LMFDB - Embedded newform 425.2.k.b.86.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] 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("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.15
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23279 - 0.895677i) q^{2} +(-0.0898893 + 0.276651i) q^{3} +(0.0995081 - 0.306255i) q^{4} +(-1.61292 + 1.54871i) q^{5} +(0.136975 + 0.421565i) q^{6} -2.08667 q^{7} +(0.790138 + 2.43179i) q^{8} +(2.35860 + 1.71362i) q^{9} +(-0.601248 + 3.35389i) q^{10} +(-2.44481 + 1.77626i) q^{11} +(0.0757809 + 0.0550580i) q^{12} +(2.17344 + 1.57910i) q^{13} +(-2.57243 + 1.86898i) q^{14} +(-0.283468 - 0.585427i) q^{15} +(3.67321 + 2.66874i) q^{16} +(0.309017 + 0.951057i) q^{17} +4.44251 q^{18} +(-0.711080 - 2.18848i) q^{19} +(0.313801 + 0.648072i) q^{20} +(0.187569 - 0.577278i) q^{21} +(-1.42299 + 4.37952i) q^{22} +(3.65519 - 2.65565i) q^{23} -0.743783 q^{24} +(0.202995 - 4.99588i) q^{25} +4.09376 q^{26} +(-1.39209 + 1.01141i) q^{27} +(-0.207640 + 0.639051i) q^{28} +(-2.92690 + 9.00806i) q^{29} +(-0.873811 - 0.467815i) q^{30} +(-1.95156 - 6.00629i) q^{31} +1.80476 q^{32} +(-0.271642 - 0.836027i) q^{33} +(1.23279 + 0.895677i) q^{34} +(3.36562 - 3.23164i) q^{35} +(0.759503 - 0.551811i) q^{36} +(4.36804 + 3.17357i) q^{37} +(-2.83678 - 2.06104i) q^{38} +(-0.632227 + 0.459340i) q^{39} +(-5.04057 - 2.69859i) q^{40} +(-0.0137059 - 0.00995792i) q^{41} +(-0.285821 - 0.879666i) q^{42} +0.729128 q^{43} +(0.300709 + 0.925488i) q^{44} +(-6.45812 + 0.888855i) q^{45} +(2.12749 - 6.54773i) q^{46} +(2.45851 - 7.56653i) q^{47} +(-1.06849 + 0.776305i) q^{48} -2.64582 q^{49} +(-4.22444 - 6.34070i) q^{50} -0.290888 q^{51} +(0.699880 - 0.508493i) q^{52} +(1.20409 - 3.70581i) q^{53} +(-0.810259 + 2.49372i) q^{54} +(1.19237 - 6.65127i) q^{55} +(-1.64875 - 5.07435i) q^{56} +0.669363 q^{57} +(4.46005 + 13.7266i) q^{58} +(9.13146 + 6.63439i) q^{59} +(-0.207497 + 0.0285586i) q^{60} +(4.57206 - 3.32180i) q^{61} +(-7.78557 - 5.65655i) q^{62} +(-4.92160 - 3.57575i) q^{63} +(-5.12153 + 3.72101i) q^{64} +(-5.95113 + 0.819078i) q^{65} +(-1.08369 - 0.787345i) q^{66} +(0.101693 + 0.312979i) q^{67} +0.322015 q^{68} +(0.406125 + 1.24993i) q^{69} +(1.25460 - 6.99845i) q^{70} +(2.23008 - 6.86347i) q^{71} +(-2.30356 + 7.08962i) q^{72} +(11.5835 - 8.41589i) q^{73} +8.22738 q^{74} +(1.36387 + 0.505235i) q^{75} -0.740989 q^{76} +(5.10151 - 3.70646i) q^{77} +(-0.367985 + 1.13254i) q^{78} +(-4.61497 + 14.2034i) q^{79} +(-10.0577 + 1.38428i) q^{80} +(2.54804 + 7.84205i) q^{81} -0.0258156 q^{82} +(-0.125996 - 0.387775i) q^{83} +(-0.158129 - 0.114888i) q^{84} +(-1.97133 - 1.05540i) q^{85} +(0.898864 - 0.653063i) q^{86} +(-2.22899 - 1.61946i) q^{87} +(-6.25124 - 4.54179i) q^{88} +(-1.73348 + 1.25945i) q^{89} +(-7.16539 + 6.88016i) q^{90} +(-4.53524 - 3.29505i) q^{91} +(-0.449584 - 1.38368i) q^{92} +1.83707 q^{93} +(-3.74632 - 11.5300i) q^{94} +(4.53623 + 2.42857i) q^{95} +(-0.162228 + 0.499288i) q^{96} +(-0.442043 + 1.36047i) q^{97} +(-3.26175 + 2.36980i) q^{98} -8.81016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.23279	−	0.895677i	0.871716	−	0.633339i	−0.0593306	−	0.998238i	$-0.518897\pi$
$2$	1.23279	−	0.895677i	0.871716	−	0.633339i	0.931047	+	0.364899i	$0.118897\pi$
$3$	−0.0898893	+	0.276651i	−0.0518976	+	0.159724i	−0.973646	−	0.228063i	$-0.926761\pi$
$3$	−0.0898893	+	0.276651i	−0.0518976	+	0.159724i	0.921749	+	0.387788i	$0.126761\pi$
$4$	0.0995081	−	0.306255i	0.0497541	−	0.153127i
$5$	−1.61292	+	1.54871i	−0.721318	+	0.692604i
$5$	−1.61292	+	1.54871i	−0.721318	+	0.692604i
$6$	0.136975	+	0.421565i	0.0559197	+	0.172103i
$7$	−2.08667			−0.788686			−0.394343	−	0.918963i	$-0.629028\pi$
$7$	−2.08667			−0.788686			−0.394343	+	0.918963i	$0.629028\pi$
$8$	0.790138	+	2.43179i	0.279356	+	0.859769i
$9$	2.35860	+	1.71362i	0.786198	+	0.571207i
$10$	−0.601248	+	3.35389i	−0.190131	+	1.06059i
$11$	−2.44481	+	1.77626i	−0.737139	+	0.535563i	−0.891814	−	0.452403i	$-0.850567\pi$
$11$	−2.44481	+	1.77626i	−0.737139	+	0.535563i	0.154675	+	0.987965i	$0.450567\pi$
$12$	0.0757809	+	0.0550580i	0.0218761	+	0.0158939i
$13$	2.17344	+	1.57910i	0.602803	+	0.437962i	0.846873	−	0.531795i	$-0.178482\pi$
$13$	2.17344	+	1.57910i	0.602803	+	0.437962i	−0.244069	+	0.969758i	$0.578482\pi$
$14$	−2.57243	+	1.86898i	−0.687510	+	0.499506i
$15$	−0.283468	−	0.585427i	−0.0731912	−	0.151157i
$16$	3.67321	+	2.66874i	0.918302	+	0.667186i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	4.44251			1.04711
$19$	−0.711080	−	2.18848i	−0.163133	−	0.502071i	0.835761	−	0.549093i	$-0.185027\pi$
$19$	−0.711080	−	2.18848i	−0.163133	−	0.502071i	−0.998894	+	0.0470221i	$0.985027\pi$
$20$	0.313801	+	0.648072i	0.0701681	+	0.144913i
$21$	0.187569	−	0.577278i	0.0409309	−	0.125972i
$22$	−1.42299	+	4.37952i	−0.303383	+	0.933718i
$23$	3.65519	−	2.65565i	0.762159	−	0.553741i	−0.137413	−	0.990514i	$-0.543879\pi$
$23$	3.65519	−	2.65565i	0.762159	−	0.553741i	0.899572	+	0.436773i	$0.143879\pi$
$24$	−0.743783			−0.151824
$25$	0.202995	−	4.99588i	0.0405990	−	0.999176i
$26$	4.09376			0.802852
$27$	−1.39209	+	1.01141i	−0.267907	+	0.194646i
$28$	−0.207640	+	0.639051i	−0.0392403	+	0.120769i
$29$	−2.92690	+	9.00806i	−0.543511	+	1.67276i	0.180993	+	0.983484i	$0.442069\pi$
$29$	−2.92690	+	9.00806i	−0.543511	+	1.67276i	−0.724504	+	0.689271i	$0.757931\pi$
$30$	−0.873811	−	0.467815i	−0.159535	−	0.0854109i
$31$	−1.95156	−	6.00629i	−0.350511	−	1.07876i	−0.958567	−	0.284868i	$-0.908050\pi$
$31$	−1.95156	−	6.00629i	−0.350511	−	1.07876i	0.608056	−	0.793894i	$-0.291950\pi$
$32$	1.80476			0.319039
$33$	−0.271642	−	0.836027i	−0.0472867	−	0.145534i
$34$	1.23279	+	0.895677i	0.211422	+	0.153607i
$35$	3.36562	−	3.23164i	0.568893	−	0.546247i
$36$	0.759503	−	0.551811i	0.126584	−	0.0919686i
$37$	4.36804	+	3.17357i	0.718101	+	0.521731i	0.885777	−	0.464111i	$-0.153626\pi$
$37$	4.36804	+	3.17357i	0.718101	+	0.521731i	−0.167676	+	0.985842i	$0.553626\pi$
$38$	−2.83678	−	2.06104i	−0.460187	−	0.334345i
$39$	−0.632227	+	0.459340i	−0.101237	+	0.0735533i
$40$	−5.04057	−	2.69859i	−0.796984	−	0.426684i
$41$	−0.0137059	−	0.00995792i	−0.00214050	−	0.00155517i	0.586714	−	0.809794i	$-0.300421\pi$
$41$	−0.0137059	−	0.00995792i	−0.00214050	−	0.00155517i	−0.588855	+	0.808239i	$0.700421\pi$
$42$	−0.285821	−	0.879666i	−0.0441031	−	0.135735i
$43$	0.729128			0.111191			0.0555955	−	0.998453i	$-0.482294\pi$
$43$	0.729128			0.111191			0.0555955	+	0.998453i	$0.482294\pi$
$44$	0.300709	+	0.925488i	0.0453336	+	0.139522i
$45$	−6.45812	+	0.888855i	−0.962719	+	0.132503i
$46$	2.12749	−	6.54773i	0.313681	−	0.965410i
$47$	2.45851	−	7.56653i	0.358611	−	1.10369i	−0.595275	−	0.803522i	$-0.702957\pi$
$47$	2.45851	−	7.56653i	0.358611	−	1.10369i	0.953886	−	0.300169i	$-0.0970431\pi$
$48$	−1.06849	+	0.776305i	−0.154224	+	0.112050i
$49$	−2.64582			−0.377974
$50$	−4.22444	−	6.34070i	−0.597426	−	0.896711i
$51$	−0.290888			−0.0407325
$52$	0.699880	−	0.508493i	0.0970559	−	0.0705152i
$53$	1.20409	−	3.70581i	0.165394	−	0.509032i	−0.833671	−	0.552262i	$-0.813765\pi$
$53$	1.20409	−	3.70581i	0.165394	−	0.509032i	0.999065	+	0.0432301i	$0.0137649\pi$
$54$	−0.810259	+	2.49372i	−0.110262	+	0.339352i
$55$	1.19237	−	6.65127i	0.160778	−	0.896856i
$56$	−1.64875	−	5.07435i	−0.220324	−	0.678088i
$57$	0.669363			0.0886593
$58$	4.46005	+	13.7266i	0.585634	+	1.80239i
$59$	9.13146	+	6.63439i	1.18881	+	0.863724i	0.993138	−	0.116945i	$-0.0373100\pi$
$59$	9.13146	+	6.63439i	1.18881	+	0.863724i	0.195676	+	0.980669i	$0.437310\pi$
$60$	−0.207497	+	0.0285586i	−0.0267878	+	0.00368690i
$61$	4.57206	−	3.32180i	0.585393	−	0.425313i	−0.255271	−	0.966869i	$-0.582165\pi$
$61$	4.57206	−	3.32180i	0.585393	−	0.425313i	0.840664	+	0.541557i	$0.182165\pi$
$62$	−7.78557	−	5.65655i	−0.988768	−	0.718382i
$63$	−4.92160	−	3.57575i	−0.620064	−	0.450503i
$64$	−5.12153	+	3.72101i	−0.640191	+	0.465126i
$65$	−5.95113	+	0.819078i	−0.738147	+	0.101594i
$66$	−1.08369	−	0.787345i	−0.133393	−	0.0969155i
$67$	0.101693	+	0.312979i	0.0124238	+	0.0382365i	0.957076	−	0.289836i	$-0.0936009\pi$
$67$	0.101693	+	0.312979i	0.0124238	+	0.0382365i	−0.944652	+	0.328073i	$0.893601\pi$
$68$	0.322015			0.0390501
$69$	0.406125	+	1.24993i	0.0488918	+	0.150473i
$70$	1.25460	−	6.99845i	0.149954	−	0.836475i
$71$	2.23008	−	6.86347i	0.264661	−	0.814544i	−0.727110	−	0.686521i	$-0.759137\pi$
$71$	2.23008	−	6.86347i	0.264661	−	0.814544i	0.991771	−	0.128023i	$-0.0408630\pi$
$72$	−2.30356	+	7.08962i	−0.271477	+	0.835519i
$73$	11.5835	−	8.41589i	1.35574	−	0.985006i	0.357041	−	0.934089i	$-0.383786\pi$
$73$	11.5835	−	8.41589i	1.35574	−	0.985006i	0.998703	−	0.0509173i	$-0.0162145\pi$
$74$	8.22738			0.956413
$75$	1.36387	+	0.505235i	0.157486	+	0.0583395i
$76$	−0.740989			−0.0849973
$77$	5.10151	−	3.70646i	0.581371	−	0.422391i
$78$	−0.367985	+	1.13254i	−0.0416661	+	0.128235i
$79$	−4.61497	+	14.2034i	−0.519225	+	1.59801i	0.256235	+	0.966614i	$0.417518\pi$
$79$	−4.61497	+	14.2034i	−0.519225	+	1.59801i	−0.775460	+	0.631396i	$0.782482\pi$
$80$	−10.0577	+	1.38428i	−1.12448	+	0.154767i
$81$	2.54804	+	7.84205i	0.283115	+	0.871339i
$82$	−0.0258156			−0.00285086
$83$	−0.125996	−	0.387775i	−0.0138298	−	0.0425638i	0.943903	−	0.330222i	$-0.107123\pi$
$83$	−0.125996	−	0.387775i	−0.0138298	−	0.0425638i	−0.957733	+	0.287658i	$0.907123\pi$
$84$	−0.158129	−	0.114888i	−0.0172533	−	0.0125353i
$85$	−1.97133	−	1.05540i	−0.213821	−	0.114474i
$86$	0.898864	−	0.653063i	0.0969270	−	0.0704216i
$87$	−2.22899	−	1.61946i	−0.238973	−	0.173624i
$88$	−6.25124	−	4.54179i	−0.666384	−	0.484157i
$89$	−1.73348	+	1.25945i	−0.183749	+	0.133501i	−0.675857	−	0.737033i	$-0.736226\pi$
$89$	−1.73348	+	1.25945i	−0.183749	+	0.133501i	0.492108	+	0.870534i	$0.336226\pi$
$90$	−7.16539	+	6.88016i	−0.755299	+	0.725232i
$91$	−4.53524	−	3.29505i	−0.475423	−	0.345415i
$92$	−0.449584	−	1.38368i	−0.0468724	−	0.144258i
$93$	1.83707			0.190495
$94$	−3.74632	−	11.5300i	−0.386404	−	1.18923i
$95$	4.53623	+	2.42857i	0.465407	+	0.249166i
$96$	−0.162228	+	0.499288i	−0.0165574	+	0.0509583i
$97$	−0.442043	+	1.36047i	−0.0448826	+	0.138135i	−0.970987	−	0.239134i	$-0.923137\pi$
$97$	−0.442043	+	1.36047i	−0.0448826	+	0.138135i	0.926104	+	0.377268i	$0.123137\pi$
$98$	−3.26175	+	2.36980i	−0.329486	+	0.239386i
$99$	−8.81016			−0.885454
$100$	−1.50981	−	0.559299i	−0.150981	−	0.0559299i
$101$	9.15637			0.911093			0.455546	−	0.890212i	$-0.349444\pi$
$101$	9.15637			0.911093			0.455546	+	0.890212i	$0.349444\pi$
$102$	−0.358605	+	0.260542i	−0.0355072	+	0.0257975i
$103$	1.01156	−	3.11325i	0.0996716	−	0.306758i	−0.888771	−	0.458351i	$-0.848440\pi$
$103$	1.01156	−	3.11325i	0.0996716	−	0.306758i	0.988443	+	0.151593i	$0.0484404\pi$
$104$	−2.12272	+	6.53306i	−0.208150	+	0.640619i
$105$	0.591504	+	1.22159i	0.0577248	+	0.119215i
$106$	−1.83481	−	5.64697i	−0.178213	−	0.548482i
$107$	9.02436			0.872418			0.436209	−	0.899845i	$-0.356321\pi$
$107$	9.02436			0.872418			0.436209	+	0.899845i	$0.356321\pi$
$108$	0.171225	+	0.526977i	0.0164761	+	0.0507083i
$109$	−14.0077	−	10.1772i	−1.34170	−	0.974799i	−0.999380	−	0.0352137i	$-0.988789\pi$
$109$	−14.0077	−	10.1772i	−1.34170	−	0.974799i	−0.342316	−	0.939585i	$-0.611211\pi$
$110$	−4.48744	−	9.26761i	−0.427861	−	0.883632i
$111$	−1.27061	+	0.923153i	−0.120601	+	0.0876218i
$112$	−7.66477	−	5.56878i	−0.724252	−	0.526200i
$113$	−4.84403	−	3.51940i	−0.455688	−	0.331077i	0.336149	−	0.941809i	$-0.390875\pi$
$113$	−4.84403	−	3.51940i	−0.455688	−	0.331077i	−0.791837	+	0.610732i	$0.790875\pi$
$114$	0.825186	−	0.599533i	0.0772857	−	0.0561514i
$115$	−1.78268	+	9.94416i	−0.166236	+	0.927298i
$116$	2.46751	+	1.79275i	0.229103	+	0.166453i
$117$	2.42029	+	7.44889i	0.223756	+	0.688651i
$118$	17.1995			1.58334
$119$	−0.644816	−	1.98454i	−0.0591102	−	0.181922i
$120$	1.19966	−	1.15190i	0.109513	−	0.105154i
$121$	−0.577178	+	1.77637i	−0.0524707	+	0.161488i
$122$	2.66115	−	8.19018i	0.240929	−	0.741504i
$123$	0.00398688	−	0.00289664i	0.000359485	−	0.000261181i
$124$	−2.03365			−0.182627
$125$	7.40975	+	8.37231i	0.662748	+	0.748842i
$126$	−9.27004			−0.825841
$127$	5.16558	−	3.75301i	0.458371	−	0.333026i	−0.334521	−	0.942388i	$-0.608575\pi$
$127$	5.16558	−	3.75301i	0.458371	−	0.333026i	0.792892	+	0.609362i	$0.208575\pi$
$128$	−4.09636	+	12.6073i	−0.362071	+	1.11434i
$129$	−0.0655408	+	0.201714i	−0.00577055	+	0.0177599i
$130$	−6.60289	+	6.34004i	−0.579112	+	0.556059i
$131$	3.29648	+	10.1455i	0.288015	+	0.886418i	0.985479	+	0.169799i	$0.0543117\pi$
$131$	3.29648	+	10.1455i	0.288015	+	0.886418i	−0.697464	+	0.716620i	$0.745688\pi$
$132$	−0.283068			−0.0246379
$133$	1.48379	+	4.56662i	0.128661	+	0.395977i
$134$	0.405694	+	0.294754i	0.0350467	+	0.0254629i
$135$	0.678938	−	3.78726i	0.0584337	−	0.325955i
$136$	−2.06861	+	1.50293i	−0.177382	+	0.128875i
$137$	15.0151	+	10.9091i	1.28283	+	0.932031i	0.999635	−	0.0270312i	$-0.00860536\pi$
$137$	15.0151	+	10.9091i	1.28283	+	0.932031i	0.283196	+	0.959062i	$0.408605\pi$
$138$	1.62020	+	1.17714i	0.137920	+	0.100205i
$139$	13.9507	−	10.1358i	1.18328	−	0.859704i	0.190743	−	0.981640i	$-0.438910\pi$
$139$	13.9507	−	10.1358i	1.18328	−	0.859704i	0.992538	+	0.121936i	$0.0389102\pi$
$140$	−0.654799	−	1.35231i	−0.0553406	−	0.114291i
$141$	1.87229	+	1.36030i	0.157675	+	0.114558i
$142$	−3.39823	−	10.4587i	−0.285173	−	0.877671i
$143$	−8.11854			−0.678906
$144$	4.09040	+	12.5890i	0.340867	+	1.04908i
$145$	−9.23004	−	19.0622i	−0.766513	−	1.58303i
$146$	6.74212	−	20.7501i	0.557982	−	1.71729i
$147$	0.237831	−	0.731969i	0.0196160	−	0.0603718i
$148$	1.40657	−	1.02194i	0.115620	−	0.0840027i
$149$	−9.33093			−0.764420			−0.382210	−	0.924075i	$-0.624837\pi$
$149$	−9.33093			−0.764420			−0.382210	+	0.924075i	$0.624837\pi$
$150$	2.13389	−	0.598734i	0.174232	−	0.0488864i
$151$	−22.8174			−1.85685			−0.928425	−	0.371520i	$-0.878837\pi$
$151$	−22.8174			−1.85685			−0.928425	+	0.371520i	$0.878837\pi$
$152$	4.76008	−	3.45840i	0.386093	−	0.280513i
$153$	−0.900903	+	2.77270i	−0.0728337	+	0.224159i
$154$	2.96931	−	9.13861i	0.239274	−	0.736410i
$155$	12.4497	+	6.66524i	0.999985	+	0.535365i
$156$	0.0777632	+	0.239331i	0.00622604	+	0.0191618i
$157$	5.59661			0.446658			0.223329	−	0.974743i	$-0.428308\pi$
$157$	5.59661			0.446658			0.223329	+	0.974743i	$0.428308\pi$
$158$	7.03237	+	21.6434i	0.559465	+	1.72186i
$159$	0.916980	+	0.666225i	0.0727213	+	0.0528351i
$160$	−2.91092	+	2.79504i	−0.230129	+	0.220968i
$161$	−7.62716	+	5.54146i	−0.601104	+	0.436728i
$162$	10.1651	+	7.38541i	0.798649	+	0.580252i
$163$	4.02307	+	2.92293i	0.315111	+	0.228941i	0.734086	−	0.679056i	$-0.237611\pi$
$163$	4.02307	+	2.92293i	0.315111	+	0.228941i	−0.418976	+	0.907998i	$0.637611\pi$
$164$	−0.00441351	+	0.00320660i	−0.000344637	+	0.000250393i
$165$	1.73290	+	0.927747i	0.134906	+	0.0722250i
$166$	−0.502647	−	0.365195i	−0.0390130	−	0.0283446i
$167$	1.05868	+	3.25829i	0.0819233	+	0.252134i	0.983626	−	0.180223i	$-0.0576820\pi$
$167$	1.05868	+	3.25829i	0.0819233	+	0.252134i	−0.901702	+	0.432357i	$0.857682\pi$
$168$	1.55203			0.119742
$169$	−1.78693	−	5.49960i	−0.137456	−	0.423046i
$170$	−3.37553	+	0.464588i	−0.258892	+	0.0356323i
$171$	2.07307	−	6.38025i	0.158532	−	0.487910i
$172$	0.0725542	−	0.223299i	0.00553220	−	0.0170264i
$173$	−5.12084	+	3.72051i	−0.389330	+	0.282865i	−0.765181	−	0.643815i	$-0.777350\pi$
$173$	−5.12084	+	3.72051i	−0.389330	+	0.282865i	0.375851	+	0.926680i	$0.377350\pi$
$174$	−4.19840			−0.318280
$175$	−0.423583	+	10.4247i	−0.0320199	+	0.788036i
$176$	−13.7207			−1.03424
$177$	−2.65623	+	1.92986i	−0.199655	+	0.145058i
$178$	−1.00897	+	3.10528i	−0.0756253	+	0.232751i
$179$	0.733079	−	2.25619i	0.0547929	−	0.168635i	−0.919915	−	0.392118i	$-0.871743\pi$
$179$	0.733079	−	2.25619i	0.0547929	−	0.168635i	0.974708	+	0.223483i	$0.0717426\pi$
$180$	−0.370419	+	2.06628i	−0.0276094	+	0.154011i
$181$	−3.15019	−	9.69530i	−0.234152	−	0.720646i	−0.997233	−	0.0743426i	$-0.976314\pi$
$181$	−3.15019	−	9.69530i	−0.234152	−	0.720646i	0.763081	−	0.646303i	$-0.223686\pi$
$182$	−8.54231			−0.633198
$183$	0.507999	+	1.56346i	0.0375524	+	0.115574i
$184$	9.34610	+	6.79034i	0.689003	+	0.500590i
$185$	−11.9602	+	1.64613i	−0.879333	+	0.121026i
$186$	2.26473	−	1.64542i	0.166058	−	0.120648i
$187$	−2.44481	−	1.77626i	−0.178782	−	0.129893i
$188$	−2.07264	−	1.50586i	−0.151163	−	0.109826i
$189$	2.90482	−	2.11048i	0.211295	−	0.153515i
$190$	7.76745	−	1.06906i	0.563510	−	0.0775580i
$191$	12.3456	+	8.96961i	0.893297	+	0.649018i	0.936736	−	0.350038i	$-0.113831\pi$
$191$	12.3456	+	8.96961i	0.893297	+	0.649018i	−0.0434386	+	0.999056i	$0.513831\pi$
$192$	−0.569049	−	1.75135i	−0.0410676	−	0.126393i
$193$	5.17024			0.372162			0.186081	−	0.982534i	$-0.440421\pi$
$193$	5.17024			0.372162			0.186081	+	0.982534i	$0.440421\pi$
$194$	0.673592	+	2.07310i	0.0483611	+	0.148840i
$195$	0.308345	−	1.72001i	0.0220810	−	0.123173i
$196$	−0.263281	+	0.810294i	−0.0188058	+	0.0578782i
$197$	6.42012	−	19.7591i	0.457415	−	1.40778i	−0.410862	−	0.911698i	$-0.634772\pi$
$197$	6.42012	−	19.7591i	0.457415	−	1.40778i	0.868277	−	0.496080i	$-0.165228\pi$
$198$	−10.8611	+	7.89105i	−0.771865	+	0.560793i
$199$	−24.2960			−1.72230			−0.861149	−	0.508353i	$-0.830255\pi$
$199$	−24.2960			−1.72230			−0.861149	+	0.508353i	$0.830255\pi$
$200$	12.3093	−	3.45379i	0.870402	−	0.244220i
$201$	−0.0957271			−0.00675207
$202$	11.2879	−	8.20115i	0.794215	−	0.577031i
$203$	6.10746	−	18.7968i	0.428660	−	1.31928i
$204$	−0.0289457	+	0.0890858i	−0.00202661	+	0.00623725i
$205$	0.0375284	−	0.00516518i	0.00262110	−	0.000360752i
$206$	−1.54143	−	4.74402i	−0.107396	−	0.330531i
$207$	13.1719			0.915509
$208$	3.76929	+	11.6007i	0.261354	+	0.804364i
$209$	5.62576	+	4.08736i	0.389142	+	0.282728i
$210$	1.82335	+	0.976174i	0.125823	+	0.0673624i
$211$	16.7182	−	12.1465i	1.15093	−	0.836197i	0.162323	−	0.986738i	$-0.448101\pi$
$211$	16.7182	−	12.1465i	1.15093	−	0.836197i	0.988604	+	0.150541i	$0.0481015\pi$
$212$	−1.01510	−	0.737516i	−0.0697176	−	0.0506528i
$213$	1.69832	+	1.23391i	0.116367	+	0.0845458i
$214$	11.1252	−	8.08291i	0.760501	−	0.552536i
$215$	−1.17602	+	1.12921i	−0.0802040	+	0.0770113i
$216$	−3.55948	−	2.58612i	−0.242192	−	0.175963i
$217$	4.07226	+	12.5331i	0.276443	+	0.850804i
$218$	−26.3841			−1.78696
$219$	1.28703	+	3.96108i	0.0869696	+	0.267665i
$220$	−1.91833	−	1.02702i	−0.129334	−	0.0692418i
$221$	−0.830180	+	2.55503i	−0.0558439	+	0.171870i
$222$	−0.739554	+	2.27611i	−0.0496356	+	0.152763i
$223$	7.43964	−	5.40522i	0.498195	−	0.361960i	−0.310132	−	0.950694i	$-0.600373\pi$
$223$	7.43964	−	5.40522i	0.498195	−	0.361960i	0.808327	+	0.588734i	$0.200373\pi$
$224$	−3.76593			−0.251622
$225$	9.03982	−	11.4354i	0.602655	−	0.762360i
$226$	−9.12393			−0.606915
$227$	14.0570	−	10.2130i	0.932999	−	0.677863i	−0.0137263	−	0.999906i	$-0.504369\pi$
$227$	14.0570	−	10.2130i	0.932999	−	0.677863i	0.946725	+	0.322042i	$0.104369\pi$
$228$	0.0666071	−	0.204995i	0.00441116	−	0.0135762i
$229$	−4.49533	+	13.8352i	−0.297060	+	0.914256i	0.685462	+	0.728109i	$0.259600\pi$
$229$	−4.49533	+	13.8352i	−0.297060	+	0.914256i	−0.982522	+	0.186148i	$0.940400\pi$
$230$	6.70908	+	13.8558i	0.442384	+	0.913625i
$231$	0.566825	+	1.74451i	0.0372944	+	0.114780i
$232$	−24.2184			−1.59002
$233$	7.61693	+	23.4425i	0.499001	+	1.53577i	0.810627	+	0.585563i	$0.199127\pi$
$233$	7.61693	+	23.4425i	0.499001	+	1.53577i	−0.311625	+	0.950205i	$0.600873\pi$
$234$	9.65552	+	7.01515i	0.631201	+	0.458594i
$235$	7.75298	+	16.0117i	0.505749	+	1.04449i
$236$	2.94047	−	2.13637i	0.191408	−	0.139066i
$237$	−3.51456	−	2.55347i	−0.228295	−	0.165866i
$238$	−2.57243	−	1.86898i	−0.166746	−	0.121148i
$239$	−1.17627	+	0.854609i	−0.0760865	+	0.0552801i	−0.625178	−	0.780482i	$-0.714974\pi$
$239$	−1.17627	+	0.854609i	−0.0760865	+	0.0552801i	0.549092	+	0.835762i	$0.314974\pi$
$240$	0.521117	−	2.90690i	0.0336379	−	0.187640i
$241$	6.49711	+	4.72042i	0.418515	+	0.304069i	0.777040	−	0.629451i	$-0.216720\pi$
$241$	6.49711	+	4.72042i	0.418515	+	0.304069i	−0.358525	+	0.933520i	$0.616720\pi$
$242$	0.879513	+	2.70686i	0.0565372	+	0.174004i
$243$	−7.56069			−0.485019
$244$	−0.562359	−	1.73076i	−0.0360013	−	0.110801i
$245$	4.26749	−	4.09761i	0.272640	−	0.261787i
$246$	0.00232055	−	0.00714191i	0.000147953	−	0.000455352i
$247$	1.91033	−	5.87938i	0.121551	−	0.374096i
$248$	13.0641	−	9.49160i	0.829569	−	0.602717i
$249$	0.118604			0.00751622
$250$	16.6336	+	3.68459i	1.05200	+	0.233034i
$251$	−11.8631			−0.748794			−0.374397	−	0.927268i	$-0.622150\pi$
$251$	−11.8631			−0.748794			−0.374397	+	0.927268i	$0.622150\pi$
$252$	−1.58483	+	1.15145i	−0.0998349	+	0.0725343i
$253$	−4.21913	+	12.9851i	−0.265254	+	0.816368i
$254$	3.00660	−	9.25337i	0.188651	−	0.580608i
$255$	0.469178	−	0.450501i	0.0293811	−	0.0282115i
$256$	2.32961	+	7.16980i	0.145600	+	0.448112i
$257$	16.3263			1.01841			0.509203	−	0.860647i	$-0.329940\pi$
$257$	16.3263			1.01841			0.509203	+	0.860647i	$0.329940\pi$
$258$	0.0998722	+	0.307375i	0.00621777	+	0.0191363i
$259$	−9.11465	−	6.62218i	−0.566357	−	0.411482i
$260$	−0.341340	+	1.90407i	−0.0211690	+	0.118085i
$261$	−22.3398	+	16.2308i	−1.38280	+	1.00466i
$262$	13.1510	+	9.55475i	0.812471	+	0.590294i
$263$	−9.67245	−	7.02744i	−0.596429	−	0.433331i	0.248181	−	0.968714i	$-0.420167\pi$
$263$	−9.67245	−	7.02744i	−0.596429	−	0.433331i	−0.844609	+	0.535383i	$0.820167\pi$
$264$	1.81841	−	1.32115i	0.111915	−	0.0813113i
$265$	3.79712	+	7.84194i	0.233256	+	0.481727i
$266$	5.91942	+	4.30071i	0.362943	+	0.263693i
$267$	−0.192606	−	0.592781i	−0.0117873	−	0.0362776i
$268$	0.105971			0.00647318
$269$	1.66066	+	5.11099i	0.101252	+	0.311622i	0.988833	−	0.149031i	$-0.0476153\pi$
$269$	1.66066	+	5.11099i	0.101252	+	0.311622i	−0.887580	+	0.460653i	$0.847615\pi$
$270$	−2.55517	−	5.27702i	−0.155503	−	0.321149i
$271$	7.82280	−	24.0761i	0.475201	−	1.46252i	−0.370484	−	0.928839i	$-0.620808\pi$
$271$	7.82280	−	24.0761i	0.475201	−	1.46252i	0.845686	−	0.533681i	$-0.179192\pi$
$272$	−1.40304	+	4.31812i	−0.0850719	+	0.261824i
$273$	1.31925	−	0.958490i	0.0798445	−	0.0580104i
$274$	28.2816			1.70856
$275$	8.37770	+	12.5746i	0.505194	+	0.758274i
$276$	0.423208			0.0254741
$277$	−20.7295	+	15.0609i	−1.24552	+	0.904921i	−0.997953	−	0.0639508i	$-0.979630\pi$
$277$	−20.7295	+	15.0609i	−1.24552	+	0.904921i	−0.247564	+	0.968872i	$0.579630\pi$
$278$	8.11994	−	24.9906i	0.487001	−	1.49884i
$279$	5.68955	−	17.5106i	0.340625	−	1.04834i
$280$	10.5180	+	5.63105i	0.628570	+	0.336520i
$281$	−0.347237	−	1.06869i	−0.0207144	−	0.0637525i	0.940165	−	0.340720i	$-0.110671\pi$
$281$	−0.347237	−	1.06869i	−0.0207144	−	0.0637525i	−0.960879	+	0.276967i	$0.910671\pi$
$282$	3.52654			0.210002
$283$	−1.44997	−	4.46254i	−0.0861915	−	0.265270i	0.898667	−	0.438632i	$-0.144537\pi$
$283$	−1.44997	−	4.46254i	−0.0861915	−	0.265270i	−0.984858	+	0.173362i	$0.944537\pi$
$284$	−1.88006	−	1.36594i	−0.111561	−	0.0810537i
$285$	−1.07963	+	1.03665i	−0.0639515	+	0.0614058i
$286$	−10.0085	+	7.27158i	−0.591813	+	0.429978i
$287$	0.0285997	+	0.0207789i	0.00168818	+	0.00122654i
$288$	4.25669	+	3.09267i	0.250828	+	0.182237i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−28.4523	−	15.2326i	−1.67077	−	0.894487i
$291$	−0.336640	−	0.244583i	−0.0197342	−	0.0143377i
$292$	−1.42475	−	4.38494i	−0.0833775	−	0.256609i
$293$	−30.0907			−1.75792			−0.878959	−	0.476897i	$-0.841762\pi$
$293$	−30.0907			−1.75792			−0.878959	+	0.476897i	$0.841762\pi$
$294$	−0.362411	−	1.11539i	−0.0211362	−	0.0650506i
$295$	−25.0030	+	3.44126i	−1.45573	+	0.200358i
$296$	−4.26611	+	13.1297i	−0.247963	+	0.763150i
$297$	1.60686	−	4.94542i	0.0932397	−	0.286962i
$298$	−11.5031	+	8.35750i	−0.666357	+	0.484137i
$299$	12.1379			0.701950
$300$	0.290446	−	0.367416i	0.0167689	−	0.0212127i
$301$	−1.52145			−0.0876948
$302$	−28.1291	+	20.4370i	−1.61865	+	1.17602i
$303$	−0.823060	+	2.53312i	−0.0472836	+	0.145524i
$304$	3.22854	−	9.93643i	0.185169	−	0.569893i
$305$	−2.22985	+	12.4386i	−0.127681	+	0.712231i
$306$	1.37281	+	4.22508i	0.0784784	+	0.241532i
$307$	−12.2499			−0.699140			−0.349570	−	0.936910i	$-0.613672\pi$
$307$	−12.2499			−0.699140			−0.349570	+	0.936910i	$0.613672\pi$
$308$	−0.627480	−	1.93118i	−0.0357540	−	0.110039i
$309$	0.770355	+	0.559696i	0.0438240	+	0.0318400i
$310$	21.3178	−	2.93405i	1.21077	−	0.166643i
$311$	−23.0937	+	16.7786i	−1.30952	+	0.951425i	−0.309524	+	0.950892i	$0.600170\pi$
$311$	−23.0937	+	16.7786i	−1.30952	+	0.951425i	−1.00000		0.000533513i	$0.999830\pi$
$312$	−1.61657	−	1.17450i	−0.0915201	−	0.0664932i
$313$	−16.5000	−	11.9879i	−0.932633	−	0.677597i	0.0140033	−	0.999902i	$-0.495542\pi$
$313$	−16.5000	−	11.9879i	−0.932633	−	0.677597i	−0.946636	+	0.322305i	$0.895542\pi$
$314$	6.89946	−	5.01275i	0.389359	−	0.282886i
$315$	13.4759	−	1.85475i	0.759283	−	0.104503i
$316$	3.89064	+	2.82671i	0.218865	+	0.159015i
$317$	7.93104	+	24.4092i	0.445451	+	1.37096i	0.881988	+	0.471272i	$0.156205\pi$
$317$	7.93104	+	24.4092i	0.445451	+	1.37096i	−0.436536	+	0.899687i	$0.643795\pi$
$318$	1.72717			0.0968548
$319$	−8.84495	−	27.2220i	−0.495222	−	1.52414i
$320$	2.49783	−	13.9334i	0.139633	−	0.778902i
$321$	−0.811194	+	2.49660i	−0.0452764	+	0.139346i
$322$	−4.43936	+	13.6629i	−0.247396	+	0.761406i
$323$	1.86163	−	1.35255i	0.103584	−	0.0752581i
$324$	2.65521			0.147512
$325$	8.33017	−	10.5377i	0.462074	−	0.584526i
$326$	7.57761			0.419685
$327$	4.07467	−	2.96042i	0.225330	−	0.163712i
$328$	0.0133861	−	0.0411981i	0.000739122	−	0.00227478i
$329$	−5.13010	+	15.7888i	−0.282831	+	0.870466i
$330$	2.96727	−	0.408396i	0.163343	−	0.0224815i
$331$	2.22955	+	6.86185i	0.122547	+	0.377161i	0.993446	−	0.114301i	$-0.0364627\pi$
$331$	2.22955	+	6.86185i	0.122547	+	0.377161i	−0.870899	+	0.491462i	$0.836463\pi$
$332$	−0.131295			−0.00720577
$333$	4.86415	+	14.9703i	0.266554	+	0.820369i
$334$	4.22351	+	3.06856i	0.231100	+	0.167904i
$335$	−0.648736	−	0.347316i	−0.0354442	−	0.0189759i
$336$	2.22959	−	1.61989i	0.121634	−	0.0883723i
$337$	8.44356	+	6.13460i	0.459950	+	0.334173i	0.793512	−	0.608555i	$-0.208251\pi$
$337$	8.44356	+	6.13460i	0.459950	+	0.334173i	−0.333562	+	0.942728i	$0.608251\pi$
$338$	−7.12878	−	5.17936i	−0.387754	−	0.281720i
$339$	1.40907	−	1.02375i	0.0765302	−	0.0556025i
$340$	−0.519383	+	0.498708i	−0.0281675	+	0.0270462i
$341$	15.4399	+	11.2178i	0.836120	+	0.607477i
$342$	−3.15898	−	9.72233i	−0.170818	−	0.525723i
$343$	20.1276			1.08679
$344$	0.576112	+	1.77309i	0.0310619	+	0.0955986i
$345$	−2.59082	−	1.38705i	−0.139485	−	0.0746765i
$346$	−2.98056	+	9.17323i	−0.160236	+	0.493156i
$347$	−3.21465	+	9.89367i	−0.172571	+	0.531120i	−0.999514	−	0.0311659i	$-0.990078\pi$
$347$	−3.21465	+	9.89367i	−0.172571	+	0.531120i	0.826943	+	0.562286i	$0.190078\pi$
$348$	−0.717769	+	0.521490i	−0.0384765	+	0.0279548i
$349$	−22.4571			−1.20210			−0.601050	−	0.799212i	$-0.705251\pi$
$349$	−22.4571			−1.20210			−0.601050	+	0.799212i	$0.705251\pi$
$350$	8.81500	+	13.2309i	0.471182	+	0.707223i
$351$	−4.62273			−0.246743
$352$	−4.41229	+	3.20572i	−0.235176	+	0.170865i
$353$	1.36411	−	4.19830i	0.0726043	−	0.223453i	−0.908169	−	0.418604i	$-0.862520\pi$
$353$	1.36411	−	4.19830i	0.0726043	−	0.223453i	0.980773	+	0.195151i	$0.0625196\pi$
$354$	−1.54605	+	4.75825i	−0.0821715	+	0.252898i
$355$	7.03260	+	14.5239i	0.373251	+	0.770851i
$356$	0.213217	+	0.656213i	0.0113005	+	0.0347792i
$357$	0.606986			0.0321251
$358$	−1.11708	−	3.43801i	−0.0590394	−	0.181705i
$359$	−14.5868	−	10.5979i	−0.769862	−	0.559337i	0.132058	−	0.991242i	$-0.457842\pi$
$359$	−14.5868	−	10.5979i	−0.769862	−	0.559337i	−0.901919	+	0.431905i	$0.857842\pi$
$360$	−7.26432	−	15.0025i	−0.382863	−	0.790701i
$361$	11.0875	−	8.05556i	0.583554	−	0.423977i
$362$	−12.5674	−	9.13074i	−0.660527	−	0.479901i
$363$	−0.439553	−	0.319354i	−0.0230705	−	0.0167617i
$364$	−1.46042	+	1.06105i	−0.0765466	+	0.0556144i
$365$	−5.64941	+	31.5136i	−0.295703	+	1.64950i
$366$	2.02661	+	1.47242i	0.105933	+	0.0769646i
$367$	−7.97556	−	24.5463i	−0.416321	−	1.28130i	−0.911064	−	0.412265i	$-0.864738\pi$
$367$	−7.97556	−	24.5463i	−0.416321	−	1.28130i	0.494743	−	0.869039i	$-0.335262\pi$
$368$	20.5135			1.06934
$369$	−0.0152626	−	0.0469734i	−0.000794538	−	0.00244534i
$370$	−13.2701	+	12.7418i	−0.689878	+	0.662416i
$371$	−2.51253	+	7.73279i	−0.130444	+	0.401466i
$372$	0.182803	−	0.562611i	0.00947792	−	0.0291700i
$373$	14.5311	−	10.5575i	0.752394	−	0.546646i	−0.144174	−	0.989552i	$-0.546053\pi$
$373$	14.5311	−	10.5575i	0.752394	−	0.546646i	0.896568	+	0.442906i	$0.146053\pi$
$374$	−4.60490			−0.238114
$375$	−2.98227	+	1.29733i	−0.154004	+	0.0669940i
$376$	20.3428			1.04910
$377$	−20.5860	+	14.9566i	−1.06023	+	0.770305i
$378$	1.69074	−	5.20356i	0.0869623	−	0.267642i
$379$	4.19621	−	12.9146i	0.215545	−	0.663379i	−0.783570	−	0.621304i	$-0.786603\pi$
$379$	4.19621	−	12.9146i	0.215545	−	0.663379i	0.999114	−	0.0420747i	$-0.0133968\pi$
$380$	1.19515	−	1.14758i	0.0613101	−	0.0588695i
$381$	0.573944	+	1.76642i	0.0294040	+	0.0904963i
$382$	23.2535			1.18975
$383$	−2.40061	−	7.38832i	−0.122666	−	0.377526i	0.870803	−	0.491632i	$-0.163599\pi$
$383$	−2.40061	−	7.38832i	−0.122666	−	0.377526i	−0.993469	+	0.114106i	$0.963599\pi$
$384$	−3.11961	−	2.26653i	−0.159197	−	0.115663i
$385$	−2.48807	+	13.8790i	−0.126804	+	0.707338i
$386$	6.37383	−	4.63086i	0.324420	−	0.235705i
$387$	1.71972	+	1.24945i	0.0874182	+	0.0635130i
$388$	0.372663	+	0.270755i	0.0189191	+	0.0137455i
$389$	0.982022	−	0.713481i	0.0497905	−	0.0361749i	−0.562612	−	0.826721i	$-0.690203\pi$
$389$	0.982022	−	0.713481i	0.0497905	−	0.0361749i	0.612402	+	0.790546i	$0.290203\pi$
$390$	−1.16045	−	2.39660i	−0.0587617	−	0.121356i
$391$	3.65519	+	2.65565i	0.184851	+	0.134302i
$392$	−2.09056	−	6.43409i	−0.105589	−	0.324971i
$393$	−3.10309			−0.156530
$394$	−9.78308	−	30.1092i	−0.492865	−	1.51688i
$395$	−14.5534	−	30.0562i	−0.732262	−	1.51229i
$396$	−0.876683	+	2.69815i	−0.0440550	+	0.135587i
$397$	8.73616	−	26.8871i	0.438455	−	1.34943i	−0.451049	−	0.892499i	$-0.648950\pi$
$397$	8.73616	−	26.8871i	0.438455	−	1.34943i	0.889504	−	0.456928i	$-0.151050\pi$
$398$	−29.9519	+	21.7614i	−1.50135	+	1.09080i
$399$	−1.39674			−0.0699243
$400$	14.0784	−	17.8092i	0.703918	−	0.890458i
$401$	−20.1402			−1.00576			−0.502878	−	0.864358i	$-0.667725\pi$
$401$	−20.1402			−1.00576			−0.502878	+	0.864358i	$0.667725\pi$
$402$	−0.118012	+	0.0857405i	−0.00588589	+	0.00427635i
$403$	5.24291	−	16.1360i	0.261168	−	0.803792i
$404$	0.911133	−	2.80418i	0.0453306	−	0.139513i
$405$	−16.2548	−	8.70240i	−0.807709	−	0.432425i
$406$	−9.30664	−	28.6429i	−0.461881	−	1.42152i
$407$	−16.3161			−0.808760
$408$	−0.229842	−	0.707380i	−0.0113789	−	0.0350205i
$409$	−0.763523	−	0.554732i	−0.0377538	−	0.0274297i	0.568748	−	0.822512i	$-0.307428\pi$
$409$	−0.763523	−	0.554732i	−0.0377538	−	0.0274297i	−0.606502	+	0.795082i	$0.707428\pi$
$410$	0.0416384	−	0.0399809i	0.00205637	−	0.00197452i
$411$	−4.36773	+	3.17334i	−0.215444	+	0.156529i
$412$	−0.852789	−	0.619587i	−0.0420139	−	0.0305249i
$413$	−19.0543	−	13.8438i	−0.937601	−	0.681207i
$414$	16.2382	−	11.7977i	0.798064	−	0.579828i
$415$	0.803771	+	0.430317i	0.0394556	+	0.0211235i
$416$	3.92253	+	2.84988i	0.192318	+	0.139727i
$417$	1.55005	+	4.77057i	0.0759063	+	0.233616i
$418$	10.5964			0.518284
$419$	1.69072	+	5.20351i	0.0825972	+	0.254208i	0.983823	−	0.179141i	$-0.0573318\pi$
$419$	1.69072	+	5.20351i	0.0825972	+	0.254208i	−0.901226	+	0.433349i	$0.857332\pi$
$420$	0.432977	−	0.0595924i	0.0211271	−	0.00290781i
$421$	5.71325	−	17.5836i	0.278447	−	0.856971i	−0.709840	−	0.704363i	$-0.751233\pi$
$421$	5.71325	−	17.5836i	0.278447	−	0.856971i	0.988287	−	0.152608i	$-0.0487672\pi$
$422$	9.73074	−	29.9481i	0.473685	−	1.45785i
$423$	18.7648	−	13.6334i	0.912375	−	0.662879i
$424$	9.96316			0.483854
$425$	4.81409	−	1.35075i	0.233518	−	0.0655211i
$426$	3.19886			0.154985
$427$	−9.54038	+	6.93149i	−0.461691	+	0.335438i
$428$	0.897997	−	2.76375i	0.0434063	−	0.133591i
$429$	0.729770	−	2.24600i	0.0352336	−	0.108438i
$430$	−0.438387	+	2.44541i	−0.0211409	+	0.117928i
$431$	−5.46036	−	16.8053i	−0.263016	−	0.809482i	−0.992144	−	0.125103i	$-0.960074\pi$
$431$	−5.46036	−	16.8053i	−0.263016	−	0.809482i	0.729127	−	0.684378i	$-0.239926\pi$
$432$	−7.81262			−0.375885
$433$	−7.10016	−	21.8520i	−0.341212	−	1.05014i	−0.963581	−	0.267418i	$-0.913830\pi$
$433$	−7.10016	−	21.8520i	−0.341212	−	1.05014i	0.622369	−	0.782724i	$-0.286170\pi$
$434$	16.2459	+	11.8033i	0.779828	+	0.566578i
$435$	6.10325	−	0.840013i	0.292628	−	0.0402756i
$436$	−4.51069	+	3.27721i	−0.216023	+	0.156950i
$437$	−8.41096	−	6.11092i	−0.402351	−	0.292325i
$438$	5.13449	+	3.73043i	0.245336	+	0.178247i
$439$	1.51023	−	1.09724i	0.0720791	−	0.0523685i	−0.551162	−	0.834398i	$-0.685815\pi$
$439$	1.51023	−	1.09724i	0.0720791	−	0.0523685i	0.623241	+	0.782030i	$0.285815\pi$
$440$	17.1166	−	2.35583i	0.816004	−	0.112310i
$441$	−6.24042	−	4.53393i	−0.297163	−	0.215901i
$442$	1.26504	+	3.89340i	0.0601719	+	0.185190i
$443$	−18.7427			−0.890494			−0.445247	−	0.895408i	$-0.646884\pi$
$443$	−18.7427			−0.890494			−0.445247	+	0.895408i	$0.646884\pi$
$444$	0.156284	+	0.480991i	0.00741689	+	0.0228268i
$445$	0.845442	−	4.71605i	0.0400778	−	0.223562i
$446$	4.33021	−	13.3270i	0.205041	−	0.631053i
$447$	0.838752	−	2.58141i	0.0396716	−	0.122097i
$448$	10.6869	−	7.76450i	0.504910	−	0.366838i
$449$	−10.7621			−0.507896			−0.253948	−	0.967218i	$-0.581729\pi$
$449$	−10.7621			−0.507896			−0.253948	+	0.967218i	$0.581729\pi$
$450$	0.901807	−	22.1942i	0.0425116	−	1.04625i
$451$	0.0511962			0.00241074
$452$	−1.55985	+	1.13330i	−0.0733692	+	0.0533059i
$453$	2.05104	−	6.31244i	0.0963661	−	0.296584i
$454$	8.18185	−	25.1811i	0.383993	−	1.18181i
$455$	12.4180	−	1.70914i	0.582167	−	0.0801258i
$456$	0.528889	+	1.62775i	0.0247675	+	0.0762265i
$457$	−28.5591			−1.33594			−0.667970	−	0.744188i	$-0.732837\pi$
$457$	−28.5591			−1.33594			−0.667970	+	0.744188i	$0.732837\pi$
$458$	6.85006	+	21.0823i	0.320082	+	0.985112i
$459$	−1.39209	−	1.01141i	−0.0649771	−	0.0472086i
$460$	2.86805	+	1.53548i	0.133724	+	0.0715921i
$461$	−2.88005	+	2.09248i	−0.134137	+	0.0974565i	−0.652831	−	0.757504i	$-0.726419\pi$
$461$	−2.88005	+	2.09248i	−0.134137	+	0.0974565i	0.518693	+	0.854960i	$0.326419\pi$
$462$	2.26129	+	1.64293i	0.105205	+	0.0764359i
$463$	−29.6840	−	21.5667i	−1.37953	−	1.00229i	−0.996924	−	0.0783787i	$-0.975026\pi$
$463$	−29.6840	−	21.5667i	−1.37953	−	1.00229i	−0.382609	−	0.923910i	$-0.624974\pi$
$464$	−34.7913	+	25.2774i	−1.61515	+	1.17347i
$465$	−2.96304	+	2.84509i	−0.137408	+	0.131938i
$466$	30.3870	+	22.0774i	1.40765	+	1.02272i
$467$	−6.45625	−	19.8703i	−0.298760	−	0.919487i	−0.981933	−	0.189231i	$-0.939401\pi$
$467$	−6.45625	−	19.8703i	−0.298760	−	0.919487i	0.683173	−	0.730257i	$-0.260599\pi$
$468$	2.52210			0.116584
$469$	−0.212200	−	0.653083i	−0.00979846	−	0.0301566i
$470$	23.8991	+	12.7949i	1.10238	+	0.590187i
$471$	−0.503076	+	1.54831i	−0.0231805	+	0.0713423i
$472$	−8.91837	+	27.4479i	−0.410501	+	1.26339i
$473$	−1.78258	+	1.29512i	−0.0819632	+	0.0595497i
$474$	−6.61981			−0.304058
$475$	−11.0777	+	3.10822i	−0.508280	+	0.142615i
$476$	−0.671938			−0.0307982
$477$	9.19030	−	6.67715i	0.420795	−	0.305726i
$478$	−0.684642	+	2.10711i	−0.0313148	+	0.0963771i
$479$	−3.29835	+	10.1513i	−0.150705	+	0.463823i	−0.997700	−	0.0677773i	$-0.978409\pi$
$479$	−3.29835	+	10.1513i	−0.150705	+	0.463823i	0.846995	+	0.531601i	$0.178409\pi$
$480$	−0.511591	−	1.05655i	−0.0233508	−	0.0482249i
$481$	4.48230	+	13.7951i	0.204375	+	0.629003i
$482$	12.2376			0.557406
$483$	−0.847449	−	2.60818i	−0.0385603	−	0.118676i
$484$	0.486588	+	0.353527i	0.0221176	+	0.0160694i
$485$	−1.39399	−	2.87892i	−0.0632979	−	0.130725i
$486$	−9.32077	+	6.77194i	−0.422799	+	0.307181i
$487$	−31.7984	−	23.1029i	−1.44093	−	1.04689i	−0.987848	−	0.155422i	$-0.950326\pi$
$487$	−31.7984	−	23.1029i	−1.44093	−	1.04689i	−0.453077	−	0.891471i	$-0.649674\pi$
$488$	11.6905	+	8.49364i	0.529204	+	0.384489i
$489$	−1.17026	+	0.850245i	−0.0529211	+	0.0384494i
$490$	1.59079	−	8.87379i	0.0718648	−	0.400877i
$491$	35.1227	+	25.5181i	1.58507	+	1.15162i	0.910582	+	0.413328i	$0.135634\pi$
$491$	35.1227	+	25.5181i	1.58507	+	1.15162i	0.674483	+	0.738290i	$0.264366\pi$
$492$	−0.000490382	−	0.00150924i	−2.21081e−5	−	6.80418e-5i
$493$	−9.47164			−0.426581
$494$	−2.91099	−	8.95910i	−0.130972	−	0.403089i
$495$	14.2100	−	13.6444i	0.638694	−	0.613269i
$496$	8.86075	−	27.2706i	0.397859	−	1.22449i
$497$	−4.65343	+	14.3218i	−0.208735	+	0.642419i
$498$	0.146214	−	0.106231i	0.00655201	−	0.00476031i
$499$	31.9577			1.43062			0.715312	−	0.698805i	$-0.246284\pi$
$499$	31.9577			1.43062			0.715312	+	0.698805i	$0.246284\pi$
$500$	3.30139	−	1.43616i	0.147643	−	0.0642269i
$501$	−0.996574			−0.0445236
$502$	−14.6248	+	10.6255i	−0.652736	+	0.474240i
$503$	5.73379	−	17.6468i	0.255657	−	0.786832i	−0.738042	−	0.674755i	$-0.764249\pi$
$503$	5.73379	−	17.6468i	0.255657	−	0.786832i	0.993699	−	0.112078i	$-0.0357505\pi$
$504$	4.80675	−	14.7937i	0.214110	−	0.658962i
$505$	−14.7685	+	14.1806i	−0.657188	+	0.631027i
$506$	6.42917	+	19.7870i	0.285812	+	0.879637i
$507$	1.68210			0.0747045
$508$	−0.635360	−	1.95544i	−0.0281895	−	0.0867585i
$509$	−6.99651	−	5.08326i	−0.310115	−	0.225312i	0.421831	−	0.906675i	$-0.361388\pi$
$509$	−6.99651	−	5.08326i	−0.310115	−	0.225312i	−0.731946	+	0.681363i	$0.761388\pi$
$510$	0.174896	−	0.975606i	0.00774452	−	0.0432006i
$511$	−24.1709	+	17.5612i	−1.06926	+	0.776860i
$512$	−12.1551	−	8.83120i	−0.537185	−	0.390288i
$513$	3.20333	+	2.32736i	0.141431	+	0.102755i
$514$	20.1269	−	14.6231i	0.887760	−	0.644996i
$515$	3.18997	+	6.58802i	0.140567	+	0.290303i
$516$	0.0552540	+	0.0401444i	0.00243242	+	0.00176726i
$517$	7.42952	+	22.8657i	0.326750	+	1.00563i
$518$	−17.1678			−0.754310
$519$	−0.568973	−	1.75112i	−0.0249751	−	0.0768656i
$520$	−6.69405	−	13.8248i	−0.293553	−	0.606255i
$521$	0.773634	−	2.38100i	0.0338935	−	0.104314i	−0.932679	−	0.360709i	$-0.882535\pi$
$521$	0.773634	−	2.38100i	0.0338935	−	0.104314i	0.966572	+	0.256395i	$0.0825348\pi$
$522$	−13.0028	+	40.0184i	−0.569116	+	1.75156i
$523$	−34.8166	+	25.2957i	−1.52242	+	1.10610i	−0.562152	+	0.827034i	$0.690026\pi$
$523$	−34.8166	+	25.2957i	−1.52242	+	1.10610i	−0.960271	+	0.279070i	$0.909974\pi$
$524$	3.43514			0.150065
$525$	−2.84594	−	1.05426i	−0.124207	−	0.0460116i
$526$	−18.2184			−0.794362
$527$	5.10926	−	3.71209i	0.222563	−	0.161701i
$528$	1.23334	−	3.79584i	0.0536744	−	0.165193i
$529$	−0.799466	+	2.46050i	−0.0347594	+	0.106978i
$530$	11.7049	+	6.26649i	0.508429	+	0.272199i
$531$	10.1686	+	31.2957i	0.441279	+	1.35812i
$532$	1.54620			0.0670362
$533$	−0.0140644	−	0.0432859i	−0.000609198	−	0.00187492i
$534$	−0.768384	−	0.558264i	−0.0332512	−	0.0241584i
$535$	−14.5555	+	13.9761i	−0.629291	+	0.604240i
$536$	−0.680749	+	0.494593i	−0.0294039	+	0.0213632i
$537$	0.558280	+	0.405614i	0.0240916	+	0.0175035i
$538$	6.62504	+	4.81338i	0.285626	+	0.207519i
$539$	6.46854	−	4.69967i	0.278620	−	0.202429i
$540$	−1.09231	−	0.584791i	−0.0470053	−	0.0251654i
$541$	29.2293	+	21.2363i	1.25666	+	0.913020i	0.998589	−	0.0531044i	$-0.0169116\pi$
$541$	29.2293	+	21.2363i	1.25666	+	0.913020i	0.258076	+	0.966125i	$0.416912\pi$
$542$	−11.9205	−	36.6876i	−0.512030	−	1.57587i
$543$	2.96538			0.127257
$544$	0.557701	+	1.71643i	0.0239112	+	0.0735911i
$545$	38.3548	−	5.27892i	1.64294	−	0.226124i
$546$	0.767863	−	2.36324i	0.0328615	−	0.101137i
$547$	−12.9066	+	39.7226i	−0.551849	+	1.69842i	0.152276	+	0.988338i	$0.451340\pi$
$547$	−12.9066	+	39.7226i	−0.551849	+	1.69842i	−0.704124	+	0.710077i	$0.748660\pi$
$548$	4.83510	−	3.51291i	0.206545	−	0.150064i
$549$	16.4760			0.703176
$550$	21.5907	+	7.99812i	0.920631	+	0.341041i
$551$	21.7952			0.928507
$552$	−2.71867	+	1.97523i	−0.115714	+	0.0840713i
$553$	9.62992	−	29.6378i	0.409506	−	1.26033i
$554$	−12.0655	+	37.1339i	−0.512616	+	1.57767i
$555$	0.619692	−	3.45677i	0.0263045	−	0.146732i
$556$	−1.71592	−	5.28105i	−0.0727711	−	0.223966i
$557$	−25.1863			−1.06718			−0.533590	−	0.845744i	$-0.679157\pi$
$557$	−25.1863			−1.06718			−0.533590	+	0.845744i	$0.679157\pi$
$558$	−8.66983	−	26.6830i	−0.367023	−	1.12958i
$559$	1.58471	+	1.15136i	0.0670263	+	0.0486974i
$560$	20.9870	−	2.88853i	0.886864	−	0.122063i
$561$	0.711167	−	0.516693i	0.0300255	−	0.0218148i
$562$	−1.38527	−	1.00646i	−0.0584340	−	0.0424548i
$563$	−36.8572	−	26.7783i	−1.55334	−	1.12857i	−0.941212	−	0.337816i	$-0.890312\pi$
$563$	−36.8572	−	26.7783i	−1.55334	−	1.12857i	−0.612133	−	0.790755i	$-0.709688\pi$
$564$	0.602906	−	0.438037i	0.0253869	−	0.0184447i
$565$	13.2635	−	1.82551i	0.558001	−	0.0767999i
$566$	−5.78450	−	4.20268i	−0.243140	−	0.176652i
$567$	−5.31690	−	16.3637i	−0.223289	−	0.687213i
$568$	18.4526			0.774254
$569$	14.4300	+	44.4110i	0.604937	+	1.86180i	0.497225	+	0.867622i	$0.334352\pi$
$569$	14.4300	+	44.4110i	0.604937	+	1.86180i	0.107712	+	0.994182i	$0.465648\pi$
$570$	−0.402453	+	2.24497i	−0.0168569	+	0.0940314i
$571$	5.60721	−	17.2572i	0.234654	−	0.722192i	−0.762513	−	0.646973i	$-0.776034\pi$
$571$	5.60721	−	17.2572i	0.234654	−	0.722192i	0.997167	−	0.0752188i	$-0.0239655\pi$
$572$	−0.807860	+	2.48634i	−0.0337783	+	0.103959i
$573$	−3.59119	+	2.60915i	−0.150024	+	0.108999i
$574$	0.0538686			0.00224843
$575$	−12.5253	−	18.8000i	−0.522342	−	0.784012i
$576$	−18.4560			−0.769000
$577$	26.9073	−	19.5493i	1.12017	−	0.813849i	0.135933	−	0.990718i	$-0.456597\pi$
$577$	26.9073	−	19.5493i	1.12017	−	0.813849i	0.984234	+	0.176869i	$0.0565968\pi$
$578$	−0.470885	+	1.44924i	−0.0195862	+	0.0602802i
$579$	−0.464749	+	1.43035i	−0.0193143	+	0.0594434i
$580$	−6.75634	+	0.929901i	−0.280542	+	0.0386120i
$581$	0.262911	+	0.809157i	0.0109074	+	0.0335695i
$582$	−0.634075			−0.0262832
$583$	3.63870	+	11.1988i	0.150700	+	0.463806i
$584$	29.6183	+	21.5189i	1.22561	+	0.890460i
$585$	−15.4399	−	8.26611i	−0.638362	−	0.341762i
$586$	−37.0956	+	26.9516i	−1.53241	+	1.11336i
$587$	23.7682	+	17.2686i	0.981018	+	0.712751i	0.957936	−	0.286982i	$-0.0926521\pi$
$587$	23.7682	+	17.2686i	0.981018	+	0.712751i	0.0230820	+	0.999734i	$0.492652\pi$
$588$	−0.200503	−	0.145674i	−0.00826859	−	0.00600748i
$589$	−11.7569	+	8.54190i	−0.484435	+	0.351963i
$590$	−27.7413	+	26.6370i	−1.14209	+	1.09663i
$591$	4.88927	+	3.55226i	0.201118	+	0.146121i
$592$	7.57529	+	23.3144i	0.311343	+	0.958214i
$593$	45.6937			1.87642			0.938209	−	0.346070i	$-0.112484\pi$
$593$	45.6937			1.87642			0.938209	+	0.346070i	$0.112484\pi$
$594$	−2.44857	−	7.53591i	−0.100466	−	0.309202i
$595$	4.11351	+	2.20226i	0.168637	+	0.0902839i
$596$	−0.928504	+	2.85764i	−0.0380330	+	0.117054i
$597$	2.18395	−	6.72151i	0.0893832	−	0.275093i
$598$	14.9635	−	10.8716i	0.611901	−	0.444572i
$599$	18.4376			0.753340			0.376670	−	0.926348i	$-0.377069\pi$
$599$	18.4376			0.753340			0.376670	+	0.926348i	$0.377069\pi$
$600$	−0.150984	+	3.71585i	−0.00616391	+	0.151699i
$601$	2.76657			0.112851			0.0564253	−	0.998407i	$-0.482030\pi$
$601$	2.76657			0.112851			0.0564253	+	0.998407i	$0.482030\pi$
$602$	−1.87563	+	1.36272i	−0.0764450	+	0.0555405i
$603$	−0.296474	+	0.912454i	−0.0120734	+	0.0371580i
$604$	−2.27051	+	6.98792i	−0.0923858	+	0.284334i
$605$	−1.82014	−	3.75902i	−0.0739994	−	0.152826i
$606$	1.25419	+	3.86001i	0.0509481	+	0.156802i
$607$	−18.1257			−0.735701			−0.367851	−	0.929885i	$-0.619906\pi$
$607$	−18.1257			−0.735701			−0.367851	+	0.929885i	$0.619906\pi$
$608$	−1.28333	−	3.94967i	−0.0520457	−	0.160180i
$609$	4.65116	+	3.37927i	0.188475	+	0.136935i
$610$	8.39200	+	17.3314i	0.339782	+	0.701729i
$611$	17.2917	−	12.5631i	0.699547	−	0.508251i
$612$	0.759503	+	0.551811i	0.0307011	+	0.0223057i
$613$	19.9940	+	14.5265i	0.807549	+	0.586719i	0.913119	−	0.407693i	$-0.133667\pi$
$613$	19.9940	+	14.5265i	0.807549	+	0.586719i	−0.105570	+	0.994412i	$0.533667\pi$
$614$	−15.1016	+	10.9720i	−0.609452	+	0.442793i
$615$	−0.00194445	+	0.0108466i	−7.84078e−5	+	0.000437375i
$616$	13.0443	+	9.47721i	0.525568	+	0.381848i
$617$	−1.09177	−	3.36012i	−0.0439529	−	0.135273i	0.926672	−	0.375871i	$-0.122656\pi$
$617$	−1.09177	−	3.36012i	−0.0439529	−	0.135273i	−0.970625	+	0.240598i	$0.922656\pi$
$618$	1.45099			0.0583676
$619$	4.91286	+	15.1202i	0.197464	+	0.607733i	0.999939	+	0.0110465i	$0.00351630\pi$
$619$	4.91286	+	15.1202i	0.197464	+	0.607733i	−0.802475	+	0.596686i	$0.796484\pi$
$620$	3.28011	−	3.14953i	0.131732	−	0.126488i
$621$	−2.40239	+	7.39379i	−0.0964045	+	0.296703i
$622$	−13.4416	+	41.3690i	−0.538959	+	1.65875i
$623$	3.61721	−	2.62805i	0.144920	−	0.105291i
$624$	−3.54816			−0.142040
$625$	−24.9176	−	2.02828i	−0.996703	−	0.0811311i
$626$	−31.0783			−1.24214
$627$	−1.63647	+	1.18896i	−0.0653542	+	0.0474826i
$628$	0.556908	−	1.71399i	0.0222231	−	0.0683956i
$629$	−1.66844	+	5.13494i	−0.0665252	+	0.204743i
$630$	14.9518	−	14.3566i	0.595694	−	0.571981i
$631$	10.5956	+	32.6099i	0.421805	+	1.29818i	0.906021	+	0.423233i	$0.139105\pi$
$631$	10.5956	+	32.6099i	0.421805	+	1.29818i	−0.484216	+	0.874948i	$0.660895\pi$
$632$	−38.1863			−1.51897
$633$	1.85754	+	5.71694i	0.0738308	+	0.227228i
$634$	31.6401	+	22.9879i	1.25659	+	0.912965i
$635$	−2.51931	+	14.0533i	−0.0999760	+	0.557687i
$636$	0.295281	−	0.214535i	0.0117087	−	0.00850685i
$637$	−5.75053	−	4.17800i	−0.227844	−	0.165538i
$638$	−35.2861	−	25.6368i	−1.39699	−	1.01497i
$639$	17.0212	−	12.3666i	0.673349	−	0.489217i
$640$	−12.9180	−	26.6786i	−0.510628	−	1.05457i
$641$	−3.83554	−	2.78668i	−0.151495	−	0.110067i	0.509456	−	0.860497i	$-0.329847\pi$
$641$	−3.83554	−	2.78668i	−0.151495	−	0.110067i	−0.660951	+	0.750429i	$0.729847\pi$
$642$	1.23611	+	3.80436i	0.0487854	+	0.150146i
$643$	24.2717			0.957183			0.478592	−	0.878038i	$-0.341147\pi$
$643$	24.2717			0.957183			0.478592	+	0.878038i	$0.341147\pi$
$644$	0.938132	+	2.88727i	0.0369676	+	0.113774i
$645$	−0.206685	−	0.426851i	−0.00813819	−	0.0168073i
$646$	1.08355	−	3.33484i	0.0426319	−	0.131207i
$647$	−0.944147	+	2.90578i	−0.0371182	+	0.114238i	−0.967899	−	0.251340i	$-0.919129\pi$
$647$	−0.944147	+	2.90578i	−0.0371182	+	0.114238i	0.930781	+	0.365578i	$0.119129\pi$
$648$	−17.0570	+	12.3926i	−0.670060	+	0.486827i
$649$	−34.1091			−1.33890
$650$	0.831013	−	20.4519i	0.0325950	−	0.802190i
$651$	−3.83336			−0.150241
$652$	1.29549	−	0.941227i	0.0507352	−	0.0368613i
$653$	3.24286	−	9.98049i	0.126903	−	0.390567i	−0.867340	−	0.497716i	$-0.834172\pi$
$653$	3.24286	−	9.98049i	0.126903	−	0.390567i	0.994243	+	0.107149i	$0.0341722\pi$
$654$	2.37165	−	7.29918i	0.0927388	−	0.285421i
$655$	−21.0294	−	11.2586i	−0.821687	−	0.439909i
$656$	−0.0237695	−	0.0731550i	−0.000928044	−	0.00285622i
$657$	41.7424			1.62853
$658$	7.81733	+	24.0593i	0.304751	+	0.937927i
$659$	−34.7144	−	25.2215i	−1.35228	−	0.982490i	−0.998894	−	0.0470132i	$-0.985030\pi$
$659$	−34.7144	−	25.2215i	−1.35228	−	0.982490i	−0.353388	−	0.935477i	$-0.614970\pi$
$660$	0.456564	−	0.438390i	0.0177717	−	0.0170643i
$661$	6.93241	−	5.03669i	0.269640	−	0.195905i	−0.444746	−	0.895657i	$-0.646706\pi$
$661$	6.93241	−	5.03669i	0.269640	−	0.195905i	0.714386	+	0.699752i	$0.246706\pi$
$662$	8.89457	+	6.46229i	0.345697	+	0.251164i
$663$	−0.632227	−	0.459340i	−0.0245537	−	0.0178393i
$664$	0.843435	−	0.612791i	0.0327316	−	0.0237809i
$665$	−9.46560	−	5.06763i	−0.367060	−	0.196514i
$666$	19.4051	+	14.0986i	0.751931	+	0.546310i
$667$	13.2239	+	40.6990i	0.512031	+	1.57587i
$668$	1.10321			0.0426846
$669$	0.826613	+	2.54405i	0.0319587	+	0.0983588i
$670$	−1.11084	+	0.152889i	−0.0429155	+	0.00590662i
$671$	−5.27746	+	16.2424i	−0.203734	+	0.627029i
$672$	0.338517	−	1.04185i	0.0130586	−	0.0401901i
$673$	14.9890	−	10.8902i	0.577784	−	0.419785i	−0.260141	−	0.965571i	$-0.583769\pi$
$673$	14.9890	−	10.8902i	0.577784	−	0.419785i	0.837924	+	0.545786i	$0.183769\pi$
$674$	15.9038			0.612591
$675$	4.77030	+	7.16001i	0.183609	+	0.275589i
$676$	−1.86209			−0.0716189
$677$	18.9166	−	13.7437i	0.727026	−	0.528215i	−0.161596	−	0.986857i	$-0.551664\pi$
$677$	18.9166	−	13.7437i	0.727026	−	0.528215i	0.888621	+	0.458642i	$0.151664\pi$
$678$	0.820144	−	2.52414i	0.0314974	−	0.0969391i
$679$	0.922396	−	2.83884i	0.0353983	−	0.108945i
$680$	1.00889	−	5.62778i	0.0386890	−	0.215815i
$681$	1.56187	+	4.80694i	0.0598510	+	0.184202i
$682$	29.0818			1.11360
$683$	−0.860527	−	2.64843i	−0.0329271	−	0.101339i	0.933242	−	0.359248i	$-0.116967\pi$
$683$	−0.860527	−	2.64843i	−0.0329271	−	0.101339i	−0.966169	+	0.257908i	$0.916967\pi$
$684$	−1.74769	−	1.26977i	−0.0668248	−	0.0485510i
$685$	−41.1133	+	5.65858i	−1.57086	+	0.216203i
$686$	24.8132	−	18.0278i	0.947372	−	0.688306i
$687$	−3.42344	−	2.48728i	−0.130612	−	0.0948955i
$688$	2.67824	+	1.94585i	0.102107	+	0.0741850i
$689$	8.46884	−	6.15297i	0.322637	−	0.234410i
$690$	−4.43630	+	0.610584i	−0.168887	+	0.0232446i
$691$	−14.2583	−	10.3593i	−0.542412	−	0.394086i	0.282568	−	0.959247i	$-0.408814\pi$
$691$	−14.2583	−	10.3593i	−0.542412	−	0.394086i	−0.824980	+	0.565162i	$0.808814\pi$
$692$	0.629857	+	1.93850i	0.0239436	+	0.0736907i
$693$	18.3839			0.698346
$694$	4.89853	+	15.0761i	0.185946	+	0.572282i
$695$	−6.80392	+	37.9537i	−0.258087	+	1.43967i
$696$	2.17698	−	6.70005i	0.0825181	−	0.253965i
$697$	0.00523519	−	0.0161123i	0.000198297	−	0.000610295i
$698$	−27.6849	+	20.1143i	−1.04789	+	0.761336i
$699$	−7.17007			−0.271197
$700$	3.15047	+	1.16707i	0.119077	+	0.0441111i
$701$	41.9829			1.58567			0.792836	−	0.609435i	$-0.208604\pi$
$701$	41.9829			1.58567			0.792836	+	0.609435i	$0.208604\pi$
$702$	−5.69887	+	4.14047i	−0.215090	+	0.156272i
$703$	3.83926	−	11.8160i	0.144800	−	0.445650i
$704$	5.91170	−	18.1943i	0.222805	−	0.685725i
$705$	−5.12656	+	0.705588i	−0.193077	+	0.0265740i
$706$	−2.07865	−	6.39744i	−0.0782312	−	0.240771i
$707$	−19.1063			−0.718566
$708$	0.326713	+	1.00552i	0.0122786	+	0.0377898i
$709$	23.3674	+	16.9774i	0.877580	+	0.637599i	0.932610	−	0.360885i	$-0.117525\pi$
$709$	23.3674	+	16.9774i	0.877580	+	0.637599i	−0.0550300	+	0.998485i	$0.517525\pi$
$710$	21.6785	+	11.6061i	0.813579	+	0.435568i
$711$	−35.2241	+	25.5918i	−1.32101	+	0.959769i
$712$	−4.43242	−	3.22034i	−0.166112	−	0.120687i
$713$	−23.0839	−	16.7715i	−0.864500	−	0.628096i
$714$	0.748289	−	0.543664i	0.0280040	−	0.0203461i
$715$	13.0945	−	12.5733i	0.489707	−	0.470213i
$716$	−0.618020	−	0.449018i	−0.0230965	−	0.0167806i
$717$	−0.130694	−	0.402236i	−0.00488087	−	0.0150218i
$718$	−27.4748			−1.02535
$719$	6.39425	+	19.6795i	0.238465	+	0.733920i	0.996643	+	0.0818722i	$0.0260899\pi$
$719$	6.39425	+	19.6795i	0.238465	+	0.733920i	−0.758178	+	0.652048i	$0.773910\pi$
$720$	−26.0941	−	13.9701i	−0.972471	−	0.520635i
$721$	−2.11078	+	6.49631i	−0.0786096	+	0.241935i
$722$	6.45345	−	19.8617i	0.240172	−	0.739175i
$723$	−1.88993	+	1.37311i	−0.0702873	+	0.0510667i
$724$	−3.28270			−0.122001
$725$	44.4090	+	16.4510i	1.64931	+	0.610975i
$726$	−0.827915			−0.0307268
$727$	−5.20155	+	3.77915i	−0.192915	+	0.140161i	−0.680050	−	0.733166i	$-0.738042\pi$
$727$	−5.20155	+	3.77915i	−0.192915	+	0.140161i	0.487135	+	0.873327i	$0.338042\pi$
$728$	4.42941	−	13.6323i	0.164165	−	0.505247i
$729$	−6.96448	+	21.4345i	−0.257944	+	0.793869i
$730$	21.2614	+	43.9098i	0.786921	+	1.62517i
$731$	0.225313	+	0.693442i	0.00833350	+	0.0256479i
$732$	0.529367			0.0195660
$733$	7.77718	+	23.9357i	0.287257	+	0.884085i	0.985713	+	0.168433i	$0.0538706\pi$
$733$	7.77718	+	23.9357i	0.287257	+	0.884085i	−0.698456	+	0.715653i	$0.746129\pi$
$734$	−31.8177	−	23.1169i	−1.17441	−	0.853262i
$735$	0.750006	+	1.54893i	0.0276644	+	0.0571333i
$736$	6.59673	−	4.79280i	0.243159	−	0.176665i
$737$	−0.804553	−	0.584542i	−0.0296361	−	0.0215319i
$738$	−0.0608886	−	0.0442381i	−0.00224134	−	0.00162843i
$739$	−1.07658	+	0.782180i	−0.0396026	+	0.0287730i	−0.607410	−	0.794388i	$-0.707792\pi$
$739$	−1.07658	+	0.782180i	−0.0396026	+	0.0287730i	0.567808	+	0.823161i	$0.307792\pi$
$740$	−0.686004	+	3.82667i	−0.0252180	+	0.140671i
$741$	1.45482	+	1.05699i	0.0534441	+	0.0388294i
$742$	3.82864	+	11.7833i	0.140554	+	0.432580i
$743$	24.9951			0.916983			0.458492	−	0.888699i	$-0.348390\pi$
$743$	24.9951			0.916983			0.458492	+	0.888699i	$0.348390\pi$
$744$	1.45154	+	4.46738i	0.0532160	+	0.163782i
$745$	15.0500	−	14.4509i	0.551390	−	0.529440i
$746$	8.45779	−	26.0304i	0.309662	−	0.953041i
$747$	0.367326	−	1.13051i	0.0134397	−	0.0413633i
$748$	−0.787267	+	0.571983i	−0.0287853	+	0.0209138i
$749$	−18.8308			−0.688064
$750$	−2.51452	+	4.27049i	−0.0918175	+	0.155936i
$751$	20.6373			0.753065			0.376532	−	0.926404i	$-0.377116\pi$
$751$	20.6373			0.753065			0.376532	+	0.926404i	$0.377116\pi$
$752$	29.2237	−	21.2323i	1.06568	−	0.774262i
$753$	1.06637	−	3.28195i	0.0388606	−	0.119601i
$754$	−11.9820	+	36.8768i	−0.436359	+	1.34298i
$755$	36.8025	−	35.3375i	1.33938	−	1.28606i
$756$	−0.357290	−	1.09962i	−0.0129945	−	0.0399930i
$757$	−6.69127			−0.243198			−0.121599	−	0.992579i	$-0.538802\pi$
$757$	−6.69127			−0.243198			−0.121599	+	0.992579i	$0.538802\pi$
$758$	−6.39425	−	19.6795i	−0.232250	−	0.714791i
$759$	−3.21309	−	2.33445i	−0.116628	−	0.0847352i
$760$	−2.32155	+	12.9501i	−0.0842114	+	0.469749i
$761$	28.1733	−	20.4691i	1.02128	−	0.742004i	0.0547358	−	0.998501i	$-0.482568\pi$
$761$	28.1733	−	20.4691i	1.02128	−	0.742004i	0.966545	+	0.256497i	$0.0825683\pi$
$762$	2.28969	+	1.66356i	0.0829468	+	0.0602644i
$763$	29.2294	+	21.2364i	1.05818	+	0.768810i
$764$	3.97547	−	2.88835i	0.143828	−	0.104497i
$765$	−2.84102	−	5.86736i	−0.102717	−	0.212135i
$766$	−9.57700	−	6.95810i	−0.346031	−	0.251406i
$767$	9.37032	+	28.8389i	0.338343	+	1.04131i
$768$	−2.19294			−0.0791308
$769$	−12.8602	−	39.5797i	−0.463751	−	1.42728i	−0.860546	−	0.509372i	$-0.829878\pi$
$769$	−12.8602	−	39.5797i	−0.463751	−	1.42728i	0.396795	−	0.917907i	$-0.370122\pi$
$770$	9.36380	+	19.3384i	0.337448	+	0.696908i
$771$	−1.46756	+	4.51668i	−0.0528528	+	0.162664i
$772$	0.514481	−	1.58341i	0.0185166	−	0.0569881i
$773$	−29.8563	+	21.6919i	−1.07386	+	0.780202i	−0.976601	−	0.215058i	$-0.931006\pi$
$773$	−29.8563	+	21.6919i	−1.07386	+	0.780202i	−0.0972543	+	0.995260i	$0.531006\pi$
$774$	3.23916			0.116429
$775$	−30.4029	+	8.53052i	−1.09210	+	0.306425i
$776$	−3.65765			−0.131302
$777$	2.65134	−	1.92631i	0.0951163	−	0.0691061i
$778$	0.571582	−	1.75915i	0.0204922	−	0.0630685i
$779$	−0.0120467	+	0.0370759i	−0.000431618	+	0.00132838i
$780$	−0.496079	−	0.265587i	−0.0177625	−	0.00950955i
$781$	6.73919	+	20.7411i	0.241147	+	0.742175i
$782$	6.88469			0.246196
$783$	−5.03635	−	15.5003i	−0.179985	−	0.553936i
$784$	−9.71865	−	7.06101i	−0.347095	−	0.252179i
$785$	−9.02686	+	8.66753i	−0.322183	+	0.309357i
$786$	−3.82546	+	2.77936i	−0.136450	+	0.0991366i
$787$	−8.50453	−	6.17890i	−0.303154	−	0.220254i	0.425800	−	0.904817i	$-0.359993\pi$
$787$	−8.50453	−	6.17890i	−0.303154	−	0.220254i	−0.728953	+	0.684563i	$0.759993\pi$
$788$	−5.41246	−	3.93238i	−0.192811	−	0.140085i
$789$	2.81360	−	2.04420i	0.100167	−	0.0727754i
$790$	−44.8620	−	24.0179i	−1.59612	−	0.854519i
$791$	10.1079	+	7.34381i	0.359395	+	0.261116i
$792$	−6.96124	−	21.4245i	−0.247357	−	0.761286i
$793$	15.1825			0.539148
$794$	−13.3123	−	40.9711i	−0.472436	−	1.45401i
$795$	−2.51080	+	0.345571i	−0.0890489	+	0.0122561i
$796$	−2.41765	+	7.44076i	−0.0856913	+	0.263731i
$797$	8.51707	−	26.2128i	0.301690	−	0.928507i	−0.679202	−	0.733952i	$-0.737674\pi$
$797$	8.51707	−	26.2128i	0.301690	−	0.928507i	0.980892	−	0.194555i	$-0.0623262\pi$
$798$	−1.72189	+	1.25103i	−0.0609542	+	0.0442858i
$799$	7.95592			0.281460
$800$	0.366357	−	9.01634i	0.0129527	−	0.318776i
$801$	−6.24681			−0.220720
$802$	−24.8287	+	18.0391i	−0.876734	+	0.636984i
$803$	−13.3706	+	41.1506i	−0.471839	+	1.45217i
$804$	−0.00952562	+	0.0293168i	−0.000335943	+	0.00103393i
$805$	3.71986	−	20.7502i	0.131108	−	0.731347i
$806$	−7.98923	−	24.5883i	−0.281408	−	0.866086i
$807$	−1.56324			−0.0550285
$808$	7.23480	+	22.2664i	0.254519	+	0.783330i
$809$	−27.0831	−	19.6771i	−0.952192	−	0.691808i	−0.000868085	−	1.00000i	$-0.500276\pi$
$809$	−27.0831	−	19.6771i	−0.952192	−	0.691808i	−0.951324	+	0.308191i	$0.900276\pi$
$810$	−27.8334	+	3.83081i	−0.977965	+	0.134601i
$811$	13.7826	−	10.0136i	0.483972	−	0.351626i	−0.318889	−	0.947792i	$-0.603310\pi$
$811$	13.7826	−	10.0136i	0.483972	−	0.351626i	0.802861	+	0.596166i	$0.203310\pi$
$812$	−5.14887	−	3.74087i	−0.180690	−	0.131279i
$813$	5.95749	+	4.32837i	0.208938	+	0.151803i
$814$	−20.1144	+	14.6140i	−0.705009	+	0.512219i
$815$	−11.0156	+	1.51612i	−0.385861	+	0.0531075i
$816$	−1.06849	−	0.776305i	−0.0374047	−	0.0271761i
$817$	−0.518468	−	1.59568i	−0.0181389	−	0.0558258i
$818$	−1.43813			−0.0502829
$819$	−5.05035	−	15.5434i	−0.176473	−	0.543129i
$820$	0.00215252	−	0.0120072i	7.51693e−5	−	0.000419310i
$821$	13.5672	−	41.7557i	0.473500	−	1.45728i	−0.374470	−	0.927239i	$-0.622175\pi$
$821$	13.5672	−	41.7557i	0.473500	−	1.45728i	0.847970	−	0.530044i	$-0.177825\pi$
$822$	−2.54222	+	7.82414i	−0.0886700	+	0.272898i
$823$	−2.35916	+	1.71403i	−0.0822350	+	0.0597472i	−0.628143	−	0.778098i	$-0.716185\pi$
$823$	−2.35916	+	1.71403i	−0.0822350	+	0.0597472i	0.545908	+	0.837845i	$0.316185\pi$
$824$	8.37005			0.291585
$825$	−4.23183	+	1.18738i	−0.147333	+	0.0413392i
$826$	−35.8896			−1.24876
$827$	29.4766	−	21.4160i	1.02500	−	0.744706i	0.0576984	−	0.998334i	$-0.481624\pi$
$827$	29.4766	−	21.4160i	1.02500	−	0.744706i	0.967302	+	0.253628i	$0.0816238\pi$
$828$	1.31071	−	4.03395i	0.0455503	−	0.140189i
$829$	12.2975	−	37.8479i	0.427111	−	1.31451i	−0.473847	−	0.880607i	$-0.657135\pi$
$829$	12.2975	−	37.8479i	0.427111	−	1.31451i	0.900958	−	0.433905i	$-0.142865\pi$
$830$	1.37631	−	0.189427i	0.0477724	−	0.00657510i
$831$	−2.30324	−	7.08866i	−0.0798987	−	0.245903i
$832$	−17.0071			−0.589617
$833$	−0.817603	−	2.51632i	−0.0283283	−	0.0871855i
$834$	6.18377	+	4.49278i	0.214127	+	0.155572i
$835$	−6.75371	−	3.61576i	−0.233722	−	0.125128i
$836$	1.81158	−	1.31619i	0.0626548	−	0.0455214i
$837$	8.79157	+	6.38745i	0.303881	+	0.220783i
$838$	6.74497	+	4.90051i	0.233001	+	0.169285i
$839$	21.9172	−	15.9238i	0.756667	−	0.549751i	−0.141219	−	0.989978i	$-0.545102\pi$
$839$	21.9172	−	15.9238i	0.756667	−	0.549751i	0.897886	+	0.440227i	$0.145102\pi$
$840$	−2.50329	+	2.40364i	−0.0863717	+	0.0829335i
$841$	−49.1170	−	35.6856i	−1.69369	−	1.23054i
$842$	−8.70594	−	26.7941i	−0.300026	−	0.923386i
$843$	0.326866			0.0112579
$844$	−2.05632	−	6.32869i	−0.0707813	−	0.217842i
$845$	11.3995	+	6.10296i	0.392153	+	0.209948i
$846$	10.9220	−	33.6144i	0.375505	−	1.15569i
$847$	1.20438	−	3.70670i	0.0413829	−	0.127364i
$848$	14.3127	−	10.3988i	0.491501	−	0.357096i
$849$	1.36490			0.0468433
$850$	4.72494	−	5.97707i	0.162064	−	0.205012i
$851$	24.3939			0.836212
$852$	0.546886	−	0.397336i	0.0187360	−	0.0136125i
$853$	−16.1863	+	49.8163i	−0.554208	+	1.70568i	0.143817	+	0.989604i	$0.454062\pi$
$853$	−16.1863	+	49.8163i	−0.554208	+	1.70568i	−0.698026	+	0.716073i	$0.745938\pi$
$854$	−5.55294	+	17.0902i	−0.190018	+	0.584814i
$855$	6.53747	+	13.5014i	0.223577	+	0.461738i
$856$	7.13049	+	21.9454i	0.243715	+	0.750078i
$857$	−12.8454			−0.438792			−0.219396	−	0.975636i	$-0.570409\pi$
$857$	−12.8454			−0.438792			−0.219396	+	0.975636i	$0.570409\pi$
$858$	−1.11203	−	3.42249i	−0.0379642	−	0.116842i
$859$	14.7381	+	10.7079i	0.502858	+	0.365348i	0.810108	−	0.586281i	$-0.199409\pi$
$859$	14.7381	+	10.7079i	0.502858	+	0.365348i	−0.307250	+	0.951629i	$0.599409\pi$
$860$	0.228801	+	0.472527i	0.00780206	+	0.0161131i
$861$	−0.00831930	+	0.00604432i	−0.000283521	+	0.000205990i
$862$	−21.7836	−	15.8267i	−0.741952	−	0.539060i
$863$	32.1165	+	23.3340i	1.09326	+	0.794299i	0.979946	−	0.199261i	$-0.0638541\pi$
$863$	32.1165	+	23.3340i	1.09326	+	0.794299i	0.113312	+	0.993559i	$0.463854\pi$
$864$	−2.51238	+	1.82535i	−0.0854729	+	0.0620997i
$865$	2.49749	−	13.9316i	0.0849174	−	0.473687i
$866$	−28.3254	−	20.5796i	−0.962536	−	0.699323i
$867$	−0.0898893	−	0.276651i	−0.00305280	−	0.00939556i
$868$	4.24355			0.144036
$869$	−13.9462	−	42.9221i	−0.473094	−	1.45603i
$870$	6.77166	−	6.50210i	0.229581	−	0.220442i
$871$	−0.273200	+	0.840824i	−0.00925703	+	0.0284902i
$872$	13.6808	−	42.1053i	0.463291	−	1.42586i
$873$	−3.37393	+	2.45130i	−0.114190	+	0.0829639i
$874$	−15.8424			−0.535876
$875$	−15.4617	−	17.4702i	−0.522700	−	0.590601i
$876$	1.34117			0.0453139
$877$	10.6515	−	7.73876i	0.359675	−	0.261319i	−0.393241	−	0.919435i	$-0.628646\pi$
$877$	10.6515	−	7.73876i	0.359675	−	0.261319i	0.752917	+	0.658116i	$0.228646\pi$
$878$	0.879020	−	2.70535i	0.0296655	−	0.0913010i
$879$	2.70484	−	8.32463i	0.0912318	−	0.280783i
$880$	22.1303	−	21.2494i	0.746013	−	0.716316i
$881$	5.72346	+	17.6150i	0.192828	+	0.593464i	0.999995	+	0.00314066i	$0.000999706\pi$
$881$	5.72346	+	17.6150i	0.192828	+	0.593464i	−0.807167	+	0.590323i	$0.799000\pi$
$882$	−11.7541			−0.395780
$883$	−4.45810	−	13.7206i	−0.150027	−	0.461736i	0.847596	−	0.530642i	$-0.178049\pi$
$883$	−4.45810	−	13.7206i	−0.150027	−	0.461736i	−0.997623	+	0.0689061i	$0.978049\pi$
$884$	0.699880	+	0.508493i	0.0235395	+	0.0171025i
$885$	1.29548	−	7.22644i	0.0435470	−	0.242914i
$886$	−23.1059	+	16.7874i	−0.776258	+	0.563985i
$887$	−0.150702	−	0.109491i	−0.00506007	−	0.00367636i	0.585252	−	0.810851i	$-0.300995\pi$
$887$	−0.150702	−	0.109491i	−0.00506007	−	0.00367636i	−0.590312	+	0.807175i	$0.700995\pi$
$888$	−3.24887	−	2.36045i	−0.109025	−	0.0792114i
$889$	−10.7788	+	7.83128i	−0.361511	+	0.262653i
$890$	−3.18180	−	6.57116i	−0.106654	−	0.220266i
$891$	−20.1590	−	14.6464i	−0.675352	−	0.490672i
$892$	−0.915067	−	2.81629i	−0.0306387	−	0.0942963i
$893$	−18.3074			−0.612633
$894$	−1.27810	−	3.93360i	−0.0427462	−	0.131559i
$895$	2.31178	+	4.77436i	0.0772743	+	0.159589i
$896$	8.54775	−	26.3073i	0.285560	−	0.878864i
$897$	−1.09106	+	3.35795i	−0.0364295	+	0.112119i
$898$	−13.2675	+	9.63938i	−0.442741	+	0.321670i
$899$	59.8171			1.99501
$900$	−2.60261	−	3.90640i	−0.0867536	−	0.130213i
$901$	3.89652			0.129812
$902$	0.0631143	−	0.0458553i	0.00210148	−	0.00152681i
$903$	0.136762	−	0.420910i	0.00455115	−	0.0140070i
$904$	4.73099	−	14.5605i	0.157350	−	0.484275i
$905$	20.0962	+	10.7590i	0.668020	+	0.357640i
$906$	−3.12540	−	9.61900i	−0.103835	−	0.319570i
$907$	18.9891			0.630524			0.315262	−	0.949005i	$-0.397908\pi$
$907$	18.9891			0.630524			0.315262	+	0.949005i	$0.397908\pi$
$908$	−1.72900	−	5.32132i	−0.0573789	−	0.176594i
$909$	21.5962	+	15.6905i	0.716300	+	0.520422i
$910$	13.7780	−	13.2296i	0.456737	−	0.438556i
$911$	−11.5366	+	8.38184i	−0.382225	+	0.277703i	−0.762262	−	0.647268i	$-0.775911\pi$
$911$	−11.5366	+	8.38184i	−0.382225	+	0.277703i	0.380037	+	0.924971i	$0.375911\pi$
$912$	2.45871	+	1.78636i	0.0814160	+	0.0591522i
$913$	0.996825	+	0.724236i	0.0329901	+	0.0239687i
$914$	−35.2075	+	25.5797i	−1.16456	+	0.846103i
$915$	−3.24071	−	1.73499i	−0.107134	−	0.0573569i
$916$	3.78977	+	2.75343i	0.125218	+	0.0909759i
$917$	−6.87866	−	21.1703i	−0.227153	−	0.699106i
$918$	−2.62205			−0.0865406
$919$	6.33744	+	19.5046i	0.209053	+	0.643398i	0.999523	+	0.0308974i	$0.00983650\pi$
$919$	6.33744	+	19.5046i	0.209053	+	0.643398i	−0.790470	+	0.612501i	$0.790163\pi$
$920$	−25.5907	+	3.52215i	−0.843701	+	0.116122i
$921$	1.10114	−	3.38895i	0.0362837	−	0.111670i
$922$	−1.67632	+	5.15919i	−0.0552067	+	0.169909i
$923$	15.6850	−	11.3958i	0.516278	−	0.375098i
$924$	0.590668			0.0194315
$925$	16.7414	−	21.1780i	0.550455	−	0.696328i
$926$	−55.9110			−1.83735
$927$	7.72078	−	5.60947i	0.253584	−	0.184239i
$928$	−5.28234	+	16.2574i	−0.173401	+	0.533674i
$929$	8.21276	−	25.2763i	0.269452	−	0.829288i	−0.721182	−	0.692745i	$-0.756401\pi$
$929$	8.21276	−	25.2763i	0.269452	−	0.829288i	0.990634	−	0.136542i	$-0.0435990\pi$
$930$	−1.10454	+	6.16133i	−0.0362191	+	0.202038i
$931$	1.88139	+	5.79032i	0.0616600	+	0.189770i
$932$	7.93732			0.259995
$933$	−2.56593	−	7.89711i	−0.0840047	−	0.258540i
$934$	−25.7566	−	18.7132i	−0.842781	−	0.612316i
$935$	6.69419	−	0.921347i	0.218923	−	0.0301313i
$936$	−16.2018	+	11.7713i	−0.529573	+	0.384757i
$937$	23.7835	+	17.2798i	0.776974	+	0.564505i	0.904069	−	0.427386i	$-0.140565\pi$
$937$	23.7835	+	17.2798i	0.776974	+	0.564505i	−0.127095	+	0.991891i	$0.540565\pi$
$938$	−0.846549	−	0.615054i	−0.0276408	−	0.0200822i
$939$	4.79964	−	3.48714i	0.156630	−	0.113799i
$940$	5.67514	−	0.781091i	0.185103	−	0.0254764i
$941$	−36.0424	−	26.1864i	−1.17495	−	0.853651i	−0.183357	−	0.983046i	$-0.558696\pi$
$941$	−36.0424	−	26.1864i	−1.17495	−	0.853651i	−0.991593	+	0.129395i	$0.958696\pi$
$942$	0.766595	+	2.35934i	0.0249770	+	0.0768713i
$943$	−0.0765424			−0.00249256
$944$	15.8363	+	48.7390i	0.515427	+	1.58632i
$945$	−1.41672	+	7.90275i	−0.0460858	+	0.257076i
$946$	−1.03754	+	3.19323i	−0.0337335	+	0.103821i
$947$	17.4879	−	53.8223i	0.568281	−	1.74899i	−0.0897152	−	0.995967i	$-0.528596\pi$
$947$	17.4879	−	53.8223i	0.568281	−	1.74899i	0.657996	−	0.753021i	$-0.271404\pi$
$948$	−1.13174	+	0.822257i	−0.0367572	+	0.0267057i
$949$	38.4655			1.24864
$950$	−10.8726	+	13.7538i	−0.352753	+	0.446233i
$951$	−7.46575			−0.242094
$952$	4.31650	−	3.13612i	0.139898	−	0.101642i
$953$	−14.1271	+	43.4789i	−0.457623	+	1.40842i	0.410405	+	0.911903i	$0.365387\pi$
$953$	−14.1271	+	43.4789i	−0.457623	+	1.40842i	−0.868028	+	0.496515i	$0.834613\pi$
$954$	5.34918	−	16.4631i	0.173186	−	0.533012i
$955$	−33.8038	+	4.65254i	−1.09386	+	0.150553i
$956$	0.144680	+	0.445278i	0.00467927	+	0.0144013i
$957$	8.32605			0.269143
$958$	5.02607	+	15.4687i	0.162385	+	0.499770i
$959$	−31.3316	−	22.7637i	−1.01175	−	0.735080i
$960$	3.63017	+	1.94349i	0.117163	+	0.0627260i
$961$	−7.18742	+	5.22196i	−0.231852	+	0.168450i
$962$	17.8817	+	12.9918i	0.576529	+	0.418873i
$963$	21.2848	+	15.4643i	0.685894	+	0.498331i
$964$	2.09217	−	1.52005i	0.0673841	−	0.0489574i
$965$	−8.33916	+	8.00720i	−0.268447	+	0.257761i
$966$	−3.38081	−	2.45630i	−0.108776	−	0.0790303i
$967$	5.50840	+	16.9531i	0.177138	+	0.545176i	0.999725	−	0.0234646i	$-0.00746969\pi$
$967$	5.50840	+	16.9531i	0.177138	+	0.545176i	−0.822586	+	0.568640i	$0.807470\pi$
$968$	−4.77582			−0.153501
$969$	0.206844	+	0.636602i	0.00664480	+	0.0204506i
$970$	−4.29708	−	2.30054i	−0.137971	−	0.0738659i
$971$	−3.36418	+	10.3539i	−0.107962	+	0.332272i	−0.990414	−	0.138130i	$-0.955891\pi$
$971$	−3.36418	+	10.3539i	−0.107962	+	0.332272i	0.882453	+	0.470401i	$0.155891\pi$
$972$	−0.752351	+	2.31550i	−0.0241317	+	0.0742696i
$973$	−29.1104	+	21.1500i	−0.933237	+	0.678037i
$974$	−59.8936			−1.91912
$975$	2.16647	+	3.25177i	0.0693825	+	0.104140i
$976$	25.6592			0.821330
$977$	18.5654	−	13.4885i	0.593958	−	0.431536i	−0.249771	−	0.968305i	$-0.580355\pi$
$977$	18.5654	−	13.4885i	0.593958	−	0.431536i	0.843729	+	0.536769i	$0.180355\pi$
$978$	−0.681146	+	2.09635i	−0.0217806	+	0.0670339i
$979$	2.00093	−	6.15824i	0.0639501	−	0.196818i
$980$	−0.830262	−	1.71468i	−0.0265217	−	0.0547735i
$981$	−15.5987	−	48.0078i	−0.498027	−	1.53277i
$982$	66.1550			2.11109
$983$	−11.2005	−	34.4716i	−0.357240	−	1.09947i	−0.954699	−	0.297573i	$-0.903823\pi$
$983$	−11.2005	−	34.4716i	−0.357240	−	1.09947i	0.597459	−	0.801900i	$-0.296177\pi$
$984$	0.0101942	+	0.00740653i	0.000324980	+	0.000236112i
$985$	20.2460	+	41.8127i	0.645091	+	1.33226i
$986$	−11.6766	+	8.48352i	−0.371858	+	0.270170i
$987$	−3.90685	−	2.83849i	−0.124356	−	0.0903502i
$988$	−1.61050	−	1.17009i	−0.0512367	−	0.0372256i
$989$	2.66510	−	1.93631i	0.0847452	−	0.0615710i
$990$	5.29709	−	29.5483i	0.168353	−	0.939107i
$991$	−10.4610	−	7.60036i	−0.332304	−	0.241433i	0.409103	−	0.912488i	$-0.365842\pi$
$991$	−10.4610	−	7.60036i	−0.332304	−	0.241433i	−0.741408	+	0.671055i	$0.765842\pi$
$992$	−3.52210	−	10.8399i	−0.111827	−	0.344167i
$993$	−2.09875			−0.0666018
$994$	7.09097	+	21.8237i	0.224912	+	0.692207i
$995$	39.1874	−	37.6275i	1.24232	−	1.19287i
$996$	0.0118021	−	0.0363230i	0.000373963	−	0.00115094i
$997$	2.31427	−	7.12258i	0.0732935	−	0.225574i	−0.907698	−	0.419623i	$-0.862162\pi$
$997$	2.31427	−	7.12258i	0.0732935	−	0.225574i	0.980992	+	0.194049i	$0.0621621\pi$
$998$	39.3973	−	28.6238i	1.24710	−	0.906071i
$999$	−9.29047			−0.293937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.15	✓	76
25.16	even	5	inner	425.2.k.b.341.15	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.15	✓	76	1.1	even	1	trivial
425.2.k.b.341.15	yes	76	25.16	even	5	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23279 - 0.895677i) q^{2} +(-0.0898893 + 0.276651i) q^{3} +(0.0995081 - 0.306255i) q^{4} +(-1.61292 + 1.54871i) q^{5} +(0.136975 + 0.421565i) q^{6} -2.08667 q^{7} +(0.790138 + 2.43179i) q^{8} +(2.35860 + 1.71362i) q^{9} +(-0.601248 + 3.35389i) q^{10} +(-2.44481 + 1.77626i) q^{11} +(0.0757809 + 0.0550580i) q^{12} +(2.17344 + 1.57910i) q^{13} +(-2.57243 + 1.86898i) q^{14} +(-0.283468 - 0.585427i) q^{15} +(3.67321 + 2.66874i) q^{16} +(0.309017 + 0.951057i) q^{17} +4.44251 q^{18} +(-0.711080 - 2.18848i) q^{19} +(0.313801 + 0.648072i) q^{20} +(0.187569 - 0.577278i) q^{21} +(-1.42299 + 4.37952i) q^{22} +(3.65519 - 2.65565i) q^{23} -0.743783 q^{24} +(0.202995 - 4.99588i) q^{25} +4.09376 q^{26} +(-1.39209 + 1.01141i) q^{27} +(-0.207640 + 0.639051i) q^{28} +(-2.92690 + 9.00806i) q^{29} +(-0.873811 - 0.467815i) q^{30} +(-1.95156 - 6.00629i) q^{31} +1.80476 q^{32} +(-0.271642 - 0.836027i) q^{33} +(1.23279 + 0.895677i) q^{34} +(3.36562 - 3.23164i) q^{35} +(0.759503 - 0.551811i) q^{36} +(4.36804 + 3.17357i) q^{37} +(-2.83678 - 2.06104i) q^{38} +(-0.632227 + 0.459340i) q^{39} +(-5.04057 - 2.69859i) q^{40} +(-0.0137059 - 0.00995792i) q^{41} +(-0.285821 - 0.879666i) q^{42} +0.729128 q^{43} +(0.300709 + 0.925488i) q^{44} +(-6.45812 + 0.888855i) q^{45} +(2.12749 - 6.54773i) q^{46} +(2.45851 - 7.56653i) q^{47} +(-1.06849 + 0.776305i) q^{48} -2.64582 q^{49} +(-4.22444 - 6.34070i) q^{50} -0.290888 q^{51} +(0.699880 - 0.508493i) q^{52} +(1.20409 - 3.70581i) q^{53} +(-0.810259 + 2.49372i) q^{54} +(1.19237 - 6.65127i) q^{55} +(-1.64875 - 5.07435i) q^{56} +0.669363 q^{57} +(4.46005 + 13.7266i) q^{58} +(9.13146 + 6.63439i) q^{59} +(-0.207497 + 0.0285586i) q^{60} +(4.57206 - 3.32180i) q^{61} +(-7.78557 - 5.65655i) q^{62} +(-4.92160 - 3.57575i) q^{63} +(-5.12153 + 3.72101i) q^{64} +(-5.95113 + 0.819078i) q^{65} +(-1.08369 - 0.787345i) q^{66} +(0.101693 + 0.312979i) q^{67} +0.322015 q^{68} +(0.406125 + 1.24993i) q^{69} +(1.25460 - 6.99845i) q^{70} +(2.23008 - 6.86347i) q^{71} +(-2.30356 + 7.08962i) q^{72} +(11.5835 - 8.41589i) q^{73} +8.22738 q^{74} +(1.36387 + 0.505235i) q^{75} -0.740989 q^{76} +(5.10151 - 3.70646i) q^{77} +(-0.367985 + 1.13254i) q^{78} +(-4.61497 + 14.2034i) q^{79} +(-10.0577 + 1.38428i) q^{80} +(2.54804 + 7.84205i) q^{81} -0.0258156 q^{82} +(-0.125996 - 0.387775i) q^{83} +(-0.158129 - 0.114888i) q^{84} +(-1.97133 - 1.05540i) q^{85} +(0.898864 - 0.653063i) q^{86} +(-2.22899 - 1.61946i) q^{87} +(-6.25124 - 4.54179i) q^{88} +(-1.73348 + 1.25945i) q^{89} +(-7.16539 + 6.88016i) q^{90} +(-4.53524 - 3.29505i) q^{91} +(-0.449584 - 1.38368i) q^{92} +1.83707 q^{93} +(-3.74632 - 11.5300i) q^{94} +(4.53623 + 2.42857i) q^{95} +(-0.162228 + 0.499288i) q^{96} +(-0.442043 + 1.36047i) q^{97} +(-3.26175 + 2.36980i) q^{98} -8.81016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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