LMFDB - Embedded newform 1110.2.ba.a.619.15

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			619.15
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18834 - 0.459547i) q^{5} +1.00000i q^{6} +(-1.07219 + 0.619032i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18834 - 0.459547i) q^{5} +1.00000i q^{6} +(-1.07219 + 0.619032i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.49215 - 1.66538i) q^{10} +2.37933 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.12200 - 1.94336i) q^{13} -1.23806i q^{14} +(-2.12493 + 0.696189i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.499820 + 0.865713i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-7.10291 + 4.10087i) q^{19} +(0.696189 + 2.12493i) q^{20} +(-0.619032 + 1.07219i) q^{21} +(-1.18966 + 2.06056i) q^{22} +1.09566 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.57763 + 2.01129i) q^{25} +2.24399 q^{26} -1.00000i q^{27} +(1.07219 + 0.619032i) q^{28} +5.72463i q^{29} +(0.459547 - 2.18834i) q^{30} +3.10566i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.06056 - 1.18966i) q^{33} +(-0.499820 - 0.865713i) q^{34} +(2.63080 - 0.861926i) q^{35} -1.00000 q^{36} +(-5.14008 + 3.25263i) q^{37} -8.20173i q^{38} +(-1.94336 - 1.12200i) q^{39} +(-2.18834 - 0.459547i) q^{40} +(4.36280 + 7.55659i) q^{41} +(-0.619032 - 1.07219i) q^{42} -6.26728 q^{43} +(-1.18966 - 2.06056i) q^{44} +(-1.49215 + 1.66538i) q^{45} +(-0.547828 + 0.948867i) q^{46} -6.29523i q^{47} +1.00000i q^{48} +(-2.73360 + 4.73473i) q^{49} +(-4.03064 + 2.95870i) q^{50} +0.999639i q^{51} +(-1.12200 + 1.94336i) q^{52} +(-10.0941 - 5.82782i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-5.20677 - 1.09341i) q^{55} +(-1.07219 + 0.619032i) q^{56} +(-4.10087 + 7.10291i) q^{57} +(-4.95768 - 2.86232i) q^{58} +(1.06936 + 0.617394i) q^{59} +(1.66538 + 1.49215i) q^{60} +(-4.52224 + 2.61091i) q^{61} +(-2.68958 - 1.55283i) q^{62} +1.23806i q^{63} +1.00000 q^{64} +(1.56224 + 4.76833i) q^{65} +2.37933i q^{66} +(-1.63569 + 0.944369i) q^{67} +0.999639 q^{68} +(0.948867 - 0.547828i) q^{69} +(-0.568948 + 2.70930i) q^{70} +(2.46057 + 4.26184i) q^{71} +(0.500000 - 0.866025i) q^{72} +0.123967i q^{73} +(-0.246818 - 6.07775i) q^{74} +(4.96999 - 0.546992i) q^{75} +(7.10291 + 4.10087i) q^{76} +(-2.55110 + 1.47288i) q^{77} +(1.94336 - 1.12200i) q^{78} +(-13.2768 + 7.66536i) q^{79} +(1.49215 - 1.66538i) q^{80} +(-0.500000 - 0.866025i) q^{81} -8.72560 q^{82} +(6.36686 + 3.67591i) q^{83} +1.23806 q^{84} +(1.49161 - 1.66478i) q^{85} +(3.13364 - 5.42762i) q^{86} +(2.86232 + 4.95768i) q^{87} +2.37933 q^{88} +(0.869603 + 0.502066i) q^{89} +(-0.696189 - 2.12493i) q^{90} +(2.40600 + 1.38910i) q^{91} +(-0.547828 - 0.948867i) q^{92} +(1.55283 + 2.68958i) q^{93} +(5.45183 + 3.14762i) q^{94} +(17.4281 - 5.70996i) q^{95} +(-0.866025 - 0.500000i) q^{96} +5.95504 q^{97} +(-2.73360 - 4.73473i) q^{98} +(1.18966 - 2.06056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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
$5$	−2.18834	−	0.459547i	−0.978654	−	0.205516i
$5$	−2.18834	−	0.459547i	−0.978654	−	0.205516i
$6$			1.00000i			0.408248i
$7$	−1.07219	+	0.619032i	−0.405251	+	0.233972i	−0.688747	−	0.725001i	$-0.741839\pi$
$7$	−1.07219	+	0.619032i	−0.405251	+	0.233972i	0.283496	+	0.958973i	$0.408506\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.49215	−	1.66538i	0.471858	−	0.526640i
$11$	2.37933			0.717394			0.358697	−	0.933454i	$-0.383221\pi$
$11$	2.37933			0.717394			0.358697	+	0.933454i	$0.383221\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.12200	−	1.94336i	−0.311186	−	0.538990i	0.667433	−	0.744670i	$-0.267393\pi$
$13$	−1.12200	−	1.94336i	−0.311186	−	0.538990i	−0.978619	+	0.205680i	$0.934060\pi$
$14$		−	1.23806i		−	0.330886i
$15$	−2.12493	+	0.696189i	−0.548654	+	0.179755i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.499820	+	0.865713i	−0.121224	+	0.209966i	−0.920251	−	0.391329i	$-0.872015\pi$
$17$	−0.499820	+	0.865713i	−0.121224	+	0.209966i	0.799027	+	0.601296i	$0.205349\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−7.10291	+	4.10087i	−1.62952	+	0.940803i	−0.645283	+	0.763944i	$0.723260\pi$
$19$	−7.10291	+	4.10087i	−1.62952	+	0.940803i	−0.984236	+	0.176859i	$0.943406\pi$
$20$	0.696189	+	2.12493i	0.155673	+	0.475148i
$21$	−0.619032	+	1.07219i	−0.135084	+	0.233972i
$22$	−1.18966	+	2.06056i	−0.253637	+	0.439312i
$23$	1.09566			0.228460			0.114230	−	0.993454i	$-0.463560\pi$
$23$	1.09566			0.228460			0.114230	+	0.993454i	$0.463560\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	4.57763	+	2.01129i	0.915527	+	0.402257i
$26$	2.24399			0.440083
$27$		−	1.00000i		−	0.192450i
$28$	1.07219	+	0.619032i	0.202626	+	0.116986i
$29$			5.72463i			1.06304i	0.847047	+	0.531519i	$0.178378\pi$
$29$			5.72463i			1.06304i	−0.847047	+	0.531519i	$0.821622\pi$
$30$	0.459547	−	2.18834i	0.0839014	−	0.399534i
$31$			3.10566i			0.557793i	0.960321	+	0.278897i	$0.0899687\pi$
$31$			3.10566i			0.557793i	−0.960321	+	0.278897i	$0.910031\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.06056	−	1.18966i	0.358697	−	0.207094i
$34$	−0.499820	−	0.865713i	−0.0857183	−	0.148469i
$35$	2.63080	−	0.861926i	0.444686	−	0.145692i
$36$	−1.00000			−0.166667
$37$	−5.14008	+	3.25263i	−0.845024	+	0.534729i
$37$	−5.14008	+	3.25263i	−0.845024	+	0.534729i
$38$		−	8.20173i		−	1.33050i
$39$	−1.94336	−	1.12200i	−0.311186	−	0.179663i
$40$	−2.18834	−	0.459547i	−0.346006	−	0.0726607i
$41$	4.36280	+	7.55659i	0.681355	+	1.18014i	0.974568	+	0.224094i	$0.0719422\pi$
$41$	4.36280	+	7.55659i	0.681355	+	1.18014i	−0.293213	+	0.956047i	$0.594724\pi$
$42$	−0.619032	−	1.07219i	−0.0955187	−	0.165443i
$43$	−6.26728			−0.955751			−0.477876	−	0.878427i	$-0.658593\pi$
$43$	−6.26728			−0.955751			−0.477876	+	0.878427i	$0.658593\pi$
$44$	−1.18966	−	2.06056i	−0.179349	−	0.310641i
$45$	−1.49215	+	1.66538i	−0.222436	+	0.248260i
$46$	−0.547828	+	0.948867i	−0.0807729	+	0.139903i
$47$		−	6.29523i		−	0.918254i	−0.888371	−	0.459127i	$-0.848162\pi$
$47$		−	6.29523i		−	0.918254i	0.888371	−	0.459127i	$-0.151838\pi$
$48$			1.00000i			0.144338i
$49$	−2.73360	+	4.73473i	−0.390514	+	0.676390i
$50$	−4.03064	+	2.95870i	−0.570019	+	0.418424i
$51$			0.999639i			0.139977i
$52$	−1.12200	+	1.94336i	−0.155593	+	0.269495i
$53$	−10.0941	−	5.82782i	−1.38653	−	0.800512i	−0.393606	−	0.919279i	$-0.628772\pi$
$53$	−10.0941	−	5.82782i	−1.38653	−	0.800512i	−0.992922	+	0.118767i	$0.962106\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−5.20677	−	1.09341i	−0.702081	−	0.147436i
$56$	−1.07219	+	0.619032i	−0.143278	+	0.0827216i
$57$	−4.10087	+	7.10291i	−0.543173	+	0.940803i
$58$	−4.95768	−	2.86232i	−0.650975	−	0.375840i
$59$	1.06936	+	0.617394i	0.139218	+	0.0803778i	0.567991	−	0.823034i	$-0.307721\pi$
$59$	1.06936	+	0.617394i	0.139218	+	0.0803778i	−0.428773	+	0.903412i	$0.641054\pi$
$60$	1.66538	+	1.49215i	0.215000	+	0.192635i
$61$	−4.52224	+	2.61091i	−0.579013	+	0.334293i	−0.760741	−	0.649055i	$-0.775164\pi$
$61$	−4.52224	+	2.61091i	−0.579013	+	0.334293i	0.181728	+	0.983349i	$0.441831\pi$
$62$	−2.68958	−	1.55283i	−0.341577	−	0.197210i
$63$			1.23806i			0.155981i
$64$	1.00000			0.125000
$65$	1.56224	+	4.76833i	0.193773	+	0.591438i
$66$			2.37933i			0.292875i
$67$	−1.63569	+	0.944369i	−0.199832	+	0.115373i	−0.596577	−	0.802556i	$-0.703473\pi$
$67$	−1.63569	+	0.944369i	−0.199832	+	0.115373i	0.396745	+	0.917929i	$0.370140\pi$
$68$	0.999639			0.121224
$69$	0.948867	−	0.547828i	0.114230	−	0.0659508i
$70$	−0.568948	+	2.70930i	−0.0680023	+	0.323823i
$71$	2.46057	+	4.26184i	0.292016	+	0.505787i	0.974286	−	0.225313i	$-0.0723405\pi$
$71$	2.46057	+	4.26184i	0.292016	+	0.505787i	−0.682270	+	0.731100i	$0.739007\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$			0.123967i			0.0145092i	0.999974	+	0.00725459i	$0.00230923\pi$
$73$			0.123967i			0.0145092i	−0.999974	+	0.00725459i	$0.997691\pi$
$74$	−0.246818	−	6.07775i	−0.0286920	−	0.706524i
$75$	4.96999	−	0.546992i	0.573885	−	0.0631612i
$76$	7.10291	+	4.10087i	0.814759	+	0.470402i
$77$	−2.55110	+	1.47288i	−0.290725	+	0.167850i
$78$	1.94336	−	1.12200i	0.220042	−	0.127041i
$79$	−13.2768	+	7.66536i	−1.49376	+	0.862420i	−0.999974	−	0.00716550i	$-0.997719\pi$
$79$	−13.2768	+	7.66536i	−1.49376	+	0.862420i	−0.493782	+	0.869586i	$0.664386\pi$
$80$	1.49215	−	1.66538i	0.166827	−	0.186195i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.72560			−0.963581
$83$	6.36686	+	3.67591i	0.698854	+	0.403483i	0.806920	−	0.590660i	$-0.201133\pi$
$83$	6.36686	+	3.67591i	0.698854	+	0.403483i	−0.108067	+	0.994144i	$0.534466\pi$
$84$	1.23806			0.135084
$85$	1.49161	−	1.66478i	0.161788	−	0.180571i
$86$	3.13364	−	5.42762i	0.337909	−	0.585276i
$87$	2.86232	+	4.95768i	0.306872	+	0.531519i
$88$	2.37933			0.253637
$89$	0.869603	+	0.502066i	0.0921778	+	0.0532189i	0.545380	−	0.838189i	$-0.316385\pi$
$89$	0.869603	+	0.502066i	0.0921778	+	0.0532189i	−0.453203	+	0.891408i	$0.649719\pi$
$90$	−0.696189	−	2.12493i	−0.0733848	−	0.223987i
$91$	2.40600	+	1.38910i	0.252217	+	0.145618i
$92$	−0.547828	−	0.948867i	−0.0571151	−	0.0989262i
$93$	1.55283	+	2.68958i	0.161021	+	0.278897i
$94$	5.45183	+	3.14762i	0.562313	+	0.324652i
$95$	17.4281	−	5.70996i	1.78808	−	0.585829i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	5.95504			0.604643			0.302321	−	0.953206i	$-0.402238\pi$
$97$	5.95504			0.604643			0.302321	+	0.953206i	$0.402238\pi$
$98$	−2.73360	−	4.73473i	−0.276135	−	0.478280i
$99$	1.18966	−	2.06056i	0.119566	−	0.207094i
$100$	−0.546992	−	4.96999i	−0.0546992	−	0.496999i
$101$	4.28415			0.426288			0.213144	−	0.977021i	$-0.431630\pi$
$101$	4.28415			0.426288			0.213144	+	0.977021i	$0.431630\pi$
$102$	−0.865713	−	0.499820i	−0.0857183	−	0.0494895i
$103$	8.69905			0.857143			0.428572	−	0.903508i	$-0.359017\pi$
$103$	8.69905			0.857143			0.428572	+	0.903508i	$0.359017\pi$
$104$	−1.12200	−	1.94336i	−0.110021	−	0.190562i
$105$	1.84737	−	2.06185i	0.180285	−	0.201216i
$106$	10.0941	−	5.82782i	0.980423	−	0.566048i
$107$	−7.24046	+	4.18028i	−0.699962	+	0.404123i	−0.807333	−	0.590096i	$-0.799090\pi$
$107$	−7.24046	+	4.18028i	−0.699962	+	0.404123i	0.107371	+	0.994219i	$0.465757\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−7.48885	−	4.32369i	−0.717302	−	0.414135i	0.0964568	−	0.995337i	$-0.469249\pi$
$109$	−7.48885	−	4.32369i	−0.717302	−	0.414135i	−0.813759	+	0.581203i	$0.802582\pi$
$110$	3.55031	−	3.96249i	0.338509	−	0.377808i
$111$	−2.82513	+	5.38690i	−0.268149	+	0.511302i
$112$		−	1.23806i		−	0.116986i
$113$	−5.72597	+	9.91767i	−0.538654	+	0.932976i	0.460323	+	0.887751i	$0.347734\pi$
$113$	−5.72597	+	9.91767i	−0.538654	+	0.932976i	−0.998977	+	0.0452242i	$0.985600\pi$
$114$	−4.10087	−	7.10291i	−0.384081	−	0.665248i
$115$	−2.39767	−	0.503506i	−0.223583	−	0.0469521i
$116$	4.95768	−	2.86232i	0.460309	−	0.265759i
$117$	−2.24399			−0.207457
$118$	−1.06936	+	0.617394i	−0.0984423	+	0.0568357i
$119$		−	1.23762i		−	0.113452i
$120$	−2.12493	+	0.696189i	−0.193979	+	0.0635531i
$121$	−5.33880			−0.485346
$122$		−	5.22183i		−	0.472762i
$123$	7.55659	+	4.36280i	0.681355	+	0.393380i
$124$	2.68958	−	1.55283i	0.241532	−	0.139448i
$125$	−9.09312	−	6.50501i	−0.813314	−	0.581826i
$126$	−1.07219	−	0.619032i	−0.0955187	−	0.0551477i
$127$	−3.39135	−	1.95799i	−0.300933	−	0.173744i	0.341929	−	0.939726i	$-0.388920\pi$
$127$	−3.39135	−	1.95799i	−0.300933	−	0.173744i	−0.642862	+	0.765982i	$0.722253\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.42762	+	3.13364i	−0.477876	+	0.275902i
$130$	−4.91061	−	1.03122i	−0.430689	−	0.0904440i
$131$	2.74014	+	1.58202i	0.239407	+	0.138222i	0.614904	−	0.788602i	$-0.289195\pi$
$131$	2.74014	+	1.58202i	0.239407	+	0.138222i	−0.375497	+	0.926823i	$0.622528\pi$
$132$	−2.06056	−	1.18966i	−0.179349	−	0.103547i
$133$	5.07713	−	8.79385i	0.440243	−	0.762524i
$134$		−	1.88874i		−	0.163162i
$135$	−0.459547	+	2.18834i	−0.0395515	+	0.188342i
$136$	−0.499820	+	0.865713i	−0.0428592	+	0.0742343i
$137$		−	8.45319i		−	0.722204i	−0.932526	−	0.361102i	$-0.882401\pi$
$137$		−	8.45319i		−	0.722204i	0.932526	−	0.361102i	$-0.117599\pi$
$138$			1.09566i			0.0932685i
$139$	−0.500249	+	0.866457i	−0.0424306	+	0.0734919i	−0.886461	−	0.462804i	$-0.846843\pi$
$139$	−0.500249	+	0.866457i	−0.0424306	+	0.0734919i	0.844030	+	0.536296i	$0.180177\pi$
$140$	−2.06185	−	1.84737i	−0.174258	−	0.156132i
$141$	−3.14762	−	5.45183i	−0.265077	−	0.459127i
$142$	−4.92115			−0.412973
$143$	−2.66960	−	4.62388i	−0.223243	−	0.386668i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	2.63074	−	12.5274i	0.218471	−	1.04035i
$146$	−0.107358	−	0.0619833i	−0.00888502	−	0.00512977i
$147$			5.46720i			0.450927i
$148$	5.38690	+	2.82513i	0.442800	+	0.232224i
$149$	22.8315			1.87043			0.935216	−	0.354076i	$-0.115205\pi$
$149$	22.8315			1.87043			0.935216	+	0.354076i	$0.115205\pi$
$150$	−2.01129	+	4.57763i	−0.164221	+	0.373762i
$151$	−5.98037	−	10.3583i	−0.486676	−	0.842947i	0.513207	−	0.858265i	$-0.328457\pi$
$151$	−5.98037	−	10.3583i	−0.486676	−	0.842947i	−0.999883	+	0.0153178i	$0.995124\pi$
$152$	−7.10291	+	4.10087i	−0.576122	+	0.332624i
$153$	0.499820	+	0.865713i	0.0404080	+	0.0699887i
$154$		−	2.94576i		−	0.237376i
$155$	1.42720	−	6.79623i	0.114635	−	0.545886i
$156$			2.24399i			0.179663i
$157$	−12.5430	−	7.24170i	−1.00104	−	0.577951i	−0.0924842	−	0.995714i	$-0.529481\pi$
$157$	−12.5430	−	7.24170i	−1.00104	−	0.577951i	−0.908556	+	0.417763i	$0.862814\pi$
$158$		−	15.3307i		−	1.21965i
$159$	−11.6556			−0.924352
$160$	0.696189	+	2.12493i	0.0550386	+	0.167990i
$161$	−1.17476	+	0.678246i	−0.0925838	+	0.0534533i
$162$	1.00000			0.0785674
$163$	−6.02844	+	10.4416i	−0.472184	+	0.817847i	−0.999493	−	0.0318265i	$-0.989868\pi$
$163$	−6.02844	+	10.4416i	−0.472184	+	0.817847i	0.527309	+	0.849673i	$0.323201\pi$
$164$	4.36280	−	7.55659i	0.340677	−	0.590071i
$165$	−5.05590	+	1.65646i	−0.393601	+	0.128955i
$166$	−6.36686	+	3.67591i	−0.494164	+	0.285306i
$167$	3.98320	+	6.89910i	0.308229	+	0.533869i	0.977975	−	0.208722i	$-0.0669303\pi$
$167$	3.98320	+	6.89910i	0.308229	+	0.533869i	−0.669746	+	0.742590i	$0.733597\pi$
$168$	−0.619032	+	1.07219i	−0.0477593	+	0.0827216i
$169$	3.98224	−	6.89745i	0.306327	−	0.530573i
$170$	0.695938	+	2.12416i	0.0533760	+	0.162916i
$171$			8.20173i			0.627202i
$172$	3.13364	+	5.42762i	0.238938	+	0.413852i
$173$	19.4302	+	11.2180i	1.47725	+	0.852890i	0.999670	−	0.0256988i	$-0.00818109\pi$
$173$	19.4302	+	11.2180i	1.47725	+	0.852890i	0.477579	+	0.878589i	$0.341514\pi$
$174$	−5.72463			−0.433983
$175$	−6.15316	+	0.677211i	−0.465135	+	0.0511923i
$176$	−1.18966	+	2.06056i	−0.0896743	+	0.155320i
$177$	1.23479			0.0928123
$178$	−0.869603	+	0.502066i	−0.0651795	+	0.0376314i
$179$		−	20.9665i		−	1.56711i	−0.621321	−	0.783556i	$-0.713404\pi$
$179$		−	20.9665i		−	1.56711i	0.621321	−	0.783556i	$-0.286596\pi$
$180$	2.18834	+	0.459547i	0.163109	+	0.0342526i
$181$	2.90937	+	5.03918i	0.216252	+	0.374560i	0.953659	−	0.300889i	$-0.0972834\pi$
$181$	2.90937	+	5.03918i	0.216252	+	0.374560i	−0.737407	+	0.675449i	$0.763950\pi$
$182$	−2.40600	+	1.38910i	−0.178344	+	0.102967i
$183$	−2.61091	+	4.52224i	−0.193004	+	0.334293i
$184$	1.09566			0.0807729
$185$	12.7430	−	4.75574i	0.936881	−	0.349649i
$186$	−3.10566			−0.227718
$187$	−1.18923	+	2.05981i	−0.0869654	+	0.150629i
$188$	−5.45183	+	3.14762i	−0.397616	+	0.229563i
$189$	0.619032	+	1.07219i	0.0450279	+	0.0779907i
$190$	−3.76908	+	17.9481i	−0.273438	+	1.30210i
$191$		−	22.1872i		−	1.60541i	−0.596377	−	0.802704i	$-0.703394\pi$
$191$		−	22.1872i		−	1.60541i	0.596377	−	0.802704i	$-0.296606\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	24.2611			1.74635			0.873176	−	0.487405i	$-0.162056\pi$
$193$	24.2611			1.74635			0.873176	+	0.487405i	$0.162056\pi$
$194$	−2.97752	+	5.15722i	−0.213774	+	0.370267i
$195$	3.73711	+	3.34837i	0.267620	+	0.239782i
$196$	5.46720			0.390514
$197$	−14.7868	−	8.53718i	−1.05352	−	0.608249i	−0.129886	−	0.991529i	$-0.541461\pi$
$197$	−14.7868	−	8.53718i	−1.05352	−	0.608249i	−0.923632	+	0.383280i	$0.874794\pi$
$198$	1.18966	+	2.06056i	0.0845457	+	0.146437i
$199$			3.69947i			0.262248i	0.991366	+	0.131124i	$0.0418586\pi$
$199$			3.69947i			0.262248i	−0.991366	+	0.131124i	$0.958141\pi$
$200$	4.57763	+	2.01129i	0.323688	+	0.142219i
$201$	−0.944369	+	1.63569i	−0.0666106	+	0.115373i
$202$	−2.14207	+	3.71018i	−0.150716	+	0.261047i
$203$	−3.54373	−	6.13792i	−0.248721	−	0.430797i
$204$	0.865713	−	0.499820i	0.0606120	−	0.0349944i
$205$	−6.07467	−	18.5413i	−0.424273	−	1.29498i
$206$	−4.34953	+	7.53360i	−0.303046	+	0.524891i
$207$	0.547828	−	0.948867i	0.0380767	−	0.0659508i
$208$	2.24399			0.155593
$209$	−16.9001	+	9.75730i	−1.16901	+	0.674927i
$210$	0.861926	+	2.63080i	0.0594786	+	0.181542i
$211$	−1.25592			−0.0864614			−0.0432307	−	0.999065i	$-0.513765\pi$
$211$	−1.25592			−0.0864614			−0.0432307	+	0.999065i	$0.513765\pi$
$212$			11.6556i			0.800512i
$213$	4.26184	+	2.46057i	0.292016	+	0.168596i
$214$		−	8.36056i		−	0.571516i
$215$	13.7149	+	2.88011i	0.935350	+	0.196422i
$216$		−	1.00000i		−	0.0680414i
$217$	−1.92250	−	3.32987i	−0.130508	−	0.226047i
$218$	7.48885	−	4.32369i	0.507209	−	0.292837i
$219$	0.0619833	+	0.107358i	0.00418844	+	0.00725459i
$220$	1.65646	+	5.05590i	0.111679	+	0.340869i
$221$	2.24318			0.150893
$222$	−3.25263	−	5.14008i	−0.218302	−	0.344980i
$223$		−	2.60823i		−	0.174660i	−0.996179	−	0.0873300i	$-0.972167\pi$
$223$		−	2.60823i		−	0.174660i	0.996179	−	0.0873300i	$-0.0278335\pi$
$224$	1.07219	+	0.619032i	0.0716390	+	0.0413608i
$225$	4.03064	−	2.95870i	0.268709	−	0.197247i
$226$	−5.72597	−	9.91767i	−0.380886	−	0.659713i
$227$	3.45993	+	5.99277i	0.229643	+	0.397754i	0.957702	−	0.287760i	$-0.0929107\pi$
$227$	3.45993	+	5.99277i	0.229643	+	0.397754i	−0.728059	+	0.685514i	$0.759577\pi$
$228$	8.20173			0.543173
$229$	4.10971	+	7.11822i	0.271577	+	0.470386i	0.969266	−	0.246016i	$-0.0791214\pi$
$229$	4.10971	+	7.11822i	0.271577	+	0.470386i	−0.697689	+	0.716401i	$0.745788\pi$
$230$	1.63488	−	1.82469i	0.107801	−	0.120316i
$231$	−1.47288	+	2.55110i	−0.0969083	+	0.167850i
$232$			5.72463i			0.375840i
$233$		−	21.4026i		−	1.40213i	−0.713097	−	0.701065i	$-0.752708\pi$
$233$		−	21.4026i		−	1.40213i	0.713097	−	0.701065i	$-0.247292\pi$
$234$	1.12200	−	1.94336i	0.0733472	−	0.127041i
$235$	−2.89295	+	13.7761i	−0.188715	+	0.898653i
$236$		−	1.23479i		−	0.0803778i
$237$	−7.66536	+	13.2768i	−0.497919	+	0.862420i
$238$	1.07181	+	0.618808i	0.0694750	+	0.0401114i
$239$	−14.7756	−	8.53068i	−0.955752	−	0.551804i	−0.0608893	−	0.998145i	$-0.519394\pi$
$239$	−14.7756	−	8.53068i	−0.955752	−	0.551804i	−0.894863	+	0.446341i	$0.852727\pi$
$240$	0.459547	−	2.18834i	0.0296636	−	0.141257i
$241$	14.1835	−	8.18883i	0.913637	−	0.527489i	0.0320375	−	0.999487i	$-0.489800\pi$
$241$	14.1835	−	8.18883i	0.913637	−	0.527489i	0.881600	+	0.471998i	$0.156467\pi$
$242$	2.66940	−	4.62354i	0.171596	−	0.297212i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	4.52224	+	2.61091i	0.289507	+	0.167147i
$245$	8.15787	−	9.10497i	0.521187	−	0.581695i
$246$	−7.55659	+	4.36280i	−0.481791	+	0.278162i
$247$	15.9389	+	9.20232i	1.01417	+	0.585530i
$248$			3.10566i			0.197210i
$249$	7.35182			0.465903
$250$	10.1801	−	4.62237i	0.643844	−	0.292344i
$251$			21.4733i			1.35539i	0.735345	+	0.677693i	$0.237020\pi$
$251$			21.4733i			1.35539i	−0.735345	+	0.677693i	$0.762980\pi$
$252$	1.07219	−	0.619032i	0.0675419	−	0.0389953i
$253$	2.60693			0.163896
$254$	3.39135	−	1.95799i	0.212792	−	0.122855i
$255$	0.459381	−	2.18755i	0.0287675	−	0.136989i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.119612	−	0.207174i	0.00746119	−	0.0129232i	−0.862271	−	0.506448i	$-0.830958\pi$
$257$	0.119612	−	0.207174i	0.00746119	−	0.0129232i	0.869732	+	0.493524i	$0.164292\pi$
$258$		−	6.26728i		−	0.390184i
$259$	3.49769	−	6.66932i	0.217336	−	0.414411i
$260$	3.34837	−	3.73711i	0.207657	−	0.231766i
$261$	4.95768	+	2.86232i	0.306872	+	0.177173i
$262$	−2.74014	+	1.58202i	−0.169286	+	0.0977374i
$263$	−24.2624	+	14.0079i	−1.49608	+	0.863765i	−0.999990	−	0.00450381i	$-0.998566\pi$
$263$	−24.2624	+	14.0079i	−1.49608	+	0.863765i	−0.496095	+	0.868269i	$0.665233\pi$
$264$	2.06056	−	1.18966i	0.126819	−	0.0732187i
$265$	19.4111	+	17.3919i	1.19241	+	1.06838i
$266$	5.07713	+	8.79385i	0.311299	+	0.539186i
$267$	1.00413			0.0614519
$268$	1.63569	+	0.944369i	0.0999160	+	0.0576865i
$269$	14.1365			0.861915			0.430958	−	0.902372i	$-0.358176\pi$
$269$	14.1365			0.861915			0.430958	+	0.902372i	$0.358176\pi$
$270$	−1.66538	−	1.49215i	−0.101352	−	0.0908092i
$271$	13.6113	−	23.5755i	0.826828	−	1.43211i	−0.0736871	−	0.997281i	$-0.523477\pi$
$271$	13.6113	−	23.5755i	0.826828	−	1.43211i	0.900515	−	0.434826i	$-0.143190\pi$
$272$	−0.499820	−	0.865713i	−0.0303060	−	0.0524916i
$273$	2.77821			0.168145
$274$	7.32067	+	4.22659i	0.442258	+	0.255338i
$275$	10.8917	+	4.78551i	0.656794	+	0.288577i
$276$	−0.948867	−	0.547828i	−0.0571151	−	0.0329754i
$277$	−11.9667	−	20.7270i	−0.719012	−	1.24537i	−0.961392	−	0.275184i	$-0.911261\pi$
$277$	−11.9667	−	20.7270i	−0.719012	−	1.24537i	0.242380	−	0.970181i	$-0.422072\pi$
$278$	−0.500249	−	0.866457i	−0.0300030	−	0.0519667i
$279$	2.68958	+	1.55283i	0.161021	+	0.0929655i
$280$	2.63080	−	0.861926i	0.157220	−	0.0515100i
$281$	12.8178	+	7.40036i	0.764646	+	0.441469i	0.830961	−	0.556330i	$-0.187791\pi$
$281$	12.8178	+	7.40036i	0.764646	+	0.441469i	−0.0663152	+	0.997799i	$0.521124\pi$
$282$	6.29523			0.374876
$283$	14.9913	+	25.9658i	0.891143	+	1.54351i	0.838507	+	0.544891i	$0.183429\pi$
$283$	14.9913	+	25.9658i	0.891143	+	1.54351i	0.0526364	+	0.998614i	$0.483238\pi$
$284$	2.46057	−	4.26184i	0.146008	−	0.252894i
$285$	12.2382	−	13.6590i	0.724928	−	0.809090i
$286$	5.33920			0.315713
$287$	−9.35554	−	5.40142i	−0.552240	−	0.318836i
$288$	−1.00000			−0.0589256
$289$	8.00036	+	13.8570i	0.470609	+	0.815119i
$290$	9.53370	+	8.54199i	0.559838	+	0.501603i
$291$	5.15722	−	2.97752i	0.302321	−	0.174545i
$292$	0.107358	−	0.0619833i	0.00628266	−	0.00362730i
$293$	−11.3931	+	6.57779i	−0.665590	+	0.384279i	−0.794404	−	0.607390i	$-0.792217\pi$
$293$	−11.3931	+	6.57779i	−0.665590	+	0.384279i	0.128813	+	0.991669i	$0.458883\pi$
$294$	−4.73473	−	2.73360i	−0.276135	−	0.159427i
$295$	−2.05639	−	1.84248i	−0.119728	−	0.107274i
$296$	−5.14008	+	3.25263i	−0.298761	+	0.189055i
$297$		−	2.37933i		−	0.138063i
$298$	−11.4158	+	19.7727i	−0.661298	+	1.14540i
$299$	−1.22932	−	2.12925i	−0.0710936	−	0.123138i
$300$	−2.95870	−	4.03064i	−0.170821	−	0.232709i
$301$	6.71974	−	3.87965i	0.387320	−	0.223619i
$302$	11.9607			0.688263
$303$	3.71018	−	2.14207i	0.213144	−	0.123059i
$304$		−	8.20173i		−	0.470402i
$305$	11.0960	−	3.63538i	0.635356	−	0.208161i
$306$	−0.999639			−0.0571456
$307$			11.1634i			0.637128i	0.947901	+	0.318564i	$0.103201\pi$
$307$			11.1634i			0.637128i	−0.947901	+	0.318564i	$0.896799\pi$
$308$	2.55110	+	1.47288i	0.145363	+	0.0839251i
$309$	7.53360	−	4.34953i	0.428572	−	0.247436i
$310$	5.17211	+	4.63410i	0.293756	+	0.263199i
$311$	−22.1416	−	12.7835i	−1.25554	−	0.724884i	−0.283332	−	0.959022i	$-0.591440\pi$
$311$	−22.1416	−	12.7835i	−1.25554	−	0.724884i	−0.972203	+	0.234138i	$0.924773\pi$
$312$	−1.94336	−	1.12200i	−0.110021	−	0.0635206i
$313$	−1.00387	+	1.73875i	−0.0567420	+	0.0982800i	−0.893001	−	0.450054i	$-0.851405\pi$
$313$	−1.00387	+	1.73875i	−0.0567420	+	0.0982800i	0.836259	+	0.548334i	$0.184738\pi$
$314$	12.5430	−	7.24170i	0.707842	−	0.408673i
$315$	0.568948	−	2.70930i	0.0320566	−	0.152652i
$316$	13.2768	+	7.66536i	0.746878	+	0.431210i
$317$	0.127184	+	0.0734298i	0.00714337	+	0.00412423i	0.503567	−	0.863956i	$-0.332021\pi$
$317$	0.127184	+	0.0734298i	0.00714337	+	0.00412423i	−0.496424	+	0.868080i	$0.665354\pi$
$318$	5.82782	−	10.0941i	0.326808	−	0.566048i
$319$			13.6208i			0.762617i
$320$	−2.18834	−	0.459547i	−0.122332	−	0.0256894i
$321$	−4.18028	+	7.24046i	−0.233321	+	0.404123i
$322$		−	1.35649i		−	0.0755944i
$323$		−	8.19877i		−	0.456192i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.22745	−	11.1526i	−0.0680865	−	0.618637i
$326$	−6.02844	−	10.4416i	−0.333885	−	0.578305i
$327$	−8.64738			−0.478201
$328$	4.36280	+	7.55659i	0.240895	+	0.417243i
$329$	3.89695	+	6.74971i	0.214846	+	0.372124i
$330$	1.09341	−	5.20677i	0.0601904	−	0.286623i
$331$	−8.53127	−	4.92553i	−0.468921	−	0.270732i	0.246867	−	0.969049i	$-0.420599\pi$
$331$	−8.53127	−	4.92553i	−0.468921	−	0.270732i	−0.715788	+	0.698318i	$0.753932\pi$
$332$		−	7.35182i		−	0.403483i
$333$	0.246818	+	6.07775i	0.0135255	+	0.333059i
$334$	−7.96640			−0.435902
$335$	4.01343	−	1.31492i	0.219277	−	0.0718417i
$336$	−0.619032	−	1.07219i	−0.0337710	−	0.0584930i
$337$	−9.95412	+	5.74702i	−0.542236	+	0.313060i	−0.745985	−	0.665963i	$-0.768021\pi$
$337$	−9.95412	+	5.74702i	−0.542236	+	0.313060i	0.203749	+	0.979023i	$0.434687\pi$
$338$	3.98224	+	6.89745i	0.216606	+	0.375172i
$339$			11.4519i			0.621984i
$340$	−2.18755	−	0.459381i	−0.118636	−	0.0249134i
$341$			7.38938i			0.400158i
$342$	−7.10291	−	4.10087i	−0.384081	−	0.221749i
$343$		−	15.4352i		−	0.833422i
$344$	−6.26728			−0.337909
$345$	−2.32819	+	0.762784i	−0.125346	+	0.0410669i
$346$	−19.4302	+	11.2180i	−1.04457	+	0.603084i
$347$	−3.73796			−0.200664			−0.100332	−	0.994954i	$-0.531991\pi$
$347$	−3.73796			−0.200664			−0.100332	+	0.994954i	$0.531991\pi$
$348$	2.86232	−	4.95768i	0.153436	−	0.265759i
$349$	−13.6535	+	23.6486i	−0.730857	+	1.26588i	0.225660	+	0.974206i	$0.427546\pi$
$349$	−13.6535	+	23.6486i	−0.730857	+	1.26588i	−0.956517	+	0.291676i	$0.905787\pi$
$350$	2.49010	−	5.66740i	0.133101	−	0.302935i
$351$	−1.94336	+	1.12200i	−0.103729	+	0.0598878i
$352$	−1.18966	−	2.06056i	−0.0634093	−	0.109828i
$353$	17.7727	−	30.7832i	0.945946	−	1.63843i	0.192100	−	0.981375i	$-0.438470\pi$
$353$	17.7727	−	30.7832i	0.945946	−	1.63843i	0.753846	−	0.657052i	$-0.228197\pi$
$354$	−0.617394	+	1.06936i	−0.0328141	+	0.0568357i
$355$	−3.42605	−	10.4571i	−0.181836	−	0.555004i
$356$		−	1.00413i		−	0.0532189i
$357$	−0.618808	−	1.07181i	−0.0327508	−	0.0567261i
$358$	18.1576	+	10.4833i	0.959656	+	0.554058i
$359$	15.8548			0.836786			0.418393	−	0.908266i	$-0.362593\pi$
$359$	15.8548			0.836786			0.418393	+	0.908266i	$0.362593\pi$
$360$	−1.49215	+	1.66538i	−0.0786431	+	0.0877733i
$361$	24.1342	−	41.8017i	1.27022	−	2.20009i
$362$	−5.81875			−0.305827
$363$	−4.62354	+	2.66940i	−0.242673	+	0.140107i
$364$		−	2.77821i		−	0.145618i
$365$	0.0569684	−	0.271280i	0.00298186	−	0.0141995i
$366$	−2.61091	−	4.52224i	−0.136475	−	0.236381i
$367$	−15.4393	+	8.91388i	−0.805925	+	0.465301i	−0.845539	−	0.533914i	$-0.820720\pi$
$367$	−15.4393	+	8.91388i	−0.805925	+	0.465301i	0.0396140	+	0.999215i	$0.487387\pi$
$368$	−0.547828	+	0.948867i	−0.0285575	+	0.0494631i
$369$	8.72560			0.454237
$370$	−2.25289	+	13.4136i	−0.117122	+	0.697340i
$371$	14.4304			0.749190
$372$	1.55283	−	2.68958i	0.0805105	−	0.139448i
$373$	4.77639	−	2.75765i	0.247312	−	0.142786i	−0.371221	−	0.928545i	$-0.621061\pi$
$373$	4.77639	−	2.75765i	0.247312	−	0.142786i	0.618533	+	0.785759i	$0.287727\pi$
$374$	−1.18923	−	2.05981i	−0.0614938	−	0.106510i
$375$	−11.1274	−	1.08694i	−0.574615	−	0.0561293i
$376$		−	6.29523i		−	0.324652i
$377$	11.1250	−	6.42302i	0.572966	−	0.330802i
$378$	−1.23806			−0.0636791
$379$	−0.979562	+	1.69665i	−0.0503167	+	0.0871511i	−0.890087	−	0.455791i	$-0.849356\pi$
$379$	−0.979562	+	1.69665i	−0.0503167	+	0.0871511i	0.839770	+	0.542942i	$0.182690\pi$
$380$	−13.6590	−	12.2382i	−0.700693	−	0.627806i
$381$	−3.91599			−0.200622
$382$	19.2147	+	11.0936i	0.983108	+	0.567598i
$383$	1.30790	+	2.26536i	0.0668308	+	0.115754i	0.897505	−	0.441005i	$-0.145378\pi$
$383$	1.30790	+	2.26536i	0.0668308	+	0.115754i	−0.830674	+	0.556759i	$0.812045\pi$
$384$			1.00000i			0.0510310i
$385$	6.25953	−	2.05081i	0.319015	−	0.104519i
$386$	−12.1306	+	21.0107i	−0.617429	+	1.06942i
$387$	−3.13364	+	5.42762i	−0.159292	+	0.275902i
$388$	−2.97752	−	5.15722i	−0.151161	−	0.261818i
$389$	−6.26174	+	3.61522i	−0.317483	+	0.183299i	−0.650270	−	0.759703i	$-0.725344\pi$
$389$	−6.26174	+	3.61522i	−0.317483	+	0.183299i	0.332787	+	0.943002i	$0.392011\pi$
$390$	−4.76833	+	1.56224i	−0.241454	+	0.0791073i
$391$	−0.547631	+	0.948524i	−0.0276949	+	0.0479689i
$392$	−2.73360	+	4.73473i	−0.138068	+	0.239140i
$393$	3.16404			0.159605
$394$	14.7868	−	8.53718i	0.744950	−	0.430097i
$395$	32.5767	−	10.6731i	1.63911	−	0.537021i
$396$	−2.37933			−0.119566
$397$			3.16094i			0.158643i	0.996849	+	0.0793216i	$0.0252754\pi$
$397$			3.16094i			0.158643i	−0.996849	+	0.0793216i	$0.974725\pi$
$398$	−3.20383	−	1.84973i	−0.160594	−	0.0927188i
$399$		−	10.1543i		−	0.508349i
$400$	−4.03064	+	2.95870i	−0.201532	+	0.147935i
$401$			13.9479i			0.696524i	0.937397	+	0.348262i	$0.113228\pi$
$401$			13.9479i			0.696524i	−0.937397	+	0.348262i	$0.886772\pi$
$402$	−0.944369	−	1.63569i	−0.0471008	−	0.0815810i
$403$	6.03541	−	3.48454i	0.300645	−	0.173577i
$404$	−2.14207	−	3.71018i	−0.106572	−	0.184588i
$405$	0.696189	+	2.12493i	0.0345939	+	0.105589i
$406$	7.08746			0.351745
$407$	−12.2299	+	7.73906i	−0.606215	+	0.383611i
$408$			0.999639i			0.0494895i
$409$	0.511337	+	0.295220i	0.0252840	+	0.0145977i	0.512589	−	0.858634i	$-0.328687\pi$
$409$	0.511337	+	0.295220i	0.0252840	+	0.0145977i	−0.487305	+	0.873232i	$0.662020\pi$
$410$	19.0945	+	4.00982i	0.943012	+	0.198031i
$411$	−4.22659	−	7.32067i	−0.208482	−	0.361102i
$412$	−4.34953	−	7.53360i	−0.214286	−	0.371154i
$413$	−1.52875			−0.0752246
$414$	0.547828	+	0.948867i	0.0269243	+	0.0466343i
$415$	−12.2436	−	10.9700i	−0.601014	−	0.538496i
$416$	−1.12200	+	1.94336i	−0.0550104	+	0.0952809i
$417$			1.00050i			0.0489946i
$418$		−	19.5146i		−	0.954490i
$419$	−5.94109	+	10.2903i	−0.290241	+	0.502712i	−0.973867	−	0.227121i	$-0.927069\pi$
$419$	−5.94109	+	10.2903i	−0.290241	+	0.502712i	0.683625	+	0.729833i	$0.260402\pi$
$420$	−2.70930	−	0.568948i	−0.132200	−	0.0277618i
$421$		−	36.7548i		−	1.79132i	−0.444743	−	0.895658i	$-0.646705\pi$
$421$		−	36.7548i		−	1.79132i	0.444743	−	0.895658i	$-0.353295\pi$
$422$	0.627962	−	1.08766i	0.0305687	−	0.0529466i
$423$	−5.45183	−	3.14762i	−0.265077	−	0.153042i
$424$	−10.0941	−	5.82782i	−0.490212	−	0.283024i
$425$	−4.02919	+	2.95764i	−0.195444	+	0.143466i
$426$	−4.26184	+	2.46057i	−0.206487	+	0.119215i
$427$	3.23248	−	5.59882i	0.156431	−	0.270946i
$428$	7.24046	+	4.18028i	0.349981	+	0.202062i
$429$	−4.62388	−	2.66960i	−0.223243	−	0.128889i
$430$	−9.35171	+	10.4374i	−0.450979	+	0.503337i
$431$	−11.2708	+	6.50722i	−0.542897	+	0.313442i	−0.746252	−	0.665663i	$-0.768149\pi$
$431$	−11.2708	+	6.50722i	−0.542897	+	0.313442i	0.203355	+	0.979105i	$0.434815\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			13.0035i			0.624910i	0.949933	+	0.312455i	$0.101151\pi$
$433$			13.0035i			0.624910i	−0.949933	+	0.312455i	$0.898849\pi$
$434$	3.84501			0.184566
$435$	−3.98543	−	12.1644i	−0.191087	−	0.583240i
$436$			8.64738i			0.414135i
$437$	−7.78235	+	4.49314i	−0.372280	+	0.214936i
$438$	−0.123967			−0.00592335
$439$	−7.58476	+	4.37906i	−0.362001	+	0.209001i	−0.669958	−	0.742399i	$-0.733688\pi$
$439$	−7.58476	+	4.37906i	−0.362001	+	0.209001i	0.307957	+	0.951400i	$0.400355\pi$
$440$	−5.20677	−	1.09341i	−0.248223	−	0.0521264i
$441$	2.73360	+	4.73473i	0.130171	+	0.225463i
$442$	−1.12159	+	1.94265i	−0.0533487	+	0.0924027i
$443$			5.44946i			0.258912i	0.991585	+	0.129456i	$0.0413230\pi$
$443$			5.44946i			0.258912i	−0.991585	+	0.129456i	$0.958677\pi$
$444$	6.07775	−	0.246818i	0.288437	−	0.0117135i
$445$	−1.67226	−	1.49831i	−0.0792728	−	0.0710268i
$446$	2.25879	+	1.30412i	0.106957	+	0.0617517i
$447$	19.7727	−	11.4158i	0.935216	−	0.539947i
$448$	−1.07219	+	0.619032i	−0.0506564	+	0.0292465i
$449$	−8.97982	+	5.18450i	−0.423784	+	0.244672i	−0.696695	−	0.717368i	$-0.745347\pi$
$449$	−8.97982	+	5.18450i	−0.423784	+	0.244672i	0.272911	+	0.962039i	$0.412013\pi$
$450$	0.546992	+	4.96999i	0.0257855	+	0.234288i
$451$	10.3805	+	17.9796i	0.488800	+	0.846626i
$452$	11.4519			0.538654
$453$	−10.3583	−	5.98037i	−0.486676	−	0.280982i
$454$	−6.91985			−0.324765
$455$	−4.62678	−	4.14550i	−0.216907	−	0.194344i
$456$	−4.10087	+	7.10291i	−0.192041	+	0.332624i
$457$	5.58456	+	9.67274i	0.261235	+	0.452472i	0.966570	−	0.256402i	$-0.0825370\pi$
$457$	5.58456	+	9.67274i	0.261235	+	0.452472i	−0.705336	+	0.708873i	$0.749204\pi$
$458$	−8.21942			−0.384068
$459$	0.865713	+	0.499820i	0.0404080	+	0.0233296i
$460$	0.762784	+	2.32819i	0.0355650	+	0.108553i
$461$	−20.0478	−	11.5746i	−0.933718	−	0.539082i	−0.0457325	−	0.998954i	$-0.514562\pi$
$461$	−20.0478	−	11.5746i	−0.933718	−	0.539082i	−0.887986	+	0.459871i	$0.847896\pi$
$462$	−1.47288	−	2.55110i	−0.0685245	−	0.118688i
$463$	−1.70132	−	2.94678i	−0.0790672	−	0.136948i	0.823781	−	0.566909i	$-0.191861\pi$
$463$	−1.70132	−	2.94678i	−0.0790672	−	0.136948i	−0.902848	+	0.429960i	$0.858528\pi$
$464$	−4.95768	−	2.86232i	−0.230154	−	0.132880i
$465$	−2.16213	−	6.59931i	−0.100266	−	0.306036i
$466$	18.5352	+	10.7013i	0.858626	+	0.495728i
$467$	−9.08042			−0.420192			−0.210096	−	0.977681i	$-0.567378\pi$
$467$	−9.08042			−0.420192			−0.210096	+	0.977681i	$0.567378\pi$
$468$	1.12200	+	1.94336i	0.0518643	+	0.0898317i
$469$	1.16919	−	2.02509i	0.0539881	−	0.0935102i
$470$	−10.4840	−	9.39341i	−0.483589	−	0.433286i
$471$	−14.4834			−0.667360
$472$	1.06936	+	0.617394i	0.0492212	+	0.0284178i
$473$	−14.9119			−0.685650
$474$	−7.66536	−	13.2768i	−0.352082	−	0.609823i
$475$	−40.7625	+	4.48628i	−1.87031	+	0.205845i
$476$	−1.07181	+	0.618808i	−0.0491262	+	0.0283630i
$477$	−10.0941	+	5.82782i	−0.462176	+	0.266837i
$478$	14.7756	−	8.53068i	0.675819	−	0.390184i
$479$	28.3565	+	16.3716i	1.29564	+	0.748038i	0.979648	−	0.200724i	$-0.0643295\pi$
$479$	28.3565	+	16.3716i	1.29564	+	0.748038i	0.315992	+	0.948762i	$0.397663\pi$
$480$	1.66538	+	1.49215i	0.0760139	+	0.0681069i
$481$	12.0882	+	6.33957i	0.551173	+	0.289059i
$482$			16.3777i			0.745982i
$483$	−0.678246	+	1.17476i	−0.0308613	+	0.0534533i
$484$	2.66940	+	4.62354i	0.121336	+	0.210161i
$485$	−13.0316	−	2.73662i	−0.591736	−	0.124263i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−8.57654			−0.388640			−0.194320	−	0.980938i	$-0.562250\pi$
$487$	−8.57654			−0.388640			−0.194320	+	0.980938i	$0.562250\pi$
$488$	−4.52224	+	2.61091i	−0.204712	+	0.118191i
$489$			12.0569i			0.545231i
$490$	3.80620	+	11.6174i	0.171947	+	0.524821i
$491$	−38.2338			−1.72547			−0.862733	−	0.505660i	$-0.831249\pi$
$491$	−38.2338			−1.72547			−0.862733	+	0.505660i	$0.831249\pi$
$492$		−	8.72560i		−	0.393380i
$493$	−4.95589	−	2.86128i	−0.223202	−	0.128866i
$494$	−15.9389	+	9.20232i	−0.717124	+	0.414032i
$495$	−3.55031	+	3.96249i	−0.159574	+	0.178101i
$496$	−2.68958	−	1.55283i	−0.120766	−	0.0697242i
$497$	−5.27643	−	3.04635i	−0.236680	−	0.136647i
$498$	−3.67591	+	6.36686i	−0.164721	+	0.285306i
$499$	−13.6781	+	7.89704i	−0.612315	+	0.353520i	−0.773871	−	0.633343i	$-0.781682\pi$
$499$	−13.6781	+	7.89704i	−0.612315	+	0.353520i	0.161556	+	0.986864i	$0.448349\pi$
$500$	−1.08694	+	11.1274i	−0.0486094	+	0.497632i
$501$	6.89910	+	3.98320i	0.308229	+	0.177956i
$502$	−18.5965	−	10.7367i	−0.830001	−	0.479201i
$503$	−13.6766	+	23.6886i	−0.609809	+	1.05622i	0.381462	+	0.924384i	$0.375421\pi$
$503$	−13.6766	+	23.6886i	−0.609809	+	1.05622i	−0.991272	+	0.131836i	$0.957913\pi$
$504$			1.23806i			0.0551477i
$505$	−9.37515	−	1.96876i	−0.417189	−	0.0876089i
$506$	−1.30346	+	2.25766i	−0.0579460	+	0.100365i
$507$		−	7.96449i		−	0.353715i
$508$			3.91599i			0.173744i
$509$	7.38847	−	12.7972i	0.327488	−	0.567226i	−0.654525	−	0.756041i	$-0.727131\pi$
$509$	7.38847	−	12.7972i	0.327488	−	0.567226i	0.982013	+	0.188815i	$0.0604645\pi$
$510$	1.66478	+	1.49161i	0.0737177	+	0.0660496i
$511$	−0.0767392	−	0.132916i	−0.00339474	−	0.00587987i
$512$	1.00000			0.0441942
$513$	4.10087	+	7.10291i	0.181058	+	0.313601i
$514$	0.119612	+	0.207174i	0.00527586	+	0.00913806i
$515$	−19.0365	−	3.99762i	−0.838846	−	0.176156i
$516$	5.42762	+	3.13364i	0.238938	+	0.137951i
$517$		−	14.9784i		−	0.658750i
$518$	4.02696	+	6.36375i	0.176934	+	0.279607i
$519$	22.4360			0.984832
$520$	1.56224	+	4.76833i	0.0685089	+	0.209105i
$521$	18.3365	+	31.7597i	0.803335	+	1.39142i	0.917409	+	0.397945i	$0.130276\pi$
$521$	18.3365	+	31.7597i	0.803335	+	1.39142i	−0.114075	+	0.993472i	$0.536390\pi$
$522$	−4.95768	+	2.86232i	−0.216992	+	0.125280i
$523$	−8.03277	−	13.9132i	−0.351249	−	0.608381i	0.635220	−	0.772331i	$-0.280910\pi$
$523$	−8.03277	−	13.9132i	−0.351249	−	0.608381i	−0.986469	+	0.163951i	$0.947576\pi$
$524$		−	3.16404i		−	0.138222i
$525$	−4.99019	+	3.66306i	−0.217790	+	0.159869i
$526$		−	28.0158i		−	1.22155i
$527$	−2.68861	−	1.55227i	−0.117118	−	0.0676180i
$528$			2.37933i			0.103547i
$529$	−21.7995			−0.947806
$530$	−24.7674	+	8.11452i	−1.07583	+	0.352472i
$531$	1.06936	−	0.617394i	0.0464061	−	0.0267926i
$532$	−10.1543			−0.440243
$533$	9.79010	−	16.9569i	0.424056	−	0.734487i
$534$	−0.502066	+	0.869603i	−0.0217265	+	0.0376314i
$535$	17.7656	−	5.82053i	0.768074	−	0.251644i
$536$	−1.63569	+	0.944369i	−0.0706513	+	0.0407905i
$537$	−10.4833	−	18.1576i	−0.452386	−	0.783556i
$538$	−7.06823	+	12.2425i	−0.304733	+	0.527813i
$539$	−6.50413	+	11.2655i	−0.280153	+	0.485239i
$540$	2.12493	−	0.696189i	0.0914424	−	0.0299592i
$541$		−	6.40179i		−	0.275234i	−0.990485	−	0.137617i	$-0.956056\pi$
$541$		−	6.40179i		−	0.275234i	0.990485	−	0.137617i	$-0.0439444\pi$
$542$	13.6113	+	23.5755i	0.584655	+	1.01265i
$543$	5.03918	+	2.90937i	0.216252	+	0.124853i
$544$	0.999639			0.0428592
$545$	14.4012	+	12.9032i	0.616879	+	0.552711i
$546$	−1.38910	+	2.40600i	−0.0594482	+	0.102967i
$547$	−23.8504			−1.01977			−0.509884	−	0.860243i	$-0.670312\pi$
$547$	−23.8504			−1.01977			−0.509884	+	0.860243i	$0.670312\pi$
$548$	−7.32067	+	4.22659i	−0.312724	+	0.180551i
$549$			5.22183i			0.222862i
$550$	−9.59022	+	7.03973i	−0.408928	+	0.300175i
$551$	−23.4759	−	40.6615i	−1.00011	−	1.73224i
$552$	0.948867	−	0.547828i	0.0403864	−	0.0233171i
$553$	9.49020	−	16.4375i	0.403564	−	0.698994i
$554$	23.9335			1.01684
$555$	8.65786	−	10.4901i	0.367506	−	0.445279i
$556$	1.00050			0.0424306
$557$	−10.5226	+	18.2256i	−0.445856	+	0.772245i	−0.998111	−	0.0614299i	$-0.980434\pi$
$557$	−10.5226	+	18.2256i	−0.445856	+	0.772245i	0.552256	+	0.833675i	$0.313767\pi$
$558$	−2.68958	+	1.55283i	−0.113859	+	0.0657366i
$559$	7.03187	+	12.1796i	0.297416	+	0.515140i
$560$	−0.568948	+	2.70930i	−0.0240424	+	0.114489i
$561$			2.37847i			0.100419i
$562$	−12.8178	+	7.40036i	−0.540687	+	0.312166i
$563$	−25.0957			−1.05766			−0.528828	−	0.848729i	$-0.677368\pi$
$563$	−25.0957			−1.05766			−0.528828	+	0.848729i	$0.677368\pi$
$564$	−3.14762	+	5.45183i	−0.132539	+	0.229563i
$565$	17.0880	−	19.0718i	0.718897	−	0.802359i
$566$	−29.9827			−1.26027
$567$	1.07219	+	0.619032i	0.0450279	+	0.0259969i
$568$	2.46057	+	4.26184i	0.103243	+	0.178823i
$569$			16.9057i			0.708723i	0.935108	+	0.354362i	$0.115302\pi$
$569$			16.9057i			0.708723i	−0.935108	+	0.354362i	$0.884698\pi$
$570$	5.70996	+	17.4281i	0.239164	+	0.729982i
$571$	−13.7384	+	23.7956i	−0.574935	+	0.995817i	0.421114	+	0.907008i	$0.361639\pi$
$571$	−13.7384	+	23.7956i	−0.574935	+	0.995817i	−0.996049	+	0.0888088i	$0.971694\pi$
$572$	−2.66960	+	4.62388i	−0.111622	+	0.193334i
$573$	−11.0936	−	19.2147i	−0.463442	−	0.802704i
$574$	9.35554	−	5.40142i	0.390493	−	0.225451i
$575$	5.01552	+	2.20368i	0.209161	+	0.0918998i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	8.05589	−	13.9532i	0.335371	−	0.580880i	−0.648185	−	0.761483i	$-0.724472\pi$
$577$	8.05589	−	13.9532i	0.335371	−	0.580880i	0.983556	+	0.180603i	$0.0578050\pi$
$578$	−16.0007			−0.665542
$579$	21.0107	−	12.1306i	0.873176	−	0.504128i
$580$	−12.1644	+	3.98543i	−0.505101	+	0.165486i
$581$	−9.10202			−0.377615
$582$			5.95504i			0.246844i
$583$	−24.0171	−	13.8663i	−0.994687	−	0.574283i
$584$			0.123967i			0.00512977i
$585$	4.91061	+	1.03122i	0.203029	+	0.0426357i
$586$		−	13.1556i		−	0.543452i
$587$	4.15035	+	7.18861i	0.171303	+	0.296706i	0.938876	−	0.344256i	$-0.111869\pi$
$587$	4.15035	+	7.18861i	0.171303	+	0.296706i	−0.767573	+	0.640962i	$0.778536\pi$
$588$	4.73473	−	2.73360i	0.195257	−	0.112732i
$589$	−12.7359	−	22.0592i	−0.524774	−	0.908935i
$590$	2.62383	−	0.859645i	0.108022	−	0.0353910i
$591$	−17.0744			−0.702345
$592$	−0.246818	−	6.07775i	−0.0101442	−	0.249794i
$593$			19.9341i			0.818597i	0.912401	+	0.409298i	$0.134226\pi$
$593$			19.9341i			0.818597i	−0.912401	+	0.409298i	$0.865774\pi$
$594$	2.06056	+	1.18966i	0.0845457	+	0.0488125i
$595$	−0.568743	+	2.70832i	−0.0233162	+	0.111030i
$596$	−11.4158	−	19.7727i	−0.467608	−	0.809921i
$597$	1.84973	+	3.20383i	0.0757046	+	0.131124i
$598$	2.45865			0.100542
$599$	8.49888	+	14.7205i	0.347255	+	0.601463i	0.985761	−	0.168154i	$-0.0537805\pi$
$599$	8.49888	+	14.7205i	0.347255	+	0.601463i	−0.638506	+	0.769617i	$0.720447\pi$
$600$	4.96999	−	0.546992i	0.202899	−	0.0223309i
$601$	20.6808	−	35.8202i	0.843588	−	1.46114i	−0.0432539	−	0.999064i	$-0.513772\pi$
$601$	20.6808	−	35.8202i	0.843588	−	1.46114i	0.886842	−	0.462073i	$-0.152894\pi$
$602$			7.75929i			0.316245i
$603$			1.88874i			0.0769153i
$604$	−5.98037	+	10.3583i	−0.243338	+	0.421474i
$605$	11.6831	+	2.45343i	0.474985	+	0.0997461i
$606$			4.28415i			0.174032i
$607$	−15.3148	+	26.5261i	−0.621610	+	1.07666i	0.367575	+	0.929994i	$0.380188\pi$
$607$	−15.3148	+	26.5261i	−0.621610	+	1.07666i	−0.989186	+	0.146667i	$0.953145\pi$
$608$	7.10291	+	4.10087i	0.288061	+	0.166312i
$609$	−6.13792	−	3.54373i	−0.248721	−	0.143599i
$610$	−2.39967	+	11.4271i	−0.0971600	+	0.462671i
$611$	−12.2339	+	7.06323i	−0.494930	+	0.285748i
$612$	0.499820	−	0.865713i	0.0202040	−	0.0349944i
$613$	−13.8680	−	8.00669i	−0.560123	−	0.323387i	0.193072	−	0.981185i	$-0.438155\pi$
$613$	−13.8680	−	8.00669i	−0.560123	−	0.323387i	−0.753195	+	0.657797i	$0.771488\pi$
$614$	−9.66777	−	5.58169i	−0.390159	−	0.225259i
$615$	−14.5315	−	13.0199i	−0.585965	−	0.525012i
$616$	−2.55110	+	1.47288i	−0.102787	+	0.0593440i
$617$	3.18990	+	1.84169i	0.128420	+	0.0741436i	0.562834	−	0.826570i	$-0.309711\pi$
$617$	3.18990	+	1.84169i	0.128420	+	0.0741436i	−0.434414	+	0.900714i	$0.643044\pi$
$618$			8.69905i			0.349927i
$619$	19.9125			0.800350			0.400175	−	0.916439i	$-0.368949\pi$
$619$	19.9125			0.800350			0.400175	+	0.916439i	$0.368949\pi$
$620$	−6.59931	+	2.16213i	−0.265035	+	0.0868331i
$621$		−	1.09566i		−	0.0439672i
$622$	22.1416	−	12.7835i	0.887798	−	0.512570i
$623$	−1.24318			−0.0498069
$624$	1.94336	−	1.12200i	0.0777965	−	0.0449158i
$625$	16.9095	+	18.4139i	0.676378	+	0.736554i
$626$	−1.00387	−	1.73875i	−0.0401226	−	0.0694944i
$627$	−9.75730	+	16.9001i	−0.389669	+	0.674927i
$628$			14.4834i			0.577951i
$629$	−0.246729	−	6.07556i	−0.00983772	−	0.242248i
$630$	2.06185	+	1.84737i	0.0821460	+	0.0736011i
$631$	−32.9638	−	19.0317i	−1.31227	−	0.757638i	−0.329797	−	0.944052i	$-0.606980\pi$
$631$	−32.9638	−	19.0317i	−1.31227	−	0.757638i	−0.982471	+	0.186414i	$0.940313\pi$
$632$	−13.2768	+	7.66536i	−0.528122	+	0.304912i
$633$	−1.08766	+	0.627962i	−0.0432307	+	0.0249593i
$634$	−0.127184	+	0.0734298i	−0.00505113	+	0.00291627i
$635$	6.52161	+	5.84323i	0.258802	+	0.231882i
$636$	5.82782	+	10.0941i	0.231088	+	0.400256i
$637$	12.2684			0.486090
$638$	−11.7959	−	6.81039i	−0.467006	−	0.269626i
$639$	4.92115			0.194678
$640$	1.49215	−	1.66538i	0.0589823	−	0.0658300i
$641$	11.7219	−	20.3029i	0.462986	−	0.801916i	−0.536122	−	0.844141i	$-0.680111\pi$
$641$	11.7219	−	20.3029i	0.462986	−	0.801916i	0.999108	+	0.0422248i	$0.0134446\pi$
$642$	−4.18028	−	7.24046i	−0.164983	−	0.285758i
$643$	−26.3688			−1.03989			−0.519943	−	0.854201i	$-0.674047\pi$
$643$	−26.3688			−1.03989			−0.519943	+	0.854201i	$0.674047\pi$
$644$	1.17476	+	0.678246i	0.0462919	+	0.0267267i
$645$	13.3175	−	4.36321i	0.524377	−	0.171801i
$646$	7.10034	+	4.09939i	0.279359	+	0.161288i
$647$	−7.15731	−	12.3968i	−0.281383	−	0.487370i	0.690343	−	0.723483i	$-0.257460\pi$
$647$	−7.15731	−	12.3968i	−0.281383	−	0.487370i	−0.971726	+	0.236113i	$0.924126\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	2.54435	+	1.46898i	0.0998745	+	0.0576626i
$650$	10.2722	+	4.51331i	0.402908	+	0.177027i
$651$	−3.32987	−	1.92250i	−0.130508	−	0.0753488i
$652$	12.0569			0.472184
$653$	−5.19792	−	9.00305i	−0.203410	−	0.352317i	0.746215	−	0.665705i	$-0.231869\pi$
$653$	−5.19792	−	9.00305i	−0.203410	−	0.352317i	−0.949625	+	0.313388i	$0.898536\pi$
$654$	4.32369	−	7.48885i	0.169070	−	0.292837i
$655$	−5.26933	−	4.72121i	−0.205890	−	0.184473i
$656$	−8.72560			−0.340677
$657$	0.107358	+	0.0619833i	0.00418844	+	0.00241820i
$658$	−7.79390			−0.303838
$659$	2.73699	+	4.74060i	0.106618	+	0.184668i	0.914398	−	0.404816i	$-0.132665\pi$
$659$	2.73699	+	4.74060i	0.106618	+	0.184668i	−0.807780	+	0.589484i	$0.799331\pi$
$660$	3.96249	+	3.55031i	0.154240	+	0.138196i
$661$	38.0482	−	21.9671i	1.47990	−	0.854423i	0.480162	−	0.877180i	$-0.340578\pi$
$661$	38.0482	−	21.9671i	1.47990	−	0.854423i	0.999741	+	0.0227571i	$0.00724443\pi$
$662$	8.53127	−	4.92553i	0.331577	−	0.191436i
$663$	1.94265	−	1.12159i	0.0754465	−	0.0435590i
$664$	6.36686	+	3.67591i	0.247082	+	0.142653i
$665$	−15.1517	+	16.9107i	−0.587556	+	0.655770i
$666$	−5.38690	−	2.82513i	−0.208738	−	0.109471i
$667$			6.27223i			0.242862i
$668$	3.98320	−	6.89910i	0.154115	−	0.266934i
$669$	−1.30412	−	2.25879i	−0.0504200	−	0.0873300i
$670$	−0.867963	+	4.13319i	−0.0335323	+	0.159679i
$671$	−10.7599	+	6.21222i	−0.415381	+	0.239820i
$672$	1.23806			0.0477593
$673$	6.80338	−	3.92793i	0.262251	−	0.151411i	−0.363110	−	0.931746i	$-0.618285\pi$
$673$	6.80338	−	3.92793i	0.262251	−	0.151411i	0.625361	+	0.780336i	$0.284952\pi$
$674$		−	11.4940i		−	0.442734i
$675$	2.01129	−	4.57763i	0.0774144	−	0.176193i
$676$	−7.96449			−0.306327
$677$		−	36.4834i		−	1.40217i	−0.713078	−	0.701085i	$-0.752700\pi$
$677$		−	36.4834i		−	1.40217i	0.713078	−	0.701085i	$-0.247300\pi$
$678$	−9.91767	−	5.72597i	−0.380886	−	0.219904i
$679$	−6.38496	+	3.68636i	−0.245032	+	0.141469i
$680$	1.49161	−	1.66478i	0.0572006	−	0.0638414i
$681$	5.99277	+	3.45993i	0.229643	+	0.132585i
$682$	−6.39940	−	3.69469i	−0.245045	−	0.141477i
$683$	−9.00252	+	15.5928i	−0.344472	+	0.596643i	−0.985258	−	0.171077i	$-0.945275\pi$
$683$	−9.00252	+	15.5928i	−0.344472	+	0.596643i	0.640786	+	0.767720i	$0.278609\pi$
$684$	7.10291	−	4.10087i	0.271586	−	0.156801i
$685$	−3.88463	+	18.4984i	−0.148424	+	0.706788i
$686$	13.3673	+	7.71759i	0.510364	+	0.294659i
$687$	7.11822	+	4.10971i	0.271577	+	0.156795i
$688$	3.13364	−	5.42762i	0.119469	−	0.206926i
$689$			26.1552i			0.996433i
$690$	0.503506	−	2.39767i	0.0191681	−	0.0912776i
$691$	−8.00024	+	13.8568i	−0.304344	+	0.527139i	−0.977115	−	0.212712i	$-0.931770\pi$
$691$	−8.00024	+	13.8568i	−0.304344	+	0.527139i	0.672771	+	0.739850i	$0.265104\pi$
$692$		−	22.4360i		−	0.852890i
$693$			2.94576i			0.111900i
$694$	1.86898	−	3.23717i	0.0709455	−	0.122881i
$695$	1.49289	−	1.66621i	0.0566286	−	0.0632030i
$696$	2.86232	+	4.95768i	0.108496	+	0.187920i
$697$	−8.72245			−0.330386
$698$	−13.6535	−	23.6486i	−0.516794	−	0.895113i
$699$	−10.7013	−	18.5352i	−0.404760	−	0.701065i
$700$	3.66306	+	4.99019i	0.138451	+	0.188611i
$701$	18.0634	+	10.4289i	0.682247	+	0.393895i	0.800701	−	0.599064i	$-0.204461\pi$
$701$	18.0634	+	10.4289i	0.682247	+	0.393895i	−0.118454	+	0.992959i	$0.537794\pi$
$702$		−	2.24399i		−	0.0846941i
$703$	23.1709	−	44.1819i	0.873908	−	1.66635i
$704$	2.37933			0.0896743
$705$	4.38267	+	13.3769i	0.165061	+	0.503804i
$706$	17.7727	+	30.7832i	0.668885	+	1.15854i
$707$	−4.59344	+	2.65202i	−0.172754	+	0.0997396i
$708$	−0.617394	−	1.06936i	−0.0232031	−	0.0401889i
$709$		−	11.6988i		−	0.439359i	−0.975572	−	0.219679i	$-0.929499\pi$
$709$		−	11.6988i		−	0.439359i	0.975572	−	0.219679i	$-0.0705011\pi$
$710$	10.7691	+	2.26150i	0.404158	+	0.0848725i
$711$			15.3307i			0.574947i
$712$	0.869603	+	0.502066i	0.0325898	+	0.0188157i
$713$			3.40274i			0.127434i
$714$	1.23762			0.0463166
$715$	3.71709	+	11.3454i	0.139011	+	0.424294i
$716$	−18.1576	+	10.4833i	−0.678580	+	0.391778i
$717$	−17.0614			−0.637168
$718$	−7.92742	+	13.7307i	−0.295849	+	0.512425i
$719$	−12.4299	+	21.5293i	−0.463559	+	0.802907i	−0.999135	−	0.0415796i	$-0.986761\pi$
$719$	−12.4299	+	21.5293i	−0.463559	+	0.802907i	0.535577	+	0.844487i	$0.320094\pi$
$720$	−0.696189	−	2.12493i	−0.0259454	−	0.0791914i
$721$	−9.32708	+	5.38499i	−0.347358	+	0.200547i
$722$	24.1342	+	41.8017i	0.898182	+	1.55570i
$723$	8.18883	−	14.1835i	0.304546	−	0.527489i
$724$	2.90937	−	5.03918i	0.108126	−	0.187280i
$725$	−11.5139	+	26.2053i	−0.427614	+	0.973239i
$726$		−	5.33880i		−	0.198142i
$727$	13.0391	+	22.5845i	0.483595	+	0.837611i	0.999823	−	0.0188403i	$-0.00599739\pi$
$727$	13.0391	+	22.5845i	0.483595	+	0.837611i	−0.516227	+	0.856452i	$0.672664\pi$
$728$	2.40600	+	1.38910i	0.0891722	+	0.0514836i
$729$	−1.00000			−0.0370370
$730$	0.206452	+	0.184976i	0.00764112	+	0.00684628i
$731$	3.13251	−	5.42567i	0.115860	−	0.200675i
$732$	5.22183			0.193004
$733$	40.4937	−	23.3790i	1.49567	−	0.863524i	0.495680	−	0.868505i	$-0.334919\pi$
$733$	40.4937	−	23.3790i	1.49567	−	0.863524i	0.999988	+	0.00498092i	$0.00158548\pi$
$734$		−	17.8278i		−	0.658035i
$735$	2.51243	−	11.9641i	0.0926725	−	0.441301i
$736$	−0.547828	−	0.948867i	−0.0201932	−	0.0349757i
$737$	−3.89185	+	2.24696i	−0.143358	+	0.0827679i
$738$	−4.36280	+	7.55659i	−0.160597	+	0.278162i
$739$	24.3403			0.895372			0.447686	−	0.894191i	$-0.352248\pi$
$739$	24.3403			0.895372			0.447686	+	0.894191i	$0.352248\pi$
$740$	−10.4901	−	8.65786i	−0.385623	−	0.318269i
$741$	18.4046			0.676111
$742$	−7.21521	+	12.4971i	−0.264879	+	0.458783i
$743$	24.0446	−	13.8822i	0.882111	−	0.509287i	0.0107573	−	0.999942i	$-0.496576\pi$
$743$	24.0446	−	13.8822i	0.882111	−	0.509287i	0.871354	+	0.490655i	$0.163242\pi$
$744$	1.55283	+	2.68958i	0.0569295	+	0.0986048i
$745$	−49.9631	−	10.4922i	−1.83051	−	0.384403i
$746$			5.51530i			0.201930i
$747$	6.36686	−	3.67591i	0.232951	−	0.134494i
$748$	2.37847			0.0869654
$749$	5.17546	−	8.96415i	0.189107	−	0.327543i
$750$	6.50501	−	9.09312i	0.237529	−	0.332034i
$751$	3.45365			0.126026			0.0630128	−	0.998013i	$-0.479929\pi$
$751$	3.45365			0.126026			0.0630128	+	0.998013i	$0.479929\pi$
$752$	5.45183	+	3.14762i	0.198808	+	0.114782i
$753$	10.7367	+	18.5965i	0.391266	+	0.677693i
$754$			12.8460i			0.467825i
$755$	8.32694	+	25.4157i	0.303048	+	0.924973i
$756$	0.619032	−	1.07219i	0.0225140	−	0.0389953i
$757$	8.28057	−	14.3424i	0.300962	−	0.521282i	−0.675392	−	0.737459i	$-0.736025\pi$
$757$	8.28057	−	14.3424i	0.300962	−	0.521282i	0.976354	+	0.216177i	$0.0693588\pi$
$758$	−0.979562	−	1.69665i	−0.0355793	−	0.0616251i
$759$	2.25766	−	1.30346i	0.0819480	−	0.0473127i
$760$	17.4281	−	5.70996i	0.632183	−	0.207122i
$761$	−13.0643	+	22.6280i	−0.473580	+	0.820265i	−0.999543	−	0.0302429i	$-0.990372\pi$
$761$	−13.0643	+	22.6280i	−0.473580	+	0.820265i	0.525962	+	0.850508i	$0.323705\pi$
$762$	1.95799	−	3.39135i	0.0709306	−	0.122855i
$763$	10.7060			0.387584
$764$	−19.2147	+	11.0936i	−0.695162	+	0.401352i
$765$	−0.695938	−	2.12416i	−0.0251617	−	0.0767992i
$766$	−2.61581			−0.0945130
$767$		−	2.77086i		−	0.100050i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$			8.68949i			0.313351i	0.987650	+	0.156675i	$0.0500777\pi$
$769$			8.68949i			0.313351i	−0.987650	+	0.156675i	$0.949922\pi$
$770$	−1.35371	+	6.44631i	−0.0487845	+	0.232309i
$771$		−	0.239224i		−	0.00861545i
$772$	−12.1306	−	21.0107i	−0.436588	−	0.756193i
$773$	−22.1990	+	12.8166i	−0.798444	+	0.460982i	−0.842927	−	0.538028i	$-0.819169\pi$
$773$	−22.1990	+	12.8166i	−0.798444	+	0.460982i	0.0444828	+	0.999010i	$0.485836\pi$
$774$	−3.13364	−	5.42762i	−0.112636	−	0.195092i
$775$	−6.24637	+	14.2166i	−0.224376	+	0.510675i
$776$	5.95504			0.213774
$777$	−0.305576	−	7.52464i	−0.0109625	−	0.269945i
$778$		−	7.23044i		−	0.259224i
$779$	−61.9771	−	35.7825i	−2.22056	−	1.28204i
$780$	1.03122	−	4.91061i	0.0369236	−	0.175828i
$781$	5.85451	+	10.1403i	0.209491	+	0.362849i
$782$	−0.547631	−	0.948524i	−0.0195832	−	0.0339192i
$783$	5.72463			0.204582
$784$	−2.73360	−	4.73473i	−0.0976285	−	0.169098i
$785$	24.1204	+	21.6114i	0.860894	+	0.771343i
$786$	−1.58202	+	2.74014i	−0.0564287	+	0.0977374i
$787$		−	50.7143i		−	1.80777i	−0.427776	−	0.903885i	$-0.640703\pi$
$787$		−	50.7143i		−	1.80777i	0.427776	−	0.903885i	$-0.359297\pi$
$788$			17.0744i			0.608249i
$789$	−14.0079	+	24.2624i	−0.498695	+	0.863765i
$790$	−7.04518	+	33.5488i	−0.250656	+	1.19361i
$791$		−	14.1782i		−	0.504120i
$792$	1.18966	−	2.06056i	0.0422729	−	0.0732187i
$793$	10.1479	+	5.85888i	0.360362	+	0.208055i
$794$	−2.73746	−	1.58047i	−0.0971487	−	0.0560888i
$795$	25.5064	+	5.35631i	0.904620	+	0.189969i
$796$	3.20383	−	1.84973i	0.113557	−	0.0655621i
$797$	4.46101	−	7.72669i	0.158017	−	0.273694i	−0.776136	−	0.630565i	$-0.782823\pi$
$797$	4.46101	−	7.72669i	0.158017	−	0.273694i	0.934154	+	0.356871i	$0.116157\pi$
$798$	8.79385	+	5.07713i	0.311299	+	0.179729i
$799$	5.44986	+	3.14648i	0.192802	+	0.111314i
$800$	−0.546992	−	4.96999i	−0.0193391	−	0.175716i
$801$	0.869603	−	0.502066i	0.0307259	−	0.0177396i
$802$	−12.0792	−	6.97395i	−0.426532	−	0.246259i
$803$			0.294957i			0.0104088i
$804$	1.88874			0.0666106
$805$	2.88245	−	0.944376i	0.101593	−	0.0332849i
$806$			6.96909i			0.245476i
$807$	12.2425	−	7.06823i	0.430958	−	0.248813i
$808$	4.28415			0.150716
$809$	31.7514	−	18.3317i	1.11632	−	0.644508i	0.175861	−	0.984415i	$-0.443729\pi$
$809$	31.7514	−	18.3317i	1.11632	−	0.644508i	0.940459	+	0.339907i	$0.110396\pi$
$810$	−2.18834	−	0.459547i	−0.0768903	−	0.0161468i
$811$	−11.9834	−	20.7559i	−0.420794	−	0.728837i	0.575223	−	0.817996i	$-0.304915\pi$
$811$	−11.9834	−	20.7559i	−0.420794	−	0.728837i	−0.996017	+	0.0891598i	$0.971582\pi$
$812$	−3.54373	+	6.13792i	−0.124361	+	0.215399i
$813$		−	27.2226i		−	0.954738i
$814$	−0.587260	−	14.4610i	−0.0205835	−	0.506857i
$815$	17.9907	−	20.0793i	0.630185	−	0.703348i
$816$	−0.865713	−	0.499820i	−0.0303060	−	0.0174972i
$817$	44.5159	−	25.7013i	1.55741	−	0.899174i
$818$	−0.511337	+	0.295220i	−0.0178785	+	0.0103221i
$819$	2.40600	−	1.38910i	0.0840724	−	0.0485392i
$820$	−13.0199	+	14.5315i	−0.454674	+	0.507460i
$821$	1.38754	+	2.40329i	0.0484255	+	0.0838754i	0.889222	−	0.457476i	$-0.151246\pi$
$821$	1.38754	+	2.40329i	0.0484255	+	0.0838754i	−0.840797	+	0.541351i	$0.817913\pi$
$822$	8.45319			0.294839
$823$	−6.62435	−	3.82457i	−0.230910	−	0.133316i	0.380082	−	0.924953i	$-0.375896\pi$
$823$	−6.62435	−	3.82457i	−0.230910	−	0.133316i	−0.610992	+	0.791637i	$0.709229\pi$
$824$	8.69905			0.303046
$825$	11.8252	−	1.30147i	0.411702	−	0.0453115i
$826$	0.764373	−	1.32393i	0.0265959	−	0.0460655i
$827$	19.2894	+	33.4102i	0.670758	+	1.16179i	0.977689	+	0.210056i	$0.0673646\pi$
$827$	19.2894	+	33.4102i	0.670758	+	1.16179i	−0.306931	+	0.951732i	$0.599302\pi$
$828$	−1.09566			−0.0380767
$829$	24.1475	+	13.9415i	0.838676	+	0.484210i	0.856814	−	0.515626i	$-0.172441\pi$
$829$	24.1475	+	13.9415i	0.838676	+	0.484210i	−0.0181381	+	0.999835i	$0.505774\pi$
$830$	15.6221	−	5.11826i	0.542251	−	0.177657i
$831$	−20.7270	−	11.9667i	−0.719012	−	0.415122i
$832$	−1.12200	−	1.94336i	−0.0388983	−	0.0673737i
$833$	−2.73261	−	4.73302i	−0.0946794	−	0.163990i
$834$	−0.866457	−	0.500249i	−0.0300030	−	0.0173222i
$835$	−5.54612	−	16.9280i	−0.191931	−	0.585818i
$836$	16.9001	+	9.75730i	0.584504	+	0.337463i
$837$	3.10566			0.107347
$838$	−5.94109	−	10.2903i	−0.205232	−	0.355471i
$839$	−19.7572	+	34.2204i	−0.682094	+	1.18142i	0.292247	+	0.956343i	$0.405597\pi$
$839$	−19.7572	+	34.2204i	−0.682094	+	1.18142i	−0.974341	+	0.225078i	$0.927736\pi$
$840$	1.84737	−	2.06185i	0.0637404	−	0.0711405i
$841$	−3.77140			−0.130048
$842$	31.8305	+	18.3774i	1.09695	+	0.633326i
$843$	14.8007			0.509764
$844$	0.627962	+	1.08766i	0.0216154	+	0.0374389i
$845$	−11.8842	+	13.2639i	−0.408829	+	0.456293i
$846$	5.45183	−	3.14762i	0.187438	−	0.108217i
$847$	5.72423	−	3.30489i	0.196687	−	0.113557i
$848$	10.0941	−	5.82782i	0.346632	−	0.200128i
$849$	25.9658	+	14.9913i	0.891143	+	0.514502i
$850$	−0.546795	−	4.96820i	−0.0187549	−	0.170408i
$851$	−5.63176	+	3.56376i	−0.193054	+	0.122164i
$852$		−	4.92115i		−	0.168596i
$853$	−20.5535	+	35.5997i	−0.703739	+	1.21891i	0.263406	+	0.964685i	$0.415154\pi$
$853$	−20.5535	+	35.5997i	−0.703739	+	1.21891i	−0.967145	+	0.254227i	$0.918179\pi$
$854$	3.23248	+	5.59882i	0.110613	+	0.191588i
$855$	3.76908	−	17.9481i	0.128900	−	0.613814i
$856$	−7.24046	+	4.18028i	−0.247474	+	0.142879i
$857$	27.5518			0.941151			0.470576	−	0.882360i	$-0.344046\pi$
$857$	27.5518			0.941151			0.470576	+	0.882360i	$0.344046\pi$
$858$	4.62388	−	2.66960i	0.157857	−	0.0911386i
$859$			30.9875i			1.05728i	0.848846	+	0.528641i	$0.177298\pi$
$859$			30.9875i			1.05728i	−0.848846	+	0.528641i	$0.822702\pi$
$860$	−4.36321	−	13.3175i	−0.148784	−	0.454124i
$861$	−10.8028			−0.368160
$862$		−	13.0144i		−	0.443274i
$863$	40.3535	+	23.2981i	1.37365	+	0.793076i	0.991385	−	0.130978i	$-0.0418116\pi$
$863$	40.3535	+	23.2981i	1.37365	+	0.793076i	0.382263	+	0.924054i	$0.375145\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−37.3646	−	33.4779i	−1.27043	−	1.13828i
$866$	−11.2614	−	6.50177i	−0.382678	−	0.220939i
$867$	13.8570	+	8.00036i	0.470609	+	0.271706i
$868$	−1.92250	+	3.32987i	−0.0652540	+	0.113023i
$869$	−31.5898	+	18.2384i	−1.07161	+	0.618695i
$870$	12.5274	+	2.63074i	0.424719	+	0.0891903i
$871$	3.67049	+	2.11916i	0.124370	+	0.0718049i
$872$	−7.48885	−	4.32369i	−0.253605	−	0.146419i
$873$	2.97752	−	5.15722i	0.100774	−	0.174545i
$874$		−	8.98628i		−	0.303966i
$875$	13.7764	+	1.34570i	0.465727	+	0.0454930i
$876$	0.0619833	−	0.107358i	0.00209422	−	0.00362730i
$877$			20.5259i			0.693110i	0.938030	+	0.346555i	$0.112649\pi$
$877$			20.5259i			0.693110i	−0.938030	+	0.346555i	$0.887351\pi$
$878$		−	8.75812i		−	0.295572i
$879$	−6.57779	+	11.3931i	−0.221863	+	0.384279i
$880$	3.55031	−	3.96249i	0.119681	−	0.133575i
$881$	−14.5639	−	25.2254i	−0.490669	−	0.849864i	0.509273	−	0.860605i	$-0.329914\pi$
$881$	−14.5639	−	25.2254i	−0.490669	−	0.849864i	−0.999942	+	0.0107408i	$0.996581\pi$
$882$	−5.46720			−0.184090
$883$	−14.4749	−	25.0713i	−0.487120	−	0.843716i	0.512771	−	0.858526i	$-0.328619\pi$
$883$	−14.4749	−	25.0713i	−0.487120	−	0.843716i	−0.999890	+	0.0148097i	$0.995286\pi$
$884$	−1.12159	−	1.94265i	−0.0377232	−	0.0653385i
$885$	−2.70213	−	0.567442i	−0.0908311	−	0.0190744i
$886$	−4.71937	−	2.72473i	−0.158550	−	0.0915391i
$887$		−	39.7064i		−	1.33321i	−0.745410	−	0.666606i	$-0.767746\pi$
$887$		−	39.7064i		−	1.33321i	0.745410	−	0.666606i	$-0.232254\pi$
$888$	−2.82513	+	5.38690i	−0.0948050	+	0.180772i
$889$	4.84824			0.162605
$890$	2.13371	−	0.699065i	0.0715220	−	0.0234327i
$891$	−1.18966	−	2.06056i	−0.0398552	−	0.0690313i
$892$	−2.25879	+	1.30412i	−0.0756300	+	0.0436650i
$893$	25.8159	+	44.7144i	0.863896	+	1.49631i
$894$			22.8315i			0.763601i
$895$	−9.63510	+	45.8818i	−0.322066	+	1.53366i
$896$		−	1.23806i		−	0.0413608i
$897$	−2.12925	−	1.22932i	−0.0710936	−	0.0410459i
$898$		−	10.3690i		−	0.346018i
$899$	−17.7788			−0.592955
$900$	−4.57763	−	2.01129i	−0.152588	−	0.0670429i
$901$	10.0904	−	5.82571i	0.336161	−	0.194083i
$902$	−20.7611			−0.691268
$903$	3.87965	−	6.71974i	0.129107	−	0.223619i
$904$	−5.72597	+	9.91767i	−0.190443	+	0.329857i
$905$	−4.05095	−	12.3644i	−0.134658	−	0.411007i
$906$	10.3583	−	5.98037i	0.344132	−	0.198685i
$907$	1.92263	+	3.33010i	0.0638400	+	0.110574i	0.896179	−	0.443693i	$-0.146332\pi$
$907$	1.92263	+	3.33010i	0.0638400	+	0.110574i	−0.832339	+	0.554267i	$0.812999\pi$
$908$	3.45993	−	5.99277i	0.114822	−	0.198877i
$909$	2.14207	−	3.71018i	0.0710481	−	0.123059i
$910$	5.90349	−	1.93416i	0.195699	−	0.0641167i
$911$			19.7562i			0.654553i	0.944929	+	0.327277i	$0.106131\pi$
$911$			19.7562i			0.654553i	−0.944929	+	0.327277i	$0.893869\pi$
$912$	−4.10087	−	7.10291i	−0.135793	−	0.235201i
$913$	15.1488	+	8.74619i	0.501354	+	0.289457i
$914$	−11.1691			−0.369442
$915$	7.79174	−	8.69634i	0.257587	−	0.287492i
$916$	4.10971	−	7.11822i	0.135789	−	0.235193i
$917$	−3.91728			−0.129360
$918$	−0.865713	+	0.499820i	−0.0285728	+	0.0164965i
$919$			10.4598i			0.345038i	0.985006	+	0.172519i	$0.0551906\pi$
$919$			10.4598i			0.345038i	−0.985006	+	0.172519i	$0.944809\pi$
$920$	−2.39767	−	0.503506i	−0.0790487	−	0.0166001i
$921$	5.58169	+	9.66777i	0.183923	+	0.318564i
$922$	20.0478	−	11.5746i	0.660238	−	0.381189i
$923$	5.52151	−	9.56354i	0.181743	−	0.314788i
$924$	2.94576			0.0969083
$925$	−30.0714	+	4.55117i	−0.988740	+	0.149641i
$926$	3.40265			0.111818
$927$	4.34953	−	7.53360i	0.142857	−	0.247436i
$928$	4.95768	−	2.86232i	0.162744	−	0.0939601i
$929$	−19.6453	−	34.0267i	−0.644542	−	1.11638i	−0.984407	−	0.175905i	$-0.943715\pi$
$929$	−19.6453	−	34.0267i	−0.644542	−	1.11638i	0.339866	−	0.940474i	$-0.389618\pi$
$930$	6.79623	+	1.42720i	0.222857	+	0.0467996i
$931$		−	44.8405i		−	1.46959i
$932$	−18.5352	+	10.7013i	−0.607140	+	0.350533i
$933$	−25.5669			−0.837024
$934$	4.54021	−	7.86388i	0.148560	−	0.257314i
$935$	3.54903	−	3.96106i	0.116066	−	0.129540i
$936$	−2.24399			−0.0733472
$937$	23.2410	+	13.4182i	0.759250	+	0.438353i	0.829027	−	0.559209i	$-0.188895\pi$
$937$	23.2410	+	13.4182i	0.759250	+	0.438353i	−0.0697761	+	0.997563i	$0.522228\pi$
$938$	1.16919	+	2.02509i	0.0381754	+	0.0661217i
$939$			2.00774i			0.0655200i
$940$	13.3769	−	4.38267i	0.436307	−	0.142947i
$941$	11.5964	−	20.0855i	0.378031	−	0.654769i	−0.612744	−	0.790281i	$-0.709935\pi$
$941$	11.5964	−	20.0855i	0.378031	−	0.654769i	0.990776	+	0.135512i	$0.0432678\pi$
$942$	7.24170	−	12.5430i	0.235947	−	0.408673i
$943$	4.78013	+	8.27943i	0.155662	+	0.269615i
$944$	−1.06936	+	0.617394i	−0.0348046	+	0.0200945i
$945$	−0.861926	−	2.63080i	−0.0280385	−	0.0855798i
$946$	7.45596	−	12.9141i	0.242414	−	0.419873i
$947$	21.9643	−	38.0433i	0.713745	−	1.23624i	−0.249697	−	0.968324i	$-0.580331\pi$
$947$	21.9643	−	38.0433i	0.713745	−	1.23624i	0.963442	−	0.267918i	$-0.0863357\pi$
$948$	15.3307			0.497919
$949$	0.240911	−	0.139090i	0.00782031	−	0.00451506i
$950$	16.4960	−	37.5445i	0.535202	−	1.21811i
$951$	0.146860			0.00476225
$952$		−	1.23762i		−	0.0401114i
$953$	37.8822	+	21.8713i	1.22712	+	0.708481i	0.966427	−	0.256940i	$-0.0827143\pi$
$953$	37.8822	+	21.8713i	1.22712	+	0.708481i	0.260697	+	0.965421i	$0.416048\pi$
$954$		−	11.6556i		−	0.377365i
$955$	−10.1961	+	48.5530i	−0.329937	+	1.57114i
$956$			17.0614i			0.551804i
$957$	6.81039	+	11.7959i	0.220149	+	0.381308i
$958$	−28.3565	+	16.3716i	−0.916155	+	0.528943i
$959$	5.23279	+	9.06346i	0.168976	+	0.292674i
$960$	−2.12493	+	0.696189i	−0.0685818	+	0.0224694i
$961$	21.3549			0.688867
$962$	−11.5343	+	7.29888i	−0.371881	+	0.235325i
$963$			8.36056i			0.269415i
$964$	−14.1835	−	8.18883i	−0.456819	−	0.263744i
$965$	−53.0915	−	11.1491i	−1.70907	−	0.358903i
$966$	−0.678246	−	1.17476i	−0.0218222	−	0.0377972i
$967$	11.8106	+	20.4566i	0.379803	+	0.657839i	0.991033	−	0.133614i	$-0.0426583\pi$
$967$	11.8106	+	20.4566i	0.379803	+	0.657839i	−0.611230	+	0.791453i	$0.709325\pi$
$968$	−5.33880			−0.171596
$969$	−4.09939	−	7.10034i	−0.131691	−	0.228096i
$970$	8.88580	−	9.91742i	0.285306	−	0.318429i
$971$	4.08436	−	7.07433i	0.131073	−	0.227026i	−0.793017	−	0.609199i	$-0.791491\pi$
$971$	4.08436	−	7.07433i	0.131073	−	0.227026i	0.924091	+	0.382173i	$0.124824\pi$
$972$			1.00000i			0.0320750i
$973$		−	1.23868i		−	0.0397103i
$974$	4.28827	−	7.42750i	0.137405	−	0.237992i
$975$	−6.63931	−	9.04474i	−0.212628	−	0.289663i
$976$		−	5.22183i		−	0.167147i
$977$	−1.14181	+	1.97767i	−0.0365297	+	0.0632713i	−0.883712	−	0.468031i	$-0.844964\pi$
$977$	−1.14181	+	1.97767i	−0.0365297	+	0.0632713i	0.847183	+	0.531302i	$0.178297\pi$
$978$	−10.4416	−	6.02844i	−0.333885	−	0.192768i
$979$	2.06907	+	1.19458i	0.0661278	+	0.0381789i
$980$	−11.9641	−	2.51243i	−0.382178	−	0.0802567i
$981$	−7.48885	+	4.32369i	−0.239101	+	0.138045i
$982$	19.1169	−	33.1114i	0.610044	−	1.05663i
$983$	35.3530	+	20.4111i	1.12759	+	0.651012i	0.943327	−	0.331866i	$-0.107678\pi$
$983$	35.3530	+	20.4111i	1.12759	+	0.651012i	0.184259	+	0.982878i	$0.441012\pi$
$984$	7.55659	+	4.36280i	0.240895	+	0.139081i
$985$	28.4353	+	25.4775i	0.906025	+	0.811780i
$986$	4.95589	−	2.86128i	0.157828	−	0.0911218i
$987$	6.74971	+	3.89695i	0.214846	+	0.124041i
$988$		−	18.4046i		−	0.585530i
$989$	−6.86679			−0.218351
$990$	−1.65646	−	5.05590i	−0.0526458	−	0.160687i
$991$			48.3652i			1.53637i	0.640227	+	0.768186i	$0.278840\pi$
$991$			48.3652i			1.53637i	−0.640227	+	0.768186i	$0.721160\pi$
$992$	2.68958	−	1.55283i	0.0853943	−	0.0493024i
$993$	−9.85106			−0.312614
$994$	5.27643	−	3.04635i	0.167358	−	0.0966242i
$995$	1.70008	−	8.09568i	0.0538961	−	0.256650i
$996$	−3.67591	−	6.36686i	−0.116476	−	0.201742i
$997$	−30.2780	+	52.4430i	−0.958913	+	1.66089i	−0.233763	+	0.972294i	$0.575104\pi$
$997$	−30.2780	+	52.4430i	−0.958913	+	1.66089i	−0.725149	+	0.688592i	$0.758229\pi$
$998$		−	15.7941i		−	0.499953i
$999$	3.25263	+	5.14008i	0.102909	+	0.162625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.619.15	yes	36
5.4	even	2		1110.2.ba.b.619.4	yes	36
37.11	even	6		1110.2.ba.b.529.4	yes	36
185.159	even	6	inner	1110.2.ba.a.529.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.15	✓	36	185.159	even	6	inner
1110.2.ba.a.619.15	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.4	yes	36	37.11	even	6
1110.2.ba.b.619.4	yes	36	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18834 - 0.459547i) q^{5} +1.00000i q^{6} +(-1.07219 + 0.619032i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18834 - 0.459547i) q^{5} +1.00000i q^{6} +(-1.07219 + 0.619032i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.49215 - 1.66538i) q^{10} +2.37933 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.12200 - 1.94336i) q^{13} -1.23806i q^{14} +(-2.12493 + 0.696189i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.499820 + 0.865713i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-7.10291 + 4.10087i) q^{19} +(0.696189 + 2.12493i) q^{20} +(-0.619032 + 1.07219i) q^{21} +(-1.18966 + 2.06056i) q^{22} +1.09566 q^{23} +(0.866025 - 0.500000i) q^{24} +(4.57763 + 2.01129i) q^{25} +2.24399 q^{26} -1.00000i q^{27} +(1.07219 + 0.619032i) q^{28} +5.72463i q^{29} +(0.459547 - 2.18834i) q^{30} +3.10566i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.06056 - 1.18966i) q^{33} +(-0.499820 - 0.865713i) q^{34} +(2.63080 - 0.861926i) q^{35} -1.00000 q^{36} +(-5.14008 + 3.25263i) q^{37} -8.20173i q^{38} +(-1.94336 - 1.12200i) q^{39} +(-2.18834 - 0.459547i) q^{40} +(4.36280 + 7.55659i) q^{41} +(-0.619032 - 1.07219i) q^{42} -6.26728 q^{43} +(-1.18966 - 2.06056i) q^{44} +(-1.49215 + 1.66538i) q^{45} +(-0.547828 + 0.948867i) q^{46} -6.29523i q^{47} +1.00000i q^{48} +(-2.73360 + 4.73473i) q^{49} +(-4.03064 + 2.95870i) q^{50} +0.999639i q^{51} +(-1.12200 + 1.94336i) q^{52} +(-10.0941 - 5.82782i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-5.20677 - 1.09341i) q^{55} +(-1.07219 + 0.619032i) q^{56} +(-4.10087 + 7.10291i) q^{57} +(-4.95768 - 2.86232i) q^{58} +(1.06936 + 0.617394i) q^{59} +(1.66538 + 1.49215i) q^{60} +(-4.52224 + 2.61091i) q^{61} +(-2.68958 - 1.55283i) q^{62} +1.23806i q^{63} +1.00000 q^{64} +(1.56224 + 4.76833i) q^{65} +2.37933i q^{66} +(-1.63569 + 0.944369i) q^{67} +0.999639 q^{68} +(0.948867 - 0.547828i) q^{69} +(-0.568948 + 2.70930i) q^{70} +(2.46057 + 4.26184i) q^{71} +(0.500000 - 0.866025i) q^{72} +0.123967i q^{73} +(-0.246818 - 6.07775i) q^{74} +(4.96999 - 0.546992i) q^{75} +(7.10291 + 4.10087i) q^{76} +(-2.55110 + 1.47288i) q^{77} +(1.94336 - 1.12200i) q^{78} +(-13.2768 + 7.66536i) q^{79} +(1.49215 - 1.66538i) q^{80} +(-0.500000 - 0.866025i) q^{81} -8.72560 q^{82} +(6.36686 + 3.67591i) q^{83} +1.23806 q^{84} +(1.49161 - 1.66478i) q^{85} +(3.13364 - 5.42762i) q^{86} +(2.86232 + 4.95768i) q^{87} +2.37933 q^{88} +(0.869603 + 0.502066i) q^{89} +(-0.696189 - 2.12493i) q^{90} +(2.40600 + 1.38910i) q^{91} +(-0.547828 - 0.948867i) q^{92} +(1.55283 + 2.68958i) q^{93} +(5.45183 + 3.14762i) q^{94} +(17.4281 - 5.70996i) q^{95} +(-0.866025 - 0.500000i) q^{96} +5.95504 q^{97} +(-2.73360 - 4.73473i) q^{98} +(1.18966 - 2.06056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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