LMFDB - Embedded newform 230.2.l.a.113.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			113.3
Character	$\chi$	$=$	230.113
Dual form			230.2.l.a.57.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977147 + 0.212565i) q^{2} +(-0.470115 + 0.628000i) q^{3} +(0.909632 - 0.415415i) q^{4} +(-2.05891 - 0.872279i) q^{5} +(0.325880 - 0.713578i) q^{6} +(1.66889 - 0.119361i) q^{7} +(-0.800541 + 0.599278i) q^{8} +(0.671822 + 2.28802i) q^{9} +(2.19728 + 0.414691i) q^{10} +(2.43931 + 3.79564i) q^{11} +(-0.166751 + 0.766541i) q^{12} +(-0.120967 + 1.69134i) q^{13} +(-1.60538 + 0.471382i) q^{14} +(1.51572 - 0.882927i) q^{15} +(0.654861 - 0.755750i) q^{16} +(-3.59932 + 1.34248i) q^{17} +(-1.14282 - 2.09292i) q^{18} +(1.30471 + 2.85692i) q^{19} +(-2.23521 + 0.0618513i) q^{20} +(-0.709611 + 1.10418i) q^{21} +(-3.19039 - 3.19039i) q^{22} +(-4.06367 + 2.54688i) q^{23} -0.784469i q^{24} +(3.47826 + 3.59190i) q^{25} +(-0.241318 - 1.67840i) q^{26} +(-3.95773 - 1.47616i) q^{27} +(1.46849 - 0.801857i) q^{28} +(8.84904 + 4.04122i) q^{29} +(-1.29340 + 1.18494i) q^{30} +(1.11608 - 7.76254i) q^{31} +(-0.479249 + 0.877679i) q^{32} +(-3.53042 - 0.252501i) q^{33} +(3.23170 - 2.07689i) q^{34} +(-3.54022 - 1.20998i) q^{35} +(1.56159 + 1.80217i) q^{36} +(10.4478 + 5.70496i) q^{37} +(-1.88217 - 2.51429i) q^{38} +(-1.00529 - 0.871092i) q^{39} +(2.17098 - 0.535566i) q^{40} +(-7.18190 - 2.10880i) q^{41} +(0.458684 - 1.22978i) q^{42} +(-4.03876 - 3.02338i) q^{43} +(3.79564 + 2.43931i) q^{44} +(0.612563 - 5.29684i) q^{45} +(3.42943 - 3.35247i) q^{46} +(2.25984 - 2.25984i) q^{47} +(0.166751 + 0.766541i) q^{48} +(-4.15780 + 0.597802i) q^{49} +(-4.16228 - 2.77045i) q^{50} +(0.849018 - 2.89149i) q^{51} +(0.592573 + 1.58875i) q^{52} +(-0.324238 - 4.53344i) q^{53} +(4.18106 + 0.601146i) q^{54} +(-1.71148 - 9.94267i) q^{55} +(-1.26448 + 1.09568i) q^{56} +(-2.40751 - 0.523721i) q^{57} +(-9.50584 - 2.06787i) q^{58} +(5.22049 - 4.52358i) q^{59} +(1.01196 - 1.43279i) q^{60} +(3.12421 + 0.449194i) q^{61} +(0.559468 + 7.82238i) q^{62} +(1.39430 + 3.73825i) q^{63} +(0.281733 - 0.959493i) q^{64} +(1.72438 - 3.37681i) q^{65} +(3.50341 - 0.503715i) q^{66} +(-0.130846 - 0.601491i) q^{67} +(-2.71637 + 2.71637i) q^{68} +(0.310953 - 3.74931i) q^{69} +(3.71651 + 0.429803i) q^{70} +(-9.57147 - 6.15121i) q^{71} +(-1.90898 - 1.42904i) q^{72} +(1.45235 - 3.89390i) q^{73} +(-11.4218 - 3.35373i) q^{74} +(-3.89089 + 0.495743i) q^{75} +(2.37361 + 2.05675i) q^{76} +(4.52400 + 6.04335i) q^{77} +(1.16748 + 0.637494i) q^{78} +(-1.72151 - 1.98673i) q^{79} +(-2.00753 + 0.984803i) q^{80} +(-3.23057 + 2.07616i) q^{81} +(7.46603 + 0.533981i) q^{82} +(2.12453 - 3.89079i) q^{83} +(-0.186793 + 1.29918i) q^{84} +(8.58170 + 0.375565i) q^{85} +(4.58913 + 2.09579i) q^{86} +(-6.69795 + 3.65736i) q^{87} +(-4.22742 - 1.57674i) q^{88} +(1.31973 + 9.17890i) q^{89} +(0.527361 + 5.30600i) q^{90} +2.83710i q^{91} +(-2.63843 + 4.00483i) q^{92} +(4.35019 + 4.35019i) q^{93} +(-1.72783 + 2.68855i) q^{94} +(-0.194259 - 7.02022i) q^{95} +(-0.325880 - 0.713578i) q^{96} +(0.636402 + 1.16548i) q^{97} +(3.93571 - 1.46795i) q^{98} +(-7.04571 + 8.13118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{22}\right)$

Coefficient data

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

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

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

$2$	−0.977147	+	0.212565i	−0.690947	+	0.150306i
$2$	−0.977147	+	0.212565i	−0.690947	+	0.150306i
$3$	−0.470115	+	0.628000i	−0.271421	+	0.362576i	−0.915455	−	0.402421i	$-0.868169\pi$
$3$	−0.470115	+	0.628000i	−0.271421	+	0.362576i	0.644034	+	0.764997i	$0.277260\pi$
$4$	0.909632	−	0.415415i	0.454816	−	0.207708i
$5$	−2.05891	−	0.872279i	−0.920775	−	0.390095i
$5$	−2.05891	−	0.872279i	−0.920775	−	0.390095i
$6$	0.325880	−	0.713578i	0.133040	−	0.291317i
$7$	1.66889	−	0.119361i	0.630781	−	0.0451143i	0.247711	−	0.968834i	$-0.420322\pi$
$7$	1.66889	−	0.119361i	0.630781	−	0.0451143i	0.383070	+	0.923720i	$0.374867\pi$
$8$	−0.800541	+	0.599278i	−0.283034	+	0.211877i
$9$	0.671822	+	2.28802i	0.223941	+	0.762672i
$10$	2.19728	+	0.414691i	0.694840	+	0.131137i
$11$	2.43931	+	3.79564i	0.735480	+	1.14443i	0.984407	+	0.175907i	$0.0562860\pi$
$11$	2.43931	+	3.79564i	0.735480	+	1.14443i	−0.248926	+	0.968522i	$0.580078\pi$
$12$	−0.166751	+	0.766541i	−0.0481368	+	0.221281i
$13$	−0.120967	+	1.69134i	−0.0335503	+	0.469094i	0.952708	+	0.303886i	$0.0982841\pi$
$13$	−0.120967	+	1.69134i	−0.0335503	+	0.469094i	−0.986259	+	0.165208i	$0.947170\pi$
$14$	−1.60538	+	0.471382i	−0.429055	+	0.125982i
$15$	1.51572	−	0.882927i	0.391356	−	0.227971i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	−3.59932	+	1.34248i	−0.872963	+	0.325598i	−0.745709	−	0.666272i	$-0.767889\pi$
$17$	−3.59932	+	1.34248i	−0.872963	+	0.325598i	−0.127254	+	0.991870i	$0.540616\pi$
$18$	−1.14282	−	2.09292i	−0.269366	−	0.493306i
$19$	1.30471	+	2.85692i	0.299321	+	0.655421i	0.998210	−	0.0598088i	$-0.0190491\pi$
$19$	1.30471	+	2.85692i	0.299321	+	0.655421i	−0.698889	+	0.715230i	$0.746322\pi$
$20$	−2.23521	+	0.0618513i	−0.499809	+	0.0138304i
$21$	−0.709611	+	1.10418i	−0.154850	+	0.240951i
$22$	−3.19039	−	3.19039i	−0.680193	−	0.680193i
$23$	−4.06367	+	2.54688i	−0.847334	+	0.531061i
$23$	−4.06367	+	2.54688i	−0.847334	+	0.531061i
$24$		−	0.784469i		−	0.160129i
$25$	3.47826	+	3.59190i	0.695652	+	0.718379i
$26$	−0.241318	−	1.67840i	−0.0473263	−	0.329162i
$27$	−3.95773	−	1.47616i	−0.761665	−	0.284087i
$28$	1.46849	−	0.801857i	0.277519	−	0.151537i
$29$	8.84904	+	4.04122i	1.64323	+	0.750436i	0.999885	−	0.0151438i	$-0.00482061\pi$
$29$	8.84904	+	4.04122i	1.64323	+	0.750436i	0.643341	+	0.765580i	$0.277548\pi$
$30$	−1.29340	+	1.18494i	−0.236141	+	0.216339i
$31$	1.11608	−	7.76254i	0.200455	−	1.39419i	−0.602484	−	0.798131i	$-0.705822\pi$
$31$	1.11608	−	7.76254i	0.200455	−	1.39419i	0.802938	−	0.596062i	$-0.203269\pi$
$32$	−0.479249	+	0.877679i	−0.0847201	+	0.155153i
$33$	−3.53042	−	0.252501i	−0.614567	−	0.0439547i
$34$	3.23170	−	2.07689i	0.554232	−	0.356183i
$35$	−3.54022	−	1.20998i	−0.598406	−	0.204524i
$36$	1.56159	+	1.80217i	0.260264	+	0.300361i
$37$	10.4478	+	5.70496i	1.71762	+	0.937889i	0.957654	+	0.287921i	$0.0929641\pi$
$37$	10.4478	+	5.70496i	1.71762	+	0.937889i	0.759962	+	0.649968i	$0.225218\pi$
$38$	−1.88217	−	2.51429i	−0.305329	−	0.407872i
$39$	−1.00529	−	0.871092i	−0.160976	−	0.139486i
$40$	2.17098	−	0.535566i	0.343263	−	0.0846805i
$41$	−7.18190	−	2.10880i	−1.12162	−	0.329339i	−0.332214	−	0.943204i	$-0.607796\pi$
$41$	−7.18190	−	2.10880i	−1.12162	−	0.329339i	−0.789411	+	0.613865i	$0.789614\pi$
$42$	0.458684	−	1.22978i	0.0707765	−	0.189759i
$43$	−4.03876	−	3.02338i	−0.615906	−	0.461061i	0.245210	−	0.969470i	$-0.421143\pi$
$43$	−4.03876	−	3.02338i	−0.615906	−	0.461061i	−0.861116	+	0.508409i	$0.830234\pi$
$44$	3.79564	+	2.43931i	0.572215	+	0.367740i
$45$	0.612563	−	5.29684i	0.0913155	−	0.789607i
$46$	3.42943	−	3.35247i	0.505641	−	0.494294i
$47$	2.25984	−	2.25984i	0.329631	−	0.329631i	−0.522815	−	0.852446i	$-0.675118\pi$
$47$	2.25984	−	2.25984i	0.329631	−	0.329631i	0.852446	+	0.522815i	$0.175118\pi$
$48$	0.166751	+	0.766541i	0.0240684	+	0.110641i
$49$	−4.15780	+	0.597802i	−0.593972	+	0.0854003i
$50$	−4.16228	−	2.77045i	−0.588636	−	0.391801i
$51$	0.849018	−	2.89149i	0.118886	−	0.404889i
$52$	0.592573	+	1.58875i	0.0821751	+	0.220320i
$53$	−0.324238	−	4.53344i	−0.0445375	−	0.622715i	−0.969880	−	0.243583i	$-0.921677\pi$
$53$	−0.324238	−	4.53344i	−0.0445375	−	0.622715i	0.925343	−	0.379132i	$-0.123777\pi$
$54$	4.18106	+	0.601146i	0.568971	+	0.0818056i
$55$	−1.71148	−	9.94267i	−0.230775	−	1.34067i
$56$	−1.26448	+	1.09568i	−0.168974	+	0.146417i
$57$	−2.40751	−	0.523721i	−0.318882	−	0.0693685i
$58$	−9.50584	−	2.06787i	−1.24818	−	0.271524i
$59$	5.22049	−	4.52358i	0.679650	−	0.588921i	−0.245098	−	0.969498i	$-0.578820\pi$
$59$	5.22049	−	4.52358i	0.679650	−	0.588921i	0.924749	+	0.380578i	$0.124275\pi$
$60$	1.01196	−	1.43279i	0.130644	−	0.184972i
$61$	3.12421	+	0.449194i	0.400014	+	0.0575134i	0.339386	−	0.940647i	$-0.389781\pi$
$61$	3.12421	+	0.449194i	0.400014	+	0.0575134i	0.0606279	+	0.998160i	$0.480690\pi$
$62$	0.559468	+	7.82238i	0.0710525	+	0.993444i
$63$	1.39430	+	3.73825i	0.175665	+	0.470976i
$64$	0.281733	−	0.959493i	0.0352166	−	0.119937i
$65$	1.72438	−	3.37681i	0.213883	−	0.418842i
$66$	3.50341	−	0.503715i	0.431240	−	0.0620030i
$67$	−0.130846	−	0.601491i	−0.0159854	−	0.0734838i	0.968463	−	0.249157i	$-0.0801535\pi$
$67$	−0.130846	−	0.601491i	−0.0159854	−	0.0734838i	−0.984449	+	0.175673i	$0.943790\pi$
$68$	−2.71637	+	2.71637i	−0.329408	+	0.329408i
$69$	0.310953	−	3.74931i	0.0374344	−	0.451364i
$70$	3.71651	+	0.429803i	0.444208	+	0.0513713i
$71$	−9.57147	−	6.15121i	−1.13592	−	0.730015i	−0.169137	−	0.985593i	$-0.554098\pi$
$71$	−9.57147	−	6.15121i	−1.13592	−	0.730015i	−0.966788	+	0.255578i	$0.917734\pi$
$72$	−1.90898	−	1.42904i	−0.224975	−	0.168414i
$73$	1.45235	−	3.89390i	0.169985	−	0.455747i	−0.823825	−	0.566845i	$-0.808164\pi$
$73$	1.45235	−	3.89390i	0.169985	−	0.455747i	0.993809	+	0.111098i	$0.0354367\pi$
$74$	−11.4218	−	3.35373i	−1.32775	−	0.389863i
$75$	−3.89089	+	0.495743i	−0.449281	+	0.0572435i
$76$	2.37361	+	2.05675i	0.272272	+	0.235925i
$77$	4.52400	+	6.04335i	0.515557	+	0.688704i
$78$	1.16748	+	0.637494i	0.132191	+	0.0721820i
$79$	−1.72151	−	1.98673i	−0.193685	−	0.223524i	0.650598	−	0.759423i	$-0.274518\pi$
$79$	−1.72151	−	1.98673i	−0.193685	−	0.223524i	−0.844282	+	0.535898i	$0.819973\pi$
$80$	−2.00753	+	0.984803i	−0.224448	+	0.110104i
$81$	−3.23057	+	2.07616i	−0.358952	+	0.230684i
$82$	7.46603	+	0.533981i	0.824485	+	0.0589684i
$83$	2.12453	−	3.89079i	0.233197	−	0.427069i	−0.734708	−	0.678383i	$-0.762681\pi$
$83$	2.12453	−	3.89079i	0.233197	−	0.427069i	0.967906	+	0.251314i	$0.0808627\pi$
$84$	−0.186793	+	1.29918i	−0.0203808	+	0.141752i
$85$	8.58170	+	0.375565i	0.930817	+	0.0407357i
$86$	4.58913	+	2.09579i	0.494859	+	0.225994i
$87$	−6.69795	+	3.65736i	−0.718096	+	0.392110i
$88$	−4.22742	−	1.57674i	−0.450644	−	0.168082i
$89$	1.31973	+	9.17890i	0.139891	+	0.972962i	0.931968	+	0.362541i	$0.118091\pi$
$89$	1.31973	+	9.17890i	0.139891	+	0.972962i	−0.792077	+	0.610421i	$0.791000\pi$
$90$	0.527361	+	5.30600i	0.0555887	+	0.559302i
$91$			2.83710i			0.297409i
$92$	−2.63843	+	4.00483i	−0.275076	+	0.417532i
$93$	4.35019	+	4.35019i	0.451093	+	0.451093i
$94$	−1.72783	+	2.68855i	−0.178212	+	0.277303i
$95$	−0.194259	−	7.02022i	−0.0199305	−	0.720259i
$96$	−0.325880	−	0.713578i	−0.0332600	−	0.0728292i
$97$	0.636402	+	1.16548i	0.0646168	+	0.118337i	0.907991	−	0.418990i	$-0.137616\pi$
$97$	0.636402	+	1.16548i	0.0646168	+	0.118337i	−0.843374	+	0.537327i	$0.819434\pi$
$98$	3.93571	−	1.46795i	0.397567	−	0.148285i
$99$	−7.04571	+	8.13118i	−0.708120	+	0.817214i
$100$	4.65606	+	1.82238i	0.465606	+	0.182238i
$101$	8.36550	−	2.45633i	0.832399	−	0.244414i	0.162352	−	0.986733i	$-0.448092\pi$
$101$	8.36550	−	2.45633i	0.832399	−	0.244414i	0.670047	+	0.742319i	$0.266274\pi$
$102$	−0.214985	+	3.00588i	−0.0212867	+	0.297627i
$103$	−2.26689	+	10.4207i	−0.223363	+	1.02678i	0.719730	+	0.694254i	$0.244266\pi$
$103$	−2.26689	+	10.4207i	−0.223363	+	1.02678i	−0.943093	+	0.332530i	$0.892098\pi$
$104$	−0.916744	−	1.42648i	−0.0898942	−	0.139878i
$105$	2.42418	−	1.65443i	0.236575	−	0.161455i
$106$	1.28048	+	4.36091i	0.124371	+	0.423569i
$107$	−1.63598	+	1.22468i	−0.158156	+	0.118394i	−0.675425	−	0.737429i	$-0.736040\pi$
$107$	−1.63598	+	1.22468i	−0.158156	+	0.118394i	0.517269	+	0.855823i	$0.326949\pi$
$108$	−4.21330	+	0.301341i	−0.405425	+	0.0289965i
$109$	−7.92219	+	17.3472i	−0.758808	+	1.66156i	−0.00894881	+	0.999960i	$0.502849\pi$
$109$	−7.92219	+	17.3472i	−0.758808	+	1.66156i	−0.749859	+	0.661598i	$0.769879\pi$
$110$	3.78583	+	9.35165i	0.360965	+	0.891645i
$111$	−8.49440	+	3.87926i	−0.806253	+	0.368203i
$112$	1.00268	−	1.33943i	0.0947446	−	0.126564i
$113$	9.86869	−	2.14680i	0.928368	−	0.201954i	0.277134	−	0.960831i	$-0.410615\pi$
$113$	9.86869	−	2.14680i	0.928368	−	0.201954i	0.651234	+	0.758877i	$0.274252\pi$
$114$	2.46381			0.230757
$115$	10.5883	−	1.69915i	0.987368	−	0.158446i
$116$	9.72816			0.903237
$117$	−3.95108	+	0.859506i	−0.365278	+	0.0794613i
$118$	−4.13963	+	5.52990i	−0.381084	+	0.509069i
$119$	−5.84663	+	2.67006i	−0.535959	+	0.244764i
$120$	−0.684276	+	1.61515i	−0.0624655	+	0.147443i
$121$	−3.88711	+	8.51158i	−0.353373	+	0.773780i
$122$	−3.14830	+	0.225171i	−0.285033	+	0.0203860i
$123$	4.70064	−	3.51886i	0.423843	−	0.317285i
$124$	−2.20945	−	7.52469i	−0.198414	−	0.675737i
$125$	−4.02830	−	10.4294i	−0.360303	−	0.932836i
$126$	−2.15706	−	3.35644i	−0.192166	−	0.299016i
$127$	4.38394	−	20.1526i	0.389012	−	1.78826i	−0.199637	−	0.979870i	$-0.563976\pi$
$127$	4.38394	−	20.1526i	0.389012	−	1.78826i	0.588649	−	0.808389i	$-0.299660\pi$
$128$	−0.0713392	+	0.997452i	−0.00630555	+	0.0881631i
$129$	3.79736	−	1.11501i	0.334339	−	0.0981708i
$130$	−0.967182	+	3.66618i	−0.0848275	+	0.321546i
$131$	−0.121623	+	0.140360i	−0.0106262	+	0.0122633i	−0.761038	−	0.648708i	$-0.775310\pi$
$131$	−0.121623	+	0.140360i	−0.0106262	+	0.0122633i	0.750412	+	0.660971i	$0.229855\pi$
$132$	−3.31628	+	1.23691i	−0.288645	+	0.107659i
$133$	2.51842	+	4.61215i	0.218375	+	0.399924i
$134$	0.255712	+	0.559932i	0.0220902	+	0.0483707i
$135$	6.86101	+	6.49153i	0.590502	+	0.558702i
$136$	2.07689	−	3.23170i	0.178092	−	0.277116i
$137$	−3.24795	−	3.24795i	−0.277491	−	0.277491i	0.554616	−	0.832107i	$-0.312865\pi$
$137$	−3.24795	−	3.24795i	−0.277491	−	0.277491i	−0.832107	+	0.554616i	$0.812865\pi$
$138$	0.493126	+	3.72972i	0.0419777	+	0.317495i
$139$		−	9.49865i		−	0.805665i	−0.915274	−	0.402833i	$-0.868026\pi$
$139$		−	9.49865i		−	0.805665i	0.915274	−	0.402833i	$-0.131974\pi$
$140$	−3.72294	+	0.370021i	−0.314646	+	0.0312725i
$141$	0.356794	+	2.48156i	0.0300475	+	0.208985i
$142$	10.6603	+	3.97608i	0.894590	+	0.333665i
$143$	−6.71481	+	3.66656i	−0.561521	+	0.306613i
$144$	2.16912	+	0.990602i	0.180760	+	0.0825502i
$145$	−14.6944	−	16.0394i	−1.22030	−	1.33200i
$146$	−0.591451	+	4.11363i	−0.0489488	+	0.340447i
$147$	1.57923	−	2.89214i	0.130252	−	0.238539i
$148$	11.8736	+	0.849218i	0.976006	+	0.0698053i
$149$	1.86660	−	1.19959i	0.152918	−	0.0982742i	−0.461944	−	0.886909i	$-0.652848\pi$
$149$	1.86660	−	1.19959i	0.152918	−	0.0982742i	0.614862	+	0.788635i	$0.289212\pi$
$150$	3.69659	−	1.31148i	0.301826	−	0.107082i
$151$	−2.09332	−	2.41581i	−0.170352	−	0.196596i	0.664154	−	0.747596i	$-0.268792\pi$
$151$	−2.09332	−	2.41581i	−0.170352	−	0.196596i	−0.834505	+	0.551000i	$0.814247\pi$
$152$	−2.75656	−	1.50520i	−0.223587	−	0.122087i
$153$	−5.48971	−	7.33339i	−0.443817	−	0.592870i
$154$	−5.70522	−	4.94360i	−0.459739	−	0.398366i
$155$	−9.06902	+	15.0089i	−0.728441	+	1.20554i
$156$	−1.27631	−	0.374759i	−0.102187	−	0.0300047i
$157$	1.13973	−	3.05572i	0.0909601	−	0.243873i	−0.883501	−	0.468429i	$-0.844820\pi$
$157$	1.13973	−	3.05572i	0.0909601	−	0.243873i	0.974461	+	0.224555i	$0.0720930\pi$
$158$	2.10448	+	1.57539i	0.167423	+	0.125331i
$159$	2.99942	+	1.92761i	0.237870	+	0.152870i
$160$	1.75231	−	1.38903i	0.138533	−	0.109812i
$161$	−6.47782	+	4.73550i	−0.510524	+	0.373210i
$162$	2.71542	−	2.71542i	0.213344	−	0.213344i
$163$	2.54751	+	11.7107i	0.199537	+	0.917255i	0.962599	+	0.270930i	$0.0873313\pi$
$163$	2.54751	+	11.7107i	0.199537	+	0.917255i	−0.763062	+	0.646325i	$0.776305\pi$
$164$	−7.40892	+	1.06524i	−0.578539	+	0.0831814i
$165$	7.04858	+	3.59939i	0.548731	+	0.280212i
$166$	−1.24893	+	4.25347i	−0.0969359	+	0.330133i
$167$	7.57243	+	20.3025i	0.585972	+	1.57105i	0.803695	+	0.595042i	$0.202864\pi$
$167$	7.57243	+	20.3025i	0.585972	+	1.57105i	−0.217723	+	0.976011i	$0.569863\pi$
$168$	−0.0936353	−	1.30919i	−0.00722412	−	0.101006i
$169$	10.0217	+	1.44090i	0.770898	+	0.110838i
$170$	−8.46542	+	1.45719i	−0.649268	+	0.111761i
$171$	−5.66013	+	4.90453i	−0.432841	+	0.375059i
$172$	−4.92975	−	1.07240i	−0.375890	−	0.0817698i
$173$	−0.268806	−	0.0584752i	−0.0204370	−	0.00444579i	0.202335	−	0.979316i	$-0.435147\pi$
$173$	−0.268806	−	0.0584752i	−0.0204370	−	0.00444579i	−0.222772	+	0.974871i	$0.571511\pi$
$174$	5.76746	−	4.99753i	0.437230	−	0.378862i
$175$	6.23356	+	5.57931i	0.471213	+	0.421756i
$176$	4.46597	+	0.642109i	0.336635	+	0.0484008i
$177$	0.386578	+	5.40507i	0.0290570	+	0.406270i
$178$	−3.24068	−	8.68861i	−0.242899	−	0.651239i
$179$	5.44259	−	18.5358i	0.406799	−	1.38543i	−0.460508	−	0.887655i	$-0.652333\pi$
$179$	5.44259	−	18.5358i	0.406799	−	1.38543i	0.867307	−	0.497773i	$-0.165849\pi$
$180$	−1.64318	−	5.07265i	−0.122476	−	0.378093i
$181$	9.05817	−	1.30237i	0.673288	−	0.0968043i	0.202813	−	0.979217i	$-0.434992\pi$
$181$	9.05817	−	1.30237i	0.673288	−	0.0968043i	0.470475	+	0.882413i	$0.344082\pi$
$182$	−0.603069	−	2.77227i	−0.0447025	−	0.205494i
$183$	−1.75083	+	1.75083i	−0.129425	+	0.129425i
$184$	1.72685	−	4.47415i	0.127305	−	0.329838i
$185$	−16.5349	−	20.8595i	−1.21567	−	1.53362i
$186$	−5.17547	−	3.32607i	−0.379484	−	0.243879i
$187$	−13.8754	−	10.3870i	−1.01467	−	0.759574i
$188$	1.11685	−	2.99439i	0.0814546	−	0.218388i
$189$	−6.78121	−	1.99114i	−0.493260	−	0.144834i
$190$	1.68207	+	6.81849i	0.122030	+	0.494665i
$191$	7.08566	+	6.13976i	0.512700	+	0.444257i	0.872387	−	0.488816i	$-0.162571\pi$
$191$	7.08566	+	6.13976i	0.512700	+	0.444257i	−0.359687	+	0.933073i	$0.617116\pi$
$192$	0.470115	+	0.628000i	0.0339276	+	0.0453220i
$193$	−6.35541	−	3.47032i	−0.457473	−	0.249799i	0.233951	−	0.972248i	$-0.424834\pi$
$193$	−6.35541	−	3.47032i	−0.457473	−	0.249799i	−0.691424	+	0.722449i	$0.743016\pi$
$194$	−0.869599	−	1.00357i	−0.0624336	−	0.0720522i
$195$	1.30998	+	2.67040i	0.0938095	+	0.191231i
$196$	−3.53374	+	2.27099i	−0.252410	+	0.162214i
$197$	11.5001	+	0.822506i	0.819351	+	0.0586011i	0.474720	−	0.880137i	$-0.342549\pi$
$197$	11.5001	+	0.822506i	0.819351	+	0.0586011i	0.344631	+	0.938738i	$0.388004\pi$
$198$	5.15629	−	9.44303i	0.366441	−	0.671087i
$199$	3.02058	−	21.0086i	0.214123	−	1.48926i	−0.545067	−	0.838393i	$-0.683496\pi$
$199$	3.02058	−	21.0086i	0.214123	−	1.48926i	0.759190	−	0.650869i	$-0.225595\pi$
$200$	−4.93703	−	0.791017i	−0.349101	−	0.0559334i
$201$	0.439249	+	0.200598i	0.0309822	+	0.0141491i
$202$	−7.65219	+	4.17841i	−0.538407	+	0.293992i
$203$	15.2504	+	5.68812i	1.07037	+	0.399228i
$204$	−0.428874	−	2.98289i	−0.0300272	−	0.208844i
$205$	12.9475	+	10.6065i	0.904290	+	0.740787i
$206$		−	10.6644i		−	0.743026i
$207$	−8.55736	−	7.58669i	−0.594777	−	0.527312i
$208$	1.19901	+	1.19901i	0.0831367	+	0.0831367i
$209$	−7.66124	+	11.9211i	−0.529939	+	0.824602i
$210$	−2.01710	+	2.13191i	−0.139193	+	0.147116i
$211$	−2.79578	−	6.12191i	−0.192470	−	0.421450i	0.788652	−	0.614839i	$-0.210779\pi$
$211$	−2.79578	−	6.12191i	−0.192470	−	0.421450i	−0.981122	+	0.193390i	$0.938052\pi$
$212$	−2.17819	−	3.98906i	−0.149599	−	0.273970i
$213$	8.36265	−	3.11911i	0.572999	−	0.213718i
$214$	1.33827	−	1.54445i	0.0914823	−	0.105576i
$215$	5.67824	+	9.74781i	0.387253	+	0.664795i
$216$	4.05295	−	1.19005i	0.275769	−	0.0809730i
$217$	0.936075	−	13.0880i	0.0635449	−	0.888474i
$218$	4.05373	−	18.6347i	0.274554	−	1.26210i
$219$	1.76260	+	2.74265i	0.119105	+	0.185331i
$220$	−5.68715	−	8.33320i	−0.383427	−	0.561824i
$221$	−1.83519	−	6.25007i	−0.123448	−	0.420426i
$222$	7.47568	−	5.59622i	0.501735	−	0.375594i
$223$	15.6910	−	1.12224i	1.05075	−	0.0751510i	0.464733	−	0.885451i	$-0.346150\pi$
$223$	15.6910	−	1.12224i	1.05075	−	0.0751510i	0.586015	+	0.810300i	$0.300696\pi$
$224$	−0.695053	+	1.52195i	−0.0464402	+	0.101690i
$225$	−5.88154	+	10.3714i	−0.392103	+	0.691428i
$226$	−9.18682	+	4.19548i	−0.611098	+	0.279079i
$227$	7.21100	−	9.63276i	0.478611	−	0.639349i	−0.494639	−	0.869098i	$-0.664700\pi$
$227$	7.21100	−	9.63276i	0.478611	−	0.639349i	0.973250	+	0.229749i	$0.0737907\pi$
$228$	−2.40751	+	0.523721i	−0.159441	+	0.0346843i
$229$	−20.2031			−1.33506			−0.667529	−	0.744584i	$-0.732648\pi$
$229$	−20.2031			−1.33506			−0.667529	+	0.744584i	$0.732648\pi$
$230$	−9.98518	+	3.91103i	−0.658403	+	0.257886i
$231$	−5.92202			−0.389640
$232$	−9.50584	+	2.06787i	−0.624089	+	0.135762i
$233$	4.94885	−	6.61089i	0.324210	−	0.433094i	−0.608592	−	0.793483i	$-0.708265\pi$
$233$	4.94885	−	6.61089i	0.324210	−	0.433094i	0.932802	+	0.360389i	$0.117356\pi$
$234$	3.67809	−	1.67973i	0.240444	−	0.109807i
$235$	−6.62402	+	2.68160i	−0.432103	+	0.174928i
$236$	2.86956	−	6.28347i	0.186793	−	0.409019i
$237$	2.05697	−	0.147117i	0.133615	−	0.00955630i
$238$	5.14545	−	3.85183i	0.333530	−	0.249677i
$239$	−4.72365	−	16.0873i	−0.305548	−	1.04060i	−0.958947	−	0.283586i	$-0.908476\pi$
$239$	−4.72365	−	16.0873i	−0.305548	−	1.04060i	0.653399	−	0.757014i	$-0.273342\pi$
$240$	0.325312	−	1.72370i	0.0209988	−	0.111264i
$241$	2.40237	+	3.73816i	0.154750	+	0.240796i	0.909969	−	0.414677i	$-0.136106\pi$
$241$	2.40237	+	3.73816i	0.154750	+	0.240796i	−0.755218	+	0.655473i	$0.772469\pi$
$242$	1.98901	−	9.14332i	0.127858	−	0.587755i
$243$	1.11893	−	15.6447i	0.0717795	−	1.00361i
$244$	3.02848	−	0.889243i	0.193879	−	0.0569280i
$245$	9.08202	+	2.39594i	0.580229	+	0.153071i
$246$	−3.84523	+	4.43763i	−0.245163	+	0.282933i
$247$	−4.98985	+	1.86112i	−0.317496	+	0.118420i
$248$	3.75845	+	6.88308i	0.238662	+	0.437076i
$249$	1.44464	+	3.16332i	0.0915503	+	0.200467i
$250$	6.15318	+	9.33480i	0.389161	+	0.590384i
$251$	−8.24727	+	12.8330i	−0.520563	+	0.810012i	−0.997627	−	0.0688568i	$-0.978065\pi$
$251$	−8.24727	+	12.8330i	−0.520563	+	0.810012i	0.477063	+	0.878869i	$0.341701\pi$
$252$	2.82122	+	2.82122i	0.177720	+	0.177720i
$253$	−19.5796	−	9.21162i	−1.23096	−	0.579130i
$254$			20.6240i			1.29406i
$255$	−4.27024	+	5.21275i	−0.267413	+	0.326435i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	18.2506	+	6.80711i	1.13844	+	0.424616i	0.846799	−	0.531913i	$-0.178527\pi$
$257$	18.2506	+	6.80711i	1.13844	+	0.424616i	0.291639	+	0.956528i	$0.405799\pi$
$258$	−3.47357	+	1.89671i	−0.216255	+	0.118084i
$259$	18.1173	+	8.27387i	1.12575	+	0.514113i
$260$	0.165776	−	3.78799i	0.0102810	−	0.234921i
$261$	−3.30140	+	22.9617i	−0.204351	+	1.42130i
$262$	0.0890076	−	0.163005i	0.00549890	−	0.0100705i
$263$	24.0296	+	1.71863i	1.48173	+	0.105975i	0.788630	−	0.614868i	$-0.210791\pi$
$263$	24.0296	+	1.71863i	1.48173	+	0.105975i	0.693098	+	0.720843i	$0.256245\pi$
$264$	2.97757	−	1.91356i	0.183256	−	0.117772i
$265$	−3.28684	+	9.61678i	−0.201909	+	0.590754i
$266$	−3.44125	−	3.97141i	−0.210997	−	0.243503i
$267$	−6.38477	−	3.48635i	−0.390742	−	0.213361i
$268$	−0.368890	−	0.492780i	−0.0225336	−	0.0301013i
$269$	−17.7119	−	15.3475i	−1.07992	−	0.935752i	−0.0817712	−	0.996651i	$-0.526058\pi$
$269$	−17.7119	−	15.3475i	−1.07992	−	0.935752i	−0.998144	+	0.0608994i	$0.980603\pi$
$270$	−8.08409	−	4.88476i	−0.491982	−	0.297277i
$271$	−0.266320	−	0.0781986i	−0.0161778	−	0.00475023i	0.273634	−	0.961834i	$-0.411774\pi$
$271$	−0.266320	−	0.0781986i	−0.0161778	−	0.00475023i	−0.289811	+	0.957084i	$0.593593\pi$
$272$	−1.34248	+	3.59932i	−0.0813996	+	0.218241i
$273$	−1.78170	−	1.33376i	−0.107833	−	0.0807230i
$274$	3.86413	+	2.48332i	0.233440	+	0.150023i
$275$	−5.14900	+	21.9640i	−0.310496	+	1.32448i
$276$	−1.27467	−	3.53967i	−0.0767259	−	0.213063i
$277$	−7.37648	+	7.37648i	−0.443210	+	0.443210i	−0.893089	−	0.449880i	$-0.851467\pi$
$277$	−7.37648	+	7.37648i	−0.443210	+	0.443210i	0.449880	+	0.893089i	$0.351467\pi$
$278$	2.01908	+	9.28158i	0.121097	+	0.556672i
$279$	18.5106	−	2.66143i	1.10820	−	0.159335i
$280$	3.55921	−	1.15293i	0.212703	−	0.0689009i
$281$	3.55550	−	12.1089i	0.212104	−	0.722358i	−0.782867	−	0.622189i	$-0.786243\pi$
$281$	3.55550	−	12.1089i	0.212104	−	0.722358i	0.994970	−	0.100169i	$-0.0319384\pi$
$282$	−0.876134	−	2.34901i	−0.0521730	−	0.139881i
$283$	0.157391	+	2.20061i	0.00935592	+	0.130813i	0.999983	−	0.00577920i	$-0.00183959\pi$
$283$	0.157391	+	2.20061i	0.00935592	+	0.130813i	−0.990627	+	0.136592i	$0.956385\pi$
$284$	−11.2618	−	1.61921i	−0.668266	−	0.0960822i
$285$	4.50002	+	3.17831i	0.266558	+	0.188267i
$286$	5.78197	−	5.01011i	0.341895	−	0.296254i
$287$	−12.2375	−	2.66211i	−0.722358	−	0.157139i
$288$	−2.33011	−	0.506885i	−0.137303	−	0.0298685i
$289$	−1.69489	+	1.46863i	−0.0996994	+	0.0863900i
$290$	17.7680	+	12.5493i	1.04337	+	0.736921i
$291$	−1.03110	−	0.148251i	−0.0604444	−	0.00869060i
$292$	−0.296481	−	4.14534i	−0.0173502	−	0.242588i
$293$	9.68400	+	25.9638i	0.565745	+	1.51682i	0.833043	+	0.553208i	$0.186596\pi$
$293$	9.68400	+	25.9638i	0.565745	+	1.51682i	−0.267298	+	0.963614i	$0.586131\pi$
$294$	−0.928368	+	3.16173i	−0.0541435	+	0.184396i
$295$	−14.6944	+	4.75995i	−0.855540	+	0.277135i
$296$	−11.7828	+	1.69411i	−0.684861	+	0.0984681i
$297$	−4.05117	−	18.6229i	−0.235073	−	1.08061i
$298$	−1.56895	+	1.56895i	−0.0908868	+	0.0908868i
$299$	−3.81607	−	7.18114i	−0.220689	−	0.415296i
$300$	−3.33334	+	2.06728i	−0.192450	+	0.119354i
$301$	−7.10112	−	4.56361i	−0.409302	−	0.263042i
$302$	2.55900	+	1.91564i	0.147254	+	0.110233i
$303$	−2.39017	+	6.40829i	−0.137312	+	0.368147i
$304$	3.01352	+	0.884848i	0.172837	+	0.0507495i
$305$	−6.04066	−	3.65003i	−0.345887	−	0.209000i
$306$	6.92308	+	5.99888i	0.395766	+	0.342933i
$307$	19.1334	+	25.5592i	1.09200	+	1.45874i	0.875976	+	0.482355i	$0.160218\pi$
$307$	19.1334	+	25.5592i	1.09200	+	1.45874i	0.216025	+	0.976388i	$0.430691\pi$
$308$	6.62567	+	3.61789i	0.377533	+	0.206148i
$309$	−5.47851	−	6.32254i	−0.311662	−	0.359677i
$310$	5.67140	−	16.5936i	0.322114	−	0.942455i
$311$	15.9063	−	10.2223i	0.901961	−	0.579655i	−0.00541011	−	0.999985i	$-0.501722\pi$
$311$	15.9063	−	10.2223i	0.901961	−	0.579655i	0.907371	+	0.420330i	$0.138086\pi$
$312$	1.32681	+	0.0948950i	0.0751155	+	0.00537237i
$313$	−8.07010	+	14.7793i	−0.456149	+	0.835374i	−0.999993	−	0.00381211i	$-0.998787\pi$
$313$	−8.07010	+	14.7793i	−0.456149	+	0.835374i	0.543844	+	0.839186i	$0.316968\pi$
$314$	−0.464139	+	3.22816i	−0.0261929	+	0.182175i
$315$	0.390062	−	8.91296i	0.0219775	−	0.502189i
$316$	−2.39125	−	1.09205i	−0.134519	−	0.0614326i
$317$	15.3648	−	8.38984i	0.862976	−	0.471220i	0.0141542	−	0.999900i	$-0.495494\pi$
$317$	15.3648	−	8.38984i	0.862976	−	0.471220i	0.848822	+	0.528679i	$0.177313\pi$
$318$	−3.34062	−	1.24599i	−0.187333	−	0.0698715i
$319$	6.24654	+	43.4456i	0.349739	+	2.43249i
$320$	−1.41701	+	1.72976i	−0.0792132	+	0.0966968i
$321$		−	1.60314i		−	0.0894784i
$322$	5.32318	−	6.00424i	0.296649	−	0.334603i
$323$	−8.53141	−	8.53141i	−0.474700	−	0.474700i
$324$	−2.07616	+	3.23057i	−0.115342	+	0.179476i
$325$	−6.49588	+	5.44842i	−0.360327	+	0.302224i
$326$	−4.97859	−	10.9016i	−0.275739	−	0.603783i
$327$	−7.16968	−	13.1303i	−0.396484	−	0.726107i
$328$	7.01317	−	2.61578i	0.387237	−	0.144432i
$329$	3.50168	−	4.04115i	0.193054	−	0.222796i
$330$	−7.65261	−	2.01885i	−0.421262	−	0.111134i
$331$	−21.3950	+	6.28213i	−1.17597	+	0.345297i	−0.810621	−	0.585571i	$-0.800870\pi$
$331$	−21.3950	+	6.28213i	−1.17597	+	0.345297i	−0.365354	+	0.930869i	$0.619052\pi$
$332$	0.316249	−	4.42175i	0.0173564	−	0.242675i
$333$	−6.03393	+	27.7376i	−0.330658	+	1.52001i
$334$	−11.7150	−	18.2289i	−0.641015	−	0.997439i
$335$	−0.255266	+	1.35255i	−0.0139467	+	0.0738979i
$336$	0.369784	+	1.25937i	0.0201734	+	0.0687042i
$337$	3.98316	−	2.98176i	0.216976	−	0.162427i	−0.485261	−	0.874369i	$-0.661275\pi$
$337$	3.98316	−	2.98176i	0.216976	−	0.162427i	0.702237	+	0.711943i	$0.252184\pi$
$338$	−10.0989	+	0.722290i	−0.549310	+	0.0392874i
$339$	−3.29122	+	7.20677i	−0.178755	+	0.391418i
$340$	7.96221	−	3.22334i	0.431811	−	0.174810i
$341$	32.1863	−	14.6990i	1.74299	−	0.795996i
$342$	4.48825	−	5.99560i	0.242697	−	0.324205i
$343$	−18.3120	+	3.98353i	−0.988754	+	0.215090i
$344$	5.04504			0.272010
$345$	−3.91067	+	7.44827i	−0.210543	+	0.401001i
$346$	0.275093			0.0147891
$347$	−5.81944	+	1.26594i	−0.312404	+	0.0679593i	−0.366034	−	0.930602i	$-0.619285\pi$
$347$	−5.81944	+	1.26594i	−0.312404	+	0.0679593i	0.0536298	+	0.998561i	$0.482921\pi$
$348$	−4.57335	+	6.10928i	−0.245157	+	0.327492i
$349$	−10.9758	+	5.01247i	−0.587520	+	0.268311i	−0.686916	−	0.726737i	$-0.741036\pi$
$349$	−10.9758	+	5.01247i	−0.587520	+	0.268311i	0.0993965	+	0.995048i	$0.468309\pi$
$350$	−7.27707	−	4.12676i	−0.388976	−	0.220585i
$351$	2.97544	−	6.51531i	0.158817	−	0.347761i
$352$	−4.50040	+	0.321875i	−0.239872	+	0.0171560i
$353$	27.0688	−	20.2635i	1.44073	−	1.07852i	0.458955	−	0.888460i	$-0.348224\pi$
$353$	27.0688	−	20.2635i	1.44073	−	1.07852i	0.981773	−	0.190056i	$-0.0608669\pi$
$354$	−1.52667	−	5.19938i	−0.0811418	−	0.276344i
$355$	14.3413	+	21.0138i	0.761156	+	1.11530i
$356$	5.01352	+	7.80119i	0.265716	+	0.413462i
$357$	1.07178	−	4.92692i	0.0567249	−	0.260760i
$358$	−1.37815	+	19.2691i	−0.0728376	+	1.01840i
$359$	28.0862	−	8.24684i	1.48233	−	0.435252i	0.562246	−	0.826970i	$-0.309938\pi$
$359$	28.0862	−	8.24684i	1.48233	−	0.435252i	0.920085	+	0.391719i	$0.128119\pi$
$360$	2.68390	+	4.60744i	0.141454	+	0.242833i
$361$	5.98265	−	6.90435i	0.314876	−	0.363387i
$362$	−8.57432	+	3.19806i	−0.450656	+	0.168086i
$363$	−3.51788	−	6.44252i	−0.184641	−	0.338145i
$364$	1.17857	+	2.58072i	0.0617741	+	0.135266i
$365$	−6.38683	+	6.75035i	−0.334302	+	0.353330i
$366$	1.33865	−	2.08298i	0.0699725	−	0.108879i
$367$	−19.4435	−	19.4435i	−1.01494	−	1.01494i	−0.999887	−	0.0150536i	$-0.995208\pi$
$367$	−19.4435	−	19.4435i	−1.01494	−	1.01494i	−0.0150536	−	0.999887i	$-0.504792\pi$
$368$	−0.736337	+	4.73897i	−0.0383842	+	0.247036i
$369$		−	17.8490i		−	0.929184i
$370$	20.5910	+	16.8680i	1.07048	+	0.876926i
$371$	−1.08223	−	7.52710i	−0.0561868	−	0.390788i
$372$	5.76420	+	2.14994i	0.298860	+	0.111469i
$373$	16.6447	−	9.08869i	0.861830	−	0.470595i	0.0134046	−	0.999910i	$-0.495733\pi$
$373$	16.6447	−	9.08869i	0.861830	−	0.470595i	0.848425	+	0.529316i	$0.177551\pi$
$374$	15.7663	+	7.20021i	0.815253	+	0.372314i
$375$	8.44344	+	2.37325i	0.436017	+	0.122554i
$376$	−0.454823	+	3.16336i	−0.0234557	+	0.163138i
$377$	−7.90553	+	14.4779i	−0.407156	+	0.745650i
$378$	7.04949	+	0.504189i	0.362586	+	0.0259327i
$379$	−11.1942	+	7.19405i	−0.575005	+	0.369533i	−0.795591	−	0.605834i	$-0.792839\pi$
$379$	−11.1942	+	7.19405i	−0.575005	+	0.369533i	0.220586	+	0.975368i	$0.429203\pi$
$380$	−3.09301	−	6.30512i	−0.158668	−	0.323446i
$381$	10.5949	+	12.2272i	0.542793	+	0.626417i
$382$	−8.22883	−	4.49328i	−0.421024	−	0.229896i
$383$	−5.70336	−	7.61880i	−0.291428	−	0.389303i	0.630802	−	0.775944i	$-0.282726\pi$
$383$	−5.70336	−	7.61880i	−0.291428	−	0.389303i	−0.922230	+	0.386641i	$0.873635\pi$
$384$	−0.592862	−	0.513718i	−0.0302544	−	0.0262156i
$385$	−4.04304	−	16.3889i	−0.206052	−	0.835257i
$386$	6.94784	+	2.04007i	0.353636	+	0.103837i
$387$	4.20421	−	11.2719i	0.213712	−	0.572984i
$388$	1.06305	+	0.795790i	0.0539682	+	0.0404001i
$389$	−18.0660	−	11.6103i	−0.915984	−	0.588667i	−0.00449402	−	0.999990i	$-0.501430\pi$
$389$	−18.0660	−	11.6103i	−0.915984	−	0.588667i	−0.911490	+	0.411323i	$0.865067\pi$
$390$	−1.84768	−	2.33092i	−0.0935607	−	0.118031i
$391$	11.2073	−	14.6224i	0.566779	−	0.739487i
$392$	2.97024	−	2.97024i	0.150020	−	0.150020i
$393$	−0.0309695	−	0.142364i	−0.00156220	−	0.00718133i
$394$	−11.4122	+	1.64082i	−0.574936	+	0.0826633i
$395$	1.81146	+	5.59214i	0.0911444	+	0.281371i
$396$	−3.03119	+	10.3233i	−0.152323	+	0.518764i
$397$	−6.75459	−	18.1098i	−0.339003	−	0.908903i	−0.988860	−	0.148847i	$-0.952444\pi$
$397$	−6.75459	−	18.1098i	−0.339003	−	0.908903i	0.649857	−	0.760057i	$-0.274829\pi$
$398$	1.51415	+	21.1706i	0.0758975	+	1.06119i
$399$	−4.08037	−	0.586669i	−0.204274	−	0.0293702i
$400$	4.99235	−	0.276502i	0.249617	−	0.0138251i
$401$	−26.8260	+	23.2449i	−1.33963	+	1.16079i	−0.366527	+	0.930407i	$0.619453\pi$
$401$	−26.8260	+	23.2449i	−1.33963	+	1.16079i	−0.973099	+	0.230386i	$0.926001\pi$
$402$	−0.471851	−	0.102645i	−0.0235338	−	0.00511946i
$403$	12.9941	+	2.82669i	0.647282	+	0.140808i
$404$	6.58913	−	5.70952i	0.327822	−	0.284059i
$405$	8.46245	−	1.45668i	0.420503	−	0.0723830i
$406$	−16.1110	−	2.31641i	−0.799576	−	0.114962i
$407$	3.83158	+	53.5725i	0.189924	+	2.65549i
$408$	1.05313	+	2.82355i	0.0521378	+	0.139787i
$409$	−7.10271	+	24.1896i	−0.351207	+	1.19610i	0.574705	+	0.818360i	$0.305117\pi$
$409$	−7.10271	+	24.1896i	−0.351207	+	1.19610i	−0.925912	+	0.377739i	$0.876702\pi$
$410$	−14.9061	−	7.61188i	−0.736162	−	0.375924i
$411$	3.56662	−	0.512803i	0.175928	−	0.0252947i
$412$	2.26689	+	10.4207i	0.111682	+	0.513392i
$413$	8.17249	−	8.17249i	0.402142	−	0.402142i
$414$	9.97446	+	5.59432i	0.490218	+	0.274946i
$415$	−7.76808	+	6.15761i	−0.381320	+	0.302265i
$416$	−1.42648	−	0.916744i	−0.0699390	−	0.0449471i
$417$	5.96515	+	4.46546i	0.292115	+	0.218674i
$418$	4.95214	−	13.2772i	0.242217	−	0.649409i
$419$	−1.91896	−	0.563457i	−0.0937472	−	0.0275267i	0.234523	−	0.972111i	$-0.424647\pi$
$419$	−1.91896	−	0.563457i	−0.0937472	−	0.0275267i	−0.328270	+	0.944584i	$0.606466\pi$
$420$	1.51784	−	2.51196i	0.0740628	−	0.122571i
$421$	7.26443	+	6.29466i	0.354046	+	0.306783i	0.813666	−	0.581333i	$-0.197469\pi$
$421$	7.26443	+	6.29466i	0.354046	+	0.306783i	−0.459619	+	0.888116i	$0.652014\pi$
$422$	4.03319	+	5.38772i	0.196333	+	0.262270i
$423$	6.68875	+	3.65233i	0.325218	+	0.177582i
$424$	2.97635	+	3.43489i	0.144544	+	0.166813i
$425$	−17.3414	−	8.25890i	−0.841181	−	0.400615i
$426$	−7.50852	+	4.82544i	−0.363789	+	0.233793i
$427$	5.26758	+	0.376745i	0.254916	+	0.0182320i
$428$	−0.979391	+	1.79362i	−0.0473406	+	0.0866979i
$429$	0.854130	−	5.94060i	0.0412378	−	0.286815i
$430$	−7.62052	−	8.31804i	−0.367494	−	0.401132i
$431$	6.40337	+	2.92432i	0.308440	+	0.140860i	0.563621	−	0.826034i	$-0.309408\pi$
$431$	6.40337	+	2.92432i	0.308440	+	0.140860i	−0.255181	+	0.966893i	$0.582135\pi$
$432$	−3.70737	+	2.02438i	−0.178371	+	0.0973978i
$433$	−32.3563	−	12.0683i	−1.55494	−	0.579964i	−0.582444	−	0.812871i	$-0.697904\pi$
$433$	−32.3563	−	12.0683i	−1.55494	−	0.579964i	−0.972499	+	0.232907i	$0.925176\pi$
$434$	1.86738	+	12.9879i	0.0896371	+	0.623440i
$435$	16.9807	−	1.68771i	0.814165	−	0.0809194i
$436$			19.0705i			0.913313i
$437$	−12.5781	−	8.28663i	−0.601693	−	0.396403i
$438$	−2.30531	−	2.30531i	−0.110152	−	0.110152i
$439$	10.0531	−	15.6429i	0.479809	−	0.746597i	−0.513989	−	0.857797i	$-0.671833\pi$
$439$	10.0531	−	15.6429i	0.479809	−	0.746597i	0.993798	+	0.111199i	$0.0354693\pi$
$440$	7.32853	+	6.93387i	0.349374	+	0.330559i
$441$	−4.16108	−	9.11150i	−0.198147	−	0.433881i
$442$	3.12180	+	5.71714i	0.148489	+	0.271937i
$443$	−15.5882	+	5.81411i	−0.740620	+	0.276237i	−0.691322	−	0.722547i	$-0.742971\pi$
$443$	−15.5882	+	5.81411i	−0.740620	+	0.276237i	−0.0492981	+	0.998784i	$0.515698\pi$
$444$	−6.11527	+	7.05740i	−0.290218	+	0.334929i
$445$	5.28936	−	20.0497i	0.250740	−	0.950449i
$446$	−15.0939	+	4.43196i	−0.714716	+	0.209859i
$447$	−0.124173	+	1.73617i	−0.00587319	+	0.0821179i
$448$	0.355654	−	1.63492i	0.0168031	−	0.0772425i
$449$	−12.0243	−	18.7101i	−0.567460	−	0.882985i	0.432365	−	0.901699i	$-0.357679\pi$
$449$	−12.0243	−	18.7101i	−0.567460	−	0.882985i	−0.999825	+	0.0187139i	$0.994043\pi$
$450$	3.54252	−	11.3846i	0.166996	−	0.536676i
$451$	−9.51466	−	32.4040i	−0.448028	−	1.52584i
$452$	8.08506	−	6.05240i	0.380289	−	0.284681i
$453$	2.50123	−	0.178891i	0.117518	−	0.00840505i
$454$	−4.99861	+	10.9454i	−0.234596	+	0.513695i
$455$	2.47474	−	5.84135i	0.116018	−	0.273847i
$456$	2.24116	−	1.02350i	0.104952	−	0.0479300i
$457$	−17.0202	+	22.7364i	−0.796173	+	1.06356i	0.200307	+	0.979733i	$0.435806\pi$
$457$	−17.0202	+	22.7364i	−0.796173	+	1.06356i	−0.996480	+	0.0838296i	$0.973285\pi$
$458$	19.7414	−	4.29448i	0.922455	−	0.200668i
$459$	16.2268			0.757404
$460$	8.92564	−	5.94415i	0.416160	−	0.277148i
$461$	32.3699			1.50761			0.753807	−	0.657095i	$-0.228215\pi$
$461$	32.3699			1.50761			0.753807	+	0.657095i	$0.228215\pi$
$462$	5.78668	−	1.25882i	0.269221	−	0.0585654i
$463$	−8.18793	+	10.9378i	−0.380526	+	0.508323i	−0.949386	−	0.314111i	$-0.898293\pi$
$463$	−8.18793	+	10.9378i	−0.380526	+	0.508323i	0.568861	+	0.822434i	$0.307384\pi$
$464$	8.84904	−	4.04122i	0.410807	−	0.187609i
$465$	−5.16209	−	12.7512i	−0.239386	−	0.591324i
$466$	−3.43051	+	7.51177i	−0.158915	+	0.347976i
$467$	−4.15491	+	0.297165i	−0.192266	+	0.0137511i	−0.167140	−	0.985933i	$-0.553453\pi$
$467$	−4.15491	+	0.297165i	−0.192266	+	0.0137511i	−0.0251260	+	0.999684i	$0.507999\pi$
$468$	−3.23698	+	2.42317i	−0.149630	+	0.112011i
$469$	−0.290163	−	0.988204i	−0.0133985	−	0.0456310i
$470$	5.90262	−	4.02836i	0.272268	−	0.185814i
$471$	1.38319	+	2.15229i	0.0637341	+	0.0991722i
$472$	−1.46834	+	6.74984i	−0.0675857	+	0.310687i
$473$	1.62387	−	22.7047i	0.0746656	−	1.04396i
$474$	−1.97869	+	0.580996i	−0.0908842	+	0.0266860i
$475$	−5.72362	+	14.6235i	−0.262618	+	0.670971i
$476$	−4.20909	+	4.85755i	−0.192923	+	0.222646i
$477$	10.1547	−	3.78752i	0.464954	−	0.173419i
$478$	8.03530	+	14.7156i	0.367526	+	0.673074i
$479$	3.31968	+	7.26909i	0.151680	+	0.332133i	0.970185	−	0.242367i	$-0.0779238\pi$
$479$	3.31968	+	7.26909i	0.151680	+	0.332133i	−0.818505	+	0.574500i	$0.805197\pi$
$480$	0.0485205	+	1.75345i	0.00221465	+	0.0800339i
$481$	−10.9129	+	16.9808i	−0.497584	+	0.774257i
$482$	−3.14207	−	3.14207i	−0.143117	−	0.143117i
$483$	0.0714242	−	6.29430i	0.00324991	−	0.286400i
$484$			9.35716i			0.425326i
$485$	−0.293671	−	2.95475i	−0.0133349	−	0.134168i
$486$	2.23216	+	15.5250i	0.101253	+	0.704230i
$487$	11.4315	+	4.26373i	0.518011	+	0.193208i	0.594852	−	0.803835i	$-0.297211\pi$
$487$	11.4315	+	4.26373i	0.518011	+	0.193208i	−0.0768410	+	0.997043i	$0.524483\pi$
$488$	−2.77025	+	1.51267i	−0.125403	+	0.0684754i
$489$	−8.55196	−	3.90555i	−0.386733	−	0.176615i
$490$	−9.38376	−	0.410666i	−0.423915	−	0.0185520i
$491$	5.67447	−	39.4668i	0.256085	−	1.78111i	−0.303994	−	0.952674i	$-0.598320\pi$
$491$	5.67447	−	39.4668i	0.256085	−	1.78111i	0.560079	−	0.828439i	$-0.310771\pi$
$492$	2.81407	−	5.15358i	0.126868	−	0.232341i
$493$	−37.2758	−	2.66602i	−1.67882	−	0.120071i
$494$	4.48021	−	2.87925i	0.201574	−	0.129544i
$495$	21.5992	−	10.5956i	0.970811	−	0.476236i
$496$	−5.13566	−	5.92686i	−0.230598	−	0.266124i
$497$	−16.7079	−	9.12323i	−0.749454	−	0.409233i
$498$	−2.08404	−	2.78395i	−0.0933879	−	0.124752i
$499$	7.59110	+	6.57772i	0.339824	+	0.294459i	0.808008	−	0.589172i	$-0.200546\pi$
$499$	7.59110	+	6.57772i	0.339824	+	0.294459i	−0.468184	+	0.883631i	$0.655091\pi$
$500$	−7.99681	−	7.81351i	−0.357628	−	0.349431i
$501$	−16.3099	−	4.78901i	−0.728671	−	0.213957i
$502$	5.33094	−	14.2928i	0.237932	−	0.637920i
$503$	−32.6726	−	24.4584i	−1.45680	−	1.09055i	−0.977018	−	0.213157i	$-0.931625\pi$
$503$	−32.6726	−	24.4584i	−1.45680	−	1.09055i	−0.479780	−	0.877389i	$-0.659284\pi$
$504$	−3.35644	−	2.15706i	−0.149508	−	0.0960829i
$505$	−19.3665	−	2.23967i	−0.861796	−	0.0996640i
$506$	21.0902	+	4.83916i	0.937575	+	0.215127i
$507$	−5.61622	+	5.61622i	−0.249425	+	0.249425i
$508$	−4.38394	−	20.1526i	−0.194506	−	0.894129i
$509$	20.9875	−	3.01754i	0.930253	−	0.133750i	0.339503	−	0.940605i	$-0.389741\pi$
$509$	20.9875	−	3.01754i	0.930253	−	0.133750i	0.590750	+	0.806855i	$0.298832\pi$
$510$	3.06460	−	6.00133i	0.135703	−	0.265743i
$511$	1.95903	−	6.67184i	0.0866624	−	0.295145i
$512$	0.349464	+	0.936950i	0.0154443	+	0.0414077i
$513$	−0.946433	−	13.2329i	−0.0417860	−	0.584245i
$514$	−19.2804	−	2.77211i	−0.850423	−	0.122272i
$515$	13.7571	−	19.4780i	0.606210	−	0.858304i
$516$	2.99101	−	2.59173i	0.131672	−	0.114094i
$517$	14.0900	+	3.06509i	0.619677	+	0.134802i
$518$	−19.4620	−	4.23369i	−0.855109	−	0.186018i
$519$	0.163092	−	0.141320i	0.00715896	−	0.00620327i
$520$	0.643208	+	3.73666i	0.0282065	+	0.163863i
$521$	−6.78921	−	0.976141i	−0.297441	−	0.0427655i	−0.00802106	−	0.999968i	$-0.502553\pi$
$521$	−6.78921	−	0.976141i	−0.297441	−	0.0427655i	−0.289420	+	0.957202i	$0.593462\pi$
$522$	−1.65492	−	23.1387i	−0.0724337	−	1.01276i
$523$	−3.90244	−	10.4629i	−0.170642	−	0.457509i	0.823275	−	0.567643i	$-0.192145\pi$
$523$	−3.90244	−	10.4629i	−0.170642	−	0.457509i	−0.993917	+	0.110134i	$0.964872\pi$
$524$	−0.0523242	+	0.178200i	−0.00228579	+	0.00778470i
$525$	−6.43429	+	1.29176i	−0.280816	+	0.0563771i
$526$	−23.8458	+	3.42850i	−1.03972	+	0.149490i
$527$	6.40388	+	29.4382i	0.278958	+	1.28235i
$528$	−2.50276	+	2.50276i	−0.108919	+	0.108919i
$529$	10.0268	−	20.6993i	0.435949	−	0.899971i
$530$	1.16753	−	10.0957i	0.0507144	−	0.438528i
$531$	13.8573	+	8.90553i	0.601354	+	0.386467i
$532$	4.20679	+	3.14916i	0.182388	+	0.136534i
$533$	4.43547	−	11.8920i	0.192122	−	0.515098i
$534$	6.97993	+	2.04949i	0.302051	+	0.0886903i
$535$	4.43661	−	1.09448i	0.191811	−	0.0473185i
$536$	0.465208	+	0.403105i	0.0200939	+	0.0174115i
$537$	9.08182	+	12.1319i	0.391909	+	0.523530i
$538$	20.5695	+	11.2318i	0.886814	+	0.484237i
$539$	−12.4112	−	14.3233i	−0.534590	−	0.616949i
$540$	8.93767	+	3.05473i	0.384616	+	0.131455i
$541$	−3.87412	+	2.48975i	−0.166561	+	0.107043i	−0.621266	−	0.783600i	$-0.713381\pi$
$541$	−3.87412	+	2.48975i	−0.166561	+	0.107043i	0.454704	+	0.890642i	$0.349745\pi$
$542$	0.276856	+	0.0198011i	0.0118920	+	0.000850531i
$543$	−3.44049	+	6.30079i	−0.147646	+	0.270393i
$544$	0.546706	−	3.80243i	0.0234398	−	0.163028i
$545$	31.4427	−	28.8060i	1.34686	−	1.23391i
$546$	2.02449	+	0.924555i	0.0866403	+	0.0395673i
$547$	8.57003	−	4.67959i	0.366428	−	0.200085i	−0.285477	−	0.958386i	$-0.592152\pi$
$547$	8.57003	−	4.67959i	0.366428	−	0.200085i	0.651905	+	0.758301i	$0.273970\pi$
$548$	−4.30369	−	1.60519i	−0.183844	−	0.0685704i
$549$	1.07115	+	7.45002i	0.0457156	+	0.317959i
$550$	0.362543	−	22.5565i	0.0154589	−	0.961814i
$551$			30.5536i			1.30163i
$552$	1.99795	+	3.18782i	0.0850382	+	0.135683i
$553$	−3.11015	−	3.11015i	−0.132257	−	0.132257i
$554$	5.63992	−	8.77589i	0.239617	−	0.372852i
$555$	20.8730	−	0.577585i	0.886011	−	0.0245171i
$556$	−3.94588	−	8.64028i	−0.167343	−	0.366429i
$557$	9.90423	+	18.1382i	0.419656	+	0.768542i	0.998914	−	0.0466025i	$-0.0148394\pi$
$557$	9.90423	+	18.1382i	0.419656	+	0.768542i	−0.579258	+	0.815144i	$0.696658\pi$
$558$	−17.5219	+	6.53532i	−0.741760	+	0.276662i
$559$	5.60213	−	6.46520i	0.236945	−	0.273449i
$560$	−3.23279	+	1.88315i	−0.136610	+	0.0795775i
$561$	13.0461	−	3.83068i	0.550806	−	0.161731i
$562$	−0.900310	+	12.5880i	−0.0379773	+	0.530992i
$563$	−5.30005	+	24.3639i	−0.223370	+	1.02682i	0.719716	+	0.694269i	$0.244272\pi$
$563$	−5.30005	+	24.3639i	−0.223370	+	1.02682i	−0.943086	+	0.332548i	$0.892092\pi$
$564$	1.35543	+	2.10909i	0.0570738	+	0.0888086i
$565$	−22.1914	−	4.18816i	−0.933599	−	0.176197i
$566$	−0.621568	−	2.11687i	−0.0261265	−	0.0889785i
$567$	−5.14365	+	3.85049i	−0.216013	+	0.161705i
$568$	11.3486	−	0.811671i	0.476179	−	0.0340570i
$569$	−11.7064	+	25.6335i	−0.490758	+	1.07461i	0.488606	+	0.872505i	$0.337506\pi$
$569$	−11.7064	+	25.6335i	−0.490758	+	1.07461i	−0.979364	+	0.202106i	$0.935222\pi$
$570$	−5.07278	−	2.14913i	−0.212475	−	0.0900172i
$571$	19.0112	−	8.68214i	0.795595	−	0.363336i	0.0242118	−	0.999707i	$-0.492292\pi$
$571$	19.0112	−	8.68214i	0.795595	−	0.363336i	0.771383	+	0.636371i	$0.219565\pi$
$572$	−4.58486	+	6.12466i	−0.191703	+	0.256085i
$573$	−7.18684	+	1.56340i	−0.300235	+	0.0653120i
$574$	12.5237			0.522730
$575$	−23.2826	−	5.73758i	−0.970952	−	0.239274i
$576$	2.38461			0.0993587
$577$	−15.6922	+	3.41363i	−0.653275	+	0.142111i	−0.526975	−	0.849881i	$-0.676674\pi$
$577$	−15.6922	+	3.41363i	−0.653275	+	0.142111i	−0.126300	+	0.991992i	$0.540310\pi$
$578$	1.34398	−	1.79534i	0.0559020	−	0.0746764i
$579$	5.16713	−	2.35975i	0.214739	−	0.0980679i
$580$	−20.0294	−	8.48567i	−0.831677	−	0.352348i
$581$	3.08120	−	6.74688i	0.127830	−	0.279908i
$582$	1.03905	−	0.0743146i	0.0430702	−	0.00308044i
$583$	16.4164	−	12.2892i	0.679897	−	0.508965i
$584$	1.17086	+	3.98759i	0.0484506	+	0.165008i
$585$	8.88467	+	1.67680i	0.367336	+	0.0693271i
$586$	−14.9817	−	23.3120i	−0.618888	−	0.963009i
$587$	−5.70114	+	26.2077i	−0.235311	+	1.08171i	0.696158	+	0.717888i	$0.254891\pi$
$587$	−5.70114	+	26.2077i	−0.235311	+	1.08171i	−0.931469	+	0.363819i	$0.881473\pi$
$588$	0.235078	−	3.28681i	0.00969443	−	0.135546i
$589$	23.6331	−	6.93930i	0.973785	−	0.285929i
$590$	13.3468	−	7.77468i	0.549478	−	0.320079i
$591$	−5.92292	+	6.83541i	−0.243636	+	0.281171i
$592$	11.1534	−	4.16000i	0.458402	−	0.170975i
$593$	−1.63363	−	2.99176i	−0.0670850	−	0.122857i	0.841984	−	0.539502i	$-0.181388\pi$
$593$	−1.63363	−	2.99176i	−0.0670850	−	0.122857i	−0.909069	+	0.416645i	$0.863206\pi$
$594$	7.91718	+	17.3362i	0.324846	+	0.711313i
$595$	14.3667	−	0.397547i	0.588979	−	0.0162978i
$596$	1.19959	−	1.86660i	0.0491371	−	0.0764589i
$597$	11.7734	+	11.7734i	0.481853	+	0.481853i
$598$	5.25532	+	6.20587i	0.214906	+	0.253777i
$599$			25.3198i			1.03454i	0.855823	+	0.517269i	$0.173051\pi$
$599$			25.3198i			1.03454i	−0.855823	+	0.517269i	$0.826949\pi$
$600$	2.81773	−	2.72859i	0.115033	−	0.111394i
$601$	1.56139	+	10.8597i	0.0636906	+	0.442978i	0.996568	+	0.0827828i	$0.0263808\pi$
$601$	1.56139	+	10.8597i	0.0636906	+	0.442978i	−0.932877	+	0.360195i	$0.882710\pi$
$602$	7.90891	+	2.94987i	0.322343	+	0.120228i
$603$	1.28831	−	0.703473i	0.0524642	−	0.0286476i
$604$	−2.90771	−	1.32791i	−0.118313	−	0.0540318i
$605$	15.4277	−	14.1340i	0.627225	−	0.574628i
$606$	0.973366	−	6.76991i	0.0395403	−	0.275009i
$607$	2.51582	−	4.60737i	0.102114	−	0.187008i	−0.821627	−	0.570025i	$-0.806933\pi$
$607$	2.51582	−	4.60737i	0.102114	−	0.187008i	0.923741	+	0.383018i	$0.125115\pi$
$608$	−3.13274	−	0.224058i	−0.127049	−	0.00908674i
$609$	−10.7416	+	6.90320i	−0.435271	+	0.279732i
$610$	6.67848	+	2.28258i	0.270404	+	0.0924192i
$611$	3.54879	+	4.09552i	0.143569	+	0.165687i
$612$	−8.04001	−	4.39018i	−0.324998	−	0.177463i
$613$	−7.76829	−	10.3772i	−0.313758	−	0.419132i	0.615745	−	0.787945i	$-0.288855\pi$
$613$	−7.76829	−	10.3772i	−0.313758	−	0.419132i	−0.929504	+	0.368813i	$0.879764\pi$
$614$	−24.1291	−	20.9080i	−0.973773	−	0.843779i
$615$	−12.7476	+	3.14476i	−0.514035	+	0.126809i
$616$	−7.24329	−	2.12682i	−0.291841	−	0.0856921i
$617$	4.30872	−	11.5521i	0.173463	−	0.465071i	−0.820904	−	0.571066i	$-0.806530\pi$
$617$	4.30872	−	11.5521i	0.173463	−	0.465071i	0.994367	+	0.105995i	$0.0338027\pi$
$618$	6.69726	+	5.01351i	0.269403	+	0.201673i
$619$	−14.1064	−	9.06563i	−0.566984	−	0.364378i	0.225526	−	0.974237i	$-0.427590\pi$
$619$	−14.1064	−	9.06563i	−0.566984	−	0.364378i	−0.792510	+	0.609859i	$0.791226\pi$
$620$	−2.01456	+	17.4200i	−0.0809068	+	0.699602i
$621$	19.8425	−	4.08124i	0.796252	−	0.163774i
$622$	−13.3698	+	13.3698i	−0.536082	+	0.536082i
$623$	3.29808	+	15.1610i	0.132135	+	0.607415i
$624$	−1.31665	+	0.189306i	−0.0527084	+	0.00757832i
$625$	−0.803424	+	24.9871i	−0.0321370	+	0.999483i
$626$	4.74411	−	16.1570i	0.189613	−	0.645762i
$627$	−3.88480	−	10.4156i	−0.155144	−	0.415957i
$628$	−0.232662	−	3.25304i	−0.00928424	−	0.129811i
$629$	−45.2639	−	6.50797i	−1.80479	−	0.259490i
$630$	1.51344	+	8.79219i	0.0602968	+	0.350289i
$631$	−16.3486	+	14.1661i	−0.650827	+	0.563944i	−0.916458	−	0.400130i	$-0.868965\pi$
$631$	−16.3486	+	14.1661i	−0.650827	+	0.563944i	0.265632	+	0.964075i	$0.414419\pi$
$632$	2.56874	+	0.558795i	0.102179	+	0.0222277i
$633$	5.15889	+	1.12225i	0.205048	+	0.0446054i
$634$	−13.2303	+	11.4641i	−0.525443	+	0.455299i
$635$	−26.6049	+	37.6686i	−1.05578	+	1.49483i
$636$	3.52913	+	0.507413i	0.139939	+	0.0201202i
$637$	−0.508130	−	7.10458i	−0.0201328	−	0.281494i
$638$	−15.3388	−	41.1250i	−0.607270	−	1.62815i
$639$	7.64374	−	26.0322i	0.302382	−	1.02982i
$640$	1.01694	−	1.99144i	0.0401980	−	0.0787186i
$641$	−6.94442	+	0.998456i	−0.274288	+	0.0394367i	−0.278086	−	0.960556i	$-0.589700\pi$
$641$	−6.94442	+	0.998456i	−0.274288	+	0.0394367i	0.00379821	+	0.999993i	$0.498791\pi$
$642$	0.340771	+	1.56650i	0.0134492	+	0.0618248i
$643$	1.78726	−	1.78726i	0.0704828	−	0.0704828i	−0.670987	−	0.741469i	$-0.734129\pi$
$643$	1.78726	−	1.78726i	0.0704828	−	0.0704828i	0.741469	+	0.670987i	$0.234129\pi$
$644$	−3.92523	+	6.99855i	−0.154676	+	0.275781i
$645$	−8.79104	−	1.01666i	−0.346147	−	0.0400308i
$646$	10.1499	+	6.52296i	0.399343	+	0.256642i
$647$	−24.2357	−	18.1426i	−0.952805	−	0.713261i	0.00520773	−	0.999986i	$-0.498342\pi$
$647$	−24.2357	−	18.1426i	−0.952805	−	0.713261i	−0.958013	+	0.286726i	$0.907433\pi$
$648$	1.34201	−	3.59806i	0.0527190	−	0.141345i
$649$	29.9043	+	8.78071i	1.17385	+	0.344673i
$650$	5.18928	−	6.70471i	0.203540	−	0.262980i
$651$	7.77922	+	6.74073i	0.304892	+	0.264190i
$652$	7.18211	+	9.59418i	0.281273	+	0.375737i
$653$	−4.22291	−	2.30588i	−0.165255	−	0.0902361i	0.394493	−	0.918899i	$-0.370920\pi$
$653$	−4.22291	−	2.30588i	−0.165255	−	0.0902361i	−0.559748	+	0.828663i	$0.689102\pi$
$654$	9.79688	+	11.3062i	0.383088	+	0.442107i
$655$	0.372844	−	0.182901i	0.0145682	−	0.00714651i
$656$	−6.29687	+	4.04675i	−0.245851	+	0.157999i
$657$	9.88502	+	0.706991i	0.385651	+	0.0275823i
$658$	−2.56265	+	4.69314i	−0.0999024	+	0.182958i
$659$	−5.27064	+	36.6581i	−0.205315	+	1.42800i	0.582873	+	0.812564i	$0.301929\pi$
$659$	−5.27064	+	36.6581i	−0.205315	+	1.42800i	−0.788188	+	0.615435i	$0.788980\pi$
$660$	7.90686	+	0.346031i	0.307774	+	0.0134693i
$661$	39.6324	+	18.0995i	1.54152	+	0.703989i	0.991372	−	0.131079i	$-0.0418440\pi$
$661$	39.6324	+	18.0995i	1.54152	+	0.703989i	0.550148	+	0.835067i	$0.314571\pi$
$662$	19.5707	−	10.6864i	0.760636	−	0.415339i
$663$	4.78779	+	1.78575i	0.185942	+	0.0693530i
$664$	0.630887	+	4.38792i	0.0244832	+	0.170284i
$665$	−1.16214	−	11.6928i	−0.0450658	−	0.453427i
$666$		−	28.3863i		−	1.09995i
$667$	−46.2521	+	6.11523i	−1.79089	+	0.236783i
$668$	15.3221	+	15.3221i	0.592829	+	0.592829i
$669$	−6.67181	+	10.3815i	−0.257947	+	0.401373i
$670$	−0.0380731	−	1.37590i	−0.00147089	−	0.0531558i
$671$	5.91595	+	12.9541i	0.228383	+	0.500088i
$672$	−0.629032	−	1.15199i	−0.0242654	−	0.0444388i
$673$	−3.46231	+	1.29137i	−0.133462	+	0.0497788i	−0.415308	−	0.909681i	$-0.636326\pi$
$673$	−3.46231	+	1.29137i	−0.133462	+	0.0497788i	0.281846	+	0.959460i	$0.409053\pi$
$674$	−3.25831	+	3.76029i	−0.125506	+	0.144841i
$675$	−8.46381	−	19.3502i	−0.325772	−	0.744790i
$676$	9.71461	−	2.85247i	0.373639	−	0.109710i
$677$	−3.18600	+	44.5462i	−0.122448	+	1.71205i	0.450766	+	0.892642i	$0.351151\pi$
$677$	−3.18600	+	44.5462i	−0.122448	+	1.71205i	−0.573214	+	0.819406i	$0.694303\pi$
$678$	1.68410	−	7.74168i	0.0646774	−	0.297317i
$679$	1.20120	+	1.86910i	0.0460978	+	0.0717295i
$680$	−7.09508	+	4.84217i	−0.272084	+	0.185689i
$681$	2.65938	+	9.05701i	0.101908	+	0.347065i
$682$	−28.3263	+	21.2048i	−1.08467	+	0.811973i
$683$	−21.8981	+	1.56618i	−0.837907	+	0.0599283i	−0.483695	−	0.875237i	$-0.660705\pi$
$683$	−21.8981	+	1.56618i	−0.837907	+	0.0599283i	−0.354212	+	0.935165i	$0.615251\pi$
$684$	−3.11122	+	6.81263i	−0.118961	+	0.260487i
$685$	3.85413	+	9.52037i	0.147259	+	0.363755i
$686$	17.0467	−	7.78498i	0.650847	−	0.297232i
$687$	9.49777	−	12.6875i	0.362363	−	0.484060i
$688$	−4.92975	+	1.07240i	−0.187945	+	0.0408849i
$689$	7.70681			0.293606
$690$	2.23805	−	8.10932i	0.0852013	−	0.308717i
$691$	19.0780			0.725762			0.362881	−	0.931836i	$-0.381793\pi$
$691$	19.0780			0.725762			0.362881	+	0.931836i	$0.381793\pi$
$692$	−0.268806	+	0.0584752i	−0.0102185	+	0.00222290i
$693$	−10.7880	+	14.4110i	−0.409801	+	0.547430i
$694$	5.41735	−	2.47402i	0.205640	−	0.0939126i
$695$	−8.28548	+	19.5569i	−0.314286	+	0.741836i
$696$	3.17021	−	6.94180i	0.120167	−	0.263128i
$697$	28.6810	−	2.05130i	1.08637	−	0.0776987i
$698$	9.65946	−	7.23098i	0.365616	−	0.273697i
$699$	1.82511	+	6.21576i	0.0690320	+	0.235101i
$700$	7.98798	+	2.48560i	0.301917	+	0.0939468i
$701$	−6.32785	−	9.84632i	−0.238999	−	0.371890i	0.700946	−	0.713214i	$-0.252761\pi$
$701$	−6.32785	−	9.84632i	−0.238999	−	0.371890i	−0.939946	+	0.341324i	$0.889125\pi$
$702$	−1.52251	+	6.99889i	−0.0574636	+	0.264156i
$703$	−2.66717	+	37.2919i	−0.100594	+	1.40649i
$704$	4.32913	−	1.27115i	0.163160	−	0.0479081i
$705$	1.43000	−	5.42054i	0.0538570	−	0.204149i
$706$	−22.1429	+	25.5543i	−0.833359	+	0.961748i
$707$	13.6679	−	5.09787i	0.514035	−	0.191725i
$708$	2.59699	+	4.75604i	0.0976009	+	0.178743i
$709$	13.8682	+	30.3671i	0.520831	+	1.14046i	0.969124	+	0.246574i	$0.0793049\pi$
$709$	13.8682	+	30.3671i	0.520831	+	1.14046i	−0.448293	+	0.893887i	$0.647968\pi$
$710$	−18.4803	−	17.4851i	−0.693555	−	0.656205i
$711$	3.38911	−	5.27356i	0.127102	−	0.197774i
$712$	−6.55721	−	6.55721i	−0.245742	−	0.245742i
$713$	15.2348	+	34.3869i	0.570549	+	1.28780i
$714$			5.04214i			0.188698i
$715$	17.0235	−	1.69196i	0.636642	−	0.0632755i
$716$	−2.74928	−	19.1217i	−0.102745	−	0.714610i
$717$	12.3235	+	4.59641i	0.460228	+	0.171656i
$718$	−25.6913	+	14.0285i	−0.958791	+	0.523540i
$719$	−20.4995	−	9.36179i	−0.764501	−	0.349136i	−0.00529470	−	0.999986i	$-0.501685\pi$
$719$	−20.4995	−	9.36179i	−0.764501	−	0.349136i	−0.759206	+	0.650850i	$0.774413\pi$
$720$	−3.60194	−	3.93164i	−0.134237	−	0.146524i
$721$	−2.53936	+	17.6616i	−0.0945706	+	0.657753i
$722$	−4.37831	+	8.01827i	−0.162944	+	0.298409i
$723$	−3.47695	−	0.248677i	−0.129309	−	0.00924838i
$724$	7.69858	−	4.94758i	0.286115	−	0.183875i
$725$	16.2636	+	45.8413i	0.604016	+	1.70250i
$726$	4.80694	+	5.54751i	0.178402	+	0.205887i
$727$	−25.8602	−	14.1208i	−0.959103	−	0.523710i	−0.0781647	−	0.996940i	$-0.524906\pi$
$727$	−25.8602	−	14.1208i	−0.959103	−	0.523710i	−0.880939	+	0.473230i	$0.843088\pi$
$728$	−1.70021	−	2.27122i	−0.0630140	−	0.0841769i
$729$	0.592199	+	0.513143i	0.0219333	+	0.0190053i
$730$	4.80598	−	7.95371i	0.177877	−	0.294380i
$731$	18.5956	+	5.46016i	0.687784	+	0.201951i
$732$	−0.865290	+	2.31993i	−0.0319821	+	0.0857472i
$733$	0.485661	+	0.363562i	0.0179383	+	0.0134285i	0.608209	−	0.793777i	$-0.291888\pi$
$733$	0.485661	+	0.363562i	0.0179383	+	0.0134285i	−0.590271	+	0.807205i	$0.700979\pi$
$734$	23.1321	+	14.8661i	0.853822	+	0.548718i
$735$	−5.77424	+	4.57714i	−0.212986	+	0.168830i
$736$	−0.287830	−	4.78719i	−0.0106096	−	0.176458i
$737$	1.96387	−	1.96387i	0.0723401	−	0.0723401i
$738$	3.79409	+	17.4411i	0.139662	+	0.642017i
$739$	47.4485	−	6.82207i	1.74542	−	0.250954i	0.805562	−	0.592512i	$-0.201864\pi$
$739$	47.4485	−	6.82207i	1.74542	−	0.250954i	0.939861	+	0.341558i	$0.110955\pi$
$740$	−23.7060	−	12.1056i	−0.871451	−	0.445010i
$741$	1.17702	−	4.00856i	0.0432389	−	0.147258i
$742$	2.65750	+	7.12504i	0.0975600	+	0.261568i
$743$	0.547219	+	7.65113i	0.0200755	+	0.280693i	0.997567	+	0.0697168i	$0.0222096\pi$
$743$	0.547219	+	7.65113i	0.0200755	+	0.280693i	−0.977491	+	0.210976i	$0.932336\pi$
$744$	−6.08947	−	0.875534i	−0.223251	−	0.0320986i
$745$	−4.88954	+	0.841659i	−0.179139	+	0.0308360i
$746$	−14.3324	+	12.4191i	−0.524745	+	0.454694i
$747$	10.3295	+	2.24704i	0.377936	+	0.0822150i
$748$	−16.9365	−	3.68430i	−0.619258	−	0.134711i
$749$	−2.58409	+	2.23913i	−0.0944207	+	0.0818160i
$750$	−8.75495	−	0.524231i	−0.319685	−	0.0191422i
$751$	−29.3300	−	4.21702i	−1.07027	−	0.153881i	−0.415411	−	0.909634i	$-0.636362\pi$
$751$	−29.3300	−	4.21702i	−1.07027	−	0.153881i	−0.654857	+	0.755752i	$0.727271\pi$
$752$	−0.227992	−	3.18775i	−0.00831402	−	0.116245i
$753$	−4.18196	−	11.2123i	−0.152399	−	0.408598i
$754$	4.64737	−	15.8275i	0.169247	−	0.576403i
$755$	2.20269	+	6.79991i	0.0801642	+	0.247474i
$756$	−6.99556	+	1.00581i	−0.254426	+	0.0365809i
$757$	−8.10922	−	37.2775i	−0.294735	−	1.35487i	−0.851566	−	0.524247i	$-0.824347\pi$
$757$	−8.10922	−	37.2775i	−0.294735	−	1.35487i	0.556832	−	0.830625i	$-0.312017\pi$
$758$	9.40913	−	9.40913i	0.341755	−	0.341755i
$759$	14.9896	−	7.96547i	0.544086	−	0.289128i
$760$	4.36257	+	5.50356i	0.158247	+	0.199635i
$761$	−18.8519	−	12.1154i	−0.683379	−	0.439181i	0.152347	−	0.988327i	$-0.451317\pi$
$761$	−18.8519	−	12.1154i	−0.683379	−	0.439181i	−0.835727	+	0.549146i	$0.814953\pi$
$762$	−12.9518	−	9.69563i	−0.469196	−	0.351236i
$763$	−11.1507	+	29.8961i	−0.403681	+	1.08231i
$764$	8.99589	+	2.64143i	0.325460	+	0.0955637i
$765$	4.90608	+	19.8874i	0.177380	+	0.719030i
$766$	7.19252	+	6.23235i	0.259876	+	0.225184i
$767$	7.01942	+	9.37685i	0.253457	+	0.338578i
$768$	0.688512	+	0.375956i	0.0248445	+	0.0135661i
$769$	−1.16713	−	1.34694i	−0.0420879	−	0.0485720i	0.734315	−	0.678809i	$-0.237503\pi$
$769$	−1.16713	−	1.34694i	−0.0420879	−	0.0485720i	−0.776403	+	0.630237i	$0.782958\pi$
$770$	7.43436	+	15.1550i	0.267916	+	0.546148i
$771$	−12.8547	+	8.26122i	−0.462951	+	0.297521i
$772$	−7.22271	−	0.516578i	−0.259951	−	0.0185921i
$773$	−7.56752	+	13.8589i	−0.272185	+	0.498469i	−0.977640	−	0.210285i	$-0.932561\pi$
$773$	−7.56752	+	13.8589i	−0.272185	+	0.498469i	0.705455	+	0.708754i	$0.250743\pi$
$774$	−1.71211	+	11.9080i	−0.0615406	+	0.428024i
$775$	31.7643	−	22.9913i	1.14101	−	0.825871i
$776$	−1.20791	−	0.551636i	−0.0433616	−	0.0198026i
$777$	−13.7132	+	7.48796i	−0.491958	+	0.268629i
$778$	20.1211	+	7.50479i	0.721377	+	0.269060i
$779$	−3.34564	−	23.2695i	−0.119870	−	0.833715i
$780$	2.30092	+	1.88490i	0.0823863	+	0.0674901i
$781$		−	51.3346i		−	1.83690i
$782$	−7.84299	+	16.6705i	−0.280465	+	0.596137i
$783$	−29.0566	−	29.0566i	−1.03840	−	1.03840i
$784$	−2.27099	+	3.53374i	−0.0811069	+	0.126205i
$785$	−5.01204	+	5.29732i	−0.178887	+	0.189069i
$786$	0.0605234	+	0.132528i	0.00215880	+	0.00472711i
$787$	3.17337	+	5.81160i	0.113118	+	0.207161i	0.928105	−	0.372319i	$-0.121437\pi$
$787$	3.17337	+	5.81160i	0.113118	+	0.207161i	−0.814986	+	0.579480i	$0.803256\pi$
$788$	10.8026	−	4.02915i	0.384826	−	0.143533i
$789$	−12.3760	+	14.2826i	−0.440596	+	0.508475i
$790$	−2.95876	−	5.07928i	−0.105268	−	0.180713i
$791$	16.2135	−	4.76071i	0.576486	−	0.169271i
$792$	0.767545	−	10.7317i	0.0272735	−	0.381334i
$793$	−1.13767	+	5.22977i	−0.0403997	+	0.185715i
$794$	10.4497	+	16.2601i	0.370847	+	0.577050i
$795$	−4.49414	−	6.58513i	−0.159391	−	0.233550i
$796$	−5.97968	−	20.3649i	−0.211944	−	0.721815i
$797$	34.1465	−	25.5617i	1.20953	−	0.905443i	0.212111	−	0.977246i	$-0.431966\pi$
$797$	34.1465	−	25.5617i	1.20953	−	0.905443i	0.997419	+	0.0718031i	$0.0228753\pi$
$798$	4.11183	−	0.294084i	0.145557	−	0.0104105i
$799$	−5.10009	+	11.1676i	−0.180428	+	0.395083i
$800$	−4.81948	+	1.33138i	−0.170394	+	0.0470715i
$801$	−20.1148	+	9.18614i	−0.710723	+	0.324576i
$802$	21.2719	−	28.4159i	0.751137	−	1.00340i
$803$	18.3226	−	3.98584i	0.646590	−	0.140657i
$804$	0.482886			0.0170301
$805$	17.4680	−	4.09953i	0.615664	−	0.144489i
$806$	−13.2980			−0.468402
$807$	17.9648	−	3.90801i	0.632392	−	0.137569i
$808$	−5.22490	+	6.97966i	−0.183812	+	0.245543i
$809$	−20.3427	+	9.29021i	−0.715212	+	0.326626i	−0.739572	−	0.673077i	$-0.764972\pi$
$809$	−20.3427	+	9.29021i	−0.715212	+	0.326626i	0.0243607	+	0.999703i	$0.492245\pi$
$810$	−7.95942	+	3.22221i	−0.279666	+	0.113217i
$811$	13.3790	−	29.2960i	0.469801	−	1.02872i	−0.515342	−	0.856985i	$-0.672335\pi$
$811$	13.3790	−	29.2960i	0.469801	−	1.02872i	0.985143	−	0.171736i	$-0.0549376\pi$
$812$	16.2352	−	1.16117i	0.569745	−	0.0407489i
$813$	0.174310	−	0.130487i	0.00611330	−	0.00457636i
$814$	−15.1317	−	51.5337i	−0.530365	−	1.80626i
$815$	4.96991	−	26.3335i	0.174088	−	0.922424i
$816$	−1.62925	−	2.53517i	−0.0570353	−	0.0887486i
$817$	3.36813	−	15.4830i	0.117836	−	0.541683i
$818$	1.79852	−	25.1466i	0.0628838	−	0.879230i
$819$	−6.49133	+	1.90603i	−0.226825	+	0.0666020i
$820$	16.1835	+	4.26940i	0.565153	+	0.149094i
$821$	9.12593	−	10.5319i	0.318497	−	0.367565i	−0.573814	−	0.818985i	$-0.694537\pi$
$821$	9.12593	−	10.5319i	0.318497	−	0.367565i	0.892312	+	0.451420i	$0.149082\pi$
$822$	−3.37611	+	1.25922i	−0.117755	+	0.0439205i
$823$	−7.90592	−	14.4786i	−0.275583	−	0.504692i	0.702828	−	0.711359i	$-0.251920\pi$
$823$	−7.90592	−	14.4786i	−0.275583	−	0.504692i	−0.978411	+	0.206667i	$0.933738\pi$
$824$	−4.43017	−	9.70071i	−0.154332	−	0.337940i
$825$	−11.3728	−	13.5592i	−0.395949	−	0.472069i
$826$	−6.24853	+	9.72291i	−0.217414	+	0.338303i
$827$	17.6102	+	17.6102i	0.612368	+	0.612368i	0.943563	−	0.331194i	$-0.107452\pi$
$827$	17.6102	+	17.6102i	0.612368	+	0.612368i	−0.331194	+	0.943563i	$0.607452\pi$
$828$	−10.9357	−	3.34624i	−0.380041	−	0.116290i
$829$			26.5027i			0.920477i	0.887795	+	0.460238i	$0.152236\pi$
$829$			26.5027i			0.920477i	−0.887795	+	0.460238i	$0.847764\pi$
$830$	6.28166	−	7.66812i	0.218039	−	0.266164i
$831$	−1.16464	−	8.10022i	−0.0404008	−	0.280993i
$832$	1.58875	+	0.592573i	0.0550800	+	0.0205438i
$833$	14.1627	−	7.73344i	0.490710	−	0.267948i
$834$	−6.77803	−	3.09542i	−0.234704	−	0.107186i
$835$	2.11843	−	48.4063i	0.0733112	−	1.67517i
$836$	−2.01670	+	14.0264i	−0.0697489	+	0.485114i
$837$	−15.8759	+	29.0745i	−0.548751	+	1.00496i
$838$	1.99487	+	0.142676i	0.0689118	+	0.00492867i
$839$	27.6812	−	17.7896i	0.955661	−	0.614166i	0.0328669	−	0.999460i	$-0.489536\pi$
$839$	27.6812	−	17.7896i	0.955661	−	0.614166i	0.922794	+	0.385294i	$0.125900\pi$
$840$	−0.949193	+	2.77719i	−0.0327503	+	0.0958222i
$841$	42.9831	+	49.6052i	1.48218	+	1.71052i
$842$	−8.43644	−	4.60664i	−0.290739	−	0.158755i
$843$	5.93291	+	7.92544i	0.204340	+	0.272967i
$844$	−5.08627	−	4.40727i	−0.175076	−	0.151705i
$845$	−19.3769	−	11.7084i	−0.666586	−	0.402781i
$846$	−7.31225	−	2.14707i	−0.251400	−	0.0738178i
$847$	−5.47120	+	14.6689i	−0.187993	+	0.504028i
$848$	−3.63847	−	2.72373i	−0.124946	−	0.0935331i
$849$	−1.45598	−	0.935699i	−0.0499690	−	0.0321131i
$850$	18.7006	+	4.38397i	0.641427	+	0.150369i
$851$	−56.9864	+	3.42632i	−1.95347	+	0.117453i
$852$	6.31121	−	6.31121i	0.216218	−	0.216218i
$853$	−5.93283	−	27.2728i	−0.203136	−	0.933802i	−0.959950	−	0.280172i	$-0.909609\pi$
$853$	−5.93283	−	27.2728i	−0.203136	−	0.933802i	0.756814	−	0.653631i	$-0.226755\pi$
$854$	−5.22728	+	0.751570i	−0.178874	+	0.0257182i
$855$	15.9319	−	5.16080i	0.544858	−	0.176496i
$856$	0.575747	−	1.96081i	0.0196786	−	0.0670193i
$857$	−11.7750	−	31.5700i	−0.402226	−	1.07841i	−0.967359	−	0.253411i	$-0.918448\pi$
$857$	−11.7750	−	31.5700i	−0.402226	−	1.07841i	0.565132	−	0.825000i	$-0.308825\pi$
$858$	0.428156	+	5.98640i	0.0146170	+	0.204372i
$859$	−40.8861	−	5.87853i	−1.39501	−	0.200573i	−0.596531	−	0.802590i	$-0.703455\pi$
$859$	−40.8861	−	5.87853i	−1.39501	−	0.200573i	−0.798483	+	0.602017i	$0.794364\pi$
$860$	9.21449	+	6.50809i	0.314212	+	0.221924i
$861$	7.42484	−	6.43366i	0.253038	−	0.219258i
$862$	−6.87865	−	1.49636i	−0.234288	−	0.0509661i
$863$	−8.38081	−	1.82313i	−0.285286	−	0.0620602i	0.0676451	−	0.997709i	$-0.478451\pi$
$863$	−8.38081	−	1.82313i	−0.285286	−	0.0620602i	−0.352931	+	0.935649i	$0.614815\pi$
$864$	3.19233	−	2.76617i	0.108605	−	0.0941070i
$865$	0.502443	+	0.354870i	0.0170836	+	0.0120659i
$866$	34.1821	+	4.91465i	1.16156	+	0.167007i
$867$	−0.125507	−	1.75481i	−0.00426243	−	0.0595966i
$868$	−4.58548	−	12.2942i	−0.155641	−	0.417291i
$869$	3.34161	−	11.3805i	0.113356	−	0.386056i
$870$	−16.2339	+	5.25866i	−0.550382	+	0.178285i
$871$	1.03315	−	0.148545i	0.0350071	−	0.00503326i
$872$	−4.05373	−	18.6347i	−0.137277	−	0.631051i
$873$	−2.23909	+	2.23909i	−0.0757819	+	0.0757819i
$874$	14.0521	+	5.42358i	0.475320	+	0.183455i
$875$	−7.96767	−	16.9247i	−0.269356	−	0.572160i
$876$	2.74265	+	1.76260i	0.0926657	+	0.0595526i
$877$	11.4044	+	8.53720i	0.385098	+	0.288281i	0.774234	−	0.632900i	$-0.218135\pi$
$877$	11.4044	+	8.53720i	0.385098	+	0.288281i	−0.389136	+	0.921180i	$0.627226\pi$
$878$	−6.49822	+	17.4224i	−0.219304	+	0.587978i
$879$	−20.8579	−	6.12442i	−0.703518	−	0.206571i
$880$	−8.63495	−	5.21762i	−0.291084	−	0.175886i
$881$	−17.0329	−	14.7591i	−0.573852	−	0.497245i	0.318904	−	0.947787i	$-0.396685\pi$
$881$	−17.0329	−	14.7591i	−0.573852	−	0.497245i	−0.892755	+	0.450542i	$0.851231\pi$
$882$	6.00278	+	8.01878i	0.202124	+	0.270006i
$883$	−21.9325	−	11.9760i	−0.738086	−	0.403025i	0.0657813	−	0.997834i	$-0.479046\pi$
$883$	−21.9325	−	11.9760i	−0.738086	−	0.403025i	−0.803867	+	0.594809i	$0.797228\pi$
$884$	−4.26572	−	4.92290i	−0.143472	−	0.165575i
$885$	3.91880	−	11.4658i	0.131729	−	0.385418i
$886$	13.9961	−	8.99476i	0.470209	−	0.302185i
$887$	−56.9868	−	4.07578i	−1.91343	−	0.136851i	−0.936535	−	0.350573i	$-0.885987\pi$
$887$	−56.9868	−	4.07578i	−1.91343	−	0.136851i	−0.976894	+	0.213722i	$0.931441\pi$
$888$	4.47536	−	8.19601i	0.150183	−	0.275040i
$889$	4.91087	−	34.1558i	0.164705	−	1.14555i
$890$	−0.906598	+	20.7159i	−0.0303892	+	0.694398i
$891$	−15.7607	−	7.19768i	−0.528004	−	0.241132i
$892$	13.8068	−	7.53911i	0.462287	−	0.252428i
$893$	9.40459	+	3.50773i	0.314713	+	0.117382i
$894$	−0.247714	−	1.72289i	−0.00828478	−	0.0576219i
$895$	−27.3742	+	33.4161i	−0.915019	+	1.11698i
$896$			1.67315i			0.0558961i
$897$	6.30375	+	0.979471i	0.210476	+	0.0327036i
$898$	15.7266	+	15.7266i	0.524803	+	0.524803i
$899$	41.2464	−	64.1807i	1.37565	−	2.14055i
$900$	−1.04159	+	11.8775i	−0.0347197	+	0.395915i
$901$	7.25306	+	15.8820i	0.241635	+	0.529106i
$902$	16.1852	+	29.6410i	0.538908	+	0.986936i
$903$	6.20429	−	2.31408i	0.206466	−	0.0770078i
$904$	−6.61376	+	7.63269i	−0.219970	+	0.253859i
$905$	−19.7860	−	5.21978i	−0.657710	−	0.173512i
$906$	−2.40604	+	0.706478i	−0.0799354	+	0.0234712i
$907$	2.23728	−	31.2813i	0.0742878	−	1.03868i	−0.814441	−	0.580246i	$-0.802956\pi$
$907$	2.23728	−	31.2813i	0.0742878	−	1.03868i	0.888729	−	0.458433i	$-0.151589\pi$
$908$	2.55776	−	11.7578i	0.0848822	−	0.390197i
$909$	11.2403	+	17.4902i	0.372816	+	0.580113i
$910$	−1.17652	+	6.23390i	−0.0390012	+	0.206652i
$911$	−0.944917	−	3.21809i	−0.0313065	−	0.106620i	0.942358	−	0.334607i	$-0.108604\pi$
$911$	−0.944917	−	3.21809i	−0.0313065	−	0.106620i	−0.973664	+	0.227987i	$0.926786\pi$
$912$	−1.97238	+	1.47651i	−0.0653121	+	0.0488920i
$913$	19.9504	−	1.42688i	0.660263	−	0.0472229i
$914$	11.7983	−	25.8347i	0.390253	−	0.854536i
$915$	5.13202	−	2.07760i	0.169659	−	0.0686833i
$916$	−18.3774	+	8.39267i	−0.607206	+	0.277302i
$917$	−0.186221	+	0.248762i	−0.00614957	+	0.00821486i
$918$	−15.8560	+	3.44926i	−0.523326	+	0.113843i
$919$	49.4619			1.63160			0.815798	−	0.578337i	$-0.196298\pi$
$919$	49.4619			1.63160			0.815798	+	0.578337i	$0.196298\pi$
$920$	−7.45814	+	7.70559i	−0.245888	+	0.254046i
$921$	−25.0461			−0.825296
$922$	−31.6301	+	6.88071i	−1.04168	+	0.226604i
$923$	11.5616	−	15.4445i	0.380556	−	0.508363i
$924$	−5.38686	+	2.46010i	−0.177215	+	0.0809312i
$925$	15.8487	+	57.3709i	0.521103	+	1.88634i
$926$	5.67582	−	12.4283i	0.186519	−	0.408419i
$927$	−25.3657	+	1.81419i	−0.833119	+	0.0595859i
$928$	−7.78779	+	5.82987i	−0.255647	+	0.191375i
$929$	14.5800	+	49.6549i	0.478354	+	1.62912i	0.746242	+	0.665674i	$0.231856\pi$
$929$	14.5800	+	49.6549i	0.478354	+	1.62912i	−0.267888	+	0.963450i	$0.586326\pi$
$930$	7.75459	+	11.3625i	0.254283	+	0.372593i
$931$	−7.13260	−	11.0985i	−0.233761	−	0.363740i
$932$	1.75537	−	8.06931i	0.0574991	−	0.264319i
$933$	−1.05814	+	14.7948i	−0.0346421	+	0.484360i
$934$	3.99679	−	1.17356i	0.130779	−	0.0384001i
$935$	19.5079	+	33.4892i	0.637978	+	1.09521i
$936$	2.64792	−	3.05587i	0.0865501	−	0.0998841i
$937$	43.2893	−	16.1461i	1.41420	−	0.527470i	0.477821	−	0.878457i	$-0.341427\pi$
$937$	43.2893	−	16.1461i	1.41420	−	0.527470i	0.936380	+	0.350988i	$0.114154\pi$
$938$	0.493590	+	0.903942i	0.0161163	+	0.0295147i
$939$	−5.48751	−	12.0160i	−0.179078	−	0.392127i
$940$	−4.91144	+	5.19099i	−0.160194	+	0.169311i
$941$	7.54865	−	11.7459i	0.246079	−	0.382906i	−0.696139	−	0.717907i	$-0.745100\pi$
$941$	7.54865	−	11.7459i	0.246079	−	0.382906i	0.942218	+	0.335001i	$0.108737\pi$
$942$	−1.80908	−	1.80908i	−0.0589431	−	0.0589431i
$943$	34.5557	−	9.72197i	1.12529	−	0.316591i
$944$		−	6.90770i		−	0.224827i
$945$	12.2251	+	10.0147i	0.397683	+	0.325778i
$946$	3.23947	+	22.5310i	0.105324	+	0.732545i
$947$	−42.2392	−	15.7544i	−1.37259	−	0.511950i	−0.448383	−	0.893841i	$-0.648000\pi$
$947$	−42.2392	−	15.7544i	−1.37259	−	0.511950i	−0.924207	+	0.381892i	$0.875273\pi$
$948$	1.80997	−	0.988319i	0.0587851	−	0.0320991i
$949$	6.41023	+	2.92745i	0.208085	+	0.0950292i
$950$	2.48438	−	15.5059i	0.0806039	−	0.503079i
$951$	−1.95442	+	13.5933i	−0.0633765	+	0.440793i
$952$	3.08036	−	5.64125i	0.0998349	−	0.182834i
$953$	54.2904	+	3.88293i	1.75864	+	0.125780i	0.912996	−	0.407969i	$-0.133763\pi$
$953$	54.2904	+	3.88293i	1.75864	+	0.125780i	0.845643	+	0.533749i	$0.179217\pi$
$954$	−9.11757	+	5.85951i	−0.295192	+	0.189709i
$955$	−9.23319	−	18.8219i	−0.298779	−	0.609063i
$956$	−10.9797	−	12.6712i	−0.355108	−	0.409817i
$957$	−30.2204	−	16.5016i	−0.976888	−	0.533421i
$958$	−4.78897	−	6.39732i	−0.154725	−	0.206688i
$959$	−5.80815	−	5.03279i	−0.187555	−	0.162517i
$960$	−0.420135	−	1.70307i	−0.0135598	−	0.0549663i
$961$	−29.2671	−	8.59360i	−0.944100	−	0.277213i
$962$	7.05396	−	18.9124i	0.227429	−	0.609760i
$963$	−3.90118	−	2.92038i	−0.125714	−	0.0941081i
$964$	3.73816	+	2.40237i	0.120398	+	0.0773751i
$965$	10.0582	+	12.6888i	0.323784	+	0.408466i
$966$	1.26816	+	6.16563i	0.0408023	+	0.198376i
$967$	30.1269	−	30.1269i	0.968814	−	0.968814i	−0.0307139	−	0.999528i	$-0.509778\pi$
$967$	30.1269	−	30.1269i	0.968814	−	0.968814i	0.999528	+	0.0307139i	$0.00977808\pi$
$968$	−1.98901	−	9.14332i	−0.0639291	−	0.293878i
$969$	9.36846	−	1.34698i	0.300958	−	0.0432713i
$970$	0.915037	+	2.82480i	0.0293801	+	0.0906989i
$971$	7.28019	−	24.7940i	0.233632	−	0.795679i	−0.756311	−	0.654213i	$-0.773000\pi$
$971$	7.28019	−	24.7940i	0.233632	−	0.795679i	0.989943	−	0.141466i	$-0.0451816\pi$
$972$	−5.48123	−	14.6958i	−0.175811	−	0.471367i
$973$	−1.13377	−	15.8522i	−0.0363471	−	0.508198i
$974$	−12.0766	−	1.73635i	−0.386959	−	0.0556363i
$975$	−0.367801	−	6.64079i	−0.0117791	−	0.212676i
$976$	2.38540	−	2.06696i	0.0763548	−	0.0661618i
$977$	−28.1706	−	6.12814i	−0.901257	−	0.196056i	−0.262017	−	0.965063i	$-0.584388\pi$
$977$	−28.1706	−	6.12814i	−0.901257	−	0.196056i	−0.639240	+	0.769007i	$0.720751\pi$
$978$	9.18670	+	1.99845i	0.293758	+	0.0639032i
$979$	−31.6206	+	27.3994i	−1.01060	+	0.875689i
$980$	9.25660	−	1.59338i	0.295691	−	0.0508987i
$981$	−45.0129	−	6.47188i	−1.43715	−	0.206631i
$982$	2.84448	+	39.7711i	0.0907711	+	1.26915i
$983$	−5.50986	−	14.7725i	−0.175737	−	0.471170i	0.818980	−	0.573822i	$-0.194540\pi$
$983$	−5.50986	−	14.7725i	−0.175737	−	0.471170i	−0.994717	+	0.102652i	$0.967267\pi$
$984$	−1.65429	+	5.63398i	−0.0527367	+	0.179605i
$985$	−22.9603	−	11.7248i	−0.731577	−	0.373583i
$986$	36.9906	−	5.31845i	1.17802	−	0.169374i
$987$	0.891652	+	4.09886i	0.0283816	+	0.130468i
$988$	−3.76579	+	3.76579i	−0.119806	+	0.119806i
$989$	24.1124	+	1.99979i	0.766729	+	0.0635896i
$990$	−18.8533	+	14.9447i	−0.599197	+	0.474973i
$991$	10.2067	+	6.55944i	0.324226	+	0.208368i	0.692621	−	0.721302i	$-0.256456\pi$
$991$	10.2067	+	6.55944i	0.324226	+	0.208368i	−0.368394	+	0.929670i	$0.620092\pi$
$992$	6.27814	+	4.69975i	0.199331	+	0.149217i
$993$	6.11292	−	16.3894i	0.193988	−	0.520101i
$994$	18.2654	+	5.36321i	0.579343	+	0.170111i
$995$	−24.5445	+	40.6202i	−0.778113	+	1.28775i
$996$	2.62818	+	2.27733i	0.0832771	+	0.0721600i
$997$	6.17450	+	8.24816i	0.195548	+	0.261222i	0.887589	−	0.460637i	$-0.152379\pi$
$997$	6.17450	+	8.24816i	0.195548	+	0.261222i	−0.692040	+	0.721859i	$0.743288\pi$
$998$	−8.81581	−	4.81380i	−0.279060	−	0.152378i
$999$	−32.9284	−	38.0013i	−1.04181	−	1.20231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.113.3	yes	240
5.2	odd	4	inner	230.2.l.a.67.4	yes	240
23.11	odd	22	inner	230.2.l.a.103.4	yes	240
115.57	even	44	inner	230.2.l.a.57.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.3	✓	240	115.57	even	44	inner
230.2.l.a.67.4	yes	240	5.2	odd	4	inner
230.2.l.a.103.4	yes	240	23.11	odd	22	inner
230.2.l.a.113.3	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.977147 + 0.212565i) q^{2} +(-0.470115 + 0.628000i) q^{3} +(0.909632 - 0.415415i) q^{4} +(-2.05891 - 0.872279i) q^{5} +(0.325880 - 0.713578i) q^{6} +(1.66889 - 0.119361i) q^{7} +(-0.800541 + 0.599278i) q^{8} +(0.671822 + 2.28802i) q^{9} +(2.19728 + 0.414691i) q^{10} +(2.43931 + 3.79564i) q^{11} +(-0.166751 + 0.766541i) q^{12} +(-0.120967 + 1.69134i) q^{13} +(-1.60538 + 0.471382i) q^{14} +(1.51572 - 0.882927i) q^{15} +(0.654861 - 0.755750i) q^{16} +(-3.59932 + 1.34248i) q^{17} +(-1.14282 - 2.09292i) q^{18} +(1.30471 + 2.85692i) q^{19} +(-2.23521 + 0.0618513i) q^{20} +(-0.709611 + 1.10418i) q^{21} +(-3.19039 - 3.19039i) q^{22} +(-4.06367 + 2.54688i) q^{23} -0.784469i q^{24} +(3.47826 + 3.59190i) q^{25} +(-0.241318 - 1.67840i) q^{26} +(-3.95773 - 1.47616i) q^{27} +(1.46849 - 0.801857i) q^{28} +(8.84904 + 4.04122i) q^{29} +(-1.29340 + 1.18494i) q^{30} +(1.11608 - 7.76254i) q^{31} +(-0.479249 + 0.877679i) q^{32} +(-3.53042 - 0.252501i) q^{33} +(3.23170 - 2.07689i) q^{34} +(-3.54022 - 1.20998i) q^{35} +(1.56159 + 1.80217i) q^{36} +(10.4478 + 5.70496i) q^{37} +(-1.88217 - 2.51429i) q^{38} +(-1.00529 - 0.871092i) q^{39} +(2.17098 - 0.535566i) q^{40} +(-7.18190 - 2.10880i) q^{41} +(0.458684 - 1.22978i) q^{42} +(-4.03876 - 3.02338i) q^{43} +(3.79564 + 2.43931i) q^{44} +(0.612563 - 5.29684i) q^{45} +(3.42943 - 3.35247i) q^{46} +(2.25984 - 2.25984i) q^{47} +(0.166751 + 0.766541i) q^{48} +(-4.15780 + 0.597802i) q^{49} +(-4.16228 - 2.77045i) q^{50} +(0.849018 - 2.89149i) q^{51} +(0.592573 + 1.58875i) q^{52} +(-0.324238 - 4.53344i) q^{53} +(4.18106 + 0.601146i) q^{54} +(-1.71148 - 9.94267i) q^{55} +(-1.26448 + 1.09568i) q^{56} +(-2.40751 - 0.523721i) q^{57} +(-9.50584 - 2.06787i) q^{58} +(5.22049 - 4.52358i) q^{59} +(1.01196 - 1.43279i) q^{60} +(3.12421 + 0.449194i) q^{61} +(0.559468 + 7.82238i) q^{62} +(1.39430 + 3.73825i) q^{63} +(0.281733 - 0.959493i) q^{64} +(1.72438 - 3.37681i) q^{65} +(3.50341 - 0.503715i) q^{66} +(-0.130846 - 0.601491i) q^{67} +(-2.71637 + 2.71637i) q^{68} +(0.310953 - 3.74931i) q^{69} +(3.71651 + 0.429803i) q^{70} +(-9.57147 - 6.15121i) q^{71} +(-1.90898 - 1.42904i) q^{72} +(1.45235 - 3.89390i) q^{73} +(-11.4218 - 3.35373i) q^{74} +(-3.89089 + 0.495743i) q^{75} +(2.37361 + 2.05675i) q^{76} +(4.52400 + 6.04335i) q^{77} +(1.16748 + 0.637494i) q^{78} +(-1.72151 - 1.98673i) q^{79} +(-2.00753 + 0.984803i) q^{80} +(-3.23057 + 2.07616i) q^{81} +(7.46603 + 0.533981i) q^{82} +(2.12453 - 3.89079i) q^{83} +(-0.186793 + 1.29918i) q^{84} +(8.58170 + 0.375565i) q^{85} +(4.58913 + 2.09579i) q^{86} +(-6.69795 + 3.65736i) q^{87} +(-4.22742 - 1.57674i) q^{88} +(1.31973 + 9.17890i) q^{89} +(0.527361 + 5.30600i) q^{90} +2.83710i q^{91} +(-2.63843 + 4.00483i) q^{92} +(4.35019 + 4.35019i) q^{93} +(-1.72783 + 2.68855i) q^{94} +(-0.194259 - 7.02022i) q^{95} +(-0.325880 - 0.713578i) q^{96} +(0.636402 + 1.16548i) q^{97} +(3.93571 - 1.46795i) q^{98} +(-7.04571 + 8.13118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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