LMFDB - Embedded newform 560.2.cz.c.453.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(157,560)] 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("560.157"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cz (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [360,2,-24,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$90$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			453.11
Character	$\chi$	$=$	560.453
Dual form			560.2.cz.c.157.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32958 + 0.481883i) q^{2} +(0.689402 - 0.398026i) q^{3} +(1.53558 - 1.28141i) q^{4} +(1.03726 - 1.98093i) q^{5} +(-0.724815 + 0.861420i) q^{6} +(-1.14153 - 2.38682i) q^{7} +(-1.42419 + 2.44370i) q^{8} +(-1.18315 + 2.04928i) q^{9} +(-0.424538 + 3.13365i) q^{10} +(0.290585 - 1.08448i) q^{11} +(0.548597 - 1.49460i) q^{12} -6.68057i q^{13} +(2.66792 + 2.62339i) q^{14} +(-0.0733779 - 1.77852i) q^{15} +(0.715996 - 3.93540i) q^{16} +(-0.386691 + 1.44315i) q^{17} +(0.585584 - 3.29482i) q^{18} +(0.744366 + 2.77801i) q^{19} +(-0.945595 - 4.37102i) q^{20} +(-1.73699 - 1.19112i) q^{21} +(0.136235 + 1.58193i) q^{22} +(-0.000156465 - 0.000583934i) q^{23} +(-0.00917984 + 2.25156i) q^{24} +(-2.84820 - 4.10947i) q^{25} +(3.21925 + 8.88237i) q^{26} +4.27186i q^{27} +(-4.81139 - 2.20239i) q^{28} +(-4.47419 - 4.47419i) q^{29} +(0.954598 + 2.32932i) q^{30} +(-9.18741 + 5.30435i) q^{31} +(0.944425 + 5.57746i) q^{32} +(-0.231321 - 0.863302i) q^{33} +(-0.181292 - 2.10513i) q^{34} +(-5.91219 - 0.214458i) q^{35} +(0.809136 + 4.66292i) q^{36} +(0.807457 - 1.39856i) q^{37} +(-2.32837 - 3.33490i) q^{38} +(-2.65904 - 4.60560i) q^{39} +(3.36357 + 5.35597i) q^{40} +6.55424 q^{41} +(2.88345 + 0.746670i) q^{42} -10.8517i q^{43} +(-0.943442 - 2.03766i) q^{44} +(2.83225 + 4.46937i) q^{45} +(0.000489421 + 0.000700991i) q^{46} +(3.32581 - 0.891149i) q^{47} +(-1.07278 - 2.99806i) q^{48} +(-4.39384 + 5.44924i) q^{49} +(5.76720 + 4.09138i) q^{50} +(0.307827 + 1.14882i) q^{51} +(-8.56052 - 10.2585i) q^{52} +(8.87517 - 5.12408i) q^{53} +(-2.05854 - 5.67979i) q^{54} +(-1.84687 - 1.70051i) q^{55} +(7.45843 + 0.609734i) q^{56} +(1.61889 + 1.61889i) q^{57} +(8.10485 + 3.79277i) q^{58} +(0.129224 - 0.482271i) q^{59} +(-2.39168 - 2.63702i) q^{60} +(3.79365 - 1.01650i) q^{61} +(9.65934 - 11.4798i) q^{62} +(6.24185 + 0.484667i) q^{63} +(-3.94337 - 6.96059i) q^{64} +(-13.2338 - 6.92946i) q^{65} +(0.723571 + 1.03636i) q^{66} +(-3.77433 + 2.17911i) q^{67} +(1.25547 + 2.71158i) q^{68} +(-0.000340288 - 0.000340288i) q^{69} +(7.96409 - 2.56385i) q^{70} -5.39800i q^{71} +(-3.32279 - 5.80982i) q^{72} +(3.40697 - 12.7150i) q^{73} +(-0.399640 + 2.24859i) q^{74} +(-3.59923 - 1.69942i) q^{75} +(4.70279 + 3.31202i) q^{76} +(-2.92017 + 0.544385i) q^{77} +(5.75478 + 4.84217i) q^{78} +(9.43202 + 5.44558i) q^{79} +(-7.05309 - 5.50036i) q^{80} +(-1.84914 - 3.20280i) q^{81} +(-8.71440 + 3.15838i) q^{82} +8.40249i q^{83} +(-4.19359 + 0.396727i) q^{84} +(2.45769 + 2.26293i) q^{85} +(5.22923 + 14.4282i) q^{86} +(-4.86537 - 1.30367i) q^{87} +(2.23630 + 2.25461i) q^{88} +(7.59633 + 4.38574i) q^{89} +(-5.91942 - 4.57757i) q^{90} +(-15.9453 + 7.62604i) q^{91} +(-0.000988521 - 0.000696181i) q^{92} +(-4.22255 + 7.31367i) q^{93} +(-3.99251 + 2.78751i) q^{94} +(6.27515 + 1.40697i) q^{95} +(2.87107 + 3.46921i) q^{96} +(-11.1142 - 11.1142i) q^{97} +(3.21607 - 9.36252i) q^{98} +(1.87859 + 1.87859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.32958	+	0.481883i	−0.940157	+	0.340743i
$2$	−1.32958	+	0.481883i	−0.940157	+	0.340743i
$3$	0.689402	−	0.398026i	0.398026	−	0.229801i	−0.287606	−	0.957749i	$-0.592859\pi$
$3$	0.689402	−	0.398026i	0.398026	−	0.229801i	0.685632	+	0.727948i	$0.259526\pi$
$4$	1.53558	−	1.28141i	0.767789	−	0.640703i
$5$	1.03726	−	1.98093i	0.463875	−	0.885901i
$5$	1.03726	−	1.98093i	0.463875	−	0.885901i
$6$	−0.724815	+	0.861420i	−0.295904	+	0.351673i
$7$	−1.14153	−	2.38682i	−0.431456	−	0.902134i
$7$	−1.14153	−	2.38682i	−0.431456	−	0.902134i
$8$	−1.42419	+	2.44370i	−0.503527	+	0.863980i
$9$	−1.18315	+	2.04928i	−0.394383	+	0.683092i
$10$	−0.424538	+	3.13365i	−0.134251	+	0.990947i
$11$	0.290585	−	1.08448i	0.0876147	−	0.326983i	−0.908182	−	0.418576i	$-0.862529\pi$
$11$	0.290585	−	1.08448i	0.0876147	−	0.326983i	0.995796	+	0.0915934i	$0.0291960\pi$
$12$	0.548597	−	1.49460i	0.158366	−	0.431455i
$13$		−	6.68057i		−	1.85286i	−0.376471	−	0.926428i	$-0.622862\pi$
$13$		−	6.68057i		−	1.85286i	0.376471	−	0.926428i	$-0.377138\pi$
$14$	2.66792	+	2.62339i	0.713032	+	0.701132i
$15$	−0.0733779	−	1.77852i	−0.0189461	−	0.459211i
$16$	0.715996	−	3.93540i	0.178999	−	0.983849i
$17$	−0.386691	+	1.44315i	−0.0937864	+	0.350016i	−0.996833	−	0.0795278i	$-0.974659\pi$
$17$	−0.386691	+	1.44315i	−0.0937864	+	0.350016i	0.903046	+	0.429543i	$0.141325\pi$
$18$	0.585584	−	3.29482i	0.138023	−	0.776597i
$19$	0.744366	+	2.77801i	0.170769	+	0.637319i	0.997234	+	0.0743304i	$0.0236820\pi$
$19$	0.744366	+	2.77801i	0.170769	+	0.637319i	−0.826464	+	0.562989i	$0.809651\pi$
$20$	−0.945595	−	4.37102i	−0.211441	−	0.977391i
$21$	−1.73699	−	1.19112i	−0.379042	−	0.259924i
$22$	0.136235	+	1.58193i	0.0290454	+	0.337269i
$23$	−0.000156465	0	0.000583934i	−3.26251e−5	0	0.000121759i	0.965910	−	0.258880i	$-0.0833534\pi$
$23$	−0.000156465	0	0.000583934i	−3.26251e−5	0	0.000121759i	−0.965942	+	0.258758i	$0.916687\pi$
$24$	−0.00917984	+	2.25156i	−0.00187383	+	0.459598i
$25$	−2.84820	−	4.10947i	−0.569640	−	0.821894i
$26$	3.21925	+	8.88237i	0.631348	+	1.74198i
$27$			4.27186i			0.822120i
$28$	−4.81139	−	2.20239i	−0.909267	−	0.416213i
$29$	−4.47419	−	4.47419i	−0.830837	−	0.830837i	0.156794	−	0.987631i	$-0.449884\pi$
$29$	−4.47419	−	4.47419i	−0.830837	−	0.830837i	−0.987631	+	0.156794i	$0.949884\pi$
$30$	0.954598	+	2.32932i	0.174285	+	0.425274i
$31$	−9.18741	+	5.30435i	−1.65011	+	0.952690i	−0.673082	+	0.739568i	$0.735030\pi$
$31$	−9.18741	+	5.30435i	−1.65011	+	0.952690i	−0.977025	+	0.213122i	$0.931637\pi$
$32$	0.944425	+	5.57746i	0.166952	+	0.985965i
$33$	−0.231321	−	0.863302i	−0.0402679	−	0.150282i
$34$	−0.181292	−	2.10513i	−0.0310914	−	0.361026i
$35$	−5.91219	−	0.214458i	−0.999343	−	0.0362500i
$36$	0.809136	+	4.66292i	0.134856	+	0.777153i
$37$	0.807457	−	1.39856i	0.132745	−	0.229921i	−0.791989	−	0.610536i	$-0.790954\pi$
$37$	0.807457	−	1.39856i	0.132745	−	0.229921i	0.924734	+	0.380615i	$0.124288\pi$
$38$	−2.32837	−	3.33490i	−0.377712	−	0.540992i
$39$	−2.65904	−	4.60560i	−0.425788	−	0.737486i
$40$	3.36357	+	5.35597i	0.531827	+	0.846853i
$41$	6.55424			1.02360			0.511800	−	0.859105i	$-0.328979\pi$
$41$	6.55424			1.02360			0.511800	+	0.859105i	$0.328979\pi$
$42$	2.88345	+	0.746670i	0.444926	+	0.115214i
$43$		−	10.8517i		−	1.65486i	−0.561566	−	0.827432i	$-0.689801\pi$
$43$		−	10.8517i		−	1.65486i	0.561566	−	0.827432i	$-0.310199\pi$
$44$	−0.943442	−	2.03766i	−0.142229	−	0.307189i
$45$	2.83225	+	4.46937i	0.422207	+	0.666254i
$46$	0.000489421	0	0.000700991i	7.21611e−5	0	0.000103355i
$47$	3.32581	−	0.891149i	0.485120	−	0.129987i	−0.00796577	−	0.999968i	$-0.502536\pi$
$47$	3.32581	−	0.891149i	0.485120	−	0.129987i	0.493086	+	0.869981i	$0.335869\pi$
$48$	−1.07278	−	2.99806i	−0.154843	−	0.432732i
$49$	−4.39384	+	5.44924i	−0.627691	+	0.778463i
$50$	5.76720	+	4.09138i	0.815605	+	0.578609i
$51$	0.307827	+	1.14882i	0.0431043	+	0.160868i
$52$	−8.56052	−	10.2585i	−1.18713	−	1.42260i
$53$	8.87517	−	5.12408i	1.21910	−	0.703847i	0.254374	−	0.967106i	$-0.418131\pi$
$53$	8.87517	−	5.12408i	1.21910	−	0.703847i	0.964725	+	0.263259i	$0.0847973\pi$
$54$	−2.05854	−	5.67979i	−0.280131	−	0.772921i
$55$	−1.84687	−	1.70051i	−0.249032	−	0.229297i
$56$	7.45843	+	0.609734i	0.996675	+	0.0814791i
$57$	1.61889	+	1.61889i	0.214427	+	0.214427i
$58$	8.10485	+	3.79277i	1.06422	+	0.498015i
$59$	0.129224	−	0.482271i	0.0168236	−	0.0627864i	−0.957004	−	0.290076i	$-0.906320\pi$
$59$	0.129224	−	0.482271i	0.0168236	−	0.0627864i	0.973827	+	0.227289i	$0.0729862\pi$
$60$	−2.39168	−	2.63702i	−0.308764	−	0.340438i
$61$	3.79365	−	1.01650i	0.485727	−	0.130150i	−0.00764124	−	0.999971i	$-0.502432\pi$
$61$	3.79365	−	1.01650i	0.485727	−	0.130150i	0.493368	+	0.869821i	$0.335766\pi$
$62$	9.65934	−	11.4798i	1.22674	−	1.45794i
$63$	6.24185	+	0.484667i	0.786399	+	0.0610623i
$64$	−3.94337	−	6.96059i	−0.492922	−	0.870074i
$65$	−13.2338	−	6.92946i	−1.64145	−	0.859494i
$66$	0.723571	+	1.03636i	0.0890655	+	0.127567i
$67$	−3.77433	+	2.17911i	−0.461108	+	0.266221i	−0.712510	−	0.701662i	$-0.752442\pi$
$67$	−3.77433	+	2.17911i	−0.461108	+	0.266221i	0.251402	+	0.967883i	$0.419108\pi$
$68$	1.25547	+	2.71158i	0.152248	+	0.328827i
$69$	−0.000340288	0	0.000340288i	−4.09659e−5	0	4.09659e-5i
$70$	7.96409	−	2.56385i	0.951891	−	0.306438i
$71$		−	5.39800i		−	0.640625i	−0.947312	−	0.320313i	$-0.896212\pi$
$71$		−	5.39800i		−	0.640625i	0.947312	−	0.320313i	$-0.103788\pi$
$72$	−3.32279	−	5.80982i	−0.391595	−	0.684694i
$73$	3.40697	−	12.7150i	0.398756	−	1.48818i	−0.416531	−	0.909121i	$-0.636754\pi$
$73$	3.40697	−	12.7150i	0.398756	−	1.48818i	0.815287	−	0.579057i	$-0.196579\pi$
$74$	−0.399640	+	2.24859i	−0.0464572	+	0.261394i
$75$	−3.59923	−	1.69942i	−0.415604	−	0.196232i
$76$	4.70279	+	3.31202i	0.539447	+	0.379914i
$77$	−2.92017	+	0.544385i	−0.332784	+	0.0620385i
$78$	5.75478	+	4.84217i	0.651600	+	0.548268i
$79$	9.43202	+	5.44558i	1.06119	+	0.612676i	0.925760	−	0.378112i	$-0.123427\pi$
$79$	9.43202	+	5.44558i	1.06119	+	0.612676i	0.135425	+	0.990788i	$0.456760\pi$
$80$	−7.05309	−	5.50036i	−0.788560	−	0.614958i
$81$	−1.84914	−	3.20280i	−0.205460	−	0.355867i
$82$	−8.71440	+	3.15838i	−0.962345	+	0.348784i
$83$			8.40249i			0.922293i	0.887324	+	0.461146i	$0.152562\pi$
$83$			8.40249i			0.922293i	−0.887324	+	0.461146i	$0.847438\pi$
$84$	−4.19359	+	0.396727i	−0.457558	+	0.0432865i
$85$	2.45769	+	2.26293i	0.266574	+	0.245449i
$86$	5.22923	+	14.4282i	0.563883	+	1.55583i
$87$	−4.86537	−	1.30367i	−0.521622	−	0.139768i
$88$	2.23630	+	2.25461i	0.238390	+	0.240342i
$89$	7.59633	+	4.38574i	0.805209	+	0.464888i	0.845289	−	0.534309i	$-0.179428\pi$
$89$	7.59633	+	4.38574i	0.805209	+	0.464888i	−0.0400802	+	0.999196i	$0.512761\pi$
$90$	−5.91942	−	4.57757i	−0.623962	−	0.482519i
$91$	−15.9453	+	7.62604i	−1.67153	+	0.799427i
$92$	−0.000988521	0	0.000696181i	−0.000103060	0	7.25819e-5i
$93$	−4.22255	+	7.31367i	−0.437858	+	0.758392i
$94$	−3.99251	+	2.78751i	−0.411796	+	0.287510i
$95$	6.27515	+	1.40697i	0.643817	+	0.144352i
$96$	2.87107	+	3.46921i	0.293027	+	0.354074i
$97$	−11.1142	−	11.1142i	−1.12847	−	1.12847i	−0.990426	−	0.138048i	$-0.955917\pi$
$97$	−11.1142	−	11.1142i	−1.12847	−	1.12847i	−0.138048	−	0.990426i	$-0.544083\pi$
$98$	3.21607	−	9.36252i	0.324872	−	0.945758i
$99$	1.87859	+	1.87859i	0.188805	+	0.188805i
$100$	−9.63953	−	2.66071i	−0.963953	−	0.266071i
$101$	9.54856	+	2.55853i	0.950117	+	0.254583i	0.700412	−	0.713739i	$-0.253000\pi$
$101$	9.54856	+	2.55853i	0.950117	+	0.254583i	0.249705	+	0.968322i	$0.419666\pi$
$102$	−0.962880	−	1.37912i	−0.0953393	−	0.136553i
$103$	−6.21615	+	1.66561i	−0.612496	+	0.164118i	−0.551714	−	0.834033i	$-0.686026\pi$
$103$	−6.21615	+	1.66561i	−0.612496	+	0.164118i	−0.0607816	+	0.998151i	$0.519359\pi$
$104$	16.3253	+	9.51439i	1.60083	+	0.932963i
$105$	−4.16124	+	2.20536i	−0.406095	+	0.215221i
$106$	−9.33106	+	11.0897i	−0.906313	+	1.07713i
$107$	−2.55973	+	4.43358i	−0.247458	+	0.428610i	−0.962820	−	0.270144i	$-0.912929\pi$
$107$	−2.55973	+	4.43358i	−0.247458	+	0.428610i	0.715362	+	0.698754i	$0.246262\pi$
$108$	5.47399	+	6.55977i	0.526735	+	0.631214i
$109$	2.42712	−	9.05814i	0.232476	−	0.867613i	−0.746794	−	0.665055i	$-0.768408\pi$
$109$	2.42712	−	9.05814i	0.232476	−	0.867613i	0.979270	−	0.202558i	$-0.0649253\pi$
$110$	3.27501	+	1.37100i	0.312260	+	0.130719i
$111$		−	1.28556i		−	0.122020i
$112$	−10.2104	+	2.78340i	−0.964794	+	0.263007i
$113$	10.1175	+	10.1175i	0.951779	+	0.951779i	0.998890	−	0.0471109i	$-0.0150014\pi$
$113$	10.1175	+	10.1175i	0.951779	+	0.951779i	−0.0471109	+	0.998890i	$0.515001\pi$
$114$	−2.93256	−	1.37233i	−0.274660	−	0.128531i
$115$	−0.00131903		0.000295743i	−0.000123000		2.75782e-5i
$116$	−12.6037	−	1.13721i	−1.17023	−	0.105587i
$117$	13.6903	+	7.90412i	1.26567	+	0.730736i
$118$	0.0605842	+	0.703490i	0.00557722	+	0.0647615i
$119$	3.88596	−	0.724431i	0.356226	−	0.0664085i
$120$	4.45067	+	2.35363i	0.406289	+	0.214856i
$121$	8.43463	+	4.86973i	0.766784	+	0.442703i
$122$	−4.55413	+	3.17962i	−0.412311	+	0.287869i
$123$	4.51851	−	2.60876i	0.407420	−	0.235224i
$124$	−7.31095	+	19.9181i	−0.656543	+	1.78869i
$125$	−11.0949	+	1.37952i	−0.992358	+	0.123388i
$126$	−8.53261	+	2.36344i	−0.760145	+	0.210552i
$127$	−4.32394	+	4.32394i	−0.383687	+	0.383687i	−0.872429	−	0.488741i	$-0.837456\pi$
$127$	−4.32394	+	4.32394i	−0.383687	+	0.383687i	0.488741	+	0.872429i	$0.337456\pi$
$128$	8.59723	+	7.35443i	0.759895	+	0.650046i
$129$	−4.31925	−	7.48116i	−0.380289	−	0.658679i
$130$	20.9346	+	2.83616i	1.83608	+	0.248748i
$131$	9.57147	−	2.56467i	0.836263	−	0.224076i	0.184819	−	0.982773i	$-0.440830\pi$
$131$	9.57147	−	2.56467i	0.836263	−	0.224076i	0.651444	+	0.758697i	$0.274164\pi$
$132$	−1.46145	−	1.02925i	−0.127203	−	0.0895848i
$133$	5.78090	−	4.94784i	0.501268	−	0.429032i
$134$	3.96821	−	4.71609i	0.342801	−	0.407409i
$135$	8.46227	+	4.43101i	0.728316	+	0.381361i
$136$	−2.97591	−	3.00028i	−0.255182	−	0.257272i
$137$	3.45869	−	12.9080i	0.295496	−	1.10280i	−0.645327	−	0.763906i	$-0.723279\pi$
$137$	3.45869	−	12.9080i	0.295496	−	1.10280i	0.940823	−	0.338898i	$-0.110054\pi$
$138$	0.000616420	0	0.000288462i	5.24732e−5	0	2.45555e-5i
$139$	7.77668	+	7.77668i	0.659609	+	0.659609i	0.955288	−	0.295678i	$-0.0955457\pi$
$139$	7.77668	+	7.77668i	0.659609	+	0.659609i	−0.295678	+	0.955288i	$0.595546\pi$
$140$	−9.35344	+	7.24660i	−0.790510	+	0.612450i
$141$	1.93812	−	1.93812i	0.163219	−	0.163219i
$142$	2.60121	+	7.17709i	0.218288	+	0.602288i
$143$	−7.24494	−	1.94127i	−0.605852	−	0.162338i
$144$	7.21758	+	6.12344i	0.601465	+	0.510287i
$145$	−13.5040	+	4.22220i	−1.12144	+	0.350635i
$146$	1.59729	+	18.5474i	0.132193	+	1.53499i
$147$	−0.860180	+	5.50558i	−0.0709465	+	0.454093i
$148$	−0.552206	−	3.18227i	−0.0453911	−	0.261581i
$149$	0.945337	+	3.52805i	0.0774450	+	0.289029i	0.993777	−	0.111392i	$-0.0355308\pi$
$149$	0.945337	+	3.52805i	0.0774450	+	0.289029i	−0.916332	+	0.400420i	$0.868864\pi$
$150$	5.60440	+	0.525107i	0.457597	+	0.0428748i
$151$	13.3247	−	7.69302i	1.08435	−	0.626049i	0.152283	−	0.988337i	$-0.451338\pi$
$151$	13.3247	−	7.69302i	1.08435	−	0.626049i	0.932066	+	0.362288i	$0.118004\pi$
$152$	−7.84875	−	2.13740i	−0.636618	−	0.173366i
$153$	−2.49990	−	2.49990i	−0.202105	−	0.202105i
$154$	3.62027	−	2.13098i	0.291730	−	0.171720i
$155$	0.977880	+	23.7016i	0.0785453	+	1.90376i
$156$	−9.98481	−	3.66494i	−0.799425	−	0.293430i
$157$	1.99716	+	3.45918i	0.159391	+	0.276073i	0.934649	−	0.355571i	$-0.115714\pi$
$157$	1.99716	+	3.45918i	0.159391	+	0.276073i	−0.775258	+	0.631644i	$0.782380\pi$
$158$	−15.1648	−	2.69521i	−1.20644	−	0.214420i
$159$	4.07904	−	7.06511i	0.323489	−	0.560300i
$160$	12.0282	+	3.91441i	0.950912	+	0.309461i
$161$	−0.00121514	+	0.00104003i	−9.57663e−5	+	8.19658e-5i
$162$	4.00195	+	3.36732i	0.314423	+	0.264561i
$163$	−2.22441	+	3.85280i	−0.174229	+	0.301774i	−0.939894	−	0.341465i	$-0.889077\pi$
$163$	−2.22441	+	3.85280i	−0.174229	+	0.301774i	0.765665	+	0.643240i	$0.222410\pi$
$164$	10.0645	−	8.39864i	0.785909	−	0.655824i
$165$	−1.95008	−	0.437233i	−0.151814	−	0.0340386i
$166$	−4.04902	−	11.1718i	−0.314265	−	0.867099i
$167$	−15.0819	+	15.0819i	−1.16707	+	1.16707i	−0.184180	+	0.982893i	$0.558963\pi$
$167$	−15.0819	+	15.0819i	−1.16707	+	1.16707i	−0.982893	+	0.184180i	$0.941037\pi$
$168$	5.38455	−	2.54830i	0.415427	−	0.196606i
$169$	−31.6300			−2.43308
$170$	−4.35817	−	1.82443i	−0.334256	−	0.139927i
$171$	−6.57361	−	1.76139i	−0.502696	−	0.134697i
$172$	−13.9054	−	16.6636i	−1.06028	−	1.27059i
$173$	15.3079	+	8.83801i	1.16384	+	0.671942i	0.952221	−	0.305411i	$-0.0987939\pi$
$173$	15.3079	+	8.83801i	1.16384	+	0.671942i	0.211616	+	0.977353i	$0.432127\pi$
$174$	7.09712	−	0.611200i	0.538031	−	0.0463349i
$175$	−6.55728	+	11.4892i	−0.495684	+	0.868503i
$176$	−4.05980	−	1.92005i	−0.306019	−	0.144729i
$177$	−0.102869	−	0.383913i	−0.00773213	−	0.0288567i
$178$	−12.2134	−	2.17066i	−0.915430	−	0.162698i
$179$	−3.68851	+	13.7657i	−0.275693	+	1.02890i	0.679683	+	0.733506i	$0.262117\pi$
$179$	−3.68851	+	13.7657i	−0.275693	+	1.02890i	−0.955376	+	0.295393i	$0.904549\pi$
$180$	10.0762	+	3.23379i	0.751037	+	0.241033i
$181$	−9.40487	+	9.40487i	−0.699059	+	0.699059i	−0.964208	−	0.265149i	$-0.914579\pi$
$181$	−9.40487	+	9.40487i	−0.699059	+	0.699059i	0.265149	+	0.964208i	$0.414579\pi$
$182$	17.5258	−	17.8232i	1.29910	−	1.32115i
$183$	2.21075	−	2.21075i	0.163423	−	0.163423i
$184$	0.00164980		0.000449279i	0.000121625		3.31213e-5i
$185$	−1.93291	−	3.05018i	−0.142110	−	0.224254i
$186$	2.08989	−	11.7589i	0.153238	−	0.862204i
$187$	1.45270	+	0.838717i	0.106232	+	0.0613330i
$188$	3.96512	−	5.63015i	0.289186	−	0.410621i
$189$	10.1962	−	4.87644i	0.741662	−	0.354709i
$190$	−9.02133	+	1.15321i	−0.654476	+	0.0836627i
$191$	−5.23759	+	9.07177i	−0.378979	+	0.656410i	−0.990914	−	0.134498i	$-0.957058\pi$
$191$	−5.23759	+	9.07177i	−0.378979	+	0.656410i	0.611935	+	0.790908i	$0.290391\pi$
$192$	−5.48907	−	3.22908i	−0.396139	−	0.233039i
$193$	2.65656	−	9.91441i	0.191223	−	0.713655i	−0.801989	−	0.597339i	$-0.796225\pi$
$193$	2.65656	−	9.91441i	0.191223	−	0.713655i	0.993212	−	0.116316i	$-0.0371086\pi$
$194$	20.1329	+	9.42148i	1.44546	+	0.676423i
$195$	−11.8815	+	0.490206i	−0.850852	+	0.0351044i
$196$	0.235608	+	13.9980i	0.0168292	+	0.999858i
$197$	14.0883			1.00375			0.501876	−	0.864939i	$-0.332643\pi$
$197$	14.0883			1.00375			0.501876	+	0.864939i	$0.332643\pi$
$198$	−3.40300	−	1.59248i	−0.241841	−	0.113173i
$199$	2.43672	−	1.40684i	0.172735	−	0.0997284i	−0.411140	−	0.911572i	$-0.634869\pi$
$199$	2.43672	−	1.40684i	0.172735	−	0.0997284i	0.583875	+	0.811844i	$0.301536\pi$
$200$	14.0987	−	1.10750i	0.996929	−	0.0783118i
$201$	−1.73469	+	3.00457i	−0.122355	+	0.211926i
$202$	−13.9285	+	1.19951i	−0.980006	+	0.0843975i
$203$	−5.57170	+	15.7865i	−0.391057	+	1.10800i
$204$	1.94480	+	1.36966i	0.136163	+	0.0958953i
$205$	6.79842	−	12.9835i	0.474823	−	0.906808i
$206$	7.46225	−	5.21003i	0.519920	−	0.363000i
$207$	0.00138176		0.000370242i	9.60392e−5		2.57336e-5i
$208$	−26.2907	−	4.78326i	−1.82293	−	0.331660i
$209$	3.22899			0.223354
$210$	4.46998	−	4.93744i	0.308458	−	0.340716i
$211$	10.4346	−	10.4346i	0.718351	−	0.718351i	−0.249917	−	0.968267i	$-0.580403\pi$
$211$	10.4346	−	10.4346i	0.718351	−	0.718351i	0.968267	+	0.249917i	$0.0804032\pi$
$212$	7.06248	−	19.2411i	0.485053	−	1.32149i
$213$	−2.14855	−	3.72139i	−0.147216	−	0.254986i
$214$	1.26690	−	7.12829i	0.0866036	−	0.487280i
$215$	−21.4964	−	11.2560i	−1.46604	−	0.767650i
$216$	−10.4392	−	6.08393i	−0.710295	−	0.413959i
$217$	23.1482	+	15.8737i	1.57140	+	1.07757i
$218$	1.13791	+	13.2131i	0.0770688	+	0.894906i
$219$	−2.71213	−	10.1218i	−0.183269	−	0.683969i
$220$	−5.01506	−	0.244678i	−0.338115	−	0.0164962i
$221$	9.64107	+	2.58332i	0.648529	+	0.173773i
$222$	0.619488	+	1.70925i	0.0415773	+	0.114718i
$223$	15.4512	−	15.4512i	1.03469	−	1.03469i	0.0353113	−	0.999376i	$-0.488758\pi$
$223$	15.4512	−	15.4512i	1.03469	−	1.03469i	0.999376	−	0.0353113i	$-0.0112423\pi$
$224$	12.2343	−	8.62099i	0.817440	−	0.576014i
$225$	11.7913	−	0.974628i	0.786086	−	0.0649752i
$226$	−18.3276	−	8.57664i	−1.21913	−	0.570509i
$227$	5.60864	+	9.71444i	0.372258	+	0.644770i	0.989913	−	0.141679i	$-0.0452502\pi$
$227$	5.60864	+	9.71444i	0.372258	+	0.644770i	−0.617654	+	0.786450i	$0.711917\pi$
$228$	4.56038	+	0.411475i	0.302019	+	0.0272506i
$229$	−5.17754	+	1.38732i	−0.342141	+	0.0916765i	−0.425798	−	0.904818i	$-0.640007\pi$
$229$	−5.17754	+	1.38732i	−0.342141	+	0.0916765i	0.0836570	+	0.996495i	$0.473340\pi$
$230$	0.00189627		0.000242403i	0.000125036		1.59836e-5i
$231$	−1.79649	+	1.53760i	−0.118200	+	0.101167i
$232$	17.3057	−	4.56151i	1.13618	−	0.299478i
$233$	0.0409163	+	0.152702i	0.00268051	+	0.0100038i	0.967253	−	0.253814i	$-0.0816850\pi$
$233$	0.0409163	+	0.152702i	0.00268051	+	0.0100038i	−0.964573	+	0.263817i	$0.915018\pi$
$234$	−22.0113	−	3.91203i	−1.43892	−	0.255738i
$235$	1.68441	−	7.51257i	0.109879	−	0.490066i
$236$	−0.419552	−	0.906154i	−0.0273105	−	0.0589856i
$237$	8.66994			0.563173
$238$	−4.81761	+	2.83577i	−0.312280	+	0.183816i
$239$		−	5.89971i		−	0.381621i	−0.981627	−	0.190810i	$-0.938888\pi$
$239$		−	5.89971i		−	0.381621i	0.981627	−	0.190810i	$-0.0611115\pi$
$240$	−7.05170	−	0.984640i	−0.455185	−	0.0635582i
$241$	0.865145	−	0.499492i	0.0557289	−	0.0321751i	−0.471877	−	0.881665i	$-0.656423\pi$
$241$	0.865145	−	0.499492i	0.0557289	−	0.0321751i	0.527606	+	0.849489i	$0.323090\pi$
$242$	−13.5612	−	2.41021i	−0.871745	−	0.154934i
$243$	−13.6482	−	7.87980i	−0.875533	−	0.505489i
$244$	4.52288	−	6.42212i	0.289548	−	0.411134i
$245$	6.23705	+	14.3562i	0.398470	+	0.917181i
$246$	−4.75061	+	5.64595i	−0.302888	+	0.359973i
$247$	18.5587	−	4.97279i	1.18086	−	0.316411i
$248$	0.122336	−	30.0057i	0.00776837	−	1.90536i
$249$	3.34441	+	5.79269i	0.211943	+	0.367097i
$250$	14.0868	−	7.18064i	0.890929	−	0.454143i
$251$	8.50132	−	8.50132i	0.536599	−	0.536599i	−0.385930	−	0.922528i	$-0.626119\pi$
$251$	8.50132	−	8.50132i	0.536599	−	0.536599i	0.922528	+	0.385930i	$0.126119\pi$
$252$	10.2059	−	7.25410i	0.642911	−	0.456966i
$253$	−0.000678730	0		−4.26714e−5	0
$254$	3.66540	−	7.83266i	0.229988	−	0.491465i
$255$	2.59504	+	0.581841i	0.162508	+	0.0364363i
$256$	−14.9747	−	5.63546i	−0.935919	−	0.352216i
$257$	−7.25364	+	1.94361i	−0.452470	+	0.121239i	−0.477855	−	0.878439i	$-0.658585\pi$
$257$	−7.25364	+	1.94361i	−0.452470	+	0.121239i	0.0253851	+	0.999678i	$0.491919\pi$
$258$	9.34784	+	7.86544i	0.581971	+	0.489681i
$259$	−4.25984	−	0.330768i	−0.264693	−	0.0205529i
$260$	−29.2009	+	6.31711i	−1.81097	+	0.391771i
$261$	14.4625	−	3.87522i	0.895206	−	0.239870i
$262$	−11.4902	+	8.02226i	−0.709866	+	0.495617i
$263$	−16.9565	−	4.54347i	−1.04558	−	0.280162i	−0.305156	−	0.952302i	$-0.598709\pi$
$263$	−16.9565	−	4.54347i	−1.04558	−	0.280162i	−0.740424	+	0.672140i	$0.765375\pi$
$264$	2.43910	+	0.664225i	0.150116	+	0.0408802i
$265$	−0.944647	−	22.8961i	−0.0580292	−	1.40650i
$266$	−5.30191	+	9.36428i	−0.325081	+	0.574161i
$267$	6.98257			0.427326
$268$	−3.00345	+	8.18265i	−0.183465	+	0.499835i
$269$	−9.16044	−	2.45453i	−0.558522	−	0.149656i	−0.0314948	−	0.999504i	$-0.510027\pi$
$269$	−9.16044	−	2.45453i	−0.558522	−	0.149656i	−0.527027	+	0.849848i	$0.676693\pi$
$270$	−13.3865	−	1.81357i	−0.814677	−	0.110370i
$271$	18.2436	+	10.5329i	1.10822	+	0.639831i	0.938368	−	0.345638i	$-0.112338\pi$
$271$	18.2436	+	10.5329i	1.10822	+	0.639831i	0.169852	+	0.985470i	$0.445671\pi$
$272$	5.40250	+	2.55507i	0.327575	+	0.154924i
$273$	−7.95738	+	11.6041i	−0.481602	+	0.702311i
$274$	1.62154	+	18.8289i	0.0979605	+	1.13750i
$275$	−5.28428	+	1.89466i	−0.318654	+	0.114252i
$276$	−0.000958587	0	8.64915e-5i	−5.77001e−5	0	5.20618e-6i
$277$	3.76115	+	6.51451i	0.225986	+	0.391419i	0.956615	−	0.291356i	$-0.0941064\pi$
$277$	3.76115	+	6.51451i	0.225986	+	0.391419i	−0.730629	+	0.682775i	$0.760773\pi$
$278$	−14.0872	−	6.59228i	−0.844893	−	0.395379i
$279$		−	25.1034i		−	1.50290i
$280$	8.94415	−	14.1422i	0.534515	−	0.845159i
$281$		−	9.45241i		−	0.563883i	−0.959432	−	0.281942i	$-0.909022\pi$
$281$		−	9.45241i		−	0.563883i	0.959432	−	0.281942i	$-0.0909785\pi$
$282$	−1.64294	+	3.51084i	−0.0978359	+	0.209068i
$283$	7.02114	+	12.1610i	0.417364	+	0.722895i	0.995673	−	0.0929223i	$-0.0296208\pi$
$283$	7.02114	+	12.1610i	0.417364	+	0.722895i	−0.578310	+	0.815817i	$0.696287\pi$
$284$	−6.91703	−	8.28905i	−0.410450	−	0.491865i
$285$	4.88611	−	1.52771i	0.289428	−	0.0904938i
$286$	10.5682	−	0.910128i	0.624911	−	0.0538170i
$287$	−7.48183	−	15.6438i	−0.441639	−	0.923425i
$288$	−12.5471	−	4.66358i	−0.739348	−	0.274804i
$289$	12.7893	+	7.38389i	0.752310	+	0.434347i
$290$	15.9200	−	12.1211i	0.934856	−	0.711775i
$291$	−12.0859	−	3.23840i	−0.708486	−	0.189838i
$292$	−11.0614	−	23.8906i	−0.647320	−	1.39809i
$293$	10.4455			0.610235			0.305117	−	0.952315i	$-0.401304\pi$
$293$	10.4455			0.610235			0.305117	+	0.952315i	$0.401304\pi$
$294$	−1.50937	−	7.73463i	−0.0880280	−	0.451093i
$295$	−0.821309	−	0.756223i	−0.0478185	−	0.0440290i
$296$	2.26769	+	3.96499i	0.131807	+	0.230460i
$297$	4.63274	+	1.24134i	0.268819	+	0.0720298i
$298$	−2.95701	−	4.23528i	−0.171295	−	0.245343i
$299$	−0.00390101	+	0.00104527i	−0.000225601	+	6.04497e-5i
$300$	−7.70455	+	2.00249i	−0.444822	+	0.115614i
$301$	−25.9010	+	12.3875i	−1.49291	+	0.714001i
$302$	−14.0092	+	16.6495i	−0.806136	+	0.958068i
$303$	7.60116	−	2.03672i	0.436675	−	0.117007i
$304$	11.4655	−	0.940329i	0.657594	−	0.0539316i
$305$	1.92135	−	8.56934i	0.110016	−	0.490679i
$306$	4.52848	+	2.11916i	0.258876	+	0.121145i
$307$	−27.9820			−1.59702			−0.798508	−	0.601984i	$-0.794377\pi$
$307$	−27.9820			−1.59702			−0.798508	+	0.601984i	$0.794377\pi$
$308$	−3.78657	+	4.57787i	−0.215760	+	0.260848i
$309$	−3.62247	+	3.62247i	−0.206075	+	0.206075i
$310$	−12.7216	−	31.0420i	−0.722537	−	1.76307i
$311$	−3.59251	−	6.22241i	−0.203713	−	0.352841i	0.746009	−	0.665936i	$-0.231967\pi$
$311$	−3.59251	−	6.22241i	−0.203713	−	0.352841i	−0.949722	+	0.313095i	$0.898634\pi$
$312$	15.0417	+	0.0613266i	0.851569	+	0.00347193i
$313$	−14.0019	+	3.75180i	−0.791435	+	0.212064i	−0.631820	−	0.775115i	$-0.717692\pi$
$313$	−14.0019	+	3.75180i	−0.791435	+	0.212064i	−0.159615	+	0.987179i	$0.551025\pi$
$314$	−4.32231	−	3.63687i	−0.243922	−	0.205240i
$315$	7.43449	−	11.8620i	0.418886	−	0.668347i
$316$	21.4616	−	3.72414i	1.20731	−	0.209499i
$317$	−4.95608	−	2.86139i	−0.278361	−	0.160712i	0.354320	−	0.935124i	$-0.384712\pi$
$317$	−4.95608	−	2.86139i	−0.278361	−	0.160712i	−0.632681	+	0.774412i	$0.718046\pi$
$318$	−2.01887	+	11.3593i	−0.113212	+	0.636996i
$319$	−6.15230	+	3.55203i	−0.344463	+	0.198876i
$320$	−17.8788	+	0.591652i	−0.999453	+	0.0330744i
$321$			4.07536i			0.227464i
$322$	0.00111445	−	0.00196836i	6.21061e−5	−	0.000109692i
$323$	−4.29693			−0.239087
$324$	−6.94358	−	2.54865i	−0.385754	−	0.141592i
$325$	−27.4536	+	19.0276i	−1.52285	+	1.05546i
$326$	1.10094	−	6.19451i	0.0609756	−	0.343082i
$327$	−1.93212	−	7.21076i	−0.106846	−	0.398756i
$328$	−9.33447	+	16.0166i	−0.515410	+	0.884370i
$329$	−5.92352	−	6.92086i	−0.326574	−	0.381559i
$330$	2.80349	−	0.358375i	0.154327	−	0.0197279i
$331$	7.73949	−	2.07379i	0.425401	−	0.113986i	−0.0397655	−	0.999209i	$-0.512661\pi$
$331$	7.73949	−	2.07379i	0.425401	−	0.113986i	0.465167	+	0.885223i	$0.345994\pi$
$332$	10.7670	+	12.9027i	0.590916	+	0.708126i
$333$	1.91068	+	3.30940i	0.104705	+	0.181354i
$334$	12.7849	−	27.3203i	0.699559	−	1.49490i
$335$	0.401729	+	9.73700i	0.0219488	+	0.531989i
$336$	−5.93122	+	5.98290i	−0.323574	+	0.326394i
$337$	13.1935	−	13.1935i	0.718694	−	0.718694i	−0.249644	−	0.968338i	$-0.580314\pi$
$337$	13.1935	−	13.1935i	0.718694	−	0.718694i	0.968338	+	0.249644i	$0.0803136\pi$
$338$	42.0547	−	15.2420i	2.28748	−	0.829054i
$339$	11.0021	+	2.94801i	0.597553	+	0.160114i
$340$	6.67370	+	0.325601i	0.361932	+	0.0176582i
$341$	3.08273	+	11.5049i	0.166939	+	0.623026i
$342$	9.58893	−	0.825793i	0.518510	−	0.0446538i
$343$	18.0220	+	4.26686i	0.973099	+	0.230389i
$344$	26.5183	+	15.4548i	1.42977	+	0.833268i
$345$	−0.00102705		0.000321123i	−5.52948e−5		1.72887e-5i
$346$	−24.6120	−	4.37425i	−1.32315	−	0.235161i
$347$	17.3989	+	30.1358i	0.934023	+	1.61778i	0.776366	+	0.630282i	$0.217061\pi$
$347$	17.3989	+	30.1358i	0.934023	+	1.61778i	0.157657	+	0.987494i	$0.449606\pi$
$348$	−9.14168	+	4.23262i	−0.490046	+	0.226892i
$349$	−3.23597	+	3.23597i	−0.173218	+	0.173218i	−0.788392	−	0.615174i	$-0.789086\pi$
$349$	−3.23597	+	3.23597i	−0.173218	+	0.173218i	0.615174	+	0.788392i	$0.289086\pi$
$350$	3.18199	−	18.4357i	0.170084	−	0.985430i
$351$	28.5385			1.52327
$352$	6.32307	+	0.596519i	0.337021	+	0.0317945i
$353$	−7.39895	−	1.98254i	−0.393806	−	0.105520i	0.0564812	−	0.998404i	$-0.482012\pi$
$353$	−7.39895	−	1.98254i	−0.393806	−	0.105520i	−0.450288	+	0.892884i	$0.648679\pi$
$354$	0.321775	+	0.460874i	0.0171021	+	0.0244952i
$355$	−10.6931	−	5.59911i	−0.567530	−	0.297170i
$356$	17.2847	−	2.99934i	0.916086	−	0.158964i
$357$	2.39065	−	2.04614i	0.126526	−	0.108293i
$358$	−1.72929	−	20.0801i	−0.0913956	−	1.06127i
$359$	14.0661	−	24.3632i	0.742381	−	1.28584i	−0.209028	−	0.977910i	$-0.567030\pi$
$359$	14.0661	−	24.3632i	0.742381	−	1.28584i	0.951409	−	0.307931i	$-0.0996367\pi$
$360$	−14.9555	+	0.555963i	−0.788222	+	0.0293018i
$361$	9.29122	−	5.36429i	0.489012	−	0.282331i
$362$	7.97250	−	17.0366i	0.419025	−	0.895424i
$363$	7.75313			0.406934
$364$	−14.7132	+	32.1428i	−0.771183	+	1.68474i
$365$	−21.6537	−	19.9377i	−1.13340	−	1.04359i
$366$	−1.87405	+	4.00470i	−0.0979583	+	0.209329i
$367$	−1.57658	+	5.88387i	−0.0822968	+	0.307136i	−0.994789	−	0.101959i	$-0.967489\pi$
$367$	−1.57658	+	5.88387i	−0.0822968	+	0.307136i	0.912492	+	0.409095i	$0.134156\pi$
$368$	−0.00241004		0.000197656i	−0.000125632		1.03035e-5i
$369$	−7.75465	+	13.4314i	−0.403691	+	0.699213i
$370$	4.03979	+	3.12403i	0.210019	+	0.162410i
$371$	−22.3615	−	15.3342i	−1.16095	−	0.796111i
$372$	2.88773	+	16.6415i	0.149722	+	0.862821i
$373$	9.57563	+	5.52849i	0.495807	+	0.286254i	0.726980	−	0.686658i	$-0.240923\pi$
$373$	9.57563	+	5.52849i	0.495807	+	0.286254i	−0.231173	+	0.972913i	$0.574256\pi$
$374$	−2.33565	−	0.415111i	−0.120773	−	0.0214649i
$375$	−7.09976	+	5.36711i	−0.366630	+	0.277157i
$376$	−2.55888	+	9.39647i	−0.131964	+	0.484586i
$377$	−29.8902	+	29.8902i	−1.53942	+	1.53942i
$378$	−11.2068	+	11.3970i	−0.576414	+	0.586198i
$379$	7.23756	−	7.23756i	0.371768	−	0.371768i	−0.496353	−	0.868121i	$-0.665328\pi$
$379$	7.23756	−	7.23756i	0.371768	−	0.371768i	0.868121	+	0.496353i	$0.165328\pi$
$380$	11.4389	−	5.88051i	0.586802	−	0.301664i
$381$	−1.25989	+	4.70197i	−0.0645461	+	0.240889i
$382$	2.59227	−	14.5856i	0.132632	−	0.746263i
$383$	−5.53650	−	20.6625i	−0.282902	−	1.05581i	−0.950359	−	0.311156i	$-0.899284\pi$
$383$	−5.53650	−	20.6625i	−0.282902	−	1.05581i	0.667457	−	0.744649i	$-0.267383\pi$
$384$	8.85421	+	1.64823i	0.451839	+	0.0841111i
$385$	−1.95057	+	6.34933i	−0.0994103	+	0.323592i
$386$	1.24547	+	14.4622i	0.0633929	+	0.736105i
$387$	22.2381	+	12.8391i	1.13042	+	0.652650i
$388$	−31.3085	−	2.82491i	−1.58945	−	0.143413i
$389$	−12.4491	−	3.33573i	−0.631195	−	0.169128i	−0.0709829	−	0.997478i	$-0.522614\pi$
$389$	−12.4491	−	3.33573i	−0.631195	−	0.169128i	−0.560212	+	0.828349i	$0.689280\pi$
$390$	15.5612	−	6.37726i	0.787972	−	0.322925i
$391$	0.000903209	0		4.56772e−5	0
$392$	−7.05867	−	18.4980i	−0.356517	−	0.934289i
$393$	5.57778	−	5.57778i	0.281362	−	0.281362i
$394$	−18.7316	+	6.78893i	−0.943685	+	0.342021i
$395$	20.5708	−	13.0358i	1.03503	−	0.655900i
$396$	5.29196	+	0.477484i	0.265931	+	0.0239945i
$397$	1.45118	−	2.51352i	0.0728328	−	0.126150i	−0.827309	−	0.561747i	$-0.810129\pi$
$397$	1.45118	−	2.51352i	0.0728328	−	0.126150i	0.900142	+	0.435597i	$0.143463\pi$
$398$	−2.56189	+	3.04473i	−0.128416	+	0.152618i
$399$	2.01600	−	5.71200i	0.100926	−	0.285958i
$400$	−18.2117	+	8.26643i	−0.910585	+	0.413322i
$401$	−4.82603	+	8.35893i	−0.241000	+	0.417425i	−0.961000	−	0.276550i	$-0.910809\pi$
$401$	−4.82603	+	8.35893i	−0.241000	+	0.417425i	0.719999	+	0.693975i	$0.244142\pi$
$402$	0.858560	−	4.83074i	0.0428211	−	0.240935i
$403$	35.4361	+	61.3772i	1.76520	+	3.05741i
$404$	17.9411	−	8.30676i	0.892601	−	0.413277i
$405$	−8.26256	+	0.340896i	−0.410570	+	0.0169393i
$406$	−0.199224	−	23.6744i	−0.00988732	−	1.17494i
$407$	−1.28207	−	1.28207i	−0.0635498	−	0.0635498i
$408$	−3.24579	−	0.883906i	−0.160691	−	0.0437599i
$409$	−14.1519	+	8.17058i	−0.699765	+	0.404009i	−0.807260	−	0.590196i	$-0.799050\pi$
$409$	−14.1519	+	8.17058i	−0.699765	+	0.404009i	0.107495	+	0.994206i	$0.465717\pi$
$410$	−2.78253	+	20.5387i	−0.137419	+	1.01433i
$411$	−2.75330	−	10.2754i	−0.135810	−	0.506850i
$412$	−7.41106	+	10.5231i	−0.365117	+	0.518436i
$413$	−1.29861	+	0.242090i	−0.0639003	+	0.0119125i
$414$	−0.00201558		0.000173581i	−9.90604e−5		8.53102e-6i
$415$	16.6448	+	8.71553i	0.817060	+	0.427828i
$416$	37.2606	−	6.30930i	1.82685	−	0.309339i
$417$	8.45658	+	2.26593i	0.414121	+	0.110963i
$418$	−4.29321	+	1.55600i	−0.209988	+	0.0761063i
$419$	0.615630	−	0.615630i	0.0300755	−	0.0300755i	−0.691909	−	0.721985i	$-0.743230\pi$
$419$	0.615630	−	0.615630i	0.0300755	−	0.0300755i	0.721985	+	0.691909i	$0.243230\pi$
$420$	−3.56394	+	8.71874i	−0.173902	+	0.425431i
$421$	−22.1332	−	22.1332i	−1.07871	−	1.07871i	−0.996626	−	0.0820818i	$-0.973843\pi$
$421$	−22.1332	−	22.1332i	−1.07871	−	1.07871i	−0.0820818	−	0.996626i	$-0.526157\pi$
$422$	−8.84544	+	18.9020i	−0.430589	+	0.920135i
$423$	−2.10873	+	7.86987i	−0.102530	+	0.382646i
$424$	−0.118179	+	28.9860i	−0.00573927	+	1.40768i
$425$	7.03196	−	2.52129i	0.341100	−	0.122300i
$426$	4.64995	+	3.91255i	0.225291	+	0.189564i
$427$	−6.75676	−	7.89439i	−0.326983	−	0.382036i
$428$	1.75055	+	10.0882i	0.0846162	+	0.487629i
$429$	−5.76735	+	1.54536i	−0.278450	+	0.0746106i
$430$	34.0053	+	4.60695i	1.63988	+	0.222167i
$431$	−12.9019	−	22.3467i	−0.621461	−	1.07640i	−0.989214	−	0.146479i	$-0.953206\pi$
$431$	−12.9019	−	22.3467i	−0.621461	−	1.07640i	0.367753	−	0.929924i	$-0.380127\pi$
$432$	16.8115	+	3.05864i	0.808842	+	0.147159i
$433$	−9.65727	+	9.65727i	−0.464099	+	0.464099i	−0.899996	−	0.435898i	$-0.856431\pi$
$433$	−9.65727	+	9.65727i	−0.464099	+	0.464099i	0.435898	+	0.899996i	$0.356431\pi$
$434$	−38.4267	−	9.95060i	−1.84454	−	0.477644i
$435$	−7.62912	+	8.28573i	−0.365788	+	0.397270i
$436$	−7.88013	−	17.0196i	−0.377390	−	0.815092i
$437$	0.00150571		0.000869321i	7.20278e−5		4.15853e-5i
$438$	8.48353	+	12.1508i	0.405359	+	0.580590i
$439$	−3.90919	−	2.25697i	−0.186576	−	0.107720i	0.403803	−	0.914846i	$-0.367688\pi$
$439$	−3.90919	−	2.25697i	−0.186576	−	0.107720i	−0.590378	+	0.807127i	$0.701022\pi$
$440$	6.78584	−	2.09135i	0.323502	−	0.0997013i
$441$	−5.96842	−	15.4514i	−0.284211	−	0.735783i
$442$	−14.0635	+	1.21114i	−0.668930	+	0.0576079i
$443$	−1.81867	−	1.05001i	−0.0864076	−	0.0498875i	0.456174	−	0.889891i	$-0.349220\pi$
$443$	−1.81867	−	1.05001i	−0.0864076	−	0.0498875i	−0.542581	+	0.840003i	$0.682553\pi$
$444$	−1.64732	−	1.97407i	−0.0781783	−	0.0936853i
$445$	16.5672	−	10.4987i	0.785361	−	0.497686i
$446$	−13.0980	+	27.9893i	−0.620206	+	1.32533i
$447$	2.05597	+	2.05597i	0.0972442	+	0.0972442i
$448$	−12.1122	+	17.3578i	−0.572249	+	0.820080i
$449$			26.2427i			1.23847i	0.785207	+	0.619234i	$0.212557\pi$
$449$			26.2427i			1.23847i	−0.785207	+	0.619234i	$0.787443\pi$
$450$	−15.2078	+	6.97787i	−0.716904	+	0.328940i
$451$	1.90457	−	7.10793i	0.0896825	−	0.334700i
$452$	28.5010	+	2.57159i	1.34057	+	0.120957i
$453$	6.12405	−	10.6072i	0.287733	−	0.498368i
$454$	−12.1384	−	10.2134i	−0.569682	−	0.479341i
$455$	−1.43270	+	39.4968i	−0.0671660	+	1.85164i
$456$	−6.26169	+	1.65048i	−0.293230	+	0.0772909i
$457$	−4.30012	+	1.15221i	−0.201151	+	0.0538983i	−0.357988	−	0.933726i	$-0.616537\pi$
$457$	−4.30012	+	1.15221i	−0.201151	+	0.0538983i	0.156837	+	0.987625i	$0.449870\pi$
$458$	6.21544	−	4.33952i	0.290428	−	0.202772i
$459$	−6.16494	−	1.65189i	−0.287755	−	0.0771036i
$460$	−0.00240444	+	0.00123608i	−0.000112108	+	5.76323e-5i
$461$	−3.95197	−	3.95197i	−0.184062	−	0.184062i	0.609061	−	0.793123i	$-0.291546\pi$
$461$	−3.95197	−	3.95197i	−0.184062	−	0.184062i	−0.793123	+	0.609061i	$0.791546\pi$
$462$	1.64764	−	2.91007i	0.0766549	−	0.135389i
$463$	15.9737	+	15.9737i	0.742362	+	0.742362i	0.973032	−	0.230670i	$-0.0740917\pi$
$463$	15.9737	+	15.9737i	0.742362	+	0.742362i	−0.230670	+	0.973032i	$0.574092\pi$
$464$	−20.8112	+	14.4042i	−0.966138	+	0.668699i
$465$	10.1080	+	15.9507i	0.468749	+	0.739697i
$466$	−0.127986	−	0.183312i	−0.00592883	−	0.00849179i
$467$	14.0428	−	24.3229i	0.649825	−	1.12553i	−0.333340	−	0.942807i	$-0.608176\pi$
$467$	14.0428	−	24.3229i	0.649825	−	1.12553i	0.983164	−	0.182723i	$-0.0584911\pi$
$468$	31.1509	−	5.40549i	1.43995	−	0.249869i
$469$	9.50965	+	6.52115i	0.439115	+	0.301119i
$470$	1.38061	+	10.8003i	0.0636830	+	0.498179i
$471$	2.75369	+	1.58984i	0.126883	+	0.0732562i
$472$	0.994488	+	1.00263i	0.0457750	+	0.0461498i
$473$	−11.7684	−	3.15333i	−0.541112	−	0.144990i
$474$	−11.5274	+	4.17790i	−0.529471	+	0.191897i
$475$	9.29605	−	10.9713i	0.426532	−	0.503397i
$476$	5.03891	−	6.09192i	0.230958	−	0.279223i
$477$			24.2502i			1.11034i
$478$	2.84297	+	7.84415i	0.130034	+	0.358783i
$479$	−12.1922	−	21.1175i	−0.557075	−	0.964881i	−0.997739	−	0.0672094i	$-0.978590\pi$
$479$	−12.1922	−	21.1175i	−0.557075	−	0.964881i	0.440664	−	0.897672i	$-0.354743\pi$
$480$	9.85030	−	2.08894i	0.449603	−	0.0953465i
$481$	−9.34315	−	5.39427i	−0.426011	−	0.245958i
$482$	−0.909585	+	1.08101i	−0.0414304	+	0.0492388i
$483$	−0.000423760		0.00120066i	−1.92817e−5		5.46317e-5i
$484$	19.1921	−	3.33033i	0.872369	−	0.151379i
$485$	−33.5447	+	10.4882i	−1.52319	+	0.476245i
$486$	21.9436	+	3.90000i	0.995380	+	0.176908i
$487$	2.42023	−	9.03244i	0.109671	−	0.409299i	−0.889162	−	0.457593i	$-0.848712\pi$
$487$	2.42023	−	9.03244i	0.109671	−	0.409299i	0.998833	+	0.0482940i	$0.0153784\pi$
$488$	−2.91883	+	10.7182i	−0.132129	+	0.485192i
$489$			3.54150i			0.160152i
$490$	−15.2107	−	16.0822i	−0.687147	−	0.726518i
$491$	−15.2153	−	15.2153i	−0.686659	−	0.686659i	0.274833	−	0.961492i	$-0.411377\pi$
$491$	−15.2153	−	15.2153i	−0.686659	−	0.686659i	−0.961492	+	0.274833i	$0.911377\pi$
$492$	3.59563	−	9.79600i	0.162104	−	0.441638i
$493$	8.18707	−	4.72681i	0.368727	−	0.212885i
$494$	−22.2790	+	15.5549i	−1.00238	+	0.699846i
$495$	5.66994	−	1.77278i	0.254845	−	0.0796807i
$496$	14.2966	+	39.9540i	0.641936	+	1.79399i
$497$	−12.8841	+	6.16196i	−0.577930	+	0.276402i
$498$	−7.23807	−	6.09024i	−0.324346	−	0.272910i
$499$	39.9154	−	10.6953i	1.78686	−	0.478787i	0.795053	−	0.606540i	$-0.207443\pi$
$499$	39.9154	−	10.6953i	1.78686	−	0.478787i	0.991806	+	0.127753i	$0.0407764\pi$
$500$	−15.2694	+	16.3354i	−0.682866	+	0.730543i
$501$	−4.39450	+	16.4005i	−0.196332	+	0.732720i
$502$	−7.20656	+	15.3998i	−0.321645	+	0.687329i
$503$	−5.91429	−	5.91429i	−0.263705	−	0.263705i	0.562852	−	0.826557i	$-0.309704\pi$
$503$	−5.91429	−	5.91429i	−0.263705	−	0.263705i	−0.826557	+	0.562852i	$0.809704\pi$
$504$	−10.0740	+	14.5630i	−0.448730	+	0.648687i
$505$	14.9726	−	16.2612i	0.666271	−	0.723615i
$506$	0.000902428	0	0.000327069i	4.01178e−5	0	1.45400e-5i
$507$	−21.8058	+	12.5896i	−0.968430	+	0.559123i
$508$	−1.09902	+	12.1805i	−0.0487612	+	0.540421i
$509$	5.65927	+	21.1207i	0.250843	+	0.936157i	0.970356	+	0.241679i	$0.0776981\pi$
$509$	5.65927	+	21.1207i	0.250843	+	0.936157i	−0.719514	+	0.694478i	$0.755635\pi$
$510$	−3.73070	+	0.476901i	−0.165198	+	0.0211175i
$511$	−34.2376	+	6.38266i	−1.51458	+	0.282352i
$512$	22.6257	+	0.276755i	0.999925	+	0.0122309i
$513$	−11.8673	+	3.17982i	−0.523953	+	0.140393i
$514$	8.70772	−	6.07959i	0.384081	−	0.268159i
$515$	−3.14827	+	14.0415i	−0.138729	+	0.618740i
$516$	−16.2189	−	5.95319i	−0.713999	−	0.262074i
$517$		−	3.86573i		−	0.170015i
$518$	5.82319	−	1.61296i	0.255856	−	0.0708694i
$519$	14.0711			0.617651
$520$	35.7809	−	22.4706i	1.56910	−	0.985399i
$521$	7.35496	+	12.7392i	0.322227	+	0.558113i	0.980947	−	0.194275i	$-0.0622353\pi$
$521$	7.35496	+	12.7392i	0.322227	+	0.558113i	−0.658720	+	0.752388i	$0.728902\pi$
$522$	−17.3617	+	12.1217i	−0.759900	+	0.530550i
$523$	1.20011	−	2.07865i	0.0524772	−	0.0908931i	−0.838594	−	0.544758i	$-0.816622\pi$
$523$	1.20011	−	2.07865i	0.0524772	−	0.0908931i	0.891071	+	0.453865i	$0.149955\pi$
$524$	11.4113	−	16.2032i	0.498507	−	0.707839i
$525$	0.0524079	+	10.5307i	0.00228727	+	0.459596i
$526$	24.7344	−	2.13011i	1.07847	−	0.0928774i
$527$	−4.10229	−	15.3100i	−0.178699	−	0.666913i
$528$	−3.56306	+	0.292219i	−0.155062	+	0.0127172i
$529$	19.9186	−	11.5000i	0.866025	−	0.500000i
$530$	12.2892	+	29.9871i	0.533810	+	1.30255i
$531$	0.835415	+	0.835415i	0.0362539	+	0.0362539i
$532$	2.53683	−	15.0055i	0.109986	−	0.650570i
$533$		−	43.7861i		−	1.89659i
$534$	−9.28390	+	3.36478i	−0.401753	+	0.145608i
$535$	6.12753	+	9.66940i	0.264916	+	0.418045i
$536$	0.0502577	−	12.3268i	0.00217080	−	0.532437i
$537$	2.93625	+	10.9582i	0.126709	+	0.472883i
$538$	13.3624	−	1.15076i	0.576092	−	0.0496127i
$539$	4.63280	+	6.34849i	0.199549	+	0.273449i
$540$	18.6724	−	4.03945i	0.803532	−	0.173830i
$541$	−0.393444	−	1.46835i	−0.0169155	−	0.0631294i	0.956952	−	0.290245i	$-0.0937370\pi$
$541$	−0.393444	−	1.46835i	−0.0169155	−	0.0631294i	−0.973868	+	0.227116i	$0.927070\pi$
$542$	−29.3320	−	5.21314i	−1.25992	−	0.223923i
$543$	−2.74035	+	10.2271i	−0.117600	+	0.438888i
$544$	−8.41432	−	0.793807i	−0.360761	−	0.0340342i
$545$	−15.4260	−	14.2036i	−0.660779	−	0.608415i
$546$	4.98818	−	19.2631i	0.213474	−	0.824384i
$547$		−	6.48504i		−	0.277280i	−0.990343	−	0.138640i	$-0.955727\pi$
$547$		−	6.48504i		−	0.277280i	0.990343	−	0.138640i	$-0.0442731\pi$
$548$	−11.2293	−	24.2532i	−0.479692	−	1.03605i
$549$	−2.40535	+	8.97690i	−0.102658	+	0.383125i
$550$	6.11288	−	5.06551i	0.260654	−	0.215994i
$551$	9.09892	−	15.7598i	0.387627	−	0.671390i
$552$	0.00131620		0.000346929i	5.60211e−5		1.47663e-5i
$553$	2.23073	−	28.7288i	0.0948605	−	1.22167i
$554$	−8.13999	−	6.84914i	−0.345835	−	0.290992i
$555$	−2.54660	−	1.33345i	−0.108097	−	0.0566018i
$556$	21.9068	+	1.97661i	0.929054	+	0.0838269i
$557$	0.964491	−	0.556849i	0.0408668	−	0.0235945i	−0.479427	−	0.877582i	$-0.659156\pi$
$557$	0.964491	−	0.556849i	0.0408668	−	0.0235945i	0.520294	+	0.853987i	$0.325822\pi$
$558$	12.0969	+	33.3770i	0.512102	+	1.41296i
$559$	−72.4953			−3.06623
$560$	−5.07708	+	23.1133i	−0.214546	+	0.976714i
$561$	1.33533			0.0563775
$562$	4.55496	+	12.5678i	0.192139	+	0.530139i
$563$	−17.1338	+	9.89219i	−0.722102	+	0.416906i	−0.815526	−	0.578721i	$-0.803552\pi$
$563$	−17.1338	+	9.89219i	−0.722102	+	0.416906i	0.0934237	+	0.995626i	$0.470219\pi$
$564$	0.492615	−	5.45966i	0.0207428	−	0.229893i
$565$	30.5367	−	9.54771i	1.28469	−	0.401675i
$566$	−15.1954	−	12.7856i	−0.638708	−	0.537421i
$567$	−5.53367	+	8.06964i	−0.232392	+	0.338893i
$568$	13.1911	+	7.68777i	0.553487	+	0.322572i
$569$	−21.6338	+	37.4708i	−0.906936	+	1.57086i	−0.0886385	+	0.996064i	$0.528252\pi$
$569$	−21.6338	+	37.4708i	−0.906936	+	1.57086i	−0.818297	+	0.574795i	$0.805082\pi$
$570$	−5.76031	+	4.38575i	−0.241273	+	0.183699i
$571$	7.70213	−	28.7447i	0.322324	−	1.20293i	−0.594651	−	0.803984i	$-0.702710\pi$
$571$	7.70213	−	28.7447i	0.322324	−	1.20293i	0.916975	−	0.398945i	$-0.130624\pi$
$572$	−13.6127	+	6.30273i	−0.569177	+	0.263530i
$573$			8.33880i			0.348358i
$574$	17.4862	+	17.1944i	0.729860	+	0.717679i
$575$	−0.00195402	+	0.00230615i	−8.14882e−5	+	9.61730e-5i
$576$	18.9298	+	0.154360i	0.788740	+	0.00643166i
$577$	−3.17960	+	11.8664i	−0.132369	+	0.494006i	−0.999995	−	0.00321070i	$-0.998978\pi$
$577$	−3.17960	+	11.8664i	−0.132369	+	0.494006i	0.867626	+	0.497217i	$0.165645\pi$
$578$	−20.5626	−	3.65456i	−0.855290	−	0.152010i
$579$	−2.11476	−	7.89240i	−0.0878865	−	0.327997i
$580$	−15.3260	+	23.7876i	−0.636379	+	0.987726i
$581$	20.0552	−	9.59165i	0.832031	−	0.397929i
$582$	17.6297	−	1.51826i	0.730774	−	0.0629338i
$583$	−2.97797	−	11.1139i	−0.123335	−	0.460292i
$584$	26.2195	+	26.4342i	1.08497	+	1.09385i
$585$	29.8579	−	18.9211i	1.23447	−	0.782289i
$586$	−13.8882	+	5.03353i	−0.573716	+	0.207933i
$587$		−	21.0376i		−	0.868315i	−0.900837	−	0.434157i	$-0.857046\pi$
$587$		−	21.0376i		−	0.868315i	0.900837	−	0.434157i	$-0.142954\pi$
$588$	5.73401	+	9.55648i	0.236467	+	0.394103i
$589$	−21.5743	−	21.5743i	−0.888955	−	0.888955i
$590$	1.45641	+	0.609686i	0.0599594	+	0.0251004i
$591$	9.71253	−	5.60753i	0.399520	−	0.230663i
$592$	−4.92574	−	4.17902i	−0.202447	−	0.171757i
$593$	−2.83260	−	10.5714i	−0.116321	−	0.434116i	0.883061	−	0.469258i	$-0.155478\pi$
$593$	−2.83260	−	10.5714i	−0.116321	−	0.434116i	−0.999382	+	0.0351417i	$0.988812\pi$
$594$	−6.75779	+	0.581977i	−0.277275	+	0.0238788i
$595$	2.59569	−	8.44926i	0.106413	−	0.346386i
$596$	5.97250	+	4.20623i	0.244643	+	0.172294i
$597$	1.11992	−	1.93976i	0.0458353	−	0.0793891i
$598$	0.00468302	−	0.00326961i	0.000191503	−	0.000133704i
$599$	15.6035	+	27.0261i	0.637542	+	1.10425i	0.985971	+	0.166920i	$0.0533821\pi$
$599$	15.6035	+	27.0261i	0.637542	+	1.10425i	−0.348429	+	0.937335i	$0.613285\pi$
$600$	9.27886	−	6.37517i	0.378808	−	0.260265i
$601$	13.5248			0.551689			0.275845	−	0.961202i	$-0.411042\pi$
$601$	13.5248			0.551689			0.275845	+	0.961202i	$0.411042\pi$
$602$	28.4682	−	28.9514i	1.16028	−	1.17997i
$603$		−	10.3129i		−	0.419972i
$604$	10.6032	−	28.8876i	0.431439	−	1.17542i
$605$	18.3955	−	11.6573i	0.747883	−	0.473936i
$606$	−9.12490	+	6.37086i	−0.370674	+	0.258799i
$607$	−6.09332	+	1.63270i	−0.247320	+	0.0662693i	−0.380349	−	0.924843i	$-0.624196\pi$
$607$	−6.09332	+	1.63270i	−0.247320	+	0.0662693i	0.133029	+	0.991112i	$0.457530\pi$
$608$	−14.7912	+	6.77529i	−0.599864	+	0.274774i
$609$	2.44231	+	13.1009i	0.0989674	+	0.530877i
$610$	1.57482	+	12.3195i	0.0637627	+	0.498802i
$611$	−5.95338	−	22.2183i	−0.240848	−	0.898858i
$612$	−7.04218	−	0.635403i	−0.284663	−	0.0256846i
$613$	−39.9147	+	23.0448i	−1.61214	+	0.930770i	−0.623268	+	0.782009i	$0.714195\pi$
$613$	−39.9147	+	23.0448i	−1.61214	+	0.930770i	−0.988873	+	0.148761i	$0.952471\pi$
$614$	37.2044	−	13.4840i	1.50145	−	0.544172i
$615$	−0.480936	−	11.6568i	−0.0193932	−	0.470048i
$616$	2.82855	−	7.91133i	0.113966	−	0.318757i
$617$	−7.05845	−	7.05845i	−0.284163	−	0.284163i	0.550604	−	0.834767i	$-0.314397\pi$
$617$	−7.05845	−	7.05845i	−0.284163	−	0.284163i	−0.834767	+	0.550604i	$0.814397\pi$
$618$	3.07076	−	6.56198i	0.123524	−	0.263961i
$619$	12.6179	−	47.0906i	0.507156	−	1.89273i	0.0601750	−	0.998188i	$-0.480834\pi$
$619$	12.6179	−	47.0906i	0.507156	−	1.89273i	0.446981	−	0.894544i	$-0.352499\pi$
$620$	31.8730	+	35.1426i	1.28005	+	1.41136i
$621$	0.00249448		0.000668395i	0.000100100		2.68218e-5i
$622$	7.77501	+	6.54204i	0.311750	+	0.262312i
$623$	1.79658	−	23.1375i	0.0719785	−	0.926985i
$624$	−20.0287	+	7.16680i	−0.801791	+	0.286902i
$625$	−8.77551	+	23.4092i	−0.351020	+	0.936368i
$626$	16.8088	−	11.7356i	0.671813	−	0.469049i
$627$	2.22608	−	1.28523i	0.0889009	−	0.0513270i
$628$	7.49941	+	2.75267i	0.299259	+	0.109843i
$629$	1.70609	+	1.70609i	0.0680263	+	0.0680263i
$630$	−4.16868	+	19.3540i	−0.166084	+	0.771083i
$631$			11.4098i			0.454217i	0.973869	+	0.227109i	$0.0729272\pi$
$631$			11.4098i			0.454217i	−0.973869	+	0.227109i	$0.927073\pi$
$632$	−26.7404	+	15.2935i	−1.06367	+	0.608344i
$633$	3.04040	−	11.3469i	0.120845	−	0.451000i
$634$	7.96837	+	1.41621i	0.316464	+	0.0562447i
$635$	4.08041	+	13.0505i	0.161926	+	0.517892i
$636$	−2.78959	−	16.0759i	−0.110614	−	0.637452i
$637$	36.4040	+	29.3533i	1.44238	+	1.16302i
$638$	6.46833	−	7.68741i	0.256084	−	0.304348i
$639$	11.0620	+	6.38665i	0.437606	+	0.252652i
$640$	23.4862	−	9.40212i	0.928372	−	0.371651i
$641$	−8.22704	−	14.2497i	−0.324949	−	0.562828i	0.656553	−	0.754280i	$-0.272014\pi$
$641$	−8.22704	−	14.2497i	−0.324949	−	0.562828i	−0.981502	+	0.191452i	$0.938680\pi$
$642$	−1.96385	−	5.41852i	−0.0775068	−	0.213852i
$643$			18.4992i			0.729537i	0.931098	+	0.364768i	$0.118852\pi$
$643$			18.4992i			0.729537i	−0.931098	+	0.364768i	$0.881148\pi$
$644$	−0.000533239		0.00315413i	−2.10126e−5		0.000124290i
$645$	−19.2999	+	0.796272i	−0.759931	+	0.0313532i
$646$	5.71312	−	2.07062i	0.224780	−	0.0814673i
$647$	−8.27963	−	2.21852i	−0.325506	−	0.0872190i	0.0923658	−	0.995725i	$-0.470557\pi$
$647$	−8.27963	−	2.21852i	−0.325506	−	0.0872190i	−0.417871	+	0.908506i	$0.637224\pi$
$648$	10.4602	+	0.0426474i	0.410916	+	0.00167535i
$649$	−0.485462	−	0.280282i	−0.0190561	−	0.0110020i
$650$	27.3328	−	38.5282i	1.07208	−	1.51120i
$651$	22.2766	+	1.72973i	0.873087	+	0.0677934i
$652$	1.52124	+	8.76664i	0.0595763	+	0.343328i
$653$	−14.8252	+	25.6780i	−0.580154	+	1.00486i	0.415306	+	0.909682i	$0.363674\pi$
$653$	−14.8252	+	25.6780i	−0.580154	+	1.00486i	−0.995461	+	0.0951751i	$0.969659\pi$
$654$	6.04365	+	8.65625i	0.236326	+	0.338486i
$655$	4.84762	−	21.6207i	0.189412	−	0.844789i
$656$	4.69281	−	25.7935i	0.183224	−	1.00707i
$657$	22.0256	+	22.0256i	0.859300	+	0.859300i
$658$	11.2108	+	6.34740i	0.437044	+	0.247448i
$659$	−23.1647	−	23.1647i	−0.902369	−	0.902369i	0.0932717	−	0.995641i	$-0.470267\pi$
$659$	−23.1647	−	23.1647i	−0.902369	−	0.902369i	−0.995641	+	0.0932717i	$0.970267\pi$
$660$	−3.55478	+	1.82744i	−0.138370	+	0.0711332i
$661$	13.8878	+	3.72123i	0.540173	+	0.144739i	0.518582	−	0.855028i	$-0.326460\pi$
$661$	13.8878	+	3.72123i	0.540173	+	0.144739i	0.0215914	+	0.999767i	$0.493127\pi$
$662$	−9.29097	+	6.48681i	−0.361104	+	0.252117i
$663$	7.67480	−	2.05646i	0.298065	−	0.0798662i
$664$	−20.5332	−	11.9667i	−0.796842	−	0.464399i
$665$	−3.80507	−	16.5838i	−0.147554	−	0.643091i
$666$	−4.13516	−	3.47940i	−0.160234	−	0.134824i
$667$	−0.00191258	+	0.00331269i	−7.40555e−5	+	0.000128268i
$668$	−3.83339	+	42.4855i	−0.148318	+	1.64381i
$669$	4.50210	−	16.8021i	0.174061	−	0.649605i
$670$	−5.22623	−	12.7526i	−0.201907	−	0.492674i
$671$		−	4.40951i		−	0.170227i
$672$	5.00298	−	10.8129i	0.192994	−	0.417117i
$673$	−3.67809	−	3.67809i	−0.141780	−	0.141780i	0.632654	−	0.774434i	$-0.281965\pi$
$673$	−3.67809	−	3.67809i	−0.141780	−	0.141780i	−0.774434	+	0.632654i	$0.781965\pi$
$674$	−11.1841	+	23.8995i	−0.430795	+	0.920574i
$675$	17.5551	−	12.1671i	0.675695	−	0.468312i
$676$	−48.5704	+	40.5309i	−1.86809	+	1.55888i
$677$	−39.6000	−	22.8631i	−1.52195	−	0.878700i	−0.999664	−	0.0259311i	$-0.991745\pi$
$677$	−39.6000	−	22.8631i	−1.52195	−	0.878700i	−0.522289	−	0.852769i	$-0.674922\pi$
$678$	−16.0488	+	1.38211i	−0.616351	+	0.0530797i
$679$	−13.8404	+	39.2147i	−0.531147	+	1.50492i
$680$	−9.03013	+	2.78303i	−0.346290	+	0.106724i
$681$	7.73321	+	4.46477i	0.296337	+	0.171090i
$682$	−9.64277	−	13.8112i	−0.369241	−	0.528859i
$683$	−26.6150	+	15.3662i	−1.01840	+	0.587971i	−0.913639	−	0.406527i	$-0.866740\pi$
$683$	−26.6150	+	15.3662i	−1.01840	+	0.587971i	−0.104757	+	0.994498i	$0.533406\pi$
$684$	−12.3513	+	5.71870i	−0.472265	+	0.218660i
$685$	−21.9823	−	20.2403i	−0.839902	−	0.773343i
$686$	−26.0179	+	3.01137i	−0.993368	+	0.114975i
$687$	−3.01722	+	3.01722i	−0.115114	+	0.115114i
$688$	−42.7056	−	7.76975i	−1.62814	−	0.296219i
$689$	−34.2318	−	59.2912i	−1.30413	−	2.25882i
$690$	0.00121081		0.000921879i	4.60948e−5		3.50953e-5i
$691$	−7.22112	+	1.93489i	−0.274704	+	0.0736068i	−0.393541	−	0.919307i	$-0.628750\pi$
$691$	−7.22112	+	1.93489i	−0.274704	+	0.0736068i	0.118837	+	0.992914i	$0.462083\pi$
$692$	34.8315	−	6.04417i	1.32410	−	0.229765i
$693$	2.33940	−	6.62832i	0.0888665	−	0.251789i
$694$	−37.6552	−	31.6838i	−1.42937	−	1.20270i
$695$	23.4715	−	7.33868i	0.890324	−	0.278372i
$696$	10.1150	−	10.0328i	0.383408	−	0.380294i
$697$	−2.53447	+	9.45876i	−0.0959998	+	0.358276i
$698$	2.74313	−	5.86185i	0.103829	−	0.221874i
$699$	0.0889870	+	0.0889870i	0.00336580	+	0.00336580i
$700$	4.65314	+	26.0451i	0.175872	+	0.984413i
$701$	27.8151	−	27.8151i	1.05056	−	1.05056i	0.0519096	−	0.998652i	$-0.483469\pi$
$701$	27.8151	−	27.8151i	1.05056	−	1.05056i	0.998652	−	0.0519096i	$-0.0165308\pi$
$702$	−37.9442	+	13.7522i	−1.43211	+	0.519043i
$703$	4.48625	+	1.20209i	0.169202	+	0.0453375i
$704$	−8.69450	+	2.25386i	−0.327686	+	0.0849456i
$705$	−1.82896	−	5.84962i	−0.0688828	−	0.220309i
$706$	10.7929	−	0.929475i	0.406195	−	0.0349813i
$707$	−4.79317	−	25.7113i	−0.180266	−	0.966974i
$708$	−0.649913	−	0.457712i	−0.0244252	−	0.0172019i
$709$	−4.89030	−	18.2508i	−0.183659	−	0.685425i	−0.994914	−	0.100732i	$-0.967882\pi$
$709$	−4.89030	−	18.2508i	−0.183659	−	0.685425i	0.811255	−	0.584693i	$-0.198785\pi$
$710$	16.9155	+	2.29166i	0.634826	+	0.0860044i
$711$	−22.3190	+	12.8859i	−0.837027	+	0.483258i
$712$	−21.5361	+	12.3171i	−0.807098	+	0.461601i
$713$	0.00453490	+	0.00453490i	0.000169833	+	0.000169833i
$714$	−2.19256	+	3.87252i	−0.0820546	+	0.144926i
$715$	−11.3604	+	12.3381i	−0.424855	+	0.461420i
$716$	11.9755	+	25.8648i	0.447545	+	0.966614i
$717$	−2.34824	−	4.06727i	−0.0876967	−	0.151895i
$718$	−6.96183	+	39.1711i	−0.259813	+	1.46185i
$719$	−15.9031	+	27.5449i	−0.593084	+	1.02725i	0.400730	+	0.916196i	$0.368756\pi$
$719$	−15.9031	+	27.5449i	−0.593084	+	1.02725i	−0.993814	+	0.111055i	$0.964577\pi$
$720$	19.6166	−	7.94598i	0.731068	−	0.296129i
$721$	11.0714	+	12.9355i	0.412321	+	0.481743i
$722$	−9.76848	+	11.6095i	−0.363545	+	0.432062i
$723$	0.397622	−	0.688701i	0.0147877	−	0.0256131i
$724$	−2.39045	+	26.4934i	−0.0888403	+	0.984618i
$725$	−5.64317	+	31.1300i	−0.209582	+	1.15614i
$726$	−10.3084	+	3.73610i	−0.382582	+	0.138660i
$727$	−33.2441	+	33.2441i	−1.23295	+	1.23295i	−0.270132	+	0.962823i	$0.587067\pi$
$727$	−33.2441	+	33.2441i	−1.23295	+	1.23295i	−0.962823	+	0.270132i	$0.912933\pi$
$728$	4.07337	−	49.8266i	0.150969	−	1.84670i
$729$	−1.45065			−0.0537279
$730$	38.3980	+	16.0743i	1.42117	+	0.594935i
$731$	15.6606	+	4.19624i	0.579228	+	0.155204i
$732$	0.561910	−	6.22765i	0.0207688	−	0.230181i
$733$	−16.4136	−	9.47639i	−0.606250	−	0.350019i	0.165246	−	0.986252i	$-0.447158\pi$
$733$	−16.4136	−	9.47639i	−0.606250	−	0.350019i	−0.771496	+	0.636234i	$0.780491\pi$
$734$	−0.739147	−	8.58282i	−0.0272824	−	0.316798i
$735$	10.0140	+	7.41465i	0.369371	+	0.273494i
$736$	0.00310910	−	0.00142416i	0.000114603	−	5.24951e-5i
$737$	1.26644	+	4.72640i	0.0466497	+	0.174099i
$738$	3.83806	−	21.5950i	0.141281	−	0.794925i
$739$	5.02591	−	18.7569i	0.184881	−	0.689985i	−0.809775	−	0.586741i	$-0.800411\pi$
$739$	5.02591	−	18.7569i	0.184881	−	0.689985i	0.994656	−	0.103245i	$-0.0329225\pi$
$740$	−6.87665	−	2.20695i	−0.252791	−	0.0811289i
$741$	10.8151	−	10.8151i	0.397303	−	0.397303i
$742$	37.1208	+	9.61243i	1.36275	+	0.352883i
$743$	31.8508	−	31.8508i	1.16849	−	1.16849i	0.185932	−	0.982563i	$-0.440470\pi$
$743$	31.8508	−	31.8508i	1.16849	−	1.16849i	0.982563	−	0.185932i	$-0.0595303\pi$
$744$	−11.8587	−	20.7347i	−0.434762	−	0.760171i
$745$	7.96938	+	1.78684i	0.291976	+	0.0654646i
$746$	−15.3957	−	2.73625i	−0.563675	−	0.100181i
$747$	−17.2190	−	9.94140i	−0.630011	−	0.363737i
$748$	3.30547	−	0.573584i	0.120860	−	0.0209723i
$749$	13.5042	+	1.04857i	0.493431	+	0.0383139i
$750$	6.85340	−	10.5573i	0.250251	−	0.385497i
$751$	−11.4665	+	19.8605i	−0.418417	+	0.724720i	−0.995780	−	0.0917675i	$-0.970748\pi$
$751$	−11.4665	+	19.8605i	−0.418417	+	0.724720i	0.577363	+	0.816487i	$0.304082\pi$
$752$	−1.12575	−	13.7265i	−0.0410521	−	0.500552i
$753$	2.47708	−	9.24458i	0.0902697	−	0.336891i
$754$	25.3379	−	54.1450i	0.922751	−	1.97185i
$755$	−1.41824	−	34.3750i	−0.0516151	−	1.25103i
$756$	9.40831	−	20.5536i	0.342177	−	0.747526i
$757$	10.8698			0.395068			0.197534	−	0.980296i	$-0.436707\pi$
$757$	10.8698			0.395068			0.197534	+	0.980296i	$0.436707\pi$
$758$	−6.13527	+	13.1106i	−0.222843	+	0.476198i
$759$	−0.000467918	0	0.000270153i	−1.69844e−5	0	9.80592e-6i
$760$	−12.3752	+	13.3308i	−0.448896	+	0.483560i
$761$	−20.3548	+	35.2555i	−0.737861	+	1.27801i	0.215596	+	0.976483i	$0.430831\pi$
$761$	−20.3548	+	35.2555i	−0.737861	+	1.27801i	−0.953457	+	0.301530i	$0.902503\pi$
$762$	−0.590674	−	6.85878i	−0.0213979	−	0.248467i
$763$	−24.3908	+	4.54700i	−0.883006	+	0.164612i
$764$	3.58190	+	20.6419i	0.129589	+	0.746797i
$765$	−7.54517	+	2.35910i	−0.272796	+	0.0852935i
$766$	17.3182	+	24.8046i	0.625730	+	0.896225i
$767$	−3.22185	−	0.863291i	−0.116334	−	0.0311716i
$768$	−12.5667	+	2.07523i	−0.453460	+	0.0748834i
$769$	47.6039			1.71664			0.858320	−	0.513114i	$-0.171508\pi$
$769$	47.6039			1.71664			0.858320	+	0.513114i	$0.171508\pi$
$770$	−0.466190	−	9.38190i	−0.0168003	−	0.338100i
$771$	−4.22707	+	4.22707i	−0.152234	+	0.152234i
$772$	−8.62504	−	18.6285i	−0.310422	−	0.670454i
$773$	24.1238	+	41.7837i	0.867674	+	1.50285i	0.864368	+	0.502860i	$0.167719\pi$
$773$	24.1238	+	41.7837i	0.867674	+	1.50285i	0.00330606	+	0.999995i	$0.498948\pi$
$774$	−35.7543	−	6.35456i	−1.28516	−	0.228410i
$775$	47.9657	+	22.6475i	1.72298	+	0.813524i
$776$	42.9884	−	11.3311i	1.54320	−	0.406762i
$777$	−3.06839	+	1.46750i	−0.110078	+	0.0526461i
$778$	18.1595	−	1.56389i	0.651051	−	0.0560681i
$779$	4.87875	+	18.2077i	0.174799	+	0.652360i
$780$	−17.6168	+	15.9778i	−0.630783	+	0.572096i
$781$	−5.85402	−	1.56858i	−0.209473	−	0.0561282i
$782$	−0.00120089		0.000435241i	−4.29437e−5		1.55642e-5i
$783$	19.1131	−	19.1131i	0.683047	−	0.683047i
$784$	18.2989	+	21.1931i	0.653534	+	0.756898i
$785$	8.92398	−	0.368185i	0.318510	−	0.0131411i
$786$	−4.72828	+	10.1040i	−0.168652	+	0.360396i
$787$	6.51046	+	11.2764i	0.232073	+	0.401962i	0.958418	−	0.285368i	$-0.0921159\pi$
$787$	6.51046	+	11.2764i	0.232073	+	0.401962i	−0.726345	+	0.687330i	$0.758783\pi$
$788$	21.6337	−	18.0529i	0.770670	−	0.643107i
$789$	−13.4982	+	3.61684i	−0.480550	+	0.128763i
$790$	−21.0688	+	27.2448i	−0.749594	+	0.969326i
$791$	12.5993	−	35.6982i	0.447981	−	1.26928i
$792$	−7.26618	+	1.91525i	−0.258193	+	0.0680555i
$793$	−6.79083	−	25.3437i	−0.241149	−	0.899982i
$794$	−0.718243	+	4.04123i	−0.0254895	+	0.143418i
$795$	−9.76450	−	15.4086i	−0.346311	−	0.546488i
$796$	1.93904	−	5.28274i	0.0687274	−	0.187242i
$797$	32.4250			1.14855			0.574276	−	0.818662i	$-0.305284\pi$
$797$	32.4250			1.14855			0.574276	+	0.818662i	$0.305284\pi$
$798$	0.0720848	+	8.56605i	0.00255177	+	0.303235i
$799$			5.14425i			0.181991i
$800$	20.2305	−	19.7668i	0.715256	−	0.698862i
$801$	−17.9752	+	10.3780i	−0.635122	+	0.366688i
$802$	2.38858	−	13.4395i	0.0843436	−	0.474564i
$803$	−12.7991	−	7.38958i	−0.451671	−	0.260773i
$804$	1.18632	+	6.83659i	0.0418384	+	0.241108i
$805$	0.000799820		0.00348589i	2.81900e−5		0.000122861i
$806$	−76.6918	−	64.5299i	−2.70135	−	2.27297i
$807$	−7.29220	+	1.95394i	−0.256698	+	0.0687819i
$808$	−19.8512	+	19.6900i	−0.698364	+	0.692693i
$809$	9.27863	+	16.0711i	0.326219	+	0.565028i	0.981758	−	0.190133i	$-0.0608919\pi$
$809$	9.27863	+	16.0711i	0.326219	+	0.565028i	−0.655539	+	0.755161i	$0.727559\pi$
$810$	10.8215	−	4.43484i	0.380228	−	0.155824i
$811$	−22.2054	+	22.2054i	−0.779739	+	0.779739i	−0.979786	−	0.200048i	$-0.935890\pi$
$811$	−22.2054	+	22.2054i	−0.779739	+	0.779739i	0.200048	+	0.979786i	$0.435890\pi$
$812$	11.6732	+	31.3810i	0.409648	+	1.10126i
$813$	16.7696			0.588134
$814$	2.32242	+	1.08681i	0.0814009	+	0.0380926i
$815$	5.32485	+	8.40275i	0.186521	+	0.294335i
$816$	4.74148	−	0.388866i	0.165985	−	0.0136130i
$817$	30.1460	−	8.07761i	1.05468	−	0.282600i
$818$	14.8788	−	17.6830i	0.520225	−	0.618272i
$819$	3.23785	−	41.6991i	0.113140	−	1.45709i
$820$	−6.19765	−	28.6487i	−0.216431	−	1.00046i
$821$	−25.0046	+	6.69996i	−0.872667	+	0.233830i	−0.667241	−	0.744842i	$-0.732525\pi$
$821$	−25.0046	+	6.69996i	−0.872667	+	0.233830i	−0.205426	+	0.978673i	$0.565858\pi$
$822$	8.61230	+	12.3353i	0.300388	+	0.430242i
$823$	−27.5479	−	7.38143i	−0.960258	−	0.257300i	−0.255549	−	0.966796i	$-0.582256\pi$
$823$	−27.5479	−	7.38143i	−0.960258	−	0.257300i	−0.704710	+	0.709496i	$0.748923\pi$
$824$	4.78271	−	17.5626i	0.166614	−	0.611821i
$825$	−2.88887	+	3.40947i	−0.100577	+	0.118702i
$826$	1.60995	−	0.947656i	0.0560172	−	0.0329732i
$827$	−25.6434			−0.891708			−0.445854	−	0.895106i	$-0.647100\pi$
$827$	−25.6434			−0.891708			−0.445854	+	0.895106i	$0.647100\pi$
$828$	0.00259624	−	0.00120206i	9.02254e−5	−	4.17746e-5i
$829$	2.39897	+	0.642803i	0.0833198	+	0.0223255i	0.300238	−	0.953864i	$-0.402934\pi$
$829$	2.39897	+	0.642803i	0.0833198	+	0.0223255i	−0.216918	+	0.976190i	$0.569601\pi$
$830$	−26.3305	−	3.56718i	−0.913943	−	0.123819i
$831$	5.18589	+	2.99408i	0.179897	+	0.103863i
$832$	−46.5007	+	26.3440i	−1.61212	+	0.913314i
$833$	−6.16501	−	8.44814i	−0.213605	−	0.292711i
$834$	−12.3356	+	1.06234i	−0.427148	+	0.0367857i
$835$	14.2325	+	45.5200i	0.492535	+	1.57529i
$836$	4.95837	−	4.13765i	0.171489	−	0.143104i
$837$	−22.6595	−	39.2473i	−0.783225	−	1.35659i
$838$	−0.521869	+	1.11519i	−0.0180277	+	0.0385237i
$839$			29.6638i			1.02411i	0.858953	+	0.512054i	$0.171115\pi$
$839$			29.6638i			1.02411i	−0.858953	+	0.512054i	$0.828885\pi$
$840$	0.537137	−	13.3097i	0.0185330	−	0.459228i
$841$			11.0368i			0.380581i
$842$	40.0936	+	18.7623i	1.38172	+	0.646592i
$843$	−3.76231	−	6.51651i	−0.129581	−	0.224441i
$844$	2.65219	−	29.3942i	0.0912921	−	1.01179i
$845$	−32.8084	+	62.6570i	−1.12864	+	2.15547i
$846$	−0.988634	−	11.4798i	−0.0339899	−	0.394684i
$847$	1.99484	−	25.6909i	0.0685436	−	0.882749i
$848$	−13.8107	−	38.5962i	−0.474262	−	1.32540i
$849$	9.68078	+	5.58920i	0.332244	+	0.191821i
$850$	−8.13460	+	6.74084i	−0.279015	+	0.231209i
$851$	−0.000943003	0	0.000252677i	−3.23257e−5	0	8.66165e-6i
$852$	−8.06788	−	2.96133i	−0.276401	−	0.101453i
$853$	31.9211			1.09296			0.546479	−	0.837473i	$-0.315968\pi$
$853$	31.9211			1.09296			0.546479	+	0.837473i	$0.315968\pi$
$854$	12.7878	+	7.24028i	0.437591	+	0.247757i
$855$	−10.3077	+	11.1949i	−0.352516	+	0.382856i
$856$	−7.18881	−	12.5695i	−0.245709	−	0.429615i
$857$	20.6038	+	5.52077i	0.703812	+	0.188586i	0.592937	−	0.805249i	$-0.297968\pi$
$857$	20.6038	+	5.52077i	0.703812	+	0.188586i	0.110874	+	0.993834i	$0.464635\pi$
$858$	6.92349	−	4.83387i	0.236364	−	0.165026i
$859$	−5.29424	+	1.41859i	−0.180637	+	0.0484016i	−0.348004	−	0.937493i	$-0.613140\pi$
$859$	−5.29424	+	1.41859i	−0.180637	+	0.0484016i	0.167366	+	0.985895i	$0.446474\pi$
$860$	−47.4329	+	10.2613i	−1.61745	+	0.349907i
$861$	−11.3846	−	7.80690i	−0.387988	−	0.266059i
$862$	27.9226	+	23.4946i	0.951047	+	0.800228i
$863$	16.0305	−	4.29537i	0.545686	−	0.146216i	0.0245639	−	0.999698i	$-0.492180\pi$
$863$	16.0305	−	4.29537i	0.545686	−	0.146216i	0.521122	+	0.853482i	$0.325514\pi$
$864$	−23.8261	+	4.03445i	−0.810581	+	0.137255i
$865$	33.3857	−	21.1566i	1.13515	−	0.719347i
$866$	8.18646	−	17.4938i	0.278187	−	0.594464i
$867$	11.7559			0.399253
$868$	55.8865	−	5.28704i	1.89691	−	0.179454i
$869$	8.64642	−	8.64642i	0.293310	−	0.293310i
$870$	6.15079	−	14.6929i	0.208531	−	0.498136i
$871$	14.5577	+	25.2147i	0.493269	+	0.854367i
$872$	18.6787	+	18.8317i	0.632542	+	0.637721i
$873$	35.9258	−	9.62628i	1.21590	−	0.325800i
$874$	−0.00158305	+	0.00188141i	−5.35475e−5	+	6.36396e-5i
$875$	15.9578	+	24.9068i	0.539472	+	0.842003i
$876$	−17.1348	−	12.0675i	−0.578933	−	0.407722i
$877$	−35.7599	−	20.6460i	−1.20753	−	0.697165i	−0.245308	−	0.969445i	$-0.578889\pi$
$877$	−35.7599	−	20.6460i	−1.20753	−	0.697165i	−0.962218	+	0.272280i	$0.912222\pi$
$878$	6.28519	+	1.11706i	0.212115	+	0.0376989i
$879$	7.20117	−	4.15760i	0.242890	−	0.140232i
$880$	−8.01454	+	6.05060i	−0.270170	+	0.203966i
$881$			6.33400i			0.213398i	0.994291	+	0.106699i	$0.0340281\pi$
$881$			6.33400i			0.213398i	−0.994291	+	0.106699i	$0.965972\pi$
$882$	15.3813	+	17.6679i	0.517915	+	0.594909i
$883$	−33.0247			−1.11137			−0.555684	−	0.831393i	$-0.687544\pi$
$883$	−33.0247			−1.11137			−0.555684	+	0.831393i	$0.687544\pi$
$884$	18.1149	−	8.38724i	0.609270	−	0.282094i
$885$	−0.867209	−	0.194439i	−0.0291509	−	0.00653600i
$886$	2.92405	+	0.519688i	0.0982355	+	0.0174593i
$887$	−7.06783	−	26.3775i	−0.237314	−	0.885670i	−0.977092	−	0.212818i	$-0.931736\pi$
$887$	−7.06783	−	26.3775i	−0.237314	−	0.885670i	0.739777	−	0.672852i	$-0.234931\pi$
$888$	3.14152	+	1.83087i	0.105422	+	0.0614401i
$889$	15.2564	+	5.38458i	0.511682	+	0.180593i
$890$	−16.9683	+	21.9423i	−0.568779	+	0.735508i
$891$	−4.01070	+	1.07466i	−0.134363	+	0.0360026i
$892$	3.92725	−	43.5257i	0.131494	−	1.45735i
$893$	4.95124	+	8.57580i	0.165687	+	0.286978i
$894$	−3.72432	−	1.74285i	−0.124560	−	0.0582895i
$895$	23.4431	+	21.5853i	0.783615	+	0.721516i
$896$	7.73976	−	28.9153i	0.258567	−	0.965993i
$897$	−0.00227332	+	0.00227332i	−7.59040e−5	+	7.59040e-5i
$898$	−12.6459	−	34.8918i	−0.421999	−	1.16435i
$899$	64.8390	+	17.3736i	2.16250	+	0.579440i
$900$	16.8575	−	16.6060i	0.561918	−	0.553535i
$901$	3.96288	+	14.7897i	0.132023	+	0.492715i
$902$	0.892917	+	10.3684i	0.0297309	+	0.345229i
$903$	−12.9257	+	18.8492i	−0.430139	+	0.627263i
$904$	−39.1336	+	10.3150i	−1.30156	+	0.343071i
$905$	8.87517	+	28.3857i	0.295021	+	0.943572i
$906$	−3.03102	+	17.0542i	−0.100699	+	0.566587i
$907$	−0.540795	−	0.936684i	−0.0179568	−	0.0311021i	0.856907	−	0.515470i	$-0.172383\pi$
$907$	−0.540795	−	0.936684i	−0.0179568	−	0.0311021i	−0.874864	+	0.484368i	$0.839049\pi$
$908$	21.0606	+	7.73034i	0.698922	+	0.256540i
$909$	−16.5405	+	16.5405i	−0.548614	+	0.548614i
$910$	−17.1280	−	53.2047i	−0.567786	−	1.76372i
$911$	−43.2692			−1.43357			−0.716786	−	0.697293i	$-0.754388\pi$
$911$	−43.2692			−1.43357			−0.716786	+	0.697293i	$0.754388\pi$
$912$	7.53009	−	5.21185i	0.249346	−	0.172582i
$913$	9.11232	+	2.44164i	0.301574	+	0.0808064i
$914$	5.16214	−	3.60412i	0.170748	−	0.119214i
$915$	−2.08624	−	6.67247i	−0.0689689	−	0.220585i
$916$	−6.17279	+	8.76486i	−0.203955	+	0.289599i
$917$	−17.0475	−	19.9178i	−0.562957	−	0.657742i
$918$	8.99281	−	0.774455i	0.296807	−	0.0255608i
$919$	1.71053	−	2.96273i	0.0564252	−	0.0977314i	−0.836433	−	0.548069i	$-0.815363\pi$
$919$	1.71053	−	2.96273i	0.0564252	−	0.0977314i	0.892858	+	0.450338i	$0.148696\pi$
$920$	0.00260125	−	0.00280212i	8.57608e−5	−	9.23832e-5i
$921$	−19.2908	+	11.1376i	−0.635655	+	0.366996i
$922$	7.15886	+	3.35008i	0.235765	+	0.110329i
$923$	−36.0617			−1.18699
$924$	−0.788354	+	4.66314i	−0.0259349	+	0.153406i
$925$	−8.04712	+	0.665148i	−0.264588	+	0.0218699i
$926$	−28.9359	−	13.5409i	−0.950892	−	0.444982i
$927$	3.94134	−	14.7093i	0.129451	−	0.483116i
$928$	20.7291	−	29.1802i	0.680466	−	0.957886i
$929$	−14.0217	+	24.2863i	−0.460037	+	0.796808i	−0.998962	−	0.0455457i	$-0.985497\pi$
$929$	−14.0217	+	24.2863i	−0.460037	+	0.796808i	0.538925	+	0.842354i	$0.318831\pi$
$930$	−21.1258	−	16.3369i	−0.692744	−	0.535709i
$931$	−18.4087	−	8.14990i	−0.603319	−	0.267102i
$932$	0.258503	+	0.182055i	0.00846754	+	0.00596340i
$933$	−4.95337	−	2.85983i	−0.162166	−	0.0936266i
$934$	−6.95031	+	39.1063i	−0.227421	+	1.27960i
$935$	3.16826	−	2.00774i	0.103613	−	0.0656601i
$936$	−38.8129	+	22.1982i	−1.26864	+	0.725570i
$937$	−0.240037	+	0.240037i	−0.00784167	+	0.00784167i	−0.711017	−	0.703175i	$-0.751765\pi$
$937$	−0.240037	+	0.240037i	−0.00784167	+	0.00784167i	0.703175	+	0.711017i	$0.251765\pi$
$938$	−15.7863	−	4.08786i	−0.515441	−	0.133473i
$939$	−8.15963	+	8.15963i	−0.266279	+	0.266279i
$940$	−7.04011	−	13.6945i	−0.229623	−	0.446667i
$941$	2.88312	−	10.7599i	0.0939869	−	0.350764i	−0.902877	−	0.429899i	$-0.858549\pi$
$941$	2.88312	−	10.7599i	0.0939869	−	0.350764i	0.996864	+	0.0791350i	$0.0252158\pi$
$942$	−4.42738	−	0.786872i	−0.144252	−	0.0256377i
$943$	−0.00102551	−	0.00382725i	−3.33951e−5	−	0.000124632i
$944$	−1.80540	−	0.853853i	−0.0587609	−	0.0277905i
$945$	0.916133	−	25.2560i	0.0298018	−	0.821579i
$946$	17.1666	−	1.47838i	0.558134	−	0.0480662i
$947$	3.64290	+	2.10323i	0.118378	+	0.0683458i	0.558020	−	0.829827i	$-0.311561\pi$
$947$	3.64290	+	2.10323i	0.118378	+	0.0683458i	−0.439642	+	0.898173i	$0.644895\pi$
$948$	13.3134	−	11.1097i	0.432398	−	0.360827i
$949$	−84.9434	−	22.7605i	−2.75738	−	0.738838i
$950$	−7.07299	+	19.0668i	−0.229478	+	0.618610i
$951$	−4.55564			−0.147727
$952$	−3.76405	+	10.5279i	−0.121993	+	0.341210i
$953$	−31.0302	+	31.0302i	−1.00517	+	1.00517i	−0.00518088	+	0.999987i	$0.501649\pi$
$953$	−31.0302	+	31.0302i	−1.00517	+	1.00517i	−0.999987	+	0.00518088i	$0.998351\pi$
$954$	−11.6858	−	32.2427i	−0.378341	−	1.04390i
$955$	12.5379	+	19.7851i	0.405716	+	0.640230i
$956$	−7.55993	−	9.05946i	−0.244505	−	0.293004i
$957$	−2.82761	+	4.89756i	−0.0914036	+	0.158316i
$958$	26.3866	+	22.2022i	0.852514	+	0.717320i
$959$	−34.7573	+	6.47954i	−1.12237	+	0.209235i
$960$	−12.0902	+	7.52410i	−0.390208	+	0.242839i
$961$	40.7723	−	70.6198i	1.31524	−	2.27806i
$962$	15.0219	+	2.66982i	0.484325	+	0.0860785i
$963$	−6.05708	−	10.4912i	−0.195187	−	0.338073i
$964$	0.688445	−	1.87561i	0.0221733	−	0.0604093i
$965$	−16.8843	−	15.5462i	−0.543524	−	0.500451i
$966$	−1.51521e−5	−	0.00180057i	−4.87512e−7	−	5.79325e-5i
$967$	2.49566	+	2.49566i	0.0802550	+	0.0802550i	0.746095	−	0.665840i	$-0.231927\pi$
$967$	2.49566	+	2.49566i	0.0802550	+	0.0802550i	−0.665840	+	0.746095i	$0.731927\pi$
$968$	−23.9127	+	13.6763i	−0.768583	+	0.439573i
$969$	−2.96231	+	1.71029i	−0.0951631	+	0.0549425i
$970$	39.5463	−	30.1096i	1.26976	−	0.966760i
$971$	12.0117	+	44.8284i	0.385475	+	1.43861i	0.837418	+	0.546564i	$0.184064\pi$
$971$	12.0117	+	44.8284i	0.385475	+	1.43861i	−0.451943	+	0.892047i	$0.649269\pi$
$972$	−31.0551	+	5.38886i	−0.996093	+	0.172848i
$973$	9.68427	−	27.4388i	0.310463	−	0.879648i
$974$	1.13468	+	13.1756i	0.0363574	+	0.422175i
$975$	−11.3531	+	24.0449i	−0.363590	+	0.770054i
$976$	−1.28411	−	15.6573i	−0.0411034	−	0.501179i
$977$	48.9736	+	13.1224i	1.56681	+	0.419824i	0.934810	−	0.355148i	$-0.115570\pi$
$977$	48.9736	+	13.1224i	1.56681	+	0.419824i	0.631995	+	0.774972i	$0.282236\pi$
$978$	−1.70659	−	4.70872i	−0.0545707	−	0.150568i
$979$	6.96362	−	6.96362i	0.222558	−	0.222558i
$980$	27.9735	+	14.0528i	0.893582	+	0.448900i
$981$	15.6910	+	15.6910i	0.500975	+	0.500975i
$982$	27.5621	+	12.8980i	0.879541	+	0.411593i
$983$	−14.2833	+	53.3062i	−0.455568	+	1.70020i	0.230845	+	0.972991i	$0.425851\pi$
$983$	−14.2833	+	53.3062i	−0.455568	+	1.70020i	−0.686413	+	0.727212i	$0.740816\pi$
$984$	−0.0601669	+	14.7573i	−0.00191805	+	0.470444i
$985$	14.6132	−	27.9081i	0.465616	−	0.889225i
$986$	−8.60761	+	10.2299i	−0.274122	+	0.325786i
$987$	−6.83837	−	2.41354i	−0.217668	−	0.0768237i
$988$	22.1262	−	31.4173i	0.703927	−	0.999518i
$989$	−0.00633666	+	0.00169790i	−0.000201494	+	5.39902e-5i
$990$	−6.68438	+	5.08931i	−0.212443	+	0.161749i
$991$	29.3073	+	50.7618i	0.930978	+	1.61250i	0.781653	+	0.623713i	$0.214377\pi$
$991$	29.3073	+	50.7618i	0.930978	+	1.61250i	0.149325	+	0.988788i	$0.452290\pi$
$992$	−38.2616	−	46.2329i	−1.21481	−	1.46789i
$993$	4.51020	−	4.51020i	0.143127	−	0.143127i
$994$	14.1611	−	14.4014i	0.449162	−	0.456786i
$995$	−0.259357	−	6.28624i	−0.00822218	−	0.199287i
$996$	12.5584	+	4.60958i	0.397928	+	0.146060i
$997$	40.0214	−	23.1064i	1.26749	−	0.731786i	0.292978	−	0.956119i	$-0.405354\pi$
$997$	40.0214	−	23.1064i	1.26749	−	0.731786i	0.974512	+	0.224334i	$0.0720205\pi$
$998$	−47.9169	+	33.4548i	−1.51678	+	1.05899i
$999$	5.97443	+	3.44934i	0.189023	+	0.109132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cz.c.453.11	yes	360
5.2	odd	4		560.2.ch.c.117.37	✓	360
7.3	odd	6	inner	560.2.cz.c.213.51	yes	360
16.13	even	4		560.2.ch.c.173.85	yes	360
35.17	even	12		560.2.ch.c.437.85	yes	360
80.77	odd	4	inner	560.2.cz.c.397.51	yes	360
112.45	odd	12		560.2.ch.c.493.37	yes	360
560.157	even	12	inner	560.2.cz.c.157.11	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.37	✓	360	5.2	odd	4
560.2.ch.c.173.85	yes	360	16.13	even	4
560.2.ch.c.437.85	yes	360	35.17	even	12
560.2.ch.c.493.37	yes	360	112.45	odd	12
560.2.cz.c.157.11	yes	360	560.157	even	12	inner
560.2.cz.c.213.51	yes	360	7.3	odd	6	inner
560.2.cz.c.397.51	yes	360	80.77	odd	4	inner
560.2.cz.c.453.11	yes	360	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32958 + 0.481883i) q^{2} +(0.689402 - 0.398026i) q^{3} +(1.53558 - 1.28141i) q^{4} +(1.03726 - 1.98093i) q^{5} +(-0.724815 + 0.861420i) q^{6} +(-1.14153 - 2.38682i) q^{7} +(-1.42419 + 2.44370i) q^{8} +(-1.18315 + 2.04928i) q^{9} +(-0.424538 + 3.13365i) q^{10} +(0.290585 - 1.08448i) q^{11} +(0.548597 - 1.49460i) q^{12} -6.68057i q^{13} +(2.66792 + 2.62339i) q^{14} +(-0.0733779 - 1.77852i) q^{15} +(0.715996 - 3.93540i) q^{16} +(-0.386691 + 1.44315i) q^{17} +(0.585584 - 3.29482i) q^{18} +(0.744366 + 2.77801i) q^{19} +(-0.945595 - 4.37102i) q^{20} +(-1.73699 - 1.19112i) q^{21} +(0.136235 + 1.58193i) q^{22} +(-0.000156465 - 0.000583934i) q^{23} +(-0.00917984 + 2.25156i) q^{24} +(-2.84820 - 4.10947i) q^{25} +(3.21925 + 8.88237i) q^{26} +4.27186i q^{27} +(-4.81139 - 2.20239i) q^{28} +(-4.47419 - 4.47419i) q^{29} +(0.954598 + 2.32932i) q^{30} +(-9.18741 + 5.30435i) q^{31} +(0.944425 + 5.57746i) q^{32} +(-0.231321 - 0.863302i) q^{33} +(-0.181292 - 2.10513i) q^{34} +(-5.91219 - 0.214458i) q^{35} +(0.809136 + 4.66292i) q^{36} +(0.807457 - 1.39856i) q^{37} +(-2.32837 - 3.33490i) q^{38} +(-2.65904 - 4.60560i) q^{39} +(3.36357 + 5.35597i) q^{40} +6.55424 q^{41} +(2.88345 + 0.746670i) q^{42} -10.8517i q^{43} +(-0.943442 - 2.03766i) q^{44} +(2.83225 + 4.46937i) q^{45} +(0.000489421 + 0.000700991i) q^{46} +(3.32581 - 0.891149i) q^{47} +(-1.07278 - 2.99806i) q^{48} +(-4.39384 + 5.44924i) q^{49} +(5.76720 + 4.09138i) q^{50} +(0.307827 + 1.14882i) q^{51} +(-8.56052 - 10.2585i) q^{52} +(8.87517 - 5.12408i) q^{53} +(-2.05854 - 5.67979i) q^{54} +(-1.84687 - 1.70051i) q^{55} +(7.45843 + 0.609734i) q^{56} +(1.61889 + 1.61889i) q^{57} +(8.10485 + 3.79277i) q^{58} +(0.129224 - 0.482271i) q^{59} +(-2.39168 - 2.63702i) q^{60} +(3.79365 - 1.01650i) q^{61} +(9.65934 - 11.4798i) q^{62} +(6.24185 + 0.484667i) q^{63} +(-3.94337 - 6.96059i) q^{64} +(-13.2338 - 6.92946i) q^{65} +(0.723571 + 1.03636i) q^{66} +(-3.77433 + 2.17911i) q^{67} +(1.25547 + 2.71158i) q^{68} +(-0.000340288 - 0.000340288i) q^{69} +(7.96409 - 2.56385i) q^{70} -5.39800i q^{71} +(-3.32279 - 5.80982i) q^{72} +(3.40697 - 12.7150i) q^{73} +(-0.399640 + 2.24859i) q^{74} +(-3.59923 - 1.69942i) q^{75} +(4.70279 + 3.31202i) q^{76} +(-2.92017 + 0.544385i) q^{77} +(5.75478 + 4.84217i) q^{78} +(9.43202 + 5.44558i) q^{79} +(-7.05309 - 5.50036i) q^{80} +(-1.84914 - 3.20280i) q^{81} +(-8.71440 + 3.15838i) q^{82} +8.40249i q^{83} +(-4.19359 + 0.396727i) q^{84} +(2.45769 + 2.26293i) q^{85} +(5.22923 + 14.4282i) q^{86} +(-4.86537 - 1.30367i) q^{87} +(2.23630 + 2.25461i) q^{88} +(7.59633 + 4.38574i) q^{89} +(-5.91942 - 4.57757i) q^{90} +(-15.9453 + 7.62604i) q^{91} +(-0.000988521 - 0.000696181i) q^{92} +(-4.22255 + 7.31367i) q^{93} +(-3.99251 + 2.78751i) q^{94} +(6.27515 + 1.40697i) q^{95} +(2.87107 + 3.46921i) q^{96} +(-11.1142 - 11.1142i) q^{97} +(3.21607 - 9.36252i) q^{98} +(1.87859 + 1.87859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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