+	0.0197193i
$560$	5.84000	−	2.84461i	0.246785	−	0.120207i
$561$	1.21554	−	0.235330i	0.0513202	−	0.00993564i
$562$		−	26.1708i		−	1.10395i
$563$	−10.8591	+	14.9463i	−0.457658	+	0.629912i	−0.974021	−	0.226458i	$-0.927285\pi$
$563$	−10.8591	+	14.9463i	−0.457658	+	0.629912i	0.516363	+	0.856370i	$0.327285\pi$
$564$	5.18408	−	15.9550i	0.218289	−	0.671825i
$565$	−3.28592	−	3.40620i	−0.138240	−	0.143300i
$566$	19.2701	−	14.0005i	0.809981	−	0.588486i
$567$	1.00760	+	1.38684i	0.0423152	+	0.0582419i
$568$	−31.3169	+	10.1755i	−1.31403	+	0.426954i
$569$	12.9706	−	39.9193i	0.543755	−	1.67351i	−0.180176	−	0.983634i	$-0.557667\pi$
$569$	12.9706	−	39.9193i	0.543755	−	1.67351i	0.723932	−	0.689872i	$-0.242333\pi$
$570$	5.30954	−	30.0208i	0.222392	−	1.25743i
$571$	−9.70741			−0.406243			−0.203121	−	0.979154i	$-0.565109\pi$
$571$	−9.70741			−0.406243			−0.203121	+	0.979154i	$0.565109\pi$
$572$	17.7957	−	38.0883i	0.744076	−	1.59255i
$573$			6.19957i			0.258991i
$574$	7.92984	+	5.76137i	0.330985	+	0.240475i
$575$	−15.7936	+	10.6291i	−0.658639	+	0.443264i
$576$	−3.60298	−	11.0888i	−0.150124	−	0.462034i
$577$	−7.65924	−	10.5420i	−0.318859	−	0.438871i	0.619260	−	0.785186i	$-0.287433\pi$
$577$	−7.65924	−	10.5420i	−0.318859	−	0.438871i	−0.938118	+	0.346315i	$0.887433\pi$
$578$	−23.4260	−	32.2431i	−0.974393	−	1.34114i
$579$	1.70689	+	5.25328i	0.0709361	+	0.218319i
$580$	−27.9374	+	3.91156i	−1.16004	+	0.162419i
$581$	10.3211	+	7.49871i	0.428191	+	0.311099i
$582$			34.6616i			1.43677i
$583$	5.92448	+	5.53300i	0.245367	+	0.229153i
$584$	56.1423			2.32319
$585$	−7.78014	−	1.37601i	−0.321669	−	0.0568911i
$586$	−5.73150	+	17.6397i	−0.236766	+	0.728691i
$587$	41.1222	−	13.3614i	1.69730	−	0.551485i	0.709158	−	0.705050i	$-0.249075\pi$
$587$	41.1222	−	13.3614i	1.69730	−	0.551485i	0.988139	+	0.153565i	$0.0490755\pi$
$588$	−8.56399	−	11.7873i	−0.353173	−	0.486101i
$589$	47.1199	−	34.2346i	1.94154	−	1.41061i
$590$	19.6691	+	20.3891i	0.809765	+	0.839408i
$591$	−3.97160	+	12.2233i	−0.163370	+	0.502800i
$592$	11.4970	−	15.8243i	0.472525	−	0.650375i
$593$		−	34.9632i		−	1.43576i	−0.696164	−	0.717882i	$-0.745112\pi$
$593$		−	34.9632i		−	1.43576i	0.696164	−	0.717882i	$-0.254888\pi$
$594$	0.961269	−	7.78058i	0.0394414	−	0.319241i
$595$	−0.626611	−	1.28644i	−0.0256886	−	0.0527388i
$596$	17.5961	+	12.7843i	0.720763	+	0.523665i
$597$	3.26051	+	1.05940i	0.133444	+	0.0433585i
$598$	30.2438	−	9.82680i	1.23676	−	0.401848i
$599$	18.2378	−	13.2505i	0.745174	−	0.541401i	−0.149153	−	0.988814i	$-0.547655\pi$
$599$	18.2378	−	13.2505i	0.745174	−	0.541401i	0.894327	+	0.447413i	$0.147655\pi$
$600$	−0.674217	+	18.7492i	−0.0275248	+	0.765434i
$601$	−6.16194	−	18.9645i	−0.251351	−	0.773578i	−0.994527	−	0.104482i	$-0.966682\pi$
$601$	−6.16194	−	18.9645i	−0.251351	−	0.773578i	0.743176	−	0.669096i	$-0.233318\pi$
$602$	0.865107	+	0.281090i	0.0352591	+	0.0114564i
$603$	−5.34290	+	7.35387i	−0.217580	+	0.299473i
$604$	26.3133			1.07067
$605$	18.2456	+	16.4954i	0.741791	+	0.670631i
$606$	14.5010			0.589063
$607$	9.64463	−	13.2747i	0.391463	−	0.538803i	−0.567113	−	0.823640i	$-0.691940\pi$
$607$	9.64463	−	13.2747i	0.391463	−	0.538803i	0.958576	+	0.284837i	$0.0919396\pi$
$608$	−19.1926	−	6.23605i	−0.778362	−	0.252905i
$609$	−1.86289	−	5.73338i	−0.0754881	−	0.232328i
$610$	−8.46068	+	15.8923i	−0.342563	+	0.643461i
$611$	−13.3677	+	9.71221i	−0.540800	+	0.392914i
$612$	1.27365	−	0.413835i	0.0514844	−	0.0167283i
$613$	−35.4555	−	11.5202i	−1.43204	−	0.465297i	−0.512631	−	0.858609i	$-0.671329\pi$
$613$	−35.4555	−	11.5202i	−1.43204	−	0.465297i	−0.919405	+	0.393313i	$0.871329\pi$
$614$	5.06179	+	3.67761i	0.204277	+	0.148416i
$615$	−4.86281	+	2.36863i	−0.196087	+	0.0955123i
$616$	2.61579	−	21.1724i	0.105393	−	0.853061i
$617$		−	28.7965i		−	1.15930i	−0.814865	−	0.579651i	$-0.803189\pi$
$617$		−	28.7965i		−	1.15930i	0.814865	−	0.579651i	$-0.196811\pi$
$618$	−10.9343	+	15.0498i	−0.439844	+	0.605393i
$619$	−2.58639	+	7.96009i	−0.103956	+	0.319943i	−0.989484	−	0.144643i	$-0.953797\pi$
$619$	−2.58639	+	7.96009i	−0.103956	+	0.319943i	0.885528	+	0.464586i	$0.153797\pi$
$620$	−58.2966	+	56.2380i	−2.34125	+	2.25857i
$621$	3.08029	−	2.23796i	0.123608	−	0.0898062i
$622$	6.26364	+	8.62116i	0.251149	+	0.345677i
$623$	−25.2796	+	8.21384i	−1.01281	+	0.329081i
$624$	1.85038	−	5.69489i	0.0740746	−	0.227978i
$625$	−9.41325	+	23.1601i	−0.376530	+	0.926404i
$626$	−22.9504			−0.917282
$627$	−13.9811	−	13.0572i	−0.558350	−	0.521454i
$628$			37.8679i			1.51109i
$629$	−3.48579	−	2.53257i	−0.138987	−	0.100980i
$630$	−8.97313	+	1.25634i	−0.357498	+	0.0500540i
$631$	−9.24911	−	28.4658i	−0.368201	−	1.13321i	−0.947952	−	0.318413i	$-0.896850\pi$
$631$	−9.24911	−	28.4658i	−0.368201	−	1.13321i	0.579751	−	0.814794i	$-0.303150\pi$
$632$	−19.3911	−	26.6895i	−0.771336	−	1.06165i
$633$	10.4797	+	14.4241i	0.416532	+	0.573307i
$634$	12.4729	+	38.3875i	0.495360	+	1.52456i
$635$	−3.70439	−	26.4577i	−0.147004	−	1.04994i
$636$	7.09365	+	5.15384i	0.281281	+	0.204363i
$637$			14.3505i			0.568588i
$638$	−11.6704	+	24.9781i	−0.462034	+	0.988894i
$639$	8.77564			0.347159
$640$	45.2774	+	8.00786i	1.78975	+	0.316538i
$641$	0.654461	−	2.01423i	0.0258497	−	0.0795571i	−0.937299	−	0.348525i	$-0.886683\pi$
$641$	0.654461	−	2.01423i	0.0258497	−	0.0795571i	0.963149	+	0.268968i	$0.0866826\pi$
$642$	11.1419	−	3.62022i	0.439735	−	0.142879i
$643$	11.3642	+	15.6415i	0.448161	+	0.616841i	0.972001	−	0.234976i	$-0.0755011\pi$
$643$	11.3642	+	15.6415i	0.448161	+	0.616841i	−0.523840	+	0.851817i	$0.675501\pi$
$644$	18.9427	−	13.7627i	0.746447	−	0.542325i
$645$	−0.361265	+	0.348507i	−0.0142248	+	0.0137225i
$646$	1.57279	−	4.84056i	0.0618808	−	0.190449i
$647$	−1.23652	+	1.70192i	−0.0486125	+	0.0669094i	−0.832631	−	0.553828i	$-0.813167\pi$
$647$	−1.23652	+	1.70192i	−0.0486125	+	0.0669094i	0.784019	+	0.620737i	$0.213167\pi$
$648$		−	3.75227i		−	0.147403i
$649$	17.4527	−	3.37886i	0.685080	−	0.132632i
$650$	25.7445	−	32.8811i	1.00978	−	1.28970i
$651$	−14.0040	−	10.1745i	−0.548861	−	0.398771i
$652$	−34.4835	−	11.2044i	−1.35048	−	0.438797i
$653$	2.49399	−	0.810347i	0.0975974	−	0.0317113i	−0.259811	−	0.965659i	$-0.583660\pi$
$653$	2.49399	−	0.810347i	0.0975974	−	0.0317113i	0.357409	+	0.933948i	$0.383660\pi$
$654$	−5.00395	+	3.63558i	−0.195670	+	0.142162i
$655$	−40.1388	−	21.3689i	−1.56835	−	0.834952i
$656$	−1.26678	−	3.89876i	−0.0494596	−	0.152221i
$657$	−14.2299	−	4.62358i	−0.555162	−	0.180383i
$658$	−11.1379	+	15.3300i	−0.434199	+	0.597624i
$659$	−36.2473			−1.41199			−0.705997	−	0.708215i	$-0.749501\pi$
$659$	−36.2473			−1.41199			−0.705997	+	0.708215i	$0.749501\pi$
$660$	21.7741	+	15.2876i	0.847555	+	0.595070i
$661$	22.6488			0.880937			0.440469	−	0.897768i	$-0.354812\pi$
$661$	22.6488			0.880937			0.440469	+	0.897768i	$0.354812\pi$
$662$	−3.88707	+	5.35010i	−0.151075	+	0.207938i
$663$	−1.25447	−	0.407603i	−0.0487197	−	0.0158300i
$664$	−8.62928	−	26.5582i	−0.334881	−	1.03066i
$665$	−10.3898	+	19.5160i	−0.402900	+	0.756797i
$666$	−22.0720	+	16.0363i	−0.855273	+	0.621392i
$667$	−12.7343	+	4.13763i	−0.493074	+	0.160210i
$668$	45.5384	+	14.7963i	1.76193	+	0.572486i
$669$	3.49260	+	2.53752i	0.135032	+	0.0981063i
$670$	−21.0391	−	43.1935i	−0.812813	−	1.66871i
$671$	5.46966	+	9.88504i	0.211154	+	0.381608i
$672$			5.99758i			0.231362i
$673$	21.7554	−	29.9438i	0.838610	−	1.15425i	−0.147649	−	0.989040i	$-0.547171\pi$
$673$	21.7554	−	29.9438i	0.838610	−	1.15425i	0.986259	−	0.165208i	$-0.0528295\pi$
$674$	−6.78421	+	20.8797i	−0.261318	+	0.804254i
$675$	1.71498	−	4.69669i	0.0660094	−	0.180776i
$676$	1.49525	−	1.08636i	0.0575097	−	0.0417832i
$677$	17.4668	+	24.0410i	0.671303	+	0.923969i	0.999789	−	0.0205398i	$-0.00653850\pi$
$677$	17.4668	+	24.0410i	0.671303	+	0.923969i	−0.328486	+	0.944509i	$0.606538\pi$
$678$	−4.75823	+	1.54604i	−0.182739	+	0.0593754i
$679$	7.76775	−	23.9067i	0.298099	−	0.917454i
$680$	−0.545493	+	3.08428i	−0.0209187	+	0.118277i
$681$	25.4363			0.974722
$682$	15.0468	+	77.7208i	0.576172	+	2.97608i
$683$		−	2.06173i		−	0.0788899i	−0.999222	−	0.0394450i	$-0.987441\pi$
$683$		−	2.06173i		−	0.0788899i	0.999222	−	0.0394450i	$-0.0125590\pi$
$684$	−16.7401	−	12.1624i	−0.640075	−	0.465042i
$685$	−1.64744	−	11.7664i	−0.0629454	−	0.449572i
$686$	13.8506	+	42.6277i	0.528817	+	1.62753i
$687$	−8.46020	−	11.6445i	−0.322777	−	0.444264i
$688$	−0.223612	−	0.307776i	−0.00852514	−	0.0117338i
$689$	−2.66873	−	8.21350i	−0.101670	−	0.312910i
$690$	2.79044	+	19.9300i	0.106230	+	0.758724i
$691$	−2.40744	−	1.74910i	−0.0915832	−	0.0665391i	0.541051	−	0.840990i	$-0.318026\pi$
$691$	−2.40744	−	1.74910i	−0.0915832	−	0.0665391i	−0.632635	+	0.774450i	$0.718026\pi$
$692$		−	64.0723i		−	2.43566i
$693$	−2.40665	+	5.15097i	−0.0914211	+	0.195669i
$694$	−22.1137			−0.839423
$695$	−5.14656	+	29.0993i	−0.195220	+	1.10380i
$696$	−4.07766	+	12.5498i	−0.154563	+	0.475697i
$697$	−0.858820	+	0.279048i	−0.0325301	+	0.0105697i
$698$	−2.34523	−	3.22793i	−0.0887683	−	0.122179i
$699$	−9.65280	+	7.01317i	−0.365102	+	0.265262i
$700$	10.5465	−	28.8830i	0.398620	−	1.09167i
$701$	13.1671	−	40.5240i	0.497313	−	1.53057i	−0.316008	−	0.948756i	$-0.602343\pi$
$701$	13.1671	−	40.5240i	0.497313	−	1.53057i	0.813321	−	0.581815i	$-0.197657\pi$
$702$	−4.90924	+	6.75700i	−0.185288	+	0.255026i
$703$			66.5733i			2.51086i
$704$	26.3942	−	28.2617i	0.994769	−	1.06515i
$705$	−4.57903	−	9.40077i	−0.172456	−	0.354054i
$706$	−18.3589	−	13.3385i	−0.690946	−	0.502002i
$707$	−10.0016	−	3.24971i	−0.376148	−	0.122218i
$708$	18.2871	−	5.94183i	0.687271	−	0.223308i
$709$	−33.6641	+	24.4584i	−1.26428	+	0.918555i	−0.998960	−	0.0456046i	$-0.985479\pi$
$709$	−33.6641	+	24.4584i	−1.26428	+	0.918555i	−0.265323	+	0.964160i	$0.585479\pi$
$710$	−21.7972	+	40.9434i	−0.818036	+	1.53658i
$711$	2.71689	+	8.36172i	0.101891	+	0.313589i
$712$	55.3343	+	17.9792i	2.07374	+	0.673800i
$713$	−22.5984	+	31.1041i	−0.846318	+	1.16486i
$714$	−1.51265			−0.0566095
$715$	−8.49980	−	24.7874i	−0.317875	−	0.926998i
$716$	−45.6936			−1.70765
$717$	−4.85363	+	6.68044i	−0.181262	+	0.249486i
$718$	61.1170	+	19.8581i	2.28087	+	0.741098i
$719$	−1.51504	−	4.66282i	−0.0565015	−	0.173894i	0.918823	−	0.394670i	$-0.129141\pi$
$719$	−1.51504	−	4.66282i	−0.0565015	−	0.173894i	−0.975325	+	0.220776i	$0.929141\pi$
$720$	3.34494	+	1.78076i	0.124659	+	0.0663651i
$721$	10.9143	−	7.92970i	0.406470	−	0.295317i
$722$	−32.0781	+	10.4228i	−1.19382	+	0.387897i
$723$	10.6031	+	3.44515i	0.394333	+	0.128127i
$724$	60.1112	+	43.6733i	2.23401	+	1.62311i
$725$	−10.8399	+	13.8447i	−0.402582	+	0.514181i
$726$	24.1228	−	9.70409i	0.895279	−	0.360153i
$727$		−	9.26283i		−	0.343539i	−0.985137	−	0.171770i	$-0.945052\pi$
$727$		−	9.26283i		−	0.343539i	0.985137	−	0.171770i	$-0.0549485\pi$
$728$	−13.3590	+	18.3870i	−0.495116	+	0.681469i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	56.9165	−	54.9066i	2.10657	−	2.03218i
$731$	−0.0677970	+	0.0492574i	−0.00250756	+	0.00182185i
$732$	7.18260	+	9.88600i	0.265477	+	0.365397i
$733$	12.9843	−	4.21886i	0.479587	−	0.155827i	−0.0592398	−	0.998244i	$-0.518868\pi$
$733$	12.9843	−	4.21886i	0.479587	−	0.155827i	0.538827	+	0.842416i	$0.318868\pi$
$734$	−5.63655	+	17.3475i	−0.208049	+	0.640308i
$735$	−8.94280	−	1.58164i	−0.329860	−	0.0583397i
$736$	13.3211			0.491022
$737$	−29.9202	−	3.69656i	−1.10213	−	0.136165i
$738$			5.71791i			0.210479i
$739$	−35.7048	−	25.9410i	−1.31342	−	0.954256i	−0.999989	−	0.00464584i	$-0.998521\pi$
$739$	−35.7048	−	25.9410i	−1.31342	−	0.954256i	−0.313432	−	0.949611i	$-0.601479\pi$
$740$	−12.8379	−	91.6916i	−0.471931	−	3.37065i
$741$	6.29787	+	19.3829i	0.231358	+	0.712047i
$742$	−5.82136	−	8.01242i	−0.213709	−	0.294145i
$743$	8.72840	+	12.0136i	0.320214	+	0.440737i	0.938532	−	0.345191i	$-0.112186\pi$
$743$	8.72840	+	12.0136i	0.320214	+	0.440737i	−0.618319	+	0.785928i	$0.712186\pi$
$744$	11.7085	+	36.0351i	0.429255	+	1.32111i
$745$	13.4260	−	1.87980i	0.491891	−	0.0688705i
$746$	38.2537	+	27.7929i	1.40057	+	1.01757i
$747$			7.44215i			0.272294i
$748$	3.24612	+	3.03161i	0.118690	+	0.110847i
$749$	−8.49605			−0.310439
$750$	17.6530	+	19.6671i	0.644597	+	0.718143i
$751$	−1.17408	+	3.61343i	−0.0428426	+	0.131856i	−0.970190	−	0.242346i	$-0.922083\pi$
$751$	−1.17408	+	3.61343i	−0.0428426	+	0.131856i	0.927347	+	0.374202i	$0.122083\pi$
$752$	7.53708	−	2.44894i	0.274849	−	0.0893038i
$753$	16.8475	+	23.1886i	0.613958	+	0.845041i
$754$	23.7623	−	17.2643i	0.865373	−	0.628730i
$755$	11.8041	−	11.3872i	0.429594	−	0.414423i
$756$	−1.90035	+	5.84866i	−0.0691149	+	0.212714i
$757$	4.18455	−	5.75954i	0.152090	−	0.209334i	−0.726173	−	0.687512i	$-0.758703\pi$
$757$	4.18455	−	5.75954i	0.152090	−	0.209334i	0.878263	+	0.478178i	$0.158703\pi$
$758$			15.8790i			0.576751i
$759$	11.4407	+	5.34536i	0.415272	+	0.194024i
$760$	43.5080	−	21.1924i	1.57820	−	0.768727i
$761$	−4.43096	−	3.21928i	−0.160622	−	0.116699i	0.504571	−	0.863370i	$-0.331651\pi$
$761$	−4.43096	−	3.21928i	−0.160622	−	0.116699i	−0.665193	+	0.746671i	$0.731651\pi$
$762$	−26.8593	−	8.72711i	−0.973009	−	0.316150i
$763$	4.26605	−	1.38612i	0.154441	−	0.0501810i
$764$	−17.9929	+	13.0726i	−0.650959	+	0.472949i
$765$	0.392267	−	0.736824i	0.0141824	−	0.0266399i
$766$	−8.29012	−	25.5144i	−0.299534	−	0.921872i
$767$	−18.0117	−	5.85235i	−0.650364	−	0.211316i
$768$	14.8634	−	20.4577i	0.536336	−	0.738203i
$769$	−40.9023			−1.47498			−0.737488	−	0.675360i	$-0.763988\pi$
$769$	−40.9023			−1.47498			−0.737488	+	0.675360i	$0.763988\pi$
$770$	−18.0545	−	24.0226i	−0.650640	−	0.865714i
$771$	2.32004			0.0835542
$772$	−11.6473	+	16.0311i	−0.419194	+	0.576971i
$773$	−26.8737	−	8.73179i	−0.966579	−	0.314061i	−0.217145	−	0.976139i	$-0.569674\pi$
$773$	−26.8737	−	8.73179i	−0.966579	−	0.314061i	−0.749434	+	0.662079i	$0.769674\pi$
$774$	0.163975	+	0.504662i	0.00589394	+	0.0181397i
$775$	−1.81439	+	50.4563i	−0.0651750	+	1.81244i
$776$	−44.5138	+	32.3412i	−1.59795	+	1.16098i
$777$	18.8172	−	6.11408i	0.675063	−	0.219341i
$778$	11.6136	+	3.77349i	0.416368	+	0.135286i
$779$	11.2878	+	8.20108i	0.404428	+	0.293834i
$780$	−12.4118	−	25.4816i	−0.444415	−	0.912387i
$781$	14.0915	+	25.4668i	0.504233	+	0.911275i
$782$			3.35972i			0.120143i
$783$	2.06706	−	2.84507i	0.0738708	−	0.101674i
$784$	2.12690	−	6.54593i	0.0759607	−	0.233783i
$785$	16.3875	+	16.9874i	0.584896	+	0.606307i
$786$	−38.8890	+	28.2545i	−1.38713	+	1.00781i
$787$	−7.61672	−	10.4835i	−0.271507	−	0.373697i	0.651391	−	0.758742i	$-0.274186\pi$
$787$	−7.61672	−	10.4835i	−0.271507	−	0.373697i	−0.922898	+	0.385045i	$0.874186\pi$
$788$	−43.8500	+	14.2477i	−1.56209	+	0.507555i
$789$	0.905327	−	2.78631i	0.0322305	−	0.0991952i
$790$	−45.7606	−	8.09330i	−1.62809	−	0.287947i
$791$	3.62830			0.129008
$792$	10.8891	−	6.02521i	0.386926	−	0.214097i
$793$		−	12.0357i		−	0.427402i
$794$	−14.1517	−	10.2818i	−0.502227	−	0.364889i
$795$	5.41253	−	0.757819i	0.191963	−	0.0268771i
$796$	3.80051	+	11.6968i	0.134706	+	0.414581i
$797$	14.8535	+	20.4441i	0.526138	+	0.724167i	0.986536	−	0.163546i	$-0.0522931\pi$
$797$	14.8535	+	20.4441i	0.526138	+	0.724167i	−0.460397	+	0.887713i	$0.652293\pi$
$798$	13.7377	+	18.9083i	0.486309	+	0.669347i
$799$	−0.539454	−	1.66027i	−0.0190845	−	0.0587361i
$800$	14.5129	−	9.76718i	0.513109	−	0.345322i
$801$	−12.5445	−	9.11409i	−0.443237	−	0.322030i
$802$		−	75.1518i		−	2.65370i
$803$	−9.43213	−	48.7195i	−0.332853	−	1.71927i
$804$	−32.6091			−1.15003
$805$	2.54176	−	14.3714i	0.0895852	−	0.506526i
$806$	26.0618	−	80.2100i	0.917988	−	2.82528i
$807$	4.31022	−	1.40047i	0.151727	−	0.0492990i
$808$	13.5302	+	18.6228i	0.475992	+	0.655146i
$809$	22.2093	−	16.1360i	0.780837	−	0.567311i	−0.124393	−	0.992233i	$-0.539698\pi$
$809$	22.2093	−	16.1360i	0.780837	−	0.567311i	0.905230	+	0.424922i	$0.139698\pi$
$810$	−3.66968	−	3.80401i	−0.128939	−	0.133659i
$811$	−11.0813	+	34.1048i	−0.389117	+	1.19758i	0.544331	+	0.838870i	$0.316783\pi$
$811$	−11.0813	+	34.1048i	−0.389117	+	1.19758i	−0.933449	+	0.358710i	$0.883217\pi$
$812$	12.7117	−	17.4962i	0.446094	−	0.613996i
$813$		−	27.1116i		−	0.950847i
$814$	−81.9793	−	38.3026i	−2.87337	−	1.34250i
$815$	−20.3179	+	9.89667i	−0.711706	+	0.346665i
$816$	0.511811	+	0.371853i	0.0179170	+	0.0130174i
$817$	1.23145	+	0.400121i	0.0430829	+	0.0139985i
$818$	26.7522	−	8.69233i	0.935370	−	0.303920i
$819$	4.90025	−	3.56024i	0.171229	−	0.124405i
$820$	−17.1282	−	9.11865i	−0.598144	−	0.318437i
$821$	16.7522	+	51.5579i	0.584655	+	1.79938i	0.600651	+	0.799512i	$0.294908\pi$
$821$	16.7522	+	51.5579i	0.584655	+	1.79938i	−0.0159955	+	0.999872i	$0.505092\pi$
$822$	−11.9450	−	3.88117i	−0.416630	−	0.135371i
$823$	2.79233	−	3.84331i	0.0973344	−	0.133969i	−0.757572	−	0.652752i	$-0.773615\pi$
$823$	2.79233	−	3.84331i	0.0973344	−	0.133969i	0.854906	+	0.518782i	$0.173615\pi$
$824$	−29.5299			−1.02872
$825$	16.3836	−	2.56487i	0.570403	−	0.0892972i
$826$	−21.7186			−0.755687
$827$	−20.3747	+	28.0434i	−0.708499	+	0.975165i	0.291329	+	0.956623i	$0.405903\pi$
$827$	−20.3747	+	28.0434i	−0.708499	+	0.975165i	−0.999828	+	0.0185425i	$0.994097\pi$
$828$	12.9903	+	4.22082i	0.451446	+	0.146684i
$829$	5.49342	+	16.9070i	0.190794	+	0.587205i	1.00000		0.000320867i	$-0.000102135\pi$
$829$	5.49342	+	16.9070i	0.190794	+	0.587205i	−0.809206	+	0.587526i	$0.800102\pi$
$830$	−34.7219	−	18.4851i	−1.20521	−	0.641626i
$831$	10.7206	−	7.78897i	0.371894	−	0.270197i
$832$	−39.1811	+	12.7307i	−1.35836	+	0.441358i
$833$	−1.44194	−	0.468514i	−0.0499602	−	0.0162331i
$834$	25.2725	+	18.3616i	0.875116	+	0.635809i
$835$	26.8315	−	13.0694i	0.928543	−	0.452284i
$836$	8.41475	−	68.1096i	0.291030	−	2.35562i
$837$		−	10.0978i		−	0.349030i
$838$	−9.12845	+	12.5642i	−0.315337	+	0.434024i
$839$	−12.8972	+	39.6936i	−0.445262	+	1.37038i	0.436934	+	0.899493i	$0.356064\pi$
$839$	−12.8972	+	39.6936i	−0.445262	+	1.37038i	−0.882196	+	0.470882i	$0.843936\pi$
$840$	−9.98588	−	10.3514i	−0.344546	−	0.357158i
$841$	13.4562	−	9.77653i	0.464008	−	0.337122i
$842$	−43.5355	−	59.9215i	−1.50033	−	2.06503i
$843$	−10.5298	+	3.42133i	−0.362664	+	0.117837i
$844$	−19.7649	+	60.8301i	−0.680336	+	2.09386i
$845$	0.200635	−	1.13442i	0.00690206	−	0.0390251i
$846$	−11.0539			−0.380039
$847$	−18.8126	+	1.28710i	−0.646408	+	0.0442254i
$848$			4.14209i			0.142240i
$849$	−8.15226	−	5.92296i	−0.279785	−	0.203276i
$850$	2.46338	+	3.66030i	0.0844933	+	0.125547i
$851$	−13.5799	−	41.7945i	−0.465512	−	1.43270i
$852$	18.5045	+	25.4693i	0.633955	+	0.872564i
$853$	−21.9653	−	30.2327i	−0.752079	−	1.03515i	−0.997832	−	0.0658151i	$-0.979035\pi$
$853$	−21.9653	−	30.2327i	−0.752079	−	1.03515i	0.245753	−	0.969332i	$-0.420965\pi$
$854$	−4.26520	−	13.1269i	−0.145952	−	0.449194i
$855$	−12.7729	+	1.78836i	−0.436824	+	0.0611606i
$856$	15.0452	+	10.9310i	0.514236	+	0.373614i
$857$		−	14.6046i		−	0.498884i	−0.968390	−	0.249442i	$-0.919753\pi$
$857$		−	14.6046i		−	0.498884i	0.968390	−	0.249442i	$-0.0802472\pi$
$858$	−27.4918	−	3.39653i	−0.938554	−	0.115956i
$859$	2.27238			0.0775325			0.0387663	−	0.999248i	$-0.487657\pi$
$859$	2.27238			0.0775325			0.0387663	+	0.999248i	$0.487657\pi$
$860$	−1.77324	−	0.313618i	−0.0604668	−	0.0106943i
$861$	1.28140	−	3.94374i	0.0436699	−	0.134402i
$862$	−28.1948	+	9.16104i	−0.960318	+	0.312026i
$863$	29.2007	+	40.1913i	0.994002	+	1.36813i	0.928934	+	0.370246i	$0.120727\pi$
$863$	29.2007	+	40.1913i	0.994002	+	1.36813i	0.0650685	+	0.997881i	$0.479273\pi$
$864$	−2.83051	+	2.05648i	−0.0962958	+	0.0699630i
$865$	−27.7276	−	28.7426i	−0.942766	−	0.977277i
$866$	−19.0087	+	58.5026i	−0.645940	+	1.98800i
$867$	−9.91044	+	13.6405i	−0.336576	+	0.463257i
$868$		−	62.0978i		−	2.10774i
$869$	−19.9030	+	21.3112i	−0.675163	+	0.722934i
$870$	8.13964	+	16.7107i	0.275960	+	0.566547i
$871$	25.9840	+	18.8785i	0.880435	+	0.639674i
$872$	−9.33791	−	3.03407i	−0.316222	−	0.102747i
$873$	13.9460	−	4.53133i	0.472000	−	0.153362i
$874$	41.9969	−	30.5125i	1.42057	−	1.03210i
$875$	−7.76813	−	17.5208i	−0.262611	−	0.592313i
$876$	−16.5867	−	51.0486i	−0.560412	−	1.72477i
$877$	−9.86924	−	3.20671i	−0.333261	−	0.108283i	0.137607	−	0.990487i	$-0.456059\pi$
$877$	−9.86924	−	3.20671i	−0.333261	−	0.108283i	−0.470867	+	0.882204i	$0.656059\pi$
$878$	48.6997	−	67.0293i	1.64353	−	2.26213i
$879$	7.84659			0.264659
$880$	0.203383	+	12.5665i	0.00685605	+	0.423615i
$881$	38.5784			1.29974			0.649869	−	0.760046i	$-0.274824\pi$
$881$	38.5784			1.29974			0.649869	+	0.760046i	$0.274824\pi$
$882$	−5.64288	+	7.76675i	−0.190006	+	0.261520i
$883$	16.9850	+	5.51877i	0.571591	+	0.185721i	0.580530	−	0.814239i	$-0.302845\pi$
$883$	16.9850	+	5.51877i	0.571591	+	0.185721i	−0.00893886	+	0.999960i	$0.502845\pi$
$884$	−1.46224	−	4.50030i	−0.0491804	−	0.151362i
$885$	5.63216	−	10.5793i	0.189323	−	0.355620i
$886$	49.8671	−	36.2305i	1.67532	−	1.21719i
$887$	38.6881	−	12.5705i	1.29902	−	0.422077i	0.423779	−	0.905766i	$-0.360703\pi$
$887$	38.6881	−	12.5705i	1.29902	−	0.422077i	0.875240	+	0.483689i	$0.160703\pi$
$888$	−41.1888	−	13.3831i	−1.38221	−	0.449106i
$889$	16.5695	+	12.0385i	0.555724	+	0.403757i
$890$	73.6809	−	35.8893i	2.46979	−	1.20301i
$891$	−3.25616	+	0.630396i	−0.109086	+	0.0211191i
$892$			15.4872i			0.518549i
$893$	−15.8543	+	21.8216i	−0.530545	+	0.730232i
$894$	4.42858	−	13.6298i	0.148114	−	0.455848i
$895$	−20.4980	+	19.7741i	−0.685172	+	0.660976i
$896$	−28.5176	+	20.7192i	−0.952705	+	0.692180i
$897$	−7.90757	−	10.8838i	−0.264026	−	0.363401i
$898$	−1.60497	+	0.521485i	−0.0535584	+	0.0174022i
$899$	−10.9735	+	33.7728i	−0.365985	+	1.12639i
$900$	17.2473	−	4.92622i	0.574910	−	0.164207i
$901$	0.912421			0.0303971
$902$	−16.5933	+	9.18154i	−0.552497	+	0.305712i
$903$		−	0.384821i		−	0.0128060i
$904$	−6.42518	−	4.66817i	−0.213698	−	0.155261i
$905$	45.8655	−	6.42171i	1.52462	−	0.213465i
$906$	−5.35775	−	16.4895i	−0.177999	−	0.547826i
$907$	10.1661	+	13.9924i	0.337559	+	0.464610i	0.943726	−	0.330727i	$-0.107294\pi$
$907$	10.1661	+	13.9924i	0.337559	+	0.464610i	−0.606168	+	0.795337i	$0.707294\pi$
$908$	53.6357	+	73.8232i	1.77996	+	2.44991i
$909$	−1.89572	−	5.83444i	−0.0628772	−	0.193516i
$910$	4.43915	+	31.7055i	0.147156	+	1.05103i
$911$	−37.8876	−	27.5270i	−1.25527	−	0.912009i	−0.256758	−	0.966476i	$-0.582654\pi$
$911$	−37.8876	−	27.5270i	−1.25527	−	0.912009i	−0.998516	+	0.0544664i	$0.982654\pi$
$912$		−	9.77482i		−	0.323677i
$913$	−21.5971	+	11.9502i	−0.714758	+	0.395495i
$914$	70.9081			2.34543
$915$	7.50030	+	1.32652i	0.247952	+	0.0438534i
$916$	15.9560	−	49.1076i	0.527202	−	1.62256i
$917$	33.1543	−	10.7725i	1.09485	−	0.355739i
$918$	−0.518666	−	0.713883i	−0.0171185	−	0.0235616i
$919$	−34.1795	+	24.8329i	−1.12748	+	0.819161i	−0.985326	−	0.170684i	$-0.945402\pi$
$919$	−34.1795	+	24.8329i	−1.12748	+	0.819161i	−0.142152	+	0.989845i	$0.545402\pi$
$920$	−22.9913	+	22.1794i	−0.758002	+	0.731234i
$921$	0.817944	−	2.51737i	0.0269522	−	0.0829503i
$922$	0.0499181	−	0.0687064i	0.00164397	−	0.00226273i
$923$		−	31.0077i		−	1.02063i
$924$	−20.0243	+	3.87671i	−0.658750	+	0.127535i
$925$	−45.4390	−	35.5768i	−1.49403	−	1.16976i
$926$	6.98907	+	5.07786i	0.229675	+	0.166869i
$927$	7.48471	+	2.43193i	0.245830	+	0.0798750i
$928$	11.7017	−	3.80210i	0.384126	−	0.124810i
$929$	9.24843	−	6.71938i	0.303431	−	0.220456i	−0.425642	−	0.904892i	$-0.639952\pi$
$929$	9.24843	−	6.71938i	0.303431	−	0.220456i	0.729073	+	0.684436i	$0.239952\pi$
$930$	47.1120	+	25.0812i	1.54486	+	0.822446i
$931$	7.23902	+	22.2794i	0.237249	+	0.730178i
$932$	−40.7083	−	13.2269i	−1.33344	−	0.433262i
$933$	2.64985	−	3.64721i	0.0867522	−	0.119404i
$934$	−36.0188			−1.17857
$935$	2.76814	−	0.0448014i	0.0905279	−	0.00146516i
$936$	−13.2582			−0.433358
$937$	−0.862330	+	1.18689i	−0.0281711	+	0.0387742i	−0.822870	−	0.568229i	$-0.807629\pi$
$937$	−0.862330	+	1.18689i	−0.0281711	+	0.0387742i	0.794699	+	0.607004i	$0.207629\pi$
$938$	35.0299	+	11.3819i	1.14377	+	0.371633i
$939$	3.00032	+	9.23403i	0.0979117	+	0.301341i
$940$	17.6282	−	33.1123i	0.574967	−	1.08000i
$941$	15.6751	−	11.3886i	0.510993	−	0.371258i	−0.302207	−	0.953242i	$-0.597723\pi$
$941$	15.6751	−	11.3886i	0.510993	−	0.371258i	0.813200	+	0.581984i	$0.197723\pi$
$942$	23.7302	−	7.71042i	0.773173	−	0.251219i
$943$	−8.75935	−	2.84609i	−0.285244	−	0.0926813i
$944$	7.34857	+	5.33905i	0.239176	+	0.173771i
$945$	1.67855	+	3.44607i	0.0546032	+	0.112101i
$946$	−1.20122	+	1.28621i	−0.0390551	+	0.0418184i
$947$			27.4774i			0.892895i	0.894810	+	0.446448i	$0.147311\pi$
$947$			27.4774i			0.892895i	−0.894810	+	0.446448i	$0.852689\pi$
$948$	−18.5391	+	25.5169i	−0.602122	+	0.828750i
$949$	−16.3369	+	50.2798i	−0.530318	+	1.63215i
$950$	23.3821	−	64.0350i	0.758616	−	2.07757i
$951$	13.8145	−	10.0368i	0.447967	−	0.325467i
$952$	−1.41139	−	1.94261i	−0.0457433	−	0.0629603i
$953$	−12.3339	+	4.00753i	−0.399534	+	0.129817i	−0.501890	−	0.864931i	$-0.667362\pi$
$953$	−12.3339	+	4.00753i	−0.399534	+	0.129817i	0.102356	+	0.994748i	$0.467362\pi$
$954$	1.78533	−	5.49468i	0.0578022	−	0.177897i
$955$	−2.41431	+	13.6508i	−0.0781252	+	0.441730i
$956$	−29.6230			−0.958075
$957$	11.5756	+	1.43013i	0.374185	+	0.0462295i
$958$			29.6908i			0.959268i
$959$	7.36890	+	5.35382i	0.237954	+	0.172884i
$960$	−3.61504	−	25.8195i	−0.116675	−	0.833322i
$961$	21.9294	+	67.4919i	0.707402	+	2.17716i
$962$	56.6623	+	77.9889i	1.82686	+	2.51446i
$963$	−2.91317	−	4.00964i	−0.0938757	−	0.129209i
$964$	12.3592	+	38.0376i	0.398062	+	1.22511i
$965$	1.71261	+	12.2319i	0.0551308	+	0.393758i
$966$	−12.4815	−	9.06833i	−0.401585	−	0.291769i
$967$		−	48.0563i		−	1.54539i	−0.634779	−	0.772694i	$-0.718909\pi$
$967$		−	48.0563i		−	1.54539i	0.634779	−	0.772694i	$-0.281091\pi$
$968$	34.9702	+	21.9250i	1.12399	+	0.704695i
$969$	−2.15320			−0.0691708
$970$	−13.4983	+	76.3212i	−0.433405	+	2.45052i
$971$	15.9783	−	49.1760i	0.512766	−	1.57813i	−0.274543	−	0.961575i	$-0.588527\pi$
$971$	15.9783	−	49.1760i	0.512766	−	1.57813i	0.787309	−	0.616558i	$-0.211473\pi$
$972$	−3.41183	+	1.10857i	−0.109434	+	0.0355574i
$973$	−13.3160	−	18.3279i	−0.426892	−	0.587566i
$974$	3.29370	−	2.39301i	0.105537	−	0.0766770i
$975$	−16.5952	−	6.05967i	−0.531472	−	0.194065i
$976$	−1.78383	+	5.49005i	−0.0570989	+	0.175732i
$977$	−7.52247	+	10.3538i	−0.240665	+	0.331247i	−0.912215	−	0.409713i	$-0.865629\pi$
$977$	−7.52247	+	10.3538i	−0.240665	+	0.331247i	0.671550	+	0.740960i	$0.265629\pi$
$978$			23.8907i			0.763941i
$979$	6.30571	−	51.0389i	0.201532	−	1.63121i
$980$	−14.2667	−	29.2895i	−0.455732	−	0.935620i
$981$	2.11693	+	1.53804i	0.0675885	+	0.0491059i
$982$	45.2373	+	14.6985i	1.44358	+	0.469048i
$983$	−13.0095	+	4.22705i	−0.414940	+	0.134822i	−0.509044	−	0.860740i	$-0.670001\pi$
$983$	−13.0095	+	4.22705i	−0.414940	+	0.134822i	0.0941048	+	0.995562i	$0.470001\pi$
$984$	−7.34317	+	5.33512i	−0.234092	+	0.170078i
$985$	−13.5052	+	25.3678i	−0.430311	+	0.808285i
$986$	0.958929	+	2.95128i	0.0305385	+	0.0939879i
$987$	7.62403	+	2.47720i	0.242675	+	0.0788500i
$988$	−42.9745	+	59.1493i	−1.36720	+	1.88179i
$989$	−0.854717			−0.0271784
$990$	5.14662	−	16.7577i	0.163570	−	0.532594i
$991$	34.7067			1.10250			0.551248	−	0.834342i	$-0.314152\pi$
$991$	34.7067			1.10250			0.551248	+	0.834342i	$0.314152\pi$
$992$	20.7659	−	28.5818i	0.659319	−	0.907474i
$993$	2.66076	+	0.864533i	0.0844366	+	0.0274351i
$994$	−10.9884	−	33.8189i	−0.348532	−	1.07267i
$995$	6.76673	+	3.60244i	0.214520	+	0.114205i
$996$	−21.5992	+	15.6927i	−0.684395	+	0.497242i
$997$	29.4014	−	9.55310i	0.931153	−	0.302550i	0.196119	−	0.980580i	$-0.437166\pi$
$997$	29.4014	−	9.55310i	0.931153	−	0.302550i	0.735034	+	0.678030i	$0.237166\pi$
$998$	−40.2099	−	13.0650i	−1.27282	−	0.413565i
$999$	9.33763	+	6.78419i	0.295430	+	0.214642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.4.11	yes	48
3.2	odd	2		495.2.ba.c.334.2		48
5.2	odd	4		825.2.n.o.301.6		24
5.3	odd	4		825.2.n.p.301.1		24
5.4	even	2	inner	165.2.s.a.4.2	✓	48
11.3	even	5	inner	165.2.s.a.124.2	yes	48
11.5	even	5		1815.2.c.j.364.22		24
11.6	odd	10		1815.2.c.k.364.3		24
15.14	odd	2		495.2.ba.c.334.11		48
33.14	odd	10		495.2.ba.c.289.11		48
55.3	odd	20		825.2.n.p.751.1		24
55.14	even	10	inner	165.2.s.a.124.11	yes	48
55.17	even	20		9075.2.a.dx.1.12		12
55.27	odd	20		9075.2.a.dz.1.1		12
55.28	even	20		9075.2.a.ea.1.1		12
55.38	odd	20		9075.2.a.dy.1.12		12
55.39	odd	10		1815.2.c.k.364.22		24
55.47	odd	20		825.2.n.o.751.6		24
55.49	even	10		1815.2.c.j.364.3		24
165.14	odd	10		495.2.ba.c.289.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.2	✓	48	5.4	even	2	inner
165.2.s.a.4.11	yes	48	1.1	even	1	trivial
165.2.s.a.124.2	yes	48	11.3	even	5	inner
165.2.s.a.124.11	yes	48	55.14	even	10	inner
495.2.ba.c.289.2		48	165.14	odd	10
495.2.ba.c.289.11		48	33.14	odd	10
495.2.ba.c.334.2		48	3.2	odd	2
495.2.ba.c.334.11		48	15.14	odd	2
825.2.n.o.301.6		24	5.2	odd	4
825.2.n.o.751.6		24	55.47	odd	20
825.2.n.p.301.1		24	5.3	odd	4
825.2.n.p.751.1		24	55.3	odd	20
1815.2.c.j.364.3		24	55.49	even	10
1815.2.c.j.364.22		24	11.5	even	5
1815.2.c.k.364.3		24	11.6	odd	10
1815.2.c.k.364.22		24	55.39	odd	10
9075.2.a.dx.1.12		12	55.17	even	20
9075.2.a.dy.1.12		12	55.38	odd	20
9075.2.a.dz.1.1		12	55.27	odd	20
9075.2.a.ea.1.1		12	55.28	even	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38939 - 1.91233i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(-1.97379 - 1.05079i) q^{5} +(-1.91233 + 1.38939i) q^{6} +(1.63033 - 0.529727i) q^{7} +(-3.56862 - 1.15951i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.38939 - 1.91233i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(-1.97379 - 1.05079i) q^{5} +(-1.91233 + 1.38939i) q^{6} +(1.63033 - 0.529727i) q^{7} +(-3.56862 - 1.15951i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-4.75182 + 2.31457i) q^{10} +(-0.406668 + 3.29160i) q^{11} +3.58741i q^{12} +(2.07687 - 2.85857i) q^{13} +(1.25215 - 3.85373i) q^{14} +(1.55247 + 1.60930i) q^{15} +(-1.37103 + 0.996109i) q^{16} +(0.219423 + 0.302010i) q^{17} +(2.24808 - 0.730445i) q^{18} +(1.78239 - 5.48564i) q^{19} +(-1.39705 + 7.89910i) q^{20} -1.71423 q^{21} +(5.72960 + 5.35099i) q^{22} +3.80745i q^{23} +(3.03565 + 2.20553i) q^{24} +(2.79166 + 4.14809i) q^{25} +(-2.58094 - 7.94332i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-3.61467 - 4.97517i) q^{28} +(1.08672 + 3.34458i) q^{29} +(5.23449 - 0.732891i) q^{30} +(8.16928 + 5.93533i) q^{31} -3.49870i q^{32} +(1.40392 - 3.00483i) q^{33} +0.882407 q^{34} +(-3.77456 - 0.667576i) q^{35} +(1.10857 - 3.41183i) q^{36} +(-10.9770 + 3.56666i) q^{37} +(-8.01391 - 11.0302i) q^{38} +(-2.85857 + 2.07687i) q^{39} +(5.82528 + 6.03852i) q^{40} +(-0.747505 + 2.30059i) q^{41} +(-2.38174 + 3.27818i) q^{42} +0.224486i q^{43} +(11.6812 - 2.26149i) q^{44} +(-0.979185 - 2.01027i) q^{45} +(7.28109 + 5.29002i) q^{46} +(-4.44749 - 1.44508i) q^{47} +(1.61174 - 0.523685i) q^{48} +(-3.28575 + 2.38724i) q^{49} +(11.8112 + 0.424728i) q^{50} +(-0.115358 - 0.355034i) q^{51} +(-12.0553 - 3.91700i) q^{52} +(1.43665 - 1.97737i) q^{53} -2.36377 q^{54} +(4.26147 - 6.06959i) q^{55} -6.43226 q^{56} +(-3.39031 + 4.66636i) q^{57} +(7.90582 + 2.56876i) q^{58} +(-1.65630 - 5.09757i) q^{59} +(3.76963 - 7.08078i) q^{60} +(2.75575 - 2.00217i) q^{61} +(22.7006 - 7.37587i) q^{62} +(1.63033 + 0.529727i) q^{63} +(-9.43272 - 6.85327i) q^{64} +(-7.10307 + 3.45984i) q^{65} +(-3.79563 - 6.85964i) q^{66} +9.08988i q^{67} +(0.787161 - 1.08343i) q^{68} +(1.17657 - 3.62110i) q^{69} +(-6.52096 + 6.29068i) q^{70} +(7.09964 - 5.15819i) q^{71} +(-2.20553 - 3.03565i) q^{72} +(-14.2299 + 4.62358i) q^{73} +(-8.43076 + 25.9472i) q^{74} +(-1.37320 - 4.80774i) q^{75} -20.6919 q^{76} +(1.08064 + 5.58182i) q^{77} +8.35211i q^{78} +(7.11291 + 5.16783i) q^{79} +(3.75282 - 0.525439i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.36090 + 4.62589i) q^{82} +(4.37438 + 6.02082i) q^{83} +(1.90035 + 5.84866i) q^{84} +(-0.115744 - 0.826672i) q^{85} +(0.429291 + 0.311898i) q^{86} -3.51670i q^{87} +(5.26790 - 11.2749i) q^{88} -15.5058 q^{89} +(-5.20477 - 0.920527i) q^{90} +(1.87173 - 5.76059i) q^{91} +(12.9903 - 4.22082i) q^{92} +(-5.93533 - 8.16928i) q^{93} +(-8.94275 + 6.49729i) q^{94} +(-9.28233 + 8.95454i) q^{95} +(-1.08116 + 3.32746i) q^{96} +(8.61910 - 11.8632i) q^{97} +9.60024i q^{98} +(-2.26375 + 2.42393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more