LMFDB - Embedded newform 1690.2.l.j.361.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(361,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,4,0,6,0,0,-4,4,6,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	1690.361
Dual form			1690.2.l.j.1161.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.547394 - 0.948114i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.948114 - 0.547394i) q^{6} +(3.45632 + 1.99551i) q^{7} -1.00000i q^{8} +(0.900720 - 1.56009i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.142181 + 0.0820885i) q^{11} -1.09479 q^{12} +3.99102 q^{14} +(0.948114 - 0.547394i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.783937 - 1.35782i) q^{17} -1.80144i q^{18} +(0.716063 + 0.413419i) q^{19} +(0.866025 + 0.500000i) q^{20} -4.36931i q^{21} +(-0.0820885 + 0.142181i) q^{22} +(3.49551 + 6.05440i) q^{23} +(-0.948114 + 0.547394i) q^{24} -1.00000 q^{25} -5.25656 q^{27} +(3.45632 - 1.99551i) q^{28} +(2.92163 + 5.06040i) q^{29} +(0.547394 - 0.948114i) q^{30} -0.0858029i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.155658 + 0.0898694i) q^{33} -1.56787i q^{34} +(-1.99551 + 3.45632i) q^{35} +(-0.900720 - 1.56009i) q^{36} +(7.24026 - 4.18016i) q^{37} +0.826838 q^{38} +1.00000 q^{40} +(-7.48652 + 4.32235i) q^{41} +(-2.18466 - 3.78394i) q^{42} +(5.62828 - 9.74846i) q^{43} +0.164177i q^{44} +(1.56009 + 0.900720i) q^{45} +(6.05440 + 3.49551i) q^{46} -5.31634i q^{47} +(-0.547394 + 0.948114i) q^{48} +(4.46410 + 7.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} -1.71649 q^{51} +10.3538 q^{53} +(-4.55231 + 2.62828i) q^{54} +(-0.0820885 - 0.142181i) q^{55} +(1.99551 - 3.45632i) q^{56} -0.905212i q^{57} +(5.06040 + 2.92163i) q^{58} +(3.00000 + 1.73205i) q^{59} -1.09479i q^{60} +(3.21606 - 5.57038i) q^{61} +(-0.0429015 - 0.0743075i) q^{62} +(6.22635 - 3.59479i) q^{63} -1.00000 q^{64} +0.179739 q^{66} +(-13.2566 + 7.65368i) q^{67} +(-0.783937 - 1.35782i) q^{68} +(3.82684 - 6.62828i) q^{69} +3.99102i q^{70} +(5.19615 + 3.00000i) q^{71} +(-1.56009 - 0.900720i) q^{72} -0.179739i q^{73} +(4.18016 - 7.24026i) q^{74} +(0.547394 + 0.948114i) q^{75} +(0.716063 - 0.413419i) q^{76} -0.655233 q^{77} -6.21257 q^{79} +(0.866025 - 0.500000i) q^{80} +(0.175247 + 0.303536i) q^{81} +(-4.32235 + 7.48652i) q^{82} -1.23952i q^{83} +(-3.78394 - 2.18466i) q^{84} +(1.35782 + 0.783937i) q^{85} -11.2566i q^{86} +(3.19856 - 5.54007i) q^{87} +(0.0820885 + 0.142181i) q^{88} +(8.98652 - 5.18837i) q^{89} +1.80144 q^{90} +6.99102 q^{92} +(-0.0813509 + 0.0469680i) q^{93} +(-2.65817 - 4.60408i) q^{94} +(-0.413419 + 0.716063i) q^{95} +1.09479i q^{96} +(-16.3853 - 9.46004i) q^{97} +(7.73205 + 4.46410i) q^{98} +0.295755i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} + 6 q^{6} - 4 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{15} - 4 q^{16} + 6 q^{17} + 6 q^{19} + 6 q^{22} + 12 q^{23} + 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} + 42 q^{33} + 4 q^{36}+ \cdots + 48 q^{98}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^4 + 6 * q^6 - 4 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^15 - 4 * q^16 + 6 * q^17 + 6 * q^19 + 6 * q^22 + 12 * q^23 + 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 + 42 * q^33 + 4 * q^36 + 30 * q^37 - 12 * q^38 + 8 * q^40 - 12 * q^41 - 6 * q^42 + 4 * q^43 + 12 * q^45 - 2 * q^48 + 8 * q^49 + 60 * q^53 - 36 * q^54 + 6 * q^55 + 24 * q^59 + 26 * q^61 + 18 * q^62 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 24 * q^67 - 6 * q^68 + 12 * q^69 - 12 * q^72 + 6 * q^74 + 2 * q^75 + 6 * q^76 - 60 * q^77 + 20 * q^79 - 28 * q^81 - 30 * q^84 + 18 * q^85 + 48 * q^87 - 6 * q^88 + 24 * q^89 - 8 * q^90 + 24 * q^92 - 48 * q^93 + 6 * q^95 + 6 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.547394	−	0.948114i	−0.316038	−	0.547394i	0.663620	−	0.748070i	$-0.269019\pi$
$3$	−0.547394	−	0.948114i	−0.316038	−	0.547394i	−0.979658	+	0.200676i	$0.935686\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.948114	−	0.547394i	−0.387066	−	0.223473i
$7$	3.45632	+	1.99551i	1.30637	+	0.754231i	0.981488	−	0.191525i	$-0.0613432\pi$
$7$	3.45632	+	1.99551i	1.30637	+	0.754231i	0.324879	+	0.945756i	$0.394677\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.900720	−	1.56009i	0.300240	−	0.520031i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.142181	+	0.0820885i	−0.0428693	+	0.0247506i	−0.521281	−	0.853385i	$-0.674546\pi$
$11$	−0.142181	+	0.0820885i	−0.0428693	+	0.0247506i	0.478412	+	0.878135i	$0.341212\pi$
$12$	−1.09479			−0.316038
$13$		0			0
$13$		0			0
$14$	3.99102			1.06664
$15$	0.948114	−	0.547394i	0.244802	−	0.141336i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.783937	−	1.35782i	0.190133	−	0.329319i	−0.755161	−	0.655539i	$-0.772442\pi$
$17$	0.783937	−	1.35782i	0.190133	−	0.329319i	0.945294	+	0.326220i	$0.105775\pi$
$18$		−	1.80144i		−	0.424604i
$19$	0.716063	+	0.413419i	0.164276	+	0.0948449i	0.579884	−	0.814699i	$-0.303098\pi$
$19$	0.716063	+	0.413419i	0.164276	+	0.0948449i	−0.415608	+	0.909544i	$0.636431\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		−	4.36931i		−	0.953462i
$22$	−0.0820885	+	0.142181i	−0.0175013	+	0.0303132i
$23$	3.49551	+	6.05440i	0.728864	+	1.26243i	0.957364	+	0.288885i	$0.0932846\pi$
$23$	3.49551	+	6.05440i	0.728864	+	1.26243i	−0.228500	+	0.973544i	$0.573382\pi$
$24$	−0.948114	+	0.547394i	−0.193533	+	0.111736i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.25656			−1.01162
$28$	3.45632	−	1.99551i	0.653183	−	0.377115i
$29$	2.92163	+	5.06040i	0.542532	+	0.939694i	0.998758	+	0.0498293i	$0.0158677\pi$
$29$	2.92163	+	5.06040i	0.542532	+	0.939694i	−0.456225	+	0.889864i	$0.650799\pi$
$30$	0.547394	−	0.948114i	0.0999400	−	0.173101i
$31$		−	0.0858029i		−	0.0154107i	−0.999970	−	0.00770533i	$-0.997547\pi$
$31$		−	0.0858029i		−	0.0154107i	0.999970	−	0.00770533i	$-0.00245271\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.155658	+	0.0898694i	0.0270967	+	0.0156443i
$34$		−	1.56787i		−	0.268888i
$35$	−1.99551	+	3.45632i	−0.337302	+	0.584225i
$36$	−0.900720	−	1.56009i	−0.150120	−	0.260015i
$37$	7.24026	−	4.18016i	1.19029	−	0.687215i	0.231918	−	0.972735i	$-0.425500\pi$
$37$	7.24026	−	4.18016i	1.19029	−	0.687215i	0.958373	+	0.285520i	$0.0921664\pi$
$38$	0.826838			0.134131
$39$		0			0
$40$	1.00000			0.158114
$41$	−7.48652	+	4.32235i	−1.16920	+	0.675037i	−0.953491	−	0.301421i	$-0.902539\pi$
$41$	−7.48652	+	4.32235i	−1.16920	+	0.675037i	−0.215707	+	0.976458i	$0.569206\pi$
$42$	−2.18466	−	3.78394i	−0.337100	−	0.583874i
$43$	5.62828	−	9.74846i	0.858304	−	1.48663i	−0.0152408	−	0.999884i	$-0.504851\pi$
$43$	5.62828	−	9.74846i	0.858304	−	1.48663i	0.873545	−	0.486743i	$-0.161815\pi$
$44$			0.164177i			0.0247506i
$45$	1.56009	+	0.900720i	0.232565	+	0.134271i
$46$	6.05440	+	3.49551i	0.892672	+	0.515384i
$47$		−	5.31634i		−	0.775468i	−0.921771	−	0.387734i	$-0.873258\pi$
$47$		−	5.31634i		−	0.775468i	0.921771	−	0.387734i	$-0.126742\pi$
$48$	−0.547394	+	0.948114i	−0.0790095	+	0.136848i
$49$	4.46410	+	7.73205i	0.637729	+	1.10458i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−1.71649			−0.240357
$52$		0			0
$53$	10.3538			1.42220			0.711099	−	0.703092i	$-0.248198\pi$
$53$	10.3538			1.42220			0.711099	+	0.703092i	$0.248198\pi$
$54$	−4.55231	+	2.62828i	−0.619491	+	0.357663i
$55$	−0.0820885	−	0.142181i	−0.0110688	−	0.0191717i
$56$	1.99551	−	3.45632i	0.266661	−	0.461870i
$57$		−	0.905212i		−	0.119898i
$58$	5.06040	+	2.92163i	0.664464	+	0.383628i
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	0.682406	−	0.730974i	$-0.260934\pi$
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	−0.291839	+	0.956467i	$0.594267\pi$
$60$		−	1.09479i		−	0.141336i
$61$	3.21606	−	5.57038i	0.411775	−	0.713215i	−0.583309	−	0.812250i	$-0.698242\pi$
$61$	3.21606	−	5.57038i	0.411775	−	0.713215i	0.995084	+	0.0990355i	$0.0315757\pi$
$62$	−0.0429015	−	0.0743075i	−0.00544849	−	0.00943706i
$63$	6.22635	−	3.59479i	0.784447	−	0.452901i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.179739			0.0221243
$67$	−13.2566	+	7.65368i	−1.61955	+	0.935045i	−0.632509	+	0.774553i	$0.717975\pi$
$67$	−13.2566	+	7.65368i	−1.61955	+	0.935045i	−0.987037	+	0.160493i	$0.948692\pi$
$68$	−0.783937	−	1.35782i	−0.0950663	−	0.164660i
$69$	3.82684	−	6.62828i	0.460697	−	0.797951i
$70$			3.99102i			0.477018i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$	−1.56009	−	0.900720i	−0.183859	−	0.106151i
$73$		−	0.179739i		−	0.0210368i	−0.999945	−	0.0105184i	$-0.996652\pi$
$73$		−	0.179739i		−	0.0210368i	0.999945	−	0.0105184i	$-0.00334818\pi$
$74$	4.18016	−	7.24026i	0.485934	−	0.841663i
$75$	0.547394	+	0.948114i	0.0632076	+	0.109479i
$76$	0.716063	−	0.413419i	0.0821381	−	0.0474224i
$77$	−0.655233			−0.0746707
$78$		0			0
$79$	−6.21257			−0.698968			−0.349484	−	0.936942i	$-0.613643\pi$
$79$	−6.21257			−0.698968			−0.349484	+	0.936942i	$0.613643\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	0.175247	+	0.303536i	0.0194718	+	0.0337262i
$82$	−4.32235	+	7.48652i	−0.477323	+	0.826748i
$83$		−	1.23952i		−	0.136055i	−0.997683	−	0.0680275i	$-0.978329\pi$
$83$		−	1.23952i		−	0.136055i	0.997683	−	0.0680275i	$-0.0216706\pi$
$84$	−3.78394	−	2.18466i	−0.412861	−	0.238366i
$85$	1.35782	+	0.783937i	0.147276	+	0.0850299i
$86$		−	11.2566i		−	1.21383i
$87$	3.19856	−	5.54007i	0.342922	−	0.593958i
$88$	0.0820885	+	0.142181i	0.00875066	+	0.0151566i
$89$	8.98652	−	5.18837i	0.952570	−	0.549966i	0.0586913	−	0.998276i	$-0.481307\pi$
$89$	8.98652	−	5.18837i	0.952570	−	0.549966i	0.893878	+	0.448310i	$0.147974\pi$
$90$	1.80144			0.189888
$91$		0			0
$92$	6.99102			0.728864
$93$	−0.0813509	+	0.0469680i	−0.00843570	+	0.00487035i
$94$	−2.65817	−	4.60408i	−0.274169	−	0.474875i
$95$	−0.413419	+	0.716063i	−0.0424159	+	0.0734665i
$96$			1.09479i			0.111736i
$97$	−16.3853	−	9.46004i	−1.66367	−	0.960521i	−0.970939	−	0.239326i	$-0.923074\pi$
$97$	−16.3853	−	9.46004i	−1.66367	−	0.960521i	−0.692732	−	0.721195i	$-0.743593\pi$
$98$	7.73205	+	4.46410i	0.781055	+	0.450942i
$99$			0.295755i			0.0297245i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.33384	−	12.7026i	−0.729745	−	1.26395i	−0.956991	−	0.290117i	$-0.906306\pi$
$101$	−7.33384	−	12.7026i	−0.729745	−	1.26395i	0.227247	−	0.973837i	$-0.427028\pi$
$102$	−1.48652	+	0.858244i	−0.147188	+	0.0849789i
$103$	−2.26795			−0.223468			−0.111734	−	0.993738i	$-0.535640\pi$
$103$	−2.26795			−0.223468			−0.111734	+	0.993738i	$0.535640\pi$
$104$		0			0
$105$	4.36931			0.426401
$106$	8.96661	−	5.17688i	0.870914	−	0.502823i
$107$	−2.34883	−	4.06830i	−0.227070	−	0.393297i	0.729868	−	0.683588i	$-0.239581\pi$
$107$	−2.34883	−	4.06830i	−0.227070	−	0.393297i	−0.956939	+	0.290290i	$0.906248\pi$
$108$	−2.62828	+	4.55231i	−0.252906	+	0.438046i
$109$		−	6.17161i		−	0.591133i	−0.955322	−	0.295566i	$-0.904492\pi$
$109$		−	6.17161i		−	0.591133i	0.955322	−	0.295566i	$-0.0955083\pi$
$110$	−0.142181	−	0.0820885i	−0.0135565	−	0.00782683i
$111$	−7.92654	−	4.57639i	−0.752354	−	0.434372i
$112$		−	3.99102i		−	0.377115i
$113$	−5.63726	+	9.76403i	−0.530309	+	0.918522i	0.469066	+	0.883163i	$0.344591\pi$
$113$	−5.63726	+	9.76403i	−0.530309	+	0.918522i	−0.999375	+	0.0353590i	$0.988743\pi$
$114$	−0.452606	−	0.783937i	−0.0423905	−	0.0734224i
$115$	−6.05440	+	3.49551i	−0.564575	+	0.325958i
$116$	5.84325			0.542532
$117$		0			0
$118$	3.46410			0.318896
$119$	5.41907	−	3.12870i	0.496766	−	0.286808i
$120$	−0.547394	−	0.948114i	−0.0499700	−	0.0865506i
$121$	−5.48652	+	9.50294i	−0.498775	+	0.863903i
$122$		−	6.43213i		−	0.582337i
$123$	8.19615	+	4.73205i	0.739022	+	0.426675i
$124$	−0.0743075	−	0.0429015i	−0.00667301	−	0.00385266i
$125$		−	1.00000i		−	0.0894427i
$126$	3.59479	−	6.22635i	0.320249	−	0.554688i
$127$	4.06218	+	7.03590i	0.360460	+	0.624335i	0.988037	−	0.154220i	$-0.0492864\pi$
$127$	4.06218	+	7.03590i	0.360460	+	0.624335i	−0.627577	+	0.778555i	$0.715953\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−12.3235			−1.08503
$130$		0			0
$131$	20.8034			1.81760			0.908802	−	0.417227i	$-0.136998\pi$
$131$	20.8034			1.81760			0.908802	+	0.417227i	$0.136998\pi$
$132$	0.155658	−	0.0898694i	0.0135483	−	0.00782213i
$133$	1.64996	+	2.85782i	0.143070	+	0.247804i
$134$	−7.65368	+	13.2566i	−0.661177	+	1.14519i
$135$		−	5.25656i		−	0.452412i
$136$	−1.35782	−	0.783937i	−0.116432	−	0.0672220i
$137$	−4.54796	−	2.62577i	−0.388559	−	0.224334i	0.292977	−	0.956120i	$-0.405354\pi$
$137$	−4.54796	−	2.62577i	−0.388559	−	0.224334i	−0.681535	+	0.731785i	$0.738687\pi$
$138$		−	7.65368i		−	0.651524i
$139$	8.36076	−	14.4813i	0.709150	−	1.22828i	−0.256023	−	0.966671i	$-0.582412\pi$
$139$	8.36076	−	14.4813i	0.709150	−	1.22828i	0.965173	−	0.261613i	$-0.0842544\pi$
$140$	1.99551	+	3.45632i	0.168651	+	0.292112i
$141$	−5.04049	+	2.91013i	−0.424486	+	0.245077i
$142$	6.00000			0.503509
$143$		0			0
$144$	−1.80144			−0.150120
$145$	−5.06040	+	2.92163i	−0.420244	+	0.242628i
$146$	−0.0898694	−	0.155658i	−0.00743765	−	0.0128824i
$147$	4.88724	−	8.46495i	0.403093	−	0.698178i
$148$		−	8.36033i		−	0.687215i
$149$	8.68868	+	5.01641i	0.711805	+	0.410961i	0.811729	−	0.584034i	$-0.198527\pi$
$149$	8.68868	+	5.01641i	0.711805	+	0.410961i	−0.0999242	+	0.994995i	$0.531860\pi$
$150$	0.948114	+	0.547394i	0.0774132	+	0.0446945i
$151$		−	10.8752i		−	0.885013i	−0.896765	−	0.442507i	$-0.854089\pi$
$151$		−	10.8752i		−	0.885013i	0.896765	−	0.442507i	$-0.145911\pi$
$152$	0.413419	−	0.716063i	0.0335327	−	0.0580804i
$153$	−1.41222	−	2.44603i	−0.114171	−	0.197750i
$154$	−0.567448	+	0.327616i	−0.0457263	+	0.0264001i
$155$	0.0858029			0.00689185
$156$		0			0
$157$	−17.6922			−1.41199			−0.705997	−	0.708215i	$-0.749501\pi$
$157$	−17.6922			−1.41199			−0.705997	+	0.708215i	$0.749501\pi$
$158$	−5.38024	+	3.10628i	−0.428029	+	0.247123i
$159$	−5.66758	−	9.81654i	−0.449468	−	0.778502i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			27.9012i			2.19893i
$162$	0.303536	+	0.175247i	0.0238480	+	0.0137687i
$163$	1.22207	+	0.705563i	0.0957200	+	0.0552640i	0.547096	−	0.837070i	$-0.315733\pi$
$163$	1.22207	+	0.705563i	0.0957200	+	0.0552640i	−0.451376	+	0.892334i	$0.649067\pi$
$164$			8.64469i			0.675037i
$165$	−0.0898694	+	0.155658i	−0.00699633	+	0.0121180i
$166$	−0.619760	−	1.07346i	−0.0481027	−	0.0833163i
$167$	−0.610092	+	0.352237i	−0.0472103	+	0.0272569i	−0.523419	−	0.852075i	$-0.675344\pi$
$167$	−0.610092	+	0.352237i	−0.0472103	+	0.0272569i	0.476209	+	0.879332i	$0.342011\pi$
$168$	−4.36931			−0.337100
$169$		0			0
$170$	1.56787			0.120250
$171$	1.28994	−	0.744750i	0.0986445	−	0.0569525i
$172$	−5.62828	−	9.74846i	−0.429152	−	0.743313i
$173$	0.327616	−	0.567448i	0.0249082	−	0.0431423i	−0.853303	−	0.521416i	$-0.825404\pi$
$173$	0.327616	−	0.567448i	0.0249082	−	0.0431423i	0.878211	+	0.478274i	$0.158737\pi$
$174$		−	6.39712i		−	0.484964i
$175$	−3.45632	−	1.99551i	−0.261273	−	0.150846i
$176$	0.142181	+	0.0820885i	0.0107173	+	0.00618765i
$177$		−	3.79246i		−	0.285058i
$178$	5.18837	−	8.98652i	0.388885	−	0.673568i
$179$	3.70665	+	6.42011i	0.277048	+	0.479862i	0.970650	−	0.240497i	$-0.0773105\pi$
$179$	3.70665	+	6.42011i	0.277048	+	0.479862i	−0.693602	+	0.720359i	$0.743977\pi$
$180$	1.56009	−	0.900720i	0.116282	−	0.0671357i
$181$	−0.496077			−0.0368731			−0.0184366	−	0.999830i	$-0.505869\pi$
$181$	−0.496077			−0.0368731			−0.0184366	+	0.999830i	$0.505869\pi$
$182$		0			0
$183$	−7.04181			−0.520546
$184$	6.05440	−	3.49551i	0.446336	−	0.257692i
$185$	4.18016	+	7.24026i	0.307332	+	0.532314i
$186$	−0.0469680	+	0.0813509i	−0.00344386	+	0.00596494i
$187$			0.257409i			0.0188236i
$188$	−4.60408	−	2.65817i	−0.335787	−	0.193867i
$189$	−18.1683	−	10.4895i	−1.32155	−	0.762999i
$190$			0.826838i			0.0599852i
$191$	−12.3972	+	21.4726i	−0.897032	+	1.55370i	−0.0657616	+	0.997835i	$0.520948\pi$
$191$	−12.3972	+	21.4726i	−0.897032	+	1.55370i	−0.831270	+	0.555869i	$0.812386\pi$
$192$	0.547394	+	0.948114i	0.0395047	+	0.0684242i
$193$	−3.34392	+	1.93061i	−0.240700	+	0.138968i	−0.615499	−	0.788138i	$-0.711045\pi$
$193$	−3.34392	+	1.93061i	−0.240700	+	0.138968i	0.374798	+	0.927106i	$0.377712\pi$
$194$	−18.9201			−1.35838
$195$		0			0
$196$	8.92820			0.637729
$197$	−4.94989	+	2.85782i	−0.352665	+	0.203611i	−0.665858	−	0.746078i	$-0.731934\pi$
$197$	−4.94989	+	2.85782i	−0.352665	+	0.203611i	0.313193	+	0.949689i	$0.398601\pi$
$198$	0.147877	+	0.256131i	0.0105092	+	0.0182025i
$199$	−0.567874	+	0.983586i	−0.0402555	+	0.0697246i	−0.885451	−	0.464732i	$-0.846151\pi$
$199$	−0.567874	+	0.983586i	−0.0402555	+	0.0697246i	0.845196	+	0.534457i	$0.179484\pi$
$200$			1.00000i			0.0707107i
$201$	14.5131	+	8.37915i	1.02368	+	0.591020i
$202$	−12.7026	−	7.33384i	−0.893751	−	0.516007i
$203$			23.3205i			1.63678i
$204$	−0.858244	+	1.48652i	−0.0600891	+	0.104077i
$205$	−4.32235	−	7.48652i	−0.301886	−	0.522881i
$206$	−1.96410	+	1.13397i	−0.136845	+	0.0790078i
$207$	12.5939			0.875336
$208$		0			0
$209$	−0.135748			−0.00938987
$210$	3.78394	−	2.18466i	0.261116	−	0.150756i
$211$	8.35475	+	14.4708i	0.575165	+	0.996214i	0.996024	+	0.0890882i	$0.0283953\pi$
$211$	8.35475	+	14.4708i	0.575165	+	0.996214i	−0.420859	+	0.907126i	$0.638271\pi$
$212$	5.17688	−	8.96661i	0.355549	−	0.615829i
$213$		−	6.56873i		−	0.450082i
$214$	−4.06830	−	2.34883i	−0.278103	−	0.160563i
$215$	9.74846	+	5.62828i	0.664840	+	0.383845i
$216$			5.25656i			0.357663i
$217$	0.171220	−	0.296562i	0.0116232	−	0.0201320i
$218$	−3.08580	−	5.34477i	−0.208997	−	0.361993i
$219$	−0.170413	+	0.0983879i	−0.0115154	+	0.00664844i
$220$	−0.164177			−0.0110688
$221$		0			0
$222$	−9.15278			−0.614295
$223$	−19.7621	+	11.4097i	−1.32337	+	0.764048i	−0.984265	−	0.176701i	$-0.943457\pi$
$223$	−19.7621	+	11.4097i	−1.32337	+	0.764048i	−0.339105	+	0.940749i	$0.610124\pi$
$224$	−1.99551	−	3.45632i	−0.133330	−	0.230935i
$225$	−0.900720	+	1.56009i	−0.0600480	+	0.104006i
$226$			11.2745i			0.749970i
$227$	3.28436	+	1.89623i	0.217991	+	0.125857i	0.605020	−	0.796211i	$-0.293165\pi$
$227$	3.28436	+	1.89623i	0.217991	+	0.125857i	−0.387029	+	0.922068i	$0.626499\pi$
$228$	−0.783937	−	0.452606i	−0.0519175	−	0.0299746i
$229$			4.69767i			0.310431i	0.987881	+	0.155215i	$0.0496071\pi$
$229$			4.69767i			0.310431i	−0.987881	+	0.155215i	$0.950393\pi$
$230$	−3.49551	+	6.05440i	−0.230487	+	0.399215i
$231$	0.358670	+	0.621235i	0.0235988	+	0.0408743i
$232$	5.06040	−	2.92163i	0.332232	−	0.191814i
$233$	−29.3752			−1.92443			−0.962216	−	0.272286i	$-0.912220\pi$
$233$	−29.3752			−1.92443			−0.962216	+	0.272286i	$0.912220\pi$
$234$		0			0
$235$	5.31634			0.346800
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$	3.40072	+	5.89022i	0.220901	+	0.382611i
$238$	3.12870	−	5.41907i	0.202804	−	0.351266i
$239$		−	4.19175i		−	0.271142i	−0.990768	−	0.135571i	$-0.956713\pi$
$239$		−	4.19175i		−	0.271142i	0.990768	−	0.135571i	$-0.0432869\pi$
$240$	−0.948114	−	0.547394i	−0.0612005	−	0.0353341i
$241$	−16.1343	−	9.31513i	−1.03930	−	0.600041i	−0.119666	−	0.992814i	$-0.538182\pi$
$241$	−16.1343	−	9.31513i	−1.03930	−	0.600041i	−0.919635	+	0.392774i	$0.871516\pi$
$242$			10.9730i			0.705374i
$243$	−7.69298	+	13.3246i	−0.493505	+	0.854775i
$244$	−3.21606	−	5.57038i	−0.205887	−	0.356607i
$245$	−7.73205	+	4.46410i	−0.493983	+	0.285201i
$246$	9.46410			0.603409
$247$		0			0
$248$	−0.0858029			−0.00544849
$249$	−1.17521	+	0.678506i	−0.0744757	+	0.0429985i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−2.28394	+	3.95589i	−0.144161	+	0.249694i	−0.929060	−	0.369930i	$-0.879382\pi$
$251$	−2.28394	+	3.95589i	−0.144161	+	0.249694i	0.784899	+	0.619624i	$0.212715\pi$
$252$		−	7.18958i		−	0.452901i
$253$	−0.993992	−	0.573882i	−0.0624918	−	0.0360796i
$254$	7.03590	+	4.06218i	0.441472	+	0.254884i
$255$		−	1.71649i		−	0.107491i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.785027	−	1.35971i	−0.0489686	−	0.0848161i	0.840502	−	0.541808i	$-0.182260\pi$
$257$	−0.785027	−	1.35971i	−0.0489686	−	0.0848161i	−0.889471	+	0.456992i	$0.848927\pi$
$258$	−10.6725	+	6.16177i	−0.664441	+	0.383615i
$259$	33.3662			2.07327
$260$		0			0
$261$	10.5263			0.651560
$262$	18.0163	−	10.4017i	1.11305	−	0.642620i
$263$	11.5167	+	19.9476i	0.710152	+	1.23002i	0.964800	+	0.262985i	$0.0847070\pi$
$263$	11.5167	+	19.9476i	0.710152	+	1.23002i	−0.254648	+	0.967034i	$0.581960\pi$
$264$	0.0898694	−	0.155658i	0.00553108	−	0.00958011i
$265$			10.3538i			0.636026i
$266$	2.85782	+	1.64996i	0.175224	+	0.101166i
$267$	−9.83833	−	5.68016i	−0.602096	−	0.347620i
$268$			15.3074i			0.935045i
$269$	−9.20708	+	15.9471i	−0.561365	+	0.972314i	0.436012	+	0.899941i	$0.356390\pi$
$269$	−9.20708	+	15.9471i	−0.561365	+	0.972314i	−0.997378	+	0.0723728i	$0.976943\pi$
$270$	−2.62828	−	4.55231i	−0.159952	−	0.277045i
$271$	7.86510	−	4.54092i	0.477771	−	0.275841i	−0.241716	−	0.970347i	$-0.577710\pi$
$271$	7.86510	−	4.54092i	0.477771	−	0.275841i	0.719487	+	0.694506i	$0.244377\pi$
$272$	−1.56787			−0.0950663
$273$		0			0
$274$	−5.25154			−0.317257
$275$	0.142181	−	0.0820885i	0.00857386	−	0.00495012i
$276$	−3.82684	−	6.62828i	−0.230349	−	0.398975i
$277$	−8.44843	+	14.6331i	−0.507617	+	0.879218i	0.492344	+	0.870400i	$0.336140\pi$
$277$	−8.44843	+	14.6331i	−0.507617	+	0.879218i	−0.999961	+	0.00881745i	$0.997193\pi$
$278$		−	16.7215i		−	1.00289i
$279$	−0.133860	−	0.0772844i	−0.00801402	−	0.00462690i
$280$	3.45632	+	1.99551i	0.206555	+	0.119254i
$281$			10.5011i			0.626443i	0.949680	+	0.313222i	$0.101408\pi$
$281$			10.5011i			0.626443i	−0.949680	+	0.313222i	$0.898592\pi$
$282$	−2.91013	+	5.04049i	−0.173296	+	0.300157i
$283$	2.86780	+	4.96717i	0.170473	+	0.295268i	0.938585	−	0.345047i	$-0.112137\pi$
$283$	2.86780	+	4.96717i	0.170473	+	0.295268i	−0.768112	+	0.640315i	$0.778804\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$	0.905212			0.0536202
$286$		0			0
$287$	−34.5011			−2.03654
$288$	−1.56009	+	0.900720i	−0.0919294	+	0.0530754i
$289$	7.27089	+	12.5935i	0.427699	+	0.740797i
$290$	−2.92163	+	5.06040i	−0.171564	+	0.297157i
$291$			20.7135i			1.21424i
$292$	−0.155658	−	0.0898694i	−0.00910922	−	0.00525921i
$293$	15.5306	+	8.96661i	0.907309	+	0.523835i	0.879564	−	0.475780i	$-0.157834\pi$
$293$	15.5306	+	8.96661i	0.907309	+	0.523835i	0.0277446	+	0.999615i	$0.491167\pi$
$294$		−	9.77449i		−	0.570060i
$295$	−1.73205	+	3.00000i	−0.100844	+	0.174667i
$296$	−4.18016	−	7.24026i	−0.242967	−	0.420831i
$297$	0.747385	−	0.431503i	0.0433676	−	0.0250383i
$298$	10.0328			0.581186
$299$		0			0
$300$	1.09479			0.0632076
$301$	38.9063	−	22.4625i	2.24252	−	1.29472i
$302$	−5.43761	−	9.41822i	−0.312900	−	0.541958i
$303$	−8.02900	+	13.9066i	−0.461254	+	0.798915i
$304$		−	0.826838i		−	0.0474224i
$305$	5.57038	+	3.21606i	0.318959	+	0.184151i
$306$	−2.44603	−	1.41222i	−0.139830	−	0.0807310i
$307$			26.7386i			1.52605i	0.646367	+	0.763027i	$0.276288\pi$
$307$			26.7386i			1.52605i	−0.646367	+	0.763027i	$0.723712\pi$
$308$	−0.327616	+	0.567448i	−0.0186677	+	0.0323334i
$309$	1.24146	+	2.15027i	0.0706243	+	0.122325i
$310$	0.0743075	−	0.0429015i	0.00422038	−	0.00243664i
$311$	25.4823			1.44497			0.722484	−	0.691388i	$-0.243000\pi$
$311$	25.4823			1.44497			0.722484	+	0.691388i	$0.243000\pi$
$312$		0			0
$313$	−8.68783			−0.491065			−0.245533	−	0.969388i	$-0.578963\pi$
$313$	−8.68783			−0.491065			−0.245533	+	0.969388i	$0.578963\pi$
$314$	−15.3219	+	8.84611i	−0.864666	+	0.499215i
$315$	3.59479	+	6.22635i	0.202543	+	0.350815i
$316$	−3.10628	+	5.38024i	−0.174742	+	0.302662i
$317$		−	35.4422i		−	1.99063i	−0.0966826	−	0.995315i	$-0.530823\pi$
$317$		−	35.4422i		−	1.99063i	0.0966826	−	0.995315i	$-0.469177\pi$
$318$	−9.81654	−	5.66758i	−0.550484	−	0.317822i
$319$	−0.830802	−	0.479664i	−0.0465160	−	0.0268560i
$320$		−	1.00000i		−	0.0559017i
$321$	−2.57147	+	4.45392i	−0.143526	+	0.248594i
$322$	13.9506	+	24.1632i	0.777438	+	1.34656i
$323$	1.12270	−	0.648189i	0.0624685	−	0.0360662i
$324$	0.350493			0.0194718
$325$		0			0
$326$	1.41113			0.0781550
$327$	−5.85139	+	3.37830i	−0.323582	+	0.186820i
$328$	4.32235	+	7.48652i	0.238662	+	0.413374i
$329$	10.6088	−	18.3750i	0.584882	−	1.01304i
$330$			0.179739i			0.00989430i
$331$	1.70362	+	0.983586i	0.0936395	+	0.0540628i	0.546089	−	0.837727i	$-0.316116\pi$
$331$	1.70362	+	0.983586i	0.0936395	+	0.0540628i	−0.452449	+	0.891790i	$0.649450\pi$
$332$	−1.07346	−	0.619760i	−0.0589135	−	0.0340138i
$333$		−	15.0606i		−	0.825318i
$334$	−0.352237	+	0.610092i	−0.0192735	+	0.0333827i
$335$	−7.65368	−	13.2566i	−0.418165	−	0.724283i
$336$	−3.78394	+	2.18466i	−0.206431	+	0.119183i
$337$	−32.4750			−1.76903			−0.884513	−	0.466516i	$-0.845509\pi$
$337$	−32.4750			−1.76903			−0.884513	+	0.466516i	$0.845509\pi$
$338$		0			0
$339$	12.3432			0.670391
$340$	1.35782	−	0.783937i	0.0736381	−	0.0425150i
$341$	0.00704343	+	0.0121996i	0.000381423	+	0.000660644i
$342$	0.744750	−	1.28994i	0.0402715	−	0.0697522i
$343$			7.69549i			0.415517i
$344$	−9.74846	−	5.62828i	−0.525602	−	0.303456i
$345$	6.62828	+	3.82684i	0.356855	+	0.206030i
$346$		−	0.655233i		−	0.0352255i
$347$	5.19209	−	8.99296i	0.278726	−	0.482767i	−0.692343	−	0.721569i	$-0.743421\pi$
$347$	5.19209	−	8.99296i	0.278726	−	0.482767i	0.971068	+	0.238802i	$0.0767546\pi$
$348$	−3.19856	−	5.54007i	−0.171461	−	0.296979i
$349$	−24.5943	+	14.1995i	−1.31650	+	0.760083i	−0.983164	−	0.182725i	$-0.941508\pi$
$349$	−24.5943	+	14.1995i	−1.31650	+	0.760083i	−0.333338	+	0.942808i	$0.608175\pi$
$350$	−3.99102			−0.213329
$351$		0			0
$352$	0.164177			0.00875066
$353$	8.14364	−	4.70173i	0.433442	−	0.250248i	−0.267370	−	0.963594i	$-0.586154\pi$
$353$	8.14364	−	4.70173i	0.433442	−	0.250248i	0.700812	+	0.713346i	$0.252821\pi$
$354$	−1.89623	−	3.28436i	−0.100783	−	0.174562i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		−	10.3767i		−	0.549966i
$357$	−5.93274	−	3.42527i	−0.313994	−	0.181284i
$358$	6.42011	+	3.70665i	0.339313	+	0.195903i
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$	0.900720	−	1.56009i	0.0474721	−	0.0822241i
$361$	−9.15817	−	15.8624i	−0.482009	−	0.834864i
$362$	−0.429615	+	0.248039i	−0.0225801	+	0.0130366i
$363$	12.0132			0.630527
$364$		0			0
$365$	0.179739			0.00940796
$366$	−6.09839	+	3.52091i	−0.318768	+	0.184041i
$367$	−15.3049	−	26.5089i	−0.798912	−	1.38376i	−0.920325	−	0.391154i	$-0.872076\pi$
$367$	−15.3049	−	26.5089i	−0.798912	−	1.38376i	0.121414	−	0.992602i	$-0.461257\pi$
$368$	3.49551	−	6.05440i	0.182216	−	0.315607i
$369$			15.5729i			0.810693i
$370$	7.24026	+	4.18016i	0.376403	+	0.217316i
$371$	35.7859	+	20.6610i	1.85791	+	1.07267i
$372$			0.0939360i			0.00487035i
$373$	11.6767	−	20.2246i	0.604595	−	1.04719i	−0.387520	−	0.921861i	$-0.626668\pi$
$373$	11.6767	−	20.2246i	0.604595	−	1.04719i	0.992115	−	0.125328i	$-0.0399983\pi$
$374$	0.128704	+	0.222922i	0.00665514	+	0.0115270i
$375$	−0.948114	+	0.547394i	−0.0489604	+	0.0282673i
$376$	−5.31634			−0.274169
$377$		0			0
$378$	−20.9790			−1.07904
$379$	15.0064	−	8.66397i	0.770829	−	0.445038i	−0.0623414	−	0.998055i	$-0.519857\pi$
$379$	15.0064	−	8.66397i	0.770829	−	0.445038i	0.833170	+	0.553017i	$0.186523\pi$
$380$	0.413419	+	0.716063i	0.0212080	+	0.0367333i
$381$	4.44722	−	7.70281i	0.227838	−	0.394627i
$382$			24.7944i			1.26859i
$383$	−16.2514	−	9.38275i	−0.830408	−	0.479436i	0.0235845	−	0.999722i	$-0.492492\pi$
$383$	−16.2514	−	9.38275i	−0.830408	−	0.479436i	−0.853992	+	0.520286i	$0.825825\pi$
$384$	0.948114	+	0.547394i	0.0483832	+	0.0279341i
$385$		−	0.655233i		−	0.0333937i
$386$	−1.93061	+	3.34392i	−0.0982655	+	0.170201i
$387$	−10.1390	−	17.5613i	−0.515395	−	0.892690i
$388$	−16.3853	+	9.46004i	−0.831836	+	0.480261i
$389$	7.13963			0.361994			0.180997	−	0.983484i	$-0.442068\pi$
$389$	7.13963			0.361994			0.180997	+	0.983484i	$0.442068\pi$
$390$		0			0
$391$	10.9610			0.554323
$392$	7.73205	−	4.46410i	0.390528	−	0.225471i
$393$	−11.3877	−	19.7240i	−0.574432	−	0.994945i
$394$	−2.85782	+	4.94989i	−0.143975	+	0.249372i
$395$		−	6.21257i		−	0.312588i
$396$	0.256131	+	0.147877i	0.0128711	+	0.00743112i
$397$	−1.81414	−	1.04739i	−0.0910490	−	0.0525672i	0.453784	−	0.891112i	$-0.350074\pi$
$397$	−1.81414	−	1.04739i	−0.0910490	−	0.0525672i	−0.544833	+	0.838544i	$0.683407\pi$
$398$			1.13575i			0.0569299i
$399$	1.80636	−	3.12870i	0.0904310	−	0.156631i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−21.8101	+	12.5921i	−1.08914	+	0.628818i	−0.933349	−	0.358971i	$-0.883128\pi$
$401$	−21.8101	+	12.5921i	−1.08914	+	0.628818i	−0.155796	+	0.987789i	$0.549794\pi$
$402$	16.7583			0.835828
$403$		0			0
$404$	−14.6677			−0.729745
$405$	−0.303536	+	0.175247i	−0.0150828	+	0.00870807i
$406$	11.6603	+	20.1962i	0.578689	+	1.00232i
$407$	−0.686287	+	1.18868i	−0.0340180	+	0.0589208i
$408$			1.71649i			0.0849789i
$409$	−8.37798	−	4.83703i	−0.414264	−	0.239176i	0.278356	−	0.960478i	$-0.410210\pi$
$409$	−8.37798	−	4.83703i	−0.414264	−	0.239176i	−0.692620	+	0.721302i	$0.743544\pi$
$410$	−7.48652	−	4.32235i	−0.369733	−	0.213465i
$411$			5.74932i			0.283593i
$412$	−1.13397	+	1.96410i	−0.0558669	+	0.0967643i
$413$	6.91264	+	11.9730i	0.340149	+	0.589155i
$414$	10.9066	−	6.29695i	0.536032	−	0.309478i
$415$	1.23952			0.0608456
$416$		0			0
$417$	−18.3065			−0.896473
$418$	−0.117561	+	0.0678739i	−0.00575010	+	0.00331982i
$419$	−4.67369	−	8.09507i	−0.228325	−	0.395470i	0.728987	−	0.684528i	$-0.239991\pi$
$419$	−4.67369	−	8.09507i	−0.228325	−	0.395470i	−0.957312	+	0.289057i	$0.906658\pi$
$420$	2.18466	−	3.78394i	0.106600	−	0.184637i
$421$			25.5243i			1.24398i	0.783026	+	0.621989i	$0.213675\pi$
$421$			25.5243i			1.24398i	−0.783026	+	0.621989i	$0.786325\pi$
$422$	14.4708	+	8.35475i	0.704430	+	0.406703i
$423$	−8.29398	−	4.78853i	−0.403267	−	0.232826i
$424$		−	10.3538i		−	0.502823i
$425$	−0.783937	+	1.35782i	−0.0380265	+	0.0658639i
$426$	−3.28436	−	5.68868i	−0.159128	−	0.275618i
$427$	22.2315	−	12.8354i	1.07586	−	0.621146i
$428$	−4.69767			−0.227070
$429$		0			0
$430$	11.2566			0.542839
$431$	3.55397	−	2.05189i	0.171189	−	0.0988359i	−0.411957	−	0.911203i	$-0.635155\pi$
$431$	3.55397	−	2.05189i	0.171189	−	0.0988359i	0.583146	+	0.812367i	$0.301821\pi$
$432$	2.62828	+	4.55231i	0.126453	+	0.219023i
$433$	1.34392	−	2.32773i	0.0645845	−	0.111864i	−0.831925	−	0.554888i	$-0.812761\pi$
$433$	1.34392	−	2.32773i	0.0645845	−	0.111864i	0.896510	+	0.443024i	$0.146094\pi$
$434$		−	0.342441i		−	0.0164377i
$435$	5.54007	+	3.19856i	0.265626	+	0.153359i
$436$	−5.34477	−	3.08580i	−0.255968	−	0.147783i
$437$			5.78044i			0.276516i
$438$	−0.0983879	+	0.170413i	−0.00470116	+	0.00814264i
$439$	−1.23848	−	2.14512i	−0.0591096	−	0.102381i	0.834956	−	0.550316i	$-0.185493\pi$
$439$	−1.23848	−	2.14512i	−0.0591096	−	0.102381i	−0.894066	+	0.447935i	$0.852159\pi$
$440$	−0.142181	+	0.0820885i	−0.00677823	+	0.00391341i
$441$	16.0836			0.765887
$442$		0			0
$443$	−17.3774			−0.825624			−0.412812	−	0.910816i	$-0.635453\pi$
$443$	−17.3774			−0.825624			−0.412812	+	0.910816i	$0.635453\pi$
$444$	−7.92654	+	4.57639i	−0.376177	+	0.217186i
$445$	5.18837	+	8.98652i	0.245952	+	0.426002i
$446$	−11.4097	+	19.7621i	−0.540263	+	0.935763i
$447$		−	10.9838i		−	0.519517i
$448$	−3.45632	−	1.99551i	−0.163296	−	0.0942789i
$449$	−25.9206	−	14.9653i	−1.22327	−	0.706255i	−0.257655	−	0.966237i	$-0.582950\pi$
$449$	−25.9206	−	14.9653i	−1.22327	−	0.706255i	−0.965613	+	0.259982i	$0.916283\pi$
$450$			1.80144i			0.0849207i
$451$	0.709629	−	1.22911i	0.0334151	−	0.0578767i
$452$	5.63726	+	9.76403i	0.265155	+	0.459261i
$453$	−10.3110	+	5.95303i	−0.484451	+	0.279698i
$454$	3.79246			0.177989
$455$		0			0
$456$	−0.905212			−0.0423905
$457$	−9.93255	+	5.73456i	−0.464625	+	0.268251i	−0.713987	−	0.700159i	$-0.753112\pi$
$457$	−9.93255	+	5.73456i	−0.464625	+	0.268251i	0.249362	+	0.968410i	$0.419779\pi$
$458$	2.34883	+	4.06830i	0.109754	+	0.190099i
$459$	−4.12081	+	7.13745i	−0.192343	+	0.333148i
$460$			6.99102i			0.325958i
$461$	−20.7904	−	12.0034i	−0.968307	−	0.559052i	−0.0695873	−	0.997576i	$-0.522168\pi$
$461$	−20.7904	−	12.0034i	−0.968307	−	0.559052i	−0.898720	+	0.438524i	$0.855502\pi$
$462$	0.621235	+	0.358670i	0.0289025	+	0.0166869i
$463$			26.3163i			1.22302i	0.791235	+	0.611512i	$0.209438\pi$
$463$			26.3163i			1.22302i	−0.791235	+	0.611512i	$0.790562\pi$
$464$	2.92163	−	5.06040i	0.135633	−	0.234923i
$465$	−0.0469680	−	0.0813509i	−0.00217809	−	0.00377256i
$466$	−25.4397	+	14.6876i	−1.17847	+	0.680390i
$467$	−16.2776			−0.753236			−0.376618	−	0.926369i	$-0.622913\pi$
$467$	−16.2776			−0.753236			−0.376618	+	0.926369i	$0.622913\pi$
$468$		0			0
$469$	−61.0919			−2.82096
$470$	4.60408	−	2.65817i	0.212371	−	0.122612i
$471$	9.68462	+	16.7742i	0.446244	+	0.772917i
$472$	1.73205	−	3.00000i	0.0797241	−	0.138086i
$473$			1.84807i			0.0849742i
$474$	5.89022	+	3.40072i	0.270547	+	0.156200i
$475$	−0.716063	−	0.413419i	−0.0328552	−	0.0189690i
$476$		−	6.25741i		−	0.286808i
$477$	9.32583	−	16.1528i	0.427001	−	0.739587i
$478$	−2.09588	−	3.63017i	−0.0958632	−	0.166040i
$479$	24.0075	−	13.8608i	1.09693	−	0.633314i	0.161519	−	0.986870i	$-0.448361\pi$
$479$	24.0075	−	13.8608i	1.09693	−	0.633314i	0.935414	+	0.353556i	$0.115027\pi$
$480$	−1.09479			−0.0499700
$481$		0			0
$482$	−18.6303			−0.848586
$483$	26.4536	−	15.2730i	1.20368	−	0.694944i
$484$	5.48652	+	9.50294i	0.249387	+	0.431952i
$485$	9.46004	−	16.3853i	0.429558	−	0.744016i
$486$			15.3860i			0.697921i
$487$	−21.0182	−	12.1349i	−0.952425	−	0.549883i	−0.0585916	−	0.998282i	$-0.518661\pi$
$487$	−21.0182	−	12.1349i	−0.952425	−	0.549883i	−0.893833	+	0.448399i	$0.851994\pi$
$488$	−5.57038	−	3.21606i	−0.252159	−	0.145584i
$489$		−	1.54488i		−	0.0698620i
$490$	−4.46410	+	7.73205i	−0.201668	+	0.349298i
$491$	5.15117	+	8.92208i	0.232469	+	0.402648i	0.958534	−	0.284978i	$-0.0919863\pi$
$491$	5.15117	+	8.92208i	0.232469	+	0.402648i	−0.726065	+	0.687626i	$0.758653\pi$
$492$	8.19615	−	4.73205i	0.369511	−	0.213337i
$493$	9.16148			0.412612
$494$		0			0
$495$	−0.295755			−0.0132932
$496$	−0.0743075	+	0.0429015i	−0.00333650	+	0.00192633i
$497$	11.9730	+	20.7379i	0.537065	+	0.930223i
$498$	−0.678506	+	1.17521i	−0.0304046	+	0.0526622i
$499$		−	28.2672i		−	1.26542i	−0.774391	−	0.632708i	$-0.781943\pi$
$499$		−	28.2672i		−	1.26542i	0.774391	−	0.632708i	$-0.218057\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	0.667921	+	0.385624i	0.0298405	+	0.0172284i
$502$			4.56787i			0.203874i
$503$	−15.3561	+	26.5976i	−0.684697	+	1.18593i	0.288835	+	0.957379i	$0.406732\pi$
$503$	−15.3561	+	26.5976i	−0.684697	+	1.18593i	−0.973532	+	0.228551i	$0.926601\pi$
$504$	−3.59479	−	6.22635i	−0.160125	−	0.277344i
$505$	12.7026	−	7.33384i	0.565258	−	0.326352i
$506$	−1.14776			−0.0510243
$507$		0			0
$508$	8.12436			0.360460
$509$	1.86255	−	1.07534i	0.0825560	−	0.0476637i	−0.458154	−	0.888873i	$-0.651489\pi$
$509$	1.86255	−	1.07534i	0.0825560	−	0.0476637i	0.540710	+	0.841209i	$0.318156\pi$
$510$	−0.858244	−	1.48652i	−0.0380037	−	0.0658243i
$511$	0.358670	−	0.621235i	0.0158666	−	0.0274818i
$512$			1.00000i			0.0441942i
$513$	−3.76403	−	2.17316i	−0.166186	−	0.0959474i
$514$	−1.35971	−	0.785027i	−0.0599741	−	0.0346260i
$515$		−	2.26795i		−	0.0999378i
$516$	−6.16177	+	10.6725i	−0.271257	+	0.469831i
$517$	0.436410	+	0.755884i	0.0191933	+	0.0332438i
$518$	28.8960	−	16.6831i	1.26962	−	0.733013i
$519$	−0.717341			−0.0314878
$520$		0			0
$521$	10.6848			0.468110			0.234055	−	0.972223i	$-0.424800\pi$
$521$	10.6848			0.468110			0.234055	+	0.972223i	$0.424800\pi$
$522$	9.11602	−	5.26313i	0.398997	−	0.230361i
$523$	−3.95601	−	6.85201i	−0.172984	−	0.299617i	0.766478	−	0.642271i	$-0.222008\pi$
$523$	−3.95601	−	6.85201i	−0.172984	−	0.299617i	−0.939462	+	0.342654i	$0.888674\pi$
$524$	10.4017	−	18.0163i	0.454401	−	0.787046i
$525$			4.36931i			0.190692i
$526$	19.9476	+	11.5167i	0.869755	+	0.502153i
$527$	−0.116505	−	0.0672641i	−0.00507503	−	0.00293007i
$528$		−	0.179739i		−	0.00782213i
$529$	−12.9371	+	22.4078i	−0.562485	+	0.974252i
$530$	5.17688	+	8.96661i	0.224869	+	0.389485i
$531$	5.40432	−	3.12019i	0.234528	−	0.135405i
$532$	3.29992			0.143070
$533$		0			0
$534$	−11.3603			−0.491610
$535$	4.06830	−	2.34883i	0.175888	−	0.101549i
$536$	7.65368	+	13.2566i	0.330588	+	0.572596i
$537$	4.05800	−	7.02866i	0.175116	−	0.303309i
$538$			18.4142i			0.793891i
$539$	−1.26942	−	0.732902i	−0.0546780	−	0.0315683i
$540$	−4.55231	−	2.62828i	−0.195900	−	0.113103i
$541$		−	34.7694i		−	1.49485i	−0.664345	−	0.747426i	$-0.731289\pi$
$541$		−	34.7694i		−	1.49485i	0.664345	−	0.747426i	$-0.268711\pi$
$542$	4.54092	−	7.86510i	0.195049	−	0.337835i
$543$	0.271550	+	0.470338i	0.0116533	+	0.0201841i
$544$	−1.35782	+	0.783937i	−0.0582160	+	0.0336110i
$545$	6.17161			0.264363
$546$		0			0
$547$	8.98506			0.384173			0.192087	−	0.981378i	$-0.438475\pi$
$547$	8.98506			0.384173			0.192087	+	0.981378i	$0.438475\pi$
$548$	−4.54796	+	2.62577i	−0.194279	+	0.112167i
$549$	−5.79355	−	10.0347i	−0.247262	−	0.428271i
$550$	0.0820885	−	0.142181i	0.00350026	−	0.00606263i
$551$			4.83143i			0.205826i
$552$	−6.62828	−	3.82684i	−0.282118	−	0.162881i
$553$	−21.4726	−	12.3972i	−0.913109	−	0.527184i
$554$			16.8969i			0.717878i
$555$	4.57639	−	7.92654i	0.194257	−	0.336463i
$556$	−8.36076	−	14.4813i	−0.354575	−	0.614142i
$557$	−26.2342	+	15.1464i	−1.11158	+	0.641771i	−0.939238	−	0.343266i	$-0.888467\pi$
$557$	−26.2342	+	15.1464i	−1.11158	+	0.641771i	−0.172342	+	0.985037i	$0.555134\pi$
$558$	−0.154569			−0.00654342
$559$		0			0
$560$	3.99102			0.168651
$561$	0.244053	−	0.140904i	0.0103039	−	0.00594897i
$562$	5.25055	+	9.09422i	0.221481	+	0.383616i
$563$	−1.20514	+	2.08736i	−0.0507905	+	0.0879717i	−0.890303	−	0.455369i	$-0.849507\pi$
$563$	−1.20514	+	2.08736i	−0.0507905	+	0.0879717i	0.839512	+	0.543341i	$0.182841\pi$
$564$			5.82026i			0.245077i
$565$	−9.76403	−	5.63726i	−0.410776	−	0.237161i
$566$	4.96717	+	2.86780i	0.208786	+	0.120543i
$567$			1.39882i			0.0587450i
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	−2.18565	−	3.78566i	−0.0916273	−	0.158703i	0.816569	−	0.577248i	$-0.195874\pi$
$569$	−2.18565	−	3.78566i	−0.0916273	−	0.158703i	−0.908196	+	0.418545i	$0.862540\pi$
$570$	0.783937	−	0.452606i	0.0328355	−	0.0189576i
$571$	−19.0050			−0.795335			−0.397668	−	0.917530i	$-0.630180\pi$
$571$	−19.0050			−0.795335			−0.397668	+	0.917530i	$0.630180\pi$
$572$		0			0
$573$	27.1447			1.13398
$574$	−29.8788	+	17.2505i	−1.24712	+	0.720024i
$575$	−3.49551	−	6.05440i	−0.145773	−	0.252486i
$576$	−0.900720	+	1.56009i	−0.0375300	+	0.0650039i
$577$		−	13.0620i		−	0.543777i	−0.962329	−	0.271888i	$-0.912352\pi$
$577$		−	13.0620i		−	0.543777i	0.962329	−	0.271888i	$-0.0876481\pi$
$578$	12.5935	+	7.27089i	0.523822	+	0.302429i
$579$	3.66088	+	2.11361i	0.152141	+	0.0878386i
$580$			5.84325i			0.242628i
$581$	2.47347	−	4.28418i	0.102617	−	0.177738i
$582$	10.3567	+	17.9384i	0.429300	+	0.743570i
$583$	−1.47211	+	0.849924i	−0.0609686	+	0.0352002i
$584$	−0.179739			−0.00743765
$585$		0			0
$586$	17.9332			0.740815
$587$	−24.2844	+	14.0206i	−1.00232	+	0.578691i	−0.908935	−	0.416938i	$-0.863103\pi$
$587$	−24.2844	+	14.0206i	−1.00232	+	0.578691i	−0.0933882	+	0.995630i	$0.529770\pi$
$588$	−4.88724	−	8.46495i	−0.201547	−	0.349089i
$589$	0.0354726	−	0.0614403i	0.00146162	−	0.00253160i
$590$			3.46410i			0.142615i
$591$	5.41907	+	3.12870i	0.222911	+	0.128698i
$592$	−7.24026	−	4.18016i	−0.297573	−	0.171804i
$593$		−	32.1848i		−	1.32167i	−0.750531	−	0.660835i	$-0.770202\pi$
$593$		−	32.1848i		−	1.32167i	0.750531	−	0.660835i	$-0.229798\pi$
$594$	0.431503	−	0.747385i	0.0177048	−	0.0306656i
$595$	3.12870	+	5.41907i	0.128264	+	0.222160i
$596$	8.68868	−	5.01641i	0.355902	−	0.205480i
$597$	1.24340			0.0508891
$598$		0			0
$599$	13.8415			0.565550			0.282775	−	0.959186i	$-0.408745\pi$
$599$	13.8415			0.565550			0.282775	+	0.959186i	$0.408745\pi$
$600$	0.948114	−	0.547394i	0.0387066	−	0.0223473i
$601$	−4.06873	−	7.04724i	−0.165967	−	0.287463i	0.771031	−	0.636797i	$-0.219741\pi$
$601$	−4.06873	−	7.04724i	−0.165967	−	0.287463i	−0.936998	+	0.349334i	$0.886408\pi$
$602$	22.4625	−	38.9063i	0.915505	−	1.58570i
$603$			27.5753i			1.12295i
$604$	−9.41822	−	5.43761i	−0.383222	−	0.221253i
$605$	−9.50294	−	5.48652i	−0.386349	−	0.223059i
$606$			16.0580i			0.652312i
$607$	22.8555	−	39.5869i	0.927676	−	1.60678i	0.140475	−	0.990084i	$-0.455137\pi$
$607$	22.8555	−	39.5869i	0.927676	−	1.60678i	0.787201	−	0.616697i	$-0.211530\pi$
$608$	−0.413419	−	0.716063i	−0.0167664	−	0.0290402i
$609$	22.1105	−	12.7655i	0.895963	−	0.517284i
$610$	6.43213			0.260429
$611$		0			0
$612$	−2.82443			−0.114171
$613$	33.1743	−	19.1532i	1.33990	−	0.773591i	0.353107	−	0.935583i	$-0.385125\pi$
$613$	33.1743	−	19.1532i	1.33990	−	0.773591i	0.986792	+	0.161992i	$0.0517919\pi$
$614$	13.3693	+	23.1563i	0.539542	+	0.934513i
$615$	−4.73205	+	8.19615i	−0.190815	+	0.330501i
$616$			0.655233i			0.0264001i
$617$	−4.67667	−	2.70008i	−0.188276	−	0.108701i	0.402899	−	0.915244i	$-0.368002\pi$
$617$	−4.67667	−	2.70008i	−0.188276	−	0.108701i	−0.591175	+	0.806543i	$0.701336\pi$
$618$	2.15027	+	1.24146i	0.0864967	+	0.0499389i
$619$		−	20.2758i		−	0.814954i	−0.913216	−	0.407477i	$-0.866409\pi$
$619$		−	20.2758i		−	0.814954i	0.913216	−	0.407477i	$-0.133591\pi$
$620$	0.0429015	−	0.0743075i	0.00172296	−	0.00298426i
$621$	−18.3743	−	31.8253i	−0.737337	−	1.27710i
$622$	22.0683	−	12.7411i	0.884858	−	0.510873i
$623$	41.4137			1.65921
$624$		0			0
$625$	1.00000			0.0400000
$626$	−7.52388	+	4.34392i	−0.300715	+	0.173618i
$627$	0.0743075	+	0.128704i	0.00296756	+	0.00513996i
$628$	−8.84611	+	15.3219i	−0.352998	+	0.611411i
$629$		−	13.1079i		−	0.522648i
$630$	6.22635	+	3.59479i	0.248064	+	0.143220i
$631$	22.1700	+	12.7999i	0.882576	+	0.509555i	0.871507	−	0.490383i	$-0.163143\pi$
$631$	22.1700	+	12.7999i	0.882576	+	0.509555i	0.0110689	+	0.999939i	$0.496477\pi$
$632$			6.21257i			0.247123i
$633$	9.14667	−	15.8425i	0.363548	−	0.629683i
$634$	−17.7211	−	30.6938i	−0.703794	−	1.21901i
$635$	−7.03590	+	4.06218i	−0.279211	+	0.161203i
$636$	−11.3352			−0.449468
$637$		0			0
$638$	−0.959327			−0.0379801
$639$	9.36056	−	5.40432i	0.370298	−	0.213792i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	0.738951	−	1.27990i	0.0291868	−	0.0505530i	−0.851063	−	0.525063i	$-0.824042\pi$
$641$	0.738951	−	1.27990i	0.0291868	−	0.0505530i	0.880250	+	0.474510i	$0.157375\pi$
$642$			5.14295i			0.202976i
$643$	35.7724	+	20.6532i	1.41073	+	0.814483i	0.995457	−	0.0952153i	$-0.0303540\pi$
$643$	35.7724	+	20.6532i	1.41073	+	0.814483i	0.415269	+	0.909698i	$0.363687\pi$
$644$	24.1632	+	13.9506i	0.952163	+	0.549732i
$645$		−	12.3235i		−	0.485239i
$646$	0.648189	−	1.12270i	0.0255027	−	0.0441719i
$647$	8.96379	+	15.5257i	0.352403	+	0.610380i	0.986670	−	0.162734i	$-0.0520313\pi$
$647$	8.96379	+	15.5257i	0.352403	+	0.610380i	−0.634267	+	0.773114i	$0.718698\pi$
$648$	0.303536	−	0.175247i	0.0119240	−	0.00688433i
$649$	−0.568726			−0.0223244
$650$		0			0
$651$	−0.374900			−0.0146935
$652$	1.22207	−	0.705563i	0.0478600	−	0.0276320i
$653$	−13.9229	−	24.1152i	−0.544846	−	0.943702i	−0.998617	−	0.0525830i	$-0.983255\pi$
$653$	−13.9229	−	24.1152i	−0.544846	−	0.943702i	0.453770	−	0.891119i	$-0.350079\pi$
$654$	−3.37830	+	5.85139i	−0.132102	+	0.228807i
$655$			20.8034i			0.812857i
$656$	7.48652	+	4.32235i	0.292300	+	0.168759i
$657$	−0.280409	−	0.161894i	−0.0109398	−	0.00631610i
$658$		−	21.2176i		−	0.827148i
$659$	−7.42915	+	12.8677i	−0.289399	+	0.501253i	−0.973666	−	0.227978i	$-0.926789\pi$
$659$	−7.42915	+	12.8677i	−0.289399	+	0.501253i	0.684268	+	0.729231i	$0.260122\pi$
$660$	0.0898694	+	0.155658i	0.00349816	+	0.00605900i
$661$	−19.5210	+	11.2705i	−0.759279	+	0.438370i	−0.829037	−	0.559194i	$-0.811111\pi$
$661$	−19.5210	+	11.2705i	−0.759279	+	0.438370i	0.0697577	+	0.997564i	$0.477777\pi$
$662$	1.96717			0.0764563
$663$		0			0
$664$	−1.23952			−0.0481027
$665$	−2.85782	+	1.64996i	−0.110821	+	0.0639828i
$666$	−7.53032	−	13.0429i	−0.291794	−	0.505402i
$667$	−20.4251	+	35.3774i	−0.790864	+	1.36982i
$668$			0.704473i			0.0272569i
$669$	21.6353	+	12.4912i	0.836470	+	0.482936i
$670$	−13.2566	−	7.65368i	−0.512145	−	0.295687i
$671$			1.05601i			0.0407667i
$672$	−2.18466	+	3.78394i	−0.0842750	+	0.145969i
$673$	13.1200	+	22.7244i	0.505737	+	0.875963i	0.999978	+	0.00663747i	$0.00211279\pi$
$673$	13.1200	+	22.7244i	0.505737	+	0.875963i	−0.494241	+	0.869325i	$0.664554\pi$
$674$	−28.1242	+	16.2375i	−1.08330	+	0.625445i
$675$	5.25656			0.202325
$676$		0			0
$677$	13.6685			0.525324			0.262662	−	0.964888i	$-0.415400\pi$
$677$	13.6685			0.525324			0.262662	+	0.964888i	$0.415400\pi$
$678$	10.6895	−	6.17161i	0.410529	−	0.237019i
$679$	−37.7551	−	65.3938i	−1.44891	−	2.50958i
$680$	0.783937	−	1.35782i	0.0300626	−	0.0520700i
$681$		−	4.15193i		−	0.159102i
$682$	0.0121996	+	0.00704343i	0.000467146	+	0.000269707i
$683$	−3.98506	−	2.30078i	−0.152484	−	0.0880368i	0.421817	−	0.906681i	$-0.361393\pi$
$683$	−3.98506	−	2.30078i	−0.152484	−	0.0880368i	−0.574301	+	0.818644i	$0.694726\pi$
$684$		−	1.48950i		−	0.0569525i
$685$	2.62577	−	4.54796i	0.100325	−	0.173769i
$686$	3.84774	+	6.66449i	0.146908	+	0.254451i
$687$	4.45392	−	2.57147i	0.169928	−	0.0981079i
$688$	−11.2566			−0.429152
$689$		0			0
$690$	7.65368			0.291370
$691$	−26.1212	+	15.0811i	−0.993699	+	0.573712i	−0.906378	−	0.422468i	$-0.861164\pi$
$691$	−26.1212	+	15.0811i	−0.993699	+	0.573712i	−0.0873208	+	0.996180i	$0.527831\pi$
$692$	−0.327616	−	0.567448i	−0.0124541	−	0.0215711i
$693$	−0.590181	+	1.02222i	−0.0224191	+	0.0388311i
$694$		−	10.3842i		−	0.394178i
$695$	14.4813	+	8.36076i	0.549305	+	0.317142i
$696$	−5.54007	−	3.19856i	−0.209996	−	0.121241i
$697$			13.5538i			0.513386i
$698$	−14.1995	+	24.5943i	−0.537460	+	0.930907i
$699$	16.0798	+	27.8510i	0.608194	+	1.05342i
$700$	−3.45632	+	1.99551i	−0.130637	+	0.0754231i
$701$	−29.3752			−1.10949			−0.554743	−	0.832022i	$-0.687183\pi$
$701$	−29.3752			−1.10949			−0.554743	+	0.832022i	$0.687183\pi$
$702$		0			0
$703$	6.91264			0.260715
$704$	0.142181	−	0.0820885i	0.00535866	−	0.00309383i
$705$	−2.91013	−	5.04049i	−0.109602	−	0.189836i
$706$	4.70173	−	8.14364i	0.176952	−	0.306490i
$707$		−	58.5389i		−	2.20158i
$708$	−3.28436	−	1.89623i	−0.123434	−	0.0712646i
$709$	13.9540	+	8.05634i	0.524053	+	0.302562i	0.738591	−	0.674153i	$-0.235491\pi$
$709$	13.9540	+	8.05634i	0.524053	+	0.302562i	−0.214538	+	0.976716i	$0.568825\pi$
$710$			6.00000i			0.225176i
$711$	−5.59578	+	9.69218i	−0.209858	+	0.363485i
$712$	−5.18837	−	8.98652i	−0.194442	−	0.336784i
$713$	0.519485	−	0.299925i	0.0194549	−	0.0112323i
$714$	−6.85053			−0.256375
$715$		0			0
$716$	7.41331			0.277048
$717$	−3.97426	+	2.29454i	−0.148421	+	0.0856912i
$718$	12.1244	+	21.0000i	0.452477	+	0.783713i
$719$	−11.3238	+	19.6133i	−0.422305	+	0.731454i	−0.996165	−	0.0874998i	$-0.972112\pi$
$719$	−11.3238	+	19.6133i	−0.422305	+	0.731454i	0.573859	+	0.818954i	$0.305446\pi$
$720$		−	1.80144i		−	0.0671357i
$721$	−7.83876	−	4.52571i	−0.291931	−	0.168546i
$722$	−15.8624	−	9.15817i	−0.590338	−	0.340832i
$723$			20.3962i			0.758542i
$724$	−0.248039	+	0.429615i	−0.00921828	+	0.0159665i
$725$	−2.92163	−	5.06040i	−0.108506	−	0.187939i
$726$	10.4037	−	6.00658i	0.386117	−	0.222925i
$727$	−4.36795			−0.161998			−0.0809991	−	0.996714i	$-0.525811\pi$
$727$	−4.36795			−0.161998			−0.0809991	+	0.996714i	$0.525811\pi$
$728$		0			0
$729$	17.8958			0.662809
$730$	0.155658	−	0.0898694i	0.00576118	−	0.00332622i
$731$	−8.82443	−	15.2844i	−0.326383	−	0.565313i
$732$	−3.52091	+	6.09839i	−0.130136	+	0.225403i
$733$		−	6.50392i		−	0.240228i	−0.992760	−	0.120114i	$-0.961674\pi$
$733$		−	6.50392i		−	0.240228i	0.992760	−	0.120114i	$-0.0383260\pi$
$734$	−26.5089	−	15.3049i	−0.978463	−	0.564916i
$735$	8.46495	+	4.88724i	0.312235	+	0.180269i
$736$		−	6.99102i		−	0.257692i
$737$	1.25656	−	2.17642i	0.0462859	−	0.0801695i
$738$	7.78645	+	13.4865i	0.286623	+	0.496446i
$739$	1.89078	−	1.09164i	0.0695535	−	0.0401567i	−0.464820	−	0.885405i	$-0.653881\pi$
$739$	1.89078	−	1.09164i	0.0695535	−	0.0401567i	0.534373	+	0.845249i	$0.320548\pi$
$740$	8.36033			0.307332
$741$		0			0
$742$	41.3220			1.51698
$743$	−8.64371	+	4.99045i	−0.317107	+	0.183082i	−0.650102	−	0.759847i	$-0.725274\pi$
$743$	−8.64371	+	4.99045i	−0.317107	+	0.183082i	0.332995	+	0.942928i	$0.391941\pi$
$744$	0.0469680	+	0.0813509i	0.00172193	+	0.00298247i
$745$	−5.01641	+	8.68868i	−0.183787	+	0.318329i
$746$		−	23.3533i		−	0.855026i
$747$	−1.93377	−	1.11646i	−0.0707528	−	0.0408492i
$748$	0.222922	+	0.128704i	0.00815085	+	0.00470590i
$749$		−	18.7485i		−	0.685054i
$750$	−0.547394	+	0.948114i	−0.0199880	+	0.0346202i
$751$	7.82026	+	13.5451i	0.285365	+	0.494267i	0.972698	−	0.232076i	$-0.0745517\pi$
$751$	7.82026	+	13.5451i	0.285365	+	0.494267i	−0.687332	+	0.726343i	$0.741218\pi$
$752$	−4.60408	+	2.65817i	−0.167894	+	0.0969335i
$753$	5.00085			0.182241
$754$		0			0
$755$	10.8752			0.395790
$756$	−18.1683	+	10.4895i	−0.660776	+	0.381499i
$757$	−2.76476	−	4.78871i	−0.100487	−	0.174049i	0.811398	−	0.584494i	$-0.198707\pi$
$757$	−2.76476	−	4.78871i	−0.100487	−	0.174049i	−0.911885	+	0.410445i	$0.865373\pi$
$758$	8.66397	−	15.0064i	0.314690	−	0.545058i
$759$			1.25656i			0.0456101i
$760$	0.716063	+	0.413419i	0.0259743	+	0.0149963i
$761$	33.3086	+	19.2308i	1.20744	+	0.697114i	0.962199	−	0.272349i	$-0.0878004\pi$
$761$	33.3086	+	19.2308i	1.20744	+	0.697114i	0.245239	+	0.969463i	$0.421134\pi$
$762$		−	8.89444i		−	0.322212i
$763$	12.3155	−	21.3310i	0.445851	−	0.772236i
$764$	12.3972	+	21.4726i	0.448516	+	0.776852i
$765$	2.44603	−	1.41222i	0.0884364	−	0.0510588i
$766$	−18.7655			−0.678025
$767$		0			0
$768$	1.09479			0.0395047
$769$	9.77174	−	5.64172i	0.352378	−	0.203445i	−0.313354	−	0.949636i	$-0.601453\pi$
$769$	9.77174	−	5.64172i	0.352378	−	0.203445i	0.665732	+	0.746191i	$0.268119\pi$
$770$	−0.327616	−	0.567448i	−0.0118065	−	0.0204494i
$771$	−0.859437	+	1.48859i	−0.0309519	+	0.0536102i
$772$			3.86122i			0.138968i
$773$	−7.84674	−	4.53032i	−0.282228	−	0.162944i	0.352204	−	0.935923i	$-0.385432\pi$
$773$	−7.84674	−	4.53032i	−0.282228	−	0.162944i	−0.634431	+	0.772979i	$0.718766\pi$
$774$	−17.5613	−	10.1390i	−0.631227	−	0.364439i
$775$			0.0858029i			0.00308213i
$776$	−9.46004	+	16.3853i	−0.339595	+	0.588197i
$777$	−18.2645	−	31.6350i	−0.655234	−	1.13490i
$778$	6.18310	−	3.56982i	0.221675	−	0.127984i
$779$	−7.14776			−0.256095
$780$		0			0
$781$	−0.985062			−0.0352483
$782$	9.49253	−	5.48052i	0.339452	−	0.195983i
$783$	−15.3577	−	26.6003i	−0.548839	−	0.950617i
$784$	4.46410	−	7.73205i	0.159432	−	0.276145i
$785$		−	17.6922i		−	0.631463i
$786$	−19.7240	−	11.3877i	−0.703533	−	0.406185i
$787$	−1.60236	−	0.925123i	−0.0571180	−	0.0329771i	0.471169	−	0.882043i	$-0.343832\pi$
$787$	−1.60236	−	0.925123i	−0.0571180	−	0.0329771i	−0.528287	+	0.849066i	$0.677165\pi$
$788$			5.71564i			0.203611i
$789$	12.6084	−	21.8383i	0.448870	−	0.777465i
$790$	−3.10628	−	5.38024i	−0.110517	−	0.191420i
$791$	−38.9684	+	22.4984i	−1.38556	+	0.799951i
$792$	0.295755			0.0105092
$793$		0			0
$794$	−2.09479			−0.0743412
$795$	9.81654	−	5.66758i	0.348157	−	0.201008i
$796$	0.567874	+	0.983586i	0.0201278	+	0.0348623i
$797$	−2.32892	+	4.03381i	−0.0824947	+	0.142885i	−0.904321	−	0.426853i	$-0.859622\pi$
$797$	−2.32892	+	4.03381i	−0.0824947	+	0.142885i	0.821826	+	0.569738i	$0.192955\pi$
$798$		−	3.61272i		−	0.127889i
$799$	−7.21862	−	4.16767i	−0.255377	−	0.147442i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		−	18.6931i		−	0.660488i
$802$	−12.5921	+	21.8101i	−0.444641	+	0.770141i
$803$	0.0147545	+	0.0255555i	0.000520674	+	0.000901835i
$804$	14.5131	−	8.37915i	0.511838	−	0.295510i
$805$	−27.9012			−0.983390
$806$		0			0
$807$	20.1596			0.709651
$808$	−12.7026	+	7.33384i	−0.446875	+	0.258004i
$809$	17.7431	+	30.7319i	0.623813	+	1.08048i	0.988769	+	0.149452i	$0.0477508\pi$
$809$	17.7431	+	30.7319i	0.623813	+	1.08048i	−0.364956	+	0.931025i	$0.618916\pi$
$810$	−0.175247	+	0.303536i	−0.00615753	+	0.0106652i
$811$		−	38.5309i		−	1.35300i	−0.736442	−	0.676501i	$-0.763496\pi$
$811$		−	38.5309i		−	1.35300i	0.736442	−	0.676501i	$-0.236504\pi$
$812$	20.1962	+	11.6603i	0.708746	+	0.409195i
$813$	−8.61062	−	4.97134i	−0.301988	−	0.174353i
$814$			1.37257i			0.0481087i
$815$	−0.705563	+	1.22207i	−0.0247148	+	0.0428073i
$816$	0.858244	+	1.48652i	0.0300446	+	0.0520387i
$817$	8.06040	−	4.65368i	0.281998	−	0.162812i
$818$	−9.67405			−0.338245
$819$		0			0
$820$	−8.64469			−0.301886
$821$	19.7784	−	11.4191i	0.690272	−	0.398528i	−0.113442	−	0.993545i	$-0.536188\pi$
$821$	19.7784	−	11.4191i	0.690272	−	0.398528i	0.803714	+	0.595016i	$0.202854\pi$
$822$	2.87466	+	4.97905i	0.100265	+	0.173664i
$823$	−1.59722	+	2.76647i	−0.0556757	+	0.0964332i	−0.892520	−	0.451008i	$-0.851065\pi$
$823$	−1.59722	+	2.76647i	−0.0556757	+	0.0964332i	0.836844	+	0.547441i	$0.184398\pi$
$824$			2.26795i			0.0790078i
$825$	−0.155658	−	0.0898694i	−0.00541933	−	0.00312885i
$826$	11.9730	+	6.91264i	0.416596	+	0.240522i
$827$		−	17.5779i		−	0.611244i	−0.952153	−	0.305622i	$-0.901136\pi$
$827$		−	17.5779i		−	0.611244i	0.952153	−	0.305622i	$-0.0988644\pi$
$828$	6.29695	−	10.9066i	0.218834	−	0.379032i
$829$	10.9566	+	18.9774i	0.380540	+	0.659114i	0.991139	−	0.132825i	$-0.0424050\pi$
$829$	10.9566	+	18.9774i	0.380540	+	0.659114i	−0.610600	+	0.791939i	$0.709072\pi$
$830$	1.07346	−	0.619760i	0.0372602	−	0.0215122i
$831$	18.4985			0.641705
$832$		0			0
$833$	13.9983			0.485012
$834$	−15.8539	+	9.15325i	−0.548976	+	0.316951i
$835$	−0.352237	−	0.610092i	−0.0121897	−	0.0211131i
$836$	−0.0678739	+	0.117561i	−0.00234747	+	0.00406593i
$837$			0.451028i			0.0155898i
$838$	−8.09507	−	4.67369i	−0.279640	−	0.161450i
$839$	28.9265	+	16.7007i	0.998655	+	0.576574i	0.907850	−	0.419295i	$-0.137723\pi$
$839$	28.9265	+	16.7007i	0.998655	+	0.576574i	0.0908051	+	0.995869i	$0.471056\pi$
$840$		−	4.36931i		−	0.150756i
$841$	−2.57180	+	4.45448i	−0.0886826	+	0.153603i
$842$	12.7621	+	22.1047i	0.439812	+	0.761777i
$843$	9.95624	−	5.74824i	0.342911	−	0.197980i
$844$	16.7095			0.575165
$845$		0			0
$846$	−9.57707			−0.329266
$847$	−37.9264	+	21.8968i	−1.30317	+	0.752383i
$848$	−5.17688	−	8.96661i	−0.177775	−	0.307915i
$849$	3.13963	−	5.43800i	0.107752	−	0.186632i
$850$			1.56787i			0.0537776i
$851$	50.6168	+	29.2236i	1.73512	+	1.00177i
$852$	−5.68868	−	3.28436i	−0.194891	−	0.112520i
$853$		−	35.3037i		−	1.20877i	−0.796691	−	0.604387i	$-0.793418\pi$
$853$		−	35.3037i		−	1.20877i	0.796691	−	0.604387i	$-0.206582\pi$
$854$	12.8354	−	22.2315i	0.439217	−	0.760746i
$855$	0.744750	+	1.28994i	0.0254699	+	0.0441152i
$856$	−4.06830	+	2.34883i	−0.139052	+	0.0802815i
$857$	−52.7645			−1.80240			−0.901200	−	0.433404i	$-0.857312\pi$
$857$	−52.7645			−1.80240			−0.901200	+	0.433404i	$0.857312\pi$
$858$		0			0
$859$	34.2305			1.16793			0.583964	−	0.811780i	$-0.301501\pi$
$859$	34.2305			1.16793			0.583964	+	0.811780i	$0.301501\pi$
$860$	9.74846	−	5.62828i	0.332420	−	0.191923i
$861$	18.8857	+	32.7110i	0.643622	+	1.11479i
$862$	2.05189	−	3.55397i	0.0698875	−	0.121049i
$863$		−	3.33252i		−	0.113440i	−0.998390	−	0.0567202i	$-0.981936\pi$
$863$		−	3.33252i		−	0.113440i	0.998390	−	0.0567202i	$-0.0180643\pi$
$864$	4.55231	+	2.62828i	0.154873	+	0.0894159i
$865$	0.567448	+	0.327616i	0.0192938	+	0.0111393i
$866$		−	2.68783i		−	0.0913362i
$867$	7.96008	−	13.7873i	0.270338	−	0.468240i
$868$	−0.171220	−	0.296562i	−0.00581160	−	0.0100660i
$869$	0.883311	−	0.509980i	0.0299643	−	0.0172999i
$870$	6.39712			0.216883
$871$		0			0
$872$	−6.17161			−0.208997
$873$	−29.5171	+	17.0417i	−0.999001	+	0.576774i
$874$	2.89022	+	5.00601i	0.0977631	+	0.169331i
$875$	1.99551	−	3.45632i	0.0674605	−	0.116845i
$876$			0.196776i			0.00664844i
$877$	14.4702	+	8.35438i	0.488624	+	0.282107i	0.724003	−	0.689796i	$-0.242300\pi$
$877$	14.4702	+	8.35438i	0.488624	+	0.282107i	−0.235379	+	0.971904i	$0.575633\pi$
$878$	−2.14512	−	1.23848i	−0.0723942	−	0.0417968i
$879$		−	19.6331i		−	0.662207i
$880$	−0.0820885	+	0.142181i	−0.00276720	+	0.00479293i
$881$	11.1797	+	19.3638i	0.376654	+	0.652383i	0.990573	−	0.136985i	$-0.0437414\pi$
$881$	11.1797	+	19.3638i	0.376654	+	0.652383i	−0.613919	+	0.789369i	$0.710408\pi$
$882$	13.9288	−	8.04181i	0.469008	−	0.270782i
$883$	−13.9499			−0.469450			−0.234725	−	0.972062i	$-0.575419\pi$
$883$	−13.9499			−0.469450			−0.234725	+	0.972062i	$0.575419\pi$
$884$		0			0
$885$	3.79246			0.127482
$886$	−15.0492	+	8.68868i	−0.505589	+	0.291902i
$887$	1.88845	+	3.27089i	0.0634078	+	0.109826i	0.895987	−	0.444081i	$-0.146470\pi$
$887$	1.88845	+	3.27089i	0.0634078	+	0.109826i	−0.832579	+	0.553907i	$0.813136\pi$
$888$	−4.57639	+	7.92654i	−0.153574	+	0.265997i
$889$			32.4244i			1.08748i
$890$	8.98652	+	5.18837i	0.301229	+	0.173915i
$891$	−0.0498336	−	0.0287714i	−0.00166949	−	0.000963879i
$892$			22.8193i			0.764048i
$893$	2.19788	−	3.80683i	0.0735491	−	0.127391i
$894$	−5.49191	−	9.51226i	−0.183677	−	0.318138i
$895$	−6.42011	+	3.70665i	−0.214601	+	0.123900i
$896$	−3.99102			−0.133330
$897$		0			0
$898$	−29.9305			−0.998795
$899$	0.434197	−	0.250684i	0.0144813	−	0.00836078i
$900$	0.900720	+	1.56009i	0.0300240	+	0.0520031i
$901$	8.11669	−	14.0585i	0.270406	−	0.468357i
$902$		−	1.41926i		−	0.0472562i
$903$	−42.5941	−	24.5917i	−1.41744	−	0.818361i
$904$	9.76403	+	5.63726i	0.324747	+	0.187493i
$905$		−	0.496077i		−	0.0164902i
$906$	−5.95303	+	10.3110i	−0.197776	+	0.342558i
$907$	1.19449	+	2.06892i	0.0396625	+	0.0686975i	0.885175	−	0.465258i	$-0.154038\pi$
$907$	1.19449	+	2.06892i	0.0396625	+	0.0686975i	−0.845513	+	0.533955i	$0.820705\pi$
$908$	3.28436	−	1.89623i	0.108995	−	0.0629285i
$909$	−26.4230			−0.876394
$910$		0			0
$911$	53.5178			1.77313			0.886563	−	0.462608i	$-0.153086\pi$
$911$	53.5178			1.77313			0.886563	+	0.462608i	$0.153086\pi$
$912$	−0.783937	+	0.452606i	−0.0259587	+	0.0149873i
$913$	0.101750	+	0.176237i	0.00336744	+	0.00583258i
$914$	−5.73456	+	9.93255i	−0.189682	+	0.328540i
$915$		−	7.04181i		−	0.232795i
$916$	4.06830	+	2.34883i	0.134420	+	0.0776077i
$917$	71.9033	+	41.5134i	2.37446	+	1.37089i
$918$			8.24162i			0.272014i
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	−0.996335	−	0.0855332i	$-0.972741\pi$
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	0.572242	+	0.820085i	$0.306074\pi$
$920$	3.49551	+	6.05440i	0.115243	+	0.199608i
$921$	25.3513	−	14.6366i	0.835353	−	0.482291i
$922$	−24.0067			−0.790619
$923$		0			0
$924$	0.717341			0.0235988
$925$	−7.24026	+	4.18016i	−0.238058	+	0.137443i
$926$	13.1582	+	22.7906i	0.432404	+	0.748946i
$927$	−2.04279	+	3.53821i	−0.0670939	+	0.116210i
$928$		−	5.84325i		−	0.191814i
$929$	−5.43127	−	3.13575i	−0.178194	−	0.102881i	0.408250	−	0.912870i	$-0.366139\pi$
$929$	−5.43127	−	3.13575i	−0.178194	−	0.102881i	−0.586444	+	0.809990i	$0.699473\pi$
$930$	−0.0813509	−	0.0469680i	−0.00266760	−	0.00154014i
$931$			7.38218i			0.241941i
$932$	−14.6876	+	25.4397i	−0.481108	+	0.833304i
$933$	−13.9488	−	24.1601i	−0.456665	−	0.790966i
$934$	−14.0968	+	8.13878i	−0.461261	+	0.266309i
$935$	−0.257409			−0.00841816
$936$		0			0
$937$	−20.7863			−0.679059			−0.339530	−	0.940595i	$-0.610268\pi$
$937$	−20.7863			−0.679059			−0.339530	+	0.940595i	$0.610268\pi$
$938$	−52.9071	+	30.5459i	−1.72748	+	0.997360i
$939$	4.75567	+	8.23705i	0.155195	+	0.268806i
$940$	2.65817	−	4.60408i	0.0866999	−	0.150169i
$941$		−	13.2566i		−	0.432151i	−0.976377	−	0.216076i	$-0.930674\pi$
$941$		−	13.2566i		−	0.432151i	0.976377	−	0.216076i	$-0.0693258\pi$
$942$	16.7742	+	9.68462i	0.546535	+	0.315542i
$943$	−52.3384	−	30.2176i	−1.70437	−	0.984020i
$944$		−	3.46410i		−	0.112747i
$945$	10.4895	−	18.1683i	0.341223	−	0.591016i
$946$	0.924033	+	1.60047i	0.0300429	+	0.0520359i
$947$	−14.2379	+	8.22023i	−0.462668	+	0.267122i	−0.713166	−	0.700996i	$-0.752739\pi$
$947$	−14.2379	+	8.22023i	−0.462668	+	0.267122i	0.250497	+	0.968117i	$0.419406\pi$
$948$	6.80144			0.220901
$949$		0			0
$950$	−0.826838			−0.0268262
$951$	−33.6032	+	19.4008i	−1.08966	+	0.629115i
$952$	−3.12870	−	5.41907i	−0.101402	−	0.175633i
$953$	13.9047	−	24.0837i	0.450419	−	0.780148i	−0.547993	−	0.836483i	$-0.684608\pi$
$953$	13.9047	−	24.0837i	0.450419	−	0.780148i	0.998412	+	0.0563345i	$0.0179413\pi$
$954$		−	18.6517i		−	0.603870i
$955$	−21.4726	−	12.3972i	−0.694838	−	0.401165i
$956$	−3.63017	−	2.09588i	−0.117408	−	0.0677855i
$957$			1.05026i			0.0339501i
$958$	13.8608	−	24.0075i	0.447821	−	0.775648i
$959$	−10.4795	−	18.1510i	−0.338400	−	0.586126i
$960$	−0.948114	+	0.547394i	−0.0306002	+	0.0176671i
$961$	30.9926			0.999763
$962$		0			0
$963$	−8.46257			−0.272702
$964$	−16.1343	+	9.31513i	−0.519650	+	0.300020i
$965$	−1.93061	−	3.34392i	−0.0621486	−	0.107644i
$966$	15.2730	−	26.4536i	0.491400	−	0.851129i
$967$		−	2.34329i		−	0.0753552i	−0.999290	−	0.0376776i	$-0.988004\pi$
$967$		−	2.34329i		−	0.0753552i	0.999290	−	0.0376776i	$-0.0119960\pi$
$968$	9.50294	+	5.48652i	0.305436	+	0.176344i
$969$	−1.22911	−	0.709629i	−0.0394848	−	0.0227966i
$970$		−	18.9201i		−	0.607487i
$971$	−1.85867	+	3.21931i	−0.0596476	+	0.103313i	−0.894307	−	0.447453i	$-0.852331\pi$
$971$	−1.85867	+	3.21931i	−0.0596476	+	0.103313i	0.834660	+	0.550766i	$0.185664\pi$
$972$	7.69298	+	13.3246i	0.246752	+	0.427388i
$973$	57.7949	−	33.3679i	1.85282	−	1.06973i
$974$	−24.2697			−0.777652
$975$		0			0
$976$	−6.43213			−0.205887
$977$	16.6990	−	9.64115i	0.534247	−	0.308448i	−0.208497	−	0.978023i	$-0.566857\pi$
$977$	16.6990	−	9.64115i	0.534247	−	0.308448i	0.742744	+	0.669575i	$0.233524\pi$
$978$	−0.772442	−	1.33791i	−0.0247000	−	0.0427816i
$979$	−0.851811	+	1.47538i	−0.0272240	+	0.0471533i
$980$			8.92820i			0.285201i
$981$	−9.62828	−	5.55889i	−0.307407	−	0.177482i
$982$	8.92208	+	5.15117i	0.284715	+	0.164380i
$983$		−	12.6837i		−	0.404546i	−0.979329	−	0.202273i	$-0.935167\pi$
$983$		−	12.6837i		−	0.404546i	0.979329	−	0.202273i	$-0.0648328\pi$
$984$	4.73205	−	8.19615i	0.150852	−	0.261284i
$985$	−2.85782	−	4.94989i	−0.0910577	−	0.157717i
$986$	7.93408	−	4.58074i	0.252672	−	0.145881i
$987$	−23.2288			−0.739379
$988$		0			0
$989$	78.6948			2.50235
$990$	−0.256131	+	0.147877i	−0.00814039	+	0.00469985i
$991$	−22.2900	−	38.6074i	−0.708065	−	1.22641i	−0.965574	−	0.260129i	$-0.916235\pi$
$991$	−22.2900	−	38.6074i	−0.708065	−	1.22641i	0.257508	−	0.966276i	$-0.417099\pi$
$992$	−0.0429015	+	0.0743075i	−0.00136212	+	0.00235927i
$993$		−	2.15364i		−	0.0683436i
$994$	20.7379	+	11.9730i	0.657767	+	0.379762i
$995$	−0.983586	−	0.567874i	−0.0311818	−	0.0180028i
$996$			1.35701i			0.0429985i
$997$	6.20142	−	10.7412i	0.196401	−	0.340177i	−0.750958	−	0.660350i	$-0.770408\pi$
$997$	6.20142	−	10.7412i	0.196401	−	0.340177i	0.947359	+	0.320174i	$0.103741\pi$
$998$	−14.1336	−	24.4802i	−0.447392	−	0.774906i
$999$	−38.0588	+	21.9733i	−1.20413	+	0.695204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.j.361.3		8
13.2	odd	12		1690.2.a.u.1.3		4
13.3	even	3		1690.2.d.k.1351.7		8
13.4	even	6	inner	1690.2.l.j.1161.3		8
13.5	odd	4		1690.2.e.s.991.2		8
13.6	odd	12		1690.2.e.s.191.2		8
13.7	odd	12		1690.2.e.t.191.2		8
13.8	odd	4		1690.2.e.t.991.2		8
13.9	even	3		130.2.l.b.121.1	yes	8
13.10	even	6		1690.2.d.k.1351.3		8
13.11	odd	12		1690.2.a.t.1.3		4
13.12	even	2		130.2.l.b.101.1	✓	8
39.35	odd	6		1170.2.bs.g.901.3		8
39.38	odd	2		1170.2.bs.g.361.3		8
52.35	odd	6		1040.2.da.d.641.3		8
52.51	odd	2		1040.2.da.d.881.3		8
65.9	even	6		650.2.m.c.251.4		8
65.12	odd	4		650.2.n.d.49.1		8
65.22	odd	12		650.2.n.e.199.4		8
65.24	odd	12		8450.2.a.cm.1.2		4
65.38	odd	4		650.2.n.e.49.4		8
65.48	odd	12		650.2.n.d.199.1		8
65.54	odd	12		8450.2.a.ci.1.2		4
65.64	even	2		650.2.m.c.101.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.1	✓	8	13.12	even	2
130.2.l.b.121.1	yes	8	13.9	even	3
650.2.m.c.101.4		8	65.64	even	2
650.2.m.c.251.4		8	65.9	even	6
650.2.n.d.49.1		8	65.12	odd	4
650.2.n.d.199.1		8	65.48	odd	12
650.2.n.e.49.4		8	65.38	odd	4
650.2.n.e.199.4		8	65.22	odd	12
1040.2.da.d.641.3		8	52.35	odd	6
1040.2.da.d.881.3		8	52.51	odd	2
1170.2.bs.g.361.3		8	39.38	odd	2
1170.2.bs.g.901.3		8	39.35	odd	6
1690.2.a.t.1.3		4	13.11	odd	12
1690.2.a.u.1.3		4	13.2	odd	12
1690.2.d.k.1351.3		8	13.10	even	6
1690.2.d.k.1351.7		8	13.3	even	3
1690.2.e.s.191.2		8	13.6	odd	12
1690.2.e.s.991.2		8	13.5	odd	4
1690.2.e.t.191.2		8	13.7	odd	12
1690.2.e.t.991.2		8	13.8	odd	4
1690.2.l.j.361.3		8	1.1	even	1	trivial
1690.2.l.j.1161.3		8	13.4	even	6	inner
8450.2.a.ci.1.2		4	65.54	odd	12
8450.2.a.cm.1.2		4	65.24	odd	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.547394 - 0.948114i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.948114 - 0.547394i) q^{6} +(3.45632 + 1.99551i) q^{7} -1.00000i q^{8} +(0.900720 - 1.56009i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.142181 + 0.0820885i) q^{11} -1.09479 q^{12} +3.99102 q^{14} +(0.948114 - 0.547394i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.783937 - 1.35782i) q^{17} -1.80144i q^{18} +(0.716063 + 0.413419i) q^{19} +(0.866025 + 0.500000i) q^{20} -4.36931i q^{21} +(-0.0820885 + 0.142181i) q^{22} +(3.49551 + 6.05440i) q^{23} +(-0.948114 + 0.547394i) q^{24} -1.00000 q^{25} -5.25656 q^{27} +(3.45632 - 1.99551i) q^{28} +(2.92163 + 5.06040i) q^{29} +(0.547394 - 0.948114i) q^{30} -0.0858029i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.155658 + 0.0898694i) q^{33} -1.56787i q^{34} +(-1.99551 + 3.45632i) q^{35} +(-0.900720 - 1.56009i) q^{36} +(7.24026 - 4.18016i) q^{37} +0.826838 q^{38} +1.00000 q^{40} +(-7.48652 + 4.32235i) q^{41} +(-2.18466 - 3.78394i) q^{42} +(5.62828 - 9.74846i) q^{43} +0.164177i q^{44} +(1.56009 + 0.900720i) q^{45} +(6.05440 + 3.49551i) q^{46} -5.31634i q^{47} +(-0.547394 + 0.948114i) q^{48} +(4.46410 + 7.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} -1.71649 q^{51} +10.3538 q^{53} +(-4.55231 + 2.62828i) q^{54} +(-0.0820885 - 0.142181i) q^{55} +(1.99551 - 3.45632i) q^{56} -0.905212i q^{57} +(5.06040 + 2.92163i) q^{58} +(3.00000 + 1.73205i) q^{59} -1.09479i q^{60} +(3.21606 - 5.57038i) q^{61} +(-0.0429015 - 0.0743075i) q^{62} +(6.22635 - 3.59479i) q^{63} -1.00000 q^{64} +0.179739 q^{66} +(-13.2566 + 7.65368i) q^{67} +(-0.783937 - 1.35782i) q^{68} +(3.82684 - 6.62828i) q^{69} +3.99102i q^{70} +(5.19615 + 3.00000i) q^{71} +(-1.56009 - 0.900720i) q^{72} -0.179739i q^{73} +(4.18016 - 7.24026i) q^{74} +(0.547394 + 0.948114i) q^{75} +(0.716063 - 0.413419i) q^{76} -0.655233 q^{77} -6.21257 q^{79} +(0.866025 - 0.500000i) q^{80} +(0.175247 + 0.303536i) q^{81} +(-4.32235 + 7.48652i) q^{82} -1.23952i q^{83} +(-3.78394 - 2.18466i) q^{84} +(1.35782 + 0.783937i) q^{85} -11.2566i q^{86} +(3.19856 - 5.54007i) q^{87} +(0.0820885 + 0.142181i) q^{88} +(8.98652 - 5.18837i) q^{89} +1.80144 q^{90} +6.99102 q^{92} +(-0.0813509 + 0.0469680i) q^{93} +(-2.65817 - 4.60408i) q^{94} +(-0.413419 + 0.716063i) q^{95} +1.09479i q^{96} +(-16.3853 - 9.46004i) q^{97} +(7.73205 + 4.46410i) q^{98} +0.295755i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} + 6 q^{6} - 4 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 6 q^{15} - 4 q^{16} + 6 q^{17} + 6 q^{19} + 6 q^{22} + 12 q^{23} + 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} + 42 q^{33} + 4 q^{36}+ \cdots + 48 q^{98}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 + 6 * q^6 - 4 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 6 * q^15 - 4 * q^16 + 6 * q^17 + 6 * q^19 + 6 * q^22 + 12 * q^23 + 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 + 42 * q^33 + 4 * q^36 + 30 * q^37 - 12 * q^38 + 8 * q^40 - 12 * q^41 - 6 * q^42 + 4 * q^43 + 12 * q^45 - 2 * q^48 + 8 * q^49 + 60 * q^53 - 36 * q^54 + 6 * q^55 + 24 * q^59 + 26 * q^61 + 18 * q^62 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 24 * q^67 - 6 * q^68 + 12 * q^69 - 12 * q^72 + 6 * q^74 + 2 * q^75 + 6 * q^76 - 60 * q^77 + 20 * q^79 - 28 * q^81 - 30 * q^84 + 18 * q^85 + 48 * q^87 - 6 * q^88 + 24 * q^89 - 8 * q^90 + 24 * q^92 - 48 * q^93 + 6 * q^95 + 6 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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