LMFDB - Embedded newform 595.2.co.a.61.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [595,2,Mod(31,595)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("595.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(595, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 595 = 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	595.co (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.75109892027$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			61.17
Character	$\chi$	$=$	595.61
Dual form			595.2.co.a.556.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.526208 - 0.685768i) q^{2} +(1.29026 + 0.0845678i) q^{3} +(0.324256 - 1.21014i) q^{4} +(-0.946930 - 0.321439i) q^{5} +(-0.620949 - 0.929316i) q^{6} +(0.450303 - 2.60715i) q^{7} +(-2.59769 + 1.07600i) q^{8} +(-1.31673 - 0.173350i) q^{9} +(0.277849 + 0.818518i) q^{10} +(2.02609 - 4.10850i) q^{11} +(0.520712 - 1.53397i) q^{12} +(2.22495 + 2.22495i) q^{13} +(-2.02485 + 1.06310i) q^{14} +(-1.19460 - 0.494819i) q^{15} +(-0.0651537 - 0.0376165i) q^{16} +(-3.52294 + 2.14216i) q^{17} +(0.573994 + 0.994186i) q^{18} +(-2.29130 + 1.75817i) q^{19} +(-0.696034 + 1.04169i) q^{20} +(0.801487 - 3.32581i) q^{21} +(-3.88362 + 0.772499i) q^{22} +(-0.361542 - 5.51606i) q^{23} +(-3.44268 + 1.16863i) q^{24} +(0.793353 + 0.608761i) q^{25} +(0.355013 - 2.69659i) q^{26} +(-5.48879 - 1.09179i) q^{27} +(-3.00900 - 1.39031i) q^{28} +(-1.01386 - 5.09702i) q^{29} +(0.289277 + 1.07960i) q^{30} +(-0.413251 + 6.30500i) q^{31} +(0.742493 + 5.63980i) q^{32} +(2.96162 - 5.12967i) q^{33} +(3.32283 + 1.28870i) q^{34} +(-1.26445 + 2.32404i) q^{35} +(-0.636734 + 1.53721i) q^{36} +(10.6466 - 5.25032i) q^{37} +(2.41140 + 0.646132i) q^{38} +(2.68260 + 3.05892i) q^{39} +(2.80570 - 0.183895i) q^{40} +(1.80555 - 9.07710i) q^{41} +(-2.70248 + 1.20043i) q^{42} +(2.51959 + 6.08284i) q^{43} +(-4.31488 - 3.78405i) q^{44} +(1.19113 + 0.587398i) q^{45} +(-3.59249 + 3.15053i) q^{46} +(-9.08508 + 2.43434i) q^{47} +(-0.0808838 - 0.0540449i) q^{48} +(-6.59445 - 2.34801i) q^{49} -0.864391i q^{50} +(-4.72666 + 2.46601i) q^{51} +(3.41396 - 1.97105i) q^{52} +(9.85071 - 1.29687i) q^{53} +(2.13953 + 4.33854i) q^{54} +(-3.23919 + 3.23919i) q^{55} +(1.63554 + 7.25708i) q^{56} +(-3.10505 + 2.07473i) q^{57} +(-2.96187 + 3.37737i) q^{58} +(5.86188 - 7.63936i) q^{59} +(-0.986155 + 1.28518i) q^{60} +(-2.02497 + 2.30903i) q^{61} +(4.54122 - 3.03434i) q^{62} +(-1.04488 + 3.35484i) q^{63} +(3.37049 - 3.37049i) q^{64} +(-1.39169 - 2.82206i) q^{65} +(-5.07619 + 0.668293i) q^{66} +(3.91238 - 2.25881i) q^{67} +(1.44998 + 4.95786i) q^{68} -7.14771i q^{69} +(2.25912 - 0.355814i) q^{70} +(-3.75431 - 2.50855i) q^{71} +(3.60696 - 0.966483i) q^{72} +(7.75495 - 6.80091i) q^{73} +(-9.20282 - 4.53833i) q^{74} +(0.972147 + 0.852550i) q^{75} +(1.38467 + 3.34289i) q^{76} +(-9.79911 - 7.13238i) q^{77} +(0.686102 - 3.44927i) q^{78} +(-5.58077 + 0.365783i) q^{79} +(0.0496046 + 0.0565632i) q^{80} +(-3.14111 - 0.841659i) q^{81} +(-7.17488 + 3.53826i) q^{82} +(-1.89327 + 4.57077i) q^{83} +(-3.76480 - 2.04832i) q^{84} +(4.02456 - 0.896065i) q^{85} +(2.84558 - 4.92870i) q^{86} +(-0.877096 - 6.66221i) q^{87} +(-0.842407 + 12.8526i) q^{88} +(0.00486531 + 0.0181576i) q^{89} +(-0.223961 - 1.12593i) q^{90} +(6.80269 - 4.79888i) q^{91} +(-6.79243 - 1.35110i) q^{92} +(-1.06640 + 8.10011i) q^{93} +(6.45003 + 4.94929i) q^{94} +(2.73485 - 0.928355i) q^{95} +(0.481061 + 7.33957i) q^{96} +(2.95338 - 0.587464i) q^{97} +(1.85986 + 5.75781i) q^{98} +(-3.38001 + 5.05854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 32 q^{14} - 64 q^{18} - 64 q^{22} - 96 q^{28} - 64 q^{37} + 16 q^{39} - 96 q^{42} - 96 q^{44} + 64 q^{46} - 64 q^{49} - 64 q^{51} + 64 q^{53} - 240 q^{54} - 240 q^{56} - 64 q^{58} + 64 q^{60} - 288 q^{61}+ \cdots - 480 q^{99}+O(q^{100}) $ 768 * q + 32 * q^14 - 64 * q^18 - 64 * q^22 - 96 * q^28 - 64 * q^37 + 16 * q^39 - 96 * q^42 - 96 * q^44 + 64 * q^46 - 64 * q^49 - 64 * q^51 + 64 * q^53 - 240 * q^54 - 240 * q^56 - 64 * q^58 + 64 * q^60 - 288 * q^61 - 96 * q^63 - 16 * q^65 + 32 * q^71 + 96 * q^77 - 48 * q^81 - 240 * q^82 - 448 * q^92 + 128 * q^93 - 272 * q^98 - 480 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/595\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.526208	−	0.685768i	−0.372085	−	0.484911i	0.569355	−	0.822092i	$-0.307193\pi$
$2$	−0.526208	−	0.685768i	−0.372085	−	0.484911i	−0.941440	+	0.337181i	$0.890527\pi$
$3$	1.29026	+	0.0845678i	0.744930	+	0.0488253i	0.433141	−	0.901326i	$-0.357405\pi$
$3$	1.29026	+	0.0845678i	0.744930	+	0.0488253i	0.311789	+	0.950151i	$0.399072\pi$
$4$	0.324256	−	1.21014i	0.162128	−	0.605069i
$5$	−0.946930	−	0.321439i	−0.423480	−	0.143752i
$5$	−0.946930	−	0.321439i	−0.423480	−	0.143752i
$6$	−0.620949	−	0.929316i	−0.253501	−	0.379392i
$7$	0.450303	−	2.60715i	0.170199	−	0.985410i
$7$	0.450303	−	2.60715i	0.170199	−	0.985410i
$8$	−2.59769	+	1.07600i	−0.918421	+	0.380422i
$9$	−1.31673	−	0.173350i	−0.438909	−	0.0577834i
$10$	0.277849	+	0.818518i	0.0878637	+	0.258838i
$11$	2.02609	−	4.10850i	0.610888	−	1.23876i	−0.343209	−	0.939259i	$-0.611514\pi$
$11$	2.02609	−	4.10850i	0.610888	−	1.23876i	0.954097	−	0.299499i	$-0.0968195\pi$
$12$	0.520712	−	1.53397i	0.150317	−	0.442818i
$13$	2.22495	+	2.22495i	0.617091	+	0.617091i	0.944784	−	0.327693i	$-0.106271\pi$
$13$	2.22495	+	2.22495i	0.617091	+	0.617091i	−0.327693	+	0.944784i	$0.606271\pi$
$14$	−2.02485	+	1.06310i	−0.541164	+	0.284125i
$15$	−1.19460	−	0.494819i	−0.308444	−	0.127762i
$16$	−0.0651537	−	0.0376165i	−0.0162884	−	0.00940413i
$17$	−3.52294	+	2.14216i	−0.854440	+	0.519551i
$17$	−3.52294	+	2.14216i	−0.854440	+	0.519551i
$18$	0.573994	+	0.994186i	0.135292	+	0.234332i
$19$	−2.29130	+	1.75817i	−0.525660	+	0.403353i	−0.837214	−	0.546875i	$-0.815817\pi$
$19$	−2.29130	+	1.75817i	−0.525660	+	0.403353i	0.311554	+	0.950228i	$0.399150\pi$
$20$	−0.696034	+	1.04169i	−0.155638	+	0.232929i
$21$	0.801487	−	3.32581i	0.174899	−	0.725751i
$22$	−3.88362	+	0.772499i	−0.827990	+	0.164697i
$23$	−0.361542	−	5.51606i	−0.0753867	−	1.15018i	−0.853165	−	0.521640i	$-0.825320\pi$
$23$	−0.361542	−	5.51606i	−0.0753867	−	1.15018i	0.777779	−	0.628538i	$-0.216346\pi$
$24$	−3.44268	+	1.16863i	−0.702733	+	0.238546i
$25$	0.793353	+	0.608761i	0.158671	+	0.121752i
$26$	0.355013	−	2.69659i	0.0696238	−	0.528845i
$27$	−5.48879	−	1.09179i	−1.05632	−	0.210115i
$28$	−3.00900	−	1.39031i	−0.568647	−	0.262744i
$29$	−1.01386	−	5.09702i	−0.188269	−	0.946494i	−0.953191	−	0.302370i	$-0.902222\pi$
$29$	−1.01386	−	5.09702i	−0.188269	−	0.946494i	0.764921	−	0.644124i	$-0.222778\pi$
$30$	0.289277	+	1.07960i	0.0528144	+	0.197106i
$31$	−0.413251	+	6.30500i	−0.0742221	+	1.13241i	0.784554	+	0.620060i	$0.212892\pi$
$31$	−0.413251	+	6.30500i	−0.0742221	+	1.13241i	−0.858776	+	0.512350i	$0.828775\pi$
$32$	0.742493	+	5.63980i	0.131256	+	0.996985i
$33$	2.96162	−	5.12967i	0.515551	−	0.892961i
$34$	3.32283	+	1.28870i	0.569860	+	0.221010i
$35$	−1.26445	+	2.32404i	−0.213730	+	0.392835i
$36$	−0.636734	+	1.53721i	−0.106122	+	0.256202i
$37$	10.6466	−	5.25032i	1.75029	−	0.863146i	0.778377	−	0.627797i	$-0.216043\pi$
$37$	10.6466	−	5.25032i	1.75029	−	0.863146i	0.971911	−	0.235349i	$-0.0756235\pi$
$38$	2.41140	+	0.646132i	0.391181	+	0.104817i
$39$	2.68260	+	3.05892i	0.429560	+	0.489819i
$40$	2.80570	−	0.183895i	0.443619	−	0.0290764i
$41$	1.80555	−	9.07710i	0.281979	−	1.41761i	−0.536903	−	0.843644i	$-0.680406\pi$
$41$	1.80555	−	9.07710i	0.281979	−	1.41761i	0.818882	−	0.573961i	$-0.194594\pi$
$42$	−2.70248	+	1.20043i	−0.417002	+	0.185231i
$43$	2.51959	+	6.08284i	0.384235	+	0.927624i	0.991136	+	0.132848i	$0.0424121\pi$
$43$	2.51959	+	6.08284i	0.384235	+	0.927624i	−0.606902	+	0.794777i	$0.707588\pi$
$44$	−4.31488	−	3.78405i	−0.650493	−	0.570467i
$45$	1.19113	+	0.587398i	0.177563	+	0.0875641i
$46$	−3.59249	+	3.15053i	−0.529684	+	0.464520i
$47$	−9.08508	+	2.43434i	−1.32520	+	0.355085i	−0.850922	−	0.525293i	$-0.823956\pi$
$47$	−9.08508	+	2.43434i	−1.32520	+	0.355085i	−0.474273	+	0.880378i	$0.657289\pi$
$48$	−0.0808838	−	0.0540449i	−0.0116746	−	0.00780070i
$49$	−6.59445	−	2.34801i	−0.942065	−	0.335431i
$50$		−	0.864391i		−	0.122243i
$51$	−4.72666	+	2.46601i	−0.661865	+	0.345311i
$52$	3.41396	−	1.97105i	0.473431	−	0.273335i
$53$	9.85071	−	1.29687i	1.35310	−	0.178139i	0.581136	−	0.813806i	$-0.302608\pi$
$53$	9.85071	−	1.29687i	1.35310	−	0.178139i	0.771963	+	0.635668i	$0.219275\pi$
$54$	2.13953	+	4.33854i	0.291154	+	0.590401i
$55$	−3.23919	+	3.23919i	−0.436773	+	0.436773i
$56$	1.63554	+	7.25708i	0.218558	+	0.969768i
$57$	−3.10505	+	2.07473i	−0.411273	+	0.274804i
$58$	−2.96187	+	3.37737i	−0.388913	+	0.443470i
$59$	5.86188	−	7.63936i	0.763152	−	0.994559i	−0.236584	−	0.971611i	$-0.576028\pi$
$59$	5.86188	−	7.63936i	0.763152	−	0.994559i	0.999737	−	0.0229485i	$-0.00730537\pi$
$60$	−0.986155	+	1.28518i	−0.127312	+	0.165916i
$61$	−2.02497	+	2.30903i	−0.259270	+	0.295641i	−0.866800	−	0.498656i	$-0.833827\pi$
$61$	−2.02497	+	2.30903i	−0.259270	+	0.295641i	0.607530	+	0.794297i	$0.292161\pi$
$62$	4.54122	−	3.03434i	0.576735	−	0.385362i
$63$	−1.04488	+	3.35484i	−0.131642	+	0.422670i
$64$	3.37049	−	3.37049i	0.421311	−	0.421311i
$65$	−1.39169	−	2.82206i	−0.172618	−	0.350034i
$66$	−5.07619	+	0.668293i	−0.624836	+	0.0822612i
$67$	3.91238	−	2.25881i	0.477973	−	0.275958i	−0.241598	−	0.970376i	$-0.577672\pi$
$67$	3.91238	−	2.25881i	0.477973	−	0.275958i	0.719571	+	0.694418i	$0.244338\pi$
$68$	1.44998	+	4.95786i	0.175836	+	0.601229i
$69$		−	7.14771i		−	0.860483i
$70$	2.25912	−	0.355814i	0.270016	−	0.0425279i
$71$	−3.75431	−	2.50855i	−0.445554	−	0.297710i	0.312480	−	0.949924i	$-0.398840\pi$
$71$	−3.75431	−	2.50855i	−0.445554	−	0.297710i	−0.758035	+	0.652214i	$0.773840\pi$
$72$	3.60696	−	0.966483i	0.425085	−	0.113901i
$73$	7.75495	−	6.80091i	0.907648	−	0.795986i	−0.0718550	−	0.997415i	$-0.522892\pi$
$73$	7.75495	−	6.80091i	0.907648	−	0.795986i	0.979503	+	0.201429i	$0.0645585\pi$
$74$	−9.20282	−	4.53833i	−1.06981	−	0.527570i
$75$	0.972147	+	0.852550i	0.112254	+	0.0984440i
$76$	1.38467	+	3.34289i	0.158832	+	0.383455i
$77$	−9.79911	−	7.13238i	−1.11671	−	0.812810i
$78$	0.686102	−	3.44927i	0.0776858	−	0.390553i
$79$	−5.58077	+	0.365783i	−0.627886	+	0.0411538i	−0.376025	−	0.926610i	$-0.622709\pi$
$79$	−5.58077	+	0.365783i	−0.627886	+	0.0411538i	−0.251861	+	0.967763i	$0.581043\pi$
$80$	0.0496046	+	0.0565632i	0.00554596	+	0.00632396i
$81$	−3.14111	−	0.841659i	−0.349013	−	0.0935177i
$82$	−7.17488	+	3.53826i	−0.792333	+	0.390735i
$83$	−1.89327	+	4.57077i	−0.207814	+	0.501707i	−0.993078	−	0.117454i	$-0.962527\pi$
$83$	−1.89327	+	4.57077i	−0.207814	+	0.501707i	0.785265	+	0.619160i	$0.212527\pi$
$84$	−3.76480	−	2.04832i	−0.410774	−	0.223490i
$85$	4.02456	−	0.896065i	0.436525	−	0.0971919i
$86$	2.84558	−	4.92870i	0.306847	−	0.531475i
$87$	−0.877096	−	6.66221i	−0.0940346	−	0.714263i
$88$	−0.842407	+	12.8526i	−0.0898009	+	1.37010i
$89$	0.00486531	+	0.0181576i	0.000515722	+	0.00192470i	0.966183	−	0.257857i	$-0.0830162\pi$
$89$	0.00486531	+	0.0181576i	0.000515722	+	0.00192470i	−0.965667	+	0.259781i	$0.916350\pi$
$90$	−0.223961	−	1.12593i	−0.0236076	−	0.118683i
$91$	6.80269	−	4.79888i	0.713116	−	0.503060i
$92$	−6.79243	−	1.35110i	−0.708160	−	0.140862i
$93$	−1.06640	+	8.10011i	−0.110581	+	0.839942i
$94$	6.45003	+	4.94929i	0.665270	+	0.510480i
$95$	2.73485	−	0.928355i	0.280589	−	0.0952472i
$96$	0.481061	+	7.33957i	0.0490981	+	0.749092i
$97$	2.95338	−	0.587464i	0.299871	−	0.0596480i	−0.0428619	−	0.999081i	$-0.513648\pi$
$97$	2.95338	−	0.587464i	0.299871	−	0.0596480i	0.342733	+	0.939433i	$0.388648\pi$
$98$	1.85986	+	5.75781i	0.187875	+	0.581626i
$99$	−3.38001	+	5.05854i	−0.339704	+	0.508402i
$100$	0.993935	−	0.762673i	0.0993935	−	0.0762673i
$101$	6.52513	+	11.3019i	0.649275	+	1.12458i	0.983296	+	0.182011i	$0.0582607\pi$
$101$	6.52513	+	11.3019i	0.649275	+	1.12458i	−0.334022	+	0.942565i	$0.608406\pi$
$102$	4.17832	+	1.94376i	0.413715	+	0.192460i
$103$	11.3679	+	6.56328i	1.12012	+	0.646700i	0.941431	−	0.337207i	$-0.109482\pi$
$103$	11.3679	+	6.56328i	1.12012	+	0.646700i	0.178686	+	0.983906i	$0.442815\pi$
$104$	−8.17378	−	3.38569i	−0.801505	−	0.331994i
$105$	−1.82800	+	2.89168i	−0.178394	+	0.282199i
$106$	−6.07287	−	6.07287i	−0.589850	−	0.589850i
$107$	2.03386	−	5.99154i	0.196620	−	0.579224i	−0.803245	−	0.595649i	$-0.796895\pi$
$107$	2.03386	−	5.99154i	0.196620	−	0.579224i	0.999865	+	0.0164245i	$0.00522830\pi$
$108$	−3.10099	+	6.28818i	−0.298393	+	0.605080i
$109$	−0.257735	−	0.759262i	−0.0246865	−	0.0727241i	0.933888	−	0.357564i	$-0.116393\pi$
$109$	−0.257735	−	0.759262i	−0.0246865	−	0.0727241i	−0.958575	+	0.284840i	$0.908059\pi$
$110$	3.92582	+	0.516845i	0.374313	+	0.0492792i
$111$	14.1808	−	5.87389i	1.34598	−	0.557525i
$112$	−0.127411	+	0.152927i	−0.0120392	+	0.0144502i
$113$	1.12565	+	1.68466i	0.105893	+	0.158479i	0.880631	−	0.473802i	$-0.157119\pi$
$113$	1.12565	+	1.68466i	0.105893	+	0.158479i	−0.774739	+	0.632281i	$0.782119\pi$
$114$	3.05668	+	1.03760i	0.286284	+	0.0971804i
$115$	−1.43073	+	5.33954i	−0.133416	+	0.497915i
$116$	−6.49686	−	0.425826i	−0.603218	−	0.0395370i
$117$	−2.54396	−	3.31535i	−0.235189	−	0.306504i
$118$	−8.32339			−0.766231
$119$	3.99855	+	10.1495i	0.366546	+	0.930400i
$120$	3.63562			0.331885
$121$	−6.07834	−	7.92144i	−0.552576	−	0.720131i
$122$	2.64901	+	0.173625i	0.239830	+	0.0157193i
$123$	3.09725	−	11.5591i	0.279270	−	1.04225i
$124$	7.49592	+	2.54452i	0.673153	+	0.228505i
$125$	−0.555570	−	0.831470i	−0.0496917	−	0.0743689i
$126$	2.85046	−	1.04880i	0.253939	−	0.0934347i
$127$	3.29613	−	1.36530i	0.292484	−	0.121151i	−0.231617	−	0.972807i	$-0.574401\pi$
$127$	3.29613	−	1.36530i	0.292484	−	0.121151i	0.524101	+	0.851656i	$0.324401\pi$
$128$	7.19464	+	0.947193i	0.635923	+	0.0837208i
$129$	2.73651	+	8.06150i	0.240936	+	0.709775i
$130$	−1.20296	+	2.43937i	−0.105507	+	0.213947i
$131$	0.215321	−	0.634314i	0.0188127	−	0.0554203i	−0.937118	−	0.349012i	$-0.886517\pi$
$131$	0.215321	−	0.634314i	0.0188127	−	0.0554203i	0.955931	+	0.293592i	$0.0948506\pi$
$132$	−5.24729	−	5.24729i	−0.456718	−	0.456718i
$133$	3.55205	+	6.76547i	0.308001	+	0.586640i
$134$	−3.60775	−	1.49438i	−0.311662	−	0.129095i
$135$	4.84656	+	2.79816i	0.417125	+	0.240827i
$136$	6.84655	−	9.35535i	0.587086	−	0.802214i
$137$	11.1465	+	19.3063i	0.952311	+	1.64945i	0.740406	+	0.672160i	$0.234633\pi$
$137$	11.1465	+	19.3063i	0.952311	+	1.64945i	0.211905	+	0.977290i	$0.432033\pi$
$138$	−4.90167	+	3.76118i	−0.417258	+	0.320173i
$139$	3.22856	−	4.83188i	0.273843	−	0.409835i	−0.668902	−	0.743351i	$-0.733235\pi$
$139$	3.22856	−	4.83188i	0.273843	−	0.409835i	0.942744	+	0.333516i	$0.108235\pi$
$140$	2.40241	+	2.28374i	0.203041	+	0.193011i
$141$	−11.9279	+	2.37262i	−1.00451	+	0.199810i
$142$	0.255266	+	3.89460i	0.0214214	+	0.326828i
$143$	13.6492	−	4.63327i	1.14140	−	0.387453i
$144$	0.0792688	+	0.0608251i	0.00660573	+	0.00506875i
$145$	−0.678329	+	5.15242i	−0.0563322	+	0.427885i
$146$	−8.74456	−	1.73940i	−0.723705	−	0.143954i
$147$	−8.30997	−	3.58722i	−0.685395	−	0.295869i
$148$	−2.90139	−	14.5863i	−0.238493	−	1.19899i
$149$	0.144177	+	0.538075i	0.0118114	+	0.0440808i	0.971580	−	0.236711i	$-0.0760695\pi$
$149$	0.144177	+	0.538075i	0.0118114	+	0.0440808i	−0.959769	+	0.280792i	$0.909403\pi$
$150$	0.0730997	−	1.11529i	0.00596857	−	0.0910627i
$151$	−1.80582	−	13.7165i	−0.146955	−	1.11624i	−0.892909	−	0.450238i	$-0.851339\pi$
$151$	−1.80582	−	13.7165i	−0.146955	−	1.11624i	0.745954	−	0.665998i	$-0.231994\pi$
$152$	4.06028	−	7.03262i	0.329332	−	0.570421i
$153$	5.01010	−	2.20994i	0.405042	−	0.178663i
$154$	0.265217	+	10.4730i	0.0213718	+	0.843940i
$155$	2.41799	−	5.83755i	0.194218	−	0.468884i
$156$	4.57157	−	2.25445i	0.366018	−	0.180500i
$157$	5.36244	+	1.43686i	0.427969	+	0.114674i	0.466373	−	0.884588i	$-0.345561\pi$
$157$	5.36244	+	1.43686i	0.427969	+	0.114674i	−0.0384034	+	0.999262i	$0.512227\pi$
$158$	3.18749	+	3.63464i	0.253583	+	0.289156i
$159$	12.8196	−	0.840242i	1.01666	−	0.0666355i
$160$	1.10976	−	5.57916i	0.0877345	−	0.441071i
$161$	−14.5440	−	1.54131i	−1.14623	−	0.121472i
$162$	1.07570	+	2.59696i	0.0845147	+	0.204037i
$163$	10.1348	+	8.88795i	0.793816	+	0.696158i	0.956888	−	0.290456i	$-0.0938070\pi$
$163$	10.1348	+	8.88795i	0.793816	+	0.696158i	−0.163072	+	0.986614i	$0.552140\pi$
$164$	−10.3991	−	5.12826i	−0.812033	−	0.400450i
$165$	−4.45332	+	3.90546i	−0.346691	+	0.304040i
$166$	4.13074	−	1.10683i	0.320608	−	0.0859065i
$167$	5.17701	+	3.45916i	0.400609	+	0.267678i	0.739512	−	0.673143i	$-0.235056\pi$
$167$	5.17701	+	3.45916i	0.400609	+	0.267678i	−0.338904	+	0.940821i	$0.610056\pi$
$168$	1.49655	+	9.50181i	0.115461	+	0.733080i
$169$		−	3.09916i		−	0.238397i
$170$	−2.73225	−	2.28840i	−0.209554	−	0.175512i
$171$	3.32179	−	1.91784i	0.254024	−	0.146661i
$172$	8.17807	−	1.07666i	0.623572	−	0.0820948i
$173$	9.96256	+	20.2021i	0.757439	+	1.53593i	0.841976	+	0.539515i	$0.181392\pi$
$173$	9.96256	+	20.2021i	0.757439	+	1.53593i	−0.0845370	+	0.996420i	$0.526941\pi$
$174$	−4.10719	+	4.10719i	−0.311365	+	0.311365i
$175$	1.94438	−	1.79426i	0.146981	−	0.135634i
$176$	−0.286554	+	0.191470i	−0.0215998	+	0.0144326i
$177$	8.20938	−	9.36100i	0.617054	−	0.703616i
$178$	0.00989172	−	0.0128911i	0.000741416	−	0.000966232i
$179$	10.6755	−	13.9126i	0.797926	−	1.03988i	−0.200264	−	0.979742i	$-0.564180\pi$
$179$	10.6755	−	13.9126i	0.797926	−	1.03988i	0.998190	−	0.0601355i	$-0.0191533\pi$
$180$	1.09706	−	1.25096i	0.0817702	−	0.0932411i
$181$	10.6135	−	7.09172i	0.788896	−	0.527123i	−0.0946264	−	0.995513i	$-0.530166\pi$
$181$	10.6135	−	7.09172i	0.788896	−	0.527123i	0.883522	+	0.468390i	$0.155166\pi$
$182$	−6.87055	−	2.13985i	−0.509279	−	0.158617i
$183$	−2.80799	+	2.80799i	−0.207573	+	0.207573i
$184$	6.87444	+	13.9400i	0.506790	+	1.02767i
$185$	−11.7692	+	1.54945i	−0.865291	+	0.113918i
$186$	6.11594	−	3.53104i	0.448443	−	0.258908i
$187$	1.66328	+	18.8142i	0.121631	+	1.37583i
$188$			11.7836i			0.859404i
$189$	−5.31807	+	13.8185i	−0.386833	+	1.00515i
$190$	−2.07573	−	1.38696i	−0.150590	−	0.100621i
$191$	−16.5354	+	4.43064i	−1.19646	+	0.320590i	−0.801436	−	0.598081i	$-0.795930\pi$
$191$	−16.5354	+	4.43064i	−1.19646	+	0.320590i	−0.395023	+	0.918671i	$0.629263\pi$
$192$	4.63383	−	4.06376i	0.334418	−	0.293277i
$193$	12.5140	+	6.17123i	0.900778	+	0.444215i	0.832865	−	0.553476i	$-0.186699\pi$
$193$	12.5140	+	6.17123i	0.900778	+	0.444215i	0.0679136	+	0.997691i	$0.478366\pi$
$194$	−1.95696	−	1.71621i	−0.140501	−	0.123216i
$195$	−1.55698	−	3.75888i	−0.111498	−	0.269179i
$196$	−4.97971	+	7.21885i	−0.355694	+	0.515632i
$197$	0.952531	−	4.78870i	0.0678650	−	0.341180i	−0.931903	−	0.362707i	$-0.881853\pi$
$197$	0.952531	−	4.78870i	0.0678650	−	0.341180i	0.999768	+	0.0215265i	$0.00685261\pi$
$198$	5.24757	−	0.343944i	0.372929	−	0.0244430i
$199$	1.70949	+	1.94929i	0.121182	+	0.138182i	0.809250	−	0.587465i	$-0.199874\pi$
$199$	1.70949	+	1.94929i	0.121182	+	0.138182i	−0.688067	+	0.725647i	$0.741541\pi$
$200$	−2.71591	−	0.727726i	−0.192044	−	0.0514580i
$201$	5.23899	−	2.58358i	0.369530	−	0.182232i
$202$	4.31687	−	10.4219i	0.303734	−	0.733279i
$203$	−13.7452	+	0.348082i	−0.964727	+	0.0244306i
$204$	1.45157	+	6.51953i	0.101630	+	0.456458i
$205$	−4.62747	+	8.01501i	−0.323196	+	0.559792i
$206$	−1.48101	−	11.2494i	−0.103187	−	0.783784i
$207$	−0.480159	+	7.32581i	−0.0333734	+	0.509179i
$208$	−0.0612690	−	0.228659i	−0.00424824	−	0.0158547i
$209$	2.58109	+	12.9760i	0.178538	+	0.897569i
$210$	2.94493	−	0.268042i	0.203219	−	0.0184967i
$211$	2.01981	+	0.401766i	0.139050	+	0.0276587i	0.264124	−	0.964489i	$-0.414917\pi$
$211$	2.01981	+	0.401766i	0.139050	+	0.0276587i	−0.125075	+	0.992147i	$0.539917\pi$
$212$	1.62476	−	12.3412i	0.111589	−	0.847600i
$213$	−4.63188	−	3.55416i	−0.317371	−	0.243527i
$214$	−5.17904	+	1.75805i	−0.354032	+	0.120178i
$215$	−0.430615	−	6.56992i	−0.0293677	−	0.448065i
$216$	15.4329	−	3.06980i	1.05008	−	0.208873i
$217$	16.2520	+	3.91657i	1.10326	+	0.265874i
$218$	−0.385055	+	0.576276i	−0.0260792	+	0.0390303i
$219$	10.5810	−	8.11909i	0.714998	−	0.548637i
$220$	2.86955	+	4.97020i	0.193465	+	0.335091i
$221$	−12.6046	−	3.07218i	−0.847877	−	0.206657i
$222$	−11.4902	−	6.63387i	−0.771171	−	0.445236i
$223$	−8.43925	−	3.49565i	−0.565134	−	0.234086i	0.0817784	−	0.996651i	$-0.473940\pi$
$223$	−8.43925	−	3.49565i	−0.565134	−	0.234086i	−0.646912	+	0.762564i	$0.723940\pi$
$224$	15.0381	+	0.603826i	1.00478	+	0.0403448i
$225$	−0.939100	−	0.939100i	−0.0626066	−	0.0626066i
$226$	0.562957	−	1.65842i	0.0374474	−	0.110316i
$227$	−9.72214	+	19.7146i	−0.645281	+	1.30850i	0.290822	+	0.956777i	$0.406071\pi$
$227$	−9.72214	+	19.7146i	−0.645281	+	1.30850i	−0.936104	+	0.351724i	$0.885596\pi$
$228$	1.50388	+	4.43028i	0.0995967	+	0.293402i
$229$	−13.2296	−	1.74170i	−0.874234	−	0.115095i	−0.319962	−	0.947431i	$-0.603670\pi$
$229$	−13.2296	−	1.74170i	−0.874234	−	0.115095i	−0.554272	+	0.832335i	$0.687003\pi$
$230$	4.41454	−	1.82856i	0.291086	−	0.120572i
$231$	−12.0402	−	10.0313i	−0.792186	−	0.660010i
$232$	8.11808	+	12.1496i	0.532978	+	0.797658i
$233$	−19.6613	−	6.67410i	−1.28805	−	0.437235i	−0.408379	−	0.912813i	$-0.633906\pi$
$233$	−19.6613	−	6.67410i	−1.28805	−	0.437235i	−0.879674	+	0.475578i	$0.842239\pi$
$234$	−0.934909	+	3.48913i	−0.0611169	+	0.228091i
$235$	9.38543	+	0.615154i	0.612238	+	0.0401282i
$236$	−7.34393	−	9.57080i	−0.478049	−	0.623006i
$237$	−7.23156			−0.469740
$238$	4.85611	−	8.08280i	0.314775	−	0.523930i
$239$	−20.3794			−1.31823			−0.659116	−	0.752041i	$-0.729069\pi$
$239$	−20.3794			−1.31823			−0.659116	+	0.752041i	$0.729069\pi$
$240$	0.0592192	+	0.0771760i	0.00382258	+	0.00498169i
$241$	8.24309	+	0.540281i	0.530984	+	0.0348025i	0.328538	−	0.944491i	$-0.393444\pi$
$241$	8.24309	+	0.540281i	0.530984	+	0.0348025i	0.202446	+	0.979293i	$0.435111\pi$
$242$	−2.23380	+	8.33665i	−0.143594	+	0.535900i
$243$	11.9163	+	4.04504i	0.764432	+	0.259490i
$244$	2.13764	+	3.19921i	0.136848	+	0.204808i
$245$	5.48974	+	4.34312i	0.350727	+	0.277472i
$246$	−9.55665	+	3.95849i	−0.609310	+	0.252384i
$247$	−9.00989	−	1.18617i	−0.573286	−	0.0754745i
$248$	−5.71066	−	16.8231i	−0.362627	−	1.06827i
$249$	−2.82935	+	5.73735i	−0.179303	+	0.363590i
$250$	−0.277849	+	0.818518i	−0.0175727	+	0.0517676i
$251$	−18.5931	−	18.5931i	−1.17358	−	1.17358i	−0.981349	−	0.192235i	$-0.938426\pi$
$251$	−18.5931	−	18.5931i	−1.17358	−	1.17358i	−0.192235	−	0.981349i	$-0.561574\pi$
$252$	3.72102	+	2.35227i	0.234402	+	0.148179i
$253$	−23.3952	−	9.69062i	−1.47085	−	0.609244i
$254$	−2.67073	−	1.54195i	−0.167577	−	0.0967504i
$255$	5.26849	−	0.815805i	0.329926	−	0.0510877i
$256$	−7.90292	−	13.6883i	−0.493932	−	0.855516i
$257$	20.5800	−	15.7916i	1.28375	−	0.985053i	0.284091	−	0.958797i	$-0.408308\pi$
$257$	20.5800	−	15.7916i	1.28375	−	0.985053i	0.999655	−	0.0262562i	$-0.00835858\pi$
$258$	4.08834	−	6.11863i	0.254529	−	0.380930i
$259$	−8.89417	−	30.1215i	−0.552657	−	1.87166i
$260$	−3.86635	+	0.769065i	−0.239781	+	0.0476954i
$261$	0.451407	+	6.88713i	0.0279414	+	0.426303i
$262$	−0.548296	+	0.186121i	−0.0338738	+	0.0114986i
$263$	−7.25844	−	5.56960i	−0.447575	−	0.343436i	0.360253	−	0.932855i	$-0.382690\pi$
$263$	−7.25844	−	5.56960i	−0.447575	−	0.343436i	−0.807828	+	0.589418i	$0.799357\pi$
$264$	−2.17384	+	16.5120i	−0.133791	+	1.01624i
$265$	−9.74480	−	1.93836i	−0.598618	−	0.119073i
$266$	2.77042	−	5.99592i	0.169866	−	0.367634i
$267$	0.00474195	+	0.0238394i	0.000290202	+	0.00145895i
$268$	−1.46487	−	5.46695i	−0.0894809	−	0.333947i
$269$	0.128046	−	1.95360i	0.00780709	−	0.119113i	−0.992176	−	0.124843i	$-0.960157\pi$
$269$	0.128046	−	1.95360i	0.00780709	−	0.119113i	0.999984	+	0.00572996i	$0.00182391\pi$
$270$	−0.631409	−	4.79603i	−0.0384263	−	0.291877i
$271$	−14.4018	+	24.9447i	−0.874850	+	1.51528i	−0.0179270	+	0.999839i	$0.505707\pi$
$271$	−14.4018	+	24.9447i	−0.874850	+	1.51528i	−0.856923	+	0.515445i	$0.827627\pi$
$272$	0.310114	−	0.00704895i	0.0188034	−	0.000427406i
$273$	9.18305	−	5.61650i	0.555783	−	0.339926i
$274$	7.37427	−	17.8031i	0.445496	−	1.07552i
$275$	4.10850	−	2.02609i	0.247752	−	0.122178i
$276$	−8.64972	−	2.31768i	−0.520652	−	0.139508i
$277$	−13.9597	−	15.9180i	−0.838755	−	0.956417i	0.160777	−	0.986991i	$-0.448600\pi$
$277$	−13.9597	−	15.9180i	−0.838755	−	0.956417i	−0.999533	+	0.0305737i	$0.990267\pi$
$278$	−5.01244	+	0.328533i	−0.300626	+	0.0197041i
$279$	1.63711	−	8.23031i	0.0980113	−	0.492736i
$280$	0.783971	−	7.39768i	0.0468512	−	0.442096i
$281$	10.3719	+	25.0399i	0.618733	+	1.49375i	0.853176	+	0.521624i	$0.174673\pi$
$281$	10.3719	+	25.0399i	0.618733	+	1.49375i	−0.234443	+	0.972130i	$0.575327\pi$
$282$	7.90364	+	6.93131i	0.470655	+	0.412754i
$283$	2.72458	+	1.34362i	0.161960	+	0.0798697i	0.521462	−	0.853275i	$-0.325387\pi$
$283$	2.72458	+	1.34362i	0.161960	+	0.0798697i	−0.359502	+	0.933144i	$0.617054\pi$
$284$	−4.25305	+	3.72982i	−0.252372	+	0.221324i
$285$	3.60716	−	0.966536i	0.213670	−	0.0572526i
$286$	−10.3596	−	6.92209i	−0.612579	−	0.409312i
$287$	−22.8523	−	8.79478i	−1.34893	−	0.519139i
$288$		−	7.55478i		−	0.445169i
$289$	7.82228	−	15.0934i	0.460134	−	0.887849i
$290$	3.89031	−	2.24607i	0.228447	−	0.131894i
$291$	3.86030	−	0.508218i	0.226295	−	0.0297923i
$292$	−5.71546	−	11.5898i	−0.334472	−	0.678242i
$293$	7.89814	−	7.89814i	0.461414	−	0.461414i	−0.437705	−	0.899119i	$-0.644208\pi$
$293$	7.89814	−	7.89814i	0.461414	−	0.461414i	0.899119	+	0.437705i	$0.144208\pi$
$294$	1.91277	+	7.58633i	0.111555	+	0.442444i
$295$	−8.00638	+	5.34970i	−0.466150	+	0.311471i
$296$	−22.0072	+	25.0944i	−1.27914	+	1.45858i
$297$	−15.6064	+	20.3386i	−0.905573	+	1.18017i
$298$	0.293128	−	0.382011i	0.0169804	−	0.0221293i
$299$	11.4686	−	13.0774i	0.663245	−	0.756286i
$300$	1.34693	−	0.899989i	0.0777649	−	0.0519609i
$301$	16.9935	−	3.82984i	0.979486	−	0.220748i
$302$	−8.45612	+	8.45612i	−0.486595	+	0.486595i
$303$	7.46331	+	15.1341i	0.428756	+	0.869432i
$304$	0.215423	−	0.0283610i	0.0123554	−	0.00162661i
$305$	2.65972	−	1.53559i	0.152295	−	0.0879275i
$306$	−4.15186	−	2.27288i	−0.237346	−	0.129932i
$307$		−	12.2920i		−	0.701540i	−0.936462	−	0.350770i	$-0.885920\pi$
$307$		−	12.2920i		−	0.701540i	0.936462	−	0.350770i	$-0.114080\pi$
$308$	−11.8086	+	9.54557i	−0.672856	+	0.543909i
$309$	14.1125	+	9.42968i	0.802833	+	0.536436i
$310$	−5.27557	+	1.41359i	−0.299632	+	0.0802863i
$311$	1.92546	−	1.68858i	0.109183	−	0.0957507i	−0.603014	−	0.797731i	$-0.706034\pi$
$311$	1.92546	−	1.68858i	0.109183	−	0.0957507i	0.712197	+	0.701980i	$0.247700\pi$
$312$	−10.2599	−	5.05965i	−0.580855	−	0.286446i
$313$	−15.2526	−	13.3762i	−0.862130	−	0.756068i	0.109145	−	0.994026i	$-0.465189\pi$
$313$	−15.2526	−	13.3762i	−0.862130	−	0.756068i	−0.971275	+	0.237958i	$0.923522\pi$
$314$	−1.83641	−	4.43348i	−0.103634	−	0.250196i
$315$	2.06780	−	2.84094i	0.116507	−	0.160069i
$316$	−1.36695	+	6.87212i	−0.0768969	+	0.386587i
$317$	−28.1189	+	1.84301i	−1.57931	+	0.103514i	−0.829641	−	0.558297i	$-0.811455\pi$
$317$	−28.1189	+	1.84301i	−1.57931	+	0.103514i	−0.749671	+	0.661811i	$0.769788\pi$
$318$	−7.32199	−	8.34913i	−0.410597	−	0.468196i
$319$	−22.9953	−	6.16156i	−1.28749	−	0.344981i
$320$	−4.27503	+	2.10821i	−0.238981	+	0.117852i
$321$	3.13089	−	7.55863i	0.174749	−	0.421881i
$322$	6.59619	+	10.7849i	0.367591	+	0.601016i
$323$	4.30582	−	11.1023i	0.239582	−	0.617748i
$324$	−2.03705	+	3.52827i	−0.113169	+	0.196015i
$325$	0.410709	+	3.11964i	0.0227820	+	0.173047i
$326$	0.762074	−	11.6270i	0.0422074	−	0.643960i
$327$	−0.268335	−	1.00144i	−0.0148389	−	0.0553797i
$328$	5.07669	+	25.5222i	0.280313	+	1.40923i
$329$	2.25565	+	24.7824i	0.124358	+	1.36630i
$330$	5.02161	+	0.998860i	0.276431	+	0.0549855i
$331$	−3.68665	+	28.0029i	−0.202636	+	1.53918i	0.523739	+	0.851879i	$0.324537\pi$
$331$	−3.68665	+	28.0029i	−0.202636	+	1.53918i	−0.726376	+	0.687298i	$0.758797\pi$
$332$	4.91736	+	3.77322i	0.269875	+	0.207082i
$333$	−14.9288	+	5.06764i	−0.818092	+	0.277705i
$334$	−0.351999	−	5.37046i	−0.0192605	−	0.293859i
$335$	−4.43082	+	0.881345i	−0.242082	+	0.0481530i
$336$	−0.177325	+	0.186540i	−0.00967389	+	0.0101766i
$337$	−8.76749	+	13.1215i	−0.477595	+	0.714772i	−0.989542	−	0.144245i	$-0.953925\pi$
$337$	−8.76749	+	13.1215i	−0.477595	+	0.714772i	0.511947	+	0.859017i	$0.328925\pi$
$338$	−2.12530	+	1.63080i	−0.115601	+	0.0887039i
$339$	1.30991	+	2.26884i	0.0711447	+	0.123226i
$340$	0.220623	−	5.16083i	0.0119650	−	0.279885i
$341$	25.0668	+	14.4723i	1.35744	+	0.783719i
$342$	−3.06314	−	1.26880i	−0.165636	−	0.0686086i
$343$	−9.09113	+	16.1354i	−0.490875	+	0.871230i
$344$	−13.0902	−	13.0902i	−0.705778	−	0.705778i
$345$	−2.29756	+	6.76838i	−0.123696	+	0.364397i
$346$	8.61155	−	17.4625i	0.462960	−	0.938789i
$347$	4.78814	+	14.1054i	0.257041	+	0.757218i	0.996467	+	0.0839809i	$0.0267635\pi$
$347$	4.78814	+	14.1054i	0.257041	+	0.757218i	−0.739426	+	0.673237i	$0.764903\pi$
$348$	−8.34660	−	1.09885i	−0.447425	−	0.0589046i
$349$	9.35660	−	3.87563i	0.500847	−	0.207458i	−0.117933	−	0.993021i	$-0.537627\pi$
$349$	9.35660	−	3.87563i	0.500847	−	0.207458i	0.618781	+	0.785564i	$0.287627\pi$
$350$	−2.25360	−	0.389238i	−0.120460	−	0.0208056i
$351$	−9.78313	−	14.6415i	−0.522185	−	0.781505i
$352$	24.6754	+	8.37618i	1.31521	+	0.446452i
$353$	−4.63007	+	17.2797i	−0.246434	+	0.919703i	0.726224	+	0.687459i	$0.241274\pi$
$353$	−4.63007	+	17.2797i	−0.246434	+	0.919703i	−0.972657	+	0.232245i	$0.925393\pi$
$354$	−10.7393	−	0.703892i	−0.570788	−	0.0374114i
$355$	2.74872	+	3.58220i	0.145887	+	0.190124i
$356$	0.0235508			0.00124819
$357$	4.30083	+	13.4336i	0.227624	+	0.710979i
$358$	−15.1584			−0.801145
$359$	3.10968	+	4.05262i	0.164123	+	0.213889i	0.868174	−	0.496261i	$-0.165294\pi$
$359$	3.10968	+	4.05262i	0.164123	+	0.213889i	−0.704051	+	0.710150i	$0.748627\pi$
$360$	−3.72621	−	0.244229i	−0.196388	−	0.0128720i
$361$	−2.75869	+	10.2956i	−0.145194	+	0.541873i
$362$	−10.4482	−	3.54668i	−0.549144	−	0.186409i
$363$	−7.17271	−	10.7347i	−0.376470	−	0.563427i
$364$	−3.60150	−	9.78827i	−0.188770	−	0.513045i
$365$	−9.52948	+	3.94724i	−0.498796	+	0.206608i
$366$	3.40322	+	0.448043i	0.177889	+	0.0234196i
$367$	−11.5227	−	33.9448i	−0.601480	−	1.77190i	−0.635057	−	0.772466i	$-0.719023\pi$
$367$	−11.5227	−	33.9448i	−0.601480	−	1.77190i	0.0335770	−	0.999436i	$-0.489310\pi$
$368$	−0.183939	+	0.372992i	−0.00958850	+	0.0194436i
$369$	−3.95093	+	11.6391i	−0.205677	+	0.605905i
$370$	7.25563	+	7.25563i	0.377202	+	0.377202i
$371$	1.05467	−	26.2663i	0.0547557	−	1.36368i
$372$	9.45647	+	3.91700i	0.490295	+	0.203087i
$373$	6.60742	+	3.81480i	0.342119	+	0.197523i	0.661209	−	0.750202i	$-0.270044\pi$
$373$	6.60742	+	3.81480i	0.342119	+	0.197523i	−0.319089	+	0.947725i	$0.603377\pi$
$374$	12.0269	−	11.0408i	0.621899	−	0.570907i
$375$	−0.646512	−	1.11979i	−0.0333857	−	0.0578258i
$376$	20.9808	−	16.0992i	1.08200	−	0.830251i
$377$	9.08485	−	13.5964i	0.467894	−	0.700252i
$378$	12.2747	−	3.62442i	0.631341	−	0.186420i
$379$	24.1226	−	4.79829i	1.23910	−	0.246472i	0.468309	−	0.883565i	$-0.344863\pi$
$379$	24.1226	−	4.79829i	1.23910	−	0.246472i	0.770787	+	0.637093i	$0.219863\pi$
$380$	−0.236649	−	3.61057i	−0.0121398	−	0.185218i
$381$	4.36831	−	1.48284i	0.223795	−	0.0759683i
$382$	11.7394	+	9.00799i	0.600642	+	0.460889i
$383$	1.59446	−	12.1111i	0.0814730	−	0.618849i	−0.901187	−	0.433431i	$-0.857303\pi$
$383$	1.59446	−	12.1111i	0.0814730	−	0.618849i	0.982660	−	0.185418i	$-0.0593639\pi$
$384$	9.20283	+	1.83056i	0.469630	+	0.0934152i
$385$	6.98644	+	9.90368i	0.356062	+	0.504738i
$386$	−2.35295	−	11.8291i	−0.119762	−	0.602083i
$387$	−2.26315	−	8.44620i	−0.115043	−	0.429345i
$388$	0.246738	−	3.76449i	0.0125262	−	0.191113i
$389$	−1.22264	−	9.28689i	−0.0619904	−	0.470864i	−0.994081	−	0.108639i	$-0.965351\pi$
$389$	−1.22264	−	9.28689i	−0.0619904	−	0.470864i	0.932091	−	0.362225i	$-0.117983\pi$
$390$	−1.75842	+	3.04568i	−0.0890412	+	0.154224i
$391$	13.0900	+	18.6583i	0.661989	+	0.943591i
$392$	19.6568	−	0.996209i	0.992817	−	0.0503161i
$393$	0.331461	−	0.800219i	0.0167200	−	0.0403657i
$394$	−3.78516	+	1.86664i	−0.190694	+	0.0940397i
$395$	5.40218	+	1.44751i	0.271813	+	0.0728321i
$396$	5.02555	+	5.73054i	0.252543	+	0.287970i
$397$	−32.5110	+	2.13088i	−1.63168	+	0.106946i	−0.853499	−	0.521095i	$-0.825524\pi$
$397$	−32.5110	+	2.13088i	−1.63168	+	0.106946i	−0.778180	+	0.628041i	$0.783857\pi$
$398$	0.437218	−	2.19804i	0.0219158	−	0.110178i
$399$	4.01091	+	9.02957i	0.200797	+	0.452044i
$400$	−0.0287904	−	0.0695063i	−0.00143952	−	0.00347531i
$401$	−13.8359	−	12.1338i	−0.690933	−	0.605932i	0.240151	−	0.970735i	$-0.422803\pi$
$401$	−13.8359	−	12.1338i	−0.690933	−	0.605932i	−0.931085	+	0.364803i	$0.881136\pi$
$402$	−4.52854	−	2.23323i	−0.225863	−	0.111383i
$403$	−14.9478	+	13.1089i	−0.744603	+	0.652999i
$404$	15.7926	−	4.23162i	0.785712	−	0.210531i
$405$	2.70387	+	1.80667i	0.134357	+	0.0897742i
$406$	7.47156	+	9.24288i	0.370807	+	0.458717i
$407$		−	54.3790i		−	2.69547i
$408$	9.62496	−	11.4918i	0.476506	−	0.568929i
$409$	3.93370	−	2.27112i	0.194509	−	0.112300i	−0.399583	−	0.916697i	$-0.630845\pi$
$409$	3.93370	−	2.27112i	0.194509	−	0.112300i	0.594092	+	0.804397i	$0.297512\pi$
$410$	7.93144	−	1.04419i	0.391706	−	0.0515691i
$411$	12.7492	+	25.8527i	0.628870	+	1.27522i
$412$	11.6286	−	11.6286i	0.572900	−	0.572900i
$413$	−17.2773	−	18.7228i	−0.850161	−	0.921290i
$414$	5.27647	−	3.52562i	0.259324	−	0.173275i
$415$	3.26202	−	3.71962i	0.160126	−	0.182589i
$416$	−10.8963	+	14.2003i	−0.534234	+	0.696227i
$417$	4.57429	−	5.96133i	0.224004	−	0.291928i
$418$	7.54033	−	8.59810i	0.368810	−	0.420547i
$419$	1.13550	−	0.758720i	0.0554730	−	0.0370659i	−0.527525	−	0.849540i	$-0.676880\pi$
$419$	1.13550	−	0.758720i	0.0554730	−	0.0370659i	0.582998	+	0.812474i	$0.301880\pi$
$420$	2.90659	+	3.14978i	0.141827	+	0.153693i
$421$	−23.6745	+	23.6745i	−1.15382	+	1.15382i	−0.168045	+	0.985779i	$0.553746\pi$
$421$	−23.6745	+	23.6745i	−1.15382	+	1.15382i	−0.985779	+	0.168045i	$0.946254\pi$
$422$	−0.787323	−	1.59653i	−0.0383263	−	0.0777181i
$423$	12.3846	−	1.63046i	0.602157	−	0.0792755i
$424$	−24.1936	+	13.9682i	−1.17495	+	0.678356i
$425$	−4.09901	−	0.445141i	−0.198831	−	0.0215925i
$426$			5.04662i			0.244510i
$427$	5.10814	+	6.31915i	0.247200	+	0.305805i
$428$	−6.59111	−	4.40404i	−0.318593	−	0.212877i
$429$	18.0027	−	4.82382i	0.869181	−	0.232896i
$430$	−4.27885	+	3.75245i	−0.206344	+	0.180959i
$431$	2.21531	+	1.09247i	0.106708	+	0.0526225i	0.494859	−	0.868973i	$-0.335220\pi$
$431$	2.21531	+	1.09247i	0.106708	+	0.0526225i	−0.388151	+	0.921596i	$0.626886\pi$
$432$	0.316546	+	0.277603i	0.0152298	+	0.0133562i
$433$	−3.23909	−	7.81985i	−0.155661	−	0.375798i	0.826740	−	0.562584i	$-0.190193\pi$
$433$	−3.23909	−	7.81985i	−0.155661	−	0.375798i	−0.982401	+	0.186786i	$0.940193\pi$
$434$	−5.86607	−	13.2060i	−0.281580	−	0.633909i
$435$	−1.31095	+	6.59058i	−0.0628551	+	0.315994i
$436$	−1.00238	+	0.0656998i	−0.0480055	+	0.00314645i
$437$	10.5266	+	12.0033i	0.503556	+	0.574195i
$438$	−11.1356	−	2.98378i	−0.532081	−	0.142571i
$439$	−17.0749	+	8.42041i	−0.814940	+	0.401884i	−0.801477	−	0.598025i	$-0.795952\pi$
$439$	−17.0749	+	8.42041i	−0.814940	+	0.401884i	−0.0134632	+	0.999909i	$0.504286\pi$
$440$	4.92905	−	11.8998i	0.234983	−	0.567300i
$441$	8.27606	+	4.23484i	0.394098	+	0.201659i
$442$	4.52584	+	10.2604i	0.215272	+	0.488039i
$443$	−8.91932	+	15.4487i	−0.423770	+	0.733991i	−0.996305	−	0.0858894i	$-0.972627\pi$
$443$	−8.91932	+	15.4487i	−0.423770	+	0.733991i	0.572535	+	0.819880i	$0.305960\pi$
$444$	−2.51001	−	19.0654i	−0.119120	−	0.904804i
$445$	0.00122946	−	0.0187579i	5.82818e−5	−	0.000889208i
$446$	2.04360	+	7.62680i	0.0967671	+	0.361140i
$447$	0.140521	+	0.706448i	0.00664642	+	0.0334138i
$448$	−7.26963	−	10.3051i	−0.343458	−	0.486871i
$449$	22.4280	+	4.46121i	1.05844	+	0.210537i	0.693473	−	0.720482i	$-0.256079\pi$
$449$	22.4280	+	4.46121i	1.05844	+	0.210537i	0.364969	+	0.931020i	$0.381079\pi$
$450$	−0.149842	+	1.13817i	−0.00706364	+	0.0536537i
$451$	−33.6350	−	25.8091i	−1.58381	−	1.21530i
$452$	2.40367	−	0.815937i	0.113059	−	0.0383784i
$453$	−1.16999	−	17.8506i	−0.0549708	−	0.838692i
$454$	18.6355	−	3.70683i	0.874606	−	0.173970i
$455$	−7.98422	+	2.35755i	−0.374306	+	0.110524i
$456$	5.83354	−	8.73051i	0.273180	−	0.408843i
$457$	3.89979	−	2.99242i	0.182425	−	0.139979i	−0.513512	−	0.858082i	$-0.671656\pi$
$457$	3.89979	−	2.99242i	0.182425	−	0.139979i	0.695937	+	0.718103i	$0.254989\pi$
$458$	5.76710	+	9.98890i	0.269479	+	0.466751i
$459$	21.6755	−	7.91157i	1.01173	−	0.369281i
$460$	5.99766	+	3.46275i	0.279642	+	0.161452i
$461$	25.7044	+	10.6471i	1.19717	+	0.495885i	0.890084	−	0.455797i	$-0.150646\pi$
$461$	25.7044	+	10.6471i	1.19717	+	0.495885i	0.307088	+	0.951681i	$0.400646\pi$
$462$	−0.543483	+	13.5353i	−0.0252851	+	0.629720i
$463$	8.44349	+	8.44349i	0.392402	+	0.392402i	0.875543	−	0.483141i	$-0.160504\pi$
$463$	8.44349	+	8.44349i	0.392402	+	0.392402i	−0.483141	+	0.875543i	$0.660504\pi$
$464$	−0.125675	+	0.370228i	−0.00583434	+	0.0171874i
$465$	3.61350	−	7.32746i	0.167572	−	0.339803i
$466$	5.76904	+	16.9950i	0.267245	+	0.787280i
$467$	12.0122	+	1.58143i	0.555858	+	0.0731801i	0.403222	−	0.915102i	$-0.367890\pi$
$467$	12.0122	+	1.58143i	0.555858	+	0.0731801i	0.152636	+	0.988282i	$0.451224\pi$
$468$	−4.83693	+	2.00352i	−0.223587	+	0.0926128i
$469$	−4.12731	−	11.2173i	−0.190581	−	0.517967i
$470$	−4.51684	−	6.75992i	−0.208346	−	0.311812i
$471$	6.79741	+	2.30741i	0.313208	+	0.106320i
$472$	−7.00741	+	26.1520i	−0.322542	+	1.20374i
$473$	30.0962	+	1.97261i	1.38383	+	0.0907008i
$474$	3.80530	+	4.95917i	0.174783	+	0.227782i
$475$	−2.88812			−0.132516
$476$	13.5788	−	1.54777i	0.622384	−	0.0709420i
$477$	−13.1955			−0.604180
$478$	10.7238	+	13.9755i	0.490495	+	0.639225i
$479$	21.8975	+	1.43524i	1.00052	+	0.0655778i	0.556852	−	0.830611i	$-0.312009\pi$
$479$	21.8975	+	1.43524i	1.00052	+	0.0655778i	0.443672	+	0.896189i	$0.353676\pi$
$480$	1.90370	−	7.10469i	0.0868915	−	0.324283i
$481$	35.3699	+	12.0065i	1.61273	+	0.547447i
$482$	−3.96707	−	5.93715i	−0.180695	−	0.270430i
$483$	−18.6351	−	3.21863i	−0.847928	−	0.146453i
$484$	−11.5570	+	4.78706i	−0.525317	+	0.217594i
$485$	−2.98548	−	0.393046i	−0.135564	−	0.0178473i
$486$	−3.49650	−	10.3004i	−0.158605	−	0.467234i
$487$	−15.4034	+	31.2349i	−0.697993	+	1.41539i	0.201956	+	0.979395i	$0.435270\pi$
$487$	−15.4034	+	31.2349i	−0.697993	+	1.41539i	−0.899949	+	0.435995i	$0.856397\pi$
$488$	2.77572	−	8.17700i	0.125651	−	0.370155i
$489$	12.3248	+	12.3248i	0.557347	+	0.557347i
$490$	0.0896264	−	6.05007i	0.00404891	−	0.273315i
$491$	−19.3852	−	8.02961i	−0.874842	−	0.362371i	−0.100348	−	0.994952i	$-0.531996\pi$
$491$	−19.3852	−	8.02961i	−0.874842	−	0.362371i	−0.774494	+	0.632581i	$0.781996\pi$
$492$	−12.9838	−	7.49620i	−0.585355	−	0.337955i
$493$	14.4904	+	15.7847i	0.652616	+	0.710906i
$494$	3.92764	+	6.80287i	0.176713	+	0.306075i
$495$	4.82665	−	3.70362i	0.216942	−	0.166465i
$496$	0.264097	−	0.395249i	0.0118583	−	0.0177472i
$497$	−8.23073	+	8.65843i	−0.369199	+	0.388384i
$498$	5.42331	−	1.07876i	0.243024	−	0.0483406i
$499$	−1.27141	−	19.3979i	−0.0569160	−	0.868370i	−0.926904	−	0.375298i	$-0.877540\pi$
$499$	−1.27141	−	19.3979i	−0.0569160	−	0.868370i	0.869988	−	0.493072i	$-0.164126\pi$
$500$	−1.18634	+	0.402708i	−0.0530548	+	0.0180097i
$501$	6.38713	+	4.90102i	0.285356	+	0.218961i
$502$	−2.96670	+	22.5343i	−0.132410	+	1.00576i
$503$	−18.1295	−	3.60618i	−0.808353	−	0.160791i	−0.226422	−	0.974029i	$-0.572703\pi$
$503$	−18.1295	−	3.60618i	−0.808353	−	0.160791i	−0.581931	+	0.813238i	$0.697703\pi$
$504$	−0.895539	−	9.83911i	−0.0398905	−	0.438269i
$505$	−2.54598	−	12.7995i	−0.113295	−	0.569570i
$506$	5.66524	+	21.1430i	0.251851	+	0.939920i
$507$	0.262089	−	3.99871i	0.0116398	−	0.177589i
$508$	−0.583416	−	4.43148i	−0.0258849	−	0.196615i
$509$	12.4957	−	21.6432i	0.553863	−	0.959319i	−0.444128	−	0.895963i	$-0.646486\pi$
$509$	12.4957	−	21.6432i	0.553863	−	0.959319i	0.997991	−	0.0633557i	$-0.0201803\pi$
$510$	−3.33177	−	3.18368i	−0.147533	−	0.140976i
$511$	−14.2389	−	23.2808i	−0.629892	−	1.02988i
$512$	0.325674	−	0.786248i	0.0143929	−	0.0347476i
$513$	14.4960	−	7.14864i	0.640015	−	0.315620i
$514$	−21.6587	−	5.80344i	−0.955326	−	0.255979i
$515$	−8.65495	−	9.86908i	−0.381383	−	0.434884i
$516$	10.6429	−	0.697570i	0.468526	−	0.0307088i
$517$	−8.40568	+	42.2582i	−0.369681	+	1.85851i
$518$	−15.9761	+	21.9495i	−0.701952	+	0.964405i
$519$	11.1458	+	26.9084i	0.489247	+	1.18115i
$520$	6.65170	+	5.83339i	0.291696	+	0.255811i
$521$	15.1731	+	7.48256i	0.664747	+	0.327817i	0.743169	−	0.669103i	$-0.233322\pi$
$521$	15.1731	+	7.48256i	0.664747	+	0.327817i	−0.0784227	+	0.996920i	$0.524988\pi$
$522$	4.48544	−	3.93363i	0.196322	−	0.172170i
$523$	−7.01916	+	1.88078i	−0.306926	+	0.0822407i	−0.408995	−	0.912537i	$-0.634121\pi$
$523$	−7.01916	+	1.88078i	−0.306926	+	0.0822407i	0.102068	+	0.994777i	$0.467454\pi$
$524$	−0.697789	−	0.466248i	−0.0304831	−	0.0203681i
$525$	2.66049	−	2.15063i	0.116113	−	0.0938611i
$526$			7.90838i			0.344822i
$527$	−12.0505	−	23.0974i	−0.524926	−	1.00614i
$528$	−0.385921	+	0.222811i	−0.0167950	+	0.00969662i
$529$	−7.49300	+	0.986472i	−0.325783	+	0.0428901i
$530$	3.79853	+	7.70265i	0.164997	+	0.334582i
$531$	−9.04278	+	9.04278i	−0.392423	+	0.392423i
$532$	9.33893	−	2.10473i	0.404894	−	0.0912515i
$533$	24.2134	−	16.1789i	1.04880	−	0.700785i
$534$	0.0138530	−	0.0157963i	0.000599479	−	0.000683575i
$535$	−3.85184	+	5.01981i	−0.166529	+	0.217025i
$536$	−7.73266	+	10.0774i	−0.334000	+	0.435277i
$537$	14.9507	−	17.0480i	0.645171	−	0.735677i
$538$	−1.40710	+	0.940191i	−0.0606642	+	0.0405345i
$539$	−23.0077	+	22.3360i	−0.991013	+	0.962080i
$540$	4.95769	−	4.95769i	0.213345	−	0.213345i
$541$	4.55823	+	9.24318i	0.195974	+	0.397395i	0.972572	−	0.232600i	$-0.0747234\pi$
$541$	4.55823	+	9.24318i	0.195974	+	0.397395i	−0.776599	+	0.629996i	$0.783057\pi$
$542$	24.6847	−	3.24980i	1.06030	−	0.139591i
$543$	14.2939	−	8.25257i	0.613409	−	0.354152i
$544$	−14.6971	−	18.2782i	−0.630134	−	0.783669i
$545$			0.801815i			0.0343460i
$546$	−8.68381	−	3.34199i	−0.371633	−	0.143024i
$547$	27.1775	+	18.1594i	1.16203	+	0.776442i	0.978434	−	0.206561i	$-0.0662271\pi$
$547$	27.1775	+	18.1594i	1.16203	+	0.776442i	0.183593	+	0.983002i	$0.441227\pi$
$548$	26.9777	−	7.22864i	1.15243	−	0.308792i
$549$	3.06660	−	2.68933i	0.130879	−	0.114778i
$550$	−3.55135	−	1.75133i	−0.151430	−	0.0746770i
$551$	11.2845	+	9.89626i	0.480737	+	0.421595i
$552$	7.69091	+	18.5675i	0.327347	+	0.790286i
$553$	−1.55939	+	14.7146i	−0.0663119	+	0.625729i
$554$	−3.57033	+	17.9492i	−0.151689	+	0.762590i
$555$	−15.3164	+	1.00389i	−0.650143	+	0.0426126i
$556$	−4.80037	−	5.47377i	−0.203581	−	0.232139i
$557$	−12.3690	−	3.31426i	−0.524090	−	0.140430i	−0.0129325	−	0.999916i	$-0.504117\pi$
$557$	−12.3690	−	3.31426i	−0.524090	−	0.140430i	−0.511158	+	0.859487i	$0.670783\pi$
$558$	−6.50554	+	3.20818i	−0.275402	+	0.135813i
$559$	−7.92806	+	19.1400i	−0.335321	+	0.809537i
$560$	0.169806	−	0.103856i	0.00717561	−	0.00438872i
$561$	0.554977	+	24.4158i	0.0234311	+	1.03084i
$562$	11.7138	−	20.2889i	0.494116	−	0.855834i
$563$	−3.98417	−	30.2628i	−0.167913	−	1.27542i	−0.843092	−	0.537770i	$-0.819267\pi$
$563$	−3.98417	−	30.2628i	−0.167913	−	1.27542i	0.675179	−	0.737654i	$-0.264066\pi$
$564$	−0.996510	+	15.2038i	−0.0419606	+	0.640196i
$565$	−0.524399	−	1.95708i	−0.0220616	−	0.0823352i
$566$	−0.512289	−	2.57545i	−0.0215331	−	0.108254i
$567$	−3.60878	+	7.81035i	−0.151555	+	0.328004i
$568$	12.4517	+	2.47680i	0.522462	+	0.103924i
$569$	3.60083	−	27.3510i	0.150955	−	1.14661i	−0.733400	−	0.679797i	$-0.762068\pi$
$569$	3.60083	−	27.3510i	0.150955	−	1.14661i	0.884354	−	0.466816i	$-0.154599\pi$
$570$	−2.56094	−	1.96508i	−0.107266	−	0.0823079i
$571$	41.3242	−	14.0277i	1.72936	−	0.587040i	0.733651	−	0.679527i	$-0.237815\pi$
$571$	41.3242	−	14.0277i	1.72936	−	0.587040i	0.995714	+	0.0924869i	$0.0294816\pi$
$572$	−1.18108	−	18.0197i	−0.0493833	−	0.753443i
$573$	−21.7096	+	4.31830i	−0.906930	+	0.180400i
$574$	5.99390	+	20.2993i	0.250180	+	0.847275i
$575$	3.07114	−	4.59628i	0.128075	−	0.191678i
$576$	−5.02228	+	3.85373i	−0.209262	+	0.160572i
$577$	10.4065	+	18.0245i	0.433227	+	0.750371i	0.997149	−	0.0754571i	$-0.0240416\pi$
$577$	10.4065	+	18.0245i	0.433227	+	0.750371i	−0.563922	+	0.825828i	$0.690708\pi$
$578$	−14.4667	+	2.57802i	−0.601737	+	0.107232i
$579$	15.6244	+	9.02075i	0.649328	+	0.374890i
$580$	6.01519	+	2.49157i	0.249767	+	0.103457i
$581$	11.0641	+	6.99428i	0.459017	+	0.290171i
$582$	−2.37984	−	2.37984i	−0.0986476	−	0.0986476i
$583$	14.6302	−	43.0992i	0.605921	−	1.78499i
$584$	−12.8272	+	26.0109i	−0.530792	+	1.07634i
$585$	1.34327	+	3.95713i	0.0555372	+	0.163607i
$586$	−9.57235	−	1.26022i	−0.395430	−	0.0520594i
$587$	−12.4427	+	5.15393i	−0.513565	+	0.212725i	−0.624388	−	0.781115i	$-0.714651\pi$
$587$	−12.4427	+	5.15393i	−0.513565	+	0.212725i	0.110823	+	0.993840i	$0.464651\pi$
$588$	−7.03559	+	8.89304i	−0.290143	+	0.366743i
$589$	−10.1384	−	15.1732i	−0.417746	−	0.625200i
$590$	7.88167	+	2.67547i	0.324483	+	0.110147i
$591$	1.63398	−	6.09809i	0.0672129	−	0.250842i
$592$	−0.891163	−	0.0584099i	−0.0366266	−	0.00240063i
$593$	1.93384	+	2.52023i	0.0794134	+	0.103494i	0.831371	−	0.555718i	$-0.187557\pi$
$593$	1.93384	+	2.52023i	0.0794134	+	0.103494i	−0.751957	+	0.659212i	$0.770890\pi$
$594$	22.1598			0.909226
$595$	−0.523904	−	10.8961i	−0.0214780	−	0.446698i
$596$	0.697896			0.0285869
$597$	2.04083	+	2.65966i	0.0835255	+	0.108852i
$598$	−15.0029	−	0.983343i	−0.613515	−	0.0402119i
$599$	−7.75843	+	28.9549i	−0.317001	+	1.18306i	0.605111	+	0.796141i	$0.293129\pi$
$599$	−7.75843	+	28.9549i	−0.317001	+	1.18306i	−0.922112	+	0.386923i	$0.873538\pi$
$600$	−3.44268	−	1.16863i	−0.140547	−	0.0477092i
$601$	15.4140	+	23.0687i	0.628751	+	0.940992i	0.999923	+	0.0124282i	$0.00395611\pi$
$601$	15.4140	+	23.0687i	0.628751	+	0.940992i	−0.371172	+	0.928564i	$0.621044\pi$
$602$	−11.5685	−	9.63827i	−0.471496	−	0.392826i
$603$	−5.54309	+	2.29602i	−0.225732	+	0.0935014i
$604$	−17.1845	−	2.26238i	−0.699225	−	0.0920548i
$605$	3.20950	+	9.45487i	0.130485	+	0.384395i
$606$	6.45122	−	13.0818i	0.262063	−	0.531411i
$607$	−2.36135	+	6.95630i	−0.0958441	+	0.282347i	−0.984270	−	0.176673i	$-0.943466\pi$
$607$	−2.36135	+	6.95630i	−0.0958441	+	0.282347i	0.888425	+	0.459021i	$0.151800\pi$
$608$	−11.6170	−	11.6170i	−0.471132	−	0.471132i
$609$	−17.7643	−	0.713291i	−0.719847	−	0.0289040i
$610$	−2.45262	−	1.01591i	−0.0993037	−	0.0411329i
$611$	−25.6302	−	14.7976i	−1.03689	−	0.598647i
$612$	−1.04978	−	6.77950i	−0.0424348	−	0.274045i
$613$	−14.7553	−	25.5570i	−0.595962	−	1.03224i	−0.993410	−	0.114612i	$-0.963438\pi$
$613$	−14.7553	−	25.5570i	−0.595962	−	1.03224i	0.397448	−	0.917624i	$-0.369896\pi$
$614$	−8.42944	+	6.46814i	−0.340185	+	0.261033i
$615$	−6.64843	+	9.95008i	−0.268090	+	0.401226i
$616$	33.1294	+	7.98387i	1.33482	+	0.321679i
$617$	16.6099	−	3.30391i	0.668689	−	0.133011i	0.150940	−	0.988543i	$-0.451770\pi$
$617$	16.6099	−	3.30391i	0.668689	−	0.133011i	0.517749	+	0.855532i	$0.326770\pi$
$618$	−0.959548	−	14.6399i	−0.0385987	−	0.588902i
$619$	−9.13523	+	3.10099i	−0.367176	+	0.124639i	−0.498928	−	0.866643i	$-0.666273\pi$
$619$	−9.13523	+	3.10099i	−0.367176	+	0.124639i	0.131752	+	0.991283i	$0.457940\pi$
$620$	−6.28020	−	4.81897i	−0.252219	−	0.193534i
$621$	−4.03795	+	30.6712i	−0.162037	+	1.23079i
$622$	−2.17117	−	0.431872i	−0.0870559	−	0.0173165i
$623$	0.0495304	−	0.00450818i	0.00198439	−	0.000180616i
$624$	−0.0597155	−	0.300210i	−0.00239053	−	0.0120180i
$625$	0.258819	+	0.965926i	0.0103528	+	0.0386370i
$626$	−1.14691	+	17.4984i	−0.0458397	+	0.699378i
$627$	2.23291	+	16.9606i	0.0891739	+	0.677343i
$628$	3.47760	−	6.02339i	0.138772	−	0.240359i
$629$	−26.2603	+	41.3033i	−1.04707	+	1.64687i
$630$	−3.03632	+	0.0768911i	−0.120970	+	0.00306342i
$631$	3.15896	−	7.62640i	0.125756	−	0.303602i	−0.848445	−	0.529283i	$-0.822461\pi$
$631$	3.15896	−	7.62640i	0.125756	−	0.303602i	0.974201	+	0.225681i	$0.0724608\pi$
$632$	14.1035	−	6.95508i	0.561008	−	0.276658i
$633$	2.57210	+	0.689192i	0.102232	+	0.0273929i
$634$	16.0602	+	18.3132i	0.637834	+	0.727310i
$635$	−3.56007	+	0.233339i	−0.141277	+	0.00925978i
$636$	3.14002	−	15.7860i	0.124510	−	0.625954i
$637$	−9.44814	−	19.8966i	−0.374349	−	0.788331i
$638$	7.87489	+	19.0117i	0.311770	+	0.752679i
$639$	4.50854	+	3.95388i	0.178355	+	0.156413i
$640$	−6.50836	−	3.20957i	−0.257265	−	0.126869i
$641$	−29.8417	+	26.1704i	−1.17867	+	1.03367i	−0.179925	+	0.983680i	$0.557585\pi$
$641$	−29.8417	+	26.1704i	−1.17867	+	1.03367i	−0.998750	+	0.0499895i	$0.984081\pi$
$642$	−6.83096	+	1.83035i	−0.269596	+	0.0722382i
$643$	−17.4409	−	11.6536i	−0.687802	−	0.459575i	0.161921	−	0.986804i	$-0.448231\pi$
$643$	−17.4409	−	11.6536i	−0.687802	−	0.459575i	−0.849723	+	0.527229i	$0.823231\pi$
$644$	−6.58117	+	17.1005i	−0.259334	+	0.673853i
$645$		−	8.51330i		−	0.335211i
$646$	−9.87935	+	2.88932i	−0.388698	+	0.113679i
$647$	10.2441	−	5.91444i	0.402738	−	0.232521i	−0.284927	−	0.958549i	$-0.591969\pi$
$647$	10.2441	−	5.91444i	0.402738	−	0.232521i	0.687665	+	0.726029i	$0.258636\pi$
$648$	9.06525	−	1.19346i	0.356117	−	0.0468837i
$649$	−19.5096	−	39.5615i	−0.765818	−	1.55293i
$650$	1.92323	−	1.92323i	0.0754353	−	0.0754353i
$651$	20.6380	+	6.42777i	0.808867	+	0.251924i
$652$	14.0419	−	9.38251i	0.549924	−	0.367447i
$653$	−8.16359	+	9.30879i	−0.319466	+	0.364281i	−0.889177	−	0.457564i	$-0.848722\pi$
$653$	−8.16359	+	9.30879i	−0.319466	+	0.364281i	0.569711	+	0.821845i	$0.307055\pi$
$654$	−0.545555	+	0.710981i	−0.0213329	+	0.0278015i
$655$	−0.407787	+	0.531439i	−0.0159336	+	0.0207650i
$656$	−0.459087	+	0.523489i	−0.0179243	+	0.0204388i
$657$	−11.3901	+	7.61061i	−0.444369	+	0.296918i
$658$	15.8080	−	14.5875i	0.616260	−	0.568681i
$659$	−8.16876	+	8.16876i	−0.318210	+	0.318210i	−0.848079	−	0.529869i	$-0.822241\pi$
$659$	−8.16876	+	8.16876i	−0.318210	+	0.318210i	0.529869	+	0.848079i	$0.322241\pi$
$660$	3.28213	+	6.65550i	0.127757	+	0.259065i
$661$	−25.9629	+	3.41809i	−1.00984	+	0.132948i	−0.617252	−	0.786766i	$-0.711754\pi$
$661$	−25.9629	+	3.41809i	−1.00984	+	0.132948i	−0.392589	+	0.919714i	$0.628421\pi$
$662$	21.1434	−	12.2071i	0.821762	−	0.474444i
$663$	−16.0034	−	5.02984i	−0.621519	−	0.195343i
$664$		−	13.9106i		−	0.539835i
$665$	−1.18885	−	7.54819i	−0.0461017	−	0.292706i
$666$	11.3309	+	7.57104i	0.439062	+	0.293372i
$667$	−27.7489	+	7.43531i	−1.07444	+	0.287896i
$668$	5.86474	−	5.14324i	0.226914	−	0.198998i
$669$	−10.5932	−	5.22397i	−0.409556	−	0.201971i
$670$	2.93593	+	2.57474i	0.113425	+	0.0994710i
$671$	5.38389	+	12.9979i	0.207843	+	0.501777i
$672$	19.3520	+	2.05083i	0.746519	+	0.0791126i
$673$	9.61589	−	48.3423i	0.370665	−	1.86346i	−0.120965	−	0.992657i	$-0.538599\pi$
$673$	9.61589	−	48.3423i	0.370665	−	1.86346i	0.491631	−	0.870804i	$-0.336401\pi$
$674$	13.6118	−	0.892165i	0.524307	−	0.0343649i
$675$	−3.68991	−	4.20754i	−0.142025	−	0.161948i
$676$	−3.75041	−	1.00492i	−0.144247	−	0.0386507i
$677$	−15.7937	+	7.78859i	−0.607001	+	0.299340i	−0.719696	−	0.694290i	$-0.755719\pi$
$677$	−15.7937	+	7.78859i	−0.607001	+	0.299340i	0.112694	+	0.993630i	$0.464052\pi$
$678$	0.866608	−	2.09218i	0.0332819	−	0.0803496i
$679$	−0.201690	−	7.96445i	−0.00774016	−	0.305647i
$680$	−9.49038	+	6.65811i	−0.363939	+	0.255327i
$681$	−14.2113	+	24.6146i	−0.544577	+	0.943235i
$682$	−3.26570	−	24.8054i	−0.125050	−	0.949848i
$683$	0.951167	−	14.5120i	0.0363954	−	0.555287i	−0.940258	−	0.340464i	$-0.889416\pi$
$683$	0.951167	−	14.5120i	0.0363954	−	0.555287i	0.976653	−	0.214823i	$-0.0689174\pi$
$684$	−1.24374	−	4.64170i	−0.0475556	−	0.177480i
$685$	−4.34915	−	21.8647i	−0.166173	−	0.835406i
$686$	15.8490	−	2.25618i	0.605116	−	0.0861414i
$687$	−16.9222	−	3.36604i	−0.645623	−	0.128422i
$688$	0.0646543	−	0.491098i	0.00246492	−	0.0187229i
$689$	24.8029	+	19.0319i	0.944914	+	0.725058i
$690$	5.85053	−	1.98599i	0.222726	−	0.0756052i
$691$	−1.46170	−	22.3013i	−0.0556058	−	0.848380i	−0.931011	−	0.364991i	$-0.881072\pi$
$691$	−1.46170	−	22.3013i	−0.0556058	−	0.848380i	0.875405	−	0.483390i	$-0.160595\pi$
$692$	27.6777	−	5.50544i	1.05215	−	0.209285i
$693$	11.6663	+	11.0901i	0.443168	+	0.421277i
$694$	7.15348	−	10.7059i	0.271542	−	0.406392i
$695$	−4.61038	+	3.53767i	−0.174882	+	0.134191i
$696$	9.44693	+	16.3626i	0.358085	+	0.620222i
$697$	13.0838	+	35.8459i	0.495584	+	1.35776i
$698$	−7.58130	−	4.37706i	−0.286956	−	0.165674i
$699$	−24.8037	−	10.2740i	−0.938161	−	0.388599i
$700$	−1.54083	−	2.93477i	−0.0582379	−	0.110924i
$701$	19.5830	+	19.5830i	0.739639	+	0.739639i	0.972508	−	0.232869i	$-0.0748115\pi$
$701$	19.5830	+	19.5830i	0.739639	+	0.739639i	−0.232869	+	0.972508i	$0.574811\pi$
$702$	−4.89270	+	14.4134i	−0.184663	+	0.544000i
$703$	−15.1635	+	30.7486i	−0.571903	+	1.15971i
$704$	−7.01874	−	20.6765i	−0.264529	−	0.779276i
$705$	12.0576	+	1.58741i	0.454115	+	0.0597854i
$706$	14.2862	−	5.91754i	0.537669	−	0.222710i
$707$	32.4039	−	11.9227i	1.21867	−	0.448400i
$708$	−8.66617	−	12.9698i	−0.325695	−	0.487436i
$709$	0.771632	+	0.261934i	0.0289793	+	0.00983713i	0.335891	−	0.941901i	$-0.390962\pi$
$709$	0.771632	+	0.261934i	0.0289793	+	0.00983713i	−0.306912	+	0.951738i	$0.599296\pi$
$710$	1.01016	−	3.76997i	0.0379106	−	0.141484i
$711$	7.41175	+	0.485792i	0.277963	+	0.0182186i
$712$	−0.0321761	−	0.0419327i	−0.00120585	−	0.00157149i
$713$	34.9282			1.30807
$714$	6.94917	−	10.0182i	0.260066	−	0.374922i
$715$	−14.4141			−0.539057
$716$	−13.3746	−	17.4301i	−0.499832	−	0.651394i
$717$	−26.2946	−	1.72344i	−0.981990	−	0.0643630i
$718$	1.14281	−	4.26504i	0.0426494	−	0.159170i
$719$	−14.6361	−	4.96830i	−0.545836	−	0.185286i	0.0348818	−	0.999391i	$-0.488895\pi$
$719$	−14.6361	−	4.96830i	−0.545836	−	0.185286i	−0.580717	+	0.814105i	$0.697228\pi$
$720$	−0.0555104	−	0.0830772i	−0.00206875	−	0.00309610i
$721$	22.2305	−	26.6825i	0.827906	−	0.993707i
$722$	8.51203	−	3.52580i	0.316785	−	0.131217i
$723$	10.5900	+	1.39420i	0.393847	+	0.0518509i
$724$	−5.14047	−	15.1433i	−0.191044	−	0.562798i
$725$	2.29852	−	4.66094i	0.0853649	−	0.173103i
$726$	−3.58719	+	10.5675i	−0.133133	+	0.392197i
$727$	−7.35145	−	7.35145i	−0.272650	−	0.272650i	0.557516	−	0.830166i	$-0.311755\pi$
$727$	−7.35145	−	7.35145i	−0.272650	−	0.272650i	−0.830166	+	0.557516i	$0.811755\pi$
$728$	−12.5077	+	19.7857i	−0.463565	+	0.733306i
$729$	24.0462	+	9.96025i	0.890599	+	0.368898i
$730$	7.72137	+	4.45794i	0.285781	+	0.164996i
$731$	−21.9068	−	16.0321i	−0.810253	−	0.592970i
$732$	2.48755	+	4.30857i	0.0919427	+	0.159249i
$733$	−36.9212	+	28.3306i	−1.36372	+	1.04642i	−0.370660	+	0.928768i	$0.620869\pi$
$733$	−36.9212	+	28.3306i	−1.36372	+	1.04642i	−0.993055	+	0.117647i	$0.962465\pi$
$734$	−17.2149	+	25.7639i	−0.635413	+	0.950963i
$735$	6.71589	+	6.06800i	0.247719	+	0.223821i
$736$	30.8410	−	6.13466i	1.13682	−	0.226127i
$737$	−1.35351	−	20.6505i	−0.0498571	−	0.760672i
$738$	10.0607	−	3.41515i	0.370340	−	0.125713i
$739$	19.9290	+	15.2921i	0.733102	+	0.562529i	0.906440	−	0.422334i	$-0.138789\pi$
$739$	19.9290	+	15.2921i	0.733102	+	0.562529i	−0.173339	+	0.984862i	$0.555456\pi$
$740$	−1.94119	+	14.7448i	−0.0713597	+	0.542030i
$741$	−11.5248	−	2.29242i	−0.423372	−	0.0842140i
$742$	−18.5675	+	13.0983i	−0.681635	+	0.480852i
$743$	7.90870	+	39.7597i	0.290142	+	1.45864i	0.800838	+	0.598881i	$0.204388\pi$
$743$	7.90870	+	39.7597i	0.290142	+	1.45864i	−0.510696	+	0.859762i	$0.670612\pi$
$744$	−5.94552	−	22.1890i	−0.217973	−	0.813488i
$745$	0.0364332	−	0.555864i	0.00133481	−	0.0203653i
$746$	−0.860814	−	6.53853i	−0.0315167	−	0.239393i
$747$	3.28526	−	5.69025i	0.120202	−	0.208195i
$748$	23.3071	+	4.08782i	0.852193	+	0.149465i
$749$	−14.7050	−	8.00057i	−0.537309	−	0.292335i
$750$	−0.427717	+	1.03260i	−0.0156180	+	0.0377053i
$751$	24.9613	−	12.3096i	0.910852	−	0.449182i	0.0744036	−	0.997228i	$-0.476295\pi$
$751$	24.9613	−	12.3096i	0.910852	−	0.449182i	0.836448	+	0.548046i	$0.184628\pi$
$752$	0.683498	+	0.183143i	0.0249246	+	0.00667853i
$753$	−22.4174	−	25.5622i	−0.816937	−	0.931538i
$754$	−14.1045	+	0.924459i	−0.513656	+	0.0336668i
$755$	−2.69905	+	13.5691i	−0.0982286	+	0.493829i
$756$	14.9978	+	10.9163i	0.545466	+	0.397023i
$757$	15.0149	+	36.2491i	0.545725	+	1.31750i	0.920631	+	0.390433i	$0.127675\pi$
$757$	15.0149	+	36.2491i	0.545725	+	1.31750i	−0.374906	+	0.927063i	$0.622325\pi$
$758$	−15.9840	−	14.0176i	−0.580566	−	0.509143i
$759$	−29.3663	−	14.4819i	−1.06593	−	0.525659i
$760$	−6.10537	+	5.35426i	−0.221465	+	0.194219i
$761$	43.8469	−	11.7487i	1.58945	−	0.425892i	0.647615	−	0.761968i	$-0.275767\pi$
$761$	43.8469	−	11.7487i	1.58945	−	0.425892i	0.941835	+	0.336076i	$0.109100\pi$
$762$	−3.31553	−	2.21536i	−0.120109	−	0.0802542i
$763$	−2.09557	+	0.330055i	−0.0758647	+	0.0119488i
$764$			21.4468i			0.775917i
$765$	−5.45457	+	0.482214i	−0.197210	+	0.0174345i
$766$	−9.14443	+	5.27954i	−0.330402	+	0.190757i
$767$	30.0396	−	3.95479i	1.08467	−	0.142799i
$768$	−9.03920	−	18.3297i	−0.326174	−	0.661415i
$769$	−15.9589	+	15.9589i	−0.575493	+	0.575493i	−0.933658	−	0.358165i	$-0.883402\pi$
$769$	−15.9589	+	15.9589i	−0.575493	+	0.575493i	0.358165	+	0.933658i	$0.383402\pi$
$770$	3.11530	−	10.0025i	0.112268	−	0.360464i
$771$	27.8890	−	18.6348i	1.00440	−	0.671116i
$772$	11.5258	−	13.1426i	0.414822	−	0.473014i
$773$	5.53270	−	7.21035i	0.198997	−	0.259338i	−0.683186	−	0.730244i	$-0.739406\pi$
$773$	5.53270	−	7.21035i	0.198997	−	0.259338i	0.882183	+	0.470906i	$0.156073\pi$
$774$	−4.60124	+	5.99646i	−0.165388	+	0.215538i
$775$	−4.16609	+	4.75052i	−0.149650	+	0.170644i
$776$	−7.03985	+	4.70388i	−0.252716	+	0.168859i
$777$	−8.92844	−	39.6166i	−0.320306	−	1.42124i
$778$	−5.72528	+	5.72528i	−0.205261	+	0.205261i
$779$	11.8221	+	23.9728i	0.423570	+	0.858915i
$780$	−5.05362	+	0.665322i	−0.180949	+	0.0238224i
$781$	−17.9129	+	10.3420i	−0.640974	+	0.370067i
$782$	5.90720	−	18.7948i	0.211241	−	0.672102i
$783$			29.0834i			1.03936i
$784$	0.341329	+	0.401042i	0.0121903	+	0.0143229i
$785$	−4.61599	−	3.08431i	−0.164752	−	0.110084i
$786$	−0.723182	+	0.193776i	−0.0257950	+	0.00691176i
$787$	−20.5343	+	18.0081i	−0.731969	+	0.641920i	−0.941937	−	0.335788i	$-0.890997\pi$
$787$	−20.5343	+	18.0081i	−0.731969	+	0.641920i	0.209968	+	0.977708i	$0.432664\pi$
$788$	−5.48612	−	2.70546i	−0.195435	−	0.0963779i
$789$	−8.89424	−	7.80004i	−0.316643	−	0.277689i
$790$	−1.85001	−	4.46633i	−0.0658206	−	0.158905i
$791$	4.89905	−	2.17614i	0.174190	−	0.0773746i
$792$	3.33723	−	16.7774i	0.118583	−	0.596158i
$793$	−9.64295	+	0.632032i	−0.342431	+	0.0224441i
$794$	18.5688	+	21.1737i	0.658983	+	0.751426i
$795$	−12.4094	−	3.32508i	−0.440115	−	0.117928i
$796$	2.91323	−	1.43664i	0.103257	−	0.0509205i
$797$	−11.5760	+	27.9470i	−0.410043	+	0.989932i	0.575082	+	0.818096i	$0.304970\pi$
$797$	−11.5760	+	27.9470i	−0.410043	+	0.989932i	−0.985126	+	0.171836i	$0.945030\pi$
$798$	4.08162	−	7.50199i	0.144488	−	0.265567i
$799$	26.7915	−	28.0378i	0.947815	−	0.991905i
$800$	−2.84423	+	4.92635i	−0.100559	+	0.174173i
$801$	−0.00325866	−	0.0247520i	−0.000115139	−	0.000874567i
$802$	−1.04038	+	15.8731i	−0.0367371	+	0.560499i
$803$	−12.2293	−	45.6404i	−0.431563	−	1.61061i
$804$	−1.42772	−	7.17765i	−0.0503519	−	0.253136i
$805$	13.2767	+	6.13452i	0.467943	+	0.216214i
$806$	16.8553	+	3.35272i	0.593702	+	0.118095i
$807$	0.330424	−	2.50982i	0.0116315	−	0.0883497i
$808$	−29.1110	−	22.3377i	−1.02412	−	0.785836i
$809$	33.1129	−	11.2403i	1.16419	−	0.395188i	0.328559	−	0.944484i	$-0.393437\pi$
$809$	33.1129	−	11.2403i	1.16419	−	0.395188i	0.835628	+	0.549295i	$0.185104\pi$
$810$	−0.183844	−	2.80491i	−0.00645961	−	0.0985546i
$811$	−0.0209422	+	0.00416566i	−0.000735379	+	0.000146276i	−0.195458	−	0.980712i	$-0.562619\pi$
$811$	−0.0209422	+	0.00416566i	−0.000735379	+	0.000146276i	0.194723	+	0.980858i	$0.437619\pi$
$812$	−4.03575	+	16.7465i	−0.141627	+	0.587688i
$813$	−20.6916	+	30.9672i	−0.725686	+	1.08607i
$814$	−37.2914	+	28.6147i	−1.30706	+	1.00294i
$815$	−6.73998	−	11.6740i	−0.236091	−	0.408922i
$816$	0.400722	+	0.0171307i	0.0140281	+	0.000599694i
$817$	−16.4678	−	9.50771i	−0.576137	−	0.332633i
$818$	−3.62740	−	1.50252i	−0.126829	−	0.0525344i
$819$	−9.78917	+	5.13957i	−0.342061	+	0.179591i
$820$	8.19879	+	8.19879i	0.286314	+	0.286314i
$821$	−11.4007	+	33.5855i	−0.397889	+	1.17214i	0.544828	+	0.838548i	$0.316595\pi$
$821$	−11.4007	+	33.5855i	−0.397889	+	1.17214i	−0.942717	+	0.333594i	$0.891738\pi$
$822$	11.0203	−	22.3469i	0.384376	−	0.779437i
$823$	−8.16771	−	24.0613i	−0.284709	−	0.838724i	−0.991361	−	0.131163i	$-0.958129\pi$
$823$	−8.16771	−	24.0613i	−0.284709	−	0.838724i	0.706652	−	0.707561i	$-0.250205\pi$
$824$	−36.5924	−	4.81748i	−1.27476	−	0.167825i
$825$	5.47235	−	2.26672i	0.190523	−	0.0789172i
$826$	−3.74805	+	21.7003i	−0.130411	+	0.755051i
$827$	30.5951	+	45.7887i	1.06389	+	1.59223i	0.771827	+	0.635833i	$0.219343\pi$
$827$	30.5951	+	45.7887i	1.06389	+	1.59223i	0.292067	+	0.956398i	$0.405657\pi$
$828$	8.70956	+	2.95650i	0.302678	+	0.102745i
$829$	1.17540	−	4.38665i	0.0408233	−	0.152355i	−0.942506	−	0.334190i	$-0.891537\pi$
$829$	1.17540	−	4.38665i	0.0408233	−	0.152355i	0.983329	+	0.181836i	$0.0582039\pi$
$830$	−4.26730	−	0.279694i	−0.148120	−	0.00970831i
$831$	−16.6654	−	21.7188i	−0.578116	−	0.753416i
$832$	14.9984			0.519975
$833$	28.2617	−	5.85447i	0.979211	−	0.202845i
$834$	−6.49511			−0.224907
$835$	−3.79035	−	4.93968i	−0.131170	−	0.170945i
$836$	16.5397	+	1.08407i	0.572037	+	0.0374933i
$837$	9.15197	−	34.1556i	0.316338	−	1.18059i
$838$	−1.11782	−	0.379448i	−0.0386144	−	0.0131078i
$839$	6.79218	+	10.1652i	0.234492	+	0.350942i	0.929989	−	0.367586i	$-0.119816\pi$
$839$	6.79218	+	10.1652i	0.234492	+	0.350942i	−0.695497	+	0.718529i	$0.744816\pi$
$840$	1.63713	−	9.47860i	0.0564863	−	0.327043i
$841$	1.84077	−	0.762472i	0.0634749	−	0.0262922i
$842$	28.6929	+	3.77749i	0.988823	+	0.130181i
$843$	11.2648	+	33.1850i	0.387980	+	1.14295i
$844$	1.14113	−	2.31398i	0.0392792	−	0.0796504i
$845$	−0.996191	+	2.93468i	−0.0342700	+	0.100956i
$846$	−7.63497	−	7.63497i	−0.262496	−	0.262496i
$847$	−23.3895	+	12.2801i	−0.803672	+	0.421949i
$848$	−0.690594	−	0.286054i	−0.0237151	−	0.00982312i
$849$	3.40178	+	1.96402i	0.116749	+	0.0674050i
$850$	1.85167	+	3.04520i	0.0635116	+	0.104450i
$851$	−32.8103	−	56.8290i	−1.12472	−	1.94807i
$852$	−5.80294	+	4.45275i	−0.198806	+	0.152549i
$853$	−9.92875	+	14.8594i	−0.339954	+	0.508777i	−0.961575	−	0.274541i	$-0.911474\pi$
$853$	−9.92875	+	14.8594i	−0.339954	+	0.508777i	0.621622	+	0.783318i	$0.286474\pi$
$854$	1.64553	−	6.82819i	0.0563087	−	0.233656i
$855$	−3.76197	+	0.748303i	−0.128657	+	0.0255914i
$856$	1.16357	+	17.7526i	0.0397698	+	0.606771i
$857$	−7.92001	+	2.68848i	−0.270542	+	0.0918367i	−0.453414	−	0.891300i	$-0.649794\pi$
$857$	−7.92001	+	2.68848i	−0.270542	+	0.0918367i	0.182872	+	0.983137i	$0.441461\pi$
$858$	−12.7812	−	9.80736i	−0.436343	−	0.334818i
$859$	2.97053	−	22.5634i	0.101353	−	0.769854i	−0.862994	−	0.505214i	$-0.831413\pi$
$859$	2.97053	−	22.5634i	0.101353	−	0.769854i	0.964347	−	0.264640i	$-0.0852532\pi$
$860$	−8.09015	−	1.60923i	−0.275872	−	0.0548743i
$861$	−28.7416	−	13.2801i	−0.979510	−	0.452584i
$862$	−0.416534	−	2.09406i	−0.0141872	−	0.0713239i
$863$	9.61549	+	35.8855i	0.327315	+	1.22156i	0.911964	+	0.410270i	$0.134566\pi$
$863$	9.61549	+	35.8855i	0.327315	+	1.22156i	−0.584649	+	0.811286i	$0.698768\pi$
$864$	2.08207	−	31.7663i	0.0708336	−	1.08071i
$865$	−2.94010	−	22.3323i	−0.0999665	−	0.759321i
$866$	−3.65817	+	6.33613i	−0.124310	+	0.215311i
$867$	11.3692	−	18.8129i	0.386117	−	0.638919i
$868$	10.0094	−	18.3972i	0.339741	−	0.624441i
$869$	−9.80430	+	23.6697i	−0.332588	+	0.802939i
$870$	5.20944	−	2.56901i	0.176616	−	0.0870976i
$871$	13.7306	+	3.67911i	0.465244	+	0.124662i
$872$	1.48648	+	1.69500i	0.0503385	+	0.0574001i
$873$	−3.99063	+	0.261560i	−0.135062	+	0.00885246i
$874$	2.69229	−	13.5350i	0.0910679	−	0.457829i
$875$	−2.41794	+	1.07404i	−0.0817413	+	0.0363092i
$876$	−6.39428	−	15.4372i	−0.216043	−	0.521573i
$877$	22.6402	+	19.8549i	0.764506	+	0.670453i	0.950020	−	0.312188i	$-0.101062\pi$
$877$	22.6402	+	19.8549i	0.764506	+	0.670453i	−0.185515	+	0.982641i	$0.559395\pi$
$878$	14.7594	+	7.27853i	0.498105	+	0.245638i
$879$	10.8586	−	9.52270i	0.366250	−	0.321193i
$880$	0.332893	−	0.0891984i	0.0112218	−	0.00300688i
$881$	−1.34126	−	0.896201i	−0.0451882	−	0.0301938i	0.532771	−	0.846259i	$-0.321151\pi$
$881$	−1.34126	−	0.896201i	−0.0451882	−	0.0301938i	−0.577959	+	0.816066i	$0.696151\pi$
$882$	−1.45081	−	7.90386i	−0.0488514	−	0.266137i
$883$		−	19.3249i		−	0.650333i	−0.945657	−	0.325167i	$-0.894580\pi$
$883$		−	19.3249i		−	0.650333i	0.945657	−	0.325167i	$-0.105420\pi$
$884$	−7.80488	+	14.2571i	−0.262506	+	0.479520i
$885$	−10.7827	+	6.22539i	−0.362456	+	0.209264i
$886$	15.2877	−	2.01266i	0.513599	−	0.0676166i
$887$	−10.7701	−	21.8396i	−0.361625	−	0.733303i	0.637691	−	0.770292i	$-0.279890\pi$
$887$	−10.7701	−	21.8396i	−0.361625	−	0.733303i	−0.999316	+	0.0369897i	$0.988223\pi$
$888$	−30.5171	+	30.5171i	−1.02409	+	1.02409i
$889$	−2.07529	−	9.20830i	−0.0696030	−	0.308837i
$890$	−0.0135105	+	0.00902742i	−0.000452873	+	0.000302600i
$891$	−9.82212	+	11.2000i	−0.329053	+	0.375213i
$892$	−6.96670	+	9.07918i	−0.233262	+	0.303993i
$893$	16.5366	−	21.5510i	0.553377	−	0.721175i
$894$	0.410516	−	0.468103i	0.0137297	−	0.0156557i
$895$	−14.5810	+	9.74274i	−0.487390	+	0.325664i
$896$	5.70924	−	18.3310i	0.190732	−	0.612395i
$897$	15.9033	−	15.9033i	0.530997	−	0.530997i
$898$	−8.74244	−	17.7279i	−0.291739	−	0.591588i
$899$	32.5557	−	4.28604i	1.08579	−	0.142947i
$900$	−1.44095	+	0.831933i	−0.0480316	+	0.0277311i
$901$	−31.9254	+	25.6706i	−1.06359	+	0.855213i
$902$			36.6468i			1.22020i
$903$	22.2498	−	3.50437i	0.740427	−	0.116618i
$904$	−4.73679	−	3.16502i	−0.157543	−	0.105267i
$905$	−12.3298	+	3.30376i	−0.409857	+	0.109821i
$906$	−11.6257	+	10.1954i	−0.386237	+	0.338721i
$907$	−2.65441	−	1.30901i	−0.0881383	−	0.0434650i	0.397685	−	0.917522i	$-0.369814\pi$
$907$	−2.65441	−	1.30901i	−0.0881383	−	0.0434650i	−0.485824	+	0.874057i	$0.661480\pi$
$908$	20.7049	+	18.1577i	0.687116	+	0.602584i
$909$	−6.63263	−	16.0126i	−0.219990	−	0.531104i
$910$	5.81810	+	4.23476i	0.192868	+	0.140381i
$911$	1.22893	−	6.17825i	0.0407163	−	0.204694i	−0.955072	−	0.296372i	$-0.904223\pi$
$911$	1.22893	−	6.17825i	0.0407163	−	0.204694i	0.995789	+	0.0916780i	$0.0292230\pi$
$912$	0.280349	−	0.0183751i	0.00928329	−	0.000608459i
$913$	14.9430	+	17.0393i	0.494542	+	0.563917i
$914$	−4.10421	−	1.09972i	−0.135755	−	0.0363755i
$915$	3.56158	−	1.75637i	0.117742	−	0.0580639i
$916$	−6.39746	+	15.4448i	−0.211378	+	0.510312i
$917$	−1.55679	−	0.847007i	−0.0514098	−	0.0279706i
$918$	−16.8313	−	10.7012i	−0.555516	−	0.353193i
$919$	23.4970	−	40.6981i	0.775096	−	1.34250i	−0.159645	−	0.987174i	$-0.551035\pi$
$919$	23.4970	−	40.6981i	0.775096	−	1.34250i	0.934741	−	0.355330i	$-0.115632\pi$
$920$	−2.02875	−	15.4099i	−0.0668860	−	0.508050i
$921$	1.03951	−	15.8598i	0.0342529	−	0.522598i
$922$	−6.22441	−	23.2298i	−0.204990	−	0.765033i
$923$	−2.77176	−	13.9346i	−0.0912335	−	0.458662i
$924$	−16.0433	+	11.3176i	−0.527787	+	0.372322i
$925$	11.6427	+	2.31588i	0.382809	+	0.0761455i
$926$	1.34724	−	10.2333i	0.0442730	−	0.336287i
$927$	−13.8307	−	10.6127i	−0.454260	−	0.348566i
$928$	27.9934	−	9.50248i	0.918928	−	0.311934i
$929$	−1.58488	−	24.1806i	−0.0519982	−	0.793339i	−0.941628	−	0.336656i	$-0.890704\pi$
$929$	−1.58488	−	24.1806i	−0.0519982	−	0.793339i	0.889629	−	0.456683i	$-0.150963\pi$
$930$	−6.92639	+	1.37774i	−0.227125	+	0.0451780i
$931$	19.2381	−	6.21420i	0.630503	−	0.203662i
$932$	−14.4519	+	21.6287i	−0.473387	+	0.708473i
$933$	2.62714	−	2.01587i	0.0860085	−	0.0659967i
$934$	−5.23641	−	9.06973i	−0.171341	−	0.296771i
$935$	4.47262	−	18.3504i	0.146270	−	0.600122i
$936$	10.1757	+	5.87495i	0.332604	+	0.192029i
$937$	−4.99006	−	2.06695i	−0.163018	−	0.0675244i	0.299682	−	0.954039i	$-0.403119\pi$
$937$	−4.99006	−	2.06695i	−0.163018	−	0.0675244i	−0.462700	+	0.886515i	$0.653119\pi$
$938$	−5.52064	+	8.73301i	−0.180255	+	0.285143i
$939$	−18.5486	−	18.5486i	−0.605311	−	0.605311i
$940$	3.78770	−	11.1582i	0.123541	−	0.363940i
$941$	−23.0084	+	46.6564i	−0.750052	+	1.52096i	0.100425	+	0.994945i	$0.467980\pi$
$941$	−23.0084	+	46.6564i	−0.750052	+	1.52096i	−0.850478	+	0.526011i	$0.823687\pi$
$942$	−1.99451	−	5.87562i	−0.0649845	−	0.191438i
$943$	−50.7226	−	6.67776i	−1.65176	−	0.217458i
$944$	−0.669290	+	0.277229i	−0.0217835	+	0.00902303i
$945$	9.47764	−	11.3757i	0.308308	−	0.370051i
$946$	−14.4841	−	21.6770i	−0.470920	−	0.704781i
$947$	−0.351157	−	0.119202i	−0.0114111	−	0.00387354i	0.315728	−	0.948850i	$-0.397751\pi$
$947$	−0.351157	−	0.119202i	−0.0114111	−	0.00387354i	−0.327139	+	0.944976i	$0.606085\pi$
$948$	−2.34487	+	8.75119i	−0.0761580	+	0.284225i
$949$	32.3861	+	2.12270i	1.05130	+	0.0689057i
$950$	1.51975	+	1.98058i	0.0493072	+	0.0642584i
$951$	−36.4364			−1.18153
$952$	−21.3078	−	22.0627i	−0.690589	−	0.715056i
$953$	−17.8650			−0.578703			−0.289352	−	0.957223i	$-0.593440\pi$
$953$	−17.8650			−0.578703			−0.289352	+	0.957223i	$0.593440\pi$
$954$	6.94358	+	9.04904i	0.224807	+	0.292974i
$955$	17.0820	+	1.11962i	0.552762	+	0.0362299i
$956$	−6.60813	+	24.6619i	−0.213722	+	0.797622i
$957$	−29.1487	−	9.89465i	−0.942244	−	0.319849i
$958$	−10.5384	−	15.7719i	−0.340481	−	0.509566i
$959$	55.3538	−	20.3669i	1.78747	−	0.657682i
$960$	−5.69416	+	2.35860i	−0.183778	+	0.0761235i
$961$	−8.84740	−	1.16478i	−0.285400	−	0.0375736i
$962$	−10.3783	−	30.5734i	−0.334609	−	0.985726i
$963$	−3.71666	+	7.53665i	−0.119768	+	0.242865i
$964$	3.32668	−	9.80010i	0.107145	−	0.315640i
$965$	−9.86622	−	9.86622i	−0.317605	−	0.317605i
$966$	7.59873	+	14.4730i	0.244485	+	0.465663i
$967$	44.5666	+	18.4601i	1.43316	+	0.593636i	0.958131	−	0.286332i	$-0.0924359\pi$
$967$	44.5666	+	18.4601i	1.43316	+	0.593636i	0.475034	+	0.879968i	$0.342436\pi$
$968$	24.3131	+	14.0372i	0.781451	+	0.451171i
$969$	6.49451	−	13.9607i	0.208634	−	0.448481i
$970$	1.30145	+	2.25417i	0.0417869	+	0.0723771i
$971$	−13.7045	+	10.5158i	−0.439799	+	0.337469i	−0.804809	−	0.593534i	$-0.797732\pi$
$971$	−13.7045	+	10.5158i	−0.439799	+	0.337469i	0.365010	+	0.931004i	$0.381066\pi$
$972$	8.75900	−	13.1088i	0.280945	−	0.420464i
$973$	−11.1436	−	10.5931i	−0.357247	−	0.339601i
$974$	29.5253	−	5.87294i	0.946051	−	0.188181i
$975$	0.266098	+	4.05987i	0.00852195	+	0.130020i
$976$	0.218792	−	0.0742698i	0.00700336	−	0.00237732i
$977$	26.7297	+	20.5104i	0.855157	+	0.656185i	0.940361	−	0.340178i	$-0.110487\pi$
$977$	26.7297	+	20.5104i	0.855157	+	0.656185i	−0.0852036	+	0.996364i	$0.527154\pi$
$978$	1.96654	−	14.9374i	0.0628831	−	0.477644i
$979$	0.0844579	+	0.0167997i	0.00269929	+	0.000536921i
$980$	7.03586	−	5.23507i	0.224752	−	0.167228i
$981$	0.207748	+	1.04442i	0.00663288	+	0.0333457i
$982$	4.69420	+	17.5190i	0.149798	+	0.559053i
$983$	0.593285	−	9.05179i	0.0189229	−	0.288707i	−0.977901	−	0.209069i	$-0.932957\pi$
$983$	0.593285	−	9.05179i	0.0189229	−	0.288707i	0.996824	−	0.0796384i	$-0.0253766\pi$
$984$	4.39187	+	33.3595i	0.140008	+	1.06346i
$985$	−2.44126	+	4.22838i	−0.0777849	+	0.134727i
$986$	3.19964	−	18.2431i	0.101897	−	0.580978i
$987$	0.814575	+	32.1663i	0.0259282	+	1.02387i
$988$	−4.35695	+	10.5186i	−0.138613	+	0.334641i
$989$	32.6424	−	16.0974i	1.03797	−	0.511869i
$990$	−5.07964	−	1.36109i	−0.161442	−	0.0432581i
$991$	−33.0596	−	37.6972i	−1.05017	−	1.19749i	−0.979802	−	0.199971i	$-0.935915\pi$
$991$	−33.0596	−	37.6972i	−1.05017	−	1.19749i	−0.0703704	−	0.997521i	$-0.522418\pi$
$992$	−35.8657	+	2.35076i	−1.13874	+	0.0746368i
$993$	−7.12486	+	35.8191i	−0.226101	+	1.13668i
$994$	10.2688	+	1.08823i	0.325705	+	0.0345167i
$995$	−0.992183	−	2.39534i	−0.0314543	−	0.0759374i
$996$	6.02556	+	5.28427i	0.190927	+	0.167439i
$997$	43.7312	+	21.5658i	1.38498	+	0.682997i	0.973556	−	0.228447i	$-0.0733649\pi$
$997$	43.7312	+	21.5658i	1.38498	+	0.682997i	0.411424	+	0.911444i	$0.365032\pi$
$998$	−12.6334	+	11.0792i	−0.399905	+	0.350707i
$999$	−64.1691	+	17.1941i	−2.03022	+	0.543996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	595.2.co.a.61.17	✓	768
7.3	odd	6	inner	595.2.co.a.486.32	yes	768
17.12	odd	16	inner	595.2.co.a.131.32	yes	768
119.80	even	48	inner	595.2.co.a.556.17	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.co.a.61.17	✓	768	1.1	even	1	trivial
595.2.co.a.131.32	yes	768	17.12	odd	16	inner
595.2.co.a.486.32	yes	768	7.3	odd	6	inner
595.2.co.a.556.17	yes	768	119.80	even	48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.co (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.526208 - 0.685768i) q^{2} +(1.29026 + 0.0845678i) q^{3} +(0.324256 - 1.21014i) q^{4} +(-0.946930 - 0.321439i) q^{5} +(-0.620949 - 0.929316i) q^{6} +(0.450303 - 2.60715i) q^{7} +(-2.59769 + 1.07600i) q^{8} +(-1.31673 - 0.173350i) q^{9} +(0.277849 + 0.818518i) q^{10} +(2.02609 - 4.10850i) q^{11} +(0.520712 - 1.53397i) q^{12} +(2.22495 + 2.22495i) q^{13} +(-2.02485 + 1.06310i) q^{14} +(-1.19460 - 0.494819i) q^{15} +(-0.0651537 - 0.0376165i) q^{16} +(-3.52294 + 2.14216i) q^{17} +(0.573994 + 0.994186i) q^{18} +(-2.29130 + 1.75817i) q^{19} +(-0.696034 + 1.04169i) q^{20} +(0.801487 - 3.32581i) q^{21} +(-3.88362 + 0.772499i) q^{22} +(-0.361542 - 5.51606i) q^{23} +(-3.44268 + 1.16863i) q^{24} +(0.793353 + 0.608761i) q^{25} +(0.355013 - 2.69659i) q^{26} +(-5.48879 - 1.09179i) q^{27} +(-3.00900 - 1.39031i) q^{28} +(-1.01386 - 5.09702i) q^{29} +(0.289277 + 1.07960i) q^{30} +(-0.413251 + 6.30500i) q^{31} +(0.742493 + 5.63980i) q^{32} +(2.96162 - 5.12967i) q^{33} +(3.32283 + 1.28870i) q^{34} +(-1.26445 + 2.32404i) q^{35} +(-0.636734 + 1.53721i) q^{36} +(10.6466 - 5.25032i) q^{37} +(2.41140 + 0.646132i) q^{38} +(2.68260 + 3.05892i) q^{39} +(2.80570 - 0.183895i) q^{40} +(1.80555 - 9.07710i) q^{41} +(-2.70248 + 1.20043i) q^{42} +(2.51959 + 6.08284i) q^{43} +(-4.31488 - 3.78405i) q^{44} +(1.19113 + 0.587398i) q^{45} +(-3.59249 + 3.15053i) q^{46} +(-9.08508 + 2.43434i) q^{47} +(-0.0808838 - 0.0540449i) q^{48} +(-6.59445 - 2.34801i) q^{49} -0.864391i q^{50} +(-4.72666 + 2.46601i) q^{51} +(3.41396 - 1.97105i) q^{52} +(9.85071 - 1.29687i) q^{53} +(2.13953 + 4.33854i) q^{54} +(-3.23919 + 3.23919i) q^{55} +(1.63554 + 7.25708i) q^{56} +(-3.10505 + 2.07473i) q^{57} +(-2.96187 + 3.37737i) q^{58} +(5.86188 - 7.63936i) q^{59} +(-0.986155 + 1.28518i) q^{60} +(-2.02497 + 2.30903i) q^{61} +(4.54122 - 3.03434i) q^{62} +(-1.04488 + 3.35484i) q^{63} +(3.37049 - 3.37049i) q^{64} +(-1.39169 - 2.82206i) q^{65} +(-5.07619 + 0.668293i) q^{66} +(3.91238 - 2.25881i) q^{67} +(1.44998 + 4.95786i) q^{68} -7.14771i q^{69} +(2.25912 - 0.355814i) q^{70} +(-3.75431 - 2.50855i) q^{71} +(3.60696 - 0.966483i) q^{72} +(7.75495 - 6.80091i) q^{73} +(-9.20282 - 4.53833i) q^{74} +(0.972147 + 0.852550i) q^{75} +(1.38467 + 3.34289i) q^{76} +(-9.79911 - 7.13238i) q^{77} +(0.686102 - 3.44927i) q^{78} +(-5.58077 + 0.365783i) q^{79} +(0.0496046 + 0.0565632i) q^{80} +(-3.14111 - 0.841659i) q^{81} +(-7.17488 + 3.53826i) q^{82} +(-1.89327 + 4.57077i) q^{83} +(-3.76480 - 2.04832i) q^{84} +(4.02456 - 0.896065i) q^{85} +(2.84558 - 4.92870i) q^{86} +(-0.877096 - 6.66221i) q^{87} +(-0.842407 + 12.8526i) q^{88} +(0.00486531 + 0.0181576i) q^{89} +(-0.223961 - 1.12593i) q^{90} +(6.80269 - 4.79888i) q^{91} +(-6.79243 - 1.35110i) q^{92} +(-1.06640 + 8.10011i) q^{93} +(6.45003 + 4.94929i) q^{94} +(2.73485 - 0.928355i) q^{95} +(0.481061 + 7.33957i) q^{96} +(2.95338 - 0.587464i) q^{97} +(1.85986 + 5.75781i) q^{98} +(-3.38001 + 5.05854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 32 q^{14} - 64 q^{18} - 64 q^{22} - 96 q^{28} - 64 q^{37} + 16 q^{39} - 96 q^{42} - 96 q^{44} + 64 q^{46} - 64 q^{49} - 64 q^{51} + 64 q^{53} - 240 q^{54} - 240 q^{56} - 64 q^{58} + 64 q^{60} - 288 q^{61}+ \cdots - 480 q^{99}+O(q^{100}) \) 768 * q + 32 * q^14 - 64 * q^18 - 64 * q^22 - 96 * q^28 - 64 * q^37 + 16 * q^39 - 96 * q^42 - 96 * q^44 + 64 * q^46 - 64 * q^49 - 64 * q^51 + 64 * q^53 - 240 * q^54 - 240 * q^56 - 64 * q^58 + 64 * q^60 - 288 * q^61 - 96 * q^63 - 16 * q^65 + 32 * q^71 + 96 * q^77 - 48 * q^81 - 240 * q^82 - 448 * q^92 + 128 * q^93 - 272 * q^98 - 480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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