LMFDB - Embedded newform 189.2.be.a.104.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] 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("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.11
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0448460 + 0.123213i) q^{2} +(-1.62941 + 0.587383i) q^{3} +(1.51892 + 1.27452i) q^{4} +(-0.231324 + 1.31190i) q^{5} +(0.000699206 - 0.227107i) q^{6} +(-2.62614 + 0.321557i) q^{7} +(-0.452264 + 0.261115i) q^{8} +(2.30996 - 1.91418i) q^{9} +(-0.151270 - 0.0873359i) q^{10} +(-4.31014 + 0.759994i) q^{11} +(-3.22358 - 1.18454i) q^{12} +(1.38870 + 3.81541i) q^{13} +(0.0781517 - 0.337996i) q^{14} +(-0.393667 - 2.27351i) q^{15} +(0.676731 + 3.83793i) q^{16} +(-1.85685 + 3.21617i) q^{17} +(0.132259 + 0.370462i) q^{18} +(4.31784 - 2.49291i) q^{19} +(-2.02342 + 1.69785i) q^{20} +(4.09018 - 2.06650i) q^{21} +(0.0996512 - 0.565150i) q^{22} +(0.242663 - 0.289194i) q^{23} +(0.583550 - 0.691115i) q^{24} +(3.03088 + 1.10315i) q^{25} -0.532388 q^{26} +(-2.63953 + 4.47581i) q^{27} +(-4.39872 - 2.85866i) q^{28} +(1.57190 - 4.31876i) q^{29} +(0.297781 + 0.0534526i) q^{30} +(0.693448 - 0.826419i) q^{31} +(-1.53182 - 0.270102i) q^{32} +(6.57659 - 3.77004i) q^{33} +(-0.313002 - 0.373021i) q^{34} +(0.185638 - 3.51963i) q^{35} +(5.94831 + 0.0366271i) q^{36} +(-0.172576 + 0.298911i) q^{37} +(0.113522 + 0.643813i) q^{38} +(-4.50387 - 5.40118i) q^{39} +(-0.237938 - 0.653729i) q^{40} +(5.09719 - 1.85523i) q^{41} +(0.0711916 + 0.596639i) q^{42} +(-0.390810 - 2.21639i) q^{43} +(-7.51538 - 4.33901i) q^{44} +(1.97686 + 3.47325i) q^{45} +(0.0247502 + 0.0428686i) q^{46} +(9.77186 - 8.19957i) q^{47} +(-3.35701 - 5.85607i) q^{48} +(6.79320 - 1.68890i) q^{49} +(-0.271846 + 0.323973i) q^{50} +(1.13646 - 6.33114i) q^{51} +(-2.75352 + 7.56523i) q^{52} +9.19872i q^{53} +(-0.433108 - 0.525947i) q^{54} -5.83030i q^{55} +(1.10374 - 0.831152i) q^{56} +(-5.57125 + 6.59819i) q^{57} +(0.461636 + 0.387359i) q^{58} +(-2.24314 + 12.7215i) q^{59} +(2.29969 - 3.95501i) q^{60} +(-1.14717 - 1.36715i) q^{61} +(0.0707275 + 0.122504i) q^{62} +(-5.45077 + 5.76967i) q^{63} +(-3.79516 + 6.57342i) q^{64} +(-5.32670 + 0.939241i) q^{65} +(0.169586 + 0.979395i) q^{66} +(5.40821 - 1.96843i) q^{67} +(-6.91949 + 2.51849i) q^{68} +(-0.225530 + 0.613753i) q^{69} +(0.425340 + 0.180714i) q^{70} +(2.30444 + 1.33047i) q^{71} +(-0.544894 + 1.46888i) q^{72} +(-4.63485 + 2.67593i) q^{73} +(-0.0290904 - 0.0346686i) q^{74} +(-5.58652 - 0.0171995i) q^{75} +(9.73572 + 1.71667i) q^{76} +(11.0746 - 3.38180i) q^{77} +(0.867479 - 0.312715i) q^{78} +(5.48206 + 1.99531i) q^{79} -5.19155 q^{80} +(1.67186 - 8.84335i) q^{81} +0.711242i q^{82} +(-4.03800 - 1.46971i) q^{83} +(8.84645 + 2.07420i) q^{84} +(-3.78977 - 3.17999i) q^{85} +(0.290615 + 0.0512433i) q^{86} +(-0.0245079 + 7.96035i) q^{87} +(1.75088 - 1.46916i) q^{88} +(-5.59352 - 9.68826i) q^{89} +(-0.516605 + 0.0878150i) q^{90} +(-4.87378 - 9.57326i) q^{91} +(0.737171 - 0.129983i) q^{92} +(-0.644488 + 1.75390i) q^{93} +(0.572067 + 1.57174i) q^{94} +(2.27163 + 6.24126i) q^{95} +(2.65463 - 0.459660i) q^{96} +(-14.5132 + 2.55906i) q^{97} +(-0.0965524 + 0.912754i) q^{98} +(-8.50151 + 10.0059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.0448460	+	0.123213i	−0.0317109	+	0.0871250i	−0.954538	−	0.298090i	$-0.903650\pi$
$2$	−0.0448460	+	0.123213i	−0.0317109	+	0.0871250i	0.922827	+	0.385215i	$0.125873\pi$
$3$	−1.62941	+	0.587383i	−0.940741	+	0.339125i
$3$	−1.62941	+	0.587383i	−0.940741	+	0.339125i
$4$	1.51892	+	1.27452i	0.759459	+	0.637262i
$5$	−0.231324	+	1.31190i	−0.103451	+	0.586701i	0.888376	+	0.459116i	$0.151834\pi$
$5$	−0.231324	+	1.31190i	−0.103451	+	0.586701i	−0.991828	+	0.127585i	$0.959277\pi$
$6$	0.000699206	−	0.227107i	0.000285450	−	0.0927161i
$7$	−2.62614	+	0.321557i	−0.992587	+	0.121537i
$7$	−2.62614	+	0.321557i	−0.992587	+	0.121537i
$8$	−0.452264	+	0.261115i	−0.159899	+	0.0923180i
$9$	2.30996	−	1.91418i	0.769988	−	0.638059i
$10$	−0.151270	−	0.0873359i	−0.0478358	−	0.0276180i
$11$	−4.31014	+	0.759994i	−1.29956	+	0.229147i	−0.780264	−	0.625450i	$-0.784915\pi$
$11$	−4.31014	+	0.759994i	−1.29956	+	0.229147i	−0.519292	+	0.854597i	$0.673804\pi$
$12$	−3.22358	−	1.18454i	−0.930566	−	0.341947i
$13$	1.38870	+	3.81541i	0.385155	+	1.05821i	0.969155	+	0.246452i	$0.0792647\pi$
$13$	1.38870	+	3.81541i	0.385155	+	1.05821i	−0.584000	+	0.811754i	$0.698513\pi$
$14$	0.0781517	−	0.337996i	0.0208869	−	0.0903332i
$15$	−0.393667	−	2.27351i	−0.101645	−	0.587017i
$16$	0.676731	+	3.83793i	0.169183	+	0.959483i
$17$	−1.85685	+	3.21617i	−0.450353	+	0.780035i	−0.998408	−	0.0564079i	$-0.982035\pi$
$17$	−1.85685	+	3.21617i	−0.450353	+	0.780035i	0.548055	+	0.836443i	$0.315369\pi$
$18$	0.132259	+	0.370462i	0.0311738	+	0.0873186i
$19$	4.31784	−	2.49291i	0.990581	−	0.571912i	0.0851328	−	0.996370i	$-0.472869\pi$
$19$	4.31784	−	2.49291i	0.990581	−	0.571912i	0.905448	+	0.424458i	$0.139535\pi$
$20$	−2.02342	+	1.69785i	−0.452450	+	0.379650i
$21$	4.09018	−	2.06650i	0.892551	−	0.450946i
$22$	0.0996512	−	0.565150i	0.0212457	−	0.120490i
$23$	0.242663	−	0.289194i	0.0505987	−	0.0603012i	−0.740152	−	0.672440i	$-0.765246\pi$
$23$	0.242663	−	0.289194i	0.0505987	−	0.0603012i	0.790750	+	0.612139i	$0.209691\pi$
$24$	0.583550	−	0.691115i	0.119117	−	0.141073i
$25$	3.03088	+	1.10315i	0.606176	+	0.220630i
$26$	−0.532388			−0.104410
$27$	−2.63953	+	4.47581i	−0.507977	+	0.861370i
$28$	−4.39872	−	2.85866i	−0.831280	−	0.540236i
$29$	1.57190	−	4.31876i	0.291895	−	0.801974i	−0.703895	−	0.710304i	$-0.748557\pi$
$29$	1.57190	−	4.31876i	0.291895	−	0.801974i	0.995789	−	0.0916699i	$-0.0292204\pi$
$30$	0.297781	+	0.0534526i	0.0543671	+	0.00975907i
$31$	0.693448	−	0.826419i	0.124547	−	0.148429i	−0.700168	−	0.713979i	$-0.746891\pi$
$31$	0.693448	−	0.826419i	0.124547	−	0.148429i	0.824714	+	0.565549i	$0.191336\pi$
$32$	−1.53182	−	0.270102i	−0.270791	−	0.0477477i
$33$	6.57659	−	3.77004i	1.14484	−	0.656281i
$34$	−0.313002	−	0.373021i	−0.0536794	−	0.0639727i
$35$	0.185638	−	3.51963i	0.0313785	−	0.594925i
$36$	5.94831	+	0.0366271i	0.991385	+	0.00610451i
$37$	−0.172576	+	0.298911i	−0.0283713	+	0.0491406i	−0.879862	−	0.475228i	$-0.842365\pi$
$37$	−0.172576	+	0.298911i	−0.0283713	+	0.0491406i	0.851491	+	0.524369i	$0.175699\pi$
$38$	0.113522	+	0.643813i	0.0184156	+	0.104440i
$39$	−4.50387	−	5.40118i	−0.721196	−	0.864882i
$40$	−0.237938	−	0.653729i	−0.0376213	−	0.103364i
$41$	5.09719	−	1.85523i	0.796047	−	0.289738i	0.0881999	−	0.996103i	$-0.471889\pi$
$41$	5.09719	−	1.85523i	0.796047	−	0.289738i	0.707848	+	0.706365i	$0.249666\pi$
$42$	0.0711916	+	0.596639i	0.0109851	+	0.0920635i
$43$	−0.390810	−	2.21639i	−0.0595979	−	0.337997i	0.940400	−	0.340071i	$-0.110451\pi$
$43$	−0.390810	−	2.21639i	−0.0595979	−	0.337997i	−0.999998	+	0.00207394i	$0.999340\pi$
$44$	−7.51538	−	4.33901i	−1.13299	−	0.654130i
$45$	1.97686	+	3.47325i	0.294694	+	0.517761i
$46$	0.0247502	+	0.0428686i	0.00364921	+	0.00632062i
$47$	9.77186	−	8.19957i	1.42537	−	1.19603i	0.476987	−	0.878910i	$-0.341729\pi$
$47$	9.77186	−	8.19957i	1.42537	−	1.19603i	0.948386	−	0.317119i	$-0.102716\pi$
$48$	−3.35701	−	5.85607i	−0.484542	−	0.845251i
$49$	6.79320	−	1.68890i	0.970458	−	0.241272i
$50$	−0.271846	+	0.323973i	−0.0384448	+	0.0458167i
$51$	1.13646	−	6.33114i	0.159136	−	0.886537i
$52$	−2.75352	+	7.56523i	−0.381844	+	1.04911i
$53$			9.19872i			1.26354i	0.775155	+	0.631771i	$0.217672\pi$
$53$			9.19872i			1.26354i	−0.775155	+	0.631771i	$0.782328\pi$
$54$	−0.433108	−	0.525947i	−0.0589385	−	0.0715724i
$55$		−	5.83030i		−	0.786157i
$56$	1.10374	−	0.831152i	0.147494	−	0.111067i
$57$	−5.57125	+	6.59819i	−0.737930	+	0.873952i
$58$	0.461636	+	0.387359i	0.0606158	+	0.0508627i
$59$	−2.24314	+	12.7215i	−0.292032	+	1.65620i	0.386993	+	0.922082i	$0.373514\pi$
$59$	−2.24314	+	12.7215i	−0.292032	+	1.65620i	−0.679026	+	0.734115i	$0.737597\pi$
$60$	2.29969	−	3.95501i	0.296889	−	0.510590i
$61$	−1.14717	−	1.36715i	−0.146880	−	0.175045i	0.687588	−	0.726101i	$-0.258670\pi$
$61$	−1.14717	−	1.36715i	−0.146880	−	0.175045i	−0.834468	+	0.551056i	$0.814225\pi$
$62$	0.0707275	+	0.122504i	0.00898240	+	0.0155580i
$63$	−5.45077	+	5.76967i	−0.686732	+	0.726911i
$64$	−3.79516	+	6.57342i	−0.474395	+	0.821677i
$65$	−5.32670	+	0.939241i	−0.660696	+	0.116498i
$66$	0.169586	+	0.979395i	0.0208746	+	0.120555i
$67$	5.40821	−	1.96843i	0.660718	−	0.240482i	0.0101714	−	0.999948i	$-0.496762\pi$
$67$	5.40821	−	1.96843i	0.660718	−	0.240482i	0.650546	+	0.759467i	$0.274540\pi$
$68$	−6.91949	+	2.51849i	−0.839111	+	0.305412i
$69$	−0.225530	+	0.613753i	−0.0271506	+	0.0738872i
$70$	0.425340	+	0.180714i	0.0508378	+	0.0215995i
$71$	2.30444	+	1.33047i	0.273487	+	0.157898i	0.630471	−	0.776213i	$-0.282862\pi$
$71$	2.30444	+	1.33047i	0.273487	+	0.157898i	−0.356984	+	0.934110i	$0.616195\pi$
$72$	−0.544894	+	1.46888i	−0.0642164	+	0.173109i
$73$	−4.63485	+	2.67593i	−0.542469	+	0.313194i	−0.746079	−	0.665858i	$-0.768066\pi$
$73$	−4.63485	+	2.67593i	−0.542469	+	0.313194i	0.203610	+	0.979052i	$0.434732\pi$
$74$	−0.0290904	−	0.0346686i	−0.00338169	−	0.00403015i
$75$	−5.58652	−	0.0171995i	−0.645076	−	0.00198603i
$76$	9.73572	+	1.71667i	1.11676	+	0.196916i
$77$	11.0746	−	3.38180i	1.26207	−	0.385392i
$78$	0.867479	−	0.312715i	0.0982226	−	0.0354080i
$79$	5.48206	+	1.99531i	0.616780	+	0.224489i	0.631467	−	0.775403i	$-0.282453\pi$
$79$	5.48206	+	1.99531i	0.616780	+	0.224489i	−0.0146875	+	0.999892i	$0.504675\pi$
$80$	−5.19155			−0.580432
$81$	1.67186	−	8.84335i	0.185763	−	0.982595i
$82$			0.711242i			0.0785435i
$83$	−4.03800	−	1.46971i	−0.443228	−	0.161322i	0.110759	−	0.993847i	$-0.464672\pi$
$83$	−4.03800	−	1.46971i	−0.443228	−	0.161322i	−0.553987	+	0.832526i	$0.686894\pi$
$84$	8.84645	+	2.07420i	0.965227	+	0.226314i
$85$	−3.78977	−	3.17999i	−0.411058	−	0.344918i
$86$	0.290615	+	0.0512433i	0.0313379	+	0.00552571i
$87$	−0.0245079	+	7.96035i	−0.00262753	+	0.853439i
$88$	1.75088	−	1.46916i	0.186644	−	0.156613i
$89$	−5.59352	−	9.68826i	−0.592912	−	1.02695i	−0.993838	−	0.110843i	$-0.964645\pi$
$89$	−5.59352	−	9.68826i	−0.592912	−	1.02695i	0.400926	−	0.916110i	$-0.368688\pi$
$90$	−0.516605	+	0.0878150i	−0.0544549	+	0.00925652i
$91$	−4.87378	−	9.57326i	−0.510911	−	1.00355i
$92$	0.737171	−	0.129983i	0.0768554	−	0.0135517i
$93$	−0.644488	+	1.75390i	−0.0668303	+	0.181871i
$94$	0.572067	+	1.57174i	0.0590042	+	0.162113i
$95$	2.27163	+	6.24126i	0.233065	+	0.640340i
$96$	2.65463	−	0.459660i	0.270937	−	0.0469138i
$97$	−14.5132	+	2.55906i	−1.47359	+	0.259833i	−0.852013	−	0.523521i	$-0.824618\pi$
$97$	−14.5132	+	2.55906i	−1.47359	+	0.259833i	−0.621575	+	0.783354i	$0.713507\pi$
$98$	−0.0965524	+	0.912754i	−0.00975327	+	0.0922021i
$99$	−8.50151	+	10.0059i	−0.854434	+	1.00563i
$100$	3.19767	+	5.53853i	0.319767	+	0.553853i
$101$	9.33893	−	7.83629i	0.929258	−	0.779740i	−0.0464262	−	0.998922i	$-0.514783\pi$
$101$	9.33893	−	7.83629i	0.929258	−	0.779740i	0.975684	+	0.219182i	$0.0703388\pi$
$102$	0.729116	+	0.423953i	0.0721932	+	0.0419776i
$103$	−8.85590	−	1.56153i	−0.872597	−	0.153862i	−0.280622	−	0.959818i	$-0.590541\pi$
$103$	−8.85590	−	1.56153i	−0.872597	−	0.153862i	−0.591976	+	0.805956i	$0.701652\pi$
$104$	−1.62432	−	1.36297i	−0.159278	−	0.133650i
$105$	1.76489	+	5.84396i	0.172235	+	0.570312i
$106$	−1.13341	−	0.412526i	−0.110086	−	0.0400680i
$107$			18.2346i			1.76280i	0.472370	+	0.881401i	$0.343399\pi$
$107$			18.2346i			1.76280i	−0.472370	+	0.881401i	$0.656601\pi$
$108$	−9.71376	+	3.43425i	−0.934707	+	0.330461i
$109$	−10.0889			−0.966342			−0.483171	−	0.875526i	$-0.660515\pi$
$109$	−10.0889			−0.966342			−0.483171	+	0.875526i	$0.660515\pi$
$110$	0.718371	+	0.261466i	0.0684940	+	0.0249298i
$111$	0.105623	−	0.588416i	0.0100253	−	0.0558500i
$112$	−3.01130	−	9.86133i	−0.284541	−	0.931809i
$113$	16.1779	+	2.85260i	1.52189	+	0.268350i	0.871175	−	0.490973i	$-0.163359\pi$
$113$	16.1779	+	2.85260i	1.52189	+	0.268350i	0.650714	+	0.759323i	$0.274470\pi$
$114$	−0.563138	−	0.982355i	−0.0527427	−	0.0920060i
$115$	0.323262	+	0.385248i	0.0301443	+	0.0359246i
$116$	7.89196	−	4.55642i	0.732750	−	0.423053i
$117$	10.5112	+	6.15526i	0.971762	+	0.569054i
$118$	−1.46686	−	0.846893i	−0.135036	−	0.0779628i
$119$	3.84218	−	9.04318i	0.352212	−	0.828987i
$120$	0.771688	+	0.925433i	0.0704452	+	0.0844801i
$121$	7.66310	−	2.78914i	0.696646	−	0.253558i
$122$	0.219897	−	0.0800359i	0.0199085	−	0.00724611i
$123$	−7.21569	+	6.01693i	−0.650617	+	0.542528i
$124$	2.10658	−	0.371447i	0.189177	−	0.0333569i
$125$	−5.47870	+	9.48939i	−0.490030	+	0.848757i
$126$	−0.466456	−	0.930354i	−0.0415552	−	0.0828826i
$127$	−10.9612	−	18.9854i	−0.972652	−	1.68468i	−0.687476	−	0.726207i	$-0.741281\pi$
$127$	−10.9612	−	18.9854i	−0.972652	−	1.68468i	−0.285175	−	0.958475i	$-0.592052\pi$
$128$	−2.63939	−	3.14550i	−0.233291	−	0.278026i
$129$	1.93866	+	3.38186i	0.170689	+	0.297756i
$130$	0.123154	−	0.698442i	0.0108013	−	0.0612574i
$131$	8.67264	+	7.27721i	0.757732	+	0.635813i	0.937535	−	0.347890i	$-0.113102\pi$
$131$	8.67264	+	7.27721i	0.757732	+	0.635813i	−0.179803	+	0.983703i	$0.557546\pi$
$132$	14.7943	+	2.65563i	1.28768	+	0.231143i
$133$	−10.5376	+	7.93515i	−0.913729	+	0.688064i
$134$			0.754639i			0.0651909i
$135$	−5.26125	−	4.49817i	−0.452816	−	0.387141i
$136$		−	1.93941i		−	0.166303i
$137$	3.91826	−	10.7653i	0.334760	−	0.919745i	−0.652095	−	0.758137i	$-0.726110\pi$
$137$	3.91826	−	10.7653i	0.334760	−	0.919745i	0.986855	−	0.161608i	$-0.0516680\pi$
$138$	−0.0655084	−	0.0553127i	−0.00557645	−	0.00470853i
$139$	−9.59685	+	11.4371i	−0.813994	+	0.970081i	−0.999922	−	0.0124827i	$-0.996027\pi$
$139$	−9.59685	+	11.4371i	−0.813994	+	0.970081i	0.185928	+	0.982563i	$0.440471\pi$
$140$	4.76782	−	5.10942i	0.402954	−	0.431825i
$141$	−11.1061	+	19.1003i	−0.935303	+	1.60853i
$142$	−0.267277	+	0.224272i	−0.0224294	+	0.0188205i
$143$	−8.88517	−	15.3896i	−0.743016	−	1.28694i
$144$	8.90970	+	7.57010i	0.742475	+	0.630842i
$145$	5.30219	+	3.06122i	0.440322	+	0.254220i
$146$	−0.121856	−	0.691081i	−0.0100849	−	0.0571943i
$147$	−10.0769	+	6.74213i	−0.831128	+	0.556081i
$148$	−0.643098	+	0.234068i	−0.0528623	+	0.0192403i
$149$	−1.04227	−	2.86360i	−0.0853857	−	0.234595i	0.889650	−	0.456643i	$-0.150948\pi$
$149$	−1.04227	−	2.86360i	−0.0853857	−	0.234595i	−0.975036	+	0.222047i	$0.928726\pi$
$150$	0.252653	−	0.687563i	0.0206290	−	0.0561393i
$151$	−0.106414	−	0.603503i	−0.00865984	−	0.0491124i	0.980172	−	0.198150i	$-0.0634934\pi$
$151$	−0.106414	−	0.603503i	−0.00865984	−	0.0491124i	−0.988831	+	0.149038i	$0.952382\pi$
$152$	−1.30187	+	2.25490i	−0.105596	+	0.182897i
$153$	1.86704	+	10.9836i	0.150941	+	0.887969i
$154$	−0.0799700	+	1.51620i	−0.00644417	+	0.122179i
$155$	0.923771	+	1.10091i	0.0741991	+	0.0884270i
$156$	0.0429309	−	13.9442i	0.00343722	−	1.11643i
$157$	1.89383	+	0.333933i	0.151144	+	0.0266507i	0.248708	−	0.968579i	$-0.419994\pi$
$157$	1.89383	+	0.333933i	0.151144	+	0.0266507i	−0.0975643	+	0.995229i	$0.531105\pi$
$158$	−0.491697	+	0.585981i	−0.0391173	+	0.0466182i
$159$	−5.40317	−	14.9885i	−0.428499	−	1.18867i
$160$	0.708696	−	1.94713i	0.0560273	−	0.153934i
$161$	−0.544274	+	0.837495i	−0.0428948	+	0.0660038i
$162$	1.01464	+	0.602585i	0.0797179	+	0.0473435i
$163$	14.3745			1.12590			0.562949	−	0.826492i	$-0.309667\pi$
$163$	14.3745			1.12590			0.562949	+	0.826492i	$0.309667\pi$
$164$	10.1067	+	3.67856i	0.789204	+	0.287247i
$165$	3.42461	+	9.49995i	0.266606	+	0.739570i
$166$	0.362176	−	0.431625i	0.0281103	−	0.0335006i
$167$	2.72667	−	15.4637i	0.210996	−	1.19662i	−0.676724	−	0.736237i	$-0.736601\pi$
$167$	2.72667	−	15.4637i	0.210996	−	1.19662i	0.887720	−	0.460383i	$-0.152288\pi$
$168$	−1.31025	+	2.00261i	−0.101088	+	0.154505i
$169$	−2.67033	+	2.24067i	−0.205410	+	0.172359i
$170$	0.561773	−	0.324340i	0.0430861	−	0.0248757i
$171$	5.20219	−	14.0236i	0.397822	−	1.07241i
$172$	2.23124	−	3.86462i	0.170130	−	0.294674i
$173$	0.759414	+	4.30685i	0.0577372	+	0.327444i	0.999972	−	0.00750984i	$-0.00239048\pi$
$173$	0.759414	+	4.30685i	0.0577372	+	0.327444i	−0.942235	+	0.334954i	$0.891279\pi$
$174$	−0.979723	−	0.360010i	−0.0742726	−	0.0272923i
$175$	−8.31424	−	1.92243i	−0.628497	−	0.145322i
$176$	−5.83361	−	16.0277i	−0.439725	−	1.20813i
$177$	−3.81738	−	22.0461i	−0.286932	−	1.65709i
$178$	1.44457	−	0.254717i	0.108275	−	0.0190918i
$179$	−12.1181	−	6.99637i	−0.905747	−	0.522933i	−0.0266868	−	0.999644i	$-0.508496\pi$
$179$	−12.1181	−	6.99637i	−0.905747	−	0.522933i	−0.879060	+	0.476710i	$0.841829\pi$
$180$	−1.42404	+	7.79514i	−0.106142	+	0.581015i
$181$	18.7936	−	10.8505i	1.39691	−	0.806509i	0.402846	−	0.915268i	$-0.368021\pi$
$181$	18.7936	−	10.8505i	1.39691	−	0.806509i	0.994068	+	0.108759i	$0.0346878\pi$
$182$	1.39812	−	0.171193i	0.103636	−	0.0126897i
$183$	2.67225	+	1.55381i	0.197539	+	0.114861i
$184$	−0.0342348	+	0.194155i	−0.00252382	+	0.0143133i
$185$	−0.352221	−	0.295548i	−0.0258958	−	0.0217292i
$186$	−0.187201	−	0.158065i	−0.0137262	−	0.0115899i
$187$	5.55904	−	15.2733i	0.406517	−	1.11690i
$188$	25.2932			1.84470
$189$	5.49254	−	12.6029i	0.399523	−	0.916723i
$190$	−0.870881			−0.0631803
$191$	−7.16981	+	19.6989i	−0.518789	+	1.42536i	0.353066	+	0.935598i	$0.385139\pi$
$191$	−7.16981	+	19.6989i	−0.518789	+	1.42536i	−0.871855	+	0.489763i	$0.837083\pi$
$192$	2.32277	−	12.9400i	0.167632	−	0.933865i
$193$	1.16810	+	0.980152i	0.0840817	+	0.0705529i	0.683860	−	0.729614i	$-0.260300\pi$
$193$	1.16810	+	0.980152i	0.0840817	+	0.0705529i	−0.599778	+	0.800166i	$0.704744\pi$
$194$	0.335547	−	1.90298i	0.0240908	−	0.136626i
$195$	8.12769	−	4.65922i	0.582036	−	0.333654i
$196$	12.4709	+	6.09279i	0.890776	+	0.435199i
$197$	21.6293	−	12.4877i	1.54102	−	0.889709i	0.542247	−	0.840219i	$-0.317574\pi$
$197$	21.6293	−	12.4877i	1.54102	−	0.889709i	0.998775	−	0.0494899i	$-0.0157596\pi$
$198$	−0.851605	−	1.49623i	−0.0605210	−	0.106332i
$199$	−0.716693	−	0.413783i	−0.0508050	−	0.0293323i	0.474382	−	0.880319i	$-0.342671\pi$
$199$	−0.716693	−	0.413783i	−0.0508050	−	0.0293323i	−0.525187	+	0.850987i	$0.676005\pi$
$200$	−1.65881	+	0.292492i	−0.117295	+	0.0206823i
$201$	−7.65597	+	6.38406i	−0.540011	+	0.450297i
$202$	0.546722	+	1.50211i	0.0384672	+	0.105688i
$203$	−2.73930	+	11.8471i	−0.192261	+	0.831505i
$204$	9.79538	−	8.16804i	0.685814	−	0.571877i
$205$	1.25478	+	7.11618i	0.0876373	+	0.497016i
$206$	0.589553	−	1.02114i	0.0410761	−	0.0711460i
$207$	0.00697361	−	1.13253i	0.000484700	−	0.0787162i
$208$	−13.7035	+	7.91174i	−0.950169	+	0.548580i
$209$	−16.7159	+	14.0263i	−1.15626	+	0.970220i
$210$	−0.799202	−	0.0446206i	−0.0551502	−	0.00307911i
$211$	1.02986	−	5.84064i	0.0708987	−	0.402086i	−0.928619	−	0.371034i	$-0.879003\pi$
$211$	1.02986	−	5.84064i	0.0708987	−	0.402086i	0.999518	−	0.0310519i	$-0.00988572\pi$
$212$	−11.7240	+	13.9721i	−0.805207	+	0.959608i
$213$	−4.53638	−	0.814294i	−0.310827	−	0.0557945i
$214$	−2.24674	−	0.817747i	−0.153584	−	0.0559000i
$215$	2.99810			0.204469
$216$	0.0250629	−	2.71347i	0.00170532	−	0.184628i
$217$	−1.55535	+	2.39327i	−0.105584	+	0.162466i
$218$	0.452447	−	1.24309i	0.0306436	−	0.0841926i
$219$	5.98029	−	7.08263i	0.404110	−	0.478600i
$220$	7.43085	−	8.85575i	0.500988	−	0.597054i
$221$	−14.8496	−	2.61839i	−0.998893	−	0.176132i
$222$	0.0677640	+	0.0394022i	0.00454802	+	0.00264451i
$223$	−9.34376	−	11.1355i	−0.625705	−	0.745686i	0.356336	−	0.934358i	$-0.384026\pi$
$223$	−9.34376	−	11.1355i	−0.625705	−	0.745686i	−0.982040	+	0.188672i	$0.939582\pi$
$224$	4.10964	+	0.216757i	0.274587	+	0.0144827i
$225$	9.11285	−	3.25340i	0.607523	−	0.216893i
$226$	−1.07699	+	1.86541i	−0.0716405	+	0.124085i
$227$	−1.15766	−	6.56541i	−0.0768366	−	0.435762i	−0.998821	−	0.0485359i	$-0.984544\pi$
$227$	−1.15766	−	6.56541i	−0.0768366	−	0.435762i	0.921985	−	0.387226i	$-0.126567\pi$
$228$	−16.8718	+	2.92143i	−1.11736	+	0.193476i
$229$	6.09035	+	16.7331i	0.402462	+	1.10575i	0.961066	+	0.276320i	$0.0891149\pi$
$229$	6.09035	+	16.7331i	0.402462	+	1.10575i	−0.558604	+	0.829434i	$0.688663\pi$
$230$	−0.0619647	+	0.0225533i	−0.00408583	+	0.00148712i
$231$	−16.0587	+	12.0154i	−1.05659	+	0.790555i
$232$	0.416778	+	2.36367i	0.0273628	+	0.155182i
$233$	−13.8987	−	8.02444i	−0.910537	−	0.525699i	−0.0299330	−	0.999552i	$-0.509529\pi$
$233$	−13.8987	−	8.02444i	−0.910537	−	0.525699i	−0.880604	+	0.473853i	$0.842863\pi$
$234$	−1.22980	+	1.01908i	−0.0803943	+	0.0666196i
$235$	8.49658	+	14.7165i	0.554256	+	0.959999i
$236$	−19.6210	+	16.4640i	−1.27722	+	1.07171i
$237$	−10.1045	−	0.0311094i	−0.656360	−	0.00202077i
$238$	0.941934	+	0.878958i	0.0610565	+	0.0569744i
$239$	−1.31201	+	1.56359i	−0.0848668	+	0.101140i	−0.806807	−	0.590815i	$-0.798806\pi$
$239$	−1.31201	+	1.56359i	−0.0848668	+	0.101140i	0.721940	+	0.691956i	$0.243251\pi$
$240$	8.45916	−	3.04942i	0.546037	−	0.196839i
$241$	3.55423	−	9.76517i	0.228948	−	0.629030i	−0.771021	−	0.636809i	$-0.780254\pi$
$241$	3.55423	−	9.76517i	0.228948	−	0.629030i	0.999970	+	0.00777897i	$0.00247615\pi$
$242$			1.06928i			0.0687359i
$243$	2.47028	+	15.3915i	0.158468	+	0.987364i
$244$		−	3.53868i		−	0.226541i
$245$	0.644249	+	9.30272i	0.0411596	+	0.594329i
$246$	−0.417771	−	1.15891i	−0.0266361	−	0.0738891i
$247$	15.5076	+	13.0125i	0.986728	+	0.827963i
$248$	−0.0978313	+	0.554829i	−0.00621230	+	0.0352317i
$249$	7.44285	+	0.0229147i	0.471671	+	0.00145216i
$250$	−0.923522	−	1.10061i	−0.0584086	−	0.0696087i
$251$	11.7343	+	20.3243i	0.740660	+	1.28286i	0.952195	+	0.305490i	$0.0988203\pi$
$251$	11.7343	+	20.3243i	0.740660	+	1.28286i	−0.211535	+	0.977370i	$0.567846\pi$
$252$	−15.6329	+	1.81653i	−0.984778	+	0.114431i
$253$	−0.826126	+	1.43089i	−0.0519381	+	0.0899594i
$254$	2.83082	−	0.499151i	0.177622	−	0.0313195i
$255$	8.04296	+	2.95547i	0.503670	+	0.185079i
$256$	−13.7592	+	5.00794i	−0.859951	+	0.312996i
$257$	4.71223	−	1.71511i	0.293941	−	0.106986i	−0.190841	−	0.981621i	$-0.561121\pi$
$257$	4.71223	−	1.71511i	0.293941	−	0.106986i	0.484781	+	0.874635i	$0.338899\pi$
$258$	−0.503632	+	0.0872059i	−0.0313547	+	0.00542920i
$259$	0.357092	−	0.840473i	0.0221886	−	0.0522245i
$260$	−9.28790	−	5.36237i	−0.576011	−	0.332560i
$261$	−4.63584	−	12.9851i	−0.286951	−	0.803756i
$262$	−1.28558	+	0.742232i	−0.0794236	+	0.0458552i
$263$	3.92830	+	4.68156i	0.242229	+	0.288678i	0.873438	−	0.486935i	$-0.161885\pi$
$263$	3.92830	+	4.68156i	0.242229	+	0.288678i	−0.631209	+	0.775613i	$0.717441\pi$
$264$	−1.98994	+	3.42230i	−0.122472	+	0.210628i
$265$	−12.0678	−	2.12789i	−0.741321	−	0.130715i
$266$	−0.505146	−	1.65424i	−0.0309725	−	0.101428i
$267$	14.8049	+	12.5006i	0.906042	+	0.765026i
$268$	10.7234	+	3.90301i	0.655038	+	0.238414i
$269$	4.75791			0.290095			0.145048	−	0.989425i	$-0.453666\pi$
$269$	4.75791			0.290095			0.145048	+	0.989425i	$0.453666\pi$
$270$	0.790181	−	0.446532i	0.0480889	−	0.0271750i
$271$			11.7607i			0.714413i	0.934025	+	0.357206i	$0.116271\pi$
$271$			11.7607i			0.714413i	−0.934025	+	0.357206i	$0.883729\pi$
$272$	−13.6000	−	4.95000i	−0.824622	−	0.300138i
$273$	13.5646	+	12.7360i	0.820965	+	0.770818i
$274$	1.15072	+	0.965565i	0.0695173	+	0.0583319i
$275$	−13.9019	−	2.45128i	−0.838317	−	0.147818i
$276$	−1.12480	+	0.644797i	−0.0677053	+	0.0388122i
$277$	−3.40027	+	2.85316i	−0.204302	+	0.171430i	−0.739198	−	0.673488i	$-0.764795\pi$
$277$	−3.40027	+	2.85316i	−0.204302	+	0.171430i	0.534896	+	0.844918i	$0.320351\pi$
$278$	−0.978821	−	1.69537i	−0.0587058	−	0.101681i
$279$	0.0199282	−	3.23638i	0.00119307	−	0.193757i
$280$	0.835069	+	1.64027i	0.0499049	+	0.0980250i
$281$	8.77039	−	1.54646i	0.523198	−	0.0922539i	0.0941892	−	0.995554i	$-0.469974\pi$
$281$	8.77039	−	1.54646i	0.523198	−	0.0922539i	0.429009	+	0.903300i	$0.358863\pi$
$282$	−1.85535	−	2.22499i	−0.110484	−	0.132496i
$283$	−8.13265	−	22.3443i	−0.483436	−	1.32823i	−0.906529	−	0.422143i	$-0.861278\pi$
$283$	−8.13265	−	22.3443i	−0.483436	−	1.32823i	0.423093	−	0.906086i	$-0.360944\pi$
$284$	1.80454	+	4.95794i	0.107080	+	0.294200i
$285$	−7.36744	−	8.83527i	−0.436409	−	0.523356i
$286$	2.29467	−	0.404612i	0.135686	−	0.0239252i
$287$	−12.7894	+	6.51111i	−0.754932	+	0.384339i
$288$	−4.05548	+	2.30826i	−0.238972	+	0.136015i
$289$	1.60419	+	2.77853i	0.0943639	+	0.163443i
$290$	−0.614965	+	0.516017i	−0.0361120	+	0.0303016i
$291$	22.1448	−	12.6945i	1.29815	−	0.744167i
$292$	−10.4505	−	1.84271i	−0.611570	−	0.107836i
$293$	−20.3420	−	17.0689i	−1.18839	−	0.997178i	−0.999886	−	0.0151056i	$-0.995192\pi$
$293$	−20.3420	−	17.0689i	−1.18839	−	0.997178i	−0.188505	−	0.982072i	$-0.560364\pi$
$294$	−0.378812	−	1.54397i	−0.0220928	−	0.0900459i
$295$	−16.1705	−	5.88558i	−0.941482	−	0.342671i
$296$		−	0.180249i		−	0.0104767i
$297$	7.97515	−	21.2974i	0.462765	−	1.23580i
$298$	0.399576			0.0231468
$299$	1.44038	+	0.524256i	0.0832995	+	0.0303185i
$300$	−8.46355	−	7.14628i	−0.488643	−	0.412591i
$301$	1.73902	+	5.69488i	0.100235	+	0.328248i
$302$	0.0791319	+	0.0139531i	0.00455353	+	0.000802910i
$303$	−10.6141	+	18.2541i	−0.609761	+	1.04867i
$304$	12.4896	+	14.8846i	0.716329	+	0.853688i
$305$	2.05893	−	1.18873i	0.117894	−	0.0680662i
$306$	−1.43705	−	0.262525i	−0.0821508	−	0.0150075i
$307$	27.6153	+	15.9437i	1.57609	+	0.909956i	0.995397	+	0.0958335i	$0.0305517\pi$
$307$	27.6153	+	15.9437i	1.57609	+	0.909956i	0.580693	+	0.814123i	$0.302782\pi$
$308$	21.1317	+	8.97821i	1.20409	+	0.511581i
$309$	15.3471	−	2.65742i	0.873067	−	0.151175i
$310$	−0.177074	+	0.0644497i	−0.0100571	+	0.00366050i
$311$	5.67000	−	2.06371i	0.321516	−	0.117022i	−0.176220	−	0.984351i	$-0.556387\pi$
$311$	5.67000	−	2.06371i	0.321516	−	0.117022i	0.497736	+	0.867328i	$0.334165\pi$
$312$	3.44727	+	1.26673i	0.195163	+	0.0717147i
$313$	4.63763	−	0.817739i	0.262134	−	0.0462213i	−0.0410364	−	0.999158i	$-0.513066\pi$
$313$	4.63763	−	0.817739i	0.262134	−	0.0462213i	0.303170	+	0.952936i	$0.401955\pi$
$314$	−0.126076	+	0.218369i	−0.00711485	+	0.0123233i
$315$	−6.30837	−	8.48555i	−0.355436	−	0.478107i
$316$	5.78373	+	10.0177i	0.325360	+	0.563541i
$317$	−9.57584	−	11.4120i	−0.537833	−	0.640964i	0.426867	−	0.904314i	$-0.359617\pi$
$317$	−9.57584	−	11.4120i	−0.537833	−	0.640964i	−0.964700	+	0.263350i	$0.915173\pi$
$318$	2.08909	+	0.00643180i	0.117151	+	0.000360678i
$319$	−3.49288	+	19.8091i	−0.195564	+	1.10910i
$320$	−7.74578	−	6.49948i	−0.433002	−	0.363332i
$321$	−10.7107	−	29.7116i	−0.597811	−	1.65834i
$322$	−0.0787820	−	0.104620i	−0.00439035	−	0.00583025i
$323$			18.5159i			1.03025i
$324$	13.8105	−	11.3015i	0.767249	−	0.627861i
$325$			13.0960i			0.726436i
$326$	−0.644639	+	1.77113i	−0.0357032	+	0.0980938i
$327$	16.4390	−	5.92605i	0.909078	−	0.327711i
$328$	−1.82085	+	2.17000i	−0.100540	+	0.119818i
$329$	−23.0256	+	24.6754i	−1.26944	+	1.36040i
$330$	−1.32410	−	0.00407658i	−0.0728894	−	0.000224408i
$331$	8.22997	−	6.90576i	0.452360	−	0.379575i	−0.387951	−	0.921680i	$-0.626817\pi$
$331$	8.22997	−	6.90576i	0.452360	−	0.379575i	0.840311	+	0.542105i	$0.182373\pi$
$332$	−4.26021	−	7.37890i	−0.233809	−	0.404970i
$333$	0.173523	+	1.02081i	0.00950899	+	0.0559402i
$334$	1.78306	+	1.02945i	0.0975646	+	0.0563290i
$335$	1.33134	+	7.55039i	0.0727388	+	0.412522i
$336$	10.6990	+	14.2994i	0.583680	+	0.780095i
$337$	−8.99836	+	3.27514i	−0.490172	+	0.178408i	−0.575268	−	0.817965i	$-0.695102\pi$
$337$	−8.99836	+	3.27514i	−0.490172	+	0.178408i	0.0850964	+	0.996373i	$0.472880\pi$
$338$	−0.156327	−	0.429506i	−0.00850308	−	0.0233620i
$339$	−28.0360	+	4.85455i	−1.52271	+	0.263663i
$340$	−1.70337	−	9.66030i	−0.0923782	−	0.523903i
$341$	−2.36078	+	4.08900i	−0.127844	+	0.221432i
$342$	1.49460	+	1.26988i	0.0808188	+	0.0686674i
$343$	−17.2968	+	6.61969i	−0.933940	+	0.357430i
$344$	0.755482	+	0.900348i	0.0407328	+	0.0485435i
$345$	−0.753014	−	0.437850i	−0.0405409	−	0.0235730i
$346$	−0.564718	−	0.0995751i	−0.0303594	−	0.00535319i
$347$	14.4006	−	17.1620i	0.773065	−	0.921303i	−0.225533	−	0.974235i	$-0.572412\pi$
$347$	14.4006	−	17.1620i	0.773065	−	0.921303i	0.998598	+	0.0529329i	$0.0168569\pi$
$348$	−10.1829	+	12.0599i	−0.545860	+	0.646478i
$349$	4.98766	−	13.7035i	0.266983	−	0.733531i	−0.731670	−	0.681659i	$-0.761259\pi$
$349$	4.98766	−	13.7035i	0.266983	−	0.733531i	0.998654	−	0.0518722i	$-0.0165189\pi$
$350$	0.609729	−	0.938212i	0.0325914	−	0.0501496i
$351$	−20.7426	−	3.85534i	−1.10716	−	0.205783i
$352$	6.80766			0.362849
$353$	7.53944	+	2.74413i	0.401284	+	0.146055i	0.534775	−	0.844995i	$-0.320396\pi$
$353$	7.53944	+	2.74413i	0.401284	+	0.146055i	−0.133491	+	0.991050i	$0.542619\pi$
$354$	2.88757	+	0.518328i	0.153473	+	0.0275488i
$355$	−2.27852	+	2.71544i	−0.120931	+	0.144120i
$356$	3.85182	−	21.8447i	0.204146	−	1.15777i
$357$	−0.948680	+	16.9919i	−0.0502095	+	0.899306i
$358$	1.40549	−	1.17935i	0.0742827	−	0.0623305i
$359$	−1.26586	+	0.730844i	−0.0668095	+	0.0385725i	−0.533033	−	0.846095i	$-0.678948\pi$
$359$	−1.26586	+	0.730844i	−0.0668095	+	0.0385725i	0.466223	+	0.884667i	$0.345614\pi$
$360$	−1.80098	−	1.05464i	−0.0949200	−	0.0555842i
$361$	2.92916	−	5.07346i	0.154167	−	0.267024i
$362$	0.494107	+	2.80222i	0.0259697	+	0.147281i
$363$	−10.8481	+	9.04583i	−0.569375	+	0.474783i
$364$	4.79847	−	20.7528i	0.251508	−	1.08774i
$365$	−2.43842	−	6.69949i	−0.127633	−	0.350668i
$366$	−0.311291	+	0.259575i	−0.0162714	+	0.0135682i
$367$	25.7879	−	4.54711i	1.34612	−	0.237357i	0.546296	−	0.837592i	$-0.316037\pi$
$367$	25.7879	−	4.54711i	1.34612	−	0.237357i	0.799824	+	0.600235i	$0.204926\pi$
$368$	1.27413	+	0.735617i	0.0664184	+	0.0383467i
$369$	8.22310	−	14.0424i	0.428077	−	0.731019i
$370$	0.0522112	−	0.0301442i	0.00271433	−	0.00156712i
$371$	−2.95791	−	24.1571i	−0.153567	−	1.25417i
$372$	−3.21431	+	1.84261i	−0.166654	+	0.0955349i
$373$	−2.15588	+	12.2266i	−0.111627	+	0.633069i	0.876738	+	0.480969i	$0.159715\pi$
$373$	−2.15588	+	12.2266i	−0.111627	+	0.633069i	−0.988365	+	0.152101i	$0.951396\pi$
$374$	1.63258	+	1.36990i	0.0844186	+	0.0708356i
$375$	3.35316	−	18.6802i	0.173156	−	0.964642i
$376$	−2.27843	+	6.25995i	−0.117501	+	0.322832i
$377$	18.6608			0.961078
$378$	1.30652	+	1.24194i	0.0672003	+	0.0638786i
$379$	7.53240			0.386913			0.193457	−	0.981109i	$-0.438030\pi$
$379$	7.53240			0.386913			0.193457	+	0.981109i	$0.438030\pi$
$380$	−4.50421	+	12.3752i	−0.231061	+	0.634835i
$381$	29.0120	+	24.4966i	1.48633	+	1.25500i
$382$	−2.10563	−	1.76683i	−0.107733	−	0.0903991i
$383$	−0.508365	+	2.88308i	−0.0259762	+	0.147319i	−0.995037	−	0.0995025i	$-0.968275\pi$
$383$	−0.508365	+	2.88308i	−0.0259762	+	0.147319i	0.969061	+	0.246821i	$0.0793860\pi$
$384$	6.14827	+	3.57499i	0.313752	+	0.182435i
$385$	1.87477	+	15.3112i	0.0955472	+	0.780329i
$386$	−0.173152	+	0.0999696i	−0.00881323	+	0.00508832i
$387$	−5.14532	−	4.37171i	−0.261551	−	0.222226i
$388$	−25.3059	−	14.6104i	−1.28471	−	0.741729i
$389$	−24.4465	+	4.31058i	−1.23949	+	0.218555i	−0.754696	−	0.656075i	$-0.772216\pi$
$389$	−24.4465	+	4.31058i	−1.23949	+	0.218555i	−0.484791	+	0.874630i	$0.661104\pi$
$390$	0.209584	+	1.21039i	0.0106127	+	0.0612904i
$391$	0.479508	+	1.31744i	0.0242497	+	0.0666256i
$392$	−2.63132	+	2.53764i	−0.132902	+	0.128170i
$393$	−18.4058	−	6.76341i	−0.928450	−	0.341169i
$394$	0.568661	+	3.22504i	0.0286487	+	0.162475i
$395$	−3.88578	+	6.73037i	−0.195515	+	0.338642i
$396$	−25.6659	+	4.36281i	−1.28976	+	0.219240i
$397$	18.3498	−	10.5942i	0.920948	−	0.531710i	0.0370106	−	0.999315i	$-0.488216\pi$
$397$	18.3498	−	10.5942i	0.920948	−	0.531710i	0.883937	+	0.467605i	$0.154883\pi$
$398$	0.0831244	−	0.0697497i	0.00416665	−	0.00349624i
$399$	12.5092	−	19.1192i	0.626242	−	0.957159i
$400$	−2.18273	+	12.3789i	−0.109136	+	0.618943i
$401$	−0.873706	+	1.04124i	−0.0436308	+	0.0519972i	−0.787419	−	0.616419i	$-0.788583\pi$
$401$	−0.873706	+	1.04124i	−0.0436308	+	0.0519972i	0.743788	+	0.668416i	$0.233027\pi$
$402$	−0.443262	−	1.22962i	−0.0221079	−	0.0613278i
$403$	4.11612	+	1.49815i	0.205039	+	0.0746279i
$404$	24.1726			1.20263
$405$	11.2149	+	4.23901i	0.557272	+	0.210638i
$406$	−1.33688	−	0.868815i	−0.0663481	−	0.0431186i
$407$	0.516657	−	1.41950i	0.0256097	−	0.0703622i
$408$	1.13917	+	3.16009i	0.0563975	+	0.156448i
$409$	17.0261	−	20.2910i	0.841889	−	1.00332i	−0.157985	−	0.987441i	$-0.550500\pi$
$409$	17.0261	−	20.2910i	0.841889	−	1.00332i	0.999874	−	0.0158823i	$-0.00505571\pi$
$410$	−0.933081	−	0.164527i	−0.0460816	−	0.00812543i
$411$	−0.0610907	+	19.8427i	−0.00301338	+	0.978768i
$412$	−11.4612	−	13.6589i	−0.564651	−	0.672925i
$413$	1.80012	−	34.1297i	0.0885782	−	1.67941i
$414$	0.139230	+	0.0516486i	0.00684278	+	0.00253839i
$415$	2.86221	−	4.95749i	0.140500	−	0.243354i
$416$	−1.09669	−	6.21964i	−0.0537696	−	0.304943i
$417$	8.91928	−	24.2727i	0.436779	−	1.18864i
$418$	−0.978588	−	2.68865i	−0.0478643	−	0.131506i
$419$	16.0247	−	5.83250i	0.782856	−	0.284936i	0.0804931	−	0.996755i	$-0.474351\pi$
$419$	16.0247	−	5.83250i	0.782856	−	0.284936i	0.702363	+	0.711819i	$0.252128\pi$
$420$	−4.76755	+	11.1259i	−0.232632	+	0.542888i
$421$	−3.15843	−	17.9124i	−0.153933	−	0.872995i	−0.959755	−	0.280838i	$-0.909388\pi$
$421$	−3.15843	−	17.9124i	−0.153933	−	0.872995i	0.805823	−	0.592157i	$-0.201724\pi$
$422$	0.673460	+	0.388822i	0.0327835	+	0.0189276i
$423$	6.87724	−	37.6458i	0.334383	−	1.83040i
$424$	−2.40192	−	4.16025i	−0.116648	−	0.202040i
$425$	−9.17582	+	7.69943i	−0.445093	+	0.373477i
$426$	0.303770	−	0.522425i	0.0147177	−	0.0253116i
$427$	3.45225	+	3.22143i	0.167066	+	0.155896i
$428$	−23.2404	+	27.6968i	−1.12337	+	1.33878i
$429$	23.5172	+	19.8570i	1.13542	+	0.958703i
$430$	−0.134453	+	0.369406i	−0.00648389	+	0.0178143i
$431$		−	3.52787i		−	0.169932i	−0.996384	−	0.0849658i	$-0.972922\pi$
$431$		−	3.52787i		−	0.169932i	0.996384	−	0.0849658i	$-0.0270781\pi$
$432$	−18.9641	−	7.10141i	−0.912412	−	0.341667i
$433$			19.5602i			0.940001i	0.882666	+	0.470001i	$0.155746\pi$
$433$			19.5602i			0.940001i	−0.882666	+	0.470001i	$0.844254\pi$
$434$	−0.225132	−	0.298969i	−0.0108067	−	0.0143510i
$435$	−10.4375	−	1.87357i	−0.500442	−	0.0898309i
$436$	−15.3242	−	12.8586i	−0.733897	−	0.615813i
$437$	0.326845	−	1.85363i	0.0156351	−	0.0886712i
$438$	0.604483	+	1.05448i	0.0288833	+	0.0503850i
$439$	−5.11723	−	6.09848i	−0.244232	−	0.291064i	0.629977	−	0.776613i	$-0.283064\pi$
$439$	−5.11723	−	6.09848i	−0.244232	−	0.291064i	−0.874209	+	0.485549i	$0.838620\pi$
$440$	1.52238	+	2.63683i	0.0725765	+	0.125706i
$441$	12.4592	−	16.9047i	0.593295	−	0.804985i
$442$	0.988566	−	1.71225i	0.0470213	−	0.0814433i
$443$	27.4654	−	4.84288i	1.30492	−	0.230092i	0.522390	−	0.852707i	$-0.325041\pi$
$443$	27.4654	−	4.84288i	1.30492	−	0.230092i	0.782529	+	0.622614i	$0.213929\pi$
$444$	0.910383	−	0.759138i	0.0432049	−	0.0360271i
$445$	14.0040	−	5.09703i	0.663852	−	0.241622i
$446$	1.79107	−	0.651896i	0.0848095	−	0.0308681i
$447$	3.38031	+	4.05378i	0.159883	+	0.191737i
$448$	7.85290	−	18.4831i	0.371015	−	0.873242i
$449$	−15.1431	−	8.74287i	−0.714647	−	0.412602i	0.0981322	−	0.995173i	$-0.468713\pi$
$449$	−15.1431	−	8.74287i	−0.714647	−	0.412602i	−0.812779	+	0.582572i	$0.802047\pi$
$450$	−0.00781227	+	1.26873i	−0.000368274	+	0.0598084i
$451$	−20.5596	+	11.8701i	−0.968116	+	0.558942i
$452$	20.9372	+	24.9520i	0.984803	+	1.17364i
$453$	0.527879	+	0.920849i	0.0248019	+	0.0432653i
$454$	0.860863	+	0.151793i	0.0404023	+	0.00712402i
$455$	13.6866	−	4.17941i	0.641639	−	0.195934i
$456$	0.796790	−	4.43886i	0.0373131	−	0.207869i
$457$	−25.2787	−	9.20069i	−1.18249	−	0.430390i	−0.325407	−	0.945574i	$-0.605501\pi$
$457$	−25.2787	−	9.20069i	−1.18249	−	0.430390i	−0.857080	+	0.515184i	$0.827724\pi$
$458$	−2.33487			−0.109101
$459$	−9.49373	−	16.8001i	−0.443130	−	0.784161i
$460$			0.997166i			0.0464931i
$461$	−17.3925	−	6.33036i	−0.810050	−	0.294834i	−0.0964058	−	0.995342i	$-0.530735\pi$
$461$	−17.3925	−	6.33036i	−0.810050	−	0.294834i	−0.713645	+	0.700508i	$0.752957\pi$
$462$	−0.760288	−	2.51749i	−0.0353718	−	0.117124i
$463$	−11.6402	−	9.76728i	−0.540966	−	0.453924i	0.330902	−	0.943665i	$-0.392647\pi$
$463$	−11.6402	−	9.76728i	−0.540966	−	0.453924i	−0.871868	+	0.489741i	$0.837091\pi$
$464$	17.6389	+	3.11021i	0.818864	+	0.144388i
$465$	−2.15186	−	1.25122i	−0.0997900	−	0.0580242i
$466$	1.61202	−	1.35265i	0.0746755	−	0.0626602i
$467$	12.8706	+	22.2926i	0.595581	+	1.03158i	0.993465	+	0.114140i	$0.0364114\pi$
$467$	12.8706	+	22.2926i	0.595581	+	1.03158i	−0.397884	+	0.917436i	$0.630255\pi$
$468$	8.12065	+	22.7461i	0.375377	+	1.05144i
$469$	−13.5697	+	6.90840i	−0.626592	+	0.319000i
$470$	−2.19431	+	0.386916i	−0.101216	+	0.0178471i
$471$	−3.28197	+	0.568287i	−0.151225	+	0.0261853i
$472$	−2.30728	−	6.33919i	−0.106201	−	0.291785i
$473$	3.36889	+	9.25595i	0.154902	+	0.425589i
$474$	0.456981	−	1.24362i	0.0209898	−	0.0571213i
$475$	15.8369	−	2.79247i	0.726647	−	0.128128i
$476$	17.3617	−	8.83891i	0.795772	−	0.405131i
$477$	17.6080	+	21.2487i	0.806213	+	0.972911i
$478$	−0.133817	−	0.231778i	−0.00612065	−	0.0106013i
$479$	1.75513	−	1.47273i	0.0801939	−	0.0672907i	−0.601810	−	0.798640i	$-0.705553\pi$
$479$	1.75513	−	1.47273i	0.0801939	−	0.0672907i	0.682003	+	0.731349i	$0.261109\pi$
$480$	−0.0110495	+	3.58895i	−0.000504337	+	0.163812i
$481$	−1.38012	−	0.243353i	−0.0629282	−	0.0110959i
$482$	1.04381	+	0.875858i	0.0475441	+	0.0398942i
$483$	0.394917	−	1.68432i	0.0179693	−	0.0766392i
$484$	15.1945	+	5.53033i	0.690657	+	0.251379i
$485$		−	19.6319i		−	0.891436i
$486$	−2.00722	−	0.385875i	−0.0910493	−	0.0175037i
$487$	35.0917			1.59016			0.795078	−	0.606507i	$-0.207430\pi$
$487$	35.0917			1.59016			0.795078	+	0.606507i	$0.207430\pi$
$488$	0.875806	+	0.318767i	0.0396459	+	0.0144299i
$489$	−23.4220	+	8.44333i	−1.05918	+	0.381820i
$490$	−1.17511	−	0.337810i	−0.0530861	−	0.0152607i
$491$	22.3682	+	3.94412i	1.00946	+	0.177996i	0.653840	−	0.756633i	$-0.273157\pi$
$491$	22.3682	+	3.94412i	1.00946	+	0.177996i	0.355624	+	0.934629i	$0.384268\pi$
$492$	−18.6288	−	0.0573534i	−0.839850	−	0.00258569i
$493$	10.9711	+	13.0748i	0.494112	+	0.588860i
$494$	−2.29877	+	1.32719i	−0.103426	+	0.0597132i
$495$	−11.1602	−	13.4678i	−0.501614	−	0.605331i
$496$	3.64102	+	2.10214i	0.163487	+	0.0943890i
$497$	−6.47960	−	2.75299i	−0.290650	−	0.123488i
$498$	−0.336605	+	0.916031i	−0.0150836	+	0.0410483i
$499$	−18.3536	+	6.68017i	−0.821621	+	0.299046i	−0.718415	−	0.695615i	$-0.755132\pi$
$499$	−18.3536	+	6.68017i	−0.821621	+	0.299046i	−0.103206	+	0.994660i	$0.532910\pi$
$500$	−20.4161	+	7.43087i	−0.913038	+	0.332319i
$501$	4.64025	+	26.7984i	0.207311	+	1.19726i
$502$	−3.03046	+	0.534353i	−0.135256	+	0.0238493i
$503$	6.03294	−	10.4494i	0.268995	−	0.465914i	−0.699607	−	0.714528i	$-0.746642\pi$
$503$	6.03294	−	10.4494i	0.268995	−	0.465914i	0.968603	+	0.248614i	$0.0799750\pi$
$504$	0.958639	−	4.03269i	0.0427012	−	0.179630i
$505$	8.12014	+	14.0645i	0.361342	+	0.625862i
$506$	−0.139257	−	0.165960i	−0.00619071	−	0.00737780i
$507$	3.03493	−	5.21948i	0.134786	−	0.231805i
$508$	7.54814	−	42.8076i	0.334895	−	1.89928i
$509$	−25.0698	−	21.0360i	−1.11120	−	0.932406i	−0.113072	−	0.993587i	$-0.536069\pi$
$509$	−25.0698	−	21.0360i	−1.11120	−	0.932406i	−0.998127	+	0.0611805i	$0.980513\pi$
$510$	−0.724848	+	0.858459i	−0.0320968	+	0.0380132i
$511$	11.3113	−	8.51774i	0.500383	−	0.376803i
$512$		−	10.1322i		−	0.447786i
$513$	−0.239280	+	25.9059i	−0.0105645	+	1.14378i
$514$			0.657525i			0.0290022i
$515$	4.09716	−	11.2569i	0.180543	−	0.496037i
$516$	−1.36560	+	7.60764i	−0.0601170	+	0.334908i
$517$	−35.8865	+	42.7678i	−1.57829	+	1.88093i
$518$	0.0875434	+	0.0816904i	0.00384644	+	0.00358927i
$519$	−3.76717	−	6.57156i	−0.165360	−	0.288460i
$520$	2.16382	−	1.81566i	0.0948900	−	0.0796221i
$521$	0.373097	+	0.646223i	0.0163457	+	0.0283115i	0.874083	−	0.485777i	$-0.161463\pi$
$521$	0.373097	+	0.646223i	0.0163457	+	0.0283115i	−0.857737	+	0.514089i	$0.828130\pi$
$522$	1.80783	+	0.0111319i	0.0791268	+	0.000487228i
$523$	−0.0341810	−	0.0197344i	−0.00149463	−	0.000862925i	0.499252	−	0.866457i	$-0.333608\pi$
$523$	−0.0341810	−	0.0197344i	−0.00149463	−	0.000862925i	−0.500747	+	0.865594i	$0.666941\pi$
$524$	3.89806	+	22.1070i	0.170287	+	0.965748i
$525$	14.6765	−	1.75122i	0.640536	−	0.0764293i
$526$	−0.753000	+	0.274070i	−0.0328324	+	0.0119500i
$527$	1.37027	+	3.76478i	0.0596898	+	0.163996i
$528$	18.9198	+	22.6892i	0.823377	+	0.987420i
$529$	3.96916	+	22.5102i	0.172572	+	0.978705i
$530$	0.803378	−	1.39149i	0.0348965	−	0.0604426i
$531$	19.1696	+	33.6799i	0.831889	+	1.46159i
$532$	−26.1193	−	1.37763i	−1.13242	−	0.0597277i
$533$	14.1569	+	16.8715i	0.613204	+	0.730788i
$534$	−2.20418	+	1.26355i	−0.0953843	+	0.0546793i
$535$	−23.9220	−	4.21809i	−1.03424	−	0.182364i
$536$	−1.93195	+	2.30241i	−0.0834476	+	0.0994490i
$537$	23.8549	+	4.28202i	1.02941	+	0.184783i
$538$	−0.213373	+	0.586239i	−0.00919918	+	0.0252745i
$539$	−27.9961	+	12.4422i	−1.20588	+	0.535924i
$540$	−2.25838	−	13.5379i	−0.0971854	−	0.582580i
$541$	−44.3075			−1.90493			−0.952465	−	0.304648i	$-0.901461\pi$
$541$	−44.3075			−1.90493			−0.952465	+	0.304648i	$0.901461\pi$
$542$	−1.44908	−	0.527421i	−0.0622432	−	0.0226547i
$543$	−24.2491	+	28.7189i	−1.04063	+	1.23244i
$544$	3.71307	−	4.42506i	0.159196	−	0.189723i
$545$	2.33381	−	13.2357i	0.0999693	−	0.566954i
$546$	−2.17756	+	1.10018i	−0.0931911	+	0.0470832i
$547$	1.85944	−	1.56025i	0.0795038	−	0.0667116i	−0.602170	−	0.798368i	$-0.705697\pi$
$547$	1.85944	−	1.56025i	0.0795038	−	0.0667116i	0.681673	+	0.731657i	$0.261252\pi$
$548$	19.6722	−	11.3578i	0.840355	−	0.485179i
$549$	−5.26688	−	0.962169i	−0.224785	−	0.0410644i
$550$	0.925476	−	1.60297i	0.0394624	−	0.0683509i
$551$	−3.97905	−	22.5663i	−0.169513	−	0.961358i
$552$	−0.0582608	−	0.336468i	−0.00247974	−	0.0143210i
$553$	−15.0382	−	3.47716i	−0.639491	−	0.147864i
$554$	−0.199059	−	0.546911i	−0.00845722	−	0.0232360i
$555$	0.747513	+	0.274682i	0.0317302	+	0.0116596i
$556$	−29.1537	+	5.14058i	−1.23639	+	0.218009i
$557$	−0.292925	−	0.169120i	−0.0124116	−	0.00716586i	0.493781	−	0.869586i	$-0.335614\pi$
$557$	−0.292925	−	0.169120i	−0.0124116	−	0.00716586i	−0.506193	+	0.862420i	$0.668948\pi$
$558$	0.397872	+	0.147594i	0.0168432	+	0.00624816i
$559$	7.91374	−	4.56900i	0.334715	−	0.193248i
$560$	13.6337	−	1.66938i	0.576130	−	0.0705440i
$561$	−0.0866724	+	28.1518i	−0.00365931	+	1.18857i
$562$	−0.202773	+	1.14998i	−0.00855346	+	0.0485091i
$563$	12.3087	+	10.3282i	0.518748	+	0.435282i	0.864195	−	0.503157i	$-0.167828\pi$
$563$	12.3087	+	10.3282i	0.518748	+	0.435282i	−0.345447	+	0.938438i	$0.612273\pi$
$564$	−41.2130	+	14.8568i	−1.73538	+	0.625584i
$565$	−7.48467	+	20.5640i	−0.314883	+	0.865133i
$566$	3.11783			0.131052
$567$	−1.54691	+	23.7615i	−0.0649639	+	0.997888i
$568$	−1.38962			−0.0583072
$569$	8.08739	−	22.2199i	0.339041	−	0.931507i	−0.646627	−	0.762807i	$-0.723821\pi$
$569$	8.08739	−	22.2199i	0.339041	−	0.931507i	0.985667	−	0.168700i	$-0.0539570\pi$
$570$	1.41902	−	0.511540i	0.0594363	−	0.0214261i
$571$	−0.278581	−	0.233758i	−0.0116583	−	0.00978245i	0.636940	−	0.770913i	$-0.280200\pi$
$571$	−0.278581	−	0.233758i	−0.0116583	−	0.00978245i	−0.648598	+	0.761131i	$0.724644\pi$
$572$	6.11852	−	34.6999i	0.255828	−	1.45087i
$573$	0.111786	−	36.3090i	0.00466995	−	1.51683i
$574$	−0.228704	−	1.86782i	−0.00954594	−	0.0779613i
$575$	1.05451	−	0.608820i	0.0439760	−	0.0253896i
$576$	3.81598	+	22.4490i	0.158999	+	0.935373i
$577$	7.66829	+	4.42729i	0.319235	+	0.184310i	0.651052	−	0.759034i	$-0.274328\pi$
$577$	7.66829	+	4.42729i	0.319235	+	0.184310i	−0.331817	+	0.943344i	$0.607661\pi$
$578$	−0.414294	+	0.0730512i	−0.0172324	+	0.00303853i
$579$	−2.47904	−	0.910950i	−0.103025	−	0.0378578i
$580$	4.15199	+	11.4075i	0.172402	+	0.473671i
$581$	11.0769	+	2.56122i	0.459549	+	0.106257i
$582$	0.571033	+	3.29783i	0.0236701	+	0.136700i
$583$	−6.99097	−	39.6478i	−0.289536	−	1.64204i
$584$	1.39745	−	2.42046i	0.0578270	−	0.100159i
$585$	−10.5066	+	12.3658i	−0.434395	+	0.511265i
$586$	3.01538	−	1.74093i	0.124564	−	0.0719171i
$587$	−22.0136	+	18.4716i	−0.908598	+	0.762405i	−0.971852	−	0.235593i	$-0.924297\pi$
$587$	−22.0136	+	18.4716i	−0.908598	+	0.762405i	0.0632534	+	0.997997i	$0.479852\pi$
$588$	−23.8990	−	2.60249i	−0.985577	−	0.107325i
$589$	0.934012	−	5.29705i	0.0384853	−	0.218261i
$590$	1.45036	−	1.72848i	0.0597105	−	0.0711602i
$591$	−27.9079	+	33.0522i	−1.14798	+	1.35959i
$592$	−1.26399	−	0.460053i	−0.0519495	−	0.0189081i
$593$	7.83158			0.321605			0.160802	−	0.986987i	$-0.448592\pi$
$593$	7.83158			0.321605			0.160802	+	0.986987i	$0.448592\pi$
$594$	2.26647	+	1.93775i	0.0929945	+	0.0795068i
$595$	10.9750	+	7.13247i	0.449931	+	0.292403i
$596$	2.06661	−	5.67797i	0.0846517	−	0.232579i
$597$	1.41084	+	0.253250i	0.0577417	+	0.0103648i
$598$	−0.129191	+	0.153964i	−0.00528300	+	0.00629604i
$599$	−25.0073	−	4.40946i	−1.02177	−	0.180166i	−0.362430	−	0.932011i	$-0.618053\pi$
$599$	−25.0073	−	4.40946i	−1.02177	−	0.180166i	−0.659339	+	0.751845i	$0.729164\pi$
$600$	2.53107	−	1.45095i	0.103331	−	0.0592346i
$601$	−28.8206	−	34.3470i	−1.17562	−	1.40104i	−0.897796	−	0.440411i	$-0.854833\pi$
$601$	−28.8206	−	34.3470i	−1.17562	−	1.40104i	−0.277819	−	0.960633i	$-0.589612\pi$
$602$	−0.779674	−	0.0411228i	−0.0317771	−	0.00167604i
$603$	8.72485	−	14.8992i	0.355303	−	0.606744i
$604$	0.607545	−	1.05230i	0.0247207	−	0.0428174i
$605$	1.88643	+	10.6985i	0.0766941	+	0.434954i
$606$	−1.77315	−	2.12642i	−0.0720292	−	0.0863797i
$607$	3.35939	+	9.22986i	0.136354	+	0.374628i	0.989011	−	0.147842i	$-0.0472327\pi$
$607$	3.35939	+	9.22986i	0.136354	+	0.374628i	−0.852657	+	0.522470i	$0.825010\pi$
$608$	−7.28751	+	2.65244i	−0.295548	+	0.107571i
$609$	−2.49534	−	20.9129i	−0.101116	−	0.847432i
$610$	0.0541320	+	0.306998i	0.00219174	+	0.0124300i
$611$	44.8549	+	25.8970i	1.81464	+	1.04768i
$612$	−11.1629	+	19.0627i	−0.451235	+	0.770565i
$613$	−16.3106	−	28.2507i	−0.658778	−	1.14104i	−0.980932	−	0.194350i	$-0.937740\pi$
$613$	−16.3106	−	28.2507i	−0.658778	−	1.14104i	0.322154	−	0.946687i	$-0.395593\pi$
$614$	−3.20292	+	2.68757i	−0.129259	+	0.108461i
$615$	−6.22447	−	10.8582i	−0.250995	−	0.437843i
$616$	−4.12562	+	4.42122i	−0.166226	+	0.178136i
$617$	0.764441	−	0.911025i	0.0307752	−	0.0366765i	−0.750437	−	0.660942i	$-0.770157\pi$
$617$	0.764441	−	0.911025i	0.0307752	−	0.0366765i	0.781213	+	0.624265i	$0.214602\pi$
$618$	−0.360827	+	2.01015i	−0.0145146	+	0.0808599i
$619$	−12.4466	+	34.1968i	−0.500271	+	1.37448i	0.390740	+	0.920501i	$0.372219\pi$
$619$	−12.4466	+	34.1968i	−0.500271	+	1.37448i	−0.891011	+	0.453982i	$0.850003\pi$
$620$			2.84956i			0.114441i
$621$	0.653864	+	1.84945i	0.0262387	+	0.0742159i
$622$			0.791169i			0.0317230i
$623$	17.8047	+	23.6441i	0.713329	+	0.947279i
$624$	17.6815	−	20.9407i	0.707825	−	0.838299i
$625$	1.17217	+	0.983570i	0.0468869	+	0.0393428i
$626$	−0.107223	+	0.608090i	−0.00428548	+	0.0243042i
$627$	18.9983	−	32.6733i	0.758718	−	1.30484i
$628$	2.45096	+	2.92094i	0.0978040	+	0.116558i
$629$	−0.640897	−	1.11007i	−0.0255542	−	0.0442612i
$630$	1.32844	−	0.396732i	0.0529263	−	0.0158062i
$631$	17.0123	−	29.4661i	0.677248	−	1.17303i	−0.298558	−	0.954391i	$-0.596506\pi$
$631$	17.0123	−	29.4661i	0.677248	−	1.17303i	0.975806	−	0.218637i	$-0.0701610\pi$
$632$	−3.00034	+	0.529041i	−0.119347	+	0.0210441i
$633$	1.75262	+	10.1217i	0.0696604	+	0.402303i
$634$	1.83556	−	0.668088i	0.0728992	−	0.0265331i
$635$	27.4426	−	9.98830i	1.08903	−	0.396374i
$636$	10.8962	−	29.6528i	0.432064	−	1.17581i
$637$	15.8776	+	23.5735i	0.629092	+	0.934016i
$638$	−2.28411	−	1.31873i	−0.0904286	−	0.0522090i
$639$	7.86993	−	1.33777i	0.311329	−	0.0529213i
$640$	4.73715	−	2.73500i	0.187252	−	0.108110i
$641$	25.3403	+	30.1994i	1.00088	+	1.19280i	0.981199	+	0.192999i	$0.0618213\pi$
$641$	25.3403	+	30.1994i	1.00088	+	1.19280i	0.0196832	+	0.999806i	$0.493734\pi$
$642$	4.14120	+	0.0127497i	0.163440	+	0.000503191i
$643$	−1.58947	−	0.280266i	−0.0626824	−	0.0110526i	0.142219	−	0.989835i	$-0.454576\pi$
$643$	−1.58947	−	0.280266i	−0.0626824	−	0.0110526i	−0.204901	+	0.978783i	$0.565687\pi$
$644$	−1.89411	+	0.578396i	−0.0746386	+	0.0227920i
$645$	−4.88513	+	1.76103i	−0.192352	+	0.0693405i
$646$	−2.28140	−	0.830362i	−0.0897605	−	0.0326702i
$647$	−20.9883			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$647$	−20.9883			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$648$	1.55301	+	4.43608i	0.0610078	+	0.174266i
$649$		−	56.5362i		−	2.21924i
$650$	−1.61360	−	0.587304i	−0.0632908	−	0.0230360i
$651$	1.12854	−	4.81321i	0.0442309	−	0.188645i
$652$	21.8337	+	18.3206i	0.855073	+	0.717492i
$653$	7.06142	+	1.24512i	0.276335	+	0.0487253i	0.310098	−	0.950705i	$-0.399638\pi$
$653$	7.06142	+	1.24512i	0.276335	+	0.0487253i	−0.0337633	+	0.999430i	$0.510749\pi$
$654$	−0.00705423	+	2.29126i	−0.000275842	+	0.0895954i
$655$	−11.5532	+	9.69428i	−0.451421	+	0.378787i
$656$	10.5697	+	18.3072i	0.412676	+	0.714776i
$657$	−5.58414	+	15.0532i	−0.217858	+	0.587283i
$658$	−2.00773	−	3.94366i	−0.0782695	−	0.153740i
$659$	−29.4274	+	5.18885i	−1.14633	+	0.202129i	−0.714372	−	0.699766i	$-0.753288\pi$
$659$	−29.4274	+	5.18885i	−1.14633	+	0.202129i	−0.431957	+	0.901894i	$0.642177\pi$
$660$	−6.90621	+	18.7944i	−0.268824	+	0.731571i
$661$	8.06882	+	22.1689i	0.313841	+	0.862270i	0.991872	+	0.127238i	$0.0406110\pi$
$661$	8.06882	+	22.1689i	0.313841	+	0.862270i	−0.678032	+	0.735033i	$0.737167\pi$
$662$	0.481801	+	1.32374i	0.0187257	+	0.0514485i
$663$	25.7341	−	4.45597i	0.999431	−	0.173056i
$664$	2.21001	−	0.389684i	0.0857649	−	0.0151227i
$665$	−7.97254	−	15.6600i	−0.309162	−	0.607267i
$666$	−0.133560	−	0.0243991i	−0.00517533	−	0.000945445i
$667$	−0.867520	−	1.50259i	−0.0335905	−	0.0581805i
$668$	23.8505	−	20.0129i	0.922803	−	0.774324i
$669$	21.7656	+	12.6559i	0.841507	+	0.489305i
$670$	−0.990015	−	0.174566i	−0.0382476	−	0.00674409i
$671$	5.98349	+	5.02075i	0.230990	+	0.193824i
$672$	−6.82361	+	2.06074i	−0.263226	+	0.0794949i
$673$	14.5070	+	5.28011i	0.559203	+	0.203533i	0.606131	−	0.795365i	$-0.292721\pi$
$673$	14.5070	+	5.28011i	0.559203	+	0.203533i	−0.0469277	+	0.998898i	$0.514943\pi$
$674$		−	1.25560i		−	0.0483637i
$675$	−12.9376	+	10.6539i	−0.497968	+	0.410067i
$676$	−6.91181			−0.265839
$677$	−35.5524	−	12.9400i	−1.36639	−	0.497325i	−0.448366	−	0.893850i	$-0.647994\pi$
$677$	−35.5524	−	12.9400i	−1.36639	−	0.497325i	−0.918024	+	0.396525i	$0.870216\pi$
$678$	0.659157	−	3.67212i	0.0253148	−	0.141027i
$679$	37.2907	−	11.3873i	1.43109	−	0.437003i
$680$	2.54432	+	0.448632i	0.0975701	+	0.0172042i
$681$	5.74271	+	10.0178i	0.220061	+	0.383882i
$682$	−0.397948	−	0.474256i	−0.0152382	−	0.0181602i
$683$	−13.2112	+	7.62750i	−0.505513	+	0.291858i	−0.730987	−	0.682391i	$-0.760940\pi$
$683$	−13.2112	+	7.62750i	−0.505513	+	0.291858i	0.225474	+	0.974249i	$0.427607\pi$
$684$	25.7752	−	14.6704i	0.985538	−	0.560938i
$685$	13.2167	+	7.63067i	0.504985	+	0.291553i
$686$	−0.0399422	−	2.42807i	−0.00152500	−	0.0927040i
$687$	−19.7524	−	23.6877i	−0.753601	−	0.903743i
$688$	8.24189	−	2.99980i	0.314219	−	0.114366i
$689$	−35.0969	+	12.7742i	−1.33709	+	0.486660i
$690$	0.0877186	−	0.0731457i	0.00333939	−	0.00278461i
$691$	−32.7662	+	5.77757i	−1.24649	+	0.219789i	−0.757693	−	0.652611i	$-0.773674\pi$
$691$	−32.7662	+	5.77757i	−1.24649	+	0.219789i	−0.488792	+	0.872400i	$0.662562\pi$
$692$	−4.33570	+	7.50964i	−0.164818	+	0.285474i
$693$	19.1087	−	29.0107i	0.725878	−	1.10202i
$694$	1.46877	+	2.54399i	0.0557539	+	0.0965686i
$695$	−12.7844	−	15.2358i	−0.484939	−	0.577928i
$696$	−2.06748	−	3.60658i	−0.0783676	−	0.136707i
$697$	−3.49803	+	19.8383i	−0.132497	+	0.751429i
$698$	1.46478	+	1.22909i	0.0554426	+	0.0465219i
$699$	27.3602	+	4.91124i	1.03486	+	0.185760i
$700$	−10.1785	−	13.5167i	−0.384710	−	0.510883i
$701$		−	1.67746i		−	0.0633567i	−0.999498	−	0.0316783i	$-0.989915\pi$
$701$		−	1.67746i		−	0.0633567i	0.999498	−	0.0316783i	$-0.0100852\pi$
$702$	1.40525	−	2.38287i	0.0530378	−	0.0899355i
$703$			1.72086i			0.0649036i
$704$	11.3619	−	31.2166i	0.428219	−	1.17652i
$705$	−22.4886	−	18.9885i	−0.846971	−	0.715148i
$706$	−0.676227	+	0.805896i	−0.0254501	+	0.0303303i
$707$	−22.0055	+	23.5822i	−0.827602	+	0.886899i
$708$	22.3000	−	38.3516i	0.838086	−	1.44134i
$709$	−21.9319	+	18.4031i	−0.823671	+	0.691142i	−0.953829	−	0.300351i	$-0.902896\pi$
$709$	−21.9319	+	18.4031i	−0.823671	+	0.691142i	0.130158	+	0.991493i	$0.458452\pi$
$710$	−0.232395	−	0.402521i	−0.00872165	−	0.0151063i
$711$	16.4827	−	5.88454i	0.618150	−	0.220687i
$712$	5.05949	+	2.92110i	0.189613	+	0.109473i
$713$	−0.0707217	−	0.401083i	−0.00264855	−	0.0150207i
$714$	−2.05108	−	0.878908i	−0.0767599	−	0.0328923i
$715$	22.2450	−	8.09652i	0.831916	−	0.302793i
$716$	−9.48932	−	26.0717i	−0.354633	−	0.974345i
$717$	1.21938	−	3.31839i	0.0455384	−	0.123927i
$718$	−0.0332810	−	0.188746i	−0.00124204	−	0.00704395i
$719$	−6.37063	+	11.0343i	−0.237584	+	0.411508i	−0.960021	−	0.279929i	$-0.909689\pi$
$719$	−6.37063	+	11.0343i	−0.237584	+	0.411508i	0.722436	+	0.691438i	$0.243022\pi$
$720$	−11.9923	+	9.93753i	−0.446926	+	0.370350i
$721$	23.7589	+	1.25313i	0.884829	+	0.0466690i
$722$	0.493757	+	0.588437i	0.0183757	+	0.0218994i
$723$	−0.0554150	+	17.9992i	−0.00206091	+	0.669397i
$724$	42.3750	+	7.47186i	1.57486	+	0.277690i
$725$	9.52849	−	11.3556i	0.353879	−	0.421737i
$726$	−0.628076	−	1.74230i	−0.0233101	−	0.0646627i
$727$	15.1297	−	41.5685i	0.561129	−	1.54169i	−0.256856	−	0.966450i	$-0.582687\pi$
$727$	15.1297	−	41.5685i	0.561129	−	1.54169i	0.817985	−	0.575240i	$-0.195091\pi$
$728$	4.70396	+	3.05702i	0.174340	+	0.113301i
$729$	−13.0658	−	23.6281i	−0.483918	−	0.875113i
$730$	0.934821			0.0345993
$731$	7.85396	+	2.85861i	0.290489	+	0.105729i
$732$	2.07856	+	5.76597i	0.0768258	+	0.213116i
$733$	13.1054	−	15.6184i	0.484060	−	0.576880i	−0.467637	−	0.883921i	$-0.654894\pi$
$733$	13.1054	−	15.6184i	0.484060	−	0.576880i	0.951696	+	0.307041i	$0.0993388\pi$
$734$	−0.596221	+	3.38134i	−0.0220069	+	0.124807i
$735$	−6.51400	−	14.7795i	−0.240272	−	0.545151i
$736$	−0.449829	+	0.377452i	−0.0165809	+	0.0139130i
$737$	−21.8141	+	12.5944i	−0.803534	+	0.463921i
$738$	1.36144	+	1.64294i	0.0501154	+	0.0604775i
$739$	−20.0545	+	34.7355i	−0.737718	+	1.27777i	0.215802	+	0.976437i	$0.430763\pi$
$739$	−20.0545	+	34.7355i	−0.737718	+	1.27777i	−0.953520	+	0.301328i	$0.902570\pi$
$740$	−0.158311	−	0.897828i	−0.00581964	−	0.0330048i
$741$	−32.9116	−	12.0937i	−1.20904	−	0.444274i
$742$	3.10913	+	0.718896i	0.114140	+	0.0263915i
$743$	−3.63149	−	9.97743i	−0.133226	−	0.366037i	0.855084	−	0.518489i	$-0.173505\pi$
$743$	−3.63149	−	9.97743i	−0.133226	−	0.366037i	−0.988311	+	0.152452i	$0.951283\pi$
$744$	−0.166489	−	0.961509i	−0.00610380	−	0.0352506i
$745$	3.99787	−	0.704933i	0.146471	−	0.0258267i
$746$	−1.40980	−	0.813947i	−0.0516164	−	0.0298007i
$747$	−12.1409	+	4.33446i	−0.444213	+	0.158590i
$748$	27.9099	−	16.1138i	1.02049	−	0.589179i
$749$	−5.86344	−	47.8865i	−0.214246	−	1.74973i
$750$	2.15128	+	1.25089i	0.0785535	+	0.0456759i
$751$	7.18177	−	40.7298i	0.262066	−	1.48625i	−0.515194	−	0.857074i	$-0.672280\pi$
$751$	7.18177	−	40.7298i	0.262066	−	1.48625i	0.777260	−	0.629179i	$-0.216609\pi$
$752$	38.0823	+	31.9549i	1.38872	+	1.16527i
$753$	−31.0581	−	26.2242i	−1.13182	−	0.955663i
$754$	−0.836861	+	2.29926i	−0.0304767	+	0.0837340i
$755$	0.816354			0.0297102
$756$	24.4054	−	12.1423i	0.887614	−	0.441613i
$757$	−23.7006			−0.861412			−0.430706	−	0.902492i	$-0.641735\pi$
$757$	−23.7006			−0.861412			−0.430706	+	0.902492i	$0.641735\pi$
$758$	−0.337798	+	0.928092i	−0.0122694	+	0.0337098i
$759$	0.505618	−	2.81676i	0.0183528	−	0.102242i
$760$	−2.65706	−	2.22954i	−0.0963818	−	0.0808740i
$761$	−2.04815	+	11.6156i	−0.0742454	+	0.421066i	0.924918	+	0.380167i	$0.124133\pi$
$761$	−2.04815	+	11.6156i	−0.0742454	+	0.421066i	−0.999163	+	0.0408995i	$0.986978\pi$
$762$	−4.31938	+	2.47610i	−0.156475	+	0.0896996i
$763$	26.4949	−	3.24415i	0.959178	−	0.117446i
$764$	−35.9971	+	20.7829i	−1.30233	+	0.751899i
$765$	−14.8413	−	0.0913861i	−0.536588	−	0.00330407i
$766$	−0.332436	−	0.191932i	−0.0120114	−	0.00693479i
$767$	−51.6528	+	9.10778i	−1.86507	+	0.328863i
$768$	19.4778	−	16.2419i	0.702846	−	0.586080i
$769$	8.33433	+	22.8984i	0.300544	+	0.825737i	0.994406	+	0.105629i	$0.0336855\pi$
$769$	8.33433	+	22.8984i	0.300544	+	0.825737i	−0.693862	+	0.720108i	$0.744092\pi$
$770$	−1.97062	−	0.455648i	−0.0710161	−	0.0164204i
$771$	−6.67073	+	5.56250i	−0.240240	+	0.200328i
$772$	0.525021	+	2.97754i	0.0188959	+	0.107164i
$773$	1.44939	−	2.51041i	0.0521309	−	0.0902933i	−0.838782	−	0.544467i	$-0.816732\pi$
$773$	1.44939	−	2.51041i	0.0521309	−	0.0902933i	0.890913	+	0.454173i	$0.150065\pi$
$774$	0.769400	−	0.437919i	0.0276555	−	0.0157407i
$775$	3.01342	−	1.73980i	0.108245	−	0.0624955i
$776$	5.89557	−	4.94697i	0.211639	−	0.177586i
$777$	−0.0881704	+	1.57923i	−0.00316309	+	0.0566544i
$778$	0.565207	−	3.20545i	0.0202637	−	0.114921i
$779$	17.3840	−	20.7174i	0.622845	−	0.742277i
$780$	18.2836	+	3.28196i	0.654657	+	0.117513i
$781$	−10.9436	−	3.98315i	−0.391593	−	0.142528i
$782$	−0.183830			−0.00657374
$783$	15.1809	+	18.4350i	0.542521	+	0.658814i
$784$	11.0791	+	24.9289i	0.395681	+	0.890319i
$785$	−0.876175	+	2.40727i	−0.0312720	+	0.0859192i
$786$	1.65877	−	1.96453i	0.0591664	−	0.0700725i
$787$	−5.60311	+	6.67753i	−0.199729	+	0.238028i	−0.856608	−	0.515969i	$-0.827432\pi$
$787$	−5.60311	+	6.67753i	−0.199729	+	0.238028i	0.656878	+	0.753997i	$0.271877\pi$
$788$	48.7689	+	8.59928i	1.73732	+	0.306337i
$789$	−9.15068	−	5.32078i	−0.325773	−	0.189425i
$790$	−0.655010	−	0.780611i	−0.0233042	−	0.0277729i
$791$	−43.4027	−	2.28921i	−1.54322	−	0.0813950i
$792$	1.23223	−	6.74519i	0.0437854	−	0.239680i
$793$	3.62315	−	6.27549i	0.128662	−	0.222849i
$794$	0.482439	+	2.73605i	0.0171211	+	0.0970986i
$795$	20.9134	−	3.62124i	0.741720	−	0.128432i
$796$	−0.561222	−	1.54195i	−0.0198920	−	0.0546528i
$797$	−11.0381	+	4.01755i	−0.390990	+	0.142309i	−0.530032	−	0.847978i	$-0.677820\pi$
$797$	−11.0381	+	4.01755i	−0.390990	+	0.142309i	0.139042	+	0.990287i	$0.455598\pi$
$798$	1.79476	+	2.39872i	0.0635338	+	0.0849138i
$799$	8.22624	+	46.6533i	0.291023	+	1.65048i
$800$	−4.34482	−	2.50848i	−0.153612	−	0.0886882i
$801$	−31.4658	−	11.6725i	−1.11179	−	0.412429i
$802$	−0.0891128	−	0.154348i	−0.00314668	−	0.00545021i
$803$	17.9432	−	15.0561i	0.633201	−	0.531319i
$804$	−19.7654	−	0.0608529i	−0.697073	−	0.00214612i
$805$	−0.972809	−	0.907768i	−0.0342870	−	0.0319946i
$806$	−0.369183	+	0.439975i	−0.0130039	+	0.0154975i
$807$	−7.75260	+	2.79471i	−0.272904	+	0.0983786i
$808$	−2.17749	+	5.98260i	−0.0766038	+	0.210467i
$809$		−	13.3913i		−	0.470814i	−0.971897	−	0.235407i	$-0.924358\pi$
$809$		−	13.3913i		−	0.470814i	0.971897	−	0.235407i	$-0.0756423\pi$
$810$	−1.02525	+	1.19172i	−0.0360234	+	0.0418728i
$811$		−	14.2545i		−	0.500543i	−0.968176	−	0.250272i	$-0.919480\pi$
$811$		−	14.2545i		−	0.500543i	0.968176	−	0.250272i	$-0.0805200\pi$
$812$	−19.2602	+	14.5035i	−0.675901	+	0.508973i
$813$	−6.90804	−	19.1631i	−0.242276	−	0.672078i
$814$	0.151732	+	0.127318i	0.00531820	+	0.00446250i
$815$	−3.32517	+	18.8580i	−0.116476	+	0.660566i
$816$	25.0676	+	0.0771768i	0.877540	+	0.00270173i
$817$	−7.21271	−	8.59577i	−0.252341	−	0.300728i
$818$	1.73656	+	3.00782i	0.0607176	+	0.105166i
$819$	−29.5832	−	12.7846i	−1.03372	−	0.446730i
$820$	−7.16385	+	12.4081i	−0.250172	+	0.433311i
$821$	53.2811	−	9.39490i	1.85952	−	0.327884i	0.872520	−	0.488579i	$-0.162485\pi$
$821$	53.2811	−	9.39490i	1.85952	−	0.327884i	0.987004	+	0.160695i	$0.0513735\pi$
$822$	−2.44215	−	0.897393i	−0.0851796	−	0.0313002i
$823$	−24.0026	+	8.73623i	−0.836678	+	0.304526i	−0.724597	−	0.689173i	$-0.757974\pi$
$823$	−24.0026	+	8.73623i	−0.836678	+	0.304526i	−0.112081	+	0.993699i	$0.535752\pi$
$824$	4.41294	−	1.60618i	0.153732	−	0.0559539i
$825$	24.0918	−	4.17159i	0.838768	−	0.145236i
$826$	4.12451	+	1.75238i	0.143510	+	0.0609731i
$827$	35.7068	+	20.6154i	1.24165	+	0.716866i	0.969430	−	0.245369i	$-0.0789092\pi$
$827$	35.7068	+	20.6154i	1.24165	+	0.716866i	0.272219	+	0.962235i	$0.412243\pi$
$828$	1.45403	−	1.71133i	0.0505309	−	0.0594728i
$829$	−19.7340	+	11.3934i	−0.685389	+	0.395710i	−0.801883	−	0.597482i	$-0.796168\pi$
$829$	−19.7340	+	11.3934i	−0.685389	+	0.395710i	0.116493	+	0.993191i	$0.462835\pi$
$830$	0.482471	+	0.574986i	0.0167468	+	0.0199581i
$831$	3.86454	−	6.64623i	0.134059	−	0.230555i
$832$	−30.3506	−	5.35164i	−1.05222	−	0.185535i
$833$	−7.18219	+	24.9841i	−0.248848	+	0.865648i
$834$	2.59073	+	2.18751i	0.0897097	+	0.0757473i
$835$	19.6562	+	7.15427i	0.680231	+	0.247584i
$836$	−43.2670			−1.49642
$837$	1.86852	+	5.28510i	0.0645855	+	0.182680i
$838$			2.23602i			0.0772420i
$839$	17.3731	+	6.32330i	0.599786	+	0.218304i	0.624028	−	0.781402i	$-0.285495\pi$
$839$	17.3731	+	6.32330i	0.599786	+	0.218304i	−0.0242419	+	0.999706i	$0.507717\pi$
$840$	−2.32414	−	2.18217i	−0.0801904	−	0.0752922i
$841$	6.03445	+	5.06350i	0.208084	+	0.174604i
$842$	2.34869	+	0.414137i	0.0809411	+	0.0142721i
$843$	−13.3822	+	7.67139i	−0.460908	+	0.264217i
$844$	9.00832	−	7.55887i	0.310079	−	0.260187i
$845$	−2.32184	−	4.02154i	−0.0798736	−	0.138345i
$846$	4.33005	+	2.53563i	0.148870	+	0.0871768i
$847$	−19.2275	+	9.78879i	−0.660665	+	0.336347i
$848$	−35.3041	+	6.22506i	−1.21235	+	0.213769i
$849$	26.3761	+	31.6311i	0.905225	+	1.08557i
$850$	−0.537174	−	1.47587i	−0.0184249	−	0.0506220i
$851$	0.0445655	+	0.122443i	0.00152768	+	0.00419728i
$852$	−5.85255	−	7.01857i	−0.200505	−	0.240452i
$853$	−52.2825	+	9.21881i	−1.79012	+	0.315646i	−0.967485	−	0.252927i	$-0.918607\pi$
$853$	−52.2825	+	9.21881i	−1.79012	+	0.315646i	−0.822633	+	0.568573i	$0.807496\pi$
$854$	−0.551743	+	0.280894i	−0.0188803	+	0.00961201i
$855$	17.1943	+	10.0688i	0.588031	+	0.344345i
$856$	−4.76131	−	8.24683i	−0.162738	−	0.281871i
$857$	5.81262	−	4.87737i	0.198555	−	0.166608i	−0.538089	−	0.842888i	$-0.680854\pi$
$857$	5.81262	−	4.87737i	0.198555	−	0.166608i	0.736644	+	0.676280i	$0.236409\pi$
$858$	−3.50129	+	2.00713i	−0.119532	+	0.0685221i
$859$	53.9268	+	9.50876i	1.83996	+	0.324435i	0.981942	−	0.189184i	$-0.0605843\pi$
$859$	53.9268	+	9.50876i	1.83996	+	0.324435i	0.858018	+	0.513619i	$0.171695\pi$
$860$	4.55387	+	3.82115i	0.155286	+	0.130300i
$861$	17.0146	−	18.1215i	0.579857	−	0.617580i
$862$	0.434681	+	0.158211i	0.0148053	+	0.00538869i
$863$		−	17.9590i		−	0.611331i	−0.952139	−	0.305666i	$-0.901121\pi$
$863$		−	17.9590i		−	0.611331i	0.952139	−	0.305666i	$-0.0988789\pi$
$864$	5.25222	−	6.14322i	0.178684	−	0.208997i
$865$	−5.82585			−0.198085
$866$	−2.41007	−	0.877195i	−0.0818976	−	0.0298083i
$867$	−4.24594	−	3.58510i	−0.144200	−	0.121756i
$868$	−5.41273	+	1.65286i	−0.183720	+	0.0561016i
$869$	−25.1449	−	4.43372i	−0.852981	−	0.150404i
$870$	0.698932	−	1.20202i	0.0236960	−	0.0407524i
$871$	15.0207	+	17.9010i	0.508958	+	0.606552i
$872$	4.56285	−	2.63436i	0.154518	−	0.0892108i
$873$	−28.6264	+	33.6921i	−0.968856	+	1.14030i
$874$	0.213735	+	0.123400i	0.00722968	+	0.00417406i
$875$	11.3364	−	26.6822i	0.383242	−	0.902021i
$876$	18.1106	−	3.13592i	0.611899	−	0.105953i
$877$	4.40950	−	1.60493i	0.148898	−	0.0541946i	−0.266496	−	0.963836i	$-0.585866\pi$
$877$	4.40950	−	1.60493i	0.148898	−	0.0541946i	0.415394	+	0.909642i	$0.363644\pi$
$878$	0.980901	−	0.357019i	0.0331038	−	0.0120488i
$879$	43.1714	+	15.8638i	1.45614	+	0.535073i
$880$	22.3763	−	3.94554i	0.754305	−	0.133004i
$881$	2.44317	−	4.23170i	0.0823125	−	0.142569i	−0.821930	−	0.569588i	$-0.807103\pi$
$881$	2.44317	−	4.23170i	0.0823125	−	0.142569i	0.904243	+	0.427019i	$0.140436\pi$
$882$	1.52414	+	2.29325i	0.0513204	+	0.0772176i
$883$	11.8954	+	20.6034i	0.400312	+	0.693361i	0.993763	−	0.111509i	$-0.0355684\pi$
$883$	11.8954	+	20.6034i	0.400312	+	0.693361i	−0.593451	+	0.804870i	$0.702235\pi$
$884$	−19.2182	−	22.9033i	−0.646376	−	0.770321i
$885$	29.8055	+	0.0917636i	1.00190	+	0.00308460i
$886$	−0.635004	+	3.60128i	−0.0213334	+	0.120988i
$887$	17.0442	+	14.3018i	0.572290	+	0.480208i	0.882405	−	0.470491i	$-0.155923\pi$
$887$	17.0442	+	14.3018i	0.572290	+	0.480208i	−0.310115	+	0.950699i	$0.600368\pi$
$888$	0.105875	+	0.293699i	0.00355293	+	0.00985590i
$889$	34.8906	+	46.3336i	1.17019	+	1.55398i
$890$			1.95406i			0.0655002i
$891$	−0.485071	+	39.3867i	−0.0162505	+	1.31950i
$892$		−	28.8227i		−	0.965056i
$893$	21.7526	−	59.7648i	0.727923	−	1.99995i
$894$	−0.651073	+	0.234704i	−0.0217751	+	0.00784967i
$895$	11.9818	−	14.2793i	0.400506	−	0.477305i
$896$	7.94286	+	7.41181i	0.265352	+	0.247611i
$897$	−2.65491	−	0.00817382i	−0.0886450	−	0.000272916i
$898$	1.75635	−	1.47375i	0.0586100	−	0.0491797i
$899$	−2.47908	−	4.29389i	−0.0826818	−	0.143209i
$900$	17.9882	+	6.67289i	0.599607	+	0.222430i
$901$	−29.5846	−	17.0807i	−0.985606	−	0.569040i
$902$	−0.540539	−	3.06555i	−0.0179980	−	0.102072i
$903$	−6.17865	−	8.25784i	−0.205613	−	0.274804i
$904$	−8.06153	+	2.93416i	−0.268123	+	0.0975887i
$905$	9.88737	+	27.1653i	0.328667	+	0.903006i
$906$	−0.137134	+	0.0237454i	−0.00455598	+	0.000788887i
$907$	−3.61323	−	20.4917i	−0.119975	−	0.680414i	−0.984166	−	0.177249i	$-0.943280\pi$
$907$	−3.61323	−	20.4917i	−0.119975	−	0.680414i	0.864191	−	0.503165i	$-0.167831\pi$
$908$	6.60939	−	11.4478i	0.219340	−	0.379908i
$909$	6.57254	−	35.9779i	0.217998	−	1.19331i
$910$	−0.0988312	+	1.87381i	−0.00327622	+	0.0621160i
$911$	−9.26438	−	11.0409i	−0.306942	−	0.365800i	0.590418	−	0.807097i	$-0.298963\pi$
$911$	−9.26438	−	11.0409i	−0.306942	−	0.365800i	−0.897361	+	0.441298i	$0.854518\pi$
$912$	−29.0937	−	16.9169i	−0.963388	−	0.560174i
$913$	18.5213	+	3.26581i	0.612966	+	0.108082i
$914$	2.26730	−	2.70206i	0.0749955	−	0.0893761i
$915$	−2.65661	+	3.14630i	−0.0878249	+	0.104014i
$916$	−12.0760	+	33.1785i	−0.399002	+	1.09625i
$917$	−25.1156	−	16.3222i	−0.829390	−	0.539007i
$918$	2.49575	−	0.416338i	0.0823721	−	0.0137412i
$919$	−23.8940			−0.788192			−0.394096	−	0.919069i	$-0.628942\pi$
$919$	−23.8940			−0.788192			−0.394096	+	0.919069i	$0.628942\pi$
$920$	−0.246794	−	0.0898255i	−0.00813655	−	0.00296146i
$921$	−54.3618	−	9.75812i	−1.79128	−	0.321541i
$922$	1.55997	−	1.85910i	0.0513749	−	0.0612262i
$923$	−1.87612	+	10.6400i	−0.0617533	+	0.350220i
$924$	−39.7058	−	2.21683i	−1.30623	−	0.0729284i
$925$	−0.852801	+	0.715585i	−0.0280399	+	0.0235283i
$926$	1.72548	−	0.996204i	0.0567027	−	0.0327373i
$927$	−23.4458	+	13.3447i	−0.770063	+	0.438296i
$928$	−3.57438	+	6.19101i	−0.117335	+	0.203230i
$929$	8.22973	+	46.6731i	0.270009	+	1.53129i	0.754383	+	0.656434i	$0.227936\pi$
$929$	8.22973	+	46.6731i	0.270009	+	1.53129i	−0.484375	+	0.874861i	$0.660953\pi$
$930$	0.250670	−	0.209025i	0.00821979	−	0.00685421i
$931$	25.1217	−	24.2272i	0.823330	−	0.794016i
$932$	−10.8837	−	29.9028i	−0.356508	−	0.979497i
$933$	−8.02658	+	6.69309i	−0.262778	+	0.219122i
$934$	−3.32394	+	0.586100i	−0.108763	+	0.0191778i
$935$	18.7512	+	10.8260i	0.613230	+	0.354048i
$936$	−6.36107	−	0.0391687i	−0.207918	−	0.00128027i
$937$	3.48018	−	2.00928i	0.113693	−	0.0656404i	−0.442075	−	0.896978i	$-0.645758\pi$
$937$	3.48018	−	2.00928i	0.113693	−	0.0656404i	0.555768	+	0.831337i	$0.312424\pi$
$938$	−0.242659	−	1.98179i	−0.00792311	−	0.0647077i
$939$	−7.07628	+	4.05649i	−0.230926	+	0.132379i
$940$	−5.85093	+	33.1823i	−0.190836	+	1.08229i
$941$	−17.4001	−	14.6004i	−0.567227	−	0.475960i	0.313497	−	0.949589i	$-0.398499\pi$
$941$	−17.4001	−	14.6004i	−0.567227	−	0.475960i	−0.880725	+	0.473629i	$0.842944\pi$
$942$	0.0771626	−	0.429868i	0.00251409	−	0.0140058i
$943$	0.700379	−	1.92427i	0.0228075	−	0.0626630i
$944$	−50.3422			−1.63850
$945$	15.2632	+	10.1210i	0.496512	+	0.329237i
$946$	−1.29154			−0.0419915
$947$	−16.2795	+	44.7277i	−0.529014	+	1.45345i	0.331220	+	0.943554i	$0.392540\pi$
$947$	−16.2795	+	44.7277i	−0.529014	+	1.45345i	−0.860234	+	0.509900i	$0.829682\pi$
$948$	−15.3083	−	12.9257i	−0.497191	−	0.419808i
$949$	−16.6462	−	13.9678i	−0.540359	−	0.453415i
$950$	−0.366152	+	2.07655i	−0.0118795	+	0.0673722i
$951$	22.3062	+	12.9702i	0.723329	+	0.420589i
$952$	0.623629	+	5.09315i	0.0202119	+	0.165070i
$953$	−33.3461	+	19.2524i	−1.08019	+	0.623646i	−0.930947	−	0.365155i	$-0.881016\pi$
$953$	−33.3461	+	19.2524i	−1.08019	+	0.623646i	−0.149240	+	0.988801i	$0.547683\pi$
$954$	−3.40777	+	1.21662i	−0.110331	+	0.0393894i
$955$	−24.1845	−	13.9629i	−0.782592	−	0.451830i
$956$	−3.98567	+	0.702781i	−0.128906	+	0.0227296i
$957$	−5.94419	−	34.3289i	−0.192148	−	1.10969i
$958$	0.102749	+	0.282301i	0.00331968	+	0.00912074i
$959$	−6.82824	+	29.5312i	−0.220495	+	0.953613i
$960$	16.4387	+	6.04059i	0.530558	+	0.194959i
$961$	5.18100	+	29.3829i	0.167129	+	0.947835i
$962$	0.0918774	−	0.159136i	0.00296225	−	0.00513076i
$963$	34.9041	+	42.1212i	1.12477	+	1.35734i
$964$	17.8445	−	10.3025i	0.574734	−	0.331823i
$965$	−1.55608	+	1.30570i	−0.0500918	+	0.0420320i
$966$	0.189820	+	0.124194i	0.00610737	+	0.00399588i
$967$	0.214600	−	1.21706i	0.00690107	−	0.0391379i	−0.981163	−	0.193183i	$-0.938119\pi$
$967$	0.214600	−	1.21706i	0.00690107	−	0.0391379i	0.988064	+	0.154045i	$0.0492301\pi$
$968$	−2.73746	+	3.26238i	−0.0879853	+	0.104857i
$969$	−10.8759	−	30.1699i	−0.349384	−	0.969198i
$970$	2.41891	+	0.880410i	0.0776664	+	0.0282683i
$971$	−55.5761			−1.78352			−0.891761	−	0.452507i	$-0.850530\pi$
$971$	−55.5761			−1.78352			−0.891761	+	0.452507i	$0.850530\pi$
$972$	−15.8647	+	26.5268i	−0.508859	+	0.850849i
$973$	21.5250	−	33.1213i	0.690059	−	1.06182i
$974$	−1.57372	+	4.32376i	−0.0504253	+	0.138542i
$975$	−7.69237	−	21.3388i	−0.246353	−	0.683388i
$976$	4.47069	−	5.32796i	0.143103	−	0.170544i
$977$	−13.4072	−	2.36405i	−0.428933	−	0.0756325i	−0.0449862	−	0.998988i	$-0.514324\pi$
$977$	−13.4072	−	2.36405i	−0.428933	−	0.0756325i	−0.383947	+	0.923355i	$0.625436\pi$
$978$	0.0100507	−	3.26455i	0.000321387	−	0.104389i
$979$	31.4719	+	37.5067i	1.00585	+	1.19872i
$980$	−10.8780	+	14.9512i	−0.347484	+	0.477598i
$981$	−23.3050	+	19.3119i	−0.744072	+	0.616583i
$982$	−1.48909	+	2.57919i	−0.0475189	+	0.0823052i
$983$	−1.53261	−	8.69187i	−0.0488827	−	0.277228i	0.950563	−	0.310533i	$-0.100508\pi$
$983$	−1.53261	−	8.69187i	−0.0488827	−	0.277228i	−0.999445	+	0.0333057i	$0.989397\pi$
$984$	1.69229	−	4.60536i	0.0539482	−	0.146814i
$985$	11.3792	+	31.2642i	0.362573	+	0.996161i
$986$	−2.10300	+	0.765429i	−0.0669732	+	0.0243762i
$987$	23.0243	−	53.7312i	0.732873	−	1.71028i
$988$	6.97016	+	39.5297i	0.221750	+	1.25761i
$989$	−0.735803	−	0.424816i	−0.0233972	−	0.0135084i
$990$	2.15990	−	0.771112i	0.0686462	−	0.0245075i
$991$	7.38836	+	12.7970i	0.234699	+	0.406511i	0.959185	−	0.282779i	$-0.0912562\pi$
$991$	7.38836	+	12.7970i	0.234699	+	0.406511i	−0.724486	+	0.689289i	$0.757923\pi$
$992$	−1.28546	+	1.07863i	−0.0408133	+	0.0342465i
$993$	−9.35368	+	16.0865i	−0.296830	+	0.510489i
$994$	0.629789	−	0.674913i	0.0199757	−	0.0214069i
$995$	0.708632	−	0.844515i	0.0224651	−	0.0267729i
$996$	11.2759	+	9.52089i	0.357290	+	0.301681i
$997$	0.491617	−	1.35071i	0.0155697	−	0.0427773i	−0.931664	−	0.363320i	$-0.881643\pi$
$997$	0.491617	−	1.35071i	0.0155697	−	0.0427773i	0.947234	+	0.320543i	$0.103865\pi$
$998$		−	2.56099i		−	0.0810667i
$999$	−0.882348	−	1.56140i	−0.0279163	−	0.0494005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.11	yes	132
3.2	odd	2		567.2.be.a.503.12		132
7.6	odd	2	inner	189.2.be.a.104.12	yes	132
21.20	even	2		567.2.be.a.503.11		132
27.7	even	9		567.2.be.a.62.11		132
27.20	odd	18	inner	189.2.be.a.20.12	yes	132
189.20	even	18	inner	189.2.be.a.20.11	✓	132
189.34	odd	18		567.2.be.a.62.12		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.11	✓	132	189.20	even	18	inner
189.2.be.a.20.12	yes	132	27.20	odd	18	inner
189.2.be.a.104.11	yes	132	1.1	even	1	trivial
189.2.be.a.104.12	yes	132	7.6	odd	2	inner
567.2.be.a.62.11		132	27.7	even	9
567.2.be.a.62.12		132	189.34	odd	18
567.2.be.a.503.11		132	21.20	even	2
567.2.be.a.503.12		132	3.2	odd	2

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0448460 + 0.123213i) q^{2} +(-1.62941 + 0.587383i) q^{3} +(1.51892 + 1.27452i) q^{4} +(-0.231324 + 1.31190i) q^{5} +(0.000699206 - 0.227107i) q^{6} +(-2.62614 + 0.321557i) q^{7} +(-0.452264 + 0.261115i) q^{8} +(2.30996 - 1.91418i) q^{9} +(-0.151270 - 0.0873359i) q^{10} +(-4.31014 + 0.759994i) q^{11} +(-3.22358 - 1.18454i) q^{12} +(1.38870 + 3.81541i) q^{13} +(0.0781517 - 0.337996i) q^{14} +(-0.393667 - 2.27351i) q^{15} +(0.676731 + 3.83793i) q^{16} +(-1.85685 + 3.21617i) q^{17} +(0.132259 + 0.370462i) q^{18} +(4.31784 - 2.49291i) q^{19} +(-2.02342 + 1.69785i) q^{20} +(4.09018 - 2.06650i) q^{21} +(0.0996512 - 0.565150i) q^{22} +(0.242663 - 0.289194i) q^{23} +(0.583550 - 0.691115i) q^{24} +(3.03088 + 1.10315i) q^{25} -0.532388 q^{26} +(-2.63953 + 4.47581i) q^{27} +(-4.39872 - 2.85866i) q^{28} +(1.57190 - 4.31876i) q^{29} +(0.297781 + 0.0534526i) q^{30} +(0.693448 - 0.826419i) q^{31} +(-1.53182 - 0.270102i) q^{32} +(6.57659 - 3.77004i) q^{33} +(-0.313002 - 0.373021i) q^{34} +(0.185638 - 3.51963i) q^{35} +(5.94831 + 0.0366271i) q^{36} +(-0.172576 + 0.298911i) q^{37} +(0.113522 + 0.643813i) q^{38} +(-4.50387 - 5.40118i) q^{39} +(-0.237938 - 0.653729i) q^{40} +(5.09719 - 1.85523i) q^{41} +(0.0711916 + 0.596639i) q^{42} +(-0.390810 - 2.21639i) q^{43} +(-7.51538 - 4.33901i) q^{44} +(1.97686 + 3.47325i) q^{45} +(0.0247502 + 0.0428686i) q^{46} +(9.77186 - 8.19957i) q^{47} +(-3.35701 - 5.85607i) q^{48} +(6.79320 - 1.68890i) q^{49} +(-0.271846 + 0.323973i) q^{50} +(1.13646 - 6.33114i) q^{51} +(-2.75352 + 7.56523i) q^{52} +9.19872i q^{53} +(-0.433108 - 0.525947i) q^{54} -5.83030i q^{55} +(1.10374 - 0.831152i) q^{56} +(-5.57125 + 6.59819i) q^{57} +(0.461636 + 0.387359i) q^{58} +(-2.24314 + 12.7215i) q^{59} +(2.29969 - 3.95501i) q^{60} +(-1.14717 - 1.36715i) q^{61} +(0.0707275 + 0.122504i) q^{62} +(-5.45077 + 5.76967i) q^{63} +(-3.79516 + 6.57342i) q^{64} +(-5.32670 + 0.939241i) q^{65} +(0.169586 + 0.979395i) q^{66} +(5.40821 - 1.96843i) q^{67} +(-6.91949 + 2.51849i) q^{68} +(-0.225530 + 0.613753i) q^{69} +(0.425340 + 0.180714i) q^{70} +(2.30444 + 1.33047i) q^{71} +(-0.544894 + 1.46888i) q^{72} +(-4.63485 + 2.67593i) q^{73} +(-0.0290904 - 0.0346686i) q^{74} +(-5.58652 - 0.0171995i) q^{75} +(9.73572 + 1.71667i) q^{76} +(11.0746 - 3.38180i) q^{77} +(0.867479 - 0.312715i) q^{78} +(5.48206 + 1.99531i) q^{79} -5.19155 q^{80} +(1.67186 - 8.84335i) q^{81} +0.711242i q^{82} +(-4.03800 - 1.46971i) q^{83} +(8.84645 + 2.07420i) q^{84} +(-3.78977 - 3.17999i) q^{85} +(0.290615 + 0.0512433i) q^{86} +(-0.0245079 + 7.96035i) q^{87} +(1.75088 - 1.46916i) q^{88} +(-5.59352 - 9.68826i) q^{89} +(-0.516605 + 0.0878150i) q^{90} +(-4.87378 - 9.57326i) q^{91} +(0.737171 - 0.129983i) q^{92} +(-0.644488 + 1.75390i) q^{93} +(0.572067 + 1.57174i) q^{94} +(2.27163 + 6.24126i) q^{95} +(2.65463 - 0.459660i) q^{96} +(-14.5132 + 2.55906i) q^{97} +(-0.0965524 + 0.912754i) q^{98} +(-8.50151 + 10.0059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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