LMFDB - Embedded newform 117.2.e.b.40.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(40,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.40"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.487558322307.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 43x^{6} + 48x^{4} + 21x^{2} + 3 $ x^10 + 13x^8 + 43x^6 + 48x^4 + 21x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.4
Root			$2.93761i$ of defining polynomial
Character	$\chi$	$=$	117.40
Dual form			117.2.e.b.79.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.565535 + 0.979535i) q^{2} +(1.19379 + 1.25494i) q^{3} +(0.360341 - 0.624129i) q^{4} +(-1.19379 + 2.06770i) q^{5} +(-0.554128 + 1.87907i) q^{6} +(-2.04404 - 3.54039i) q^{7} +3.07728 q^{8} +(-0.149744 + 2.99626i) q^{9} -2.70051 q^{10} +(-1.92720 - 3.33800i) q^{11} +(1.21341 - 0.292871i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(2.31196 - 4.00442i) q^{14} +(-4.01997 + 0.970264i) q^{15} +(1.01963 + 1.76605i) q^{16} +2.15906 q^{17} +(-3.01963 + 1.54781i) q^{18} -0.284952 q^{19} +(0.860341 + 1.49015i) q^{20} +(2.00282 - 6.79162i) q^{21} +(2.17979 - 3.77551i) q^{22} +(-1.79481 + 3.10870i) q^{23} +(3.67362 + 3.86180i) q^{24} +(-0.350256 - 0.606662i) q^{25} -1.13107 q^{26} +(-3.93889 + 3.38898i) q^{27} -2.94621 q^{28} +(-1.48859 - 2.57832i) q^{29} +(-3.22384 - 3.38898i) q^{30} +(5.00988 - 8.67737i) q^{31} +(1.92401 - 3.33249i) q^{32} +(1.88833 - 6.40338i) q^{33} +(1.22102 + 2.11487i) q^{34} +9.76061 q^{35} +(1.81609 + 1.17313i) q^{36} -7.86324 q^{37} +(-0.161150 - 0.279120i) q^{38} +(-1.68370 + 0.406381i) q^{39} +(-3.67362 + 6.36289i) q^{40} +(-2.78754 + 4.82816i) q^{41} +(7.78529 - 1.87907i) q^{42} +(1.41165 + 2.44505i) q^{43} -2.77779 q^{44} +(-6.01661 - 3.88652i) q^{45} -4.06010 q^{46} +(4.21039 + 7.29262i) q^{47} +(-0.999062 + 3.38785i) q^{48} +(-4.85623 + 8.41124i) q^{49} +(0.396164 - 0.686177i) q^{50} +(2.57745 + 2.70948i) q^{51} +(0.360341 + 0.624129i) q^{52} -4.34724 q^{53} +(-5.54720 - 1.94169i) q^{54} +9.20266 q^{55} +(-6.29010 - 10.8948i) q^{56} +(-0.340172 - 0.357597i) q^{57} +(1.68370 - 2.91626i) q^{58} +(-4.79328 + 8.30221i) q^{59} +(-0.842989 + 2.85860i) q^{60} +(3.84333 + 6.65684i) q^{61} +11.3330 q^{62} +(10.9140 - 5.59434i) q^{63} +8.43089 q^{64} +(-1.19379 - 2.06770i) q^{65} +(7.34025 - 1.77165i) q^{66} +(-0.730767 + 1.26572i) q^{67} +(0.777996 - 1.34753i) q^{68} +(-6.04384 + 1.45875i) q^{69} +(5.51997 + 9.56086i) q^{70} -8.81244 q^{71} +(-0.460803 + 9.22033i) q^{72} +15.7860 q^{73} +(-4.44693 - 7.70231i) q^{74} +(0.343192 - 1.16378i) q^{75} +(-0.102680 + 0.177847i) q^{76} +(-7.87855 + 13.6461i) q^{77} +(-1.35026 - 1.41942i) q^{78} +(-4.91481 - 8.51270i) q^{79} -4.86887 q^{80} +(-8.95515 - 0.897342i) q^{81} -6.30580 q^{82} +(-0.336467 - 0.582777i) q^{83} +(-3.51715 - 3.69731i) q^{84} +(-2.57745 + 4.46428i) q^{85} +(-1.59668 + 2.76553i) q^{86} +(1.45857 - 4.94606i) q^{87} +(-5.93053 - 10.2720i) q^{88} +3.26322 q^{89} +(0.404385 - 8.09144i) q^{90} +4.08809 q^{91} +(1.29348 + 2.24038i) q^{92} +(16.8703 - 4.07184i) q^{93} +(-4.76225 + 8.24846i) q^{94} +(0.340172 - 0.589195i) q^{95} +(6.47893 - 1.56376i) q^{96} +(4.43889 + 7.68838i) q^{97} -10.9855 q^{98} +(10.2901 - 5.27454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} + 13 q^{6} + 2 q^{7} + 24 q^{8} - 13 q^{9} - 4 q^{10} - 11 q^{11} - 19 q^{12} - 5 q^{13} + 5 q^{14} - 10 q^{15} - 10 q^{16} + 14 q^{17} - 10 q^{18} + 6 q^{19}+ \cdots + 17 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 + 13 * q^6 + 2 * q^7 + 24 * q^8 - 13 * q^9 - 4 * q^10 - 11 * q^11 - 19 * q^12 - 5 * q^13 + 5 * q^14 - 10 * q^15 - 10 * q^16 + 14 * q^17 - 10 * q^18 + 6 * q^19 + q^20 + 8 * q^21 + 7 * q^22 - 18 * q^23 + 18 * q^24 + 8 * q^25 + 4 * q^26 - 11 * q^27 - 38 * q^28 - 4 * q^29 + 5 * q^30 + 16 * q^31 - 31 * q^32 + 19 * q^33 - 13 * q^34 + 22 * q^35 - 5 * q^36 + 10 * q^37 - 24 * q^38 - 2 * q^39 - 18 * q^40 - 12 * q^41 + 59 * q^42 + 2 * q^44 - 14 * q^45 + 12 * q^46 - 15 * q^47 + 29 * q^48 - 3 * q^49 + 5 * q^50 - 7 * q^51 - 4 * q^52 - 6 * q^53 - 11 * q^54 - 34 * q^55 + 24 * q^56 + 12 * q^57 + 2 * q^58 - 3 * q^59 + 19 * q^60 + q^61 - 8 * q^62 - 14 * q^63 + 124 * q^64 - q^65 - 11 * q^66 + 4 * q^67 + 16 * q^68 + 25 * q^70 + 30 * q^71 - 66 * q^72 - 10 * q^73 - 11 * q^74 + 14 * q^75 - 9 * q^76 - q^77 - 2 * q^78 - 13 * q^79 + 64 * q^80 - 25 * q^81 - 42 * q^82 - 26 * q^83 - 17 * q^84 + 7 * q^85 + 6 * q^86 - 13 * q^87 - 3 * q^88 + 58 * q^89 - 26 * q^90 - 4 * q^91 + 6 * q^92 + 58 * q^93 - 12 * q^94 - 12 * q^95 - 67 * q^96 + 16 * q^97 - 78 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.565535	+	0.979535i	0.399893	+	0.692636i	0.993712	−	0.111963i	$-0.0357138\pi$
$2$	0.565535	+	0.979535i	0.399893	+	0.692636i	−0.593819	+	0.804599i	$0.702380\pi$
$3$	1.19379	+	1.25494i	0.689233	+	0.724539i
$3$	1.19379	+	1.25494i	0.689233	+	0.724539i
$4$	0.360341	−	0.624129i	0.180170	−	0.312064i
$5$	−1.19379	+	2.06770i	−0.533878	+	0.924704i	0.465339	+	0.885133i	$0.345932\pi$
$5$	−1.19379	+	2.06770i	−0.533878	+	0.924704i	−0.999217	+	0.0395711i	$0.987401\pi$
$6$	−0.554128	+	1.87907i	−0.226222	+	0.767126i
$7$	−2.04404	−	3.54039i	−0.772576	−	1.33814i	−0.936147	−	0.351609i	$-0.885635\pi$
$7$	−2.04404	−	3.54039i	−0.772576	−	1.33814i	0.163571	−	0.986532i	$-0.447699\pi$
$8$	3.07728			1.08798
$9$	−0.149744	+	2.99626i	−0.0499146	+	0.998753i
$10$	−2.70051			−0.853977
$11$	−1.92720	−	3.33800i	−0.581072	−	1.00645i	−0.995353	−	0.0962969i	$-0.969300\pi$
$11$	−1.92720	−	3.33800i	−0.581072	−	1.00645i	0.414281	−	0.910149i	$-0.364033\pi$
$12$	1.21341	−	0.292871i	0.350282	−	0.0845446i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	2.31196	−	4.00442i	0.617896	−	1.07023i
$15$	−4.01997	+	0.970264i	−1.03795	+	0.250521i
$16$	1.01963	+	1.76605i	0.254907	+	0.441511i
$17$	2.15906			0.523648			0.261824	−	0.965116i	$-0.415676\pi$
$17$	2.15906			0.523648			0.261824	+	0.965116i	$0.415676\pi$
$18$	−3.01963	+	1.54781i	−0.711733	+	0.364822i
$19$	−0.284952			−0.0653724			−0.0326862	−	0.999466i	$-0.510406\pi$
$19$	−0.284952			−0.0653724			−0.0326862	+	0.999466i	$0.510406\pi$
$20$	0.860341	+	1.49015i	0.192378	+	0.333209i
$21$	2.00282	−	6.79162i	0.437050	−	1.48205i
$22$	2.17979	−	3.77551i	0.464734	−	0.804942i
$23$	−1.79481	+	3.10870i	−0.374243	+	0.648208i	−0.990213	−	0.139561i	$-0.955431\pi$
$23$	−1.79481	+	3.10870i	−0.374243	+	0.648208i	0.615970	+	0.787769i	$0.288764\pi$
$24$	3.67362	+	3.86180i	0.749874	+	0.788286i
$25$	−0.350256	−	0.606662i	−0.0700513	−	0.121332i
$26$	−1.13107			−0.221821
$27$	−3.93889	+	3.38898i	−0.758039	+	0.652209i
$28$	−2.94621			−0.556781
$29$	−1.48859	−	2.57832i	−0.276425	−	0.478782i	0.694069	−	0.719909i	$-0.255816\pi$
$29$	−1.48859	−	2.57832i	−0.276425	−	0.478782i	−0.970494	+	0.241127i	$0.922483\pi$
$30$	−3.22384	−	3.38898i	−0.588590	−	0.618740i
$31$	5.00988	−	8.67737i	0.899801	−	1.55850i	0.0720537	−	0.997401i	$-0.477045\pi$
$31$	5.00988	−	8.67737i	0.899801	−	1.55850i	0.827748	−	0.561101i	$-0.189622\pi$
$32$	1.92401	−	3.33249i	0.340120	−	0.589106i
$33$	1.88833	−	6.40338i	0.328716	−	1.11469i
$34$	1.22102	+	2.11487i	0.209403	+	0.362697i
$35$	9.76061			1.64984
$36$	1.81609	+	1.17313i	0.302682	+	0.195522i
$37$	−7.86324			−1.29271			−0.646354	−	0.763038i	$-0.723707\pi$
$37$	−7.86324			−1.29271			−0.646354	+	0.763038i	$0.723707\pi$
$38$	−0.161150	−	0.279120i	−0.0261420	−	0.0452793i
$39$	−1.68370	+	0.406381i	−0.269608	+	0.0650730i
$40$	−3.67362	+	6.36289i	−0.580850	+	1.00606i
$41$	−2.78754	+	4.82816i	−0.435340	+	0.754032i	−0.997323	−	0.0731172i	$-0.976705\pi$
$41$	−2.78754	+	4.82816i	−0.435340	+	0.754032i	0.561983	+	0.827149i	$0.310039\pi$
$42$	7.78529	−	1.87907i	1.20130	−	0.289946i
$43$	1.41165	+	2.44505i	0.215275	+	0.372867i	0.953358	−	0.301843i	$-0.0976019\pi$
$43$	1.41165	+	2.44505i	0.215275	+	0.372867i	−0.738083	+	0.674710i	$0.764269\pi$
$44$	−2.77779			−0.418768
$45$	−6.01661	−	3.88652i	−0.896903	−	0.579369i
$46$	−4.06010			−0.598629
$47$	4.21039	+	7.29262i	0.614149	+	1.06374i	0.990533	+	0.137274i	$0.0438340\pi$
$47$	4.21039	+	7.29262i	0.614149	+	1.06374i	−0.376384	+	0.926464i	$0.622833\pi$
$48$	−0.999062	+	3.38785i	−0.144202	+	0.488994i
$49$	−4.85623	+	8.41124i	−0.693747	+	1.20161i
$50$	0.396164	−	0.686177i	0.0560261	−	0.0970400i
$51$	2.57745	+	2.70948i	0.360916	+	0.379404i
$52$	0.360341	+	0.624129i	0.0499703	+	0.0865511i
$53$	−4.34724			−0.597139			−0.298569	−	0.954388i	$-0.596509\pi$
$53$	−4.34724			−0.597139			−0.298569	+	0.954388i	$0.596509\pi$
$54$	−5.54720	−	1.94169i	−0.754878	−	0.264231i
$55$	9.20266			1.24089
$56$	−6.29010	−	10.8948i	−0.840549	−	1.45587i
$57$	−0.340172	−	0.357597i	−0.0450568	−	0.0473649i
$58$	1.68370	−	2.91626i	0.221081	−	0.382924i
$59$	−4.79328	+	8.30221i	−0.624032	+	1.08086i	0.364695	+	0.931127i	$0.381173\pi$
$59$	−4.79328	+	8.30221i	−0.624032	+	1.08086i	−0.988727	+	0.149728i	$0.952160\pi$
$60$	−0.842989	+	2.85860i	−0.108829	+	0.369044i
$61$	3.84333	+	6.65684i	0.492088	+	0.852321i	0.999958	−	0.00911240i	$-0.00290061\pi$
$61$	3.84333	+	6.65684i	0.492088	+	0.852321i	−0.507871	+	0.861433i	$0.669567\pi$
$62$	11.3330			1.43930
$63$	10.9140	−	5.59434i	1.37504	−	0.704820i
$64$	8.43089			1.05386
$65$	−1.19379	−	2.06770i	−0.148071	−	0.256467i
$66$	7.34025	−	1.77165i	0.903522	−	0.218075i
$67$	−0.730767	+	1.26572i	−0.0892773	+	0.154633i	−0.907206	−	0.420687i	$-0.861789\pi$
$67$	−0.730767	+	1.26572i	−0.0892773	+	0.154633i	0.817929	+	0.575320i	$0.195122\pi$
$68$	0.777996	−	1.34753i	0.0943459	−	0.163412i
$69$	−6.04384	+	1.45875i	−0.727593	+	0.175613i
$70$	5.51997	+	9.56086i	0.659762	+	1.14274i
$71$	−8.81244			−1.04584			−0.522922	−	0.852381i	$-0.675158\pi$
$71$	−8.81244			−1.04584			−0.522922	+	0.852381i	$0.675158\pi$
$72$	−0.460803	+	9.22033i	−0.0543062	+	1.08663i
$73$	15.7860			1.84761			0.923806	−	0.382860i	$-0.125061\pi$
$73$	15.7860			1.84761			0.923806	+	0.382860i	$0.125061\pi$
$74$	−4.44693	−	7.70231i	−0.516945	−	0.895376i
$75$	0.343192	−	1.16378i	0.0396284	−	0.134381i
$76$	−0.102680	+	0.177847i	−0.0117782	+	0.0204004i
$77$	−7.87855	+	13.6461i	−0.897844	+	1.55511i
$78$	−1.35026	−	1.41942i	−0.152886	−	0.160718i
$79$	−4.91481	−	8.51270i	−0.552959	−	0.957753i	−0.998059	−	0.0622725i	$-0.980165\pi$
$79$	−4.91481	−	8.51270i	−0.552959	−	0.957753i	0.445100	−	0.895481i	$-0.353168\pi$
$80$	−4.86887			−0.544356
$81$	−8.95515	−	0.897342i	−0.995017	−	0.0997047i
$82$	−6.30580			−0.696359
$83$	−0.336467	−	0.582777i	−0.0369320	−	0.0639681i	0.846969	−	0.531643i	$-0.178425\pi$
$83$	−0.336467	−	0.582777i	−0.0369320	−	0.0639681i	−0.883901	+	0.467675i	$0.845092\pi$
$84$	−3.51715	−	3.69731i	−0.383752	−	0.403410i
$85$	−2.57745	+	4.46428i	−0.279564	+	0.484219i
$86$	−1.59668	+	2.76553i	−0.172174	+	0.298214i
$87$	1.45857	−	4.94606i	0.156375	−	0.530273i
$88$	−5.93053	−	10.2720i	−0.632196	−	1.09500i
$89$	3.26322			0.345901			0.172951	−	0.984931i	$-0.444670\pi$
$89$	3.26322			0.345901			0.172951	+	0.984931i	$0.444670\pi$
$90$	0.404385	−	8.09144i	0.0426259	−	0.852913i
$91$	4.08809			0.428548
$92$	1.29348	+	2.24038i	0.134855	+	0.233576i
$93$	16.8703	−	4.07184i	1.74937	−	0.422230i
$94$	−4.76225	+	8.24846i	−0.491188	+	0.850763i
$95$	0.340172	−	0.589195i	0.0349009	−	0.0604501i
$96$	6.47893	−	1.56376i	0.661253	−	0.159601i
$97$	4.43889	+	7.68838i	0.450701	+	0.780636i	0.998430	−	0.0560194i	$-0.0178409\pi$
$97$	4.43889	+	7.68838i	0.450701	+	0.780636i	−0.547729	+	0.836656i	$0.684508\pi$
$98$	−10.9855			−1.10970
$99$	10.2901	−	5.27454i	1.03420	−	0.530111i
$100$	−0.504847			−0.0504847
$101$	−6.09349	−	10.5542i	−0.606325	−	1.05019i	−0.991841	−	0.127484i	$-0.959310\pi$
$101$	−6.09349	−	10.5542i	−0.606325	−	1.05019i	0.385516	−	0.922701i	$-0.374024\pi$
$102$	−1.19639	+	4.05701i	−0.118461	+	0.401704i
$103$	6.36686	−	11.0277i	0.627346	−	1.08659i	−0.360737	−	0.932668i	$-0.617475\pi$
$103$	6.36686	−	11.0277i	0.627346	−	1.08659i	0.988082	−	0.153927i	$-0.0491920\pi$
$104$	−1.53864	+	2.66500i	−0.150876	+	0.261325i
$105$	11.6521	+	12.2490i	1.13713	+	1.19538i
$106$	−2.45851	−	4.25827i	−0.238792	−	0.413600i
$107$	6.83490			0.660755			0.330378	−	0.943849i	$-0.392824\pi$
$107$	6.83490			0.660755			0.330378	+	0.943849i	$0.392824\pi$
$108$	0.695817	+	3.67956i	0.0669551	+	0.354066i
$109$	−9.06573			−0.868340			−0.434170	−	0.900831i	$-0.642958\pi$
$109$	−9.06573			−0.868340			−0.434170	+	0.900831i	$0.642958\pi$
$110$	5.20442	+	9.01432i	0.496222	+	0.859482i
$111$	−9.38703	−	9.86788i	−0.890978	−	0.936618i
$112$	4.16832	−	7.21975i	0.393870	−	0.682202i
$113$	6.61682	−	11.4607i	0.622458	−	1.07813i	−0.366569	−	0.930391i	$-0.619468\pi$
$113$	6.61682	−	11.4607i	0.622458	−	1.07813i	0.989027	−	0.147737i	$-0.0471991\pi$
$114$	0.157900	−	0.535444i	0.0147887	−	0.0501489i
$115$	−4.28523	−	7.42224i	−0.399600	−	0.692128i
$116$	−2.14561			−0.199214
$117$	−2.51997	−	1.62781i	−0.232971	−	0.150491i
$118$	−10.8431			−0.998185
$119$	−4.41320	−	7.64389i	−0.404558	−	0.700715i
$120$	−12.3706	+	2.98577i	−1.12927	+	0.272563i
$121$	−1.92818	+	3.33971i	−0.175289	+	0.303610i
$122$	−4.34707	+	7.52935i	−0.393565	+	0.681675i
$123$	−9.38677	+	2.26560i	−0.846377	+	0.204283i
$124$	−3.61053	−	6.25362i	−0.324235	−	0.561592i
$125$	−10.2653			−0.918161
$126$	11.6521	+	7.52686i	1.03805	+	0.670546i
$127$	18.9491			1.68146			0.840732	−	0.541451i	$-0.182125\pi$
$127$	18.9491			1.68146			0.840732	+	0.541451i	$0.182125\pi$
$128$	0.919937	+	1.59338i	0.0813117	+	0.140836i
$129$	−1.38318	+	4.69041i	−0.121782	+	0.412968i
$130$	1.35026	−	2.33871i	0.118425	−	0.205119i
$131$	8.78133	−	15.2097i	0.767229	−	1.32888i	−0.171832	−	0.985126i	$-0.554969\pi$
$131$	8.78133	−	15.2097i	0.767229	−	1.32888i	0.939060	−	0.343753i	$-0.111698\pi$
$132$	−3.31609	−	3.48596i	−0.288629	−	0.303414i
$133$	0.582454	+	1.00884i	0.0505051	+	0.0874775i
$134$	−1.65310			−0.142806
$135$	−2.30520	−	12.1902i	−0.198400	−	1.04916i
$136$	6.64402			0.569720
$137$	0.383097	+	0.663543i	0.0327302	+	0.0566903i	0.881927	−	0.471387i	$-0.156246\pi$
$137$	0.383097	+	0.663543i	0.0327302	+	0.0566903i	−0.849196	+	0.528077i	$0.822913\pi$
$138$	−4.84690	−	5.09518i	−0.412595	−	0.433730i
$139$	−7.27125	+	12.5942i	−0.616739	+	1.06822i	0.373338	+	0.927696i	$0.378213\pi$
$139$	−7.27125	+	12.5942i	−0.616739	+	1.06822i	−0.990077	+	0.140528i	$0.955120\pi$
$140$	3.51715	−	6.09188i	0.297253	−	0.514858i
$141$	−4.12547	+	13.9896i	−0.347428	+	1.17814i
$142$	−4.98374	−	8.63209i	−0.418226	−	0.724389i
$143$	3.85439			0.322321
$144$	−5.44421	+	2.79061i	−0.453685	+	0.232551i
$145$	7.10826			0.590309
$146$	8.92754	+	15.4629i	0.738848	+	1.27972i
$147$	−16.3529	+	3.94696i	−1.34876	+	0.325539i
$148$	−2.83345	+	4.90767i	−0.232908	+	0.403408i
$149$	−1.26220	+	2.18619i	−0.103403	+	0.179099i	−0.913085	−	0.407770i	$-0.866307\pi$
$149$	−1.26220	+	2.18619i	−0.103403	+	0.179099i	0.809682	+	0.586869i	$0.199640\pi$
$150$	1.33405	−	0.321987i	0.108924	−	0.0262901i
$151$	3.10510	+	5.37819i	0.252690	+	0.437671i	0.964265	−	0.264938i	$-0.0853515\pi$
$151$	3.10510	+	5.37819i	0.252690	+	0.437671i	−0.711576	+	0.702609i	$0.752018\pi$
$152$	−0.876876			−0.0711241
$153$	−0.323305	+	6.46909i	−0.0261377	+	0.522995i
$154$	−17.8224			−1.43617
$155$	11.9615	+	20.7179i	0.960768	+	1.66410i
$156$	−0.353073	+	1.19728i	−0.0282685	+	0.0958594i
$157$	1.33928	−	2.31971i	0.106886	−	0.185133i	−0.807621	−	0.589702i	$-0.799245\pi$
$157$	1.33928	−	2.31971i	0.106886	−	0.185133i	0.914507	+	0.404569i	$0.132579\pi$
$158$	5.55899	−	9.62845i	0.442249	−	0.765999i
$159$	−5.18968	−	5.45552i	−0.411568	−	0.432651i
$160$	4.59372	+	7.95656i	0.363166	+	0.629021i
$161$	14.6746			1.15652
$162$	−4.18547	−	9.27936i	−0.328842	−	0.729056i
$163$	−0.158596			−0.0124222			−0.00621109	−	0.999981i	$-0.501977\pi$
$163$	−0.158596			−0.0124222			−0.00621109	+	0.999981i	$0.501977\pi$
$164$	2.00893	+	3.47957i	0.156871	+	0.271708i
$165$	10.9860	+	11.5488i	0.855260	+	0.899071i
$166$	0.380567	−	0.659161i	0.0295377	−	0.0511609i
$167$	5.35729	−	9.27910i	0.414560	−	0.718038i	−0.580823	−	0.814030i	$-0.697269\pi$
$167$	5.35729	−	9.27910i	0.414560	−	0.718038i	0.995382	+	0.0959919i	$0.0306023\pi$
$168$	6.16323	−	20.8997i	0.475503	−	1.61245i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−5.83056			−0.447183
$171$	0.0426697	−	0.853789i	0.00326303	−	0.0652909i
$172$	2.03470			0.155145
$173$	5.08367	+	8.80517i	0.386504	+	0.669445i	0.991977	−	0.126422i	$-0.0403492\pi$
$173$	5.08367	+	8.80517i	0.386504	+	0.669445i	−0.605473	+	0.795866i	$0.707016\pi$
$174$	5.66971	−	1.36845i	0.429820	−	0.103742i
$175$	−1.43188	+	2.48009i	−0.108240	+	0.187477i
$176$	3.93004	−	6.80704i	0.296238	−	0.513100i
$177$	−16.1409	+	3.89579i	−1.21323	+	0.292826i
$178$	1.84547	+	3.19644i	0.138324	+	0.239583i
$179$	6.34718			0.474411			0.237205	−	0.971460i	$-0.423769\pi$
$179$	6.34718			0.474411			0.237205	+	0.971460i	$0.423769\pi$
$180$	−4.59372	+	2.35466i	−0.342396	+	0.175506i
$181$	−7.20318			−0.535408			−0.267704	−	0.963501i	$-0.586265\pi$
$181$	−7.20318			−0.535408			−0.267704	+	0.963501i	$0.586265\pi$
$182$	2.31196	+	4.00442i	0.171374	+	0.296828i
$183$	−3.76581	+	12.7700i	−0.278377	+	0.943985i
$184$	−5.52312	+	9.56633i	−0.407170	+	0.705239i
$185$	9.38703	−	16.2588i	0.690148	−	1.19537i
$186$	13.5292	+	14.2223i	0.992013	+	1.04283i
$187$	−4.16093	−	7.20694i	−0.304277	−	0.527023i
$188$	6.06871			0.442606
$189$	20.0496	+	7.01796i	1.45839	+	0.510482i
$190$	0.769516			0.0558265
$191$	−1.81775	−	3.14844i	−0.131528	−	0.227813i	0.792738	−	0.609563i	$-0.208655\pi$
$191$	−1.81775	−	3.14844i	−0.131528	−	0.227813i	−0.924266	+	0.381750i	$0.875322\pi$
$192$	10.0647	+	10.5803i	0.726356	+	0.763564i
$193$	−1.95630	+	3.38841i	−0.140818	+	0.243903i	−0.927805	−	0.373066i	$-0.878306\pi$
$193$	−1.95630	+	3.38841i	−0.140818	+	0.243903i	0.786987	+	0.616969i	$0.211640\pi$
$194$	−5.02069	+	8.69609i	−0.360464	+	0.624343i
$195$	1.16971	−	3.96652i	0.0837646	−	0.284049i
$196$	3.49980	+	6.06183i	0.249985	+	0.432988i
$197$	6.56674			0.467861			0.233930	−	0.972253i	$-0.424841\pi$
$197$	6.56674			0.467861			0.233930	+	0.972253i	$0.424841\pi$
$198$	10.9860	+	7.09659i	0.780742	+	0.504333i
$199$	−1.95403			−0.138517			−0.0692587	−	0.997599i	$-0.522063\pi$
$199$	−1.95403			−0.138517			−0.0692587	+	0.997599i	$0.522063\pi$
$200$	−1.07784	−	1.86687i	−0.0762146	−	0.132008i
$201$	−2.46079	+	0.593939i	−0.173571	+	0.0418932i
$202$	6.89216	−	11.9376i	0.484931	−	0.839925i
$203$	−6.08550	+	10.5404i	−0.427118	+	0.739791i
$204$	2.61983	−	0.632325i	0.183425	−	0.0442716i
$205$	−6.65546	−	11.5276i	−0.464837	−	0.805122i
$206$	14.4027			1.00349
$207$	−9.04570	−	5.84321i	−0.628720	−	0.406131i
$208$	−2.03925			−0.141397
$209$	0.549158	+	0.951170i	0.0379861	+	0.0657938i
$210$	−5.40863	+	18.3409i	−0.373231	+	1.26564i
$211$	10.1083	−	17.5082i	0.695887	−	1.20531i	−0.273994	−	0.961731i	$-0.588345\pi$
$211$	10.1083	−	17.5082i	0.695887	−	1.20531i	0.969881	−	0.243580i	$-0.0783217\pi$
$212$	−1.56649	+	2.71324i	−0.107587	+	0.186346i
$213$	−10.5202	−	11.0591i	−0.720831	−	0.757755i
$214$	3.86538	+	6.69503i	0.264232	+	0.457663i
$215$	−6.74085			−0.459722
$216$	−12.1211	+	10.4288i	−0.824733	+	0.709592i
$217$	−40.9617			−2.78066
$218$	−5.12699	−	8.88020i	−0.347243	−	0.601443i
$219$	18.8451	+	19.8105i	1.27344	+	1.33867i
$220$	3.31609	−	5.74364i	0.223571	−	0.387236i
$221$	−1.07953	+	1.86980i	−0.0726169	+	0.125776i
$222$	4.35724	−	14.7756i	0.292439	−	0.991670i
$223$	−3.12848	−	5.41869i	−0.209499	−	0.362862i	0.742058	−	0.670336i	$-0.233850\pi$
$223$	−3.12848	−	5.41869i	−0.209499	−	0.362862i	−0.951557	+	0.307473i	$0.900517\pi$
$224$	−15.7311			−1.05108
$225$	1.87017	−	0.958615i	0.124678	−	0.0639077i
$226$	14.9682			0.995667
$227$	−3.62042	−	6.27074i	−0.240295	−	0.416204i	0.720503	−	0.693452i	$-0.243911\pi$
$227$	−3.62042	−	6.27074i	−0.240295	−	0.416204i	−0.960798	+	0.277248i	$0.910578\pi$
$228$	−0.345764	+	0.0834541i	−0.0228988	+	0.00552689i
$229$	1.13576	−	1.96719i	0.0750530	−	0.129996i	−0.826056	−	0.563588i	$-0.809421\pi$
$229$	1.13576	−	1.96719i	0.0750530	−	0.129996i	0.901109	+	0.433592i	$0.142754\pi$
$230$	4.84690	−	8.39507i	0.319595	−	0.553555i
$231$	−26.5303	+	6.40338i	−1.74556	+	0.421312i
$232$	−4.58082	−	7.93421i	−0.300746	−	0.520907i
$233$	−13.9715			−0.915303			−0.457651	−	0.889132i	$-0.651309\pi$
$233$	−13.9715			−0.915303			−0.457651	+	0.889132i	$0.651309\pi$
$234$	0.169370	−	3.38898i	0.0110721	−	0.221544i
$235$	−20.1053			−1.31152
$236$	3.45443	+	5.98325i	0.224864	+	0.389476i
$237$	4.81568	−	16.3301i	0.312812	−	1.06076i
$238$	4.99164	−	8.64577i	0.323560	−	0.560422i
$239$	−13.2645	+	22.9747i	−0.858007	+	1.48611i	0.0158202	+	0.999875i	$0.494964\pi$
$239$	−13.2645	+	22.9747i	−0.858007	+	1.48611i	−0.873827	+	0.486237i	$0.838369\pi$
$240$	−5.81240	−	6.11014i	−0.375189	−	0.394408i
$241$	2.00055	+	3.46505i	0.128867	+	0.223204i	0.923238	−	0.384229i	$-0.125533\pi$
$241$	2.00055	+	3.46505i	0.128867	+	0.223204i	−0.794371	+	0.607433i	$0.792199\pi$
$242$	−4.36181			−0.280388
$243$	−9.56444	−	12.3094i	−0.613559	−	0.789649i
$244$	5.53963			0.354639
$245$	−11.5946	−	20.0825i	−0.740752	−	1.28302i
$246$	−7.52778	−	7.91339i	−0.479954	−	0.504540i
$247$	0.142476	−	0.246775i	0.00906552	−	0.0157019i
$248$	15.4168	−	26.7027i	0.978968	−	1.69562i
$249$	0.329680	−	1.11796i	0.0208926	−	0.0708476i
$250$	−5.80541	−	10.0553i	−0.367166	−	0.635951i
$251$	3.96080			0.250003			0.125002	−	0.992157i	$-0.460106\pi$
$251$	3.96080			0.250003			0.125002	+	0.992157i	$0.460106\pi$
$252$	0.441176	−	8.82761i	0.0277915	−	0.556087i
$253$	13.8358			0.869848
$254$	10.7164	+	18.5613i	0.672407	+	1.16464i
$255$	−8.67933	+	2.09485i	−0.543521	+	0.131185i
$256$	7.39038	−	12.8005i	0.461898	−	0.800032i
$257$	−6.62299	+	11.4714i	−0.413131	+	0.715564i	−0.995230	−	0.0975540i	$-0.968898\pi$
$257$	−6.62299	+	11.4714i	−0.413131	+	0.715564i	0.582099	+	0.813118i	$0.302231\pi$
$258$	−5.37666	+	1.29772i	−0.334736	+	0.0807923i
$259$	16.0728	+	27.8389i	0.998715	+	1.72983i
$260$	−1.72068			−0.106712
$261$	7.94822	−	4.07413i	0.491983	−	0.252182i
$262$	19.8646			1.22724
$263$	−2.64411	−	4.57973i	−0.163043	−	0.282398i	0.772916	−	0.634509i	$-0.218797\pi$
$263$	−2.64411	−	4.57973i	−0.163043	−	0.282398i	−0.935958	+	0.352110i	$0.885464\pi$
$264$	5.81091	−	19.7050i	0.357637	−	1.21276i
$265$	5.18968	−	8.98878i	0.318799	−	0.552176i
$266$	−0.658796	+	1.14107i	−0.0403933	+	0.0699633i
$267$	3.89560	+	4.09515i	0.238407	+	0.250619i
$268$	0.526650	+	0.912185i	0.0321703	+	0.0557206i
$269$	−8.01270			−0.488543			−0.244271	−	0.969707i	$-0.578549\pi$
$269$	−8.01270			−0.488543			−0.244271	+	0.969707i	$0.578549\pi$
$270$	10.6370	−	9.15198i	0.647348	−	0.556972i
$271$	−15.9840			−0.970956			−0.485478	−	0.874249i	$-0.661354\pi$
$271$	−15.9840			−0.970956			−0.485478	+	0.874249i	$0.661354\pi$
$272$	2.20143	+	3.81299i	0.133481	+	0.231197i
$273$	4.88031	+	5.13030i	0.295370	+	0.310500i
$274$	−0.433309	+	0.750514i	−0.0261772	+	0.0453402i
$275$	−1.35003	+	2.33831i	−0.0814096	+	0.141006i
$276$	−1.26740	+	4.29778i	−0.0762883	+	0.258696i
$277$	3.14563	+	5.44839i	0.189003	+	0.327362i	0.944918	−	0.327307i	$-0.106141\pi$
$277$	3.14563	+	5.44839i	0.189003	+	0.327362i	−0.755915	+	0.654669i	$0.772808\pi$
$278$	−16.4486			−0.986520
$279$	25.2495	+	16.3103i	1.51165	+	0.976472i
$280$	30.0361			1.79500
$281$	−8.49232	−	14.7091i	−0.506609	−	0.877473i	−0.999971	−	0.00764859i	$-0.997565\pi$
$281$	−8.49232	−	14.7091i	−0.506609	−	0.877473i	0.493361	−	0.869824i	$-0.335768\pi$
$282$	−16.0364	+	3.87057i	−0.954955	+	0.230489i
$283$	−13.7365	+	23.7924i	−0.816552	+	1.41431i	0.0916556	+	0.995791i	$0.470784\pi$
$283$	−13.7365	+	23.7924i	−0.816552	+	1.41431i	−0.908208	+	0.418519i	$0.862549\pi$
$284$	−3.17548	+	5.50010i	−0.188430	+	0.326371i
$285$	1.14550	−	0.276478i	0.0678533	−	0.0163772i
$286$	2.17979	+	3.77551i	0.128894	+	0.223251i
$287$	22.7914			1.34533
$288$	9.69689	+	6.26386i	0.571395	+	0.369101i
$289$	−12.3385			−0.725793
$290$	4.01997	+	6.96279i	0.236061	+	0.408869i
$291$	−4.34936	+	14.7488i	−0.254964	+	0.864591i
$292$	5.68835	−	9.85250i	0.332885	−	0.576574i
$293$	13.9323	−	24.1315i	0.813934	−	1.40977i	−0.0961570	−	0.995366i	$-0.530655\pi$
$293$	13.9323	−	24.1315i	0.813934	−	1.40977i	0.910091	−	0.414409i	$-0.136012\pi$
$294$	−13.1143	−	13.7861i	−0.764842	−	0.804021i
$295$	−11.4443	−	19.8221i	−0.666314	−	1.15409i
$296$	−24.1974			−1.40644
$297$	18.9034	+	6.61679i	1.09689	+	0.383945i
$298$	−2.85526			−0.165401
$299$	−1.79481	−	3.10870i	−0.103796	−	0.179781i
$300$	−0.602680	−	0.633552i	−0.0347957	−	0.0365781i
$301$	5.77096	−	9.99559i	0.332633	−	0.576136i
$302$	−3.51208	+	6.08311i	−0.202098	+	0.350044i
$303$	5.97059	−	20.2465i	0.343001	−	1.16313i
$304$	−0.290544	−	0.503238i	−0.0166639	−	0.0288627i
$305$	−18.3525			−1.05086
$306$	−6.51954	+	3.34181i	−0.372697	+	0.191038i
$307$	15.3680			0.877096			0.438548	−	0.898708i	$-0.355493\pi$
$307$	15.3680			0.877096			0.438548	+	0.898708i	$0.355493\pi$
$308$	5.67793	+	9.83446i	0.323530	+	0.560371i
$309$	21.4398	−	5.17474i	1.21967	−	0.294381i
$310$	−13.5292	+	23.4333i	−0.768410	+	1.33092i
$311$	5.63733	−	9.76415i	0.319664	−	0.553674i	−0.660754	−	0.750603i	$-0.729763\pi$
$311$	5.63733	−	9.76415i	0.319664	−	0.553674i	0.980418	+	0.196928i	$0.0630967\pi$
$312$	−5.18122	+	1.25055i	−0.293329	+	0.0707983i
$313$	5.41008	+	9.37052i	0.305796	+	0.529653i	0.977438	−	0.211222i	$-0.0677443\pi$
$313$	5.41008	+	9.37052i	0.305796	+	0.529653i	−0.671643	+	0.740875i	$0.734411\pi$
$314$	3.02964			0.170973
$315$	−1.46159	+	29.2453i	−0.0823513	+	1.64779i
$316$	−7.08403			−0.398508
$317$	8.22337	+	14.2433i	0.461871	+	0.799984i	0.999054	−	0.0434819i	$-0.0138451\pi$
$317$	8.22337	+	14.2433i	0.461871	+	0.799984i	−0.537184	+	0.843465i	$0.680512\pi$
$318$	2.40893	−	8.16875i	0.135086	−	0.458081i
$319$	−5.73763	+	9.93786i	−0.321245	+	0.556413i
$320$	−10.0647	+	17.4326i	−0.562633	+	0.974509i
$321$	8.15942	+	8.57739i	0.455414	+	0.478743i
$322$	8.29902	+	14.3743i	0.462487	+	0.801050i
$323$	−0.615227			−0.0342321
$324$	−3.78697	+	5.26582i	−0.210387	+	0.292546i
$325$	0.700513			0.0388575
$326$	−0.0896914	−	0.155350i	−0.00496754	−	0.00860404i
$327$	−10.8226	−	11.3769i	−0.598489	−	0.629146i
$328$	−8.57804	+	14.8576i	−0.473643	+	0.820373i
$329$	17.2125	−	29.8129i	0.948954	−	1.64364i
$330$	−5.09945	+	17.2924i	−0.280716	+	0.951916i
$331$	−2.86109	−	4.95556i	−0.157260	−	0.272382i	0.776620	−	0.629970i	$-0.216933\pi$
$331$	−2.86109	−	4.95556i	−0.157260	−	0.272382i	−0.933880	+	0.357588i	$0.883599\pi$
$332$	−0.484971			−0.0266162
$333$	1.17747	−	23.5603i	0.0645249	−	1.29110i
$334$	12.1189			0.663119
$335$	−1.74476	−	3.02201i	−0.0953264	−	0.165110i
$336$	14.0364	−	3.38785i	0.765750	−	0.184822i
$337$	2.37586	−	4.11510i	0.129421	−	0.224164i	−0.794031	−	0.607877i	$-0.792021\pi$
$337$	2.37586	−	4.11510i	0.129421	−	0.224164i	0.923452	+	0.383713i	$0.125355\pi$
$338$	0.565535	−	0.979535i	0.0307610	−	0.0532797i
$339$	22.2815	−	5.37789i	1.21017	−	0.292087i
$340$	1.85752	+	3.21733i	0.100738	+	0.174484i
$341$	−38.6201			−2.09140
$342$	0.860448	−	0.441051i	0.0465277	−	0.0238493i
$343$	11.0888			0.598737
$344$	4.34405	+	7.52412i	0.234215	+	0.405673i
$345$	4.19880	−	14.2383i	0.226056	−	0.766564i
$346$	−5.74998	+	9.95926i	−0.309121	+	0.535413i
$347$	−5.46573	+	9.46692i	−0.293416	+	0.508211i	−0.974615	−	0.223887i	$-0.928125\pi$
$347$	−5.46573	+	9.46692i	−0.293416	+	0.508211i	0.681199	+	0.732098i	$0.261459\pi$
$348$	−2.56140	−	2.69260i	−0.137305	−	0.144339i
$349$	13.0535	+	22.6094i	0.698739	+	1.21025i	0.968904	+	0.247437i	$0.0795884\pi$
$349$	13.0535	+	22.6094i	0.698739	+	1.21025i	−0.270165	+	0.962814i	$0.587078\pi$
$350$	−3.23911			−0.173138
$351$	−0.965499	−	5.10566i	−0.0515345	−	0.272520i
$352$	−14.8318			−0.790538
$353$	5.74760	+	9.95514i	0.305914	+	0.529859i	0.977464	−	0.211100i	$-0.0677046\pi$
$353$	5.74760	+	9.95514i	0.305914	+	0.529859i	−0.671550	+	0.740959i	$0.734371\pi$
$354$	−12.9443	−	13.6074i	−0.687983	−	0.723225i
$355$	10.5202	−	18.2215i	0.558353	−	0.967096i
$356$	1.17587	−	2.03667i	0.0623212	−	0.107943i
$357$	4.32419	−	14.6635i	0.228861	−	0.776074i
$358$	3.58955	+	6.21729i	0.189714	+	0.328594i
$359$	7.42296			0.391769			0.195884	−	0.980627i	$-0.437242\pi$
$359$	7.42296			0.391769			0.195884	+	0.980627i	$0.437242\pi$
$360$	−18.5148	−	11.9599i	−0.975815	−	0.630343i
$361$	−18.9188			−0.995726
$362$	−4.07365	−	7.05576i	−0.214106	−	0.370843i
$363$	−6.49296	+	1.56715i	−0.340792	+	0.0822541i
$364$	1.47311	−	2.55149i	0.0772117	−	0.133735i
$365$	−18.8451	+	32.6407i	−0.986400	+	1.70849i
$366$	−14.6383	+	3.53313i	−0.765159	+	0.184680i
$367$	2.99575	+	5.18880i	0.156377	+	0.270853i	0.933560	−	0.358422i	$-0.116685\pi$
$367$	2.99575	+	5.18880i	0.156377	+	0.270853i	−0.777183	+	0.629275i	$0.783352\pi$
$368$	−7.32013			−0.381588
$369$	−14.0490	−	9.07518i	−0.731362	−	0.472435i
$370$	21.2348			1.10394
$371$	8.88594	+	15.3909i	0.461335	+	0.799056i
$372$	3.53771	−	11.9965i	0.183422	−	0.621989i
$373$	−13.3589	+	23.1382i	−0.691696	+	1.19805i	0.279586	+	0.960121i	$0.409803\pi$
$373$	−13.3589	+	23.1382i	−0.691696	+	1.19805i	−0.971282	+	0.237932i	$0.923531\pi$
$374$	4.70630	−	8.15155i	0.243357	−	0.421506i
$375$	−12.2546	−	12.8824i	−0.632827	−	0.665243i
$376$	12.9566	+	22.4414i	0.668184	+	1.15733i
$377$	2.97719			0.153333
$378$	4.46438	+	23.6081i	0.229623	+	1.21427i
$379$	−17.3941			−0.893474			−0.446737	−	0.894665i	$-0.647414\pi$
$379$	−17.3941			−0.893474			−0.446737	+	0.894665i	$0.647414\pi$
$380$	−0.245156	−	0.424622i	−0.0125762	−	0.0217826i
$381$	22.6212	+	23.7800i	1.15892	+	1.21829i
$382$	2.05601	−	3.56111i	0.105194	−	0.182202i
$383$	−17.3071	+	29.9769i	−0.884354	+	1.53175i	−0.0379018	+	0.999281i	$0.512067\pi$
$383$	−17.3071	+	29.9769i	−0.884354	+	1.53175i	−0.846452	+	0.532465i	$0.821266\pi$
$384$	−0.901383	+	3.05662i	−0.0459985	+	0.155982i
$385$	−18.8106	−	32.5810i	−0.958678	−	1.66048i
$386$	−4.42543			−0.225248
$387$	−7.53740	+	3.86355i	−0.383148	+	0.196395i
$388$	6.39805			0.324812
$389$	−17.8721	−	30.9554i	−0.906152	−	1.56950i	−0.819364	−	0.573274i	$-0.805673\pi$
$389$	−17.8721	−	30.9554i	−0.906152	−	1.56950i	−0.0867879	−	0.996227i	$-0.527660\pi$
$390$	4.54686	−	1.09744i	0.230239	−	0.0555708i
$391$	−3.87509	+	6.71185i	−0.195972	+	0.339433i
$392$	−14.9440	+	25.8837i	−0.754785	+	1.30733i
$393$	29.5703	−	7.13713i	1.49162	−	0.360020i
$394$	3.71372	+	6.43235i	0.187094	+	0.324057i
$395$	23.4689			1.18085
$396$	0.415957	−	8.32299i	0.0209026	−	0.418246i
$397$	13.6734			0.686246			0.343123	−	0.939290i	$-0.388515\pi$
$397$	13.6734			0.686246			0.343123	+	0.939290i	$0.388515\pi$
$398$	−1.10507	−	1.91404i	−0.0553922	−	0.0959421i
$399$	−0.570706	+	1.93528i	−0.0285710	+	0.0968854i
$400$	0.714262	−	1.23714i	0.0357131	−	0.0618569i
$401$	16.7932	−	29.0866i	0.838610	−	1.45252i	−0.0524466	−	0.998624i	$-0.516702\pi$
$401$	16.7932	−	29.0866i	0.838610	−	1.45252i	0.891057	−	0.453892i	$-0.149965\pi$
$402$	−1.97344	−	2.07453i	−0.0984265	−	0.103468i
$403$	5.00988	+	8.67737i	0.249560	+	0.432251i
$404$	−8.78294			−0.436967
$405$	12.5460	−	17.4453i	0.623415	−	0.866866i
$406$	−13.7662			−0.683207
$407$	15.1540	+	26.2475i	0.751156	+	1.30104i
$408$	7.93155	+	8.33784i	0.392670	+	0.412785i
$409$	−1.46727	+	2.54138i	−0.0725517	+	0.125663i	−0.900019	−	0.435851i	$-0.856448\pi$
$409$	−1.46727	+	2.54138i	−0.0725517	+	0.125663i	0.827467	+	0.561514i	$0.189781\pi$
$410$	7.52778	−	13.0385i	0.371771	−	0.643926i
$411$	−0.375370	+	1.27289i	−0.0185156	+	0.0627872i
$412$	−4.58848	−	7.94749i	−0.226058	−	0.391545i
$413$	39.1907			1.92845
$414$	0.607974	−	12.1651i	0.0298803	−	0.597883i
$415$	1.60668			0.0788687
$416$	1.92401	+	3.33249i	0.0943324	+	0.163389i
$417$	−24.4852	+	5.90979i	−1.19905	+	0.289404i
$418$	−0.621136	+	1.07584i	−0.0303808	+	0.0526210i
$419$	4.26665	−	7.39005i	0.208439	−	0.361028i	−0.742784	−	0.669531i	$-0.766495\pi$
$419$	4.26665	−	7.39005i	0.208439	−	0.361028i	0.951223	+	0.308504i	$0.0998283\pi$
$420$	11.8437	−	2.85860i	0.577912	−	0.139486i
$421$	10.9240	+	18.9208i	0.532401	+	0.922146i	0.999284	+	0.0378266i	$0.0120435\pi$
$421$	10.9240	+	18.9208i	0.532401	+	0.922146i	−0.466883	+	0.884319i	$0.654623\pi$
$422$	22.8665			1.11312
$423$	−22.4811	+	11.5234i	−1.09307	+	0.560288i
$424$	−13.3777			−0.649677
$425$	−0.756223	−	1.30982i	−0.0366822	−	0.0635354i
$426$	4.88322	−	16.5592i	0.236593	−	0.802294i
$427$	15.7119	−	27.2137i	0.760350	−	1.31697i
$428$	2.46290	−	4.26586i	0.119049	−	0.206198i
$429$	4.60133	+	4.83703i	0.222154	+	0.233534i
$430$	−3.81219	−	6.60290i	−0.183840	−	0.318420i
$431$	35.1630			1.69374			0.846872	−	0.531797i	$-0.178483\pi$
$431$	35.1630			1.69374			0.846872	+	0.531797i	$0.178483\pi$
$432$	−10.0013	−	3.50076i	−0.481187	−	0.168430i
$433$	24.9431			1.19869			0.599344	−	0.800491i	$-0.295428\pi$
$433$	24.9431			1.19869			0.599344	+	0.800491i	$0.295428\pi$
$434$	−23.1652	−	40.1234i	−1.11197	−	1.92598i
$435$	8.48575	+	8.92043i	0.406860	+	0.427702i
$436$	−3.26676	+	5.65819i	−0.156449	+	0.270978i
$437$	0.511433	−	0.885828i	0.0244652	−	0.0423749i
$438$	−8.74747	+	29.6630i	−0.417971	+	1.41735i
$439$	−6.76343	−	11.7146i	−0.322801	−	0.559108i	0.658264	−	0.752787i	$-0.271291\pi$
$439$	−6.76343	−	11.7146i	−0.322801	−	0.559108i	−0.981065	+	0.193680i	$0.937958\pi$
$440$	28.3191			1.35006
$441$	−24.4751	−	15.8101i	−1.16548	−	0.752860i
$442$	−2.44204			−0.116156
$443$	−16.7288	−	28.9751i	−0.794808	−	1.37665i	−0.922961	−	0.384894i	$-0.874238\pi$
$443$	−16.7288	−	28.9751i	−0.794808	−	1.37665i	0.128152	−	0.991754i	$-0.459095\pi$
$444$	−9.54136	+	2.30292i	−0.452813	+	0.109292i
$445$	−3.89560	+	6.74737i	−0.184669	+	0.319856i
$446$	3.53853	−	6.12892i	0.167554	−	0.290213i
$447$	−4.25032	+	1.02586i	−0.201033	+	0.0485217i
$448$	−17.2331	−	29.8486i	−0.814188	−	1.41021i
$449$	−7.63995			−0.360552			−0.180276	−	0.983616i	$-0.557699\pi$
$449$	−7.63995			−0.360552			−0.180276	+	0.983616i	$0.557699\pi$
$450$	1.99664	+	1.28976i	0.0941225	+	0.0608000i
$451$	21.4885			1.01186
$452$	−4.76862	−	8.25949i	−0.224297	−	0.388494i
$453$	−3.04247	+	10.3171i	−0.142948	+	0.484741i
$454$	4.09494	−	7.09265i	0.192185	−	0.332874i
$455$	−4.88031	+	8.45294i	−0.228792	+	0.396280i
$456$	−1.04680	−	1.10043i	−0.0490211	−	0.0515322i
$457$	−7.06564	−	12.2381i	−0.330517	−	0.572472i	0.652096	−	0.758136i	$-0.273890\pi$
$457$	−7.06564	−	12.2381i	−0.330517	−	0.572472i	−0.982613	+	0.185664i	$0.940556\pi$
$458$	2.56924			0.120053
$459$	−8.50427	+	7.31699i	−0.396946	+	0.341528i
$460$	−6.17658			−0.287985
$461$	2.31409	+	4.00813i	0.107778	+	0.186677i	0.914870	−	0.403749i	$-0.132293\pi$
$461$	2.31409	+	4.00813i	0.107778	+	0.186677i	−0.807092	+	0.590426i	$0.798960\pi$
$462$	−21.2761	−	22.3660i	−0.989855	−	1.04056i
$463$	−8.94322	+	15.4901i	−0.415627	+	0.719887i	−0.995494	−	0.0948242i	$-0.969771\pi$
$463$	−8.94322	+	15.4901i	−0.415627	+	0.719887i	0.579867	+	0.814711i	$0.303104\pi$
$464$	3.03562	−	5.25785i	0.140925	−	0.244089i
$465$	−11.7202	+	39.7436i	−0.543512	+	1.84307i
$466$	−7.90136	−	13.6856i	−0.366024	−	0.633972i
$467$	−16.6357			−0.769808			−0.384904	−	0.922957i	$-0.625765\pi$
$467$	−16.6357			−0.769808			−0.384904	+	0.922957i	$0.625765\pi$
$468$	−1.92401	+	0.986216i	−0.0889375	+	0.0455879i
$469$	5.97488			0.275894
$470$	−11.3702	−	19.6938i	−0.524469	−	0.908407i
$471$	4.50991	−	1.08852i	0.207806	−	0.0501562i
$472$	−14.7503	+	25.5482i	−0.678936	+	1.17595i
$473$	5.44107	−	9.42420i	0.250180	−	0.433325i
$474$	18.7194	−	4.51813i	0.859809	−	0.207525i
$475$	0.0998061	+	0.172869i	0.00457942	+	0.00793179i
$476$	−6.36103			−0.291557
$477$	0.650971	−	13.0255i	0.0298059	−	0.596394i
$478$	−30.0061			−1.37245
$479$	−18.8372	−	32.6271i	−0.860695	−	1.49077i	−0.871259	−	0.490824i	$-0.836696\pi$
$479$	−18.8372	−	32.6271i	−0.860695	−	1.49077i	0.0105634	−	0.999944i	$-0.496637\pi$
$480$	−4.50107	+	15.2633i	−0.205445	+	0.696670i
$481$	3.93162	−	6.80976i	0.179266	−	0.310498i
$482$	−2.26276	+	3.91922i	−0.103066	+	0.178515i
$483$	17.5184	+	18.4158i	0.797115	+	0.837947i
$484$	1.38960	+	2.40687i	0.0631638	+	0.109403i
$485$	−21.1963			−0.962476
$486$	6.64847	−	16.3301i	0.301581	−	0.740748i
$487$	−34.2388			−1.55151			−0.775754	−	0.631035i	$-0.782630\pi$
$487$	−34.2388			−1.55151			−0.775754	+	0.631035i	$0.782630\pi$
$488$	11.8270	+	20.4850i	0.535383	+	0.927310i
$489$	−0.189329	−	0.199028i	−0.00856178	−	0.00900035i
$490$	13.1143	−	22.7146i	0.592444	−	1.02614i
$491$	−14.9575	+	25.9072i	−0.675024	+	1.16918i	0.301438	+	0.953486i	$0.402533\pi$
$491$	−14.9575	+	25.9072i	−0.675024	+	1.16918i	−0.976462	+	0.215690i	$0.930800\pi$
$492$	−1.96841	+	6.67495i	−0.0887428	+	0.300930i
$493$	−3.21396	−	5.56674i	−0.144749	−	0.250713i
$494$	0.322300			0.0145010
$495$	−1.37804	+	27.5736i	−0.0619383	+	1.23934i
$496$	20.4328			0.917461
$497$	18.0130	+	31.1994i	0.807994	+	1.39949i
$498$	1.28152	−	0.309310i	0.0574264	−	0.0138605i
$499$	10.4792	−	18.1504i	0.469111	−	0.812525i	−0.530265	−	0.847832i	$-0.677908\pi$
$499$	10.4792	−	18.1504i	0.469111	−	0.812525i	0.999377	+	0.0353070i	$0.0112409\pi$
$500$	−3.69903	+	6.40690i	−0.165425	+	0.286525i
$501$	18.0402	−	4.35420i	0.805975	−	0.194531i
$502$	2.23997	+	3.87974i	0.0999747	+	0.173161i
$503$	−21.1599			−0.943473			−0.471737	−	0.881739i	$-0.656373\pi$
$503$	−21.1599			−0.943473			−0.471737	+	0.881739i	$0.656373\pi$
$504$	33.5855	−	17.2153i	1.49601	−	0.766832i
$505$	29.0973			1.29481
$506$	7.82462	+	13.5526i	0.347847	+	0.602488i
$507$	0.489915	−	1.66132i	0.0217579	−	0.0737818i
$508$	6.82815	−	11.8267i	0.302950	−	0.524725i
$509$	−1.51495	+	2.62396i	−0.0671488	+	0.116305i	−0.897645	−	0.440719i	$-0.854724\pi$
$509$	−1.51495	+	2.62396i	−0.0671488	+	0.116305i	0.830496	+	0.557024i	$0.188057\pi$
$510$	−6.96045	−	7.31699i	−0.308214	−	0.324002i
$511$	−32.2673	−	55.8886i	−1.42742	−	2.47237i
$512$	20.3978			0.901464
$513$	1.12239	−	0.965695i	0.0495548	−	0.0426365i
$514$	−14.9821			−0.660833
$515$	15.2014	+	26.3295i	0.669852	+	1.16022i
$516$	2.42900	+	2.55343i	0.106931	+	0.112409i
$517$	16.2285	−	28.1086i	0.713730	−	1.23622i
$518$	−18.1795	+	31.4877i	−0.798759	+	1.38349i
$519$	−4.98113	+	16.8912i	−0.218647	+	0.741441i
$520$	−3.67362	−	6.36289i	−0.161099	−	0.279031i
$521$	−12.5546			−0.550026			−0.275013	−	0.961441i	$-0.588682\pi$
$521$	−12.5546			−0.550026			−0.275013	+	0.961441i	$0.588682\pi$
$522$	8.48575	+	5.48150i	0.371411	+	0.239919i
$523$	−8.54696			−0.373733			−0.186866	−	0.982385i	$-0.559833\pi$
$523$	−8.54696			−0.373733			−0.186866	+	0.982385i	$0.559833\pi$
$524$	−6.32855	−	10.9614i	−0.276464	−	0.478849i
$525$	−4.82172	+	1.16378i	−0.210437	+	0.0507913i
$526$	2.99067	−	5.17999i	0.130399	−	0.225858i
$527$	10.8166	−	18.7349i	0.471179	−	0.816106i
$528$	13.2341	−	3.19419i	0.575938	−	0.139009i
$529$	5.05734	+	8.75957i	0.219884	+	0.380851i
$530$	11.7398			0.509943
$531$	−24.1578	−	15.6051i	−1.04836	−	0.677205i
$532$	0.839528			0.0363981
$533$	−2.78754	−	4.82816i	−0.120742	−	0.209131i
$534$	−1.80824	+	6.13182i	−0.0782504	+	0.265350i
$535$	−8.15942	+	14.1325i	−0.352763	+	0.611003i
$536$	−2.24877	+	3.89499i	−0.0971322	+	0.168238i
$537$	7.57719	+	7.96533i	0.326980	+	0.343729i
$538$	−4.53146	−	7.84872i	−0.195365	−	0.338382i
$539$	37.4356			1.61247
$540$	−8.43889	−	2.95387i	−0.363152	−	0.127114i
$541$	−4.74799			−0.204132			−0.102066	−	0.994778i	$-0.532545\pi$
$541$	−4.74799			−0.204132			−0.102066	+	0.994778i	$0.532545\pi$
$542$	−9.03948	−	15.6568i	−0.388279	−	0.672519i
$543$	−8.59906	−	9.03955i	−0.369021	−	0.387924i
$544$	4.15405	−	7.19502i	0.178103	−	0.308484i
$545$	10.8226	−	18.7452i	0.463587	−	0.802957i
$546$	−2.26532	+	7.68179i	−0.0969470	+	0.328750i
$547$	0.977794	+	1.69359i	0.0418074	+	0.0724126i	0.886172	−	0.463357i	$-0.153355\pi$
$547$	0.977794	+	1.69359i	0.0418074	+	0.0724126i	−0.844365	+	0.535769i	$0.820022\pi$
$548$	0.552182			0.0235881
$549$	−20.5211	+	10.5188i	−0.875821	+	0.448931i
$550$	−3.05395			−0.130221
$551$	0.424177	+	0.734697i	0.0180706	+	0.0312991i
$552$	−18.5986	+	4.48898i	−0.791609	+	0.191064i
$553$	−20.0922	+	34.8007i	−0.854406	+	1.47987i
$554$	−3.55793	+	6.16251i	−0.151162	+	0.261820i
$555$	31.6099	−	7.62942i	1.34177	−	0.323851i
$556$	5.24026	+	9.07639i	0.222236	+	0.384925i
$557$	26.8657			1.13833			0.569167	−	0.822222i	$-0.307266\pi$
$557$	26.8657			1.13833			0.569167	+	0.822222i	$0.307266\pi$
$558$	−1.69705	+	33.9568i	−0.0718419	+	1.43750i
$559$	−2.82330			−0.119413
$560$	9.95218	+	17.2377i	0.420557	+	0.728425i
$561$	4.07700	−	13.8253i	0.172131	−	0.583703i
$562$	9.60540	−	16.6370i	0.405179	−	0.701791i
$563$	−20.9340	+	36.2588i	−0.882265	+	1.52813i	−0.0334482	+	0.999440i	$0.510649\pi$
$563$	−20.9340	+	36.2588i	−0.882265	+	1.52813i	−0.848817	+	0.528687i	$0.822684\pi$
$564$	7.24475	+	7.61586i	0.305059	+	0.320686i
$565$	15.7981	+	27.3632i	0.664633	+	1.15118i
$566$	−31.0740			−1.30614
$567$	15.1278	+	33.5389i	0.635307	+	1.40850i
$568$	−27.1183			−1.13786
$569$	13.1717	+	22.8141i	0.552188	+	0.956417i	0.998116	+	0.0613487i	$0.0195402\pi$
$569$	13.1717	+	22.8141i	0.552188	+	0.956417i	−0.445929	+	0.895068i	$0.647127\pi$
$570$	0.918638	+	0.965695i	0.0384775	+	0.0404485i
$571$	−1.35759	+	2.35141i	−0.0568133	+	0.0984035i	−0.893033	−	0.449991i	$-0.851427\pi$
$571$	−1.35759	+	2.35141i	−0.0568133	+	0.0984035i	0.836220	+	0.548394i	$0.184761\pi$
$572$	1.38890	−	2.40564i	0.0580727	−	0.100585i
$573$	1.78109	−	6.03974i	0.0744062	−	0.252314i
$574$	12.8893	+	22.3250i	0.537990	+	0.931826i
$575$	2.51457			0.104865
$576$	−1.26247	+	25.2611i	−0.0526030	+	1.05255i
$577$	−16.4988			−0.686855			−0.343427	−	0.939179i	$-0.611588\pi$
$577$	−16.4988			−0.686855			−0.343427	+	0.939179i	$0.611588\pi$
$578$	−6.97784	−	12.0860i	−0.290240	−	0.502710i
$579$	−6.58766	+	1.59001i	−0.273774	+	0.0660784i
$580$	2.56140	−	4.43647i	0.106356	−	0.184214i
$581$	−1.37550	+	2.38244i	−0.0570656	+	0.0988404i
$582$	−16.9067	+	4.08062i	−0.700805	+	0.169147i
$583$	8.37798	+	14.5111i	0.346981	+	0.600988i
$584$	48.5780			2.01017
$585$	6.37413	−	3.26727i	0.263538	−	0.135085i
$586$	31.5168			1.30195
$587$	−18.2523	−	31.6139i	−0.753353	−	1.30485i	−0.946189	−	0.323615i	$-0.895102\pi$
$587$	−18.2523	−	31.6139i	−0.753353	−	1.30485i	0.192836	−	0.981231i	$-0.438232\pi$
$588$	−3.42921	+	11.6286i	−0.141418	+	0.479554i
$589$	−1.42757	+	2.47263i	−0.0588222	+	0.101883i
$590$	12.9443	−	22.4202i	0.532909	−	0.923026i
$591$	7.83929	+	8.24086i	0.322465	+	0.338984i
$592$	−8.01757	−	13.8868i	−0.329520	−	0.570745i
$593$	6.45481			0.265067			0.132534	−	0.991178i	$-0.457689\pi$
$593$	6.45481			0.265067			0.132534	+	0.991178i	$0.457689\pi$
$594$	4.20918	+	22.2586i	0.172705	+	0.913281i
$595$	21.0737			0.863938
$596$	0.909642	+	1.57555i	0.0372604	+	0.0645369i
$597$	−2.33269	−	2.45219i	−0.0954708	−	0.100361i
$598$	2.03005	−	3.51615i	0.0830149	−	0.143786i
$599$	16.2944	−	28.2227i	0.665770	−	1.15315i	−0.313306	−	0.949652i	$-0.601437\pi$
$599$	16.2944	−	28.2227i	0.665770	−	1.15315i	0.979076	−	0.203495i	$-0.0652301\pi$
$600$	1.05610	−	3.58126i	0.0431150	−	0.146204i
$601$	−2.17773	−	3.77194i	−0.0888315	−	0.153861i	0.818186	−	0.574954i	$-0.194980\pi$
$601$	−2.17773	−	3.77194i	−0.0888315	−	0.153861i	−0.907017	+	0.421093i	$0.861647\pi$
$602$	13.0547			0.532070
$603$	−3.68301	−	2.37910i	−0.149984	−	0.0968845i
$604$	4.47558			0.182109
$605$	−4.60367	−	7.97380i	−0.187166	−	0.324181i
$606$	23.2087	−	5.60168i	0.942789	−	0.227553i
$607$	0.694133	−	1.20227i	0.0281740	−	0.0487988i	−0.851595	−	0.524201i	$-0.824364\pi$
$607$	0.694133	−	1.20227i	0.0281740	−	0.0487988i	0.879769	+	0.475402i	$0.157697\pi$
$608$	−0.548250	+	0.949597i	−0.0222345	+	0.0385113i
$609$	−20.4923	+	4.94606i	−0.830392	+	0.200424i
$610$	−10.3790	−	17.9769i	−0.420232	−	0.727862i
$611$	−8.42079			−0.340669
$612$	3.92105	+	2.53286i	0.158499	+	0.102385i
$613$	−17.9268			−0.724056			−0.362028	−	0.932167i	$-0.617916\pi$
$613$	−17.9268			−0.724056			−0.362028	+	0.932167i	$0.617916\pi$
$614$	8.69112	+	15.0535i	0.350745	+	0.607508i
$615$	6.52122	−	22.1137i	0.262961	−	0.891710i
$616$	−24.2445	+	41.9927i	−0.976839	+	1.69194i
$617$	7.93721	−	13.7477i	0.319540	−	0.553460i	−0.660852	−	0.750516i	$-0.729805\pi$
$617$	7.93721	−	13.7477i	0.319540	−	0.553460i	0.980392	+	0.197056i	$0.0631382\pi$
$618$	17.1938	+	18.0745i	0.691636	+	0.727065i
$619$	−7.02684	−	12.1708i	−0.282432	−	0.489187i	0.689551	−	0.724237i	$-0.257808\pi$
$619$	−7.02684	−	12.1708i	−0.282432	−	0.489187i	−0.971983	+	0.235050i	$0.924475\pi$
$620$	17.2408			0.692408
$621$	−3.46577	−	18.3274i	−0.139076	−	0.735452i
$622$	12.7524			0.511326
$623$	−6.67017	−	11.5531i	−0.267235	−	0.462864i
$624$	−2.43444	−	2.55914i	−0.0974554	−	0.102448i
$625$	14.0059	−	24.2590i	0.560237	−	0.970359i
$626$	−6.11917	+	10.5987i	−0.244571	+	0.423610i
$627$	−0.538082	+	1.82465i	−0.0214889	+	0.0728697i
$628$	−0.965197	−	1.67177i	−0.0385156	−	0.0667109i
$629$	−16.9772			−0.676924
$630$	−29.4734	+	15.1076i	−1.17425	+	0.601900i
$631$	3.10018			0.123416			0.0617081	−	0.998094i	$-0.480345\pi$
$631$	3.10018			0.123416			0.0617081	+	0.998094i	$0.480345\pi$
$632$	−15.1242	−	26.1960i	−0.601610	−	1.04202i
$633$	34.0389	−	8.21566i	1.35292	−	0.326543i
$634$	−9.30121	+	16.1102i	−0.369398	+	0.639816i
$635$	−22.6212	+	39.1811i	−0.897697	+	1.55486i
$636$	−5.27500	+	1.27318i	−0.209167	+	0.0504849i
$637$	−4.85623	−	8.41124i	−0.192411	−	0.333265i
$638$	−12.9793			−0.513856
$639$	1.31961	−	26.4044i	0.0522028	−	1.04454i
$640$	−4.39284			−0.173642
$641$	2.73944	+	4.74485i	0.108201	+	0.187410i	0.915042	−	0.403359i	$-0.132158\pi$
$641$	2.73944	+	4.74485i	0.108201	+	0.187410i	−0.806840	+	0.590770i	$0.798824\pi$
$642$	−3.78741	+	12.8432i	−0.149477	+	0.506883i
$643$	−10.9177	+	18.9100i	−0.430552	+	0.745738i	−0.996921	−	0.0784137i	$-0.975015\pi$
$643$	−10.9177	+	18.9100i	−0.430552	+	0.745738i	0.566369	+	0.824152i	$0.308348\pi$
$644$	5.28788	−	9.15887i	0.208372	−	0.360910i
$645$	−8.04714	−	8.45936i	−0.316856	−	0.333087i
$646$	−0.347932	−	0.602636i	−0.0136892	−	0.0237104i
$647$	−0.921997			−0.0362474			−0.0181237	−	0.999836i	$-0.505769\pi$
$647$	−0.921997			−0.0362474			−0.0181237	+	0.999836i	$0.505769\pi$
$648$	−27.5575	−	2.76137i	−1.08256	−	0.108477i
$649$	36.9504			1.45043
$650$	0.396164	+	0.686177i	0.0155388	+	0.0269141i
$651$	−48.8995	−	51.4044i	−1.91652	−	2.01470i
$652$	−0.0571485	+	0.0989841i	−0.00223811	+	0.00387652i
$653$	2.23080	−	3.86387i	0.0872981	−	0.151205i	−0.819070	−	0.573694i	$-0.805510\pi$
$653$	2.23080	−	3.86387i	0.0872981	−	0.151205i	0.906368	+	0.422489i	$0.138843\pi$
$654$	5.02358	−	17.0351i	0.196438	−	0.666126i
$655$	20.9661	+	36.3143i	0.819213	+	1.41892i
$656$	−11.3690			−0.443885
$657$	−2.36385	+	47.2990i	−0.0922228	+	1.84531i
$658$	38.9370			1.51792
$659$	5.05884	+	8.76217i	0.197065	+	0.341326i	0.947575	−	0.319532i	$-0.103526\pi$
$659$	5.05884	+	8.76217i	0.197065	+	0.341326i	−0.750511	+	0.660858i	$0.770192\pi$
$660$	11.1666	−	2.69519i	0.434661	−	0.104910i
$661$	−24.9917	+	43.2869i	−0.972065	+	1.68367i	−0.282767	+	0.959189i	$0.591252\pi$
$661$	−24.9917	+	43.2869i	−0.972065	+	1.68367i	−0.689298	+	0.724478i	$0.742081\pi$
$662$	3.23610	−	5.60508i	0.125774	−	0.217848i
$663$	−3.63521	+	0.877399i	−0.141180	+	0.0340753i
$664$	−1.03540	−	1.79337i	−0.0401814	−	0.0695962i
$665$	−2.78130			−0.107854
$666$	23.7440	−	12.1708i	0.920063	−	0.471609i
$667$	10.6869			0.413800
$668$	−3.86090	−	6.68728i	−0.149383	−	0.258739i
$669$	3.06538	−	10.3948i	0.118515	−	0.401887i
$670$	1.97344	−	3.41811i	0.0762408	−	0.132053i
$671$	14.8137	−	25.6581i	0.571877	−	0.990519i
$672$	−18.7795	−	19.7415i	−0.724436	−	0.761545i
$673$	−14.2027	−	24.5998i	−0.547474	−	0.948252i	−0.998447	−	0.0557147i	$-0.982256\pi$
$673$	−14.2027	−	24.5998i	−0.547474	−	0.948252i	0.450973	−	0.892538i	$-0.351077\pi$
$674$	5.37452			0.207019
$675$	3.43558	+	1.20256i	0.132236	+	0.0462866i
$676$	−0.720682			−0.0277185
$677$	23.0900	+	39.9931i	0.887421	+	1.53706i	0.842913	+	0.538050i	$0.180839\pi$
$677$	23.0900	+	39.9931i	0.887421	+	1.53706i	0.0445081	+	0.999009i	$0.485828\pi$
$678$	17.8688	+	18.7841i	0.686247	+	0.721400i
$679$	18.1466	−	31.4308i	0.696401	−	1.20620i
$680$	−7.93155	+	13.7378i	−0.304161	+	0.526822i
$681$	3.54739	−	12.0293i	0.135936	−	0.460965i
$682$	−21.8410	−	37.8298i	−0.836336	−	1.44858i
$683$	6.42699			0.245922			0.122961	−	0.992412i	$-0.460761\pi$
$683$	6.42699			0.245922			0.122961	+	0.992412i	$0.460761\pi$
$684$	−0.517499	−	0.334287i	−0.0197871	−	0.0127818i
$685$	−1.82935			−0.0698957
$686$	6.27108	+	10.8618i	0.239431	+	0.414707i
$687$	3.82456	−	0.923100i	0.145916	−	0.0352184i
$688$	−2.87872	+	4.98608i	−0.109750	+	0.190093i
$689$	2.17362	−	3.76482i	0.0828083	−	0.143428i
$690$	16.3215	−	3.93937i	0.621348	−	0.149969i
$691$	17.1715	+	29.7418i	0.653233	+	1.13143i	0.982334	+	0.187138i	$0.0599211\pi$
$691$	17.1715	+	29.7418i	0.653233	+	1.13143i	−0.329101	+	0.944295i	$0.606746\pi$
$692$	7.32741			0.278546
$693$	−39.7074	−	25.6496i	−1.50836	−	0.974348i
$694$	−12.3642			−0.469340
$695$	−17.3606	−	30.0695i	−0.658527	−	1.14060i
$696$	4.48843	−	15.2204i	0.170133	−	0.576928i
$697$	−6.01845	+	10.4243i	−0.227965	+	0.394847i
$698$	−14.7644	+	25.5728i	−0.558842	+	0.967943i
$699$	−16.6790	−	17.5334i	−0.630857	−	0.663173i
$700$	1.03193	+	1.78735i	0.0390033	+	0.0675556i
$701$	9.36636			0.353763			0.176881	−	0.984232i	$-0.443399\pi$
$701$	9.36636			0.353763			0.176881	+	0.984232i	$0.443399\pi$
$702$	4.45515	−	3.83317i	0.168149	−	0.144674i
$703$	2.24064			0.0845074
$704$	−16.2480	−	28.1423i	−0.612369	−	1.06065i
$705$	−24.0014	−	25.2309i	−0.903945	−	0.950250i
$706$	−6.50094	+	11.2600i	−0.244666	+	0.423774i
$707$	−24.9107	+	43.1466i	−0.936864	+	1.62270i
$708$	−3.38476	+	11.4778i	−0.127207	+	0.431363i
$709$	−0.929096	−	1.60924i	−0.0348929	−	0.0604363i	0.848052	−	0.529914i	$-0.177776\pi$
$709$	−0.929096	−	1.60924i	−0.0348929	−	0.0604363i	−0.882945	+	0.469477i	$0.844442\pi$
$710$	23.7981			0.893127
$711$	26.2422	−	13.4513i	0.984160	−	0.504464i
$712$	10.0419			0.376334
$713$	17.9835	+	31.1484i	0.673489	+	1.16652i
$714$	16.8089	−	4.05701i	0.629056	−	0.151830i
$715$	−4.60133	+	7.96973i	−0.172080	+	0.298051i
$716$	2.28715	−	3.96146i	0.0854748	−	0.148047i
$717$	−44.6668	+	10.7808i	−1.66811	+	0.402618i
$718$	4.19794	+	7.27105i	0.156666	+	0.271353i
$719$	−39.6078			−1.47712			−0.738561	−	0.674186i	$-0.764494\pi$
$719$	−39.6078			−1.47712			−0.738561	+	0.674186i	$0.764494\pi$
$720$	0.729082	−	14.5884i	0.0271713	−	0.543678i
$721$	−52.0566			−1.93869
$722$	−10.6992	−	18.5316i	−0.398184	−	0.689676i
$723$	−1.96020	+	6.64710i	−0.0729006	+	0.247208i
$724$	−2.59560	+	4.49571i	−0.0964647	+	0.167082i
$725$	−1.04278	+	1.80615i	−0.0387278	+	0.0670786i
$726$	−5.20708	−	5.47381i	−0.193253	−	0.203152i
$727$	11.9312	+	20.6654i	0.442502	+	0.766436i	0.997874	−	0.0651657i	$-0.0207576\pi$
$727$	11.9312	+	20.6654i	0.442502	+	0.766436i	−0.555372	+	0.831602i	$0.687424\pi$
$728$	12.5802			0.466253
$729$	4.02965	−	26.6976i	0.149246	−	0.988800i
$730$	−42.6303			−1.57782
$731$	3.04784	+	5.27901i	0.112728	+	0.195251i
$732$	6.61314	+	6.95190i	0.244429	+	0.256950i
$733$	14.8302	−	25.6867i	0.547767	−	0.948760i	−0.450660	−	0.892695i	$-0.648811\pi$
$733$	14.8302	−	25.6867i	0.547767	−	0.948760i	0.998427	−	0.0560644i	$-0.0178552\pi$
$734$	−3.38840	+	5.86889i	−0.125068	+	0.216625i
$735$	11.3608	−	38.5247i	0.419048	−	1.42101i
$736$	6.90646	+	11.9623i	0.254575	+	0.440937i
$737$	5.63333			0.207506
$738$	0.944253	−	18.8938i	0.0347584	−	0.695491i
$739$	−5.87088			−0.215964			−0.107982	−	0.994153i	$-0.534439\pi$
$739$	−5.87088			−0.215964			−0.107982	+	0.994153i	$0.534439\pi$
$740$	−6.76506	−	11.7174i	−0.248689	−	0.430742i
$741$	0.479774	−	0.115799i	0.0176249	−	0.00425398i
$742$	−10.0506	+	17.4082i	−0.368970	+	0.639074i
$743$	4.54037	−	7.86414i	0.166570	−	0.288507i	−0.770642	−	0.637269i	$-0.780064\pi$
$743$	4.54037	−	7.86414i	0.166570	−	0.288507i	0.937212	+	0.348761i	$0.113398\pi$
$744$	51.9146	−	12.5302i	1.90328	−	0.459379i
$745$	−3.01359	−	5.21968i	−0.110409	−	0.191234i
$746$	−30.2196			−1.10642
$747$	1.79654	−	0.920874i	0.0657318	−	0.0336930i
$748$	−5.99741			−0.219287
$749$	−13.9708	−	24.1982i	−0.510483	−	0.884183i
$750$	5.68832	−	19.2893i	0.207708	−	0.704345i
$751$	27.0520	−	46.8555i	0.987142	−	1.70978i	0.355142	−	0.934812i	$-0.384433\pi$
$751$	27.0520	−	46.8555i	0.987142	−	1.70978i	0.632000	−	0.774968i	$-0.282234\pi$
$752$	−8.58606	+	14.8715i	−0.313101	+	0.542308i
$753$	4.72835	+	4.97056i	0.172311	+	0.181137i
$754$	1.68370	+	2.91626i	0.0613168	+	0.106204i
$755$	−14.8273			−0.539621
$756$	11.6048	−	9.98465i	0.422062	−	0.363138i
$757$	42.6779			1.55116			0.775578	−	0.631252i	$-0.217459\pi$
$757$	42.6779			1.55116			0.775578	+	0.631252i	$0.217459\pi$
$758$	−9.83696	−	17.0381i	−0.357294	−	0.618852i
$759$	16.5170	+	17.3631i	0.599529	+	0.630239i
$760$	1.04680	−	1.81312i	0.0379716	−	0.0657687i
$761$	0.955252	−	1.65454i	0.0346278	−	0.0599772i	−0.848192	−	0.529689i	$-0.822309\pi$
$761$	0.955252	−	1.65454i	0.0346278	−	0.0599772i	0.882820	+	0.469712i	$0.155642\pi$
$762$	−10.5003	+	35.6067i	−0.380384	+	1.28990i
$763$	18.5308	+	32.0962i	0.670858	+	1.16196i
$764$	−2.62005			−0.0947899
$765$	−12.9902	−	8.39122i	−0.469661	−	0.303385i
$766$	−39.1512			−1.41459
$767$	−4.79328	−	8.30221i	−0.173075	−	0.299775i
$768$	24.8864	−	6.00661i	0.898010	−	0.216745i
$769$	10.1790	−	17.6306i	0.367066	−	0.635777i	−0.622040	−	0.782986i	$-0.713696\pi$
$769$	10.1790	−	17.6306i	0.367066	−	0.635777i	0.989105	+	0.147209i	$0.0470290\pi$
$770$	21.2761	−	36.8513i	0.766738	−	1.32803i
$771$	−22.3023	+	5.38291i	−0.803198	+	0.193861i
$772$	1.40987	+	2.44197i	0.0507424	+	0.0878884i
$773$	−37.6497			−1.35417			−0.677083	−	0.735906i	$-0.736756\pi$
$773$	−37.6497			−1.35417			−0.677083	+	0.735906i	$0.736756\pi$
$774$	−8.04714	−	5.19818i	−0.289249	−	0.186845i
$775$	−7.01897			−0.252129
$776$	13.6597	+	23.6593i	0.490355	+	0.849319i
$777$	−15.7486	+	53.4041i	−0.564979	+	1.91586i
$778$	20.2146	−	35.0127i	0.724728	−	1.25527i
$779$	0.794314	−	1.37579i	0.0284592	−	0.0492929i
$780$	−2.05413	−	2.15935i	−0.0735496	−	0.0773172i
$781$	16.9833	+	29.4160i	0.607711	+	1.05259i
$782$	−8.76598			−0.313471
$783$	14.6013	+	5.11090i	0.521807	+	0.182649i
$784$	−19.8062			−0.707363
$785$	3.19764	+	5.53847i	0.114129	+	0.197677i
$786$	23.7141	+	24.9289i	0.845854	+	0.889183i
$787$	16.7913	−	29.0834i	0.598545	−	1.03671i	−0.394491	−	0.918900i	$-0.629079\pi$
$787$	16.7913	−	29.0834i	0.598545	−	1.03671i	0.993036	−	0.117810i	$-0.0375874\pi$
$788$	2.36627	−	4.09849i	0.0842947	−	0.146003i
$789$	2.59078	−	8.78541i	0.0922341	−	0.312769i
$790$	13.2725	+	22.9886i	0.472214	+	0.817899i
$791$	−54.1002			−1.92358
$792$	31.6656	−	16.2312i	1.12519	−	0.576752i
$793$	−7.68666			−0.272961
$794$	7.73276	+	13.3935i	0.274425	+	0.475319i
$795$	17.4757	−	4.21797i	0.619801	−	0.149596i
$796$	−0.704116	+	1.21957i	−0.0249567	+	0.0432263i
$797$	3.54428	−	6.13887i	0.125545	−	0.217450i	−0.796401	−	0.604769i	$-0.793265\pi$
$797$	3.54428	−	6.13887i	0.125545	−	0.217450i	0.921946	+	0.387319i	$0.126599\pi$
$798$	−2.21843	+	0.535444i	−0.0785316	+	0.0189545i
$799$	9.09048	+	15.7452i	0.321598	+	0.557024i
$800$	−2.69559			−0.0953035
$801$	−0.488647	+	9.77747i	−0.0172655	+	0.345470i
$802$	37.9885			1.34142
$803$	−30.4228	−	52.6938i	−1.07360	−	1.85952i
$804$	−0.516028	+	1.74987i	−0.0181989	+	0.0617131i
$805$	−17.5184	+	30.3428i	−0.617443	+	1.06944i
$806$	−5.66652	+	9.81471i	−0.199595	+	0.345708i
$807$	−9.56546	−	10.0554i	−0.336720	−	0.353968i
$808$	−18.7514	−	32.4783i	−0.659671	−	1.14258i
$809$	−9.32644			−0.327900			−0.163950	−	0.986469i	$-0.552424\pi$
$809$	−9.32644			−0.327900			−0.163950	+	0.986469i	$0.552424\pi$
$810$	24.1835	+	2.42328i	0.849722	+	0.0851455i
$811$	−11.0677			−0.388638			−0.194319	−	0.980938i	$-0.562250\pi$
$811$	−11.0677			−0.388638			−0.194319	+	0.980938i	$0.562250\pi$
$812$	4.38571	+	7.59627i	0.153908	+	0.266577i
$813$	−19.0814	−	20.0589i	−0.669216	−	0.703496i
$814$	−17.1402	+	29.6878i	−0.600765	+	1.04056i
$815$	0.189329	−	0.327928i	0.00663192	−	0.0114868i
$816$	−2.15703	+	7.31456i	−0.0755112	+	0.256061i
$817$	−0.402253	−	0.696722i	−0.0140730	−	0.0243752i
$818$	−3.31916			−0.116052
$819$	−0.612165	+	12.2490i	−0.0213908	+	0.428014i
$820$	−9.59293			−0.335000
$821$	14.6037	+	25.2943i	0.509672	+	0.882778i	0.999937	+	0.0112043i	$0.00356653\pi$
$821$	14.6037	+	25.2943i	0.509672	+	0.882778i	−0.490265	+	0.871573i	$0.663100\pi$
$822$	−1.45913	+	0.352177i	−0.0508929	+	0.0122836i
$823$	−6.01230	+	10.4136i	−0.209576	+	0.362996i	−0.951581	−	0.307398i	$-0.900542\pi$
$823$	−6.01230	+	10.4136i	−0.209576	+	0.362996i	0.742005	+	0.670394i	$0.233875\pi$
$824$	19.5926	−	33.9354i	0.682541	−	1.18220i
$825$	−4.54609	+	1.09725i	−0.158274	+	0.0382013i
$826$	22.1637	+	38.3887i	0.771174	+	1.33571i
$827$	19.0243			0.661540			0.330770	−	0.943711i	$-0.392692\pi$
$827$	19.0243			0.661540			0.330770	+	0.943711i	$0.392692\pi$
$828$	−6.90646	+	3.54013i	−0.240016	+	0.123028i
$829$	30.3433			1.05387			0.526934	−	0.849906i	$-0.323342\pi$
$829$	30.3433			1.05387			0.526934	+	0.849906i	$0.323342\pi$
$830$	0.908632	+	1.57380i	0.0315391	+	0.0546273i
$831$	−3.08219	+	10.4518i	−0.106920	+	0.362569i
$832$	−4.21544	+	7.30136i	−0.146144	+	0.253129i
$833$	−10.4849	+	18.1603i	−0.363279	+	0.629218i
$834$	−19.6361	−	20.6420i	−0.679942	−	0.714772i
$835$	12.7909	+	22.1545i	0.442648	+	0.766690i
$836$	0.791537			0.0273759
$837$	9.67407	+	51.1575i	0.334385	+	1.76826i
$838$	9.65175			0.333414
$839$	−3.01735	−	5.22621i	−0.104171	−	0.180429i	0.809228	−	0.587494i	$-0.199885\pi$
$839$	−3.01735	−	5.22621i	−0.104171	−	0.180429i	−0.913399	+	0.407065i	$0.866552\pi$
$840$	35.8568	+	37.6935i	1.23718	+	1.30055i
$841$	10.0682	−	17.4386i	0.347179	−	0.601331i
$842$	−12.3558	+	21.4008i	−0.425807	+	0.737520i
$843$	8.32103	−	28.2169i	0.286592	−	0.971842i
$844$	−7.28489	−	12.6178i	−0.250756	−	0.434323i
$845$	2.38757			0.0821351
$846$	−24.0014	−	15.5041i	−0.825185	−	0.533042i
$847$	15.7651			0.541697
$848$	−4.43256	−	7.67742i	−0.152215	−	0.263644i
$849$	−46.2565	+	11.1645i	−1.58752	+	0.383166i
$850$	0.855341	−	1.48149i	0.0293379	−	0.0508148i
$851$	14.1130	−	24.4444i	0.483787	−	0.837944i
$852$	−10.6931	+	2.58091i	−0.366341	+	0.0884205i
$853$	11.8596	+	20.5414i	0.406065	+	0.703325i	0.994445	−	0.105260i	$-0.0335674\pi$
$853$	11.8596	+	20.5414i	0.406065	+	0.703325i	−0.588380	+	0.808585i	$0.700234\pi$
$854$	35.5424			1.21624
$855$	1.71444	+	1.10747i	0.0586327	+	0.0378747i
$856$	21.0329			0.718890
$857$	14.7407	+	25.5317i	0.503533	+	0.872145i	0.999992	+	0.00408483i	$0.00130025\pi$
$857$	14.7407	+	25.5317i	0.503533	+	0.872145i	−0.496458	+	0.868061i	$0.665366\pi$
$858$	−2.13583	+	7.24267i	−0.0729160	+	0.247261i
$859$	14.2969	−	24.7630i	0.487805	−	0.844903i	−0.512097	−	0.858928i	$-0.671131\pi$
$859$	14.2969	−	24.7630i	0.487805	−	0.844903i	0.999902	+	0.0140250i	$0.00446444\pi$
$860$	−2.42900	+	4.20716i	−0.0828284	+	0.143463i
$861$	27.2081	+	28.6018i	0.927249	+	0.974747i
$862$	19.8859	+	34.4434i	0.677317	+	1.17315i
$863$	48.3938			1.64734			0.823672	−	0.567066i	$-0.191922\pi$
$863$	48.3938			1.64734			0.823672	+	0.567066i	$0.191922\pi$
$864$	3.71526	+	19.6467i	0.126396	+	0.668395i
$865$	−24.2753			−0.825384
$866$	14.1062	+	24.4326i	0.479348	+	0.830255i
$867$	−14.7295	−	15.4840i	−0.500241	−	0.525865i
$868$	−14.7602	+	25.5654i	−0.500993	+	0.867745i
$869$	−18.9436	+	32.8113i	−0.642618	+	1.11305i
$870$	−3.93889	+	13.3569i	−0.133541	+	0.452841i
$871$	−0.730767	−	1.26572i	−0.0247611	−	0.0428875i
$872$	−27.8978			−0.944739
$873$	−23.7011	+	12.1488i	−0.802160	+	0.411174i
$874$	1.15693			0.0391338
$875$	20.9828	+	36.3433i	0.709349	+	1.22863i
$876$	19.1550	−	4.62327i	0.647186	−	0.156206i
$877$	13.2759	−	22.9945i	0.448294	−	0.776468i	−0.549981	−	0.835177i	$-0.685365\pi$
$877$	13.2759	−	22.9945i	0.448294	−	0.776468i	0.998275	+	0.0587091i	$0.0186984\pi$
$878$	7.64991	−	13.2500i	0.258172	−	0.447167i
$879$	46.9157	−	11.3236i	1.58243	−	0.381937i
$880$	9.38327	+	16.2523i	0.316310	+	0.547865i
$881$	−14.6581			−0.493843			−0.246921	−	0.969036i	$-0.579419\pi$
$881$	−14.6581			−0.493843			−0.246921	+	0.969036i	$0.579419\pi$
$882$	1.64500	−	32.9153i	0.0553902	−	1.10832i
$883$	−37.2159			−1.25241			−0.626207	−	0.779657i	$-0.715394\pi$
$883$	−37.2159			−1.25241			−0.626207	+	0.779657i	$0.715394\pi$
$884$	0.777996	+	1.34753i	0.0261668	+	0.0453223i
$885$	11.2135	−	38.0253i	0.376937	−	1.27821i
$886$	18.9214	−	32.7729i	0.635677	−	1.10103i
$887$	1.31165	−	2.27184i	0.0440408	−	0.0762809i	−0.843165	−	0.537655i	$-0.819310\pi$
$887$	1.31165	−	2.27184i	0.0440408	−	0.0762809i	0.887206	+	0.461374i	$0.152644\pi$
$888$	−28.8865	−	30.3662i	−0.969368	−	1.01902i
$889$	−38.7329	−	67.0873i	−1.29906	−	2.25004i
$890$	−8.81238			−0.295392
$891$	14.2630	+	31.6217i	0.477829	+	1.05937i
$892$	−4.50928			−0.150982
$893$	−1.19976	−	2.07804i	−0.0401484	−	0.0695391i
$894$	−3.40858	−	3.58318i	−0.114000	−	0.119839i
$895$	−7.57719	+	13.1241i	−0.253277	+	0.438689i
$896$	3.76078	−	6.51387i	0.125639	−	0.217613i
$897$	1.75861	−	5.96349i	0.0587182	−	0.199115i
$898$	−4.32066	−	7.48360i	−0.144182	−	0.249731i
$899$	−29.8307			−0.994910
$900$	0.0755976	−	1.51265i	0.00251992	−	0.0504218i
$901$	−9.38593			−0.312691
$902$	12.1525	+	21.0488i	0.404635	+	0.700848i
$903$	19.4332	−	4.69041i	0.646695	−	0.156087i
$904$	20.3618	−	35.2677i	0.677223	−	1.17299i
$905$	8.59906	−	14.8940i	0.285842	−	0.495094i
$906$	−11.8266	+	2.85449i	−0.392913	+	0.0948340i
$907$	17.7295	+	30.7084i	0.588698	+	1.01965i	0.994403	+	0.105650i	$0.0336925\pi$
$907$	17.7295	+	30.7084i	0.588698	+	1.01965i	−0.405706	+	0.914004i	$0.632974\pi$
$908$	−5.21834			−0.173177
$909$	32.5357	−	16.6773i	1.07914	−	0.553150i
$910$	−11.0399			−0.365970
$911$	27.4104	+	47.4762i	0.908147	+	1.57296i	0.816637	+	0.577152i	$0.195836\pi$
$911$	27.4104	+	47.4762i	0.908147	+	1.57296i	0.0915103	+	0.995804i	$0.470831\pi$
$912$	0.284684	−	0.965374i	0.00942684	−	0.0319667i
$913$	−1.29688	+	2.24625i	−0.0429203	+	0.0743401i
$914$	7.99173	−	13.8421i	0.264343	−	0.457856i
$915$	−21.9089	−	23.0312i	−0.724287	−	0.761389i
$916$	−0.818520	−	1.41772i	−0.0270447	−	0.0468427i
$917$	−71.7977			−2.37097
$918$	−11.9767	−	4.19222i	−0.395290	−	0.138364i
$919$	23.5096			0.775511			0.387755	−	0.921762i	$-0.373251\pi$
$919$	23.5096			0.775511			0.387755	+	0.921762i	$0.373251\pi$
$920$	−13.1869	−	22.8403i	−0.434758	−	0.753023i
$921$	18.3461	+	19.2859i	0.604524	+	0.635491i
$922$	−2.61740	+	4.53347i	−0.0861995	+	0.149302i
$923$	4.40622	−	7.63179i	0.145032	−	0.251204i
$924$	−5.56341	+	18.8657i	−0.183023	+	0.620636i
$925$	2.75415	+	4.77033i	0.0905558	+	0.156847i
$926$	−20.2308			−0.664826
$927$	32.0886	+	20.7281i	1.05393	+	0.680801i
$928$	−11.4563			−0.376071
$929$	17.7694	+	30.7775i	0.582994	+	1.00978i	0.995122	+	0.0986498i	$0.0314524\pi$
$929$	17.7694	+	30.7775i	0.582994	+	1.00978i	−0.412128	+	0.911126i	$0.635214\pi$
$930$	−45.5585	+	10.9960i	−1.49392	+	0.360575i
$931$	1.38379	−	2.39680i	0.0453519	−	0.0785518i
$932$	−5.03450	+	8.72001i	−0.164911	+	0.285634i
$933$	18.9832	−	4.58181i	0.621482	−	0.150002i
$934$	−9.40806	−	16.2952i	−0.307841	−	0.533196i
$935$	19.8690			0.649787
$936$	−7.75464	−	5.00923i	−0.253468	−	0.163732i
$937$	29.5466			0.965246			0.482623	−	0.875828i	$-0.339684\pi$
$937$	29.5466			0.965246			0.482623	+	0.875828i	$0.339684\pi$
$938$	3.37900	+	5.85260i	0.110328	+	0.191094i
$939$	−5.30096	+	17.9757i	−0.172990	+	0.586616i
$940$	−7.24475	+	12.5483i	−0.236298	+	0.409280i
$941$	2.48107	−	4.29734i	0.0808806	−	0.140089i	−0.822748	−	0.568407i	$-0.807560\pi$
$941$	2.48107	−	4.29734i	0.0808806	−	0.140089i	0.903628	+	0.428317i	$0.140893\pi$
$942$	3.61675	+	3.80202i	0.117840	+	0.123876i
$943$	−10.0062	−	17.3312i	−0.325846	−	0.564382i
$944$	−19.5494			−0.636280
$945$	−38.4459	+	33.0785i	−1.25065	+	1.07604i
$946$	12.3084			0.400182
$947$	−12.9736	−	22.4710i	−0.421587	−	0.730209i	0.574508	−	0.818499i	$-0.305193\pi$
$947$	−12.9736	−	22.4710i	−0.421587	−	0.730209i	−0.996095	+	0.0882894i	$0.971860\pi$
$948$	−8.45682	−	8.89002i	−0.274665	−	0.288734i
$949$	−7.89300	+	13.6711i	−0.256218	+	0.443782i
$950$	−0.112888	+	0.195527i	−0.00366256	+	0.00634374i
$951$	−8.05751	+	27.3233i	−0.261283	+	0.886019i
$952$	−13.5807	−	23.5224i	−0.440152	−	0.762365i
$953$	17.5273			0.567765			0.283883	−	0.958859i	$-0.408377\pi$
$953$	17.5273			0.567765			0.283883	+	0.958859i	$0.408377\pi$
$954$	13.1270	−	6.72870i	0.425003	−	0.217850i
$955$	8.68005			0.280880
$956$	9.55946	+	16.5575i	0.309175	+	0.535507i
$957$	−19.3209	+	4.66332i	−0.624557	+	0.150744i
$958$	21.3062	−	36.9035i	0.688373	−	1.19230i
$959$	1.56613	−	2.71262i	0.0505731	−	0.0875952i
$960$	−33.8919	+	8.18019i	−1.09386	+	0.264014i
$961$	−34.6978	−	60.0984i	−1.11928	−	1.93866i
$962$	8.89387			0.286750
$963$	−1.02348	+	20.4792i	−0.0329813	+	0.659931i
$964$	2.88352			0.0928719
$965$	−4.67082	−	8.09009i	−0.150359	−	0.260429i
$966$	−8.13164	+	27.5747i	−0.261631	+	0.887200i
$967$	−18.8264	+	32.6083i	−0.605417	+	1.04861i	0.386569	+	0.922261i	$0.373660\pi$
$967$	−18.8264	+	32.6083i	−0.605417	+	1.04861i	−0.991985	+	0.126352i	$0.959673\pi$
$968$	−5.93355	+	10.2772i	−0.190712	+	0.330322i
$969$	−0.734450	−	0.772072i	−0.0235939	−	0.0248025i
$970$	−11.9873	−	20.7626i	−0.384888	−	0.666646i
$971$	4.27036			0.137042			0.0685211	−	0.997650i	$-0.478172\pi$
$971$	4.27036			0.137042			0.0685211	+	0.997650i	$0.478172\pi$
$972$	−11.1291	+	1.53386i	−0.356967	+	0.0491986i
$973$	59.4510			1.90591
$974$	−19.3632	−	33.5381i	−0.620438	−	1.07463i
$975$	0.836263	+	0.879101i	0.0267819	+	0.0281538i
$976$	−7.83752	+	13.5750i	−0.250873	+	0.434525i
$977$	−2.12998	+	3.68923i	−0.0681440	+	0.118029i	−0.898084	−	0.439823i	$-0.855041\pi$
$977$	−2.12998	+	3.68923i	−0.0681440	+	0.118029i	0.829940	+	0.557852i	$0.188374\pi$
$978$	0.0878823	−	0.298012i	0.00281017	−	0.00952937i
$979$	−6.28888	−	10.8927i	−0.200993	−	0.348131i
$980$	−16.7121			−0.533847
$981$	1.35754	−	27.1633i	0.0433428	−	0.867257i
$982$	−33.8360			−1.07975
$983$	0.558030	+	0.966536i	0.0177984	+	0.0308277i	0.874787	−	0.484507i	$-0.161001\pi$
$983$	0.558030	+	0.966536i	0.0177984	+	0.0308277i	−0.856989	+	0.515335i	$0.827668\pi$
$984$	−28.8857	+	6.97190i	−0.920843	+	0.222256i
$985$	−7.83929	+	13.5780i	−0.249781	+	0.432633i
$986$	3.63521	−	6.29637i	0.115769	−	0.200517i
$987$	57.9613	−	13.9896i	1.84493	−	0.445295i
$988$	−0.102680	−	0.177847i	−0.00326668	−	0.00565805i
$989$	−10.1346			−0.322261
$990$	−27.7886	+	14.2440i	−0.883179	+	0.452703i
$991$	−25.3057			−0.803862			−0.401931	−	0.915670i	$-0.631661\pi$
$991$	−25.3057			−0.803862			−0.401931	+	0.915670i	$0.631661\pi$
$992$	−19.2781	−	33.3907i	−0.612081	−	1.06016i
$993$	2.80339	−	9.50638i	0.0889628	−	0.301676i
$994$	−20.3740	+	35.2887i	−0.646223	+	1.11929i
$995$	2.33269	−	4.04034i	0.0739514	−	0.128088i
$996$	−0.578952	−	0.608609i	−0.0183448	−	0.0192845i
$997$	−8.32092	−	14.4123i	−0.263526	−	0.456441i	0.703650	−	0.710546i	$-0.251552\pi$
$997$	−8.32092	−	14.4123i	−0.263526	−	0.456441i	−0.967176	+	0.254106i	$0.918219\pi$
$998$	23.7053			0.750378
$999$	30.9724	−	26.6483i	0.979923	−	0.843116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.e.b.40.4	✓	10
3.2	odd	2		351.2.e.b.118.2		10
9.2	odd	6		351.2.e.b.235.2		10
9.4	even	3		1053.2.a.k.1.2		5
9.5	odd	6		1053.2.a.j.1.4		5
9.7	even	3	inner	117.2.e.b.79.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.b.40.4	✓	10	1.1	even	1	trivial
117.2.e.b.79.4	yes	10	9.7	even	3	inner
351.2.e.b.118.2		10	3.2	odd	2
351.2.e.b.235.2		10	9.2	odd	6
1053.2.a.j.1.4		5	9.5	odd	6
1053.2.a.k.1.2		5	9.4	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.565535 + 0.979535i) q^{2} +(1.19379 + 1.25494i) q^{3} +(0.360341 - 0.624129i) q^{4} +(-1.19379 + 2.06770i) q^{5} +(-0.554128 + 1.87907i) q^{6} +(-2.04404 - 3.54039i) q^{7} +3.07728 q^{8} +(-0.149744 + 2.99626i) q^{9} -2.70051 q^{10} +(-1.92720 - 3.33800i) q^{11} +(1.21341 - 0.292871i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(2.31196 - 4.00442i) q^{14} +(-4.01997 + 0.970264i) q^{15} +(1.01963 + 1.76605i) q^{16} +2.15906 q^{17} +(-3.01963 + 1.54781i) q^{18} -0.284952 q^{19} +(0.860341 + 1.49015i) q^{20} +(2.00282 - 6.79162i) q^{21} +(2.17979 - 3.77551i) q^{22} +(-1.79481 + 3.10870i) q^{23} +(3.67362 + 3.86180i) q^{24} +(-0.350256 - 0.606662i) q^{25} -1.13107 q^{26} +(-3.93889 + 3.38898i) q^{27} -2.94621 q^{28} +(-1.48859 - 2.57832i) q^{29} +(-3.22384 - 3.38898i) q^{30} +(5.00988 - 8.67737i) q^{31} +(1.92401 - 3.33249i) q^{32} +(1.88833 - 6.40338i) q^{33} +(1.22102 + 2.11487i) q^{34} +9.76061 q^{35} +(1.81609 + 1.17313i) q^{36} -7.86324 q^{37} +(-0.161150 - 0.279120i) q^{38} +(-1.68370 + 0.406381i) q^{39} +(-3.67362 + 6.36289i) q^{40} +(-2.78754 + 4.82816i) q^{41} +(7.78529 - 1.87907i) q^{42} +(1.41165 + 2.44505i) q^{43} -2.77779 q^{44} +(-6.01661 - 3.88652i) q^{45} -4.06010 q^{46} +(4.21039 + 7.29262i) q^{47} +(-0.999062 + 3.38785i) q^{48} +(-4.85623 + 8.41124i) q^{49} +(0.396164 - 0.686177i) q^{50} +(2.57745 + 2.70948i) q^{51} +(0.360341 + 0.624129i) q^{52} -4.34724 q^{53} +(-5.54720 - 1.94169i) q^{54} +9.20266 q^{55} +(-6.29010 - 10.8948i) q^{56} +(-0.340172 - 0.357597i) q^{57} +(1.68370 - 2.91626i) q^{58} +(-4.79328 + 8.30221i) q^{59} +(-0.842989 + 2.85860i) q^{60} +(3.84333 + 6.65684i) q^{61} +11.3330 q^{62} +(10.9140 - 5.59434i) q^{63} +8.43089 q^{64} +(-1.19379 - 2.06770i) q^{65} +(7.34025 - 1.77165i) q^{66} +(-0.730767 + 1.26572i) q^{67} +(0.777996 - 1.34753i) q^{68} +(-6.04384 + 1.45875i) q^{69} +(5.51997 + 9.56086i) q^{70} -8.81244 q^{71} +(-0.460803 + 9.22033i) q^{72} +15.7860 q^{73} +(-4.44693 - 7.70231i) q^{74} +(0.343192 - 1.16378i) q^{75} +(-0.102680 + 0.177847i) q^{76} +(-7.87855 + 13.6461i) q^{77} +(-1.35026 - 1.41942i) q^{78} +(-4.91481 - 8.51270i) q^{79} -4.86887 q^{80} +(-8.95515 - 0.897342i) q^{81} -6.30580 q^{82} +(-0.336467 - 0.582777i) q^{83} +(-3.51715 - 3.69731i) q^{84} +(-2.57745 + 4.46428i) q^{85} +(-1.59668 + 2.76553i) q^{86} +(1.45857 - 4.94606i) q^{87} +(-5.93053 - 10.2720i) q^{88} +3.26322 q^{89} +(0.404385 - 8.09144i) q^{90} +4.08809 q^{91} +(1.29348 + 2.24038i) q^{92} +(16.8703 - 4.07184i) q^{93} +(-4.76225 + 8.24846i) q^{94} +(0.340172 - 0.589195i) q^{95} +(6.47893 - 1.56376i) q^{96} +(4.43889 + 7.68838i) q^{97} -10.9855 q^{98} +(10.2901 - 5.27454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} + 13 q^{6} + 2 q^{7} + 24 q^{8} - 13 q^{9} - 4 q^{10} - 11 q^{11} - 19 q^{12} - 5 q^{13} + 5 q^{14} - 10 q^{15} - 10 q^{16} + 14 q^{17} - 10 q^{18} + 6 q^{19}+ \cdots + 17 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 + 13 * q^6 + 2 * q^7 + 24 * q^8 - 13 * q^9 - 4 * q^10 - 11 * q^11 - 19 * q^12 - 5 * q^13 + 5 * q^14 - 10 * q^15 - 10 * q^16 + 14 * q^17 - 10 * q^18 + 6 * q^19 + q^20 + 8 * q^21 + 7 * q^22 - 18 * q^23 + 18 * q^24 + 8 * q^25 + 4 * q^26 - 11 * q^27 - 38 * q^28 - 4 * q^29 + 5 * q^30 + 16 * q^31 - 31 * q^32 + 19 * q^33 - 13 * q^34 + 22 * q^35 - 5 * q^36 + 10 * q^37 - 24 * q^38 - 2 * q^39 - 18 * q^40 - 12 * q^41 + 59 * q^42 + 2 * q^44 - 14 * q^45 + 12 * q^46 - 15 * q^47 + 29 * q^48 - 3 * q^49 + 5 * q^50 - 7 * q^51 - 4 * q^52 - 6 * q^53 - 11 * q^54 - 34 * q^55 + 24 * q^56 + 12 * q^57 + 2 * q^58 - 3 * q^59 + 19 * q^60 + q^61 - 8 * q^62 - 14 * q^63 + 124 * q^64 - q^65 - 11 * q^66 + 4 * q^67 + 16 * q^68 + 25 * q^70 + 30 * q^71 - 66 * q^72 - 10 * q^73 - 11 * q^74 + 14 * q^75 - 9 * q^76 - q^77 - 2 * q^78 - 13 * q^79 + 64 * q^80 - 25 * q^81 - 42 * q^82 - 26 * q^83 - 17 * q^84 + 7 * q^85 + 6 * q^86 - 13 * q^87 - 3 * q^88 + 58 * q^89 - 26 * q^90 - 4 * q^91 + 6 * q^92 + 58 * q^93 - 12 * q^94 - 12 * q^95 - 67 * q^96 + 16 * q^97 - 78 * q^98 + 17 * q^99

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