LMFDB - Embedded newform 126.2.f.c.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(43,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("126.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.f (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			85.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	126.85
Dual form			126.2.f.c.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.724745 - 1.25529i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.724745 - 1.25529i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -1.44949 q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.724745 + 1.57313i) q^{12} +(-2.44949 + 4.24264i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(-1.94949 + 2.28024i) q^{18} +2.55051 q^{19} +(0.724745 + 1.25529i) q^{20} +(1.72474 + 0.158919i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.00000 - 1.41421i) q^{24} +(1.44949 + 2.51059i) q^{25} +4.89898 q^{26} +(-5.00000 - 1.41421i) q^{27} -1.00000 q^{28} +(3.44949 + 5.97469i) q^{29} +(-1.44949 + 2.04989i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.44949 - 0.317837i) q^{33} +(-1.00000 - 1.73205i) q^{34} +1.44949 q^{35} +(2.94949 + 0.548188i) q^{36} +11.7980 q^{37} +(-1.27526 - 2.20881i) q^{38} +(3.55051 + 7.70674i) q^{39} +(0.724745 - 1.25529i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(-0.724745 - 1.57313i) q^{42} +(-3.44949 - 5.97469i) q^{43} +2.00000 q^{44} +(-4.27526 - 0.794593i) q^{45} -1.00000 q^{46} +(-4.89898 - 8.48528i) q^{47} +(-1.72474 - 0.158919i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.44949 - 2.51059i) q^{50} +(2.00000 - 2.82843i) q^{51} +(-2.44949 - 4.24264i) q^{52} -10.8990 q^{53} +(1.27526 + 5.03723i) q^{54} -2.89898 q^{55} +(0.500000 + 0.866025i) q^{56} +(2.55051 - 3.60697i) q^{57} +(3.44949 - 5.97469i) q^{58} +(1.00000 - 1.73205i) q^{59} +(2.50000 + 0.230351i) q^{60} +(-3.27526 - 5.67291i) q^{61} +6.00000 q^{62} +(1.94949 - 2.28024i) q^{63} +1.00000 q^{64} +(3.55051 + 6.14966i) q^{65} +(1.44949 + 3.14626i) q^{66} +(6.44949 - 11.1708i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-0.724745 - 1.57313i) q^{69} +(-0.724745 - 1.25529i) q^{70} +0.101021 q^{71} +(-1.00000 - 2.82843i) q^{72} -6.89898 q^{73} +(-5.89898 - 10.2173i) q^{74} +(5.00000 + 0.460702i) q^{75} +(-1.27526 + 2.20881i) q^{76} +(1.00000 - 1.73205i) q^{77} +(4.89898 - 6.92820i) q^{78} +(0.949490 + 1.64456i) q^{79} -1.44949 q^{80} +(-7.00000 + 5.65685i) q^{81} +9.79796 q^{82} +(-1.00000 - 1.73205i) q^{83} +(-1.00000 + 1.41421i) q^{84} +(1.44949 - 2.51059i) q^{85} +(-3.44949 + 5.97469i) q^{86} +(11.8990 + 1.09638i) q^{87} +(-1.00000 - 1.73205i) q^{88} -16.8990 q^{89} +(1.44949 + 4.09978i) q^{90} -4.89898 q^{91} +(0.500000 + 0.866025i) q^{92} +(4.34847 + 9.43879i) q^{93} +(-4.89898 + 8.48528i) q^{94} +(1.84847 - 3.20164i) q^{95} +(0.724745 + 1.57313i) q^{96} +(-1.44949 - 2.51059i) q^{97} +1.00000 q^{98} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{10} - 4 q^{11} - 2 q^{12} + 2 q^{14} - 14 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} + 20 q^{19} - 2 q^{20} + 2 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 4 q^{25} - 20 q^{27} - 4 q^{28} + 4 q^{29} + 4 q^{30} - 12 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 8 q^{37} - 10 q^{38} + 24 q^{39} - 2 q^{40} + 2 q^{42} - 4 q^{43} + 8 q^{44} - 22 q^{45} - 4 q^{46} - 2 q^{48} - 2 q^{49} - 4 q^{50} + 8 q^{51} - 24 q^{53} + 10 q^{54} + 8 q^{55} + 2 q^{56} + 20 q^{57} + 4 q^{58} + 4 q^{59} + 10 q^{60} - 18 q^{61} + 24 q^{62} - 2 q^{63} + 4 q^{64} + 24 q^{65} - 4 q^{66} + 16 q^{67} - 4 q^{68} + 2 q^{69} + 2 q^{70} + 20 q^{71} - 4 q^{72} - 8 q^{73} - 4 q^{74} + 20 q^{75} - 10 q^{76} + 4 q^{77} - 6 q^{79} + 4 q^{80} - 28 q^{81} - 4 q^{83} - 4 q^{84} - 4 q^{85} - 4 q^{86} + 28 q^{87} - 4 q^{88} - 48 q^{89} - 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} - 2 q^{96} + 4 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^10 - 4 * q^11 - 2 * q^12 + 2 * q^14 - 14 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 + 20 * q^19 - 2 * q^20 + 2 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 4 * q^25 - 20 * q^27 - 4 * q^28 + 4 * q^29 + 4 * q^30 - 12 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 8 * q^37 - 10 * q^38 + 24 * q^39 - 2 * q^40 + 2 * q^42 - 4 * q^43 + 8 * q^44 - 22 * q^45 - 4 * q^46 - 2 * q^48 - 2 * q^49 - 4 * q^50 + 8 * q^51 - 24 * q^53 + 10 * q^54 + 8 * q^55 + 2 * q^56 + 20 * q^57 + 4 * q^58 + 4 * q^59 + 10 * q^60 - 18 * q^61 + 24 * q^62 - 2 * q^63 + 4 * q^64 + 24 * q^65 - 4 * q^66 + 16 * q^67 - 4 * q^68 + 2 * q^69 + 2 * q^70 + 20 * q^71 - 4 * q^72 - 8 * q^73 - 4 * q^74 + 20 * q^75 - 10 * q^76 + 4 * q^77 - 6 * q^79 + 4 * q^80 - 28 * q^81 - 4 * q^83 - 4 * q^84 - 4 * q^85 - 4 * q^86 + 28 * q^87 - 4 * q^88 - 48 * q^89 - 4 * q^90 + 2 * q^92 - 12 * q^93 - 22 * q^95 - 2 * q^96 + 4 * q^97 + 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.724745	−	1.25529i	0.324116	−	0.561385i	−0.657217	−	0.753701i	$-0.728267\pi$
$5$	0.724745	−	1.25529i	0.324116	−	0.561385i	0.981333	+	0.192316i	$0.0615999\pi$
$6$	−1.72474	−	0.158919i	−0.704124	−	0.0648783i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	−1.44949			−0.458369
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	0.724745	+	1.57313i	0.209216	+	0.454124i
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	0.295806	+	0.955248i	$0.404412\pi$
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	−0.975172	+	0.221449i	$0.928921\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	−1.05051	−	2.28024i	−0.271241	−	0.588755i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.94949	+	2.28024i	−0.459499	+	0.537457i
$19$	2.55051			0.585127			0.292564	−	0.956246i	$-0.405492\pi$
$19$	2.55051			0.585127			0.292564	+	0.956246i	$0.405492\pi$
$20$	0.724745	+	1.25529i	0.162058	+	0.280692i
$21$	1.72474	+	0.158919i	0.376370	+	0.0346789i
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	1.00000	−	1.41421i	0.204124	−	0.288675i
$25$	1.44949	+	2.51059i	0.289898	+	0.502118i
$26$	4.89898			0.960769
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	−1.00000			−0.188982
$29$	3.44949	+	5.97469i	0.640554	+	1.10947i	0.985309	+	0.170780i	$0.0546286\pi$
$29$	3.44949	+	5.97469i	0.640554	+	1.10947i	−0.344755	+	0.938693i	$0.612038\pi$
$30$	−1.44949	+	2.04989i	−0.264639	+	0.374257i
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.44949	−	0.317837i	−0.600479	−	0.0553284i
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$	1.44949			0.245008
$36$	2.94949	+	0.548188i	0.491582	+	0.0913647i
$37$	11.7980			1.93957			0.969786	−	0.243956i	$-0.0784453\pi$
$37$	11.7980			1.93957			0.969786	+	0.243956i	$0.0784453\pi$
$38$	−1.27526	−	2.20881i	−0.206874	−	0.358316i
$39$	3.55051	+	7.70674i	0.568537	+	1.23407i
$40$	0.724745	−	1.25529i	0.114592	−	0.198480i
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	0.175106	+	0.984550i	$0.443973\pi$
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	−0.940198	+	0.340629i	$0.889360\pi$
$42$	−0.724745	−	1.57313i	−0.111831	−	0.242740i
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	−0.999540	−	0.0303367i	$-0.990342\pi$
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	0.473497	−	0.880795i	$-0.342991\pi$
$44$	2.00000			0.301511
$45$	−4.27526	−	0.794593i	−0.637317	−	0.118451i
$46$	−1.00000			−0.147442
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	−0.963118	−	0.269081i	$-0.913280\pi$
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	0.248528	−	0.968625i	$-0.420053\pi$
$48$	−1.72474	−	0.158919i	−0.248945	−	0.0229379i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	1.44949	−	2.51059i	0.204989	−	0.355051i
$51$	2.00000	−	2.82843i	0.280056	−	0.396059i
$52$	−2.44949	−	4.24264i	−0.339683	−	0.588348i
$53$	−10.8990			−1.49709			−0.748545	−	0.663084i	$-0.769247\pi$
$53$	−10.8990			−1.49709			−0.748545	+	0.663084i	$0.769247\pi$
$54$	1.27526	+	5.03723i	0.173540	+	0.685481i
$55$	−2.89898			−0.390898
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	2.55051	−	3.60697i	0.337823	−	0.477754i
$58$	3.44949	−	5.97469i	0.452940	−	0.784515i
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	−0.793560	−	0.608492i	$-0.791775\pi$
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	0.923749	+	0.382998i	$0.125108\pi$
$60$	2.50000	+	0.230351i	0.322749	+	0.0297382i
$61$	−3.27526	−	5.67291i	−0.419353	−	0.726341i	0.576521	−	0.817082i	$-0.304410\pi$
$61$	−3.27526	−	5.67291i	−0.419353	−	0.726341i	−0.995875	+	0.0907408i	$0.971077\pi$
$62$	6.00000			0.762001
$63$	1.94949	−	2.28024i	0.245613	−	0.287283i
$64$	1.00000			0.125000
$65$	3.55051	+	6.14966i	0.440387	+	0.762772i
$66$	1.44949	+	3.14626i	0.178420	+	0.387278i
$67$	6.44949	−	11.1708i	0.787931	−	1.36474i	−0.139302	−	0.990250i	$-0.544486\pi$
$67$	6.44949	−	11.1708i	0.787931	−	1.36474i	0.927233	−	0.374486i	$-0.122181\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	−0.724745	−	1.57313i	−0.0872490	−	0.189383i
$70$	−0.724745	−	1.25529i	−0.0866236	−	0.150036i
$71$	0.101021			0.0119889			0.00599446	−	0.999982i	$-0.498092\pi$
$71$	0.101021			0.0119889			0.00599446	+	0.999982i	$0.498092\pi$
$72$	−1.00000	−	2.82843i	−0.117851	−	0.333333i
$73$	−6.89898			−0.807464			−0.403732	−	0.914877i	$-0.632287\pi$
$73$	−6.89898			−0.807464			−0.403732	+	0.914877i	$0.632287\pi$
$74$	−5.89898	−	10.2173i	−0.685742	−	1.18774i
$75$	5.00000	+	0.460702i	0.577350	+	0.0531973i
$76$	−1.27526	+	2.20881i	−0.146282	+	0.253368i
$77$	1.00000	−	1.73205i	0.113961	−	0.197386i
$78$	4.89898	−	6.92820i	0.554700	−	0.784465i
$79$	0.949490	+	1.64456i	0.106826	+	0.185028i	0.914483	−	0.404625i	$-0.132598\pi$
$79$	0.949490	+	1.64456i	0.106826	+	0.185028i	−0.807657	+	0.589653i	$0.799265\pi$
$80$	−1.44949			−0.162058
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	9.79796			1.08200
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$	−1.00000	+	1.41421i	−0.109109	+	0.154303i
$85$	1.44949	−	2.51059i	0.157219	−	0.272312i
$86$	−3.44949	+	5.97469i	−0.371968	+	0.644268i
$87$	11.8990	+	1.09638i	1.27570	+	0.117544i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	−16.8990			−1.79129			−0.895644	−	0.444771i	$-0.853285\pi$
$89$	−16.8990			−1.79129			−0.895644	+	0.444771i	$0.853285\pi$
$90$	1.44949	+	4.09978i	0.152790	+	0.432154i
$91$	−4.89898			−0.513553
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	4.34847	+	9.43879i	0.450915	+	0.978757i
$94$	−4.89898	+	8.48528i	−0.505291	+	0.875190i
$95$	1.84847	−	3.20164i	0.189649	−	0.328482i
$96$	0.724745	+	1.57313i	0.0739690	+	0.160557i
$97$	−1.44949	−	2.51059i	−0.147173	−	0.254912i	0.783008	−	0.622011i	$-0.213684\pi$
$97$	−1.44949	−	2.51059i	−0.147173	−	0.254912i	−0.930182	+	0.367099i	$0.880351\pi$
$98$	1.00000			0.101015
$99$	−3.89898	+	4.56048i	−0.391862	+	0.458345i
$100$	−2.89898			−0.289898
$101$	8.62372	+	14.9367i	0.858093	+	1.48626i	0.873746	+	0.486383i	$0.161684\pi$
$101$	8.62372	+	14.9367i	0.858093	+	1.48626i	−0.0156533	+	0.999877i	$0.504983\pi$
$102$	−3.44949	−	0.317837i	−0.341550	−	0.0314706i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	−2.44949	+	4.24264i	−0.240192	+	0.416025i
$105$	1.44949	−	2.04989i	0.141456	−	0.200049i
$106$	5.44949	+	9.43879i	0.529301	+	0.916777i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	3.72474	−	3.62302i	0.358414	−	0.348625i
$109$	12.6969			1.21615			0.608073	−	0.793881i	$-0.291943\pi$
$109$	12.6969			1.21615			0.608073	+	0.793881i	$0.291943\pi$
$110$	1.44949	+	2.51059i	0.138203	+	0.239375i
$111$	11.7980	−	16.6848i	1.11981	−	1.58365i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	3.05051	−	5.28364i	0.286968	−	0.497043i	−0.686117	−	0.727492i	$-0.740686\pi$
$113$	3.05051	−	5.28364i	0.286968	−	0.497043i	0.973084	+	0.230449i	$0.0740194\pi$
$114$	−4.39898	−	0.405324i	−0.412002	−	0.0379620i
$115$	−0.724745	−	1.25529i	−0.0675828	−	0.117057i
$116$	−6.89898			−0.640554
$117$	14.4495	+	2.68556i	1.33586	+	0.248280i
$118$	−2.00000			−0.184115
$119$	1.00000	+	1.73205i	0.0916698	+	0.158777i
$120$	−1.05051	−	2.28024i	−0.0958980	−	0.208156i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−3.27526	+	5.67291i	−0.296528	+	0.513601i
$123$	7.10102	+	15.4135i	0.640277	+	1.38979i
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	11.4495			1.02407
$126$	−2.94949	−	0.548188i	−0.262761	−	0.0488365i
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−11.8990	−	1.09638i	−1.04765	−	0.0965306i
$130$	3.55051	−	6.14966i	0.311400	−	0.539361i
$131$	4.27526	−	7.40496i	0.373531	−	0.646974i	−0.616575	−	0.787296i	$-0.711480\pi$
$131$	4.27526	−	7.40496i	0.373531	−	0.646974i	0.990106	+	0.140322i	$0.0448137\pi$
$132$	2.00000	−	2.82843i	0.174078	−	0.246183i
$133$	1.27526	+	2.20881i	0.110579	+	0.191528i
$134$	−12.8990			−1.11430
$135$	−5.39898	+	5.25153i	−0.464670	+	0.451980i
$136$	2.00000			0.171499
$137$	−3.89898	−	6.75323i	−0.333112	−	0.576967i	0.650008	−	0.759927i	$-0.274765\pi$
$137$	−3.89898	−	6.75323i	−0.333112	−	0.576967i	−0.983120	+	0.182960i	$0.941432\pi$
$138$	−1.00000	+	1.41421i	−0.0851257	+	0.120386i
$139$	−2.27526	+	3.94086i	−0.192985	+	0.334259i	−0.946238	−	0.323471i	$-0.895150\pi$
$139$	−2.27526	+	3.94086i	−0.192985	+	0.334259i	0.753253	+	0.657730i	$0.228483\pi$
$140$	−0.724745	+	1.25529i	−0.0612521	+	0.106092i
$141$	−16.8990	−	1.55708i	−1.42315	−	0.131130i
$142$	−0.0505103	−	0.0874863i	−0.00423873	−	0.00734169i
$143$	9.79796			0.819346
$144$	−1.94949	+	2.28024i	−0.162457	+	0.190020i
$145$	10.0000			0.830455
$146$	3.44949	+	5.97469i	0.285482	+	0.494469i
$147$	0.724745	+	1.57313i	0.0597759	+	0.129750i
$148$	−5.89898	+	10.2173i	−0.484893	+	0.839860i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−2.10102	−	4.56048i	−0.171548	−	0.372361i
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	0.949637	−	0.313353i	$-0.101452\pi$
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	−0.746190	+	0.665733i	$0.768119\pi$
$152$	2.55051			0.206874
$153$	−2.00000	−	5.65685i	−0.161690	−	0.457330i
$154$	−2.00000			−0.161165
$155$	4.34847	+	7.53177i	0.349277	+	0.604966i
$156$	−8.44949	−	0.778539i	−0.676501	−	0.0623330i
$157$	4.17423	−	7.22999i	0.333140	−	0.577016i	−0.649986	−	0.759947i	$-0.725225\pi$
$157$	4.17423	−	7.22999i	0.333140	−	0.577016i	0.983126	+	0.182931i	$0.0585584\pi$
$158$	0.949490	−	1.64456i	0.0755373	−	0.130835i
$159$	−10.8990	+	15.4135i	−0.864345	+	1.22237i
$160$	0.724745	+	1.25529i	0.0572961	+	0.0992398i
$161$	1.00000			0.0788110
$162$	8.39898	+	3.23375i	0.659886	+	0.254067i
$163$	−19.7980			−1.55070			−0.775348	−	0.631534i	$-0.782425\pi$
$163$	−19.7980			−1.55070			−0.775348	+	0.631534i	$0.782425\pi$
$164$	−4.89898	−	8.48528i	−0.382546	−	0.662589i
$165$	−2.89898	+	4.09978i	−0.225685	+	0.319167i
$166$	−1.00000	+	1.73205i	−0.0776151	+	0.134433i
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	−0.581433	−	0.813594i	$-0.697508\pi$
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	0.995310	+	0.0967384i	$0.0308410\pi$
$168$	1.72474	+	0.158919i	0.133067	+	0.0122608i
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	−2.89898			−0.222342
$171$	−2.55051	−	7.21393i	−0.195042	−	0.551663i
$172$	6.89898			0.526042
$173$	1.55051	+	2.68556i	0.117883	+	0.204180i	0.918929	−	0.394424i	$-0.129056\pi$
$173$	1.55051	+	2.68556i	0.117883	+	0.204180i	−0.801045	+	0.598604i	$0.795723\pi$
$174$	−5.00000	−	10.8530i	−0.379049	−	0.822764i
$175$	−1.44949	+	2.51059i	−0.109571	+	0.189783i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	−1.44949	−	3.14626i	−0.108950	−	0.236488i
$178$	8.44949	+	14.6349i	0.633316	+	1.09694i
$179$	20.6969			1.54696			0.773481	−	0.633820i	$-0.218514\pi$
$179$	20.6969			1.54696			0.773481	+	0.633820i	$0.218514\pi$
$180$	2.82577	−	3.30518i	0.210620	−	0.246354i
$181$	−10.3485			−0.769196			−0.384598	−	0.923084i	$-0.625660\pi$
$181$	−10.3485			−0.769196			−0.384598	+	0.923084i	$0.625660\pi$
$182$	2.44949	+	4.24264i	0.181568	+	0.314485i
$183$	−11.2980	−	1.04100i	−0.835169	−	0.0769528i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	8.55051	−	14.8099i	0.628646	−	1.08885i
$186$	6.00000	−	8.48528i	0.439941	−	0.622171i
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	9.79796			0.714590
$189$	−1.27526	−	5.03723i	−0.0927612	−	0.366405i
$190$	−3.69694			−0.268204
$191$	−2.05051	−	3.55159i	−0.148370	−	0.256984i	0.782255	−	0.622958i	$-0.214069\pi$
$191$	−2.05051	−	3.55159i	−0.148370	−	0.256984i	−0.930625	+	0.365974i	$0.880736\pi$
$192$	1.00000	−	1.41421i	0.0721688	−	0.102062i
$193$	8.94949	−	15.5010i	0.644198	−	1.11578i	−0.340288	−	0.940321i	$-0.610524\pi$
$193$	8.94949	−	15.5010i	0.644198	−	1.11578i	0.984486	−	0.175463i	$-0.0561422\pi$
$194$	−1.44949	+	2.51059i	−0.104067	+	0.180250i
$195$	12.2474	+	1.12848i	0.877058	+	0.0808124i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	16.6969			1.18961			0.594804	−	0.803871i	$-0.297230\pi$
$197$	16.6969			1.18961			0.594804	+	0.803871i	$0.297230\pi$
$198$	5.89898	+	1.09638i	0.419222	+	0.0779161i
$199$	−2.89898			−0.205503			−0.102752	−	0.994707i	$-0.532765\pi$
$199$	−2.89898			−0.205503			−0.102752	+	0.994707i	$0.532765\pi$
$200$	1.44949	+	2.51059i	0.102494	+	0.177526i
$201$	−9.34847	−	20.2918i	−0.659390	−	1.43127i
$202$	8.62372	−	14.9367i	0.606763	−	1.05094i
$203$	−3.44949	+	5.97469i	−0.242107	+	0.419341i
$204$	1.44949	+	3.14626i	0.101485	+	0.220283i
$205$	7.10102	+	12.2993i	0.495957	+	0.859022i
$206$	14.0000			0.975426
$207$	−2.94949	−	0.548188i	−0.205004	−	0.0381017i
$208$	4.89898			0.339683
$209$	−2.55051	−	4.41761i	−0.176422	−	0.305573i
$210$	−2.50000	−	0.230351i	−0.172516	−	0.0158957i
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	−0.997982	−	0.0634968i	$-0.979775\pi$
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	0.553981	+	0.832529i	$0.313108\pi$
$212$	5.44949	−	9.43879i	0.374272	−	0.648259i
$213$	0.101021	−	0.142865i	0.00692181	−	0.00978892i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−10.0000			−0.681994
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$	−6.00000			−0.407307
$218$	−6.34847	−	10.9959i	−0.429973	−	0.744734i
$219$	−6.89898	+	9.75663i	−0.466190	+	0.659292i
$220$	1.44949	−	2.51059i	0.0977246	−	0.169264i
$221$	−4.89898	+	8.48528i	−0.329541	+	0.570782i
$222$	−20.3485	−	1.87492i	−1.36570	−	0.125836i
$223$	5.55051	+	9.61377i	0.371690	+	0.643785i	0.989826	−	0.142286i	$-0.0454452\pi$
$223$	5.55051	+	9.61377i	0.371690	+	0.643785i	−0.618136	+	0.786071i	$0.712112\pi$
$224$	−1.00000			−0.0668153
$225$	5.65153	−	6.61037i	0.376769	−	0.440691i
$226$	−6.10102			−0.405834
$227$	2.72474	+	4.71940i	0.180848	+	0.313237i	0.942169	−	0.335137i	$-0.108783\pi$
$227$	2.72474	+	4.71940i	0.180848	+	0.313237i	−0.761322	+	0.648374i	$0.775449\pi$
$228$	1.84847	+	4.01229i	0.122418	+	0.265720i
$229$	−0.623724	+	1.08032i	−0.0412169	+	0.0713897i	−0.885898	−	0.463880i	$-0.846457\pi$
$229$	−0.623724	+	1.08032i	−0.0412169	+	0.0713897i	0.844681	+	0.535270i	$0.179790\pi$
$230$	−0.724745	+	1.25529i	−0.0477883	+	0.0827717i
$231$	−1.44949	−	3.14626i	−0.0953694	−	0.207009i
$232$	3.44949	+	5.97469i	0.226470	+	0.392258i
$233$	−7.00000			−0.458585			−0.229293	−	0.973358i	$-0.573641\pi$
$233$	−7.00000			−0.458585			−0.229293	+	0.973358i	$0.573641\pi$
$234$	−4.89898	−	13.8564i	−0.320256	−	0.905822i
$235$	−14.2020			−0.926439
$236$	1.00000	+	1.73205i	0.0650945	+	0.112747i
$237$	3.27526	+	0.301783i	0.212751	+	0.0196029i
$238$	1.00000	−	1.73205i	0.0648204	−	0.112272i
$239$	−3.39898	+	5.88721i	−0.219862	+	0.380812i	−0.954766	−	0.297360i	$-0.903894\pi$
$239$	−3.39898	+	5.88721i	−0.219862	+	0.380812i	0.734904	+	0.678171i	$0.237227\pi$
$240$	−1.44949	+	2.04989i	−0.0935642	+	0.132320i
$241$	−0.449490	−	0.778539i	−0.0289542	−	0.0501501i	0.851185	−	0.524865i	$-0.175884\pi$
$241$	−0.449490	−	0.778539i	−0.0289542	−	0.0501501i	−0.880139	+	0.474715i	$0.842551\pi$
$242$	−7.00000			−0.449977
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$	6.55051			0.419353
$245$	0.724745	+	1.25529i	0.0463023	+	0.0801979i
$246$	9.79796	−	13.8564i	0.624695	−	0.883452i
$247$	−6.24745	+	10.8209i	−0.397516	+	0.688517i
$248$	−3.00000	+	5.19615i	−0.190500	+	0.329956i
$249$	−3.44949	−	0.317837i	−0.218603	−	0.0201421i
$250$	−5.72474	−	9.91555i	−0.362065	−	0.627114i
$251$	17.4495			1.10140			0.550701	−	0.834703i	$-0.314360\pi$
$251$	17.4495			1.10140			0.550701	+	0.834703i	$0.314360\pi$
$252$	1.00000	+	2.82843i	0.0629941	+	0.178174i
$253$	−2.00000			−0.125739
$254$	1.50000	+	2.59808i	0.0941184	+	0.163018i
$255$	−2.10102	−	4.56048i	−0.131571	−	0.285588i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.10102	+	7.10318i	−0.255815	+	0.443084i	−0.965116	−	0.261821i	$-0.915677\pi$
$257$	−4.10102	+	7.10318i	−0.255815	+	0.443084i	0.709302	+	0.704905i	$0.249010\pi$
$258$	5.00000	+	10.8530i	0.311286	+	0.675679i
$259$	5.89898	+	10.2173i	0.366545	+	0.634874i
$260$	−7.10102			−0.440387
$261$	13.4495	−	15.7313i	0.832503	−	0.973744i
$262$	−8.55051			−0.528252
$263$	−12.9495	−	22.4292i	−0.798500	−	1.38304i	−0.920593	−	0.390523i	$-0.872294\pi$
$263$	−12.9495	−	22.4292i	−0.798500	−	1.38304i	0.122093	−	0.992519i	$-0.461039\pi$
$264$	−3.44949	−	0.317837i	−0.212301	−	0.0195615i
$265$	−7.89898	+	13.6814i	−0.485230	+	0.840444i
$266$	1.27526	−	2.20881i	0.0781909	−	0.135431i
$267$	−16.8990	+	23.8988i	−1.03420	+	1.46258i
$268$	6.44949	+	11.1708i	0.393965	+	0.682368i
$269$	−18.3485			−1.11873			−0.559363	−	0.828923i	$-0.688954\pi$
$269$	−18.3485			−1.11873			−0.559363	+	0.828923i	$0.688954\pi$
$270$	7.24745	+	2.04989i	0.441066	+	0.124752i
$271$	7.10102			0.431356			0.215678	−	0.976465i	$-0.430804\pi$
$271$	7.10102			0.431356			0.215678	+	0.976465i	$0.430804\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$	−4.89898	+	6.92820i	−0.296500	+	0.419314i
$274$	−3.89898	+	6.75323i	−0.235546	+	0.407978i
$275$	2.89898	−	5.02118i	0.174815	−	0.302789i
$276$	1.72474	+	0.158919i	0.103817	+	0.00956578i
$277$	9.34847	+	16.1920i	0.561695	+	0.972884i	0.997349	+	0.0727700i	$0.0231839\pi$
$277$	9.34847	+	16.1920i	0.561695	+	0.972884i	−0.435654	+	0.900114i	$0.643483\pi$
$278$	4.55051			0.272921
$279$	17.6969	+	3.28913i	1.05949	+	0.196915i
$280$	1.44949			0.0866236
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	0.996887	+	0.0788417i	$0.0251222\pi$
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	−0.430165	+	0.902750i	$0.641545\pi$
$282$	7.10102	+	15.4135i	0.422860	+	0.917860i
$283$	12.7247	−	22.0399i	0.756408	−	1.31014i	−0.188264	−	0.982118i	$-0.560286\pi$
$283$	12.7247	−	22.0399i	0.756408	−	1.31014i	0.944672	−	0.328018i	$-0.106381\pi$
$284$	−0.0505103	+	0.0874863i	−0.00299723	+	0.00519136i
$285$	−2.67934	−	5.81577i	−0.158710	−	0.344497i
$286$	−4.89898	−	8.48528i	−0.289683	−	0.501745i
$287$	−9.79796			−0.578355
$288$	2.94949	+	0.548188i	0.173800	+	0.0323023i
$289$	−13.0000			−0.764706
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$	−5.00000	−	0.460702i	−0.293105	−	0.0270068i
$292$	3.44949	−	5.97469i	0.201866	−	0.349642i
$293$	−1.37628	+	2.38378i	−0.0804029	+	0.139262i	−0.903423	−	0.428750i	$-0.858954\pi$
$293$	−1.37628	+	2.38378i	−0.0804029	+	0.139262i	0.823020	+	0.568012i	$0.192287\pi$
$294$	1.00000	−	1.41421i	0.0583212	−	0.0824786i
$295$	−1.44949	−	2.51059i	−0.0843926	−	0.146172i
$296$	11.7980			0.685742
$297$	2.55051	+	10.0745i	0.147996	+	0.584580i
$298$	−6.00000			−0.347571
$299$	2.44949	+	4.24264i	0.141658	+	0.245358i
$300$	−2.89898	+	4.09978i	−0.167373	+	0.236701i
$301$	3.44949	−	5.97469i	0.198825	−	0.344375i
$302$	2.50000	−	4.33013i	0.143859	−	0.249171i
$303$	29.7474	+	2.74094i	1.70895	+	0.157463i
$304$	−1.27526	−	2.20881i	−0.0731409	−	0.126684i
$305$	−9.49490			−0.543676
$306$	−3.89898	+	4.56048i	−0.222890	+	0.260705i
$307$	25.2474			1.44095			0.720474	−	0.693482i	$-0.243924\pi$
$307$	25.2474			1.44095			0.720474	+	0.693482i	$0.243924\pi$
$308$	1.00000	+	1.73205i	0.0569803	+	0.0986928i
$309$	10.1464	+	22.0239i	0.577210	+	1.25289i
$310$	4.34847	−	7.53177i	0.246976	−	0.427776i
$311$	−15.3485	+	26.5843i	−0.870332	+	1.50746i	−0.00867810	+	0.999962i	$0.502762\pi$
$311$	−15.3485	+	26.5843i	−0.870332	+	1.50746i	−0.861654	+	0.507497i	$0.830571\pi$
$312$	3.55051	+	7.70674i	0.201008	+	0.436308i
$313$	2.34847	+	4.06767i	0.132743	+	0.229918i	0.924733	−	0.380616i	$-0.124288\pi$
$313$	2.34847	+	4.06767i	0.132743	+	0.229918i	−0.791990	+	0.610534i	$0.790955\pi$
$314$	−8.34847			−0.471131
$315$	−1.44949	−	4.09978i	−0.0816695	−	0.230996i
$316$	−1.89898			−0.106826
$317$	−10.3485	−	17.9241i	−0.581228	−	1.00672i	−0.995334	−	0.0964878i	$-0.969239\pi$
$317$	−10.3485	−	17.9241i	−0.581228	−	1.00672i	0.414106	−	0.910229i	$-0.364094\pi$
$318$	18.7980	+	1.73205i	1.05414	+	0.0971286i
$319$	6.89898	−	11.9494i	0.386269	−	0.669037i
$320$	0.724745	−	1.25529i	0.0405145	−	0.0701731i
$321$	−12.0000	+	16.9706i	−0.669775	+	0.947204i
$322$	−0.500000	−	0.866025i	−0.0278639	−	0.0482617i
$323$	5.10102			0.283828
$324$	−1.39898	−	8.89060i	−0.0777211	−	0.493922i
$325$	−14.2020			−0.787787
$326$	9.89898	+	17.1455i	0.548254	+	0.949603i
$327$	12.6969	−	17.9562i	0.702142	−	0.992979i
$328$	−4.89898	+	8.48528i	−0.270501	+	0.468521i
$329$	4.89898	−	8.48528i	0.270089	−	0.467809i
$330$	5.00000	+	0.460702i	0.275241	+	0.0253608i
$331$	−2.34847	−	4.06767i	−0.129084	−	0.223579i	0.794238	−	0.607606i	$-0.207870\pi$
$331$	−2.34847	−	4.06767i	−0.129084	−	0.223579i	−0.923322	+	0.384027i	$0.874537\pi$
$332$	2.00000			0.109764
$333$	−11.7980	−	33.3697i	−0.646524	−	1.82865i
$334$	−10.6969			−0.585310
$335$	−9.34847	−	16.1920i	−0.510761	−	0.884665i
$336$	−0.724745	−	1.57313i	−0.0395381	−	0.0858214i
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	−0.348877	−	0.937168i	$-0.613437\pi$
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	0.986050	−	0.166447i	$-0.0532296\pi$
$338$	−5.50000	+	9.52628i	−0.299161	+	0.518161i
$339$	−4.42168	−	9.59771i	−0.240153	−	0.521276i
$340$	1.44949	+	2.51059i	0.0786096	+	0.136156i
$341$	12.0000			0.649836
$342$	−4.97219	+	5.81577i	−0.268865	+	0.314481i
$343$	−1.00000			−0.0539949
$344$	−3.44949	−	5.97469i	−0.185984	−	0.322134i
$345$	−2.50000	−	0.230351i	−0.134595	−	0.0124017i
$346$	1.55051	−	2.68556i	0.0833559	−	0.144377i
$347$	−9.79796	+	16.9706i	−0.525982	+	0.911028i	0.473560	+	0.880762i	$0.342969\pi$
$347$	−9.79796	+	16.9706i	−0.525982	+	0.911028i	−0.999542	+	0.0302659i	$0.990365\pi$
$348$	−6.89898	+	9.75663i	−0.369824	+	0.523010i
$349$	−5.55051	−	9.61377i	−0.297112	−	0.514613i	0.678362	−	0.734728i	$-0.262690\pi$
$349$	−5.55051	−	9.61377i	−0.297112	−	0.514613i	−0.975474	+	0.220115i	$0.929357\pi$
$350$	2.89898			0.154957
$351$	18.2474	−	17.7491i	0.973977	−	0.947377i
$352$	2.00000			0.106600
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$	−2.00000	+	2.82843i	−0.106299	+	0.150329i
$355$	0.0732141	−	0.126811i	0.00388580	−	0.00673040i
$356$	8.44949	−	14.6349i	0.447822	−	0.775651i
$357$	3.44949	+	0.317837i	0.182566	+	0.0168217i
$358$	−10.3485	−	17.9241i	−0.546934	−	0.947317i
$359$	−8.79796			−0.464339			−0.232169	−	0.972675i	$-0.574582\pi$
$359$	−8.79796			−0.464339			−0.232169	+	0.972675i	$0.574582\pi$
$360$	−4.27526	−	0.794593i	−0.225326	−	0.0418787i
$361$	−12.4949			−0.657626
$362$	5.17423	+	8.96204i	0.271952	+	0.471034i
$363$	−5.07321	−	11.0119i	−0.266275	−	0.577976i
$364$	2.44949	−	4.24264i	0.128388	−	0.222375i
$365$	−5.00000	+	8.66025i	−0.261712	+	0.453298i
$366$	4.74745	+	10.3048i	0.248153	+	0.538641i
$367$	6.89898	+	11.9494i	0.360124	+	0.623753i	0.987981	−	0.154576i	$-0.0494011\pi$
$367$	6.89898	+	11.9494i	0.360124	+	0.623753i	−0.627857	+	0.778329i	$0.716068\pi$
$368$	−1.00000			−0.0521286
$369$	28.8990	+	5.37113i	1.50442	+	0.279610i
$370$	−17.1010			−0.889040
$371$	−5.44949	−	9.43879i	−0.282923	−	0.490038i
$372$	−10.3485	−	0.953512i	−0.536543	−	0.0494373i
$373$	3.44949	−	5.97469i	0.178608	−	0.309358i	−0.762796	−	0.646639i	$-0.776174\pi$
$373$	3.44949	−	5.97469i	0.178608	−	0.309358i	0.941404	+	0.337281i	$0.109507\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$	11.4495	−	16.1920i	0.591249	−	0.836153i
$376$	−4.89898	−	8.48528i	−0.252646	−	0.437595i
$377$	−33.7980			−1.74068
$378$	−3.72474	+	3.62302i	−0.191580	+	0.186348i
$379$	22.4949			1.15549			0.577743	−	0.816219i	$-0.303934\pi$
$379$	22.4949			1.15549			0.577743	+	0.816219i	$0.303934\pi$
$380$	1.84847	+	3.20164i	0.0948245	+	0.164241i
$381$	−3.00000	+	4.24264i	−0.153695	+	0.217357i
$382$	−2.05051	+	3.55159i	−0.104913	+	0.181715i
$383$	1.44949	−	2.51059i	0.0740655	−	0.128285i	−0.826614	−	0.562769i	$-0.809736\pi$
$383$	1.44949	−	2.51059i	0.0740655	−	0.128285i	0.900679	+	0.434484i	$0.143069\pi$
$384$	−1.72474	−	0.158919i	−0.0880155	−	0.00810978i
$385$	−1.44949	−	2.51059i	−0.0738728	−	0.127952i
$386$	−17.8990			−0.911034
$387$	−13.4495	+	15.7313i	−0.683676	+	0.799668i
$388$	2.89898			0.147173
$389$	12.4495	+	21.5631i	0.631214	+	1.09330i	0.987304	+	0.158843i	$0.0507764\pi$
$389$	12.4495	+	21.5631i	0.631214	+	1.09330i	−0.356090	+	0.934452i	$0.615890\pi$
$390$	−5.14643	−	11.1708i	−0.260600	−	0.565658i
$391$	1.00000	−	1.73205i	0.0505722	−	0.0875936i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−6.19694	−	13.4511i	−0.312594	−	0.678517i
$394$	−8.34847	−	14.4600i	−0.420590	−	0.728483i
$395$	2.75255			0.138496
$396$	−2.00000	−	5.65685i	−0.100504	−	0.284268i
$397$	38.6969			1.94214			0.971072	−	0.238788i	$-0.0767500\pi$
$397$	38.6969			1.94214			0.971072	+	0.238788i	$0.0767500\pi$
$398$	1.44949	+	2.51059i	0.0726564	+	0.125844i
$399$	4.39898	+	0.405324i	0.220224	+	0.0202916i
$400$	1.44949	−	2.51059i	0.0724745	−	0.125529i
$401$	9.94949	−	17.2330i	0.496854	−	0.860576i	−0.503140	−	0.864205i	$-0.667822\pi$
$401$	9.94949	−	17.2330i	0.496854	−	0.860576i	0.999993	+	0.00362911i	$0.00115518\pi$
$402$	−12.8990	+	18.2419i	−0.643343	+	0.909824i
$403$	−14.6969	−	25.4558i	−0.732107	−	1.26805i
$404$	−17.2474			−0.858093
$405$	2.02781	+	12.8868i	0.100763	+	0.640352i
$406$	6.89898			0.342391
$407$	−11.7980	−	20.4347i	−0.584803	−	1.01291i
$408$	2.00000	−	2.82843i	0.0990148	−	0.140028i
$409$	6.89898	−	11.9494i	0.341133	−	0.590859i	−0.643511	−	0.765437i	$-0.722523\pi$
$409$	6.89898	−	11.9494i	0.341133	−	0.590859i	0.984643	+	0.174578i	$0.0558562\pi$
$410$	7.10102	−	12.2993i	0.350694	−	0.607421i
$411$	−13.4495	−	1.23924i	−0.663414	−	0.0611272i
$412$	−7.00000	−	12.1244i	−0.344865	−	0.597324i
$413$	2.00000			0.0984136
$414$	1.00000	+	2.82843i	0.0491473	+	0.139010i
$415$	−2.89898			−0.142305
$416$	−2.44949	−	4.24264i	−0.120096	−	0.208013i
$417$	3.29796	+	7.15855i	0.161502	+	0.350556i
$418$	−2.55051	+	4.41761i	−0.124750	+	0.216073i
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	0.241906	+	0.970300i	$0.422227\pi$
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	−0.961257	+	0.275653i	$0.911106\pi$
$420$	1.05051	+	2.28024i	0.0512597	+	0.111264i
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	−0.997662	−	0.0683385i	$-0.978230\pi$
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	0.439648	−	0.898170i	$-0.355103\pi$
$422$	12.8990			0.627912
$423$	−19.1010	+	22.3417i	−0.928723	+	1.08629i
$424$	−10.8990			−0.529301
$425$	2.89898	+	5.02118i	0.140621	+	0.243563i
$426$	−0.174235	−	0.0160540i	−0.00844169	−	0.000777821i
$427$	3.27526	−	5.67291i	0.158501	−	0.274531i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$	9.79796	−	13.8564i	0.473050	−	0.668994i
$430$	5.00000	+	8.66025i	0.241121	+	0.417635i
$431$	31.5959			1.52192			0.760961	−	0.648798i	$-0.224728\pi$
$431$	31.5959			1.52192			0.760961	+	0.648798i	$0.224728\pi$
$432$	1.27526	+	5.03723i	0.0613557	+	0.242354i
$433$	−7.79796			−0.374746			−0.187373	−	0.982289i	$-0.559997\pi$
$433$	−7.79796			−0.374746			−0.187373	+	0.982289i	$0.559997\pi$
$434$	3.00000	+	5.19615i	0.144005	+	0.249423i
$435$	10.0000	−	14.1421i	0.479463	−	0.678064i
$436$	−6.34847	+	10.9959i	−0.304037	+	0.526607i
$437$	1.27526	−	2.20881i	0.0610037	−	0.105662i
$438$	11.8990	+	1.09638i	0.568555	+	0.0523869i
$439$	−1.10102	−	1.90702i	−0.0525488	−	0.0910173i	0.838554	−	0.544818i	$-0.183401\pi$
$439$	−1.10102	−	1.90702i	−0.0525488	−	0.0910173i	−0.891103	+	0.453801i	$0.850068\pi$
$440$	−2.89898			−0.138203
$441$	2.94949	+	0.548188i	0.140452	+	0.0261042i
$442$	9.79796			0.466041
$443$	7.44949	+	12.9029i	0.353936	+	0.613035i	0.986935	−	0.161117i	$-0.0515098\pi$
$443$	7.44949	+	12.9029i	0.353936	+	0.613035i	−0.632999	+	0.774152i	$0.718176\pi$
$444$	8.55051	+	18.5597i	0.405789	+	0.880807i
$445$	−12.2474	+	21.2132i	−0.580585	+	1.00560i
$446$	5.55051	−	9.61377i	0.262824	−	0.455225i
$447$	−4.34847	−	9.43879i	−0.205676	−	0.446440i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	20.5959			0.971981			0.485991	−	0.873964i	$-0.338459\pi$
$449$	20.5959			0.971981			0.485991	+	0.873964i	$0.338459\pi$
$450$	−8.55051	−	1.58919i	−0.403075	−	0.0749150i
$451$	19.5959			0.922736
$452$	3.05051	+	5.28364i	0.143484	+	0.248521i
$453$	8.62372	+	0.794593i	0.405178	+	0.0373332i
$454$	2.72474	−	4.71940i	0.127879	−	0.221492i
$455$	−3.55051	+	6.14966i	−0.166450	+	0.288301i
$456$	2.55051	−	3.60697i	0.119439	−	0.168912i
$457$	8.74745	+	15.1510i	0.409188	+	0.708735i	0.994799	−	0.101857i	$-0.0324785\pi$
$457$	8.74745	+	15.1510i	0.409188	+	0.708735i	−0.585611	+	0.810593i	$0.699145\pi$
$458$	1.24745			0.0582895
$459$	−10.0000	−	2.82843i	−0.466760	−	0.132020i
$460$	1.44949			0.0675828
$461$	−2.82577	−	4.89437i	−0.131609	−	0.227954i	0.792688	−	0.609628i	$-0.208681\pi$
$461$	−2.82577	−	4.89437i	−0.131609	−	0.227954i	−0.924297	+	0.381674i	$0.875348\pi$
$462$	−2.00000	+	2.82843i	−0.0930484	+	0.131590i
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	−0.905777	−	0.423755i	$-0.860712\pi$
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	0.819871	+	0.572548i	$0.194045\pi$
$464$	3.44949	−	5.97469i	0.160139	−	0.277368i
$465$	15.0000	+	1.38211i	0.695608	+	0.0640936i
$466$	3.50000	+	6.06218i	0.162134	+	0.280825i
$467$	10.0000			0.462745			0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000			0.462745			0.231372	+	0.972865i	$0.425678\pi$
$468$	−9.55051	+	11.1708i	−0.441472	+	0.516372i
$469$	12.8990			0.595620
$470$	7.10102	+	12.2993i	0.327546	+	0.567326i
$471$	−6.05051	−	13.1332i	−0.278793	−	0.605148i
$472$	1.00000	−	1.73205i	0.0460287	−	0.0797241i
$473$	−6.89898	+	11.9494i	−0.317215	+	0.549433i
$474$	−1.37628	−	2.98735i	−0.0632144	−	0.137213i
$475$	3.69694	+	6.40329i	0.169627	+	0.293803i
$476$	−2.00000			−0.0916698
$477$	10.8990	+	30.8270i	0.499030	+	1.41147i
$478$	6.79796			0.310931
$479$	−4.79796	−	8.31031i	−0.219224	−	0.379708i	0.735347	−	0.677691i	$-0.237019\pi$
$479$	−4.79796	−	8.31031i	−0.219224	−	0.379708i	−0.954571	+	0.297983i	$0.903686\pi$
$480$	2.50000	+	0.230351i	0.114109	+	0.0105140i
$481$	−28.8990	+	50.0545i	−1.31768	+	2.28229i
$482$	−0.449490	+	0.778539i	−0.0204737	+	0.0354615i
$483$	1.00000	−	1.41421i	0.0455016	−	0.0643489i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−4.20204			−0.190805
$486$	12.9722	−	8.64420i	0.588431	−	0.392109i
$487$	−36.3939			−1.64916			−0.824582	−	0.565742i	$-0.808590\pi$
$487$	−36.3939			−1.64916			−0.824582	+	0.565742i	$0.808590\pi$
$488$	−3.27526	−	5.67291i	−0.148264	−	0.256800i
$489$	−19.7980	+	27.9985i	−0.895295	+	1.26614i
$490$	0.724745	−	1.25529i	0.0327406	−	0.0567084i
$491$	−7.89898	+	13.6814i	−0.356476	+	0.617434i	−0.987369	−	0.158435i	$-0.949355\pi$
$491$	−7.89898	+	13.6814i	−0.356476	+	0.617434i	0.630893	+	0.775869i	$0.282688\pi$
$492$	−16.8990	−	1.55708i	−0.761865	−	0.0701985i
$493$	6.89898	+	11.9494i	0.310714	+	0.538173i
$494$	12.4949			0.562172
$495$	2.89898	+	8.19955i	0.130299	+	0.368542i
$496$	6.00000			0.269408
$497$	0.0505103	+	0.0874863i	0.00226569	+	0.00392430i
$498$	1.44949	+	3.14626i	0.0649532	+	0.140987i
$499$	12.6969	−	21.9917i	0.568393	−	0.984486i	−0.428332	−	0.903621i	$-0.640899\pi$
$499$	12.6969	−	21.9917i	0.568393	−	0.984486i	0.996725	−	0.0808642i	$-0.0257680\pi$
$500$	−5.72474	+	9.91555i	−0.256018	+	0.443437i
$501$	−7.75255	−	16.8277i	−0.346358	−	0.751806i
$502$	−8.72474	−	15.1117i	−0.389404	−	0.674468i
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$	1.94949	−	2.28024i	0.0868372	−	0.101570i
$505$	25.0000			1.11249
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$	−18.9722	−	1.74810i	−0.842585	−	0.0776361i
$508$	1.50000	−	2.59808i	0.0665517	−	0.115271i
$509$	3.55051	−	6.14966i	0.157374	−	0.272579i	−0.776547	−	0.630059i	$-0.783031\pi$
$509$	3.55051	−	6.14966i	0.157374	−	0.272579i	0.933921	+	0.357480i	$0.116364\pi$
$510$	−2.89898	+	4.09978i	−0.128369	+	0.181541i
$511$	−3.44949	−	5.97469i	−0.152596	−	0.264305i
$512$	1.00000			0.0441942
$513$	−12.7526	−	3.60697i	−0.563039	−	0.159251i
$514$	8.20204			0.361777
$515$	10.1464	+	17.5741i	0.447105	+	0.774409i
$516$	6.89898	−	9.75663i	0.303711	−	0.429512i
$517$	−9.79796	+	16.9706i	−0.430914	+	0.746364i
$518$	5.89898	−	10.2173i	0.259186	−	0.448924i
$519$	5.34847	+	0.492810i	0.234772	+	0.0216320i
$520$	3.55051	+	6.14966i	0.155700	+	0.269681i
$521$	−9.30306			−0.407575			−0.203787	−	0.979015i	$-0.565325\pi$
$521$	−9.30306			−0.407575			−0.203787	+	0.979015i	$0.565325\pi$
$522$	−20.3485	−	3.78194i	−0.890628	−	0.165531i
$523$	−14.3485			−0.627415			−0.313707	−	0.949520i	$-0.601571\pi$
$523$	−14.3485			−0.627415			−0.313707	+	0.949520i	$0.601571\pi$
$524$	4.27526	+	7.40496i	0.186765	+	0.323487i
$525$	2.10102	+	4.56048i	0.0916961	+	0.199036i
$526$	−12.9495	+	22.4292i	−0.564625	+	0.977958i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	1.44949	+	3.14626i	0.0630809	+	0.136924i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	15.7980			0.686219
$531$	−5.89898	−	1.09638i	−0.255994	−	0.0475787i
$532$	−2.55051			−0.110579
$533$	−24.0000	−	41.5692i	−1.03956	−	1.80056i
$534$	29.1464	+	2.68556i	1.26129	+	0.116216i
$535$	−8.69694	+	15.0635i	−0.376001	+	0.651254i
$536$	6.44949	−	11.1708i	0.278576	−	0.482507i
$537$	20.6969	−	29.2699i	0.893139	−	1.26309i
$538$	9.17423	+	15.8902i	0.395529	+	0.685077i
$539$	2.00000			0.0861461
$540$	−1.84847	−	7.30142i	−0.0795455	−	0.314203i
$541$	−18.4949			−0.795158			−0.397579	−	0.917568i	$-0.630149\pi$
$541$	−18.4949			−0.795158			−0.397579	+	0.917568i	$0.630149\pi$
$542$	−3.55051	−	6.14966i	−0.152507	−	0.264151i
$543$	−10.3485	+	14.6349i	−0.444095	+	0.628046i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	9.20204	−	15.9384i	0.394172	−	0.682726i
$546$	8.44949	+	0.778539i	0.361605	+	0.0333184i
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	0.935725	−	0.352730i	$-0.114747\pi$
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	−0.773336	+	0.633996i	$0.781413\pi$
$548$	7.79796			0.333112
$549$	−12.7702	+	14.9367i	−0.545017	+	0.637484i
$550$	−5.79796			−0.247226
$551$	8.79796	+	15.2385i	0.374806	+	0.649182i
$552$	−0.724745	−	1.57313i	−0.0308472	−	0.0669570i
$553$	−0.949490	+	1.64456i	−0.0403764	+	0.0699340i
$554$	9.34847	−	16.1920i	0.397178	−	0.687933i
$555$	−12.3939	−	26.9022i	−0.526091	−	1.14193i
$556$	−2.27526	−	3.94086i	−0.0964923	−	0.167130i
$557$	−12.8990			−0.546547			−0.273274	−	0.961936i	$-0.588106\pi$
$557$	−12.8990			−0.546547			−0.273274	+	0.961936i	$0.588106\pi$
$558$	−6.00000	−	16.9706i	−0.254000	−	0.718421i
$559$	33.7980			1.42950
$560$	−0.724745	−	1.25529i	−0.0306261	−	0.0530459i
$561$	−6.89898	−	0.635674i	−0.291275	−	0.0268382i
$562$	9.50000	−	16.4545i	0.400733	−	0.694090i
$563$	19.9722	−	34.5929i	0.841728	−	1.45791i	−0.0467054	−	0.998909i	$-0.514872\pi$
$563$	19.9722	−	34.5929i	0.841728	−	1.45791i	0.888433	−	0.459006i	$-0.151794\pi$
$564$	9.79796	−	13.8564i	0.412568	−	0.583460i
$565$	−4.42168	−	7.65858i	−0.186022	−	0.322199i
$566$	−25.4495			−1.06972
$567$	−8.39898	−	3.23375i	−0.352724	−	0.135805i
$568$	0.101021			0.00423873
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$	−3.69694	+	5.22826i	−0.154848	+	0.218988i
$571$	−16.8990	+	29.2699i	−0.707200	+	1.22491i	0.258691	+	0.965960i	$0.416709\pi$
$571$	−16.8990	+	29.2699i	−0.707200	+	1.22491i	−0.965892	+	0.258947i	$0.916625\pi$
$572$	−4.89898	+	8.48528i	−0.204837	+	0.354787i
$573$	−7.07321	−	0.651729i	−0.295488	−	0.0272263i
$574$	4.89898	+	8.48528i	0.204479	+	0.354169i
$575$	2.89898			0.120896
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	−15.5959			−0.649267			−0.324633	−	0.945840i	$-0.605241\pi$
$577$	−15.5959			−0.649267			−0.324633	+	0.945840i	$0.605241\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−12.9722	−	28.1575i	−0.539106	−	1.17018i
$580$	−5.00000	+	8.66025i	−0.207614	+	0.359597i
$581$	1.00000	−	1.73205i	0.0414870	−	0.0718576i
$582$	2.10102	+	4.56048i	0.0870901	+	0.189038i
$583$	10.8990	+	18.8776i	0.451390	+	0.781830i
$584$	−6.89898			−0.285482
$585$	13.8434	−	16.1920i	0.572353	−	0.669458i
$586$	2.75255			0.113707
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	0.649924	−	0.760000i	$-0.274801\pi$
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	−0.983141	+	0.182850i	$0.941468\pi$
$588$	−1.72474	−	0.158919i	−0.0711273	−	0.00655369i
$589$	−7.65153	+	13.2528i	−0.315276	+	0.546074i
$590$	−1.44949	+	2.51059i	−0.0596745	+	0.103359i
$591$	16.6969	−	23.6130i	0.686820	−	0.971311i
$592$	−5.89898	−	10.2173i	−0.242447	−	0.419930i
$593$	14.6969			0.603531			0.301765	−	0.953382i	$-0.402424\pi$
$593$	14.6969			0.603531			0.301765	+	0.953382i	$0.402424\pi$
$594$	7.44949	−	7.24604i	0.305656	−	0.297309i
$595$	2.89898			0.118847
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	−2.89898	+	4.09978i	−0.118647	+	0.167793i
$598$	2.44949	−	4.24264i	0.100167	−	0.173494i
$599$	16.8990	−	29.2699i	0.690474	−	1.19594i	−0.281209	−	0.959646i	$-0.590736\pi$
$599$	16.8990	−	29.2699i	0.690474	−	1.19594i	0.971683	−	0.236289i	$-0.0759312\pi$
$600$	5.00000	+	0.460702i	0.204124	+	0.0188081i
$601$	−8.34847	−	14.4600i	−0.340541	−	0.589835i	0.643992	−	0.765032i	$-0.277277\pi$
$601$	−8.34847	−	14.4600i	−0.340541	−	0.589835i	−0.984533	+	0.175198i	$0.943944\pi$
$602$	−6.89898			−0.281181
$603$	−38.0454	−	7.07107i	−1.54933	−	0.287956i
$604$	−5.00000			−0.203447
$605$	−5.07321	−	8.78706i	−0.206255	−	0.357245i
$606$	−12.5000	−	27.1325i	−0.507778	−	1.10218i
$607$	−10.3485	+	17.9241i	−0.420031	+	0.727516i	−0.995942	−	0.0899969i	$-0.971314\pi$
$607$	−10.3485	+	17.9241i	−0.420031	+	0.727516i	0.575911	+	0.817513i	$0.304648\pi$
$608$	−1.27526	+	2.20881i	−0.0517184	+	0.0895789i
$609$	5.00000	+	10.8530i	0.202610	+	0.439786i
$610$	4.74745	+	8.22282i	0.192219	+	0.332932i
$611$	48.0000			1.94187
$612$	5.89898	+	1.09638i	0.238452	+	0.0443184i
$613$	−14.6969			−0.593604			−0.296802	−	0.954939i	$-0.595920\pi$
$613$	−14.6969			−0.593604			−0.296802	+	0.954939i	$0.595920\pi$
$614$	−12.6237	−	21.8649i	−0.509452	−	0.882397i
$615$	24.4949	+	2.25697i	0.987730	+	0.0910098i
$616$	1.00000	−	1.73205i	0.0402911	−	0.0697863i
$617$	7.69694	−	13.3315i	0.309867	−	0.536706i	−0.668466	−	0.743743i	$-0.733049\pi$
$617$	7.69694	−	13.3315i	0.309867	−	0.536706i	0.978333	+	0.207037i	$0.0663821\pi$
$618$	14.0000	−	19.7990i	0.563163	−	0.796432i
$619$	−15.0732	−	26.1076i	−0.605844	−	1.04935i	−0.991918	−	0.126884i	$-0.959502\pi$
$619$	−15.0732	−	26.1076i	−0.605844	−	1.04935i	0.386074	−	0.922468i	$-0.373831\pi$
$620$	−8.69694			−0.349277
$621$	−3.72474	+	3.62302i	−0.149469	+	0.145387i
$622$	30.6969			1.23084
$623$	−8.44949	−	14.6349i	−0.338522	−	0.586337i
$624$	4.89898	−	6.92820i	0.196116	−	0.277350i
$625$	1.05051	−	1.81954i	0.0420204	−	0.0727815i
$626$	2.34847	−	4.06767i	0.0938637	−	0.162577i
$627$	−8.79796	−	0.810647i	−0.351357	−	0.0323741i
$628$	4.17423	+	7.22999i	0.166570	+	0.288508i
$629$	23.5959			0.940831
$630$	−2.82577	+	3.30518i	−0.112581	+	0.131682i
$631$	27.8990			1.11064			0.555320	−	0.831636i	$-0.312596\pi$
$631$	27.8990			1.11064			0.555320	+	0.831636i	$0.312596\pi$
$632$	0.949490	+	1.64456i	0.0377687	+	0.0654173i
$633$	9.34847	+	20.2918i	0.371568	+	0.806527i
$634$	−10.3485	+	17.9241i	−0.410990	+	0.711856i
$635$	−2.17423	+	3.76588i	−0.0862819	+	0.149445i
$636$	−7.89898	−	17.1455i	−0.313215	−	0.679865i
$637$	−2.44949	−	4.24264i	−0.0970523	−	0.168100i
$638$	−13.7980			−0.546266
$639$	−0.101021	−	0.285729i	−0.00399631	−	0.0113033i
$640$	−1.44949			−0.0572961
$641$	3.74745	+	6.49077i	0.148015	+	0.256370i	0.930494	−	0.366308i	$-0.119378\pi$
$641$	3.74745	+	6.49077i	0.148015	+	0.256370i	−0.782479	+	0.622678i	$0.786045\pi$
$642$	20.6969	+	1.90702i	0.816843	+	0.0752642i
$643$	19.6969	−	34.1161i	0.776771	−	1.34541i	−0.157022	−	0.987595i	$-0.550189\pi$
$643$	19.6969	−	34.1161i	0.776771	−	1.34541i	0.933793	−	0.357812i	$-0.116477\pi$
$644$	−0.500000	+	0.866025i	−0.0197028	+	0.0341262i
$645$	−10.0000	+	14.1421i	−0.393750	+	0.556846i
$646$	−2.55051	−	4.41761i	−0.100348	−	0.173809i
$647$	−50.6969			−1.99310			−0.996551	−	0.0829807i	$-0.973556\pi$
$647$	−50.6969			−1.99310			−0.996551	+	0.0829807i	$0.973556\pi$
$648$	−7.00000	+	5.65685i	−0.274986	+	0.222222i
$649$	−4.00000			−0.157014
$650$	7.10102	+	12.2993i	0.278525	+	0.482419i
$651$	−6.00000	+	8.48528i	−0.235159	+	0.332564i
$652$	9.89898	−	17.1455i	0.387674	−	0.671471i
$653$	−4.89898	+	8.48528i	−0.191712	+	0.332055i	−0.945818	−	0.324698i	$-0.894737\pi$
$653$	−4.89898	+	8.48528i	−0.191712	+	0.332055i	0.754106	+	0.656753i	$0.228071\pi$
$654$	−21.8990	−	2.01778i	−0.856318	−	0.0789014i
$655$	−6.19694	−	10.7334i	−0.242134	−	0.419389i
$656$	9.79796			0.382546
$657$	6.89898	+	19.5133i	0.269155	+	0.761285i
$658$	−9.79796			−0.381964
$659$	12.3485	+	21.3882i	0.481028	+	0.833165i	0.999763	−	0.0217701i	$-0.00693018\pi$
$659$	12.3485	+	21.3882i	0.481028	+	0.833165i	−0.518735	+	0.854935i	$0.673597\pi$
$660$	−2.10102	−	4.56048i	−0.0817821	−	0.177516i
$661$	−2.27526	+	3.94086i	−0.0884972	+	0.153282i	−0.906876	−	0.421397i	$-0.861540\pi$
$661$	−2.27526	+	3.94086i	−0.0884972	+	0.153282i	0.818379	+	0.574679i	$0.194873\pi$
$662$	−2.34847	+	4.06767i	−0.0912758	+	0.158094i
$663$	7.10102	+	15.4135i	0.275781	+	0.598610i
$664$	−1.00000	−	1.73205i	−0.0388075	−	0.0672166i
$665$	3.69694			0.143361
$666$	−23.0000	+	26.9022i	−0.891232	+	1.04244i
$667$	6.89898			0.267130
$668$	5.34847	+	9.26382i	0.206938	+	0.358428i
$669$	19.1464	+	1.76416i	0.740244	+	0.0682063i
$670$	−9.34847	+	16.1920i	−0.361163	+	0.625552i
$671$	−6.55051	+	11.3458i	−0.252880	+	0.438000i
$672$	−1.00000	+	1.41421i	−0.0385758	+	0.0545545i
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	0.936894	−	0.349612i	$-0.113687\pi$
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	−0.771220	+	0.636568i	$0.780353\pi$
$674$	−23.3939			−0.901098
$675$	−3.69694	−	14.6028i	−0.142295	−	0.562063i
$676$	11.0000			0.423077
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	0.689557	−	0.724232i	$-0.257805\pi$
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	−0.971981	+	0.235058i	$0.924472\pi$
$678$	−6.10102	+	8.62815i	−0.234308	+	0.331362i
$679$	1.44949	−	2.51059i	0.0556263	−	0.0963476i
$680$	1.44949	−	2.51059i	0.0555854	−	0.0962767i
$681$	9.39898	+	0.866025i	0.360170	+	0.0331862i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	51.7980			1.98199			0.990997	−	0.133885i	$-0.0427452\pi$
$683$	51.7980			1.98199			0.990997	+	0.133885i	$0.0427452\pi$
$684$	7.52270	+	1.39816i	0.287638	+	0.0534600i
$685$	−11.3031			−0.431868
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	0.904082	+	1.96240i	0.0344929	+	0.0748703i
$688$	−3.44949	+	5.97469i	−0.131511	+	0.227783i
$689$	26.6969	−	46.2405i	1.01707	−	1.76162i
$690$	1.05051	+	2.28024i	0.0399922	+	0.0868072i
$691$	−25.5227	−	44.2066i	−0.970929	−	1.68170i	−0.692762	−	0.721167i	$-0.743606\pi$
$691$	−25.5227	−	44.2066i	−0.970929	−	1.68170i	−0.278168	−	0.960533i	$-0.589727\pi$
$692$	−3.10102			−0.117883
$693$	−5.89898	−	1.09638i	−0.224084	−	0.0416479i
$694$	19.5959			0.743851
$695$	3.29796	+	5.71223i	0.125099	+	0.216677i
$696$	11.8990	+	1.09638i	0.451030	+	0.0415580i
$697$	−9.79796	+	16.9706i	−0.371124	+	0.642806i
$698$	−5.55051	+	9.61377i	−0.210090	+	0.363886i
$699$	−7.00000	+	9.89949i	−0.264764	+	0.374433i
$700$	−1.44949	−	2.51059i	−0.0547856	−	0.0948914i
$701$	−7.39388			−0.279263			−0.139631	−	0.990204i	$-0.544592\pi$
$701$	−7.39388			−0.279263			−0.139631	+	0.990204i	$0.544592\pi$
$702$	−24.4949	−	6.92820i	−0.924500	−	0.261488i
$703$	30.0908			1.13490
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	−14.2020	+	20.0847i	−0.534880	+	0.756434i
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$	−8.62372	+	14.9367i	−0.324329	+	0.561754i
$708$	3.44949	+	0.317837i	0.129640	+	0.0119451i
$709$	−13.7980	−	23.8988i	−0.518193	−	0.897537i	−0.999777	−	0.0211367i	$-0.993271\pi$
$709$	−13.7980	−	23.8988i	−0.518193	−	0.897537i	0.481583	−	0.876400i	$-0.340062\pi$
$710$	−0.146428			−0.00549535
$711$	3.70204	−	4.33013i	0.138837	−	0.162392i
$712$	−16.8990			−0.633316
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$	−1.44949	−	3.14626i	−0.0542458	−	0.117746i
$715$	7.10102	−	12.2993i	0.265563	−	0.459969i
$716$	−10.3485	+	17.9241i	−0.386740	+	0.669854i
$717$	4.92679	+	10.6941i	0.183994	+	0.399378i
$718$	4.39898	+	7.61926i	0.164168	+	0.284348i
$719$	9.79796			0.365402			0.182701	−	0.983169i	$-0.441516\pi$
$719$	9.79796			0.365402			0.182701	+	0.983169i	$0.441516\pi$
$720$	1.44949	+	4.09978i	0.0540193	+	0.152790i
$721$	−14.0000			−0.521387
$722$	6.24745	+	10.8209i	0.232506	+	0.402712i
$723$	−1.55051	−	0.142865i	−0.0576641	−	0.00531319i
$724$	5.17423	−	8.96204i	0.192299	−	0.333071i
$725$	−10.0000	+	17.3205i	−0.371391	+	0.643268i
$726$	−7.00000	+	9.89949i	−0.259794	+	0.367405i
$727$	4.24745	+	7.35680i	0.157529	+	0.272848i	0.933977	−	0.357333i	$-0.116314\pi$
$727$	4.24745	+	7.35680i	0.157529	+	0.272848i	−0.776448	+	0.630181i	$0.782981\pi$
$728$	−4.89898			−0.181568
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	10.0000			0.370117
$731$	−6.89898	−	11.9494i	−0.255168	−	0.441964i
$732$	6.55051	−	9.26382i	0.242114	−	0.342401i
$733$	8.72474	−	15.1117i	0.322256	−	0.558163i	−0.658697	−	0.752408i	$-0.728892\pi$
$733$	8.72474	−	15.1117i	0.322256	−	0.558163i	0.980953	+	0.194245i	$0.0622255\pi$
$734$	6.89898	−	11.9494i	0.254646	−	0.441060i
$735$	2.50000	+	0.230351i	0.0922139	+	0.00849662i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−25.7980			−0.950280
$738$	−9.79796	−	27.7128i	−0.360668	−	1.02012i
$739$	13.5959			0.500134			0.250067	−	0.968229i	$-0.419547\pi$
$739$	13.5959			0.500134			0.250067	+	0.968229i	$0.419547\pi$
$740$	8.55051	+	14.8099i	0.314323	+	0.544423i
$741$	9.05561	+	19.6561i	0.332666	+	0.722086i
$742$	−5.44949	+	9.43879i	−0.200057	+	0.346509i
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$	4.34847	+	9.43879i	0.159423	+	0.346043i
$745$	−4.34847	−	7.53177i	−0.159316	−	0.275943i
$746$	−6.89898			−0.252590
$747$	−3.89898	+	4.56048i	−0.142656	+	0.166859i
$748$	4.00000			0.146254
$749$	−6.00000	−	10.3923i	−0.219235	−	0.379727i
$750$	−19.7474	−	1.81954i	−0.721075	−	0.0664401i
$751$	−0.702041	+	1.21597i	−0.0256178	+	0.0443714i	−0.878550	−	0.477650i	$-0.841489\pi$
$751$	−0.702041	+	1.21597i	−0.0256178	+	0.0443714i	0.852932	+	0.522022i	$0.174822\pi$
$752$	−4.89898	+	8.48528i	−0.178647	+	0.309426i
$753$	17.4495	−	24.6773i	0.635895	−	0.899291i
$754$	16.8990	+	29.2699i	0.615425	+	1.06595i
$755$	7.24745			0.263762
$756$	5.00000	+	1.41421i	0.181848	+	0.0514344i
$757$	−35.3939			−1.28641			−0.643206	−	0.765693i	$-0.722396\pi$
$757$	−35.3939			−1.28641			−0.643206	+	0.765693i	$0.722396\pi$
$758$	−11.2474	−	19.4812i	−0.408526	−	0.707587i
$759$	−2.00000	+	2.82843i	−0.0725954	+	0.102665i
$760$	1.84847	−	3.20164i	0.0670510	−	0.116136i
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	−0.883581	−	0.468278i	$-0.844875\pi$
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	0.847331	+	0.531065i	$0.178208\pi$
$762$	5.17423	+	0.476756i	0.187443	+	0.0172710i
$763$	6.34847	+	10.9959i	0.229830	+	0.398077i
$764$	4.10102			0.148370
$765$	−8.55051	−	1.58919i	−0.309144	−	0.0574571i
$766$	−2.89898			−0.104744
$767$	4.89898	+	8.48528i	0.176892	+	0.306386i
$768$	0.724745	+	1.57313i	0.0261520	+	0.0567655i
$769$	17.0454	−	29.5235i	0.614673	−	1.06465i	−0.375769	−	0.926714i	$-0.622621\pi$
$769$	17.0454	−	29.5235i	0.614673	−	1.06465i	0.990442	−	0.137932i	$-0.0440454\pi$
$770$	−1.44949	+	2.51059i	−0.0522360	+	0.0904754i
$771$	5.94439	+	12.9029i	0.214082	+	0.464686i
$772$	8.94949	+	15.5010i	0.322099	+	0.557892i
$773$	33.9444			1.22089			0.610447	−	0.792057i	$-0.290990\pi$
$773$	33.9444			1.22089			0.610447	+	0.792057i	$0.290990\pi$
$774$	20.3485	+	3.78194i	0.731411	+	0.135939i
$775$	−17.3939			−0.624807
$776$	−1.44949	−	2.51059i	−0.0520336	−	0.0901249i
$777$	20.3485	+	1.87492i	0.729997	+	0.0672622i
$778$	12.4495	−	21.5631i	0.446336	−	0.773076i
$779$	−12.4949	+	21.6418i	−0.447676	+	0.775398i
$780$	−7.10102	+	10.0424i	−0.254257	+	0.359574i
$781$	−0.101021	−	0.174973i	−0.00361480	−	0.00626101i
$782$	−2.00000			−0.0715199
$783$	−8.79796	−	34.7518i	−0.314413	−	1.24193i
$784$	1.00000			0.0357143
$785$	−6.05051	−	10.4798i	−0.215952	−	0.374040i
$786$	−8.55051	+	12.0922i	−0.304987	+	0.431316i
$787$	5.69694	−	9.86739i	0.203074	−	0.351734i	−0.746443	−	0.665449i	$-0.768240\pi$
$787$	5.69694	−	9.86739i	0.203074	−	0.351734i	0.949517	+	0.313715i	$0.101573\pi$
$788$	−8.34847	+	14.4600i	−0.297402	+	0.515115i
$789$	−44.6691	−	4.11583i	−1.59026	−	0.146527i
$790$	−1.37628	−	2.38378i	−0.0489657	−	0.0848111i
$791$	6.10102			0.216927
$792$	−3.89898	+	4.56048i	−0.138544	+	0.162050i
$793$	32.0908			1.13958
$794$	−19.3485	−	33.5125i	−0.686651	−	1.18932i
$795$	11.4495	+	24.8523i	0.406072	+	0.881419i
$796$	1.44949	−	2.51059i	0.0513758	−	0.0889855i
$797$	8.97219	−	15.5403i	0.317811	−	0.550465i	−0.662220	−	0.749310i	$-0.730385\pi$
$797$	8.97219	−	15.5403i	0.317811	−	0.550465i	0.980031	+	0.198844i	$0.0637188\pi$
$798$	−1.84847	−	4.01229i	−0.0654351	−	0.142034i
$799$	−9.79796	−	16.9706i	−0.346627	−	0.600375i
$800$	−2.89898			−0.102494
$801$	16.8990	+	47.7975i	0.597096	+	1.68884i
$802$	−19.8990			−0.702657
$803$	6.89898	+	11.9494i	0.243460	+	0.421685i
$804$	22.2474	+	2.04989i	0.784607	+	0.0722940i
$805$	0.724745	−	1.25529i	0.0255439	−	0.0442433i
$806$	−14.6969	+	25.4558i	−0.517678	+	0.896644i
$807$	−18.3485	+	25.9487i	−0.645897	+	0.913436i
$808$	8.62372	+	14.9367i	0.303382	+	0.525472i
$809$	−16.2020			−0.569633			−0.284817	−	0.958582i	$-0.591933\pi$
$809$	−16.2020			−0.569633			−0.284817	+	0.958582i	$0.591933\pi$
$810$	10.1464	−	8.19955i	0.356509	−	0.288103i
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−3.44949	−	5.97469i	−0.121053	−	0.209671i
$813$	7.10102	−	10.0424i	0.249044	−	0.352201i
$814$	−11.7980	+	20.4347i	−0.413518	+	0.716235i
$815$	−14.3485	+	24.8523i	−0.502605	+	0.870537i
$816$	−3.44949	−	0.317837i	−0.120756	−	0.0111265i
$817$	−8.79796	−	15.2385i	−0.307802	−	0.533128i
$818$	−13.7980			−0.482434
$819$	4.89898	+	13.8564i	0.171184	+	0.484182i
$820$	−14.2020			−0.495957
$821$	−0.202041	−	0.349945i	−0.00705128	−	0.0122132i	0.862478	−	0.506094i	$-0.168911\pi$
$821$	−0.202041	−	0.349945i	−0.00705128	−	0.0122132i	−0.869530	+	0.493881i	$0.835578\pi$
$822$	5.65153	+	12.2672i	0.197120	+	0.427868i
$823$	6.69694	−	11.5994i	0.233441	−	0.404331i	−0.725378	−	0.688351i	$-0.758335\pi$
$823$	6.69694	−	11.5994i	0.233441	−	0.404331i	0.958818	+	0.284020i	$0.0916682\pi$
$824$	−7.00000	+	12.1244i	−0.243857	+	0.422372i
$825$	−4.20204	−	9.12096i	−0.146296	−	0.317551i
$826$	−1.00000	−	1.73205i	−0.0347945	−	0.0602658i
$827$	−36.4949			−1.26905			−0.634526	−	0.772902i	$-0.718805\pi$
$827$	−36.4949			−1.26905			−0.634526	+	0.772902i	$0.718805\pi$
$828$	1.94949	−	2.28024i	0.0677495	−	0.0792438i
$829$	1.30306			0.0452572			0.0226286	−	0.999744i	$-0.492796\pi$
$829$	1.30306			0.0452572			0.0226286	+	0.999744i	$0.492796\pi$
$830$	1.44949	+	2.51059i	0.0503125	+	0.0871438i
$831$	32.2474	+	2.97129i	1.11865	+	0.103073i
$832$	−2.44949	+	4.24264i	−0.0849208	+	0.147087i
$833$	−1.00000	+	1.73205i	−0.0346479	+	0.0600120i
$834$	4.55051	−	6.43539i	0.157571	−	0.222839i
$835$	−7.75255	−	13.4278i	−0.268288	−	0.464689i
$836$	5.10102			0.176422
$837$	22.3485	−	21.7381i	0.772476	−	0.751379i
$838$	29.4495			1.01732
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	0.991907	+	0.126968i	$0.0405245\pi$
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	−0.385996	+	0.922500i	$0.626142\pi$
$840$	1.44949	−	2.04989i	0.0500121	−	0.0707279i
$841$	−9.29796	+	16.1045i	−0.320619	+	0.555329i
$842$	−11.4495	+	19.8311i	−0.394575	+	0.683425i
$843$	32.7702	+	3.01945i	1.12866	+	0.103996i
$844$	−6.44949	−	11.1708i	−0.222001	−	0.384516i
$845$	−15.9444			−0.548504
$846$	28.8990	+	5.37113i	0.993567	+	0.184663i
$847$	7.00000			0.240523
$848$	5.44949	+	9.43879i	0.187136	+	0.324129i
$849$	−18.4444	−	40.0354i	−0.633010	−	1.37401i
$850$	2.89898	−	5.02118i	0.0994342	−	0.172225i
$851$	5.89898	−	10.2173i	0.202214	−	0.350246i
$852$	0.0732141	+	0.158919i	0.00250827	+	0.00544446i
$853$	−12.4217	−	21.5150i	−0.425310	−	0.736659i	0.571139	−	0.820853i	$-0.306502\pi$
$853$	−12.4217	−	21.5150i	−0.425310	−	0.736659i	−0.996449	+	0.0841942i	$0.973168\pi$
$854$	−6.55051			−0.224154
$855$	−10.9041	−	2.02662i	−0.372912	−	0.0693089i
$856$	−12.0000			−0.410152
$857$	17.4495	+	30.2234i	0.596063	+	1.03241i	0.993396	+	0.114737i	$0.0366026\pi$
$857$	17.4495	+	30.2234i	0.596063	+	1.03241i	−0.397333	+	0.917675i	$0.630064\pi$
$858$	−16.8990	−	1.55708i	−0.576922	−	0.0531578i
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	−0.768031	−	0.640412i	$-0.778763\pi$
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	0.938629	+	0.344928i	$0.112097\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$	−9.79796	+	13.8564i	−0.333914	+	0.472225i
$862$	−15.7980	−	27.3629i	−0.538081	−	0.931983i
$863$	11.8990			0.405046			0.202523	−	0.979278i	$-0.435086\pi$
$863$	11.8990			0.405046			0.202523	+	0.979278i	$0.435086\pi$
$864$	3.72474	−	3.62302i	0.126718	−	0.123258i
$865$	4.49490			0.152831
$866$	3.89898	+	6.75323i	0.132493	+	0.229484i
$867$	−13.0000	+	18.3848i	−0.441503	+	0.624380i
$868$	3.00000	−	5.19615i	0.101827	−	0.176369i
$869$	1.89898	−	3.28913i	0.0644185	−	0.111576i
$870$	−17.2474	−	1.58919i	−0.584743	−	0.0538785i
$871$	31.5959	+	54.7257i	1.07059	+	1.85431i
$872$	12.6969			0.429973
$873$	−5.65153	+	6.61037i	−0.191275	+	0.223727i
$874$	−2.55051			−0.0862723
$875$	5.72474	+	9.91555i	0.193532	+	0.335207i
$876$	−5.00000	−	10.8530i	−0.168934	−	0.366689i
$877$	−11.2474	+	19.4812i	−0.379799	+	0.657832i	−0.991033	−	0.133619i	$-0.957340\pi$
$877$	−11.2474	+	19.4812i	−0.379799	+	0.657832i	0.611233	+	0.791450i	$0.290674\pi$
$878$	−1.10102	+	1.90702i	−0.0371576	+	0.0643589i
$879$	1.99490	+	4.33013i	0.0672862	+	0.146052i
$880$	1.44949	+	2.51059i	0.0488623	+	0.0846320i
$881$	19.5959			0.660203			0.330102	−	0.943945i	$-0.392917\pi$
$881$	19.5959			0.660203			0.330102	+	0.943945i	$0.392917\pi$
$882$	−1.00000	−	2.82843i	−0.0336718	−	0.0952381i
$883$	−19.7980			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$883$	−19.7980			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$884$	−4.89898	−	8.48528i	−0.164771	−	0.285391i
$885$	−5.00000	−	0.460702i	−0.168073	−	0.0154863i
$886$	7.44949	−	12.9029i	0.250271	−	0.433481i
$887$	7.10102	−	12.2993i	0.238429	−	0.412971i	−0.721835	−	0.692065i	$-0.756701\pi$
$887$	7.10102	−	12.2993i	0.238429	−	0.412971i	0.960264	+	0.279094i	$0.0900343\pi$
$888$	11.7980	−	16.6848i	0.395914	−	0.559906i
$889$	−1.50000	−	2.59808i	−0.0503084	−	0.0871367i
$890$	24.4949			0.821071
$891$	16.7980	+	6.46750i	0.562753	+	0.216669i
$892$	−11.1010			−0.371690
$893$	−12.4949	−	21.6418i	−0.418126	−	0.724215i
$894$	−6.00000	+	8.48528i	−0.200670	+	0.283790i
$895$	15.0000	−	25.9808i	0.501395	−	0.868441i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	8.44949	+	0.778539i	0.282120	+	0.0259947i
$898$	−10.2980	−	17.8366i	−0.343647	−	0.595215i
$899$	−41.3939			−1.38056
$900$	2.89898	+	8.19955i	0.0966326	+	0.273318i
$901$	−21.7980			−0.726195
$902$	−9.79796	−	16.9706i	−0.326236	−	0.565058i
$903$	−5.00000	−	10.8530i	−0.166390	−	0.361165i
$904$	3.05051	−	5.28364i	0.101458	−	0.175731i
$905$	−7.50000	+	12.9904i	−0.249308	+	0.431815i
$906$	−3.62372	−	7.86566i	−0.120390	−	0.261319i
$907$	−1.34847	−	2.33562i	−0.0447752	−	0.0775529i	0.842769	−	0.538275i	$-0.180924\pi$
$907$	−1.34847	−	2.33562i	−0.0447752	−	0.0775529i	−0.887544	+	0.460722i	$0.847590\pi$
$908$	−5.44949			−0.180848
$909$	33.6237	−	39.3283i	1.11523	−	1.30444i
$910$	7.10102			0.235397
$911$	−25.9949	−	45.0245i	−0.861249	−	1.49173i	−0.870724	−	0.491773i	$-0.836349\pi$
$911$	−25.9949	−	45.0245i	−0.861249	−	1.49173i	0.00947432	−	0.999955i	$-0.496984\pi$
$912$	−4.39898	−	0.405324i	−0.145665	−	0.0134216i
$913$	−2.00000	+	3.46410i	−0.0661903	+	0.114645i
$914$	8.74745	−	15.1510i	0.289340	−	0.501151i
$915$	−9.49490	+	13.4278i	−0.313892	+	0.443910i
$916$	−0.623724	−	1.08032i	−0.0206084	−	0.0356949i
$917$	8.55051			0.282363
$918$	2.55051	+	10.0745i	0.0841794	+	0.332507i
$919$	−25.6969			−0.847664			−0.423832	−	0.905741i	$-0.639315\pi$
$919$	−25.6969			−0.847664			−0.423832	+	0.905741i	$0.639315\pi$
$920$	−0.724745	−	1.25529i	−0.0238941	−	0.0413858i
$921$	25.2474	−	35.7053i	0.831932	−	1.17653i
$922$	−2.82577	+	4.89437i	−0.0930616	+	0.161187i
$923$	−0.247449	+	0.428594i	−0.00814487	+	0.0141073i
$924$	3.44949	+	0.317837i	0.113480	+	0.0104561i
$925$	17.1010	+	29.6198i	0.562278	+	0.973894i
$926$	3.69694			0.121489
$927$	41.2929	+	7.67463i	1.35624	+	0.252068i
$928$	−6.89898			−0.226470
$929$	−17.1464	−	29.6985i	−0.562556	−	0.974376i	−0.997272	−	0.0738083i	$-0.976485\pi$
$929$	−17.1464	−	29.6985i	−0.562556	−	0.974376i	0.434716	−	0.900567i	$-0.356849\pi$
$930$	−6.30306	−	13.6814i	−0.206686	−	0.448632i
$931$	−1.27526	+	2.20881i	−0.0417948	+	0.0723907i
$932$	3.50000	−	6.06218i	0.114646	−	0.198573i
$933$	22.2474	+	48.2903i	0.728349	+	1.58095i
$934$	−5.00000	−	8.66025i	−0.163605	−	0.283372i
$935$	−5.79796			−0.189614
$936$	14.4495	+	2.68556i	0.472296	+	0.0877804i
$937$	45.5959			1.48955			0.744777	−	0.667314i	$-0.232556\pi$
$937$	45.5959			1.48955			0.744777	+	0.667314i	$0.232556\pi$
$938$	−6.44949	−	11.1708i	−0.210583	−	0.364741i
$939$	8.10102	+	0.746431i	0.264367	+	0.0243589i
$940$	7.10102	−	12.2993i	0.231610	−	0.401160i
$941$	0.724745	−	1.25529i	0.0236260	−	0.0409214i	−0.853971	−	0.520321i	$-0.825812\pi$
$941$	0.724745	−	1.25529i	0.0236260	−	0.0409214i	0.877597	+	0.479400i	$0.159146\pi$
$942$	−8.34847	+	11.8065i	−0.272008	+	0.384677i
$943$	4.89898	+	8.48528i	0.159533	+	0.276319i
$944$	−2.00000			−0.0650945
$945$	−7.24745	−	2.04989i	−0.235760	−	0.0666829i
$946$	13.7980			0.448610
$947$	−26.2474	−	45.4619i	−0.852927	−	1.47731i	−0.878554	−	0.477642i	$-0.841492\pi$
$947$	−26.2474	−	45.4619i	−0.852927	−	1.47731i	0.0256270	−	0.999672i	$-0.491842\pi$
$948$	−1.89898	+	2.68556i	−0.0616760	+	0.0872230i
$949$	16.8990	−	29.2699i	0.548564	−	0.950141i
$950$	3.69694	−	6.40329i	0.119945	−	0.207750i
$951$	−35.6969	−	3.28913i	−1.15755	−	0.106657i
$952$	1.00000	+	1.73205i	0.0324102	+	0.0561361i
$953$	−3.39388			−0.109938			−0.0549692	−	0.998488i	$-0.517506\pi$
$953$	−3.39388			−0.109938			−0.0549692	+	0.998488i	$0.517506\pi$
$954$	21.2474	−	24.8523i	0.687912	−	0.804622i
$955$	−5.94439			−0.192356
$956$	−3.39898	−	5.88721i	−0.109931	−	0.190406i
$957$	−10.0000	−	21.7060i	−0.323254	−	0.701656i
$958$	−4.79796	+	8.31031i	−0.155015	+	0.268494i
$959$	3.89898	−	6.75323i	0.125905	−	0.218073i
$960$	−1.05051	−	2.28024i	−0.0339051	−	0.0735944i
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	57.7980			1.86348
$963$	12.0000	+	33.9411i	0.386695	+	1.09374i
$964$	0.898979			0.0289542
$965$	−12.9722	−	22.4685i	−0.417590	−	0.723287i
$966$	−1.72474	−	0.158919i	−0.0554928	−	0.00511312i
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	−0.993162	−	0.116746i	$-0.962754\pi$
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	0.597686	+	0.801730i	$0.296087\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	5.10102	−	7.21393i	0.163868	−	0.231745i
$970$	2.10102	+	3.63907i	0.0674597	+	0.116844i
$971$	−0.0556128			−0.00178470			−0.000892350	−	1.00000i	$-0.500284\pi$
$971$	−0.0556128			−0.00178470			−0.000892350		1.00000i	$0.500284\pi$
$972$	−13.9722	−	6.91215i	−0.448158	−	0.221707i
$973$	−4.55051			−0.145883
$974$	18.1969	+	31.5180i	0.583068	+	1.00990i
$975$	−14.2020	+	20.0847i	−0.454829	+	0.643226i
$976$	−3.27526	+	5.67291i	−0.104838	+	0.181585i
$977$	18.7980	−	32.5590i	0.601400	−	1.04166i	−0.391209	−	0.920302i	$-0.627943\pi$
$977$	18.7980	−	32.5590i	0.601400	−	1.04166i	0.992609	−	0.121354i	$-0.0387235\pi$
$978$	34.1464	+	3.14626i	1.09188	+	0.100606i
$979$	16.8990	+	29.2699i	0.540094	+	0.935470i
$980$	−1.44949			−0.0463023
$981$	−12.6969	−	35.9124i	−0.405382	−	1.14659i
$982$	15.7980			0.504133
$983$	16.5959	+	28.7450i	0.529328	+	0.916822i	0.999415	+	0.0342024i	$0.0108891\pi$
$983$	16.5959	+	28.7450i	0.529328	+	0.916822i	−0.470087	+	0.882620i	$0.655778\pi$
$984$	7.10102	+	15.4135i	0.226372	+	0.491364i
$985$	12.1010	−	20.9596i	0.385571	−	0.667828i
$986$	6.89898	−	11.9494i	0.219708	−	0.380546i
$987$	−7.10102	−	15.4135i	−0.226028	−	0.490617i
$988$	−6.24745	−	10.8209i	−0.198758	−	0.344259i
$989$	−6.89898			−0.219375
$990$	5.65153	−	6.61037i	0.179617	−	0.210091i
$991$	−1.79796			−0.0571140			−0.0285570	−	0.999592i	$-0.509091\pi$
$991$	−1.79796			−0.0571140			−0.0285570	+	0.999592i	$0.509091\pi$
$992$	−3.00000	−	5.19615i	−0.0952501	−	0.164978i
$993$	−8.10102	−	0.746431i	−0.257078	−	0.0236873i
$994$	0.0505103	−	0.0874863i	0.00160209	−	0.00277490i
$995$	−2.10102	+	3.63907i	−0.0666068	+	0.115366i
$996$	2.00000	−	2.82843i	0.0633724	−	0.0896221i
$997$	−26.0732	−	45.1601i	−0.825747	−	1.43024i	−0.901347	−	0.433097i	$-0.857421\pi$
$997$	−26.0732	−	45.1601i	−0.825747	−	1.43024i	0.0756001	−	0.997138i	$-0.475913\pi$
$998$	−25.3939			−0.803829
$999$	−58.9898	−	16.6848i	−1.86635	−	0.527885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.f.c.85.1	yes	4
3.2	odd	2		378.2.f.d.253.1		4
4.3	odd	2		1008.2.r.e.337.2		4
7.2	even	3		882.2.h.k.67.2		4
7.3	odd	6		882.2.e.n.373.2		4
7.4	even	3		882.2.e.m.373.1		4
7.5	odd	6		882.2.h.l.67.1		4
7.6	odd	2		882.2.f.j.589.2		4
9.2	odd	6		378.2.f.d.127.1		4
9.4	even	3		1134.2.a.p.1.1		2
9.5	odd	6		1134.2.a.i.1.2		2
9.7	even	3	inner	126.2.f.c.43.2	✓	4
12.11	even	2		3024.2.r.e.1009.1		4
21.2	odd	6		2646.2.h.m.361.2		4
21.5	even	6		2646.2.h.n.361.1		4
21.11	odd	6		2646.2.e.l.1549.1		4
21.17	even	6		2646.2.e.k.1549.2		4
21.20	even	2		2646.2.f.k.1765.2		4
36.7	odd	6		1008.2.r.e.673.1		4
36.11	even	6		3024.2.r.e.2017.1		4
36.23	even	6		9072.2.a.bd.1.2		2
36.31	odd	6		9072.2.a.bk.1.1		2
63.2	odd	6		2646.2.e.l.2125.1		4
63.11	odd	6		2646.2.h.m.667.2		4
63.13	odd	6		7938.2.a.bn.1.2		2
63.16	even	3		882.2.e.m.655.1		4
63.20	even	6		2646.2.f.k.883.2		4
63.25	even	3		882.2.h.k.79.2		4
63.34	odd	6		882.2.f.j.295.1		4
63.38	even	6		2646.2.h.n.667.1		4
63.41	even	6		7938.2.a.bm.1.1		2
63.47	even	6		2646.2.e.k.2125.2		4
63.52	odd	6		882.2.h.l.79.1		4
63.61	odd	6		882.2.e.n.655.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	9.7	even	3	inner
126.2.f.c.85.1	yes	4	1.1	even	1	trivial
378.2.f.d.127.1		4	9.2	odd	6
378.2.f.d.253.1		4	3.2	odd	2
882.2.e.m.373.1		4	7.4	even	3
882.2.e.m.655.1		4	63.16	even	3
882.2.e.n.373.2		4	7.3	odd	6
882.2.e.n.655.2		4	63.61	odd	6
882.2.f.j.295.1		4	63.34	odd	6
882.2.f.j.589.2		4	7.6	odd	2
882.2.h.k.67.2		4	7.2	even	3
882.2.h.k.79.2		4	63.25	even	3
882.2.h.l.67.1		4	7.5	odd	6
882.2.h.l.79.1		4	63.52	odd	6
1008.2.r.e.337.2		4	4.3	odd	2
1008.2.r.e.673.1		4	36.7	odd	6
1134.2.a.i.1.2		2	9.5	odd	6
1134.2.a.p.1.1		2	9.4	even	3
2646.2.e.k.1549.2		4	21.17	even	6
2646.2.e.k.2125.2		4	63.47	even	6
2646.2.e.l.1549.1		4	21.11	odd	6
2646.2.e.l.2125.1		4	63.2	odd	6
2646.2.f.k.883.2		4	63.20	even	6
2646.2.f.k.1765.2		4	21.20	even	2
2646.2.h.m.361.2		4	21.2	odd	6
2646.2.h.m.667.2		4	63.11	odd	6
2646.2.h.n.361.1		4	21.5	even	6
2646.2.h.n.667.1		4	63.38	even	6
3024.2.r.e.1009.1		4	12.11	even	2
3024.2.r.e.2017.1		4	36.11	even	6
7938.2.a.bm.1.1		2	63.41	even	6
7938.2.a.bn.1.2		2	63.13	odd	6
9072.2.a.bd.1.2		2	36.23	even	6
9072.2.a.bk.1.1		2	36.31	odd	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.724745 - 1.25529i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.724745 - 1.25529i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -1.44949 q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.724745 + 1.57313i) q^{12} +(-2.44949 + 4.24264i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} +(-1.94949 + 2.28024i) q^{18} +2.55051 q^{19} +(0.724745 + 1.25529i) q^{20} +(1.72474 + 0.158919i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.00000 - 1.41421i) q^{24} +(1.44949 + 2.51059i) q^{25} +4.89898 q^{26} +(-5.00000 - 1.41421i) q^{27} -1.00000 q^{28} +(3.44949 + 5.97469i) q^{29} +(-1.44949 + 2.04989i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.44949 - 0.317837i) q^{33} +(-1.00000 - 1.73205i) q^{34} +1.44949 q^{35} +(2.94949 + 0.548188i) q^{36} +11.7980 q^{37} +(-1.27526 - 2.20881i) q^{38} +(3.55051 + 7.70674i) q^{39} +(0.724745 - 1.25529i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(-0.724745 - 1.57313i) q^{42} +(-3.44949 - 5.97469i) q^{43} +2.00000 q^{44} +(-4.27526 - 0.794593i) q^{45} -1.00000 q^{46} +(-4.89898 - 8.48528i) q^{47} +(-1.72474 - 0.158919i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.44949 - 2.51059i) q^{50} +(2.00000 - 2.82843i) q^{51} +(-2.44949 - 4.24264i) q^{52} -10.8990 q^{53} +(1.27526 + 5.03723i) q^{54} -2.89898 q^{55} +(0.500000 + 0.866025i) q^{56} +(2.55051 - 3.60697i) q^{57} +(3.44949 - 5.97469i) q^{58} +(1.00000 - 1.73205i) q^{59} +(2.50000 + 0.230351i) q^{60} +(-3.27526 - 5.67291i) q^{61} +6.00000 q^{62} +(1.94949 - 2.28024i) q^{63} +1.00000 q^{64} +(3.55051 + 6.14966i) q^{65} +(1.44949 + 3.14626i) q^{66} +(6.44949 - 11.1708i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-0.724745 - 1.57313i) q^{69} +(-0.724745 - 1.25529i) q^{70} +0.101021 q^{71} +(-1.00000 - 2.82843i) q^{72} -6.89898 q^{73} +(-5.89898 - 10.2173i) q^{74} +(5.00000 + 0.460702i) q^{75} +(-1.27526 + 2.20881i) q^{76} +(1.00000 - 1.73205i) q^{77} +(4.89898 - 6.92820i) q^{78} +(0.949490 + 1.64456i) q^{79} -1.44949 q^{80} +(-7.00000 + 5.65685i) q^{81} +9.79796 q^{82} +(-1.00000 - 1.73205i) q^{83} +(-1.00000 + 1.41421i) q^{84} +(1.44949 - 2.51059i) q^{85} +(-3.44949 + 5.97469i) q^{86} +(11.8990 + 1.09638i) q^{87} +(-1.00000 - 1.73205i) q^{88} -16.8990 q^{89} +(1.44949 + 4.09978i) q^{90} -4.89898 q^{91} +(0.500000 + 0.866025i) q^{92} +(4.34847 + 9.43879i) q^{93} +(-4.89898 + 8.48528i) q^{94} +(1.84847 - 3.20164i) q^{95} +(0.724745 + 1.57313i) q^{96} +(-1.44949 - 2.51059i) q^{97} +1.00000 q^{98} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{10} - 4 q^{11} - 2 q^{12} + 2 q^{14} - 14 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} + 20 q^{19} - 2 q^{20} + 2 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 4 q^{25} - 20 q^{27} - 4 q^{28} + 4 q^{29} + 4 q^{30} - 12 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 8 q^{37} - 10 q^{38} + 24 q^{39} - 2 q^{40} + 2 q^{42} - 4 q^{43} + 8 q^{44} - 22 q^{45} - 4 q^{46} - 2 q^{48} - 2 q^{49} - 4 q^{50} + 8 q^{51} - 24 q^{53} + 10 q^{54} + 8 q^{55} + 2 q^{56} + 20 q^{57} + 4 q^{58} + 4 q^{59} + 10 q^{60} - 18 q^{61} + 24 q^{62} - 2 q^{63} + 4 q^{64} + 24 q^{65} - 4 q^{66} + 16 q^{67} - 4 q^{68} + 2 q^{69} + 2 q^{70} + 20 q^{71} - 4 q^{72} - 8 q^{73} - 4 q^{74} + 20 q^{75} - 10 q^{76} + 4 q^{77} - 6 q^{79} + 4 q^{80} - 28 q^{81} - 4 q^{83} - 4 q^{84} - 4 q^{85} - 4 q^{86} + 28 q^{87} - 4 q^{88} - 48 q^{89} - 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} - 2 q^{96} + 4 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^10 - 4 * q^11 - 2 * q^12 + 2 * q^14 - 14 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 + 20 * q^19 - 2 * q^20 + 2 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 4 * q^25 - 20 * q^27 - 4 * q^28 + 4 * q^29 + 4 * q^30 - 12 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 8 * q^37 - 10 * q^38 + 24 * q^39 - 2 * q^40 + 2 * q^42 - 4 * q^43 + 8 * q^44 - 22 * q^45 - 4 * q^46 - 2 * q^48 - 2 * q^49 - 4 * q^50 + 8 * q^51 - 24 * q^53 + 10 * q^54 + 8 * q^55 + 2 * q^56 + 20 * q^57 + 4 * q^58 + 4 * q^59 + 10 * q^60 - 18 * q^61 + 24 * q^62 - 2 * q^63 + 4 * q^64 + 24 * q^65 - 4 * q^66 + 16 * q^67 - 4 * q^68 + 2 * q^69 + 2 * q^70 + 20 * q^71 - 4 * q^72 - 8 * q^73 - 4 * q^74 + 20 * q^75 - 10 * q^76 + 4 * q^77 - 6 * q^79 + 4 * q^80 - 28 * q^81 - 4 * q^83 - 4 * q^84 - 4 * q^85 - 4 * q^86 + 28 * q^87 - 4 * q^88 - 48 * q^89 - 4 * q^90 + 2 * q^92 - 12 * q^93 - 22 * q^95 - 2 * q^96 + 4 * q^97 + 4 * q^98 + 4 * q^99

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