LMFDB - Embedded newform 1110.2.ba.b.619.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.1
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.b.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.62555 + 1.53544i) q^{5} +1.00000i q^{6} +(2.75229 - 1.58904i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.62555 + 1.53544i) q^{5} +1.00000i q^{6} +(2.75229 - 1.58904i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.516959 + 2.17549i) q^{10} -3.88035 q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.379707 - 0.657673i) q^{13} -3.17807i q^{14} +(0.640045 - 2.14251i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.69434 + 2.93468i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.55166 - 2.62790i) q^{19} +(2.14251 + 0.640045i) q^{20} +(-1.58904 + 2.75229i) q^{21} +(-1.94018 + 3.36048i) q^{22} -6.61653 q^{23} +(0.866025 - 0.500000i) q^{24} +(0.284822 - 4.99188i) q^{25} -0.759415 q^{26} +1.00000i q^{27} +(-2.75229 - 1.58904i) q^{28} +1.30709i q^{29} +(-1.53544 - 1.62555i) q^{30} -6.12433i q^{31} +(0.500000 + 0.866025i) q^{32} +(3.36048 - 1.94018i) q^{33} +(1.69434 + 2.93468i) q^{34} +(-2.03411 + 6.80904i) q^{35} -1.00000 q^{36} +(-6.05221 + 0.608935i) q^{37} -5.25580i q^{38} +(0.657673 + 0.379707i) q^{39} +(1.62555 - 1.53544i) q^{40} +(-5.17175 - 8.95773i) q^{41} +(1.58904 + 2.75229i) q^{42} -9.41844 q^{43} +(1.94018 + 3.36048i) q^{44} +(0.516959 + 2.17549i) q^{45} +(-3.30827 + 5.73009i) q^{46} -5.34620i q^{47} -1.00000i q^{48} +(1.55007 - 2.68480i) q^{49} +(-4.18068 - 2.74260i) q^{50} -3.38867i q^{51} +(-0.379707 + 0.657673i) q^{52} +(2.76662 + 1.59731i) q^{53} +(0.866025 + 0.500000i) q^{54} +(6.30770 - 5.95806i) q^{55} +(-2.75229 + 1.58904i) q^{56} +(-2.62790 + 4.55166i) q^{57} +(1.13197 + 0.653545i) q^{58} +(-5.34529 - 3.08610i) q^{59} +(-2.17549 + 0.516959i) q^{60} +(-8.45447 + 4.88119i) q^{61} +(-5.30382 - 3.06216i) q^{62} -3.17807i q^{63} +1.00000 q^{64} +(1.62705 + 0.486060i) q^{65} -3.88035i q^{66} +(-8.72817 + 5.03921i) q^{67} +3.38867 q^{68} +(5.73009 - 3.30827i) q^{69} +(4.87975 + 5.16611i) q^{70} +(-3.22083 - 5.57863i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.84525i q^{73} +(-2.49875 + 5.54583i) q^{74} +(2.24928 + 4.46551i) q^{75} +(-4.55166 - 2.62790i) q^{76} +(-10.6799 + 6.16602i) q^{77} +(0.657673 - 0.379707i) q^{78} +(7.39006 - 4.26665i) q^{79} +(-0.516959 - 2.17549i) q^{80} +(-0.500000 - 0.866025i) q^{81} -10.3435 q^{82} +(6.05368 + 3.49509i) q^{83} +3.17807 q^{84} +(-1.75181 - 7.37202i) q^{85} +(-4.70922 + 8.15661i) q^{86} +(-0.653545 - 1.13197i) q^{87} +3.88035 q^{88} +(-1.93582 - 1.11765i) q^{89} +(2.14251 + 0.640045i) q^{90} +(-2.09013 - 1.20674i) q^{91} +(3.30827 + 5.73009i) q^{92} +(3.06216 + 5.30382i) q^{93} +(-4.62995 - 2.67310i) q^{94} +(-3.36395 + 11.2606i) q^{95} +(-0.866025 - 0.500000i) q^{96} -4.77178 q^{97} +(-1.55007 - 2.68480i) q^{98} +(-1.94018 + 3.36048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * 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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.62555	+	1.53544i	−0.726968	+	0.686672i
$5$	−1.62555	+	1.53544i	−0.726968	+	0.686672i
$6$			1.00000i			0.408248i
$7$	2.75229	−	1.58904i	1.04027	−	0.600599i	0.120359	−	0.992730i	$-0.461595\pi$
$7$	2.75229	−	1.58904i	1.04027	−	0.600599i	0.919909	+	0.392131i	$0.128262\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.516959	+	2.17549i	0.163477	+	0.687950i
$11$	−3.88035			−1.16997			−0.584985	−	0.811044i	$-0.698900\pi$
$11$	−3.88035			−1.16997			−0.584985	+	0.811044i	$0.698900\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.379707	−	0.657673i	−0.105312	−	0.182406i	0.808554	−	0.588422i	$-0.200251\pi$
$13$	−0.379707	−	0.657673i	−0.105312	−	0.182406i	−0.913866	+	0.406017i	$0.866917\pi$
$14$		−	3.17807i		−	0.849375i
$15$	0.640045	−	2.14251i	0.165259	−	0.553193i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.69434	+	2.93468i	−0.410937	+	0.711764i	−0.994992	−	0.0999499i	$-0.968132\pi$
$17$	−1.69434	+	2.93468i	−0.410937	+	0.711764i	0.584055	+	0.811714i	$0.301465\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	4.55166	−	2.62790i	1.04422	−	0.602882i	0.123196	−	0.992382i	$-0.460686\pi$
$19$	4.55166	−	2.62790i	1.04422	−	0.602882i	0.921026	+	0.389501i	$0.127352\pi$
$20$	2.14251	+	0.640045i	0.479079	+	0.143118i
$21$	−1.58904	+	2.75229i	−0.346756	+	0.600599i
$22$	−1.94018	+	3.36048i	−0.413647	+	0.716457i
$23$	−6.61653			−1.37964			−0.689821	−	0.723980i	$-0.742311\pi$
$23$	−6.61653			−1.37964			−0.689821	+	0.723980i	$0.742311\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.284822	−	4.99188i	0.0569645	−	0.998376i
$26$	−0.759415			−0.148934
$27$			1.00000i			0.192450i
$28$	−2.75229	−	1.58904i	−0.520134	−	0.300300i
$29$			1.30709i			0.242721i	0.992609	+	0.121360i	$0.0387256\pi$
$29$			1.30709i			0.242721i	−0.992609	+	0.121360i	$0.961274\pi$
$30$	−1.53544	−	1.62555i	−0.280332	−	0.296783i
$31$		−	6.12433i		−	1.09996i	−0.835177	−	0.549981i	$-0.814635\pi$
$31$		−	6.12433i		−	1.09996i	0.835177	−	0.549981i	$-0.185365\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.36048	−	1.94018i	0.584985	−	0.337741i
$34$	1.69434	+	2.93468i	0.290576	+	0.503293i
$35$	−2.03411	+	6.80904i	−0.343827	+	1.15094i
$36$	−1.00000			−0.166667
$37$	−6.05221	+	0.608935i	−0.994977	+	0.100108i
$37$	−6.05221	+	0.608935i	−0.994977	+	0.100108i
$38$		−	5.25580i		−	0.852604i
$39$	0.657673	+	0.379707i	0.105312	+	0.0608019i
$40$	1.62555	−	1.53544i	0.257022	−	0.242775i
$41$	−5.17175	−	8.95773i	−0.807691	−	1.39896i	−0.914459	−	0.404678i	$-0.867384\pi$
$41$	−5.17175	−	8.95773i	−0.807691	−	1.39896i	0.106768	−	0.994284i	$-0.465950\pi$
$42$	1.58904	+	2.75229i	0.245194	+	0.424688i
$43$	−9.41844			−1.43630			−0.718149	−	0.695889i	$-0.755011\pi$
$43$	−9.41844			−1.43630			−0.718149	+	0.695889i	$0.755011\pi$
$44$	1.94018	+	3.36048i	0.292492	+	0.506612i
$45$	0.516959	+	2.17549i	0.0770637	+	0.324303i
$46$	−3.30827	+	5.73009i	−0.487777	+	0.844855i
$47$		−	5.34620i		−	0.779824i	−0.920852	−	0.389912i	$-0.872505\pi$
$47$		−	5.34620i		−	0.779824i	0.920852	−	0.389912i	$-0.127495\pi$
$48$		−	1.00000i		−	0.144338i
$49$	1.55007	−	2.68480i	0.221438	−	0.383543i
$50$	−4.18068	−	2.74260i	−0.591238	−	0.387863i
$51$		−	3.38867i		−	0.474509i
$52$	−0.379707	+	0.657673i	−0.0526559	+	0.0912028i
$53$	2.76662	+	1.59731i	0.380024	+	0.219407i	0.677829	−	0.735220i	$-0.262921\pi$
$53$	2.76662	+	1.59731i	0.380024	+	0.219407i	−0.297804	+	0.954627i	$0.596254\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	6.30770	−	5.95806i	0.850530	−	0.803385i
$56$	−2.75229	+	1.58904i	−0.367790	+	0.212344i
$57$	−2.62790	+	4.55166i	−0.348074	+	0.602882i
$58$	1.13197	+	0.653545i	0.148635	+	0.0858147i
$59$	−5.34529	−	3.08610i	−0.695897	−	0.401776i	0.109920	−	0.993940i	$-0.464940\pi$
$59$	−5.34529	−	3.08610i	−0.695897	−	0.401776i	−0.805817	+	0.592164i	$0.798274\pi$
$60$	−2.17549	+	0.516959i	−0.280854	+	0.0667391i
$61$	−8.45447	+	4.88119i	−1.08248	+	0.624973i	−0.931565	−	0.363574i	$-0.881557\pi$
$61$	−8.45447	+	4.88119i	−1.08248	+	0.624973i	−0.150919	+	0.988546i	$0.548223\pi$
$62$	−5.30382	−	3.06216i	−0.673586	−	0.388895i
$63$		−	3.17807i		−	0.400399i
$64$	1.00000			0.125000
$65$	1.62705	+	0.486060i	0.201811	+	0.0602883i
$66$		−	3.88035i		−	0.477638i
$67$	−8.72817	+	5.03921i	−1.06632	+	0.615638i	−0.927173	−	0.374634i	$-0.877768\pi$
$67$	−8.72817	+	5.03921i	−1.06632	+	0.615638i	−0.139144	+	0.990272i	$0.544435\pi$
$68$	3.38867			0.410937
$69$	5.73009	−	3.30827i	0.689821	−	0.398269i
$70$	4.87975	+	5.16611i	0.583242	+	0.617469i
$71$	−3.22083	−	5.57863i	−0.382242	−	0.662062i	0.609141	−	0.793062i	$-0.291514\pi$
$71$	−3.22083	−	5.57863i	−0.382242	−	0.662062i	−0.991382	+	0.131000i	$0.958181\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$			5.84525i			0.684135i	0.939675	+	0.342067i	$0.111127\pi$
$73$			5.84525i			0.684135i	−0.939675	+	0.342067i	$0.888873\pi$
$74$	−2.49875	+	5.54583i	−0.290474	+	0.644690i
$75$	2.24928	+	4.46551i	0.259724	+	0.515632i
$76$	−4.55166	−	2.62790i	−0.522111	−	0.301441i
$77$	−10.6799	+	6.16602i	−1.21708	+	0.702683i
$78$	0.657673	−	0.379707i	0.0744668	−	0.0429934i
$79$	7.39006	−	4.26665i	0.831446	−	0.480036i	−0.0229014	−	0.999738i	$-0.507290\pi$
$79$	7.39006	−	4.26665i	0.831446	−	0.480036i	0.854348	+	0.519702i	$0.173957\pi$
$80$	−0.516959	−	2.17549i	−0.0577978	−	0.243227i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.3435			−1.14225
$83$	6.05368	+	3.49509i	0.664477	+	0.383636i	0.793981	−	0.607943i	$-0.208005\pi$
$83$	6.05368	+	3.49509i	0.664477	+	0.383636i	−0.129504	+	0.991579i	$0.541338\pi$
$84$	3.17807			0.346756
$85$	−1.75181	−	7.37202i	−0.190010	−	0.799608i
$86$	−4.70922	+	8.15661i	−0.507808	+	0.879550i
$87$	−0.653545	−	1.13197i	−0.0700674	−	0.121360i
$88$	3.88035			0.413647
$89$	−1.93582	−	1.11765i	−0.205197	−	0.118470i	0.393880	−	0.919162i	$-0.371132\pi$
$89$	−1.93582	−	1.11765i	−0.205197	−	0.118470i	−0.599077	+	0.800691i	$0.704466\pi$
$90$	2.14251	+	0.640045i	0.225840	+	0.0674667i
$91$	−2.09013	−	1.20674i	−0.219105	−	0.126500i
$92$	3.30827	+	5.73009i	0.344911	+	0.597403i
$93$	3.06216	+	5.30382i	0.317532	+	0.549981i
$94$	−4.62995	−	2.67310i	−0.477543	−	0.275709i
$95$	−3.36395	+	11.2606i	−0.345134	+	1.15531i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−4.77178			−0.484501			−0.242250	−	0.970214i	$-0.577886\pi$
$97$	−4.77178			−0.484501			−0.242250	+	0.970214i	$0.577886\pi$
$98$	−1.55007	−	2.68480i	−0.156581	−	0.271206i
$99$	−1.94018	+	3.36048i	−0.194995	+	0.337741i
$100$	−4.46551	+	2.24928i	−0.446551	+	0.224928i
$101$	2.01613			0.200612			0.100306	−	0.994957i	$-0.468018\pi$
$101$	2.01613			0.200612			0.100306	+	0.994957i	$0.468018\pi$
$102$	−2.93468	−	1.69434i	−0.290576	−	0.167764i
$103$	−8.06815			−0.794978			−0.397489	−	0.917607i	$-0.630118\pi$
$103$	−8.06815			−0.794978			−0.397489	+	0.917607i	$0.630118\pi$
$104$	0.379707	+	0.657673i	0.0372334	+	0.0644901i
$105$	−1.64293	−	6.91386i	−0.160334	−	0.674724i
$106$	2.76662	−	1.59731i	0.268718	−	0.155144i
$107$	4.44127	−	2.56417i	0.429354	−	0.247887i	−0.269718	−	0.962939i	$-0.586930\pi$
$107$	4.44127	−	2.56417i	0.429354	−	0.247887i	0.699071	+	0.715052i	$0.253597\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−4.29464	−	2.47951i	−0.411352	−	0.237494i	0.280018	−	0.959995i	$-0.409659\pi$
$109$	−4.29464	−	2.47951i	−0.411352	−	0.237494i	−0.691371	+	0.722500i	$0.742993\pi$
$110$	−2.00598	−	8.44166i	−0.191263	−	0.804881i
$111$	4.93690	−	3.55346i	0.468589	−	0.337279i
$112$			3.17807i			0.300300i
$113$	5.50508	−	9.53507i	0.517874	−	0.896984i	−0.481910	−	0.876221i	$-0.660057\pi$
$113$	5.50508	−	9.53507i	0.517874	−	0.896984i	0.999784	−	0.0207636i	$-0.00660974\pi$
$114$	2.62790	+	4.55166i	0.246125	+	0.426302i
$115$	10.7555	−	10.1593i	1.00296	−	0.947361i
$116$	1.13197	−	0.653545i	0.105101	−	0.0606802i
$117$	−0.759415			−0.0702079
$118$	−5.34529	+	3.08610i	−0.492074	+	0.284099i
$119$			10.7694i			0.987234i
$120$	−0.640045	+	2.14251i	−0.0584279	+	0.195583i
$121$	4.05712			0.368829
$122$			9.76238i			0.883845i
$123$	8.95773	+	5.17175i	0.807691	+	0.466321i
$124$	−5.30382	+	3.06216i	−0.476297	+	0.274990i
$125$	7.20176	+	8.55188i	0.644145	+	0.764903i
$126$	−2.75229	−	1.58904i	−0.245194	−	0.141563i
$127$	13.0596	+	7.53996i	1.15885	+	0.669063i	0.951029	−	0.309103i	$-0.100029\pi$
$127$	13.0596	+	7.53996i	1.15885	+	0.669063i	0.207823	+	0.978166i	$0.433362\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	8.15661	−	4.70922i	0.718149	−	0.414624i
$130$	1.23447	−	1.16604i	0.108270	−	0.102268i
$131$	9.51251	+	5.49205i	0.831112	+	0.479843i	0.854233	−	0.519890i	$-0.174027\pi$
$131$	9.51251	+	5.49205i	0.831112	+	0.479843i	−0.0231214	+	0.999733i	$0.507360\pi$
$132$	−3.36048	−	1.94018i	−0.292492	−	0.168871i
$133$	8.35166	−	14.4655i	0.724180	−	1.25432i
$134$			10.0784i			0.870644i
$135$	−1.53544	−	1.62555i	−0.132150	−	0.139905i
$136$	1.69434	−	2.93468i	0.145288	−	0.251647i
$137$		−	1.70269i		−	0.145471i	−0.997351	−	0.0727353i	$-0.976827\pi$
$137$		−	1.70269i		−	0.145471i	0.997351	−	0.0727353i	$-0.0231728\pi$
$138$		−	6.61653i		−	0.563237i
$139$	8.79340	−	15.2306i	0.745846	−	1.29184i	−0.203952	−	0.978981i	$-0.565379\pi$
$139$	8.79340	−	15.2306i	0.745846	−	1.29184i	0.949798	−	0.312863i	$-0.101288\pi$
$140$	6.91386	−	1.64293i	0.584328	−	0.138853i
$141$	2.67310	+	4.62995i	0.225116	+	0.389912i
$142$	−6.44165			−0.540571
$143$	1.47340	+	2.55200i	0.123212	+	0.213409i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−2.00696	−	2.12474i	−0.166669	−	0.176450i
$146$	5.06214	+	2.92263i	0.418945	+	0.241878i
$147$			3.10014i			0.255695i
$148$	3.55346	+	4.93690i	0.292092	+	0.405810i
$149$	18.0769			1.48092			0.740458	−	0.672103i	$-0.234609\pi$
$149$	18.0769			1.48092			0.740458	+	0.672103i	$0.234609\pi$
$150$	4.99188	+	0.284822i	0.407585	+	0.0232556i
$151$	7.75253	+	13.4278i	0.630892	+	1.09274i	0.987370	+	0.158433i	$0.0506441\pi$
$151$	7.75253	+	13.4278i	0.630892	+	1.09274i	−0.356478	+	0.934304i	$0.616023\pi$
$152$	−4.55166	+	2.62790i	−0.369188	+	0.213151i
$153$	1.69434	+	2.93468i	0.136979	+	0.237255i
$154$			12.3320i			0.993744i
$155$	9.40356	+	9.95540i	0.755312	+	0.799637i
$156$		−	0.759415i		−	0.0608019i
$157$	−4.26063	−	2.45988i	−0.340035	−	0.196320i	0.320252	−	0.947332i	$-0.396232\pi$
$157$	−4.26063	−	2.45988i	−0.340035	−	0.196320i	−0.660288	+	0.751013i	$0.729566\pi$
$158$		−	8.53330i		−	0.678873i
$159$	−3.19462			−0.253350
$160$	−2.14251	−	0.640045i	−0.169380	−	0.0506000i
$161$	−18.2106	+	10.5139i	−1.43520	+	0.828612i
$162$	−1.00000			−0.0785674
$163$	−3.02056	+	5.23176i	−0.236588	+	0.409783i	−0.959733	−	0.280914i	$-0.909363\pi$
$163$	−3.02056	+	5.23176i	−0.236588	+	0.409783i	0.723145	+	0.690696i	$0.242696\pi$
$164$	−5.17175	+	8.95773i	−0.403845	+	0.699481i
$165$	−2.48360	+	8.31368i	−0.193348	+	0.647219i
$166$	6.05368	−	3.49509i	0.469856	−	0.271272i
$167$	9.53467	+	16.5145i	0.737815	+	1.27793i	0.953477	+	0.301465i	$0.0974755\pi$
$167$	9.53467	+	16.5145i	0.737815	+	1.27793i	−0.215663	+	0.976468i	$0.569191\pi$
$168$	1.58904	−	2.75229i	0.122597	−	0.212344i
$169$	6.21164	−	10.7589i	0.477819	−	0.827606i
$170$	−7.26026	−	2.16890i	−0.556837	−	0.166347i
$171$		−	5.25580i		−	0.401921i
$172$	4.70922	+	8.15661i	0.359075	+	0.621936i
$173$	−17.6459	−	10.1879i	−1.34160	−	0.774571i	−0.354554	−	0.935035i	$-0.615367\pi$
$173$	−17.6459	−	10.1879i	−1.34160	−	0.774571i	−0.987042	+	0.160465i	$0.948701\pi$
$174$	−1.30709			−0.0990903
$175$	−7.14836	−	14.1917i	−0.540365	−	1.07279i
$176$	1.94018	−	3.36048i	0.146246	−	0.253306i
$177$	6.17221			0.463931
$178$	−1.93582	+	1.11765i	−0.145096	+	0.0837713i
$179$			1.86502i			0.139398i	0.997568	+	0.0696989i	$0.0222039\pi$
$179$			1.86502i			0.139398i	−0.997568	+	0.0696989i	$0.977796\pi$
$180$	1.62555	−	1.53544i	0.121161	−	0.114445i
$181$	6.08878	+	10.5461i	0.452575	+	0.783884i	0.998545	−	0.0539212i	$-0.0171720\pi$
$181$	6.08878	+	10.5461i	0.452575	+	0.783884i	−0.545970	+	0.837805i	$0.683839\pi$
$182$	−2.09013	+	1.20674i	−0.154931	+	0.0894493i
$183$	4.88119	−	8.45447i	0.360828	−	0.624973i
$184$	6.61653			0.487777
$185$	8.90317	−	10.2827i	0.654574	−	0.755998i
$186$	6.12433			0.449057
$187$	6.57462	−	11.3876i	0.480784	−	0.832742i
$188$	−4.62995	+	2.67310i	−0.337674	+	0.194956i
$189$	1.58904	+	2.75229i	0.115585	+	0.200200i
$190$	8.06999	+	8.54356i	0.585459	+	0.619815i
$191$		−	21.9186i		−	1.58597i	−0.609240	−	0.792986i	$-0.708525\pi$
$191$		−	21.9186i		−	1.58597i	0.609240	−	0.792986i	$-0.291475\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	6.01088			0.432672			0.216336	−	0.976319i	$-0.430589\pi$
$193$	6.01088			0.432672			0.216336	+	0.976319i	$0.430589\pi$
$194$	−2.38589	+	4.13248i	−0.171297	+	0.296695i
$195$	−1.65210	+	0.392586i	−0.118309	+	0.0281137i
$196$	−3.10014			−0.221438
$197$	−16.0895	−	9.28928i	−1.14633	−	0.661834i	−0.198340	−	0.980133i	$-0.563555\pi$
$197$	−16.0895	−	9.28928i	−1.14633	−	0.661834i	−0.947990	+	0.318299i	$0.896888\pi$
$198$	1.94018	+	3.36048i	0.137882	+	0.238819i
$199$		−	2.04121i		−	0.144697i	−0.997379	−	0.0723487i	$-0.976951\pi$
$199$		−	2.04121i		−	0.144697i	0.997379	−	0.0723487i	$-0.0230495\pi$
$200$	−0.284822	+	4.99188i	−0.0201400	+	0.352979i
$201$	5.03921	−	8.72817i	0.355439	−	0.615638i
$202$	1.00807	−	1.74602i	0.0709272	−	0.122850i
$203$	2.07701	+	3.59749i	0.145778	+	0.252494i
$204$	−2.93468	+	1.69434i	−0.205469	+	0.118627i
$205$	22.1610	+	6.62030i	1.54779	+	0.462382i
$206$	−4.03407	+	6.98722i	−0.281067	+	0.486823i
$207$	−3.30827	+	5.73009i	−0.229940	+	0.398269i
$208$	0.759415			0.0526559
$209$	−17.6620	+	10.1972i	−1.22171	+	0.705353i
$210$	−6.80904	−	2.03411i	−0.469869	−	0.140367i
$211$	13.3152			0.916658			0.458329	−	0.888783i	$-0.348448\pi$
$211$	13.3152			0.916658			0.458329	+	0.888783i	$0.348448\pi$
$212$		−	3.19462i		−	0.219407i
$213$	5.57863	+	3.22083i	0.382242	+	0.220687i
$214$		−	5.12833i		−	0.350566i
$215$	15.3101	−	14.4615i	1.04414	−	0.986265i
$216$		−	1.00000i		−	0.0680414i
$217$	−9.73177	−	16.8559i	−0.660636	−	1.14425i
$218$	−4.29464	+	2.47951i	−0.290870	+	0.167934i
$219$	−2.92263	−	5.06214i	−0.197493	−	0.342067i
$220$	−8.31368	−	2.48360i	−0.560508	−	0.167444i
$221$	2.57341			0.173106
$222$	−0.608935	−	6.05221i	−0.0408691	−	0.406197i
$223$		−	14.8913i		−	0.997193i	−0.866834	−	0.498597i	$-0.833849\pi$
$223$		−	14.8913i		−	0.997193i	0.866834	−	0.498597i	$-0.166151\pi$
$224$	2.75229	+	1.58904i	0.183895	+	0.106172i
$225$	−4.18068	−	2.74260i	−0.278712	−	0.182840i
$226$	−5.50508	−	9.53507i	−0.366192	−	0.634264i
$227$	0.708052	+	1.22638i	0.0469951	+	0.0813979i	0.888566	−	0.458749i	$-0.151702\pi$
$227$	0.708052	+	1.22638i	0.0469951	+	0.0813979i	−0.841571	+	0.540146i	$0.818369\pi$
$228$	5.25580			0.348074
$229$	−13.9106	−	24.0938i	−0.919237	−	1.59217i	−0.800576	−	0.599231i	$-0.795473\pi$
$229$	−13.9106	−	24.0938i	−0.919237	−	1.59217i	−0.118661	−	0.992935i	$-0.537860\pi$
$230$	−3.42048	−	14.3942i	−0.225540	−	0.949125i
$231$	6.16602	−	10.6799i	0.405694	−	0.702683i
$232$		−	1.30709i		−	0.0858147i
$233$			21.1423i			1.38508i	0.721382	+	0.692538i	$0.243507\pi$
$233$			21.1423i			1.38508i	−0.721382	+	0.692538i	$0.756493\pi$
$234$	−0.379707	+	0.657673i	−0.0248223	+	0.0429934i
$235$	8.20879	+	8.69052i	0.535483	+	0.566907i
$236$			6.17221i			0.401776i
$237$	−4.26665	+	7.39006i	−0.277149	+	0.480036i
$238$	9.32662	+	5.38472i	0.604555	+	0.349040i
$239$	−5.13952	−	2.96731i	−0.332448	−	0.191939i	0.324479	−	0.945893i	$-0.394811\pi$
$239$	−5.13952	−	2.96731i	−0.332448	−	0.191939i	−0.656927	+	0.753954i	$0.728144\pi$
$240$	1.53544	+	1.62555i	0.0991125	+	0.104929i
$241$	−21.6064	+	12.4744i	−1.39179	+	0.803550i	−0.993513	−	0.113716i	$-0.963725\pi$
$241$	−21.6064	+	12.4744i	−1.39179	+	0.803550i	−0.398276	+	0.917266i	$0.630391\pi$
$242$	2.02856	−	3.51357i	0.130401	−	0.225861i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	8.45447	+	4.88119i	0.541242	+	0.312486i
$245$	1.60264	+	6.74432i	0.102389	+	0.430879i
$246$	8.95773	−	5.17175i	0.571124	−	0.329738i
$247$	−3.45660	−	1.99567i	−0.219938	−	0.126981i
$248$			6.12433i			0.388895i
$249$	−6.99018			−0.442985
$250$	11.0070	−	1.96097i	0.696145	−	0.124023i
$251$			5.08160i			0.320748i	0.987056	+	0.160374i	$0.0512700\pi$
$251$			5.08160i			0.320748i	−0.987056	+	0.160374i	$0.948730\pi$
$252$	−2.75229	+	1.58904i	−0.173378	+	0.100100i
$253$	25.6745			1.61414
$254$	13.0596	−	7.53996i	0.819432	−	0.473099i
$255$	5.20312	+	5.50846i	0.325832	+	0.344953i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.08288	+	8.80380i	−0.317061	+	0.549166i	−0.979873	−	0.199620i	$-0.936029\pi$
$257$	−5.08288	+	8.80380i	−0.317061	+	0.549166i	0.662812	+	0.748786i	$0.269363\pi$
$258$		−	9.41844i		−	0.586366i
$259$	−15.6898	+	11.2931i	−0.974917	+	0.701722i
$260$	−0.392586	−	1.65210i	−0.0243472	−	0.102459i
$261$	1.13197	+	0.653545i	0.0700674	+	0.0404534i
$262$	9.51251	−	5.49205i	0.587685	−	0.339300i
$263$	13.5376	−	7.81597i	0.834767	−	0.481953i	−0.0207149	−	0.999785i	$-0.506594\pi$
$263$	13.5376	−	7.81597i	0.834767	−	0.481953i	0.855482	+	0.517832i	$0.173261\pi$
$264$	−3.36048	+	1.94018i	−0.206823	+	0.119410i
$265$	−6.94986	+	1.65149i	−0.426926	+	0.101450i
$266$	−8.35166	−	14.4655i	−0.512073	−	0.886936i
$267$	2.23530			0.136798
$268$	8.72817	+	5.03921i	0.533158	+	0.307819i
$269$	−17.1683			−1.04677			−0.523384	−	0.852097i	$-0.675330\pi$
$269$	−17.1683			−1.04677			−0.523384	+	0.852097i	$0.675330\pi$
$270$	−2.17549	+	0.516959i	−0.132396	+	0.0314611i
$271$	−4.20412	+	7.28174i	−0.255382	+	0.442334i	−0.964999	−	0.262253i	$-0.915535\pi$
$271$	−4.20412	+	7.28174i	−0.255382	+	0.442334i	0.709617	+	0.704587i	$0.248868\pi$
$272$	−1.69434	−	2.93468i	−0.102734	−	0.177941i
$273$	2.41347			0.146070
$274$	−1.47457	−	0.851345i	−0.0890822	−	0.0514316i
$275$	−1.10521	+	19.3703i	−0.0666467	+	1.16807i
$276$	−5.73009	−	3.30827i	−0.344911	−	0.199134i
$277$	14.0962	+	24.4154i	0.846960	+	1.46698i	0.883908	+	0.467661i	$0.154903\pi$
$277$	14.0962	+	24.4154i	0.846960	+	1.46698i	−0.0369475	+	0.999317i	$0.511763\pi$
$278$	−8.79340	−	15.2306i	−0.527393	−	0.913472i
$279$	−5.30382	−	3.06216i	−0.317532	−	0.183327i
$280$	2.03411	−	6.80904i	0.121561	−	0.406918i
$281$	−18.0402	−	10.4155i	−1.07619	−	0.621339i	−0.146324	−	0.989237i	$-0.546744\pi$
$281$	−18.0402	−	10.4155i	−1.07619	−	0.621339i	−0.929866	+	0.367898i	$0.880078\pi$
$282$	5.34620			0.318362
$283$	7.70394	+	13.3436i	0.457952	+	0.793196i	0.998853	−	0.0478906i	$-0.0152499\pi$
$283$	7.70394	+	13.3436i	0.457952	+	0.793196i	−0.540901	+	0.841086i	$0.681917\pi$
$284$	−3.22083	+	5.57863i	−0.191121	+	0.331031i
$285$	−2.71703	−	11.4339i	−0.160943	−	0.677288i
$286$	2.94680			0.174248
$287$	−28.4683	−	16.4362i	−1.68043	−	0.970197i
$288$	1.00000			0.0589256
$289$	2.75844	+	4.77777i	0.162261	+	0.281045i
$290$	−2.84356	+	0.675712i	−0.166980	+	0.0396792i
$291$	4.13248	−	2.38589i	0.242250	−	0.139863i
$292$	5.06214	−	2.92263i	0.296239	−	0.171034i
$293$	−10.7757	+	6.22135i	−0.629523	+	0.363455i	−0.780567	−	0.625072i	$-0.785070\pi$
$293$	−10.7757	+	6.22135i	−0.629523	+	0.363455i	0.151044	+	0.988527i	$0.451736\pi$
$294$	2.68480	+	1.55007i	0.156581	+	0.0904019i
$295$	13.4276	−	3.19078i	0.781783	−	0.185774i
$296$	6.05221	−	0.608935i	0.351777	−	0.0353937i
$297$		−	3.88035i		−	0.225161i
$298$	9.03844	−	15.6550i	0.523583	−	0.906872i
$299$	2.51235	+	4.35151i	0.145293	+	0.251654i
$300$	2.74260	−	4.18068i	0.158344	−	0.241372i
$301$	−25.9223	+	14.9662i	−1.49414	+	0.862640i
$302$	15.5051			0.892215
$303$	−1.74602	+	1.00807i	−0.100306	+	0.0579118i
$304$			5.25580i			0.301441i
$305$	6.24837	−	20.9160i	0.357780	−	1.19765i
$306$	3.38867			0.193718
$307$			28.9874i			1.65440i	0.561910	+	0.827199i	$0.310067\pi$
$307$			28.9874i			1.65440i	−0.561910	+	0.827199i	$0.689933\pi$
$308$	10.6799	+	6.16602i	0.608541	+	0.351341i
$309$	6.98722	−	4.03407i	0.397489	−	0.229490i
$310$	13.3234	−	3.16603i	0.756719	−	0.179818i
$311$	−0.445283	−	0.257084i	−0.0252497	−	0.0145779i	0.487322	−	0.873222i	$-0.337974\pi$
$311$	−0.445283	−	0.257084i	−0.0252497	−	0.0145779i	−0.512572	+	0.858644i	$0.671307\pi$
$312$	−0.657673	−	0.379707i	−0.0372334	−	0.0214967i
$313$	11.2521	−	19.4892i	0.636006	−	1.10160i	−0.350295	−	0.936640i	$-0.613919\pi$
$313$	11.2521	−	19.4892i	0.636006	−	1.10160i	0.986301	−	0.164956i	$-0.0527481\pi$
$314$	−4.26063	+	2.45988i	−0.240441	+	0.138819i
$315$	4.87975	+	5.16611i	0.274943	+	0.291077i
$316$	−7.39006	−	4.26665i	−0.415723	−	0.240018i
$317$	6.11367	+	3.52973i	0.343378	+	0.198249i	0.661765	−	0.749712i	$-0.269808\pi$
$317$	6.11367	+	3.52973i	0.343378	+	0.198249i	−0.318387	+	0.947961i	$0.603141\pi$
$318$	−1.59731	+	2.76662i	−0.0895726	+	0.155144i
$319$		−	5.07197i		−	0.283976i
$320$	−1.62555	+	1.53544i	−0.0908710	+	0.0858339i
$321$	−2.56417	+	4.44127i	−0.143118	+	0.247887i
$322$			21.0278i			1.17183i
$323$			17.8102i			0.990986i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−3.39117	+	1.70813i	−0.188108	+	0.0947503i
$326$	3.02056	+	5.23176i	0.167293	+	0.289760i
$327$	4.95903			0.274235
$328$	5.17175	+	8.95773i	0.285562	+	0.494608i
$329$	−8.49531	−	14.7143i	−0.468361	−	0.811226i
$330$	5.95806	+	6.30770i	0.327981	+	0.347228i
$331$	11.4620	+	6.61756i	0.630006	+	0.363734i	0.780754	−	0.624838i	$-0.214835\pi$
$331$	11.4620	+	6.61756i	0.630006	+	0.363734i	−0.150748	+	0.988572i	$0.548168\pi$
$332$		−	6.99018i		−	0.383636i
$333$	−2.49875	+	5.54583i	−0.136931	+	0.303910i
$334$	19.0693			1.04343
$335$	6.45065	−	21.5931i	0.352437	−	1.17976i
$336$	−1.58904	−	2.75229i	−0.0866890	−	0.150150i
$337$	8.19202	−	4.72967i	0.446248	−	0.257641i	−0.259996	−	0.965610i	$-0.583721\pi$
$337$	8.19202	−	4.72967i	0.446248	−	0.257641i	0.706244	+	0.707968i	$0.250388\pi$
$338$	−6.21164	−	10.7589i	−0.337869	−	0.585206i
$339$			11.0102i			0.597989i
$340$	−5.50846	+	5.20312i	−0.298738	+	0.282179i
$341$			23.7645i			1.28692i
$342$	−4.55166	−	2.62790i	−0.246125	−	0.142101i
$343$			12.3940i			0.669215i
$344$	9.41844			0.507808
$345$	−4.23488	+	14.1760i	−0.227998	+	0.763209i
$346$	−17.6459	+	10.1879i	−0.948652	+	0.547704i
$347$	6.97276			0.374317			0.187159	−	0.982330i	$-0.440072\pi$
$347$	6.97276			0.374317			0.187159	+	0.982330i	$0.440072\pi$
$348$	−0.653545	+	1.13197i	−0.0350337	+	0.0606802i
$349$	−4.99936	+	8.65914i	−0.267609	+	0.463513i	−0.968244	−	0.250007i	$-0.919567\pi$
$349$	−4.99936	+	8.65914i	−0.267609	+	0.463513i	0.700635	+	0.713520i	$0.252900\pi$
$350$	−15.8646	−	0.905186i	−0.847996	−	0.0483842i
$351$	0.657673	−	0.379707i	0.0351040	−	0.0202673i
$352$	−1.94018	−	3.36048i	−0.103412	−	0.179114i
$353$	−0.898282	+	1.55587i	−0.0478107	+	0.0828106i	−0.888940	−	0.458023i	$-0.848558\pi$
$353$	−0.898282	+	1.55587i	−0.0478107	+	0.0828106i	0.841130	+	0.540834i	$0.181891\pi$
$354$	3.08610	−	5.34529i	0.164025	−	0.284099i
$355$	13.8013	+	4.12295i	0.732497	+	0.218823i
$356$			2.23530i			0.118470i
$357$	−5.38472	−	9.32662i	−0.284990	−	0.493617i
$358$	1.61515	+	0.932508i	0.0853634	+	0.0492846i
$359$	36.2514			1.91327			0.956637	−	0.291283i	$-0.0940822\pi$
$359$	36.2514			1.91327			0.956637	+	0.291283i	$0.0940822\pi$
$360$	−0.516959	−	2.17549i	−0.0272461	−	0.114658i
$361$	4.31172	−	7.46812i	0.226933	−	0.393059i
$362$	12.1776			0.640038
$363$	−3.51357	+	2.02856i	−0.184415	+	0.106472i
$364$			2.41347i			0.126500i
$365$	−8.97506	−	9.50174i	−0.469776	−	0.497344i
$366$	−4.88119	−	8.45447i	−0.255144	−	0.441922i
$367$	−24.0265	+	13.8717i	−1.25417	+	0.724096i	−0.971935	−	0.235249i	$-0.924409\pi$
$367$	−24.0265	+	13.8717i	−1.25417	+	0.724096i	−0.282236	+	0.959345i	$0.591076\pi$
$368$	3.30827	−	5.73009i	0.172455	−	0.298701i
$369$	−10.3435			−0.538461
$370$	−4.45347	−	12.8517i	−0.231525	−	0.668129i
$371$	10.1527			0.527103
$372$	3.06216	−	5.30382i	0.158766	−	0.274990i
$373$	13.7243	−	7.92370i	0.710615	−	0.410274i	−0.100674	−	0.994919i	$-0.532100\pi$
$373$	13.7243	−	7.92370i	0.710615	−	0.410274i	0.811289	+	0.584646i	$0.198767\pi$
$374$	−6.57462	−	11.3876i	−0.339966	−	0.588838i
$375$	−10.5128	−	3.80526i	−0.542881	−	0.196503i
$376$			5.34620i			0.275709i
$377$	0.859638	−	0.496312i	0.0442736	−	0.0255614i
$378$	3.17807			0.163462
$379$	12.5851	−	21.7980i	0.646453	−	1.11969i	−0.337511	−	0.941322i	$-0.609585\pi$
$379$	12.5851	−	21.7980i	0.646453	−	1.11969i	0.983964	−	0.178367i	$-0.0570816\pi$
$380$	11.4339	−	2.71703i	0.586549	−	0.139381i
$381$	−15.0799			−0.772568
$382$	−18.9820	−	10.9593i	−0.971205	−	0.560726i
$383$	−7.99822	−	13.8533i	−0.408690	−	0.707872i	0.586053	−	0.810273i	$-0.300681\pi$
$383$	−7.99822	−	13.8533i	−0.408690	−	0.707872i	−0.994743	+	0.102401i	$0.967348\pi$
$384$			1.00000i			0.0510310i
$385$	7.89306	−	26.4215i	0.402267	−	1.34656i
$386$	3.00544	−	5.20557i	0.152973	−	0.264957i
$387$	−4.70922	+	8.15661i	−0.239383	+	0.414624i
$388$	2.38589	+	4.13248i	0.121125	+	0.209795i
$389$	5.81063	−	3.35477i	0.294611	−	0.170093i	−0.345409	−	0.938452i	$-0.612260\pi$
$389$	5.81063	−	3.35477i	0.294611	−	0.170093i	0.640019	+	0.768359i	$0.278926\pi$
$390$	−0.486060	+	1.62705i	−0.0246126	+	0.0823890i
$391$	11.2106	−	19.4174i	0.566946	−	0.981980i
$392$	−1.55007	+	2.68480i	−0.0782903	+	0.135603i
$393$	−10.9841			−0.554074
$394$	−16.0895	+	9.28928i	−0.810578	+	0.467987i
$395$	−5.46170	+	18.2827i	−0.274808	+	0.919901i
$396$	3.88035			0.194995
$397$		−	19.4407i		−	0.975703i	−0.872927	−	0.487851i	$-0.837781\pi$
$397$		−	19.4407i		−	0.975703i	0.872927	−	0.487851i	$-0.162219\pi$
$398$	−1.76774	−	1.02060i	−0.0886087	−	0.0511583i
$399$			16.7033i			0.836212i
$400$	4.18068	+	2.74260i	0.209034	+	0.137130i
$401$		−	0.994109i		−	0.0496434i	−0.999692	−	0.0248217i	$-0.992098\pi$
$401$		−	0.994109i		−	0.0496434i	0.999692	−	0.0248217i	$-0.00790181\pi$
$402$	−5.03921	−	8.72817i	−0.251333	−	0.435322i
$403$	−4.02780	+	2.32545i	−0.200639	+	0.115839i
$404$	−1.00807	−	1.74602i	−0.0501531	−	0.0868677i
$405$	2.14251	+	0.640045i	0.106462	+	0.0318041i
$406$	4.15403			0.206161
$407$	23.4847	−	2.36288i	1.16409	−	0.117124i
$408$			3.38867i			0.167764i
$409$	−26.9360	−	15.5515i	−1.33190	−	0.768973i	−0.346309	−	0.938120i	$-0.612565\pi$
$409$	−26.9360	−	15.5515i	−1.33190	−	0.768973i	−0.985591	+	0.169148i	$0.945898\pi$
$410$	16.8139	−	15.8819i	0.830377	−	0.784349i
$411$	0.851345	+	1.47457i	0.0419938	+	0.0727353i
$412$	4.03407	+	6.98722i	0.198745	+	0.344236i
$413$	−19.6157			−0.965226
$414$	3.30827	+	5.73009i	0.162592	+	0.281618i
$415$	−15.2071	+	3.61364i	−0.746486	+	0.177386i
$416$	0.379707	−	0.657673i	0.0186167	−	0.0322451i
$417$			17.5868i			0.861229i
$418$			20.3944i			0.997520i
$419$	19.2268	−	33.3019i	0.939293	−	1.62690i	0.172498	−	0.985010i	$-0.444816\pi$
$419$	19.2268	−	33.3019i	0.939293	−	1.62690i	0.766794	−	0.641893i	$-0.221851\pi$
$420$	−5.16611	+	4.87975i	−0.252080	+	0.238107i
$421$		−	9.18954i		−	0.447871i	−0.974604	−	0.223935i	$-0.928110\pi$
$421$		−	9.18954i		−	0.447871i	0.974604	−	0.223935i	$-0.0718905\pi$
$422$	6.65761	−	11.5313i	0.324088	−	0.561336i
$423$	−4.62995	−	2.67310i	−0.225116	−	0.129971i
$424$	−2.76662	−	1.59731i	−0.134359	−	0.0775722i
$425$	14.1670	+	9.29379i	0.687199	+	0.450815i
$426$	5.57863	−	3.22083i	0.270286	−	0.156050i
$427$	−15.5128	+	26.8689i	−0.750716	+	1.30028i
$428$	−4.44127	−	2.56417i	−0.214677	−	0.123944i
$429$	−2.55200	−	1.47340i	−0.123212	−	0.0711363i
$430$	−4.86895	−	20.4897i	−0.234801	−	0.988102i
$431$	−9.79127	+	5.65299i	−0.471629	+	0.272295i	−0.716921	−	0.697154i	$-0.754449\pi$
$431$	−9.79127	+	5.65299i	−0.471629	+	0.272295i	0.245293	+	0.969449i	$0.421116\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	19.1591i		−	0.920727i	−0.887731	−	0.460363i	$-0.847719\pi$
$433$		−	19.1591i		−	0.920727i	0.887731	−	0.460363i	$-0.152281\pi$
$434$	−19.4635			−0.934280
$435$	2.80045	+	0.836597i	0.134271	+	0.0401117i
$436$			4.95903i			0.237494i
$437$	−30.1162	+	17.3876i	−1.44065	+	0.831761i
$438$	−5.84525			−0.279297
$439$	28.6432	−	16.5371i	1.36706	−	0.789274i	0.376511	−	0.926412i	$-0.377124\pi$
$439$	28.6432	−	16.5371i	1.36706	−	0.789274i	0.990552	+	0.137138i	$0.0437903\pi$
$440$	−6.30770	+	5.95806i	−0.300708	+	0.284039i
$441$	−1.55007	−	2.68480i	−0.0738128	−	0.127848i
$442$	1.28670	−	2.22864i	0.0612023	−	0.106005i
$443$		−	0.475614i		−	0.0225971i	−0.999936	−	0.0112985i	$-0.996403\pi$
$443$		−	0.475614i		−	0.0225971i	0.999936	−	0.0112985i	$-0.00359651\pi$
$444$	−5.54583	−	2.49875i	−0.263194	−	0.118585i
$445$	4.86286	−	1.15556i	0.230522	−	0.0547786i
$446$	−12.8962	−	7.44563i	−0.610654	−	0.352561i
$447$	−15.6550	+	9.03844i	−0.740458	+	0.427503i
$448$	2.75229	−	1.58904i	0.130034	−	0.0750749i
$449$	−33.9306	+	19.5898i	−1.60128	+	0.924502i	−0.610053	+	0.792360i	$0.708852\pi$
$449$	−33.9306	+	19.5898i	−1.60128	+	0.924502i	−0.991231	+	0.132141i	$0.957815\pi$
$450$	−4.46551	+	2.24928i	−0.210506	+	0.106032i
$451$	20.0682	+	34.7591i	0.944974	+	1.63674i
$452$	−11.0102			−0.517874
$453$	−13.4278	−	7.75253i	−0.630892	−	0.364245i
$454$	1.41610			0.0664611
$455$	5.25049	−	1.24767i	0.246147	−	0.0584915i
$456$	2.62790	−	4.55166i	0.123063	−	0.213151i
$457$	−6.27814	−	10.8741i	−0.293679	−	0.508667i	0.680998	−	0.732286i	$-0.261546\pi$
$457$	−6.27814	−	10.8741i	−0.293679	−	0.508667i	−0.974677	+	0.223618i	$0.928213\pi$
$458$	−27.8212			−1.30000
$459$	−2.93468	−	1.69434i	−0.136979	−	0.0790849i
$460$	−14.1760	−	4.23488i	−0.660958	−	0.197452i
$461$	−4.06075	−	2.34448i	−0.189128	−	0.109193i	0.402446	−	0.915444i	$-0.368160\pi$
$461$	−4.06075	−	2.34448i	−0.189128	−	0.109193i	−0.591574	+	0.806250i	$0.701493\pi$
$462$	−6.16602	−	10.6799i	−0.286869	−	0.496872i
$463$	−6.13895	−	10.6330i	−0.285301	−	0.494156i	0.687381	−	0.726297i	$-0.258760\pi$
$463$	−6.13895	−	10.6330i	−0.285301	−	0.494156i	−0.972682	+	0.232141i	$0.925427\pi$
$464$	−1.13197	−	0.653545i	−0.0525506	−	0.0303401i
$465$	−13.1214	−	3.91985i	−0.608491	−	0.181778i
$466$	18.3097	+	10.5711i	0.848182	+	0.489698i
$467$	12.6856			0.587021			0.293511	−	0.955956i	$-0.405176\pi$
$467$	12.6856			0.587021			0.293511	+	0.955956i	$0.405176\pi$
$468$	0.379707	+	0.657673i	0.0175520	+	0.0304009i
$469$	−16.0150	+	27.7388i	−0.739503	+	1.28086i
$470$	11.6306	−	2.76377i	0.536480	−	0.127483i
$471$	4.91975			0.226690
$472$	5.34529	+	3.08610i	0.246037	+	0.142049i
$473$	36.5468			1.68043
$474$	4.26665	+	7.39006i	0.195974	+	0.339436i
$475$	−11.8218	−	23.4698i	−0.542419	−	1.07687i
$476$	9.32662	−	5.38472i	0.427485	−	0.246808i
$477$	2.76662	−	1.59731i	0.126675	−	0.0731357i
$478$	−5.13952	+	2.96731i	−0.235076	+	0.135721i
$479$	−2.51613	−	1.45269i	−0.114965	−	0.0663750i	0.441415	−	0.897303i	$-0.354477\pi$
$479$	−2.51613	−	1.45269i	−0.114965	−	0.0663750i	−0.556380	+	0.830928i	$0.687810\pi$
$480$	2.17549	−	0.516959i	0.0992970	−	0.0235958i
$481$	2.69855	+	3.74915i	0.123043	+	0.170947i
$482$			24.9489i			1.13639i
$483$	10.5139	−	18.2106i	0.478399	−	0.828612i
$484$	−2.02856	−	3.51357i	−0.0922073	−	0.159708i
$485$	7.75676	−	7.32680i	0.352216	−	0.332693i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	0.439955			0.0199363			0.00996814	−	0.999950i	$-0.496827\pi$
$487$	0.439955			0.0199363			0.00996814	+	0.999950i	$0.496827\pi$
$488$	8.45447	−	4.88119i	0.382716	−	0.220961i
$489$		−	6.04111i		−	0.273189i
$490$	6.64207	+	1.98423i	0.300058	+	0.0896383i
$491$	38.7496			1.74875			0.874373	−	0.485254i	$-0.161273\pi$
$491$	38.7496			1.74875			0.874373	+	0.485254i	$0.161273\pi$
$492$		−	10.3435i		−	0.466321i
$493$	−3.83589	−	2.21465i	−0.172760	−	0.0997429i
$494$	−3.45660	+	1.99567i	−0.155520	+	0.0897893i
$495$	−2.00598	−	8.44166i	−0.0901622	−	0.379424i
$496$	5.30382	+	3.06216i	0.238149	+	0.137495i
$497$	−17.7293	−	10.2360i	−0.795268	−	0.459148i
$498$	−3.49509	+	6.05368i	−0.156619	+	0.271272i
$499$	−32.7624	+	18.9154i	−1.46665	+	0.846768i	−0.999304	−	0.0373082i	$-0.988122\pi$
$499$	−32.7624	+	18.9154i	−1.46665	+	0.846768i	−0.467342	+	0.884077i	$0.654788\pi$
$500$	3.80526	−	10.5128i	0.170177	−	0.470149i
$501$	−16.5145	−	9.53467i	−0.737815	−	0.425978i
$502$	4.40080	+	2.54080i	0.196417	+	0.113401i
$503$	−13.0136	+	22.5402i	−0.580246	+	1.00502i	0.415203	+	0.909729i	$0.363710\pi$
$503$	−13.0136	+	22.5402i	−0.580246	+	1.00502i	−0.995450	+	0.0952875i	$0.969623\pi$
$504$			3.17807i			0.141563i
$505$	−3.27732	+	3.09566i	−0.145839	+	0.137755i
$506$	12.8372	−	22.2347i	0.570685	−	0.988455i
$507$			12.4233i			0.551738i
$508$		−	15.0799i		−	0.669063i
$509$	−18.3204	+	31.7319i	−0.812038	+	1.40649i	0.0993971	+	0.995048i	$0.468309\pi$
$509$	−18.3204	+	31.7319i	−0.812038	+	1.40649i	−0.911435	+	0.411444i	$0.865025\pi$
$510$	7.37202	−	1.75181i	0.326439	−	0.0775712i
$511$	9.28831	+	16.0878i	0.410891	+	0.711684i
$512$	−1.00000			−0.0441942
$513$	2.62790	+	4.55166i	0.116025	+	0.200961i
$514$	5.08288	+	8.80380i	0.224196	+	0.388319i
$515$	13.1152	−	12.3882i	0.577924	−	0.545889i
$516$	−8.15661	−	4.70922i	−0.359075	−	0.207312i
$517$			20.7451i			0.912370i
$518$	1.93524	+	19.2343i	0.0850296	+	0.845109i
$519$	20.3758			0.894397
$520$	−1.62705	−	0.486060i	−0.0713510	−	0.0213151i
$521$	−6.87938	−	11.9154i	−0.301391	−	0.522025i	0.675060	−	0.737763i	$-0.264118\pi$
$521$	−6.87938	−	11.9154i	−0.301391	−	0.522025i	−0.976451	+	0.215738i	$0.930784\pi$
$522$	1.13197	−	0.653545i	0.0495451	−	0.0286049i
$523$	−0.135209	−	0.234189i	−0.00591228	−	0.0102404i	0.863054	−	0.505111i	$-0.168549\pi$
$523$	−0.135209	−	0.234189i	−0.00591228	−	0.0102404i	−0.868966	+	0.494871i	$0.835215\pi$
$524$		−	10.9841i		−	0.479843i
$525$	13.2865	+	8.71619i	0.579871	+	0.380406i
$526$		−	15.6319i		−	0.681585i
$527$	17.9729	+	10.3767i	0.782913	+	0.452015i
$528$			3.88035i			0.168871i
$529$	20.7785			0.903414
$530$	−2.04470	+	6.84449i	−0.0888160	+	0.297306i
$531$	−5.34529	+	3.08610i	−0.231966	+	0.133925i
$532$	−16.7033			−0.724180
$533$	−3.92750	+	6.80263i	−0.170119	+	0.294655i
$534$	1.11765	−	1.93582i	0.0483654	−	0.0837713i
$535$	−3.28237	+	10.9875i	−0.141909	+	0.475031i
$536$	8.72817	−	5.03921i	0.377000	−	0.217661i
$537$	−0.932508	−	1.61515i	−0.0402407	−	0.0696989i
$538$	−8.58413	+	14.8681i	−0.370088	+	0.641011i
$539$	−6.01481	+	10.4180i	−0.259076	+	0.448733i
$540$	−0.640045	+	2.14251i	−0.0275432	+	0.0921989i
$541$			33.4724i			1.43909i	0.694446	+	0.719545i	$0.255650\pi$
$541$			33.4724i			1.43909i	−0.694446	+	0.719545i	$0.744350\pi$
$542$	4.20412	+	7.28174i	0.180582	+	0.312778i
$543$	−10.5461	−	6.08878i	−0.452575	−	0.261295i
$544$	−3.38867			−0.145288
$545$	10.7883	−	2.56361i	0.462120	−	0.109813i
$546$	1.20674	−	2.09013i	0.0516436	−	0.0894493i
$547$	−41.8398			−1.78894			−0.894471	−	0.447126i	$-0.852448\pi$
$547$	−41.8398			−1.78894			−0.894471	+	0.447126i	$0.852448\pi$
$548$	−1.47457	+	0.851345i	−0.0629906	+	0.0363677i
$549$			9.76238i			0.416648i
$550$	16.2225	+	10.6423i	0.691731	+	0.453788i
$551$	3.43490	+	5.94943i	0.146332	+	0.253454i
$552$	−5.73009	+	3.30827i	−0.243889	+	0.140809i
$553$	13.5597	−	23.4861i	0.576618	−	0.998732i
$554$	28.1925			1.19778
$555$	−2.56904	+	13.3566i	−0.109049	+	0.566958i
$556$	−17.5868			−0.745846
$557$	−18.9097	+	32.7526i	−0.801230	+	1.38777i	0.117576	+	0.993064i	$0.462488\pi$
$557$	−18.9097	+	32.7526i	−0.801230	+	1.38777i	−0.918807	+	0.394708i	$0.870846\pi$
$558$	−5.30382	+	3.06216i	−0.224529	+	0.129632i
$559$	3.57625	+	6.19425i	0.151259	+	0.261989i
$560$	−4.87975	−	5.16611i	−0.206207	−	0.218308i
$561$			13.1492i			0.555162i
$562$	−18.0402	+	10.4155i	−0.760981	+	0.439353i
$563$	−38.4439			−1.62022			−0.810109	−	0.586280i	$-0.800592\pi$
$563$	−38.4439			−1.62022			−0.810109	+	0.586280i	$0.800592\pi$
$564$	2.67310	−	4.62995i	0.112558	−	0.194956i
$565$	5.69180	+	23.9525i	0.239456	+	1.00769i
$566$	15.4079			0.647642
$567$	−2.75229	−	1.58904i	−0.115585	−	0.0667332i
$568$	3.22083	+	5.57863i	0.135143	+	0.234074i
$569$		−	42.4265i		−	1.77861i	−0.457315	−	0.889305i	$-0.651189\pi$
$569$		−	42.4265i		−	1.77861i	0.457315	−	0.889305i	$-0.348811\pi$
$570$	−11.2606	−	3.36395i	−0.471655	−	0.140900i
$571$	−2.51703	+	4.35962i	−0.105334	+	0.182444i	−0.913875	−	0.405996i	$-0.866925\pi$
$571$	−2.51703	+	4.35962i	−0.105334	+	0.182444i	0.808540	+	0.588441i	$0.200258\pi$
$572$	1.47340	−	2.55200i	0.0616059	−	0.106704i
$573$	10.9593	+	18.9820i	0.457831	+	0.792986i
$574$	−28.4683	+	16.4362i	−1.18824	+	0.686033i
$575$	−1.88454	+	33.0289i	−0.0785906	+	1.37740i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−4.83557	+	8.37546i	−0.201308	+	0.348675i	−0.948950	−	0.315427i	$-0.897852\pi$
$577$	−4.83557	+	8.37546i	−0.201308	+	0.348675i	0.747642	+	0.664102i	$0.231186\pi$
$578$	5.51689			0.229472
$579$	−5.20557	+	3.00544i	−0.216336	+	0.124902i
$580$	−0.836597	+	2.80045i	−0.0347378	+	0.116282i
$581$	22.2153			0.921646
$582$		−	4.77178i		−	0.197797i
$583$	−10.7355	−	6.19812i	−0.444617	−	0.256700i
$584$		−	5.84525i		−	0.241878i
$585$	1.23447	−	1.16604i	0.0510389	−	0.0482098i
$586$			12.4427i			0.514003i
$587$	−11.6533	−	20.1840i	−0.480981	−	0.833084i	0.518780	−	0.854908i	$-0.326386\pi$
$587$	−11.6533	−	20.1840i	−0.480981	−	0.833084i	−0.999762	+	0.0218233i	$0.993053\pi$
$588$	2.68480	−	1.55007i	0.110719	−	0.0639238i
$589$	−16.0941	−	27.8758i	−0.663147	−	1.14860i
$590$	3.95049	−	13.2240i	0.162639	−	0.544424i
$591$	18.5786			0.764220
$592$	2.49875	−	5.54583i	0.102698	−	0.227932i
$593$		−	28.4421i		−	1.16798i	−0.811762	−	0.583989i	$-0.801491\pi$
$593$		−	28.4421i		−	1.16798i	0.811762	−	0.583989i	$-0.198509\pi$
$594$	−3.36048	−	1.94018i	−0.137882	−	0.0796064i
$595$	−16.5359	−	17.5063i	−0.677905	−	0.717687i
$596$	−9.03844	−	15.6550i	−0.370229	−	0.641255i
$597$	1.02060	+	1.76774i	0.0417706	+	0.0723487i
$598$	5.02469			0.205475
$599$	13.7454	+	23.8078i	0.561623	+	0.972759i	0.997355	+	0.0726826i	$0.0231560\pi$
$599$	13.7454	+	23.8078i	0.561623	+	0.972759i	−0.435733	+	0.900076i	$0.643511\pi$
$600$	−2.24928	−	4.46551i	−0.0918264	−	0.182304i
$601$	−22.0281	+	38.1539i	−0.898547	+	1.55633i	−0.0691938	+	0.997603i	$0.522043\pi$
$601$	−22.0281	+	38.1539i	−0.898547	+	1.55633i	−0.829353	+	0.558725i	$0.811291\pi$
$602$			29.9325i			1.21996i
$603$			10.0784i			0.410425i
$604$	7.75253	−	13.4278i	0.315446	−	0.546368i
$605$	−6.59505	+	6.22949i	−0.268127	+	0.253265i
$606$			2.01613i			0.0818997i
$607$	22.3880	−	38.7772i	0.908702	−	1.57392i	0.0928326	−	0.995682i	$-0.470408\pi$
$607$	22.3880	−	38.7772i	0.908702	−	1.57392i	0.815869	−	0.578236i	$-0.196259\pi$
$608$	4.55166	+	2.62790i	0.184594	+	0.106575i
$609$	−3.59749	−	2.07701i	−0.145778	−	0.0841648i
$610$	−14.9896	−	15.8692i	−0.606911	−	0.642527i
$611$	−3.51605	+	2.02999i	−0.142244	+	0.0821247i
$612$	1.69434	−	2.93468i	0.0684895	−	0.118627i
$613$	−21.4944	−	12.4098i	−0.868150	−	0.501227i	−0.00141717	−	0.999999i	$-0.500451\pi$
$613$	−21.4944	−	12.4098i	−0.868150	−	0.501227i	−0.866733	+	0.498772i	$0.833784\pi$
$614$	25.1038	+	14.4937i	1.01311	+	0.584918i
$615$	−22.5022	+	5.34716i	−0.907374	+	0.215618i
$616$	10.6799	−	6.16602i	0.430304	−	0.248436i
$617$	−34.1390	−	19.7101i	−1.37438	−	0.793500i	−0.382906	−	0.923787i	$-0.625077\pi$
$617$	−34.1390	−	19.7101i	−1.37438	−	0.793500i	−0.991476	+	0.130287i	$0.958410\pi$
$618$		−	8.06815i		−	0.324549i
$619$	9.70430			0.390049			0.195024	−	0.980798i	$-0.437521\pi$
$619$	9.70430			0.390049			0.195024	+	0.980798i	$0.437521\pi$
$620$	3.91985	−	13.1214i	0.157425	−	0.526969i
$621$		−	6.61653i		−	0.265512i
$622$	−0.445283	+	0.257084i	−0.0178542	+	0.0103081i
$623$	−7.10393			−0.284613
$624$	−0.657673	+	0.379707i	−0.0263280	+	0.0152005i
$625$	−24.8378	−	2.84360i	−0.993510	−	0.113744i
$626$	−11.2521	−	19.4892i	−0.449724	−	0.778945i
$627$	10.1972	−	17.6620i	0.407236	−	0.705353i
$628$			4.91975i			0.196320i
$629$	8.46745	−	18.7930i	0.337619	−	0.749327i
$630$	6.91386	−	1.64293i	0.275455	−	0.0654560i
$631$	−11.6902	−	6.74933i	−0.465379	−	0.268687i	0.248924	−	0.968523i	$-0.419923\pi$
$631$	−11.6902	−	6.74933i	−0.465379	−	0.268687i	−0.714303	+	0.699836i	$0.753256\pi$
$632$	−7.39006	+	4.26665i	−0.293961	+	0.169718i
$633$	−11.5313	+	6.65761i	−0.458329	+	0.264616i
$634$	6.11367	−	3.52973i	0.242805	−	0.140183i
$635$	−32.8062	+	7.79570i	−1.30187	+	0.309363i
$636$	1.59731	+	2.76662i	0.0633374	+	0.109704i
$637$	−2.35429			−0.0932804
$638$	−4.39245	−	2.53598i	−0.173899	−	0.100401i
$639$	−6.44165			−0.254828
$640$	0.516959	+	2.17549i	0.0204346	+	0.0859938i
$641$	8.41425	−	14.5739i	0.332343	−	0.575635i	−0.650628	−	0.759397i	$-0.725494\pi$
$641$	8.41425	−	14.5739i	0.332343	−	0.575635i	0.982971	+	0.183762i	$0.0588275\pi$
$642$	2.56417	+	4.44127i	0.101200	+	0.175283i
$643$	18.4589			0.727949			0.363975	−	0.931409i	$-0.381419\pi$
$643$	18.4589			0.727949			0.363975	+	0.931409i	$0.381419\pi$
$644$	18.2106	+	10.5139i	0.717599	+	0.414306i
$645$	−6.02823	+	20.1791i	−0.237361	+	0.794551i
$646$	15.4241	+	8.90510i	0.606852	+	0.350366i
$647$	2.42149	+	4.19414i	0.0951985	+	0.164889i	0.909691	−	0.415285i	$-0.136318\pi$
$647$	2.42149	+	4.19414i	0.0951985	+	0.164889i	−0.814493	+	0.580173i	$0.802985\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	20.7416	+	11.9752i	0.814179	+	0.470066i
$650$	−0.216298	+	3.79091i	−0.00848392	+	0.148692i
$651$	16.8559	+	9.73177i	0.660636	+	0.381418i
$652$	6.04111			0.236588
$653$	0.412819	+	0.715023i	0.0161549	+	0.0279810i	0.873990	−	0.485944i	$-0.161524\pi$
$653$	0.412819	+	0.715023i	0.0161549	+	0.0279810i	−0.857835	+	0.513925i	$0.828191\pi$
$654$	2.47951	−	4.29464i	0.0969566	−	0.167934i
$655$	−23.8958	+	5.67833i	−0.933686	+	0.221871i
$656$	10.3435			0.403845
$657$	5.06214	+	2.92263i	0.197493	+	0.114022i
$658$	−16.9906			−0.662363
$659$	−12.4134	−	21.5006i	−0.483557	−	0.837546i	0.516264	−	0.856429i	$-0.327322\pi$
$659$	−12.4134	−	21.5006i	−0.483557	−	0.837546i	−0.999822	+	0.0188834i	$0.993989\pi$
$660$	8.44166	−	2.00598i	0.328591	−	0.0780827i
$661$	14.5538	−	8.40263i	0.566077	−	0.326825i	−0.189504	−	0.981880i	$-0.560688\pi$
$661$	14.5538	−	8.40263i	0.566077	−	0.326825i	0.755581	+	0.655055i	$0.227355\pi$
$662$	11.4620	−	6.61756i	0.445482	−	0.257199i
$663$	−2.22864	+	1.28670i	−0.0865531	+	0.0499715i
$664$	−6.05368	−	3.49509i	−0.234928	−	0.135636i
$665$	8.63493	+	36.3379i	0.334848	+	1.40912i
$666$	3.55346	+	4.93690i	0.137694	+	0.191301i
$667$		−	8.64841i		−	0.334868i
$668$	9.53467	−	16.5145i	0.368907	−	0.638966i
$669$	7.44563	+	12.8962i	0.287865	+	0.498597i
$670$	−15.4749	−	16.3830i	−0.597846	−	0.632930i
$671$	32.8063	−	18.9407i	1.26647	−	0.731199i
$672$	−3.17807			−0.122597
$673$	1.06009	−	0.612042i	0.0408634	−	0.0235925i	−0.479429	−	0.877581i	$-0.659156\pi$
$673$	1.06009	−	0.612042i	0.0408634	−	0.0235925i	0.520293	+	0.853988i	$0.325823\pi$
$674$		−	9.45934i		−	0.364360i
$675$	4.99188	+	0.284822i	0.192138	+	0.0109628i
$676$	−12.4233			−0.477819
$677$			19.9522i			0.766825i	0.923577	+	0.383412i	$0.125251\pi$
$677$			19.9522i			0.766825i	−0.923577	+	0.383412i	$0.874749\pi$
$678$	9.53507	+	5.50508i	0.366192	+	0.211421i
$679$	−13.1333	+	7.58253i	−0.504011	+	0.290991i
$680$	1.75181	+	7.37202i	0.0671787	+	0.282704i
$681$	−1.22638	−	0.708052i	−0.0469951	−	0.0271326i
$682$	20.5807	+	11.8823i	0.788075	+	0.454996i
$683$	−7.80416	+	13.5172i	−0.298618	+	0.517221i	−0.975820	−	0.218576i	$-0.929859\pi$
$683$	−7.80416	+	13.5172i	−0.298618	+	0.517221i	0.677202	+	0.735797i	$0.263192\pi$
$684$	−4.55166	+	2.62790i	−0.174037	+	0.100480i
$685$	2.61439	+	2.76781i	0.0998905	+	0.105752i
$686$	10.7336	+	6.19702i	0.409809	+	0.236603i
$687$	24.0938	+	13.9106i	0.919237	+	0.530722i
$688$	4.70922	−	8.15661i	0.179537	−	0.310968i
$689$		−	2.42604i		−	0.0924248i
$690$	10.1593	+	10.7555i	0.386759	+	0.409455i
$691$	−19.8289	+	34.3447i	−0.754328	+	1.30654i	0.191379	+	0.981516i	$0.438704\pi$
$691$	−19.8289	+	34.3447i	−0.754328	+	1.30654i	−0.945707	+	0.325019i	$0.894629\pi$
$692$			20.3758i			0.774571i
$693$			12.3320i			0.468455i
$694$	3.48638	−	6.03859i	0.132341	−	0.229222i
$695$	9.09165	+	38.2599i	0.344866	+	1.45128i
$696$	0.653545	+	1.13197i	0.0247726	+	0.0429073i
$697$	35.0507			1.32764
$698$	4.99936	+	8.65914i	0.189228	+	0.327753i
$699$	−10.5711	−	18.3097i	−0.399837	−	0.692538i
$700$	−8.71619	+	13.2865i	−0.329441	+	0.502183i
$701$	30.5819	+	17.6564i	1.15506	+	0.666875i	0.950115	−	0.311899i	$-0.100965\pi$
$701$	30.5819	+	17.6564i	1.15506	+	0.666875i	0.204945	+	0.978773i	$0.434298\pi$
$702$		−	0.759415i		−	0.0286623i
$703$	−25.9473	+	18.6763i	−0.978623	+	0.704389i
$704$	−3.88035			−0.146246
$705$	−11.4543	−	3.42181i	−0.431393	−	0.128873i
$706$	0.898282	+	1.55587i	0.0338073	+	0.0585559i
$707$	5.54898	−	3.20370i	0.208691	−	0.120488i
$708$	−3.08610	−	5.34529i	−0.115983	−	0.200888i
$709$			11.4844i			0.431305i	0.976470	+	0.215652i	$0.0691878\pi$
$709$			11.4844i			0.431305i	−0.976470	+	0.215652i	$0.930812\pi$
$710$	10.4712	−	9.89080i	0.392978	−	0.371195i
$711$		−	8.53330i		−	0.320024i
$712$	1.93582	+	1.11765i	0.0725481	+	0.0418856i
$713$			40.5218i			1.51755i
$714$	−10.7694			−0.403036
$715$	−6.31354	−	1.88608i	−0.236113	−	0.0705355i
$716$	1.61515	−	0.932508i	0.0603610	−	0.0348494i
$717$	5.93461			0.221632
$718$	18.1257	−	31.3946i	0.676444	−	1.17164i
$719$	6.73406	−	11.6637i	0.251138	−	0.434984i	−0.712701	−	0.701468i	$-0.752529\pi$
$719$	6.73406	−	11.6637i	0.251138	−	0.434984i	0.963839	+	0.266484i	$0.0858619\pi$
$720$	−2.14251	−	0.640045i	−0.0798466	−	0.0238531i
$721$	−22.2059	+	12.8206i	−0.826991	+	0.477463i
$722$	−4.31172	−	7.46812i	−0.160466	−	0.277935i
$723$	12.4744	−	21.6064i	0.463930	−	0.803550i
$724$	6.08878	−	10.5461i	0.226288	−	0.391942i
$725$	6.52484	+	0.372289i	0.242326	+	0.0138264i
$726$			4.05712i			0.150574i
$727$	−8.17953	−	14.1674i	−0.303362	−	0.525439i	0.673533	−	0.739157i	$-0.264776\pi$
$727$	−8.17953	−	14.1674i	−0.303362	−	0.525439i	−0.976895	+	0.213718i	$0.931443\pi$
$728$	2.09013	+	1.20674i	0.0774654	+	0.0447247i
$729$	−1.00000			−0.0370370
$730$	−12.7163	+	3.02175i	−0.470651	+	0.111840i
$731$	15.9580	−	27.6401i	0.590228	−	1.02231i
$732$	−9.76238			−0.360828
$733$	33.0277	−	19.0685i	1.21991	−	0.704313i	0.255008	−	0.966939i	$-0.417922\pi$
$733$	33.0277	−	19.0685i	1.21991	−	0.704313i	0.964898	+	0.262626i	$0.0845886\pi$
$734$			27.7434i			1.02403i
$735$	−4.76009	−	5.03943i	−0.175579	−	0.185882i
$736$	−3.30827	−	5.73009i	−0.121944	−	0.211214i
$737$	33.8684	−	19.5539i	1.24756	−	0.720278i
$738$	−5.17175	+	8.95773i	−0.190375	+	0.329738i
$739$	−36.2617			−1.33391			−0.666954	−	0.745099i	$-0.732402\pi$
$739$	−36.2617			−1.33391			−0.666954	+	0.745099i	$0.732402\pi$
$740$	−13.3566	−	2.56904i	−0.491000	−	0.0944396i
$741$	3.99133			0.146625
$742$	5.07636	−	8.79251i	0.186359	−	0.322783i
$743$	5.97478	−	3.44954i	0.219193	−	0.126551i	−0.386383	−	0.922338i	$-0.626276\pi$
$743$	5.97478	−	3.44954i	0.219193	−	0.126551i	0.605577	+	0.795787i	$0.292942\pi$
$744$	−3.06216	−	5.30382i	−0.112264	−	0.194448i
$745$	−29.3849	+	27.7560i	−1.07658	+	1.01690i
$746$		−	15.8474i		−	0.580215i
$747$	6.05368	−	3.49509i	0.221492	−	0.127879i
$748$	−13.1492			−0.480784
$749$	8.14911	−	14.1147i	0.297762	−	0.515739i
$750$	−8.55188	+	7.20176i	−0.312270	+	0.262971i
$751$	−27.9667			−1.02052			−0.510260	−	0.860020i	$-0.670451\pi$
$751$	−27.9667			−1.02052			−0.510260	+	0.860020i	$0.670451\pi$
$752$	4.62995	+	2.67310i	0.168837	+	0.0974780i
$753$	−2.54080	−	4.40080i	−0.0925919	−	0.160374i
$754$		−	0.992624i		−	0.0361492i
$755$	−33.2197	−	9.92393i	−1.20899	−	0.361169i
$756$	1.58904	−	2.75229i	0.0577927	−	0.100100i
$757$	22.6799	−	39.2828i	0.824316	−	1.42776i	−0.0781247	−	0.996944i	$-0.524893\pi$
$757$	22.6799	−	39.2828i	0.824316	−	1.42776i	0.902441	−	0.430814i	$-0.141773\pi$
$758$	−12.5851	−	21.7980i	−0.457111	−	0.791740i
$759$	−22.2347	+	12.8372i	−0.807070	+	0.465962i
$760$	3.36395	−	11.2606i	0.122023	−	0.408465i
$761$	4.81085	−	8.33263i	0.174393	−	0.302058i	−0.765558	−	0.643367i	$-0.777537\pi$
$761$	4.81085	−	8.33263i	0.174393	−	0.302058i	0.939951	+	0.341309i	$0.110870\pi$
$762$	−7.53996	+	13.0596i	−0.273144	+	0.473099i
$763$	−15.7601			−0.570555
$764$	−18.9820	+	10.9593i	−0.686746	+	0.396493i
$765$	−7.26026	−	2.16890i	−0.262495	−	0.0784169i
$766$	−15.9964			−0.577975
$767$			4.68726i			0.169247i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$		−	31.0987i		−	1.12145i	−0.828002	−	0.560725i	$-0.810523\pi$
$769$		−	31.0987i		−	1.12145i	0.828002	−	0.560725i	$-0.189477\pi$
$770$	−18.9351	−	20.0463i	−0.682375	−	0.722420i
$771$		−	10.1658i		−	0.366111i
$772$	−3.00544	−	5.20557i	−0.108168	−	0.187353i
$773$	3.09863	−	1.78899i	0.111450	−	0.0643456i	−0.443239	−	0.896404i	$-0.646171\pi$
$773$	3.09863	−	1.78899i	0.111450	−	0.0643456i	0.554689	+	0.832058i	$0.312837\pi$
$774$	4.70922	+	8.15661i	0.169269	+	0.293183i
$775$	−30.5719	−	1.74435i	−1.09818	−	0.0626587i
$776$	4.77178			0.171297
$777$	7.94120	−	17.6251i	0.284889	−	0.632295i
$778$		−	6.70954i		−	0.240548i
$779$	−47.0800	−	27.1817i	−1.68682	−	0.973884i
$780$	1.16604	+	1.23447i	0.0417509	+	0.0442010i
$781$	12.4979	+	21.6471i	0.447211	+	0.774593i
$782$	−11.2106	−	19.4174i	−0.400892	−	0.694365i
$783$	−1.30709			−0.0467116
$784$	1.55007	+	2.68480i	0.0553596	+	0.0958857i
$785$	10.7029	−	2.54331i	0.382002	−	0.0907747i
$786$	−5.49205	+	9.51251i	−0.195895	+	0.339300i
$787$		−	31.7684i		−	1.13242i	−0.824260	−	0.566211i	$-0.808409\pi$
$787$		−	31.7684i		−	1.13242i	0.824260	−	0.566211i	$-0.191591\pi$
$788$			18.5786i			0.661834i
$789$	−7.81597	+	13.5376i	−0.278256	+	0.481953i
$790$	13.1024	+	13.8713i	0.466163	+	0.493519i
$791$		−	34.9911i		−	1.24414i
$792$	1.94018	−	3.36048i	0.0689411	−	0.119410i
$793$	6.42045	+	3.70685i	0.227997	+	0.131634i
$794$	−16.8362	−	9.72037i	−0.597493	−	0.344963i
$795$	5.19301	−	4.90516i	0.184177	−	0.173968i
$796$	−1.76774	+	1.02060i	−0.0626558	+	0.0361744i
$797$	8.31378	−	14.3999i	0.294489	−	0.510070i	−0.680377	−	0.732863i	$-0.738184\pi$
$797$	8.31378	−	14.3999i	0.294489	−	0.510070i	0.974866	+	0.222792i	$0.0715172\pi$
$798$	14.4655	+	8.35166i	0.512073	+	0.295645i
$799$	15.6894	+	9.05827i	0.555050	+	0.320458i
$800$	4.46551	−	2.24928i	0.157880	−	0.0795240i
$801$	−1.93582	+	1.11765i	−0.0683990	+	0.0394902i
$802$	−0.860924	−	0.497054i	−0.0304003	−	0.0175516i
$803$		−	22.6816i		−	0.800417i
$804$	−10.0784			−0.355439
$805$	13.4588	−	45.0523i	0.474359	−	1.58788i
$806$			4.65090i			0.163821i
$807$	14.8681	−	8.58413i	0.523384	−	0.302176i
$808$	−2.01613			−0.0709272
$809$	−16.5235	+	9.53987i	−0.580937	+	0.335404i	−0.761506	−	0.648158i	$-0.775539\pi$
$809$	−16.5235	+	9.53987i	−0.580937	+	0.335404i	0.180569	+	0.983562i	$0.442206\pi$
$810$	1.62555	−	1.53544i	0.0571160	−	0.0539500i
$811$	−26.6866	−	46.2226i	−0.937094	−	1.62309i	−0.770857	−	0.637008i	$-0.780172\pi$
$811$	−26.6866	−	46.2226i	−0.937094	−	1.62309i	−0.166237	−	0.986086i	$-0.553162\pi$
$812$	2.07701	−	3.59749i	0.0728889	−	0.126247i
$813$		−	8.40823i		−	0.294890i
$814$	9.69602	−	21.5198i	0.339845	−	0.754268i
$815$	−3.12301	−	13.1424i	−0.109394	−	0.460357i
$816$	2.93468	+	1.69434i	0.102734	+	0.0593137i
$817$	−42.8695	+	24.7507i	−1.49981	+	0.865918i
$818$	−26.9360	+	15.5515i	−0.941795	+	0.543746i
$819$	−2.09013	+	1.20674i	−0.0730351	+	0.0421668i
$820$	−5.34716	−	22.5022i	−0.186731	−	0.785809i
$821$	−5.62460	−	9.74210i	−0.196300	−	0.340001i	0.751026	−	0.660273i	$-0.229559\pi$
$821$	−5.62460	−	9.74210i	−0.196300	−	0.340001i	−0.947326	+	0.320271i	$0.896226\pi$
$822$	1.70269			0.0593881
$823$	−16.0481	−	9.26537i	−0.559401	−	0.322970i	0.193504	−	0.981099i	$-0.438015\pi$
$823$	−16.0481	−	9.26537i	−0.559401	−	0.322970i	−0.752905	+	0.658129i	$0.771348\pi$
$824$	8.06815			0.281067
$825$	−8.72798	−	17.3277i	−0.303869	−	0.603274i
$826$	−9.80786	+	16.9877i	−0.341259	+	0.591078i
$827$	−20.4765	−	35.4663i	−0.712037	−	1.23328i	−0.964091	−	0.265572i	$-0.914439\pi$
$827$	−20.4765	−	35.4663i	−0.712037	−	1.23328i	0.252054	−	0.967713i	$-0.418894\pi$
$828$	6.61653			0.229940
$829$	37.5169	+	21.6604i	1.30301	+	0.752296i	0.980920	−	0.194412i	$-0.0622798\pi$
$829$	37.5169	+	21.6604i	1.30301	+	0.752296i	0.322094	+	0.946708i	$0.395613\pi$
$830$	−4.47403	+	14.9765i	−0.155296	+	0.519843i
$831$	−24.4154	−	14.0962i	−0.846960	−	0.488993i
$832$	−0.379707	−	0.657673i	−0.0131640	−	0.0228007i
$833$	5.25268	+	9.09791i	0.181995	+	0.315224i
$834$	15.2306	+	8.79340i	0.527393	+	0.304491i
$835$	−40.8562	−	12.2052i	−1.41389	−	0.422380i
$836$	17.6620	+	10.1972i	0.610854	+	0.352677i
$837$	6.12433			0.211688
$838$	−19.2268	−	33.3019i	−0.664180	−	1.15039i
$839$	6.10865	−	10.5805i	0.210894	−	0.365279i	−0.741101	−	0.671394i	$-0.765696\pi$
$839$	6.10865	−	10.5805i	0.210894	−	0.365279i	0.951995	+	0.306115i	$0.0990292\pi$
$840$	1.64293	+	6.91386i	0.0566866	+	0.238551i
$841$	27.2915			0.941087
$842$	−7.95838	−	4.59477i	−0.274264	−	0.158346i
$843$	20.8311			0.717460
$844$	−6.65761	−	11.5313i	−0.229165	−	0.396925i
$845$	6.42233	+	27.0267i	0.220935	+	0.929748i
$846$	−4.62995	+	2.67310i	−0.159181	+	0.0919031i
$847$	11.1664	−	6.44691i	0.383681	−	0.221519i
$848$	−2.76662	+	1.59731i	−0.0950061	+	0.0548518i
$849$	−13.3436	−	7.70394i	−0.457952	−	0.264399i
$850$	15.1321	−	7.62207i	0.519028	−	0.261435i
$851$	40.0446	−	4.02904i	1.37271	−	0.138114i
$852$		−	6.44165i		−	0.220687i
$853$	−25.4152	+	44.0204i	−0.870199	+	1.50723i	−0.00840753	+	0.999965i	$0.502676\pi$
$853$	−25.4152	+	44.0204i	−0.870199	+	1.50723i	−0.861791	+	0.507263i	$0.830657\pi$
$854$	15.5128	+	26.8689i	0.530836	+	0.919435i
$855$	8.06999	+	8.54356i	0.275988	+	0.292184i
$856$	−4.44127	+	2.56417i	−0.151799	+	0.0876414i
$857$	52.0353			1.77749			0.888746	−	0.458400i	$-0.151577\pi$
$857$	52.0353			1.77749			0.888746	+	0.458400i	$0.151577\pi$
$858$	−2.55200	+	1.47340i	−0.0871239	+	0.0503010i
$859$		−	37.8302i		−	1.29075i	−0.763866	−	0.645375i	$-0.776701\pi$
$859$		−	37.8302i		−	1.29075i	0.763866	−	0.645375i	$-0.223299\pi$
$860$	−20.1791	−	6.02823i	−0.688101	−	0.205561i
$861$	32.8724			1.12029
$862$			11.3060i			0.385083i
$863$	1.07588	+	0.621161i	0.0366235	+	0.0211446i	0.518200	−	0.855259i	$-0.326602\pi$
$863$	1.07588	+	0.621161i	0.0366235	+	0.0211446i	−0.481576	+	0.876404i	$0.659936\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	44.3273	−	10.5334i	1.50717	−	0.358148i
$866$	−16.5923	−	9.57954i	−0.563828	−	0.325526i
$867$	−4.77777	−	2.75844i	−0.162261	−	0.0936817i
$868$	−9.73177	+	16.8559i	−0.330318	+	0.572127i
$869$	−28.6760	+	16.5561i	−0.972767	+	0.561627i
$870$	2.12474	−	2.00696i	0.0720354	−	0.0680425i
$871$	6.62831	+	3.82685i	0.224592	+	0.129668i
$872$	4.29464	+	2.47951i	0.145435	+	0.0839669i
$873$	−2.38589	+	4.13248i	−0.0807501	+	0.139863i
$874$			34.7752i			1.17629i
$875$	33.4106	+	12.0934i	1.12948	+	0.408831i
$876$	−2.92263	+	5.06214i	−0.0987464	+	0.171034i
$877$			9.31872i			0.314671i	0.987545	+	0.157335i	$0.0502904\pi$
$877$			9.31872i			0.314671i	−0.987545	+	0.157335i	$0.949710\pi$
$878$		−	33.0743i		−	1.11620i
$879$	6.22135	−	10.7757i	0.209841	−	0.363455i
$880$	2.00598	+	8.44166i	0.0676216	+	0.284568i
$881$	−6.24610	−	10.8186i	−0.210436	−	0.364486i	0.741415	−	0.671047i	$-0.234155\pi$
$881$	−6.24610	−	10.8186i	−0.210436	−	0.364486i	−0.951851	+	0.306561i	$0.900822\pi$
$882$	−3.10014			−0.104387
$883$	1.69119	+	2.92923i	0.0569131	+	0.0985764i	0.893078	−	0.449901i	$-0.148541\pi$
$883$	1.69119	+	2.92923i	0.0569131	+	0.0985764i	−0.836165	+	0.548478i	$0.815208\pi$
$884$	−1.28670	−	2.22864i	−0.0432766	−	0.0749572i
$885$	−10.0332	+	9.47708i	−0.337263	+	0.318568i
$886$	−0.411893	−	0.237807i	−0.0138378	−	0.00798927i
$887$			1.02834i			0.0345283i	0.999851	+	0.0172642i	$0.00549563\pi$
$887$			1.02834i			0.0345283i	−0.999851	+	0.0172642i	$0.994504\pi$
$888$	−4.93690	+	3.55346i	−0.165671	+	0.119246i
$889$	47.9251			1.60736
$890$	1.43069	−	4.78914i	0.0479569	−	0.160532i
$891$	1.94018	+	3.36048i	0.0649983	+	0.112580i
$892$	−12.8962	+	7.44563i	−0.431797	+	0.249298i
$893$	−14.0493	−	24.3341i	−0.470141	−	0.814309i
$894$			18.0769i			0.604581i
$895$	−2.86363	−	3.03167i	−0.0957205	−	0.101338i
$896$		−	3.17807i		−	0.106172i
$897$	−4.35151	−	2.51235i	−0.145293	−	0.0838848i
$898$			39.1797i			1.30744i
$899$	8.00505			0.266983
$900$	−0.284822	+	4.99188i	−0.00949408	+	0.166396i
$901$	−9.37517	+	5.41276i	−0.312332	+	0.180325i
$902$	40.1364			1.33640
$903$	14.9662	−	25.9223i	0.498045	−	0.862640i
$904$	−5.50508	+	9.53507i	−0.183096	+	0.317132i
$905$	−26.0905	−	7.79419i	−0.867278	−	0.259088i
$906$	−13.4278	+	7.75253i	−0.446108	+	0.257560i
$907$	−9.56237	−	16.5625i	−0.317513	−	0.549949i	0.662455	−	0.749101i	$-0.269514\pi$
$907$	−9.56237	−	16.5625i	−0.317513	−	0.549949i	−0.979969	+	0.199152i	$0.936181\pi$
$908$	0.708052	−	1.22638i	0.0234975	−	0.0406989i
$909$	1.00807	−	1.74602i	0.0334354	−	0.0579118i
$910$	1.54473	−	5.17089i	0.0512074	−	0.171413i
$911$			39.6440i			1.31346i	0.754124	+	0.656732i	$0.228062\pi$
$911$			39.6440i			1.31346i	−0.754124	+	0.656732i	$0.771938\pi$
$912$	−2.62790	−	4.55166i	−0.0870185	−	0.150720i
$913$	−23.4904	−	13.5622i	−0.777418	−	0.448843i
$914$	−12.5563			−0.415325
$915$	5.04675	+	21.2380i	0.166840	+	0.702105i
$916$	−13.9106	+	24.0938i	−0.459619	+	0.796083i
$917$	34.9083			1.15277
$918$	−2.93468	+	1.69434i	−0.0968588	+	0.0559215i
$919$		−	32.9069i		−	1.08550i	−0.839895	−	0.542749i	$-0.817384\pi$
$919$		−	32.9069i		−	1.08550i	0.839895	−	0.542749i	$-0.182616\pi$
$920$	−10.7555	+	10.1593i	−0.354598	+	0.334943i
$921$	−14.4937	−	25.1038i	−0.477583	−	0.827199i
$922$	−4.06075	+	2.34448i	−0.133734	+	0.0772113i
$923$	−2.44594	+	4.23650i	−0.0805092	+	0.139446i
$924$	−12.3320			−0.405694
$925$	1.31593	+	30.3853i	0.0432675	+	0.999064i
$926$	−12.2779			−0.403477
$927$	−4.03407	+	6.98722i	−0.132496	+	0.229490i
$928$	−1.13197	+	0.653545i	−0.0371589	+	0.0214537i
$929$	−15.3383	−	26.5668i	−0.503235	−	0.871628i	−0.999993	−	0.00373929i	$-0.998810\pi$
$929$	−15.3383	−	26.5668i	−0.503235	−	0.871628i	0.496758	−	0.867889i	$-0.334524\pi$
$930$	−9.95540	+	9.40356i	−0.326450	+	0.308355i
$931$		−	16.2937i		−	0.534005i
$932$	18.3097	−	10.5711i	0.599755	−	0.346269i
$933$	0.514169			0.0168331
$934$	6.34282	−	10.9861i	0.207543	−	0.359476i
$935$	6.79762	+	28.6060i	0.222306	+	0.935517i
$936$	0.759415			0.0248223
$937$	−12.2218	−	7.05627i	−0.399269	−	0.230518i	0.286899	−	0.957961i	$-0.407375\pi$
$937$	−12.2218	−	7.05627i	−0.399269	−	0.230518i	−0.686169	+	0.727442i	$0.740709\pi$
$938$	16.0150	+	27.7388i	0.522908	+	0.905703i
$939$			22.5042i			0.734397i
$940$	3.42181	−	11.4543i	0.111607	−	0.373598i
$941$	−15.2622	+	26.4350i	−0.497535	+	0.861756i	−0.999996	−	0.00284385i	$-0.999095\pi$
$941$	−15.2622	+	26.4350i	−0.497535	+	0.861756i	0.502461	+	0.864600i	$0.332428\pi$
$942$	2.45988	−	4.26063i	0.0801471	−	0.138819i
$943$	34.2190	+	59.2691i	1.11432	+	1.93007i
$944$	5.34529	−	3.08610i	0.173974	−	0.100444i
$945$	−6.80904	−	2.03411i	−0.221498	−	0.0661696i
$946$	18.2734	−	31.6505i	0.594120	−	1.02905i
$947$	24.2928	−	42.0764i	0.789411	−	1.36730i	−0.136916	−	0.990583i	$-0.543719\pi$
$947$	24.2928	−	42.0764i	0.789411	−	1.36730i	0.926328	−	0.376718i	$-0.122947\pi$
$948$	8.53330			0.277149
$949$	3.84426	−	2.21949i	0.124790	−	0.0720475i
$950$	−26.2363	−	1.49697i	−0.851219	−	0.0485681i
$951$	−7.05946			−0.228919
$952$		−	10.7694i		−	0.349040i
$953$	31.8214	+	18.3721i	1.03080	+	0.595131i	0.917213	−	0.398397i	$-0.130433\pi$
$953$	31.8214	+	18.3721i	1.03080	+	0.595131i	0.113585	+	0.993528i	$0.463767\pi$
$954$		−	3.19462i		−	0.103430i
$955$	33.6547	+	35.6297i	1.08904	+	1.15295i
$956$			5.93461i			0.191939i
$957$	2.53598	+	4.39245i	0.0819767	+	0.141988i
$958$	−2.51613	+	1.45269i	−0.0812925	+	0.0469342i
$959$	−2.70564	−	4.68630i	−0.0873695	−	0.151328i
$960$	0.640045	−	2.14251i	0.0206574	−	0.0691492i
$961$	−6.50738			−0.209915
$962$	4.59614	−	0.462435i	0.148185	−	0.0149095i
$963$		−	5.12833i		−	0.165258i
$964$	21.6064	+	12.4744i	0.695895	+	0.401775i
$965$	−9.77098	+	9.22937i	−0.314539	+	0.297104i
$966$	−10.5139	−	18.2106i	−0.338279	−	0.585917i
$967$	27.1750	+	47.0685i	0.873890	+	1.51362i	0.857941	+	0.513749i	$0.171744\pi$
$967$	27.1750	+	47.0685i	0.873890	+	1.51362i	0.0159491	+	0.999873i	$0.494923\pi$
$968$	−4.05712			−0.130401
$969$	−8.90510	−	15.4241i	−0.286073	−	0.495493i
$970$	−2.46681	−	10.3810i	−0.0792046	−	0.333312i
$971$	26.2816	−	45.5210i	0.843416	−	1.46084i	−0.0435737	−	0.999050i	$-0.513874\pi$
$971$	26.2816	−	45.5210i	0.843416	−	1.46084i	0.886990	−	0.461789i	$-0.152792\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	55.8921i		−	1.79182i
$974$	0.219978	−	0.381012i	0.00704854	−	0.0122084i
$975$	2.08277	−	3.17487i	0.0667022	−	0.101677i
$976$		−	9.76238i		−	0.312486i
$977$	−22.6877	+	39.2962i	−0.725843	+	1.25720i	0.232782	+	0.972529i	$0.425217\pi$
$977$	−22.6877	+	39.2962i	−0.725843	+	1.25720i	−0.958626	+	0.284669i	$0.908116\pi$
$978$	−5.23176	−	3.02056i	−0.167293	−	0.0965867i
$979$	7.51167	+	4.33687i	0.240074	+	0.138607i
$980$	5.03943	−	4.76009i	0.160979	−	0.152055i
$981$	−4.29464	+	2.47951i	−0.137117	+	0.0791648i
$982$	19.3748	−	33.5582i	0.618275	−	1.07088i
$983$	3.52063	+	2.03263i	0.112291	+	0.0648310i	0.555093	−	0.831788i	$-0.312683\pi$
$983$	3.52063	+	2.03263i	0.112291	+	0.0648310i	−0.442803	+	0.896619i	$0.646016\pi$
$984$	−8.95773	−	5.17175i	−0.285562	−	0.164869i
$985$	40.4175	−	9.60435i	1.28781	−	0.306020i
$986$	−3.83589	+	2.21465i	−0.122160	+	0.0705289i
$987$	14.7143	+	8.49531i	0.468361	+	0.270409i
$988$			3.99133i			0.126981i
$989$	62.3174			1.98158
$990$	−8.31368	−	2.48360i	−0.264226	−	0.0789340i
$991$			56.8201i			1.80495i	0.430744	+	0.902474i	$0.358251\pi$
$991$			56.8201i			1.80495i	−0.430744	+	0.902474i	$0.641749\pi$
$992$	5.30382	−	3.06216i	0.168397	−	0.0972238i
$993$	−13.2351			−0.420004
$994$	−17.7293	+	10.2360i	−0.562339	+	0.324667i
$995$	3.13416	+	3.31809i	0.0993596	+	0.105190i
$996$	3.49509	+	6.05368i	0.110746	+	0.191818i
$997$	9.73005	−	16.8529i	0.308154	−	0.533738i	−0.669805	−	0.742537i	$-0.733622\pi$
$997$	9.73005	−	16.8529i	0.308154	−	0.533738i	0.977959	+	0.208799i	$0.0669555\pi$
$998$			37.8307i			1.19751i
$999$	−0.608935	−	6.05221i	−0.0192659	−	0.191483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.619.1	yes	36
5.4	even	2		1110.2.ba.a.619.18	yes	36
37.11	even	6		1110.2.ba.a.529.18	✓	36
185.159	even	6	inner	1110.2.ba.b.529.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.18	✓	36	37.11	even	6
1110.2.ba.a.619.18	yes	36	5.4	even	2
1110.2.ba.b.529.1	yes	36	185.159	even	6	inner
1110.2.ba.b.619.1	yes	36	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.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.62555 + 1.53544i) q^{5} +1.00000i q^{6} +(2.75229 - 1.58904i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.62555 + 1.53544i) q^{5} +1.00000i q^{6} +(2.75229 - 1.58904i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.516959 + 2.17549i) q^{10} -3.88035 q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.379707 - 0.657673i) q^{13} -3.17807i q^{14} +(0.640045 - 2.14251i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.69434 + 2.93468i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.55166 - 2.62790i) q^{19} +(2.14251 + 0.640045i) q^{20} +(-1.58904 + 2.75229i) q^{21} +(-1.94018 + 3.36048i) q^{22} -6.61653 q^{23} +(0.866025 - 0.500000i) q^{24} +(0.284822 - 4.99188i) q^{25} -0.759415 q^{26} +1.00000i q^{27} +(-2.75229 - 1.58904i) q^{28} +1.30709i q^{29} +(-1.53544 - 1.62555i) q^{30} -6.12433i q^{31} +(0.500000 + 0.866025i) q^{32} +(3.36048 - 1.94018i) q^{33} +(1.69434 + 2.93468i) q^{34} +(-2.03411 + 6.80904i) q^{35} -1.00000 q^{36} +(-6.05221 + 0.608935i) q^{37} -5.25580i q^{38} +(0.657673 + 0.379707i) q^{39} +(1.62555 - 1.53544i) q^{40} +(-5.17175 - 8.95773i) q^{41} +(1.58904 + 2.75229i) q^{42} -9.41844 q^{43} +(1.94018 + 3.36048i) q^{44} +(0.516959 + 2.17549i) q^{45} +(-3.30827 + 5.73009i) q^{46} -5.34620i q^{47} -1.00000i q^{48} +(1.55007 - 2.68480i) q^{49} +(-4.18068 - 2.74260i) q^{50} -3.38867i q^{51} +(-0.379707 + 0.657673i) q^{52} +(2.76662 + 1.59731i) q^{53} +(0.866025 + 0.500000i) q^{54} +(6.30770 - 5.95806i) q^{55} +(-2.75229 + 1.58904i) q^{56} +(-2.62790 + 4.55166i) q^{57} +(1.13197 + 0.653545i) q^{58} +(-5.34529 - 3.08610i) q^{59} +(-2.17549 + 0.516959i) q^{60} +(-8.45447 + 4.88119i) q^{61} +(-5.30382 - 3.06216i) q^{62} -3.17807i q^{63} +1.00000 q^{64} +(1.62705 + 0.486060i) q^{65} -3.88035i q^{66} +(-8.72817 + 5.03921i) q^{67} +3.38867 q^{68} +(5.73009 - 3.30827i) q^{69} +(4.87975 + 5.16611i) q^{70} +(-3.22083 - 5.57863i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.84525i q^{73} +(-2.49875 + 5.54583i) q^{74} +(2.24928 + 4.46551i) q^{75} +(-4.55166 - 2.62790i) q^{76} +(-10.6799 + 6.16602i) q^{77} +(0.657673 - 0.379707i) q^{78} +(7.39006 - 4.26665i) q^{79} +(-0.516959 - 2.17549i) q^{80} +(-0.500000 - 0.866025i) q^{81} -10.3435 q^{82} +(6.05368 + 3.49509i) q^{83} +3.17807 q^{84} +(-1.75181 - 7.37202i) q^{85} +(-4.70922 + 8.15661i) q^{86} +(-0.653545 - 1.13197i) q^{87} +3.88035 q^{88} +(-1.93582 - 1.11765i) q^{89} +(2.14251 + 0.640045i) q^{90} +(-2.09013 - 1.20674i) q^{91} +(3.30827 + 5.73009i) q^{92} +(3.06216 + 5.30382i) q^{93} +(-4.62995 - 2.67310i) q^{94} +(-3.36395 + 11.2606i) q^{95} +(-0.866025 - 0.500000i) q^{96} -4.77178 q^{97} +(-1.55007 - 2.68480i) q^{98} +(-1.94018 + 3.36048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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