LMFDB - Embedded newform 110.2.j.b.59.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(9,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.4
Root			$1.89162 - 1.19237i$ of defining polynomial
Character	$\chi$	$=$	110.59
Dual form			110.2.j.b.69.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 - 0.809017i) q^{2} +(1.53884 + 0.500000i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.71856 + 1.43058i) q^{5} +(1.30902 - 0.951057i) q^{6} +(-4.76878 + 1.54947i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.224514i) q^{9} +(2.16751 - 0.549472i) q^{10} +(-0.969425 - 3.17178i) q^{11} -1.61803i q^{12} +(1.37249 - 1.88906i) q^{13} +(-1.54947 + 4.76878i) q^{14} +(1.92930 + 3.06071i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.0359433 + 0.0494717i) q^{17} +(-0.363271 + 0.118034i) q^{18} +(0.636930 - 1.96027i) q^{19} +(0.829496 - 2.07652i) q^{20} -8.11314 q^{21} +(-3.13584 - 1.08005i) q^{22} +3.91525i q^{23} +(-1.30902 - 0.951057i) q^{24} +(0.906896 + 4.91707i) q^{25} +(-0.721558 - 2.22073i) q^{26} +(-3.21644 - 4.42705i) q^{27} +(2.94727 + 4.05657i) q^{28} +(1.27844 + 3.93464i) q^{29} +(3.61018 + 0.238203i) q^{30} +(7.18170 + 5.21781i) q^{31} +1.00000i q^{32} +(0.0941007 - 5.36559i) q^{33} +0.0611504 q^{34} +(-10.4121 - 4.15925i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(4.33385 - 1.40815i) q^{37} +(-1.21151 - 1.66751i) q^{38} +(3.05657 - 2.22073i) q^{39} +(-1.19237 - 1.89162i) q^{40} +(-1.41525 + 4.35570i) q^{41} +(-4.76878 + 6.56367i) q^{42} +3.61803i q^{43} +(-2.71698 + 1.90211i) q^{44} +(-0.209880 - 0.827913i) q^{45} +(3.16751 + 2.30133i) q^{46} +(-8.44260 - 2.74317i) q^{47} +(-1.53884 + 0.500000i) q^{48} +(14.6773 - 10.6637i) q^{49} +(4.51105 + 2.15649i) q^{50} +(0.0305752 + 0.0941007i) q^{51} +(-2.22073 - 0.721558i) q^{52} +(1.30598 - 1.79753i) q^{53} -5.47214 q^{54} +(2.87147 - 6.83774i) q^{55} +5.01420 q^{56} +(1.96027 - 2.69808i) q^{57} +(3.93464 + 1.27844i) q^{58} +(-0.599137 - 1.84396i) q^{59} +(2.31472 - 2.78069i) q^{60} +(7.84211 - 5.69763i) q^{61} +(8.44260 - 2.74317i) q^{62} +(1.82151 + 0.591846i) q^{63} +(0.809017 + 0.587785i) q^{64} +(5.06115 - 1.28302i) q^{65} +(-4.28554 - 3.22994i) q^{66} -2.49573i q^{67} +(0.0359433 - 0.0494717i) q^{68} +(-1.95763 + 6.02495i) q^{69} +(-9.48497 + 5.97880i) q^{70} +(-7.13254 + 5.18210i) q^{71} +(0.224514 + 0.309017i) q^{72} +(-5.13205 + 1.66751i) q^{73} +(1.40815 - 4.33385i) q^{74} +(-1.06296 + 8.02003i) q^{75} -2.06115 q^{76} +(9.53757 + 13.6235i) q^{77} -3.77813i q^{78} +(-5.38417 - 3.91183i) q^{79} +(-2.23122 - 0.147217i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(2.69197 + 3.70518i) q^{82} +(-6.49620 - 8.94125i) q^{83} +(2.50710 + 7.71605i) q^{84} +(-0.00900240 + 0.136440i) q^{85} +(2.92705 + 2.12663i) q^{86} +6.69401i q^{87} +(-0.0581575 + 3.31611i) q^{88} -6.09017 q^{89} +(-0.793160 - 0.316839i) q^{90} +(-3.61803 + 11.1352i) q^{91} +(3.72363 - 1.20988i) q^{92} +(8.44260 + 11.6202i) q^{93} +(-7.18170 + 5.21781i) q^{94} +(3.89892 - 2.45766i) q^{95} +(-0.500000 + 1.53884i) q^{96} +(4.29216 - 5.90765i) q^{97} -18.1422i q^{98} +(-0.412541 + 1.19778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 20 q^{11} - 12 q^{14} + 2 q^{15} - 4 q^{16} - 16 q^{19} + 6 q^{20} - 16 q^{21} - 12 q^{24} - 16 q^{26} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{34}+ \cdots - 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 20 * q^11 - 12 * q^14 + 2 * q^15 - 4 * q^16 - 16 * q^19 + 6 * q^20 - 16 * q^21 - 12 * q^24 - 16 * q^26 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^34 - 48 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 + 40 * q^41 - 4 * q^45 + 20 * q^46 + 84 * q^49 + 4 * q^50 - 4 * q^51 - 16 * q^54 + 32 * q^55 - 8 * q^56 + 8 * q^60 + 20 * q^61 + 4 * q^64 + 72 * q^65 - 20 * q^66 + 36 * q^70 - 56 * q^71 + 4 * q^74 + 32 * q^75 - 24 * q^76 + 36 * q^79 + 4 * q^80 - 56 * q^81 - 4 * q^84 - 54 * q^85 + 20 * q^86 - 8 * q^89 - 4 * q^90 - 40 * q^91 + 4 * q^94 - 50 * q^95 - 8 * q^96 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	1.53884	+	0.500000i	0.888451	+	0.288675i	0.717462	−	0.696598i	$-0.245304\pi$
$3$	1.53884	+	0.500000i	0.888451	+	0.288675i	0.170989	+	0.985273i	$0.445304\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.71856	+	1.43058i	0.768563	+	0.639774i
$5$	1.71856	+	1.43058i	0.768563	+	0.639774i
$6$	1.30902	−	0.951057i	0.534404	−	0.388267i
$7$	−4.76878	+	1.54947i	−1.80243	+	0.585645i	−0.999939	−	0.0110184i	$-0.996493\pi$
$7$	−4.76878	+	1.54947i	−1.80243	+	0.585645i	−0.802491	+	0.596664i	$0.796493\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.309017	−	0.224514i	−0.103006	−	0.0748380i
$10$	2.16751	−	0.549472i	0.685425	−	0.173758i
$11$	−0.969425	−	3.17178i	−0.292293	−	0.956329i
$11$	−0.969425	−	3.17178i	−0.292293	−	0.956329i
$12$		−	1.61803i		−	0.467086i
$13$	1.37249	−	1.88906i	0.380659	−	0.523932i	−0.575100	−	0.818083i	$-0.695037\pi$
$13$	1.37249	−	1.88906i	0.380659	−	0.523932i	0.955759	+	0.294151i	$0.0950369\pi$
$14$	−1.54947	+	4.76878i	−0.414114	+	1.27451i
$15$	1.92930	+	3.06071i	0.498144	+	0.790273i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.0359433	+	0.0494717i	0.00871753	+	0.0119986i	0.813354	−	0.581770i	$-0.197640\pi$
$17$	0.0359433	+	0.0494717i	0.00871753	+	0.0119986i	−0.804636	+	0.593768i	$0.797640\pi$
$18$	−0.363271	+	0.118034i	−0.0856239	+	0.0278209i
$19$	0.636930	−	1.96027i	0.146122	−	0.449717i	−0.851032	−	0.525114i	$-0.824023\pi$
$19$	0.636930	−	1.96027i	0.146122	−	0.449717i	0.997154	+	0.0753974i	$0.0240226\pi$
$20$	0.829496	−	2.07652i	0.185481	−	0.464324i
$21$	−8.11314			−1.77043
$22$	−3.13584	−	1.08005i	−0.668564	−	0.230267i
$23$			3.91525i			0.816387i	0.912896	+	0.408193i	$0.133841\pi$
$23$			3.91525i			0.816387i	−0.912896	+	0.408193i	$0.866159\pi$
$24$	−1.30902	−	0.951057i	−0.267202	−	0.194134i
$25$	0.906896	+	4.91707i	0.181379	+	0.983413i
$26$	−0.721558	−	2.22073i	−0.141509	−	0.435521i
$27$	−3.21644	−	4.42705i	−0.619004	−	0.851986i
$28$	2.94727	+	4.05657i	0.556982	+	0.766620i
$29$	1.27844	+	3.93464i	0.237401	+	0.730644i	0.996794	+	0.0800122i	$0.0254959\pi$
$29$	1.27844	+	3.93464i	0.237401	+	0.730644i	−0.759393	+	0.650632i	$0.774504\pi$
$30$	3.61018	+	0.238203i	0.659126	+	0.0434897i
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.999803	−	0.0198592i	$-0.00632179\pi$
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.290069	+	0.957006i	$0.406322\pi$
$32$			1.00000i			0.176777i
$33$	0.0941007	−	5.36559i	0.0163808	−	0.934029i
$34$	0.0611504			0.0104872
$35$	−10.4121	−	4.15925i	−1.75996	−	0.703042i
$36$	−0.118034	+	0.363271i	−0.0196723	+	0.0605452i
$37$	4.33385	−	1.40815i	0.712481	−	0.231499i	0.0697209	−	0.997567i	$-0.477789\pi$
$37$	4.33385	−	1.40815i	0.712481	−	0.231499i	0.642760	+	0.766067i	$0.277789\pi$
$38$	−1.21151	−	1.66751i	−0.196533	−	0.270505i
$39$	3.05657	−	2.22073i	0.489443	−	0.355601i
$40$	−1.19237	−	1.89162i	−0.188531	−	0.299092i
$41$	−1.41525	+	4.35570i	−0.221025	+	0.680246i	0.777646	+	0.628703i	$0.216414\pi$
$41$	−1.41525	+	4.35570i	−0.221025	+	0.680246i	−0.998671	+	0.0515429i	$0.983586\pi$
$42$	−4.76878	+	6.56367i	−0.735839	+	1.01280i
$43$			3.61803i			0.551745i	0.961194	+	0.275873i	$0.0889668\pi$
$43$			3.61803i			0.551745i	−0.961194	+	0.275873i	$0.911033\pi$
$44$	−2.71698	+	1.90211i	−0.409600	+	0.286754i
$45$	−0.209880	−	0.827913i	−0.0312870	−	0.123418i
$46$	3.16751	+	2.30133i	0.467023	+	0.339312i
$47$	−8.44260	−	2.74317i	−1.23148	−	0.400132i	−0.380229	−	0.924892i	$-0.624155\pi$
$47$	−8.44260	−	2.74317i	−1.23148	−	0.400132i	−0.851250	+	0.524760i	$0.824155\pi$
$48$	−1.53884	+	0.500000i	−0.222113	+	0.0721688i
$49$	14.6773	−	10.6637i	2.09676	−	1.52338i
$50$	4.51105	+	2.15649i	0.637959	+	0.304973i
$51$	0.0305752	+	0.0941007i	0.00428138	+	0.0131767i
$52$	−2.22073	−	0.721558i	−0.307960	−	0.100062i
$53$	1.30598	−	1.79753i	0.179391	−	0.246910i	−0.709847	−	0.704356i	$-0.751236\pi$
$53$	1.30598	−	1.79753i	0.179391	−	0.246910i	0.889237	+	0.457446i	$0.151236\pi$
$54$	−5.47214			−0.744663
$55$	2.87147	−	6.83774i	0.387189	−	0.922000i
$56$	5.01420			0.670050
$57$	1.96027	−	2.69808i	0.259644	−	0.357370i
$58$	3.93464	+	1.27844i	0.516643	+	0.167868i
$59$	−0.599137	−	1.84396i	−0.0780011	−	0.240063i	0.904451	−	0.426577i	$-0.140281\pi$
$59$	−0.599137	−	1.84396i	−0.0780011	−	0.240063i	−0.982452	+	0.186515i	$0.940281\pi$
$60$	2.31472	−	2.78069i	0.298829	−	0.358985i
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.0411202	−	0.999154i	$-0.486907\pi$
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.962959	+	0.269648i	$0.0869073\pi$
$62$	8.44260	−	2.74317i	1.07221	−	0.348382i
$63$	1.82151	+	0.591846i	0.229489	+	0.0745655i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	5.06115	−	1.28302i	0.627758	−	0.159139i
$66$	−4.28554	−	3.22994i	−0.527513	−	0.397578i
$67$		−	2.49573i		−	0.304902i	−0.988311	−	0.152451i	$-0.951283\pi$
$67$		−	2.49573i		−	0.304902i	0.988311	−	0.152451i	$-0.0487167\pi$
$68$	0.0359433	−	0.0494717i	0.00435876	−	0.00599932i
$69$	−1.95763	+	6.02495i	−0.235670	+	0.725319i
$70$	−9.48497	+	5.97880i	−1.13367	+	0.714603i
$71$	−7.13254	+	5.18210i	−0.846477	+	0.615002i	−0.924172	−	0.381975i	$-0.875244\pi$
$71$	−7.13254	+	5.18210i	−0.846477	+	0.615002i	0.0776953	+	0.996977i	$0.475244\pi$
$72$	0.224514	+	0.309017i	0.0264592	+	0.0364180i
$73$	−5.13205	+	1.66751i	−0.600662	+	0.195167i	−0.593535	−	0.804808i	$-0.702268\pi$
$73$	−5.13205	+	1.66751i	−0.600662	+	0.195167i	−0.00712611	+	0.999975i	$0.502268\pi$
$74$	1.40815	−	4.33385i	0.163695	−	0.503800i
$75$	−1.06296	+	8.02003i	−0.122741	+	0.926074i
$76$	−2.06115			−0.236430
$77$	9.53757	+	13.6235i	1.08691	+	1.55254i
$78$		−	3.77813i		−	0.427789i
$79$	−5.38417	−	3.91183i	−0.605766	−	0.440115i	0.242155	−	0.970238i	$-0.422146\pi$
$79$	−5.38417	−	3.91183i	−0.605766	−	0.440115i	−0.847921	+	0.530123i	$0.822146\pi$
$80$	−2.23122	−	0.147217i	−0.249458	−	0.0164594i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	2.69197	+	3.70518i	0.297278	+	0.409169i
$83$	−6.49620	−	8.94125i	−0.713050	−	0.981429i	−0.999726	−	0.0234017i	$-0.992550\pi$
$83$	−6.49620	−	8.94125i	−0.713050	−	0.981429i	0.286676	−	0.958028i	$-0.407450\pi$
$84$	2.50710	+	7.71605i	0.273547	+	0.841890i
$85$	−0.00900240	+	0.136440i	−0.000976448	+	0.0147990i
$86$	2.92705	+	2.12663i	0.315632	+	0.229320i
$87$			6.69401i			0.717673i
$88$	−0.0581575	+	3.31611i	−0.00619961	+	0.353499i
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$	−0.793160	−	0.316839i	−0.0836064	−	0.0333978i
$91$	−3.61803	+	11.1352i	−0.379273	+	1.16728i
$92$	3.72363	−	1.20988i	0.388215	−	0.126139i
$93$	8.44260	+	11.6202i	0.875456	+	1.20496i
$94$	−7.18170	+	5.21781i	−0.740736	+	0.538176i
$95$	3.89892	−	2.45766i	0.400021	−	0.252151i
$96$	−0.500000	+	1.53884i	−0.0510310	+	0.157057i
$97$	4.29216	−	5.90765i	0.435802	−	0.599831i	−0.533470	−	0.845819i	$-0.679112\pi$
$97$	4.29216	−	5.90765i	0.435802	−	0.599831i	0.969273	+	0.245988i	$0.0791124\pi$
$98$		−	18.1422i		−	1.83263i
$99$	−0.412541	+	1.19778i	−0.0414620	+	0.120382i
$100$	4.39616	−	2.38197i	0.439616	−	0.238197i
$101$	0.179498	+	0.130413i	0.0178608	+	0.0129766i	0.596680	−	0.802479i	$-0.296486\pi$
$101$	0.179498	+	0.130413i	0.0178608	+	0.0129766i	−0.578819	+	0.815456i	$0.696486\pi$
$102$	0.0941007	+	0.0305752i	0.00931736	+	0.00302739i
$103$	−0.538341	+	0.174918i	−0.0530443	+	0.0172351i	−0.335419	−	0.942069i	$-0.608878\pi$
$103$	−0.538341	+	0.174918i	−0.0530443	+	0.0172351i	0.282375	+	0.959304i	$0.408878\pi$
$104$	−1.88906	+	1.37249i	−0.185238	+	0.134583i
$105$	−13.9429	−	11.6065i	−1.36069	−	1.13268i
$106$	−0.686596	−	2.11313i	−0.0666881	−	0.205245i
$107$	2.12087	+	0.689113i	0.205033	+	0.0666191i	0.409733	−	0.912206i	$-0.365622\pi$
$107$	2.12087	+	0.689113i	0.205033	+	0.0666191i	−0.204700	+	0.978825i	$0.565622\pi$
$108$	−3.21644	+	4.42705i	−0.309502	+	0.425993i
$109$	−7.86288			−0.753127			−0.376563	−	0.926391i	$-0.622894\pi$
$109$	−7.86288			−0.753127			−0.376563	+	0.926391i	$0.622894\pi$
$110$	−3.84404	−	6.34219i	−0.366515	−	0.604704i
$111$	7.37319			0.699832
$112$	2.94727	−	4.05657i	0.278491	−	0.383310i
$113$	−11.9469	−	3.88177i	−1.12387	−	0.365166i	−0.312624	−	0.949877i	$-0.601208\pi$
$113$	−11.9469	−	3.88177i	−1.12387	−	0.365166i	−0.811242	+	0.584710i	$0.801208\pi$
$114$	−1.03058	−	3.17178i	−0.0965222	−	0.297065i
$115$	−5.60107	+	6.72860i	−0.522303	+	0.627445i
$116$	3.34700	−	2.43174i	0.310762	−	0.225781i
$117$	−0.848243	+	0.275611i	−0.0784200	+	0.0254802i
$118$	−1.84396	−	0.599137i	−0.169750	−	0.0551551i
$119$	−0.248061	−	0.180227i	−0.0227397	−	0.0165214i
$120$	−0.889064	−	3.50710i	−0.0811601	−	0.320153i
$121$	−9.12043	+	6.14961i	−0.829130	+	0.559056i
$122$		−	9.69338i		−	0.877597i
$123$	−4.35570	+	5.99511i	−0.392740	+	0.540560i
$124$	2.74317	−	8.44260i	0.246344	−	0.758168i
$125$	−5.47569	+	9.74766i	−0.489761	+	0.871857i
$126$	1.54947	−	1.12576i	0.138038	−	0.100290i
$127$	8.50112	+	11.7008i	0.754353	+	1.03828i	0.997663	+	0.0683289i	$0.0217667\pi$
$127$	8.50112	+	11.7008i	0.754353	+	1.03828i	−0.243310	+	0.969949i	$0.578233\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−1.80902	+	5.56758i	−0.159275	+	0.490198i
$130$	1.93688	−	4.84870i	0.169876	−	0.425259i
$131$	15.3256			1.33900			0.669502	−	0.742810i	$-0.266507\pi$
$131$	15.3256			1.33900			0.669502	+	0.742810i	$0.266507\pi$
$132$	−5.13205	+	1.56856i	−0.446688	+	0.136526i
$133$			10.3350i			0.896159i
$134$	−2.01909	−	1.46696i	−0.174423	−	0.126726i
$135$	0.805594	−	12.2095i	0.0693345	−	1.05083i
$136$	−0.0188965	−	0.0581575i	−0.00162036	−	0.00498696i
$137$	−0.649130	−	0.893451i	−0.0554589	−	0.0763326i	0.780387	−	0.625297i	$-0.215022\pi$
$137$	−0.649130	−	0.893451i	−0.0554589	−	0.0763326i	−0.835846	+	0.548964i	$0.815022\pi$
$138$	3.72363	+	5.12513i	0.316976	+	0.436280i
$139$	3.06115	+	9.42125i	0.259643	+	0.799100i	0.992879	+	0.119126i	$0.0380092\pi$
$139$	3.06115	+	9.42125i	0.259643	+	0.799100i	−0.733236	+	0.679974i	$0.761991\pi$
$140$	−0.738177	+	11.1878i	−0.0623874	+	0.945538i
$141$	−11.6202	−	8.44260i	−0.978600	−	0.710995i
$142$			8.81631i			0.739848i
$143$	−7.32222	−	2.52192i	−0.612315	−	0.210894i
$144$	0.381966			0.0318305
$145$	−3.43173	+	8.59082i	−0.284990	+	0.713429i
$146$	−1.66751	+	5.13205i	−0.138004	+	0.424732i
$147$	27.9179	−	9.07108i	2.30263	−	0.748170i
$148$	−2.67847	−	3.68660i	−0.220169	−	0.303036i
$149$	7.11314	−	5.16800i	0.582731	−	0.423379i	−0.256977	−	0.966418i	$-0.582726\pi$
$149$	7.11314	−	5.16800i	0.582731	−	0.423379i	0.839708	+	0.543039i	$0.182726\pi$
$150$	5.86355	+	5.57401i	0.478757	+	0.455116i
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	−0.182894	−	0.983133i	$-0.558547\pi$
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	0.725835	−	0.687868i	$-0.241453\pi$
$152$	−1.21151	+	1.66751i	−0.0982667	+	0.135253i
$153$		−	0.0233574i		−	0.00188833i
$154$	16.6276	+	0.291613i	1.33989	+	0.0234988i
$155$	4.87770	+	19.2411i	0.391786	+	1.54548i
$156$	−3.05657	−	2.22073i	−0.244721	−	0.177801i
$157$	−3.24760	−	1.05521i	−0.259186	−	0.0842148i	0.176542	−	0.984293i	$-0.443509\pi$
$157$	−3.24760	−	1.05521i	−0.259186	−	0.0842148i	−0.435728	+	0.900078i	$0.643509\pi$
$158$	−6.32947	+	2.05657i	−0.503546	+	0.163612i
$159$	2.90847	−	2.11313i	0.230657	−	0.167582i
$160$	−1.43058	+	1.71856i	−0.113097	+	0.135864i
$161$	−6.06657	−	18.6710i	−0.478113	−	1.47148i
$162$	−7.33094	−	2.38197i	−0.575973	−	0.187145i
$163$	10.2336	−	14.0853i	0.801554	−	1.10324i	−0.191019	−	0.981586i	$-0.561179\pi$
$163$	10.2336	−	14.0853i	0.801554	−	1.10324i	0.992572	−	0.121657i	$-0.0388209\pi$
$164$	4.57985			0.357626
$165$	7.83761	−	9.08646i	0.610157	−	0.707380i
$166$	−11.0520			−0.857801
$167$	−1.94321	+	2.67460i	−0.150370	+	0.206967i	−0.877556	−	0.479473i	$-0.840828\pi$
$167$	−1.94321	+	2.67460i	−0.150370	+	0.206967i	0.727186	+	0.686440i	$0.240828\pi$
$168$	7.71605	+	2.50710i	0.595306	+	0.193427i
$169$	2.33237	+	7.17831i	0.179413	+	0.552178i
$170$	0.105091	+	0.0874803i	0.00806008	+	0.00670944i
$171$	−0.636930	+	0.462757i	−0.0487073	+	0.0353879i
$172$	3.44095	−	1.11803i	0.262370	−	0.0852493i
$173$	4.87758	+	1.58482i	0.370836	+	0.120492i	0.488505	−	0.872561i	$-0.337542\pi$
$173$	4.87758	+	1.58482i	0.370836	+	0.120492i	−0.117670	+	0.993053i	$0.537542\pi$
$174$	5.41557	+	3.93464i	0.410553	+	0.298284i
$175$	−11.9436	−	22.0432i	−0.902855	−	1.66631i
$176$	2.64861	+	1.99621i	0.199646	+	0.150470i
$177$		−	3.13712i		−	0.235801i
$178$	−3.57971	+	4.92705i	−0.268311	+	0.369298i
$179$	4.46201	−	13.7327i	0.333507	−	1.02643i	−0.633947	−	0.773377i	$-0.718566\pi$
$179$	4.46201	−	13.7327i	0.333507	−	1.02643i	0.967453	−	0.253051i	$-0.0814339\pi$
$180$	−0.722536	+	0.455447i	−0.0538547	+	0.0339470i
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	−0.885090	−	0.465419i	$-0.845903\pi$
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	0.169132	+	0.985593i	$0.445903\pi$
$182$	6.88191	+	9.47214i	0.510121	+	0.702121i
$183$	14.9166	−	4.84669i	1.10267	−	0.358278i
$184$	1.20988	−	3.72363i	0.0891935	−	0.274509i
$185$	9.46246	+	3.77992i	0.695694	+	0.277905i
$186$	14.3634			1.05318
$187$	0.122069	−	0.161963i	0.00892658	−	0.0118439i
$188$			8.87707i			0.647427i
$189$	22.1981	+	16.1279i	1.61467	+	1.17313i
$190$	0.303437	−	4.59887i	0.0220137	−	0.333637i
$191$	3.25026	+	10.0033i	0.235181	+	0.723812i	0.997097	+	0.0761369i	$0.0242586\pi$
$191$	3.25026	+	10.0033i	0.235181	+	0.723812i	−0.761917	+	0.647675i	$0.775741\pi$
$192$	0.951057	+	1.30902i	0.0686366	+	0.0944702i
$193$	−2.86174	−	3.93885i	−0.205993	−	0.283525i	0.693503	−	0.720453i	$-0.256066\pi$
$193$	−2.86174	−	3.93885i	−0.205993	−	0.283525i	−0.899496	+	0.436929i	$0.856066\pi$
$194$	−2.25652	−	6.94485i	−0.162009	−	0.498612i
$195$	8.42982	+	0.556206i	0.603672	+	0.0398308i
$196$	−14.6773	−	10.6637i	−1.04838	−	0.761692i
$197$			15.9760i			1.13824i	0.822253	+	0.569122i	$0.192717\pi$
$197$			15.9760i			1.13824i	−0.822253	+	0.569122i	$0.807283\pi$
$198$	0.726543	+	1.03779i	0.0516331	+	0.0737527i
$199$	−16.7076			−1.18437			−0.592184	−	0.805803i	$-0.701734\pi$
$199$	−16.7076			−1.18437			−0.592184	+	0.805803i	$0.701734\pi$
$200$	0.656948	−	4.95665i	0.0464532	−	0.350488i
$201$	1.24787	−	3.84054i	0.0880177	−	0.270891i
$202$	0.211013	−	0.0685623i	0.0148468	−	0.00482403i
$203$	−12.1932	−	16.7825i	−0.855797	−	1.17790i
$204$	0.0800469	−	0.0581575i	0.00560440	−	0.00407184i
$205$	−8.66336	+	5.46090i	−0.605075	+	0.381406i
$206$	−0.174918	+	0.538341i	−0.0121871	+	0.0375080i
$207$	0.879029	−	1.20988i	0.0610967	−	0.0840924i
$208$			2.33501i			0.161904i
$209$	−6.83501	−	0.119871i	−0.472788	−	0.00829167i
$210$	−17.5853	+	4.45794i	−1.21350	+	0.307627i
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	0.932449	−	0.361301i	$-0.117667\pi$
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	−0.0554754	+	0.998460i	$0.517667\pi$
$212$	−2.11313	−	0.686596i	−0.145130	−	0.0471556i
$213$	−13.5669	+	4.40815i	−0.929589	+	0.302042i
$214$	1.80412	−	1.31077i	0.123327	−	0.0896025i
$215$	−5.17588	+	6.21781i	−0.352992	+	0.424051i
$216$	1.69098	+	5.20431i	0.115057	+	0.354108i
$217$	−42.3328	−	13.7548i	−2.87374	−	0.933735i
$218$	−4.62168	+	6.36120i	−0.313020	+	0.430835i
$219$	−8.73117			−0.589998
$220$	−7.39041	−	0.617952i	−0.498261	−	0.0416623i
$221$	0.142787			0.00960488
$222$	4.33385	−	5.96504i	0.290869	−	0.400347i
$223$	13.8432	+	4.49794i	0.927011	+	0.301204i	0.733340	−	0.679862i	$-0.237961\pi$
$223$	13.8432	+	4.49794i	0.927011	+	0.301204i	0.193671	+	0.981067i	$0.437961\pi$
$224$	−1.54947	−	4.76878i	−0.103528	−	0.318628i
$225$	0.823704	−	1.72307i	0.0549136	−	0.114871i
$226$	−10.1626	+	7.38357i	−0.676007	+	0.491148i
$227$	−9.35512	+	3.03966i	−0.620921	+	0.201749i	−0.602549	−	0.798082i	$-0.705848\pi$
$227$	−9.35512	+	3.03966i	−0.620921	+	0.201749i	−0.0183719	+	0.999831i	$0.505848\pi$
$228$	−3.17178	−	1.03058i	−0.210057	−	0.0682515i
$229$	−12.5785	−	9.13881i	−0.831210	−	0.603909i	0.0886913	−	0.996059i	$-0.471732\pi$
$229$	−12.5785	−	9.13881i	−0.831210	−	0.603909i	−0.919901	+	0.392150i	$0.871732\pi$
$230$	2.15132	+	8.48633i	0.141854	+	0.559572i
$231$	7.86508	+	25.7331i	0.517484	+	1.69312i
$232$		−	4.13712i		−	0.271616i
$233$	15.2217	−	20.9509i	0.997206	−	1.37254i	0.0701824	−	0.997534i	$-0.477642\pi$
$233$	15.2217	−	20.9509i	0.997206	−	1.37254i	0.927024	−	0.375002i	$-0.122358\pi$
$234$	−0.275611	+	0.848243i	−0.0180172	+	0.0554513i
$235$	−10.5848	−	16.7921i	−0.690476	−	1.09539i
$236$	−1.56856	+	1.13963i	−0.102105	+	0.0741834i
$237$	−6.32947	−	8.71177i	−0.411143	−	0.565890i
$238$	−0.291613	+	0.0947508i	−0.0189025	+	0.00614178i
$239$	−6.17911	+	19.0173i	−0.399693	+	1.23013i	0.525552	+	0.850761i	$0.323859\pi$
$239$	−6.17911	+	19.0173i	−0.399693	+	1.23013i	−0.925246	+	0.379369i	$0.876141\pi$
$240$	−3.35988	−	1.34215i	−0.216879	−	0.0866356i
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$	−0.385714	+	10.9932i	−0.0247946	+	0.706672i
$243$			3.94427i			0.253025i
$244$	−7.84211	−	5.69763i	−0.502040	−	0.364753i
$245$	40.4791	+	2.67084i	2.58611	+	0.170634i
$246$	2.28993	+	7.04767i	0.146000	+	0.449343i
$247$	−2.82890	−	3.89364i	−0.179998	−	0.247747i
$248$	−5.21781	−	7.18170i	−0.331331	−	0.456038i
$249$	−5.52599	−	17.0073i	−0.350196	−	1.07779i
$250$	4.66749	+	10.1595i	0.295198	+	0.642540i
$251$	−1.06115	−	0.770971i	−0.0669792	−	0.0486632i	0.553792	−	0.832655i	$-0.313180\pi$
$251$	−1.06115	−	0.770971i	−0.0669792	−	0.0486632i	−0.620771	+	0.783992i	$0.713180\pi$
$252$		−	1.91525i		−	0.120650i
$253$	12.4183	−	3.79554i	0.780734	−	0.238624i
$254$	14.4630			0.907488
$255$	−0.0820731	+	0.205458i	−0.00513962	+	0.0128663i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.24551	−	1.37945i	0.264827	−	0.0860477i	−0.173594	−	0.984817i	$-0.555538\pi$
$257$	4.24551	−	1.37945i	0.264827	−	0.0860477i	0.438421	+	0.898770i	$0.355538\pi$
$258$	3.44095	+	4.73607i	0.214224	+	0.294855i
$259$	−18.4853	+	13.4304i	−1.14862	+	0.834522i
$260$	−2.78421	−	4.41696i	−0.172669	−	0.273928i
$261$	0.488321	−	1.50290i	0.0302263	−	0.0930271i
$262$	9.00817	−	12.3987i	0.556526	−	0.765993i
$263$			14.1791i			0.874320i	0.899384	+	0.437160i	$0.144016\pi$
$263$			14.1791i			0.874320i	−0.899384	+	0.437160i	$0.855984\pi$
$264$	−1.74755	+	5.07390i	−0.107554	+	0.312277i
$265$	4.81592	−	1.22086i	0.295840	−	0.0749966i
$266$	8.36120	+	6.07477i	0.512658	+	0.372468i
$267$	−9.37181	−	3.04508i	−0.573545	−	0.186356i
$268$	−2.37358	+	0.771224i	−0.144990	+	0.0471100i
$269$	−25.8847	+	18.8063i	−1.57822	+	1.14664i	−0.659516	+	0.751691i	$0.729239\pi$
$269$	−25.8847	+	18.8063i	−1.57822	+	1.14664i	−0.918702	+	0.394952i	$0.870761\pi$
$270$	−9.40419	−	7.82831i	−0.572321	−	0.476416i
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	0.960524	−	0.278197i	$-0.0897367\pi$
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	−0.940600	+	0.339516i	$0.889737\pi$
$272$	−0.0581575	−	0.0188965i	−0.00352631	−	0.00114577i
$273$	−11.1352	+	15.3262i	−0.673931	+	0.927586i
$274$	−1.10437			−0.0667172
$275$	14.7167	−	7.64320i	0.887451	−	0.460902i
$276$	6.33501			0.381323
$277$	3.89892	−	5.36641i	0.234264	−	0.322436i	−0.675659	−	0.737214i	$-0.736141\pi$
$277$	3.89892	−	5.36641i	0.234264	−	0.322436i	0.909923	+	0.414778i	$0.136141\pi$
$278$	9.42125	+	3.06115i	0.565049	+	0.183596i
$279$	−1.04780	−	3.22478i	−0.0627299	−	0.193063i
$280$	8.61720	+	7.17320i	0.514976	+	0.428680i
$281$	−12.6582	+	9.19674i	−0.755126	+	0.548631i	−0.897412	−	0.441194i	$-0.854555\pi$
$281$	−12.6582	+	9.19674i	−0.755126	+	0.548631i	0.142285	+	0.989826i	$0.454555\pi$
$282$	−13.6604	+	4.43854i	−0.813465	+	0.264311i
$283$	21.3993	+	6.95305i	1.27205	+	0.413316i	0.865775	−	0.500433i	$-0.166826\pi$
$283$	21.3993	+	6.95305i	1.27205	+	0.413316i	0.406280	+	0.913749i	$0.366826\pi$
$284$	7.13254	+	5.18210i	0.423239	+	0.307501i
$285$	7.22866	−	1.83249i	0.428189	−	0.108548i
$286$	−6.34417	+	4.44146i	−0.375139	+	0.262629i
$287$		−	22.9643i		−	1.35554i
$288$	0.224514	−	0.309017i	0.0132296	−	0.0182090i
$289$	5.25213	−	16.1644i	0.308949	−	0.950847i
$290$	4.93300	+	7.82589i	0.289676	+	0.459552i
$291$	9.55877	−	6.94485i	0.560345	−	0.407115i
$292$	3.17178	+	4.36559i	0.185615	+	0.255477i
$293$	−17.2985	+	5.62063i	−1.01059	+	0.328360i	−0.767089	−	0.641540i	$-0.778296\pi$
$293$	−17.2985	+	5.62063i	−1.01059	+	0.328360i	−0.243500	+	0.969901i	$0.578296\pi$
$294$	9.07108	−	27.9179i	0.529036	−	1.62821i
$295$	1.60827	−	4.02606i	0.0936370	−	0.234406i
$296$	−4.55688			−0.264863
$297$	−10.9236	+	14.4935i	−0.633849	+	0.841001i
$298$		−	8.79232i		−	0.509326i
$299$	7.39616	+	5.37363i	0.427731	+	0.310765i
$300$	7.95598	−	1.46739i	0.459339	−	0.0847197i
$301$	−5.60604	−	17.2536i	−0.323127	−	0.994482i
$302$	−12.6905	−	17.4669i	−0.730254	−	1.00511i
$303$	0.211013	+	0.290435i	0.0121224	+	0.0166850i
$304$	0.636930	+	1.96027i	0.0365305	+	0.112429i
$305$	21.6280	+	1.42703i	1.23842	+	0.0817118i
$306$	−0.0188965	−	0.0137291i	−0.00108024	−	0.000784841i
$307$			12.3820i			0.706676i	0.935496	+	0.353338i	$0.114953\pi$
$307$			12.3820i			0.706676i	−0.935496	+	0.353338i	$0.885047\pi$
$308$	10.0094	−	13.2806i	0.570339	−	0.756735i
$309$	−0.915880			−0.0521026
$310$	18.4334	+	7.36349i	1.04695	+	0.418218i
$311$	2.90784	−	8.94941i	0.164889	−	0.507475i	−0.834140	−	0.551553i	$-0.814035\pi$
$311$	2.90784	−	8.94941i	0.164889	−	0.507475i	0.999028	+	0.0440788i	$0.0140353\pi$
$312$	−3.59321	+	1.16751i	−0.203426	+	0.0660970i
$313$	8.95297	+	12.3227i	0.506052	+	0.696520i	0.983247	−	0.182277i	$-0.0583467\pi$
$313$	8.95297	+	12.3227i	0.506052	+	0.696520i	−0.477196	+	0.878797i	$0.658347\pi$
$314$	−2.76257	+	2.00712i	−0.155901	+	0.113269i
$315$	2.28370	+	3.62294i	0.128672	+	0.204129i
$316$	−2.05657	+	6.32947i	−0.115691	+	0.356061i
$317$	−7.90964	+	10.8867i	−0.444250	+	0.611457i	−0.971150	−	0.238470i	$-0.923354\pi$
$317$	−7.90964	+	10.8867i	−0.444250	+	0.611457i	0.526900	+	0.849927i	$0.323354\pi$
$318$		−	3.59506i		−	0.201601i
$319$	11.2405	−	7.86928i	0.629346	−	0.440595i
$320$	0.549472	+	2.16751i	0.0307164	+	0.121167i
$321$	2.91913	+	2.12087i	0.162930	+	0.118376i
$322$	−18.6710	−	6.06657i	−1.04049	−	0.338077i
$323$	0.119871	−	0.0389485i	0.00666982	−	0.00216715i
$324$	−6.23607	+	4.53077i	−0.346448	+	0.251709i
$325$	10.5334	+	5.03542i	0.584285	+	0.279315i
$326$	−5.38010	−	16.5582i	−0.297976	−	0.917076i
$327$	−12.0997	−	3.93144i	−0.669116	−	0.217409i
$328$	2.69197	−	3.70518i	0.148639	−	0.204584i
$329$	44.5114			2.45399
$330$	−2.74427	−	11.6816i	−0.151067	−	0.643053i
$331$	−3.82236			−0.210096			−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236			−0.210096			−0.105048	+	0.994467i	$0.533500\pi$
$332$	−6.49620	+	8.94125i	−0.356525	+	0.490715i
$333$	−1.65538	−	0.537867i	−0.0907145	−	0.0294749i
$334$	1.02161	+	3.14419i	0.0558999	+	0.172042i
$335$	3.57034	−	4.28907i	0.195069	−	0.234337i
$336$	6.56367	−	4.76878i	0.358077	−	0.260158i
$337$	9.00338	−	2.92538i	0.490445	−	0.159355i	−0.0533455	−	0.998576i	$-0.516988\pi$
$337$	9.00338	−	2.92538i	0.490445	−	0.159355i	0.543791	+	0.839221i	$0.316988\pi$
$338$	7.17831	+	2.33237i	0.390449	+	0.126864i
$339$	−16.4434	−	11.9469i	−0.893086	−	0.648865i
$340$	0.132544	−	0.0336004i	0.00718820	−	0.00182224i
$341$	9.58765	−	27.8371i	0.519201	−	1.50746i
$342$			0.787289i			0.0425717i
$343$	−32.8390	+	45.1989i	−1.77314	+	2.44051i
$344$	1.11803	−	3.44095i	0.0602804	−	0.185524i
$345$	−11.9835	+	7.55371i	−0.645168	+	0.406678i
$346$	4.14912	−	3.01451i	0.223058	−	0.162061i
$347$	9.72341	+	13.3831i	0.521980	+	0.718444i	0.985882	−	0.167443i	$-0.0535510\pi$
$347$	9.72341	+	13.3831i	0.521980	+	0.718444i	−0.463902	+	0.885887i	$0.653551\pi$
$348$	6.36638	−	2.06856i	0.341274	−	0.110887i
$349$	−9.03161	+	27.7964i	−0.483451	+	1.48791i	0.350761	+	0.936465i	$0.385923\pi$
$349$	−9.03161	+	27.7964i	−0.483451	+	1.48791i	−0.834212	+	0.551444i	$0.814077\pi$
$350$	−24.8536	−	3.29407i	−1.32848	−	0.176075i
$351$	−12.7775			−0.682012
$352$	3.17178	−	0.969425i	0.169057	−	0.0516705i
$353$		−	27.9200i		−	1.48603i	−0.669272	−	0.743017i	$-0.733394\pi$
$353$		−	27.9200i		−	1.48603i	0.669272	−	0.743017i	$-0.266606\pi$
$354$	−2.53799	−	1.84396i	−0.134892	−	0.0980051i
$355$	−19.6711	−	1.29791i	−1.04403	−	0.0688862i
$356$	1.88197	+	5.79210i	0.0997440	+	0.306980i
$357$	−0.291613	−	0.401371i	−0.0154338	−	0.0212428i
$358$	−8.48725	−	11.6817i	−0.448565	−	0.617397i
$359$	−5.25768	−	16.1815i	−0.277490	−	0.854025i	−0.988550	−	0.150894i	$-0.951785\pi$
$359$	−5.25768	−	16.1815i	−0.277490	−	0.854025i	0.711060	−	0.703131i	$-0.248215\pi$
$360$	−0.0562321	+	0.852249i	−0.00296369	+	0.0449175i
$361$	11.9343	+	8.67081i	0.628123	+	0.456358i
$362$			11.9061i			0.625770i
$363$	−17.1097	+	4.90307i	−0.898027	+	0.257344i
$364$	11.7082			0.613677
$365$	−11.2052	−	4.47609i	−0.586509	−	0.234289i
$366$	4.84669	−	14.9166i	0.253341	−	0.779702i
$367$	27.9983	−	9.09719i	1.46150	−	0.474870i	0.532971	−	0.846133i	$-0.321075\pi$
$367$	27.9983	−	9.09719i	1.46150	−	0.474870i	0.928527	+	0.371264i	$0.121075\pi$
$368$	−2.30133	−	3.16751i	−0.119965	−	0.165118i
$369$	1.41525	−	1.02824i	0.0736751	−	0.0535281i
$370$	8.61991	−	5.43351i	0.448128	−	0.282475i
$371$	−3.44273	+	10.5956i	−0.178738	+	0.550098i
$372$	8.44260	−	11.6202i	0.437728	−	0.602481i
$373$		−	16.0743i		−	0.832297i	−0.909297	−	0.416149i	$-0.863380\pi$
$373$		−	16.0743i		−	0.832297i	0.909297	−	0.416149i	$-0.136620\pi$
$374$	−0.0592807	−	0.193956i	−0.00306533	−	0.0100292i
$375$	−13.3000	+	12.2623i	−0.686812	+	0.633220i
$376$	7.18170	+	5.21781i	0.370368	+	0.269088i
$377$	9.18743	+	2.98518i	0.473177	+	0.153744i
$378$	26.0954	−	8.47892i	1.34220	−	0.436109i
$379$	14.6618	−	10.6524i	0.753125	−	0.547178i	−0.143669	−	0.989626i	$-0.545890\pi$
$379$	14.6618	−	10.6524i	0.753125	−	0.547178i	0.896794	+	0.442448i	$0.145890\pi$
$380$	−3.54221	−	2.94864i	−0.181712	−	0.151262i
$381$	7.23149	+	22.2562i	0.370480	+	1.14022i
$382$	10.0033	+	3.25026i	0.511812	+	0.166298i
$383$	7.76587	−	10.6888i	0.396817	−	0.546172i	−0.563124	−	0.826372i	$-0.690401\pi$
$383$	7.76587	−	10.6888i	0.396817	−	0.546172i	0.959942	+	0.280200i	$0.0904008\pi$
$384$	1.61803			0.0825700
$385$	−3.09853	+	37.0570i	−0.157916	+	1.88860i
$386$	−4.86869			−0.247810
$387$	0.812299	−	1.11803i	0.0412915	−	0.0568329i
$388$	−6.94485	−	2.25652i	−0.352572	−	0.114557i
$389$	8.19653	+	25.2263i	0.415580	+	1.27902i	0.911731	+	0.410788i	$0.134746\pi$
$389$	8.19653	+	25.2263i	0.415580	+	1.27902i	−0.496150	+	0.868237i	$0.665254\pi$
$390$	5.40490	−	6.49294i	0.273688	−	0.328783i
$391$	−0.193694	+	0.140727i	−0.00979553	+	0.00711687i
$392$	−17.2542	+	5.60624i	−0.871470	+	0.283158i
$393$	23.5837	+	7.66280i	1.18964	+	0.386537i
$394$	12.9249	+	9.39047i	0.651145	+	0.473085i
$395$	−3.65684	−	14.4252i	−0.183996	−	0.725810i
$396$	1.26664	+	0.0222142i	0.0636512	+	0.00111630i
$397$		−	30.3246i		−	1.52195i	−0.648783	−	0.760974i	$-0.724722\pi$
$397$		−	30.3246i		−	1.52195i	0.648783	−	0.760974i	$-0.275278\pi$
$398$	−9.82047	+	13.5167i	−0.492256	+	0.677532i
$399$	−5.16751	+	15.9039i	−0.258699	+	0.796193i
$400$	−3.62387	−	3.44493i	−0.181194	−	0.172247i
$401$	−15.7565	+	11.4478i	−0.786844	+	0.571676i	−0.907025	−	0.421076i	$-0.861652\pi$
$401$	−15.7565	+	11.4478i	−0.786844	+	0.571676i	0.120181	+	0.992752i	$0.461652\pi$
$402$	−2.37358	−	3.26696i	−0.118384	−	0.162941i
$403$	19.7136	−	6.40532i	0.982002	−	0.319072i
$404$	0.0685623	−	0.211013i	0.00341110	−	0.0104983i
$405$	6.39392	−	16.0062i	0.317717	−	0.795357i
$406$	−20.7444			−1.02952
$407$	−8.66771	−	12.3809i	−0.429642	−	0.613701i
$408$		−	0.0989434i		−	0.00489843i
$409$	−22.9197	−	16.6521i	−1.13330	−	0.823394i	−0.147132	−	0.989117i	$-0.547004\pi$
$409$	−22.9197	−	16.6521i	−1.13330	−	0.823394i	−0.986172	+	0.165723i	$0.947004\pi$
$410$	−0.674234	+	10.2186i	−0.0332981	+	0.504663i
$411$	−0.552183	−	1.69944i	−0.0272372	−	0.0838274i
$412$	0.332713	+	0.457940i	0.0163916	+	0.0225611i
$413$	5.71431	+	7.86508i	0.281183	+	0.387015i
$414$	−0.462133	−	1.42230i	−0.0227126	−	0.0699022i
$415$	1.62705	−	24.6594i	0.0798685	−	1.21048i
$416$	1.88906	+	1.37249i	0.0926190	+	0.0672916i
$417$			16.0284i			0.784914i
$418$	−4.11450	+	5.45918i	−0.201247	+	0.267017i
$419$	15.4826			0.756374			0.378187	−	0.925729i	$-0.376548\pi$
$419$	15.4826			0.756374			0.378187	+	0.925729i	$0.376548\pi$
$420$	−6.72982	+	16.8471i	−0.328381	+	0.822054i
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	−0.648474	−	0.761237i	$-0.724592\pi$
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	0.972070	−	0.234690i	$-0.0754076\pi$
$422$	14.9753	−	4.86578i	0.728988	−	0.236862i
$423$	1.99303	+	2.74317i	0.0969043	+	0.133377i
$424$	−1.79753	+	1.30598i	−0.0872959	+	0.0634242i
$425$	−0.210659	+	0.221601i	−0.0102185	+	0.0107492i
$426$	−4.40815	+	13.5669i	−0.213576	+	0.657319i
$427$	−28.5690	+	39.3219i	−1.38255	+	1.90292i
$428$		−	2.23002i		−	0.107792i
$429$	−10.0068	−	7.54195i	−0.483132	−	0.364129i
$430$	1.98801	+	7.84211i	0.0958702	+	0.378180i
$431$	−21.3896	−	15.5404i	−1.03030	−	0.748557i	−0.0619316	−	0.998080i	$-0.519726\pi$
$431$	−21.3896	−	15.5404i	−1.03030	−	0.748557i	−0.968369	+	0.249523i	$0.919726\pi$
$432$	5.20431	+	1.69098i	0.250393	+	0.0813575i
$433$	−31.2725	+	10.1611i	−1.50286	+	0.488309i	−0.940851	−	0.338821i	$-0.889972\pi$
$433$	−31.2725	+	10.1611i	−1.50286	+	0.488309i	−0.562010	+	0.827130i	$0.689972\pi$
$434$	−36.0105	+	26.1631i	−1.72856	+	1.25587i
$435$	−9.57630	+	11.5041i	−0.459148	+	0.551577i
$436$	2.42976	+	7.47804i	0.116365	+	0.358133i
$437$	7.67495	+	2.49374i	0.367143	+	0.119292i
$438$	−5.13205	+	7.06367i	−0.245219	+	0.337515i
$439$	12.1796			0.581299			0.290649	−	0.956830i	$-0.406129\pi$
$439$	12.1796			0.581299			0.290649	+	0.956830i	$0.406129\pi$
$440$	−4.84391	+	5.61574i	−0.230924	+	0.267720i
$441$	−6.92969			−0.329985
$442$	0.0839280	−	0.115517i	0.00399205	−	0.00549458i
$443$	−15.7961	−	5.13247i	−0.750496	−	0.243851i	−0.0913015	−	0.995823i	$-0.529103\pi$
$443$	−15.7961	−	5.13247i	−0.750496	−	0.243851i	−0.659195	+	0.751972i	$0.729103\pi$
$444$	−2.27844	−	7.01232i	−0.108130	−	0.332790i
$445$	−10.4663	−	8.71246i	−0.496151	−	0.413010i
$446$	11.7757	−	8.55558i	0.557598	−	0.405119i
$447$	13.5300	−	4.39616i	0.639947	−	0.207931i
$448$	−4.76878	−	1.54947i	−0.225304	−	0.0732057i
$449$	−4.33928	−	3.15267i	−0.204783	−	0.148784i	0.480667	−	0.876903i	$-0.340395\pi$
$449$	−4.33928	−	3.15267i	−0.204783	−	0.148784i	−0.685450	+	0.728119i	$0.740395\pi$
$450$	−0.909830	−	1.67918i	−0.0428898	−	0.0791575i
$451$	15.1873	+	0.266353i	0.715143	+	0.0125421i
$452$			12.5617i			0.590852i
$453$	20.5336	−	28.2621i	0.964753	−	1.32787i
$454$	−3.03966	+	9.35512i	−0.142658	+	0.439058i
$455$	−22.1475	+	13.9606i	−1.03829	+	0.654481i
$456$	−2.69808	+	1.96027i	−0.126349	+	0.0917981i
$457$	−2.12330	−	2.92247i	−0.0993237	−	0.136707i	0.756462	−	0.654037i	$-0.226926\pi$
$457$	−2.12330	−	2.92247i	−0.0993237	−	0.136707i	−0.855786	+	0.517330i	$0.826926\pi$
$458$	−14.7869	+	4.80456i	−0.690947	+	0.224502i
$459$	0.103404	−	0.318246i	0.00482650	−	0.0148544i
$460$	8.13010	+	3.24769i	0.379068	+	0.151424i
$461$	−40.6625			−1.89384			−0.946922	−	0.321464i	$-0.895825\pi$
$461$	−40.6625			−1.89384			−0.946922	+	0.321464i	$0.895825\pi$
$462$	25.4415	+	8.76257i	1.18365	+	0.407672i
$463$		−	2.11880i		−	0.0984690i	−0.998787	−	0.0492345i	$-0.984322\pi$
$463$		−	2.11880i		−	0.0984690i	0.998787	−	0.0492345i	$-0.0156782\pi$
$464$	−3.34700	−	2.43174i	−0.155381	−	0.112891i
$465$	−2.11454	+	32.0479i	−0.0980596	+	1.48618i
$466$	−8.00252	−	24.6292i	−0.370709	−	1.14093i
$467$	−8.08494	−	11.1280i	−0.374126	−	0.514941i	0.579890	−	0.814695i	$-0.303095\pi$
$467$	−8.08494	−	11.1280i	−0.374126	−	0.514941i	−0.954017	+	0.299754i	$0.903095\pi$
$468$	0.524243	+	0.721558i	0.0242331	+	0.0333540i
$469$	3.86707	+	11.9016i	0.178565	+	0.549565i
$470$	−19.8067	−	1.30686i	−0.913613	−	0.0602810i
$471$	−4.46993	−	3.24760i	−0.205964	−	0.149641i
$472$			1.93885i			0.0892428i
$473$	11.4756	−	3.50741i	0.527650	−	0.161271i
$474$	−10.7683			−0.494606
$475$	10.2164	+	1.35407i	0.468761	+	0.0621289i
$476$	−0.0947508	+	0.291613i	−0.00434289	+	0.0133661i
$477$	−0.807142	+	0.262256i	−0.0369565	+	0.0120079i
$478$	11.7534	+	16.1771i	0.537586	+	0.739924i
$479$	25.4118	−	18.4628i	1.16110	−	0.843586i	0.171180	−	0.985240i	$-0.445242\pi$
$479$	25.4118	−	18.4628i	1.16110	−	0.843586i	0.989916	+	0.141654i	$0.0452421\pi$
$480$	−3.06071	+	1.92930i	−0.139702	+	0.0880602i
$481$	3.28806	−	10.1196i	0.149922	−	0.461414i
$482$	5.29818	−	7.29232i	0.241326	−	0.332156i
$483$		−	31.7650i		−	1.44536i
$484$	8.66700	+	6.77371i	0.393954	+	0.307896i
$485$	15.8277	−	4.01238i	0.718698	−	0.182193i
$486$	3.19098	+	2.31838i	0.144746	+	0.105164i
$487$	7.14274	+	2.32082i	0.323668	+	0.105166i	0.466344	−	0.884603i	$-0.345571\pi$
$487$	7.14274	+	2.32082i	0.323668	+	0.105166i	−0.142676	+	0.989769i	$0.545571\pi$
$488$	−9.21895	+	2.99542i	−0.417322	+	0.135596i
$489$	22.7905	−	16.5582i	1.03062	−	0.748789i
$490$	25.9538	−	31.1784i	1.17247	−	1.40850i
$491$	3.48008	+	10.7106i	0.157054	+	0.483361i	0.998363	−	0.0571923i	$-0.0182148\pi$
$491$	3.48008	+	10.7106i	0.157054	+	0.483361i	−0.841310	+	0.540554i	$0.818215\pi$
$492$	7.04767	+	2.28993i	0.317733	+	0.103238i
$493$	−0.148702	+	0.204671i	−0.00669719	+	0.00921790i
$494$	−4.81281			−0.216539
$495$	−2.42250	+	1.46829i	−0.108883	+	0.0659948i
$496$	−8.87707			−0.398592
$497$	25.9840	−	35.7640i	1.16554	−	1.60423i
$498$	−17.0073	−	5.52599i	−0.762114	−	0.247626i
$499$	8.33753	+	25.6603i	0.373239	+	1.14871i	0.944659	+	0.328054i	$0.106393\pi$
$499$	8.33753	+	25.6603i	0.373239	+	1.14871i	−0.571420	+	0.820658i	$0.693607\pi$
$500$	10.9627	+	2.19550i	0.490265	+	0.0981857i
$501$	−4.32760	+	3.14419i	−0.193343	+	0.140472i
$502$	−1.24746	+	0.405323i	−0.0556767	+	0.0180905i
$503$	−30.5818	−	9.93662i	−1.36357	−	0.443052i	−0.466339	−	0.884606i	$-0.654427\pi$
$503$	−30.5818	−	9.93662i	−1.36357	−	0.443052i	−0.897235	+	0.441554i	$0.854427\pi$
$504$	−1.54947	−	1.12576i	−0.0690190	−	0.0501452i
$505$	0.121913	+	0.480909i	0.00542504	+	0.0214002i
$506$	4.22866	−	12.2776i	0.187987	−	0.545806i
$507$			12.2125i			0.542375i
$508$	8.50112	−	11.7008i	0.377176	−	0.519139i
$509$	−3.64048	+	11.2043i	−0.161362	+	0.496620i	−0.998750	−	0.0499888i	$-0.984081\pi$
$509$	−3.64048	+	11.2043i	−0.161362	+	0.496620i	0.837388	+	0.546609i	$0.184081\pi$
$510$	0.117978	+	0.187164i	0.00522414	+	0.00828775i
$511$	21.8899	−	15.9039i	0.968352	−	0.703549i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−10.7269	+	3.48537i	−0.473603	+	0.153883i
$514$	1.37945	−	4.24551i	0.0608449	−	0.187261i
$515$	−1.17540	−	0.469532i	−0.0517945	−	0.0206901i
$516$	5.85410			0.257712
$517$	−0.516268	+	29.4374i	−0.0227054	+	1.29465i
$518$			22.8491i			1.00393i
$519$	6.71341	+	4.87758i	0.294686	+	0.214102i
$520$	−5.20992	−	0.343754i	−0.228470	−	0.0150746i
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	0.965568	−	0.260152i	$-0.0837728\pi$
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	−0.934074	+	0.357079i	$0.883773\pi$
$522$	−0.928842	−	1.27844i	−0.0406543	−	0.0559559i
$523$	−0.901612	−	1.24096i	−0.0394248	−	0.0542635i	0.788850	−	0.614586i	$-0.210677\pi$
$523$	−0.901612	−	1.24096i	−0.0394248	−	0.0542635i	−0.828274	+	0.560323i	$0.810677\pi$
$524$	−4.73587	−	14.5755i	−0.206888	−	0.636735i
$525$	−7.35777	−	39.8928i	−0.321119	−	1.74107i
$526$	11.4711	+	8.33426i	0.500165	+	0.363391i
$527$			0.542836i			0.0236463i
$528$	3.07768	+	4.39616i	0.133939	+	0.191318i
$529$	7.67080			0.333513
$530$	1.84303	−	4.61376i	0.0800563	−	0.200409i
$531$	−0.228850	+	0.704328i	−0.00993125	+	0.0305652i
$532$	9.82918	−	3.19369i	0.426149	−	0.138464i
$533$	6.28578	+	8.65163i	0.272267	+	0.374744i
$534$	−7.97214	+	5.79210i	−0.344988	+	0.250648i
$535$	2.65902	+	4.21836i	0.114959	+	0.182375i
$536$	−0.771224	+	2.37358i	−0.0333118	+	0.102523i
$537$	13.7327	−	18.9014i	0.592608	−	0.815655i
$538$			31.9952i			1.37941i
$539$	−48.0515	−	36.2156i	−2.06972	−	1.55992i
$540$	−11.8609	+	3.00678i	−0.510411	+	0.129391i
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	0.823008	−	0.568029i	$-0.192294\pi$
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	−0.285904	+	0.958258i	$0.592294\pi$
$542$	1.00944	+	0.327988i	0.0433593	+	0.0140883i
$543$	−18.3216	+	5.95305i	−0.786255	+	0.255470i
$544$	−0.0494717	+	0.0359433i	−0.00212108	+	0.00154106i
$545$	−13.5128	−	11.2485i	−0.578826	−	0.481831i
$546$	5.85410	+	18.0171i	0.250532	+	0.771060i
$547$	10.1261	+	3.29017i	0.432960	+	0.140677i	0.517385	−	0.855752i	$-0.326905\pi$
$547$	10.1261	+	3.29017i	0.432960	+	0.140677i	−0.0844251	+	0.996430i	$0.526905\pi$
$548$	−0.649130	+	0.893451i	−0.0277295	+	0.0381663i
$549$	−3.70254			−0.158021
$550$	2.46678	−	16.3986i	0.105184	−	0.699240i
$551$	8.52724			0.363272
$552$	3.72363	−	5.12513i	0.158488	−	0.218140i
$553$	31.7372	+	10.3120i	1.34960	+	0.438513i
$554$	−2.04979	−	6.30859i	−0.0870871	−	0.268026i
$555$	12.6713	+	10.5479i	0.537866	+	0.447734i
$556$	8.01420	−	5.82265i	0.339878	−	0.246936i
$557$	32.2595	−	10.4818i	1.36688	−	0.444126i	0.468545	−	0.883439i	$-0.344778\pi$
$557$	32.2595	−	10.4818i	1.36688	−	0.444126i	0.898334	+	0.439313i	$0.144778\pi$
$558$	−3.22478	−	1.04780i	−0.136516	−	0.0443567i
$559$	6.83470	+	4.96570i	0.289077	+	0.210027i
$560$	10.8683	−	2.75516i	0.459269	−	0.116427i
$561$	0.268827	−	0.188201i	0.0113499	−	0.00794587i
$562$			15.6464i			0.660005i
$563$	0.789857	−	1.08714i	0.0332885	−	0.0458177i	−0.792048	−	0.610458i	$-0.790985\pi$
$563$	0.789857	−	1.08714i	0.0332885	−	0.0458177i	0.825337	+	0.564641i	$0.190985\pi$
$564$	−4.43854	+	13.6604i	−0.186896	+	0.575207i
$565$	−14.9782	−	23.7620i	−0.630139	−	0.999674i
$566$	18.2033	−	13.2255i	0.765142	−	0.555908i
$567$	22.7182	+	31.2689i	0.954073	+	1.31317i
$568$	8.38481	−	2.72439i	0.351819	−	0.114313i
$569$	9.70595	−	29.8718i	0.406894	−	1.25229i	−0.512409	−	0.858742i	$-0.671247\pi$
$569$	9.70595	−	29.8718i	0.406894	−	1.25229i	0.919303	−	0.393550i	$-0.128753\pi$
$570$	2.76638	−	6.92522i	0.115871	−	0.290065i
$571$	9.25361			0.387252			0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361			0.387252			0.193626	+	0.981075i	$0.437975\pi$
$572$	−0.135798	+	7.74317i	−0.00567801	+	0.323758i
$573$			17.0186i			0.710962i
$574$	−18.5785	−	13.4981i	−0.775451	−	0.563398i
$575$	−19.2516	+	3.55073i	−0.802845	+	0.148075i
$576$	−0.118034	−	0.363271i	−0.00491808	−	0.0151363i
$577$	25.4998	+	35.0975i	1.06157	+	1.46113i	0.878327	+	0.478060i	$0.158660\pi$
$577$	25.4998	+	35.0975i	1.06157	+	1.46113i	0.183244	+	0.983068i	$0.441340\pi$
$578$	−9.99015	−	13.7503i	−0.415536	−	0.571936i
$579$	−2.43434	−	7.49214i	−0.101168	−	0.311363i
$580$	9.23082	+	0.609057i	0.383289	+	0.0252897i
$581$	44.8332	+	32.5732i	1.85999	+	1.35136i
$582$		−	11.8153i		−	0.489760i
$583$	−6.96744	−	2.39973i	−0.288562	−	0.0993865i
$584$	5.39616			0.223295
$585$	−1.85204	−	0.739823i	−0.0765723	−	0.0305879i
$586$	−5.62063	+	17.2985i	−0.232186	+	0.714595i
$587$	−3.05524	+	0.992708i	−0.126103	+	0.0409734i	−0.371389	−	0.928477i	$-0.621118\pi$
$587$	−3.05524	+	0.992708i	−0.126103	+	0.0409734i	0.245285	+	0.969451i	$0.421118\pi$
$588$	−17.2542	−	23.7484i	−0.711552	−	0.979367i
$589$	14.8026	−	10.7547i	0.609929	−	0.443139i
$590$	−2.31184	−	3.66758i	−0.0951768	−	0.150992i
$591$	−7.98801	+	24.5846i	−0.328583	+	1.01127i
$592$	−2.67847	+	3.68660i	−0.110084	+	0.151518i
$593$			0.0315027i			0.00129366i	1.00000		0.000646829i	$0.000205892\pi$
$593$			0.0315027i			0.00129366i	−1.00000		0.000646829i	$0.999794\pi$
$594$	5.30482	+	17.3564i	0.217660	+	0.712143i
$595$	−0.168479	−	0.664600i	−0.00690696	−	0.0272460i
$596$	−7.11314	−	5.16800i	−0.291366	−	0.211689i
$597$	−25.7103	−	8.35379i	−1.05225	−	0.341898i
$598$	8.69471	−	2.82508i	0.355553	−	0.115526i
$599$	−8.50993	+	6.18283i	−0.347706	+	0.252623i	−0.747906	−	0.663804i	$-0.768941\pi$
$599$	−8.50993	+	6.18283i	−0.347706	+	0.252623i	0.400200	+	0.916428i	$0.368941\pi$
$600$	3.48927	−	7.29903i	0.142449	−	0.297982i
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	0.980043	+	0.198788i	$0.0637005\pi$
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	−0.676026	+	0.736877i	$0.736300\pi$
$602$	−17.2536	−	5.60604i	−0.703205	−	0.228485i
$603$	−0.560327	+	0.771224i	−0.0228183	+	0.0314067i
$604$	−21.5903			−0.878497
$605$	−24.4715	−	2.47901i	−0.994908	−	0.100786i
$606$	0.358997			0.0145833
$607$	−1.46340	+	2.01420i	−0.0593975	+	0.0817537i	−0.837682	−	0.546158i	$-0.816090\pi$
$607$	−1.46340	+	2.01420i	−0.0593975	+	0.0817537i	0.778285	+	0.627911i	$0.216090\pi$
$608$	1.96027	+	0.636930i	0.0794995	+	0.0258309i
$609$	−10.3722	−	31.9223i	−0.420302	−	1.29356i
$610$	13.8671	−	16.6587i	0.561464	−	0.674489i
$611$	−16.7694	+	12.1836i	−0.678415	+	0.492898i
$612$	−0.0222142	+	0.00721782i	−0.000897955	+	0.000291763i
$613$	−35.7338	−	11.6106i	−1.44328	−	0.468949i	−0.520359	−	0.853948i	$-0.674202\pi$
$613$	−35.7338	−	11.6106i	−1.44328	−	0.468949i	−0.922917	+	0.384999i	$0.874202\pi$
$614$	10.0172	+	7.27794i	0.404262	+	0.293714i
$615$	−16.0620	+	4.07178i	−0.647682	+	0.164190i
$616$	−4.86089	−	15.9039i	−0.195851	−	0.640788i
$617$			45.5803i			1.83499i	0.397744	+	0.917496i	$0.369793\pi$
$617$			45.5803i			1.83499i	−0.397744	+	0.917496i	$0.630207\pi$
$618$	−0.538341	+	0.740963i	−0.0216553	+	0.0298059i
$619$	−1.77382	+	5.45924i	−0.0712957	+	0.219425i	−0.980355	−	0.197241i	$-0.936802\pi$
$619$	−1.77382	+	5.45924i	−0.0712957	+	0.219425i	0.909059	+	0.416667i	$0.136802\pi$
$620$	16.7921	−	10.5848i	0.674386	−	0.425096i
$621$	17.3330	−	12.5932i	0.695550	−	0.505347i
$622$	−5.53104	−	7.61283i	−0.221775	−	0.305246i
$623$	29.0427	−	9.43655i	1.16357	−	0.378067i
$624$	−1.16751	+	3.59321i	−0.0467376	+	0.143844i
$625$	−23.3551	+	8.91853i	−0.934203	+	0.356741i
$626$	15.2317			0.608781
$627$	−10.4581	−	3.60197i	−0.417655	−	0.143849i
$628$			3.41472i			0.136262i
$629$	0.225437	+	0.163789i	0.00898875	+	0.00653071i
$630$	4.27334	+	0.281959i	0.170254	+	0.0112335i
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	0.997304	−	0.0733811i	$-0.0233790\pi$
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	−0.849968	+	0.526834i	$0.823379\pi$
$632$	3.91183	+	5.38417i	0.155604	+	0.214171i
$633$	14.9753	+	20.6118i	0.595216	+	0.819245i
$634$	4.15834	+	12.7981i	0.165149	+	0.508276i
$635$	−2.12920	+	32.2700i	−0.0844948	+	1.28060i
$636$	−2.90847	−	2.11313i	−0.115328	−	0.0837909i
$637$		−	42.3621i		−	1.67845i
$638$	0.240605	−	13.7192i	0.00952563	−	0.543148i
$639$	3.36753			0.133217
$640$	2.07652	+	0.829496i	0.0820817	+	0.0327887i
$641$	−10.8526	+	33.4007i	−0.428650	+	1.31925i	0.470805	+	0.882237i	$0.343964\pi$
$641$	−10.8526	+	33.4007i	−0.428650	+	1.31925i	−0.899455	+	0.437013i	$0.856036\pi$
$642$	3.43164	−	1.11501i	0.135436	−	0.0440059i
$643$	−20.9529	−	28.8392i	−0.826302	−	1.13731i	−0.988600	−	0.150565i	$-0.951891\pi$
$643$	−20.9529	−	28.8392i	−0.826302	−	1.13731i	0.162298	−	0.986742i	$-0.448109\pi$
$644$	−15.8825	+	11.5393i	−0.625858	+	0.454712i
$645$	−11.0738	+	6.98028i	−0.436029	+	0.274848i
$646$	0.0389485	−	0.119871i	0.00153241	−	0.00471627i
$647$	11.8476	−	16.3068i	0.465778	−	0.641088i	−0.509917	−	0.860224i	$-0.670324\pi$
$647$	11.8476	−	16.3068i	0.465778	−	0.641088i	0.975694	+	0.219136i	$0.0703238\pi$
$648$			7.70820i			0.302807i
$649$	−5.26781	+	3.68791i	−0.206780	+	0.144763i
$650$	10.2651	−	5.56192i	0.402630	−	0.218156i
$651$	−58.2661	−	42.3328i	−2.28363	−	1.65915i
$652$	−16.5582	−	5.38010i	−0.648470	−	0.210701i
$653$	23.1905	−	7.53504i	0.907513	−	0.294869i	0.182178	−	0.983266i	$-0.441685\pi$
$653$	23.1905	−	7.53504i	0.907513	−	0.294869i	0.725334	+	0.688397i	$0.241685\pi$
$654$	−10.2926	+	7.47804i	−0.402474	+	0.292414i
$655$	26.3380	+	21.9245i	1.02911	+	0.856660i
$656$	−1.41525	−	4.35570i	−0.0552563	−	0.170061i
$657$	1.96027	+	0.636930i	0.0764774	+	0.0248490i
$658$	26.1631	−	36.0105i	1.01994	−	1.40383i
$659$	6.98788			0.272209			0.136104	−	0.990694i	$-0.456542\pi$
$659$	6.98788			0.272209			0.136104	+	0.990694i	$0.456542\pi$
$660$	−11.0637	−	4.64613i	−0.430654	−	0.180851i
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$	−2.24673	+	3.09235i	−0.0873215	+	0.120188i
$663$	0.219726	+	0.0713934i	0.00853346	+	0.00277269i
$664$	3.41525	+	10.5111i	0.132537	+	0.407908i
$665$	−14.7850	+	17.7613i	−0.573339	+	0.688755i
$666$	−1.40815	+	1.02308i	−0.0545649	+	0.0396437i
$667$	−15.4051	+	5.00542i	−0.596488	+	0.193811i
$668$	3.14419	+	1.02161i	0.121652	+	0.0395272i
$669$	19.0536	+	13.8432i	0.736653	+	0.535210i
$670$	−1.37133	−	5.40952i	−0.0529793	−	0.208988i
$671$	−25.6740	−	19.3501i	−0.991133	−	0.747001i
$672$		−	8.11314i		−	0.312971i
$673$	−4.68377	+	6.44665i	−0.180546	+	0.248500i	−0.889692	−	0.456562i	$-0.849081\pi$
$673$	−4.68377	+	6.44665i	−0.180546	+	0.248500i	0.709146	+	0.705062i	$0.249081\pi$
$674$	2.92538	−	9.00338i	0.112681	−	0.346797i
$675$	18.8511	−	19.8303i	0.725580	−	0.763270i
$676$	6.10624	−	4.43644i	0.234855	−	0.170632i
$677$	−8.48443	−	11.6778i	−0.326083	−	0.448815i	0.614229	−	0.789128i	$-0.289467\pi$
$677$	−8.48443	−	11.6778i	−0.326083	−	0.448815i	−0.940312	+	0.340313i	$0.889467\pi$
$678$	−19.3304	+	6.28084i	−0.742381	+	0.241214i
$679$	−11.3146	+	34.8229i	−0.434216	+	1.33638i
$680$	0.0507240	−	0.126980i	0.00194518	−	0.00486946i
$681$	−15.9159			−0.609898
$682$	−16.8852	−	24.1188i	−0.646567	−	0.923557i
$683$			29.6723i			1.13538i	0.823242	+	0.567690i	$0.192163\pi$
$683$			29.6723i			1.13538i	−0.823242	+	0.567690i	$0.807837\pi$
$684$	0.636930	+	0.462757i	0.0243536	+	0.0176940i
$685$	0.162582	−	2.46408i	0.00621194	−	0.0941476i
$686$	17.2645	+	53.1345i	0.659160	+	2.02869i
$687$	−14.7869	−	20.3524i	−0.564156	−	0.776493i
$688$	−2.12663	−	2.92705i	−0.0810769	−	0.111593i
$689$	−1.60321	−	4.93417i	−0.0610774	−	0.187977i
$690$	−0.932624	+	14.1348i	−0.0355044	+	0.538102i
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.0347577	−	0.999396i	$-0.511066\pi$
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.961223	+	0.275774i	$0.911066\pi$
$692$		−	5.12859i		−	0.194960i
$693$	0.111386	−	6.35120i	0.00423121	−	0.241262i
$694$	16.5424			0.627943
$695$	−8.21706	+	20.5702i	−0.311691	+	0.780272i
$696$	2.06856	−	6.36638i	0.0784087	−	0.241317i
$697$	−0.266353	+	0.0865432i	−0.0100888	+	0.00327806i
$698$	17.1791	+	23.6451i	0.650240	+	0.894979i
$699$	33.8992	−	24.6292i	1.28219	−	0.931562i
$700$	−17.2736	+	18.1708i	−0.652879	+	0.686792i
$701$	5.86089	−	18.0380i	0.221363	−	0.681284i	−0.777278	−	0.629157i	$-0.783400\pi$
$701$	5.86089	−	18.0380i	0.221363	−	0.681284i	0.998640	−	0.0521266i	$-0.0165999\pi$
$702$	−7.51043	+	10.3372i	−0.283463	+	0.390153i
$703$		−	9.39242i		−	0.354242i
$704$	1.08005	−	3.13584i	0.0407058	−	0.118186i
$705$	−7.89228	−	31.1328i	−0.297241	−	1.17253i
$706$	−22.5878	−	16.4110i	−0.850103	−	0.617636i
$707$	−1.05806	−	0.343785i	−0.0397925	−	0.0129294i
$708$	−2.98358	+	0.969425i	−0.112130	+	0.0364332i
$709$	6.78617	−	4.93044i	0.254860	−	0.185167i	−0.453018	−	0.891501i	$-0.649653\pi$
$709$	6.78617	−	4.93044i	0.254860	−	0.185167i	0.707878	+	0.706335i	$0.249653\pi$
$710$	−12.6124	+	15.1514i	−0.473335	+	0.568620i
$711$	0.785540	+	2.41764i	0.0294600	+	0.0906687i
$712$	5.79210	+	1.88197i	0.217068	+	0.0705297i
$713$	−20.4290	+	28.1182i	−0.765074	+	1.05303i
$714$	−0.496121			−0.0185669
$715$	−8.97588	−	14.8091i	−0.335679	−	0.553828i
$716$	−14.4394			−0.539625
$717$	−19.0173	+	26.1751i	−0.710216	+	0.977528i
$718$	−16.1815	−	5.25768i	−0.603887	−	0.196215i
$719$	−2.33218	−	7.17771i	−0.0869756	−	0.267684i	0.898104	−	0.439783i	$-0.144945\pi$
$719$	−2.33218	−	7.17771i	−0.0869756	−	0.267684i	−0.985079	+	0.172100i	$0.944945\pi$
$720$	0.656431	+	0.546432i	0.0244638	+	0.0203643i
$721$	2.29620	−	1.66829i	0.0855150	−	0.0621303i
$722$	14.0297	−	4.55851i	0.522130	−	0.169650i
$723$	13.8708	+	4.50690i	0.515861	+	0.167614i
$724$	9.63223	+	6.99822i	0.357979	+	0.260087i
$725$	−18.1875	+	9.85449i	−0.675466	+	0.365987i
$726$	−6.09017	+	16.7240i	−0.226027	+	0.620686i
$727$		−	24.2826i		−	0.900593i	−0.892879	−	0.450297i	$-0.851318\pi$
$727$		−	24.2826i		−	0.900593i	0.892879	−	0.450297i	$-0.148682\pi$
$728$	6.88191	−	9.47214i	0.255061	−	0.351061i
$729$	−9.11803	+	28.0624i	−0.337705	+	1.03935i
$730$	−10.2075	+	6.43425i	−0.377797	+	0.238142i
$731$	−0.178990	+	0.130044i	−0.00662019	+	0.00480985i
$732$	−9.21895	−	12.6888i	−0.340742	−	0.468992i
$733$	−20.3541	+	6.61345i	−0.751796	+	0.244273i	−0.659754	−	0.751482i	$-0.729340\pi$
$733$	−20.3541	+	6.61345i	−0.751796	+	0.244273i	−0.0920424	+	0.995755i	$0.529340\pi$
$734$	9.09719	−	27.9983i	0.335784	−	1.03344i
$735$	60.9555	+	24.3495i	2.24838	+	0.898147i
$736$	−3.91525			−0.144318
$737$	−7.91593	+	2.41943i	−0.291587	+	0.0891207i
$738$		−	1.74935i		−	0.0643944i
$739$	28.4419	+	20.6642i	1.04625	+	0.760147i	0.971496	−	0.237055i	$-0.0761823\pi$
$739$	28.4419	+	20.6642i	1.04625	+	0.760147i	0.0747558	+	0.997202i	$0.476182\pi$
$740$	0.670853	−	10.1674i	0.0246610	−	0.373761i
$741$	−2.40640	−	7.40615i	−0.0884015	−	0.272072i
$742$	6.54846	+	9.01318i	0.240401	+	0.330884i
$743$	20.0435	+	27.5875i	0.735324	+	1.01209i	0.998874	+	0.0474407i	$0.0151065\pi$
$743$	20.0435	+	27.5875i	0.735324	+	1.01209i	−0.263550	+	0.964646i	$0.584893\pi$
$744$	−4.43854	−	13.6604i	−0.162725	−	0.500815i
$745$	19.6176	+	1.29438i	0.718732	+	0.0474225i
$746$	−13.0044	−	9.44825i	−0.476125	−	0.345925i
$747$			4.22148i			0.154456i
$748$	−0.191758	−	0.0660453i	−0.00701136	−	0.00241485i
$749$	−11.1817			−0.408572
$750$	2.10280	+	17.9675i	0.0767834	+	0.656082i
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	0.517884	+	0.855451i	$0.326720\pi$
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	−0.921799	+	0.387669i	$0.873280\pi$
$752$	8.44260	−	2.74317i	0.307870	−	0.100033i
$753$	−1.24746	−	1.71698i	−0.0454599	−	0.0625701i
$754$	7.81529	−	5.67814i	0.284616	−	0.206786i
$755$	40.8408	−	25.7437i	1.48635	−	0.936911i
$756$	8.47892	−	26.0954i	0.308375	−	0.949082i
$757$	−14.2408	+	19.6008i	−0.517592	+	0.712404i	−0.985176	−	0.171544i	$-0.945124\pi$
$757$	−14.2408	+	19.6008i	−0.517592	+	0.712404i	0.467584	+	0.883948i	$0.345124\pi$
$758$		−	18.1230i		−	0.658256i
$759$	21.0076	+	0.368428i	0.762528	+	0.0133731i
$760$	−4.46756	+	1.13254i	−0.162055	+	0.0410817i
$761$	−8.62191	−	6.26419i	−0.312544	−	0.227077i	0.420443	−	0.907319i	$-0.361875\pi$
$761$	−8.62191	−	6.26419i	−0.312544	−	0.227077i	−0.732987	+	0.680242i	$0.761875\pi$
$762$	22.2562	+	7.23149i	0.806258	+	0.261969i
$763$	37.4964	−	12.1833i	1.35746	−	0.441065i
$764$	8.50930	−	6.18237i	0.307856	−	0.223670i
$765$	0.0334145	−	0.0401410i	0.00120810	−	0.00145130i
$766$	−4.08276	−	12.5654i	−0.147516	−	0.454008i
$767$	−4.30566	−	1.39899i	−0.155468	−	0.0505147i
$768$	0.951057	−	1.30902i	0.0343183	−	0.0472351i
$769$	−25.8297			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$769$	−25.8297			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$770$	28.1584	+	24.2883i	1.01476	+	0.875289i
$771$	7.22289			0.260126
$772$	−2.86174	+	3.93885i	−0.102996	+	0.141762i
$773$	−11.4679	−	3.72614i	−0.412471	−	0.134020i	0.0954286	−	0.995436i	$-0.469578\pi$
$773$	−11.4679	−	3.72614i	−0.412471	−	0.134020i	−0.507899	+	0.861416i	$0.669578\pi$
$774$	−0.427051	−	1.31433i	−0.0153500	−	0.0472425i
$775$	−19.1433	+	40.0449i	−0.687647	+	1.43846i
$776$	−5.90765	+	4.29216i	−0.212072	+	0.154079i
$777$	−35.1612	+	11.4246i	−1.26140	+	0.409854i
$778$	25.2263	+	8.19653i	0.904407	+	0.293860i
$779$	7.63693	+	5.54855i	0.273621	+	0.198798i
$780$	−2.07597	−	8.18911i	−0.0743318	−	0.293217i
$781$	23.3510	+	17.5992i	0.835563	+	0.629750i
$782$			0.239419i			0.00856161i
$783$	13.3068	−	18.3153i	0.475547	−	0.654534i
$784$	−5.60624	+	17.2542i	−0.200223	+	0.616222i
$785$	−4.07163	−	6.45938i	−0.145323	−	0.230545i
$786$	20.0615	−	14.5755i	0.715569	−	0.519892i
$787$	−10.6725	−	14.6895i	−0.380435	−	0.523624i	0.575265	−	0.817967i	$-0.304899\pi$
$787$	−10.6725	−	14.6895i	−0.380435	−	0.523624i	−0.955700	+	0.294343i	$0.904899\pi$
$788$	15.1941	−	4.93686i	0.541267	−	0.175868i
$789$	−7.08954	+	21.8194i	−0.252394	+	0.776790i
$790$	−13.8197	−	5.52046i	−0.491681	−	0.196409i
$791$	62.9867			2.23955
$792$	0.762486	−	1.01168i	0.0270938	−	0.0359484i
$793$		−	22.6342i		−	0.803762i
$794$	−24.5331	−	17.8243i	−0.870648	−	0.632562i
$795$	8.02137	+	0.529256i	0.284489	+	0.0187708i
$796$	5.16292	+	15.8898i	0.182995	+	0.563201i
$797$	0.946725	+	1.30306i	0.0335347	+	0.0461566i	0.825455	−	0.564468i	$-0.190919\pi$
$797$	0.946725	+	1.30306i	0.0335347	+	0.0461566i	−0.791920	+	0.610624i	$0.790919\pi$
$798$	9.82918	+	13.5287i	0.347949	+	0.478911i
$799$	−0.167746	−	0.516268i	−0.00593441	−	0.0182642i
$800$	−4.91707	+	0.906896i	−0.173845	+	0.0320636i
$801$	1.88197	+	1.36733i	0.0664960	+	0.0483122i
$802$			19.4762i			0.687727i
$803$	10.2641	+	14.6612i	0.362213	+	0.517384i
$804$	−4.03818			−0.142416
$805$	16.2845	−	40.7659i	0.573954	−	1.43681i
$806$	6.40532	−	19.7136i	0.225618	−	0.694380i
$807$	−49.2356	+	15.9976i	−1.73318	+	0.563143i
$808$	−0.130413	−	0.179498i	−0.00458792	−	0.00631473i
$809$	20.7273	−	15.0593i	0.728733	−	0.529455i	−0.160429	−	0.987047i	$-0.551288\pi$
$809$	20.7273	−	15.0593i	0.728733	−	0.529455i	0.889162	+	0.457592i	$0.151288\pi$
$810$	−9.19107	−	14.5810i	−0.322941	−	0.512325i
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	−0.369012	−	0.929424i	$-0.620304\pi$
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	0.844839	−	0.535020i	$-0.179696\pi$
$812$	−12.1932	+	16.7825i	−0.427898	+	0.588951i
$813$			1.71737i			0.0602306i
$814$	−15.1111	−	0.265017i	−0.529646	−	0.00928883i
$815$	37.7370	−	9.56650i	1.32187	−	0.335100i
$816$	−0.0800469	−	0.0581575i	−0.00280220	−	0.00203592i
$817$	7.09233	+	2.30444i	0.248129	+	0.0806220i
$818$	−26.9437	+	8.75453i	−0.942063	+	0.306095i
$819$	3.61803	−	2.62866i	0.126424	−	0.0918527i
$820$	7.87075	+	6.55183i	0.274859	+	0.228800i
$821$	−5.43938	−	16.7407i	−0.189836	−	0.584254i	0.810163	−	0.586205i	$-0.199379\pi$
$821$	−5.43938	−	16.7407i	−0.189836	−	0.584254i	−0.999998	+	0.00195152i	$0.999379\pi$
$822$	−1.69944	−	0.552183i	−0.0592749	−	0.0192596i
$823$	−7.43854	+	10.2383i	−0.259291	+	0.356884i	−0.918738	−	0.394867i	$-0.870791\pi$
$823$	−7.43854	+	10.2383i	−0.259291	+	0.356884i	0.659447	+	0.751751i	$0.270791\pi$
$824$	0.566045			0.0197191
$825$	26.4683	−	4.40333i	0.921507	−	0.153304i
$826$	9.72177			0.338264
$827$	−5.19856	+	7.15520i	−0.180772	+	0.248811i	−0.889780	−	0.456389i	$-0.849143\pi$
$827$	−5.19856	+	7.15520i	−0.180772	+	0.248811i	0.709009	+	0.705200i	$0.249143\pi$
$828$	−1.42230	−	0.462133i	−0.0494283	−	0.0160602i
$829$	−11.6571	−	35.8767i	−0.404866	−	1.24605i	−0.921007	−	0.389546i	$-0.872632\pi$
$829$	−11.6571	−	35.8767i	−0.404866	−	1.24605i	0.516141	−	0.856504i	$-0.327368\pi$
$830$	−18.9935	−	15.8107i	−0.659274	−	0.548798i
$831$	8.68303	−	6.30859i	0.301211	−	0.218843i
$832$	2.22073	−	0.721558i	0.0769899	−	0.0250155i
$833$	1.05510	+	0.342823i	0.0365571	+	0.0118781i
$834$	12.9672	+	9.42125i	0.449019	+	0.326231i
$835$	−7.16576	+	1.81655i	−0.247981	+	0.0628643i
$836$	1.99813	+	6.53752i	0.0691068	+	0.226105i
$837$		−	48.5765i		−	1.67905i
$838$	9.10044	−	12.5257i	0.314369	−	0.432692i
$839$	11.8934	−	36.6041i	0.410606	−	1.26372i	−0.505517	−	0.862817i	$-0.668698\pi$
$839$	11.8934	−	36.6041i	0.410606	−	1.26372i	0.916123	−	0.400898i	$-0.131302\pi$
$840$	9.67390	+	15.3470i	0.333781	+	0.529522i
$841$	9.61452	−	6.98536i	0.331535	−	0.240874i
$842$	−12.6293	−	17.3828i	−0.435236	−	0.599051i
$843$	−24.0774	+	7.82321i	−0.829269	+	0.269446i
$844$	4.86578	−	14.9753i	0.167487	−	0.515472i
$845$	−6.26080	+	15.6730i	−0.215378	+	0.539168i
$846$	3.39074			0.116576
$847$	33.9647	−	43.4580i	1.16704	−	1.49324i
$848$			2.22187i			0.0762994i
$849$	29.4536	+	21.3993i	1.01084	+	0.734421i
$850$	0.0554570	+	0.300680i	0.00190216	+	0.0103133i
$851$	5.51328	+	16.9681i	0.188993	+	0.581660i
$852$	8.38481	+	11.5407i	0.287259	+	0.395378i
$853$	−29.9122	−	41.1706i	−1.02417	−	1.40965i	−0.909237	−	0.416280i	$-0.863334\pi$
$853$	−29.9122	−	41.1706i	−1.02417	−	1.40965i	−0.114936	−	0.993373i	$-0.536666\pi$
$854$	15.0196	+	46.2256i	0.513961	+	1.58181i
$855$	−1.75661	−	0.115903i	−0.0600749	−	0.00396379i
$856$	−1.80412	−	1.31077i	−0.0616636	−	0.0448012i
$857$		−	11.5197i		−	0.393506i	−0.980453	−	0.196753i	$-0.936960\pi$
$857$		−	11.5197i		−	0.393506i	0.980453	−	0.196753i	$-0.0630397\pi$
$858$	−11.9834	+	3.66261i	−0.409107	+	0.125039i
$859$	−23.9497			−0.817153			−0.408577	−	0.912724i	$-0.633975\pi$
$859$	−23.9497			−0.817153			−0.408577	+	0.912724i	$0.633975\pi$
$860$	7.51292	+	3.00114i	0.256188	+	0.102338i
$861$	11.4821	−	35.3384i	0.391310	−	1.20433i
$862$	−25.1450	+	8.17010i	−0.856441	+	0.278275i
$863$	23.5170	+	32.3684i	0.800530	+	1.10183i	0.992716	+	0.120476i	$0.0384421\pi$
$863$	23.5170	+	32.3684i	0.800530	+	1.10183i	−0.192187	+	0.981358i	$0.561558\pi$
$864$	4.42705	−	3.21644i	0.150611	−	0.109426i
$865$	6.11520	+	9.70137i	0.207923	+	0.329856i
$866$	−10.1611	+	31.2725i	−0.345287	+	1.06268i
$867$	16.1644	−	22.2484i	0.548972	−	0.755595i
$868$			44.5114i			1.51081i
$869$	−7.18793	+	20.8696i	−0.243834	+	0.707954i
$870$	3.67817	+	14.5093i	0.124702	+	0.491911i
$871$	−4.71460	−	3.42536i	−0.159748	−	0.116064i
$872$	7.47804	+	2.42976i	0.253238	+	0.0822821i
$873$	−2.65270	+	0.861914i	−0.0897802	+	0.0291714i
$874$	6.52871	−	4.74338i	0.220837	−	0.160447i
$875$	11.0087	−	54.9689i	0.372161	−	1.85829i
$876$	2.69808	+	8.30384i	0.0911597	+	0.280561i
$877$	24.7104	+	8.02891i	0.834413	+	0.271117i	0.694903	−	0.719104i	$-0.255447\pi$
$877$	24.7104	+	8.02891i	0.834413	+	0.271117i	0.139510	+	0.990221i	$0.455447\pi$
$878$	7.15897	−	9.85347i	0.241603	−	0.332539i
$879$	−29.4300			−0.992648
$880$	1.69605	+	7.21965i	0.0571740	+	0.243374i
$881$	25.1372			0.846893			0.423446	−	0.905921i	$-0.360820\pi$
$881$	25.1372			0.846893			0.423446	+	0.905921i	$0.360820\pi$
$882$	−4.07317	+	5.60624i	−0.137151	+	0.188772i
$883$	41.3431	+	13.4332i	1.39131	+	0.452063i	0.906369	−	0.422486i	$-0.138843\pi$
$883$	41.3431	+	13.4332i	1.39131	+	0.452063i	0.484937	+	0.874549i	$0.338843\pi$
$884$	−0.0441236	−	0.135798i	−0.00148404	−	0.00456739i
$885$	4.48790	−	5.39134i	0.150859	−	0.181228i
$886$	−13.4370	+	9.76254i	−0.451424	+	0.327979i
$887$	−27.2078	+	8.84036i	−0.913549	+	0.296830i	−0.727818	−	0.685770i	$-0.759465\pi$
$887$	−27.2078	+	8.84036i	−0.913549	+	0.296830i	−0.185731	+	0.982601i	$0.559465\pi$
$888$	−7.01232	−	2.27844i	−0.235318	−	0.0764595i
$889$	−58.6701	−	42.6263i	−1.96773	−	1.42964i
$890$	−13.2005	+	3.34638i	−0.442481	+	0.112171i
$891$	−20.9430	+	14.6619i	−0.701617	+	0.491191i
$892$		−	14.5556i		−	0.487358i
$893$	−10.7547	+	14.8026i	−0.359892	+	0.495349i
$894$	4.39616	−	13.5300i	0.147030	−	0.452511i
$895$	27.3139	−	17.2171i	0.913002	−	0.575506i
$896$	−4.05657	+	2.94727i	−0.135520	+	0.0984614i
$897$	8.69471	+	11.9672i	0.290308	+	0.399575i
$898$	−5.10113	+	1.65746i	−0.170227	+	0.0553100i
$899$	−11.3488	+	34.9281i	−0.378504	+	1.16492i
$900$	−1.89327	−	0.250932i	−0.0631091	−	0.00836439i
$901$	0.135868			0.00452643
$902$	9.14237	−	12.1302i	0.304407	−	0.403893i
$903$		−	29.3536i		−	0.976827i
$904$	10.1626	+	7.38357i	0.338003	+	0.245574i
$905$	−26.5651	−	1.75278i	−0.883053	−	0.0582645i
$906$	−10.7952	−	33.2241i	−0.358645	−	1.10380i
$907$	−28.0438	−	38.5990i	−0.931179	−	1.28166i	−0.959398	−	0.282056i	$-0.908983\pi$
$907$	−28.0438	−	38.5990i	−0.931179	−	1.28166i	0.0282187	−	0.999602i	$-0.491017\pi$
$908$	5.78178	+	7.95794i	0.191875	+	0.264094i
$909$	−0.0261885	−	0.0805998i	−0.000868617	−	0.00267333i
$910$	−1.72365	+	26.1235i	−0.0571385	+	0.865987i
$911$	−40.3003	−	29.2799i	−1.33521	−	0.970085i	−0.999606	−	0.0280809i	$-0.991060\pi$
$911$	−40.3003	−	29.2799i	−1.33521	−	0.970085i	−0.335602	−	0.942004i	$-0.608940\pi$
$912$			3.33501i			0.110433i
$913$	−22.0621	+	29.2724i	−0.730150	+	0.968775i
$914$	−3.61237			−0.119487
$915$	32.5686	+	13.0100i	1.07668	+	0.430097i
$916$	−4.80456	+	14.7869i	−0.158747	+	0.488573i
$917$	−73.0845	+	23.7466i	−2.41346	+	0.784182i
$918$	−0.196687	−	0.270716i	−0.00649162	−	0.00893495i
$919$	−34.7058	+	25.2153i	−1.14484	+	0.831775i	−0.987786	−	0.155815i	$-0.950199\pi$
$919$	−34.7058	+	25.2153i	−1.14484	+	0.831775i	−0.157053	+	0.987590i	$0.550199\pi$
$920$	7.40619	−	4.66845i	0.244175	−	0.153914i
$921$	−6.19098	+	19.0539i	−0.204000	+	0.627847i
$922$	−23.9008	+	32.8967i	−0.787132	+	1.08339i
$923$			20.5862i			0.677602i
$924$	22.0432	−	15.4321i	0.725169	−	0.507679i
$925$	10.8543	+	20.0328i	0.356889	+	0.658674i
$926$	−1.71415	−	1.24540i	−0.0563303	−	0.0409264i
$927$	0.205628	+	0.0668126i	0.00675371	+	0.00219441i
$928$	−3.93464	+	1.27844i	−0.129161	+	0.0419669i
$929$	−3.20719	+	2.33016i	−0.105224	+	0.0764500i	−0.639153	−	0.769079i	$-0.720715\pi$
$929$	−3.20719	+	2.33016i	−0.105224	+	0.0764500i	0.533929	+	0.845529i	$0.320715\pi$
$930$	24.6844	+	20.5480i	0.809432	+	0.673794i
$931$	−11.5553	−	35.5635i	−0.378709	−	1.16555i
$932$	−24.6292	−	8.00252i	−0.806757	−	0.262131i
$933$	8.94941	−	12.3178i	0.292991	−	0.403267i
$934$	−13.7549			−0.450075
$935$	0.441484	−	0.103714i	0.0144381	−	0.00339182i
$936$	0.891895			0.0291525
$937$	−1.24563	+	1.71446i	−0.0406929	+	0.0560090i	−0.828879	−	0.559429i	$-0.811021\pi$
$937$	−1.24563	+	1.71446i	−0.0406929	+	0.0560090i	0.788186	+	0.615437i	$0.211021\pi$
$938$	11.9016	+	3.86707i	0.388601	+	0.126264i
$939$	7.61585	+	23.4392i	0.248534	+	0.764909i
$940$	−12.6993	+	15.2558i	−0.414207	+	0.497589i
$941$	−4.08118	+	2.96515i	−0.133043	+	0.0966612i	−0.652316	−	0.757947i	$-0.726203\pi$
$941$	−4.08118	+	2.96515i	−0.133043	+	0.0966612i	0.519274	+	0.854608i	$0.326203\pi$
$942$	−5.25472	+	1.70736i	−0.171208	+	0.0556289i
$943$	−17.0537	−	5.54107i	−0.555344	−	0.180442i
$944$	1.56856	+	1.13963i	0.0510524	+	0.0370917i
$945$	15.0766	+	59.4728i	0.490442	+	1.93465i
$946$	3.90765	−	11.3456i	0.127049	−	0.368877i
$947$		−	0.986192i		−	0.0320470i	−0.999872	−	0.0160235i	$-0.994899\pi$
$947$		−	0.986192i		−	0.0320470i	0.999872	−	0.0160235i	$-0.00510065\pi$
$948$	−6.32947	+	8.71177i	−0.205572	+	0.282945i
$949$	−3.89364	+	11.9834i	−0.126393	+	0.388998i
$950$	7.10052	−	7.46935i	0.230371	−	0.242338i
$951$	−17.6150	+	12.7981i	−0.571206	+	0.415006i
$952$	0.180227	+	0.248061i	0.00584118	+	0.00803969i
$953$	21.8386	−	7.09580i	0.707422	−	0.229855i	0.0668608	−	0.997762i	$-0.478702\pi$
$953$	21.8386	−	7.09580i	0.707422	−	0.229855i	0.640562	+	0.767907i	$0.278702\pi$
$954$	−0.262256	+	0.807142i	−0.00849087	+	0.0261322i
$955$	−8.72470	+	21.8410i	−0.282325	+	0.706758i
$956$	19.9960			0.646718
$957$	21.2320	−	6.48934i	0.686331	−	0.209770i
$958$		−	31.4107i		−	1.01484i
$959$	4.47994	+	3.25486i	0.144665	+	0.105105i
$960$	−0.238203	+	3.61018i	−0.00768796	+	0.116518i
$961$	14.7718	+	45.4628i	0.476508	+	1.46654i
$962$	−6.25426	−	8.60824i	−0.201645	−	0.277541i
$963$	−0.500670	−	0.689113i	−0.0161339	−	0.0222064i
$964$	−2.78542	−	8.57264i	−0.0897123	−	0.276106i
$965$	0.716756	−	10.8631i	0.0230732	−	0.349695i
$966$	−25.6984	−	18.6710i	−0.826833	−	0.600729i
$967$			20.1267i			0.647231i	0.946189	+	0.323616i	$0.104898\pi$
$967$			20.1267i			0.647231i	−0.946189	+	0.323616i	$0.895102\pi$
$968$	10.5744	−	3.03026i	0.339873	−	0.0973963i
$969$	0.203937			0.00655141
$970$	6.05719	−	15.1633i	0.194485	−	0.486863i
$971$	−6.77852	+	20.8621i	−0.217533	+	0.669498i	0.781431	+	0.623991i	$0.214490\pi$
$971$	−6.77852	+	20.8621i	−0.217533	+	0.669498i	−0.998964	+	0.0455060i	$0.985510\pi$
$972$	3.75123	−	1.21885i	0.120321	−	0.0390945i
$973$	−29.1959	−	40.1847i	−0.935978	−	1.28826i
$974$	6.07597	−	4.41445i	0.194687	−	0.141448i
$975$	13.6915	+	13.0154i	0.438477	+	0.416826i
$976$	−2.99542	+	9.21895i	−0.0958810	+	0.295091i
$977$	34.7133	−	47.7788i	1.11058	−	1.52858i	0.290015	−	0.957022i	$-0.406340\pi$
$977$	34.7133	−	47.7788i	1.11058	−	1.52858i	0.820562	−	0.571557i	$-0.193660\pi$
$978$		−	28.1706i		−	0.900795i
$979$	5.90396	+	19.3167i	0.188691	+	0.617365i
$980$	−9.96860	−	39.3232i	−0.318435	−	1.25613i
$981$	2.42976	+	1.76533i	0.0775763	+	0.0563625i
$982$	10.7106	+	3.48008i	0.341788	+	0.111054i
$983$	45.9751	−	14.9382i	1.46638	−	0.476455i	0.536367	−	0.843985i	$-0.319796\pi$
$983$	45.9751	−	14.9382i	1.46638	−	0.476455i	0.930012	+	0.367530i	$0.119796\pi$
$984$	5.99511	−	4.35570i	0.191117	−	0.138855i
$985$	−22.8549	+	27.4557i	−0.728219	+	0.874813i
$986$	0.0781772	+	0.240605i	0.00248967	+	0.00766241i
$987$	68.4960	+	22.2557i	2.18025	+	0.708406i
$988$	−2.82890	+	3.89364i	−0.0899992	+	0.123873i
$989$	−14.1655			−0.450437
$990$	−0.236037	+	2.82288i	−0.00750174	+	0.0897172i
$991$	−55.0154			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$992$	−5.21781	+	7.18170i	−0.165666	+	0.228019i
$993$	−5.88201	−	1.91118i	−0.186660	−	0.0606495i
$994$	−13.6606	−	42.0431i	−0.433289	−	1.33353i
$995$	−28.7130	−	23.9015i	−0.910262	−	0.757728i
$996$	−14.4672	+	10.5111i	−0.458412	+	0.333056i
$997$	21.8457	−	7.09810i	0.691861	−	0.224799i	0.0580799	−	0.998312i	$-0.481502\pi$
$997$	21.8457	−	7.09810i	0.691861	−	0.224799i	0.633781	+	0.773513i	$0.281502\pi$
$998$	25.6603	+	8.33753i	0.812262	+	0.263920i
$999$	−20.1736	−	14.6569i	−0.638263	−	0.463725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.j.b.59.4	yes	16
3.2	odd	2		990.2.ba.h.829.1		16
4.3	odd	2		880.2.cd.b.609.2		16
5.2	odd	4		550.2.h.n.301.1		8
5.3	odd	4		550.2.h.j.301.2		8
5.4	even	2	inner	110.2.j.b.59.2	✓	16
11.3	even	5	inner	110.2.j.b.69.2	yes	16
11.5	even	5		1210.2.b.k.969.7		8
11.6	odd	10		1210.2.b.l.969.3		8
15.14	odd	2		990.2.ba.h.829.3		16
20.19	odd	2		880.2.cd.b.609.4		16
33.14	odd	10		990.2.ba.h.289.3		16
44.3	odd	10		880.2.cd.b.289.4		16
55.3	odd	20		550.2.h.j.201.2		8
55.14	even	10	inner	110.2.j.b.69.4	yes	16
55.17	even	20		6050.2.a.dl.1.4		4
55.27	odd	20		6050.2.a.dd.1.3		4
55.28	even	20		6050.2.a.da.1.1		4
55.38	odd	20		6050.2.a.di.1.2		4
55.39	odd	10		1210.2.b.l.969.5		8
55.47	odd	20		550.2.h.n.201.1		8
55.49	even	10		1210.2.b.k.969.1		8
165.14	odd	10		990.2.ba.h.289.1		16
220.179	odd	10		880.2.cd.b.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	5.4	even	2	inner
110.2.j.b.59.4	yes	16	1.1	even	1	trivial
110.2.j.b.69.2	yes	16	11.3	even	5	inner
110.2.j.b.69.4	yes	16	55.14	even	10	inner
550.2.h.j.201.2		8	55.3	odd	20
550.2.h.j.301.2		8	5.3	odd	4
550.2.h.n.201.1		8	55.47	odd	20
550.2.h.n.301.1		8	5.2	odd	4
880.2.cd.b.289.2		16	220.179	odd	10
880.2.cd.b.289.4		16	44.3	odd	10
880.2.cd.b.609.2		16	4.3	odd	2
880.2.cd.b.609.4		16	20.19	odd	2
990.2.ba.h.289.1		16	165.14	odd	10
990.2.ba.h.289.3		16	33.14	odd	10
990.2.ba.h.829.1		16	3.2	odd	2
990.2.ba.h.829.3		16	15.14	odd	2
1210.2.b.k.969.1		8	55.49	even	10
1210.2.b.k.969.7		8	11.5	even	5
1210.2.b.l.969.3		8	11.6	odd	10
1210.2.b.l.969.5		8	55.39	odd	10
6050.2.a.da.1.1		4	55.28	even	20
6050.2.a.dd.1.3		4	55.27	odd	20
6050.2.a.di.1.2		4	55.38	odd	20
6050.2.a.dl.1.4		4	55.17	even	20

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(1.53884 + 0.500000i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.71856 + 1.43058i) q^{5} +(1.30902 - 0.951057i) q^{6} +(-4.76878 + 1.54947i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.224514i) q^{9} +(2.16751 - 0.549472i) q^{10} +(-0.969425 - 3.17178i) q^{11} -1.61803i q^{12} +(1.37249 - 1.88906i) q^{13} +(-1.54947 + 4.76878i) q^{14} +(1.92930 + 3.06071i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.0359433 + 0.0494717i) q^{17} +(-0.363271 + 0.118034i) q^{18} +(0.636930 - 1.96027i) q^{19} +(0.829496 - 2.07652i) q^{20} -8.11314 q^{21} +(-3.13584 - 1.08005i) q^{22} +3.91525i q^{23} +(-1.30902 - 0.951057i) q^{24} +(0.906896 + 4.91707i) q^{25} +(-0.721558 - 2.22073i) q^{26} +(-3.21644 - 4.42705i) q^{27} +(2.94727 + 4.05657i) q^{28} +(1.27844 + 3.93464i) q^{29} +(3.61018 + 0.238203i) q^{30} +(7.18170 + 5.21781i) q^{31} +1.00000i q^{32} +(0.0941007 - 5.36559i) q^{33} +0.0611504 q^{34} +(-10.4121 - 4.15925i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(4.33385 - 1.40815i) q^{37} +(-1.21151 - 1.66751i) q^{38} +(3.05657 - 2.22073i) q^{39} +(-1.19237 - 1.89162i) q^{40} +(-1.41525 + 4.35570i) q^{41} +(-4.76878 + 6.56367i) q^{42} +3.61803i q^{43} +(-2.71698 + 1.90211i) q^{44} +(-0.209880 - 0.827913i) q^{45} +(3.16751 + 2.30133i) q^{46} +(-8.44260 - 2.74317i) q^{47} +(-1.53884 + 0.500000i) q^{48} +(14.6773 - 10.6637i) q^{49} +(4.51105 + 2.15649i) q^{50} +(0.0305752 + 0.0941007i) q^{51} +(-2.22073 - 0.721558i) q^{52} +(1.30598 - 1.79753i) q^{53} -5.47214 q^{54} +(2.87147 - 6.83774i) q^{55} +5.01420 q^{56} +(1.96027 - 2.69808i) q^{57} +(3.93464 + 1.27844i) q^{58} +(-0.599137 - 1.84396i) q^{59} +(2.31472 - 2.78069i) q^{60} +(7.84211 - 5.69763i) q^{61} +(8.44260 - 2.74317i) q^{62} +(1.82151 + 0.591846i) q^{63} +(0.809017 + 0.587785i) q^{64} +(5.06115 - 1.28302i) q^{65} +(-4.28554 - 3.22994i) q^{66} -2.49573i q^{67} +(0.0359433 - 0.0494717i) q^{68} +(-1.95763 + 6.02495i) q^{69} +(-9.48497 + 5.97880i) q^{70} +(-7.13254 + 5.18210i) q^{71} +(0.224514 + 0.309017i) q^{72} +(-5.13205 + 1.66751i) q^{73} +(1.40815 - 4.33385i) q^{74} +(-1.06296 + 8.02003i) q^{75} -2.06115 q^{76} +(9.53757 + 13.6235i) q^{77} -3.77813i q^{78} +(-5.38417 - 3.91183i) q^{79} +(-2.23122 - 0.147217i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(2.69197 + 3.70518i) q^{82} +(-6.49620 - 8.94125i) q^{83} +(2.50710 + 7.71605i) q^{84} +(-0.00900240 + 0.136440i) q^{85} +(2.92705 + 2.12663i) q^{86} +6.69401i q^{87} +(-0.0581575 + 3.31611i) q^{88} -6.09017 q^{89} +(-0.793160 - 0.316839i) q^{90} +(-3.61803 + 11.1352i) q^{91} +(3.72363 - 1.20988i) q^{92} +(8.44260 + 11.6202i) q^{93} +(-7.18170 + 5.21781i) q^{94} +(3.89892 - 2.45766i) q^{95} +(-0.500000 + 1.53884i) q^{96} +(4.29216 - 5.90765i) q^{97} -18.1422i q^{98} +(-0.412541 + 1.19778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 20 q^{11} - 12 q^{14} + 2 q^{15} - 4 q^{16} - 16 q^{19} + 6 q^{20} - 16 q^{21} - 12 q^{24} - 16 q^{26} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{34}+ \cdots - 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 20 * q^11 - 12 * q^14 + 2 * q^15 - 4 * q^16 - 16 * q^19 + 6 * q^20 - 16 * q^21 - 12 * q^24 - 16 * q^26 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^34 - 48 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 + 40 * q^41 - 4 * q^45 + 20 * q^46 + 84 * q^49 + 4 * q^50 - 4 * q^51 - 16 * q^54 + 32 * q^55 - 8 * q^56 + 8 * q^60 + 20 * q^61 + 4 * q^64 + 72 * q^65 - 20 * q^66 + 36 * q^70 - 56 * q^71 + 4 * q^74 + 32 * q^75 - 24 * q^76 + 36 * q^79 + 4 * q^80 - 56 * q^81 - 4 * q^84 - 54 * q^85 + 20 * q^86 - 8 * q^89 - 4 * q^90 - 40 * q^91 + 4 * q^94 - 50 * q^95 - 8 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more