LMFDB - Embedded newform 1110.2.x.b.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.b.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.36603 + 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.36603 + 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +3.73205 q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.50000 - 0.866025i) q^{13} -2.73205i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.76795 + 1.59808i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.73205 + 1.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.36603 + 2.36603i) q^{21} +(-3.23205 - 1.86603i) q^{22} -2.00000i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.73205 q^{26} -1.00000 q^{27} +(-1.36603 + 2.36603i) q^{28} -7.73205i q^{29} +(0.500000 + 0.866025i) q^{30} +6.92820i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.86603 + 3.23205i) q^{33} +(-1.59808 - 2.76795i) q^{34} +(-2.36603 - 1.36603i) q^{35} -1.00000 q^{36} +(-0.500000 + 6.06218i) q^{37} +2.00000 q^{38} +(1.50000 + 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(1.09808 + 1.90192i) q^{41} +(2.36603 - 1.36603i) q^{42} +7.46410i q^{43} +(1.86603 + 3.23205i) q^{44} -1.00000i q^{45} +(-1.00000 + 1.73205i) q^{46} +1.73205 q^{47} -1.00000 q^{48} +(-0.232051 + 0.401924i) q^{49} +(-0.866025 + 0.500000i) q^{50} +3.19615i q^{51} +(1.50000 + 0.866025i) q^{52} +(-1.09808 + 1.90192i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-3.23205 + 1.86603i) q^{55} +(2.36603 - 1.36603i) q^{56} +(-1.73205 - 1.00000i) q^{57} +(-3.86603 + 6.69615i) q^{58} +(-5.59808 - 3.23205i) q^{59} -1.00000i q^{60} +(-4.09808 + 2.36603i) q^{61} +(3.46410 - 6.00000i) q^{62} -2.73205 q^{63} -1.00000 q^{64} +(-0.866025 + 1.50000i) q^{65} -3.73205i q^{66} +(3.33013 + 5.76795i) q^{67} +3.19615i q^{68} +(1.73205 - 1.00000i) q^{69} +(1.36603 + 2.36603i) q^{70} +(1.09808 + 1.90192i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.39230 q^{73} +(3.46410 - 5.00000i) q^{74} +1.00000 q^{75} +(-1.73205 - 1.00000i) q^{76} +(5.09808 + 8.83013i) q^{77} +(-0.866025 - 1.50000i) q^{78} +(-7.73205 + 4.46410i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -2.19615i q^{82} +(-2.09808 + 3.63397i) q^{83} -2.73205 q^{84} -3.19615 q^{85} +(3.73205 - 6.46410i) q^{86} +(6.69615 - 3.86603i) q^{87} -3.73205i q^{88} +(0.803848 + 0.464102i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(4.09808 + 2.36603i) q^{91} +(1.73205 - 1.00000i) q^{92} +(-6.00000 + 3.46410i) q^{93} +(-1.50000 - 0.866025i) q^{94} +(1.00000 - 1.73205i) q^{95} +(0.866025 + 0.500000i) q^{96} -4.53590i q^{97} +(0.401924 - 0.232051i) q^{98} +(-1.86603 + 3.23205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{16} + 18 q^{17} - 2 q^{21} - 6 q^{22} + 2 q^{25} - 4 q^{27} - 2 q^{28} + 2 q^{30} + 4 q^{33} + 4 q^{34} - 6 q^{35} - 4 q^{36} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 4 q^{44} - 4 q^{46} - 4 q^{48} + 6 q^{49} + 6 q^{52} + 6 q^{53} - 6 q^{55} + 6 q^{56} - 12 q^{58} - 12 q^{59} - 6 q^{61} - 4 q^{63} - 4 q^{64} - 4 q^{67} + 2 q^{70} - 6 q^{71} - 8 q^{73} + 4 q^{75} + 10 q^{77} - 24 q^{79} - 2 q^{81} + 2 q^{83} - 4 q^{84} + 8 q^{85} + 8 q^{86} + 6 q^{87} + 24 q^{89} - 2 q^{90} + 6 q^{91} - 24 q^{93} - 6 q^{94} + 4 q^{95} + 12 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^16 + 18 * q^17 - 2 * q^21 - 6 * q^22 + 2 * q^25 - 4 * q^27 - 2 * q^28 + 2 * q^30 + 4 * q^33 + 4 * q^34 - 6 * q^35 - 4 * q^36 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 4 * q^44 - 4 * q^46 - 4 * q^48 + 6 * q^49 + 6 * q^52 + 6 * q^53 - 6 * q^55 + 6 * q^56 - 12 * q^58 - 12 * q^59 - 6 * q^61 - 4 * q^63 - 4 * q^64 - 4 * q^67 + 2 * q^70 - 6 * q^71 - 8 * q^73 + 4 * q^75 + 10 * q^77 - 24 * q^79 - 2 * q^81 + 2 * q^83 - 4 * q^84 + 8 * q^85 + 8 * q^86 + 6 * q^87 + 24 * q^89 - 2 * q^90 + 6 * q^91 - 24 * q^93 - 6 * q^94 + 4 * q^95 + 12 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	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
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	1.36603	+	2.36603i	0.516309	+	0.894274i	0.999821	+	0.0189356i	$0.00602775\pi$
$7$	1.36603	+	2.36603i	0.516309	+	0.894274i	−0.483512	+	0.875338i	$0.660639\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	3.73205			1.12526			0.562628	−	0.826710i	$-0.309790\pi$
$11$	3.73205			1.12526			0.562628	+	0.826710i	$0.309790\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	0.693375	+	0.720577i	$0.256123\pi$
$14$		−	2.73205i		−	0.730171i
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.76795	+	1.59808i	0.671326	+	0.387590i	0.796579	−	0.604534i	$-0.206641\pi$
$17$	2.76795	+	1.59808i	0.671326	+	0.387590i	−0.125253	+	0.992125i	$0.539974\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−1.73205	+	1.00000i	−0.397360	+	0.229416i	−0.685344	−	0.728219i	$-0.740348\pi$
$19$	−1.73205	+	1.00000i	−0.397360	+	0.229416i	0.287984	+	0.957635i	$0.407015\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−1.36603	+	2.36603i	−0.298091	+	0.516309i
$22$	−3.23205	−	1.86603i	−0.689076	−	0.397838i
$23$		−	2.00000i		−	0.417029i	−0.978019	−	0.208514i	$-0.933137\pi$
$23$		−	2.00000i		−	0.417029i	0.978019	−	0.208514i	$-0.0668628\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.73205			−0.339683
$27$	−1.00000			−0.192450
$28$	−1.36603	+	2.36603i	−0.258155	+	0.447137i
$29$		−	7.73205i		−	1.43581i	−0.696143	−	0.717903i	$-0.745102\pi$
$29$		−	7.73205i		−	1.43581i	0.696143	−	0.717903i	$-0.254898\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$			6.92820i			1.24434i	0.782881	+	0.622171i	$0.213749\pi$
$31$			6.92820i			1.24434i	−0.782881	+	0.622171i	$0.786251\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.86603	+	3.23205i	0.324833	+	0.562628i
$34$	−1.59808	−	2.76795i	−0.274068	−	0.474699i
$35$	−2.36603	−	1.36603i	−0.399931	−	0.230900i
$36$	−1.00000			−0.166667
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$37$	−0.500000	+	6.06218i	−0.0821995	+	0.996616i
$38$	2.00000			0.324443
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	1.09808	+	1.90192i	0.171491	+	0.297031i	0.938941	−	0.344078i	$-0.111808\pi$
$41$	1.09808	+	1.90192i	0.171491	+	0.297031i	−0.767451	+	0.641108i	$0.778475\pi$
$42$	2.36603	−	1.36603i	0.365086	−	0.210782i
$43$			7.46410i			1.13826i	0.822246	+	0.569132i	$0.192721\pi$
$43$			7.46410i			1.13826i	−0.822246	+	0.569132i	$0.807279\pi$
$44$	1.86603	+	3.23205i	0.281314	+	0.487250i
$45$		−	1.00000i		−	0.149071i
$46$	−1.00000	+	1.73205i	−0.147442	+	0.255377i
$47$	1.73205			0.252646			0.126323	−	0.991989i	$-0.459682\pi$
$47$	1.73205			0.252646			0.126323	+	0.991989i	$0.459682\pi$
$48$	−1.00000			−0.144338
$49$	−0.232051	+	0.401924i	−0.0331501	+	0.0574177i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$			3.19615i			0.447551i
$52$	1.50000	+	0.866025i	0.208013	+	0.120096i
$53$	−1.09808	+	1.90192i	−0.150832	+	0.261249i	−0.931534	−	0.363655i	$-0.881529\pi$
$53$	−1.09808	+	1.90192i	−0.150832	+	0.261249i	0.780701	+	0.624904i	$0.214862\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−3.23205	+	1.86603i	−0.435810	+	0.251615i
$56$	2.36603	−	1.36603i	0.316173	−	0.182543i
$57$	−1.73205	−	1.00000i	−0.229416	−	0.132453i
$58$	−3.86603	+	6.69615i	−0.507634	+	0.879248i
$59$	−5.59808	−	3.23205i	−0.728807	−	0.420777i	0.0891783	−	0.996016i	$-0.471576\pi$
$59$	−5.59808	−	3.23205i	−0.728807	−	0.420777i	−0.817986	+	0.575239i	$0.804909\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−4.09808	+	2.36603i	−0.524705	+	0.302939i	−0.738857	−	0.673862i	$-0.764634\pi$
$61$	−4.09808	+	2.36603i	−0.524705	+	0.302939i	0.214153	+	0.976800i	$0.431301\pi$
$62$	3.46410	−	6.00000i	0.439941	−	0.762001i
$63$	−2.73205			−0.344206
$64$	−1.00000			−0.125000
$65$	−0.866025	+	1.50000i	−0.107417	+	0.186052i
$66$		−	3.73205i		−	0.459384i
$67$	3.33013	+	5.76795i	0.406840	+	0.704667i	0.994534	−	0.104416i	$-0.0332974\pi$
$67$	3.33013	+	5.76795i	0.406840	+	0.704667i	−0.587694	+	0.809083i	$0.699964\pi$
$68$			3.19615i			0.387590i
$69$	1.73205	−	1.00000i	0.208514	−	0.120386i
$70$	1.36603	+	2.36603i	0.163271	+	0.282794i
$71$	1.09808	+	1.90192i	0.130318	+	0.225717i	0.923799	−	0.382878i	$-0.125067\pi$
$71$	1.09808	+	1.90192i	0.130318	+	0.225717i	−0.793481	+	0.608595i	$0.791734\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	8.39230			0.982245			0.491122	−	0.871091i	$-0.336587\pi$
$73$	8.39230			0.982245			0.491122	+	0.871091i	$0.336587\pi$
$74$	3.46410	−	5.00000i	0.402694	−	0.581238i
$75$	1.00000			0.115470
$76$	−1.73205	−	1.00000i	−0.198680	−	0.114708i
$77$	5.09808	+	8.83013i	0.580980	+	1.00629i
$78$	−0.866025	−	1.50000i	−0.0980581	−	0.169842i
$79$	−7.73205	+	4.46410i	−0.869924	+	0.502251i	−0.867323	−	0.497746i	$-0.834161\pi$
$79$	−7.73205	+	4.46410i	−0.869924	+	0.502251i	−0.00260080	+	0.999997i	$0.500828\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	2.19615i		−	0.242524i
$83$	−2.09808	+	3.63397i	−0.230294	+	0.398881i	−0.957895	−	0.287120i	$-0.907302\pi$
$83$	−2.09808	+	3.63397i	−0.230294	+	0.398881i	0.727601	+	0.686001i	$0.240635\pi$
$84$	−2.73205			−0.298091
$85$	−3.19615			−0.346671
$86$	3.73205	−	6.46410i	0.402437	−	0.697042i
$87$	6.69615	−	3.86603i	0.717903	−	0.414481i
$88$		−	3.73205i		−	0.397838i
$89$	0.803848	+	0.464102i	0.0852077	+	0.0491947i	0.541998	−	0.840379i	$-0.317668\pi$
$89$	0.803848	+	0.464102i	0.0852077	+	0.0491947i	−0.456791	+	0.889574i	$0.651001\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	4.09808	+	2.36603i	0.429595	+	0.248027i
$92$	1.73205	−	1.00000i	0.180579	−	0.104257i
$93$	−6.00000	+	3.46410i	−0.622171	+	0.359211i
$94$	−1.50000	−	0.866025i	−0.154713	−	0.0893237i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$		−	4.53590i		−	0.460551i	−0.973126	−	0.230275i	$-0.926037\pi$
$97$		−	4.53590i		−	0.460551i	0.973126	−	0.230275i	$-0.0739627\pi$
$98$	0.401924	−	0.232051i	0.0406004	−	0.0234407i
$99$	−1.86603	+	3.23205i	−0.187543	+	0.324833i
$100$	1.00000			0.100000
$101$	1.53590			0.152828			0.0764138	−	0.997076i	$-0.475653\pi$
$101$	1.53590			0.152828			0.0764138	+	0.997076i	$0.475653\pi$
$102$	1.59808	−	2.76795i	0.158233	−	0.274068i
$103$		−	0.196152i		−	0.0193275i	−0.999953	−	0.00966374i	$-0.996924\pi$
$103$		−	0.196152i		−	0.0193275i	0.999953	−	0.00966374i	$-0.00307611\pi$
$104$	−0.866025	−	1.50000i	−0.0849208	−	0.147087i
$105$		−	2.73205i		−	0.266621i
$106$	1.90192	−	1.09808i	0.184731	−	0.106655i
$107$	6.09808	+	10.5622i	0.589523	+	1.02108i	0.994295	+	0.106666i	$0.0340177\pi$
$107$	6.09808	+	10.5622i	0.589523	+	1.02108i	−0.404772	+	0.914418i	$0.632649\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.83013	−	3.36603i	−0.558425	−	0.322407i	0.194088	−	0.980984i	$-0.437825\pi$
$109$	−5.83013	−	3.36603i	−0.558425	−	0.322407i	−0.752513	+	0.658577i	$0.771159\pi$
$110$	3.73205			0.355837
$111$	−5.50000	+	2.59808i	−0.522037	+	0.246598i
$112$	−2.73205			−0.258155
$113$	−2.30385	−	1.33013i	−0.216728	−	0.125128i	0.387706	−	0.921783i	$-0.373267\pi$
$113$	−2.30385	−	1.33013i	−0.216728	−	0.125128i	−0.604434	+	0.796655i	$0.706601\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$	6.69615	−	3.86603i	0.621722	−	0.358951i
$117$			1.73205i			0.160128i
$118$	3.23205	+	5.59808i	0.297534	+	0.515345i
$119$			8.73205i			0.800466i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	2.92820			0.266200
$122$	4.73205			0.428420
$123$	−1.09808	+	1.90192i	−0.0990102	+	0.171491i
$124$	−6.00000	+	3.46410i	−0.538816	+	0.311086i
$125$			1.00000i			0.0894427i
$126$	2.36603	+	1.36603i	0.210782	+	0.121695i
$127$	1.36603	−	2.36603i	0.121215	−	0.209951i	−0.799032	−	0.601289i	$-0.794654\pi$
$127$	1.36603	−	2.36603i	0.121215	−	0.209951i	0.920247	+	0.391338i	$0.127988\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.46410	+	3.73205i	−0.569132	+	0.328589i
$130$	1.50000	−	0.866025i	0.131559	−	0.0759555i
$131$	−9.86603	−	5.69615i	−0.861999	−	0.497675i	0.00268243	−	0.999996i	$-0.499146\pi$
$131$	−9.86603	−	5.69615i	−0.861999	−	0.497675i	−0.864681	+	0.502321i	$0.832479\pi$
$132$	−1.86603	+	3.23205i	−0.162417	+	0.281314i
$133$	−4.73205	−	2.73205i	−0.410321	−	0.236899i
$134$		−	6.66025i		−	0.575358i
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$	1.59808	−	2.76795i	0.137034	−	0.237350i
$137$	11.0000			0.939793			0.469897	−	0.882721i	$-0.344291\pi$
$137$	11.0000			0.939793			0.469897	+	0.882721i	$0.344291\pi$
$138$	−2.00000			−0.170251
$139$	2.19615	−	3.80385i	0.186275	−	0.322638i	−0.757730	−	0.652568i	$-0.773692\pi$
$139$	2.19615	−	3.80385i	0.186275	−	0.322638i	0.944005	+	0.329930i	$0.107025\pi$
$140$		−	2.73205i		−	0.230900i
$141$	0.866025	+	1.50000i	0.0729325	+	0.126323i
$142$		−	2.19615i		−	0.184297i
$143$	5.59808	−	3.23205i	0.468135	−	0.270278i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.86603	+	6.69615i	0.321056	+	0.556085i
$146$	−7.26795	−	4.19615i	−0.601500	−	0.347276i
$147$	−0.464102			−0.0382785
$148$	−5.50000	+	2.59808i	−0.452097	+	0.213561i
$149$	−9.92820			−0.813350			−0.406675	−	0.913573i	$-0.633312\pi$
$149$	−9.92820			−0.813350			−0.406675	+	0.913573i	$0.633312\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$	9.46410	+	16.3923i	0.770178	+	1.33399i	0.937465	+	0.348079i	$0.113166\pi$
$151$	9.46410	+	16.3923i	0.770178	+	1.33399i	−0.167288	+	0.985908i	$0.553501\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	−2.76795	+	1.59808i	−0.223775	+	0.129197i
$154$		−	10.1962i		−	0.821629i
$155$	−3.46410	−	6.00000i	−0.278243	−	0.481932i
$156$			1.73205i			0.138675i
$157$	7.76795	−	13.4545i	0.619950	−	1.07378i	−0.369545	−	0.929213i	$-0.620486\pi$
$157$	7.76795	−	13.4545i	0.619950	−	1.07378i	0.989494	−	0.144572i	$-0.0461804\pi$
$158$	8.92820			0.710290
$159$	−2.19615			−0.174166
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	4.73205	−	2.73205i	0.372938	−	0.215316i
$162$			1.00000i			0.0785674i
$163$	13.4545	+	7.76795i	1.05384	+	0.608433i	0.923721	−	0.383066i	$-0.125132\pi$
$163$	13.4545	+	7.76795i	1.05384	+	0.608433i	0.130115	+	0.991499i	$0.458465\pi$
$164$	−1.09808	+	1.90192i	−0.0857453	+	0.148515i
$165$	−3.23205	−	1.86603i	−0.251615	−	0.145270i
$166$	3.63397	−	2.09808i	0.282051	−	0.162842i
$167$	20.5981	−	11.8923i	1.59393	−	0.920254i	0.601303	−	0.799021i	$-0.294649\pi$
$167$	20.5981	−	11.8923i	1.59393	−	0.920254i	0.992624	−	0.121233i	$-0.0386848\pi$
$168$	2.36603	+	1.36603i	0.182543	+	0.105391i
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$	2.76795	+	1.59808i	0.212292	+	0.122567i
$171$		−	2.00000i		−	0.152944i
$172$	−6.46410	+	3.73205i	−0.492883	+	0.284566i
$173$	0.169873	−	0.294229i	0.0129152	−	0.0223698i	−0.859496	−	0.511143i	$-0.829222\pi$
$173$	0.169873	−	0.294229i	0.0129152	−	0.0223698i	0.872411	+	0.488773i	$0.162556\pi$
$174$	−7.73205			−0.586165
$175$	2.73205			0.206524
$176$	−1.86603	+	3.23205i	−0.140657	+	0.243625i
$177$		−	6.46410i		−	0.485872i
$178$	−0.464102	−	0.803848i	−0.0347859	−	0.0602509i
$179$		−	4.92820i		−	0.368351i	−0.982893	−	0.184176i	$-0.941038\pi$
$179$		−	4.92820i		−	0.368351i	0.982893	−	0.184176i	$-0.0589615\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	0.900794	−	0.434246i	$-0.142985\pi$
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	−0.826465	+	0.562988i	$0.809652\pi$
$182$	−2.36603	−	4.09808i	−0.175381	−	0.303770i
$183$	−4.09808	−	2.36603i	−0.302939	−	0.174902i
$184$	−2.00000			−0.147442
$185$	−2.59808	−	5.50000i	−0.191014	−	0.404368i
$186$	6.92820			0.508001
$187$	10.3301	+	5.96410i	0.755414	+	0.436138i
$188$	0.866025	+	1.50000i	0.0631614	+	0.109399i
$189$	−1.36603	−	2.36603i	−0.0993637	−	0.172103i
$190$	−1.73205	+	1.00000i	−0.125656	+	0.0725476i
$191$		−	10.1962i		−	0.737768i	−0.929476	−	0.368884i	$-0.879740\pi$
$191$		−	10.1962i		−	0.737768i	0.929476	−	0.368884i	$-0.120260\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$		−	0.196152i		−	0.0141194i	−0.999975	−	0.00705968i	$-0.997753\pi$
$193$		−	0.196152i		−	0.0141194i	0.999975	−	0.00705968i	$-0.00224718\pi$
$194$	−2.26795	+	3.92820i	−0.162829	+	0.282029i
$195$	−1.73205			−0.124035
$196$	−0.464102			−0.0331501
$197$	−4.46410	+	7.73205i	−0.318054	+	0.550886i	−0.980082	−	0.198593i	$-0.936363\pi$
$197$	−4.46410	+	7.73205i	−0.318054	+	0.550886i	0.662028	+	0.749479i	$0.269696\pi$
$198$	3.23205	−	1.86603i	0.229692	−	0.132613i
$199$		−	26.3205i		−	1.86581i	−0.360121	−	0.932906i	$-0.617265\pi$
$199$		−	26.3205i		−	1.86581i	0.360121	−	0.932906i	$-0.382735\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−3.33013	+	5.76795i	−0.234889	+	0.406840i
$202$	−1.33013	−	0.767949i	−0.0935874	−	0.0540327i
$203$	18.2942	−	10.5622i	1.28400	−	0.741320i
$204$	−2.76795	+	1.59808i	−0.193795	+	0.111888i
$205$	−1.90192	−	1.09808i	−0.132836	−	0.0766930i
$206$	−0.0980762	+	0.169873i	−0.00683329	+	0.0118356i
$207$	1.73205	+	1.00000i	0.120386	+	0.0695048i
$208$			1.73205i			0.120096i
$209$	−6.46410	+	3.73205i	−0.447131	+	0.258151i
$210$	−1.36603	+	2.36603i	−0.0942647	+	0.163271i
$211$	11.3205			0.779336			0.389668	−	0.920955i	$-0.372590\pi$
$211$	11.3205			0.779336			0.389668	+	0.920955i	$0.372590\pi$
$212$	−2.19615			−0.150832
$213$	−1.09808	+	1.90192i	−0.0752389	+	0.130318i
$214$		−	12.1962i		−	0.833712i
$215$	−3.73205	−	6.46410i	−0.254524	−	0.440848i
$216$			1.00000i			0.0680414i
$217$	−16.3923	+	9.46410i	−1.11278	+	0.642465i
$218$	3.36603	+	5.83013i	0.227976	+	0.394866i
$219$	4.19615	+	7.26795i	0.283550	+	0.491122i
$220$	−3.23205	−	1.86603i	−0.217905	−	0.125807i
$221$	5.53590			0.372385
$222$	6.06218	+	0.500000i	0.406867	+	0.0335578i
$223$	−21.4641			−1.43734			−0.718671	−	0.695350i	$-0.755249\pi$
$223$	−21.4641			−1.43734			−0.718671	+	0.695350i	$0.755249\pi$
$224$	2.36603	+	1.36603i	0.158087	+	0.0912714i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	1.33013	+	2.30385i	0.0884787	+	0.153250i
$227$	4.09808	−	2.36603i	0.271999	−	0.157039i	−0.357797	−	0.933799i	$-0.616472\pi$
$227$	4.09808	−	2.36603i	0.271999	−	0.157039i	0.629796	+	0.776761i	$0.283139\pi$
$228$		−	2.00000i		−	0.132453i
$229$	−11.0263	−	19.0981i	−0.728637	−	1.26204i	−0.957459	−	0.288568i	$-0.906821\pi$
$229$	−11.0263	−	19.0981i	−0.728637	−	1.26204i	0.228822	−	0.973468i	$-0.426513\pi$
$230$		−	2.00000i		−	0.131876i
$231$	−5.09808	+	8.83013i	−0.335429	+	0.580980i
$232$	−7.73205			−0.507634
$233$	−9.46410			−0.620014			−0.310007	−	0.950734i	$-0.600331\pi$
$233$	−9.46410			−0.620014			−0.310007	+	0.950734i	$0.600331\pi$
$234$	0.866025	−	1.50000i	0.0566139	−	0.0980581i
$235$	−1.50000	+	0.866025i	−0.0978492	+	0.0564933i
$236$		−	6.46410i		−	0.420777i
$237$	−7.73205	−	4.46410i	−0.502251	−	0.289975i
$238$	4.36603	−	7.56218i	0.283007	−	0.490183i
$239$	−18.5885	−	10.7321i	−1.20239	−	0.694199i	−0.241302	−	0.970450i	$-0.577574\pi$
$239$	−18.5885	−	10.7321i	−1.20239	−	0.694199i	−0.961085	+	0.276251i	$0.910908\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	0.232051	−	0.133975i	0.0149477	−	0.00863006i	−0.492508	−	0.870308i	$-0.663920\pi$
$241$	0.232051	−	0.133975i	0.0149477	−	0.00863006i	0.507455	+	0.861678i	$0.330586\pi$
$242$	−2.53590	−	1.46410i	−0.163014	−	0.0941160i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.09808	−	2.36603i	−0.262352	−	0.151469i
$245$		−	0.464102i		−	0.0296504i
$246$	1.90192	−	1.09808i	0.121262	−	0.0700108i
$247$	−1.73205	+	3.00000i	−0.110208	+	0.190885i
$248$	6.92820			0.439941
$249$	−4.19615			−0.265920
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$		−	26.3205i		−	1.66134i	−0.556768	−	0.830668i	$-0.687959\pi$
$251$		−	26.3205i		−	1.66134i	0.556768	−	0.830668i	$-0.312041\pi$
$252$	−1.36603	−	2.36603i	−0.0860515	−	0.149046i
$253$		−	7.46410i		−	0.469264i
$254$	−2.36603	+	1.36603i	−0.148458	+	0.0857121i
$255$	−1.59808	−	2.76795i	−0.100075	−	0.173336i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.23205	−	5.33013i	−0.575880	−	0.332484i	0.183615	−	0.982998i	$-0.441220\pi$
$257$	−9.23205	−	5.33013i	−0.575880	−	0.332484i	−0.759494	+	0.650514i	$0.774553\pi$
$258$	7.46410			0.464695
$259$	−15.0263	+	7.09808i	−0.933688	+	0.441053i
$260$	−1.73205			−0.107417
$261$	6.69615	+	3.86603i	0.414481	+	0.239301i
$262$	5.69615	+	9.86603i	0.351909	+	0.609525i
$263$	5.66025	+	9.80385i	0.349026	+	0.604531i	0.986077	−	0.166291i	$-0.0531791\pi$
$263$	5.66025	+	9.80385i	0.349026	+	0.604531i	−0.637051	+	0.770822i	$0.719846\pi$
$264$	3.23205	−	1.86603i	0.198919	−	0.114846i
$265$		−	2.19615i		−	0.134909i
$266$	2.73205	+	4.73205i	0.167513	+	0.290141i
$267$			0.928203i			0.0568051i
$268$	−3.33013	+	5.76795i	−0.203420	+	0.352334i
$269$	−14.9282			−0.910189			−0.455094	−	0.890443i	$-0.650394\pi$
$269$	−14.9282			−0.910189			−0.455094	+	0.890443i	$0.650394\pi$
$270$	−1.00000			−0.0608581
$271$	11.3301	−	19.6244i	0.688256	−	1.19209i	−0.284145	−	0.958781i	$-0.591710\pi$
$271$	11.3301	−	19.6244i	0.688256	−	1.19209i	0.972402	−	0.233313i	$-0.0749568\pi$
$272$	−2.76795	+	1.59808i	−0.167832	+	0.0968976i
$273$			4.73205i			0.286397i
$274$	−9.52628	−	5.50000i	−0.575504	−	0.332267i
$275$	1.86603	−	3.23205i	0.112526	−	0.194900i
$276$	1.73205	+	1.00000i	0.104257	+	0.0601929i
$277$	−4.16025	+	2.40192i	−0.249965	+	0.144318i	−0.619748	−	0.784801i	$-0.712765\pi$
$277$	−4.16025	+	2.40192i	−0.249965	+	0.144318i	0.369783	+	0.929118i	$0.379432\pi$
$278$	−3.80385	+	2.19615i	−0.228140	+	0.131716i
$279$	−6.00000	−	3.46410i	−0.359211	−	0.207390i
$280$	−1.36603	+	2.36603i	−0.0816356	+	0.141397i
$281$	−3.00000	−	1.73205i	−0.178965	−	0.103325i	0.407841	−	0.913053i	$-0.366282\pi$
$281$	−3.00000	−	1.73205i	−0.178965	−	0.103325i	−0.586806	+	0.809727i	$0.699615\pi$
$282$		−	1.73205i		−	0.103142i
$283$	20.3827	−	11.7679i	1.21162	−	0.699532i	0.248512	−	0.968629i	$-0.420059\pi$
$283$	20.3827	−	11.7679i	1.21162	−	0.699532i	0.963113	+	0.269097i	$0.0867252\pi$
$284$	−1.09808	+	1.90192i	−0.0651588	+	0.112858i
$285$	2.00000			0.118470
$286$	−6.46410			−0.382230
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$			1.00000i			0.0589256i
$289$	−3.39230	−	5.87564i	−0.199547	−	0.345626i
$290$		−	7.73205i		−	0.454042i
$291$	3.92820	−	2.26795i	0.230275	−	0.132950i
$292$	4.19615	+	7.26795i	0.245561	+	0.425325i
$293$	−1.73205	−	3.00000i	−0.101187	−	0.175262i	0.810987	−	0.585065i	$-0.198931\pi$
$293$	−1.73205	−	3.00000i	−0.101187	−	0.175262i	−0.912174	+	0.409803i	$0.865598\pi$
$294$	0.401924	+	0.232051i	0.0234407	+	0.0135335i
$295$	6.46410			0.376355
$296$	6.06218	+	0.500000i	0.352357	+	0.0290619i
$297$	−3.73205			−0.216556
$298$	8.59808	+	4.96410i	0.498073	+	0.287563i
$299$	−1.73205	−	3.00000i	−0.100167	−	0.173494i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−17.6603	+	10.1962i	−1.01792	+	0.587696i
$302$		−	18.9282i		−	1.08920i
$303$	0.767949	+	1.33013i	0.0441175	+	0.0764138i
$304$		−	2.00000i		−	0.114708i
$305$	2.36603	−	4.09808i	0.135478	−	0.234655i
$306$	3.19615			0.182712
$307$	−12.5359			−0.715462			−0.357731	−	0.933825i	$-0.616449\pi$
$307$	−12.5359			−0.715462			−0.357731	+	0.933825i	$0.616449\pi$
$308$	−5.09808	+	8.83013i	−0.290490	+	0.503143i
$309$	0.169873	−	0.0980762i	0.00966374	−	0.00557936i
$310$			6.92820i			0.393496i
$311$	1.09808	+	0.633975i	0.0622662	+	0.0359494i	0.530810	−	0.847491i	$-0.321888\pi$
$311$	1.09808	+	0.633975i	0.0622662	+	0.0359494i	−0.468544	+	0.883440i	$0.655221\pi$
$312$	0.866025	−	1.50000i	0.0490290	−	0.0849208i
$313$	7.73205	+	4.46410i	0.437041	+	0.252326i	0.702342	−	0.711840i	$-0.252138\pi$
$313$	7.73205	+	4.46410i	0.437041	+	0.252326i	−0.265300	+	0.964166i	$0.585471\pi$
$314$	−13.4545	+	7.76795i	−0.759280	+	0.438371i
$315$	2.36603	−	1.36603i	0.133310	−	0.0769668i
$316$	−7.73205	−	4.46410i	−0.434962	−	0.251125i
$317$	4.36603	−	7.56218i	0.245220	−	0.424734i	−0.716973	−	0.697101i	$-0.754473\pi$
$317$	4.36603	−	7.56218i	0.245220	−	0.424734i	0.962194	+	0.272367i	$0.0878063\pi$
$318$	1.90192	+	1.09808i	0.106655	+	0.0615771i
$319$		−	28.8564i		−	1.61565i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−6.09808	+	10.5622i	−0.340361	+	0.589523i
$322$	−5.46410			−0.304502
$323$	−6.39230			−0.355677
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		−	1.73205i		−	0.0960769i
$326$	−7.76795	−	13.4545i	−0.430227	−	0.745175i
$327$		−	6.73205i		−	0.372283i
$328$	1.90192	−	1.09808i	0.105016	−	0.0606311i
$329$	2.36603	+	4.09808i	0.130443	+	0.225934i
$330$	1.86603	+	3.23205i	0.102721	+	0.177919i
$331$	−8.95448	−	5.16987i	−0.492183	−	0.284162i	0.233297	−	0.972406i	$-0.425049\pi$
$331$	−8.95448	−	5.16987i	−0.492183	−	0.284162i	−0.725480	+	0.688244i	$0.758382\pi$
$332$	−4.19615			−0.230294
$333$	−5.00000	−	3.46410i	−0.273998	−	0.189832i
$334$	−23.7846			−1.30144
$335$	−5.76795	−	3.33013i	−0.315137	−	0.181944i
$336$	−1.36603	−	2.36603i	−0.0745228	−	0.129077i
$337$	3.83013	+	6.63397i	0.208640	+	0.361376i	0.951286	−	0.308308i	$-0.0997629\pi$
$337$	3.83013	+	6.63397i	0.208640	+	0.361376i	−0.742646	+	0.669684i	$0.766430\pi$
$338$	8.66025	−	5.00000i	0.471056	−	0.271964i
$339$		−	2.66025i		−	0.144485i
$340$	−1.59808	−	2.76795i	−0.0866679	−	0.150113i
$341$			25.8564i			1.40020i
$342$	−1.00000	+	1.73205i	−0.0540738	+	0.0936586i
$343$	17.8564			0.964155
$344$	7.46410			0.402437
$345$	−1.00000	+	1.73205i	−0.0538382	+	0.0932505i
$346$	−0.294229	+	0.169873i	−0.0158178	+	0.00913243i
$347$		−	15.0718i		−	0.809096i	−0.914517	−	0.404548i	$-0.867429\pi$
$347$		−	15.0718i		−	0.809096i	0.914517	−	0.404548i	$-0.132571\pi$
$348$	6.69615	+	3.86603i	0.358951	+	0.207241i
$349$	8.19615	−	14.1962i	0.438730	−	0.759903i	−0.558862	−	0.829261i	$-0.688762\pi$
$349$	8.19615	−	14.1962i	0.438730	−	0.759903i	0.997592	+	0.0693582i	$0.0220951\pi$
$350$	−2.36603	−	1.36603i	−0.126469	−	0.0730171i
$351$	−1.50000	+	0.866025i	−0.0800641	+	0.0462250i
$352$	3.23205	−	1.86603i	0.172269	−	0.0994595i
$353$	−6.80385	−	3.92820i	−0.362132	−	0.209077i	0.307883	−	0.951424i	$-0.400379\pi$
$353$	−6.80385	−	3.92820i	−0.362132	−	0.209077i	−0.670016	+	0.742347i	$0.733713\pi$
$354$	−3.23205	+	5.59808i	−0.171782	+	0.297534i
$355$	−1.90192	−	1.09808i	−0.100944	−	0.0582798i
$356$			0.928203i			0.0491947i
$357$	−7.56218	+	4.36603i	−0.400233	+	0.231075i
$358$	−2.46410	+	4.26795i	−0.130232	+	0.225568i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$	−1.00000			−0.0527046
$361$	−7.50000	+	12.9904i	−0.394737	+	0.683704i
$362$		−	2.00000i		−	0.105118i
$363$	1.46410	+	2.53590i	0.0768454	+	0.133100i
$364$			4.73205i			0.248027i
$365$	−7.26795	+	4.19615i	−0.380422	+	0.219637i
$366$	2.36603	+	4.09808i	0.123674	+	0.214210i
$367$	10.1962	+	17.6603i	0.532235	+	0.921858i	0.999292	+	0.0376305i	$0.0119810\pi$
$367$	10.1962	+	17.6603i	0.532235	+	0.921858i	−0.467057	+	0.884227i	$0.654686\pi$
$368$	1.73205	+	1.00000i	0.0902894	+	0.0521286i
$369$	−2.19615			−0.114327
$370$	−0.500000	+	6.06218i	−0.0259938	+	0.315158i
$371$	−6.00000			−0.311504
$372$	−6.00000	−	3.46410i	−0.311086	−	0.179605i
$373$	−18.1962	−	31.5167i	−0.942161	−	1.63187i	−0.761338	−	0.648355i	$-0.775457\pi$
$373$	−18.1962	−	31.5167i	−0.942161	−	1.63187i	−0.180823	−	0.983516i	$-0.557876\pi$
$374$	−5.96410	−	10.3301i	−0.308396	−	0.534158i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$		−	1.73205i		−	0.0893237i
$377$	−6.69615	−	11.5981i	−0.344869	−	0.597331i
$378$			2.73205i			0.140522i
$379$	11.7583	−	20.3660i	0.603985	−	1.04613i	−0.388226	−	0.921564i	$-0.626912\pi$
$379$	11.7583	−	20.3660i	0.603985	−	1.04613i	0.992211	−	0.124568i	$-0.0397546\pi$
$380$	2.00000			0.102598
$381$	2.73205			0.139967
$382$	−5.09808	+	8.83013i	−0.260840	+	0.451789i
$383$	19.6699	−	11.3564i	1.00508	−	0.580285i	0.0953351	−	0.995445i	$-0.469608\pi$
$383$	19.6699	−	11.3564i	1.00508	−	0.580285i	0.909748	+	0.415160i	$0.136274\pi$
$384$			1.00000i			0.0510310i
$385$	−8.83013	−	5.09808i	−0.450025	−	0.259822i
$386$	−0.0980762	+	0.169873i	−0.00499195	+	0.00864631i
$387$	−6.46410	−	3.73205i	−0.328589	−	0.189711i
$388$	3.92820	−	2.26795i	0.199424	−	0.115138i
$389$	1.39230	−	0.803848i	0.0705927	−	0.0407567i	−0.464288	−	0.885684i	$-0.653690\pi$
$389$	1.39230	−	0.803848i	0.0705927	−	0.0407567i	0.534881	+	0.844927i	$0.320356\pi$
$390$	1.50000	+	0.866025i	0.0759555	+	0.0438529i
$391$	3.19615	−	5.53590i	0.161636	−	0.279962i
$392$	0.401924	+	0.232051i	0.0203002	+	0.0117203i
$393$		−	11.3923i		−	0.574666i
$394$	7.73205	−	4.46410i	0.389535	−	0.224898i
$395$	4.46410	−	7.73205i	0.224613	−	0.389042i
$396$	−3.73205			−0.187543
$397$	−18.4641			−0.926687			−0.463343	−	0.886179i	$-0.653350\pi$
$397$	−18.4641			−0.926687			−0.463343	+	0.886179i	$0.653350\pi$
$398$	−13.1603	+	22.7942i	−0.659664	+	1.14257i
$399$		−	5.46410i		−	0.273547i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			8.87564i			0.443229i	0.975134	+	0.221614i	$0.0711326\pi$
$401$			8.87564i			0.443229i	−0.975134	+	0.221614i	$0.928867\pi$
$402$	5.76795	−	3.33013i	0.287679	−	0.166092i
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$	0.767949	+	1.33013i	0.0382069	+	0.0661763i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−21.1244			−1.04838
$407$	−1.86603	+	22.6244i	−0.0924954	+	1.12145i
$408$	3.19615			0.158233
$409$	19.1603	+	11.0622i	0.947414	+	0.546989i	0.892277	−	0.451489i	$-0.149107\pi$
$409$	19.1603	+	11.0622i	0.947414	+	0.546989i	0.0551371	+	0.998479i	$0.482440\pi$
$410$	1.09808	+	1.90192i	0.0542301	+	0.0939293i
$411$	5.50000	+	9.52628i	0.271295	+	0.469897i
$412$	0.169873	−	0.0980762i	0.00836904	−	0.00483187i
$413$		−	17.6603i		−	0.869004i
$414$	−1.00000	−	1.73205i	−0.0491473	−	0.0851257i
$415$		−	4.19615i		−	0.205981i
$416$	0.866025	−	1.50000i	0.0424604	−	0.0735436i
$417$	4.39230			0.215092
$418$	7.46410			0.365081
$419$	−18.9282	+	32.7846i	−0.924703	+	1.60163i	−0.132665	+	0.991161i	$0.542354\pi$
$419$	−18.9282	+	32.7846i	−0.924703	+	1.60163i	−0.792038	+	0.610472i	$0.790980\pi$
$420$	2.36603	−	1.36603i	0.115450	−	0.0666552i
$421$		−	12.3397i		−	0.601402i	−0.953718	−	0.300701i	$-0.902779\pi$
$421$		−	12.3397i		−	0.601402i	0.953718	−	0.300701i	$-0.0972207\pi$
$422$	−9.80385	−	5.66025i	−0.477244	−	0.275537i
$423$	−0.866025	+	1.50000i	−0.0421076	+	0.0729325i
$424$	1.90192	+	1.09808i	0.0923656	+	0.0533273i
$425$	2.76795	−	1.59808i	0.134265	−	0.0775181i
$426$	1.90192	−	1.09808i	0.0921485	−	0.0532020i
$427$	−11.1962	−	6.46410i	−0.541820	−	0.312820i
$428$	−6.09808	+	10.5622i	−0.294762	+	0.510542i
$429$	5.59808	+	3.23205i	0.270278	+	0.156045i
$430$			7.46410i			0.359951i
$431$	−30.7583	+	17.7583i	−1.48158	+	0.855389i	−0.999782	−	0.0208953i	$-0.993348\pi$
$431$	−30.7583	+	17.7583i	−1.48158	+	0.855389i	−0.481795	+	0.876284i	$0.660015\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	13.0718			0.628190			0.314095	−	0.949391i	$-0.398299\pi$
$433$	13.0718			0.628190			0.314095	+	0.949391i	$0.398299\pi$
$434$	18.9282			0.908583
$435$	−3.86603	+	6.69615i	−0.185362	+	0.321056i
$436$		−	6.73205i		−	0.322407i
$437$	2.00000	+	3.46410i	0.0956730	+	0.165710i
$438$		−	8.39230i		−	0.401000i
$439$	32.0429	−	18.5000i	1.52933	−	0.882957i	0.529936	−	0.848038i	$-0.322216\pi$
$439$	32.0429	−	18.5000i	1.52933	−	0.882957i	0.999390	−	0.0349192i	$-0.0111174\pi$
$440$	1.86603	+	3.23205i	0.0889593	+	0.154082i
$441$	−0.232051	−	0.401924i	−0.0110500	−	0.0191392i
$442$	−4.79423	−	2.76795i	−0.228038	−	0.131658i
$443$	37.3731			1.77565			0.887824	−	0.460183i	$-0.152216\pi$
$443$	37.3731			1.77565			0.887824	+	0.460183i	$0.152216\pi$
$444$	−5.00000	−	3.46410i	−0.237289	−	0.164399i
$445$	−0.928203			−0.0440011
$446$	18.5885	+	10.7321i	0.880189	+	0.508177i
$447$	−4.96410	−	8.59808i	−0.234794	−	0.406675i
$448$	−1.36603	−	2.36603i	−0.0645386	−	0.111784i
$449$	14.5359	−	8.39230i	0.685991	−	0.396057i	−0.116117	−	0.993236i	$-0.537045\pi$
$449$	14.5359	−	8.39230i	0.685991	−	0.396057i	0.802109	+	0.597178i	$0.203711\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	4.09808	+	7.09808i	0.192971	+	0.334235i
$452$		−	2.66025i		−	0.125128i
$453$	−9.46410	+	16.3923i	−0.444662	+	0.770178i
$454$	−4.73205			−0.222086
$455$	−4.73205			−0.221842
$456$	−1.00000	+	1.73205i	−0.0468293	+	0.0811107i
$457$	16.7321	−	9.66025i	0.782692	−	0.451888i	−0.0546913	−	0.998503i	$-0.517417\pi$
$457$	16.7321	−	9.66025i	0.782692	−	0.451888i	0.837384	+	0.546616i	$0.184084\pi$
$458$			22.0526i			1.03045i
$459$	−2.76795	−	1.59808i	−0.129197	−	0.0745918i
$460$	−1.00000	+	1.73205i	−0.0466252	+	0.0807573i
$461$	30.8205	+	17.7942i	1.43545	+	0.828760i	0.997529	−	0.0702517i	$-0.0223803\pi$
$461$	30.8205	+	17.7942i	1.43545	+	0.828760i	0.437925	+	0.899012i	$0.355714\pi$
$462$	8.83013	−	5.09808i	0.410815	−	0.237184i
$463$	6.46410	−	3.73205i	0.300412	−	0.173443i	−0.342216	−	0.939621i	$-0.611177\pi$
$463$	6.46410	−	3.73205i	0.300412	−	0.173443i	0.642628	+	0.766178i	$0.277844\pi$
$464$	6.69615	+	3.86603i	0.310861	+	0.179476i
$465$	3.46410	−	6.00000i	0.160644	−	0.278243i
$466$	8.19615	+	4.73205i	0.379679	+	0.219208i
$467$			11.8564i			0.548649i	0.961637	+	0.274325i	$0.0884542\pi$
$467$			11.8564i			0.548649i	−0.961637	+	0.274325i	$0.911546\pi$
$468$	−1.50000	+	0.866025i	−0.0693375	+	0.0400320i
$469$	−9.09808	+	15.7583i	−0.420110	+	0.727652i
$470$	1.73205			0.0798935
$471$	15.5359			0.715856
$472$	−3.23205	+	5.59808i	−0.148767	+	0.257672i
$473$			27.8564i			1.28084i
$474$	4.46410	+	7.73205i	0.205043	+	0.355145i
$475$			2.00000i			0.0917663i
$476$	−7.56218	+	4.36603i	−0.346612	+	0.200116i
$477$	−1.09808	−	1.90192i	−0.0502775	−	0.0870831i
$478$	10.7321	+	18.5885i	0.490873	+	0.850216i
$479$	27.9282	+	16.1244i	1.27607	+	0.736741i	0.976124	−	0.217215i	$-0.0696972\pi$
$479$	27.9282	+	16.1244i	1.27607	+	0.736741i	0.299948	+	0.953955i	$0.403031\pi$
$480$	−1.00000			−0.0456435
$481$	4.50000	+	9.52628i	0.205182	+	0.434361i
$482$	−0.267949			−0.0122048
$483$	4.73205	+	2.73205i	0.215316	+	0.124313i
$484$	1.46410	+	2.53590i	0.0665501	+	0.115268i
$485$	2.26795	+	3.92820i	0.102982	+	0.178371i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$			24.9282i			1.12960i	0.825226	+	0.564802i	$0.191048\pi$
$487$			24.9282i			1.12960i	−0.825226	+	0.564802i	$0.808952\pi$
$488$	2.36603	+	4.09808i	0.107105	+	0.185511i
$489$			15.5359i			0.702558i
$490$	−0.232051	+	0.401924i	−0.0104830	+	0.0181571i
$491$	16.0000			0.722070			0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000			0.722070			0.361035	+	0.932552i	$0.382424\pi$
$492$	−2.19615			−0.0990102
$493$	12.3564	−	21.4019i	0.556505	−	0.963894i
$494$	3.00000	−	1.73205i	0.134976	−	0.0779287i
$495$		−	3.73205i		−	0.167743i
$496$	−6.00000	−	3.46410i	−0.269408	−	0.155543i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$	3.63397	+	2.09808i	0.162842	+	0.0940170i
$499$	26.3660	−	15.2224i	1.18031	−	0.681450i	0.224220	−	0.974539i	$-0.428017\pi$
$499$	26.3660	−	15.2224i	1.18031	−	0.681450i	0.956085	+	0.293089i	$0.0946832\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	20.5981	+	11.8923i	0.920254	+	0.531309i
$502$	−13.1603	+	22.7942i	−0.587371	+	1.01736i
$503$	−20.5981	−	11.8923i	−0.918423	−	0.530252i	−0.0352913	−	0.999377i	$-0.511236\pi$
$503$	−20.5981	−	11.8923i	−0.918423	−	0.530252i	−0.883132	+	0.469125i	$0.844569\pi$
$504$			2.73205i			0.121695i
$505$	−1.33013	+	0.767949i	−0.0591899	+	0.0341733i
$506$	−3.73205	+	6.46410i	−0.165910	+	0.287364i
$507$	−10.0000			−0.444116
$508$	2.73205			0.121215
$509$	−17.3923	+	30.1244i	−0.770900	+	1.33524i	0.166170	+	0.986097i	$0.446860\pi$
$509$	−17.3923	+	30.1244i	−0.770900	+	1.33524i	−0.937070	+	0.349141i	$0.886473\pi$
$510$			3.19615i			0.141528i
$511$	11.4641	+	19.8564i	0.507142	+	0.878396i
$512$			1.00000i			0.0441942i
$513$	1.73205	−	1.00000i	0.0764719	−	0.0441511i
$514$	5.33013	+	9.23205i	0.235102	+	0.407208i
$515$	0.0980762	+	0.169873i	0.00432175	+	0.00748550i
$516$	−6.46410	−	3.73205i	−0.284566	−	0.164294i
$517$	6.46410			0.284291
$518$	16.5622	+	1.36603i	0.727700	+	0.0600197i
$519$	0.339746			0.0149132
$520$	1.50000	+	0.866025i	0.0657794	+	0.0379777i
$521$	−8.19615	−	14.1962i	−0.359080	−	0.621945i	0.628727	−	0.777626i	$-0.283576\pi$
$521$	−8.19615	−	14.1962i	−0.359080	−	0.621945i	−0.987807	+	0.155681i	$0.950243\pi$
$522$	−3.86603	−	6.69615i	−0.169211	−	0.293083i
$523$	4.85641	−	2.80385i	0.212356	−	0.122604i	−0.390050	−	0.920794i	$-0.627542\pi$
$523$	4.85641	−	2.80385i	0.212356	−	0.122604i	0.602406	+	0.798190i	$0.294209\pi$
$524$		−	11.3923i		−	0.497675i
$525$	1.36603	+	2.36603i	0.0596182	+	0.103262i
$526$		−	11.3205i		−	0.493598i
$527$	−11.0718	+	19.1769i	−0.482295	+	0.835360i
$528$	−3.73205			−0.162417
$529$	19.0000			0.826087
$530$	−1.09808	+	1.90192i	−0.0476974	+	0.0826143i
$531$	5.59808	−	3.23205i	0.242936	−	0.140259i
$532$		−	5.46410i		−	0.236899i
$533$	3.29423	+	1.90192i	0.142689	+	0.0823815i
$534$	0.464102	−	0.803848i	0.0200836	−	0.0347859i
$535$	−10.5622	−	6.09808i	−0.456643	−	0.263643i
$536$	5.76795	−	3.33013i	0.249137	−	0.143840i
$537$	4.26795	−	2.46410i	0.184176	−	0.106334i
$538$	12.9282	+	7.46410i	0.557374	+	0.321800i
$539$	−0.866025	+	1.50000i	−0.0373024	+	0.0646096i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$		−	38.5885i		−	1.65905i	−0.558472	−	0.829524i	$-0.688612\pi$
$541$		−	38.5885i		−	1.65905i	0.558472	−	0.829524i	$-0.311388\pi$
$542$	−19.6244	+	11.3301i	−0.842938	+	0.486671i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	3.19615			0.137034
$545$	6.73205			0.288369
$546$	2.36603	−	4.09808i	0.101257	−	0.175381i
$547$			28.9282i			1.23688i	0.785832	+	0.618440i	$0.212235\pi$
$547$			28.9282i			1.23688i	−0.785832	+	0.618440i	$0.787765\pi$
$548$	5.50000	+	9.52628i	0.234948	+	0.406942i
$549$		−	4.73205i		−	0.201959i
$550$	−3.23205	+	1.86603i	−0.137815	+	0.0795676i
$551$	7.73205	+	13.3923i	0.329396	+	0.570531i
$552$	−1.00000	−	1.73205i	−0.0425628	−	0.0737210i
$553$	−21.1244	−	12.1962i	−0.898299	−	0.518633i
$554$	4.80385			0.204096
$555$	3.46410	−	5.00000i	0.147043	−	0.212238i
$556$	4.39230			0.186275
$557$	−36.3731	−	21.0000i	−1.54118	−	0.889799i	−0.998765	−	0.0496855i	$-0.984178\pi$
$557$	−36.3731	−	21.0000i	−1.54118	−	0.889799i	−0.542411	−	0.840113i	$-0.682489\pi$
$558$	3.46410	+	6.00000i	0.146647	+	0.254000i
$559$	6.46410	+	11.1962i	0.273402	+	0.473547i
$560$	2.36603	−	1.36603i	0.0999828	−	0.0577251i
$561$			11.9282i			0.503609i
$562$	1.73205	+	3.00000i	0.0730622	+	0.126547i
$563$		−	6.33975i		−	0.267188i	−0.991036	−	0.133594i	$-0.957348\pi$
$563$		−	6.33975i		−	0.267188i	0.991036	−	0.133594i	$-0.0426519\pi$
$564$	−0.866025	+	1.50000i	−0.0364662	+	0.0631614i
$565$	2.66025			0.111918
$566$	−23.5359			−0.989288
$567$	1.36603	−	2.36603i	0.0573677	−	0.0993637i
$568$	1.90192	−	1.09808i	0.0798029	−	0.0460743i
$569$			40.9808i			1.71800i	0.511973	+	0.859001i	$0.328915\pi$
$569$			40.9808i			1.71800i	−0.511973	+	0.859001i	$0.671085\pi$
$570$	−1.73205	−	1.00000i	−0.0725476	−	0.0418854i
$571$	14.4641	−	25.0526i	0.605304	−	1.04842i	−0.386700	−	0.922206i	$-0.626385\pi$
$571$	14.4641	−	25.0526i	0.605304	−	1.04842i	0.992003	−	0.126211i	$-0.0402817\pi$
$572$	5.59808	+	3.23205i	0.234067	+	0.135139i
$573$	8.83013	−	5.09808i	0.368884	−	0.212975i
$574$	5.19615	−	3.00000i	0.216883	−	0.125218i
$575$	−1.73205	−	1.00000i	−0.0722315	−	0.0417029i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	24.8827	+	14.3660i	1.03588	+	0.598065i	0.918664	−	0.395041i	$-0.129270\pi$
$577$	24.8827	+	14.3660i	1.03588	+	0.598065i	0.117216	+	0.993106i	$0.462603\pi$
$578$			6.78461i			0.282203i
$579$	0.169873	−	0.0980762i	0.00705968	−	0.00407591i
$580$	−3.86603	+	6.69615i	−0.160528	+	0.278043i
$581$	−11.4641			−0.475611
$582$	−4.53590			−0.188019
$583$	−4.09808	+	7.09808i	−0.169725	+	0.293972i
$584$		−	8.39230i		−	0.347276i
$585$	−0.866025	−	1.50000i	−0.0358057	−	0.0620174i
$586$			3.46410i			0.143101i
$587$	−23.3660	+	13.4904i	−0.964419	+	0.556808i	−0.897530	−	0.440953i	$-0.854641\pi$
$587$	−23.3660	+	13.4904i	−0.964419	+	0.556808i	−0.0668888	+	0.997760i	$0.521307\pi$
$588$	−0.232051	−	0.401924i	−0.00956961	−	0.0165751i
$589$	−6.92820	−	12.0000i	−0.285472	−	0.494451i
$590$	−5.59808	−	3.23205i	−0.230469	−	0.133061i
$591$	−8.92820			−0.367257
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	−31.9282			−1.31113			−0.655567	−	0.755137i	$-0.727570\pi$
$593$	−31.9282			−1.31113			−0.655567	+	0.755137i	$0.727570\pi$
$594$	3.23205	+	1.86603i	0.132613	+	0.0765639i
$595$	−4.36603	−	7.56218i	−0.178990	−	0.310019i
$596$	−4.96410	−	8.59808i	−0.203338	−	0.352191i
$597$	22.7942	−	13.1603i	0.932906	−	0.538613i
$598$			3.46410i			0.141658i
$599$	−12.2942	−	21.2942i	−0.502329	−	0.870059i	−0.999996	−	0.00269088i	$-0.999143\pi$
$599$	−12.2942	−	21.2942i	−0.502329	−	0.870059i	0.497668	−	0.867368i	$-0.334190\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−16.4282	+	28.4545i	−0.670120	+	1.16068i	0.307749	+	0.951467i	$0.400424\pi$
$601$	−16.4282	+	28.4545i	−0.670120	+	1.16068i	−0.977870	+	0.209215i	$0.932909\pi$
$602$	20.3923			0.831128
$603$	−6.66025			−0.271227
$604$	−9.46410	+	16.3923i	−0.385089	+	0.666993i
$605$	−2.53590	+	1.46410i	−0.103099	+	0.0595242i
$606$		−	1.53590i		−	0.0623916i
$607$	3.00000	+	1.73205i	0.121766	+	0.0703018i	0.559646	−	0.828732i	$-0.310937\pi$
$607$	3.00000	+	1.73205i	0.121766	+	0.0703018i	−0.437880	+	0.899034i	$0.644270\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$	18.2942	+	10.5622i	0.741320	+	0.428001i
$610$	−4.09808	+	2.36603i	−0.165926	+	0.0957976i
$611$	2.59808	−	1.50000i	0.105107	−	0.0606835i
$612$	−2.76795	−	1.59808i	−0.111888	−	0.0645984i
$613$	−5.69615	+	9.86603i	−0.230065	+	0.398485i	−0.957827	−	0.287345i	$-0.907227\pi$
$613$	−5.69615	+	9.86603i	−0.230065	+	0.398485i	0.727762	+	0.685830i	$0.240561\pi$
$614$	10.8564	+	6.26795i	0.438129	+	0.252954i
$615$		−	2.19615i		−	0.0885574i
$616$	8.83013	−	5.09808i	0.355776	−	0.205407i
$617$	13.6244	−	23.5981i	0.548496	−	0.950023i	−0.449882	−	0.893088i	$-0.648534\pi$
$617$	13.6244	−	23.5981i	0.548496	−	0.950023i	0.998378	−	0.0569348i	$-0.0181327\pi$
$618$	−0.196152			−0.00789041
$619$	15.8038			0.635210			0.317605	−	0.948223i	$-0.397121\pi$
$619$	15.8038			0.635210			0.317605	+	0.948223i	$0.397121\pi$
$620$	3.46410	−	6.00000i	0.139122	−	0.240966i
$621$			2.00000i			0.0802572i
$622$	−0.633975	−	1.09808i	−0.0254201	−	0.0440288i
$623$			2.53590i			0.101599i
$624$	−1.50000	+	0.866025i	−0.0600481	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.46410	−	7.73205i	−0.178421	−	0.309035i
$627$	−6.46410	−	3.73205i	−0.258151	−	0.149044i
$628$	15.5359			0.619950
$629$	−11.0718	+	15.9808i	−0.441461	+	0.637195i
$630$	−2.73205			−0.108848
$631$	24.0622	+	13.8923i	0.957900	+	0.553044i	0.895526	−	0.445009i	$-0.146799\pi$
$631$	24.0622	+	13.8923i	0.957900	+	0.553044i	0.0623740	+	0.998053i	$0.480133\pi$
$632$	4.46410	+	7.73205i	0.177572	+	0.307564i
$633$	5.66025	+	9.80385i	0.224975	+	0.389668i
$634$	−7.56218	+	4.36603i	−0.300332	+	0.173397i
$635$			2.73205i			0.108418i
$636$	−1.09808	−	1.90192i	−0.0435416	−	0.0754162i
$637$			0.803848i			0.0318496i
$638$	−14.4282	+	24.9904i	−0.571218	+	0.989379i
$639$	−2.19615			−0.0868784
$640$	−1.00000			−0.0395285
$641$	17.0263	−	29.4904i	0.672498	−	1.16480i	−0.304696	−	0.952450i	$-0.598555\pi$
$641$	17.0263	−	29.4904i	0.672498	−	1.16480i	0.977194	−	0.212350i	$-0.0681118\pi$
$642$	10.5622	−	6.09808i	0.416856	−	0.240672i
$643$		−	35.3923i		−	1.39574i	−0.716226	−	0.697868i	$-0.754132\pi$
$643$		−	35.3923i		−	1.39574i	0.716226	−	0.697868i	$-0.245868\pi$
$644$	4.73205	+	2.73205i	0.186469	+	0.107658i
$645$	3.73205	−	6.46410i	0.146949	−	0.254524i
$646$	5.53590	+	3.19615i	0.217807	+	0.125751i
$647$	0.186533	−	0.107695i	0.00733339	−	0.00423393i	−0.496329	−	0.868135i	$-0.665319\pi$
$647$	0.186533	−	0.107695i	0.00733339	−	0.00423393i	0.503662	+	0.863901i	$0.331986\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−20.8923	−	12.0622i	−0.820095	−	0.473482i
$650$	−0.866025	+	1.50000i	−0.0339683	+	0.0588348i
$651$	−16.3923	−	9.46410i	−0.642465	−	0.370927i
$652$			15.5359i			0.608433i
$653$	−15.7128	+	9.07180i	−0.614890	+	0.355007i	−0.774877	−	0.632112i	$-0.782188\pi$
$653$	−15.7128	+	9.07180i	−0.614890	+	0.355007i	0.159987	+	0.987119i	$0.448855\pi$
$654$	−3.36603	+	5.83013i	−0.131622	+	0.227976i
$655$	11.3923			0.445134
$656$	−2.19615			−0.0857453
$657$	−4.19615	+	7.26795i	−0.163707	+	0.283550i
$658$		−	4.73205i		−	0.184475i
$659$	0.937822	+	1.62436i	0.0365324	+	0.0632759i	0.883713	−	0.468028i	$-0.155035\pi$
$659$	0.937822	+	1.62436i	0.0365324	+	0.0632759i	−0.847181	+	0.531304i	$0.821702\pi$
$660$		−	3.73205i		−	0.145270i
$661$	−32.4449	+	18.7321i	−1.26196	+	0.728592i	−0.973453	−	0.228886i	$-0.926492\pi$
$661$	−32.4449	+	18.7321i	−1.26196	+	0.728592i	−0.288506	+	0.957478i	$0.593158\pi$
$662$	5.16987	+	8.95448i	0.200933	+	0.348026i
$663$	2.76795	+	4.79423i	0.107498	+	0.186192i
$664$	3.63397	+	2.09808i	0.141026	+	0.0814211i
$665$	5.46410			0.211889
$666$	2.59808	+	5.50000i	0.100673	+	0.213121i
$667$	−15.4641			−0.598772
$668$	20.5981	+	11.8923i	0.796963	+	0.460127i
$669$	−10.7321	−	18.5885i	−0.414925	−	0.718671i
$670$	3.33013	+	5.76795i	0.128654	+	0.222835i
$671$	−15.2942	+	8.83013i	−0.590427	+	0.340883i
$672$			2.73205i			0.105391i
$673$	20.5622	+	35.6147i	0.792614	+	1.37285i	0.924343	+	0.381562i	$0.124614\pi$
$673$	20.5622	+	35.6147i	0.792614	+	1.37285i	−0.131730	+	0.991286i	$0.542053\pi$
$674$		−	7.66025i		−	0.295062i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−10.0000			−0.384615
$677$	17.6603			0.678739			0.339369	−	0.940653i	$-0.389786\pi$
$677$	17.6603			0.678739			0.339369	+	0.940653i	$0.389786\pi$
$678$	−1.33013	+	2.30385i	−0.0510832	+	0.0884787i
$679$	10.7321	−	6.19615i	0.411858	−	0.237787i
$680$			3.19615i			0.122567i
$681$	4.09808	+	2.36603i	0.157039	+	0.0906663i
$682$	12.9282	−	22.3923i	0.495046	−	0.857446i
$683$	−7.05256	−	4.07180i	−0.269859	−	0.155803i	0.358965	−	0.933351i	$-0.383130\pi$
$683$	−7.05256	−	4.07180i	−0.269859	−	0.155803i	−0.628823	+	0.777548i	$0.716463\pi$
$684$	1.73205	−	1.00000i	0.0662266	−	0.0382360i
$685$	−9.52628	+	5.50000i	−0.363980	+	0.210144i
$686$	−15.4641	−	8.92820i	−0.590422	−	0.340880i
$687$	11.0263	−	19.0981i	0.420679	−	0.728637i
$688$	−6.46410	−	3.73205i	−0.246442	−	0.142283i
$689$			3.80385i			0.144915i
$690$	1.73205	−	1.00000i	0.0659380	−	0.0380693i
$691$	3.19615	−	5.53590i	0.121587	−	0.210595i	−0.798806	−	0.601588i	$-0.794535\pi$
$691$	3.19615	−	5.53590i	0.121587	−	0.210595i	0.920394	+	0.390993i	$0.127868\pi$
$692$	0.339746			0.0129152
$693$	−10.1962			−0.387320
$694$	−7.53590	+	13.0526i	−0.286059	+	0.495468i
$695$			4.39230i			0.166610i
$696$	−3.86603	−	6.69615i	−0.146541	−	0.253817i
$697$			7.01924i			0.265873i
$698$	−14.1962	+	8.19615i	−0.537332	+	0.310229i
$699$	−4.73205	−	8.19615i	−0.178983	−	0.310007i
$700$	1.36603	+	2.36603i	0.0516309	+	0.0894274i
$701$	7.03590	+	4.06218i	0.265742	+	0.153426i	0.626951	−	0.779059i	$-0.284303\pi$
$701$	7.03590	+	4.06218i	0.265742	+	0.153426i	−0.361209	+	0.932485i	$0.617636\pi$
$702$	1.73205			0.0653720
$703$	−5.19615	−	11.0000i	−0.195977	−	0.414873i
$704$	−3.73205			−0.140657
$705$	−1.50000	−	0.866025i	−0.0564933	−	0.0326164i
$706$	3.92820	+	6.80385i	0.147840	+	0.256066i
$707$	2.09808	+	3.63397i	0.0789063	+	0.136670i
$708$	5.59808	−	3.23205i	0.210389	−	0.121468i
$709$			3.66025i			0.137464i	0.997635	+	0.0687319i	$0.0218953\pi$
$709$			3.66025i			0.137464i	−0.997635	+	0.0687319i	$0.978105\pi$
$710$	1.09808	+	1.90192i	0.0412101	+	0.0713779i
$711$		−	8.92820i		−	0.334834i
$712$	0.464102	−	0.803848i	0.0173929	−	0.0301255i
$713$	13.8564			0.518927
$714$	8.73205			0.326789
$715$	−3.23205	+	5.59808i	−0.120872	+	0.209356i
$716$	4.26795	−	2.46410i	0.159501	−	0.0920878i
$717$		−	21.4641i		−	0.801592i
$718$	−15.5885	−	9.00000i	−0.581756	−	0.335877i
$719$	24.8827	−	43.0981i	0.927968	−	1.60729i	0.141250	−	0.989974i	$-0.454888\pi$
$719$	24.8827	−	43.0981i	0.927968	−	1.60729i	0.786718	−	0.617313i	$-0.211779\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	0.464102	−	0.267949i	0.0172840	−	0.00997895i
$722$	12.9904	−	7.50000i	0.483452	−	0.279121i
$723$	0.232051	+	0.133975i	0.00863006	+	0.00498257i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−6.69615	−	3.86603i	−0.248689	−	0.143581i
$726$		−	2.92820i		−	0.108676i
$727$	−10.7321	+	6.19615i	−0.398030	+	0.229803i	−0.685633	−	0.727947i	$-0.740475\pi$
$727$	−10.7321	+	6.19615i	−0.398030	+	0.229803i	0.287604	+	0.957749i	$0.407141\pi$
$728$	2.36603	−	4.09808i	0.0876907	−	0.151885i
$729$	1.00000			0.0370370
$730$	8.39230			0.310613
$731$	−11.9282	+	20.6603i	−0.441181	+	0.764147i
$732$		−	4.73205i		−	0.174902i
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	−0.999136	−	0.0415715i	$-0.986764\pi$
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	0.463566	−	0.886062i	$-0.346570\pi$
$734$		−	20.3923i		−	0.752694i
$735$	0.401924	−	0.232051i	0.0148252	−	0.00855932i
$736$	−1.00000	−	1.73205i	−0.0368605	−	0.0638442i
$737$	12.4282	+	21.5263i	0.457799	+	0.792931i
$738$	1.90192	+	1.09808i	0.0700108	+	0.0404207i
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	3.46410	−	5.00000i	0.127343	−	0.183804i
$741$	−3.46410			−0.127257
$742$	5.19615	+	3.00000i	0.190757	+	0.110133i
$743$	−19.2583	−	33.3564i	−0.706520	−	1.22373i	−0.966140	−	0.258017i	$-0.916931\pi$
$743$	−19.2583	−	33.3564i	−0.706520	−	1.22373i	0.259621	−	0.965711i	$-0.416402\pi$
$744$	3.46410	+	6.00000i	0.127000	+	0.219971i
$745$	8.59808	−	4.96410i	0.315009	−	0.181871i
$746$			36.3923i			1.33242i
$747$	−2.09808	−	3.63397i	−0.0767646	−	0.132960i
$748$			11.9282i			0.436138i
$749$	−16.6603	+	28.8564i	−0.608752	+	1.05439i
$750$	1.00000			0.0365148
$751$	47.4449			1.73129			0.865644	−	0.500660i	$-0.166909\pi$
$751$	47.4449			1.73129			0.865644	+	0.500660i	$0.166909\pi$
$752$	−0.866025	+	1.50000i	−0.0315807	+	0.0546994i
$753$	22.7942	−	13.1603i	0.830668	−	0.479586i
$754$			13.3923i			0.487719i
$755$	−16.3923	−	9.46410i	−0.596577	−	0.344434i
$756$	1.36603	−	2.36603i	0.0496819	−	0.0860515i
$757$	30.0000	+	17.3205i	1.09037	+	0.629525i	0.933675	−	0.358123i	$-0.116583\pi$
$757$	30.0000	+	17.3205i	1.09037	+	0.629525i	0.156694	+	0.987647i	$0.449916\pi$
$758$	−20.3660	+	11.7583i	−0.739727	+	0.427082i
$759$	6.46410	−	3.73205i	0.234632	−	0.135465i
$760$	−1.73205	−	1.00000i	−0.0628281	−	0.0362738i
$761$	−5.90192	+	10.2224i	−0.213945	+	0.370563i	−0.952946	−	0.303141i	$-0.901965\pi$
$761$	−5.90192	+	10.2224i	−0.213945	+	0.370563i	0.739001	+	0.673704i	$0.235298\pi$
$762$	−2.36603	−	1.36603i	−0.0857121	−	0.0494859i
$763$		−	18.3923i		−	0.665846i
$764$	8.83013	−	5.09808i	0.319463	−	0.184442i
$765$	1.59808	−	2.76795i	0.0577786	−	0.100075i
$766$	−22.7128			−0.820647
$767$	−11.1962			−0.404270
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	23.1962i		−	0.836475i	−0.908338	−	0.418237i	$-0.862648\pi$
$769$		−	23.1962i		−	0.836475i	0.908338	−	0.418237i	$-0.137352\pi$
$770$	5.09808	+	8.83013i	0.183722	+	0.318216i
$771$		−	10.6603i		−	0.383920i
$772$	0.169873	−	0.0980762i	0.00611386	−	0.00352984i
$773$	−7.29423	−	12.6340i	−0.262355	−	0.454412i	0.704512	−	0.709692i	$-0.251166\pi$
$773$	−7.29423	−	12.6340i	−0.262355	−	0.454412i	−0.966867	+	0.255279i	$0.917833\pi$
$774$	3.73205	+	6.46410i	0.134146	+	0.232347i
$775$	6.00000	+	3.46410i	0.215526	+	0.124434i
$776$	−4.53590			−0.162829
$777$	−13.6603	−	9.46410i	−0.490059	−	0.339523i
$778$	−1.60770			−0.0576387
$779$	−3.80385	−	2.19615i	−0.136287	−	0.0786853i
$780$	−0.866025	−	1.50000i	−0.0310087	−	0.0537086i
$781$	4.09808	+	7.09808i	0.146641	+	0.253989i
$782$	−5.53590	+	3.19615i	−0.197963	+	0.114294i
$783$			7.73205i			0.276321i
$784$	−0.232051	−	0.401924i	−0.00828753	−	0.0143544i
$785$			15.5359i			0.554500i
$786$	−5.69615	+	9.86603i	−0.203175	+	0.351909i
$787$	24.3731			0.868806			0.434403	−	0.900719i	$-0.356959\pi$
$787$	24.3731			0.868806			0.434403	+	0.900719i	$0.356959\pi$
$788$	−8.92820			−0.318054
$789$	−5.66025	+	9.80385i	−0.201510	+	0.349026i
$790$	−7.73205	+	4.46410i	−0.275094	+	0.158826i
$791$		−	7.26795i		−	0.258419i
$792$	3.23205	+	1.86603i	0.114846	+	0.0663063i
$793$	−4.09808	+	7.09808i	−0.145527	+	0.252060i
$794$	15.9904	+	9.23205i	0.567477	+	0.327633i
$795$	1.90192	−	1.09808i	0.0674543	−	0.0389447i
$796$	22.7942	−	13.1603i	0.807920	−	0.466453i
$797$	−7.60770	−	4.39230i	−0.269478	−	0.155583i	0.359172	−	0.933271i	$-0.383059\pi$
$797$	−7.60770	−	4.39230i	−0.269478	−	0.155583i	−0.628651	+	0.777688i	$0.716392\pi$
$798$	−2.73205	+	4.73205i	−0.0967136	+	0.167513i
$799$	4.79423	+	2.76795i	0.169608	+	0.0979230i
$800$		−	1.00000i		−	0.0353553i
$801$	−0.803848	+	0.464102i	−0.0284026	+	0.0163982i
$802$	4.43782	−	7.68653i	0.156705	−	0.271421i
$803$	31.3205			1.10528
$804$	−6.66025			−0.234889
$805$	−2.73205	+	4.73205i	−0.0962921	+	0.166783i
$806$		−	12.0000i		−	0.422682i
$807$	−7.46410	−	12.9282i	−0.262749	−	0.455094i
$808$		−	1.53590i		−	0.0540327i
$809$	−35.1962	+	20.3205i	−1.23743	+	0.714431i	−0.968568	−	0.248748i	$-0.919981\pi$
$809$	−35.1962	+	20.3205i	−1.23743	+	0.714431i	−0.268862	+	0.963179i	$0.586648\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	11.8301	+	20.4904i	0.415412	+	0.719515i	0.995472	−	0.0950594i	$-0.0303041\pi$
$811$	11.8301	+	20.4904i	0.415412	+	0.719515i	−0.580060	+	0.814574i	$0.696971\pi$
$812$	18.2942	+	10.5622i	0.642002	+	0.370660i
$813$	22.6603			0.794730
$814$	12.9282	−	18.6603i	0.453133	−	0.654042i
$815$	−15.5359			−0.544199
$816$	−2.76795	−	1.59808i	−0.0968976	−	0.0559439i
$817$	−7.46410	−	12.9282i	−0.261136	−	0.452301i
$818$	−11.0622	−	19.1603i	−0.386780	−	0.669923i
$819$	−4.09808	+	2.36603i	−0.143198	+	0.0826756i
$820$		−	2.19615i		−	0.0766930i
$821$	−12.8205	−	22.2058i	−0.447439	−	0.774987i	0.550780	−	0.834651i	$-0.314330\pi$
$821$	−12.8205	−	22.2058i	−0.447439	−	0.774987i	−0.998219	+	0.0596639i	$0.980997\pi$
$822$		−	11.0000i		−	0.383669i
$823$	−25.2224	+	43.6865i	−0.879199	+	1.52282i	−0.0269770	+	0.999636i	$0.508588\pi$
$823$	−25.2224	+	43.6865i	−0.879199	+	1.52282i	−0.852222	+	0.523181i	$0.824745\pi$
$824$	−0.196152			−0.00683329
$825$	3.73205			0.129933
$826$	−8.83013	+	15.2942i	−0.307239	+	0.532154i
$827$	27.0000	−	15.5885i	0.938882	−	0.542064i	0.0492723	−	0.998785i	$-0.484310\pi$
$827$	27.0000	−	15.5885i	0.938882	−	0.542064i	0.889610	+	0.456722i	$0.150976\pi$
$828$			2.00000i			0.0695048i
$829$	−30.4186	−	17.5622i	−1.05648	−	0.609960i	−0.132024	−	0.991246i	$-0.542148\pi$
$829$	−30.4186	−	17.5622i	−1.05648	−	0.609960i	−0.924457	+	0.381287i	$0.875481\pi$
$830$	−2.09808	+	3.63397i	−0.0728253	+	0.126137i
$831$	−4.16025	−	2.40192i	−0.144318	−	0.0833218i
$832$	−1.50000	+	0.866025i	−0.0520031	+	0.0300240i
$833$	−1.28461	+	0.741670i	−0.0445091	+	0.0256973i
$834$	−3.80385	−	2.19615i	−0.131716	−	0.0760465i
$835$	−11.8923	+	20.5981i	−0.411550	+	0.712826i
$836$	−6.46410	−	3.73205i	−0.223566	−	0.129076i
$837$		−	6.92820i		−	0.239474i
$838$	32.7846	−	18.9282i	1.13253	−	0.653864i
$839$	−15.6865	+	27.1699i	−0.541559	+	0.938008i	0.457255	+	0.889335i	$0.348832\pi$
$839$	−15.6865	+	27.1699i	−0.541559	+	0.938008i	−0.998815	+	0.0486728i	$0.984501\pi$
$840$	−2.73205			−0.0942647
$841$	−30.7846			−1.06154
$842$	−6.16987	+	10.6865i	−0.212628	+	0.368282i
$843$		−	3.46410i		−	0.119310i
$844$	5.66025	+	9.80385i	0.194834	+	0.337462i
$845$		−	10.0000i		−	0.344010i
$846$	1.50000	−	0.866025i	0.0515711	−	0.0297746i
$847$	4.00000	+	6.92820i	0.137442	+	0.238056i
$848$	−1.09808	−	1.90192i	−0.0377081	−	0.0653123i
$849$	20.3827	+	11.7679i	0.699532	+	0.403875i
$850$	−3.19615			−0.109627
$851$	12.1244	+	1.00000i	0.415618	+	0.0342796i
$852$	−2.19615			−0.0752389
$853$	−33.6051	−	19.4019i	−1.15062	−	0.664309i	−0.201580	−	0.979472i	$-0.564608\pi$
$853$	−33.6051	−	19.4019i	−1.15062	−	0.664309i	−0.949038	+	0.315163i	$0.897941\pi$
$854$	6.46410	+	11.1962i	0.221197	+	0.383124i
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	10.5622	−	6.09808i	0.361008	−	0.208428i
$857$		−	18.1244i		−	0.619116i	−0.950881	−	0.309558i	$-0.899819\pi$
$857$		−	18.1244i		−	0.619116i	0.950881	−	0.309558i	$-0.100181\pi$
$858$	−3.23205	−	5.59808i	−0.110340	−	0.191115i
$859$		−	26.9808i		−	0.920572i	−0.887771	−	0.460286i	$-0.847747\pi$
$859$		−	26.9808i		−	0.920572i	0.887771	−	0.460286i	$-0.152253\pi$
$860$	3.73205	−	6.46410i	0.127262	−	0.220424i
$861$	−6.00000			−0.204479
$862$	35.5167			1.20970
$863$	10.3301	−	17.8923i	0.351642	−	0.609061i	−0.634896	−	0.772598i	$-0.718957\pi$
$863$	10.3301	−	17.8923i	0.351642	−	0.609061i	0.986537	+	0.163537i	$0.0522902\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$			0.339746i			0.0115517i
$866$	−11.3205	−	6.53590i	−0.384687	−	0.222099i
$867$	3.39230	−	5.87564i	0.115209	−	0.199547i
$868$	−16.3923	−	9.46410i	−0.556391	−	0.321233i
$869$	−28.8564	+	16.6603i	−0.978887	+	0.565160i
$870$	6.69615	−	3.86603i	0.227021	−	0.131071i
$871$	9.99038	+	5.76795i	0.338511	+	0.195440i
$872$	−3.36603	+	5.83013i	−0.113988	+	0.197433i
$873$	3.92820	+	2.26795i	0.132950	+	0.0767585i
$874$		−	4.00000i		−	0.135302i
$875$	−2.36603	+	1.36603i	−0.0799863	+	0.0461801i
$876$	−4.19615	+	7.26795i	−0.141775	+	0.245561i
$877$	−44.1769			−1.49175			−0.745874	−	0.666087i	$-0.767968\pi$
$877$	−44.1769			−1.49175			−0.745874	+	0.666087i	$0.767968\pi$
$878$	−37.0000			−1.24869
$879$	1.73205	−	3.00000i	0.0584206	−	0.101187i
$880$		−	3.73205i		−	0.125807i
$881$	1.07180	+	1.85641i	0.0361098	+	0.0625439i	0.883515	−	0.468402i	$-0.155170\pi$
$881$	1.07180	+	1.85641i	0.0361098	+	0.0625439i	−0.847406	+	0.530946i	$0.821837\pi$
$882$			0.464102i			0.0156271i
$883$	0.741670	−	0.428203i	0.0249592	−	0.0144102i	−0.487468	−	0.873141i	$-0.662080\pi$
$883$	0.741670	−	0.428203i	0.0249592	−	0.0144102i	0.512428	+	0.858730i	$0.328746\pi$
$884$	2.76795	+	4.79423i	0.0930962	+	0.161247i
$885$	3.23205	+	5.59808i	0.108644	+	0.188177i
$886$	−32.3660	−	18.6865i	−1.08736	−	0.627786i
$887$	−56.7846			−1.90664			−0.953320	−	0.301961i	$-0.902359\pi$
$887$	−56.7846			−1.90664			−0.953320	+	0.301961i	$0.902359\pi$
$888$	2.59808	+	5.50000i	0.0871857	+	0.184568i
$889$	7.46410			0.250338
$890$	0.803848	+	0.464102i	0.0269450	+	0.0155567i
$891$	−1.86603	−	3.23205i	−0.0625142	−	0.108278i
$892$	−10.7321	−	18.5885i	−0.359336	−	0.622388i
$893$	−3.00000	+	1.73205i	−0.100391	+	0.0579609i
$894$			9.92820i			0.332049i
$895$	2.46410	+	4.26795i	0.0823658	+	0.142662i
$896$			2.73205i			0.0912714i
$897$	1.73205	−	3.00000i	0.0578315	−	0.100167i
$898$	−16.7846			−0.560110
$899$	53.5692			1.78663
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−6.07884	+	3.50962i	−0.202515	+	0.116922i
$902$		−	8.19615i		−	0.272902i
$903$	−17.6603	−	10.1962i	−0.587696	−	0.339307i
$904$	−1.33013	+	2.30385i	−0.0442394	+	0.0766248i
$905$	−1.73205	−	1.00000i	−0.0575753	−	0.0332411i
$906$	16.3923	−	9.46410i	0.544598	−	0.314424i
$907$	0.124356	−	0.0717968i	0.00412916	−	0.00238397i	−0.497934	−	0.867215i	$-0.665908\pi$
$907$	0.124356	−	0.0717968i	0.00412916	−	0.00238397i	0.502063	+	0.864831i	$0.332574\pi$
$908$	4.09808	+	2.36603i	0.135999	+	0.0785193i
$909$	−0.767949	+	1.33013i	−0.0254713	+	0.0441175i
$910$	4.09808	+	2.36603i	0.135850	+	0.0784330i
$911$			35.5692i			1.17846i	0.807965	+	0.589230i	$0.200569\pi$
$911$			35.5692i			1.17846i	−0.807965	+	0.589230i	$0.799431\pi$
$912$	1.73205	−	1.00000i	0.0573539	−	0.0331133i
$913$	−7.83013	+	13.5622i	−0.259139	+	0.448843i
$914$	−19.3205			−0.639066
$915$	4.73205			0.156437
$916$	11.0263	−	19.0981i	0.364319	−	0.631018i
$917$		−	31.1244i		−	1.02782i
$918$	1.59808	+	2.76795i	0.0527444	+	0.0913559i
$919$			6.75129i			0.222704i	0.993781	+	0.111352i	$0.0355182\pi$
$919$			6.75129i			0.222704i	−0.993781	+	0.111352i	$0.964482\pi$
$920$	1.73205	−	1.00000i	0.0571040	−	0.0329690i
$921$	−6.26795	−	10.8564i	−0.206536	−	0.357731i
$922$	−17.7942	−	30.8205i	−0.586022	−	1.01502i
$923$	3.29423	+	1.90192i	0.108431	+	0.0626026i
$924$	−10.1962			−0.335429
$925$	5.00000	+	3.46410i	0.164399	+	0.113899i
$926$	−7.46410			−0.245286
$927$	0.169873	+	0.0980762i	0.00557936	+	0.00322125i
$928$	−3.86603	−	6.69615i	−0.126909	−	0.219812i
$929$	13.8564	+	24.0000i	0.454614	+	0.787414i	0.998666	−	0.0516371i	$-0.0164439\pi$
$929$	13.8564	+	24.0000i	0.454614	+	0.787414i	−0.544052	+	0.839052i	$0.683111\pi$
$930$	−6.00000	+	3.46410i	−0.196748	+	0.113592i
$931$		−	0.928203i		−	0.0304206i
$932$	−4.73205	−	8.19615i	−0.155003	−	0.268474i
$933$			1.26795i			0.0415108i
$934$	5.92820	−	10.2679i	0.193977	−	0.335978i
$935$	−11.9282			−0.390094
$936$	1.73205			0.0566139
$937$	6.70577	−	11.6147i	0.219068	−	0.379437i	−0.735455	−	0.677573i	$-0.763032\pi$
$937$	6.70577	−	11.6147i	0.219068	−	0.379437i	0.954523	+	0.298136i	$0.0963650\pi$
$938$	15.7583	−	9.09808i	0.514528	−	0.297063i
$939$			8.92820i			0.291361i
$940$	−1.50000	−	0.866025i	−0.0489246	−	0.0282466i
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$	−13.4545	−	7.76795i	−0.438371	−	0.253093i
$943$	3.80385	−	2.19615i	0.123870	−	0.0715166i
$944$	5.59808	−	3.23205i	0.182202	−	0.105194i
$945$	2.36603	+	1.36603i	0.0769668	+	0.0444368i
$946$	13.9282	−	24.1244i	0.452845	−	0.784350i
$947$	−9.24871	−	5.33975i	−0.300543	−	0.173518i	0.342144	−	0.939648i	$-0.388847\pi$
$947$	−9.24871	−	5.33975i	−0.300543	−	0.173518i	−0.642687	+	0.766129i	$0.722180\pi$
$948$		−	8.92820i		−	0.289975i
$949$	12.5885	−	7.26795i	0.408639	−	0.235928i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	8.73205			0.283156
$952$	8.73205			0.283007
$953$	−16.1603	+	27.9904i	−0.523482	+	0.906697i	0.476144	+	0.879367i	$0.342034\pi$
$953$	−16.1603	+	27.9904i	−0.523482	+	0.906697i	−0.999626	+	0.0273303i	$0.991299\pi$
$954$			2.19615i			0.0711031i
$955$	5.09808	+	8.83013i	0.164970	+	0.285736i
$956$		−	21.4641i		−	0.694199i
$957$	24.9904	−	14.4282i	0.807824	−	0.466398i
$958$	−16.1244	−	27.9282i	−0.520954	−	0.902319i
$959$	15.0263	+	26.0263i	0.485224	+	0.840432i
$960$	0.866025	+	0.500000i	0.0279508	+	0.0161374i
$961$	−17.0000			−0.548387
$962$	0.866025	−	10.5000i	0.0279218	−	0.338534i
$963$	−12.1962			−0.393016
$964$	0.232051	+	0.133975i	0.00747385	+	0.00431503i
$965$	0.0980762	+	0.169873i	0.00315718	+	0.00546840i
$966$	−2.73205	−	4.73205i	−0.0879023	−	0.152251i
$967$	−11.6147	+	6.70577i	−0.373505	+	0.215643i	−0.674989	−	0.737828i	$-0.735851\pi$
$967$	−11.6147	+	6.70577i	−0.373505	+	0.215643i	0.301484	+	0.953471i	$0.402518\pi$
$968$		−	2.92820i		−	0.0941160i
$969$	−3.19615	−	5.53590i	−0.102675	−	0.177839i
$970$		−	4.53590i		−	0.145639i
$971$	4.73205	−	8.19615i	0.151859	−	0.263027i	−0.780052	−	0.625715i	$-0.784807\pi$
$971$	4.73205	−	8.19615i	0.151859	−	0.263027i	0.931911	+	0.362688i	$0.118141\pi$
$972$	1.00000			0.0320750
$973$	12.0000			0.384702
$974$	12.4641	−	21.5885i	0.399376	−	0.691739i
$975$	1.50000	−	0.866025i	0.0480384	−	0.0277350i
$976$		−	4.73205i		−	0.151469i
$977$	23.6769	+	13.6699i	0.757492	+	0.437338i	0.828394	−	0.560145i	$-0.189255\pi$
$977$	23.6769	+	13.6699i	0.757492	+	0.437338i	−0.0709028	+	0.997483i	$0.522588\pi$
$978$	7.76795	−	13.4545i	0.248392	−	0.430227i
$979$	3.00000	+	1.73205i	0.0958804	+	0.0553566i
$980$	0.401924	−	0.232051i	0.0128390	−	0.00741259i
$981$	5.83013	−	3.36603i	0.186142	−	0.107469i
$982$	−13.8564	−	8.00000i	−0.442176	−	0.255290i
$983$	−1.46410	+	2.53590i	−0.0466976	+	0.0808826i	−0.888429	−	0.459013i	$-0.848203\pi$
$983$	−1.46410	+	2.53590i	−0.0466976	+	0.0808826i	0.841732	+	0.539896i	$0.181536\pi$
$984$	1.90192	+	1.09808i	0.0606311	+	0.0350054i
$985$		−	8.92820i		−	0.284476i
$986$	−21.4019	+	12.3564i	−0.681576	+	0.393508i
$987$	−2.36603	+	4.09808i	−0.0753114	+	0.130443i
$988$	−3.46410			−0.110208
$989$	14.9282			0.474689
$990$	−1.86603	+	3.23205i	−0.0593062	+	0.102721i
$991$		−	16.1769i		−	0.513877i	−0.966428	−	0.256938i	$-0.917286\pi$
$991$		−	16.1769i		−	0.513877i	0.966428	−	0.256938i	$-0.0827137\pi$
$992$	3.46410	+	6.00000i	0.109985	+	0.190500i
$993$		−	10.3397i		−	0.328122i
$994$	5.19615	−	3.00000i	0.164812	−	0.0951542i
$995$	13.1603	+	22.7942i	0.417208	+	0.722626i
$996$	−2.09808	−	3.63397i	−0.0664801	−	0.115147i
$997$	−21.8205	−	12.5981i	−0.691062	−	0.398985i	0.112947	−	0.993601i	$-0.463971\pi$
$997$	−21.8205	−	12.5981i	−0.691062	−	0.398985i	−0.804010	+	0.594616i	$0.797304\pi$
$998$	−30.4449			−0.963715
$999$	0.500000	−	6.06218i	0.0158193	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.b.841.1	yes	4
37.11	even	6	inner	1110.2.x.b.751.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.b.751.1	✓	4	37.11	even	6	inner
1110.2.x.b.841.1	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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.36603 + 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.36603 + 2.36603i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +3.73205 q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.50000 - 0.866025i) q^{13} -2.73205i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.76795 + 1.59808i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.73205 + 1.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.36603 + 2.36603i) q^{21} +(-3.23205 - 1.86603i) q^{22} -2.00000i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.73205 q^{26} -1.00000 q^{27} +(-1.36603 + 2.36603i) q^{28} -7.73205i q^{29} +(0.500000 + 0.866025i) q^{30} +6.92820i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.86603 + 3.23205i) q^{33} +(-1.59808 - 2.76795i) q^{34} +(-2.36603 - 1.36603i) q^{35} -1.00000 q^{36} +(-0.500000 + 6.06218i) q^{37} +2.00000 q^{38} +(1.50000 + 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(1.09808 + 1.90192i) q^{41} +(2.36603 - 1.36603i) q^{42} +7.46410i q^{43} +(1.86603 + 3.23205i) q^{44} -1.00000i q^{45} +(-1.00000 + 1.73205i) q^{46} +1.73205 q^{47} -1.00000 q^{48} +(-0.232051 + 0.401924i) q^{49} +(-0.866025 + 0.500000i) q^{50} +3.19615i q^{51} +(1.50000 + 0.866025i) q^{52} +(-1.09808 + 1.90192i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-3.23205 + 1.86603i) q^{55} +(2.36603 - 1.36603i) q^{56} +(-1.73205 - 1.00000i) q^{57} +(-3.86603 + 6.69615i) q^{58} +(-5.59808 - 3.23205i) q^{59} -1.00000i q^{60} +(-4.09808 + 2.36603i) q^{61} +(3.46410 - 6.00000i) q^{62} -2.73205 q^{63} -1.00000 q^{64} +(-0.866025 + 1.50000i) q^{65} -3.73205i q^{66} +(3.33013 + 5.76795i) q^{67} +3.19615i q^{68} +(1.73205 - 1.00000i) q^{69} +(1.36603 + 2.36603i) q^{70} +(1.09808 + 1.90192i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.39230 q^{73} +(3.46410 - 5.00000i) q^{74} +1.00000 q^{75} +(-1.73205 - 1.00000i) q^{76} +(5.09808 + 8.83013i) q^{77} +(-0.866025 - 1.50000i) q^{78} +(-7.73205 + 4.46410i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -2.19615i q^{82} +(-2.09808 + 3.63397i) q^{83} -2.73205 q^{84} -3.19615 q^{85} +(3.73205 - 6.46410i) q^{86} +(6.69615 - 3.86603i) q^{87} -3.73205i q^{88} +(0.803848 + 0.464102i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(4.09808 + 2.36603i) q^{91} +(1.73205 - 1.00000i) q^{92} +(-6.00000 + 3.46410i) q^{93} +(-1.50000 - 0.866025i) q^{94} +(1.00000 - 1.73205i) q^{95} +(0.866025 + 0.500000i) q^{96} -4.53590i q^{97} +(0.401924 - 0.232051i) q^{98} +(-1.86603 + 3.23205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{7} - 2 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{16} + 18 q^{17} - 2 q^{21} - 6 q^{22} + 2 q^{25} - 4 q^{27} - 2 q^{28} + 2 q^{30} + 4 q^{33} + 4 q^{34} - 6 q^{35} - 4 q^{36} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 4 q^{44} - 4 q^{46} - 4 q^{48} + 6 q^{49} + 6 q^{52} + 6 q^{53} - 6 q^{55} + 6 q^{56} - 12 q^{58} - 12 q^{59} - 6 q^{61} - 4 q^{63} - 4 q^{64} - 4 q^{67} + 2 q^{70} - 6 q^{71} - 8 q^{73} + 4 q^{75} + 10 q^{77} - 24 q^{79} - 2 q^{81} + 2 q^{83} - 4 q^{84} + 8 q^{85} + 8 q^{86} + 6 q^{87} + 24 q^{89} - 2 q^{90} + 6 q^{91} - 24 q^{93} - 6 q^{94} + 4 q^{95} + 12 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^7 - 2 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^16 + 18 * q^17 - 2 * q^21 - 6 * q^22 + 2 * q^25 - 4 * q^27 - 2 * q^28 + 2 * q^30 + 4 * q^33 + 4 * q^34 - 6 * q^35 - 4 * q^36 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 4 * q^44 - 4 * q^46 - 4 * q^48 + 6 * q^49 + 6 * q^52 + 6 * q^53 - 6 * q^55 + 6 * q^56 - 12 * q^58 - 12 * q^59 - 6 * q^61 - 4 * q^63 - 4 * q^64 - 4 * q^67 + 2 * q^70 - 6 * q^71 - 8 * q^73 + 4 * q^75 + 10 * q^77 - 24 * q^79 - 2 * q^81 + 2 * q^83 - 4 * q^84 + 8 * q^85 + 8 * q^86 + 6 * q^87 + 24 * q^89 - 2 * q^90 + 6 * q^91 - 24 * q^93 - 6 * q^94 + 4 * q^95 + 12 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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