LMFDB - Embedded newform 595.2.co.a.486.32

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			486.32
Character	$\chi$	$=$	595.486
Dual form			595.2.co.a.131.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.856996 - 0.112826i) q^{2} +(0.571890 + 1.15968i) q^{3} +(-1.21014 + 0.324256i) q^{4} +(-0.751840 + 0.659346i) q^{5} +(0.620949 + 0.929316i) q^{6} +(-0.581687 + 2.58102i) q^{7} +(-2.59769 + 1.07600i) q^{8} +(0.808489 - 1.05364i) q^{9} +(-0.569933 + 0.649884i) q^{10} +(-4.57110 + 0.299606i) q^{11} +(-1.06810 - 1.21793i) q^{12} +(-2.22495 - 2.22495i) q^{13} +(-0.207299 + 2.27755i) q^{14} +(-1.19460 - 0.494819i) q^{15} +(0.0651537 - 0.0376165i) q^{16} +(-3.61664 - 1.97988i) q^{17} +(0.573994 - 0.994186i) q^{18} +(0.376975 + 2.86341i) q^{19} +(0.696034 - 1.04169i) q^{20} +(-3.32581 + 0.801487i) q^{21} +(-3.88362 + 0.772499i) q^{22} +(4.95782 + 2.44493i) q^{23} +(-2.73340 - 2.39713i) q^{24} +(0.130526 - 0.991445i) q^{25} +(-2.15781 - 1.65575i) q^{26} +(5.48879 + 1.09179i) q^{27} +(-0.132987 - 3.31200i) q^{28} +(-1.01386 - 5.09702i) q^{29} +(-1.07960 - 0.289277i) q^{30} +(-5.66691 + 2.79461i) q^{31} +(4.51296 - 3.46292i) 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} +(-0.776387 + 11.8454i) q^{37} +(0.646132 + 2.41140i) q^{38} +(1.30780 - 3.85266i) q^{39} +(1.24359 - 2.52175i) q^{40} +(-1.80555 + 9.07710i) q^{41} +(-2.75978 + 1.06211i) q^{42} +(2.51959 + 6.08284i) q^{43} +(5.43452 - 1.84477i) q^{44} +(0.0868611 + 1.32524i) q^{45} +(4.52468 + 1.53592i) q^{46} +(-2.43434 + 9.08508i) q^{47} +(0.0808838 + 0.0540449i) q^{48} +(-6.32328 - 3.00269i) q^{49} -0.864391i q^{50} +(0.227702 - 5.32641i) q^{51} +(3.41396 + 1.97105i) q^{52} +(-6.04848 - 7.88253i) q^{53} +(4.82706 + 0.316382i) q^{54} +(3.23919 - 3.23919i) q^{55} +(-1.26612 - 7.33056i) q^{56} +(-3.10505 + 2.07473i) q^{57} +(-1.44395 - 4.25374i) q^{58} +(9.54682 + 1.25686i) q^{59} +(1.60608 + 0.211444i) q^{60} +(0.987197 + 2.90819i) q^{61} +(-4.54122 + 3.03434i) q^{62} +(2.24918 + 2.69961i) q^{63} +(3.37049 - 3.37049i) q^{64} +(3.13982 + 0.205795i) q^{65} +(-3.11685 - 4.06196i) q^{66} +(-3.91238 - 2.25881i) q^{67} +(5.01862 + 1.22321i) q^{68} +7.14771i q^{69} +(-1.34584 - 1.84903i) q^{70} +(-3.75431 - 2.50855i) q^{71} +(-0.966483 + 3.60696i) q^{72} +(9.76723 + 3.31553i) q^{73} +(0.671102 + 10.2390i) q^{74} +(1.22440 - 0.415629i) q^{75} +(-1.38467 - 3.34289i) q^{76} +(1.88566 - 11.9724i) q^{77} +(0.686102 - 3.44927i) q^{78} +(2.47361 - 5.01598i) q^{79} +(-0.0241829 + 0.0712404i) q^{80} +(0.841659 + 3.14111i) q^{81} +(-0.523217 + 7.98275i) 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} +(5.33109 - 4.09069i) q^{87} +(11.5519 - 5.69678i) q^{88} +(0.0181576 + 0.00486531i) q^{89} +(0.223961 + 1.12593i) q^{90} +(7.03687 - 4.44841i) q^{91} +(-6.79243 - 1.35110i) q^{92} +(-6.48170 - 4.97358i) q^{93} +(-1.06119 + 8.06054i) q^{94} +(-2.17140 - 1.90427i) q^{95} +(6.59679 + 3.25318i) q^{96} +(-2.95338 + 0.587464i) q^{97} +(-5.75781 - 1.85986i) 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 $\left(\mathbb{Z}/595\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.856996	−	0.112826i	0.605988	−	0.0797798i	0.178712	−	0.983901i	$-0.442807\pi$
$2$	0.856996	−	0.112826i	0.605988	−	0.0797798i	0.427275	+	0.904122i	$0.359473\pi$
$3$	0.571890	+	1.15968i	0.330181	+	0.669541i	0.997142	−	0.0755520i	$-0.0240719\pi$
$3$	0.571890	+	1.15968i	0.330181	+	0.669541i	−0.666961	+	0.745093i	$0.732405\pi$
$4$	−1.21014	+	0.324256i	−0.605069	+	0.162128i
$5$	−0.751840	+	0.659346i	−0.336233	+	0.294868i
$5$	−0.751840	+	0.659346i	−0.336233	+	0.294868i
$6$	0.620949	+	0.929316i	0.253501	+	0.379392i
$7$	−0.581687	+	2.58102i	−0.219857	+	0.975532i
$7$	−0.581687	+	2.58102i	−0.219857	+	0.975532i
$8$	−2.59769	+	1.07600i	−0.918421	+	0.380422i
$9$	0.808489	−	1.05364i	0.269496	−	0.351214i
$10$	−0.569933	+	0.649884i	−0.180229	+	0.205511i
$11$	−4.57110	+	0.299606i	−1.37824	+	0.0903346i	−0.736422	−	0.676523i	$-0.763486\pi$
$11$	−4.57110	+	0.299606i	−1.37824	+	0.0903346i	−0.641818	+	0.766857i	$0.721819\pi$
$12$	−1.06810	−	1.21793i	−0.308334	−	0.351587i
$13$	−2.22495	−	2.22495i	−0.617091	−	0.617091i	0.327693	−	0.944784i	$-0.393729\pi$
$13$	−2.22495	−	2.22495i	−0.617091	−	0.617091i	−0.944784	+	0.327693i	$0.893729\pi$
$14$	−0.207299	+	2.27755i	−0.0554029	+	0.608701i
$15$	−1.19460	−	0.494819i	−0.308444	−	0.127762i
$16$	0.0651537	−	0.0376165i	0.0162884	−	0.00940413i
$17$	−3.61664	−	1.97988i	−0.877164	−	0.480191i
$17$	−3.61664	−	1.97988i	−0.877164	−	0.480191i
$18$	0.573994	−	0.994186i	0.135292	−	0.234332i
$19$	0.376975	+	2.86341i	0.0864840	+	0.656911i	0.978699	+	0.205300i	$0.0658171\pi$
$19$	0.376975	+	2.86341i	0.0864840	+	0.656911i	−0.892215	+	0.451611i	$0.850850\pi$
$20$	0.696034	−	1.04169i	0.155638	−	0.232929i
$21$	−3.32581	+	0.801487i	−0.725751	+	0.174899i
$22$	−3.88362	+	0.772499i	−0.827990	+	0.164697i
$23$	4.95782	+	2.44493i	1.03378	+	0.509802i	0.878337	−	0.478043i	$-0.158654\pi$
$23$	4.95782	+	2.44493i	1.03378	+	0.509802i	0.155441	+	0.987845i	$0.450320\pi$
$24$	−2.73340	−	2.39713i	−0.557953	−	0.489312i
$25$	0.130526	−	0.991445i	0.0261052	−	0.198289i
$26$	−2.15781	−	1.65575i	−0.423181	−	0.324718i
$27$	5.48879	+	1.09179i	1.05632	+	0.210115i
$28$	−0.132987	−	3.31200i	−0.0251321	−	0.625910i
$29$	−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	$-0.222778\pi$
$30$	−1.07960	−	0.289277i	−0.197106	−	0.0528144i
$31$	−5.66691	+	2.79461i	−1.01781	+	0.501927i	−0.873097	−	0.487547i	$-0.837892\pi$
$31$	−5.66691	+	2.79461i	−1.01781	+	0.501927i	−0.144711	+	0.989474i	$0.546225\pi$
$32$	4.51296	−	3.46292i	0.797786	−	0.612163i
$33$	−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
$37$	−0.776387	+	11.8454i	−0.127637	+	1.94737i	0.154500	+	0.987993i	$0.450623\pi$
$37$	−0.776387	+	11.8454i	−0.127637	+	1.94737i	−0.282137	+	0.959374i	$0.591043\pi$
$38$	0.646132	+	2.41140i	0.104817	+	0.391181i
$39$	1.30780	−	3.85266i	0.209416	−	0.616919i
$40$	1.24359	−	2.52175i	0.196629	−	0.398724i
$41$	−1.80555	+	9.07710i	−0.281979	+	1.41761i	0.536903	+	0.843644i	$0.319594\pi$
$41$	−1.80555	+	9.07710i	−0.281979	+	1.41761i	−0.818882	+	0.573961i	$0.805406\pi$
$42$	−2.75978	+	1.06211i	−0.425843	+	0.163887i
$43$	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	$0.707588\pi$
$44$	5.43452	−	1.84477i	0.819285	−	0.278110i
$45$	0.0868611	+	1.32524i	0.0129485	+	0.197556i
$46$	4.52468	+	1.53592i	0.667128	+	0.226460i
$47$	−2.43434	+	9.08508i	−0.355085	+	1.32520i	0.525293	+	0.850922i	$0.323956\pi$
$47$	−2.43434	+	9.08508i	−0.355085	+	1.32520i	−0.880378	+	0.474273i	$0.842711\pi$
$48$	0.0808838	+	0.0540449i	0.0116746	+	0.00780070i
$49$	−6.32328	−	3.00269i	−0.903326	−	0.428955i
$50$		−	0.864391i		−	0.122243i
$51$	0.227702	−	5.32641i	0.0318846	−	0.745847i
$52$	3.41396	+	1.97105i	0.473431	+	0.273335i
$53$	−6.04848	−	7.88253i	−0.830822	−	1.08275i	−0.995345	−	0.0963754i	$-0.969275\pi$
$53$	−6.04848	−	7.88253i	−0.830822	−	1.08275i	0.164523	−	0.986373i	$-0.447392\pi$
$54$	4.82706	+	0.316382i	0.656879	+	0.0430541i
$55$	3.23919	−	3.23919i	0.436773	−	0.436773i
$56$	−1.26612	−	7.33056i	−0.169193	−	0.979588i
$57$	−3.10505	+	2.07473i	−0.411273	+	0.274804i
$58$	−1.44395	−	4.25374i	−0.189600	−	0.558543i
$59$	9.54682	+	1.25686i	1.24289	+	0.163630i	0.723148	−	0.690694i	$-0.242695\pi$
$59$	9.54682	+	1.25686i	1.24289	+	0.163630i	0.519742	+	0.854323i	$0.326028\pi$
$60$	1.60608	+	0.211444i	0.207344	+	0.0272973i
$61$	0.987197	+	2.90819i	0.126398	+	0.372355i	0.991646	−	0.128988i	$-0.0411728\pi$
$61$	0.987197	+	2.90819i	0.126398	+	0.372355i	−0.865249	+	0.501343i	$0.832839\pi$
$62$	−4.54122	+	3.03434i	−0.576735	+	0.385362i
$63$	2.24918	+	2.69961i	0.283370	+	0.340119i
$64$	3.37049	−	3.37049i	0.421311	−	0.421311i
$65$	3.13982	+	0.205795i	0.389447	+	0.0255257i
$66$	−3.11685	−	4.06196i	−0.383658	−	0.499993i
$67$	−3.91238	−	2.25881i	−0.477973	−	0.275958i	0.241598	−	0.970376i	$-0.422328\pi$
$67$	−3.91238	−	2.25881i	−0.477973	−	0.275958i	−0.719571	+	0.694418i	$0.755662\pi$
$68$	5.01862	+	1.22321i	0.608597	+	0.148336i
$69$			7.14771i			0.860483i
$70$	−1.34584	−	1.84903i	−0.160858	−	0.221002i
$71$	−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	$0.773840\pi$
$72$	−0.966483	+	3.60696i	−0.113901	+	0.425085i
$73$	9.76723	+	3.31553i	1.14317	+	0.388053i	0.827859	−	0.560936i	$-0.189559\pi$
$73$	9.76723	+	3.31553i	1.14317	+	0.388053i	0.315309	+	0.948989i	$0.397892\pi$
$74$	0.671102	+	10.2390i	0.0780140	+	1.19026i
$75$	1.22440	−	0.415629i	0.141382	−	0.0479927i
$76$	−1.38467	−	3.34289i	−0.158832	−	0.383455i
$77$	1.88566	−	11.9724i	0.214891	−	1.36438i
$78$	0.686102	−	3.44927i	0.0776858	−	0.390553i
$79$	2.47361	−	5.01598i	0.278303	−	0.564342i	−0.712177	−	0.702000i	$-0.752291\pi$
$79$	2.47361	−	5.01598i	0.278303	−	0.564342i	0.990480	+	0.137658i	$0.0439574\pi$
$80$	−0.0241829	+	0.0712404i	−0.00270373	+	0.00796492i
$81$	0.841659	+	3.14111i	0.0935177	+	0.349013i
$82$	−0.523217	+	7.98275i	−0.0577797	+	0.881548i
$83$	1.89327	−	4.57077i	0.207814	−	0.501707i	−0.785265	−	0.619160i	$-0.787473\pi$
$83$	1.89327	−	4.57077i	0.207814	−	0.501707i	0.993078	+	0.117454i	$0.0374731\pi$
$84$	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
$87$	5.33109	−	4.09069i	0.571553	−	0.438568i
$88$	11.5519	−	5.69678i	1.23144	−	0.607279i
$89$	0.0181576	+	0.00486531i	0.00192470	+	0.000515722i	0.259781	−	0.965667i	$-0.416350\pi$
$89$	0.0181576	+	0.00486531i	0.00192470	+	0.000515722i	−0.257857	+	0.966183i	$0.583016\pi$
$90$	0.223961	+	1.12593i	0.0236076	+	0.118683i
$91$	7.03687	−	4.44841i	0.737664	−	0.466320i
$92$	−6.79243	−	1.35110i	−0.708160	−	0.140862i
$93$	−6.48170	−	4.97358i	−0.672121	−	0.515737i
$94$	−1.06119	+	8.06054i	−0.109453	+	0.831381i
$95$	−2.17140	−	1.90427i	−0.222781	−	0.195374i
$96$	6.59679	+	3.25318i	0.673282	+	0.332026i
$97$	−2.95338	+	0.587464i	−0.299871	+	0.0596480i	−0.342733	−	0.939433i	$-0.611352\pi$
$97$	−2.95338	+	0.587464i	−0.299871	+	0.0596480i	0.0428619	+	0.999081i	$0.486352\pi$
$98$	−5.75781	−	1.85986i	−0.581626	−	0.187875i
$99$	−3.38001	+	5.05854i	−0.339704	+	0.508402i
$100$	0.163527	+	1.24211i	0.0163527	+	0.124211i
$101$	−6.52513	+	11.3019i	−0.649275	+	1.12458i	0.334022	+	0.942565i	$0.391594\pi$
$101$	−6.52513	+	11.3019i	−0.649275	+	1.12458i	−0.983296	+	0.182011i	$0.941739\pi$
$102$	−0.405817	−	4.59041i	−0.0401818	−	0.454518i
$103$	11.3679	−	6.56328i	1.12012	−	0.646700i	0.178686	−	0.983906i	$-0.442815\pi$
$103$	11.3679	−	6.56328i	1.12012	−	0.646700i	0.941431	+	0.337207i	$0.109482\pi$
$104$	8.17378	+	3.38569i	0.801505	+	0.331994i
$105$	1.97202	−	2.79545i	0.192449	−	0.272808i
$106$	−6.07287	−	6.07287i	−0.589850	−	0.589850i
$107$	4.17190	+	4.75714i	0.403313	+	0.459890i	0.917470	−	0.397806i	$-0.130228\pi$
$107$	4.17190	+	4.75714i	0.403313	+	0.459890i	−0.514157	+	0.857696i	$0.671895\pi$
$108$	−6.99622	+	0.458556i	−0.673211	+	0.0441246i
$109$	−0.528673	+	0.602836i	−0.0506377	+	0.0577412i	−0.776604	−	0.629989i	$-0.783059\pi$
$109$	−0.528673	+	0.602836i	−0.0506377	+	0.0577412i	0.725966	+	0.687730i	$0.241393\pi$
$110$	2.41051	−	3.14144i	0.229833	−	0.299525i
$111$	−14.1808	+	5.87389i	−1.34598	+	0.557525i
$112$	0.0591897	+	0.190044i	0.00559290	+	0.0179575i
$113$	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	$0.782119\pi$
$114$	−2.42693	+	2.12836i	−0.227303	+	0.199339i
$115$	−5.33954	+	1.43073i	−0.497915	+	0.133416i
$116$	2.87965	+	5.83936i	0.267369	+	0.542171i
$117$	−4.14316	+	0.545457i	−0.383035	+	0.0504275i
$118$	8.32339			0.766231
$119$	7.21385	−	8.18293i	0.661292	−	0.750128i
$120$	3.63562			0.331885
$121$	9.89934	−	1.30327i	0.899940	−	0.118479i
$122$	1.17414	+	2.38092i	0.106302	+	0.215559i
$123$	−11.5591	+	3.09725i	−1.04225	+	0.279270i
$124$	5.95158	−	5.21940i	0.534468	−	0.468716i
$125$	0.555570	+	0.831470i	0.0496917	+	0.0743689i
$126$	2.23212	+	2.05979i	0.198853	+	0.183501i
$127$	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	$0.324401\pi$
$128$	−4.41761	+	5.75715i	−0.390466	+	0.508865i
$129$	−5.61321	+	6.40064i	−0.494215	+	0.563545i
$130$	2.71404	−	0.177887i	0.238037	−	0.0156017i
$131$	−0.441672	−	0.503630i	−0.0385891	−	0.0440024i	0.732223	−	0.681065i	$-0.238483\pi$
$131$	−0.441672	−	0.503630i	−0.0385891	−	0.0440024i	−0.770812	+	0.637062i	$0.780149\pi$
$132$	5.24729	+	5.24729i	0.456718	+	0.456718i
$133$	−7.60979	−	0.692630i	−0.659852	−	0.0600587i
$134$	−3.60775	−	1.49438i	−0.311662	−	0.129095i
$135$	−4.84656	+	2.79816i	−0.417125	+	0.240827i
$136$	11.5252	+	1.25161i	0.988281	+	0.107325i
$137$	11.1465	−	19.3063i	0.952311	−	1.64945i	0.211905	−	0.977290i	$-0.432033\pi$
$137$	11.1465	−	19.3063i	0.952311	−	1.64945i	0.740406	−	0.672160i	$-0.234633\pi$
$138$	0.806445	+	6.12556i	0.0686492	+	0.521442i
$139$	−3.22856	+	4.83188i	−0.273843	+	0.409835i	−0.942744	−	0.333516i	$-0.891765\pi$
$139$	−3.22856	+	4.83188i	−0.273843	+	0.409835i	0.668902	+	0.743351i	$0.266765\pi$
$140$	2.28374	+	2.40241i	0.193011	+	0.203041i
$141$	−11.9279	+	2.37262i	−1.00451	+	0.199810i
$142$	−3.50046	−	1.72623i	−0.293752	−	0.144862i
$143$	10.8371	+	9.50389i	0.906245	+	0.794755i
$144$	0.0130417	−	0.0990613i	0.00108681	−	0.00825511i
$145$	4.12296	+	3.16366i	0.342393	+	0.262728i
$146$	8.74456	+	1.73940i	0.723705	+	0.143954i
$147$	−0.134070	−	9.05018i	−0.0110579	−	0.746446i
$148$	−2.90139	−	14.5863i	−0.238493	−	1.19899i
$149$	−0.538075	−	0.144177i	−0.0440808	−	0.0118114i	0.236711	−	0.971580i	$-0.423930\pi$
$149$	−0.538075	−	0.144177i	−0.0440808	−	0.0118114i	−0.280792	+	0.959769i	$0.590597\pi$
$150$	1.00242	−	0.494337i	0.0818469	−	0.0403624i
$151$	−10.9760	+	8.42215i	−0.893211	+	0.685385i	−0.949748	−	0.313016i	$-0.898661\pi$
$151$	−10.9760	+	8.42215i	−0.893211	+	0.685385i	0.0565373	+	0.998400i	$0.481994\pi$
$152$	−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
$156$	−0.333375	+	5.08632i	−0.0266913	+	0.407231i
$157$	1.43686	+	5.36244i	0.114674	+	0.427969i	0.999262	−	0.0384034i	$-0.0122272\pi$
$157$	1.43686	+	5.36244i	0.114674	+	0.427969i	−0.884588	+	0.466373i	$0.845561\pi$
$158$	1.55394	−	4.57776i	0.123625	−	0.364187i
$159$	5.68214	−	11.5222i	0.450623	−	0.913772i
$160$	−1.10976	+	5.57916i	−0.0877345	+	0.441071i
$161$	−9.19429	+	11.3740i	−0.724612	+	0.896399i
$162$	1.07570	+	2.59696i	0.0845147	+	0.204037i
$163$	−12.7646	+	4.33299i	−0.999799	+	0.339386i	−0.772897	−	0.634532i	$-0.781193\pi$
$163$	−12.7646	+	4.33299i	−0.999799	+	0.339386i	−0.226902	+	0.973918i	$0.572860\pi$
$164$	−0.758339	−	11.5700i	−0.0592163	−	0.903466i
$165$	5.60889	+	1.90396i	0.436651	+	0.148223i
$166$	1.10683	−	4.13074i	0.0859065	−	0.320608i
$167$	−5.17701	−	3.45916i	−0.400609	−	0.267678i	0.338904	−	0.940821i	$-0.389944\pi$
$167$	−5.17701	−	3.45916i	−0.400609	−	0.267678i	−0.739512	+	0.673143i	$0.764944\pi$
$168$	7.77701	−	5.66057i	0.600009	−	0.436723i
$169$		−	3.09916i		−	0.238397i
$170$	3.34793	−	1.22200i	0.256775	−	0.0937230i
$171$	3.32179	+	1.91784i	0.254024	+	0.146661i
$172$	−5.02145	−	6.54409i	−0.382882	−	0.498982i
$173$	22.4768	+	1.47321i	1.70888	+	0.112006i	0.888221	−	0.459416i	$-0.151941\pi$
$173$	22.4768	+	1.47321i	1.70888	+	0.112006i	0.820657	+	0.571421i	$0.193608\pi$
$174$	4.10719	−	4.10719i	0.311365	−	0.311365i
$175$	2.48301	+	0.913601i	0.187698	+	0.0690617i
$176$	−0.286554	+	0.191470i	−0.0215998	+	0.0144326i
$177$	4.00217	+	11.7900i	0.300822	+	0.886193i
$178$	0.0161099	+	0.00212091i	0.00120749	+	0.000158969i
$179$	−17.3864	−	2.28897i	−1.29952	−	0.171085i	−0.551174	−	0.834390i	$-0.685820\pi$
$179$	−17.3864	−	2.28897i	−1.29952	−	0.171085i	−0.748349	+	0.663305i	$0.769153\pi$
$180$	−0.534832	−	1.57556i	−0.0398640	−	0.117436i
$181$	−10.6135	+	7.09172i	−0.788896	+	0.527123i	−0.883522	−	0.468390i	$-0.844834\pi$
$181$	−10.6135	+	7.09172i	−0.788896	+	0.527123i	0.0946264	+	0.995513i	$0.469834\pi$
$182$	5.52867	−	4.60621i	0.409813	−	0.341435i
$183$	−2.80799	+	2.80799i	−0.207573	+	0.207573i
$184$	−15.5096	−	1.01655i	−1.14338	−	0.0749413i
$185$	−7.22648	−	9.41773i	−0.531301	−	0.692405i
$186$	−6.11594	−	3.53104i	−0.448443	−	0.258908i
$187$	17.1252	+	7.96666i	1.25232	+	0.582580i
$188$		−	11.7836i		−	0.859404i
$189$	−6.01068	+	13.5316i	−0.437213	+	0.984277i
$190$	−2.07573	−	1.38696i	−0.150590	−	0.100621i
$191$	4.43064	−	16.5354i	0.320590	−	1.19646i	−0.598081	−	0.801436i	$-0.704070\pi$
$191$	4.43064	−	16.5354i	0.320590	−	1.19646i	0.918671	−	0.395023i	$-0.129263\pi$
$192$	5.83623	+	1.98113i	0.421194	+	0.142976i
$193$	−0.912566	−	13.9231i	−0.0656879	−	1.00220i	−0.895757	−	0.444544i	$-0.853366\pi$
$193$	−0.912566	−	13.9231i	−0.0656879	−	1.00220i	0.830069	−	0.557661i	$-0.188301\pi$
$194$	−2.46476	+	0.836672i	−0.176959	+	0.0600696i
$195$	1.55698	+	3.75888i	0.111498	+	0.269179i
$196$	8.62568	+	1.58331i	0.616120	+	0.113093i
$197$	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	$0.00685261\pi$
$198$	−2.32592	+	4.71650i	−0.165296	+	0.335187i
$199$	−0.833396	+	2.45511i	−0.0590779	+	0.174038i	−0.972462	−	0.233060i	$-0.925126\pi$
$199$	−0.833396	+	2.45511i	−0.0590779	+	0.174038i	0.913384	+	0.407098i	$0.133459\pi$
$200$	0.727726	+	2.71591i	0.0514580	+	0.192044i
$201$	0.382046	−	5.82889i	0.0269474	−	0.411138i
$202$	−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
$206$	9.00178	−	6.90731i	0.627184	−	0.481255i
$207$	6.58442	−	3.24708i	0.457649	−	0.225687i
$208$	−0.228659	−	0.0612690i	−0.0158547	−	0.00424824i
$209$	−2.58109	−	12.9760i	−0.178538	−	0.897569i
$210$	1.37461	−	2.61818i	0.0948574	−	0.180672i
$211$	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	$0.539917\pi$
$212$	9.87545	+	7.57770i	0.678249	+	0.520439i
$213$	0.762058	−	5.78840i	0.0522153	−	0.396615i
$214$	4.11203	+	3.60616i	0.281093	+	0.246512i
$215$	−5.90503	−	2.91204i	−0.402719	−	0.198599i
$216$	−15.4329	+	3.06980i	−1.05008	+	0.208873i
$217$	−3.91657	−	16.2520i	−0.265874	−	1.10326i
$218$	−0.385055	+	0.576276i	−0.0260792	+	0.0390303i
$219$	1.74084	+	13.2230i	0.117635	+	0.893525i
$220$	−2.86955	+	4.97020i	−0.193465	+	0.335091i
$221$	3.64172	+	12.4520i	0.244969	+	0.837612i
$222$	−11.4902	+	6.63387i	−0.771171	+	0.445236i
$223$	8.43925	+	3.49565i	0.565134	+	0.234086i	0.646912	−	0.762564i	$-0.276060\pi$
$223$	8.43925	+	3.49565i	0.565134	+	0.234086i	−0.0817784	+	0.996651i	$0.526060\pi$
$224$	6.31271	+	13.6624i	0.421786	+	0.912854i
$225$	−0.939100	−	0.939100i	−0.0626066	−	0.0626066i
$226$	1.15475	+	1.31674i	0.0768131	+	0.0875886i
$227$	−21.9344	+	1.43766i	−1.45584	+	0.0954205i	−0.772654	−	0.634828i	$-0.781071\pi$
$227$	−21.9344	+	1.43766i	−1.45584	+	0.0954205i	−0.683182	+	0.730248i	$0.739404\pi$
$228$	3.08480	−	3.51753i	0.204296	−	0.232954i
$229$	−8.12314	+	10.5863i	−0.536792	+	0.699561i	−0.980480	−	0.196620i	$-0.937003\pi$
$229$	−8.12314	+	10.5863i	−0.536792	+	0.699561i	0.443688	+	0.896182i	$0.353670\pi$
$230$	−4.41454	+	1.82856i	−0.291086	+	0.120572i
$231$	14.9625	−	4.66011i	0.984460	−	0.306613i
$232$	8.11808	+	12.1496i	0.532978	+	0.797658i
$233$	15.6106	−	13.6901i	1.02268	−	0.896869i	0.0279746	−	0.999609i	$-0.491094\pi$
$233$	15.6106	−	13.6901i	1.02268	−	0.896869i	0.994708	+	0.102740i	$0.0327609\pi$
$234$	−3.48913	+	0.934909i	−0.228091	+	0.0611169i
$235$	−4.15998	−	8.43560i	−0.271367	−	0.550278i
$236$	−11.9605	+	1.57463i	−0.778563	+	0.102500i
$237$	7.23156			0.469740
$238$	5.25900	−	7.82665i	0.340890	−	0.507326i
$239$	−20.3794			−1.31823			−0.659116	−	0.752041i	$-0.729069\pi$
$239$	−20.3794			−1.31823			−0.659116	+	0.752041i	$0.729069\pi$
$240$	−0.0964460	+	0.0126974i	−0.00622556	+	0.000819610i
$241$	3.65365	+	7.40887i	0.235352	+	0.477247i	0.982222	−	0.187723i	$-0.0601108\pi$
$241$	3.65365	+	7.40887i	0.235352	+	0.477247i	−0.746870	+	0.664970i	$0.768444\pi$
$242$	8.33665	−	2.23380i	0.535900	−	0.143594i
$243$	9.46127	−	8.29731i	0.606941	−	0.532273i
$244$	−2.13764	−	3.19921i	−0.136848	−	0.204808i
$245$	6.73390	−	1.91169i	0.430213	−	0.122133i
$246$	−9.55665	+	3.95849i	−0.609310	+	0.252384i
$247$	5.53220	−	7.20971i	0.352006	−	0.458743i
$248$	11.7139	−	13.3571i	0.743831	−	0.848177i
$249$	6.38336	−	0.418388i	0.404529	−	0.0265142i
$250$	0.569933	+	0.649884i	0.0360457	+	0.0411023i
$251$	18.5931	+	18.5931i	1.17358	+	1.17358i	0.981349	+	0.192235i	$0.0615736\pi$
$251$	18.5931	+	18.5931i	1.17358	+	1.17358i	0.192235	+	0.981349i	$0.438426\pi$
$252$	−3.59719	−	2.53759i	−0.226601	−	0.159853i
$253$	−23.3952	−	9.69062i	−1.47085	−	0.609244i
$254$	2.67073	−	1.54195i	0.167577	−	0.0967504i
$255$	3.34075	+	4.15474i	0.209206	+	0.260180i
$256$	−7.90292	+	13.6883i	−0.493932	+	0.855516i
$257$	−3.38592	−	25.7186i	−0.211208	−	1.60428i	−0.688297	−	0.725429i	$-0.741641\pi$
$257$	−3.38592	−	25.7186i	−0.211208	−	1.60428i	0.477089	−	0.878855i	$-0.341692\pi$
$258$	−4.08834	+	6.11863i	−0.254529	+	0.380930i
$259$	−30.1215	−	8.89417i	−1.87166	−	0.552657i
$260$	−3.86635	+	0.769065i	−0.239781	+	0.0476954i
$261$	−6.19014	−	3.05264i	−0.383160	−	0.188954i
$262$	−0.435334	−	0.381777i	−0.0268950	−	0.0235863i
$263$	−1.19419	+	9.07080i	−0.0736371	+	0.559329i	0.914365	+	0.404890i	$0.132690\pi$
$263$	−1.19419	+	9.07080i	−0.0736371	+	0.559329i	−0.988002	+	0.154439i	$0.950643\pi$
$264$	13.2129	+	10.1386i	0.813195	+	0.623987i
$265$	9.74480	+	1.93836i	0.598618	+	0.119073i
$266$	−6.59970	+	0.264998i	−0.404654	+	0.0162481i
$267$	0.00474195	+	0.0238394i	0.000290202	+	0.00145895i
$268$	5.46695	+	1.46487i	0.333947	+	0.0894809i
$269$	1.75589	−	0.865910i	0.107059	−	0.0527954i	−0.387971	−	0.921672i	$-0.626824\pi$
$269$	1.75589	−	0.865910i	0.107059	−	0.0527954i	0.495030	+	0.868876i	$0.335157\pi$
$270$	−3.83778	+	2.94483i	−0.233560	+	0.179217i
$271$	14.4018	+	24.9447i	0.874850	+	1.51528i	0.856923	+	0.515445i	$0.172373\pi$
$271$	14.4018	+	24.9447i	0.874850	+	1.51528i	0.0179270	+	0.999839i	$0.494293\pi$
$272$	−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
$275$	−0.299606	+	4.57110i	−0.0180669	+	0.275648i
$276$	−2.31768	−	8.64972i	−0.139508	−	0.520652i
$277$	−6.80552	+	20.0484i	−0.408904	+	1.20459i	0.526244	+	0.850334i	$0.323600\pi$
$277$	−6.80552	+	20.0484i	−0.408904	+	1.20459i	−0.935148	+	0.354258i	$0.884733\pi$
$278$	−2.22170	+	4.50517i	−0.133249	+	0.270202i
$279$	−1.63711	+	8.23031i	−0.0980113	+	0.492736i
$280$	5.78530	+	4.67660i	0.345738	+	0.279480i
$281$	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	$0.575327\pi$
$282$	−9.95451	+	3.37910i	−0.592783	+	0.201223i
$283$	0.198686	+	3.03137i	0.0118107	+	0.180196i	0.999688	+	0.0249620i	$0.00794648\pi$
$283$	0.198686	+	3.03137i	0.0118107	+	0.180196i	−0.987878	+	0.155234i	$0.950387\pi$
$284$	5.35664	+	1.81834i	0.317858	+	0.107898i
$285$	0.966536	−	3.60716i	0.0572526	−	0.213670i
$286$	10.3596	+	6.92209i	0.612579	+	0.409312i
$287$	−22.3779	−	9.94018i	−1.32092	−	0.586750i
$288$		−	7.55478i		−	0.445169i
$289$	9.16016	+	14.3210i	0.538833	+	0.842412i
$290$	3.89031	+	2.24607i	0.228447	+	0.131894i
$291$	−2.37028	−	3.08901i	−0.138948	−	0.181081i
$292$	−12.8948	−	0.845169i	−0.754610	−	0.0494598i
$293$	−7.89814	+	7.89814i	−0.461414	+	0.461414i	−0.899119	−	0.437705i	$-0.855792\pi$
$293$	−7.89814	+	7.89814i	−0.461414	+	0.461414i	0.437705	+	0.899119i	$0.355792\pi$
$294$	−1.13599	−	7.74084i	−0.0662523	−	0.451455i
$295$	−8.00638	+	5.34970i	−0.466150	+	0.311471i
$296$	−10.7288	−	31.6060i	−0.623597	−	1.83706i
$297$	−25.4169	−	3.34620i	−1.47484	−	0.194166i
$298$	−0.477395	−	0.0628503i	−0.0276548	−	0.00364082i
$299$	−5.59108	−	16.4708i	−0.323340	−	0.952530i
$300$	−1.34693	+	0.899989i	−0.0777649	+	0.0519609i
$301$	−17.1655	+	2.96480i	−0.989404	+	0.170888i
$302$	−8.45612	+	8.45612i	−0.486595	+	0.486595i
$303$	−16.8382	−	1.10363i	−0.967328	−	0.0634020i
$304$	0.132273	+	0.172381i	0.00758637	+	0.00988675i
$305$	−2.65972	−	1.53559i	−0.152295	−	0.0879275i
$306$	−4.04430	+	2.45918i	−0.231197	+	0.140582i
$307$			12.2920i			0.701540i	0.936462	+	0.350770i	$0.114080\pi$
$307$			12.2920i			0.701540i	−0.936462	+	0.350770i	$0.885920\pi$
$308$	1.60019	+	15.0997i	0.0911794	+	0.860383i
$309$	14.1125	+	9.42968i	0.802833	+	0.536436i
$310$	1.41359	−	5.27557i	0.0802863	−	0.299632i
$311$	2.42508	+	0.823205i	0.137514	+	0.0466797i	0.389348	−	0.921091i	$-0.372700\pi$
$311$	2.42508	+	0.823205i	0.137514	+	0.0466797i	−0.251834	+	0.967770i	$0.581034\pi$
$312$	0.748192	+	11.4152i	0.0423580	+	0.646258i
$313$	−19.2105	+	6.52107i	−1.08584	+	0.368593i	−0.806279	−	0.591536i	$-0.798522\pi$
$313$	−19.2105	+	6.52107i	−1.08584	+	0.368593i	−0.279560	+	0.960128i	$0.590189\pi$
$314$	1.83641	+	4.43348i	0.103634	+	0.250196i
$315$	−3.47100	−	0.546688i	−0.195569	−	0.0308024i
$316$	−1.36695	+	6.87212i	−0.0768969	+	0.386587i
$317$	12.4633	−	25.2731i	0.700011	−	1.41948i	−0.198309	−	0.980139i	$-0.563545\pi$
$317$	12.4633	−	25.2731i	0.700011	−	1.41948i	0.898320	−	0.439342i	$-0.144788\pi$
$318$	3.56956	−	10.5156i	0.200171	−	0.589685i
$319$	6.16156	+	22.9953i	0.344981	+	1.28749i
$320$	−0.311750	+	4.75639i	−0.0174274	+	0.265890i
$321$	−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
$325$	−2.49633	+	1.91550i	−0.138472	+	0.106253i
$326$	−10.4503	+	5.15353i	−0.578790	+	0.285428i
$327$	−1.00144	−	0.268335i	−0.0553797	−	0.0148389i
$328$	−5.07669	−	25.5222i	−0.280313	−	1.40923i
$329$	−22.0327	−	11.5677i	−1.21470	−	0.637750i
$330$	5.02161	+	0.998860i	0.276431	+	0.0549855i
$331$	−22.4079	−	17.1942i	−1.23165	−	0.945077i	−0.232030	−	0.972709i	$-0.574537\pi$
$331$	−22.4079	−	17.1942i	−1.23165	−	0.945077i	−0.999618	+	0.0276321i	$0.991203\pi$
$332$	−0.809026	+	6.14517i	−0.0444011	+	0.337260i
$333$	11.8531	+	10.3949i	0.649545	+	0.569636i
$334$	−4.82696	−	2.38039i	−0.264119	−	0.130249i
$335$	4.43082	−	0.881345i	0.242082	−	0.0481530i
$336$	−0.186540	+	0.177325i	−0.0101766	+	0.00967389i
$337$	−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	$0.328925\pi$
$338$	−0.349664	−	2.65597i	−0.0190192	−	0.144465i
$339$	−1.30991	+	2.26884i	−0.0711447	+	0.123226i
$340$	−4.57972	+	2.38935i	−0.248370	+	0.129581i
$341$	25.0668	−	14.4723i	1.35744	−	0.783719i
$342$	3.06314	+	1.26880i	0.165636	+	0.0686086i
$343$	11.4282	−	14.5739i	0.617062	−	0.786914i
$344$	−13.0902	−	13.0902i	−0.705778	−	0.705778i
$345$	−4.71281	−	5.37393i	−0.253729	−	0.289323i
$346$	19.4287	−	1.27343i	1.04450	−	0.0684598i
$347$	9.82158	−	11.1994i	0.527250	−	0.601213i	−0.425504	−	0.904957i	$-0.639903\pi$
$347$	9.82158	−	11.1994i	0.527250	−	0.601213i	0.952754	+	0.303743i	$0.0982365\pi$
$348$	−5.12493	+	6.67894i	−0.274725	+	0.358029i
$349$	−9.35660	+	3.87563i	−0.500847	+	0.207458i	−0.618781	−	0.785564i	$-0.712373\pi$
$349$	−9.35660	+	3.87563i	−0.500847	+	0.207458i	0.117933	+	0.993021i	$0.462373\pi$
$350$	2.23101	+	0.502805i	0.119252	+	0.0268761i
$351$	−9.78313	−	14.6415i	−0.522185	−	0.781505i
$352$	−19.5917	+	17.1815i	−1.04424	+	0.915775i
$353$	−17.2797	+	4.63007i	−0.919703	+	0.246434i	−0.687459	−	0.726224i	$-0.741274\pi$
$353$	−17.2797	+	4.63007i	−0.919703	+	0.246434i	−0.232245	+	0.972657i	$0.574607\pi$
$354$	4.76007	+	9.65246i	0.252995	+	0.513022i
$355$	4.47664	−	0.589361i	0.237595	−	0.0312800i
$356$	−0.0235508			−0.00124819
$357$	13.6151	+	3.68601i	0.720587	+	0.195084i
$358$	−15.1584			−0.801145
$359$	−5.06451	+	0.666755i	−0.267295	+	0.0351900i	−0.262982	−	0.964801i	$-0.584706\pi$
$359$	−5.06451	+	0.666755i	−0.267295	+	0.0351900i	−0.00431245	+	0.999991i	$0.501373\pi$
$360$	−1.65160	−	3.34911i	−0.0870468	−	0.176513i
$361$	10.2956	−	2.75869i	0.541873	−	0.145194i
$362$	−8.29561	+	7.27505i	−0.436007	+	0.382368i
$363$	7.17271	+	10.7347i	0.376470	+	0.563427i
$364$	−7.07316	+	7.66494i	−0.370735	+	0.401752i
$365$	−9.52948	+	3.94724i	−0.498796	+	0.206608i
$366$	−2.08963	+	2.72325i	−0.109227	+	0.142347i
$367$	23.6357	−	26.9513i	1.23377	−	1.40685i	0.351447	−	0.936208i	$-0.385690\pi$
$367$	23.6357	−	26.9513i	1.23377	−	1.40685i	0.882326	−	0.470639i	$-0.155977\pi$
$368$	0.414990	−	0.0271999i	0.0216329	−	0.00141789i
$369$	8.10426	+	9.24113i	0.421891	+	0.481074i
$370$	−7.25563	−	7.25563i	−0.377202	−	0.377202i
$371$	23.8633	−	11.0260i	1.23892	−	0.572444i
$372$	9.45647	+	3.91700i	0.490295	+	0.203087i
$373$	−6.60742	+	3.81480i	−0.342119	+	0.197523i	−0.661209	−	0.750202i	$-0.729956\pi$
$373$	−6.60742	+	3.81480i	−0.342119	+	0.197523i	0.319089	+	0.947725i	$0.396623\pi$
$374$	15.5751	+	4.89524i	0.805369	+	0.253127i
$375$	−0.646512	+	1.11979i	−0.0333857	+	0.0578258i
$376$	−3.45187	−	26.2195i	−0.178016	−	1.35217i
$377$	−9.08485	+	13.5964i	−0.467894	+	0.700252i
$378$	−3.62442	+	12.2747i	−0.186420	+	0.631341i
$379$	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	$0.219863\pi$
$380$	3.24517	+	1.60034i	0.166474	+	0.0820957i
$381$	3.46834	+	3.04165i	0.177688	+	0.155828i
$382$	1.93143	−	14.6707i	0.0988205	−	0.750616i
$383$	−9.69130	−	7.43640i	−0.495202	−	0.379982i	0.330753	−	0.943717i	$-0.392697\pi$
$383$	−9.69130	−	7.43640i	−0.495202	−	0.379982i	−0.825956	+	0.563735i	$0.809364\pi$
$384$	−9.20283	−	1.83056i	−0.469630	−	0.0934152i
$385$	6.47621	+	10.2446i	0.330058	+	0.522114i
$386$	−2.35295	−	11.8291i	−0.119762	−	0.602083i
$387$	8.44620	+	2.26315i	0.429345	+	0.115043i
$388$	3.38351	−	1.66856i	0.171772	−	0.0847085i
$389$	−7.43136	+	5.70228i	−0.376785	+	0.289117i	−0.779741	−	0.626102i	$-0.784649\pi$
$389$	−7.43136	+	5.70228i	−0.376785	+	0.289117i	0.402956	+	0.915219i	$0.367983\pi$
$390$	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
$394$	0.276027	−	4.21136i	0.0139061	−	0.212165i
$395$	1.44751	+	5.40218i	0.0728321	+	0.271813i
$396$	2.45002	−	7.21752i	0.123118	−	0.362694i
$397$	−14.4101	+	29.2208i	−0.723222	+	1.46655i	0.154809	+	0.987944i	$0.450524\pi$
$397$	−14.4101	+	29.2208i	−0.723222	+	1.46655i	−0.878031	+	0.478604i	$0.841143\pi$
$398$	−0.437218	+	2.19804i	−0.0219158	+	0.110178i
$399$	−3.54873	−	9.22101i	−0.177659	−	0.461628i
$400$	−0.0287904	−	0.0695063i	−0.00143952	−	0.00347531i
$401$	17.4261	−	5.91537i	0.870219	−	0.295400i	0.149613	−	0.988745i	$-0.452197\pi$
$401$	17.4261	−	5.91537i	0.870219	−	0.295400i	0.720606	+	0.693345i	$0.243864\pi$
$402$	−0.330237	−	5.03844i	−0.0164707	−	0.251295i
$403$	18.8265	+	6.39074i	0.937815	+	0.318345i
$404$	4.23162	−	15.7926i	0.210531	−	0.785712i
$405$	−2.70387	−	1.80667i	−0.134357	−	0.0897742i
$406$	11.8189	−	1.25251i	0.586562	−	0.0621611i
$407$		−	54.3790i		−	2.69547i
$408$	5.13971	+	14.0814i	0.254453	+	0.697131i
$409$	3.93370	+	2.27112i	0.194509	+	0.112300i	0.594092	−	0.804397i	$-0.297512\pi$
$409$	3.93370	+	2.27112i	0.194509	+	0.112300i	−0.399583	+	0.916697i	$0.630845\pi$
$410$	−4.87002	−	6.34673i	−0.240513	−	0.313443i
$411$	28.7637	+	1.88527i	1.41881	+	0.0929937i
$412$	−11.6286	+	11.6286i	−0.572900	+	0.572900i
$413$	−8.79724	+	23.9094i	−0.432884	+	1.17650i
$414$	5.27647	−	3.52562i	0.259324	−	0.173275i
$415$	1.59028	+	4.68481i	0.0780636	+	0.229968i
$416$	−17.7460	−	2.33630i	−0.870067	−	0.114547i
$417$	−7.44981	−	0.980786i	−0.364819	−	0.0480293i
$418$	−3.67601	−	10.8292i	−0.179799	−	0.529672i
$419$	−1.13550	+	0.758720i	−0.0554730	+	0.0370659i	−0.582998	−	0.812474i	$-0.698120\pi$
$419$	−1.13550	+	0.758720i	−0.0554730	+	0.0370659i	0.527525	+	0.849540i	$0.323120\pi$
$420$	−1.47998	+	4.02232i	−0.0722154	+	0.196269i
$421$	−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	$0.946254\pi$
$422$	1.77630	+	0.116425i	0.0864690	+	0.00566748i
$423$	7.60429	+	9.91011i	0.369733	+	0.481846i
$424$	24.1936	+	13.9682i	1.17495	+	0.678356i
$425$	−2.43501	+	3.32727i	−0.118115	+	0.161396i
$426$		−	5.04662i		−	0.244510i
$427$	−8.08032	+	0.856314i	−0.391034	+	0.0414400i
$428$	−6.59111	−	4.40404i	−0.318593	−	0.212877i
$429$	−4.82382	+	18.0027i	−0.232896	+	0.869181i
$430$	−5.38914	−	1.82937i	−0.259887	−	0.0882199i
$431$	−0.161548	−	2.46475i	−0.00778152	−	0.118723i	0.992201	−	0.124649i	$-0.0397804\pi$
$431$	−0.161548	−	2.46475i	−0.00778152	−	0.118723i	−0.999982	+	0.00592581i	$0.998114\pi$
$432$	0.398685	−	0.135335i	0.0191817	−	0.00651132i
$433$	3.23909	+	7.81985i	0.155661	+	0.375798i	0.982401	−	0.186786i	$-0.0598072\pi$
$433$	3.23909	+	7.81985i	0.155661	+	0.375798i	−0.826740	+	0.562584i	$0.809807\pi$
$434$	−5.19012	−	13.4860i	−0.249134	−	0.647348i
$435$	−1.31095	+	6.59058i	−0.0628551	+	0.315994i
$436$	0.444295	−	0.900941i	0.0212779	−	0.0431472i
$437$	−5.13185	+	15.1180i	−0.245490	+	0.723190i
$438$	2.98378	+	11.1356i	0.142571	+	0.532081i
$439$	−1.24516	+	18.9975i	−0.0594283	+	0.906701i	0.859215	+	0.511614i	$0.170952\pi$
$439$	−1.24516	+	18.9975i	−0.0594283	+	0.906701i	−0.918644	+	0.395087i	$0.870714\pi$
$440$	−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	0.572535	−	0.819880i	$-0.305960\pi$
$443$	−8.91932	−	15.4487i	−0.423770	−	0.733991i	−0.996305	+	0.0858894i	$0.972627\pi$
$444$	15.2561	−	11.7064i	0.724024	−	0.555563i
$445$	−0.0168595	+	0.00831419i	−0.000799218	+	0.000394131i
$446$	7.62680	+	2.04360i	0.361140	+	0.0967671i
$447$	−0.140521	−	0.706448i	−0.00664642	−	0.0334138i
$448$	6.73871	+	10.6599i	0.318374	+	0.503631i
$449$	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	$0.381079\pi$
$450$	−0.910760	−	0.698850i	−0.0429336	−	0.0329441i
$451$	5.53379	−	42.0333i	0.260576	−	1.97927i
$452$	−1.90846	−	1.67367i	−0.0897663	−	0.0787229i
$453$	−16.0440	−	7.91204i	−0.753814	−	0.371740i
$454$	−18.6355	+	3.70683i	−0.874606	+	0.173970i
$455$	−2.35755	+	7.98422i	−0.110524	+	0.374306i
$456$	5.83354	−	8.73051i	0.273180	−	0.408843i
$457$	0.641612	+	4.87353i	0.0300134	+	0.227974i	0.999877	−	0.0156736i	$-0.00498926\pi$
$457$	0.641612	+	4.87353i	0.0300134	+	0.227974i	−0.969864	+	0.243648i	$0.921656\pi$
$458$	−5.76710	+	9.98890i	−0.269479	+	0.466751i
$459$	−17.6894	−	14.8157i	−0.825669	−	0.691540i
$460$	5.99766	−	3.46275i	0.279642	−	0.161452i
$461$	−25.7044	−	10.6471i	−1.19717	−	0.495885i	−0.307088	−	0.951681i	$-0.599354\pi$
$461$	−25.7044	−	10.6471i	−1.19717	−	0.495885i	−0.890084	+	0.455797i	$0.849354\pi$
$462$	12.2970	−	5.68185i	0.572109	−	0.264344i
$463$	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	$0.660504\pi$
$464$	−0.257789	−	0.293952i	−0.0119676	−	0.0136464i
$465$	8.15251	−	0.534344i	0.378064	−	0.0247796i
$466$	11.8336	−	13.4936i	0.548181	−	0.625081i
$467$	7.37566	−	9.61214i	0.341305	−	0.444797i	−0.590891	−	0.806751i	$-0.701224\pi$
$467$	7.37566	−	9.61214i	0.341305	−	0.444797i	0.932196	+	0.361954i	$0.117890\pi$
$468$	4.83693	−	2.00352i	0.223587	−	0.0926128i
$469$	8.10581	−	8.78399i	0.374291	−	0.405607i
$470$	−4.51684	−	6.75992i	−0.208346	−	0.311812i
$471$	−5.39698	+	4.73303i	−0.248680	+	0.218086i
$472$	−26.1520	+	7.00741i	−1.20374	+	0.322542i
$473$	−13.3398	−	27.0504i	−0.613364	−	1.24378i
$474$	6.19742	−	0.815906i	0.284657	−	0.0374758i
$475$	2.88812			0.132516
$476$	−6.07640	+	12.2416i	−0.278511	+	0.561094i
$477$	−13.1955			−0.604180
$478$	−17.4650	+	2.29932i	−0.798832	+	0.105168i
$479$	9.70582	+	19.6814i	0.443470	+	0.899268i	0.997757	+	0.0669426i	$0.0213244\pi$
$479$	9.70582	+	19.6814i	0.443470	+	0.899268i	−0.554287	+	0.832326i	$0.687009\pi$
$480$	−7.10469	+	1.90370i	−0.324283	+	0.0868915i
$481$	28.0828	−	24.6280i	1.28047	−	1.12294i
$482$	3.96707	+	5.93715i	0.180695	+	0.270430i
$483$	−18.4483	−	4.15773i	−0.839429	−	0.189183i
$484$	−11.5570	+	4.78706i	−0.525317	+	0.217594i
$485$	1.83313	−	2.38898i	0.0832381	−	0.108478i
$486$	7.17212	−	8.17824i	0.325334	−	0.370972i
$487$	34.7519	−	2.27776i	1.57476	−	0.103215i	0.747202	−	0.664597i	$-0.231397\pi$
$487$	34.7519	−	2.27776i	1.57476	−	0.103215i	0.827557	+	0.561381i	$0.189730\pi$
$488$	−5.69363	−	6.49234i	−0.257739	−	0.293894i
$489$	−12.3248	−	12.3248i	−0.557347	−	0.557347i
$490$	5.55524	−	2.39807i	0.250960	−	0.108334i
$491$	−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
$493$	−6.42472	+	20.4414i	−0.289355	+	0.920635i
$494$	3.92764	−	6.80287i	0.176713	−	0.306075i
$495$	−0.794102	−	6.03180i	−0.0356922	−	0.271109i
$496$	−0.264097	+	0.395249i	−0.0118583	+	0.0177472i
$497$	8.65843	−	8.23073i	0.388384	−	0.369199i
$498$	5.42331	−	1.07876i	0.243024	−	0.0483406i
$499$	17.4348	+	8.59789i	0.780489	+	0.384894i	0.788470	−	0.615074i	$-0.210874\pi$
$499$	17.4348	+	8.59789i	0.780489	+	0.384894i	−0.00798091	+	0.999968i	$0.502540\pi$
$500$	−0.941926	−	0.826047i	−0.0421242	−	0.0369419i
$501$	1.05084	−	7.98192i	0.0469481	−	0.356606i
$502$	18.0320	+	13.8364i	0.804806	+	0.617549i
$503$	18.1295	+	3.60618i	0.808353	+	0.160791i	0.581931	−	0.813238i	$-0.302297\pi$
$503$	18.1295	+	3.60618i	0.808353	+	0.160791i	0.226422	+	0.974029i	$0.427297\pi$
$504$	−8.74744	−	4.59263i	−0.389642	−	0.204572i
$505$	−2.54598	−	12.7995i	−0.113295	−	0.569570i
$506$	−21.1430	−	5.66524i	−0.939920	−	0.251851i
$507$	3.59402	−	1.77238i	0.159616	−	0.0787140i
$508$	−3.54607	+	2.72099i	−0.157331	+	0.120725i
$509$	−12.4957	−	21.6432i	−0.553863	−	0.959319i	−0.997991	−	0.0633557i	$-0.979820\pi$
$509$	−12.4957	−	21.6432i	−0.553863	−	0.959319i	0.444128	−	0.895963i	$-0.353514\pi$
$510$	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
$513$	−1.05710	+	16.1282i	−0.0466721	+	0.712079i
$514$	−5.80344	−	21.6587i	−0.255979	−	0.955326i
$515$	−4.21940	+	12.4299i	−0.185929	+	0.547729i
$516$	4.71732	−	9.56577i	0.207668	−	0.421110i
$517$	8.40568	−	42.2582i	0.369681	−	1.85851i
$518$	−26.8175	−	4.22379i	−1.17829	−	0.185583i
$519$	11.1458	+	26.9084i	0.489247	+	1.18115i
$520$	−8.37771	+	2.84385i	−0.367387	+	0.124711i
$521$	1.10648	+	16.8816i	0.0484757	+	0.739596i	0.951045	+	0.309052i	$0.100012\pi$
$521$	1.10648	+	16.8816i	0.0484757	+	0.739596i	−0.902570	+	0.430544i	$0.858322\pi$
$522$	−5.64934	−	1.91769i	−0.247265	−	0.0839351i
$523$	−1.88078	+	7.01916i	−0.0822407	+	0.306926i	−0.994777	−	0.102068i	$-0.967454\pi$
$523$	−1.88078	+	7.01916i	−0.0822407	+	0.306926i	0.912537	+	0.408995i	$0.134121\pi$
$524$	0.697789	+	0.466248i	0.0304831	+	0.0203681i
$525$	0.360525	+	3.40197i	0.0157346	+	0.148474i
$526$			7.90838i			0.344822i
$527$	26.0282	+	1.11269i	1.13380	+	0.0484696i
$528$	−0.385921	−	0.222811i	−0.0167950	−	0.00969662i
$529$	4.60081	+	5.99589i	0.200035	+	0.260691i
$530$	8.56995	+	0.561704i	0.372255	+	0.0243989i
$531$	9.04278	−	9.04278i	0.392423	−	0.392423i
$532$	9.43349	−	1.62934i	0.408993	−	0.0706408i
$533$	24.2134	−	16.1789i	1.04880	−	0.700785i
$534$	0.00675353	+	0.0198952i	0.000292254	+	0.000860951i
$535$	−6.27320	−	0.825883i	−0.271214	−	0.0357060i
$536$	12.5936	+	1.65798i	0.543961	+	0.0716138i
$537$	−7.28866	−	21.4717i	−0.314529	−	0.926573i
$538$	1.40710	−	0.940191i	0.0606642	−	0.0405345i
$539$	29.8040	+	11.8311i	1.28375	+	0.509602i
$540$	4.95769	−	4.95769i	0.213345	−	0.213345i
$541$	−10.2839	−	0.674045i	−0.442141	−	0.0289795i	−0.157293	−	0.987552i	$-0.550277\pi$
$541$	−10.2839	−	0.674045i	−0.442141	−	0.0289795i	−0.284849	+	0.958573i	$0.591943\pi$
$542$	15.1567	+	19.7526i	0.651037	+	0.848448i
$543$	−14.2939	−	8.25257i	−0.613409	−	0.354152i
$544$	−23.1779	+	3.58901i	−0.993745	+	0.153877i
$545$		−	0.801815i		−	0.0343460i
$546$	8.50352	+	3.77724i	0.363917	+	0.161651i
$547$	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	$0.441227\pi$
$548$	−7.22864	+	26.9777i	−0.308792	+	1.15243i
$549$	3.86233	+	1.31108i	0.164840	+	0.0559557i
$550$	0.258977	+	3.95122i	0.0110428	+	0.168481i
$551$	14.2127	−	4.82455i	0.605480	−	0.205533i
$552$	−7.69091	−	18.5675i	−0.327347	−	0.790286i
$553$	11.5075	+	9.30215i	0.489347	+	0.395568i
$554$	−3.57033	+	17.9492i	−0.151689	+	0.762590i
$555$	6.78879	−	13.7663i	0.288168	−	0.584347i
$556$	2.34024	−	6.89412i	0.0992483	−	0.292376i
$557$	3.31426	+	12.3690i	0.140430	+	0.524090i	0.999916	+	0.0129325i	$0.00411664\pi$
$557$	3.31426	+	12.3690i	0.140430	+	0.524090i	−0.859487	+	0.511158i	$0.829217\pi$
$558$	−0.474407	+	7.23805i	−0.0200833	+	0.306411i
$559$	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
$563$	24.2162	−	18.5818i	1.02059	−	0.783128i	0.0441762	−	0.999024i	$-0.485934\pi$
$563$	24.2162	−	18.5818i	1.02059	−	0.783128i	0.976416	+	0.215895i	$0.0692670\pi$
$564$	13.6651	−	6.73890i	0.575406	−	0.283759i
$565$	−1.95708	−	0.524399i	−0.0823352	−	0.0220616i
$566$	0.512289	+	2.57545i	0.0215331	+	0.108254i
$567$	−8.59685	+	0.345189i	−0.361034	+	0.0144966i
$568$	12.4517	+	2.47680i	0.522462	+	0.103924i
$569$	21.8862	+	16.7939i	0.917519	+	0.704037i	0.955422	−	0.295244i	$-0.0954010\pi$
$569$	21.8862	+	16.7939i	0.917519	+	0.704037i	−0.0379026	+	0.999281i	$0.512068\pi$
$570$	0.421337	−	3.20037i	0.0176479	−	0.134049i
$571$	−32.8104	−	28.7740i	−1.37307	−	1.20415i	−0.955313	−	0.295596i	$-0.904482\pi$
$571$	−32.8104	−	28.7740i	−1.37307	−	1.20415i	−0.417761	−	0.908557i	$-0.637185\pi$
$572$	−16.1961	−	7.98703i	−0.677193	−	0.333954i
$573$	21.7096	−	4.31830i	0.906930	−	0.180400i
$574$	−20.2993	−	5.99390i	−0.847275	−	0.250180i
$575$	3.07114	−	4.59628i	0.128075	−	0.191678i
$576$	−0.826290	−	6.27629i	−0.0344287	−	0.261512i
$577$	−10.4065	+	18.0245i	−0.433227	+	0.750371i	−0.997149	−	0.0754571i	$-0.975958\pi$
$577$	−10.4065	+	18.0245i	−0.433227	+	0.750371i	0.563922	+	0.825828i	$0.309292\pi$
$578$	9.46600	+	11.2396i	0.393734	+	0.467504i
$579$	15.6244	−	9.02075i	0.649328	−	0.374890i
$580$	−6.01519	−	2.49157i	−0.249767	−	0.103457i
$581$	10.6959	+	7.54532i	0.443742	+	0.313033i
$582$	−2.37984	−	2.37984i	−0.0986476	−	0.0986476i
$583$	30.0099	+	34.2197i	1.24288	+	1.41724i
$584$	−28.9397	+	1.89681i	−1.19753	+	0.0784905i
$585$	2.75535	−	3.14187i	0.113920	−	0.129900i
$586$	−5.87756	+	7.65979i	−0.242800	+	0.316423i
$587$	12.4427	−	5.15393i	0.513565	−	0.212725i	−0.110823	−	0.993840i	$-0.535349\pi$
$587$	12.4427	−	5.15393i	0.513565	−	0.212725i	0.624388	+	0.781115i	$0.285349\pi$
$588$	3.09682	+	10.9085i	0.127711	+	0.449859i
$589$	−10.1384	−	15.1732i	−0.417746	−	0.625200i
$590$	−6.25786	+	5.48799i	−0.257632	+	0.225937i
$591$	6.09809	−	1.63398i	0.250842	−	0.0672129i
$592$	0.394997	+	0.800975i	0.0162343	+	0.0329199i
$593$	3.14951	−	0.414640i	0.129335	−	0.0170272i	−0.0655809	−	0.997847i	$-0.520890\pi$
$593$	3.14951	−	0.414640i	0.129335	−	0.0170272i	0.194916	+	0.980820i	$0.437557\pi$
$594$	−22.1598			−0.909226
$595$	−0.0282765	+	10.9087i	−0.00115922	+	0.447212i
$596$	0.697896			0.0285869
$597$	−3.32374	+	0.437579i	−0.136032	+	0.0179089i
$598$	−6.64986	−	13.4846i	−0.271933	−	0.551425i
$599$	28.9549	−	7.75843i	1.18306	−	0.317001i	0.386923	−	0.922112i	$-0.373538\pi$
$599$	28.9549	−	7.75843i	1.18306	−	0.317001i	0.796141	+	0.605111i	$0.206871\pi$
$600$	−2.73340	+	2.39713i	−0.111591	+	0.0978624i
$601$	−15.4140	−	23.0687i	−0.628751	−	0.940992i	−0.999923	−	0.0124282i	$-0.996044\pi$
$601$	−15.4140	−	23.0687i	−0.628751	−	0.940992i	0.371172	−	0.928564i	$-0.378956\pi$
$602$	−14.3763	+	4.47754i	−0.585933	+	0.182491i
$603$	−5.54309	+	2.29602i	−0.225732	+	0.0935014i
$604$	10.5515	−	13.7510i	0.429334	−	0.559520i
$605$	−6.58341	+	7.50694i	−0.267654	+	0.305200i
$606$	−14.5548	+	0.953970i	−0.591247	+	0.0387524i
$607$	4.84366	+	5.52314i	0.196598	+	0.224177i	0.841736	−	0.539889i	$-0.181534\pi$
$607$	4.84366	+	5.52314i	0.196598	+	0.224177i	−0.645138	+	0.764066i	$0.723200\pi$
$608$	11.6170	+	11.6170i	0.471132	+	0.471132i
$609$	7.45711	+	16.1391i	0.302177	+	0.653991i
$610$	−2.45262	−	1.01591i	−0.0993037	−	0.0411329i
$611$	25.6302	−	14.7976i	1.03689	−	0.598647i
$612$	5.34633	−	4.29888i	0.216112	−	0.173772i
$613$	−14.7553	+	25.5570i	−0.595962	+	1.03224i	0.397448	+	0.917624i	$0.369896\pi$
$613$	−14.7553	+	25.5570i	−0.595962	+	1.03224i	−0.993410	+	0.114612i	$0.963438\pi$
$614$	1.38685	+	10.5342i	0.0559688	+	0.425125i
$615$	6.64843	−	9.95008i	0.268090	−	0.401226i
$616$	7.98387	+	33.1294i	0.321679	+	1.33482i
$617$	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	$0.326770\pi$
$618$	13.1583	+	6.48895i	0.529304	+	0.261024i
$619$	−7.25316	−	6.36085i	−0.291529	−	0.255664i	0.501071	−	0.865406i	$-0.332940\pi$
$619$	−7.25316	−	6.36085i	−0.291529	−	0.255664i	−0.792600	+	0.609742i	$0.791273\pi$
$620$	−1.03325	+	7.84830i	−0.0414962	+	0.315195i
$621$	24.5431	+	18.8326i	0.984881	+	0.755726i
$622$	2.17117	+	0.431872i	0.0870559	+	0.0173165i
$623$	−0.0231195	+	0.0440349i	−0.000926262	+	0.00176422i
$624$	−0.0597155	−	0.300210i	−0.00239053	−	0.0120180i
$625$	−0.965926	−	0.258819i	−0.0386370	−	0.0103528i
$626$	−15.7275	+	7.75596i	−0.628599	+	0.309991i
$627$	13.5719	−	10.4141i	0.542009	−	0.415898i
$628$	−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	$0.0724608\pi$
$632$	−1.02848	+	15.6915i	−0.0409107	+	0.624176i
$633$	0.689192	+	2.57210i	0.0273929	+	0.102232i
$634$	7.82957	−	23.0652i	0.310952	−	0.916035i
$635$	−1.57796	+	3.19978i	−0.0626193	+	0.126979i
$636$	−3.14002	+	15.7860i	−0.124510	+	0.625954i
$637$	7.38817	+	20.7499i	0.292730	+	0.822139i
$638$	7.87489	+	19.0117i	0.311770	+	0.752679i
$639$	−5.67843	+	1.92757i	−0.224635	+	0.0762534i
$640$	−0.474613	−	7.24119i	−0.0187607	−	0.286233i
$641$	37.5851	+	12.7584i	1.48452	+	0.503927i	0.941855	−	0.336021i	$-0.109081\pi$
$641$	37.5851	+	12.7584i	1.48452	+	0.503927i	0.542667	+	0.839948i	$0.317415\pi$
$642$	−1.83035	+	6.83096i	−0.0722382	+	0.269596i
$643$	17.4409	+	11.6536i	0.687802	+	0.459575i	0.849723	−	0.527229i	$-0.176769\pi$
$643$	17.4409	+	11.6536i	0.687802	+	0.459575i	−0.161921	+	0.986804i	$0.551769\pi$
$644$	7.43828	−	16.7455i	0.293109	−	0.659863i
$645$		−	8.51330i		−	0.335211i
$646$	2.43745	−	10.0004i	0.0959001	−	0.393461i
$647$	10.2441	+	5.91444i	0.402738	+	0.232521i	0.687665	−	0.726029i	$-0.258636\pi$
$647$	10.2441	+	5.91444i	0.402738	+	0.232521i	−0.284927	+	0.958549i	$0.591969\pi$
$648$	−5.56620	−	7.25401i	−0.218661	−	0.284964i
$649$	−44.0161	−	2.88497i	−1.72778	−	0.113245i
$650$	−1.92323	+	1.92323i	−0.0754353	+	0.0754353i
$651$	16.6072	−	13.8363i	0.650888	−	0.542287i
$652$	14.0419	−	9.38251i	0.549924	−	0.367447i
$653$	−3.97985	−	11.7243i	−0.155744	−	0.458806i	0.840851	−	0.541267i	$-0.182055\pi$
$653$	−3.97985	−	11.7243i	−0.155744	−	0.458806i	−0.996594	+	0.0824611i	$0.973722\pi$
$654$	−0.888504	−	0.116974i	−0.0347433	−	0.00457404i
$655$	0.664133	+	0.0874348i	0.0259498	+	0.00341636i
$656$	0.223811	+	0.659325i	0.00873834	+	0.0257423i
$657$	11.3901	−	7.61061i	0.444369	−	0.296918i
$658$	−20.1871	−	7.42766i	−0.786975	−	0.289560i
$659$	−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	$0.322241\pi$
$660$	−7.40490	−	0.485343i	−0.288235	−	0.0188919i
$661$	−15.9416	−	20.7755i	−0.620057	−	0.808074i	0.372733	−	0.927939i	$-0.378421\pi$
$661$	−15.9416	−	20.7755i	−0.620057	−	0.808074i	−0.992790	+	0.119864i	$0.961754\pi$
$662$	−21.1434	−	12.2071i	−0.821762	−	0.474444i
$663$	−12.3576	+	11.3444i	−0.479931	+	0.440580i
$664$			13.9106i			0.539835i
$665$	6.17802	−	4.49673i	0.239573	−	0.174376i
$666$	11.3309	+	7.57104i	0.439062	+	0.293372i
$667$	7.43531	−	27.7489i	0.287896	−	1.07444i
$668$	7.38655	+	2.50740i	0.285794	+	0.0970140i
$669$	0.772492	+	11.7859i	0.0298663	+	0.455671i
$670$	3.69776	−	1.25522i	0.142857	−	0.0484934i
$671$	−5.38389	−	12.9979i	−0.207843	−	0.501777i
$672$	−12.2338	+	15.1341i	−0.471928	+	0.583810i
$673$	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	$-0.336401\pi$
$674$	−6.03326	+	12.2342i	−0.232393	+	0.471246i
$675$	1.79888	−	5.29933i	0.0692389	−	0.203971i
$676$	1.00492	+	3.75041i	0.0386507	+	0.144247i
$677$	−1.15173	+	17.5720i	−0.0442647	+	0.675348i	0.916856	+	0.399219i	$0.130719\pi$
$677$	−1.15173	+	17.5720i	−0.0442647	+	0.675348i	−0.961120	+	0.276130i	$0.910948\pi$
$678$	−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
$682$	19.8493	−	15.2309i	0.760068	−	0.583221i
$683$	−13.0434	+	6.43227i	−0.499090	+	0.246124i	−0.674369	−	0.738395i	$-0.735584\pi$
$683$	−13.0434	+	6.43227i	−0.499090	+	0.246124i	0.175279	+	0.984519i	$0.443917\pi$
$684$	−4.64170	−	1.24374i	−0.177480	−	0.0475556i
$685$	4.34915	+	21.8647i	0.166173	+	0.835406i
$686$	8.14958	−	13.7791i	0.311152	−	0.526090i
$687$	−16.9222	−	3.36604i	−0.645623	−	0.128422i
$688$	0.392976	+	0.301541i	0.0149821	+	0.0114962i
$689$	−4.08068	+	30.9959i	−0.155462	+	1.18085i
$690$	−4.64518	−	4.07371i	−0.176839	−	0.155084i
$691$	−20.0443	−	9.88476i	−0.762522	−	0.376034i	0.0190750	−	0.999818i	$-0.493928\pi$
$691$	−20.0443	−	9.88476i	−0.762522	−	0.376034i	−0.781597	+	0.623784i	$0.785595\pi$
$692$	−27.6777	+	5.50544i	−1.05215	+	0.209285i
$693$	−11.0901	−	11.6663i	−0.421277	−	0.443168i
$694$	7.15348	−	10.7059i	0.271542	−	0.406392i
$695$	−0.758521	−	5.76154i	−0.0287723	−	0.218548i
$696$	−9.44693	+	16.3626i	−0.358085	+	0.620222i
$697$	24.5016	−	29.2538i	0.928063	−	1.10807i
$698$	−7.58130	+	4.37706i	−0.286956	+	0.165674i
$699$	24.8037	+	10.2740i	0.938161	+	0.388599i
$700$	−3.30103	−	0.300454i	−0.124767	−	0.0113561i
$701$	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	$0.574811\pi$
$702$	−10.0360	−	11.4439i	−0.378786	−	0.431923i
$703$	−34.2108	+	2.24230i	−1.29029	+	0.0845698i
$704$	−14.3970	+	16.4167i	−0.542609	+	0.618727i
$705$	7.40353	−	9.64847i	0.278833	−	0.363382i
$706$	−14.2862	+	5.91754i	−0.537669	+	0.222710i
$707$	−25.3747	−	23.4156i	−0.954313	−	0.880634i
$708$	−8.66617	−	12.9698i	−0.325695	−	0.487436i
$709$	−0.612658	+	0.537286i	−0.0230088	+	0.0201782i	−0.670773	−	0.741663i	$-0.734038\pi$
$709$	−0.612658	+	0.537286i	−0.0230088	+	0.0201782i	0.647764	+	0.761841i	$0.275704\pi$
$710$	3.76997	−	1.01016i	0.141484	−	0.0379106i
$711$	−3.28517	−	6.66166i	−0.123203	−	0.249832i
$712$	−0.0524028	+	0.00689896i	−0.00196388	+	0.000258549i
$713$	−34.9282			−1.30807
$714$	12.0840	+	1.62276i	0.452231	+	0.0607303i
$715$	−14.4141			−0.539057
$716$	21.7822	−	2.86768i	0.814039	−	0.107170i
$717$	−11.6548	−	23.6335i	−0.435255	−	0.882610i
$718$	−4.26504	+	1.14281i	−0.159170	+	0.0426494i
$719$	−11.6207	+	10.1911i	−0.433380	+	0.380064i	−0.848057	−	0.529904i	$-0.822228\pi$
$719$	−11.6207	+	10.1911i	−0.433380	+	0.380064i	0.414677	+	0.909969i	$0.363895\pi$
$720$	0.0555104	+	0.0830772i	0.00206875	+	0.00309610i
$721$	10.3274	+	33.1586i	0.384611	+	1.23489i
$722$	8.51203	−	3.52580i	0.316785	−	0.131217i
$723$	−6.50242	+	8.47412i	−0.241828	+	0.315156i
$724$	10.5443	−	12.0235i	0.391875	−	0.446848i
$725$	−5.18575	+	0.339892i	−0.192594	+	0.0126233i
$726$	7.35814	+	8.39035i	0.273086	+	0.311395i
$727$	7.35145	+	7.35145i	0.272650	+	0.272650i	0.830166	−	0.557516i	$-0.188245\pi$
$727$	7.35145	+	7.35145i	0.272650	+	0.272650i	−0.557516	+	0.830166i	$0.688245\pi$
$728$	−13.4931	+	19.1272i	−0.500088	+	0.708903i
$729$	24.0462	+	9.96025i	0.890599	+	0.368898i
$730$	−7.72137	+	4.45794i	−0.285781	+	0.164996i
$731$	2.93082	−	26.9879i	0.108400	−	0.998185i
$732$	2.48755	−	4.30857i	0.0919427	−	0.159249i
$733$	6.07445	+	46.1400i	0.224365	+	1.70422i	0.619007	+	0.785386i	$0.287535\pi$
$733$	6.07445	+	46.1400i	0.224365	+	1.70422i	−0.394642	+	0.918835i	$0.629131\pi$
$734$	17.2149	−	25.7639i	0.635413	−	0.950963i
$735$	6.06800	+	6.71589i	0.223821	+	0.247719i
$736$	30.8410	−	6.13466i	1.13682	−	0.226127i
$737$	18.5606	+	9.15310i	0.683690	+	0.337159i
$738$	7.98796	+	7.00525i	0.294041	+	0.257867i
$739$	3.27882	−	24.9051i	0.120613	−	0.916149i	−0.818972	−	0.573834i	$-0.805456\pi$
$739$	3.27882	−	24.9051i	0.120613	−	0.916149i	0.939585	−	0.342315i	$-0.111211\pi$
$740$	11.7988	+	9.05353i	0.433732	+	0.332814i
$741$	11.5248	+	2.29242i	0.423372	+	0.0842140i
$742$	19.2067	−	12.1417i	0.705100	−	0.445735i
$743$	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	$0.670612\pi$
$744$	22.1890	+	5.94552i	0.813488	+	0.217973i
$745$	0.499609	−	0.246380i	0.0183042	−	0.00902666i
$746$	−5.23213	+	4.01475i	−0.191562	+	0.146991i
$747$	−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
$751$	−1.82027	+	27.7719i	−0.0664225	+	1.01341i	0.826423	+	0.563050i	$0.190372\pi$
$751$	−1.82027	+	27.7719i	−0.0664225	+	1.01341i	−0.892846	+	0.450363i	$0.851295\pi$
$752$	0.183143	+	0.683498i	0.00667853	+	0.0249246i
$753$	−10.9288	+	32.1952i	−0.398267	+	1.17326i
$754$	−6.25165	+	12.6771i	−0.227672	+	0.461673i
$755$	2.69905	−	13.5691i	0.0982286	−	0.493829i
$756$	2.88607	−	18.3241i	0.104965	−	0.666440i
$757$	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	$0.622325\pi$
$758$	20.1316	−	6.83377i	0.731214	−	0.248214i
$759$	−2.14150	−	32.6729i	−0.0777314	−	1.18595i
$760$	7.68961	+	2.61027i	0.278931	+	0.0946845i
$761$	11.7487	−	43.8469i	0.425892	−	1.58945i	−0.336076	−	0.941835i	$-0.609100\pi$
$761$	11.7487	−	43.8469i	0.425892	−	1.58945i	0.761968	−	0.647615i	$-0.224233\pi$
$762$	3.31553	+	2.21536i	0.120109	+	0.0802542i
$763$	−1.24841	−	1.71518i	−0.0451954	−	0.0620935i
$764$			21.4468i			0.775917i
$765$	2.30968	−	4.96490i	0.0835065	−	0.179507i
$766$	−9.14443	−	5.27954i	−0.330402	−	0.190757i
$767$	−18.4448	−	24.0377i	−0.666002	−	0.867951i
$768$	−20.3936	−	1.33667i	−0.735890	−	0.0482328i
$769$	15.9589	−	15.9589i	0.575493	−	0.575493i	−0.358165	−	0.933658i	$-0.616598\pi$
$769$	15.9589	−	15.9589i	0.575493	−	0.575493i	0.933658	+	0.358165i	$0.116598\pi$
$770$	6.70594	+	8.04891i	0.241665	+	0.290062i
$771$	27.8890	−	18.6348i	1.00440	−	0.671116i
$772$	5.61897	+	16.5529i	0.202231	+	0.595753i
$773$	9.01070	+	1.18628i	0.324092	+	0.0426676i	0.290817	−	0.956779i	$-0.406073\pi$
$773$	9.01070	+	1.18628i	0.324092	+	0.0426676i	0.0332752	+	0.999446i	$0.489406\pi$
$774$	7.49371	+	0.986565i	0.269356	+	0.0354614i
$775$	2.03102	+	5.98320i	0.0729565	+	0.214923i
$776$	7.03985	−	4.70388i	0.252716	−	0.168859i
$777$	−6.91180	−	40.0177i	−0.247959	−	1.43563i
$778$	−5.72528	+	5.72528i	−0.205261	+	0.205261i
$779$	−26.6721	−	1.74818i	−0.955627	−	0.0626351i
$780$	−3.10300	−	4.04390i	−0.111105	−	0.144795i
$781$	17.9129	+	10.3420i	0.640974	+	0.370067i
$782$	−13.3232	−	14.5132i	−0.476437	−	0.518991i
$783$		−	29.0834i		−	1.03936i
$784$	−0.524936	+	0.0422236i	−0.0187477	+	0.00150798i
$785$	−4.61599	−	3.08431i	−0.164752	−	0.110084i
$786$	0.193776	−	0.723182i	0.00691176	−	0.0257950i
$787$	−25.8626	−	8.77918i	−0.921904	−	0.312944i	−0.180167	−	0.983636i	$-0.557664\pi$
$787$	−25.8626	−	8.77918i	−0.921904	−	0.312944i	−0.741736	+	0.670692i	$0.765997\pi$
$788$	0.400067	+	6.10385i	0.0142518	+	0.217441i
$789$	−11.2022	+	3.80262i	−0.398807	+	0.135377i
$790$	1.85001	+	4.46633i	0.0658206	+	0.158905i
$791$	−5.00291	+	1.92538i	−0.177883	+	0.0684588i
$792$	3.33723	−	16.7774i	0.118583	−	0.596158i
$793$	4.27412	−	8.66705i	0.151778	−	0.307776i
$794$	−9.05254	+	26.6679i	−0.321263	+	0.946409i
$795$	3.32508	+	12.4094i	0.117928	+	0.440115i
$796$	0.212443	−	3.24125i	0.00752984	−	0.114883i
$797$	11.5760	−	27.9470i	0.410043	−	0.989932i	−0.575082	−	0.818096i	$-0.695030\pi$
$797$	11.5760	−	27.9470i	0.410043	−	0.989932i	0.985126	−	0.171836i	$-0.0549700\pi$
$798$	−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
$801$	0.0198065	−	0.0151981i	0.000699828	−	0.000536997i
$802$	14.2667	−	7.03557i	0.503775	−	0.248434i
$803$	−45.6404	−	12.2293i	−1.61061	−	0.431563i
$804$	1.42772	+	7.17765i	0.0503519	+	0.253136i
$805$	−0.586782	−	14.6137i	−0.0206814	−	0.515064i
$806$	16.8553	+	3.35272i	0.593702	+	0.118095i
$807$	2.00835	+	1.54106i	0.0706974	+	0.0542480i
$808$	4.78948	−	36.3797i	0.168493	−	1.27983i
$809$	−26.2908	−	23.0564i	−0.924336	−	0.810621i	0.0578897	−	0.998323i	$-0.481563\pi$
$809$	−26.2908	−	23.0564i	−0.924336	−	0.810621i	−0.982226	+	0.187702i	$0.939896\pi$
$810$	−2.52105	−	1.24324i	−0.0885806	−	0.0436831i
$811$	0.0209422	−	0.00416566i	0.000735379	−	0.000146276i	−0.194723	−	0.980858i	$-0.562381\pi$
$811$	0.0209422	−	0.00416566i	0.000735379	−	0.000146276i	0.195458	+	0.980712i	$0.437381\pi$
$812$	−16.7465	+	4.03575i	−0.587688	+	0.141627i
$813$	−20.6916	+	30.9672i	−0.725686	+	1.08607i
$814$	−6.13535	−	46.6026i	−0.215044	−	1.63342i
$815$	6.73998	−	11.6740i	0.236091	−	0.408922i
$816$	−0.185525	−	0.355601i	−0.00649469	−	0.0124485i
$817$	−16.4678	+	9.50771i	−0.576137	+	0.332633i
$818$	3.62740	+	1.50252i	0.126829	+	0.0525344i
$819$	1.00219	−	11.0108i	0.0350193	−	0.384750i
$820$	8.19879	+	8.19879i	0.286314	+	0.286314i
$821$	−23.3855	−	26.6661i	−0.816160	−	0.930653i	0.182457	−	0.983214i	$-0.441595\pi$
$821$	−23.3855	−	26.6661i	−0.816160	−	0.930653i	−0.998618	+	0.0525612i	$0.983262\pi$
$822$	24.8631	−	1.62961i	0.867200	−	0.0568393i
$823$	−16.7538	+	19.1041i	−0.584002	+	0.665927i	−0.966092	−	0.258198i	$-0.916871\pi$
$823$	−16.7538	+	19.1041i	−0.584002	+	0.665927i	0.382090	+	0.924125i	$0.375205\pi$
$824$	−22.4683	+	29.2812i	−0.782720	+	1.02006i
$825$	−5.47235	+	2.26672i	−0.190523	+	0.0789172i
$826$	−4.84161	+	21.4828i	−0.168461	+	0.747482i
$827$	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	$0.405657\pi$
$828$	−6.91518	+	6.06445i	−0.240319	+	0.210754i
$829$	4.38665	−	1.17540i	0.152355	−	0.0408233i	−0.181836	−	0.983329i	$-0.558204\pi$
$829$	4.38665	−	1.17540i	0.152355	−	0.0408233i	0.334190	+	0.942506i	$0.391537\pi$
$830$	1.89143	+	3.83544i	0.0656524	+	0.133130i
$831$	−27.1417	+	3.57327i	−0.941535	+	0.123955i
$832$	−14.9984			−0.519975
$833$	16.9241	+	23.3790i	0.586384	+	0.810033i
$834$	−6.49511			−0.224907
$835$	6.17306	−	0.812699i	0.213628	−	0.0281246i
$836$	7.33102	+	14.8658i	0.253548	+	0.514145i
$837$	−34.1556	+	9.15197i	−1.18059	+	0.316338i
$838$	−0.887520	+	0.778334i	−0.0306589	+	0.0268871i
$839$	−6.79218	−	10.1652i	−0.234492	−	0.350942i	0.695497	−	0.718529i	$-0.255184\pi$
$839$	−6.79218	−	10.1652i	−0.234492	−	0.350942i	−0.929989	+	0.367586i	$0.880184\pi$
$840$	−2.11479	+	9.38358i	−0.0729673	+	0.323764i
$841$	1.84077	−	0.762472i	0.0634749	−	0.0262922i
$842$	−17.6179	+	22.9601i	−0.607152	+	0.791256i
$843$	−23.1066	+	26.3481i	−0.795835	+	0.907476i
$844$	−2.57453	+	0.168743i	−0.0886189	+	0.00580839i
$845$	2.04342	+	2.33007i	0.0702956	+	0.0801568i
$846$	7.63497	+	7.63497i	0.262496	+	0.262496i
$847$	−2.39455	+	26.3084i	−0.0822777	+	0.903969i
$848$	−0.690594	−	0.286054i	−0.0237151	−	0.00982312i
$849$	−3.40178	+	1.96402i	−0.116749	+	0.0674050i
$850$	−1.71139	+	3.12619i	−0.0587002	+	0.107227i
$851$	−32.8103	+	56.8290i	−1.12472	+	1.94807i
$852$	0.954727	+	7.25187i	0.0327084	+	0.248445i
$853$	9.92875	−	14.8594i	0.339954	−	0.508777i	−0.621622	−	0.783318i	$-0.713526\pi$
$853$	9.92875	−	14.8594i	0.339954	−	0.508777i	0.961575	+	0.274541i	$0.0885258\pi$
$854$	−6.82819	+	1.64553i	−0.233656	+	0.0563087i
$855$	−3.76197	+	0.748303i	−0.128657	+	0.0255914i
$856$	−15.9560	−	7.86861i	−0.545364	−	0.268944i
$857$	−6.28829	−	5.51469i	−0.214804	−	0.188378i	0.545182	−	0.838318i	$-0.316461\pi$
$857$	−6.28829	−	5.51469i	−0.214804	−	0.188378i	−0.759986	+	0.649940i	$0.774794\pi$
$858$	−2.10282	+	15.9725i	−0.0717892	+	0.545293i
$859$	−18.0552	−	13.8543i	−0.616037	−	0.472702i	0.252989	−	0.967469i	$-0.418587\pi$
$859$	−18.0552	−	13.8543i	−0.616037	−	0.472702i	−0.869025	+	0.494768i	$0.835253\pi$
$860$	8.09015	+	1.60923i	0.275872	+	0.0548743i
$861$	−1.27027	−	31.6358i	−0.0432908	−	1.07815i
$862$	−0.416534	−	2.09406i	−0.0141872	−	0.0713239i
$863$	−35.8855	−	9.61549i	−1.22156	−	0.327315i	−0.410270	−	0.911964i	$-0.634566\pi$
$863$	−35.8855	−	9.61549i	−1.22156	−	0.327315i	−0.811286	+	0.584649i	$0.801232\pi$
$864$	28.5515	−	14.0800i	0.971341	−	0.479012i
$865$	−17.8703	+	13.7124i	−0.607608	+	0.466234i
$866$	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
$870$	−0.379890	+	5.79601i	−0.0128795	+	0.196503i
$871$	3.67911	+	13.7306i	0.124662	+	0.465244i
$872$	0.724677	−	2.13483i	0.0245407	−	0.0722945i
$873$	−1.76880	+	3.58677i	−0.0598648	+	0.121394i
$874$	−2.69229	+	13.5350i	−0.0910679	+	0.457829i
$875$	−2.46920	+	0.950280i	−0.0834743	+	0.0321253i
$876$	−6.39428	−	15.4372i	−0.216043	−	0.521573i
$877$	−28.5150	+	9.67953i	−0.962883	+	0.326855i	−0.758235	−	0.651981i	$-0.773938\pi$
$877$	−28.5150	+	9.67953i	−0.962883	+	0.326855i	−0.204647	+	0.978836i	$0.565605\pi$
$878$	1.07631	+	16.4213i	0.0363236	+	0.554191i
$879$	−13.6762	−	4.64243i	−0.461286	−	0.156585i
$880$	0.0891984	−	0.332893i	0.00300688	−	0.0112218i
$881$	1.34126	+	0.896201i	0.0451882	+	0.0301938i	0.577959	−	0.816066i	$-0.303849\pi$
$881$	1.34126	+	0.896201i	0.0451882	+	0.0301938i	−0.532771	+	0.846259i	$0.678849\pi$
$882$	−6.61475	+	4.56299i	−0.222730	+	0.153644i
$883$		−	19.3249i		−	0.650333i	−0.945657	−	0.325167i	$-0.894580\pi$
$883$		−	19.3249i		−	0.650333i	0.945657	−	0.325167i	$-0.105420\pi$
$884$	−8.44462	−	13.8878i	−0.284023	−	0.467097i
$885$	−10.7827	−	6.22539i	−0.362456	−	0.209264i
$886$	−9.38684	−	12.2332i	−0.315357	−	0.410981i
$887$	−24.2987	−	1.59262i	−0.815871	−	0.0534750i	−0.348247	−	0.937403i	$-0.613223\pi$
$887$	−24.2987	−	1.59262i	−0.815871	−	0.0534750i	−0.467624	+	0.883928i	$0.654890\pi$
$888$	30.5171	−	30.5171i	1.02409	−	1.02409i
$889$	1.60655	+	9.30154i	0.0538819	+	0.311964i
$890$	−0.0135105	+	0.00902742i	−0.000452873	+	0.000302600i
$891$	−4.78841	−	14.1062i	−0.160418	−	0.472575i
$892$	−11.3461	−	1.49375i	−0.379897	−	0.0500144i
$893$	−26.9320	−	3.54566i	−0.901245	−	0.118651i
$894$	−0.200132	−	0.589568i	−0.00669340	−	0.0197181i
$895$	14.5810	−	9.74274i	0.487390	−	0.325664i
$896$	−12.2896	−	14.7508i	−0.410567	−	0.492789i
$897$	15.9033	−	15.9033i	0.530997	−	0.530997i
$898$	19.7241	+	1.29278i	0.658200	+	0.0431407i
$899$	19.9897	+	26.0510i	0.666693	+	0.868851i
$900$	1.44095	+	0.831933i	0.0480316	+	0.0277311i
$901$	6.26871	+	40.4835i	0.208841	+	1.34870i
$902$		−	36.6468i		−	1.22020i
$903$	−13.2550	−	18.2109i	−0.441099	−	0.606022i
$904$	−4.73679	−	3.16502i	−0.157543	−	0.105267i
$905$	3.30376	−	12.3298i	0.109821	−	0.409857i
$906$	−14.6423	−	4.97041i	−0.486459	−	0.165131i
$907$	0.193569	+	2.95329i	0.00642736	+	0.0980625i	0.999867	−	0.0162929i	$-0.00518641\pi$
$907$	0.193569	+	2.95329i	0.00642736	+	0.0980625i	−0.993440	+	0.114355i	$0.963520\pi$
$908$	26.0775	−	8.85211i	0.865411	−	0.293768i
$909$	6.63263	+	16.0126i	0.219990	+	0.531104i
$910$	−1.11959	+	7.10844i	−0.0371140	+	0.235643i
$911$	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	$0.0292230\pi$
$912$	−0.124261	+	0.251977i	−0.00411471	+	0.00834380i
$913$	−7.28492	+	21.4607i	−0.241096	+	0.710245i
$914$	1.09972	+	4.10421i	0.0363755	+	0.135755i
$915$	0.259723	−	3.96260i	0.00858617	−	0.131000i
$916$	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	0.934741	+	0.355330i	$0.115632\pi$
$919$	23.4970	+	40.6981i	0.775096	+	1.34250i	−0.159645	+	0.987174i	$0.551035\pi$
$920$	12.3310	−	9.46191i	0.406541	−	0.311950i
$921$	−14.2547	+	7.02966i	−0.469710	+	0.231635i
$922$	−23.2298	−	6.22441i	−0.765033	−	0.204990i
$923$	2.77176	+	13.9346i	0.0912335	+	0.458662i
$924$	−16.5956	+	10.4911i	−0.545956	+	0.345130i
$925$	11.6427	+	2.31588i	0.382809	+	0.0761455i
$926$	8.18868	+	6.28339i	0.269097	+	0.206485i
$927$	2.27549	−	17.2841i	0.0747370	−	0.567684i
$928$	−22.2261	−	19.4918i	−0.729607	−	0.639848i
$929$	−21.7334	−	10.7177i	−0.713051	−	0.351638i	0.0493156	−	0.998783i	$-0.484296\pi$
$929$	−21.7334	−	10.7177i	−0.713051	−	0.351638i	−0.762367	+	0.647145i	$0.775963\pi$
$930$	6.92639	−	1.37774i	0.227125	−	0.0451780i
$931$	6.21420	−	19.2381i	0.203662	−	0.630503i
$932$	−14.4519	+	21.6287i	−0.473387	+	0.708473i
$933$	0.432229	+	3.28310i	0.0141505	+	0.107484i
$934$	5.23641	−	9.06973i	0.171341	−	0.296771i
$935$	−18.1282	+	5.30179i	−0.592856	+	0.173387i
$936$	10.1757	−	5.87495i	0.332604	−	0.192029i
$937$	4.99006	+	2.06695i	0.163018	+	0.0675244i	0.462700	−	0.886515i	$-0.346881\pi$
$937$	4.99006	+	2.06695i	0.163018	+	0.0675244i	−0.299682	+	0.954039i	$0.596881\pi$
$938$	5.95559	−	8.44239i	0.194457	−	0.275654i
$939$	−18.5486	−	18.5486i	−0.605311	−	0.605311i
$940$	7.76944	+	8.85935i	0.253411	+	0.288960i
$941$	−51.9098	+	3.40235i	−1.69221	+	0.110913i	−0.880778	−	0.473530i	$-0.842980\pi$
$941$	−51.9098	+	3.40235i	−1.69221	+	0.110913i	−0.811435	+	0.584443i	$0.801313\pi$
$942$	−4.09119	+	4.66510i	−0.133298	+	0.151997i
$943$	−31.1444	+	40.5882i	−1.01420	+	1.32173i
$944$	0.669290	−	0.277229i	0.0217835	−	0.00902303i
$945$	−4.40292	−	14.1367i	−0.143227	−	0.459867i
$946$	−14.4841	−	21.6770i	−0.470920	−	0.704781i
$947$	0.278810	−	0.244510i	0.00906012	−	0.00794551i	−0.654804	−	0.755799i	$-0.727249\pi$
$947$	0.278810	−	0.244510i	0.00906012	−	0.00794551i	0.663864	+	0.747853i	$0.268915\pi$
$948$	−8.75119	+	2.34487i	−0.284225	+	0.0761580i
$949$	−14.3547	−	29.1085i	−0.465975	−	0.944904i
$950$	2.47511	−	0.325854i	0.0803031	−	0.0105721i
$951$	36.4364			1.18153
$952$	−9.93451	+	29.0188i	−0.321979	+	0.940504i
$953$	−17.8650			−0.578703			−0.289352	−	0.957223i	$-0.593440\pi$
$953$	−17.8650			−0.578703			−0.289352	+	0.957223i	$0.593440\pi$
$954$	−11.3085	+	1.48879i	−0.366126	+	0.0482014i
$955$	7.57140	+	15.3533i	0.245005	+	0.496821i
$956$	24.6619	−	6.60813i	0.797622	−	0.213722i
$957$	−23.1434	+	20.2962i	−0.748119	+	0.656083i
$958$	10.5384	+	15.7719i	0.340481	+	0.509566i
$959$	43.3461	+	39.9996i	1.39972	+	1.29165i
$960$	−5.69416	+	2.35860i	−0.183778	+	0.0761235i
$961$	5.43243	−	7.07968i	0.175240	−	0.228377i
$962$	21.2882	−	24.2746i	0.686360	−	0.782643i
$963$	8.38526	−	0.549599i	0.270211	−	0.0177106i
$964$	−6.82379	−	7.78104i	−0.219779	−	0.250610i
$965$	9.86622	+	9.86622i	0.317605	+	0.317605i
$966$	−16.2793	−	1.48171i	−0.523777	−	0.0476733i
$967$	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
$969$	15.3375	−	1.35592i	0.492713	−	0.0435585i
$970$	1.30145	−	2.25417i	0.0417869	−	0.0723771i
$971$	2.25473	+	17.1264i	0.0723577	+	0.549611i	0.988778	+	0.149394i	$0.0477322\pi$
$971$	2.25473	+	17.1264i	0.0723577	+	0.549611i	−0.916420	+	0.400218i	$0.868934\pi$
$972$	−8.75900	+	13.1088i	−0.280945	+	0.420464i
$973$	−10.5931	−	11.1436i	−0.339601	−	0.357247i
$974$	29.5253	−	5.87294i	0.946051	−	0.188181i
$975$	−3.64900	−	1.79949i	−0.116861	−	0.0576297i
$976$	0.173715	+	0.152344i	0.00556050	+	0.00487642i
$977$	4.39769	−	33.4038i	0.140694	−	1.06868i	−0.764783	−	0.644287i	$-0.777154\pi$
$977$	4.39769	−	33.4038i	0.140694	−	1.06868i	0.905478	−	0.424393i	$-0.139513\pi$
$978$	−11.9529	−	9.17176i	−0.382211	−	0.293281i
$979$	−0.0844579	−	0.0167997i	−0.00269929	−	0.000536921i
$980$	−7.52908	+	4.49691i	−0.240508	+	0.143649i
$981$	0.207748	+	1.04442i	0.00663288	+	0.0333457i
$982$	−17.5190	−	4.69420i	−0.559053	−	0.149798i
$983$	8.13572	−	4.01209i	0.259489	−	0.127966i	−0.307892	−	0.951421i	$-0.599623\pi$
$983$	8.13572	−	4.01209i	0.259489	−	0.127966i	0.567381	+	0.823456i	$0.307957\pi$
$984$	26.6943	−	20.4832i	0.850982	−	0.652982i
$985$	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
$989$	−2.38040	+	36.3179i	−0.0756923	+	1.15484i
$990$	−1.36109	−	5.07964i	−0.0432581	−	0.161442i
$991$	−16.1170	+	47.4790i	−0.511972	+	1.50822i	0.316721	+	0.948519i	$0.397418\pi$
$991$	−16.1170	+	47.4790i	−0.511972	+	1.50822i	−0.828693	+	0.559703i	$0.810915\pi$
$992$	−15.8970	+	32.2360i	−0.504732	+	1.02349i
$993$	7.12486	−	35.8191i	0.226101	−	1.13668i
$994$	6.49161	−	8.03060i	0.205901	−	0.254715i
$995$	−0.992183	−	2.39534i	−0.0314543	−	0.0759374i
$996$	−7.58909	+	2.57615i	−0.240470	+	0.0816284i
$997$	3.18903	+	48.6552i	0.100998	+	1.54093i	0.684619	+	0.728901i	$0.259968\pi$
$997$	3.18903	+	48.6552i	0.100998	+	1.54093i	−0.583622	+	0.812026i	$0.698365\pi$
$998$	15.9116	+	5.40127i	0.503673	+	0.170974i
$999$	−17.1941	+	64.1691i	−0.543996	+	2.03022i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.co.a.61.17	✓	768	7.5	odd	6	inner
595.2.co.a.131.32	yes	768	119.12	even	48	inner
595.2.co.a.486.32	yes	768	1.1	even	1	trivial
595.2.co.a.556.17	yes	768	17.12	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(0.856996 - 0.112826i) q^{2} +(0.571890 + 1.15968i) q^{3} +(-1.21014 + 0.324256i) q^{4} +(-0.751840 + 0.659346i) q^{5} +(0.620949 + 0.929316i) q^{6} +(-0.581687 + 2.58102i) q^{7} +(-2.59769 + 1.07600i) q^{8} +(0.808489 - 1.05364i) q^{9} +(-0.569933 + 0.649884i) q^{10} +(-4.57110 + 0.299606i) q^{11} +(-1.06810 - 1.21793i) q^{12} +(-2.22495 - 2.22495i) q^{13} +(-0.207299 + 2.27755i) q^{14} +(-1.19460 - 0.494819i) q^{15} +(0.0651537 - 0.0376165i) q^{16} +(-3.61664 - 1.97988i) q^{17} +(0.573994 - 0.994186i) q^{18} +(0.376975 + 2.86341i) q^{19} +(0.696034 - 1.04169i) q^{20} +(-3.32581 + 0.801487i) q^{21} +(-3.88362 + 0.772499i) q^{22} +(4.95782 + 2.44493i) q^{23} +(-2.73340 - 2.39713i) q^{24} +(0.130526 - 0.991445i) q^{25} +(-2.15781 - 1.65575i) q^{26} +(5.48879 + 1.09179i) q^{27} +(-0.132987 - 3.31200i) q^{28} +(-1.01386 - 5.09702i) q^{29} +(-1.07960 - 0.289277i) q^{30} +(-5.66691 + 2.79461i) q^{31} +(4.51296 - 3.46292i) 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} +(-0.776387 + 11.8454i) q^{37} +(0.646132 + 2.41140i) q^{38} +(1.30780 - 3.85266i) q^{39} +(1.24359 - 2.52175i) q^{40} +(-1.80555 + 9.07710i) q^{41} +(-2.75978 + 1.06211i) q^{42} +(2.51959 + 6.08284i) q^{43} +(5.43452 - 1.84477i) q^{44} +(0.0868611 + 1.32524i) q^{45} +(4.52468 + 1.53592i) q^{46} +(-2.43434 + 9.08508i) q^{47} +(0.0808838 + 0.0540449i) q^{48} +(-6.32328 - 3.00269i) q^{49} -0.864391i q^{50} +(0.227702 - 5.32641i) q^{51} +(3.41396 + 1.97105i) q^{52} +(-6.04848 - 7.88253i) q^{53} +(4.82706 + 0.316382i) q^{54} +(3.23919 - 3.23919i) q^{55} +(-1.26612 - 7.33056i) q^{56} +(-3.10505 + 2.07473i) q^{57} +(-1.44395 - 4.25374i) q^{58} +(9.54682 + 1.25686i) q^{59} +(1.60608 + 0.211444i) q^{60} +(0.987197 + 2.90819i) q^{61} +(-4.54122 + 3.03434i) q^{62} +(2.24918 + 2.69961i) q^{63} +(3.37049 - 3.37049i) q^{64} +(3.13982 + 0.205795i) q^{65} +(-3.11685 - 4.06196i) q^{66} +(-3.91238 - 2.25881i) q^{67} +(5.01862 + 1.22321i) q^{68} +7.14771i q^{69} +(-1.34584 - 1.84903i) q^{70} +(-3.75431 - 2.50855i) q^{71} +(-0.966483 + 3.60696i) q^{72} +(9.76723 + 3.31553i) q^{73} +(0.671102 + 10.2390i) q^{74} +(1.22440 - 0.415629i) q^{75} +(-1.38467 - 3.34289i) q^{76} +(1.88566 - 11.9724i) q^{77} +(0.686102 - 3.44927i) q^{78} +(2.47361 - 5.01598i) q^{79} +(-0.0241829 + 0.0712404i) q^{80} +(0.841659 + 3.14111i) q^{81} +(-0.523217 + 7.98275i) 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} +(5.33109 - 4.09069i) q^{87} +(11.5519 - 5.69678i) q^{88} +(0.0181576 + 0.00486531i) q^{89} +(0.223961 + 1.12593i) q^{90} +(7.03687 - 4.44841i) q^{91} +(-6.79243 - 1.35110i) q^{92} +(-6.48170 - 4.97358i) q^{93} +(-1.06119 + 8.06054i) q^{94} +(-2.17140 - 1.90427i) q^{95} +(6.59679 + 3.25318i) q^{96} +(-2.95338 + 0.587464i) q^{97} +(-5.75781 - 1.85986i) 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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