LMFDB - Embedded newform 240.2.bb.a.173.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.18
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.418005 + 1.35103i) q^{2} +(-1.65521 + 0.510164i) q^{3} +(-1.65054 - 1.12947i) q^{4} +(-0.369196 + 2.20538i) q^{5} +(0.00264245 - 2.44949i) q^{6} +(-2.84513 - 2.84513i) q^{7} +(2.21588 - 1.75780i) q^{8} +(2.47947 - 1.68886i) q^{9} +O(q^{10})$	\(q+(-0.418005 + 1.35103i) q^{2} +(-1.65521 + 0.510164i) q^{3} +(-1.65054 - 1.12947i) q^{4} +(-0.369196 + 2.20538i) q^{5} +(0.00264245 - 2.44949i) q^{6} +(-2.84513 - 2.84513i) q^{7} +(2.21588 - 1.75780i) q^{8} +(2.47947 - 1.68886i) q^{9} +(-2.82520 - 1.42065i) q^{10} +(-0.897797 - 0.897797i) q^{11} +(3.30822 + 1.02747i) q^{12} +1.68555i q^{13} +(5.03313 - 2.65457i) q^{14} +(-0.514007 - 3.83872i) q^{15} +(1.44859 + 3.72848i) q^{16} +(-3.30858 - 3.30858i) q^{17} +(1.24527 + 4.05577i) q^{18} +(4.55983 - 4.55983i) q^{19} +(3.10029 - 3.22308i) q^{20} +(6.16079 + 3.25782i) q^{21} +(1.58823 - 0.837664i) q^{22} +(-1.41506 - 1.41506i) q^{23} +(-2.77099 + 4.04000i) q^{24} +(-4.72739 - 1.62843i) q^{25} +(-2.27722 - 0.704566i) q^{26} +(-3.24245 + 4.06036i) q^{27} +(1.48252 + 7.90951i) q^{28} +(-3.73404 - 3.73404i) q^{29} +(5.40107 + 0.910169i) q^{30} -4.39950 q^{31} +(-5.64280 + 0.398557i) q^{32} +(1.94407 + 1.02802i) q^{33} +(5.85299 - 3.08698i) q^{34} +(7.32500 - 5.22418i) q^{35} +(-5.99999 - 0.0129453i) q^{36} +3.05850i q^{37} +(4.25442 + 8.06648i) q^{38} +(-0.859905 - 2.78994i) q^{39} +(3.05853 + 5.53583i) q^{40} -2.50291 q^{41} +(-6.97664 + 6.96160i) q^{42} -10.5667 q^{43} +(0.467817 + 2.49589i) q^{44} +(2.80917 + 6.09168i) q^{45} +(2.50329 - 1.32028i) q^{46} +(2.69473 + 2.69473i) q^{47} +(-4.29986 - 5.43242i) q^{48} +9.18955i q^{49} +(4.17613 - 5.70613i) q^{50} +(7.16433 + 3.78849i) q^{51} +(1.90378 - 2.78207i) q^{52} -2.43012i q^{53} +(-4.13029 - 6.07788i) q^{54} +(2.31145 - 1.64852i) q^{55} +(-11.3057 - 1.30329i) q^{56} +(-5.22123 + 9.87375i) q^{57} +(6.60563 - 3.48394i) q^{58} +(-0.429791 + 0.429791i) q^{59} +(-3.48734 + 6.91654i) q^{60} +(0.751106 + 0.751106i) q^{61} +(1.83901 - 5.94384i) q^{62} +(-11.8594 - 2.24937i) q^{63} +(1.82026 - 7.79016i) q^{64} +(-3.71727 - 0.622296i) q^{65} +(-2.20152 + 2.19677i) q^{66} -10.4823 q^{67} +(1.72401 + 9.19791i) q^{68} +(3.06415 + 1.62032i) q^{69} +(3.99612 + 12.0800i) q^{70} -13.4420 q^{71} +(2.52551 - 8.10073i) q^{72} +(8.58741 - 8.58741i) q^{73} +(-4.13211 - 1.27847i) q^{74} +(8.65561 + 0.283661i) q^{75} +(-12.6764 + 2.37600i) q^{76} +5.10870i q^{77} +(4.12872 + 0.00445397i) q^{78} +9.85894i q^{79} +(-8.75753 + 1.81815i) q^{80} +(3.29549 - 8.37495i) q^{81} +(1.04623 - 3.38150i) q^{82} +15.6541 q^{83} +(-6.48904 - 12.3356i) q^{84} +(8.51819 - 6.07516i) q^{85} +(4.41691 - 14.2758i) q^{86} +(8.08560 + 4.27566i) q^{87} +(-3.56756 - 0.411261i) q^{88} -10.8149i q^{89} +(-9.40427 + 1.24891i) q^{90} +(4.79560 - 4.79560i) q^{91} +(0.737351 + 3.93390i) q^{92} +(7.28211 - 2.24447i) q^{93} +(-4.76706 + 2.51424i) q^{94} +(8.37268 + 11.7396i) q^{95} +(9.13670 - 3.53845i) q^{96} +(1.65415 - 1.65415i) q^{97} +(-12.4153 - 3.84128i) q^{98} +(-3.74231 - 0.709802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.418005	+	1.35103i	−0.295574	+	0.955320i
$2$	−0.418005	+	1.35103i	−0.295574	+	0.955320i
$3$	−1.65521	+	0.510164i	−0.955638	+	0.294543i
$3$	−1.65521	+	0.510164i	−0.955638	+	0.294543i
$4$	−1.65054	−	1.12947i	−0.825272	−	0.564736i
$5$	−0.369196	+	2.20538i	−0.165109	+	0.986275i
$5$	−0.369196	+	2.20538i	−0.165109	+	0.986275i
$6$	0.00264245	−	2.44949i	0.00107878	−	0.999999i
$7$	−2.84513	−	2.84513i	−1.07536	−	1.07536i	−0.996919	−	0.0784400i	$-0.975006\pi$
$7$	−2.84513	−	2.84513i	−1.07536	−	1.07536i	−0.0784400	−	0.996919i	$-0.524994\pi$
$8$	2.21588	−	1.75780i	0.783432	−	0.621477i
$9$	2.47947	−	1.68886i	0.826488	−	0.562954i
$10$	−2.82520	−	1.42065i	−0.893406	−	0.449250i
$11$	−0.897797	−	0.897797i	−0.270696	−	0.270696i	0.558684	−	0.829380i	$-0.311306\pi$
$11$	−0.897797	−	0.897797i	−0.270696	−	0.270696i	−0.829380	+	0.558684i	$0.811306\pi$
$12$	3.30822	+	1.02747i	0.955000	+	0.296605i
$13$			1.68555i			0.467486i	0.972298	+	0.233743i	$0.0750975\pi$
$13$			1.68555i			0.467486i	−0.972298	+	0.233743i	$0.924903\pi$
$14$	5.03313	−	2.65457i	1.34516	−	0.709463i
$15$	−0.514007	−	3.83872i	−0.132716	−	0.991154i
$16$	1.44859	+	3.72848i	0.362147	+	0.932121i
$17$	−3.30858	−	3.30858i	−0.802449	−	0.802449i	0.181029	−	0.983478i	$-0.442057\pi$
$17$	−3.30858	−	3.30858i	−0.802449	−	0.802449i	−0.983478	+	0.181029i	$0.942057\pi$
$18$	1.24527	+	4.05577i	0.293512	+	0.955955i
$19$	4.55983	−	4.55983i	1.04610	−	1.04610i	0.0472113	−	0.998885i	$-0.484967\pi$
$19$	4.55983	−	4.55983i	1.04610	−	1.04610i	0.998885	−	0.0472113i	$-0.0150334\pi$
$20$	3.10029	−	3.22308i	0.693245	−	0.720702i
$21$	6.16079	+	3.25782i	1.34439	+	0.710914i
$22$	1.58823	−	0.837664i	0.338612	−	0.178591i
$23$	−1.41506	−	1.41506i	−0.295061	−	0.295061i	0.544015	−	0.839076i	$-0.316904\pi$
$23$	−1.41506	−	1.41506i	−0.295061	−	0.295061i	−0.839076	+	0.544015i	$0.816904\pi$
$24$	−2.77099	+	4.04000i	−0.565626	+	0.824662i
$25$	−4.72739	−	1.62843i	−0.945478	−	0.325687i
$26$	−2.27722	−	0.704566i	−0.446599	−	0.138177i
$27$	−3.24245	+	4.06036i	−0.624009	+	0.781417i
$28$	1.48252	+	7.90951i	0.280170	+	1.49476i
$29$	−3.73404	−	3.73404i	−0.693393	−	0.693393i	0.269584	−	0.962977i	$-0.413114\pi$
$29$	−3.73404	−	3.73404i	−0.693393	−	0.693393i	−0.962977	+	0.269584i	$0.913114\pi$
$30$	5.40107	+	0.910169i	0.986097	+	0.166173i
$31$	−4.39950			−0.790173			−0.395087	−	0.918644i	$-0.629285\pi$
$31$	−4.39950			−0.790173			−0.395087	+	0.918644i	$0.629285\pi$
$32$	−5.64280	+	0.398557i	−0.997515	+	0.0704556i
$33$	1.94407	+	1.02802i	0.338419	+	0.178956i
$34$	5.85299	−	3.08698i	1.00378	−	0.529412i
$35$	7.32500	−	5.22418i	1.23815	−	0.883048i
$36$	−5.99999	−	0.0129453i	−0.999998	−	0.00215755i
$37$			3.05850i			0.502814i	0.967881	+	0.251407i	$0.0808933\pi$
$37$			3.05850i			0.502814i	−0.967881	+	0.251407i	$0.919107\pi$
$38$	4.25442	+	8.06648i	0.690157	+	1.30856i
$39$	−0.859905	−	2.78994i	−0.137695	−	0.446748i
$40$	3.05853	+	5.53583i	0.483596	+	0.875292i
$41$	−2.50291			−0.390889			−0.195444	−	0.980715i	$-0.562615\pi$
$41$	−2.50291			−0.390889			−0.195444	+	0.980715i	$0.562615\pi$
$42$	−6.97664	+	6.96160i	−1.07652	+	1.07420i
$43$	−10.5667			−1.61140			−0.805700	−	0.592324i	$-0.798211\pi$
$43$	−10.5667			−1.61140			−0.805700	+	0.592324i	$0.798211\pi$
$44$	0.467817	+	2.49589i	0.0705261	+	0.376270i
$45$	2.80917	+	6.09168i	0.418766	+	0.908094i
$46$	2.50329	−	1.32028i	0.369090	−	0.194665i
$47$	2.69473	+	2.69473i	0.393067	+	0.393067i	0.875779	−	0.482712i	$-0.160348\pi$
$47$	2.69473	+	2.69473i	0.393067	+	0.393067i	−0.482712	+	0.875779i	$0.660348\pi$
$48$	−4.29986	−	5.43242i	−0.620632	−	0.784102i
$49$			9.18955i			1.31279i
$50$	4.17613	−	5.70613i	0.590594	−	0.806969i
$51$	7.16433	+	3.78849i	1.00321	+	0.530495i
$52$	1.90378	−	2.78207i	0.264006	−	0.385803i
$53$		−	2.43012i		−	0.333802i	−0.985974	−	0.166901i	$-0.946624\pi$
$53$		−	2.43012i		−	0.333802i	0.985974	−	0.166901i	$-0.0533760\pi$
$54$	−4.13029	−	6.07788i	−0.562062	−	0.827095i
$55$	2.31145	−	1.64852i	0.311675	−	0.222286i
$56$	−11.3057	−	1.30329i	−1.51078	−	0.174160i
$57$	−5.22123	+	9.87375i	−0.691569	+	1.30781i
$58$	6.60563	−	3.48394i	0.867362	−	0.457463i
$59$	−0.429791	+	0.429791i	−0.0559540	+	0.0559540i	−0.734530	−	0.678576i	$-0.762597\pi$
$59$	−0.429791	+	0.429791i	−0.0559540	+	0.0559540i	0.678576	+	0.734530i	$0.262597\pi$
$60$	−3.48734	+	6.91654i	−0.450213	+	0.892921i
$61$	0.751106	+	0.751106i	0.0961693	+	0.0961693i	0.753555	−	0.657385i	$-0.228338\pi$
$61$	0.751106	+	0.751106i	0.0961693	+	0.0961693i	−0.657385	+	0.753555i	$0.728338\pi$
$62$	1.83901	−	5.94384i	0.233555	−	0.754868i
$63$	−11.8594	−	2.24937i	−1.49415	−	0.283394i
$64$	1.82026	−	7.79016i	0.227532	−	0.973771i
$65$	−3.71727	−	0.622296i	−0.461070	−	0.0771864i
$66$	−2.20152	+	2.19677i	−0.270988	+	0.270404i
$67$	−10.4823			−1.28061			−0.640306	−	0.768120i	$-0.721193\pi$
$67$	−10.4823			−1.28061			−0.640306	+	0.768120i	$0.721193\pi$
$68$	1.72401	+	9.19791i	0.209067	+	1.11541i
$69$	3.06415	+	1.62032i	0.368880	+	0.195063i
$70$	3.99612	+	12.0800i	0.477628	+	1.44384i
$71$	−13.4420			−1.59527			−0.797634	−	0.603141i	$-0.793916\pi$
$71$	−13.4420			−1.59527			−0.797634	+	0.603141i	$0.793916\pi$
$72$	2.52551	−	8.10073i	0.297635	−	0.954680i
$73$	8.58741	−	8.58741i	1.00508	−	1.00508i	0.00509303	−	0.999987i	$-0.498379\pi$
$73$	8.58741	−	8.58741i	1.00508	−	1.00508i	0.999987	−	0.00509303i	$-0.00162117\pi$
$74$	−4.13211	−	1.27847i	−0.480349	−	0.148619i
$75$	8.65561	+	0.283661i	0.999463	+	0.0327544i
$76$	−12.6764	+	2.37600i	−1.45408	+	0.272546i
$77$			5.10870i			0.582191i
$78$	4.12872	+	0.00445397i	0.467486	+	0.000504313i
$79$			9.85894i			1.10922i	0.832111	+	0.554609i	$0.187132\pi$
$79$			9.85894i			1.10922i	−0.832111	+	0.554609i	$0.812868\pi$
$80$	−8.75753	+	1.81815i	−0.979122	+	0.203275i
$81$	3.29549	−	8.37495i	0.366166	−	0.930550i
$82$	1.04623	−	3.38150i	0.115537	−	0.373424i
$83$	15.6541			1.71827			0.859133	−	0.511753i	$-0.171004\pi$
$83$	15.6541			1.71827			0.859133	+	0.511753i	$0.171004\pi$
$84$	−6.48904	−	12.3356i	−0.708012	−	1.34592i
$85$	8.51819	−	6.07516i	0.923928	−	0.658944i
$86$	4.41691	−	14.2758i	0.476288	−	1.53940i
$87$	8.08560	+	4.27566i	0.866868	+	0.458399i
$88$	−3.56756	−	0.411261i	−0.380304	−	0.0438406i
$89$		−	10.8149i		−	1.14638i	−0.819424	−	0.573188i	$-0.805707\pi$
$89$		−	10.8149i		−	1.14638i	0.819424	−	0.573188i	$-0.194293\pi$
$90$	−9.40427	+	1.24891i	−0.991297	+	0.131647i
$91$	4.79560	−	4.79560i	0.502715	−	0.502715i
$92$	0.737351	+	3.93390i	0.0768741	+	0.410137i
$93$	7.28211	−	2.24447i	0.755120	−	0.232740i
$94$	−4.76706	+	2.51424i	−0.491685	+	0.259324i
$95$	8.37268	+	11.7396i	0.859018	+	1.20446i
$96$	9.13670	−	3.53845i	0.932511	−	0.361141i
$97$	1.65415	−	1.65415i	0.167954	−	0.167954i	−0.618126	−	0.786079i	$-0.712108\pi$
$97$	1.65415	−	1.65415i	0.167954	−	0.167954i	0.786079	+	0.618126i	$0.212108\pi$
$98$	−12.4153	−	3.84128i	−1.25414	−	0.388028i
$99$	−3.74231	−	0.709802i	−0.376117	−	0.0713378i
$100$	5.96349	+	8.02725i	0.596349	+	0.802725i
$101$	11.7459	+	11.7459i	1.16876	+	1.16876i	0.982500	+	0.186265i	$0.0596381\pi$
$101$	11.7459	+	11.7459i	1.16876	+	1.16876i	0.186265	+	0.982500i	$0.440362\pi$
$102$	−8.11308	+	8.09559i	−0.803314	+	0.801583i
$103$	−3.09454	+	3.09454i	−0.304914	+	0.304914i	−0.842933	−	0.538019i	$-0.819173\pi$
$103$	−3.09454	+	3.09454i	−0.304914	+	0.304914i	0.538019	+	0.842933i	$0.319173\pi$
$104$	2.96286	+	3.73497i	0.290532	+	0.366244i
$105$	−9.45926	+	12.3841i	−0.923129	+	1.20856i
$106$	3.28315	+	1.01580i	0.318888	+	0.0986633i
$107$	7.08042			0.684490			0.342245	−	0.939611i	$-0.388813\pi$
$107$	7.08042			0.684490			0.342245	+	0.939611i	$0.388813\pi$
$108$	9.93786	−	3.03955i	0.956271	−	0.292481i
$109$	−6.54083	+	6.54083i	−0.626498	+	0.626498i	−0.947185	−	0.320687i	$-0.896086\pi$
$109$	−6.54083	+	6.54083i	−0.626498	+	0.626498i	0.320687	+	0.947185i	$0.396086\pi$
$110$	1.26100	+	3.81191i	0.120231	+	0.363452i
$111$	−1.56034	−	5.06247i	−0.148101	−	0.480509i
$112$	6.48660	−	14.7295i	0.612926	−	1.39180i
$113$	6.53213	−	6.53213i	0.614491	−	0.614491i	−0.329622	−	0.944113i	$-0.606921\pi$
$113$	6.53213	−	6.53213i	0.614491	−	0.614491i	0.944113	+	0.329622i	$0.106921\pi$
$114$	−11.1572	−	11.1813i	−1.04497	−	1.04722i
$115$	3.64319	−	2.59832i	0.339729	−	0.242294i
$116$	1.94570	+	10.3807i	0.180654	+	0.963822i
$117$	2.84665	+	4.17925i	0.263173	+	0.386372i
$118$	−0.401004	−	0.760314i	−0.0369154	−	0.0699926i
$119$			18.8267i			1.72584i
$120$	−7.88670	−	7.60263i	−0.719954	−	0.694022i
$121$		−	9.38792i		−	0.853447i
$122$	−1.32873	+	0.700798i	−0.120298	+	0.0634472i
$123$	4.14285	−	1.27689i	0.373548	−	0.115134i
$124$	7.26157	+	4.96911i	0.652108	+	0.446239i
$125$	5.33665	−	9.82447i	0.477324	−	0.878727i
$126$	7.99627	−	15.0822i	0.712364	−	1.34363i
$127$	9.03070	−	9.03070i	0.801345	−	0.801345i	−0.181961	−	0.983306i	$-0.558244\pi$
$127$	9.03070	−	9.03070i	0.801345	−	0.801345i	0.983306	+	0.181961i	$0.0582444\pi$
$128$	9.76384	+	5.71554i	0.863010	+	0.505187i
$129$	17.4901	−	5.39073i	1.53992	−	0.474627i
$130$	2.39457	−	4.76200i	0.210018	−	0.417655i
$131$	−6.09302	+	6.09302i	−0.532350	+	0.532350i	−0.921271	−	0.388921i	$-0.872848\pi$
$131$	−6.09302	+	6.09302i	−0.532350	+	0.532350i	0.388921	+	0.921271i	$0.372848\pi$
$132$	−2.04765	−	3.89257i	−0.178225	−	0.338805i
$133$	−25.9466			−2.24986
$134$	4.38164	−	14.1618i	0.378516	−	1.22339i
$135$	−7.75753	−	8.64989i	−0.667662	−	0.744464i
$136$	−13.1473	−	1.51559i	−1.12737	−	0.129961i
$137$	−5.70036	+	5.70036i	−0.487015	+	0.487015i	−0.907363	−	0.420348i	$-0.861908\pi$
$137$	−5.70036	+	5.70036i	−0.487015	+	0.487015i	0.420348	+	0.907363i	$0.361908\pi$
$138$	−3.46992	+	3.46244i	−0.295379	+	0.294743i
$139$	−1.07274	−	1.07274i	−0.0909889	−	0.0909889i	0.660147	−	0.751136i	$-0.270494\pi$
$139$	−1.07274	−	1.07274i	−0.0909889	−	0.0909889i	−0.751136	+	0.660147i	$0.770494\pi$
$140$	−17.9908	+	0.349358i	−1.52050	+	0.0295262i
$141$	−5.83511	−	3.08560i	−0.491405	−	0.259855i
$142$	5.61881	−	18.1605i	0.471520	−	1.52399i
$143$	1.51328	−	1.51328i	0.126547	−	0.126547i
$144$	9.88862	+	6.79818i	0.824051	+	0.566515i
$145$	9.61356	−	6.85638i	0.798363	−	0.569391i
$146$	8.01223	+	15.1914i	0.663097	+	1.25725i
$147$	−4.68818	−	15.2107i	−0.386675	−	1.25456i
$148$	3.45449	−	5.04819i	0.283957	−	0.414959i
$149$	−6.22464	+	6.22464i	−0.509943	+	0.509943i	−0.914509	−	0.404566i	$-0.867423\pi$
$149$	−6.22464	+	6.22464i	−0.509943	+	0.509943i	0.404566	+	0.914509i	$0.367423\pi$
$150$	−4.00132	+	11.5754i	−0.326706	+	0.945126i
$151$		−	1.53152i		−	0.124633i	−0.998056	−	0.0623167i	$-0.980151\pi$
$151$		−	1.53152i		−	0.124633i	0.998056	−	0.0623167i	$-0.0198489\pi$
$152$	2.08876	−	18.1193i	0.169420	−	1.46967i
$153$	−13.7913	−	2.61578i	−1.11496	−	0.211473i
$154$	−6.90199	−	2.13546i	−0.556178	−	0.172081i
$155$	1.62428	−	9.70256i	0.130465	−	0.779329i
$156$	−1.73184	+	5.57615i	−0.138659	+	0.446449i
$157$	−8.64080			−0.689611			−0.344806	−	0.938674i	$-0.612055\pi$
$157$	−8.64080			−0.689611			−0.344806	+	0.938674i	$0.612055\pi$
$158$	−13.3197	−	4.12109i	−1.05966	−	0.327856i
$159$	1.23976	+	4.02236i	0.0983192	+	0.318994i
$160$	1.20433	−	12.5916i	0.0952105	−	0.995457i
$161$			8.05209i			0.634593i
$162$	9.93724	+	7.95307i	0.780743	+	0.624852i
$163$			8.12334i			0.636269i	0.948046	+	0.318135i	$0.103056\pi$
$163$			8.12334i			0.636269i	−0.948046	+	0.318135i	$0.896944\pi$
$164$	4.13116	+	2.82696i	0.322589	+	0.220749i
$165$	−2.98492	+	3.90787i	−0.232376	+	0.304227i
$166$	−6.54351	+	21.1492i	−0.507875	+	1.64149i
$167$	0.792638	−	0.792638i	0.0613362	−	0.0613362i	−0.675773	−	0.737110i	$-0.736190\pi$
$167$	0.792638	−	0.792638i	0.0613362	−	0.0613362i	0.737110	+	0.675773i	$0.236190\pi$
$168$	19.3782	−	3.61051i	1.49506	−	0.278557i
$169$	10.1589			0.781457
$170$	4.64706	+	14.0477i	0.356413	+	1.07741i
$171$	3.60502	−	19.0069i	0.275683	−	1.45349i
$172$	17.4407	+	11.9347i	1.32984	+	0.910015i
$173$	−19.3251			−1.46926			−0.734631	−	0.678467i	$-0.762645\pi$
$173$	−19.3251			−1.46926			−0.734631	+	0.678467i	$0.762645\pi$
$174$	−9.15635	+	9.13662i	−0.694141	+	0.692645i
$175$	8.81694	+	18.0832i	0.666498	+	1.36696i
$176$	2.04688	−	4.64796i	0.154290	−	0.350353i
$177$	0.492132	−	0.930660i	0.0369909	−	0.0699527i
$178$	14.6112	+	4.52068i	1.09516	+	0.338839i
$179$	−3.78196	−	3.78196i	−0.282677	−	0.282677i	0.551499	−	0.834176i	$-0.314056\pi$
$179$	−3.78196	−	3.78196i	−0.282677	−	0.282677i	−0.834176	+	0.551499i	$0.814056\pi$
$180$	2.24372	−	13.2275i	0.167237	−	0.985917i
$181$	−16.8741	+	16.8741i	−1.25425	+	1.25425i	−0.300447	+	0.953799i	$0.597136\pi$
$181$	−16.8741	+	16.8741i	−1.25425	+	1.25425i	−0.953799	+	0.300447i	$0.902864\pi$
$182$	4.47440	+	8.48356i	0.331664	+	0.628844i
$183$	−1.62643	−	0.860053i	−0.120229	−	0.0635770i
$184$	−5.62302	−	0.648209i	−0.414534	−	0.0477866i
$185$	−6.74515	−	1.12919i	−0.495913	−	0.0830194i
$186$	−0.0116255	+	10.7765i	−0.000852421	+	0.790173i
$187$			5.94087i			0.434440i
$188$	−1.40415	−	7.49139i	−0.102408	−	0.546366i
$189$	20.7775	−	2.32707i	1.51134	−	0.169269i
$190$	−19.3603	+	6.40449i	−1.40455	+	0.464630i
$191$		−	4.30900i		−	0.311788i	−0.987774	−	0.155894i	$-0.950174\pi$
$191$		−	4.30900i		−	0.311788i	0.987774	−	0.155894i	$-0.0498259\pi$
$192$	0.961350	+	13.8230i	0.0693795	+	0.997590i
$193$	−15.5869	−	15.5869i	−1.12197	−	1.12197i	−0.991445	−	0.130527i	$-0.958333\pi$
$193$	−15.5869	−	15.5869i	−1.12197	−	1.12197i	−0.130527	−	0.991445i	$-0.541667\pi$
$194$	1.54336	+	2.92625i	0.110807	+	0.210092i
$195$	6.47034	−	0.866382i	0.463351	−	0.0620429i
$196$	10.3793	−	15.1678i	0.741381	−	1.08341i
$197$	11.0384			0.786452			0.393226	−	0.919442i	$-0.371359\pi$
$197$	11.0384			0.786452			0.393226	+	0.919442i	$0.371359\pi$
$198$	2.52327	−	4.75926i	0.179321	−	0.338226i
$199$	0.862986			0.0611755			0.0305877	−	0.999532i	$-0.490262\pi$
$199$	0.862986			0.0611755			0.0305877	+	0.999532i	$0.490262\pi$
$200$	−13.3378	+	4.70140i	−0.943125	+	0.332439i
$201$	17.3504	−	5.34768i	1.22380	−	0.377196i
$202$	−20.7789	+	10.9592i	−1.46200	+	0.771087i
$203$			21.2477i			1.49129i
$204$	−7.54605	−	14.3450i	−0.528329	−	1.00435i
$205$	0.924064	−	5.51986i	0.0645394	−	0.385524i
$206$	−2.88727	−	5.47434i	−0.201166	−	0.381416i
$207$	−5.89845	−	1.11875i	−0.409970	−	0.0777588i
$208$	−6.28453	+	2.44166i	−0.435754	+	0.169299i
$209$	−8.18760			−0.566348
$210$	−12.7772	−	17.9563i	−0.881712	−	1.23910i
$211$	−3.14109	−	3.14109i	−0.216241	−	0.216241i	0.590671	−	0.806912i	$-0.298863\pi$
$211$	−3.14109	−	3.14109i	−0.216241	−	0.216241i	−0.806912	+	0.590671i	$0.798863\pi$
$212$	−2.74475	+	4.01101i	−0.188510	+	0.275477i
$213$	22.2493	−	6.85761i	1.52450	−	0.469876i
$214$	−2.95965	+	9.56583i	−0.202318	+	0.653907i
$215$	3.90117	−	23.3035i	0.266057	−	1.58928i
$216$	−0.0475641	+	14.6969i	−0.00323633	+	0.999995i
$217$	12.5172	+	12.5172i	0.849720	+	0.849720i
$218$	−6.10273	−	11.5709i	−0.413329	−	0.783682i
$219$	−9.83301	+	18.5950i	−0.664453	+	1.25653i
$220$	−5.67710	+	0.110242i	−0.382750	+	0.00743251i
$221$	5.57677	−	5.57677i	0.375134	−	0.375134i
$222$	7.49176	+	0.00808195i	0.502814	+	0.000542425i
$223$	0.135826	+	0.135826i	0.00909556	+	0.00909556i	0.711640	−	0.702544i	$-0.247953\pi$
$223$	0.135826	+	0.135826i	0.00909556	+	0.00909556i	−0.702544	+	0.711640i	$0.747953\pi$
$224$	17.1884	+	14.9206i	1.14845	+	0.996921i
$225$	−14.4716	+	3.94626i	−0.964773	+	0.263084i
$226$	6.09462	+	11.5555i	0.405408	+	0.768663i
$227$			11.1670i			0.741182i	0.928796	+	0.370591i	$0.120845\pi$
$227$			11.1670i			0.741182i	−0.928796	+	0.370591i	$0.879155\pi$
$228$	19.7700	−	10.3998i	1.30930	−	0.688745i
$229$	−0.647593	−	0.647593i	−0.0427941	−	0.0427941i	0.685386	−	0.728180i	$-0.259634\pi$
$229$	−0.647593	−	0.647593i	−0.0427941	−	0.0427941i	−0.728180	+	0.685386i	$0.759634\pi$
$230$	1.98752	+	6.00815i	0.131053	+	0.396166i
$231$	−2.60628	−	8.45600i	−0.171480	−	0.556364i
$232$	−14.8379	−	1.71048i	−0.974155	−	0.112298i
$233$	4.46060	+	4.46060i	0.292224	+	0.292224i	0.837958	−	0.545735i	$-0.183749\pi$
$233$	4.46060	+	4.46060i	0.292224	+	0.292224i	−0.545735	+	0.837958i	$0.683749\pi$
$234$	−6.83619	+	2.09895i	−0.446896	+	0.137213i
$235$	−6.93779	+	4.94802i	−0.452571	+	0.322773i
$236$	1.19483	−	0.223952i	0.0777765	−	0.0145781i
$237$	−5.02968	−	16.3187i	−0.326713	−	1.06001i
$238$	−25.4354	−	7.86966i	−1.64873	−	0.510114i
$239$	−17.8621			−1.15540			−0.577702	−	0.816248i	$-0.696050\pi$
$239$	−17.8621			−1.15540			−0.577702	+	0.816248i	$0.696050\pi$
$240$	13.5680	−	7.47720i	0.875813	−	0.482651i
$241$	4.98671			0.321223			0.160611	−	0.987018i	$-0.448653\pi$
$241$	4.98671			0.321223			0.160611	+	0.987018i	$0.448653\pi$
$242$	12.6833	+	3.92420i	0.815315	+	0.252257i
$243$	−1.18215	+	15.5436i	−0.0758350	+	0.997120i
$244$	−0.391381	−	2.08809i	−0.0250556	−	0.133676i
$245$	−20.2664	−	3.39275i	−1.29478	−	0.216755i
$246$	−0.00661382	+	6.13085i	−0.000421682	+	0.390888i
$247$	7.68580	+	7.68580i	0.489035	+	0.489035i
$248$	−9.74877	+	7.73345i	−0.619047	+	0.491075i
$249$	−25.9109	+	7.98618i	−1.64204	+	0.506104i
$250$	11.0424	+	11.3166i	0.698381	+	0.715726i
$251$	−4.21768	−	4.21768i	−0.266218	−	0.266218i	0.561356	−	0.827574i	$-0.310280\pi$
$251$	−4.21768	−	4.21768i	−0.266218	−	0.266218i	−0.827574	+	0.561356i	$0.810280\pi$
$252$	17.0339	+	17.1076i	1.07304	+	1.07768i
$253$			2.54088i			0.159744i
$254$	8.42583	+	15.9756i	0.528684	+	1.00240i
$255$	−11.0001	+	14.4014i	−0.688853	+	0.901849i
$256$	−11.8032	+	10.8021i	−0.737699	+	0.675130i
$257$	−13.4226	−	13.4226i	−0.837279	−	0.837279i	0.151221	−	0.988500i	$-0.451679\pi$
$257$	−13.4226	−	13.4226i	−0.837279	−	0.837279i	−0.988500	+	0.151221i	$0.951679\pi$
$258$	−0.0279219	+	25.8829i	−0.00173834	+	1.61140i
$259$	8.70184	−	8.70184i	0.540706	−	0.540706i
$260$	5.43264	+	5.22567i	0.336918	+	0.324082i
$261$	−15.5647	−	2.95214i	−0.963430	−	0.182733i
$262$	−5.68492	−	10.7787i	−0.351216	−	0.665913i
$263$	8.49417	+	8.49417i	0.523773	+	0.523773i	0.918709	−	0.394936i	$-0.129233\pi$
$263$	8.49417	+	8.49417i	0.523773	+	0.523773i	−0.394936	+	0.918709i	$0.629233\pi$
$264$	6.11489	−	1.13932i	0.376345	−	0.0701202i
$265$	5.35933	+	0.897189i	0.329221	+	0.0551139i
$266$	10.8458	−	35.0546i	0.665000	−	2.14933i
$267$	5.51737	+	17.9009i	0.337657	+	1.09552i
$268$	17.3014	+	11.8394i	1.05685	+	0.723208i
$269$	−2.63108	−	2.63108i	−0.160420	−	0.160420i	0.622333	−	0.782753i	$-0.286185\pi$
$269$	−2.63108	−	2.63108i	−0.160420	−	0.160420i	−0.782753	+	0.622333i	$0.786185\pi$
$270$	14.9289	−	6.86493i	0.908545	−	0.417786i
$271$	15.0210			0.912463			0.456231	−	0.889861i	$-0.349199\pi$
$271$	15.0210			0.912463			0.456231	+	0.889861i	$0.349199\pi$
$272$	7.54322	−	17.1288i	0.457375	−	1.03858i
$273$	−5.49120	+	10.3843i	−0.332342	+	0.628485i
$274$	−5.31856	−	10.0841i	−0.321306	−	0.609204i
$275$	2.78223	+	5.70624i	0.167775	+	0.344099i
$276$	−3.22741	−	6.13527i	−0.194267	−	0.369300i
$277$		−	26.7895i		−	1.60963i	−0.593528	−	0.804813i	$-0.702266\pi$
$277$		−	26.7895i		−	1.60963i	0.593528	−	0.804813i	$-0.297734\pi$
$278$	1.89772	−	1.00089i	0.113818	−	0.0600296i
$279$	−10.9084	+	7.43014i	−0.653069	+	0.444831i
$280$	7.04825	−	24.4521i	0.421214	−	1.46129i
$281$	6.99005			0.416992			0.208496	−	0.978023i	$-0.433143\pi$
$281$	6.99005			0.416992			0.208496	+	0.978023i	$0.433143\pi$
$282$	6.60783	−	6.59359i	0.393491	−	0.392643i
$283$	25.6879			1.52699			0.763495	−	0.645814i	$-0.223482\pi$
$283$	25.6879			1.52699			0.763495	+	0.645814i	$0.223482\pi$
$284$	22.1866	+	15.1823i	1.31653	+	0.900905i
$285$	−19.8477	−	15.1601i	−1.17568	−	0.898009i
$286$	1.41192	+	2.67704i	0.0834886	+	0.158296i
$287$	7.12111	+	7.12111i	0.420346	+	0.420346i
$288$	−13.3180	+	10.5181i	−0.784771	+	0.619786i
$289$			4.89343i			0.287849i
$290$	5.24463	+	15.8542i	0.307975	+	0.930989i
$291$	−1.89409	+	3.58187i	−0.111033	+	0.209973i
$292$	−23.8731	+	4.47466i	−1.39707	+	0.261860i
$293$		−	25.0148i		−	1.46138i	−0.682709	−	0.730691i	$-0.739198\pi$
$293$		−	25.0148i		−	1.46138i	0.682709	−	0.730691i	$-0.260802\pi$
$294$	22.5097	+	0.0242830i	1.31279	+	0.00141621i
$295$	−0.789175	−	1.10653i	−0.0459475	−	0.0644246i
$296$	5.37624	+	6.77727i	0.312488	+	0.393921i
$297$	6.55644	−	0.734320i	0.380443	−	0.0426095i
$298$	−5.80773	−	11.0116i	−0.336432	−	0.637884i
$299$	2.38515	−	2.38515i	0.137937	−	0.137937i
$300$	−13.9661	−	10.2445i	−0.806331	−	0.591464i
$301$	30.0635	+	30.0635i	1.73283	+	1.73283i
$302$	2.06912	+	0.640183i	0.119065	+	0.0368384i
$303$	−25.4344	−	13.4497i	−1.46117	−	0.772664i
$304$	23.6066	+	10.3959i	1.35393	+	0.596247i
$305$	−1.93378	+	1.37917i	−0.110728	+	0.0789709i
$306$	9.29880	−	17.5389i	0.531577	−	1.00263i
$307$	6.11979			0.349275			0.174637	−	0.984633i	$-0.444125\pi$
$307$	6.11979			0.349275			0.174637	+	0.984633i	$0.444125\pi$
$308$	5.77014	−	8.43214i	0.328784	−	0.480466i
$309$	3.54341	−	6.70085i	0.201577	−	0.381198i
$310$	12.4295	+	6.25016i	0.705946	+	0.354985i
$311$	22.0550			1.25062			0.625312	−	0.780375i	$-0.284972\pi$
$311$	22.0550			1.25062			0.625312	+	0.780375i	$0.284972\pi$
$312$	−6.80961	−	4.67063i	−0.385518	−	0.264422i
$313$	−2.07489	+	2.07489i	−0.117280	+	0.117280i	−0.763311	−	0.646031i	$-0.776428\pi$
$313$	−2.07489	+	2.07489i	−0.117280	+	0.117280i	0.646031	+	0.763311i	$0.276428\pi$
$314$	3.61190	−	11.6739i	0.203831	−	0.658799i
$315$	9.33917	−	25.3241i	0.526203	−	1.42685i
$316$	11.1354	−	16.2726i	0.626415	−	0.915406i
$317$			1.46508i			0.0822871i	0.999153	+	0.0411435i	$0.0131001\pi$
$317$			1.46508i			0.0822871i	−0.999153	+	0.0411435i	$0.986900\pi$
$318$	−5.95254	−	0.00642147i	−0.333802	−	0.000360098i
$319$			6.70482i			0.375398i
$320$	16.5082	+	6.89045i	0.922838	+	0.385188i
$321$	−11.7196	+	3.61218i	−0.654125	+	0.201612i
$322$	−10.8786	−	3.36581i	−0.606240	−	0.187569i
$323$	−30.1731			−1.67888
$324$	−14.8986	+	10.1010i	−0.827701	+	0.561169i
$325$	2.74480	−	7.96823i	0.152254	−	0.441998i
$326$	−10.9748	−	3.39560i	−0.607841	−	0.188065i
$327$	7.48957	−	14.1634i	0.414174	−	0.783236i
$328$	−5.54615	+	4.39962i	−0.306235	+	0.242928i
$329$		−	15.3337i		−	0.845376i
$330$	−4.03192	−	5.66622i	−0.221950	−	0.311915i
$331$	−14.6641	+	14.6641i	−0.806010	+	0.806010i	−0.984027	−	0.178018i	$-0.943032\pi$
$331$	−14.6641	+	14.6641i	−0.806010	+	0.806010i	0.178018	+	0.984027i	$0.443032\pi$
$332$	−25.8378	−	17.6809i	−1.41804	−	0.970366i
$333$	5.16538	+	7.58345i	0.283061	+	0.415570i
$334$	0.739549	+	1.40220i	0.0404663	+	0.0767251i
$335$	3.87001	−	23.1174i	0.211441	−	1.26304i
$336$	−3.22227	+	27.6896i	−0.175789	+	1.51059i
$337$	−11.9292	+	11.9292i	−0.649827	+	0.649827i	−0.952951	−	0.303124i	$-0.901970\pi$
$337$	−11.9292	+	11.9292i	−0.649827	+	0.649827i	0.303124	+	0.952951i	$0.401970\pi$
$338$	−4.24649	+	13.7250i	−0.230978	+	0.746541i
$339$	−7.47961	+	14.1445i	−0.406237	+	0.768226i
$340$	−20.9214	+	0.406266i	−1.13462	+	0.0220329i
$341$	3.94986	+	3.94986i	0.213897	+	0.213897i
$342$	24.1718	+	12.8154i	1.30706	+	0.692979i
$343$	6.22957	−	6.22957i	0.336365	−	0.336365i
$344$	−23.4145	+	18.5741i	−1.26242	+	1.00145i
$345$	−4.70469	+	6.15939i	−0.253292	+	0.331610i
$346$	8.07800	−	26.1088i	0.434276	−	1.40362i
$347$	−5.65825			−0.303751			−0.151876	−	0.988400i	$-0.548531\pi$
$347$	−5.65825			−0.303751			−0.151876	+	0.988400i	$0.548531\pi$
$348$	−8.51641	−	16.1896i	−0.456527	−	0.867855i
$349$	16.9458	−	16.9458i	0.907090	−	0.907090i	−0.0889460	−	0.996036i	$-0.528350\pi$
$349$	16.9458	−	16.9458i	0.907090	−	0.907090i	0.996036	+	0.0889460i	$0.0283499\pi$
$350$	−28.1163	+	4.35306i	−1.50288	+	0.232681i
$351$	−6.84392	−	5.46529i	−0.365302	−	0.291716i
$352$	5.42391	+	4.70826i	0.289095	+	0.250951i
$353$	11.0587	−	11.0587i	0.588596	−	0.588596i	−0.348655	−	0.937251i	$-0.613361\pi$
$353$	11.0587	−	11.0587i	0.588596	−	0.588596i	0.937251	+	0.348655i	$0.113361\pi$
$354$	1.05163	+	1.05390i	0.0558936	+	0.0560144i
$355$	4.96272	−	29.6446i	0.263394	−	1.57337i
$356$	−12.2151	+	17.8504i	−0.647399	+	0.946072i
$357$	−9.60471	−	31.1622i	−0.508335	−	1.64928i
$358$	6.69041	−	3.52865i	0.353599	−	0.186495i
$359$			0.811093i			0.0428079i	0.999771	+	0.0214039i	$0.00681360\pi$
$359$			0.811093i			0.0428079i	−0.999771	+	0.0214039i	$0.993186\pi$
$360$	16.9328	+	8.56047i	0.892435	+	0.451176i
$361$		−	22.5841i		−	1.18863i
$362$	−15.7439	−	29.8509i	−0.827483	−	1.56893i
$363$	4.78938	+	15.5390i	0.251377	+	0.815587i
$364$	−13.3318	+	2.49885i	−0.698778	+	0.130976i
$365$	15.7680	+	22.1089i	0.825337	+	1.15723i
$366$	1.84181	−	1.83784i	0.0962729	−	0.0960654i
$367$	18.0288	−	18.0288i	0.941097	−	0.941097i	−0.0572624	−	0.998359i	$-0.518237\pi$
$367$	18.0288	−	18.0288i	0.941097	−	0.941097i	0.998359	+	0.0572624i	$0.0182372\pi$
$368$	3.22620	−	7.32589i	0.168177	−	0.381888i
$369$	−6.20587	+	4.22707i	−0.323065	+	0.220052i
$370$	4.34507	−	8.64087i	0.225889	−	0.449218i
$371$	−6.91400	+	6.91400i	−0.358957	+	0.358957i
$372$	−14.5545	−	4.52035i	−0.754616	−	0.234369i
$373$	5.38763			0.278961			0.139480	−	0.990225i	$-0.455457\pi$
$373$	5.38763			0.278961			0.139480	+	0.990225i	$0.455457\pi$
$374$	−8.02628	−	2.48331i	−0.415029	−	0.128409i
$375$	−3.82120	+	18.9842i	−0.197326	+	0.980338i
$376$	10.7080	+	1.23440i	0.552224	+	0.0636591i
$377$	6.29389	−	6.29389i	0.324152	−	0.324152i
$378$	−5.54115	+	29.0436i	−0.285006	+	1.49384i
$379$	−26.5638	−	26.5638i	−1.36449	−	1.36449i	−0.868101	−	0.496388i	$-0.834659\pi$
$379$	−26.5638	−	26.5638i	−1.36449	−	1.36449i	−0.496388	−	0.868101i	$-0.665341\pi$
$380$	−0.559908	−	28.8334i	−0.0287227	−	1.47912i
$381$	−10.3406	+	19.5549i	−0.529765	+	1.00183i
$382$	5.82157	+	1.80118i	0.297858	+	0.0921566i
$383$	12.8154	−	12.8154i	0.654836	−	0.654836i	−0.299317	−	0.954154i	$-0.596759\pi$
$383$	12.8154	−	12.8154i	0.654836	−	0.654836i	0.954154	+	0.299317i	$0.0967589\pi$
$384$	−19.0771	−	4.47928i	−0.973525	−	0.228582i
$385$	−11.2666	−	1.88611i	−0.574200	−	0.0961252i
$386$	27.5738	−	14.5429i	1.40347	−	0.740216i
$387$	−26.1997	+	17.8456i	−1.33180	+	0.907144i
$388$	−4.59857	+	0.861933i	−0.233457	+	0.0437580i
$389$	3.79806	−	3.79806i	0.192569	−	0.192569i	−0.604236	−	0.796805i	$-0.706522\pi$
$389$	3.79806	−	3.79806i	0.192569	−	0.192569i	0.796805	+	0.604236i	$0.206522\pi$
$390$	−1.53413	+	9.10375i	−0.0776837	+	0.460986i
$391$			9.36371i			0.473543i
$392$	16.1534	+	20.3630i	0.815871	+	1.02848i
$393$	6.97681	−	13.1937i	0.351934	−	0.665534i
$394$	−4.61410	+	14.9131i	−0.232455	+	0.751313i
$395$	−21.7427	−	3.63988i	−1.09399	−	0.183142i
$396$	5.37515	+	5.39839i	0.270111	+	0.271280i
$397$	−23.7190			−1.19042			−0.595210	−	0.803570i	$-0.702931\pi$
$397$	−23.7190			−1.19042			−0.595210	+	0.803570i	$0.702931\pi$
$398$	−0.360733	+	1.16592i	−0.0180819	+	0.0584421i
$399$	42.9472	−	13.2370i	2.15005	−	0.662681i
$400$	−0.776456	−	19.9849i	−0.0388228	−	0.999246i
$401$			31.6884i			1.58245i	0.611528	+	0.791223i	$0.290555\pi$
$401$			31.6884i			1.58245i	−0.611528	+	0.791223i	$0.709445\pi$
$402$	−0.0276989	+	25.6762i	−0.00138150	+	1.28061i
$403$		−	7.41556i		−	0.369395i
$404$	−6.12048	−	32.6539i	−0.304505	−	1.62459i
$405$	17.2532	+	10.3598i	0.857320	+	0.514783i
$406$	−28.7061	−	8.88163i	−1.42466	−	0.440788i
$407$	2.74591	−	2.74591i	0.136110	−	0.136110i
$408$	22.5347	−	4.19864i	1.11564	−	0.207864i
$409$	−3.30520			−0.163431			−0.0817157	−	0.996656i	$-0.526040\pi$
$409$	−3.30520			−0.163431			−0.0817157	+	0.996656i	$0.526040\pi$
$410$	7.07121	+	3.55576i	0.349222	+	0.175607i
$411$	6.52720	−	12.3434i	0.321963	−	0.608857i
$412$	8.60288	−	1.61248i	0.423833	−	0.0794412i
$413$	2.44562			0.120341
$414$	3.97705	−	7.50131i	0.195461	−	0.368669i
$415$	−5.77944	+	34.5233i	−0.283702	+	1.69468i
$416$	−0.671786	−	9.51119i	−0.0329370	−	0.466324i
$417$	2.32290	+	1.22835i	0.113753	+	0.0601523i
$418$	3.42246	−	11.0617i	0.167398	−	0.541044i
$419$	4.43180	+	4.43180i	0.216507	+	0.216507i	0.807025	−	0.590517i	$-0.201076\pi$
$419$	4.43180	+	4.43180i	0.216507	+	0.216507i	−0.590517	+	0.807025i	$0.701076\pi$
$420$	29.6004	−	9.75653i	1.44435	−	0.476070i
$421$	−7.92088	+	7.92088i	−0.386040	+	0.386040i	−0.873272	−	0.487232i	$-0.838006\pi$
$421$	−7.92088	+	7.92088i	−0.386040	+	0.386040i	0.487232	+	0.873272i	$0.338006\pi$
$422$	5.55668	−	2.93070i	0.270495	−	0.142664i
$423$	11.2325	+	2.13047i	0.546144	+	0.103587i
$424$	−4.27167	−	5.38485i	−0.207450	−	0.261511i
$425$	10.2531	+	21.0288i	0.497351	+	1.02004i
$426$	−0.0355198	+	32.9260i	−0.00172094	+	1.59527i
$427$		−	4.27399i		−	0.206833i
$428$	−11.6865	−	7.99713i	−0.564890	−	0.386556i
$429$	−1.73278	+	3.27682i	−0.0836593	+	0.158206i
$430$	29.8529	+	15.0115i	1.43963	+	0.723921i
$431$		−	28.1361i		−	1.35527i	−0.735399	−	0.677634i	$-0.763005\pi$
$431$		−	28.1361i		−	1.35527i	0.735399	−	0.677634i	$-0.236995\pi$
$432$	−19.8360	−	6.20762i	−0.954358	−	0.298664i
$433$	26.7435	+	26.7435i	1.28521	+	1.28521i	0.937661	+	0.347551i	$0.112987\pi$
$433$	26.7435	+	26.7435i	1.28521	+	1.28521i	0.347551	+	0.937661i	$0.387013\pi$
$434$	−22.1432	+	11.6788i	−1.06291	+	0.560599i
$435$	−12.4146	+	16.2533i	−0.595235	+	0.779284i
$436$	18.1836	−	3.40824i	0.870837	−	0.163225i
$437$	−12.9049			−0.617325
$438$	−21.0121	−	21.0574i	−1.00400	−	1.00616i
$439$	−19.6650			−0.938557			−0.469279	−	0.883050i	$-0.655486\pi$
$439$	−19.6650			−0.938557			−0.469279	+	0.883050i	$0.655486\pi$
$440$	2.22412	−	7.71599i	0.106031	−	0.367845i
$441$	15.5199	+	22.7852i	0.739042	+	1.08501i
$442$	5.20324	+	9.86547i	0.247493	+	0.469253i
$443$		−	26.1817i		−	1.24393i	−0.783045	−	0.621965i	$-0.786335\pi$
$443$		−	26.1817i		−	1.24393i	0.783045	−	0.621965i	$-0.213665\pi$
$444$	−3.14251	+	10.1182i	−0.149137	+	0.480188i
$445$	23.8509	+	3.99281i	1.13064	+	0.189277i
$446$	−0.240280	+	0.126728i	−0.0113776	+	0.00600076i
$447$	7.12753	−	13.4787i	0.337120	−	0.637521i
$448$	−27.3429	+	16.9852i	−1.29183	+	0.802474i
$449$	10.7835			0.508905			0.254452	−	0.967085i	$-0.418105\pi$
$449$	10.7835			0.508905			0.254452	+	0.967085i	$0.418105\pi$
$450$	0.717698	−	21.2011i	0.0338326	−	0.999428i
$451$	2.24710	+	2.24710i	0.105812	+	0.105812i
$452$	−18.1594	+	3.40371i	−0.854147	+	0.160097i
$453$	0.781327	+	2.53499i	0.0367099	+	0.119104i
$454$	−15.0870	−	4.66787i	−0.708066	−	0.219074i
$455$	8.80560	+	12.3466i	0.412813	+	0.578819i
$456$	5.78649	+	31.0569i	0.270977	+	1.45437i
$457$	7.76727	+	7.76727i	0.363338	+	0.363338i	0.865040	−	0.501703i	$-0.167293\pi$
$457$	7.76727	+	7.76727i	0.363338	+	0.363338i	−0.501703	+	0.865040i	$0.667293\pi$
$458$	1.14561	−	0.604218i	0.0535309	−	0.0282332i
$459$	24.1619	−	2.70613i	1.12778	−	0.126311i
$460$	−8.94796	+	0.173758i	−0.417201	+	0.00810150i
$461$	7.82882	−	7.82882i	0.364625	−	0.364625i	−0.500888	−	0.865512i	$-0.666993\pi$
$461$	7.82882	−	7.82882i	0.364625	−	0.364625i	0.865512	+	0.500888i	$0.166993\pi$
$462$	12.5137	+	0.0134995i	0.582191	+	0.000628054i
$463$	11.3472	+	11.3472i	0.527349	+	0.527349i	0.919781	−	0.392432i	$-0.128366\pi$
$463$	11.3472	+	11.3472i	0.527349	+	0.527349i	−0.392432	+	0.919781i	$0.628366\pi$
$464$	8.51321	−	19.3314i	0.395216	−	0.897437i
$465$	2.26137	+	16.8885i	0.104869	+	0.783184i
$466$	−7.89094	+	4.16183i	−0.365541	+	0.192793i
$467$			4.05635i			0.187706i	0.995586	+	0.0938529i	$0.0299183\pi$
$467$			4.05635i			0.187706i	−0.995586	+	0.0938529i	$0.970082\pi$
$468$	0.0218199	−	10.1132i	0.00100863	−	0.467485i
$469$	29.8234	+	29.8234i	1.37712	+	1.37712i
$470$	−3.78487	−	11.4414i	−0.174583	−	0.527754i
$471$	14.3024	−	4.40823i	0.659019	−	0.203120i
$472$	−0.196878	+	1.70785i	−0.00906203	+	0.0786104i
$473$	9.48672	+	9.48672i	0.436200	+	0.436200i
$474$	24.1494	+	0.0260518i	1.10922	+	0.00119660i
$475$	−28.9815	+	14.1307i	−1.32976	+	0.648361i
$476$	21.2642	−	31.0743i	0.974644	−	1.42429i
$477$	−4.10413	−	6.02539i	−0.187915	−	0.275884i
$478$	7.46645	−	24.1322i	0.341508	−	1.10378i
$479$	−27.3485			−1.24958			−0.624792	−	0.780791i	$-0.714816\pi$
$479$	−27.3485			−1.24958			−0.624792	+	0.780791i	$0.714816\pi$
$480$	4.43039	+	21.4563i	0.202219	+	0.979340i
$481$	−5.15524			−0.235059
$482$	−2.08447	+	6.73718i	−0.0949451	+	0.306870i
$483$	−4.10789	−	13.3279i	−0.186915	−	0.606442i
$484$	−10.6034	+	15.4952i	−0.481972	+	0.704326i
$485$	3.03733	+	4.25874i	0.137918	+	0.193379i
$486$	−20.5056	−	8.09441i	−0.930154	−	0.367170i
$487$	6.28745	+	6.28745i	0.284911	+	0.284911i	0.835064	−	0.550153i	$-0.185430\pi$
$487$	6.28745	+	6.28745i	0.284911	+	0.284911i	−0.550153	+	0.835064i	$0.685430\pi$
$488$	2.98466	+	0.344065i	0.135109	+	0.0155751i
$489$	−4.14424	−	13.4459i	−0.187409	−	0.608043i
$490$	13.0552	−	25.9623i	0.589772	−	1.17286i
$491$	14.6684	+	14.6684i	0.661974	+	0.661974i	0.955845	−	0.293871i	$-0.0949436\pi$
$491$	14.6684	+	14.6684i	0.661974	+	0.661974i	−0.293871	+	0.955845i	$0.594944\pi$
$492$	−8.28017	−	2.57166i	−0.373299	−	0.115939i
$493$			24.7087i			1.11283i
$494$	−13.5964	+	7.17101i	−0.611732	+	0.322639i
$495$	2.94703	−	7.99116i	0.132459	−	0.359176i
$496$	−6.37307	−	16.4035i	−0.286159	−	0.736537i
$497$	38.2442	+	38.2442i	1.71549	+	1.71549i
$498$	0.0413653	−	38.3446i	0.00185362	−	1.71826i
$499$	8.95304	−	8.95304i	0.400793	−	0.400793i	−0.477720	−	0.878512i	$-0.658536\pi$
$499$	8.95304	−	8.95304i	0.400793	−	0.400793i	0.878512	+	0.477720i	$0.158536\pi$
$500$	−19.9048	+	10.1881i	−0.890171	+	0.455627i
$501$	−0.907610	+	1.71636i	−0.0405490	+	0.0766814i
$502$	7.46121	−	3.93519i	0.333010	−	0.175636i
$503$	6.06706	+	6.06706i	0.270517	+	0.270517i	0.829308	−	0.558791i	$-0.188735\pi$
$503$	6.06706	+	6.06706i	0.270517	+	0.270517i	−0.558791	+	0.829308i	$0.688735\pi$
$504$	−30.2331	+	15.8622i	−1.34669	+	0.706559i
$505$	−30.2408	+	21.5677i	−1.34570	+	0.959749i
$506$	−3.43280	−	1.06210i	−0.152606	−	0.0472161i
$507$	−16.8152	+	5.18273i	−0.746790	+	0.230173i
$508$	−25.1055	+	4.70565i	−1.11388	+	0.208779i
$509$	−1.69973	−	1.69973i	−0.0753390	−	0.0753390i	0.668433	−	0.743772i	$-0.266965\pi$
$509$	−1.69973	−	1.69973i	−0.0753390	−	0.0753390i	−0.743772	+	0.668433i	$0.766965\pi$
$510$	−14.8585	−	20.8813i	−0.657947	−	0.924638i
$511$	−48.8646			−2.16164
$512$	−9.66011	−	20.4617i	−0.426920	−	0.904289i
$513$	3.72954	+	33.2996i	0.164663	+	1.47021i
$514$	23.7450	−	12.5236i	1.04735	−	0.552391i
$515$	−5.68215	−	7.96713i	−0.250385	−	0.351074i
$516$	−34.9568	−	10.8569i	−1.53889	−	0.477949i
$517$		−	4.83865i		−	0.212803i
$518$	8.11900	+	15.3938i	0.356728	+	0.676366i
$519$	31.9872	−	9.85899i	1.40408	−	0.432761i
$520$	−9.33089	+	5.15529i	−0.409187	+	0.226074i
$521$	12.9756			0.568472			0.284236	−	0.958754i	$-0.408260\pi$
$521$	12.9756			0.568472			0.284236	+	0.958754i	$0.408260\pi$
$522$	10.4945	−	19.7943i	0.459334	−	0.866373i
$523$	9.09422			0.397663			0.198831	−	0.980034i	$-0.436285\pi$
$523$	9.09422			0.397663			0.198831	+	0.980034i	$0.436285\pi$
$524$	16.9387	−	3.17491i	0.739970	−	0.138696i
$525$	−23.8193	−	25.4334i	−1.03956	−	1.11000i
$526$	−15.0265	+	7.92524i	−0.655185	+	0.345557i
$527$	14.5561	+	14.5561i	0.634074	+	0.634074i
$528$	−1.01681	+	8.73762i	−0.0442508	+	0.380256i
$529$		−	18.9952i		−	0.825878i
$530$	−3.45235	+	6.86556i	−0.149961	+	0.298221i
$531$	−0.339794	+	1.79151i	−0.0147458	+	0.0777449i
$532$	42.8260	+	29.3060i	1.85674	+	1.27057i
$533$		−	4.21877i		−	0.182735i
$534$	−26.4909	−	0.0285778i	−1.14638	−	0.00123668i
$535$	−2.61406	+	15.6150i	−0.113016	+	0.675096i
$536$	−23.2275	+	18.4258i	−1.00327	+	0.795872i
$537$	8.18938	+	4.33053i	0.353398	+	0.186876i
$538$	4.65446	−	2.45485i	0.200668	−	0.105836i
$539$	8.25036	−	8.25036i	0.355368	−	0.355368i
$540$	3.03434	+	23.0389i	0.130577	+	0.991438i
$541$	−25.3761	−	25.3761i	−1.09100	−	1.09100i	−0.995422	−	0.0955815i	$-0.969529\pi$
$541$	−25.3761	−	25.3761i	−1.09100	−	1.09100i	−0.0955815	−	0.995422i	$-0.530471\pi$
$542$	−6.27887	+	20.2938i	−0.269700	+	0.871694i
$543$	19.3217	−	36.5389i	0.829175	−	1.56803i
$544$	19.9883	+	17.3510i	0.856992	+	0.743918i
$545$	−12.0102	−	16.8398i	−0.514459	−	0.721340i
$546$	−11.7341	−	11.7594i	−0.502173	−	0.503257i
$547$	−0.671566			−0.0287141			−0.0143570	−	0.999897i	$-0.504570\pi$
$547$	−0.671566			−0.0287141			−0.0143570	+	0.999897i	$0.504570\pi$
$548$	15.8471	−	2.97030i	0.676954	−	0.126885i
$549$	3.13085	+	0.593827i	0.133622	+	0.0253439i
$550$	−8.87227	+	1.37363i	−0.378315	+	0.0585720i
$551$	−34.0531			−1.45071
$552$	9.63799	−	1.79574i	0.410220	−	0.0764316i
$553$	28.0500	−	28.0500i	1.19281	−	1.19281i
$554$	36.1933	+	11.1982i	1.53771	+	0.475764i
$555$	11.7407	−	1.57209i	0.498367	−	0.0667315i
$556$	0.558977	+	2.98224i	0.0237059	+	0.126475i
$557$			8.61480i			0.365021i	0.983204	+	0.182510i	$0.0584223\pi$
$557$			8.61480i			0.365021i	−0.983204	+	0.182510i	$0.941578\pi$
$558$	−5.47855	−	17.8434i	−0.231926	−	0.755370i
$559$		−	17.8106i		−	0.753307i
$560$	30.0892	+	19.7435i	1.27150	+	0.834314i
$561$	−3.03082	−	9.83341i	−0.127961	−	0.415167i
$562$	−2.92188	+	9.44375i	−0.123252	+	0.398360i
$563$	10.1462			0.427612			0.213806	−	0.976876i	$-0.431414\pi$
$563$	10.1462			0.427612			0.213806	+	0.976876i	$0.431414\pi$
$564$	6.14601	+	11.6835i	0.258794	+	0.491965i
$565$	11.9942	+	16.8175i	0.504599	+	0.707516i
$566$	−10.7377	+	34.7051i	−0.451339	+	1.45876i
$567$	−33.2039	+	14.4517i	−1.39443	+	0.606915i
$568$	−29.7858	+	23.6283i	−1.24978	+	0.991423i
$569$			29.8857i			1.25287i	0.779472	+	0.626437i	$0.215487\pi$
$569$			29.8857i			1.25287i	−0.779472	+	0.626437i	$0.784513\pi$
$570$	28.7782	−	20.4778i	1.20539	−	0.857719i
$571$	8.74319	−	8.74319i	0.365891	−	0.365891i	−0.500085	−	0.865976i	$-0.666698\pi$
$571$	8.74319	−	8.74319i	0.365891	−	0.365891i	0.865976	+	0.500085i	$0.166698\pi$
$572$	−4.20694	+	0.788527i	−0.175901	+	0.0329700i
$573$	2.19830	+	7.13232i	0.0918352	+	0.297957i
$574$	−12.5975	+	6.64414i	−0.525808	+	0.277321i
$575$	4.38522	+	8.99389i	0.182876	+	0.375071i
$576$	−8.64325	−	22.3896i	−0.360135	−	0.932900i
$577$	14.9148	−	14.9148i	0.620913	−	0.620913i	−0.324852	−	0.945765i	$-0.605315\pi$
$577$	14.9148	−	14.9148i	0.620913	−	0.620913i	0.945765	+	0.324852i	$0.105315\pi$
$578$	−6.61116	−	2.04548i	−0.274988	−	0.0850807i
$579$	33.7516	+	17.8478i	1.40267	+	0.741730i
$580$	−23.6117	+	0.458508i	−0.980422	+	0.0190385i
$581$	−44.5381	−	44.5381i	−1.84775	−	1.84775i
$582$	−4.04746	−	4.05620i	−0.167772	−	0.168135i
$583$	−2.18175	+	2.18175i	−0.0903589	+	0.0903589i
$584$	3.93370	−	34.1236i	0.162778	−	1.41205i
$585$	−10.2678	+	4.73498i	−0.424521	+	0.195767i
$586$	33.7957	+	10.4563i	1.39609	+	0.431947i
$587$	−7.62049			−0.314531			−0.157266	−	0.987556i	$-0.550268\pi$
$587$	−7.62049			−0.314531			−0.157266	+	0.987556i	$0.550268\pi$
$588$	−9.44197	+	30.4010i	−0.389380	+	1.25372i
$589$	−20.0610	+	20.0610i	−0.826597	+	0.826597i
$590$	1.82483	−	0.603661i	0.0751270	−	0.0248523i
$591$	−18.2709	+	5.63139i	−0.751564	+	0.231644i
$592$	−11.4036	+	4.43051i	−0.468684	+	0.182093i
$593$	−22.8113	+	22.8113i	−0.936749	+	0.936749i	−0.998115	−	0.0613661i	$-0.980454\pi$
$593$	−22.8113	+	22.8113i	−0.936749	+	0.936749i	0.0613661	+	0.998115i	$0.480454\pi$
$594$	−1.74854	+	9.16488i	−0.0717435	+	0.376039i
$595$	−41.5200	−	6.95074i	−1.70215	−	0.284953i
$596$	17.3046	−	3.24349i	0.708824	−	0.132859i
$597$	−1.42843	+	0.440265i	−0.0584616	+	0.0180188i
$598$	2.22540	+	4.21941i	0.0910033	+	0.172545i
$599$		−	46.2096i		−	1.88807i	−0.329843	−	0.944036i	$-0.606996\pi$
$599$		−	46.2096i		−	1.88807i	0.329843	−	0.944036i	$-0.393004\pi$
$600$	19.6784	−	14.5863i	0.803368	−	0.595483i
$601$			0.711114i			0.0290070i	0.999895	+	0.0145035i	$0.00461676\pi$
$601$			0.711114i			0.0290070i	−0.999895	+	0.0145035i	$0.995383\pi$
$602$	−53.1833	+	28.0499i	−2.16759	+	1.14323i
$603$	−25.9904	+	17.7031i	−1.05841	+	0.720926i
$604$	−1.72981	+	2.52784i	−0.0703849	+	0.102856i
$605$	20.7039	+	3.46598i	0.841734	+	0.140912i
$606$	28.8026	−	28.7405i	1.17002	−	1.16750i
$607$	25.5282	−	25.5282i	1.03616	−	1.03616i	0.0368357	−	0.999321i	$-0.488272\pi$
$607$	25.5282	−	25.5282i	1.03616	−	1.03616i	0.999321	−	0.0368357i	$-0.0117278\pi$
$608$	−23.9128	+	27.5475i	−0.969793	+	1.11720i
$609$	−10.8398	−	35.1694i	−0.439251	−	1.42514i
$610$	−1.05496	−	3.18908i	−0.0427142	−	0.129122i
$611$	−4.54209	+	4.54209i	−0.183753	+	0.183753i
$612$	19.8086	+	19.8943i	0.800716	+	0.804179i
$613$	−17.8559			−0.721192			−0.360596	−	0.932722i	$-0.617427\pi$
$613$	−17.8559			−0.721192			−0.360596	+	0.932722i	$0.617427\pi$
$614$	−2.55810	+	8.26800i	−0.103237	+	0.333669i
$615$	1.28651	+	9.60797i	0.0518772	+	0.387431i
$616$	8.98010	+	11.3203i	0.361818	+	0.456107i
$617$	−10.7537	+	10.7537i	−0.432926	+	0.432926i	−0.889622	−	0.456697i	$-0.849032\pi$
$617$	−10.7537	+	10.7537i	−0.432926	+	0.432926i	0.456697	+	0.889622i	$0.349032\pi$
$618$	7.57187	+	7.58822i	0.304585	+	0.305243i
$619$	−13.9757	−	13.9757i	−0.561732	−	0.561732i	0.368067	−	0.929799i	$-0.380020\pi$
$619$	−13.9757	−	13.9757i	−0.561732	−	0.561732i	−0.929799	+	0.368067i	$0.880020\pi$
$620$	−13.6397	+	14.1799i	−0.547784	+	0.569480i
$621$	10.3339	−	1.15740i	0.414687	−	0.0464448i
$622$	−9.21910	+	29.7969i	−0.369652	+	1.19475i
$623$	−30.7698	+	30.7698i	−1.23277	+	1.23277i
$624$	9.15659	−	7.24761i	0.366557	−	0.290137i
$625$	19.6964	+	15.3965i	0.787856	+	0.615859i
$626$	−1.93592	−	3.67055i	−0.0773749	−	0.146705i
$627$	13.5522	−	4.17702i	0.541224	−	0.166814i
$628$	14.2620	+	9.75954i	0.569117	+	0.389448i
$629$	10.1193	−	10.1193i	0.403483	−	0.403483i
$630$	30.3097	+	23.2031i	1.20757	+	0.924432i
$631$		−	7.35150i		−	0.292659i	−0.989236	−	0.146329i	$-0.953254\pi$
$631$		−	7.35150i		−	0.292659i	0.989236	−	0.146329i	$-0.0467459\pi$
$632$	17.3301	+	21.8462i	0.689354	+	0.868997i
$633$	6.80164	+	3.59670i	0.270341	+	0.142956i
$634$	−1.97936	−	0.612411i	−0.0786105	−	0.0243219i
$635$	16.5820	+	23.2502i	0.658037	+	0.922656i
$636$	2.49687	−	8.03935i	0.0990072	−	0.318781i
$637$	−15.4894			−0.613713
$638$	−9.05839	−	2.80265i	−0.358625	−	0.110958i
$639$	−33.3289	+	22.7016i	−1.31847	+	0.898063i
$640$	−16.2097	+	19.4228i	−0.640745	+	0.767754i
$641$			6.25676i			0.247127i	0.992337	+	0.123563i	$0.0394323\pi$
$641$			6.25676i			0.247127i	−0.992337	+	0.123563i	$0.960568\pi$
$642$	0.0187097	−	17.3434i	0.000738412	−	0.684490i
$643$			25.1807i			0.993031i	0.868028	+	0.496516i	$0.165387\pi$
$643$			25.1807i			0.993031i	−0.868028	+	0.496516i	$0.834613\pi$
$644$	9.09460	−	13.2903i	0.358377	−	0.523712i
$645$	5.43133	+	40.5625i	0.213859	+	1.59715i
$646$	12.6125	−	40.7647i	0.496233	−	1.60387i
$647$	6.52820	−	6.52820i	0.256650	−	0.256650i	−0.567040	−	0.823690i	$-0.691912\pi$
$647$	6.52820	−	6.52820i	0.256650	−	0.256650i	0.823690	+	0.567040i	$0.191912\pi$
$648$	−7.41908	−	24.3507i	−0.291449	−	0.956586i
$649$	0.771731			0.0302931
$650$	9.61795	+	7.03905i	0.377247	+	0.276094i
$651$	−27.1044	−	14.3328i	−1.06230	−	0.561745i
$652$	9.17508	−	13.4079i	0.359324	−	0.525095i
$653$	−4.64684			−0.181845			−0.0909225	−	0.995858i	$-0.528982\pi$
$653$	−4.64684			−0.181845			−0.0909225	+	0.995858i	$0.528982\pi$
$654$	16.0044	+	16.0390i	0.625822	+	0.627173i
$655$	−11.1879	−	15.6869i	−0.437148	−	0.612940i
$656$	−3.62569	−	9.33205i	−0.141559	−	0.364355i
$657$	6.78924	−	35.7951i	0.264873	−	1.39650i
$658$	20.7163	+	6.40958i	0.807605	+	0.249871i
$659$	−18.1412	−	18.1412i	−0.706681	−	0.706681i	0.259155	−	0.965836i	$-0.416556\pi$
$659$	−18.1412	−	18.1412i	−0.706681	−	0.706681i	−0.965836	+	0.259155i	$0.916556\pi$
$660$	9.34057	−	3.07873i	0.363581	−	0.119839i
$661$	34.0918	−	34.0918i	1.32602	−	1.32602i	0.417201	−	0.908814i	$-0.363011\pi$
$661$	34.0918	−	34.0918i	1.32602	−	1.32602i	0.908814	−	0.417201i	$-0.136989\pi$
$662$	−13.6819	−	25.9412i	−0.531761	−	1.00823i
$663$	−6.38567	+	12.0758i	−0.247999	+	0.468985i
$664$	34.6877	−	27.5169i	1.34614	−	1.06786i
$665$	9.57939	−	57.2221i	0.371473	−	2.21898i
$666$	−12.4046	+	3.80865i	−0.480668	+	0.147582i
$667$			10.5678i			0.409187i
$668$	−2.20355	+	0.413022i	−0.0852578	+	0.0159803i
$669$	−0.294114	−	0.155527i	−0.0113711	−	0.00601303i
$670$	29.6145	+	14.8917i	1.14411	+	0.575315i
$671$		−	1.34868i		−	0.0520653i
$672$	−36.0625	−	15.9278i	−1.39114	−	0.614427i
$673$	−25.9877	−	25.9877i	−1.00175	−	1.00175i	−0.999998	−	0.00175260i	$-0.999442\pi$
$673$	−25.9877	−	25.9877i	−1.00175	−	1.00175i	−0.00175260	−	0.999998i	$-0.500558\pi$
$674$	−11.1302	−	21.1032i	−0.428721	−	0.812865i
$675$	21.9403	−	13.9148i	0.844484	−	0.535581i
$676$	−16.7678	−	11.4742i	−0.644914	−	0.441316i
$677$	−12.0573			−0.463401			−0.231701	−	0.972787i	$-0.574429\pi$
$677$	−12.0573			−0.463401			−0.231701	+	0.972787i	$0.574429\pi$
$678$	−15.9831	−	16.0176i	−0.613828	−	0.615154i
$679$	−9.41257			−0.361221
$680$	8.19636	−	28.4351i	0.314316	−	1.09044i
$681$	−5.69702	−	18.4838i	−0.218310	−	0.708302i
$682$	−6.98742	+	3.68530i	−0.267562	+	0.141118i
$683$		−	19.8952i		−	0.761269i	−0.924726	−	0.380634i	$-0.875706\pi$
$683$		−	19.8952i		−	0.761269i	0.924726	−	0.380634i	$-0.124294\pi$
$684$	−27.4179	+	27.2999i	−1.04835	+	1.04384i
$685$	−10.4669	−	14.6760i	−0.399920	−	0.560741i
$686$	5.81232	+	11.0203i	0.221915	+	0.420757i
$687$	1.40228	+	0.741526i	0.0535004	+	0.0282910i
$688$	−15.3067	−	39.3976i	−0.583564	−	1.50202i
$689$	4.09607			0.156048
$690$	−6.35492	−	8.93081i	−0.241928	−	0.339990i
$691$	6.29828	+	6.29828i	0.239598	+	0.239598i	0.816684	−	0.577086i	$-0.195810\pi$
$691$	6.29828	+	6.29828i	0.239598	+	0.239598i	−0.577086	+	0.816684i	$0.695810\pi$
$692$	31.8970	+	21.8272i	1.21254	+	0.829745i
$693$	8.62789	+	12.6669i	0.327747	+	0.481174i
$694$	2.36518	−	7.64445i	0.0897809	−	0.290179i
$695$	2.76186	−	1.96975i	0.104763	−	0.0747170i
$696$	25.4325	−	4.73855i	0.964016	−	0.179614i
$697$	8.28108	+	8.28108i	0.313668	+	0.313668i
$698$	15.8108	+	29.9777i	0.598449	+	1.13467i
$699$	−9.65888	−	5.10761i	−0.365333	−	0.193187i
$700$	5.87166	−	39.8055i	0.221928	−	1.50451i
$701$	−10.6698	+	10.6698i	−0.402994	+	0.402994i	−0.879287	−	0.476292i	$-0.841980\pi$
$701$	−10.6698	+	10.6698i	−0.402994	+	0.402994i	0.476292	+	0.879287i	$0.341980\pi$
$702$	10.2445	−	6.96180i	0.386656	−	0.262756i
$703$	13.9462	+	13.9462i	0.525992	+	0.525992i
$704$	−8.62821	+	5.35977i	−0.325188	+	0.202004i
$705$	8.95922	−	11.7294i	0.337424	−	0.441756i
$706$	10.3180	+	19.5632i	0.388324	+	0.736272i
$707$		−	66.8375i		−	2.51368i
$708$	−1.86344	+	0.980246i	−0.0700323	+	0.0368399i
$709$	−24.9541	−	24.9541i	−0.937170	−	0.937170i	0.0609695	−	0.998140i	$-0.480581\pi$
$709$	−24.9541	−	24.9541i	−0.937170	−	0.937170i	−0.998140	+	0.0609695i	$0.980581\pi$
$710$	37.9762	+	19.0964i	1.42522	+	0.716674i
$711$	16.6504	+	24.4449i	0.624438	+	0.916755i
$712$	−19.0104	−	23.9645i	−0.712446	−	0.898108i
$713$	6.22557	+	6.22557i	0.233150	+	0.233150i
$714$	46.1158	+	0.0497487i	1.72584	+	0.00186180i
$715$	2.77866	+	3.89605i	0.103916	+	0.145704i
$716$	1.97068	+	10.5139i	0.0736476	+	0.392923i
$717$	29.5656	−	9.11261i	1.10415	−	0.340317i
$718$	−1.09581	−	0.339041i	−0.0408952	−	0.0126529i
$719$	−6.98626			−0.260543			−0.130272	−	0.991478i	$-0.541585\pi$
$719$	−6.98626			−0.260543			−0.130272	+	0.991478i	$0.541585\pi$
$720$	−18.6434	+	19.2983i	−0.694798	+	0.719205i
$721$	17.6088			0.655785
$722$	30.5117	+	9.44025i	1.13553	+	0.351330i
$723$	−8.25408	+	2.54404i	−0.306972	+	0.0946140i
$724$	46.9104	−	8.79265i	1.74341	−	0.326776i
$725$	11.5716	+	23.7329i	0.429759	+	0.881417i
$726$	−22.9956	−	0.0248071i	−0.853447	−	0.000920679i
$727$	−11.5528	−	11.5528i	−0.428468	−	0.428468i	0.459638	−	0.888106i	$-0.347979\pi$
$727$	−11.5528	−	11.5528i	−0.428468	−	0.428468i	−0.888106	+	0.459638i	$0.847979\pi$
$728$	2.19676	−	19.0562i	0.0814172	−	0.706270i
$729$	−5.97306	−	26.3310i	−0.221224	−	0.975223i
$730$	−36.4609	+	12.0614i	−1.34948	+	0.446413i
$731$	34.9607	+	34.9607i	1.29307	+	1.29307i
$732$	1.71308	+	3.25656i	0.0633174	+	0.120366i
$733$		−	28.8013i		−	1.06380i	−0.846807	−	0.531901i	$-0.821478\pi$
$733$		−	28.8013i		−	1.06380i	0.846807	−	0.531901i	$-0.178522\pi$
$734$	16.8213	+	31.8935i	0.620884	+	1.17721i
$735$	35.2762	−	4.72349i	1.30118	−	0.174229i
$736$	8.54890	+	7.42093i	0.315117	+	0.273539i
$737$	9.41095	+	9.41095i	0.346657	+	0.346657i
$738$	−3.11679	−	10.1512i	−0.114731	−	0.373672i
$739$	−5.64414	+	5.64414i	−0.207623	+	0.207623i	−0.803256	−	0.595633i	$-0.796901\pi$
$739$	−5.64414	+	5.64414i	−0.207623	+	0.207623i	0.595633	+	0.803256i	$0.296901\pi$
$740$	9.85779	+	9.48223i	0.362379	+	0.348574i
$741$	−16.6427	−	8.80062i	−0.611383	−	0.323299i
$742$	−6.45091	−	12.2311i	−0.236820	−	0.449017i
$743$	22.5360	+	22.5360i	0.826766	+	0.826766i	0.987068	−	0.160302i	$-0.0512469\pi$
$743$	22.5360	+	22.5360i	0.826766	+	0.826766i	−0.160302	+	0.987068i	$0.551247\pi$
$744$	12.1910	−	17.7740i	0.446942	−	0.651626i
$745$	−11.4296	−	16.0258i	−0.418748	−	0.587140i
$746$	−2.25205	+	7.27883i	−0.0824536	+	0.266497i
$747$	38.8139	−	26.4377i	1.42013	−	0.967304i
$748$	6.71005	−	9.80567i	0.245344	−	0.358531i
$749$	−20.1447	−	20.1447i	−0.736072	−	0.736072i
$750$	−24.0508	−	13.0980i	−0.878212	−	0.478272i
$751$	−16.6940			−0.609174			−0.304587	−	0.952484i	$-0.598519\pi$
$751$	−16.6940			−0.609174			−0.304587	+	0.952484i	$0.598519\pi$
$752$	−6.14370	+	13.9508i	−0.224038	+	0.508734i
$753$	9.13287	+	4.82945i	0.332820	+	0.175995i
$754$	5.87233	+	11.1341i	0.213858	+	0.405480i
$755$	3.37758	+	0.565431i	0.122923	+	0.0205781i
$756$	−36.9225	−	19.6266i	−1.34286	−	0.713813i
$757$			3.11900i			0.113362i	0.998392	+	0.0566810i	$0.0180518\pi$
$757$			3.11900i			0.113362i	−0.998392	+	0.0566810i	$0.981948\pi$
$758$	46.9921	−	24.7846i	1.70683	−	0.900216i
$759$	−1.29627	−	4.20570i	−0.0470515	−	0.152657i
$760$	39.1888	+	11.2961i	1.42153	+	0.409752i
$761$	−51.3818			−1.86259			−0.931294	−	0.364267i	$-0.881319\pi$
$761$	−51.3818			−1.86259			−0.931294	+	0.364267i	$0.881319\pi$
$762$	−22.0967	−	22.1445i	−0.800480	−	0.802209i
$763$	37.2190			1.34742
$764$	−4.86689	+	7.11219i	−0.176078	+	0.257310i
$765$	10.8605	−	29.4492i	0.392661	−	1.06474i
$766$	11.9570	+	22.6708i	0.432026	+	0.819131i
$767$	−0.724432	−	0.724432i	−0.0261577	−	0.0261577i
$768$	14.0260	−	23.9013i	0.506118	−	0.862464i
$769$			25.3743i			0.915021i	0.889204	+	0.457511i	$0.151259\pi$
$769$			25.3743i			0.915021i	−0.889204	+	0.457511i	$0.848741\pi$
$770$	7.25769	−	14.4331i	0.261549	−	0.520133i
$771$	29.0650	+	15.3695i	1.04675	+	0.553521i
$772$	8.12192	+	43.3319i	0.292314	+	1.55955i
$773$			48.1095i			1.73038i	0.501447	+	0.865188i	$0.332801\pi$
$773$			48.1095i			1.73038i	−0.501447	+	0.865188i	$0.667199\pi$
$774$	−13.1583	−	42.8560i	−0.472966	−	1.54043i
$775$	20.7981	+	7.16429i	0.747091	+	0.257349i
$776$	0.757730	−	6.57308i	0.0272009	−	0.235960i
$777$	−9.96404	+	18.8428i	−0.357458	+	0.675981i
$778$	3.54367	+	6.71889i	0.127047	+	0.240884i
$779$	−11.4128	+	11.4128i	−0.408907	+	0.408907i
$780$	−11.6581	−	5.87806i	−0.417428	−	0.210468i
$781$	12.0682	+	12.0682i	0.431833	+	0.431833i
$782$	−12.6506	−	3.91408i	−0.452385	−	0.139967i
$783$	27.2690	−	3.05412i	0.974513	−	0.109145i
$784$	−34.2631	+	13.3119i	−1.22368	+	0.475425i
$785$	3.19015	−	19.0562i	0.113861	−	0.680146i
$786$	14.9087	+	14.9409i	0.531775	+	0.532924i
$787$	−31.4648			−1.12160			−0.560799	−	0.827952i	$-0.689506\pi$
$787$	−31.4648			−1.12160			−0.560799	+	0.827952i	$0.689506\pi$
$788$	−18.2193	−	12.4675i	−0.649037	−	0.444138i
$789$	−18.3931	−	9.72625i	−0.654811	−	0.346264i
$790$	14.0061	−	27.8535i	0.498316	−	0.990982i
$791$	−37.1696			−1.32160
$792$	−9.54021	+	5.00541i	−0.338997	+	0.177860i
$793$	−1.26602	+	1.26602i	−0.0449578	+	0.0449578i
$794$	9.91464	−	32.0449i	0.351857	−	1.13723i
$795$	−9.32854	+	1.24910i	−0.330849	+	0.0443009i
$796$	−1.42440	−	0.974718i	−0.0504864	−	0.0345480i
$797$			16.4469i			0.582578i	0.956635	+	0.291289i	$0.0940841\pi$
$797$			16.4469i			0.582578i	−0.956635	+	0.291289i	$0.905916\pi$
$798$	−0.0685627	+	63.5560i	−0.00242709	+	2.24986i
$799$		−	17.8315i		−	0.630833i
$800$	27.3247	+	7.30478i	0.966075	+	0.258263i
$801$	−18.2648	−	26.8151i	−0.645357	−	0.947466i
$802$	−42.8119	−	13.2459i	−1.51174	−	0.467730i
$803$	−15.4195			−0.544143
$804$	−34.6776	−	10.7702i	−1.22299	−	0.379835i
$805$	−17.7579	−	2.97280i	−0.625884	−	0.104777i
$806$	10.0186	+	3.09974i	0.352890	+	0.109184i
$807$	5.69728	+	3.01272i	0.200554	+	0.106053i
$808$	46.6746	+	5.38055i	1.64201	+	0.189287i
$809$			50.6943i			1.78232i	0.453694	+	0.891158i	$0.350106\pi$
$809$			50.6943i			1.78232i	−0.453694	+	0.891158i	$0.649894\pi$
$810$	−21.2083	+	18.9791i	−0.745184	+	0.666859i
$811$	26.5200	−	26.5200i	0.931243	−	0.931243i	−0.0665406	−	0.997784i	$-0.521196\pi$
$811$	26.5200	−	26.5200i	0.931243	−	0.931243i	0.997784	+	0.0665406i	$0.0211962\pi$
$812$	23.9986	−	35.0702i	0.842187	−	1.23072i
$813$	−24.8630	+	7.66319i	−0.871984	+	0.268760i
$814$	2.56200	+	4.85761i	0.0897979	+	0.170259i
$815$	−17.9150	−	2.99910i	−0.627536	−	0.105054i
$816$	−3.74715	+	32.2001i	−0.131177	+	1.12723i
$817$	−48.1821	+	48.1821i	−1.68568	+	1.68568i
$818$	1.38159	−	4.46541i	0.0483061	−	0.156129i
$819$	3.79142	−	19.9896i	0.132483	−	0.698494i
$820$	−7.75973	+	8.06707i	−0.270982	+	0.281714i
$821$	30.3566	+	30.3566i	1.05945	+	1.05945i	0.998117	+	0.0613353i	$0.0195359\pi$
$821$	30.3566	+	30.3566i	1.05945	+	1.05945i	0.0613353	+	0.998117i	$0.480464\pi$
$822$	13.9479	+	13.9780i	0.486489	+	0.487540i
$823$	21.1974	−	21.1974i	0.738893	−	0.738893i	−0.233471	−	0.972364i	$-0.575008\pi$
$823$	21.1974	−	21.1974i	0.738893	−	0.738893i	0.972364	+	0.233471i	$0.0750082\pi$
$824$	−1.41754	+	12.2967i	−0.0493824	+	0.428377i
$825$	−7.51631	−	8.02565i	−0.261684	−	0.279417i
$826$	−1.02228	+	3.30410i	−0.0355698	+	0.114964i
$827$	−35.1166			−1.22112			−0.610562	−	0.791969i	$-0.709056\pi$
$827$	−35.1166			−1.22112			−0.610562	+	0.791969i	$0.709056\pi$
$828$	8.47204	+	8.50868i	0.294424	+	0.295697i
$829$	−2.61688	+	2.61688i	−0.0908881	+	0.0908881i	−0.751089	−	0.660201i	$-0.770471\pi$
$829$	−2.61688	+	2.61688i	−0.0908881	+	0.0908881i	0.660201	+	0.751089i	$0.270471\pi$
$830$	−44.2261	−	22.2391i	−1.53511	−	0.771930i
$831$	13.6671	+	44.3424i	0.474105	+	1.53822i
$832$	13.1307	+	3.06812i	0.455224	+	0.106368i
$833$	30.4044	−	30.4044i	1.05345	−	1.05345i
$834$	−2.63051	+	2.62484i	−0.0910871	+	0.0908907i
$835$	1.45543	+	2.04071i	0.0503672	+	0.0706216i
$836$	13.5140	+	9.24766i	0.467391	+	0.319837i
$837$	14.2651	−	17.8636i	0.493076	−	0.617455i
$838$	−7.83999	+	4.13496i	−0.270828	+	0.142840i
$839$			8.12625i			0.280549i	0.990113	+	0.140275i	$0.0447985\pi$
$839$			8.12625i			0.280549i	−0.990113	+	0.140275i	$0.955201\pi$
$840$	0.808209	+	44.0692i	0.0278859	+	1.52053i
$841$		−	1.11392i		−	0.0384111i
$842$	−7.39035	−	14.0123i	−0.254688	−	0.482895i
$843$	−11.5700	+	3.56607i	−0.398493	+	0.122822i
$844$	1.63673	+	8.73227i	0.0563387	+	0.300577i
$845$	−3.75064	+	22.4043i	−0.129026	+	0.770731i
$846$	−7.57356	+	14.2849i	−0.260384	+	0.491124i
$847$	−26.7099	+	26.7099i	−0.917762	+	0.917762i
$848$	9.06065	−	3.52024i	0.311144	−	0.120886i
$849$	−42.5190	+	13.1051i	−1.45925	+	0.449765i
$850$	−32.6963	+	5.06215i	−1.12147	+	0.173630i
$851$	4.32797	−	4.32797i	0.148361	−	0.148361i
$852$	−44.4690	−	13.8112i	−1.52348	−	0.473164i
$853$	−32.0739			−1.09819			−0.549095	−	0.835760i	$-0.685027\pi$
$853$	−32.0739			−1.09819			−0.549095	+	0.835760i	$0.685027\pi$
$854$	5.77427	+	1.78655i	0.197592	+	0.0611345i
$855$	40.5863	+	14.9677i	1.38802	+	0.511884i
$856$	15.6894	−	12.4460i	0.536252	−	0.425395i
$857$	19.1655	−	19.1655i	0.654682	−	0.654682i	−0.299435	−	0.954117i	$-0.596798\pi$
$857$	19.1655	−	19.1655i	0.654682	−	0.654682i	0.954117	+	0.299435i	$0.0967980\pi$
$858$	−3.70276	−	3.71076i	−0.126410	−	0.126683i
$859$	20.7901	+	20.7901i	0.709349	+	0.709349i	0.966398	−	0.257049i	$-0.0827502\pi$
$859$	20.7901	+	20.7901i	0.709349	+	0.709349i	−0.257049	+	0.966398i	$0.582750\pi$
$860$	−32.7597	+	34.0572i	−1.11709	+	1.16134i
$861$	−15.4199	−	8.15402i	−0.525508	−	0.277888i
$862$	38.0126	+	11.7610i	1.29471	+	0.400582i
$863$	−1.44188	+	1.44188i	−0.0490822	+	0.0490822i	−0.731222	−	0.682140i	$-0.761050\pi$
$863$	−1.44188	+	1.44188i	−0.0490822	+	0.0490822i	0.682140	+	0.731222i	$0.261050\pi$
$864$	16.6782	−	24.2041i	0.567404	−	0.823440i
$865$	7.13476	−	42.6192i	0.242589	−	1.44910i
$866$	−47.3101	+	24.9523i	−1.60766	+	0.847913i
$867$	−2.49645	−	8.09968i	−0.0847840	−	0.275079i
$868$	−6.52234	−	34.7979i	−0.221383	−	1.18112i
$869$	8.85133	−	8.85133i	0.300261	−	0.300261i
$870$	−16.7692	−	23.5664i	−0.568529	−	0.798976i
$871$		−	17.6683i		−	0.598669i
$872$	−2.99621	+	25.9912i	−0.101464	+	0.880173i
$873$	1.30778	−	6.89505i	0.0442616	−	0.233362i
$874$	5.39431	−	17.4348i	0.182465	−	0.589743i
$875$	−43.1354	+	12.7685i	−1.45824	+	0.431653i
$876$	37.2323	−	19.5857i	1.25796	−	0.661741i
$877$	21.2987			0.719206			0.359603	−	0.933105i	$-0.382912\pi$
$877$	21.2987			0.719206			0.359603	+	0.933105i	$0.382912\pi$
$878$	8.22005	−	26.5679i	0.277413	−	0.896623i
$879$	12.7617	+	41.4049i	0.430440	+	1.39655i
$880$	9.49482	+	6.23016i	0.320070	+	0.210019i
$881$		−	36.8723i		−	1.24226i	−0.783708	−	0.621130i	$-0.786674\pi$
$881$		−	36.8723i		−	1.24226i	0.783708	−	0.621130i	$-0.213326\pi$
$882$	−37.2708	+	11.4434i	−1.25497	+	0.385321i
$883$			7.54042i			0.253755i	0.991918	+	0.126878i	$0.0404956\pi$
$883$			7.54042i			0.253755i	−0.991918	+	0.126878i	$0.959504\pi$
$884$	−15.5035	+	2.90590i	−0.521439	+	0.0977359i
$885$	1.87076	+	1.42893i	0.0628851	+	0.0480331i
$886$	35.3722	+	10.9441i	1.18835	+	0.367673i
$887$	−12.9867	+	12.9867i	−0.436051	+	0.436051i	−0.890681	−	0.454629i	$-0.849772\pi$
$887$	−12.9867	+	12.9867i	−0.436051	+	0.436051i	0.454629	+	0.890681i	$0.349772\pi$
$888$	−12.3564	−	8.47507i	−0.414652	−	0.284405i
$889$	−51.3871			−1.72347
$890$	−15.3642	+	30.5542i	−0.515009	+	1.02418i
$891$	−10.4777	+	4.56032i	−0.351016	+	0.152776i
$892$	−0.0707750	−	0.377598i	−0.00236972	−	0.0126429i
$893$	24.5750			0.822372
$894$	15.2307	+	15.2636i	0.509392	+	0.510493i
$895$	9.73694	−	6.94437i	0.325470	−	0.232125i
$896$	−11.5179	−	44.0409i	−0.384788	−	1.47130i
$897$	−2.73112	+	5.16476i	−0.0911894	+	0.172446i
$898$	−4.50756	+	14.5688i	−0.150419	+	0.486167i
$899$	16.4279	+	16.4279i	0.547901	+	0.547901i
$900$	28.3432	+	9.83178i	0.944773	+	0.327726i
$901$	−8.04024	+	8.04024i	−0.267859	+	0.267859i
$902$	−3.97520	+	2.09660i	−0.132360	+	0.0698090i
$903$	−65.0989	−	34.4242i	−2.16636	−	1.14557i
$904$	2.99222	−	25.9566i	0.0995199	−	0.863305i
$905$	−30.9840	−	43.4437i	−1.02994	−	1.44412i
$906$	−3.75144	−	0.00404697i	−0.124633	−	0.000134452i
$907$			17.5700i			0.583402i	0.956510	+	0.291701i	$0.0942211\pi$
$907$			17.5700i			0.583402i	−0.956510	+	0.291701i	$0.905779\pi$
$908$	12.6128	−	18.4317i	0.418572	−	0.611677i
$909$	48.9609	+	9.28638i	1.62393	+	0.308010i
$910$	−20.3614	+	6.73564i	−0.674974	+	0.223284i
$911$			26.4654i			0.876838i	0.898771	+	0.438419i	$0.144461\pi$
$911$			26.4654i			0.876838i	−0.898771	+	0.438419i	$0.855539\pi$
$912$	−44.3775	−	5.16426i	−1.46949	−	0.171006i
$913$	−14.0542	−	14.0542i	−0.465128	−	0.465128i
$914$	−13.7405	+	7.24703i	−0.454497	+	0.239710i
$915$	2.49721	−	3.26936i	0.0825554	−	0.108082i
$916$	0.337443	+	1.80032i	0.0111494	+	0.0594842i
$917$	34.6709			1.14493
$918$	−6.44376	+	33.7746i	−0.212676	+	1.11473i
$919$	48.0566			1.58524			0.792620	−	0.609716i	$-0.208717\pi$
$919$	48.0566			1.58524			0.792620	+	0.609716i	$0.208717\pi$
$920$	3.50554	−	12.1616i	0.115574	−	0.400955i
$921$	−10.1296	+	3.12210i	−0.333780	+	0.102877i
$922$	7.30446	+	13.8494i	0.240559	+	0.456107i
$923$		−	22.6571i		−	0.745766i
$924$	−5.24903	+	16.9007i	−0.172680	+	0.555993i
$925$	4.98057	−	14.4587i	0.163760	−	0.475400i
$926$	−20.0736	+	10.5872i	−0.659658	+	0.347916i
$927$	−2.44656	+	12.8991i	−0.0803555	+	0.423661i
$928$	22.5586	+	19.5822i	0.740524	+	0.642817i
$929$	5.96630			0.195748			0.0978739	−	0.995199i	$-0.468796\pi$
$929$	5.96630			0.195748			0.0978739	+	0.995199i	$0.468796\pi$
$930$	−23.7620	−	4.00429i	−0.779187	−	0.131306i
$931$	41.9028	+	41.9028i	1.37331	+	1.37331i
$932$	−2.32430	−	12.4005i	−0.0761348	−	0.406193i
$933$	−36.5057	+	11.2517i	−1.19514	+	0.368363i
$934$	−5.48024	−	1.69558i	−0.179319	−	0.0554810i
$935$	−13.1019	−	2.19335i	−0.428477	−	0.0717301i
$936$	13.6541	+	4.25687i	0.446300	+	0.139140i
$937$	20.1483	+	20.1483i	0.658215	+	0.658215i	0.954958	−	0.296742i	$-0.0959003\pi$
$937$	20.1483	+	20.1483i	0.658215	+	0.658215i	−0.296742	+	0.954958i	$0.595900\pi$
$938$	−52.7586	+	27.8259i	−1.72263	+	0.908548i
$939$	2.37586	−	4.49293i	0.0775331	−	0.146621i
$940$	17.0398	−	0.330890i	0.555776	−	0.0107925i
$941$	20.6426	−	20.6426i	0.672931	−	0.672931i	−0.285460	−	0.958391i	$-0.592146\pi$
$941$	20.6426	−	20.6426i	0.672931	−	0.672931i	0.958391	+	0.285460i	$0.0921463\pi$
$942$	−0.0228329	+	21.1655i	−0.000743937	+	0.689611i
$943$	3.54178	+	3.54178i	0.115336	+	0.115336i
$944$	−2.22506	−	0.979878i	−0.0724195	−	0.0318923i
$945$	−2.53889	+	46.6813i	−0.0825899	+	1.51854i
$946$	−16.7823	+	8.85131i	−0.545640	+	0.287781i
$947$			36.0909i			1.17280i	0.810023	+	0.586399i	$0.199455\pi$
$947$			36.0909i			1.17280i	−0.810023	+	0.586399i	$0.800545\pi$
$948$	−10.1298	+	32.6155i	−0.328999	+	1.05930i
$949$	14.4745	+	14.4745i	0.469861	+	0.469861i
$950$	−6.97656	−	45.0614i	−0.226349	−	1.46199i
$951$	−0.747431	−	2.42502i	−0.0242371	−	0.0786367i
$952$	33.0936	+	41.7177i	1.07257	+	1.35208i
$953$	20.8050	+	20.8050i	0.673939	+	0.673939i	0.958622	−	0.284683i	$-0.0918882\pi$
$953$	20.8050	+	20.8050i	0.673939	+	0.673939i	−0.284683	+	0.958622i	$0.591888\pi$
$954$	9.85600	−	3.02614i	0.319100	−	0.0979750i
$955$	9.50298	+	1.59087i	0.307509	+	0.0514792i
$956$	29.4822	+	20.1747i	0.953522	+	0.652498i
$957$	−3.42056	−	11.0979i	−0.110571	−	0.358744i
$958$	11.4318	−	36.9485i	0.369345	−	1.19375i
$959$	32.4366			1.04743
$960$	−30.8399	−	2.98326i	−0.995354	−	0.0962843i
$961$	−11.6444			−0.375626
$962$	2.15492	−	6.96487i	0.0694773	−	0.224556i
$963$	17.5557	−	11.9578i	0.565723	−	0.385336i
$964$	−8.23079	−	5.63235i	−0.265096	−	0.181406i
$965$	40.1297	−	28.6205i	1.29182	−	0.921325i
$966$	19.7235	+	0.0212773i	0.634593	+	0.000684585i
$967$	−42.2100	−	42.2100i	−1.35738	−	1.35738i	−0.877130	−	0.480252i	$-0.840545\pi$
$967$	−42.2100	−	42.2100i	−1.35738	−	1.35738i	−0.480252	−	0.877130i	$-0.659455\pi$
$968$	−16.5021	−	20.8025i	−0.530398	−	0.668618i
$969$	49.9430	−	15.3932i	1.60440	−	0.494502i
$970$	−7.02329	+	2.32333i	−0.225504	+	0.0745977i
$971$	1.42380	+	1.42380i	0.0456918	+	0.0456918i	0.729584	−	0.683892i	$-0.239714\pi$
$971$	1.42380	+	1.42380i	0.0456918	+	0.0456918i	−0.683892	+	0.729584i	$0.739714\pi$
$972$	19.5072	−	24.3201i	0.625694	−	0.780069i
$973$			6.10420i			0.195692i
$974$	−11.1227	+	5.86632i	−0.356394	+	0.187969i
$975$	−0.478124	+	14.5894i	−0.0153122	+	0.467235i
$976$	−1.71244	+	3.88853i	−0.0548139	+	0.124469i
$977$	−42.5772	−	42.5772i	−1.36216	−	1.36216i	−0.871154	−	0.491010i	$-0.836628\pi$
$977$	−42.5772	−	42.5772i	−1.36216	−	1.36216i	−0.491010	−	0.871154i	$-0.663372\pi$
$978$	19.8980	+	0.0214655i	0.636269	+	0.000686393i
$979$	−9.70958	+	9.70958i	−0.310319	+	0.310319i
$980$	29.6186	+	28.4902i	0.946133	+	0.910087i
$981$	−5.17120	+	27.2643i	−0.165104	+	0.870482i
$982$	−25.9488	+	13.6859i	−0.828060	+	0.436735i
$983$	−40.4211	−	40.4211i	−1.28923	−	1.28923i	−0.935252	−	0.353982i	$-0.884827\pi$
$983$	−40.4211	−	40.4211i	−1.28923	−	1.28923i	−0.353982	−	0.935252i	$-0.615173\pi$
$984$	6.93553	−	10.1118i	0.221097	−	0.322351i
$985$	−4.07533	+	24.3438i	−0.129851	+	0.775658i
$986$	−33.3822	−	10.3284i	−1.06310	−	0.328923i
$987$	7.82272	+	25.3806i	0.249000	+	0.807874i
$988$	−4.00486	−	21.3666i	−0.127411	−	0.679763i
$989$	14.9525	+	14.9525i	0.475462	+	0.475462i
$990$	9.56439	+	7.32186i	0.303976	+	0.232704i
$991$	−4.85693			−0.154285			−0.0771427	−	0.997020i	$-0.524580\pi$
$991$	−4.85693			−0.154285			−0.0771427	+	0.997020i	$0.524580\pi$
$992$	24.8255	−	1.75345i	0.788210	−	0.0556722i
$993$	16.7911	−	31.7532i	0.532849	−	1.00766i
$994$	−67.6552	+	35.6826i	−2.14589	+	1.13178i
$995$	−0.318611	+	1.90321i	−0.0101006	+	0.0603359i
$996$	51.7873	+	16.0841i	1.64094	+	0.509645i
$997$			30.4969i			0.965845i	0.875663	+	0.482923i	$0.160425\pi$
$997$			30.4969i			0.965845i	−0.875663	+	0.482923i	$0.839575\pi$
$998$	8.35337	+	15.8382i	0.264421	+	0.501349i
$999$	−12.4186	−	9.91703i	−0.392908	−	0.313761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.18	✓	88
3.2	odd	2	inner	240.2.bb.a.173.27	yes	88
4.3	odd	2		960.2.bb.a.593.40		88
5.2	odd	4		240.2.bf.a.77.5	yes	88
12.11	even	2		960.2.bb.a.593.5		88
15.2	even	4		240.2.bf.a.77.40	yes	88
16.5	even	4		240.2.bf.a.53.40	yes	88
16.11	odd	4		960.2.bf.a.113.17		88
20.7	even	4		960.2.bf.a.17.17		88
48.5	odd	4		240.2.bf.a.53.5	yes	88
48.11	even	4		960.2.bf.a.113.18		88
60.47	odd	4		960.2.bf.a.17.18		88
80.27	even	4		960.2.bb.a.497.5		88
80.37	odd	4	inner	240.2.bb.a.197.27	yes	88
240.107	odd	4		960.2.bb.a.497.40		88
240.197	even	4	inner	240.2.bb.a.197.18	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.18	✓	88	1.1	even	1	trivial
240.2.bb.a.173.27	yes	88	3.2	odd	2	inner
240.2.bb.a.197.18	yes	88	240.197	even	4	inner
240.2.bb.a.197.27	yes	88	80.37	odd	4	inner
240.2.bf.a.53.5	yes	88	48.5	odd	4
240.2.bf.a.53.40	yes	88	16.5	even	4
240.2.bf.a.77.5	yes	88	5.2	odd	4
240.2.bf.a.77.40	yes	88	15.2	even	4
960.2.bb.a.497.5		88	80.27	even	4
960.2.bb.a.497.40		88	240.107	odd	4
960.2.bb.a.593.5		88	12.11	even	2
960.2.bb.a.593.40		88	4.3	odd	2
960.2.bf.a.17.17		88	20.7	even	4
960.2.bf.a.17.18		88	60.47	odd	4
960.2.bf.a.113.17		88	16.11	odd	4
960.2.bf.a.113.18		88	48.11	even	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.418005 + 1.35103i) q^{2} +(-1.65521 + 0.510164i) q^{3} +(-1.65054 - 1.12947i) q^{4} +(-0.369196 + 2.20538i) q^{5} +(0.00264245 - 2.44949i) q^{6} +(-2.84513 - 2.84513i) q^{7} +(2.21588 - 1.75780i) q^{8} +(2.47947 - 1.68886i) q^{9} +O(q^{10})\)	\(q+(-0.418005 + 1.35103i) q^{2} +(-1.65521 + 0.510164i) q^{3} +(-1.65054 - 1.12947i) q^{4} +(-0.369196 + 2.20538i) q^{5} +(0.00264245 - 2.44949i) q^{6} +(-2.84513 - 2.84513i) q^{7} +(2.21588 - 1.75780i) q^{8} +(2.47947 - 1.68886i) q^{9} +(-2.82520 - 1.42065i) q^{10} +(-0.897797 - 0.897797i) q^{11} +(3.30822 + 1.02747i) q^{12} +1.68555i q^{13} +(5.03313 - 2.65457i) q^{14} +(-0.514007 - 3.83872i) q^{15} +(1.44859 + 3.72848i) q^{16} +(-3.30858 - 3.30858i) q^{17} +(1.24527 + 4.05577i) q^{18} +(4.55983 - 4.55983i) q^{19} +(3.10029 - 3.22308i) q^{20} +(6.16079 + 3.25782i) q^{21} +(1.58823 - 0.837664i) q^{22} +(-1.41506 - 1.41506i) q^{23} +(-2.77099 + 4.04000i) q^{24} +(-4.72739 - 1.62843i) q^{25} +(-2.27722 - 0.704566i) q^{26} +(-3.24245 + 4.06036i) q^{27} +(1.48252 + 7.90951i) q^{28} +(-3.73404 - 3.73404i) q^{29} +(5.40107 + 0.910169i) q^{30} -4.39950 q^{31} +(-5.64280 + 0.398557i) q^{32} +(1.94407 + 1.02802i) q^{33} +(5.85299 - 3.08698i) q^{34} +(7.32500 - 5.22418i) q^{35} +(-5.99999 - 0.0129453i) q^{36} +3.05850i q^{37} +(4.25442 + 8.06648i) q^{38} +(-0.859905 - 2.78994i) q^{39} +(3.05853 + 5.53583i) q^{40} -2.50291 q^{41} +(-6.97664 + 6.96160i) q^{42} -10.5667 q^{43} +(0.467817 + 2.49589i) q^{44} +(2.80917 + 6.09168i) q^{45} +(2.50329 - 1.32028i) q^{46} +(2.69473 + 2.69473i) q^{47} +(-4.29986 - 5.43242i) q^{48} +9.18955i q^{49} +(4.17613 - 5.70613i) q^{50} +(7.16433 + 3.78849i) q^{51} +(1.90378 - 2.78207i) q^{52} -2.43012i q^{53} +(-4.13029 - 6.07788i) q^{54} +(2.31145 - 1.64852i) q^{55} +(-11.3057 - 1.30329i) q^{56} +(-5.22123 + 9.87375i) q^{57} +(6.60563 - 3.48394i) q^{58} +(-0.429791 + 0.429791i) q^{59} +(-3.48734 + 6.91654i) q^{60} +(0.751106 + 0.751106i) q^{61} +(1.83901 - 5.94384i) q^{62} +(-11.8594 - 2.24937i) q^{63} +(1.82026 - 7.79016i) q^{64} +(-3.71727 - 0.622296i) q^{65} +(-2.20152 + 2.19677i) q^{66} -10.4823 q^{67} +(1.72401 + 9.19791i) q^{68} +(3.06415 + 1.62032i) q^{69} +(3.99612 + 12.0800i) q^{70} -13.4420 q^{71} +(2.52551 - 8.10073i) q^{72} +(8.58741 - 8.58741i) q^{73} +(-4.13211 - 1.27847i) q^{74} +(8.65561 + 0.283661i) q^{75} +(-12.6764 + 2.37600i) q^{76} +5.10870i q^{77} +(4.12872 + 0.00445397i) q^{78} +9.85894i q^{79} +(-8.75753 + 1.81815i) q^{80} +(3.29549 - 8.37495i) q^{81} +(1.04623 - 3.38150i) q^{82} +15.6541 q^{83} +(-6.48904 - 12.3356i) q^{84} +(8.51819 - 6.07516i) q^{85} +(4.41691 - 14.2758i) q^{86} +(8.08560 + 4.27566i) q^{87} +(-3.56756 - 0.411261i) q^{88} -10.8149i q^{89} +(-9.40427 + 1.24891i) q^{90} +(4.79560 - 4.79560i) q^{91} +(0.737351 + 3.93390i) q^{92} +(7.28211 - 2.24447i) q^{93} +(-4.76706 + 2.51424i) q^{94} +(8.37268 + 11.7396i) q^{95} +(9.13670 - 3.53845i) q^{96} +(1.65415 - 1.65415i) q^{97} +(-12.4153 - 3.84128i) q^{98} +(-3.74231 - 0.709802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Introduction

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