LMFDB - Embedded newform 1110.2.i.m.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.m.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -1.37228 q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +2.37228 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.313859 + 0.543620i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.18614 + 2.05446i) q^{21} +(-0.686141 - 1.18843i) q^{22} +7.37228 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(1.18614 + 2.05446i) q^{28} +2.74456 q^{29} +(-0.500000 + 0.866025i) q^{30} +9.11684 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.686141 - 1.18843i) q^{33} +(-3.00000 + 5.19615i) q^{34} +(-1.18614 - 2.05446i) q^{35} +1.00000 q^{36} +(6.05842 - 0.543620i) q^{37} -0.627719 q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.37228 - 2.37686i) q^{41} +(-1.18614 + 2.05446i) q^{42} -11.1168 q^{43} +(0.686141 - 1.18843i) q^{44} -1.00000 q^{45} +(3.68614 + 6.38458i) q^{46} +7.37228 q^{47} +1.00000 q^{48} +(0.686141 + 1.18843i) q^{49} +(0.500000 - 0.866025i) q^{50} -6.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(1.37228 + 2.37686i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.686141 + 1.18843i) q^{55} +(-1.18614 + 2.05446i) q^{56} +(-0.313859 - 0.543620i) q^{57} +(1.37228 + 2.37686i) q^{58} +(-0.686141 - 1.18843i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(4.55842 + 7.89542i) q^{62} -2.37228 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +1.37228 q^{66} +(-1.81386 + 3.14170i) q^{67} -6.00000 q^{68} +(-3.68614 + 6.38458i) q^{69} +(1.18614 - 2.05446i) q^{70} +(-4.37228 + 7.57301i) q^{71} +(0.500000 + 0.866025i) q^{72} -11.1168 q^{73} +(3.50000 + 4.97494i) q^{74} +1.00000 q^{75} +(-0.313859 - 0.543620i) q^{76} +(-1.62772 + 2.81929i) q^{77} +(-0.500000 + 0.866025i) q^{78} +(8.55842 - 14.8236i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +2.74456 q^{82} +(-5.74456 - 9.94987i) q^{83} -2.37228 q^{84} +6.00000 q^{85} +(-5.55842 - 9.62747i) q^{86} +(-1.37228 + 2.37686i) q^{87} +1.37228 q^{88} +(8.05842 + 13.9576i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-1.18614 - 2.05446i) q^{91} +(-3.68614 + 6.38458i) q^{92} +(-4.55842 + 7.89542i) q^{93} +(3.68614 + 6.38458i) q^{94} +(0.313859 + 0.543620i) q^{95} +(0.500000 + 0.866025i) q^{96} +0.883156 q^{97} +(-0.686141 + 1.18843i) q^{98} +(0.686141 + 1.18843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} - 2 q^{9} + 4 q^{10} + 6 q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} + 12 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 18 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - q^{28} - 12 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} - 3 q^{33} - 12 q^{34} + q^{35} + 4 q^{36} + 7 q^{37} - 14 q^{38} + 2 q^{39} - 2 q^{40} - 6 q^{41} + q^{42} - 10 q^{43} - 3 q^{44} - 4 q^{45} + 9 q^{46} + 18 q^{47} + 4 q^{48} - 3 q^{49} + 2 q^{50} - 24 q^{51} + 2 q^{52} - 6 q^{53} + 2 q^{54} + 3 q^{55} + q^{56} - 7 q^{57} - 6 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} + q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{65} - 6 q^{66} - 13 q^{67} - 24 q^{68} - 9 q^{69} - q^{70} - 6 q^{71} + 2 q^{72} - 10 q^{73} + 14 q^{74} + 4 q^{75} - 7 q^{76} - 18 q^{77} - 2 q^{78} + 17 q^{79} - 4 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{84} + 24 q^{85} - 5 q^{86} + 6 q^{87} - 6 q^{88} + 15 q^{89} - 2 q^{90} + q^{91} - 9 q^{92} - q^{93} + 9 q^{94} + 7 q^{95} + 2 q^{96} + 38 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - q^7 - 4 * q^8 - 2 * q^9 + 4 * q^10 + 6 * q^11 - 2 * q^12 + 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 + 12 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 - q^21 + 3 * q^22 + 18 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - q^28 - 12 * q^29 - 2 * q^30 + 2 * q^31 + 2 * q^32 - 3 * q^33 - 12 * q^34 + q^35 + 4 * q^36 + 7 * q^37 - 14 * q^38 + 2 * q^39 - 2 * q^40 - 6 * q^41 + q^42 - 10 * q^43 - 3 * q^44 - 4 * q^45 + 9 * q^46 + 18 * q^47 + 4 * q^48 - 3 * q^49 + 2 * q^50 - 24 * q^51 + 2 * q^52 - 6 * q^53 + 2 * q^54 + 3 * q^55 + q^56 - 7 * q^57 - 6 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 + q^62 + 2 * q^63 + 4 * q^64 - 2 * q^65 - 6 * q^66 - 13 * q^67 - 24 * q^68 - 9 * q^69 - q^70 - 6 * q^71 + 2 * q^72 - 10 * q^73 + 14 * q^74 + 4 * q^75 - 7 * q^76 - 18 * q^77 - 2 * q^78 + 17 * q^79 - 4 * q^80 - 2 * q^81 - 12 * q^82 + 2 * q^84 + 24 * q^85 - 5 * q^86 + 6 * q^87 - 6 * q^88 + 15 * q^89 - 2 * q^90 + q^91 - 9 * q^92 - q^93 + 9 * q^94 + 7 * q^95 + 2 * q^96 + 38 * q^97 + 3 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$	1.18614	−	2.05446i	0.448319	−	0.776511i	−0.549958	−	0.835192i	$-0.685356\pi$
$7$	1.18614	−	2.05446i	0.448319	−	0.776511i	0.998277	+	0.0586811i	$0.0186895\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	−1.37228			−0.413758			−0.206879	−	0.978366i	$-0.566331\pi$
$11$	−1.37228			−0.413758			−0.206879	+	0.978366i	$0.566331\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	2.37228			0.634019
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−0.313859	+	0.543620i	−0.0720043	+	0.124715i	−0.899780	−	0.436345i	$-0.856273\pi$
$19$	−0.313859	+	0.543620i	−0.0720043	+	0.124715i	0.827775	+	0.561060i	$0.189606\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.18614	+	2.05446i	0.258837	+	0.448319i
$22$	−0.686141	−	1.18843i	−0.146286	−	0.253374i
$23$	7.37228			1.53723			0.768613	−	0.639713i	$-0.220947\pi$
$23$	7.37228			1.53723			0.768613	+	0.639713i	$0.220947\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$	1.00000			0.192450
$28$	1.18614	+	2.05446i	0.224160	+	0.388256i
$29$	2.74456			0.509652			0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456			0.509652			0.254826	+	0.966987i	$0.417982\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	9.11684			1.63743			0.818717	−	0.574198i	$-0.194686\pi$
$31$	9.11684			1.63743			0.818717	+	0.574198i	$0.194686\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.686141	−	1.18843i	0.119442	−	0.206879i
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$	−1.18614	−	2.05446i	−0.200494	−	0.347266i
$36$	1.00000			0.166667
$37$	6.05842	−	0.543620i	0.995998	−	0.0893706i
$37$	6.05842	−	0.543620i	0.995998	−	0.0893706i
$38$	−0.627719			−0.101829
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	1.37228	−	2.37686i	0.214314	−	0.371203i	−0.738746	−	0.673984i	$-0.764582\pi$
$41$	1.37228	−	2.37686i	0.214314	−	0.371203i	0.953060	+	0.302781i	$0.0979150\pi$
$42$	−1.18614	+	2.05446i	−0.183025	+	0.317009i
$43$	−11.1168			−1.69530			−0.847651	−	0.530554i	$-0.821984\pi$
$43$	−11.1168			−1.69530			−0.847651	+	0.530554i	$0.821984\pi$
$44$	0.686141	−	1.18843i	0.103440	−	0.179163i
$45$	−1.00000			−0.149071
$46$	3.68614	+	6.38458i	0.543492	+	0.941355i
$47$	7.37228			1.07536			0.537679	−	0.843150i	$-0.319301\pi$
$47$	7.37228			1.07536			0.537679	+	0.843150i	$0.319301\pi$
$48$	1.00000			0.144338
$49$	0.686141	+	1.18843i	0.0980201	+	0.169776i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−6.00000			−0.840168
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	1.37228	+	2.37686i	0.188497	+	0.326487i	0.944749	−	0.327793i	$-0.106305\pi$
$53$	1.37228	+	2.37686i	0.188497	+	0.326487i	−0.756252	+	0.654280i	$0.772972\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−0.686141	+	1.18843i	−0.0925192	+	0.160248i
$56$	−1.18614	+	2.05446i	−0.158505	+	0.274538i
$57$	−0.313859	−	0.543620i	−0.0415717	−	0.0720043i
$58$	1.37228	+	2.37686i	0.180189	+	0.312097i
$59$	−0.686141	−	1.18843i	−0.0893279	−	0.154720i	0.817899	−	0.575361i	$-0.195139\pi$
$59$	−0.686141	−	1.18843i	−0.0893279	−	0.154720i	−0.907227	+	0.420641i	$0.861805\pi$
$60$	−1.00000			−0.129099
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	4.55842	+	7.89542i	0.578920	+	1.00272i
$63$	−2.37228			−0.298879
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	1.37228			0.168916
$67$	−1.81386	+	3.14170i	−0.221598	+	0.383819i	−0.955293	−	0.295659i	$-0.904461\pi$
$67$	−1.81386	+	3.14170i	−0.221598	+	0.383819i	0.733695	+	0.679479i	$0.237794\pi$
$68$	−6.00000			−0.727607
$69$	−3.68614	+	6.38458i	−0.443759	+	0.768613i
$70$	1.18614	−	2.05446i	0.141771	−	0.245554i
$71$	−4.37228	+	7.57301i	−0.518894	+	0.898751i	0.480865	+	0.876795i	$0.340323\pi$
$71$	−4.37228	+	7.57301i	−0.518894	+	0.898751i	−0.999759	+	0.0219565i	$0.993010\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−11.1168			−1.30113			−0.650564	−	0.759451i	$-0.725467\pi$
$73$	−11.1168			−1.30113			−0.650564	+	0.759451i	$0.725467\pi$
$74$	3.50000	+	4.97494i	0.406867	+	0.578325i
$75$	1.00000			0.115470
$76$	−0.313859	−	0.543620i	−0.0360021	−	0.0623575i
$77$	−1.62772	+	2.81929i	−0.185496	+	0.321288i
$78$	−0.500000	+	0.866025i	−0.0566139	+	0.0980581i
$79$	8.55842	−	14.8236i	0.962898	−	1.66779i	0.247737	−	0.968827i	$-0.420313\pi$
$79$	8.55842	−	14.8236i	0.962898	−	1.66779i	0.715160	−	0.698961i	$-0.246354\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.74456			0.303086
$83$	−5.74456	−	9.94987i	−0.630548	−	1.09214i	−0.987440	−	0.157995i	$-0.949497\pi$
$83$	−5.74456	−	9.94987i	−0.630548	−	1.09214i	0.356892	−	0.934146i	$-0.383836\pi$
$84$	−2.37228			−0.258837
$85$	6.00000			0.650791
$86$	−5.55842	−	9.62747i	−0.599380	−	1.03816i
$87$	−1.37228	+	2.37686i	−0.147124	+	0.254826i
$88$	1.37228			0.146286
$89$	8.05842	+	13.9576i	0.854191	+	1.47950i	0.877393	+	0.479771i	$0.159280\pi$
$89$	8.05842	+	13.9576i	0.854191	+	1.47950i	−0.0232025	+	0.999731i	$0.507386\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−1.18614	−	2.05446i	−0.124341	−	0.215365i
$92$	−3.68614	+	6.38458i	−0.384307	+	0.665639i
$93$	−4.55842	+	7.89542i	−0.472686	+	0.818717i
$94$	3.68614	+	6.38458i	0.380196	+	0.658519i
$95$	0.313859	+	0.543620i	0.0322013	+	0.0557743i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	0.883156			0.0896709			0.0448355	−	0.998994i	$-0.485724\pi$
$97$	0.883156			0.0896709			0.0448355	+	0.998994i	$0.485724\pi$
$98$	−0.686141	+	1.18843i	−0.0693107	+	0.120050i
$99$	0.686141	+	1.18843i	0.0689597	+	0.119442i
$100$	1.00000			0.100000
$101$	−3.25544			−0.323928			−0.161964	−	0.986797i	$-0.551783\pi$
$101$	−3.25544			−0.323928			−0.161964	+	0.986797i	$0.551783\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−2.11684			−0.208579			−0.104289	−	0.994547i	$-0.533257\pi$
$103$	−2.11684			−0.208579			−0.104289	+	0.994547i	$0.533257\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$	2.37228			0.231511
$106$	−1.37228	+	2.37686i	−0.133288	+	0.230861i
$107$	4.37228	−	7.57301i	0.422684	−	0.732111i	−0.573517	−	0.819194i	$-0.694421\pi$
$107$	4.37228	−	7.57301i	0.422684	−	0.732111i	0.996201	+	0.0870831i	$0.0277546\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	1.18614	+	2.05446i	0.113612	+	0.196781i	0.917224	−	0.398372i	$-0.130425\pi$
$109$	1.18614	+	2.05446i	0.113612	+	0.196781i	−0.803612	+	0.595153i	$0.797091\pi$
$110$	−1.37228			−0.130842
$111$	−2.55842	+	5.51856i	−0.242835	+	0.523798i
$112$	−2.37228			−0.224160
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$	0.313859	−	0.543620i	0.0293956	−	0.0509147i
$115$	3.68614	−	6.38458i	0.343734	−	0.595365i
$116$	−1.37228	+	2.37686i	−0.127413	+	0.220686i
$117$	−1.00000			−0.0924500
$118$	0.686141	−	1.18843i	0.0631644	−	0.109404i
$119$	14.2337			1.30480
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−9.11684			−0.828804
$122$	−2.00000			−0.181071
$123$	1.37228	+	2.37686i	0.123734	+	0.214314i
$124$	−4.55842	+	7.89542i	−0.409358	+	0.709030i
$125$	−1.00000			−0.0894427
$126$	−1.18614	−	2.05446i	−0.105670	−	0.183025i
$127$	−9.61684	−	16.6569i	−0.853357	−	1.47806i	−0.878161	−	0.478365i	$-0.841230\pi$
$127$	−9.61684	−	16.6569i	−0.853357	−	1.47806i	0.0248041	−	0.999692i	$-0.492104\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.55842	−	9.62747i	0.489392	−	0.847651i
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	4.37228	+	7.57301i	0.382008	+	0.661657i	0.991349	−	0.131251i	$-0.0418993\pi$
$131$	4.37228	+	7.57301i	0.382008	+	0.661657i	−0.609341	+	0.792908i	$0.708566\pi$
$132$	0.686141	+	1.18843i	0.0597209	+	0.103440i
$133$	0.744563	+	1.28962i	0.0645618	+	0.111824i
$134$	−3.62772			−0.313387
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	2.74456			0.234484			0.117242	−	0.993103i	$-0.462595\pi$
$137$	2.74456			0.234484			0.117242	+	0.993103i	$0.462595\pi$
$138$	−7.37228			−0.627570
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	2.37228			0.200494
$141$	−3.68614	+	6.38458i	−0.310429	+	0.537679i
$142$	−8.74456			−0.733827
$143$	−0.686141	+	1.18843i	−0.0573780	+	0.0993815i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.37228	−	2.37686i	0.113962	−	0.197388i
$146$	−5.55842	−	9.62747i	−0.460018	−	0.796775i
$147$	−1.37228			−0.113184
$148$	−2.55842	+	5.51856i	−0.210301	+	0.453623i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−10.3030	+	17.8453i	−0.838445	+	1.45223i	0.0527494	+	0.998608i	$0.483202\pi$
$151$	−10.3030	+	17.8453i	−0.838445	+	1.45223i	−0.891194	+	0.453622i	$0.850132\pi$
$152$	0.313859	−	0.543620i	0.0254574	−	0.0440934i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$	−3.25544			−0.262331
$155$	4.55842	−	7.89542i	0.366141	−	0.634175i
$156$	−1.00000			−0.0800641
$157$	−3.87228	−	6.70699i	−0.309042	−	0.535276i	0.669111	−	0.743162i	$-0.266675\pi$
$157$	−3.87228	−	6.70699i	−0.309042	−	0.535276i	−0.978153	+	0.207886i	$0.933342\pi$
$158$	17.1168			1.36174
$159$	−2.74456			−0.217658
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	8.74456	−	15.1460i	0.689168	−	1.19367i
$162$	−1.00000			−0.0785674
$163$	−11.3723	−	19.6974i	−0.890746	−	1.54282i	−0.838983	−	0.544158i	$-0.816849\pi$
$163$	−11.3723	−	19.6974i	−0.890746	−	1.54282i	−0.0517628	−	0.998659i	$-0.516484\pi$
$164$	1.37228	+	2.37686i	0.107157	+	0.185602i
$165$	−0.686141	−	1.18843i	−0.0534160	−	0.0925192i
$166$	5.74456	−	9.94987i	0.445865	−	0.772260i
$167$	8.74456	−	15.1460i	0.676675	−	1.17203i	−0.299302	−	0.954158i	$-0.596754\pi$
$167$	8.74456	−	15.1460i	0.676675	−	1.17203i	0.975976	−	0.217876i	$-0.0699129\pi$
$168$	−1.18614	−	2.05446i	−0.0915127	−	0.158505i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	3.00000	+	5.19615i	0.230089	+	0.398527i
$171$	0.627719			0.0480028
$172$	5.55842	−	9.62747i	0.423826	−	0.734088i
$173$	0.941578	+	1.63086i	0.0715869	+	0.123992i	0.899597	−	0.436721i	$-0.143860\pi$
$173$	0.941578	+	1.63086i	0.0715869	+	0.123992i	−0.828010	+	0.560713i	$0.810527\pi$
$174$	−2.74456			−0.208065
$175$	−2.37228			−0.179328
$176$	0.686141	+	1.18843i	0.0517198	+	0.0895813i
$177$	1.37228			0.103147
$178$	−8.05842	+	13.9576i	−0.604004	+	1.04617i
$179$	10.6277			0.794353			0.397176	−	0.917742i	$-0.369990\pi$
$179$	10.6277			0.794353			0.397176	+	0.917742i	$0.369990\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	4.44158	−	7.69304i	0.330140	−	0.571819i	−0.652399	−	0.757876i	$-0.726237\pi$
$181$	4.44158	−	7.69304i	0.330140	−	0.571819i	0.982539	+	0.186056i	$0.0595707\pi$
$182$	1.18614	−	2.05446i	0.0879226	−	0.152286i
$183$	−1.00000	−	1.73205i	−0.0739221	−	0.128037i
$184$	−7.37228			−0.543492
$185$	2.55842	−	5.51856i	0.188099	−	0.405732i
$186$	−9.11684			−0.668479
$187$	−4.11684	−	7.13058i	−0.301053	−	0.521440i
$188$	−3.68614	+	6.38458i	−0.268839	+	0.465644i
$189$	1.18614	−	2.05446i	0.0862790	−	0.149440i
$190$	−0.313859	+	0.543620i	−0.0227697	+	0.0394384i
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−14.3723			−1.03454			−0.517270	−	0.855822i	$-0.673052\pi$
$193$	−14.3723			−1.03454			−0.517270	+	0.855822i	$0.673052\pi$
$194$	0.441578	+	0.764836i	0.0317035	+	0.0549120i
$195$	1.00000			0.0716115
$196$	−1.37228			−0.0980201
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$	−0.686141	+	1.18843i	−0.0487619	+	0.0844581i
$199$	9.62772			0.682491			0.341245	−	0.939974i	$-0.389151\pi$
$199$	9.62772			0.682491			0.341245	+	0.939974i	$0.389151\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−1.81386	−	3.14170i	−0.127940	−	0.221598i
$202$	−1.62772	−	2.81929i	−0.114526	−	0.198365i
$203$	3.25544	−	5.63858i	0.228487	−	0.395751i
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$	−1.37228	−	2.37686i	−0.0958443	−	0.166007i
$206$	−1.05842	−	1.83324i	−0.0737438	−	0.127728i
$207$	−3.68614	−	6.38458i	−0.256204	−	0.443759i
$208$	−1.00000			−0.0693375
$209$	0.430703	−	0.746000i	0.0297924	−	0.0516019i
$210$	1.18614	+	2.05446i	0.0818515	+	0.141771i
$211$	19.2337			1.32410			0.662051	−	0.749459i	$-0.269686\pi$
$211$	19.2337			1.32410			0.662051	+	0.749459i	$0.269686\pi$
$212$	−2.74456			−0.188497
$213$	−4.37228	−	7.57301i	−0.299584	−	0.518894i
$214$	8.74456			0.597766
$215$	−5.55842	+	9.62747i	−0.379081	+	0.656588i
$216$	−1.00000			−0.0680414
$217$	10.8139	−	18.7302i	0.734093	−	1.27149i
$218$	−1.18614	+	2.05446i	−0.0803356	+	0.139145i
$219$	5.55842	−	9.62747i	0.375603	−	0.650564i
$220$	−0.686141	−	1.18843i	−0.0462596	−	0.0801240i
$221$	6.00000			0.403604
$222$	−6.05842	+	0.543620i	−0.406615	+	0.0364854i
$223$	−23.9783			−1.60570			−0.802851	−	0.596179i	$-0.796685\pi$
$223$	−23.9783			−1.60570			−0.802851	+	0.596179i	$0.796685\pi$
$224$	−1.18614	−	2.05446i	−0.0792524	−	0.137269i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$	0.627719			0.0415717
$229$	−13.5584	+	23.4839i	−0.895966	+	1.55186i	−0.0633609	+	0.997991i	$0.520182\pi$
$229$	−13.5584	+	23.4839i	−0.895966	+	1.55186i	−0.832605	+	0.553868i	$0.813151\pi$
$230$	7.37228			0.486114
$231$	−1.62772	−	2.81929i	−0.107096	−	0.185496i
$232$	−2.74456			−0.180189
$233$	−14.2337			−0.932480			−0.466240	−	0.884658i	$-0.654392\pi$
$233$	−14.2337			−0.932480			−0.466240	+	0.884658i	$0.654392\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	3.68614	−	6.38458i	0.240457	−	0.416484i
$236$	1.37228			0.0893279
$237$	8.55842	+	14.8236i	0.555929	+	0.962898i
$238$	7.11684	+	12.3267i	0.461316	+	0.799024i
$239$	3.25544	+	5.63858i	0.210577	+	0.364730i	0.951895	−	0.306424i	$-0.0991325\pi$
$239$	3.25544	+	5.63858i	0.210577	+	0.364730i	−0.741318	+	0.671153i	$0.765799\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.12772	+	1.95327i	−0.0726427	+	0.125821i	−0.900059	−	0.435769i	$-0.856477\pi$
$241$	−1.12772	+	1.95327i	−0.0726427	+	0.125821i	0.827416	+	0.561589i	$0.189810\pi$
$242$	−4.55842	−	7.89542i	−0.293026	−	0.507537i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	1.37228			0.0876718
$246$	−1.37228	+	2.37686i	−0.0874935	+	0.151543i
$247$	0.313859	+	0.543620i	0.0199704	+	0.0345897i
$248$	−9.11684			−0.578920
$249$	11.4891			0.728094
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−21.6060			−1.36376			−0.681878	−	0.731466i	$-0.738837\pi$
$251$	−21.6060			−1.36376			−0.681878	+	0.731466i	$0.738837\pi$
$252$	1.18614	−	2.05446i	0.0747198	−	0.129419i
$253$	−10.1168			−0.636041
$254$	9.61684	−	16.6569i	0.603414	−	1.04514i
$255$	−3.00000	+	5.19615i	−0.187867	+	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.1168	+	17.5229i	0.631071	+	1.09305i	0.987333	+	0.158661i	$0.0507178\pi$
$257$	10.1168	+	17.5229i	0.631071	+	1.09305i	−0.356262	+	0.934386i	$0.615949\pi$
$258$	11.1168			0.692104
$259$	6.06930	−	13.0916i	0.377128	−	0.813471i
$260$	1.00000			0.0620174
$261$	−1.37228	−	2.37686i	−0.0849421	−	0.147124i
$262$	−4.37228	+	7.57301i	−0.270120	+	0.467862i
$263$	−3.94158	+	6.82701i	−0.243048	+	0.420972i	−0.961581	−	0.274521i	$-0.911481\pi$
$263$	−3.94158	+	6.82701i	−0.243048	+	0.420972i	0.718533	+	0.695493i	$0.244814\pi$
$264$	−0.686141	+	1.18843i	−0.0422290	+	0.0731428i
$265$	2.74456			0.168597
$266$	−0.744563	+	1.28962i	−0.0456521	+	0.0790717i
$267$	−16.1168			−0.986335
$268$	−1.81386	−	3.14170i	−0.110799	−	0.191910i
$269$	21.2554			1.29597			0.647983	−	0.761654i	$-0.275613\pi$
$269$	21.2554			1.29597			0.647983	+	0.761654i	$0.275613\pi$
$270$	1.00000			0.0608581
$271$	−13.5584	−	23.4839i	−0.823615	−	1.42654i	−0.902973	−	0.429698i	$-0.858620\pi$
$271$	−13.5584	−	23.4839i	−0.823615	−	1.42654i	0.0793574	−	0.996846i	$-0.474713\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$	2.37228			0.143577
$274$	1.37228	+	2.37686i	0.0829025	+	0.143591i
$275$	0.686141	+	1.18843i	0.0413758	+	0.0716651i
$276$	−3.68614	−	6.38458i	−0.221880	−	0.384307i
$277$	1.74456	−	3.02167i	0.104821	−	0.181555i	−0.808844	−	0.588023i	$-0.799906\pi$
$277$	1.74456	−	3.02167i	0.104821	−	0.181555i	0.913665	+	0.406468i	$0.133240\pi$
$278$	2.50000	−	4.33013i	0.149940	−	0.259704i
$279$	−4.55842	−	7.89542i	−0.272906	−	0.472686i
$280$	1.18614	+	2.05446i	0.0708855	+	0.122777i
$281$	8.05842	+	13.9576i	0.480725	+	0.832640i	0.999755	−	0.0221155i	$-0.00704015\pi$
$281$	8.05842	+	13.9576i	0.480725	+	0.832640i	−0.519030	+	0.854756i	$0.673707\pi$
$282$	−7.37228			−0.439013
$283$	5.81386	−	10.0699i	0.345598	−	0.598593i	−0.639864	−	0.768488i	$-0.721009\pi$
$283$	5.81386	−	10.0699i	0.345598	−	0.598593i	0.985462	+	0.169895i	$0.0543427\pi$
$284$	−4.37228	−	7.57301i	−0.259447	−	0.449376i
$285$	−0.627719			−0.0371828
$286$	−1.37228			−0.0811447
$287$	−3.25544	−	5.63858i	−0.192162	−	0.332835i
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	2.74456			0.161166
$291$	−0.441578	+	0.764836i	−0.0258858	+	0.0448355i
$292$	5.55842	−	9.62747i	0.325282	−	0.563405i
$293$	11.0584	−	19.1537i	0.646040	−	1.11897i	−0.338020	−	0.941139i	$-0.609757\pi$
$293$	11.0584	−	19.1537i	0.646040	−	1.11897i	0.984060	−	0.177835i	$-0.0569094\pi$
$294$	−0.686141	−	1.18843i	−0.0400165	−	0.0693107i
$295$	−1.37228			−0.0798973
$296$	−6.05842	+	0.543620i	−0.352139	+	0.0315973i
$297$	−1.37228			−0.0796278
$298$		0			0
$299$	3.68614	−	6.38458i	0.213175	−	0.369230i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−13.1861	+	22.8391i	−0.760037	+	1.31642i
$302$	−20.6060			−1.18574
$303$	1.62772	−	2.81929i	0.0935100	−	0.161964i
$304$	0.627719			0.0360021
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	6.00000			0.342997
$307$	−22.6060			−1.29019			−0.645095	−	0.764102i	$-0.723182\pi$
$307$	−22.6060			−1.29019			−0.645095	+	0.764102i	$0.723182\pi$
$308$	−1.62772	−	2.81929i	−0.0927479	−	0.160644i
$309$	1.05842	−	1.83324i	0.0602115	−	0.104289i
$310$	9.11684			0.517802
$311$	2.74456	+	4.75372i	0.155630	+	0.269559i	0.933288	−	0.359128i	$-0.116926\pi$
$311$	2.74456	+	4.75372i	0.155630	+	0.269559i	−0.777658	+	0.628687i	$0.783593\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	3.93070	+	6.80818i	0.222176	+	0.384821i	0.955469	−	0.295093i	$-0.0953506\pi$
$313$	3.93070	+	6.80818i	0.222176	+	0.384821i	−0.733292	+	0.679914i	$0.762017\pi$
$314$	3.87228	−	6.70699i	0.218525	−	0.378497i
$315$	−1.18614	+	2.05446i	−0.0668315	+	0.115755i
$316$	8.55842	+	14.8236i	0.481449	+	0.833894i
$317$	14.0584	+	24.3499i	0.789600	+	1.36763i	0.926212	+	0.377002i	$0.123045\pi$
$317$	14.0584	+	24.3499i	0.789600	+	1.36763i	−0.136613	+	0.990625i	$0.543622\pi$
$318$	−1.37228	−	2.37686i	−0.0769537	−	0.133288i
$319$	−3.76631			−0.210873
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	4.37228	+	7.57301i	0.244037	+	0.422684i
$322$	17.4891			0.974631
$323$	−3.76631			−0.209563
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000			−0.0554700
$326$	11.3723	−	19.6974i	0.629852	−	1.09094i
$327$	−2.37228			−0.131187
$328$	−1.37228	+	2.37686i	−0.0757716	+	0.131240i
$329$	8.74456	−	15.1460i	0.482103	−	0.835027i
$330$	0.686141	−	1.18843i	0.0377708	−	0.0654209i
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$	11.4891			0.630548
$333$	−3.50000	−	4.97494i	−0.191799	−	0.272625i
$334$	17.4891			0.956962
$335$	1.81386	+	3.14170i	0.0991017	+	0.171649i
$336$	1.18614	−	2.05446i	0.0647093	−	0.112080i
$337$	2.81386	−	4.87375i	0.153281	−	0.265490i	−0.779151	−	0.626836i	$-0.784349\pi$
$337$	2.81386	−	4.87375i	0.153281	−	0.265490i	0.932432	+	0.361346i	$0.117683\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−12.5109			−0.677502
$342$	0.313859	+	0.543620i	0.0169716	+	0.0293956i
$343$	19.8614			1.07242
$344$	11.1168			0.599380
$345$	3.68614	+	6.38458i	0.198455	+	0.343734i
$346$	−0.941578	+	1.63086i	−0.0506195	+	0.0876756i
$347$	−26.7446			−1.43572			−0.717862	−	0.696186i	$-0.754879\pi$
$347$	−26.7446			−1.43572			−0.717862	+	0.696186i	$0.754879\pi$
$348$	−1.37228	−	2.37686i	−0.0735620	−	0.127413i
$349$	−17.1168	−	29.6472i	−0.916244	−	1.58698i	−0.805070	−	0.593180i	$-0.797872\pi$
$349$	−17.1168	−	29.6472i	−0.916244	−	1.58698i	−0.111173	−	0.993801i	$-0.535461\pi$
$350$	−1.18614	−	2.05446i	−0.0634019	−	0.109815i
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$	−0.686141	+	1.18843i	−0.0365714	+	0.0633436i
$353$	−1.37228	−	2.37686i	−0.0730392	−	0.126508i	0.827193	−	0.561918i	$-0.189936\pi$
$353$	−1.37228	−	2.37686i	−0.0730392	−	0.126508i	−0.900232	+	0.435411i	$0.856603\pi$
$354$	0.686141	+	1.18843i	0.0364680	+	0.0631644i
$355$	4.37228	+	7.57301i	0.232057	+	0.401934i
$356$	−16.1168			−0.854191
$357$	−7.11684	+	12.3267i	−0.376663	+	0.652400i
$358$	5.31386	+	9.20387i	0.280846	+	0.486440i
$359$	−11.4891			−0.606373			−0.303186	−	0.952931i	$-0.598050\pi$
$359$	−11.4891			−0.606373			−0.303186	+	0.952931i	$0.598050\pi$
$360$	1.00000			0.0527046
$361$	9.30298	+	16.1132i	0.489631	+	0.848065i
$362$	8.88316			0.466888
$363$	4.55842	−	7.89542i	0.239255	−	0.414402i
$364$	2.37228			0.124341
$365$	−5.55842	+	9.62747i	−0.290941	+	0.503925i
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	3.75544	−	6.50461i	0.196032	−	0.339538i	−0.751206	−	0.660068i	$-0.770528\pi$
$367$	3.75544	−	6.50461i	0.196032	−	0.339538i	0.947238	+	0.320530i	$0.103861\pi$
$368$	−3.68614	−	6.38458i	−0.192153	−	0.332819i
$369$	−2.74456			−0.142876
$370$	6.05842	−	0.543620i	0.314962	−	0.0282615i
$371$	6.51087			0.338028
$372$	−4.55842	−	7.89542i	−0.236343	−	0.409358i
$373$	−15.3614	+	26.6067i	−0.795383	+	1.37764i	0.127212	+	0.991876i	$0.459397\pi$
$373$	−15.3614	+	26.6067i	−0.795383	+	1.37764i	−0.922595	+	0.385769i	$0.873936\pi$
$374$	4.11684	−	7.13058i	0.212877	−	0.368714i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−7.37228			−0.380196
$377$	1.37228	−	2.37686i	0.0706761	−	0.122415i
$378$	2.37228			0.122017
$379$	−1.25544	−	2.17448i	−0.0644875	−	0.111696i	0.831979	−	0.554807i	$-0.187208\pi$
$379$	−1.25544	−	2.17448i	−0.0644875	−	0.111696i	−0.896467	+	0.443111i	$0.853875\pi$
$380$	−0.627719			−0.0322013
$381$	19.2337			0.985372
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	−9.17527	+	15.8920i	−0.468834	+	0.812045i	−0.999365	−	0.0356208i	$-0.988659\pi$
$383$	−9.17527	+	15.8920i	−0.468834	+	0.812045i	0.530531	+	0.847665i	$0.321992\pi$
$384$	−1.00000			−0.0510310
$385$	1.62772	+	2.81929i	0.0829562	+	0.143684i
$386$	−7.18614	−	12.4468i	−0.365765	−	0.633523i
$387$	5.55842	+	9.62747i	0.282550	+	0.489392i
$388$	−0.441578	+	0.764836i	−0.0224177	+	0.0388286i
$389$	1.37228	−	2.37686i	0.0695774	−	0.120512i	−0.829138	−	0.559044i	$-0.811168\pi$
$389$	1.37228	−	2.37686i	0.0695774	−	0.120512i	0.898715	+	0.438532i	$0.144502\pi$
$390$	0.500000	+	0.866025i	0.0253185	+	0.0438529i
$391$	22.1168	+	38.3075i	1.11850	+	1.93729i
$392$	−0.686141	−	1.18843i	−0.0346553	−	0.0600248i
$393$	−8.74456			−0.441105
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−8.55842	−	14.8236i	−0.430621	−	0.745857i
$396$	−1.37228			−0.0689597
$397$	29.0000			1.45547			0.727734	−	0.685859i	$-0.240573\pi$
$397$	29.0000			1.45547			0.727734	+	0.685859i	$0.240573\pi$
$398$	4.81386	+	8.33785i	0.241297	+	0.417939i
$399$	−1.48913			−0.0745495
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−21.6060			−1.07895			−0.539475	−	0.842001i	$-0.681377\pi$
$401$	−21.6060			−1.07895			−0.539475	+	0.842001i	$0.681377\pi$
$402$	1.81386	−	3.14170i	0.0904671	−	0.156694i
$403$	4.55842	−	7.89542i	0.227071	−	0.393299i
$404$	1.62772	−	2.81929i	0.0809820	−	0.140265i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	6.51087			0.323129
$407$	−8.31386	+	0.746000i	−0.412103	+	0.0369778i
$408$	6.00000			0.297044
$409$	14.0475	+	24.3311i	0.694607	+	1.20309i	0.970313	+	0.241852i	$0.0777548\pi$
$409$	14.0475	+	24.3311i	0.694607	+	1.20309i	−0.275707	+	0.961242i	$0.588912\pi$
$410$	1.37228	−	2.37686i	0.0677721	−	0.117385i
$411$	−1.37228	+	2.37686i	−0.0676896	+	0.117242i
$412$	1.05842	−	1.83324i	0.0521447	−	0.0903173i
$413$	−3.25544			−0.160190
$414$	3.68614	−	6.38458i	0.181164	−	0.313785i
$415$	−11.4891			−0.563979
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	5.00000			0.244851
$418$	0.861407			0.0421328
$419$	−3.94158	−	6.82701i	−0.192559	−	0.333521i	0.753539	−	0.657403i	$-0.228345\pi$
$419$	−3.94158	−	6.82701i	−0.192559	−	0.333521i	−0.946097	+	0.323882i	$0.895012\pi$
$420$	−1.18614	+	2.05446i	−0.0578777	+	0.100247i
$421$	−30.2337			−1.47350			−0.736750	−	0.676165i	$-0.763640\pi$
$421$	−30.2337			−1.47350			−0.736750	+	0.676165i	$0.763640\pi$
$422$	9.61684	+	16.6569i	0.468141	+	0.810843i
$423$	−3.68614	−	6.38458i	−0.179226	−	0.310429i
$424$	−1.37228	−	2.37686i	−0.0666439	−	0.115431i
$425$	3.00000	−	5.19615i	0.145521	−	0.252050i
$426$	4.37228	−	7.57301i	0.211838	−	0.366914i
$427$	2.37228	+	4.10891i	0.114803	+	0.198844i
$428$	4.37228	+	7.57301i	0.211342	+	0.366055i
$429$	−0.686141	−	1.18843i	−0.0331272	−	0.0573780i
$430$	−11.1168			−0.536102
$431$	11.4891	−	19.8997i	0.553412	−	0.958537i	−0.444614	−	0.895723i	$-0.646659\pi$
$431$	11.4891	−	19.8997i	0.553412	−	0.958537i	0.998025	−	0.0628147i	$-0.0200077\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−32.9783			−1.58483			−0.792417	−	0.609980i	$-0.791177\pi$
$433$	−32.9783			−1.58483			−0.792417	+	0.609980i	$0.791177\pi$
$434$	21.6277			1.03816
$435$	1.37228	+	2.37686i	0.0657959	+	0.113962i
$436$	−2.37228			−0.113612
$437$	−2.31386	+	4.00772i	−0.110687	+	0.191715i
$438$	11.1168			0.531183
$439$	−4.81386	+	8.33785i	−0.229753	+	0.397944i	−0.957735	−	0.287653i	$-0.907125\pi$
$439$	−4.81386	+	8.33785i	−0.229753	+	0.397944i	0.727982	+	0.685596i	$0.240458\pi$
$440$	0.686141	−	1.18843i	0.0327105	−	0.0566562i
$441$	0.686141	−	1.18843i	0.0326734	−	0.0565919i
$442$	3.00000	+	5.19615i	0.142695	+	0.247156i
$443$	8.74456			0.415467			0.207733	−	0.978185i	$-0.433391\pi$
$443$	8.74456			0.415467			0.207733	+	0.978185i	$0.433391\pi$
$444$	−3.50000	−	4.97494i	−0.166103	−	0.236100i
$445$	16.1168			0.764012
$446$	−11.9891	−	20.7658i	−0.567702	−	0.983288i
$447$		0			0
$448$	1.18614	−	2.05446i	0.0560399	−	0.0970639i
$449$	−13.3723	+	23.1615i	−0.631077	+	1.09306i	0.356255	+	0.934389i	$0.384053\pi$
$449$	−13.3723	+	23.1615i	−0.631077	+	1.09306i	−0.987332	+	0.158669i	$0.949280\pi$
$450$	−1.00000			−0.0471405
$451$	−1.88316	+	3.26172i	−0.0886744	+	0.153588i
$452$		0			0
$453$	−10.3030	−	17.8453i	−0.484076	−	0.838445i
$454$	−6.00000			−0.281594
$455$	−2.37228			−0.111214
$456$	0.313859	+	0.543620i	0.0146978	+	0.0254574i
$457$	3.11684	−	5.39853i	0.145800	−	0.252533i	−0.783871	−	0.620923i	$-0.786758\pi$
$457$	3.11684	−	5.39853i	0.145800	−	0.252533i	0.929671	+	0.368391i	$0.120091\pi$
$458$	−27.1168			−1.26709
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$	3.68614	+	6.38458i	0.171867	+	0.297683i
$461$	−10.3723	−	17.9653i	−0.483085	−	0.836728i	0.516726	−	0.856151i	$-0.327151\pi$
$461$	−10.3723	−	17.9653i	−0.483085	−	0.836728i	−0.999811	+	0.0194225i	$0.993817\pi$
$462$	1.62772	−	2.81929i	0.0757283	−	0.131165i
$463$	5.55842	−	9.62747i	0.258322	−	0.447426i	−0.707471	−	0.706743i	$-0.750164\pi$
$463$	5.55842	−	9.62747i	0.258322	−	0.447426i	0.965792	+	0.259316i	$0.0834972\pi$
$464$	−1.37228	−	2.37686i	−0.0637066	−	0.110343i
$465$	4.55842	+	7.89542i	0.211392	+	0.366141i
$466$	−7.11684	−	12.3267i	−0.329681	−	0.571025i
$467$	−30.0000			−1.38823			−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000			−1.38823			−0.694117	+	0.719862i	$0.744205\pi$
$468$	0.500000	−	0.866025i	0.0231125	−	0.0400320i
$469$	4.30298	+	7.45299i	0.198693	+	0.344147i
$470$	7.37228			0.340058
$471$	7.74456			0.356851
$472$	0.686141	+	1.18843i	0.0315822	+	0.0547019i
$473$	15.2554			0.701446
$474$	−8.55842	+	14.8236i	−0.393101	+	0.680871i
$475$	0.627719			0.0288017
$476$	−7.11684	+	12.3267i	−0.326200	+	0.564995i
$477$	1.37228	−	2.37686i	0.0628324	−	0.108829i
$478$	−3.25544	+	5.63858i	−0.148900	+	0.257903i
$479$	−5.48913	−	9.50744i	−0.250805	−	0.434406i	0.712943	−	0.701222i	$-0.247362\pi$
$479$	−5.48913	−	9.50744i	−0.250805	−	0.434406i	−0.963748	+	0.266816i	$0.914028\pi$
$480$	1.00000			0.0456435
$481$	2.55842	−	5.51856i	0.116654	−	0.251625i
$482$	−2.25544			−0.102732
$483$	8.74456	+	15.1460i	0.397891	+	0.689168i
$484$	4.55842	−	7.89542i	0.207201	−	0.358883i
$485$	0.441578	−	0.764836i	0.0200510	−	0.0347294i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	13.4891			0.611251			0.305625	−	0.952152i	$-0.401135\pi$
$487$	13.4891			0.611251			0.305625	+	0.952152i	$0.401135\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	22.7446			1.02854
$490$	0.686141	+	1.18843i	0.0309967	+	0.0536878i
$491$	16.6277			0.750398			0.375199	−	0.926944i	$-0.377574\pi$
$491$	16.6277			0.750398			0.375199	+	0.926944i	$0.377574\pi$
$492$	−2.74456			−0.123734
$493$	8.23369	+	14.2612i	0.370827	+	0.642291i
$494$	−0.313859	+	0.543620i	−0.0141212	+	0.0244586i
$495$	1.37228			0.0616795
$496$	−4.55842	−	7.89542i	−0.204679	−	0.354515i
$497$	10.3723	+	17.9653i	0.465260	+	0.805855i
$498$	5.74456	+	9.94987i	0.257420	+	0.445865i
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	8.74456	+	15.1460i	0.390678	+	0.676675i
$502$	−10.8030	−	18.7113i	−0.482161	−	0.835127i
$503$	1.62772	+	2.81929i	0.0725764	+	0.125706i	0.900030	−	0.435828i	$-0.143545\pi$
$503$	1.62772	+	2.81929i	0.0725764	+	0.125706i	−0.827453	+	0.561534i	$0.810211\pi$
$504$	2.37228			0.105670
$505$	−1.62772	+	2.81929i	−0.0724325	+	0.125457i
$506$	−5.05842	−	8.76144i	−0.224874	−	0.389494i
$507$	−12.0000			−0.532939
$508$	19.2337			0.853357
$509$	−12.0000	−	20.7846i	−0.531891	−	0.921262i	−0.999307	−	0.0372243i	$-0.988148\pi$
$509$	−12.0000	−	20.7846i	−0.531891	−	0.921262i	0.467416	−	0.884037i	$-0.345185\pi$
$510$	−6.00000			−0.265684
$511$	−13.1861	+	22.8391i	−0.583321	+	1.01034i
$512$	−1.00000			−0.0441942
$513$	−0.313859	+	0.543620i	−0.0138572	+	0.0240014i
$514$	−10.1168	+	17.5229i	−0.446235	+	0.772901i
$515$	−1.05842	+	1.83324i	−0.0466396	+	0.0807822i
$516$	5.55842	+	9.62747i	0.244696	+	0.423826i
$517$	−10.1168			−0.444938
$518$	14.3723	−	1.28962i	0.631482	−	0.0566627i
$519$	−1.88316			−0.0826614
$520$	0.500000	+	0.866025i	0.0219265	+	0.0379777i
$521$	5.31386	−	9.20387i	0.232804	−	0.403229i	−0.725828	−	0.687876i	$-0.758543\pi$
$521$	5.31386	−	9.20387i	0.232804	−	0.403229i	0.958632	+	0.284647i	$0.0918765\pi$
$522$	1.37228	−	2.37686i	0.0600631	−	0.104032i
$523$	−3.18614	+	5.51856i	−0.139320	+	0.241310i	−0.927239	−	0.374469i	$-0.877825\pi$
$523$	−3.18614	+	5.51856i	−0.139320	+	0.241310i	0.787919	+	0.615779i	$0.211158\pi$
$524$	−8.74456			−0.382008
$525$	1.18614	−	2.05446i	0.0517674	−	0.0896638i
$526$	−7.88316			−0.343722
$527$	27.3505	+	47.3725i	1.19141	+	2.06358i
$528$	−1.37228			−0.0597209
$529$	31.3505			1.36307
$530$	1.37228	+	2.37686i	0.0596081	+	0.103244i
$531$	−0.686141	+	1.18843i	−0.0297760	+	0.0515735i
$532$	−1.48913			−0.0645618
$533$	−1.37228	−	2.37686i	−0.0594401	−	0.102953i
$534$	−8.05842	−	13.9576i	−0.348722	−	0.604004i
$535$	−4.37228	−	7.57301i	−0.189030	−	0.327410i
$536$	1.81386	−	3.14170i	0.0783468	−	0.135701i
$537$	−5.31386	+	9.20387i	−0.229310	+	0.397176i
$538$	10.6277	+	18.4077i	0.458193	+	0.793614i
$539$	−0.941578	−	1.63086i	−0.0405566	−	0.0702462i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	17.8614			0.767922			0.383961	−	0.923349i	$-0.374560\pi$
$541$	17.8614			0.767922			0.383961	+	0.923349i	$0.374560\pi$
$542$	13.5584	−	23.4839i	0.582384	−	1.00872i
$543$	4.44158	+	7.69304i	0.190606	+	0.330140i
$544$	6.00000			0.257248
$545$	2.37228			0.101617
$546$	1.18614	+	2.05446i	0.0507621	+	0.0879226i
$547$	6.88316			0.294302			0.147151	−	0.989114i	$-0.452990\pi$
$547$	6.88316			0.294302			0.147151	+	0.989114i	$0.452990\pi$
$548$	−1.37228	+	2.37686i	−0.0586210	+	0.101534i
$549$	2.00000			0.0853579
$550$	−0.686141	+	1.18843i	−0.0292571	+	0.0506748i
$551$	−0.861407	+	1.49200i	−0.0366972	+	0.0635613i
$552$	3.68614	−	6.38458i	0.156893	−	0.271746i
$553$	−20.3030	−	35.1658i	−0.863371	−	1.49540i
$554$	3.48913			0.148239
$555$	3.50000	+	4.97494i	0.148567	+	0.211174i
$556$	5.00000			0.212047
$557$	6.68614	+	11.5807i	0.283301	+	0.490692i	0.972196	−	0.234170i	$-0.0752372\pi$
$557$	6.68614	+	11.5807i	0.283301	+	0.490692i	−0.688895	+	0.724861i	$0.741904\pi$
$558$	4.55842	−	7.89542i	0.192973	−	0.334240i
$559$	−5.55842	+	9.62747i	−0.235096	+	0.407199i
$560$	−1.18614	+	2.05446i	−0.0501236	+	0.0868166i
$561$	8.23369			0.347627
$562$	−8.05842	+	13.9576i	−0.339924	+	0.588766i
$563$	−41.4891			−1.74856			−0.874279	−	0.485424i	$-0.838665\pi$
$563$	−41.4891			−1.74856			−0.874279	+	0.485424i	$0.838665\pi$
$564$	−3.68614	−	6.38458i	−0.155215	−	0.268839i
$565$		0			0
$566$	11.6277			0.488749
$567$	1.18614	+	2.05446i	0.0498132	+	0.0862790i
$568$	4.37228	−	7.57301i	0.183457	−	0.317757i
$569$	1.37228			0.0575290			0.0287645	−	0.999586i	$-0.490843\pi$
$569$	1.37228			0.0575290			0.0287645	+	0.999586i	$0.490843\pi$
$570$	−0.313859	−	0.543620i	−0.0131461	−	0.0227697i
$571$	2.12772	+	3.68532i	0.0890423	+	0.154226i	0.907107	−	0.420901i	$-0.138286\pi$
$571$	2.12772	+	3.68532i	0.0890423	+	0.154226i	−0.818064	+	0.575127i	$0.804953\pi$
$572$	−0.686141	−	1.18843i	−0.0286890	−	0.0496908i
$573$	−3.00000	+	5.19615i	−0.125327	+	0.217072i
$574$	3.25544	−	5.63858i	0.135879	−	0.235350i
$575$	−3.68614	−	6.38458i	−0.153723	−	0.266256i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.1168	−	19.2549i	−0.462800	−	0.801594i	0.536299	−	0.844028i	$-0.319822\pi$
$577$	−11.1168	−	19.2549i	−0.462800	−	0.801594i	−0.999099	+	0.0424345i	$0.986489\pi$
$578$	−19.0000			−0.790296
$579$	7.18614	−	12.4468i	0.298646	−	0.517270i
$580$	1.37228	+	2.37686i	0.0569809	+	0.0986938i
$581$	−27.2554			−1.13075
$582$	−0.883156			−0.0366080
$583$	−1.88316	−	3.26172i	−0.0779924	−	0.135087i
$584$	11.1168			0.460018
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$	22.1168			0.913638
$587$	−16.3723	+	28.3576i	−0.675756	+	1.17044i	0.300491	+	0.953785i	$0.402850\pi$
$587$	−16.3723	+	28.3576i	−0.675756	+	1.17044i	−0.976247	+	0.216660i	$0.930484\pi$
$588$	0.686141	−	1.18843i	0.0282960	−	0.0490100i
$589$	−2.86141	+	4.95610i	−0.117902	+	0.204213i
$590$	−0.686141	−	1.18843i	−0.0282480	−	0.0489269i
$591$	6.00000			0.246807
$592$	−3.50000	−	4.97494i	−0.143849	−	0.204469i
$593$	−6.51087			−0.267370			−0.133685	−	0.991024i	$-0.542681\pi$
$593$	−6.51087			−0.267370			−0.133685	+	0.991024i	$0.542681\pi$
$594$	−0.686141	−	1.18843i	−0.0281527	−	0.0487619i
$595$	7.11684	−	12.3267i	0.291762	−	0.505347i
$596$		0			0
$597$	−4.81386	+	8.33785i	−0.197018	+	0.341245i
$598$	7.37228			0.301475
$599$	−3.25544	+	5.63858i	−0.133014	+	0.230386i	−0.924837	−	0.380364i	$-0.875799\pi$
$599$	−3.25544	+	5.63858i	−0.133014	+	0.230386i	0.791823	+	0.610750i	$0.209132\pi$
$600$	−1.00000			−0.0408248
$601$	−12.8723	−	22.2954i	−0.525071	−	0.909450i	−0.999574	−	0.0291960i	$-0.990705\pi$
$601$	−12.8723	−	22.2954i	−0.525071	−	0.909450i	0.474502	−	0.880254i	$-0.342628\pi$
$602$	−26.3723			−1.07485
$603$	3.62772			0.147732
$604$	−10.3030	−	17.8453i	−0.419222	−	0.726115i
$605$	−4.55842	+	7.89542i	−0.185326	+	0.320994i
$606$	3.25544			0.132243
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	0.313859	+	0.543620i	0.0127287	+	0.0220467i
$609$	3.25544	+	5.63858i	0.131917	+	0.228487i
$610$	−1.00000	+	1.73205i	−0.0404888	+	0.0701287i
$611$	3.68614	−	6.38458i	0.149125	−	0.258293i
$612$	3.00000	+	5.19615i	0.121268	+	0.210042i
$613$	11.9416	+	20.6834i	0.482316	+	0.835395i	0.999794	−	0.0203010i	$-0.00646245\pi$
$613$	11.9416	+	20.6834i	0.482316	+	0.835395i	−0.517478	+	0.855696i	$0.673129\pi$
$614$	−11.3030	−	19.5773i	−0.456151	−	0.790077i
$615$	2.74456			0.110671
$616$	1.62772	−	2.81929i	0.0655827	−	0.113592i
$617$	2.74456	+	4.75372i	0.110492	+	0.191378i	0.915969	−	0.401250i	$-0.131424\pi$
$617$	2.74456	+	4.75372i	0.110492	+	0.191378i	−0.805477	+	0.592627i	$0.798091\pi$
$618$	2.11684			0.0851520
$619$	7.39403			0.297191			0.148596	−	0.988898i	$-0.452525\pi$
$619$	7.39403			0.297191			0.148596	+	0.988898i	$0.452525\pi$
$620$	4.55842	+	7.89542i	0.183071	+	0.317088i
$621$	7.37228			0.295839
$622$	−2.74456	+	4.75372i	−0.110047	+	0.190607i
$623$	38.2337			1.53180
$624$	0.500000	−	0.866025i	0.0200160	−	0.0346688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.93070	+	6.80818i	−0.157103	+	0.272110i
$627$	0.430703	+	0.746000i	0.0172006	+	0.0297924i
$628$	7.74456			0.309042
$629$	21.0000	+	29.8496i	0.837325	+	1.19018i
$630$	−2.37228			−0.0945140
$631$	−6.44158	−	11.1571i	−0.256435	−	0.444159i	0.708849	−	0.705360i	$-0.249215\pi$
$631$	−6.44158	−	11.1571i	−0.256435	−	0.444159i	−0.965284	+	0.261201i	$0.915881\pi$
$632$	−8.55842	+	14.8236i	−0.340436	+	0.589652i
$633$	−9.61684	+	16.6569i	−0.382235	+	0.662051i
$634$	−14.0584	+	24.3499i	−0.558331	+	0.967058i
$635$	−19.2337			−0.763266
$636$	1.37228	−	2.37686i	0.0544145	−	0.0942487i
$637$	1.37228			0.0543718
$638$	−1.88316	−	3.26172i	−0.0745549	−	0.129133i
$639$	8.74456			0.345930
$640$	1.00000			0.0395285
$641$	17.0584	+	29.5461i	0.673767	+	1.16700i	0.976828	+	0.214028i	$0.0686583\pi$
$641$	17.0584	+	29.5461i	0.673767	+	1.16700i	−0.303060	+	0.952971i	$0.598008\pi$
$642$	−4.37228	+	7.57301i	−0.172560	+	0.298883i
$643$	9.11684			0.359533			0.179767	−	0.983709i	$-0.442466\pi$
$643$	9.11684			0.359533			0.179767	+	0.983709i	$0.442466\pi$
$644$	8.74456	+	15.1460i	0.344584	+	0.596837i
$645$	−5.55842	−	9.62747i	−0.218863	−	0.379081i
$646$	−1.88316	−	3.26172i	−0.0740918	−	0.128331i
$647$	−21.4307	+	37.1191i	−0.842528	+	1.45930i	0.0452230	+	0.998977i	$0.485600\pi$
$647$	−21.4307	+	37.1191i	−0.842528	+	1.45930i	−0.887751	+	0.460324i	$0.847733\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	0.941578	+	1.63086i	0.0369602	+	0.0640169i
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$	10.8139	+	18.7302i	0.423829	+	0.734093i
$652$	22.7446			0.890746
$653$	3.94158	−	6.82701i	0.154246	−	0.267162i	−0.778538	−	0.627597i	$-0.784039\pi$
$653$	3.94158	−	6.82701i	0.154246	−	0.267162i	0.932784	+	0.360435i	$0.117372\pi$
$654$	−1.18614	−	2.05446i	−0.0463818	−	0.0803356i
$655$	8.74456			0.341678
$656$	−2.74456			−0.107157
$657$	5.55842	+	9.62747i	0.216855	+	0.375603i
$658$	17.4891			0.681797
$659$	−24.1753	+	41.8728i	−0.941735	+	1.63113i	−0.179574	+	0.983744i	$0.557472\pi$
$659$	−24.1753	+	41.8728i	−0.941735	+	1.63113i	−0.762161	+	0.647388i	$0.775861\pi$
$660$	1.37228			0.0534160
$661$	5.55842	−	9.62747i	0.216198	−	0.374465i	−0.737445	−	0.675407i	$-0.763968\pi$
$661$	5.55842	−	9.62747i	0.216198	−	0.374465i	0.953642	+	0.300942i	$0.0973011\pi$
$662$	8.50000	−	14.7224i	0.330362	−	0.572204i
$663$	−3.00000	+	5.19615i	−0.116510	+	0.201802i
$664$	5.74456	+	9.94987i	0.222932	+	0.386130i
$665$	1.48913			0.0577458
$666$	2.55842	−	5.51856i	0.0991368	−	0.213840i
$667$	20.2337			0.783452
$668$	8.74456	+	15.1460i	0.338337	+	0.586017i
$669$	11.9891	−	20.7658i	0.463526	−	0.802851i
$670$	−1.81386	+	3.14170i	−0.0700755	+	0.121374i
$671$	1.37228	−	2.37686i	0.0529763	−	0.0917577i
$672$	2.37228			0.0915127
$673$	0.883156	−	1.52967i	0.0340432	−	0.0589645i	−0.848502	−	0.529192i	$-0.822495\pi$
$673$	0.883156	−	1.52967i	0.0340432	−	0.0589645i	0.882545	+	0.470228i	$0.155828\pi$
$674$	5.62772			0.216772
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−12.0000			−0.461538
$677$	−31.8832			−1.22537			−0.612685	−	0.790328i	$-0.709910\pi$
$677$	−31.8832			−1.22537			−0.612685	+	0.790328i	$0.709910\pi$
$678$		0			0
$679$	1.04755	−	1.81441i	0.0402012	−	0.0696305i
$680$	−6.00000			−0.230089
$681$	−3.00000	−	5.19615i	−0.114960	−	0.199117i
$682$	−6.25544	−	10.8347i	−0.239533	−	0.414883i
$683$	−15.6060	−	27.0303i	−0.597146	−	1.03429i	−0.993240	−	0.116077i	$-0.962968\pi$
$683$	−15.6060	−	27.0303i	−0.597146	−	1.03429i	0.396094	−	0.918210i	$-0.370365\pi$
$684$	−0.313859	+	0.543620i	−0.0120007	+	0.0207858i
$685$	1.37228	−	2.37686i	0.0524322	−	0.0908152i
$686$	9.93070	+	17.2005i	0.379156	+	0.656717i
$687$	−13.5584	−	23.4839i	−0.517286	−	0.895966i
$688$	5.55842	+	9.62747i	0.211913	+	0.367044i
$689$	2.74456			0.104560
$690$	−3.68614	+	6.38458i	−0.140329	+	0.243057i
$691$	11.5584	+	20.0198i	0.439703	+	0.761588i	0.997666	−	0.0682775i	$-0.0217503\pi$
$691$	11.5584	+	20.0198i	0.439703	+	0.761588i	−0.557963	+	0.829866i	$0.688417\pi$
$692$	−1.88316			−0.0715869
$693$	3.25544			0.123664
$694$	−13.3723	−	23.1615i	−0.507605	−	0.879197i
$695$	−5.00000			−0.189661
$696$	1.37228	−	2.37686i	0.0520162	−	0.0900947i
$697$	16.4674			0.623746
$698$	17.1168	−	29.6472i	0.647882	−	1.12216i
$699$	7.11684	−	12.3267i	0.269184	−	0.466240i
$700$	1.18614	−	2.05446i	0.0448319	−	0.0776511i
$701$	9.86141	+	17.0805i	0.372460	+	0.645120i	0.989943	−	0.141464i	$-0.0451810\pi$
$701$	9.86141	+	17.0805i	0.372460	+	0.645120i	−0.617483	+	0.786584i	$0.711848\pi$
$702$	1.00000			0.0377426
$703$	−1.60597	+	3.46410i	−0.0605703	+	0.130651i
$704$	−1.37228			−0.0517198
$705$	3.68614	+	6.38458i	0.138828	+	0.240457i
$706$	1.37228	−	2.37686i	0.0516465	−	0.0894543i
$707$	−3.86141	+	6.68815i	−0.145223	+	0.251534i
$708$	−0.686141	+	1.18843i	−0.0257867	+	0.0446640i
$709$	−5.11684			−0.192167			−0.0960836	−	0.995373i	$-0.530632\pi$
$709$	−5.11684			−0.192167			−0.0960836	+	0.995373i	$0.530632\pi$
$710$	−4.37228	+	7.57301i	−0.164089	+	0.284210i
$711$	−17.1168			−0.641932
$712$	−8.05842	−	13.9576i	−0.302002	−	0.523083i
$713$	67.2119			2.51711
$714$	−14.2337			−0.532682
$715$	0.686141	+	1.18843i	0.0256602	+	0.0444448i
$716$	−5.31386	+	9.20387i	−0.198588	+	0.343965i
$717$	−6.51087			−0.243153
$718$	−5.74456	−	9.94987i	−0.214385	−	0.371326i
$719$	−24.8614	−	43.0612i	−0.927174	−	1.60591i	−0.788027	−	0.615641i	$-0.788897\pi$
$719$	−24.8614	−	43.0612i	−0.927174	−	1.60591i	−0.139147	−	0.990272i	$-0.544436\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−2.51087	+	4.34896i	−0.0935099	+	0.161964i
$722$	−9.30298	+	16.1132i	−0.346221	+	0.599673i
$723$	−1.12772	−	1.95327i	−0.0419403	−	0.0726427i
$724$	4.44158	+	7.69304i	0.165070	+	0.285910i
$725$	−1.37228	−	2.37686i	−0.0509652	−	0.0882744i
$726$	9.11684			0.338358
$727$	−0.872281	+	1.51084i	−0.0323511	+	0.0560338i	−0.881748	−	0.471721i	$-0.843633\pi$
$727$	−0.872281	+	1.51084i	−0.0323511	+	0.0560338i	0.849397	+	0.527755i	$0.176966\pi$
$728$	1.18614	+	2.05446i	0.0439613	+	0.0761432i
$729$	1.00000			0.0370370
$730$	−11.1168			−0.411453
$731$	−33.3505	−	57.7648i	−1.23351	−	2.13651i
$732$	2.00000			0.0739221
$733$	−1.38316	+	2.39570i	−0.0510880	+	0.0884871i	−0.890439	−	0.455104i	$-0.849602\pi$
$733$	−1.38316	+	2.39570i	−0.0510880	+	0.0884871i	0.839350	+	0.543591i	$0.182936\pi$
$734$	7.51087			0.277231
$735$	−0.686141	+	1.18843i	−0.0253087	+	0.0438359i
$736$	3.68614	−	6.38458i	0.135873	−	0.235339i
$737$	2.48913	−	4.31129i	0.0916881	−	0.158808i
$738$	−1.37228	−	2.37686i	−0.0505144	−	0.0874935i
$739$	9.88316			0.363558			0.181779	−	0.983339i	$-0.441814\pi$
$739$	9.88316			0.363558			0.181779	+	0.983339i	$0.441814\pi$
$740$	3.50000	+	4.97494i	0.128663	+	0.182882i
$741$	−0.627719			−0.0230598
$742$	3.25544	+	5.63858i	0.119511	+	0.206999i
$743$	−17.3139	+	29.9885i	−0.635184	+	1.10017i	0.351292	+	0.936266i	$0.385742\pi$
$743$	−17.3139	+	29.9885i	−0.635184	+	1.10017i	−0.986476	+	0.163905i	$0.947591\pi$
$744$	4.55842	−	7.89542i	0.167120	−	0.289460i
$745$		0			0
$746$	−30.7228			−1.12484
$747$	−5.74456	+	9.94987i	−0.210183	+	0.364047i
$748$	8.23369			0.301053
$749$	−10.3723	−	17.9653i	−0.378995	−	0.656438i
$750$	1.00000			0.0365148
$751$	15.1168			0.551621			0.275811	−	0.961212i	$-0.411054\pi$
$751$	15.1168			0.551621			0.275811	+	0.961212i	$0.411054\pi$
$752$	−3.68614	−	6.38458i	−0.134420	−	0.232822i
$753$	10.8030	−	18.7113i	0.393683	−	0.681878i
$754$	2.74456			0.0999511
$755$	10.3030	+	17.8453i	0.374964	+	0.649457i
$756$	1.18614	+	2.05446i	0.0431395	+	0.0747198i
$757$	13.3614	+	23.1426i	0.485629	+	0.841133i	0.999864	−	0.0165159i	$-0.00525742\pi$
$757$	13.3614	+	23.1426i	0.485629	+	0.841133i	−0.514235	+	0.857649i	$0.671924\pi$
$758$	1.25544	−	2.17448i	0.0455995	−	0.0789807i
$759$	5.05842	−	8.76144i	0.183609	−	0.318020i
$760$	−0.313859	−	0.543620i	−0.0113849	−	0.0197192i
$761$	23.3139	+	40.3808i	0.845127	+	1.46380i	0.885511	+	0.464618i	$0.153808\pi$
$761$	23.3139	+	40.3808i	0.845127	+	1.46380i	−0.0403844	+	0.999184i	$0.512858\pi$
$762$	9.61684	+	16.6569i	0.348381	+	0.603414i
$763$	5.62772			0.203737
$764$	−3.00000	+	5.19615i	−0.108536	+	0.187990i
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$	−18.3505			−0.663032
$767$	−1.37228			−0.0495502
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	8.09509			0.291917			0.145958	−	0.989291i	$-0.453373\pi$
$769$	8.09509			0.291917			0.145958	+	0.989291i	$0.453373\pi$
$770$	−1.62772	+	2.81929i	−0.0586589	+	0.101600i
$771$	−20.2337			−0.728698
$772$	7.18614	−	12.4468i	0.258635	−	0.447969i
$773$	12.9416	−	22.4155i	0.465476	−	0.806228i	−0.533747	−	0.845644i	$-0.679216\pi$
$773$	12.9416	−	22.4155i	0.465476	−	0.806228i	0.999223	+	0.0394160i	$0.0125497\pi$
$774$	−5.55842	+	9.62747i	−0.199793	+	0.346052i
$775$	−4.55842	−	7.89542i	−0.163743	−	0.283612i
$776$	−0.883156			−0.0317035
$777$	8.30298	+	11.8020i	0.297868	+	0.423393i
$778$	2.74456			0.0983973
$779$	0.861407	+	1.49200i	0.0308631	+	0.0534564i
$780$	−0.500000	+	0.866025i	−0.0179029	+	0.0310087i
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	−22.1168	+	38.3075i	−0.790897	+	1.36987i
$783$	2.74456			0.0980827
$784$	0.686141	−	1.18843i	0.0245050	−	0.0424439i
$785$	−7.74456			−0.276415
$786$	−4.37228	−	7.57301i	−0.155954	−	0.270120i
$787$	30.3723			1.08265			0.541327	−	0.840812i	$-0.317922\pi$
$787$	30.3723			1.08265			0.541327	+	0.840812i	$0.317922\pi$
$788$	6.00000			0.213741
$789$	−3.94158	−	6.82701i	−0.140324	−	0.243048i
$790$	8.55842	−	14.8236i	0.304495	−	0.527401i
$791$		0			0
$792$	−0.686141	−	1.18843i	−0.0243809	−	0.0422290i
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$	−1.37228	+	2.37686i	−0.0486698	+	0.0842986i
$796$	−4.81386	+	8.33785i	−0.170623	+	0.295527i
$797$	5.31386	+	9.20387i	0.188227	+	0.326018i	0.944659	−	0.328054i	$-0.106393\pi$
$797$	5.31386	+	9.20387i	0.188227	+	0.326018i	−0.756432	+	0.654072i	$0.773059\pi$
$798$	−0.744563	−	1.28962i	−0.0263572	−	0.0456521i
$799$	22.1168	+	38.3075i	0.782438	+	1.35522i
$800$	−1.00000			−0.0353553
$801$	8.05842	−	13.9576i	0.284730	−	0.493167i
$802$	−10.8030	−	18.7113i	−0.381467	−	0.660720i
$803$	15.2554			0.538353
$804$	3.62772			0.127940
$805$	−8.74456	−	15.1460i	−0.308205	−	0.533827i
$806$	9.11684			0.321127
$807$	−10.6277	+	18.4077i	−0.374113	+	0.647983i
$808$	3.25544			0.114526
$809$	2.31386	−	4.00772i	0.0813510	−	0.140904i	−0.822479	−	0.568795i	$-0.807410\pi$
$809$	2.31386	−	4.00772i	0.0813510	−	0.140904i	0.903830	+	0.427891i	$0.140743\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	9.80298	−	16.9793i	0.344229	−	0.596223i	−0.640984	−	0.767554i	$-0.721474\pi$
$811$	9.80298	−	16.9793i	0.344229	−	0.596223i	0.985213	+	0.171331i	$0.0548069\pi$
$812$	3.25544	+	5.63858i	0.114243	+	0.197875i
$813$	27.1168			0.951029
$814$	−4.80298	−	6.82701i	−0.168345	−	0.239287i
$815$	−22.7446			−0.796707
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	3.48913	−	6.04334i	0.122069	−	0.211430i
$818$	−14.0475	+	24.3311i	−0.491161	+	0.850716i
$819$	−1.18614	+	2.05446i	−0.0414471	+	0.0717885i
$820$	2.74456			0.0958443
$821$	−13.1168	+	22.7190i	−0.457781	+	0.792900i	−0.998843	−	0.0480825i	$-0.984689\pi$
$821$	−13.1168	+	22.7190i	−0.457781	+	0.792900i	0.541062	+	0.840982i	$0.318022\pi$
$822$	−2.74456			−0.0957276
$823$	23.5584	+	40.8044i	0.821195	+	1.42235i	0.904793	+	0.425852i	$0.140026\pi$
$823$	23.5584	+	40.8044i	0.821195	+	1.42235i	−0.0835979	+	0.996500i	$0.526641\pi$
$824$	2.11684			0.0737438
$825$	−1.37228			−0.0477767
$826$	−1.62772	−	2.81929i	−0.0566356	−	0.0980957i
$827$	−8.48913	+	14.7036i	−0.295196	+	0.511294i	−0.975030	−	0.222071i	$-0.928718\pi$
$827$	−8.48913	+	14.7036i	−0.295196	+	0.511294i	0.679835	+	0.733365i	$0.262052\pi$
$828$	7.37228			0.256204
$829$	−17.6753	−	30.6145i	−0.613887	−	1.06328i	−0.990579	−	0.136945i	$-0.956272\pi$
$829$	−17.6753	−	30.6145i	−0.613887	−	1.06328i	0.376691	−	0.926339i	$-0.377062\pi$
$830$	−5.74456	−	9.94987i	−0.199397	−	0.345365i
$831$	1.74456	+	3.02167i	0.0605182	+	0.104821i
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	−4.11684	+	7.13058i	−0.142640	+	0.247060i
$834$	2.50000	+	4.33013i	0.0865679	+	0.149940i
$835$	−8.74456	−	15.1460i	−0.302618	−	0.524150i
$836$	0.430703	+	0.746000i	0.0148962	+	0.0258009i
$837$	9.11684			0.315124
$838$	3.94158	−	6.82701i	0.136160	−	0.235835i
$839$	−20.7446	−	35.9306i	−0.716182	−	1.24046i	−0.962502	−	0.271275i	$-0.912555\pi$
$839$	−20.7446	−	35.9306i	−0.716182	−	1.24046i	0.246320	−	0.969189i	$-0.420779\pi$
$840$	−2.37228			−0.0818515
$841$	−21.4674			−0.740254
$842$	−15.1168	−	26.1831i	−0.520961	−	0.902331i
$843$	−16.1168			−0.555094
$844$	−9.61684	+	16.6569i	−0.331025	+	0.573353i
$845$	12.0000			0.412813
$846$	3.68614	−	6.38458i	0.126732	−	0.219506i
$847$	−10.8139	+	18.7302i	−0.371569	+	0.643576i
$848$	1.37228	−	2.37686i	0.0471243	−	0.0816217i
$849$	5.81386	+	10.0699i	0.199531	+	0.345598i
$850$	6.00000			0.205798
$851$	44.6644	−	4.00772i	1.53108	−	0.137383i
$852$	8.74456			0.299584
$853$	−26.2921	−	45.5393i	−0.900225	−	1.55923i	−0.827202	−	0.561905i	$-0.810069\pi$
$853$	−26.2921	−	45.5393i	−0.900225	−	1.55923i	−0.0730227	−	0.997330i	$-0.523265\pi$
$854$	−2.37228	+	4.10891i	−0.0811778	+	0.140604i
$855$	0.313859	−	0.543620i	0.0107338	−	0.0185914i
$856$	−4.37228	+	7.57301i	−0.149441	+	0.258840i
$857$	38.2337			1.30604			0.653019	−	0.757342i	$-0.273502\pi$
$857$	38.2337			1.30604			0.653019	+	0.757342i	$0.273502\pi$
$858$	0.686141	−	1.18843i	0.0234245	−	0.0405723i
$859$	29.0000			0.989467			0.494734	−	0.869045i	$-0.335266\pi$
$859$	29.0000			0.989467			0.494734	+	0.869045i	$0.335266\pi$
$860$	−5.55842	−	9.62747i	−0.189541	−	0.328294i
$861$	6.51087			0.221890
$862$	22.9783			0.782642
$863$	−19.5475	−	33.8573i	−0.665406	−	1.15252i	−0.979175	−	0.203018i	$-0.934925\pi$
$863$	−19.5475	−	33.8573i	−0.665406	−	1.15252i	0.313769	−	0.949499i	$-0.398408\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	1.88316			0.0640292
$866$	−16.4891	−	28.5600i	−0.560323	−	0.970508i
$867$	−9.50000	−	16.4545i	−0.322637	−	0.558824i
$868$	10.8139	+	18.7302i	0.367046	+	0.635743i
$869$	−11.7446	+	20.3422i	−0.398407	+	0.690061i
$870$	−1.37228	+	2.37686i	−0.0465247	+	0.0805831i
$871$	1.81386	+	3.14170i	0.0614603	+	0.106452i
$872$	−1.18614	−	2.05446i	−0.0401678	−	0.0695727i
$873$	−0.441578	−	0.764836i	−0.0149452	−	0.0258858i
$874$	−4.62772			−0.156535
$875$	−1.18614	+	2.05446i	−0.0400989	+	0.0694533i
$876$	5.55842	+	9.62747i	0.187802	+	0.325282i
$877$	−4.25544			−0.143696			−0.0718480	−	0.997416i	$-0.522890\pi$
$877$	−4.25544			−0.143696			−0.0718480	+	0.997416i	$0.522890\pi$
$878$	−9.62772			−0.324920
$879$	11.0584	+	19.1537i	0.372991	+	0.646040i
$880$	1.37228			0.0462596
$881$	7.54755	−	13.0727i	0.254283	−	0.440432i	−0.710417	−	0.703781i	$-0.751494\pi$
$881$	7.54755	−	13.0727i	0.254283	−	0.440432i	0.964701	+	0.263349i	$0.0848271\pi$
$882$	1.37228			0.0462071
$883$	−17.3723	+	30.0897i	−0.584624	+	1.01260i	0.410298	+	0.911951i	$0.365425\pi$
$883$	−17.3723	+	30.0897i	−0.584624	+	1.01260i	−0.994922	+	0.100647i	$0.967909\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$	0.686141	−	1.18843i	0.0230644	−	0.0399487i
$886$	4.37228	+	7.57301i	0.146890	+	0.254420i
$887$	9.76631			0.327921			0.163960	−	0.986467i	$-0.447573\pi$
$887$	9.76631			0.327921			0.163960	+	0.986467i	$0.447573\pi$
$888$	2.55842	−	5.51856i	0.0858550	−	0.185191i
$889$	−45.6277			−1.53030
$890$	8.05842	+	13.9576i	0.270119	+	0.467860i
$891$	0.686141	−	1.18843i	0.0229866	−	0.0398139i
$892$	11.9891	−	20.7658i	0.401426	−	0.695290i
$893$	−2.31386	+	4.00772i	−0.0774304	+	0.134113i
$894$		0			0
$895$	5.31386	−	9.20387i	0.177623	−	0.307652i
$896$	2.37228			0.0792524
$897$	3.68614	+	6.38458i	0.123077	+	0.213175i
$898$	−26.7446			−0.892478
$899$	25.0217			0.834522
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−8.23369	+	14.2612i	−0.274304	+	0.475108i
$902$	−3.76631			−0.125404
$903$	−13.1861	−	22.8391i	−0.438807	−	0.760037i
$904$		0			0
$905$	−4.44158	−	7.69304i	−0.147643	−	0.255725i
$906$	10.3030	−	17.8453i	0.342294	−	0.592870i
$907$	26.5584	−	46.0005i	0.881858	−	1.52742i	0.0325848	−	0.999469i	$-0.489626\pi$
$907$	26.5584	−	46.0005i	0.881858	−	1.52742i	0.849273	−	0.527954i	$-0.177041\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$	1.62772	+	2.81929i	0.0539880	+	0.0935100i
$910$	−1.18614	−	2.05446i	−0.0393202	−	0.0681045i
$911$	−12.5109			−0.414504			−0.207252	−	0.978288i	$-0.566452\pi$
$911$	−12.5109			−0.414504			−0.207252	+	0.978288i	$0.566452\pi$
$912$	−0.313859	+	0.543620i	−0.0103929	+	0.0180011i
$913$	7.88316	+	13.6540i	0.260894	+	0.451882i
$914$	6.23369			0.206192
$915$	−2.00000			−0.0661180
$916$	−13.5584	−	23.4839i	−0.447983	−	0.775929i
$917$	20.7446			0.685046
$918$	−3.00000	+	5.19615i	−0.0990148	+	0.171499i
$919$	32.0951			1.05872			0.529360	−	0.848397i	$-0.322432\pi$
$919$	32.0951			1.05872			0.529360	+	0.848397i	$0.322432\pi$
$920$	−3.68614	+	6.38458i	−0.121528	+	0.210493i
$921$	11.3030	−	19.5773i	0.372446	−	0.645095i
$922$	10.3723	−	17.9653i	0.341593	−	0.591656i
$923$	4.37228	+	7.57301i	0.143915	+	0.249269i
$924$	3.25544			0.107096
$925$	−3.50000	−	4.97494i	−0.115079	−	0.163575i
$926$	11.1168			0.365322
$927$	1.05842	+	1.83324i	0.0347631	+	0.0602115i
$928$	1.37228	−	2.37686i	0.0450473	−	0.0780243i
$929$	10.1970	−	17.6617i	0.334553	−	0.579463i	−0.648846	−	0.760920i	$-0.724748\pi$
$929$	10.1970	−	17.6617i	0.334553	−	0.579463i	0.983399	+	0.181457i	$0.0580813\pi$
$930$	−4.55842	+	7.89542i	−0.149477	+	0.258901i
$931$	−0.861407			−0.0282315
$932$	7.11684	−	12.3267i	0.233120	−	0.403776i
$933$	−5.48913			−0.179706
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$	−8.23369			−0.269270
$936$	1.00000			0.0326860
$937$	−15.7921	−	27.3527i	−0.515906	−	0.893575i	−0.999830	−	0.0184648i	$-0.994122\pi$
$937$	−15.7921	−	27.3527i	−0.515906	−	0.893575i	0.483924	−	0.875110i	$-0.339211\pi$
$938$	−4.30298	+	7.45299i	−0.140497	+	0.243349i
$939$	−7.86141			−0.256547
$940$	3.68614	+	6.38458i	0.120229	+	0.208242i
$941$	10.1168	+	17.5229i	0.329800	+	0.571230i	0.982472	−	0.186411i	$-0.0596855\pi$
$941$	10.1168	+	17.5229i	0.329800	+	0.571230i	−0.652672	+	0.757640i	$0.726352\pi$
$942$	3.87228	+	6.70699i	0.126166	+	0.218525i
$943$	10.1168	−	17.5229i	0.329450	−	0.570624i
$944$	−0.686141	+	1.18843i	−0.0223320	+	0.0386801i
$945$	−1.18614	−	2.05446i	−0.0385852	−	0.0668315i
$946$	7.62772	+	13.2116i	0.247999	+	0.429546i
$947$	−12.2554	−	21.2270i	−0.398248	−	0.689786i	0.595262	−	0.803532i	$-0.297048\pi$
$947$	−12.2554	−	21.2270i	−0.398248	−	0.689786i	−0.993510	+	0.113746i	$0.963715\pi$
$948$	−17.1168			−0.555929
$949$	−5.55842	+	9.62747i	−0.180434	+	0.312521i
$950$	0.313859	+	0.543620i	0.0101829	+	0.0176374i
$951$	−28.1168			−0.911751
$952$	−14.2337			−0.461316
$953$	−24.0000	−	41.5692i	−0.777436	−	1.34656i	−0.933415	−	0.358799i	$-0.883186\pi$
$953$	−24.0000	−	41.5692i	−0.777436	−	1.34656i	0.155979	−	0.987760i	$-0.450147\pi$
$954$	2.74456			0.0888585
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$	−6.51087			−0.210577
$957$	1.88316	−	3.26172i	0.0608738	−	0.105436i
$958$	5.48913	−	9.50744i	0.177346	−	0.307172i
$959$	3.25544	−	5.63858i	0.105124	−	0.182079i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	52.1168			1.68119
$962$	6.05842	−	0.543620i	0.195331	−	0.0175270i
$963$	−8.74456			−0.281790
$964$	−1.12772	−	1.95327i	−0.0363214	−	0.0629105i
$965$	−7.18614	+	12.4468i	−0.231330	+	0.400675i
$966$	−8.74456	+	15.1460i	−0.281352	+	0.487315i
$967$	13.6168	−	23.5851i	0.437888	−	0.758445i	−0.559638	−	0.828737i	$-0.689060\pi$
$967$	13.6168	−	23.5851i	0.437888	−	0.758445i	0.997526	+	0.0702924i	$0.0223932\pi$
$968$	9.11684			0.293026
$969$	1.88316	−	3.26172i	0.0604957	−	0.104782i
$970$	0.883156			0.0283564
$971$	13.8030	+	23.9075i	0.442959	+	0.767227i	0.997908	−	0.0646573i	$-0.0205954\pi$
$971$	13.8030	+	23.9075i	0.442959	+	0.767227i	−0.554949	+	0.831885i	$0.687262\pi$
$972$	1.00000			0.0320750
$973$	−11.8614			−0.380259
$974$	6.74456	+	11.6819i	0.216110	+	0.374313i
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	2.00000			0.0640184
$977$	−28.9783	−	50.1918i	−0.927096	−	1.60578i	−0.788154	−	0.615477i	$-0.788963\pi$
$977$	−28.9783	−	50.1918i	−0.927096	−	1.60578i	−0.138942	−	0.990301i	$-0.544370\pi$
$978$	11.3723	+	19.6974i	0.363645	+	0.629852i
$979$	−11.0584	−	19.1537i	−0.353429	−	0.612156i
$980$	−0.686141	+	1.18843i	−0.0219180	+	0.0379630i
$981$	1.18614	−	2.05446i	0.0378706	−	0.0655937i
$982$	8.31386	+	14.4000i	0.265306	+	0.459523i
$983$	−28.5475	−	49.4458i	−0.910525	−	1.57708i	−0.813324	−	0.581811i	$-0.802344\pi$
$983$	−28.5475	−	49.4458i	−0.910525	−	1.57708i	−0.0972017	−	0.995265i	$-0.530989\pi$
$984$	−1.37228	−	2.37686i	−0.0437467	−	0.0757716i
$985$	−6.00000			−0.191176
$986$	−8.23369	+	14.2612i	−0.262214	+	0.454168i
$987$	8.74456	+	15.1460i	0.278342	+	0.482103i
$988$	−0.627719			−0.0199704
$989$	−81.9565			−2.60607
$990$	0.686141	+	1.18843i	0.0218070	+	0.0377708i
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	4.55842	−	7.89542i	0.144730	−	0.250680i
$993$	17.0000			0.539479
$994$	−10.3723	+	17.9653i	−0.328989	+	0.569825i
$995$	4.81386	−	8.33785i	0.152610	−	0.264328i
$996$	−5.74456	+	9.94987i	−0.182023	+	0.315274i
$997$	−22.1753	−	38.4087i	−0.702298	−	1.21642i	−0.967658	−	0.252266i	$-0.918824\pi$
$997$	−22.1753	−	38.4087i	−0.702298	−	1.21642i	0.265360	−	0.964149i	$-0.414509\pi$
$998$	−20.0000			−0.633089
$999$	6.05842	−	0.543620i	0.191680	−	0.0171994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.m.211.2	yes	4
37.10	even	3	inner	1110.2.i.m.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.m.121.2	✓	4	37.10	even	3	inner
1110.2.i.m.211.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -1.37228 q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +2.37228 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.313859 + 0.543620i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.18614 + 2.05446i) q^{21} +(-0.686141 - 1.18843i) q^{22} +7.37228 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(1.18614 + 2.05446i) q^{28} +2.74456 q^{29} +(-0.500000 + 0.866025i) q^{30} +9.11684 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.686141 - 1.18843i) q^{33} +(-3.00000 + 5.19615i) q^{34} +(-1.18614 - 2.05446i) q^{35} +1.00000 q^{36} +(6.05842 - 0.543620i) q^{37} -0.627719 q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.37228 - 2.37686i) q^{41} +(-1.18614 + 2.05446i) q^{42} -11.1168 q^{43} +(0.686141 - 1.18843i) q^{44} -1.00000 q^{45} +(3.68614 + 6.38458i) q^{46} +7.37228 q^{47} +1.00000 q^{48} +(0.686141 + 1.18843i) q^{49} +(0.500000 - 0.866025i) q^{50} -6.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(1.37228 + 2.37686i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.686141 + 1.18843i) q^{55} +(-1.18614 + 2.05446i) q^{56} +(-0.313859 - 0.543620i) q^{57} +(1.37228 + 2.37686i) q^{58} +(-0.686141 - 1.18843i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(4.55842 + 7.89542i) q^{62} -2.37228 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +1.37228 q^{66} +(-1.81386 + 3.14170i) q^{67} -6.00000 q^{68} +(-3.68614 + 6.38458i) q^{69} +(1.18614 - 2.05446i) q^{70} +(-4.37228 + 7.57301i) q^{71} +(0.500000 + 0.866025i) q^{72} -11.1168 q^{73} +(3.50000 + 4.97494i) q^{74} +1.00000 q^{75} +(-0.313859 - 0.543620i) q^{76} +(-1.62772 + 2.81929i) q^{77} +(-0.500000 + 0.866025i) q^{78} +(8.55842 - 14.8236i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +2.74456 q^{82} +(-5.74456 - 9.94987i) q^{83} -2.37228 q^{84} +6.00000 q^{85} +(-5.55842 - 9.62747i) q^{86} +(-1.37228 + 2.37686i) q^{87} +1.37228 q^{88} +(8.05842 + 13.9576i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-1.18614 - 2.05446i) q^{91} +(-3.68614 + 6.38458i) q^{92} +(-4.55842 + 7.89542i) q^{93} +(3.68614 + 6.38458i) q^{94} +(0.313859 + 0.543620i) q^{95} +(0.500000 + 0.866025i) q^{96} +0.883156 q^{97} +(-0.686141 + 1.18843i) q^{98} +(0.686141 + 1.18843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} - 2 q^{9} + 4 q^{10} + 6 q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} + 12 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 18 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - q^{28} - 12 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} - 3 q^{33} - 12 q^{34} + q^{35} + 4 q^{36} + 7 q^{37} - 14 q^{38} + 2 q^{39} - 2 q^{40} - 6 q^{41} + q^{42} - 10 q^{43} - 3 q^{44} - 4 q^{45} + 9 q^{46} + 18 q^{47} + 4 q^{48} - 3 q^{49} + 2 q^{50} - 24 q^{51} + 2 q^{52} - 6 q^{53} + 2 q^{54} + 3 q^{55} + q^{56} - 7 q^{57} - 6 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} + q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{65} - 6 q^{66} - 13 q^{67} - 24 q^{68} - 9 q^{69} - q^{70} - 6 q^{71} + 2 q^{72} - 10 q^{73} + 14 q^{74} + 4 q^{75} - 7 q^{76} - 18 q^{77} - 2 q^{78} + 17 q^{79} - 4 q^{80} - 2 q^{81} - 12 q^{82} + 2 q^{84} + 24 q^{85} - 5 q^{86} + 6 q^{87} - 6 q^{88} + 15 q^{89} - 2 q^{90} + q^{91} - 9 q^{92} - q^{93} + 9 q^{94} + 7 q^{95} + 2 q^{96} + 38 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - q^7 - 4 * q^8 - 2 * q^9 + 4 * q^10 + 6 * q^11 - 2 * q^12 + 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 + 12 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 - q^21 + 3 * q^22 + 18 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - q^28 - 12 * q^29 - 2 * q^30 + 2 * q^31 + 2 * q^32 - 3 * q^33 - 12 * q^34 + q^35 + 4 * q^36 + 7 * q^37 - 14 * q^38 + 2 * q^39 - 2 * q^40 - 6 * q^41 + q^42 - 10 * q^43 - 3 * q^44 - 4 * q^45 + 9 * q^46 + 18 * q^47 + 4 * q^48 - 3 * q^49 + 2 * q^50 - 24 * q^51 + 2 * q^52 - 6 * q^53 + 2 * q^54 + 3 * q^55 + q^56 - 7 * q^57 - 6 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 + q^62 + 2 * q^63 + 4 * q^64 - 2 * q^65 - 6 * q^66 - 13 * q^67 - 24 * q^68 - 9 * q^69 - q^70 - 6 * q^71 + 2 * q^72 - 10 * q^73 + 14 * q^74 + 4 * q^75 - 7 * q^76 - 18 * q^77 - 2 * q^78 + 17 * q^79 - 4 * q^80 - 2 * q^81 - 12 * q^82 + 2 * q^84 + 24 * q^85 - 5 * q^86 + 6 * q^87 - 6 * q^88 + 15 * q^89 - 2 * q^90 + q^91 - 9 * q^92 - q^93 + 9 * q^94 + 7 * q^95 + 2 * q^96 + 38 * q^97 + 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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