LMFDB - Embedded newform 78.2.i.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(43,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("78.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.43
Dual form			78.2.i.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.267949i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.267949i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.133975 - 0.232051i) q^{10} +(-4.09808 - 2.36603i) q^{11} -1.00000 q^{12} +(2.59808 - 2.50000i) q^{13} +0.732051 q^{14} +(0.232051 + 0.133975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.13397 - 1.96410i) q^{17} -1.00000i q^{18} +(-1.09808 + 0.633975i) q^{19} +(0.232051 - 0.133975i) q^{20} +0.732051i q^{21} +(-2.36603 - 4.09808i) q^{22} +(-3.09808 + 5.36603i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.92820 q^{25} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(0.633975 + 0.366025i) q^{28} +(-1.23205 + 2.13397i) q^{29} +(0.133975 + 0.232051i) q^{30} +5.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.09808 - 2.36603i) q^{33} -2.26795i q^{34} +(-0.0980762 - 0.169873i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-9.06218 - 5.23205i) q^{37} -1.26795 q^{38} +(0.866025 + 3.50000i) q^{39} +0.267949 q^{40} +(9.86603 + 5.69615i) q^{41} +(-0.366025 + 0.633975i) q^{42} +(3.83013 + 6.63397i) q^{43} -4.73205i q^{44} +(-0.232051 + 0.133975i) q^{45} +(-5.36603 + 3.09808i) q^{46} -8.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(4.26795 + 2.46410i) q^{50} +2.26795 q^{51} +(3.46410 + 1.00000i) q^{52} +0.464102 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.633975 + 1.09808i) q^{55} +(0.366025 + 0.633975i) q^{56} -1.26795i q^{57} +(-2.13397 + 1.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +0.267949i q^{60} +(-0.598076 - 1.03590i) q^{61} +(-2.73205 + 4.73205i) q^{62} +(-0.633975 - 0.366025i) q^{63} -1.00000 q^{64} +(-0.669873 - 0.696152i) q^{65} +4.73205 q^{66} +(-9.63397 - 5.56218i) q^{67} +(1.13397 - 1.96410i) q^{68} +(-3.09808 - 5.36603i) q^{69} -0.196152i q^{70} +(-1.09808 + 0.633975i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.73205i q^{73} +(-5.23205 - 9.06218i) q^{74} +(-2.46410 + 4.26795i) q^{75} +(-1.09808 - 0.633975i) q^{76} -3.46410 q^{77} +(-1.00000 + 3.46410i) q^{78} -9.46410 q^{79} +(0.232051 + 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.69615 + 9.86603i) q^{82} -10.1962i q^{83} +(-0.633975 + 0.366025i) q^{84} +(-0.526279 + 0.303848i) q^{85} +7.66025i q^{86} +(-1.23205 - 2.13397i) q^{87} +(2.36603 - 4.09808i) q^{88} +(2.19615 + 1.26795i) q^{89} -0.267949 q^{90} +(0.732051 - 2.53590i) q^{91} -6.19615 q^{92} +(-4.73205 - 2.73205i) q^{93} +(4.09808 - 7.09808i) q^{94} +(0.169873 + 0.294229i) q^{95} -1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(-5.59808 + 3.23205i) q^{98} +4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 14 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + 4 q^{30} + 6 q^{33} + 10 q^{35} + 2 q^{36} - 12 q^{37} - 12 q^{38} + 8 q^{40} + 36 q^{41} + 2 q^{42} - 2 q^{43} + 6 q^{45} - 18 q^{46} - 2 q^{48} - 6 q^{49} + 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 8 q^{61} - 4 q^{62} - 6 q^{63} - 4 q^{64} - 20 q^{65} + 12 q^{66} - 42 q^{67} + 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 24 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 6 q^{84} + 36 q^{85} + 2 q^{87} + 6 q^{88} - 12 q^{89} - 8 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 4 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 2 * q^23 - 8 * q^25 + 14 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^33 + 10 * q^35 + 2 * q^36 - 12 * q^37 - 12 * q^38 + 8 * q^40 + 36 * q^41 + 2 * q^42 - 2 * q^43 + 6 * q^45 - 18 * q^46 - 2 * q^48 - 6 * q^49 + 24 * q^50 + 16 * q^51 - 12 * q^53 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 8 * q^61 - 4 * q^62 - 6 * q^63 - 4 * q^64 - 20 * q^65 + 12 * q^66 - 42 * q^67 + 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 4 * q^75 + 6 * q^76 - 4 * q^78 - 24 * q^79 - 6 * q^80 - 2 * q^81 + 2 * q^82 - 6 * q^84 + 36 * q^85 + 2 * q^87 + 6 * q^88 - 12 * q^89 - 8 * q^90 - 4 * q^91 - 4 * q^92 - 12 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−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
$5$		−	0.267949i		−	0.119831i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$		−	0.267949i		−	0.119831i	0.998203	−	0.0599153i	$-0.0190830\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	−0.375382	−	0.926870i	$-0.622489\pi$
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	0.615002	+	0.788526i	$0.289155\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.133975	−	0.232051i	0.0423665	−	0.0733809i
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.267421	−	0.963580i	$-0.586172\pi$
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.968195	+	0.250196i	$0.919505\pi$
$12$	−1.00000			−0.288675
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$14$	0.732051			0.195649
$15$	0.232051	+	0.133975i	0.0599153	+	0.0345921i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.13397	−	1.96410i	−0.275029	−	0.476365i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	−1.13397	−	1.96410i	−0.275029	−	0.476365i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	−0.620641	−	0.784095i	$-0.713128\pi$
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	0.368725	+	0.929538i	$0.379794\pi$
$20$	0.232051	−	0.133975i	0.0518881	−	0.0299576i
$21$			0.732051i			0.159747i
$22$	−2.36603	−	4.09808i	−0.504438	−	0.873713i
$23$	−3.09808	+	5.36603i	−0.645994	+	1.11889i	0.338078	+	0.941118i	$0.390223\pi$
$23$	−3.09808	+	5.36603i	−0.645994	+	1.11889i	−0.984071	+	0.177775i	$0.943110\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	4.92820			0.985641
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	1.00000			0.192450
$28$	0.633975	+	0.366025i	0.119810	+	0.0691723i
$29$	−1.23205	+	2.13397i	−0.228786	+	0.396269i	−0.957449	−	0.288604i	$-0.906809\pi$
$29$	−1.23205	+	2.13397i	−0.228786	+	0.396269i	0.728663	+	0.684873i	$0.240142\pi$
$30$	0.133975	+	0.232051i	0.0244603	+	0.0423665i
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	4.09808	−	2.36603i	0.713384	−	0.411872i
$34$		−	2.26795i		−	0.388950i
$35$	−0.0980762	−	0.169873i	−0.0165779	−	0.0287138i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−9.06218	−	5.23205i	−1.48981	−	0.860144i	−0.489881	−	0.871789i	$-0.662960\pi$
$37$	−9.06218	−	5.23205i	−1.48981	−	0.860144i	−0.999932	+	0.0116456i	$0.996293\pi$
$38$	−1.26795			−0.205689
$39$	0.866025	+	3.50000i	0.138675	+	0.560449i
$40$	0.267949			0.0423665
$41$	9.86603	+	5.69615i	1.54081	+	0.889590i	0.998788	+	0.0492283i	$0.0156762\pi$
$41$	9.86603	+	5.69615i	1.54081	+	0.889590i	0.542027	+	0.840361i	$0.317657\pi$
$42$	−0.366025	+	0.633975i	−0.0564789	+	0.0978244i
$43$	3.83013	+	6.63397i	0.584089	+	1.01167i	0.994988	+	0.0999910i	$0.0318814\pi$
$43$	3.83013	+	6.63397i	0.584089	+	1.01167i	−0.410899	+	0.911681i	$0.634785\pi$
$44$		−	4.73205i		−	0.713384i
$45$	−0.232051	+	0.133975i	−0.0345921	+	0.0199718i
$46$	−5.36603	+	3.09808i	−0.791177	+	0.456786i
$47$		−	8.19615i		−	1.19553i	−0.801671	−	0.597766i	$-0.796055\pi$
$47$		−	8.19615i		−	1.19553i	0.801671	−	0.597766i	$-0.203945\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$	4.26795	+	2.46410i	0.603579	+	0.348477i
$51$	2.26795			0.317576
$52$	3.46410	+	1.00000i	0.480384	+	0.138675i
$53$	0.464102			0.0637493			0.0318746	−	0.999492i	$-0.489852\pi$
$53$	0.464102			0.0637493			0.0318746	+	0.999492i	$0.489852\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.633975	+	1.09808i	−0.0854851	+	0.148065i
$56$	0.366025	+	0.633975i	0.0489122	+	0.0847184i
$57$		−	1.26795i		−	0.167944i
$58$	−2.13397	+	1.23205i	−0.280205	+	0.161776i
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.0241347	−	0.999709i	$-0.492317\pi$
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.877841	+	0.478953i	$0.158984\pi$
$60$			0.267949i			0.0345921i
$61$	−0.598076	−	1.03590i	−0.0765758	−	0.132633i	0.825195	−	0.564848i	$-0.191065\pi$
$61$	−0.598076	−	1.03590i	−0.0765758	−	0.132633i	−0.901770	+	0.432215i	$0.857732\pi$
$62$	−2.73205	+	4.73205i	−0.346971	+	0.600971i
$63$	−0.633975	−	0.366025i	−0.0798733	−	0.0461149i
$64$	−1.00000			−0.125000
$65$	−0.669873	−	0.696152i	−0.0830875	−	0.0863471i
$66$	4.73205			0.582475
$67$	−9.63397	−	5.56218i	−1.17698	−	0.679528i	−0.221664	−	0.975123i	$-0.571149\pi$
$67$	−9.63397	−	5.56218i	−1.17698	−	0.679528i	−0.955313	+	0.295595i	$0.904482\pi$
$68$	1.13397	−	1.96410i	0.137515	−	0.238182i
$69$	−3.09808	−	5.36603i	−0.372965	−	0.645994i
$70$		−	0.196152i		−	0.0234447i
$71$	−1.09808	+	0.633975i	−0.130318	+	0.0752389i	−0.563742	−	0.825951i	$-0.690639\pi$
$71$	−1.09808	+	0.633975i	−0.130318	+	0.0752389i	0.433424	+	0.901190i	$0.357305\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	9.73205i		−	1.13905i	−0.821974	−	0.569525i	$-0.807127\pi$
$73$		−	9.73205i		−	1.13905i	0.821974	−	0.569525i	$-0.192873\pi$
$74$	−5.23205	−	9.06218i	−0.608214	−	1.05346i
$75$	−2.46410	+	4.26795i	−0.284530	+	0.492820i
$76$	−1.09808	−	0.633975i	−0.125958	−	0.0727219i
$77$	−3.46410			−0.394771
$78$	−1.00000	+	3.46410i	−0.113228	+	0.392232i
$79$	−9.46410			−1.06479			−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410			−1.06479			−0.532397	+	0.846495i	$0.678709\pi$
$80$	0.232051	+	0.133975i	0.0259441	+	0.0149788i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.69615	+	9.86603i	0.629035	+	1.08952i
$83$		−	10.1962i		−	1.11917i	−0.828772	−	0.559587i	$-0.810960\pi$
$83$		−	10.1962i		−	1.11917i	0.828772	−	0.559587i	$-0.189040\pi$
$84$	−0.633975	+	0.366025i	−0.0691723	+	0.0399366i
$85$	−0.526279	+	0.303848i	−0.0570830	+	0.0329569i
$86$			7.66025i			0.826026i
$87$	−1.23205	−	2.13397i	−0.132090	−	0.228786i
$88$	2.36603	−	4.09808i	0.252219	−	0.436856i
$89$	2.19615	+	1.26795i	0.232792	+	0.134402i	0.611859	−	0.790967i	$-0.290422\pi$
$89$	2.19615	+	1.26795i	0.232792	+	0.134402i	−0.379068	+	0.925369i	$0.623755\pi$
$90$	−0.267949			−0.0282443
$91$	0.732051	−	2.53590i	0.0767398	−	0.265834i
$92$	−6.19615			−0.645994
$93$	−4.73205	−	2.73205i	−0.490691	−	0.283300i
$94$	4.09808	−	7.09808i	0.422684	−	0.732111i
$95$	0.169873	+	0.294229i	0.0174286	+	0.0301872i
$96$		−	1.00000i		−	0.102062i
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$	−5.59808	+	3.23205i	−0.565491	+	0.326486i
$99$			4.73205i			0.475589i
$100$	2.46410	+	4.26795i	0.246410	+	0.426795i
$101$	−5.96410	+	10.3301i	−0.593450	+	1.02789i	0.400313	+	0.916378i	$0.368901\pi$
$101$	−5.96410	+	10.3301i	−0.593450	+	1.02789i	−0.993764	+	0.111508i	$0.964432\pi$
$102$	1.96410	+	1.13397i	0.194475	+	0.112280i
$103$	18.7321			1.84572			0.922862	−	0.385131i	$-0.125844\pi$
$103$	18.7321			1.84572			0.922862	+	0.385131i	$0.125844\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$	0.196152			0.0191425
$106$	0.401924	+	0.232051i	0.0390383	+	0.0225388i
$107$	0.0980762	−	0.169873i	0.00948139	−	0.0164222i	−0.861246	−	0.508189i	$-0.830315\pi$
$107$	0.0980762	−	0.169873i	0.00948139	−	0.0164222i	0.870727	+	0.491766i	$0.163649\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			5.46410i			0.523366i	0.965154	+	0.261683i	$0.0842775\pi$
$109$			5.46410i			0.523366i	−0.965154	+	0.261683i	$0.915723\pi$
$110$	−1.09808	+	0.633975i	−0.104697	+	0.0604471i
$111$	9.06218	−	5.23205i	0.860144	−	0.496604i
$112$			0.732051i			0.0691723i
$113$	9.33013	+	16.1603i	0.877705	+	1.52023i	0.853854	+	0.520513i	$0.174259\pi$
$113$	9.33013	+	16.1603i	0.877705	+	1.52023i	0.0238510	+	0.999716i	$0.492407\pi$
$114$	0.633975	−	1.09808i	0.0593772	−	0.102844i
$115$	1.43782	+	0.830127i	0.134078	+	0.0774097i
$116$	−2.46410			−0.228786
$117$	−3.46410	−	1.00000i	−0.320256	−	0.0924500i
$118$	8.00000			0.736460
$119$	−1.43782	−	0.830127i	−0.131805	−	0.0760976i
$120$	−0.133975	+	0.232051i	−0.0122302	+	0.0211832i
$121$	5.69615	+	9.86603i	0.517832	+	0.896911i
$122$		−	1.19615i		−	0.108295i
$123$	−9.86603	+	5.69615i	−0.889590	+	0.513605i
$124$	−4.73205	+	2.73205i	−0.424951	+	0.245345i
$125$		−	2.66025i		−	0.237940i
$126$	−0.366025	−	0.633975i	−0.0326081	−	0.0564789i
$127$	8.92820	−	15.4641i	0.792250	−	1.37222i	−0.132321	−	0.991207i	$-0.542243\pi$
$127$	8.92820	−	15.4641i	0.792250	−	1.37222i	0.924571	−	0.381010i	$-0.124424\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−7.66025			−0.674448
$130$	−0.232051	−	0.937822i	−0.0203522	−	0.0822524i
$131$	13.4641			1.17636			0.588182	−	0.808729i	$-0.299844\pi$
$131$	13.4641			1.17636			0.588182	+	0.808729i	$0.299844\pi$
$132$	4.09808	+	2.36603i	0.356692	+	0.205936i
$133$	−0.464102	+	0.803848i	−0.0402427	+	0.0697024i
$134$	−5.56218	−	9.63397i	−0.480499	−	0.832249i
$135$		−	0.267949i		−	0.0230614i
$136$	1.96410	−	1.13397i	0.168420	−	0.0972375i
$137$	−1.66987	+	0.964102i	−0.142667	+	0.0823688i	−0.569634	−	0.821898i	$-0.692915\pi$
$137$	−1.66987	+	0.964102i	−0.142667	+	0.0823688i	0.426968	+	0.904267i	$0.359582\pi$
$138$		−	6.19615i		−	0.527452i
$139$	4.92820	+	8.53590i	0.418005	+	0.724005i	0.995739	−	0.0922197i	$-0.0293962\pi$
$139$	4.92820	+	8.53590i	0.418005	+	0.724005i	−0.577734	+	0.816225i	$0.696063\pi$
$140$	0.0980762	−	0.169873i	0.00828895	−	0.0143569i
$141$	7.09808	+	4.09808i	0.597766	+	0.345120i
$142$	−1.26795			−0.106404
$143$	−16.5622	+	4.09808i	−1.38500	+	0.342698i
$144$	1.00000			0.0833333
$145$	0.571797	+	0.330127i	0.0474851	+	0.0274156i
$146$	4.86603	−	8.42820i	0.402715	−	0.697523i
$147$	−3.23205	−	5.59808i	−0.266575	−	0.461722i
$148$		−	10.4641i		−	0.860144i
$149$	−2.42820	+	1.40192i	−0.198926	+	0.114850i	−0.596154	−	0.802870i	$-0.703305\pi$
$149$	−2.42820	+	1.40192i	−0.198926	+	0.114850i	0.397228	+	0.917720i	$0.369972\pi$
$150$	−4.26795	+	2.46410i	−0.348477	+	0.201193i
$151$			3.26795i			0.265942i	0.991120	+	0.132971i	$0.0424517\pi$
$151$			3.26795i			0.265942i	−0.991120	+	0.132971i	$0.957548\pi$
$152$	−0.633975	−	1.09808i	−0.0514221	−	0.0890657i
$153$	−1.13397	+	1.96410i	−0.0916764	+	0.158788i
$154$	−3.00000	−	1.73205i	−0.241747	−	0.139573i
$155$	1.46410			0.117599
$156$	−2.59808	+	2.50000i	−0.208013	+	0.200160i
$157$	−23.5885			−1.88256			−0.941282	−	0.337622i	$-0.890378\pi$
$157$	−23.5885			−1.88256			−0.941282	+	0.337622i	$0.890378\pi$
$158$	−8.19615	−	4.73205i	−0.652051	−	0.376462i
$159$	−0.232051	+	0.401924i	−0.0184028	+	0.0318746i
$160$	0.133975	+	0.232051i	0.0105916	+	0.0183452i
$161$			4.53590i			0.357479i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−5.66025	+	3.26795i	−0.443345	+	0.255966i	−0.705016	−	0.709192i	$-0.749060\pi$
$163$	−5.66025	+	3.26795i	−0.443345	+	0.255966i	0.261670	+	0.965157i	$0.415727\pi$
$164$			11.3923i			0.889590i
$165$	−0.633975	−	1.09808i	−0.0493549	−	0.0854851i
$166$	5.09808	−	8.83013i	0.395687	−	0.685351i
$167$	2.19615	+	1.26795i	0.169943	+	0.0981169i	0.582559	−	0.812788i	$-0.302051\pi$
$167$	2.19615	+	1.26795i	0.169943	+	0.0981169i	−0.412616	+	0.910905i	$0.635385\pi$
$168$	−0.732051			−0.0564789
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$	−0.607695			−0.0466081
$171$	1.09808	+	0.633975i	0.0839720	+	0.0484812i
$172$	−3.83013	+	6.63397i	−0.292044	+	0.505836i
$173$	−8.19615	−	14.1962i	−0.623142	−	1.07931i	−0.988897	−	0.148602i	$-0.952523\pi$
$173$	−8.19615	−	14.1962i	−0.623142	−	1.07931i	0.365755	−	0.930711i	$-0.380811\pi$
$174$		−	2.46410i		−	0.186803i
$175$	3.12436	−	1.80385i	0.236179	−	0.136358i
$176$	4.09808	−	2.36603i	0.308904	−	0.178346i
$177$			8.00000i			0.601317i
$178$	1.26795	+	2.19615i	0.0950368	+	0.164609i
$179$	11.0263	−	19.0981i	0.824143	−	1.42746i	−0.0784298	−	0.996920i	$-0.524991\pi$
$179$	11.0263	−	19.0981i	0.824143	−	1.42746i	0.902573	−	0.430538i	$-0.141676\pi$
$180$	−0.232051	−	0.133975i	−0.0172960	−	0.00998588i
$181$	−8.80385			−0.654385			−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385			−0.654385			−0.327192	+	0.944958i	$0.606103\pi$
$182$	1.90192	−	1.83013i	0.140980	−	0.135658i
$183$	1.19615			0.0884221
$184$	−5.36603	−	3.09808i	−0.395589	−	0.228393i
$185$	−1.40192	+	2.42820i	−0.103071	+	0.178525i
$186$	−2.73205	−	4.73205i	−0.200324	−	0.346971i
$187$			10.7321i			0.784805i
$188$	7.09808	−	4.09808i	0.517680	−	0.298883i
$189$	0.633975	−	0.366025i	0.0461149	−	0.0266244i
$190$			0.339746i			0.0246478i
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	0.713052	−	0.701111i	$-0.247312\pi$
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	−0.963706	+	0.266966i	$0.913979\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	7.16025	+	4.13397i	0.515406	+	0.297570i	0.735053	−	0.678009i	$-0.237157\pi$
$193$	7.16025	+	4.13397i	0.515406	+	0.297570i	−0.219647	+	0.975579i	$0.570490\pi$
$194$	6.00000			0.430775
$195$	0.937822	−	0.232051i	0.0671588	−	0.0166175i
$196$	−6.46410			−0.461722
$197$	8.53590	+	4.92820i	0.608158	+	0.351120i	0.772244	−	0.635326i	$-0.219134\pi$
$197$	8.53590	+	4.92820i	0.608158	+	0.351120i	−0.164086	+	0.986446i	$0.552468\pi$
$198$	−2.36603	+	4.09808i	−0.168146	+	0.291238i
$199$	−1.90192	−	3.29423i	−0.134824	−	0.233522i	0.790706	−	0.612196i	$-0.209714\pi$
$199$	−1.90192	−	3.29423i	−0.134824	−	0.233522i	−0.925530	+	0.378674i	$0.876380\pi$
$200$			4.92820i			0.348477i
$201$	9.63397	−	5.56218i	0.679528	−	0.392326i
$202$	−10.3301	+	5.96410i	−0.726825	+	0.419633i
$203$			1.80385i			0.126605i
$204$	1.13397	+	1.96410i	0.0793941	+	0.137515i
$205$	1.52628	−	2.64359i	0.106600	−	0.184637i
$206$	16.2224	+	9.36603i	1.13027	+	0.652562i
$207$	6.19615			0.430662
$208$	0.866025	+	3.50000i	0.0600481	+	0.242681i
$209$	6.00000			0.415029
$210$	0.169873	+	0.0980762i	0.0117223	+	0.00676790i
$211$	2.19615	−	3.80385i	0.151189	−	0.261868i	−0.780476	−	0.625186i	$-0.785023\pi$
$211$	2.19615	−	3.80385i	0.151189	−	0.261868i	0.931665	+	0.363319i	$0.118356\pi$
$212$	0.232051	+	0.401924i	0.0159373	+	0.0276042i
$213$		−	1.26795i		−	0.0868784i
$214$	0.169873	−	0.0980762i	0.0116123	−	0.00670435i
$215$	1.77757	−	1.02628i	0.121229	−	0.0699917i
$216$			1.00000i			0.0680414i
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	−2.73205	+	4.73205i	−0.185038	+	0.320495i
$219$	8.42820	+	4.86603i	0.569525	+	0.328816i
$220$	−1.26795			−0.0854851
$221$	−7.85641	−	2.26795i	−0.528479	−	0.152559i
$222$	10.4641			0.702305
$223$	−11.3205	−	6.53590i	−0.758077	−	0.437676i	0.0705277	−	0.997510i	$-0.477532\pi$
$223$	−11.3205	−	6.53590i	−0.758077	−	0.437676i	−0.828605	+	0.559834i	$0.810865\pi$
$224$	−0.366025	+	0.633975i	−0.0244561	+	0.0423592i
$225$	−2.46410	−	4.26795i	−0.164273	−	0.284530i
$226$			18.6603i			1.24126i
$227$	1.56218	−	0.901924i	0.103685	−	0.0598628i	−0.447261	−	0.894404i	$-0.647600\pi$
$227$	1.56218	−	0.901924i	0.103685	−	0.0598628i	0.550946	+	0.834541i	$0.314267\pi$
$228$	1.09808	−	0.633975i	0.0727219	−	0.0419860i
$229$			15.8564i			1.04782i	0.851773	+	0.523910i	$0.175527\pi$
$229$			15.8564i			1.04782i	−0.851773	+	0.523910i	$0.824473\pi$
$230$	0.830127	+	1.43782i	0.0547370	+	0.0948072i
$231$	1.73205	−	3.00000i	0.113961	−	0.197386i
$232$	−2.13397	−	1.23205i	−0.140102	−	0.0808881i
$233$	−19.8564			−1.30084			−0.650418	−	0.759576i	$-0.725406\pi$
$233$	−19.8564			−1.30084			−0.650418	+	0.759576i	$0.725406\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$	−2.19615			−0.143261
$236$	6.92820	+	4.00000i	0.450988	+	0.260378i
$237$	4.73205	−	8.19615i	0.307380	−	0.532397i
$238$	−0.830127	−	1.43782i	−0.0538091	−	0.0932002i
$239$			9.66025i			0.624870i	0.949939	+	0.312435i	$0.101145\pi$
$239$			9.66025i			0.624870i	−0.949939	+	0.312435i	$0.898855\pi$
$240$	−0.232051	+	0.133975i	−0.0149788	+	0.00864802i
$241$	−15.2321	+	8.79423i	−0.981183	+	0.566486i	−0.902627	−	0.430424i	$-0.858364\pi$
$241$	−15.2321	+	8.79423i	−0.981183	+	0.566486i	−0.0785557	+	0.996910i	$0.525031\pi$
$242$			11.3923i			0.732325i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.598076	−	1.03590i	0.0382879	−	0.0663166i
$245$	1.50000	+	0.866025i	0.0958315	+	0.0553283i
$246$	−11.3923			−0.726347
$247$	−1.26795	+	4.39230i	−0.0806777	+	0.279476i
$248$	−5.46410			−0.346971
$249$	8.83013	+	5.09808i	0.559587	+	0.323077i
$250$	1.33013	−	2.30385i	0.0841246	−	0.145708i
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	0.950537	−	0.310611i	$-0.100534\pi$
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	−0.744266	+	0.667883i	$0.767200\pi$
$252$		−	0.732051i		−	0.0461149i
$253$	25.3923	−	14.6603i	1.59640	−	0.921682i
$254$	15.4641	−	8.92820i	0.970304	−	0.560205i
$255$		−	0.607695i		−	0.0380553i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.3301	−	23.0885i	0.831510	−	1.44022i	−0.0653297	−	0.997864i	$-0.520810\pi$
$257$	13.3301	−	23.0885i	0.831510	−	1.44022i	0.896840	−	0.442355i	$-0.145857\pi$
$258$	−6.63397	−	3.83013i	−0.413013	−	0.238453i
$259$	−7.66025			−0.475985
$260$	0.267949	−	0.928203i	0.0166175	−	0.0575647i
$261$	2.46410			0.152524
$262$	11.6603	+	6.73205i	0.720373	+	0.415907i
$263$	−14.0263	+	24.2942i	−0.864897	+	1.49805i	0.00225153	+	0.999997i	$0.499283\pi$
$263$	−14.0263	+	24.2942i	−0.864897	+	1.49805i	−0.867149	+	0.498049i	$0.834050\pi$
$264$	2.36603	+	4.09808i	0.145619	+	0.252219i
$265$		−	0.124356i		−	0.00763911i
$266$	−0.803848	+	0.464102i	−0.0492871	+	0.0284559i
$267$	−2.19615	+	1.26795i	−0.134402	+	0.0775972i
$268$		−	11.1244i		−	0.679528i
$269$	0.732051	+	1.26795i	0.0446339	+	0.0773082i	0.887479	−	0.460848i	$-0.152455\pi$
$269$	0.732051	+	1.26795i	0.0446339	+	0.0773082i	−0.842845	+	0.538156i	$0.819121\pi$
$270$	0.133975	−	0.232051i	0.00815343	−	0.0141222i
$271$	−5.07180	−	2.92820i	−0.308090	−	0.177876i	0.337982	−	0.941153i	$-0.390256\pi$
$271$	−5.07180	−	2.92820i	−0.308090	−	0.177876i	−0.646071	+	0.763277i	$0.723589\pi$
$272$	2.26795			0.137515
$273$	1.83013	+	1.90192i	0.110764	+	0.115110i
$274$	−1.92820			−0.116487
$275$	−20.1962	−	11.6603i	−1.21787	−	0.703140i
$276$	3.09808	−	5.36603i	0.186482	−	0.322997i
$277$	−1.13397	−	1.96410i	−0.0681339	−	0.118011i	0.829946	−	0.557844i	$-0.188371\pi$
$277$	−1.13397	−	1.96410i	−0.0681339	−	0.118011i	−0.898080	+	0.439832i	$0.855038\pi$
$278$			9.85641i			0.591148i
$279$	4.73205	−	2.73205i	0.283300	−	0.163564i
$280$	0.169873	−	0.0980762i	0.0101519	−	0.00586117i
$281$		−	22.3205i		−	1.33153i	−0.746162	−	0.665765i	$-0.768105\pi$
$281$		−	22.3205i		−	1.33153i	0.746162	−	0.665765i	$-0.231895\pi$
$282$	4.09808	+	7.09808i	0.244037	+	0.422684i
$283$	4.16987	−	7.22243i	0.247873	−	0.429329i	−0.715062	−	0.699061i	$-0.753602\pi$
$283$	4.16987	−	7.22243i	0.247873	−	0.429329i	0.962936	+	0.269732i	$0.0869350\pi$
$284$	−1.09808	−	0.633975i	−0.0651588	−	0.0376195i
$285$	−0.339746			−0.0201248
$286$	−16.3923	−	4.73205i	−0.969297	−	0.279812i
$287$	8.33975			0.492280
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	5.92820	−	10.2679i	0.348718	−	0.603997i
$290$	0.330127	+	0.571797i	0.0193857	+	0.0335771i
$291$			6.00000i			0.351726i
$292$	8.42820	−	4.86603i	0.493223	−	0.284763i
$293$	−12.5718	+	7.25833i	−0.734452	+	0.424036i	−0.820049	−	0.572294i	$-0.806054\pi$
$293$	−12.5718	+	7.25833i	−0.734452	+	0.424036i	0.0855965	+	0.996330i	$0.472720\pi$
$294$		−	6.46410i		−	0.376994i
$295$	−1.07180	−	1.85641i	−0.0624024	−	0.108084i
$296$	5.23205	−	9.06218i	0.304107	−	0.526728i
$297$	−4.09808	−	2.36603i	−0.237795	−	0.137291i
$298$	−2.80385			−0.162423
$299$	5.36603	+	21.6865i	0.310325	+	1.25416i
$300$	−4.92820			−0.284530
$301$	4.85641	+	2.80385i	0.279919	+	0.161611i
$302$	−1.63397	+	2.83013i	−0.0940247	+	0.162856i
$303$	−5.96410	−	10.3301i	−0.342629	−	0.593450i
$304$		−	1.26795i		−	0.0727219i
$305$	−0.277568	+	0.160254i	−0.0158935	+	0.00917612i
$306$	−1.96410	+	1.13397i	−0.112280	+	0.0648250i
$307$			8.58846i			0.490169i	0.969502	+	0.245085i	$0.0788157\pi$
$307$			8.58846i			0.490169i	−0.969502	+	0.245085i	$0.921184\pi$
$308$	−1.73205	−	3.00000i	−0.0986928	−	0.170941i
$309$	−9.36603	+	16.2224i	−0.532815	+	0.922862i
$310$	1.26795	+	0.732051i	0.0720147	+	0.0415777i
$311$	−15.6603			−0.888012			−0.444006	−	0.896024i	$-0.646443\pi$
$311$	−15.6603			−0.888012			−0.444006	+	0.896024i	$0.646443\pi$
$312$	−3.50000	+	0.866025i	−0.198148	+	0.0490290i
$313$	13.4641			0.761036			0.380518	−	0.924774i	$-0.375746\pi$
$313$	13.4641			0.761036			0.380518	+	0.924774i	$0.375746\pi$
$314$	−20.4282	−	11.7942i	−1.15283	−	0.665587i
$315$	−0.0980762	+	0.169873i	−0.00552597	+	0.00957126i
$316$	−4.73205	−	8.19615i	−0.266199	−	0.461070i
$317$		−	3.33975i		−	0.187579i	−0.995592	−	0.0937894i	$-0.970102\pi$
$317$		−	3.33975i		−	0.187579i	0.995592	−	0.0937894i	$-0.0298980\pi$
$318$	−0.401924	+	0.232051i	−0.0225388	+	0.0130128i
$319$	10.0981	−	5.83013i	0.565384	−	0.326424i
$320$			0.267949i			0.0149788i
$321$	0.0980762	+	0.169873i	0.00547408	+	0.00948139i
$322$	−2.26795	+	3.92820i	−0.126388	+	0.218910i
$323$	2.49038	+	1.43782i	0.138569	+	0.0800026i
$324$	−1.00000			−0.0555556
$325$	12.8038	−	12.3205i	0.710230	−	0.683419i
$326$	−6.53590			−0.361990
$327$	−4.73205	−	2.73205i	−0.261683	−	0.151083i
$328$	−5.69615	+	9.86603i	−0.314517	+	0.544760i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		−	1.26795i		−	0.0697983i
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.893708	−	0.448649i	$-0.851905\pi$
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.0583130	+	0.998298i	$0.518572\pi$
$332$	8.83013	−	5.09808i	0.484616	−	0.279793i
$333$			10.4641i			0.573429i
$334$	1.26795	+	2.19615i	0.0693791	+	0.120168i
$335$	−1.49038	+	2.58142i	−0.0814282	+	0.141038i
$336$	−0.633975	−	0.366025i	−0.0345861	−	0.0199683i
$337$	−6.85641			−0.373492			−0.186746	−	0.982408i	$-0.559794\pi$
$337$	−6.85641			−0.373492			−0.186746	+	0.982408i	$0.559794\pi$
$338$	6.92820	−	11.0000i	0.376845	−	0.598321i
$339$	−18.6603			−1.01349
$340$	−0.526279	−	0.303848i	−0.0285415	−	0.0164784i
$341$	12.9282	−	22.3923i	0.700101	−	1.21261i
$342$	0.633975	+	1.09808i	0.0342814	+	0.0593772i
$343$			9.85641i			0.532196i
$344$	−6.63397	+	3.83013i	−0.357680	+	0.206507i
$345$	−1.43782	+	0.830127i	−0.0774097	+	0.0446925i
$346$		−	16.3923i		−	0.881256i
$347$	−4.43782	−	7.68653i	−0.238235	−	0.412635i	0.721973	−	0.691921i	$-0.243235\pi$
$347$	−4.43782	−	7.68653i	−0.238235	−	0.412635i	−0.960208	+	0.279286i	$0.909902\pi$
$348$	1.23205	−	2.13397i	0.0660449	−	0.114393i
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.0198610	+	0.999803i	$0.493678\pi$
$350$	3.60770			0.192839
$351$	2.59808	−	2.50000i	0.138675	−	0.133440i
$352$	4.73205			0.252219
$353$	17.1340	+	9.89230i	0.911949	+	0.526514i	0.881058	−	0.473008i	$-0.156832\pi$
$353$	17.1340	+	9.89230i	0.911949	+	0.526514i	0.0308916	+	0.999523i	$0.490165\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$	0.169873	+	0.294229i	0.00901592	+	0.0156160i
$356$			2.53590i			0.134402i
$357$	1.43782	−	0.830127i	0.0760976	−	0.0439350i
$358$	19.0981	−	11.0263i	1.00936	−	0.582757i
$359$			23.1244i			1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$359$			23.1244i			1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$360$	−0.133975	−	0.232051i	−0.00706108	−	0.0122302i
$361$	−8.69615	+	15.0622i	−0.457692	+	0.792746i
$362$	−7.62436	−	4.40192i	−0.400727	−	0.231360i
$363$	−11.3923			−0.597941
$364$	2.56218	−	0.633975i	0.134295	−	0.0332293i
$365$	−2.60770			−0.136493
$366$	1.03590	+	0.598076i	0.0541473	+	0.0312619i
$367$	7.36603	−	12.7583i	0.384503	−	0.665979i	−0.607197	−	0.794551i	$-0.707706\pi$
$367$	7.36603	−	12.7583i	0.384503	−	0.665979i	0.991700	+	0.128572i	$0.0410394\pi$
$368$	−3.09808	−	5.36603i	−0.161498	−	0.279723i
$369$		−	11.3923i		−	0.593060i
$370$	−2.42820	+	1.40192i	−0.126236	+	0.0728825i
$371$	0.294229	−	0.169873i	0.0152756	−	0.00881937i
$372$		−	5.46410i		−	0.283300i
$373$	5.13397	+	8.89230i	0.265827	+	0.460426i	0.967780	−	0.251797i	$-0.0810216\pi$
$373$	5.13397	+	8.89230i	0.265827	+	0.460426i	−0.701953	+	0.712223i	$0.747688\pi$
$374$	−5.36603	+	9.29423i	−0.277471	+	0.480593i
$375$	2.30385	+	1.33013i	0.118970	+	0.0686875i
$376$	8.19615			0.422684
$377$	2.13397	+	8.62436i	0.109905	+	0.444177i
$378$	0.732051			0.0376526
$379$	1.26795	+	0.732051i	0.0651302	+	0.0376029i	0.532211	−	0.846611i	$-0.321361\pi$
$379$	1.26795	+	0.732051i	0.0651302	+	0.0376029i	−0.467081	+	0.884214i	$0.654694\pi$
$380$	−0.169873	+	0.294229i	−0.00871430	+	0.0150936i
$381$	8.92820	+	15.4641i	0.457406	+	0.792250i
$382$		−	6.92820i		−	0.354478i
$383$	−4.73205	+	2.73205i	−0.241797	+	0.139601i	−0.616002	−	0.787744i	$-0.711249\pi$
$383$	−4.73205	+	2.73205i	−0.241797	+	0.139601i	0.374206	+	0.927346i	$0.377915\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$			0.928203i			0.0473056i
$386$	4.13397	+	7.16025i	0.210414	+	0.364447i
$387$	3.83013	−	6.63397i	0.194696	−	0.337224i
$388$	5.19615	+	3.00000i	0.263795	+	0.152302i
$389$	29.7846			1.51014			0.755070	−	0.655644i	$-0.227603\pi$
$389$	29.7846			1.51014			0.755070	+	0.655644i	$0.227603\pi$
$390$	0.928203	+	0.267949i	0.0470014	+	0.0135681i
$391$	14.0526			0.710668
$392$	−5.59808	−	3.23205i	−0.282746	−	0.163243i
$393$	−6.73205	+	11.6603i	−0.339587	+	0.588182i
$394$	4.92820	+	8.53590i	0.248279	+	0.430032i
$395$			2.53590i			0.127595i
$396$	−4.09808	+	2.36603i	−0.205936	+	0.118897i
$397$	−0.339746	+	0.196152i	−0.0170514	+	0.00984461i	−0.508501	−	0.861061i	$-0.669800\pi$
$397$	−0.339746	+	0.196152i	−0.0170514	+	0.00984461i	0.491450	+	0.870906i	$0.336467\pi$
$398$		−	3.80385i		−	0.190670i
$399$	−0.464102	−	0.803848i	−0.0232341	−	0.0402427i
$400$	−2.46410	+	4.26795i	−0.123205	+	0.213397i
$401$	−18.9904	−	10.9641i	−0.948334	−	0.547521i	−0.0557713	−	0.998444i	$-0.517762\pi$
$401$	−18.9904	−	10.9641i	−0.948334	−	0.547521i	−0.892563	+	0.450922i	$0.851095\pi$
$402$	11.1244			0.554832
$403$	13.6603	+	14.1962i	0.680466	+	0.707161i
$404$	−11.9282			−0.593450
$405$	0.232051	+	0.133975i	0.0115307	+	0.00665725i
$406$	−0.901924	+	1.56218i	−0.0447617	+	0.0775296i
$407$	24.7583	+	42.8827i	1.22722	+	2.12562i
$408$			2.26795i			0.112280i
$409$	−12.3564	+	7.13397i	−0.610985	+	0.352752i	−0.773351	−	0.633978i	$-0.781421\pi$
$409$	−12.3564	+	7.13397i	−0.610985	+	0.352752i	0.162366	+	0.986731i	$0.448088\pi$
$410$	2.64359	−	1.52628i	0.130558	−	0.0753776i
$411$		−	1.92820i		−	0.0951113i
$412$	9.36603	+	16.2224i	0.461431	+	0.799222i
$413$	2.92820	−	5.07180i	0.144087	−	0.249567i
$414$	5.36603	+	3.09808i	0.263726	+	0.152262i
$415$	−2.73205			−0.134111
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	−9.85641			−0.482670
$418$	5.19615	+	3.00000i	0.254152	+	0.146735i
$419$	5.26795	−	9.12436i	0.257356	−	0.445754i	−0.708177	−	0.706035i	$-0.750482\pi$
$419$	5.26795	−	9.12436i	0.257356	−	0.445754i	0.965533	+	0.260281i	$0.0838153\pi$
$420$	0.0980762	+	0.169873i	0.00478563	+	0.00828895i
$421$		−	32.7128i		−	1.59432i	−0.603765	−	0.797162i	$-0.706333\pi$
$421$		−	32.7128i		−	1.59432i	0.603765	−	0.797162i	$-0.293667\pi$
$422$	3.80385	−	2.19615i	0.185168	−	0.106907i
$423$	−7.09808	+	4.09808i	−0.345120	+	0.199255i
$424$			0.464102i			0.0225388i
$425$	−5.58846	−	9.67949i	−0.271080	−	0.469524i
$426$	0.633975	−	1.09808i	0.0307162	−	0.0532020i
$427$	−0.758330	−	0.437822i	−0.0366982	−	0.0211877i
$428$	0.196152			0.00948139
$429$	4.73205	−	16.3923i	0.228466	−	0.791428i
$430$	2.05256			0.0989832
$431$	−9.63397	−	5.56218i	−0.464052	−	0.267921i	0.249694	−	0.968325i	$-0.419670\pi$
$431$	−9.63397	−	5.56218i	−0.464052	−	0.267921i	−0.713747	+	0.700404i	$0.753003\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−7.42820	−	12.8660i	−0.356977	−	0.618302i	0.630478	−	0.776208i	$-0.282859\pi$
$433$	−7.42820	−	12.8660i	−0.356977	−	0.618302i	−0.987454	+	0.157906i	$0.949526\pi$
$434$			4.00000i			0.192006i
$435$	−0.571797	+	0.330127i	−0.0274156	+	0.0158284i
$436$	−4.73205	+	2.73205i	−0.226624	+	0.130842i
$437$		−	7.85641i		−	0.375823i
$438$	4.86603	+	8.42820i	0.232508	+	0.402715i
$439$	−8.83013	+	15.2942i	−0.421439	+	0.729954i	−0.996080	−	0.0884515i	$-0.971808\pi$
$439$	−8.83013	+	15.2942i	−0.421439	+	0.729954i	0.574642	+	0.818405i	$0.305141\pi$
$440$	−1.09808	−	0.633975i	−0.0523487	−	0.0302236i
$441$	6.46410			0.307814
$442$	−5.66987	−	5.89230i	−0.269688	−	0.280268i
$443$	36.3923			1.72905			0.864525	−	0.502589i	$-0.167619\pi$
$443$	36.3923			1.72905			0.864525	+	0.502589i	$0.167619\pi$
$444$	9.06218	+	5.23205i	0.430072	+	0.248302i
$445$	0.339746	−	0.588457i	0.0161055	−	0.0278955i
$446$	−6.53590	−	11.3205i	−0.309484	−	0.536042i
$447$		−	2.80385i		−	0.132617i
$448$	−0.633975	+	0.366025i	−0.0299525	+	0.0172931i
$449$	−20.1962	+	11.6603i	−0.953115	+	0.550281i	−0.894047	−	0.447973i	$-0.852146\pi$
$449$	−20.1962	+	11.6603i	−0.953115	+	0.550281i	−0.0590680	+	0.998254i	$0.518813\pi$
$450$		−	4.92820i		−	0.232318i
$451$	−26.9545	−	46.6865i	−1.26924	−	2.19838i
$452$	−9.33013	+	16.1603i	−0.438852	+	0.760114i
$453$	−2.83013	−	1.63397i	−0.132971	−	0.0767708i
$454$	1.80385			0.0846588
$455$	−0.679492	−	0.196152i	−0.0318551	−	0.00919577i
$456$	1.26795			0.0593772
$457$	16.1603	+	9.33013i	0.755945	+	0.436445i	0.827838	−	0.560967i	$-0.189571\pi$
$457$	16.1603	+	9.33013i	0.755945	+	0.436445i	−0.0718931	+	0.997412i	$0.522904\pi$
$458$	−7.92820	+	13.7321i	−0.370461	+	0.641657i
$459$	−1.13397	−	1.96410i	−0.0529294	−	0.0916764i
$460$			1.66025i			0.0774097i
$461$	−22.2846	+	12.8660i	−1.03790	+	0.599231i	−0.919237	−	0.393704i	$-0.871193\pi$
$461$	−22.2846	+	12.8660i	−1.03790	+	0.599231i	−0.118661	+	0.992935i	$0.537860\pi$
$462$	3.00000	−	1.73205i	0.139573	−	0.0805823i
$463$		−	28.0526i		−	1.30371i	−0.758342	−	0.651856i	$-0.773990\pi$
$463$		−	28.0526i		−	1.30371i	0.758342	−	0.651856i	$-0.226010\pi$
$464$	−1.23205	−	2.13397i	−0.0571965	−	0.0990673i
$465$	−0.732051	+	1.26795i	−0.0339480	+	0.0587997i
$466$	−17.1962	−	9.92820i	−0.796596	−	0.459915i
$467$	12.5885			0.582524			0.291262	−	0.956643i	$-0.405925\pi$
$467$	12.5885			0.582524			0.291262	+	0.956643i	$0.405925\pi$
$468$	−0.866025	−	3.50000i	−0.0400320	−	0.161788i
$469$	−8.14359			−0.376036
$470$	−1.90192	−	1.09808i	−0.0877292	−	0.0506505i
$471$	11.7942	−	20.4282i	0.543449	−	0.941282i
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$		−	36.2487i		−	1.66672i
$474$	8.19615	−	4.73205i	0.376462	−	0.217350i
$475$	−5.41154	+	3.12436i	−0.248299	+	0.143355i
$476$		−	1.66025i		−	0.0760976i
$477$	−0.232051	−	0.401924i	−0.0106249	−	0.0184028i
$478$	−4.83013	+	8.36603i	−0.220925	+	0.382653i
$479$	−22.9808	−	13.2679i	−1.05002	−	0.606228i	−0.127363	−	0.991856i	$-0.540651\pi$
$479$	−22.9808	−	13.2679i	−1.05002	−	0.606228i	−0.922654	+	0.385628i	$0.873985\pi$
$480$	−0.267949			−0.0122302
$481$	−36.6244	+	9.06218i	−1.66993	+	0.413200i
$482$	−17.5885			−0.801132
$483$	−3.92820	−	2.26795i	−0.178739	−	0.103195i
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	−0.803848	−	1.39230i	−0.0365008	−	0.0632213i
$486$		−	1.00000i		−	0.0453609i
$487$	−18.2942	+	10.5622i	−0.828991	+	0.478618i	−0.853507	−	0.521081i	$-0.825529\pi$
$487$	−18.2942	+	10.5622i	−0.828991	+	0.478618i	0.0245163	+	0.999699i	$0.492195\pi$
$488$	1.03590	−	0.598076i	0.0468929	−	0.0270736i
$489$		−	6.53590i		−	0.295564i
$490$	0.866025	+	1.50000i	0.0391230	+	0.0677631i
$491$	2.63397	−	4.56218i	0.118870	−	0.205888i	−0.800450	−	0.599399i	$-0.795406\pi$
$491$	2.63397	−	4.56218i	0.118870	−	0.205888i	0.919320	+	0.393511i	$0.128740\pi$
$492$	−9.86603	−	5.69615i	−0.444795	−	0.256802i
$493$	5.58846			0.251691
$494$	−3.29423	+	3.16987i	−0.148214	+	0.142619i
$495$	1.26795			0.0569901
$496$	−4.73205	−	2.73205i	−0.212475	−	0.122673i
$497$	−0.464102	+	0.803848i	−0.0208178	+	0.0360575i
$498$	5.09808	+	8.83013i	0.228450	+	0.395687i
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$	2.30385	−	1.33013i	0.103031	−	0.0594851i
$501$	−2.19615	+	1.26795i	−0.0981169	+	0.0566478i
$502$			6.53590i			0.291711i
$503$	5.49038	+	9.50962i	0.244804	+	0.424013i	0.962076	−	0.272780i	$-0.0879431\pi$
$503$	5.49038	+	9.50962i	0.244804	+	0.424013i	−0.717272	+	0.696793i	$0.754610\pi$
$504$	0.366025	−	0.633975i	0.0163041	−	0.0282395i
$505$	2.76795	+	1.59808i	0.123172	+	0.0711135i
$506$	29.3205			1.30346
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$	17.8564			0.792250
$509$	8.89230	+	5.13397i	0.394144	+	0.227559i	0.683954	−	0.729525i	$-0.260259\pi$
$509$	8.89230	+	5.13397i	0.394144	+	0.227559i	−0.289810	+	0.957084i	$0.593592\pi$
$510$	0.303848	−	0.526279i	0.0134546	−	0.0233040i
$511$	−3.56218	−	6.16987i	−0.157581	−	0.272939i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.09808	+	0.633975i	−0.0484812	+	0.0279907i
$514$	23.0885	−	13.3301i	1.01839	−	0.587967i
$515$		−	5.01924i		−	0.221174i
$516$	−3.83013	−	6.63397i	−0.168612	−	0.292044i
$517$	−19.3923	+	33.5885i	−0.852873	+	1.47722i
$518$	−6.63397	−	3.83013i	−0.291480	−	0.168286i
$519$	16.3923			0.719542
$520$	0.696152	−	0.669873i	0.0305283	−	0.0293759i
$521$	−17.4449			−0.764273			−0.382137	−	0.924106i	$-0.624812\pi$
$521$	−17.4449			−0.764273			−0.382137	+	0.924106i	$0.624812\pi$
$522$	2.13397	+	1.23205i	0.0934015	+	0.0539254i
$523$	−18.2224	+	31.5622i	−0.796811	+	1.38012i	0.124871	+	0.992173i	$0.460148\pi$
$523$	−18.2224	+	31.5622i	−0.796811	+	1.38012i	−0.921683	+	0.387945i	$0.873185\pi$
$524$	6.73205	+	11.6603i	0.294091	+	0.509381i
$525$			3.60770i			0.157453i
$526$	−24.2942	+	14.0263i	−1.05928	+	0.611575i
$527$	10.7321	−	6.19615i	0.467495	−	0.269909i
$528$			4.73205i			0.205936i
$529$	−7.69615	−	13.3301i	−0.334615	−	0.579571i
$530$	0.0621778	−	0.107695i	0.00270083	−	0.00467798i
$531$	−6.92820	−	4.00000i	−0.300658	−	0.173585i
$532$	−0.928203			−0.0402427
$533$	39.8731	−	9.86603i	1.72709	−	0.427345i
$534$	−2.53590			−0.109739
$535$	−0.0455173	−	0.0262794i	−0.00196789	−	0.00113616i
$536$	5.56218	−	9.63397i	0.240249	−	0.416124i
$537$	11.0263	+	19.0981i	0.475819	+	0.824143i
$538$			1.46410i			0.0631219i
$539$	26.4904	−	15.2942i	1.14102	−	0.658769i
$540$	0.232051	−	0.133975i	0.00998588	−	0.00576535i
$541$			40.3205i			1.73351i	0.498731	+	0.866757i	$0.333800\pi$
$541$			40.3205i			1.73351i	−0.498731	+	0.866757i	$0.666200\pi$
$542$	−2.92820	−	5.07180i	−0.125777	−	0.217852i
$543$	4.40192	−	7.62436i	0.188905	−	0.327192i
$544$	1.96410	+	1.13397i	0.0842102	+	0.0486188i
$545$	1.46410			0.0627152
$546$	0.633975	+	2.56218i	0.0271316	+	0.109651i
$547$	6.19615			0.264928			0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615			0.264928			0.132464	+	0.991188i	$0.457711\pi$
$548$	−1.66987	−	0.964102i	−0.0713334	−	0.0411844i
$549$	−0.598076	+	1.03590i	−0.0255253	+	0.0442111i
$550$	−11.6603	−	20.1962i	−0.497195	−	0.861167i
$551$		−	3.12436i		−	0.133102i
$552$	5.36603	−	3.09808i	0.228393	−	0.131863i
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$		−	2.26795i		−	0.0963559i
$555$	−1.40192	−	2.42820i	−0.0595084	−	0.103071i
$556$	−4.92820	+	8.53590i	−0.209002	+	0.362003i
$557$	26.3038	+	15.1865i	1.11453	+	0.643474i	0.939999	−	0.341178i	$-0.110826\pi$
$557$	26.3038	+	15.1865i	1.11453	+	0.643474i	0.174531	+	0.984652i	$0.444159\pi$
$558$	5.46410			0.231314
$559$	26.5359	+	7.66025i	1.12235	+	0.323994i
$560$	0.196152			0.00828895
$561$	−9.29423	−	5.36603i	−0.392403	−	0.226554i
$562$	11.1603	−	19.3301i	0.470767	−	0.815392i
$563$	10.5359	+	18.2487i	0.444035	+	0.769091i	0.997984	−	0.0634589i	$-0.0202132\pi$
$563$	10.5359	+	18.2487i	0.444035	+	0.769091i	−0.553949	+	0.832550i	$0.686880\pi$
$564$			8.19615i			0.345120i
$565$	4.33013	−	2.50000i	0.182170	−	0.105176i
$566$	7.22243	−	4.16987i	0.303581	−	0.175273i
$567$			0.732051i			0.0307432i
$568$	−0.633975	−	1.09808i	−0.0266010	−	0.0460743i
$569$	−19.3205	+	33.4641i	−0.809958	+	1.40289i	0.102935	+	0.994688i	$0.467177\pi$
$569$	−19.3205	+	33.4641i	−0.809958	+	1.40289i	−0.912893	+	0.408200i	$0.866157\pi$
$570$	−0.294229	−	0.169873i	−0.0123239	−	0.00711520i
$571$	24.0526			1.00657			0.503284	−	0.864121i	$-0.332125\pi$
$571$	24.0526			1.00657			0.503284	+	0.864121i	$0.332125\pi$
$572$	−11.8301	−	12.2942i	−0.494642	−	0.514048i
$573$	6.92820			0.289430
$574$	7.22243	+	4.16987i	0.301458	+	0.174047i
$575$	−15.2679	+	26.4449i	−0.636717	+	1.10283i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	0.267949i		−	0.0111549i	−0.999984	−	0.00557744i	$-0.998225\pi$
$577$		−	0.267949i		−	0.0111549i	0.999984	−	0.00557744i	$-0.00177536\pi$
$578$	10.2679	−	5.92820i	0.427090	−	0.246581i
$579$	−7.16025	+	4.13397i	−0.297570	+	0.171802i
$580$			0.660254i			0.0274156i
$581$	−3.73205	−	6.46410i	−0.154832	−	0.268176i
$582$	−3.00000	+	5.19615i	−0.124354	+	0.215387i
$583$	−1.90192	−	1.09808i	−0.0787696	−	0.0454777i
$584$	9.73205			0.402715
$585$	−0.267949	+	0.928203i	−0.0110783	+	0.0383765i
$586$	−14.5167			−0.599678
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	0.757914	−	0.652355i	$-0.226219\pi$
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	−0.185999	+	0.982550i	$0.559552\pi$
$588$	3.23205	−	5.59808i	0.133288	−	0.230861i
$589$	−3.46410	−	6.00000i	−0.142736	−	0.247226i
$590$		−	2.14359i		−	0.0882503i
$591$	−8.53590	+	4.92820i	−0.351120	+	0.202719i
$592$	9.06218	−	5.23205i	0.372453	−	0.215036i
$593$		−	36.8564i		−	1.51351i	−0.653698	−	0.756756i	$-0.726783\pi$
$593$		−	36.8564i		−	1.51351i	0.653698	−	0.756756i	$-0.273217\pi$
$594$	−2.36603	−	4.09808i	−0.0970792	−	0.168146i
$595$	−0.222432	+	0.385263i	−0.00911882	+	0.0157943i
$596$	−2.42820	−	1.40192i	−0.0994631	−	0.0574250i
$597$	3.80385			0.155681
$598$	−6.19615	+	21.4641i	−0.253380	+	0.877732i
$599$	−9.46410			−0.386693			−0.193346	−	0.981131i	$-0.561934\pi$
$599$	−9.46410			−0.386693			−0.193346	+	0.981131i	$0.561934\pi$
$600$	−4.26795	−	2.46410i	−0.174238	−	0.100597i
$601$	2.96410	−	5.13397i	0.120908	−	0.209419i	−0.799218	−	0.601041i	$-0.794753\pi$
$601$	2.96410	−	5.13397i	0.120908	−	0.209419i	0.920126	+	0.391622i	$0.128086\pi$
$602$	2.80385	+	4.85641i	0.114276	+	0.197932i
$603$			11.1244i			0.453019i
$604$	−2.83013	+	1.63397i	−0.115156	+	0.0664855i
$605$	2.64359	−	1.52628i	0.107477	−	0.0620521i
$606$		−	11.9282i		−	0.484550i
$607$	−0.392305	−	0.679492i	−0.0159232	−	0.0275797i	0.857954	−	0.513726i	$-0.171735\pi$
$607$	−0.392305	−	0.679492i	−0.0159232	−	0.0275797i	−0.873877	+	0.486147i	$0.838402\pi$
$608$	0.633975	−	1.09808i	0.0257111	−	0.0445329i
$609$	−1.56218	−	0.901924i	−0.0633026	−	0.0365478i
$610$	−0.320508			−0.0129770
$611$	−20.4904	−	21.2942i	−0.828952	−	0.861472i
$612$	−2.26795			−0.0916764
$613$	9.86603	+	5.69615i	0.398485	+	0.230065i	0.685830	−	0.727762i	$-0.259439\pi$
$613$	9.86603	+	5.69615i	0.398485	+	0.230065i	−0.287345	+	0.957827i	$0.592773\pi$
$614$	−4.29423	+	7.43782i	−0.173301	+	0.300166i
$615$	1.52628	+	2.64359i	0.0615455	+	0.106600i
$616$		−	3.46410i		−	0.139573i
$617$	−30.5263	+	17.6244i	−1.22894	+	0.709530i	−0.966809	−	0.255502i	$-0.917759\pi$
$617$	−30.5263	+	17.6244i	−1.22894	+	0.709530i	−0.262133	+	0.965032i	$0.584426\pi$
$618$	−16.2224	+	9.36603i	−0.652562	+	0.376757i
$619$			10.5359i			0.423474i	0.977327	+	0.211737i	$0.0679119\pi$
$619$			10.5359i			0.423474i	−0.977327	+	0.211737i	$0.932088\pi$
$620$	0.732051	+	1.26795i	0.0293999	+	0.0509221i
$621$	−3.09808	+	5.36603i	−0.124322	+	0.215331i
$622$	−13.5622	−	7.83013i	−0.543794	−	0.313959i
$623$	1.85641			0.0743754
$624$	−3.46410	−	1.00000i	−0.138675	−	0.0400320i
$625$	23.9282			0.957128
$626$	11.6603	+	6.73205i	0.466037	+	0.269067i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	−11.7942	−	20.4282i	−0.470641	−	0.815174i
$629$			23.7321i			0.946259i
$630$	−0.169873	+	0.0980762i	−0.00676790	+	0.00390745i
$631$	41.3205	−	23.8564i	1.64494	−	0.949709i	0.665904	−	0.746037i	$-0.268046\pi$
$631$	41.3205	−	23.8564i	1.64494	−	0.949709i	0.979039	−	0.203671i	$-0.0652874\pi$
$632$		−	9.46410i		−	0.376462i
$633$	2.19615	+	3.80385i	0.0872892	+	0.151189i
$634$	1.66987	−	2.89230i	0.0663191	−	0.114868i
$635$	−4.14359	−	2.39230i	−0.164433	−	0.0949357i
$636$	−0.464102			−0.0184028
$637$	5.59808	+	22.6244i	0.221804	+	0.896410i
$638$	11.6603			0.461634
$639$	1.09808	+	0.633975i	0.0434392	+	0.0250796i
$640$	−0.133975	+	0.232051i	−0.00529581	+	0.00917261i
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	0.999885	+	0.0151806i	$0.00483233\pi$
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	−0.486796	+	0.873516i	$0.661834\pi$
$642$			0.196152i			0.00774152i
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	−0.717592	−	0.696463i	$-0.754756\pi$
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	0.244359	+	0.969685i	$0.421423\pi$
$644$	−3.92820	+	2.26795i	−0.154793	+	0.0893697i
$645$			2.05256i			0.0808194i
$646$	1.43782	+	2.49038i	0.0565704	+	0.0979827i
$647$	13.1244	−	22.7321i	0.515972	−	0.893689i	−0.483856	−	0.875147i	$-0.660764\pi$
$647$	13.1244	−	22.7321i	0.515972	−	0.893689i	0.999828	−	0.0185417i	$-0.00590236\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−37.8564			−1.48599
$650$	17.2487	−	4.26795i	0.676550	−	0.167403i
$651$	−4.00000			−0.156772
$652$	−5.66025	−	3.26795i	−0.221673	−	0.127983i
$653$	5.26795	−	9.12436i	0.206151	−	0.357064i	−0.744348	−	0.667792i	$-0.767240\pi$
$653$	5.26795	−	9.12436i	0.206151	−	0.357064i	0.950499	+	0.310728i	$0.100573\pi$
$654$	−2.73205	−	4.73205i	−0.106832	−	0.185038i
$655$		−	3.60770i		−	0.140964i
$656$	−9.86603	+	5.69615i	−0.385204	+	0.222397i
$657$	−8.42820	+	4.86603i	−0.328816	+	0.189842i
$658$		−	6.00000i		−	0.233904i
$659$	−19.1244	−	33.1244i	−0.744979	−	1.29034i	−0.950205	−	0.311627i	$-0.899126\pi$
$659$	−19.1244	−	33.1244i	−0.744979	−	1.29034i	0.205225	−	0.978715i	$-0.434207\pi$
$660$	0.633975	−	1.09808i	0.0246774	−	0.0427426i
$661$	8.13397	+	4.69615i	0.316375	+	0.182659i	0.649776	−	0.760126i	$-0.274863\pi$
$661$	8.13397	+	4.69615i	0.316375	+	0.182659i	−0.333401	+	0.942785i	$0.608196\pi$
$662$	−20.0000			−0.777322
$663$	5.89230	−	5.66987i	0.228838	−	0.220200i
$664$	10.1962			0.395687
$665$	0.215390	+	0.124356i	0.00835248	+	0.00482231i
$666$	−5.23205	+	9.06218i	−0.202738	+	0.351152i
$667$	−7.63397	−	13.2224i	−0.295589	−	0.511975i
$668$			2.53590i			0.0981169i
$669$	11.3205	−	6.53590i	0.437676	−	0.252692i
$670$	−2.58142	+	1.49038i	−0.0997288	+	0.0575784i
$671$			5.66025i			0.218512i
$672$	−0.366025	−	0.633975i	−0.0141197	−	0.0244561i
$673$	7.03590	−	12.1865i	0.271214	−	0.469756i	−0.697959	−	0.716138i	$-0.745908\pi$
$673$	7.03590	−	12.1865i	0.271214	−	0.469756i	0.969173	+	0.246381i	$0.0792416\pi$
$674$	−5.93782	−	3.42820i	−0.228716	−	0.132049i
$675$	4.92820			0.189687
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	−38.5359			−1.48105			−0.740527	−	0.672026i	$-0.765424\pi$
$677$	−38.5359			−1.48105			−0.740527	+	0.672026i	$0.765424\pi$
$678$	−16.1603	−	9.33013i	−0.620631	−	0.358321i
$679$	2.19615	−	3.80385i	0.0842806	−	0.145978i
$680$	−0.303848	−	0.526279i	−0.0116520	−	0.0201819i
$681$			1.80385i			0.0691236i
$682$	22.3923	−	12.9282i	0.857446	−	0.495046i
$683$	−32.7846	+	18.9282i	−1.25447	+	0.724268i	−0.971994	−	0.235007i	$-0.924489\pi$
$683$	−32.7846	+	18.9282i	−1.25447	+	0.724268i	−0.282475	+	0.959275i	$0.591155\pi$
$684$			1.26795i			0.0484812i
$685$	0.258330	+	0.447441i	0.00987029	+	0.0170958i
$686$	−4.92820	+	8.53590i	−0.188160	+	0.325902i
$687$	−13.7321	−	7.92820i	−0.523910	−	0.302480i
$688$	−7.66025			−0.292044
$689$	1.20577	−	1.16025i	0.0459362	−	0.0442022i
$690$	−1.66025			−0.0632048
$691$	22.8109	+	13.1699i	0.867767	+	0.501006i	0.866606	−	0.498994i	$-0.166297\pi$
$691$	22.8109	+	13.1699i	0.867767	+	0.501006i	0.00116153	+	0.999999i	$0.499630\pi$
$692$	8.19615	−	14.1962i	0.311571	−	0.539657i
$693$	1.73205	+	3.00000i	0.0657952	+	0.113961i
$694$		−	8.87564i		−	0.336915i
$695$	2.28719	−	1.32051i	0.0867580	−	0.0500897i
$696$	2.13397	−	1.23205i	0.0808881	−	0.0467008i
$697$		−	25.8372i		−	0.978653i
$698$	9.66025	+	16.7321i	0.365646	+	0.633317i
$699$	9.92820	−	17.1962i	0.375519	−	0.650418i
$700$	3.12436	+	1.80385i	0.118090	+	0.0681790i
$701$	−31.3205			−1.18296			−0.591480	−	0.806320i	$-0.701456\pi$
$701$	−31.3205			−1.18296			−0.591480	+	0.806320i	$0.701456\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	13.2679			0.500410
$704$	4.09808	+	2.36603i	0.154452	+	0.0891729i
$705$	1.09808	−	1.90192i	0.0413559	−	0.0716306i
$706$	9.89230	+	17.1340i	0.372302	+	0.644846i
$707$			8.73205i			0.328403i
$708$	−6.92820	+	4.00000i	−0.260378	+	0.150329i
$709$	35.3827	−	20.4282i	1.32882	−	0.767197i	0.343707	−	0.939077i	$-0.388317\pi$
$709$	35.3827	−	20.4282i	1.32882	−	0.767197i	0.985118	+	0.171880i	$0.0549841\pi$
$710$			0.339746i			0.0127504i
$711$	4.73205	+	8.19615i	0.177466	+	0.307380i
$712$	−1.26795	+	2.19615i	−0.0475184	+	0.0823043i
$713$	−29.3205	−	16.9282i	−1.09806	−	0.633966i
$714$	1.66025			0.0621334
$715$	1.09808	+	4.43782i	0.0410657	+	0.165965i
$716$	22.0526			0.824143
$717$	−8.36603	−	4.83013i	−0.312435	−	0.180384i
$718$	−11.5622	+	20.0263i	−0.431497	+	0.747374i
$719$	−11.2679	−	19.5167i	−0.420224	−	0.727849i	0.575737	−	0.817635i	$-0.304715\pi$
$719$	−11.2679	−	19.5167i	−0.420224	−	0.727849i	−0.995961	+	0.0897860i	$0.971382\pi$
$720$		−	0.267949i		−	0.00998588i
$721$	11.8756	−	6.85641i	0.442272	−	0.255346i
$722$	−15.0622	+	8.69615i	−0.560556	+	0.323637i
$723$		−	17.5885i		−	0.654122i
$724$	−4.40192	−	7.62436i	−0.163596	−	0.283357i
$725$	−6.07180	+	10.5167i	−0.225501	+	0.390579i
$726$	−9.86603	−	5.69615i	−0.366163	−	0.211404i
$727$	−20.9808			−0.778133			−0.389067	−	0.921210i	$-0.627202\pi$
$727$	−20.9808			−0.778133			−0.389067	+	0.921210i	$0.627202\pi$
$728$	2.53590	+	0.732051i	0.0939866	+	0.0271316i
$729$	1.00000			0.0370370
$730$	−2.25833	−	1.30385i	−0.0835846	−	0.0482576i
$731$	8.68653	−	15.0455i	0.321283	−	0.556479i
$732$	0.598076	+	1.03590i	0.0221055	+	0.0382879i
$733$		−	19.0000i		−	0.701781i	−0.936416	−	0.350891i	$-0.885879\pi$
$733$		−	19.0000i		−	0.701781i	0.936416	−	0.350891i	$-0.114121\pi$
$734$	12.7583	−	7.36603i	0.470919	−	0.271885i
$735$	−1.50000	+	0.866025i	−0.0553283	+	0.0319438i
$736$		−	6.19615i		−	0.228393i
$737$	26.3205	+	45.5885i	0.969528	+	1.67927i
$738$	5.69615	−	9.86603i	0.209678	−	0.363173i
$739$	9.46410	+	5.46410i	0.348143	+	0.201000i	0.663867	−	0.747851i	$-0.268914\pi$
$739$	9.46410	+	5.46410i	0.348143	+	0.201000i	−0.315724	+	0.948851i	$0.602247\pi$
$740$	−2.80385			−0.103071
$741$	−3.16987	−	3.29423i	−0.116448	−	0.121017i
$742$	0.339746			0.0124725
$743$	−23.9090	−	13.8038i	−0.877135	−	0.506414i	−0.00742221	−	0.999972i	$-0.502363\pi$
$743$	−23.9090	−	13.8038i	−0.877135	−	0.506414i	−0.869713	+	0.493558i	$0.835696\pi$
$744$	2.73205	−	4.73205i	0.100162	−	0.173485i
$745$	0.375644	+	0.650635i	0.0137625	+	0.0238374i
$746$			10.2679i			0.375936i
$747$	−8.83013	+	5.09808i	−0.323077	+	0.186529i
$748$	−9.29423	+	5.36603i	−0.339831	+	0.196201i
$749$		−	0.143594i		−	0.00524679i
$750$	1.33013	+	2.30385i	0.0485694	+	0.0841246i
$751$	7.95448	−	13.7776i	0.290263	−	0.502751i	−0.683609	−	0.729849i	$-0.739590\pi$
$751$	7.95448	−	13.7776i	0.290263	−	0.502751i	0.973872	+	0.227098i	$0.0729238\pi$
$752$	7.09808	+	4.09808i	0.258840	+	0.149441i
$753$	−6.53590			−0.238181
$754$	−2.46410	+	8.53590i	−0.0897373	+	0.310859i
$755$	0.875644			0.0318680
$756$	0.633975	+	0.366025i	0.0230574	+	0.0133122i
$757$	−3.53590	+	6.12436i	−0.128514	+	0.222593i	−0.923101	−	0.384557i	$-0.874354\pi$
$757$	−3.53590	+	6.12436i	−0.128514	+	0.222593i	0.794587	+	0.607151i	$0.207688\pi$
$758$	0.732051	+	1.26795i	0.0265893	+	0.0460540i
$759$			29.3205i			1.06427i
$760$	−0.294229	+	0.169873i	−0.0106728	+	0.00616194i
$761$	−20.1962	+	11.6603i	−0.732110	+	0.422684i	−0.819194	−	0.573517i	$-0.805579\pi$
$761$	−20.1962	+	11.6603i	−0.732110	+	0.422684i	0.0870836	+	0.996201i	$0.472245\pi$
$762$			17.8564i			0.646869i
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	3.46410	−	6.00000i	0.125327	−	0.217072i
$765$	0.526279	+	0.303848i	0.0190277	+	0.0109856i
$766$	−5.46410			−0.197426
$767$	8.00000	−	27.7128i	0.288863	−	1.00065i
$768$	1.00000			0.0360844
$769$	−13.9808	−	8.07180i	−0.504159	−	0.291076i	0.226270	−	0.974065i	$-0.427347\pi$
$769$	−13.9808	−	8.07180i	−0.504159	−	0.291076i	−0.730429	+	0.682988i	$0.760680\pi$
$770$	−0.464102	+	0.803848i	−0.0167251	+	0.0289687i
$771$	13.3301	+	23.0885i	0.480073	+	0.831510i
$772$			8.26795i			0.297570i
$773$	30.3731	−	17.5359i	1.09244	−	0.630722i	0.158217	−	0.987404i	$-0.449425\pi$
$773$	30.3731	−	17.5359i	1.09244	−	0.630722i	0.934226	+	0.356682i	$0.116092\pi$
$774$	6.63397	−	3.83013i	0.238453	−	0.137671i
$775$			26.9282i			0.967290i
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	3.83013	−	6.63397i	0.137405	−	0.237993i
$778$	25.7942	+	14.8923i	0.924768	+	0.533915i
$779$	−14.4449			−0.517541
$780$	0.669873	+	0.696152i	0.0239853	+	0.0249263i
$781$	6.00000			0.214697
$782$	12.1699	+	7.02628i	0.435194	+	0.251259i
$783$	−1.23205	+	2.13397i	−0.0440299	+	0.0762620i
$784$	−3.23205	−	5.59808i	−0.115430	−	0.199931i
$785$			6.32051i			0.225589i
$786$	−11.6603	+	6.73205i	−0.415907	+	0.240124i
$787$	34.0526	−	19.6603i	1.21384	−	0.700812i	0.250248	−	0.968182i	$-0.419488\pi$
$787$	34.0526	−	19.6603i	1.21384	−	0.700812i	0.963594	+	0.267369i	$0.0861544\pi$
$788$			9.85641i			0.351120i
$789$	−14.0263	−	24.2942i	−0.499349	−	0.864897i
$790$	−1.26795	+	2.19615i	−0.0451116	+	0.0781356i
$791$	11.8301	+	6.83013i	0.420631	+	0.242851i
$792$	−4.73205			−0.168146
$793$	−4.14359	−	1.19615i	−0.147143	−	0.0424766i
$794$	−0.392305			−0.0139224
$795$	0.107695	+	0.0621778i	0.00381955	+	0.00220522i
$796$	1.90192	−	3.29423i	0.0674119	−	0.116761i
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	−0.992492	−	0.122312i	$-0.960969\pi$
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	0.390321	−	0.920679i	$-0.372364\pi$
$798$		−	0.928203i		−	0.0328580i
$799$	−16.0981	+	9.29423i	−0.569509	+	0.328806i
$800$	−4.26795	+	2.46410i	−0.150895	+	0.0871191i
$801$		−	2.53590i		−	0.0896016i
$802$	−10.9641	−	18.9904i	−0.387156	−	0.670574i
$803$	−23.0263	+	39.8827i	−0.812580	+	1.40743i
$804$	9.63397	+	5.56218i	0.339764	+	0.196163i
$805$	1.21539			0.0428369
$806$	4.73205	+	19.1244i	0.166679	+	0.673627i
$807$	−1.46410			−0.0515388
$808$	−10.3301	−	5.96410i	−0.363413	−	0.209816i
$809$	11.2058	−	19.4090i	0.393974	−	0.682383i	−0.598996	−	0.800752i	$-0.704433\pi$
$809$	11.2058	−	19.4090i	0.393974	−	0.682383i	0.992970	+	0.118369i	$0.0377667\pi$
$810$	0.133975	+	0.232051i	0.00470739	+	0.00815343i
$811$			45.1769i			1.58638i	0.608977	+	0.793188i	$0.291580\pi$
$811$			45.1769i			1.58638i	−0.608977	+	0.793188i	$0.708420\pi$
$812$	−1.56218	+	0.901924i	−0.0548217	+	0.0316513i
$813$	5.07180	−	2.92820i	0.177876	−	0.102697i
$814$			49.5167i			1.73556i
$815$	0.875644	+	1.51666i	0.0306725	+	0.0531263i
$816$	−1.13397	+	1.96410i	−0.0396971	+	0.0687573i
$817$	−8.41154	−	4.85641i	−0.294283	−	0.169904i
$818$	−14.2679			−0.498867
$819$	−2.56218	+	0.633975i	−0.0895297	+	0.0221529i
$820$	3.05256			0.106600
$821$	11.1962	+	6.46410i	0.390748	+	0.225599i	0.682484	−	0.730900i	$-0.260900\pi$
$821$	11.1962	+	6.46410i	0.390748	+	0.225599i	−0.291736	+	0.956499i	$0.594233\pi$
$822$	0.964102	−	1.66987i	0.0336269	−	0.0582435i
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	−0.959177	−	0.282806i	$-0.908735\pi$
$823$	−20.7846	−	36.0000i	−0.724506	−	1.25488i	0.234671	−	0.972075i	$-0.424599\pi$
$824$			18.7321i			0.652562i
$825$	20.1962	−	11.6603i	0.703140	−	0.405958i
$826$	5.07180	−	2.92820i	0.176470	−	0.101885i
$827$			33.4641i			1.16366i	0.813310	+	0.581830i	$0.197663\pi$
$827$			33.4641i			1.16366i	−0.813310	+	0.581830i	$0.802337\pi$
$828$	3.09808	+	5.36603i	0.107666	+	0.186482i
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	−0.741338	−	0.671132i	$-0.765808\pi$
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	0.951886	+	0.306452i	$0.0991418\pi$
$830$	−2.36603	−	1.36603i	−0.0821259	−	0.0474154i
$831$	2.26795			0.0786743
$832$	−2.59808	+	2.50000i	−0.0900721	+	0.0866719i
$833$	14.6603			0.507948
$834$	−8.53590	−	4.92820i	−0.295574	−	0.170650i
$835$	0.339746	−	0.588457i	0.0117574	−	0.0203644i
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$			5.46410i			0.188867i
$838$	9.12436	−	5.26795i	0.315196	−	0.181978i
$839$	12.2487	−	7.07180i	0.422872	−	0.244146i	−0.273433	−	0.961891i	$-0.588159\pi$
$839$	12.2487	−	7.07180i	0.422872	−	0.244146i	0.696306	+	0.717745i	$0.254826\pi$
$840$			0.196152i			0.00676790i
$841$	11.4641	+	19.8564i	0.395314	+	0.684704i
$842$	16.3564	−	28.3301i	0.563679	−	0.976321i
$843$	19.3301	+	11.1603i	0.665765	+	0.384380i
$844$	4.39230			0.151189
$845$	−3.48076	−	0.133975i	−0.119742	−	0.00460887i
$846$	−8.19615			−0.281790
$847$	7.22243	+	4.16987i	0.248166	+	0.143279i
$848$	−0.232051	+	0.401924i	−0.00796866	+	0.0138021i
$849$	4.16987	+	7.22243i	0.143110	+	0.247873i
$850$		−	11.1769i		−	0.383365i
$851$	56.1506	−	32.4186i	1.92482	−	1.11129i
$852$	1.09808	−	0.633975i	0.0376195	−	0.0217196i
$853$			8.17691i			0.279972i	0.990153	+	0.139986i	$0.0447058\pi$
$853$			8.17691i			0.279972i	−0.990153	+	0.139986i	$0.955294\pi$
$854$	−0.437822	−	0.758330i	−0.0149820	−	0.0259495i
$855$	0.169873	−	0.294229i	0.00580953	−	0.0100624i
$856$	0.169873	+	0.0980762i	0.00580614	+	0.00335218i
$857$	19.4449			0.664224			0.332112	−	0.943240i	$-0.392239\pi$
$857$	19.4449			0.664224			0.332112	+	0.943240i	$0.392239\pi$
$858$	12.2942	−	11.8301i	0.419718	−	0.403874i
$859$	−22.8756			−0.780507			−0.390253	−	0.920707i	$-0.627613\pi$
$859$	−22.8756			−0.780507			−0.390253	+	0.920707i	$0.627613\pi$
$860$	1.77757	+	1.02628i	0.0606146	+	0.0349958i
$861$	−4.16987	+	7.22243i	−0.142109	+	0.246140i
$862$	−5.56218	−	9.63397i	−0.189449	−	0.328134i
$863$		−	7.12436i		−	0.242516i	−0.992621	−	0.121258i	$-0.961307\pi$
$863$		−	7.12436i		−	0.242516i	0.992621	−	0.121258i	$-0.0386928\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−3.80385	+	2.19615i	−0.129335	+	0.0746714i
$866$		−	14.8564i		−	0.504841i
$867$	5.92820	+	10.2679i	0.201332	+	0.348718i
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	38.7846	+	22.3923i	1.31568	+	0.759607i
$870$	−0.660254			−0.0223847
$871$	−38.9352	+	9.63397i	−1.31927	+	0.326435i
$872$	−5.46410			−0.185038
$873$	−5.19615	−	3.00000i	−0.175863	−	0.101535i
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$	−0.973721	−	1.68653i	−0.0329178	−	0.0570152i
$876$			9.73205i			0.328816i
$877$	−8.72243	+	5.03590i	−0.294536	+	0.170050i	−0.639985	−	0.768387i	$-0.721060\pi$
$877$	−8.72243	+	5.03590i	−0.294536	+	0.170050i	0.345450	+	0.938437i	$0.387726\pi$
$878$	−15.2942	+	8.83013i	−0.516155	+	0.298002i
$879$		−	14.5167i		−	0.489635i
$880$	−0.633975	−	1.09808i	−0.0213713	−	0.0370161i
$881$	25.9186	−	44.8923i	0.873219	−	1.51246i	0.0145717	−	0.999894i	$-0.495362\pi$
$881$	25.9186	−	44.8923i	0.873219	−	1.51246i	0.858648	−	0.512566i	$-0.171305\pi$
$882$	5.59808	+	3.23205i	0.188497	+	0.108829i
$883$	−29.0718			−0.978344			−0.489172	−	0.872187i	$-0.662701\pi$
$883$	−29.0718			−0.978344			−0.489172	+	0.872187i	$0.662701\pi$
$884$	−1.96410	−	7.93782i	−0.0660599	−	0.266978i
$885$	2.14359			0.0720561
$886$	31.5167	+	18.1962i	1.05882	+	0.611312i
$887$	−5.07180	+	8.78461i	−0.170294	+	0.294958i	−0.938523	−	0.345217i	$-0.887805\pi$
$887$	−5.07180	+	8.78461i	−0.170294	+	0.294958i	0.768228	+	0.640176i	$0.221138\pi$
$888$	5.23205	+	9.06218i	0.175576	+	0.304107i
$889$		−	13.0718i		−	0.438414i
$890$	0.588457	−	0.339746i	0.0197251	−	0.0113883i
$891$	4.09808	−	2.36603i	0.137291	−	0.0792648i
$892$		−	13.0718i		−	0.437676i
$893$	5.19615	+	9.00000i	0.173883	+	0.301174i
$894$	1.40192	−	2.42820i	0.0468873	−	0.0812113i
$895$	−5.11731	−	2.95448i	−0.171053	−	0.0987575i
$896$	−0.732051			−0.0244561
$897$	−21.4641	−	6.19615i	−0.716665	−	0.206884i
$898$	−23.3205			−0.778215
$899$	−11.6603	−	6.73205i	−0.388891	−	0.224526i
$900$	2.46410	−	4.26795i	0.0821367	−	0.142265i
$901$	−0.526279	−	0.911543i	−0.0175329	−	0.0303679i
$902$		−	53.9090i		−	1.79497i
$903$	−4.85641	+	2.80385i	−0.161611	+	0.0933062i
$904$	−16.1603	+	9.33013i	−0.537482	+	0.310315i
$905$			2.35898i			0.0784153i
$906$	−1.63397	−	2.83013i	−0.0542852	−	0.0940247i
$907$	7.80385	−	13.5167i	0.259123	−	0.448813i	−0.706885	−	0.707329i	$-0.749900\pi$
$907$	7.80385	−	13.5167i	0.259123	−	0.448813i	0.966007	+	0.258516i	$0.0832333\pi$
$908$	1.56218	+	0.901924i	0.0518427	+	0.0299314i
$909$	11.9282			0.395634
$910$	−0.490381	−	0.509619i	−0.0162560	−	0.0168937i
$911$	−9.46410			−0.313560			−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410			−0.313560			−0.156780	+	0.987634i	$0.550111\pi$
$912$	1.09808	+	0.633975i	0.0363609	+	0.0209930i
$913$	−24.1244	+	41.7846i	−0.798400	+	1.38287i
$914$	9.33013	+	16.1603i	0.308613	+	0.534534i
$915$		−	0.320508i		−	0.0105957i
$916$	−13.7321	+	7.92820i	−0.453720	+	0.261955i
$917$	8.53590	−	4.92820i	0.281880	−	0.162744i
$918$		−	2.26795i		−	0.0748535i
$919$	28.9808	+	50.1962i	0.955987	+	1.65582i	0.732093	+	0.681205i	$0.238544\pi$
$919$	28.9808	+	50.1962i	0.955987	+	1.65582i	0.223894	+	0.974613i	$0.428123\pi$
$920$	−0.830127	+	1.43782i	−0.0273685	+	0.0474036i
$921$	−7.43782	−	4.29423i	−0.245085	−	0.141500i
$922$	−25.7321			−0.847440
$923$	−1.26795	+	4.39230i	−0.0417351	+	0.144574i
$924$	3.46410			0.113961
$925$	−44.6603	−	25.7846i	−1.46842	−	0.847793i
$926$	14.0263	−	24.2942i	0.460932	−	0.798358i
$927$	−9.36603	−	16.2224i	−0.307621	−	0.532815i
$928$		−	2.46410i		−	0.0808881i
$929$	−8.00962	+	4.62436i	−0.262787	+	0.151720i	−0.625605	−	0.780140i	$-0.715148\pi$
$929$	−8.00962	+	4.62436i	−0.262787	+	0.151720i	0.362818	+	0.931860i	$0.381815\pi$
$930$	−1.26795	+	0.732051i	−0.0415777	+	0.0240049i
$931$		−	8.19615i		−	0.268618i
$932$	−9.92820	−	17.1962i	−0.325209	−	0.563279i
$933$	7.83013	−	13.5622i	0.256347	−	0.444006i
$934$	10.9019	+	6.29423i	0.356722	+	0.205953i
$935$	2.87564			0.0940436
$936$	1.00000	−	3.46410i	0.0326860	−	0.113228i
$937$	43.2487			1.41287			0.706437	−	0.707776i	$-0.250301\pi$
$937$	43.2487			1.41287			0.706437	+	0.707776i	$0.250301\pi$
$938$	−7.05256	−	4.07180i	−0.230274	−	0.132949i
$939$	−6.73205	+	11.6603i	−0.219692	+	0.380518i
$940$	−1.09808	−	1.90192i	−0.0358153	−	0.0620339i
$941$			56.6410i			1.84644i	0.384267	+	0.923222i	$0.374454\pi$
$941$			56.6410i			1.84644i	−0.384267	+	0.923222i	$0.625546\pi$
$942$	20.4282	−	11.7942i	0.665587	−	0.384277i
$943$	−61.1314	+	35.2942i	−1.99071	+	1.14934i
$944$			8.00000i			0.260378i
$945$	−0.0980762	−	0.169873i	−0.00319042	−	0.00552597i
$946$	18.1244	−	31.3923i	0.589274	−	1.02065i
$947$	−30.2487	−	17.4641i	−0.982951	−	0.567507i	−0.0797913	−	0.996812i	$-0.525425\pi$
$947$	−30.2487	−	17.4641i	−0.982951	−	0.567507i	−0.903160	+	0.429305i	$0.858759\pi$
$948$	9.46410			0.307380
$949$	−24.3301	−	25.2846i	−0.789789	−	0.820773i
$950$	−6.24871			−0.202735
$951$	2.89230	+	1.66987i	0.0937894	+	0.0541493i
$952$	0.830127	−	1.43782i	0.0269046	−	0.0466001i
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	−0.976969	−	0.213383i	$-0.931552\pi$
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	0.303689	−	0.952771i	$-0.401782\pi$
$954$		−	0.464102i		−	0.0150258i
$955$	−1.60770	+	0.928203i	−0.0520238	+	0.0300360i
$956$	−8.36603	+	4.83013i	−0.270577	+	0.156217i
$957$			11.6603i			0.376922i
$958$	−13.2679	−	22.9808i	−0.428668	−	0.742475i
$959$	−0.705771	+	1.22243i	−0.0227905	+	0.0394744i
$960$	−0.232051	−	0.133975i	−0.00748941	−	0.00432401i
$961$	1.14359			0.0368901
$962$	−36.2487	−	10.4641i	−1.16871	−	0.337376i
$963$	−0.196152			−0.00632092
$964$	−15.2321	−	8.79423i	−0.490591	−	0.283243i
$965$	1.10770	−	1.91858i	0.0356580	−	0.0617614i
$966$	−2.26795	−	3.92820i	−0.0729701	−	0.126388i
$967$			18.8756i			0.607000i	0.952831	+	0.303500i	$0.0981552\pi$
$967$			18.8756i			0.607000i	−0.952831	+	0.303500i	$0.901845\pi$
$968$	−9.86603	+	5.69615i	−0.317106	+	0.183081i
$969$	−2.49038	+	1.43782i	−0.0800026	+	0.0461895i
$970$		−	1.60770i		−	0.0516200i
$971$	9.12436	+	15.8038i	0.292815	+	0.507170i	0.974474	−	0.224500i	$-0.0720748\pi$
$971$	9.12436	+	15.8038i	0.292815	+	0.507170i	−0.681660	+	0.731669i	$0.738741\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	6.24871	+	3.60770i	0.200324	+	0.115657i
$974$	−21.1244			−0.676868
$975$	4.26795	+	17.2487i	0.136684	+	0.552401i
$976$	1.19615			0.0382879
$977$	27.7750	+	16.0359i	0.888601	+	0.513034i	0.873485	−	0.486852i	$-0.161855\pi$
$977$	27.7750	+	16.0359i	0.888601	+	0.513034i	0.0151161	+	0.999886i	$0.495188\pi$
$978$	3.26795	−	5.66025i	0.104497	−	0.180995i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$			1.73205i			0.0553283i
$981$	4.73205	−	2.73205i	0.151083	−	0.0872277i
$982$	4.56218	−	2.63397i	0.145585	−	0.0840535i
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$	−5.69615	−	9.86603i	−0.181587	−	0.314517i
$985$	1.32051	−	2.28719i	0.0420749	−	0.0728758i
$986$	4.83975	+	2.79423i	0.154129	+	0.0889864i
$987$	6.00000			0.190982
$988$	−4.43782	+	1.09808i	−0.141186	+	0.0349345i
$989$	−47.4641			−1.50927
$990$	1.09808	+	0.633975i	0.0348992	+	0.0201490i
$991$	4.29423	−	7.43782i	0.136411	−	0.236270i	−0.789725	−	0.613461i	$-0.789777\pi$
$991$	4.29423	−	7.43782i	0.136411	−	0.236270i	0.926135	+	0.377191i	$0.123110\pi$
$992$	−2.73205	−	4.73205i	−0.0867427	−	0.150243i
$993$		−	20.0000i		−	0.634681i
$994$	−0.803848	+	0.464102i	−0.0254965	+	0.0147204i
$995$	−0.882686	+	0.509619i	−0.0279830	+	0.0161560i
$996$			10.1962i			0.323077i
$997$	−19.3301	−	33.4808i	−0.612191	−	1.06035i	−0.990870	−	0.134818i	$-0.956955\pi$
$997$	−19.3301	−	33.4808i	−0.612191	−	1.06035i	0.378679	−	0.925528i	$-0.376378\pi$
$998$	16.0000	−	27.7128i	0.506471	−	0.877234i
$999$	−9.06218	−	5.23205i	−0.286715	−	0.165535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.i.a.43.2	✓	4
3.2	odd	2		234.2.l.c.199.1		4
4.3	odd	2		624.2.bv.e.433.1		4
5.2	odd	4		1950.2.y.b.199.2		4
5.3	odd	4		1950.2.y.g.199.1		4
5.4	even	2		1950.2.bc.d.901.1		4
12.11	even	2		1872.2.by.h.433.2		4
13.2	odd	12		1014.2.e.i.991.2		4
13.3	even	3		1014.2.i.a.361.1		4
13.4	even	6		1014.2.b.e.337.3		4
13.5	odd	4		1014.2.e.i.529.2		4
13.6	odd	12		1014.2.a.i.1.2		2
13.7	odd	12		1014.2.a.k.1.1		2
13.8	odd	4		1014.2.e.g.529.1		4
13.9	even	3		1014.2.b.e.337.2		4
13.10	even	6	inner	78.2.i.a.49.2	yes	4
13.11	odd	12		1014.2.e.g.991.1		4
13.12	even	2		1014.2.i.a.823.1		4
39.17	odd	6		3042.2.b.i.1351.2		4
39.20	even	12		3042.2.a.p.1.2		2
39.23	odd	6		234.2.l.c.127.1		4
39.32	even	12		3042.2.a.y.1.1		2
39.35	odd	6		3042.2.b.i.1351.3		4
52.7	even	12		8112.2.a.bp.1.1		2
52.19	even	12		8112.2.a.bj.1.2		2
52.23	odd	6		624.2.bv.e.49.2		4
65.23	odd	12		1950.2.y.b.49.2		4
65.49	even	6		1950.2.bc.d.751.1		4
65.62	odd	12		1950.2.y.g.49.1		4
156.23	even	6		1872.2.by.h.1297.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	1.1	even	1	trivial
78.2.i.a.49.2	yes	4	13.10	even	6	inner
234.2.l.c.127.1		4	39.23	odd	6
234.2.l.c.199.1		4	3.2	odd	2
624.2.bv.e.49.2		4	52.23	odd	6
624.2.bv.e.433.1		4	4.3	odd	2
1014.2.a.i.1.2		2	13.6	odd	12
1014.2.a.k.1.1		2	13.7	odd	12
1014.2.b.e.337.2		4	13.9	even	3
1014.2.b.e.337.3		4	13.4	even	6
1014.2.e.g.529.1		4	13.8	odd	4
1014.2.e.g.991.1		4	13.11	odd	12
1014.2.e.i.529.2		4	13.5	odd	4
1014.2.e.i.991.2		4	13.2	odd	12
1014.2.i.a.361.1		4	13.3	even	3
1014.2.i.a.823.1		4	13.12	even	2
1872.2.by.h.433.2		4	12.11	even	2
1872.2.by.h.1297.1		4	156.23	even	6
1950.2.y.b.49.2		4	65.23	odd	12
1950.2.y.b.199.2		4	5.2	odd	4
1950.2.y.g.49.1		4	65.62	odd	12
1950.2.y.g.199.1		4	5.3	odd	4
1950.2.bc.d.751.1		4	65.49	even	6
1950.2.bc.d.901.1		4	5.4	even	2
3042.2.a.p.1.2		2	39.20	even	12
3042.2.a.y.1.1		2	39.32	even	12
3042.2.b.i.1351.2		4	39.17	odd	6
3042.2.b.i.1351.3		4	39.35	odd	6
8112.2.a.bj.1.2		2	52.19	even	12
8112.2.a.bp.1.1		2	52.7	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.267949i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.267949i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.633975 - 0.366025i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.133975 - 0.232051i) q^{10} +(-4.09808 - 2.36603i) q^{11} -1.00000 q^{12} +(2.59808 - 2.50000i) q^{13} +0.732051 q^{14} +(0.232051 + 0.133975i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.13397 - 1.96410i) q^{17} -1.00000i q^{18} +(-1.09808 + 0.633975i) q^{19} +(0.232051 - 0.133975i) q^{20} +0.732051i q^{21} +(-2.36603 - 4.09808i) q^{22} +(-3.09808 + 5.36603i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.92820 q^{25} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(0.633975 + 0.366025i) q^{28} +(-1.23205 + 2.13397i) q^{29} +(0.133975 + 0.232051i) q^{30} +5.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.09808 - 2.36603i) q^{33} -2.26795i q^{34} +(-0.0980762 - 0.169873i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-9.06218 - 5.23205i) q^{37} -1.26795 q^{38} +(0.866025 + 3.50000i) q^{39} +0.267949 q^{40} +(9.86603 + 5.69615i) q^{41} +(-0.366025 + 0.633975i) q^{42} +(3.83013 + 6.63397i) q^{43} -4.73205i q^{44} +(-0.232051 + 0.133975i) q^{45} +(-5.36603 + 3.09808i) q^{46} -8.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(4.26795 + 2.46410i) q^{50} +2.26795 q^{51} +(3.46410 + 1.00000i) q^{52} +0.464102 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.633975 + 1.09808i) q^{55} +(0.366025 + 0.633975i) q^{56} -1.26795i q^{57} +(-2.13397 + 1.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +0.267949i q^{60} +(-0.598076 - 1.03590i) q^{61} +(-2.73205 + 4.73205i) q^{62} +(-0.633975 - 0.366025i) q^{63} -1.00000 q^{64} +(-0.669873 - 0.696152i) q^{65} +4.73205 q^{66} +(-9.63397 - 5.56218i) q^{67} +(1.13397 - 1.96410i) q^{68} +(-3.09808 - 5.36603i) q^{69} -0.196152i q^{70} +(-1.09808 + 0.633975i) q^{71} +(0.866025 - 0.500000i) q^{72} -9.73205i q^{73} +(-5.23205 - 9.06218i) q^{74} +(-2.46410 + 4.26795i) q^{75} +(-1.09808 - 0.633975i) q^{76} -3.46410 q^{77} +(-1.00000 + 3.46410i) q^{78} -9.46410 q^{79} +(0.232051 + 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.69615 + 9.86603i) q^{82} -10.1962i q^{83} +(-0.633975 + 0.366025i) q^{84} +(-0.526279 + 0.303848i) q^{85} +7.66025i q^{86} +(-1.23205 - 2.13397i) q^{87} +(2.36603 - 4.09808i) q^{88} +(2.19615 + 1.26795i) q^{89} -0.267949 q^{90} +(0.732051 - 2.53590i) q^{91} -6.19615 q^{92} +(-4.73205 - 2.73205i) q^{93} +(4.09808 - 7.09808i) q^{94} +(0.169873 + 0.294229i) q^{95} -1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(-5.59808 + 3.23205i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 14 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + 4 q^{30} + 6 q^{33} + 10 q^{35} + 2 q^{36} - 12 q^{37} - 12 q^{38} + 8 q^{40} + 36 q^{41} + 2 q^{42} - 2 q^{43} + 6 q^{45} - 18 q^{46} - 2 q^{48} - 6 q^{49} + 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 8 q^{61} - 4 q^{62} - 6 q^{63} - 4 q^{64} - 20 q^{65} + 12 q^{66} - 42 q^{67} + 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 24 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 6 q^{84} + 36 q^{85} + 2 q^{87} + 6 q^{88} - 12 q^{89} - 8 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 4 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 2 * q^23 - 8 * q^25 + 14 * q^26 + 4 * q^27 + 6 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^33 + 10 * q^35 + 2 * q^36 - 12 * q^37 - 12 * q^38 + 8 * q^40 + 36 * q^41 + 2 * q^42 - 2 * q^43 + 6 * q^45 - 18 * q^46 - 2 * q^48 - 6 * q^49 + 24 * q^50 + 16 * q^51 - 12 * q^53 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 8 * q^61 - 4 * q^62 - 6 * q^63 - 4 * q^64 - 20 * q^65 + 12 * q^66 - 42 * q^67 + 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 4 * q^75 + 6 * q^76 - 4 * q^78 - 24 * q^79 - 6 * q^80 - 2 * q^81 + 2 * q^82 - 6 * q^84 + 36 * q^85 + 2 * q^87 + 6 * q^88 - 12 * q^89 - 8 * q^90 - 4 * q^91 - 4 * q^92 - 12 * q^93 + 6 * q^94 + 18 * q^95 - 12 * q^98

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