LMFDB - Embedded newform 966.2.l.d.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.20460 + 1.24456i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.662008 - 1.14663i) q^{5} +(1.66550 - 0.475517i) q^{6} +(2.07946 + 1.63580i) q^{7} -1.00000i q^{8} +(-0.0978548 - 2.99840i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.20460 + 1.24456i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.662008 - 1.14663i) q^{5} +(1.66550 - 0.475517i) q^{6} +(2.07946 + 1.63580i) q^{7} -1.00000i q^{8} +(-0.0978548 - 2.99840i) q^{9} +(-1.14663 + 0.662008i) q^{10} +(-5.14427 + 2.97005i) q^{11} +(-1.68012 - 0.420939i) q^{12} -0.431364i q^{13} +(-0.982969 - 2.45637i) q^{14} +(0.629593 + 2.20515i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.767229 + 1.32888i) q^{17} +(-1.41446 + 2.64562i) q^{18} +(2.99058 + 1.72661i) q^{19} +1.32402 q^{20} +(-4.54078 + 0.617525i) q^{21} +5.94009 q^{22} +(-0.866025 - 0.500000i) q^{23} +(1.24456 + 1.20460i) q^{24} +(1.62349 + 2.81197i) q^{25} +(-0.215682 + 0.373572i) q^{26} +(3.84957 + 3.49011i) q^{27} +(-0.376911 + 2.61877i) q^{28} -4.54331i q^{29} +(0.557330 - 2.22451i) q^{30} +(-6.56402 + 3.78974i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.50042 - 9.98008i) q^{33} -1.53446i q^{34} +(3.25228 - 1.30147i) q^{35} +(2.54777 - 1.58395i) q^{36} +(1.58338 - 2.74249i) q^{37} +(-1.72661 - 2.99058i) q^{38} +(0.536858 + 0.519623i) q^{39} +(-1.14663 - 0.662008i) q^{40} -0.950042 q^{41} +(4.24119 + 1.73560i) q^{42} -6.81513 q^{43} +(-5.14427 - 2.97005i) q^{44} +(-3.50284 - 1.87276i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-2.43049 + 4.20973i) q^{47} +(-0.475517 - 1.66550i) q^{48} +(1.64833 + 6.80316i) q^{49} -3.24698i q^{50} +(-2.57808 - 0.645913i) q^{51} +(0.373572 - 0.215682i) q^{52} +(-2.00861 + 1.15967i) q^{53} +(-1.58877 - 4.94730i) q^{54} +7.86478i q^{55} +(1.63580 - 2.07946i) q^{56} +(-5.75133 + 1.64207i) q^{57} +(-2.27166 + 3.93462i) q^{58} +(-1.84910 - 3.20274i) q^{59} +(-1.59492 + 1.64782i) q^{60} +(6.47975 + 3.74108i) q^{61} +7.57947 q^{62} +(4.70130 - 6.39514i) q^{63} -1.00000 q^{64} +(-0.494615 - 0.285566i) q^{65} +(-7.15547 + 7.39280i) q^{66} +(4.35534 + 7.54367i) q^{67} +(-0.767229 + 1.32888i) q^{68} +(1.66550 - 0.475517i) q^{69} +(-3.46729 - 0.499036i) q^{70} +13.2414i q^{71} +(-2.99840 + 0.0978548i) q^{72} +(-11.1193 + 6.41976i) q^{73} +(-2.74249 + 1.58338i) q^{74} +(-5.45533 - 1.36678i) q^{75} +3.45322i q^{76} +(-15.5557 - 2.23889i) q^{77} +(-0.205121 - 0.718436i) q^{78} +(-6.48480 + 11.2320i) q^{79} +(0.662008 + 1.14663i) q^{80} +(-8.98085 + 0.586816i) q^{81} +(0.822761 + 0.475021i) q^{82} -3.35408 q^{83} +(-2.80518 - 3.62367i) q^{84} +2.03165 q^{85} +(5.90208 + 3.40757i) q^{86} +(5.65442 + 5.47290i) q^{87} +(2.97005 + 5.14427i) q^{88} +(-8.29910 + 14.3745i) q^{89} +(2.09717 + 3.37328i) q^{90} +(0.705624 - 0.897005i) q^{91} -1.00000i q^{92} +(3.19049 - 12.7344i) q^{93} +(4.20973 - 2.43049i) q^{94} +(3.95957 - 2.28606i) q^{95} +(-0.420939 + 1.68012i) q^{96} -10.3531i q^{97} +(1.97408 - 6.71588i) q^{98} +(9.40879 + 15.1340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.20460	+	1.24456i	−0.695479	+	0.718547i
$3$	−1.20460	+	1.24456i	−0.695479	+	0.718547i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.662008	−	1.14663i	0.296059	−	0.512789i	−0.679172	−	0.733979i	$-0.737661\pi$
$5$	0.662008	−	1.14663i	0.296059	−	0.512789i	0.975231	+	0.221190i	$0.0709942\pi$
$6$	1.66550	−	0.475517i	0.679937	−	0.194129i
$7$	2.07946	+	1.63580i	0.785963	+	0.618273i
$7$	2.07946	+	1.63580i	0.785963	+	0.618273i
$8$		−	1.00000i		−	0.353553i
$9$	−0.0978548	−	2.99840i	−0.0326183	−	0.999468i
$10$	−1.14663	+	0.662008i	−0.362597	+	0.209345i
$11$	−5.14427	+	2.97005i	−1.55106	+	0.895503i	−0.553000	+	0.833181i	$0.686517\pi$
$11$	−5.14427	+	2.97005i	−1.55106	+	0.895503i	−0.998056	+	0.0623219i	$0.980149\pi$
$12$	−1.68012	−	0.420939i	−0.485009	−	0.121515i
$13$		−	0.431364i		−	0.119639i	−0.998209	−	0.0598194i	$-0.980948\pi$
$13$		−	0.431364i		−	0.119639i	0.998209	−	0.0598194i	$-0.0190525\pi$
$14$	−0.982969	−	2.45637i	−0.262709	−	0.656494i
$15$	0.629593	+	2.20515i	0.162560	+	0.569366i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.767229	+	1.32888i	0.186080	+	0.322301i	0.943940	−	0.330117i	$-0.107088\pi$
$17$	0.767229	+	1.32888i	0.186080	+	0.322301i	−0.757860	+	0.652418i	$0.773755\pi$
$18$	−1.41446	+	2.64562i	−0.333391	+	0.623579i
$19$	2.99058	+	1.72661i	0.686085	+	0.396111i	0.802144	−	0.597131i	$-0.203693\pi$
$19$	2.99058	+	1.72661i	0.686085	+	0.396111i	−0.116059	+	0.993242i	$0.537026\pi$
$20$	1.32402			0.296059
$21$	−4.54078	+	0.617525i	−0.990879	+	0.134755i
$22$	5.94009			1.26643
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	1.24456	+	1.20460i	0.254045	+	0.245889i
$25$	1.62349	+	2.81197i	0.324698	+	0.562394i
$26$	−0.215682	+	0.373572i	−0.0422987	+	0.0732635i
$27$	3.84957	+	3.49011i	0.740849	+	0.671671i
$28$	−0.376911	+	2.61877i	−0.0712295	+	0.494900i
$29$		−	4.54331i		−	0.843672i	−0.906672	−	0.421836i	$-0.861386\pi$
$29$		−	4.54331i		−	0.843672i	0.906672	−	0.421836i	$-0.138614\pi$
$30$	0.557330	−	2.22451i	0.101754	−	0.406138i
$31$	−6.56402	+	3.78974i	−1.17893	+	0.680657i	−0.955767	−	0.294124i	$-0.904972\pi$
$31$	−6.56402	+	3.78974i	−1.17893	+	0.680657i	−0.223165	+	0.974781i	$0.571639\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.50042	−	9.98008i	0.435267	−	1.73731i
$34$		−	1.53446i		−	0.263157i
$35$	3.25228	−	1.30147i	0.549735	−	0.219988i
$36$	2.54777	−	1.58395i	0.424628	−	0.263991i
$37$	1.58338	−	2.74249i	0.260306	−	0.450863i	−0.706017	−	0.708195i	$-0.749510\pi$
$37$	1.58338	−	2.74249i	0.260306	−	0.450863i	0.966323	+	0.257332i	$0.0828432\pi$
$38$	−1.72661	−	2.99058i	−0.280093	−	0.485135i
$39$	0.536858	+	0.519623i	0.0859661	+	0.0832063i
$40$	−1.14663	−	0.662008i	−0.181298	−	0.104673i
$41$	−0.950042			−0.148372			−0.0741859	−	0.997244i	$-0.523636\pi$
$41$	−0.950042			−0.148372			−0.0741859	+	0.997244i	$0.523636\pi$
$42$	4.24119	+	1.73560i	0.654430	+	0.267808i
$43$	−6.81513			−1.03930			−0.519649	−	0.854380i	$-0.673937\pi$
$43$	−6.81513			−1.03930			−0.519649	+	0.854380i	$0.673937\pi$
$44$	−5.14427	−	2.97005i	−0.775528	−	0.447751i
$45$	−3.50284	−	1.87276i	−0.522173	−	0.279175i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−2.43049	+	4.20973i	−0.354523	+	0.614052i	−0.987036	−	0.160497i	$-0.948690\pi$
$47$	−2.43049	+	4.20973i	−0.354523	+	0.614052i	0.632513	+	0.774550i	$0.282023\pi$
$48$	−0.475517	−	1.66550i	−0.0686350	−	0.240394i
$49$	1.64833	+	6.80316i	0.235476	+	0.971880i
$50$		−	3.24698i		−	0.459193i
$51$	−2.57808	−	0.645913i	−0.361003	−	0.0904459i
$52$	0.373572	−	0.215682i	0.0518051	−	0.0299097i
$53$	−2.00861	+	1.15967i	−0.275904	+	0.159293i	−0.631568	−	0.775321i	$-0.717588\pi$
$53$	−2.00861	+	1.15967i	−0.275904	+	0.159293i	0.355664	+	0.934614i	$0.384255\pi$
$54$	−1.58877	−	4.94730i	−0.216204	−	0.673243i
$55$			7.86478i			1.06049i
$56$	1.63580	−	2.07946i	0.218593	−	0.277880i
$57$	−5.75133	+	1.64207i	−0.761782	+	0.217497i
$58$	−2.27166	+	3.93462i	−0.298283	+	0.516642i
$59$	−1.84910	−	3.20274i	−0.240733	−	0.416961i	0.720190	−	0.693776i	$-0.244054\pi$
$59$	−1.84910	−	3.20274i	−0.240733	−	0.416961i	−0.960923	+	0.276815i	$0.910721\pi$
$60$	−1.59492	+	1.64782i	−0.205903	+	0.212732i
$61$	6.47975	+	3.74108i	0.829647	+	0.478997i	0.853732	−	0.520713i	$-0.174334\pi$
$61$	6.47975	+	3.74108i	0.829647	+	0.478997i	−0.0240850	+	0.999710i	$0.507667\pi$
$62$	7.57947			0.962594
$63$	4.70130	−	6.39514i	0.592308	−	0.805712i
$64$	−1.00000			−0.125000
$65$	−0.494615	−	0.285566i	−0.0613495	−	0.0354201i
$66$	−7.15547	+	7.39280i	−0.880777	+	0.909991i
$67$	4.35534	+	7.54367i	0.532089	+	0.921606i	0.999298	+	0.0374589i	$0.0119263\pi$
$67$	4.35534	+	7.54367i	0.532089	+	0.921606i	−0.467209	+	0.884147i	$0.654740\pi$
$68$	−0.767229	+	1.32888i	−0.0930402	+	0.161150i
$69$	1.66550	−	0.475517i	0.200502	−	0.0572456i
$70$	−3.46729	−	0.499036i	−0.414420	−	0.0596462i
$71$			13.2414i			1.57147i	0.618566	+	0.785733i	$0.287714\pi$
$71$			13.2414i			1.57147i	−0.618566	+	0.785733i	$0.712286\pi$
$72$	−2.99840	+	0.0978548i	−0.353365	+	0.0115323i
$73$	−11.1193	+	6.41976i	−1.30142	+	0.751376i	−0.980648	−	0.195780i	$-0.937276\pi$
$73$	−11.1193	+	6.41976i	−1.30142	+	0.751376i	−0.320773	+	0.947156i	$0.603943\pi$
$74$	−2.74249	+	1.58338i	−0.318808	+	0.184064i
$75$	−5.45533	−	1.36678i	−0.629927	−	0.157822i
$76$			3.45322i			0.396111i
$77$	−15.5557	−	2.23889i	−1.77274	−	0.255145i
$78$	−0.205121	−	0.718436i	−0.0232254	−	0.0813468i
$79$	−6.48480	+	11.2320i	−0.729597	+	1.26370i	0.227457	+	0.973788i	$0.426959\pi$
$79$	−6.48480	+	11.2320i	−0.729597	+	1.26370i	−0.957054	+	0.289911i	$0.906374\pi$
$80$	0.662008	+	1.14663i	0.0740147	+	0.128197i
$81$	−8.98085	+	0.586816i	−0.997872	+	0.0652018i
$82$	0.822761	+	0.475021i	0.0908587	+	0.0524573i
$83$	−3.35408			−0.368158			−0.184079	−	0.982911i	$-0.558930\pi$
$83$	−3.35408			−0.368158			−0.184079	+	0.982911i	$0.558930\pi$
$84$	−2.80518	−	3.62367i	−0.306070	−	0.395374i
$85$	2.03165			0.220363
$86$	5.90208	+	3.40757i	0.636438	+	0.367447i
$87$	5.65442	+	5.47290i	0.606218	+	0.586756i
$88$	2.97005	+	5.14427i	0.316608	+	0.548381i
$89$	−8.29910	+	14.3745i	−0.879703	+	1.52369i	−0.0280365	+	0.999607i	$0.508925\pi$
$89$	−8.29910	+	14.3745i	−0.879703	+	1.52369i	−0.851667	+	0.524084i	$0.824408\pi$
$90$	2.09717	+	3.37328i	0.221061	+	0.355575i
$91$	0.705624	−	0.897005i	0.0739695	−	0.0940317i
$92$		−	1.00000i		−	0.104257i
$93$	3.19049	−	12.7344i	0.330839	−	1.32050i
$94$	4.20973	−	2.43049i	0.434201	−	0.250686i
$95$	3.95957	−	2.28606i	0.406243	−	0.234545i
$96$	−0.420939	+	1.68012i	−0.0429619	+	0.171477i
$97$		−	10.3531i		−	1.05120i	−0.850732	−	0.525599i	$-0.823841\pi$
$97$		−	10.3531i		−	1.05120i	0.850732	−	0.525599i	$-0.176159\pi$
$98$	1.97408	−	6.71588i	0.199412	−	0.678406i
$99$	9.40879	+	15.1340i	0.945619	+	1.52102i
$100$	−1.62349	+	2.81197i	−0.162349	+	0.281197i
$101$	−8.12460	−	14.0722i	−0.808427	−	1.40024i	−0.913953	−	0.405821i	$-0.866986\pi$
$101$	−8.12460	−	14.0722i	−0.808427	−	1.40024i	0.105525	−	0.994417i	$-0.466348\pi$
$102$	1.90972	+	1.84842i	0.189091	+	0.183020i
$103$	−14.1321	−	8.15920i	−1.39248	−	0.803949i	−0.398892	−	0.916998i	$-0.630605\pi$
$103$	−14.1321	−	8.15920i	−1.39248	−	0.803949i	−0.993589	+	0.113049i	$0.963938\pi$
$104$	−0.431364			−0.0422987
$105$	−2.29796	+	5.61540i	−0.224258	+	0.548007i
$106$	2.31934			0.225274
$107$	12.5081	+	7.22158i	1.20921	+	0.698137i	0.962586	−	0.270975i	$-0.0873461\pi$
$107$	12.5081	+	7.22158i	1.20921	+	0.698137i	0.246622	+	0.969112i	$0.420679\pi$
$108$	−1.09774	+	5.07888i	−0.105630	+	0.488715i
$109$	4.14273	+	7.17542i	0.396802	+	0.687281i	0.993329	−	0.115312i	$-0.0367868\pi$
$109$	4.14273	+	7.17542i	0.396802	+	0.687281i	−0.596528	+	0.802592i	$0.703453\pi$
$110$	3.93239	−	6.81110i	0.374939	−	0.649413i
$111$	1.50585	+	5.27423i	0.142929	+	0.500608i
$112$	−2.45637	+	0.982969i	−0.232106	+	0.0928818i
$113$			8.85205i			0.832731i	0.909197	+	0.416365i	$0.136696\pi$
$113$			8.85205i			0.832731i	−0.909197	+	0.416365i	$0.863304\pi$
$114$	5.80183	+	1.45359i	0.543391	+	0.136142i
$115$	−1.14663	+	0.662008i	−0.106924	+	0.0617326i
$116$	3.93462	−	2.27166i	0.365321	−	0.210918i
$117$	−1.29340	+	0.0422110i	−0.119575	+	0.00390241i
$118$			3.69821i			0.340448i
$119$	−0.578354	+	4.01839i	−0.0530176	+	0.368365i
$120$	2.20515	−	0.629593i	0.201301	−	0.0574737i
$121$	12.1424	−	21.0312i	1.10385	−	1.91193i
$122$	−3.74108	−	6.47975i	−0.338702	−	0.586649i
$123$	1.14443	−	1.18238i	0.103189	−	0.106612i
$124$	−6.56402	−	3.78974i	−0.589466	−	0.340328i
$125$	10.9191			0.976637
$126$	−7.26901	+	3.18771i	−0.647575	+	0.283983i
$127$	−12.9091			−1.14550			−0.572749	−	0.819731i	$-0.694123\pi$
$127$	−12.9091			−1.14550			−0.572749	+	0.819731i	$0.694123\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.20954	−	8.48184i	0.722810	−	0.746784i
$130$	0.285566	+	0.494615i	0.0250458	+	0.0433806i
$131$	6.44820	−	11.1686i	0.563381	−	0.975805i	−0.433817	−	0.901001i	$-0.642833\pi$
$131$	6.44820	−	11.1686i	0.563381	−	0.975805i	0.997198	−	0.0748042i	$-0.0238332\pi$
$132$	9.89321	−	2.82462i	0.861094	−	0.245851i
$133$	3.39441	+	8.48240i	0.294332	+	0.735517i
$134$		−	8.71068i		−	0.752488i
$135$	6.55031	−	2.10356i	0.563761	−	0.181045i
$136$	1.32888	−	0.767229i	0.113951	−	0.0657894i
$137$	−13.2390	+	7.64352i	−1.13108	+	0.653030i	−0.944207	−	0.329354i	$-0.893169\pi$
$137$	−13.2390	+	7.64352i	−1.13108	+	0.653030i	−0.186874	+	0.982384i	$0.559836\pi$
$138$	−1.68012	−	0.420939i	−0.143021	−	0.0358327i
$139$		−	11.6576i		−	0.988783i	−0.869239	−	0.494391i	$-0.835391\pi$
$139$		−	11.6576i		−	0.988783i	0.869239	−	0.494391i	$-0.164609\pi$
$140$	2.75324	+	2.16582i	0.232691	+	0.183045i
$141$	−2.31148	−	8.09595i	−0.194662	−	0.681802i
$142$	6.62071	−	11.4674i	0.555597	−	0.962323i
$143$	1.28117	+	2.21905i	0.107137	+	0.185567i
$144$	2.64562	+	1.41446i	0.220468	+	0.117871i
$145$	−5.20951	−	3.00771i	−0.432626	−	0.249777i
$146$	12.8395			1.06261
$147$	−10.4525	−	6.14367i	−0.862110	−	0.506722i
$148$	3.16676			0.260306
$149$	−4.78584	−	2.76311i	−0.392072	−	0.226363i	0.290986	−	0.956727i	$-0.406017\pi$
$149$	−4.78584	−	2.76311i	−0.392072	−	0.226363i	−0.683057	+	0.730365i	$0.739350\pi$
$150$	4.04106	+	3.91133i	0.329951	+	0.319359i
$151$	4.94694	+	8.56835i	0.402576	+	0.697283i	0.994036	−	0.109052i	$-0.0347815\pi$
$151$	4.94694	+	8.56835i	0.402576	+	0.697283i	−0.591460	+	0.806335i	$0.701448\pi$
$152$	1.72661	−	2.99058i	0.140047	−	0.242568i
$153$	3.90944	−	2.43050i	0.316060	−	0.196494i
$154$	12.3522	+	9.71679i	0.995369	+	0.783001i
$155$			10.0353i			0.806058i
$156$	−0.181578	+	0.724744i	−0.0145379	+	0.0580260i
$157$	−2.98159	+	1.72142i	−0.237956	+	0.137384i	−0.614237	−	0.789122i	$-0.710536\pi$
$157$	−2.98159	+	1.72142i	−0.237956	+	0.137384i	0.376281	+	0.926506i	$0.377203\pi$
$158$	11.2320	−	6.48480i	0.893570	−	0.515903i
$159$	0.976301	−	3.89678i	0.0774257	−	0.309035i
$160$		−	1.32402i		−	0.104673i
$161$	−0.982969	−	2.45637i	−0.0774688	−	0.193589i
$162$	8.07105	+	3.98223i	0.634122	+	0.312873i
$163$	8.75656	−	15.1668i	0.685867	−	1.18796i	−0.287297	−	0.957842i	$-0.592757\pi$
$163$	8.75656	−	15.1668i	0.685867	−	1.18796i	0.973164	−	0.230114i	$-0.0739100\pi$
$164$	−0.475021	−	0.822761i	−0.0370929	−	0.0642468i
$165$	−9.78818	−	9.47395i	−0.762009	−	0.737546i
$166$	2.90472	+	1.67704i	0.225450	+	0.130164i
$167$	−6.31100			−0.488360			−0.244180	−	0.969730i	$-0.578519\pi$
$167$	−6.31100			−0.488360			−0.244180	+	0.969730i	$0.578519\pi$
$168$	0.617525	+	4.54078i	0.0476431	+	0.350329i
$169$	12.8139			0.985687
$170$	−1.75946	−	1.01582i	−0.134944	−	0.0779101i
$171$	4.88443	−	9.13591i	0.373522	−	0.698641i
$172$	−3.40757	−	5.90208i	−0.259825	−	0.450029i
$173$	−2.31313	+	4.00646i	−0.175864	+	0.304606i	−0.940460	−	0.339904i	$-0.889605\pi$
$173$	−2.31313	+	4.00646i	−0.175864	+	0.304606i	0.764596	+	0.644510i	$0.222939\pi$
$174$	−2.16042	−	7.56688i	−0.163781	−	0.573644i
$175$	−1.22382	+	8.50309i	−0.0925123	+	0.642773i
$176$		−	5.94009i		−	0.447751i
$177$	6.21344	+	1.55672i	0.467031	+	0.117010i
$178$	14.3745	−	8.29910i	1.07741	−	0.622044i
$179$	18.2428	−	10.5325i	1.36353	−	0.787236i	0.373441	−	0.927654i	$-0.378178\pi$
$179$	18.2428	−	10.5325i	1.36353	−	0.787236i	0.990092	+	0.140417i	$0.0448444\pi$
$180$	−0.129561	−	3.96993i	−0.00965693	−	0.295901i
$181$			6.37728i			0.474019i	0.971507	+	0.237010i	$0.0761673\pi$
$181$			6.37728i			0.474019i	−0.971507	+	0.237010i	$0.923833\pi$
$182$	−1.05959	+	0.424017i	−0.0785421	+	0.0314303i
$183$	−12.4615	+	3.55790i	−0.921183	+	0.263008i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−2.09642	−	3.63110i	−0.154132	−	0.266964i
$186$	−9.13027	+	9.43310i	−0.669464	+	0.691669i
$187$	−7.89367	−	4.55741i	−0.577242	−	0.333271i
$188$	−4.86098			−0.354523
$189$	2.29593	+	13.5547i	0.167004	+	0.985956i
$190$	−4.57212			−0.331696
$191$	6.66406	+	3.84750i	0.482195	+	0.278395i	0.721331	−	0.692591i	$-0.243531\pi$
$191$	6.66406	+	3.84750i	0.482195	+	0.278395i	−0.239136	+	0.970986i	$0.576864\pi$
$192$	1.20460	−	1.24456i	0.0869349	−	0.0898183i
$193$	5.99384	+	10.3816i	0.431446	+	0.747286i	0.996998	−	0.0774262i	$-0.0246702\pi$
$193$	5.99384	+	10.3816i	0.431446	+	0.747286i	−0.565552	+	0.824713i	$0.691337\pi$
$194$	−5.17655	+	8.96605i	−0.371655	+	0.643725i
$195$	0.951220	−	0.271584i	0.0681183	−	0.0194485i
$196$	−5.06754	+	4.82908i	−0.361967	+	0.344934i
$197$			15.1707i			1.08087i	0.841386	+	0.540435i	$0.181740\pi$
$197$			15.1707i			1.08087i	−0.841386	+	0.540435i	$0.818260\pi$
$198$	−0.581267	−	17.8108i	−0.0413088	−	1.26576i
$199$	20.9478	−	12.0942i	1.48495	−	0.857335i	0.485094	−	0.874462i	$-0.338785\pi$
$199$	20.9478	−	12.0942i	1.48495	−	0.857335i	0.999853	+	0.0171271i	$0.00545199\pi$
$200$	2.81197	−	1.62349i	0.198836	−	0.114798i
$201$	−14.6350	−	3.66666i	−1.03227	−	0.258626i
$202$			16.2492i			1.14329i
$203$	7.43194	−	9.44765i	0.521620	−	0.663095i
$204$	−0.729662	−	2.55564i	−0.0510865	−	0.178930i
$205$	−0.628936	+	1.08935i	−0.0439268	+	0.0760834i
$206$	8.15920	+	14.1321i	0.568478	+	0.984633i
$207$	−1.41446	+	2.64562i	−0.0983116	+	0.183883i
$208$	0.373572	+	0.215682i	0.0259026	+	0.0149549i
$209$	−20.5125			−1.41888
$210$	4.79779	−	3.71410i	0.331079	−	0.256298i
$211$	−2.61273			−0.179868			−0.0899340	−	0.995948i	$-0.528666\pi$
$211$	−2.61273			−0.179868			−0.0899340	+	0.995948i	$0.528666\pi$
$212$	−2.00861	−	1.15967i	−0.137952	−	0.0796466i
$213$	−16.4797	−	15.9507i	−1.12917	−	1.09292i
$214$	−7.22158	−	12.5081i	−0.493657	−	0.855039i
$215$	−4.51167	+	7.81445i	−0.307693	+	0.532941i
$216$	3.49011	−	3.84957i	0.237472	−	0.261930i
$217$	−19.8489	−	2.85679i	−1.34743	−	0.193931i
$218$		−	8.28546i		−	0.561162i
$219$	5.40465	−	21.5720i	0.365212	−	1.45770i
$220$	−6.81110	+	3.93239i	−0.459204	+	0.265122i
$221$	0.573231	−	0.330955i	0.0385597	−	0.0222624i
$222$	1.33301	−	5.32054i	0.0894659	−	0.357091i
$223$		−	0.232863i		−	0.0155936i	−0.999970	−	0.00779682i	$-0.997518\pi$
$223$		−	0.232863i		−	0.0155936i	0.999970	−	0.00779682i	$-0.00248183\pi$
$224$	2.61877	+	0.376911i	0.174974	+	0.0251834i
$225$	8.27255	−	5.14305i	0.551503	−	0.342870i
$226$	4.42603	−	7.66610i	0.294415	−	0.509941i
$227$	−3.83498	−	6.64239i	−0.254537	−	0.440871i	0.710233	−	0.703967i	$-0.248590\pi$
$227$	−3.83498	−	6.64239i	−0.254537	−	0.440871i	−0.964770	+	0.263096i	$0.915256\pi$
$228$	−4.29774	−	4.15976i	−0.284625	−	0.275487i
$229$	5.44588	+	3.14418i	0.359874	+	0.207773i	0.669025	−	0.743239i	$-0.266712\pi$
$229$	5.44588	+	3.14418i	0.359874	+	0.207773i	−0.309152	+	0.951013i	$0.600045\pi$
$230$	1.32402			0.0873030
$231$	21.5249	−	16.6630i	1.41624	−	1.09635i
$232$	−4.54331			−0.298283
$233$	10.3737	+	5.98926i	0.679603	+	0.392369i	0.799706	−	0.600392i	$-0.204989\pi$
$233$	10.3737	+	5.98926i	0.679603	+	0.392369i	−0.120102	+	0.992762i	$0.538322\pi$
$234$	1.14123	+	0.610146i	0.0746043	+	0.0398865i
$235$	3.21801	+	5.57375i	0.209920	+	0.363591i
$236$	1.84910	−	3.20274i	0.120366	−	0.208481i
$237$	−6.16727	−	21.6008i	−0.400607	−	1.40313i
$238$	2.51006	−	3.19085i	0.162703	−	0.206832i
$239$			22.3020i			1.44260i	0.692623	+	0.721300i	$0.256455\pi$
$239$			22.3020i			1.44260i	−0.692623	+	0.721300i	$0.743545\pi$
$240$	−2.22451	−	0.557330i	−0.143591	−	0.0359755i
$241$	23.5248	−	13.5820i	1.51536	−	0.874896i	0.515526	−	0.856874i	$-0.327596\pi$
$241$	23.5248	−	13.5820i	1.51536	−	0.874896i	0.999838	−	0.0180218i	$-0.00573684\pi$
$242$	−21.0312	+	12.1424i	−1.35194	+	0.780540i
$243$	10.0880	−	11.8841i	0.647148	−	0.762364i
$244$			7.48217i			0.478997i
$245$	8.89193	+	2.61372i	0.568084	+	0.166984i
$246$	−1.58229	+	0.451762i	−0.100883	+	0.0288033i
$247$	0.744797	−	1.29003i	0.0473903	−	0.0820824i
$248$	3.78974	+	6.56402i	0.240648	+	0.416815i
$249$	4.04034	−	4.17435i	0.256046	−	0.264539i
$250$	−9.45625	−	5.45957i	−0.598066	−	0.345293i
$251$	8.74556			0.552015			0.276007	−	0.961155i	$-0.410989\pi$
$251$	8.74556			0.552015			0.276007	+	0.961155i	$0.410989\pi$
$252$	7.88900	+	0.873872i	0.496960	+	0.0550488i
$253$	5.94009			0.373451
$254$	11.1796	+	6.45455i	0.701471	+	0.404994i
$255$	−2.44733	+	2.52850i	−0.153258	+	0.158341i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.21182	−	7.29509i	0.262726	−	0.455055i	−0.704239	−	0.709963i	$-0.748712\pi$
$257$	4.21182	−	7.29509i	0.262726	−	0.455055i	0.966965	+	0.254907i	$0.0820450\pi$
$258$	−11.3506	+	3.24071i	−0.706657	+	0.201758i
$259$	7.77874	−	3.11283i	0.483348	−	0.193422i
$260$		−	0.571133i		−	0.0354201i
$261$	−13.6227	+	0.444585i	−0.843223	+	0.0275191i
$262$	−11.1686	+	6.44820i	−0.689999	+	0.398371i
$263$	11.8646	−	6.85000i	0.731600	−	0.422389i	−0.0874074	−	0.996173i	$-0.527858\pi$
$263$	11.8646	−	6.85000i	0.731600	−	0.422389i	0.819007	+	0.573783i	$0.194525\pi$
$264$	−9.98008	−	2.50042i	−0.614232	−	0.153890i
$265$			3.07085i			0.188641i
$266$	1.30156	−	9.04318i	0.0798035	−	0.554473i
$267$	−7.89274	−	27.6443i	−0.483028	−	1.69180i
$268$	−4.35534	+	7.54367i	−0.266045	+	0.460803i
$269$	1.16768	+	2.02248i	0.0711945	+	0.123313i	0.899425	−	0.437075i	$-0.143986\pi$
$269$	1.16768	+	2.02248i	0.0711945	+	0.123313i	−0.828231	+	0.560387i	$0.810652\pi$
$270$	−6.72451	−	1.45342i	−0.409241	−	0.0884523i
$271$	−1.51793	−	0.876376i	−0.0922076	−	0.0532361i	0.453187	−	0.891415i	$-0.350287\pi$
$271$	−1.51793	−	0.876376i	−0.0922076	−	0.0532361i	−0.545395	+	0.838179i	$0.683620\pi$
$272$	−1.53446			−0.0930402
$273$	0.266378	+	1.95873i	0.0161219	+	0.118548i
$274$	15.2870			0.923524
$275$	−16.7034	−	9.64369i	−1.00725	−	0.581536i
$276$	1.24456	+	1.20460i	0.0749137	+	0.0725087i
$277$	3.92403	+	6.79662i	0.235772	+	0.408370i	0.959497	−	0.281719i	$-0.0909047\pi$
$277$	3.92403	+	6.79662i	0.235772	+	0.408370i	−0.723725	+	0.690089i	$0.757571\pi$
$278$	−5.82879	+	10.0958i	−0.349588	+	0.605503i
$279$	12.0055	+	19.3107i	0.718749	+	1.15610i
$280$	−1.30147	−	3.25228i	−0.0777775	−	0.194361i
$281$		−	7.04104i		−	0.420033i	−0.977698	−	0.210016i	$-0.932648\pi$
$281$		−	7.04104i		−	0.420033i	0.977698	−	0.210016i	$-0.0673518\pi$
$282$	−2.04617	+	8.16704i	−0.121848	+	0.486340i
$283$	4.79548	−	2.76867i	0.285062	−	0.164580i	−0.350651	−	0.936506i	$-0.614040\pi$
$283$	4.79548	−	2.76867i	0.285062	−	0.164580i	0.635713	+	0.771926i	$0.280706\pi$
$284$	−11.4674	+	6.62071i	−0.680465	+	0.392867i
$285$	−1.92458	+	7.68172i	−0.114002	+	0.455026i
$286$		−	2.56234i		−	0.151514i
$287$	−1.97558	−	1.55408i	−0.116615	−	0.0917343i
$288$	−1.58395	−	2.54777i	−0.0933349	−	0.150129i
$289$	7.32272	−	12.6833i	0.430748	−	0.746078i
$290$	3.00771	+	5.20951i	0.176619	+	0.305913i
$291$	12.8850	+	12.4714i	0.755335	+	0.731086i
$292$	−11.1193	−	6.41976i	−0.650711	−	0.375688i
$293$	−0.902583			−0.0527294			−0.0263647	−	0.999652i	$-0.508393\pi$
$293$	−0.902583			−0.0527294			−0.0263647	+	0.999652i	$0.508393\pi$
$294$	5.98032	+	10.5468i	0.348779	+	0.615104i
$295$	−4.89648			−0.285084
$296$	−2.74249	−	1.58338i	−0.159404	−	0.0920320i
$297$	−30.1690	−	6.52066i	−1.75058	−	0.378367i
$298$	2.76311	+	4.78584i	0.160063	+	0.277236i
$299$	−0.215682	+	0.373572i	−0.0124732	+	0.0216042i
$300$	−1.54400	−	5.40784i	−0.0891427	−	0.312222i
$301$	−14.1718	−	11.1482i	−0.816850	−	0.642570i
$302$		−	9.89388i		−	0.569329i
$303$	27.3006	+	6.83991i	1.56838	+	0.392943i
$304$	−2.99058	+	1.72661i	−0.171521	+	0.0990279i
$305$	8.57929	−	4.95325i	0.491249	−	0.283622i
$306$	−4.60093	+	0.150154i	−0.263017	+	0.00858374i
$307$		−	28.2740i		−	1.61369i	−0.590766	−	0.806843i	$-0.701175\pi$
$307$		−	28.2740i		−	1.61369i	0.590766	−	0.806843i	$-0.298825\pi$
$308$	−5.83893	−	14.5911i	−0.332704	−	0.831405i
$309$	27.1782	−	7.75968i	1.54612	−	0.441433i
$310$	5.01767	−	8.69086i	0.284985	−	0.493608i
$311$	7.92530	+	13.7270i	0.449403	+	0.778388i	0.998347	−	0.0574706i	$-0.0183035\pi$
$311$	7.92530	+	13.7270i	0.449403	+	0.778388i	−0.548945	+	0.835859i	$0.684970\pi$
$312$	0.519623	−	0.536858i	0.0294179	−	0.0303936i
$313$	−28.5410	−	16.4782i	−1.61323	−	0.931400i	−0.988615	−	0.150470i	$-0.951921\pi$
$313$	−28.5410	−	16.4782i	−1.61323	−	0.931400i	−0.624618	−	0.780931i	$-0.714745\pi$
$314$	3.44284			0.194291
$315$	−4.22057	−	9.62429i	−0.237802	−	0.542267i
$316$	−12.9696			−0.729597
$317$	−18.1446	−	10.4758i	−1.01910	−	0.588380i	−0.105259	−	0.994445i	$-0.533567\pi$
$317$	−18.1446	−	10.4758i	−1.01910	−	0.588380i	−0.913844	+	0.406065i	$0.866901\pi$
$318$	−2.79389	+	2.88656i	−0.156674	+	0.161870i
$319$	13.4939	+	23.3720i	0.755511	+	1.30858i
$320$	−0.662008	+	1.14663i	−0.0370074	+	0.0640986i
$321$	−24.0551	+	6.86798i	−1.34262	+	0.383333i
$322$	−0.376911	+	2.61877i	−0.0210044	+	0.145938i
$323$			5.29882i			0.294834i
$324$	−4.99862	−	7.48424i	−0.277701	−	0.415791i
$325$	1.21298	−	0.700316i	0.0672841	−	0.0388465i
$326$	−15.1668	+	8.75656i	−0.840012	+	0.484981i
$327$	−13.9206	−	3.48767i	−0.769810	−	0.192869i
$328$			0.950042i			0.0524573i
$329$	−11.9404	+	4.77819i	−0.658294	+	0.263430i
$330$	3.73984	+	13.0988i	0.205871	+	0.721064i
$331$	−11.2718	+	19.5234i	−0.619556	+	1.07310i	0.370011	+	0.929027i	$0.379354\pi$
$331$	−11.2718	+	19.5234i	−0.619556	+	1.07310i	−0.989567	+	0.144075i	$0.953979\pi$
$332$	−1.67704	−	2.90472i	−0.0920395	−	0.159417i
$333$	−8.37804	−	4.47924i	−0.459114	−	0.245461i
$334$	5.46548	+	3.15550i	0.299058	+	0.172661i
$335$	11.5331			0.630119
$336$	1.73560	−	4.24119i	0.0946846	−	0.231376i
$337$	11.7877			0.642116			0.321058	−	0.947060i	$-0.395962\pi$
$337$	11.7877			0.642116			0.321058	+	0.947060i	$0.395962\pi$
$338$	−11.0972	−	6.40696i	−0.603607	−	0.348493i
$339$	−11.0169	−	10.6632i	−0.598356	−	0.579147i
$340$	1.01582	+	1.75946i	0.0550908	+	0.0954200i
$341$	22.5114	−	38.9909i	1.21906	−	2.11147i
$342$	−8.79800	+	5.46972i	−0.475741	+	0.295768i
$343$	−7.70095	+	16.8433i	−0.415812	+	0.909451i
$344$			6.81513i			0.367447i
$345$	0.557330	−	2.22451i	0.0300056	−	0.119763i
$346$	4.00646	−	2.31313i	0.215389	−	0.124355i
$347$	−13.2116	+	7.62773i	−0.709237	+	0.409478i	−0.810778	−	0.585353i	$-0.800956\pi$
$347$	−13.2116	+	7.62773i	−0.709237	+	0.409478i	0.101542	+	0.994831i	$0.467623\pi$
$348$	−1.91246	+	7.63332i	−0.102518	+	0.409189i
$349$		−	3.90282i		−	0.208913i	−0.994529	−	0.104457i	$-0.966690\pi$
$349$		−	3.90282i		−	0.208913i	0.994529	−	0.104457i	$-0.0333103\pi$
$350$	5.31141	−	6.75198i	0.283907	−	0.360908i
$351$	1.50551	−	1.66056i	0.0803580	−	0.0886344i
$352$	−2.97005	+	5.14427i	−0.158304	+	0.274191i
$353$	9.66433	+	16.7391i	0.514380	+	0.890933i	0.999861	+	0.0166851i	$0.00531129\pi$
$353$	9.66433	+	16.7391i	0.514380	+	0.890933i	−0.485481	+	0.874247i	$0.661355\pi$
$354$	−4.60264	−	4.45488i	−0.244627	−	0.236774i
$355$	15.1830	+	8.76592i	0.805831	+	0.465247i
$356$	−16.5982			−0.879703
$357$	−4.30443	−	5.56036i	−0.227815	−	0.294286i
$358$	−21.0650			−1.11332
$359$	−11.3768	−	6.56842i	−0.600446	−	0.346668i	0.168771	−	0.985655i	$-0.446020\pi$
$359$	−11.3768	−	6.56842i	−0.600446	−	0.346668i	−0.769217	+	0.638988i	$0.779354\pi$
$360$	−1.87276	+	3.50284i	−0.0987033	+	0.184616i
$361$	−3.53764	−	6.12737i	−0.186191	−	0.322493i
$362$	3.18864	−	5.52288i	0.167591	−	0.290276i
$363$	11.5478	+	40.4461i	0.606103	+	2.12287i
$364$	1.12964	+	0.162586i	0.0592093	+	0.00852181i
$365$			16.9997i			0.889806i
$366$	12.5710	+	3.14953i	0.657094	+	0.164629i
$367$	2.19574	−	1.26771i	0.114617	−	0.0661740i	−0.441596	−	0.897214i	$-0.645587\pi$
$367$	2.19574	−	1.26771i	0.114617	−	0.0661740i	0.556212	+	0.831040i	$0.312254\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	0.0929662	+	2.84861i	0.00483963	+	0.148293i
$370$			4.19284i			0.217975i
$371$	−6.07382	−	0.874185i	−0.315337	−	0.0453854i
$372$	12.6236	−	3.60417i	0.654503	−	0.186868i
$373$	−14.6671	+	25.4042i	−0.759433	+	1.31538i	0.183706	+	0.982981i	$0.441190\pi$
$373$	−14.6671	+	25.4042i	−0.759433	+	1.31538i	−0.943140	+	0.332396i	$0.892143\pi$
$374$	4.55741	+	7.89367i	0.235658	+	0.408172i
$375$	−13.1532	+	13.5895i	−0.679230	+	0.701759i
$376$	4.20973	+	2.43049i	0.217100	+	0.125343i
$377$	−1.95982			−0.100936
$378$	4.78900	−	12.8866i	0.246319	−	0.662817i
$379$	23.0909			1.18610			0.593049	−	0.805166i	$-0.297924\pi$
$379$	23.0909			1.18610			0.593049	+	0.805166i	$0.297924\pi$
$380$	3.95957	+	2.28606i	0.203122	+	0.117272i
$381$	15.5504	−	16.0661i	0.796669	−	0.823093i
$382$	−3.84750	−	6.66406i	−0.196855	−	0.340963i
$383$	0.298968	−	0.517829i	0.0152766	−	0.0264598i	−0.858286	−	0.513172i	$-0.828470\pi$
$383$	0.298968	−	0.517829i	0.0152766	−	0.0264598i	0.873563	+	0.486712i	$0.161804\pi$
$384$	−1.66550	+	0.475517i	−0.0849921	+	0.0242661i
$385$	−12.8652	+	16.3545i	−0.655671	+	0.833503i
$386$		−	11.9877i		−	0.610157i
$387$	0.666893	+	20.4345i	0.0339001	+	1.03875i
$388$	8.96605	−	5.17655i	0.455182	−	0.262800i
$389$	9.88043	−	5.70447i	0.500957	−	0.289228i	−0.228151	−	0.973626i	$-0.573268\pi$
$389$	9.88043	−	5.70447i	0.500957	−	0.289228i	0.729109	+	0.684398i	$0.239935\pi$
$390$	−0.959573	−	0.240412i	−0.0485899	−	0.0121737i
$391$		−	1.53446i		−	0.0776009i
$392$	6.80316	−	1.64833i	0.343612	−	0.0832533i
$393$	6.13246	+	21.4789i	0.309342	+	1.08347i
$394$	7.58537	−	13.1383i	0.382146	−	0.661895i
$395$	8.58597	+	14.8713i	0.432007	+	0.748259i
$396$	−8.40201	+	15.7152i	−0.422217	+	0.789720i
$397$	14.5065	+	8.37532i	0.728059	+	0.420345i	0.817712	−	0.575628i	$-0.195242\pi$
$397$	14.5065	+	8.37532i	0.728059	+	0.420345i	−0.0896524	+	0.995973i	$0.528576\pi$
$398$	−24.1884			−1.21245
$399$	−14.6458	−	5.99340i	−0.733205	−	0.300045i
$400$	−3.24698			−0.162349
$401$	9.27098	+	5.35260i	0.462971	+	0.267296i	0.713293	−	0.700866i	$-0.247203\pi$
$401$	9.27098	+	5.35260i	0.462971	+	0.267296i	−0.250322	+	0.968163i	$0.580536\pi$
$402$	10.8410	+	10.4929i	0.540698	+	0.523340i
$403$	1.63476	+	2.83148i	0.0814330	+	0.141046i
$404$	8.12460	−	14.0722i	0.404214	−	0.700119i
$405$	−5.27253	+	10.6862i	−0.261994	+	0.531002i
$406$	−11.1601	+	4.46594i	−0.553865	+	0.221641i
$407$			18.8108i			0.932419i
$408$	−0.645913	+	2.57808i	−0.0319775	+	0.127634i
$409$	6.23426	−	3.59935i	0.308264	−	0.177976i	−0.337885	−	0.941187i	$-0.609712\pi$
$409$	6.23426	−	3.59935i	0.308264	−	0.177976i	0.646150	+	0.763211i	$0.276378\pi$
$410$	1.08935	−	0.628936i	0.0537991	−	0.0310609i
$411$	6.43491	−	25.6841i	0.317411	−	1.26690i
$412$		−	16.3184i		−	0.803949i
$413$	1.39389	−	9.68474i	0.0685891	−	0.476555i
$414$	2.54777	−	1.58395i	0.125216	−	0.0778467i
$415$	−2.22043	+	3.84589i	−0.108996	+	0.188787i
$416$	−0.215682	−	0.373572i	−0.0105747	−	0.0183159i
$417$	14.5085	+	14.0428i	0.710487	+	0.687678i
$418$	17.7643	+	10.2562i	0.868880	+	0.501648i
$419$	13.9562			0.681804			0.340902	−	0.940099i	$-0.389268\pi$
$419$	13.9562			0.681804			0.340902	+	0.940099i	$0.389268\pi$
$420$	−6.01206	+	0.817613i	−0.293359	+	0.0398954i
$421$	−28.5137			−1.38967			−0.694837	−	0.719168i	$-0.744523\pi$
$421$	−28.5137			−1.38967			−0.694837	+	0.719168i	$0.744523\pi$
$422$	2.26269	+	1.30637i	0.110146	+	0.0635930i
$423$	12.8603	+	6.87565i	0.625290	+	0.334305i
$424$	1.15967	+	2.00861i	0.0563186	+	0.0975467i
$425$	−2.49118	+	4.31485i	−0.120840	+	0.209301i
$426$	6.29652	+	22.0535i	0.305067	+	1.06850i
$427$	7.35474	+	18.3790i	0.355921	+	0.889422i
$428$			14.4432i			0.698137i
$429$	−4.30505	−	1.07859i	−0.207850	−	0.0520748i
$430$	7.81445	−	4.51167i	0.376846	−	0.217572i
$431$	35.4458	−	20.4647i	1.70737	−	0.985748i	0.769570	−	0.638562i	$-0.220470\pi$
$431$	35.4458	−	20.4647i	1.70737	−	0.985748i	0.937796	−	0.347186i	$-0.112863\pi$
$432$	−4.94730	+	1.58877i	−0.238027	+	0.0764397i
$433$		−	8.15508i		−	0.391908i	−0.980613	−	0.195954i	$-0.937220\pi$
$433$		−	8.15508i		−	0.391908i	0.980613	−	0.195954i	$-0.0627804\pi$
$434$	15.7612	+	12.3985i	0.756563	+	0.595146i
$435$	10.0187	−	2.86044i	0.480358	−	0.137147i
$436$	−4.14273	+	7.17542i	−0.198401	+	0.343640i
$437$	−1.72661	−	2.99058i	−0.0825950	−	0.143059i
$438$	−15.4665	+	15.9795i	−0.739020	+	0.763532i
$439$	−21.1201	−	12.1937i	−1.00801	−	0.581973i	−0.0973992	−	0.995245i	$-0.531052\pi$
$439$	−21.1201	−	12.1937i	−1.00801	−	0.581973i	−0.910607	+	0.413272i	$0.864386\pi$
$440$	7.86478			0.374939
$441$	20.2373	−	5.60809i	0.963682	−	0.267052i
$442$	−0.661910			−0.0314838
$443$	24.9142	+	14.3842i	1.18371	+	0.683416i	0.956870	−	0.290516i	$-0.0938268\pi$
$443$	24.9142	+	14.3842i	1.18371	+	0.683416i	0.226841	+	0.973932i	$0.427160\pi$
$444$	−3.81469	+	3.94122i	−0.181037	+	0.187042i
$445$	10.9881	+	19.0320i	0.520888	+	0.902204i
$446$	−0.116431	+	0.201665i	−0.00551318	+	0.00954911i
$447$	9.20390	−	2.62781i	0.435330	−	0.124291i
$448$	−2.07946	−	1.63580i	−0.0982454	−	0.0772842i
$449$			10.5522i			0.497988i	0.968505	+	0.248994i	$0.0800999\pi$
$449$			10.5522i			0.497988i	−0.968505	+	0.248994i	$0.919900\pi$
$450$	−9.73576	+	0.317733i	−0.458948	+	0.0149781i
$451$	4.88728	−	2.82167i	0.230133	−	0.132867i
$452$	−7.66610	+	4.42603i	−0.360583	+	0.208183i
$453$	−16.6229	−	4.16472i	−0.781013	−	0.195676i
$454$			7.66997i			0.359970i
$455$	−0.561406	−	1.40292i	−0.0263191	−	0.0657697i
$456$	1.64207	+	5.75133i	0.0768968	+	0.269331i
$457$	8.83043	−	15.2948i	0.413070	−	0.715459i	−0.582154	−	0.813079i	$-0.697790\pi$
$457$	8.83043	−	15.2948i	0.413070	−	0.715459i	0.995224	+	0.0976203i	$0.0311231\pi$
$458$	−3.14418	−	5.44588i	−0.146918	−	0.254469i
$459$	−1.68443	+	7.79332i	−0.0786225	+	0.363761i
$460$	−1.14663	−	0.662008i	−0.0534620	−	0.0308663i
$461$	17.3436			0.807771			0.403886	−	0.914810i	$-0.367659\pi$
$461$	17.3436			0.807771			0.403886	+	0.914810i	$0.367659\pi$
$462$	−26.9726	+	3.66816i	−1.25488	+	0.170658i
$463$	−0.550380			−0.0255783			−0.0127892	−	0.999918i	$-0.504071\pi$
$463$	−0.550380			−0.0255783			−0.0127892	+	0.999918i	$0.504071\pi$
$464$	3.93462	+	2.27166i	0.182660	+	0.105459i
$465$	−12.4896	−	12.0886i	−0.579190	−	0.560596i
$466$	−5.98926	−	10.3737i	−0.277447	−	0.480552i
$467$	−3.14205	+	5.44218i	−0.145397	+	0.251834i	−0.929521	−	0.368770i	$-0.879779\pi$
$467$	−3.14205	+	5.44218i	−0.145397	+	0.251834i	0.784124	+	0.620604i	$0.213112\pi$
$468$	−0.683258	−	1.09901i	−0.0315836	−	0.0508020i
$469$	−3.28315	+	22.8112i	−0.151602	+	1.05333i
$470$		−	6.43601i		−	0.296871i
$471$	1.44922	−	5.78439i	0.0667767	−	0.266531i
$472$	−3.20274	+	1.84910i	−0.147418	+	0.0851119i
$473$	35.0589	−	20.2413i	1.61201	−	0.930694i
$474$	−5.45941	+	21.7905i	−0.250759	+	1.00087i
$475$			11.2125i			0.514467i
$476$	−3.76920	+	1.50832i	−0.172761	+	0.0691339i
$477$	3.67371	+	5.90914i	0.168208	+	0.270561i
$478$	11.1510	−	19.3141i	0.510036	−	0.883408i
$479$	8.68863	+	15.0491i	0.396994	+	0.687613i	0.993353	−	0.115104i	$-0.0367202\pi$
$479$	8.68863	+	15.0491i	0.396994	+	0.687613i	−0.596360	+	0.802717i	$0.703387\pi$
$480$	1.64782	+	1.59492i	0.0752122	+	0.0727976i
$481$	−1.18301	−	0.683013i	−0.0539407	−	0.0311427i
$482$	−27.1641			−1.23729
$483$	4.24119	+	1.73560i	0.192981	+	0.0789724i
$484$	24.2847			1.10385
$485$	−11.8712	−	6.85383i	−0.539043	−	0.311217i
$486$	−14.6785	+	5.24789i	−0.665832	+	0.238049i
$487$	−12.1339	−	21.0165i	−0.549839	−	0.952350i	−0.998285	−	0.0585397i	$-0.981356\pi$
$487$	−12.1339	−	21.0165i	−0.549839	−	0.952350i	0.448446	−	0.893810i	$-0.351978\pi$
$488$	3.74108	−	6.47975i	0.169351	−	0.293324i
$489$	8.32779	+	29.1681i	0.376596	+	1.31903i
$490$	−6.39378	−	6.70951i	−0.288841	−	0.303105i
$491$			8.38198i			0.378274i	0.981951	+	0.189137i	$0.0605690\pi$
$491$			8.38198i			0.378274i	−0.981951	+	0.189137i	$0.939431\pi$
$492$	1.59619	+	0.399910i	0.0719617	+	0.0180293i
$493$	6.03752	−	3.48576i	0.271916	−	0.156991i
$494$	−1.29003	+	0.744797i	−0.0580411	+	0.0335100i
$495$	23.5818	−	0.769606i	1.05992	−	0.0345912i
$496$		−	7.57947i		−	0.340328i
$497$	−21.6603	+	27.5350i	−0.971596	+	1.23511i
$498$	−5.58621	+	1.59492i	−0.250324	+	0.0714702i
$499$	14.8966	−	25.8017i	0.666863	−	1.15504i	−0.311914	−	0.950110i	$-0.600970\pi$
$499$	14.8966	−	25.8017i	0.666863	−	1.15504i	0.978777	−	0.204930i	$-0.0656967\pi$
$500$	5.45957	+	9.45625i	0.244159	+	0.422896i
$501$	7.60226	−	7.85441i	0.339644	−	0.350909i
$502$	−7.57388	−	4.37278i	−0.338039	−	0.195167i
$503$	−37.7983			−1.68534			−0.842671	−	0.538428i	$-0.819018\pi$
$503$	−37.7983			−1.68534			−0.842671	+	0.538428i	$0.819018\pi$
$504$	−6.39514	−	4.70130i	−0.284862	−	0.209412i
$505$	−21.5142			−0.957369
$506$	−5.14427	−	2.97005i	−0.228691	−	0.132035i
$507$	−15.4357	+	15.9477i	−0.685524	+	0.708262i
$508$	−6.45455	−	11.1796i	−0.286374	−	0.496015i
$509$	−20.1561	+	34.9114i	−0.893403	+	1.54742i	−0.0576334	+	0.998338i	$0.518355\pi$
$509$	−20.1561	+	34.9114i	−0.893403	+	1.54742i	−0.835769	+	0.549081i	$0.814978\pi$
$510$	3.38370	−	0.966083i	0.149833	−	0.0427789i
$511$	−33.6237	−	4.83935i	−1.48742	−	0.214080i
$512$			1.00000i			0.0441942i
$513$	5.48637	+	17.0841i	0.242229	+	0.754283i
$514$	−7.29509	+	4.21182i	−0.321773	+	0.185776i
$515$	−18.7112	+	10.8029i	−0.824513	+	0.476033i
$516$	11.4503	+	2.86875i	0.504069	+	0.126290i
$517$		−	28.8747i		−	1.26991i
$518$	−8.29300	−	1.19359i	−0.364374	−	0.0524431i
$519$	−2.19987	−	7.70503i	−0.0965636	−	0.338213i
$520$	−0.285566	+	0.494615i	−0.0125229	+	0.0216903i
$521$	7.27692	+	12.6040i	0.318808	+	0.552191i	0.980240	−	0.197814i	$-0.0633843\pi$
$521$	7.27692	+	12.6040i	0.318808	+	0.552191i	−0.661432	+	0.750005i	$0.730051\pi$
$522$	12.0199	+	6.42632i	0.526096	+	0.281272i
$523$	11.0289	+	6.36755i	0.482261	+	0.278433i	0.721358	−	0.692562i	$-0.243518\pi$
$523$	11.0289	+	6.36755i	0.482261	+	0.278433i	−0.239097	+	0.970996i	$0.576852\pi$
$524$	12.8964			0.563381
$525$	−9.10837	−	11.7660i	−0.397522	−	0.513510i
$526$	−13.7000			−0.597349
$527$	−10.0722	−	5.81519i	−0.438752	−	0.253314i
$528$	7.39280	+	7.15547i	0.321730	+	0.311402i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	1.53542	−	2.65943i	0.0666945	−	0.115518i
$531$	−9.42217	+	5.85776i	−0.408887	+	0.254205i
$532$	−5.64877	+	7.18084i	−0.244905	+	0.311329i
$533$			0.409814i			0.0177510i
$534$	−6.98683	+	27.8870i	−0.302350	+	1.20679i
$535$	16.5610	−	9.56149i	0.715994	−	0.413379i
$536$	7.54367	−	4.35534i	0.325837	−	0.188122i
$537$	−8.86708	+	35.3918i	−0.382643	+	1.52727i
$538$		−	2.33535i		−	0.100684i
$539$	−28.6852	−	30.1017i	−1.23556	−	1.29657i
$540$	5.09689	+	4.62095i	0.219335	+	0.198854i
$541$	5.76926	−	9.99265i	0.248040	−	0.429618i	−0.714942	−	0.699184i	$-0.753547\pi$
$541$	5.76926	−	9.99265i	0.248040	−	0.429618i	0.962982	+	0.269566i	$0.0868803\pi$
$542$	0.876376	+	1.51793i	0.0376436	+	0.0652006i
$543$	−7.93690	−	7.68210i	−0.340605	−	0.329670i
$544$	1.32888	+	0.767229i	0.0569753	+	0.0328947i
$545$	10.9701			0.469907
$546$	0.748674	−	1.82950i	0.0320403	−	0.0782953i
$547$	−34.2942			−1.46631			−0.733156	−	0.680060i	$-0.761954\pi$
$547$	−34.2942			−1.46631			−0.733156	+	0.680060i	$0.761954\pi$
$548$	−13.2390	−	7.64352i	−0.565540	−	0.326515i
$549$	10.5832	−	19.7950i	0.451680	−	0.844829i
$550$	9.64369	+	16.7034i	0.411208	+	0.712234i
$551$	7.84453	−	13.5871i	0.334188	−	0.578831i
$552$	−0.475517	−	1.66550i	−0.0202394	−	0.0708883i
$553$	−31.8582	+	12.7487i	−1.35475	+	0.542130i
$554$		−	7.84807i		−	0.333432i
$555$	7.04448	+	1.76493i	0.299022	+	0.0749170i
$556$	10.0958	−	5.82879i	0.428156	−	0.247196i
$557$	7.99915	−	4.61831i	0.338935	−	0.195684i	−0.320866	−	0.947125i	$-0.603974\pi$
$557$	7.99915	−	4.61831i	0.338935	−	0.195684i	0.659801	+	0.751440i	$0.270641\pi$
$558$	−0.741687	−	22.7263i	−0.0313981	−	0.962082i
$559$			2.93980i			0.124340i
$560$	−0.499036	+	3.46729i	−0.0210881	+	0.146520i
$561$	15.1807	−	4.33426i	0.640931	−	0.182993i
$562$	−3.52052	+	6.09772i	−0.148504	+	0.257217i
$563$	0.0487491	+	0.0844359i	0.00205453	+	0.00355855i	0.867051	−	0.498220i	$-0.166013\pi$
$563$	0.0487491	+	0.0844359i	0.00205453	+	0.00355855i	−0.864996	+	0.501778i	$0.832679\pi$
$564$	5.85556	−	6.04977i	0.246563	−	0.254741i
$565$	10.1500	+	5.86013i	0.427015	+	0.246537i
$566$	−5.53734			−0.232752
$567$	−19.6353	−	13.4706i	−0.824603	−	0.565712i
$568$	13.2414			0.555597
$569$	10.1195	+	5.84250i	0.424231	+	0.244930i	0.696886	−	0.717182i	$-0.254568\pi$
$569$	10.1195	+	5.84250i	0.424231	+	0.244930i	−0.272655	+	0.962112i	$0.587902\pi$
$570$	5.50759	−	5.69027i	0.230688	−	0.238339i
$571$	6.08543	+	10.5403i	0.254667	+	0.441096i	0.964805	−	0.262966i	$-0.0847008\pi$
$571$	6.08543	+	10.5403i	0.254667	+	0.441096i	−0.710138	+	0.704063i	$0.751367\pi$
$572$	−1.28117	+	2.21905i	−0.0535685	+	0.0927833i
$573$	−12.8160	+	3.65911i	−0.535396	+	0.152861i
$574$	0.933862	+	2.33366i	0.0389787	+	0.0974051i
$575$		−	3.24698i		−	0.135409i
$576$	0.0978548	+	2.99840i	0.00407728	+	0.124933i
$577$	6.38984	−	3.68918i	0.266013	−	0.153582i	−0.361062	−	0.932542i	$-0.617586\pi$
$577$	6.38984	−	3.68918i	0.266013	−	0.153582i	0.627074	+	0.778960i	$0.284252\pi$
$578$	−12.6833	+	7.32272i	−0.527557	+	0.304585i
$579$	−20.1408	−	5.04608i	−0.837022	−	0.209708i
$580$		−	6.01542i		−	0.249777i
$581$	−6.97468	−	5.48659i	−0.289359	−	0.227622i
$582$	−4.92308	−	17.2431i	−0.204068	−	0.714748i
$583$	6.88856	−	11.9313i	0.285295	−	0.494145i
$584$	6.41976	+	11.1193i	0.265652	+	0.460122i
$585$	−0.807843	+	1.51100i	−0.0334002	+	0.0624722i
$586$	0.781660	+	0.451291i	0.0322901	+	0.0186427i
$587$	−21.3626			−0.881728			−0.440864	−	0.897574i	$-0.645328\pi$
$587$	−21.3626			−0.881728			−0.440864	+	0.897574i	$0.645328\pi$
$588$	0.0943147	−	12.1240i	0.00388947	−	0.499985i
$589$	−26.1736			−1.07846
$590$	4.24048	+	2.44824i	0.174578	+	0.100793i
$591$	−18.8809	−	18.2748i	−0.776656	−	0.751723i
$592$	1.58338	+	2.74249i	0.0650765	+	0.112716i
$593$	15.5202	−	26.8817i	0.637338	−	1.10390i	−0.348677	−	0.937243i	$-0.613369\pi$
$593$	15.5202	−	26.8817i	0.637338	−	1.10390i	0.986015	−	0.166658i	$-0.0532976\pi$
$594$	22.8668	+	20.7316i	0.938236	+	0.850626i
$595$	4.22473	+	3.32336i	0.173197	+	0.136245i
$596$		−	5.52622i		−	0.226363i
$597$	−10.1818	+	40.6395i	−0.416715	+	1.66326i
$598$	0.373572	−	0.215682i	0.0152765	−	0.00881989i
$599$	22.6228	−	13.0613i	0.924343	−	0.533669i	0.0393247	−	0.999226i	$-0.487479\pi$
$599$	22.6228	−	13.0613i	0.924343	−	0.533669i	0.885018	+	0.465557i	$0.154146\pi$
$600$	−1.36678	+	5.45533i	−0.0557986	+	0.222713i
$601$			31.4368i			1.28233i	0.767401	+	0.641167i	$0.221549\pi$
$601$			31.4368i			1.28233i	−0.767401	+	0.641167i	$0.778451\pi$
$602$	6.69906	+	16.7405i	0.273033	+	0.682292i
$603$	22.1928	−	13.7973i	0.903760	−	0.561868i
$604$	−4.94694	+	8.56835i	−0.201288	+	0.348641i
$605$	−16.0767	−	27.8456i	−0.653610	−	1.13209i
$606$	−20.2231	−	19.5739i	−0.821506	−	0.795133i
$607$	−17.2647	−	9.96780i	−0.700754	−	0.404580i	0.106874	−	0.994273i	$-0.465916\pi$
$607$	−17.2647	−	9.96780i	−0.700754	−	0.404580i	−0.807628	+	0.589692i	$0.799249\pi$
$608$	3.45322			0.140047
$609$	2.80561	+	20.6302i	0.113689	+	0.835977i
$610$	−9.90651			−0.401103
$611$	1.81593	+	1.04843i	0.0734645	+	0.0424148i
$612$	4.05959	+	2.17043i	0.164099	+	0.0877342i
$613$	−4.88790	−	8.46610i	−0.197421	−	0.341942i	0.750271	−	0.661131i	$-0.229923\pi$
$613$	−4.88790	−	8.46610i	−0.197421	−	0.341942i	−0.947691	+	0.319188i	$0.896590\pi$
$614$	−14.1370	+	24.4860i	−0.570524	+	0.988176i
$615$	−0.598140	−	2.09498i	−0.0241193	−	0.0844778i
$616$	−2.23889	+	15.5557i	−0.0902073	+	0.626758i
$617$		−	46.6722i		−	1.87895i	−0.342615	−	0.939476i	$-0.611313\pi$
$617$		−	46.6722i		−	1.87895i	0.342615	−	0.939476i	$-0.388687\pi$
$618$	−27.4169	−	6.86904i	−1.10287	−	0.276313i
$619$	−11.1566	+	6.44124i	−0.448420	+	0.258895i	−0.707163	−	0.707051i	$-0.750025\pi$
$619$	−11.1566	+	6.44124i	−0.448420	+	0.258895i	0.258743	+	0.965946i	$0.416692\pi$
$620$	−8.69086	+	5.01767i	−0.349033	+	0.201514i
$621$	−1.58877	−	4.94730i	−0.0637551	−	0.198528i
$622$		−	15.8506i		−	0.635551i
$623$	−40.7714	+	16.3155i	−1.63347	+	0.653668i
$624$	−0.718436	+	0.205121i	−0.0287605	+	0.00821142i
$625$	−0.888903	+	1.53962i	−0.0355561	+	0.0615850i
$626$	16.4782	+	28.5410i	0.658599	+	1.14073i
$627$	24.7094	−	25.5290i	0.986798	−	1.01953i
$628$	−2.98159	−	1.72142i	−0.118978	−	0.0686921i
$629$	4.85926			0.193751
$630$	−1.15702	+	10.4452i	−0.0460968	+	0.416145i
$631$	25.4564			1.01340			0.506702	−	0.862121i	$-0.330864\pi$
$631$	25.4564			1.01340			0.506702	+	0.862121i	$0.330864\pi$
$632$	11.2320	+	6.48480i	0.446785	+	0.257951i
$633$	3.14731	−	3.25170i	0.125094	−	0.129244i
$634$	10.4758	+	18.1446i	0.416047	+	0.720615i
$635$	−8.54593	+	14.8020i	−0.339135	+	0.587399i
$636$	3.86286	−	1.10289i	0.153172	−	0.0437323i
$637$	2.93464	−	0.711031i	0.116275	−	0.0281721i
$638$		−	26.9877i		−	1.06845i
$639$	39.7031	−	1.29574i	1.57063	−	0.0512585i
$640$	1.14663	−	0.662008i	0.0453246	−	0.0261682i
$641$	−11.3251	+	6.53858i	−0.447316	+	0.258258i	−0.706696	−	0.707517i	$-0.749815\pi$
$641$	−11.3251	+	6.53858i	−0.447316	+	0.258258i	0.259380	+	0.965775i	$0.416482\pi$
$642$	24.2663	+	6.07969i	0.957714	+	0.239946i
$643$			15.8515i			0.625123i	0.949898	+	0.312561i	$0.101187\pi$
$643$			15.8515i			0.625123i	−0.949898	+	0.312561i	$0.898813\pi$
$644$	1.63580	−	2.07946i	0.0644595	−	0.0819423i
$645$	−4.29076	−	15.0284i	−0.168948	−	0.591741i
$646$	2.64941	−	4.58891i	0.104240	−	0.180548i
$647$	−1.08917	−	1.88651i	−0.0428199	−	0.0741662i	0.843821	−	0.536624i	$-0.180301\pi$
$647$	−1.08917	−	1.88651i	−0.0428199	−	0.0741662i	−0.886641	+	0.462458i	$0.846967\pi$
$648$	0.586816	+	8.98085i	0.0230523	+	0.352801i
$649$	19.0246	+	10.9838i	0.746780	+	0.431154i
$650$	−1.40063			−0.0549373
$651$	27.4655	−	21.2618i	1.07646	−	0.833315i
$652$	17.5131			0.685867
$653$	1.31906	+	0.761562i	0.0516190	+	0.0298022i	0.525587	−	0.850740i	$-0.323846\pi$
$653$	1.31906	+	0.761562i	0.0516190	+	0.0298022i	−0.473968	+	0.880542i	$0.657179\pi$
$654$	10.3117	+	9.98071i	0.403221	+	0.390276i
$655$	−8.53751	−	14.7874i	−0.333588	−	0.577792i
$656$	0.475021	−	0.822761i	0.0185465	−	0.0321234i
$657$	20.3371	+	32.7121i	0.793426	+	1.27622i
$658$	12.7298	+	1.83216i	0.496258	+	0.0714249i
$659$		−	0.495255i		−	0.0192924i	−0.999953	−	0.00964620i	$-0.996929\pi$
$659$		−	0.495255i		−	0.0192924i	0.999953	−	0.00964620i	$-0.00307053\pi$
$660$	3.31059	−	13.2138i	0.128865	−	0.514346i
$661$	12.5499	−	7.24567i	0.488133	−	0.281824i	−0.235667	−	0.971834i	$-0.575727\pi$
$661$	12.5499	−	7.24567i	0.488133	−	0.281824i	0.723800	+	0.690010i	$0.242394\pi$
$662$	19.5234	−	11.2718i	0.758798	−	0.438092i
$663$	−0.278624	+	1.11209i	−0.0108208	+	0.0431900i
$664$			3.35408i			0.130164i
$665$	11.9733	+	1.72328i	0.464305	+	0.0668260i
$666$	5.01598	+	8.06816i	0.194365	+	0.312635i
$667$	−2.27166	+	3.93462i	−0.0879589	+	0.152349i
$668$	−3.15550	−	5.46548i	−0.122090	−	0.211466i
$669$	0.289811	+	0.280507i	0.0112048	+	0.0108450i
$670$	−9.98794	−	5.76654i	−0.385868	−	0.222781i
$671$	−44.4448			−1.71577
$672$	−3.62367	+	2.80518i	−0.139786	+	0.108212i
$673$	−17.2937			−0.666623			−0.333312	−	0.942817i	$-0.608166\pi$
$673$	−17.2937			−0.666623			−0.333312	+	0.942817i	$0.608166\pi$
$674$	−10.2084	−	5.89384i	−0.393214	−	0.227022i
$675$	−3.56433	+	16.4910i	−0.137191	+	0.634740i
$676$	6.40696	+	11.0972i	0.246422	+	0.426815i
$677$	14.2617	−	24.7019i	0.548120	−	0.949372i	−0.450283	−	0.892886i	$-0.648677\pi$
$677$	14.2617	−	24.7019i	0.548120	−	0.949372i	0.998403	−	0.0564865i	$-0.0179898\pi$
$678$	4.20930	+	14.7431i	0.161657	+	0.566204i
$679$	16.9356	−	21.5289i	0.649928	−	0.826203i
$680$		−	2.03165i		−	0.0779101i
$681$	12.8865	+	3.22859i	0.493811	+	0.123720i
$682$	−38.9909	+	22.5114i	−1.49304	+	0.862006i
$683$	−4.64981	+	2.68457i	−0.177920	+	0.102722i	−0.586315	−	0.810083i	$-0.699422\pi$
$683$	−4.64981	+	2.68457i	−0.177920	+	0.102722i	0.408395	+	0.912805i	$0.366089\pi$
$684$	10.3541	−	0.337914i	0.395901	−	0.0129205i
$685$			20.2403i			0.773341i
$686$	15.0908	−	10.7362i	0.576171	−	0.409911i
$687$	−10.4733	+	2.99023i	−0.399580	+	0.114084i
$688$	3.40757	−	5.90208i	0.129912	−	0.225015i
$689$	0.500240	+	0.866442i	0.0190576	+	0.0330088i
$690$	−1.59492	+	1.64782i	−0.0607174	+	0.0627313i
$691$	−16.1930	−	9.34901i	−0.616009	−	0.355653i	0.159304	−	0.987230i	$-0.449075\pi$
$691$	−16.1930	−	9.34901i	−0.616009	−	0.355653i	−0.775314	+	0.631576i	$0.782408\pi$
$692$	−4.62626			−0.175864
$693$	−5.19088	+	46.8614i	−0.197185	+	1.78012i
$694$	15.2555			0.579089
$695$	−13.3669	−	7.71741i	−0.507037	−	0.292738i
$696$	5.47290	−	5.65442i	0.207450	−	0.214330i
$697$	−0.728900	−	1.26249i	−0.0276091	−	0.0478203i
$698$	−1.95141	+	3.37994i	−0.0738620	+	0.127933i
$699$	−19.9502	+	5.69599i	−0.754585	+	0.215442i
$700$	−7.97580	+	3.19168i	−0.301457	+	0.120634i
$701$		−	35.7422i		−	1.34996i	−0.737834	−	0.674982i	$-0.764151\pi$
$701$		−	35.7422i		−	1.34996i	0.737834	−	0.674982i	$-0.235849\pi$
$702$	−2.13409	+	0.685338i	−0.0805460	+	0.0258664i
$703$	9.47043	−	5.46776i	0.357184	−	0.206220i
$704$	5.14427	−	2.97005i	0.193882	−	0.111938i
$705$	−10.8133	−	2.70917i	−0.407252	−	0.102033i
$706$		−	19.3287i		−	0.727443i
$707$	6.12450	−	42.5528i	0.230335	−	1.60036i
$708$	1.75856	+	6.15936i	0.0660908	+	0.231483i
$709$	3.25992	−	5.64635i	0.122429	−	0.212053i	−0.798296	−	0.602265i	$-0.794265\pi$
$709$	3.25992	−	5.64635i	0.122429	−	0.212053i	0.920725	+	0.390212i	$0.127598\pi$
$710$	−8.76592	−	15.1830i	−0.328979	−	0.569808i
$711$	34.3126	+	18.3449i	1.28682	+	0.687989i
$712$	14.3745	+	8.29910i	0.538706	+	0.311022i
$713$	7.57947			0.283853
$714$	0.947566	+	6.96763i	0.0354618	+	0.260757i
$715$	3.39258			0.126875
$716$	18.2428	+	10.5325i	0.681767	+	0.393618i
$717$	−27.7562	−	26.8651i	−1.03657	−	1.00330i
$718$	6.56842	+	11.3768i	0.245131	+	0.424580i
$719$	−10.1906	+	17.6506i	−0.380045	+	0.658257i	−0.991068	−	0.133355i	$-0.957425\pi$
$719$	−10.1906	+	17.6506i	−0.380045	+	0.658257i	0.611023	+	0.791613i	$0.290758\pi$
$720$	3.37328	−	2.09717i	0.125715	−	0.0781569i
$721$	−16.0405	−	40.0841i	−0.597378	−	1.49281i
$722$			7.07527i			0.263314i
$723$	−11.4344	+	45.6390i	−0.425250	+	1.69733i
$724$	−5.52288	+	3.18864i	−0.205256	+	0.118505i
$725$	12.7757	−	7.37603i	0.474476	−	0.273939i
$726$	10.2224	−	40.8013i	0.379388	−	1.51428i
$727$			10.5786i			0.392337i	0.980570	+	0.196169i	$0.0628500\pi$
$727$			10.5786i			0.392337i	−0.980570	+	0.196169i	$0.937150\pi$
$728$	−0.897005	−	0.705624i	−0.0332452	−	0.0261522i
$729$	2.63833	+	26.8708i	0.0977160	+	0.995214i
$730$	8.49986	−	14.7222i	0.314594	−	0.544893i
$731$	−5.22877	−	9.05649i	−0.193393	−	0.334967i
$732$	−9.31200	−	9.01305i	−0.344181	−	0.333132i
$733$	41.6777	+	24.0626i	1.53940	+	0.888774i	0.998874	+	0.0474473i	$0.0151086\pi$
$733$	41.6777	+	24.0626i	1.53940	+	0.888774i	0.540527	+	0.841326i	$0.318225\pi$
$734$	−2.53542			−0.0935842
$735$	−13.9642	+	7.91803i	−0.515077	+	0.292061i
$736$	−1.00000			−0.0368605
$737$	−44.8101	−	25.8711i	−1.65060	−	0.952975i
$738$	1.34379	−	2.51345i	0.0494658	−	0.0925215i
$739$	0.111573	+	0.193251i	0.00410430	+	0.00710885i	0.868070	−	0.496441i	$-0.165360\pi$
$739$	0.111573	+	0.193251i	0.00410430	+	0.00710885i	−0.863966	+	0.503550i	$0.832027\pi$
$740$	2.09642	−	3.63110i	0.0770659	−	0.133482i
$741$	0.708328	+	2.48092i	0.0260211	+	0.0911388i
$742$	4.82299	+	3.79398i	0.177057	+	0.139281i
$743$		−	9.67336i		−	0.354881i	−0.984132	−	0.177441i	$-0.943218\pi$
$743$		−	9.67336i		−	0.354881i	0.984132	−	0.177441i	$-0.0567818\pi$
$744$	−12.7344	−	3.19049i	−0.466867	−	0.116969i
$745$	−6.33653	+	3.65840i	−0.232153	+	0.134033i
$746$	25.4042	−	14.6671i	0.930112	−	0.537001i
$747$	0.328213	+	10.0569i	0.0120087	+	0.367962i
$748$		−	9.11483i		−	0.333271i
$749$	14.1972	+	35.4778i	0.518754	+	1.29633i
$750$	18.1858	−	5.19224i	0.664051	−	0.189594i
$751$	−4.08105	+	7.06859i	−0.148920	+	0.257936i	−0.930828	−	0.365456i	$-0.880913\pi$
$751$	−4.08105	+	7.06859i	−0.148920	+	0.257936i	0.781909	+	0.623393i	$0.214246\pi$
$752$	−2.43049	−	4.20973i	−0.0886308	−	0.153513i
$753$	−10.5349	+	10.8844i	−0.383915	+	0.396648i
$754$	1.69726	+	0.979911i	0.0618104	+	0.0356863i
$755$	13.0997			0.476745
$756$	−10.5907	+	8.76566i	−0.385181	+	0.318804i
$757$	−14.0515			−0.510710			−0.255355	−	0.966847i	$-0.582192\pi$
$757$	−14.0515			−0.510710			−0.255355	+	0.966847i	$0.582192\pi$
$758$	−19.9973	−	11.5454i	−0.726334	−	0.419349i
$759$	−7.15547	+	7.39280i	−0.259727	+	0.268342i
$760$	−2.28606	−	3.95957i	−0.0829241	−	0.143629i
$761$	−22.1322	+	38.3341i	−0.802291	+	1.38961i	0.115814	+	0.993271i	$0.463052\pi$
$761$	−22.1322	+	38.3341i	−0.802291	+	1.38961i	−0.918105	+	0.396337i	$0.870281\pi$
$762$	−21.5001	+	6.13850i	−0.778866	+	0.222374i
$763$	−3.12288	+	21.6977i	−0.113056	+	0.785509i
$764$			7.69500i			0.278395i
$765$	−0.198806	−	6.09170i	−0.00718786	−	0.220246i
$766$	−0.517829	+	0.298968i	−0.0187099	+	0.0108022i
$767$	−1.38155	+	0.797637i	−0.0498848	+	0.0288010i
$768$	1.68012	+	0.420939i	0.0606262	+	0.0151893i
$769$		−	37.9898i		−	1.36995i	−0.728568	−	0.684974i	$-0.759814\pi$
$769$		−	37.9898i		−	1.36995i	0.728568	−	0.684974i	$-0.240186\pi$
$770$	19.3188	−	7.73083i	0.696202	−	0.278600i
$771$	4.00559	+	14.0296i	0.144258	+	0.505263i
$772$	−5.99384	+	10.3816i	−0.215723	+	0.373643i
$773$	7.66410	+	13.2746i	0.275658	+	0.477454i	0.970301	−	0.241901i	$-0.0777708\pi$
$773$	7.66410	+	13.2746i	0.275658	+	0.477454i	−0.694643	+	0.719355i	$0.744437\pi$
$774$	9.63971	−	18.0303i	0.346492	−	0.648084i
$775$	−21.3132	−	12.3052i	−0.765594	−	0.442016i
$776$	−10.3531			−0.371655
$777$	−5.49622	+	13.4308i	−0.197176	+	0.481828i
$778$	−11.4089			−0.409030
$779$	−2.84117	−	1.64035i	−0.101796	−	0.0587717i
$780$	0.710808	+	0.687989i	0.0254510	+	0.0246340i
$781$	−39.3276	−	68.1174i	−1.40725	−	2.43743i
$782$	−0.767229	+	1.32888i	−0.0274361	+	0.0475206i
$783$	15.8566	−	17.4898i	0.566670	−	0.625034i
$784$	−6.71588	−	1.97408i	−0.239853	−	0.0705030i
$785$			4.55837i			0.162695i
$786$	5.42859	−	21.6675i	0.193631	−	0.772855i
$787$	−15.8484	+	9.15010i	−0.564936	+	0.326166i	−0.755124	−	0.655582i	$-0.772423\pi$
$787$	−15.8484	+	9.15010i	−0.564936	+	0.326166i	0.190188	+	0.981748i	$0.439090\pi$
$788$	−13.1383	+	7.58537i	−0.468031	+	0.270218i
$789$	−5.76686	+	23.0177i	−0.205306	+	0.819451i
$790$		−	17.1719i		−	0.610951i
$791$	−14.4802	+	18.4075i	−0.514855	+	0.654496i
$792$	15.1340	−	9.40879i	0.537762	−	0.334327i
$793$	1.61377	−	2.79513i	0.0573066	−	0.0992580i
$794$	−8.37532	−	14.5065i	−0.297229	−	0.514816i
$795$	−3.82185	−	3.69916i	−0.135547	−	0.131196i
$796$	20.9478	+	12.0942i	0.742474	+	0.428667i
$797$	−24.4087			−0.864602			−0.432301	−	0.901729i	$-0.642298\pi$
$797$	−24.4087			−0.864602			−0.432301	+	0.901729i	$0.642298\pi$
$798$	9.68691	+	12.5133i	0.342913	+	0.442967i
$799$	−7.45897			−0.263879
$800$	2.81197	+	1.62349i	0.0994181	+	0.0573991i
$801$	43.9126	+	23.4775i	1.55157	+	0.829535i
$802$	−5.35260	−	9.27098i	−0.189007	−	0.327370i
$803$	38.1340	−	66.0500i	1.34572	−	2.33085i
$804$	−4.14208	−	14.5076i	−0.146080	−	0.511644i
$805$	−3.46729	−	0.499036i	−0.122206	−	0.0175887i
$806$		−	3.26951i		−	0.115164i
$807$	−3.92368	−	0.983041i	−0.138120	−	0.0346047i
$808$	−14.0722	+	8.12460i	−0.495059	+	0.285822i
$809$	13.0928	−	7.55911i	0.460317	−	0.265764i	−0.251860	−	0.967764i	$-0.581042\pi$
$809$	13.0928	−	7.55911i	0.460317	−	0.265764i	0.712178	+	0.701999i	$0.247709\pi$
$810$	9.90925	−	6.61825i	0.348175	−	0.232542i
$811$			5.82703i			0.204615i	0.994753	+	0.102307i	$0.0326225\pi$
$811$			5.82703i			0.204615i	−0.994753	+	0.102307i	$0.967377\pi$
$812$	11.8979	+	1.71242i	0.417534	+	0.0600943i
$813$	2.91921	−	0.833464i	0.102381	−	0.0292309i
$814$	9.40542	−	16.2907i	0.329660	−	0.570988i
$815$	−11.5938	−	20.0811i	−0.406114	−	0.703410i
$816$	1.84842	−	1.90972i	0.0647075	−	0.0668537i
$817$	−20.3812	−	11.7671i	−0.713047	−	0.411678i
$818$	−7.19870			−0.251697
$819$	−2.75863	−	2.02797i	−0.0963944	−	0.0708630i
$820$	−1.25787			−0.0439268
$821$	31.3346	+	18.0910i	1.09358	+	0.631381i	0.934528	−	0.355889i	$-0.115822\pi$
$821$	31.3346	+	18.0910i	1.09358	+	0.631381i	0.159055	+	0.987270i	$0.449155\pi$
$822$	−18.4148	+	19.0256i	−0.642291	+	0.663595i
$823$	−11.0267	−	19.0989i	−0.384368	−	0.665744i	0.607314	−	0.794462i	$-0.292247\pi$
$823$	−11.0267	−	19.0989i	−0.384368	−	0.665744i	−0.991681	+	0.128718i	$0.958914\pi$
$824$	−8.15920	+	14.1321i	−0.284239	+	0.492316i
$825$	32.1231	−	9.17149i	1.11838	−	0.319310i
$826$	−6.04952	+	7.69028i	−0.210490	+	0.267579i
$827$			47.1121i			1.63825i	0.573616	+	0.819125i	$0.305540\pi$
$827$			47.1121i			1.63825i	−0.573616	+	0.819125i	$0.694460\pi$
$828$	−2.99840	+	0.0978548i	−0.104202	+	0.00340069i
$829$	40.0510	−	23.1234i	1.39103	−	0.803110i	0.397599	−	0.917559i	$-0.369844\pi$
$829$	40.0510	−	23.1234i	1.39103	−	0.803110i	0.993429	+	0.114449i	$0.0365103\pi$
$830$	3.84589	−	2.22043i	0.133493	−	0.0770721i
$831$	−13.1857	−	3.30355i	−0.457407	−	0.114599i
$832$			0.431364i			0.0149549i
$833$	−7.77593	+	7.41002i	−0.269420	+	0.256742i
$834$	−5.54338	−	19.4157i	−0.191952	−	0.672310i
$835$	−4.17793	+	7.23639i	−0.144583	+	0.250425i
$836$	−10.2562	−	17.7643i	−0.354719	−	0.614391i
$837$	−38.4952	−	8.32026i	−1.33059	−	0.287590i
$838$	−12.0864	−	6.97809i	−0.417518	−	0.241054i
$839$	−28.0500			−0.968393			−0.484197	−	0.874959i	$-0.660888\pi$
$839$	−28.0500			−0.968393			−0.484197	+	0.874959i	$0.660888\pi$
$840$	5.61540	+	2.29796i	0.193750	+	0.0792871i
$841$	8.35830			0.288217
$842$	24.6936	+	14.2569i	0.850998	+	0.491324i
$843$	8.76299	+	8.48167i	0.301813	+	0.292124i
$844$	−1.30637	−	2.26269i	−0.0449670	−	0.0778852i
$845$	8.48292	−	14.6928i	0.291821	−	0.505449i
$846$	−7.69953	−	12.3846i	−0.264715	−	0.425793i
$847$	59.6523	−	23.8711i	2.04968	−	0.820221i
$848$		−	2.31934i		−	0.0796466i
$849$	−2.33088	+	9.30342i	−0.0799957	+	0.319292i
$850$	4.31485	−	2.49118i	0.147998	−	0.0854467i
$851$	−2.74249	+	1.58338i	−0.0940115	+	0.0542775i
$852$	5.57382	−	22.2472i	0.190956	−	0.762176i
$853$		−	47.7792i		−	1.63593i	−0.575268	−	0.817965i	$-0.695102\pi$
$853$		−	47.7792i		−	1.63593i	0.575268	−	0.817965i	$-0.304898\pi$
$854$	2.82011	−	19.5940i	0.0965022	−	0.670495i
$855$	−7.24199	−	11.6487i	−0.247671	−	0.398377i
$856$	7.22158	−	12.5081i	0.246829	−	0.427520i
$857$	14.0384	+	24.3153i	0.479544	+	0.830594i	0.999725	−	0.0234618i	$-0.00746881\pi$
$857$	14.0384	+	24.3153i	0.479544	+	0.830594i	−0.520181	+	0.854056i	$0.674135\pi$
$858$	3.18899	+	3.08661i	0.108870	+	0.105375i
$859$	22.4563	+	12.9652i	0.766200	+	0.442366i	0.831517	−	0.555499i	$-0.187473\pi$
$859$	22.4563	+	12.9652i	0.766200	+	0.442366i	−0.0653176	+	0.997865i	$0.520806\pi$
$860$	−9.02334			−0.307693
$861$	4.31393	−	0.586675i	0.147018	−	0.0199938i
$862$	−40.9293			−1.39406
$863$	37.4012	+	21.5936i	1.27315	+	0.735054i	0.975580	−	0.219645i	$-0.0704900\pi$
$863$	37.4012	+	21.5936i	1.27315	+	0.735054i	0.297571	+	0.954700i	$0.403823\pi$
$864$	5.07888	+	1.09774i	0.172787	+	0.0373457i
$865$	3.06262	+	5.30462i	0.104132	+	0.180362i
$866$	−4.07754	+	7.06251i	−0.138561	+	0.239994i
$867$	6.96416	+	24.3919i	0.236515	+	0.828394i
$868$	−7.45039	−	18.6180i	−0.252883	−	0.631937i
$869$		−	77.0406i		−	2.61342i
$870$	−10.1066	−	2.53212i	−0.342647	−	0.0858470i
$871$	3.25407	−	1.87874i	0.110260	−	0.0636586i
$872$	7.17542	−	4.14273i	0.242990	−	0.140291i
$873$	−31.0428	+	1.01310i	−1.05064	+	0.0342882i
$874$			3.45322i			0.116807i
$875$	22.7059	+	17.8615i	0.767601	+	0.603829i
$876$	21.3842	−	6.10541i	0.722505	−	0.206283i
$877$	2.64342	−	4.57854i	0.0892620	−	0.154606i	−0.817937	−	0.575307i	$-0.804882\pi$
$877$	2.64342	−	4.57854i	0.0892620	−	0.154606i	0.907199	+	0.420701i	$0.138216\pi$
$878$	12.1937	+	21.1201i	0.411517	+	0.712768i
$879$	1.08726	−	1.12332i	0.0366722	−	0.0378886i
$880$	−6.81110	−	3.93239i	−0.229602	−	0.132561i
$881$	18.2562			0.615067			0.307534	−	0.951537i	$-0.400496\pi$
$881$	18.2562			0.615067			0.307534	+	0.951537i	$0.400496\pi$
$882$	−20.3301	−	5.26192i	−0.684549	−	0.177178i
$883$	43.3057			1.45735			0.728677	−	0.684857i	$-0.240135\pi$
$883$	43.3057			1.45735			0.728677	+	0.684857i	$0.240135\pi$
$884$	0.573231	+	0.330955i	0.0192798	+	0.0111312i
$885$	5.89833	−	6.09396i	0.198270	−	0.204846i
$886$	−14.3842	−	24.9142i	−0.483248	−	0.837010i
$887$	−0.722966	+	1.25221i	−0.0242748	+	0.0420452i	−0.877908	−	0.478830i	$-0.841061\pi$
$887$	−0.722966	+	1.25221i	−0.0242748	+	0.0420452i	0.853633	+	0.520875i	$0.174394\pi$
$888$	5.27423	−	1.50585i	0.176992	−	0.0505330i
$889$	−26.8440	−	21.1167i	−0.900319	−	0.708231i
$890$		−	21.9763i		−	0.736647i
$891$	44.4571	−	29.6923i	1.48937	−	0.994729i
$892$	0.201665	−	0.116431i	0.00675224	−	0.00389841i
$893$	−14.5371	+	8.39301i	−0.486466	+	0.280861i
$894$	−9.28472	−	2.32620i	−0.310527	−	0.0777997i
$895$		−	27.8904i		−	0.932274i
$896$	0.982969	+	2.45637i	0.0328387	+	0.0820617i
$897$	−0.205121	−	0.718436i	−0.00684879	−	0.0239879i
$898$	5.27609	−	9.13845i	0.176065	−	0.304954i
$899$	17.2180	+	29.8224i	0.574251	+	0.994632i
$900$	8.59028	+	4.59272i	0.286343	+	0.153091i
$901$	−3.08213	−	1.77947i	−0.102681	−	0.0592826i
$902$	−5.64334			−0.187903
$903$	30.9460	−	4.20852i	1.02982	−	0.140051i
$904$	8.85205			0.294415
$905$	7.31239	+	4.22181i	0.243072	+	0.140338i
$906$	12.3135	+	11.9182i	0.409089	+	0.395956i
$907$	−18.6824	−	32.3588i	−0.620338	−	1.07446i	−0.989423	−	0.145061i	$-0.953662\pi$
$907$	−18.6824	−	32.3588i	−0.620338	−	1.07446i	0.369085	−	0.929396i	$-0.379671\pi$
$908$	3.83498	−	6.64239i	0.127268	−	0.220435i
$909$	−41.3991	+	25.7378i	−1.37312	+	0.853671i
$910$	−0.215266	+	1.49566i	−0.00713600	+	0.0495808i
$911$		−	38.1364i		−	1.26351i	−0.775166	−	0.631757i	$-0.782334\pi$
$911$		−	38.1364i		−	1.26351i	0.775166	−	0.631757i	$-0.217666\pi$
$912$	1.45359	−	5.80183i	0.0481333	−	0.192118i
$913$	17.2543	−	9.96177i	0.571034	−	0.329687i
$914$	−15.2948	+	8.83043i	−0.505906	+	0.292085i
$915$	−4.17003	+	16.6441i	−0.137857	+	0.550238i
$916$			6.28836i			0.207773i
$917$	31.6784	−	12.6768i	1.04611	−	0.418623i
$918$	5.35542	−	5.90700i	0.176755	−	0.194960i
$919$	−5.62761	+	9.74731i	−0.185638	+	0.321534i	−0.943791	−	0.330542i	$-0.892768\pi$
$919$	−5.62761	+	9.74731i	−0.185638	+	0.321534i	0.758153	+	0.652076i	$0.226102\pi$
$920$	0.662008	+	1.14663i	0.0218258	+	0.0378033i
$921$	35.1887	+	34.0591i	1.15951	+	1.12228i
$922$	−15.0200	−	8.67179i	−0.494657	−	0.285590i
$923$	5.71187			0.188008
$924$	25.1931	+	10.3096i	0.828791	+	0.339161i
$925$	10.2824			0.338084
$926$	0.476643	+	0.275190i	0.0156635	+	0.00904330i
$927$	−23.0817	+	43.1723i	−0.758101	+	1.41796i
$928$	−2.27166	−	3.93462i	−0.0745708	−	0.129160i
$929$	−21.0957	+	36.5387i	−0.692126	+	1.19880i	0.279014	+	0.960287i	$0.409992\pi$
$929$	−21.0957	+	36.5387i	−0.692126	+	1.19880i	−0.971140	+	0.238510i	$0.923341\pi$
$930$	4.77198	+	16.7138i	0.156479	+	0.548068i
$931$	−6.81694	+	23.1914i	−0.223416	+	0.760067i
$932$			11.9785i			0.392369i
$933$	−26.6310	−	6.67213i	−0.871858	−	0.218436i
$934$	5.44218	−	3.14205i	0.178074	−	0.102811i
$935$	−10.4513	+	6.03409i	−0.341796	+	0.197336i
$936$	0.0422110	+	1.29340i	0.00137971	+	0.0422762i
$937$			44.8813i			1.46621i	0.680117	+	0.733104i	$0.261929\pi$
$937$			44.8813i			1.46621i	−0.680117	+	0.733104i	$0.738071\pi$
$938$	14.2489	−	18.1135i	0.465243	−	0.591428i
$939$	54.8887	−	15.6713i	1.79122	−	0.511413i
$940$	−3.21801	+	5.57375i	−0.104960	+	0.181796i
$941$	−4.90439	−	8.49466i	−0.159879	−	0.276918i	0.774946	−	0.632027i	$-0.217777\pi$
$941$	−4.90439	−	8.49466i	−0.159879	−	0.276918i	−0.934825	+	0.355109i	$0.884444\pi$
$942$	−4.14726	+	4.28482i	−0.135125	+	0.139607i
$943$	0.822761	+	0.475021i	0.0267928	+	0.0154688i
$944$	3.69821			0.120366
$945$	17.0621	+	6.34071i	0.555031	+	0.206263i
$946$	−40.4825			−1.31620
$947$	−14.3409	−	8.27971i	−0.466016	−	0.269054i	0.248555	−	0.968618i	$-0.420044\pi$
$947$	−14.3409	−	8.27971i	−0.466016	−	0.269054i	−0.714570	+	0.699563i	$0.753378\pi$
$948$	15.6232	−	16.1414i	0.507419	−	0.524249i
$949$	2.76925	+	4.79649i	0.0898938	+	0.155701i
$950$	5.60627	−	9.71035i	0.181891	−	0.315045i
$951$	34.8949	−	9.96285i	1.13154	−	0.323068i
$952$	4.01839	+	0.578354i	0.130237	+	0.0187446i
$953$			50.7649i			1.64444i	0.569172	+	0.822218i	$0.307264\pi$
$953$			50.7649i			1.64444i	−0.569172	+	0.822218i	$0.692736\pi$
$954$	−0.226959	−	6.95433i	−0.00734806	−	0.225155i
$955$	8.82333	−	5.09415i	0.285516	−	0.164843i
$956$	−19.3141	+	11.1510i	−0.624664	+	0.360650i
$957$	−45.3427	−	11.3602i	−1.46572	−	0.367222i
$958$		−	17.3773i		−	0.561434i
$959$	−40.0332	−	5.76185i	−1.29274	−	0.186060i
$960$	−0.629593	−	2.20515i	−0.0203200	−	0.0711708i
$961$	13.2242	−	22.9050i	0.426587	−	0.738871i
$962$	0.683013	+	1.18301i	0.0220212	+	0.0381419i
$963$	20.4292	−	38.2111i	0.658323	−	1.23134i
$964$	23.5248	+	13.5820i	0.757682	+	0.437448i
$965$	15.8719			0.510934
$966$	−2.80518	−	3.62367i	−0.0902552	−	0.116590i
$967$	30.6129			0.984443			0.492222	−	0.870470i	$-0.336185\pi$
$967$	30.6129			0.984443			0.492222	+	0.870470i	$0.336185\pi$
$968$	−21.0312	−	12.1424i	−0.675968	−	0.390270i
$969$	−6.59470	−	6.38299i	−0.211852	−	0.205051i
$970$	6.85383	+	11.8712i	0.220063	+	0.381161i
$971$	−16.2236	+	28.1002i	−0.520642	+	0.901778i	0.479070	+	0.877776i	$0.340974\pi$
$971$	−16.2236	+	28.1002i	−0.520642	+	0.901778i	−0.999712	+	0.0240011i	$0.992359\pi$
$972$	15.3359	+	2.79446i	0.491900	+	0.0896325i
$973$	19.0694	−	24.2415i	0.611338	−	0.777147i
$974$			24.2678i			0.777590i
$975$	−0.589580	+	2.35323i	−0.0188817	+	0.0753637i
$976$	−6.47975	+	3.74108i	−0.207412	+	0.119749i
$977$	8.25549	−	4.76631i	0.264117	−	0.152488i	−0.362094	−	0.932141i	$-0.617938\pi$
$977$	8.25549	−	4.76631i	0.264117	−	0.152488i	0.626211	+	0.779654i	$0.284605\pi$
$978$	7.37195	−	29.4242i	0.235729	−	0.940882i
$979$		−	98.5949i		−	3.15111i
$980$	2.18242	+	9.00749i	0.0697148	+	0.287734i
$981$	21.1094	−	13.1237i	0.673972	−	0.419008i
$982$	4.19099	−	7.25901i	0.133740	−	0.231644i
$983$	−18.2133	−	31.5464i	−0.580914	−	1.00617i	−0.995371	−	0.0961038i	$-0.969362\pi$
$983$	−18.2133	−	31.5464i	−0.580914	−	1.00617i	0.414457	−	0.910069i	$-0.363971\pi$
$984$	−1.18238	−	1.14443i	−0.0376930	−	0.0364830i
$985$	17.3953	+	10.0432i	0.554259	+	0.320001i
$986$	−6.97152			−0.222019
$987$	8.43670	−	20.6163i	0.268543	−	0.656225i
$988$	1.48959			0.0473903
$989$	5.90208	+	3.40757i	0.187675	+	0.108354i
$990$	−20.8072	−	11.1244i	−0.661297	−	0.353556i
$991$	18.1027	+	31.3548i	0.575051	+	0.996018i	0.996036	+	0.0889503i	$0.0283512\pi$
$991$	18.1027	+	31.3548i	0.575051	+	0.996018i	−0.420985	+	0.907068i	$0.638315\pi$
$992$	−3.78974	+	6.56402i	−0.120324	+	0.208408i
$993$	−10.7199	−	37.5464i	−0.340186	−	1.19150i
$994$	32.5259	−	13.0159i	1.03166	−	0.412839i
$995$		−	32.0258i		−	1.01529i
$996$	5.63526	+	1.41186i	0.178560	+	0.0447366i
$997$	−51.9932	+	30.0183i	−1.64664	+	0.950689i	−0.668249	+	0.743938i	$0.732956\pi$
$997$	−51.9932	+	30.0183i	−1.64664	+	0.950689i	−0.978394	+	0.206751i	$0.933711\pi$
$998$	−25.8017	+	14.8966i	−0.816737	+	0.471543i
$999$	15.6669	−	5.03125i	0.495679	−	0.159182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.4	✓	56
3.2	odd	2	inner	966.2.l.d.47.16	yes	56
7.3	odd	6	inner	966.2.l.d.185.16	yes	56
21.17	even	6	inner	966.2.l.d.185.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.4	✓	56	1.1	even	1	trivial
966.2.l.d.47.16	yes	56	3.2	odd	2	inner
966.2.l.d.185.4	yes	56	21.17	even	6	inner
966.2.l.d.185.16	yes	56	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.20460 + 1.24456i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.662008 - 1.14663i) q^{5} +(1.66550 - 0.475517i) q^{6} +(2.07946 + 1.63580i) q^{7} -1.00000i q^{8} +(-0.0978548 - 2.99840i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.20460 + 1.24456i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.662008 - 1.14663i) q^{5} +(1.66550 - 0.475517i) q^{6} +(2.07946 + 1.63580i) q^{7} -1.00000i q^{8} +(-0.0978548 - 2.99840i) q^{9} +(-1.14663 + 0.662008i) q^{10} +(-5.14427 + 2.97005i) q^{11} +(-1.68012 - 0.420939i) q^{12} -0.431364i q^{13} +(-0.982969 - 2.45637i) q^{14} +(0.629593 + 2.20515i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.767229 + 1.32888i) q^{17} +(-1.41446 + 2.64562i) q^{18} +(2.99058 + 1.72661i) q^{19} +1.32402 q^{20} +(-4.54078 + 0.617525i) q^{21} +5.94009 q^{22} +(-0.866025 - 0.500000i) q^{23} +(1.24456 + 1.20460i) q^{24} +(1.62349 + 2.81197i) q^{25} +(-0.215682 + 0.373572i) q^{26} +(3.84957 + 3.49011i) q^{27} +(-0.376911 + 2.61877i) q^{28} -4.54331i q^{29} +(0.557330 - 2.22451i) q^{30} +(-6.56402 + 3.78974i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.50042 - 9.98008i) q^{33} -1.53446i q^{34} +(3.25228 - 1.30147i) q^{35} +(2.54777 - 1.58395i) q^{36} +(1.58338 - 2.74249i) q^{37} +(-1.72661 - 2.99058i) q^{38} +(0.536858 + 0.519623i) q^{39} +(-1.14663 - 0.662008i) q^{40} -0.950042 q^{41} +(4.24119 + 1.73560i) q^{42} -6.81513 q^{43} +(-5.14427 - 2.97005i) q^{44} +(-3.50284 - 1.87276i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-2.43049 + 4.20973i) q^{47} +(-0.475517 - 1.66550i) q^{48} +(1.64833 + 6.80316i) q^{49} -3.24698i q^{50} +(-2.57808 - 0.645913i) q^{51} +(0.373572 - 0.215682i) q^{52} +(-2.00861 + 1.15967i) q^{53} +(-1.58877 - 4.94730i) q^{54} +7.86478i q^{55} +(1.63580 - 2.07946i) q^{56} +(-5.75133 + 1.64207i) q^{57} +(-2.27166 + 3.93462i) q^{58} +(-1.84910 - 3.20274i) q^{59} +(-1.59492 + 1.64782i) q^{60} +(6.47975 + 3.74108i) q^{61} +7.57947 q^{62} +(4.70130 - 6.39514i) q^{63} -1.00000 q^{64} +(-0.494615 - 0.285566i) q^{65} +(-7.15547 + 7.39280i) q^{66} +(4.35534 + 7.54367i) q^{67} +(-0.767229 + 1.32888i) q^{68} +(1.66550 - 0.475517i) q^{69} +(-3.46729 - 0.499036i) q^{70} +13.2414i q^{71} +(-2.99840 + 0.0978548i) q^{72} +(-11.1193 + 6.41976i) q^{73} +(-2.74249 + 1.58338i) q^{74} +(-5.45533 - 1.36678i) q^{75} +3.45322i q^{76} +(-15.5557 - 2.23889i) q^{77} +(-0.205121 - 0.718436i) q^{78} +(-6.48480 + 11.2320i) q^{79} +(0.662008 + 1.14663i) q^{80} +(-8.98085 + 0.586816i) q^{81} +(0.822761 + 0.475021i) q^{82} -3.35408 q^{83} +(-2.80518 - 3.62367i) q^{84} +2.03165 q^{85} +(5.90208 + 3.40757i) q^{86} +(5.65442 + 5.47290i) q^{87} +(2.97005 + 5.14427i) q^{88} +(-8.29910 + 14.3745i) q^{89} +(2.09717 + 3.37328i) q^{90} +(0.705624 - 0.897005i) q^{91} -1.00000i q^{92} +(3.19049 - 12.7344i) q^{93} +(4.20973 - 2.43049i) q^{94} +(3.95957 - 2.28606i) q^{95} +(-0.420939 + 1.68012i) q^{96} -10.3531i q^{97} +(1.97408 - 6.71588i) q^{98} +(9.40879 + 15.1340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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