LMFDB - Embedded newform 960.2.cn.a.611.82

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			611.82
Character	$\chi$	$=$	960.611
Dual form			960.2.cn.a.11.82

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557061 - 1.29988i) q^{2} +(-0.0725476 - 1.73053i) q^{3} +(-1.37937 - 1.44822i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-2.28989 - 0.869709i) q^{6} +(-0.966631 - 2.33365i) q^{7} +(-2.65091 + 0.986257i) q^{8} +(-2.98947 + 0.251092i) q^{9} +O(q^{10})$	\(q+(0.557061 - 1.29988i) q^{2} +(-0.0725476 - 1.73053i) q^{3} +(-1.37937 - 1.44822i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-2.28989 - 0.869709i) q^{6} +(-0.966631 - 2.33365i) q^{7} +(-2.65091 + 0.986257i) q^{8} +(-2.98947 + 0.251092i) q^{9} +(-1.18535 + 0.771322i) q^{10} +(0.314221 + 1.57970i) q^{11} +(-2.40613 + 2.49210i) q^{12} +(-0.595243 - 0.890844i) q^{13} +(-3.57194 - 0.0434862i) q^{14} +(-0.901110 + 1.47919i) q^{15} +(-0.194704 + 3.99526i) q^{16} +(3.51577 - 3.51577i) q^{17} +(-1.33893 + 4.02582i) q^{18} +(-1.27827 - 1.91306i) q^{19} +(0.342310 + 1.97049i) q^{20} +(-3.96833 + 1.84209i) q^{21} +(2.22845 + 0.471539i) q^{22} +(-1.44382 + 3.48568i) q^{23} +(1.89906 + 4.51592i) q^{24} +(0.382683 + 0.923880i) q^{25} +(-1.48958 + 0.277488i) q^{26} +(0.651401 + 5.15516i) q^{27} +(-2.04632 + 4.61886i) q^{28} +(1.64464 + 0.327140i) q^{29} +(1.42079 + 1.99533i) 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} +(4.48721 + 3.98308i) q^{36} +(-0.709876 - 0.474324i) q^{37} +(-3.19882 + 0.595898i) q^{38} +(-1.49845 + 1.09472i) q^{39} +(2.75208 + 0.652721i) q^{40} +(0.102308 + 0.0423775i) q^{41} +(0.183881 + 6.18450i) q^{42} +(0.442995 + 2.22709i) q^{43} +(1.85433 - 2.63404i) q^{44} +(2.62516 + 1.45209i) q^{45} +(3.72667 + 3.81853i) q^{46} +(-3.58215 - 3.58215i) q^{47} +(6.92804 + 0.0470943i) q^{48} +(0.438183 - 0.438183i) q^{49} +(1.41411 + 0.0172159i) q^{50} +(-6.33920 - 5.82908i) q^{51} +(-0.469084 + 2.09084i) q^{52} +(10.6251 - 2.11347i) q^{53} +(7.06395 + 2.02500i) q^{54} +(0.616367 - 1.48804i) q^{55} +(4.86403 + 5.23295i) q^{56} +(-3.21787 + 2.35087i) q^{57} +(1.34141 - 1.95560i) q^{58} +(-1.61569 + 2.41805i) q^{59} +(3.38516 - 0.735333i) 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} +(0.654344 - 3.89062i) q^{66} +(2.21625 - 11.1418i) q^{67} +(-9.94114 - 0.242091i) q^{68} +(6.13683 + 2.24569i) q^{69} +(2.94580 + 2.02062i) q^{70} +(-5.24577 + 2.17287i) q^{71} +(7.67717 - 3.61401i) q^{72} +(-4.27949 - 1.77262i) q^{73} +(-1.01201 + 0.658525i) q^{74} +(1.57104 - 0.729271i) q^{75} +(-1.00734 + 4.49002i) q^{76} +(3.38273 - 2.26027i) q^{77} +(0.588267 + 2.55763i) q^{78} +(-10.8259 - 10.8259i) q^{79} +(2.38154 - 3.21376i) q^{80} +(8.87391 - 1.50126i) q^{81} +(0.112078 - 0.109382i) q^{82} +(-9.64161 + 6.44232i) q^{83} +(8.14153 + 3.20612i) q^{84} +(-4.87651 + 0.969998i) q^{85} +(3.14171 + 0.664784i) q^{86} +(0.446810 - 2.86984i) q^{87} +(-2.39096 - 3.87772i) q^{88} +(-12.1021 + 5.01286i) q^{89} +(3.34991 - 2.60348i) q^{90} +(-1.50354 + 2.25021i) q^{91} +(7.03960 - 2.71706i) q^{92} +(0.362080 + 8.63696i) q^{93} +(-6.65184 + 2.66088i) q^{94} +2.30082i q^{95} +(3.92056 - 8.97938i) q^{96} +0.469233i q^{97} +(-0.325490 - 0.813680i) q^{98} +(-1.33600 - 4.64356i) 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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{11}{16}\right)$

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
$3$	−0.0725476	−	1.73053i	−0.0418854	−	0.999122i
$3$	−0.0725476	−	1.73053i	−0.0418854	−	0.999122i
$4$	−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
$6$	−2.28989	−	0.869709i	−0.934845	−	0.355057i
$7$	−0.966631	−	2.33365i	−0.365352	−	0.882038i	−0.994498	−	0.104751i	$-0.966595\pi$
$7$	−0.966631	−	2.33365i	−0.365352	−	0.882038i	0.629146	−	0.777287i	$-0.283405\pi$
$8$	−2.65091	+	0.986257i	−0.937236	+	0.348694i
$9$	−2.98947	+	0.251092i	−0.996491	+	0.0836972i
$10$	−1.18535	+	0.771322i	−0.374842	+	0.243914i
$11$	0.314221	+	1.57970i	0.0947413	+	0.476297i	0.998804	+	0.0488965i	$0.0155704\pi$
$11$	0.314221	+	1.57970i	0.0947413	+	0.476297i	−0.904063	+	0.427400i	$0.859430\pi$
$12$	−2.40613	+	2.49210i	−0.694589	+	0.719407i
$13$	−0.595243	−	0.890844i	−0.165091	−	0.247076i	0.739696	−	0.672942i	$-0.234970\pi$
$13$	−0.595243	−	0.890844i	−0.165091	−	0.247076i	−0.904786	+	0.425866i	$0.859970\pi$
$14$	−3.57194	−	0.0434862i	−0.954641	−	0.0116222i
$15$	−0.901110	+	1.47919i	−0.232666	+	0.381925i
$16$	−0.194704	+	3.99526i	−0.0486759	+	0.998815i
$17$	3.51577	−	3.51577i	0.852698	−	0.852698i	−0.137766	−	0.990465i	$-0.543992\pi$
$17$	3.51577	−	3.51577i	0.852698	−	0.852698i	0.990465	+	0.137766i	$0.0439923\pi$
$18$	−1.33893	+	4.02582i	−0.315589	+	0.948896i
$19$	−1.27827	−	1.91306i	−0.293254	−	0.438886i	0.655362	−	0.755315i	$-0.272516\pi$
$19$	−1.27827	−	1.91306i	−0.293254	−	0.438886i	−0.948616	+	0.316429i	$0.897516\pi$
$20$	0.342310	+	1.97049i	0.0765429	+	0.440615i
$21$	−3.96833	+	1.84209i	−0.865961	+	0.401976i
$22$	2.22845	+	0.471539i	0.475108	+	0.100532i
$23$	−1.44382	+	3.48568i	−0.301057	+	0.726815i	0.698876	+	0.715243i	$0.253684\pi$
$23$	−1.44382	+	3.48568i	−0.301057	+	0.726815i	−0.999933	+	0.0115727i	$0.996316\pi$
$24$	1.89906	+	4.51592i	0.387645	+	0.921809i
$25$	0.382683	+	0.923880i	0.0765367	+	0.184776i
$26$	−1.48958	+	0.277488i	−0.292130	+	0.0544200i
$27$	0.651401	+	5.15516i	0.125362	+	0.992111i
$28$	−2.04632	+	4.61886i	−0.386717	+	0.872882i
$29$	1.64464	+	0.327140i	0.305402	+	0.0607483i	0.345412	−	0.938451i	$-0.387739\pi$
$29$	1.64464	+	0.327140i	0.305402	+	0.0607483i	−0.0400102	+	0.999199i	$0.512739\pi$
$30$	1.42079	+	1.99533i	0.259400	+	0.364296i
$31$	−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
$36$	4.48721	+	3.98308i	0.747869	+	0.663847i
$37$	−0.709876	−	0.474324i	−0.116703	−	0.0779784i	0.495849	−	0.868409i	$-0.334857\pi$
$37$	−0.709876	−	0.474324i	−0.116703	−	0.0779784i	−0.612552	+	0.790430i	$0.709857\pi$
$38$	−3.19882	+	0.595898i	−0.518917	+	0.0966674i
$39$	−1.49845	+	1.09472i	−0.239944	+	0.175295i
$40$	2.75208	+	0.652721i	0.435142	+	0.103204i
$41$	0.102308	+	0.0423775i	0.0159779	+	0.00661826i	0.390658	−	0.920536i	$-0.372247\pi$
$41$	0.102308	+	0.0423775i	0.0159779	+	0.00661826i	−0.374680	+	0.927154i	$0.622247\pi$
$42$	0.183881	+	6.18450i	0.0283735	+	0.954290i
$43$	0.442995	+	2.22709i	0.0675561	+	0.339627i	0.999751	−	0.0223302i	$-0.00710851\pi$
$43$	0.442995	+	2.22709i	0.0675561	+	0.339627i	−0.932195	+	0.361958i	$0.882109\pi$
$44$	1.85433	−	2.63404i	0.279551	−	0.397097i
$45$	2.62516	+	1.45209i	0.391335	+	0.216464i
$46$	3.72667	+	3.81853i	0.549467	+	0.563011i
$47$	−3.58215	−	3.58215i	−0.522511	−	0.522511i	0.395818	−	0.918329i	$-0.370461\pi$
$47$	−3.58215	−	3.58215i	−0.522511	−	0.522511i	−0.918329	+	0.395818i	$0.870461\pi$
$48$	6.92804	+	0.0470943i	0.999977	+	0.00679748i
$49$	0.438183	−	0.438183i	0.0625976	−	0.0625976i
$50$	1.41411	+	0.0172159i	0.199985	+	0.00243470i
$51$	−6.33920	−	5.82908i	−0.887666	−	0.816235i
$52$	−0.469084	+	2.09084i	−0.0650503	+	0.289948i
$53$	10.6251	−	2.11347i	1.45947	−	0.290307i	0.599387	−	0.800459i	$-0.295411\pi$
$53$	10.6251	−	2.11347i	1.45947	−	0.290307i	0.860084	+	0.510152i	$0.170411\pi$
$54$	7.06395	+	2.02500i	0.961282	+	0.275567i
$55$	0.616367	−	1.48804i	0.0831109	−	0.200648i
$56$	4.86403	+	5.23295i	0.649983	+	0.699282i
$57$	−3.21787	+	2.35087i	−0.426218	+	0.311380i
$58$	1.34141	−	1.95560i	0.176135	−	0.256782i
$59$	−1.61569	+	2.41805i	−0.210345	+	0.314803i	−0.921608	−	0.388123i	$-0.873124\pi$
$59$	−1.61569	+	2.41805i	−0.210345	+	0.314803i	0.711263	+	0.702926i	$0.248124\pi$
$60$	3.38516	−	0.735333i	0.437022	−	0.0949310i
$61$	−7.53033	−	1.49788i	−0.964160	−	0.191783i	−0.312183	−	0.950022i	$-0.601060\pi$
$61$	−7.53033	−	1.49788i	−0.964160	−	0.191783i	−0.651977	+	0.758239i	$0.726060\pi$
$62$	−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
$66$	0.654344	−	3.89062i	0.0805442	−	0.478902i
$67$	2.21625	−	11.1418i	0.270758	−	1.36119i	−0.570829	−	0.821069i	$-0.693378\pi$
$67$	2.21625	−	11.1418i	0.270758	−	1.36119i	0.841587	−	0.540122i	$-0.181622\pi$
$68$	−9.94114	−	0.242091i	−1.20554	−	0.0293578i
$69$	6.13683	+	2.24569i	0.738787	+	0.270350i
$70$	2.94580	+	2.02062i	0.352090	+	0.241510i
$71$	−5.24577	+	2.17287i	−0.622558	+	0.257872i	−0.671587	−	0.740925i	$-0.734387\pi$
$71$	−5.24577	+	2.17287i	−0.622558	+	0.257872i	0.0490295	+	0.998797i	$0.484387\pi$
$72$	7.67717	−	3.61401i	0.904763	−	0.425915i
$73$	−4.27949	−	1.77262i	−0.500876	−	0.207470i	0.117917	−	0.993023i	$-0.462378\pi$
$73$	−4.27949	−	1.77262i	−0.500876	−	0.207470i	−0.618793	+	0.785554i	$0.712378\pi$
$74$	−1.01201	+	0.658525i	−0.117644	+	0.0765519i
$75$	1.57104	−	0.729271i	0.181408	−	0.0842089i
$76$	−1.00734	+	4.49002i	−0.115550	+	0.515041i
$77$	3.38273	−	2.26027i	0.385498	−	0.257581i
$78$	0.588267	+	2.55763i	0.0666082	+	0.289594i
$79$	−10.8259	−	10.8259i	−1.21801	−	1.21801i	−0.968326	−	0.249687i	$-0.919672\pi$
$79$	−10.8259	−	10.8259i	−1.21801	−	1.21801i	−0.249687	−	0.968326i	$-0.580328\pi$
$80$	2.38154	−	3.21376i	0.266264	−	0.359310i
$81$	8.87391	−	1.50126i	0.985990	−	0.166807i
$82$	0.112078	−	0.109382i	0.0123769	−	0.0120792i
$83$	−9.64161	+	6.44232i	−1.05830	+	0.707136i	−0.957694	−	0.287790i	$-0.907080\pi$
$83$	−9.64161	+	6.44232i	−1.05830	+	0.707136i	−0.100610	+	0.994926i	$0.532080\pi$
$84$	8.14153	+	3.20612i	0.888314	+	0.349817i
$85$	−4.87651	+	0.969998i	−0.528931	+	0.105211i
$86$	3.14171	+	0.664784i	0.338780	+	0.0716855i
$87$	0.446810	−	2.86984i	0.0479031	−	0.307679i
$88$	−2.39096	−	3.87772i	−0.254877	−	0.413367i
$89$	−12.1021	+	5.01286i	−1.28282	+	0.531362i	−0.916838	−	0.399259i	$-0.869267\pi$
$89$	−12.1021	+	5.01286i	−1.28282	+	0.531362i	−0.365983	+	0.930621i	$0.619267\pi$
$90$	3.34991	−	2.60348i	0.353111	−	0.274431i
$91$	−1.50354	+	2.25021i	−0.157614	+	0.235886i
$92$	7.03960	−	2.71706i	0.733929	−	0.283273i
$93$	0.362080	+	8.63696i	0.0375459	+	0.895611i
$94$	−6.65184	+	2.66088i	−0.686085	+	0.274449i
$95$			2.30082i			0.236059i
$96$	3.92056	−	8.97938i	0.400141	−	0.916454i
$97$			0.469233i			0.0476434i	0.999716	+	0.0238217i	$0.00758341\pi$
$97$			0.469233i			0.0476434i	−0.999716	+	0.0238217i	$0.992417\pi$
$98$	−0.325490	−	0.813680i	−0.0328794	−	0.0821941i
$99$	−1.33600	−	4.64356i	−0.134274	−	0.466696i
$100$	0.810124	−	1.82858i	0.0810124	−	0.182858i
$101$	−3.79478	+	5.67929i	−0.377595	+	0.565111i	−0.970785	−	0.239952i	$-0.922868\pi$
$101$	−3.79478	+	5.67929i	−0.377595	+	0.565111i	0.593190	+	0.805063i	$0.297868\pi$
$102$	−11.1084	+	4.99303i	−1.09990	+	0.494384i
$103$	−1.92201	+	0.796123i	−0.189381	+	0.0784443i	−0.475359	−	0.879792i	$-0.657682\pi$
$103$	−1.92201	+	0.796123i	−0.189381	+	0.0784443i	0.285978	+	0.958236i	$0.407682\pi$
$104$	2.45653	+	1.77448i	0.240883	+	0.174002i
$105$	4.32296	+	0.673049i	0.421877	+	0.0656829i
$106$	3.17159	−	14.9887i	0.308052	−	1.45583i
$107$	12.1160	−	2.41003i	1.17130	−	0.232986i	0.429158	−	0.903229i	$-0.358810\pi$
$107$	12.1160	−	2.41003i	1.17130	−	0.232986i	0.742142	+	0.670243i	$0.233810\pi$
$108$	6.56731	−	8.05422i	0.631939	−	0.775018i
$109$	5.72085	−	3.82255i	0.547958	−	0.366134i	−0.250564	−	0.968100i	$-0.580616\pi$
$109$	5.72085	−	3.82255i	0.547958	−	0.366134i	0.798521	+	0.601967i	$0.205616\pi$
$110$	−1.59092	−	1.63013i	−0.151688	−	0.155427i
$111$	−0.769332	+	1.26287i	−0.0730218	+	0.119867i
$112$	9.51176	−	3.40757i	0.898777	−	0.321985i
$113$	3.28149	+	3.28149i	0.308696	+	0.308696i	0.844404	−	0.535707i	$-0.179955\pi$
$113$	3.28149	+	3.28149i	0.308696	+	0.308696i	−0.535707	+	0.844404i	$0.679955\pi$
$114$	1.26329	+	5.49242i	0.118318	+	0.514412i
$115$	3.13703	−	2.09610i	0.292530	−	0.195462i
$116$	−1.79479	−	2.83305i	−0.166642	−	0.263042i
$117$	2.00315	+	2.51370i	0.185191	+	0.232391i
$118$	2.24313	+	3.44720i	0.206497	+	0.317341i
$119$	−11.6030	−	4.80613i	−1.06365	−	0.440577i
$120$	0.929898	−	4.80992i	0.0848877	−	0.439083i
$121$	7.76597	−	3.21677i	0.705997	−	0.292434i
$122$	−6.14191	+	8.95410i	−0.556063	+	0.810667i
$123$	0.0659134	−	0.180122i	0.00594321	−	0.0162411i
$124$	6.88431	+	7.22798i	0.618230	+	0.649092i
$125$	0.195090	−	0.980785i	0.0174494	−	0.0877241i
$126$	10.6891	−	0.766883i	0.952264	−	0.0683194i
$127$			0.606243i			0.0537954i	0.999638	+	0.0268977i	$0.00856283\pi$
$127$			0.606243i			0.0537954i	−0.999638	+	0.0268977i	$0.991437\pi$
$128$	−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	$-0.767500\pi$
$131$	−19.3247	−	3.84392i	−1.68841	−	0.335845i	−0.943512	+	0.331339i	$0.892500\pi$
$132$	−4.69282	−	3.01788i	−0.408457	−	0.262673i
$133$	−3.22881	+	4.83225i	−0.279973	+	0.419010i
$134$	−13.2484	−	9.08753i	−1.14449	−	0.785043i
$135$	2.32243	−	4.64826i	0.199883	−	0.400058i
$136$	−5.85251	+	12.7874i	−0.501849	+	1.09651i
$137$	1.38073	−	3.33337i	0.117964	−	0.284789i	−0.853858	−	0.520505i	$-0.825744\pi$
$137$	1.38073	−	3.33337i	0.117964	−	0.284789i	0.971822	+	0.235716i	$0.0757435\pi$
$138$	6.33772	−	6.72614i	0.539502	−	0.572567i
$139$	17.2378	−	3.42881i	1.46209	−	0.290828i	0.600987	−	0.799259i	$-0.294774\pi$
$139$	17.2378	−	3.42881i	1.46209	−	0.290828i	0.861103	+	0.508431i	$0.169774\pi$
$140$	4.26755	−	2.70357i	0.360674	−	0.228493i
$141$	−5.93915	+	6.45890i	−0.500167	+	0.543938i
$142$	−0.0977515	+	8.02928i	−0.00820313	+	0.673802i
$143$	1.22023	−	1.22023i	0.102040	−	0.102040i
$144$	−0.421115	−	11.9926i	−0.0350929	−	0.999384i
$145$	−1.18572	−	1.18572i	−0.0984687	−	0.0984687i
$146$	−4.68813	+	4.57535i	−0.387992	+	0.378659i
$147$	−0.790079	−	0.726500i	−0.0651646	−	0.0599207i
$148$	0.292251	+	1.68233i	0.0240229	+	0.138286i
$149$	0.0269648	+	0.135561i	0.00220904	+	0.0111056i	0.981874	−	0.189534i	$-0.0606979\pi$
$149$	0.0269648	+	0.135561i	0.00220904	+	0.0111056i	−0.979665	+	0.200640i	$0.935698\pi$
$150$	−0.0727975	−	2.44841i	−0.00594389	−	0.199912i
$151$	−15.9569	−	6.60957i	−1.29856	−	0.537879i	−0.377031	−	0.926201i	$-0.623055\pi$
$151$	−15.9569	−	6.60957i	−1.29856	−	0.537879i	−0.921524	+	0.388321i	$0.873055\pi$
$152$	5.27533	+	3.81064i	0.427886	+	0.309084i
$153$	−9.62751	+	11.3931i	−0.778338	+	0.921075i
$154$	−1.05368	−	5.65624i	−0.0849083	−	0.455793i
$155$	4.14981	+	2.77281i	0.333320	+	0.222718i
$156$	3.65230	+	0.660079i	0.292418	+	0.0528486i
$157$	−2.75438	+	13.8472i	−0.219823	+	1.10513i	0.700405	+	0.713745i	$0.253003\pi$
$157$	−2.75438	+	13.8472i	−0.219823	+	1.10513i	−0.920229	+	0.391381i	$0.871997\pi$
$158$	−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
$162$	2.99185	−	12.3713i	0.235062	−	0.971980i
$163$	20.2967	+	4.03727i	1.58976	+	0.316223i	0.909166	−	0.416435i	$-0.136721\pi$
$163$	20.2967	+	4.03727i	1.58976	+	0.316223i	0.680597	+	0.732658i	$0.261721\pi$
$164$	−0.0797485	−	0.206620i	−0.00622731	−	0.0161343i
$165$	−2.61982	−	0.958689i	−0.203953	−	0.0746338i
$166$	3.00326	+	16.1217i	0.233098	+	1.25128i
$167$	−8.52477	−	20.5806i	−0.659667	−	1.59258i	−0.798319	−	0.602235i	$-0.794277\pi$
$167$	−8.52477	−	20.5806i	−0.659667	−	1.59258i	0.138652	−	0.990341i	$-0.455723\pi$
$168$	8.70290	−	8.79699i	0.671444	−	0.678702i
$169$	4.53560	−	10.9499i	0.348892	−	0.842300i
$170$	−1.45564	+	6.87921i	−0.111642	+	0.527612i
$171$	4.30170	+	5.39808i	0.328959	+	0.412802i
$172$	2.61427	−	3.71352i	0.199336	−	0.283153i
$173$	−1.89330	−	2.83353i	−0.143945	−	0.215429i	0.752491	−	0.658603i	$-0.228852\pi$
$173$	−1.89330	−	2.83353i	−0.143945	−	0.215429i	−0.896436	+	0.443174i	$0.853852\pi$
$174$	−3.48154	−	2.17947i	−0.263935	−	0.165225i
$175$	1.78610	−	1.78610i	0.135017	−	0.135017i
$176$	−6.37248	+	0.947822i	−0.480344	+	0.0714448i
$177$	4.30173	+	2.62058i	0.323338	+	0.196975i
$178$	−0.225515	+	18.5237i	−0.0169031	+	1.38841i
$179$	−3.13337	−	4.68943i	−0.234199	−	0.350504i	0.695691	−	0.718341i	$-0.255098\pi$
$179$	−3.13337	−	4.68943i	−0.234199	−	0.350504i	−0.929890	+	0.367837i	$0.880098\pi$
$180$	−1.51810	−	5.80477i	−0.113153	−	0.432662i
$181$	−3.51297	−	17.6609i	−0.261117	−	1.31272i	−0.859344	−	0.511397i	$-0.829128\pi$
$181$	−3.51297	−	17.6609i	−0.261117	−	1.31272i	0.598227	−	0.801326i	$-0.295872\pi$
$182$	2.08743	+	3.20793i	0.154731	+	0.237787i
$183$	−2.04581	+	13.1401i	−0.151231	+	0.971347i
$184$	0.389644	−	10.6642i	0.0287249	−	0.786175i
$185$	0.326720	+	0.788772i	0.0240209	+	0.0579917i
$186$	11.4287	+	4.34066i	0.837992	+	0.318272i
$187$	6.65857	+	4.44912i	0.486923	+	0.325352i
$188$	−0.246662	+	10.1289i	−0.0179897	+	0.738723i
$189$	11.4007	−	6.50328i	0.829279	−	0.473044i
$190$	2.99078	+	1.28170i	0.216974	+	0.0929841i
$191$	−12.1089			−0.876169			−0.438085	−	0.898934i	$-0.644343\pi$
$191$	−12.1089			−0.876169			−0.438085	+	0.898934i	$0.644343\pi$
$192$	−9.48810	−	10.0983i	−0.684744	−	0.728783i
$193$	−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
$195$	1.85411	−	0.0777282i	0.132775	−	0.00556623i
$196$	−1.23900	−	0.0301727i	−0.0885001	−	0.00215519i
$197$	−5.10176	−	3.40888i	−0.363485	−	0.242873i	0.360393	−	0.932800i	$-0.382642\pi$
$197$	−5.10176	−	3.40888i	−0.363485	−	0.242873i	−0.723879	+	0.689927i	$0.757642\pi$
$198$	−6.78030	−	0.850107i	−0.481855	−	0.0604145i
$199$	−7.48686	−	18.0749i	−0.530729	−	1.28129i	−0.931041	−	0.364915i	$-0.881098\pi$
$199$	−7.48686	−	18.0749i	−0.530729	−	1.28129i	0.400312	−	0.916379i	$-0.368902\pi$
$200$	−1.92564	−	2.07169i	−0.136163	−	0.146491i
$201$	−19.4421	−	3.02697i	−1.37134	−	0.213506i
$202$	5.26846	+	8.09647i	0.370688	+	0.569665i
$203$	−0.826331	−	4.15425i	−0.0579971	−	0.291571i
$204$	0.302261	+	17.2210i	0.0211625	+	1.20571i
$205$	−0.0615226	−	0.0920751i	−0.00429693	−	0.00643081i
$206$	−0.0358154	+	2.94187i	−0.00249538	+	0.204970i
$207$	3.44103	−	10.7829i	0.239168	−	0.749463i
$208$	3.67505	−	2.20470i	0.254819	−	0.152868i
$209$	2.62040	−	2.62040i	0.181257	−	0.181257i
$210$	3.28303	−	5.24439i	0.226551	−	0.361897i
$211$	11.6914	+	17.4975i	0.804871	+	1.20458i	0.975665	+	0.219268i	$0.0703670\pi$
$211$	11.6914	+	17.4975i	0.804871	+	1.20458i	−0.170793	+	0.985307i	$0.554633\pi$
$212$	−17.7167	−	12.4723i	−1.21679	−	0.856601i
$213$	4.14078	+	8.92032i	0.283722	+	0.611210i
$214$	3.61663	−	17.0919i	0.247228	−	1.16838i
$215$	0.868966	−	2.09787i	0.0592630	−	0.143073i
$216$	−6.81111	−	13.0234i	−0.463438	−	0.886130i
$217$	4.82439	+	11.6471i	0.327501	+	0.790657i
$218$	−1.78198	−	9.56579i	−0.120691	−	0.647877i
$219$	−2.75711	+	7.53438i	−0.186308	+	0.509126i
$220$	−3.00521	+	1.15992i	−0.202611	+	0.0782015i
$221$	−5.22474	−	1.03926i	−0.351454	−	0.0699085i
$222$	1.21302	+	1.70354i	0.0814123	+	0.114334i
$223$	−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	$-0.992207\pi$
$227$	−1.00537	+	5.05436i	−0.0667291	+	0.335470i	0.932971	+	0.359951i	$0.117207\pi$
$228$	7.84320	+	1.41750i	0.519429	+	0.0938762i
$229$	16.1855	+	10.8148i	1.06957	+	0.714663i	0.960193	−	0.279337i	$-0.0901148\pi$
$229$	16.1855	+	10.8148i	1.06957	+	0.714663i	0.109376	+	0.994000i	$0.465115\pi$
$230$	−0.977152	−	5.24541i	−0.0644315	−	0.345872i
$231$	−4.15687	−	5.68994i	−0.273502	−	0.374371i
$232$	−4.68243	+	0.754823i	−0.307417	+	0.0495565i
$233$	17.2061	+	7.12698i	1.12721	+	0.466904i	0.866830	−	0.498603i	$-0.166154\pi$
$233$	17.2061	+	7.12698i	1.12721	+	0.466904i	0.260376	+	0.965507i	$0.416154\pi$
$234$	4.38337	−	1.20356i	0.286550	−	0.0786795i
$235$	0.988314	+	4.96859i	0.0644705	+	0.324115i
$236$	5.73051	−	0.995495i	0.373024	−	0.0648012i
$237$	−17.9492	+	19.5200i	−1.16593	+	1.26796i
$238$	−12.7110	+	12.4052i	−0.823931	+	0.804110i
$239$	−5.56958	−	5.56958i	−0.360266	−	0.360266i	0.503645	−	0.863911i	$-0.331992\pi$
$239$	−5.56958	−	5.56958i	−0.360266	−	0.360266i	−0.863911	+	0.503645i	$0.831992\pi$
$240$	−5.73429	−	3.88817i	−0.370147	−	0.250980i
$241$	10.3957	−	10.3957i	0.669644	−	0.669644i	−0.287989	−	0.957634i	$-0.592987\pi$
$241$	10.3957	−	10.3957i	0.669644	−	0.669644i	0.957634	+	0.287989i	$0.0929867\pi$
$242$	0.144714	−	11.8867i	0.00930256	−	0.764109i
$243$	−3.24176	−	15.2477i	−0.207959	−	0.978137i
$244$	8.21782	+	12.9717i	0.526092	+	0.830430i
$245$	−0.607778	+	0.120894i	−0.0388295	+	0.00772367i
$246$	−0.197419	−	0.186018i	−0.0125870	−	0.0118601i
$247$	−0.943360	+	2.27747i	−0.0600245	+	0.144912i
$248$	13.2305	−	4.92234i	0.840136	−	0.312569i
$249$	11.8481	+	16.2177i	0.750843	+	1.02776i
$250$	−1.16622	−	0.799951i	−0.0737585	−	0.0505934i
$251$	−2.18096	+	3.26404i	−0.137661	+	0.206025i	−0.893894	−	0.448278i	$-0.852038\pi$
$251$	−2.18096	+	3.26404i	−0.137661	+	0.206025i	0.756233	+	0.654302i	$0.227038\pi$
$252$	4.95765	−	14.3218i	0.312303	−	0.902187i
$253$	−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	$-0.208790\pi$
$258$	0.922506	−	5.48506i	0.0574327	−	0.341485i
$259$	−0.420720	+	2.11510i	−0.0261423	+	0.131426i
$260$	1.55164	−	1.47786i	0.0962287	−	0.0916533i
$261$	−4.99875	−	0.565019i	−0.309415	−	0.0349738i
$262$	−15.7617	+	22.9784i	−0.973759	+	1.41961i
$263$	13.9244	−	5.76766i	0.858613	−	0.355649i	0.0904482	−	0.995901i	$-0.471170\pi$
$263$	13.9244	−	5.76766i	0.858613	−	0.355649i	0.768165	+	0.640252i	$0.221170\pi$
$264$	−6.53706	+	4.41895i	−0.402328	+	0.271967i
$265$	−10.0086	−	4.14571i	−0.614826	−	0.254669i
$266$	4.48269	+	6.88892i	0.274852	+	0.422387i
$267$	9.55289	+	20.5794i	0.584627	+	1.25944i
$268$	−19.1929	+	12.1590i	−1.17239	+	0.742730i
$269$	18.3536	−	12.2635i	1.11904	−	0.747718i	0.148560	−	0.988903i	$-0.452536\pi$
$269$	18.3536	−	12.2635i	1.11904	−	0.747718i	0.970479	+	0.241186i	$0.0775362\pi$
$270$	−4.74843	−	5.60825i	−0.288980	−	0.341307i
$271$	2.20350	+	2.20350i	0.133853	+	0.133853i	0.770859	−	0.637006i	$-0.219827\pi$
$271$	2.20350	+	2.20350i	0.133853	+	0.133853i	−0.637006	+	0.770859i	$0.719827\pi$
$272$	13.3619	+	14.7309i	0.810182	+	0.893194i
$273$	4.00313	+	2.43868i	0.242281	+	0.147596i
$274$	−3.56383	−	3.65167i	−0.215299	−	0.220606i
$275$	−1.33920	+	0.894827i	−0.0807569	+	0.0539601i
$276$	−5.21266	−	11.9851i	−0.313765	−	0.721420i
$277$	3.48459	−	0.693129i	0.209369	−	0.0416461i	−0.0892914	−	0.996006i	$-0.528460\pi$
$277$	3.48459	−	0.693129i	0.209369	−	0.0416461i	0.298660	+	0.954359i	$0.403460\pi$
$278$	5.14547	−	24.3171i	0.308605	−	1.45844i
$279$	14.9203	−	1.25318i	0.893252	−	0.0750260i
$280$	−1.13702	−	7.05335i	−0.0679501	−	0.421518i
$281$	6.98120	−	2.89171i	0.416464	−	0.172505i	−0.164605	−	0.986360i	$-0.552635\pi$
$281$	6.98120	−	2.89171i	0.416464	−	0.172505i	0.581068	+	0.813855i	$0.302635\pi$
$282$	5.08731	+	11.3182i	0.302945	+	0.673988i
$283$	−5.79540	+	8.67344i	−0.344501	+	0.515582i	−0.962747	−	0.270402i	$-0.912843\pi$
$283$	−5.79540	+	8.67344i	−0.344501	+	0.515582i	0.618246	+	0.785984i	$0.287843\pi$
$284$	10.3826	+	4.59986i	0.616095	+	0.272952i
$285$	3.98164	−	0.166919i	0.235852	−	0.00988741i
$286$	−0.906404	−	2.26589i	−0.0535968	−	0.133985i
$287$		−	0.279716i		−	0.0165111i
$288$	−15.8235	−	6.13322i	−0.932409	−	0.361404i
$289$		−	7.72122i		−	0.454189i
$290$	−2.20181	+	0.880773i	−0.129295	+	0.0517208i
$291$	0.812023	−	0.0340418i	0.0476016	−	0.00199556i
$292$	3.33582	+	8.64274i	0.195214	+	0.505778i
$293$	−12.2310	+	18.3049i	−0.714540	+	1.06938i	0.279476	+	0.960153i	$0.409839\pi$
$293$	−12.2310	+	18.3049i	−0.714540	+	1.06938i	−0.994016	+	0.109232i	$0.965161\pi$
$294$	−1.38448	+	0.622300i	−0.0807448	+	0.0362933i
$295$	2.68679	−	1.11291i	0.156431	−	0.0647959i
$296$	2.34962	+	0.557268i	0.136569	+	0.0323905i
$297$	−7.93891	+	2.64888i	−0.460662	+	0.153703i
$298$	0.191234	+	0.0404650i	0.0110779	+	0.00234407i
$299$	3.96462	−	0.788613i	0.229280	−	0.0456066i
$300$	−3.22318	−	1.26929i	−0.186091	−	0.0732822i
$301$	4.76903	−	3.18657i	0.274883	−	0.183671i
$302$	−17.4806	+	17.0601i	−1.00590	+	0.981699i
$303$	10.1035	+	6.15497i	0.580430	+	0.353594i
$304$	7.89205	−	4.73452i	0.452640	−	0.271544i
$305$	5.42907	+	5.42907i	0.310868	+	0.310868i
$306$	9.44648	+	18.8612i	0.540020	+	1.07822i
$307$	24.4837	−	16.3595i	1.39736	−	0.933687i	0.397490	−	0.917606i	$-0.369881\pi$
$307$	24.4837	−	16.3595i	1.39736	−	0.933687i	0.999871	−	0.0160802i	$-0.00511870\pi$
$308$	−7.93939	−	1.78121i	−0.452389	−	0.101494i
$309$	1.51715	+	3.26834i	0.0863077	+	0.185929i
$310$	5.91601	−	3.84961i	0.336007	−	0.218643i
$311$	−8.99525	−	3.72595i	−0.510074	−	0.211279i	0.112777	−	0.993620i	$-0.464025\pi$
$311$	−8.99525	−	3.72595i	−0.510074	−	0.211279i	−0.622850	+	0.782341i	$0.714025\pi$
$312$	2.89258	−	4.37984i	0.163760	−	0.247960i
$313$	15.8402	−	6.56123i	0.895342	−	0.370863i	0.112914	−	0.993605i	$-0.463981\pi$
$313$	15.8402	−	6.56123i	0.895342	−	0.370863i	0.782427	+	0.622742i	$0.213981\pi$
$314$	16.4653	+	11.2941i	0.929191	+	0.637362i
$315$	0.851113	−	7.52984i	0.0479548	−	0.424258i
$316$	−0.745459	+	30.6113i	−0.0419353	+	1.72202i
$317$	−0.000568099		0.00285603i	−3.19076e−5		0.000160411i	−0.980801	−	0.195010i	$-0.937526\pi$
$317$	−0.000568099		0.00285603i	−3.19076e−5		0.000160411i	0.980769	+	0.195171i	$0.0625260\pi$
$318$	−26.1685	−	4.40115i	−1.46745	−	0.246804i
$319$			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
$324$	−14.4145	−	10.7806i	−0.800807	−	0.598923i
$325$	0.595243	−	0.890844i	0.0330181	−	0.0494152i
$326$	16.5545	−	24.1343i	0.916868	−	1.33667i
$327$	−7.03007	−	9.62278i	−0.388764	−	0.532141i
$328$	−0.313005	−	0.0114365i	−0.0172828	−	0.000631472i
$329$	−4.89689	+	11.8221i	−0.269974	+	0.651775i
$330$	−2.70558	+	2.87140i	−0.148937	+	0.158065i
$331$	27.7143	−	5.51273i	1.52332	−	0.303007i	0.638749	−	0.769416i	$-0.279452\pi$
$331$	27.7143	−	5.51273i	1.52332	−	0.303007i	0.884569	+	0.466409i	$0.154452\pi$
$332$	22.6292	+	5.07690i	1.24194	+	0.278631i
$333$	2.24125	+	1.23974i	0.122820	+	0.0679371i
$334$	−31.5011	−	0.383507i	−1.72366	−	0.0209846i
$335$	−8.03281	+	8.03281i	−0.438879	+	0.438879i
$336$	−6.58696	−	16.2132i	−0.359348	−	0.884501i
$337$	22.0273	+	22.0273i	1.19990	+	1.19990i	0.974196	+	0.225705i	$0.0724686\pi$
$337$	22.0273	+	22.0273i	1.19990	+	1.19990i	0.225705	+	0.974196i	$0.427531\pi$
$338$	−11.7069	−	11.9955i	−0.636773	−	0.652468i
$339$	5.44065	−	5.91678i	0.295496	−	0.321355i
$340$	8.13126	+	5.72429i	0.440979	+	0.310443i
$341$	−1.56826	−	7.88416i	−0.0849258	−	0.426951i
$342$	9.41316	−	2.58462i	0.509005	−	0.139760i
$343$	−17.7817	−	7.36542i	−0.960122	−	0.397695i
$344$	−3.37082	−	5.46689i	−0.181742	−	0.294755i
$345$	−3.85495	−	5.27666i	−0.207543	−	0.284086i
$346$	−4.73792	+	0.882613i	−0.254712	+	0.0474496i
$347$	−13.4739	−	9.00295i	−0.723315	−	0.483304i	0.138605	−	0.990348i	$-0.455738\pi$
$347$	−13.4739	−	9.00295i	−0.723315	−	0.483304i	−0.861920	+	0.507044i	$0.830738\pi$
$348$	−4.77248	+	3.31147i	−0.255832	+	0.177513i
$349$	0.514040	−	2.58425i	0.0275159	−	0.138332i	−0.964585	−	0.263771i	$-0.915034\pi$
$349$	0.514040	−	2.58425i	0.0275159	−	0.138332i	0.992101	+	0.125439i	$0.0400338\pi$
$350$	−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	$-0.254483\pi$
$353$	26.1938			1.39415			0.697077	+	0.716996i	$0.254483\pi$
$354$	5.80276	−	4.13190i	0.308413	−	0.219608i
$355$	5.56888	+	1.10772i	0.295565	+	0.0587916i
$356$	23.9530	+	10.6120i	1.26951	+	0.562435i
$357$	−7.47539	+	20.4281i	−0.395639	+	1.08117i
$358$	−7.84116	+	1.46071i	−0.414418	+	0.0772007i
$359$	3.70332	+	8.94061i	0.195454	+	0.471867i	0.990973	−	0.134061i	$-0.0428018\pi$
$359$	3.70332	+	8.94061i	0.195454	+	0.471867i	−0.795519	+	0.605928i	$0.792802\pi$
$360$	−8.39117	−	1.26027i	−0.442253	−	0.0664220i
$361$	5.24515	−	12.6629i	0.276061	−	0.666469i
$362$	−24.9139	−	5.27177i	−1.30945	−	0.277078i
$363$	−6.13012	−	13.2059i	−0.321748	−	0.693129i
$364$	5.33274	−	0.926395i	0.279511	−	0.0485563i
$365$	2.57345	+	3.85144i	0.134700	+	0.201593i
$366$	15.9409	+	9.97917i	0.833246	+	0.521620i
$367$	22.1495	−	22.1495i	1.15619	−	1.15619i	0.170907	−	0.985287i	$-0.445330\pi$
$367$	22.1495	−	22.1495i	1.15619	−	1.15619i	0.985287	−	0.170907i	$-0.0546698\pi$
$368$	−13.6451	−	6.44710i	−0.711299	−	0.336078i
$369$	−0.316489	−	0.100998i	−0.0164758	−	0.00525773i
$370$	1.20731	+	0.0146983i	0.0627651	+	0.000764127i
$371$	−15.2027	−	22.7524i	−0.789283	−	1.18125i
$372$	12.0088	−	12.4379i	0.622627	−	0.644874i
$373$	0.728316	+	3.66149i	0.0377108	+	0.189585i	0.995049	−	0.0993846i	$-0.0316874\pi$
$373$	0.728316	+	3.66149i	0.0377108	+	0.189585i	−0.957338	+	0.288969i	$0.906687\pi$
$374$	9.49254	−	6.17690i	0.490848	−	0.319400i
$375$	−1.71143	−	0.266456i	−0.0883780	−	0.0137597i
$376$	13.0289	+	5.96303i	0.671913	+	0.307520i
$377$	−0.687531	−	1.65985i	−0.0354097	−	0.0854865i
$378$	−2.10259	−	18.4422i	−0.108145	−	0.948566i
$379$	−15.2798	−	10.2097i	−0.784872	−	0.524435i	0.0973601	−	0.995249i	$-0.468960\pi$
$379$	−15.2798	−	10.2097i	−0.784872	−	0.524435i	−0.882232	+	0.470814i	$0.843960\pi$
$380$	3.33210	−	3.17367i	0.170933	−	0.162806i
$381$	1.04912	−	0.0439815i	0.0537481	−	0.00225324i
$382$	−6.74540	+	15.7401i	−0.345125	+	0.805333i
$383$	−0.661932			−0.0338231			−0.0169116	−	0.999857i	$-0.505383\pi$
$383$	−0.661932			−0.0338231			−0.0169116	+	0.999857i	$0.505383\pi$
$384$	−18.4120	+	6.70799i	−0.939585	+	0.342316i
$385$	−4.06837			−0.207344
$386$	−14.8650	+	34.6869i	−0.756610	+	1.76552i
$387$	−1.88352	−	6.54658i	−0.0957449	−	0.332781i
$388$	0.679555	−	0.647244i	0.0344992	−	0.0328588i
$389$	13.7921	+	9.21558i	0.699287	+	0.467248i	0.853705	−	0.520757i	$-0.174350\pi$
$389$	13.7921	+	9.21558i	0.699287	+	0.467248i	−0.154418	+	0.988006i	$0.549350\pi$
$390$	0.931814	−	2.45341i	0.0471843	−	0.124233i
$391$	7.17872	+	17.3310i	0.363044	+	0.876465i
$392$	−0.729421	+	1.59374i	−0.0368413	+	0.0804962i
$393$	−5.25006	+	33.7208i	−0.264831	+	1.70099i
$394$	−7.27313	+	4.73270i	−0.366415	+	0.238430i
$395$	2.98687	+	15.0160i	0.150286	+	0.755538i
$396$	−4.88208	+	8.34001i	−0.245334	+	0.419101i
$397$	10.0550	+	15.0484i	0.504647	+	0.755258i	0.993092	−	0.117337i	$-0.0374357\pi$
$397$	10.0550	+	15.0484i	0.504647	+	0.755258i	−0.488445	+	0.872595i	$0.662436\pi$
$398$	−27.6658	−	0.336814i	−1.38676	−	0.0168830i
$399$	8.59661	+	5.23698i	0.430369	+	0.262177i
$400$	−3.76565	+	1.34904i	−0.188282	+	0.0674518i
$401$	−16.0793	+	16.0793i	−0.802963	+	0.802963i	−0.983558	−	0.180595i	$-0.942198\pi$
$401$	−16.0793	+	16.0793i	−0.802963	+	0.802963i	0.180595	+	0.983558i	$0.442198\pi$
$402$	−14.7651	+	23.5861i	−0.736417	+	1.17637i
$403$	2.97082	+	4.44614i	0.147987	+	0.221478i
$404$	13.4593	−	2.33812i	0.669624	−	0.116326i
$405$	−8.21244	−	3.68182i	−0.408079	−	0.182951i
$406$	−5.86033	−	1.24004i	−0.290843	−	0.0615422i
$407$	0.526230	−	1.27043i	0.0260843	−	0.0629730i
$408$	22.5536	+	9.20026i	1.11657	+	0.455481i
$409$	−2.93979	−	7.09728i	−0.145363	−	0.350938i	0.834382	−	0.551187i	$-0.185825\pi$
$409$	−2.93979	−	7.09728i	−0.145363	−	0.350938i	−0.979745	+	0.200249i	$0.935825\pi$
$410$	−0.153958	+	0.0286804i	−0.00760346	+	0.00141642i
$411$	−5.86868	−	2.14757i	−0.289480	−	0.105932i
$412$	3.80412	+	1.68536i	0.187415	+	0.0830316i
$413$	7.20467	+	1.43310i	0.354519	+	0.0705181i
$414$	−12.0996	−	10.4796i	−0.594662	−	0.515047i
$415$	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	$-0.935879\pi$
$419$	0.0406751	−	0.204488i	0.00198711	−	0.00998988i	0.981766	+	0.190093i	$0.0608789\pi$
$420$	−4.98821	−	7.18899i	−0.243400	−	0.350787i
$421$	4.89688	+	3.27199i	0.238659	+	0.159467i	0.669149	−	0.743129i	$-0.266659\pi$
$421$	4.89688	+	3.27199i	0.238659	+	0.159467i	−0.430489	+	0.902596i	$0.641659\pi$
$422$	29.2574	−	5.45027i	1.42423	−	0.265315i
$423$	11.6082	+	9.80930i	0.564410	+	0.476945i
$424$	−26.0817	+	16.0817i	−1.26664	+	0.780996i
$425$	4.59357	+	1.90272i	0.222821	+	0.0922954i
$426$	13.9020	−	0.413342i	0.673554	−	0.0200265i
$427$	3.78353	+	19.0211i	0.183098	+	0.920495i
$428$	−20.2027	−	14.2224i	−0.976533	−	0.687466i
$429$	−2.20016	−	2.02311i	−0.106225	−	0.0976769i
$430$	−2.24291	−	2.29819i	−0.108163	−	0.110829i
$431$	23.2684	+	23.2684i	1.12080	+	1.12080i	0.991622	+	0.129175i	$0.0412330\pi$
$431$	23.2684	+	23.2684i	1.12080	+	1.12080i	0.129175	+	0.991622i	$0.458767\pi$
$432$	−20.7230	+	1.59879i	−0.997037	+	0.0769216i
$433$	19.9489	−	19.9489i	0.958682	−	0.958682i	−0.0404977	−	0.999180i	$-0.512894\pi$
$433$	19.9489	−	19.9489i	0.958682	−	0.958682i	0.999180	+	0.0404977i	$0.0128944\pi$
$434$	17.8273	+	0.217036i	0.855737	+	0.0104181i
$435$	−1.96590	+	2.13795i	−0.0942579	+	0.102507i
$436$	−13.4270	−	3.01238i	−0.643038	−	0.144267i
$437$	8.51390	−	1.69352i	0.407275	−	0.0810121i
$438$	8.25790	+	7.78102i	0.394578	+	0.371791i
$439$	3.07196	−	7.41636i	0.146617	−	0.353964i	−0.833461	−	0.552578i	$-0.813644\pi$
$439$	3.07196	−	7.41636i	0.146617	−	0.353964i	0.980078	+	0.198614i	$0.0636441\pi$
$440$	−0.166339	+	4.55255i	−0.00792992	+	0.217035i
$441$	−1.19991	+	1.41996i	−0.0571387	+	0.0676172i
$442$	−4.26142	+	6.21258i	−0.202695	+	0.295502i
$443$	2.85713	−	4.27599i	0.135746	−	0.203158i	−0.757368	−	0.652988i	$-0.773515\pi$
$443$	2.85713	−	4.27599i	0.135746	−	0.203158i	0.893114	+	0.449829i	$0.148515\pi$
$444$	2.89011	−	0.627798i	0.137159	−	0.0297940i
$445$	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	$0.871165\pi$
$450$	−4.23176	+	0.303604i	−0.199487	+	0.0143120i
$451$	−0.0347962	+	0.174932i	−0.00163849	+	0.00823723i
$452$	0.225958	−	9.27870i	0.0106282	−	0.436433i
$453$	−10.2804	+	28.0934i	−0.483017	+	1.31994i
$454$	6.01000	+	4.12245i	0.282063	+	0.193476i
$455$	2.50030	−	1.03566i	0.117216	−	0.0485524i
$456$	6.21172	−	9.40557i	0.290891	−	0.440456i
$457$	−20.9382	−	8.67287i	−0.979446	−	0.405700i	−0.165226	−	0.986256i	$-0.552835\pi$
$457$	−20.9382	−	8.67287i	−0.979446	−	0.405700i	−0.814220	+	0.580556i	$0.802835\pi$
$458$	23.0743	−	15.0147i	1.07819	−	0.701590i
$459$	20.4145	+	15.8342i	0.952868	+	0.739075i
$460$	−7.36273	−	1.65184i	−0.343289	−	0.0770174i
$461$	−3.91190	+	2.61385i	−0.182196	+	0.121739i	−0.643323	−	0.765595i	$-0.722445\pi$
$461$	−3.91190	+	2.61385i	−0.182196	+	0.121739i	0.461128	+	0.887334i	$0.347445\pi$
$462$	−9.71186	+	2.23378i	−0.451837	+	0.103925i
$463$	5.13941	+	5.13941i	0.238849	+	0.238849i	0.816373	−	0.577525i	$-0.195981\pi$
$463$	5.13941	+	5.13941i	0.238849	+	0.238849i	−0.577525	+	0.816373i	$0.695981\pi$
$464$	−1.62722	+	6.50707i	−0.0755420	+	0.302083i
$465$	4.49738	−	7.38253i	0.208561	−	0.342356i
$466$	18.8490	−	18.3956i	0.873164	−	0.852160i
$467$	−5.30296	+	3.54333i	−0.245392	+	0.163966i	−0.672184	−	0.740384i	$-0.734644\pi$
$467$	−5.30296	+	3.54333i	−0.245392	+	0.163966i	0.426792	+	0.904350i	$0.359644\pi$
$468$	0.877321	−	6.36831i	0.0405542	−	0.294375i
$469$	−28.1434	+	5.59808i	−1.29954	+	0.258495i
$470$	7.00911	+	1.48312i	0.323306	+	0.0684113i
$471$	24.1628	+	3.76196i	1.11336	+	0.173342i
$472$	1.89822	−	8.00351i	0.0873728	−	0.368391i
$473$	−3.37892	+	1.39960i	−0.155363	+	0.0643535i
$474$	15.3748	+	34.2057i	0.706189	+	1.57112i
$475$	1.27827	−	1.91306i	0.0586509	−	0.0877772i
$476$	9.04446	+	23.4332i	0.414552	+	1.07406i
$477$	−31.2328	+	8.98603i	−1.43005	+	0.411442i
$478$	−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	$0.737761\pi$
$480$	−8.24850	+	5.28793i	−0.376491	+	0.241360i
$481$			0.914727i			0.0417080i
$482$	−7.72208	−	19.3041i	−0.351731	−	0.879280i
$483$	−0.691380	−	16.4920i	−0.0314589	−	0.750411i
$484$	−15.3707	−	6.80976i	−0.698668	−	0.309534i
$485$	0.260692	−	0.390153i	0.0118374	−	0.0177160i
$486$	−21.6260	−	4.27998i	−0.980973	−	0.194144i
$487$	22.7425	−	9.42027i	1.03056	−	0.426873i	0.197647	−	0.980273i	$-0.436670\pi$
$487$	22.7425	−	9.42027i	1.03056	−	0.426873i	0.832916	+	0.553400i	$0.186670\pi$
$488$	21.4395	−	3.45611i	0.970520	−	0.156451i
$489$	5.51414	−	35.4170i	0.249358	−	1.60161i
$490$	−0.181421	+	0.857382i	−0.00819578	+	0.0387326i
$491$	11.7783	−	2.34285i	0.531546	−	0.105731i	0.0779822	−	0.996955i	$-0.475152\pi$
$491$	11.7783	−	2.34285i	0.531546	−	0.105731i	0.453564	+	0.891224i	$0.350152\pi$
$492$	−0.351776	+	0.152997i	−0.0158593	+	0.00689764i
$493$	6.93232	−	4.63203i	0.312216	−	0.208616i
$494$	2.43493	+	2.49494i	0.109553	+	0.112253i
$495$	−1.46898	+	4.60323i	−0.0660257	+	0.206900i
$496$	0.971752	−	19.9401i	0.0436330	−	0.895335i
$497$	10.1414	+	10.1414i	0.454906	+	0.454906i
$498$	27.6812	−	6.36682i	1.24042	−	0.285304i
$499$	−1.40249	+	0.937117i	−0.0627843	+	0.0419511i	−0.586566	−	0.809901i	$-0.699521\pi$
$499$	−1.40249	+	0.937117i	−0.0627843	+	0.0419511i	0.523782	+	0.851852i	$0.324521\pi$
$500$	−1.68950	+	1.07033i	−0.0755566	+	0.0478665i
$501$	−34.9970	+	16.2455i	−1.56355	+	0.725793i
$502$	3.02793	+	4.65326i	0.135143	+	0.207685i
$503$	21.4968	+	8.90428i	0.958497	+	0.397022i	0.806418	−	0.591346i	$-0.201403\pi$
$503$	21.4968	+	8.90428i	0.958497	+	0.397022i	0.152079	+	0.988368i	$0.451403\pi$
$504$	−15.8548	−	14.4224i	−0.706231	−	0.642427i
$505$	6.31049	−	2.61389i	0.280813	−	0.116317i
$506$	−4.86112	+	7.08687i	−0.216103	+	0.315050i
$507$	−19.2782	−	7.05460i	−0.856174	−	0.313306i
$508$	0.877975	−	0.836230i	0.0389539	−	0.0371017i
$509$	4.41384	−	22.1899i	0.195640	−	0.983549i	−0.750766	−	0.660569i	$-0.770315\pi$
$509$	4.41384	−	22.1899i	0.195640	−	0.983549i	0.946406	−	0.322980i	$-0.104685\pi$
$510$	12.0103	+	2.01995i	0.531825	+	0.0894450i
$511$			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
$516$	−6.61602	−	4.25466i	−0.291254	−	0.187301i
$517$	4.53313	−	6.78431i	0.199367	−	0.298373i
$518$	2.51501	+	1.72513i	0.110503	+	0.0757977i
$519$	−4.76615	+	3.48198i	−0.209211	+	0.152842i
$520$	−1.05668	−	2.84020i	−0.0463387	−	0.124551i
$521$	7.11760	−	17.1834i	0.311828	−	0.752819i	−0.687810	−	0.725891i	$-0.741428\pi$
$521$	7.11760	−	17.1834i	0.311828	−	0.752819i	0.999637	−	0.0269278i	$-0.00857241\pi$
$522$	−3.51907	+	6.18302i	−0.154025	+	0.270623i
$523$	−8.78136	+	1.74672i	−0.383982	+	0.0763788i	−0.383307	−	0.923621i	$-0.625215\pi$
$523$	−8.78136	+	1.74672i	−0.383982	+	0.0763788i	−0.000675031		1.00000i	$0.500215\pi$
$524$	21.0889	+	33.2886i	0.921275	+	1.45422i
$525$	−3.22048	−	2.96133i	−0.140553	−	0.129243i
$526$	0.259472	−	21.3129i	0.0113135	−	0.929287i
$527$	−17.5469	+	17.5469i	−0.764357	+	0.764357i
$528$	2.10254	+	10.9590i	0.0915015	+	0.476930i
$529$	6.19808	+	6.19808i	0.269482	+	0.269482i
$530$	−10.9643	+	10.7006i	−0.476261	+	0.464804i
$531$	4.22291	−	7.63439i	0.183259	−	0.331304i
$532$	11.4519	−	1.98941i	0.496502	−	0.0862516i
$533$	−0.0231466	−	0.116366i	−0.00100259	−	0.00504036i
$534$	32.0723	−	0.953592i	1.38790	−	0.0412659i
$535$	−11.4130	−	4.72744i	−0.493429	−	0.204385i
$536$	5.11364	+	31.7217i	0.220876	+	1.37017i
$537$	−7.88788	+	5.76261i	−0.340387	+	0.248675i
$538$	−5.71695	−	30.6890i	−0.246475	−	1.32309i
$539$	0.829883	+	0.554510i	0.0357456	+	0.0238844i
$540$	−9.93520	+	3.04824i	−0.427543	+	0.131175i
$541$	1.31313	−	6.60154i	0.0564558	−	0.283822i	−0.942236	−	0.334949i	$-0.891281\pi$
$541$	1.31313	−	6.60154i	0.0564558	−	0.283822i	0.998692	+	0.0511262i	$0.0162811\pi$
$542$	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
$546$	5.39998	−	3.84509i	0.231098	−	0.164555i
$547$	−8.56950	−	1.70458i	−0.366405	−	0.0728825i	0.00845400	−	0.999964i	$-0.497309\pi$
$547$	−8.56950	−	1.70458i	−0.366405	−	0.0728825i	−0.374859	+	0.927082i	$0.622309\pi$
$548$	−6.73200	+	2.59834i	−0.287577	+	0.110995i
$549$	22.8878	+	2.58706i	0.976829	+	0.110413i
$550$	0.417147	+	2.23927i	0.0177872	+	0.0954829i
$551$	−1.47645	−	3.56447i	−0.0628990	−	0.151852i
$552$	−18.4830	+	0.0993701i	−0.786688	+	0.00422947i
$553$	−14.7993	+	35.7287i	−0.629331	+	1.51934i
$554$	1.04015	−	4.91566i	0.0441917	−	0.208846i
$555$	1.34129	−	0.622623i	0.0569347	−	0.0264289i
$556$	−28.7429	−	20.2346i	−1.21897	−	0.858138i
$557$	−20.8881	−	31.2612i	−0.885056	−	1.32458i	−0.945234	−	0.326392i	$-0.894167\pi$
$557$	−20.8881	−	31.2612i	−0.885056	−	1.32458i	0.0601782	−	0.998188i	$-0.480833\pi$
$558$	6.68251	−	20.0926i	0.282893	−	0.850588i
$559$	1.72030	−	1.72030i	0.0727608	−	0.0727608i
$560$	−9.80188	−	2.45116i	−0.414205	−	0.103580i
$561$	7.21627	−	11.8456i	0.304671	−	0.500123i
$562$	0.130090	−	10.6856i	0.00548753	−	0.450744i
$563$	21.6831	+	32.4511i	0.913835	+	1.36765i	0.929913	+	0.367780i	$0.119882\pi$
$563$	21.6831	+	32.4511i	0.913835	+	1.36765i	−0.0160783	+	0.999871i	$0.505118\pi$
$564$	17.5462	−	0.307968i	0.738828	−	0.0129678i
$565$	−0.905360	−	4.55155i	−0.0380888	−	0.191485i
$566$	8.04601	+	12.3650i	0.338199	+	0.519738i
$567$	−12.0812	−	19.2575i	−0.507364	−	0.808737i
$568$	11.7630	−	10.9337i	0.493565	−	0.458769i
$569$	11.1604	+	26.9437i	0.467870	+	1.12954i	0.965091	+	0.261914i	$0.0843535\pi$
$569$	11.1604	+	26.9437i	0.467870	+	1.12954i	−0.497222	+	0.867623i	$0.665646\pi$
$570$	2.00104	−	5.26863i	0.0838144	−	0.220678i
$571$	9.73116	+	6.50215i	0.407236	+	0.272107i	0.742272	−	0.670099i	$-0.233748\pi$
$571$	9.73116	+	6.50215i	0.407236	+	0.272107i	−0.335036	+	0.942205i	$0.608748\pi$
$572$	−3.45030	−	0.0840230i	−0.144264	−	0.00351318i
$573$	0.878471	+	20.9548i	0.0366987	+	0.875400i
$574$	−0.363596	−	0.155819i	−0.0151762	−	0.00650375i
$575$	−3.77288			−0.157340
$576$	−16.7871	+	17.1521i	−0.699463	+	0.714669i
$577$	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
$579$	1.93591	+	46.1788i	0.0804538	+	1.91912i
$580$	−0.0816470	+	3.35273i	−0.00339021	+	0.139215i
$581$	24.3540	+	16.2728i	1.01037	+	0.675111i
$582$	0.408097	−	1.07449i	0.0169161	−	0.0445392i
$583$	6.67727	+	16.1204i	0.276544	+	0.667637i
$584$	13.0928	+	0.478379i	0.541783	+	0.0197954i
$585$	−0.269022	−	3.20295i	−0.0111227	−	0.132426i
$586$	16.9808	+	26.0957i	0.701469	+	1.07800i
$587$	5.05908	+	25.4337i	0.208810	+	1.04976i	0.932922	+	0.360078i	$0.117250\pi$
$587$	5.05908	+	25.4337i	0.208810	+	1.04976i	−0.724112	+	0.689683i	$0.757750\pi$
$588$	0.0376719	+	2.14632i	0.00155356	+	0.0885128i
$589$	6.37973	+	9.54795i	0.262872	+	0.393416i
$590$	0.0500667	−	4.11246i	0.00206121	−	0.169307i
$591$	−5.52906	+	9.07605i	−0.227435	+	0.373339i
$592$	2.03326	−	2.74379i	0.0835666	−	0.112769i
$593$	23.3893	−	23.3893i	0.960482	−	0.960482i	−0.0387660	−	0.999248i	$-0.512343\pi$
$593$	23.3893	−	23.3893i	0.960482	−	0.960482i	0.999248	+	0.0387660i	$0.0123427\pi$
$594$	−0.979242	+	11.7952i	−0.0401788	+	0.483963i
$595$	6.97742	+	10.4424i	0.286046	+	0.428099i
$596$	0.159129	−	0.226039i	0.00651816	−	0.00925894i
$597$	−30.7360	+	14.2675i	−1.25794	+	0.583931i
$598$	1.18344	−	5.59283i	0.0483944	−	0.228708i
$599$	14.7425	−	35.5915i	0.602362	−	1.45423i	−0.268782	−	0.963201i	$-0.586621\pi$
$599$	14.7425	−	35.5915i	0.602362	−	1.45423i	0.871143	−	0.491029i	$-0.163379\pi$
$600$	−3.44543	+	3.48268i	−0.140659	+	0.142180i
$601$	−9.47695	−	22.8794i	−0.386573	−	0.933269i	−0.990661	−	0.136352i	$-0.956462\pi$
$601$	−9.47695	−	22.8794i	−0.386573	−	0.933269i	0.604088	−	0.796918i	$-0.293538\pi$
$602$	−1.48550	−	7.97428i	−0.0605446	−	0.325007i
$603$	−3.82779	+	33.8647i	−0.155880	+	1.37908i
$604$	12.4383	+	32.2262i	0.506106	+	1.31127i
$605$	−8.24431	−	1.63989i	−0.335179	−	0.0666712i
$606$	13.6290	−	9.70461i	0.553639	−	0.394223i
$607$	−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
$612$	29.7796	−	1.77241i	1.20377	−	0.0716456i
$613$	32.4040	+	21.6517i	1.30879	+	0.874503i	0.997131	−	0.0756918i	$-0.0241165\pi$
$613$	32.4040	+	21.6517i	1.30879	+	0.874503i	0.311656	+	0.950195i	$0.399117\pi$
$614$	−7.62642	−	40.9391i	−0.307777	−	1.65217i
$615$	−0.154876	+	0.113147i	−0.00624518	+	0.00456251i
$616$	−6.73809	+	9.32800i	−0.271485	+	0.375836i
$617$	−29.7498	−	12.3228i	−1.19768	−	0.496096i	−0.307432	−	0.951570i	$-0.599470\pi$
$617$	−29.7498	−	12.3228i	−1.19768	−	0.496096i	−0.890249	+	0.455474i	$0.849470\pi$
$618$	5.09359	−	0.151446i	0.204894	−	0.00609204i
$619$	−0.732516	−	3.68261i	−0.0294423	−	0.148016i	0.963268	−	0.268542i	$-0.0865419\pi$
$619$	−0.732516	−	3.68261i	−0.0294423	−	0.148016i	−0.992710	+	0.120526i	$0.961542\pi$
$620$	−1.70845	−	9.83457i	−0.0686128	−	0.394966i
$621$	−18.9098	−	5.17253i	−0.758823	−	0.207567i
$622$	−9.85419	+	9.61714i	−0.395117	+	0.385612i
$623$	23.3966	+	23.3966i	0.937363	+	0.937363i
$624$	−4.08192	−	6.19984i	−0.163407	−	0.248192i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	0.295172	−	24.2453i	0.0117975	−	0.969039i
$627$	−4.72478	−	4.34457i	−0.188690	−	0.173506i
$628$	23.8531	−	15.1114i	0.951843	−	0.603010i
$629$	−4.16337	+	0.828146i	−0.166004	+	0.0330203i
$630$	−9.31375	−	5.30092i	−0.371069	−	0.211194i
$631$	−10.2998	+	24.8659i	−0.410029	+	0.989897i	0.575100	+	0.818083i	$0.304963\pi$
$631$	−10.2998	+	24.8659i	−0.410029	+	0.989897i	−0.985129	+	0.171815i	$0.945037\pi$
$632$	39.3757	+	18.0214i	1.56628	+	0.716852i
$633$	29.4317	−	21.5018i	1.16981	−	0.854619i
$634$	0.00339602	+	0.00232944i	0.000134873	+	9.25140e-5i
$635$	0.336810	−	0.504073i	0.0133659	−	0.0200035i
$636$	−20.2984	+	31.5641i	−0.804884	+	1.25160i
$637$	−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	$-0.0733902\pi$
$642$	−29.8404	−	5.01871i	−1.17771	−	0.198073i
$643$	3.23824	−	16.2797i	0.127704	−	0.642010i	−0.862914	−	0.505350i	$-0.831363\pi$
$643$	3.23824	−	16.2797i	0.127704	−	0.642010i	0.990618	−	0.136660i	$-0.0436366\pi$
$644$	−13.1454	−	13.8016i	−0.518000	−	0.543859i
$645$	−3.69347	−	1.35158i	−0.145430	−	0.0532183i
$646$	−9.15126	+	13.3413i	−0.360051	+	0.524908i
$647$	−7.69523	+	3.18747i	−0.302531	+	0.125312i	−0.528785	−	0.848756i	$-0.677352\pi$
$647$	−7.69523	+	3.18747i	−0.302531	+	0.125312i	0.226254	+	0.974068i	$0.427352\pi$
$648$	−22.0433	+	12.7317i	−0.865941	+	0.500147i
$649$	−4.32747	−	1.79250i	−0.169868	−	0.0703617i
$650$	−0.826402	−	1.27000i	−0.0324141	−	0.0498134i
$651$	19.8057	−	9.19372i	0.776245	−	0.360330i
$652$	−22.1497	−	34.9631i	−0.867450	−	1.36926i
$653$	8.43770	−	5.63789i	0.330193	−	0.220628i	−0.379412	−	0.925228i	$-0.623874\pi$
$653$	8.43770	−	5.63789i	0.330193	−	0.220628i	0.709604	+	0.704600i	$0.248874\pi$
$654$	−16.4246	+	3.77775i	−0.642254	+	0.147722i
$655$	13.9323	+	13.9323i	0.544381	+	0.544381i
$656$	−0.189229	+	0.400497i	−0.00738815	+	0.0156368i
$657$	13.2385	+	4.22466i	0.516483	+	0.164820i
$658$	12.6395	+	12.9510i	0.492737	+	0.504883i
$659$	−40.6038	+	27.1306i	−1.58170	+	1.05686i	−0.619327	+	0.785133i	$0.712594\pi$
$659$	−40.6038	+	27.1306i	−1.58170	+	1.05686i	−0.962375	+	0.271726i	$0.912406\pi$
$660$	2.22529	+	5.11647i	0.0866193	+	0.199158i
$661$	−8.33263	+	1.65746i	−0.324102	+	0.0644678i	−0.354460	−	0.935071i	$-0.615335\pi$
$661$	−8.33263	+	1.65746i	−0.324102	+	0.0644678i	0.0303581	+	0.999539i	$0.490335\pi$
$662$	8.27272	−	39.0962i	0.321528	−	1.51952i
$663$	−1.41944	+	9.11696i	−0.0551264	+	0.354073i
$664$	19.2052	−	26.5871i	0.745307	−	1.03178i
$665$	5.36931	−	2.22404i	0.208213	−	0.0862447i
$666$	2.86002	−	2.22275i	0.110824	−	0.0861298i
$667$	−3.51487	+	5.26037i	−0.136096	+	0.203682i
$668$	−18.0466	+	40.7340i	−0.698243	+	1.57604i
$669$	1.71677	+	40.9514i	0.0663741	+	1.58327i
$670$	5.96690	+	14.9164i	0.230522	+	0.576272i
$671$		−	12.3663i		−	0.477396i
$672$	−24.7445	−	0.469492i	−0.954539	−	0.0181110i
$673$		−	4.07049i		−	0.156906i	−0.996918	−	0.0784529i	$-0.975002\pi$
$673$		−	4.07049i		−	0.156906i	0.996918	−	0.0784529i	$-0.0249980\pi$
$674$	40.9033	−	16.3622i	1.57554	−	0.630249i
$675$	−4.51347	+	2.57461i	−0.173723	+	0.0990968i
$676$	−22.1141	+	8.53535i	−0.850544	+	0.328283i
$677$	−18.6377	+	27.8934i	−0.716307	+	1.07203i	0.277480	+	0.960731i	$0.410501\pi$
$677$	−18.6377	+	27.8934i	−0.716307	+	1.07203i	−0.993787	+	0.111298i	$0.964499\pi$
$678$	−4.66031	−	10.3682i	−0.178978	−	0.398188i
$679$	1.09503	−	0.453576i	0.0420233	−	0.0174066i
$680$	11.9705	−	7.38086i	0.459047	−	0.283043i
$681$	8.81966	+	1.37315i	0.337970	+	0.0526192i
$682$	−11.1221	−	2.35342i	−0.425885	−	0.0901170i
$683$	13.2346	−	2.63253i	0.506408	−	0.100731i	0.0647273	−	0.997903i	$-0.479382\pi$
$683$	13.2346	−	2.63253i	0.506408	−	0.100731i	0.441681	+	0.897172i	$0.354382\pi$
$684$	1.88402	−	13.6757i	0.0720373	−	0.522905i
$685$	−2.99996	+	2.00451i	−0.114622	+	0.0765883i
$686$	−19.4797	+	19.0111i	−0.743737	+	0.725845i
$687$	17.5412	−	28.7941i	0.669237	−	1.09856i
$688$	−8.98404	+	1.33626i	−0.342513	+	0.0509443i
$689$	−8.20730	−	8.20730i	−0.312673	−	0.312673i
$690$	−9.00646	+	2.07153i	−0.342870	+	0.0788619i
$691$	−18.8347	+	12.5849i	−0.716505	+	0.478753i	−0.859608	−	0.510954i	$-0.829292\pi$
$691$	−18.8347	+	12.5849i	−0.716505	+	0.478753i	0.143103	+	0.989708i	$0.454292\pi$
$692$	−1.49203	+	6.65039i	−0.0567183	+	0.252810i
$693$	−9.54505	+	7.60639i	−0.362586	+	0.288943i
$694$	−19.2085	+	12.4992i	−0.729145	+	0.474463i
$695$	−16.2376	−	6.72585i	−0.615929	−	0.255126i
$696$	1.64594	+	8.04833i	0.0623893	+	0.305071i
$697$	0.508682	−	0.210703i	0.0192677	−	0.00798094i
$698$	−3.07286	−	2.10778i	−0.116310	−	0.0797805i
$699$	11.0852	−	30.2926i	0.419281	−	1.14577i
$700$	−5.05036	−	0.122988i	−0.190886	−	0.00464852i
$701$	7.59487	−	38.1820i	0.286854	−	1.44211i	−0.521417	−	0.853302i	$-0.674596\pi$
$701$	7.59487	−	38.1820i	0.286854	−	1.44211i	0.808271	−	0.588811i	$-0.200404\pi$
$702$	−2.40081	−	7.49825i	−0.0906127	−	0.283003i
$703$			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
$708$	−2.13847	−	9.84460i	−0.0803686	−	0.369983i
$709$	−3.23386	+	4.83982i	−0.121450	+	0.181763i	−0.887213	−	0.461360i	$-0.847362\pi$
$709$	−3.23386	+	4.83982i	−0.121450	+	0.181763i	0.765763	+	0.643123i	$0.222362\pi$
$710$	4.54210	−	6.62179i	0.170462	−	0.248511i
$711$	35.0822	+	29.6456i	1.31568	+	1.11180i
$712$	27.1376	−	25.2244i	1.01702	−	0.945325i
$713$	7.20599	−	17.3968i	0.269866	−	0.651515i
$714$	22.3897	+	21.0968i	0.837915	+	0.789527i
$715$	−1.69250	+	0.336660i	−0.0632960	+	0.0125904i
$716$	−2.46927	+	11.0063i	−0.0922810	+	0.411323i
$717$	−9.23427	+	10.0424i	−0.344860	+	0.375040i
$718$	13.6847	+	0.166603i	0.510708	+	0.00621755i
$719$	−36.7344	+	36.7344i	−1.36996	+	1.36996i	−0.509480	+	0.860482i	$0.670162\pi$
$719$	−36.7344	+	36.7344i	−1.36996	+	1.36996i	−0.860482	+	0.509480i	$0.829838\pi$
$720$	−6.31259	+	10.2054i	−0.235256	+	0.380335i
$721$	3.71575	+	3.71575i	0.138382	+	0.138382i
$722$	−13.5384	−	13.8721i	−0.503846	−	0.516265i
$723$	−18.7442	−	17.2359i	−0.697105	−	0.641009i
$724$	−20.7313	+	29.4484i	−0.770471	+	1.09444i
$725$	0.327140	+	1.64464i	0.0121497	+	0.0610805i
$726$	−20.5809	+	0.611923i	−0.763828	+	0.0227106i
$727$	−38.1535	−	15.8037i	−1.41503	−	0.586126i	−0.461426	−	0.887179i	$-0.652662\pi$
$727$	−38.1535	−	15.8037i	−1.41503	−	0.586126i	−0.953608	+	0.301052i	$0.902662\pi$
$728$	1.76646	−	7.44797i	0.0654695	−	0.276040i
$729$	−26.1514	+	6.71615i	−0.968569	+	0.248746i
$730$	6.43996	−	1.19968i	0.238354	−	0.0444022i
$731$	9.38738	+	6.27245i	0.347205	+	0.231995i
$732$	21.8518	−	15.1623i	0.807665	−	0.560413i
$733$	6.21965	−	31.2683i	0.229728	−	1.15492i	−0.677903	−	0.735152i	$-0.737111\pi$
$733$	6.21965	−	31.2683i	0.229728	−	1.15492i	0.907631	−	0.419769i	$-0.137889\pi$
$734$	−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
$738$	−0.307588	+	0.355135i	−0.0113225	+	0.0130727i
$739$	−9.24774	−	1.83949i	−0.340183	−	0.0676667i	0.0220424	−	0.999757i	$-0.492983\pi$
$739$	−9.24774	−	1.83949i	−0.340183	−	0.0676667i	−0.362226	+	0.932090i	$0.617983\pi$
$740$	0.691652	−	1.56117i	0.0254256	−	0.0573897i
$741$	4.00967	+	1.46729i	0.147299	+	0.0539022i
$742$	−38.0442	+	7.08713i	−1.39664	+	0.260177i
$743$	1.53949	+	3.71665i	0.0564783	+	0.136351i	0.949600	−	0.313465i	$-0.101490\pi$
$743$	1.53949	+	3.71665i	0.0564783	+	0.136351i	−0.893122	+	0.449815i	$0.851490\pi$
$744$	−9.47809	−	22.5386i	−0.347484	−	0.826307i
$745$	0.0528934	−	0.127696i	0.00193786	−	0.00467841i
$746$	5.16521	+	1.09295i	0.189112	+	0.0400159i
$747$	27.2057	−	21.6801i	0.995405	−	0.793232i
$748$	−2.74129	−	15.7801i	−0.100231	−	0.576976i
$749$	−17.3359	−	25.9450i	−0.633440	−	0.948009i
$750$	−1.29973	+	2.07622i	−0.0474596	+	0.0758129i
$751$	2.82090	−	2.82090i	0.102936	−	0.102936i	−0.653763	−	0.756699i	$-0.726811\pi$
$751$	2.82090	−	2.82090i	0.102936	−	0.102936i	0.756699	+	0.653763i	$0.226811\pi$
$752$	15.0091	−	13.6142i	0.547325	−	0.496458i
$753$	5.80675	+	3.53743i	0.211610	+	0.128911i
$754$	−2.54060	−	0.0309302i	−0.0925230	−	0.00112641i
$755$	9.59561	+	14.3608i	0.349220	+	0.522645i
$756$	−25.1439	−	7.54036i	−0.914476	−	0.274240i
$757$	0.316732	+	1.59232i	0.0115118	+	0.0578738i	0.986114	−	0.166068i	$-0.0531073\pi$
$757$	0.316732	+	1.59232i	0.0115118	+	0.0578738i	−0.974602	+	0.223942i	$0.928107\pi$
$758$	−21.7831	+	14.1745i	−0.791198	+	0.514841i
$759$	−1.61919	+	10.4000i	−0.0587729	+	0.377495i
$760$	−2.26920	−	6.09925i	−0.0823124	−	0.221243i
$761$	−17.4189	−	42.0529i	−0.631434	−	1.52442i	−0.837820	−	0.545947i	$-0.816170\pi$
$761$	−17.4189	−	42.0529i	−0.631434	−	1.52442i	0.206385	−	0.978471i	$-0.433830\pi$
$762$	0.527255	−	1.38823i	0.0191004	−	0.0502903i
$763$	−14.4504	−	9.65548i	−0.523141	−	0.349552i
$764$	16.7026	+	17.5364i	0.604278	+	0.634444i
$765$	14.3346	−	4.12423i	0.518270	−	0.149112i
$766$	−0.368737	+	0.860431i	−0.0133230	+	0.0310886i
$767$	3.11584			0.112506
$768$	−1.53707	+	27.6702i	−0.0554642	+	0.998461i
$769$	−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
$771$	−33.8403	+	1.41866i	−1.21873	+	0.0510917i
$772$	36.8080	+	38.6455i	1.32475	+	1.39088i
$773$	−4.12556	−	2.75661i	−0.148386	−	0.0991483i	0.479161	−	0.877727i	$-0.340941\pi$
$773$	−4.12556	−	2.75661i	−0.148386	−	0.0991483i	−0.627547	+	0.778579i	$0.715941\pi$
$774$	−9.55900	−	1.19850i	−0.343591	−	0.0430791i
$775$	−1.90995	−	4.61102i	−0.0686073	−	0.165633i
$776$	−0.462785	−	1.24389i	−0.0166130	−	0.0446532i
$777$	3.69077	+	0.574623i	0.132406	+	0.0206145i
$778$	19.6622	−	12.7944i	0.704923	−	0.458701i
$779$	−0.0497066	−	0.249892i	−0.00178092	−	0.00895330i
$780$	−2.67006	−	2.57795i	−0.0956034	−	0.0923053i
$781$	−5.08080	−	7.60396i	−0.181805	−	0.272091i
$782$	26.5271	+	0.322952i	0.948608	+	0.0115487i
$783$	−0.615136	+	8.69149i	−0.0219832	+	0.310608i
$784$	1.66534	+	1.83597i	0.0594764	+	0.0655704i
$785$	9.98327	−	9.98327i	0.356318	−	0.356318i
$786$	40.9084	+	25.6090i	1.45915	+	0.913443i
$787$	−18.4242	−	27.5737i	−0.656750	−	0.982896i	−0.999062	−	0.0433095i	$-0.986210\pi$
$787$	−18.4242	−	27.5737i	−0.656750	−	0.982896i	0.342312	−	0.939586i	$-0.388790\pi$
$788$	2.10036	+	12.0906i	0.0748221	+	0.430709i
$789$	−10.9913	−	23.6781i	−0.391300	−	0.842963i
$790$	21.1829	+	4.48228i	0.753652	+	0.159472i
$791$	4.48587	−	10.8298i	0.159499	−	0.385065i
$792$	8.12137	+	10.9920i	0.288580	+	0.390584i
$793$	3.14800	+	7.59996i	0.111789	+	0.269882i
$794$	25.1624	−	4.68742i	0.892978	−	0.166350i
$795$	−6.44818	+	17.6210i	−0.228693	+	0.624953i
$796$	−15.8494	+	35.7745i	−0.561765	+	1.26799i
$797$	−46.5142	−	9.25224i	−1.64762	−	0.327731i	−0.717939	−	0.696106i	$-0.754914\pi$
$797$	−46.5142	−	9.25224i	−1.64762	−	0.327731i	−0.929677	+	0.368375i	$0.879914\pi$
$798$	11.5963	−	8.25722i	0.410504	−	0.292302i
$799$	−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
$804$	22.4340	+	32.3317i	0.791185	+	1.14025i
$805$	−7.92392	−	5.29459i	−0.279281	−	0.186610i
$806$	7.43437	−	1.38492i	0.261864	−	0.0487819i
$807$	−22.5538	−	30.8718i	−0.793933	−	1.08674i
$808$	4.45837	−	18.7979i	0.156845	−	0.661308i
$809$	−38.3206	−	15.8729i	−1.34728	−	0.558063i	−0.411748	−	0.911298i	$-0.635082\pi$
$809$	−38.3206	−	15.8729i	−1.34728	−	0.558063i	−0.935535	+	0.353235i	$0.885082\pi$
$810$	−9.36075	+	8.62417i	−0.328903	+	0.303022i
$811$	1.66928	+	8.39202i	0.0586163	+	0.294684i	0.998963	−	0.0455344i	$-0.0144991\pi$
$811$	1.66928	+	8.39202i	0.0586163	+	0.294684i	−0.940347	+	0.340218i	$0.889499\pi$
$812$	−4.87647	+	6.92694i	−0.171130	+	0.243088i
$813$	3.65336	−	3.97308i	0.128129	−	0.139342i
$814$	−1.35826	−	1.39174i	−0.0476071	−	0.0487806i
$815$	−14.6331	−	14.6331i	−0.512576	−	0.512576i
$816$	24.5230	−	24.1918i	0.858475	−	0.846883i
$817$	3.69428	−	3.69428i	0.129247	−	0.129247i
$818$	−10.8632	−	0.132253i	−0.379824	−	0.00462413i
$819$	3.92979	−	7.10447i	0.137318	−	0.248250i
$820$	−0.0484832	+	0.216104i	−0.00169311	+	0.00754667i
$821$	54.7983	−	10.9001i	1.91248	−	0.380415i	0.912863	−	0.408266i	$-0.133866\pi$
$821$	54.7983	−	10.9001i	1.91248	−	0.380415i	0.999612	+	0.0278512i	$0.00886646\pi$
$822$	−6.06079	+	6.43224i	−0.211394	+	0.224350i
$823$	11.4434	−	27.6268i	0.398892	−	0.963011i	−0.589037	−	0.808106i	$-0.700493\pi$
$823$	11.4434	−	27.6268i	0.398892	−	0.963011i	0.987929	−	0.154905i	$-0.0495071\pi$
$824$	4.30988	−	4.00604i	0.150142	−	0.139557i
$825$	1.64568	+	2.25261i	0.0572952	+	0.0784259i
$826$	5.87630	−	8.56687i	0.204463	−	0.298079i
$827$	7.60870	−	11.3872i	0.264580	−	0.395972i	−0.675264	−	0.737576i	$-0.735970\pi$
$827$	7.60870	−	11.3872i	0.264580	−	0.395972i	0.939844	+	0.341604i	$0.110970\pi$
$828$	−20.3625	+	9.89016i	−0.707645	+	0.343707i
$829$	26.6849	+	5.30795i	0.926804	+	0.184353i	0.635343	−	0.772230i	$-0.280859\pi$
$829$	26.6849	+	5.30795i	0.926804	+	0.184353i	0.291461	+	0.956583i	$0.405859\pi$
$830$	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
$834$	−42.4547	−	7.14025i	−1.47009	−	0.247247i
$835$	−4.34589	+	21.8483i	−0.150396	+	0.756091i
$836$	−7.40941	−	0.180437i	−0.256260	−	0.00624054i
$837$	−3.25110	−	25.7290i	−0.112374	−	0.889326i
$838$	−0.243151	−	0.166785i	−0.00839950	−	0.00576149i
$839$	14.6562	−	6.07080i	0.505989	−	0.209587i	−0.115061	−	0.993358i	$-0.536706\pi$
$839$	14.6562	−	6.07080i	0.505989	−	0.209587i	0.621050	+	0.783771i	$0.286706\pi$
$840$	−12.1235	+	2.47935i	−0.418302	+	0.0855459i
$841$	−24.1947	−	10.0218i	−0.834299	−	0.345578i
$842$	6.98105	−	4.54264i	0.240583	−	0.156550i
$843$	−5.51066	−	11.8714i	−0.189797	−	0.408873i
$844$	9.21349	−	41.0672i	0.317141	−	1.41359i
$845$	−9.85465	+	6.58466i	−0.339010	+	0.226519i
$846$	19.2174	−	9.62486i	0.660707	−	0.330910i
$847$	−15.0136	−	15.0136i	−0.515875	−	0.515875i
$848$	6.37510	+	42.8616i	0.218922	+	1.47187i
$849$	15.4301	+	9.39989i	0.529559	+	0.322603i
$850$	5.03220	−	4.91115i	0.172603	−	0.168451i
$851$	2.67827	−	1.78957i	0.0918101	−	0.0613455i
$852$	7.20697	−	18.3012i	0.246907	−	0.626987i
$853$	−54.1584	+	10.7728i	−1.85435	+	0.368853i	−0.990791	−	0.135397i	$-0.956769\pi$
$853$	−54.1584	+	10.7728i	−1.85435	+	0.368853i	−0.863558	+	0.504250i	$0.831769\pi$
$854$	26.8327	+	5.67779i	0.918198	+	0.194290i
$855$	−0.577716	−	6.87823i	−0.0197575	−	0.235231i
$856$	−29.7415	+	18.3383i	−1.01654	+	0.626789i
$857$	34.8180	−	14.4221i	1.18936	−	0.492649i	0.301813	−	0.953367i	$-0.402408\pi$
$857$	34.8180	−	14.4221i	1.18936	−	0.492649i	0.887547	+	0.460718i	$0.152408\pi$
$858$	−3.85543	+	1.73294i	−0.131622	+	0.0591618i
$859$	0.695116	−	1.04031i	0.0237170	−	0.0354951i	−0.819422	−	0.573191i	$-0.805705\pi$
$859$	0.695116	−	1.04031i	0.0237170	−	0.0354951i	0.843139	+	0.537696i	$0.180705\pi$
$860$	−4.23680	+	1.63527i	−0.144474	+	0.0557623i
$861$	−0.484057	+	0.0202927i	−0.0164966	+	0.000691573i
$862$	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	$0.770829\pi$
$864$	−9.46577	+	27.8280i	−0.322032	+	0.946729i
$865$			3.40785i			0.115870i
$866$	−14.8184	−	37.0439i	−0.503548	−	1.25880i
$867$	−13.3618	+	0.560156i	−0.453791	+	0.0190239i
$868$	10.2130	−	23.0524i	0.346652	−	0.782449i
$869$	13.7000	−	20.5035i	0.464740	−	0.695532i
$870$	1.68394	+	3.74640i	0.0570909	+	0.127015i
$871$	−11.2448	+	4.65776i	−0.381017	+	0.157822i
$872$	−11.3954	+	15.7754i	−0.385897	+	0.534223i
$873$	−0.117821	−	1.40276i	−0.00398762	−	0.0474763i
$874$	2.54140	−	12.0104i	0.0859641	−	0.406259i
$875$	−2.47739	+	0.492784i	−0.0837512	+	0.0166591i
$876$	14.7145	−	6.39975i	0.497158	−	0.216228i
$877$	19.2860	−	12.8865i	0.651243	−	0.435146i	−0.185574	−	0.982630i	$-0.559414\pi$
$877$	19.2860	−	12.8865i	0.651243	−	0.435146i	0.836816	+	0.547484i	$0.184414\pi$
$878$	−7.92910	−	8.12454i	−0.267594	−	0.274190i
$879$	32.5645	+	19.8381i	1.09837	+	0.669121i
$880$	5.82510	+	2.75227i	0.196364	+	0.0927791i
$881$	−4.17139	−	4.17139i	−0.140538	−	0.140538i	0.633338	−	0.773876i	$-0.281684\pi$
$881$	−4.17139	−	4.17139i	−0.140538	−	0.140538i	−0.773876	+	0.633338i	$0.781684\pi$
$882$	1.17735	+	2.35075i	0.0396435	+	0.0791537i
$883$	44.1573	−	29.5050i	1.48601	−	0.992922i	0.493638	−	0.869668i	$-0.335667\pi$
$883$	44.1573	−	29.5050i	1.48601	−	0.992922i	0.992375	−	0.123254i	$-0.0393331\pi$
$884$	5.70173	+	9.00011i	0.191770	+	0.302706i
$885$	−2.12084	−	4.56884i	−0.0712913	−	0.153580i
$886$	−3.96667	−	6.09590i	−0.133263	−	0.204796i
$887$	46.7599	+	19.3686i	1.57004	+	0.650333i	0.986797	−	0.161962i	$-0.0517822\pi$
$887$	46.7599	+	19.3686i	1.57004	+	0.650333i	0.583246	+	0.812295i	$0.301782\pi$
$888$	0.793910	−	4.10652i	0.0266419	−	0.137806i
$889$	1.41476	−	0.586013i	0.0474496	−	0.0196543i
$890$	10.4787	−	15.2766i	0.351248	−	0.512074i
$891$	5.15991	+	13.5464i	0.172864	+	0.453820i
$892$	32.6414	+	34.2708i	1.09291	+	1.14747i
$893$	−2.27393	+	11.4318i	−0.0760942	+	0.382551i
$894$	0.0561523	−	0.333872i	0.00187801	−	0.0111664i
$895$			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
$900$	−1.96270	+	5.66990i	−0.0654235	+	0.188997i
$901$	29.9250	−	44.7859i	0.996945	−	1.49203i
$902$	0.208007	+	0.142679i	0.00692587	+	0.00475068i
$903$	−5.86043	−	8.02178i	−0.195023	−	0.266948i
$904$	−11.9353	−	5.46252i	−0.396962	−	0.181681i
$905$	−6.89094	+	16.6362i	−0.229063	+	0.553006i
$906$	30.7912	+	29.0131i	1.02297	+	0.963895i
$907$	−0.207808	+	0.0413356i	−0.00690015	+	0.00137252i	−0.198539	−	0.980093i	$-0.563620\pi$
$907$	−0.207808	+	0.0413356i	−0.00690015	+	0.00137252i	0.191639	+	0.981465i	$0.438620\pi$
$908$	8.70662	−	5.51580i	0.288939	−	0.183048i
$909$	9.91838	−	17.9309i	0.328972	−	0.594731i
$910$	0.0465915	−	3.82701i	0.00154449	−	0.126864i
$911$	−23.9481	+	23.9481i	−0.793436	+	0.793436i	−0.982051	−	0.188615i	$-0.939600\pi$
$911$	−23.9481	+	23.9481i	−0.793436	+	0.793436i	0.188615	+	0.982051i	$0.439600\pi$
$912$	−8.76579	−	13.3140i	−0.290264	−	0.440869i
$913$	−13.2065	−	13.2065i	−0.437072	−	0.437072i
$914$	−22.9375	+	22.3857i	−0.758706	+	0.740454i
$915$	9.00130	−	9.78903i	0.297574	−	0.323616i
$916$	−6.66346	−	38.3578i	−0.220167	−	1.26738i
$917$	9.70946	+	48.8128i	0.320635	+	1.61194i
$918$	31.9546	−	17.7158i	1.05466	−	0.584707i
$919$	−44.3805	−	18.3830i	−1.46398	−	0.606399i	−0.498500	−	0.866890i	$-0.666116\pi$
$919$	−44.3805	−	18.3830i	−1.46398	−	0.606399i	−0.965476	+	0.260491i	$0.916116\pi$
$920$	−6.24868	+	8.65048i	−0.206013	+	0.285198i
$921$	−30.0869	−	41.1830i	−0.991396	−	1.35703i
$922$	1.21852	+	6.54107i	0.0401297	+	0.215419i
$923$	5.05819	+	3.37978i	0.166492	+	0.111247i
$924$	−2.50646	+	13.8686i	−0.0824566	+	0.456243i
$925$	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	$-0.672037\pi$
$929$	−31.3659			−1.02908			−0.514540	+	0.857466i	$0.672037\pi$
$930$	−7.09107	−	9.95856i	−0.232525	−	0.326554i
$931$	−1.39839	−	0.278156i	−0.0458302	−	0.00911620i
$932$	−13.4120	−	34.7489i	−0.439324	−	1.13824i
$933$	−5.79529	+	15.8369i	−0.189729	+	0.518475i
$934$	1.65182	+	8.86706i	0.0540491	+	0.290139i
$935$	−3.06460	−	7.39861i	−0.100223	−	0.241960i
$936$	−7.78930	−	4.68795i	−0.254601	−	0.153230i
$937$	−8.95148	+	21.6108i	−0.292432	+	0.705993i	−1.00000		0.000652178i	$-0.999792\pi$
$937$	−8.95148	+	21.6108i	−0.292432	+	0.705993i	0.707568	+	0.706645i	$0.249792\pi$
$938$	−8.40081	+	39.7015i	−0.274296	+	1.29630i
$939$	−12.5036	−	26.9360i	−0.408039	−	0.879022i
$940$	5.83238	−	8.28480i	0.190231	−	0.270220i
$941$	−25.3501	−	37.9391i	−0.826389	−	1.23678i	−0.969015	−	0.247002i	$-0.920555\pi$
$941$	−25.3501	−	37.9391i	−0.826389	−	1.23678i	0.142626	−	0.989777i	$-0.454445\pi$
$942$	18.3503	−	29.3131i	0.597884	−	0.955071i
$943$	−0.295429	+	0.295429i	−0.00962050	+	0.00962050i
$944$	−9.34616	−	6.92590i	−0.304192	−	0.225419i
$945$	−13.0924	−	0.926605i	−0.425895	−	0.0301425i
$946$	−0.0629641	+	5.17185i	−0.00204714	+	0.168151i
$947$	22.5872	+	33.8041i	0.733984	+	1.09849i	0.991231	+	0.132139i	$0.0421847\pi$
$947$	22.5872	+	33.8041i	0.733984	+	1.09849i	−0.257247	+	0.966346i	$0.582815\pi$
$948$	53.0279	−	0.930738i	1.72227	−	0.0302290i
$949$	0.968205	+	4.86750i	0.0314293	+	0.158006i
$950$	−1.77467	−	2.72728i	−0.0575780	−	0.0884847i
$951$	0.00498366		0.000775916i	0.000161606		2.51608e-5i
$952$	35.4986	+	1.29703i	1.15052	+	0.0420371i
$953$	−1.51175	−	3.64969i	−0.0489705	−	0.118225i	0.897501	−	0.441012i	$-0.145380\pi$
$953$	−1.51175	−	3.64969i	−0.0489705	−	0.118225i	−0.946472	+	0.322787i	$0.895380\pi$
$954$	−5.71786	+	45.6046i	−0.185123	+	1.47650i
$955$	10.0682	+	6.72734i	0.325799	+	0.217692i
$956$	−0.383513	+	15.7485i	−0.0124037	+	0.509343i
$957$	4.67387	−	0.195939i	0.151085	−	0.00633380i
$958$	41.7501	+	17.8919i	1.34888	+	0.578063i
$959$	−9.11360			−0.294293
$960$	2.27874	+	13.6677i	0.0735461	+	0.441125i
$961$	−6.09063			−0.196472
$962$	1.18903	+	0.509559i	0.0383360	+	0.0164288i
$963$	−35.6154	+	10.2469i	−1.14769	+	0.330203i
$964$	−29.3947	−	0.715831i	−0.946740	−	0.0230554i
$965$	22.1875	+	14.8252i	0.714242	+	0.477242i
$966$	−21.8227	−	8.28834i	−0.702134	−	0.266673i
$967$	11.8698	+	28.6561i	0.381706	+	0.921519i	0.991636	+	0.129064i	$0.0411973\pi$
$967$	11.8698	+	28.6561i	0.381706	+	0.921519i	−0.609931	+	0.792455i	$0.708803\pi$
$968$	−17.4143	+	16.1866i	−0.559716	+	0.520257i
$969$	−3.04820	+	19.5784i	−0.0979222	+	0.628949i
$970$	−0.361930	−	0.556207i	−0.0116209	−	0.0178587i
$971$	−1.45646	−	7.32211i	−0.0467400	−	0.234978i	0.950353	−	0.311174i	$-0.100722\pi$
$971$	−1.45646	−	7.32211i	−0.0467400	−	0.234978i	−0.997093	+	0.0761967i	$0.975722\pi$
$972$	−17.6104	+	25.7269i	−0.564855	+	0.825190i
$973$	−24.6642	−	36.9126i	−0.790699	−	1.18336i
$974$	0.423793	−	34.8102i	0.0135792	−	1.11539i
$975$	−1.58482	−	0.965458i	−0.0507548	−	0.0309194i
$976$	7.45059	−	29.7940i	0.238487	−	0.953682i
$977$	33.8171	−	33.8171i	1.08191	−	1.08191i	0.0855740	−	0.996332i	$-0.472728\pi$
$977$	33.8171	−	33.8171i	1.08191	−	1.08191i	0.996332	−	0.0855740i	$-0.0272724\pi$
$978$	−42.9661	−	26.8972i	−1.37390	−	0.860076i
$979$	−11.7215	−	17.5425i	−0.374622	−	0.560662i
$980$	1.01343	+	0.713440i	0.0323728	+	0.0227900i
$981$	−16.1425	+	12.8639i	−0.515391	+	0.410711i
$982$	3.51581	−	16.6154i	0.112194	−	0.530220i
$983$	11.4150	−	27.5582i	0.364081	−	0.878970i	−0.630613	−	0.776097i	$-0.717197\pi$
$983$	11.4150	−	27.5582i	0.364081	−	0.878970i	0.994695	−	0.102873i	$-0.0328034\pi$
$984$	0.00291662	+	0.542494i	9.29783e−5	+	0.0172941i
$985$	2.34808	+	5.66877i	0.0748161	+	0.180622i
$986$	−2.15934	−	11.5915i	−0.0687675	−	0.369148i
$987$	20.8138	+	7.61654i	0.662511	+	0.242437i
$988$	4.59953	−	1.77527i	0.146330	−	0.0564788i
$989$	−8.40252	−	1.67137i	−0.267185	−	0.0531463i
$990$	5.16532	+	4.47377i	0.164165	+	0.142186i
$991$	−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
$996$	7.14403	−	39.5289i	0.226367	−	1.25252i
$997$	27.1264	+	18.1253i	0.859101	+	0.574033i	0.905239	−	0.424902i	$-0.139692\pi$
$997$	27.1264	+	18.1253i	0.859101	+	0.574033i	−0.0461384	+	0.998935i	$0.514692\pi$
$998$	0.436862	+	2.34510i	0.0138286	+	0.0742329i
$999$	1.98280	−	3.96850i	0.0627331	−	0.125558i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.11.47	✓	1024	64.11	odd	16	inner
960.2.cn.a.11.82	yes	1024	192.11	even	16	inner
960.2.cn.a.611.47	yes	1024	3.2	odd	2	inner
960.2.cn.a.611.82	yes	1024	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.557061 - 1.29988i) q^{2} +(-0.0725476 - 1.73053i) q^{3} +(-1.37937 - 1.44822i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-2.28989 - 0.869709i) q^{6} +(-0.966631 - 2.33365i) q^{7} +(-2.65091 + 0.986257i) q^{8} +(-2.98947 + 0.251092i) q^{9} +O(q^{10})\)	\(q+(0.557061 - 1.29988i) q^{2} +(-0.0725476 - 1.73053i) q^{3} +(-1.37937 - 1.44822i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-2.28989 - 0.869709i) q^{6} +(-0.966631 - 2.33365i) q^{7} +(-2.65091 + 0.986257i) q^{8} +(-2.98947 + 0.251092i) q^{9} +(-1.18535 + 0.771322i) q^{10} +(0.314221 + 1.57970i) q^{11} +(-2.40613 + 2.49210i) q^{12} +(-0.595243 - 0.890844i) q^{13} +(-3.57194 - 0.0434862i) q^{14} +(-0.901110 + 1.47919i) q^{15} +(-0.194704 + 3.99526i) q^{16} +(3.51577 - 3.51577i) q^{17} +(-1.33893 + 4.02582i) q^{18} +(-1.27827 - 1.91306i) q^{19} +(0.342310 + 1.97049i) q^{20} +(-3.96833 + 1.84209i) q^{21} +(2.22845 + 0.471539i) q^{22} +(-1.44382 + 3.48568i) q^{23} +(1.89906 + 4.51592i) q^{24} +(0.382683 + 0.923880i) q^{25} +(-1.48958 + 0.277488i) q^{26} +(0.651401 + 5.15516i) q^{27} +(-2.04632 + 4.61886i) q^{28} +(1.64464 + 0.327140i) q^{29} +(1.42079 + 1.99533i) 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} +(4.48721 + 3.98308i) q^{36} +(-0.709876 - 0.474324i) q^{37} +(-3.19882 + 0.595898i) q^{38} +(-1.49845 + 1.09472i) q^{39} +(2.75208 + 0.652721i) q^{40} +(0.102308 + 0.0423775i) q^{41} +(0.183881 + 6.18450i) q^{42} +(0.442995 + 2.22709i) q^{43} +(1.85433 - 2.63404i) q^{44} +(2.62516 + 1.45209i) q^{45} +(3.72667 + 3.81853i) q^{46} +(-3.58215 - 3.58215i) q^{47} +(6.92804 + 0.0470943i) q^{48} +(0.438183 - 0.438183i) q^{49} +(1.41411 + 0.0172159i) q^{50} +(-6.33920 - 5.82908i) q^{51} +(-0.469084 + 2.09084i) q^{52} +(10.6251 - 2.11347i) q^{53} +(7.06395 + 2.02500i) q^{54} +(0.616367 - 1.48804i) q^{55} +(4.86403 + 5.23295i) q^{56} +(-3.21787 + 2.35087i) q^{57} +(1.34141 - 1.95560i) q^{58} +(-1.61569 + 2.41805i) q^{59} +(3.38516 - 0.735333i) 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} +(0.654344 - 3.89062i) q^{66} +(2.21625 - 11.1418i) q^{67} +(-9.94114 - 0.242091i) q^{68} +(6.13683 + 2.24569i) q^{69} +(2.94580 + 2.02062i) q^{70} +(-5.24577 + 2.17287i) q^{71} +(7.67717 - 3.61401i) q^{72} +(-4.27949 - 1.77262i) q^{73} +(-1.01201 + 0.658525i) q^{74} +(1.57104 - 0.729271i) q^{75} +(-1.00734 + 4.49002i) q^{76} +(3.38273 - 2.26027i) q^{77} +(0.588267 + 2.55763i) q^{78} +(-10.8259 - 10.8259i) q^{79} +(2.38154 - 3.21376i) q^{80} +(8.87391 - 1.50126i) q^{81} +(0.112078 - 0.109382i) q^{82} +(-9.64161 + 6.44232i) q^{83} +(8.14153 + 3.20612i) q^{84} +(-4.87651 + 0.969998i) q^{85} +(3.14171 + 0.664784i) q^{86} +(0.446810 - 2.86984i) q^{87} +(-2.39096 - 3.87772i) q^{88} +(-12.1021 + 5.01286i) q^{89} +(3.34991 - 2.60348i) q^{90} +(-1.50354 + 2.25021i) q^{91} +(7.03960 - 2.71706i) q^{92} +(0.362080 + 8.63696i) q^{93} +(-6.65184 + 2.66088i) q^{94} +2.30082i q^{95} +(3.92056 - 8.97938i) q^{96} +0.469233i q^{97} +(-0.325490 - 0.813680i) q^{98} +(-1.33600 - 4.64356i) 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

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