LMFDB - Embedded newform 462.2.i.f.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(67,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.i (of order $3$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.500000 + 1.51496i$ of defining polynomial
Character	$\chi$	$=$	462.67
Dual form			462.2.i.f.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.227452 - 0.393958i) q^{5} +1.00000 q^{6} +(-0.227452 - 2.63596i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.227452 - 0.393958i) q^{5} +1.00000 q^{6} +(-0.227452 - 2.63596i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.227452 + 0.393958i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +0.909808 q^{13} +(-2.16908 + 1.51496i) q^{14} +0.454904 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.94163 - 3.36300i) q^{19} +0.454904 q^{20} +(2.39653 + 1.12100i) q^{21} +1.00000 q^{22} +(-4.16908 - 7.22106i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.39653 - 4.15091i) q^{25} +(-0.454904 - 0.787917i) q^{26} +1.00000 q^{27} +(2.39653 + 1.12100i) q^{28} -2.79306 q^{29} +(-0.227452 - 0.393958i) q^{30} +(4.79306 - 8.30183i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(-0.986723 + 0.689160i) q^{35} +1.00000 q^{36} +(-3.94163 - 6.82710i) q^{37} +(-1.94163 + 3.36300i) q^{38} +(-0.454904 + 0.787917i) q^{39} +(-0.227452 - 0.393958i) q^{40} -1.79306 q^{41} +(-0.227452 - 2.63596i) q^{42} +7.88325 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.227452 + 0.393958i) q^{45} +(-4.16908 + 7.22106i) q^{46} +(-0.169079 - 0.292854i) q^{47} +1.00000 q^{48} +(-6.89653 + 1.19911i) q^{49} -4.79306 q^{50} +(-0.500000 - 0.866025i) q^{51} +(-0.454904 + 0.787917i) q^{52} +(-0.454904 + 0.787917i) q^{53} +(-0.500000 - 0.866025i) q^{54} +0.454904 q^{55} +(-0.227452 - 2.63596i) q^{56} +3.88325 q^{57} +(1.39653 + 2.41886i) q^{58} +(-3.48672 + 6.03918i) q^{59} +(-0.227452 + 0.393958i) q^{60} +(7.02051 + 12.1599i) q^{61} -9.58612 q^{62} +(-2.16908 + 1.51496i) q^{63} +1.00000 q^{64} +(-0.206938 - 0.358427i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(1.89653 - 3.28489i) q^{67} +(-0.500000 - 0.866025i) q^{68} +8.33816 q^{69} +(1.09019 + 0.509947i) q^{70} -4.79306 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.33816 + 9.24596i) q^{73} +(-3.94163 + 6.82710i) q^{74} +(2.39653 + 4.15091i) q^{75} +3.88325 q^{76} +(2.39653 + 1.12100i) q^{77} +0.909808 q^{78} +(-2.68236 - 4.64598i) q^{79} +(-0.227452 + 0.393958i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.896531 + 1.55284i) q^{82} +1.97345 q^{83} +(-2.16908 + 1.51496i) q^{84} +0.454904 q^{85} +(-3.94163 - 6.82710i) q^{86} +(1.39653 - 2.41886i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(5.54510 + 9.60439i) q^{89} +0.454904 q^{90} +(-0.206938 - 2.39821i) q^{91} +8.33816 q^{92} +(4.79306 + 8.30183i) q^{93} +(-0.169079 + 0.292854i) q^{94} +(-0.883254 + 1.52984i) q^{95} +(-0.500000 - 0.866025i) q^{96} +14.5861 q^{97} +(4.48672 + 5.37302i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{21} + 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 6 q^{27} - 3 q^{28} + 18 q^{29} - 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} + 6 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} + 24 q^{41} + 18 q^{43} - 3 q^{44} - 9 q^{46} + 15 q^{47} + 6 q^{48} - 24 q^{49} + 6 q^{50} - 3 q^{51} - 3 q^{54} - 6 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 3 q^{63} + 6 q^{64} - 36 q^{65} - 3 q^{66} - 6 q^{67} - 3 q^{68} + 18 q^{69} + 12 q^{70} + 6 q^{71} - 3 q^{72} - 9 q^{74} - 3 q^{75} - 6 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} - 12 q^{83} + 3 q^{84} - 9 q^{86} - 9 q^{87} - 3 q^{88} + 36 q^{89} - 36 q^{91} + 18 q^{92} - 6 q^{93} + 15 q^{94} + 24 q^{95} - 3 q^{96} + 18 q^{97} + 15 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^21 + 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 6 * q^27 - 3 * q^28 + 18 * q^29 - 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 + 6 * q^35 + 6 * q^36 - 9 * q^37 + 3 * q^38 + 24 * q^41 + 18 * q^43 - 3 * q^44 - 9 * q^46 + 15 * q^47 + 6 * q^48 - 24 * q^49 + 6 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 3 * q^63 + 6 * q^64 - 36 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 + 18 * q^69 + 12 * q^70 + 6 * q^71 - 3 * q^72 - 9 * q^74 - 3 * q^75 - 6 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 - 12 * q^83 + 3 * q^84 - 9 * q^86 - 9 * q^87 - 3 * q^88 + 36 * q^89 - 36 * q^91 + 18 * q^92 - 6 * q^93 + 15 * q^94 + 24 * q^95 - 3 * q^96 + 18 * q^97 + 15 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.227452	−	0.393958i	−0.101720	−	0.176184i	0.810674	−	0.585498i	$-0.199101\pi$
$5$	−0.227452	−	0.393958i	−0.101720	−	0.176184i	−0.912393	+	0.409315i	$0.865768\pi$
$6$	1.00000			0.408248
$7$	−0.227452	−	2.63596i	−0.0859688	−	0.996298i
$7$	−0.227452	−	2.63596i	−0.0859688	−	0.996298i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.227452	+	0.393958i	−0.0719267	+	0.124581i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.909808			0.252335			0.126168	−	0.992009i	$-0.459732\pi$
$13$	0.909808			0.252335			0.126168	+	0.992009i	$0.459732\pi$
$14$	−2.16908	+	1.51496i	−0.579711	+	0.404889i
$15$	0.454904			0.117456
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−1.94163	−	3.36300i	−0.445440	−	0.771524i	0.552643	−	0.833418i	$-0.313619\pi$
$19$	−1.94163	−	3.36300i	−0.445440	−	0.771524i	−0.998083	+	0.0618938i	$0.980286\pi$
$20$	0.454904			0.101720
$21$	2.39653	+	1.12100i	0.522966	+	0.244622i
$22$	1.00000			0.213201
$23$	−4.16908	−	7.22106i	−0.869313	−	1.50569i	−0.862700	−	0.505716i	$-0.831228\pi$
$23$	−4.16908	−	7.22106i	−0.869313	−	1.50569i	−0.00661323	−	0.999978i	$-0.502105\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.39653	−	4.15091i	0.479306	−	0.830183i
$26$	−0.454904	−	0.787917i	−0.0892140	−	0.154523i
$27$	1.00000			0.192450
$28$	2.39653	+	1.12100i	0.452902	+	0.211849i
$29$	−2.79306			−0.518659			−0.259329	−	0.965789i	$-0.583502\pi$
$29$	−2.79306			−0.518659			−0.259329	+	0.965789i	$0.583502\pi$
$30$	−0.227452	−	0.393958i	−0.0415269	−	0.0719267i
$31$	4.79306	−	8.30183i	0.860859	−	1.49105i	−0.0102412	−	0.999948i	$-0.503260\pi$
$31$	4.79306	−	8.30183i	0.860859	−	1.49105i	0.871101	−	0.491105i	$-0.163407\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	1.00000			0.171499
$35$	−0.986723	+	0.689160i	−0.166787	+	0.116489i
$36$	1.00000			0.166667
$37$	−3.94163	−	6.82710i	−0.647999	−	1.12237i	−0.983600	−	0.180364i	$-0.942273\pi$
$37$	−3.94163	−	6.82710i	−0.647999	−	1.12237i	0.335601	−	0.942004i	$-0.391061\pi$
$38$	−1.94163	+	3.36300i	−0.314973	+	0.545550i
$39$	−0.454904	+	0.787917i	−0.0728430	+	0.126168i
$40$	−0.227452	−	0.393958i	−0.0359633	−	0.0622903i
$41$	−1.79306			−0.280029			−0.140015	−	0.990149i	$-0.544715\pi$
$41$	−1.79306			−0.280029			−0.140015	+	0.990149i	$0.544715\pi$
$42$	−0.227452	−	2.63596i	−0.0350966	−	0.406737i
$43$	7.88325			1.20218			0.601092	−	0.799179i	$-0.294732\pi$
$43$	7.88325			1.20218			0.601092	+	0.799179i	$0.294732\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−0.227452	+	0.393958i	−0.0339065	+	0.0587279i
$46$	−4.16908	+	7.22106i	−0.614697	+	1.06469i
$47$	−0.169079	−	0.292854i	−0.0246627	−	0.0427171i	0.853431	−	0.521206i	$-0.174518\pi$
$47$	−0.169079	−	0.292854i	−0.0246627	−	0.0427171i	−0.878093	+	0.478489i	$0.841185\pi$
$48$	1.00000			0.144338
$49$	−6.89653	+	1.19911i	−0.985219	+	0.171301i
$50$	−4.79306			−0.677841
$51$	−0.500000	−	0.866025i	−0.0700140	−	0.121268i
$52$	−0.454904	+	0.787917i	−0.0630838	+	0.109264i
$53$	−0.454904	+	0.787917i	−0.0624859	+	0.108229i	−0.895576	−	0.444909i	$-0.853236\pi$
$53$	−0.454904	+	0.787917i	−0.0624859	+	0.108229i	0.833090	+	0.553137i	$0.186570\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	0.454904			0.0613393
$56$	−0.227452	−	2.63596i	−0.0303946	−	0.352244i
$57$	3.88325			0.514350
$58$	1.39653	+	2.41886i	0.183374	+	0.317612i
$59$	−3.48672	+	6.03918i	−0.453933	+	0.786234i	−0.998626	−	0.0524008i	$-0.983313\pi$
$59$	−3.48672	+	6.03918i	−0.453933	+	0.786234i	0.544693	+	0.838635i	$0.316646\pi$
$60$	−0.227452	+	0.393958i	−0.0293639	+	0.0508598i
$61$	7.02051	+	12.1599i	0.898885	+	1.55691i	0.828922	+	0.559364i	$0.188955\pi$
$61$	7.02051	+	12.1599i	0.898885	+	1.55691i	0.0699629	+	0.997550i	$0.477712\pi$
$62$	−9.58612			−1.21744
$63$	−2.16908	+	1.51496i	−0.273278	+	0.190867i
$64$	1.00000			0.125000
$65$	−0.206938	−	0.358427i	−0.0256675	−	0.0444574i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	1.89653	−	3.28489i	0.231698	−	0.401313i	−0.726610	−	0.687050i	$-0.758905\pi$
$67$	1.89653	−	3.28489i	0.231698	−	0.401313i	0.958308	+	0.285737i	$0.0922385\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	8.33816			1.00380
$70$	1.09019	+	0.509947i	0.130303	+	0.0609503i
$71$	−4.79306			−0.568832			−0.284416	−	0.958701i	$-0.591800\pi$
$71$	−4.79306			−0.568832			−0.284416	+	0.958701i	$0.591800\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−5.33816	+	9.24596i	−0.624784	+	1.08216i	0.363798	+	0.931478i	$0.381480\pi$
$73$	−5.33816	+	9.24596i	−0.624784	+	1.08216i	−0.988583	+	0.150680i	$0.951854\pi$
$74$	−3.94163	+	6.82710i	−0.458205	+	0.793634i
$75$	2.39653	+	4.15091i	0.276728	+	0.479306i
$76$	3.88325			0.445440
$77$	2.39653	+	1.12100i	0.273110	+	0.127750i
$78$	0.909808			0.103015
$79$	−2.68236	−	4.64598i	−0.301789	−	0.522713i	0.674753	−	0.738044i	$-0.264250\pi$
$79$	−2.68236	−	4.64598i	−0.301789	−	0.522713i	−0.976541	+	0.215331i	$0.930917\pi$
$80$	−0.227452	+	0.393958i	−0.0254299	+	0.0440459i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.896531	+	1.55284i	0.0990053	+	0.171482i
$83$	1.97345			0.216614			0.108307	−	0.994118i	$-0.465457\pi$
$83$	1.97345			0.216614			0.108307	+	0.994118i	$0.465457\pi$
$84$	−2.16908	+	1.51496i	−0.236666	+	0.165295i
$85$	0.454904			0.0493413
$86$	−3.94163	−	6.82710i	−0.425037	−	0.736185i
$87$	1.39653	−	2.41886i	0.149724	−	0.259329i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	5.54510	+	9.60439i	0.587779	+	1.01806i	0.994523	+	0.104521i	$0.0333309\pi$
$89$	5.54510	+	9.60439i	0.587779	+	1.01806i	−0.406744	+	0.913542i	$0.633336\pi$
$90$	0.454904			0.0479511
$91$	−0.206938	−	2.39821i	−0.0216930	−	0.251401i
$92$	8.33816			0.869313
$93$	4.79306	+	8.30183i	0.497017	+	0.860859i
$94$	−0.169079	+	0.292854i	−0.0174392	+	0.0302055i
$95$	−0.883254	+	1.52984i	−0.0906200	+	0.156958i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	14.5861			1.48100			0.740498	−	0.672058i	$-0.234590\pi$
$97$	14.5861			1.48100			0.740498	+	0.672058i	$0.234590\pi$
$98$	4.48672	+	5.37302i	0.453227	+	0.542757i
$99$	1.00000			0.100504
$100$	2.39653	+	4.15091i	0.239653	+	0.415091i
$101$	4.03182	−	6.98332i	0.401181	−	0.694866i	−0.592688	−	0.805432i	$-0.701933\pi$
$101$	4.03182	−	6.98332i	0.401181	−	0.694866i	0.993869	+	0.110566i	$0.0352665\pi$
$102$	−0.500000	+	0.866025i	−0.0495074	+	0.0857493i
$103$	−2.88325	−	4.99394i	−0.284095	−	0.492068i	0.688294	−	0.725432i	$-0.258360\pi$
$103$	−2.88325	−	4.99394i	−0.284095	−	0.492068i	−0.972389	+	0.233364i	$0.925027\pi$
$104$	0.909808			0.0892140
$105$	−0.103469	−	1.19911i	−0.0100975	−	0.117021i
$106$	0.909808			0.0883684
$107$	−7.80634	−	13.5210i	−0.754667	−	1.30712i	−0.945540	−	0.325507i	$-0.894465\pi$
$107$	−7.80634	−	13.5210i	−0.754667	−	1.30712i	0.190872	−	0.981615i	$-0.438868\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−7.02051	+	12.1599i	−0.672443	+	1.16471i	0.304766	+	0.952427i	$0.401422\pi$
$109$	−7.02051	+	12.1599i	−0.672443	+	1.16471i	−0.977209	+	0.212279i	$0.931912\pi$
$110$	−0.227452	−	0.393958i	−0.0216867	−	0.0375625i
$111$	7.88325			0.748245
$112$	−2.16908	+	1.51496i	−0.204959	+	0.143150i
$113$	7.58612			0.713643			0.356821	−	0.934173i	$-0.383861\pi$
$113$	7.58612			0.713643			0.356821	+	0.934173i	$0.383861\pi$
$114$	−1.94163	−	3.36300i	−0.181850	−	0.314973i
$115$	−1.89653	+	3.28489i	−0.176852	+	0.306317i
$116$	1.39653	−	2.41886i	0.129665	−	0.224586i
$117$	−0.454904	−	0.787917i	−0.0420559	−	0.0728430i
$118$	6.97345			0.641958
$119$	2.39653	+	1.12100i	0.219690	+	0.102762i
$120$	0.454904			0.0415269
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	7.02051	−	12.1599i	0.635608	−	1.10090i
$123$	0.896531	−	1.55284i	0.0808375	−	0.140015i
$124$	4.79306	+	8.30183i	0.430430	+	0.745526i
$125$	−4.45490			−0.398459
$126$	2.39653	+	1.12100i	0.213500	+	0.0998665i
$127$	7.42835			0.659159			0.329580	−	0.944128i	$-0.393093\pi$
$127$	7.42835			0.659159			0.329580	+	0.944128i	$0.393093\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.94163	+	6.82710i	−0.347041	+	0.601092i
$130$	−0.206938	+	0.358427i	−0.0181496	+	0.0314361i
$131$	9.70287	+	16.8059i	0.847744	+	1.46834i	0.883217	+	0.468965i	$0.155373\pi$
$131$	9.70287	+	16.8059i	0.847744	+	1.46834i	−0.0354732	+	0.999371i	$0.511294\pi$
$132$	1.00000			0.0870388
$133$	−8.42309	+	5.88296i	−0.730374	+	0.510118i
$134$	−3.79306			−0.327671
$135$	−0.227452	−	0.393958i	−0.0195760	−	0.0339065i
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	−0.454904	+	0.787917i	−0.0388651	+	0.0673163i	−0.884804	−	0.465964i	$-0.845708\pi$
$137$	−0.454904	+	0.787917i	−0.0388651	+	0.0673163i	0.845939	+	0.533280i	$0.179041\pi$
$138$	−4.16908	−	7.22106i	−0.354896	−	0.614697i
$139$	−8.37919			−0.710713			−0.355357	−	0.934731i	$-0.615641\pi$
$139$	−8.37919			−0.710713			−0.355357	+	0.934731i	$0.615641\pi$
$140$	−0.103469	−	1.19911i	−0.00874472	−	0.101343i
$141$	0.338158			0.0284781
$142$	2.39653	+	4.15091i	0.201112	+	0.348337i
$143$	−0.454904	+	0.787917i	−0.0380410	+	0.0658889i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.635288	+	1.10035i	0.0527578	+	0.0913791i
$146$	10.6763			0.883578
$147$	2.40981	−	6.57212i	0.198758	−	0.542060i
$148$	7.88325			0.647999
$149$	−2.05837	−	3.56521i	−0.168628	−	0.292073i	0.769309	−	0.638876i	$-0.220600\pi$
$149$	−2.05837	−	3.56521i	−0.168628	−	0.292073i	−0.937938	+	0.346803i	$0.887267\pi$
$150$	2.39653	−	4.15091i	0.195676	−	0.338921i
$151$	3.07889	−	5.33279i	0.250556	−	0.433976i	−0.713123	−	0.701039i	$-0.752720\pi$
$151$	3.07889	−	5.33279i	0.250556	−	0.433976i	0.963679	+	0.267063i	$0.0860531\pi$
$152$	−1.94163	−	3.36300i	−0.157487	−	0.272775i
$153$	1.00000			0.0808452
$154$	−0.227452	−	2.63596i	−0.0183286	−	0.212411i
$155$	−4.36077			−0.350265
$156$	−0.454904	−	0.787917i	−0.0364215	−	0.0630838i
$157$	8.82488	−	15.2851i	0.704302	−	1.21989i	−0.262641	−	0.964894i	$-0.584593\pi$
$157$	8.82488	−	15.2851i	0.704302	−	1.21989i	0.966943	−	0.254993i	$-0.0820733\pi$
$158$	−2.68236	+	4.64598i	−0.213397	+	0.369614i
$159$	−0.454904	−	0.787917i	−0.0360762	−	0.0624859i
$160$	0.454904			0.0359633
$161$	−18.0861	+	12.6320i	−1.42539	+	0.995537i
$162$	1.00000			0.0785674
$163$	5.80634	+	10.0569i	0.454788	+	0.787715i	0.998676	−	0.0514424i	$-0.0163818\pi$
$163$	5.80634	+	10.0569i	0.454788	+	0.787715i	−0.543888	+	0.839158i	$0.683049\pi$
$164$	0.896531	−	1.55284i	0.0700073	−	0.121256i
$165$	−0.227452	+	0.393958i	−0.0177071	+	0.0306696i
$166$	−0.986723	−	1.70905i	−0.0765846	−	0.132648i
$167$	−4.85670			−0.375823			−0.187911	−	0.982186i	$-0.560172\pi$
$167$	−4.85670			−0.375823			−0.187911	+	0.982186i	$0.560172\pi$
$168$	2.39653	+	1.12100i	0.184896	+	0.0864869i
$169$	−12.1722			−0.936327
$170$	−0.227452	−	0.393958i	−0.0174448	−	0.0302152i
$171$	−1.94163	+	3.36300i	−0.148480	+	0.257175i
$172$	−3.94163	+	6.82710i	−0.300546	+	0.520561i
$173$	12.7931	+	22.1582i	0.972639	+	1.68466i	0.687518	+	0.726168i	$0.258700\pi$
$173$	12.7931	+	22.1582i	0.972639	+	1.68466i	0.285121	+	0.958492i	$0.407966\pi$
$174$	−2.79306			−0.211742
$175$	−11.4867	−	5.37302i	−0.868315	−	0.406162i
$176$	1.00000			0.0753778
$177$	−3.48672	−	6.03918i	−0.262078	−	0.453933i
$178$	5.54510	−	9.60439i	0.415623	−	0.719879i
$179$	7.85144	−	13.5991i	0.586844	−	1.01644i	−0.407799	−	0.913072i	$-0.633704\pi$
$179$	7.85144	−	13.5991i	0.586844	−	1.01644i	0.994643	−	0.103372i	$-0.0329631\pi$
$180$	−0.227452	−	0.393958i	−0.0169533	−	0.0293639i
$181$	−2.49593			−0.185521			−0.0927606	−	0.995688i	$-0.529569\pi$
$181$	−2.49593			−0.185521			−0.0927606	+	0.995688i	$0.529569\pi$
$182$	−1.97345	+	1.37832i	−0.146282	+	0.102168i
$183$	−14.0410			−1.03794
$184$	−4.16908	−	7.22106i	−0.307349	−	0.532343i
$185$	−1.79306	+	3.10567i	−0.131829	+	0.228334i
$186$	4.79306	−	8.30183i	0.351444	−	0.608720i
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	0.338158			0.0246627
$189$	−0.227452	−	2.63596i	−0.0165447	−	0.191738i
$190$	1.76651			0.128156
$191$	−4.90981	−	8.50404i	−0.355261	−	0.615331i	0.631901	−	0.775049i	$-0.282275\pi$
$191$	−4.90981	−	8.50404i	−0.355261	−	0.615331i	−0.987163	+	0.159718i	$0.948941\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−3.42835	+	5.93808i	−0.246778	+	0.427432i	−0.962630	−	0.270820i	$-0.912705\pi$
$193$	−3.42835	+	5.93808i	−0.246778	+	0.427432i	0.715852	+	0.698252i	$0.246039\pi$
$194$	−7.29306	−	12.6320i	−0.523611	−	0.906921i
$195$	0.413875			0.0296382
$196$	2.40981	−	6.57212i	0.172129	−	0.469437i
$197$	23.4694			1.67212			0.836062	−	0.548635i	$-0.184852\pi$
$197$	23.4694			1.67212			0.836062	+	0.548635i	$0.184852\pi$
$198$	−0.500000	−	0.866025i	−0.0355335	−	0.0615457i
$199$	1.11675	−	1.93426i	0.0791640	−	0.137116i	−0.823725	−	0.566989i	$-0.808108\pi$
$199$	1.11675	−	1.93426i	0.0791640	−	0.137116i	0.902889	+	0.429873i	$0.141442\pi$
$200$	2.39653	−	4.15091i	0.169460	−	0.293514i
$201$	1.89653	+	3.28489i	0.133771	+	0.231698i
$202$	−8.06364			−0.567356
$203$	0.635288	+	7.36239i	0.0445885	+	0.516738i
$204$	1.00000			0.0700140
$205$	0.407836	+	0.706392i	0.0284845	+	0.0493366i
$206$	−2.88325	+	4.99394i	−0.200886	+	0.347944i
$207$	−4.16908	+	7.22106i	−0.289771	+	0.501898i
$208$	−0.454904	−	0.787917i	−0.0315419	−	0.0546322i
$209$	3.88325			0.268610
$210$	−0.986723	+	0.689160i	−0.0680904	+	0.0475566i
$211$	−18.2624			−1.25724			−0.628619	−	0.777713i	$-0.716380\pi$
$211$	−18.2624			−1.25724			−0.628619	+	0.777713i	$0.716380\pi$
$212$	−0.454904	−	0.787917i	−0.0312429	−	0.0541144i
$213$	2.39653	−	4.15091i	0.164208	−	0.284416i
$214$	−7.80634	+	13.5210i	−0.533630	+	0.924275i
$215$	−1.79306	−	3.10567i	−0.122286	−	0.211805i
$216$	1.00000			0.0680414
$217$	−22.9734	−	10.7460i	−1.55954	−	0.729488i
$218$	14.0410			0.950978
$219$	−5.33816	−	9.24596i	−0.360719	−	0.624784i
$220$	−0.227452	+	0.393958i	−0.0153348	+	0.0265607i
$221$	−0.454904	+	0.787917i	−0.0306002	+	0.0530010i
$222$	−3.94163	−	6.82710i	−0.264545	−	0.458205i
$223$	12.4959			0.836790			0.418395	−	0.908265i	$-0.362593\pi$
$223$	12.4959			0.836790			0.418395	+	0.908265i	$0.362593\pi$
$224$	2.39653	+	1.12100i	0.160125	+	0.0748999i
$225$	−4.79306			−0.319537
$226$	−3.79306	−	6.56978i	−0.252311	−	0.437015i
$227$	−4.89653	+	8.48104i	−0.324994	+	0.562906i	−0.981511	−	0.191405i	$-0.938696\pi$
$227$	−4.89653	+	8.48104i	−0.324994	+	0.562906i	0.656517	+	0.754311i	$0.272029\pi$
$228$	−1.94163	+	3.36300i	−0.128587	+	0.222720i
$229$	−4.33816	−	7.51391i	−0.286674	−	0.496533i	0.686340	−	0.727281i	$-0.259216\pi$
$229$	−4.33816	−	7.51391i	−0.286674	−	0.496533i	−0.973014	+	0.230748i	$0.925883\pi$
$230$	3.79306			0.250107
$231$	−2.16908	+	1.51496i	−0.142715	+	0.0996769i
$232$	−2.79306			−0.183374
$233$	−8.38325	−	14.5202i	−0.549205	−	0.951251i	−0.998329	−	0.0577819i	$-0.981597\pi$
$233$	−8.38325	−	14.5202i	−0.549205	−	0.951251i	0.449124	−	0.893469i	$-0.351736\pi$
$234$	−0.454904	+	0.787917i	−0.0297380	+	0.0515077i
$235$	−0.0769148	+	0.133220i	−0.00501737	+	0.00869033i
$236$	−3.48672	−	6.03918i	−0.226966	−	0.393117i
$237$	5.36471			0.348476
$238$	−0.227452	−	2.63596i	−0.0147435	−	0.170864i
$239$	−26.2624			−1.69878			−0.849388	−	0.527769i	$-0.823029\pi$
$239$	−26.2624			−1.69878			−0.849388	+	0.527769i	$0.823029\pi$
$240$	−0.227452	−	0.393958i	−0.0146820	−	0.0254299i
$241$	−3.97345	+	6.88221i	−0.255952	+	0.443322i	−0.965154	−	0.261684i	$-0.915722\pi$
$241$	−3.97345	+	6.88221i	−0.255952	+	0.443322i	0.709202	+	0.705006i	$0.249056\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−14.0410			−0.898885
$245$	2.04103	+	2.44421i	0.130397	+	0.156155i
$246$	−1.79306			−0.114321
$247$	−1.76651	−	3.05968i	−0.112400	−	0.194683i
$248$	4.79306	−	8.30183i	0.304360	−	0.527167i
$249$	−0.986723	+	1.70905i	−0.0625310	+	0.108307i
$250$	2.22745	+	3.85806i	0.140876	+	0.244005i
$251$	−3.93636			−0.248461			−0.124230	−	0.992253i	$-0.539646\pi$
$251$	−3.93636			−0.248461			−0.124230	+	0.992253i	$0.539646\pi$
$252$	−0.227452	−	2.63596i	−0.0143281	−	0.166050i
$253$	8.33816			0.524216
$254$	−3.71417	−	6.43314i	−0.233048	−	0.403651i
$255$	−0.227452	+	0.393958i	−0.0142436	+	0.0246706i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.54510	+	13.0685i	0.470650	+	0.815190i	0.999437	−	0.0335650i	$-0.0106861\pi$
$257$	7.54510	+	13.0685i	0.470650	+	0.815190i	−0.528786	+	0.848755i	$0.677353\pi$
$258$	7.88325			0.490790
$259$	−17.0994	+	11.9428i	−1.06251	+	0.742089i
$260$	0.413875			0.0256675
$261$	1.39653	+	2.41886i	0.0864431	+	0.149724i
$262$	9.70287	−	16.8059i	0.599445	−	1.03827i
$263$	14.3116	−	24.7884i	0.882491	−	1.52852i	0.0339291	−	0.999424i	$-0.489198\pi$
$263$	14.3116	−	24.7884i	0.882491	−	1.52852i	0.848562	−	0.529096i	$-0.177469\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	0.413875			0.0254242
$266$	9.30634	+	4.35312i	0.570608	+	0.266907i
$267$	−11.0902			−0.678709
$268$	1.89653	+	3.28489i	0.115849	+	0.200656i
$269$	11.4754	−	19.8760i	0.699669	−	1.21186i	−0.268913	−	0.963165i	$-0.586664\pi$
$269$	11.4754	−	19.8760i	0.699669	−	1.21186i	0.968581	−	0.248697i	$-0.0800023\pi$
$270$	−0.227452	+	0.393958i	−0.0138423	+	0.0239756i
$271$	−4.90981	−	8.50404i	−0.298250	−	0.516583i	0.677486	−	0.735536i	$-0.263069\pi$
$271$	−4.90981	−	8.50404i	−0.298250	−	0.516583i	−0.975736	+	0.218952i	$0.929736\pi$
$272$	1.00000			0.0606339
$273$	2.18038	+	1.01989i	0.131963	+	0.0617268i
$274$	0.909808			0.0549635
$275$	2.39653	+	4.15091i	0.144516	+	0.250310i
$276$	−4.16908	+	7.22106i	−0.250949	+	0.434657i
$277$	−5.36471	+	9.29195i	−0.322334	+	0.558299i	−0.980969	−	0.194163i	$-0.937801\pi$
$277$	−5.36471	+	9.29195i	−0.322334	+	0.558299i	0.658635	+	0.752463i	$0.271134\pi$
$278$	4.18959	+	7.25659i	0.251275	+	0.435221i
$279$	−9.58612			−0.573906
$280$	−0.986723	+	0.689160i	−0.0589680	+	0.0411852i
$281$	2.58612			0.154275			0.0771376	−	0.997020i	$-0.475422\pi$
$281$	2.58612			0.154275			0.0771376	+	0.997020i	$0.475422\pi$
$282$	−0.169079	−	0.292854i	−0.0100685	−	0.0174392i
$283$	10.0410	−	17.3916i	0.596877	−	1.03382i	−0.396402	−	0.918077i	$-0.629741\pi$
$283$	10.0410	−	17.3916i	0.596877	−	1.03382i	0.993279	−	0.115745i	$-0.0369254\pi$
$284$	2.39653	−	4.15091i	0.142208	−	0.246311i
$285$	−0.883254	−	1.52984i	−0.0523195	−	0.0906200i
$286$	0.909808			0.0537981
$287$	0.407836	+	4.72643i	0.0240738	+	0.278993i
$288$	1.00000			0.0589256
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	0.635288	−	1.10035i	0.0373054	−	0.0646148i
$291$	−7.29306	+	12.6320i	−0.427527	+	0.740498i
$292$	−5.33816	−	9.24596i	−0.312392	−	0.541079i
$293$	10.3792			0.606359			0.303179	−	0.952934i	$-0.401952\pi$
$293$	10.3792			0.606359			0.303179	+	0.952934i	$0.401952\pi$
$294$	−6.89653	+	1.19911i	−0.402214	+	0.0699334i
$295$	3.17225			0.184695
$296$	−3.94163	−	6.82710i	−0.229102	−	0.396817i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−2.05837	+	3.56521i	−0.119238	+	0.206527i
$299$	−3.79306	−	6.56978i	−0.219358	−	0.379940i
$300$	−4.79306			−0.276728
$301$	−1.79306	−	20.7799i	−0.103350	−	1.19773i
$302$	−6.15777			−0.354340
$303$	4.03182	+	6.98332i	0.231622	+	0.401181i
$304$	−1.94163	+	3.36300i	−0.111360	+	0.192881i
$305$	3.19366	−	5.53158i	0.182868	−	0.316737i
$306$	−0.500000	−	0.866025i	−0.0285831	−	0.0495074i
$307$	9.76651			0.557404			0.278702	−	0.960378i	$-0.410096\pi$
$307$	9.76651			0.557404			0.278702	+	0.960378i	$0.410096\pi$
$308$	−2.16908	+	1.51496i	−0.123595	+	0.0863227i
$309$	5.76651			0.328045
$310$	2.18038	+	3.77654i	0.123837	+	0.214493i
$311$	3.25927	−	5.64522i	0.184816	−	0.320111i	−0.758698	−	0.651442i	$-0.774164\pi$
$311$	3.25927	−	5.64522i	0.184816	−	0.320111i	0.943515	+	0.331331i	$0.107498\pi$
$312$	−0.454904	+	0.787917i	−0.0257539	+	0.0446070i
$313$	−15.3965	−	26.6676i	−0.870263	−	1.50734i	−0.861724	−	0.507377i	$-0.830615\pi$
$313$	−15.3965	−	26.6676i	−0.870263	−	1.50734i	−0.00853913	−	0.999964i	$-0.502718\pi$
$314$	−17.6498			−0.996034
$315$	1.09019	+	0.509947i	0.0614254	+	0.0287323i
$316$	5.36471			0.301789
$317$	13.8136	+	23.9258i	0.775848	+	1.34381i	0.934317	+	0.356444i	$0.116011\pi$
$317$	13.8136	+	23.9258i	0.775848	+	1.34381i	−0.158469	+	0.987364i	$0.550656\pi$
$318$	−0.454904	+	0.787917i	−0.0255098	+	0.0441842i
$319$	1.39653	−	2.41886i	0.0781907	−	0.135430i
$320$	−0.227452	−	0.393958i	−0.0127150	−	0.0220229i
$321$	15.6127			0.871415
$322$	19.9827	+	9.34707i	1.11359	+	0.520892i
$323$	3.88325			0.216070
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.18038	−	3.77654i	0.120946	−	0.209484i
$326$	5.80634	−	10.0569i	0.321583	−	0.556999i
$327$	−7.02051	−	12.1599i	−0.388235	−	0.672443i
$328$	−1.79306			−0.0990053
$329$	−0.733492	+	0.512295i	−0.0404387	+	0.0282438i
$330$	0.454904			0.0250416
$331$	14.4827	+	25.0847i	0.796039	+	1.37878i	0.922177	+	0.386767i	$0.126408\pi$
$331$	14.4827	+	25.0847i	0.796039	+	1.37878i	−0.126139	+	0.992013i	$0.540258\pi$
$332$	−0.986723	+	1.70905i	−0.0541535	+	0.0937965i
$333$	−3.94163	+	6.82710i	−0.216000	+	0.374123i
$334$	2.42835	+	4.20603i	0.132873	+	0.230143i
$335$	−1.72548			−0.0942730
$336$	−0.227452	−	2.63596i	−0.0124085	−	0.143803i
$337$	−9.03708			−0.492281			−0.246141	−	0.969234i	$-0.579163\pi$
$337$	−9.03708			−0.492281			−0.246141	+	0.969234i	$0.579163\pi$
$338$	6.08612	+	10.5415i	0.331042	+	0.573381i
$339$	−3.79306	+	6.56978i	−0.206011	+	0.356821i
$340$	−0.227452	+	0.393958i	−0.0123353	+	0.0213654i
$341$	4.79306	+	8.30183i	0.259559	+	0.449569i
$342$	3.88325			0.209982
$343$	4.72942	+	17.9062i	0.255365	+	0.966845i
$344$	7.88325			0.425037
$345$	−1.89653	−	3.28489i	−0.102106	−	0.176852i
$346$	12.7931	−	22.1582i	0.687759	−	1.19123i
$347$	10.8063	−	18.7171i	0.580115	−	1.00479i	−0.415350	−	0.909661i	$-0.636341\pi$
$347$	10.8063	−	18.7171i	0.580115	−	1.00479i	0.995465	−	0.0951267i	$-0.0303256\pi$
$348$	1.39653	+	2.41886i	0.0748619	+	0.129665i
$349$	14.2745			0.764098			0.382049	−	0.924142i	$-0.375219\pi$
$349$	14.2745			0.764098			0.382049	+	0.924142i	$0.375219\pi$
$350$	1.09019	+	12.6343i	0.0582732	+	0.675332i
$351$	0.909808			0.0485620
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	14.2480	−	24.6782i	0.758343	−	1.31349i	−0.185353	−	0.982672i	$-0.559343\pi$
$353$	14.2480	−	24.6782i	0.758343	−	1.31349i	0.943695	−	0.330816i	$-0.107324\pi$
$354$	−3.48672	+	6.03918i	−0.185317	+	0.320979i
$355$	1.09019	+	1.88827i	0.0578614	+	0.100219i
$356$	−11.0902			−0.587779
$357$	−2.16908	+	1.51496i	−0.114800	+	0.0801800i
$358$	−15.7029			−0.829922
$359$	6.81962	+	11.8119i	0.359926	+	0.623409i	0.987948	−	0.154786i	$-0.0494687\pi$
$359$	6.81962	+	11.8119i	0.359926	+	0.623409i	−0.628022	+	0.778195i	$0.716135\pi$
$360$	−0.227452	+	0.393958i	−0.0119878	+	0.0207634i
$361$	1.96017	−	3.39511i	0.103167	−	0.178690i
$362$	1.24797	+	2.16154i	0.0655917	+	0.113608i
$363$	1.00000			0.0524864
$364$	2.18038	+	1.01989i	0.114283	+	0.0534570i
$365$	4.85670			0.254211
$366$	7.02051	+	12.1599i	0.366968	+	0.635608i
$367$	−11.3647	+	19.6843i	−0.593233	+	1.02751i	0.400560	+	0.916270i	$0.368815\pi$
$367$	−11.3647	+	19.6843i	−0.593233	+	1.02751i	−0.993794	+	0.111240i	$0.964518\pi$
$368$	−4.16908	+	7.22106i	−0.217328	+	0.376424i
$369$	0.896531	+	1.55284i	0.0466715	+	0.0808375i
$370$	3.58612			0.186434
$371$	2.18038	+	1.01989i	0.113200	+	0.0529503i
$372$	−9.58612			−0.497017
$373$	−5.20090	−	9.00822i	−0.269292	−	0.466428i	0.699387	−	0.714743i	$-0.253456\pi$
$373$	−5.20090	−	9.00822i	−0.269292	−	0.466428i	−0.968679	+	0.248315i	$0.920123\pi$
$374$	−0.500000	+	0.866025i	−0.0258544	+	0.0447811i
$375$	2.22745	−	3.85806i	0.115025	−	0.199229i
$376$	−0.169079	−	0.292854i	−0.00871959	−	0.0151028i
$377$	−2.54115			−0.130876
$378$	−2.16908	+	1.51496i	−0.111565	+	0.0779210i
$379$	7.61268			0.391037			0.195519	−	0.980700i	$-0.437361\pi$
$379$	7.61268			0.391037			0.195519	+	0.980700i	$0.437361\pi$
$380$	−0.883254	−	1.52984i	−0.0453100	−	0.0784792i
$381$	−3.71417	+	6.43314i	−0.190283	+	0.329580i
$382$	−4.90981	+	8.50404i	−0.251208	+	0.435104i
$383$	11.0728	+	19.1787i	0.565796	+	0.979988i	0.996975	+	0.0777212i	$0.0247644\pi$
$383$	11.0728	+	19.1787i	0.565796	+	0.979988i	−0.431179	+	0.902266i	$0.641902\pi$
$384$	1.00000			0.0510310
$385$	−0.103469	−	1.19911i	−0.00527326	−	0.0611122i
$386$	6.85670			0.348997
$387$	−3.94163	−	6.82710i	−0.200364	−	0.347041i
$388$	−7.29306	+	12.6320i	−0.370249	+	0.641290i
$389$	1.77255	−	3.07014i	0.0898717	−	0.155662i	−0.817585	−	0.575808i	$-0.804688\pi$
$389$	1.77255	−	3.07014i	0.0898717	−	0.155662i	0.907457	+	0.420145i	$0.138021\pi$
$390$	−0.206938	−	0.358427i	−0.0104787	−	0.0181496i
$391$	8.33816			0.421679
$392$	−6.89653	+	1.19911i	−0.348327	+	0.0605641i
$393$	−19.4057			−0.978890
$394$	−11.7347	−	20.3251i	−0.591185	−	1.02396i
$395$	−1.22021	+	2.11347i	−0.0613957	+	0.106340i
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	1.27979	+	2.21665i	0.0642306	+	0.111251i	0.896352	−	0.443342i	$-0.146207\pi$
$397$	1.27979	+	2.21665i	0.0642306	+	0.111251i	−0.832122	+	0.554593i	$0.812874\pi$
$398$	−2.23349			−0.111955
$399$	−0.883254	−	10.2361i	−0.0442180	−	0.512445i
$400$	−4.79306			−0.239653
$401$	−5.24797	−	9.08974i	−0.262071	−	0.453920i	0.704721	−	0.709484i	$-0.251072\pi$
$401$	−5.24797	−	9.08974i	−0.262071	−	0.453920i	−0.966792	+	0.255564i	$0.917739\pi$
$402$	1.89653	−	3.28489i	0.0945904	−	0.163835i
$403$	4.36077	−	7.55307i	0.217225	−	0.376245i
$404$	4.03182	+	6.98332i	0.200590	+	0.347433i
$405$	0.454904			0.0226044
$406$	6.05837	−	4.23137i	0.300672	−	0.209999i
$407$	7.88325			0.390758
$408$	−0.500000	−	0.866025i	−0.0247537	−	0.0428746i
$409$	−7.92428	+	13.7253i	−0.391831	+	0.678670i	−0.992691	−	0.120683i	$-0.961491\pi$
$409$	−7.92428	+	13.7253i	−0.391831	+	0.678670i	0.600860	+	0.799354i	$0.294825\pi$
$410$	0.407836	−	0.706392i	0.0201416	−	0.0348862i
$411$	−0.454904	−	0.787917i	−0.0224388	−	0.0388651i
$412$	5.76651			0.284095
$413$	16.7121	+	7.81723i	0.822348	+	0.384661i
$414$	8.33816			0.409798
$415$	−0.448864	−	0.777456i	−0.0220339	−	0.0381638i
$416$	−0.454904	+	0.787917i	−0.0223035	+	0.0386308i
$417$	4.18959	−	7.25659i	0.205165	−	0.355357i
$418$	−1.94163	−	3.36300i	−0.0949681	−	0.164490i
$419$	−9.52249			−0.465204			−0.232602	−	0.972572i	$-0.574724\pi$
$419$	−9.52249			−0.465204			−0.232602	+	0.972572i	$0.574724\pi$
$420$	1.09019	+	0.509947i	0.0531959	+	0.0248829i
$421$	−0.530621			−0.0258609			−0.0129305	−	0.999916i	$-0.504116\pi$
$421$	−0.530621			−0.0258609			−0.0129305	+	0.999916i	$0.504116\pi$
$422$	9.13122	+	15.8157i	0.444501	+	0.769898i
$423$	−0.169079	+	0.292854i	−0.00822091	+	0.0142390i
$424$	−0.454904	+	0.787917i	−0.0220921	+	0.0382646i
$425$	2.39653	+	4.15091i	0.116249	+	0.201349i
$426$	−4.79306			−0.232225
$427$	30.4561	−	21.2716i	1.47387	−	1.02940i
$428$	15.6127			0.754667
$429$	−0.454904	−	0.787917i	−0.0219630	−	0.0380410i
$430$	−1.79306	+	3.10567i	−0.0864691	+	0.149769i
$431$	−10.4018	+	18.0164i	−0.501037	+	0.867821i	0.498962	+	0.866624i	$0.333715\pi$
$431$	−10.4018	+	18.0164i	−0.501037	+	0.867821i	−0.999999	+	0.00119770i	$0.999619\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−4.40574			−0.211726			−0.105863	−	0.994381i	$-0.533761\pi$
$433$	−4.40574			−0.211726			−0.105863	+	0.994381i	$0.533761\pi$
$434$	2.18038	+	25.2686i	0.104662	+	1.21293i
$435$	−1.27058			−0.0609194
$436$	−7.02051	−	12.1599i	−0.336222	−	0.582353i
$437$	−16.1896	+	28.0412i	−0.774453	+	1.34139i
$438$	−5.33816	+	9.24596i	−0.255067	+	0.441789i
$439$	7.59743	+	13.1591i	0.362606	+	0.628051i	0.988389	−	0.151946i	$-0.0485539\pi$
$439$	7.59743	+	13.1591i	0.362606	+	0.628051i	−0.625783	+	0.779997i	$0.715221\pi$
$440$	0.454904			0.0216867
$441$	4.48672	+	5.37302i	0.213653	+	0.255858i
$442$	0.909808			0.0432752
$443$	5.69366	+	9.86171i	0.270514	+	0.468544i	0.968994	−	0.247086i	$-0.0794730\pi$
$443$	5.69366	+	9.86171i	0.270514	+	0.468544i	−0.698480	+	0.715630i	$0.746140\pi$
$444$	−3.94163	+	6.82710i	−0.187061	+	0.324000i
$445$	2.52249	−	4.36908i	0.119577	−	0.207114i
$446$	−6.24797	−	10.8218i	−0.295850	−	0.512427i
$447$	4.11675			0.194715
$448$	−0.227452	−	2.63596i	−0.0107461	−	0.124537i
$449$	−24.0821			−1.13650			−0.568251	−	0.822855i	$-0.692380\pi$
$449$	−24.0821			−1.13650			−0.568251	+	0.822855i	$0.692380\pi$
$450$	2.39653	+	4.15091i	0.112974	+	0.195676i
$451$	0.896531	−	1.55284i	0.0422160	−	0.0731203i
$452$	−3.79306	+	6.56978i	−0.178411	+	0.309016i
$453$	3.07889	+	5.33279i	0.144659	+	0.250556i
$454$	9.79306			0.459611
$455$	−0.897729	+	0.627004i	−0.0420862	+	0.0293944i
$456$	3.88325			0.181850
$457$	14.7665	+	25.5763i	0.690748	+	1.19641i	0.971593	+	0.236658i	$0.0760520\pi$
$457$	14.7665	+	25.5763i	0.690748	+	1.19641i	−0.280845	+	0.959753i	$0.590615\pi$
$458$	−4.33816	+	7.51391i	−0.202709	+	0.351102i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$	−1.89653	−	3.28489i	−0.0884262	−	0.153159i
$461$	4.14569			0.193084			0.0965421	−	0.995329i	$-0.469222\pi$
$461$	4.14569			0.193084			0.0965421	+	0.995329i	$0.469222\pi$
$462$	2.39653	+	1.12100i	0.111497	+	0.0521536i
$463$	−9.32368			−0.433308			−0.216654	−	0.976248i	$-0.569514\pi$
$463$	−9.32368			−0.433308			−0.216654	+	0.976248i	$0.569514\pi$
$464$	1.39653	+	2.41886i	0.0648323	+	0.112293i
$465$	2.18038	−	3.77654i	0.101113	−	0.175133i
$466$	−8.38325	+	14.5202i	−0.388347	+	0.672636i
$467$	−18.2798	−	31.6615i	−0.845888	−	1.46512i	−0.884848	−	0.465880i	$-0.845738\pi$
$467$	−18.2798	−	31.6615i	−0.845888	−	1.46512i	0.0389606	−	0.999241i	$-0.487595\pi$
$468$	0.909808			0.0420559
$469$	−9.09019	−	4.25202i	−0.419746	−	0.196340i
$470$	0.153830			0.00709563
$471$	8.82488	+	15.2851i	0.406629	+	0.704302i
$472$	−3.48672	+	6.03918i	−0.160489	+	0.277976i
$473$	−3.94163	+	6.82710i	−0.181236	+	0.313910i
$474$	−2.68236	−	4.64598i	−0.123205	−	0.213397i
$475$	−18.6127			−0.854008
$476$	−2.16908	+	1.51496i	−0.0994196	+	0.0694380i
$477$	0.909808			0.0416573
$478$	13.1312	+	22.7439i	0.600608	+	1.04028i
$479$	−0.364712	+	0.631700i	−0.0166641	+	0.0288631i	−0.874237	−	0.485499i	$-0.838638\pi$
$479$	−0.364712	+	0.631700i	−0.0166641	+	0.0288631i	0.857573	+	0.514362i	$0.171971\pi$
$480$	−0.227452	+	0.393958i	−0.0103817	+	0.0179817i
$481$	−3.58612	−	6.21135i	−0.163513	−	0.283213i
$482$	7.94689			0.361971
$483$	−1.89653	−	21.9790i	−0.0862952	−	1.00008i
$484$	1.00000			0.0454545
$485$	−3.31764	−	5.74633i	−0.150646	−	0.260927i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	18.4283	−	31.9188i	0.835068	−	1.44638i	−0.0589066	−	0.998263i	$-0.518761\pi$
$487$	18.4283	−	31.9188i	0.835068	−	1.44638i	0.893975	−	0.448117i	$-0.147905\pi$
$488$	7.02051	+	12.1599i	0.317804	+	0.550452i
$489$	−11.6127			−0.525143
$490$	1.09623	−	2.98969i	0.0495227	−	0.135060i
$491$	25.5065			1.15109			0.575545	−	0.817770i	$-0.304790\pi$
$491$	25.5065			1.15109			0.575545	+	0.817770i	$0.304790\pi$
$492$	0.896531	+	1.55284i	0.0404187	+	0.0700073i
$493$	1.39653	−	2.41886i	0.0628966	−	0.108940i
$494$	−1.76651	+	3.05968i	−0.0794790	+	0.137662i
$495$	−0.227452	−	0.393958i	−0.0102232	−	0.0177071i
$496$	−9.58612			−0.430430
$497$	1.09019	+	12.6343i	0.0489018	+	0.566726i
$498$	1.97345			0.0884322
$499$	2.06364	+	3.57433i	0.0923811	+	0.160009i	0.908513	−	0.417857i	$-0.137219\pi$
$499$	2.06364	+	3.57433i	0.0923811	+	0.160009i	−0.816131	+	0.577866i	$0.803886\pi$
$500$	2.22745	−	3.85806i	0.0996147	−	0.172538i
$501$	2.42835	−	4.20603i	0.108491	−	0.187911i
$502$	1.96818	+	3.40899i	0.0878442	+	0.152151i
$503$	−6.85670			−0.305725			−0.152863	−	0.988247i	$-0.548849\pi$
$503$	−6.85670			−0.305725			−0.152863	+	0.988247i	$0.548849\pi$
$504$	−2.16908	+	1.51496i	−0.0966185	+	0.0674816i
$505$	−3.66818			−0.163232
$506$	−4.16908	−	7.22106i	−0.185338	−	0.321015i
$507$	6.08612	−	10.5415i	0.270294	−	0.468163i
$508$	−3.71417	+	6.43314i	−0.164790	+	0.285424i
$509$	−8.22141	−	14.2399i	−0.364408	−	0.631173i	0.624273	−	0.781206i	$-0.285395\pi$
$509$	−8.22141	−	14.2399i	−0.364408	−	0.631173i	−0.988681	+	0.150033i	$0.952062\pi$
$510$	0.454904			0.0201435
$511$	25.5861	+	11.9681i	1.13186	+	0.529439i
$512$	1.00000			0.0441942
$513$	−1.94163	−	3.36300i	−0.0857249	−	0.148480i
$514$	7.54510	−	13.0685i	0.332800	−	0.576426i
$515$	−1.31160	+	2.27176i	−0.0577962	+	0.100106i
$516$	−3.94163	−	6.82710i	−0.173520	−	0.300546i
$517$	0.338158			0.0148722
$518$	18.8925	+	8.83712i	0.830087	+	0.388281i
$519$	−25.5861			−1.12311
$520$	−0.206938	−	0.358427i	−0.00907482	−	0.0157180i
$521$	2.81962	−	4.88372i	0.123530	−	0.213960i	−0.797628	−	0.603150i	$-0.793912\pi$
$521$	2.81962	−	4.88372i	0.123530	−	0.213960i	0.921157	+	0.389191i	$0.127245\pi$
$522$	1.39653	−	2.41886i	0.0611245	−	0.105871i
$523$	2.04103	+	3.53517i	0.0892480	+	0.154582i	0.907193	−	0.420714i	$-0.138220\pi$
$523$	2.04103	+	3.53517i	0.0892480	+	0.154582i	−0.817946	+	0.575296i	$0.804887\pi$
$524$	−19.4057			−0.847744
$525$	10.3965	−	7.26129i	0.453742	−	0.316908i
$526$	−28.6232			−1.24803
$527$	4.79306	+	8.30183i	0.208789	+	0.361633i
$528$	−0.500000	+	0.866025i	−0.0217597	+	0.0376889i
$529$	−23.2624	+	40.2917i	−1.01141	+	1.75181i
$530$	−0.206938	−	0.358427i	−0.00898880	−	0.0155691i
$531$	6.97345			0.302622
$532$	−0.883254	−	10.2361i	−0.0382939	−	0.443791i
$533$	−1.63134			−0.0706613
$534$	5.54510	+	9.60439i	0.239960	+	0.415623i
$535$	−3.55114	+	6.15075i	−0.153529	+	0.265920i
$536$	1.89653	−	3.28489i	0.0819177	−	0.141886i
$537$	7.85144	+	13.5991i	0.338814	+	0.586844i
$538$	−22.9508			−0.989481
$539$	2.40981	−	6.57212i	0.103798	−	0.283081i
$540$	0.454904			0.0195760
$541$	2.44886	+	4.24156i	0.105285	+	0.182359i	0.913855	−	0.406042i	$-0.133091\pi$
$541$	2.44886	+	4.24156i	0.105285	+	0.182359i	−0.808570	+	0.588400i	$0.799758\pi$
$542$	−4.90981	+	8.50404i	−0.210894	+	0.365280i
$543$	1.24797	−	2.16154i	0.0535554	−	0.0927606i
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	6.38732			0.273603
$546$	−0.206938	−	2.39821i	−0.00885612	−	0.102634i
$547$	21.4694			0.917964			0.458982	−	0.888445i	$-0.348214\pi$
$547$	21.4694			0.917964			0.458982	+	0.888445i	$0.348214\pi$
$548$	−0.454904	−	0.787917i	−0.0194325	−	0.0336581i
$549$	7.02051	−	12.1599i	0.299628	−	0.518971i
$550$	2.39653	−	4.15091i	0.102188	−	0.176996i
$551$	5.42309	+	9.39306i	0.231031	+	0.400158i
$552$	8.33816			0.354896
$553$	−11.6365	+	8.12731i	−0.494834	+	0.345608i
$554$	10.7294			0.455850
$555$	−1.79306	−	3.10567i	−0.0761113	−	0.131829i
$556$	4.18959	−	7.25659i	0.177678	−	0.307748i
$557$	19.7347	−	34.1815i	0.836186	−	1.44832i	−0.0568758	−	0.998381i	$-0.518114\pi$
$557$	19.7347	−	34.1815i	0.836186	−	1.44832i	0.893061	−	0.449935i	$-0.148553\pi$
$558$	4.79306	+	8.30183i	0.202907	+	0.351444i
$559$	7.17225			0.303354
$560$	1.09019	+	0.509947i	0.0460690	+	0.0215492i
$561$	1.00000			0.0422200
$562$	−1.29306	−	2.23965i	−0.0545445	−	0.0944739i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	−0.169079	+	0.292854i	−0.00711951	+	0.0123314i
$565$	−1.72548	−	2.98862i	−0.0725915	−	0.125732i
$566$	−20.0821			−0.844112
$567$	2.39653	+	1.12100i	0.100645	+	0.0470775i
$568$	−4.79306			−0.201112
$569$	−17.0994	−	29.6170i	−0.716844	−	1.24161i	−0.962244	−	0.272189i	$-0.912253\pi$
$569$	−17.0994	−	29.6170i	−0.716844	−	1.24161i	0.245400	−	0.969422i	$-0.421081\pi$
$570$	−0.883254	+	1.52984i	−0.0369954	+	0.0640780i
$571$	−7.39653	+	12.8112i	−0.309535	+	0.536131i	−0.978261	−	0.207379i	$-0.933507\pi$
$571$	−7.39653	+	12.8112i	−0.309535	+	0.536131i	0.668726	+	0.743509i	$0.266840\pi$
$572$	−0.454904	−	0.787917i	−0.0190205	−	0.0329445i
$573$	9.81962			0.410220
$574$	3.88929	−	2.71641i	0.162336	−	0.113381i
$575$	−39.9653			−1.66667
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.59940	−	6.23435i	0.149845	−	0.259539i	−0.781325	−	0.624124i	$-0.785456\pi$
$577$	3.59940	−	6.23435i	0.149845	−	0.259539i	0.931170	+	0.364585i	$0.118789\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	−3.42835	−	5.93808i	−0.142477	−	0.246778i
$580$	−1.27058			−0.0527578
$581$	−0.448864	−	5.20192i	−0.0186220	−	0.215812i
$582$	14.5861			0.604614
$583$	−0.454904	−	0.787917i	−0.0188402	−	0.0326322i
$584$	−5.33816	+	9.24596i	−0.220895	+	0.382601i
$585$	−0.206938	+	0.358427i	−0.00855582	+	0.0148191i
$586$	−5.18959	−	8.98864i	−0.214380	−	0.371317i
$587$	−44.4959			−1.83654			−0.918272	−	0.395951i	$-0.870415\pi$
$587$	−44.4959			−1.83654			−0.918272	+	0.395951i	$0.870415\pi$
$588$	4.48672	+	5.37302i	0.185029	+	0.221580i
$589$	−37.2254			−1.53384
$590$	−1.58612	−	2.74725i	−0.0652997	−	0.113102i
$591$	−11.7347	+	20.3251i	−0.482701	+	0.836062i
$592$	−3.94163	+	6.82710i	−0.162000	+	0.280592i
$593$	−8.98266	−	15.5584i	−0.368873	−	0.638908i	0.620516	−	0.784194i	$-0.286923\pi$
$593$	−8.98266	−	15.5584i	−0.368873	−	0.638908i	−0.989390	+	0.145286i	$0.953590\pi$
$594$	1.00000			0.0410305
$595$	−0.103469	−	1.19911i	−0.00424181	−	0.0491586i
$596$	4.11675			0.168628
$597$	1.11675	+	1.93426i	0.0457054	+	0.0791640i
$598$	−3.79306	+	6.56978i	−0.155110	+	0.268658i
$599$	12.9038	−	22.3500i	0.527234	−	0.913196i	−0.472263	−	0.881458i	$-0.656563\pi$
$599$	12.9038	−	22.3500i	0.527234	−	0.913196i	0.999496	−	0.0317376i	$-0.0101041\pi$
$600$	2.39653	+	4.15091i	0.0978380	+	0.169460i
$601$	10.4139			0.424791			0.212395	−	0.977184i	$-0.431874\pi$
$601$	10.4139			0.424791			0.212395	+	0.977184i	$0.431874\pi$
$602$	−17.0994	+	11.9428i	−0.696920	+	0.486752i
$603$	−3.79306			−0.154465
$604$	3.07889	+	5.33279i	0.125278	+	0.216988i
$605$	−0.227452	+	0.393958i	−0.00924724	+	0.0160167i
$606$	4.03182	−	6.98332i	0.163781	−	0.283678i
$607$	4.44886	+	7.70566i	0.180574	+	0.312763i	0.942076	−	0.335399i	$-0.108871\pi$
$607$	4.44886	+	7.70566i	0.180574	+	0.312763i	−0.761502	+	0.648162i	$0.775538\pi$
$608$	3.88325			0.157487
$609$	−6.69366	−	3.13102i	−0.271241	−	0.126875i
$610$	−6.38732			−0.258615
$611$	−0.153830	−	0.266441i	−0.00622328	−	0.0107790i
$612$	−0.500000	+	0.866025i	−0.0202113	+	0.0350070i
$613$	11.8136	−	20.4617i	0.477146	−	0.826441i	−0.522511	−	0.852632i	$-0.675005\pi$
$613$	11.8136	−	20.4617i	0.477146	−	0.826441i	0.999657	+	0.0261916i	$0.00833800\pi$
$614$	−4.88325	−	8.45804i	−0.197072	−	0.341339i
$615$	−0.815671			−0.0328910
$616$	2.39653	+	1.12100i	0.0965590	+	0.0451663i
$617$	−35.8486			−1.44321			−0.721604	−	0.692306i	$-0.756595\pi$
$617$	−35.8486			−1.44321			−0.721604	+	0.692306i	$0.756595\pi$
$618$	−2.88325	−	4.99394i	−0.115981	−	0.200886i
$619$	−13.9602	+	24.1797i	−0.561107	+	0.971865i	0.436294	+	0.899804i	$0.356291\pi$
$619$	−13.9602	+	24.1797i	−0.561107	+	0.971865i	−0.997400	+	0.0720607i	$0.977042\pi$
$620$	2.18038	−	3.77654i	0.0875663	−	0.151669i
$621$	−4.16908	−	7.22106i	−0.167299	−	0.289771i
$622$	−6.51854			−0.261370
$623$	24.0555	−	16.8012i	0.963763	−	0.673125i
$624$	0.909808			0.0364215
$625$	−10.9694	−	18.9995i	−0.438775	−	0.759981i
$626$	−15.3965	+	26.6676i	−0.615369	+	1.06585i
$627$	−1.94163	+	3.36300i	−0.0775411	+	0.134305i
$628$	8.82488	+	15.2851i	0.352151	+	0.609944i
$629$	7.88325			0.314326
$630$	−0.103469	−	1.19911i	−0.00412230	−	0.0477736i
$631$	43.6682			1.73840			0.869201	−	0.494458i	$-0.164633\pi$
$631$	43.6682			1.73840			0.869201	+	0.494458i	$0.164633\pi$
$632$	−2.68236	−	4.64598i	−0.106698	−	0.184807i
$633$	9.13122	−	15.8157i	0.362933	−	0.628619i
$634$	13.8136	−	23.9258i	0.548607	−	0.950216i
$635$	−1.68959	−	2.92646i	−0.0670495	−	0.116133i
$636$	0.909808			0.0360762
$637$	−6.27452	+	1.09096i	−0.248606	+	0.0432253i
$638$	−2.79306			−0.110578
$639$	2.39653	+	4.15091i	0.0948053	+	0.164208i
$640$	−0.227452	+	0.393958i	−0.00899083	+	0.0155726i
$641$	9.88325	−	17.1183i	0.390365	−	0.676132i	−0.602133	−	0.798396i	$-0.705682\pi$
$641$	9.88325	−	17.1183i	0.390365	−	0.676132i	0.992498	+	0.122264i	$0.0390155\pi$
$642$	−7.80634	−	13.5210i	−0.308092	−	0.533630i
$643$	24.7584			0.976375			0.488187	−	0.872739i	$-0.337658\pi$
$643$	24.7584			0.976375			0.488187	+	0.872739i	$0.337658\pi$
$644$	−1.89653	−	21.9790i	−0.0747338	−	0.866095i
$645$	3.58612			0.141204
$646$	−1.94163	−	3.36300i	−0.0763923	−	0.132315i
$647$	−15.5391	+	26.9144i	−0.610903	+	1.05812i	0.380185	+	0.924910i	$0.375860\pi$
$647$	−15.5391	+	26.9144i	−0.610903	+	1.05812i	−0.991088	+	0.133205i	$0.957473\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−3.48672	−	6.03918i	−0.136866	−	0.237059i
$650$	−4.36077			−0.171043
$651$	20.7931	−	14.5226i	0.814944	−	0.569184i
$652$	−11.6127			−0.454788
$653$	−11.3587	−	19.6738i	−0.444499	−	0.769895i	0.553518	−	0.832837i	$-0.313285\pi$
$653$	−11.3587	−	19.6738i	−0.444499	−	0.769895i	−0.998017	+	0.0629420i	$0.979952\pi$
$654$	−7.02051	+	12.1599i	−0.274524	+	0.475489i
$655$	4.41388	−	7.64506i	0.172464	−	0.298717i
$656$	0.896531	+	1.55284i	0.0350037	+	0.0606281i
$657$	10.6763			0.416523
$658$	0.810407	+	0.379075i	0.0315929	+	0.0147779i
$659$	43.6127			1.69891			0.849454	−	0.527662i	$-0.176931\pi$
$659$	43.6127			1.69891			0.849454	+	0.527662i	$0.176931\pi$
$660$	−0.227452	−	0.393958i	−0.00885356	−	0.0153348i
$661$	3.96818	−	6.87309i	0.154344	−	0.267332i	−0.778476	−	0.627675i	$-0.784007\pi$
$661$	3.96818	−	6.87309i	0.154344	−	0.267332i	0.932820	+	0.360342i	$0.117340\pi$
$662$	14.4827	−	25.0847i	0.562884	−	0.974944i
$663$	−0.454904	−	0.787917i	−0.0176670	−	0.0306002i
$664$	1.97345			0.0765846
$665$	4.23349	+	1.98025i	0.164168	+	0.0767909i
$666$	7.88325			0.305470
$667$	11.6445	+	20.1689i	0.450877	+	0.780941i
$668$	2.42835	−	4.20603i	0.0939557	−	0.162736i
$669$	−6.24797	+	10.8218i	−0.241560	+	0.418395i
$670$	0.862740	+	1.49431i	0.0333305	+	0.0577302i
$671$	−14.0410			−0.542048
$672$	−2.16908	+	1.51496i	−0.0836740	+	0.0584408i
$673$	36.9388			1.42388			0.711942	−	0.702238i	$-0.247816\pi$
$673$	36.9388			1.42388			0.711942	+	0.702238i	$0.247816\pi$
$674$	4.51854	+	7.82634i	0.174048	+	0.301460i
$675$	2.39653	−	4.15091i	0.0922425	−	0.159769i
$676$	6.08612	−	10.5415i	0.234082	−	0.405441i
$677$	19.8249	+	34.3377i	0.761932	+	1.31971i	0.941853	+	0.336024i	$0.109082\pi$
$677$	19.8249	+	34.3377i	0.761932	+	1.31971i	−0.179921	+	0.983681i	$0.557584\pi$
$678$	7.58612			0.291343
$679$	−3.31764	−	38.4484i	−0.127319	−	1.47551i
$680$	0.454904			0.0174448
$681$	−4.89653	−	8.48104i	−0.187635	−	0.324994i
$682$	4.79306	−	8.30183i	0.183536	−	0.317893i
$683$	22.7757	−	39.4487i	0.871489	−	1.50946i	0.0110318	−	0.999939i	$-0.496488\pi$
$683$	22.7757	−	39.4487i	0.871489	−	1.50946i	0.860457	−	0.509523i	$-0.170178\pi$
$684$	−1.94163	−	3.36300i	−0.0742400	−	0.128587i
$685$	0.413875			0.0158134
$686$	13.1425	−	13.0489i	0.501784	−	0.498210i
$687$	8.67632			0.331022
$688$	−3.94163	−	6.82710i	−0.150273	−	0.260281i
$689$	−0.413875	+	0.716853i	−0.0157674	+	0.0273099i
$690$	−1.89653	+	3.28489i	−0.0721997	+	0.125054i
$691$	9.59940	+	16.6267i	0.365178	+	0.632508i	0.988805	−	0.149215i	$-0.0476746\pi$
$691$	9.59940	+	16.6267i	0.365178	+	0.632508i	−0.623626	+	0.781723i	$0.714341\pi$
$692$	−25.5861			−0.972639
$693$	−0.227452	−	2.63596i	−0.00864019	−	0.100132i
$694$	−21.6127			−0.820406
$695$	1.90586	+	3.30105i	0.0722935	+	0.125216i
$696$	1.39653	−	2.41886i	0.0529354	−	0.0916868i
$697$	0.896531	−	1.55284i	0.0339585	−	0.0588179i
$698$	−7.13726	−	12.3621i	−0.270149	−	0.467912i
$699$	16.7665			0.634168
$700$	10.3965	−	7.26129i	0.392952	−	0.274451i
$701$	23.2890			0.879613			0.439807	−	0.898093i	$-0.355047\pi$
$701$	23.2890			0.879613			0.439807	+	0.898093i	$0.355047\pi$
$702$	−0.454904	−	0.787917i	−0.0171692	−	0.0297380i
$703$	−15.3063	+	26.5114i	−0.577290	+	0.999895i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−0.0769148	−	0.133220i	−0.00289678	−	0.00501737i
$706$	−28.4959			−1.07246
$707$	−19.3248	−	9.03933i	−0.726782	−	0.339959i
$708$	6.97345			0.262078
$709$	10.3965	+	18.0073i	0.390450	+	0.676279i	0.992509	−	0.122173i	$-0.0389861\pi$
$709$	10.3965	+	18.0073i	0.390450	+	0.676279i	−0.602059	+	0.798452i	$0.705653\pi$
$710$	1.09019	−	1.88827i	0.0409142	−	0.0708654i
$711$	−2.68236	+	4.64598i	−0.100596	+	0.174238i
$712$	5.54510	+	9.60439i	0.207811	+	0.359940i
$713$	−79.9306			−2.99343
$714$	2.39653	+	1.12100i	0.0896879	+	0.0419523i
$715$	0.413875			0.0154781
$716$	7.85144	+	13.5991i	0.293422	+	0.508222i
$717$	13.1312	−	22.7439i	0.490394	−	0.849388i
$718$	6.81962	−	11.8119i	0.254506	−	0.440817i
$719$	2.74073	+	4.74708i	0.102212	+	0.177036i	0.912596	−	0.408863i	$-0.134075\pi$
$719$	2.74073	+	4.74708i	0.102212	+	0.177036i	−0.810384	+	0.585899i	$0.800741\pi$
$720$	0.454904			0.0169533
$721$	−12.5080	+	8.73601i	−0.465823	+	0.325346i
$722$	−3.92034			−0.145900
$723$	−3.97345	−	6.88221i	−0.147774	−	0.255952i
$724$	1.24797	−	2.16154i	0.0463803	−	0.0803330i
$725$	−6.69366	+	11.5938i	−0.248596	+	0.430581i
$726$	−0.500000	−	0.866025i	−0.0185567	−	0.0321412i
$727$	25.5330			0.946967			0.473484	−	0.880803i	$-0.342996\pi$
$727$	25.5330			0.946967			0.473484	+	0.880803i	$0.342996\pi$
$728$	−0.206938	−	2.39821i	−0.00766962	−	0.0888837i
$729$	1.00000			0.0370370
$730$	−2.42835	−	4.20603i	−0.0898773	−	0.155672i
$731$	−3.94163	+	6.82710i	−0.145786	+	0.252509i
$732$	7.02051	−	12.1599i	0.259486	−	0.449442i
$733$	−8.11071	−	14.0482i	−0.299576	−	0.518880i	0.676463	−	0.736476i	$-0.263512\pi$
$733$	−8.11071	−	14.0482i	−0.299576	−	0.518880i	−0.976039	+	0.217596i	$0.930178\pi$
$734$	22.7294			0.838958
$735$	−3.13726	+	0.545479i	−0.115720	+	0.0201203i
$736$	8.33816			0.307349
$737$	1.89653	+	3.28489i	0.0698596	+	0.121000i
$738$	0.896531	−	1.55284i	0.0330018	−	0.0571607i
$739$	−9.37919	+	16.2452i	−0.345019	+	0.597590i	−0.985357	−	0.170503i	$-0.945461\pi$
$739$	−9.37919	+	16.2452i	−0.345019	+	0.597590i	0.640338	+	0.768093i	$0.278794\pi$
$740$	−1.79306	−	3.10567i	−0.0659143	−	0.114167i
$741$	3.53302			0.129789
$742$	−0.206938	−	2.39821i	−0.00759692	−	0.0880412i
$743$	−44.6763			−1.63902			−0.819508	−	0.573068i	$-0.805753\pi$
$743$	−44.6763			−1.63902			−0.819508	+	0.573068i	$0.805753\pi$
$744$	4.79306	+	8.30183i	0.175722	+	0.304360i
$745$	−0.936362	+	1.62183i	−0.0343057	+	0.0594191i
$746$	−5.20090	+	9.00822i	−0.190418	+	0.329814i
$747$	−0.986723	−	1.70905i	−0.0361023	−	0.0625310i
$748$	1.00000			0.0365636
$749$	−33.8651	+	23.6525i	−1.23741	+	0.864245i
$750$	−4.45490			−0.162670
$751$	1.48146	+	2.56596i	0.0540592	+	0.0936332i	0.891789	−	0.452452i	$-0.149451\pi$
$751$	1.48146	+	2.56596i	0.0540592	+	0.0936332i	−0.837729	+	0.546085i	$0.816117\pi$
$752$	−0.169079	+	0.292854i	−0.00616568	+	0.0106793i
$753$	1.96818	−	3.40899i	0.0717245	−	0.124230i
$754$	1.27058	+	2.20070i	0.0462716	+	0.0801448i
$755$	−2.80120			−0.101946
$756$	2.39653	+	1.12100i	0.0871610	+	0.0407703i
$757$	26.1988			0.952212			0.476106	−	0.879388i	$-0.342048\pi$
$757$	26.1988			0.952212			0.476106	+	0.879388i	$0.342048\pi$
$758$	−3.80634	−	6.59277i	−0.138252	−	0.239460i
$759$	−4.16908	+	7.22106i	−0.151328	+	0.262108i
$760$	−0.883254	+	1.52984i	−0.0320390	+	0.0554932i
$761$	−12.8965	−	22.3374i	−0.467499	−	0.809732i	0.531812	−	0.846863i	$-0.321511\pi$
$761$	−12.8965	−	22.3374i	−0.467499	−	0.809732i	−0.999310	+	0.0371309i	$0.988178\pi$
$762$	7.42835			0.269101
$763$	33.6498	+	15.7400i	1.21820	+	0.569825i
$764$	9.81962			0.355261
$765$	−0.227452	−	0.393958i	−0.00822355	−	0.0142436i
$766$	11.0728	−	19.1787i	0.400078	−	0.692956i
$767$	−3.17225	+	5.49450i	−0.114543	+	0.198395i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−37.2012			−1.34151			−0.670755	−	0.741679i	$-0.734030\pi$
$769$	−37.2012			−1.34151			−0.670755	+	0.741679i	$0.734030\pi$
$770$	−0.986723	+	0.689160i	−0.0355590	+	0.0248356i
$771$	−15.0902			−0.543460
$772$	−3.42835	−	5.93808i	−0.123389	−	0.213716i
$773$	20.3852	−	35.3082i	0.733206	−	1.26995i	−0.222300	−	0.974978i	$-0.571357\pi$
$773$	20.3852	−	35.3082i	0.733206	−	1.26995i	0.955506	−	0.294971i	$-0.0953101\pi$
$774$	−3.94163	+	6.82710i	−0.141679	+	0.245395i
$775$	−22.9734	−	39.7912i	−0.825231	−	1.42934i
$776$	14.5861			0.523611
$777$	−1.79306	−	20.7799i	−0.0643258	−	0.745475i
$778$	−3.54510			−0.127098
$779$	3.48146	+	6.03006i	0.124736	+	0.216049i
$780$	−0.206938	+	0.358427i	−0.00740956	+	0.0128337i
$781$	2.39653	−	4.15091i	0.0857546	−	0.148531i
$782$	−4.16908	−	7.22106i	−0.149086	−	0.258224i
$783$	−2.79306			−0.0998159
$784$	4.48672	+	5.37302i	0.160240	+	0.191893i
$785$	−8.02895			−0.286565
$786$	9.70287	+	16.8059i	0.346090	+	0.599445i
$787$	−27.2943	+	47.2750i	−0.972935	+	1.68517i	−0.286348	+	0.958126i	$0.592441\pi$
$787$	−27.2943	+	47.2750i	−0.972935	+	1.68517i	−0.686587	+	0.727048i	$0.740892\pi$
$788$	−11.7347	+	20.3251i	−0.418031	+	0.724051i
$789$	14.3116	+	24.7884i	0.509507	+	0.882491i
$790$	2.44043			0.0868266
$791$	−1.72548	−	19.9967i	−0.0613510	−	0.711001i
$792$	1.00000			0.0355335
$793$	6.38732	+	11.0632i	0.226820	+	0.392865i
$794$	1.27979	−	2.21665i	0.0454179	−	0.0786661i
$795$	−0.206938	+	0.358427i	−0.00733933	+	0.0127121i
$796$	1.11675	+	1.93426i	0.0395820	+	0.0685581i
$797$	−16.7705			−0.594040			−0.297020	−	0.954871i	$-0.595993\pi$
$797$	−16.7705			−0.594040			−0.297020	+	0.954871i	$0.595993\pi$
$798$	−8.42309	+	5.88296i	−0.298174	+	0.208255i
$799$	0.338158			0.0119632
$800$	2.39653	+	4.15091i	0.0847302	+	0.146757i
$801$	5.54510	−	9.60439i	0.195926	−	0.339354i
$802$	−5.24797	+	9.08974i	−0.185312	+	0.320970i
$803$	−5.33816	−	9.24596i	−0.188380	−	0.326283i
$804$	−3.79306			−0.133771
$805$	9.09019	+	4.25202i	0.320387	+	0.149864i
$806$	−8.72153			−0.307203
$807$	11.4754	+	19.8760i	0.403954	+	0.699669i
$808$	4.03182	−	6.98332i	0.141839	−	0.245672i
$809$	5.10347	−	8.83947i	0.179428	−	0.310779i	−0.762257	−	0.647275i	$-0.775909\pi$
$809$	5.10347	−	8.83947i	0.179428	−	0.310779i	0.941685	+	0.336496i	$0.109242\pi$
$810$	−0.227452	−	0.393958i	−0.00799185	−	0.0138423i
$811$	−28.4139			−0.997746			−0.498873	−	0.866675i	$-0.666253\pi$
$811$	−28.4139			−0.997746			−0.498873	+	0.866675i	$0.666253\pi$
$812$	−6.69366	−	3.13102i	−0.234901	−	0.109877i
$813$	9.81962			0.344389
$814$	−3.94163	−	6.82710i	−0.138154	−	0.239290i
$815$	2.64133	−	4.57491i	0.0925217	−	0.160252i
$816$	−0.500000	+	0.866025i	−0.0175035	+	0.0303170i
$817$	−15.3063	−	26.5114i	−0.535501	−	0.927515i
$818$	15.8486			0.554132
$819$	−1.97345	+	1.37832i	−0.0689578	+	0.0481624i
$820$	−0.815671			−0.0284845
$821$	1.70287	+	2.94946i	0.0594306	+	0.102937i	0.894210	−	0.447648i	$-0.147738\pi$
$821$	1.70287	+	2.94946i	0.0594306	+	0.102937i	−0.834779	+	0.550585i	$0.814405\pi$
$822$	−0.454904	+	0.787917i	−0.0158666	+	0.0274818i
$823$	19.0145	−	32.9340i	0.662803	−	1.14801i	−0.317073	−	0.948401i	$-0.602700\pi$
$823$	19.0145	−	32.9340i	0.662803	−	1.14801i	0.979876	−	0.199607i	$-0.0639666\pi$
$824$	−2.88325	−	4.99394i	−0.100443	−	0.173972i
$825$	−4.79306			−0.166873
$826$	−1.58612	−	18.3817i	−0.0551883	−	0.639581i
$827$	−12.9653			−0.450848			−0.225424	−	0.974261i	$-0.572377\pi$
$827$	−12.9653			−0.450848			−0.225424	+	0.974261i	$0.572377\pi$
$828$	−4.16908	−	7.22106i	−0.144886	−	0.250949i
$829$	−25.9416	+	44.9322i	−0.900990	+	1.56056i	−0.0747785	+	0.997200i	$0.523825\pi$
$829$	−25.9416	+	44.9322i	−0.900990	+	1.56056i	−0.826211	+	0.563360i	$0.809508\pi$
$830$	−0.448864	+	0.777456i	−0.0155803	+	0.0269859i
$831$	−5.36471	−	9.29195i	−0.186100	−	0.322334i
$832$	0.909808			0.0315419
$833$	2.40981	−	6.57212i	0.0834949	−	0.227711i
$834$	−8.37919			−0.290148
$835$	1.10467	+	1.91334i	0.0382286	+	0.0662138i
$836$	−1.94163	+	3.36300i	−0.0671526	+	0.116312i
$837$	4.79306	−	8.30183i	0.165672	−	0.286953i
$838$	4.76124	+	8.24672i	0.164474	+	0.284878i
$839$	−50.2504			−1.73484			−0.867418	−	0.497581i	$-0.834222\pi$
$839$	−50.2504			−1.73484			−0.867418	+	0.497581i	$0.834222\pi$
$840$	−0.103469	−	1.19911i	−0.00357002	−	0.0413731i
$841$	−21.1988			−0.730993
$842$	0.265311	+	0.459532i	0.00914321	+	0.0158365i
$843$	−1.29306	+	2.23965i	−0.0445354	+	0.0771376i
$844$	9.13122	−	15.8157i	0.314310	−	0.544400i
$845$	2.76860	+	4.79536i	0.0952428	+	0.164965i
$846$	0.338158			0.0116261
$847$	−2.16908	+	1.51496i	−0.0745304	+	0.0520546i
$848$	0.909808			0.0312429
$849$	10.0410	+	17.3916i	0.344607	+	0.596877i
$850$	2.39653	−	4.15091i	0.0822003	−	0.142375i
$851$	−32.8659	+	56.9254i	−1.12663	+	1.95138i
$852$	2.39653	+	4.15091i	0.0821038	+	0.142208i
$853$	13.3647			0.457599			0.228800	−	0.973474i	$-0.426520\pi$
$853$	13.3647			0.457599			0.228800	+	0.973474i	$0.426520\pi$
$854$	−33.6498	−	15.7400i	−1.15147	−	0.538611i
$855$	1.76651			0.0604133
$856$	−7.80634	−	13.5210i	−0.266815	−	0.462137i
$857$	−13.1763	+	22.8220i	−0.450094	+	0.779586i	−0.998391	−	0.0566973i	$-0.981943\pi$
$857$	−13.1763	+	22.8220i	−0.450094	+	0.779586i	0.548297	+	0.836284i	$0.315276\pi$
$858$	−0.454904	+	0.787917i	−0.0155302	+	0.0268990i
$859$	−0.986723	−	1.70905i	−0.0336666	−	0.0583122i	0.848701	−	0.528873i	$-0.177385\pi$
$859$	−0.986723	−	1.70905i	−0.0336666	−	0.0583122i	−0.882368	+	0.470560i	$0.844052\pi$
$860$	3.58612			0.122286
$861$	−4.29713	−	2.01002i	−0.146446	−	0.0685013i
$862$	20.8036			0.708573
$863$	24.9038	+	43.1346i	0.847734	+	1.46832i	0.883225	+	0.468949i	$0.155367\pi$
$863$	24.9038	+	43.1346i	0.847734	+	1.46832i	−0.0354913	+	0.999370i	$0.511300\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	5.81962	−	10.0799i	0.197873	−	0.342726i
$866$	2.20287	+	3.81548i	0.0748566	+	0.129655i
$867$	−16.0000			−0.543388
$868$	20.7931	−	14.5226i	0.705763	−	0.492928i
$869$	5.36471			0.181985
$870$	0.635288	+	1.10035i	0.0215383	+	0.0373054i
$871$	1.72548	−	2.98862i	0.0584656	−	0.101265i
$872$	−7.02051	+	12.1599i	−0.237745	+	0.411786i
$873$	−7.29306	−	12.6320i	−0.246833	−	0.427527i
$874$	32.3792			1.09524
$875$	1.01328	+	11.7429i	0.0342550	+	0.396984i
$876$	10.6763			0.360719
$877$	12.2685	+	21.2496i	0.414277	+	0.717549i	0.995352	−	0.0963008i	$-0.0307011\pi$
$877$	12.2685	+	21.2496i	0.414277	+	0.717549i	−0.581075	+	0.813850i	$0.697368\pi$
$878$	7.59743	−	13.1591i	0.256401	−	0.444099i
$879$	−5.18959	+	8.98864i	−0.175041	+	0.303179i
$880$	−0.227452	−	0.393958i	−0.00766741	−	0.0132803i
$881$	11.5861			0.390346			0.195173	−	0.980769i	$-0.437473\pi$
$881$	11.5861			0.390346			0.195173	+	0.980769i	$0.437473\pi$
$882$	2.40981	−	6.57212i	0.0811425	−	0.221295i
$883$	−44.1376			−1.48535			−0.742674	−	0.669654i	$-0.766443\pi$
$883$	−44.1376			−1.48535			−0.742674	+	0.669654i	$0.766443\pi$
$884$	−0.454904	−	0.787917i	−0.0153001	−	0.0265005i
$885$	−1.58612	+	2.74725i	−0.0533170	+	0.0923477i
$886$	5.69366	−	9.86171i	0.191282	−	0.331311i
$887$	10.0145	+	17.3456i	0.336253	+	0.582408i	0.983725	−	0.179682i	$-0.0575069\pi$
$887$	10.0145	+	17.3456i	0.336253	+	0.582408i	−0.647472	+	0.762090i	$0.724174\pi$
$888$	7.88325			0.264545
$889$	−1.68959	−	19.5808i	−0.0566671	−	0.656719i
$890$	−5.04497			−0.169108
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−6.24797	+	10.8218i	−0.209197	+	0.362341i
$893$	−0.656577	+	1.13722i	−0.0219715	+	0.0380558i
$894$	−2.05837	−	3.56521i	−0.0688423	−	0.119238i
$895$	−7.14330			−0.238774
$896$	−2.16908	+	1.51496i	−0.0724638	+	0.0506112i
$897$	7.58612			0.253293
$898$	12.0410	+	20.8557i	0.401814	+	0.695963i
$899$	−13.3873	+	23.1875i	−0.446492	+	0.773347i
$900$	2.39653	−	4.15091i	0.0798844	−	0.138364i
$901$	−0.454904	−	0.787917i	−0.0151551	−	0.0262493i
$902$	−1.79306			−0.0597024
$903$	18.8925	+	8.83712i	0.628702	+	0.294081i
$904$	7.58612			0.252311
$905$	0.567705	+	0.983294i	0.0188712	+	0.0326858i
$906$	3.07889	−	5.33279i	0.102289	−	0.177170i
$907$	8.96017	−	15.5195i	0.297518	−	0.515315i	−0.678050	−	0.735016i	$-0.737175\pi$
$907$	8.96017	−	15.5195i	0.297518	−	0.515315i	0.975567	+	0.219700i	$0.0705080\pi$
$908$	−4.89653	−	8.48104i	−0.162497	−	0.281453i
$909$	−8.06364			−0.267454
$910$	0.991865	+	0.463954i	0.0328800	+	0.0153799i
$911$	13.9695			0.462830			0.231415	−	0.972855i	$-0.425664\pi$
$911$	13.9695			0.462830			0.231415	+	0.972855i	$0.425664\pi$
$912$	−1.94163	−	3.36300i	−0.0642937	−	0.111360i
$913$	−0.986723	+	1.70905i	−0.0326558	+	0.0565614i
$914$	14.7665	−	25.5763i	0.488433	−	0.845990i
$915$	3.19366	+	5.53158i	0.105579	+	0.182868i
$916$	8.67632			0.286674
$917$	42.0926	−	29.3989i	1.39002	−	0.970836i
$918$	1.00000			0.0330049
$919$	21.4807	+	37.2056i	0.708582	+	1.22730i	0.965383	+	0.260836i	$0.0839983\pi$
$919$	21.4807	+	37.2056i	0.708582	+	1.22730i	−0.256801	+	0.966464i	$0.582668\pi$
$920$	−1.89653	+	3.28489i	−0.0625268	+	0.108300i
$921$	−4.88325	+	8.45804i	−0.160909	+	0.278702i
$922$	−2.07285	−	3.59028i	−0.0682656	−	0.118239i
$923$	−4.36077			−0.143536
$924$	−0.227452	−	2.63596i	−0.00748262	−	0.0867166i
$925$	−37.7849			−1.24236
$926$	4.66184	+	8.07455i	0.153198	+	0.265346i
$927$	−2.88325	+	4.99394i	−0.0946985	+	0.164023i
$928$	1.39653	−	2.41886i	0.0458434	−	0.0794031i
$929$	12.8341	+	22.2293i	0.421073	+	0.729320i	0.996045	−	0.0888536i	$-0.0283203\pi$
$929$	12.8341	+	22.2293i	0.421073	+	0.729320i	−0.574972	+	0.818173i	$0.694987\pi$
$930$	−4.36077			−0.142995
$931$	17.4231	+	20.8648i	0.571019	+	0.683816i
$932$	16.7665			0.549205
$933$	3.25927	+	5.64522i	0.106704	+	0.184816i
$934$	−18.2798	+	31.6615i	−0.598133	+	1.03600i
$935$	−0.227452	+	0.393958i	−0.00743848	+	0.0128838i
$936$	−0.454904	−	0.787917i	−0.0148690	−	0.0257539i
$937$	26.7584			0.874158			0.437079	−	0.899423i	$-0.356013\pi$
$937$	26.7584			0.874158			0.437079	+	0.899423i	$0.356013\pi$
$938$	0.862740	+	9.99835i	0.0281695	+	0.326458i
$939$	30.7931			1.00489
$940$	−0.0769148	−	0.133220i	−0.00250868	−	0.00434517i
$941$	7.81041	−	13.5280i	0.254612	−	0.441001i	−0.710178	−	0.704022i	$-0.751386\pi$
$941$	7.81041	−	13.5280i	0.254612	−	0.441001i	0.964790	+	0.263021i	$0.0847189\pi$
$942$	8.82488	−	15.2851i	0.287530	−	0.498017i
$943$	7.47542	+	12.9478i	0.243433	+	0.421639i
$944$	6.97345			0.226966
$945$	−0.986723	+	0.689160i	−0.0320981	+	0.0224184i
$946$	7.88325			0.256307
$947$	−9.89246	−	17.1343i	−0.321462	−	0.556788i	0.659328	−	0.751855i	$-0.270841\pi$
$947$	−9.89246	−	17.1343i	−0.321462	−	0.556788i	−0.980790	+	0.195067i	$0.937508\pi$
$948$	−2.68236	+	4.64598i	−0.0871189	+	0.150894i
$949$	−4.85670	+	8.41205i	−0.157655	+	0.273067i
$950$	9.30634	+	16.1191i	0.301938	+	0.522971i
$951$	−27.6272			−0.895872
$952$	2.39653	+	1.12100i	0.0776720	+	0.0363318i
$953$	43.5065			1.40931			0.704656	−	0.709549i	$-0.251101\pi$
$953$	43.5065			1.40931			0.704656	+	0.709549i	$0.251101\pi$
$954$	−0.454904	−	0.787917i	−0.0147281	−	0.0255098i
$955$	−2.23349	+	3.86852i	−0.0722741	+	0.125182i
$956$	13.1312	−	22.7439i	0.424694	−	0.735592i
$957$	1.39653	+	2.41886i	0.0451434	+	0.0781907i
$958$	0.729425			0.0235666
$959$	2.18038	+	1.01989i	0.0704083	+	0.0329341i
$960$	0.454904			0.0146820
$961$	−30.4469	−	52.7356i	−0.982158	−	1.70115i
$962$	−3.58612	+	6.21135i	−0.115621	+	0.200262i
$963$	−7.80634	+	13.5210i	−0.251556	+	0.435707i
$964$	−3.97345	−	6.88221i	−0.127976	−	0.221661i
$965$	3.11914			0.100409
$966$	−18.0861	+	12.6320i	−0.581912	+	0.406426i
$967$	34.5185			1.11004			0.555021	−	0.831837i	$-0.312710\pi$
$967$	34.5185			1.11004			0.555021	+	0.831837i	$0.312710\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−1.94163	+	3.36300i	−0.0623740	+	0.108035i
$970$	−3.31764	+	5.74633i	−0.106523	+	0.184503i
$971$	22.4694	+	38.9181i	0.721077	+	1.24894i	0.960569	+	0.278043i	$0.0896858\pi$
$971$	22.4694	+	38.9181i	0.721077	+	1.24894i	−0.239492	+	0.970898i	$0.576981\pi$
$972$	1.00000			0.0320750
$973$	1.90586	+	22.0872i	0.0610992	+	0.708082i
$974$	−36.8567			−1.18096
$975$	2.18038	+	3.77654i	0.0698282	+	0.120946i
$976$	7.02051	−	12.1599i	0.224721	−	0.389229i
$977$	−16.2624	+	28.1674i	−0.520282	+	0.901154i	0.479440	+	0.877574i	$0.340840\pi$
$977$	−16.2624	+	28.1674i	−0.520282	+	0.901154i	−0.999722	+	0.0235797i	$0.992494\pi$
$978$	5.80634	+	10.0569i	0.185666	+	0.321583i
$979$	−11.0902			−0.354444
$980$	−3.13726	+	0.545479i	−0.100216	+	0.0174247i
$981$	14.0410			0.448296
$982$	−12.7532	−	22.0892i	−0.406972	−	0.704896i
$983$	23.5974	−	40.8719i	0.752641	−	1.30361i	−0.193897	−	0.981022i	$-0.562113\pi$
$983$	23.5974	−	40.8719i	0.752641	−	1.30361i	0.946539	−	0.322591i	$-0.104554\pi$
$984$	0.896531	−	1.55284i	0.0285804	−	0.0495027i
$985$	−5.33816	−	9.24596i	−0.170088	−	0.294601i
$986$	−2.79306			−0.0889492
$987$	−0.0769148	−	0.891370i	−0.00244822	−	0.0283726i
$988$	3.53302			0.112400
$989$	−32.8659	−	56.9254i	−1.04508	−	1.81012i
$990$	−0.227452	+	0.393958i	−0.00722890	+	0.0125208i
$991$	−6.27452	+	10.8678i	−0.199317	+	0.345227i	−0.948307	−	0.317354i	$-0.897206\pi$
$991$	−6.27452	+	10.8678i	−0.199317	+	0.345227i	0.748990	+	0.662581i	$0.230539\pi$
$992$	4.79306	+	8.30183i	0.152180	+	0.263583i
$993$	−28.9653			−0.919186
$994$	10.3965	−	7.26129i	0.329758	−	0.230314i
$995$	−1.01602			−0.0322101
$996$	−0.986723	−	1.70905i	−0.0312655	−	0.0541535i
$997$	−20.4549	+	35.4289i	−0.647813	+	1.12205i	0.335831	+	0.941922i	$0.390983\pi$
$997$	−20.4549	+	35.4289i	−0.647813	+	1.12205i	−0.983644	+	0.180123i	$0.942350\pi$
$998$	2.06364	−	3.57433i	0.0653233	−	0.113143i
$999$	−3.94163	−	6.82710i	−0.124708	−	0.216000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.i.f.67.2	✓	6
3.2	odd	2		1386.2.k.w.991.2		6
7.2	even	3	inner	462.2.i.f.331.2	yes	6
7.3	odd	6		3234.2.a.bg.1.2		3
7.4	even	3		3234.2.a.bi.1.2		3
21.2	odd	6		1386.2.k.w.793.2		6
21.11	odd	6		9702.2.a.dt.1.2		3
21.17	even	6		9702.2.a.du.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.f.67.2	✓	6	1.1	even	1	trivial
462.2.i.f.331.2	yes	6	7.2	even	3	inner
1386.2.k.w.793.2		6	21.2	odd	6
1386.2.k.w.991.2		6	3.2	odd	2
3234.2.a.bg.1.2		3	7.3	odd	6
3234.2.a.bi.1.2		3	7.4	even	3
9702.2.a.dt.1.2		3	21.11	odd	6
9702.2.a.du.1.2		3	21.17	even	6

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.227452 - 0.393958i) q^{5} +1.00000 q^{6} +(-0.227452 - 2.63596i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.227452 - 0.393958i) q^{5} +1.00000 q^{6} +(-0.227452 - 2.63596i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.227452 + 0.393958i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +0.909808 q^{13} +(-2.16908 + 1.51496i) q^{14} +0.454904 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.94163 - 3.36300i) q^{19} +0.454904 q^{20} +(2.39653 + 1.12100i) q^{21} +1.00000 q^{22} +(-4.16908 - 7.22106i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.39653 - 4.15091i) q^{25} +(-0.454904 - 0.787917i) q^{26} +1.00000 q^{27} +(2.39653 + 1.12100i) q^{28} -2.79306 q^{29} +(-0.227452 - 0.393958i) q^{30} +(4.79306 - 8.30183i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +1.00000 q^{34} +(-0.986723 + 0.689160i) q^{35} +1.00000 q^{36} +(-3.94163 - 6.82710i) q^{37} +(-1.94163 + 3.36300i) q^{38} +(-0.454904 + 0.787917i) q^{39} +(-0.227452 - 0.393958i) q^{40} -1.79306 q^{41} +(-0.227452 - 2.63596i) q^{42} +7.88325 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.227452 + 0.393958i) q^{45} +(-4.16908 + 7.22106i) q^{46} +(-0.169079 - 0.292854i) q^{47} +1.00000 q^{48} +(-6.89653 + 1.19911i) q^{49} -4.79306 q^{50} +(-0.500000 - 0.866025i) q^{51} +(-0.454904 + 0.787917i) q^{52} +(-0.454904 + 0.787917i) q^{53} +(-0.500000 - 0.866025i) q^{54} +0.454904 q^{55} +(-0.227452 - 2.63596i) q^{56} +3.88325 q^{57} +(1.39653 + 2.41886i) q^{58} +(-3.48672 + 6.03918i) q^{59} +(-0.227452 + 0.393958i) q^{60} +(7.02051 + 12.1599i) q^{61} -9.58612 q^{62} +(-2.16908 + 1.51496i) q^{63} +1.00000 q^{64} +(-0.206938 - 0.358427i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(1.89653 - 3.28489i) q^{67} +(-0.500000 - 0.866025i) q^{68} +8.33816 q^{69} +(1.09019 + 0.509947i) q^{70} -4.79306 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.33816 + 9.24596i) q^{73} +(-3.94163 + 6.82710i) q^{74} +(2.39653 + 4.15091i) q^{75} +3.88325 q^{76} +(2.39653 + 1.12100i) q^{77} +0.909808 q^{78} +(-2.68236 - 4.64598i) q^{79} +(-0.227452 + 0.393958i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.896531 + 1.55284i) q^{82} +1.97345 q^{83} +(-2.16908 + 1.51496i) q^{84} +0.454904 q^{85} +(-3.94163 - 6.82710i) q^{86} +(1.39653 - 2.41886i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(5.54510 + 9.60439i) q^{89} +0.454904 q^{90} +(-0.206938 - 2.39821i) q^{91} +8.33816 q^{92} +(4.79306 + 8.30183i) q^{93} +(-0.169079 + 0.292854i) q^{94} +(-0.883254 + 1.52984i) q^{95} +(-0.500000 - 0.866025i) q^{96} +14.5861 q^{97} +(4.48672 + 5.37302i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 6 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{19} - 3 q^{21} + 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 6 q^{27} - 3 q^{28} + 18 q^{29} - 6 q^{31} - 3 q^{32} - 3 q^{33} + 6 q^{34} + 6 q^{35} + 6 q^{36} - 9 q^{37} + 3 q^{38} + 24 q^{41} + 18 q^{43} - 3 q^{44} - 9 q^{46} + 15 q^{47} + 6 q^{48} - 24 q^{49} + 6 q^{50} - 3 q^{51} - 3 q^{54} - 6 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 3 q^{63} + 6 q^{64} - 36 q^{65} - 3 q^{66} - 6 q^{67} - 3 q^{68} + 18 q^{69} + 12 q^{70} + 6 q^{71} - 3 q^{72} - 9 q^{74} - 3 q^{75} - 6 q^{76} - 3 q^{77} - 12 q^{79} - 3 q^{81} - 12 q^{82} - 12 q^{83} + 3 q^{84} - 9 q^{86} - 9 q^{87} - 3 q^{88} + 36 q^{89} - 36 q^{91} + 18 q^{92} - 6 q^{93} + 15 q^{94} + 24 q^{95} - 3 q^{96} + 18 q^{97} + 15 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 6 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^19 - 3 * q^21 + 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 6 * q^27 - 3 * q^28 + 18 * q^29 - 6 * q^31 - 3 * q^32 - 3 * q^33 + 6 * q^34 + 6 * q^35 + 6 * q^36 - 9 * q^37 + 3 * q^38 + 24 * q^41 + 18 * q^43 - 3 * q^44 - 9 * q^46 + 15 * q^47 + 6 * q^48 - 24 * q^49 + 6 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 3 * q^63 + 6 * q^64 - 36 * q^65 - 3 * q^66 - 6 * q^67 - 3 * q^68 + 18 * q^69 + 12 * q^70 + 6 * q^71 - 3 * q^72 - 9 * q^74 - 3 * q^75 - 6 * q^76 - 3 * q^77 - 12 * q^79 - 3 * q^81 - 12 * q^82 - 12 * q^83 + 3 * q^84 - 9 * q^86 - 9 * q^87 - 3 * q^88 + 36 * q^89 - 36 * q^91 + 18 * q^92 - 6 * q^93 + 15 * q^94 + 24 * q^95 - 3 * q^96 + 18 * q^97 + 15 * q^98 + 6 * q^99

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