LMFDB - Embedded newform 165.2.s.a.4.2

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			4.2
Character	$\chi$	$=$	165.4
Dual form			165.2.s.a.124.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38939 + 1.91233i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(0.389432 + 2.20190i) q^{5} +(-1.91233 + 1.38939i) q^{6} +(-1.63033 + 0.529727i) q^{7} +(3.56862 + 1.15951i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.38939 + 1.91233i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(0.389432 + 2.20190i) 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} +(-0.310052 + 2.21447i) 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} +(7.08078 - 3.76963i) q^{20} -1.71423 q^{21} +(-5.72960 - 5.35099i) q^{22} -3.80745i q^{23} +(3.03565 + 2.20553i) q^{24} +(-4.69669 + 1.71498i) 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} +(-3.80401 - 3.66968i) q^{30} +(8.16928 + 5.93533i) q^{31} +3.49870i q^{32} +(-1.40392 + 3.00483i) q^{33} +0.882407 q^{34} +(-1.80131 - 3.38353i) 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} +(-1.16340 + 8.30928i) 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} +(3.24593 - 11.3644i) q^{50} +(-0.115358 - 0.355034i) q^{51} +(12.0553 + 3.91700i) q^{52} +(-1.43665 + 1.97737i) q^{53} -2.36377 q^{54} +(-7.40612 + 0.386413i) q^{55} -6.43226 q^{56} +(3.39031 - 4.66636i) q^{57} +(-7.90582 - 2.56876i) q^{58} +(-1.65630 - 5.09757i) q^{59} +(7.89910 - 1.39705i) 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} +(8.97313 + 1.25634i) 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} +(-4.99677 + 0.179682i) q^{75} -20.6919 q^{76} +(-1.08064 - 5.58182i) q^{77} -8.35211i q^{78} +(7.11291 + 5.16783i) q^{79} +(-2.72725 - 2.63094i) 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} +(0.579544 - 0.600759i) q^{85} +(0.429291 + 0.311898i) q^{86} +3.51670i q^{87} +(-5.26790 + 11.2749i) q^{88} -15.5058 q^{89} +(-2.48384 - 4.66558i) 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} +(12.7729 + 1.78836i) 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	$0.514949\pi$
$2$	−1.38939	+	1.91233i	−0.982446	+	1.35222i	−0.935501	+	0.353324i	$0.885051\pi$
$3$	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
$5$	0.389432	+	2.20190i	0.174159	+	0.984718i
$5$	0.389432	+	2.20190i	0.174159	+	0.984718i
$6$	−1.91233	+	1.38939i	−0.780705	+	0.567216i
$7$	−1.63033	+	0.529727i	−0.616207	+	0.200218i	−0.600456	−	0.799658i	$-0.705014\pi$
$7$	−1.63033	+	0.529727i	−0.616207	+	0.200218i	−0.0157517	+	0.999876i	$0.505014\pi$
$8$	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	−0.993252	−	0.115976i	$-0.963000\pi$
$13$	−2.07687	+	2.85857i	−0.576020	+	0.792824i	0.417232	+	0.908800i	$0.363000\pi$
$14$	1.25215	−	3.85373i	0.334652	−	1.02995i
$15$	−0.310052	+	2.21447i	−0.0800550	+	0.571773i
$16$	−1.37103	+	0.996109i	−0.342757	+	0.249027i
$17$	−0.219423	−	0.302010i	−0.0532180	−	0.0732482i	0.781579	−	0.623807i	$-0.214415\pi$
$17$	−0.219423	−	0.302010i	−0.0532180	−	0.0732482i	−0.834797	+	0.550559i	$0.814415\pi$
$18$	−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	$-0.130134\pi$
$20$	7.08078	−	3.76963i	1.58331	−	0.842915i
$21$	−1.71423			−0.374076
$22$	−5.72960	−	5.35099i	−1.22156	−	1.14084i
$23$		−	3.80745i		−	0.793907i	−0.917839	−	0.396954i	$-0.870067\pi$
$23$		−	3.80745i		−	0.793907i	0.917839	−	0.396954i	$-0.129933\pi$
$24$	3.03565	+	2.20553i	0.619649	+	0.450201i
$25$	−4.69669	+	1.71498i	−0.939337	+	0.342995i
$26$	−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	$0.794125\pi$
$30$	−3.80401	−	3.66968i	−0.694514	−	0.669989i
$31$	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
$35$	−1.80131	−	3.38353i	−0.304476	−	0.571920i
$36$	1.10857	−	3.41183i	0.184762	−	0.568638i
$37$	10.9770	−	3.56666i	1.80462	−	0.586355i	0.804643	−	0.593759i	$-0.202357\pi$
$37$	10.9770	−	3.56666i	1.80462	−	0.586355i	0.999973	+	0.00740399i	$0.00235678\pi$
$38$	8.01391	+	11.0302i	1.30003	+	1.78933i
$39$	−2.85857	+	2.07687i	−0.457737	+	0.332565i
$40$	−1.16340	+	8.30928i	−0.183949	+	1.31381i
$41$	−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	$-0.994551\pi$
$43$		−	0.224486i		−	0.0342338i	0.999853	−	0.0171169i	$-0.00544874\pi$
$44$	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	0.614855	−	0.788640i	$-0.289214\pi$
$47$	4.44749	+	1.44508i	0.648733	+	0.210786i	0.0338775	+	0.999426i	$0.489214\pi$
$48$	−1.61174	+	0.523685i	−0.232634	+	0.0755875i
$49$	−3.28575	+	2.38724i	−0.469393	+	0.341034i
$50$	3.24593	−	11.3644i	0.459043	−	1.60717i
$51$	−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	−0.896206	−	0.443638i	$-0.853688\pi$
$53$	−1.43665	+	1.97737i	−0.197339	+	0.271613i	0.698868	+	0.715251i	$0.253688\pi$
$54$	−2.36377			−0.321668
$55$	−7.40612	+	0.386413i	−0.998642	+	0.0521039i
$56$	−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	$-0.213445\pi$
$60$	7.89910	−	1.39705i	1.01977	−	0.180358i
$61$	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	$-0.812621\pi$
$67$		−	9.08988i		−	1.11051i	0.831682	−	0.555253i	$-0.187379\pi$
$68$	−0.787161	+	1.08343i	−0.0954573	+	0.131386i
$69$	1.17657	−	3.62110i	0.141642	−	0.435929i
$70$	8.97313	+	1.25634i	1.07249	+	0.150162i
$71$	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	0.683476	−	0.729973i	$-0.260467\pi$
$73$	14.2299	−	4.62358i	1.66549	−	0.541150i	0.982011	+	0.188823i	$0.0604673\pi$
$74$	−8.43076	+	25.9472i	−0.980056	+	3.01630i
$75$	−4.99677	+	0.179682i	−0.576977	+	0.0207479i
$76$	−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	$0.535318\pi$
$80$	−2.72725	−	2.63094i	−0.304916	−	0.294148i
$81$	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	0.498383	−	0.866957i	$-0.333927\pi$
$83$	−4.37438	−	6.02082i	−0.480151	−	0.660871i	−0.978534	+	0.206086i	$0.933927\pi$
$84$	1.90035	+	5.84866i	0.207345	+	0.638142i
$85$	0.579544	−	0.600759i	0.0628604	−	0.0651615i
$86$	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	$0.807034\pi$
$90$	−2.48384	−	4.66558i	−0.261819	−	0.491795i
$91$	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
$95$	12.7729	+	1.78836i	1.31047	+	0.183482i
$96$	−1.08116	+	3.32746i	−0.110345	+	0.339607i
$97$	−8.61910	+	11.8632i	−0.875137	+	1.20452i	0.102608	+	0.994722i	$0.467281\pi$
$97$	−8.61910	+	11.8632i	−0.875137	+	1.20452i	−0.977744	+	0.209800i	$0.932719\pi$
$98$		−	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	−0.653590	−	0.756849i	$-0.726738\pi$
$103$	−7.48471	+	2.43193i	−0.737490	+	0.239625i	−0.0839005	+	0.996474i	$0.526738\pi$
$104$	−10.7261	+	7.79298i	−1.05178	+	0.764164i
$105$	−0.667576	−	3.77456i	−0.0651488	−	0.368359i
$106$	−1.78533	−	5.49468i	−0.173407	−	0.533691i
$107$	4.71361	+	1.53155i	0.455682	+	0.148060i	0.527859	−	0.849332i	$-0.322995\pi$
$107$	4.71361	+	1.53155i	0.455682	+	0.148060i	−0.0721774	+	0.997392i	$0.522995\pi$
$108$	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	$0.460006\pi$
$110$	9.55104	−	14.6998i	0.910656	−	1.40157i
$111$	11.5420			1.09551
$112$	1.70756	−	2.35026i	0.161349	−	0.222078i
$113$	−2.01298	−	0.654058i	−0.189366	−	0.0615286i	0.212799	−	0.977096i	$-0.431742\pi$
$113$	−2.01298	−	0.654058i	−0.189366	−	0.0615286i	−0.402165	+	0.915567i	$0.631742\pi$
$114$	4.21316	+	12.9668i	0.394599	+	1.21445i
$115$	8.38360	−	1.48274i	0.781774	−	0.138266i
$116$	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
$125$	−5.60523	−	9.67375i	−0.501347	−	0.865246i
$126$	3.27818	−	2.38174i	0.292043	−	0.212182i
$127$	−7.02266	−	9.66586i	−0.623160	−	0.857707i	0.374418	−	0.927260i	$-0.377843\pi$
$127$	−7.02266	−	9.66586i	−0.623160	−	0.857707i	−0.997578	+	0.0695535i	$0.977843\pi$
$128$	19.5565	−	6.35430i	1.72857	−	0.561646i
$129$	0.0693699	−	0.213499i	0.00610768	−	0.0187975i
$130$	16.4853	−	8.77635i	1.44585	−	0.769737i
$131$	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
$135$	−1.55247	+	1.60930i	−0.133615	+	0.138506i
$136$	−0.432853	−	1.33218i	−0.0371168	−	0.114234i
$137$	−3.12316	−	4.29866i	−0.266829	−	0.367259i	0.654487	−	0.756073i	$-0.272885\pi$
$137$	−3.12316	−	4.29866i	−0.266829	−	0.367259i	−0.921316	+	0.388814i	$0.872885\pi$
$138$	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	$-0.289378\pi$
$140$	−9.54714	+	9.89662i	−0.806880	+	0.836417i
$141$	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
$145$	−6.94121	+	3.69533i	−0.576436	+	0.306880i
$146$	−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	$0.379886\pi$
$150$	6.59885	−	9.80512i	0.538794	−	0.800585i
$151$	−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	0.680871	−	0.732403i	$-0.261601\pi$
$157$	10.0392	+	3.26192i	0.801212	+	0.260329i	0.120340	+	0.992733i	$0.461601\pi$
$158$	−19.7652	+	6.42210i	−1.57243	+	0.510915i
$159$	−1.97737	+	1.43665i	−0.156816	+	0.113933i
$160$	−7.70377	+	1.36250i	−0.609036	+	0.107715i
$161$	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	−0.975601	−	0.219552i	$-0.929540\pi$
$163$	−5.94077	+	8.17677i	−0.465317	+	0.640454i	0.510284	+	0.860006i	$0.329540\pi$
$164$	8.67786			0.677627
$165$	−7.16305	−	1.92112i	−0.557643	−	0.149559i
$166$	17.5915			1.36537
$167$	7.84529	−	10.7981i	0.607087	−	0.835583i	−0.389247	−	0.921133i	$-0.627265\pi$
$167$	7.84529	−	10.7981i	0.607087	−	0.835583i	0.996334	+	0.0855502i	$0.0272648\pi$
$168$	−6.11744	−	1.98768i	−0.471971	−	0.153353i
$169$	0.159206	+	0.489985i	0.0122466	+	0.0376911i
$170$	0.343637	+	1.94297i	0.0263558	+	0.149019i
$171$	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	−0.418841	−	0.908059i	$-0.637564\pi$
$173$	−16.9862	−	5.51914i	−1.29144	−	0.419613i	−0.872594	+	0.488447i	$0.837564\pi$
$174$	−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	$-0.0579181\pi$
$180$	7.94420	+	1.11228i	0.592126	+	0.0829046i
$181$	−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
$185$	12.1282	+	22.7813i	0.891684	+	1.67492i
$186$	−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
$190$	−21.1665	+	21.9413i	−1.53558	+	1.59179i
$191$	−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	0.909721	−	0.415221i	$-0.136296\pi$
$193$	3.24670	+	4.46870i	0.233703	+	0.321664i	−0.676018	+	0.736885i	$0.736296\pi$
$194$	−10.7110	−	32.9651i	−0.769006	−	2.36676i
$195$	−5.68627	−	5.48547i	−0.407202	−	0.392822i
$196$	11.7873	+	8.56399i	0.841952	+	0.611714i
$197$			12.8524i			0.915693i	0.889031	+	0.457846i	$0.151379\pi$
$197$			12.8524i			0.915693i	−0.889031	+	0.457846i	$0.848621\pi$
$198$	−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	$0.538775\pi$
$200$	−18.7492	+	0.674217i	−1.32577	+	0.0476743i
$201$	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
$205$	−5.35675	−	0.750008i	−0.374132	−	0.0523828i
$206$	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
$215$	0.494294	−	0.0874219i	0.0337106	−	0.00596212i
$216$	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
$220$	9.52858	+	24.8401i	0.642417	+	1.67472i
$221$	1.31903			0.0887276
$222$	−16.0363	+	22.0720i	−1.07628	+	1.48138i
$223$	4.10580	+	1.33405i	0.274944	+	0.0893349i	0.443244	−	0.896401i	$-0.353828\pi$
$223$	4.10580	+	1.33405i	0.274944	+	0.0893349i	−0.168299	+	0.985736i	$0.553828\pi$
$224$	−1.85335	−	5.70404i	−0.123832	−	0.381117i
$225$	−4.80774	−	1.37320i	−0.320516	−	0.0915466i
$226$	4.04759	−	2.94075i	0.269242	−	0.195616i
$227$	24.1914	−	7.86025i	1.60564	−	0.521703i	0.637145	−	0.770744i	$-0.280115\pi$
$227$	24.1914	−	7.86025i	1.60564	−	0.521703i	0.968493	+	0.249041i	$0.0801153\pi$
$228$	−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	−0.974394	−	0.224847i	$-0.927812\pi$
$233$	−7.01317	+	9.65280i	−0.459448	+	0.632376i	0.514946	+	0.857223i	$0.327812\pi$
$234$	2.58094	−	7.94332i	0.168722	−	0.519271i
$235$	−1.44991	+	10.3557i	−0.0945820	+	0.675529i
$236$	−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	$0.0139458\pi$
$240$	−1.78076	−	3.34494i	−0.114948	−	0.215915i
$241$	−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
$245$	−6.53602	−	6.30521i	−0.417571	−	0.402825i
$246$	−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
$250$	26.2872	+	2.72154i	1.66255	+	0.172125i
$251$	−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
$255$	0.736824	−	0.392267i	0.0461417	−	0.0245647i
$256$	−7.81414	+	24.0494i	−0.488384	+	1.50309i
$257$	2.20649	−	0.716932i	0.137637	−	0.0447210i	−0.239388	−	0.970924i	$-0.576947\pi$
$257$	2.20649	−	0.716932i	0.137637	−	0.0447210i	0.377025	+	0.926203i	$0.376947\pi$
$258$	0.311898	+	0.429291i	0.0194179	+	0.0267265i
$259$	−16.0069	+	11.6297i	−0.994619	+	0.722633i
$260$	−3.93012	+	28.0699i	−0.243736	+	1.74082i
$261$	−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	$-0.971209\pi$
$263$		−	2.92970i		−	0.180653i	0.995912	−	0.0903265i	$-0.0287910\pi$
$264$	−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	$0.344119\pi$
$270$	−0.920527	−	5.20477i	−0.0560215	−	0.316752i
$271$	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
$275$	−3.73502	−	16.1570i	−0.225230	−	0.974306i
$276$	−13.6589			−0.822167
$277$	7.78897	−	10.7206i	0.467994	−	0.644139i	−0.508148	−	0.861270i	$-0.669670\pi$
$277$	7.78897	−	10.7206i	0.467994	−	0.644139i	0.976142	+	0.217131i	$0.0696698\pi$
$278$	29.7096	+	9.65325i	1.78187	+	0.578963i
$279$	3.12039	+	9.60356i	0.186813	+	0.574950i
$280$	−2.50492	−	14.1632i	−0.149698	−	0.846411i
$281$	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	0.00999031	−	0.999950i	$-0.496820\pi$
$283$	−9.58356	−	3.11389i	−0.569683	−	0.185101i	−0.579674	+	0.814849i	$0.696820\pi$
$284$	−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
$290$	2.57736	−	18.4081i	0.151348	−	1.08096i
$291$	−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	−0.0828074	−	0.996566i	$-0.526389\pi$
$293$	7.46255	−	2.42473i	0.435967	−	0.141654i	0.518774	+	0.854911i	$0.326389\pi$
$294$	2.96664	−	9.13037i	0.173018	−	0.532494i
$295$	10.5793	−	5.63216i	0.615951	−	0.327917i
$296$	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
$300$	6.15232	+	16.8489i	0.355204	+	0.972773i
$301$	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
$305$	5.48174	+	5.28817i	0.313884	+	0.302799i
$306$	0.713883	+	0.518666i	0.0408099	+	0.0296502i
$307$		−	2.64692i		−	0.151068i	−0.997143	−	0.0755339i	$-0.975934\pi$
$307$		−	2.64692i		−	0.151068i	0.997143	−	0.0755339i	$-0.0240661\pi$
$308$	−17.8462	+	9.87481i	−1.01688	+	0.562670i
$309$	−7.86989			−0.447702
$310$	−25.0812	−	47.1120i	−1.42452	−	2.67578i
$311$	−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	0.939251	−	0.343230i	$-0.111521\pi$
$313$	5.70694	+	7.85494i	0.322576	+	0.443987i	−0.616676	+	0.787217i	$0.711521\pi$
$314$	−20.1862	+	14.6661i	−1.13917	+	0.827656i
$315$	0.531500	−	3.79611i	0.0299467	−	0.213887i
$316$	9.74659	−	29.9969i	0.548288	−	1.68746i
$317$	10.0368	−	13.8145i	0.563725	−	0.775901i	−0.428069	−	0.903746i	$-0.640806\pi$
$317$	10.0368	−	13.8145i	0.563725	−	0.775901i	0.991794	+	0.127845i	$0.0408060\pi$
$318$		−	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
$325$	4.85204	−	16.9876i	0.269143	−	0.942301i
$326$	−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
$330$	13.6261	−	11.0289i	0.750091	−	0.607123i
$331$	−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
$335$	20.0150	−	3.53989i	1.09353	−	0.193405i
$336$	2.35026	−	1.70756i	0.128217	−	0.0931551i
$337$	8.83320	−	2.87008i	0.481175	−	0.156343i	−0.0583785	−	0.998295i	$-0.518593\pi$
$337$	8.83320	−	2.87008i	0.481175	−	0.156343i	0.539554	+	0.841951i	$0.318593\pi$
$338$	−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
$345$	8.43147	+	1.18050i	0.453935	+	0.0635562i
$346$	34.1548	−	24.8149i	1.83618	−	1.33406i
$347$	5.49888	+	7.56856i	0.295195	+	0.406301i	0.930693	−	0.365801i	$-0.119205\pi$
$347$	5.49888	+	7.56856i	0.295195	+	0.406301i	−0.635498	+	0.772103i	$0.719205\pi$
$348$	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	$0.0856148\pi$
$350$	0.728082	+	20.2472i	0.0389176	+	1.08226i
$351$	−3.53338			−0.188598
$352$	−11.5163	−	1.42281i	−0.613821	−	0.0758359i
$353$			9.60028i			0.510971i	0.966813	+	0.255486i	$0.0822353\pi$
$353$			9.60028i			0.510971i	−0.966813	+	0.255486i	$0.917765\pi$
$354$	10.2499	+	7.44700i	0.544777	+	0.395803i
$355$	14.1226	+	13.6239i	0.749551	+	0.723082i
$356$	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	$0.645323\pi$
$360$	−5.82528	+	6.03852i	−0.307019	+	0.318258i
$361$	−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
$365$	15.7222	+	29.5322i	0.822939	+	1.54579i
$366$	−2.48811	+	7.65762i	−0.130056	+	0.400270i
$367$	7.33892	−	2.38456i	0.383088	−	0.124473i	−0.111141	−	0.993805i	$-0.535450\pi$
$367$	7.33892	−	2.38456i	0.383088	−	0.124473i	0.494229	+	0.869332i	$0.335450\pi$
$368$	3.79263	+	5.22011i	0.197705	+	0.272117i
$369$	−1.95699	+	1.42184i	−0.101877	+	0.0740180i
$370$	−60.4163	−	8.45899i	−3.14089	−	0.439762i
$371$	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	$-0.826723\pi$
$373$		−	20.0037i		−	1.03575i	0.855456	−	0.517876i	$-0.173277\pi$
$374$	−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	$0.355195\pi$
$380$	−8.05810	−	45.5615i	−0.413372	−	2.33726i
$381$	−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	−0.944696	−	0.327947i	$-0.893643\pi$
$383$	−6.67102	+	9.18187i	−0.340873	+	0.469171i	0.603823	+	0.797118i	$0.293643\pi$
$384$	20.5629			1.04935
$385$	11.8697	−	4.55320i	0.604938	−	0.232053i
$386$	−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	$0.858193\pi$
$390$	18.3905	−	3.25257i	0.931237	−	0.164700i
$391$	−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	$0.0594566\pi$
$397$			7.40026i			0.371408i	−0.982606	+	0.185704i	$0.940543\pi$
$398$	4.76324	−	6.55604i	0.238760	−	0.328625i
$399$	−3.05543	+	9.40365i	−0.152963	+	0.470771i
$400$	4.73098	−	7.02969i	0.236549	−	0.351484i
$401$	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
$405$	−1.97379	+	1.05079i	−0.0980782	+	0.0522144i
$406$	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	$0.604944\pi$
$410$	8.87687	−	9.20182i	0.438398	−	0.454446i
$411$	−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
$415$	11.5537	−	11.9766i	0.567149	−	0.587910i
$416$	−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	$0.551306\pi$
$420$	−12.1381	+	6.46202i	−0.592278	+	0.315314i
$421$	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
$425$	1.54850	+	1.04214i	0.0751134	+	0.0505513i
$426$	−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	0.353546	−	0.935417i	$-0.384976\pi$
$433$	24.7497	−	8.04167i	1.18939	−	0.386458i	0.835849	+	0.548959i	$0.184976\pi$
$434$	33.1023	−	24.0502i	1.58896	−	1.15445i
$435$	−7.74340	+	1.36951i	−0.371268	+	0.0656632i
$436$	−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	$0.184627\pi$
$440$	−26.8777	−	7.20855i	−1.28134	−	0.343654i
$441$	−4.06141			−0.193400
$442$	−1.83265	+	2.52242i	−0.0871701	+	0.119979i
$443$	−24.8003	−	8.05811i	−1.17830	−	0.382852i	−0.346564	−	0.938026i	$-0.612652\pi$
$443$	−24.8003	−	8.05811i	−1.17830	−	0.382852i	−0.831734	+	0.555174i	$0.812652\pi$
$444$	−12.7951	−	39.3792i	−0.607227	−	1.86885i
$445$	−6.03845	−	34.1422i	−0.286250	−	1.61849i
$446$	−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
$455$	13.4131	+	1.87799i	0.628817	+	0.0880418i
$456$	17.5094	−	12.7213i	0.819954	−	0.595732i
$457$	−17.6323	−	24.2688i	−0.824805	−	1.13525i	−0.988868	−	0.148796i	$-0.952460\pi$
$457$	−17.6323	−	24.2688i	−0.824805	−	1.13525i	0.164063	−	0.986450i	$-0.447540\pi$
$458$	−32.3574	+	10.5136i	−1.51196	+	0.491266i
$459$	0.115358	−	0.355034i	0.00538443	−	0.0165716i
$460$	−14.3527	−	26.9597i	−0.669196	−	1.25700i
$461$	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	$-0.972935\pi$
$463$		−	3.65474i		−	0.169850i	0.996387	−	0.0849251i	$-0.0270651\pi$
$464$	−4.82149	−	3.50302i	−0.223832	−	0.162623i
$465$	−15.6765	+	16.2503i	−0.726980	+	0.753592i
$466$	−8.71532	−	26.8230i	−0.403729	−	1.24255i
$467$	8.95659	+	12.3277i	0.414462	+	0.570457i	0.964300	−	0.264814i	$-0.0853105\pi$
$467$	8.95659	+	12.3277i	0.414462	+	0.570457i	−0.549838	+	0.835271i	$0.685311\pi$
$468$	7.45058	+	10.2548i	0.344403	+	0.474031i
$469$	4.81515	+	14.8195i	0.222343	+	0.684302i
$470$	−17.7889	−	17.1608i	−0.820543	−	0.791567i
$471$	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
$475$	1.03640	+	28.8211i	0.0475532	+	1.32240i
$476$	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	$0.392644\pi$
$480$	−7.74775	−	1.08478i	−0.353635	−	0.0495131i
$481$	−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	0.271668	−	0.962391i	$-0.412425\pi$
$487$	−1.63805	−	0.532235i	−0.0742271	−	0.0241179i	−0.345895	+	0.938273i	$0.612425\pi$
$488$	12.1558	−	3.94965i	0.550266	−	0.178792i
$489$	−8.17677	+	5.94077i	−0.369766	+	0.268651i
$490$	21.1387	−	3.73864i	0.954950	−	0.168894i
$491$	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
$495$	−6.21881	−	4.04060i	−0.279515	−	0.181611i
$496$	−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	$-0.231112\pi$
$500$	−26.7914	+	29.8481i	−1.19815	+	1.33485i
$501$	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	0.635042	−	0.772478i	$-0.280983\pi$
$503$	15.5816	+	5.06278i	0.694750	+	0.225738i	0.0597085	+	0.998216i	$0.480983\pi$
$504$	−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	$0.100992\pi$
$510$	−0.273592	+	1.95406i	−0.0121149	+	0.0865274i
$511$	−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
$515$	−8.26963	−	15.5335i	−0.364404	−	0.684487i
$516$	−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
$520$	−21.3364	−	20.5829i	−0.935663	−	0.902622i
$521$	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	0.979965	−	0.199168i	$-0.0638238\pi$
$523$	11.1538	+	15.3518i	0.487720	+	0.671289i	−0.492246	+	0.870456i	$0.663824\pi$
$524$	−22.5438	−	69.3827i	−0.984831	−	3.03100i
$525$	8.05121	−	2.93987i	0.351384	−	0.128306i
$526$	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
$530$	11.4035	−	6.07092i	0.495334	−	0.263704i
$531$	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
$535$	−1.53667	+	10.9753i	−0.0664362	+	0.474504i
$536$	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
$545$	1.01902	+	5.76164i	0.0436498	+	0.246802i
$546$	4.42433	+	13.6167i	0.189344	+	0.582741i
$547$	−29.3476	−	9.53561i	−1.25481	−	0.407713i	−0.395169	−	0.918608i	$-0.629314\pi$
$547$	−29.3476	−	9.53561i	−1.25481	−	0.407713i	−0.859643	+	0.510895i	$0.829314\pi$
$548$	−11.2040	+	15.4210i	−0.478613	+	0.658754i
$549$	3.40629			0.145377
$550$	36.0870	+	15.3058i	1.53875	+	0.652642i
$551$	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
$555$	4.49480	+	25.4142i	0.190794	+	1.07877i
$556$	−38.3552	+	27.8667i	−1.62662	+	1.18181i
$557$	−35.4614	+	11.5221i	−1.50255	+	0.488207i	−0.940759	−	0.339075i	$-0.889886\pi$
$557$	−35.4614	+	11.5221i	−1.50255	+	0.488207i	−0.561787	+	0.827282i	$0.689886\pi$
$558$	−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	−0.516363	−	0.856370i	$-0.672715\pi$
$563$	10.8591	−	14.9463i	0.457658	−	0.629912i	0.974021	+	0.226458i	$0.0727145\pi$
$564$	5.18408	−	15.9550i	0.218289	−	0.671825i
$565$	0.656248	−	4.68709i	0.0276086	−	0.197187i
$566$	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	$-0.242333\pi$
$570$	−26.9108	+	14.3266i	−1.12717	+	0.600076i
$571$	−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
$575$	6.52967	+	17.8824i	0.272306	+	0.745747i
$576$	−3.60298	−	11.0888i	−0.150124	−	0.462034i
$577$	7.65924	+	10.5420i	0.318859	+	0.438871i	0.938118	−	0.346315i	$-0.112567\pi$
$577$	7.65924	+	10.5420i	0.318859	+	0.438871i	−0.619260	+	0.785186i	$0.712567\pi$
$578$	23.4260	+	32.2431i	0.974393	+	1.34114i
$579$	1.70689	+	5.25328i	0.0709361	+	0.218319i
$580$	20.3026	+	19.5857i	0.843021	+	0.813251i
$581$	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
$585$	−3.71286	−	6.97414i	−0.153508	−	0.288345i
$586$	−5.73150	+	17.6397i	−0.236766	+	0.728691i
$587$	−41.1222	+	13.3614i	−1.69730	+	0.551485i	−0.988139	−	0.153565i	$-0.950925\pi$
$587$	−41.1222	+	13.3614i	−1.69730	+	0.551485i	−0.709158	+	0.705050i	$0.750925\pi$
$588$	8.56399	+	11.7873i	0.353173	+	0.486101i
$589$	47.1199	−	34.2346i	1.94154	−	1.41061i
$590$	−3.92823	+	28.0564i	−0.161723	+	1.15506i
$591$	−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	$0.254888\pi$
$593$			34.9632i			1.43576i	−0.696164	+	0.717882i	$0.745112\pi$
$594$	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	$0.147655\pi$
$600$	−18.0399	−	5.15261i	−0.736476	−	0.210354i
$601$	−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
$605$	1.73992	−	24.5351i	0.0707377	−	0.997495i
$606$	14.5010			0.589063
$607$	−9.64463	+	13.2747i	−0.391463	+	0.538803i	−0.958576	−	0.284837i	$-0.908060\pi$
$607$	−9.64463	+	13.2747i	−0.391463	+	0.538803i	0.567113	+	0.823640i	$0.308060\pi$
$608$	19.1926	+	6.23605i	0.778362	+	0.252905i
$609$	−1.86289	−	5.73338i	−0.0754881	−	0.232328i
$610$	−17.7290	+	3.13558i	−0.717826	+	0.126956i
$611$	−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	0.919405	−	0.393313i	$-0.128671\pi$
$613$	35.4555	+	11.5202i	1.43204	+	0.465297i	0.512631	+	0.858609i	$0.328671\pi$
$614$	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	$0.196811\pi$
$617$			28.7965i			1.15930i	−0.814865	+	0.579651i	$0.803189\pi$
$618$	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	$0.153797\pi$
$620$	80.2188	+	11.2316i	3.22166	+	0.451071i
$621$	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
$625$	19.1177	−	16.1094i	0.764709	−	0.644376i
$626$	−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
$630$	6.52096	+	6.29068i	0.259801	+	0.250627i
$631$	−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
$635$	18.5484	−	19.2274i	0.736070	−	0.763014i
$636$	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
$640$	21.6074	+	40.5868i	0.854108	+	1.60434i
$641$	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	0.523840	−	0.851817i	$-0.324499\pi$
$643$	−11.3642	−	15.6415i	−0.448161	−	0.616841i	−0.972001	+	0.234976i	$0.924499\pi$
$644$	18.9427	−	13.7627i	0.746447	−	0.542325i
$645$	0.497117	+	0.0696022i	0.0195739	+	0.00274058i
$646$	1.57279	−	4.84056i	0.0618808	−	0.190449i
$647$	1.23652	−	1.70192i	0.0486125	−	0.0669094i	−0.784019	−	0.620737i	$-0.786833\pi$
$647$	1.23652	−	1.70192i	0.0486125	−	0.0669094i	0.832631	+	0.553828i	$0.186833\pi$
$648$			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	−0.357409	−	0.933948i	$-0.616340\pi$
$653$	−2.49399	+	0.810347i	−0.0975974	+	0.0317113i	0.259811	+	0.965659i	$0.416340\pi$
$654$	−5.00395	+	3.63558i	−0.195670	+	0.142162i
$655$	7.91946	+	44.7776i	0.309439	+	1.74961i
$656$	−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	$0.749501\pi$
$660$	1.38622	+	26.5688i	0.0539585	+	1.03419i
$661$	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
$665$	−21.7714	+	3.85054i	−0.844260	+	0.149317i
$666$	−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	$0.452829\pi$
$673$	−21.7554	+	29.9438i	−0.838610	+	1.15425i	−0.986259	+	0.165208i	$0.947171\pi$
$674$	−6.78421	+	20.8797i	−0.261318	+	0.804254i
$675$	−4.14809	−	2.79166i	−0.159660	−	0.107451i
$676$	1.49525	−	1.08636i	0.0575097	−	0.0417832i
$677$	−17.4668	−	24.0410i	−0.671303	−	0.923969i	0.328486	−	0.944509i	$-0.393462\pi$
$677$	−17.4668	−	24.0410i	−0.671303	−	0.923969i	−0.999789	+	0.0205398i	$0.993462\pi$
$678$	4.75823	−	1.54604i	0.182739	−	0.0593754i
$679$	7.76775	−	23.9067i	0.298099	−	0.917454i
$680$	2.76476	−	1.47189i	0.106024	−	0.0564444i
$681$	25.4363			0.974722
$682$	−15.0468	−	77.7208i	−0.576172	−	2.97608i
$683$			2.06173i			0.0788899i	0.999222	+	0.0394450i	$0.0125590\pi$
$683$			2.06173i			0.0788899i	−0.999222	+	0.0394450i	$0.987441\pi$
$684$	−16.7401	−	12.1624i	−0.640075	−	0.465042i
$685$	8.24894	−	8.55090i	0.315176	−	0.326713i
$686$	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
$690$	−13.9721	+	14.4836i	−0.531909	+	0.551380i
$691$	−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
$695$	26.0847	−	13.8868i	0.989449	−	0.526758i
$696$	−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
$700$	−25.5093	−	17.1677i	−0.964160	−	0.648880i
$701$	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	$0.585479\pi$
$710$	−45.6752	+	8.07821i	−1.71416	+	0.303170i
$711$	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
$715$	14.2770	−	21.9734i	0.533929	−	0.821760i
$716$	−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	$0.929141\pi$
$720$	−0.659963	−	3.73151i	−0.0245954	−	0.139065i
$721$	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	$0.0549485\pi$
$727$			9.26283i			0.343539i	−0.985137	+	0.171770i	$0.945052\pi$
$728$	13.3590	−	18.3870i	0.495116	−	0.681469i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−78.3197	−	10.9657i	−2.89874	−	0.405858i
$731$	−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	−0.538827	−	0.842416i	$-0.681132\pi$
$733$	−12.9843	+	4.21886i	−0.479587	+	0.155827i	0.0592398	+	0.998244i	$0.481132\pi$
$734$	−5.63655	+	17.3475i	−0.208049	+	0.640308i
$735$	−4.26771	−	8.01635i	−0.157417	−	0.295688i
$736$	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	$-0.601479\pi$
$740$	64.2810	−	66.6341i	2.36302	−	2.44952i
$741$	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	0.618319	−	0.785928i	$-0.287814\pi$
$743$	−8.72840	−	12.0136i	−0.320214	−	0.440737i	−0.938532	+	0.345191i	$0.887814\pi$
$744$	11.7085	+	36.0351i	0.429255	+	1.32111i
$745$	−9.75695	−	9.41239i	−0.357467	−	0.344843i
$746$	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
$750$	24.1597	+	10.7115i	0.882186	+	0.391130i
$751$	−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
$755$	−16.2429	−	2.27420i	−0.591141	−	0.0827667i
$756$	−1.90035	+	5.84866i	−0.0691149	+	0.212714i
$757$	−4.18455	+	5.75954i	−0.152090	+	0.209334i	−0.878263	−	0.478178i	$-0.841297\pi$
$757$	−4.18455	+	5.75954i	−0.152090	+	0.209334i	0.726173	+	0.687512i	$0.241297\pi$
$758$		−	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
$765$	0.821979	−	0.145377i	0.0297187	−	0.00525611i
$766$	−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	$0.763988\pi$
$770$	−7.78447	+	29.0250i	−0.280533	+	1.04599i
$771$	2.32004			0.0835542
$772$	11.6473	−	16.0311i	0.419194	−	0.576971i
$773$	26.8737	+	8.73179i	0.966579	+	0.314061i	0.749434	−	0.662079i	$-0.230326\pi$
$773$	26.8737	+	8.73179i	0.966579	+	0.314061i	0.217145	+	0.976139i	$0.430326\pi$
$774$	0.163975	+	0.504662i	0.00589394	+	0.0181397i
$775$	−48.5475	−	13.8663i	−1.74388	−	0.498091i
$776$	−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
$785$	−3.27284	+	23.3755i	−0.116813	+	0.834306i
$786$	−38.8890	+	28.2545i	−1.38713	+	1.00781i
$787$	7.61672	+	10.4835i	0.271507	+	0.373697i	0.922898	−	0.385045i	$-0.125814\pi$
$787$	7.61672	+	10.4835i	0.271507	+	0.373697i	−0.651391	+	0.758742i	$0.725814\pi$
$788$	43.8500	−	14.2477i	1.56209	−	0.507555i
$789$	0.905327	−	2.78631i	0.0322305	−	0.0991952i
$790$	−21.8380	−	41.0199i	−0.776961	−	1.45942i
$791$	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
$795$	−3.93340	−	3.79450i	−0.139503	−	0.134577i
$796$	3.80051	+	11.6968i	0.134706	+	0.414581i
$797$	−14.8535	−	20.4441i	−0.526138	−	0.724167i	0.460397	−	0.887713i	$-0.347707\pi$
$797$	−14.8535	−	20.4441i	−0.526138	−	0.724167i	−0.986536	+	0.163546i	$0.947707\pi$
$798$	−13.7377	−	18.9083i	−0.486309	−	0.669347i
$799$	−0.539454	−	1.66027i	−0.0190845	−	0.0587361i
$800$	−6.00018	−	16.4323i	−0.212138	−	0.580969i
$801$	−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
$805$	−12.8826	+	6.85837i	−0.454052	+	0.241726i
$806$	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	$0.139698\pi$
$810$	0.732891	−	5.23449i	0.0257512	−	0.183921i
$811$	−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
$820$	3.37943	+	19.1077i	0.118015	+	0.667271i
$821$	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	−0.854906	−	0.518782i	$-0.826385\pi$
$823$	−2.79233	+	3.84331i	−0.0973344	+	0.133969i	0.757572	+	0.652752i	$0.226385\pi$
$824$	−29.5299			−1.02872
$825$	1.44058	−	16.5204i	0.0501547	−	0.575168i
$826$	−21.7186			−0.755687
$827$	20.3747	−	28.0434i	0.708499	−	0.975165i	−0.291329	−	0.956623i	$-0.594097\pi$
$827$	20.3747	−	28.0434i	0.708499	−	0.975165i	0.999828	−	0.0185425i	$-0.00590261\pi$
$828$	−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	$0.800102\pi$
$830$	6.85070	+	38.7347i	0.237791	+	1.34450i
$831$	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	$0.843936\pi$
$840$	1.99433	−	14.2440i	0.0688110	−	0.491466i
$841$	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
$845$	−1.01689	+	0.541370i	−0.0349822	+	0.0186237i
$846$	−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
$850$	−4.14439	+	1.51331i	−0.142151	+	0.0519060i
$851$	−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	$0.0209648\pi$
$853$	21.9653	+	30.2327i	0.752079	+	1.03515i	−0.245753	+	0.969332i	$0.579035\pi$
$854$	−4.26520	−	13.1269i	−0.145952	−	0.449194i
$855$	9.28233	+	8.95454i	0.317449	+	0.306239i
$856$	15.0452	+	10.9310i	0.514236	+	0.373614i
$857$			14.6046i			0.498884i	0.968390	+	0.249442i	$0.0802472\pi$
$857$			14.6046i			0.498884i	−0.968390	+	0.249442i	$0.919753\pi$
$858$	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	$0.487657\pi$
$860$	−0.846228	−	1.58953i	−0.0288561	−	0.0542026i
$861$	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	$-0.879273\pi$
$863$	−29.2007	−	40.1913i	−0.994002	−	1.36813i	−0.0650685	−	0.997881i	$-0.520727\pi$
$864$	−2.83051	+	2.05648i	−0.0962958	+	0.0699630i
$865$	5.53762	−	39.5511i	0.188285	−	1.34478i
$866$	−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
$875$	14.2628	+	12.8022i	0.482172	+	0.432792i
$876$	−16.5867	−	51.0486i	−0.560412	−	1.72477i
$877$	9.86924	+	3.20671i	0.333261	+	0.108283i	0.470867	−	0.882204i	$-0.343941\pi$
$877$	9.86924	+	3.20671i	0.333261	+	0.108283i	−0.137607	+	0.990487i	$0.543941\pi$
$878$	−48.6997	+	67.0293i	−1.64353	+	2.26213i
$879$	7.84659			0.264659
$880$	9.76908	−	7.90709i	0.329316	−	0.266548i
$881$	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	0.00893886	−	0.999960i	$-0.497155\pi$
$883$	−16.9850	−	5.51877i	−0.571591	−	0.185721i	−0.580530	+	0.814239i	$0.697155\pi$
$884$	−1.46224	−	4.50030i	−0.0491804	−	0.151362i
$885$	11.8020	−	2.08732i	0.396718	−	0.0701644i
$886$	49.8671	−	36.2305i	1.67532	−	1.21719i
$887$	−38.6881	+	12.5705i	−1.29902	+	0.422077i	−0.875240	−	0.483689i	$-0.839297\pi$
$887$	−38.6881	+	12.5705i	−1.29902	+	0.422077i	−0.423779	+	0.905766i	$0.639297\pi$
$888$	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
$895$	28.2061	+	3.94919i	0.942827	+	0.132007i
$896$	−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
$900$	0.644594	+	17.9255i	0.0214865	+	0.597515i
$901$	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
$905$	−33.3314	−	32.1543i	−1.10797	−	1.06885i
$906$	−5.35775	−	16.4895i	−0.177999	−	0.547826i
$907$	−10.1661	−	13.9924i	−0.337559	−	0.464610i	0.606168	−	0.795337i	$-0.292706\pi$
$907$	−10.1661	−	13.9924i	−0.337559	−	0.464610i	−0.943726	+	0.330727i	$0.892706\pi$
$908$	−53.6357	−	73.8232i	−1.77996	−	2.44991i
$909$	−1.89572	−	5.83444i	−0.0628772	−	0.193516i
$910$	−22.2274	+	23.0410i	−0.736831	+	0.763803i
$911$	−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
$915$	3.57932	+	6.72330i	0.118329	+	0.222265i
$916$	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	$0.545402\pi$
$920$	31.6371	+	4.42957i	1.04304	+	0.146039i
$921$	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	$0.239952\pi$
$930$	−9.29528	−	52.5567i	−0.304804	−	1.72340i
$931$	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
$935$	1.74178	+	2.15194i	0.0569622	+	0.0703759i
$936$	−13.2582			−0.433358
$937$	0.862330	−	1.18689i	0.0281711	−	0.0387742i	−0.794699	−	0.607004i	$-0.792371\pi$
$937$	0.862330	−	1.18689i	0.0281711	−	0.0387742i	0.822870	+	0.568229i	$0.192371\pi$
$938$	−35.0299	−	11.3819i	−1.14377	−	0.371633i
$939$	3.00032	+	9.23403i	0.0979117	+	0.301341i
$940$	36.9391	−	6.53312i	1.20482	−	0.213087i
$941$	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	$-0.852689\pi$
$947$		−	27.4774i		−	0.892895i	0.894810	−	0.446448i	$-0.147311\pi$
$948$	18.5391	−	25.5169i	0.602122	−	0.828750i
$949$	−16.3369	+	50.2798i	−0.530318	+	1.63215i
$950$	−56.5553	−	38.0617i	−1.83490	−	1.23489i
$951$	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	−0.102356	−	0.994748i	$-0.532638\pi$
$953$	12.3339	−	4.00753i	0.399534	−	0.129817i	0.501890	+	0.864931i	$0.332638\pi$
$954$	1.78533	−	5.49468i	0.0578022	−	0.177897i
$955$	12.2366	−	6.51448i	0.395968	−	0.210803i
$956$	−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
$960$	18.1010	−	18.7636i	0.584207	−	0.605592i
$961$	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
$965$	−8.57525	+	8.88916i	−0.276047	+	0.286152i
$966$	−12.4815	−	9.06833i	−0.401585	−	0.291769i
$967$			48.0563i			1.54539i	0.634779	+	0.772694i	$0.281091\pi$
$967$			48.0563i			1.54539i	−0.634779	+	0.772694i	$0.718909\pi$
$968$	−34.9702	−	21.9250i	−1.12399	−	0.704695i
$969$	−2.15320			−0.0691708
$970$	68.4145	−	36.4222i	2.19666	−	1.16945i
$971$	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
$975$	9.86401	−	14.6568i	0.315901	−	0.469393i
$976$	−1.78383	+	5.49005i	−0.0570989	+	0.175732i
$977$	7.52247	−	10.3538i	0.240665	−	0.331247i	−0.671550	−	0.740960i	$-0.734371\pi$
$977$	7.52247	−	10.3538i	0.240665	−	0.331247i	0.912215	+	0.409713i	$0.134371\pi$
$978$		−	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	−0.0941048	−	0.995562i	$-0.529999\pi$
$983$	13.0095	−	4.22705i	0.414940	−	0.134822i	0.509044	+	0.860740i	$0.329999\pi$
$984$	−7.34317	+	5.33512i	−0.234092	+	0.170078i
$985$	−28.2995	+	5.00511i	−0.901699	+	0.159476i
$986$	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
$990$	16.3673	−	6.27845i	0.520187	−	0.199542i
$991$	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
$995$	−1.33509	−	7.54876i	−0.0423252	−	0.239312i
$996$	−21.5992	+	15.6927i	−0.684395	+	0.497242i
$997$	−29.4014	+	9.55310i	−0.931153	+	0.302550i	−0.735034	−	0.678030i	$-0.762834\pi$
$997$	−29.4014	+	9.55310i	−0.931153	+	0.302550i	−0.196119	+	0.980580i	$0.562834\pi$
$998$	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.4.2	✓	48
3.2	odd	2		495.2.ba.c.334.11		48
5.2	odd	4		825.2.n.p.301.1		24
5.3	odd	4		825.2.n.o.301.6		24
5.4	even	2	inner	165.2.s.a.4.11	yes	48
11.3	even	5	inner	165.2.s.a.124.11	yes	48
11.5	even	5		1815.2.c.j.364.3		24
11.6	odd	10		1815.2.c.k.364.22		24
15.14	odd	2		495.2.ba.c.334.2		48
33.14	odd	10		495.2.ba.c.289.2		48
55.3	odd	20		825.2.n.o.751.6		24
55.14	even	10	inner	165.2.s.a.124.2	yes	48
55.17	even	20		9075.2.a.ea.1.1		12
55.27	odd	20		9075.2.a.dy.1.12		12
55.28	even	20		9075.2.a.dx.1.12		12
55.38	odd	20		9075.2.a.dz.1.1		12
55.39	odd	10		1815.2.c.k.364.3		24
55.47	odd	20		825.2.n.p.751.1		24
55.49	even	10		1815.2.c.j.364.22		24
165.14	odd	10		495.2.ba.c.289.11		48

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

\(f(q)\)	\(=\)	\(q+(-1.38939 + 1.91233i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(0.389432 + 2.20190i) q^{5} +(-1.91233 + 1.38939i) q^{6} +(-1.63033 + 0.529727i) q^{7} +(3.56862 + 1.15951i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.38939 + 1.91233i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.10857 - 3.41183i) q^{4} +(0.389432 + 2.20190i) 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} +(-0.310052 + 2.21447i) 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} +(7.08078 - 3.76963i) q^{20} -1.71423 q^{21} +(-5.72960 - 5.35099i) q^{22} -3.80745i q^{23} +(3.03565 + 2.20553i) q^{24} +(-4.69669 + 1.71498i) 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} +(-3.80401 - 3.66968i) q^{30} +(8.16928 + 5.93533i) q^{31} +3.49870i q^{32} +(-1.40392 + 3.00483i) q^{33} +0.882407 q^{34} +(-1.80131 - 3.38353i) 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} +(-1.16340 + 8.30928i) 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} +(3.24593 - 11.3644i) q^{50} +(-0.115358 - 0.355034i) q^{51} +(12.0553 + 3.91700i) q^{52} +(-1.43665 + 1.97737i) q^{53} -2.36377 q^{54} +(-7.40612 + 0.386413i) q^{55} -6.43226 q^{56} +(3.39031 - 4.66636i) q^{57} +(-7.90582 - 2.56876i) q^{58} +(-1.65630 - 5.09757i) q^{59} +(7.89910 - 1.39705i) 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} +(8.97313 + 1.25634i) 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} +(-4.99677 + 0.179682i) q^{75} -20.6919 q^{76} +(-1.08064 - 5.58182i) q^{77} -8.35211i q^{78} +(7.11291 + 5.16783i) q^{79} +(-2.72725 - 2.63094i) 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} +(0.579544 - 0.600759i) q^{85} +(0.429291 + 0.311898i) q^{86} +3.51670i q^{87} +(-5.26790 + 11.2749i) q^{88} -15.5058 q^{89} +(-2.48384 - 4.66558i) 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} +(12.7729 + 1.78836i) 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

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