LMFDB - Embedded newform 185.2.p.a.103.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] 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([3, 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("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (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			103.9
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0525355 + 0.0909942i) q^{2} +(0.518767 + 1.93607i) q^{3} +(0.994480 - 1.72249i) q^{4} +(2.22012 + 0.266603i) q^{5} +(-0.148917 + 0.148917i) q^{6} +(-1.16902 - 4.36283i) q^{7} +0.419124 q^{8} +(-0.881153 + 0.508734i) q^{9} +(0.0923757 + 0.216024i) q^{10} +2.44344i q^{11} +(3.85076 + 1.03181i) q^{12} +(-2.32245 + 4.02259i) q^{13} +(0.335578 - 0.335578i) q^{14} +(0.635563 + 4.43660i) q^{15} +(-1.96694 - 3.40684i) q^{16} +(-6.61533 + 3.81936i) q^{17} +(-0.0925836 - 0.0534532i) q^{18} +(1.19934 - 0.321362i) q^{19} +(2.66708 - 3.55900i) q^{20} +(7.84028 - 4.52659i) q^{21} +(-0.222339 + 0.128367i) q^{22} -0.150193 q^{23} +(0.217428 + 0.811452i) q^{24} +(4.85785 + 1.18378i) q^{25} -0.488044 q^{26} +(2.80984 + 2.80984i) q^{27} +(-8.67750 - 2.32513i) q^{28} +(-0.503427 + 0.503427i) q^{29} +(-0.370315 + 0.290912i) q^{30} +(-5.31753 - 5.31753i) q^{31} +(0.625793 - 1.08391i) q^{32} +(-4.73065 + 1.26757i) q^{33} +(-0.695080 - 0.401304i) q^{34} +(-1.43221 - 9.99767i) q^{35} +2.02370i q^{36} +(-5.61531 + 2.33845i) q^{37} +(0.0922501 + 0.0922501i) q^{38} +(-8.99281 - 2.40962i) q^{39} +(0.930505 + 0.111740i) q^{40} +(4.77325 + 2.75584i) q^{41} +(0.823787 + 0.475614i) q^{42} +1.79435 q^{43} +(4.20880 + 2.42995i) q^{44} +(-2.09189 + 0.894531i) 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} +(0.147492 + 0.504226i) q^{50} +(-10.8263 - 10.8263i) q^{51} +(4.61925 + 8.00078i) q^{52} +(3.03376 - 11.3222i) q^{53} +(-0.108063 + 0.403296i) q^{54} +(-0.651427 + 5.42472i) q^{55} +(-0.489964 - 1.82857i) q^{56} +(1.24436 + 2.15529i) q^{57} +(-0.0722567 - 0.0193611i) q^{58} +(0.0783231 - 0.292306i) q^{59} +(8.27405 + 3.31736i) q^{60} +(-2.65533 + 0.711494i) q^{61} +(0.204505 - 0.763224i) q^{62} +(3.24960 + 3.24960i) q^{63} -7.73626 q^{64} +(-6.22854 + 8.31146i) q^{65} +(-0.363869 - 0.363869i) q^{66} +(12.3061 - 3.29741i) q^{67} +15.1931i q^{68} +(-0.0779154 - 0.290784i) q^{69} +(0.834488 - 0.655556i) q^{70} +(5.25961 - 9.10991i) q^{71} +(-0.369312 + 0.213223i) 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} +(10.6603 - 2.85642i) q^{77} +(-0.253181 - 0.944884i) q^{78} +(4.95543 - 1.32780i) q^{79} +(-3.45857 - 8.08798i) q^{80} +(-5.50858 + 9.54114i) q^{81} +0.579117i q^{82} +(-0.236629 + 0.883111i) q^{83} -18.0064i q^{84} +(-15.7051 + 6.71577i) q^{85} +(0.0942673 + 0.163276i) q^{86} +(-1.23583 - 0.713506i) q^{87} +1.02410i q^{88} +(7.43872 + 1.99320i) q^{89} +(-0.191296 - 0.143355i) q^{90} +(20.2649 + 5.42996i) q^{91} +(-0.149364 + 0.258707i) q^{92} +(7.53653 - 13.0536i) q^{93} +(0.237428 + 0.0636187i) q^{94} +(2.74835 - 0.393715i) q^{95} +(2.42315 + 0.649281i) q^{96} -1.75339i q^{97} +(-1.21941 - 0.704025i) q^{98} +(-1.24306 - 2.15304i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

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

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	0.0525355	+	0.0909942i	0.0371482	+	0.0643426i	0.884002	−	0.467484i	$-0.154839\pi$
$2$	0.0525355	+	0.0909942i	0.0371482	+	0.0643426i	−0.846854	+	0.531826i	$0.821506\pi$
$3$	0.518767	+	1.93607i	0.299510	+	1.11779i	0.937569	+	0.347800i	$0.113071\pi$
$3$	0.518767	+	1.93607i	0.299510	+	1.11779i	−0.638059	+	0.769988i	$0.720262\pi$
$4$	0.994480	−	1.72249i	0.497240	−	0.861245i
$5$	2.22012	+	0.266603i	0.992867	+	0.119228i
$5$	2.22012	+	0.266603i	0.992867	+	0.119228i
$6$	−0.148917	+	0.148917i	−0.0607951	+	0.0607951i
$7$	−1.16902	−	4.36283i	−0.441847	−	1.64900i	−0.724129	−	0.689665i	$-0.757758\pi$
$7$	−1.16902	−	4.36283i	−0.441847	−	1.64900i	0.282282	−	0.959332i	$-0.408909\pi$
$8$	0.419124			0.148183
$9$	−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	$0.120081\pi$
$11$			2.44344i			0.736724i	−0.929682	+	0.368362i	$0.879919\pi$
$12$	3.85076	+	1.03181i	1.11162	+	0.297857i
$13$	−2.32245	+	4.02259i	−0.644131	+	1.11567i	0.340371	+	0.940291i	$0.389447\pi$
$13$	−2.32245	+	4.02259i	−0.644131	+	1.11567i	−0.984502	+	0.175376i	$0.943886\pi$
$14$	0.335578	−	0.335578i	0.0896869	−	0.0896869i
$15$	0.635563	+	4.43660i	0.164102	+	1.14552i
$16$	−1.96694	−	3.40684i	−0.491735	−	0.851711i
$17$	−6.61533	+	3.81936i	−1.60445	+	0.926331i	−0.613871	+	0.789406i	$0.710389\pi$
$17$	−6.61533	+	3.81936i	−1.60445	+	0.926331i	−0.990581	+	0.136925i	$0.956278\pi$
$18$	−0.0925836	−	0.0534532i	−0.0218222	−	0.0125990i
$19$	1.19934	−	0.321362i	0.275148	−	0.0737256i	−0.118607	−	0.992941i	$-0.537843\pi$
$19$	1.19934	−	0.321362i	0.275148	−	0.0737256i	0.393754	+	0.919216i	$0.371176\pi$
$20$	2.66708	−	3.55900i	0.596378	−	0.795816i
$21$	7.84028	−	4.52659i	1.71089	−	0.987783i
$22$	−0.222339	+	0.128367i	−0.0474028	+	0.0273680i
$23$	−0.150193			−0.0313175			−0.0156587	−	0.999877i	$-0.504985\pi$
$23$	−0.150193			−0.0313175			−0.0156587	+	0.999877i	$0.504985\pi$
$24$	0.217428	+	0.811452i	0.0443823	+	0.165637i
$25$	4.85785	+	1.18378i	0.971569	+	0.236756i
$26$	−0.488044			−0.0957132
$27$	2.80984	+	2.80984i	0.540754	+	0.540754i
$28$	−8.67750	−	2.32513i	−1.63989	−	0.439408i
$29$	−0.503427	+	0.503427i	−0.0934840	+	0.0934840i	−0.752302	−	0.658818i	$-0.771057\pi$
$29$	−0.503427	+	0.503427i	−0.0934840	+	0.0934840i	0.658818	+	0.752302i	$0.271057\pi$
$30$	−0.370315	+	0.290912i	−0.0676100	+	0.0531129i
$31$	−5.31753	−	5.31753i	−0.955057	−	0.955057i	0.0439759	−	0.999033i	$-0.485998\pi$
$31$	−5.31753	−	5.31753i	−0.955057	−	0.955057i	−0.999033	+	0.0439759i	$0.985998\pi$
$32$	0.625793	−	1.08391i	0.110626	−	0.191609i
$33$	−4.73065	+	1.26757i	−0.823501	+	0.220656i
$34$	−0.695080	−	0.401304i	−0.119205	−	0.0688231i
$35$	−1.43221	−	9.99767i	−0.242088	−	1.68991i
$36$			2.02370i			0.337284i
$37$	−5.61531	+	2.33845i	−0.923151	+	0.384438i
$37$	−5.61531	+	2.33845i	−0.923151	+	0.384438i
$38$	0.0922501	+	0.0922501i	0.0149649	+	0.0149649i
$39$	−8.99281	−	2.40962i	−1.44000	−	0.385847i
$40$	0.930505	+	0.111740i	0.147126	+	0.0176676i
$41$	4.77325	+	2.75584i	0.745456	+	0.430389i	0.824050	−	0.566518i	$-0.191710\pi$
$41$	4.77325	+	2.75584i	0.745456	+	0.430389i	−0.0785937	+	0.996907i	$0.525043\pi$
$42$	0.823787	+	0.475614i	0.127113	+	0.0733888i
$43$	1.79435			0.273636			0.136818	−	0.990596i	$-0.456312\pi$
$43$	1.79435			0.273636			0.136818	+	0.990596i	$0.456312\pi$
$44$	4.20880	+	2.42995i	0.634500	+	0.366329i
$45$	−2.09189	+	0.894531i	−0.311841	+	0.133349i
$46$	−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
$50$	0.147492	+	0.504226i	0.0208586	+	0.0713084i
$51$	−10.8263	−	10.8263i	−1.51599	−	1.51599i
$52$	4.61925	+	8.00078i	0.640575	+	1.10951i
$53$	3.03376	−	11.3222i	0.416720	−	1.55522i	−0.364647	−	0.931146i	$-0.618810\pi$
$53$	3.03376	−	11.3222i	0.416720	−	1.55522i	0.781366	−	0.624073i	$-0.214523\pi$
$54$	−0.108063	+	0.403296i	−0.0147055	+	0.0548816i
$55$	−0.651427	+	5.42472i	−0.0878384	+	0.731469i
$56$	−0.489964	−	1.82857i	−0.0654742	−	0.244353i
$57$	1.24436	+	2.15529i	0.164819	+	0.285475i
$58$	−0.0722567	−	0.0193611i	−0.00948777	−	0.00254224i
$59$	0.0783231	−	0.292306i	0.0101968	−	0.0380550i	−0.960640	−	0.277796i	$-0.910396\pi$
$59$	0.0783231	−	0.292306i	0.0101968	−	0.0380550i	0.970837	+	0.239741i	$0.0770626\pi$
$60$	8.27405	+	3.31736i	1.06818	+	0.428269i
$61$	−2.65533	+	0.711494i	−0.339980	+	0.0910974i	−0.424770	−	0.905301i	$-0.639645\pi$
$61$	−2.65533	+	0.711494i	−0.339980	+	0.0910974i	0.0847894	+	0.996399i	$0.472978\pi$
$62$	0.204505	−	0.763224i	0.0259722	−	0.0969295i
$63$	3.24960	+	3.24960i	0.409412	+	0.409412i
$64$	−7.73626			−0.967032
$65$	−6.22854	+	8.31146i	−0.772555	+	1.03091i
$66$	−0.363869	−	0.363869i	−0.0447892	−	0.0447892i
$67$	12.3061	−	3.29741i	1.50343	−	0.402843i	0.589183	−	0.807999i	$-0.299450\pi$
$67$	12.3061	−	3.29741i	1.50343	−	0.402843i	0.914247	+	0.405156i	$0.132783\pi$
$68$			15.1931i			1.84244i
$69$	−0.0779154	−	0.290784i	−0.00937991	−	0.0350063i
$70$	0.834488	−	0.655556i	0.0997404	−	0.0783539i
$71$	5.25961	−	9.10991i	0.624201	−	1.08115i	−0.364494	−	0.931206i	$-0.618758\pi$
$71$	5.25961	−	9.10991i	0.624201	−	1.08115i	0.988695	−	0.149941i	$-0.0479085\pi$
$72$	−0.369312	+	0.213223i	−0.0435239	+	0.0251285i
$73$	−6.35187	+	6.35187i	−0.743431	+	0.743431i	−0.973237	−	0.229806i	$-0.926191\pi$
$73$	−6.35187	+	6.35187i	−0.743431	+	0.743431i	0.229806	+	0.973237i	$0.426191\pi$
$74$	−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
$77$	10.6603	−	2.85642i	1.21486	−	0.325519i
$78$	−0.253181	−	0.944884i	−0.0286671	−	0.106987i
$79$	4.95543	−	1.32780i	0.557530	−	0.149390i	0.0309586	−	0.999521i	$-0.490144\pi$
$79$	4.95543	−	1.32780i	0.557530	−	0.149390i	0.526571	+	0.850131i	$0.323477\pi$
$80$	−3.45857	−	8.08798i	−0.386680	−	0.904264i
$81$	−5.50858	+	9.54114i	−0.612065	+	1.06013i
$82$			0.579117i			0.0639528i
$83$	−0.236629	+	0.883111i	−0.0259734	+	0.0969340i	−0.977696	−	0.210026i	$-0.932645\pi$
$83$	−0.236629	+	0.883111i	−0.0259734	+	0.0969340i	0.951722	+	0.306960i	$0.0993118\pi$
$84$		−	18.0064i		−	1.96466i
$85$	−15.7051	+	6.71577i	−1.70345	+	0.728427i
$86$	0.0942673	+	0.163276i	0.0101651	+	0.0176065i
$87$	−1.23583	−	0.713506i	−0.132495	−	0.0764958i
$88$			1.02410i			0.109170i
$89$	7.43872	+	1.99320i	0.788503	+	0.211279i	0.630530	−	0.776165i	$-0.282838\pi$
$89$	7.43872	+	1.99320i	0.788503	+	0.211279i	0.157973	+	0.987444i	$0.449504\pi$
$90$	−0.191296	−	0.143355i	−0.0201643	−	0.0151110i
$91$	20.2649	+	5.42996i	2.12434	+	0.569215i
$92$	−0.149364	+	0.258707i	−0.0155723	+	0.0269720i
$93$	7.53653	−	13.0536i	0.781501	−	1.35360i
$94$	0.237428	+	0.0636187i	0.0244889	+	0.00656177i
$95$	2.74835	−	0.393715i	0.281975	−	0.0403943i
$96$	2.42315	+	0.649281i	0.247312	+	0.0662670i
$97$		−	1.75339i		−	0.178030i	−0.996030	−	0.0890150i	$-0.971628\pi$
$97$		−	1.75339i		−	0.178030i	0.996030	−	0.0890150i	$-0.0283719\pi$
$98$	−1.21941	−	0.704025i	−0.123179	−	0.0711172i
$99$	−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	$0.0294485\pi$
$101$			1.85688i			0.184766i	−0.995724	+	0.0923831i	$0.970552\pi$
$102$	0.416367	−	1.55390i	0.0412265	−	0.153859i
$103$			3.56156i			0.350931i	0.984486	+	0.175466i	$0.0561431\pi$
$103$			3.56156i			0.350931i	−0.984486	+	0.175466i	$0.943857\pi$
$104$	−0.973393	+	1.68597i	−0.0954491	+	0.165323i
$105$	18.6132	−	7.95932i	1.81646	−	0.776750i
$106$	1.18963	−	0.318761i	0.115547	−	0.0309608i
$107$	−2.94924	−	11.0067i	−0.285114	−	1.06406i	−0.948756	−	0.316010i	$-0.897657\pi$
$107$	−2.94924	−	11.0067i	−0.285114	−	1.06406i	0.663642	−	0.748050i	$-0.269010\pi$
$108$	7.63425	−	2.04559i	0.734606	−	0.196837i
$109$	1.72341	−	6.43186i	0.165073	−	0.616061i	−0.832958	−	0.553336i	$-0.813354\pi$
$109$	1.72341	−	6.43186i	0.165073	−	0.616061i	0.998031	−	0.0627245i	$-0.0199789\pi$
$110$	−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
$113$	−7.19065	+	4.15153i	−0.676440	+	0.390543i	−0.798512	−	0.601978i	$-0.794379\pi$
$113$	−7.19065	+	4.15153i	−0.676440	+	0.390543i	0.122073	+	0.992521i	$0.461046\pi$
$114$	−0.130746	+	0.226459i	−0.0122455	+	0.0212098i
$115$	−0.333447	−	0.0400420i	−0.0310941	−	0.00373393i
$116$	0.366500	+	1.36779i	0.0340286	+	0.126997i
$117$		−	4.72603i		−	0.436921i
$118$	0.0307129	−	0.00822949i	0.00282735	−	0.000757586i
$119$	24.3967	+	24.3967i	2.23644	+	2.23644i
$120$	0.266380	+	1.85949i	0.0243171	+	0.169747i
$121$	5.02962			0.457238
$122$	−0.204241	−	0.204241i	−0.0184911	−	0.0184911i
$123$	−2.85927	+	10.6710i	−0.257812	+	0.962168i
$124$	−14.4476	+	3.87122i	−1.29743	+	0.347645i
$125$	10.4694	+	3.92325i	0.936411	+	0.350906i
$126$	−0.124975	+	0.466415i	−0.0111337	+	0.0415515i
$127$	−4.78938	−	1.28331i	−0.424988	−	0.113875i	0.0399843	−	0.999200i	$-0.487269\pi$
$127$	−4.78938	−	1.28331i	−0.424988	−	0.113875i	−0.464973	+	0.885325i	$0.653936\pi$
$128$	−1.65801	−	2.87176i	−0.146549	−	0.253831i
$129$	0.930851	+	3.47398i	0.0819569	+	0.305867i
$130$	−1.08351	−	0.130114i	−0.0950305	−	0.0114117i
$131$	−3.53198	+	13.1815i	−0.308590	+	1.15168i	0.621220	+	0.783636i	$0.286637\pi$
$131$	−3.53198	+	13.1815i	−0.308590	+	1.15168i	−0.929810	+	0.368039i	$0.880029\pi$
$132$	−2.52116	+	9.40908i	−0.219438	+	0.818955i
$133$	−2.80410	−	4.85685i	−0.243146	−	0.421142i
$134$	0.946554	+	0.946554i	0.0817698	+	0.0817698i
$135$	5.48906	+	6.98729i	0.472423	+	0.601370i
$136$	−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	$-0.273230\pi$
$139$	−3.87366	−	6.70937i	−0.328559	−	0.569081i	−0.982226	+	0.187701i	$0.939896\pi$
$140$	−18.6452	−	7.47551i	−1.57581	−	0.631796i
$141$	4.06081	+	2.34451i	0.341982	+	0.197443i
$142$	1.10527			0.0927518
$143$	−9.82895	−	5.67475i	−0.821938	−	0.474546i
$144$	3.46635	+	2.00130i	0.288863	+	0.166775i
$145$	−1.25188	+	0.983451i	−0.103963	+	0.0816712i
$146$	−0.911683	−	0.244285i	−0.0754514	−	0.0202171i
$147$	−18.9931	−	18.9931i	−1.56652	−	1.56652i
$148$	−1.55636	+	11.9978i	−0.127932	+	0.986217i
$149$		−	1.69346i		−	0.138734i	−0.997591	−	0.0693670i	$-0.977902\pi$
$149$		−	1.69346i		−	0.138734i	0.997591	−	0.0693670i	$-0.0220980\pi$
$150$	−0.899701	+	0.547131i	−0.0734603	+	0.0446731i
$151$	−9.78475	−	5.64923i	−0.796271	−	0.459727i	0.0458944	−	0.998946i	$-0.485386\pi$
$151$	−9.78475	−	5.64923i	−0.796271	−	0.459727i	−0.842166	+	0.539219i	$0.818720\pi$
$152$	0.502673	−	0.134691i	0.0407722	−	0.0109249i
$153$	3.88608	−	6.73088i	0.314171	−	0.544159i
$154$	0.819963	+	0.819963i	0.0660745	+	0.0660745i
$155$	−10.3879	−	13.2232i	−0.834374	−	1.06211i
$156$	−13.0937	+	13.0937i	−1.04834	+	1.04834i
$157$	9.08776	+	2.43506i	0.725282	+	0.194339i	0.602527	−	0.798098i	$-0.294160\pi$
$157$	9.08776	+	2.43506i	0.725282	+	0.194339i	0.122755	+	0.992437i	$0.460827\pi$
$158$	0.381159	+	0.381159i	0.0303234	+	0.0303234i
$159$	23.4943			1.86322
$160$	1.67831	−	2.23956i	0.132682	−	0.177053i
$161$	0.175579	+	0.655269i	0.0138375	+	0.0516424i
$162$	−1.15758			−0.0909485
$163$	13.7365	−	7.93075i	1.07592	−	0.621184i	0.146129	−	0.989266i	$-0.453318\pi$
$163$	13.7365	−	7.93075i	1.07592	−	0.621184i	0.929794	+	0.368081i	$0.119985\pi$
$164$	9.49380	−	5.48125i	0.741341	−	0.428013i
$165$	−10.8405	+	1.55296i	−0.843935	+	0.120898i
$166$	−0.0927894	+	0.0248628i	−0.00720185	+	0.00192973i
$167$	−0.459399	−	0.265234i	−0.0355494	−	0.0205244i	0.482120	−	0.876105i	$-0.339867\pi$
$167$	−0.459399	−	0.265234i	−0.0355494	−	0.0205244i	−0.517669	+	0.855581i	$0.673200\pi$
$168$	3.28605	−	1.89720i	0.253524	−	0.146372i
$169$	−4.28751	−	7.42618i	−0.329808	−	0.571245i
$170$	−1.43617	−	1.07625i	−0.110149	−	0.0825448i
$171$	−0.893314	+	0.893314i	−0.0683135	+	0.0683135i
$172$	1.78445	−	3.09076i	0.136063	−	0.235668i
$173$	2.68675	+	0.719913i	0.204270	+	0.0547340i	0.359503	−	0.933144i	$-0.382946\pi$
$173$	2.68675	+	0.719913i	0.204270	+	0.0547340i	−0.155233	+	0.987878i	$0.549613\pi$
$174$		−	0.149938i		−	0.0113667i
$175$	−0.514274	−	22.5778i	−0.0388755	−	1.70672i
$176$	8.32440	−	4.80610i	0.627476	−	0.362273i
$177$	0.606555			0.0455914
$178$	0.209427	+	0.781594i	0.0156973	+	0.0585829i
$179$	−6.41009	+	6.41009i	−0.479112	+	0.479112i	−0.904848	−	0.425735i	$-0.860015\pi$
$179$	−6.41009	+	6.41009i	−0.479112	+	0.479112i	0.425735	+	0.904848i	$0.360015\pi$
$180$	−0.539525	+	4.49286i	−0.0402138	+	0.334878i
$181$	0.557213	−	0.965121i	0.0414173	−	0.0717369i	−0.844574	−	0.535439i	$-0.820146\pi$
$181$	0.557213	−	0.965121i	0.0414173	−	0.0717369i	0.885991	+	0.463703i	$0.153479\pi$
$182$	0.570532	+	2.12925i	0.0422906	+	0.157831i
$183$	−2.75500	−	4.77179i	−0.203655	−	0.352741i
$184$	−0.0629497			−0.00464071
$185$	−13.0901	+	3.69457i	−0.962402	+	0.271630i
$186$	1.58374			0.116126
$187$	−9.33237	−	16.1641i	−0.682450	−	1.18204i
$188$	−1.20428	−	4.49444i	−0.0878312	−	0.327791i
$189$	8.97411	−	15.5436i	0.652771	−	1.13063i
$190$	0.180212	+	0.229400i	0.0130740	+	0.0166424i
$191$	−12.9182	+	12.9182i	−0.934729	+	0.934729i	−0.997997	−	0.0632677i	$-0.979848\pi$
$191$	−12.9182	+	12.9182i	−0.934729	+	0.934729i	0.0632677	+	0.997997i	$0.479848\pi$
$192$	−4.01332	−	14.9779i	−0.289636	−	1.08094i
$193$	−6.70355			−0.482532			−0.241266	−	0.970459i	$-0.577563\pi$
$193$	−6.70355			−0.482532			−0.241266	+	0.970459i	$0.577563\pi$
$194$	0.159549	−	0.0921154i	0.0114549	−	0.00661350i
$195$	−19.3227	−	7.74714i	−1.38373	−	0.554784i
$196$			26.6539i			1.90385i
$197$	13.9325	+	3.73320i	0.992650	+	0.265980i	0.718363	−	0.695668i	$-0.244892\pi$
$197$	13.9325	+	3.73320i	0.992650	+	0.265980i	0.274287	+	0.961648i	$0.411558\pi$
$198$	0.130609	−	0.226222i	0.00928201	−	0.0160769i
$199$	6.68443	−	6.68443i	0.473847	−	0.473847i	−0.429310	−	0.903157i	$-0.641243\pi$
$199$	6.68443	−	6.68443i	0.473847	−	0.473847i	0.903157	+	0.429310i	$0.141243\pi$
$200$	2.03604	+	0.496151i	0.143970	+	0.0350832i
$201$	12.7680	+	22.1148i	0.900586	+	1.55986i
$202$	−0.168965	+	0.0975521i	−0.0118883	+	0.00686374i
$203$	2.78488	+	1.60785i	0.195460	+	0.112849i
$204$	−29.4149	+	7.88169i	−2.05945	+	0.551829i
$205$	9.86246	+	7.39084i	0.688824	+	0.516199i
$206$	−0.324082	+	0.187109i	−0.0225798	+	0.0130365i
$207$	0.132343	−	0.0764084i	0.00919849	−	0.00531075i
$208$	18.2725			1.26697
$209$	0.785229	+	2.93051i	0.0543154	+	0.202708i
$210$	1.70210	+	1.27554i	0.117456	+	0.0880208i
$211$	−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
$213$	20.3659	+	5.45702i	1.39545	+	0.373909i
$214$	0.846608	−	0.846608i	0.0578729	−	0.0578729i
$215$	3.98368	+	0.478380i	0.271684	+	0.0326252i
$216$	1.17767	+	1.17767i	0.0801304	+	0.0801304i
$217$	−16.9832	+	29.4158i	−1.15290	+	1.99687i
$218$	0.675803	−	0.181081i	0.0457711	−	0.0122643i
$219$	−15.5928	−	9.00250i	−1.05366	−	0.608333i
$220$	8.69619	+	6.51685i	0.586297	+	0.439366i
$221$		−	35.4810i		−	2.38671i
$222$	0.487980	−	1.18445i	0.0327511	−	0.0794950i
$223$	−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
$225$	−4.88273	+	1.42826i	−0.325515	+	0.0952173i
$226$	−0.755530	−	0.436205i	−0.0502571	−	0.0290159i
$227$	5.98267	+	3.45410i	0.397084	+	0.229256i	0.685225	−	0.728332i	$-0.259704\pi$
$227$	5.98267	+	3.45410i	0.397084	+	0.229256i	−0.288141	+	0.957588i	$0.593037\pi$
$228$	4.94995			0.327819
$229$	20.4243	+	11.7920i	1.34967	+	0.779235i	0.988203	−	0.153148i	$-0.0489411\pi$
$229$	20.4243	+	11.7920i	1.34967	+	0.779235i	0.361472	+	0.932383i	$0.382274\pi$
$230$	−0.0138742	−	0.0324454i	−0.000914839	−	0.00213938i
$231$	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	−0.259375	−	0.965777i	$-0.583516\pi$
$233$	10.7828	−	10.7828i	0.706402	−	0.706402i	0.965777	+	0.259375i	$0.0835165\pi$
$234$	0.430041	−	0.248284i	0.0281127	−	0.0162308i
$235$	4.11356	−	3.23152i	0.268339	−	0.210801i
$236$	−0.425603	−	0.425603i	−0.0277044	−	0.0277044i
$237$	5.14143	+	8.90522i	0.333972	+	0.578456i
$238$	−0.938264	+	3.50165i	−0.0608186	+	0.226978i
$239$	−4.28082	+	15.9763i	−0.276903	+	1.03342i	0.677652	+	0.735383i	$0.262998\pi$
$239$	−4.28082	+	15.9763i	−0.276903	+	1.03342i	−0.954555	+	0.298035i	$0.903669\pi$
$240$	13.8647	−	10.8918i	0.894961	−	0.703062i
$241$	−0.943969	−	3.52294i	−0.0608064	−	0.226933i	0.928835	−	0.370493i	$-0.120811\pi$
$241$	−0.943969	−	3.52294i	−0.0608064	−	0.226933i	−0.989641	+	0.143561i	$0.954145\pi$
$242$	0.264234	+	0.457666i	0.0169856	+	0.0294199i
$243$	−9.81501	−	2.62992i	−0.629633	−	0.168710i
$244$	−1.41513	+	5.28135i	−0.0905946	+	0.338104i
$245$	−27.5520	+	11.7817i	−1.76023	+	0.752708i
$246$	−1.12121	+	0.300427i	−0.0714856	+	0.0191545i
$247$	−1.49269	+	5.57081i	−0.0949778	+	0.354462i
$248$	−2.22871	−	2.22871i	−0.141523	−	0.141523i
$249$	−1.83251			−0.116131
$250$	0.193022	+	1.15876i	0.0122078	+	0.0732867i
$251$	5.49768	+	5.49768i	0.347010	+	0.347010i	0.858995	−	0.511984i	$-0.171089\pi$
$251$	5.49768	+	5.49768i	0.347010	+	0.347010i	−0.511984	+	0.858995i	$0.671089\pi$
$252$	8.82908	−	2.36574i	0.556180	−	0.149028i
$253$		−	0.366988i		−	0.0230723i
$254$	−0.134839	−	0.503225i	−0.00846053	−	0.0315751i
$255$	−21.1494	−	26.9221i	−1.32443	−	1.68593i
$256$	−7.56205	+	13.0979i	−0.472628	+	0.818616i
$257$	23.3649	−	13.4897i	1.45746	−	0.841467i	0.458578	−	0.888654i	$-0.348359\pi$
$257$	23.3649	−	13.4897i	1.45746	−	0.841467i	0.998886	+	0.0471867i	$0.0150256\pi$
$258$	−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
$262$	−1.38500	+	0.371109i	−0.0855654	+	0.0229272i
$263$	−1.40124	−	5.22951i	−0.0864043	−	0.322465i	0.909172	−	0.416421i	$-0.136716\pi$
$263$	−1.40124	−	5.22951i	−0.0864043	−	0.322465i	−0.995576	+	0.0939553i	$0.970049\pi$
$264$	−1.98273	+	0.531271i	−0.122029	+	0.0326975i
$265$	9.75384	−	24.3277i	0.599173	−	1.49444i
$266$	0.294630	−	0.510314i	0.0180649	−	0.0312894i
$267$			15.4358i			0.944659i
$268$	6.55842	−	24.4764i	0.400619	−	1.49513i
$269$			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	0.513007	−	0.858385i	$-0.328532\pi$
$271$	−8.01505	−	13.8825i	−0.486879	−	0.843300i	−0.999886	+	0.0150847i	$0.995198\pi$
$272$	26.0239	+	15.0249i	1.57793	+	0.911019i
$273$			42.0510i			2.54504i
$274$	−1.07151	−	0.287110i	−0.0647323	−	0.0173450i
$275$	−2.89249	+	11.8698i	−0.174424	+	0.715778i
$276$	−0.578358	−	0.154971i	−0.0348131	−	0.00932813i
$277$	11.5109	−	19.9375i	0.691626	−	1.19793i	−0.279679	−	0.960093i	$-0.590228\pi$
$277$	11.5109	−	19.9375i	0.691626	−	1.19793i	0.971305	−	0.237837i	$-0.0764385\pi$
$278$	0.407009	−	0.704961i	0.0244108	−	0.0422807i
$279$	7.39076	+	1.98035i	0.442473	+	0.118560i
$280$	−0.600275	−	4.19027i	−0.0358733	−	0.250416i
$281$	26.6973	+	7.15352i	1.59263	+	0.426743i	0.942805	−	0.333343i	$-0.108177\pi$
$281$	26.6973	+	7.15352i	1.59263	+	0.426743i	0.649822	+	0.760087i	$0.274844\pi$
$282$			0.492680i			0.0293387i
$283$	−4.91260	−	2.83629i	−0.292024	−	0.168600i	0.346830	−	0.937928i	$-0.387258\pi$
$283$	−4.91260	−	2.83629i	−0.292024	−	0.168600i	−0.638854	+	0.769328i	$0.720591\pi$
$284$	−10.4611	−	18.1192i	−0.620755	−	1.07518i
$285$	2.18801	+	5.11675i	0.129607	+	0.303090i
$286$		−	1.19250i		−	0.0705142i
$287$	6.44324	−	24.0465i	0.380333	−	1.41942i
$288$			1.27345i			0.0750386i
$289$	20.6750	−	35.8102i	1.21618	−	2.10648i
$290$	−0.155257	−	0.0622478i	−0.00911698	−	0.00365532i
$291$	3.39468	−	0.909603i	0.199000	−	0.0533218i
$292$	4.62423	+	17.2579i	0.270612	+	1.00994i
$293$	−13.4613	+	3.60695i	−0.786418	+	0.210720i	−0.629612	−	0.776909i	$-0.716786\pi$
$293$	−13.4613	+	3.60695i	−0.786418	+	0.210720i	−0.156806	+	0.987629i	$0.550120\pi$
$294$	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
$298$	0.154095	−	0.0889671i	0.00892651	−	0.00515372i
$299$	0.348816	−	0.604167i	0.0201725	−	0.0349399i
$300$	17.4849	+	9.57081i	1.00949	+	0.552571i
$301$	−2.09763	−	7.82847i	−0.120905	−	0.451225i
$302$		−	1.18714i		−	0.0683122i
$303$	−3.59504	+	0.963287i	−0.206529	+	0.0553394i
$304$	−3.45386	−	3.45386i	−0.198093	−	0.198093i
$305$	−6.08483	+	0.871681i	−0.348417	+	0.0499123i
$306$	0.816628			0.0466835
$307$	−7.33300	−	7.33300i	−0.418516	−	0.418516i	0.466176	−	0.884692i	$-0.345631\pi$
$307$	−7.33300	−	7.33300i	−0.418516	−	0.418516i	−0.884692	+	0.466176i	$0.845631\pi$
$308$	5.68131	−	21.2029i	0.323723	−	1.20815i
$309$	−6.89542	+	1.84762i	−0.392267	+	0.105108i
$310$	0.657503	−	1.63993i	0.0373437	−	0.0931415i
$311$	−0.463544	+	1.72997i	−0.0262852	+	0.0980975i	−0.977822	−	0.209436i	$-0.932837\pi$
$311$	−0.463544	+	1.72997i	−0.0262852	+	0.0980975i	0.951537	+	0.307534i	$0.0995038\pi$
$312$	−3.76911	−	1.00993i	−0.213384	−	0.0571760i
$313$	−13.5807	−	23.5224i	−0.767625	−	1.32957i	−0.938848	−	0.344333i	$-0.888105\pi$
$313$	−13.5807	−	23.5224i	−0.767625	−	1.32957i	0.171223	−	0.985232i	$-0.445228\pi$
$314$	0.255854	+	0.954861i	0.0144387	+	0.0538859i
$315$	6.34815	+	8.08086i	0.357678	+	0.455305i
$316$	2.64095	−	9.85616i	0.148565	−	0.554452i
$317$	1.69565	−	6.32825i	0.0952372	−	0.355430i	−0.901818	−	0.432116i	$-0.857767\pi$
$317$	1.69565	−	6.32825i	0.0952372	−	0.355430i	0.997055	+	0.0766857i	$0.0244338\pi$
$318$	1.23428	+	2.13784i	0.0692152	+	0.119884i
$319$	−1.23009	−	1.23009i	−0.0688719	−	0.0688719i
$320$	−17.1754	−	2.06251i	−0.960134	−	0.115298i
$321$	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
$325$	−16.0439	+	16.7919i	−0.889958	+	0.931446i
$326$	1.44330	+	0.833292i	0.0799373	+	0.0461518i
$327$	13.3466			0.738066
$328$	2.00058	+	1.15504i	0.110464	+	0.0637763i
$329$	−9.15085	−	5.28324i	−0.504502	−	0.291275i
$330$	−0.710824	−	0.904841i	−0.0391296	−	0.0498099i
$331$	27.9515	+	7.48959i	1.53635	+	0.411665i	0.925086	−	0.379758i	$-0.123993\pi$
$331$	27.9515	+	7.48959i	1.53635	+	0.411665i	0.611268	+	0.791423i	$0.290660\pi$
$332$	1.28583	+	1.28583i	0.0705689	+	0.0705689i
$333$	3.75829	−	4.91722i	0.205953	−	0.269462i
$334$		−	0.0557369i		−	0.00304979i
$335$	28.2001	−	4.03980i	1.54074	−	0.220718i
$336$	−30.8428	−	17.8071i	−1.68261	−	0.971455i
$337$	7.88127	−	2.11178i	0.429320	−	0.115036i	−0.0376867	−	0.999290i	$-0.511999\pi$
$337$	7.88127	−	2.11178i	0.429320	−	0.115036i	0.467007	+	0.884254i	$0.345332\pi$
$338$	0.450493	−	0.780277i	0.0245036	−	0.0424415i
$339$	−11.7679	−	11.7679i	−0.639145	−	0.639145i
$340$	−4.05053	+	33.7305i	−0.219671	+	1.82929i
$341$	12.9931	−	12.9931i	0.703613	−	0.703613i
$342$	−0.128217	−	0.0343557i	−0.00693319	−	0.00185774i
$343$	20.4434	+	20.4434i	1.10384	+	1.10384i
$344$	0.752057			0.0405482
$345$	−0.0954574	−	0.666347i	−0.00513925	−	0.0358749i
$346$	0.0756421	+	0.282300i	0.00406654	+	0.0151765i
$347$	−24.8690			−1.33504			−0.667519	−	0.744592i	$-0.732644\pi$
$347$	−24.8690			−1.33504			−0.667519	+	0.744592i	$0.732644\pi$
$348$	−2.45801	+	1.41913i	−0.131763	+	0.0760736i
$349$	−16.0098	+	9.24327i	−0.856985	+	0.494781i	−0.863002	−	0.505201i	$-0.831418\pi$
$349$	−16.0098	+	9.24327i	−0.856985	+	0.494781i	0.00601629	+	0.999982i	$0.498085\pi$
$350$	2.02743	−	1.23293i	0.108371	−	0.0659031i
$351$	−17.8285	+	4.77714i	−0.951617	+	0.254985i
$352$	2.64845	+	1.52909i	0.141163	+	0.0815005i
$353$	−15.7652	+	9.10206i	−0.839099	+	0.484454i	−0.856958	−	0.515387i	$-0.827648\pi$
$353$	−15.7652	+	9.10206i	−0.839099	+	0.484454i	0.0178589	+	0.999841i	$0.494315\pi$
$354$	0.0318657	+	0.0551930i	0.00169364	+	0.00293347i
$355$	14.1057	−	18.8228i	0.748652	−	0.999013i
$356$	10.8309	−	10.8309i	0.574038	−	0.574038i
$357$	−34.5774	+	59.8897i	−1.83003	+	3.16970i
$358$	−0.920038	−	0.246524i	−0.0486255	−	0.0130292i
$359$			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
$362$	0.117094			0.00615432
$363$	2.60920	+	9.73766i	0.136947	+	0.511095i
$364$	29.5061	−	29.5061i	1.54654	−	1.54654i
$365$	−15.7953	+	12.4085i	−0.826766	+	0.649490i
$366$	0.289470	−	0.501377i	0.0151309	−	0.0262074i
$367$	−2.93236	−	10.9437i	−0.153068	−	0.571258i	−0.999263	−	0.0383846i	$-0.987779\pi$
$367$	−2.93236	−	10.9437i	−0.153068	−	0.571258i	0.846195	−	0.532874i	$-0.178888\pi$
$368$	0.295421	+	0.511685i	0.0153999	+	0.0266734i
$369$	−5.60795			−0.291938
$370$	−1.02388	−	0.997025i	−0.0532289	−	0.0518329i
$371$	−52.9432			−2.74868
$372$	−14.9898	−	25.9632i	−0.777187	−	1.34613i
$373$	7.91372	+	29.5344i	0.409757	+	1.52923i	0.795110	+	0.606465i	$0.207413\pi$
$373$	7.91372	+	29.5344i	0.409757	+	1.52923i	−0.385354	+	0.922769i	$0.625921\pi$
$374$	0.980562	−	1.69838i	0.0507036	−	0.0878213i
$375$	−2.16448	+	22.3047i	−0.111773	+	1.15181i
$376$	0.693320	−	0.693320i	0.0357552	−	0.0357552i
$377$	−0.855900	−	3.19426i	−0.0440811	−	0.164513i
$378$	1.88584			0.0969971
$379$	−6.07630	+	3.50815i	−0.312119	+	0.180202i	−0.647874	−	0.761747i	$-0.724342\pi$
$379$	−6.07630	+	3.50815i	−0.312119	+	0.180202i	0.335756	+	0.941949i	$0.391008\pi$
$380$	2.05501	−	5.12555i	0.105420	−	0.262935i
$381$		−	9.93828i		−	0.509154i
$382$	−1.85415	−	0.496817i	−0.0948664	−	0.0254194i
$383$	10.5184	−	18.2184i	0.537466	−	0.930919i	−0.461573	−	0.887102i	$-0.652715\pi$
$383$	10.5184	−	18.2184i	0.537466	−	0.930919i	0.999040	−	0.0438170i	$-0.0139518\pi$
$384$	4.69980	−	4.69980i	0.239836	−	0.239836i
$385$	24.4287	−	3.49952i	1.24500	−	0.178352i
$386$	−0.352175	−	0.609984i	−0.0179252	−	0.0310474i
$387$	−1.58110	+	0.912848i	−0.0803718	+	0.0464027i
$388$	−3.02020	−	1.74371i	−0.153328	−	0.0885237i
$389$	−28.1825	+	7.55149i	−1.42891	+	0.382876i	−0.888636	−	0.458612i	$-0.848347\pi$
$389$	−28.1825	+	7.55149i	−1.42891	+	0.382876i	−0.540275	+	0.841488i	$0.681680\pi$
$390$	−0.310183	−	2.16525i	−0.0157067	−	0.109642i
$391$	0.993578	−	0.573643i	0.0502474	−	0.0290104i
$392$	−4.86416	+	2.80833i	−0.245677	+	0.141842i
$393$	−27.3526			−1.37975
$394$	0.392252	+	1.46390i	0.0197614	+	0.0737504i
$395$	11.3556	−	1.62675i	0.571364	−	0.0818506i
$396$	−4.94479			−0.248485
$397$	1.11923	+	1.11923i	0.0561727	+	0.0561727i	0.734635	−	0.678462i	$-0.237353\pi$
$397$	1.11923	+	1.11923i	0.0561727	+	0.0561727i	−0.678462	+	0.734635i	$0.737353\pi$
$398$	0.959415	+	0.257074i	0.0480911	+	0.0128860i
$399$	7.94850	−	7.94850i	0.397923	−	0.397923i
$400$	−5.52215	−	18.8783i	−0.276107	−	0.943917i
$401$	2.72947	+	2.72947i	0.136303	+	0.136303i	0.771966	−	0.635663i	$-0.219273\pi$
$401$	2.72947	+	2.72947i	0.136303	+	0.136303i	−0.635663	+	0.771966i	$0.719273\pi$
$402$	−1.34155	+	2.32363i	−0.0669104	+	0.115892i
$403$	33.7399	−	9.04059i	1.68071	−	0.450344i
$404$	3.19845	+	1.84663i	0.159129	+	0.0918732i
$405$	−14.7734	+	19.7139i	−0.734096	+	0.979589i
$406$			0.337877i			0.0167686i
$407$	−5.71385	−	13.7206i	−0.283225	−	0.680107i
$408$	−4.53758	−	4.53758i	−0.224644	−	0.224644i
$409$	15.9537	+	4.27479i	0.788862	+	0.211375i	0.630688	−	0.776037i	$-0.282773\pi$
$409$	15.9537	+	4.27479i	0.788862	+	0.211375i	0.158174	+	0.987411i	$0.449439\pi$
$410$	−0.154394	+	1.28571i	−0.00762499	+	0.0634966i
$411$	−18.3264	−	10.5807i	−0.903973	−	0.521909i
$412$	6.13476	+	3.54190i	0.302238	+	0.174497i
$413$	−1.36684			−0.0672580
$414$	0.0139054	+	0.00802831i	0.000683415	+	0.000394570i
$415$	−0.760784	+	1.89752i	−0.0373454	+	0.0931458i
$416$	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	$-0.526281\pi$
$419$	15.1345	−	8.73792i	0.739370	−	0.426875i	0.821840	+	0.569718i	$0.192948\pi$
$420$	4.80056	−	39.9764i	0.234243	−	1.95065i
$421$	−7.21676	−	7.21676i	−0.351723	−	0.351723i	0.509027	−	0.860750i	$-0.330005\pi$
$421$	−7.21676	−	7.21676i	−0.351723	−	0.351723i	−0.860750	+	0.509027i	$0.830005\pi$
$422$	−0.812038	−	1.40649i	−0.0395294	−	0.0684669i
$423$	−0.616059	+	2.29916i	−0.0299538	+	0.111789i
$424$	1.27152	−	4.74539i	0.0617507	−	0.230457i
$425$	−36.6575	+	10.7228i	−1.77815	+	0.520131i
$426$	0.573375	+	2.13987i	0.0277801	+	0.103677i
$427$	6.20826	+	10.7530i	0.300439	+	0.520375i
$428$	−21.8919	−	5.86592i	−1.05819	−	0.283540i
$429$	5.88775	−	21.9734i	0.284263	−	1.06088i
$430$	0.165755	+	0.387623i	0.00799340	+	0.0186929i
$431$	27.7849	−	7.44493i	1.33835	−	0.358610i	0.482528	−	0.875880i	$-0.339719\pi$
$431$	27.7849	−	7.44493i	1.33835	−	0.358610i	0.855822	+	0.517270i	$0.173052\pi$
$432$	4.04589	−	15.0995i	0.194658	−	0.726474i
$433$	−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
$435$	−2.55346	−	1.91354i	−0.122429	−	0.0917473i
$436$	−9.36492	−	9.36492i	−0.448498	−	0.448498i
$437$	−0.180133	+	0.0482665i	−0.00861693	+	0.00230890i
$438$		−	1.89180i		−	0.0903939i
$439$	2.60805	+	9.73336i	0.124475	+	0.464548i	0.999820	−	0.0189505i	$-0.00603251\pi$
$439$	2.60805	+	9.73336i	0.124475	+	0.464548i	−0.875345	+	0.483499i	$0.839366\pi$
$440$	−0.273029	+	2.27363i	−0.0130161	+	0.108391i
$441$	6.81750	−	11.8083i	0.324643	−	0.562298i
$442$	3.22857	−	1.86402i	0.153567	−	0.0886622i
$443$	−27.4924	+	27.4924i	−1.30620	+	1.30620i	−0.382069	+	0.924134i	$0.624788\pi$
$443$	−27.4924	+	27.4924i	−1.30620	+	1.30620i	−0.924134	+	0.382069i	$0.875212\pi$
$444$	−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
$447$	3.27866	−	0.878514i	0.155075	−	0.0415523i
$448$	9.04383	+	33.7520i	0.427281	+	1.59463i
$449$	−24.2566	+	6.49953i	−1.14474	+	0.306732i	−0.780855	−	0.624713i	$-0.785216\pi$
$449$	−24.2566	+	6.49953i	−1.14474	+	0.306732i	−0.363883	+	0.931444i	$0.618549\pi$
$450$	−0.386480	−	0.369266i	−0.0182189	−	0.0174074i
$451$	−6.73371	+	11.6631i	−0.317078	+	0.549195i
$452$			16.5144i			0.776774i
$453$	5.86126	−	21.8745i	0.275386	−	1.02776i
$454$			0.725851i			0.0340659i
$455$	43.5428	+	17.4578i	2.04132	+	0.818436i
$456$	0.521540	+	0.903334i	0.0244234	+	0.0423025i
$457$	1.51738	+	0.876059i	0.0709800	+	0.0409803i	0.535070	−	0.844808i	$-0.320285\pi$
$457$	1.51738	+	0.876059i	0.0709800	+	0.0409803i	−0.464090	+	0.885788i	$0.653619\pi$
$458$			2.47799i			0.115789i
$459$	−29.3198	−	7.85622i	−1.36853	−	0.366697i
$460$	−0.400578	+	0.534538i	−0.0186771	+	0.0249230i
$461$	−17.9341	−	4.80544i	−0.835276	−	0.223812i	−0.184262	−	0.982877i	$-0.558990\pi$
$461$	−17.9341	−	4.80544i	−0.835276	−	0.223812i	−0.651014	+	0.759066i	$0.725656\pi$
$462$	−1.16213	+	2.01287i	−0.0540673	+	0.0936472i
$463$	−10.4787	+	18.1497i	−0.486988	+	0.843488i	−0.999888	−	0.0149605i	$-0.995238\pi$
$463$	−10.4787	+	18.1497i	−0.486988	+	0.843488i	0.512900	+	0.858448i	$0.328571\pi$
$464$	2.70531	+	0.724884i	0.125591	+	0.0336519i
$465$	20.2121	−	26.9714i	0.937314	−	1.25077i
$466$	1.54765	+	0.414691i	0.0716933	+	0.0192102i
$467$		−	22.0375i		−	1.01977i	−0.860241	−	0.509887i	$-0.829687\pi$
$467$		−	22.0375i		−	1.01977i	0.860241	−	0.509887i	$-0.170313\pi$
$468$	−8.14053	−	4.69994i	−0.376296	−	0.217255i
$469$	−28.7721	−	49.8348i	−1.32857	−	2.30116i
$470$	0.510158	+	0.204540i	0.0235318	+	0.00943473i
$471$			18.8577i			0.868918i
$472$	0.0328271	−	0.122512i	0.00151099	−	0.00563909i
$473$			4.38439i			0.201594i
$474$	−0.540216	+	0.935681i	−0.0248129	+	0.0429773i
$475$	6.20664	−	0.141374i	0.284780	−	0.00648667i
$476$	66.2850	−	17.7610i	3.03817	−	0.814075i
$477$	3.08676	+	11.5199i	0.141333	+	0.527461i
$478$	−1.67864	+	0.449791i	−0.0767793	+	0.0205729i
$479$	−7.10617	+	26.5206i	−0.324689	+	1.21176i	0.589935	+	0.807451i	$0.299153\pi$
$479$	−7.10617	+	26.5206i	−0.324689	+	1.21176i	−0.914624	+	0.404305i	$0.867513\pi$
$480$	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
$483$	−1.17756	+	0.679864i	−0.0535808	+	0.0309349i
$484$	5.00185	−	8.66346i	0.227357	−	0.393794i
$485$	0.467460	−	3.89274i	0.0212263	−	0.176760i
$486$	−0.276329	−	1.03127i	−0.0125345	−	0.0467795i
$487$			35.4750i			1.60752i	0.594951	+	0.803762i	$0.297171\pi$
$487$			35.4750i			1.60752i	−0.594951	+	0.803762i	$0.702829\pi$
$488$	−1.11291	+	0.298204i	−0.0503792	+	0.0134991i
$489$	22.4805	+	22.4805i	1.01660	+	1.01660i
$490$	−2.51953	−	1.88812i	−0.113821	−	0.0852963i
$491$	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
$493$	1.40756	−	5.25310i	0.0633935	−	0.236588i
$494$	−0.585331	+	0.156839i	−0.0263353	+	0.00705652i
$495$	−2.18573	−	5.11141i	−0.0982412	−	0.229741i
$496$	−7.65672	+	28.5753i	−0.343797	+	1.28307i
$497$	−45.8936	−	12.2972i	−2.05861	−	0.551603i
$498$	−0.0962721	−	0.166748i	−0.00431406	−	0.00747217i
$499$	5.71230	+	21.3186i	0.255718	+	0.954352i	0.967690	+	0.252144i	$0.0811357\pi$
$499$	5.71230	+	21.3186i	0.255718	+	0.954352i	−0.711972	+	0.702208i	$0.752198\pi$
$500$	17.1694	−	14.1318i	0.767837	−	0.631995i
$501$	0.275190	−	1.02702i	0.0122946	−	0.0458839i
$502$	−0.211433	+	0.789080i	−0.00943673	+	0.0352184i
$503$	1.97683	+	3.42397i	0.0881424	+	0.152667i	0.906726	−	0.421720i	$-0.138574\pi$
$503$	1.97683	+	3.42397i	0.0881424	+	0.152667i	−0.818584	+	0.574388i	$0.805240\pi$
$504$	1.36199	+	1.36199i	0.0606678	+	0.0606678i
$505$	−0.495049	+	4.12249i	−0.0220294	+	0.183448i
$506$	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	$-0.0465762\pi$
$509$	8.31123	+	14.3955i	0.368389	+	0.638068i	−0.620925	+	0.783870i	$0.713243\pi$
$510$	1.33866	−	3.33884i	0.0592768	−	0.147846i
$511$	35.1376	+	20.2867i	1.55440	+	0.897432i
$512$	−8.22116			−0.363327
$513$	4.27293	+	2.46698i	0.188655	+	0.108920i
$514$	2.45498	+	1.41738i	0.108284	+	0.0625180i
$515$	−0.949523	+	7.90709i	−0.0418410	+	0.348428i
$516$	6.90962	+	1.85143i	0.304179	+	0.0815045i
$517$	4.04196	+	4.04196i	0.177765	+	0.177765i
$518$	−1.09964	+	2.66910i	−0.0483154	+	0.117274i
$519$			5.57520i			0.244724i
$520$	−2.61053	+	3.48354i	−0.114479	+	0.152763i
$521$	−1.01799	−	0.587738i	−0.0445990	−	0.0257493i	0.477535	−	0.878613i	$-0.341530\pi$
$521$	−1.01799	−	0.587738i	−0.0445990	−	0.0257493i	−0.522134	+	0.852864i	$0.674864\pi$
$522$	0.0735188	−	0.0196993i	0.00321783	−	0.000862215i
$523$	17.4391	−	30.2054i	0.762560	−	1.32079i	−0.178968	−	0.983855i	$-0.557276\pi$
$523$	17.4391	−	30.2054i	0.762560	−	1.32079i	0.941527	−	0.336937i	$-0.109391\pi$
$524$	19.1926	+	19.1926i	0.838431	+	0.838431i
$525$	43.4454	−	12.7083i	1.89611	−	0.554636i
$526$	0.402240	−	0.402240i	0.0175385	−	0.0175385i
$527$	55.4868	+	14.8676i	2.41704	+	0.647644i
$528$	13.6233	+	13.6233i	0.592880	+	0.592880i
$529$	−22.9774			−0.999019
$530$	2.72610	−	0.390527i	0.118414	−	0.0169634i
$531$	0.0796912	+	0.297412i	0.00345830	+	0.0129066i
$532$	−11.1545			−0.483609
$533$	−22.1712	+	12.8006i	−0.960342	+	0.554454i
$534$	−1.40457	+	0.810931i	−0.0607818	+	0.0350924i
$535$	−3.61324	−	25.2225i	−0.156214	−	1.09046i
$536$	5.15779	−	1.38203i	0.222783	−	0.0596944i
$537$	−15.7357	−	9.08500i	−0.679045	−	0.392047i
$538$	−1.66276	+	0.959996i	−0.0716868	+	0.0413884i
$539$	−16.3722	−	28.3574i	−0.705199	−	1.22144i
$540$	17.4943	−	2.50614i	0.752835	−	0.107847i
$541$	−4.65504	+	4.65504i	−0.200136	+	0.200136i	−0.800058	−	0.599922i	$-0.795198\pi$
$541$	−4.65504	+	4.65504i	−0.200136	+	0.200136i	0.599922	+	0.800058i	$0.295198\pi$
$542$	0.842149	−	1.45865i	0.0361734	−	0.0626542i
$543$	2.15760	+	0.578127i	0.0925915	+	0.0248098i
$544$			9.56052i			0.409904i
$545$	5.54093	−	13.8200i	0.237348	−	0.591985i
$546$	−3.82640	+	2.20917i	−0.163755	+	0.0945439i
$547$	−15.3538			−0.656482			−0.328241	−	0.944594i	$-0.606456\pi$
$547$	−15.3538			−0.656482			−0.328241	+	0.944594i	$0.606456\pi$
$548$	5.43490	+	20.2833i	0.232167	+	0.866461i
$549$	1.97779	−	1.97779i	0.0844100	−	0.0844100i
$550$	−1.23205	+	0.360388i	−0.0525346	+	0.0153670i
$551$	−0.441998	+	0.765562i	−0.0188297	+	0.0326141i
$552$	−0.0326562	−	0.121875i	−0.00138994	−	0.00518733i
$553$	−11.5860	−	20.0675i	−0.492686	−	0.853357i
$554$	2.41893			0.102771
$555$	−13.9436	−	23.4266i	−0.591874	−	0.994405i
$556$	−15.4091			−0.653491
$557$	−8.19437	−	14.1931i	−0.347207	−	0.601379i	0.638546	−	0.769584i	$-0.279536\pi$
$557$	−8.19437	−	14.1931i	−0.347207	−	0.601379i	−0.985752	+	0.168205i	$0.946203\pi$
$558$	0.208077	+	0.776555i	0.00880862	+	0.0328742i
$559$	−4.16729	+	7.21795i	−0.176258	+	0.305287i
$560$	−31.2434	+	24.5442i	−1.32027	+	1.03718i
$561$	26.4535	−	26.4535i	1.11687	−	1.11687i
$562$	0.751628	+	2.80511i	0.0317055	+	0.118327i
$563$	−34.2468			−1.44333			−0.721665	−	0.692242i	$-0.756623\pi$
$563$	−34.2468			−1.44333			−0.721665	+	0.692242i	$0.756623\pi$
$564$	8.07679	−	4.66313i	0.340094	−	0.196353i
$565$	−17.0709	+	7.29983i	−0.718178	+	0.307106i
$566$		−	0.596025i		−	0.0250528i
$567$	48.0661	+	12.8793i	2.01858	+	0.540878i
$568$	2.20443	−	3.81818i	0.0924958	−	0.160207i
$569$	12.1154	−	12.1154i	0.507904	−	0.507904i	−0.405979	−	0.913882i	$-0.633069\pi$
$569$	12.1154	−	12.1154i	0.507904	−	0.507904i	0.913882	+	0.405979i	$0.133069\pi$
$570$	−0.350646	+	0.467907i	−0.0146869	+	0.0195985i
$571$	−4.07340	−	7.05533i	−0.170466	−	0.295257i	0.768117	−	0.640310i	$-0.221194\pi$
$571$	−4.07340	−	7.05533i	−0.170466	−	0.295257i	−0.938583	+	0.345053i	$0.887861\pi$
$572$	−19.5494	+	11.2869i	−0.817401	+	0.471927i
$573$	−31.7120	−	18.3090i	−1.32479	−	0.764868i
$574$	2.52659	−	0.676998i	0.105458	−	0.0282574i
$575$	−0.729616	−	0.177796i	−0.0304271	−	0.00741460i
$576$	6.81682	−	3.93570i	0.284034	−	0.163987i
$577$	10.8128	−	6.24278i	0.450143	−	0.259890i	−0.257748	−	0.966212i	$-0.582980\pi$
$577$	10.8128	−	6.24278i	0.450143	−	0.259890i	0.707891	+	0.706322i	$0.249647\pi$
$578$	4.34470			0.180716
$579$	−3.47758	−	12.9785i	−0.144523	−	0.539369i
$580$	0.449014	+	3.13438i	0.0186443	+	0.130148i
$581$	4.12949			0.171320
$582$	0.261110	+	0.261110i	0.0108234	+	0.0108234i
$583$	27.6650	+	7.41281i	1.14577	+	0.307007i
$584$	−2.66222	+	2.66222i	−0.110164	+	0.110164i
$585$	1.25997	−	10.4923i	0.0520934	−	0.433805i
$586$	−1.03541	−	1.03541i	−0.0427723	−	0.0427723i
$587$	−3.20283	+	5.54747i	−0.132195	+	0.228969i	−0.924522	−	0.381128i	$-0.875536\pi$
$587$	−3.20283	+	5.54747i	−0.132195	+	0.228969i	0.792327	+	0.610096i	$0.208869\pi$
$588$	−51.6037	+	13.8272i	−2.12810	+	0.570223i
$589$	−8.08639	−	4.66868i	−0.333194	−	0.192370i
$590$	0.0703802	−	0.0100823i	0.00289751	−	0.000415082i
$591$			28.9109i			1.18924i
$592$	19.0117	+	14.5309i	0.781376	+	0.597215i
$593$	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
$595$	47.6593	+	60.6677i	1.95384	+	2.48713i
$596$	−2.91698	−	1.68412i	−0.119484	−	0.0689841i
$597$	16.4092	+	9.47384i	0.671582	+	0.387738i
$598$	0.0733009			0.00299750
$599$	−25.2199	−	14.5607i	−1.03046	−	0.594934i	−0.113341	−	0.993556i	$-0.536155\pi$
$599$	−25.2199	−	14.5607i	−1.03046	−	0.594934i	−0.917115	+	0.398622i	$0.869489\pi$
$600$	0.0956509	+	4.19929i	0.00390493	+	0.171435i
$601$	−8.70660	−	15.0803i	−0.355150	−	0.615137i	0.631994	−	0.774973i	$-0.282237\pi$
$601$	−8.70660	−	15.0803i	−0.355150	−	0.615137i	−0.987144	+	0.159836i	$0.948903\pi$
$602$	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
$605$	11.1663	+	1.34091i	0.453976	+	0.0545157i
$606$	−0.276521	−	0.276521i	−0.0112329	−	0.0112329i
$607$	10.9126	+	18.9011i	0.442927	+	0.767172i	0.997905	−	0.0646926i	$-0.0206067\pi$
$607$	10.9126	+	18.9011i	0.442927	+	0.767172i	−0.554978	+	0.831865i	$0.687273\pi$
$608$	0.402213	−	1.50108i	0.0163119	−	0.0608767i
$609$	−1.66820	+	6.22581i	−0.0675989	+	0.252283i
$610$	−0.398988	−	0.507890i	−0.0161545	−	0.0205639i
$611$	2.81240	+	10.4960i	0.113778	+	0.424624i
$612$	−7.72925	−	13.3875i	−0.312436	−	0.541156i
$613$	39.5877	+	10.6075i	1.59893	+	0.428432i	0.944720	−	0.327879i	$-0.106334\pi$
$613$	39.5877	+	10.6075i	1.59893	+	0.428432i	0.654212	+	0.756312i	$0.273001\pi$
$614$	0.282017	−	1.05250i	0.0113813	−	0.0424756i
$615$	−9.19283	+	22.9285i	−0.370691	+	0.924566i
$616$	4.46799	−	1.19720i	0.180021	−	0.0482364i
$617$	−0.473071	+	1.76552i	−0.0190451	+	0.0710773i	−0.974794	−	0.223105i	$-0.928381\pi$
$617$	−0.473071	+	1.76552i	−0.0190451	+	0.0710773i	0.955749	+	0.294182i	$0.0950473\pi$
$618$	−0.530377	−	0.530377i	−0.0213349	−	0.0213349i
$619$	−28.5279			−1.14663			−0.573317	−	0.819334i	$-0.694343\pi$
$619$	−28.5279			−1.14663			−0.573317	+	0.819334i	$0.694343\pi$
$620$	−33.1074	+	4.74279i	−1.32962	+	0.190475i
$621$	−0.422019	−	0.422019i	−0.0169350	−	0.0169350i
$622$	−0.181770	+	0.0487050i	−0.00728830	+	0.00195289i
$623$		−	34.7840i		−	1.39359i
$624$	9.47915	+	35.3767i	0.379470	+	1.41620i
$625$	22.1973	+	11.5012i	0.887893	+	0.460050i
$626$	1.42694	−	2.47152i	0.0570318	−	0.0987820i
$627$	−5.26631	+	3.04051i	−0.210316	+	0.121426i
$628$	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	−0.802060	−	0.597244i	$-0.796262\pi$
$631$	4.80204	−	17.9215i	0.191166	−	0.713442i	0.993226	−	0.116199i	$-0.0370709\pi$
$632$	2.07694	−	0.556515i	0.0826163	−	0.0221370i
$633$	−8.01854	−	29.9256i	−0.318709	−	1.18944i
$634$	0.664916	−	0.178164i	0.0264072	−	0.00707579i
$635$	−10.2908	−	4.12596i	−0.408380	−	0.163734i
$636$	23.3646	−	40.4686i	0.926466	−	1.60469i
$637$		−	62.2458i		−	2.46627i
$638$	0.0473077	−	0.176555i	0.00187293	−	0.00698987i
$639$			10.7030i			0.423402i
$640$	−2.91537	−	6.81769i	−0.115240	−	0.269493i
$641$	5.12828	+	8.88244i	0.202555	+	0.350835i	0.949351	−	0.314218i	$-0.101742\pi$
$641$	5.12828	+	8.88244i	0.202555	+	0.350835i	−0.746796	+	0.665053i	$0.768409\pi$
$642$	2.07828	+	1.19990i	0.0820232	+	0.0473561i
$643$		−	12.2193i		−	0.481883i	−0.970540	−	0.240942i	$-0.922544\pi$
$643$		−	12.2193i		−	0.481883i	0.970540	−	0.240942i	$-0.0774562\pi$
$644$	1.30330	+	0.349219i	0.0513573	+	0.0137612i
$645$	1.14043	+	7.96082i	0.0449042	+	0.313457i
$646$	−0.962601	−	0.257928i	−0.0378730	−	0.0101481i
$647$	7.64866	−	13.2479i	0.300700	−	0.520828i	−0.675595	−	0.737273i	$-0.736113\pi$
$647$	7.64866	−	13.2479i	0.300700	−	0.520828i	0.976295	+	0.216446i	$0.0694464\pi$
$648$	−2.30878	+	3.99892i	−0.0906974	+	0.157093i
$649$	0.714231	+	0.191378i	0.0280360	+	0.00751223i
$650$	−2.37084	−	0.577736i	−0.0929920	−	0.0226607i
$651$	−65.7612	−	17.6207i	−2.57739	−	0.690608i
$652$		−	31.5479i		−	1.23551i
$653$	39.2103	+	22.6381i	1.53442	+	0.885897i	0.999150	+	0.0412146i	$0.0131227\pi$
$653$	39.2103	+	22.6381i	1.53442	+	0.885897i	0.535268	+	0.844682i	$0.320211\pi$
$654$	0.701169	+	1.21446i	0.0274179	+	0.0474891i
$655$	−11.3556	+	28.3229i	−0.443702	+	1.10667i
$656$		−	21.6823i		−	0.846550i
$657$	2.36556	−	8.82838i	0.0922892	−	0.344428i
$658$		−	1.11023i		−	0.0432813i
$659$	20.6457	−	35.7594i	0.804243	−	1.39299i	−0.112559	−	0.993645i	$-0.535905\pi$
$659$	20.6457	−	35.7594i	0.804243	−	1.39299i	0.916801	−	0.399344i	$-0.130762\pi$
$660$	−8.10575	+	20.2171i	−0.315516	+	0.786950i
$661$	−22.9847	+	6.15874i	−0.894003	+	0.239547i	−0.676439	−	0.736499i	$-0.736478\pi$
$661$	−22.9847	+	6.15874i	−0.894003	+	0.239547i	−0.217564	+	0.976046i	$0.569811\pi$
$662$	0.786939	+	2.93690i	0.0305852	+	0.114146i
$663$	68.6936	−	18.4064i	2.66784	−	0.714845i
$664$	−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
$668$	−0.913727	+	0.527540i	−0.0353531	+	0.0204111i
$669$	10.3045	−	17.8479i	0.398395	−	0.690040i
$670$	1.84911	+	2.35381i	0.0714372	+	0.0909358i
$671$	−1.73849	−	6.48813i	−0.0671137	−	0.250472i
$672$		−	11.3308i		−	0.437096i
$673$	−21.5596	+	5.77687i	−0.831060	+	0.222682i	−0.649176	−	0.760638i	$-0.724886\pi$
$673$	−21.5596	+	5.77687i	−0.831060	+	0.222682i	−0.181884	+	0.983320i	$0.558220\pi$
$674$	0.606207	+	0.606207i	0.0233502	+	0.0233502i
$675$	10.3235	+	16.9760i	0.397353	+	0.653406i
$676$	−17.0554			−0.655976
$677$	19.1688	+	19.1688i	0.736715	+	0.736715i	0.971941	−	0.235225i	$-0.0755828\pi$
$677$	19.1688	+	19.1688i	0.736715	+	0.736715i	−0.235225	+	0.971941i	$0.575583\pi$
$678$	0.452578	−	1.68904i	0.0173811	−	0.0648673i
$679$	−7.64976	+	2.04975i	−0.293571	+	0.0786621i
$680$	−6.58237	+	2.81474i	−0.252422	+	0.107940i
$681$	−3.58374	+	13.3747i	−0.137329	+	0.512520i
$682$	1.86489	+	0.499696i	0.0714103	+	0.0191343i
$683$	11.1086	+	19.2407i	0.425059	+	0.736224i	0.996426	−	0.0844709i	$-0.0269200\pi$
$683$	11.1086	+	19.2407i	0.425059	+	0.736224i	−0.571367	+	0.820695i	$0.693587\pi$
$684$	0.650342	+	2.42711i	0.0248664	+	0.0928028i
$685$	−18.5644	+	14.5838i	−0.709310	+	0.557219i
$686$	−0.786225	+	2.93423i	−0.0300182	+	0.112030i
$687$	−12.2346	+	45.6600i	−0.466778	+	1.74204i
$688$	−3.52939	−	6.11308i	−0.134557	−	0.233059i
$689$	38.4987	+	38.4987i	1.46668	+	1.46668i
$690$	0.0556188	−	0.0436930i	0.00211737	−	0.00166336i
$691$	−36.9526	+	21.3346i	−1.40574	+	0.811606i	−0.994974	−	0.100134i	$-0.968073\pi$
$691$	−36.9526	+	21.3346i	−1.40574	+	0.811606i	−0.410769	+	0.911740i	$0.634740\pi$
$692$	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
$695$	−6.81124	−	15.9283i	−0.258365	−	0.604196i
$696$	−0.517965	−	0.299047i	−0.0196334	−	0.0113354i
$697$	−42.1021			−1.59473
$698$	−1.68217	−	0.971200i	−0.0636710	−	0.0367605i
$699$	26.4699	+	15.2824i	1.00118	+	0.578033i
$700$	−39.4015	−	21.5674i	−1.48924	−	0.815170i
$701$	−12.0518	−	3.22926i	−0.455189	−	0.121967i	0.0239375	−	0.999713i	$-0.492380\pi$
$701$	−12.0518	−	3.22926i	−0.455189	−	0.121967i	−0.479126	+	0.877746i	$0.659046\pi$
$702$	−1.37132	−	1.37132i	−0.0517573	−	0.0517573i
$703$	−5.98318	+	4.60914i	−0.225660	+	0.173837i
$704$		−	18.9031i		−	0.712436i
$705$	8.39042	+	6.28771i	0.316001	+	0.236809i
$706$	−1.65647	−	0.956364i	−0.0623421	−	0.0359932i
$707$	8.10125	−	2.17072i	0.304679	−	0.0816385i
$708$	0.603206	−	1.04478i	0.0226699	−	0.0392654i
$709$	−36.3631	−	36.3631i	−1.36565	−	1.36565i	−0.866542	−	0.499104i	$-0.833663\pi$
$709$	−36.3631	−	36.3631i	−1.36565	−	1.36565i	−0.499104	−	0.866542i	$-0.666337\pi$
$710$	2.45382	+	0.294667i	0.0920902	+	0.0110587i
$711$	−3.69099	+	3.69099i	−0.138423	+	0.138423i
$712$	3.11775	+	0.835398i	0.116843	+	0.0313079i
$713$	0.798658	+	0.798658i	0.0299100	+	0.0299100i
$714$	−7.26616			−0.271929
$715$	−20.3085	−	15.2190i	−0.759496	−	0.569160i
$716$	4.66661	+	17.4160i	0.174399	+	0.650867i
$717$	−33.1518			−1.23808
$718$	−2.31557	+	1.33690i	−0.0864165	+	0.0498926i
$719$	14.6985	−	8.48621i	0.548163	−	0.316482i	−0.200218	−	0.979751i	$-0.564165\pi$
$719$	14.6985	−	8.48621i	0.548163	−	0.316482i	0.748381	+	0.663269i	$0.230832\pi$
$720$	7.16215	+	5.36726i	0.266918	+	0.200026i
$721$	15.5385	−	4.16353i	0.578684	−	0.155058i
$722$	−1.58860	−	0.917181i	−0.0591218	−	0.0341340i
$723$	6.33094	−	3.65517i	0.235450	−	0.135937i
$724$	−1.10827	−	1.91959i	−0.0411887	−	0.0713409i
$725$	−3.04151	+	1.84962i	−0.112959	+	0.0686933i
$726$	−0.748995	+	0.748995i	−0.0277978	+	0.0277978i
$727$	−7.32860	+	12.6935i	−0.271803	+	0.470776i	−0.969323	−	0.245788i	$-0.920953\pi$
$727$	−7.32860	+	12.6935i	−0.271803	+	0.470776i	0.697521	+	0.716565i	$0.254286\pi$
$728$	8.49351	+	2.27583i	0.314790	+	0.0843478i
$729$			12.6847i			0.469803i
$730$	−1.95892	−	0.785398i	−0.0725027	−	0.0290689i
$731$	−11.8702	+	6.85328i	−0.439037	+	0.253478i
$732$	−10.9592			−0.405062
$733$	−5.04961	−	18.8454i	−0.186512	−	0.696071i	−0.994302	−	0.106601i	$-0.966003\pi$
$733$	−5.04961	−	18.8454i	−0.186512	−	0.696071i	0.807790	−	0.589470i	$-0.200663\pi$
$734$	0.841763	−	0.841763i	0.0310700	−	0.0310700i
$735$	−37.1033	−	47.2305i	−1.36858	−	1.74212i
$736$	−0.0939899	+	0.162795i	−0.00346451	+	0.00600072i
$737$	8.05702	+	30.0692i	0.296784	+	1.10761i
$738$	−0.294616	−	0.510291i	−0.0108450	−	0.0187841i
$739$	0.970989			0.0357184			0.0178592	−	0.999841i	$-0.494315\pi$
$739$	0.970989			0.0357184			0.0178592	+	0.999841i	$0.494315\pi$
$740$	−6.65396	+	26.2217i	−0.244604	+	0.963929i
$741$	−11.5598			−0.424660
$742$	−2.78140	−	4.81753i	−0.102108	−	0.176857i
$743$	−5.91126	−	22.0611i	−0.216863	−	0.809344i	−0.985502	−	0.169662i	$-0.945732\pi$
$743$	−5.91126	−	22.0611i	−0.216863	−	0.809344i	0.768639	−	0.639683i	$-0.220934\pi$
$744$	3.15874	−	5.47110i	0.115805	−	0.200580i
$745$	0.451483	−	3.75969i	0.0165410	−	0.137744i
$746$	−2.27171	+	2.27171i	−0.0831732	+	0.0831732i
$747$	−0.240762	−	0.898536i	−0.00880902	−	0.0328757i
$748$	−37.1234			−1.35737
$749$	−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	$-0.746043\pi$
$751$		−	39.2344i		−	1.43168i	0.698262	−	0.715842i	$-0.253957\pi$
$752$	−8.88937	−	2.38190i	−0.324162	−	0.0868589i
$753$	−7.79185	+	13.4959i	−0.283951	+	0.491817i
$754$	0.245694	−	0.245694i	0.00894765	−	0.00894765i
$755$	−20.2172	−	15.1506i	−0.735779	−	0.551386i
$756$	−17.8491	−	30.9156i	−0.649167	−	1.12439i
$757$	29.8205	−	17.2169i	1.08384	−	0.625757i	0.151913	−	0.988394i	$-0.451457\pi$
$757$	29.8205	−	17.2169i	1.08384	−	0.625757i	0.931931	+	0.362637i	$0.118123\pi$
$758$	−0.638443	−	0.368605i	−0.0231893	−	0.0133884i
$759$	0.710513	−	0.190381i	0.0257900	−	0.00691040i
$760$	1.15190	−	0.165015i	0.0417839	−	0.00598574i
$761$	13.3522	−	7.70889i	0.484016	−	0.279447i	−0.238072	−	0.971247i	$-0.576516\pi$
$761$	13.3522	−	7.70889i	0.484016	−	0.279447i	0.722089	+	0.691800i	$0.243182\pi$
$762$	0.904326	−	0.522113i	0.0327603	−	0.0189142i
$763$	−30.0759			−1.08882
$764$	9.40459	+	35.0984i	0.340246	+	1.26982i
$765$	10.4220	−	13.9073i	0.376809	−	0.502820i
$766$	2.21036			0.0798637
$767$	0.993927	+	0.993927i	0.0358886	+	0.0358886i
$768$	−29.2812	−	7.84589i	−1.05660	−	0.283114i
$769$	8.34198	−	8.34198i	0.300819	−	0.300819i	−0.540515	−	0.841334i	$-0.681771\pi$
$769$	8.34198	−	8.34198i	0.300819	−	0.300819i	0.841334	+	0.540515i	$0.181771\pi$
$770$	1.60181	+	2.03902i	0.0577252	+	0.0734811i
$771$	38.2380	+	38.2380i	1.37711	+	1.37711i
$772$	−6.66655	+	11.5468i	−0.239934	+	0.415578i
$773$	29.4170	−	7.88226i	1.05806	−	0.283505i	0.312479	−	0.949925i	$-0.398841\pi$
$773$	29.4170	−	7.88226i	1.05806	−	0.283505i	0.745577	+	0.666420i	$0.232174\pi$
$774$	−0.166128	−	0.0959139i	−0.00597134	−	0.00344755i
$775$	−19.5370	−	32.1265i	−0.701788	−	1.15402i
$776$		−	0.734890i		−	0.0263810i
$777$	−33.4404	+	43.7523i	−1.19967	+	1.56960i
$778$	−2.16773	−	2.16773i	−0.0777168	−	0.0777168i
$779$	6.61037	+	1.77124i	0.236841	+	0.0634614i
$780$	−32.5604	+	25.5788i	−1.16585	+	0.915867i
$781$	22.2595	+	12.8515i	0.796507	+	0.459864i
$782$	0.104396	+	0.0602732i	0.00373320	+	0.00215537i
$783$	−2.82910			−0.101104
$784$	45.6548	+	26.3588i	1.63053	+	0.941387i
$785$	19.5267	+	7.82894i	0.696938	+	0.279427i
$786$	−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
$790$	0.744599	+	0.947836i	0.0264917	+	0.0337225i
$791$	26.5184	+	26.5184i	0.942886	+	0.942886i
$792$	−0.520996	−	0.902392i	−0.0185128	−	0.0320651i
$793$	3.30481	−	12.3337i	0.117357	−	0.437983i
$794$	−0.0430442	+	0.160643i	−0.00152758	+	0.00570101i
$795$	52.1600	+	6.26364i	1.84993	+	0.222148i
$796$	−4.86633	−	18.1614i	−0.172483	−	0.643714i
$797$	−6.63356	−	11.4897i	−0.234973	−	0.406985i	0.724292	−	0.689493i	$-0.242167\pi$
$797$	−6.63356	−	11.4897i	−0.234973	−	0.406985i	−0.959265	+	0.282509i	$0.908833\pi$
$798$	1.14085	+	0.305689i	0.0403855	+	0.0108213i
$799$	−4.62512	+	17.2612i	−0.163625	+	0.610656i
$800$	4.32311	−	4.52464i	0.152845	−	0.159970i
$801$	−7.56865	+	2.02801i	−0.267425	+	0.0716564i
$802$	−0.104972	+	0.391760i	−0.00370668	+	0.0138335i
$803$	−15.5204	−	15.5204i	−0.547703	−	0.547703i
$804$	50.7901			1.79123
$805$	0.215109	+	1.50158i	0.00758159	+	0.0529239i
$806$	2.59519	+	2.59519i	0.0914116	+	0.0914116i
$807$	−35.3782	+	9.47957i	−1.24537	+	0.333697i
$808$			0.778263i			0.0273792i
$809$	−7.16080	−	26.7245i	−0.251760	−	0.939582i	−0.969864	−	0.243646i	$-0.921656\pi$
$809$	−7.16080	−	26.7245i	−0.251760	−	0.939582i	0.718104	−	0.695936i	$-0.245010\pi$
$810$	−2.56997	−	0.308615i	−0.0902997	−	0.0108436i
$811$	1.13841	−	1.97178i	0.0399749	−	0.0692385i	−0.845346	−	0.534220i	$-0.820606\pi$
$811$	1.13841	−	1.97178i	0.0399749	−	0.0692385i	0.885321	+	0.464981i	$0.153939\pi$
$812$	5.53902	−	3.19795i	0.194381	−	0.112226i
$813$	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
$817$	2.15204	−	0.576638i	0.0752904	−	0.0201740i
$818$	0.449157	+	1.67628i	0.0157044	+	0.0586096i
$819$	−20.6189	+	5.52481i	−0.720481	+	0.193052i
$820$	22.5387	−	9.63794i	0.787084	−	0.336571i
$821$	−13.8253	+	23.9461i	−0.482507	+	0.835726i	−0.999798	−	0.0200830i	$-0.993607\pi$
$821$	−13.8253	+	23.9461i	−0.482507	+	0.835726i	0.517292	+	0.855809i	$0.326940\pi$
$822$		−	2.22346i		−	0.0775520i
$823$	−0.923299	+	3.44580i	−0.0321842	+	0.120113i	−0.980149	−	0.198262i	$-0.936470\pi$
$823$	−0.923299	+	3.44580i	−0.0321842	+	0.120113i	0.947965	+	0.318375i	$0.103137\pi$
$824$			1.49274i			0.0520020i
$825$	−24.4813	+	0.557632i	−0.852330	+	0.0194142i
$826$	−0.0718078	−	0.124375i	−0.00249851	−	0.00432755i
$827$	−29.8888	−	17.2563i	−1.03934	−	0.600060i	−0.119690	−	0.992811i	$-0.538190\pi$
$827$	−29.8888	−	17.2563i	−1.03934	−	0.600060i	−0.919645	+	0.392751i	$0.871523\pi$
$828$		−	0.303947i		−	0.0105629i
$829$	−12.0971	−	3.24141i	−0.420150	−	0.112579i	0.0425488	−	0.999094i	$-0.486452\pi$
$829$	−12.0971	−	3.24141i	−0.420150	−	0.112579i	−0.462699	+	0.886516i	$0.653119\pi$
$830$	−0.212632	+	0.0304605i	−0.00738056	+	0.00105730i
$831$	44.5719	+	11.9430i	1.54618	+	0.414298i
$832$	17.9670	−	31.1198i	0.622895	−	1.07889i
$833$	51.1830	−	88.6515i	1.77338	−	3.07159i
$834$	1.57599	+	0.422286i	0.0545722	+	0.0146226i
$835$	−0.949208	−	0.711328i	−0.0328487	−	0.0246165i
$836$	5.82868	+	1.56179i	0.201589	+	0.0540156i
$837$		−	29.8828i		−	1.03290i
$838$	1.59020	+	0.918102i	0.0549326	+	0.0317153i
$839$	15.9229	+	27.5792i	0.549719	+	0.952141i	0.998294	+	0.0583957i	$0.0185985\pi$
$839$	15.9229	+	27.5792i	0.549719	+	0.952141i	−0.448575	+	0.893745i	$0.648068\pi$
$840$	7.80122	−	3.33594i	0.269168	−	0.115101i
$841$			28.4931i			0.982521i
$842$	0.277547	−	1.03582i	0.00956490	−	0.0356967i
$843$			55.3987i			1.90803i
$844$	−15.3716	+	26.6244i	−0.529112	+	0.916450i
$845$	−7.53893	−	17.6301i	−0.259347	−	0.606493i
$846$	−0.241576	+	0.0647300i	−0.00830554	+	0.00222546i
$847$	−5.87971	−	21.9434i	−0.202029	−	0.753983i
$848$	−44.5401	+	11.9345i	−1.52951	+	0.409831i
$849$	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
$853$	−14.8064	+	8.54847i	−0.506961	+	0.292694i	−0.731583	−	0.681752i	$-0.761218\pi$
$853$	−14.8064	+	8.54847i	−0.506961	+	0.292694i	0.224623	+	0.974446i	$0.427885\pi$
$854$	−0.652308	+	1.12983i	−0.0223215	+	0.0386620i
$855$	−2.22142	+	1.74510i	−0.0759711	+	0.0596813i
$856$	−1.23610	−	4.61318i	−0.0422490	−	0.157675i
$857$			13.4046i			0.457892i	0.973439	+	0.228946i	$0.0735280\pi$
$857$			13.4046i			0.457892i	−0.973439	+	0.228946i	$0.926472\pi$
$858$	2.30877	−	0.618632i	0.0788199	−	0.0211197i
$859$	7.23511	+	7.23511i	0.246859	+	0.246859i	0.819680	−	0.572821i	$-0.194151\pi$
$859$	7.23511	+	7.23511i	0.246859	+	0.246859i	−0.572821	+	0.819680i	$0.694151\pi$
$860$	4.78569	−	6.38610i	0.163191	−	0.217764i
$861$	49.8981			1.70052
$862$	2.13714	+	2.13714i	0.0727912	+	0.0727912i
$863$	0.644292	−	2.40453i	0.0219320	−	0.0818512i	−0.954092	−	0.299512i	$-0.903176\pi$
$863$	0.644292	−	2.40453i	0.0219320	−	0.0818512i	0.976024	+	0.217661i	$0.0698427\pi$
$864$	4.80398	−	1.28722i	0.163435	−	0.0437922i
$865$	5.77298	+	2.31459i	0.196287	+	0.0786984i
$866$	0.465314	−	1.73658i	0.0158120	−	0.0590113i
$867$	80.0565	+	21.4511i	2.71886	+	0.728516i
$868$	33.7789	+	58.5068i	1.14653	+	1.98585i
$869$	3.24441	+	12.1083i	0.110059	+	0.410746i
$870$	0.0399738	−	0.332879i	0.00135524	−	0.0112857i
$871$	−15.3161	+	57.1606i	−0.518967	+	1.93681i
$872$	0.722324	−	2.69575i	0.0244610	−	0.0912896i
$873$	0.892010	+	1.54501i	0.0301900	+	0.0522906i
$874$	−0.0138554	−	0.0138554i	−0.000468664	−	0.000468664i
$875$	4.87757	−	50.2626i	0.164892	−	1.69918i
$876$	−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
$880$	19.7625	−	8.45079i	0.666193	−	0.284876i
$881$	−46.0684	−	26.5976i	−1.55208	−	0.896096i	−0.997972	−	0.0636536i	$-0.979725\pi$
$881$	−46.0684	−	26.5976i	−1.55208	−	0.896096i	−0.554112	−	0.832442i	$-0.686942\pi$
$882$	1.43264			0.0482396
$883$	23.0566	+	13.3117i	0.775916	+	0.447975i	0.834981	−	0.550279i	$-0.185479\pi$
$883$	23.0566	+	13.3117i	0.775916	+	0.447975i	−0.0590650	+	0.998254i	$0.518812\pi$
$884$	−61.1157	−	35.2852i	−2.05554	−	1.18677i
$885$	1.34662	+	0.161709i	0.0452662	+	0.00543580i
$886$	−3.94598	−	1.05732i	−0.132568	−	0.0355214i
$887$	−21.7089	−	21.7089i	−0.728912	−	0.728912i	0.241491	−	0.970403i	$-0.422364\pi$
$887$	−21.7089	−	21.7089i	−0.728912	−	0.728912i	−0.970403	+	0.241491i	$0.922364\pi$
$888$	−3.11846	−	4.04811i	−0.104649	−	0.135846i
$889$			22.3955i			0.751120i
$890$	0.256578	+	1.79106i	0.00860053	+	0.0600366i
$891$	−23.3132	−	13.4599i	−0.781021	−	0.450923i
$892$	−19.7538	+	5.29301i	−0.661405	+	0.177223i
$893$	1.45236	−	2.51556i	0.0486014	−	0.0841801i
$894$	0.252186	+	0.252186i	0.00843435	+	0.00843435i
$895$	−15.9401	+	12.5222i	−0.532819	+	0.418571i
$896$	−10.5908	+	10.5908i	−0.353813	+	0.353813i
$897$	1.35066	+	0.361908i	0.0450972	+	0.0120838i
$898$	−1.86575	−	1.86575i	−0.0622609	−	0.0622609i
$899$	5.35397			0.178565
$900$	−2.39562	+	9.83083i	−0.0798539	+	0.327694i
$901$	23.1741	+	86.4869i	0.772041	+	2.88130i
$902$	−1.41504			−0.0471156
$903$	14.0682	−	8.12230i	0.468162	−	0.270293i
$904$	−3.01378	+	1.74001i	−0.100237	+	0.0578717i
$905$	1.49438	−	1.99413i	0.0496749	−	0.0662870i
$906$	2.29838	−	0.615849i	0.0763586	−	0.0204602i
$907$	−9.23231	−	5.33028i	−0.306554	−	0.176989i	0.338830	−	0.940848i	$-0.389969\pi$
$907$	−9.23231	−	5.33028i	−0.306554	−	0.176989i	−0.645383	+	0.763859i	$0.723302\pi$
$908$	11.8993	−	6.87006i	0.394892	−	0.227991i
$909$	−0.944656	−	1.63619i	−0.0313323	−	0.0542691i
$910$	0.698983	+	4.87930i	0.0231710	+	0.161747i
$911$	10.7665	−	10.7665i	0.356708	−	0.356708i	−0.505890	−	0.862598i	$-0.668836\pi$
$911$	10.7665	−	10.7665i	0.356708	−	0.356708i	0.862598	+	0.505890i	$0.168836\pi$
$912$	4.89515	−	8.47866i	0.162095	−	0.280756i
$913$	−2.15783	−	0.578188i	−0.0714136	−	0.0191352i
$914$			0.184097i			0.00608938i
$915$	−4.84424	−	11.3284i	−0.160146	−	0.374506i
$916$	40.6231	−	23.4538i	1.34222	−	0.774934i
$917$	61.6378			2.03546
$918$	−0.825461	−	3.08066i	−0.0272443	−	0.101677i
$919$	13.7345	−	13.7345i	0.453059	−	0.453059i	−0.443310	−	0.896368i	$-0.646196\pi$
$919$	13.7345	−	13.7345i	0.453059	−	0.453059i	0.896368	+	0.443310i	$0.146196\pi$
$920$	−0.139756	−	0.0167826i	−0.00460761	−	0.000553305i
$921$	10.3930	−	18.0013i	0.342463	−	0.593162i
$922$	−0.504913	−	1.88436i	−0.0166284	−	0.0620581i
$923$	24.4303	+	42.3145i	0.804133	+	1.39280i
$924$	43.9975			1.44741
$925$	−30.0465	+	4.71253i	−0.987923	+	0.154947i
$926$	−2.20202			−0.0723629
$927$	−1.81189	−	3.13828i	−0.0595102	−	0.103075i
$928$	0.230626	+	0.860707i	0.00757066	+	0.0282541i
$929$	2.36184	−	4.09083i	0.0774895	−	0.134216i	−0.824677	−	0.565604i	$-0.808643\pi$
$929$	2.36184	−	4.09083i	0.0774895	−	0.134216i	0.902166	+	0.431389i	$0.141976\pi$
$930$	3.51609	+	0.422230i	0.115297	+	0.0138455i
$931$	−11.7657	+	11.7657i	−0.385606	+	0.385606i
$932$	−7.84996	−	29.2964i	−0.257134	−	0.959637i
$933$	−3.58980			−0.117525
$934$	2.00529	−	1.15775i	0.0656149	−	0.0378828i
$935$	−16.4096	−	38.3743i	−0.536650	−	1.25497i
$936$		−	1.98079i		−	0.0647442i
$937$	−37.8706	−	10.1474i	−1.23718	−	0.331501i	−0.419808	−	0.907613i	$-0.637903\pi$
$937$	−37.8706	−	10.1474i	−1.23718	−	0.331501i	−0.817371	+	0.576112i	$0.804569\pi$
$938$	3.02312	−	5.23619i	0.0987083	−	0.170968i
$939$	38.4957	−	38.4957i	1.25626	−	1.25626i
$940$	−1.47542	−	10.2992i	−0.0481228	−	0.335924i
$941$	3.93030	+	6.80748i	0.128124	+	0.221917i	0.922950	−	0.384920i	$-0.125771\pi$
$941$	3.93030	+	6.80748i	0.128124	+	0.221917i	−0.794826	+	0.606838i	$0.792438\pi$
$942$	−1.71594	+	0.990700i	−0.0559085	+	0.0322788i
$943$	−0.716910	−	0.413908i	−0.0233458	−	0.0134787i
$944$	−1.14990	+	0.308114i	−0.0374260	+	0.0100283i
$945$	24.0676	−	32.1161i	0.782918	−	1.04474i
$946$	−0.398954	+	0.230336i	−0.0129711	+	0.00748888i
$947$	−34.8825	+	20.1394i	−1.13353	+	0.654444i	−0.944820	−	0.327589i	$-0.893764\pi$
$947$	−34.8825	+	20.1394i	−1.13353	+	0.654444i	−0.188710	+	0.982033i	$0.560431\pi$
$948$	20.4522			0.664257
$949$	−10.7991	−	40.3029i	−0.350555	−	1.30829i
$950$	0.338933	+	0.557341i	0.0109964	+	0.0180825i
$951$	13.1316			0.425820
$952$	10.2252	+	10.2252i	0.331402	+	0.331402i
$953$	−29.5341	−	7.91365i	−0.956705	−	0.256348i	−0.253500	−	0.967335i	$-0.581582\pi$
$953$	−29.5341	−	7.91365i	−0.956705	−	0.256348i	−0.703205	+	0.710987i	$0.748248\pi$
$954$	−0.886083	+	0.886083i	−0.0286880	+	0.0286880i
$955$	−32.1240	+	25.2359i	−1.03951	+	0.816615i
$956$	23.2617	+	23.2617i	0.752338	+	0.752338i
$957$	1.74341	−	3.01967i	0.0563563	−	0.0976120i
$958$	−2.78654	+	0.746652i	−0.0900292	+	0.0241232i
$959$	41.2976	+	23.8432i	1.33357	+	0.769937i
$960$	−4.91688	−	34.3227i	−0.158692	−	1.10776i
$961$			25.5523i			0.824267i
$962$	2.74051	−	1.14126i	0.0883577	−	0.0367958i
$963$	8.19822	+	8.19822i	0.264184	+	0.264184i
$964$	−7.00699	−	1.87752i	−0.225680	−	0.0604707i
$965$	−14.8827	−	1.78719i	−0.479090	−	0.0575316i
$966$	−0.123727	−	0.0714340i	−0.00398086	−	0.00229835i
$967$	17.4848	+	10.0949i	0.562273	+	0.324629i	0.754057	−	0.656809i	$-0.228094\pi$
$967$	17.4848	+	10.0949i	0.562273	+	0.324629i	−0.191784	+	0.981437i	$0.561427\pi$
$968$	2.10803			0.0677548
$969$	−16.4637	−	9.50530i	−0.528889	−	0.305354i
$970$	0.378775	−	0.161971i	0.0121617	−	0.00520058i
$971$	−13.3211	−	23.0728i	−0.427494	−	0.740441i	0.569156	−	0.822230i	$-0.307270\pi$
$971$	−13.3211	−	23.0728i	−0.427494	−	0.740441i	−0.996650	+	0.0817885i	$0.973937\pi$
$972$	−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
$975$	−40.8332	−	22.3511i	−1.30771	−	0.715807i
$976$	7.64683	+	7.64683i	0.244769	+	0.244769i
$977$	3.06529	+	5.30924i	0.0980674	+	0.169858i	0.910885	−	0.412661i	$-0.135401\pi$
$977$	3.06529	+	5.30924i	0.0980674	+	0.169858i	−0.812817	+	0.582519i	$0.802067\pi$
$978$	−0.864569	+	3.22662i	−0.0276459	+	0.103176i
$979$	−4.87026	+	18.1760i	−0.155654	+	0.580909i
$980$	−7.10601	+	59.1748i	−0.226993	+	1.89027i
$981$	1.75352	+	6.54421i	0.0559855	+	0.208941i
$982$	0.0781165	+	0.135302i	0.00249280	+	0.00431765i
$983$	20.4463	+	5.47856i	0.652134	+	0.174739i	0.569694	−	0.821857i	$-0.307062\pi$
$983$	20.4463	+	5.47856i	0.652134	+	0.174739i	0.0824406	+	0.996596i	$0.473729\pi$
$984$	−1.19839	+	4.47246i	−0.0382033	+	0.142577i
$985$	29.9365	+	12.0026i	0.953857	+	0.382435i
$986$	0.551949	−	0.147894i	0.0175776	−	0.00470991i
$987$	5.48155	−	20.4574i	0.174480	−	0.651166i
$988$	8.11121	+	8.11121i	0.258052	+	0.258052i
$989$	−0.269500			−0.00856960
$990$	0.350280	−	0.467419i	0.0111326	−	0.0148556i
$991$	−24.8692	−	24.8692i	−0.789997	−	0.789997i	0.191497	−	0.981493i	$-0.438666\pi$
$991$	−24.8692	−	24.8692i	−0.789997	−	0.789997i	−0.981493	+	0.191497i	$0.938666\pi$
$992$	−9.09137	+	2.43603i	−0.288651	+	0.0773439i
$993$			58.0013i			1.84062i
$994$	−1.29207	−	4.82209i	−0.0409821	−	0.152947i
$995$	16.6223	−	13.0581i	0.526963	−	0.413971i
$996$	−1.82240	+	3.15649i	−0.0577449	+	0.100017i
$997$	−15.4481	+	8.91895i	−0.489245	+	0.282466i	−0.724261	−	0.689526i	$-0.757819\pi$
$997$	−15.4481	+	8.91895i	−0.489245	+	0.282466i	0.235016	+	0.971992i	$0.424486\pi$
$998$	−1.63977	+	1.63977i	−0.0519060	+	0.0519060i
$999$	−22.3488	−	9.20745i	−0.707084	−	0.291311i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.9	✓	68	185.97	even	12	inner
185.2.p.a.103.9	yes	68	1.1	even	1	trivial
185.2.u.a.23.9	yes	68	37.23	odd	12
185.2.u.a.177.9	yes	68	5.2	odd	4
925.2.t.b.282.9		68	185.23	even	12
925.2.t.b.843.9		68	5.4	even	2
925.2.y.b.393.9		68	185.134	odd	12
925.2.y.b.732.9		68	5.3	odd	4

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

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.9

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$