LMFDB - Embedded newform 165.2.s.a.4.10

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			4.10
Character	$\chi$	$=$	165.4
Dual form			165.2.s.a.124.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12116 - 1.54314i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.506258 - 1.55810i) q^{4} +(1.25493 - 1.85071i) q^{5} +(1.54314 - 1.12116i) q^{6} +(-4.23918 + 1.37739i) q^{7} +(0.656175 + 0.213204i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.12116 - 1.54314i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.506258 - 1.55810i) q^{4} +(1.25493 - 1.85071i) q^{5} +(1.54314 - 1.12116i) q^{6} +(-4.23918 + 1.37739i) q^{7} +(0.656175 + 0.213204i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.44894 - 4.01149i) q^{10} +(-1.22140 + 3.08354i) q^{11} -1.63829i q^{12} +(0.313882 - 0.432021i) q^{13} +(-2.62728 + 8.08594i) q^{14} +(1.76541 - 1.37234i) q^{15} +(3.71548 - 2.69946i) q^{16} +(-2.67102 - 3.67635i) q^{17} +(1.81407 - 0.589428i) q^{18} +(-0.594714 + 1.83034i) q^{19} +(-3.51892 - 1.01838i) q^{20} -4.45734 q^{21} +(3.38895 + 5.34192i) q^{22} +5.18745i q^{23} +(0.558176 + 0.405538i) q^{24} +(-1.85028 - 4.64505i) q^{25} +(-0.314759 - 0.968729i) q^{26} +(0.587785 + 0.809017i) q^{27} +(4.29224 + 5.90776i) q^{28} +(1.46923 + 4.52183i) q^{29} +(-0.138403 - 4.26290i) q^{30} +(-2.82936 - 2.05565i) q^{31} -7.38016i q^{32} +(-2.11448 + 2.55518i) q^{33} -8.66777 q^{34} +(-2.77073 + 9.57405i) q^{35} +(0.506258 - 1.55810i) q^{36} +(0.501344 - 0.162896i) q^{37} +(2.15771 + 2.96983i) q^{38} +(0.432021 - 0.313882i) q^{39} +(1.21804 - 0.946835i) q^{40} +(1.45107 - 4.46595i) q^{41} +(-4.99738 + 6.87831i) q^{42} -3.02459i q^{43} +(5.42281 + 0.341997i) q^{44} +(2.10308 - 0.759628i) q^{45} +(8.00498 + 5.81596i) q^{46} +(11.4010 + 3.70442i) q^{47} +(4.36781 - 1.41919i) q^{48} +(10.4103 - 7.56354i) q^{49} +(-9.24243 - 2.35258i) q^{50} +(-1.40424 - 4.32181i) q^{51} +(-0.832039 - 0.270346i) q^{52} +(-2.95328 + 4.06485i) q^{53} +1.90743 q^{54} +(4.17397 + 6.13009i) q^{55} -3.07531 q^{56} +(-1.13121 + 1.55698i) q^{57} +(8.62507 + 2.80246i) q^{58} +(-4.21793 - 12.9815i) q^{59} +(-3.03200 - 2.05594i) q^{60} +(-9.45864 + 6.87210i) q^{61} +(-6.34433 + 2.06140i) q^{62} +(-4.23918 - 1.37739i) q^{63} +(-3.95767 - 2.87541i) q^{64} +(-0.405647 - 1.12306i) q^{65} +(1.57234 + 6.12771i) q^{66} -11.5622i q^{67} +(-4.37590 + 6.02291i) q^{68} +(-1.60301 + 4.93356i) q^{69} +(11.6677 + 15.0097i) q^{70} +(-2.72305 + 1.97841i) q^{71} +(0.405538 + 0.558176i) q^{72} +(-0.618559 + 0.200982i) q^{73} +(0.310714 - 0.956278i) q^{74} +(-0.324328 - 4.98947i) q^{75} +3.15294 q^{76} +(0.930481 - 14.7540i) q^{77} -1.01858i q^{78} +(-14.3357 - 10.4155i) q^{79} +(-0.333239 - 10.2639i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.26471 - 7.24625i) q^{82} +(2.49655 + 3.43620i) q^{83} +(2.25656 + 6.94499i) q^{84} +(-10.1558 + 0.329729i) q^{85} +(-4.66738 - 3.39105i) q^{86} +4.75453i q^{87} +(-1.45887 + 1.76293i) q^{88} +8.24094 q^{89} +(1.18568 - 4.09702i) q^{90} +(-0.735538 + 2.26375i) q^{91} +(8.08259 - 2.62619i) q^{92} +(-2.05565 - 2.82936i) q^{93} +(18.4988 - 13.4402i) q^{94} +(2.64111 + 3.39760i) q^{95} +(2.28059 - 7.01895i) q^{96} +(0.669130 - 0.920978i) q^{97} -24.5445i q^{98} +(-2.80059 + 1.77671i) 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 $

$2$	1.12116	−	1.54314i	0.792779	−	1.09117i	−0.200977	−	0.979596i	$-0.564412\pi$
$2$	1.12116	−	1.54314i	0.792779	−	1.09117i	0.993756	−	0.111571i	$-0.0355882\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.506258	−	1.55810i	−0.253129	−	0.779052i
$5$	1.25493	−	1.85071i	0.561223	−	0.827664i
$5$	1.25493	−	1.85071i	0.561223	−	0.827664i
$6$	1.54314	−	1.12116i	0.629985	−	0.457711i
$7$	−4.23918	+	1.37739i	−1.60226	+	0.520606i	−0.967665	−	0.252239i	$-0.918833\pi$
$7$	−4.23918	+	1.37739i	−1.60226	+	0.520606i	−0.634595	+	0.772845i	$0.718833\pi$
$8$	0.656175	+	0.213204i	0.231993	+	0.0753790i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−1.44894	−	4.01149i	−0.458194	−	1.26854i
$11$	−1.22140	+	3.08354i	−0.368265	+	0.929721i
$11$	−1.22140	+	3.08354i	−0.368265	+	0.929721i
$12$		−	1.63829i		−	0.472933i
$13$	0.313882	−	0.432021i	0.0870551	−	0.119821i	−0.763268	−	0.646082i	$-0.776406\pi$
$13$	0.313882	−	0.432021i	0.0870551	−	0.119821i	0.850323	+	0.526261i	$0.176406\pi$
$14$	−2.62728	+	8.08594i	−0.702170	+	2.16106i
$15$	1.76541	−	1.37234i	0.455828	−	0.354336i
$16$	3.71548	−	2.69946i	0.928871	−	0.674864i
$17$	−2.67102	−	3.67635i	−0.647818	−	0.891645i	0.351184	−	0.936306i	$-0.385779\pi$
$17$	−2.67102	−	3.67635i	−0.647818	−	0.891645i	−0.999002	+	0.0446611i	$0.985779\pi$
$18$	1.81407	−	0.589428i	0.427581	−	0.138930i
$19$	−0.594714	+	1.83034i	−0.136437	+	0.419909i	−0.995811	−	0.0914385i	$-0.970853\pi$
$19$	−0.594714	+	1.83034i	−0.136437	+	0.419909i	0.859374	+	0.511348i	$0.170853\pi$
$20$	−3.51892	−	1.01838i	−0.786855	−	0.227716i
$21$	−4.45734			−0.972671
$22$	3.38895	+	5.34192i	0.722528	+	1.13890i
$23$			5.18745i			1.08166i	0.841132	+	0.540830i	$0.181890\pi$
$23$			5.18745i			1.08166i	−0.841132	+	0.540830i	$0.818110\pi$
$24$	0.558176	+	0.405538i	0.113937	+	0.0827801i
$25$	−1.85028	−	4.64505i	−0.370057	−	0.929009i
$26$	−0.314759	−	0.968729i	−0.0617293	−	0.189983i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	4.29224	+	5.90776i	0.811157	+	1.11646i
$29$	1.46923	+	4.52183i	0.272829	+	0.839683i	0.989786	+	0.142564i	$0.0455348\pi$
$29$	1.46923	+	4.52183i	0.272829	+	0.839683i	−0.716956	+	0.697118i	$0.754465\pi$
$30$	−0.138403	−	4.26290i	−0.0252689	−	0.778295i
$31$	−2.82936	−	2.05565i	−0.508168	−	0.369206i	0.303960	−	0.952685i	$-0.401691\pi$
$31$	−2.82936	−	2.05565i	−0.508168	−	0.369206i	−0.812128	+	0.583479i	$0.801691\pi$
$32$		−	7.38016i		−	1.30464i
$33$	−2.11448	+	2.55518i	−0.368084	+	0.444800i
$34$	−8.66777			−1.48651
$35$	−2.77073	+	9.57405i	−0.468338	+	1.61831i
$36$	0.506258	−	1.55810i	0.0843764	−	0.259684i
$37$	0.501344	−	0.162896i	0.0824204	−	0.0267800i	−0.267517	−	0.963553i	$-0.586203\pi$
$37$	0.501344	−	0.162896i	0.0824204	−	0.0267800i	0.349937	+	0.936773i	$0.386203\pi$
$38$	2.15771	+	2.96983i	0.350027	+	0.481770i
$39$	0.432021	−	0.313882i	0.0691787	−	0.0502613i
$40$	1.21804	−	0.946835i	0.192588	−	0.149708i
$41$	1.45107	−	4.46595i	0.226620	−	0.697464i	−0.771503	−	0.636225i	$-0.780495\pi$
$41$	1.45107	−	4.46595i	0.226620	−	0.697464i	0.998123	−	0.0612387i	$-0.0195051\pi$
$42$	−4.99738	+	6.87831i	−0.771113	+	1.06135i
$43$		−	3.02459i		−	0.461246i	−0.973043	−	0.230623i	$-0.925924\pi$
$43$		−	3.02459i		−	0.461246i	0.973043	−	0.230623i	$-0.0740765\pi$
$44$	5.42281	+	0.341997i	0.817519	+	0.0515580i
$45$	2.10308	−	0.759628i	0.313509	−	0.113239i
$46$	8.00498	+	5.81596i	1.18027	+	0.857517i
$47$	11.4010	+	3.70442i	1.66301	+	0.540346i	0.981500	−	0.191461i	$-0.0613225\pi$
$47$	11.4010	+	3.70442i	1.66301	+	0.540346i	0.681512	+	0.731807i	$0.261323\pi$
$48$	4.36781	−	1.41919i	0.630439	−	0.204842i
$49$	10.4103	−	7.56354i	1.48719	−	1.08051i
$50$	−9.24243	−	2.35258i	−1.30708	−	0.332705i
$51$	−1.40424	−	4.32181i	−0.196633	−	0.605174i
$52$	−0.832039	−	0.270346i	−0.115383	−	0.0374902i
$53$	−2.95328	+	4.06485i	−0.405665	+	0.558350i	−0.962154	−	0.272505i	$-0.912148\pi$
$53$	−2.95328	+	4.06485i	−0.405665	+	0.558350i	0.556490	+	0.830855i	$0.312148\pi$
$54$	1.90743			0.259568
$55$	4.17397	+	6.13009i	0.562818	+	0.826581i
$56$	−3.07531			−0.410955
$57$	−1.13121	+	1.55698i	−0.149833	+	0.206227i
$58$	8.62507	+	2.80246i	1.13253	+	0.367980i
$59$	−4.21793	−	12.9815i	−0.549128	−	1.69004i	−0.710967	−	0.703225i	$-0.751742\pi$
$59$	−4.21793	−	12.9815i	−0.549128	−	1.69004i	0.161839	−	0.986817i	$-0.448258\pi$
$60$	−3.03200	−	2.05594i	−0.391430	−	0.265421i
$61$	−9.45864	+	6.87210i	−1.21105	+	0.879883i	−0.995326	−	0.0965707i	$-0.969213\pi$
$61$	−9.45864	+	6.87210i	−1.21105	+	0.879883i	−0.215728	+	0.976453i	$0.569213\pi$
$62$	−6.34433	+	2.06140i	−0.805730	+	0.261798i
$63$	−4.23918	−	1.37739i	−0.534087	−	0.173535i
$64$	−3.95767	−	2.87541i	−0.494708	−	0.359427i
$65$	−0.405647	−	1.12306i	−0.0503143	−	0.139299i
$66$	1.57234	+	6.12771i	0.193542	+	0.754270i
$67$		−	11.5622i		−	1.41255i	−0.707936	−	0.706276i	$-0.750374\pi$
$67$		−	11.5622i		−	1.41255i	0.707936	−	0.706276i	$-0.249626\pi$
$68$	−4.37590	+	6.02291i	−0.530656	+	0.730385i
$69$	−1.60301	+	4.93356i	−0.192980	+	0.593931i
$70$	11.6677	+	15.0097i	1.39456	+	1.79400i
$71$	−2.72305	+	1.97841i	−0.323166	+	0.234794i	−0.737525	−	0.675319i	$-0.764006\pi$
$71$	−2.72305	+	1.97841i	−0.323166	+	0.234794i	0.414359	+	0.910113i	$0.364006\pi$
$72$	0.405538	+	0.558176i	0.0477931	+	0.0657816i
$73$	−0.618559	+	0.200982i	−0.0723969	+	0.0235232i	−0.344992	−	0.938606i	$-0.612118\pi$
$73$	−0.618559	+	0.200982i	−0.0723969	+	0.0235232i	0.272595	+	0.962129i	$0.412118\pi$
$74$	0.310714	−	0.956278i	0.0361197	−	0.111165i
$75$	−0.324328	−	4.98947i	−0.0374501	−	0.576134i
$76$	3.15294			0.361667
$77$	0.930481	−	14.7540i	0.106038	−	1.68137i
$78$		−	1.01858i		−	0.115332i
$79$	−14.3357	−	10.4155i	−1.61289	−	1.17184i	−0.853265	−	0.521477i	$-0.825381\pi$
$79$	−14.3357	−	10.4155i	−1.61289	−	1.17184i	−0.759628	−	0.650358i	$-0.774619\pi$
$80$	−0.333239	−	10.2639i	−0.0372572	−	1.14754i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−5.26471	−	7.24625i	−0.581390	−	0.800215i
$83$	2.49655	+	3.43620i	0.274031	+	0.377172i	0.923746	−	0.383007i	$-0.125111\pi$
$83$	2.49655	+	3.43620i	0.274031	+	0.377172i	−0.649714	+	0.760179i	$0.725111\pi$
$84$	2.25656	+	6.94499i	0.246211	+	0.757761i
$85$	−10.1558	+	0.329729i	−1.10155	+	0.0357641i
$86$	−4.66738	−	3.39105i	−0.503297	−	0.365666i
$87$			4.75453i			0.509739i
$88$	−1.45887	+	1.76293i	−0.155516	+	0.187929i
$89$	8.24094			0.873538			0.436769	−	0.899574i	$-0.356123\pi$
$89$	8.24094			0.873538			0.436769	+	0.899574i	$0.356123\pi$
$90$	1.18568	−	4.09702i	0.124981	−	0.431864i
$91$	−0.735538	+	2.26375i	−0.0771054	+	0.237306i
$92$	8.08259	−	2.62619i	0.842668	−	0.273799i
$93$	−2.05565	−	2.82936i	−0.213161	−	0.293391i
$94$	18.4988	−	13.4402i	1.90801	−	1.38625i
$95$	2.64111	+	3.39760i	0.270972	+	0.348586i
$96$	2.28059	−	7.01895i	0.232762	−	0.716368i
$97$	0.669130	−	0.920978i	0.0679398	−	0.0935112i	−0.773695	−	0.633558i	$-0.781594\pi$
$97$	0.669130	−	0.920978i	0.0679398	−	0.0935112i	0.841635	+	0.540047i	$0.181594\pi$
$98$		−	24.5445i		−	2.47937i
$99$	−2.80059	+	1.77671i	−0.281470	+	0.178566i
$100$	−6.30074	+	5.23453i	−0.630074	+	0.523453i
$101$	0.828229	+	0.601744i	0.0824119	+	0.0598757i	0.628228	−	0.778029i	$-0.283780\pi$
$101$	0.828229	+	0.601744i	0.0824119	+	0.0598757i	−0.545816	+	0.837905i	$0.683780\pi$
$102$	−8.24354	−	2.67849i	−0.816232	−	0.265210i
$103$	4.55623	−	1.48041i	0.448939	−	0.145869i	−0.0758171	−	0.997122i	$-0.524157\pi$
$103$	4.55623	−	1.48041i	0.448939	−	0.145869i	0.524756	+	0.851253i	$0.324157\pi$
$104$	0.298070	−	0.216560i	0.0292282	−	0.0212355i
$105$	−5.59366	+	8.24926i	−0.545885	+	0.805045i
$106$	2.96154	+	9.11468i	0.287650	+	0.885296i
$107$	0.699950	+	0.227427i	0.0676667	+	0.0219862i	0.342655	−	0.939461i	$-0.388674\pi$
$107$	0.699950	+	0.227427i	0.0676667	+	0.0219862i	−0.274988	+	0.961448i	$0.588674\pi$
$108$	0.962961	−	1.32540i	0.0926609	−	0.127537i
$109$	0.0433994			0.00415691			0.00207845	−	0.999998i	$-0.499338\pi$
$109$	0.0433994			0.00415691			0.00207845	+	0.999998i	$0.499338\pi$
$110$	14.1393	+	0.431770i	1.34813	+	0.0411676i
$111$	0.527144			0.0500343
$112$	−12.0324	+	16.5612i	−1.13695	+	1.56488i
$113$	10.6524	+	3.46117i	1.00209	+	0.325600i	0.763701	−	0.645570i	$-0.223380\pi$
$113$	10.6524	+	3.46117i	1.00209	+	0.325600i	0.238391	+	0.971169i	$0.423380\pi$
$114$	1.13437	+	3.49125i	0.106244	+	0.326985i
$115$	9.60049	+	6.50991i	0.895251	+	0.607052i
$116$	6.30167	−	4.57843i	0.585095	−	0.425096i
$117$	0.507871	−	0.165017i	0.0469527	−	0.0152559i
$118$	−24.7612	−	8.04541i	−2.27946	−	0.740640i
$119$	16.3867	+	11.9057i	1.50217	+	1.09139i
$120$	1.45101	−	0.524100i	0.132458	−	0.0478435i
$121$	−8.01638	−	7.53244i	−0.728762	−	0.684767i
$122$			22.3007i			2.01901i
$123$	2.76011	−	3.79896i	0.248871	−	0.342541i
$124$	−1.77053	+	5.44913i	−0.158998	+	0.489346i
$125$	−10.9186	−	2.40487i	−0.976592	−	0.215098i
$126$	−6.87831	+	4.99738i	−0.612768	+	0.445202i
$127$	4.80507	+	6.61362i	0.426381	+	0.586863i	0.967118	−	0.254328i	$-0.0818544\pi$
$127$	4.80507	+	6.61362i	0.426381	+	0.586863i	−0.540737	+	0.841192i	$0.681854\pi$
$128$	5.16355	−	1.67774i	0.456397	−	0.148292i
$129$	0.934651	−	2.87656i	0.0822914	−	0.253267i
$130$	−2.18784	−	0.633161i	−0.191886	−	0.0555319i
$131$	17.7054			1.54693			0.773465	−	0.633839i	$-0.218522\pi$
$131$	17.7054			1.54693			0.773465	+	0.633839i	$0.218522\pi$
$132$	5.05171	+	2.00100i	0.439695	+	0.174165i
$133$		−	8.57830i		−	0.743833i
$134$	−17.8422	−	12.9631i	−1.54133	−	1.11984i
$135$	2.23489	−	0.0725601i	0.192349	−	0.00624498i
$136$	−0.968845	−	2.98180i	−0.0830778	−	0.255687i
$137$	−3.22449	−	4.43814i	−0.275487	−	0.379176i	0.648745	−	0.761006i	$-0.275294\pi$
$137$	−3.22449	−	4.43814i	−0.275487	−	0.379176i	−0.924233	+	0.381830i	$0.875294\pi$
$138$	5.81596	+	8.00498i	0.495087	+	0.681429i
$139$	−1.00725	−	3.09999i	−0.0854337	−	0.262938i	0.899209	−	0.437519i	$-0.144143\pi$
$139$	−1.00725	−	3.09999i	−0.0854337	−	0.262938i	−0.984643	+	0.174581i	$0.944143\pi$
$140$	16.3201	−	0.529862i	1.37930	−	0.0447816i
$141$	9.69830	+	7.04623i	0.816745	+	0.593400i
$142$			6.42016i			0.538768i
$143$	0.948778	+	1.49553i	0.0793408	+	0.125063i
$144$	4.59259			0.382716
$145$	10.2124	+	2.95547i	0.848094	+	0.245438i
$146$	−0.383359	+	1.17986i	−0.0317270	+	0.0976457i
$147$	12.2381	−	3.97639i	1.00938	−	0.327967i
$148$	−0.507619	−	0.698678i	−0.0417260	−	0.0574310i
$149$	2.27038	−	1.64953i	0.185997	−	0.135135i	−0.490890	−	0.871221i	$-0.663328\pi$
$149$	2.27038	−	1.64953i	0.185997	−	0.135135i	0.676887	+	0.736087i	$0.263328\pi$
$150$	−8.06309	−	5.09350i	−0.658348	−	0.415883i
$151$	−4.37685	+	13.4706i	−0.356183	+	1.09622i	0.599137	+	0.800647i	$0.295511\pi$
$151$	−4.37685	+	13.4706i	−0.356183	+	1.09622i	−0.955320	+	0.295573i	$0.904489\pi$
$152$	−0.780472	+	1.07423i	−0.0633047	+	0.0871314i
$153$		−	4.54422i		−	0.367378i
$154$	−21.7243	−	17.9774i	−1.75060	−	1.44866i
$155$	−7.35508	+	2.65663i	−0.590774	+	0.213386i
$156$	−0.707774	−	0.514228i	−0.0566673	−	0.0411712i
$157$	2.95859	+	0.961303i	0.236121	+	0.0767204i	0.424687	−	0.905340i	$-0.360384\pi$
$157$	2.95859	+	0.961303i	0.236121	+	0.0767204i	−0.188566	+	0.982060i	$0.560384\pi$
$158$	−32.1452	+	10.4446i	−2.55734	+	0.830929i
$159$	−4.06485	+	2.95328i	−0.322363	+	0.234211i
$160$	−13.6586	−	9.26160i	−1.07980	−	0.732194i
$161$	−7.14516	−	21.9906i	−0.563118	−	1.73310i
$162$	1.81407	+	0.589428i	0.142527	+	0.0463098i
$163$	−11.3880	+	15.6743i	−0.891978	+	1.22770i	0.0809786	+	0.996716i	$0.474195\pi$
$163$	−11.3880	+	15.6743i	−0.891978	+	1.22770i	−0.972957	+	0.230987i	$0.925805\pi$
$164$	−7.69303			−0.600724
$165$	2.07538	+	7.11989i	0.161568	+	0.554282i
$166$	8.10157			0.628804
$167$	2.43926	−	3.35735i	0.188756	−	0.259800i	−0.704142	−	0.710059i	$-0.748668\pi$
$167$	2.43926	−	3.35735i	0.188756	−	0.259800i	0.892898	+	0.450259i	$0.148668\pi$
$168$	−2.92479	−	0.950323i	−0.225653	−	0.0733190i
$169$	3.92910	+	12.0925i	0.302238	+	0.930194i
$170$	−10.8775	+	16.0416i	−0.834264	+	1.23033i
$171$	−1.55698	+	1.13121i	−0.119065	+	0.0865060i
$172$	−4.71263	+	1.53123i	−0.359335	+	0.116755i
$173$	10.1434	+	3.29580i	0.771191	+	0.250575i	0.668075	−	0.744094i	$-0.267119\pi$
$173$	10.1434	+	3.29580i	0.771191	+	0.250575i	0.103116	+	0.994669i	$0.467119\pi$
$174$	7.33692	+	5.33059i	0.556211	+	0.404111i
$175$	14.2417	+	17.1426i	1.07657	+	1.29586i
$176$	3.78579	+	14.7539i	0.285365	+	1.11212i
$177$		−	13.6495i		−	1.02596i
$178$	9.23940	−	12.7169i	0.692523	−	0.953175i
$179$	−6.99420	+	21.5259i	−0.522771	+	1.60892i	0.245910	+	0.969293i	$0.420913\pi$
$179$	−6.99420	+	21.5259i	−0.522771	+	1.60892i	−0.768681	+	0.639632i	$0.779087\pi$
$180$	−2.24828	−	2.89225i	−0.167577	−	0.215576i
$181$	−11.7973	+	8.57121i	−0.876883	+	0.637093i	−0.932425	−	0.361363i	$-0.882311\pi$
$181$	−11.7973	+	8.57121i	−0.876883	+	0.637093i	0.0555418	+	0.998456i	$0.482311\pi$
$182$	2.66864	+	3.67307i	0.197813	+	0.272266i
$183$	−11.1193	+	3.61288i	−0.821962	+	0.267072i
$184$	−1.10599	+	3.40388i	−0.0815344	+	0.250937i
$185$	0.327678	−	1.13227i	0.0240914	−	0.0832460i
$186$	−6.67082			−0.489128
$187$	14.5985	−	3.74591i	1.06755	−	0.273928i
$188$		−	19.6394i		−	1.43235i
$189$	−3.60606	−	2.61996i	−0.262302	−	0.190574i
$190$	8.20409	−	0.266362i	0.595187	−	0.0193239i
$191$	1.22505	+	3.77031i	0.0886414	+	0.272810i	0.985544	−	0.169417i	$-0.0541885\pi$
$191$	1.22505	+	3.77031i	0.0886414	+	0.272810i	−0.896903	+	0.442227i	$0.854188\pi$
$192$	−2.87541	−	3.95767i	−0.207515	−	0.285620i
$193$	−0.0176648	−	0.0243135i	−0.00127154	−	0.00175012i	0.808381	−	0.588660i	$-0.200344\pi$
$193$	−0.0176648	−	0.0243135i	−0.00127154	−	0.00175012i	−0.809652	+	0.586910i	$0.800344\pi$
$194$	−0.671000	−	2.06513i	−0.0481750	−	0.148267i
$195$	−0.0387476	−	1.19345i	−0.00277478	−	0.0854646i
$196$	−17.0551	−	12.3912i	−1.21822	−	0.885089i
$197$			5.50562i			0.392259i	0.980578	+	0.196130i	$0.0628373\pi$
$197$			5.50562i			0.392259i	−0.980578	+	0.196130i	$0.937163\pi$
$198$	−0.398181	+	6.31368i	−0.0282975	+	0.448694i
$199$	3.12623			0.221612			0.110806	−	0.993842i	$-0.464657\pi$
$199$	3.12623			0.221612			0.110806	+	0.993842i	$0.464657\pi$
$200$	−0.223768	−	3.44245i	−0.0158228	−	0.243418i
$201$	3.57293	−	10.9963i	0.252015	−	0.775622i
$202$	1.85715	−	0.603426i	0.130669	−	0.0424569i
$203$	−12.4567	−	17.1451i	−0.874287	−	1.20335i
$204$	−6.02291	+	4.37590i	−0.421688	+	0.306374i
$205$	−6.44419	−	8.28999i	−0.450082	−	0.578998i
$206$	2.82378	−	8.69069i	0.196742	−	0.605509i
$207$	−3.04911	+	4.19674i	−0.211928	+	0.291694i
$208$		−	2.45248i		−	0.170049i
$209$	−4.91754	−	4.06939i	−0.340153	−	0.281486i
$210$	6.45840	+	17.8805i	0.445672	+	1.23387i
$211$	16.4962	+	11.9852i	1.13564	+	0.825094i	0.986506	−	0.163722i	$-0.0523501\pi$
$211$	16.4962	+	11.9852i	1.13564	+	0.825094i	0.149138	+	0.988816i	$0.452350\pi$
$212$	7.82857	+	2.54366i	0.537669	+	0.174699i
$213$	−3.20113	+	1.04011i	−0.219338	+	0.0712673i
$214$	1.13571	−	0.825140i	0.0776354	−	0.0564054i
$215$	−5.59766	−	3.79566i	−0.381757	−	0.258862i
$216$	0.213204	+	0.656175i	0.0145067	+	0.0446470i
$217$	14.8256	+	4.81713i	1.00643	+	0.327008i
$218$	0.0486576	−	0.0669715i	0.00329551	−	0.00453588i
$219$	−0.650391			−0.0439494
$220$	7.43820	−	9.60688i	0.501483	−	0.647696i
$221$	−2.42665			−0.163234
$222$	0.591012	−	0.813459i	0.0396661	−	0.0545958i
$223$	−9.79767	−	3.18346i	−0.656101	−	0.213180i	−0.0379985	−	0.999278i	$-0.512098\pi$
$223$	−9.79767	−	3.18346i	−0.656101	−	0.213180i	−0.618102	+	0.786098i	$0.712098\pi$
$224$	10.1654	+	31.2858i	0.679203	+	2.09037i
$225$	1.23338	−	4.84549i	0.0822251	−	0.323033i
$226$	17.2841	−	12.5576i	1.14972	−	0.835321i
$227$	−5.96545	+	1.93829i	−0.395941	+	0.128649i	−0.500218	−	0.865899i	$-0.666747\pi$
$227$	−5.96545	+	1.93829i	−0.395941	+	0.128649i	0.104278	+	0.994548i	$0.466747\pi$
$228$	2.99862	+	0.974312i	0.198589	+	0.0645254i
$229$	1.11734	+	0.811793i	0.0738358	+	0.0536448i	0.624091	−	0.781352i	$-0.285470\pi$
$229$	1.11734	+	0.811793i	0.0738358	+	0.0536448i	−0.550255	+	0.834997i	$0.685470\pi$
$230$	20.8094	−	7.51629i	1.37213	−	0.495610i
$231$	5.44418	−	13.7444i	0.358201	−	0.904312i
$232$			3.28036i			0.215366i
$233$	4.88123	−	6.71844i	0.319780	−	0.440139i	−0.618620	−	0.785690i	$-0.712308\pi$
$233$	4.88123	−	6.71844i	0.319780	−	0.440139i	0.938400	+	0.345551i	$0.112308\pi$
$234$	0.314759	−	0.968729i	0.0205764	−	0.0633278i
$235$	21.1634	−	16.4513i	1.38055	−	1.07316i
$236$	−18.0911	+	13.1440i	−1.17763	+	0.855598i
$237$	−10.4155	−	14.3357i	−0.676559	−	0.931204i
$238$	36.7442	−	11.9389i	2.38178	−	0.773886i
$239$	−3.18134	+	9.79117i	−0.205784	+	0.633338i	0.793896	+	0.608053i	$0.208049\pi$
$239$	−3.18134	+	9.79117i	−0.205784	+	0.633338i	−0.999680	+	0.0252850i	$0.991951\pi$
$240$	2.85480	−	9.86456i	0.184277	−	0.636755i
$241$	12.2340			0.788060			0.394030	−	0.919097i	$-0.371081\pi$
$241$	12.2340			0.788060			0.394030	+	0.919097i	$0.371081\pi$
$242$	−20.6113	+	3.92535i	−1.32494	+	0.252331i
$243$			1.00000i			0.0641500i
$244$	15.4960	+	11.2585i	0.992027	+	0.720750i
$245$	−0.933693	−	28.7583i	−0.0596515	−	1.83730i
$246$	−2.76782	−	8.51848i	−0.176470	−	0.543118i
$247$	0.604076	+	0.831439i	0.0384364	+	0.0529032i
$248$	−1.41828	−	1.95210i	−0.0900610	−	0.123958i
$249$	1.31251	+	4.03950i	0.0831770	+	0.255993i
$250$	−15.9526	+	14.1528i	−1.00893	+	0.895100i
$251$	3.76725	+	2.73707i	0.237787	+	0.172762i	0.700297	−	0.713852i	$-0.253051\pi$
$251$	3.76725	+	2.73707i	0.237787	+	0.172762i	−0.462510	+	0.886614i	$0.653051\pi$
$252$			7.30240i			0.460008i
$253$	−15.9957	−	6.33594i	−1.00564	−	0.398337i
$254$	15.5930			0.978392
$255$	−9.76065	−	2.82473i	−0.611236	−	0.176892i
$256$	6.22355	−	19.1541i	0.388972	−	1.19713i
$257$	−17.4390	+	5.66627i	−1.08781	+	0.353452i	−0.797401	−	0.603449i	$-0.793793\pi$
$257$	−17.4390	+	5.66627i	−1.08781	+	0.353452i	−0.290413	+	0.956901i	$0.593793\pi$
$258$	−3.39105	−	4.66738i	−0.211118	−	0.290578i
$259$	−1.90091	+	1.38110i	−0.118117	+	0.0858171i
$260$	−1.54449	+	1.20060i	−0.0957849	+	0.0744580i
$261$	−1.46923	+	4.52183i	−0.0909432	+	0.279894i
$262$	19.8506	−	27.3220i	1.22637	−	1.68796i
$263$			9.80198i			0.604416i	0.953242	+	0.302208i	$0.0977237\pi$
$263$			9.80198i			0.604416i	−0.953242	+	0.302208i	$0.902276\pi$
$264$	−1.93225	+	1.22583i	−0.118921	+	0.0754447i
$265$	3.81669	+	10.5668i	0.234458	+	0.649113i
$266$	−13.2375	−	9.61764i	−0.811646	−	0.589695i
$267$	7.83760	+	2.54659i	0.479653	+	0.155849i
$268$	−18.0152	+	5.85348i	−1.10045	+	0.357558i
$269$	9.65232	−	7.01282i	0.588512	−	0.427579i	−0.253270	−	0.967396i	$-0.581506\pi$
$269$	9.65232	−	7.01282i	0.588512	−	0.427579i	0.841783	+	0.539816i	$0.181506\pi$
$270$	2.39370	−	3.53011i	0.145676	−	0.214835i
$271$	−9.39561	−	28.9167i	−0.570743	−	1.75657i	−0.650239	−	0.759730i	$-0.725331\pi$
$271$	−9.39561	−	28.9167i	−0.570743	−	1.75657i	0.0794962	−	0.996835i	$-0.474669\pi$
$272$	−19.8483	−	6.44910i	−1.20348	−	0.391034i
$273$	−1.39908	+	1.92566i	−0.0846760	+	0.116547i
$274$	−10.4638			−0.632144
$275$	16.5831	−	0.0319748i	0.999998	−	0.00192815i
$276$	8.49854			0.511552
$277$	13.0162	−	17.9152i	0.782065	−	1.07642i	−0.212986	−	0.977055i	$-0.568319\pi$
$277$	13.0162	−	17.9152i	0.782065	−	1.07642i	0.995051	−	0.0993645i	$-0.0316810\pi$
$278$	−5.91302	−	1.92126i	−0.354639	−	0.115229i
$279$	−1.08072	−	3.32611i	−0.0647010	−	0.199129i
$280$	−3.85931	+	5.69152i	−0.230638	+	0.340133i
$281$	−13.7794	+	10.0113i	−0.822009	+	0.597225i	−0.917287	−	0.398226i	$-0.869626\pi$
$281$	−13.7794	+	10.0113i	−0.822009	+	0.597225i	0.0952780	+	0.995451i	$0.469626\pi$
$282$	21.7467	−	7.06592i	1.29500	−	0.420770i
$283$	7.53379	+	2.44788i	0.447838	+	0.145511i	0.524249	−	0.851565i	$-0.324346\pi$
$283$	7.53379	+	2.44788i	0.447838	+	0.145511i	−0.0764113	+	0.997076i	$0.524346\pi$
$284$	4.46113	+	3.24120i	0.264719	+	0.192330i
$285$	1.46193	+	4.04746i	0.0865972	+	0.239751i
$286$	3.37155	+	0.212632i	0.199364	+	0.0125732i
$287$			20.9307i			1.23550i
$288$	4.33795	−	5.97067i	0.255616	−	0.351825i
$289$	−1.12788	+	3.47126i	−0.0663459	+	0.204192i
$290$	16.0104	−	12.4456i	0.940165	−	0.730833i
$291$	0.920978	−	0.669130i	0.0539887	−	0.0392251i
$292$	0.626301	+	0.862030i	0.0366515	+	0.0504465i
$293$	21.2462	−	6.90330i	1.24121	−	0.403295i	0.386450	−	0.922310i	$-0.373701\pi$
$293$	21.2462	−	6.90330i	1.24121	−	0.403295i	0.854765	+	0.519015i	$0.173701\pi$
$294$	7.58468	−	23.3432i	0.442347	−	1.36141i
$295$	−29.3182	−	8.48468i	−1.70697	−	0.493997i
$296$	0.363699			0.0211396
$297$	−3.21255	+	0.824326i	−0.186411	+	0.0478322i
$298$		−	5.35291i		−	0.310086i
$299$	2.24109	+	1.62825i	0.129606	+	0.0941640i
$300$	−7.60992	+	3.03130i	−0.439359	+	0.175012i
$301$	4.16606	+	12.8218i	0.240127	+	0.739036i
$302$	15.8799	+	21.8568i	0.913784	+	1.25772i
$303$	0.601744	+	0.828229i	0.0345693	+	0.0475805i
$304$	2.73128	+	8.40601i	0.156649	+	0.482117i
$305$	0.848338	+	26.1293i	0.0485757	+	1.49616i
$306$	−7.01237	−	5.09479i	−0.400871	−	0.291250i
$307$		−	9.33327i		−	0.532678i	−0.963879	−	0.266339i	$-0.914186\pi$
$307$		−	9.33327i		−	0.532678i	0.963879	−	0.266339i	$-0.0858140\pi$
$308$	−23.4593	+	6.01955i	−1.33672	+	0.342996i
$309$	4.79071			0.272534
$310$	−4.14665	+	14.3284i	−0.235514	+	0.813801i
$311$	−3.47582	+	10.6975i	−0.197096	+	0.606598i	0.802850	+	0.596181i	$0.203316\pi$
$311$	−3.47582	+	10.6975i	−0.197096	+	0.606598i	−0.999946	+	0.0104169i	$0.996684\pi$
$312$	0.350402	−	0.113853i	0.0198376	−	0.00644563i
$313$	6.38570	+	8.78916i	0.360941	+	0.496792i	0.950411	−	0.310998i	$-0.100663\pi$
$313$	6.38570	+	8.78916i	0.360941	+	0.496792i	−0.589470	+	0.807790i	$0.700663\pi$
$314$	4.80047	−	3.48775i	0.270906	−	0.196825i
$315$	−7.86905	+	6.11697i	−0.443371	+	0.344652i
$316$	−8.97085	+	27.6094i	−0.504650	+	1.55315i
$317$	−7.45871	+	10.2660i	−0.418923	+	0.576598i	−0.965366	−	0.260898i	$-0.915981\pi$
$317$	−7.45871	+	10.2660i	−0.418923	+	0.576598i	0.546443	+	0.837496i	$0.315981\pi$
$318$			9.58374i			0.537429i
$319$	−15.7377	−	0.992522i	−0.881144	−	0.0555706i
$320$	−10.2882	+	3.71606i	−0.575126	+	0.207734i
$321$	0.595413	+	0.432593i	0.0332327	+	0.0241450i
$322$	−41.9454	−	13.6289i	−2.33753	−	0.759509i
$323$	8.31746	−	2.70251i	0.462796	−	0.150372i
$324$	1.32540	−	0.962961i	0.0736334	−	0.0534978i
$325$	−2.58753	−	0.658633i	−0.143530	−	0.0365344i
$326$	11.4198	+	35.1467i	0.632487	+	1.94659i
$327$	0.0412753	+	0.0134112i	0.00228253	+	0.000741638i
$328$	1.90432	−	2.62107i	0.105148	−	0.144724i
$329$	−53.4335			−2.94588
$330$	13.3138	+	4.77992i	0.732902	+	0.263126i
$331$	−23.0627			−1.26764			−0.633821	−	0.773480i	$-0.718514\pi$
$331$	−23.0627			−1.26764			−0.633821	+	0.773480i	$0.718514\pi$
$332$	4.09006	−	5.62948i	0.224471	−	0.308958i
$333$	0.501344	+	0.162896i	0.0274735	+	0.00892667i
$334$	−2.44608	−	7.52826i	−0.133843	−	0.411928i
$335$	−21.3984	−	14.5098i	−1.16912	−	0.792757i
$336$	−16.5612	+	12.0324i	−0.903486	+	0.656421i
$337$	−30.7791	+	10.0007i	−1.67664	+	0.544774i	−0.984255	−	0.176753i	$-0.943441\pi$
$337$	−30.7791	+	10.0007i	−1.67664	+	0.544774i	−0.692386	+	0.721527i	$0.743441\pi$
$338$	23.0656	+	7.49448i	1.25461	+	0.407646i
$339$	9.06146	+	6.58354i	0.492151	+	0.357569i
$340$	5.65522	+	15.6569i	0.306698	+	0.849114i
$341$	9.79444	−	6.21367i	0.530399	−	0.336489i
$342$			3.67091i			0.198500i
$343$	−15.3735	+	21.1599i	−0.830093	+	1.14253i
$344$	0.644856	−	1.98466i	0.0347683	−	0.107006i
$345$	7.11894	+	9.15801i	0.383271	+	0.493051i
$346$	16.4583	−	11.9576i	0.884803	−	0.642847i
$347$	−17.0953	−	23.5297i	−0.917725	−	1.26314i	−0.964459	−	0.264233i	$-0.914881\pi$
$347$	−17.0953	−	23.5297i	−0.917725	−	1.26314i	0.0467340	−	0.998907i	$-0.485119\pi$
$348$	7.40805	−	2.40702i	0.397113	−	0.129030i
$349$	4.45099	−	13.6987i	0.238256	−	0.733276i	−0.758417	−	0.651770i	$-0.774027\pi$
$349$	4.45099	−	13.6987i	0.238256	−	0.733276i	0.996673	−	0.0815064i	$-0.0259731\pi$
$350$	42.4208	−	2.75745i	2.26748	−	0.147392i
$351$	0.534008			0.0285032
$352$	22.7570	+	9.01410i	1.21295	+	0.480453i
$353$		−	28.9227i		−	1.53940i	−0.638406	−	0.769700i	$-0.720406\pi$
$353$		−	28.9227i		−	1.53940i	0.638406	−	0.769700i	$-0.279594\pi$
$354$	−21.0632	−	15.3033i	−1.11949	−	0.813360i
$355$	0.244228	+	7.52235i	0.0129623	+	0.399245i
$356$	−4.17205	−	12.8402i	−0.221118	−	0.680531i
$357$	11.9057	+	16.3867i	0.630114	+	0.867277i
$358$	25.3760	+	34.9271i	1.34116	+	1.84595i
$359$	−7.26682	−	22.3650i	−0.383528	−	1.18038i	−0.937542	−	0.347871i	$-0.886905\pi$
$359$	−7.26682	−	22.3650i	−0.383528	−	1.18038i	0.554014	−	0.832507i	$-0.313095\pi$
$360$	1.54195	−	0.0500623i	0.0812677	−	0.00263852i
$361$	12.3749	+	8.99086i	0.651308	+	0.473203i
$362$			27.8145i			1.46190i
$363$	−5.29638	−	9.64097i	−0.277988	−	0.506020i
$364$	3.89953			0.204391
$365$	−0.404290	+	1.39699i	−0.0211615	+	0.0731220i
$366$	−6.89131	+	21.2093i	−0.360215	+	1.10863i
$367$	−24.0653	+	7.81928i	−1.25620	+	0.408163i	−0.860137	−	0.510062i	$-0.829622\pi$
$367$	−24.0653	+	7.81928i	−1.25620	+	0.408163i	−0.396059	+	0.918225i	$0.629622\pi$
$368$	14.0033	+	19.2739i	0.729973	+	1.00472i
$369$	3.79896	−	2.76011i	0.197766	−	0.143685i
$370$	−1.37987	−	1.77511i	−0.0717361	−	0.0922834i
$371$	6.92061	−	21.2994i	0.359300	−	1.10581i
$372$	−3.36775	+	4.63530i	−0.174609	+	0.240329i
$373$			16.2682i			0.842334i	0.906983	+	0.421167i	$0.138379\pi$
$373$			16.2682i			0.842334i	−0.906983	+	0.421167i	$0.861621\pi$
$374$	10.5868	−	26.7274i	0.547430	−	1.38204i
$375$	−9.64109	−	5.66121i	−0.497864	−	0.292344i
$376$	6.69128	+	4.86150i	0.345076	+	0.250713i
$377$	2.41469	+	0.784581i	0.124363	+	0.0404080i
$378$	−8.08594	+	2.62728i	−0.415896	+	0.135133i
$379$	20.2467	−	14.7101i	1.04000	−	0.755607i	0.0697177	−	0.997567i	$-0.477790\pi$
$379$	20.2467	−	14.7101i	1.04000	−	0.755607i	0.970286	+	0.241960i	$0.0777902\pi$
$380$	3.95673	−	5.83519i	0.202976	−	0.299339i
$381$	2.52618	+	7.77477i	0.129420	+	0.398314i
$382$	7.19160	+	2.33669i	0.367954	+	0.119556i
$383$	−7.69944	+	10.5974i	−0.393423	+	0.541500i	−0.959078	−	0.283142i	$-0.908623\pi$
$383$	−7.69944	+	10.5974i	−0.393423	+	0.541500i	0.565655	+	0.824642i	$0.308623\pi$
$384$	5.42927			0.277061
$385$	−26.1378	−	20.2373i	−1.33210	−	1.03139i
$386$	−0.0573242			−0.00291772
$387$	1.77781	−	2.44695i	0.0903713	−	0.124385i
$388$	−1.77373	−	0.576320i	−0.0900476	−	0.0292582i
$389$	−5.16480	−	15.8956i	−0.261866	−	0.805940i	−0.992399	−	0.123063i	$-0.960728\pi$
$389$	−5.16480	−	15.8956i	−0.261866	−	0.805940i	0.730533	−	0.682877i	$-0.239272\pi$
$390$	−1.88510	−	1.27825i	−0.0954559	−	0.0647268i
$391$	19.0709	−	13.8558i	0.964456	−	0.700718i
$392$	8.44356	−	2.74348i	0.426464	−	0.138567i
$393$	16.8389	+	5.47128i	0.849408	+	0.275990i
$394$	8.49596	+	6.17267i	0.428020	+	0.310975i
$395$	−37.2665	+	13.4605i	−1.87508	+	0.677273i
$396$	4.18612	+	3.46413i	0.210361	+	0.174079i
$397$			4.22375i			0.211984i	0.994367	+	0.105992i	$0.0338018\pi$
$397$			4.22375i			0.211984i	−0.994367	+	0.105992i	$0.966198\pi$
$398$	3.50500	−	4.82421i	0.175690	−	0.241816i
$399$	2.65084	−	8.15845i	0.132708	−	0.408433i
$400$	−19.4138	−	12.2638i	−0.970690	−	0.613191i
$401$	16.9460	−	12.3120i	0.846241	−	0.614830i	−0.0778663	−	0.996964i	$-0.524811\pi$
$401$	16.9460	−	12.3120i	0.846241	−	0.614830i	0.924107	+	0.382134i	$0.124811\pi$
$402$	−12.9631	−	17.8422i	−0.646541	−	0.889887i
$403$	−1.77617	+	0.577112i	−0.0884773	+	0.0287480i
$404$	0.518281	−	1.59510i	0.0257854	−	0.0793594i
$405$	2.14793	+	0.621610i	0.106731	+	0.0308881i
$406$	−40.4233			−2.00618
$407$	−0.110043	+	1.74487i	−0.00545462	+	0.0864901i
$408$		−	3.13525i		−	0.155218i
$409$	−5.54999	−	4.03231i	−0.274429	−	0.199385i	0.442055	−	0.896988i	$-0.354250\pi$
$409$	−5.54999	−	4.03231i	−0.274429	−	0.199385i	−0.716484	+	0.697603i	$0.754250\pi$
$410$	−20.0176	+	0.649910i	−0.988599	+	0.0320968i
$411$	−1.69522	−	5.21734i	−0.0836189	−	0.257353i
$412$	−4.61326	−	6.34961i	−0.227279	−	0.312823i
$413$	35.7612	+	49.2210i	1.75969	+	2.42201i
$414$	3.05763	+	9.41042i	0.150274	+	0.462497i
$415$	9.49242	−	0.308190i	0.465965	−	0.0151285i
$416$	−3.18838	−	2.31650i	−0.156323	−	0.113576i
$417$		−	3.25952i		−	0.159620i
$418$	−11.7930	+	3.02603i	−0.576814	+	0.148008i
$419$	19.0865			0.932435			0.466217	−	0.884670i	$-0.345616\pi$
$419$	19.0865			0.932435			0.466217	+	0.884670i	$0.345616\pi$
$420$	15.6850	+	4.53925i	0.765351	+	0.221492i
$421$	−3.78642	+	11.6534i	−0.184539	+	0.567952i	−0.999940	−	0.0109440i	$-0.996516\pi$
$421$	−3.78642	+	11.6534i	−0.184539	+	0.567952i	0.815401	+	0.578896i	$0.196516\pi$
$422$	36.9897	−	12.0187i	1.80063	−	0.585060i
$423$	7.04623	+	9.69830i	0.342599	+	0.471548i
$424$	−2.80451	+	2.03760i	−0.136199	+	0.0989545i
$425$	−12.1346	+	19.2093i	−0.588617	+	0.931789i
$426$	−1.98394	+	6.10594i	−0.0961222	+	0.295834i
$427$	30.6313	−	42.1603i	1.48235	−	2.04028i
$428$		−	1.20573i		−	0.0582812i
$429$	0.440196	+	1.71553i	0.0212529	+	0.0828264i
$430$	−12.1331	+	4.38244i	−0.585111	+	0.211340i
$431$	5.68128	+	4.12769i	0.273658	+	0.198824i	0.716146	−	0.697950i	$-0.245904\pi$
$431$	5.68128	+	4.12769i	0.273658	+	0.198824i	−0.442489	+	0.896774i	$0.645904\pi$
$432$	4.36781	+	1.41919i	0.210146	+	0.0682807i
$433$	−26.1445	+	8.49487i	−1.25643	+	0.408238i	−0.860220	−	0.509924i	$-0.829674\pi$
$433$	−26.1445	+	8.49487i	−1.25643	+	0.408238i	−0.396207	+	0.918161i	$0.629674\pi$
$434$	24.0554	−	17.4773i	1.15470	−	0.838935i
$435$	8.79928	+	5.96662i	0.421893	+	0.286078i
$436$	−0.0219713	−	0.0676207i	−0.00105223	−	0.00323845i
$437$	−9.49481	−	3.08505i	−0.454198	−	0.147578i
$438$	−0.729192	+	1.00365i	−0.0348421	+	0.0479561i
$439$	17.6992			0.844736			0.422368	−	0.906425i	$-0.361199\pi$
$439$	17.6992			0.844736			0.422368	+	0.906425i	$0.361199\pi$
$440$	1.43189	+	4.91232i	0.0682629	+	0.234185i
$441$	12.8679			0.612755
$442$	−2.72065	+	3.74466i	−0.129408	+	0.178115i
$443$	−15.7780	−	5.12660i	−0.749638	−	0.243572i	−0.0908124	−	0.995868i	$-0.528946\pi$
$443$	−15.7780	−	5.12660i	−0.749638	−	0.243572i	−0.658825	+	0.752296i	$0.728946\pi$
$444$	−0.266871	−	0.821345i	−0.0126651	−	0.0389793i
$445$	10.3418	−	15.2516i	0.490250	−	0.722996i
$446$	−15.8973	+	11.5500i	−0.752758	+	0.546911i
$447$	2.66900	−	0.867210i	0.126239	−	0.0410176i
$448$	20.7378	+	6.73813i	0.979771	+	0.318347i
$449$	−21.2665	−	15.4510i	−1.00363	−	0.729179i	−0.0407653	−	0.999169i	$-0.512980\pi$
$449$	−21.2665	−	15.4510i	−1.00363	−	0.729179i	−0.962863	+	0.269990i	$0.912980\pi$
$450$	−6.09447	−	7.33584i	−0.287296	−	0.345815i
$451$	11.9986	+	9.92913i	0.564991	+	0.467545i
$452$		−	18.3498i		−	0.863100i
$453$	−8.32527	+	11.4588i	−0.391155	+	0.538379i
$454$	−3.69715	+	11.3787i	−0.173516	+	0.534027i
$455$	3.26651	+	4.20213i	0.153136	+	0.196999i
$456$	−1.07423	+	0.780472i	−0.0503053	+	0.0365490i
$457$	16.1356	+	22.2087i	0.754790	+	1.03888i	0.997630	+	0.0688132i	$0.0219212\pi$
$457$	16.1356	+	22.2087i	0.754790	+	1.03888i	−0.242839	+	0.970067i	$0.578079\pi$
$458$	2.50543	−	0.814062i	0.117071	−	0.0380386i
$459$	1.40424	−	4.32181i	0.0655443	−	0.201725i
$460$	5.28278	−	18.2543i	0.246311	−	0.851109i
$461$	16.7991			0.782410			0.391205	−	0.920304i	$-0.372058\pi$
$461$	16.7991			0.782410			0.391205	+	0.920304i	$0.372058\pi$
$462$	−15.1057	−	23.8108i	−0.702782	−	1.10778i
$463$		−	32.2574i		−	1.49913i	−0.661930	−	0.749565i	$-0.730263\pi$
$463$		−	32.2574i		−	1.49913i	0.661930	−	0.749565i	$-0.269737\pi$
$464$	17.6654	+	12.8347i	0.820095	+	0.595834i
$465$	−7.81604	+	0.253763i	−0.362460	+	0.0117680i
$466$	−4.89487	−	15.0649i	−0.226751	−	0.697866i
$467$	1.34967	+	1.85767i	0.0624555	+	0.0859626i	0.839102	−	0.543974i	$-0.183081\pi$
$467$	1.34967	+	1.85767i	0.0624555	+	0.0859626i	−0.776647	+	0.629936i	$0.783081\pi$
$468$	−0.514228	−	0.707774i	−0.0237702	−	0.0327169i
$469$	15.9258	+	49.0144i	0.735383	+	2.26328i
$470$	−1.65915	−	51.1026i	−0.0765307	−	2.35719i
$471$	2.51672	+	1.82851i	0.115965	+	0.0842532i
$472$		−	9.41739i		−	0.433470i
$473$	9.32644	+	3.69423i	0.428830	+	0.169861i
$474$	−33.7995			−1.55246
$475$	9.60241	−	0.624180i	0.440589	−	0.0286393i
$476$	10.2543	−	31.5595i	0.470006	−	1.44653i
$477$	−4.77851	+	1.55263i	−0.218793	+	0.0710902i
$478$	11.5424	+	15.8867i	0.527936	+	0.726642i
$479$	0.275970	−	0.200504i	0.0126094	−	0.00916125i	−0.581463	−	0.813573i	$-0.697519\pi$
$479$	0.275970	−	0.200504i	0.0126094	−	0.00916125i	0.594072	+	0.804412i	$0.297519\pi$
$480$	−10.1281	−	13.0290i	−0.462281	−	0.594691i
$481$	0.0869880	−	0.267721i	0.00396631	−	0.0122070i
$482$	13.7162	−	18.8788i	0.624758	−	0.859905i
$483$		−	23.1222i		−	1.05210i
$484$	−7.67796	+	16.3037i	−0.348998	+	0.741078i
$485$	−0.864754	−	2.39413i	−0.0392665	−	0.108712i
$486$	1.54314	+	1.12116i	0.0699984	+	0.0508568i
$487$	−15.0793	−	4.89955i	−0.683306	−	0.222020i	−0.0532640	−	0.998580i	$-0.516962\pi$
$487$	−15.0793	−	4.89955i	−0.683306	−	0.222020i	−0.630042	+	0.776561i	$0.716962\pi$
$488$	−7.67168	+	2.49268i	−0.347281	+	0.112838i
$489$	−15.6743	+	11.3880i	−0.708815	+	0.514984i
$490$	−45.4249	−	30.8018i	−2.05209	−	1.39148i
$491$	9.27370	+	28.5415i	0.418516	+	1.28806i	0.909068	+	0.416648i	$0.136795\pi$
$491$	9.27370	+	28.5415i	0.418516	+	1.28806i	−0.490552	+	0.871412i	$0.663205\pi$
$492$	−7.31650	−	2.37728i	−0.329853	−	0.107176i
$493$	12.6995	−	17.4793i	0.571955	−	0.787229i
$494$	1.96030			0.0881978
$495$	−0.226362	+	7.41274i	−0.0101742	+	0.333178i
$496$	−16.0616			−0.721186
$497$	8.81844	−	12.1375i	0.395561	−	0.544443i
$498$	7.70505	+	2.50352i	0.345272	+	0.112186i
$499$	−1.12951	−	3.47626i	−0.0505636	−	0.155619i	0.922586	−	0.385790i	$-0.126071\pi$
$499$	−1.12951	−	3.47626i	−0.0505636	−	0.155619i	−0.973150	+	0.230172i	$0.926071\pi$
$500$	1.78061	+	18.2298i	0.0796313	+	0.815263i
$501$	3.35735	−	2.43926i	0.149996	−	0.108978i
$502$	8.44737	−	2.74472i	0.377025	−	0.122503i
$503$	−29.6522	−	9.63458i	−1.32213	−	0.429585i	−0.438901	−	0.898535i	$-0.644632\pi$
$503$	−29.6522	−	9.63458i	−1.32213	−	0.429585i	−0.883224	+	0.468951i	$0.844632\pi$
$504$	−2.48798	−	1.80762i	−0.110823	−	0.0805178i
$505$	2.15303	−	0.777667i	0.0958085	−	0.0346057i
$506$	−27.7110	+	17.5800i	−1.23190	+	0.781529i
$507$			12.7148i			0.564686i
$508$	7.87209	−	10.8350i	0.349267	−	0.480725i
$509$	4.55180	−	14.0090i	0.201755	−	0.620938i	−0.798076	−	0.602557i	$-0.794149\pi$
$509$	4.55180	−	14.0090i	0.201755	−	0.620938i	0.999831	−	0.0183813i	$-0.00585128\pi$
$510$	−15.3022	+	11.8951i	−0.677593	+	0.526724i
$511$	2.34535	−	1.70400i	0.103752	−	0.0753804i
$512$	−16.1975	−	22.2939i	−0.715834	−	0.985261i
$513$	−1.83034	+	0.594714i	−0.0808115	+	0.0262573i
$514$	−10.8080	+	33.2636i	−0.476721	+	1.46720i
$515$	2.97795	−	10.2901i	0.131224	−	0.453436i
$516$	−4.95515			−0.218138
$517$	−25.3479	+	30.6309i	−1.11480	+	1.34715i
$518$			4.48181i			0.196919i
$519$	8.62852	+	6.26898i	0.378750	+	0.275178i
$520$	−0.0267336	−	0.823411i	−0.00117235	−	0.0361090i
$521$	−0.400394	−	1.23229i	−0.0175416	−	0.0539875i	0.941903	−	0.335886i	$-0.109036\pi$
$521$	−0.400394	−	1.23229i	−0.0175416	−	0.0539875i	−0.959444	+	0.281899i	$0.909036\pi$
$522$	5.33059	+	7.33692i	0.233313	+	0.321128i
$523$	−18.0736	−	24.8762i	−0.790305	−	1.08776i	−0.994070	−	0.108742i	$-0.965318\pi$
$523$	−18.0736	−	24.8762i	−0.790305	−	1.08776i	0.203765	−	0.979020i	$-0.434682\pi$
$524$	−8.96352	−	27.5869i	−0.391573	−	1.20514i
$525$	8.24735	+	20.7045i	0.359944	+	0.903620i
$526$	15.1259	+	10.9896i	0.659519	+	0.479168i
$527$			15.8924i			0.692284i
$528$	−0.958716	+	15.2017i	−0.0417227	+	0.661569i
$529$	−3.90968			−0.169986
$530$	20.5852	+	5.95735i	0.894164	+	0.258771i
$531$	4.21793	−	12.9815i	0.183043	−	0.563348i
$532$	−13.3659	+	4.34284i	−0.579484	+	0.188286i
$533$	−1.47392	−	2.02867i	−0.0638425	−	0.0878716i
$534$	12.7169	−	9.23940i	0.550316	−	0.399828i
$535$	1.29929	−	1.01000i	0.0561734	−	0.0436661i
$536$	2.46512	−	7.58685i	0.106477	−	0.327702i
$537$	−13.3038	+	18.3111i	−0.574100	+	0.790181i
$538$		−	22.7574i		−	0.981141i
$539$	10.6073	+	41.3387i	0.456889	+	1.78058i
$540$	−1.24449	−	3.44546i	−0.0535542	−	0.148269i
$541$	−12.7461	−	9.26058i	−0.547998	−	0.398144i	0.279049	−	0.960277i	$-0.409981\pi$
$541$	−12.7461	−	9.26058i	−0.547998	−	0.398144i	−0.827047	+	0.562133i	$0.809981\pi$
$542$	−55.1566	−	17.9215i	−2.36918	−	0.769793i
$543$	−13.8685	+	4.50615i	−0.595155	+	0.193377i
$544$	−27.1320	+	19.7126i	−1.16328	+	0.845169i
$545$	0.0544633	−	0.0803199i	0.00233295	−	0.00344053i
$546$	1.40299	+	4.31795i	0.0600423	+	0.184791i
$547$	14.6079	+	4.74641i	0.624591	+	0.202942i	0.604178	−	0.796850i	$-0.293502\pi$
$547$	14.6079	+	4.74641i	0.624591	+	0.202942i	0.0204133	+	0.999792i	$0.493502\pi$
$548$	−5.28265	+	7.27094i	−0.225663	+	0.310599i
$549$	−11.6915			−0.498982
$550$	18.5429	−	25.6259i	0.790674	−	1.09269i
$551$	−9.15026			−0.389814
$552$	−2.10371	+	2.89551i	−0.0895399	+	0.123241i
$553$	75.1179	+	24.4073i	3.19434	+	1.03790i
$554$	−13.0525	−	40.1716i	−0.554549	−	1.70673i
$555$	0.661531	−	0.975593i	0.0280804	−	0.0414116i
$556$	−4.32018	+	3.13879i	−0.183216	+	0.133115i
$557$	34.1609	−	11.0996i	1.44745	−	0.470303i	0.523235	−	0.852188i	$-0.324725\pi$
$557$	34.1609	−	11.0996i	1.44745	−	0.470303i	0.924210	+	0.381885i	$0.124725\pi$
$558$	−6.34433	−	2.06140i	−0.268577	−	0.0872659i
$559$	−1.30669	−	0.949365i	−0.0552670	−	0.0401539i
$560$	15.5501	+	43.0517i	0.657113	+	1.81927i
$561$	15.0416	+	0.948618i	0.635056	+	0.0400507i
$562$			32.4878i			1.37042i
$563$	18.1981	−	25.0475i	0.766958	−	1.05563i	−0.229645	−	0.973274i	$-0.573756\pi$
$563$	18.1981	−	25.0475i	0.766958	−	1.05563i	0.996603	−	0.0823531i	$-0.0262435\pi$
$564$	6.06891	−	18.6782i	0.255547	−	0.786493i
$565$	19.7737	−	15.3710i	0.831885	−	0.646662i
$566$	12.2240	−	8.88126i	0.513813	−	0.373307i
$567$	−2.61996	−	3.60606i	−0.110028	−	0.151440i
$568$	−2.20860	+	0.717618i	−0.0926708	+	0.0301106i
$569$	−0.721169	+	2.21953i	−0.0302330	+	0.0930475i	−0.965034	−	0.262123i	$-0.915577\pi$
$569$	−0.721169	+	2.21953i	−0.0302330	+	0.0930475i	0.934801	+	0.355171i	$0.115577\pi$
$570$	7.88486	+	2.28188i	0.330261	+	0.0955773i
$571$	−26.6093			−1.11357			−0.556783	−	0.830658i	$-0.687964\pi$
$571$	−26.6093			−1.11357			−0.556783	+	0.830658i	$0.687964\pi$
$572$	1.84987	−	2.23542i	0.0773470	−	0.0934677i
$573$			3.96434i			0.165613i
$574$	32.2990	+	23.4666i	1.34813	+	0.979477i
$575$	24.0960	−	9.59827i	1.00487	−	0.400275i
$576$	−1.51169	−	4.65252i	−0.0629872	−	0.193855i
$577$	−2.17403	−	2.99229i	−0.0905059	−	0.124571i	0.761363	−	0.648326i	$-0.224531\pi$
$577$	−2.17403	−	2.99229i	−0.0905059	−	0.124571i	−0.851869	+	0.523755i	$0.824531\pi$
$578$	4.09212	+	5.63231i	0.170210	+	0.234273i
$579$	−0.00928692	−	0.0285822i	−0.000385951	−	0.00118784i
$580$	−0.565191	−	17.4082i	−0.0234683	−	0.722836i
$581$	−15.3163	−	11.1279i	−0.635427	−	0.461665i
$582$		−	2.17140i		−	0.0900075i
$583$	−8.92696	−	14.0713i	−0.369717	−	0.582776i
$584$	−0.448733			−0.0185687
$585$	0.331945	−	1.14701i	0.0137242	−	0.0474230i
$586$	13.1676	−	40.5256i	0.543947	−	1.67410i
$587$	29.8228	−	9.69003i	1.23092	−	0.399950i	0.379873	−	0.925039i	$-0.375968\pi$
$587$	29.8228	−	9.69003i	1.23092	−	0.399950i	0.851048	+	0.525088i	$0.175968\pi$
$588$	−12.3912	−	17.0551i	−0.511006	−	0.703340i
$589$	5.44520	−	3.95617i	0.224366	−	0.163011i
$590$	−45.9634	+	35.7295i	−1.89228	+	1.47096i
$591$	−1.70133	+	5.23616i	−0.0699834	+	0.215387i
$592$	1.42300	−	1.95860i	0.0584851	−	0.0804978i
$593$			32.0728i			1.31707i	0.752550	+	0.658535i	$0.228824\pi$
$593$			32.0728i			1.31707i	−0.752550	+	0.658535i	$0.771176\pi$
$594$	−2.32973	+	5.88163i	−0.0955899	+	0.241326i
$595$	42.5982	−	15.3863i	1.74636	−	0.630779i
$596$	−3.71954	−	2.70240i	−0.152358	−	0.110695i
$597$	2.97322	+	0.966057i	0.121686	+	0.0395381i
$598$	5.02524	−	1.63280i	0.205497	−	0.0667701i
$599$	−16.4442	+	11.9474i	−0.671892	+	0.488158i	−0.870658	−	0.491889i	$-0.836307\pi$
$599$	−16.4442	+	11.9474i	−0.671892	+	0.488158i	0.198766	+	0.980047i	$0.436307\pi$
$600$	0.850960	−	3.34311i	0.0347403	−	0.136482i
$601$	−3.59254	−	11.0567i	−0.146543	−	0.451012i	0.850663	−	0.525711i	$-0.176201\pi$
$601$	−3.59254	−	11.0567i	−0.146543	−	0.451012i	−0.997206	+	0.0746984i	$0.976201\pi$
$602$	24.4567	+	7.94646i	0.996780	+	0.323873i
$603$	6.79611	−	9.35405i	0.276759	−	0.380926i
$604$	23.2044			0.944172
$605$	−24.0004	+	5.38331i	−0.975756	+	0.218863i
$606$	1.95273			0.0793241
$607$	−15.0927	+	20.7734i	−0.612595	+	0.843164i	−0.996788	−	0.0800885i	$-0.974480\pi$
$607$	−15.0927	+	20.7734i	−0.612595	+	0.843164i	0.384193	+	0.923253i	$0.374480\pi$
$608$	13.5082	+	4.38908i	0.547830	+	0.178001i
$609$	−6.54886	−	20.1553i	−0.265373	−	0.816735i
$610$	41.2723	+	27.9860i	1.67107	+	1.13312i
$611$	5.17897	−	3.76274i	0.209519	−	0.152224i
$612$	−7.08036	+	2.30055i	−0.286206	+	0.0929941i
$613$	−6.26213	−	2.03469i	−0.252925	−	0.0821804i	0.179810	−	0.983701i	$-0.442452\pi$
$613$	−6.26213	−	2.03469i	−0.252925	−	0.0821804i	−0.432736	+	0.901521i	$0.642452\pi$
$614$	−14.4026	−	10.4641i	−0.581240	−	0.422296i
$615$	−3.56704	−	9.87561i	−0.143837	−	0.398223i
$616$	3.75617	−	9.48282i	0.151341	−	0.382074i
$617$		−	25.4721i		−	1.02547i	−0.858548	−	0.512734i	$-0.828633\pi$
$617$		−	25.4721i		−	1.02547i	0.858548	−	0.512734i	$-0.171367\pi$
$618$	5.37114	−	7.39274i	0.216059	−	0.297380i
$619$	0.334663	−	1.02999i	0.0134513	−	0.0413987i	−0.944106	−	0.329643i	$-0.893072\pi$
$619$	0.334663	−	1.02999i	0.0134513	−	0.0413987i	0.957557	+	0.288244i	$0.0930716\pi$
$620$	7.86288	+	10.1150i	0.315781	+	0.406229i
$621$	−4.19674	+	3.04911i	−0.168409	+	0.122357i
$622$	12.6108	+	17.3572i	0.505646	+	0.695962i
$623$	−34.9348	+	11.3510i	−1.39963	+	0.454769i
$624$	0.757857	−	2.33244i	0.0303386	−	0.0933725i
$625$	−18.1529	+	17.1893i	−0.726116	+	0.687573i
$626$	20.7223			0.828230
$627$	−3.41935	−	5.38983i	−0.136556	−	0.215249i
$628$		−	5.09645i		−	0.203371i
$629$	−1.93797	−	1.40801i	−0.0772717	−	0.0561412i
$630$	0.616910	+	19.0012i	0.0245783	+	0.757025i
$631$	9.59703	+	29.5366i	0.382052	+	1.17583i	0.938597	+	0.345017i	$0.112127\pi$
$631$	9.59703	+	29.5366i	0.382052	+	1.17583i	−0.556545	+	0.830817i	$0.687873\pi$
$632$	−7.18610	−	9.89082i	−0.285848	−	0.393436i
$633$	11.9852	+	16.4962i	0.476368	+	0.655665i
$634$	7.47956	+	23.0197i	0.297051	+	0.914230i
$635$	18.2700	−	0.593170i	0.725021	−	0.0235392i
$636$	6.65938	+	4.83832i	0.264062	+	0.191852i
$637$		−	6.87153i		−	0.272260i
$638$	−19.1761	+	23.1728i	−0.759189	+	0.917420i
$639$	−3.36587			−0.133152
$640$	3.37489	−	11.6617i	0.133404	−	0.460969i
$641$	−6.92776	+	21.3214i	−0.273630	+	0.842147i	0.715949	+	0.698153i	$0.245994\pi$
$641$	−6.92776	+	21.3214i	−0.273630	+	0.842147i	−0.989579	+	0.143994i	$0.954006\pi$
$642$	1.33510	−	0.433802i	0.0526924	−	0.0171208i
$643$	−8.12166	−	11.1785i	−0.320287	−	0.440837i	0.618268	−	0.785968i	$-0.287835\pi$
$643$	−8.12166	−	11.1785i	−0.320287	−	0.440837i	−0.938555	+	0.345130i	$0.887835\pi$
$644$	−30.6463	+	22.2658i	−1.20763	+	0.877396i
$645$	−4.15077	−	5.33966i	−0.163436	−	0.210249i
$646$	5.15484	−	15.8650i	0.202815	−	0.624199i
$647$	−14.6642	+	20.1836i	−0.576511	+	0.793499i	−0.993307	−	0.115501i	$-0.963153\pi$
$647$	−14.6642	+	20.1836i	−0.576511	+	0.793499i	0.416797	+	0.909000i	$0.363153\pi$
$648$			0.689943i			0.0271035i
$649$	45.1806	+	2.84937i	1.77349	+	0.111848i
$650$	−3.91739	+	3.25449i	−0.153653	+	0.127652i
$651$	12.6114	+	9.16273i	0.494280	+	0.359116i
$652$	30.1874	+	9.80848i	1.18223	+	0.384130i
$653$	17.9388	−	5.82866i	0.701999	−	0.228093i	0.0637975	−	0.997963i	$-0.479679\pi$
$653$	17.9388	−	5.82866i	0.701999	−	0.228093i	0.638201	+	0.769870i	$0.279679\pi$
$654$	0.0669715	−	0.0486576i	0.00261879	−	0.00190266i
$655$	22.2191	−	32.7677i	0.868173	−	1.28034i
$656$	−6.66419	−	20.5103i	−0.260193	−	0.800791i
$657$	−0.618559	−	0.200982i	−0.0241323	−	0.00784105i
$658$	−59.9075	+	82.4555i	−2.33544	+	3.21445i
$659$	2.97553			0.115910			0.0579550	−	0.998319i	$-0.481542\pi$
$659$	2.97553			0.115910			0.0579550	+	0.998319i	$0.481542\pi$
$660$	10.0428	−	6.83816i	0.390917	−	0.266175i
$661$	−39.0164			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$661$	−39.0164			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$662$	−25.8570	+	35.5891i	−1.00496	+	1.38321i
$663$	−2.30788	−	0.749875i	−0.0896305	−	0.0291227i
$664$	0.905558	+	2.78702i	0.0351425	+	0.108157i
$665$	−15.8760	−	10.7652i	−0.615644	−	0.417456i
$666$	0.813459	−	0.591012i	0.0315209	−	0.0229013i
$667$	−23.4568	+	7.62157i	−0.908250	+	0.295108i
$668$	−6.46600	−	2.10093i	−0.250177	−	0.0812875i
$669$	−8.33440	−	6.05529i	−0.322226	−	0.234111i
$670$	−46.3818	+	16.7530i	−1.79188	+	0.647223i
$671$	−9.63762	−	37.5596i	−0.372056	−	1.44997i
$672$			32.8958i			1.26898i
$673$	8.95090	−	12.3199i	0.345032	−	0.474896i	−0.600871	−	0.799346i	$-0.705179\pi$
$673$	8.95090	−	12.3199i	0.345032	−	0.474896i	0.945903	+	0.324450i	$0.105179\pi$
$674$	−19.0757	+	58.7089i	−0.734767	+	2.26138i
$675$	2.67035	−	4.22720i	0.102782	−	0.162705i
$676$	16.8523	−	12.2439i	0.648164	−	0.470919i
$677$	−0.487311	−	0.670727i	−0.0187289	−	0.0257781i	0.799550	−	0.600600i	$-0.205071\pi$
$677$	−0.487311	−	0.670727i	−0.0187289	−	0.0257781i	−0.818279	+	0.574822i	$0.805071\pi$
$678$	20.3187	−	6.60194i	0.780334	−	0.253546i
$679$	−1.56801	+	4.82585i	−0.0601748	+	0.185199i
$680$	−6.73429	−	1.94890i	−0.258248	−	0.0747370i
$681$	−6.27244			−0.240361
$682$	1.39255	−	22.0807i	0.0533236	−	0.845515i
$683$		−	1.03468i		−	0.0395910i	−0.999804	−	0.0197955i	$-0.993698\pi$
$683$		−	1.03468i		−	0.0395910i	0.999804	−	0.0197955i	$-0.00630151\pi$
$684$	2.55078	+	1.85325i	0.0975315	+	0.0708608i
$685$	−12.2602	+	0.398053i	−0.468440	+	0.0152088i
$686$	15.4165	+	47.4472i	0.588605	+	1.81154i
$687$	0.811793	+	1.11734i	0.0309718	+	0.0426291i
$688$	−8.16476	−	11.2378i	−0.311279	−	0.428438i
$689$	0.829118	+	2.55176i	0.0315869	+	0.0972144i
$690$	22.1136	−	0.717960i	0.841849	−	0.0273323i
$691$	−15.5969	−	11.3318i	−0.593332	−	0.431081i	0.250174	−	0.968201i	$-0.419512\pi$
$691$	−15.5969	−	11.3318i	−0.593332	−	0.431081i	−0.843506	+	0.537120i	$0.819512\pi$
$692$		−	17.4730i		−	0.664225i
$693$	9.42496	−	11.3893i	0.358025	−	0.432644i
$694$	−55.4762			−2.10585
$695$	−7.00123	−	2.02615i	−0.265572	−	0.0768564i
$696$	−1.01369	+	3.11980i	−0.0384237	+	0.118256i
$697$	−20.2942	+	6.59400i	−0.768699	+	0.249765i
$698$	−16.1488	−	22.2270i	−0.611242	−	0.841303i
$699$	6.71844	−	4.88123i	0.254115	−	0.184625i
$700$	19.5000	−	30.8687i	0.737029	−	1.16673i
$701$	1.01927	−	3.13700i	0.0384974	−	0.118483i	−0.929961	−	0.367658i	$-0.880160\pi$
$701$	1.01927	−	3.13700i	0.0384974	−	0.118483i	0.968458	+	0.249175i	$0.0801596\pi$
$702$	0.598707	−	0.824050i	0.0225967	−	0.0311018i
$703$			1.01451i			0.0382629i
$704$	13.7003	−	8.69158i	0.516350	−	0.327576i
$705$	25.2113	−	9.10624i	0.949512	−	0.342961i
$706$	−44.6318	−	32.4269i	−1.67974	−	1.22040i
$707$	−4.33985	−	1.41010i	−0.163217	−	0.0530324i
$708$	−21.2674	+	6.91018i	−0.799276	+	0.259701i
$709$	−30.5479	+	22.1943i	−1.14725	+	0.833526i	−0.988113	−	0.153730i	$-0.950871\pi$
$709$	−30.5479	+	22.1943i	−1.14725	+	0.833526i	−0.159137	+	0.987256i	$0.550871\pi$
$710$	11.8819	+	8.05687i	0.445919	+	0.302369i
$711$	−5.47575	−	16.8526i	−0.205357	−	0.632023i
$712$	5.40750	+	1.75700i	0.202654	+	0.0658464i
$713$	10.6636	−	14.6772i	0.399355	−	0.549665i
$714$	38.6352			1.44589
$715$	3.95846	+	0.120879i	0.148038	+	0.00452062i
$716$	37.0805			1.38576
$717$	−6.05128	+	8.32887i	−0.225989	+	0.311047i
$718$	−42.6596	−	13.8610i	−1.59204	−	0.517286i
$719$	8.99176	+	27.6738i	0.335336	+	1.03206i	0.966556	+	0.256455i	$0.0825545\pi$
$719$	8.99176	+	27.6738i	0.335336	+	1.03206i	−0.631220	+	0.775604i	$0.717446\pi$
$720$	5.76339	−	8.49957i	0.214789	−	0.316760i
$721$	−17.2756	+	12.5514i	−0.643377	+	0.467440i
$722$	27.7484	−	9.01599i	1.03269	−	0.335540i
$723$	11.6352	+	3.78051i	0.432718	+	0.140599i
$724$	19.3273	+	14.0421i	0.718293	+	0.521870i
$725$	18.2856	−	15.1913i	0.679110	−	0.564192i
$726$	−20.8155	−	2.63600i	−0.772535	−	0.0978310i
$727$			38.1331i			1.41428i	0.707074	+	0.707140i	$0.250015\pi$
$727$			38.1331i			1.41428i	−0.707074	+	0.707140i	$0.749985\pi$
$728$	−0.965283	+	1.32860i	−0.0357758	+	0.0492411i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	1.70249	+	2.19013i	0.0630119	+	0.0810604i
$731$	−11.1195	+	8.07876i	−0.411268	+	0.298804i
$732$	11.2585	+	15.4960i	0.416125	+	0.572747i
$733$	38.0468	−	12.3622i	1.40529	−	0.456607i	0.494393	−	0.869238i	$-0.335390\pi$
$733$	38.0468	−	12.3622i	1.40529	−	0.456607i	0.910898	+	0.412632i	$0.135390\pi$
$734$	−14.9147	+	45.9028i	−0.550512	+	1.69430i
$735$	7.99880	−	27.6393i	0.295040	−	1.01949i
$736$	38.2842			1.41118
$737$	35.6526	+	14.1221i	1.31328	+	0.520194i
$738$		−	8.95686i		−	0.329707i
$739$	−33.5714	−	24.3910i	−1.23494	−	0.897238i	−0.237692	−	0.971341i	$-0.576391\pi$
$739$	−33.5714	−	24.3910i	−1.23494	−	0.897238i	−0.997251	+	0.0741026i	$0.976391\pi$
$740$	−1.93008	+	0.0626638i	−0.0709512	+	0.00230357i
$741$	0.317582	+	0.977416i	0.0116667	+	0.0359063i
$742$	−25.1090	−	34.5596i	−0.921780	−	1.26872i
$743$	1.58408	+	2.18030i	0.0581144	+	0.0799876i	0.837085	−	0.547073i	$-0.184258\pi$
$743$	1.58408	+	2.18030i	0.0581144	+	0.0799876i	−0.778971	+	0.627060i	$0.784258\pi$
$744$	−0.745635	−	2.29483i	−0.0273363	−	0.0841325i
$745$	−0.203629	−	6.27188i	−0.00746039	−	0.229784i
$746$	25.1041	+	18.2392i	0.919127	+	0.667785i
$747$			4.24738i			0.155403i
$748$	−13.2271	−	20.8496i	−0.483632	−	0.762337i
$749$	−3.28047			−0.119866
$750$	−19.5453	+	8.53046i	−0.713692	+	0.311488i
$751$	−14.1019	+	43.4012i	−0.514586	+	1.58373i	0.269448	+	0.963015i	$0.413159\pi$
$751$	−14.1019	+	43.4012i	−0.514586	+	1.58373i	−0.784034	+	0.620718i	$0.786841\pi$
$752$	52.3603	−	17.0129i	1.90938	−	0.620396i
$753$	2.73707	+	3.76725i	0.0997443	+	0.137286i
$754$	3.91797	−	2.84657i	0.142684	−	0.103666i
$755$	19.4375	+	25.0050i	0.707404	+	0.910024i
$756$	−2.25656	+	6.94499i	−0.0820705	+	0.252587i
$757$	5.28529	−	7.27458i	0.192097	−	0.264399i	−0.702094	−	0.712084i	$-0.747751\pi$
$757$	5.28529	−	7.27458i	0.192097	−	0.264399i	0.894191	+	0.447685i	$0.147751\pi$
$758$		−	47.7359i		−	1.73385i
$759$	−13.2549	−	10.9688i	−0.481122	−	0.398142i
$760$	1.00865	+	2.79252i	0.0365875	+	0.101295i
$761$	12.1822	+	8.85092i	0.441606	+	0.320845i	0.786273	−	0.617880i	$-0.212008\pi$
$761$	12.1822	+	8.85092i	0.441606	+	0.320845i	−0.344667	+	0.938725i	$0.612008\pi$
$762$	14.8298	+	4.81850i	0.537228	+	0.174556i
$763$	−0.183978	+	0.0597780i	−0.00666045	+	0.00216411i
$764$	5.25434	−	3.81750i	0.190095	−	0.138112i
$765$	−8.41004	−	5.70269i	−0.304066	−	0.206181i
$766$	7.72096	+	23.7627i	0.278970	+	0.858580i
$767$	−6.93220	−	2.25241i	−0.250307	−	0.0813297i
$768$	11.8379	−	16.2935i	0.427164	−	0.587940i
$769$	48.1314			1.73566			0.867831	−	0.496859i	$-0.165513\pi$
$769$	48.1314			1.73566			0.867831	+	0.496859i	$0.165513\pi$
$770$	−60.5337	+	17.6450i	−2.18148	+	0.635882i
$771$	−18.3364			−0.660371
$772$	−0.0289400	+	0.0398324i	−0.00104157	+	0.00143360i
$773$	−27.1575	−	8.82402i	−0.976789	−	0.317378i	−0.223235	−	0.974765i	$-0.571662\pi$
$773$	−27.1575	−	8.82402i	−0.976789	−	0.317378i	−0.753553	+	0.657387i	$0.771662\pi$
$774$	−1.78278	−	5.48683i	−0.0640807	−	0.197220i
$775$	−4.31347	+	16.9460i	−0.154944	+	0.608720i
$776$	0.635422	−	0.461661i	0.0228103	−	0.0165727i
$777$	−2.23466	+	0.726085i	−0.0801679	+	0.0260481i
$778$	−30.3198	−	9.85149i	−1.08702	−	0.353193i
$779$	7.31123	+	5.31192i	0.261952	+	0.190319i
$780$	−1.83990	+	0.664566i	−0.0658790	+	0.0237953i
$781$	−2.77457	−	10.8130i	−0.0992821	−	0.386921i
$782$		−	44.9637i		−	1.60790i
$783$	−2.79464	+	3.84650i	−0.0998724	+	0.137463i
$784$	18.2619	−	56.2044i	0.652211	−	2.00730i
$785$	5.49193	−	4.26913i	0.196015	−	0.152372i
$786$	27.3220	−	19.8506i	0.974544	−	0.708047i
$787$	−25.1054	−	34.5547i	−0.894912	−	1.23174i	−0.972063	−	0.234721i	$-0.924582\pi$
$787$	−25.1054	−	34.5547i	−0.894912	−	1.23174i	0.0771507	−	0.997019i	$-0.475418\pi$
$788$	8.57832	−	2.78727i	0.305590	−	0.0992923i
$789$	−3.02898	+	9.32224i	−0.107834	+	0.331880i
$790$	−21.0101	+	72.5989i	−0.747506	+	2.58295i
$791$	−49.9248			−1.77512
$792$	−2.21648	+	0.568738i	−0.0787591	+	0.0202092i
$793$			6.24336i			0.221708i
$794$	6.51784	+	4.73549i	0.231310	+	0.168056i
$795$	0.364573	+	11.2290i	0.0129301	+	0.398253i
$796$	−1.58268	−	4.87098i	−0.0560966	−	0.172647i
$797$	5.02481	+	6.91606i	0.177988	+	0.244979i	0.888684	−	0.458519i	$-0.151620\pi$
$797$	5.02481	+	6.91606i	0.177988	+	0.244979i	−0.710696	+	0.703499i	$0.751620\pi$
$798$	−9.61764	−	13.2375i	−0.340461	−	0.468604i
$799$	−16.8337	−	51.8088i	−0.595533	−	1.83286i
$800$	−34.2812	+	13.6554i	−1.21202	+	0.482791i
$801$	6.66706	+	4.84390i	0.235569	+	0.171151i
$802$		−	39.9537i		−	1.41081i
$803$	0.135771	−	2.15283i	0.00479125	−	0.0759716i
$804$	−18.9423			−0.668042
$805$	−49.6649	−	14.3730i	−1.75046	−	0.506582i
$806$	−1.10080	+	3.38792i	−0.0387741	+	0.119334i
$807$	11.3470	−	3.68686i	0.399433	−	0.129784i
$808$	0.415169	+	0.571431i	0.0146056	+	0.0201029i
$809$	10.3702	−	7.53436i	0.364595	−	0.264894i	−0.390371	−	0.920658i	$-0.627653\pi$
$809$	10.3702	−	7.53436i	0.364595	−	0.264894i	0.754966	+	0.655764i	$0.227653\pi$
$810$	3.36740	−	2.61764i	0.118318	−	0.0919744i
$811$	10.5227	−	32.3855i	0.369502	−	1.13721i	−0.577612	−	0.816312i	$-0.696015\pi$
$811$	10.5227	−	32.3855i	0.369502	−	1.13721i	0.947114	−	0.320898i	$-0.103985\pi$
$812$	−20.4076	+	28.0887i	−0.716166	+	0.985719i
$813$		−	30.4048i		−	1.06634i
$814$	2.56921	+	2.12609i	0.0900508	+	0.0745195i
$815$	14.7174	+	40.7461i	0.515527	+	1.42727i
$816$	−16.8840	−	12.2669i	−0.591057	−	0.429428i
$817$	5.53604	+	1.79877i	0.193681	+	0.0629309i
$818$	−12.4448	+	4.04358i	−0.435124	+	0.141380i
$819$	−1.92566	+	1.39908i	−0.0672882	+	0.0488877i
$820$	−9.65423	+	14.2376i	−0.337140	+	0.497198i
$821$	5.35752	+	16.4888i	0.186979	+	0.575462i	0.999977	−	0.00680474i	$-0.00216603\pi$
$821$	5.35752	+	16.4888i	0.186979	+	0.575462i	−0.812998	+	0.582266i	$0.802166\pi$
$822$	−9.95171	−	3.23351i	−0.347106	−	0.112782i
$823$	13.8525	−	19.0664i	0.482868	−	0.664611i	−0.496185	−	0.868217i	$-0.665266\pi$
$823$	13.8525	−	19.0664i	0.482868	−	0.664611i	0.979053	+	0.203606i	$0.0652661\pi$
$824$	3.30531			0.115146
$825$	15.7813	+	5.09405i	0.549436	+	0.177352i
$826$	116.049			4.03786
$827$	9.01142	−	12.4032i	0.313358	−	0.431300i	−0.623067	−	0.782169i	$-0.714114\pi$
$827$	9.01142	−	12.4032i	0.313358	−	0.431300i	0.936425	+	0.350869i	$0.114114\pi$
$828$	8.08259	+	2.62619i	0.280889	+	0.0912665i
$829$	6.93630	+	21.3477i	0.240908	+	0.741437i	0.996283	+	0.0861445i	$0.0274547\pi$
$829$	6.93630	+	21.3477i	0.240908	+	0.741437i	−0.755375	+	0.655293i	$0.772545\pi$
$830$	10.1669	−	14.9937i	0.352899	−	0.520439i
$831$	17.9152	−	13.0162i	0.621471	−	0.451525i
$832$	−2.48448	+	0.807256i	−0.0861338	+	0.0279866i
$833$	−55.6124	−	18.0696i	−1.92686	−	0.626073i
$834$	−5.02991	−	3.65444i	−0.174172	−	0.126543i
$835$	−3.15239	−	8.72763i	−0.109093	−	0.302032i
$836$	−3.85099	+	9.72220i	−0.133189	+	0.336249i
$837$		−	3.49728i		−	0.120884i
$838$	21.3990	−	29.4531i	0.739215	−	1.01744i
$839$	14.3542	−	44.1776i	0.495561	−	1.52518i	−0.320519	−	0.947242i	$-0.603857\pi$
$839$	14.3542	−	44.1776i	0.495561	−	1.52518i	0.816080	−	0.577939i	$-0.196143\pi$
$840$	−5.42919	+	4.22036i	−0.187325	+	0.145616i
$841$	5.17319	−	3.75854i	0.178386	−	0.129605i
$842$	13.7377	+	18.9083i	0.473432	+	0.651623i
$843$	−16.1986	+	5.26326i	−0.557911	+	0.181276i
$844$	10.3228	−	31.7704i	0.355326	−	1.09358i
$845$	27.3106	+	7.90367i	0.939512	+	0.271895i
$846$	22.8658			0.786143
$847$	44.3580	+	20.8897i	1.52416	+	0.717778i
$848$			23.0751i			0.792403i
$849$	6.40863	+	4.65614i	0.219944	+	0.159798i
$850$	16.0378	+	40.2622i	0.550094	+	1.38098i
$851$	0.845018	+	2.60070i	0.0289669	+	0.0891508i
$852$	3.24120	+	4.46113i	0.111042	+	0.152836i
$853$	20.9440	+	28.8270i	0.717109	+	0.987016i	0.999615	+	0.0277505i	$0.00883438\pi$
$853$	20.9440	+	28.8270i	0.717109	+	0.987016i	−0.282506	+	0.959266i	$0.591166\pi$
$854$	−30.7169	−	94.5369i	−1.05111	−	3.23499i
$855$	0.139644	+	4.30112i	0.00477574	+	0.147095i
$856$	0.410801	+	0.298464i	0.0140409	+	0.0102013i
$857$			12.7176i			0.434424i	0.976124	+	0.217212i	$0.0696962\pi$
$857$			12.7176i			0.434424i	−0.976124	+	0.217212i	$0.930304\pi$
$858$	3.14083	+	1.24409i	0.107226	+	0.0424726i
$859$	12.9964			0.443431			0.221715	−	0.975111i	$-0.428834\pi$
$859$	12.9964			0.443431			0.221715	+	0.975111i	$0.428834\pi$
$860$	−3.08017	+	10.6433i	−0.105033	+	0.362934i
$861$	−6.46793	+	19.9062i	−0.220426	+	0.678403i
$862$	12.7392	−	4.13923i	0.433900	−	0.140983i
$863$	−31.2607	−	43.0267i	−1.06413	−	1.46465i	−0.875883	−	0.482523i	$-0.839720\pi$
$863$	−31.2607	−	43.0267i	−1.06413	−	1.46465i	−0.188244	−	0.982122i	$-0.560280\pi$
$864$	5.97067	−	4.33795i	0.203126	−	0.147580i
$865$	18.8289	−	14.6366i	0.640202	−	0.497659i
$866$	−16.2034	+	49.8689i	−0.550613	+	1.69461i
$867$	−2.14536	+	2.95283i	−0.0728601	+	0.100283i
$868$		−	25.5385i		−	0.866835i
$869$	49.6262	−	31.4832i	1.68345	−	1.06799i
$870$	19.0727	−	6.88902i	0.646627	−	0.233560i
$871$	−4.99513	−	3.62918i	−0.169254	−	0.122970i
$872$	0.0284776	+	0.00925293i	0.000964373	+	0.000313344i
$873$	1.08267	−	0.351782i	0.0366430	−	0.0119060i
$874$	−15.4059	+	11.1930i	−0.521111	+	0.378609i
$875$	49.5985	−	4.84456i	1.67674	−	0.163776i
$876$	0.329266	+	1.01338i	0.0111249	+	0.0342388i
$877$	−8.94641	−	2.90686i	−0.302099	−	0.0981578i	0.154045	−	0.988064i	$-0.450770\pi$
$877$	−8.94641	−	2.90686i	−0.302099	−	0.0981578i	−0.456144	+	0.889906i	$0.650770\pi$
$878$	19.8436	−	27.3124i	0.669689	−	0.921747i
$879$	22.3396			0.753494
$880$	32.0562	+	11.5088i	1.08062	+	0.387961i
$881$	−26.5160			−0.893345			−0.446673	−	0.894697i	$-0.647391\pi$
$881$	−26.5160			−0.893345			−0.446673	+	0.894697i	$0.647391\pi$
$882$	14.4269	−	19.8569i	0.485780	−	0.668618i
$883$	−10.9394	−	3.55444i	−0.368141	−	0.119616i	0.119103	−	0.992882i	$-0.461998\pi$
$883$	−10.9394	−	3.55444i	−0.368141	−	0.119616i	−0.487245	+	0.873266i	$0.661998\pi$
$884$	1.22851	+	3.78096i	0.0413192	+	0.127168i
$885$	−25.2614	−	17.1292i	−0.849151	−	0.575793i
$886$	−25.6008	+	18.6001i	−0.860075	+	0.624881i
$887$	−30.6974	+	9.97420i	−1.03072	+	0.334901i	−0.775074	−	0.631870i	$-0.782288\pi$
$887$	−30.6974	+	9.97420i	−1.03072	+	0.334901i	−0.255645	+	0.966771i	$0.582288\pi$
$888$	0.345899	+	0.112389i	0.0116076	+	0.00377154i
$889$	−29.4791	−	21.4178i	−0.988698	−	0.718331i
$890$	−11.9406	−	33.0584i	−0.400250	−	1.10812i
$891$	−3.31005	−	0.208753i	−0.110891	−	0.00699348i
$892$			16.8774i			0.565098i
$893$	−13.5607	+	18.6647i	−0.453792	+	0.624591i
$894$	1.65414	−	5.09092i	0.0553228	−	0.170266i
$895$	31.0611	+	39.9579i	1.03826	+	1.33565i
$896$	−19.5783	+	14.2245i	−0.654065	+	0.475206i
$897$	1.62825	+	2.24109i	0.0543656	+	0.0748278i
$898$	−47.6863	+	15.4942i	−1.59131	+	0.517048i
$899$	5.13832	−	15.8141i	0.171372	−	0.527430i
$900$	−8.17418	+	0.531342i	−0.272473	+	0.0177114i
$901$	22.8321			0.760647
$902$	28.7744	−	7.38337i	0.958082	−	0.245839i
$903$			13.4816i			0.448641i
$904$	6.25189	+	4.54226i	0.207935	+	0.151073i
$905$	1.05809	+	32.5896i	0.0351720	+	1.08332i
$906$	8.34854	+	25.6942i	0.277362	+	0.853631i
$907$	13.5243	+	18.6147i	0.449068	+	0.618090i	0.972197	−	0.234164i	$-0.0752353\pi$
$907$	13.5243	+	18.6147i	0.449068	+	0.618090i	−0.523129	+	0.852254i	$0.675235\pi$
$908$	6.04011	+	8.31350i	0.200448	+	0.275893i
$909$	0.316355	+	0.973642i	0.0104928	+	0.0322937i
$910$	10.1468	−	0.329435i	0.336362	−	0.0109206i
$911$	24.4145	+	17.7382i	0.808888	+	0.587692i	0.913508	−	0.406820i	$-0.133363\pi$
$911$	24.4145	+	17.7382i	0.808888	+	0.587692i	−0.104620	+	0.994512i	$0.533363\pi$
$912$			8.83860i			0.292675i
$913$	−13.6449	+	3.50122i	−0.451581	+	0.115874i
$914$	52.3618			1.73197
$915$	−7.26757	+	25.1126i	−0.240258	+	0.830196i
$916$	0.699196	−	2.15190i	0.0231021	−	0.0711009i
$917$	−75.0565	+	24.3873i	−2.47858	+	0.805341i
$918$	−5.09479	−	7.01237i	−0.168153	−	0.231443i
$919$	−22.9351	+	16.6633i	−0.756558	+	0.549672i	−0.897853	−	0.440296i	$-0.854874\pi$
$919$	−22.9351	+	16.6633i	−0.756558	+	0.549672i	0.141294	+	0.989968i	$0.454874\pi$
$920$	4.91166	+	6.31850i	0.161933	+	0.208315i
$921$	2.88414	−	8.87647i	0.0950356	−	0.292490i
$922$	18.8344	−	25.9233i	0.620278	−	0.853740i
$923$			1.79740i			0.0591622i
$924$	−24.1713	−	1.52440i	−0.795177	−	0.0501489i
$925$	−1.68429	−	2.02736i	−0.0553791	−	0.0666592i
$926$	−49.7778	−	36.1657i	−1.63580	−	1.18848i
$927$	4.55623	+	1.48041i	0.149646	+	0.0486230i
$928$	33.3718	−	10.8432i	1.09548	−	0.355944i
$929$	−25.7821	+	18.7318i	−0.845885	+	0.614571i	−0.924008	−	0.382372i	$-0.875107\pi$
$929$	−25.7821	+	18.7318i	−0.845885	+	0.614571i	0.0781235	+	0.996944i	$0.475107\pi$
$930$	−8.37143	+	12.3458i	−0.274510	+	0.404834i
$931$	7.65269	+	23.5526i	0.250807	+	0.771904i
$932$	−12.9392	−	4.20419i	−0.423837	−	0.137713i
$933$	−6.61140	+	9.09981i	−0.216447	+	0.297914i
$934$	4.37985			0.143313
$935$	11.3876	−	31.7186i	0.372413	−	1.03731i
$936$	0.368435			0.0120427
$937$	13.0657	−	17.9834i	0.426839	−	0.587494i	−0.540385	−	0.841418i	$-0.681721\pi$
$937$	13.0657	−	17.9834i	0.426839	−	0.587494i	0.967224	+	0.253924i	$0.0817214\pi$
$938$	93.4915	+	30.3772i	3.05261	+	0.991852i
$939$	3.35716	+	10.3323i	0.109557	+	0.337181i
$940$	−36.3469	−	24.6461i	−1.18551	−	0.803868i
$941$	1.16490	−	0.846351i	0.0379747	−	0.0275903i	−0.568636	−	0.822589i	$-0.692529\pi$
$941$	1.16490	−	0.846351i	0.0379747	−	0.0275903i	0.606611	+	0.794999i	$0.292529\pi$
$942$	5.64330	−	1.83362i	0.183869	−	0.0597425i
$943$	23.1669	+	7.52738i	0.754418	+	0.245125i
$944$	−50.7146	−	36.8463i	−1.65062	−	1.19924i
$945$	−9.37416	+	3.38592i	−0.304941	+	0.110144i
$946$	16.1571	−	10.2502i	0.525314	−	0.333263i
$947$		−	22.8848i		−	0.743655i	−0.928302	−	0.371827i	$-0.878731\pi$
$947$		−	22.8848i		−	0.743655i	0.928302	−	0.371827i	$-0.121269\pi$
$948$	−17.0636	+	23.4860i	−0.554199	+	0.762790i
$949$	−0.107326	+	0.330315i	−0.00348395	+	0.0107225i
$950$	9.80262	−	15.5177i	0.318039	−	0.503460i
$951$	−10.2660	+	7.45871i	−0.332899	+	0.241865i
$952$	8.21422	+	11.3059i	0.266224	+	0.366426i
$953$	13.3026	−	4.32227i	0.430913	−	0.140012i	−0.0855263	−	0.996336i	$-0.527257\pi$
$953$	13.3026	−	4.32227i	0.430913	−	0.140012i	0.516439	+	0.856324i	$0.327257\pi$
$954$	−2.96154	+	9.11468i	−0.0958833	+	0.295099i
$955$	8.51512	+	2.46428i	0.275543	+	0.0797421i
$956$	16.8662			0.545493
$957$	−14.6608	−	5.80717i	−0.473915	−	0.187719i
$958$		−	0.650657i		−	0.0210218i
$959$	19.7823	+	14.3727i	0.638803	+	0.464118i
$960$	−10.9330	+	0.354960i	−0.352860	+	0.0114563i
$961$	−5.79995	−	17.8504i	−0.187095	−	0.575819i
$962$	−0.315605	−	0.434393i	−0.0101755	−	0.0140054i
$963$	0.432593	+	0.595413i	0.0139401	+	0.0191869i
$964$	−6.19356	−	19.0618i	−0.199481	−	0.613940i
$965$	−0.0671654	+	0.00218066i	−0.00216213	+	7.01978e-5i
$966$	−35.6809	−	25.9237i	−1.14801	−	0.834081i
$967$			34.3901i			1.10591i	0.833211	+	0.552955i	$0.186500\pi$
$967$			34.3901i			1.10591i	−0.833211	+	0.552955i	$0.813500\pi$
$968$	−3.65420	−	6.65172i	−0.117450	−	0.213794i
$969$	8.74550			0.280946
$970$	−4.66402	−	1.34977i	−0.149753	−	0.0433384i
$971$	12.4857	−	38.4271i	0.400686	−	1.23318i	−0.523758	−	0.851867i	$-0.675471\pi$
$971$	12.4857	−	38.4271i	0.400686	−	1.23318i	0.924444	−	0.381317i	$-0.124529\pi$
$972$	1.55810	−	0.506258i	0.0499762	−	0.0162382i
$973$	8.53982	+	11.7540i	0.273774	+	0.376817i
$974$	−24.4669	+	17.7763i	−0.783971	+	0.569589i
$975$	−2.25736	−	1.42599i	−0.0722933	−	0.0456681i
$976$	−16.5925	+	51.0664i	−0.531112	+	1.63459i
$977$	−28.7264	+	39.5384i	−0.919038	+	1.26495i	0.0449470	+	0.998989i	$0.485688\pi$
$977$	−28.7264	+	39.5384i	−0.919038	+	1.26495i	−0.963985	+	0.265958i	$0.914312\pi$
$978$			36.9554i			1.18170i
$979$	−10.0655	+	25.4112i	−0.321693	+	0.812146i
$980$	−44.3356	+	16.0139i	−1.41625	+	0.511545i
$981$	0.0351108	+	0.0255095i	0.00112100	+	0.000814456i
$982$	54.4409	+	17.6889i	1.73728	+	0.564476i
$983$	−9.51959	+	3.09310i	−0.303628	+	0.0986546i	−0.456868	−	0.889534i	$-0.651029\pi$
$983$	−9.51959	+	3.09310i	−0.303628	+	0.0986546i	0.153241	+	0.988189i	$0.451029\pi$
$984$	2.62107	−	1.90432i	0.0835566	−	0.0607074i
$985$	10.1893	+	6.90919i	0.324659	+	0.220145i
$986$	−12.7350	−	39.1942i	−0.405564	−	1.24820i
$987$	−50.8183	−	16.5119i	−1.61756	−	0.525578i
$988$	0.989650	−	1.36214i	0.0314850	−	0.0433353i
$989$	15.6899			0.498911
$990$	11.1851	+	8.66017i	0.355487	+	0.275238i
$991$	31.6029			1.00390			0.501949	−	0.864897i	$-0.332617\pi$
$991$	31.6029			1.00390			0.501949	+	0.864897i	$0.332617\pi$
$992$	−15.1710	+	20.8811i	−0.481680	+	0.662976i
$993$	−21.9340	−	7.12678i	−0.696053	−	0.226161i
$994$	−8.84309	−	27.2162i	−0.280486	−	0.863246i
$995$	3.92321	−	5.78575i	0.124374	−	0.183421i
$996$	5.62948	−	4.09006i	0.178377	−	0.129598i
$997$	−50.7872	+	16.5018i	−1.60845	+	0.522616i	−0.969177	−	0.246365i	$-0.920764\pi$
$997$	−50.7872	+	16.5018i	−1.60845	+	0.522616i	−0.639271	+	0.768982i	$0.720764\pi$
$998$	−6.63072	−	2.15445i	−0.209892	−	0.0681980i
$999$	0.426469	+	0.309848i	0.0134929	+	0.00980314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.4.10	yes	48
3.2	odd	2		495.2.ba.c.334.3		48
5.2	odd	4		825.2.n.p.301.5		24
5.3	odd	4		825.2.n.o.301.2		24
5.4	even	2	inner	165.2.s.a.4.3	✓	48
11.3	even	5	inner	165.2.s.a.124.3	yes	48
11.5	even	5		1815.2.c.j.364.19		24
11.6	odd	10		1815.2.c.k.364.6		24
15.14	odd	2		495.2.ba.c.334.10		48
33.14	odd	10		495.2.ba.c.289.10		48
55.3	odd	20		825.2.n.o.751.2		24
55.14	even	10	inner	165.2.s.a.124.10	yes	48
55.17	even	20		9075.2.a.ea.1.9		12
55.27	odd	20		9075.2.a.dy.1.4		12
55.28	even	20		9075.2.a.dx.1.4		12
55.38	odd	20		9075.2.a.dz.1.9		12
55.39	odd	10		1815.2.c.k.364.19		24
55.47	odd	20		825.2.n.p.751.5		24
55.49	even	10		1815.2.c.j.364.6		24
165.14	odd	10		495.2.ba.c.289.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.3	✓	48	5.4	even	2	inner
165.2.s.a.4.10	yes	48	1.1	even	1	trivial
165.2.s.a.124.3	yes	48	11.3	even	5	inner
165.2.s.a.124.10	yes	48	55.14	even	10	inner
495.2.ba.c.289.3		48	165.14	odd	10
495.2.ba.c.289.10		48	33.14	odd	10
495.2.ba.c.334.3		48	3.2	odd	2
495.2.ba.c.334.10		48	15.14	odd	2
825.2.n.o.301.2		24	5.3	odd	4
825.2.n.o.751.2		24	55.3	odd	20
825.2.n.p.301.5		24	5.2	odd	4
825.2.n.p.751.5		24	55.47	odd	20
1815.2.c.j.364.6		24	55.49	even	10
1815.2.c.j.364.19		24	11.5	even	5
1815.2.c.k.364.6		24	11.6	odd	10
1815.2.c.k.364.19		24	55.39	odd	10
9075.2.a.dx.1.4		12	55.28	even	20
9075.2.a.dy.1.4		12	55.27	odd	20
9075.2.a.dz.1.9		12	55.38	odd	20
9075.2.a.ea.1.9		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)

\(f(q)\)	\(=\)	\(q+(1.12116 - 1.54314i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.506258 - 1.55810i) q^{4} +(1.25493 - 1.85071i) q^{5} +(1.54314 - 1.12116i) q^{6} +(-4.23918 + 1.37739i) q^{7} +(0.656175 + 0.213204i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.12116 - 1.54314i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.506258 - 1.55810i) q^{4} +(1.25493 - 1.85071i) q^{5} +(1.54314 - 1.12116i) q^{6} +(-4.23918 + 1.37739i) q^{7} +(0.656175 + 0.213204i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.44894 - 4.01149i) q^{10} +(-1.22140 + 3.08354i) q^{11} -1.63829i q^{12} +(0.313882 - 0.432021i) q^{13} +(-2.62728 + 8.08594i) q^{14} +(1.76541 - 1.37234i) q^{15} +(3.71548 - 2.69946i) q^{16} +(-2.67102 - 3.67635i) q^{17} +(1.81407 - 0.589428i) q^{18} +(-0.594714 + 1.83034i) q^{19} +(-3.51892 - 1.01838i) q^{20} -4.45734 q^{21} +(3.38895 + 5.34192i) q^{22} +5.18745i q^{23} +(0.558176 + 0.405538i) q^{24} +(-1.85028 - 4.64505i) q^{25} +(-0.314759 - 0.968729i) q^{26} +(0.587785 + 0.809017i) q^{27} +(4.29224 + 5.90776i) q^{28} +(1.46923 + 4.52183i) q^{29} +(-0.138403 - 4.26290i) q^{30} +(-2.82936 - 2.05565i) q^{31} -7.38016i q^{32} +(-2.11448 + 2.55518i) q^{33} -8.66777 q^{34} +(-2.77073 + 9.57405i) q^{35} +(0.506258 - 1.55810i) q^{36} +(0.501344 - 0.162896i) q^{37} +(2.15771 + 2.96983i) q^{38} +(0.432021 - 0.313882i) q^{39} +(1.21804 - 0.946835i) q^{40} +(1.45107 - 4.46595i) q^{41} +(-4.99738 + 6.87831i) q^{42} -3.02459i q^{43} +(5.42281 + 0.341997i) q^{44} +(2.10308 - 0.759628i) q^{45} +(8.00498 + 5.81596i) q^{46} +(11.4010 + 3.70442i) q^{47} +(4.36781 - 1.41919i) q^{48} +(10.4103 - 7.56354i) q^{49} +(-9.24243 - 2.35258i) q^{50} +(-1.40424 - 4.32181i) q^{51} +(-0.832039 - 0.270346i) q^{52} +(-2.95328 + 4.06485i) q^{53} +1.90743 q^{54} +(4.17397 + 6.13009i) q^{55} -3.07531 q^{56} +(-1.13121 + 1.55698i) q^{57} +(8.62507 + 2.80246i) q^{58} +(-4.21793 - 12.9815i) q^{59} +(-3.03200 - 2.05594i) q^{60} +(-9.45864 + 6.87210i) q^{61} +(-6.34433 + 2.06140i) q^{62} +(-4.23918 - 1.37739i) q^{63} +(-3.95767 - 2.87541i) q^{64} +(-0.405647 - 1.12306i) q^{65} +(1.57234 + 6.12771i) q^{66} -11.5622i q^{67} +(-4.37590 + 6.02291i) q^{68} +(-1.60301 + 4.93356i) q^{69} +(11.6677 + 15.0097i) q^{70} +(-2.72305 + 1.97841i) q^{71} +(0.405538 + 0.558176i) q^{72} +(-0.618559 + 0.200982i) q^{73} +(0.310714 - 0.956278i) q^{74} +(-0.324328 - 4.98947i) q^{75} +3.15294 q^{76} +(0.930481 - 14.7540i) q^{77} -1.01858i q^{78} +(-14.3357 - 10.4155i) q^{79} +(-0.333239 - 10.2639i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-5.26471 - 7.24625i) q^{82} +(2.49655 + 3.43620i) q^{83} +(2.25656 + 6.94499i) q^{84} +(-10.1558 + 0.329729i) q^{85} +(-4.66738 - 3.39105i) q^{86} +4.75453i q^{87} +(-1.45887 + 1.76293i) q^{88} +8.24094 q^{89} +(1.18568 - 4.09702i) q^{90} +(-0.735538 + 2.26375i) q^{91} +(8.08259 - 2.62619i) q^{92} +(-2.05565 - 2.82936i) q^{93} +(18.4988 - 13.4402i) q^{94} +(2.64111 + 3.39760i) q^{95} +(2.28059 - 7.01895i) q^{96} +(0.669130 - 0.920978i) q^{97} -24.5445i q^{98} +(-2.80059 + 1.77671i) 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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