LMFDB - Embedded newform 70.2.i.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,2,Mod(9,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("70.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	70.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:	$0.558952814149$
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			9.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	70.9
Dual form			70.2.i.a.39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} -3.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} -3.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(1.86603 + 1.23205i) q^{10} +(2.59808 + 1.50000i) q^{12} +2.00000i q^{13} +(2.00000 - 1.73205i) q^{14} +(-6.00000 + 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(1.50000 + 7.79423i) q^{21} +(-0.866025 - 0.500000i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(4.96410 + 0.598076i) q^{25} +(1.00000 - 1.73205i) q^{26} -9.00000i q^{27} +(-2.59808 + 0.500000i) q^{28} +1.00000 q^{29} +(6.69615 + 0.401924i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(2.26795 - 5.46410i) q^{35} +6.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(-0.133975 + 2.23205i) q^{40} -3.00000 q^{41} +(2.59808 - 7.50000i) q^{42} -5.00000i q^{43} +(-7.39230 + 11.1962i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-6.92820 - 4.00000i) q^{47} +3.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(2.50000 + 0.866025i) q^{56} +6.00000i q^{57} +(-0.866025 - 0.500000i) q^{58} +(1.00000 + 1.73205i) q^{59} +(-5.59808 - 3.69615i) q^{60} +(4.50000 - 7.79423i) q^{61} +10.0000i q^{62} +(10.3923 + 12.0000i) q^{63} -1.00000 q^{64} +(0.267949 - 4.46410i) q^{65} +(-6.06218 + 3.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} -3.00000 q^{69} +(-4.69615 + 3.59808i) q^{70} +6.00000 q^{71} +(-5.19615 - 3.00000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(13.7942 - 5.89230i) q^{75} -2.00000 q^{76} -6.00000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(1.23205 - 1.86603i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 1.50000i) q^{82} +9.00000i q^{83} +(-6.00000 + 5.19615i) q^{84} +(4.00000 - 2.00000i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(2.59808 - 1.50000i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(12.0000 - 6.00000i) q^{90} +(-5.00000 - 1.73205i) q^{91} -1.00000i q^{92} +(-25.9808 - 15.0000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(2.46410 - 3.73205i) q^{95} +(1.50000 - 2.59808i) q^{96} +(2.59808 + 6.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 12 * q^9	$ 4 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 12 q^{9} + 4 q^{10} + 8 q^{14} - 24 q^{15} - 2 q^{16} - 4 q^{19} - 4 q^{20} + 6 q^{21} - 6 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{29} + 6 q^{30} - 20 q^{31} + 8 q^{34} + 16 q^{35} + 24 q^{36} + 12 q^{39} - 4 q^{40} - 12 q^{41} + 12 q^{45} + 2 q^{46} - 22 q^{49} - 16 q^{50} - 12 q^{51} - 18 q^{54} + 10 q^{56} + 4 q^{59} - 12 q^{60} + 18 q^{61} - 4 q^{64} + 8 q^{65} - 12 q^{69} + 2 q^{70} + 24 q^{71} - 16 q^{74} + 24 q^{75} - 8 q^{76} - 20 q^{79} - 2 q^{80} - 18 q^{81} - 24 q^{84} + 16 q^{85} - 10 q^{86} - 14 q^{89} + 48 q^{90} - 20 q^{91} + 16 q^{94} - 4 q^{95} + 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 12 * q^9 + 4 * q^10 + 8 * q^14 - 24 * q^15 - 2 * q^16 - 4 * q^19 - 4 * q^20 + 6 * q^21 - 6 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^29 + 6 * q^30 - 20 * q^31 + 8 * q^34 + 16 * q^35 + 24 * q^36 + 12 * q^39 - 4 * q^40 - 12 * q^41 + 12 * q^45 + 2 * q^46 - 22 * q^49 - 16 * q^50 - 12 * q^51 - 18 * q^54 + 10 * q^56 + 4 * q^59 - 12 * q^60 + 18 * q^61 - 4 * q^64 + 8 * q^65 - 12 * q^69 + 2 * q^70 + 24 * q^71 - 16 * q^74 + 24 * q^75 - 8 * q^76 - 20 * q^79 - 2 * q^80 - 18 * q^81 - 24 * q^84 + 16 * q^85 - 10 * q^86 - 14 * q^89 + 48 * q^90 - 20 * q^91 + 16 * q^94 - 4 * q^95 + 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	2.59808	−	1.50000i	1.50000	−	0.866025i	1.00000			$0$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$6$	−3.00000			−1.22474
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$8$		−	1.00000i		−	0.353553i
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$	1.86603	+	1.23205i	0.590089	+	0.389609i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	2.59808	+	1.50000i	0.750000	+	0.433013i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−6.00000	+	3.00000i	−1.54919	+	0.774597i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$	−5.19615	+	3.00000i	−1.22474	+	0.707107i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$	1.50000	+	7.79423i	0.327327	+	1.70084i
$22$		0			0
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	0.406986	−	0.913434i	$-0.366580\pi$
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	−0.587565	+	0.809177i	$0.699913\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$		−	9.00000i		−	1.73205i
$28$	−2.59808	+	0.500000i	−0.490990	+	0.0944911i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	6.69615	+	0.401924i	1.22254	+	0.0733809i
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	2.00000			0.342997
$35$	2.26795	−	5.46410i	0.383353	−	0.923602i
$36$	6.00000			1.00000
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.946180	−	0.323640i	$-0.104907\pi$
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.192809	+	0.981236i	$0.438240\pi$
$38$	1.73205	−	1.00000i	0.280976	−	0.162221i
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$	−0.133975	+	2.23205i	−0.0211832	+	0.352918i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	2.59808	−	7.50000i	0.400892	−	1.15728i
$43$		−	5.00000i		−	0.762493i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$		−	5.00000i		−	0.762493i	0.924473	−	0.381246i	$-0.124505\pi$
$44$		0			0
$45$	−7.39230	+	11.1962i	−1.10198	+	1.66902i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.0992202	−	0.995066i	$-0.531635\pi$
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.911362	+	0.411606i	$0.864968\pi$
$48$			3.00000i			0.433013i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$		0			0
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$			6.00000i			0.794719i
$58$	−0.866025	−	0.500000i	−0.113715	−	0.0656532i
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$	−5.59808	−	3.69615i	−0.722709	−	0.477171i
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$			10.0000i			1.27000i
$63$	10.3923	+	12.0000i	1.30931	+	1.51186i
$64$	−1.00000			−0.125000
$65$	0.267949	−	4.46410i	0.0332350	−	0.553704i
$66$		0			0
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	−1.73205	−	1.00000i	−0.210042	−	0.121268i
$69$	−3.00000			−0.361158
$70$	−4.69615	+	3.59808i	−0.561298	+	0.430052i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−5.19615	−	3.00000i	−0.612372	−	0.353553i
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.101361	−	0.994850i	$-0.467680\pi$
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.912245	+	0.409644i	$0.134347\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	13.7942	−	5.89230i	1.59282	−	0.680385i
$76$	−2.00000			−0.229416
$77$		0			0
$78$		−	6.00000i		−	0.679366i
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	1.23205	−	1.86603i	0.137747	−	0.208628i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.59808	+	1.50000i	0.286910	+	0.165647i
$83$			9.00000i			0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$			9.00000i			0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$	−6.00000	+	5.19615i	−0.654654	+	0.566947i
$85$	4.00000	−	2.00000i	0.433861	−	0.216930i
$86$	−2.50000	+	4.33013i	−0.269582	+	0.466930i
$87$	2.59808	−	1.50000i	0.278543	−	0.160817i
$88$		0			0
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$	12.0000	−	6.00000i	1.26491	−	0.632456i
$91$	−5.00000	−	1.73205i	−0.524142	−	0.181568i
$92$		−	1.00000i		−	0.104257i
$93$	−25.9808	−	15.0000i	−2.69408	−	1.55543i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	2.46410	−	3.73205i	0.252811	−	0.382900i
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	2.59808	+	6.50000i	0.262445	+	0.656599i
$99$		0			0
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$	5.19615	−	3.00000i	0.514496	−	0.297044i
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.0491146	−	0.998793i	$-0.515640\pi$
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.889538	+	0.456862i	$0.848973\pi$
$104$	2.00000			0.196116
$105$	−2.30385	−	17.5981i	−0.224833	−	1.71740i
$106$	−6.00000			−0.582772
$107$	6.06218	+	3.50000i	0.586053	+	0.338358i	0.763535	−	0.645766i	$-0.223462\pi$
$107$	6.06218	+	3.50000i	0.586053	+	0.338358i	−0.177482	+	0.984124i	$0.556795\pi$
$108$	7.79423	−	4.50000i	0.750000	−	0.433013i
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$		0			0
$111$	24.0000			2.27798
$112$	−1.73205	−	2.00000i	−0.163663	−	0.188982i
$113$			10.0000i			0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$			10.0000i			0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$	1.86603	+	1.23205i	0.174008	+	0.114889i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	10.3923	+	6.00000i	0.960769	+	0.554700i
$118$		−	2.00000i		−	0.184115i
$119$	−1.00000	−	5.19615i	−0.0916698	−	0.476331i
$120$	3.00000	+	6.00000i	0.273861	+	0.547723i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−7.79423	+	4.50000i	−0.705656	+	0.407411i
$123$	−7.79423	+	4.50000i	−0.702782	+	0.405751i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−3.00000	−	15.5885i	−0.267261	−	1.38873i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−7.50000	−	12.9904i	−0.660338	−	1.14374i
$130$	−2.46410	+	3.73205i	−0.216116	+	0.327323i
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.0155672	+	0.999879i	$0.504955\pi$
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.858137	+	0.513421i	$0.828378\pi$
$132$		0			0
$133$	−3.46410	−	4.00000i	−0.300376	−	0.346844i
$134$	7.00000			0.604708
$135$	−1.20577	+	20.0885i	−0.103776	+	1.72894i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	13.8564	−	8.00000i	1.18383	−	0.683486i	0.226935	−	0.973910i	$-0.427130\pi$
$137$	13.8564	−	8.00000i	1.18383	−	0.683486i	0.956898	+	0.290424i	$0.0937963\pi$
$138$	2.59808	+	1.50000i	0.221163	+	0.127688i
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	5.86603	−	0.767949i	0.495770	−	0.0649036i
$141$	−24.0000			−2.02116
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$		0			0
$144$	3.00000	+	5.19615i	0.250000	+	0.433013i
$145$	−2.23205	−	0.133975i	−0.185362	−	0.0111260i
$146$	−10.0000			−0.827606
$147$	−20.7846	−	3.00000i	−1.71429	−	0.247436i
$148$			8.00000i			0.657596i
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$	−14.8923	−	1.79423i	−1.21595	−	0.146498i
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	0.717752	−	0.696299i	$-0.245171\pi$
$151$	−3.00000	−	5.19615i	−0.244137	−	0.422857i	−0.961888	+	0.273442i	$0.911838\pi$
$152$	1.73205	+	1.00000i	0.140488	+	0.0811107i
$153$			12.0000i			0.970143i
$154$		0			0
$155$	10.0000	+	20.0000i	0.803219	+	1.60644i
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	8.66025	−	5.00000i	0.688973	−	0.397779i
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$			9.00000i			0.707107i
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	0.848339	−	0.529454i	$-0.177603\pi$
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	−0.0343508	+	0.999410i	$0.510936\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$		−	9.00000i		−	0.696441i	−0.937413	−	0.348220i	$-0.886786\pi$
$167$		−	9.00000i		−	0.696441i	0.937413	−	0.348220i	$-0.113214\pi$
$168$	7.79423	−	1.50000i	0.601338	−	0.115728i
$169$	9.00000			0.692308
$170$	−4.46410	−	0.267949i	−0.342381	−	0.0205508i
$171$	6.00000	+	10.3923i	0.458831	+	0.794719i
$172$	4.33013	−	2.50000i	0.330169	−	0.190623i
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	0.840002	−	0.542583i	$-0.182554\pi$
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	−0.0498898	+	0.998755i	$0.515887\pi$
$174$	−3.00000			−0.227429
$175$	−5.79423	+	11.8923i	−0.438003	+	0.898974i
$176$		0			0
$177$	5.19615	+	3.00000i	0.390567	+	0.225494i
$178$	6.06218	−	3.50000i	0.454379	−	0.262336i
$179$	−13.0000	−	22.5167i	−0.971666	−	1.68297i	−0.690526	−	0.723307i	$-0.742621\pi$
$179$	−13.0000	−	22.5167i	−0.971666	−	1.68297i	−0.281139	−	0.959667i	$-0.590712\pi$
$180$	−13.3923	−	0.803848i	−0.998203	−	0.0599153i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	3.46410	+	4.00000i	0.256776	+	0.296500i
$183$		−	27.0000i		−	1.99590i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−14.9282	−	9.85641i	−1.09754	−	0.724657i
$186$	15.0000	+	25.9808i	1.09985	+	1.90500i
$187$		0			0
$188$		−	8.00000i		−	0.583460i
$189$	22.5000	+	7.79423i	1.63663	+	0.566947i
$190$	−4.00000	+	2.00000i	−0.290191	+	0.145095i
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$	−2.59808	+	1.50000i	−0.187500	+	0.108253i
$193$	−17.3205	+	10.0000i	−1.24676	+	0.719816i	−0.970461	−	0.241257i	$-0.922440\pi$
$193$	−17.3205	+	10.0000i	−1.24676	+	0.719816i	−0.276296	+	0.961073i	$0.589107\pi$
$194$		0			0
$195$	−6.00000	−	12.0000i	−0.429669	−	0.859338i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$	6.00000	+	10.3923i	0.425329	+	0.736691i	0.996451	−	0.0841740i	$-0.0268252\pi$
$199$	6.00000	+	10.3923i	0.425329	+	0.736691i	−0.571122	+	0.820865i	$0.693492\pi$
$200$	0.598076	−	4.96410i	0.0422904	−	0.351015i
$201$	−10.5000	+	18.1865i	−0.740613	+	1.28278i
$202$		−	15.0000i		−	1.05540i
$203$	−0.866025	+	2.50000i	−0.0607831	+	0.175466i
$204$	−6.00000			−0.420084
$205$	6.69615	+	0.401924i	0.467680	+	0.0280716i
$206$	5.50000	+	9.52628i	0.383203	+	0.663727i
$207$	−5.19615	+	3.00000i	−0.361158	+	0.208514i
$208$	−1.73205	−	1.00000i	−0.120096	−	0.0693375i
$209$		0			0
$210$	−6.80385	+	16.3923i	−0.469510	+	1.13118i
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$	15.5885	−	9.00000i	1.06810	−	0.616670i
$214$	−3.50000	−	6.06218i	−0.239255	−	0.414402i
$215$	−0.669873	+	11.1603i	−0.0456850	+	0.761123i
$216$	−9.00000			−0.612372
$217$	25.9808	−	5.00000i	1.76369	−	0.339422i
$218$		−	5.00000i		−	0.338643i
$219$	15.0000	−	25.9808i	1.01361	−	1.75562i
$220$		0			0
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$	−20.7846	−	12.0000i	−1.39497	−	0.805387i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$	18.0000	−	24.0000i	1.20000	−	1.60000i
$226$	5.00000	−	8.66025i	0.332595	−	0.576072i
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$	−5.19615	+	3.00000i	−0.344124	+	0.198680i
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	−1.00000	−	2.00000i	−0.0659380	−	0.131876i
$231$		0			0
$232$		−	1.00000i		−	0.0656532i
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	0.0471787	−	0.998886i	$-0.484977\pi$
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	−0.841472	+	0.540301i	$0.818310\pi$
$234$	−6.00000	−	10.3923i	−0.392232	−	0.679366i
$235$	14.9282	+	9.85641i	0.973809	+	0.642961i
$236$	−1.00000	+	1.73205i	−0.0650945	+	0.112747i
$237$			30.0000i			1.94871i
$238$	−1.73205	+	5.00000i	−0.112272	+	0.324102i
$239$	10.0000			0.646846			0.323423	−	0.946254i	$-0.395166\pi$
$239$	10.0000			0.646846			0.323423	+	0.946254i	$0.395166\pi$
$240$	0.401924	−	6.69615i	0.0259441	−	0.432235i
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	−9.52628	+	5.50000i	−0.612372	+	0.353553i
$243$		0			0
$244$	9.00000			0.576166
$245$	11.6962	+	10.4019i	0.747240	+	0.664555i
$246$	9.00000			0.573819
$247$	−3.46410	−	2.00000i	−0.220416	−	0.127257i
$248$	−8.66025	+	5.00000i	−0.549927	+	0.317500i
$249$	13.5000	+	23.3827i	0.855528	+	1.48182i
$250$	8.52628	+	7.23205i	0.539249	+	0.457395i
$251$	−10.0000			−0.631194			−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000			−0.631194			−0.315597	+	0.948893i	$0.602205\pi$
$252$	−5.19615	+	15.0000i	−0.327327	+	0.944911i
$253$		0			0
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	7.39230	−	11.1962i	0.462924	−	0.701130i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$			15.0000i			0.933859i
$259$	−16.0000	+	13.8564i	−0.994192	+	0.860995i
$260$	4.00000	−	2.00000i	0.248069	−	0.124035i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	17.3205	−	10.0000i	1.07006	−	0.617802i
$263$	−18.1865	+	10.5000i	−1.12143	+	0.647458i	−0.941766	−	0.336270i	$-0.890834\pi$
$263$	−18.1865	+	10.5000i	−1.12143	+	0.647458i	−0.179664	+	0.983728i	$0.557501\pi$
$264$		0			0
$265$	−12.0000	+	6.00000i	−0.737154	+	0.368577i
$266$	1.00000	+	5.19615i	0.0613139	+	0.318597i
$267$			21.0000i			1.28518i
$268$	−6.06218	−	3.50000i	−0.370306	−	0.213797i
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	0.932119	−	0.362151i	$-0.117958\pi$
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	−0.779692	+	0.626164i	$0.784624\pi$
$270$	11.0885	−	16.7942i	0.674822	−	1.02206i
$271$	−3.00000	+	5.19615i	−0.182237	+	0.315644i	−0.942642	−	0.333805i	$-0.891667\pi$
$271$	−3.00000	+	5.19615i	−0.182237	+	0.315644i	0.760405	+	0.649449i	$0.225000\pi$
$272$		−	2.00000i		−	0.121268i
$273$	−15.5885	+	3.00000i	−0.943456	+	0.181568i
$274$	−16.0000			−0.966595
$275$		0			0
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.988654	−	0.150210i	$-0.952005\pi$
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.364241	+	0.931305i	$0.618672\pi$
$278$	−6.92820	−	4.00000i	−0.415526	−	0.239904i
$279$	−60.0000			−3.59211
$280$	−5.46410	−	2.26795i	−0.326543	−	0.135536i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	20.7846	+	12.0000i	1.23771	+	0.714590i
$283$	−6.92820	+	4.00000i	−0.411839	+	0.237775i	−0.691580	−	0.722300i	$-0.743085\pi$
$283$	−6.92820	+	4.00000i	−0.411839	+	0.237775i	0.279741	+	0.960076i	$0.409752\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	0.803848	−	13.3923i	0.0476158	−	0.793292i
$286$		0			0
$287$	2.59808	−	7.50000i	0.153360	−	0.442711i
$288$		−	6.00000i		−	0.353553i
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$	1.86603	+	1.23205i	0.109577	+	0.0723485i
$291$		0			0
$292$	8.66025	+	5.00000i	0.506803	+	0.292603i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$	16.5000	+	12.9904i	0.962300	+	0.757614i
$295$	−2.00000	−	4.00000i	−0.116445	−	0.232889i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$	12.9904	−	7.50000i	0.752513	−	0.434463i
$299$	1.00000	−	1.73205i	0.0578315	−	0.100167i
$300$	12.0000	+	9.00000i	0.692820	+	0.519615i
$301$	12.5000	+	4.33013i	0.720488	+	0.249584i
$302$			6.00000i			0.345261i
$303$	38.9711	+	22.5000i	2.23883	+	1.29259i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	−11.0885	+	16.7942i	−0.634923	+	0.961635i
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$		−	19.0000i		−	1.08439i	−0.840254	−	0.542194i	$-0.817594\pi$
$307$		−	19.0000i		−	1.08439i	0.840254	−	0.542194i	$-0.182406\pi$
$308$		0			0
$309$	−33.0000			−1.87730
$310$	1.33975	−	22.3205i	0.0760925	−	1.26772i
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$	5.19615	−	3.00000i	0.294174	−	0.169842i
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	0.682855	−	0.730554i	$-0.260738\pi$
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	−0.291250	+	0.956647i	$0.594071\pi$
$314$	12.0000			0.677199
$315$	−21.5885	−	28.1769i	−1.21637	−	1.58759i
$316$	−10.0000			−0.562544
$317$	−19.0526	−	11.0000i	−1.07010	−	0.617822i	−0.141890	−	0.989882i	$-0.545318\pi$
$317$	−19.0526	−	11.0000i	−1.07010	−	0.617822i	−0.928208	+	0.372061i	$0.878651\pi$
$318$	−15.5885	+	9.00000i	−0.874157	+	0.504695i
$319$		0			0
$320$	2.23205	+	0.133975i	0.124775	+	0.00748941i
$321$	21.0000			1.17211
$322$	−2.59808	+	0.500000i	−0.144785	+	0.0278639i
$323$		−	4.00000i		−	0.222566i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−1.19615	+	9.92820i	−0.0663506	+	0.550718i
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$	12.9904	+	7.50000i	0.718370	+	0.414751i
$328$			3.00000i			0.165647i
$329$	16.0000	−	13.8564i	0.882109	−	0.763928i
$330$		0			0
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$332$	−7.79423	+	4.50000i	−0.427764	+	0.246970i
$333$	41.5692	−	24.0000i	2.27798	−	1.31519i
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$	14.0000	−	7.00000i	0.764902	−	0.382451i
$336$	−7.50000	−	2.59808i	−0.409159	−	0.141737i
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$	−7.79423	−	4.50000i	−0.423950	−	0.244768i
$339$	15.0000	+	25.9808i	0.814688	+	1.41108i
$340$	3.73205	+	2.46410i	0.202399	+	0.133635i
$341$		0			0
$342$		−	12.0000i		−	0.648886i
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−5.00000			−0.269582
$345$	6.69615	+	0.401924i	0.360509	+	0.0216388i
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	18.1865	−	10.5000i	0.976304	−	0.563670i	0.0751519	−	0.997172i	$-0.476056\pi$
$347$	18.1865	−	10.5000i	0.976304	−	0.563670i	0.901152	+	0.433503i	$0.142722\pi$
$348$	2.59808	+	1.50000i	0.139272	+	0.0804084i
$349$	9.00000			0.481759			0.240879	−	0.970555i	$-0.422564\pi$
$349$	9.00000			0.481759			0.240879	+	0.970555i	$0.422564\pi$
$350$	10.9641	−	7.40192i	0.586056	−	0.395649i
$351$	18.0000			0.960769
$352$		0			0
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	−0.355303	−	0.934751i	$-0.615622\pi$
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	0.631867	+	0.775077i	$0.282289\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	−13.3923	−	0.803848i	−0.710790	−	0.0426638i
$356$	−7.00000			−0.370999
$357$	−10.3923	−	12.0000i	−0.550019	−	0.635107i
$358$			26.0000i			1.37414i
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	−0.989479	−	0.144677i	$-0.953786\pi$
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	0.620033	+	0.784576i	$0.287119\pi$
$360$	11.1962	+	7.39230i	0.590089	+	0.389609i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−4.33013	−	2.50000i	−0.227586	−	0.131397i
$363$		−	33.0000i		−	1.73205i
$364$	−1.00000	−	5.19615i	−0.0524142	−	0.272352i
$365$	−20.0000	+	10.0000i	−1.04685	+	0.523424i
$366$	−13.5000	+	23.3827i	−0.705656	+	1.22223i
$367$	−19.9186	+	11.5000i	−1.03974	+	0.600295i	−0.919760	−	0.392481i	$-0.871617\pi$
$367$	−19.9186	+	11.5000i	−1.03974	+	0.600295i	−0.119982	+	0.992776i	$0.538284\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$	8.00000	+	16.0000i	0.415900	+	0.831800i
$371$	3.00000	+	15.5885i	0.155752	+	0.809312i
$372$		−	30.0000i		−	1.55543i
$373$	6.92820	+	4.00000i	0.358729	+	0.207112i	0.668523	−	0.743691i	$-0.266927\pi$
$373$	6.92820	+	4.00000i	0.358729	+	0.207112i	−0.309794	+	0.950804i	$0.600260\pi$
$374$		0			0
$375$	−31.5788	+	11.3038i	−1.63072	+	0.583728i
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$			2.00000i			0.103005i
$378$	−15.5885	−	18.0000i	−0.801784	−	0.925820i
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	4.46410	+	0.267949i	0.229004	+	0.0137455i
$381$	−12.0000	−	20.7846i	−0.614779	−	1.06483i
$382$	−17.3205	+	10.0000i	−0.886194	+	0.511645i
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	0.287469	−	0.957790i	$-0.407186\pi$
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	−0.685736	+	0.727851i	$0.740519\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	20.0000			1.01797
$387$	−25.9808	−	15.0000i	−1.32068	−	0.762493i
$388$		0			0
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$	−0.803848	+	13.3923i	−0.0407044	+	0.678146i
$391$	2.00000			0.101144
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$			60.0000i			3.02660i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	12.3205	−	18.6603i	0.619912	−	0.938899i
$396$		0			0
$397$	27.7128	+	16.0000i	1.39087	+	0.803017i	0.993411	−	0.114605i	$-0.0365601\pi$
$397$	27.7128	+	16.0000i	1.39087	+	0.803017i	0.397455	+	0.917622i	$0.369893\pi$
$398$		−	12.0000i		−	0.601506i
$399$	−15.0000	−	5.19615i	−0.750939	−	0.260133i
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	18.1865	−	10.5000i	0.907062	−	0.523692i
$403$	17.3205	−	10.0000i	0.862796	−	0.498135i
$404$	−7.50000	+	12.9904i	−0.373139	+	0.646296i
$405$	9.00000	+	18.0000i	0.447214	+	0.894427i
$406$	2.00000	−	1.73205i	0.0992583	−	0.0859602i
$407$		0			0
$408$	5.19615	+	3.00000i	0.257248	+	0.148522i
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	0.575670	−	0.817682i	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$	−5.59808	−	3.69615i	−0.276469	−	0.182540i
$411$	24.0000	−	41.5692i	1.18383	−	2.05046i
$412$		−	11.0000i		−	0.541931i
$413$	−5.19615	+	1.00000i	−0.255686	+	0.0492068i
$414$	6.00000			0.294884
$415$	1.20577	−	20.0885i	0.0591890	−	0.986104i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	20.7846	−	12.0000i	1.01783	−	0.587643i
$418$		0			0
$419$	40.0000			1.95413			0.977064	−	0.212946i	$-0.0683059\pi$
$419$	40.0000			1.95413			0.977064	+	0.212946i	$0.0683059\pi$
$420$	14.0885	−	10.7942i	0.687446	−	0.526704i
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$	15.5885	+	9.00000i	0.758834	+	0.438113i
$423$	−41.5692	+	24.0000i	−2.02116	+	1.16692i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$	−18.0000			−0.872103
$427$	15.5885	+	18.0000i	0.754378	+	0.871081i
$428$			7.00000i			0.338358i
$429$		0			0
$430$	6.16025	−	9.33013i	0.297074	−	0.449939i
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	−0.937184	−	0.348836i	$-0.886577\pi$
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	0.166491	−	0.986043i	$-0.446756\pi$
$432$	7.79423	+	4.50000i	0.375000	+	0.216506i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	−25.0000	−	8.66025i	−1.20004	−	0.415705i
$435$	−6.00000	+	3.00000i	−0.287678	+	0.143839i
$436$	−2.50000	+	4.33013i	−0.119728	+	0.207375i
$437$	1.73205	−	1.00000i	0.0828552	−	0.0478365i
$438$	−25.9808	+	15.0000i	−1.24141	+	0.716728i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$	−39.0000	+	15.5885i	−1.85714	+	0.742307i
$442$			4.00000i			0.190261i
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	0.437009	−	0.899457i	$-0.356038\pi$
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	−0.560448	+	0.828190i	$0.689371\pi$
$444$	12.0000	+	20.7846i	0.569495	+	0.986394i
$445$	8.62436	−	13.0622i	0.408834	−	0.619207i
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$			45.0000i			2.12843i
$448$	0.866025	−	2.50000i	0.0409159	−	0.118114i
$449$	−23.0000			−1.08544			−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000			−1.08544			−0.542719	+	0.839915i	$0.682605\pi$
$450$	−27.5885	+	11.7846i	−1.30053	+	0.555532i
$451$		0			0
$452$	−8.66025	+	5.00000i	−0.407344	+	0.235180i
$453$	−15.5885	−	9.00000i	−0.732410	−	0.422857i
$454$	−12.0000			−0.563188
$455$	10.9282	+	4.53590i	0.512322	+	0.212646i
$456$	6.00000			0.280976
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.316579	−	0.948566i	$-0.602534\pi$
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.979772	+	0.200118i	$0.935868\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$	9.00000	+	15.5885i	0.420084	+	0.727607i
$460$	−0.133975	+	2.23205i	−0.00624660	+	0.104070i
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$		−	25.0000i		−	1.16185i	−0.813958	−	0.580924i	$-0.802691\pi$
$463$		−	25.0000i		−	1.16185i	0.813958	−	0.580924i	$-0.197309\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	55.9808	+	36.9615i	2.59605	+	1.71405i
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−0.866025	−	0.500000i	−0.0400749	−	0.0231372i	0.479829	−	0.877362i	$-0.340699\pi$
$467$	−0.866025	−	0.500000i	−0.0400749	−	0.0231372i	−0.519904	+	0.854225i	$0.674032\pi$
$468$			12.0000i			0.554700i
$469$	−3.50000	−	18.1865i	−0.161615	−	0.839776i
$470$	−8.00000	−	16.0000i	−0.369012	−	0.738025i
$471$	−18.0000	+	31.1769i	−0.829396	+	1.43656i
$472$	1.73205	−	1.00000i	0.0797241	−	0.0460287i
$473$		0			0
$474$	15.0000	−	25.9808i	0.688973	−	1.19334i
$475$	−6.00000	+	8.00000i	−0.275299	+	0.367065i
$476$	4.00000	−	3.46410i	0.183340	−	0.158777i
$477$		−	36.0000i		−	1.64833i
$478$	−8.66025	−	5.00000i	−0.396111	−	0.228695i
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$	−3.69615	+	5.59808i	−0.168706	+	0.255516i
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$			18.0000i			0.819878i
$483$	2.59808	−	7.50000i	0.118217	−	0.341262i
$484$	11.0000			0.500000
$485$		0			0
$486$		0			0
$487$	3.46410	−	2.00000i	0.156973	−	0.0906287i	−0.419456	−	0.907776i	$-0.637779\pi$
$487$	3.46410	−	2.00000i	0.156973	−	0.0906287i	0.576429	+	0.817147i	$0.304446\pi$
$488$	−7.79423	−	4.50000i	−0.352828	−	0.203705i
$489$	36.0000			1.62798
$490$	−4.92820	−	14.8564i	−0.222634	−	0.671144i
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	−7.79423	−	4.50000i	−0.351391	−	0.202876i
$493$	−1.73205	+	1.00000i	−0.0780076	+	0.0450377i
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$		0			0
$496$	10.0000			0.449013
$497$	−5.19615	+	15.0000i	−0.233079	+	0.672842i
$498$		−	27.0000i		−	1.20990i
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	−3.76795	−	10.5263i	−0.168508	−	0.470750i
$501$	−13.5000	−	23.3827i	−0.603136	−	1.04466i
$502$	8.66025	+	5.00000i	0.386526	+	0.223161i
$503$			5.00000i			0.222939i	0.993768	+	0.111469i	$0.0355557\pi$
$503$			5.00000i			0.222939i	−0.993768	+	0.111469i	$0.964444\pi$
$504$	12.0000	−	10.3923i	0.534522	−	0.462910i
$505$	−15.0000	−	30.0000i	−0.667491	−	1.33498i
$506$		0			0
$507$	23.3827	−	13.5000i	1.03846	−	0.599556i
$508$	6.92820	−	4.00000i	0.307389	−	0.177471i
$509$	17.5000	−	30.3109i	0.775674	−	1.34351i	−0.158741	−	0.987320i	$-0.550744\pi$
$509$	17.5000	−	30.3109i	0.775674	−	1.34351i	0.934415	−	0.356186i	$-0.115923\pi$
$510$	−12.0000	+	6.00000i	−0.531369	+	0.265684i
$511$	5.00000	+	25.9808i	0.221187	+	1.14932i
$512$			1.00000i			0.0441942i
$513$	15.5885	+	9.00000i	0.688247	+	0.397360i
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$	20.5263	+	13.5526i	0.904496	+	0.597197i
$516$	7.50000	−	12.9904i	0.330169	−	0.571870i
$517$		0			0
$518$	20.7846	−	4.00000i	0.913223	−	0.175750i
$519$	36.0000			1.58022
$520$	−4.46410	−	0.267949i	−0.195764	−	0.0117503i
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	0.573822	−	0.818980i	$-0.305460\pi$
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	−0.422347	+	0.906434i	$0.638794\pi$
$524$	−20.0000			−0.873704
$525$	2.78461	+	39.5885i	0.121530	+	1.72778i
$526$	21.0000			0.915644
$527$	17.3205	+	10.0000i	0.754493	+	0.435607i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$	13.3923	+	0.803848i	0.581725	+	0.0349169i
$531$	12.0000			0.520756
$532$	1.73205	−	5.00000i	0.0750939	−	0.216777i
$533$		−	6.00000i		−	0.259889i
$534$	10.5000	−	18.1865i	0.454379	−	0.787008i
$535$	−13.0622	−	8.62436i	−0.564727	−	0.372863i
$536$	3.50000	+	6.06218i	0.151177	+	0.261846i
$537$	−67.5500	−	39.0000i	−2.91500	−	1.68297i
$538$		−	5.00000i		−	0.215565i
$539$		0			0
$540$	−18.0000	+	9.00000i	−0.774597	+	0.387298i
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	5.19615	−	3.00000i	0.223194	−	0.128861i
$543$	12.9904	−	7.50000i	0.557471	−	0.321856i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−5.00000	−	10.0000i	−0.214176	−	0.428353i
$546$	15.0000	+	5.19615i	0.641941	+	0.222375i
$547$			37.0000i			1.58201i	0.611812	+	0.791003i	$0.290441\pi$
$547$			37.0000i			1.58201i	−0.611812	+	0.791003i	$0.709559\pi$
$548$	13.8564	+	8.00000i	0.591916	+	0.341743i
$549$	−27.0000	−	46.7654i	−1.15233	−	1.99590i
$550$		0			0
$551$	−1.00000	+	1.73205i	−0.0426014	+	0.0737878i
$552$			3.00000i			0.127688i
$553$	−17.3205	−	20.0000i	−0.736543	−	0.850487i
$554$	26.0000			1.10463
$555$	−53.5692	−	3.21539i	−2.27389	−	0.136486i
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	−3.46410	+	2.00000i	−0.146779	+	0.0847427i	−0.571591	−	0.820539i	$-0.693674\pi$
$557$	−3.46410	+	2.00000i	−0.146779	+	0.0847427i	0.424812	+	0.905282i	$0.360340\pi$
$558$	51.9615	+	30.0000i	2.19971	+	1.27000i
$559$	10.0000			0.422955
$560$	3.59808	+	4.69615i	0.152046	+	0.198449i
$561$		0			0
$562$	−15.5885	−	9.00000i	−0.657559	−	0.379642i
$563$	−9.52628	+	5.50000i	−0.401485	+	0.231797i	−0.687124	−	0.726540i	$-0.741127\pi$
$563$	−9.52628	+	5.50000i	−0.401485	+	0.231797i	0.285640	+	0.958337i	$0.407794\pi$
$564$	−12.0000	−	20.7846i	−0.505291	−	0.875190i
$565$	1.33975	−	22.3205i	0.0563635	−	0.939031i
$566$	8.00000			0.336265
$567$	23.3827	−	4.50000i	0.981981	−	0.188982i
$568$		−	6.00000i		−	0.251754i
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$	−7.39230	+	11.1962i	−0.309630	+	0.468955i
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	0.951476	−	0.307722i	$-0.0995665\pi$
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	−0.742233	+	0.670142i	$0.766233\pi$
$572$		0			0
$573$		−	60.0000i		−	2.50654i
$574$	−6.00000	+	5.19615i	−0.250435	+	0.216883i
$575$	−4.00000	−	3.00000i	−0.166812	−	0.125109i
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	−13.8564	+	8.00000i	−0.576850	+	0.333044i	−0.759880	−	0.650063i	$-0.774743\pi$
$577$	−13.8564	+	8.00000i	−0.576850	+	0.333044i	0.183031	+	0.983107i	$0.441409\pi$
$578$	11.2583	−	6.50000i	0.468285	−	0.270364i
$579$	−30.0000	+	51.9615i	−1.24676	+	2.15945i
$580$	−1.00000	−	2.00000i	−0.0415227	−	0.0830455i
$581$	−22.5000	−	7.79423i	−0.933457	−	0.323359i
$582$		0			0
$583$		0			0
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$	−22.3923	−	14.7846i	−0.925808	−	0.611268i
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$	−7.79423	−	19.5000i	−0.321429	−	0.804166i
$589$	20.0000			0.824086
$590$	−0.267949	+	4.46410i	−0.0110313	+	0.183784i
$591$	−12.0000	−	20.7846i	−0.493614	−	0.854965i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.999974	−	0.00727173i	$-0.00231468\pi$
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.493689	+	0.869638i	$0.335648\pi$
$594$		0			0
$595$	1.53590	+	11.7321i	0.0629657	+	0.480967i
$596$	−15.0000			−0.614424
$597$	31.1769	+	18.0000i	1.27599	+	0.736691i
$598$	−1.73205	+	1.00000i	−0.0708288	+	0.0408930i
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$	−5.89230	−	13.7942i	−0.240552	−	0.563147i
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−8.66025	−	10.0000i	−0.352966	−	0.407570i
$603$			42.0000i			1.71037i
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$	−13.5526	+	20.5263i	−0.550990	+	0.834512i
$606$	−22.5000	−	38.9711i	−0.914000	−	1.58309i
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	0.409542	−	0.912291i	$-0.365689\pi$
$607$	−4.33013	−	2.50000i	−0.175754	−	0.101472i	−0.585296	+	0.810819i	$0.699022\pi$
$608$			2.00000i			0.0811107i
$609$	1.50000	+	7.79423i	0.0607831	+	0.315838i
$610$	18.0000	−	9.00000i	0.728799	−	0.364399i
$611$	8.00000	−	13.8564i	0.323645	−	0.560570i
$612$	−10.3923	+	6.00000i	−0.420084	+	0.242536i
$613$	−15.5885	+	9.00000i	−0.629612	+	0.363507i	−0.780602	−	0.625029i	$-0.785087\pi$
$613$	−15.5885	+	9.00000i	−0.629612	+	0.363507i	0.150990	+	0.988535i	$0.451754\pi$
$614$	−9.50000	+	16.4545i	−0.383389	+	0.664049i
$615$	18.0000	−	9.00000i	0.725830	−	0.362915i
$616$		0			0
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$	28.5788	+	16.5000i	1.14961	+	0.663727i
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	−12.3205	+	18.6603i	−0.494804	+	0.749414i
$621$	−4.50000	+	7.79423i	−0.180579	+	0.312772i
$622$			6.00000i			0.240578i
$623$	−12.1244	−	14.0000i	−0.485752	−	0.560898i
$624$	−6.00000			−0.240192
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$		0			0
$628$	−10.3923	−	6.00000i	−0.414698	−	0.239426i
$629$	−16.0000			−0.637962
$630$	4.60770	+	35.1962i	0.183575	+	1.40225i
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$	8.66025	+	5.00000i	0.344486	+	0.198889i
$633$	−46.7654	+	27.0000i	−1.85876	+	1.07315i
$634$	11.0000	+	19.0526i	0.436866	+	0.756674i
$635$	−1.07180	+	17.8564i	−0.0425330	+	0.708610i
$636$	18.0000			0.713746
$637$	8.66025	−	11.0000i	0.343132	−	0.435836i
$638$		0			0
$639$	18.0000	−	31.1769i	0.712069	−	1.23334i
$640$	−1.86603	−	1.23205i	−0.0737611	−	0.0487011i
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	0.971442	+	0.237276i	$0.0762547\pi$
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	−0.280234	+	0.959932i	$0.590412\pi$
$642$	−18.1865	−	10.5000i	−0.717765	−	0.414402i
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$	2.50000	+	0.866025i	0.0985138	+	0.0341262i
$645$	15.0000	+	30.0000i	0.590624	+	1.18125i
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	−0.0979182	−	0.995194i	$-0.531218\pi$
$647$	18.1865	−	10.5000i	0.714986	−	0.412798i	0.812905	+	0.582397i	$0.197885\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$		0			0
$650$	6.00000	−	8.00000i	0.235339	−	0.313786i
$651$	60.0000	−	51.9615i	2.35159	−	2.03653i
$652$			12.0000i			0.469956i
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.996587	−	0.0825519i	$-0.0263070\pi$
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.426801	+	0.904345i	$0.359640\pi$
$654$	−7.50000	−	12.9904i	−0.293273	−	0.507964i
$655$	24.6410	−	37.3205i	0.962804	−	1.45823i
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$		−	60.0000i		−	2.34082i
$658$	−20.7846	+	4.00000i	−0.810268	+	0.155936i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	0.921331	+	0.388778i	$0.127103\pi$
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	−0.123974	+	0.992286i	$0.539564\pi$
$662$	12.1244	−	7.00000i	0.471226	−	0.272063i
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$	9.00000			0.349268
$665$	7.19615	+	9.39230i	0.279055	+	0.364218i
$666$	−48.0000			−1.85996
$667$	−0.866025	−	0.500000i	−0.0335326	−	0.0193601i
$668$	7.79423	−	4.50000i	0.301568	−	0.174110i
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$	−15.6244	−	0.937822i	−0.603622	−	0.0362312i
$671$		0			0
$672$	5.19615	+	6.00000i	0.200446	+	0.231455i
$673$		−	20.0000i		−	0.770943i	−0.922720	−	0.385472i	$-0.874039\pi$
$673$		−	20.0000i		−	0.770943i	0.922720	−	0.385472i	$-0.125961\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	5.38269	−	44.6769i	0.207180	−	1.71962i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	0.532915	−	0.846169i	$-0.321097\pi$
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	−0.466347	+	0.884602i	$0.654430\pi$
$678$		−	30.0000i		−	1.15214i
$679$		0			0
$680$	−2.00000	−	4.00000i	−0.0766965	−	0.153393i
$681$	18.0000	−	31.1769i	0.689761	−	1.19470i
$682$		0			0
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	−0.853318	−	0.521391i	$-0.825413\pi$
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	0.0248792	+	0.999690i	$0.492080\pi$
$684$	−6.00000	+	10.3923i	−0.229416	+	0.397360i
$685$	−32.0000	+	16.0000i	−1.22266	+	0.611329i
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$		−	30.0000i		−	1.14457i
$688$	4.33013	+	2.50000i	0.165085	+	0.0953116i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$	−5.59808	−	3.69615i	−0.213115	−	0.140710i
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	−21.0000			−0.797149
$695$	−17.8564	−	1.07180i	−0.677332	−	0.0406556i
$696$	−1.50000	−	2.59808i	−0.0568574	−	0.0984798i
$697$	5.19615	−	3.00000i	0.196818	−	0.113633i
$698$	−7.79423	−	4.50000i	−0.295016	−	0.170328i
$699$	−42.0000			−1.58859
$700$	−13.1962	+	0.928203i	−0.498768	+	0.0350828i
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$	−15.5885	−	9.00000i	−0.588348	−	0.339683i
$703$	−13.8564	+	8.00000i	−0.522604	+	0.301726i
$704$		0			0
$705$	53.5692	+	3.21539i	2.01753	+	0.121099i
$706$	−6.00000			−0.225813
$707$	−38.9711	+	7.50000i	−1.46566	+	0.282067i
$708$			6.00000i			0.225494i
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	−0.938069	−	0.346449i	$-0.887387\pi$
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	0.769068	+	0.639167i	$0.220721\pi$
$710$	11.1962	+	7.39230i	0.420184	+	0.277428i
$711$	30.0000	+	51.9615i	1.12509	+	1.94871i
$712$	6.06218	+	3.50000i	0.227190	+	0.131168i
$713$			10.0000i			0.374503i
$714$	3.00000	+	15.5885i	0.112272	+	0.583383i
$715$		0			0
$716$	13.0000	−	22.5167i	0.485833	−	0.841487i
$717$	25.9808	−	15.0000i	0.970269	−	0.560185i
$718$	12.1244	−	7.00000i	0.452477	−	0.261238i
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	−0.617079	−	0.786901i	$-0.711684\pi$
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	0.990016	+	0.140955i	$0.0450174\pi$
$720$	−6.00000	−	12.0000i	−0.223607	−	0.447214i
$721$	22.0000	−	19.0526i	0.819323	−	0.709554i
$722$		−	15.0000i		−	0.558242i
$723$	−46.7654	−	27.0000i	−1.73922	−	1.00414i
$724$	2.50000	+	4.33013i	0.0929118	+	0.160928i
$725$	4.96410	+	0.598076i	0.184362	+	0.0222120i
$726$	−16.5000	+	28.5788i	−0.612372	+	1.06066i
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$	−1.73205	+	5.00000i	−0.0641941	+	0.185312i
$729$	27.0000			1.00000
$730$	22.3205	+	1.33975i	0.826119	+	0.0495862i
$731$	5.00000	+	8.66025i	0.184932	+	0.320311i
$732$	23.3827	−	13.5000i	0.864249	−	0.498974i
$733$	−13.8564	−	8.00000i	−0.511798	−	0.295487i	0.221774	−	0.975098i	$-0.428815\pi$
$733$	−13.8564	−	8.00000i	−0.511798	−	0.295487i	−0.733572	+	0.679611i	$0.762148\pi$
$734$	23.0000			0.848945
$735$	45.9904	+	9.48076i	1.69638	+	0.349703i
$736$	−1.00000			−0.0368605
$737$		0			0
$738$	15.5885	−	9.00000i	0.573819	−	0.331295i
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	1.07180	−	17.8564i	0.0394000	−	0.656415i
$741$	−12.0000			−0.440831
$742$	5.19615	−	15.0000i	0.190757	−	0.550667i
$743$			3.00000i			0.110059i	0.998485	+	0.0550297i	$0.0175253\pi$
$743$			3.00000i			0.110059i	−0.998485	+	0.0550297i	$0.982475\pi$
$744$	−15.0000	+	25.9808i	−0.549927	+	0.952501i
$745$	18.4808	−	27.9904i	0.677083	−	1.02549i
$746$	−4.00000	−	6.92820i	−0.146450	−	0.253660i
$747$	46.7654	+	27.0000i	1.71106	+	0.987878i
$748$		0			0
$749$	−14.0000	+	12.1244i	−0.511549	+	0.443014i
$750$	33.0000	+	6.00000i	1.20499	+	0.219089i
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$	−25.9808	+	15.0000i	−0.946792	+	0.546630i
$754$	1.00000	−	1.73205i	0.0364179	−	0.0630776i
$755$	6.00000	+	12.0000i	0.218362	+	0.436725i
$756$	4.50000	+	23.3827i	0.163663	+	0.850420i
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$	−1.73205	−	1.00000i	−0.0629109	−	0.0363216i
$759$		0			0
$760$	−3.73205	−	2.46410i	−0.135376	−	0.0893824i
$761$	25.0000	−	43.3013i	0.906249	−	1.56967i	0.0870179	−	0.996207i	$-0.472266\pi$
$761$	25.0000	−	43.3013i	0.906249	−	1.56967i	0.819231	−	0.573463i	$-0.194400\pi$
$762$			24.0000i			0.869428i
$763$	−12.9904	+	2.50000i	−0.470283	+	0.0905061i
$764$	20.0000			0.723575
$765$	1.60770	−	26.7846i	0.0581263	−	0.968400i
$766$	4.50000	+	7.79423i	0.162592	+	0.281617i
$767$	−3.46410	+	2.00000i	−0.125081	+	0.0722158i
$768$	−2.59808	−	1.50000i	−0.0937500	−	0.0541266i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$	−17.3205	−	10.0000i	−0.623379	−	0.359908i
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$	15.0000	+	25.9808i	0.539164	+	0.933859i
$775$	−19.6410	−	45.9808i	−0.705526	−	1.65168i
$776$		0			0
$777$	−20.7846	+	60.0000i	−0.745644	+	2.15249i
$778$			18.0000i			0.645331i
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	7.39230	−	11.1962i	0.264687	−	0.400887i
$781$		0			0
$782$	−1.73205	−	1.00000i	−0.0619380	−	0.0357599i
$783$		−	9.00000i		−	0.321634i
$784$	6.50000	−	2.59808i	0.232143	−	0.0927884i
$785$	24.0000	−	12.0000i	0.856597	−	0.428298i
$786$	30.0000	−	51.9615i	1.07006	−	1.85341i
$787$	18.1865	−	10.5000i	0.648280	−	0.374285i	−0.139517	−	0.990220i	$-0.544555\pi$
$787$	18.1865	−	10.5000i	0.648280	−	0.374285i	0.787797	+	0.615935i	$0.211222\pi$
$788$	6.92820	−	4.00000i	0.246807	−	0.142494i
$789$	−31.5000	+	54.5596i	−1.12143	+	1.94237i
$790$	−20.0000	+	10.0000i	−0.711568	+	0.355784i
$791$	−25.0000	−	8.66025i	−0.888898	−	0.307923i
$792$		0			0
$793$	15.5885	+	9.00000i	0.553562	+	0.319599i
$794$	−16.0000	−	27.7128i	−0.567819	−	0.983491i
$795$	−22.1769	+	33.5885i	−0.786534	+	1.19126i
$796$	−6.00000	+	10.3923i	−0.212664	+	0.368345i
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$	10.3923	+	12.0000i	0.367884	+	0.424795i
$799$	16.0000			0.566039
$800$	4.59808	−	1.96410i	0.162567	−	0.0694415i
$801$	21.0000	+	36.3731i	0.741999	+	1.28518i
$802$	2.59808	−	1.50000i	0.0917413	−	0.0529668i
$803$		0			0
$804$	−21.0000			−0.740613
$805$	−4.69615	+	3.59808i	−0.165518	+	0.126816i
$806$	−20.0000			−0.704470
$807$	12.9904	+	7.50000i	0.457283	+	0.264013i
$808$	12.9904	−	7.50000i	0.457000	−	0.263849i
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	0.997649	−	0.0685291i	$-0.0218306\pi$
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	−0.558173	+	0.829725i	$0.688497\pi$
$810$	1.20577	−	20.0885i	0.0423665	−	0.705836i
$811$	6.00000			0.210688			0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000			0.210688			0.105344	+	0.994436i	$0.466406\pi$
$812$	−2.59808	+	0.500000i	−0.0911746	+	0.0175466i
$813$			18.0000i			0.631288i
$814$		0			0
$815$	−22.3923	−	14.7846i	−0.784368	−	0.517882i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	8.66025	+	5.00000i	0.302984	+	0.174928i
$818$			17.0000i			0.594391i
$819$	−24.0000	+	20.7846i	−0.838628	+	0.726273i
$820$	3.00000	+	6.00000i	0.104765	+	0.209529i
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$	−41.5692	+	24.0000i	−1.44989	+	0.837096i
$823$	38.9711	−	22.5000i	1.35845	−	0.784301i	0.369034	−	0.929416i	$-0.379689\pi$
$823$	38.9711	−	22.5000i	1.35845	−	0.784301i	0.989415	+	0.145115i	$0.0463553\pi$
$824$	−5.50000	+	9.52628i	−0.191602	+	0.331864i
$825$		0			0
$826$	5.00000	+	1.73205i	0.173972	+	0.0602658i
$827$		−	37.0000i		−	1.28662i	−0.765607	−	0.643308i	$-0.777561\pi$
$827$		−	37.0000i		−	1.28662i	0.765607	−	0.643308i	$-0.222439\pi$
$828$	−5.19615	−	3.00000i	−0.180579	−	0.104257i
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	0.994174	+	0.107788i	$0.0343769\pi$
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	−0.403739	+	0.914874i	$0.632290\pi$
$830$	−11.0885	+	16.7942i	−0.384886	+	0.582936i
$831$	−39.0000	+	67.5500i	−1.35290	+	2.34328i
$832$		−	2.00000i		−	0.0693375i
$833$	13.8564	+	2.00000i	0.480096	+	0.0692959i
$834$	−24.0000			−0.831052
$835$	−1.20577	+	20.0885i	−0.0417274	+	0.695190i
$836$		0			0
$837$	−77.9423	+	45.0000i	−2.69408	+	1.55543i
$838$	−34.6410	−	20.0000i	−1.19665	−	0.690889i
$839$	−32.0000			−1.10476			−0.552381	−	0.833592i	$-0.686281\pi$
$839$	−32.0000			−1.10476			−0.552381	+	0.833592i	$0.686281\pi$
$840$	−17.5981	+	2.30385i	−0.607191	+	0.0794903i
$841$	−28.0000			−0.965517
$842$	−26.8468	−	15.5000i	−0.925201	−	0.534165i
$843$	46.7654	−	27.0000i	1.61068	−	0.929929i
$844$	−9.00000	−	15.5885i	−0.309793	−	0.536577i
$845$	−20.0885	−	1.20577i	−0.691064	−	0.0414798i
$846$	48.0000			1.65027
$847$	19.0526	+	22.0000i	0.654654	+	0.755929i
$848$			6.00000i			0.206041i
$849$	−12.0000	+	20.7846i	−0.411839	+	0.713326i
$850$	9.92820	+	1.19615i	0.340535	+	0.0410277i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$	15.5885	+	9.00000i	0.534052	+	0.308335i
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$	−4.50000	−	23.3827i	−0.153987	−	0.800139i
$855$	−12.0000	−	24.0000i	−0.410391	−	0.820783i
$856$	3.50000	−	6.06218i	0.119628	−	0.207201i
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	−0.557998	−	0.829843i	$-0.688430\pi$
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	0.439666	+	0.898161i	$0.355097\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	−10.0000	+	5.00000i	−0.340997	+	0.170499i
$861$	−4.50000	−	23.3827i	−0.153360	−	0.796880i
$862$			32.0000i			1.08992i
$863$	−9.52628	−	5.50000i	−0.324278	−	0.187222i	0.329020	−	0.944323i	$-0.393282\pi$
$863$	−9.52628	−	5.50000i	−0.324278	−	0.187222i	−0.653298	+	0.757101i	$0.726615\pi$
$864$	−4.50000	−	7.79423i	−0.153093	−	0.265165i
$865$	−22.3923	−	14.7846i	−0.761361	−	0.502692i
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$			39.0000i			1.32451i
$868$	17.3205	+	20.0000i	0.587896	+	0.678844i
$869$		0			0
$870$	6.69615	+	0.401924i	0.227021	+	0.0136265i
$871$	−7.00000	−	12.1244i	−0.237186	−	0.410818i
$872$	4.33013	−	2.50000i	0.146637	−	0.0846607i
$873$		0			0
$874$	−2.00000			−0.0676510
$875$	14.5263	−	25.7679i	0.491078	−	0.871116i
$876$	30.0000			1.01361
$877$	12.1244	+	7.00000i	0.409410	+	0.236373i	0.690536	−	0.723298i	$-0.257375\pi$
$877$	12.1244	+	7.00000i	0.409410	+	0.236373i	−0.281126	+	0.959671i	$0.590708\pi$
$878$	−6.92820	+	4.00000i	−0.233816	+	0.134993i
$879$	−36.0000	−	62.3538i	−1.21425	−	2.10314i
$880$		0			0
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$	41.5692	+	6.00000i	1.39971	+	0.202031i
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$	−11.1962	−	7.39230i	−0.376355	−	0.248490i
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	0.363407	−	0.931630i	$-0.381613\pi$
$887$	−7.79423	−	4.50000i	−0.261705	−	0.151095i	−0.625112	+	0.780535i	$0.714947\pi$
$888$		−	24.0000i		−	0.805387i
$889$	20.0000	+	6.92820i	0.670778	+	0.232364i
$890$	−14.0000	+	7.00000i	−0.469281	+	0.234641i
$891$		0			0
$892$	−6.92820	+	4.00000i	−0.231973	+	0.133930i
$893$	13.8564	−	8.00000i	0.463687	−	0.267710i
$894$	22.5000	−	38.9711i	0.752513	−	1.30339i
$895$	26.0000	+	52.0000i	0.869084	+	1.73817i
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		−	6.00000i		−	0.200334i
$898$	19.9186	+	11.5000i	0.664692	+	0.383760i
$899$	−5.00000	−	8.66025i	−0.166759	−	0.288836i
$900$	29.7846	+	3.58846i	0.992820	+	0.119615i
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$	38.9711	−	7.50000i	1.29688	−	0.249584i
$904$	10.0000			0.332595
$905$	−11.1603	−	0.669873i	−0.370979	−	0.0222673i
$906$	9.00000	+	15.5885i	0.299005	+	0.517892i
$907$	−21.6506	+	12.5000i	−0.718898	+	0.415056i	−0.814347	−	0.580379i	$-0.802905\pi$
$907$	−21.6506	+	12.5000i	−0.718898	+	0.415056i	0.0954492	+	0.995434i	$0.469571\pi$
$908$	10.3923	+	6.00000i	0.344881	+	0.199117i
$909$	90.0000			2.98511
$910$	−7.19615	−	9.39230i	−0.238550	−	0.311352i
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$	−5.19615	−	3.00000i	−0.172062	−	0.0993399i
$913$		0			0
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$	−3.61731	+	60.2654i	−0.119585	+	1.99231i
$916$	10.0000			0.330409
$917$	−34.6410	−	40.0000i	−1.14395	−	1.32092i
$918$		−	18.0000i		−	0.594089i
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	0.996770	+	0.0803145i	$0.0255924\pi$
$920$	1.23205	−	1.86603i	0.0406195	−	0.0615210i
$921$	−28.5000	−	49.3634i	−0.939107	−	1.62658i
$922$	12.1244	+	7.00000i	0.399294	+	0.230533i
$923$			12.0000i			0.394985i
$924$		0			0
$925$	32.0000	+	24.0000i	1.05215	+	0.789115i
$926$	−12.5000	+	21.6506i	−0.410775	+	0.711484i
$927$	−57.1577	+	33.0000i	−1.87730	+	1.08386i
$928$	0.866025	−	0.500000i	0.0284287	−	0.0164133i
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$	−30.0000	−	60.0000i	−0.983739	−	1.96748i
$931$	13.0000	−	5.19615i	0.426058	−	0.170297i
$932$		−	14.0000i		−	0.458585i
$933$	−15.5885	−	9.00000i	−0.510343	−	0.294647i
$934$	0.500000	+	0.866025i	0.0163605	+	0.0283372i
$935$		0			0
$936$	6.00000	−	10.3923i	0.196116	−	0.339683i
$937$		−	56.0000i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$937$		−	56.0000i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$938$	−6.06218	+	17.5000i	−0.197937	+	0.571395i
$939$	24.0000			0.783210
$940$	−1.07180	+	17.8564i	−0.0349582	+	0.582412i
$941$	−7.00000	−	12.1244i	−0.228193	−	0.395243i	0.729079	−	0.684429i	$-0.239949\pi$
$941$	−7.00000	−	12.1244i	−0.228193	−	0.395243i	−0.957273	+	0.289187i	$0.906615\pi$
$942$	31.1769	−	18.0000i	1.01580	−	0.586472i
$943$	2.59808	+	1.50000i	0.0846050	+	0.0488467i
$944$	−2.00000			−0.0650945
$945$	−49.1769	−	20.4115i	−1.59973	−	0.663988i
$946$		0			0
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	0.541619	−	0.840624i	$-0.317812\pi$
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	−0.457193	+	0.889368i	$0.651145\pi$
$948$	−25.9808	+	15.0000i	−0.843816	+	0.487177i
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$	9.19615	−	3.92820i	0.298363	−	0.127448i
$951$	−66.0000			−2.14020
$952$	−5.19615	+	1.00000i	−0.168408	+	0.0324102i
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$	−18.0000	+	31.1769i	−0.582772	+	1.00939i
$955$	−24.6410	+	37.3205i	−0.797365	+	1.20766i
$956$	5.00000	+	8.66025i	0.161712	+	0.280093i
$957$		0			0
$958$		−	18.0000i		−	0.581554i
$959$	8.00000	+	41.5692i	0.258333	+	1.34234i
$960$	6.00000	−	3.00000i	0.193649	−	0.0968246i
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	13.8564	−	8.00000i	0.446748	−	0.257930i
$963$	36.3731	−	21.0000i	1.17211	−	0.676716i
$964$	9.00000	−	15.5885i	0.289870	−	0.502070i
$965$	40.0000	−	20.0000i	1.28765	−	0.643823i
$966$	−6.00000	+	5.19615i	−0.193047	+	0.167183i
$967$			17.0000i			0.546683i	0.961917	+	0.273342i	$0.0881289\pi$
$967$			17.0000i			0.546683i	−0.961917	+	0.273342i	$0.911871\pi$
$968$	−9.52628	−	5.50000i	−0.306186	−	0.176777i
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	−6.92820	+	20.0000i	−0.222108	+	0.641171i
$974$	−4.00000			−0.128168
$975$	11.7846	+	27.5885i	0.377410	+	0.883538i
$976$	4.50000	+	7.79423i	0.144041	+	0.249487i
$977$	31.1769	−	18.0000i	0.997438	−	0.575871i	0.0899487	−	0.995946i	$-0.471330\pi$
$977$	31.1769	−	18.0000i	0.997438	−	0.575871i	0.907489	+	0.420075i	$0.137996\pi$
$978$	−31.1769	−	18.0000i	−0.996928	−	0.575577i
$979$		0			0
$980$	−3.16025	+	15.3301i	−0.100951	+	0.489703i
$981$	30.0000			0.957826
$982$	15.5885	+	9.00000i	0.497448	+	0.287202i
$983$	−21.6506	+	12.5000i	−0.690548	+	0.398688i	−0.803817	−	0.594876i	$-0.797201\pi$
$983$	−21.6506	+	12.5000i	−0.690548	+	0.398688i	0.113269	+	0.993564i	$0.463868\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	−1.07180	+	17.8564i	−0.0341503	+	0.568952i
$986$	2.00000			0.0636930
$987$	20.7846	−	60.0000i	0.661581	−	1.90982i
$988$		−	4.00000i		−	0.127257i
$989$	−2.50000	+	4.33013i	−0.0794954	+	0.137690i
$990$		0			0
$991$	13.0000	+	22.5167i	0.412959	+	0.715265i	0.995212	−	0.0977423i	$-0.0311621\pi$
$991$	13.0000	+	22.5167i	0.412959	+	0.715265i	−0.582253	+	0.813008i	$0.697829\pi$
$992$	−8.66025	−	5.00000i	−0.274963	−	0.158750i
$993$			42.0000i			1.33283i
$994$	12.0000	−	10.3923i	0.380617	−	0.329624i
$995$	−12.0000	−	24.0000i	−0.380426	−	0.760851i
$996$	−13.5000	+	23.3827i	−0.427764	+	0.740909i
$997$	29.4449	−	17.0000i	0.932528	−	0.538395i	0.0449179	−	0.998991i	$-0.485697\pi$
$997$	29.4449	−	17.0000i	0.932528	−	0.538395i	0.887610	+	0.460595i	$0.152364\pi$
$998$	−13.8564	+	8.00000i	−0.438617	+	0.253236i
$999$	36.0000	−	62.3538i	1.13899	−	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.i.a.9.1	✓	4
3.2	odd	2		630.2.u.b.289.2		4
4.3	odd	2		560.2.bw.c.289.1		4
5.2	odd	4		350.2.e.g.51.1		2
5.3	odd	4		350.2.e.f.51.1		2
5.4	even	2	inner	70.2.i.a.9.2	yes	4
7.2	even	3		490.2.c.c.99.2		2
7.3	odd	6		490.2.i.b.459.2		4
7.4	even	3	inner	70.2.i.a.39.2	yes	4
7.5	odd	6		490.2.c.b.99.2		2
7.6	odd	2		490.2.i.b.79.1		4
15.14	odd	2		630.2.u.b.289.1		4
20.19	odd	2		560.2.bw.c.289.2		4
21.11	odd	6		630.2.u.b.109.1		4
28.11	odd	6		560.2.bw.c.529.2		4
35.2	odd	12		2450.2.a.r.1.1		1
35.4	even	6	inner	70.2.i.a.39.1	yes	4
35.9	even	6		490.2.c.c.99.1		2
35.12	even	12		2450.2.a.c.1.1		1
35.18	odd	12		350.2.e.f.151.1		2
35.19	odd	6		490.2.c.b.99.1		2
35.23	odd	12		2450.2.a.s.1.1		1
35.24	odd	6		490.2.i.b.459.1		4
35.32	odd	12		350.2.e.g.151.1		2
35.33	even	12		2450.2.a.bh.1.1		1
35.34	odd	2		490.2.i.b.79.2		4
105.74	odd	6		630.2.u.b.109.2		4
140.39	odd	6		560.2.bw.c.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	1.1	even	1	trivial
70.2.i.a.9.2	yes	4	5.4	even	2	inner
70.2.i.a.39.1	yes	4	35.4	even	6	inner
70.2.i.a.39.2	yes	4	7.4	even	3	inner
350.2.e.f.51.1		2	5.3	odd	4
350.2.e.f.151.1		2	35.18	odd	12
350.2.e.g.51.1		2	5.2	odd	4
350.2.e.g.151.1		2	35.32	odd	12
490.2.c.b.99.1		2	35.19	odd	6
490.2.c.b.99.2		2	7.5	odd	6
490.2.c.c.99.1		2	35.9	even	6
490.2.c.c.99.2		2	7.2	even	3
490.2.i.b.79.1		4	7.6	odd	2
490.2.i.b.79.2		4	35.34	odd	2
490.2.i.b.459.1		4	35.24	odd	6
490.2.i.b.459.2		4	7.3	odd	6
560.2.bw.c.289.1		4	4.3	odd	2
560.2.bw.c.289.2		4	20.19	odd	2
560.2.bw.c.529.1		4	140.39	odd	6
560.2.bw.c.529.2		4	28.11	odd	6
630.2.u.b.109.1		4	21.11	odd	6
630.2.u.b.109.2		4	105.74	odd	6
630.2.u.b.289.1		4	15.14	odd	2
630.2.u.b.289.2		4	3.2	odd	2
2450.2.a.c.1.1		1	35.12	even	12
2450.2.a.r.1.1		1	35.2	odd	12
2450.2.a.s.1.1		1	35.23	odd	12
2450.2.a.bh.1.1		1	35.33	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} -3.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(2.59808 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.23205 - 0.133975i) q^{5} -3.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(1.86603 + 1.23205i) q^{10} +(2.59808 + 1.50000i) q^{12} +2.00000i q^{13} +(2.00000 - 1.73205i) q^{14} +(-6.00000 + 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.00000 - 2.00000i) q^{20} +(1.50000 + 7.79423i) q^{21} +(-0.866025 - 0.500000i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(4.96410 + 0.598076i) q^{25} +(1.00000 - 1.73205i) q^{26} -9.00000i q^{27} +(-2.59808 + 0.500000i) q^{28} +1.00000 q^{29} +(6.69615 + 0.401924i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(2.26795 - 5.46410i) q^{35} +6.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(1.73205 - 1.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(-0.133975 + 2.23205i) q^{40} -3.00000 q^{41} +(2.59808 - 7.50000i) q^{42} -5.00000i q^{43} +(-7.39230 + 11.1962i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-6.92820 - 4.00000i) q^{47} +3.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(2.50000 + 0.866025i) q^{56} +6.00000i q^{57} +(-0.866025 - 0.500000i) q^{58} +(1.00000 + 1.73205i) q^{59} +(-5.59808 - 3.69615i) q^{60} +(4.50000 - 7.79423i) q^{61} +10.0000i q^{62} +(10.3923 + 12.0000i) q^{63} -1.00000 q^{64} +(0.267949 - 4.46410i) q^{65} +(-6.06218 + 3.50000i) q^{67} +(-1.73205 - 1.00000i) q^{68} -3.00000 q^{69} +(-4.69615 + 3.59808i) q^{70} +6.00000 q^{71} +(-5.19615 - 3.00000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(13.7942 - 5.89230i) q^{75} -2.00000 q^{76} -6.00000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(1.23205 - 1.86603i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 1.50000i) q^{82} +9.00000i q^{83} +(-6.00000 + 5.19615i) q^{84} +(4.00000 - 2.00000i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(2.59808 - 1.50000i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(12.0000 - 6.00000i) q^{90} +(-5.00000 - 1.73205i) q^{91} -1.00000i q^{92} +(-25.9808 - 15.0000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(2.46410 - 3.73205i) q^{95} +(1.50000 - 2.59808i) q^{96} +(2.59808 + 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 12 * q^9	\( 4 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 12 q^{9} + 4 q^{10} + 8 q^{14} - 24 q^{15} - 2 q^{16} - 4 q^{19} - 4 q^{20} + 6 q^{21} - 6 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{29} + 6 q^{30} - 20 q^{31} + 8 q^{34} + 16 q^{35} + 24 q^{36} + 12 q^{39} - 4 q^{40} - 12 q^{41} + 12 q^{45} + 2 q^{46} - 22 q^{49} - 16 q^{50} - 12 q^{51} - 18 q^{54} + 10 q^{56} + 4 q^{59} - 12 q^{60} + 18 q^{61} - 4 q^{64} + 8 q^{65} - 12 q^{69} + 2 q^{70} + 24 q^{71} - 16 q^{74} + 24 q^{75} - 8 q^{76} - 20 q^{79} - 2 q^{80} - 18 q^{81} - 24 q^{84} + 16 q^{85} - 10 q^{86} - 14 q^{89} + 48 q^{90} - 20 q^{91} + 16 q^{94} - 4 q^{95} + 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 12 * q^9 + 4 * q^10 + 8 * q^14 - 24 * q^15 - 2 * q^16 - 4 * q^19 - 4 * q^20 + 6 * q^21 - 6 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^29 + 6 * q^30 - 20 * q^31 + 8 * q^34 + 16 * q^35 + 24 * q^36 + 12 * q^39 - 4 * q^40 - 12 * q^41 + 12 * q^45 + 2 * q^46 - 22 * q^49 - 16 * q^50 - 12 * q^51 - 18 * q^54 + 10 * q^56 + 4 * q^59 - 12 * q^60 + 18 * q^61 - 4 * q^64 + 8 * q^65 - 12 * q^69 + 2 * q^70 + 24 * q^71 - 16 * q^74 + 24 * q^75 - 8 * q^76 - 20 * q^79 - 2 * q^80 - 18 * q^81 - 24 * q^84 + 16 * q^85 - 10 * q^86 - 14 * q^89 + 48 * q^90 - 20 * q^91 + 16 * q^94 - 4 * q^95 + 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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