LMFDB - Embedded newform 960.2.cn.a.11.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.47
Character	$\chi$	$=$	960.11
Dual form			960.2.cn.a.611.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.557061 - 1.29988i) q^{2} +(0.729271 + 1.57104i) q^{3} +(-1.37937 + 1.44822i) q^{4} +(0.831470 - 0.555570i) q^{5} +(1.63591 - 1.82313i) q^{6} +(-0.966631 + 2.33365i) q^{7} +(2.65091 + 0.986257i) q^{8} +(-1.93633 + 2.29143i) q^{9} +O(q^{10})$	\(q+(-0.557061 - 1.29988i) q^{2} +(0.729271 + 1.57104i) q^{3} +(-1.37937 + 1.44822i) q^{4} +(0.831470 - 0.555570i) q^{5} +(1.63591 - 1.82313i) q^{6} +(-0.966631 + 2.33365i) q^{7} +(2.65091 + 0.986257i) q^{8} +(-1.93633 + 2.29143i) q^{9} +(-1.18535 - 0.771322i) q^{10} +(-0.314221 + 1.57970i) q^{11} +(-3.28115 - 1.11089i) q^{12} +(-0.595243 + 0.890844i) q^{13} +(3.57194 - 0.0434862i) q^{14} +(1.47919 + 0.901110i) q^{15} +(-0.194704 - 3.99526i) q^{16} +(-3.51577 - 3.51577i) q^{17} +(4.05723 + 1.24053i) q^{18} +(-1.27827 + 1.91306i) q^{19} +(-0.342310 + 1.97049i) q^{20} +(-4.37120 + 0.183250i) q^{21} +(2.22845 - 0.471539i) q^{22} +(1.44382 + 3.48568i) q^{23} +(0.383779 + 4.88392i) q^{24} +(0.382683 - 0.923880i) q^{25} +(1.48958 + 0.277488i) q^{26} +(-5.01203 - 1.37098i) q^{27} +(-2.04632 - 4.61886i) q^{28} +(-1.64464 + 0.327140i) q^{29} +(0.347334 - 2.42474i) q^{30} -4.99093 q^{31} +(-5.08489 + 2.47870i) q^{32} +(-2.71092 + 0.658373i) q^{33} +(-2.61157 + 6.52856i) q^{34} +(0.492784 + 2.47739i) q^{35} +(-0.647593 - 5.96495i) q^{36} +(-0.709876 + 0.474324i) q^{37} +(3.19882 + 0.595898i) q^{38} +(-1.83364 - 0.285484i) q^{39} +(2.75208 - 0.652721i) q^{40} +(-0.102308 + 0.0423775i) q^{41} +(2.67323 + 5.57994i) q^{42} +(0.442995 - 2.22709i) q^{43} +(-1.85433 - 2.63404i) q^{44} +(-0.336950 + 2.98102i) q^{45} +(3.72667 - 3.81853i) q^{46} +(3.58215 - 3.58215i) q^{47} +(6.13472 - 3.21951i) q^{48} +(0.438183 + 0.438183i) q^{49} +(-1.41411 + 0.0172159i) q^{50} +(2.95946 - 8.08735i) q^{51} +(-0.469084 - 2.09084i) q^{52} +(-10.6251 - 2.11347i) q^{53} +(1.00990 + 7.27874i) q^{54} +(0.616367 + 1.48804i) q^{55} +(-4.86403 + 5.23295i) q^{56} +(-3.93769 - 0.613067i) q^{57} +(1.34141 + 1.95560i) q^{58} +(1.61569 + 2.41805i) q^{59} +(-3.34535 + 0.899236i) q^{60} +(-7.53033 + 1.49788i) q^{61} +(2.78025 + 6.48760i) q^{62} +(-3.47568 - 6.73368i) q^{63} +(6.05460 + 5.22895i) q^{64} +1.07141i q^{65} +(2.36595 + 3.15711i) q^{66} +(2.21625 + 11.1418i) q^{67} +(9.94114 - 0.242091i) q^{68} +(-4.42321 + 4.81030i) q^{69} +(2.94580 - 2.02062i) q^{70} +(5.24577 + 2.17287i) q^{71} +(-7.39296 + 4.16464i) q^{72} +(-4.27949 + 1.77262i) q^{73} +(1.01201 + 0.658525i) q^{74} +(1.73053 - 0.0725476i) q^{75} +(-1.00734 - 4.49002i) q^{76} +(-3.38273 - 2.26027i) q^{77} +(0.650359 + 2.54255i) q^{78} +(-10.8259 + 10.8259i) q^{79} +(-2.38154 - 3.21376i) q^{80} +(-1.50126 - 8.87391i) q^{81} +(0.112078 + 0.109382i) q^{82} +(9.64161 + 6.44232i) q^{83} +(5.76409 - 6.58324i) q^{84} +(-4.87651 - 0.969998i) q^{85} +(-3.14171 + 0.664784i) q^{86} +(-1.71334 - 2.34522i) q^{87} +(-2.39096 + 3.87772i) q^{88} +(12.1021 + 5.01286i) q^{89} +(4.06266 - 1.22262i) q^{90} +(-1.50354 - 2.25021i) q^{91} +(-7.03960 - 2.71706i) q^{92} +(-3.63974 - 7.84094i) q^{93} +(-6.65184 - 2.66088i) q^{94} +2.30082i q^{95} +(-7.60239 - 6.18092i) q^{96} -0.469233i q^{97} +(0.325490 - 0.813680i) q^{98} +(-3.01132 - 3.77883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	−0.557061	−	1.29988i	−0.393902	−	0.919152i
$2$	−0.557061	−	1.29988i	−0.393902	−	0.919152i
$3$	0.729271	+	1.57104i	0.421045	+	0.907040i
$3$	0.729271	+	1.57104i	0.421045	+	0.907040i
$4$	−1.37937	+	1.44822i	−0.689683	+	0.724112i
$5$	0.831470	−	0.555570i	0.371845	−	0.248459i
$5$	0.831470	−	0.555570i	0.371845	−	0.248459i
$6$	1.63591	−	1.82313i	0.667858	−	0.744289i
$7$	−0.966631	+	2.33365i	−0.365352	+	0.882038i	0.629146	+	0.777287i	$0.283405\pi$
$7$	−0.966631	+	2.33365i	−0.365352	+	0.882038i	−0.994498	+	0.104751i	$0.966595\pi$
$8$	2.65091	+	0.986257i	0.937236	+	0.348694i
$9$	−1.93633	+	2.29143i	−0.645443	+	0.763809i
$10$	−1.18535	−	0.771322i	−0.374842	−	0.243914i
$11$	−0.314221	+	1.57970i	−0.0947413	+	0.476297i	0.904063	+	0.427400i	$0.140570\pi$
$11$	−0.314221	+	1.57970i	−0.0947413	+	0.476297i	−0.998804	+	0.0488965i	$0.984430\pi$
$12$	−3.28115	−	1.11089i	−0.947185	−	0.320686i
$13$	−0.595243	+	0.890844i	−0.165091	+	0.247076i	−0.904786	−	0.425866i	$-0.859970\pi$
$13$	−0.595243	+	0.890844i	−0.165091	+	0.247076i	0.739696	+	0.672942i	$0.234970\pi$
$14$	3.57194	−	0.0434862i	0.954641	−	0.0116222i
$15$	1.47919	+	0.901110i	0.381925	+	0.232666i
$16$	−0.194704	−	3.99526i	−0.0486759	−	0.998815i
$17$	−3.51577	−	3.51577i	−0.852698	−	0.852698i	0.137766	−	0.990465i	$-0.456008\pi$
$17$	−3.51577	−	3.51577i	−0.852698	−	0.852698i	−0.990465	+	0.137766i	$0.956008\pi$
$18$	4.05723	+	1.24053i	0.956298	+	0.292395i
$19$	−1.27827	+	1.91306i	−0.293254	+	0.438886i	−0.948616	−	0.316429i	$-0.897516\pi$
$19$	−1.27827	+	1.91306i	−0.293254	+	0.438886i	0.655362	+	0.755315i	$0.272516\pi$
$20$	−0.342310	+	1.97049i	−0.0765429	+	0.440615i
$21$	−4.37120	+	0.183250i	−0.953873	+	0.0399884i
$22$	2.22845	−	0.471539i	0.475108	−	0.100532i
$23$	1.44382	+	3.48568i	0.301057	+	0.726815i	0.999933	+	0.0115727i	$0.00368378\pi$
$23$	1.44382	+	3.48568i	0.301057	+	0.726815i	−0.698876	+	0.715243i	$0.746316\pi$
$24$	0.383779	+	4.88392i	0.0783386	+	0.996927i
$25$	0.382683	−	0.923880i	0.0765367	−	0.184776i
$26$	1.48958	+	0.277488i	0.292130	+	0.0544200i
$27$	−5.01203	−	1.37098i	−0.964565	−	0.263845i
$28$	−2.04632	−	4.61886i	−0.386717	−	0.872882i
$29$	−1.64464	+	0.327140i	−0.305402	+	0.0607483i	−0.345412	−	0.938451i	$-0.612261\pi$
$29$	−1.64464	+	0.327140i	−0.305402	+	0.0607483i	0.0400102	+	0.999199i	$0.487261\pi$
$30$	0.347334	−	2.42474i	0.0634143	−	0.442695i
$31$	−4.99093			−0.896397			−0.448199	−	0.893934i	$-0.647934\pi$
$31$	−4.99093			−0.896397			−0.448199	+	0.893934i	$0.647934\pi$
$32$	−5.08489	+	2.47870i	−0.898889	+	0.438176i
$33$	−2.71092	+	0.658373i	−0.471910	+	0.114608i
$34$	−2.61157	+	6.52856i	−0.447880	+	1.11964i
$35$	0.492784	+	2.47739i	0.0832957	+	0.418756i
$36$	−0.647593	−	5.96495i	−0.107932	−	0.994158i
$37$	−0.709876	+	0.474324i	−0.116703	+	0.0779784i	−0.612552	−	0.790430i	$-0.709857\pi$
$37$	−0.709876	+	0.474324i	−0.116703	+	0.0779784i	0.495849	+	0.868409i	$0.334857\pi$
$38$	3.19882	+	0.595898i	0.518917	+	0.0966674i
$39$	−1.83364	−	0.285484i	−0.293618	−	0.0457140i
$40$	2.75208	−	0.652721i	0.435142	−	0.103204i
$41$	−0.102308	+	0.0423775i	−0.0159779	+	0.00661826i	−0.390658	−	0.920536i	$-0.627753\pi$
$41$	−0.102308	+	0.0423775i	−0.0159779	+	0.00661826i	0.374680	+	0.927154i	$0.377753\pi$
$42$	2.67323	+	5.57994i	0.412488	+	0.861004i
$43$	0.442995	−	2.22709i	0.0675561	−	0.339627i	−0.932195	−	0.361958i	$-0.882109\pi$
$43$	0.442995	−	2.22709i	0.0675561	−	0.339627i	0.999751	+	0.0223302i	$0.00710851\pi$
$44$	−1.85433	−	2.63404i	−0.279551	−	0.397097i
$45$	−0.336950	+	2.98102i	−0.0502296	+	0.444384i
$46$	3.72667	−	3.81853i	0.549467	−	0.563011i
$47$	3.58215	−	3.58215i	0.522511	−	0.522511i	−0.395818	−	0.918329i	$-0.629539\pi$
$47$	3.58215	−	3.58215i	0.522511	−	0.522511i	0.918329	+	0.395818i	$0.129539\pi$
$48$	6.13472	−	3.21951i	0.885470	−	0.464697i
$49$	0.438183	+	0.438183i	0.0625976	+	0.0625976i
$50$	−1.41411	+	0.0172159i	−0.199985	+	0.00243470i
$51$	2.95946	−	8.08735i	0.414407	−	1.13246i
$52$	−0.469084	−	2.09084i	−0.0650503	−	0.289948i
$53$	−10.6251	−	2.11347i	−1.45947	−	0.290307i	−0.599387	−	0.800459i	$-0.704589\pi$
$53$	−10.6251	−	2.11347i	−1.45947	−	0.290307i	−0.860084	+	0.510152i	$0.829589\pi$
$54$	1.00990	+	7.27874i	0.137430	+	0.990511i
$55$	0.616367	+	1.48804i	0.0831109	+	0.200648i
$56$	−4.86403	+	5.23295i	−0.649983	+	0.699282i
$57$	−3.93769	−	0.613067i	−0.521560	−	0.0812027i
$58$	1.34141	+	1.95560i	0.176135	+	0.256782i
$59$	1.61569	+	2.41805i	0.210345	+	0.314803i	0.921608	−	0.388123i	$-0.126876\pi$
$59$	1.61569	+	2.41805i	0.210345	+	0.314803i	−0.711263	+	0.702926i	$0.751876\pi$
$60$	−3.34535	+	0.899236i	−0.431883	+	0.116091i
$61$	−7.53033	+	1.49788i	−0.964160	+	0.191783i	−0.651977	−	0.758239i	$-0.726060\pi$
$61$	−7.53033	+	1.49788i	−0.964160	+	0.191783i	−0.312183	+	0.950022i	$0.601060\pi$
$62$	2.78025	+	6.48760i	0.353093	+	0.823926i
$63$	−3.47568	−	6.73368i	−0.437894	−	0.848364i
$64$	6.05460	+	5.22895i	0.756824	+	0.653618i
$65$			1.07141i			0.132892i
$66$	2.36595	+	3.15711i	0.291229	+	0.388613i
$67$	2.21625	+	11.1418i	0.270758	+	1.36119i	0.841587	+	0.540122i	$0.181622\pi$
$67$	2.21625	+	11.1418i	0.270758	+	1.36119i	−0.570829	+	0.821069i	$0.693378\pi$
$68$	9.94114	−	0.242091i	1.20554	−	0.0293578i
$69$	−4.42321	+	4.81030i	−0.532492	+	0.579092i
$70$	2.94580	−	2.02062i	0.352090	−	0.241510i
$71$	5.24577	+	2.17287i	0.622558	+	0.257872i	0.671587	−	0.740925i	$-0.265613\pi$
$71$	5.24577	+	2.17287i	0.622558	+	0.257872i	−0.0490295	+	0.998797i	$0.515613\pi$
$72$	−7.39296	+	4.16464i	−0.871268	+	0.490807i
$73$	−4.27949	+	1.77262i	−0.500876	+	0.207470i	−0.618793	−	0.785554i	$-0.712378\pi$
$73$	−4.27949	+	1.77262i	−0.500876	+	0.207470i	0.117917	+	0.993023i	$0.462378\pi$
$74$	1.01201	+	0.658525i	0.117644	+	0.0765519i
$75$	1.73053	−	0.0725476i	0.199824	−	0.00837707i
$76$	−1.00734	−	4.49002i	−0.115550	−	0.515041i
$77$	−3.38273	−	2.26027i	−0.385498	−	0.257581i
$78$	0.650359	+	2.54255i	0.0736386	+	0.287887i
$79$	−10.8259	+	10.8259i	−1.21801	+	1.21801i	−0.249687	+	0.968326i	$0.580328\pi$
$79$	−10.8259	+	10.8259i	−1.21801	+	1.21801i	−0.968326	+	0.249687i	$0.919672\pi$
$80$	−2.38154	−	3.21376i	−0.266264	−	0.359310i
$81$	−1.50126	−	8.87391i	−0.166807	−	0.985990i
$82$	0.112078	+	0.109382i	0.0123769	+	0.0120792i
$83$	9.64161	+	6.44232i	1.05830	+	0.707136i	0.957694	−	0.287790i	$-0.0929205\pi$
$83$	9.64161	+	6.44232i	1.05830	+	0.707136i	0.100610	+	0.994926i	$0.467920\pi$
$84$	5.76409	−	6.58324i	0.628914	−	0.718290i
$85$	−4.87651	−	0.969998i	−0.528931	−	0.105211i
$86$	−3.14171	+	0.664784i	−0.338780	+	0.0716855i
$87$	−1.71334	−	2.34522i	−0.183689	−	0.251434i
$88$	−2.39096	+	3.87772i	−0.254877	+	0.413367i
$89$	12.1021	+	5.01286i	1.28282	+	0.531362i	0.916838	−	0.399259i	$-0.130733\pi$
$89$	12.1021	+	5.01286i	1.28282	+	0.531362i	0.365983	+	0.930621i	$0.380733\pi$
$90$	4.06266	−	1.22262i	0.428242	−	0.128875i
$91$	−1.50354	−	2.25021i	−0.157614	−	0.235886i
$92$	−7.03960	−	2.71706i	−0.733929	−	0.283273i
$93$	−3.63974	−	7.84094i	−0.377423	−	0.813068i
$94$	−6.65184	−	2.66088i	−0.686085	−	0.274449i
$95$			2.30082i			0.236059i
$96$	−7.60239	−	6.18092i	−0.775915	−	0.630837i
$97$		−	0.469233i		−	0.0476434i	−0.999716	−	0.0238217i	$-0.992417\pi$
$97$		−	0.469233i		−	0.0476434i	0.999716	−	0.0238217i	$-0.00758341\pi$
$98$	0.325490	−	0.813680i	0.0328794	−	0.0821941i
$99$	−3.01132	−	3.77883i	−0.302649	−	0.379786i
$100$	0.810124	+	1.82858i	0.0810124	+	0.182858i
$101$	3.79478	+	5.67929i	0.377595	+	0.565111i	0.970785	−	0.239952i	$-0.0771317\pi$
$101$	3.79478	+	5.67929i	0.377595	+	0.565111i	−0.593190	+	0.805063i	$0.702132\pi$
$102$	−12.1612	+	0.658213i	−1.20414	+	0.0651728i
$103$	−1.92201	−	0.796123i	−0.189381	−	0.0784443i	0.285978	−	0.958236i	$-0.407682\pi$
$103$	−1.92201	−	0.796123i	−0.189381	−	0.0784443i	−0.475359	+	0.879792i	$0.657682\pi$
$104$	−2.45653	+	1.77448i	−0.240883	+	0.174002i
$105$	−3.53271	+	2.58087i	−0.344757	+	0.251868i
$106$	3.17159	+	14.9887i	0.308052	+	1.45583i
$107$	−12.1160	−	2.41003i	−1.17130	−	0.232986i	−0.429158	−	0.903229i	$-0.641190\pi$
$107$	−12.1160	−	2.41003i	−1.17130	−	0.232986i	−0.742142	+	0.670243i	$0.766190\pi$
$108$	8.89890	−	5.36746i	0.856297	−	0.516484i
$109$	5.72085	+	3.82255i	0.547958	+	0.366134i	0.798521	−	0.601967i	$-0.205616\pi$
$109$	5.72085	+	3.82255i	0.547958	+	0.366134i	−0.250564	+	0.968100i	$0.580616\pi$
$110$	1.59092	−	1.63013i	0.151688	−	0.155427i
$111$	−1.26287	−	0.769332i	−0.119867	−	0.0730218i
$112$	9.51176	+	3.40757i	0.898777	+	0.321985i
$113$	−3.28149	+	3.28149i	−0.308696	+	0.308696i	−0.844404	−	0.535707i	$-0.820045\pi$
$113$	−3.28149	+	3.28149i	−0.308696	+	0.308696i	0.535707	+	0.844404i	$0.320045\pi$
$114$	1.39663	+	5.46004i	0.130806	+	0.511379i
$115$	3.13703	+	2.09610i	0.292530	+	0.195462i
$116$	1.79479	−	2.83305i	0.166642	−	0.263042i
$117$	−0.888717	−	3.08892i	−0.0821619	−	0.285571i
$118$	2.24313	−	3.44720i	0.206497	−	0.317341i
$119$	11.6030	−	4.80613i	1.06365	−	0.440577i
$120$	3.03246	+	3.84762i	0.276825	+	0.351238i
$121$	7.76597	+	3.21677i	0.705997	+	0.292434i
$122$	6.14191	+	8.95410i	0.556063	+	0.810667i
$123$	−0.141187	−	0.129826i	−0.0127304	−	0.0117060i
$124$	6.88431	−	7.22798i	0.618230	−	0.649092i
$125$	−0.195090	−	0.980785i	−0.0174494	−	0.0877241i
$126$	−6.81680	+	8.26903i	−0.607289	+	0.736664i
$127$		−	0.606243i		−	0.0537954i	−0.999638	−	0.0268977i	$-0.991437\pi$
$127$		−	0.606243i		−	0.0537954i	0.999638	−	0.0268977i	$-0.00856283\pi$
$128$	3.42421	−	10.7831i	0.302660	−	0.953099i
$129$	3.82190	−	0.928186i	0.336500	−	0.0817222i
$130$	1.39270	−	0.596841i	0.122148	−	0.0523464i
$131$	19.3247	−	3.84392i	1.68841	−	0.335845i	0.744894	−	0.667183i	$-0.232500\pi$
$131$	19.3247	−	3.84392i	1.68841	−	0.335845i	0.943512	+	0.331339i	$0.107500\pi$
$132$	2.78588	−	4.83415i	0.242479	−	0.420759i
$133$	−3.22881	−	4.83225i	−0.279973	−	0.419010i
$134$	13.2484	−	9.08753i	1.14449	−	0.785043i
$135$	−4.92902	+	1.64461i	−0.424223	+	0.141545i
$136$	−5.85251	−	12.7874i	−0.501849	−	1.09651i
$137$	−1.38073	−	3.33337i	−0.117964	−	0.284789i	0.853858	−	0.520505i	$-0.174256\pi$
$137$	−1.38073	−	3.33337i	−0.117964	−	0.284789i	−0.971822	+	0.235716i	$0.924256\pi$
$138$	8.71680	+	3.07000i	0.742024	+	0.261336i
$139$	17.2378	+	3.42881i	1.46209	+	0.290828i	0.861103	−	0.508431i	$-0.169774\pi$
$139$	17.2378	+	3.42881i	1.46209	+	0.290828i	0.600987	+	0.799259i	$0.294774\pi$
$140$	−4.26755	−	2.70357i	−0.360674	−	0.228493i
$141$	8.24006	+	3.01534i	0.693938	+	0.253938i
$142$	−0.0977515	−	8.02928i	−0.00820313	−	0.673802i
$143$	−1.22023	−	1.22023i	−0.102040	−	0.102040i
$144$	9.53185	+	7.28998i	0.794321	+	0.607499i
$145$	−1.18572	+	1.18572i	−0.0984687	+	0.0984687i
$146$	4.68813	+	4.57535i	0.387992	+	0.378659i
$147$	−0.368849	+	1.00796i	−0.0304221	+	0.0831349i
$148$	0.292251	−	1.68233i	0.0240229	−	0.138286i
$149$	−0.0269648	+	0.135561i	−0.00220904	+	0.0111056i	−0.981874	−	0.189534i	$-0.939302\pi$
$149$	−0.0269648	+	0.135561i	−0.00220904	+	0.0111056i	0.979665	+	0.200640i	$0.0643021\pi$
$150$	−1.05831	−	2.20907i	−0.0864111	−	0.180369i
$151$	−15.9569	+	6.60957i	−1.29856	+	0.537879i	−0.921524	−	0.388321i	$-0.873055\pi$
$151$	−15.9569	+	6.60957i	−1.29856	+	0.537879i	−0.377031	+	0.926201i	$0.623055\pi$
$152$	−5.27533	+	3.81064i	−0.427886	+	0.309084i
$153$	14.8638	−	1.24844i	1.20167	−	0.100930i
$154$	−1.05368	+	5.65624i	−0.0849083	+	0.455793i
$155$	−4.14981	+	2.77281i	−0.333320	+	0.222718i
$156$	2.94271	−	2.26174i	0.235605	−	0.181084i
$157$	−2.75438	−	13.8472i	−0.219823	−	1.10513i	−0.920229	−	0.391381i	$-0.871997\pi$
$157$	−2.75438	−	13.8472i	−0.219823	−	1.10513i	0.700405	−	0.713745i	$-0.253003\pi$
$158$	20.1031	+	8.04169i	1.59932	+	0.639763i
$159$	−4.42825	−	18.2338i	−0.351183	−	1.44603i
$160$	−2.85084	+	4.88597i	−0.225379	+	0.386270i
$161$	−9.53002			−0.751071
$162$	−10.6987	+	6.89477i	−0.840569	+	0.541704i
$163$	20.2967	−	4.03727i	1.58976	−	0.316223i	0.680597	−	0.732658i	$-0.261721\pi$
$163$	20.2967	−	4.03727i	1.58976	−	0.316223i	0.909166	+	0.416435i	$0.136721\pi$
$164$	0.0797485	−	0.206620i	0.00622731	−	0.0161343i
$165$	−1.88827	+	2.05352i	−0.147002	+	0.159867i
$166$	3.00326	−	16.1217i	0.233098	−	1.25128i
$167$	8.52477	−	20.5806i	0.659667	−	1.59258i	−0.138652	−	0.990341i	$-0.544277\pi$
$167$	8.52477	−	20.5806i	0.659667	−	1.59258i	0.798319	−	0.602235i	$-0.205723\pi$
$168$	−11.7684	−	3.82534i	−0.907949	−	0.295132i
$169$	4.53560	+	10.9499i	0.348892	+	0.842300i
$170$	1.45564	+	6.87921i	0.111642	+	0.527612i
$171$	−1.90849	−	6.63336i	−0.145946	−	0.507266i
$172$	2.61427	+	3.71352i	0.199336	+	0.283153i
$173$	1.89330	−	2.83353i	0.143945	−	0.215429i	−0.752491	−	0.658603i	$-0.771148\pi$
$173$	1.89330	−	2.83353i	0.143945	−	0.215429i	0.896436	+	0.443174i	$0.146148\pi$
$174$	−2.09407	+	3.53356i	−0.158751	+	0.267879i
$175$	1.78610	+	1.78610i	0.135017	+	0.135017i
$176$	6.37248	+	0.947822i	0.480344	+	0.0714448i
$177$	−2.62058	+	4.30173i	−0.196975	+	0.323338i
$178$	−0.225515	−	18.5237i	−0.0169031	−	1.38841i
$179$	3.13337	−	4.68943i	0.234199	−	0.350504i	−0.695691	−	0.718341i	$-0.744902\pi$
$179$	3.13337	−	4.68943i	0.234199	−	0.350504i	0.929890	+	0.367837i	$0.119902\pi$
$180$	−3.85240	−	4.59989i	−0.287141	−	0.342856i
$181$	−3.51297	+	17.6609i	−0.261117	+	1.31272i	0.598227	+	0.801326i	$0.295872\pi$
$181$	−3.51297	+	17.6609i	−0.261117	+	1.31272i	−0.859344	+	0.511397i	$0.829128\pi$
$182$	−2.08743	+	3.20793i	−0.154731	+	0.237787i
$183$	−7.84487	−	10.7381i	−0.579910	−	0.793783i
$184$	0.389644	+	10.6642i	0.0287249	+	0.786175i
$185$	−0.326720	+	0.788772i	−0.0240209	+	0.0579917i
$186$	−8.16471	+	9.09910i	−0.598666	+	0.667179i
$187$	6.65857	−	4.44912i	0.486923	−	0.325352i
$188$	0.246662	+	10.1289i	0.0179897	+	0.738723i
$189$	8.04417	−	10.3711i	0.585127	−	0.754387i
$190$	2.99078	−	1.28170i	0.216974	−	0.0929841i
$191$	12.1089			0.876169			0.438085	−	0.898934i	$-0.355657\pi$
$191$	12.1089			0.876169			0.438085	+	0.898934i	$0.355657\pi$
$192$	−3.79944	+	13.3253i	−0.274201	+	0.961672i
$193$	−26.6847			−1.92081			−0.960405	−	0.278609i	$-0.910127\pi$
$193$	−26.6847			−1.92081			−0.960405	+	0.278609i	$0.910127\pi$
$194$	−0.609946	+	0.261392i	−0.0437916	+	0.0187668i
$195$	−1.68323	+	0.781347i	−0.120538	+	0.0559535i
$196$	−1.23900	+	0.0301727i	−0.0885001	+	0.00215519i
$197$	5.10176	−	3.40888i	0.363485	−	0.242873i	−0.360393	−	0.932800i	$-0.617358\pi$
$197$	5.10176	−	3.40888i	0.363485	−	0.242873i	0.723879	+	0.689927i	$0.242358\pi$
$198$	−3.23452	+	6.01939i	−0.229867	+	0.427779i
$199$	−7.48686	+	18.0749i	−0.530729	+	1.28129i	0.400312	+	0.916379i	$0.368902\pi$
$199$	−7.48686	+	18.0749i	−0.530729	+	1.28129i	−0.931041	+	0.364915i	$0.881098\pi$
$200$	1.92564	−	2.07169i	0.136163	−	0.146491i
$201$	−15.8880	+	11.6072i	−1.12065	+	0.818710i
$202$	5.26846	−	8.09647i	0.370688	−	0.569665i
$203$	0.826331	−	4.15425i	0.0579971	−	0.291571i
$204$	7.63012	+	15.4414i	0.534215	+	1.08111i
$205$	−0.0615226	+	0.0920751i	−0.00429693	+	0.00643081i
$206$	0.0358154	+	2.94187i	0.00249538	+	0.204970i
$207$	−10.7829	−	3.44103i	−0.749463	−	0.239168i
$208$	3.67505	+	2.20470i	0.254819	+	0.152868i
$209$	−2.62040	−	2.62040i	−0.181257	−	0.181257i
$210$	5.32276	+	3.15439i	0.367305	+	0.217673i
$211$	11.6914	−	17.4975i	0.804871	−	1.20458i	−0.170793	−	0.985307i	$-0.554633\pi$
$211$	11.6914	−	17.4975i	0.804871	−	1.20458i	0.975665	−	0.219268i	$-0.0703670\pi$
$212$	17.7167	−	12.4723i	1.21679	−	0.856601i
$213$	0.411923	+	9.82591i	0.0282245	+	0.673260i
$214$	3.61663	+	17.0919i	0.247228	+	1.16838i
$215$	−0.868966	−	2.09787i	−0.0592630	−	0.143073i
$216$	−11.9343	−	8.57748i	−0.812024	−	0.583624i
$217$	4.82439	−	11.6471i	0.327501	−	0.790657i
$218$	1.78198	−	9.56579i	0.120691	−	0.647877i
$219$	−5.90576	−	5.43052i	−0.399074	−	0.366961i
$220$	−3.00521	−	1.15992i	−0.202611	−	0.0782015i
$221$	5.22474	−	1.03926i	0.351454	−	0.0699085i
$222$	−0.296540	+	2.07015i	−0.0199025	+	0.138939i
$223$	−23.6640			−1.58466			−0.792331	−	0.610092i	$-0.791133\pi$
$223$	−23.6640			−1.58466			−0.792331	+	0.610092i	$0.791133\pi$
$224$	−0.869208	−	14.2623i	−0.0580764	−	0.952943i
$225$	1.37600	+	2.66582i	0.0917334	+	0.177722i
$226$	6.09352	+	2.43754i	0.405335	+	0.162143i
$227$	1.00537	+	5.05436i	0.0667291	+	0.335470i	0.999700	−	0.0244813i	$-0.00779342\pi$
$227$	1.00537	+	5.05436i	0.0667291	+	0.335470i	−0.932971	+	0.359951i	$0.882793\pi$
$228$	6.31938	−	4.85702i	0.418511	−	0.321664i
$229$	16.1855	−	10.8148i	1.06957	−	0.714663i	0.109376	−	0.994000i	$-0.465115\pi$
$229$	16.1855	−	10.8148i	1.06957	−	0.714663i	0.960193	+	0.279337i	$0.0901148\pi$
$230$	0.977152	−	5.24541i	0.0644315	−	0.345872i
$231$	1.08404	−	6.96275i	0.0713248	−	0.458115i
$232$	−4.68243	−	0.754823i	−0.307417	−	0.0495565i
$233$	−17.2061	+	7.12698i	−1.12721	+	0.466904i	−0.866830	−	0.498603i	$-0.833846\pi$
$233$	−17.2061	+	7.12698i	−1.12721	+	0.466904i	−0.260376	+	0.965507i	$0.583846\pi$
$234$	−3.52015	+	2.87594i	−0.230120	+	0.188006i
$235$	0.988314	−	4.96859i	0.0644705	−	0.324115i
$236$	−5.73051	−	0.995495i	−0.373024	−	0.0648012i
$237$	−24.9030	−	9.11294i	−1.61763	−	0.591949i
$238$	−12.7110	−	12.4052i	−0.823931	−	0.804110i
$239$	5.56958	−	5.56958i	0.360266	−	0.360266i	−0.503645	−	0.863911i	$-0.668008\pi$
$239$	5.56958	−	5.56958i	0.360266	−	0.360266i	0.863911	+	0.503645i	$0.168008\pi$
$240$	3.31217	−	6.08519i	0.213799	−	0.392797i
$241$	10.3957	+	10.3957i	0.669644	+	0.669644i	0.957634	−	0.287989i	$-0.0929867\pi$
$241$	10.3957	+	10.3957i	0.669644	+	0.669644i	−0.287989	+	0.957634i	$0.592987\pi$
$242$	−0.144714	−	11.8867i	−0.00930256	−	0.764109i
$243$	12.8464	−	8.83002i	0.824099	−	0.566446i
$244$	8.21782	−	12.9717i	0.526092	−	0.830430i
$245$	0.607778	+	0.120894i	0.0388295	+	0.00772367i
$246$	−0.0901077	+	0.255847i	−0.00574506	+	0.0163122i
$247$	−0.943360	−	2.27747i	−0.0600245	−	0.144912i
$248$	−13.2305	−	4.92234i	−0.840136	−	0.312569i
$249$	−3.08979	+	19.8455i	−0.195807	+	1.25766i
$250$	−1.16622	+	0.799951i	−0.0737585	+	0.0505934i
$251$	2.18096	+	3.26404i	0.137661	+	0.206025i	0.893894	−	0.448278i	$-0.147962\pi$
$251$	2.18096	+	3.26404i	0.137661	+	0.206025i	−0.756233	+	0.654302i	$0.772962\pi$
$252$	14.5461	+	4.25465i	0.916319	+	0.268018i
$253$	−5.96000	+	1.18552i	−0.374702	+	0.0745329i
$254$	−0.788042	+	0.337715i	−0.0494461	+	0.0211901i
$255$	−2.03239	−	8.36858i	−0.127273	−	0.524061i
$256$	−15.9242	+	1.55578i	−0.995261	+	0.0972364i
$257$		−	19.5549i		−	1.21980i	−0.792479	−	0.609899i	$-0.791210\pi$
$257$		−	19.5549i		−	1.21980i	0.792479	−	0.609899i	$-0.208790\pi$
$258$	−3.33556	−	4.45095i	−0.207663	−	0.277104i
$259$	−0.420720	−	2.11510i	−0.0261423	−	0.131426i
$260$	−1.55164	−	1.47786i	−0.0962287	−	0.0916533i
$261$	2.43495	−	4.40202i	0.150720	−	0.272478i
$262$	−15.7617	−	22.9784i	−0.973759	−	1.41961i
$263$	−13.9244	−	5.76766i	−0.858613	−	0.355649i	−0.0904482	−	0.995901i	$-0.528830\pi$
$263$	−13.9244	−	5.76766i	−0.858613	−	0.355649i	−0.768165	+	0.640252i	$0.778830\pi$
$264$	−7.83571	−	0.928378i	−0.482255	−	0.0571377i
$265$	−10.0086	+	4.14571i	−0.614826	+	0.254669i
$266$	−4.48269	+	6.88892i	−0.274852	+	0.422387i
$267$	0.950318	+	22.6686i	0.0581585	+	1.38730i
$268$	−19.1929	−	12.1590i	−1.17239	−	0.742730i
$269$	−18.3536	−	12.2635i	−1.11904	−	0.747718i	−0.148560	−	0.988903i	$-0.547464\pi$
$269$	−18.3536	−	12.2635i	−1.11904	−	0.747718i	−0.970479	+	0.241186i	$0.922464\pi$
$270$	4.88356	+	5.49098i	0.297204	+	0.334171i
$271$	2.20350	−	2.20350i	0.133853	−	0.133853i	−0.637006	−	0.770859i	$-0.719827\pi$
$271$	2.20350	−	2.20350i	0.133853	−	0.133853i	0.770859	+	0.637006i	$0.219827\pi$
$272$	−13.3619	+	14.7309i	−0.810182	+	0.893194i
$273$	2.43868	−	4.00313i	0.147596	−	0.242281i
$274$	−3.56383	+	3.65167i	−0.215299	+	0.220606i
$275$	1.33920	+	0.894827i	0.0807569	+	0.0539601i
$276$	−0.865167	−	13.0410i	−0.0520769	−	0.784974i
$277$	3.48459	+	0.693129i	0.209369	+	0.0416461i	0.298660	−	0.954359i	$-0.403460\pi$
$277$	3.48459	+	0.693129i	0.209369	+	0.0416461i	−0.0892914	+	0.996006i	$0.528460\pi$
$278$	−5.14547	−	24.3171i	−0.308605	−	1.45844i
$279$	9.66408	−	11.4363i	0.578573	−	0.684676i
$280$	−1.13702	+	7.05335i	−0.0679501	+	0.421518i
$281$	−6.98120	−	2.89171i	−0.416464	−	0.172505i	0.164605	−	0.986360i	$-0.447365\pi$
$281$	−6.98120	−	2.89171i	−0.416464	−	0.172505i	−0.581068	+	0.813855i	$0.697365\pi$
$282$	−0.670642	−	12.3908i	−0.0399362	−	0.737862i
$283$	−5.79540	−	8.67344i	−0.344501	−	0.515582i	0.618246	−	0.785984i	$-0.287843\pi$
$283$	−5.79540	−	8.67344i	−0.344501	−	0.515582i	−0.962747	+	0.270402i	$0.912843\pi$
$284$	−10.3826	+	4.59986i	−0.616095	+	0.272952i
$285$	−3.61468	+	1.67792i	−0.214115	+	0.0993914i
$286$	−0.906404	+	2.26589i	−0.0535968	+	0.133985i
$287$		−	0.279716i		−	0.0165111i
$288$	4.16626	−	16.4512i	0.245499	−	0.969397i
$289$			7.72122i			0.454189i
$290$	2.20181	+	0.880773i	0.129295	+	0.0517208i
$291$	0.737184	−	0.342198i	0.0432145	−	0.0200600i
$292$	3.33582	−	8.64274i	0.195214	−	0.505778i
$293$	12.2310	+	18.3049i	0.714540	+	1.06938i	0.994016	+	0.109232i	$0.0348391\pi$
$293$	12.2310	+	18.3049i	0.714540	+	1.06938i	−0.279476	+	0.960153i	$0.590161\pi$
$294$	1.51569	−	0.0820356i	0.0883970	−	0.00478441i
$295$	2.68679	+	1.11291i	0.156431	+	0.0647959i
$296$	−2.34962	+	0.557268i	−0.136569	+	0.0323905i
$297$	3.74062	−	7.48669i	0.217053	−	0.434422i
$298$	0.191234	−	0.0404650i	0.0110779	−	0.00234407i
$299$	−3.96462	−	0.788613i	−0.229280	−	0.0456066i
$300$	−2.28197	+	2.60627i	−0.131750	+	0.150473i
$301$	4.76903	+	3.18657i	0.274883	+	0.183671i
$302$	17.4806	+	17.0601i	1.00590	+	0.981699i
$303$	−6.15497	+	10.1035i	−0.353594	+	0.580430i
$304$	7.89205	+	4.73452i	0.452640	+	0.271544i
$305$	−5.42907	+	5.42907i	−0.310868	+	0.310868i
$306$	−9.90286	−	18.6257i	−0.566109	−	1.06476i
$307$	24.4837	+	16.3595i	1.39736	+	0.933687i	0.999871	+	0.0160802i	$0.00511870\pi$
$307$	24.4837	+	16.3595i	1.39736	+	0.933687i	0.397490	+	0.917606i	$0.369881\pi$
$308$	7.93939	−	1.78121i	0.452389	−	0.101494i
$309$	−0.150926	−	3.60014i	−0.00858586	−	0.204805i
$310$	5.91601	+	3.84961i	0.336007	+	0.218643i
$311$	8.99525	−	3.72595i	0.510074	−	0.211279i	−0.112777	−	0.993620i	$-0.535975\pi$
$311$	8.99525	−	3.72595i	0.510074	−	0.211279i	0.622850	+	0.782341i	$0.285975\pi$
$312$	−4.57926	−	2.56523i	−0.259249	−	0.145228i
$313$	15.8402	+	6.56123i	0.895342	+	0.370863i	0.782427	−	0.622742i	$-0.213981\pi$
$313$	15.8402	+	6.56123i	0.895342	+	0.370863i	0.112914	+	0.993605i	$0.463981\pi$
$314$	−16.4653	+	11.2941i	−0.929191	+	0.637362i
$315$	−6.63096	−	3.66787i	−0.373612	−	0.206661i
$316$	−0.745459	−	30.6113i	−0.0419353	−	1.72202i
$317$	0.000568099		0.00285603i	3.19076e−5		0.000160411i	0.980801	−	0.195010i	$-0.0624740\pi$
$317$	0.000568099		0.00285603i	3.19076e−5		0.000160411i	−0.980769	+	0.195171i	$0.937474\pi$
$318$	−21.2349	+	15.9135i	−1.19079	+	0.892385i
$319$		−	2.70083i		−	0.151217i
$320$	7.93926	+	0.983957i	0.443818	+	0.0550048i
$321$	−5.04961	−	20.7923i	−0.281842	−	1.16051i
$322$	5.30880	+	12.3879i	0.295848	+	0.690348i
$323$	11.2200	−	2.23179i	0.624295	−	0.124180i
$324$	14.9222	+	10.0662i	0.829011	+	0.559233i
$325$	0.595243	+	0.890844i	0.0330181	+	0.0494152i
$326$	−16.5545	−	24.1343i	−0.916868	−	1.33667i
$327$	−1.83333	+	11.7753i	−0.101383	+	0.651178i
$328$	−0.313005	+	0.0114365i	−0.0172828	+	0.000631472i
$329$	4.89689	+	11.8221i	0.269974	+	0.651775i
$330$	3.72121	+	1.31059i	0.204846	+	0.0721455i
$331$	27.7143	+	5.51273i	1.52332	+	0.303007i	0.884569	−	0.466409i	$-0.154452\pi$
$331$	27.7143	+	5.51273i	1.52332	+	0.303007i	0.638749	+	0.769416i	$0.279452\pi$
$332$	−22.6292	+	5.07690i	−1.24194	+	0.278631i
$333$	0.287675	−	2.54508i	0.0157645	−	0.139469i
$334$	−31.5011	+	0.383507i	−1.72366	+	0.0209846i
$335$	8.03281	+	8.03281i	0.438879	+	0.438879i
$336$	1.58322	+	17.4284i	0.0863717	+	0.950796i
$337$	22.0273	−	22.0273i	1.19990	−	1.19990i	0.225705	−	0.974196i	$-0.427531\pi$
$337$	22.0273	−	22.0273i	1.19990	−	1.19990i	0.974196	−	0.225705i	$-0.0724686\pi$
$338$	11.7069	−	11.9955i	0.636773	−	0.652468i
$339$	−7.54844	−	2.76225i	−0.409975	−	0.150025i
$340$	8.13126	−	5.72429i	0.440979	−	0.310443i
$341$	1.56826	−	7.88416i	0.0849258	−	0.426951i
$342$	−7.55942	+	6.17600i	−0.408766	+	0.333960i
$343$	−17.7817	+	7.36542i	−0.960122	+	0.397695i
$344$	3.37082	−	5.46689i	0.181742	−	0.294755i
$345$	−1.00531	+	6.45702i	−0.0541239	+	0.347634i
$346$	−4.73792	−	0.882613i	−0.254712	−	0.0474496i
$347$	13.4739	−	9.00295i	0.723315	−	0.483304i	−0.138605	−	0.990348i	$-0.544262\pi$
$347$	13.4739	−	9.00295i	0.723315	−	0.483304i	0.861920	+	0.507044i	$0.169262\pi$
$348$	5.75973	+	0.753622i	0.308754	+	0.0403984i
$349$	0.514040	+	2.58425i	0.0275159	+	0.138332i	0.992101	−	0.125439i	$-0.0400338\pi$
$349$	0.514040	+	2.58425i	0.0275159	+	0.138332i	−0.964585	+	0.263771i	$0.915034\pi$
$350$	1.32675	−	3.31668i	0.0709175	−	0.177284i
$351$	4.20470	−	3.64887i	0.224430	−	0.194762i
$352$	−2.31781	−	8.81144i	−0.123540	−	0.469651i
$353$	−26.1938			−1.39415			−0.697077	−	0.716996i	$-0.745517\pi$
$353$	−26.1938			−1.39415			−0.697077	+	0.716996i	$0.745517\pi$
$354$	7.05154	+	1.01011i	0.374785	+	0.0536865i
$355$	5.56888	−	1.10772i	0.295565	−	0.0587916i
$356$	−23.9530	+	10.6120i	−1.26951	+	0.562435i
$357$	16.0124	+	14.7238i	0.847464	+	0.779268i
$358$	−7.84116	−	1.46071i	−0.414418	−	0.0772007i
$359$	−3.70332	+	8.94061i	−0.195454	+	0.471867i	−0.990973	−	0.134061i	$-0.957198\pi$
$359$	−3.70332	+	8.94061i	−0.195454	+	0.471867i	0.795519	+	0.605928i	$0.207198\pi$
$360$	−3.83327	+	7.57007i	−0.202031	+	0.398978i
$361$	5.24515	+	12.6629i	0.276061	+	0.666469i
$362$	24.9139	−	5.27177i	1.30945	−	0.277078i
$363$	0.609822	+	14.5465i	0.0320074	+	0.763495i
$364$	5.33274	+	0.926395i	0.279511	+	0.0485563i
$365$	−2.57345	+	3.85144i	−0.134700	+	0.201593i
$366$	−9.58813	+	16.1792i	−0.501180	+	0.845698i
$367$	22.1495	+	22.1495i	1.15619	+	1.15619i	0.985287	+	0.170907i	$0.0546698\pi$
$367$	22.1495	+	22.1495i	1.15619	+	1.15619i	0.170907	+	0.985287i	$0.445330\pi$
$368$	13.6451	−	6.44710i	0.711299	−	0.336078i
$369$	0.100998	−	0.316489i	0.00525773	−	0.0164758i
$370$	1.20731	−	0.0146983i	0.0627651	−	0.000764127i
$371$	15.2027	−	22.7524i	0.789283	−	1.18125i
$372$	16.3760	+	5.54437i	0.849054	+	0.287462i
$373$	0.728316	−	3.66149i	0.0377108	−	0.189585i	−0.957338	−	0.288969i	$-0.906687\pi$
$373$	0.728316	−	3.66149i	0.0377108	−	0.189585i	0.995049	+	0.0993846i	$0.0316874\pi$
$374$	−9.49254	−	6.17690i	−0.490848	−	0.319400i
$375$	1.39858	−	1.02175i	0.0722223	−	0.0527631i
$376$	13.0289	−	5.96303i	0.671913	−	0.307520i
$377$	0.687531	−	1.65985i	0.0354097	−	0.0854865i
$378$	−17.9623	−	4.67910i	−0.923879	−	0.240667i
$379$	−15.2798	+	10.2097i	−0.784872	+	0.524435i	−0.882232	−	0.470814i	$-0.843960\pi$
$379$	−15.2798	+	10.2097i	−0.784872	+	0.524435i	0.0973601	+	0.995249i	$0.468960\pi$
$380$	−3.33210	−	3.17367i	−0.170933	−	0.162806i
$381$	0.952431	−	0.442115i	0.0487945	−	0.0226502i
$382$	−6.74540	−	15.7401i	−0.345125	−	0.805333i
$383$	0.661932			0.0338231			0.0169116	−	0.999857i	$-0.494617\pi$
$383$	0.661932			0.0338231			0.0169116	+	0.999857i	$0.494617\pi$
$384$	19.4378	−	2.48422i	0.991932	−	0.126772i
$385$	−4.06837			−0.207344
$386$	14.8650	+	34.6869i	0.756610	+	1.76552i
$387$	4.24542	+	5.32746i	0.215807	+	0.270810i
$388$	0.679555	+	0.647244i	0.0344992	+	0.0328588i
$389$	−13.7921	+	9.21558i	−0.699287	+	0.467248i	−0.853705	−	0.520757i	$-0.825650\pi$
$389$	−13.7921	+	9.21558i	−0.699287	+	0.467248i	0.154418	+	0.988006i	$0.450650\pi$
$390$	1.95332	+	1.75273i	0.0989100	+	0.0887529i
$391$	7.17872	−	17.3310i	0.363044	−	0.876465i
$392$	0.729421	+	1.59374i	0.0368413	+	0.0804962i
$393$	20.1319	+	27.5566i	1.01552	+	1.39005i
$394$	−7.27313	−	4.73270i	−0.366415	−	0.238430i
$395$	−2.98687	+	15.0160i	−0.150286	+	0.755538i
$396$	9.62630	+	0.851313i	0.483740	+	0.0427801i
$397$	10.0550	−	15.0484i	0.504647	−	0.755258i	−0.488445	−	0.872595i	$-0.662436\pi$
$397$	10.0550	−	15.0484i	0.504647	−	0.755258i	0.993092	+	0.117337i	$0.0374357\pi$
$398$	27.6658	−	0.336814i	1.38676	−	0.0168830i
$399$	5.23698	−	8.59661i	0.262177	−	0.430369i
$400$	−3.76565	−	1.34904i	−0.188282	−	0.0674518i
$401$	16.0793	+	16.0793i	0.802963	+	0.802963i	0.983558	−	0.180595i	$-0.0578023\pi$
$401$	16.0793	+	16.0793i	0.802963	+	0.802963i	−0.180595	+	0.983558i	$0.557802\pi$
$402$	23.9386	+	14.1865i	1.19395	+	0.707560i
$403$	2.97082	−	4.44614i	0.147987	−	0.221478i
$404$	−13.4593	−	2.33812i	−0.669624	−	0.116326i
$405$	−6.17833	−	6.54433i	−0.307004	−	0.325190i
$406$	−5.86033	+	1.24004i	−0.290843	+	0.0615422i
$407$	−0.526230	−	1.27043i	−0.0260843	−	0.0629730i
$408$	15.8215	−	18.5200i	0.783279	−	0.916877i
$409$	−2.93979	+	7.09728i	−0.145363	+	0.350938i	−0.979745	−	0.200249i	$-0.935825\pi$
$409$	−2.93979	+	7.09728i	−0.145363	+	0.350938i	0.834382	+	0.551187i	$0.185825\pi$
$410$	0.153958	+	0.0286804i	0.00760346	+	0.00141642i
$411$	4.22994	−	4.60011i	0.208647	−	0.226907i
$412$	3.80412	−	1.68536i	0.187415	−	0.0830316i
$413$	−7.20467	+	1.43310i	−0.354519	+	0.0705181i
$414$	1.53382	+	15.9333i	0.0753829	+	0.783079i
$415$	11.5959			0.569219
$416$	0.818612	−	6.00527i	0.0401358	−	0.294433i
$417$	7.18422	+	29.5818i	0.351813	+	1.44863i
$418$	−1.94647	+	4.86592i	−0.0952052	+	0.238000i
$419$	−0.0406751	−	0.204488i	−0.00198711	−	0.00998988i	0.979779	−	0.200083i	$-0.0641211\pi$
$419$	−0.0406751	−	0.204488i	−0.00198711	−	0.00998988i	−0.981766	+	0.190093i	$0.939121\pi$
$420$	1.13521	−	8.67612i	0.0553927	−	0.423351i
$421$	4.89688	−	3.27199i	0.238659	−	0.159467i	−0.430489	−	0.902596i	$-0.641659\pi$
$421$	4.89688	−	3.27199i	0.238659	−	0.159467i	0.669149	+	0.743129i	$0.266659\pi$
$422$	−29.2574	−	5.45027i	−1.42423	−	0.265315i
$423$	1.27201	+	15.1445i	0.0618474	+	0.736349i
$424$	−26.0817	−	16.0817i	−1.26664	−	0.780996i
$425$	−4.59357	+	1.90272i	−0.222821	+	0.0922954i
$426$	12.5430	−	6.00909i	0.607711	−	0.291141i
$427$	3.78353	−	19.0211i	0.183098	−	0.920495i
$428$	20.2027	−	14.2224i	0.976533	−	0.687466i
$429$	1.02715	−	2.80690i	0.0495912	−	0.135518i
$430$	−2.24291	+	2.29819i	−0.108163	+	0.110829i
$431$	−23.2684	+	23.2684i	−1.12080	+	1.12080i	−0.129175	+	0.991622i	$0.541233\pi$
$431$	−23.2684	+	23.2684i	−1.12080	+	1.12080i	−0.991622	+	0.129175i	$0.958767\pi$
$432$	−4.50155	+	20.2913i	−0.216581	+	0.976265i
$433$	19.9489	+	19.9489i	0.958682	+	0.958682i	0.999180	−	0.0404977i	$-0.0128944\pi$
$433$	19.9489	+	19.9489i	0.958682	+	0.958682i	−0.0404977	+	0.999180i	$0.512894\pi$
$434$	−17.8273	+	0.217036i	−0.855737	+	0.0104181i
$435$	−2.72752	−	0.998102i	−0.130775	−	0.0478553i
$436$	−13.4270	+	3.01238i	−0.643038	+	0.144267i
$437$	−8.51390	−	1.69352i	−0.407275	−	0.0810121i
$438$	−3.76914	+	10.7019i	−0.180097	+	0.511357i
$439$	3.07196	+	7.41636i	0.146617	+	0.353964i	0.980078	−	0.198614i	$-0.0636441\pi$
$439$	3.07196	+	7.41636i	0.146617	+	0.353964i	−0.833461	+	0.552578i	$0.813644\pi$
$440$	0.166339	+	4.55255i	0.00792992	+	0.217035i
$441$	−1.85253	+	0.155598i	−0.0882158	+	0.00740941i
$442$	−4.26142	−	6.21258i	−0.202695	−	0.295502i
$443$	−2.85713	−	4.27599i	−0.135746	−	0.203158i	0.757368	−	0.652988i	$-0.226485\pi$
$443$	−2.85713	−	4.27599i	−0.135746	−	0.203158i	−0.893114	+	0.449829i	$0.851485\pi$
$444$	2.85613	−	0.767733i	0.135546	−	0.0364350i
$445$	12.8475	−	2.55553i	0.609032	−	0.121144i
$446$	13.1823	+	30.7604i	0.624201	+	1.45655i
$447$	−0.232637	+	0.0564981i	−0.0110033	+	0.00267227i
$448$	−18.0551	+	9.07487i	−0.853024	+	0.428747i
$449$			16.6884i			0.787573i	0.919202	+	0.393786i	$0.128835\pi$
$449$			16.6884i			0.787573i	−0.919202	+	0.393786i	$0.871165\pi$
$450$	2.69873	−	3.27366i	0.127219	−	0.154322i
$451$	−0.0347962	−	0.174932i	−0.00163849	−	0.00823723i
$452$	−0.225958	−	9.27870i	−0.0106282	−	0.436433i
$453$	−22.0208	−	20.2488i	−1.03463	−	0.951370i
$454$	6.01000	−	4.12245i	0.282063	−	0.193476i
$455$	−2.50030	−	1.03566i	−0.117216	−	0.0485524i
$456$	−9.83381	−	5.50876i	−0.460510	−	0.257971i
$457$	−20.9382	+	8.67287i	−0.979446	+	0.405700i	−0.814220	−	0.580556i	$-0.802835\pi$
$457$	−20.9382	+	8.67287i	−0.979446	+	0.405700i	−0.165226	+	0.986256i	$0.552835\pi$
$458$	−23.0743	−	15.0147i	−1.07819	−	0.701590i
$459$	12.8011	+	22.4412i	0.597503	+	1.04746i
$460$	−7.36273	+	1.65184i	−0.343289	+	0.0770174i
$461$	3.91190	+	2.61385i	0.182196	+	0.121739i	0.643323	−	0.765595i	$-0.277555\pi$
$461$	3.91190	+	2.61385i	0.182196	+	0.121739i	−0.461128	+	0.887334i	$0.652555\pi$
$462$	−9.65460	+	2.46955i	−0.449173	+	0.114894i
$463$	5.13941	−	5.13941i	0.238849	−	0.238849i	−0.577525	−	0.816373i	$-0.695981\pi$
$463$	5.13941	−	5.13941i	0.238849	−	0.238849i	0.816373	+	0.577525i	$0.195981\pi$
$464$	1.62722	+	6.50707i	0.0755420	+	0.302083i
$465$	−7.38253	−	4.49738i	−0.342356	−	0.208561i
$466$	18.8490	+	18.3956i	0.873164	+	0.852160i
$467$	5.30296	+	3.54333i	0.245392	+	0.163966i	0.672184	−	0.740384i	$-0.265356\pi$
$467$	5.30296	+	3.54333i	0.245392	+	0.163966i	−0.426792	+	0.904350i	$0.640356\pi$
$468$	5.69932	+	2.97369i	0.263451	+	0.137459i
$469$	−28.1434	−	5.59808i	−1.29954	−	0.258495i
$470$	−7.00911	+	1.48312i	−0.323306	+	0.0684113i
$471$	19.7458	−	14.4256i	0.909838	−	0.664696i
$472$	1.89822	+	8.00351i	0.0873728	+	0.368391i
$473$	3.37892	+	1.39960i	0.155363	+	0.0643535i
$474$	2.02681	+	37.4474i	0.0930943	+	1.72001i
$475$	1.27827	+	1.91306i	0.0586509	+	0.0877772i
$476$	−9.04446	+	23.4332i	−0.414552	+	1.07406i
$477$	25.4166	−	20.2543i	1.16374	−	0.927380i
$478$	−10.3424	−	4.13718i	−0.473049	−	0.189230i
$479$			32.1184i			1.46753i	0.679404	+	0.733765i	$0.262239\pi$
$479$			32.1184i			1.46753i	−0.679404	+	0.733765i	$0.737761\pi$
$480$	−9.75509	−	0.915584i	−0.445257	−	0.0417905i
$481$		−	0.914727i		−	0.0417080i
$482$	7.72208	−	19.3041i	0.351731	−	0.879280i
$483$	−6.94996	−	14.9720i	−0.316234	−	0.681251i
$484$	−15.3707	+	6.80976i	−0.698668	+	0.309534i
$485$	−0.260692	−	0.390153i	−0.0118374	−	0.0177160i
$486$	−18.6342	−	11.7799i	−0.845265	−	0.534348i
$487$	22.7425	+	9.42027i	1.03056	+	0.426873i	0.832916	−	0.553400i	$-0.186670\pi$
$487$	22.7425	+	9.42027i	1.03056	+	0.426873i	0.197647	+	0.980273i	$0.436670\pi$
$488$	−21.4395	−	3.45611i	−0.970520	−	0.156451i
$489$	21.1445	+	28.9427i	0.956188	+	1.30883i
$490$	−0.181421	−	0.857382i	−0.00819578	−	0.0387326i
$491$	−11.7783	−	2.34285i	−0.531546	−	0.105731i	−0.0779822	−	0.996955i	$-0.524848\pi$
$491$	−11.7783	−	2.34285i	−0.531546	−	0.105731i	−0.453564	+	0.891224i	$0.649848\pi$
$492$	0.382766	−	0.0253935i	0.0172564	−	0.00114483i
$493$	6.93232	+	4.63203i	0.312216	+	0.208616i
$494$	−2.43493	+	2.49494i	−0.109553	+	0.112253i
$495$	−4.60323	−	1.46898i	−0.206900	−	0.0660257i
$496$	0.971752	+	19.9401i	0.0436330	+	0.895335i
$497$	−10.1414	+	10.1414i	−0.454906	+	0.454906i
$498$	27.5180	−	7.03883i	1.23311	−	0.315418i
$499$	−1.40249	−	0.937117i	−0.0627843	−	0.0419511i	0.523782	−	0.851852i	$-0.324521\pi$
$499$	−1.40249	−	0.937117i	−0.0627843	−	0.0419511i	−0.586566	+	0.809901i	$0.699521\pi$
$500$	1.68950	+	1.07033i	0.0755566	+	0.0478665i
$501$	38.5498	−	1.61609i	1.72228	−	0.0722017i
$502$	3.02793	−	4.65326i	0.135143	−	0.207685i
$503$	−21.4968	+	8.90428i	−0.958497	+	0.397022i	−0.806418	−	0.591346i	$-0.798597\pi$
$503$	−21.4968	+	8.90428i	−0.958497	+	0.397022i	−0.152079	+	0.988368i	$0.548597\pi$
$504$	−2.57255	−	21.2783i	−0.114591	−	0.947809i
$505$	6.31049	+	2.61389i	0.280813	+	0.116317i
$506$	4.86112	+	7.08687i	0.216103	+	0.315050i
$507$	−13.8950	+	15.1110i	−0.617100	+	0.671105i
$508$	0.877975	+	0.836230i	0.0389539	+	0.0371017i
$509$	−4.41384	−	22.1899i	−0.195640	−	0.983549i	−0.946406	−	0.322980i	$-0.895315\pi$
$509$	−4.41384	−	22.1899i	−0.195640	−	0.983549i	0.750766	−	0.660569i	$-0.229685\pi$
$510$	−9.74596	+	7.30367i	−0.431558	+	0.323412i
$511$		−	11.7003i		−	0.517591i
$512$	10.8931	+	19.8328i	0.481410	+	0.876495i
$513$	9.02947	−	7.83584i	0.398661	−	0.345961i
$514$	−25.4189	+	10.8933i	−1.12118	+	0.480481i
$515$	−2.04039	+	0.405860i	−0.0899105	+	0.0178843i
$516$	−3.92758	+	6.81528i	−0.172902	+	0.300026i
$517$	4.53313	+	6.78431i	0.199367	+	0.298373i
$518$	−2.51501	+	1.72513i	−0.110503	+	0.0757977i
$519$	5.83231	+	0.908043i	0.256010	+	0.0398587i
$520$	−1.05668	+	2.84020i	−0.0463387	+	0.124551i
$521$	−7.11760	−	17.1834i	−0.311828	−	0.752819i	−0.999637	−	0.0269278i	$-0.991428\pi$
$521$	−7.11760	−	17.1834i	−0.311828	−	0.752819i	0.687810	−	0.725891i	$-0.258572\pi$
$522$	−7.07851	−	0.712941i	−0.309818	−	0.0312046i
$523$	−8.78136	−	1.74672i	−0.383982	−	0.0763788i	−0.000675031	−	1.00000i	$-0.500215\pi$
$523$	−8.78136	−	1.74672i	−0.383982	−	0.0763788i	−0.383307	+	0.923621i	$0.625215\pi$
$524$	−21.0889	+	33.2886i	−0.921275	+	1.45422i
$525$	−1.50348	+	4.10859i	−0.0656174	+	0.179313i
$526$	0.259472	+	21.3129i	0.0113135	+	0.929287i
$527$	17.5469	+	17.5469i	0.764357	+	0.764357i
$528$	3.15820	+	10.7026i	0.137443	+	0.465772i
$529$	6.19808	−	6.19808i	0.269482	−	0.269482i
$530$	10.9643	+	10.7006i	0.476261	+	0.464804i
$531$	−8.66929	−	0.979908i	−0.376215	−	0.0425244i
$532$	11.4519	+	1.98941i	0.496502	+	0.0862516i
$533$	0.0231466	−	0.116366i	0.00100259	−	0.00504036i
$534$	28.9371	−	13.8631i	1.25223	−	0.599916i
$535$	−11.4130	+	4.72744i	−0.493429	+	0.204385i
$536$	−5.11364	+	31.7217i	−0.220876	+	1.37017i
$537$	9.65235	+	1.50279i	0.416530	+	0.0648503i
$538$	−5.71695	+	30.6890i	−0.246475	+	1.32309i
$539$	−0.829883	+	0.554510i	−0.0357456	+	0.0238844i
$540$	4.41717	−	9.40684i	0.190085	−	0.404806i
$541$	1.31313	+	6.60154i	0.0564558	+	0.283822i	0.998692	−	0.0511262i	$-0.0162811\pi$
$541$	1.31313	+	6.60154i	0.0564558	+	0.283822i	−0.942236	+	0.334949i	$0.891281\pi$
$542$	−4.09176	−	1.63679i	−0.175756	−	0.0703063i
$543$	−30.3079	+	7.36056i	−1.30063	+	0.315872i
$544$	26.5918	+	9.16276i	1.14011	+	0.392850i
$545$	6.88040			0.294724
$546$	−6.56208	−	0.939992i	−0.280831	−	0.0402279i
$547$	−8.56950	+	1.70458i	−0.366405	+	0.0728825i	−0.374859	−	0.927082i	$-0.622309\pi$
$547$	−8.56950	+	1.70458i	−0.366405	+	0.0728825i	0.00845400	+	0.999964i	$0.497309\pi$
$548$	6.73200	+	2.59834i	0.287577	+	0.110995i
$549$	11.1489	−	20.1556i	0.475825	−	0.860219i
$550$	0.417147	−	2.23927i	0.0177872	−	0.0954829i
$551$	1.47645	−	3.56447i	0.0628990	−	0.151852i
$552$	−16.4697	+	8.38923i	−0.700997	+	0.357069i
$553$	−14.7993	−	35.7287i	−0.629331	−	1.51934i
$554$	−1.04015	−	4.91566i	−0.0441917	−	0.208846i
$555$	−1.47746	+	0.0619383i	−0.0627146	+	0.00262913i
$556$	−28.7429	+	20.2346i	−1.21897	+	0.858138i
$557$	20.8881	−	31.2612i	0.885056	−	1.32458i	−0.0601782	−	0.998188i	$-0.519167\pi$
$557$	20.8881	−	31.2612i	0.885056	−	1.32458i	0.945234	−	0.326392i	$-0.105833\pi$
$558$	−20.2493	−	6.19138i	−0.857223	−	0.262102i
$559$	1.72030	+	1.72030i	0.0727608	+	0.0727608i
$560$	9.80188	−	2.45116i	0.414205	−	0.103580i
$561$	11.8456	+	7.21627i	0.500123	+	0.304671i
$562$	0.130090	+	10.6856i	0.00548753	+	0.450744i
$563$	−21.6831	+	32.4511i	−0.913835	+	1.36765i	0.0160783	+	0.999871i	$0.494882\pi$
$563$	−21.6831	+	32.4511i	−0.913835	+	1.36765i	−0.929913	+	0.367780i	$0.880118\pi$
$564$	−15.7329	+	7.77419i	−0.662477	+	0.327353i
$565$	−0.905360	+	4.55155i	−0.0380888	+	0.191485i
$566$	−8.04601	+	12.3650i	−0.338199	+	0.519738i
$567$	22.1598	+	5.07436i	0.930624	+	0.213103i
$568$	11.7630	+	10.9337i	0.493565	+	0.458769i
$569$	−11.1604	+	26.9437i	−0.467870	+	1.12954i	0.497222	+	0.867623i	$0.334354\pi$
$569$	−11.1604	+	26.9437i	−0.467870	+	1.12954i	−0.965091	+	0.261914i	$0.915646\pi$
$570$	4.19469	+	3.76393i	0.175696	+	0.157654i
$571$	9.73116	−	6.50215i	0.407236	−	0.272107i	−0.335036	−	0.942205i	$-0.608748\pi$
$571$	9.73116	−	6.50215i	0.407236	−	0.272107i	0.742272	+	0.670099i	$0.233748\pi$
$572$	3.45030	−	0.0840230i	0.144264	−	0.00351318i
$573$	8.83066	+	19.0236i	0.368906	+	0.794720i
$574$	−0.363596	+	0.155819i	−0.0151762	+	0.00650375i
$575$	3.77288			0.157340
$576$	−23.7054	+	3.74870i	−0.987726	+	0.156196i
$577$	12.9165			0.537721			0.268860	−	0.963179i	$-0.413353\pi$
$577$	12.9165			0.537721			0.268860	+	0.963179i	$0.413353\pi$
$578$	10.0366	−	4.30119i	0.417469	−	0.178906i
$579$	−19.4604	−	41.9228i	−0.808746	−	1.74225i
$580$	−0.0816470	−	3.35273i	−0.00339021	−	0.139215i
$581$	−24.3540	+	16.2728i	−1.01037	+	0.675111i
$582$	−0.855473	−	0.767624i	−0.0354605	−	0.0318190i
$583$	6.67727	−	16.1204i	0.276544	−	0.667637i
$584$	−13.0928	+	0.478379i	−0.541783	+	0.0197954i
$585$	−2.45505	−	2.07460i	−0.101504	−	0.0857742i
$586$	16.9808	−	26.0957i	0.701469	−	1.07800i
$587$	−5.05908	+	25.4337i	−0.208810	+	1.04976i	0.724112	+	0.689683i	$0.242250\pi$
$587$	−5.05908	+	25.4337i	−0.208810	+	1.04976i	−0.932922	+	0.360078i	$0.882750\pi$
$588$	−0.950970	−	1.92452i	−0.0392174	−	0.0793657i
$589$	6.37973	−	9.54795i	0.262872	−	0.393416i
$590$	−0.0500667	−	4.11246i	−0.00206121	−	0.169307i
$591$	9.07605	+	5.52906i	0.373339	+	0.227435i
$592$	2.03326	+	2.74379i	0.0835666	+	0.112769i
$593$	−23.3893	−	23.3893i	−0.960482	−	0.960482i	0.0387660	−	0.999248i	$-0.487657\pi$
$593$	−23.3893	−	23.3893i	−0.960482	−	0.960482i	−0.999248	+	0.0387660i	$0.987657\pi$
$594$	−11.8155	−	0.691796i	−0.484798	−	0.0283847i
$595$	6.97742	−	10.4424i	0.286046	−	0.428099i
$596$	−0.159129	−	0.226039i	−0.00651816	−	0.00925894i
$597$	−33.8563	+	1.41933i	−1.38565	+	0.0580892i
$598$	1.18344	+	5.59283i	0.0483944	+	0.228708i
$599$	−14.7425	−	35.5915i	−0.602362	−	1.45423i	−0.871143	−	0.491029i	$-0.836621\pi$
$599$	−14.7425	−	35.5915i	−0.602362	−	1.45423i	0.268782	−	0.963201i	$-0.413379\pi$
$600$	4.65902	+	1.51443i	0.190204	+	0.0618264i
$601$	−9.47695	+	22.8794i	−0.386573	+	0.933269i	0.604088	+	0.796918i	$0.293538\pi$
$601$	−9.47695	+	22.8794i	−0.386573	+	0.933269i	−0.990661	+	0.136352i	$0.956462\pi$
$602$	1.48550	−	7.97428i	0.0605446	−	0.325007i
$603$	−29.8220	−	16.4959i	−1.21445	−	0.671764i
$604$	12.4383	−	32.2262i	0.506106	−	1.31127i
$605$	8.24431	−	1.63989i	0.335179	−	0.0666712i
$606$	16.5620	+	2.37244i	0.672785	+	0.0963738i
$607$	−43.8635			−1.78036			−0.890182	−	0.455605i	$-0.849423\pi$
$607$	−43.8635			−1.78036			−0.890182	+	0.455605i	$0.849423\pi$
$608$	1.75794	−	12.8961i	0.0712940	−	0.523007i
$609$	7.12910	−	1.73137i	0.288886	−	0.0701587i
$610$	10.0814	+	4.03280i	0.408186	+	0.163283i
$611$	1.05889	+	5.32339i	0.0428381	+	0.215361i
$612$	−18.6946	+	23.2482i	−0.755684	+	0.939751i
$613$	32.4040	−	21.6517i	1.30879	−	0.874503i	0.311656	−	0.950195i	$-0.399117\pi$
$613$	32.4040	−	21.6517i	1.30879	−	0.874503i	0.997131	+	0.0756918i	$0.0241165\pi$
$614$	7.62642	−	40.9391i	0.307777	−	1.65217i
$615$	−0.189520	−	0.0295068i	−0.00764219	−	0.00118983i
$616$	−6.73809	−	9.32800i	−0.271485	−	0.375836i
$617$	29.7498	−	12.3228i	1.19768	−	0.496096i	0.307432	−	0.951570i	$-0.400530\pi$
$617$	29.7498	−	12.3228i	1.19768	−	0.496096i	0.890249	+	0.455474i	$0.150530\pi$
$618$	−4.59567	+	2.20169i	−0.184865	+	0.0885648i
$619$	−0.732516	+	3.68261i	−0.0294423	+	0.148016i	−0.992710	−	0.120526i	$-0.961542\pi$
$619$	−0.732516	+	3.68261i	−0.0294423	+	0.148016i	0.963268	+	0.268542i	$0.0865419\pi$
$620$	1.70845	−	9.83457i	0.0686128	−	0.394966i
$621$	−2.45766	−	19.4498i	−0.0986223	−	0.780493i
$622$	−9.85419	−	9.61714i	−0.395117	−	0.385612i
$623$	−23.3966	+	23.3966i	−0.937363	+	0.937363i
$624$	−0.783564	+	7.38147i	−0.0313677	+	0.295495i
$625$	−0.707107	−	0.707107i	−0.0282843	−	0.0282843i
$626$	−0.295172	−	24.2453i	−0.0117975	−	0.969039i
$627$	2.20577	−	6.02773i	0.0880899	−	0.240724i
$628$	23.8531	+	15.1114i	0.951843	+	0.603010i
$629$	4.16337	+	0.828146i	0.166004	+	0.0330203i
$630$	−1.07393	+	10.6627i	−0.0427865	+	0.424811i
$631$	−10.2998	−	24.8659i	−0.410029	−	0.989897i	−0.985129	−	0.171815i	$-0.945037\pi$
$631$	−10.2998	−	24.8659i	−0.410029	−	0.989897i	0.575100	−	0.818083i	$-0.304963\pi$
$632$	−39.3757	+	18.0214i	−1.56628	+	0.716852i
$633$	36.0154	+	5.60731i	1.43148	+	0.222871i
$634$	0.00339602	−	0.00232944i	0.000134873	−	9.25140e-5i
$635$	−0.336810	−	0.504073i	−0.0133659	−	0.0200035i
$636$	32.5147	+	18.7379i	1.28929	+	0.743007i
$637$	−0.651179	+	0.129527i	−0.0258006	+	0.00513207i
$638$	−3.51075	+	1.50453i	−0.138992	+	0.0595648i
$639$	−15.1365	+	7.81290i	−0.598790	+	0.309073i
$640$	−3.14363	−	10.8682i	−0.124263	−	0.429603i
$641$		−	11.5716i		−	0.457049i	−0.973538	−	0.228525i	$-0.926610\pi$
$641$		−	11.5716i		−	0.457049i	0.973538	−	0.228525i	$-0.0733902\pi$
$642$	−24.2145	+	18.1465i	−0.955671	+	0.716184i
$643$	3.23824	+	16.2797i	0.127704	+	0.642010i	0.990618	+	0.136660i	$0.0436366\pi$
$643$	3.23824	+	16.2797i	0.127704	+	0.642010i	−0.862914	+	0.505350i	$0.831363\pi$
$644$	13.1454	−	13.8016i	0.518000	−	0.543859i
$645$	2.66212	−	2.89509i	0.104821	−	0.113994i
$646$	−9.15126	−	13.3413i	−0.360051	−	0.524908i
$647$	7.69523	+	3.18747i	0.302531	+	0.125312i	0.528785	−	0.848756i	$-0.322648\pi$
$647$	7.69523	+	3.18747i	0.302531	+	0.125312i	−0.226254	+	0.974068i	$0.572648\pi$
$648$	4.77224	−	25.0045i	0.187471	−	0.982270i
$649$	−4.32747	+	1.79250i	−0.169868	+	0.0703617i
$650$	0.826402	−	1.27000i	0.0324141	−	0.0498134i
$651$	21.8163	−	0.914588i	0.855050	−	0.0358455i
$652$	−22.1497	+	34.9631i	−0.867450	+	1.36926i
$653$	−8.43770	−	5.63789i	−0.330193	−	0.220628i	0.379412	−	0.925228i	$-0.376126\pi$
$653$	−8.43770	−	5.63789i	−0.330193	−	0.220628i	−0.709604	+	0.704600i	$0.751126\pi$
$654$	16.3278	−	4.17649i	0.638467	−	0.163314i
$655$	13.9323	−	13.9323i	0.544381	−	0.544381i
$656$	0.189229	+	0.400497i	0.00738815	+	0.0156368i
$657$	4.22466	−	13.2385i	0.164820	−	0.516483i
$658$	12.6395	−	12.9510i	0.492737	−	0.504883i
$659$	40.6038	+	27.1306i	1.58170	+	1.05686i	0.962375	+	0.271726i	$0.0875943\pi$
$659$	40.6038	+	27.1306i	1.58170	+	1.05686i	0.619327	+	0.785133i	$0.287406\pi$
$660$	−0.369341	−	5.56720i	−0.0143766	−	0.216703i
$661$	−8.33263	−	1.65746i	−0.324102	−	0.0644678i	0.0303581	−	0.999539i	$-0.490335\pi$
$661$	−8.33263	−	1.65746i	−0.324102	−	0.0644678i	−0.354460	+	0.935071i	$0.615335\pi$
$662$	−8.27272	−	39.0962i	−0.321528	−	1.51952i
$663$	5.44297	+	7.45036i	0.211388	+	0.289348i
$664$	19.2052	+	26.5871i	0.745307	+	1.03178i
$665$	−5.36931	−	2.22404i	−0.208213	−	0.0862447i
$666$	−3.46854	+	1.04382i	−0.134403	+	0.0404472i
$667$	−3.51487	−	5.26037i	−0.136096	−	0.203682i
$668$	18.0466	+	40.7340i	0.698243	+	1.57604i
$669$	−17.2575	−	37.1771i	−0.667213	−	1.43735i
$670$	5.96690	−	14.9164i	0.230522	−	0.576272i
$671$		−	12.3663i		−	0.477396i
$672$	21.7728	−	11.7667i	0.839905	−	0.453909i
$673$			4.07049i			0.156906i	0.996918	+	0.0784529i	$0.0249980\pi$
$673$			4.07049i			0.156906i	−0.996918	+	0.0784529i	$0.975002\pi$
$674$	−40.9033	−	16.3622i	−1.57554	−	0.630249i
$675$	−3.18464	+	4.10586i	−0.122577	+	0.158035i
$676$	−22.1141	−	8.53535i	−0.850544	−	0.328283i
$677$	18.6377	+	27.8934i	0.716307	+	1.07203i	0.993787	+	0.111298i	$0.0355007\pi$
$677$	18.6377	+	27.8934i	0.716307	+	1.07203i	−0.277480	+	0.960731i	$0.589499\pi$
$678$	0.614352	+	11.3508i	0.0235940	+	0.435924i
$679$	1.09503	+	0.453576i	0.0420233	+	0.0174066i
$680$	−11.9705	−	7.38086i	−0.459047	−	0.283043i
$681$	−7.20741	+	5.26548i	−0.276188	+	0.201774i
$682$	−11.1221	+	2.35342i	−0.425885	+	0.0901170i
$683$	−13.2346	−	2.63253i	−0.506408	−	0.100731i	−0.0647273	−	0.997903i	$-0.520618\pi$
$683$	−13.2346	−	2.63253i	−0.506408	−	0.100731i	−0.441681	+	0.897172i	$0.645618\pi$
$684$	12.2391	+	6.38591i	0.467974	+	0.244171i
$685$	−2.99996	−	2.00451i	−0.114622	−	0.0765883i
$686$	19.4797	+	19.0111i	0.743737	+	0.725845i
$687$	28.7941	+	17.5412i	1.09856	+	0.669237i
$688$	−8.98404	−	1.33626i	−0.342513	−	0.0509443i
$689$	8.20730	−	8.20730i	0.312673	−	0.312673i
$690$	8.95336	−	2.29018i	0.340849	−	0.0871858i
$691$	−18.8347	−	12.5849i	−0.716505	−	0.478753i	0.143103	−	0.989708i	$-0.454292\pi$
$691$	−18.8347	−	12.5849i	−0.716505	−	0.478753i	−0.859608	+	0.510954i	$0.829292\pi$
$692$	1.49203	+	6.65039i	0.0567183	+	0.252810i
$693$	11.7293	−	3.37465i	0.445560	−	0.128192i
$694$	−19.2085	−	12.4992i	−0.729145	−	0.474463i
$695$	16.2376	−	6.72585i	0.615929	−	0.255126i
$696$	−2.22890	−	7.90675i	−0.0844864	−	0.299705i
$697$	0.508682	+	0.210703i	0.0192677	+	0.00798094i
$698$	3.07286	−	2.10778i	0.116310	−	0.0797805i
$699$	−23.7446	−	21.8339i	−0.898104	−	0.825833i
$700$	−5.05036	+	0.122988i	−0.190886	+	0.00464852i
$701$	−7.59487	−	38.1820i	−0.286854	−	1.44211i	−0.808271	−	0.588811i	$-0.799596\pi$
$701$	−7.59487	−	38.1820i	−0.286854	−	1.44211i	0.521417	−	0.853302i	$-0.325404\pi$
$702$	−7.08536	−	3.43296i	−0.267420	−	0.129569i
$703$		−	1.96435i		−	0.0740868i
$704$	−10.1626	+	7.92138i	−0.383019	+	0.298548i
$705$	8.52660	−	2.07077i	0.321130	−	0.0779896i
$706$	14.5915	+	34.0487i	0.549160	+	1.28144i
$707$	−16.9217	+	3.36593i	−0.636404	+	0.126589i
$708$	−2.61513	−	9.72883i	−0.0982825	−	0.365632i
$709$	−3.23386	−	4.83982i	−0.121450	−	0.181763i	0.765763	−	0.643123i	$-0.222362\pi$
$709$	−3.23386	−	4.83982i	−0.121450	−	0.181763i	−0.887213	+	0.461360i	$0.847362\pi$
$710$	−4.54210	−	6.62179i	−0.170462	−	0.248511i
$711$	−3.84426	−	45.7694i	−0.144171	−	1.71649i
$712$	27.1376	+	25.2244i	1.01702	+	0.945325i
$713$	−7.20599	−	17.3968i	−0.269866	−	0.651515i
$714$	10.2193	−	29.0162i	0.382449	−	1.08590i
$715$	−1.69250	−	0.336660i	−0.0632960	−	0.0125904i
$716$	2.46927	+	11.0063i	0.0922810	+	0.411323i
$717$	12.8118	+	4.68830i	0.478464	+	0.175088i
$718$	13.6847	−	0.166603i	0.510708	−	0.00621755i
$719$	36.7344	+	36.7344i	1.36996	+	1.36996i	0.860482	+	0.509480i	$0.170162\pi$
$719$	36.7344	+	36.7344i	1.36996	+	1.36996i	0.509480	+	0.860482i	$0.329838\pi$
$720$	11.9755	+	0.765789i	0.446302	+	0.0285393i
$721$	3.71575	−	3.71575i	0.138382	−	0.138382i
$722$	13.5384	−	13.8721i	0.503846	−	0.516265i
$723$	−8.75075	+	23.9133i	−0.325444	+	0.889344i
$724$	−20.7313	−	29.4484i	−0.770471	−	1.09444i
$725$	−0.327140	+	1.64464i	−0.0121497	+	0.0610805i
$726$	18.5690	−	8.89601i	0.689161	−	0.330162i
$727$	−38.1535	+	15.8037i	−1.41503	+	0.586126i	−0.953608	−	0.301052i	$-0.902662\pi$
$727$	−38.1535	+	15.8037i	−1.41503	+	0.586126i	−0.461426	+	0.887179i	$0.652662\pi$
$728$	−1.76646	−	7.44797i	−0.0654695	−	0.276040i
$729$	23.2408	+	13.7428i	0.860772	+	0.508991i
$730$	6.43996	+	1.19968i	0.238354	+	0.0444022i
$731$	−9.38738	+	6.27245i	−0.347205	+	0.231995i
$732$	26.3721	+	3.45062i	0.974741	+	0.127538i
$733$	6.21965	+	31.2683i	0.229728	+	1.15492i	0.907631	+	0.419769i	$0.137889\pi$
$733$	6.21965	+	31.2683i	0.229728	+	1.15492i	−0.677903	+	0.735152i	$0.737111\pi$
$734$	16.4530	−	41.1303i	0.607292	−	1.51815i
$735$	0.253304	+	1.04301i	0.00934327	+	0.0384719i
$736$	−15.9816	−	14.1455i	−0.589089	−	0.521411i
$737$	−18.2971			−0.673982
$738$	−0.467659	+	0.0450191i	−0.0172148	+	0.00165717i
$739$	−9.24774	+	1.83949i	−0.340183	+	0.0676667i	−0.362226	−	0.932090i	$-0.617983\pi$
$739$	−9.24774	+	1.83949i	−0.340183	+	0.0676667i	0.0220424	+	0.999757i	$0.492983\pi$
$740$	−0.691652	−	1.56117i	−0.0254256	−	0.0573897i
$741$	2.89003	−	3.14295i	0.106168	−	0.115459i
$742$	−38.0442	−	7.08713i	−1.39664	−	0.260177i
$743$	−1.53949	+	3.71665i	−0.0564783	+	0.136351i	−0.949600	−	0.313465i	$-0.898510\pi$
$743$	−1.53949	+	3.71665i	−0.0564783	+	0.136351i	0.893122	+	0.449815i	$0.148510\pi$
$744$	−1.91542	−	24.3753i	−0.0702225	−	0.893642i
$745$	0.0528934	+	0.127696i	0.00193786	+	0.00467841i
$746$	−5.16521	+	1.09295i	−0.189112	+	0.0400159i
$747$	−33.4314	+	9.61859i	−1.22319	+	0.351926i
$748$	−2.74129	+	15.7801i	−0.100231	+	0.576976i
$749$	17.3359	−	25.9450i	0.633440	−	0.948009i
$750$	−2.10725	−	1.24880i	−0.0769458	−	0.0455998i
$751$	2.82090	+	2.82090i	0.102936	+	0.102936i	0.756699	−	0.653763i	$-0.226811\pi$
$751$	2.82090	+	2.82090i	0.102936	+	0.102936i	−0.653763	+	0.756699i	$0.726811\pi$
$752$	−15.0091	−	13.6142i	−0.547325	−	0.496458i
$753$	−3.53743	+	5.80675i	−0.128911	+	0.211610i
$754$	−2.54060	+	0.0309302i	−0.0925230	+	0.00112641i
$755$	−9.59561	+	14.3608i	−0.349220	+	0.522645i
$756$	3.92383	+	25.9553i	0.142708	+	0.943985i
$757$	0.316732	−	1.59232i	0.0115118	−	0.0578738i	−0.974602	−	0.223942i	$-0.928107\pi$
$757$	0.316732	−	1.59232i	0.0115118	−	0.0578738i	0.986114	+	0.166068i	$0.0531073\pi$
$758$	21.7831	+	14.1745i	0.791198	+	0.514841i
$759$	−6.20895	−	8.49883i	−0.225371	−	0.308488i
$760$	−2.26920	+	6.09925i	−0.0823124	+	0.221243i
$761$	17.4189	−	42.0529i	0.631434	−	1.52442i	−0.206385	−	0.978471i	$-0.566170\pi$
$761$	17.4189	−	42.0529i	0.631434	−	1.52442i	0.837820	−	0.545947i	$-0.183830\pi$
$762$	−1.10526	−	0.991759i	−0.0400393	−	0.0359276i
$763$	−14.4504	+	9.65548i	−0.523141	+	0.349552i
$764$	−16.7026	+	17.5364i	−0.604278	+	0.634444i
$765$	11.6652	−	9.29592i	0.421756	−	0.336095i
$766$	−0.368737	−	0.860431i	−0.0133230	−	0.0310886i
$767$	−3.11584			−0.112506
$768$	−14.0572	−	23.8829i	−0.507247	−	0.861801i
$769$	−37.8121			−1.36354			−0.681769	−	0.731567i	$-0.738789\pi$
$769$	−37.8121			−1.36354			−0.681769	+	0.731567i	$0.738789\pi$
$770$	2.26633	+	5.28839i	0.0816730	+	0.190580i
$771$	30.7214	−	14.2608i	1.10641	−	0.513590i
$772$	36.8080	−	38.6455i	1.32475	−	1.39088i
$773$	4.12556	−	2.75661i	0.148386	−	0.0991483i	−0.479161	−	0.877727i	$-0.659059\pi$
$773$	4.12556	−	2.75661i	0.148386	−	0.0991483i	0.627547	+	0.778579i	$0.284059\pi$
$774$	4.56009	−	8.48625i	0.163909	−	0.305032i
$775$	−1.90995	+	4.61102i	−0.0686073	+	0.165633i
$776$	0.462785	−	1.24389i	0.0166130	−	0.0446532i
$777$	3.01609	−	2.20345i	0.108202	−	0.0790483i
$778$	19.6622	+	12.7944i	0.704923	+	0.458701i
$779$	0.0497066	−	0.249892i	0.00178092	−	0.00895330i
$780$	1.19022	−	3.51545i	0.0426166	−	0.125873i
$781$	−5.08080	+	7.60396i	−0.181805	+	0.272091i
$782$	−26.5271	+	0.322952i	−0.948608	+	0.0115487i
$783$	8.69149	+	0.615136i	0.310608	+	0.0219832i
$784$	1.66534	−	1.83597i	0.0594764	−	0.0655704i
$785$	−9.98327	−	9.98327i	−0.356318	−	0.356318i
$786$	24.6055	−	41.5197i	0.877649	−	1.48096i
$787$	−18.4242	+	27.5737i	−0.656750	+	0.982896i	0.342312	+	0.939586i	$0.388790\pi$
$787$	−18.4242	+	27.5737i	−0.656750	+	0.982896i	−0.999062	+	0.0433095i	$0.986210\pi$
$788$	−2.10036	+	12.0906i	−0.0748221	+	0.430709i
$789$	−1.09341	−	26.0819i	−0.0389264	−	0.928541i
$790$	21.1829	−	4.48228i	0.753652	−	0.159472i
$791$	−4.48587	−	10.8298i	−0.159499	−	0.385065i
$792$	−4.25584	−	12.9872i	−0.151225	−	0.461482i
$793$	3.14800	−	7.59996i	0.111789	−	0.269882i
$794$	−25.1624	−	4.68742i	−0.892978	−	0.166350i
$795$	−13.8121	−	12.7006i	−0.489864	−	0.450444i
$796$	−15.8494	−	35.7745i	−0.561765	−	1.26799i
$797$	46.5142	−	9.25224i	1.64762	−	0.327731i	0.717939	−	0.696106i	$-0.245086\pi$
$797$	46.5142	−	9.25224i	1.64762	−	0.327731i	0.929677	+	0.368375i	$0.120086\pi$
$798$	−14.0919	−	2.01860i	−0.498846	−	0.0714578i
$799$	−25.1880			−0.891088
$800$	0.344114	+	5.64638i	0.0121663	+	0.199630i
$801$	−34.9203	+	18.0246i	−1.23385	+	0.636866i
$802$	11.9440	−	29.8583i	0.421757	−	1.05433i
$803$	−1.45550	−	7.31729i	−0.0513634	−	0.258221i
$804$	5.10551	−	39.0200i	0.180057	−	1.37613i
$805$	−7.92392	+	5.29459i	−0.279281	+	0.186610i
$806$	−7.43437	−	1.38492i	−0.261864	−	0.0487819i
$807$	5.88167	−	37.7776i	0.207045	−	1.32984i
$808$	4.45837	+	18.7979i	0.156845	+	0.661308i
$809$	38.3206	−	15.8729i	1.34728	−	0.558063i	0.411748	−	0.911298i	$-0.364918\pi$
$809$	38.3206	−	15.8729i	1.34728	−	0.558063i	0.935535	+	0.353235i	$0.114918\pi$
$810$	−5.06511	+	11.6767i	−0.177970	+	0.410276i
$811$	1.66928	−	8.39202i	0.0586163	−	0.294684i	−0.940347	−	0.340218i	$-0.889499\pi$
$811$	1.66928	−	8.39202i	0.0586163	−	0.294684i	0.998963	+	0.0455344i	$0.0144991\pi$
$812$	4.87647	+	6.92694i	0.171130	+	0.243088i
$813$	5.06873	+	1.85483i	0.177768	+	0.0650519i
$814$	−1.35826	+	1.39174i	−0.0476071	+	0.0487806i
$815$	14.6331	−	14.6331i	0.512576	−	0.512576i
$816$	−32.8873	−	10.2492i	−1.15128	−	0.358793i
$817$	3.69428	+	3.69428i	0.129247	+	0.129247i
$818$	10.8632	−	0.132253i	0.379824	−	0.00462413i
$819$	8.06754	+	0.911890i	0.281903	+	0.0318640i
$820$	−0.0484832	−	0.216104i	−0.00169311	−	0.00754667i
$821$	−54.7983	−	10.9001i	−1.91248	−	0.380415i	−0.912863	−	0.408266i	$-0.866134\pi$
$821$	−54.7983	−	10.9001i	−1.91248	−	0.380415i	−0.999612	+	0.0278512i	$0.991134\pi$
$822$	−8.33592	−	2.93586i	−0.290749	−	0.102400i
$823$	11.4434	+	27.6268i	0.398892	+	0.963011i	0.987929	+	0.154905i	$0.0495071\pi$
$823$	11.4434	+	27.6268i	0.398892	+	0.963011i	−0.589037	+	0.808106i	$0.700493\pi$
$824$	−4.30988	−	4.00604i	−0.150142	−	0.139557i
$825$	−0.429166	+	2.75651i	−0.0149417	+	0.0959694i
$826$	5.87630	+	8.56687i	0.204463	+	0.298079i
$827$	−7.60870	−	11.3872i	−0.264580	−	0.395972i	0.675264	−	0.737576i	$-0.264030\pi$
$827$	−7.60870	−	11.3872i	−0.264580	−	0.395972i	−0.939844	+	0.341604i	$0.889030\pi$
$828$	19.8569	−	10.8696i	0.690076	−	0.377745i
$829$	26.6849	−	5.30795i	0.926804	−	0.184353i	0.291461	−	0.956583i	$-0.405859\pi$
$829$	26.6849	−	5.30795i	0.926804	−	0.184353i	0.635343	+	0.772230i	$0.280859\pi$
$830$	−6.45961	−	15.0732i	−0.224216	−	0.523199i
$831$	1.45228	+	5.97991i	0.0503790	+	0.207441i
$832$	−8.26213	+	2.28121i	−0.286438	+	0.0790866i
$833$		−	3.08110i		−	0.106754i
$834$	34.4506	−	25.8175i	1.19293	−	0.893986i
$835$	−4.34589	−	21.8483i	−0.150396	−	0.756091i
$836$	7.40941	−	0.180437i	0.256260	−	0.00624054i
$837$	25.0147	+	6.84246i	0.864634	+	0.236510i
$838$	−0.243151	+	0.166785i	−0.00839950	+	0.00576149i
$839$	−14.6562	−	6.07080i	−0.505989	−	0.209587i	0.115061	−	0.993358i	$-0.463294\pi$
$839$	−14.6562	−	6.07080i	−0.505989	−	0.209587i	−0.621050	+	0.783771i	$0.713294\pi$
$840$	−11.9103	+	3.35749i	−0.410944	+	0.115845i
$841$	−24.1947	+	10.0218i	−0.834299	+	0.345578i
$842$	−6.98105	−	4.54264i	−0.240583	−	0.156550i
$843$	−0.548199	−	13.0766i	−0.0188810	−	0.450382i
$844$	9.21349	+	41.0672i	0.317141	+	1.41359i
$845$	9.85465	+	6.58466i	0.339010	+	0.226519i
$846$	18.9774	−	10.0899i	0.652455	−	0.346896i
$847$	−15.0136	+	15.0136i	−0.515875	+	0.515875i
$848$	−6.37510	+	42.8616i	−0.218922	+	1.47187i
$849$	9.39989	−	15.4301i	0.322603	−	0.529559i
$850$	5.03220	+	4.91115i	0.172603	+	0.168451i
$851$	−2.67827	−	1.78957i	−0.0918101	−	0.0613455i
$852$	−14.7983	−	12.9570i	−0.506982	−	0.443898i
$853$	−54.1584	−	10.7728i	−1.85435	−	0.368853i	−0.863558	−	0.504250i	$-0.831769\pi$
$853$	−54.1584	−	10.7728i	−1.85435	−	0.368853i	−0.990791	+	0.135397i	$0.956769\pi$
$854$	−26.8327	+	5.67779i	−0.918198	+	0.194290i
$855$	−5.27215	−	4.45514i	−0.180304	−	0.152363i
$856$	−29.7415	−	18.3383i	−1.01654	−	0.626789i
$857$	−34.8180	−	14.4221i	−1.18936	−	0.492649i	−0.301813	−	0.953367i	$-0.597592\pi$
$857$	−34.8180	−	14.4221i	−1.18936	−	0.492649i	−0.887547	+	0.460718i	$0.847592\pi$
$858$	−4.22081	+	0.228448i	−0.144096	+	0.00779908i
$859$	0.695116	+	1.04031i	0.0237170	+	0.0354951i	0.843139	−	0.537696i	$-0.180705\pi$
$859$	0.695116	+	1.04031i	0.0237170	+	0.0354951i	−0.819422	+	0.573191i	$0.805705\pi$
$860$	4.23680	+	1.63527i	0.144474	+	0.0557623i
$861$	0.439444	−	0.203989i	0.0149762	−	0.00695191i
$862$	43.2079	+	17.2841i	1.47167	+	0.588699i
$863$			38.7397i			1.31871i	0.751830	+	0.659357i	$0.229171\pi$
$863$			38.7397i			1.31871i	−0.751830	+	0.659357i	$0.770829\pi$
$864$	28.8838	−	5.45202i	0.982648	−	0.185481i
$865$		−	3.40785i		−	0.115870i
$866$	14.8184	−	37.0439i	0.503548	−	1.25880i
$867$	−12.1303	+	5.63086i	−0.411968	+	0.191234i
$868$	10.2130	+	23.0524i	0.346652	+	0.782449i
$869$	−13.7000	−	20.5035i	−0.464740	−	0.695532i
$870$	0.221988	+	4.10145i	0.00752609	+	0.139052i
$871$	−11.2448	−	4.65776i	−0.381017	−	0.157822i
$872$	11.3954	+	15.7754i	0.385897	+	0.534223i
$873$	1.07521	+	0.908590i	0.0363905	+	0.0307511i
$874$	2.54140	+	12.0104i	0.0859641	+	0.406259i
$875$	2.47739	+	0.492784i	0.0837512	+	0.0166591i
$876$	16.0108	−	1.06219i	0.540955	−	0.0358882i
$877$	19.2860	+	12.8865i	0.651243	+	0.435146i	0.836816	−	0.547484i	$-0.184414\pi$
$877$	19.2860	+	12.8865i	0.651243	+	0.435146i	−0.185574	+	0.982630i	$0.559414\pi$
$878$	7.92910	−	8.12454i	0.267594	−	0.274190i
$879$	−19.8381	+	32.5645i	−0.669121	+	1.09837i
$880$	5.82510	−	2.75227i	0.196364	−	0.0927791i
$881$	4.17139	−	4.17139i	0.140538	−	0.140538i	−0.633338	−	0.773876i	$-0.718316\pi$
$881$	4.17139	−	4.17139i	0.140538	−	0.140538i	0.773876	+	0.633338i	$0.218316\pi$
$882$	1.23423	+	2.32139i	0.0415587	+	0.0781652i
$883$	44.1573	+	29.5050i	1.48601	+	0.992922i	0.992375	+	0.123254i	$0.0393331\pi$
$883$	44.1573	+	29.5050i	1.48601	+	0.992922i	0.493638	+	0.869668i	$0.335667\pi$
$884$	−5.70173	+	9.00011i	−0.191770	+	0.302706i
$885$	0.210980	+	5.03267i	0.00709203	+	0.169171i
$886$	−3.96667	+	6.09590i	−0.133263	+	0.204796i
$887$	−46.7599	+	19.3686i	−1.57004	+	0.650333i	−0.986797	−	0.161962i	$-0.948218\pi$
$887$	−46.7599	+	19.3686i	−1.57004	+	0.650333i	−0.583246	+	0.812295i	$0.698218\pi$
$888$	−2.58900	−	3.28494i	−0.0868811	−	0.110236i
$889$	1.41476	+	0.586013i	0.0474496	+	0.0196543i
$890$	−10.4787	−	15.2766i	−0.351248	−	0.512074i
$891$	14.4898	+	0.416828i	0.485427	+	0.0139643i
$892$	32.6414	−	34.2708i	1.09291	−	1.14747i
$893$	2.27393	+	11.4318i	0.0760942	+	0.382551i
$894$	0.203033	+	0.270926i	0.00679045	+	0.00906113i
$895$		−	5.63992i		−	0.188522i
$896$	21.8540	+	18.4142i	0.730092	+	0.615175i
$897$	−1.65234	−	6.80369i	−0.0551701	−	0.227169i
$898$	21.6928	−	9.29644i	0.723899	−	0.310226i
$899$	8.20829	−	1.63273i	0.273762	−	0.0544546i
$900$	−5.75872	−	1.68439i	−0.191957	−	0.0561463i
$901$	29.9250	+	44.7859i	0.996945	+	1.49203i
$902$	−0.208007	+	0.142679i	−0.00692587	+	0.00475068i
$903$	−1.52830	+	9.81621i	−0.0508588	+	0.326663i
$904$	−11.9353	+	5.46252i	−0.396962	+	0.181681i
$905$	6.89094	+	16.6362i	0.229063	+	0.553006i
$906$	−14.0540	+	39.9042i	−0.466913	+	1.32573i
$907$	−0.207808	−	0.0413356i	−0.00690015	−	0.00137252i	0.191639	−	0.981465i	$-0.438620\pi$
$907$	−0.207808	−	0.0413356i	−0.00690015	−	0.00137252i	−0.198539	+	0.980093i	$0.563620\pi$
$908$	−8.70662	−	5.51580i	−0.288939	−	0.183048i
$909$	−20.3616	−	2.30151i	−0.675352	−	0.0763364i
$910$	0.0465915	+	3.82701i	0.00154449	+	0.126864i
$911$	23.9481	+	23.9481i	0.793436	+	0.793436i	0.982051	−	0.188615i	$-0.0603999\pi$
$911$	23.9481	+	23.9481i	0.793436	+	0.793436i	−0.188615	+	0.982051i	$0.560400\pi$
$912$	−1.68268	+	15.8515i	−0.0557191	+	0.524895i
$913$	−13.2065	+	13.2065i	−0.437072	+	0.437072i
$914$	22.9375	+	22.3857i	0.758706	+	0.740454i
$915$	−12.4885	−	4.57002i	−0.412858	−	0.151080i
$916$	−6.66346	+	38.3578i	−0.220167	+	1.26738i
$917$	−9.70946	+	48.8128i	−0.320635	+	1.61194i
$918$	22.0398	−	29.1409i	0.727421	−	0.961794i
$919$	−44.3805	+	18.3830i	−1.46398	+	0.606399i	−0.965476	−	0.260491i	$-0.916116\pi$
$919$	−44.3805	+	18.3830i	−1.46398	+	0.606399i	−0.498500	+	0.866890i	$0.666116\pi$
$920$	6.24868	+	8.65048i	0.206013	+	0.285198i
$921$	−7.84616	+	50.3954i	−0.258540	+	1.66059i
$922$	1.21852	−	6.54107i	0.0401297	−	0.215419i
$923$	−5.05819	+	3.37978i	−0.166492	+	0.111247i
$924$	8.58833	+	11.1741i	0.282535	+	0.367601i
$925$	0.166560	+	0.837356i	0.00547647	+	0.0275321i
$926$	−9.54357	−	3.81764i	−0.313621	−	0.125455i
$927$	5.54590	−	2.86259i	0.182151	−	0.0940197i
$928$	7.55194	−	5.74003i	0.247904	−	0.188426i
$929$	31.3659			1.02908			0.514540	−	0.857466i	$-0.327963\pi$
$929$	31.3659			1.02908			0.514540	+	0.857466i	$0.327963\pi$
$930$	−1.73352	+	12.1017i	−0.0568444	+	0.396830i
$931$	−1.39839	+	0.278156i	−0.0458302	+	0.00911620i
$932$	13.4120	−	34.7489i	0.439324	−	1.13824i
$933$	12.4136	+	11.4147i	0.406403	+	0.373699i
$934$	1.65182	−	8.86706i	0.0540491	−	0.290139i
$935$	3.06460	−	7.39861i	0.100223	−	0.241960i
$936$	0.690566	−	9.06494i	0.0225718	−	0.296297i
$937$	−8.95148	−	21.6108i	−0.292432	−	0.705993i	0.707568	−	0.706645i	$-0.249792\pi$
$937$	−8.95148	−	21.6108i	−0.292432	−	0.705993i	−1.00000		0.000652178i	$0.999792\pi$
$938$	8.40081	+	39.7015i	0.274296	+	1.29630i
$939$	1.24385	+	29.6705i	0.0405916	+	0.968260i
$940$	5.83238	+	8.28480i	0.190231	+	0.270220i
$941$	25.3501	−	37.9391i	0.826389	−	1.23678i	−0.142626	−	0.989777i	$-0.545555\pi$
$941$	25.3501	−	37.9391i	0.826389	−	1.23678i	0.969015	−	0.247002i	$-0.0794454\pi$
$942$	−29.7511	−	17.6312i	−0.969344	−	0.574455i
$943$	−0.295429	−	0.295429i	−0.00962050	−	0.00962050i
$944$	9.34616	−	6.92590i	0.304192	−	0.225419i
$945$	0.926605	−	13.0924i	0.0301425	−	0.425895i
$946$	−0.0629641	−	5.17185i	−0.00204714	−	0.168151i
$947$	−22.5872	+	33.8041i	−0.733984	+	1.09849i	0.257247	+	0.966346i	$0.417185\pi$
$947$	−22.5872	+	33.8041i	−0.733984	+	1.09849i	−0.991231	+	0.132139i	$0.957815\pi$
$948$	47.5479	−	23.4951i	1.54429	−	0.763085i
$949$	0.968205	−	4.86750i	0.0314293	−	0.158006i
$950$	1.77467	−	2.72728i	0.0575780	−	0.0884847i
$951$	−0.00407263	+	0.00297532i	−0.000132064	+	9.64815e-5i
$952$	35.4986	−	1.29703i	1.15052	−	0.0420371i
$953$	1.51175	−	3.64969i	0.0489705	−	0.118225i	−0.897501	−	0.441012i	$-0.854620\pi$
$953$	1.51175	−	3.64969i	0.0489705	−	0.118225i	0.946472	+	0.322787i	$0.104620\pi$
$954$	−40.4867	−	21.7555i	−1.31081	−	0.704362i
$955$	10.0682	−	6.72734i	0.325799	−	0.217692i
$956$	0.383513	+	15.7485i	0.0124037	+	0.509343i
$957$	4.24311	−	1.96964i	0.137160	−	0.0636693i
$958$	41.7501	−	17.8919i	1.34888	−	0.578063i
$959$	9.11360			0.294293
$960$	4.24403	+	13.1905i	0.136976	+	0.425720i
$961$	−6.09063			−0.196472
$962$	−1.18903	+	0.509559i	−0.0383360	+	0.0164288i
$963$	28.9830	−	23.0964i	0.933964	−	0.744270i
$964$	−29.3947	+	0.715831i	−0.946740	+	0.0230554i
$965$	−22.1875	+	14.8252i	−0.714242	+	0.477242i
$966$	−15.5903	+	17.3744i	−0.501608	+	0.559014i
$967$	11.8698	−	28.6561i	0.381706	−	0.921519i	−0.609931	−	0.792455i	$-0.708803\pi$
$967$	11.8698	−	28.6561i	0.381706	−	0.921519i	0.991636	−	0.129064i	$-0.0411973\pi$
$968$	17.4143	+	16.1866i	0.559716	+	0.520257i
$969$	11.6886	+	15.9994i	0.375492	+	0.513975i
$970$	−0.361930	+	0.556207i	−0.0116209	+	0.0178587i
$971$	1.45646	−	7.32211i	0.0467400	−	0.234978i	−0.950353	−	0.311174i	$-0.899278\pi$
$971$	1.45646	−	7.32211i	0.0467400	−	0.234978i	0.997093	+	0.0761967i	$0.0242777\pi$
$972$	−4.93206	+	30.7843i	−0.158196	+	0.987408i
$973$	−24.6642	+	36.9126i	−0.790699	+	1.18336i
$974$	−0.423793	−	34.8102i	−0.0135792	−	1.11539i
$975$	−0.965458	+	1.58482i	−0.0309194	+	0.0507548i
$976$	7.45059	+	29.7940i	0.238487	+	0.953682i
$977$	−33.8171	−	33.8171i	−1.08191	−	1.08191i	−0.996332	−	0.0855740i	$-0.972728\pi$
$977$	−33.8171	−	33.8171i	−1.08191	−	1.08191i	−0.0855740	−	0.996332i	$-0.527272\pi$
$978$	25.8432	−	43.6081i	0.826373	−	1.39443i
$979$	−11.7215	+	17.5425i	−0.374622	+	0.560662i
$980$	−1.01343	+	0.713440i	−0.0323728	+	0.0227900i
$981$	−19.8365	+	5.70719i	−0.633331	+	0.182216i
$982$	3.51581	+	16.6154i	0.112194	+	0.530220i
$983$	−11.4150	−	27.5582i	−0.364081	−	0.878970i	−0.994695	−	0.102873i	$-0.967197\pi$
$983$	−11.4150	−	27.5582i	−0.364081	−	0.878970i	0.630613	−	0.776097i	$-0.282803\pi$
$984$	−0.246232	−	0.483403i	−0.00784960	−	0.0154103i
$985$	2.34808	−	5.66877i	0.0748161	−	0.180622i
$986$	2.15934	−	11.5915i	0.0687675	−	0.369148i
$987$	−15.0019	+	16.3147i	−0.477515	+	0.519304i
$988$	4.59953	+	1.77527i	0.146330	+	0.0564788i
$989$	8.40252	−	1.67137i	0.267185	−	0.0531463i
$990$	0.654788	+	6.80194i	0.0208105	+	0.216180i
$991$	−11.0297			−0.350371			−0.175185	−	0.984535i	$-0.556052\pi$
$991$	−11.0297			−0.350371			−0.175185	+	0.984535i	$0.556052\pi$
$992$	25.3783	−	12.3710i	0.805762	−	0.392779i
$993$	11.5505	+	47.5606i	0.366546	+	1.50929i
$994$	18.8320	+	7.53323i	0.597316	+	0.238940i
$995$	3.81677	+	19.1882i	0.121000	+	0.608306i
$996$	−24.4788	−	31.8489i	−0.775641	−	1.00917i
$997$	27.1264	−	18.1253i	0.859101	−	0.574033i	−0.0461384	−	0.998935i	$-0.514692\pi$
$997$	27.1264	−	18.1253i	0.859101	−	0.574033i	0.905239	+	0.424902i	$0.139692\pi$
$998$	−0.436862	+	2.34510i	−0.0138286	+	0.0742329i
$999$	4.20821	−	1.40410i	0.133142	−	0.0444238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.11.47	✓	1024
3.2	odd	2	inner	960.2.cn.a.11.82	yes	1024
64.35	odd	16	inner	960.2.cn.a.611.82	yes	1024
192.35	even	16	inner	960.2.cn.a.611.47	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.11.47	✓	1024	1.1	even	1	trivial
960.2.cn.a.11.82	yes	1024	3.2	odd	2	inner
960.2.cn.a.611.47	yes	1024	192.35	even	16	inner
960.2.cn.a.611.82	yes	1024	64.35	odd	16	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557061 - 1.29988i) q^{2} +(0.729271 + 1.57104i) q^{3} +(-1.37937 + 1.44822i) q^{4} +(0.831470 - 0.555570i) q^{5} +(1.63591 - 1.82313i) q^{6} +(-0.966631 + 2.33365i) q^{7} +(2.65091 + 0.986257i) q^{8} +(-1.93633 + 2.29143i) q^{9} +O(q^{10})\)	\(q+(-0.557061 - 1.29988i) q^{2} +(0.729271 + 1.57104i) q^{3} +(-1.37937 + 1.44822i) q^{4} +(0.831470 - 0.555570i) q^{5} +(1.63591 - 1.82313i) q^{6} +(-0.966631 + 2.33365i) q^{7} +(2.65091 + 0.986257i) q^{8} +(-1.93633 + 2.29143i) q^{9} +(-1.18535 - 0.771322i) q^{10} +(-0.314221 + 1.57970i) q^{11} +(-3.28115 - 1.11089i) q^{12} +(-0.595243 + 0.890844i) q^{13} +(3.57194 - 0.0434862i) q^{14} +(1.47919 + 0.901110i) q^{15} +(-0.194704 - 3.99526i) q^{16} +(-3.51577 - 3.51577i) q^{17} +(4.05723 + 1.24053i) q^{18} +(-1.27827 + 1.91306i) q^{19} +(-0.342310 + 1.97049i) q^{20} +(-4.37120 + 0.183250i) q^{21} +(2.22845 - 0.471539i) q^{22} +(1.44382 + 3.48568i) q^{23} +(0.383779 + 4.88392i) q^{24} +(0.382683 - 0.923880i) q^{25} +(1.48958 + 0.277488i) q^{26} +(-5.01203 - 1.37098i) q^{27} +(-2.04632 - 4.61886i) q^{28} +(-1.64464 + 0.327140i) q^{29} +(0.347334 - 2.42474i) q^{30} -4.99093 q^{31} +(-5.08489 + 2.47870i) q^{32} +(-2.71092 + 0.658373i) q^{33} +(-2.61157 + 6.52856i) q^{34} +(0.492784 + 2.47739i) q^{35} +(-0.647593 - 5.96495i) q^{36} +(-0.709876 + 0.474324i) q^{37} +(3.19882 + 0.595898i) q^{38} +(-1.83364 - 0.285484i) q^{39} +(2.75208 - 0.652721i) q^{40} +(-0.102308 + 0.0423775i) q^{41} +(2.67323 + 5.57994i) q^{42} +(0.442995 - 2.22709i) q^{43} +(-1.85433 - 2.63404i) q^{44} +(-0.336950 + 2.98102i) q^{45} +(3.72667 - 3.81853i) q^{46} +(3.58215 - 3.58215i) q^{47} +(6.13472 - 3.21951i) q^{48} +(0.438183 + 0.438183i) q^{49} +(-1.41411 + 0.0172159i) q^{50} +(2.95946 - 8.08735i) q^{51} +(-0.469084 - 2.09084i) q^{52} +(-10.6251 - 2.11347i) q^{53} +(1.00990 + 7.27874i) q^{54} +(0.616367 + 1.48804i) q^{55} +(-4.86403 + 5.23295i) q^{56} +(-3.93769 - 0.613067i) q^{57} +(1.34141 + 1.95560i) q^{58} +(1.61569 + 2.41805i) q^{59} +(-3.34535 + 0.899236i) q^{60} +(-7.53033 + 1.49788i) q^{61} +(2.78025 + 6.48760i) q^{62} +(-3.47568 - 6.73368i) q^{63} +(6.05460 + 5.22895i) q^{64} +1.07141i q^{65} +(2.36595 + 3.15711i) q^{66} +(2.21625 + 11.1418i) q^{67} +(9.94114 - 0.242091i) q^{68} +(-4.42321 + 4.81030i) q^{69} +(2.94580 - 2.02062i) q^{70} +(5.24577 + 2.17287i) q^{71} +(-7.39296 + 4.16464i) q^{72} +(-4.27949 + 1.77262i) q^{73} +(1.01201 + 0.658525i) q^{74} +(1.73053 - 0.0725476i) q^{75} +(-1.00734 - 4.49002i) q^{76} +(-3.38273 - 2.26027i) q^{77} +(0.650359 + 2.54255i) q^{78} +(-10.8259 + 10.8259i) q^{79} +(-2.38154 - 3.21376i) q^{80} +(-1.50126 - 8.87391i) q^{81} +(0.112078 + 0.109382i) q^{82} +(9.64161 + 6.44232i) q^{83} +(5.76409 - 6.58324i) q^{84} +(-4.87651 - 0.969998i) q^{85} +(-3.14171 + 0.664784i) q^{86} +(-1.71334 - 2.34522i) q^{87} +(-2.39096 + 3.87772i) q^{88} +(12.1021 + 5.01286i) q^{89} +(4.06266 - 1.22262i) q^{90} +(-1.50354 - 2.25021i) q^{91} +(-7.03960 - 2.71706i) q^{92} +(-3.63974 - 7.84094i) q^{93} +(-6.65184 - 2.66088i) q^{94} +2.30082i q^{95} +(-7.60239 - 6.18092i) q^{96} -0.469233i q^{97} +(0.325490 - 0.813680i) q^{98} +(-3.01132 - 3.77883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more