LMFDB - Embedded newform 1110.2.i.n.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:	$\Q(\zeta_{12})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.n.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.366025 - 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(0.366025 - 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +6.46410 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.232051 - 0.401924i) q^{13} +0.732051 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.13397 - 3.69615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.73205 + 3.00000i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.366025 - 0.633975i) q^{21} +(3.23205 + 5.59808i) q^{22} +8.92820 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.464102 q^{26} -1.00000 q^{27} +(0.366025 + 0.633975i) q^{28} -5.19615 q^{29} +(-0.500000 + 0.866025i) q^{30} +3.46410 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.23205 - 5.59808i) q^{33} +(2.13397 - 3.69615i) q^{34} +(0.366025 + 0.633975i) q^{35} +1.00000 q^{36} +(5.69615 + 2.13397i) q^{37} -3.46410 q^{38} +(-0.232051 - 0.401924i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-3.63397 + 6.29423i) q^{41} +(0.366025 - 0.633975i) q^{42} +12.3923 q^{43} +(-3.23205 + 5.59808i) q^{44} +1.00000 q^{45} +(4.46410 + 7.73205i) q^{46} -2.46410 q^{47} -1.00000 q^{48} +(3.23205 + 5.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} -4.26795 q^{51} +(0.232051 + 0.401924i) q^{52} +(1.63397 + 2.83013i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-3.23205 + 5.59808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +(1.73205 + 3.00000i) q^{57} +(-2.59808 - 4.50000i) q^{58} +(-0.232051 - 0.401924i) q^{59} -1.00000 q^{60} +(5.83013 - 10.0981i) q^{61} +(1.73205 + 3.00000i) q^{62} -0.732051 q^{63} +1.00000 q^{64} +(0.232051 + 0.401924i) q^{65} +6.46410 q^{66} +(-2.13397 + 3.69615i) q^{67} +4.26795 q^{68} +(4.46410 - 7.73205i) q^{69} +(-0.366025 + 0.633975i) q^{70} +(1.63397 - 2.83013i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 + 6.00000i) q^{74} -1.00000 q^{75} +(-1.73205 - 3.00000i) q^{76} +(2.36603 - 4.09808i) q^{77} +(0.232051 - 0.401924i) q^{78} +(-2.00000 + 3.46410i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -7.26795 q^{82} +(-6.83013 - 11.8301i) q^{83} +0.732051 q^{84} +4.26795 q^{85} +(6.19615 + 10.7321i) q^{86} +(-2.59808 + 4.50000i) q^{87} -6.46410 q^{88} +(1.73205 + 3.00000i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-0.169873 - 0.294229i) q^{91} +(-4.46410 + 7.73205i) q^{92} +(1.73205 - 3.00000i) q^{93} +(-1.23205 - 2.13397i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-0.500000 - 0.866025i) q^{96} +8.92820 q^{97} +(-3.23205 + 5.59808i) q^{98} +(-3.23205 - 5.59808i) 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} - 2 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 - 2 * 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} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 12 q^{11} + 2 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{20} + 2 q^{21} + 6 q^{22} + 8 q^{23} - 2 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 6 q^{33} + 12 q^{34} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 6 q^{39} + 2 q^{40} - 18 q^{41} - 2 q^{42} + 8 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 6 q^{49} + 2 q^{50} - 24 q^{51} - 6 q^{52} + 10 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 6 q^{59} - 4 q^{60} + 6 q^{61} + 4 q^{63} + 4 q^{64} - 6 q^{65} + 12 q^{66} - 12 q^{67} + 24 q^{68} + 4 q^{69} + 2 q^{70} + 10 q^{71} + 2 q^{72} + 4 q^{74} - 4 q^{75} + 6 q^{77} - 6 q^{78} - 8 q^{79} + 4 q^{80} - 2 q^{81} - 36 q^{82} - 10 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} - 12 q^{88} + 2 q^{90} - 18 q^{91} - 4 q^{92} + 2 q^{94} - 2 q^{96} + 8 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 12 * q^11 + 2 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^20 + 2 * q^21 + 6 * q^22 + 8 * q^23 - 2 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 6 * q^33 + 12 * q^34 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 6 * q^39 + 2 * q^40 - 18 * q^41 - 2 * q^42 + 8 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 4 * q^47 - 4 * q^48 + 6 * q^49 + 2 * q^50 - 24 * q^51 - 6 * q^52 + 10 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 6 * q^59 - 4 * q^60 + 6 * q^61 + 4 * q^63 + 4 * q^64 - 6 * q^65 + 12 * q^66 - 12 * q^67 + 24 * q^68 + 4 * q^69 + 2 * q^70 + 10 * q^71 + 2 * q^72 + 4 * q^74 - 4 * q^75 + 6 * q^77 - 6 * q^78 - 8 * q^79 + 4 * q^80 - 2 * q^81 - 36 * q^82 - 10 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 - 12 * q^88 + 2 * q^90 - 18 * q^91 - 4 * q^92 + 2 * q^94 - 2 * q^96 + 8 * q^97 - 6 * q^98 - 6 * 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
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	−0.788526	−	0.615002i	$-0.789155\pi$
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	0.926870	+	0.375382i	$0.122489\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	6.46410			1.94900			0.974500	−	0.224388i	$-0.0720382\pi$
$11$	6.46410			1.94900			0.974500	+	0.224388i	$0.0720382\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.232051	−	0.401924i	0.0643593	−	0.111474i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	0.232051	−	0.401924i	0.0643593	−	0.111474i	0.896410	+	0.443227i	$0.146166\pi$
$14$	0.732051			0.195649
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.13397	−	3.69615i	−0.517565	−	0.896449i	−0.999792	−	0.0204023i	$-0.993505\pi$
$17$	−2.13397	−	3.69615i	−0.517565	−	0.896449i	0.482227	−	0.876046i	$-0.339828\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.73205	+	3.00000i	−0.397360	+	0.688247i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−1.73205	+	3.00000i	−0.397360	+	0.688247i	0.596040	+	0.802955i	$0.296740\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−0.366025	−	0.633975i	−0.0798733	−	0.138345i
$22$	3.23205	+	5.59808i	0.689076	+	1.19351i
$23$	8.92820			1.86166			0.930830	−	0.365454i	$-0.119086\pi$
$23$	8.92820			1.86166			0.930830	+	0.365454i	$0.119086\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.464102			0.0910178
$27$	−1.00000			−0.192450
$28$	0.366025	+	0.633975i	0.0691723	+	0.119810i
$29$	−5.19615			−0.964901			−0.482451	−	0.875923i	$-0.660253\pi$
$29$	−5.19615			−0.964901			−0.482451	+	0.875923i	$0.660253\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.23205	−	5.59808i	0.562628	−	0.974500i
$34$	2.13397	−	3.69615i	0.365974	−	0.633885i
$35$	0.366025	+	0.633975i	0.0618696	+	0.107161i
$36$	1.00000			0.166667
$37$	5.69615	+	2.13397i	0.936442	+	0.350823i
$37$	5.69615	+	2.13397i	0.936442	+	0.350823i
$38$	−3.46410			−0.561951
$39$	−0.232051	−	0.401924i	−0.0371579	−	0.0643593i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−3.63397	+	6.29423i	−0.567531	+	0.982993i	0.429278	+	0.903173i	$0.358768\pi$
$41$	−3.63397	+	6.29423i	−0.567531	+	0.982993i	−0.996809	+	0.0798208i	$0.974565\pi$
$42$	0.366025	−	0.633975i	0.0564789	−	0.0978244i
$43$	12.3923			1.88981			0.944904	−	0.327346i	$-0.106154\pi$
$43$	12.3923			1.88981			0.944904	+	0.327346i	$0.106154\pi$
$44$	−3.23205	+	5.59808i	−0.487250	+	0.843942i
$45$	1.00000			0.149071
$46$	4.46410	+	7.73205i	0.658196	+	1.14003i
$47$	−2.46410			−0.359426			−0.179713	−	0.983719i	$-0.557517\pi$
$47$	−2.46410			−0.359426			−0.179713	+	0.983719i	$0.557517\pi$
$48$	−1.00000			−0.144338
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−4.26795			−0.597632
$52$	0.232051	+	0.401924i	0.0321797	+	0.0557368i
$53$	1.63397	+	2.83013i	0.224444	+	0.388748i	0.956152	−	0.292870i	$-0.0946102\pi$
$53$	1.63397	+	2.83013i	0.224444	+	0.388748i	−0.731709	+	0.681617i	$0.761277\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−3.23205	+	5.59808i	−0.435810	+	0.754844i
$56$	−0.366025	+	0.633975i	−0.0489122	+	0.0847184i
$57$	1.73205	+	3.00000i	0.229416	+	0.397360i
$58$	−2.59808	−	4.50000i	−0.341144	−	0.590879i
$59$	−0.232051	−	0.401924i	−0.0302104	−	0.0523260i	0.850525	−	0.525935i	$-0.176284\pi$
$59$	−0.232051	−	0.401924i	−0.0302104	−	0.0523260i	−0.880735	+	0.473609i	$0.842951\pi$
$60$	−1.00000			−0.129099
$61$	5.83013	−	10.0981i	0.746471	−	1.29293i	−0.203033	−	0.979172i	$-0.565080\pi$
$61$	5.83013	−	10.0981i	0.746471	−	1.29293i	0.949504	−	0.313754i	$-0.101587\pi$
$62$	1.73205	+	3.00000i	0.219971	+	0.381000i
$63$	−0.732051			−0.0922297
$64$	1.00000			0.125000
$65$	0.232051	+	0.401924i	0.0287824	+	0.0498525i
$66$	6.46410			0.795676
$67$	−2.13397	+	3.69615i	−0.260706	+	0.451557i	−0.966430	−	0.256931i	$-0.917289\pi$
$67$	−2.13397	+	3.69615i	−0.260706	+	0.451557i	0.705723	+	0.708487i	$0.250622\pi$
$68$	4.26795			0.517565
$69$	4.46410	−	7.73205i	0.537415	−	0.930830i
$70$	−0.366025	+	0.633975i	−0.0437484	+	0.0757745i
$71$	1.63397	−	2.83013i	0.193917	−	0.335874i	−0.752628	−	0.658446i	$-0.771214\pi$
$71$	1.63397	−	2.83013i	0.193917	−	0.335874i	0.946545	+	0.322572i	$0.104547\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	1.00000	+	6.00000i	0.116248	+	0.697486i
$75$	−1.00000			−0.115470
$76$	−1.73205	−	3.00000i	−0.198680	−	0.344124i
$77$	2.36603	−	4.09808i	0.269634	−	0.467019i
$78$	0.232051	−	0.401924i	0.0262746	−	0.0455089i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	1.00000			0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.26795			−0.802611
$83$	−6.83013	−	11.8301i	−0.749704	−	1.29853i	−0.947965	−	0.318376i	$-0.896863\pi$
$83$	−6.83013	−	11.8301i	−0.749704	−	1.29853i	0.198261	−	0.980149i	$-0.436471\pi$
$84$	0.732051			0.0798733
$85$	4.26795			0.462924
$86$	6.19615	+	10.7321i	0.668148	+	1.15727i
$87$	−2.59808	+	4.50000i	−0.278543	+	0.482451i
$88$	−6.46410			−0.689076
$89$	1.73205	+	3.00000i	0.183597	+	0.317999i	0.943103	−	0.332501i	$-0.107893\pi$
$89$	1.73205	+	3.00000i	0.183597	+	0.317999i	−0.759506	+	0.650500i	$0.774559\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−0.169873	−	0.294229i	−0.0178075	−	0.0308435i
$92$	−4.46410	+	7.73205i	−0.465415	+	0.806122i
$93$	1.73205	−	3.00000i	0.179605	−	0.311086i
$94$	−1.23205	−	2.13397i	−0.127076	−	0.220103i
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	8.92820			0.906522			0.453261	−	0.891378i	$-0.350261\pi$
$97$	8.92820			0.906522			0.453261	+	0.891378i	$0.350261\pi$
$98$	−3.23205	+	5.59808i	−0.326486	+	0.565491i
$99$	−3.23205	−	5.59808i	−0.324833	−	0.562628i
$100$	1.00000			0.100000
$101$	−16.1244			−1.60443			−0.802217	−	0.597033i	$-0.796346\pi$
$101$	−16.1244			−1.60443			−0.802217	+	0.597033i	$0.796346\pi$
$102$	−2.13397	−	3.69615i	−0.211295	−	0.365974i
$103$	−9.66025			−0.951853			−0.475927	−	0.879485i	$-0.657887\pi$
$103$	−9.66025			−0.951853			−0.475927	+	0.879485i	$0.657887\pi$
$104$	−0.232051	+	0.401924i	−0.0227545	+	0.0394119i
$105$	0.732051			0.0714408
$106$	−1.63397	+	2.83013i	−0.158706	+	0.274886i
$107$	−3.36603	+	5.83013i	−0.325406	+	0.563620i	−0.981594	−	0.190977i	$-0.938834\pi$
$107$	−3.36603	+	5.83013i	−0.325406	+	0.563620i	0.656188	+	0.754597i	$0.272168\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−8.83013	−	15.2942i	−0.845773	−	1.46492i	−0.884948	−	0.465689i	$-0.845807\pi$
$109$	−8.83013	−	15.2942i	−0.845773	−	1.46492i	0.0391756	−	0.999232i	$-0.487527\pi$
$110$	−6.46410			−0.616328
$111$	4.69615	−	3.86603i	0.445739	−	0.366947i
$112$	−0.732051			−0.0691723
$113$	−1.86603	−	3.23205i	−0.175541	−	0.304046i	0.764807	−	0.644259i	$-0.222834\pi$
$113$	−1.86603	−	3.23205i	−0.175541	−	0.304046i	−0.940348	+	0.340213i	$0.889501\pi$
$114$	−1.73205	+	3.00000i	−0.162221	+	0.280976i
$115$	−4.46410	+	7.73205i	−0.416280	+	0.721017i
$116$	2.59808	−	4.50000i	0.241225	−	0.417815i
$117$	−0.464102			−0.0429062
$118$	0.232051	−	0.401924i	0.0213620	−	0.0370001i
$119$	−3.12436			−0.286409
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	30.7846			2.79860
$122$	11.6603			1.05567
$123$	3.63397	+	6.29423i	0.327664	+	0.567531i
$124$	−1.73205	+	3.00000i	−0.155543	+	0.269408i
$125$	1.00000			0.0894427
$126$	−0.366025	−	0.633975i	−0.0326081	−	0.0564789i
$127$	−2.56218	−	4.43782i	−0.227357	−	0.393793i	0.729667	−	0.683802i	$-0.239675\pi$
$127$	−2.56218	−	4.43782i	−0.227357	−	0.393793i	−0.957024	+	0.290009i	$0.906342\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.19615	−	10.7321i	0.545541	−	0.944904i
$130$	−0.232051	+	0.401924i	−0.0203522	+	0.0352510i
$131$	−3.69615	−	6.40192i	−0.322934	−	0.559339i	0.658158	−	0.752880i	$-0.271336\pi$
$131$	−3.69615	−	6.40192i	−0.322934	−	0.559339i	−0.981092	+	0.193541i	$0.938003\pi$
$132$	3.23205	+	5.59808i	0.281314	+	0.487250i
$133$	1.26795	+	2.19615i	0.109945	+	0.190431i
$134$	−4.26795			−0.368695
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	2.13397	+	3.69615i	0.182987	+	0.316942i
$137$	−5.73205			−0.489722			−0.244861	−	0.969558i	$-0.578742\pi$
$137$	−5.73205			−0.489722			−0.244861	+	0.969558i	$0.578742\pi$
$138$	8.92820			0.760019
$139$	−4.73205	−	8.19615i	−0.401367	−	0.695189i	0.592524	−	0.805553i	$-0.298132\pi$
$139$	−4.73205	−	8.19615i	−0.401367	−	0.695189i	−0.993891	+	0.110364i	$0.964798\pi$
$140$	−0.732051			−0.0618696
$141$	−1.23205	+	2.13397i	−0.103757	+	0.179713i
$142$	3.26795			0.274240
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.59808	−	4.50000i	0.215758	−	0.373705i
$146$		0			0
$147$	6.46410			0.533150
$148$	−4.69615	+	3.86603i	−0.386021	+	0.317785i
$149$	−4.26795			−0.349644			−0.174822	−	0.984600i	$-0.555935\pi$
$149$	−4.26795			−0.349644			−0.174822	+	0.984600i	$0.555935\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−8.92820	+	15.4641i	−0.726567	+	1.25845i	0.231759	+	0.972773i	$0.425552\pi$
$151$	−8.92820	+	15.4641i	−0.726567	+	1.25845i	−0.958326	+	0.285677i	$0.907781\pi$
$152$	1.73205	−	3.00000i	0.140488	−	0.243332i
$153$	−2.13397	+	3.69615i	−0.172522	+	0.298816i
$154$	4.73205			0.381320
$155$	−1.73205	+	3.00000i	−0.139122	+	0.240966i
$156$	0.464102			0.0371579
$157$	−1.96410	−	3.40192i	−0.156752	−	0.271503i	0.776943	−	0.629571i	$-0.216769\pi$
$157$	−1.96410	−	3.40192i	−0.156752	−	0.271503i	−0.933696	+	0.358067i	$0.883436\pi$
$158$	−4.00000			−0.318223
$159$	3.26795			0.259165
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	3.26795	−	5.66025i	0.257550	−	0.446091i
$162$	−1.00000			−0.0785674
$163$	1.06218	+	1.83975i	0.0831962	+	0.144100i	0.904621	−	0.426217i	$-0.140154\pi$
$163$	1.06218	+	1.83975i	0.0831962	+	0.144100i	−0.821425	+	0.570317i	$0.806821\pi$
$164$	−3.63397	−	6.29423i	−0.283766	−	0.491497i
$165$	3.23205	+	5.59808i	0.251615	+	0.435810i
$166$	6.83013	−	11.8301i	0.530121	−	0.918196i
$167$	−0.696152	+	1.20577i	−0.0538699	+	0.0933054i	−0.891703	−	0.452621i	$-0.850489\pi$
$167$	−0.696152	+	1.20577i	−0.0538699	+	0.0933054i	0.837833	+	0.545927i	$0.183822\pi$
$168$	0.366025	+	0.633975i	0.0282395	+	0.0489122i
$169$	6.39230	+	11.0718i	0.491716	+	0.851677i
$170$	2.13397	+	3.69615i	0.163668	+	0.283482i
$171$	3.46410			0.264906
$172$	−6.19615	+	10.7321i	−0.472452	+	0.818311i
$173$	−8.36603	−	14.4904i	−0.636057	−	1.10168i	−0.986290	−	0.165021i	$-0.947231\pi$
$173$	−8.36603	−	14.4904i	−0.636057	−	1.10168i	0.350233	−	0.936663i	$-0.386102\pi$
$174$	−5.19615			−0.393919
$175$	−0.732051			−0.0553378
$176$	−3.23205	−	5.59808i	−0.243625	−	0.421971i
$177$	−0.464102			−0.0348840
$178$	−1.73205	+	3.00000i	−0.129823	+	0.224860i
$179$	−7.85641			−0.587215			−0.293608	−	0.955926i	$-0.594856\pi$
$179$	−7.85641			−0.587215			−0.293608	+	0.955926i	$0.594856\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−10.4641	+	18.1244i	−0.777791	+	1.34717i	0.155422	+	0.987848i	$0.450326\pi$
$181$	−10.4641	+	18.1244i	−0.777791	+	1.34717i	−0.933213	+	0.359325i	$0.883007\pi$
$182$	0.169873	−	0.294229i	0.0125918	−	0.0218097i
$183$	−5.83013	−	10.0981i	−0.430975	−	0.746471i
$184$	−8.92820			−0.658196
$185$	−4.69615	+	3.86603i	−0.345268	+	0.284236i
$186$	3.46410			0.254000
$187$	−13.7942	−	23.8923i	−1.00873	−	1.74718i
$188$	1.23205	−	2.13397i	0.0898565	−	0.155636i
$189$	−0.366025	+	0.633975i	−0.0266244	+	0.0461149i
$190$	1.73205	−	3.00000i	0.125656	−	0.217643i
$191$	−27.1244			−1.96265			−0.981325	−	0.192358i	$-0.938386\pi$
$191$	−27.1244			−1.96265			−0.981325	+	0.192358i	$0.938386\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−14.7321			−1.06044			−0.530218	−	0.847861i	$-0.677890\pi$
$193$	−14.7321			−1.06044			−0.530218	+	0.847861i	$0.677890\pi$
$194$	4.46410	+	7.73205i	0.320504	+	0.555129i
$195$	0.464102			0.0332350
$196$	−6.46410			−0.461722
$197$	7.73205	+	13.3923i	0.550886	+	0.954162i	0.998211	+	0.0597908i	$0.0190434\pi$
$197$	7.73205	+	13.3923i	0.550886	+	0.954162i	−0.447325	+	0.894371i	$0.647623\pi$
$198$	3.23205	−	5.59808i	0.229692	−	0.397838i
$199$	−7.58846			−0.537931			−0.268966	−	0.963150i	$-0.586682\pi$
$199$	−7.58846			−0.537931			−0.268966	+	0.963150i	$0.586682\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	2.13397	+	3.69615i	0.150519	+	0.260706i
$202$	−8.06218	−	13.9641i	−0.567253	−	0.982511i
$203$	−1.90192	+	3.29423i	−0.133489	+	0.231210i
$204$	2.13397	−	3.69615i	0.149408	−	0.258782i
$205$	−3.63397	−	6.29423i	−0.253808	−	0.439608i
$206$	−4.83013	−	8.36603i	−0.336531	−	0.582889i
$207$	−4.46410	−	7.73205i	−0.310277	−	0.537415i
$208$	−0.464102			−0.0321797
$209$	−11.1962	+	19.3923i	−0.774454	+	1.34139i
$210$	0.366025	+	0.633975i	0.0252582	+	0.0437484i
$211$	9.46410			0.651536			0.325768	−	0.945450i	$-0.394377\pi$
$211$	9.46410			0.651536			0.325768	+	0.945450i	$0.394377\pi$
$212$	−3.26795			−0.224444
$213$	−1.63397	−	2.83013i	−0.111958	−	0.193917i
$214$	−6.73205			−0.460194
$215$	−6.19615	+	10.7321i	−0.422574	+	0.731920i
$216$	1.00000			0.0680414
$217$	1.26795	−	2.19615i	0.0860740	−	0.149085i
$218$	8.83013	−	15.2942i	0.598052	−	1.03586i
$219$		0			0
$220$	−3.23205	−	5.59808i	−0.217905	−	0.377422i
$221$	−1.98076			−0.133240
$222$	5.69615	+	2.13397i	0.382301	+	0.143223i
$223$	21.8564			1.46361			0.731807	−	0.681512i	$-0.238677\pi$
$223$	21.8564			1.46361			0.731807	+	0.681512i	$0.238677\pi$
$224$	−0.366025	−	0.633975i	−0.0244561	−	0.0423592i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	1.86603	−	3.23205i	0.124126	−	0.214993i
$227$	−6.09808	+	10.5622i	−0.404744	+	0.701036i	−0.994292	−	0.106697i	$-0.965973\pi$
$227$	−6.09808	+	10.5622i	−0.404744	+	0.701036i	0.589548	+	0.807733i	$0.299306\pi$
$228$	−3.46410			−0.229416
$229$	−13.0981	+	22.6865i	−0.865545	+	1.49917i	0.000959532		1.00000i	$0.499695\pi$
$229$	−13.0981	+	22.6865i	−0.865545	+	1.49917i	−0.866505	+	0.499169i	$0.833639\pi$
$230$	−8.92820			−0.588708
$231$	−2.36603	−	4.09808i	−0.155673	−	0.269634i
$232$	5.19615			0.341144
$233$	16.9282			1.10900			0.554502	−	0.832183i	$-0.312909\pi$
$233$	16.9282			1.10900			0.554502	+	0.832183i	$0.312909\pi$
$234$	−0.232051	−	0.401924i	−0.0151696	−	0.0262746i
$235$	1.23205	−	2.13397i	0.0803701	−	0.139205i
$236$	0.464102			0.0302104
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$	−1.56218	−	2.70577i	−0.101261	−	0.175389i
$239$	−10.7321	−	18.5885i	−0.694199	−	1.20239i	−0.970450	−	0.241302i	$-0.922426\pi$
$239$	−10.7321	−	18.5885i	−0.694199	−	1.20239i	0.276251	−	0.961085i	$-0.410908\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	10.6244	−	18.4019i	0.684375	−	1.18537i	−0.289258	−	0.957251i	$-0.593409\pi$
$241$	10.6244	−	18.4019i	0.684375	−	1.18537i	0.973633	−	0.228121i	$-0.0732582\pi$
$242$	15.3923	+	26.6603i	0.989455	+	1.71379i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	5.83013	+	10.0981i	0.373236	+	0.646463i
$245$	−6.46410			−0.412976
$246$	−3.63397	+	6.29423i	−0.231694	+	0.401305i
$247$	0.803848	+	1.39230i	0.0511476	+	0.0885902i
$248$	−3.46410			−0.219971
$249$	−13.6603			−0.865683
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−0.464102			−0.0292938			−0.0146469	−	0.999893i	$-0.504662\pi$
$251$	−0.464102			−0.0292938			−0.0146469	+	0.999893i	$0.504662\pi$
$252$	0.366025	−	0.633975i	0.0230574	−	0.0399366i
$253$	57.7128			3.62837
$254$	2.56218	−	4.43782i	0.160765	−	0.278454i
$255$	2.13397	−	3.69615i	0.133635	−	0.231462i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.06218	+	8.76795i	0.315770	+	0.546930i	0.979601	−	0.200953i	$-0.0644039\pi$
$257$	5.06218	+	8.76795i	0.315770	+	0.546930i	−0.663831	+	0.747883i	$0.731071\pi$
$258$	12.3923			0.771511
$259$	3.43782	−	2.83013i	0.213616	−	0.175856i
$260$	−0.464102			−0.0287824
$261$	2.59808	+	4.50000i	0.160817	+	0.278543i
$262$	3.69615	−	6.40192i	0.228349	−	0.395512i
$263$	−4.80385	+	8.32051i	−0.296218	+	0.513065i	−0.975267	−	0.221028i	$-0.929059\pi$
$263$	−4.80385	+	8.32051i	−0.296218	+	0.513065i	0.679050	+	0.734092i	$0.262392\pi$
$264$	−3.23205	+	5.59808i	−0.198919	+	0.344538i
$265$	−3.26795			−0.200749
$266$	−1.26795	+	2.19615i	−0.0777430	+	0.134655i
$267$	3.46410			0.212000
$268$	−2.13397	−	3.69615i	−0.130353	−	0.225778i
$269$	−9.32051			−0.568281			−0.284141	−	0.958783i	$-0.591708\pi$
$269$	−9.32051			−0.568281			−0.284141	+	0.958783i	$0.591708\pi$
$270$	1.00000			0.0608581
$271$	−10.0622	−	17.4282i	−0.611234	−	1.05869i	−0.991033	−	0.133619i	$-0.957340\pi$
$271$	−10.0622	−	17.4282i	−0.611234	−	1.05869i	0.379799	−	0.925069i	$-0.375993\pi$
$272$	−2.13397	+	3.69615i	−0.129391	+	0.224112i
$273$	−0.339746			−0.0205624
$274$	−2.86603	−	4.96410i	−0.173143	−	0.299892i
$275$	−3.23205	−	5.59808i	−0.194900	−	0.337577i
$276$	4.46410	+	7.73205i	0.268707	+	0.465415i
$277$	3.42820	−	5.93782i	0.205981	−	0.356769i	−0.744464	−	0.667663i	$-0.767295\pi$
$277$	3.42820	−	5.93782i	0.205981	−	0.356769i	0.950445	+	0.310893i	$0.100628\pi$
$278$	4.73205	−	8.19615i	0.283810	−	0.491573i
$279$	−1.73205	−	3.00000i	−0.103695	−	0.179605i
$280$	−0.366025	−	0.633975i	−0.0218742	−	0.0378872i
$281$	−14.6603	−	25.3923i	−0.874557	−	1.51478i	−0.857233	−	0.514928i	$-0.827819\pi$
$281$	−14.6603	−	25.3923i	−0.874557	−	1.51478i	−0.0173240	−	0.999850i	$-0.505515\pi$
$282$	−2.46410			−0.146735
$283$	7.86603	−	13.6244i	0.467587	−	0.809884i	−0.531727	−	0.846916i	$-0.678457\pi$
$283$	7.86603	−	13.6244i	0.467587	−	0.809884i	0.999314	+	0.0370317i	$0.0117902\pi$
$284$	1.63397	+	2.83013i	0.0969586	+	0.167937i
$285$	−3.46410			−0.205196
$286$	3.00000			0.177394
$287$	2.66025	+	4.60770i	0.157030	+	0.271984i
$288$	−1.00000			−0.0589256
$289$	−0.607695	+	1.05256i	−0.0357468	+	0.0619152i
$290$	5.19615			0.305129
$291$	4.46410	−	7.73205i	0.261690	−	0.453261i
$292$		0			0
$293$	5.19615	−	9.00000i	0.303562	−	0.525786i	−0.673378	−	0.739299i	$-0.735157\pi$
$293$	5.19615	−	9.00000i	0.303562	−	0.525786i	0.976940	+	0.213513i	$0.0684906\pi$
$294$	3.23205	+	5.59808i	0.188497	+	0.326486i
$295$	0.464102			0.0270210
$296$	−5.69615	−	2.13397i	−0.331082	−	0.124035i
$297$	−6.46410			−0.375085
$298$	−2.13397	−	3.69615i	−0.123618	−	0.214112i
$299$	2.07180	−	3.58846i	0.119815	−	0.207526i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	4.53590	−	7.85641i	0.261445	−	0.452836i
$302$	−17.8564			−1.02752
$303$	−8.06218	+	13.9641i	−0.463160	+	0.802217i
$304$	3.46410			0.198680
$305$	5.83013	+	10.0981i	0.333832	+	0.578214i
$306$	−4.26795			−0.243982
$307$	12.5359			0.715462			0.357731	−	0.933825i	$-0.383551\pi$
$307$	12.5359			0.715462			0.357731	+	0.933825i	$0.383551\pi$
$308$	2.36603	+	4.09808i	0.134817	+	0.233510i
$309$	−4.83013	+	8.36603i	−0.274776	+	0.475927i
$310$	−3.46410			−0.196748
$311$	−3.09808	−	5.36603i	−0.175676	−	0.304279i	0.764719	−	0.644364i	$-0.222878\pi$
$311$	−3.09808	−	5.36603i	−0.175676	−	0.304279i	−0.940395	+	0.340084i	$0.889544\pi$
$312$	0.232051	+	0.401924i	0.0131373	+	0.0227545i
$313$	−9.19615	−	15.9282i	−0.519797	−	0.900315i	−0.999735	−	0.0230128i	$-0.992674\pi$
$313$	−9.19615	−	15.9282i	−0.519797	−	0.900315i	0.479938	−	0.877302i	$-0.340659\pi$
$314$	1.96410	−	3.40192i	0.110841	−	0.191982i
$315$	0.366025	−	0.633975i	0.0206232	−	0.0357204i
$316$	−2.00000	−	3.46410i	−0.112509	−	0.194871i
$317$	−0.169873	−	0.294229i	−0.00954102	−	0.0165255i	0.861215	−	0.508240i	$-0.169704\pi$
$317$	−0.169873	−	0.294229i	−0.00954102	−	0.0165255i	−0.870756	+	0.491714i	$0.836370\pi$
$318$	1.63397	+	2.83013i	0.0916287	+	0.158706i
$319$	−33.5885			−1.88059
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	3.36603	+	5.83013i	0.187873	+	0.325406i
$322$	6.53590			0.364231
$323$	14.7846			0.822638
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.464102			−0.0257437
$326$	−1.06218	+	1.83975i	−0.0588286	+	0.101894i
$327$	−17.6603			−0.976614
$328$	3.63397	−	6.29423i	0.200653	−	0.347541i
$329$	−0.901924	+	1.56218i	−0.0497247	+	0.0861257i
$330$	−3.23205	+	5.59808i	−0.177919	+	0.308164i
$331$	6.63397	+	11.4904i	0.364636	+	0.631568i	0.988718	−	0.149791i	$-0.0478600\pi$
$331$	6.63397	+	11.4904i	0.364636	+	0.631568i	−0.624081	+	0.781359i	$0.714527\pi$
$332$	13.6603			0.749704
$333$	−1.00000	−	6.00000i	−0.0547997	−	0.328798i
$334$	−1.39230			−0.0761835
$335$	−2.13397	−	3.69615i	−0.116591	−	0.201942i
$336$	−0.366025	+	0.633975i	−0.0199683	+	0.0345861i
$337$	16.0981	−	27.8827i	0.876918	−	1.51887i	0.0222127	−	0.999753i	$-0.492929\pi$
$337$	16.0981	−	27.8827i	0.876918	−	1.51887i	0.854705	−	0.519113i	$-0.173738\pi$
$338$	−6.39230	+	11.0718i	−0.347696	+	0.602226i
$339$	−3.73205			−0.202697
$340$	−2.13397	+	3.69615i	−0.115731	+	0.200452i
$341$	22.3923			1.21261
$342$	1.73205	+	3.00000i	0.0936586	+	0.162221i
$343$	9.85641			0.532196
$344$	−12.3923			−0.668148
$345$	4.46410	+	7.73205i	0.240339	+	0.416280i
$346$	8.36603	−	14.4904i	0.449760	−	0.779008i
$347$	−3.07180			−0.164903			−0.0824513	−	0.996595i	$-0.526275\pi$
$347$	−3.07180			−0.164903			−0.0824513	+	0.996595i	$0.526275\pi$
$348$	−2.59808	−	4.50000i	−0.139272	−	0.241225i
$349$	9.85641	+	17.0718i	0.527601	+	0.913832i	0.999482	+	0.0321701i	$0.0102418\pi$
$349$	9.85641	+	17.0718i	0.527601	+	0.913832i	−0.471881	+	0.881662i	$0.656425\pi$
$350$	−0.366025	−	0.633975i	−0.0195649	−	0.0338874i
$351$	−0.232051	+	0.401924i	−0.0123860	+	0.0214531i
$352$	3.23205	−	5.59808i	0.172269	−	0.298378i
$353$	9.53590	+	16.5167i	0.507545	+	0.879093i	0.999962	+	0.00873384i	$0.00278010\pi$
$353$	9.53590	+	16.5167i	0.507545	+	0.879093i	−0.492417	+	0.870359i	$0.663887\pi$
$354$	−0.232051	−	0.401924i	−0.0123334	−	0.0213620i
$355$	1.63397	+	2.83013i	0.0867224	+	0.150208i
$356$	−3.46410			−0.183597
$357$	−1.56218	+	2.70577i	−0.0826792	+	0.143205i
$358$	−3.92820	−	6.80385i	−0.207612	−	0.359595i
$359$	−18.3923			−0.970709			−0.485354	−	0.874318i	$-0.661309\pi$
$359$	−18.3923			−0.970709			−0.485354	+	0.874318i	$0.661309\pi$
$360$	−1.00000			−0.0527046
$361$	3.50000	+	6.06218i	0.184211	+	0.319062i
$362$	−20.9282			−1.09996
$363$	15.3923	−	26.6603i	0.807886	−	1.39930i
$364$	0.339746			0.0178075
$365$		0			0
$366$	5.83013	−	10.0981i	0.304746	−	0.527835i
$367$	9.66025	−	16.7321i	0.504261	−	0.873406i	−0.495727	−	0.868479i	$-0.665098\pi$
$367$	9.66025	−	16.7321i	0.504261	−	0.873406i	0.999988	−	0.00492737i	$-0.00156844\pi$
$368$	−4.46410	−	7.73205i	−0.232707	−	0.403061i
$369$	7.26795			0.378354
$370$	−5.69615	−	2.13397i	−0.296129	−	0.110940i
$371$	2.39230			0.124202
$372$	1.73205	+	3.00000i	0.0898027	+	0.155543i
$373$	−15.2679	+	26.4449i	−0.790544	+	1.36926i	0.135086	+	0.990834i	$0.456869\pi$
$373$	−15.2679	+	26.4449i	−0.790544	+	1.36926i	−0.925630	+	0.378429i	$0.876464\pi$
$374$	13.7942	−	23.8923i	0.713283	−	1.23544i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	2.46410			0.127076
$377$	−1.20577	+	2.08846i	−0.0621004	+	0.107561i
$378$	−0.732051			−0.0376526
$379$	11.0981	+	19.2224i	0.570070	+	0.987390i	0.996558	+	0.0828969i	$0.0264172\pi$
$379$	11.0981	+	19.2224i	0.570070	+	0.987390i	−0.426488	+	0.904493i	$0.640249\pi$
$380$	3.46410			0.177705
$381$	−5.12436			−0.262529
$382$	−13.5622	−	23.4904i	−0.693901	−	1.20187i
$383$	−8.76795	+	15.1865i	−0.448021	+	0.775996i	−0.998257	−	0.0590136i	$-0.981204\pi$
$383$	−8.76795	+	15.1865i	−0.448021	+	0.775996i	0.550236	+	0.835009i	$0.314538\pi$
$384$	1.00000			0.0510310
$385$	2.36603	+	4.09808i	0.120584	+	0.208857i
$386$	−7.36603	−	12.7583i	−0.374921	−	0.649382i
$387$	−6.19615	−	10.7321i	−0.314968	−	0.545541i
$388$	−4.46410	+	7.73205i	−0.226630	+	0.392535i
$389$	13.7321	−	23.7846i	0.696243	−	1.20593i	−0.273517	−	0.961867i	$-0.588187\pi$
$389$	13.7321	−	23.7846i	0.696243	−	1.20593i	0.969760	−	0.244061i	$-0.0784796\pi$
$390$	0.232051	+	0.401924i	0.0117503	+	0.0203522i
$391$	−19.0526	−	33.0000i	−0.963529	−	1.66888i
$392$	−3.23205	−	5.59808i	−0.163243	−	0.282746i
$393$	−7.39230			−0.372892
$394$	−7.73205	+	13.3923i	−0.389535	+	0.674695i
$395$	−2.00000	−	3.46410i	−0.100631	−	0.174298i
$396$	6.46410			0.324833
$397$	−27.9282			−1.40168			−0.700838	−	0.713320i	$-0.747190\pi$
$397$	−27.9282			−1.40168			−0.700838	+	0.713320i	$0.747190\pi$
$398$	−3.79423	−	6.57180i	−0.190187	−	0.329414i
$399$	2.53590			0.126954
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−10.1962			−0.509172			−0.254586	−	0.967050i	$-0.581939\pi$
$401$	−10.1962			−0.509172			−0.254586	+	0.967050i	$0.581939\pi$
$402$	−2.13397	+	3.69615i	−0.106433	+	0.184347i
$403$	0.803848	−	1.39230i	0.0400425	−	0.0693556i
$404$	8.06218	−	13.9641i	0.401108	−	0.694740i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−3.80385			−0.188782
$407$	36.8205	+	13.7942i	1.82512	+	0.683755i
$408$	4.26795			0.211295
$409$	13.6244	+	23.5981i	0.673681	+	1.16685i	0.976853	+	0.213914i	$0.0686212\pi$
$409$	13.6244	+	23.5981i	0.673681	+	1.16685i	−0.303172	+	0.952936i	$0.598046\pi$
$410$	3.63397	−	6.29423i	0.179469	−	0.310850i
$411$	−2.86603	+	4.96410i	−0.141371	+	0.244861i
$412$	4.83013	−	8.36603i	0.237963	−	0.412164i
$413$	−0.339746			−0.0167178
$414$	4.46410	−	7.73205i	0.219399	−	0.380010i
$415$	13.6603			0.670555
$416$	−0.232051	−	0.401924i	−0.0113772	−	0.0197059i
$417$	−9.46410			−0.463459
$418$	−22.3923			−1.09524
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$	−0.366025	+	0.633975i	−0.0178602	+	0.0309348i
$421$	−29.8038			−1.45255			−0.726275	−	0.687404i	$-0.758750\pi$
$421$	−29.8038			−1.45255			−0.726275	+	0.687404i	$0.758750\pi$
$422$	4.73205	+	8.19615i	0.230353	+	0.398982i
$423$	1.23205	+	2.13397i	0.0599044	+	0.103757i
$424$	−1.63397	−	2.83013i	−0.0793528	−	0.137443i
$425$	−2.13397	+	3.69615i	−0.103513	+	0.179290i
$426$	1.63397	−	2.83013i	0.0791663	−	0.137120i
$427$	−4.26795	−	7.39230i	−0.206541	−	0.357739i
$428$	−3.36603	−	5.83013i	−0.162703	−	0.281810i
$429$	−1.50000	−	2.59808i	−0.0724207	−	0.125436i
$430$	−12.3923			−0.597610
$431$	6.56218	−	11.3660i	0.316089	−	0.547482i	−0.663579	−	0.748106i	$-0.730964\pi$
$431$	6.56218	−	11.3660i	0.316089	−	0.547482i	0.979668	+	0.200624i	$0.0642968\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	2.92820			0.140720			0.0703602	−	0.997522i	$-0.477585\pi$
$433$	2.92820			0.140720			0.0703602	+	0.997522i	$0.477585\pi$
$434$	2.53590			0.121727
$435$	−2.59808	−	4.50000i	−0.124568	−	0.215758i
$436$	17.6603			0.845773
$437$	−15.4641	+	26.7846i	−0.739748	+	1.28128i
$438$		0			0
$439$	−5.99038	+	10.3756i	−0.285905	+	0.495202i	−0.972828	−	0.231528i	$-0.925628\pi$
$439$	−5.99038	+	10.3756i	−0.285905	+	0.495202i	0.686923	+	0.726730i	$0.258961\pi$
$440$	3.23205	−	5.59808i	0.154082	−	0.266878i
$441$	3.23205	−	5.59808i	0.153907	−	0.266575i
$442$	−0.990381	−	1.71539i	−0.0471076	−	0.0815928i
$443$	40.1962			1.90978			0.954888	−	0.296965i	$-0.0959744\pi$
$443$	40.1962			1.90978			0.954888	+	0.296965i	$0.0959744\pi$
$444$	1.00000	+	6.00000i	0.0474579	+	0.284747i
$445$	−3.46410			−0.164214
$446$	10.9282	+	18.9282i	0.517465	+	0.896276i
$447$	−2.13397	+	3.69615i	−0.100934	+	0.174822i
$448$	0.366025	−	0.633975i	0.0172931	−	0.0299525i
$449$	1.07180	−	1.85641i	0.0505812	−	0.0876092i	−0.839626	−	0.543165i	$-0.817226\pi$
$449$	1.07180	−	1.85641i	0.0505812	−	0.0876092i	0.890207	+	0.455555i	$0.150559\pi$
$450$	−1.00000			−0.0471405
$451$	−23.4904	+	40.6865i	−1.10612	+	1.91585i
$452$	3.73205			0.175541
$453$	8.92820	+	15.4641i	0.419484	+	0.726567i
$454$	−12.1962			−0.572394
$455$	0.339746			0.0159275
$456$	−1.73205	−	3.00000i	−0.0811107	−	0.140488i
$457$	2.19615	−	3.80385i	0.102732	−	0.177936i	−0.810078	−	0.586323i	$-0.800575\pi$
$457$	2.19615	−	3.80385i	0.102732	−	0.177936i	0.912809	+	0.408386i	$0.133908\pi$
$458$	−26.1962			−1.22407
$459$	2.13397	+	3.69615i	0.0996054	+	0.172522i
$460$	−4.46410	−	7.73205i	−0.208140	−	0.360509i
$461$	8.52628	+	14.7679i	0.397108	+	0.687812i	0.993368	−	0.114980i	$-0.0366804\pi$
$461$	8.52628	+	14.7679i	0.397108	+	0.687812i	−0.596259	+	0.802792i	$0.703347\pi$
$462$	2.36603	−	4.09808i	0.110077	−	0.190660i
$463$	−15.9282	+	27.5885i	−0.740246	+	1.28214i	0.212137	+	0.977240i	$0.431958\pi$
$463$	−15.9282	+	27.5885i	−0.740246	+	1.28214i	−0.952383	+	0.304904i	$0.901376\pi$
$464$	2.59808	+	4.50000i	0.120613	+	0.208907i
$465$	1.73205	+	3.00000i	0.0803219	+	0.139122i
$466$	8.46410	+	14.6603i	0.392092	+	0.679123i
$467$	4.53590			0.209896			0.104948	−	0.994478i	$-0.466532\pi$
$467$	4.53590			0.209896			0.104948	+	0.994478i	$0.466532\pi$
$468$	0.232051	−	0.401924i	0.0107266	−	0.0185789i
$469$	1.56218	+	2.70577i	0.0721347	+	0.124941i
$470$	2.46410			0.113661
$471$	−3.92820			−0.181002
$472$	0.232051	+	0.401924i	0.0106810	+	0.0185000i
$473$	80.1051			3.68324
$474$	−2.00000	+	3.46410i	−0.0918630	+	0.159111i
$475$	3.46410			0.158944
$476$	1.56218	−	2.70577i	0.0716023	−	0.124019i
$477$	1.63397	−	2.83013i	0.0748146	−	0.129583i
$478$	10.7321	−	18.5885i	0.490873	−	0.850216i
$479$	19.0000	+	32.9090i	0.868132	+	1.50365i	0.863903	+	0.503658i	$0.168013\pi$
$479$	19.0000	+	32.9090i	0.868132	+	1.50365i	0.00422900	+	0.999991i	$0.498654\pi$
$480$	1.00000			0.0456435
$481$	2.17949	−	1.79423i	0.0993763	−	0.0818098i
$482$	21.2487			0.967852
$483$	−3.26795	−	5.66025i	−0.148697	−	0.257550i
$484$	−15.3923	+	26.6603i	−0.699650	+	1.21183i
$485$	−4.46410	+	7.73205i	−0.202704	+	0.351094i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−6.39230			−0.289663			−0.144831	−	0.989456i	$-0.546264\pi$
$487$	−6.39230			−0.289663			−0.144831	+	0.989456i	$0.546264\pi$
$488$	−5.83013	+	10.0981i	−0.263917	+	0.457118i
$489$	2.12436			0.0960667
$490$	−3.23205	−	5.59808i	−0.146009	−	0.252895i
$491$	−29.7128			−1.34092			−0.670460	−	0.741945i	$-0.733903\pi$
$491$	−29.7128			−1.34092			−0.670460	+	0.741945i	$0.733903\pi$
$492$	−7.26795			−0.327664
$493$	11.0885	+	19.2058i	0.499399	+	0.864984i
$494$	−0.803848	+	1.39230i	−0.0361668	+	0.0626428i
$495$	6.46410			0.290540
$496$	−1.73205	−	3.00000i	−0.0777714	−	0.134704i
$497$	−1.19615	−	2.07180i	−0.0536548	−	0.0929328i
$498$	−6.83013	−	11.8301i	−0.306065	−	0.530121i
$499$	3.90192	−	6.75833i	0.174674	−	0.302544i	−0.765374	−	0.643585i	$-0.777446\pi$
$499$	3.90192	−	6.75833i	0.174674	−	0.302544i	0.940048	+	0.341041i	$0.110779\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	0.696152	+	1.20577i	0.0311018	+	0.0538699i
$502$	−0.232051	−	0.401924i	−0.0103569	−	0.0179387i
$503$	4.62436	+	8.00962i	0.206190	+	0.357131i	0.950511	−	0.310690i	$-0.100560\pi$
$503$	4.62436	+	8.00962i	0.206190	+	0.357131i	−0.744321	+	0.667822i	$0.767227\pi$
$504$	0.732051			0.0326081
$505$	8.06218	−	13.9641i	0.358762	−	0.621394i
$506$	28.8564	+	49.9808i	1.28282	+	2.22192i
$507$	12.7846			0.567784
$508$	5.12436			0.227357
$509$	4.39230	+	7.60770i	0.194685	+	0.337205i	0.946797	−	0.321830i	$-0.104298\pi$
$509$	4.39230	+	7.60770i	0.194685	+	0.337205i	−0.752112	+	0.659035i	$0.770965\pi$
$510$	4.26795			0.188988
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	1.73205	−	3.00000i	0.0764719	−	0.132453i
$514$	−5.06218	+	8.76795i	−0.223283	+	0.386738i
$515$	4.83013	−	8.36603i	0.212841	−	0.368651i
$516$	6.19615	+	10.7321i	0.272770	+	0.472452i
$517$	−15.9282			−0.700522
$518$	4.16987	+	1.56218i	0.183214	+	0.0686382i
$519$	−16.7321			−0.734456
$520$	−0.232051	−	0.401924i	−0.0101761	−	0.0176255i
$521$	−11.8038	+	20.4449i	−0.517136	+	0.895706i	0.482666	+	0.875805i	$0.339669\pi$
$521$	−11.8038	+	20.4449i	−0.517136	+	0.895706i	−0.999802	+	0.0199012i	$0.993665\pi$
$522$	−2.59808	+	4.50000i	−0.113715	+	0.196960i
$523$	−13.6603	+	23.6603i	−0.597321	+	1.03459i	0.395894	+	0.918296i	$0.370435\pi$
$523$	−13.6603	+	23.6603i	−0.597321	+	1.03459i	−0.993215	+	0.116294i	$0.962898\pi$
$524$	7.39230			0.322934
$525$	−0.366025	+	0.633975i	−0.0159747	+	0.0276689i
$526$	−9.60770			−0.418915
$527$	−7.39230	−	12.8038i	−0.322014	−	0.557744i
$528$	−6.46410			−0.281314
$529$	56.7128			2.46577
$530$	−1.63397	−	2.83013i	−0.0709753	−	0.122933i
$531$	−0.232051	+	0.401924i	−0.0100701	+	0.0174420i
$532$	−2.53590			−0.109945
$533$	1.68653	+	2.92116i	0.0730519	+	0.126530i
$534$	1.73205	+	3.00000i	0.0749532	+	0.129823i
$535$	−3.36603	−	5.83013i	−0.145526	−	0.252058i
$536$	2.13397	−	3.69615i	0.0921737	−	0.159649i
$537$	−3.92820	+	6.80385i	−0.169514	+	0.293608i
$538$	−4.66025	−	8.07180i	−0.200918	−	0.348000i
$539$	20.8923	+	36.1865i	0.899895	+	1.55866i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	8.05256			0.346207			0.173103	−	0.984904i	$-0.444621\pi$
$541$	8.05256			0.346207			0.173103	+	0.984904i	$0.444621\pi$
$542$	10.0622	−	17.4282i	0.432208	−	0.748605i
$543$	10.4641	+	18.1244i	0.449058	+	0.777791i
$544$	−4.26795			−0.182987
$545$	17.6603			0.756482
$546$	−0.169873	−	0.294229i	−0.00726989	−	0.0125918i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	2.86603	−	4.96410i	0.122431	−	0.212056i
$549$	−11.6603			−0.497648
$550$	3.23205	−	5.59808i	0.137815	−	0.238703i
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$	−4.46410	+	7.73205i	−0.190005	+	0.329098i
$553$	1.46410	+	2.53590i	0.0622599	+	0.107837i
$554$	6.85641			0.291301
$555$	1.00000	+	6.00000i	0.0424476	+	0.254686i
$556$	9.46410			0.401367
$557$	−19.9282	−	34.5167i	−0.844385	−	1.46252i	−0.886154	−	0.463391i	$-0.846633\pi$
$557$	−19.9282	−	34.5167i	−0.844385	−	1.46252i	0.0417691	−	0.999127i	$-0.486701\pi$
$558$	1.73205	−	3.00000i	0.0733236	−	0.127000i
$559$	2.87564	−	4.98076i	0.121627	−	0.210664i
$560$	0.366025	−	0.633975i	0.0154674	−	0.0267903i
$561$	−27.5885			−1.16479
$562$	14.6603	−	25.3923i	0.618405	−	1.07111i
$563$	−19.6603			−0.828581			−0.414290	−	0.910145i	$-0.635970\pi$
$563$	−19.6603			−0.828581			−0.414290	+	0.910145i	$0.635970\pi$
$564$	−1.23205	−	2.13397i	−0.0518787	−	0.0898565i
$565$	3.73205			0.157009
$566$	15.7321			0.661267
$567$	0.366025	+	0.633975i	0.0153716	+	0.0266244i
$568$	−1.63397	+	2.83013i	−0.0685601	+	0.118749i
$569$	−10.1962			−0.427445			−0.213722	−	0.976894i	$-0.568559\pi$
$569$	−10.1962			−0.427445			−0.213722	+	0.976894i	$0.568559\pi$
$570$	−1.73205	−	3.00000i	−0.0725476	−	0.125656i
$571$	2.46410	+	4.26795i	0.103119	+	0.178608i	0.912968	−	0.408030i	$-0.133784\pi$
$571$	2.46410	+	4.26795i	0.103119	+	0.178608i	−0.809849	+	0.586639i	$0.800451\pi$
$572$	1.50000	+	2.59808i	0.0627182	+	0.108631i
$573$	−13.5622	+	23.4904i	−0.566568	+	0.981325i
$574$	−2.66025	+	4.60770i	−0.111037	+	0.192321i
$575$	−4.46410	−	7.73205i	−0.186166	−	0.322449i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	6.75833	+	11.7058i	0.281353	+	0.487318i	0.971718	−	0.236143i	$-0.0758835\pi$
$577$	6.75833	+	11.7058i	0.281353	+	0.487318i	−0.690365	+	0.723461i	$0.742550\pi$
$578$	−1.21539			−0.0505536
$579$	−7.36603	+	12.7583i	−0.306122	+	0.530218i
$580$	2.59808	+	4.50000i	0.107879	+	0.186852i
$581$	−10.0000			−0.414870
$582$	8.92820			0.370086
$583$	10.5622	+	18.2942i	0.437441	+	0.757670i
$584$		0			0
$585$	0.232051	−	0.401924i	0.00959412	−	0.0166175i
$586$	10.3923			0.429302
$587$	−7.75833	+	13.4378i	−0.320221	+	0.554638i	−0.980533	−	0.196352i	$-0.937090\pi$
$587$	−7.75833	+	13.4378i	−0.320221	+	0.554638i	0.660313	+	0.750991i	$0.270424\pi$
$588$	−3.23205	+	5.59808i	−0.133288	+	0.230861i
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$	0.232051	+	0.401924i	0.00955338	+	0.0165469i
$591$	15.4641			0.636108
$592$	−1.00000	−	6.00000i	−0.0410997	−	0.246598i
$593$	−32.6603			−1.34120			−0.670598	−	0.741821i	$-0.733962\pi$
$593$	−32.6603			−1.34120			−0.670598	+	0.741821i	$0.733962\pi$
$594$	−3.23205	−	5.59808i	−0.132613	−	0.229692i
$595$	1.56218	−	2.70577i	0.0640430	−	0.110926i
$596$	2.13397	−	3.69615i	0.0874110	−	0.151400i
$597$	−3.79423	+	6.57180i	−0.155287	+	0.268966i
$598$	4.14359			0.169444
$599$	−9.16987	+	15.8827i	−0.374671	+	0.648949i	−0.990278	−	0.139104i	$-0.955578\pi$
$599$	−9.16987	+	15.8827i	−0.374671	+	0.648949i	0.615607	+	0.788053i	$0.288911\pi$
$600$	1.00000			0.0408248
$601$	1.96410	+	3.40192i	0.0801174	+	0.138767i	0.903300	−	0.429009i	$-0.141137\pi$
$601$	1.96410	+	3.40192i	0.0801174	+	0.138767i	−0.823183	+	0.567776i	$0.807804\pi$
$602$	9.07180			0.369739
$603$	4.26795			0.173804
$604$	−8.92820	−	15.4641i	−0.363283	−	0.629225i
$605$	−15.3923	+	26.6603i	−0.625786	+	1.08389i
$606$	−16.1244			−0.655007
$607$	−19.7846	−	34.2679i	−0.803033	−	1.39089i	−0.917611	−	0.397479i	$-0.869885\pi$
$607$	−19.7846	−	34.2679i	−0.803033	−	1.39089i	0.114579	−	0.993414i	$-0.463448\pi$
$608$	1.73205	+	3.00000i	0.0702439	+	0.121666i
$609$	1.90192	+	3.29423i	0.0770698	+	0.133489i
$610$	−5.83013	+	10.0981i	−0.236055	+	0.408859i
$611$	−0.571797	+	0.990381i	−0.0231324	+	0.0400665i
$612$	−2.13397	−	3.69615i	−0.0862608	−	0.149408i
$613$	19.8923	+	34.4545i	0.803443	+	1.39160i	0.917337	+	0.398111i	$0.130334\pi$
$613$	19.8923	+	34.4545i	0.803443	+	1.39160i	−0.113895	+	0.993493i	$0.536333\pi$
$614$	6.26795	+	10.8564i	0.252954	+	0.438129i
$615$	−7.26795			−0.293072
$616$	−2.36603	+	4.09808i	−0.0953299	+	0.165116i
$617$	4.79423	+	8.30385i	0.193008	+	0.334300i	0.946246	−	0.323448i	$-0.104842\pi$
$617$	4.79423	+	8.30385i	0.193008	+	0.334300i	−0.753237	+	0.657749i	$0.771509\pi$
$618$	−9.66025			−0.388592
$619$	−23.2679			−0.935218			−0.467609	−	0.883935i	$-0.654884\pi$
$619$	−23.2679			−0.935218			−0.467609	+	0.883935i	$0.654884\pi$
$620$	−1.73205	−	3.00000i	−0.0695608	−	0.120483i
$621$	−8.92820			−0.358276
$622$	3.09808	−	5.36603i	0.124222	−	0.215158i
$623$	2.53590			0.101599
$624$	−0.232051	+	0.401924i	−0.00928947	+	0.0160898i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.19615	−	15.9282i	0.367552	−	0.636619i
$627$	11.1962	+	19.3923i	0.447131	+	0.774454i
$628$	3.92820			0.156752
$629$	−4.26795	−	25.6077i	−0.170174	−	1.02105i
$630$	0.732051			0.0291656
$631$	3.59808	+	6.23205i	0.143237	+	0.248094i	0.928714	−	0.370797i	$-0.120916\pi$
$631$	3.59808	+	6.23205i	0.143237	+	0.248094i	−0.785477	+	0.618891i	$0.787582\pi$
$632$	2.00000	−	3.46410i	0.0795557	−	0.137795i
$633$	4.73205	−	8.19615i	0.188082	−	0.325768i
$634$	0.169873	−	0.294229i	0.00674652	−	0.0116853i
$635$	5.12436			0.203354
$636$	−1.63397	+	2.83013i	−0.0647913	+	0.112222i
$637$	3.00000			0.118864
$638$	−16.7942	−	29.0885i	−0.664890	−	1.15162i
$639$	−3.26795			−0.129278
$640$	−1.00000			−0.0395285
$641$	−0.973721	−	1.68653i	−0.0384596	−	0.0666141i	0.846155	−	0.532937i	$-0.178912\pi$
$641$	−0.973721	−	1.68653i	−0.0384596	−	0.0666141i	−0.884615	+	0.466323i	$0.845578\pi$
$642$	−3.36603	+	5.83013i	−0.132846	+	0.230097i
$643$	2.12436			0.0837764			0.0418882	−	0.999122i	$-0.486663\pi$
$643$	2.12436			0.0837764			0.0418882	+	0.999122i	$0.486663\pi$
$644$	3.26795	+	5.66025i	0.128775	+	0.223045i
$645$	6.19615	+	10.7321i	0.243973	+	0.422574i
$646$	7.39230	+	12.8038i	0.290846	+	0.503761i
$647$	22.1603	−	38.3827i	0.871209	−	1.50898i	0.0104630	−	0.999945i	$-0.496669\pi$
$647$	22.1603	−	38.3827i	0.871209	−	1.50898i	0.860747	−	0.509034i	$-0.169997\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−1.50000	−	2.59808i	−0.0588802	−	0.101983i
$650$	−0.232051	−	0.401924i	−0.00910178	−	0.0157647i
$651$	−1.26795	−	2.19615i	−0.0496948	−	0.0860740i
$652$	−2.12436			−0.0831962
$653$	10.7321	−	18.5885i	0.419978	−	0.727423i	−0.575959	−	0.817479i	$-0.695371\pi$
$653$	10.7321	−	18.5885i	0.419978	−	0.727423i	0.995937	+	0.0900560i	$0.0287046\pi$
$654$	−8.83013	−	15.2942i	−0.345285	−	0.598052i
$655$	7.39230			0.288841
$656$	7.26795			0.283766
$657$		0			0
$658$	−1.80385			−0.0703213
$659$	−24.6962	+	42.7750i	−0.962026	+	1.66628i	−0.244623	+	0.969618i	$0.578664\pi$
$659$	−24.6962	+	42.7750i	−0.962026	+	1.66628i	−0.717403	+	0.696659i	$0.754669\pi$
$660$	−6.46410			−0.251615
$661$	5.80385	−	10.0526i	0.225744	−	0.390999i	−0.730799	−	0.682593i	$-0.760852\pi$
$661$	5.80385	−	10.0526i	0.225744	−	0.390999i	0.956542	+	0.291594i	$0.0941855\pi$
$662$	−6.63397	+	11.4904i	−0.257837	+	0.446586i
$663$	−0.990381	+	1.71539i	−0.0384632	+	0.0666202i
$664$	6.83013	+	11.8301i	0.265060	+	0.459098i
$665$	−2.53590			−0.0983379
$666$	4.69615	−	3.86603i	0.181972	−	0.149805i
$667$	−46.3923			−1.79632
$668$	−0.696152	−	1.20577i	−0.0269349	−	0.0466527i
$669$	10.9282	−	18.9282i	0.422509	−	0.731807i
$670$	2.13397	−	3.69615i	0.0824426	−	0.142795i
$671$	37.6865	−	65.2750i	1.45487	−	2.51991i
$672$	−0.732051			−0.0282395
$673$	7.95448	−	13.7776i	0.306623	−	0.531086i	−0.670999	−	0.741459i	$-0.734134\pi$
$673$	7.95448	−	13.7776i	0.306623	−	0.531086i	0.977621	+	0.210372i	$0.0674677\pi$
$674$	32.1962			1.24015
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−12.7846			−0.491716
$677$	14.7321			0.566199			0.283099	−	0.959091i	$-0.408637\pi$
$677$	14.7321			0.566199			0.283099	+	0.959091i	$0.408637\pi$
$678$	−1.86603	−	3.23205i	−0.0716643	−	0.124126i
$679$	3.26795	−	5.66025i	0.125412	−	0.217221i
$680$	−4.26795			−0.163668
$681$	6.09808	+	10.5622i	0.233679	+	0.404744i
$682$	11.1962	+	19.3923i	0.428723	+	0.742570i
$683$	−11.7321	−	20.3205i	−0.448914	−	0.777543i	0.549401	−	0.835559i	$-0.314856\pi$
$683$	−11.7321	−	20.3205i	−0.448914	−	0.777543i	−0.998316	+	0.0580161i	$0.981523\pi$
$684$	−1.73205	+	3.00000i	−0.0662266	+	0.114708i
$685$	2.86603	−	4.96410i	0.109505	−	0.189669i
$686$	4.92820	+	8.53590i	0.188160	+	0.325902i
$687$	13.0981	+	22.6865i	0.499723	+	0.865545i
$688$	−6.19615	−	10.7321i	−0.236226	−	0.409156i
$689$	1.51666			0.0577802
$690$	−4.46410	+	7.73205i	−0.169945	+	0.294354i
$691$	22.6603	+	39.2487i	0.862037	+	1.49309i	0.869960	+	0.493123i	$0.164145\pi$
$691$	22.6603	+	39.2487i	0.862037	+	1.49309i	−0.00792306	+	0.999969i	$0.502522\pi$
$692$	16.7321			0.636057
$693$	−4.73205			−0.179756
$694$	−1.53590	−	2.66025i	−0.0583019	−	0.100982i
$695$	9.46410			0.358994
$696$	2.59808	−	4.50000i	0.0984798	−	0.170572i
$697$	31.0192			1.17494
$698$	−9.85641	+	17.0718i	−0.373070	+	0.646177i
$699$	8.46410	−	14.6603i	0.320142	−	0.554502i
$700$	0.366025	−	0.633975i	0.0138345	−	0.0239620i
$701$	10.2583	+	17.7679i	0.387452	+	0.671086i	0.992106	−	0.125402i	$-0.0400220\pi$
$701$	10.2583	+	17.7679i	0.387452	+	0.671086i	−0.604654	+	0.796488i	$0.706689\pi$
$702$	−0.464102			−0.0175164
$703$	−16.2679	+	13.3923i	−0.613557	+	0.505100i
$704$	6.46410			0.243625
$705$	−1.23205	−	2.13397i	−0.0464017	−	0.0803701i
$706$	−9.53590	+	16.5167i	−0.358888	+	0.621613i
$707$	−5.90192	+	10.2224i	−0.221965	+	0.384454i
$708$	0.232051	−	0.401924i	0.00872100	−	0.0151052i
$709$	0.732051			0.0274927			0.0137464	−	0.999906i	$-0.495624\pi$
$709$	0.732051			0.0274927			0.0137464	+	0.999906i	$0.495624\pi$
$710$	−1.63397	+	2.83013i	−0.0613220	+	0.106213i
$711$	4.00000			0.150012
$712$	−1.73205	−	3.00000i	−0.0649113	−	0.112430i
$713$	30.9282			1.15827
$714$	−3.12436			−0.116926
$715$	1.50000	+	2.59808i	0.0560968	+	0.0971625i
$716$	3.92820	−	6.80385i	0.146804	−	0.254272i
$717$	−21.4641			−0.801592
$718$	−9.19615	−	15.9282i	−0.343197	−	0.594435i
$719$	−4.43782	−	7.68653i	−0.165503	−	0.286659i	0.771331	−	0.636434i	$-0.219591\pi$
$719$	−4.43782	−	7.68653i	−0.165503	−	0.286659i	−0.936834	+	0.349775i	$0.886258\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	−3.53590	+	6.12436i	−0.131684	+	0.228083i
$722$	−3.50000	+	6.06218i	−0.130257	+	0.225611i
$723$	−10.6244	−	18.4019i	−0.395124	−	0.684375i
$724$	−10.4641	−	18.1244i	−0.388895	−	0.673586i
$725$	2.59808	+	4.50000i	0.0964901	+	0.167126i
$726$	30.7846			1.14252
$727$	9.66025	−	16.7321i	0.358279	−	0.620557i	−0.629394	−	0.777086i	$-0.716697\pi$
$727$	9.66025	−	16.7321i	0.358279	−	0.620557i	0.987673	+	0.156529i	$0.0500303\pi$
$728$	0.169873	+	0.294229i	0.00629591	+	0.0109048i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−26.4449	−	45.8038i	−0.978099	−	1.69412i
$732$	11.6603			0.430975
$733$	−19.5526	+	33.8660i	−0.722190	+	1.25087i	0.237930	+	0.971282i	$0.423531\pi$
$733$	−19.5526	+	33.8660i	−0.722190	+	1.25087i	−0.960120	+	0.279588i	$0.909802\pi$
$734$	19.3205			0.713133
$735$	−3.23205	+	5.59808i	−0.119216	+	0.206488i
$736$	4.46410	−	7.73205i	0.164549	−	0.285007i
$737$	−13.7942	+	23.8923i	−0.508117	+	0.880084i
$738$	3.63397	+	6.29423i	0.133768	+	0.231694i
$739$	−27.4641			−1.01028			−0.505142	−	0.863036i	$-0.668560\pi$
$739$	−27.4641			−1.01028			−0.505142	+	0.863036i	$0.668560\pi$
$740$	−1.00000	−	6.00000i	−0.0367607	−	0.220564i
$741$	1.60770			0.0590602
$742$	1.19615	+	2.07180i	0.0439121	+	0.0760581i
$743$	8.08846	−	14.0096i	0.296737	−	0.513963i	−0.678651	−	0.734461i	$-0.737435\pi$
$743$	8.08846	−	14.0096i	0.296737	−	0.513963i	0.975387	+	0.220498i	$0.0707683\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$	2.13397	−	3.69615i	0.0781828	−	0.135417i
$746$	−30.5359			−1.11800
$747$	−6.83013	+	11.8301i	−0.249901	+	0.432842i
$748$	27.5885			1.00873
$749$	2.46410	+	4.26795i	0.0900363	+	0.155947i
$750$	1.00000			0.0365148
$751$	−11.0526			−0.403314			−0.201657	−	0.979456i	$-0.564633\pi$
$751$	−11.0526			−0.403314			−0.201657	+	0.979456i	$0.564633\pi$
$752$	1.23205	+	2.13397i	0.0449283	+	0.0778180i
$753$	−0.232051	+	0.401924i	−0.00845640	+	0.0146469i
$754$	−2.41154			−0.0878232
$755$	−8.92820	−	15.4641i	−0.324931	−	0.562796i
$756$	−0.366025	−	0.633975i	−0.0133122	−	0.0230574i
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	−0.527011	+	0.849858i	$0.676688\pi$
$758$	−11.0981	+	19.2224i	−0.403100	+	0.698190i
$759$	28.8564	−	49.9808i	1.04742	−	1.81419i
$760$	1.73205	+	3.00000i	0.0628281	+	0.108821i
$761$	25.2224	+	43.6865i	0.914312	+	1.58364i	0.807905	+	0.589313i	$0.200602\pi$
$761$	25.2224	+	43.6865i	0.914312	+	1.58364i	0.106408	+	0.994323i	$0.466065\pi$
$762$	−2.56218	−	4.43782i	−0.0928179	−	0.160765i
$763$	−12.9282			−0.468032
$764$	13.5622	−	23.4904i	0.490662	−	0.849852i
$765$	−2.13397	−	3.69615i	−0.0771540	−	0.133635i
$766$	−17.5359			−0.633598
$767$	−0.215390			−0.00777729
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	44.4641			1.60342			0.801708	−	0.597716i	$-0.203925\pi$
$769$	44.4641			1.60342			0.801708	+	0.597716i	$0.203925\pi$
$770$	−2.36603	+	4.09808i	−0.0852656	+	0.147684i
$771$	10.1244			0.364620
$772$	7.36603	−	12.7583i	0.265109	−	0.459182i
$773$	5.09808	−	8.83013i	0.183365	−	0.317598i	−0.759659	−	0.650321i	$-0.774634\pi$
$773$	5.09808	−	8.83013i	0.183365	−	0.317598i	0.943024	+	0.332724i	$0.107968\pi$
$774$	6.19615	−	10.7321i	0.222716	−	0.385756i
$775$	−1.73205	−	3.00000i	−0.0622171	−	0.107763i
$776$	−8.92820			−0.320504
$777$	−0.732051	−	4.39230i	−0.0262622	−	0.157573i
$778$	27.4641			0.984636
$779$	−12.5885	−	21.8038i	−0.451028	−	0.781204i
$780$	−0.232051	+	0.401924i	−0.00830875	+	0.0143912i
$781$	10.5622	−	18.2942i	0.377944	−	0.654619i
$782$	19.0526	−	33.0000i	0.681318	−	1.18008i
$783$	5.19615			0.185695
$784$	3.23205	−	5.59808i	0.115430	−	0.199931i
$785$	3.92820			0.140204
$786$	−3.69615	−	6.40192i	−0.131837	−	0.228349i
$787$	−26.5167			−0.945217			−0.472608	−	0.881273i	$-0.656687\pi$
$787$	−26.5167			−0.945217			−0.472608	+	0.881273i	$0.656687\pi$
$788$	−15.4641			−0.550886
$789$	4.80385	+	8.32051i	0.171022	+	0.296218i
$790$	2.00000	−	3.46410i	0.0711568	−	0.123247i
$791$	−2.73205			−0.0971405
$792$	3.23205	+	5.59808i	0.114846	+	0.198919i
$793$	−2.70577	−	4.68653i	−0.0960848	−	0.166424i
$794$	−13.9641	−	24.1865i	−0.495567	−	0.858348i
$795$	−1.63397	+	2.83013i	−0.0579511	+	0.100374i
$796$	3.79423	−	6.57180i	0.134483	−	0.232931i
$797$	−2.92820	−	5.07180i	−0.103722	−	0.179652i	0.809493	−	0.587129i	$-0.199742\pi$
$797$	−2.92820	−	5.07180i	−0.103722	−	0.179652i	−0.913215	+	0.407477i	$0.866409\pi$
$798$	1.26795	+	2.19615i	0.0448849	+	0.0777430i
$799$	5.25833	+	9.10770i	0.186026	+	0.322207i
$800$	−1.00000			−0.0353553
$801$	1.73205	−	3.00000i	0.0611990	−	0.106000i
$802$	−5.09808	−	8.83013i	−0.180019	−	0.311803i
$803$		0			0
$804$	−4.26795			−0.150519
$805$	3.26795	+	5.66025i	0.115180	+	0.199498i
$806$	1.60770			0.0566286
$807$	−4.66025	+	8.07180i	−0.164049	+	0.284141i
$808$	16.1244			0.567253
$809$	7.58846	−	13.1436i	0.266796	−	0.462104i	−0.701237	−	0.712929i	$-0.747368\pi$
$809$	7.58846	−	13.1436i	0.266796	−	0.462104i	0.968033	+	0.250824i	$0.0807017\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−14.6865	+	25.4378i	−0.515714	+	0.893243i	0.484120	+	0.875002i	$0.339140\pi$
$811$	−14.6865	+	25.4378i	−0.515714	+	0.893243i	−0.999834	+	0.0182410i	$0.994193\pi$
$812$	−1.90192	−	3.29423i	−0.0667444	−	0.115605i
$813$	−20.1244			−0.705792
$814$	6.46410	+	38.7846i	0.226567	+	1.35940i
$815$	−2.12436			−0.0744129
$816$	2.13397	+	3.69615i	0.0747041	+	0.129391i
$817$	−21.4641	+	37.1769i	−0.750934	+	1.30066i
$818$	−13.6244	+	23.5981i	−0.476364	+	0.825087i
$819$	−0.169873	+	0.294229i	−0.00593584	+	0.0102812i
$820$	7.26795			0.253808
$821$	12.7942	−	22.1603i	0.446522	−	0.773398i	−0.551635	−	0.834086i	$-0.685996\pi$
$821$	12.7942	−	22.1603i	0.446522	−	0.773398i	0.998157	+	0.0606873i	$0.0193292\pi$
$822$	−5.73205			−0.199928
$823$	−21.2942	−	36.8827i	−0.742270	−	1.28565i	−0.951459	−	0.307774i	$-0.900416\pi$
$823$	−21.2942	−	36.8827i	−0.742270	−	1.28565i	0.209189	−	0.977875i	$-0.432918\pi$
$824$	9.66025			0.336531
$825$	−6.46410			−0.225051
$826$	−0.169873	−	0.294229i	−0.00591064	−	0.0102375i
$827$	21.7846	−	37.7321i	0.757525	−	1.31207i	−0.186584	−	0.982439i	$-0.559742\pi$
$827$	21.7846	−	37.7321i	0.757525	−	1.31207i	0.944109	−	0.329633i	$-0.106925\pi$
$828$	8.92820			0.310277
$829$	15.1699	+	26.2750i	0.526871	+	0.912568i	0.999510	+	0.0313116i	$0.00996842\pi$
$829$	15.1699	+	26.2750i	0.526871	+	0.912568i	−0.472638	+	0.881257i	$0.656698\pi$
$830$	6.83013	+	11.8301i	0.237077	+	0.410630i
$831$	−3.42820	−	5.93782i	−0.118923	−	0.205981i
$832$	0.232051	−	0.401924i	0.00804491	−	0.0139342i
$833$	13.7942	−	23.8923i	0.477942	−	0.827819i
$834$	−4.73205	−	8.19615i	−0.163858	−	0.283810i
$835$	−0.696152	−	1.20577i	−0.0240913	−	0.0417274i
$836$	−11.1962	−	19.3923i	−0.387227	−	0.670697i
$837$	−3.46410			−0.119737
$838$	15.0000	−	25.9808i	0.518166	−	0.897491i
$839$	6.16987	+	10.6865i	0.213008	+	0.368940i	0.952654	−	0.304055i	$-0.0983407\pi$
$839$	6.16987	+	10.6865i	0.213008	+	0.368940i	−0.739647	+	0.672995i	$0.765007\pi$
$840$	−0.732051			−0.0252582
$841$	−2.00000			−0.0689655
$842$	−14.9019	−	25.8109i	−0.513554	−	0.889502i
$843$	−29.3205			−1.00985
$844$	−4.73205	+	8.19615i	−0.162884	+	0.282123i
$845$	−12.7846			−0.439804
$846$	−1.23205	+	2.13397i	−0.0423588	+	0.0733676i
$847$	11.2679	−	19.5167i	0.387171	−	0.670600i
$848$	1.63397	−	2.83013i	0.0561109	−	0.0971870i
$849$	−7.86603	−	13.6244i	−0.269961	−	0.467587i
$850$	−4.26795			−0.146389
$851$	50.8564	+	19.0526i	1.74334	+	0.653113i
$852$	3.26795			0.111958
$853$	3.30385	+	5.72243i	0.113122	+	0.195932i	0.917027	−	0.398824i	$-0.130582\pi$
$853$	3.30385	+	5.72243i	0.113122	+	0.195932i	−0.803906	+	0.594757i	$0.797248\pi$
$854$	4.26795	−	7.39230i	0.146046	−	0.252959i
$855$	−1.73205	+	3.00000i	−0.0592349	+	0.102598i
$856$	3.36603	−	5.83013i	0.115048	−	0.199270i
$857$	42.1244			1.43894			0.719470	−	0.694523i	$-0.244385\pi$
$857$	42.1244			1.43894			0.719470	+	0.694523i	$0.244385\pi$
$858$	1.50000	−	2.59808i	0.0512092	−	0.0886969i
$859$	−40.0526			−1.36658			−0.683288	−	0.730149i	$-0.739451\pi$
$859$	−40.0526			−1.36658			−0.683288	+	0.730149i	$0.739451\pi$
$860$	−6.19615	−	10.7321i	−0.211287	−	0.365960i
$861$	5.32051			0.181322
$862$	13.1244			0.447017
$863$	4.83975	+	8.38269i	0.164747	+	0.285350i	0.936565	−	0.350493i	$-0.113986\pi$
$863$	4.83975	+	8.38269i	0.164747	+	0.285350i	−0.771818	+	0.635843i	$0.780653\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	16.7321			0.568907
$866$	1.46410	+	2.53590i	0.0497522	+	0.0861733i
$867$	0.607695	+	1.05256i	0.0206384	+	0.0357468i
$868$	1.26795	+	2.19615i	0.0430370	+	0.0745423i
$869$	−12.9282	+	22.3923i	−0.438559	+	0.759607i
$870$	2.59808	−	4.50000i	0.0880830	−	0.152564i
$871$	0.990381	+	1.71539i	0.0335578	+	0.0581238i
$872$	8.83013	+	15.2942i	0.299026	+	0.517928i
$873$	−4.46410	−	7.73205i	−0.151087	−	0.261690i
$874$	−30.9282			−1.04616
$875$	0.366025	−	0.633975i	0.0123739	−	0.0214323i
$876$		0			0
$877$	−51.7846			−1.74864			−0.874321	−	0.485348i	$-0.838693\pi$
$877$	−51.7846			−1.74864			−0.874321	+	0.485348i	$0.838693\pi$
$878$	−11.9808			−0.404331
$879$	−5.19615	−	9.00000i	−0.175262	−	0.303562i
$880$	6.46410			0.217905
$881$	4.39230	−	7.60770i	0.147981	−	0.256310i	−0.782500	−	0.622650i	$-0.786056\pi$
$881$	4.39230	−	7.60770i	0.147981	−	0.256310i	0.930481	+	0.366340i	$0.119389\pi$
$882$	6.46410			0.217658
$883$	−10.9904	+	19.0359i	−0.369856	+	0.640609i	−0.989543	−	0.144240i	$-0.953926\pi$
$883$	−10.9904	+	19.0359i	−0.369856	+	0.640609i	0.619687	+	0.784849i	$0.287260\pi$
$884$	0.990381	−	1.71539i	0.0333101	−	0.0576948i
$885$	0.232051	−	0.401924i	0.00780030	−	0.0135105i
$886$	20.0981	+	34.8109i	0.675208	+	1.16949i
$887$	50.7846			1.70518			0.852590	−	0.522580i	$-0.175030\pi$
$887$	50.7846			1.70518			0.852590	+	0.522580i	$0.175030\pi$
$888$	−4.69615	+	3.86603i	−0.157593	+	0.129735i
$889$	−3.75129			−0.125814
$890$	−1.73205	−	3.00000i	−0.0580585	−	0.100560i
$891$	−3.23205	+	5.59808i	−0.108278	+	0.187543i
$892$	−10.9282	+	18.9282i	−0.365903	+	0.633763i
$893$	4.26795	−	7.39230i	0.142821	−	0.247374i
$894$	−4.26795			−0.142742
$895$	3.92820	−	6.80385i	0.131305	−	0.227428i
$896$	0.732051			0.0244561
$897$	−2.07180	−	3.58846i	−0.0691753	−	0.119815i
$898$	2.14359			0.0715326
$899$	−18.0000			−0.600334
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	6.97372	−	12.0788i	0.232328	−	0.402404i
$902$	−46.9808			−1.56429
$903$	−4.53590	−	7.85641i	−0.150945	−	0.261445i
$904$	1.86603	+	3.23205i	0.0620631	+	0.107496i
$905$	−10.4641	−	18.1244i	−0.347839	−	0.602474i
$906$	−8.92820	+	15.4641i	−0.296620	+	0.513760i
$907$	15.4641	−	26.7846i	0.513477	−	0.889368i	−0.486401	−	0.873736i	$-0.661690\pi$
$907$	15.4641	−	26.7846i	0.513477	−	0.889368i	0.999878	−	0.0156325i	$-0.00497619\pi$
$908$	−6.09808	−	10.5622i	−0.202372	−	0.350518i
$909$	8.06218	+	13.9641i	0.267406	+	0.463160i
$910$	0.169873	+	0.294229i	0.00563123	+	0.00975358i
$911$	−29.3205			−0.971432			−0.485716	−	0.874117i	$-0.661441\pi$
$911$	−29.3205			−0.971432			−0.485716	+	0.874117i	$0.661441\pi$
$912$	1.73205	−	3.00000i	0.0573539	−	0.0993399i
$913$	−44.1506	−	76.4711i	−1.46117	−	2.53083i
$914$	4.39230			0.145285
$915$	11.6603			0.385476
$916$	−13.0981	−	22.6865i	−0.432773	−	0.749584i
$917$	−5.41154			−0.178705
$918$	−2.13397	+	3.69615i	−0.0704317	+	0.121991i
$919$	9.73205			0.321031			0.160515	−	0.987033i	$-0.448684\pi$
$919$	9.73205			0.321031			0.160515	+	0.987033i	$0.448684\pi$
$920$	4.46410	−	7.73205i	0.147177	−	0.254918i
$921$	6.26795	−	10.8564i	0.206536	−	0.357731i
$922$	−8.52628	+	14.7679i	−0.280798	+	0.486357i
$923$	−0.758330	−	1.31347i	−0.0249607	−	0.0432333i
$924$	4.73205			0.155673
$925$	−1.00000	−	6.00000i	−0.0328798	−	0.197279i
$926$	−31.8564			−1.04687
$927$	4.83013	+	8.36603i	0.158642	+	0.274776i
$928$	−2.59808	+	4.50000i	−0.0852860	+	0.147720i
$929$	6.33975	−	10.9808i	0.208000	−	0.360267i	−0.743084	−	0.669198i	$-0.766638\pi$
$929$	6.33975	−	10.9808i	0.208000	−	0.360267i	0.951085	+	0.308931i	$0.0999712\pi$
$930$	−1.73205	+	3.00000i	−0.0567962	+	0.0983739i
$931$	−22.3923			−0.733878
$932$	−8.46410	+	14.6603i	−0.277251	+	0.480213i
$933$	−6.19615			−0.202853
$934$	2.26795	+	3.92820i	0.0742096	+	0.128535i
$935$	27.5885			0.902239
$936$	0.464102			0.0151696
$937$	−24.6865	−	42.7583i	−0.806474	−	1.39685i	−0.915292	−	0.402792i	$-0.868040\pi$
$937$	−24.6865	−	42.7583i	−0.806474	−	1.39685i	0.108818	−	0.994062i	$-0.465294\pi$
$938$	−1.56218	+	2.70577i	−0.0510069	+	0.0883466i
$939$	−18.3923			−0.600210
$940$	1.23205	+	2.13397i	0.0401851	+	0.0696026i
$941$	−14.7846	−	25.6077i	−0.481965	−	0.834787i	0.517821	−	0.855489i	$-0.326743\pi$
$941$	−14.7846	−	25.6077i	−0.481965	−	0.834787i	−0.999786	+	0.0207019i	$0.993410\pi$
$942$	−1.96410	−	3.40192i	−0.0639939	−	0.110841i
$943$	−32.4449	+	56.1962i	−1.05655	+	1.83000i
$944$	−0.232051	+	0.401924i	−0.00755261	+	0.0130815i
$945$	−0.366025	−	0.633975i	−0.0119068	−	0.0206232i
$946$	40.0526	+	69.3731i	1.30222	+	2.25551i
$947$	−4.60770	−	7.98076i	−0.149730	−	0.259340i	0.781398	−	0.624033i	$-0.214507\pi$
$947$	−4.60770	−	7.98076i	−0.149730	−	0.259340i	−0.931128	+	0.364694i	$0.881174\pi$
$948$	−4.00000			−0.129914
$949$		0			0
$950$	1.73205	+	3.00000i	0.0561951	+	0.0973329i
$951$	−0.339746			−0.0110170
$952$	3.12436			0.101261
$953$	25.3301	+	43.8731i	0.820523	+	1.42119i	0.905293	+	0.424787i	$0.139651\pi$
$953$	25.3301	+	43.8731i	0.820523	+	1.42119i	−0.0847698	+	0.996401i	$0.527015\pi$
$954$	3.26795			0.105804
$955$	13.5622	−	23.4904i	0.438862	−	0.760131i
$956$	21.4641			0.694199
$957$	−16.7942	+	29.0885i	−0.542880	+	0.940296i
$958$	−19.0000	+	32.9090i	−0.613862	+	1.06324i
$959$	−2.09808	+	3.63397i	−0.0677504	+	0.117347i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−19.0000			−0.612903
$962$	2.64359	+	0.990381i	0.0852329	+	0.0319312i
$963$	6.73205			0.216937
$964$	10.6244	+	18.4019i	0.342187	+	0.592686i
$965$	7.36603	−	12.7583i	0.237121	−	0.410705i
$966$	3.26795	−	5.66025i	0.105145	−	0.182116i
$967$	20.6147	−	35.7058i	0.662925	−	1.14822i	−0.316918	−	0.948453i	$-0.602648\pi$
$967$	20.6147	−	35.7058i	0.662925	−	1.14822i	0.979843	−	0.199767i	$-0.0640186\pi$
$968$	−30.7846			−0.989455
$969$	7.39230	−	12.8038i	0.237475	−	0.411319i
$970$	−8.92820			−0.286667
$971$	3.58846	+	6.21539i	0.115159	+	0.199461i	0.917843	−	0.396943i	$-0.129929\pi$
$971$	3.58846	+	6.21539i	0.115159	+	0.199461i	−0.802684	+	0.596404i	$0.796596\pi$
$972$	−1.00000			−0.0320750
$973$	−6.92820			−0.222108
$974$	−3.19615	−	5.53590i	−0.102411	−	0.177382i
$975$	−0.232051	+	0.401924i	−0.00743157	+	0.0128719i
$976$	−11.6603			−0.373236
$977$	−28.0622	−	48.6051i	−0.897789	−	1.55502i	−0.830315	−	0.557294i	$-0.811839\pi$
$977$	−28.0622	−	48.6051i	−0.897789	−	1.55502i	−0.0674737	−	0.997721i	$-0.521494\pi$
$978$	1.06218	+	1.83975i	0.0339647	+	0.0588286i
$979$	11.1962	+	19.3923i	0.357831	+	0.619781i
$980$	3.23205	−	5.59808i	0.103244	−	0.178824i
$981$	−8.83013	+	15.2942i	−0.281924	+	0.488307i
$982$	−14.8564	−	25.7321i	−0.474087	−	0.821143i
$983$	−4.85641	−	8.41154i	−0.154895	−	0.268287i	0.778126	−	0.628109i	$-0.216171\pi$
$983$	−4.85641	−	8.41154i	−0.154895	−	0.268287i	−0.933021	+	0.359822i	$0.882837\pi$
$984$	−3.63397	−	6.29423i	−0.115847	−	0.200653i
$985$	−15.4641			−0.492727
$986$	−11.0885	+	19.2058i	−0.353128	+	0.611636i
$987$	0.901924	+	1.56218i	0.0287086	+	0.0497247i
$988$	−1.60770			−0.0511476
$989$	110.641			3.51818
$990$	3.23205	+	5.59808i	0.102721	+	0.177919i
$991$	−4.94744			−0.157161			−0.0785803	−	0.996908i	$-0.525039\pi$
$991$	−4.94744			−0.157161			−0.0785803	+	0.996908i	$0.525039\pi$
$992$	1.73205	−	3.00000i	0.0549927	−	0.0952501i
$993$	13.2679			0.421046
$994$	1.19615	−	2.07180i	0.0379397	−	0.0657134i
$995$	3.79423	−	6.57180i	0.120285	−	0.208340i
$996$	6.83013	−	11.8301i	0.216421	−	0.374852i
$997$	−5.08846	−	8.81347i	−0.161153	−	0.279125i	0.774129	−	0.633027i	$-0.218188\pi$
$997$	−5.08846	−	8.81347i	−0.161153	−	0.279125i	−0.935282	+	0.353902i	$0.884855\pi$
$998$	7.80385			0.247026
$999$	−5.69615	−	2.13397i	−0.180218	−	0.0675160i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.n.121.2	✓	4	37.10	even	3	inner
1110.2.i.n.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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(0.366025 - 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(0.366025 - 0.633975i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +6.46410 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.232051 - 0.401924i) q^{13} +0.732051 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.13397 - 3.69615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.73205 + 3.00000i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.366025 - 0.633975i) q^{21} +(3.23205 + 5.59808i) q^{22} +8.92820 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.464102 q^{26} -1.00000 q^{27} +(0.366025 + 0.633975i) q^{28} -5.19615 q^{29} +(-0.500000 + 0.866025i) q^{30} +3.46410 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.23205 - 5.59808i) q^{33} +(2.13397 - 3.69615i) q^{34} +(0.366025 + 0.633975i) q^{35} +1.00000 q^{36} +(5.69615 + 2.13397i) q^{37} -3.46410 q^{38} +(-0.232051 - 0.401924i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-3.63397 + 6.29423i) q^{41} +(0.366025 - 0.633975i) q^{42} +12.3923 q^{43} +(-3.23205 + 5.59808i) q^{44} +1.00000 q^{45} +(4.46410 + 7.73205i) q^{46} -2.46410 q^{47} -1.00000 q^{48} +(3.23205 + 5.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} -4.26795 q^{51} +(0.232051 + 0.401924i) q^{52} +(1.63397 + 2.83013i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-3.23205 + 5.59808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +(1.73205 + 3.00000i) q^{57} +(-2.59808 - 4.50000i) q^{58} +(-0.232051 - 0.401924i) q^{59} -1.00000 q^{60} +(5.83013 - 10.0981i) q^{61} +(1.73205 + 3.00000i) q^{62} -0.732051 q^{63} +1.00000 q^{64} +(0.232051 + 0.401924i) q^{65} +6.46410 q^{66} +(-2.13397 + 3.69615i) q^{67} +4.26795 q^{68} +(4.46410 - 7.73205i) q^{69} +(-0.366025 + 0.633975i) q^{70} +(1.63397 - 2.83013i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 + 6.00000i) q^{74} -1.00000 q^{75} +(-1.73205 - 3.00000i) q^{76} +(2.36603 - 4.09808i) q^{77} +(0.232051 - 0.401924i) q^{78} +(-2.00000 + 3.46410i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -7.26795 q^{82} +(-6.83013 - 11.8301i) q^{83} +0.732051 q^{84} +4.26795 q^{85} +(6.19615 + 10.7321i) q^{86} +(-2.59808 + 4.50000i) q^{87} -6.46410 q^{88} +(1.73205 + 3.00000i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-0.169873 - 0.294229i) q^{91} +(-4.46410 + 7.73205i) q^{92} +(1.73205 - 3.00000i) q^{93} +(-1.23205 - 2.13397i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-0.500000 - 0.866025i) q^{96} +8.92820 q^{97} +(-3.23205 + 5.59808i) q^{98} +(-3.23205 - 5.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 12 q^{11} + 2 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{20} + 2 q^{21} + 6 q^{22} + 8 q^{23} - 2 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 6 q^{33} + 12 q^{34} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 6 q^{39} + 2 q^{40} - 18 q^{41} - 2 q^{42} + 8 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 6 q^{49} + 2 q^{50} - 24 q^{51} - 6 q^{52} + 10 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 6 q^{59} - 4 q^{60} + 6 q^{61} + 4 q^{63} + 4 q^{64} - 6 q^{65} + 12 q^{66} - 12 q^{67} + 24 q^{68} + 4 q^{69} + 2 q^{70} + 10 q^{71} + 2 q^{72} + 4 q^{74} - 4 q^{75} + 6 q^{77} - 6 q^{78} - 8 q^{79} + 4 q^{80} - 2 q^{81} - 36 q^{82} - 10 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} - 12 q^{88} + 2 q^{90} - 18 q^{91} - 4 q^{92} + 2 q^{94} - 2 q^{96} + 8 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 12 * q^11 + 2 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^20 + 2 * q^21 + 6 * q^22 + 8 * q^23 - 2 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 6 * q^33 + 12 * q^34 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 6 * q^39 + 2 * q^40 - 18 * q^41 - 2 * q^42 + 8 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 4 * q^47 - 4 * q^48 + 6 * q^49 + 2 * q^50 - 24 * q^51 - 6 * q^52 + 10 * q^53 - 2 * q^54 - 6 * q^55 + 2 * q^56 + 6 * q^59 - 4 * q^60 + 6 * q^61 + 4 * q^63 + 4 * q^64 - 6 * q^65 + 12 * q^66 - 12 * q^67 + 24 * q^68 + 4 * q^69 + 2 * q^70 + 10 * q^71 + 2 * q^72 + 4 * q^74 - 4 * q^75 + 6 * q^77 - 6 * q^78 - 8 * q^79 + 4 * q^80 - 2 * q^81 - 36 * q^82 - 10 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 - 12 * q^88 + 2 * q^90 - 18 * q^91 - 4 * q^92 + 2 * q^94 - 2 * q^96 + 8 * q^97 - 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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