LMFDB - Embedded newform 185.2.u.a.23.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(8,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.u (of order $12$, degree $4$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	185.23
Dual form			185.2.u.a.177.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0909942 - 0.0525355i) q^{2} +(1.93607 + 0.518767i) q^{3} +(-0.994480 - 1.72249i) q^{4} +(-1.78938 - 1.34094i) q^{5} +(-0.148917 - 0.148917i) q^{6} +(4.36283 + 1.16902i) q^{7} +0.419124i q^{8} +(0.881153 + 0.508734i) q^{9} +(0.0923757 + 0.216024i) q^{10} -2.44344i q^{11} +(-1.03181 - 3.85076i) q^{12} +(4.02259 - 2.32245i) q^{13} +(-0.335578 - 0.335578i) q^{14} +(-2.76871 - 3.52442i) q^{15} +(-1.96694 + 3.40684i) q^{16} +(-3.81936 + 6.61533i) q^{17} +(-0.0534532 - 0.0925836i) q^{18} +(-1.19934 - 0.321362i) q^{19} +(-0.530263 + 4.41573i) q^{20} +(7.84028 + 4.52659i) q^{21} +(-0.128367 + 0.222339i) q^{22} -0.150193i q^{23} +(-0.217428 + 0.811452i) q^{24} +(1.40374 + 4.79891i) q^{25} -0.488044 q^{26} +(-2.80984 - 2.80984i) q^{27} +(-2.32513 - 8.67750i) q^{28} +(0.503427 + 0.503427i) q^{29} +(0.0667793 + 0.466158i) q^{30} +(-5.31753 + 5.31753i) q^{31} +(1.08391 - 0.625793i) q^{32} +(1.26757 - 4.73065i) q^{33} +(0.695080 - 0.401304i) q^{34} +(-6.23917 - 7.94213i) q^{35} -2.02370i q^{36} +(-2.33845 + 5.61531i) q^{37} +(0.0922501 + 0.0922501i) q^{38} +(8.99281 - 2.40962i) q^{39} +(0.562022 - 0.749971i) q^{40} +(4.77325 - 2.75584i) q^{41} +(-0.475614 - 0.823787i) q^{42} +1.79435i q^{43} +(-4.20880 + 2.42995i) q^{44} +(-0.894531 - 2.09189i) q^{45} +(-0.00789049 + 0.0136667i) q^{46} +(1.65421 - 1.65421i) q^{47} +(-5.57548 + 5.57548i) q^{48} +(11.6055 + 6.70046i) q^{49} +(0.124381 - 0.510419i) q^{50} +(-10.8263 + 10.8263i) q^{51} +(-8.00078 - 4.61925i) q^{52} +(-11.3222 + 3.03376i) q^{53} +(0.108063 + 0.403296i) q^{54} +(-3.27651 + 4.37223i) q^{55} +(-0.489964 + 1.82857i) q^{56} +(-2.15529 - 1.24436i) q^{57} +(-0.0193611 - 0.0722567i) q^{58} +(-0.0783231 - 0.292306i) q^{59} +(-3.31736 + 8.27405i) q^{60} +(-2.65533 - 0.711494i) q^{61} +(0.763224 - 0.204505i) q^{62} +(3.24960 + 3.24960i) q^{63} +7.73626 q^{64} +(-10.3122 - 1.23834i) q^{65} +(-0.363869 + 0.363869i) q^{66} +(3.29741 - 12.3061i) q^{67} +15.1931 q^{68} +(0.0779154 - 0.290784i) q^{69} +(0.150484 + 1.05047i) q^{70} +(5.25961 + 9.10991i) q^{71} +(-0.213223 + 0.369312i) q^{72} +(6.35187 - 6.35187i) q^{73} +(0.507788 - 0.388109i) q^{74} +(0.228216 + 10.0192i) q^{75} +(0.639177 + 2.38544i) q^{76} +(2.85642 - 10.6603i) q^{77} +(-0.944884 - 0.253181i) q^{78} +(-4.95543 - 1.32780i) q^{79} +(8.08798 - 3.45857i) q^{80} +(-5.50858 - 9.54114i) q^{81} -0.579117 q^{82} +(0.883111 - 0.236629i) q^{83} -18.0064i q^{84} +(15.7051 - 6.71577i) q^{85} +(0.0942673 - 0.163276i) q^{86} +(0.713506 + 1.23583i) q^{87} +1.02410 q^{88} +(-7.43872 + 1.99320i) q^{89} +(-0.0285015 + 0.237345i) q^{90} +(20.2649 - 5.42996i) q^{91} +(-0.258707 + 0.149364i) q^{92} +(-13.0536 + 7.53653i) q^{93} +(-0.237428 + 0.0636187i) q^{94} +(1.71514 + 2.18329i) q^{95} +(2.42315 - 0.649281i) q^{96} +1.75339 q^{97} +(-0.704025 - 1.21941i) q^{98} +(1.24306 - 2.15304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0909942	−	0.0525355i	−0.0643426	−	0.0371482i	0.467484	−	0.884002i	$-0.345161\pi$
$2$	−0.0909942	−	0.0525355i	−0.0643426	−	0.0371482i	−0.531826	+	0.846854i	$0.678494\pi$
$3$	1.93607	+	0.518767i	1.11779	+	0.299510i	0.769988	−	0.638059i	$-0.220262\pi$
$3$	1.93607	+	0.518767i	1.11779	+	0.299510i	0.347800	+	0.937569i	$0.386929\pi$
$4$	−0.994480	−	1.72249i	−0.497240	−	0.861245i
$5$	−1.78938	−	1.34094i	−0.800234	−	0.599688i
$5$	−1.78938	−	1.34094i	−0.800234	−	0.599688i
$6$	−0.148917	−	0.148917i	−0.0607951	−	0.0607951i
$7$	4.36283	+	1.16902i	1.64900	+	0.441847i	0.959332	−	0.282282i	$-0.0910912\pi$
$7$	4.36283	+	1.16902i	1.64900	+	0.441847i	0.689665	+	0.724129i	$0.257758\pi$
$8$			0.419124i			0.148183i
$9$	0.881153	+	0.508734i	0.293718	+	0.169578i
$10$	0.0923757	+	0.216024i	0.0292118	+	0.0683128i
$11$		−	2.44344i		−	0.736724i	−0.929682	−	0.368362i	$-0.879919\pi$
$11$		−	2.44344i		−	0.736724i	0.929682	−	0.368362i	$-0.120081\pi$
$12$	−1.03181	−	3.85076i	−0.297857	−	1.11162i
$13$	4.02259	−	2.32245i	1.11567	−	0.644131i	0.175376	−	0.984502i	$-0.443886\pi$
$13$	4.02259	−	2.32245i	1.11567	−	0.644131i	0.940291	+	0.340371i	$0.110553\pi$
$14$	−0.335578	−	0.335578i	−0.0896869	−	0.0896869i
$15$	−2.76871	−	3.52442i	−0.714879	−	0.910002i
$16$	−1.96694	+	3.40684i	−0.491735	+	0.851711i
$17$	−3.81936	+	6.61533i	−0.926331	+	1.60445i	−0.136925	+	0.990581i	$0.543722\pi$
$17$	−3.81936	+	6.61533i	−0.926331	+	1.60445i	−0.789406	+	0.613871i	$0.789611\pi$
$18$	−0.0534532	−	0.0925836i	−0.0125990	−	0.0218222i
$19$	−1.19934	−	0.321362i	−0.275148	−	0.0737256i	0.118607	−	0.992941i	$-0.462157\pi$
$19$	−1.19934	−	0.321362i	−0.275148	−	0.0737256i	−0.393754	+	0.919216i	$0.628824\pi$
$20$	−0.530263	+	4.41573i	−0.118570	+	0.987386i
$21$	7.84028	+	4.52659i	1.71089	+	0.987783i
$22$	−0.128367	+	0.222339i	−0.0273680	+	0.0474028i
$23$		−	0.150193i		−	0.0313175i	−0.999877	−	0.0156587i	$-0.995015\pi$
$23$		−	0.150193i		−	0.0313175i	0.999877	−	0.0156587i	$-0.00498454\pi$
$24$	−0.217428	+	0.811452i	−0.0443823	+	0.165637i
$25$	1.40374	+	4.79891i	0.280748	+	0.959782i
$26$	−0.488044			−0.0957132
$27$	−2.80984	−	2.80984i	−0.540754	−	0.540754i
$28$	−2.32513	−	8.67750i	−0.439408	−	1.63989i
$29$	0.503427	+	0.503427i	0.0934840	+	0.0934840i	0.752302	−	0.658818i	$-0.228943\pi$
$29$	0.503427	+	0.503427i	0.0934840	+	0.0934840i	−0.658818	+	0.752302i	$0.728943\pi$
$30$	0.0667793	+	0.466158i	0.0121922	+	0.0851084i
$31$	−5.31753	+	5.31753i	−0.955057	+	0.955057i	−0.999033	−	0.0439759i	$-0.985998\pi$
$31$	−5.31753	+	5.31753i	−0.955057	+	0.955057i	0.0439759	+	0.999033i	$0.485998\pi$
$32$	1.08391	−	0.625793i	0.191609	−	0.110626i
$33$	1.26757	−	4.73065i	0.220656	−	0.823501i
$34$	0.695080	−	0.401304i	0.119205	−	0.0688231i
$35$	−6.23917	−	7.94213i	−1.05461	−	1.34246i
$36$		−	2.02370i		−	0.337284i
$37$	−2.33845	+	5.61531i	−0.384438	+	0.923151i
$37$	−2.33845	+	5.61531i	−0.384438	+	0.923151i
$38$	0.0922501	+	0.0922501i	0.0149649	+	0.0149649i
$39$	8.99281	−	2.40962i	1.44000	−	0.385847i
$40$	0.562022	−	0.749971i	0.0888635	−	0.118581i
$41$	4.77325	−	2.75584i	0.745456	−	0.430389i	−0.0785937	−	0.996907i	$-0.525043\pi$
$41$	4.77325	−	2.75584i	0.745456	−	0.430389i	0.824050	+	0.566518i	$0.191710\pi$
$42$	−0.475614	−	0.823787i	−0.0733888	−	0.127113i
$43$			1.79435i			0.273636i	0.990596	+	0.136818i	$0.0436876\pi$
$43$			1.79435i			0.273636i	−0.990596	+	0.136818i	$0.956312\pi$
$44$	−4.20880	+	2.42995i	−0.634500	+	0.366329i
$45$	−0.894531	−	2.09189i	−0.133349	−	0.311841i
$46$	−0.00789049	+	0.0136667i	−0.00116339	+	0.00201505i
$47$	1.65421	−	1.65421i	0.241291	−	0.241291i	−0.576093	−	0.817384i	$-0.695423\pi$
$47$	1.65421	−	1.65421i	0.241291	−	0.241291i	0.817384	+	0.576093i	$0.195423\pi$
$48$	−5.57548	+	5.57548i	−0.804752	+	0.804752i
$49$	11.6055	+	6.70046i	1.65793	+	0.957209i
$50$	0.124381	−	0.510419i	0.0175901	−	0.0721841i
$51$	−10.8263	+	10.8263i	−1.51599	+	1.51599i
$52$	−8.00078	−	4.61925i	−1.10951	−	0.640575i
$53$	−11.3222	+	3.03376i	−1.55522	+	0.416720i	−0.931146	−	0.364647i	$-0.881190\pi$
$53$	−11.3222	+	3.03376i	−1.55522	+	0.416720i	−0.624073	+	0.781366i	$0.714523\pi$
$54$	0.108063	+	0.403296i	0.0147055	+	0.0548816i
$55$	−3.27651	+	4.37223i	−0.441805	+	0.589551i
$56$	−0.489964	+	1.82857i	−0.0654742	+	0.244353i
$57$	−2.15529	−	1.24436i	−0.285475	−	0.164819i
$58$	−0.0193611	−	0.0722567i	−0.00254224	−	0.00948777i
$59$	−0.0783231	−	0.292306i	−0.0101968	−	0.0380550i	0.960640	−	0.277796i	$-0.0896040\pi$
$59$	−0.0783231	−	0.292306i	−0.0101968	−	0.0380550i	−0.970837	+	0.239741i	$0.922937\pi$
$60$	−3.31736	+	8.27405i	−0.428269	+	1.06818i
$61$	−2.65533	−	0.711494i	−0.339980	−	0.0910974i	0.0847894	−	0.996399i	$-0.472978\pi$
$61$	−2.65533	−	0.711494i	−0.339980	−	0.0910974i	−0.424770	+	0.905301i	$0.639645\pi$
$62$	0.763224	−	0.204505i	0.0969295	−	0.0259722i
$63$	3.24960	+	3.24960i	0.409412	+	0.409412i
$64$	7.73626			0.967032
$65$	−10.3122	−	1.23834i	−1.27907	−	0.153597i
$66$	−0.363869	+	0.363869i	−0.0447892	+	0.0447892i
$67$	3.29741	−	12.3061i	0.402843	−	1.50343i	−0.405156	−	0.914247i	$-0.632783\pi$
$67$	3.29741	−	12.3061i	0.402843	−	1.50343i	0.807999	−	0.589183i	$-0.200550\pi$
$68$	15.1931			1.84244
$69$	0.0779154	−	0.290784i	0.00937991	−	0.0350063i
$70$	0.150484	+	1.05047i	0.0179863	+	0.125555i
$71$	5.25961	+	9.10991i	0.624201	+	1.08115i	0.988695	+	0.149941i	$0.0479085\pi$
$71$	5.25961	+	9.10991i	0.624201	+	1.08115i	−0.364494	+	0.931206i	$0.618758\pi$
$72$	−0.213223	+	0.369312i	−0.0251285	+	0.0435239i
$73$	6.35187	−	6.35187i	0.743431	−	0.743431i	−0.229806	−	0.973237i	$-0.573809\pi$
$73$	6.35187	−	6.35187i	0.743431	−	0.743431i	0.973237	+	0.229806i	$0.0738091\pi$
$74$	0.507788	−	0.388109i	0.0590292	−	0.0451167i
$75$	0.228216	+	10.0192i	0.0263521	+	1.15692i
$76$	0.639177	+	2.38544i	0.0733186	+	0.273629i
$77$	2.85642	−	10.6603i	0.325519	−	1.21486i
$78$	−0.944884	−	0.253181i	−0.106987	−	0.0286671i
$79$	−4.95543	−	1.32780i	−0.557530	−	0.149390i	−0.0309586	−	0.999521i	$-0.509856\pi$
$79$	−4.95543	−	1.32780i	−0.557530	−	0.149390i	−0.526571	+	0.850131i	$0.676523\pi$
$80$	8.08798	−	3.45857i	0.904264	−	0.386680i
$81$	−5.50858	−	9.54114i	−0.612065	−	1.06013i
$82$	−0.579117			−0.0639528
$83$	0.883111	−	0.236629i	0.0969340	−	0.0259734i	−0.210026	−	0.977696i	$-0.567355\pi$
$83$	0.883111	−	0.236629i	0.0969340	−	0.0259734i	0.306960	+	0.951722i	$0.400688\pi$
$84$		−	18.0064i		−	1.96466i
$85$	15.7051	−	6.71577i	1.70345	−	0.728427i
$86$	0.0942673	−	0.163276i	0.0101651	−	0.0176065i
$87$	0.713506	+	1.23583i	0.0764958	+	0.132495i
$88$	1.02410			0.109170
$89$	−7.43872	+	1.99320i	−0.788503	+	0.211279i	−0.630530	−	0.776165i	$-0.717162\pi$
$89$	−7.43872	+	1.99320i	−0.788503	+	0.211279i	−0.157973	+	0.987444i	$0.550496\pi$
$90$	−0.0285015	+	0.237345i	−0.00300433	+	0.0250183i
$91$	20.2649	−	5.42996i	2.12434	−	0.569215i
$92$	−0.258707	+	0.149364i	−0.0269720	+	0.0155723i
$93$	−13.0536	+	7.53653i	−1.35360	+	0.781501i
$94$	−0.237428	+	0.0636187i	−0.0244889	+	0.00656177i
$95$	1.71514	+	2.18329i	0.175970	+	0.224001i
$96$	2.42315	−	0.649281i	0.247312	−	0.0662670i
$97$	1.75339			0.178030			0.0890150	−	0.996030i	$-0.471628\pi$
$97$	1.75339			0.178030			0.0890150	+	0.996030i	$0.471628\pi$
$98$	−0.704025	−	1.21941i	−0.0711172	−	0.123179i
$99$	1.24306	−	2.15304i	0.124932	−	0.216389i
$100$	6.87008	−	7.19035i	0.687008	−	0.719035i
$101$		−	1.85688i		−	0.184766i	−0.995724	−	0.0923831i	$-0.970552\pi$
$101$		−	1.85688i		−	0.184766i	0.995724	−	0.0923831i	$-0.0294485\pi$
$102$	1.55390	−	0.416367i	0.153859	−	0.0412265i
$103$	3.56156			0.350931			0.175466	−	0.984486i	$-0.443857\pi$
$103$	3.56156			0.350931			0.175466	+	0.984486i	$0.443857\pi$
$104$	0.973393	+	1.68597i	0.0954491	+	0.165323i
$105$	−7.95932	−	18.6132i	−0.776750	−	1.81646i
$106$	1.18963	+	0.318761i	0.115547	+	0.0309608i
$107$	11.0067	+	2.94924i	1.06406	+	0.285114i	0.748050	−	0.663642i	$-0.230990\pi$
$107$	11.0067	+	2.94924i	1.06406	+	0.285114i	0.316010	+	0.948756i	$0.397657\pi$
$108$	−2.04559	+	7.63425i	−0.196837	+	0.734606i
$109$	−1.72341	−	6.43186i	−0.165073	−	0.616061i	−0.998031	−	0.0627245i	$-0.980021\pi$
$109$	−1.72341	−	6.43186i	−0.165073	−	0.616061i	0.832958	−	0.553336i	$-0.186646\pi$
$110$	0.527841	−	0.225714i	0.0503277	−	0.0215210i
$111$	−7.44042	+	9.65849i	−0.706214	+	0.916743i
$112$	−12.5641	+	12.5641i	−1.18720	+	1.18720i
$113$	4.15153	−	7.19065i	0.390543	−	0.676440i	−0.601978	−	0.798512i	$-0.705621\pi$
$113$	4.15153	−	7.19065i	0.390543	−	0.676440i	0.992521	+	0.122073i	$0.0389540\pi$
$114$	0.130746	+	0.226459i	0.0122455	+	0.0212098i
$115$	−0.201401	+	0.268753i	−0.0187807	+	0.0250613i
$116$	0.366500	−	1.36779i	0.0340286	−	0.126997i
$117$	4.72603			0.436921
$118$	−0.00822949	+	0.0307129i	−0.000757586	+	0.00282735i
$119$	−24.3967	+	24.3967i	−2.23644	+	2.23644i
$120$	1.47717	−	1.16043i	0.134847	−	0.105933i
$121$	5.02962			0.457238
$122$	0.204241	+	0.204241i	0.0184911	+	0.0184911i
$123$	10.6710	−	2.85927i	0.962168	−	0.257812i
$124$	14.4476	+	3.87122i	1.29743	+	0.347645i
$125$	3.92325	−	10.4694i	0.350906	−	0.936411i
$126$	−0.124975	−	0.466415i	−0.0111337	−	0.0415515i
$127$	1.28331	+	4.78938i	0.113875	+	0.424988i	0.999200	−	0.0399843i	$-0.0127308\pi$
$127$	1.28331	+	4.78938i	0.113875	+	0.424988i	−0.885325	+	0.464973i	$0.846064\pi$
$128$	−2.87176	−	1.65801i	−0.253831	−	0.146549i
$129$	−0.930851	+	3.47398i	−0.0819569	+	0.305867i
$130$	0.873294	+	0.654439i	0.0765930	+	0.0573981i
$131$	−3.53198	−	13.1815i	−0.308590	−	1.15168i	−0.929810	−	0.368039i	$-0.880029\pi$
$131$	−3.53198	−	13.1815i	−0.308590	−	1.15168i	0.621220	−	0.783636i	$-0.286637\pi$
$132$	−9.40908	+	2.52116i	−0.818955	+	0.219438i
$133$	−4.85685	−	2.80410i	−0.421142	−	0.243146i
$134$	−0.946554	+	0.946554i	−0.0817698	+	0.0817698i
$135$	1.26003	+	8.79570i	0.108446	+	0.757013i
$136$	−2.77264	−	1.60079i	−0.237752	−	0.137266i
$137$	−7.46542	+	7.46542i	−0.637814	+	0.637814i	−0.950016	−	0.312202i	$-0.898933\pi$
$137$	−7.46542	+	7.46542i	−0.637814	+	0.637814i	0.312202	+	0.950016i	$0.398933\pi$
$138$	−0.0223663	+	0.0223663i	−0.00190395	+	0.00190395i
$139$	3.87366	−	6.70937i	0.328559	−	0.569081i	−0.653667	−	0.756782i	$-0.726770\pi$
$139$	3.87366	−	6.70937i	0.328559	−	0.569081i	0.982226	+	0.187701i	$0.0601036\pi$
$140$	−7.47551	+	18.6452i	−0.631796	+	1.57581i
$141$	4.06081	−	2.34451i	0.341982	−	0.197443i
$142$		−	1.10527i		−	0.0927518i
$143$	−5.67475	−	9.82895i	−0.474546	−	0.821938i
$144$	−3.46635	+	2.00130i	−0.288863	+	0.166775i
$145$	−0.225753	−	1.57589i	−0.0187478	−	0.130870i
$146$	−0.911683	+	0.244285i	−0.0754514	+	0.0202171i
$147$	18.9931	+	18.9931i	1.56652	+	1.56652i
$148$	11.9978	−	1.55636i	0.986217	−	0.127932i
$149$		−	1.69346i		−	0.138734i	−0.997591	−	0.0693670i	$-0.977902\pi$
$149$		−	1.69346i		−	0.138734i	0.997591	−	0.0693670i	$-0.0220980\pi$
$150$	0.505598	−	0.923680i	0.0412819	−	0.0754181i
$151$	−9.78475	+	5.64923i	−0.796271	+	0.459727i	−0.842166	−	0.539219i	$-0.818720\pi$
$151$	−9.78475	+	5.64923i	−0.796271	+	0.459727i	0.0458944	+	0.998946i	$0.485386\pi$
$152$	0.134691	−	0.502673i	0.0109249	−	0.0407722i
$153$	−6.73088	+	3.88608i	−0.544159	+	0.314171i
$154$	−0.819963	+	0.819963i	−0.0660745	+	0.0660745i
$155$	16.6456	−	2.38456i	1.33700	−	0.191532i
$156$	−13.0937	−	13.0937i	−1.04834	−	1.04834i
$157$	−2.43506	−	9.08776i	−0.194339	−	0.725282i	−0.992437	−	0.122755i	$-0.960827\pi$
$157$	−2.43506	−	9.08776i	−0.194339	−	0.725282i	0.798098	−	0.602527i	$-0.205840\pi$
$158$	0.381159	+	0.381159i	0.0303234	+	0.0303234i
$159$	−23.4943			−1.86322
$160$	−2.77867	−	0.333676i	−0.219673	−	0.0263794i
$161$	0.175579	−	0.655269i	0.0138375	−	0.0516424i
$162$			1.15758i			0.0909485i
$163$	−7.93075	+	13.7365i	−0.621184	+	1.07592i	0.368081	+	0.929794i	$0.380015\pi$
$163$	−7.93075	+	13.7365i	−0.621184	+	1.07592i	−0.989266	+	0.146129i	$0.953318\pi$
$164$	−9.49380	−	5.48125i	−0.741341	−	0.428013i
$165$	−8.61171	+	6.76518i	−0.670421	+	0.526668i
$166$	−0.0927894	−	0.0248628i	−0.00720185	−	0.00192973i
$167$	0.265234	+	0.459399i	0.0205244	+	0.0355494i	0.876105	−	0.482120i	$-0.160133\pi$
$167$	0.265234	+	0.459399i	0.0205244	+	0.0355494i	−0.855581	+	0.517669i	$0.826800\pi$
$168$	−1.89720	+	3.28605i	−0.146372	+	0.253524i
$169$	4.28751	−	7.42618i	0.329808	−	0.571245i
$170$	−1.78189	−	0.213978i	−0.136664	−	0.0164113i
$171$	−0.893314	−	0.893314i	−0.0683135	−	0.0683135i
$172$	3.09076	−	1.78445i	0.235668	−	0.136063i
$173$	0.719913	+	2.68675i	0.0547340	+	0.204270i	0.987878	−	0.155233i	$-0.0496129\pi$
$173$	0.719913	+	2.68675i	0.0547340	+	0.204270i	−0.933144	+	0.359503i	$0.882946\pi$
$174$		−	0.149938i		−	0.0113667i
$175$	0.514274	+	22.5778i	0.0388755	+	1.70672i
$176$	8.32440	+	4.80610i	0.627476	+	0.362273i
$177$		−	0.606555i		−	0.0455914i
$178$	0.781594	+	0.209427i	0.0585829	+	0.0156973i
$179$	6.41009	+	6.41009i	0.479112	+	0.479112i	0.904848	−	0.425735i	$-0.139985\pi$
$179$	6.41009	+	6.41009i	0.479112	+	0.479112i	−0.425735	+	0.904848i	$0.639985\pi$
$180$	−2.71367	+	3.62117i	−0.202265	+	0.269906i
$181$	0.557213	+	0.965121i	0.0414173	+	0.0717369i	0.885991	−	0.463703i	$-0.153479\pi$
$181$	0.557213	+	0.965121i	0.0414173	+	0.0717369i	−0.844574	+	0.535439i	$0.820146\pi$
$182$	−2.12925	−	0.570532i	−0.157831	−	0.0422906i
$183$	−4.77179	−	2.75500i	−0.352741	−	0.203655i
$184$	0.0629497			0.00464071
$185$	11.7142	−	6.91217i	0.861243	−	0.508193i
$186$	1.58374			0.116126
$187$	16.1641	+	9.33237i	1.18204	+	0.682450i
$188$	−4.49444	−	1.20428i	−0.327791	−	0.0878312i
$189$	−8.97411	−	15.5436i	−0.652771	−	1.13063i
$190$	−0.0413680	−	0.288772i	−0.00300115	−	0.0209498i
$191$	−12.9182	−	12.9182i	−0.934729	−	0.934729i	0.0632677	−	0.997997i	$-0.479848\pi$
$191$	−12.9182	−	12.9182i	−0.934729	−	0.934729i	−0.997997	+	0.0632677i	$0.979848\pi$
$192$	14.9779	+	4.01332i	1.08094	+	0.289636i
$193$		−	6.70355i		−	0.482532i	−0.970459	−	0.241266i	$-0.922437\pi$
$193$		−	6.70355i		−	0.482532i	0.970459	−	0.241266i	$-0.0775627\pi$
$194$	−0.159549	−	0.0921154i	−0.0114549	−	0.00661350i
$195$	−19.3227	−	7.74714i	−1.38373	−	0.554784i
$196$		−	26.6539i		−	1.90385i
$197$	−3.73320	−	13.9325i	−0.265980	−	0.992650i	−0.961648	−	0.274287i	$-0.911558\pi$
$197$	−3.73320	−	13.9325i	−0.265980	−	0.992650i	0.695668	−	0.718363i	$-0.255108\pi$
$198$	−0.226222	+	0.130609i	−0.0160769	+	0.00928201i
$199$	−6.68443	−	6.68443i	−0.473847	−	0.473847i	0.429310	−	0.903157i	$-0.358757\pi$
$199$	−6.68443	−	6.68443i	−0.473847	−	0.473847i	−0.903157	+	0.429310i	$0.858757\pi$
$200$	−2.01134	+	0.588341i	−0.142223	+	0.0416020i
$201$	12.7680	−	22.1148i	0.900586	−	1.55986i
$202$	−0.0975521	+	0.168965i	−0.00686374	+	0.0118883i
$203$	1.60785	+	2.78488i	0.112849	+	0.195460i
$204$	29.4149	+	7.88169i	2.05945	+	0.551829i
$205$	−12.2366	−	1.46943i	−0.854638	−	0.102629i
$206$	−0.324082	−	0.187109i	−0.0225798	−	0.0130365i
$207$	0.0764084	−	0.132343i	0.00531075	−	0.00919849i
$208$			18.2725i			1.26697i
$209$	−0.785229	+	2.93051i	−0.0543154	+	0.202708i
$210$	−0.253600	+	2.11184i	−0.0175001	+	0.145731i
$211$	−15.4569			−1.06410			−0.532049	−	0.846713i	$-0.678578\pi$
$211$	−15.4569			−1.06410			−0.532049	+	0.846713i	$0.678578\pi$
$212$	16.4853	+	16.4853i	1.13221	+	1.13221i
$213$	5.45702	+	20.3659i	0.373909	+	1.39545i
$214$	−0.846608	−	0.846608i	−0.0578729	−	0.0578729i
$215$	2.40613	−	3.21077i	0.164096	−	0.218973i
$216$	1.17767	−	1.17767i	0.0801304	−	0.0801304i
$217$	−29.4158	+	16.9832i	−1.99687	+	1.15290i
$218$	−0.181081	+	0.675803i	−0.0122643	+	0.0457711i
$219$	15.5928	−	9.00250i	1.05366	−	0.608333i
$220$	10.7895	+	1.29566i	0.727431	+	0.0873536i
$221$			35.4810i			2.38671i
$222$	1.18445	−	0.487980i	0.0794950	−	0.0327511i
$223$	−7.27052	−	7.27052i	−0.486870	−	0.486870i	0.420447	−	0.907317i	$-0.361873\pi$
$223$	−7.27052	−	7.27052i	−0.486870	−	0.486870i	−0.907317	+	0.420447i	$0.861873\pi$
$224$	5.46046	−	1.46313i	0.364842	−	0.0977592i
$225$	−1.20446	+	4.94270i	−0.0802971	+	0.329513i
$226$	−0.755530	+	0.436205i	−0.0502571	+	0.0290159i
$227$	−3.45410	−	5.98267i	−0.229256	−	0.397084i	0.728332	−	0.685225i	$-0.240296\pi$
$227$	−3.45410	−	5.98267i	−0.229256	−	0.397084i	−0.957588	+	0.288141i	$0.906963\pi$
$228$			4.94995i			0.327819i
$229$	−20.4243	+	11.7920i	−1.34967	+	0.779235i	−0.988203	−	0.153148i	$-0.951059\pi$
$229$	−20.4243	+	11.7920i	−1.34967	+	0.779235i	−0.361472	+	0.932383i	$0.617726\pi$
$230$	0.0324454	−	0.0138742i	0.00213938	−	0.000914839i
$231$	11.0604	−	19.1572i	0.727723	−	1.26045i
$232$	−0.210998	+	0.210998i	−0.0138527	+	0.0138527i
$233$	−10.7828	+	10.7828i	−0.706402	+	0.706402i	−0.965777	−	0.259375i	$-0.916484\pi$
$233$	−10.7828	+	10.7828i	−0.706402	+	0.706402i	0.259375	+	0.965777i	$0.416484\pi$
$234$	−0.430041	−	0.248284i	−0.0281127	−	0.0162308i
$235$	−5.17821	+	0.741803i	−0.337789	+	0.0483899i
$236$	−0.425603	+	0.425603i	−0.0277044	+	0.0277044i
$237$	−8.90522	−	5.14143i	−0.578456	−	0.333972i
$238$	3.50165	−	0.938264i	0.226978	−	0.0608186i
$239$	4.28082	+	15.9763i	0.276903	+	1.03342i	0.954555	+	0.298035i	$0.0963311\pi$
$239$	4.28082	+	15.9763i	0.276903	+	1.03342i	−0.677652	+	0.735383i	$0.737002\pi$
$240$	17.4531	−	2.50023i	1.12659	−	0.161389i
$241$	−0.943969	+	3.52294i	−0.0608064	+	0.226933i	−0.989641	−	0.143561i	$-0.954145\pi$
$241$	−0.943969	+	3.52294i	−0.0608064	+	0.226933i	0.928835	+	0.370493i	$0.120811\pi$
$242$	−0.457666	−	0.264234i	−0.0294199	−	0.0169856i
$243$	−2.62992	−	9.81501i	−0.168710	−	0.629633i
$244$	1.41513	+	5.28135i	0.0905946	+	0.338104i
$245$	−11.7817	−	27.5520i	−0.752708	−	1.76023i
$246$	−1.12121	−	0.300427i	−0.0714856	−	0.0191545i
$247$	−5.57081	+	1.49269i	−0.354462	+	0.0949778i
$248$	−2.22871	−	2.22871i	−0.141523	−	0.141523i
$249$	1.83251			0.116131
$250$	−0.907008	+	0.746544i	−0.0573642	+	0.0472156i
$251$	5.49768	−	5.49768i	0.347010	−	0.347010i	−0.511984	−	0.858995i	$-0.671089\pi$
$251$	5.49768	−	5.49768i	0.347010	−	0.347010i	0.858995	+	0.511984i	$0.171089\pi$
$252$	2.36574	−	8.82908i	0.149028	−	0.556180i
$253$	−0.366988			−0.0230723
$254$	0.134839	−	0.503225i	0.00846053	−	0.0315751i
$255$	33.8899	−	4.85489i	2.12227	−	0.304025i
$256$	−7.56205	−	13.0979i	−0.472628	−	0.818616i
$257$	13.4897	−	23.3649i	0.841467	−	1.45746i	−0.0471867	−	0.998886i	$-0.515026\pi$
$257$	13.4897	−	23.3649i	0.841467	−	1.45746i	0.888654	−	0.458578i	$-0.151641\pi$
$258$	0.267210	−	0.267210i	0.0166358	−	0.0166358i
$259$	−16.7667	+	21.7650i	−1.04183	+	1.35241i
$260$	8.12225	+	18.9942i	0.503721	+	1.17797i
$261$	0.187486	+	0.699706i	0.0116051	+	0.0433107i
$262$	−0.371109	+	1.38500i	−0.0229272	+	0.0855654i
$263$	−5.22951	−	1.40124i	−0.322465	−	0.0864043i	0.0939553	−	0.995576i	$-0.470049\pi$
$263$	−5.22951	−	1.40124i	−0.322465	−	0.0864043i	−0.416421	+	0.909172i	$0.636716\pi$
$264$	1.98273	+	0.531271i	0.122029	+	0.0326975i
$265$	24.3277	+	9.75384i	1.49444	+	0.599173i
$266$	0.294630	+	0.510314i	0.0180649	+	0.0312894i
$267$	−15.4358			−0.944659
$268$	−24.4764	+	6.55842i	−1.49513	+	0.400619i
$269$			18.2733i			1.11414i	0.830465	+	0.557071i	$0.188075\pi$
$269$			18.2733i			1.11414i	−0.830465	+	0.557071i	$0.811925\pi$
$270$	0.347432	−	0.866554i	0.0211440	−	0.0527368i
$271$	−8.01505	+	13.8825i	−0.486879	+	0.843300i	−0.999886	−	0.0150847i	$-0.995198\pi$
$271$	−8.01505	+	13.8825i	−0.486879	+	0.843300i	0.513007	+	0.858385i	$0.328532\pi$
$272$	−15.0249	−	26.0239i	−0.911019	−	1.57793i
$273$	42.0510			2.54504
$274$	1.07151	−	0.287110i	0.0647323	−	0.0173450i
$275$	11.7258	−	3.42995i	0.707094	−	0.206834i
$276$	−0.578358	+	0.154971i	−0.0348131	+	0.00932813i
$277$	19.9375	−	11.5109i	1.19793	−	0.691626i	0.237837	−	0.971305i	$-0.423561\pi$
$277$	19.9375	−	11.5109i	1.19793	−	0.691626i	0.960093	+	0.279679i	$0.0902281\pi$
$278$	−0.704961	+	0.407009i	−0.0422807	+	0.0244108i
$279$	−7.39076	+	1.98035i	−0.442473	+	0.118560i
$280$	3.32874	−	2.61499i	0.198930	−	0.156275i
$281$	26.6973	−	7.15352i	1.59263	−	0.426743i	0.649822	−	0.760087i	$-0.274844\pi$
$281$	26.6973	−	7.15352i	1.59263	−	0.426743i	0.942805	+	0.333343i	$0.108177\pi$
$282$	−0.492680			−0.0293387
$283$	−2.83629	−	4.91260i	−0.168600	−	0.292024i	0.769328	−	0.638854i	$-0.220591\pi$
$283$	−2.83629	−	4.91260i	−0.168600	−	0.292024i	−0.937928	+	0.346830i	$0.887258\pi$
$284$	10.4611	−	18.1192i	0.620755	−	1.07518i
$285$	2.18801	+	5.11675i	0.129607	+	0.303090i
$286$			1.19250i			0.0705142i
$287$	24.0465	−	6.44324i	1.41942	−	0.380333i
$288$	1.27345			0.0750386
$289$	−20.6750	−	35.8102i	−1.21618	−	2.10648i
$290$	−0.0622478	+	0.155257i	−0.00365532	+	0.00911698i
$291$	3.39468	+	0.909603i	0.199000	+	0.0533218i
$292$	−17.2579	−	4.62423i	−1.00994	−	0.270612i
$293$	3.60695	−	13.4613i	0.210720	−	0.786418i	−0.776909	−	0.629612i	$-0.783214\pi$
$293$	3.60695	−	13.4613i	0.210720	−	0.786418i	0.987629	−	0.156806i	$-0.0501196\pi$
$294$	−0.730450	−	2.72608i	−0.0426007	−	0.158988i
$295$	−0.251816	+	0.628072i	−0.0146613	+	0.0365678i
$296$	−2.35351	−	0.980100i	−0.136795	−	0.0569671i
$297$	−6.86567	+	6.86567i	−0.398386	+	0.398386i
$298$	−0.0889671	+	0.154095i	−0.00515372	+	0.00892651i
$299$	−0.348816	−	0.604167i	−0.0201725	−	0.0349399i
$300$	17.0310	−	10.3570i	0.983287	−	0.597962i
$301$	−2.09763	+	7.82847i	−0.120905	+	0.451225i
$302$	1.18714			0.0683122
$303$	0.963287	−	3.59504i	0.0553394	−	0.206529i
$304$	3.45386	−	3.45386i	0.198093	−	0.198093i
$305$	3.79731	+	4.83378i	0.217434	+	0.276781i
$306$	0.816628			0.0466835
$307$	7.33300	+	7.33300i	0.418516	+	0.418516i	0.884692	−	0.466176i	$-0.154369\pi$
$307$	7.33300	+	7.33300i	0.418516	+	0.418516i	−0.466176	+	0.884692i	$0.654369\pi$
$308$	−21.2029	+	5.68131i	−1.20815	+	0.323723i
$309$	6.89542	+	1.84762i	0.392267	+	0.105108i
$310$	−1.63993	−	0.657503i	−0.0931415	−	0.0373437i
$311$	−0.463544	−	1.72997i	−0.0262852	−	0.0980975i	0.951537	−	0.307534i	$-0.0995038\pi$
$311$	−0.463544	−	1.72997i	−0.0262852	−	0.0980975i	−0.977822	+	0.209436i	$0.932837\pi$
$312$	1.00993	+	3.76911i	0.0571760	+	0.213384i
$313$	−23.5224	−	13.5807i	−1.32957	−	0.767625i	−0.344333	−	0.938848i	$-0.611895\pi$
$313$	−23.5224	−	13.5807i	−1.32957	−	0.767625i	−0.985232	+	0.171223i	$0.945228\pi$
$314$	−0.255854	+	0.954861i	−0.0144387	+	0.0538859i
$315$	−1.45723	−	10.1723i	−0.0821056	−	0.573144i
$316$	2.64095	+	9.85616i	0.148565	+	0.554452i
$317$	6.32825	−	1.69565i	0.355430	−	0.0952372i	−0.0766857	−	0.997055i	$-0.524434\pi$
$317$	6.32825	−	1.69565i	0.355430	−	0.0952372i	0.432116	+	0.901818i	$0.357767\pi$
$318$	2.13784	+	1.23428i	0.119884	+	0.0692152i
$319$	1.23009	−	1.23009i	0.0688719	−	0.0688719i
$320$	−13.8431	−	10.3739i	−0.773852	−	0.579918i
$321$	19.7798	+	11.4198i	1.10400	+	0.637394i
$322$	−0.0504015	+	0.0504015i	−0.00280877	+	0.00280877i
$323$	6.70663	−	6.70663i	0.373167	−	0.373167i
$324$	−10.9563	+	18.9770i	−0.608686	+	1.05428i
$325$	16.7919	+	16.0439i	0.931446	+	0.889958i
$326$	1.44330	−	0.833292i	0.0799373	−	0.0461518i
$327$		−	13.3466i		−	0.738066i
$328$	1.15504	+	2.00058i	0.0637763	+	0.110464i
$329$	9.15085	−	5.28324i	0.504502	−	0.291275i
$330$	1.13903	−	0.163171i	0.0627014	−	0.00898227i
$331$	27.9515	−	7.48959i	1.53635	−	0.411665i	0.611268	−	0.791423i	$-0.290660\pi$
$331$	27.9515	−	7.48959i	1.53635	−	0.411665i	0.925086	+	0.379758i	$0.123993\pi$
$332$	−1.28583	−	1.28583i	−0.0705689	−	0.0705689i
$333$	−4.91722	+	3.75829i	−0.269462	+	0.205953i
$334$		−	0.0557369i		−	0.00304979i
$335$	−22.4021	+	17.5986i	−1.22396	+	0.961516i
$336$	−30.8428	+	17.8071i	−1.68261	+	0.971455i
$337$	2.11178	−	7.88127i	0.115036	−	0.429320i	−0.884254	−	0.467007i	$-0.845332\pi$
$337$	2.11178	−	7.88127i	0.115036	−	0.429320i	0.999290	+	0.0376867i	$0.0119989\pi$
$338$	−0.780277	+	0.450493i	−0.0424415	+	0.0245036i
$339$	11.7679	−	11.7679i	0.639145	−	0.639145i
$340$	−27.1862	−	20.3731i	−1.47438	−	1.10489i
$341$	12.9931	+	12.9931i	0.703613	+	0.703613i
$342$	0.0343557	+	0.128217i	0.00185774	+	0.00693319i
$343$	20.4434	+	20.4434i	1.10384	+	1.10384i
$344$	−0.752057			−0.0405482
$345$	−0.529345	+	0.415842i	−0.0284990	+	0.0223882i
$346$	0.0756421	−	0.282300i	0.00406654	−	0.0151765i
$347$			24.8690i			1.33504i	0.744592	+	0.667519i	$0.232644\pi$
$347$			24.8690i			1.33504i	−0.744592	+	0.667519i	$0.767356\pi$
$348$	1.41913	−	2.45801i	0.0760736	−	0.131763i
$349$	16.0098	+	9.24327i	0.856985	+	0.494781i	0.863002	−	0.505201i	$-0.168582\pi$
$349$	16.0098	+	9.24327i	0.856985	+	0.494781i	−0.00601629	+	0.999982i	$0.501915\pi$
$350$	1.13934	−	2.08147i	0.0609004	−	0.111259i
$351$	−17.8285	−	4.77714i	−0.951617	−	0.254985i
$352$	−1.52909	−	2.64845i	−0.0815005	−	0.141163i
$353$	9.10206	−	15.7652i	0.484454	−	0.839099i	−0.515387	−	0.856958i	$-0.672352\pi$
$353$	9.10206	−	15.7652i	0.484454	−	0.839099i	0.999841	+	0.0178589i	$0.00568497\pi$
$354$	−0.0318657	+	0.0551930i	−0.00169364	+	0.00293347i
$355$	2.80445	−	23.3539i	0.148845	−	1.23950i
$356$	10.8309	+	10.8309i	0.574038	+	0.574038i
$357$	−59.8897	+	34.5774i	−3.16970	+	1.83003i
$358$	−0.246524	−	0.920038i	−0.0130292	−	0.0486255i
$359$			25.4475i			1.34307i	0.740974	+	0.671534i	$0.234364\pi$
$359$			25.4475i			1.34307i	−0.740974	+	0.671534i	$0.765636\pi$
$360$	0.876763	−	0.374920i	0.0462095	−	0.0197600i
$361$	−15.1193	−	8.72915i	−0.795755	−	0.459429i
$362$		−	0.117094i		−	0.00615432i
$363$	9.73766	+	2.60920i	0.511095	+	0.136947i
$364$	−29.5061	−	29.5061i	−1.54654	−	1.54654i
$365$	−19.8834	+	2.84839i	−1.04074	+	0.149092i
$366$	0.289470	+	0.501377i	0.0151309	+	0.0262074i
$367$	10.9437	+	2.93236i	0.571258	+	0.153068i	0.532874	−	0.846195i	$-0.321112\pi$
$367$	10.9437	+	2.93236i	0.571258	+	0.153068i	0.0383846	+	0.999263i	$0.487779\pi$
$368$	0.511685	+	0.295421i	0.0266734	+	0.0153999i
$369$	5.60795			0.291938
$370$	−1.42906	+	0.0135575i	−0.0742931	+	0.000704820i
$371$	−52.9432			−2.74868
$372$	25.9632	+	14.9898i	1.34613	+	0.777187i
$373$	29.5344	+	7.91372i	1.52923	+	0.409757i	0.922769	−	0.385354i	$-0.125921\pi$
$373$	29.5344	+	7.91372i	1.52923	+	0.409757i	0.606465	+	0.795110i	$0.292587\pi$
$374$	−0.980562	−	1.69838i	−0.0507036	−	0.0878213i
$375$	13.0268	−	18.2342i	0.672703	−	0.941609i
$376$	0.693320	+	0.693320i	0.0357552	+	0.0357552i
$377$	3.19426	+	0.855900i	0.164513	+	0.0440811i
$378$			1.88584i			0.0969971i
$379$	6.07630	+	3.50815i	0.312119	+	0.180202i	0.647874	−	0.761747i	$-0.275658\pi$
$379$	6.07630	+	3.50815i	0.312119	+	0.180202i	−0.335756	+	0.941949i	$0.608992\pi$
$380$	2.05501	−	5.12555i	0.105420	−	0.262935i
$381$			9.93828i			0.509154i
$382$	0.496817	+	1.85415i	0.0254194	+	0.0948664i
$383$	−18.2184	+	10.5184i	−0.930919	+	0.537466i	−0.887102	−	0.461573i	$-0.847285\pi$
$383$	−18.2184	+	10.5184i	−0.930919	+	0.537466i	−0.0438170	+	0.999040i	$0.513952\pi$
$384$	−4.69980	−	4.69980i	−0.239836	−	0.239836i
$385$	−19.4061	+	15.2450i	−0.989026	+	0.776958i
$386$	−0.352175	+	0.609984i	−0.0179252	+	0.0310474i
$387$	−0.912848	+	1.58110i	−0.0464027	+	0.0803718i
$388$	−1.74371	−	3.02020i	−0.0885237	−	0.153328i
$389$	28.1825	+	7.55149i	1.42891	+	0.382876i	0.888636	−	0.458612i	$-0.151653\pi$
$389$	28.1825	+	7.55149i	1.42891	+	0.382876i	0.540275	+	0.841488i	$0.318320\pi$
$390$	1.35125	+	1.72007i	0.0684233	+	0.0870993i
$391$	0.993578	+	0.573643i	0.0502474	+	0.0290104i
$392$	−2.80833	+	4.86416i	−0.141842	+	0.245677i
$393$		−	27.3526i		−	1.37975i
$394$	−0.392252	+	1.46390i	−0.0197614	+	0.0737504i
$395$	7.08663	+	9.02090i	0.356567	+	0.453891i
$396$	−4.94479			−0.248485
$397$	−1.11923	−	1.11923i	−0.0561727	−	0.0561727i	0.678462	−	0.734635i	$-0.262647\pi$
$397$	−1.11923	−	1.11923i	−0.0561727	−	0.0561727i	−0.734635	+	0.678462i	$0.762647\pi$
$398$	0.257074	+	0.959415i	0.0128860	+	0.0480911i
$399$	−7.94850	−	7.94850i	−0.397923	−	0.397923i
$400$	−19.1102	−	4.65685i	−0.955510	−	0.232842i
$401$	2.72947	−	2.72947i	0.136303	−	0.136303i	−0.635663	−	0.771966i	$-0.719273\pi$
$401$	2.72947	−	2.72947i	0.136303	−	0.136303i	0.771966	+	0.635663i	$0.219273\pi$
$402$	−2.32363	+	1.34155i	−0.115892	+	0.0669104i
$403$	−9.04059	+	33.7399i	−0.450344	+	1.68071i
$404$	−3.19845	+	1.84663i	−0.159129	+	0.0918732i
$405$	−2.93721	+	24.4594i	−0.145951	+	1.21540i
$406$		−	0.337877i		−	0.0167686i
$407$	13.7206	+	5.71385i	0.680107	+	0.283225i
$408$	−4.53758	−	4.53758i	−0.224644	−	0.224644i
$409$	−15.9537	+	4.27479i	−0.788862	+	0.211375i	−0.630688	−	0.776037i	$-0.717227\pi$
$409$	−15.9537	+	4.27479i	−0.788862	+	0.211375i	−0.158174	+	0.987411i	$0.550561\pi$
$410$	1.03626	+	0.776564i	0.0511772	+	0.0383517i
$411$	−18.3264	+	10.5807i	−0.903973	+	0.521909i
$412$	−3.54190	−	6.13476i	−0.174497	−	0.302238i
$413$		−	1.36684i		−	0.0672580i
$414$	−0.0139054	+	0.00802831i	−0.000683415	+	0.000394570i
$415$	−1.89752	−	0.760784i	−0.0931458	−	0.0373454i
$416$	2.90674	−	5.03462i	0.142515	−	0.246843i
$417$	10.9803	−	10.9803i	0.537705	−	0.537705i
$418$	0.225407	−	0.225407i	0.0110250	−	0.0110250i
$419$	−15.1345	−	8.73792i	−0.739370	−	0.426875i	0.0824704	−	0.996594i	$-0.473719\pi$
$419$	−15.1345	−	8.73792i	−0.739370	−	0.426875i	−0.821840	+	0.569718i	$0.807052\pi$
$420$	−24.1456	+	32.2203i	−1.17818	+	1.57219i
$421$	−7.21676	+	7.21676i	−0.351723	+	0.351723i	−0.860750	−	0.509027i	$-0.830005\pi$
$421$	−7.21676	+	7.21676i	−0.351723	+	0.351723i	0.509027	+	0.860750i	$0.330005\pi$
$422$	1.40649	+	0.812038i	0.0684669	+	0.0395294i
$423$	2.29916	−	0.616059i	0.111789	−	0.0299538i
$424$	−1.27152	−	4.74539i	−0.0617507	−	0.230457i
$425$	−37.1077	−	9.04256i	−1.79999	−	0.438629i
$426$	0.573375	−	2.13987i	0.0277801	−	0.103677i
$427$	−10.7530	−	6.20826i	−0.520375	−	0.300439i
$428$	−5.86592	−	21.8919i	−0.283540	−	1.05819i
$429$	−5.88775	−	21.9734i	−0.284263	−	1.06088i
$430$	−0.387623	+	0.165755i	−0.0186929	+	0.00799340i
$431$	27.7849	+	7.44493i	1.33835	+	0.358610i	0.855822	−	0.517270i	$-0.173052\pi$
$431$	27.7849	+	7.44493i	1.33835	+	0.358610i	0.482528	+	0.875880i	$0.339719\pi$
$432$	15.0995	−	4.04589i	0.726474	−	0.194658i
$433$	−12.0991	−	12.0991i	−0.581444	−	0.581444i	0.353856	−	0.935300i	$-0.384870\pi$
$433$	−12.0991	−	12.0991i	−0.581444	−	0.581444i	−0.935300	+	0.353856i	$0.884870\pi$
$434$	3.56889			0.171312
$435$	0.380445	−	3.16813i	0.0182410	−	0.151900i
$436$	−9.36492	+	9.36492i	−0.448498	+	0.448498i
$437$	−0.0482665	+	0.180133i	−0.00230890	+	0.00861693i
$438$	−1.89180			−0.0903939
$439$	−2.60805	+	9.73336i	−0.124475	+	0.464548i	−0.999820	−	0.0189505i	$-0.993967\pi$
$439$	−2.60805	+	9.73336i	−0.124475	+	0.464548i	0.875345	+	0.483499i	$0.160634\pi$
$440$	−1.83251	−	1.37327i	−0.0873614	−	0.0654679i
$441$	6.81750	+	11.8083i	0.324643	+	0.562298i
$442$	1.86402	−	3.22857i	0.0886622	−	0.153567i
$443$	27.4924	−	27.4924i	1.30620	−	1.30620i	0.382069	−	0.924134i	$-0.375212\pi$
$443$	27.4924	−	27.4924i	1.30620	−	1.30620i	0.924134	−	0.382069i	$-0.124788\pi$
$444$	24.0360	+	3.21088i	1.14070	+	0.152381i
$445$	15.9834	+	6.40832i	0.757688	+	0.303783i
$446$	0.279614	+	1.04354i	0.0132401	+	0.0494128i
$447$	0.878514	−	3.27866i	0.0415523	−	0.155075i
$448$	33.7520	+	9.04383i	1.59463	+	0.427281i
$449$	24.2566	+	6.49953i	1.14474	+	0.306732i	0.780855	−	0.624713i	$-0.214784\pi$
$449$	24.2566	+	6.49953i	1.14474	+	0.306732i	0.363883	+	0.931444i	$0.381451\pi$
$450$	0.369266	−	0.386480i	0.0174074	−	0.0182189i
$451$	−6.73371	−	11.6631i	−0.317078	−	0.549195i
$452$	−16.5144			−0.776774
$453$	−21.8745	+	5.86126i	−1.02776	+	0.275386i
$454$			0.725851i			0.0340659i
$455$	−43.5428	−	17.4578i	−2.04132	−	0.818436i
$456$	0.521540	−	0.903334i	0.0244234	−	0.0423025i
$457$	−0.876059	−	1.51738i	−0.0409803	−	0.0709800i	0.844808	−	0.535070i	$-0.179715\pi$
$457$	−0.876059	−	1.51738i	−0.0409803	−	0.0709800i	−0.885788	+	0.464090i	$0.846381\pi$
$458$	2.47799			0.115789
$459$	29.3198	−	7.85622i	1.36853	−	0.366697i
$460$	0.663213	+	0.0796419i	0.0309224	+	0.00371332i
$461$	−17.9341	+	4.80544i	−0.835276	+	0.223812i	−0.651014	−	0.759066i	$-0.725656\pi$
$461$	−17.9341	+	4.80544i	−0.835276	+	0.223812i	−0.184262	+	0.982877i	$0.558990\pi$
$462$	−2.01287	+	1.16213i	−0.0936472	+	0.0540673i
$463$	18.1497	−	10.4787i	0.843488	−	0.486988i	−0.0149605	−	0.999888i	$-0.504762\pi$
$463$	18.1497	−	10.4787i	0.843488	−	0.486988i	0.858448	+	0.512900i	$0.171429\pi$
$464$	−2.70531	+	0.724884i	−0.125591	+	0.0336519i
$465$	33.4639	+	4.01852i	1.55185	+	0.186354i
$466$	1.54765	−	0.414691i	0.0716933	−	0.0192102i
$467$	22.0375			1.01977			0.509887	−	0.860241i	$-0.329687\pi$
$467$	22.0375			1.01977			0.509887	+	0.860241i	$0.329687\pi$
$468$	−4.69994	−	8.14053i	−0.217255	−	0.376296i
$469$	28.7721	−	49.8348i	1.32857	−	2.30116i
$470$	0.510158	+	0.204540i	0.0235318	+	0.00943473i
$471$		−	18.8577i		−	0.868918i
$472$	0.122512	−	0.0328271i	0.00563909	−	0.00151099i
$473$	4.38439			0.201594
$474$	0.540216	+	0.935681i	0.0248129	+	0.0429773i
$475$	−0.141374	−	6.20664i	−0.00648667	−	0.284780i
$476$	66.2850	+	17.7610i	3.03817	+	0.814075i
$477$	−11.5199	−	3.08676i	−0.527461	−	0.141333i
$478$	0.449791	−	1.67864i	0.0205729	−	0.0767793i
$479$	7.10617	+	26.5206i	0.324689	+	1.21176i	0.914624	+	0.404305i	$0.132487\pi$
$479$	7.10617	+	26.5206i	0.324689	+	1.21176i	−0.589935	+	0.807451i	$0.700847\pi$
$480$	−5.20658	−	2.08750i	−0.237647	−	0.0952809i
$481$	3.63462	+	28.0190i	0.165724	+	1.27756i
$482$	0.270975	−	0.270975i	0.0123426	−	0.0123426i
$483$	0.679864	−	1.17756i	0.0309349	−	0.0535808i
$484$	−5.00185	−	8.66346i	−0.227357	−	0.393794i
$485$	−3.13748	−	2.35120i	−0.142466	−	0.106763i
$486$	−0.276329	+	1.03127i	−0.0125345	+	0.0467795i
$487$	−35.4750			−1.60752			−0.803762	−	0.594951i	$-0.797171\pi$
$487$	−35.4750			−1.60752			−0.803762	+	0.594951i	$0.797171\pi$
$488$	0.298204	−	1.11291i	0.0134991	−	0.0503792i
$489$	−22.4805	+	22.4805i	−1.01660	+	1.01660i
$490$	−0.375390	+	3.12604i	−0.0169584	+	0.141220i
$491$	1.48693			0.0671041			0.0335521	−	0.999437i	$-0.489318\pi$
$491$	1.48693			0.0671041			0.0335521	+	0.999437i	$0.489318\pi$
$492$	−15.5371	−	15.5371i	−0.700467	−	0.700467i
$493$	−5.25310	+	1.40756i	−0.236588	+	0.0633935i
$494$	0.585331	+	0.156839i	0.0263353	+	0.00705652i
$495$	−5.11141	+	2.18573i	−0.229741	+	0.0982412i
$496$	−7.65672	−	28.5753i	−0.343797	−	1.28307i
$497$	12.2972	+	45.8936i	0.551603	+	2.05861i
$498$	−0.166748	−	0.0962721i	−0.00747217	−	0.00431406i
$499$	−5.71230	+	21.3186i	−0.255718	+	0.954352i	0.711972	+	0.702208i	$0.247802\pi$
$499$	−5.71230	+	21.3186i	−0.255718	+	0.954352i	−0.967690	+	0.252144i	$0.918864\pi$
$500$	−21.9350	+	3.65385i	−0.980963	+	0.163405i
$501$	0.275190	+	1.02702i	0.0122946	+	0.0458839i
$502$	−0.789080	+	0.211433i	−0.0352184	+	0.00943673i
$503$	3.42397	+	1.97683i	0.152667	+	0.0881424i	0.574388	−	0.818584i	$-0.305240\pi$
$503$	3.42397	+	1.97683i	0.152667	+	0.0881424i	−0.421720	+	0.906726i	$0.638574\pi$
$504$	−1.36199	+	1.36199i	−0.0606678	+	0.0606678i
$505$	−2.48997	+	3.32265i	−0.110802	+	0.147856i
$506$	0.0333938	+	0.0192799i	0.00148453	+	0.000857096i
$507$	12.1534	−	12.1534i	0.539749	−	0.539749i
$508$	6.97343	−	6.97343i	0.309396	−	0.309396i
$509$	−8.31123	+	14.3955i	−0.368389	+	0.638068i	−0.989314	−	0.145802i	$-0.953424\pi$
$509$	−8.31123	+	14.3955i	−0.368389	+	0.638068i	0.620925	+	0.783870i	$0.286757\pi$
$510$	−3.33884	−	1.33866i	−0.147846	−	0.0592768i
$511$	35.1376	−	20.2867i	1.55440	−	0.897432i
$512$			8.22116i			0.363327i
$513$	2.46698	+	4.27293i	0.108920	+	0.188655i
$514$	−2.45498	+	1.41738i	−0.108284	+	0.0625180i
$515$	−6.37298	−	4.77586i	−0.280827	−	0.210449i
$516$	6.90962	−	1.85143i	0.304179	−	0.0815045i
$517$	−4.04196	−	4.04196i	−0.177765	−	0.177765i
$518$	2.66910	−	1.09964i	0.117274	−	0.0483154i
$519$			5.57520i			0.244724i
$520$	0.519019	−	4.32210i	0.0227605	−	0.189536i
$521$	−1.01799	+	0.587738i	−0.0445990	+	0.0257493i	−0.522134	−	0.852864i	$-0.674864\pi$
$521$	−1.01799	+	0.587738i	−0.0445990	+	0.0257493i	0.477535	+	0.878613i	$0.341530\pi$
$522$	0.0196993	−	0.0735188i	0.000862215	−	0.00321783i
$523$	−30.2054	+	17.4391i	−1.32079	+	0.762560i	−0.983855	−	0.178968i	$-0.942724\pi$
$523$	−30.2054	+	17.4391i	−1.32079	+	0.762560i	−0.336937	+	0.941527i	$0.609391\pi$
$524$	−19.1926	+	19.1926i	−0.838431	+	0.838431i
$525$	−10.7170	+	43.9789i	−0.467727	+	1.91940i
$526$	0.402240	+	0.402240i	0.0175385	+	0.0175385i
$527$	−14.8676	−	55.4868i	−0.647644	−	2.41704i
$528$	13.6233	+	13.6233i	0.592880	+	0.592880i
$529$	22.9774			0.999019
$530$	−1.70126	−	2.16561i	−0.0738980	−	0.0940682i
$531$	0.0796912	−	0.297412i	0.00345830	−	0.0129066i
$532$			11.1545i			0.483609i
$533$	12.8006	−	22.1712i	0.554454	−	0.960342i
$534$	1.40457	+	0.810931i	0.0607818	+	0.0350924i
$535$	−15.7404	−	20.0367i	−0.680517	−	0.866262i
$536$	5.15779	+	1.38203i	0.222783	+	0.0596944i
$537$	9.08500	+	15.7357i	0.392047	+	0.679045i
$538$	0.959996	−	1.66276i	0.0413884	−	0.0716868i
$539$	16.3722	−	28.3574i	0.705199	−	1.22144i
$540$	13.8974	−	10.9175i	0.598050	−	0.469816i
$541$	−4.65504	−	4.65504i	−0.200136	−	0.200136i	0.599922	−	0.800058i	$-0.295198\pi$
$541$	−4.65504	−	4.65504i	−0.200136	−	0.200136i	−0.800058	+	0.599922i	$0.795198\pi$
$542$	1.45865	−	0.842149i	0.0626542	−	0.0361734i
$543$	0.578127	+	2.15760i	0.0248098	+	0.0925915i
$544$			9.56052i			0.409904i
$545$	−5.54093	+	13.8200i	−0.237348	+	0.591985i
$546$	−3.82640	−	2.20917i	−0.163755	−	0.0945439i
$547$			15.3538i			0.656482i	0.944594	+	0.328241i	$0.106456\pi$
$547$			15.3538i			0.656482i	−0.944594	+	0.328241i	$0.893544\pi$
$548$	20.2833	+	5.43490i	0.866461	+	0.232167i
$549$	−1.97779	−	1.97779i	−0.0844100	−	0.0844100i
$550$	−1.24718	−	0.303917i	−0.0531798	−	0.0129591i
$551$	−0.441998	−	0.765562i	−0.0188297	−	0.0326141i
$552$	0.121875	+	0.0326562i	0.00518733	+	0.00138994i
$553$	−20.0675	−	11.5860i	−0.853357	−	0.492686i
$554$	−2.41893			−0.102771
$555$	26.2652	−	7.30549i	1.11490	−	0.310101i
$556$	−15.4091			−0.653491
$557$	14.1931	+	8.19437i	0.601379	+	0.347207i	0.769584	−	0.638546i	$-0.220464\pi$
$557$	14.1931	+	8.19437i	0.601379	+	0.347207i	−0.168205	+	0.985752i	$0.553797\pi$
$558$	0.776555	+	0.208077i	0.0328742	+	0.00880862i
$559$	4.16729	+	7.21795i	0.176258	+	0.305287i
$560$	39.3297	−	5.63416i	1.66198	−	0.238087i
$561$	26.4535	+	26.4535i	1.11687	+	1.11687i
$562$	−2.80511	−	0.751628i	−0.118327	−	0.0317055i
$563$		−	34.2468i		−	1.44333i	−0.692242	−	0.721665i	$-0.743377\pi$
$563$		−	34.2468i		−	1.44333i	0.692242	−	0.721665i	$-0.256623\pi$
$564$	−8.07679	−	4.66313i	−0.340094	−	0.196353i
$565$	−17.0709	+	7.29983i	−0.718178	+	0.307106i
$566$			0.596025i			0.0250528i
$567$	−12.8793	−	48.0661i	−0.540878	−	2.01858i
$568$	−3.81818	+	2.20443i	−0.160207	+	0.0924958i
$569$	−12.1154	−	12.1154i	−0.507904	−	0.507904i	0.405979	−	0.913882i	$-0.366931\pi$
$569$	−12.1154	−	12.1154i	−0.507904	−	0.507904i	−0.913882	+	0.405979i	$0.866931\pi$
$570$	0.0697145	−	0.580543i	0.00292002	−	0.0243163i
$571$	−4.07340	+	7.05533i	−0.170466	+	0.295257i	−0.938583	−	0.345053i	$-0.887861\pi$
$571$	−4.07340	+	7.05533i	−0.170466	+	0.295257i	0.768117	+	0.640310i	$0.221194\pi$
$572$	−11.2869	+	19.5494i	−0.471927	+	0.817401i
$573$	−18.3090	−	31.7120i	−0.764868	−	1.32479i
$574$	−2.52659	−	0.676998i	−0.105458	−	0.0282574i
$575$	0.720764	−	0.210832i	0.0300579	−	0.00879232i
$576$	6.81682	+	3.93570i	0.284034	+	0.163987i
$577$	6.24278	−	10.8128i	0.259890	−	0.450143i	−0.706322	−	0.707891i	$-0.749647\pi$
$577$	6.24278	−	10.8128i	0.259890	−	0.450143i	0.966212	+	0.257748i	$0.0829803\pi$
$578$			4.34470i			0.180716i
$579$	3.47758	−	12.9785i	0.144523	−	0.539369i
$580$	−2.48994	+	1.95605i	−0.103389	+	0.0812204i
$581$	4.12949			0.171320
$582$	−0.261110	−	0.261110i	−0.0108234	−	0.0108234i
$583$	7.41281	+	27.6650i	0.307007	+	1.14577i
$584$	2.66222	+	2.66222i	0.110164	+	0.110164i
$585$	−8.45664	−	6.33733i	−0.349639	−	0.262017i
$586$	−1.03541	+	1.03541i	−0.0427723	+	0.0427723i
$587$	−5.54747	+	3.20283i	−0.228969	+	0.132195i	−0.610096	−	0.792327i	$-0.708869\pi$
$587$	−5.54747	+	3.20283i	−0.228969	+	0.132195i	0.381128	+	0.924522i	$0.375536\pi$
$588$	13.8272	−	51.6037i	0.570223	−	2.12810i
$589$	8.08639	−	4.66868i	0.333194	−	0.192370i
$590$	0.0559099	−	0.0439216i	0.00230177	−	0.00180823i
$591$		−	28.9109i		−	1.18924i
$592$	−14.5309	−	19.0117i	−0.597215	−	0.781376i
$593$	29.3715	+	29.3715i	1.20614	+	1.20614i	0.972267	+	0.233875i	$0.0751408\pi$
$593$	29.3715	+	29.3715i	1.20614	+	1.20614i	0.233875	+	0.972267i	$0.424859\pi$
$594$	0.985427	−	0.264044i	0.0404326	−	0.0108339i
$595$	76.3694	−	10.9403i	3.13084	−	0.448508i
$596$	−2.91698	+	1.68412i	−0.119484	+	0.0689841i
$597$	−9.47384	−	16.4092i	−0.387738	−	0.671582i
$598$			0.0733009i			0.00299750i
$599$	25.2199	−	14.5607i	1.03046	−	0.594934i	0.113341	−	0.993556i	$-0.463845\pi$
$599$	25.2199	−	14.5607i	1.03046	−	0.594934i	0.917115	+	0.398622i	$0.130511\pi$
$600$	−4.19929	+	0.0956509i	−0.171435	+	0.00390493i
$601$	−8.70660	+	15.0803i	−0.355150	+	0.615137i	−0.987144	−	0.159836i	$-0.948903\pi$
$601$	−8.70660	+	15.0803i	−0.355150	+	0.615137i	0.631994	+	0.774973i	$0.282237\pi$
$602$	0.602145	−	0.602145i	0.0245416	−	0.0245416i
$603$	9.16606	−	9.16606i	0.373271	−	0.373271i
$604$	19.4615	+	11.2361i	0.791876	+	0.457190i
$605$	−8.99988	−	6.74443i	−0.365897	−	0.274200i
$606$	−0.276521	+	0.276521i	−0.0112329	+	0.0112329i
$607$	−18.9011	−	10.9126i	−0.767172	−	0.442927i	0.0646926	−	0.997905i	$-0.479393\pi$
$607$	−18.9011	−	10.9126i	−0.767172	−	0.442927i	−0.831865	+	0.554978i	$0.812727\pi$
$608$	−1.50108	+	0.402213i	−0.0608767	+	0.0163119i
$609$	1.66820	+	6.22581i	0.0675989	+	0.252283i
$610$	−0.0915884	−	0.639340i	−0.00370831	−	0.0258861i
$611$	2.81240	−	10.4960i	0.113778	−	0.424624i
$612$	13.3875	+	7.72925i	0.541156	+	0.312436i
$613$	10.6075	+	39.5877i	0.428432	+	1.59893i	0.756312	+	0.654212i	$0.226999\pi$
$613$	10.6075	+	39.5877i	0.428432	+	1.59893i	−0.327879	+	0.944720i	$0.606334\pi$
$614$	−0.282017	−	1.05250i	−0.0113813	−	0.0424756i
$615$	−22.9285	−	9.19283i	−0.924566	−	0.370691i
$616$	4.46799	+	1.19720i	0.180021	+	0.0482364i
$617$	−1.76552	+	0.473071i	−0.0710773	+	0.0190451i	−0.294182	−	0.955749i	$-0.595047\pi$
$617$	−1.76552	+	0.473071i	−0.0710773	+	0.0190451i	0.223105	+	0.974794i	$0.428381\pi$
$618$	−0.530377	−	0.530377i	−0.0213349	−	0.0213349i
$619$	28.5279			1.14663			0.573317	−	0.819334i	$-0.305657\pi$
$619$	28.5279			1.14663			0.573317	+	0.819334i	$0.305657\pi$
$620$	−20.6611	−	26.3004i	−0.829769	−	1.05625i
$621$	−0.422019	+	0.422019i	−0.0169350	+	0.0169350i
$622$	−0.0487050	+	0.181770i	−0.00195289	+	0.00728830i
$623$	−34.7840			−1.39359
$624$	−9.47915	+	35.3767i	−0.379470	+	1.41620i
$625$	−21.0590	+	13.4728i	−0.842361	+	0.538913i
$626$	1.42694	+	2.47152i	0.0570318	+	0.0987820i
$627$	−3.04051	+	5.26631i	−0.121426	+	0.210316i
$628$	−13.2320	+	13.2320i	−0.528013	+	0.528013i
$629$	−28.2157	−	36.9165i	−1.12503	−	1.47196i
$630$	−0.401808	+	1.00218i	−0.0160084	+	0.0399277i
$631$	4.80204	+	17.9215i	0.191166	+	0.713442i	0.993226	+	0.116199i	$0.0370709\pi$
$631$	4.80204	+	17.9215i	0.191166	+	0.713442i	−0.802060	+	0.597244i	$0.796262\pi$
$632$	0.556515	−	2.07694i	0.0221370	−	0.0826163i
$633$	−29.9256	−	8.01854i	−1.18944	−	0.318709i
$634$	−0.664916	−	0.178164i	−0.0264072	−	0.00707579i
$635$	4.12596	−	10.2908i	0.163734	−	0.408380i
$636$	23.3646	+	40.4686i	0.926466	+	1.60469i
$637$	62.2458			2.46627
$638$	−0.176555	+	0.0473077i	−0.00698987	+	0.00187293i
$639$			10.7030i			0.423402i
$640$	2.91537	+	6.81769i	0.115240	+	0.269493i
$641$	5.12828	−	8.88244i	0.202555	−	0.350835i	−0.746796	−	0.665053i	$-0.768409\pi$
$641$	5.12828	−	8.88244i	0.202555	−	0.350835i	0.949351	+	0.314218i	$0.101742\pi$
$642$	−1.19990	−	2.07828i	−0.0473561	−	0.0820232i
$643$	−12.2193			−0.481883			−0.240942	−	0.970540i	$-0.577456\pi$
$643$	−12.2193			−0.481883			−0.240942	+	0.970540i	$0.577456\pi$
$644$	−1.30330	+	0.349219i	−0.0513573	+	0.0137612i
$645$	6.32406	−	4.96805i	0.249010	−	0.195617i
$646$	−0.962601	+	0.257928i	−0.0378730	+	0.0101481i
$647$	13.2479	−	7.64866i	0.520828	−	0.300700i	−0.216446	−	0.976295i	$-0.569446\pi$
$647$	13.2479	−	7.64866i	0.520828	−	0.300700i	0.737273	+	0.675595i	$0.236113\pi$
$648$	3.99892	−	2.30878i	0.157093	−	0.0906974i
$649$	−0.714231	+	0.191378i	−0.0280360	+	0.00751223i
$650$	−0.685086	−	2.34208i	−0.0268713	−	0.0918638i
$651$	−65.7612	+	17.6207i	−2.57739	+	0.690608i
$652$	31.5479			1.23551
$653$	22.6381	+	39.2103i	0.885897	+	1.53442i	0.844682	+	0.535268i	$0.179789\pi$
$653$	22.6381	+	39.2103i	0.885897	+	1.53442i	0.0412146	+	0.999150i	$0.486877\pi$
$654$	−0.701169	+	1.21446i	−0.0274179	+	0.0474891i
$655$	−11.3556	+	28.3229i	−0.443702	+	1.10667i
$656$			21.6823i			0.846550i
$657$	8.82838	−	2.36556i	0.344428	−	0.0922892i
$658$	−1.11023			−0.0432813
$659$	−20.6457	−	35.7594i	−0.804243	−	1.39299i	−0.916801	−	0.399344i	$-0.869238\pi$
$659$	−20.6457	−	35.7594i	−0.804243	−	1.39299i	0.112559	−	0.993645i	$-0.464095\pi$
$660$	20.2171	+	8.10575i	0.786950	+	0.315516i
$661$	−22.9847	−	6.15874i	−0.894003	−	0.239547i	−0.217564	−	0.976046i	$-0.569811\pi$
$661$	−22.9847	−	6.15874i	−0.894003	−	0.239547i	−0.676439	+	0.736499i	$0.736478\pi$
$662$	−2.93690	−	0.786939i	−0.114146	−	0.0305852i
$663$	−18.4064	+	68.6936i	−0.714845	+	2.66784i
$664$	0.0991769	+	0.370133i	0.00384881	+	0.0143640i
$665$	4.93059	+	11.5304i	0.191200	+	0.447128i
$666$	0.644883	−	0.0836541i	0.0249887	−	0.00324153i
$667$	0.0756113	−	0.0756113i	0.00292768	−	0.00292768i
$668$	0.527540	−	0.913727i	0.0204111	−	0.0353531i
$669$	−10.3045	−	17.8479i	−0.398395	−	0.690040i
$670$	2.96302	−	0.424466i	0.114471	−	0.0163986i
$671$	−1.73849	+	6.48813i	−0.0671137	+	0.250472i
$672$	11.3308			0.437096
$673$	5.77687	−	21.5596i	0.222682	−	0.831060i	−0.760638	−	0.649176i	$-0.775114\pi$
$673$	5.77687	−	21.5596i	0.222682	−	0.831060i	0.983320	−	0.181884i	$-0.0582195\pi$
$674$	−0.606207	+	0.606207i	−0.0233502	+	0.0233502i
$675$	9.53988	−	17.4284i	0.367190	−	0.670821i
$676$	−17.0554			−0.655976
$677$	−19.1688	−	19.1688i	−0.736715	−	0.736715i	0.235225	−	0.971941i	$-0.424417\pi$
$677$	−19.1688	−	19.1688i	−0.736715	−	0.736715i	−0.971941	+	0.235225i	$0.924417\pi$
$678$	−1.68904	+	0.452578i	−0.0648673	+	0.0173811i
$679$	7.64976	+	2.04975i	0.293571	+	0.0786621i
$680$	2.81474	+	6.58237i	0.107940	+	0.252422i
$681$	−3.58374	−	13.3747i	−0.137329	−	0.512520i
$682$	−0.499696	−	1.86489i	−0.0191343	−	0.0714103i
$683$	19.2407	+	11.1086i	0.736224	+	0.425059i	0.820695	−	0.571367i	$-0.193587\pi$
$683$	19.2407	+	11.1086i	0.736224	+	0.425059i	−0.0844709	+	0.996426i	$0.526920\pi$
$684$	−0.650342	+	2.42711i	−0.0248664	+	0.0928028i
$685$	23.3692	−	3.34774i	0.892890	−	0.127911i
$686$	−0.786225	−	2.93423i	−0.0300182	−	0.112030i
$687$	−45.6600	+	12.2346i	−1.74204	+	0.466778i
$688$	−6.11308	−	3.52939i	−0.233059	−	0.134557i
$689$	−38.4987	+	38.4987i	−1.46668	+	1.46668i
$690$	0.0700138	−	0.0100298i	0.00266538	−	0.000381828i
$691$	−36.9526	−	21.3346i	−1.40574	−	0.811606i	−0.410769	−	0.911740i	$-0.634740\pi$
$691$	−36.9526	−	21.3346i	−1.40574	−	0.811606i	−0.994974	+	0.100134i	$0.968073\pi$
$692$	3.91197	−	3.91197i	0.148711	−	0.148711i
$693$	7.94020	−	7.94020i	0.301623	−	0.301623i
$694$	1.30651	−	2.26294i	0.0495943	−	0.0858999i
$695$	−15.9283	+	6.81124i	−0.604196	+	0.258365i
$696$	−0.517965	+	0.299047i	−0.0196334	+	0.0113354i
$697$			42.1021i			1.59473i
$698$	−0.971200	−	1.68217i	−0.0367605	−	0.0636710i
$699$	−26.4699	+	15.2824i	−1.00118	+	0.578033i
$700$	38.3787	−	23.3390i	1.45058	−	0.882133i
$701$	−12.0518	+	3.22926i	−0.455189	+	0.121967i	−0.479126	−	0.877746i	$-0.659046\pi$
$701$	−12.0518	+	3.22926i	−0.455189	+	0.121967i	0.0239375	+	0.999713i	$0.492380\pi$
$702$	1.37132	+	1.37132i	0.0517573	+	0.0517573i
$703$	4.60914	−	5.98318i	0.173837	−	0.225660i
$704$		−	18.9031i		−	0.712436i
$705$	−10.4102	−	1.25011i	−0.392070	−	0.0470817i
$706$	−1.65647	+	0.956364i	−0.0623421	+	0.0359932i
$707$	2.17072	−	8.10125i	0.0816385	−	0.304679i
$708$	−1.04478	+	0.603206i	−0.0392654	+	0.0226699i
$709$	36.3631	−	36.3631i	1.36565	−	1.36565i	0.499104	−	0.866542i	$-0.333663\pi$
$709$	36.3631	−	36.3631i	1.36565	−	1.36565i	0.866542	−	0.499104i	$-0.166337\pi$
$710$	−1.48210	+	1.97774i	−0.0556222	+	0.0742231i
$711$	−3.69099	−	3.69099i	−0.138423	−	0.138423i
$712$	−0.835398	−	3.11775i	−0.0313079	−	0.116843i
$713$	0.798658	+	0.798658i	0.0299100	+	0.0299100i
$714$	7.26616			0.271929
$715$	−3.02581	+	25.1972i	−0.113159	+	0.942323i
$716$	4.66661	−	17.4160i	0.174399	−	0.650867i
$717$			33.1518i			1.23808i
$718$	1.33690	−	2.31557i	0.0498926	−	0.0864165i
$719$	−14.6985	−	8.48621i	−0.548163	−	0.316482i	0.200218	−	0.979751i	$-0.435835\pi$
$719$	−14.6985	−	8.48621i	−0.548163	−	0.316482i	−0.748381	+	0.663269i	$0.769168\pi$
$720$	8.88624	+	1.06710i	0.331170	+	0.0397686i
$721$	15.5385	+	4.16353i	0.578684	+	0.155058i
$722$	0.917181	+	1.58860i	0.0341340	+	0.0591218i
$723$	−3.65517	+	6.33094i	−0.135937	+	0.235450i
$724$	1.10827	−	1.91959i	0.0411887	−	0.0713409i
$725$	−1.70922	+	3.12258i	−0.0634788	+	0.115970i
$726$	−0.748995	−	0.748995i	−0.0277978	−	0.0277978i
$727$	−12.6935	+	7.32860i	−0.470776	+	0.271803i	−0.716565	−	0.697521i	$-0.754286\pi$
$727$	−12.6935	+	7.32860i	−0.470776	+	0.271803i	0.245788	+	0.969323i	$0.420953\pi$
$728$	2.27583	+	8.49351i	0.0843478	+	0.314790i
$729$			12.6847i			0.469803i
$730$	1.95892	+	0.785398i	0.0725027	+	0.0290689i
$731$	−11.8702	−	6.85328i	−0.439037	−	0.253478i
$732$			10.9592i			0.405062i
$733$	−18.8454	−	5.04961i	−0.696071	−	0.186512i	−0.106601	−	0.994302i	$-0.533997\pi$
$733$	−18.8454	−	5.04961i	−0.696071	−	0.186512i	−0.589470	+	0.807790i	$0.700663\pi$
$734$	−0.841763	−	0.841763i	−0.0310700	−	0.0310700i
$735$	−8.51714	−	59.4545i	−0.314159	−	2.19301i
$736$	−0.0939899	−	0.162795i	−0.00346451	−	0.00600072i
$737$	−30.0692	−	8.05702i	−1.10761	−	0.296784i
$738$	−0.510291	−	0.294616i	−0.0187841	−	0.0108450i
$739$	−0.970989			−0.0357184			−0.0178592	−	0.999841i	$-0.505685\pi$
$739$	−0.970989			−0.0357184			−0.0178592	+	0.999841i	$0.505685\pi$
$740$	−23.5557	−	13.3035i	−0.865923	−	0.489047i
$741$	−11.5598			−0.424660
$742$	4.81753	+	2.78140i	0.176857	+	0.102108i
$743$	−22.0611	−	5.91126i	−0.809344	−	0.216863i	−0.169662	−	0.985502i	$-0.554268\pi$
$743$	−22.0611	−	5.91126i	−0.809344	−	0.216863i	−0.639683	+	0.768639i	$0.720934\pi$
$744$	−3.15874	−	5.47110i	−0.115805	−	0.200580i
$745$	−2.27084	+	3.03025i	−0.0831972	+	0.111020i
$746$	−2.27171	−	2.27171i	−0.0831732	−	0.0831732i
$747$	0.898536	+	0.240762i	0.0328757	+	0.00880902i
$748$		−	37.1234i		−	1.35737i
$749$	44.5728	+	25.7341i	1.62865	+	0.940304i
$750$	−2.14331	+	0.974832i	−0.0782626	+	0.0355958i
$751$			39.2344i			1.43168i	0.698262	+	0.715842i	$0.253957\pi$
$751$			39.2344i			1.43168i	−0.698262	+	0.715842i	$0.746043\pi$
$752$	2.38190	+	8.88937i	0.0868589	+	0.324162i
$753$	13.4959	−	7.79185i	0.491817	−	0.283951i
$754$	−0.245694	−	0.245694i	−0.00894765	−	0.00894765i
$755$	25.0839	+	3.01220i	0.912896	+	0.109625i
$756$	−17.8491	+	30.9156i	−0.649167	+	1.12439i
$757$	17.2169	−	29.8205i	0.625757	−	1.08384i	−0.362637	−	0.931931i	$-0.618123\pi$
$757$	17.2169	−	29.8205i	0.625757	−	1.08384i	0.988394	−	0.151913i	$-0.0485432\pi$
$758$	−0.368605	−	0.638443i	−0.0133884	−	0.0231893i
$759$	−0.710513	−	0.190381i	−0.0257900	−	0.00691040i
$760$	−0.915069	+	0.718858i	−0.0331930	+	0.0260757i
$761$	13.3522	+	7.70889i	0.484016	+	0.279447i	0.722089	−	0.691800i	$-0.243182\pi$
$761$	13.3522	+	7.70889i	0.484016	+	0.279447i	−0.238072	+	0.971247i	$0.576516\pi$
$762$	0.522113	−	0.904326i	0.0189142	−	0.0327603i
$763$		−	30.0759i		−	1.08882i
$764$	−9.40459	+	35.0984i	−0.340246	+	1.26982i
$765$	17.2551	+	2.07208i	0.623859	+	0.0749161i
$766$	2.21036			0.0798637
$767$	−0.993927	−	0.993927i	−0.0358886	−	0.0358886i
$768$	−7.84589	−	29.2812i	−0.283114	−	1.05660i
$769$	−8.34198	−	8.34198i	−0.300819	−	0.300819i	0.540515	−	0.841334i	$-0.318229\pi$
$769$	−8.34198	−	8.34198i	−0.300819	−	0.300819i	−0.841334	+	0.540515i	$0.818229\pi$
$770$	2.56675	−	0.367699i	0.0924991	−	0.0132509i
$771$	38.2380	−	38.2380i	1.37711	−	1.37711i
$772$	−11.5468	+	6.66655i	−0.415578	+	0.239934i
$773$	−7.88226	+	29.4170i	−0.283505	+	1.05806i	0.666420	+	0.745577i	$0.267826\pi$
$773$	−7.88226	+	29.4170i	−0.283505	+	1.05806i	−0.949925	+	0.312479i	$0.898841\pi$
$774$	0.166128	−	0.0959139i	0.00597134	−	0.00344755i
$775$	−32.9828	−	18.0539i	−1.18478	−	0.648516i
$776$			0.734890i			0.0263810i
$777$	−43.7523	+	33.4404i	−1.56960	+	1.19967i
$778$	−2.16773	−	2.16773i	−0.0777168	−	0.0777168i
$779$	−6.61037	+	1.77124i	−0.236841	+	0.0634614i
$780$	5.87166	+	40.9875i	0.210239	+	1.46759i
$781$	22.2595	−	12.8515i	0.796507	−	0.459864i
$782$	−0.0602732	−	0.104396i	−0.00215537	−	0.00373320i
$783$		−	2.82910i		−	0.101104i
$784$	−45.6548	+	26.3588i	−1.63053	+	0.941387i
$785$	−7.82894	+	19.5267i	−0.279427	+	0.696938i
$786$	−1.43698	+	2.48893i	−0.0512554	+	0.0887770i
$787$	−12.7741	+	12.7741i	−0.455348	+	0.455348i	−0.897125	−	0.441777i	$-0.854348\pi$
$787$	−12.7741	+	12.7741i	−0.455348	+	0.455348i	0.441777	+	0.897125i	$0.354348\pi$
$788$	−20.2860	+	20.2860i	−0.722659	+	0.722659i
$789$	−9.39775	−	5.42579i	−0.334569	−	0.193163i
$790$	−0.170924	−	1.19315i	−0.00608121	−	0.0424504i
$791$	26.5184	−	26.5184i	0.942886	−	0.942886i
$792$	0.902392	+	0.520996i	0.0320651	+	0.0185128i
$793$	−12.3337	+	3.30481i	−0.437983	+	0.117357i
$794$	0.0430442	+	0.160643i	0.00152758	+	0.00570101i
$795$	42.0401	+	31.5045i	1.49101	+	1.11735i
$796$	−4.86633	+	18.1614i	−0.172483	+	0.643714i
$797$	11.4897	+	6.63356i	0.406985	+	0.234973i	0.689493	−	0.724292i	$-0.257833\pi$
$797$	11.4897	+	6.63356i	0.406985	+	0.234973i	−0.282509	+	0.959265i	$0.591167\pi$
$798$	0.305689	+	1.14085i	0.0108213	+	0.0403855i
$799$	4.62512	+	17.2612i	0.163625	+	0.610656i
$800$	4.52464	+	4.32311i	0.159970	+	0.152845i
$801$	−7.56865	−	2.02801i	−0.267425	−	0.0716564i
$802$	−0.391760	+	0.104972i	−0.0138335	+	0.00370668i
$803$	−15.5204	−	15.5204i	−0.547703	−	0.547703i
$804$	−50.7901			−1.79123
$805$	−1.19285	+	0.937081i	−0.0420426	+	0.0330278i
$806$	2.59519	−	2.59519i	0.0914116	−	0.0914116i
$807$	−9.47957	+	35.3782i	−0.333697	+	1.24537i
$808$	0.778263			0.0273792
$809$	7.16080	−	26.7245i	0.251760	−	0.939582i	−0.718104	−	0.695936i	$-0.754990\pi$
$809$	7.16080	−	26.7245i	0.251760	−	0.939582i	0.969864	−	0.243646i	$-0.0783435\pi$
$810$	1.55226	−	2.07136i	0.0545407	−	0.0727800i
$811$	1.13841	+	1.97178i	0.0399749	+	0.0692385i	0.885321	−	0.464981i	$-0.153939\pi$
$811$	1.13841	+	1.97178i	0.0399749	+	0.0692385i	−0.845346	+	0.534220i	$0.820606\pi$
$812$	3.19795	−	5.53902i	0.112226	−	0.194381i
$813$	−22.7194	+	22.7194i	−0.796805	+	0.796805i
$814$	−0.948319	−	1.24075i	−0.0332386	−	0.0434882i
$815$	32.6109	−	13.9450i	1.14231	−	0.488473i
$816$	−15.5889	−	58.1784i	−0.545719	−	2.03665i
$817$	0.576638	−	2.15204i	0.0201740	−	0.0752904i
$818$	1.67628	+	0.449157i	0.0586096	+	0.0157044i
$819$	20.6189	+	5.52481i	0.720481	+	0.193052i
$820$	9.63794	+	22.5387i	0.336571	+	0.787084i
$821$	−13.8253	−	23.9461i	−0.482507	−	0.835726i	0.517292	−	0.855809i	$-0.326940\pi$
$821$	−13.8253	−	23.9461i	−0.482507	−	0.835726i	−0.999798	+	0.0200830i	$0.993607\pi$
$822$	2.22346			0.0775520
$823$	3.44580	−	0.923299i	0.120113	−	0.0321842i	−0.198262	−	0.980149i	$-0.563530\pi$
$823$	3.44580	−	0.923299i	0.120113	−	0.0321842i	0.318375	+	0.947965i	$0.396863\pi$
$824$			1.49274i			0.0520020i
$825$	24.4813	−	0.557632i	0.852330	−	0.0194142i
$826$	−0.0718078	+	0.124375i	−0.00249851	+	0.00432755i
$827$	17.2563	+	29.8888i	0.600060	+	1.03934i	0.992811	+	0.119690i	$0.0381901\pi$
$827$	17.2563	+	29.8888i	0.600060	+	1.03934i	−0.392751	+	0.919645i	$0.628477\pi$
$828$	−0.303947			−0.0105629
$829$	12.0971	−	3.24141i	0.420150	−	0.112579i	−0.0425488	−	0.999094i	$-0.513548\pi$
$829$	12.0971	−	3.24141i	0.420150	−	0.112579i	0.462699	+	0.886516i	$0.346881\pi$
$830$	0.132695	+	0.168914i	0.00460593	+	0.00586310i
$831$	44.5719	−	11.9430i	1.54618	−	0.414298i
$832$	31.1198	−	17.9670i	1.07889	−	0.622895i
$833$	−88.6515	+	51.1830i	−3.07159	+	1.77338i
$834$	−1.57599	+	0.422286i	−0.0545722	+	0.0146226i
$835$	0.141424	−	1.17770i	0.00489419	−	0.0407561i
$836$	5.82868	−	1.56179i	0.201589	−	0.0540156i
$837$	29.8828			1.03290
$838$	0.918102	+	1.59020i	0.0317153	+	0.0549326i
$839$	−15.9229	+	27.5792i	−0.549719	+	0.952141i	0.448575	+	0.893745i	$0.351932\pi$
$839$	−15.9229	+	27.5792i	−0.549719	+	0.952141i	−0.998294	+	0.0583957i	$0.981401\pi$
$840$	7.80122	−	3.33594i	0.269168	−	0.115101i
$841$		−	28.4931i		−	0.982521i
$842$	1.03582	−	0.277547i	0.0356967	−	0.00956490i
$843$	55.3987			1.90803
$844$	15.3716	+	26.6244i	0.529112	+	0.916450i
$845$	−17.6301	+	7.53893i	−0.606493	+	0.259347i
$846$	−0.241576	−	0.0647300i	−0.00830554	−	0.00222546i
$847$	21.9434	+	5.87971i	0.753983	+	0.202029i
$848$	11.9345	−	44.5401i	0.409831	−	1.52951i
$849$	−2.94275	−	10.9825i	−0.100995	−	0.376918i
$850$	2.90153	+	2.77230i	0.0995218	+	0.0950890i
$851$	0.843382	+	0.351219i	0.0289108	+	0.0120396i
$852$	29.6531	−	29.6531i	1.01590	−	1.01590i
$853$	8.54847	−	14.8064i	0.292694	−	0.506961i	−0.681752	−	0.731583i	$-0.738782\pi$
$853$	8.54847	−	14.8064i	0.292694	−	0.506961i	0.974446	+	0.224623i	$0.0721150\pi$
$854$	0.652308	+	1.12983i	0.0223215	+	0.0386620i
$855$	0.400592	+	2.79636i	0.0137000	+	0.0956335i
$856$	−1.23610	+	4.61318i	−0.0422490	+	0.157675i
$857$	−13.4046			−0.457892			−0.228946	−	0.973439i	$-0.573528\pi$
$857$	−13.4046			−0.457892			−0.228946	+	0.973439i	$0.573528\pi$
$858$	−0.618632	+	2.30877i	−0.0211197	+	0.0788199i
$859$	−7.23511	+	7.23511i	−0.246859	+	0.246859i	−0.819680	−	0.572821i	$-0.805849\pi$
$859$	−7.23511	+	7.23511i	−0.246859	+	0.246859i	0.572821	+	0.819680i	$0.305849\pi$
$860$	−7.92337	−	0.951478i	−0.270185	−	0.0324451i
$861$	49.8981			1.70052
$862$	−2.13714	−	2.13714i	−0.0727912	−	0.0727912i
$863$	−2.40453	+	0.644292i	−0.0818512	+	0.0219320i	−0.299512	−	0.954092i	$-0.596824\pi$
$863$	−2.40453	+	0.644292i	−0.0818512	+	0.0219320i	0.217661	+	0.976024i	$0.430157\pi$
$864$	−4.80398	−	1.28722i	−0.163435	−	0.0437922i
$865$	2.31459	−	5.77298i	0.0786984	−	0.196287i
$866$	0.465314	+	1.73658i	0.0158120	+	0.0590113i
$867$	−21.4511	−	80.0565i	−0.728516	−	2.71886i
$868$	58.5068	+	33.7789i	1.98585	+	1.14653i
$869$	−3.24441	+	12.1083i	−0.110059	+	0.410746i
$870$	−0.201058	+	0.268295i	−0.00681650	+	0.00909605i
$871$	−15.3161	−	57.1606i	−0.518967	−	1.93681i
$872$	2.69575	−	0.722324i	0.0912896	−	0.0244610i
$873$	1.54501	+	0.892010i	0.0522906	+	0.0301900i
$874$	0.0138554	−	0.0138554i	0.000468664	−	0.000468664i
$875$	29.3554	−	41.0899i	0.992393	−	1.38909i
$876$	−31.0134	−	17.9056i	−1.04785	−	0.604975i
$877$	11.4866	−	11.4866i	0.387875	−	0.387875i	−0.486054	−	0.873929i	$-0.661564\pi$
$877$	11.4866	−	11.4866i	0.387875	−	0.387875i	0.873929	+	0.486054i	$0.161564\pi$
$878$	0.748664	−	0.748664i	0.0252662	−	0.0252662i
$879$	13.9666	−	24.1908i	0.471081	−	0.815935i
$880$	−8.45079	−	19.7625i	−0.284876	−	0.666193i
$881$	−46.0684	+	26.5976i	−1.55208	+	0.896096i	−0.554112	+	0.832442i	$0.686942\pi$
$881$	−46.0684	+	26.5976i	−1.55208	+	0.896096i	−0.997972	+	0.0636536i	$0.979725\pi$
$882$		−	1.43264i		−	0.0482396i
$883$	13.3117	+	23.0566i	0.447975	+	0.775916i	0.998254	−	0.0590650i	$-0.0188119\pi$
$883$	13.3117	+	23.0566i	0.447975	+	0.775916i	−0.550279	+	0.834981i	$0.685479\pi$
$884$	61.1157	−	35.2852i	2.05554	−	1.18677i
$885$	−0.813356	+	1.08535i	−0.0273406	+	0.0364838i
$886$	−3.94598	+	1.05732i	−0.132568	+	0.0355214i
$887$	21.7089	+	21.7089i	0.728912	+	0.728912i	0.970403	−	0.241491i	$-0.0776364\pi$
$887$	21.7089	+	21.7089i	0.728912	+	0.728912i	−0.241491	+	0.970403i	$0.577636\pi$
$888$	−4.04811	−	3.11846i	−0.135846	−	0.104649i
$889$			22.3955i			0.751120i
$890$	−1.11774	−	1.42282i	−0.0374666	−	0.0476930i
$891$	−23.3132	+	13.4599i	−0.781021	+	0.450923i
$892$	−5.29301	+	19.7538i	−0.177223	+	0.661405i
$893$	−2.51556	+	1.45236i	−0.0841801	+	0.0486014i
$894$	−0.252186	+	0.252186i	−0.00843435	+	0.00843435i
$895$	−2.87450	−	20.0656i	−0.0960838	−	0.670720i
$896$	−10.5908	−	10.5908i	−0.353813	−	0.353813i
$897$	−0.361908	−	1.35066i	−0.0120838	−	0.0450972i
$898$	−1.86575	−	1.86575i	−0.0622609	−	0.0622609i
$899$	−5.35397			−0.178565
$900$	9.71156	−	2.84075i	0.323719	−	0.0946917i
$901$	23.1741	−	86.4869i	0.772041	−	2.88130i
$902$			1.41504i			0.0471156i
$903$	−8.12230	+	14.0682i	−0.270293	+	0.468162i
$904$	3.01378	+	1.74001i	0.100237	+	0.0578717i
$905$	0.297109	−	2.47416i	0.00987624	−	0.0822437i
$906$	2.29838	+	0.615849i	0.0763586	+	0.0204602i
$907$	5.33028	+	9.23231i	0.176989	+	0.306554i	0.940848	−	0.338830i	$-0.110031\pi$
$907$	5.33028	+	9.23231i	0.176989	+	0.306554i	−0.763859	+	0.645383i	$0.776698\pi$
$908$	−6.87006	+	11.8993i	−0.227991	+	0.394892i
$909$	0.944656	−	1.63619i	0.0313323	−	0.0542691i
$910$	3.04499	+	3.87611i	0.100940	+	0.128492i
$911$	10.7665	+	10.7665i	0.356708	+	0.356708i	0.862598	−	0.505890i	$-0.168836\pi$
$911$	10.7665	+	10.7665i	0.356708	+	0.356708i	−0.505890	+	0.862598i	$0.668836\pi$
$912$	8.47866	−	4.89515i	0.280756	−	0.162095i
$913$	−0.578188	−	2.15783i	−0.0191352	−	0.0714136i
$914$			0.184097i			0.00608938i
$915$	4.84424	+	11.3284i	0.160146	+	0.374506i
$916$	40.6231	+	23.4538i	1.34222	+	0.774934i
$917$		−	61.6378i		−	2.03546i
$918$	−3.08066	−	0.825461i	−0.101677	−	0.0272443i
$919$	−13.7345	−	13.7345i	−0.453059	−	0.453059i	0.443310	−	0.896368i	$-0.353804\pi$
$919$	−13.7345	−	13.7345i	−0.453059	−	0.453059i	−0.896368	+	0.443310i	$0.853804\pi$
$920$	−0.112641	−	0.0844120i	−0.00371365	−	0.00278298i
$921$	10.3930	+	18.0013i	0.342463	+	0.593162i
$922$	1.88436	+	0.504913i	0.0620581	+	0.0166284i
$923$	42.3145	+	24.4303i	1.39280	+	0.804133i
$924$	−43.9975			−1.44741
$925$	−30.2299	−	3.33956i	−0.993953	−	0.109804i
$926$	−2.20202			−0.0723629
$927$	3.13828	+	1.81189i	0.103075	+	0.0595102i
$928$	0.860707	+	0.230626i	0.0282541	+	0.00757066i
$929$	−2.36184	−	4.09083i	−0.0774895	−	0.134216i	0.824677	−	0.565604i	$-0.191357\pi$
$929$	−2.36184	−	4.09083i	−0.0774895	−	0.134216i	−0.902166	+	0.431389i	$0.858024\pi$
$930$	−2.83391	−	2.12371i	−0.0929276	−	0.0696391i
$931$	−11.7657	−	11.7657i	−0.385606	−	0.385606i
$932$	29.2964	+	7.84996i	0.959637	+	0.257134i
$933$		−	3.58980i		−	0.117525i
$934$	−2.00529	−	1.15775i	−0.0656149	−	0.0378828i
$935$	−16.4096	−	38.3743i	−0.536650	−	1.25497i
$936$			1.98079i			0.0647442i
$937$	10.1474	+	37.8706i	0.331501	+	1.23718i	0.907613	+	0.419808i	$0.137903\pi$
$937$	10.1474	+	37.8706i	0.331501	+	1.23718i	−0.576112	+	0.817371i	$0.695431\pi$
$938$	−5.23619	+	3.02312i	−0.170968	+	0.0987083i
$939$	−38.4957	−	38.4957i	−1.25626	−	1.25626i
$940$	6.42737	+	8.18170i	0.209638	+	0.266858i
$941$	3.93030	−	6.80748i	0.128124	−	0.221917i	−0.794826	−	0.606838i	$-0.792438\pi$
$941$	3.93030	−	6.80748i	0.128124	−	0.221917i	0.922950	+	0.384920i	$0.125771\pi$
$942$	−0.990700	+	1.71594i	−0.0322788	+	0.0559085i
$943$	−0.413908	−	0.716910i	−0.0134787	−	0.0233458i
$944$	1.14990	+	0.308114i	0.0374260	+	0.0100283i
$945$	−4.78505	+	39.8472i	−0.155658	+	1.29623i
$946$	−0.398954	−	0.230336i	−0.0129711	−	0.00748888i
$947$	−20.1394	+	34.8825i	−0.654444	+	1.13353i	0.327589	+	0.944820i	$0.393764\pi$
$947$	−20.1394	+	34.8825i	−0.654444	+	1.13353i	−0.982033	+	0.188710i	$0.939569\pi$
$948$			20.4522i			0.664257i
$949$	10.7991	−	40.3029i	0.350555	−	1.30829i
$950$	−0.313205	+	0.572195i	−0.0101617	+	0.0185645i
$951$	13.1316			0.425820
$952$	−10.2252	−	10.2252i	−0.331402	−	0.331402i
$953$	−7.91365	−	29.5341i	−0.256348	−	0.956705i	−0.967335	−	0.253500i	$-0.918418\pi$
$953$	−7.91365	−	29.5341i	−0.256348	−	0.956705i	0.710987	−	0.703205i	$-0.248248\pi$
$954$	0.886083	+	0.886083i	0.0286880	+	0.0286880i
$955$	5.79295	+	40.4381i	0.187456	+	1.30855i
$956$	23.2617	−	23.2617i	0.752338	−	0.752338i
$957$	3.01967	−	1.74341i	0.0976120	−	0.0563563i
$958$	0.746652	−	2.78654i	0.0241232	−	0.0900292i
$959$	−41.2976	+	23.8432i	−1.33357	+	0.769937i
$960$	−21.4195	−	27.2659i	−0.691311	−	0.880002i
$961$		−	25.5523i		−	0.824267i
$962$	1.14126	−	2.74051i	0.0367958	−	0.0883577i
$963$	8.19822	+	8.19822i	0.264184	+	0.264184i
$964$	7.00699	−	1.87752i	0.225680	−	0.0604707i
$965$	−8.98909	+	11.9952i	−0.289369	+	0.386138i
$966$	−0.123727	+	0.0714340i	−0.00398086	+	0.00229835i
$967$	−10.0949	−	17.4848i	−0.324629	−	0.562273i	0.656809	−	0.754057i	$-0.271906\pi$
$967$	−10.0949	−	17.4848i	−0.324629	−	0.562273i	−0.981437	+	0.191784i	$0.938573\pi$
$968$			2.10803i			0.0677548i
$969$	16.4637	−	9.50530i	0.528889	−	0.305354i
$970$	0.161971	+	0.378775i	0.00520058	+	0.0121617i
$971$	−13.3211	+	23.0728i	−0.427494	+	0.740441i	−0.996650	−	0.0817885i	$-0.973937\pi$
$971$	−13.3211	+	23.0728i	−0.427494	+	0.740441i	0.569156	+	0.822230i	$0.307270\pi$
$972$	−14.2908	+	14.2908i	−0.458379	+	0.458379i
$973$	24.7435	−	24.7435i	0.793240	−	0.793240i
$974$	3.22802	+	1.86370i	0.103432	+	0.0597167i
$975$	24.1871	+	39.7732i	0.774607	+	1.27376i
$976$	7.64683	−	7.64683i	0.244769	−	0.244769i
$977$	−5.30924	−	3.06529i	−0.169858	−	0.0980674i	0.412661	−	0.910885i	$-0.364599\pi$
$977$	−5.30924	−	3.06529i	−0.169858	−	0.0980674i	−0.582519	+	0.812817i	$0.697933\pi$
$978$	3.22662	−	0.864569i	0.103176	−	0.0276459i
$979$	4.87026	+	18.1760i	0.155654	+	0.580909i
$980$	−35.7414	+	47.6939i	−1.14172	+	1.52353i
$981$	1.75352	−	6.54421i	0.0559855	−	0.208941i
$982$	−0.135302	−	0.0781165i	−0.00431765	−	0.00249280i
$983$	5.47856	+	20.4463i	0.174739	+	0.652134i	0.996596	+	0.0824406i	$0.0262715\pi$
$983$	5.47856	+	20.4463i	0.174739	+	0.652134i	−0.821857	+	0.569694i	$0.807062\pi$
$984$	1.19839	+	4.47246i	0.0382033	+	0.142577i
$985$	−12.0026	+	29.9365i	−0.382435	+	0.953857i
$986$	0.551949	+	0.147894i	0.0175776	+	0.00470991i
$987$	20.4574	−	5.48155i	0.651166	−	0.174480i
$988$	8.11121	+	8.11121i	0.258052	+	0.258052i
$989$	0.269500			0.00856960
$990$	0.579937	+	0.0696417i	0.0184316	+	0.00221336i
$991$	−24.8692	+	24.8692i	−0.789997	+	0.789997i	−0.981493	−	0.191497i	$-0.938666\pi$
$991$	−24.8692	+	24.8692i	−0.789997	+	0.789997i	0.191497	+	0.981493i	$0.438666\pi$
$992$	−2.43603	+	9.09137i	−0.0773439	+	0.288651i
$993$	58.0013			1.84062
$994$	1.29207	−	4.82209i	0.0409821	−	0.152947i
$995$	2.99752	+	20.9244i	0.0950278	+	0.663349i
$996$	−1.82240	−	3.15649i	−0.0577449	−	0.100017i
$997$	−8.91895	+	15.4481i	−0.282466	+	0.489245i	−0.971992	−	0.235016i	$-0.924486\pi$
$997$	−8.91895	+	15.4481i	−0.282466	+	0.489245i	0.689526	+	0.724261i	$0.257819\pi$
$998$	1.63977	−	1.63977i	0.0519060	−	0.0519060i
$999$	22.3488	−	9.20745i	0.707084	−	0.291311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.u.a.23.9	yes	68
5.2	odd	4		185.2.p.a.97.9	✓	68
5.3	odd	4		925.2.t.b.282.9		68
5.4	even	2		925.2.y.b.393.9		68
37.29	odd	12		185.2.p.a.103.9	yes	68
185.29	odd	12		925.2.t.b.843.9		68
185.103	even	12		925.2.y.b.732.9		68
185.177	even	12	inner	185.2.u.a.177.9	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.9	✓	68	5.2	odd	4
185.2.p.a.103.9	yes	68	37.29	odd	12
185.2.u.a.23.9	yes	68	1.1	even	1	trivial
185.2.u.a.177.9	yes	68	185.177	even	12	inner
925.2.t.b.282.9		68	5.3	odd	4
925.2.t.b.843.9		68	185.29	odd	12
925.2.y.b.393.9		68	5.4	even	2
925.2.y.b.732.9		68	185.103	even	12

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0909942 - 0.0525355i) q^{2} +(1.93607 + 0.518767i) q^{3} +(-0.994480 - 1.72249i) q^{4} +(-1.78938 - 1.34094i) q^{5} +(-0.148917 - 0.148917i) q^{6} +(4.36283 + 1.16902i) q^{7} +0.419124i q^{8} +(0.881153 + 0.508734i) q^{9} +(0.0923757 + 0.216024i) q^{10} -2.44344i q^{11} +(-1.03181 - 3.85076i) q^{12} +(4.02259 - 2.32245i) q^{13} +(-0.335578 - 0.335578i) q^{14} +(-2.76871 - 3.52442i) q^{15} +(-1.96694 + 3.40684i) q^{16} +(-3.81936 + 6.61533i) q^{17} +(-0.0534532 - 0.0925836i) q^{18} +(-1.19934 - 0.321362i) q^{19} +(-0.530263 + 4.41573i) q^{20} +(7.84028 + 4.52659i) q^{21} +(-0.128367 + 0.222339i) q^{22} -0.150193i q^{23} +(-0.217428 + 0.811452i) q^{24} +(1.40374 + 4.79891i) q^{25} -0.488044 q^{26} +(-2.80984 - 2.80984i) q^{27} +(-2.32513 - 8.67750i) q^{28} +(0.503427 + 0.503427i) q^{29} +(0.0667793 + 0.466158i) q^{30} +(-5.31753 + 5.31753i) q^{31} +(1.08391 - 0.625793i) q^{32} +(1.26757 - 4.73065i) q^{33} +(0.695080 - 0.401304i) q^{34} +(-6.23917 - 7.94213i) q^{35} -2.02370i q^{36} +(-2.33845 + 5.61531i) q^{37} +(0.0922501 + 0.0922501i) q^{38} +(8.99281 - 2.40962i) q^{39} +(0.562022 - 0.749971i) q^{40} +(4.77325 - 2.75584i) q^{41} +(-0.475614 - 0.823787i) q^{42} +1.79435i q^{43} +(-4.20880 + 2.42995i) q^{44} +(-0.894531 - 2.09189i) q^{45} +(-0.00789049 + 0.0136667i) q^{46} +(1.65421 - 1.65421i) q^{47} +(-5.57548 + 5.57548i) q^{48} +(11.6055 + 6.70046i) q^{49} +(0.124381 - 0.510419i) q^{50} +(-10.8263 + 10.8263i) q^{51} +(-8.00078 - 4.61925i) q^{52} +(-11.3222 + 3.03376i) q^{53} +(0.108063 + 0.403296i) q^{54} +(-3.27651 + 4.37223i) q^{55} +(-0.489964 + 1.82857i) q^{56} +(-2.15529 - 1.24436i) q^{57} +(-0.0193611 - 0.0722567i) q^{58} +(-0.0783231 - 0.292306i) q^{59} +(-3.31736 + 8.27405i) q^{60} +(-2.65533 - 0.711494i) q^{61} +(0.763224 - 0.204505i) q^{62} +(3.24960 + 3.24960i) q^{63} +7.73626 q^{64} +(-10.3122 - 1.23834i) q^{65} +(-0.363869 + 0.363869i) q^{66} +(3.29741 - 12.3061i) q^{67} +15.1931 q^{68} +(0.0779154 - 0.290784i) q^{69} +(0.150484 + 1.05047i) q^{70} +(5.25961 + 9.10991i) q^{71} +(-0.213223 + 0.369312i) q^{72} +(6.35187 - 6.35187i) q^{73} +(0.507788 - 0.388109i) q^{74} +(0.228216 + 10.0192i) q^{75} +(0.639177 + 2.38544i) q^{76} +(2.85642 - 10.6603i) q^{77} +(-0.944884 - 0.253181i) q^{78} +(-4.95543 - 1.32780i) q^{79} +(8.08798 - 3.45857i) q^{80} +(-5.50858 - 9.54114i) q^{81} -0.579117 q^{82} +(0.883111 - 0.236629i) q^{83} -18.0064i q^{84} +(15.7051 - 6.71577i) q^{85} +(0.0942673 - 0.163276i) q^{86} +(0.713506 + 1.23583i) q^{87} +1.02410 q^{88} +(-7.43872 + 1.99320i) q^{89} +(-0.0285015 + 0.237345i) q^{90} +(20.2649 - 5.42996i) q^{91} +(-0.258707 + 0.149364i) q^{92} +(-13.0536 + 7.53653i) q^{93} +(-0.237428 + 0.0636187i) q^{94} +(1.71514 + 2.18329i) q^{95} +(2.42315 - 0.649281i) q^{96} +1.75339 q^{97} +(-0.704025 - 1.21941i) q^{98} +(1.24306 - 2.15304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Introduction

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