LMFDB - Embedded newform 714.2.t.c.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(67,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("714.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.t (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:	$5.70131870432$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	714.67
Dual form			714.2.t.c.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.59808 - 1.50000i) q^{10} +(1.73205 + 1.00000i) q^{11} +(-0.866025 + 0.500000i) q^{12} +4.00000 q^{13} +(1.73205 + 2.00000i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.96410 + 2.86603i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +3.00000i q^{20} +(-2.50000 - 0.866025i) q^{21} -2.00000i q^{22} +(0.866025 - 0.500000i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} -6.00000i q^{29} +(-1.50000 - 2.59808i) q^{30} +(6.92820 + 4.00000i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(1.00000 - 4.00000i) q^{34} +(-6.00000 + 5.19615i) q^{35} -1.00000 q^{36} +(6.06218 - 3.50000i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(3.46410 + 2.00000i) q^{39} +(2.59808 - 1.50000i) q^{40} +8.00000i q^{41} +(0.500000 + 2.59808i) q^{42} -9.00000 q^{43} +(-1.73205 + 1.00000i) q^{44} +(2.59808 + 1.50000i) q^{45} +(-0.866025 - 0.500000i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(1.13397 + 3.96410i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(0.866025 - 0.500000i) q^{54} +6.00000 q^{55} +(-2.59808 + 0.500000i) q^{56} -5.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(0.500000 - 0.866025i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.73205 - 1.00000i) q^{61} -8.00000i q^{62} +(-1.73205 - 2.00000i) q^{63} +1.00000 q^{64} +(10.3923 - 6.00000i) q^{65} +(1.00000 - 1.73205i) q^{66} +(2.50000 - 4.33013i) q^{67} +(-3.96410 + 1.13397i) q^{68} +1.00000 q^{69} +(7.50000 + 2.59808i) q^{70} -1.00000i q^{71} +(0.500000 + 0.866025i) q^{72} +(8.66025 + 5.00000i) q^{73} +(-6.06218 - 3.50000i) q^{74} +(3.46410 - 2.00000i) q^{75} +5.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} -4.00000i q^{78} +(-3.46410 + 2.00000i) q^{79} +(-2.59808 - 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.92820 - 4.00000i) q^{82} -4.00000 q^{83} +(2.00000 - 1.73205i) q^{84} +(12.0000 + 3.00000i) q^{85} +(4.50000 + 7.79423i) q^{86} +(3.00000 - 5.19615i) q^{87} +(1.73205 + 1.00000i) q^{88} +(-7.50000 - 12.9904i) q^{89} -3.00000i q^{90} +(-10.3923 + 2.00000i) q^{91} +1.00000i q^{92} +(4.00000 + 6.92820i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-12.9904 - 7.50000i) q^{95} +(-0.866025 + 0.500000i) q^{96} -12.0000i q^{97} +(-5.50000 - 4.33013i) q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 16 q^{13} + 12 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} - 10 q^{19} - 10 q^{21} + 8 q^{25} - 8 q^{26} - 6 q^{30} - 2 q^{32} + 4 q^{33} + 4 q^{34} - 24 q^{35} - 4 q^{36} - 10 q^{38} + 2 q^{42} - 36 q^{43} - 12 q^{47} + 26 q^{49} - 16 q^{50} + 8 q^{51} - 8 q^{52} - 8 q^{53} + 24 q^{55} + 2 q^{59} - 6 q^{60} + 4 q^{64} + 4 q^{66} + 10 q^{67} - 2 q^{68} + 4 q^{69} + 30 q^{70} + 2 q^{72} + 20 q^{76} - 20 q^{77} - 2 q^{81} - 16 q^{83} + 8 q^{84} + 48 q^{85} + 18 q^{86} + 12 q^{87} - 30 q^{89} + 16 q^{93} - 12 q^{94} - 22 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9 + 16 * q^13 + 12 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 - 10 * q^19 - 10 * q^21 + 8 * q^25 - 8 * q^26 - 6 * q^30 - 2 * q^32 + 4 * q^33 + 4 * q^34 - 24 * q^35 - 4 * q^36 - 10 * q^38 + 2 * q^42 - 36 * q^43 - 12 * q^47 + 26 * q^49 - 16 * q^50 + 8 * q^51 - 8 * q^52 - 8 * q^53 + 24 * q^55 + 2 * q^59 - 6 * q^60 + 4 * q^64 + 4 * q^66 + 10 * q^67 - 2 * q^68 + 4 * q^69 + 30 * q^70 + 2 * q^72 + 20 * q^76 - 20 * q^77 - 2 * q^81 - 16 * q^83 + 8 * q^84 + 48 * q^85 + 18 * q^86 + 12 * q^87 - 30 * q^89 + 16 * q^93 - 12 * q^94 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.59808	−	1.50000i	1.16190	−	0.670820i	0.210138	−	0.977672i	$-0.432609\pi$
$5$	2.59808	−	1.50000i	1.16190	−	0.670820i	0.951757	+	0.306851i	$0.0992755\pi$
$6$		−	1.00000i		−	0.408248i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.59808	−	1.50000i	−0.821584	−	0.474342i
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	0.737848	−	0.674967i	$-0.235842\pi$
$11$	1.73205	+	1.00000i	0.522233	+	0.301511i	−0.215615	+	0.976478i	$0.569176\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	1.73205	+	2.00000i	0.462910	+	0.534522i
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.96410	+	2.86603i	0.718900	+	0.695113i
$17$	2.96410	+	2.86603i	0.718900	+	0.695113i
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$			3.00000i			0.670820i
$21$	−2.50000	−	0.866025i	−0.545545	−	0.188982i
$22$		−	2.00000i		−	0.426401i
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	−0.406986	−	0.913434i	$-0.633420\pi$
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	0.587565	+	0.809177i	$0.300087\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$			1.00000i			0.192450i
$28$	0.866025	−	2.50000i	0.163663	−	0.472456i
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	6.92820	+	4.00000i	1.24434	+	0.718421i	0.969975	−	0.243204i	$-0.0781984\pi$
$31$	6.92820	+	4.00000i	1.24434	+	0.718421i	0.274367	+	0.961625i	$0.411532\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	1.00000	−	4.00000i	0.171499	−	0.685994i
$35$	−6.00000	+	5.19615i	−1.01419	+	0.878310i
$36$	−1.00000			−0.166667
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.0893706	−	0.995998i	$-0.471514\pi$
$37$	6.06218	−	3.50000i	0.996616	−	0.575396i	0.907245	+	0.420602i	$0.138181\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$	3.46410	+	2.00000i	0.554700	+	0.320256i
$40$	2.59808	−	1.50000i	0.410792	−	0.237171i
$41$			8.00000i			1.24939i	0.780869	+	0.624695i	$0.214777\pi$
$41$			8.00000i			1.24939i	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0.500000	+	2.59808i	0.0771517	+	0.400892i
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$	−1.73205	+	1.00000i	−0.261116	+	0.150756i
$45$	2.59808	+	1.50000i	0.387298	+	0.223607i
$46$	−0.866025	−	0.500000i	−0.127688	−	0.0737210i
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$	−4.00000			−0.565685
$51$	1.13397	+	3.96410i	0.158788	+	0.555085i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	6.00000			0.809040
$56$	−2.59808	+	0.500000i	−0.347183	+	0.0668153i
$57$		−	5.00000i		−	0.662266i
$58$	−5.19615	+	3.00000i	−0.682288	+	0.393919i
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	−0.831641	−	0.555313i	$-0.812598\pi$
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	0.896736	+	0.442566i	$0.145932\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	1.73205	−	1.00000i	0.221766	−	0.128037i	−0.385002	−	0.922916i	$-0.625799\pi$
$61$	1.73205	−	1.00000i	0.221766	−	0.128037i	0.606768	+	0.794879i	$0.292466\pi$
$62$		−	8.00000i		−	1.01600i
$63$	−1.73205	−	2.00000i	−0.218218	−	0.251976i
$64$	1.00000			0.125000
$65$	10.3923	−	6.00000i	1.28901	−	0.744208i
$66$	1.00000	−	1.73205i	0.123091	−	0.213201i
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$	−3.96410	+	1.13397i	−0.480718	+	0.137515i
$69$	1.00000			0.120386
$70$	7.50000	+	2.59808i	0.896421	+	0.310530i
$71$		−	1.00000i		−	0.118678i	−0.998238	−	0.0593391i	$-0.981101\pi$
$71$		−	1.00000i		−	0.118678i	0.998238	−	0.0593391i	$-0.0188993\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.912245	−	0.409644i	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$	−6.06218	−	3.50000i	−0.704714	−	0.406867i
$75$	3.46410	−	2.00000i	0.400000	−	0.230940i
$76$	5.00000			0.573539
$77$	−5.00000	−	1.73205i	−0.569803	−	0.197386i
$78$		−	4.00000i		−	0.452911i
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$	−2.59808	−	1.50000i	−0.290474	−	0.167705i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.92820	−	4.00000i	0.765092	−	0.441726i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$	12.0000	+	3.00000i	1.30158	+	0.325396i
$86$	4.50000	+	7.79423i	0.485247	+	0.840473i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	1.73205	+	1.00000i	0.184637	+	0.106600i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		−	3.00000i		−	0.316228i
$91$	−10.3923	+	2.00000i	−1.08941	+	0.209657i
$92$			1.00000i			0.104257i
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	−12.9904	−	7.50000i	−1.33278	−	0.769484i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$			2.00000i			0.201008i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−8.00000	+	13.8564i	−0.796030	+	1.37876i	0.126153	+	0.992011i	$0.459737\pi$
$101$	−8.00000	+	13.8564i	−0.796030	+	1.37876i	−0.922183	+	0.386753i	$0.873597\pi$
$102$	2.86603	−	2.96410i	0.283779	−	0.293490i
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	0.679525	−	0.733652i	$-0.262186\pi$
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	−0.975124	+	0.221660i	$0.928852\pi$
$104$	4.00000			0.392232
$105$	−7.79423	+	1.50000i	−0.760639	+	0.146385i
$106$	4.00000			0.388514
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	−0.729676	−	0.683793i	$-0.760329\pi$
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	0.227345	+	0.973814i	$0.426996\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−6.06218	−	3.50000i	−0.580651	−	0.335239i	0.180741	−	0.983531i	$-0.442150\pi$
$109$	−6.06218	−	3.50000i	−0.580651	−	0.335239i	−0.761392	+	0.648292i	$0.775484\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$	7.00000			0.664411
$112$	1.73205	+	2.00000i	0.163663	+	0.188982i
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$	−4.33013	+	2.50000i	−0.405554	+	0.234146i
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	5.19615	+	3.00000i	0.482451	+	0.278543i
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$	−1.00000			−0.0920575
$119$	−9.13397	−	5.96410i	−0.837310	−	0.546728i
$120$	3.00000			0.273861
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	−1.73205	−	1.00000i	−0.156813	−	0.0905357i
$123$	−4.00000	+	6.92820i	−0.360668	+	0.624695i
$124$	−6.92820	+	4.00000i	−0.622171	+	0.359211i
$125$			3.00000i			0.268328i
$126$	−0.866025	+	2.50000i	−0.0771517	+	0.222718i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−7.79423	−	4.50000i	−0.686244	−	0.396203i
$130$	−10.3923	−	6.00000i	−0.911465	−	0.526235i
$131$	−3.46410	+	2.00000i	−0.302660	+	0.174741i	−0.643637	−	0.765331i	$-0.722575\pi$
$131$	−3.46410	+	2.00000i	−0.302660	+	0.174741i	0.340977	+	0.940072i	$0.389242\pi$
$132$	−2.00000			−0.174078
$133$	8.66025	+	10.0000i	0.750939	+	0.867110i
$134$	−5.00000			−0.431934
$135$	1.50000	+	2.59808i	0.129099	+	0.223607i
$136$	2.96410	+	2.86603i	0.254170	+	0.245760i
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	−0.886594	−	0.462549i	$-0.846935\pi$
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	0.843876	+	0.536538i	$0.180268\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$			2.00000i			0.169638i	0.996396	+	0.0848189i	$0.0270312\pi$
$139$			2.00000i			0.169638i	−0.996396	+	0.0848189i	$0.972969\pi$
$140$	−1.50000	−	7.79423i	−0.126773	−	0.658733i
$141$		−	6.00000i		−	0.505291i
$142$	−0.866025	+	0.500000i	−0.0726752	+	0.0419591i
$143$	6.92820	+	4.00000i	0.579365	+	0.334497i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−9.00000	−	15.5885i	−0.747409	−	1.29455i
$146$		−	10.0000i		−	0.827606i
$147$	6.92820	+	1.00000i	0.571429	+	0.0824786i
$148$			7.00000i			0.575396i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$	−3.46410	−	2.00000i	−0.282843	−	0.163299i
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	−1.00000	+	4.00000i	−0.0808452	+	0.323381i
$154$	1.00000	+	5.19615i	0.0805823	+	0.418718i
$155$	24.0000			1.92773
$156$	−3.46410	+	2.00000i	−0.277350	+	0.160128i
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.0242497	+	0.999706i	$0.507720\pi$
$157$	−11.0000	+	19.0526i	−0.877896	+	1.52056i	−0.853646	+	0.520854i	$0.825614\pi$
$158$	3.46410	+	2.00000i	0.275589	+	0.159111i
$159$	−3.46410	+	2.00000i	−0.274721	+	0.158610i
$160$			3.00000i			0.237171i
$161$	−2.00000	+	1.73205i	−0.157622	+	0.136505i
$162$	1.00000			0.0785674
$163$	−12.1244	+	7.00000i	−0.949653	+	0.548282i	−0.892973	−	0.450110i	$-0.851385\pi$
$163$	−12.1244	+	7.00000i	−0.949653	+	0.548282i	−0.0566798	+	0.998392i	$0.518051\pi$
$164$	−6.92820	−	4.00000i	−0.541002	−	0.312348i
$165$	5.19615	+	3.00000i	0.404520	+	0.233550i
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$			15.0000i			1.16073i	0.814355	+	0.580367i	$0.197091\pi$
$167$			15.0000i			1.16073i	−0.814355	+	0.580367i	$0.802909\pi$
$168$	−2.50000	−	0.866025i	−0.192879	−	0.0668153i
$169$	3.00000			0.230769
$170$	−3.40192	−	11.8923i	−0.260916	−	0.912098i
$171$	2.50000	−	4.33013i	0.191180	−	0.331133i
$172$	4.50000	−	7.79423i	0.343122	−	0.594304i
$173$	−11.2583	+	6.50000i	−0.855955	+	0.494186i	−0.862656	−	0.505792i	$-0.831200\pi$
$173$	−11.2583	+	6.50000i	−0.855955	+	0.494186i	0.00670064	+	0.999978i	$0.497867\pi$
$174$	−6.00000			−0.454859
$175$	−3.46410	+	10.0000i	−0.261861	+	0.755929i
$176$		−	2.00000i		−	0.150756i
$177$	0.866025	−	0.500000i	0.0650945	−	0.0375823i
$178$	−7.50000	+	12.9904i	−0.562149	+	0.973670i
$179$	−5.50000	+	9.52628i	−0.411089	+	0.712028i	−0.995009	−	0.0997838i	$-0.968185\pi$
$179$	−5.50000	+	9.52628i	−0.411089	+	0.712028i	0.583920	+	0.811811i	$0.301518\pi$
$180$	−2.59808	+	1.50000i	−0.193649	+	0.111803i
$181$		−	11.0000i		−	0.817624i	−0.912619	−	0.408812i	$-0.865943\pi$
$181$		−	11.0000i		−	0.817624i	0.912619	−	0.408812i	$-0.134057\pi$
$182$	6.92820	+	8.00000i	0.513553	+	0.592999i
$183$	2.00000			0.147844
$184$	0.866025	−	0.500000i	0.0638442	−	0.0368605i
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$	2.26795	+	7.92820i	0.165849	+	0.579768i
$188$	6.00000			0.437595
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$			15.0000i			1.08821i
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−5.19615	−	3.00000i	−0.374027	−	0.215945i	0.301189	−	0.953564i	$-0.402616\pi$
$193$	−5.19615	−	3.00000i	−0.374027	−	0.215945i	−0.675216	+	0.737620i	$0.735950\pi$
$194$	−10.3923	+	6.00000i	−0.746124	+	0.430775i
$195$	12.0000			0.859338
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			15.0000i			1.06871i	0.845262	+	0.534353i	$0.179445\pi$
$197$			15.0000i			1.06871i	−0.845262	+	0.534353i	$0.820555\pi$
$198$	1.73205	−	1.00000i	0.123091	−	0.0710669i
$199$	−12.9904	−	7.50000i	−0.920864	−	0.531661i	−0.0369532	−	0.999317i	$-0.511765\pi$
$199$	−12.9904	−	7.50000i	−0.920864	−	0.531661i	−0.883911	+	0.467656i	$0.845099\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	4.33013	−	2.50000i	0.305424	−	0.176336i
$202$	16.0000			1.12576
$203$	3.00000	+	15.5885i	0.210559	+	1.09410i
$204$	−4.00000	−	1.00000i	−0.280056	−	0.0700140i
$205$	12.0000	+	20.7846i	0.838116	+	1.45166i
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	0.866025	+	0.500000i	0.0601929	+	0.0347524i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$		−	10.0000i		−	0.691714i
$210$	5.19615	+	6.00000i	0.358569	+	0.414039i
$211$		−	12.0000i		−	0.826114i	−0.910705	−	0.413057i	$-0.864461\pi$
$211$		−	12.0000i		−	0.826114i	0.910705	−	0.413057i	$-0.135539\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$	0.500000	−	0.866025i	0.0342594	−	0.0593391i
$214$	5.19615	+	3.00000i	0.355202	+	0.205076i
$215$	−23.3827	+	13.5000i	−1.59469	+	0.920692i
$216$			1.00000i			0.0680414i
$217$	−20.0000	−	6.92820i	−1.35769	−	0.470317i
$218$			7.00000i			0.474100i
$219$	5.00000	+	8.66025i	0.337869	+	0.585206i
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	11.8564	+	11.4641i	0.797548	+	0.771159i
$222$	−3.50000	−	6.06218i	−0.234905	−	0.406867i
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$	0.866025	−	2.50000i	0.0578638	−	0.167038i
$225$	4.00000			0.266667
$226$	15.5885	−	9.00000i	1.03693	−	0.598671i
$227$	−13.8564	−	8.00000i	−0.919682	−	0.530979i	−0.0361484	−	0.999346i	$-0.511509\pi$
$227$	−13.8564	−	8.00000i	−0.919682	−	0.530979i	−0.883534	+	0.468368i	$0.844842\pi$
$228$	4.33013	+	2.50000i	0.286770	+	0.165567i
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$	−3.00000			−0.197814
$231$	−3.46410	−	4.00000i	−0.227921	−	0.263181i
$232$		−	6.00000i		−	0.393919i
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.106773	−	0.994283i	$-0.465948\pi$
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.914461	+	0.404674i	$0.132615\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$	−15.5885	−	9.00000i	−1.01688	−	0.587095i
$236$	0.500000	+	0.866025i	0.0325472	+	0.0563735i
$237$	−4.00000			−0.259828
$238$	−0.598076	+	10.8923i	−0.0387675	+	0.706043i
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	−17.3205	−	10.0000i	−1.11571	−	0.644157i	−0.175409	−	0.984496i	$-0.556125\pi$
$241$	−17.3205	−	10.0000i	−1.11571	−	0.644157i	−0.940303	+	0.340339i	$0.889458\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$			2.00000i			0.128037i
$245$	12.9904	−	16.5000i	0.829925	−	1.05415i
$246$	8.00000			0.510061
$247$	−10.0000	−	17.3205i	−0.636285	−	1.10208i
$248$	6.92820	+	4.00000i	0.439941	+	0.254000i
$249$	−3.46410	−	2.00000i	−0.219529	−	0.126745i
$250$	2.59808	−	1.50000i	0.164317	−	0.0948683i
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$	2.59808	−	0.500000i	0.163663	−	0.0314970i
$253$	2.00000			0.125739
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$	8.89230	+	8.59808i	0.556858	+	0.538432i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	0.981901	+	0.189396i	$0.0606529\pi$
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	−0.326929	+	0.945049i	$0.606014\pi$
$258$			9.00000i			0.560316i
$259$	−14.0000	+	12.1244i	−0.869918	+	0.753371i
$260$			12.0000i			0.744208i
$261$	5.19615	−	3.00000i	0.321634	−	0.185695i
$262$	3.46410	+	2.00000i	0.214013	+	0.123560i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$			12.0000i			0.737154i
$266$	4.33013	−	12.5000i	0.265497	−	0.766424i
$267$		−	15.0000i		−	0.917985i
$268$	2.50000	+	4.33013i	0.152712	+	0.264505i
$269$	−16.4545	−	9.50000i	−1.00325	−	0.579225i	−0.0940400	−	0.995568i	$-0.529978\pi$
$269$	−16.4545	−	9.50000i	−1.00325	−	0.579225i	−0.909208	+	0.416343i	$0.863311\pi$
$270$	1.50000	−	2.59808i	0.0912871	−	0.158114i
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	0.571221	−	0.820796i	$-0.306470\pi$
$271$	−7.00000	−	12.1244i	−0.425220	−	0.736502i	−0.996441	+	0.0842940i	$0.973137\pi$
$272$	1.00000	−	4.00000i	0.0606339	−	0.242536i
$273$	−10.0000	−	3.46410i	−0.605228	−	0.209657i
$274$	1.00000			0.0604122
$275$	6.92820	−	4.00000i	0.417786	−	0.241209i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	15.5885	+	9.00000i	0.936620	+	0.540758i	0.888899	−	0.458103i	$-0.151471\pi$
$277$	15.5885	+	9.00000i	0.936620	+	0.540758i	0.0477206	+	0.998861i	$0.484804\pi$
$278$	1.73205	−	1.00000i	0.103882	−	0.0599760i
$279$			8.00000i			0.478947i
$280$	−6.00000	+	5.19615i	−0.358569	+	0.310530i
$281$	−27.0000			−1.61068			−0.805342	−	0.592810i	$-0.798019\pi$
$281$	−27.0000			−1.61068			−0.805342	+	0.592810i	$0.798019\pi$
$282$	−5.19615	+	3.00000i	−0.309426	+	0.178647i
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	0.815017	−	0.579437i	$-0.196728\pi$
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	−0.0942988	+	0.995544i	$0.530061\pi$
$284$	0.866025	+	0.500000i	0.0513892	+	0.0296695i
$285$	−7.50000	−	12.9904i	−0.444262	−	0.769484i
$286$		−	8.00000i		−	0.473050i
$287$	−4.00000	−	20.7846i	−0.236113	−	1.22688i
$288$	−1.00000			−0.0589256
$289$	0.571797	+	16.9904i	0.0336351	+	0.999434i
$290$	−9.00000	+	15.5885i	−0.528498	+	0.915386i
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	−8.66025	+	5.00000i	−0.506803	+	0.292603i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	−2.59808	−	6.50000i	−0.151523	−	0.379088i
$295$		−	3.00000i		−	0.174667i
$296$	6.06218	−	3.50000i	0.352357	−	0.203433i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$		0			0
$299$	3.46410	−	2.00000i	0.200334	−	0.115663i
$300$			4.00000i			0.230940i
$301$	23.3827	−	4.50000i	1.34776	−	0.259376i
$302$	10.0000			0.575435
$303$	−13.8564	+	8.00000i	−0.796030	+	0.459588i
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	3.96410	−	1.13397i	0.226613	−	0.0648250i
$307$	−31.0000			−1.76926			−0.884632	−	0.466290i	$-0.845590\pi$
$307$	−31.0000			−1.76926			−0.884632	+	0.466290i	$0.845590\pi$
$308$	4.00000	−	3.46410i	0.227921	−	0.197386i
$309$		−	6.00000i		−	0.341328i
$310$	−12.0000	−	20.7846i	−0.681554	−	1.18049i
$311$	−26.8468	−	15.5000i	−1.52234	−	0.878924i	−0.999651	−	0.0264017i	$-0.991595\pi$
$311$	−26.8468	−	15.5000i	−1.52234	−	0.878924i	−0.522690	−	0.852523i	$-0.675072\pi$
$312$	3.46410	+	2.00000i	0.196116	+	0.113228i
$313$	5.19615	−	3.00000i	0.293704	−	0.169570i	−0.345907	−	0.938269i	$-0.612429\pi$
$313$	5.19615	−	3.00000i	0.293704	−	0.169570i	0.639611	+	0.768699i	$0.279095\pi$
$314$	22.0000			1.24153
$315$	−7.50000	−	2.59808i	−0.422577	−	0.146385i
$316$		−	4.00000i		−	0.225018i
$317$	6.06218	−	3.50000i	0.340486	−	0.196580i	−0.320001	−	0.947417i	$-0.603683\pi$
$317$	6.06218	−	3.50000i	0.340486	−	0.196580i	0.660487	+	0.750838i	$0.270350\pi$
$318$	3.46410	+	2.00000i	0.194257	+	0.112154i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$	2.59808	−	1.50000i	0.145237	−	0.0838525i
$321$	−6.00000			−0.334887
$322$	2.50000	+	0.866025i	0.139320	+	0.0482617i
$323$	5.00000	−	20.0000i	0.278207	−	1.11283i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	12.1244	+	7.00000i	0.671506	+	0.387694i
$327$	−3.50000	−	6.06218i	−0.193550	−	0.335239i
$328$			8.00000i			0.441726i
$329$	10.3923	+	12.0000i	0.572946	+	0.661581i
$330$		−	6.00000i		−	0.330289i
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	0.999667	+	0.0257885i	$0.00820965\pi$
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	−0.477500	+	0.878632i	$0.658457\pi$
$332$	2.00000	−	3.46410i	0.109764	−	0.190117i
$333$	6.06218	+	3.50000i	0.332205	+	0.191799i
$334$	12.9904	−	7.50000i	0.710802	−	0.410382i
$335$		−	15.0000i		−	0.819538i
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$		−	22.0000i		−	1.19842i	−0.800593	−	0.599208i	$-0.795482\pi$
$337$		−	22.0000i		−	1.19842i	0.800593	−	0.599208i	$-0.204518\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$	−8.59808	+	8.89230i	−0.466296	+	0.482253i
$341$	8.00000	+	13.8564i	0.433224	+	0.750366i
$342$	−5.00000			−0.270369
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−9.00000			−0.485247
$345$	2.59808	−	1.50000i	0.139876	−	0.0807573i
$346$	11.2583	+	6.50000i	0.605252	+	0.349442i
$347$	3.46410	+	2.00000i	0.185963	+	0.107366i	0.590091	−	0.807337i	$-0.299092\pi$
$347$	3.46410	+	2.00000i	0.185963	+	0.107366i	−0.404128	+	0.914702i	$0.632425\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$	10.3923	−	2.00000i	0.555492	−	0.106904i
$351$			4.00000i			0.213504i
$352$	−1.73205	+	1.00000i	−0.0923186	+	0.0533002i
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$	−0.866025	−	0.500000i	−0.0460287	−	0.0265747i
$355$	−1.50000	−	2.59808i	−0.0796117	−	0.137892i
$356$	15.0000			0.794998
$357$	−4.92820	−	9.73205i	−0.260828	−	0.515075i
$358$	11.0000			0.581368
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	0.924932	+	0.380131i	$0.124121\pi$
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	−0.133263	+	0.991081i	$0.542545\pi$
$360$	2.59808	+	1.50000i	0.136931	+	0.0790569i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−9.52628	+	5.50000i	−0.500690	+	0.289074i
$363$		−	7.00000i		−	0.367405i
$364$	3.46410	−	10.0000i	0.181568	−	0.524142i
$365$	30.0000			1.57027
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	26.8468	+	15.5000i	1.40139	+	0.809093i	0.994535	−	0.104399i	$-0.0332919\pi$
$367$	26.8468	+	15.5000i	1.40139	+	0.809093i	0.406855	+	0.913493i	$0.366625\pi$
$368$	−0.866025	−	0.500000i	−0.0451447	−	0.0260643i
$369$	−6.92820	+	4.00000i	−0.360668	+	0.208232i
$370$	−21.0000			−1.09174
$371$	3.46410	−	10.0000i	0.179847	−	0.519174i
$372$	−8.00000			−0.414781
$373$	−8.00000	−	13.8564i	−0.414224	−	0.717458i	0.581122	−	0.813816i	$-0.302614\pi$
$373$	−8.00000	−	13.8564i	−0.414224	−	0.717458i	−0.995347	+	0.0963587i	$0.969280\pi$
$374$	5.73205	−	5.92820i	0.296397	−	0.306540i
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$		−	24.0000i		−	1.23606i
$378$	−2.00000	+	1.73205i	−0.102869	+	0.0890871i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$	12.9904	−	7.50000i	0.666392	−	0.384742i
$381$	1.73205	+	1.00000i	0.0887357	+	0.0512316i
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	0.987573	−	0.157159i	$-0.0502334\pi$
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	−0.629890	+	0.776684i	$0.716900\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−15.5885	+	3.00000i	−0.794461	+	0.152894i
$386$			6.00000i			0.305392i
$387$	−4.50000	−	7.79423i	−0.228748	−	0.396203i
$388$	10.3923	+	6.00000i	0.527589	+	0.304604i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$	−6.00000	−	10.3923i	−0.303822	−	0.526235i
$391$	4.00000	+	1.00000i	0.202289	+	0.0505722i
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	−4.00000			−0.201773
$394$	12.9904	−	7.50000i	0.654446	−	0.377845i
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$	−1.73205	−	1.00000i	−0.0870388	−	0.0502519i
$397$	25.1147	−	14.5000i	1.26047	−	0.727734i	0.287307	−	0.957839i	$-0.407240\pi$
$397$	25.1147	−	14.5000i	1.26047	−	0.727734i	0.973166	+	0.230105i	$0.0739068\pi$
$398$			15.0000i			0.751882i
$399$	2.50000	+	12.9904i	0.125157	+	0.650332i
$400$	−4.00000			−0.200000
$401$	25.9808	−	15.0000i	1.29742	−	0.749064i	0.317460	−	0.948272i	$-0.397170\pi$
$401$	25.9808	−	15.0000i	1.29742	−	0.749064i	0.979957	+	0.199207i	$0.0638367\pi$
$402$	−4.33013	−	2.50000i	−0.215967	−	0.124689i
$403$	27.7128	+	16.0000i	1.38047	+	0.797017i
$404$	−8.00000	−	13.8564i	−0.398015	−	0.689382i
$405$			3.00000i			0.149071i
$406$	12.0000	−	10.3923i	0.595550	−	0.515761i
$407$	14.0000			0.693954
$408$	1.13397	+	3.96410i	0.0561401	+	0.196252i
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$	12.0000	−	20.7846i	0.592638	−	1.02648i
$411$	−0.866025	+	0.500000i	−0.0427179	+	0.0246632i
$412$	6.00000			0.295599
$413$	−0.866025	+	2.50000i	−0.0426143	+	0.123017i
$414$		−	1.00000i		−	0.0491473i
$415$	−10.3923	+	6.00000i	−0.510138	+	0.294528i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	−1.00000	+	1.73205i	−0.0489702	+	0.0848189i
$418$	−8.66025	+	5.00000i	−0.423587	+	0.244558i
$419$		−	6.00000i		−	0.293119i	−0.989202	−	0.146560i	$-0.953180\pi$
$419$		−	6.00000i		−	0.293119i	0.989202	−	0.146560i	$-0.0468200\pi$
$420$	2.59808	−	7.50000i	0.126773	−	0.365963i
$421$	24.0000			1.16969			0.584844	−	0.811146i	$-0.301156\pi$
$421$	24.0000			1.16969			0.584844	+	0.811146i	$0.301156\pi$
$422$	−10.3923	+	6.00000i	−0.505889	+	0.292075i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	15.8564	−	4.53590i	0.769149	−	0.220023i
$426$	−1.00000			−0.0484502
$427$	−4.00000	+	3.46410i	−0.193574	+	0.167640i
$428$		−	6.00000i		−	0.290021i
$429$	4.00000	+	6.92820i	0.193122	+	0.334497i
$430$	23.3827	+	13.5000i	1.12761	+	0.651028i
$431$	6.06218	+	3.50000i	0.292005	+	0.168589i	0.638846	−	0.769335i	$-0.279412\pi$
$431$	6.06218	+	3.50000i	0.292005	+	0.168589i	−0.346841	+	0.937924i	$0.612746\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	39.0000			1.87422			0.937110	−	0.349034i	$-0.113490\pi$
$433$	39.0000			1.87422			0.937110	+	0.349034i	$0.113490\pi$
$434$	4.00000	+	20.7846i	0.192006	+	0.997693i
$435$		−	18.0000i		−	0.863034i
$436$	6.06218	−	3.50000i	0.290326	−	0.167620i
$437$	−4.33013	−	2.50000i	−0.207138	−	0.119591i
$438$	5.00000	−	8.66025i	0.238909	−	0.413803i
$439$	7.79423	−	4.50000i	0.371998	−	0.214773i	−0.302333	−	0.953202i	$-0.597765\pi$
$439$	7.79423	−	4.50000i	0.371998	−	0.214773i	0.674331	+	0.738429i	$0.264432\pi$
$440$	6.00000			0.286039
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$	4.00000	−	16.0000i	0.190261	−	0.761042i
$443$	2.50000	+	4.33013i	0.118779	+	0.205731i	0.919284	−	0.393595i	$-0.128769\pi$
$443$	2.50000	+	4.33013i	0.118779	+	0.205731i	−0.800505	+	0.599326i	$0.795435\pi$
$444$	−3.50000	+	6.06218i	−0.166103	+	0.287698i
$445$	−38.9711	−	22.5000i	−1.84741	−	1.06660i
$446$	−13.0000	−	22.5167i	−0.615568	−	1.06619i
$447$		0			0
$448$	−2.59808	+	0.500000i	−0.122748	+	0.0236228i
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$	−2.00000	−	3.46410i	−0.0942809	−	0.163299i
$451$	−8.00000	+	13.8564i	−0.376705	+	0.652473i
$452$	−15.5885	−	9.00000i	−0.733219	−	0.423324i
$453$	−8.66025	+	5.00000i	−0.406894	+	0.234920i
$454$			16.0000i			0.750917i
$455$	−24.0000	+	20.7846i	−1.12514	+	0.974398i
$456$		−	5.00000i		−	0.234146i
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$	−2.86603	+	2.96410i	−0.133775	+	0.138352i
$460$	1.50000	+	2.59808i	0.0699379	+	0.121136i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$	−1.73205	+	5.00000i	−0.0805823	+	0.232621i
$463$	−28.0000			−1.30127			−0.650635	−	0.759390i	$-0.725497\pi$
$463$	−28.0000			−1.30127			−0.650635	+	0.759390i	$0.725497\pi$
$464$	−5.19615	+	3.00000i	−0.241225	+	0.139272i
$465$	20.7846	+	12.0000i	0.963863	+	0.556487i
$466$	−15.5885	−	9.00000i	−0.722121	−	0.416917i
$467$	−8.50000	−	14.7224i	−0.393333	−	0.681273i	0.599554	−	0.800334i	$-0.295345\pi$
$467$	−8.50000	−	14.7224i	−0.393333	−	0.681273i	−0.992887	+	0.119062i	$0.962011\pi$
$468$	−4.00000			−0.184900
$469$	−4.33013	+	12.5000i	−0.199947	+	0.577196i
$470$			18.0000i			0.830278i
$471$	−19.0526	+	11.0000i	−0.877896	+	0.506853i
$472$	0.500000	−	0.866025i	0.0230144	−	0.0398621i
$473$	−15.5885	−	9.00000i	−0.716758	−	0.413820i
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$	−20.0000			−0.917663
$476$	9.73205	−	4.92820i	0.446068	−	0.225884i
$477$	−4.00000			−0.183147
$478$	−11.0000	−	19.0526i	−0.503128	−	0.871444i
$479$	25.1147	+	14.5000i	1.14752	+	0.662522i	0.948282	−	0.317429i	$-0.102819\pi$
$479$	25.1147	+	14.5000i	1.14752	+	0.662522i	0.199240	+	0.979951i	$0.436153\pi$
$480$	−1.50000	+	2.59808i	−0.0684653	+	0.118585i
$481$	24.2487	−	14.0000i	1.10565	−	0.638345i
$482$			20.0000i			0.910975i
$483$	−2.59808	+	0.500000i	−0.118217	+	0.0227508i
$484$	7.00000			0.318182
$485$	−18.0000	−	31.1769i	−0.817338	−	1.41567i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	26.8468	+	15.5000i	1.21654	+	0.702372i	0.964177	−	0.265260i	$-0.0854576\pi$
$487$	26.8468	+	15.5000i	1.21654	+	0.702372i	0.252367	+	0.967632i	$0.418791\pi$
$488$	1.73205	−	1.00000i	0.0784063	−	0.0452679i
$489$	−14.0000			−0.633102
$490$	−20.7846	−	3.00000i	−0.938953	−	0.135526i
$491$	11.0000			0.496423			0.248212	−	0.968706i	$-0.420157\pi$
$491$	11.0000			0.496423			0.248212	+	0.968706i	$0.420157\pi$
$492$	−4.00000	−	6.92820i	−0.180334	−	0.312348i
$493$	17.1962	−	17.7846i	0.774476	−	0.800979i
$494$	−10.0000	+	17.3205i	−0.449921	+	0.779287i
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$		−	8.00000i		−	0.359211i
$497$	0.500000	+	2.59808i	0.0224281	+	0.116540i
$498$			4.00000i			0.179244i
$499$	−17.3205	+	10.0000i	−0.775372	+	0.447661i	−0.834788	−	0.550572i	$-0.814410\pi$
$499$	−17.3205	+	10.0000i	−0.775372	+	0.447661i	0.0594153	+	0.998233i	$0.481076\pi$
$500$	−2.59808	−	1.50000i	−0.116190	−	0.0670820i
$501$	−7.50000	+	12.9904i	−0.335075	+	0.580367i
$502$	10.0000	+	17.3205i	0.446322	+	0.773052i
$503$			33.0000i			1.47140i	0.677309	+	0.735699i	$0.263146\pi$
$503$			33.0000i			1.47140i	−0.677309	+	0.735699i	$0.736854\pi$
$504$	−1.73205	−	2.00000i	−0.0771517	−	0.0890871i
$505$			48.0000i			2.13597i
$506$	−1.00000	−	1.73205i	−0.0444554	−	0.0769991i
$507$	2.59808	+	1.50000i	0.115385	+	0.0666173i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$	3.00000	−	12.0000i	0.132842	−	0.531369i
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$	1.00000			0.0441942
$513$	4.33013	−	2.50000i	0.191180	−	0.110378i
$514$	10.5000	−	18.1865i	0.463135	−	0.802174i
$515$	−15.5885	−	9.00000i	−0.686909	−	0.396587i
$516$	7.79423	−	4.50000i	0.343122	−	0.198101i
$517$		−	12.0000i		−	0.527759i
$518$	17.5000	+	6.06218i	0.768906	+	0.266357i
$519$	−13.0000			−0.570637
$520$	10.3923	−	6.00000i	0.455733	−	0.263117i
$521$	−15.5885	−	9.00000i	−0.682943	−	0.394297i	0.118020	−	0.993011i	$-0.462345\pi$
$521$	−15.5885	−	9.00000i	−0.682943	−	0.394297i	−0.800963	+	0.598714i	$0.795679\pi$
$522$	−5.19615	−	3.00000i	−0.227429	−	0.131306i
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	−0.927746	−	0.373213i	$-0.878256\pi$
$523$	−18.0000	−	31.1769i	−0.787085	−	1.36327i	0.140660	−	0.990058i	$-0.455077\pi$
$524$		−	4.00000i		−	0.174741i
$525$	−8.00000	+	6.92820i	−0.349149	+	0.302372i
$526$	−24.0000			−1.04645
$527$	9.07180	+	31.7128i	0.395174	+	1.38143i
$528$	1.00000	−	1.73205i	0.0435194	−	0.0753778i
$529$	−11.0000	+	19.0526i	−0.478261	+	0.828372i
$530$	10.3923	−	6.00000i	0.451413	−	0.260623i
$531$	1.00000			0.0433963
$532$	−12.9904	+	2.50000i	−0.563204	+	0.108389i
$533$			32.0000i			1.38607i
$534$	−12.9904	+	7.50000i	−0.562149	+	0.324557i
$535$	−9.00000	+	15.5885i	−0.389104	+	0.673948i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	−9.52628	+	5.50000i	−0.411089	+	0.237343i
$538$			19.0000i			0.819148i
$539$	13.8564	+	2.00000i	0.596838	+	0.0861461i
$540$	−3.00000			−0.129099
$541$	−32.9090	+	19.0000i	−1.41487	+	0.816874i	−0.995842	−	0.0911008i	$-0.970961\pi$
$541$	−32.9090	+	19.0000i	−1.41487	+	0.816874i	−0.419025	+	0.907975i	$0.637628\pi$
$542$	−7.00000	+	12.1244i	−0.300676	+	0.520786i
$543$	5.50000	−	9.52628i	0.236028	−	0.408812i
$544$	−3.96410	+	1.13397i	−0.169959	+	0.0486188i
$545$	−21.0000			−0.899541
$546$	2.00000	+	10.3923i	0.0855921	+	0.444750i
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$	−0.500000	−	0.866025i	−0.0213589	−	0.0369948i
$549$	1.73205	+	1.00000i	0.0739221	+	0.0426790i
$550$	−6.92820	−	4.00000i	−0.295420	−	0.170561i
$551$	−25.9808	+	15.0000i	−1.10682	+	0.639021i
$552$	1.00000			0.0425628
$553$	8.00000	−	6.92820i	0.340195	−	0.294617i
$554$		−	18.0000i		−	0.764747i
$555$	18.1865	−	10.5000i	0.771975	−	0.445700i
$556$	−1.73205	−	1.00000i	−0.0734553	−	0.0424094i
$557$	−14.0000	+	24.2487i	−0.593199	+	1.02745i	0.400599	+	0.916253i	$0.368802\pi$
$557$	−14.0000	+	24.2487i	−0.593199	+	1.02745i	−0.993798	+	0.111198i	$0.964531\pi$
$558$	6.92820	−	4.00000i	0.293294	−	0.169334i
$559$	−36.0000			−1.52264
$560$	7.50000	+	2.59808i	0.316933	+	0.109789i
$561$	−2.00000	+	8.00000i	−0.0844401	+	0.337760i
$562$	13.5000	+	23.3827i	0.569463	+	0.986339i
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$	5.19615	+	3.00000i	0.218797	+	0.126323i
$565$	27.0000	+	46.7654i	1.13590	+	1.96743i
$566$		−	14.0000i		−	0.588464i
$567$	0.866025	−	2.50000i	0.0363696	−	0.104990i
$568$		−	1.00000i		−	0.0419591i
$569$	−17.5000	−	30.3109i	−0.733638	−	1.27070i	−0.955318	−	0.295579i	$-0.904487\pi$
$569$	−17.5000	−	30.3109i	−0.733638	−	1.27070i	0.221680	−	0.975119i	$-0.428846\pi$
$570$	−7.50000	+	12.9904i	−0.314140	+	0.544107i
$571$	10.3923	+	6.00000i	0.434904	+	0.251092i	0.701434	−	0.712735i	$-0.252544\pi$
$571$	10.3923	+	6.00000i	0.434904	+	0.251092i	−0.266529	+	0.963827i	$0.585877\pi$
$572$	−6.92820	+	4.00000i	−0.289683	+	0.167248i
$573$			16.0000i			0.668410i
$574$	−16.0000	+	13.8564i	−0.667827	+	0.578355i
$575$		−	4.00000i		−	0.166812i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	14.4282	−	8.99038i	0.600134	−	0.373951i
$579$	−3.00000	−	5.19615i	−0.124676	−	0.215945i
$580$	18.0000			0.747409
$581$	10.3923	−	2.00000i	0.431145	−	0.0829740i
$582$	−12.0000			−0.497416
$583$	−6.92820	+	4.00000i	−0.286937	+	0.165663i
$584$	8.66025	+	5.00000i	0.358364	+	0.206901i
$585$	10.3923	+	6.00000i	0.429669	+	0.248069i
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	11.0000			0.454019			0.227009	−	0.973893i	$-0.427105\pi$
$587$	11.0000			0.454019			0.227009	+	0.973893i	$0.427105\pi$
$588$	−4.33013	+	5.50000i	−0.178571	+	0.226816i
$589$		−	40.0000i		−	1.64817i
$590$	−2.59808	+	1.50000i	−0.106961	+	0.0617540i
$591$	−7.50000	+	12.9904i	−0.308509	+	0.534353i
$592$	−6.06218	−	3.50000i	−0.249154	−	0.143849i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$	2.00000			0.0820610
$595$	−32.6769	−	1.79423i	−1.33962	−	0.0735562i
$596$		0			0
$597$	−7.50000	−	12.9904i	−0.306955	−	0.531661i
$598$	−3.46410	−	2.00000i	−0.141658	−	0.0817861i
$599$	11.0000	−	19.0526i	0.449448	−	0.778466i	−0.548902	−	0.835887i	$-0.684954\pi$
$599$	11.0000	−	19.0526i	0.449448	−	0.778466i	0.998350	+	0.0574201i	$0.0182874\pi$
$600$	3.46410	−	2.00000i	0.141421	−	0.0816497i
$601$		−	22.0000i		−	0.897399i	−0.893683	−	0.448699i	$-0.851887\pi$
$601$		−	22.0000i		−	0.897399i	0.893683	−	0.448699i	$-0.148113\pi$
$602$	−15.5885	−	18.0000i	−0.635338	−	0.733625i
$603$	5.00000			0.203616
$604$	−5.00000	−	8.66025i	−0.203447	−	0.352381i
$605$	−18.1865	−	10.5000i	−0.739388	−	0.426886i
$606$	13.8564	+	8.00000i	0.562878	+	0.324978i
$607$	−28.5788	+	16.5000i	−1.15998	+	0.669714i	−0.951299	−	0.308270i	$-0.900250\pi$
$607$	−28.5788	+	16.5000i	−1.15998	+	0.669714i	−0.208680	+	0.977984i	$0.566917\pi$
$608$	5.00000			0.202777
$609$	−5.19615	+	15.0000i	−0.210559	+	0.607831i
$610$	−6.00000			−0.242933
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$	−2.96410	−	2.86603i	−0.119817	−	0.115852i
$613$	23.0000	−	39.8372i	0.928961	−	1.60901i	0.143898	−	0.989593i	$-0.454036\pi$
$613$	23.0000	−	39.8372i	0.928961	−	1.60901i	0.785063	−	0.619416i	$-0.212630\pi$
$614$	15.5000	+	26.8468i	0.625529	+	1.08345i
$615$			24.0000i			0.967773i
$616$	−5.00000	−	1.73205i	−0.201456	−	0.0697863i
$617$		−	4.00000i		−	0.161034i	−0.996753	−	0.0805170i	$-0.974343\pi$
$617$		−	4.00000i		−	0.161034i	0.996753	−	0.0805170i	$-0.0256571\pi$
$618$	−5.19615	+	3.00000i	−0.209020	+	0.120678i
$619$	−20.7846	−	12.0000i	−0.835404	−	0.482321i	0.0202954	−	0.999794i	$-0.493539\pi$
$619$	−20.7846	−	12.0000i	−0.835404	−	0.482321i	−0.855699	+	0.517473i	$0.826873\pi$
$620$	−12.0000	+	20.7846i	−0.481932	+	0.834730i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$			31.0000i			1.24299i
$623$	25.9808	+	30.0000i	1.04090	+	1.20192i
$624$		−	4.00000i		−	0.160128i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−5.19615	−	3.00000i	−0.207680	−	0.119904i
$627$	5.00000	−	8.66025i	0.199681	−	0.345857i
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$	28.0000	+	7.00000i	1.11643	+	0.279108i
$630$	1.50000	+	7.79423i	0.0597614	+	0.310530i
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−3.46410	+	2.00000i	−0.137795	+	0.0795557i
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$	−6.06218	−	3.50000i	−0.240760	−	0.139003i
$635$	5.19615	−	3.00000i	0.206203	−	0.119051i
$636$		−	4.00000i		−	0.158610i
$637$	26.0000	−	10.3923i	1.03016	−	0.411758i
$638$	−12.0000			−0.475085
$639$	0.866025	−	0.500000i	0.0342594	−	0.0197797i
$640$	−2.59808	−	1.50000i	−0.102698	−	0.0592927i
$641$	6.92820	+	4.00000i	0.273648	+	0.157991i	0.630544	−	0.776153i	$-0.282832\pi$
$641$	6.92820	+	4.00000i	0.273648	+	0.157991i	−0.356897	+	0.934144i	$0.616165\pi$
$642$	3.00000	+	5.19615i	0.118401	+	0.205076i
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$	−0.500000	−	2.59808i	−0.0197028	−	0.102379i
$645$	−27.0000			−1.06312
$646$	−19.8205	+	5.66987i	−0.779827	+	0.223078i
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	−0.404559	−	0.914512i	$-0.632575\pi$
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	0.994270	−	0.106897i	$-0.0340916\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	1.73205	−	1.00000i	0.0679889	−	0.0392534i
$650$	−16.0000			−0.627572
$651$	−13.8564	−	16.0000i	−0.543075	−	0.627089i
$652$		−	14.0000i		−	0.548282i
$653$	−12.9904	+	7.50000i	−0.508353	+	0.293498i	−0.732156	−	0.681137i	$-0.761486\pi$
$653$	−12.9904	+	7.50000i	−0.508353	+	0.293498i	0.223803	+	0.974634i	$0.428153\pi$
$654$	−3.50000	+	6.06218i	−0.136861	+	0.237050i
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$	6.92820	−	4.00000i	0.270501	−	0.156174i
$657$			10.0000i			0.390137i
$658$	5.19615	−	15.0000i	0.202567	−	0.584761i
$659$	15.0000			0.584317			0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000			0.584317			0.292159	+	0.956370i	$0.405627\pi$
$660$	−5.19615	+	3.00000i	−0.202260	+	0.116775i
$661$	16.0000	−	27.7128i	0.622328	−	1.07790i	−0.366723	−	0.930330i	$-0.619520\pi$
$661$	16.0000	−	27.7128i	0.622328	−	1.07790i	0.989051	−	0.147573i	$-0.0471463\pi$
$662$	9.50000	−	16.4545i	0.369228	−	0.639522i
$663$	4.53590	+	15.8564i	0.176160	+	0.615812i
$664$	−4.00000			−0.155230
$665$	37.5000	+	12.9904i	1.45419	+	0.503745i
$666$		−	7.00000i		−	0.271244i
$667$	−3.00000	−	5.19615i	−0.116160	−	0.201196i
$668$	−12.9904	−	7.50000i	−0.502613	−	0.290184i
$669$	22.5167	+	13.0000i	0.870544	+	0.502609i
$670$	−12.9904	+	7.50000i	−0.501862	+	0.289750i
$671$	4.00000			0.154418
$672$	2.00000	−	1.73205i	0.0771517	−	0.0668153i
$673$			40.0000i			1.54189i	0.636904	+	0.770943i	$0.280215\pi$
$673$			40.0000i			1.54189i	−0.636904	+	0.770943i	$0.719785\pi$
$674$	−19.0526	+	11.0000i	−0.733877	+	0.423704i
$675$	3.46410	+	2.00000i	0.133333	+	0.0769800i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−5.19615	+	3.00000i	−0.199704	+	0.115299i	−0.596518	−	0.802600i	$-0.703449\pi$
$677$	−5.19615	+	3.00000i	−0.199704	+	0.115299i	0.396813	+	0.917899i	$0.370116\pi$
$678$	18.0000			0.691286
$679$	6.00000	+	31.1769i	0.230259	+	1.19646i
$680$	12.0000	+	3.00000i	0.460179	+	0.115045i
$681$	−8.00000	−	13.8564i	−0.306561	−	0.530979i
$682$	8.00000	−	13.8564i	0.306336	−	0.530589i
$683$	15.5885	+	9.00000i	0.596476	+	0.344375i	0.767654	−	0.640865i	$-0.221424\pi$
$683$	15.5885	+	9.00000i	0.596476	+	0.344375i	−0.171178	+	0.985240i	$0.554757\pi$
$684$	2.50000	+	4.33013i	0.0955899	+	0.165567i
$685$			3.00000i			0.114624i
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$		−	22.0000i		−	0.839352i
$688$	4.50000	+	7.79423i	0.171561	+	0.297152i
$689$	−8.00000	+	13.8564i	−0.304776	+	0.527887i
$690$	−2.59808	−	1.50000i	−0.0989071	−	0.0571040i
$691$	20.7846	−	12.0000i	0.790684	−	0.456502i	−0.0495194	−	0.998773i	$-0.515769\pi$
$691$	20.7846	−	12.0000i	0.790684	−	0.456502i	0.840203	+	0.542272i	$0.182436\pi$
$692$		−	13.0000i		−	0.494186i
$693$	−1.00000	−	5.19615i	−0.0379869	−	0.197386i
$694$		−	4.00000i		−	0.151838i
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	−22.9282	+	23.7128i	−0.868468	+	0.898187i
$698$	17.0000	+	29.4449i	0.643459	+	1.11450i
$699$	18.0000			0.680823
$700$	−6.92820	−	8.00000i	−0.261861	−	0.302372i
$701$	−24.0000			−0.906467			−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000			−0.906467			−0.453234	+	0.891392i	$0.649730\pi$
$702$	3.46410	−	2.00000i	0.130744	−	0.0754851i
$703$	−30.3109	−	17.5000i	−1.14320	−	0.660025i
$704$	1.73205	+	1.00000i	0.0652791	+	0.0376889i
$705$	−9.00000	−	15.5885i	−0.338960	−	0.587095i
$706$	−15.0000			−0.564532
$707$	13.8564	−	40.0000i	0.521124	−	1.50435i
$708$			1.00000i			0.0375823i
$709$	7.79423	−	4.50000i	0.292718	−	0.169001i	−0.346449	−	0.938069i	$-0.612613\pi$
$709$	7.79423	−	4.50000i	0.292718	−	0.169001i	0.639167	+	0.769068i	$0.279279\pi$
$710$	−1.50000	+	2.59808i	−0.0562940	+	0.0975041i
$711$	−3.46410	−	2.00000i	−0.129914	−	0.0750059i
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	8.00000			0.299602
$714$	−5.96410	+	9.13397i	−0.223201	+	0.341830i
$715$	24.0000			0.897549
$716$	−5.50000	−	9.52628i	−0.205545	−	0.356014i
$717$	19.0526	+	11.0000i	0.711531	+	0.410803i
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−27.7128	+	16.0000i	−1.03351	+	0.596699i	−0.917989	−	0.396605i	$-0.870188\pi$
$719$	−27.7128	+	16.0000i	−1.03351	+	0.596699i	−0.115524	+	0.993305i	$0.536855\pi$
$720$		−	3.00000i		−	0.111803i
$721$	10.3923	+	12.0000i	0.387030	+	0.446903i
$722$	6.00000			0.223297
$723$	−10.0000	−	17.3205i	−0.371904	−	0.644157i
$724$	9.52628	+	5.50000i	0.354041	+	0.204406i
$725$	−20.7846	−	12.0000i	−0.771921	−	0.445669i
$726$	−6.06218	+	3.50000i	−0.224989	+	0.129897i
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$	−10.3923	+	2.00000i	−0.385164	+	0.0741249i
$729$	−1.00000			−0.0370370
$730$	−15.0000	−	25.9808i	−0.555175	−	0.961591i
$731$	−26.6769	−	25.7942i	−0.986681	−	0.954034i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	19.0000	+	32.9090i	0.701781	+	1.21552i	0.967841	+	0.251564i	$0.0809448\pi$
$733$	19.0000	+	32.9090i	0.701781	+	1.21552i	−0.266060	+	0.963957i	$0.585722\pi$
$734$		−	31.0000i		−	1.14423i
$735$	19.5000	−	7.79423i	0.719268	−	0.287494i
$736$			1.00000i			0.0368605i
$737$	8.66025	−	5.00000i	0.319005	−	0.184177i
$738$	6.92820	+	4.00000i	0.255031	+	0.147242i
$739$	11.5000	−	19.9186i	0.423034	−	0.732717i	−0.573200	−	0.819415i	$-0.694298\pi$
$739$	11.5000	−	19.9186i	0.423034	−	0.732717i	0.996235	+	0.0866983i	$0.0276316\pi$
$740$	10.5000	+	18.1865i	0.385988	+	0.668550i
$741$		−	20.0000i		−	0.734718i
$742$	−10.3923	+	2.00000i	−0.381514	+	0.0734223i
$743$			28.0000i			1.02722i	0.858024	+	0.513610i	$0.171692\pi$
$743$			28.0000i			1.02722i	−0.858024	+	0.513610i	$0.828308\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$		0			0
$746$	−8.00000	+	13.8564i	−0.292901	+	0.507319i
$747$	−2.00000	−	3.46410i	−0.0731762	−	0.126745i
$748$	−8.00000	−	2.00000i	−0.292509	−	0.0731272i
$749$	12.0000	−	10.3923i	0.438470	−	0.379727i
$750$	3.00000			0.109545
$751$	12.9904	−	7.50000i	0.474026	−	0.273679i	−0.243898	−	0.969801i	$-0.578426\pi$
$751$	12.9904	−	7.50000i	0.474026	−	0.273679i	0.717923	+	0.696122i	$0.245093\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	−17.3205	−	10.0000i	−0.631194	−	0.364420i
$754$	−20.7846	+	12.0000i	−0.756931	+	0.437014i
$755$			30.0000i			1.09181i
$756$	2.50000	+	0.866025i	0.0909241	+	0.0314970i
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	−6.92820	+	4.00000i	−0.251644	+	0.145287i
$759$	1.73205	+	1.00000i	0.0628695	+	0.0362977i
$760$	−12.9904	−	7.50000i	−0.471211	−	0.272054i
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	0.772863	−	0.634573i	$-0.218824\pi$
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	−0.935988	+	0.352032i	$0.885491\pi$
$762$		−	2.00000i		−	0.0724524i
$763$	17.5000	+	6.06218i	0.633543	+	0.219466i
$764$	−16.0000			−0.578860
$765$	3.40192	+	11.8923i	0.122997	+	0.429967i
$766$	7.00000	−	12.1244i	0.252920	−	0.438071i
$767$	2.00000	−	3.46410i	0.0722158	−	0.125081i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−37.0000			−1.33425			−0.667127	−	0.744944i	$-0.732476\pi$
$769$	−37.0000			−1.33425			−0.667127	+	0.744944i	$0.732476\pi$
$770$	10.3923	+	12.0000i	0.374513	+	0.432450i
$771$			21.0000i			0.756297i
$772$	5.19615	−	3.00000i	0.187014	−	0.107972i
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	0.189899	+	0.981804i	$0.439184\pi$
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	−0.945216	+	0.326445i	$0.894149\pi$
$774$	−4.50000	+	7.79423i	−0.161749	+	0.280158i
$775$	27.7128	−	16.0000i	0.995474	−	0.574737i
$776$		−	12.0000i		−	0.430775i
$777$	−18.1865	+	3.50000i	−0.652438	+	0.125562i
$778$	−26.0000			−0.932145
$779$	34.6410	−	20.0000i	1.24114	−	0.716574i
$780$	−6.00000	+	10.3923i	−0.214834	+	0.372104i
$781$	1.00000	−	1.73205i	0.0357828	−	0.0619777i
$782$	−1.13397	−	3.96410i	−0.0405508	−	0.141756i
$783$	6.00000			0.214423
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$			66.0000i			2.35564i
$786$	2.00000	+	3.46410i	0.0713376	+	0.123560i
$787$	19.0526	+	11.0000i	0.679150	+	0.392108i	0.799535	−	0.600620i	$-0.205079\pi$
$787$	19.0526	+	11.0000i	0.679150	+	0.392108i	−0.120384	+	0.992727i	$0.538413\pi$
$788$	−12.9904	−	7.50000i	−0.462763	−	0.267176i
$789$	20.7846	−	12.0000i	0.739952	−	0.427211i
$790$	12.0000			0.426941
$791$	−9.00000	−	46.7654i	−0.320003	−	1.66279i
$792$			2.00000i			0.0710669i
$793$	6.92820	−	4.00000i	0.246028	−	0.142044i
$794$	−25.1147	−	14.5000i	−0.891289	−	0.514586i
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$	12.9904	−	7.50000i	0.460432	−	0.265830i
$797$	−38.0000			−1.34603			−0.673015	−	0.739629i	$-0.735001\pi$
$797$	−38.0000			−1.34603			−0.673015	+	0.739629i	$0.735001\pi$
$798$	10.0000	−	8.66025i	0.353996	−	0.306570i
$799$	6.00000	−	24.0000i	0.212265	−	0.849059i
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	7.50000	−	12.9904i	0.264999	−	0.458993i
$802$	−25.9808	−	15.0000i	−0.917413	−	0.529668i
$803$	10.0000	+	17.3205i	0.352892	+	0.611227i
$804$			5.00000i			0.176336i
$805$	−2.59808	+	7.50000i	−0.0915702	+	0.264340i
$806$		−	32.0000i		−	1.12715i
$807$	−9.50000	−	16.4545i	−0.334416	−	0.579225i
$808$	−8.00000	+	13.8564i	−0.281439	+	0.487467i
$809$	−25.9808	−	15.0000i	−0.913435	−	0.527372i	−0.0319002	−	0.999491i	$-0.510156\pi$
$809$	−25.9808	−	15.0000i	−0.913435	−	0.527372i	−0.881535	+	0.472119i	$0.843489\pi$
$810$	2.59808	−	1.50000i	0.0912871	−	0.0527046i
$811$			4.00000i			0.140459i	0.997531	+	0.0702295i	$0.0223732\pi$
$811$			4.00000i			0.140459i	−0.997531	+	0.0702295i	$0.977627\pi$
$812$	−15.0000	−	5.19615i	−0.526397	−	0.182349i
$813$		−	14.0000i		−	0.491001i
$814$	−7.00000	−	12.1244i	−0.245350	−	0.424958i
$815$	−21.0000	+	36.3731i	−0.735598	+	1.27409i
$816$	2.86603	−	2.96410i	0.100331	−	0.103764i
$817$	22.5000	+	38.9711i	0.787175	+	1.36343i
$818$	−26.0000			−0.909069
$819$	−6.92820	−	8.00000i	−0.242091	−	0.279543i
$820$	−24.0000			−0.838116
$821$	−40.7032	+	23.5000i	−1.42055	+	0.820156i	−0.996346	−	0.0854103i	$-0.972780\pi$
$821$	−40.7032	+	23.5000i	−1.42055	+	0.820156i	−0.424205	+	0.905566i	$0.639447\pi$
$822$	0.866025	+	0.500000i	0.0302061	+	0.0174395i
$823$	34.6410	+	20.0000i	1.20751	+	0.697156i	0.962215	−	0.272292i	$-0.0877817\pi$
$823$	34.6410	+	20.0000i	1.20751	+	0.697156i	0.245295	+	0.969448i	$0.421115\pi$
$824$	−3.00000	−	5.19615i	−0.104510	−	0.181017i
$825$	8.00000			0.278524
$826$	2.59808	−	0.500000i	0.0903986	−	0.0173972i
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$	−0.866025	+	0.500000i	−0.0300965	+	0.0173762i
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$	10.3923	+	6.00000i	0.360722	+	0.208263i
$831$	9.00000	+	15.5885i	0.312207	+	0.540758i
$832$	4.00000			0.138675
$833$	26.7128	+	10.9282i	0.925544	+	0.378640i
$834$	2.00000			0.0692543
$835$	22.5000	+	38.9711i	0.778645	+	1.34865i
$836$	8.66025	+	5.00000i	0.299521	+	0.172929i
$837$	−4.00000	+	6.92820i	−0.138260	+	0.239474i
$838$	−5.19615	+	3.00000i	−0.179498	+	0.103633i
$839$		−	45.0000i		−	1.55357i	−0.629764	−	0.776786i	$-0.716849\pi$
$839$		−	45.0000i		−	1.55357i	0.629764	−	0.776786i	$-0.283151\pi$
$840$	−7.79423	+	1.50000i	−0.268926	+	0.0517549i
$841$	−7.00000			−0.241379
$842$	−12.0000	−	20.7846i	−0.413547	−	0.716285i
$843$	−23.3827	−	13.5000i	−0.805342	−	0.464965i
$844$	10.3923	+	6.00000i	0.357718	+	0.206529i
$845$	7.79423	−	4.50000i	0.268130	−	0.154805i
$846$	−6.00000			−0.206284
$847$	12.1244	+	14.0000i	0.416598	+	0.481046i
$848$	4.00000			0.137361
$849$	7.00000	+	12.1244i	0.240239	+	0.416107i
$850$	−11.8564	−	11.4641i	−0.406671	−	0.393215i
$851$	3.50000	−	6.06218i	0.119978	−	0.207809i
$852$	0.500000	+	0.866025i	0.0171297	+	0.0296695i
$853$			14.0000i			0.479351i	0.970853	+	0.239675i	$0.0770410\pi$
$853$			14.0000i			0.479351i	−0.970853	+	0.239675i	$0.922959\pi$
$854$	5.00000	+	1.73205i	0.171096	+	0.0592696i
$855$		−	15.0000i		−	0.512989i
$856$	−5.19615	+	3.00000i	−0.177601	+	0.102538i
$857$	5.19615	+	3.00000i	0.177497	+	0.102478i	0.586116	−	0.810227i	$-0.300656\pi$
$857$	5.19615	+	3.00000i	0.177497	+	0.102478i	−0.408619	+	0.912705i	$0.633990\pi$
$858$	4.00000	−	6.92820i	0.136558	−	0.236525i
$859$	−14.5000	−	25.1147i	−0.494734	−	0.856904i	0.505248	−	0.862974i	$-0.331401\pi$
$859$	−14.5000	−	25.1147i	−0.494734	−	0.856904i	−0.999982	+	0.00607046i	$0.998068\pi$
$860$		−	27.0000i		−	0.920692i
$861$	6.92820	−	20.0000i	0.236113	−	0.681598i
$862$		−	7.00000i		−	0.238421i
$863$	13.0000	+	22.5167i	0.442525	+	0.766476i	0.997876	−	0.0651400i	$-0.0207494\pi$
$863$	13.0000	+	22.5167i	0.442525	+	0.766476i	−0.555351	+	0.831616i	$0.687416\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−19.5000	+	33.7750i	−0.663020	+	1.14838i
$866$	−19.5000	−	33.7750i	−0.662637	−	1.14772i
$867$	−8.00000	+	15.0000i	−0.271694	+	0.509427i
$868$	16.0000	−	13.8564i	0.543075	−	0.470317i
$869$	−8.00000			−0.271381
$870$	−15.5885	+	9.00000i	−0.528498	+	0.305129i
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$	−6.06218	−	3.50000i	−0.205291	−	0.118525i
$873$	10.3923	−	6.00000i	0.351726	−	0.203069i
$874$			5.00000i			0.169128i
$875$	−1.50000	−	7.79423i	−0.0507093	−	0.263493i
$876$	−10.0000			−0.337869
$877$	39.8372	−	23.0000i	1.34521	−	0.776655i	0.357640	−	0.933860i	$-0.383582\pi$
$877$	39.8372	−	23.0000i	1.34521	−	0.776655i	0.987566	+	0.157205i	$0.0502483\pi$
$878$	−7.79423	−	4.50000i	−0.263042	−	0.151868i
$879$	−15.5885	−	9.00000i	−0.525786	−	0.303562i
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$		−	16.0000i		−	0.539054i	−0.962993	−	0.269527i	$-0.913133\pi$
$881$		−	16.0000i		−	0.539054i	0.962993	−	0.269527i	$-0.0868673\pi$
$882$	1.00000	−	6.92820i	0.0336718	−	0.233285i
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−15.8564	+	4.53590i	−0.533309	+	0.152559i
$885$	1.50000	−	2.59808i	0.0504219	−	0.0873334i
$886$	2.50000	−	4.33013i	0.0839891	−	0.145473i
$887$	48.4974	−	28.0000i	1.62838	−	0.940148i	0.643809	−	0.765186i	$-0.277353\pi$
$887$	48.4974	−	28.0000i	1.62838	−	0.940148i	0.984575	−	0.174962i	$-0.0559801\pi$
$888$	7.00000			0.234905
$889$	−5.19615	+	1.00000i	−0.174273	+	0.0335389i
$890$			45.0000i			1.50840i
$891$	−1.73205	+	1.00000i	−0.0580259	+	0.0335013i
$892$	−13.0000	+	22.5167i	−0.435272	+	0.753914i
$893$	−15.0000	+	25.9808i	−0.501956	+	0.869413i
$894$		0			0
$895$			33.0000i			1.10307i
$896$	1.73205	+	2.00000i	0.0578638	+	0.0668153i
$897$	4.00000			0.133556
$898$	−5.19615	+	3.00000i	−0.173398	+	0.100111i
$899$	24.0000	−	41.5692i	0.800445	−	1.38641i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	−15.8564	+	4.53590i	−0.528253	+	0.151113i
$902$	16.0000			0.532742
$903$	22.5000	+	7.79423i	0.748753	+	0.259376i
$904$			18.0000i			0.598671i
$905$	−16.5000	−	28.5788i	−0.548479	−	0.949993i
$906$	8.66025	+	5.00000i	0.287718	+	0.166114i
$907$	−43.3013	−	25.0000i	−1.43780	−	0.830111i	−0.440099	−	0.897949i	$-0.645057\pi$
$907$	−43.3013	−	25.0000i	−1.43780	−	0.830111i	−0.997696	+	0.0678380i	$0.978390\pi$
$908$	13.8564	−	8.00000i	0.459841	−	0.265489i
$909$	−16.0000			−0.530687
$910$	30.0000	+	10.3923i	0.994490	+	0.344502i
$911$			33.0000i			1.09334i	0.837349	+	0.546669i	$0.184105\pi$
$911$			33.0000i			1.09334i	−0.837349	+	0.546669i	$0.815895\pi$
$912$	−4.33013	+	2.50000i	−0.143385	+	0.0827833i
$913$	−6.92820	−	4.00000i	−0.229290	−	0.132381i
$914$	8.50000	−	14.7224i	0.281155	−	0.486975i
$915$	5.19615	−	3.00000i	0.171780	−	0.0991769i
$916$	22.0000			0.726900
$917$	8.00000	−	6.92820i	0.264183	−	0.228789i
$918$	4.00000	+	1.00000i	0.132020	+	0.0330049i
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	0.882048	−	0.471160i	$-0.156165\pi$
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	−0.849061	+	0.528295i	$0.822831\pi$
$920$	1.50000	−	2.59808i	0.0494535	−	0.0856560i
$921$	−26.8468	−	15.5000i	−0.884632	−	0.510742i
$922$	−9.00000	−	15.5885i	−0.296399	−	0.513378i
$923$		−	4.00000i		−	0.131662i
$924$	5.19615	−	1.00000i	0.170941	−	0.0328976i
$925$		−	28.0000i		−	0.920634i
$926$	14.0000	+	24.2487i	0.460069	+	0.796862i
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$	5.19615	+	3.00000i	0.170572	+	0.0984798i
$929$	−19.0526	+	11.0000i	−0.625094	+	0.360898i	−0.778850	−	0.627211i	$-0.784197\pi$
$929$	−19.0526	+	11.0000i	−0.625094	+	0.360898i	0.153755	+	0.988109i	$0.450863\pi$
$930$		−	24.0000i		−	0.786991i
$931$	−27.5000	−	21.6506i	−0.901276	−	0.709571i
$932$			18.0000i			0.589610i
$933$	−15.5000	−	26.8468i	−0.507447	−	0.878924i
$934$	−8.50000	+	14.7224i	−0.278128	+	0.481733i
$935$	17.7846	+	17.1962i	0.581619	+	0.562374i
$936$	2.00000	+	3.46410i	0.0653720	+	0.113228i
$937$	−13.0000			−0.424691			−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000			−0.424691			−0.212346	+	0.977195i	$0.568110\pi$
$938$	12.9904	−	2.50000i	0.424151	−	0.0816279i
$939$	6.00000			0.195803
$940$	15.5885	−	9.00000i	0.508439	−	0.293548i
$941$	−19.9186	−	11.5000i	−0.649327	−	0.374889i	0.138871	−	0.990310i	$-0.455653\pi$
$941$	−19.9186	−	11.5000i	−0.649327	−	0.374889i	−0.788198	+	0.615421i	$0.788986\pi$
$942$	19.0526	+	11.0000i	0.620766	+	0.358399i
$943$	4.00000	+	6.92820i	0.130258	+	0.225613i
$944$	−1.00000			−0.0325472
$945$	−5.19615	−	6.00000i	−0.169031	−	0.195180i
$946$			18.0000i			0.585230i
$947$	13.8564	−	8.00000i	0.450273	−	0.259965i	−0.257673	−	0.966232i	$-0.582956\pi$
$947$	13.8564	−	8.00000i	0.450273	−	0.259965i	0.707945	+	0.706267i	$0.249622\pi$
$948$	2.00000	−	3.46410i	0.0649570	−	0.112509i
$949$	34.6410	+	20.0000i	1.12449	+	0.649227i
$950$	10.0000	+	17.3205i	0.324443	+	0.561951i
$951$	7.00000			0.226991
$952$	−9.13397	−	5.96410i	−0.296034	−	0.193298i
$953$	−19.0000			−0.615470			−0.307735	−	0.951472i	$-0.599571\pi$
$953$	−19.0000			−0.615470			−0.307735	+	0.951472i	$0.599571\pi$
$954$	2.00000	+	3.46410i	0.0647524	+	0.112154i
$955$	41.5692	+	24.0000i	1.34515	+	0.776622i
$956$	−11.0000	+	19.0526i	−0.355765	+	0.616204i
$957$	10.3923	−	6.00000i	0.335936	−	0.193952i
$958$		−	29.0000i		−	0.936947i
$959$	0.866025	−	2.50000i	0.0279654	−	0.0807292i
$960$	3.00000			0.0968246
$961$	16.5000	+	28.5788i	0.532258	+	0.921898i
$962$	−24.2487	−	14.0000i	−0.781810	−	0.451378i
$963$	−5.19615	−	3.00000i	−0.167444	−	0.0966736i
$964$	17.3205	−	10.0000i	0.557856	−	0.322078i
$965$	−18.0000			−0.579441
$966$	1.73205	+	2.00000i	0.0557278	+	0.0643489i
$967$	6.00000			0.192947			0.0964735	−	0.995336i	$-0.469244\pi$
$967$	6.00000			0.192947			0.0964735	+	0.995336i	$0.469244\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$	14.3301	−	14.8205i	0.460350	−	0.476103i
$970$	−18.0000	+	31.1769i	−0.577945	+	1.00103i
$971$	−4.50000	−	7.79423i	−0.144412	−	0.250129i	0.784741	−	0.619823i	$-0.212796\pi$
$971$	−4.50000	−	7.79423i	−0.144412	−	0.250129i	−0.929153	+	0.369694i	$0.879462\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−1.00000	−	5.19615i	−0.0320585	−	0.166581i
$974$		−	31.0000i		−	0.993304i
$975$	13.8564	−	8.00000i	0.443760	−	0.256205i
$976$	−1.73205	−	1.00000i	−0.0554416	−	0.0320092i
$977$	−5.50000	+	9.52628i	−0.175961	+	0.304773i	−0.940493	−	0.339812i	$-0.889636\pi$
$977$	−5.50000	+	9.52628i	−0.175961	+	0.304773i	0.764533	+	0.644585i	$0.222970\pi$
$978$	7.00000	+	12.1244i	0.223835	+	0.387694i
$979$		−	30.0000i		−	0.958804i
$980$	7.79423	+	19.5000i	0.248978	+	0.622905i
$981$		−	7.00000i		−	0.223493i
$982$	−5.50000	−	9.52628i	−0.175512	−	0.303996i
$983$	38.9711	+	22.5000i	1.24299	+	0.717639i	0.969701	−	0.244294i	$-0.0785563\pi$
$983$	38.9711	+	22.5000i	1.24299	+	0.717639i	0.273285	+	0.961933i	$0.411890\pi$
$984$	−4.00000	+	6.92820i	−0.127515	+	0.220863i
$985$	22.5000	+	38.9711i	0.716910	+	1.24172i
$986$	−24.0000	−	6.00000i	−0.764316	−	0.191079i
$987$	3.00000	+	15.5885i	0.0954911	+	0.496186i
$988$	20.0000			0.636285
$989$	−7.79423	+	4.50000i	−0.247842	+	0.143092i
$990$	3.00000	−	5.19615i	0.0953463	−	0.165145i
$991$	7.79423	+	4.50000i	0.247592	+	0.142947i	0.618661	−	0.785658i	$-0.287675\pi$
$991$	7.79423	+	4.50000i	0.247592	+	0.142947i	−0.371069	+	0.928605i	$0.621009\pi$
$992$	−6.92820	+	4.00000i	−0.219971	+	0.127000i
$993$			19.0000i			0.602947i
$994$	2.00000	−	1.73205i	0.0634361	−	0.0549373i
$995$	−45.0000			−1.42660
$996$	3.46410	−	2.00000i	0.109764	−	0.0633724i
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	0.295567	−	0.955322i	$-0.404491\pi$
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$998$	17.3205	+	10.0000i	0.548271	+	0.316544i
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.t.c.67.2	yes	4
7.2	even	3	inner	714.2.t.c.373.1	yes	4
17.16	even	2	inner	714.2.t.c.67.1	✓	4
119.16	even	6	inner	714.2.t.c.373.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.t.c.67.1	✓	4	17.16	even	2	inner
714.2.t.c.67.2	yes	4	1.1	even	1	trivial
714.2.t.c.373.1	yes	4	7.2	even	3	inner
714.2.t.c.373.2	yes	4	119.16	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} -1.00000i q^{6} +(-2.59808 + 0.500000i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.59808 - 1.50000i) q^{10} +(1.73205 + 1.00000i) q^{11} +(-0.866025 + 0.500000i) q^{12} +4.00000 q^{13} +(1.73205 + 2.00000i) q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.96410 + 2.86603i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +3.00000i q^{20} +(-2.50000 - 0.866025i) q^{21} -2.00000i q^{22} +(0.866025 - 0.500000i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} -6.00000i q^{29} +(-1.50000 - 2.59808i) q^{30} +(6.92820 + 4.00000i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{33} +(1.00000 - 4.00000i) q^{34} +(-6.00000 + 5.19615i) q^{35} -1.00000 q^{36} +(6.06218 - 3.50000i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(3.46410 + 2.00000i) q^{39} +(2.59808 - 1.50000i) q^{40} +8.00000i q^{41} +(0.500000 + 2.59808i) q^{42} -9.00000 q^{43} +(-1.73205 + 1.00000i) q^{44} +(2.59808 + 1.50000i) q^{45} +(-0.866025 - 0.500000i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(1.13397 + 3.96410i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(0.866025 - 0.500000i) q^{54} +6.00000 q^{55} +(-2.59808 + 0.500000i) q^{56} -5.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(0.500000 - 0.866025i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.73205 - 1.00000i) q^{61} -8.00000i q^{62} +(-1.73205 - 2.00000i) q^{63} +1.00000 q^{64} +(10.3923 - 6.00000i) q^{65} +(1.00000 - 1.73205i) q^{66} +(2.50000 - 4.33013i) q^{67} +(-3.96410 + 1.13397i) q^{68} +1.00000 q^{69} +(7.50000 + 2.59808i) q^{70} -1.00000i q^{71} +(0.500000 + 0.866025i) q^{72} +(8.66025 + 5.00000i) q^{73} +(-6.06218 - 3.50000i) q^{74} +(3.46410 - 2.00000i) q^{75} +5.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} -4.00000i q^{78} +(-3.46410 + 2.00000i) q^{79} +(-2.59808 - 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.92820 - 4.00000i) q^{82} -4.00000 q^{83} +(2.00000 - 1.73205i) q^{84} +(12.0000 + 3.00000i) q^{85} +(4.50000 + 7.79423i) q^{86} +(3.00000 - 5.19615i) q^{87} +(1.73205 + 1.00000i) q^{88} +(-7.50000 - 12.9904i) q^{89} -3.00000i q^{90} +(-10.3923 + 2.00000i) q^{91} +1.00000i q^{92} +(4.00000 + 6.92820i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-12.9904 - 7.50000i) q^{95} +(-0.866025 + 0.500000i) q^{96} -12.0000i q^{97} +(-5.50000 - 4.33013i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 16 q^{13} + 12 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} - 10 q^{19} - 10 q^{21} + 8 q^{25} - 8 q^{26} - 6 q^{30} - 2 q^{32} + 4 q^{33} + 4 q^{34} - 24 q^{35} - 4 q^{36} - 10 q^{38} + 2 q^{42} - 36 q^{43} - 12 q^{47} + 26 q^{49} - 16 q^{50} + 8 q^{51} - 8 q^{52} - 8 q^{53} + 24 q^{55} + 2 q^{59} - 6 q^{60} + 4 q^{64} + 4 q^{66} + 10 q^{67} - 2 q^{68} + 4 q^{69} + 30 q^{70} + 2 q^{72} + 20 q^{76} - 20 q^{77} - 2 q^{81} - 16 q^{83} + 8 q^{84} + 48 q^{85} + 18 q^{86} + 12 q^{87} - 30 q^{89} + 16 q^{93} - 12 q^{94} - 22 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9 + 16 * q^13 + 12 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 - 10 * q^19 - 10 * q^21 + 8 * q^25 - 8 * q^26 - 6 * q^30 - 2 * q^32 + 4 * q^33 + 4 * q^34 - 24 * q^35 - 4 * q^36 - 10 * q^38 + 2 * q^42 - 36 * q^43 - 12 * q^47 + 26 * q^49 - 16 * q^50 + 8 * q^51 - 8 * q^52 - 8 * q^53 + 24 * q^55 + 2 * q^59 - 6 * q^60 + 4 * q^64 + 4 * q^66 + 10 * q^67 - 2 * q^68 + 4 * q^69 + 30 * q^70 + 2 * q^72 + 20 * q^76 - 20 * q^77 - 2 * q^81 - 16 * q^83 + 8 * q^84 + 48 * q^85 + 18 * q^86 + 12 * q^87 - 30 * q^89 + 16 * q^93 - 12 * q^94 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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