LMFDB - Embedded newform 456.2.bk.a.61.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.10
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01758 - 0.982103i) q^{2} +(-0.984808 + 0.173648i) q^{3} +(0.0709471 + 1.99874i) q^{4} +(2.00499 + 2.38946i) q^{5} +(1.17266 + 0.790481i) q^{6} +(-0.650971 + 1.12751i) q^{7} +(1.89078 - 2.10356i) q^{8} +(0.939693 - 0.342020i) q^{9} +(0.306449 - 4.40058i) q^{10} +(-3.19277 + 1.84334i) q^{11} +(-0.416947 - 1.95606i) q^{12} +(2.28774 + 0.403390i) q^{13} +(1.76975 - 0.508018i) q^{14} +(-2.38946 - 2.00499i) q^{15} +(-3.98993 + 0.283610i) q^{16} +(-4.34949 - 1.58309i) q^{17} +(-1.29211 - 0.574841i) q^{18} +(-1.36918 + 4.13828i) q^{19} +(-4.63366 + 4.17699i) q^{20} +(0.445290 - 1.22343i) q^{21} +(5.05926 + 1.25987i) q^{22} +(-4.32214 - 3.62671i) q^{23} +(-1.49677 + 2.39993i) q^{24} +(-0.821270 + 4.65765i) q^{25} +(-1.93179 - 2.65728i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-2.29979 - 1.22113i) q^{28} +(0.617421 + 1.69635i) q^{29} +(0.462360 + 4.38694i) q^{30} +(-2.13633 + 3.70023i) q^{31} +(4.33862 + 3.62993i) q^{32} +(2.82417 - 2.36976i) q^{33} +(2.87121 + 5.88257i) q^{34} +(-3.99934 + 0.705192i) q^{35} +(0.750278 + 1.85394i) q^{36} +0.384977i q^{37} +(5.45747 - 2.86636i) q^{38} -2.32303 q^{39} +(8.81736 + 0.300303i) q^{40} +(-0.439300 - 2.49139i) q^{41} +(-1.65465 + 0.807615i) q^{42} +(7.88287 + 9.39444i) q^{43} +(-3.91089 - 6.25073i) q^{44} +(2.70132 + 1.55961i) q^{45} +(0.836334 + 7.93526i) q^{46} +(1.33097 - 0.484434i) q^{47} +(3.88007 - 0.972146i) q^{48} +(2.65247 + 4.59422i) q^{49} +(5.41001 - 3.93297i) q^{50} +(4.55832 + 0.803754i) q^{51} +(-0.643964 + 4.60121i) q^{52} +(-2.65275 + 3.16143i) q^{53} +(1.37230 + 0.341735i) q^{54} +(-10.8061 - 3.93309i) q^{55} +(1.14096 + 3.50123i) q^{56} +(0.629778 - 4.31316i) q^{57} +(1.03771 - 2.33255i) q^{58} +(0.866732 - 2.38133i) q^{59} +(3.83794 - 4.91816i) q^{60} +(-5.61539 + 6.69216i) q^{61} +(5.80790 - 1.66719i) q^{62} +(-0.226080 + 1.28216i) q^{63} +(-0.849937 - 7.95472i) q^{64} +(3.62302 + 6.27525i) q^{65} +(-5.20117 - 0.362200i) q^{66} +(0.167931 + 0.461387i) q^{67} +(2.85560 - 8.80583i) q^{68} +(4.88625 + 2.82108i) q^{69} +(4.76223 + 3.21017i) q^{70} +(0.995420 - 0.835257i) q^{71} +(1.05729 - 2.62338i) q^{72} +(-0.785927 - 4.45721i) q^{73} +(0.378087 - 0.391746i) q^{74} -4.72951i q^{75} +(-8.36848 - 2.44304i) q^{76} -4.79985i q^{77} +(2.36387 + 2.28145i) q^{78} +(-1.91386 - 10.8540i) q^{79} +(-8.67746 - 8.96514i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.99978 + 2.96664i) q^{82} +(-11.6759 - 6.74107i) q^{83} +(2.47690 + 0.803222i) q^{84} +(-4.93799 - 13.5670i) q^{85} +(1.20484 - 17.3014i) q^{86} +(-0.902610 - 1.56337i) q^{87} +(-2.15922 + 10.2015i) q^{88} +(-3.11073 + 17.6418i) q^{89} +(-1.21712 - 4.24000i) q^{90} +(-1.94408 + 2.31686i) q^{91} +(6.94220 - 8.89614i) q^{92} +(1.46134 - 4.01499i) q^{93} +(-1.83014 - 0.814201i) q^{94} +(-12.6334 + 5.02561i) q^{95} +(-4.90304 - 2.82139i) q^{96} +(17.8103 + 6.48241i) q^{97} +(1.81289 - 7.28000i) q^{98} +(-2.36976 + 2.82417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.01758	−	0.982103i	−0.719539	−	0.694452i
$2$	−1.01758	−	0.982103i	−0.719539	−	0.694452i
$3$	−0.984808	+	0.173648i	−0.568579	+	0.100256i
$3$	−0.984808	+	0.173648i	−0.568579	+	0.100256i
$4$	0.0709471	+	1.99874i	0.0354735	+	0.999371i
$5$	2.00499	+	2.38946i	0.896660	+	1.06860i	0.997282	+	0.0736733i	$0.0234722\pi$
$5$	2.00499	+	2.38946i	0.896660	+	1.06860i	−0.100622	+	0.994925i	$0.532083\pi$
$6$	1.17266	+	0.790481i	0.478738	+	0.322713i
$7$	−0.650971	+	1.12751i	−0.246044	+	0.426161i	−0.962425	−	0.271549i	$-0.912464\pi$
$7$	−0.650971	+	1.12751i	−0.246044	+	0.426161i	0.716381	+	0.697710i	$0.245797\pi$
$8$	1.89078	−	2.10356i	0.668490	−	0.743721i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	0.306449	−	4.40058i	0.0969075	−	1.39159i
$11$	−3.19277	+	1.84334i	−0.962655	+	0.555789i	−0.896989	−	0.442052i	$-0.854250\pi$
$11$	−3.19277	+	1.84334i	−0.962655	+	0.555789i	−0.0656659	+	0.997842i	$0.520917\pi$
$12$	−0.416947	−	1.95606i	−0.120362	−	0.564665i
$13$	2.28774	+	0.403390i	0.634504	+	0.111880i	0.481643	−	0.876367i	$-0.340040\pi$
$13$	2.28774	+	0.403390i	0.634504	+	0.111880i	0.152861	+	0.988248i	$0.451151\pi$
$14$	1.76975	−	0.508018i	0.472986	−	0.135774i
$15$	−2.38946	−	2.00499i	−0.616955	−	0.517687i
$16$	−3.98993	+	0.283610i	−0.997483	+	0.0709024i
$17$	−4.34949	−	1.58309i	−1.05491	−	0.383955i	−0.244395	−	0.969676i	$-0.578589\pi$
$17$	−4.34949	−	1.58309i	−1.05491	−	0.383955i	−0.810513	+	0.585721i	$0.800811\pi$
$18$	−1.29211	−	0.574841i	−0.304554	−	0.135491i
$19$	−1.36918	+	4.13828i	−0.314112	+	0.949386i
$19$	−1.36918	+	4.13828i	−0.314112	+	0.949386i
$20$	−4.63366	+	4.17699i	−1.03612	+	0.934003i
$21$	0.445290	−	1.22343i	0.0971703	−	0.266973i
$22$	5.05926	+	1.25987i	1.07864	+	0.268605i
$23$	−4.32214	−	3.62671i	−0.901229	−	0.756221i	0.0692016	−	0.997603i	$-0.477955\pi$
$23$	−4.32214	−	3.62671i	−0.901229	−	0.756221i	−0.970430	+	0.241382i	$0.922399\pi$
$24$	−1.49677	+	2.39993i	−0.305527	+	0.489884i
$25$	−0.821270	+	4.65765i	−0.164254	+	0.931531i
$26$	−1.93179	−	2.65728i	−0.378855	−	0.521135i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−2.29979	−	1.22113i	−0.434620	−	0.230772i
$29$	0.617421	+	1.69635i	0.114652	+	0.315005i	0.983725	−	0.179679i	$-0.0575060\pi$
$29$	0.617421	+	1.69635i	0.114652	+	0.315005i	−0.869073	+	0.494684i	$0.835284\pi$
$30$	0.462360	+	4.38694i	0.0844150	+	0.800942i
$31$	−2.13633	+	3.70023i	−0.383696	+	0.664582i	−0.991587	−	0.129439i	$-0.958682\pi$
$31$	−2.13633	+	3.70023i	−0.383696	+	0.664582i	0.607891	+	0.794020i	$0.292016\pi$
$32$	4.33862	+	3.62993i	0.766967	+	0.641687i
$33$	2.82417	−	2.36976i	0.491624	−	0.412522i
$34$	2.87121	+	5.88257i	0.492409	+	1.00885i
$35$	−3.99934	+	0.705192i	−0.676012	+	0.119199i
$36$	0.750278	+	1.85394i	0.125046	+	0.308990i
$37$			0.384977i			0.0632898i	0.999499	+	0.0316449i	$0.0100746\pi$
$37$			0.384977i			0.0632898i	−0.999499	+	0.0316449i	$0.989925\pi$
$38$	5.45747	−	2.86636i	0.885319	−	0.464985i
$39$	−2.32303			−0.371982
$40$	8.81736	+	0.300303i	1.39415	+	0.0474821i
$41$	−0.439300	−	2.49139i	−0.0686071	−	0.389090i	−0.999704	−	0.0243190i	$-0.992258\pi$
$41$	−0.439300	−	2.49139i	−0.0686071	−	0.389090i	0.931097	−	0.364771i	$-0.118853\pi$
$42$	−1.65465	+	0.807615i	−0.255318	+	0.124618i
$43$	7.88287	+	9.39444i	1.20213	+	1.43264i	0.872560	+	0.488506i	$0.162458\pi$
$43$	7.88287	+	9.39444i	1.20213	+	1.43264i	0.329566	+	0.944133i	$0.393098\pi$
$44$	−3.91089	−	6.25073i	−0.589588	−	0.942333i
$45$	2.70132	+	1.55961i	0.402689	+	0.232493i
$46$	0.836334	+	7.93526i	0.123311	+	1.16999i
$47$	1.33097	−	0.484434i	0.194142	−	0.0706620i	−0.243119	−	0.969996i	$-0.578171\pi$
$47$	1.33097	−	0.484434i	0.194142	−	0.0706620i	0.437262	+	0.899334i	$0.355948\pi$
$48$	3.88007	−	0.972146i	0.560040	−	0.140317i
$49$	2.65247	+	4.59422i	0.378925	+	0.656317i
$50$	5.41001	−	3.93297i	0.765091	−	0.556207i
$51$	4.55832	+	0.803754i	0.638292	+	0.112548i
$52$	−0.643964	+	4.60121i	−0.0893017	+	0.638074i
$53$	−2.65275	+	3.16143i	−0.364384	+	0.434255i	−0.916821	−	0.399299i	$-0.869254\pi$
$53$	−2.65275	+	3.16143i	−0.364384	+	0.434255i	0.552437	+	0.833555i	$0.313698\pi$
$54$	1.37230	+	0.341735i	0.186747	+	0.0465043i
$55$	−10.8061	−	3.93309i	−1.45709	−	0.530337i
$56$	1.14096	+	3.50123i	0.152467	+	0.467872i
$57$	0.629778	−	4.31316i	0.0834161	−	0.571292i
$58$	1.03771	−	2.33255i	0.136259	−	0.306279i
$59$	0.866732	−	2.38133i	0.112839	−	0.310022i	−0.870400	−	0.492346i	$-0.836140\pi$
$59$	0.866732	−	2.38133i	0.112839	−	0.310022i	0.983239	+	0.182323i	$0.0583618\pi$
$60$	3.83794	−	4.91816i	0.495476	−	0.634931i
$61$	−5.61539	+	6.69216i	−0.718977	+	0.856843i	−0.994531	−	0.104442i	$-0.966694\pi$
$61$	−5.61539	+	6.69216i	−0.718977	+	0.856843i	0.275554	+	0.961286i	$0.411139\pi$
$62$	5.80790	−	1.66719i	0.737604	−	0.211734i
$63$	−0.226080	+	1.28216i	−0.0284834	+	0.161537i
$64$	−0.849937	−	7.95472i	−0.106242	−	0.994340i
$65$	3.62302	+	6.27525i	0.449380	+	0.778349i
$66$	−5.20117	−	0.362200i	−0.640220	−	0.0445837i
$67$	0.167931	+	0.461387i	0.0205161	+	0.0563674i	0.949528	−	0.313683i	$-0.101563\pi$
$67$	0.167931	+	0.461387i	0.0205161	+	0.0563674i	−0.929012	+	0.370050i	$0.879341\pi$
$68$	2.85560	−	8.80583i	0.346292	−	1.06786i
$69$	4.88625	+	2.82108i	0.588235	+	0.339618i
$70$	4.76223	+	3.21017i	0.569195	+	0.383689i
$71$	0.995420	−	0.835257i	0.118135	−	0.0991268i	−0.581807	−	0.813327i	$-0.697654\pi$
$71$	0.995420	−	0.835257i	0.118135	−	0.0991268i	0.699941	+	0.714200i	$0.253209\pi$
$72$	1.05729	−	2.62338i	0.124603	−	0.309169i
$73$	−0.785927	−	4.45721i	−0.0919858	−	0.521677i	−0.995629	−	0.0933921i	$-0.970229\pi$
$73$	−0.785927	−	4.45721i	−0.0919858	−	0.521677i	0.903644	−	0.428285i	$-0.140882\pi$
$74$	0.378087	−	0.391746i	0.0439517	−	0.0455395i
$75$		−	4.72951i		−	0.546116i
$76$	−8.36848	−	2.44304i	−0.959931	−	0.280236i
$77$		−	4.79985i		−	0.546994i
$78$	2.36387	+	2.28145i	0.267656	+	0.258324i
$79$	−1.91386	−	10.8540i	−0.215326	−	1.22117i	−0.880341	−	0.474342i	$-0.842686\pi$
$79$	−1.91386	−	10.8540i	−0.215326	−	1.22117i	0.665015	−	0.746830i	$-0.268425\pi$
$80$	−8.67746	−	8.96514i	−0.970170	−	1.00233i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.99978	+	2.96664i	−0.220839	+	0.327610i
$83$	−11.6759	−	6.74107i	−1.28159	−	0.739928i	−0.304454	−	0.952527i	$-0.598474\pi$
$83$	−11.6759	−	6.74107i	−1.28159	−	0.739928i	−0.977140	+	0.212599i	$0.931807\pi$
$84$	2.47690	+	0.803222i	0.270252	+	0.0876387i
$85$	−4.93799	−	13.5670i	−0.535600	−	1.47155i
$86$	1.20484	−	17.3014i	0.129921	−	1.86566i
$87$	−0.902610	−	1.56337i	−0.0967699	−	0.167610i
$88$	−2.15922	+	10.2015i	−0.230173	+	1.08749i
$89$	−3.11073	+	17.6418i	−0.329737	+	1.87003i	0.144310	+	0.989533i	$0.453904\pi$
$89$	−3.11073	+	17.6418i	−0.329737	+	1.87003i	−0.474047	+	0.880499i	$0.657207\pi$
$90$	−1.21712	−	4.24000i	−0.128296	−	0.446936i
$91$	−1.94408	+	2.31686i	−0.203795	+	0.242873i
$92$	6.94220	−	8.89614i	0.723775	−	0.927487i
$93$	1.46134	−	4.01499i	0.151534	−	0.416335i
$94$	−1.83014	−	0.814201i	−0.188764	−	0.0839784i
$95$	−12.6334	+	5.02561i	−1.29616	+	0.515617i
$96$	−4.90304	−	2.82139i	−0.500414	−	0.287957i
$97$	17.8103	+	6.48241i	1.80836	+	0.658189i	0.997317	+	0.0732013i	$0.0233216\pi$
$97$	17.8103	+	6.48241i	1.80836	+	0.658189i	0.811042	+	0.584988i	$0.198901\pi$
$98$	1.81289	−	7.28000i	0.183129	−	0.735391i
$99$	−2.36976	+	2.82417i	−0.238170	+	0.283839i
$100$	−9.36771	−	1.31106i	−0.936771	−	0.131106i
$101$	−9.48803	−	1.67300i	−0.944094	−	0.166469i	−0.319647	−	0.947537i	$-0.603564\pi$
$101$	−9.48803	−	1.67300i	−0.944094	−	0.166469i	−0.624447	+	0.781067i	$0.714676\pi$
$102$	−3.84909	−	5.29462i	−0.381117	−	0.524246i
$103$	5.71644	+	9.90116i	0.563257	+	0.975590i	0.997209	+	0.0746544i	$0.0237854\pi$
$103$	5.71644	+	9.90116i	0.563257	+	0.975590i	−0.433952	+	0.900936i	$0.642881\pi$
$104$	5.17415	−	4.04968i	0.507367	−	0.397103i
$105$	3.81613	−	1.38896i	0.372416	−	0.135548i
$106$	5.80424	−	0.611736i	0.563758	−	0.0594170i
$107$	6.90179	+	3.98475i	0.667221	+	0.385220i	0.795023	−	0.606579i	$-0.207459\pi$
$107$	6.90179	+	3.98475i	0.667221	+	0.385220i	−0.127802	+	0.991800i	$0.540792\pi$
$108$	−1.06081	−	1.69549i	−0.102077	−	0.163148i
$109$	−7.53219	−	8.97652i	−0.721453	−	0.859794i	0.273318	−	0.961924i	$-0.411879\pi$
$109$	−7.53219	−	8.97652i	−0.721453	−	0.859794i	−0.994771	+	0.102129i	$0.967434\pi$
$110$	7.13337	+	14.6149i	0.680140	+	1.39348i
$111$	−0.0668505	−	0.379128i	−0.00634517	−	0.0359853i
$112$	2.27756	−	4.68333i	0.215209	−	0.442533i
$113$	5.73694			0.539686			0.269843	−	0.962904i	$-0.413028\pi$
$113$	5.73694			0.539686			0.269843	+	0.962904i	$0.413028\pi$
$114$	−4.87682	+	3.77049i	−0.456756	+	0.353139i
$115$		−	17.5991i		−	1.64112i
$116$	−3.34676	+	1.35442i	−0.310739	+	0.125754i
$117$	2.28774	−	0.403390i	0.211501	−	0.0372934i
$118$	−3.22068	+	1.57198i	−0.296488	+	0.144712i
$119$	4.61635	−	3.87358i	0.423180	−	0.355090i
$120$	−8.73555	+	1.23538i	−0.797443	+	0.112774i
$121$	1.29584	−	2.24445i	0.117803	−	0.204041i
$122$	12.2865	−	1.29493i	1.11237	−	0.117238i
$123$	0.865252	+	2.37726i	0.0780172	+	0.214350i
$124$	−7.54738	−	4.00745i	−0.677774	−	0.359880i
$125$	0.730689	−	0.421864i	0.0653548	−	0.0377326i
$126$	1.48927	−	1.08267i	0.132675	−	0.0964521i
$127$	3.61684	−	20.5121i	0.320943	−	1.82016i	−0.215833	−	0.976430i	$-0.569247\pi$
$127$	3.61684	−	20.5121i	0.320943	−	1.82016i	0.536775	−	0.843725i	$-0.319642\pi$
$128$	−6.94748	+	8.92931i	−0.614076	+	0.789247i
$129$	−9.39444	−	7.88287i	−0.827134	−	0.694048i
$130$	2.47622	−	9.94375i	0.217179	−	0.872125i
$131$	−2.04947	+	5.63088i	−0.179063	+	0.491973i	−0.996457	−	0.0841074i	$-0.973196\pi$
$131$	−2.04947	+	5.63088i	−0.179063	+	0.491973i	0.817393	+	0.576080i	$0.195418\pi$
$132$	4.93690	+	5.47665i	0.429702	+	0.476681i
$133$	−3.77467	−	4.23767i	−0.327305	−	0.367453i
$134$	0.282246	−	0.634425i	0.0243823	−	0.0548060i
$135$	−2.93110	−	1.06683i	−0.252269	−	0.0918185i
$136$	−11.5540	+	6.15617i	−0.990750	+	0.527887i
$137$	11.3380	+	9.51371i	0.968671	+	0.812811i	0.982342	−	0.187095i	$-0.0599073\pi$
$137$	11.3380	+	9.51371i	0.968671	+	0.812811i	−0.0136709	+	0.999907i	$0.504352\pi$
$138$	−2.20157	−	7.66948i	−0.187410	−	0.652869i
$139$	17.0965	+	3.01457i	1.45010	+	0.255692i	0.842563	−	0.538597i	$-0.181046\pi$
$139$	17.0965	+	3.01457i	1.45010	+	0.255692i	0.607539	+	0.794290i	$0.292157\pi$
$140$	−1.69324	−	7.94362i	−0.143105	−	0.671358i
$141$	−1.22663	+	0.708196i	−0.103301	+	0.0596408i
$142$	−1.83323	−	0.127663i	−0.153841	−	0.0107132i
$143$	−8.04780	+	2.92916i	−0.672991	+	0.244949i
$144$	−3.65231	+	1.63114i	−0.304359	+	0.135929i
$145$	−2.81543	+	4.87647i	−0.233809	+	0.404969i
$146$	−3.57770	+	5.30744i	−0.296092	+	0.439247i
$147$	−3.40995	−	4.06383i	−0.281248	−	0.335179i
$148$	−0.769469	+	0.0273130i	−0.0632500	+	0.00224511i
$149$	10.1938	−	1.79745i	0.835110	−	0.147252i	0.260288	−	0.965531i	$-0.416182\pi$
$149$	10.1938	−	1.79745i	0.835110	−	0.147252i	0.574822	+	0.818279i	$0.305071\pi$
$150$	−4.64486	+	4.81266i	−0.379251	+	0.392952i
$151$	15.0751			1.22679			0.613396	−	0.789775i	$-0.289803\pi$
$151$	15.0751			1.22679			0.613396	+	0.789775i	$0.289803\pi$
$152$	6.11630	+	10.7047i	0.496097	+	0.868267i
$153$	−4.62864			−0.374203
$154$	−4.71395	+	4.88425i	−0.379861	+	0.393584i
$155$	−13.1249	+	2.31427i	−1.05422	+	0.185887i
$156$	−0.164812	−	4.64314i	−0.0131955	−	0.371748i
$157$	−1.40767	−	1.67759i	−0.112344	−	0.133887i	0.706942	−	0.707272i	$-0.250074\pi$
$157$	−1.40767	−	1.67759i	−0.112344	−	0.133887i	−0.819286	+	0.573385i	$0.805630\pi$
$158$	−8.71225	+	12.9245i	−0.693110	+	1.02821i
$159$	2.06348	−	3.57404i	0.163644	−	0.283440i
$160$	0.0253383	+	17.6449i	0.00200317	+	1.39495i
$161$	6.90275	−	2.51240i	0.544013	−	0.198005i
$162$	−1.41080	−	0.0982454i	−0.110843	−	0.00771889i
$163$	−1.81606	+	1.04850i	−0.142245	+	0.0821252i	−0.569434	−	0.822037i	$-0.692837\pi$
$163$	−1.81606	+	1.04850i	−0.142245	+	0.0821252i	0.427189	+	0.904163i	$0.359504\pi$
$164$	4.94849	−	1.05480i	0.386412	−	0.0823664i
$165$	11.3249	+	1.99688i	0.881640	+	0.155457i
$166$	5.26074	+	18.3265i	0.408312	+	1.42241i
$167$	11.0398	+	9.26353i	0.854289	+	0.716833i	0.960730	−	0.277486i	$-0.0895011\pi$
$167$	11.0398	+	9.26353i	0.854289	+	0.716833i	−0.106441	+	0.994319i	$0.533946\pi$
$168$	−1.73161	−	3.24992i	−0.133596	−	0.250737i
$169$	−7.14498	−	2.60056i	−0.549614	−	0.200043i
$170$	−8.29939	+	18.6552i	−0.636534	+	1.43079i
$171$	0.128763	+	4.35700i	0.00984676	+	0.333188i
$172$	−18.2178	+	16.4223i	−1.38909	+	1.25219i
$173$	8.41717	−	23.1260i	0.639946	−	1.75824i	−0.0119499	−	0.999929i	$-0.503804\pi$
$173$	8.41717	−	23.1260i	0.639946	−	1.75824i	0.651896	−	0.758308i	$-0.273974\pi$
$174$	−0.616907	+	2.47731i	−0.0467676	+	0.187804i
$175$	−4.71695	−	3.95799i	−0.356568	−	0.299196i
$176$	12.2161	−	8.26032i	0.920826	−	0.622645i
$177$	−0.440051	+	2.49566i	−0.0330763	+	0.187585i
$178$	20.4915	−	14.8970i	1.53591	−	1.11657i
$179$	2.80848	−	1.62148i	0.209916	−	0.121195i	−0.391356	−	0.920239i	$-0.627994\pi$
$179$	2.80848	−	1.62148i	0.209916	−	0.121195i	0.601272	+	0.799044i	$0.294661\pi$
$180$	−2.92560	+	5.50989i	−0.218061	+	0.410683i
$181$	−0.643278	−	1.76739i	−0.0478145	−	0.131369i	0.913487	−	0.406868i	$-0.133379\pi$
$181$	−0.643278	−	1.76739i	−0.0478145	−	0.131369i	−0.961301	+	0.275499i	$0.911157\pi$
$182$	4.25366	−	0.448313i	0.315302	−	0.0332311i
$183$	4.36800	−	7.56559i	0.322892	−	0.559265i
$184$	−15.8012	+	2.23460i	−1.16488	+	0.164737i
$185$	−0.919886	+	0.771876i	−0.0676314	+	0.0567495i
$186$	−5.43016	+	2.65040i	−0.398159	+	0.194337i
$187$	16.8051	−	2.96319i	1.22891	−	0.216690i
$188$	1.06269	+	2.62590i	0.0775045	+	0.191514i
$189$		−	1.30194i		−	0.0947023i
$190$	17.7912	+	7.29337i	1.29071	+	0.529116i
$191$	9.13375			0.660895			0.330447	−	0.943824i	$-0.392800\pi$
$191$	9.13375			0.660895			0.330447	+	0.943824i	$0.392800\pi$
$192$	2.21835	+	7.68628i	0.160095	+	0.554710i
$193$	−2.80629	−	15.9153i	−0.202001	−	1.14561i	−0.902089	−	0.431550i	$-0.857967\pi$
$193$	−2.80629	−	15.9153i	−0.202001	−	1.14561i	0.700088	−	0.714057i	$-0.253144\pi$
$194$	−11.7570	−	24.0879i	−0.844105	−	1.72941i
$195$	−4.65766	−	5.55078i	−0.333542	−	0.397500i
$196$	−8.99447	+	5.62755i	−0.642462	+	0.401968i
$197$	20.4328	+	11.7969i	1.45578	+	0.840492i	0.998799	−	0.0489870i	$-0.0155993\pi$
$197$	20.4328	+	11.7969i	1.45578	+	0.840492i	0.456976	+	0.889479i	$0.348933\pi$
$198$	5.18505	−	0.546476i	0.368485	−	0.0388364i
$199$	−16.4961	+	6.00409i	−1.16938	+	0.425619i	−0.852439	−	0.522827i	$-0.824877\pi$
$199$	−16.4961	+	6.00409i	−1.16938	+	0.425619i	−0.316940	+	0.948446i	$0.602655\pi$
$200$	8.24482	+	10.5342i	0.582997	+	0.744878i
$201$	−0.245499	−	0.425217i	−0.0173162	−	0.0299925i
$202$	8.01179	+	11.0206i	0.563708	+	0.775409i
$203$	−2.31458	−	0.408124i	−0.162452	−	0.0286447i
$204$	−1.28310	+	9.16792i	−0.0898348	+	0.641883i
$205$	5.07229	−	6.04492i	0.354264	−	0.422195i
$206$	3.90701	−	15.6894i	0.272215	−	1.09313i
$207$	−5.30189	−	1.92973i	−0.368507	−	0.134126i
$208$	−9.24233	−	0.960674i	−0.640840	−	0.0666107i
$209$	−3.25679	−	15.7364i	−0.225277	−	1.08851i
$210$	−5.24732	−	2.33445i	−0.362100	−	0.161093i
$211$	−4.47567	+	12.2968i	−0.308117	+	0.846546i	0.684906	+	0.728631i	$0.259843\pi$
$211$	−4.47567	+	12.2968i	−0.308117	+	0.846546i	−0.993024	+	0.117915i	$0.962379\pi$
$212$	−6.50708	−	5.07787i	−0.446908	−	0.348750i
$213$	−0.835257	+	0.995420i	−0.0572309	+	0.0682051i
$214$	−3.10970	−	10.8331i	−0.212575	−	0.740534i
$215$	−6.64252	+	37.6716i	−0.453016	+	2.56918i
$216$	−0.585679	+	2.76712i	−0.0398504	+	0.188279i
$217$	−2.78138	−	4.81749i	−0.188812	−	0.327032i
$218$	−1.15124	+	16.5317i	−0.0779718	+	1.11967i
$219$	1.54797	+	4.25302i	0.104602	+	0.287393i
$220$	7.09456	−	21.8776i	0.478315	−	1.47499i
$221$	−9.31190	−	5.37623i	−0.626386	−	0.361644i
$222$	−0.304317	+	0.451448i	−0.0204244	+	0.0302992i
$223$	19.8647	−	16.6685i	1.33024	−	1.11620i	0.346219	−	0.938154i	$-0.387466\pi$
$223$	19.8647	−	16.6685i	1.33024	−	1.11620i	0.984021	−	0.178050i	$-0.0569789\pi$
$224$	−6.91711	+	2.52888i	−0.462169	+	0.168968i
$225$	0.821270	+	4.65765i	0.0547513	+	0.310510i
$226$	−5.83781	−	5.63427i	−0.388325	−	0.374786i
$227$		−	3.75371i		−	0.249143i	−0.992211	−	0.124571i	$-0.960244\pi$
$227$		−	3.75371i		−	0.249143i	0.992211	−	0.124571i	$-0.0397556\pi$
$228$	8.66558	+	0.952756i	0.573892	+	0.0630978i
$229$			13.5819i			0.897518i	0.893653	+	0.448759i	$0.148134\pi$
$229$			13.5819i			0.897518i	−0.893653	+	0.448759i	$0.851866\pi$
$230$	−17.2841	+	17.9085i	−1.13968	+	1.18085i
$231$	0.833486	+	4.72693i	0.0548393	+	0.311009i
$232$	4.73578	+	1.90864i	0.310919	+	0.125308i
$233$	20.5073	−	17.2077i	1.34348	−	1.12731i	0.362762	−	0.931882i	$-0.381834\pi$
$233$	20.5073	−	17.2077i	1.34348	−	1.12731i	0.980717	−	0.195431i	$-0.0626106\pi$
$234$	−2.72413	−	1.83631i	−0.178082	−	0.120043i
$235$	3.82613	+	2.20902i	0.249589	+	0.144100i
$236$	4.82115	+	1.56342i	0.313830	+	0.101770i
$237$	3.76956	+	10.3568i	0.244859	+	0.672745i
$238$	−8.50176	−	0.592048i	−0.551088	−	0.0383768i
$239$	−4.87458	−	8.44302i	−0.315310	−	0.546133i	0.664193	−	0.747561i	$-0.268775\pi$
$239$	−4.87458	−	8.44302i	−0.315310	−	0.546133i	−0.979503	+	0.201428i	$0.935442\pi$
$240$	10.1024	+	7.32212i	0.652108	+	0.472640i
$241$	−4.27315	+	24.2342i	−0.275258	+	1.56106i	0.462884	+	0.886419i	$0.346815\pi$
$241$	−4.27315	+	24.2342i	−0.275258	+	1.56106i	−0.738142	+	0.674645i	$0.764297\pi$
$242$	−3.52290	+	1.01127i	−0.226461	+	0.0650070i
$243$	−0.642788	+	0.766044i	−0.0412348	+	0.0491418i
$244$	−13.7743	−	10.7489i	−0.881809	−	0.688129i
$245$	−5.65950	+	15.5494i	−0.361572	+	0.993412i
$246$	1.45425	−	3.26883i	0.0927196	−	0.208413i
$247$	−4.80167	+	8.91498i	−0.305523	+	0.567246i
$248$	3.74434	+	11.4902i	0.237766	+	0.729629i
$249$	12.6691	+	4.61116i	0.802869	+	0.292221i
$250$	−1.15785	−	0.288331i	−0.0732288	−	0.0182357i
$251$	−13.1795	+	15.7067i	−0.831882	+	0.991398i	0.168102	+	0.985770i	$0.446236\pi$
$251$	−13.1795	+	15.7067i	−0.831882	+	0.991398i	−0.999984	+	0.00562884i	$0.998208\pi$
$252$	−2.57875	−	0.360909i	−0.162446	−	0.0227352i
$253$	20.4848	+	3.61203i	1.28787	+	0.227086i
$254$	−23.8254	+	17.3207i	−1.49494	+	1.08679i
$255$	7.21886	+	12.5034i	0.452062	+	0.782995i
$256$	15.8391	−	2.26317i	0.989946	−	0.141448i
$257$	−0.0314622	+	0.0114513i	−0.00196256	+	0.000714312i	−0.343001	−	0.939335i	$-0.611444\pi$
$257$	−0.0314622	+	0.0114513i	−0.00196256	+	0.000714312i	0.341039	+	0.940049i	$0.389221\pi$
$258$	1.81782	+	17.2478i	0.113173	+	1.07380i
$259$	−0.434067	−	0.250609i	−0.0269716	−	0.0155721i
$260$	−12.2856	+	7.68668i	−0.761918	+	0.476708i
$261$	1.16037	+	1.38288i	0.0718253	+	0.0855980i
$262$	7.61562	−	3.71709i	0.470494	−	0.229643i
$263$	2.78379	+	15.7877i	0.171656	+	0.973509i	0.941933	+	0.335800i	$0.109007\pi$
$263$	2.78379	+	15.7877i	0.171656	+	0.973509i	−0.770278	+	0.637709i	$0.779882\pi$
$264$	0.354936	−	10.4215i	0.0218448	−	0.641398i
$265$	−12.8728			−0.790773
$266$	−0.320794	+	8.01930i	−0.0196691	+	0.491695i
$267$		−	17.9140i		−	1.09632i
$268$	−0.910280	+	0.368385i	−0.0556042	+	0.0225027i
$269$	−15.1320	+	2.66819i	−0.922617	+	0.162682i	−0.614727	−	0.788740i	$-0.710734\pi$
$269$	−15.1320	+	2.66819i	−0.922617	+	0.162682i	−0.307890	+	0.951422i	$0.599623\pi$
$270$	1.93490	+	3.96424i	0.117754	+	0.241256i
$271$	13.9599	−	11.7138i	0.848005	−	0.711561i	−0.111344	−	0.993782i	$-0.535516\pi$
$271$	13.9599	−	11.7138i	0.848005	−	0.711561i	0.959349	+	0.282221i	$0.0910712\pi$
$272$	17.8032	+	5.08285i	1.07948	+	0.308193i
$273$	1.51222	−	2.61925i	0.0915240	−	0.158524i
$274$	−2.19390	−	20.8161i	−0.132538	−	1.25754i
$275$	−5.96354	−	16.3847i	−0.359615	−	0.988034i
$276$	−5.29194	+	9.96649i	−0.318537	+	0.599912i
$277$	−13.6933	+	7.90585i	−0.822753	+	0.475017i	−0.851365	−	0.524574i	$-0.824225\pi$
$277$	−13.6933	+	7.90585i	−0.822753	+	0.475017i	0.0286118	+	0.999591i	$0.490891\pi$
$278$	−14.4364	−	19.8581i	−0.865840	−	1.19101i
$279$	−0.741940	+	4.20775i	−0.0444188	+	0.251911i
$280$	−6.07844	+	9.74622i	−0.363256	+	0.582448i
$281$	7.07946	+	5.94037i	0.422325	+	0.354373i	0.829047	−	0.559179i	$-0.188884\pi$
$281$	7.07946	+	5.94037i	0.422325	+	0.354373i	−0.406722	+	0.913552i	$0.633328\pi$
$282$	1.94372	+	0.484031i	0.115747	+	0.0288236i
$283$	0.933412	−	2.56453i	0.0554856	−	0.152445i	−0.908853	−	0.417116i	$-0.863041\pi$
$283$	0.933412	−	2.56453i	0.0554856	−	0.152445i	0.964339	+	0.264670i	$0.0852632\pi$
$284$	1.74008	+	1.93033i	0.103255	+	0.114544i
$285$	11.5688	−	7.14304i	0.685278	−	0.423117i
$286$	11.0660	+	4.92311i	0.654348	+	0.291109i
$287$	3.09506	+	1.12651i	0.182695	+	0.0664957i
$288$	5.31848	+	1.92712i	0.313394	+	0.113557i
$289$	3.38918	+	2.84386i	0.199364	+	0.167286i
$290$	7.65414	−	2.19717i	0.449466	−	0.129022i
$291$	−18.6654	−	3.29121i	−1.09418	−	0.192934i
$292$	8.85306	−	1.88709i	0.518086	−	0.110434i
$293$	−26.7806	+	15.4618i	−1.56454	+	0.903286i	−0.567749	+	0.823201i	$0.692186\pi$
$293$	−26.7806	+	15.4618i	−1.56454	+	0.903286i	−0.996788	+	0.0800848i	$0.974481\pi$
$294$	−0.521187	+	7.48420i	−0.0303962	+	0.436488i
$295$	7.42787	−	2.70352i	0.432467	−	0.157405i
$296$	0.809822	+	0.727905i	0.0470700	+	0.0423086i
$297$	1.84334	−	3.19277i	0.106962	−	0.185263i
$298$	−12.1383	−	8.18233i	−0.703154	−	0.473990i
$299$	−8.42495	−	10.0405i	−0.487227	−	0.580655i
$300$	9.45306	−	0.335545i	0.545773	−	0.0193727i
$301$	−15.7239	+	2.77255i	−0.906310	+	0.159807i
$302$	−15.3401	−	14.8053i	−0.882726	−	0.851948i
$303$	9.63440			0.553482
$304$	4.28929	−	16.8998i	0.246008	−	0.969268i
$305$	−27.2494			−1.56030
$306$	4.71002	+	4.54580i	0.269254	+	0.259866i
$307$	34.2751	−	6.04362i	1.95618	−	0.344928i	0.957846	−	0.287283i	$-0.0927521\pi$
$307$	34.2751	−	6.04362i	1.95618	−	0.344928i	0.998337	−	0.0576445i	$-0.0183590\pi$
$308$	9.59367	−	0.340536i	0.546650	−	0.0194038i
$309$	−7.34891	−	8.75809i	−0.418065	−	0.498230i
$310$	15.6285	+	10.5350i	0.887639	+	0.598349i
$311$	5.39321	−	9.34132i	0.305821	−	0.529697i	−0.671623	−	0.740893i	$-0.734402\pi$
$311$	5.39321	−	9.34132i	0.305821	−	0.529697i	0.977444	+	0.211196i	$0.0677358\pi$
$312$	−4.39233	+	4.88663i	−0.248667	+	0.276651i
$313$	−21.6482	+	7.87928i	−1.22363	+	0.445364i	−0.871410	−	0.490555i	$-0.836794\pi$
$313$	−21.6482	+	7.87928i	−1.22363	+	0.445364i	−0.352216	+	0.935919i	$0.614572\pi$
$314$	−0.215152	+	3.08957i	−0.0121417	+	0.174354i
$315$	−3.51696	+	2.03052i	−0.198158	+	0.114407i
$316$	21.5586	−	4.59536i	1.21276	−	0.258509i
$317$	5.87530	+	1.03597i	0.329990	+	0.0581861i	0.336189	−	0.941795i	$-0.390862\pi$
$317$	5.87530	+	1.03597i	0.329990	+	0.0581861i	−0.00619884	+	0.999981i	$0.501973\pi$
$318$	−5.60984	+	1.61034i	−0.314584	+	0.0903033i
$319$	−5.09824	−	4.27793i	−0.285447	−	0.239518i
$320$	17.3034	−	17.9801i	0.967287	−	1.00512i
$321$	−7.48888	−	2.72573i	−0.417989	−	0.152135i
$322$	−9.49155	−	4.22264i	−0.528943	−	0.235319i
$323$	12.5065	−	15.8319i	0.695880	−	0.880909i
$324$	1.33911	+	1.48552i	0.0743953	+	0.0825289i
$325$	−3.75770	+	10.3242i	−0.208440	+	0.572684i
$326$	2.87773	+	0.716621i	0.159383	+	0.0396900i
$327$	8.97652	+	7.53219i	0.496402	+	0.416531i
$328$	−6.07142	−	3.78657i	−0.335238	−	0.209079i
$329$	−0.320218	+	1.81604i	−0.0176542	+	0.100122i
$330$	−9.56285	−	13.1542i	−0.526417	−	0.724114i
$331$	−2.50377	+	1.44555i	−0.137620	+	0.0794547i	−0.567229	−	0.823560i	$-0.691985\pi$
$331$	−2.50377	+	1.44555i	−0.137620	+	0.0794547i	0.429609	+	0.903015i	$0.358651\pi$
$332$	12.6453	−	23.8153i	0.694000	−	1.30703i
$333$	0.131670	+	0.361760i	0.00721546	+	0.0198243i
$334$	−2.13621	−	20.2687i	−0.116888	−	1.10905i
$335$	−0.765764	+	1.32634i	−0.0418382	+	0.0724659i
$336$	−1.42970	+	5.00767i	−0.0779967	+	0.273191i
$337$	1.09985	−	0.922884i	0.0599127	−	0.0502727i	−0.612340	−	0.790595i	$-0.709771\pi$
$337$	1.09985	−	0.922884i	0.0599127	−	0.0502727i	0.672252	+	0.740322i	$0.265327\pi$
$338$	4.71659	+	9.66340i	0.256549	+	0.525619i
$339$	−5.64978	+	0.996209i	−0.306854	+	0.0541066i
$340$	26.7666	−	10.8323i	1.45162	−	0.587464i
$341$		−	15.7520i		−	0.853017i
$342$	4.14799	−	4.56006i	0.224298	−	0.246580i
$343$	−16.0203			−0.865016
$344$	34.6665	+	1.18068i	1.86909	+	0.0636578i
$345$	3.05605	+	17.3317i	0.164532	+	0.933109i
$346$	−31.2773	+	15.2661i	−1.68148	+	0.820709i
$347$	16.7590	+	19.9726i	0.899671	+	1.07219i	0.997036	+	0.0769369i	$0.0245140\pi$
$347$	16.7590	+	19.9726i	0.899671	+	1.07219i	−0.0973655	+	0.995249i	$0.531042\pi$
$348$	3.06073	−	1.91500i	0.164072	−	0.102655i
$349$	1.20631	+	0.696465i	0.0645724	+	0.0372809i	0.531939	−	0.846783i	$-0.321464\pi$
$349$	1.20631	+	0.696465i	0.0645724	+	0.0372809i	−0.467366	+	0.884064i	$0.654797\pi$
$350$	0.912730	+	8.66012i	0.0487874	+	0.462903i
$351$	−2.18293	+	0.794523i	−0.116516	+	0.0424085i
$352$	−20.5434	−	3.59195i	−1.09497	−	0.191451i
$353$	−10.7974	−	18.7016i	−0.574686	−	0.995386i	−0.996076	−	0.0885059i	$-0.971791\pi$
$353$	−10.7974	−	18.7016i	−0.574686	−	0.995386i	0.421390	−	0.906880i	$-0.361543\pi$
$354$	2.89878	−	2.10736i	0.154068	−	0.112005i
$355$	3.99162	+	0.703831i	0.211853	+	0.0373555i
$356$	−35.4822	−	4.96591i	−1.88055	−	0.263193i
$357$	−3.87358	+	4.61635i	−0.205011	+	0.244323i
$358$	−4.45032	−	1.10823i	−0.235207	−	0.0585719i
$359$	−8.57617	−	3.12147i	−0.452633	−	0.164745i	0.105636	−	0.994405i	$-0.466312\pi$
$359$	−8.57617	−	3.12147i	−0.452633	−	0.164745i	−0.558269	+	0.829660i	$0.688534\pi$
$360$	8.38832	−	2.73352i	0.442103	−	0.144069i
$361$	−15.2507	−	11.3321i	−0.802667	−	0.596427i
$362$	−1.08117	+	2.43023i	−0.0568251	+	0.127730i
$363$	−0.886404	+	2.43537i	−0.0465241	+	0.127824i
$364$	−4.76874	−	3.72134i	−0.249950	−	0.195051i
$365$	9.07454	−	10.8146i	0.474983	−	0.566063i
$366$	−11.8750	+	3.40879i	−0.620716	+	0.178180i
$367$	−2.72696	+	15.4654i	−0.142346	+	0.807286i	0.827113	+	0.562035i	$0.189981\pi$
$367$	−2.72696	+	15.4654i	−0.142346	+	0.807286i	−0.969460	+	0.245251i	$0.921130\pi$
$368$	18.2736	+	13.2445i	0.952578	+	0.690418i
$369$	−1.26491	−	2.19090i	−0.0658488	−	0.114053i
$370$	1.69412	+	0.117976i	0.0880732	+	0.00613326i
$371$	−1.83769	−	5.04902i	−0.0954082	−	0.262132i
$372$	8.12860	+	2.63598i	0.421448	+	0.136669i
$373$	−23.6990	−	13.6826i	−1.22709	−	0.708458i	−0.260666	−	0.965429i	$-0.583942\pi$
$373$	−23.6990	−	13.6826i	−1.22709	−	0.708458i	−0.966419	+	0.256971i	$0.917276\pi$
$374$	−20.0107	−	13.4890i	−1.03473	−	0.697502i
$375$	−0.646332	+	0.542337i	−0.0333765	+	0.0280062i
$376$	1.49753	−	3.71574i	0.0772294	−	0.191625i
$377$	0.728207	+	4.12987i	0.0375046	+	0.212699i
$378$	−1.27864	+	1.32483i	−0.0657662	+	0.0681421i
$379$		−	7.31910i		−	0.375957i	−0.982173	−	0.187978i	$-0.939807\pi$
$379$		−	7.31910i		−	0.375957i	0.982173	−	0.187978i	$-0.0601935\pi$
$380$	−10.9412	−	24.8944i	−0.561272	−	1.27706i
$381$			20.8285i			1.06708i
$382$	−9.29434	−	8.97028i	−0.475540	−	0.458960i
$383$	−1.34812	−	7.64559i	−0.0688859	−	0.390671i	−0.999684	−	0.0251377i	$-0.991998\pi$
$383$	−1.34812	−	7.64559i	−0.0688859	−	0.390671i	0.930798	−	0.365534i	$-0.119114\pi$
$384$	5.29137	−	10.0001i	0.270024	−	0.510314i
$385$	11.4690	−	9.62368i	0.584517	−	0.490468i
$386$	−12.7748	+	18.9512i	−0.650221	+	0.964589i
$387$	10.6206	+	6.13179i	0.539874	+	0.311696i
$388$	−11.6931	+	36.0580i	−0.593626	+	1.83057i
$389$	4.99243	+	13.7166i	0.253126	+	0.695458i	0.999550	+	0.0299877i	$0.00954682\pi$
$389$	4.99243	+	13.7166i	0.253126	+	0.695458i	−0.746424	+	0.665470i	$0.768231\pi$
$390$	−0.711889	+	10.2227i	−0.0360479	+	0.517645i
$391$	13.0577	+	22.6167i	0.660358	+	1.14377i
$392$	14.6795	+	3.10700i	0.741424	+	0.156927i
$393$	1.04055	−	5.90123i	0.0524886	−	0.297677i
$394$	−9.20629	−	32.0714i	−0.463806	−	1.61573i
$395$	22.0979	−	26.3353i	1.11187	−	1.32507i
$396$	−5.81291	−	4.53617i	−0.292110	−	0.227951i
$397$	12.0424	−	33.0863i	0.604392	−	1.66055i	−0.137875	−	0.990450i	$-0.544027\pi$
$397$	12.0424	−	33.0863i	0.604392	−	1.66055i	0.742267	−	0.670104i	$-0.233751\pi$
$398$	22.6828	+	10.0912i	1.13699	+	0.505827i
$399$	4.45319	+	3.51783i	0.222938	+	0.176112i
$400$	1.95586	−	18.8167i	0.0977928	−	0.940833i
$401$	−10.1959	−	3.71101i	−0.509159	−	0.185319i	0.0746498	−	0.997210i	$-0.476216\pi$
$401$	−10.1959	−	3.71101i	−0.509159	−	0.185319i	−0.583809	+	0.811891i	$0.698438\pi$
$402$	−0.167791	+	0.673798i	−0.00836867	+	0.0336060i
$403$	−6.38000	+	7.60339i	−0.317810	+	0.378752i
$404$	2.67074	−	19.0828i	0.132874	−	0.949405i
$405$	3.07183	+	0.541646i	0.152640	+	0.0269146i
$406$	1.95446	+	2.68846i	0.0969982	+	0.133426i
$407$	−0.709645	−	1.22914i	−0.0351758	−	0.0609263i
$408$	10.3095	−	8.06898i	0.510396	−	0.399474i
$409$	16.0563	−	5.84403i	0.793934	−	0.288968i	0.0869638	−	0.996211i	$-0.472284\pi$
$409$	16.0563	−	5.84403i	0.793934	−	0.288968i	0.706971	+	0.707243i	$0.250061\pi$
$410$	−11.0982	+	1.16969i	−0.548101	+	0.0577669i
$411$	−12.8178	−	7.40036i	−0.632255	−	0.365033i
$412$	−19.3843	+	12.1281i	−0.954996	+	0.597510i
$413$	2.12076	+	2.52743i	0.104356	+	0.124367i
$414$	3.49991	+	7.17066i	0.172011	+	0.352419i
$415$	−7.30255	−	41.4148i	−0.358468	−	2.03297i
$416$	8.46134	+	10.0545i	0.414852	+	0.492961i
$417$	−17.3602			−0.850133
$418$	−12.1407	+	19.2116i	−0.593823	+	0.939671i
$419$			7.66550i			0.374484i	0.982314	+	0.187242i	$0.0599549\pi$
$419$			7.66550i			0.374484i	−0.982314	+	0.187242i	$0.940045\pi$
$420$	3.04691	+	7.52891i	0.148674	+	0.367373i
$421$	10.0506	−	1.77220i	0.489838	−	0.0863716i	0.0767264	−	0.997052i	$-0.475553\pi$
$421$	10.0506	−	1.77220i	0.489838	−	0.0863716i	0.413111	+	0.910681i	$0.364442\pi$
$422$	16.6311	−	8.11743i	0.809588	−	0.395150i
$423$	1.08502	−	0.910439i	0.0527554	−	0.0442671i
$424$	1.63450	+	11.5578i	0.0793781	+	0.561295i
$425$	10.9456	−	18.9583i	0.530939	−	0.919613i
$426$	1.82755	−	0.192614i	0.0885450	−	0.00933217i
$427$	−3.89005	−	10.6878i	−0.188253	−	0.517221i
$428$	−7.47482	+	14.0776i	−0.361309	+	0.680466i
$429$	7.41689	−	4.28214i	0.358091	−	0.206744i
$430$	43.7567	−	31.8103i	2.11013	−	1.53403i
$431$	6.18693	−	35.0878i	0.298014	−	1.69012i	−0.356679	−	0.934227i	$-0.616091\pi$
$431$	6.18693	−	35.0878i	0.298014	−	1.69012i	0.654693	−	0.755895i	$-0.272798\pi$
$432$	3.31358	−	2.24058i	0.159425	−	0.107800i
$433$	−1.39414	−	1.16983i	−0.0669983	−	0.0562182i	0.608674	−	0.793421i	$-0.291702\pi$
$433$	−1.39414	−	1.16983i	−0.0669983	−	0.0562182i	−0.675672	+	0.737203i	$0.736146\pi$
$434$	−1.90099	+	7.63379i	−0.0912504	+	0.366434i
$435$	1.92587	−	5.29129i	0.0923384	−	0.253698i
$436$	17.4073	−	15.6918i	0.833661	−	0.751499i
$437$	20.9261	−	12.9206i	1.00103	−	0.618076i
$438$	2.60172	−	5.84807i	0.124315	−	0.279432i
$439$	28.8757	+	10.5099i	1.37816	+	0.501610i	0.921620	−	0.388093i	$-0.126866\pi$
$439$	28.8757	+	10.5099i	1.37816	+	0.501610i	0.456541	+	0.889702i	$0.349088\pi$
$440$	−28.7053	+	15.2946i	−1.36847	+	0.729143i
$441$	4.06383	+	3.40995i	0.193515	+	0.162379i
$442$	4.19561	+	14.6160i	0.199565	+	0.695212i
$443$	−15.3244	−	2.70211i	−0.728086	−	0.128381i	−0.202695	−	0.979242i	$-0.564970\pi$
$443$	−15.3244	−	2.70211i	−0.728086	−	0.128381i	−0.525391	+	0.850861i	$0.676081\pi$
$444$	0.753036	−	0.160515i	0.0357375	−	0.00761770i
$445$	−48.3914	+	27.9388i	−2.29397	+	1.32443i
$446$	−36.5841	−	2.54765i	−1.73231	−	0.120635i
$447$	−9.72683	+	3.54028i	−0.460063	+	0.167449i
$448$	9.52235	+	4.21998i	0.449889	+	0.199375i
$449$	−12.4104	+	21.4954i	−0.585681	+	1.01443i	0.409109	+	0.912485i	$0.365839\pi$
$449$	−12.4104	+	21.4954i	−0.585681	+	1.01443i	−0.994790	+	0.101943i	$0.967494\pi$
$450$	3.73859	−	5.54612i	0.176239	−	0.261447i
$451$	5.99508	+	7.14466i	0.282297	+	0.336429i
$452$	0.407019	+	11.4667i	0.0191446	+	0.539346i
$453$	−14.8461	+	2.61776i	−0.697529	+	0.122993i
$454$	−3.68653	+	3.81971i	−0.173018	+	0.179268i
$455$	−9.43391			−0.442269
$456$	−7.88223	−	9.48000i	−0.369119	−	0.443942i
$457$	−24.4839			−1.14531			−0.572654	−	0.819797i	$-0.694086\pi$
$457$	−24.4839			−1.14531			−0.572654	+	0.819797i	$0.694086\pi$
$458$	13.3388	−	13.8207i	0.623283	−	0.645799i
$459$	4.55832	−	0.803754i	0.212764	−	0.0375160i
$460$	35.1760	−	1.24860i	1.64009	−	0.0582165i
$461$	22.9664	+	27.3702i	1.06965	+	1.27476i	0.959762	+	0.280815i	$0.0906047\pi$
$461$	22.9664	+	27.3702i	1.06965	+	1.27476i	0.109888	+	0.993944i	$0.464951\pi$
$462$	3.79420	−	5.62861i	0.176522	−	0.261867i
$463$	−6.95171	+	12.0407i	−0.323073	+	0.559579i	−0.981121	−	0.193397i	$-0.938049\pi$
$463$	−6.95171	+	12.0407i	−0.323073	+	0.559579i	0.658047	+	0.752977i	$0.271383\pi$
$464$	−2.94457	−	6.59322i	−0.136698	−	0.306083i
$465$	12.5236	−	4.55822i	0.580769	−	0.211383i
$466$	−37.7676	−	2.63007i	−1.74955	−	0.121836i
$467$	9.70731	−	5.60452i	0.449201	−	0.259346i	−0.258292	−	0.966067i	$-0.583160\pi$
$467$	9.70731	−	5.60452i	0.449201	−	0.259346i	0.707493	+	0.706721i	$0.249826\pi$
$468$	0.968580	+	4.54398i	0.0447726	+	0.210045i
$469$	−0.629539	−	0.111005i	−0.0290694	−	0.00512572i
$470$	−1.72392	−	6.00551i	−0.0795184	−	0.277013i
$471$	1.67759	+	1.40767i	0.0772995	+	0.0648620i
$472$	−3.37047	−	6.32578i	−0.155138	−	0.291167i
$473$	−42.4853	−	15.4634i	−1.95348	−	0.711008i
$474$	6.33559	−	14.2410i	0.291003	−	0.654109i
$475$	−18.1502	−	9.77583i	−0.832788	−	0.448546i
$476$	8.06979	+	8.95207i	0.369878	+	0.410317i
$477$	−1.41150	+	3.87807i	−0.0646282	+	0.177564i
$478$	−3.33163	+	13.3788i	−0.152385	+	0.611932i
$479$	27.9975	+	23.4927i	1.27924	+	1.07341i	0.993349	+	0.115145i	$0.0367334\pi$
$479$	27.9975	+	23.4927i	1.27924	+	1.07341i	0.285889	+	0.958263i	$0.407711\pi$
$480$	−3.08896	−	17.3725i	−0.140991	−	0.792941i
$481$	−0.155296	+	0.880726i	−0.00708088	+	0.0401577i
$482$	28.1488	−	20.4637i	1.28214	−	0.932094i
$483$	−6.36161	+	3.67288i	−0.289463	+	0.167122i
$484$	4.57802	+	2.43080i	0.208092	+	0.110491i
$485$	20.2200	+	55.5541i	0.918144	+	2.52258i
$486$	1.40642	−	0.148230i	0.0637967	−	0.00672383i
$487$	4.79231	−	8.30052i	0.217160	−	0.376132i	−0.736779	−	0.676134i	$-0.763654\pi$
$487$	4.79231	−	8.30052i	0.217160	−	0.376132i	0.953939	+	0.300002i	$0.0969873\pi$
$488$	3.45993	+	24.4657i	0.156623	+	1.10751i
$489$	1.60640	−	1.34793i	0.0726440	−	0.0609555i
$490$	21.0301	−	10.2645i	0.950042	−	0.463704i
$491$	−12.2970	+	2.16830i	−0.554956	+	0.0978538i	−0.444091	−	0.895982i	$-0.646473\pi$
$491$	−12.2970	+	2.16830i	−0.554956	+	0.0978538i	−0.110865	+	0.993835i	$0.535362\pi$
$492$	−4.69014	+	1.89807i	−0.211448	+	0.0855718i
$493$		−	8.35570i		−	0.376322i
$494$	13.6415	−	4.35599i	0.613761	−	0.195985i
$495$	−11.4996			−0.516868
$496$	7.47439	−	15.3696i	0.335610	−	0.690114i
$497$	0.293775	+	1.66608i	0.0131776	+	0.0747339i
$498$	−8.36318	−	17.1346i	−0.374763	−	0.767818i
$499$	22.3458	+	26.6307i	1.00034	+	1.19216i	0.981329	+	0.192336i	$0.0616064\pi$
$499$	22.3458	+	26.6307i	1.00034	+	1.19216i	0.0190081	+	0.999819i	$0.493949\pi$
$500$	0.895036	+	1.43053i	0.0400272	+	0.0639752i
$501$	−12.4807	−	7.20575i	−0.557597	−	0.321929i
$502$	28.8368	−	3.03925i	1.28705	−	0.135648i
$503$	−6.92624	+	2.52094i	−0.308826	+	0.112403i	−0.491784	−	0.870717i	$-0.663655\pi$
$503$	−6.92624	+	2.52094i	−0.308826	+	0.112403i	0.182958	+	0.983121i	$0.441433\pi$
$504$	2.26964	+	2.89985i	0.101098	+	0.129170i
$505$	−15.0259	−	26.0256i	−0.668643	−	1.15812i
$506$	−17.2976	−	23.7938i	−0.768973	−	1.05776i
$507$	7.48802	+	1.32034i	0.332555	+	0.0586383i
$508$	41.2550	+	5.77385i	1.83039	+	0.256173i
$509$	12.0487	−	14.3591i	0.534050	−	0.636456i	−0.429793	−	0.902927i	$-0.641413\pi$
$509$	12.0487	−	14.3591i	0.534050	−	0.636456i	0.963843	+	0.266472i	$0.0858579\pi$
$510$	4.93387	−	19.8129i	0.218476	−	0.877331i
$511$	5.53719	+	2.01537i	0.244951	+	0.0891548i
$512$	−18.3403	−	13.2527i	−0.810534	−	0.585692i
$513$	−0.883391	−	4.26844i	−0.0390027	−	0.188456i
$514$	0.0432617	+	0.0192465i	0.00190819	+	0.000848925i
$515$	−12.1970	+	33.5109i	−0.537463	+	1.47667i
$516$	15.0893	−	19.3363i	0.664270	−	0.851234i
$517$	−3.35650	+	4.00013i	−0.147619	+	0.175925i
$518$	0.195575	+	0.681314i	0.00859309	+	0.0299352i
$519$	−4.27351	+	24.2363i	−0.187586	+	1.06386i
$520$	20.0507	+	4.24385i	0.879280	+	0.186105i
$521$	0.207337	+	0.359118i	0.00908359	+	0.0157332i	0.870531	−	0.492113i	$-0.163775\pi$
$521$	0.207337	+	0.359118i	0.00908359	+	0.0157332i	−0.861448	+	0.507846i	$0.830442\pi$
$522$	0.177354	−	2.54680i	0.00776259	−	0.111470i
$523$	−0.412793	−	1.13414i	−0.0180502	−	0.0495925i	0.930340	−	0.366697i	$-0.119512\pi$
$523$	−0.412793	−	1.13414i	−0.0180502	−	0.0495925i	−0.948391	+	0.317105i	$0.897289\pi$
$524$	−11.4001	−	3.69687i	−0.498015	−	0.161499i
$525$	5.33259	+	3.07877i	0.232733	+	0.134369i
$526$	12.6724	−	18.7992i	0.552542	−	0.819684i
$527$	15.1497	−	12.7121i	0.659933	−	0.553750i
$528$	−10.5962	+	10.2561i	−0.461138	+	0.446341i
$529$	1.53399	+	8.69969i	0.0666952	+	0.378247i
$530$	13.0992	+	12.6425i	0.568992	+	0.549154i
$531$		−	2.53415i		−	0.109973i
$532$	8.20221	−	7.84524i	0.355611	−	0.340134i
$533$		−	5.87687i		−	0.254555i
$534$	−17.5934	+	18.2290i	−0.761341	+	0.788845i
$535$	4.31665	+	24.4809i	0.186625	+	1.05840i
$536$	1.28808	+	0.519126i	0.0556364	+	0.0224228i
$537$	−2.48425	+	2.08453i	−0.107203	+	0.0899543i
$538$	18.0185	+	12.1461i	0.776834	+	0.523657i
$539$	−16.9375	−	9.77884i	−0.729548	−	0.421205i
$540$	1.92437	−	5.93421i	0.0828118	−	0.255368i
$541$	1.54188	+	4.23628i	0.0662905	+	0.182132i	0.968415	−	0.249344i	$-0.0802151\pi$
$541$	1.54188	+	4.23628i	0.0662905	+	0.182132i	−0.902124	+	0.431476i	$0.857993\pi$
$542$	−25.7095	−	1.79036i	−1.10432	−	0.0769027i
$543$	0.940409	+	1.62884i	0.0403568	+	0.0699001i
$544$	−13.1243	−	22.6568i	−0.562700	−	0.971401i
$545$	6.34701	−	35.9957i	0.271876	−	1.54189i
$546$	−4.11119	+	1.18014i	−0.175943	+	0.0505054i
$547$	−7.47133	+	8.90398i	−0.319451	+	0.380707i	−0.901743	−	0.432273i	$-0.857712\pi$
$547$	−7.47133	+	8.90398i	−0.319451	+	0.380707i	0.582292	+	0.812980i	$0.302156\pi$
$548$	−18.2111	+	23.3367i	−0.777938	+	0.996894i
$549$	−2.98789	+	8.20915i	−0.127520	+	0.350358i
$550$	−10.0231	+	22.5296i	−0.427385	+	0.960664i
$551$	−7.86533	+	0.232446i	−0.335075	+	0.00990251i
$552$	15.1731	−	4.94450i	0.645810	−	0.210452i
$553$	13.4839	+	4.90775i	0.573395	+	0.208699i
$554$	21.6985	+	5.40342i	0.921879	+	0.229569i
$555$	0.771876	−	0.919886i	0.0327643	−	0.0390470i
$556$	−4.81239	+	34.3853i	−0.204091	+	1.45826i
$557$	−35.2996	−	6.22427i	−1.49569	−	0.263731i	−0.634862	−	0.772626i	$-0.718943\pi$
$557$	−35.2996	−	6.22427i	−1.49569	−	0.263731i	−0.860829	+	0.508895i	$0.830054\pi$
$558$	4.88743	−	3.55307i	0.206901	−	0.150413i
$559$	14.2443	+	24.6719i	0.602470	+	1.04351i
$560$	15.7571	−	3.94792i	0.665859	−	0.166830i
$561$	−16.0352	+	5.83635i	−0.677008	+	0.246411i
$562$	−1.36987	−	12.9976i	−0.0577847	−	0.548270i
$563$	9.35349	+	5.40024i	0.394203	+	0.227593i	0.683979	−	0.729501i	$-0.260248\pi$
$563$	9.35349	+	5.40024i	0.394203	+	0.227593i	−0.289777	+	0.957094i	$0.593581\pi$
$564$	−1.50253	−	2.40147i	−0.0632678	−	0.101120i
$565$	11.5025	+	13.7082i	0.483915	+	0.576707i
$566$	−3.46846	+	1.69291i	−0.145790	+	0.0711584i
$567$	0.226080	+	1.28216i	0.00949446	+	0.0538458i
$568$	0.125103	−	3.67321i	0.00524919	−	0.154125i
$569$	−17.9301			−0.751668			−0.375834	−	0.926687i	$-0.622644\pi$
$569$	−17.9301			−0.751668			−0.375834	+	0.926687i	$0.622644\pi$
$570$	−18.7874	−	4.09315i	−0.786919	−	0.171443i
$571$		−	5.01990i		−	0.210076i	−0.994468	−	0.105038i	$-0.966504\pi$
$571$		−	5.01990i		−	0.210076i	0.994468	−	0.105038i	$-0.0334965\pi$
$572$	−6.42560	−	15.8776i	−0.268668	−	0.663878i
$573$	−8.99499	+	1.58606i	−0.375771	+	0.0662586i
$574$	−2.04313	−	4.18598i	−0.0852785	−	0.174719i
$575$	20.4416	−	17.1525i	0.852473	−	0.715310i
$576$	−3.51935	−	7.18430i	−0.146640	−	0.299346i
$577$	−9.54806	+	16.5377i	−0.397491	+	0.688474i	−0.993416	−	0.114566i	$-0.963452\pi$
$577$	−9.54806	+	16.5377i	−0.397491	+	0.688474i	0.595925	+	0.803040i	$0.296786\pi$
$578$	−0.655806	−	6.22239i	−0.0272780	−	0.258817i
$579$	5.52732	+	15.1862i	0.229708	+	0.631116i
$580$	−9.94656	−	5.28135i	−0.413008	−	0.219296i
$581$	15.2013	−	8.77648i	0.630657	−	0.364110i
$582$	15.7612	+	21.6804i	0.653324	+	0.898680i
$583$	2.64202	−	14.9836i	0.109421	−	0.620559i
$584$	−10.8620	−	6.77434i	−0.449474	−	0.280324i
$585$	5.55078	+	4.65766i	0.229497	+	0.192570i
$586$	42.4365	+	10.5677i	1.75303	+	0.436546i
$587$	−14.1021	+	38.7451i	−0.582054	+	1.59918i	0.202611	+	0.979259i	$0.435057\pi$
$587$	−14.1021	+	38.7451i	−0.582054	+	1.59918i	−0.784665	+	0.619921i	$0.787165\pi$
$588$	7.88061	−	7.10393i	0.324991	−	0.292961i
$589$	−12.3876	−	13.9070i	−0.510421	−	0.573029i
$590$	−10.2136	−	4.54388i	−0.420488	−	0.187068i
$591$	−22.1709	−	8.06953i	−0.911987	−	0.331936i
$592$	−0.109183	−	1.53603i	−0.00448740	−	0.0631305i
$593$	29.2985	+	24.5844i	1.20314	+	1.00956i	0.999535	+	0.0305063i	$0.00971195\pi$
$593$	29.2985	+	24.5844i	1.20314	+	1.00956i	0.203610	+	0.979052i	$0.434732\pi$
$594$	−5.01138	+	1.43855i	−0.205619	+	0.0590243i
$595$	18.5115	+	3.26408i	0.758897	+	0.133814i
$596$	4.31585	+	20.2473i	0.176784	+	0.829361i
$597$	15.2029	−	8.77740i	0.622213	−	0.359235i
$598$	−1.28769	+	18.4912i	−0.0526576	+	0.756160i
$599$	−13.3940	+	4.87501i	−0.547263	+	0.199188i	−0.600830	−	0.799377i	$-0.705163\pi$
$599$	−13.3940	+	4.87501i	−0.547263	+	0.199188i	0.0535668	+	0.998564i	$0.482941\pi$
$600$	−9.94881	−	8.94243i	−0.406158	−	0.365073i
$601$	3.66471	−	6.34746i	0.149487	−	0.258918i	−0.781551	−	0.623841i	$-0.785571\pi$
$601$	3.66471	−	6.34746i	0.149487	−	0.258918i	0.931038	+	0.364923i	$0.118905\pi$
$602$	18.7233	+	12.6212i	0.763104	+	0.514401i
$603$	0.315607	+	0.376126i	0.0128525	+	0.0153170i
$604$	1.06953	+	30.1312i	0.0435187	+	1.22602i
$605$	7.96117	−	1.40377i	0.323668	−	0.0570713i
$606$	−9.80379	−	9.46197i	−0.398252	−	0.384366i
$607$	−37.4001			−1.51802			−0.759012	−	0.651077i	$-0.774318\pi$
$607$	−37.4001			−1.51802			−0.759012	+	0.651077i	$0.774318\pi$
$608$	−20.9620	+	12.9844i	−0.850122	+	0.526586i
$609$	2.35029			0.0952386
$610$	27.7286	+	26.7618i	1.12270	+	1.08355i
$611$	3.24033	−	0.571358i	0.131090	−	0.0231147i
$612$	−0.328388	−	9.25144i	−0.0132743	−	0.373967i
$613$	−16.2519	−	19.3682i	−0.656407	−	0.782275i	0.330459	−	0.943820i	$-0.392797\pi$
$613$	−16.2519	−	19.3682i	−0.656407	−	0.782275i	−0.986865	+	0.161546i	$0.948352\pi$
$614$	−40.8132	−	27.5118i	−1.64709	−	1.11029i
$615$	−3.94554	+	6.83388i	−0.159100	+	0.275568i
$616$	−10.0968	−	9.07545i	−0.406811	−	0.365660i
$617$	−9.18042	+	3.34140i	−0.369590	+	0.134520i	−0.520136	−	0.854083i	$-0.674119\pi$
$617$	−9.18042	+	3.34140i	−0.369590	+	0.134520i	0.150547	+	0.988603i	$0.451897\pi$
$618$	−1.12323	+	16.1295i	−0.0451828	+	0.648822i
$619$	−34.1675	+	19.7266i	−1.37331	+	0.792879i	−0.991343	−	0.131299i	$-0.958085\pi$
$619$	−34.1675	+	19.7266i	−1.37331	+	0.792879i	−0.381963	+	0.924177i	$0.624752\pi$
$620$	−5.55680	−	26.0690i	−0.223166	−	1.04696i
$621$	5.55644	+	0.979750i	0.222972	+	0.0393160i
$622$	−14.6622	+	4.20887i	−0.587899	+	0.168760i
$623$	−17.8664	−	14.9917i	−0.715804	−	0.600631i
$624$	9.26873	−	0.658834i	0.371046	−	0.0263745i
$625$	24.6945	+	8.98805i	0.987779	+	0.359522i
$626$	29.7670	+	13.2429i	1.18973	+	0.529293i
$627$	5.93991	+	14.9318i	0.237217	+	0.596319i
$628$	3.25321	−	2.93259i	0.129817	−	0.117023i
$629$	0.609452	−	1.67445i	0.0243004	−	0.0667649i
$630$	5.57298	+	1.38780i	0.222033	+	0.0552912i
$631$	9.16731	+	7.69229i	0.364945	+	0.306225i	0.806758	−	0.590882i	$-0.201220\pi$
$631$	9.16731	+	7.69229i	0.364945	+	0.306225i	−0.441813	+	0.897107i	$0.645665\pi$
$632$	−26.4507	−	16.4966i	−1.05215	−	0.656199i
$633$	2.27235	−	12.8872i	0.0903180	−	0.512219i
$634$	−4.96117	−	6.82434i	−0.197033	−	0.271029i
$635$	56.2646	−	32.4844i	2.23279	−	1.28910i
$636$	7.28999	+	3.87079i	0.289067	+	0.153487i
$637$	4.21490	+	11.5803i	0.167001	+	0.458830i
$638$	0.986509	+	9.36015i	0.0390563	+	0.370572i
$639$	0.649715	−	1.12534i	0.0257023	−	0.0445177i
$640$	−35.2659	+	1.30250i	−1.39401	+	0.0514859i
$641$	−23.0194	+	19.3155i	−0.909210	+	0.762918i	−0.971968	−	0.235111i	$-0.924455\pi$
$641$	−23.0194	+	19.3155i	−0.909210	+	0.762918i	0.0627587	+	0.998029i	$0.480010\pi$
$642$	4.94360	+	10.1285i	0.195108	+	0.399740i
$643$	−43.6118	+	7.68994i	−1.71988	+	0.303262i	−0.944569	−	0.328314i	$-0.893520\pi$
$643$	−43.6118	+	7.68994i	−1.71988	+	0.303262i	−0.775314	+	0.631576i	$0.782408\pi$
$644$	5.51136	+	13.6186i	0.217178	+	0.536647i
$645$		−	38.2527i		−	1.50620i
$646$	−28.2749	+	3.82756i	−1.11246	+	0.150593i
$647$	31.4426			1.23614			0.618068	−	0.786125i	$-0.287916\pi$
$647$	31.4426			1.23614			0.618068	+	0.786125i	$0.287916\pi$
$648$	0.0962751	−	2.82679i	0.00378204	−	0.111047i
$649$	1.62233	+	9.20070i	0.0636821	+	0.361159i
$650$	13.9632	−	6.81527i	0.547682	−	0.267317i
$651$	3.57567	+	4.26132i	0.140142	+	0.167014i
$652$	−2.22453	−	3.55545i	−0.0871194	−	0.139242i
$653$	−6.97881	−	4.02922i	−0.273102	−	0.157675i	0.357195	−	0.934030i	$-0.383733\pi$
$653$	−6.97881	−	4.02922i	−0.273102	−	0.157675i	−0.630296	+	0.776355i	$0.717067\pi$
$654$	−1.73695	−	16.4805i	−0.0679203	−	0.644438i
$655$	−17.5639	+	6.39275i	−0.686280	+	0.249786i
$656$	2.45936	+	9.81591i	0.0960219	+	0.383247i
$657$	−2.26299	−	3.91961i	−0.0882875	−	0.152918i
$658$	2.10939	−	1.53349i	0.0822326	−	0.0597816i
$659$	27.9633	+	4.93068i	1.08929	+	0.192072i	0.689322	−	0.724455i	$-0.257909\pi$
$659$	27.9633	+	4.93068i	1.08929	+	0.192072i	0.399972	+	0.916527i	$0.369020\pi$
$660$	−3.18778	+	22.7772i	−0.124084	+	0.886600i
$661$	16.2232	−	19.3341i	0.631011	−	0.752009i	−0.351911	−	0.936033i	$-0.614468\pi$
$661$	16.2232	−	19.3341i	0.631011	−	0.752009i	0.982922	+	0.184024i	$0.0589125\pi$
$662$	3.96747	+	0.987992i	0.154200	+	0.0383994i
$663$	10.1040	+	3.67756i	0.392407	+	0.142824i
$664$	−36.2567	+	11.8151i	−1.40703	+	0.458513i
$665$	2.55755	−	17.5159i	0.0991776	−	0.679238i
$666$	0.221301	−	0.497434i	0.00857523	−	0.0192752i
$667$	3.48359	−	9.57107i	0.134885	−	0.370593i
$668$	−17.7322	+	22.7230i	−0.686078	+	0.879180i
$669$	−16.6685	+	19.8647i	−0.644441	+	0.768014i
$670$	2.08183	−	0.597603i	0.0804283	−	0.0230874i
$671$	5.59267	−	31.7176i	0.215903	−	1.22444i
$672$	6.37289	−	3.69160i	0.245840	−	0.142407i
$673$	7.32065	+	12.6797i	0.282190	+	0.488768i	0.971924	−	0.235295i	$-0.0756058\pi$
$673$	7.32065	+	12.6797i	0.282190	+	0.488768i	−0.689734	+	0.724063i	$0.742272\pi$
$674$	−2.02556	−	0.141056i	−0.0780215	−	0.00543328i
$675$	−1.61759	−	4.44428i	−0.0622609	−	0.171061i
$676$	4.69093	−	14.4655i	0.180421	−	0.556364i
$677$	−5.53405	−	3.19509i	−0.212691	−	0.122797i	0.389870	−	0.920870i	$-0.372520\pi$
$677$	−5.53405	−	3.19509i	−0.212691	−	0.122797i	−0.602561	+	0.798073i	$0.705853\pi$
$678$	6.72750	+	4.53494i	0.258368	+	0.174163i
$679$	−18.9030	+	15.8615i	−0.725430	+	0.608708i
$680$	−37.8757	−	15.2648i	−1.45247	−	0.585379i
$681$	0.651826	+	3.69669i	0.0249780	+	0.141657i
$682$	−15.4701	+	16.0289i	−0.592379	+	0.613779i
$683$			4.83949i			0.185178i	0.995704	+	0.0925889i	$0.0295142\pi$
$683$			4.83949i			0.185178i	−0.995704	+	0.0925889i	$0.970486\pi$
$684$	−8.69937	+	0.566480i	−0.332629	+	0.0216599i
$685$			46.1666i			1.76394i
$686$	16.3020	+	15.7336i	0.622413	+	0.600712i
$687$	−2.35847	−	13.3756i	−0.0899814	−	0.510310i
$688$	−34.1165	−	35.2475i	−1.30068	−	1.34380i
$689$	−7.34409	+	6.16242i	−0.279788	+	0.234770i
$690$	13.9118	−	20.6378i	0.529612	−	0.785668i
$691$	−9.32490	−	5.38373i	−0.354736	−	0.204807i	0.312033	−	0.950071i	$-0.398990\pi$
$691$	−9.32490	−	5.38373i	−0.354736	−	0.204807i	−0.666769	+	0.745264i	$0.732323\pi$
$692$	46.8201	+	15.1830i	1.77983	+	0.577172i
$693$	−1.64165	−	4.51039i	−0.0623610	−	0.171335i
$694$	2.56149	−	36.7828i	0.0972329	−	1.39626i
$695$	27.0751	+	46.8955i	1.02702	+	1.77885i
$696$	−4.99527	−	1.05728i	−0.189345	−	0.0400761i
$697$	−2.03336	+	11.5318i	−0.0770190	+	0.436796i
$698$	−0.543522	−	1.89343i	−0.0205726	−	0.0716675i
$699$	−17.2077	+	20.5073i	−0.650854	+	0.775658i
$700$	7.57635	−	9.70877i	0.286359	−	0.366957i
$701$	9.50376	−	26.1114i	0.358952	−	0.986213i	−0.620442	−	0.784253i	$-0.713047\pi$
$701$	9.50376	−	26.1114i	0.358952	−	0.986213i	0.979394	−	0.201960i	$-0.0647312\pi$
$702$	3.00162	+	1.33537i	0.113289	+	0.0504004i
$703$	−1.59314	−	0.527104i	−0.0600865	−	0.0198801i
$704$	17.3769	+	23.8308i	0.654918	+	0.898159i
$705$	−4.15159	−	1.51106i	−0.156358	−	0.0569096i
$706$	−7.37968	+	29.6345i	−0.277738	+	1.11531i
$707$	8.06276	−	9.60882i	0.303231	−	0.361377i
$708$	−5.01939	−	0.702489i	−0.188640	−	0.0264012i
$709$	−0.703205	−	0.123994i	−0.0264094	−	0.00465669i	0.160428	−	0.987048i	$-0.448713\pi$
$709$	−0.703205	−	0.123994i	−0.0264094	−	0.00465669i	−0.186837	+	0.982391i	$0.559824\pi$
$710$	−3.37057	−	4.63639i	−0.126495	−	0.174001i
$711$	−5.51073	−	9.54486i	−0.206668	−	0.357960i
$712$	31.2290	+	39.9004i	1.17036	+	1.49533i
$713$	22.6532	−	8.24508i	0.848368	−	0.308781i
$714$	8.47541	−	0.893263i	0.317184	−	0.0334295i
$715$	−23.1349	−	13.3569i	−0.865195	−	0.499521i
$716$	3.44017	+	5.49839i	0.128565	+	0.205485i
$717$	6.26664	+	7.46829i	0.234032	+	0.278908i
$718$	5.66135	+	11.5990i	0.211280	+	0.432872i
$719$	−6.11879	−	34.7014i	−0.228192	−	1.29414i	−0.856488	−	0.516168i	$-0.827358\pi$
$719$	−6.11879	−	34.7014i	−0.228192	−	1.29414i	0.628295	−	0.777975i	$-0.283753\pi$
$720$	−11.2204	−	5.45661i	−0.418160	−	0.203356i
$721$	−14.8849			−0.554344
$722$	4.38951	+	26.5091i	0.163361	+	0.986566i
$723$		−	24.6081i		−	0.915185i
$724$	3.48692	−	1.41114i	0.129590	−	0.0524445i
$725$	−8.40809	+	1.48257i	−0.312269	+	0.0550614i
$726$	3.29378	−	1.60765i	0.122244	−	0.0596656i
$727$	−13.6528	+	11.4560i	−0.506354	+	0.424881i	−0.859844	−	0.510557i	$-0.829439\pi$
$727$	−13.6528	+	11.4560i	−0.506354	+	0.424881i	0.353490	+	0.935438i	$0.384995\pi$
$728$	1.19785	+	8.47016i	0.0443951	+	0.313925i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−19.8552	+	2.09263i	−0.734873	+	0.0774516i
$731$	−19.4143	−	53.3403i	−0.718064	−	1.97286i
$732$	15.4316	+	8.19374i	0.570367	+	0.302849i
$733$	−0.580968	+	0.335422i	−0.0214585	+	0.0123891i	−0.510691	−	0.859764i	$-0.670610\pi$
$733$	−0.580968	+	0.335422i	−0.0214585	+	0.0123891i	0.489232	+	0.872153i	$0.337277\pi$
$734$	17.9635	−	13.0591i	0.663045	−	0.482021i
$735$	2.87340	−	16.2959i	0.105987	−	0.601083i
$736$	−5.58743	−	31.4240i	−0.205955	−	1.15830i
$737$	−1.38666	−	1.16355i	−0.0510783	−	0.0428598i
$738$	−0.864531	+	3.47169i	−0.0318238	+	0.127795i
$739$	12.7598	−	35.0573i	0.469377	−	1.28960i	−0.448871	−	0.893597i	$-0.648174\pi$
$739$	12.7598	−	35.0573i	0.469377	−	1.28960i	0.918248	−	0.396006i	$-0.129604\pi$
$740$	−1.60804	−	1.78385i	−0.0591129	−	0.0655757i
$741$	3.18065	−	9.61334i	0.116844	−	0.353155i
$742$	−3.08865	+	6.94259i	−0.113388	+	0.254871i
$743$	−30.4479	−	11.0821i	−1.11703	−	0.406564i	−0.283460	−	0.958984i	$-0.591482\pi$
$743$	−30.4479	−	11.0821i	−1.11703	−	0.406564i	−0.833566	+	0.552420i	$0.813705\pi$
$744$	−5.68271	−	10.6655i	−0.208338	−	0.391014i
$745$	24.7335	+	20.7538i	0.906164	+	0.760362i
$746$	10.6779	+	37.1980i	0.390946	+	1.36192i
$747$	−13.2773	−	2.34115i	−0.485791	−	0.0856581i
$748$	7.11492	+	33.3788i	0.260147	+	1.22045i
$749$	−8.98573	+	5.18791i	−0.328331	+	0.189562i
$750$	1.19033	+	0.0828923i	0.0434646	+	0.00302680i
$751$	24.7702	−	9.01561i	0.903877	−	0.328984i	0.152072	−	0.988369i	$-0.451406\pi$
$751$	24.7702	−	9.01561i	0.903877	−	0.328984i	0.751805	+	0.659385i	$0.229183\pi$
$752$	−5.17310	+	2.31034i	−0.188644	+	0.0842494i
$753$	10.2518	−	17.7567i	0.373597	−	0.647089i
$754$	3.31495	−	4.91765i	0.120723	−	0.179090i
$755$	30.2254	+	36.0213i	1.10002	+	1.31095i
$756$	2.60225	−	0.0923690i	0.0946427	−	0.00335943i
$757$	−1.02702	+	0.181092i	−0.0373278	+	0.00658189i	−0.192281	−	0.981340i	$-0.561588\pi$
$757$	−1.02702	+	0.181092i	−0.0373278	+	0.00658189i	0.154953	+	0.987922i	$0.450477\pi$
$758$	−7.18811	+	7.44778i	−0.261084	+	0.270516i
$759$	−20.8009			−0.755023
$760$	−13.3153	+	36.0775i	−0.482997	+	1.30867i
$761$	2.45334			0.0889334			0.0444667	−	0.999011i	$-0.485841\pi$
$761$	2.45334			0.0889334			0.0444667	+	0.999011i	$0.485841\pi$
$762$	20.4558	−	21.1948i	0.741035	−	0.767805i
$763$	15.0244	−	2.64921i	0.543920	−	0.0959077i
$764$	0.648013	+	18.2560i	0.0234443	+	0.660479i
$765$	−9.28038	−	11.0599i	−0.335533	−	0.399873i
$766$	−6.13693	+	9.10401i	−0.221736	+	0.328941i
$767$	2.94346	−	5.09822i	0.106282	−	0.184086i
$768$	−15.2055	+	4.97922i	−0.548681	+	0.179672i
$769$	13.6054	−	4.95195i	0.490622	−	0.178572i	−0.0848491	−	0.996394i	$-0.527041\pi$
$769$	13.6054	−	4.95195i	0.490622	−	0.178572i	0.575471	+	0.817822i	$0.304819\pi$
$770$	−21.1221	−	1.47091i	−0.761189	−	0.0530079i
$771$	0.0289957	−	0.0167407i	0.00104425	−	0.000602900i
$772$	31.6114	−	6.73820i	1.13772	−	0.242513i
$773$	−23.4550	−	4.13575i	−0.843617	−	0.148752i	−0.264895	−	0.964277i	$-0.585337\pi$
$773$	−23.4550	−	4.13575i	−0.843617	−	0.148752i	−0.578722	+	0.815525i	$0.696448\pi$
$774$	−4.78525	−	16.6701i	−0.172002	−	0.599194i
$775$	−15.4799	−	12.9892i	−0.556055	−	0.466585i
$776$	47.3114	−	25.2082i	1.69838	−	0.904922i
$777$	0.470990	+	0.171427i	0.0168967	+	0.00614989i
$778$	8.39089	−	18.8608i	0.300828	−	0.676193i
$779$	10.9116	+	1.59323i	0.390947	+	0.0570834i
$780$	10.7641	−	9.70327i	0.385418	−	0.347433i
$781$	−1.63848	+	4.50168i	−0.0586294	+	0.161083i
$782$	8.92457	−	35.8384i	0.319142	−	1.28158i
$783$	−1.38288	−	1.16037i	−0.0494200	−	0.0414683i
$784$	−11.8862	−	17.5784i	−0.424506	−	0.627799i
$785$	1.18618	−	6.72713i	0.0423364	−	0.240102i
$786$	−6.85445	+	4.98306i	−0.244490	+	0.177740i
$787$	14.8256	−	8.55957i	0.528476	−	0.305116i	−0.211920	−	0.977287i	$-0.567972\pi$
$787$	14.8256	−	8.55957i	0.528476	−	0.305116i	0.740396	+	0.672171i	$0.234638\pi$
$788$	−22.1292	+	41.6768i	−0.788322	+	1.48467i
$789$	−5.48300	−	15.0644i	−0.195200	−	0.536307i
$790$	−48.3504	+	5.09588i	−1.72023	+	0.181303i
$791$	−3.73458	+	6.46848i	−0.132786	+	0.229993i
$792$	1.46013	+	10.3248i	0.0518834	+	0.366876i
$793$	−15.5461	+	13.0447i	−0.552058	+	0.463231i
$794$	−44.7483	+	21.8411i	−1.58806	+	0.775112i
$795$	12.6773	−	2.23535i	0.449617	−	0.0792796i
$796$	−13.1710	−	32.5455i	−0.466833	−	1.15354i
$797$			27.7477i			0.982873i	0.870913	+	0.491437i	$0.163528\pi$
$797$			27.7477i			0.982873i	−0.870913	+	0.491437i	$0.836472\pi$
$798$	−1.07662	−	7.95317i	−0.0381118	−	0.281539i
$799$	−6.55596			−0.231933
$800$	−20.4701	+	17.2266i	−0.723729	+	0.609054i
$801$	3.11073	+	17.6418i	0.109912	+	0.623344i
$802$	6.73058	+	13.7897i	0.237665	+	0.486931i
$803$	10.7255	+	12.7821i	0.378493	+	0.451071i
$804$	0.832481	−	0.520857i	0.0293593	−	0.0183692i
$805$	19.8432	+	11.4565i	0.699382	+	0.403789i
$806$	13.9595	−	1.47125i	0.491702	−	0.0518227i
$807$	14.4388	−	5.25531i	0.508271	−	0.184996i
$808$	−21.4590	+	16.7954i	−0.754924	+	0.590860i
$809$	13.8788	+	24.0388i	0.487952	+	0.845158i	0.999904	−	0.0138561i	$-0.00441068\pi$
$809$	13.8788	+	24.0388i	0.487952	+	0.845158i	−0.511952	+	0.859014i	$0.671077\pi$
$810$	−2.59388	−	3.56802i	−0.0911398	−	0.125367i
$811$	−3.86510	−	0.681522i	−0.135722	−	0.0239315i	0.105374	−	0.994433i	$-0.466396\pi$
$811$	−3.86510	−	0.681522i	−0.135722	−	0.0239315i	−0.241096	+	0.970501i	$0.577507\pi$
$812$	0.651521	−	4.65521i	0.0228639	−	0.163366i
$813$	−11.7138	+	13.9599i	−0.410820	+	0.489596i
$814$	−0.485021	+	1.94770i	−0.0170000	+	0.0682667i
$815$	−6.14655	−	2.23716i	−0.215304	−	0.0783643i
$816$	−18.4153	−	1.91414i	−0.644665	−	0.0670084i
$817$	−49.6699	+	19.7588i	−1.73773	+	0.691273i
$818$	−22.0781	−	9.82219i	−0.771942	−	0.343425i
$819$	−1.03442	+	2.84205i	−0.0361457	+	0.0993094i
$820$	12.4421	+	9.70932i	0.434497	+	0.339064i
$821$	15.4891	−	18.4592i	0.540573	−	0.644229i	−0.424743	−	0.905314i	$-0.639636\pi$
$821$	15.4891	−	18.4592i	0.540573	−	0.644229i	0.965316	+	0.261084i	$0.0840801\pi$
$822$	5.77524	+	20.1189i	0.201435	+	0.701726i
$823$	−0.647058	+	3.66965i	−0.0225550	+	0.127916i	−0.994006	−	0.109324i	$-0.965131\pi$
$823$	−0.647058	+	3.66965i	−0.0225550	+	0.127916i	0.971451	+	0.237239i	$0.0762426\pi$
$824$	31.6362	+	6.69600i	1.10210	+	0.233266i
$825$	8.71811	+	15.1002i	0.303526	+	0.525722i
$826$	0.324143	−	4.65467i	0.0112784	−	0.161957i
$827$	−6.56614	−	18.0403i	−0.228327	−	0.627323i	0.771635	−	0.636066i	$-0.219439\pi$
$827$	−6.56614	−	18.0403i	−0.228327	−	0.627323i	−0.999962	+	0.00874244i	$0.997217\pi$
$828$	3.48088	−	10.7340i	0.120969	−	0.373033i
$829$	39.8149	+	22.9872i	1.38283	+	0.798377i	0.992494	−	0.122296i	$-0.0390256\pi$
$829$	39.8149	+	22.9872i	1.38283	+	0.798377i	0.390336	+	0.920673i	$0.372359\pi$
$830$	−33.2427	+	49.3148i	−1.15387	+	1.71174i
$831$	12.1125	−	10.1636i	0.420177	−	0.352570i
$832$	1.26442	−	18.5412i	0.0438360	−	0.642800i
$833$	−4.26387	−	24.1816i	−0.147734	−	0.837844i
$834$	17.6654	+	17.0495i	0.611704	+	0.590376i
$835$			44.9526i			1.55565i
$836$	31.2220	−	7.62593i	1.07983	−	0.263748i
$837$		−	4.27266i		−	0.147685i
$838$	7.52831	−	7.80028i	0.260061	−	0.269456i
$839$	0.434355	+	2.46335i	0.0149956	+	0.0850443i	0.991387	−	0.130964i	$-0.0418073\pi$
$839$	0.434355	+	2.46335i	0.0149956	+	0.0850443i	−0.976392	+	0.216008i	$0.930696\pi$
$840$	4.29368	−	10.6537i	0.148146	−	0.367586i
$841$	19.7189	−	16.5461i	0.679962	−	0.570556i
$842$	−11.9678	−	8.06740i	−0.412438	−	0.278021i
$843$	−8.00344	−	4.62079i	−0.275653	−	0.159148i
$844$	−24.8956	−	8.07328i	−0.856943	−	0.277894i
$845$	−8.11171	−	22.2867i	−0.279051	−	0.766687i
$846$	−1.99824	−	0.139154i	−0.0687009	−	0.00478421i
$847$	1.68710	+	2.92215i	0.0579695	+	0.100406i
$848$	9.68769	−	13.3662i	0.332677	−	0.458998i
$849$	−0.473906	+	2.68765i	−0.0162644	+	0.0922400i
$850$	−29.7570	+	8.54194i	−1.02066	+	0.292986i
$851$	1.39620	−	1.66392i	0.0478611	−	0.0570386i
$852$	−2.04885	−	1.59884i	−0.0701923	−	0.0547754i
$853$	15.7544	−	43.2848i	0.539420	−	1.48204i	−0.308139	−	0.951341i	$-0.599706\pi$
$853$	15.7544	−	43.2848i	0.539420	−	1.48204i	0.847558	−	0.530702i	$-0.178072\pi$
$854$	−6.53811	+	14.6962i	−0.223729	+	0.502893i
$855$	−10.1527	+	9.04342i	−0.347215	+	0.309279i
$856$	21.4319	−	6.98407i	0.732527	−	0.238710i
$857$	40.9609	+	14.9085i	1.39920	+	0.509266i	0.927940	−	0.372730i	$-0.121578\pi$
$857$	40.9609	+	14.9085i	1.39920	+	0.509266i	0.471257	+	0.881996i	$0.343800\pi$
$858$	−11.7528	−	2.92672i	−0.401234	−	0.0999165i
$859$	−4.68324	+	5.58127i	−0.159790	+	0.190430i	−0.839999	−	0.542588i	$-0.817445\pi$
$859$	−4.68324	+	5.58127i	−0.159790	+	0.190430i	0.680209	+	0.733018i	$0.261889\pi$
$860$	−75.7670	−	10.6040i	−2.58363	−	0.361593i
$861$	−3.24365	−	0.571943i	−0.110543	−	0.0194918i
$862$	−40.7556	+	29.6286i	−1.38814	+	1.00915i
$863$	−15.5176	−	26.8773i	−0.528226	−	0.914915i	−0.999458	−	0.0329058i	$-0.989524\pi$
$863$	−15.5176	−	26.8773i	−0.528226	−	0.914915i	0.471232	−	0.882009i	$-0.343809\pi$
$864$	−5.57232	−	0.974302i	−0.189574	−	0.0331464i
$865$	72.1350	−	26.2550i	2.45266	−	0.892696i
$866$	0.269767	+	2.55959i	0.00916704	+	0.0869783i
$867$	−3.83152	−	2.21213i	−0.130125	−	0.0751279i
$868$	9.43158	−	5.90104i	0.320129	−	0.200294i
$869$	26.1182	+	31.1264i	0.885998	+	1.05589i
$870$	−7.15632	+	3.49291i	−0.242622	+	0.118421i
$871$	0.198064	+	1.12327i	0.00671113	+	0.0380607i
$872$	−33.1243	−	1.12815i	−1.12173	−	0.0382041i
$873$	18.9533			0.641472
$874$	−33.9834	−	7.40384i	−1.14951	−	0.250439i
$875$			1.09848i			0.0371355i
$876$	−8.39087	+	3.39574i	−0.283501	+	0.114731i
$877$	1.09136	−	0.192437i	0.0368527	−	0.00649812i	−0.155191	−	0.987884i	$-0.549599\pi$
$877$	1.09136	−	0.192437i	0.0368527	−	0.00649812i	0.192044	+	0.981386i	$0.438488\pi$
$878$	−19.0616	−	39.0536i	−0.643297	−	1.31799i
$879$	23.6888	−	19.8773i	0.799004	−	0.670444i
$880$	44.2309	+	12.6280i	1.49102	+	0.425691i
$881$	21.2054	−	36.7288i	0.714427	−	1.23742i	−0.248753	−	0.968567i	$-0.580021\pi$
$881$	21.2054	−	36.7288i	0.714427	−	1.23742i	0.963180	−	0.268857i	$-0.0866459\pi$
$882$	−0.786350	−	7.46100i	−0.0264778	−	0.251225i
$883$	−2.97946	−	8.18600i	−0.100267	−	0.275481i	0.879409	−	0.476066i	$-0.157938\pi$
$883$	−2.97946	−	8.18600i	−0.100267	−	0.275481i	−0.979676	+	0.200586i	$0.935716\pi$
$884$	10.0850	−	18.9935i	0.339197	−	0.638821i
$885$	−6.84556	+	3.95229i	−0.230111	+	0.132855i
$886$	12.9401	+	17.7998i	0.434732	+	0.597996i
$887$	6.63363	−	37.6212i	0.222736	−	1.26320i	−0.644231	−	0.764831i	$-0.722823\pi$
$887$	6.63363	−	37.6212i	0.222736	−	1.26320i	0.866967	−	0.498366i	$-0.166066\pi$
$888$	−0.923919	−	0.576222i	−0.0310047	−	0.0193368i
$889$	20.7733	+	17.4308i	0.696712	+	0.584611i
$890$	76.6811	+	19.0953i	2.57036	+	0.640078i
$891$	−1.26092	+	3.46435i	−0.0422425	+	0.116060i
$892$	34.7253	+	38.5219i	1.16269	+	1.28981i
$893$	0.182379	+	6.17121i	0.00610308	+	0.206512i
$894$	13.3748	+	5.95023i	0.447319	+	0.199005i
$895$	9.50545	+	3.45970i	0.317732	+	0.115645i
$896$	−5.54532	−	13.6461i	−0.185256	−	0.455884i
$897$	10.0405	+	8.42495i	0.335241	+	0.281301i
$898$	33.7392	−	9.68505i	1.12589	−	0.323194i
$899$	−7.59591	−	1.33936i	−0.253338	−	0.0446703i
$900$	−9.25118	+	1.97195i	−0.308373	+	0.0657318i
$901$	16.5429	−	9.55107i	0.551125	−	0.318192i
$902$	0.916304	−	13.1581i	0.0305096	−	0.438116i
$903$	15.0036	−	5.46085i	0.499287	−	0.181726i
$904$	10.8473	−	12.0680i	0.360775	−	0.401376i
$905$	2.93334	−	5.08069i	0.0975075	−	0.168888i
$906$	17.6780	+	11.9166i	0.587312	+	0.395902i
$907$	−7.59462	−	9.05092i	−0.252175	−	0.300531i	0.625074	−	0.780565i	$-0.285069\pi$
$907$	−7.59462	−	9.05092i	−0.252175	−	0.300531i	−0.877250	+	0.480034i	$0.840624\pi$
$908$	7.50270	−	0.266315i	0.248986	−	0.00883798i
$909$	−9.48803	+	1.67300i	−0.314698	+	0.0554897i
$910$	9.59978	+	9.26507i	0.318230	+	0.307134i
$911$	−18.6435			−0.617685			−0.308843	−	0.951113i	$-0.599942\pi$
$911$	−18.6435			−0.617685			−0.308843	+	0.951113i	$0.599942\pi$
$912$	−1.28952	+	17.3878i	−0.0427001	+	0.575769i
$913$	49.7044			1.64498
$914$	24.9144	+	24.0457i	0.824094	+	0.795361i
$915$	26.8355	−	4.73182i	0.887153	−	0.156429i
$916$	−27.1467	+	0.963597i	−0.896953	+	0.0318381i
$917$	−5.01476	−	5.97635i	−0.165602	−	0.197357i
$918$	−5.42783	−	3.65885i	−0.179145	−	0.120760i
$919$	−15.0889	+	26.1348i	−0.497737	+	0.862106i	−0.999997	−	0.00261081i	$-0.999169\pi$
$919$	−15.0889	+	26.1348i	−0.497737	+	0.862106i	0.502259	+	0.864717i	$0.332502\pi$
$920$	−37.0208	−	33.2759i	−1.22054	−	1.09708i
$921$	−32.7049	+	11.9036i	−1.07766	+	0.392237i
$922$	3.51024	−	50.4068i	0.115604	−	1.66006i
$923$	2.61420	−	1.50931i	0.0860473	−	0.0496794i
$924$	−9.38878	+	2.00128i	−0.308868	+	0.0658374i
$925$	−1.79309	−	0.316170i	−0.0589564	−	0.0103956i
$926$	18.8992	−	5.42512i	0.621065	−	0.178281i
$927$	8.75809	+	7.34891i	0.287653	+	0.241370i
$928$	−3.47888	+	9.60102i	−0.114200	+	0.315169i
$929$	24.8402	+	9.04110i	0.814981	+	0.296629i	0.715680	−	0.698428i	$-0.246117\pi$
$929$	24.8402	+	9.04110i	0.814981	+	0.296629i	0.0993015	+	0.995057i	$0.468339\pi$
$930$	−17.2205	−	7.66111i	−0.564681	−	0.251218i
$931$	−22.6439	+	4.68634i	−0.742123	+	0.153589i
$932$	35.8486	+	39.7680i	1.17426	+	1.30264i
$933$	−3.68917	+	10.1359i	−0.120778	+	0.331835i
$934$	−15.3822	−	3.83052i	−0.503321	−	0.125338i
$935$	40.7745	+	34.2139i	1.33347	+	1.11891i
$936$	3.47704	−	5.57511i	0.113651	−	0.182228i
$937$	3.06016	−	17.3550i	0.0999712	−	0.566965i	−0.893139	−	0.449781i	$-0.851502\pi$
$937$	3.06016	−	17.3550i	0.0999712	−	0.566965i	0.993110	−	0.117184i	$-0.0373867\pi$
$938$	0.531590	+	0.731229i	0.0173570	+	0.0238755i
$939$	19.9510	−	11.5187i	0.651078	−	0.375900i
$940$	−4.14380	+	7.80416i	−0.135156	+	0.254544i
$941$	−3.69369	−	10.1483i	−0.120411	−	0.330826i	0.864814	−	0.502093i	$-0.167436\pi$
$941$	−3.69369	−	10.1483i	−0.120411	−	0.330826i	−0.985225	+	0.171266i	$0.945214\pi$
$942$	−0.324614	−	3.07999i	−0.0105765	−	0.100352i
$943$	−7.13684	+	12.3614i	−0.232407	+	0.402542i
$944$	−2.78283	+	9.74715i	−0.0905736	+	0.317243i
$945$	3.11094	−	2.61038i	0.101199	−	0.0849158i
$946$	28.0457	+	57.4603i	0.911844	+	1.86819i
$947$	−9.62126	+	1.69649i	−0.312649	+	0.0551284i	−0.327771	−	0.944757i	$-0.606297\pi$
$947$	−9.62126	+	1.69649i	−0.312649	+	0.0551284i	0.0151221	+	0.999886i	$0.495186\pi$
$948$	−20.4331	+	8.26916i	−0.663636	+	0.268570i
$949$		−	10.5140i		−	0.341298i
$950$	8.86845	+	27.7731i	0.287731	+	0.901077i
$951$	−5.96594			−0.193459
$952$	0.580175	−	17.0348i	0.0188036	−	0.552102i
$953$	4.28863	+	24.3221i	0.138922	+	0.787869i	0.972048	+	0.234784i	$0.0754383\pi$
$953$	4.28863	+	24.3221i	0.138922	+	0.787869i	−0.833125	+	0.553085i	$0.813451\pi$
$954$	5.24498	−	2.56001i	0.169812	−	0.0828834i
$955$	18.3131	+	21.8247i	0.592598	+	0.706231i
$956$	16.5296	−	10.3420i	0.534605	−	0.334485i
$957$	5.76364	+	3.32764i	0.186312	+	0.107567i
$958$	−5.41751	−	51.4022i	−0.175032	−	1.66073i
$959$	−18.1076	+	6.59061i	−0.584724	+	0.212822i
$960$	−13.9183	+	20.7116i	−0.449210	+	0.668464i
$961$	6.37218	+	11.0369i	0.205554	+	0.356030i
$962$	1.02299	−	0.743695i	0.0329825	−	0.0239777i
$963$	7.84843	+	1.38389i	0.252912	+	0.0445952i
$964$	−48.7411	−	6.82157i	−1.56985	−	0.219708i
$965$	32.4023	−	38.6155i	1.04307	−	1.24308i
$966$	10.0806	+	2.51030i	0.324338	+	0.0807677i
$967$	12.7192	+	4.62941i	0.409022	+	0.148872i	0.538333	−	0.842732i	$-0.319054\pi$
$967$	12.7192	+	4.62941i	0.409022	+	0.148872i	−0.129311	+	0.991604i	$0.541277\pi$
$968$	−2.27121	−	6.96963i	−0.0729995	−	0.224012i
$969$	−9.56733	+	17.7631i	−0.307347	+	0.570633i
$970$	33.9843	−	76.3890i	1.09117	−	2.45270i
$971$	−9.42078	+	25.8834i	−0.302327	+	0.830638i	0.691767	+	0.722121i	$0.256832\pi$
$971$	−9.42078	+	25.8834i	−0.302327	+	0.830638i	−0.994095	+	0.108517i	$0.965390\pi$
$972$	−1.57673	−	1.23042i	−0.0505736	−	0.0394657i
$973$	−14.5283	+	17.3141i	−0.465755	+	0.555065i
$974$	−13.0285	+	3.73992i	−0.417461	+	0.119835i
$975$	1.90784	−	10.8199i	0.0610996	−	0.346513i
$976$	20.5071	−	28.2938i	0.656415	−	0.905664i
$977$	17.2065	+	29.8026i	0.550486	+	0.953469i	0.998239	+	0.0593121i	$0.0188907\pi$
$977$	17.2065	+	29.8026i	0.550486	+	0.953469i	−0.447754	+	0.894157i	$0.647776\pi$
$978$	−2.95845	−	0.206021i	−0.0946009	−	0.00658784i
$979$	−22.5882	−	62.0604i	−0.721920	−	1.98346i
$980$	−31.4807	−	10.2087i	−1.00561	−	0.326105i
$981$	−10.1481	−	5.85900i	−0.324004	−	0.187064i
$982$	14.6427	+	9.87052i	0.467268	+	0.314981i
$983$	−45.5584	+	38.2280i	−1.45309	+	1.21928i	−0.522798	+	0.852456i	$0.675112\pi$
$983$	−45.5584	+	38.2280i	−1.45309	+	1.21928i	−0.930289	+	0.366828i	$0.880444\pi$
$984$	6.63671	+	2.67476i	0.211571	+	0.0852681i
$985$	12.7795	+	72.4759i	0.407187	+	2.30927i
$986$	−8.20616	+	8.50261i	−0.261337	+	0.270778i
$987$		−	1.84406i		−	0.0586971i
$988$	−18.1594	−	8.96480i	−0.577727	−	0.285208i
$989$		−	69.1929i		−	2.20021i
$990$	11.7018	+	11.2938i	0.371906	+	0.358940i
$991$	−2.37659	−	13.4783i	−0.0754947	−	0.428152i	−0.999006	−	0.0445802i	$-0.985805\pi$
$991$	−2.37659	−	13.4783i	−0.0754947	−	0.428152i	0.923511	−	0.383572i	$-0.125306\pi$
$992$	−22.7003	+	8.29917i	−0.720736	+	0.263499i
$993$	2.21471	−	1.85837i	0.0702818	−	0.0589734i
$994$	1.33732	−	1.98389i	0.0424173	−	0.0629252i
$995$	−47.4211	−	27.3786i	−1.50335	−	0.867960i
$996$	−8.31769	+	25.6493i	−0.263556	+	0.812730i
$997$	5.36013	+	14.7268i	0.169757	+	0.466403i	0.995175	−	0.0981191i	$-0.0312826\pi$
$997$	5.36013	+	14.7268i	0.169757	+	0.466403i	−0.825418	+	0.564522i	$0.809060\pi$
$998$	3.41540	−	49.0449i	0.108113	−	1.55249i
$999$	−0.192488	−	0.333400i	−0.00609007	−	0.0105483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.61.10	yes	240
8.5	even	2	inner	456.2.bk.a.61.1	✓	240
19.5	even	9	inner	456.2.bk.a.157.1	yes	240
152.5	even	18	inner	456.2.bk.a.157.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.1	✓	240	8.5	even	2	inner
456.2.bk.a.61.10	yes	240	1.1	even	1	trivial
456.2.bk.a.157.1	yes	240	19.5	even	9	inner
456.2.bk.a.157.10	yes	240	152.5	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01758 - 0.982103i) q^{2} +(-0.984808 + 0.173648i) q^{3} +(0.0709471 + 1.99874i) q^{4} +(2.00499 + 2.38946i) q^{5} +(1.17266 + 0.790481i) q^{6} +(-0.650971 + 1.12751i) q^{7} +(1.89078 - 2.10356i) q^{8} +(0.939693 - 0.342020i) q^{9} +(0.306449 - 4.40058i) q^{10} +(-3.19277 + 1.84334i) q^{11} +(-0.416947 - 1.95606i) q^{12} +(2.28774 + 0.403390i) q^{13} +(1.76975 - 0.508018i) q^{14} +(-2.38946 - 2.00499i) q^{15} +(-3.98993 + 0.283610i) q^{16} +(-4.34949 - 1.58309i) q^{17} +(-1.29211 - 0.574841i) q^{18} +(-1.36918 + 4.13828i) q^{19} +(-4.63366 + 4.17699i) q^{20} +(0.445290 - 1.22343i) q^{21} +(5.05926 + 1.25987i) q^{22} +(-4.32214 - 3.62671i) q^{23} +(-1.49677 + 2.39993i) q^{24} +(-0.821270 + 4.65765i) q^{25} +(-1.93179 - 2.65728i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-2.29979 - 1.22113i) q^{28} +(0.617421 + 1.69635i) q^{29} +(0.462360 + 4.38694i) q^{30} +(-2.13633 + 3.70023i) q^{31} +(4.33862 + 3.62993i) q^{32} +(2.82417 - 2.36976i) q^{33} +(2.87121 + 5.88257i) q^{34} +(-3.99934 + 0.705192i) q^{35} +(0.750278 + 1.85394i) q^{36} +0.384977i q^{37} +(5.45747 - 2.86636i) q^{38} -2.32303 q^{39} +(8.81736 + 0.300303i) q^{40} +(-0.439300 - 2.49139i) q^{41} +(-1.65465 + 0.807615i) q^{42} +(7.88287 + 9.39444i) q^{43} +(-3.91089 - 6.25073i) q^{44} +(2.70132 + 1.55961i) q^{45} +(0.836334 + 7.93526i) q^{46} +(1.33097 - 0.484434i) q^{47} +(3.88007 - 0.972146i) q^{48} +(2.65247 + 4.59422i) q^{49} +(5.41001 - 3.93297i) q^{50} +(4.55832 + 0.803754i) q^{51} +(-0.643964 + 4.60121i) q^{52} +(-2.65275 + 3.16143i) q^{53} +(1.37230 + 0.341735i) q^{54} +(-10.8061 - 3.93309i) q^{55} +(1.14096 + 3.50123i) q^{56} +(0.629778 - 4.31316i) q^{57} +(1.03771 - 2.33255i) q^{58} +(0.866732 - 2.38133i) q^{59} +(3.83794 - 4.91816i) q^{60} +(-5.61539 + 6.69216i) q^{61} +(5.80790 - 1.66719i) q^{62} +(-0.226080 + 1.28216i) q^{63} +(-0.849937 - 7.95472i) q^{64} +(3.62302 + 6.27525i) q^{65} +(-5.20117 - 0.362200i) q^{66} +(0.167931 + 0.461387i) q^{67} +(2.85560 - 8.80583i) q^{68} +(4.88625 + 2.82108i) q^{69} +(4.76223 + 3.21017i) q^{70} +(0.995420 - 0.835257i) q^{71} +(1.05729 - 2.62338i) q^{72} +(-0.785927 - 4.45721i) q^{73} +(0.378087 - 0.391746i) q^{74} -4.72951i q^{75} +(-8.36848 - 2.44304i) q^{76} -4.79985i q^{77} +(2.36387 + 2.28145i) q^{78} +(-1.91386 - 10.8540i) q^{79} +(-8.67746 - 8.96514i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.99978 + 2.96664i) q^{82} +(-11.6759 - 6.74107i) q^{83} +(2.47690 + 0.803222i) q^{84} +(-4.93799 - 13.5670i) q^{85} +(1.20484 - 17.3014i) q^{86} +(-0.902610 - 1.56337i) q^{87} +(-2.15922 + 10.2015i) q^{88} +(-3.11073 + 17.6418i) q^{89} +(-1.21712 - 4.24000i) q^{90} +(-1.94408 + 2.31686i) q^{91} +(6.94220 - 8.89614i) q^{92} +(1.46134 - 4.01499i) q^{93} +(-1.83014 - 0.814201i) q^{94} +(-12.6334 + 5.02561i) q^{95} +(-4.90304 - 2.82139i) q^{96} +(17.8103 + 6.48241i) q^{97} +(1.81289 - 7.28000i) q^{98} +(-2.36976 + 2.82417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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