LMFDB - Embedded newform 1110.2.ba.b.619.4

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			619.4
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.b.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.696189 + 2.12493i) q^{5} +1.00000i q^{6} +(1.07219 - 0.619032i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.696189 + 2.12493i) 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} +(-0.459547 - 2.18834i) 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} +(2.18834 - 0.459547i) q^{20} +(-0.619032 + 1.07219i) q^{21} +(1.18966 - 2.06056i) q^{22} -1.09566 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.03064 - 2.95870i) q^{25} +2.24399 q^{26} +1.00000i q^{27} +(-1.07219 - 0.619032i) q^{28} +5.72463i q^{29} +(-2.12493 - 0.696189i) q^{30} +3.10566i q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.06056 + 1.18966i) q^{33} +(-0.499820 - 0.865713i) q^{34} +(0.568948 + 2.70930i) q^{35} -1.00000 q^{36} +(5.14008 - 3.25263i) q^{37} +8.20173i q^{38} +(-1.94336 - 1.12200i) q^{39} +(0.696189 - 2.12493i) 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} +(-4.57763 + 2.01129i) q^{50} +0.999639i q^{51} +(1.12200 - 1.94336i) q^{52} +(10.0941 + 5.82782i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.65646 + 5.05590i) 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} +(-4.91061 + 1.03122i) q^{65} +2.37933i q^{66} +(1.63569 - 0.944369i) q^{67} -0.999639 q^{68} +(0.948867 - 0.547828i) q^{69} +(2.63080 + 0.861926i) 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} +(2.18834 - 0.459547i) 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} +(-3.76908 - 17.9481i) 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} + 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
$5$	−0.696189	+	2.12493i	−0.311345	+	0.950297i
$5$	−0.696189	+	2.12493i	−0.311345	+	0.950297i
$6$			1.00000i			0.408248i
$7$	1.07219	−	0.619032i	0.405251	−	0.233972i	−0.283496	−	0.958973i	$-0.591494\pi$
$7$	1.07219	−	0.619032i	0.405251	−	0.233972i	0.688747	+	0.725001i	$0.258161\pi$
$8$	−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	0.978619	−	0.205680i	$-0.0659404\pi$
$13$	1.12200	+	1.94336i	0.311186	+	0.538990i	−0.667433	+	0.744670i	$0.732607\pi$
$14$		−	1.23806i		−	0.330886i
$15$	−0.459547	−	2.18834i	−0.118654	−	0.565026i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.499820	−	0.865713i	0.121224	−	0.209966i	−0.799027	−	0.601296i	$-0.794651\pi$
$17$	0.499820	−	0.865713i	0.121224	−	0.209966i	0.920251	+	0.391329i	$0.127985\pi$
$18$	−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	$0.943406\pi$
$20$	2.18834	−	0.459547i	0.489327	−	0.102758i
$21$	−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	$-0.536440\pi$
$23$	−1.09566			−0.228460			−0.114230	+	0.993454i	$0.536440\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.03064	−	2.95870i	−0.806128	−	0.591741i
$26$	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	$0.821622\pi$
$30$	−2.12493	−	0.696189i	−0.387957	−	0.127106i
$31$			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
$35$	0.568948	+	2.70930i	0.0961698	+	0.457955i
$36$	−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
$40$	0.696189	−	2.12493i	0.110077	−	0.335981i
$41$	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	$-0.341407\pi$
$43$	6.26728			0.955751			0.477876	+	0.878427i	$0.341407\pi$
$44$	−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	$0.151838\pi$
$47$			6.29523i			0.918254i	−0.888371	+	0.459127i	$0.848162\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−2.73360	+	4.73473i	−0.390514	+	0.676390i
$50$	−4.57763	+	2.01129i	−0.647375	+	0.284439i
$51$			0.999639i			0.139977i
$52$	1.12200	−	1.94336i	0.155593	−	0.269495i
$53$	10.0941	+	5.82782i	1.38653	+	0.800512i	0.992922	−	0.118767i	$-0.0378942\pi$
$53$	10.0941	+	5.82782i	1.38653	+	0.800512i	0.393606	+	0.919279i	$0.371228\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−1.65646	+	5.05590i	−0.223357	+	0.681737i
$56$	−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
$65$	−4.91061	+	1.03122i	−0.609087	+	0.127907i
$66$			2.37933i			0.292875i
$67$	1.63569	−	0.944369i	0.199832	−	0.115373i	−0.396745	−	0.917929i	$-0.629860\pi$
$67$	1.63569	−	0.944369i	0.199832	−	0.115373i	0.596577	+	0.802556i	$0.296527\pi$
$68$	−0.999639			−0.121224
$69$	0.948867	−	0.547828i	0.114230	−	0.0659508i
$70$	2.63080	+	0.861926i	0.314440	+	0.103020i
$71$	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	$-0.997691\pi$
$73$		−	0.123967i		−	0.0145092i	0.999974	−	0.00725459i	$-0.00230923\pi$
$74$	−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	0.108067	−	0.994144i	$-0.465534\pi$
$83$	−6.36686	−	3.67591i	−0.698854	−	0.403483i	−0.806920	+	0.590660i	$0.798867\pi$
$84$	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	$0.649719\pi$
$90$	2.18834	−	0.459547i	0.230671	−	0.0484405i
$91$	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
$95$	−3.76908	−	17.9481i	−0.386699	−	1.84144i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−5.95504			−0.604643			−0.302321	−	0.953206i	$-0.597762\pi$
$97$	−5.95504			−0.604643			−0.302321	+	0.953206i	$0.597762\pi$
$98$	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	$-0.640983\pi$
$103$	−8.69905			−0.857143			−0.428572	+	0.903508i	$0.640983\pi$
$104$	−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	−0.107371	−	0.994219i	$-0.534243\pi$
$107$	7.24046	−	4.18028i	0.699962	−	0.404123i	0.807333	+	0.590096i	$0.200910\pi$
$108$	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	$-0.652266\pi$
$113$	5.72597	−	9.91767i	0.538654	−	0.932976i	0.998977	−	0.0452242i	$-0.0144002\pi$
$114$	−4.10087	−	7.10291i	−0.384081	−	0.665248i
$115$	0.762784	−	2.32819i	0.0711300	−	0.217105i
$116$	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
$120$	0.459547	+	2.18834i	0.0419507	+	0.199767i
$121$	−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	0.642862	−	0.765982i	$-0.277747\pi$
$127$	3.39135	+	1.95799i	0.300933	+	0.173744i	−0.341929	+	0.939726i	$0.611080\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.42762	+	3.13364i	−0.477876	+	0.275902i
$130$	−1.56224	+	4.76833i	−0.137018	+	0.418210i
$131$	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
$135$	−2.12493	−	0.696189i	−0.182885	−	0.0599184i
$136$	−0.499820	+	0.865713i	−0.0428592	+	0.0742343i
$137$			8.45319i			0.722204i	0.932526	+	0.361102i	$0.117599\pi$
$137$			8.45319i			0.722204i	−0.932526	+	0.361102i	$0.882401\pi$
$138$		−	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
$145$	−12.1644	−	3.98543i	−1.01020	−	0.330972i
$146$	−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	$0.115205\pi$
$150$	2.95870	−	4.03064i	0.241577	−	0.329100i
$151$	−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
$155$	−6.59931	−	2.16213i	−0.530069	−	0.173666i
$156$			2.24399i			0.179663i
$157$	12.5430	+	7.24170i	1.00104	+	0.577951i	0.908556	−	0.417763i	$-0.137186\pi$
$157$	12.5430	+	7.24170i	1.00104	+	0.577951i	0.0924842	+	0.995714i	$0.470519\pi$
$158$			15.3307i			1.21965i
$159$	−11.6556			−0.924352
$160$	−2.18834	+	0.459547i	−0.173003	+	0.0363304i
$161$	−1.17476	+	0.678246i	−0.0925838	+	0.0534533i
$162$	−1.00000			−0.0785674
$163$	6.02844	−	10.4416i	0.472184	−	0.817847i	−0.527309	−	0.849673i	$-0.676799\pi$
$163$	6.02844	−	10.4416i	0.472184	−	0.817847i	0.999493	+	0.0318265i	$0.0101324\pi$
$164$	4.36280	−	7.55659i	0.340677	−	0.590071i
$165$	−1.09341	−	5.20677i	−0.0851220	−	0.405346i
$166$	−6.36686	+	3.67591i	−0.494164	+	0.285306i
$167$	−3.98320	−	6.89910i	−0.308229	−	0.533869i	0.669746	−	0.742590i	$-0.266403\pi$
$167$	−3.98320	−	6.89910i	−0.308229	−	0.533869i	−0.977975	+	0.208722i	$0.933070\pi$
$168$	0.619032	−	1.07219i	0.0477593	−	0.0827216i
$169$	3.98224	−	6.89745i	0.306327	−	0.530573i
$170$	2.18755	−	0.459381i	0.167777	−	0.0352329i
$171$			8.20173i			0.627202i
$172$	−3.13364	−	5.42762i	−0.238938	−	0.413852i
$173$	−19.4302	−	11.2180i	−1.47725	−	0.852890i	−0.477579	−	0.878589i	$-0.658486\pi$
$173$	−19.4302	−	11.2180i	−1.47725	−	0.852890i	−0.999670	+	0.0256988i	$0.991819\pi$
$174$	−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	$-0.286596\pi$
$180$	0.696189	−	2.12493i	0.0518909	−	0.158383i
$181$	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
$185$	3.33313	+	13.1867i	0.245057	+	0.969509i
$186$	−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
$190$	−17.4281	−	5.70996i	−1.26437	−	0.414244i
$191$		−	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	$-0.837944\pi$
$193$	−24.2611			−1.74635			−0.873176	+	0.487405i	$0.837944\pi$
$194$	−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	0.923632	−	0.383280i	$-0.125206\pi$
$197$	14.7868	+	8.53718i	1.05352	+	0.608249i	0.129886	+	0.991529i	$0.458539\pi$
$198$	−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	$0.958141\pi$
$200$	4.03064	+	2.95870i	0.285009	+	0.209212i
$201$	−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
$205$	−19.0945	+	4.00982i	−1.33362	+	0.280058i
$206$	−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
$210$	−2.70930	+	0.568948i	−0.186959	+	0.0392611i
$211$	−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
$215$	−4.36321	+	13.3175i	−0.297569	+	0.908247i
$216$		−	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
$220$	5.20677	−	1.09341i	0.351040	−	0.0737178i
$221$	2.24318			0.150893
$222$	3.25263	+	5.14008i	0.218302	+	0.344980i
$223$			2.60823i			0.174660i	0.996179	+	0.0873300i	$0.0278335\pi$
$223$			2.60823i			0.174660i	−0.996179	+	0.0873300i	$0.972167\pi$
$224$	1.07219	+	0.619032i	0.0716390	+	0.0413608i
$225$	−4.57763	+	2.01129i	−0.305176	+	0.134086i
$226$	−5.72597	−	9.91767i	−0.380886	−	0.659713i
$227$	−3.45993	−	5.99277i	−0.229643	−	0.397754i	0.728059	−	0.685514i	$-0.240423\pi$
$227$	−3.45993	−	5.99277i	−0.229643	−	0.397754i	−0.957702	+	0.287760i	$0.907089\pi$
$228$	−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	$0.247292\pi$
$233$			21.4026i			1.40213i	−0.713097	+	0.701065i	$0.752708\pi$
$234$	1.12200	−	1.94336i	0.0733472	−	0.127041i
$235$	−13.3769	−	4.38267i	−0.872614	−	0.285894i
$236$		−	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	$0.852727\pi$
$240$	2.12493	+	0.696189i	0.137164	+	0.0449388i
$241$	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
$250$	−1.08694	−	11.1274i	−0.0687441	−	0.703757i
$251$			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
$255$	−2.12416	−	0.695938i	−0.133020	−	0.0435813i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.119612	+	0.207174i	−0.00746119	+	0.0129232i	−0.869732	−	0.493524i	$-0.835708\pi$
$257$	−0.119612	+	0.207174i	−0.00746119	+	0.0129232i	0.862271	+	0.506448i	$0.169042\pi$
$258$			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	0.496095	−	0.868269i	$-0.334767\pi$
$263$	24.2624	−	14.0079i	1.49608	−	0.863765i	0.999990	+	0.00450381i	$0.00143361\pi$
$264$	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
$275$	−9.59022	−	7.03973i	−0.578312	−	0.424511i
$276$	−0.948867	−	0.547828i	−0.0571151	−	0.0329754i
$277$	11.9667	+	20.7270i	0.719012	+	1.24537i	0.961392	+	0.275184i	$0.0887387\pi$
$277$	11.9667	+	20.7270i	0.719012	+	1.24537i	−0.242380	+	0.970181i	$0.577928\pi$
$278$	0.500249	+	0.866457i	0.0300030	+	0.0519667i
$279$	2.68958	+	1.55283i	0.161021	+	0.0929655i
$280$	−0.568948	−	2.70930i	−0.0340012	−	0.161912i
$281$	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	$-0.816571\pi$
$283$	−14.9913	−	25.9658i	−0.891143	−	1.54351i	−0.0526364	−	0.998614i	$-0.516762\pi$
$284$	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	−0.128813	−	0.991669i	$-0.541117\pi$
$293$	11.3931	−	6.57779i	0.665590	−	0.384279i	0.794404	+	0.607390i	$0.207783\pi$
$294$	−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
$300$	−2.01129	−	4.57763i	−0.116122	−	0.264290i
$301$	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
$305$	−2.39967	−	11.4271i	−0.137405	−	0.654315i
$306$	−0.999639			−0.0571456
$307$		−	11.1634i		−	0.637128i	−0.947901	−	0.318564i	$-0.896799\pi$
$307$		−	11.1634i		−	0.637128i	0.947901	−	0.318564i	$-0.103201\pi$
$308$	−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	−0.836259	−	0.548334i	$-0.815262\pi$
$313$	1.00387	−	1.73875i	0.0567420	−	0.0982800i	0.893001	+	0.450054i	$0.148595\pi$
$314$	12.5430	−	7.24170i	0.707842	−	0.408673i
$315$	2.63080	+	0.861926i	0.148229	+	0.0485641i
$316$	13.2768	+	7.66536i	0.746878	+	0.431210i
$317$	−0.127184	−	0.0734298i	−0.00714337	−	0.00412423i	0.496424	−	0.868080i	$-0.334646\pi$
$317$	−0.127184	−	0.0734298i	−0.00714337	−	0.00412423i	−0.503567	+	0.863956i	$0.667979\pi$
$318$	−5.82782	+	10.0941i	−0.326808	+	0.566048i
$319$			13.6208i			0.762617i
$320$	−0.696189	+	2.12493i	−0.0389182	+	0.118787i
$321$	−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
$330$	−5.05590	−	1.65646i	−0.278318	−	0.0911852i
$331$	−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
$335$	0.867963	+	4.13319i	0.0474219	+	0.225821i
$336$	−0.619032	−	1.07219i	−0.0337710	−	0.0584930i
$337$	9.95412	−	5.74702i	0.542236	−	0.313060i	−0.203749	−	0.979023i	$-0.565313\pi$
$337$	9.95412	−	5.74702i	0.542236	−	0.313060i	0.745985	+	0.665963i	$0.231979\pi$
$338$	−3.98224	−	6.89745i	−0.216606	−	0.375172i
$339$			11.4519i			0.621984i
$340$	0.695938	−	2.12416i	0.0377425	−	0.115199i
$341$			7.38938i			0.400158i
$342$	7.10291	+	4.10087i	0.384081	+	0.221749i
$343$			15.4352i			0.833422i
$344$	−6.26728			−0.337909
$345$	0.503506	+	2.39767i	0.0271078	+	0.129086i
$346$	−19.4302	+	11.2180i	−1.04457	+	0.603084i
$347$	3.73796			0.200664			0.100332	−	0.994954i	$-0.468009\pi$
$347$	3.73796			0.200664			0.100332	+	0.994954i	$0.468009\pi$
$348$	−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	$0.905787\pi$
$350$	−3.66306	+	4.99019i	−0.195799	+	0.266737i
$351$	−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	$0.561530\pi$
$353$	−17.7727	+	30.7832i	−0.945946	+	1.63843i	−0.753846	+	0.657052i	$0.771803\pi$
$354$	−0.617394	+	1.06936i	−0.0328141	+	0.0568357i
$355$	−10.7691	+	2.26150i	−0.571566	+	0.120028i
$356$		−	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
$365$	0.263420	+	0.0863041i	0.0137880	+	0.00451737i
$366$	−2.61091	−	4.52224i	−0.136475	−	0.236381i
$367$	15.4393	−	8.91388i	0.805925	−	0.465301i	−0.0396140	−	0.999215i	$-0.512613\pi$
$367$	15.4393	−	8.91388i	0.805925	−	0.465301i	0.845539	+	0.533914i	$0.179280\pi$
$368$	0.547828	−	0.948867i	0.0285575	−	0.0494631i
$369$	8.72560			0.454237
$370$	13.0866	+	3.70680i	0.680341	+	0.192707i
$371$	14.4304			0.749190
$372$	−1.55283	+	2.68958i	−0.0805105	+	0.139448i
$373$	−4.77639	+	2.75765i	−0.247312	+	0.142786i	−0.618533	−	0.785759i	$-0.712273\pi$
$373$	−4.77639	+	2.75765i	−0.247312	+	0.142786i	0.371221	+	0.928545i	$0.378939\pi$
$374$	−1.18923	−	2.05981i	−0.0614938	−	0.106510i
$375$	−4.62237	+	10.1801i	−0.238698	+	0.525696i
$376$		−	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	0.830674	−	0.556759i	$-0.187955\pi$
$383$	−1.30790	−	2.26536i	−0.0668308	−	0.115754i	−0.897505	+	0.441005i	$0.854622\pi$
$384$			1.00000i			0.0510310i
$385$	1.35371	+	6.44631i	0.0689916	+	0.328534i
$386$	−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	$0.392011\pi$
$390$	−1.03122	−	4.91061i	−0.0522179	−	0.248659i
$391$	−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
$395$	−7.04518	−	33.5488i	−0.354482	−	1.68802i
$396$	−2.37933			−0.119566
$397$		−	3.16094i		−	0.158643i	−0.996849	−	0.0793216i	$-0.974725\pi$
$397$		−	3.16094i		−	0.158643i	0.996849	−	0.0793216i	$-0.0252754\pi$
$398$	3.20383	+	1.84973i	0.160594	+	0.0927188i
$399$		−	10.1543i		−	0.508349i
$400$	4.57763	−	2.01129i	0.228882	−	0.100564i
$401$			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
$405$	2.18834	−	0.459547i	0.108739	−	0.0228351i
$406$	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	$0.662020\pi$
$410$	−6.07467	+	18.5413i	−0.300006	+	0.915688i
$411$	−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	$0.260402\pi$
$420$	−0.861926	+	2.63080i	−0.0420577	+	0.128370i
$421$		−	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
$425$	−4.57598	+	2.01056i	−0.221968	+	0.0975265i
$426$	−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	$-0.898849\pi$
$433$		−	13.0035i		−	0.624910i	0.949933	−	0.312455i	$-0.101151\pi$
$434$	3.84501			0.184566
$435$	12.5274	−	2.63074i	0.600644	−	0.126134i
$436$			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	$0.400355\pi$
$440$	1.65646	−	5.05590i	0.0789687	−	0.241031i
$441$	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	$-0.958677\pi$
$443$		−	5.44946i		−	0.258912i	0.991585	−	0.129456i	$-0.0413230\pi$
$444$	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	0.705336	−	0.708873i	$-0.250796\pi$
$457$	−5.58456	−	9.67274i	−0.261235	−	0.452472i	−0.966570	+	0.256402i	$0.917463\pi$
$458$	8.21942			0.384068
$459$	0.865713	+	0.499820i	0.0404080	+	0.0233296i
$460$	−2.39767	+	0.503506i	−0.111792	+	0.0234761i
$461$	−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	0.902848	−	0.429960i	$-0.141472\pi$
$463$	1.70132	+	2.94678i	0.0790672	+	0.136948i	−0.823781	+	0.566909i	$0.808139\pi$
$464$	−4.95768	−	2.86232i	−0.230154	−	0.132880i
$465$	6.79623	−	1.42720i	0.315168	−	0.0661847i
$466$	18.5352	+	10.7013i	0.858626	+	0.495728i
$467$	9.08042			0.420192			0.210096	−	0.977681i	$-0.432622\pi$
$467$	9.08042			0.420192			0.210096	+	0.977681i	$0.432622\pi$
$468$	−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
$485$	4.14583	−	12.6540i	0.188253	−	0.574590i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	8.57654			0.388640			0.194320	−	0.980938i	$-0.437750\pi$
$487$	8.57654			0.388640			0.194320	+	0.980938i	$0.437750\pi$
$488$	4.52224	−	2.61091i	0.204712	−	0.118191i
$489$			12.0569i			0.545231i
$490$	−11.9641	+	2.51243i	−0.540482	+	0.113500i
$491$	−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	$0.448349\pi$
$500$	−10.1801	−	4.62237i	−0.455266	−	0.206719i
$501$	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	$-0.624579\pi$
$503$	13.6766	−	23.6886i	0.609809	−	1.05622i	0.991272	−	0.131836i	$-0.0420872\pi$
$504$			1.23806i			0.0551477i
$505$	−2.98258	+	9.10350i	−0.132723	+	0.405101i
$506$	−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
$515$	6.05619	−	18.4849i	0.266867	−	0.814540i
$516$	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
$520$	4.91061	−	1.03122i	0.215345	−	0.0452220i
$521$	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	0.986469	−	0.163951i	$-0.0524238\pi$
$523$	8.03277	+	13.9132i	0.351249	+	0.608381i	−0.635220	+	0.772331i	$0.719090\pi$
$524$		−	3.16404i		−	0.138222i
$525$	5.66740	−	2.49010i	0.247346	−	0.108677i
$526$		−	28.0158i		−	1.22155i
$527$	2.68861	+	1.55227i	0.117118	+	0.0676180i
$528$		−	2.37933i		−	0.103547i
$529$	−21.7995			−0.947806
$530$	5.35631	+	25.5064i	0.232663	+	1.10793i
$531$	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
$535$	3.84207	+	18.2957i	0.166107	+	0.790993i
$536$	−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
$540$	0.459547	+	2.18834i	0.0197757	+	0.0941710i
$541$		−	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	$-0.329688\pi$
$547$	23.8504			1.01977			0.509884	+	0.860243i	$0.329688\pi$
$548$	7.32067	−	4.22659i	0.312724	−	0.180551i
$549$			5.22183i			0.222862i
$550$	−10.8917	+	4.78551i	−0.464423	+	0.204055i
$551$	−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
$555$	−9.47995	−	9.75349i	−0.402401	−	0.414013i
$556$	1.00050			0.0424306
$557$	10.5226	−	18.2256i	0.445856	−	0.772245i	−0.552256	−	0.833675i	$-0.686233\pi$
$557$	10.5226	−	18.2256i	0.445856	−	0.772245i	0.998111	+	0.0614299i	$0.0195661\pi$
$558$	2.68958	−	1.55283i	0.113859	−	0.0657366i
$559$	7.03187	+	12.1796i	0.297416	+	0.515140i
$560$	−2.63080	−	0.861926i	−0.111171	−	0.0364230i
$561$			2.37847i			0.100419i
$562$	12.8178	−	7.40036i	0.540687	−	0.312166i
$563$	25.0957			1.05766			0.528828	−	0.848729i	$-0.322632\pi$
$563$	25.0957			1.05766			0.528828	+	0.848729i	$0.322632\pi$
$564$	−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	$0.884698\pi$
$570$	17.9481	−	3.76908i	0.751765	−	0.157869i
$571$	−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
$575$	4.41620	+	3.24172i	0.184168	+	0.135189i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−8.05589	+	13.9532i	−0.335371	+	0.580880i	−0.983556	−	0.180603i	$-0.942195\pi$
$577$	−8.05589	+	13.9532i	−0.335371	+	0.580880i	0.648185	+	0.761483i	$0.275528\pi$
$578$	16.0007			0.665542
$579$	21.0107	−	12.1306i	0.873176	−	0.504128i
$580$	2.63074	+	12.5274i	0.109235	+	0.520173i
$581$	−9.10202			−0.377615
$582$		−	5.95504i		−	0.246844i
$583$	24.0171	+	13.8663i	0.994687	+	0.574283i
$584$			0.123967i			0.00512977i
$585$	−1.56224	+	4.76833i	−0.0645909	+	0.197146i
$586$		−	13.1556i		−	0.543452i
$587$	−4.15035	−	7.18861i	−0.171303	−	0.296706i	0.767573	−	0.640962i	$-0.221464\pi$
$587$	−4.15035	−	7.18861i	−0.171303	−	0.296706i	−0.938876	+	0.344256i	$0.888131\pi$
$588$	−4.73473	+	2.73360i	−0.195257	+	0.112732i
$589$	−12.7359	−	22.0592i	−0.524774	−	0.908935i
$590$	0.567442	+	2.70213i	0.0233612	+	0.111245i
$591$	−17.0744			−0.702345
$592$	0.246818	+	6.07775i	0.0101442	+	0.249794i
$593$		−	19.9341i		−	0.818597i	−0.912401	−	0.409298i	$-0.865774\pi$
$593$		−	19.9341i		−	0.818597i	0.912401	−	0.409298i	$-0.134226\pi$
$594$	2.06056	+	1.18966i	0.0845457	+	0.0488125i
$595$	2.62985	+	0.861615i	0.107813	+	0.0353228i
$596$	−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
$605$	3.71682	−	11.3446i	0.151110	−	0.461222i
$606$			4.28415i			0.174032i
$607$	15.3148	−	26.5261i	0.621610	−	1.07666i	−0.367575	−	0.929994i	$-0.619812\pi$
$607$	15.3148	−	26.5261i	0.621610	−	1.07666i	0.989186	−	0.146667i	$-0.0468546\pi$
$608$	−7.10291	−	4.10087i	−0.288061	−	0.166312i
$609$	−6.13792	−	3.54373i	−0.248721	−	0.143599i
$610$	−11.0960	−	3.63538i	−0.449264	−	0.147192i
$611$	−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	0.753195	−	0.657797i	$-0.228512\pi$
$613$	13.8680	+	8.00669i	0.560123	+	0.323387i	−0.193072	+	0.981185i	$0.561845\pi$
$614$	−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	0.434414	−	0.900714i	$-0.356956\pi$
$617$	−3.18990	−	1.84169i	−0.128420	−	0.0741436i	−0.562834	+	0.826570i	$0.690289\pi$
$618$		−	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	$0.368949\pi$
$620$	1.42720	+	6.79623i	0.0573176	+	0.272943i
$621$		−	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
$625$	7.49214	+	23.8510i	0.299686	+	0.954038i
$626$	−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	$-0.325953\pi$
$643$	26.3688			1.03989			0.519943	+	0.854201i	$0.325953\pi$
$644$	1.17476	+	0.678246i	0.0462919	+	0.0267267i
$645$	−2.88011	−	13.7149i	−0.113404	−	0.540024i
$646$	7.10034	+	4.09939i	0.279359	+	0.161288i
$647$	7.15731	+	12.3968i	0.281383	+	0.487370i	0.971726	−	0.236113i	$-0.0758736\pi$
$647$	7.15731	+	12.3968i	0.281383	+	0.487370i	−0.690343	+	0.723483i	$0.742540\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	2.54435	+	1.46898i	0.0998745	+	0.0576626i
$650$	−9.04474	−	6.63931i	−0.354764	−	0.260415i
$651$	−3.32987	−	1.92250i	−0.130508	−	0.0753488i
$652$	−12.0569			−0.472184
$653$	5.19792	+	9.00305i	0.203410	+	0.352317i	0.949625	−	0.313388i	$-0.101464\pi$
$653$	5.19792	+	9.00305i	0.203410	+	0.352317i	−0.746215	+	0.665705i	$0.768131\pi$
$654$	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
$670$	4.01343	+	1.31492i	0.155052	+	0.0507997i
$671$	−10.7599	+	6.21222i	−0.415381	+	0.239820i
$672$	−1.23806			−0.0477593
$673$	−6.80338	+	3.92793i	−0.262251	+	0.151411i	−0.625361	−	0.780336i	$-0.715048\pi$
$673$	−6.80338	+	3.92793i	−0.262251	+	0.151411i	0.363110	+	0.931746i	$0.381715\pi$
$674$		−	11.4940i		−	0.442734i
$675$	2.95870	−	4.03064i	0.113881	−	0.155139i
$676$	−7.96449			−0.306327
$677$			36.4834i			1.40217i	0.713078	+	0.701085i	$0.247300\pi$
$677$			36.4834i			1.40217i	−0.713078	+	0.701085i	$0.752700\pi$
$678$	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	−0.640786	−	0.767720i	$-0.721391\pi$
$683$	9.00252	−	15.5928i	0.344472	−	0.596643i	0.985258	+	0.171077i	$0.0547247\pi$
$684$	7.10291	−	4.10087i	0.271586	−	0.156801i
$685$	−17.9624	−	5.88502i	−0.686309	−	0.224855i
$686$	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
$690$	2.32819	+	0.762784i	0.0886328	+	0.0290387i
$691$	−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
$700$	2.49010	+	5.66740i	0.0941169	+	0.214208i
$701$	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
$705$	13.7761	−	2.89295i	0.518837	−	0.108955i
$706$	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	$-0.0705011\pi$
$710$	−3.42605	+	10.4571i	−0.128577	+	0.392447i
$711$			15.3307i			0.574947i
$712$	−0.869603	−	0.502066i	−0.0325898	−	0.0188157i
$713$		−	3.40274i		−	0.127434i
$714$	1.23762			0.0463166
$715$	−11.6840	+	2.45361i	−0.436955	+	0.0917598i
$716$	−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	$0.320094\pi$
$720$	−2.18834	+	0.459547i	−0.0815545	+	0.0171263i
$721$	−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
$725$	16.9375	−	23.0739i	0.629043	−	0.856944i
$726$		−	5.33880i		−	0.198142i
$727$	−13.0391	−	22.5845i	−0.483595	−	0.837611i	0.516227	−	0.856452i	$-0.327336\pi$
$727$	−13.0391	−	22.5845i	−0.483595	−	0.837611i	−0.999823	+	0.0188403i	$0.994003\pi$
$728$	−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	−0.999988	−	0.00498092i	$-0.998415\pi$
$733$	−40.4937	+	23.3790i	−1.49567	+	0.863524i	−0.495680	+	0.868505i	$0.665081\pi$
$734$		−	17.8278i		−	0.658035i
$735$	11.6174	+	3.80620i	0.428514	+	0.140394i
$736$	−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	$0.352248\pi$
$740$	9.75349	−	9.47995i	0.358545	−	0.348490i
$741$	18.4046			0.676111
$742$	7.21521	−	12.4971i	0.264879	−	0.458783i
$743$	−24.0446	+	13.8822i	−0.882111	+	0.509287i	−0.871354	−	0.490655i	$-0.836758\pi$
$743$	−24.0446	+	13.8822i	−0.882111	+	0.509287i	−0.0107573	+	0.999942i	$0.503424\pi$
$744$	1.55283	+	2.68958i	0.0569295	+	0.0986048i
$745$	−15.8951	+	48.5154i	−0.582350	+	1.77747i
$746$			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
$755$	26.1741	−	5.49652i	0.952574	−	0.200039i
$756$	0.619032	−	1.07219i	0.0225140	−	0.0389953i
$757$	−8.28057	+	14.3424i	−0.300962	+	0.521282i	−0.976354	−	0.216177i	$-0.930641\pi$
$757$	−8.28057	+	14.3424i	−0.300962	+	0.521282i	0.675392	+	0.737459i	$0.263975\pi$
$758$	0.979562	+	1.69665i	0.0355793	+	0.0616251i
$759$	2.25766	−	1.30346i	0.0819480	−	0.0473127i
$760$	3.76908	+	17.9481i	0.136719	+	0.651048i
$761$	−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
$765$	2.18755	−	0.459381i	0.0790909	−	0.0166090i
$766$	−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	$0.949922\pi$
$770$	6.25953	+	2.05081i	0.225578	+	0.0739059i
$771$		−	0.239224i		−	0.00861545i
$772$	12.1306	+	21.0107i	0.436588	+	0.756193i
$773$	22.1990	−	12.8166i	0.798444	−	0.460982i	−0.0444828	−	0.999010i	$-0.514164\pi$
$773$	22.1990	−	12.8166i	0.798444	−	0.460982i	0.842927	+	0.538028i	$0.180831\pi$
$774$	−3.13364	−	5.42762i	−0.112636	−	0.195092i
$775$	9.18873	−	12.5178i	0.330069	−	0.449653i
$776$	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
$780$	−4.76833	−	1.56224i	−0.170734	−	0.0559373i
$781$	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	$0.359297\pi$
$787$			50.7143i			1.80777i	−0.427776	+	0.903885i	$0.640703\pi$
$788$		−	17.0744i		−	0.608249i
$789$	−14.0079	+	24.2624i	−0.498695	+	0.863765i
$790$	−32.5767	−	10.6731i	−1.15903	−	0.379731i
$791$		−	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
$795$	8.11452	−	24.7674i	0.287793	−	0.878409i
$796$	3.20383	−	1.84973i	0.113557	−	0.0655621i
$797$	−4.46101	+	7.72669i	−0.158017	+	0.273694i	−0.934154	−	0.356871i	$-0.883843\pi$
$797$	−4.46101	+	7.72669i	−0.158017	+	0.273694i	0.776136	+	0.630565i	$0.217177\pi$
$798$	−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
$805$	−0.623372	−	2.96846i	−0.0219710	−	0.104625i
$806$			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	$0.110396\pi$
$810$	0.696189	−	2.12493i	0.0244616	−	0.0746624i
$811$	−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	0.610992	−	0.791637i	$-0.290771\pi$
$823$	6.62435	+	3.82457i	0.230910	+	0.133316i	−0.380082	+	0.924953i	$0.624104\pi$
$824$	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	$-0.932635\pi$
$827$	−19.2894	−	33.4102i	−0.670758	−	1.16179i	0.306931	−	0.951732i	$-0.400698\pi$
$828$	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	$0.505774\pi$
$830$	−3.37850	−	16.0883i	−0.117270	−	0.558431i
$831$	−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
$835$	17.4332	−	3.66093i	0.603299	−	0.126692i
$836$	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	$-0.584846\pi$
$853$	20.5535	−	35.5997i	0.703739	−	1.21891i	0.967145	−	0.254227i	$-0.0818209\pi$
$854$	3.23248	+	5.59882i	0.110613	+	0.191588i
$855$	−17.4281	−	5.70996i	−0.596028	−	0.195276i
$856$	−7.24046	+	4.18028i	−0.247474	+	0.142879i
$857$	−27.5518			−0.941151			−0.470576	−	0.882360i	$-0.655954\pi$
$857$	−27.5518			−0.941151			−0.470576	+	0.882360i	$0.655954\pi$
$858$	−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	$0.822702\pi$
$860$	13.7149	−	2.88011i	0.467675	−	0.0982109i
$861$	−10.8028			−0.368160
$862$			13.0144i			0.443274i
$863$	−40.3535	−	23.2981i	−1.37365	−	0.793076i	−0.382263	−	0.924054i	$-0.624855\pi$
$863$	−40.3535	−	23.2981i	−1.37365	−	0.793076i	−0.991385	+	0.130978i	$0.958188\pi$
$864$	−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
$870$	3.98543	−	12.1644i	0.135119	−	0.412413i
$871$	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
$875$	5.72279	−	12.6036i	0.193466	−	0.426078i
$876$	0.0619833	−	0.107358i	0.00209422	−	0.00362730i
$877$		−	20.5259i		−	0.693110i	−0.938030	−	0.346555i	$-0.887351\pi$
$877$		−	20.5259i		−	0.693110i	0.938030	−	0.346555i	$-0.112649\pi$
$878$			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	0.999890	−	0.0148097i	$-0.00471425\pi$
$883$	14.4749	+	25.0713i	0.487120	+	0.843716i	−0.512771	+	0.858526i	$0.671381\pi$
$884$	−1.12159	−	1.94265i	−0.0377232	−	0.0653385i
$885$	0.859645	−	2.62383i	0.0288967	−	0.0881992i
$886$	−4.71937	−	2.72473i	−0.158550	−	0.0915391i
$887$			39.7064i			1.33321i	0.745410	+	0.666606i	$0.232254\pi$
$887$			39.7064i			1.33321i	−0.745410	+	0.666606i	$0.767746\pi$
$888$	2.82513	−	5.38690i	0.0948050	−	0.180772i
$889$	4.84824			0.162605
$890$	0.461445	+	2.19738i	0.0154677	+	0.0736563i
$891$	−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
$895$	44.5524	+	14.5967i	1.48922	+	0.487913i
$896$		−	1.23806i		−	0.0413608i
$897$	2.12925	+	1.22932i	0.0710936	+	0.0410459i
$898$			10.3690i			0.346018i
$899$	−17.7788			−0.592955
$900$	4.03064	+	2.95870i	0.134355	+	0.0986235i
$901$	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
$905$	−12.7334	+	2.67399i	−0.423272	+	0.0888863i
$906$	10.3583	−	5.98037i	0.344132	−	0.198685i
$907$	−1.92263	−	3.33010i	−0.0638400	−	0.110574i	0.832339	−	0.554267i	$-0.187001\pi$
$907$	−1.92263	−	3.33010i	−0.0638400	−	0.110574i	−0.896179	+	0.443693i	$0.853668\pi$
$908$	−3.45993	+	5.99277i	−0.114822	+	0.198877i
$909$	2.14207	−	3.71018i	0.0710481	−	0.123059i
$910$	1.27672	+	6.07965i	0.0423227	+	0.201539i
$911$			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	$0.944809\pi$
$920$	−0.762784	+	2.32819i	−0.0251483	+	0.0767582i
$921$	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
$925$	−30.3414	−	2.09780i	−0.997618	−	0.0689753i
$926$	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	$-0.389618\pi$
$930$	2.16213	−	6.59931i	0.0708990	−	0.216400i
$931$		−	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	0.0697761	−	0.997563i	$-0.477772\pi$
$937$	−23.2410	−	13.4182i	−0.759250	−	0.438353i	−0.829027	+	0.559209i	$0.811105\pi$
$938$	−1.16919	−	2.02509i	−0.0381754	−	0.0661217i
$939$			2.00774i			0.0655200i
$940$	2.89295	+	13.7761i	0.0943577	+	0.449326i
$941$	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
$945$	−2.70930	+	0.568948i	−0.0881335	+	0.0185079i
$946$	7.45596	−	12.9141i	0.242414	−	0.419873i
$947$	−21.9643	+	38.0433i	−0.713745	+	1.23624i	0.249697	+	0.968324i	$0.419669\pi$
$947$	−21.9643	+	38.0433i	−0.713745	+	1.23624i	−0.963442	+	0.267918i	$0.913664\pi$
$948$	−15.3307			−0.497919
$949$	0.240911	−	0.139090i	0.00782031	−	0.00451506i
$950$	24.2665	−	33.0582i	0.787309	−	1.07255i
$951$	0.146860			0.00476225
$952$			1.23762i			0.0401114i
$953$	−37.8822	−	21.8713i	−1.22712	−	0.708481i	−0.260697	−	0.965421i	$-0.583952\pi$
$953$	−37.8822	−	21.8713i	−1.22712	−	0.708481i	−0.966427	+	0.256940i	$0.917286\pi$
$954$		−	11.6556i		−	0.377365i
$955$	47.1462	+	15.4465i	1.52562	+	0.499836i
$956$			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
$960$	−0.459547	−	2.18834i	−0.0148318	−	0.0706283i
$961$	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
$965$	16.8903	−	51.5531i	0.543718	−	1.65955i
$966$	−0.678246	−	1.17476i	−0.0218222	−	0.0377972i
$967$	−11.8106	−	20.4566i	−0.379803	−	0.657839i	0.611230	−	0.791453i	$-0.290675\pi$
$967$	−11.8106	−	20.4566i	−0.379803	−	0.657839i	−0.991033	+	0.133614i	$0.957342\pi$
$968$	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
$975$	4.51331	+	10.2722i	0.144542	+	0.328973i
$976$		−	5.22183i		−	0.167147i
$977$	1.14181	−	1.97767i	0.0365297	−	0.0632713i	−0.847183	−	0.531302i	$-0.821703\pi$
$977$	1.14181	−	1.97767i	0.0365297	−	0.0632713i	0.883712	+	0.468031i	$0.155036\pi$
$978$	10.4416	+	6.02844i	0.333885	+	0.192768i
$979$	2.06907	+	1.19458i	0.0661278	+	0.0381789i
$980$	−3.80620	+	11.6174i	−0.121585	+	0.371104i
$981$	−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	−0.184259	−	0.982878i	$-0.558988\pi$
$983$	−35.3530	−	20.4111i	−1.12759	−	0.651012i	−0.943327	+	0.331866i	$0.892322\pi$
$984$	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
$990$	5.20677	−	1.09341i	0.165482	−	0.0347509i
$991$			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
$995$	−7.86110	−	2.57553i	−0.249214	−	0.0816497i
$996$	−3.67591	−	6.36686i	−0.116476	−	0.201742i
$997$	30.2780	−	52.4430i	0.958913	−	1.66089i	0.233763	−	0.972294i	$-0.424896\pi$
$997$	30.2780	−	52.4430i	0.958913	−	1.66089i	0.725149	−	0.688592i	$-0.241771\pi$
$998$			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.b.619.4	yes	36
5.4	even	2		1110.2.ba.a.619.15	yes	36
37.11	even	6		1110.2.ba.a.529.15	✓	36
185.159	even	6	inner	1110.2.ba.b.529.4	yes	36

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.696189 + 2.12493i) q^{5} +1.00000i q^{6} +(1.07219 - 0.619032i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.696189 + 2.12493i) 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} +(-0.459547 - 2.18834i) 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} +(2.18834 - 0.459547i) q^{20} +(-0.619032 + 1.07219i) q^{21} +(1.18966 - 2.06056i) q^{22} -1.09566 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.03064 - 2.95870i) q^{25} +2.24399 q^{26} +1.00000i q^{27} +(-1.07219 - 0.619032i) q^{28} +5.72463i q^{29} +(-2.12493 - 0.696189i) q^{30} +3.10566i q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.06056 + 1.18966i) q^{33} +(-0.499820 - 0.865713i) q^{34} +(0.568948 + 2.70930i) q^{35} -1.00000 q^{36} +(5.14008 - 3.25263i) q^{37} +8.20173i q^{38} +(-1.94336 - 1.12200i) q^{39} +(0.696189 - 2.12493i) 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} +(-4.57763 + 2.01129i) q^{50} +0.999639i q^{51} +(1.12200 - 1.94336i) q^{52} +(10.0941 + 5.82782i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.65646 + 5.05590i) 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} +(-4.91061 + 1.03122i) q^{65} +2.37933i q^{66} +(1.63569 - 0.944369i) q^{67} -0.999639 q^{68} +(0.948867 - 0.547828i) q^{69} +(2.63080 + 0.861926i) 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} +(2.18834 - 0.459547i) 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} +(-3.76908 - 17.9481i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 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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