LMFDB - Embedded newform 210.2.u.b.187.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(73,210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("210.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,12,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			187.2
Root			$-0.424637 - 3.22544i$ of defining polynomial
Character	$\chi$	$=$	210.187
Dual form			210.2.u.b.73.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.23435 - 0.0876265i) q^{5} +1.00000i q^{6} +(-0.703686 - 2.55046i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.13554 + 0.662933i) q^{10} +(0.989376 + 1.71365i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-2.19222 - 2.19222i) q^{13} +(1.33981 + 2.28142i) q^{14} +(0.493652 - 2.18090i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.44599 + 1.19130i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.10939 - 3.65357i) q^{19} +(1.89119 - 1.19306i) q^{20} +(-2.64568 + 0.0196015i) q^{21} +(-1.39919 - 1.39919i) q^{22} +(-1.52249 - 5.68202i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.98464 - 0.391577i) q^{25} +(2.68491 + 1.55013i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.88464 - 1.85692i) q^{28} +8.94996i q^{29} +(0.0876265 + 2.23435i) q^{30} +(-1.50157 + 0.866930i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.91133 - 0.512139i) q^{33} -4.60282 q^{34} +(-1.79577 - 5.63695i) q^{35} -1.00000 q^{36} +(2.67747 - 0.717425i) q^{37} +(-1.09190 + 4.07503i) q^{38} +(-2.68491 + 1.55013i) q^{39} +(-1.51796 + 1.64189i) q^{40} +6.55691i q^{41} +(2.55046 - 0.703686i) q^{42} +(-6.33724 + 6.33724i) q^{43} +(1.71365 + 0.989376i) q^{44} +(-1.97882 - 1.04129i) q^{45} +(2.94123 + 5.09436i) q^{46} +(1.57366 + 5.87298i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.00965 + 3.58944i) q^{49} +(-4.71345 + 1.66835i) q^{50} +(2.30141 - 3.98616i) q^{51} +(-2.99462 - 0.802407i) q^{52} +(-11.0441 - 2.95926i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.36077 + 3.74220i) q^{55} +(2.30103 + 1.30586i) q^{56} +(-2.98313 - 2.98313i) q^{57} +(-2.31642 - 8.64500i) q^{58} +(-2.10351 - 3.64339i) q^{59} +(-0.662933 - 2.13554i) q^{60} +(9.63018 + 5.55999i) q^{61} +(1.22602 - 1.22602i) q^{62} +(-0.665818 + 2.56060i) q^{63} -1.00000i q^{64} +(-5.09028 - 4.70608i) q^{65} +(-1.71365 + 0.989376i) q^{66} +(1.42665 - 5.32434i) q^{67} +(4.44599 - 1.19130i) q^{68} -5.88246 q^{69} +(3.19353 + 4.98010i) q^{70} -3.86002 q^{71} +(0.965926 - 0.258819i) q^{72} +(-3.93920 + 14.7013i) q^{73} +(-2.40055 + 1.38596i) q^{74} +(0.911886 - 4.91614i) q^{75} -4.21878i q^{76} +(3.67438 - 3.72923i) q^{77} +(2.19222 - 2.19222i) q^{78} +(2.21282 + 1.27757i) q^{79} +(1.04129 - 1.97882i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.69705 - 6.33349i) q^{82} +(9.52969 + 9.52969i) q^{83} +(-2.28142 + 1.33981i) q^{84} +(10.0383 + 2.27219i) q^{85} +(4.48111 - 7.76151i) q^{86} +(8.64500 + 2.31642i) q^{87} +(-1.91133 - 0.512139i) q^{88} +(3.09593 - 5.36231i) q^{89} +(2.18090 + 0.493652i) q^{90} +(-4.04852 + 7.13378i) q^{91} +(-4.15953 - 4.15953i) q^{92} +(0.448756 + 1.67478i) q^{93} +(-3.04008 - 5.26557i) q^{94} +(4.39297 - 8.34821i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-1.48031 + 1.48031i) q^{97} +(4.87586 - 5.02254i) q^{98} -1.97875i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.23435	−	0.0876265i	0.999232	−	0.0391878i
$5$	2.23435	−	0.0876265i	0.999232	−	0.0391878i
$6$			1.00000i			0.408248i
$7$	−0.703686	−	2.55046i	−0.265968	−	0.963982i
$7$	−0.703686	−	2.55046i	−0.265968	−	0.963982i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−2.13554	+	0.662933i	−0.675316	+	0.209638i
$11$	0.989376	+	1.71365i	0.298308	+	0.516685i	0.975749	−	0.218892i	$-0.0702443\pi$
$11$	0.989376	+	1.71365i	0.298308	+	0.516685i	−0.677441	+	0.735577i	$0.736911\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	−2.19222	−	2.19222i	−0.608011	−	0.608011i	0.334415	−	0.942426i	$-0.391461\pi$
$13$	−2.19222	−	2.19222i	−0.608011	−	0.608011i	−0.942426	+	0.334415i	$0.891461\pi$
$14$	1.33981	+	2.28142i	0.358081	+	0.609736i
$15$	0.493652	−	2.18090i	0.127460	−	0.563105i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.44599	+	1.19130i	1.07831	+	0.288932i	0.753903	−	0.656985i	$-0.228169\pi$
$17$	4.44599	+	1.19130i	1.07831	+	0.288932i	0.324407	+	0.945918i	$0.394835\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	2.10939	−	3.65357i	0.483928	−	0.838188i	−0.515902	−	0.856648i	$-0.672543\pi$
$19$	2.10939	−	3.65357i	0.483928	−	0.838188i	0.999830	+	0.0184602i	$0.00587639\pi$
$20$	1.89119	−	1.19306i	0.422883	−	0.266777i
$21$	−2.64568	+	0.0196015i	−0.577334	+	0.00427740i
$22$	−1.39919	−	1.39919i	−0.298308	−	0.298308i
$23$	−1.52249	−	5.68202i	−0.317462	−	1.18478i	−0.921676	−	0.387961i	$-0.873179\pi$
$23$	−1.52249	−	5.68202i	−0.317462	−	1.18478i	0.604214	−	0.796822i	$-0.293487\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.98464	−	0.391577i	0.996929	−	0.0783154i
$26$	2.68491	+	1.55013i	0.526553	+	0.304006i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.88464	−	1.85692i	−0.356163	−	0.350924i
$29$			8.94996i			1.66197i	0.556298	+	0.830983i	$0.312221\pi$
$29$			8.94996i			1.66197i	−0.556298	+	0.830983i	$0.687779\pi$
$30$	0.0876265	+	2.23435i	0.0159983	+	0.407935i
$31$	−1.50157	+	0.866930i	−0.269689	+	0.155705i	−0.628747	−	0.777610i	$-0.716432\pi$
$31$	−1.50157	+	0.866930i	−0.269689	+	0.155705i	0.359057	+	0.933316i	$0.383098\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	1.91133	−	0.512139i	0.332720	−	0.0891519i
$34$	−4.60282			−0.789378
$35$	−1.79577	−	5.63695i	−0.303540	−	0.952819i
$36$	−1.00000			−0.166667
$37$	2.67747	−	0.717425i	0.440173	−	0.117944i	−0.0319248	−	0.999490i	$-0.510164\pi$
$37$	2.67747	−	0.717425i	0.440173	−	0.117944i	0.472097	+	0.881546i	$0.343497\pi$
$38$	−1.09190	+	4.07503i	−0.177130	+	0.661058i
$39$	−2.68491	+	1.55013i	−0.429929	+	0.248220i
$40$	−1.51796	+	1.64189i	−0.240011	+	0.259605i
$41$			6.55691i			1.02402i	0.858980	+	0.512008i	$0.171098\pi$
$41$			6.55691i			1.02402i	−0.858980	+	0.512008i	$0.828902\pi$
$42$	2.55046	−	0.703686i	0.393544	−	0.108581i
$43$	−6.33724	+	6.33724i	−0.966421	+	0.966421i	−0.999454	−	0.0330335i	$-0.989483\pi$
$43$	−6.33724	+	6.33724i	−0.966421	+	0.966421i	0.0330335	+	0.999454i	$0.489483\pi$
$44$	1.71365	+	0.989376i	0.258342	+	0.149154i
$45$	−1.97882	−	1.04129i	−0.294985	−	0.155226i
$46$	2.94123	+	5.09436i	0.433661	+	0.751122i
$47$	1.57366	+	5.87298i	0.229542	+	0.856663i	0.980534	+	0.196351i	$0.0629091\pi$
$47$	1.57366	+	5.87298i	0.229542	+	0.856663i	−0.750992	+	0.660312i	$0.770424\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−6.00965	+	3.58944i	−0.858522	+	0.512777i
$50$	−4.71345	+	1.66835i	−0.666582	+	0.235941i
$51$	2.30141	−	3.98616i	0.322262	−	0.558174i
$52$	−2.99462	−	0.802407i	−0.415280	−	0.111274i
$53$	−11.0441	−	2.95926i	−1.51702	−	0.406485i	−0.598263	−	0.801300i	$-0.704142\pi$
$53$	−11.0441	−	2.95926i	−1.51702	−	0.406485i	−0.918761	+	0.394814i	$0.870809\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.36077	+	3.74220i	0.318327	+	0.504598i
$56$	2.30103	+	1.30586i	0.307487	+	0.174503i
$57$	−2.98313	−	2.98313i	−0.395125	−	0.395125i
$58$	−2.31642	−	8.64500i	−0.304161	−	1.13514i
$59$	−2.10351	−	3.64339i	−0.273854	−	0.474329i	0.695991	−	0.718050i	$-0.254965\pi$
$59$	−2.10351	−	3.64339i	−0.273854	−	0.474329i	−0.969845	+	0.243721i	$0.921632\pi$
$60$	−0.662933	−	2.13554i	−0.0855843	−	0.275697i
$61$	9.63018	+	5.55999i	1.23302	+	0.711883i	0.967658	−	0.252266i	$-0.0811759\pi$
$61$	9.63018	+	5.55999i	1.23302	+	0.711883i	0.265360	+	0.964149i	$0.414509\pi$
$62$	1.22602	−	1.22602i	0.155705	−	0.155705i
$63$	−0.665818	+	2.56060i	−0.0838852	+	0.322606i
$64$		−	1.00000i		−	0.125000i
$65$	−5.09028	−	4.70608i	−0.631371	−	0.583718i
$66$	−1.71365	+	0.989376i	−0.210936	+	0.121784i
$67$	1.42665	−	5.32434i	0.174294	−	0.650472i	−0.822377	−	0.568942i	$-0.807353\pi$
$67$	1.42665	−	5.32434i	0.174294	−	0.650472i	0.996671	−	0.0815298i	$-0.0259806\pi$
$68$	4.44599	−	1.19130i	0.539155	−	0.144466i
$69$	−5.88246			−0.708165
$70$	3.19353	+	4.98010i	0.381700	+	0.595236i
$71$	−3.86002			−0.458100			−0.229050	−	0.973415i	$-0.573562\pi$
$71$	−3.86002			−0.458100			−0.229050	+	0.973415i	$0.573562\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−3.93920	+	14.7013i	−0.461048	+	1.72066i	0.208621	+	0.977997i	$0.433103\pi$
$73$	−3.93920	+	14.7013i	−0.461048	+	1.72066i	−0.669669	+	0.742660i	$0.733564\pi$
$74$	−2.40055	+	1.38596i	−0.279058	+	0.161114i
$75$	0.911886	−	4.91614i	0.105296	−	0.567667i
$76$		−	4.21878i		−	0.483928i
$77$	3.67438	−	3.72923i	0.418734	−	0.424985i
$78$	2.19222	−	2.19222i	0.248220	−	0.248220i
$79$	2.21282	+	1.27757i	0.248962	+	0.143738i	0.619289	−	0.785163i	$-0.287421\pi$
$79$	2.21282	+	1.27757i	0.248962	+	0.143738i	−0.370327	+	0.928901i	$0.620754\pi$
$80$	1.04129	−	1.97882i	0.116420	−	0.221239i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−1.69705	−	6.33349i	−0.187408	−	0.699416i
$83$	9.52969	+	9.52969i	1.04602	+	1.04602i	0.998889	+	0.0471311i	$0.0150078\pi$
$83$	9.52969	+	9.52969i	1.04602	+	1.04602i	0.0471311	+	0.998889i	$0.484992\pi$
$84$	−2.28142	+	1.33981i	−0.248924	+	0.146186i
$85$	10.0383	+	2.27219i	1.08880	+	0.246454i
$86$	4.48111	−	7.76151i	0.483210	−	0.836945i
$87$	8.64500	+	2.31642i	0.926841	+	0.248346i
$88$	−1.91133	−	0.512139i	−0.203748	−	0.0545942i
$89$	3.09593	−	5.36231i	0.328168	−	0.568404i	−0.653980	−	0.756512i	$-0.726902\pi$
$89$	3.09593	−	5.36231i	0.328168	−	0.568404i	0.982148	+	0.188108i	$0.0602354\pi$
$90$	2.18090	+	0.493652i	0.229887	+	0.0520355i
$91$	−4.04852	+	7.13378i	−0.424400	+	0.747824i
$92$	−4.15953	−	4.15953i	−0.433661	−	0.433661i
$93$	0.448756	+	1.67478i	0.0465339	+	0.173667i
$94$	−3.04008	−	5.26557i	−0.313560	−	0.543102i
$95$	4.39297	−	8.34821i	0.450709	−	0.856508i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−1.48031	+	1.48031i	−0.150303	+	0.150303i	−0.778253	−	0.627951i	$-0.783894\pi$
$97$	−1.48031	+	1.48031i	−0.150303	+	0.150303i	0.627951	+	0.778253i	$0.283894\pi$
$98$	4.87586	−	5.02254i	0.492537	−	0.507354i
$99$		−	1.97875i		−	0.198872i
$100$	4.12104	−	2.83144i	0.412104	−	0.283144i
$101$	−8.70112	+	5.02360i	−0.865794	+	0.499866i	−0.865948	−	0.500134i	$-0.833284\pi$
$101$	−8.70112	+	5.02360i	−0.865794	+	0.499866i	0.000154194		1.00000i	$0.499951\pi$
$102$	−1.19130	+	4.44599i	−0.117956	+	0.440218i
$103$	4.81790	−	1.29095i	0.474722	−	0.127201i	−0.0135219	−	0.999909i	$-0.504304\pi$
$103$	4.81790	−	1.29095i	0.474722	−	0.127201i	0.488244	+	0.872707i	$0.337638\pi$
$104$	3.10026			0.304006
$105$	−5.90966	+	0.275628i	−0.576723	+	0.0268986i
$106$	11.4337			1.11054
$107$	−5.84351	+	1.56576i	−0.564913	+	0.151368i	−0.529963	−	0.848021i	$-0.677794\pi$
$107$	−5.84351	+	1.56576i	−0.564913	+	0.151368i	−0.0349507	+	0.999389i	$0.511127\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	8.44287	−	4.87449i	0.808680	−	0.466892i	−0.0378171	−	0.999285i	$-0.512040\pi$
$109$	8.44287	−	4.87449i	0.808680	−	0.466892i	0.846497	+	0.532393i	$0.178707\pi$
$110$	−3.24889	−	3.00367i	−0.309769	−	0.286389i
$111$		−	2.77192i		−	0.263099i
$112$	−2.56060	−	0.665818i	−0.241954	−	0.0629139i
$113$	6.02504	−	6.02504i	0.566788	−	0.566788i	−0.364439	−	0.931227i	$-0.618739\pi$
$113$	6.02504	−	6.02504i	0.566788	−	0.566788i	0.931227	+	0.364439i	$0.118739\pi$
$114$	3.65357	+	2.10939i	0.342189	+	0.197563i
$115$	−3.89968	−	12.5622i	−0.363647	−	1.17143i
$116$	4.47498	+	7.75089i	0.415491	+	0.719652i
$117$	0.802407	+	2.99462i	0.0741826	+	0.276853i
$118$	2.97481	+	2.97481i	0.273854	+	0.273854i
$119$	−0.0902224	−	12.1776i	−0.00827067	−	1.11632i
$120$	1.19306	+	1.89119i	0.108911	+	0.172641i
$121$	3.54227	−	6.13539i	0.322024	−	0.557763i
$122$	−10.7411	−	2.87806i	−0.972451	−	0.260567i
$123$	6.33349	+	1.69705i	0.571071	+	0.153018i
$124$	−0.866930	+	1.50157i	−0.0778527	+	0.134845i
$125$	11.1031	−	1.31171i	0.993094	−	0.117323i
$126$	−0.0196015	−	2.64568i	−0.00174624	−	0.235696i
$127$	−8.92770	−	8.92770i	−0.792205	−	0.792205i	0.189647	−	0.981852i	$-0.439266\pi$
$127$	−8.92770	−	8.92770i	−0.792205	−	0.792205i	−0.981852	+	0.189647i	$0.939266\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	4.48111	+	7.76151i	0.394540	+	0.683363i
$130$	6.13485	+	3.22827i	0.538062	+	0.283138i
$131$	−4.43543	−	2.56080i	−0.387526	−	0.223738i	0.293562	−	0.955940i	$-0.405159\pi$
$131$	−4.43543	−	2.56080i	−0.387526	−	0.223738i	−0.681087	+	0.732202i	$0.738493\pi$
$132$	1.39919	−	1.39919i	0.121784	−	0.121784i
$133$	−10.8026	−	2.80894i	−0.936707	−	0.243566i
$134$			5.51217i			0.476179i
$135$	−1.51796	+	1.64189i	−0.130645	+	0.141311i
$136$	−3.98616	+	2.30141i	−0.341811	+	0.197344i
$137$	−2.99773	+	11.1877i	−0.256114	+	0.955829i	0.711354	+	0.702834i	$0.248082\pi$
$137$	−2.99773	+	11.1877i	−0.256114	+	0.955829i	−0.967468	+	0.252995i	$0.918584\pi$
$138$	5.68202	−	1.52249i	0.483686	−	0.129603i
$139$	2.87054			0.243476			0.121738	−	0.992562i	$-0.461153\pi$
$139$	2.87054			0.243476			0.121738	+	0.992562i	$0.461153\pi$
$140$	−4.37366	−	3.98386i	−0.369641	−	0.336698i
$141$	6.08016			0.512042
$142$	3.72849	−	0.999046i	0.312888	−	0.0838381i
$143$	1.58776	−	5.92562i	0.132776	−	0.495525i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	0.784254	+	19.9973i	0.0651288	+	1.66069i
$146$		−	15.2199i		−	1.25961i
$147$	1.91172	+	6.73389i	0.157676	+	0.555402i
$148$	1.96004	−	1.96004i	0.161114	−	0.161114i
$149$	−13.4924	−	7.78982i	−1.10534	−	0.638167i	−0.167720	−	0.985835i	$-0.553640\pi$
$149$	−13.4924	−	7.78982i	−1.10534	−	0.638167i	−0.937618	+	0.347668i	$0.886974\pi$
$150$	0.391577	+	4.98464i	0.0319721	+	0.406994i
$151$	−10.5953	−	18.3516i	−0.862232	−	1.49343i	−0.869769	−	0.493459i	$-0.835732\pi$
$151$	−10.5953	−	18.3516i	−0.862232	−	1.49343i	0.00753703	−	0.999972i	$-0.497601\pi$
$152$	1.09190	+	4.07503i	0.0885649	+	0.330529i
$153$	−3.25469	−	3.25469i	−0.263126	−	0.263126i
$154$	−2.58398	+	4.55316i	−0.208223	+	0.366904i
$155$	−3.27906	+	2.06860i	−0.263381	+	0.166154i
$156$	−1.55013	+	2.68491i	−0.124110	+	0.214965i
$157$	14.6660	+	3.92974i	1.17047	+	0.313627i	0.791141	−	0.611633i	$-0.209487\pi$
$157$	14.6660	+	3.92974i	1.17047	+	0.313627i	0.379332	+	0.925261i	$0.376154\pi$
$158$	−2.46808	−	0.661320i	−0.196350	−	0.0526118i
$159$	−5.71685	+	9.90187i	−0.453375	+	0.785269i
$160$	−0.493652	+	2.18090i	−0.0390266	+	0.172415i
$161$	−13.4204	+	7.88141i	−1.05767	+	0.621142i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	5.77762	+	21.5624i	0.452538	+	1.68890i	0.695225	+	0.718792i	$0.255305\pi$
$163$	5.77762	+	21.5624i	0.452538	+	1.68890i	−0.242687	+	0.970105i	$0.578029\pi$
$164$	3.27845	+	5.67845i	0.256004	+	0.443412i
$165$	4.22570	−	1.31178i	0.328970	−	0.102122i
$166$	−11.6714	−	6.73851i	−0.905880	−	0.523010i
$167$	−6.91224	+	6.91224i	−0.534885	+	0.534885i	−0.922022	−	0.387137i	$-0.873464\pi$
$167$	−6.91224	+	6.91224i	−0.534885	+	0.534885i	0.387137	+	0.922022i	$0.373464\pi$
$168$	1.85692	−	1.88464i	0.143264	−	0.145403i
$169$		−	3.38837i		−	0.260644i
$170$	−10.2843	+	0.403330i	−0.788771	+	0.0309340i
$171$	−3.65357	+	2.10939i	−0.279396	+	0.161309i
$172$	−2.31959	+	8.65684i	−0.176867	+	0.660078i
$173$	−4.37334	+	1.17183i	−0.332499	+	0.0890928i	−0.421206	−	0.906965i	$-0.638393\pi$
$173$	−4.37334	+	1.17183i	−0.332499	+	0.0890928i	0.0887072	+	0.996058i	$0.471726\pi$
$174$	−8.94996			−0.678495
$175$	−4.50632	−	12.4376i	−0.340646	−	0.940192i
$176$	1.97875			0.149154
$177$	−4.06367	+	1.08886i	−0.305444	+	0.0818436i
$178$	−1.60257	+	5.98088i	−0.120118	+	0.448286i
$179$	1.79084	−	1.03394i	0.133853	−	0.0772803i	−0.431578	−	0.902076i	$-0.642043\pi$
$179$	1.79084	−	1.03394i	0.133853	−	0.0772803i	0.565431	+	0.824795i	$0.308710\pi$
$180$	−2.23435	+	0.0876265i	−0.166539	+	0.00653130i
$181$			6.13199i			0.455787i	0.973686	+	0.227894i	$0.0731839\pi$
$181$			6.13199i			0.455787i	−0.973686	+	0.227894i	$0.926816\pi$
$182$	2.06421	−	7.93854i	0.153010	−	0.588444i
$183$	7.86301	−	7.86301i	0.581250	−	0.581250i
$184$	5.09436	+	2.94123i	0.375561	+	0.216830i
$185$	5.91953	−	1.83760i	0.435212	−	0.135103i
$186$	−0.866930	−	1.50157i	−0.0635664	−	0.110100i
$187$	2.35728	+	8.79751i	0.172382	+	0.643337i
$188$	4.29932	+	4.29932i	0.313560	+	0.313560i
$189$	2.30103	+	1.30586i	0.167375	+	0.0949876i
$190$	−2.08261	+	9.20073i	−0.151088	+	0.667491i
$191$	8.08306	−	14.0003i	0.584869	−	1.01302i	−0.410022	−	0.912075i	$-0.634479\pi$
$191$	8.08306	−	14.0003i	0.584869	−	1.01302i	0.994892	−	0.100948i	$-0.0321876\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−21.0484	−	5.63991i	−1.51510	−	0.405969i	−0.596973	−	0.802261i	$-0.703630\pi$
$193$	−21.0484	−	5.63991i	−1.51510	−	0.405969i	−0.918125	+	0.396292i	$0.870297\pi$
$194$	1.04674	−	1.81300i	0.0751514	−	0.130166i
$195$	−5.86319	+	3.69881i	−0.419872	+	0.264877i
$196$	−3.40979	+	6.11337i	−0.243557	+	0.436669i
$197$	−0.628120	−	0.628120i	−0.0447517	−	0.0447517i	0.684377	−	0.729129i	$-0.260074\pi$
$197$	−0.628120	−	0.628120i	−0.0447517	−	0.0447517i	−0.729129	+	0.684377i	$0.760074\pi$
$198$	0.512139	+	1.91133i	0.0363961	+	0.135832i
$199$	−4.81248	−	8.33546i	−0.341147	−	0.590885i	0.643499	−	0.765447i	$-0.277482\pi$
$199$	−4.81248	−	8.33546i	−0.341147	−	0.590885i	−0.984646	+	0.174563i	$0.944149\pi$
$200$	−3.24779	+	3.80156i	−0.229653	+	0.268811i
$201$	−4.77368	−	2.75608i	−0.336709	−	0.194399i
$202$	7.10444	−	7.10444i	0.499866	−	0.499866i
$203$	22.8265	−	6.29796i	1.60210	−	0.442030i
$204$		−	4.60282i		−	0.322262i
$205$	0.574559	+	14.6504i	0.0401289	+	1.02323i
$206$	−4.31961	+	2.49393i	−0.300962	+	0.173760i
$207$	−1.52249	+	5.68202i	−0.105821	+	0.394928i
$208$	−2.99462	+	0.802407i	−0.207640	+	0.0556369i
$209$	8.34793			0.577439
$210$	5.63695	−	1.79577i	0.388987	−	0.123920i
$211$	11.2669			0.775648			0.387824	−	0.921733i	$-0.373227\pi$
$211$	11.2669			0.775648			0.387824	+	0.921733i	$0.373227\pi$
$212$	−11.0441	+	2.95926i	−0.758512	+	0.203243i
$213$	−0.999046	+	3.72849i	−0.0684535	+	0.255472i
$214$	5.23915	−	3.02482i	0.358141	−	0.206773i
$215$	−13.6043	+	14.7149i	−0.927807	+	1.00355i
$216$		−	1.00000i		−	0.0680414i
$217$	3.26770	+	3.21964i	0.221826	+	0.218563i
$218$	−6.89357	+	6.89357i	−0.466892	+	0.466892i
$219$	13.1808	+	7.60995i	0.890677	+	0.514233i
$220$	3.91559	+	2.06045i	0.263989	+	0.138916i
$221$	−7.13498	−	12.3581i	−0.479951	−	0.831299i
$222$	0.717425	+	2.67747i	0.0481504	+	0.179700i
$223$	−13.1718	−	13.1718i	−0.882048	−	0.882048i	0.111694	−	0.993743i	$-0.464372\pi$
$223$	−13.1718	−	13.1718i	−0.882048	−	0.882048i	−0.993743	+	0.111694i	$0.964372\pi$
$224$	2.64568	−	0.0196015i	0.176772	−	0.00130968i
$225$	−4.51262	−	2.15321i	−0.300841	−	0.143547i
$226$	−4.26035	+	7.37914i	−0.283394	+	0.490853i
$227$	25.9971	+	6.96589i	1.72549	+	0.462343i	0.979135	−	0.203210i	$-0.0651373\pi$
$227$	25.9971	+	6.96589i	1.72549	+	0.462343i	0.746351	+	0.665552i	$0.231804\pi$
$228$	−4.07503	−	1.09190i	−0.269876	−	0.0723130i
$229$	13.4452	−	23.2878i	0.888486	−	1.53890i	0.0468199	−	0.998903i	$-0.485091\pi$
$229$	13.4452	−	23.2878i	0.888486	−	1.53890i	0.841666	−	0.539999i	$-0.181575\pi$
$230$	7.01814	+	11.1249i	0.462762	+	0.733551i
$231$	−2.65116	−	4.51437i	−0.174434	−	0.297024i
$232$	−6.32858	−	6.32858i	−0.415491	−	0.415491i
$233$	−0.238436	−	0.889853i	−0.0156204	−	0.0582962i	0.957676	−	0.287849i	$-0.0929402\pi$
$233$	−0.238436	−	0.889853i	−0.0156204	−	0.0582962i	−0.973296	+	0.229553i	$0.926274\pi$
$234$	−1.55013	−	2.68491i	−0.101335	−	0.175518i
$235$	4.03074	+	12.9844i	0.262936	+	0.847009i
$236$	−3.64339	−	2.10351i	−0.237164	−	0.136927i
$237$	1.80676	−	1.80676i	0.117362	−	0.117362i
$238$	3.23894	+	11.7393i	0.209949	+	0.760946i
$239$			25.3432i			1.63931i	0.572856	+	0.819656i	$0.305836\pi$
$239$			25.3432i			1.63931i	−0.572856	+	0.819656i	$0.694164\pi$
$240$	−1.64189	−	1.51796i	−0.105983	−	0.0979841i
$241$	18.2905	−	10.5600i	1.17819	−	0.680230i	0.222597	−	0.974911i	$-0.428547\pi$
$241$	18.2905	−	10.5600i	1.17819	−	0.680230i	0.955596	+	0.294681i	$0.0952134\pi$
$242$	−1.83361	+	6.84314i	−0.117869	+	0.439894i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	11.1200			0.711883
$245$	−13.1131	+	8.54667i	−0.837768	+	0.546027i
$246$	−6.55691			−0.418053
$247$	−12.6337	+	3.38518i	−0.803861	+	0.215394i
$248$	0.448756	−	1.67478i	0.0284960	−	0.106349i
$249$	11.6714	−	6.73851i	0.739648	−	0.427036i
$250$	−10.3853	+	4.14071i	−0.656824	+	0.261882i
$251$			2.70623i			0.170816i	0.996346	+	0.0854078i	$0.0272193\pi$
$251$			2.70623i			0.170816i	−0.996346	+	0.0854078i	$0.972781\pi$
$252$	0.703686	+	2.55046i	0.0443280	+	0.160664i
$253$	8.23068	−	8.23068i	0.517458	−	0.517458i
$254$	10.9342	+	6.31283i	0.686070	+	0.396102i
$255$	4.79287	−	9.10815i	0.300141	−	0.570374i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.21737	−	23.2035i	−0.387829	−	1.44740i	−0.833660	−	0.552279i	$-0.813758\pi$
$257$	−6.21737	−	23.2035i	−0.387829	−	1.44740i	0.445831	−	0.895117i	$-0.352908\pi$
$258$	−6.33724	−	6.33724i	−0.394540	−	0.394540i
$259$	−3.71385	−	6.32392i	−0.230768	−	0.392949i
$260$	−6.76135	−	1.53045i	−0.419321	−	0.0949145i
$261$	4.47498	−	7.75089i	0.276994	−	0.479768i
$262$	4.94708	+	1.32557i	0.305632	+	0.0818938i
$263$	−0.821351	−	0.220080i	−0.0506467	−	0.0135707i	0.233407	−	0.972379i	$-0.425013\pi$
$263$	−0.821351	−	0.220080i	−0.0506467	−	0.0135707i	−0.284053	+	0.958808i	$0.591679\pi$
$264$	−0.989376	+	1.71365i	−0.0608919	+	0.105468i
$265$	−24.9357	−	5.64426i	−1.53179	−	0.346724i
$266$	11.1615	−	0.0826946i	0.684359	−	0.00507033i
$267$	−4.37831	−	4.37831i	−0.267948	−	0.267948i
$268$	−1.42665	−	5.32434i	−0.0871468	−	0.325236i
$269$	−5.82171	−	10.0835i	−0.354956	−	0.614802i	0.632154	−	0.774842i	$-0.282171\pi$
$269$	−5.82171	−	10.0835i	−0.354956	−	0.614802i	−0.987110	+	0.160041i	$0.948837\pi$
$270$	1.04129	−	1.97882i	0.0633708	−	0.120427i
$271$	−20.2171	−	11.6724i	−1.22810	−	0.709046i	−0.261471	−	0.965211i	$-0.584208\pi$
$271$	−20.2171	−	11.6724i	−1.22810	−	0.709046i	−0.966633	+	0.256165i	$0.917541\pi$
$272$	3.25469	−	3.25469i	0.197344	−	0.197344i
$273$	5.84287	+	5.75693i	0.353627	+	0.348425i
$274$		−	11.5824i		−	0.699715i
$275$	5.60271	+	8.15452i	0.337856	+	0.491736i
$276$	−5.09436	+	2.94123i	−0.306644	+	0.177041i
$277$	2.44577	−	9.12775i	0.146952	−	0.548433i	−0.852708	−	0.522387i	$-0.825042\pi$
$277$	2.44577	−	9.12775i	0.146952	−	0.548433i	0.999661	−	0.0260462i	$-0.00829171\pi$
$278$	−2.77273	+	0.742949i	−0.166297	+	0.0445591i
$279$	1.73386			0.103804
$280$	5.25573	+	2.71613i	0.314090	+	0.162320i
$281$	−11.7320			−0.699871			−0.349935	−	0.936774i	$-0.613796\pi$
$281$	−11.7320			−0.699871			−0.349935	+	0.936774i	$0.613796\pi$
$282$	−5.87298	+	1.57366i	−0.349731	+	0.0937101i
$283$	0.944117	−	3.52349i	0.0561219	−	0.209450i	−0.932171	−	0.362018i	$-0.882088\pi$
$283$	0.944117	−	3.52349i	0.0561219	−	0.209450i	0.988293	+	0.152568i	$0.0487544\pi$
$284$	−3.34287	+	1.93001i	−0.198363	+	0.114525i
$285$	−6.92676	−	6.40396i	−0.410306	−	0.379338i
$286$			6.13465i			0.362750i
$287$	16.7231	−	4.61400i	0.987133	−	0.272356i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	3.62517	+	2.09299i	0.213245	+	0.123117i
$290$	−5.93323	−	19.1130i	−0.348411	−	1.12235i
$291$	1.04674	+	1.81300i	0.0613609	+	0.106280i
$292$	3.93920	+	14.7013i	0.230524	+	0.860328i
$293$	8.62354	+	8.62354i	0.503793	+	0.503793i	0.912614	−	0.408822i	$-0.134060\pi$
$293$	8.62354	+	8.62354i	0.503793	+	0.503793i	−0.408822	+	0.912614i	$0.634060\pi$
$294$	−3.58944	−	6.00965i	−0.209340	−	0.350490i
$295$	−5.01924	−	7.95628i	−0.292231	−	0.463233i
$296$	−1.38596	+	2.40055i	−0.0805572	+	0.139529i
$297$	−1.91133	−	0.512139i	−0.110907	−	0.0297173i
$298$	15.0488	+	4.03231i	0.871752	+	0.233585i
$299$	−9.11859	+	15.7939i	−0.527341	+	0.913382i
$300$	−1.66835	−	4.71345i	−0.0963225	−	0.272131i
$301$	20.6223	+	11.7034i	1.18865	+	0.674575i
$302$	14.9840	+	14.9840i	0.862232	+	0.862232i
$303$	2.60040	+	9.70484i	0.149389	+	0.557529i
$304$	−2.10939	−	3.65357i	−0.120982	−	0.209547i
$305$	22.0044	+	11.5791i	1.25997	+	0.663017i
$306$	3.98616	+	2.30141i	0.227874	+	0.131563i
$307$	−15.9933	+	15.9933i	−0.912785	+	0.912785i	−0.996490	−	0.0837060i	$-0.973324\pi$
$307$	−15.9933	+	15.9933i	−0.912785	+	0.912785i	0.0837060	+	0.996490i	$0.473324\pi$
$308$	1.31749	−	5.06680i	0.0750710	−	0.288708i
$309$		−	4.98786i		−	0.283750i
$310$	2.63194	−	2.84680i	0.149484	−	0.161687i
$311$	6.70522	−	3.87126i	0.380218	−	0.219519i	−0.297695	−	0.954661i	$-0.596218\pi$
$311$	6.70522	−	3.87126i	0.380218	−	0.219519i	0.677913	+	0.735142i	$0.262885\pi$
$312$	0.802407	−	2.99462i	0.0454273	−	0.169537i
$313$	19.3623	−	5.18810i	1.09442	−	0.293249i	0.333929	−	0.942598i	$-0.391625\pi$
$313$	19.3623	−	5.18810i	1.09442	−	0.293249i	0.760490	+	0.649349i	$0.224959\pi$
$314$	−15.1833			−0.856846
$315$	−1.26329	+	5.77963i	−0.0711786	+	0.325645i
$316$	2.55514			0.143738
$317$	2.87877	−	0.771364i	0.161688	−	0.0433241i	−0.177067	−	0.984199i	$-0.556661\pi$
$317$	2.87877	−	0.771364i	0.161688	−	0.0433241i	0.338755	+	0.940875i	$0.389994\pi$
$318$	2.95926	−	11.0441i	0.165947	−	0.619322i
$319$	−15.3371	+	8.85488i	−0.858713	+	0.495778i
$320$	−0.0876265	−	2.23435i	−0.00489847	−	0.124904i
$321$			6.04965i			0.337658i
$322$	10.9232	−	11.0863i	0.608728	−	0.617816i
$323$	13.7308	−	13.7308i	0.764004	−	0.764004i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	−11.7858	−	10.0690i	−0.653761	−	0.558527i
$326$	−11.1615	−	19.3323i	−0.618179	−	1.07072i
$327$	−2.52322	−	9.41680i	−0.139535	−	0.520750i
$328$	−4.63643	−	4.63643i	−0.256004	−	0.256004i
$329$	13.8714	−	8.14629i	0.764756	−	0.449119i
$330$	−3.74220	+	2.36077i	−0.206001	+	0.129956i
$331$	−13.9186	+	24.1077i	−0.765035	+	1.32508i	0.175194	+	0.984534i	$0.443945\pi$
$331$	−13.9186	+	24.1077i	−0.765035	+	1.32508i	−0.940228	+	0.340545i	$0.889388\pi$
$332$	13.0178	+	3.48811i	0.714445	+	0.191435i
$333$	−2.67747	−	0.717425i	−0.146724	−	0.0393146i
$334$	4.88769	−	8.46573i	0.267442	−	0.463224i
$335$	2.72109	−	12.0215i	0.148669	−	0.656803i
$336$	−1.30586	+	2.30103i	−0.0712407	+	0.125531i
$337$	−17.1567	−	17.1567i	−0.934583	−	0.934583i	0.0634051	−	0.997988i	$-0.479804\pi$
$337$	−17.1567	−	17.1567i	−0.934583	−	0.934583i	−0.997988	+	0.0634051i	$0.979804\pi$
$338$	0.876975	+	3.27292i	0.0477012	+	0.178023i
$339$	−4.26035	−	7.37914i	−0.231390	−	0.400780i
$340$	9.82950	−	3.05136i	0.533080	−	0.165483i
$341$	−2.97123	−	1.71544i	−0.160901	−	0.0928963i
$342$	2.98313	−	2.98313i	0.161309	−	0.161309i
$343$	13.3836	+	12.8015i	0.722647	+	0.691217i
$344$		−	8.96222i		−	0.483210i
$345$	−13.1435	+	0.515460i	−0.707621	+	0.0277514i
$346$	3.92103	−	2.26381i	0.210796	−	0.121703i
$347$	−6.48156	+	24.1895i	−0.347948	+	1.29856i	0.541181	+	0.840906i	$0.317977\pi$
$347$	−6.48156	+	24.1895i	−0.347948	+	1.29856i	−0.889130	+	0.457655i	$0.848689\pi$
$348$	8.64500	−	2.31642i	0.463421	−	0.124173i
$349$	18.0130			0.964212			0.482106	−	0.876113i	$-0.339872\pi$
$349$	18.0130			0.964212			0.482106	+	0.876113i	$0.339872\pi$
$350$	7.57185	+	10.8474i	0.404732	+	0.579820i
$351$	3.10026			0.165480
$352$	−1.91133	+	0.512139i	−0.101874	+	0.0272971i
$353$	1.96651	−	7.33911i	0.104667	−	0.390621i	−0.893641	−	0.448784i	$-0.851857\pi$
$353$	1.96651	−	7.33911i	0.104667	−	0.390621i	0.998307	+	0.0581623i	$0.0185241\pi$
$354$	3.64339	−	2.10351i	0.193644	−	0.111800i
$355$	−8.62463	+	0.338240i	−0.457748	+	0.0179519i
$356$		−	6.19187i		−	0.328168i
$357$	−11.7860	−	3.06464i	−0.623781	−	0.162198i
$358$	−1.46221	+	1.46221i	−0.0772803	+	0.0772803i
$359$	2.84638	+	1.64336i	0.150226	+	0.0867332i	0.573229	−	0.819395i	$-0.305691\pi$
$359$	2.84638	+	1.64336i	0.150226	+	0.0867332i	−0.423003	+	0.906128i	$0.639024\pi$
$360$	2.13554	−	0.662933i	0.112553	−	0.0349396i
$361$	0.600927	+	1.04084i	0.0316277	+	0.0547808i
$362$	−1.58708	−	5.92305i	−0.0834149	−	0.311309i
$363$	−5.00952	−	5.00952i	−0.262932	−	0.262932i
$364$	0.0607699	+	8.20230i	0.00318521	+	0.429917i
$365$	−7.51333	+	33.1930i	−0.393266	+	1.73740i
$366$	−5.55999	+	9.63018i	−0.290625	+	0.503377i
$367$	−3.13693	−	0.840538i	−0.163746	−	0.0438757i	0.176014	−	0.984388i	$-0.443679\pi$
$367$	−3.13693	−	0.840538i	−0.163746	−	0.0438757i	−0.339761	+	0.940512i	$0.610346\pi$
$368$	−5.68202	−	1.52249i	−0.296196	−	0.0793654i
$369$	3.27845	−	5.67845i	0.170669	−	0.295608i
$370$	−5.24222	+	3.30707i	−0.272530	+	0.171926i
$371$	0.224118	+	30.2499i	0.0116356	+	1.57050i
$372$	1.22602	+	1.22602i	0.0635664	+	0.0635664i
$373$	−4.08060	−	15.2290i	−0.211286	−	0.788529i	−0.987441	−	0.157987i	$-0.949500\pi$
$373$	−4.08060	−	15.2290i	−0.211286	−	0.788529i	0.776156	−	0.630542i	$-0.217167\pi$
$374$	−4.55392	−	7.88763i	−0.235478	−	0.407860i
$375$	1.60669	−	11.0643i	0.0829691	−	0.571358i
$376$	−5.26557	−	3.04008i	−0.271551	−	0.156780i
$377$	19.6203	−	19.6203i	1.01049	−	1.01049i
$378$	−2.56060	−	0.665818i	−0.131703	−	0.0342460i
$379$			21.7428i			1.11685i	0.829555	+	0.558426i	$0.188594\pi$
$379$			21.7428i			1.11685i	−0.829555	+	0.558426i	$0.811406\pi$
$380$	−0.369678	−	9.42624i	−0.0189641	−	0.483556i
$381$	−10.9342	+	6.31283i	−0.560174	+	0.323416i
$382$	−4.18410	+	15.6153i	−0.214077	+	0.798946i
$383$	−17.2784	+	4.62973i	−0.882883	+	0.236568i	−0.671651	−	0.740868i	$-0.734414\pi$
$383$	−17.2784	+	4.62973i	−0.882883	+	0.236568i	−0.211233	+	0.977436i	$0.567748\pi$
$384$	1.00000			0.0510310
$385$	7.88307	−	8.65438i	0.401759	−	0.441068i
$386$	21.7909			1.10913
$387$	8.65684	−	2.31959i	0.440052	−	0.117912i
$388$	−0.541831	+	2.02214i	−0.0275073	+	0.102659i
$389$	−4.36130	+	2.51800i	−0.221127	+	0.127667i	−0.606472	−	0.795105i	$-0.707416\pi$
$389$	−4.36130	+	2.51800i	−0.221127	+	0.127667i	0.385345	+	0.922772i	$0.374082\pi$
$390$	4.70608	−	5.09028i	0.238302	−	0.257756i
$391$		−	27.0759i		−	1.36929i
$392$	1.71135	−	6.78758i	0.0864362	−	0.342825i
$393$	−3.62152	+	3.62152i	−0.182681	+	0.182681i
$394$	0.769287	+	0.444148i	0.0387561	+	0.0223759i
$395$	5.05616	+	2.66064i	0.254403	+	0.133871i
$396$	−0.989376	−	1.71365i	−0.0497180	−	0.0861142i
$397$	−3.81880	−	14.2520i	−0.191660	−	0.715285i	−0.993106	−	0.117218i	$-0.962602\pi$
$397$	−3.81880	−	14.2520i	−0.191660	−	0.715285i	0.801446	−	0.598067i	$-0.204064\pi$
$398$	6.80587	+	6.80587i	0.341147	+	0.341147i
$399$	−5.50916	+	9.70753i	−0.275803	+	0.485984i
$400$	2.15321	−	4.51262i	0.107660	−	0.225631i
$401$	4.34686	−	7.52897i	0.217072	−	0.375979i	−0.736840	−	0.676067i	$-0.763683\pi$
$401$	4.34686	−	7.52897i	0.217072	−	0.375979i	0.953911	+	0.300088i	$0.0970162\pi$
$402$	5.32434	+	1.42665i	0.265554	+	0.0711550i
$403$	5.19226	+	1.39126i	0.258645	+	0.0693037i
$404$	−5.02360	+	8.70112i	−0.249933	+	0.432897i
$405$	1.19306	+	1.89119i	0.0592837	+	0.0939740i
$406$	−20.4187	+	11.9913i	−1.01336	+	0.595118i
$407$	3.87844	+	3.87844i	0.192247	+	0.192247i
$408$	1.19130	+	4.44599i	0.0589781	+	0.220109i
$409$	9.49095	+	16.4388i	0.469297	+	0.812847i	0.999384	−	0.0350966i	$-0.0111739\pi$
$409$	9.49095	+	16.4388i	0.469297	+	0.812847i	−0.530087	+	0.847944i	$0.677841\pi$
$410$	−4.34679	−	14.0025i	−0.214673	−	0.691535i
$411$	10.0306	+	5.79118i	0.494774	+	0.285658i
$412$	3.52695	−	3.52695i	0.173760	−	0.173760i
$413$	−7.81209	+	7.92871i	−0.384408	+	0.390147i
$414$		−	5.88246i		−	0.289107i
$415$	22.1277	+	20.4576i	1.08621	+	1.00423i
$416$	2.68491	−	1.55013i	0.131638	−	0.0760014i
$417$	0.742949	−	2.77273i	0.0363824	−	0.135781i
$418$	−8.06348	+	2.16060i	−0.394398	+	0.105679i
$419$	−11.9171			−0.582188			−0.291094	−	0.956695i	$-0.594019\pi$
$419$	−11.9171			−0.582188			−0.291094	+	0.956695i	$0.594019\pi$
$420$	−4.98010	+	3.19353i	−0.243004	+	0.155828i
$421$	6.95263			0.338850			0.169425	−	0.985543i	$-0.445809\pi$
$421$	6.95263			0.338850			0.169425	+	0.985543i	$0.445809\pi$
$422$	−10.8830	+	2.91610i	−0.529778	+	0.141953i
$423$	1.57366	−	5.87298i	0.0765140	−	0.285554i
$424$	9.90187	−	5.71685i	0.480877	−	0.277635i
$425$	22.6281	+	4.19725i	1.09763	+	0.203597i
$426$		−	3.86002i		−	0.187018i
$427$	7.40388	−	28.4738i	0.358299	−	1.37795i
$428$	−4.27775	+	4.27775i	−0.206773	+	0.206773i
$429$	−5.31277	−	3.06733i	−0.256503	−	0.148092i
$430$	9.33225	−	17.7346i	0.450041	−	0.855238i
$431$	−3.12392	−	5.41078i	−0.150474	−	0.260628i	0.780928	−	0.624621i	$-0.214747\pi$
$431$	−3.12392	−	5.41078i	−0.150474	−	0.260628i	−0.931402	+	0.363993i	$0.881413\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	−15.1544	−	15.1544i	−0.728274	−	0.728274i	0.242002	−	0.970276i	$-0.422196\pi$
$433$	−15.1544	−	15.1544i	−0.728274	−	0.728274i	−0.970276	+	0.242002i	$0.922196\pi$
$434$	−3.98966	−	2.26419i	−0.191510	−	0.108684i
$435$	19.5189	+	4.41816i	0.935861	+	0.211835i
$436$	4.87449	−	8.44287i	0.233446	−	0.404340i
$437$	−23.9712	−	6.42307i	−1.14670	−	0.307257i
$438$	−14.7013	−	3.93920i	−0.702455	−	0.188222i
$439$	−16.3729	+	28.3588i	−0.781438	+	1.35349i	0.149666	+	0.988737i	$0.452180\pi$
$439$	−16.3729	+	28.3588i	−0.781438	+	1.35349i	−0.931104	+	0.364753i	$0.881153\pi$
$440$	−4.31545	−	0.976815i	−0.205731	−	0.0465678i
$441$	6.99923	−	0.103719i	0.333297	−	0.00493899i
$442$	10.0904	+	10.0904i	0.479951	+	0.479951i
$443$	7.95895	+	29.7032i	0.378141	+	1.41124i	0.848701	+	0.528874i	$0.177385\pi$
$443$	7.95895	+	29.7032i	0.378141	+	1.41124i	−0.470559	+	0.882368i	$0.655948\pi$
$444$	−1.38596	−	2.40055i	−0.0657747	−	0.113925i
$445$	6.44752	−	12.2526i	0.305642	−	0.580828i
$446$	16.1321	+	9.31386i	0.763876	+	0.441024i
$447$	−11.0165	+	11.0165i	−0.521061	+	0.521061i
$448$	−2.55046	+	0.703686i	−0.120498	+	0.0332460i
$449$			16.8713i			0.796207i	0.917341	+	0.398103i	$0.130331\pi$
$449$			16.8713i			0.796207i	−0.917341	+	0.398103i	$0.869669\pi$
$450$	4.91614	+	0.911886i	0.231749	+	0.0429867i
$451$	−11.2362	+	6.48725i	−0.529094	+	0.305473i
$452$	2.20532	−	8.23036i	0.103729	−	0.387123i
$453$	−20.4685	+	5.48452i	−0.961695	+	0.257685i
$454$	−26.9142			−1.26314
$455$	−8.42071	+	16.2941i	−0.394769	+	0.763881i
$456$	4.21878			0.197563
$457$	−19.1714	+	5.13696i	−0.896800	+	0.240297i	−0.677641	−	0.735393i	$-0.736998\pi$
$457$	−19.1714	+	5.13696i	−0.896800	+	0.240297i	−0.219158	+	0.975689i	$0.570331\pi$
$458$	−6.95976	+	25.9742i	−0.325208	+	1.21369i
$459$	−3.98616	+	2.30141i	−0.186058	+	0.107421i
$460$	−9.65833	−	8.92936i	−0.450322	−	0.416333i
$461$			15.7775i			0.734830i	0.930057	+	0.367415i	$0.119757\pi$
$461$			15.7775i			0.734830i	−0.930057	+	0.367415i	$0.880243\pi$
$462$	3.72923	+	3.67438i	0.173500	+	0.170948i
$463$	4.48617	−	4.48617i	0.208490	−	0.208490i	−0.595135	−	0.803625i	$-0.702902\pi$
$463$	4.48617	−	4.48617i	0.208490	−	0.208490i	0.803625	+	0.595135i	$0.202902\pi$
$464$	7.75089	+	4.47498i	0.359826	+	0.207746i
$465$	1.14943	+	3.70272i	0.0533037	+	0.171710i
$466$	0.460622	+	0.797821i	0.0213379	+	0.0369583i
$467$	−4.51639	−	16.8554i	−0.208994	−	0.779975i	−0.988195	−	0.153201i	$-0.951042\pi$
$467$	−4.51639	−	16.8554i	−0.208994	−	0.779975i	0.779201	−	0.626774i	$-0.215625\pi$
$468$	2.19222	+	2.19222i	0.101335	+	0.101335i
$469$	−14.5834	+	0.108047i	−0.673400	+	0.00498914i
$470$	−7.25401	−	11.4987i	−0.334602	−	0.530397i
$471$	7.59167	−	13.1492i	0.349806	−	0.605881i
$472$	4.06367	+	1.08886i	0.187046	+	0.0501187i
$473$	−17.1297	−	4.58990i	−0.787626	−	0.211044i
$474$	−1.27757	+	2.21282i	−0.0586808	+	0.101638i
$475$	9.08391	−	19.0378i	0.416799	−	0.873512i
$476$	−6.16693	−	10.5010i	−0.282661	−	0.481312i
$477$	8.08484	+	8.08484i	0.370180	+	0.370180i
$478$	−6.55929	−	24.4796i	−0.300015	−	1.11967i
$479$	−15.8748	−	27.4960i	−0.725339	−	1.25632i	−0.958834	−	0.283966i	$-0.908350\pi$
$479$	−15.8748	−	27.4960i	−0.725339	−	1.25632i	0.233495	−	0.972358i	$-0.424984\pi$
$480$	1.97882	+	1.04129i	0.0903202	+	0.0475281i
$481$	−7.44233	−	4.29683i	−0.339341	−	0.195919i
$482$	−14.9341	+	14.9341i	−0.680230	+	0.680230i
$483$	4.13940	+	15.0030i	0.188349	+	0.682658i
$484$		−	7.08454i		−	0.322024i
$485$	−3.17782	+	3.43725i	−0.144297	+	0.156077i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−7.74077	+	28.8890i	−0.350768	+	1.30908i	0.534960	+	0.844878i	$0.320327\pi$
$487$	−7.74077	+	28.8890i	−0.350768	+	1.30908i	−0.885727	+	0.464206i	$0.846340\pi$
$488$	−10.7411	+	2.87806i	−0.486225	+	0.130284i
$489$	22.3230			1.00948
$490$	10.4543	−	11.6494i	0.472276	−	0.526265i
$491$	1.57179			0.0709340			0.0354670	−	0.999371i	$-0.488708\pi$
$491$	1.57179			0.0709340			0.0354670	+	0.999371i	$0.488708\pi$
$492$	6.33349	−	1.69705i	0.285536	−	0.0765090i
$493$	−10.6621	+	39.7914i	−0.480196	+	1.79211i
$494$	11.3270	−	6.53967i	0.509628	−	0.294234i
$495$	−0.173391	−	4.42123i	−0.00779336	−	0.198719i
$496$			1.73386i			0.0778527i
$497$	2.71624	+	9.84480i	0.121840	+	0.441600i
$498$	−9.52969	+	9.52969i	−0.427036	+	0.427036i
$499$	−12.3491	−	7.12977i	−0.552823	−	0.319172i	0.197437	−	0.980316i	$-0.436738\pi$
$499$	−12.3491	−	7.12977i	−0.552823	−	0.319172i	−0.750260	+	0.661143i	$0.770072\pi$
$500$	8.95974	−	6.68753i	0.400692	−	0.299076i
$501$	4.88769	+	8.46573i	0.218366	+	0.378221i
$502$	−0.700423	−	2.61401i	−0.0312614	−	0.116669i
$503$	−28.7896	−	28.7896i	−1.28367	−	1.28367i	−0.938566	−	0.345100i	$-0.887845\pi$
$503$	−28.7896	−	28.7896i	−1.28367	−	1.28367i	−0.345100	−	0.938566i	$-0.612155\pi$
$504$	−1.33981	−	2.28142i	−0.0596801	−	0.101623i
$505$	−19.0012	+	11.9869i	−0.845540	+	0.533411i
$506$	−5.81997	+	10.0805i	−0.258729	+	0.448132i
$507$	−3.27292	−	0.876975i	−0.145355	−	0.0389478i
$508$	−12.1955	−	3.26776i	−0.541086	−	0.144984i
$509$	−7.30942	+	12.6603i	−0.323984	+	0.561157i	−0.981306	−	0.192453i	$-0.938356\pi$
$509$	−7.30942	+	12.6603i	−0.323984	+	0.561157i	0.657322	+	0.753610i	$0.271689\pi$
$510$	−2.27219	+	10.0383i	−0.100614	+	0.444502i
$511$	40.2670	−	0.298333i	1.78131	−	0.0131975i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.09190	+	4.07503i	0.0482086	+	0.179917i
$514$	12.0110	+	20.8037i	0.529784	+	0.917612i
$515$	10.6518	−	3.30662i	0.469373	−	0.145707i
$516$	7.76151	+	4.48111i	0.341681	+	0.197270i
$517$	−8.50729	+	8.50729i	−0.374150	+	0.374150i
$518$	5.22406	+	5.14722i	0.229532	+	0.226156i
$519$			4.52762i			0.198740i
$520$	6.92707	−	0.271665i	0.303772	−	0.0119133i
$521$	−13.3153	+	7.68757i	−0.583352	+	0.336798i	−0.762464	−	0.647030i	$-0.776011\pi$
$521$	−13.3153	+	7.68757i	−0.583352	+	0.336798i	0.179112	+	0.983829i	$0.442677\pi$
$522$	−2.31642	+	8.64500i	−0.101387	+	0.378381i
$523$	22.6178	−	6.06041i	0.989006	−	0.265003i	0.272173	−	0.962248i	$-0.412258\pi$
$523$	22.6178	−	6.06041i	0.989006	−	0.265003i	0.716833	+	0.697245i	$0.245591\pi$
$524$	−5.12160			−0.223738
$525$	−13.1801	+	1.13369i	−0.575226	+	0.0494784i
$526$	0.850325			0.0370759
$527$	−7.70872	+	2.06555i	−0.335797	+	0.0899766i
$528$	0.512139	−	1.91133i	0.0222880	−	0.0831799i
$529$	−10.0488	+	5.80167i	−0.436904	+	0.252247i
$530$	25.5469	−	1.00190i	1.10969	−	0.0435195i
$531$			4.20702i			0.182569i
$532$	−10.7598	+	2.96870i	−0.466498	+	0.128709i
$533$	14.3742	−	14.3742i	0.622614	−	0.622614i
$534$	5.36231	+	3.09593i	0.232050	+	0.133974i
$535$	−12.9192	+	4.01051i	−0.558548	+	0.173390i
$536$	2.75608	+	4.77368i	0.119045	+	0.206191i
$537$	−0.535206	−	1.99742i	−0.0230959	−	0.0861949i
$538$	8.23314	+	8.23314i	0.354956	+	0.354956i
$539$	−12.0969	−	6.74714i	−0.521048	−	0.290620i
$540$	−0.493652	+	2.18090i	−0.0212434	+	0.0938508i
$541$	−3.98437	+	6.90113i	−0.171301	+	0.296703i	−0.938875	−	0.344258i	$-0.888131\pi$
$541$	−3.98437	+	6.90113i	−0.171301	+	0.296703i	0.767574	+	0.640961i	$0.221464\pi$
$542$	22.5493	+	6.04206i	0.968575	+	0.259529i
$543$	5.92305	+	1.58708i	0.254182	+	0.0681080i
$544$	−2.30141	+	3.98616i	−0.0986722	+	0.170905i
$545$	18.4372	−	11.6311i	0.789763	−	0.498224i
$546$	−7.13378	−	4.04852i	−0.305298	−	0.173261i
$547$	−5.88082	−	5.88082i	−0.251446	−	0.251446i	0.570117	−	0.821563i	$-0.306898\pi$
$547$	−5.88082	−	5.88082i	−0.251446	−	0.251446i	−0.821563	+	0.570117i	$0.806898\pi$
$548$	2.99773	+	11.1877i	0.128057	+	0.477915i
$549$	−5.55999	−	9.63018i	−0.237294	−	0.411006i
$550$	−7.52235	−	6.42657i	−0.320754	−	0.274030i
$551$	32.6994	+	18.8790i	1.39304	+	0.804272i
$552$	4.15953	−	4.15953i	0.177041	−	0.177041i
$553$	1.70126	−	6.54271i	0.0723450	−	0.278224i
$554$			9.44974i			0.401481i
$555$	−0.242893	−	6.19343i	−0.0103103	−	0.262897i
$556$	2.48596	−	1.43527i	0.105428	−	0.0608689i
$557$	6.78443	−	25.3198i	0.287466	−	1.07284i	−0.659553	−	0.751658i	$-0.729254\pi$
$557$	6.78443	−	25.3198i	0.287466	−	1.07284i	0.947019	−	0.321178i	$-0.104079\pi$
$558$	−1.67478	+	0.448756i	−0.0708991	+	0.0189974i
$559$	27.7852			1.17519
$560$	−5.77963	−	1.26329i	−0.244234	−	0.0533840i
$561$	9.10785			0.384534
$562$	11.3322	−	3.03646i	0.478020	−	0.128085i
$563$	0.226316	−	0.844624i	0.00953810	−	0.0355967i	−0.960993	−	0.276573i	$-0.910801\pi$
$563$	0.226316	−	0.844624i	0.00953810	−	0.0355967i	0.970531	+	0.240977i	$0.0774678\pi$
$564$	5.26557	−	3.04008i	0.221721	−	0.128010i
$565$	12.9341	−	13.9900i	0.544141	−	0.588564i
$566$			3.64779i			0.153328i
$567$	1.85692	−	1.88464i	0.0779832	−	0.0791473i
$568$	2.72944	−	2.72944i	0.114525	−	0.114525i
$569$	−28.5877	−	16.5051i	−1.19846	−	0.691929i	−0.238246	−	0.971205i	$-0.576572\pi$
$569$	−28.5877	−	16.5051i	−1.19846	−	0.691929i	−0.960211	+	0.279275i	$0.909906\pi$
$570$	8.34821	+	4.39297i	0.349668	+	0.184001i
$571$	−2.39594	−	4.14989i	−0.100267	−	0.173668i	0.811528	−	0.584314i	$-0.198636\pi$
$571$	−2.39594	−	4.14989i	−0.100267	−	0.173668i	−0.911795	+	0.410646i	$0.865303\pi$
$572$	−1.58776	−	5.92562i	−0.0663878	−	0.247763i
$573$	−11.4312	−	11.4312i	−0.477544	−	0.477544i
$574$	−14.9591	+	8.78504i	−0.624380	+	0.366680i
$575$	−9.81403	−	27.7267i	−0.409273	−	1.15628i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	31.5375	+	8.45046i	1.31293	+	0.351797i	0.846323	−	0.532670i	$-0.178811\pi$
$577$	31.5375	+	8.45046i	1.31293	+	0.351797i	0.466602	+	0.884467i	$0.345478\pi$
$578$	−4.04335	−	1.08341i	−0.168181	−	0.0450640i
$579$	−10.8955	+	18.8715i	−0.452800	+	0.784272i
$580$	10.6779	+	16.9261i	0.443374	+	0.702817i
$581$	17.5992	−	31.0110i	0.730136	−	1.28655i
$582$	−1.48031	−	1.48031i	−0.0613609	−	0.0613609i
$583$	−5.85564	−	21.8535i	−0.242516	−	0.905081i
$584$	−7.60995	−	13.1808i	−0.314902	−	0.545426i
$585$	2.05527	+	6.62073i	0.0849748	+	0.273733i
$586$	−10.5616	−	6.09777i	−0.436297	−	0.251896i
$587$	−6.03856	+	6.03856i	−0.249238	+	0.249238i	−0.820658	−	0.571420i	$-0.806393\pi$
$587$	−6.03856	+	6.03856i	−0.249238	+	0.249238i	0.571420	+	0.820658i	$0.306393\pi$
$588$	5.02254	+	4.87586i	0.207126	+	0.201077i
$589$			7.31479i			0.301401i
$590$	6.90745	+	6.38610i	0.284375	+	0.262912i
$591$	−0.769287	+	0.444148i	−0.0316442	+	0.0182698i
$592$	0.717425	−	2.67747i	0.0294860	−	0.110043i
$593$	3.93171	−	1.05350i	0.161456	−	0.0432620i	−0.177186	−	0.984177i	$-0.556699\pi$
$593$	3.93171	−	1.05350i	0.161456	−	0.0432620i	0.338642	+	0.940915i	$0.390033\pi$
$594$	1.97875			0.0811892
$595$	−1.26867	−	27.2011i	−0.0520103	−	1.11514i
$596$	−15.5796			−0.638167
$597$	−9.29699	+	2.49112i	−0.380501	+	0.101955i
$598$	4.72013	−	17.6158i	0.193020	−	0.720362i
$599$	29.5547	−	17.0634i	1.20757	−	0.697193i	0.245345	−	0.969436i	$-0.421099\pi$
$599$	29.5547	−	17.0634i	1.20757	−	0.697193i	0.962229	+	0.272243i	$0.0877654\pi$
$600$	2.83144	+	4.12104i	0.115593	+	0.168241i
$601$			9.99405i			0.407666i	0.979006	+	0.203833i	$0.0653399\pi$
$601$			9.99405i			0.407666i	−0.979006	+	0.203833i	$0.934660\pi$
$602$	−22.9487	−	5.96721i	−0.935318	−	0.243205i
$603$	−3.89769	+	3.89769i	−0.158726	+	0.158726i
$604$	−18.3516	−	10.5953i	−0.746715	−	0.431116i
$605$	7.37705	−	14.0190i	0.299920	−	0.569954i
$606$	−5.02360	−	8.70112i	−0.204070	−	0.353459i
$607$	4.73109	+	17.6567i	0.192029	+	0.716662i	0.993016	+	0.117980i	$0.0376419\pi$
$607$	4.73109	+	17.6567i	0.192029	+	0.716662i	−0.800987	+	0.598682i	$0.795691\pi$
$608$	2.98313	+	2.98313i	0.120982	+	0.120982i
$609$	−0.175433	−	23.6787i	−0.00710890	−	0.959510i
$610$	−24.2515	−	5.48939i	−0.981915	−	0.222259i
$611$	9.42504	−	16.3247i	0.381296	−	0.660425i
$612$	−4.44599	−	1.19130i	−0.179718	−	0.0481554i
$613$	28.8155	+	7.72109i	1.16385	+	0.311852i	0.788501	−	0.615033i	$-0.210857\pi$
$613$	28.8155	+	7.72109i	1.16385	+	0.311852i	0.375346	+	0.926885i	$0.377524\pi$
$614$	11.3090	−	19.5877i	0.456392	−	0.790495i
$615$	14.2999	+	3.23683i	0.576629	+	0.130521i
$616$	0.0387866	+	5.23514i	0.00156276	+	0.210930i
$617$	−35.0246	−	35.0246i	−1.41004	−	1.41004i	−0.759317	−	0.650721i	$-0.774467\pi$
$617$	−35.0246	−	35.0246i	−1.41004	−	1.41004i	−0.650721	−	0.759317i	$-0.725533\pi$
$618$	1.29095	+	4.81790i	0.0519298	+	0.193805i
$619$	5.75770	+	9.97263i	0.231422	+	0.400834i	0.958227	−	0.286010i	$-0.0923290\pi$
$619$	5.75770	+	9.97263i	0.231422	+	0.400834i	−0.726805	+	0.686844i	$0.758996\pi$
$620$	−1.80545	+	3.43099i	−0.0725086	+	0.137792i
$621$	5.09436	+	2.94123i	0.204430	+	0.118028i
$622$	−5.47479	+	5.47479i	−0.219519	+	0.219519i
$623$	−15.8549	−	4.12266i	−0.635214	−	0.165171i
$624$			3.10026i			0.124110i
$625$	24.6933	−	3.90374i	0.987733	−	0.156150i
$626$	−17.3597	+	10.0226i	−0.693834	+	0.400585i
$627$	2.16060	−	8.06348i	0.0862862	−	0.322024i
$628$	14.6660	−	3.92974i	0.585237	−	0.156814i
$629$	12.7586			0.508720
$630$	−0.275628	−	5.90966i	−0.0109813	−	0.235446i
$631$	18.4477			0.734390			0.367195	−	0.930144i	$-0.380318\pi$
$631$	18.4477			0.734390			0.367195	+	0.930144i	$0.380318\pi$
$632$	−2.46808	+	0.661320i	−0.0981749	+	0.0263059i
$633$	2.91610	−	10.8830i	0.115905	−	0.432562i
$634$	−2.58104	+	1.49016i	−0.102506	+	0.0591819i
$635$	−20.7299	−	19.1653i	−0.822641	−	0.760552i
$636$			11.4337i			0.453375i
$637$	21.0433	+	5.30563i	0.833765	+	0.210217i
$638$	12.5227	−	12.5227i	0.495778	−	0.495778i
$639$	3.34287	+	1.93001i	0.132242	+	0.0763499i
$640$	0.662933	+	2.13554i	0.0262047	+	0.0844145i
$641$	9.74229	+	16.8741i	0.384797	+	0.666488i	0.991741	−	0.128256i	$-0.0409380\pi$
$641$	9.74229	+	16.8741i	0.384797	+	0.666488i	−0.606944	+	0.794745i	$0.707605\pi$
$642$	−1.56576	−	5.84351i	−0.0617958	−	0.230625i
$643$	28.2707	+	28.2707i	1.11489	+	1.11489i	0.992480	+	0.122408i	$0.0390615\pi$
$643$	28.2707	+	28.2707i	1.11489	+	1.11489i	0.122408	+	0.992480i	$0.460938\pi$
$644$	−7.68169	+	13.5357i	−0.302701	+	0.533381i
$645$	10.6925	+	16.9493i	0.421016	+	0.667377i
$646$	−9.70916	+	16.8168i	−0.382002	+	0.661647i
$647$	−24.0797	−	6.45214i	−0.946672	−	0.253660i	−0.247722	−	0.968831i	$-0.579682\pi$
$647$	−24.0797	−	6.45214i	−0.946672	−	0.253660i	−0.698949	+	0.715171i	$0.746349\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	4.16233	−	7.20937i	0.163386	−	0.282992i
$650$	13.9903	+	6.67550i	0.548744	+	0.261835i
$651$	3.95567	−	2.32305i	0.155035	−	0.0910476i
$652$	15.7848	+	15.7848i	0.618179	+	0.618179i
$653$	−12.8743	−	48.0477i	−0.503812	−	1.88025i	−0.473666	−	0.880705i	$-0.657070\pi$
$653$	−12.8743	−	48.0477i	−0.503812	−	1.88025i	−0.0301458	−	0.999546i	$-0.509597\pi$
$654$	4.87449	+	8.44287i	0.190608	+	0.330142i
$655$	−10.1347	−	5.33306i	−0.395996	−	0.208380i
$656$	5.67845	+	3.27845i	0.221706	+	0.128002i
$657$	10.7621	−	10.7621i	0.419869	−	0.419869i
$658$	−11.2903	+	11.4589i	−0.440144	+	0.446714i
$659$		−	39.5644i		−	1.54121i	−0.637312	−	0.770606i	$-0.719954\pi$
$659$		−	39.5644i		−	1.54121i	0.637312	−	0.770606i	$-0.280046\pi$
$660$	3.00367	−	3.24889i	0.116918	−	0.126463i
$661$	−1.74995	+	1.01033i	−0.0680651	+	0.0392974i	−0.533646	−	0.845708i	$-0.679179\pi$
$661$	−1.74995	+	1.01033i	−0.0680651	+	0.0392974i	0.465581	+	0.885005i	$0.345845\pi$
$662$	7.20479	−	26.8886i	0.280022	−	1.04506i
$663$	−13.7837	+	3.69334i	−0.535315	+	0.143437i
$664$	−13.4770			−0.523010
$665$	−24.3830	−	5.32957i	−0.945532	−	0.206672i
$666$	2.77192			0.107410
$667$	50.8539	−	13.6263i	1.96907	−	0.527611i
$668$	−2.53005	+	9.44229i	−0.0978907	+	0.365333i
$669$	−16.1321	+	9.31386i	−0.623702	+	0.360095i
$670$	0.483012	+	12.3161i	0.0186604	+	0.475813i
$671$			22.0037i			0.849442i
$672$	0.665818	−	2.56060i	0.0256845	−	0.0987774i
$673$	−19.7775	+	19.7775i	−0.762366	+	0.762366i	−0.976750	−	0.214383i	$-0.931226\pi$
$673$	−19.7775	+	19.7775i	−0.762366	+	0.762366i	0.214383	+	0.976750i	$0.431226\pi$
$674$	21.0125	+	12.1316i	0.809372	+	0.467291i
$675$	−3.24779	+	3.80156i	−0.125007	+	0.146322i
$676$	−1.69419	−	2.93442i	−0.0651610	−	0.112862i
$677$	−4.44120	−	16.5748i	−0.170689	−	0.637021i	−0.997246	−	0.0741672i	$-0.976370\pi$
$677$	−4.44120	−	16.5748i	−0.170689	−	0.637021i	0.826557	−	0.562854i	$-0.190297\pi$
$678$	6.02504	+	6.02504i	0.231390	+	0.231390i
$679$	4.81714	+	2.73379i	0.184865	+	0.104913i
$680$	−8.70482	+	5.49145i	−0.333815	+	0.210588i
$681$	13.4571	−	23.3083i	0.515676	−	0.893177i
$682$	3.31398	+	0.887978i	0.126899	+	0.0340024i
$683$	−0.487181	−	0.130540i	−0.0186414	−	0.00499496i	0.249486	−	0.968378i	$-0.419738\pi$
$683$	−0.487181	−	0.130540i	−0.0186414	−	0.00499496i	−0.268128	+	0.963383i	$0.586405\pi$
$684$	−2.10939	+	3.65357i	−0.0806546	+	0.139698i
$685$	−5.71765	+	25.2599i	−0.218460	+	0.965131i
$686$	−16.2409	−	8.90138i	−0.620079	−	0.339856i
$687$	−19.0144	−	19.0144i	−0.725445	−	0.725445i
$688$	2.31959	+	8.65684i	0.0884336	+	0.330039i
$689$	17.7237	+	30.6984i	0.675220	+	1.16952i
$690$	12.5622	−	3.89968i	0.478235	−	0.148458i
$691$	13.5396	+	7.81710i	0.515071	+	0.297376i	0.734916	−	0.678158i	$-0.237222\pi$
$691$	13.5396	+	7.81710i	0.515071	+	0.297376i	−0.219845	+	0.975535i	$0.570555\pi$
$692$	−3.20151	+	3.20151i	−0.121703	+	0.121703i
$693$	−5.04672	+	1.39242i	−0.191709	+	0.0528937i
$694$		−	25.0428i		−	0.950613i
$695$	6.41378	−	0.251535i	0.243289	−	0.00954127i
$696$	−7.75089	+	4.47498i	−0.293797	+	0.169624i
$697$	−7.81123	+	29.1519i	−0.295871	+	1.10421i
$698$	−17.3992	+	4.66210i	−0.658569	+	0.176463i
$699$	−0.921244			−0.0348447
$700$	−10.1214	−	8.51809i	−0.382552	−	0.321953i
$701$	8.02724			0.303185			0.151592	−	0.988443i	$-0.451560\pi$
$701$	8.02724			0.303185			0.151592	+	0.988443i	$0.451560\pi$
$702$	−2.99462	+	0.802407i	−0.113025	+	0.0302849i
$703$	3.02666	−	11.2956i	0.114153	−	0.426023i
$704$	1.71365	−	0.989376i	0.0645856	−	0.0372885i
$705$	13.5852	−	0.532783i	0.511648	−	0.0200658i
$706$			7.59800i			0.285955i
$707$	18.9353	+	18.6568i	0.712136	+	0.701661i
$708$	−2.97481	+	2.97481i	−0.111800	+	0.111800i
$709$	−11.8457	−	6.83914i	−0.444876	−	0.256849i	0.260788	−	0.965396i	$-0.416018\pi$
$709$	−11.8457	−	6.83914i	−0.444876	−	0.256849i	−0.705664	+	0.708547i	$0.749351\pi$
$710$	8.24321	−	2.55893i	0.309362	−	0.0960350i
$711$	−1.27757	−	2.21282i	−0.0479127	−	0.0829872i
$712$	1.60257	+	5.98088i	0.0600590	+	0.224143i
$713$	7.21204	+	7.21204i	0.270093	+	0.270093i
$714$	12.1776	−	0.0902224i	0.455735	−	0.00337649i
$715$	3.02838	−	13.3790i	0.113255	−	0.500348i
$716$	1.03394	−	1.79084i	0.0386401	−	0.0669267i
$717$	24.4796	+	6.55929i	0.914208	+	0.244961i
$718$	−3.17473	−	0.850665i	−0.118480	−	0.0317465i
$719$	10.5235	−	18.2273i	0.392462	−	0.679764i	−0.600312	−	0.799766i	$-0.704957\pi$
$719$	10.5235	−	18.2273i	0.392462	−	0.679764i	0.992774	+	0.120002i	$0.0382901\pi$
$720$	−1.89119	+	1.19306i	−0.0704805	+	0.0444628i
$721$	−6.68281	−	11.3794i	−0.248881	−	0.423792i
$722$	−0.849839	−	0.849839i	−0.0316277	−	0.0316277i
$723$	−5.46626	−	20.4004i	−0.203292	−	0.758698i
$724$	3.06600	+	5.31046i	0.113947	+	0.197362i
$725$	3.50460	+	44.6124i	0.130157	+	1.65686i
$726$	6.13539	+	3.54227i	0.227706	+	0.131466i
$727$	11.2251	−	11.2251i	0.416317	−	0.416317i	−0.467615	−	0.883932i	$-0.654887\pi$
$727$	11.2251	−	11.2251i	0.416317	−	0.416317i	0.883932	+	0.467615i	$0.154887\pi$
$728$	−2.18161	−	7.90708i	−0.0808559	−	0.293056i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.33367	−	34.0066i	−0.0493612	−	1.25864i
$731$	−35.7248	+	20.6258i	−1.32133	+	0.762871i
$732$	2.87806	−	10.7411i	0.106376	−	0.397001i
$733$	27.7719	−	7.44145i	1.02578	−	0.274856i	0.293570	−	0.955938i	$-0.405157\pi$
$733$	27.7719	−	7.44145i	1.02578	−	0.274856i	0.732208	+	0.681081i	$0.238490\pi$
$734$	3.24759			0.119871
$735$	4.86152	+	14.8784i	0.179320	+	0.548797i
$736$	5.88246			0.216830
$737$	10.5356	−	2.82300i	0.388082	−	0.103986i
$738$	−1.69705	+	6.33349i	−0.0624694	+	0.233139i
$739$	−36.3593	+	20.9921i	−1.33750	+	0.772205i	−0.986436	−	0.164147i	$-0.947513\pi$
$739$	−36.3593	+	20.9921i	−1.33750	+	0.772205i	−0.351063	+	0.936352i	$0.614180\pi$
$740$	4.20767	−	4.55117i	0.154677	−	0.167304i
$741$			13.0793i			0.480482i
$742$	−8.04573	−	29.1611i	−0.295368	−	1.07054i
$743$	8.63799	−	8.63799i	0.316897	−	0.316897i	−0.530677	−	0.847574i	$-0.678062\pi$
$743$	8.63799	−	8.63799i	0.316897	−	0.316897i	0.847574	+	0.530677i	$0.178062\pi$
$744$	−1.50157	−	0.866930i	−0.0550501	−	0.0317832i
$745$	−30.8293	−	16.2229i	−1.12950	−	0.594361i
$746$	7.88312	+	13.6540i	0.288622	+	0.499907i
$747$	−3.48811	−	13.0178i	−0.127623	−	0.476297i
$748$	6.44022	+	6.44022i	0.235478	+	0.235478i
$749$	8.10541	+	13.8018i	0.296165	+	0.504307i
$750$	1.31171	+	11.1031i	0.0478968	+	0.405429i
$751$	−15.8723	+	27.4916i	−0.579188	+	1.00318i	0.416384	+	0.909189i	$0.363297\pi$
$751$	−15.8723	+	27.4916i	−0.579188	+	1.00318i	−0.995573	+	0.0939948i	$0.970036\pi$
$752$	5.87298	+	1.57366i	0.214166	+	0.0573855i
$753$	2.61401	+	0.700423i	0.0952600	+	0.0255248i
$754$	−13.8736	+	24.0298i	−0.505247	+	0.875114i
$755$	−25.2817	−	40.0754i	−0.920094	−	1.45849i
$756$	2.64568	−	0.0196015i	0.0962224	−	0.000712901i
$757$	−9.81959	−	9.81959i	−0.356899	−	0.356899i	0.505770	−	0.862669i	$-0.331209\pi$
$757$	−9.81959	−	9.81959i	−0.356899	−	0.356899i	−0.862669	+	0.505770i	$0.831209\pi$
$758$	−5.62744	−	21.0019i	−0.204398	−	0.762824i
$759$	−5.81997	−	10.0805i	−0.211251	−	0.365898i
$760$	2.79677	+	9.00937i	0.101450	+	0.326804i
$761$	27.6636	+	15.9716i	1.00280	+	0.578970i	0.909077	−	0.416628i	$-0.136788\pi$
$761$	27.6636	+	15.9716i	1.00280	+	0.578970i	0.0937278	+	0.995598i	$0.470122\pi$
$762$	8.92770	−	8.92770i	0.323416	−	0.323416i
$763$	−18.3733	−	18.1031i	−0.665158	−	0.655375i
$764$		−	16.1661i		−	0.584869i
$765$	−7.55731	−	6.98692i	−0.273235	−	0.252612i
$766$	15.4914	−	8.94394i	0.559726	−	0.323158i
$767$	−3.37574	+	12.5985i	−0.121891	+	0.454904i
$768$	−0.965926	+	0.258819i	−0.0348548	+	0.00933933i
$769$	26.3715			0.950981			0.475490	−	0.879721i	$-0.342271\pi$
$769$	26.3715			0.950981			0.475490	+	0.879721i	$0.342271\pi$
$770$	−5.37454	+	10.3998i	−0.193685	+	0.374782i
$771$	−24.0221			−0.865133
$772$	−21.0484	+	5.63991i	−0.757549	+	0.202985i
$773$	−11.9120	+	44.4561i	−0.428444	+	1.59898i	0.327841	+	0.944733i	$0.393679\pi$
$773$	−11.9120	+	44.4561i	−0.428444	+	1.59898i	−0.756285	+	0.654242i	$0.772988\pi$
$774$	−7.76151	+	4.48111i	−0.278982	+	0.161070i
$775$	−7.14531	+	4.90932i	−0.256667	+	0.176348i
$776$		−	2.09348i		−	0.0751514i
$777$	−7.06965	+	1.95056i	−0.253622	+	0.0699759i
$778$	3.56098	−	3.56098i	0.127667	−	0.127667i
$779$	23.9561	+	13.8311i	0.858318	+	0.495550i
$780$	−3.22827	+	6.13485i	−0.115591	+	0.219663i
$781$	−3.81901	−	6.61472i	−0.136655	−	0.236693i
$782$	7.00777	+	26.1533i	0.250597	+	0.935241i
$783$	−6.32858	−	6.32858i	−0.226165	−	0.226165i
$784$	0.103719	+	6.99923i	0.00370424	+	0.249973i
$785$	33.1133	+	7.49528i	1.18186	+	0.267518i
$786$	2.56080	−	4.43543i	0.0913407	−	0.158207i
$787$	−10.9433	−	2.93226i	−0.390088	−	0.104524i	0.0584437	−	0.998291i	$-0.481386\pi$
$787$	−10.9433	−	2.93226i	−0.390088	−	0.104524i	−0.448532	+	0.893767i	$0.648053\pi$
$788$	−0.858028	−	0.229908i	−0.0305660	−	0.00819013i
$789$	−0.425163	+	0.736403i	−0.0151362	+	0.0262167i
$790$	−5.57250	−	1.26135i	−0.198261	−	0.0448768i
$791$	−19.6063	−	11.1269i	−0.697121	−	0.395626i
$792$	1.39919	+	1.39919i	0.0497180	+	0.0497180i
$793$	−8.92274	−	33.3001i	−0.316856	−	1.18252i
$794$	7.37735	+	12.7780i	0.261813	+	0.453473i
$795$	−11.9058	+	22.6252i	−0.422254	+	0.802433i
$796$	−8.33546	−	4.81248i	−0.295442	−	0.170574i
$797$	−24.7239	+	24.7239i	−0.875767	+	0.875767i	−0.993093	−	0.117327i	$-0.962568\pi$
$797$	−24.7239	+	24.7239i	−0.875767	+	0.875767i	0.117327	+	0.993093i	$0.462568\pi$
$798$	2.80894	−	10.8026i	0.0994356	−	0.382409i
$799$			27.9859i			0.990070i
$800$	−0.911886	+	4.91614i	−0.0322401	+	0.173812i
$801$	−5.36231	+	3.09593i	−0.189468	+	0.109389i
$802$	−2.25010	+	8.39748i	−0.0794537	+	0.296525i
$803$	−29.0902	+	7.79470i	−1.02657	+	0.275069i
$804$	−5.51217			−0.194399
$805$	−29.2952	+	18.7858i	−1.03252	+	0.662113i
$806$	−5.37542			−0.189341
$807$	−11.2467	+	3.01354i	−0.395902	+	0.106082i
$808$	2.60040	−	9.70484i	0.0914819	−	0.341415i
$809$	−5.02215	+	2.89954i	−0.176569	+	0.101942i	−0.585680	−	0.810542i	$-0.699172\pi$
$809$	−5.02215	+	2.89954i	−0.176569	+	0.101942i	0.409110	+	0.912485i	$0.365839\pi$
$810$	−1.64189	−	1.51796i	−0.0576900	−	0.0533358i
$811$		−	28.8064i		−	1.01153i	−0.862671	−	0.505765i	$-0.831210\pi$
$811$		−	28.8064i		−	1.01153i	0.862671	−	0.505765i	$-0.168790\pi$
$812$	16.6193	−	16.8674i	0.583224	−	0.591931i
$813$	−16.5072	+	16.5072i	−0.578934	+	0.578934i
$814$	−4.75009	−	2.74247i	−0.166491	−	0.0961235i
$815$	14.7987	+	47.6717i	0.518375	+	1.66987i
$816$	−2.30141	−	3.98616i	−0.0805655	−	0.139544i
$817$	9.78586	+	36.5213i	0.342364	+	1.27772i
$818$	−13.4222	−	13.4222i	−0.469297	−	0.469297i
$819$	7.07301	−	4.15378i	0.247151	−	0.145145i
$820$	7.82280	+	12.4004i	0.273184	+	0.433039i
$821$	−2.25899	+	3.91269i	−0.0788395	+	0.136554i	−0.902749	−	0.430167i	$-0.858455\pi$
$821$	−2.25899	+	3.91269i	−0.0788395	+	0.136554i	0.823910	+	0.566721i	$0.191788\pi$
$822$	−11.1877	−	2.99773i	−0.390216	−	0.104558i
$823$	21.6187	+	5.79271i	0.753580	+	0.201921i	0.615105	−	0.788445i	$-0.289113\pi$
$823$	21.6187	+	5.79271i	0.753580	+	0.201921i	0.138474	+	0.990366i	$0.455780\pi$
$824$	−2.49393	+	4.31961i	−0.0868802	+	0.150481i
$825$	9.32675	−	3.30126i	0.324716	−	0.114935i
$826$	5.49380	−	9.68047i	0.191154	−	0.336827i
$827$	22.5410	+	22.5410i	0.783826	+	0.783826i	0.980474	−	0.196648i	$-0.0630057\pi$
$827$	22.5410	+	22.5410i	0.783826	+	0.783826i	−0.196648	+	0.980474i	$0.563006\pi$
$828$	1.52249	+	5.68202i	0.0529103	+	0.197464i
$829$	−3.61347	−	6.25871i	−0.125501	−	0.217374i	0.796428	−	0.604734i	$-0.206720\pi$
$829$	−3.61347	−	6.25871i	−0.125501	−	0.217374i	−0.921929	+	0.387360i	$0.873387\pi$
$830$	−26.6686	−	14.0335i	−0.925679	−	0.487109i
$831$	−8.18372	−	4.72487i	−0.283890	−	0.163904i
$832$	−2.19222	+	2.19222i	−0.0760014	+	0.0760014i
$833$	−30.9949	+	8.79930i	−1.07391	+	0.304878i
$834$			2.87054i			0.0993985i
$835$	−14.8387	+	16.0501i	−0.513513	+	0.555435i
$836$	7.22952	−	4.17397i	0.250038	−	0.144360i
$837$	0.448756	−	1.67478i	0.0155113	−	0.0578889i
$838$	11.5110	−	3.08437i	0.397642	−	0.106548i
$839$	−5.52622			−0.190786			−0.0953932	−	0.995440i	$-0.530411\pi$
$839$	−5.52622			−0.190786			−0.0953932	+	0.995440i	$0.530411\pi$
$840$	3.98386	−	4.37366i	0.137456	−	0.150905i
$841$	−51.1018			−1.76213
$842$	−6.71572	+	1.79947i	−0.231439	+	0.0620139i
$843$	−3.03646	+	11.3322i	−0.104581	+	0.390302i
$844$	9.75746	−	5.63347i	0.335866	−	0.193912i
$845$	−0.296911	−	7.57081i	−0.0102141	−	0.260444i
$846$			6.08016i			0.209040i
$847$	−18.1407	−	4.71702i	−0.623321	−	0.162079i
$848$	−8.08484	+	8.08484i	−0.277635	+	0.277635i
$849$	−3.15908	−	1.82389i	−0.108419	−	0.0625959i
$850$	−22.9434	+	1.80236i	−0.786953	+	0.0618204i
$851$	−8.15284	−	14.1211i	−0.279476	−	0.484066i
$852$	0.999046	+	3.72849i	0.0342267	+	0.127736i
$853$	10.4649	+	10.4649i	0.358313	+	0.358313i	0.863191	−	0.504878i	$-0.168462\pi$
$853$	10.4649	+	10.4649i	0.358313	+	0.358313i	−0.504878	+	0.863191i	$0.668462\pi$
$854$	0.217968	+	29.4199i	0.00745873	+	1.00673i
$855$	−7.97853	+	5.03327i	−0.272860	+	0.172134i
$856$	3.02482	−	5.23915i	0.103386	−	0.179070i
$857$	2.07640	+	0.556370i	0.0709286	+	0.0190053i	0.294109	−	0.955772i	$-0.404977\pi$
$857$	2.07640	+	0.556370i	0.0709286	+	0.0190053i	−0.223180	+	0.974777i	$0.571644\pi$
$858$	5.92562	+	1.58776i	0.202297	+	0.0542054i
$859$	3.59455	−	6.22594i	0.122644	−	0.212426i	−0.798165	−	0.602439i	$-0.794196\pi$
$859$	3.59455	−	6.22594i	0.122644	−	0.212426i	0.920810	+	0.390012i	$0.127529\pi$
$860$	−4.42421	+	19.5457i	−0.150864	+	0.666502i
$861$	−0.128525	−	17.3475i	−0.00438013	−	0.591200i
$862$	4.41788	+	4.41788i	0.150474	+	0.150474i
$863$	10.4926	+	39.1589i	0.357172	+	1.33298i	0.877729	+	0.479157i	$0.159057\pi$
$863$	10.4926	+	39.1589i	0.357172	+	1.33298i	−0.520557	+	0.853827i	$0.674276\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−9.66889	+	3.00151i	−0.328752	+	0.102054i
$866$	18.5603	+	10.7158i	0.630704	+	0.364137i
$867$	2.95994	−	2.95994i	0.100525	−	0.100525i
$868$	4.43973	+	1.15444i	0.150694	+	0.0391841i
$869$			5.05600i			0.171513i
$870$	−19.9973	+	0.784254i	−0.677974	+	0.0265887i
$871$	−14.7997	+	8.54458i	−0.501467	+	0.289522i
$872$	−2.52322	+	9.41680i	−0.0854471	+	0.318893i
$873$	2.02214	−	0.541831i	0.0684391	−	0.0183382i
$874$	24.8168			0.839442
$875$	−11.1586	−	27.3950i	−0.377228	−	0.926120i
$876$	15.2199			0.514233
$877$	49.3516	−	13.2237i	1.66648	−	0.446533i	0.702325	−	0.711857i	$-0.252145\pi$
$877$	49.3516	−	13.2237i	1.66648	−	0.446533i	0.964159	+	0.265324i	$0.0854788\pi$
$878$	8.47526	−	31.6301i	0.286026	−	1.06746i
$879$	10.5616	−	6.09777i	0.356235	−	0.205673i
$880$	4.42123	−	0.173391i	0.149040	−	0.00584502i
$881$		−	27.9972i		−	0.943251i	−0.881799	−	0.471625i	$-0.843667\pi$
$881$		−	27.9972i		−	0.943251i	0.881799	−	0.471625i	$-0.156333\pi$
$882$	−6.73389	+	1.91172i	−0.226742	+	0.0643709i
$883$	4.66131	−	4.66131i	0.156865	−	0.156865i	−0.624311	−	0.781176i	$-0.714620\pi$
$883$	4.66131	−	4.66131i	0.156865	−	0.156865i	0.781176	+	0.624311i	$0.214620\pi$
$884$	−12.3581	−	7.13498i	−0.415650	−	0.239975i
$885$	−8.98425	+	2.78898i	−0.302002	+	0.0937504i
$886$	−15.3755	−	26.6312i	−0.516550	−	0.894692i
$887$	−3.60517	−	13.4547i	−0.121050	−	0.451763i	0.878619	−	0.477524i	$-0.158466\pi$
$887$	−3.60517	−	13.4547i	−0.121050	−	0.451763i	−0.999668	+	0.0257610i	$0.991799\pi$
$888$	1.96004	+	1.96004i	0.0657747	+	0.0657747i
$889$	−16.4874	+	29.0520i	−0.552970	+	0.974372i
$890$	−3.05663	+	13.5038i	−0.102458	+	0.452649i
$891$	−0.989376	+	1.71365i	−0.0331454	+	0.0574094i
$892$	−17.9930	−	4.82121i	−0.602450	−	0.161426i
$893$	24.7768	+	6.63894i	0.829126	+	0.222164i
$894$	7.78982	−	13.4924i	0.260531	−	0.451252i
$895$	3.91075	−	2.46711i	0.130722	−	0.0824663i
$896$	2.28142	−	1.33981i	0.0762170	−	0.0447601i
$897$	12.8956	+	12.8956i	0.430573	+	0.430573i
$898$	−4.36662	−	16.2964i	−0.145716	−	0.543819i
$899$	−7.75899	−	13.4390i	−0.258777	−	0.448215i
$900$	−4.98464	+	0.391577i	−0.166155	+	0.0130526i
$901$	−45.5766	−	26.3136i	−1.51838	−	0.876634i
$902$	9.17435	−	9.17435i	0.305473	−	0.305473i
$903$	16.6421	−	16.8905i	0.553814	−	0.562082i
$904$			8.52069i			0.283394i
$905$	0.537325	+	13.7010i	0.0178613	+	0.455437i
$906$	18.3516	−	10.5953i	0.609690	−	0.352005i
$907$	6.98519	−	26.0691i	0.231939	−	0.865610i	−0.747565	−	0.664188i	$-0.768777\pi$
$907$	6.98519	−	26.0691i	0.231939	−	0.865610i	0.979505	−	0.201421i	$-0.0645560\pi$
$908$	25.9971	−	6.96589i	0.862743	−	0.231171i
$909$	10.0472			0.333244
$910$	3.91655	−	17.9184i	0.129832	−	0.593988i
$911$	−15.5364			−0.514744			−0.257372	−	0.966312i	$-0.582857\pi$
$911$	−15.5364			−0.514744			−0.257372	+	0.966312i	$0.582857\pi$
$912$	−4.07503	+	1.09190i	−0.134938	+	0.0361565i
$913$	−6.90211	+	25.7590i	−0.228426	+	0.852499i
$914$	17.1886	−	9.92384i	0.568548	−	0.328251i
$915$	16.8797	−	18.2577i	0.558026	−	0.603582i
$916$		−	26.8905i		−	0.888486i
$917$	−3.41005	+	13.1144i	−0.112610	+	0.433075i
$918$	3.25469	−	3.25469i	0.107421	−	0.107421i
$919$	−32.7915	−	18.9322i	−1.08169	−	0.624515i	−0.150339	−	0.988634i	$-0.548037\pi$
$919$	−32.7915	−	18.9322i	−1.08169	−	0.624515i	−0.931352	+	0.364120i	$0.881370\pi$
$920$	11.6403	+	6.12534i	0.383770	+	0.201946i
$921$	11.3090	+	19.5877i	0.372643	+	0.645436i
$922$	−4.08351	−	15.2399i	−0.134483	−	0.501898i
$923$	8.46199	+	8.46199i	0.278530	+	0.278530i
$924$	−4.55316	−	2.58398i	−0.149788	−	0.0850068i
$925$	13.0653	−	4.62454i	0.429584	−	0.152054i
$926$	−3.17220	+	5.49441i	−0.104245	+	0.180558i
$927$	−4.81790	−	1.29095i	−0.158241	−	0.0424005i
$928$	−8.64500	−	2.31642i	−0.283786	−	0.0760402i
$929$	−8.75685	+	15.1673i	−0.287303	+	0.497624i	−0.973165	−	0.230108i	$-0.926092\pi$
$929$	−8.75685	+	15.1673i	−0.287303	+	0.497624i	0.685862	+	0.727732i	$0.259425\pi$
$930$	−2.06860	−	3.27906i	−0.0678322	−	0.107525i
$931$	0.437567	+	29.5283i	0.0143407	+	0.967749i
$932$	−0.651418	−	0.651418i	−0.0213379	−	0.0213379i
$933$	−2.00391	−	7.47870i	−0.0656051	−	0.244842i
$934$	8.72500	+	15.1121i	0.285491	+	0.494484i
$935$	6.03790	+	19.4502i	0.197460	+	0.636088i
$936$	−2.68491	−	1.55013i	−0.0877589	−	0.0506676i
$937$	−2.68964	+	2.68964i	−0.0878666	+	0.0878666i	−0.749674	−	0.661807i	$-0.769790\pi$
$937$	−2.68964	+	2.68964i	−0.0878666	+	0.0878666i	0.661807	+	0.749674i	$0.269790\pi$
$938$	14.0585	−	3.87883i	0.459028	−	0.126648i
$939$		−	20.0453i		−	0.654153i
$940$	9.98293	+	9.22946i	0.325607	+	0.301032i
$941$	28.0634	−	16.2024i	0.914839	−	0.528183i	0.0328543	−	0.999460i	$-0.489540\pi$
$941$	28.0634	−	16.2024i	0.914839	−	0.528183i	0.881985	+	0.471277i	$0.156207\pi$
$942$	−3.92974	+	14.6660i	−0.128038	+	0.477844i
$943$	37.2565	−	9.98284i	1.21324	−	0.325086i
$944$	−4.20702			−0.136927
$945$	5.25573	+	2.71613i	0.170969	+	0.0883556i
$946$	17.7340			0.576582
$947$	37.0654	−	9.93164i	1.20446	−	0.322735i	0.399876	−	0.916569i	$-0.369053\pi$
$947$	37.0654	−	9.93164i	1.20446	−	0.322735i	0.804587	+	0.593834i	$0.202386\pi$
$948$	0.661320	−	2.46808i	0.0214787	−	0.0801595i
$949$	40.8640	−	23.5928i	1.32650	−	0.765856i
$950$	−3.84705	+	20.7402i	−0.124815	+	0.672899i
$951$		−	2.98032i		−	0.0966436i
$952$	8.67465	+	8.54706i	0.281147	+	0.277012i
$953$	12.2232	−	12.2232i	0.395949	−	0.395949i	−0.480853	−	0.876801i	$-0.659673\pi$
$953$	12.2232	−	12.2232i	0.395949	−	0.395949i	0.876801	+	0.480853i	$0.159673\pi$
$954$	−9.90187	−	5.71685i	−0.320585	−	0.185090i
$955$	16.8336	−	31.9898i	0.544722	−	1.03517i
$956$	12.6716	+	21.9478i	0.409828	+	0.709843i
$957$	4.58362	+	17.1063i	0.148167	+	0.552969i
$958$	22.4504	+	22.4504i	0.725339	+	0.725339i
$959$	30.6432	−	0.227032i	0.989520	−	0.00733124i
$960$	−2.18090	−	0.493652i	−0.0703881	−	0.0159325i
$961$	−13.9969	+	24.2433i	−0.451512	+	0.782041i
$962$	8.30084	+	2.22420i	0.267630	+	0.0717112i
$963$	5.84351	+	1.56576i	0.188304	+	0.0504560i
$964$	10.5600	−	18.2905i	0.340115	−	0.589096i
$965$	−47.5237	−	10.7571i	−1.52984	−	0.346284i
$966$	−7.88141	−	13.4204i	−0.253580	−	0.431794i
$967$	24.7551	+	24.7551i	0.796071	+	0.796071i	0.982474	−	0.186402i	$-0.0596827\pi$
$967$	24.7551	+	24.7551i	0.796071	+	0.796071i	−0.186402	+	0.982474i	$0.559683\pi$
$968$	1.83361	+	6.84314i	0.0589346	+	0.219947i
$969$	−9.70916	−	16.8168i	−0.311903	−	0.540232i
$970$	2.17991	−	4.14261i	0.0699927	−	0.133011i
$971$	8.84412	+	5.10615i	0.283821	+	0.163864i	0.635152	−	0.772387i	$-0.280937\pi$
$971$	8.84412	+	5.10615i	0.283821	+	0.163864i	−0.351331	+	0.936251i	$0.614271\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−2.01996	−	7.32118i	−0.0647568	−	0.234706i
$974$		−	29.9080i		−	0.958316i
$975$	−12.7763	+	8.77820i	−0.409169	+	0.281127i
$976$	9.63018	−	5.55999i	0.308254	−	0.177971i
$977$	−4.14558	+	15.4715i	−0.132629	+	0.494977i	−0.999996	−	0.00269080i	$-0.999143\pi$
$977$	−4.14558	+	15.4715i	−0.132629	+	0.494977i	0.867368	+	0.497668i	$0.165810\pi$
$978$	−21.5624	+	5.77762i	−0.689489	+	0.184748i
$979$	12.2522			0.391581
$980$	−7.08298	+	13.9582i	−0.226257	+	0.445878i
$981$	−9.74899			−0.311261
$982$	−1.51824	+	0.406810i	−0.0484488	+	0.0129818i
$983$	1.97394	−	7.36683i	0.0629588	−	0.234965i	−0.927275	−	0.374380i	$-0.877855\pi$
$983$	1.97394	−	7.36683i	0.0629588	−	0.234965i	0.990234	+	0.139415i	$0.0445221\pi$
$984$	−5.67845	+	3.27845i	−0.181022	+	0.104513i
$985$	−1.45848	−	1.34840i	−0.0464711	−	0.0429636i
$986$		−	41.1951i		−	1.31192i
$987$	−4.27852	−	15.5072i	−0.136187	−	0.493599i
$988$	−9.24849	+	9.24849i	−0.294234	+	0.294234i
$989$	45.6568	+	26.3599i	1.45180	+	0.838198i
$990$	1.31178	+	4.22570i	0.0416911	+	0.134302i
$991$	−25.4379	−	44.0597i	−0.808060	−	1.39960i	−0.914206	−	0.405251i	$-0.867184\pi$
$991$	−25.4379	−	44.0597i	−0.808060	−	1.39960i	0.106145	−	0.994351i	$-0.466149\pi$
$992$	−0.448756	−	1.67478i	−0.0142480	−	0.0531743i
$993$	19.6839	+	19.6839i	0.624648	+	0.624648i
$994$	−5.17171	−	8.80633i	−0.164037	−	0.279320i
$995$	−11.4832	−	18.2026i	−0.364041	−	0.577062i
$996$	6.73851	−	11.6714i	0.213518	−	0.369824i
$997$	−39.3361	−	10.5401i	−1.24579	−	0.333808i	−0.425080	−	0.905156i	$-0.639754\pi$
$997$	−39.3361	−	10.5401i	−1.24579	−	0.333808i	−0.820708	+	0.571348i	$0.806421\pi$
$998$	13.7737	+	3.69064i	0.435997	+	0.116825i
$999$	−1.38596	+	2.40055i	−0.0438498	+	0.0759500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.b.187.2	yes	16
3.2	odd	2		630.2.bv.b.397.3		16
5.2	odd	4		1050.2.bc.h.943.2		16
5.3	odd	4		210.2.u.a.103.3	✓	16
5.4	even	2		1050.2.bc.g.607.4		16
7.2	even	3		1470.2.m.e.97.6		16
7.3	odd	6		210.2.u.a.157.3	yes	16
7.5	odd	6		1470.2.m.d.97.7		16
15.8	even	4		630.2.bv.a.523.2		16
21.17	even	6		630.2.bv.a.577.2		16
35.3	even	12	inner	210.2.u.b.73.2	yes	16
35.17	even	12		1050.2.bc.g.493.4		16
35.23	odd	12		1470.2.m.d.1273.7		16
35.24	odd	6		1050.2.bc.h.157.2		16
35.33	even	12		1470.2.m.e.1273.6		16
105.38	odd	12		630.2.bv.b.73.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.3	✓	16	5.3	odd	4
210.2.u.a.157.3	yes	16	7.3	odd	6
210.2.u.b.73.2	yes	16	35.3	even	12	inner
210.2.u.b.187.2	yes	16	1.1	even	1	trivial
630.2.bv.a.523.2		16	15.8	even	4
630.2.bv.a.577.2		16	21.17	even	6
630.2.bv.b.73.3		16	105.38	odd	12
630.2.bv.b.397.3		16	3.2	odd	2
1050.2.bc.g.493.4		16	35.17	even	12
1050.2.bc.g.607.4		16	5.4	even	2
1050.2.bc.h.157.2		16	35.24	odd	6
1050.2.bc.h.943.2		16	5.2	odd	4
1470.2.m.d.97.7		16	7.5	odd	6
1470.2.m.d.1273.7		16	35.23	odd	12
1470.2.m.e.97.6		16	7.2	even	3
1470.2.m.e.1273.6		16	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.23435 - 0.0876265i) q^{5} +1.00000i q^{6} +(-0.703686 - 2.55046i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.13554 + 0.662933i) q^{10} +(0.989376 + 1.71365i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-2.19222 - 2.19222i) q^{13} +(1.33981 + 2.28142i) q^{14} +(0.493652 - 2.18090i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.44599 + 1.19130i) q^{17} +(0.965926 + 0.258819i) q^{18} +(2.10939 - 3.65357i) q^{19} +(1.89119 - 1.19306i) q^{20} +(-2.64568 + 0.0196015i) q^{21} +(-1.39919 - 1.39919i) q^{22} +(-1.52249 - 5.68202i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.98464 - 0.391577i) q^{25} +(2.68491 + 1.55013i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.88464 - 1.85692i) q^{28} +8.94996i q^{29} +(0.0876265 + 2.23435i) q^{30} +(-1.50157 + 0.866930i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.91133 - 0.512139i) q^{33} -4.60282 q^{34} +(-1.79577 - 5.63695i) q^{35} -1.00000 q^{36} +(2.67747 - 0.717425i) q^{37} +(-1.09190 + 4.07503i) q^{38} +(-2.68491 + 1.55013i) q^{39} +(-1.51796 + 1.64189i) q^{40} +6.55691i q^{41} +(2.55046 - 0.703686i) q^{42} +(-6.33724 + 6.33724i) q^{43} +(1.71365 + 0.989376i) q^{44} +(-1.97882 - 1.04129i) q^{45} +(2.94123 + 5.09436i) q^{46} +(1.57366 + 5.87298i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-6.00965 + 3.58944i) q^{49} +(-4.71345 + 1.66835i) q^{50} +(2.30141 - 3.98616i) q^{51} +(-2.99462 - 0.802407i) q^{52} +(-11.0441 - 2.95926i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.36077 + 3.74220i) q^{55} +(2.30103 + 1.30586i) q^{56} +(-2.98313 - 2.98313i) q^{57} +(-2.31642 - 8.64500i) q^{58} +(-2.10351 - 3.64339i) q^{59} +(-0.662933 - 2.13554i) q^{60} +(9.63018 + 5.55999i) q^{61} +(1.22602 - 1.22602i) q^{62} +(-0.665818 + 2.56060i) q^{63} -1.00000i q^{64} +(-5.09028 - 4.70608i) q^{65} +(-1.71365 + 0.989376i) q^{66} +(1.42665 - 5.32434i) q^{67} +(4.44599 - 1.19130i) q^{68} -5.88246 q^{69} +(3.19353 + 4.98010i) q^{70} -3.86002 q^{71} +(0.965926 - 0.258819i) q^{72} +(-3.93920 + 14.7013i) q^{73} +(-2.40055 + 1.38596i) q^{74} +(0.911886 - 4.91614i) q^{75} -4.21878i q^{76} +(3.67438 - 3.72923i) q^{77} +(2.19222 - 2.19222i) q^{78} +(2.21282 + 1.27757i) q^{79} +(1.04129 - 1.97882i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.69705 - 6.33349i) q^{82} +(9.52969 + 9.52969i) q^{83} +(-2.28142 + 1.33981i) q^{84} +(10.0383 + 2.27219i) q^{85} +(4.48111 - 7.76151i) q^{86} +(8.64500 + 2.31642i) q^{87} +(-1.91133 - 0.512139i) q^{88} +(3.09593 - 5.36231i) q^{89} +(2.18090 + 0.493652i) q^{90} +(-4.04852 + 7.13378i) q^{91} +(-4.15953 - 4.15953i) q^{92} +(0.448756 + 1.67478i) q^{93} +(-3.04008 - 5.26557i) q^{94} +(4.39297 - 8.34821i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-1.48031 + 1.48031i) q^{97} +(4.87586 - 5.02254i) q^{98} -1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more