LMFDB - Embedded newform 1110.2.ba.a.529.17

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			529.17
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.a.619.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.581519 - 2.15913i) q^{5} -1.00000i q^{6} +(1.29297 + 0.746494i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.581519 - 2.15913i) q^{5} -1.00000i q^{6} +(1.29297 + 0.746494i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.57910 + 1.58317i) q^{10} -4.99238 q^{11} +(-0.866025 + 0.500000i) q^{12} +(-3.55888 + 6.16416i) q^{13} -1.49299i q^{14} +(0.575954 - 2.16062i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.24427 - 3.88718i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.68637 + 1.55098i) q^{19} +(2.16062 + 0.575954i) q^{20} +(0.746494 + 1.29297i) q^{21} +(2.49619 + 4.32353i) q^{22} -7.83788 q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.32367 + 2.51115i) q^{25} +7.11776 q^{26} +1.00000i q^{27} +(-1.29297 + 0.746494i) q^{28} +8.24378i q^{29} +(-2.15913 + 0.581519i) q^{30} -0.925166i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.32353 - 2.49619i) q^{33} +(-2.24427 + 3.88718i) q^{34} +(0.859892 - 3.22578i) q^{35} -1.00000 q^{36} +(-4.87320 - 3.64031i) q^{37} -3.10196i q^{38} +(-6.16416 + 3.55888i) q^{39} +(-0.581519 - 2.15913i) q^{40} +(3.23677 - 5.60626i) q^{41} +(0.746494 - 1.29297i) q^{42} +8.04319 q^{43} +(2.49619 - 4.32353i) q^{44} +(1.57910 - 1.58317i) q^{45} +(3.91894 + 6.78780i) q^{46} +4.51871i q^{47} -1.00000i q^{48} +(-2.38549 - 4.13180i) q^{49} +(4.33655 + 2.48883i) q^{50} -4.48853i q^{51} +(-3.55888 - 6.16416i) q^{52} +(-3.66104 + 2.11370i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.90317 + 10.7792i) q^{55} +(1.29297 + 0.746494i) q^{56} +(1.55098 + 2.68637i) q^{57} +(7.13932 - 4.12189i) q^{58} +(-4.55609 + 2.63046i) q^{59} +(1.58317 + 1.57910i) q^{60} +(8.38002 + 4.83821i) q^{61} +(-0.801217 + 0.462583i) q^{62} +1.49299i q^{63} +1.00000 q^{64} +(15.3788 + 4.09950i) q^{65} +4.99238i q^{66} +(-11.5321 - 6.65806i) q^{67} +4.48853 q^{68} +(-6.78780 - 3.91894i) q^{69} +(-3.22355 + 0.868201i) q^{70} +(0.259078 - 0.448736i) q^{71} +(0.500000 + 0.866025i) q^{72} +13.8195i q^{73} +(-0.716002 + 6.04048i) q^{74} +(-4.99998 + 0.0128835i) q^{75} +(-2.68637 + 1.55098i) q^{76} +(-6.45498 - 3.72678i) q^{77} +(6.16416 + 3.55888i) q^{78} +(-0.836264 - 0.482817i) q^{79} +(-1.57910 + 1.58317i) q^{80} +(-0.500000 + 0.866025i) q^{81} -6.47355 q^{82} +(-7.83972 + 4.52626i) q^{83} -1.49299 q^{84} +(-7.08784 + 7.10613i) q^{85} +(-4.02159 - 6.96561i) q^{86} +(-4.12189 + 7.13932i) q^{87} -4.99238 q^{88} +(6.79186 - 3.92128i) q^{89} +(-2.16062 - 0.575954i) q^{90} +(-9.20301 + 5.31336i) q^{91} +(3.91894 - 6.78780i) q^{92} +(0.462583 - 0.801217i) q^{93} +(3.91331 - 2.25935i) q^{94} +(1.78658 - 6.70215i) q^{95} +(-0.866025 + 0.500000i) q^{96} -9.48892 q^{97} +(-2.38549 + 4.13180i) q^{98} +(-2.49619 - 4.32353i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−0.581519	−	2.15913i	−0.260063	−	0.965592i
$5$	−0.581519	−	2.15913i	−0.260063	−	0.965592i
$6$		−	1.00000i		−	0.408248i
$7$	1.29297	+	0.746494i	0.488695	+	0.282148i	0.724033	−	0.689765i	$-0.242286\pi$
$7$	1.29297	+	0.746494i	0.488695	+	0.282148i	−0.235338	+	0.971914i	$0.575620\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.57910	+	1.58317i	−0.499355	+	0.500644i
$11$	−4.99238			−1.50526			−0.752630	−	0.658443i	$-0.771215\pi$
$11$	−4.99238			−1.50526			−0.752630	+	0.658443i	$0.771215\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	−3.55888	+	6.16416i	−0.987055	+	1.70963i	−0.354634	+	0.935005i	$0.615395\pi$
$13$	−3.55888	+	6.16416i	−0.987055	+	1.70963i	−0.632421	+	0.774625i	$0.717939\pi$
$14$		−	1.49299i		−	0.399018i
$15$	0.575954	−	2.16062i	0.148711	−	0.557870i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.24427	−	3.88718i	−0.544314	−	0.942780i	−0.998650	−	0.0519493i	$-0.983457\pi$
$17$	−2.24427	−	3.88718i	−0.544314	−	0.942780i	0.454335	−	0.890831i	$-0.349877\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.68637	+	1.55098i	0.616296	+	0.355819i	0.775426	−	0.631439i	$-0.217535\pi$
$19$	2.68637	+	1.55098i	0.616296	+	0.355819i	−0.159129	+	0.987258i	$0.550869\pi$
$20$	2.16062	+	0.575954i	0.483129	+	0.128787i
$21$	0.746494	+	1.29297i	0.162898	+	0.282148i
$22$	2.49619	+	4.32353i	0.532190	+	0.921780i
$23$	−7.83788			−1.63431			−0.817155	−	0.576417i	$-0.804450\pi$
$23$	−7.83788			−1.63431			−0.817155	+	0.576417i	$0.804450\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−4.32367	+	2.51115i	−0.864734	+	0.502230i
$26$	7.11776			1.39591
$27$			1.00000i			0.192450i
$28$	−1.29297	+	0.746494i	−0.244347	+	0.141074i
$29$			8.24378i			1.53083i	0.643537	+	0.765415i	$0.277466\pi$
$29$			8.24378i			1.53083i	−0.643537	+	0.765415i	$0.722534\pi$
$30$	−2.15913	+	0.581519i	−0.394201	+	0.106170i
$31$		−	0.925166i		−	0.166165i	−0.996543	−	0.0830823i	$-0.973524\pi$
$31$		−	0.925166i		−	0.166165i	0.996543	−	0.0830823i	$-0.0264764\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−4.32353	−	2.49619i	−0.752630	−	0.434531i
$34$	−2.24427	+	3.88718i	−0.384888	+	0.666646i
$35$	0.859892	−	3.22578i	0.145348	−	0.545256i
$36$	−1.00000			−0.166667
$37$	−4.87320	−	3.64031i	−0.801150	−	0.598464i
$37$	−4.87320	−	3.64031i	−0.801150	−	0.598464i
$38$		−	3.10196i		−	0.503204i
$39$	−6.16416	+	3.55888i	−0.987055	+	0.569877i
$40$	−0.581519	−	2.15913i	−0.0919463	−	0.341388i
$41$	3.23677	−	5.60626i	0.505499	−	0.875550i	−0.494481	−	0.869189i	$-0.664642\pi$
$41$	3.23677	−	5.60626i	0.505499	−	0.875550i	0.999980	−	0.00636146i	$-0.00202493\pi$
$42$	0.746494	−	1.29297i	0.115187	−	0.199509i
$43$	8.04319			1.22657			0.613287	−	0.789860i	$-0.289847\pi$
$43$	8.04319			1.22657			0.613287	+	0.789860i	$0.289847\pi$
$44$	2.49619	−	4.32353i	0.376315	−	0.651797i
$45$	1.57910	−	1.58317i	0.235398	−	0.236006i
$46$	3.91894	+	6.78780i	0.577816	+	1.00081i
$47$			4.51871i			0.659121i	0.944134	+	0.329560i	$0.106901\pi$
$47$			4.51871i			0.659121i	−0.944134	+	0.329560i	$0.893099\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−2.38549	−	4.13180i	−0.340785	−	0.590257i
$50$	4.33655	+	2.48883i	0.613281	+	0.351974i
$51$		−	4.48853i		−	0.628520i
$52$	−3.55888	−	6.16416i	−0.493528	−	0.854815i
$53$	−3.66104	+	2.11370i	−0.502882	+	0.290339i	−0.729903	−	0.683551i	$-0.760435\pi$
$53$	−3.66104	+	2.11370i	−0.502882	+	0.290339i	0.227021	+	0.973890i	$0.427101\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	2.90317	+	10.7792i	0.391463	+	1.45347i
$56$	1.29297	+	0.746494i	0.172780	+	0.0997544i
$57$	1.55098	+	2.68637i	0.205432	+	0.355819i
$58$	7.13932	−	4.12189i	0.937439	−	0.541230i
$59$	−4.55609	+	2.63046i	−0.593153	+	0.342457i	−0.766343	−	0.642431i	$-0.777926\pi$
$59$	−4.55609	+	2.63046i	−0.593153	+	0.342457i	0.173190	+	0.984888i	$0.444592\pi$
$60$	1.58317	+	1.57910i	0.204387	+	0.203861i
$61$	8.38002	+	4.83821i	1.07295	+	0.619469i	0.928986	−	0.370114i	$-0.120681\pi$
$61$	8.38002	+	4.83821i	1.07295	+	0.619469i	0.143965	+	0.989583i	$0.454015\pi$
$62$	−0.801217	+	0.462583i	−0.101755	+	0.0587481i
$63$			1.49299i			0.188099i
$64$	1.00000			0.125000
$65$	15.3788	+	4.09950i	1.90750	+	0.508480i
$66$			4.99238i			0.614520i
$67$	−11.5321	−	6.65806i	−1.40887	−	0.813412i	−0.413592	−	0.910463i	$-0.635726\pi$
$67$	−11.5321	−	6.65806i	−1.40887	−	0.813412i	−0.995279	+	0.0970505i	$0.969059\pi$
$68$	4.48853			0.544314
$69$	−6.78780	−	3.91894i	−0.817155	−	0.471785i
$70$	−3.22355	+	0.868201i	−0.385288	+	0.103770i
$71$	0.259078	−	0.448736i	0.0307469	−	0.0532552i	−0.850243	−	0.526391i	$-0.823545\pi$
$71$	0.259078	−	0.448736i	0.0307469	−	0.0532552i	0.880989	+	0.473136i	$0.156878\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$			13.8195i			1.61745i	0.588185	+	0.808726i	$0.299843\pi$
$73$			13.8195i			1.61745i	−0.588185	+	0.808726i	$0.700157\pi$
$74$	−0.716002	+	6.04048i	−0.0832335	+	0.702191i
$75$	−4.99998	+	0.0128835i	−0.577348	+	0.00148766i
$76$	−2.68637	+	1.55098i	−0.308148	+	0.177909i
$77$	−6.45498	−	3.72678i	−0.735613	−	0.424707i
$78$	6.16416	+	3.55888i	0.697953	+	0.402964i
$79$	−0.836264	−	0.482817i	−0.0940870	−	0.0543212i	0.452218	−	0.891907i	$-0.350633\pi$
$79$	−0.836264	−	0.482817i	−0.0940870	−	0.0543212i	−0.546305	+	0.837586i	$0.683966\pi$
$80$	−1.57910	+	1.58317i	−0.176549	+	0.177004i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.47355			−0.714884
$83$	−7.83972	+	4.52626i	−0.860521	+	0.496822i	−0.864187	−	0.503171i	$-0.832166\pi$
$83$	−7.83972	+	4.52626i	−0.860521	+	0.496822i	0.00366573	+	0.999993i	$0.498833\pi$
$84$	−1.49299			−0.162898
$85$	−7.08784	+	7.10613i	−0.768784	+	0.770768i
$86$	−4.02159	−	6.96561i	−0.433660	−	0.751121i
$87$	−4.12189	+	7.13932i	−0.441913	+	0.765415i
$88$	−4.99238			−0.532190
$89$	6.79186	−	3.92128i	0.719935	−	0.415655i	−0.0947935	−	0.995497i	$-0.530219\pi$
$89$	6.79186	−	3.92128i	0.719935	−	0.415655i	0.814729	+	0.579842i	$0.196886\pi$
$90$	−2.16062	−	0.575954i	−0.227749	−	0.0607109i
$91$	−9.20301	+	5.31336i	−0.964738	+	0.556992i
$92$	3.91894	−	6.78780i	0.408578	−	0.707677i
$93$	0.462583	−	0.801217i	0.0479676	−	0.0830823i
$94$	3.91331	−	2.25935i	0.403628	−	0.233034i
$95$	1.78658	−	6.70215i	0.183300	−	0.687626i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−9.48892			−0.963454			−0.481727	−	0.876321i	$-0.659990\pi$
$97$	−9.48892			−0.963454			−0.481727	+	0.876321i	$0.659990\pi$
$98$	−2.38549	+	4.13180i	−0.240971	+	0.417374i
$99$	−2.49619	−	4.32353i	−0.250877	−	0.434531i
$100$	−0.0128835	−	4.99998i	−0.00128835	−	0.499998i
$101$	8.49427			0.845211			0.422606	−	0.906314i	$-0.361116\pi$
$101$	8.49427			0.845211			0.422606	+	0.906314i	$0.361116\pi$
$102$	−3.88718	+	2.24427i	−0.384888	+	0.222215i
$103$	5.32885			0.525068			0.262534	−	0.964923i	$-0.415442\pi$
$103$	5.32885			0.525068			0.262534	+	0.964923i	$0.415442\pi$
$104$	−3.55888	+	6.16416i	−0.348977	+	0.604445i
$105$	2.35758	−	2.36366i	0.230076	−	0.230670i
$106$	3.66104	+	2.11370i	0.355591	+	0.205301i
$107$	−5.06411	−	2.92376i	−0.489566	−	0.282651i	0.234829	−	0.972037i	$-0.424547\pi$
$107$	−5.06411	−	2.92376i	−0.489566	−	0.282651i	−0.724394	+	0.689386i	$0.757880\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−6.74554	+	3.89454i	−0.646105	+	0.373029i	−0.786962	−	0.617001i	$-0.788347\pi$
$109$	−6.74554	+	3.89454i	−0.646105	+	0.373029i	0.140857	+	0.990030i	$0.455014\pi$
$110$	7.88348	−	7.90382i	0.751660	−	0.753599i
$111$	−2.40016	−	5.58921i	−0.227813	−	0.530504i
$112$		−	1.49299i		−	0.141074i
$113$	0.919606	+	1.59280i	0.0865092	+	0.149838i	0.906033	−	0.423206i	$-0.139095\pi$
$113$	0.919606	+	1.59280i	0.0865092	+	0.149838i	−0.819524	+	0.573045i	$0.805762\pi$
$114$	1.55098	−	2.68637i	0.145262	−	0.251602i
$115$	4.55788	+	16.9230i	0.425024	+	1.57808i
$116$	−7.13932	−	4.12189i	−0.662869	−	0.382708i
$117$	−7.11776			−0.658037
$118$	4.55609	+	2.63046i	0.419423	+	0.242154i
$119$		−	6.70132i		−	0.614309i
$120$	0.575954	−	2.16062i	0.0525772	−	0.197237i
$121$	13.9239			1.26581
$122$		−	9.67642i		−	0.876062i
$123$	5.60626	−	3.23677i	0.505499	−	0.291850i
$124$	0.801217	+	0.462583i	0.0719514	+	0.0415412i
$125$	7.93619	+	7.87508i	0.709834	+	0.704369i
$126$	1.29297	−	0.746494i	0.115187	−	0.0665030i
$127$	−7.96186	+	4.59678i	−0.706501	+	0.407899i	−0.809764	−	0.586755i	$-0.800405\pi$
$127$	−7.96186	+	4.59678i	−0.706501	+	0.407899i	0.103263	+	0.994654i	$0.467072\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	6.96561	+	4.02159i	0.613287	+	0.354082i
$130$	−4.13911	−	15.3682i	−0.363024	−	1.34788i
$131$	−6.67622	+	3.85452i	−0.583304	+	0.336771i	−0.762445	−	0.647053i	$-0.776001\pi$
$131$	−6.67622	+	3.85452i	−0.583304	+	0.336771i	0.179141	+	0.983823i	$0.442668\pi$
$132$	4.32353	−	2.49619i	0.376315	−	0.217266i
$133$	2.31559	+	4.01072i	0.200787	+	0.347774i
$134$			13.3161i			1.15034i
$135$	2.15913	−	0.581519i	0.185828	−	0.0500492i
$136$	−2.24427	−	3.88718i	−0.192444	−	0.333323i
$137$			5.30952i			0.453623i	0.973939	+	0.226812i	$0.0728301\pi$
$137$			5.30952i			0.453623i	−0.973939	+	0.226812i	$0.927170\pi$
$138$			7.83788i			0.667205i
$139$	−3.98426	−	6.90094i	−0.337941	−	0.585330i	0.646105	−	0.763249i	$-0.276397\pi$
$139$	−3.98426	−	6.90094i	−0.337941	−	0.585330i	−0.984045	+	0.177919i	$0.943064\pi$
$140$	2.36366	+	2.35758i	0.199766	+	0.199252i
$141$	−2.25935	+	3.91331i	−0.190272	+	0.329560i
$142$	−0.518156			−0.0434827
$143$	17.7673	−	30.7738i	1.48578	−	2.57344i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	17.7994	−	4.79391i	1.47816	−	0.398113i
$146$	11.9681	−	6.90976i	0.990484	−	0.571856i
$147$		−	4.77099i		−	0.393504i
$148$	5.58921	−	2.40016i	0.459430	−	0.197292i
$149$	8.88053			0.727521			0.363760	−	0.931493i	$-0.381493\pi$
$149$	8.88053			0.727521			0.363760	+	0.931493i	$0.381493\pi$
$150$	2.51115	+	4.32367i	0.205034	+	0.353026i
$151$	5.35526	−	9.27558i	0.435805	−	0.754836i	−0.561556	−	0.827439i	$-0.689797\pi$
$151$	5.35526	−	9.27558i	0.435805	−	0.754836i	0.997361	+	0.0726027i	$0.0231305\pi$
$152$	2.68637	+	1.55098i	0.217894	+	0.125801i
$153$	2.24427	−	3.88718i	0.181438	−	0.314260i
$154$			7.45357i			0.600626i
$155$	−1.99755	+	0.538002i	−0.160447	+	0.0432133i
$156$		−	7.11776i		−	0.569877i
$157$	5.76364	−	3.32764i	0.459988	−	0.265574i	−0.252051	−	0.967714i	$-0.581105\pi$
$157$	5.76364	−	3.32764i	0.459988	−	0.265574i	0.712039	+	0.702140i	$0.247772\pi$
$158$			0.965634i			0.0768217i
$159$	−4.22740			−0.335255
$160$	2.16062	+	0.575954i	0.170812	+	0.0455331i
$161$	−10.1341	−	5.85093i	−0.798679	−	0.461118i
$162$	1.00000			0.0785674
$163$	1.39135	+	2.40989i	0.108979	+	0.188757i	0.915357	−	0.402644i	$-0.131909\pi$
$163$	1.39135	+	2.40989i	0.108979	+	0.188757i	−0.806378	+	0.591401i	$0.798575\pi$
$164$	3.23677	+	5.60626i	0.252750	+	0.437775i
$165$	−2.87538	+	10.7866i	−0.223848	+	0.839739i
$166$	7.83972	+	4.52626i	0.608480	+	0.351306i
$167$	−7.54017	+	13.0600i	−0.583476	+	1.01061i	0.411588	+	0.911370i	$0.364974\pi$
$167$	−7.54017	+	13.0600i	−0.583476	+	1.01061i	−0.995064	+	0.0992397i	$0.968359\pi$
$168$	0.746494	+	1.29297i	0.0575933	+	0.0997544i
$169$	−18.8312	−	32.6167i	−1.44856	−	2.50897i
$170$	9.69801	+	2.58519i	0.743803	+	0.198275i
$171$			3.10196i			0.237213i
$172$	−4.02159	+	6.96561i	−0.306644	+	0.531123i
$173$	15.2577	−	8.80902i	1.16002	−	0.669737i	0.208711	−	0.977977i	$-0.433073\pi$
$173$	15.2577	−	8.80902i	1.16002	−	0.669737i	0.951309	+	0.308240i	$0.0997400\pi$
$174$	8.24378			0.624959
$175$	−7.46491	+	0.0192349i	−0.564294	+	0.00145402i
$176$	2.49619	+	4.32353i	0.188158	+	0.325898i
$177$	−5.26092			−0.395435
$178$	−6.79186	−	3.92128i	−0.509071	−	0.293912i
$179$			6.17151i			0.461280i	0.973039	+	0.230640i	$0.0740820\pi$
$179$			6.17151i			0.461280i	−0.973039	+	0.230640i	$0.925918\pi$
$180$	0.581519	+	2.15913i	0.0433439	+	0.160932i
$181$	4.96675	−	8.60266i	0.369176	−	0.639431i	−0.620261	−	0.784395i	$-0.712973\pi$
$181$	4.96675	−	8.60266i	0.369176	−	0.639431i	0.989437	+	0.144964i	$0.0463068\pi$
$182$	9.20301	+	5.31336i	0.682173	+	0.393853i
$183$	4.83821	+	8.38002i	0.357651	+	0.619469i
$184$	−7.83788			−0.577816
$185$	−5.02604	+	12.6388i	−0.369522	+	0.929222i
$186$	−0.925166			−0.0678364
$187$	11.2042	+	19.4063i	0.819335	+	1.41913i
$188$	−3.91331	−	2.25935i	−0.285408	−	0.164780i
$189$	−0.746494	+	1.29297i	−0.0542994	+	0.0940494i
$190$	−6.69752	+	1.80385i	−0.485889	+	0.130865i
$191$		−	9.91473i		−	0.717404i	−0.933452	−	0.358702i	$-0.883219\pi$
$191$		−	9.91473i		−	0.717404i	0.933452	−	0.358702i	$-0.116781\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−16.2324			−1.16843			−0.584217	−	0.811597i	$-0.698598\pi$
$193$	−16.2324			−1.16843			−0.584217	+	0.811597i	$0.698598\pi$
$194$	4.74446	+	8.21765i	0.340633	+	0.589993i
$195$	11.2687	+	11.2397i	0.806965	+	0.804888i
$196$	4.77099			0.340785
$197$	5.62897	−	3.24989i	0.401047	−	0.231545i	−0.285888	−	0.958263i	$-0.592289\pi$
$197$	5.62897	−	3.24989i	0.401047	−	0.231545i	0.686936	+	0.726718i	$0.258955\pi$
$198$	−2.49619	+	4.32353i	−0.177397	+	0.307260i
$199$			19.9907i			1.41710i	0.705660	+	0.708550i	$0.250650\pi$
$199$			19.9907i			1.41710i	−0.705660	+	0.708550i	$0.749350\pi$
$200$	−4.32367	+	2.51115i	−0.305730	+	0.177565i
$201$	−6.65806	−	11.5321i	−0.469624	−	0.813412i
$202$	−4.24713	−	7.35625i	−0.298827	−	0.517584i
$203$	−6.15393	+	10.6589i	−0.431921	+	0.748109i
$204$	3.88718	+	2.24427i	0.272157	+	0.157130i
$205$	−13.9869	−	3.72846i	−0.976886	−	0.260407i
$206$	−2.66443	−	4.61492i	−0.185639	−	0.321537i
$207$	−3.91894	−	6.78780i	−0.272385	−	0.471785i
$208$	7.11776			0.493528
$209$	−13.4114	−	7.74308i	−0.927686	−	0.535600i
$210$	−3.22578	−	0.859892i	−0.222600	−	0.0593382i
$211$	−3.12799			−0.215339			−0.107670	−	0.994187i	$-0.534339\pi$
$211$	−3.12799			−0.215339			−0.107670	+	0.994187i	$0.534339\pi$
$212$		−	4.22740i		−	0.290339i
$213$	0.448736	−	0.259078i	0.0307469	−	0.0177517i
$214$			5.84753i			0.399729i
$215$	−4.67727	−	17.3663i	−0.318987	−	1.18437i
$216$			1.00000i			0.0680414i
$217$	0.690630	−	1.19621i	0.0468830	−	0.0812038i
$218$	6.74554	+	3.89454i	0.456865	+	0.263771i
$219$	−6.90976	+	11.9681i	−0.466918	+	0.808726i
$220$	−10.7866	−	2.87538i	−0.727235	−	0.193858i
$221$	31.9483			2.14907
$222$	−3.64031	+	4.87320i	−0.244322	+	0.327068i
$223$		−	27.7499i		−	1.85827i	−0.369741	−	0.929135i	$-0.620554\pi$
$223$		−	27.7499i		−	1.85827i	0.369741	−	0.929135i	$-0.379446\pi$
$224$	−1.29297	+	0.746494i	−0.0863899	+	0.0498772i
$225$	−4.33655	−	2.48883i	−0.289104	−	0.165922i
$226$	0.919606	−	1.59280i	0.0611713	−	0.105952i
$227$	9.89438	−	17.1376i	0.656713	−	1.13746i	−0.324748	−	0.945800i	$-0.605280\pi$
$227$	9.89438	−	17.1376i	0.656713	−	1.13746i	0.981461	−	0.191660i	$-0.0613870\pi$
$228$	−3.10196			−0.205432
$229$	4.33595	−	7.51008i	0.286527	−	0.496280i	−0.686451	−	0.727176i	$-0.740832\pi$
$229$	4.33595	−	7.51008i	0.286527	−	0.496280i	0.972978	+	0.230896i	$0.0741657\pi$
$230$	12.3768	−	12.4087i	0.816102	−	0.818207i
$231$	−3.72678	−	6.45498i	−0.245204	−	0.424707i
$232$			8.24378i			0.541230i
$233$		−	2.13736i		−	0.140023i	−0.997546	−	0.0700115i	$-0.977696\pi$
$233$		−	2.13736i		−	0.140023i	0.997546	−	0.0700115i	$-0.0223036\pi$
$234$	3.55888	+	6.16416i	0.232651	+	0.402964i
$235$	9.75647	−	2.62771i	0.636442	−	0.171413i
$236$		−	5.26092i		−	0.342457i
$237$	−0.482817	−	0.836264i	−0.0313623	−	0.0543212i
$238$	−5.80351	+	3.35066i	−0.376186	+	0.217191i
$239$	2.00088	−	1.15521i	0.129426	−	0.0747241i	−0.433889	−	0.900966i	$-0.642859\pi$
$239$	2.00088	−	1.15521i	0.129426	−	0.0747241i	0.563315	+	0.826242i	$0.309526\pi$
$240$	−2.15913	+	0.581519i	−0.139371	+	0.0375369i
$241$	18.1405	+	10.4734i	1.16853	+	0.674652i	0.953334	−	0.301919i	$-0.0976272\pi$
$241$	18.1405	+	10.4734i	1.16853	+	0.674652i	0.215197	+	0.976571i	$0.430960\pi$
$242$	−6.96195	−	12.0585i	−0.447531	−	0.775147i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−8.38002	+	4.83821i	−0.536476	+	0.309735i
$245$	−7.53387	+	7.55331i	−0.481321	+	0.482563i
$246$	−5.60626	−	3.23677i	−0.357442	−	0.206369i
$247$	−19.1210	+	11.0395i	−1.21664	+	0.702426i
$248$		−	0.925166i		−	0.0587481i
$249$	−9.05253			−0.573681
$250$	2.85192	−	10.8105i	0.180371	−	0.683715i
$251$			17.3320i			1.09399i	0.837137	+	0.546993i	$0.184228\pi$
$251$			17.3320i			1.09399i	−0.837137	+	0.546993i	$0.815772\pi$
$252$	−1.29297	−	0.746494i	−0.0814492	−	0.0470247i
$253$	39.1297			2.46006
$254$	7.96186	+	4.59678i	0.499572	+	0.288428i
$255$	−9.69131	+	2.61017i	−0.606894	+	0.163455i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.45518	−	4.25250i	−0.153150	−	0.265263i	0.779234	−	0.626733i	$-0.215608\pi$
$257$	−2.45518	−	4.25250i	−0.153150	−	0.265263i	−0.932384	+	0.361470i	$0.882275\pi$
$258$		−	8.04319i		−	0.500747i
$259$	−3.58341	−	8.34462i	−0.222662	−	0.518509i
$260$	−11.2397	+	11.2687i	−0.697054	+	0.698852i
$261$	−7.13932	+	4.12189i	−0.441913	+	0.255138i
$262$	6.67622	+	3.85452i	0.412458	+	0.238133i
$263$	16.2980	+	9.40967i	1.00498	+	0.580225i	0.909718	−	0.415227i	$-0.136298\pi$
$263$	16.2980	+	9.40967i	1.00498	+	0.580225i	0.0952619	+	0.995452i	$0.469631\pi$
$264$	−4.32353	−	2.49619i	−0.266095	−	0.153630i
$265$	6.69271	+	6.67549i	0.411130	+	0.410072i
$266$	2.31559	−	4.01072i	0.141978	−	0.245913i
$267$	7.84256			0.479957
$268$	11.5321	−	6.65806i	0.704436	−	0.406706i
$269$	12.5071			0.762571			0.381285	−	0.924457i	$-0.375482\pi$
$269$	12.5071			0.762571			0.381285	+	0.924457i	$0.375482\pi$
$270$	−1.58317	−	1.57910i	−0.0963489	−	0.0961010i
$271$	−12.1046	−	20.9658i	−0.735302	−	1.27358i	−0.954591	−	0.297920i	$-0.903707\pi$
$271$	−12.1046	−	20.9658i	−0.735302	−	1.27358i	0.219289	−	0.975660i	$-0.429626\pi$
$272$	−2.24427	+	3.88718i	−0.136079	+	0.235695i
$273$	−10.6267			−0.643159
$274$	4.59818	−	2.65476i	0.277786	−	0.160380i
$275$	21.5854	−	12.5366i	1.30165	−	0.755987i
$276$	6.78780	−	3.91894i	0.408578	−	0.235892i
$277$	12.6092	−	21.8397i	0.757611	−	1.31222i	−0.186454	−	0.982464i	$-0.559700\pi$
$277$	12.6092	−	21.8397i	0.757611	−	1.31222i	0.944066	−	0.329758i	$-0.106967\pi$
$278$	−3.98426	+	6.90094i	−0.238960	+	0.413891i
$279$	0.801217	−	0.462583i	0.0479676	−	0.0276941i
$280$	0.859892	−	3.22578i	0.0513884	−	0.192777i
$281$	3.24794	−	1.87520i	0.193756	−	0.111865i	−0.399984	−	0.916522i	$-0.630984\pi$
$281$	3.24794	−	1.87520i	0.193756	−	0.111865i	0.593740	+	0.804657i	$0.297651\pi$
$282$	4.51871			0.269085
$283$	−15.0869	+	26.1313i	−0.896824	+	1.55334i	−0.0652929	+	0.997866i	$0.520798\pi$
$283$	−15.0869	+	26.1313i	−0.896824	+	1.55334i	−0.831531	+	0.555478i	$0.812535\pi$
$284$	0.259078	+	0.448736i	0.0153734	+	0.0266276i
$285$	4.89830	−	4.91094i	0.290150	−	0.290899i
$286$	−35.5346			−2.10120
$287$	8.37007	−	4.83246i	0.494070	−	0.285251i
$288$	−1.00000			−0.0589256
$289$	−1.57345	+	2.72530i	−0.0925560	+	0.160312i
$290$	−13.0513	−	13.0178i	−0.766401	−	0.764429i
$291$	−8.21765	−	4.74446i	−0.481727	−	0.278125i
$292$	−11.9681	−	6.90976i	−0.700378	−	0.404363i
$293$	−24.3362	−	14.0505i	−1.42174	−	0.820841i	−0.425291	−	0.905057i	$-0.639828\pi$
$293$	−24.3362	−	14.0505i	−1.42174	−	0.820841i	−0.996448	+	0.0842159i	$0.973161\pi$
$294$	−4.13180	+	2.38549i	−0.240971	+	0.139125i
$295$	8.32896	+	8.30753i	0.484931	+	0.483683i
$296$	−4.87320	−	3.64031i	−0.283249	−	0.211589i
$297$		−	4.99238i		−	0.289688i
$298$	−4.44026	−	7.69076i	−0.257218	−	0.445514i
$299$	27.8941	−	48.3139i	1.61316	−	2.79407i
$300$	2.48883	−	4.33655i	0.143693	−	0.250371i
$301$	10.3996	+	6.00419i	0.599421	+	0.346076i
$302$	−10.7105			−0.616321
$303$	7.35625	+	4.24713i	0.422606	+	0.243992i
$304$		−	3.10196i		−	0.177909i
$305$	5.57317	−	20.9071i	0.319119	−	1.19713i
$306$	−4.48853			−0.256592
$307$			13.0437i			0.744446i	0.928143	+	0.372223i	$0.121404\pi$
$307$			13.0437i			0.744446i	−0.928143	+	0.372223i	$0.878596\pi$
$308$	6.45498	−	3.72678i	0.367807	−	0.212353i
$309$	4.61492	+	2.66443i	0.262534	+	0.151574i
$310$	1.46470	+	1.46093i	0.0831893	+	0.0829752i
$311$	−18.1342	+	10.4698i	−1.02830	+	0.593687i	−0.916496	−	0.400044i	$-0.868995\pi$
$311$	−18.1342	+	10.4698i	−1.02830	+	0.593687i	−0.111800	+	0.993731i	$0.535662\pi$
$312$	−6.16416	+	3.55888i	−0.348977	+	0.201482i
$313$	−7.90172	−	13.6862i	−0.446632	−	0.773589i	0.551533	−	0.834153i	$-0.314043\pi$
$313$	−7.90172	−	13.6862i	−0.446632	−	0.773589i	−0.998164	+	0.0605646i	$0.980710\pi$
$314$	−5.76364	−	3.32764i	−0.325261	−	0.187789i
$315$	3.22355	−	0.868201i	0.181627	−	0.0489176i
$316$	0.836264	−	0.482817i	0.0470435	−	0.0271606i
$317$	−16.8545	+	9.73093i	−0.946641	+	0.546543i	−0.892036	−	0.451965i	$-0.850723\pi$
$317$	−16.8545	+	9.73093i	−0.946641	+	0.546543i	−0.0546048	+	0.998508i	$0.517390\pi$
$318$	2.11370	+	3.66104i	0.118530	+	0.205301i
$319$		−	41.1561i		−	2.30430i
$320$	−0.581519	−	2.15913i	−0.0325079	−	0.120699i
$321$	−2.92376	−	5.06411i	−0.163189	−	0.282651i
$322$			11.7019i			0.652119i
$323$		−	13.9232i		−	0.774709i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.0917014	−	35.5887i	−0.00508668	−	1.97410i
$326$	1.39135	−	2.40989i	0.0770597	−	0.133471i
$327$	−7.78907			−0.430737
$328$	3.23677	−	5.60626i	0.178721	−	0.309554i
$329$	−3.37319	+	5.84253i	−0.185970	+	0.322109i
$330$	10.7792	−	2.90317i	0.593375	−	0.159814i
$331$	−3.62395	+	2.09229i	−0.199190	+	0.115003i	−0.596278	−	0.802778i	$-0.703354\pi$
$331$	−3.62395	+	2.09229i	−0.199190	+	0.115003i	0.397087	+	0.917781i	$0.370021\pi$
$332$		−	9.05253i		−	0.496822i
$333$	0.716002	−	6.04048i	0.0392367	−	0.331016i
$334$	15.0803			0.825160
$335$	−7.66948	+	28.7711i	−0.419028	+	1.57193i
$336$	0.746494	−	1.29297i	0.0407246	−	0.0705370i
$337$	−11.0981	−	6.40748i	−0.604551	−	0.349038i	0.166279	−	0.986079i	$-0.446825\pi$
$337$	−11.0981	−	6.40748i	−0.604551	−	0.349038i	−0.770830	+	0.637041i	$0.780158\pi$
$338$	−18.8312	+	32.6167i	−1.02428	+	1.77411i
$339$			1.83921i			0.0998923i
$340$	−2.61017	−	9.69131i	−0.141556	−	0.525585i
$341$			4.61878i			0.250121i
$342$	2.68637	−	1.55098i	0.145262	−	0.0838673i
$343$		−	17.5739i		−	0.948904i
$344$	8.04319			0.433660
$345$	−4.51426	+	16.9347i	−0.243039	+	0.911732i
$346$	−15.2577	−	8.80902i	−0.820257	−	0.473576i
$347$	12.0755			0.648247			0.324123	−	0.946015i	$-0.394931\pi$
$347$	12.0755			0.648247			0.324123	+	0.946015i	$0.394931\pi$
$348$	−4.12189	−	7.13932i	−0.220956	−	0.382708i
$349$	3.57899	+	6.19899i	0.191579	+	0.331824i	0.945774	−	0.324827i	$-0.105306\pi$
$349$	3.57899	+	6.19899i	0.191579	+	0.331824i	−0.754195	+	0.656651i	$0.771973\pi$
$350$	3.74911	+	6.45519i	0.200399	+	0.345044i
$351$	−6.16416	−	3.55888i	−0.329018	−	0.189959i
$352$	2.49619	−	4.32353i	0.133047	−	0.230445i
$353$	−16.3563	−	28.3299i	−0.870556	−	1.50785i	−0.861422	−	0.507889i	$-0.830426\pi$
$353$	−16.3563	−	28.3299i	−0.870556	−	1.50785i	−0.00913392	−	0.999958i	$-0.502907\pi$
$354$	2.63046	+	4.55609i	0.139808	+	0.242154i
$355$	−1.11954	−	0.298434i	−0.0594189	−	0.0158392i
$356$			7.84256i			0.415655i
$357$	3.35066	−	5.80351i	0.177336	−	0.307155i
$358$	5.34469	−	3.08576i	0.282475	−	0.163087i
$359$	−26.3836			−1.39247			−0.696236	−	0.717813i	$-0.745143\pi$
$359$	−26.3836			−1.39247			−0.696236	+	0.717813i	$0.745143\pi$
$360$	1.57910	−	1.58317i	0.0832259	−	0.0834406i
$361$	−4.68893	−	8.12147i	−0.246786	−	0.427446i
$362$	−9.93350			−0.522093
$363$	12.0585	+	6.96195i	0.632905	+	0.365408i
$364$		−	10.6267i		−	0.556992i
$365$	29.8381	−	8.03632i	1.56180	−	0.420640i
$366$	4.83821	−	8.38002i	0.252897	−	0.438031i
$367$	1.34639	+	0.777339i	0.0702810	+	0.0405768i	0.534729	−	0.845024i	$-0.320414\pi$
$367$	1.34639	+	0.777339i	0.0702810	+	0.0405768i	−0.464448	+	0.885601i	$0.653747\pi$
$368$	3.91894	+	6.78780i	0.204289	+	0.353839i
$369$	6.47355			0.336999
$370$	13.4585	−	1.96671i	0.699676	−	0.102244i
$371$	−6.31146			−0.327675
$372$	0.462583	+	0.801217i	0.0239838	+	0.0415412i
$373$	23.6846	+	13.6743i	1.22634	+	0.708028i	0.966262	−	0.257560i	$-0.0829184\pi$
$373$	23.6846	+	13.6743i	1.22634	+	0.708028i	0.260078	+	0.965588i	$0.416252\pi$
$374$	11.2042	−	19.4063i	0.579357	−	1.00348i
$375$	2.93540	+	10.7881i	0.151584	+	0.557096i
$376$			4.51871i			0.233034i
$377$	−50.8159	−	29.3386i	−2.61715	−	1.51101i
$378$	1.49299			0.0767910
$379$	3.06678	+	5.31181i	0.157530	+	0.272849i	0.933977	−	0.357332i	$-0.116314\pi$
$379$	3.06678	+	5.31181i	0.157530	+	0.272849i	−0.776448	+	0.630182i	$0.782980\pi$
$380$	4.91094	+	4.89830i	0.251926	+	0.251278i
$381$	−9.19357			−0.471001
$382$	−8.58641	+	4.95736i	−0.439319	+	0.253641i
$383$	−17.4879	+	30.2900i	−0.893591	+	1.54774i	−0.0580512	+	0.998314i	$0.518489\pi$
$383$	−17.4879	+	30.2900i	−0.893591	+	1.54774i	−0.835539	+	0.549431i	$0.814845\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−4.29291	+	16.1043i	−0.218787	+	0.820753i
$386$	8.11621	+	14.0577i	0.413104	+	0.715517i
$387$	4.02159	+	6.96561i	0.204429	+	0.354082i
$388$	4.74446	−	8.21765i	0.240864	−	0.417188i
$389$	−16.4618	−	9.50424i	−0.834648	−	0.481884i	0.0207936	−	0.999784i	$-0.493381\pi$
$389$	−16.4618	−	9.50424i	−0.834648	−	0.481884i	−0.855441	+	0.517900i	$0.826714\pi$
$390$	4.09950	−	15.3788i	0.207586	−	0.778734i
$391$	17.5903	+	30.4673i	0.889579	+	1.54080i
$392$	−2.38549	−	4.13180i	−0.120486	−	0.208687i
$393$	−7.70903			−0.388869
$394$	−5.62897	−	3.24989i	−0.283583	−	0.163727i
$395$	−0.556161	+	2.08637i	−0.0279835	+	0.104977i
$396$	4.99238			0.250877
$397$			15.0132i			0.753492i	0.926317	+	0.376746i	$0.122957\pi$
$397$			15.0132i			0.753492i	−0.926317	+	0.376746i	$0.877043\pi$
$398$	17.3124	−	9.99533i	0.867793	−	0.501021i
$399$			4.63118i			0.231849i
$400$	4.33655	+	2.48883i	0.216828	+	0.124442i
$401$		−	2.84609i		−	0.142127i	−0.997472	−	0.0710634i	$-0.977361\pi$
$401$		−	2.84609i		−	0.142127i	0.997472	−	0.0710634i	$-0.0226393\pi$
$402$	−6.65806	+	11.5321i	−0.332074	+	0.575169i
$403$	5.70287	+	3.29255i	0.284080	+	0.164014i
$404$	−4.24713	+	7.35625i	−0.211303	+	0.365987i
$405$	2.16062	+	0.575954i	0.107362	+	0.0286194i
$406$	12.3079			0.610829
$407$	24.3289	+	18.1738i	1.20594	+	0.900844i
$408$		−	4.48853i		−	0.222215i
$409$	12.4387	−	7.18152i	0.615057	−	0.355103i	−0.159885	−	0.987136i	$-0.551112\pi$
$409$	12.4387	−	7.18152i	0.615057	−	0.355103i	0.774942	+	0.632033i	$0.217779\pi$
$410$	3.76449	+	13.9772i	0.185915	+	0.690286i
$411$	−2.65476	+	4.59818i	−0.130950	+	0.226812i
$412$	−2.66443	+	4.61492i	−0.131267	+	0.227361i
$413$	−7.85450			−0.386495
$414$	−3.91894	+	6.78780i	−0.192605	+	0.333602i
$415$	14.3317	+	14.2949i	0.703517	+	0.701707i
$416$	−3.55888	−	6.16416i	−0.174488	−	0.302223i
$417$		−	7.96852i		−	0.390220i
$418$			15.4862i			0.757453i
$419$	0.643425	+	1.11444i	0.0314334	+	0.0544442i	0.881314	−	0.472531i	$-0.156659\pi$
$419$	0.643425	+	1.11444i	0.0314334	+	0.0544442i	−0.849881	+	0.526975i	$0.823326\pi$
$420$	0.868201	+	3.22355i	0.0423639	+	0.157293i
$421$			40.0359i			1.95123i	0.219484	+	0.975616i	$0.429563\pi$
$421$			40.0359i			1.95123i	−0.219484	+	0.975616i	$0.570437\pi$
$422$	1.56399	+	2.70892i	0.0761340	+	0.131868i
$423$	−3.91331	+	2.25935i	−0.190272	+	0.109853i
$424$	−3.66104	+	2.11370i	−0.177796	+	0.102650i
$425$	19.4648	+	11.1712i	0.944179	+	0.541883i
$426$	−0.448736	−	0.259078i	−0.0217413	−	0.0125524i
$427$	7.22339	+	12.5113i	0.349564	+	0.605463i
$428$	5.06411	−	2.92376i	0.244783	−	0.141325i
$429$	30.7738	−	17.7673i	1.48578	−	0.857813i
$430$	−12.7010	+	12.7338i	−0.612497	+	0.614077i
$431$	6.33783	+	3.65915i	0.305283	+	0.176255i	0.644814	−	0.764340i	$-0.276935\pi$
$431$	6.33783	+	3.65915i	0.305283	+	0.176255i	−0.339531	+	0.940595i	$0.610268\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	7.62286i		−	0.366332i	−0.983082	−	0.183166i	$-0.941365\pi$
$433$		−	7.62286i		−	0.366332i	0.983082	−	0.183166i	$-0.0586345\pi$
$434$	−1.38126			−0.0663026
$435$	17.8117	+	4.74803i	0.854004	+	0.227651i
$436$		−	7.78907i		−	0.373029i
$437$	−21.0555	−	12.1564i	−1.00722	−	0.581519i
$438$	13.8195			0.660322
$439$	21.6063	+	12.4744i	1.03121	+	0.595370i	0.917331	−	0.398125i	$-0.130339\pi$
$439$	21.6063	+	12.4744i	1.03121	+	0.595370i	0.113880	+	0.993495i	$0.463672\pi$
$440$	2.90317	+	10.7792i	0.138403	+	0.513878i
$441$	2.38549	−	4.13180i	0.113595	−	0.196752i
$442$	−15.9741	−	27.6680i	−0.759812	−	1.31603i
$443$			18.3769i			0.873111i	0.899677	+	0.436555i	$0.143802\pi$
$443$			18.3769i			0.873111i	−0.899677	+	0.436555i	$0.856198\pi$
$444$	6.04048	+	0.716002i	0.286668	+	0.0339799i
$445$	−12.4161	−	12.3842i	−0.588582	−	0.587067i
$446$	−24.0321	+	13.8749i	−1.13795	+	0.656998i
$447$	7.69076	+	4.44026i	0.363760	+	0.210017i
$448$	1.29297	+	0.746494i	0.0610869	+	0.0352685i
$449$	5.69834	+	3.28994i	0.268921	+	0.155262i	0.628397	−	0.777893i	$-0.283711\pi$
$449$	5.69834	+	3.28994i	0.268921	+	0.155262i	−0.359476	+	0.933154i	$0.617045\pi$
$450$	0.0128835	+	4.99998i	0.000607333	+	0.235701i
$451$	−16.1592	+	27.9886i	−0.760908	+	1.31793i
$452$	−1.83921			−0.0865092
$453$	9.27558	−	5.35526i	0.435805	−	0.251612i
$454$	−19.7888			−0.928732
$455$	16.8240	+	16.7807i	0.788719	+	0.786690i
$456$	1.55098	+	2.68637i	0.0726312	+	0.125801i
$457$	−11.7495	+	20.3508i	−0.549619	+	0.951968i	0.448681	+	0.893692i	$0.351894\pi$
$457$	−11.7495	+	20.3508i	−0.549619	+	0.951968i	−0.998300	+	0.0582764i	$0.981440\pi$
$458$	−8.67189			−0.405211
$459$	3.88718	−	2.24427i	0.181438	−	0.104753i
$460$	−16.9347	−	4.51426i	−0.789583	−	0.210478i
$461$	9.55328	−	5.51559i	0.444941	−	0.256887i	−0.260750	−	0.965406i	$-0.583970\pi$
$461$	9.55328	−	5.51559i	0.444941	−	0.256887i	0.705691	+	0.708520i	$0.250637\pi$
$462$	−3.72678	+	6.45498i	−0.173386	+	0.300313i
$463$	−6.03232	+	10.4483i	−0.280346	+	0.485573i	−0.971470	−	0.237163i	$-0.923782\pi$
$463$	−6.03232	+	10.4483i	−0.280346	+	0.485573i	0.691124	+	0.722736i	$0.257116\pi$
$464$	7.13932	−	4.12189i	0.331435	−	0.191354i
$465$	−1.99893	−	0.532853i	−0.0926982	−	0.0247105i
$466$	−1.85101	+	1.06868i	−0.0857462	+	0.0495056i
$467$	8.08233			0.374005			0.187003	−	0.982359i	$-0.440123\pi$
$467$	8.08233			0.374005			0.187003	+	0.982359i	$0.440123\pi$
$468$	3.55888	−	6.16416i	0.164509	−	0.284938i
$469$	−9.94041	−	17.2173i	−0.459005	−	0.795021i
$470$	−7.15390	−	7.13549i	−0.329985	−	0.329136i
$471$	6.65528			0.306659
$472$	−4.55609	+	2.63046i	−0.209711	+	0.121077i
$473$	−40.1547			−1.84631
$474$	−0.482817	+	0.836264i	−0.0221765	+	0.0384109i
$475$	−15.5097	+	0.0399640i	−0.711635	+	0.00183367i
$476$	5.80351	+	3.35066i	0.266004	+	0.153577i
$477$	−3.66104	−	2.11370i	−0.167627	−	0.0967797i
$478$	−2.00088	−	1.15521i	−0.0915180	−	0.0528379i
$479$	−14.6391	+	8.45188i	−0.668877	+	0.386176i	−0.795651	−	0.605755i	$-0.792871\pi$
$479$	−14.6391	+	8.45188i	−0.668877	+	0.386176i	0.126774	+	0.991932i	$0.459538\pi$
$480$	1.58317	+	1.57910i	0.0722617	+	0.0720757i
$481$	39.7826	−	17.0838i	1.81393	−	0.778953i
$482$		−	20.9468i		−	0.954102i
$483$	−5.85093	−	10.1341i	−0.266226	−	0.461118i
$484$	−6.96195	+	12.0585i	−0.316452	+	0.548112i
$485$	5.51799	+	20.4878i	0.250559	+	0.930303i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	33.2218			1.50542			0.752711	−	0.658351i	$-0.228746\pi$
$487$	33.2218			1.50542			0.752711	+	0.658351i	$0.228746\pi$
$488$	8.38002	+	4.83821i	0.379346	+	0.219015i
$489$			2.78270i			0.125838i
$490$	10.3083	+	2.74787i	0.465681	+	0.124136i
$491$	2.40662			0.108609			0.0543046	−	0.998524i	$-0.482706\pi$
$491$	2.40662			0.108609			0.0543046	+	0.998524i	$0.482706\pi$
$492$			6.47355i			0.291850i
$493$	32.0451	−	18.5012i	1.44324	−	0.833253i
$494$	19.1210	+	11.0395i	0.860292	+	0.496690i
$495$	−7.88348	+	7.90382i	−0.354336	+	0.355250i
$496$	−0.801217	+	0.462583i	−0.0359757	+	0.0207706i
$497$	0.669958	−	0.386800i	0.0300517	−	0.0173504i
$498$	4.52626	+	7.83972i	0.202827	+	0.351306i
$499$	−14.3350	−	8.27632i	−0.641723	−	0.370499i	0.143555	−	0.989642i	$-0.454147\pi$
$499$	−14.3350	−	8.27632i	−0.641723	−	0.370499i	−0.785278	+	0.619143i	$0.787480\pi$
$500$	−10.7881	+	2.93540i	−0.482459	+	0.131275i
$501$	−13.0600	+	7.54017i	−0.583476	+	0.336870i
$502$	15.0099	−	8.66600i	0.669927	−	0.386782i
$503$	11.7871	+	20.4159i	0.525562	+	0.910299i	0.999557	+	0.0297718i	$0.00947807\pi$
$503$	11.7871	+	20.4159i	0.525562	+	0.910299i	−0.473995	+	0.880527i	$0.657189\pi$
$504$			1.49299i			0.0665030i
$505$	−4.93958	−	18.3402i	−0.219808	−	0.816129i
$506$	−19.5649	−	33.8873i	−0.869764	−	1.50648i
$507$		−	37.6625i		−	1.67265i
$508$		−	9.19357i		−	0.407899i
$509$	−2.31738	−	4.01382i	−0.102716	−	0.177909i	0.810087	−	0.586310i	$-0.199420\pi$
$509$	−2.31738	−	4.01382i	−0.102716	−	0.177909i	−0.912803	+	0.408401i	$0.866087\pi$
$510$	7.10613	+	7.08784i	0.314665	+	0.313855i
$511$	−10.3162	+	17.8682i	−0.456361	+	0.790441i
$512$	1.00000			0.0441942
$513$	−1.55098	+	2.68637i	−0.0684774	+	0.118606i
$514$	−2.45518	+	4.25250i	−0.108293	+	0.187570i
$515$	−3.09883	−	11.5057i	−0.136551	−	0.507001i
$516$	−6.96561	+	4.02159i	−0.306644	+	0.177041i
$517$		−	22.5591i		−	0.992149i
$518$	−5.43494	+	7.27563i	−0.238798	+	0.319673i
$519$	17.6180			0.773346
$520$	15.3788	+	4.09950i	0.674403	+	0.179775i
$521$	−10.8756	+	18.8371i	−0.476468	+	0.825267i	−0.999636	−	0.0269626i	$-0.991416\pi$
$521$	−10.8756	+	18.8371i	−0.476468	+	0.825267i	0.523169	+	0.852229i	$0.324750\pi$
$522$	7.13932	+	4.12189i	0.312480	+	0.180410i
$523$	−16.7885	+	29.0785i	−0.734108	+	1.27151i	0.221005	+	0.975273i	$0.429066\pi$
$523$	−16.7885	+	29.0785i	−0.734108	+	1.27151i	−0.955113	+	0.296240i	$0.904267\pi$
$524$		−	7.70903i		−	0.336771i
$525$	−6.47442	−	3.71580i	−0.282567	−	0.162171i
$526$		−	18.8193i		−	0.820563i
$527$	−3.59629	+	2.07632i	−0.156657	+	0.0904458i
$528$			4.99238i			0.217266i
$529$	38.4323			1.67097
$530$	2.43479	−	9.13381i	0.105760	−	0.396747i
$531$	−4.55609	−	2.63046i	−0.197718	−	0.114152i
$532$	−4.63118			−0.200787
$533$	23.0386	+	39.9040i	0.997911	+	1.72843i
$534$	−3.92128	−	6.79186i	−0.169690	−	0.293912i
$535$	−3.36790	+	12.6343i	−0.145607	+	0.546228i
$536$	−11.5321	−	6.65806i	−0.498111	−	0.287585i
$537$	−3.08576	+	5.34469i	−0.133160	+	0.230640i
$538$	−6.25354	−	10.8315i	−0.269609	−	0.466977i
$539$	11.9093	+	20.6275i	0.512970	+	0.888490i
$540$	−0.575954	+	2.16062i	−0.0247851	+	0.0929783i
$541$		−	2.98441i		−	0.128310i	−0.997940	−	0.0641548i	$-0.979565\pi$
$541$		−	2.98441i		−	0.128310i	0.997940	−	0.0641548i	$-0.0204352\pi$
$542$	−12.1046	+	20.9658i	−0.519937	+	0.900557i
$543$	8.60266	−	4.96675i	0.369176	−	0.213144i
$544$	4.48853			0.192444
$545$	12.3315	+	12.2997i	0.528222	+	0.526863i
$546$	5.31336	+	9.20301i	0.227391	+	0.393853i
$547$	−19.7115			−0.842802			−0.421401	−	0.906874i	$-0.638461\pi$
$547$	−19.7115			−0.842802			−0.421401	+	0.906874i	$0.638461\pi$
$548$	−4.59818	−	2.65476i	−0.196425	−	0.113406i
$549$			9.67642i			0.412979i
$550$	−21.6497	−	12.4252i	−0.923148	−	0.529813i
$551$	−12.7859	+	22.1459i	−0.544698	+	0.943445i
$552$	−6.78780	−	3.91894i	−0.288908	−	0.166801i
$553$	−0.720840	−	1.24853i	−0.0306532	−	0.0530930i
$554$	−25.2183			−1.07142
$555$	−10.6721	+	8.43249i	−0.453004	+	0.357939i
$556$	7.96852			0.337941
$557$	6.44022	+	11.1548i	0.272881	+	0.472643i	0.969598	−	0.244702i	$-0.0786902\pi$
$557$	6.44022	+	11.1548i	0.272881	+	0.472643i	−0.696717	+	0.717346i	$0.745357\pi$
$558$	−0.801217	−	0.462583i	−0.0339182	−	0.0195827i
$559$	−28.6247	+	49.5795i	−1.21070	+	2.09699i
$560$	−3.22355	+	0.868201i	−0.136220	+	0.0366882i
$561$			22.4085i			0.946086i
$562$	−3.24794	−	1.87520i	−0.137006	−	0.0791004i
$563$	−4.71733			−0.198812			−0.0994059	−	0.995047i	$-0.531694\pi$
$563$	−4.71733			−0.198812			−0.0994059	+	0.995047i	$0.531694\pi$
$564$	−2.25935	−	3.91331i	−0.0951359	−	0.164780i
$565$	2.90430	−	2.91179i	0.122185	−	0.122500i
$566$	30.1738			1.26830
$567$	−1.29297	+	0.746494i	−0.0542994	+	0.0313498i
$568$	0.259078	−	0.448736i	0.0108707	−	0.0188286i
$569$			40.6559i			1.70438i	0.523230	+	0.852191i	$0.324727\pi$
$569$			40.6559i			1.70438i	−0.523230	+	0.852191i	$0.675273\pi$
$570$	−6.70215	−	1.78658i	−0.280722	−	0.0748318i
$571$	5.57259	+	9.65201i	0.233206	+	0.403924i	0.958750	−	0.284252i	$-0.0917451\pi$
$571$	5.57259	+	9.65201i	0.233206	+	0.403924i	−0.725544	+	0.688176i	$0.758412\pi$
$572$	17.7673	+	30.7738i	0.742888	+	1.28672i
$573$	4.95736	−	8.58641i	0.207097	−	0.358702i
$574$	−8.37007	−	4.83246i	−0.349360	−	0.201703i
$575$	33.8884	−	19.6821i	1.41324	−	0.820800i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−18.0545	−	31.2713i	−0.751619	−	1.30184i	−0.947038	−	0.321122i	$-0.895940\pi$
$577$	−18.0545	−	31.2713i	−0.751619	−	1.30184i	0.195419	−	0.980720i	$-0.437393\pi$
$578$	3.14690			0.130894
$579$	−14.0577	−	8.11621i	−0.584217	−	0.337298i
$580$	−4.74803	+	17.8117i	−0.197151	+	0.739589i
$581$	−13.5153			−0.560710
$582$			9.48892i			0.393329i
$583$	18.2773	−	10.5524i	0.756969	−	0.437036i
$584$			13.8195i			0.571856i
$585$	4.13911	+	15.3682i	0.171131	+	0.635395i
$586$			28.1011i			1.16084i
$587$	−15.0657	+	26.0945i	−0.621827	+	1.07704i	0.367318	+	0.930095i	$0.380276\pi$
$587$	−15.0657	+	26.0945i	−0.621827	+	1.07704i	−0.989145	+	0.146941i	$0.953057\pi$
$588$	4.13180	+	2.38549i	0.170392	+	0.0983761i
$589$	1.43491	−	2.48534i	0.0591245	−	0.102407i
$590$	3.03005	−	11.3669i	0.124745	−	0.467966i
$591$	6.49977			0.267365
$592$	−0.716002	+	6.04048i	−0.0294275	+	0.248262i
$593$		−	20.9906i		−	0.861981i	−0.902356	−	0.430991i	$-0.858164\pi$
$593$		−	20.9906i		−	0.861981i	0.902356	−	0.430991i	$-0.141836\pi$
$594$	−4.32353	+	2.49619i	−0.177397	+	0.102420i
$595$	−14.4690	+	3.89695i	−0.593172	+	0.159759i
$596$	−4.44026	+	7.69076i	−0.181880	+	0.315026i
$597$	−9.99533	+	17.3124i	−0.409082	+	0.708550i
$598$	−55.7881			−2.28135
$599$	−17.7246	+	30.6999i	−0.724207	+	1.25436i	0.235092	+	0.971973i	$0.424461\pi$
$599$	−17.7246	+	30.6999i	−0.724207	+	1.25436i	−0.959300	+	0.282390i	$0.908873\pi$
$600$	−4.99998	+	0.0128835i	−0.204123	+	0.000525966i
$601$	17.9480	+	31.0868i	0.732114	+	1.26806i	0.955978	+	0.293438i	$0.0947994\pi$
$601$	17.9480	+	31.0868i	0.732114	+	1.26806i	−0.223864	+	0.974620i	$0.571867\pi$
$602$		−	12.0084i		−	0.489425i
$603$		−	13.3161i		−	0.542275i
$604$	5.35526	+	9.27558i	0.217902	+	0.377418i
$605$	−8.09702	−	30.0635i	−0.329191	−	1.22225i
$606$		−	8.49427i		−	0.345056i
$607$	−20.3935	−	35.3226i	−0.827746	−	1.43370i	−0.899802	−	0.436298i	$-0.856289\pi$
$607$	−20.3935	−	35.3226i	−0.827746	−	1.43370i	0.0720560	−	0.997401i	$-0.477044\pi$
$608$	−2.68637	+	1.55098i	−0.108947	+	0.0629005i
$609$	−10.6589	+	6.15393i	−0.431921	+	0.249370i
$610$	−20.8926	+	5.62702i	−0.845918	+	0.227831i
$611$	−27.8540	−	16.0815i	−1.12685	−	0.650589i
$612$	2.24427	+	3.88718i	0.0907190	+	0.157130i
$613$	19.2575	−	11.1183i	0.777805	−	0.449066i	−0.0578469	−	0.998325i	$-0.518424\pi$
$613$	19.2575	−	11.1183i	0.777805	−	0.449066i	0.835652	+	0.549260i	$0.185090\pi$
$614$	11.2962	−	6.52187i	0.455878	−	0.263201i
$615$	−10.2488	−	10.2224i	−0.413270	−	0.412206i
$616$	−6.45498	−	3.72678i	−0.260079	−	0.150156i
$617$	−9.51843	+	5.49547i	−0.383197	+	0.221239i	−0.679208	−	0.733945i	$-0.737677\pi$
$617$	−9.51843	+	5.49547i	−0.383197	+	0.221239i	0.296011	+	0.955184i	$0.404343\pi$
$618$		−	5.32885i		−	0.214358i
$619$	43.9421			1.76618			0.883092	−	0.469200i	$-0.155458\pi$
$619$	43.9421			1.76618			0.883092	+	0.469200i	$0.155458\pi$
$620$	0.532853	−	1.99893i	0.0213999	−	0.0802790i
$621$		−	7.83788i		−	0.314523i
$622$	18.1342	+	10.4698i	0.727115	+	0.419800i
$623$	11.7088			0.469105
$624$	6.16416	+	3.55888i	0.246764	+	0.142469i
$625$	12.3883	−	21.7148i	0.495530	−	0.868591i
$626$	−7.90172	+	13.6862i	−0.315816	+	0.547010i
$627$	−7.74308	−	13.4114i	−0.309229	−	0.535600i
$628$			6.65528i			0.265574i
$629$	−3.21380	+	27.1129i	−0.128142	+	1.08106i
$630$	−2.36366	−	2.35758i	−0.0941705	−	0.0939281i
$631$	13.5638	−	7.83107i	0.539967	−	0.311750i	−0.205098	−	0.978741i	$-0.565751\pi$
$631$	13.5638	−	7.83107i	0.539967	−	0.311750i	0.745066	+	0.666991i	$0.232418\pi$
$632$	−0.836264	−	0.482817i	−0.0332648	−	0.0192054i
$633$	−2.70892	−	1.56399i	−0.107670	−	0.0621631i
$634$	16.8545	+	9.73093i	0.669376	+	0.386464i
$635$	14.5550	+	14.5176i	0.577598	+	0.576112i
$636$	2.11370	−	3.66104i	0.0838137	−	0.145170i
$637$	33.9587			1.34549
$638$	−35.6422	+	20.5780i	−1.41109	+	0.814693i
$639$	0.518156			0.0204979
$640$	−1.57910	+	1.58317i	−0.0624194	+	0.0625805i
$641$	−9.61289	−	16.6500i	−0.379686	−	0.657636i	0.611330	−	0.791376i	$-0.290635\pi$
$641$	−9.61289	−	16.6500i	−0.379686	−	0.657636i	−0.991017	+	0.133740i	$0.957301\pi$
$642$	−2.92376	+	5.06411i	−0.115392	+	0.199864i
$643$	−29.7837			−1.17456			−0.587278	−	0.809385i	$-0.699801\pi$
$643$	−29.7837			−1.17456			−0.587278	+	0.809385i	$0.699801\pi$
$644$	10.1341	−	5.85093i	0.399340	−	0.230559i
$645$	4.63251	−	17.3783i	0.182405	−	0.684269i
$646$	−12.0579	+	6.96161i	−0.474410	+	0.273901i
$647$	−9.75527	+	16.8966i	−0.383519	+	0.664275i	−0.991563	−	0.129629i	$-0.958621\pi$
$647$	−9.75527	+	16.8966i	−0.383519	+	0.664275i	0.608043	+	0.793904i	$0.291955\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	22.7458	−	13.1323i	0.892850	−	0.515487i
$650$	−30.7748	+	17.8737i	−1.20709	+	0.701066i
$651$	1.19621	−	0.690630i	0.0468830	−	0.0270679i
$652$	−2.78270			−0.108979
$653$	6.40287	−	11.0901i	0.250563	−	0.433989i	−0.713118	−	0.701044i	$-0.752717\pi$
$653$	6.40287	−	11.0901i	0.250563	−	0.433989i	0.963681	+	0.267056i	$0.0860508\pi$
$654$	3.89454	+	6.74554i	0.152288	+	0.263771i
$655$	12.2047	+	12.1733i	0.476879	+	0.475652i
$656$	−6.47355			−0.252750
$657$	−11.9681	+	6.90976i	−0.466918	+	0.269575i
$658$	6.74637			0.263001
$659$	7.16675	−	12.4132i	0.279177	−	0.483548i	−0.692004	−	0.721894i	$-0.743272\pi$
$659$	7.16675	−	12.4132i	0.279177	−	0.483548i	0.971180	+	0.238346i	$0.0766051\pi$
$660$	−7.90382	−	7.88348i	−0.307656	−	0.306864i
$661$	21.4678	+	12.3944i	0.834999	+	0.482087i	0.855561	−	0.517702i	$-0.173212\pi$
$661$	21.4678	+	12.3944i	0.834999	+	0.482087i	−0.0205623	+	0.999789i	$0.506546\pi$
$662$	3.62395	+	2.09229i	0.140849	+	0.0813192i
$663$	27.6680	+	15.9741i	1.07454	+	0.620384i
$664$	−7.83972	+	4.52626i	−0.304240	+	0.175653i
$665$	7.31310	−	7.33197i	0.283590	−	0.284322i
$666$	−5.58921	+	2.40016i	−0.216577	+	0.0930044i
$667$		−	64.6137i		−	2.50185i
$668$	−7.54017	−	13.0600i	−0.291738	−	0.505305i
$669$	13.8749	−	24.0321i	0.536436	−	0.929135i
$670$	28.7512	−	7.74358i	1.11076	−	0.299161i
$671$	−41.8363	−	24.1542i	−1.61507	−	0.932462i
$672$	−1.49299			−0.0575933
$673$	−9.21745	−	5.32170i	−0.355307	−	0.205136i	0.311713	−	0.950176i	$-0.399097\pi$
$673$	−9.21745	−	5.32170i	−0.355307	−	0.205136i	−0.667020	+	0.745040i	$0.732430\pi$
$674$			12.8150i			0.493614i
$675$	−2.51115	−	4.32367i	−0.0966542	−	0.166418i
$676$	37.6625			1.44856
$677$			21.2505i			0.816725i	0.912820	+	0.408362i	$0.133900\pi$
$677$			21.2505i			0.816725i	−0.912820	+	0.408362i	$0.866100\pi$
$678$	1.59280	−	0.919606i	0.0611713	−	0.0353172i
$679$	−12.2689	−	7.08342i	−0.470835	−	0.271837i
$680$	−7.08784	+	7.10613i	−0.271806	+	0.272508i
$681$	17.1376	−	9.89438i	0.656713	−	0.379153i
$682$	3.99998	−	2.30939i	0.153167	−	0.0884312i
$683$	14.8676	+	25.7514i	0.568893	+	0.985351i	0.996676	+	0.0814698i	$0.0259614\pi$
$683$	14.8676	+	25.7514i	0.568893	+	0.985351i	−0.427783	+	0.903881i	$0.640705\pi$
$684$	−2.68637	−	1.55098i	−0.102716	−	0.0593031i
$685$	11.4639	−	3.08759i	0.438015	−	0.117971i
$686$	−15.2195	+	8.78697i	−0.581082	+	0.335488i
$687$	7.51008	−	4.33595i	0.286527	−	0.165427i
$688$	−4.02159	−	6.96561i	−0.153322	−	0.265561i
$689$		−	30.0896i		−	1.14632i
$690$	16.9230	−	4.55788i	0.644247	−	0.173515i
$691$	16.1943	+	28.0494i	0.616060	+	1.06705i	0.990197	+	0.139675i	$0.0446056\pi$
$691$	16.1943	+	28.0494i	0.616060	+	1.06705i	−0.374137	+	0.927373i	$0.622061\pi$
$692$			17.6180i			0.669737i
$693$		−	7.45357i		−	0.283138i
$694$	−6.03775	−	10.4577i	−0.229190	−	0.396969i
$695$	−12.5831	+	12.6156i	−0.477304	+	0.478535i
$696$	−4.12189	+	7.13932i	−0.156240	+	0.270615i
$697$	−29.0567			−1.10060
$698$	3.57899	−	6.19899i	0.135467	−	0.234635i
$699$	1.06868	−	1.85101i	0.0404212	−	0.0700115i
$700$	3.71580	−	6.47442i	0.140444	−	0.244710i
$701$	−22.1818	+	12.8066i	−0.837793	+	0.483700i	−0.856514	−	0.516125i	$-0.827374\pi$
$701$	−22.1818	+	12.8066i	−0.837793	+	0.483700i	0.0187202	+	0.999825i	$0.494041\pi$
$702$			7.11776i			0.268642i
$703$	−7.44520	−	17.3375i	−0.280801	−	0.653895i
$704$	−4.99238			−0.188158
$705$	9.76320	+	2.60257i	0.367704	+	0.0980183i
$706$	−16.3563	+	28.3299i	−0.615576	+	1.06621i
$707$	10.9828	+	6.34092i	0.413051	+	0.238475i
$708$	2.63046	−	4.55609i	0.0988588	−	0.171229i
$709$		−	36.3231i		−	1.36414i	−0.731286	−	0.682071i	$-0.761080\pi$
$709$		−	36.3231i		−	1.36414i	0.731286	−	0.682071i	$-0.238920\pi$
$710$	0.301318	+	1.11877i	0.0113082	+	0.0419865i
$711$		−	0.965634i		−	0.0362141i
$712$	6.79186	−	3.92128i	0.254536	−	0.146956i
$713$			7.25134i			0.271565i
$714$	−6.70132			−0.250791
$715$	−76.7767	−	20.4663i	−2.87129	−	0.765395i
$716$	−5.34469	−	3.08576i	−0.199740	−	0.115320i
$717$	2.31041			0.0862840
$718$	13.1918	+	22.8488i	0.492313	+	0.852711i
$719$	−2.41440	−	4.18186i	−0.0900419	−	0.155957i	0.817487	−	0.575948i	$-0.195367\pi$
$719$	−2.41440	−	4.18186i	−0.0900419	−	0.155957i	−0.907529	+	0.419990i	$0.862033\pi$
$720$	−2.16062	−	0.575954i	−0.0805215	−	0.0214645i
$721$	6.89002	+	3.97796i	0.256598	+	0.148147i
$722$	−4.68893	+	8.12147i	−0.174504	+	0.302250i
$723$	10.4734	+	18.1405i	0.389510	+	0.674652i
$724$	4.96675	+	8.60266i	0.184588	+	0.319715i
$725$	−20.7014	−	35.6434i	−0.768829	−	1.32376i
$726$		−	13.9239i		−	0.516764i
$727$	1.93804	−	3.35679i	0.0718780	−	0.124496i	−0.827846	−	0.560955i	$-0.810434\pi$
$727$	1.93804	−	3.35679i	0.0718780	−	0.124496i	0.899724	+	0.436459i	$0.143767\pi$
$728$	−9.20301	+	5.31336i	−0.341086	+	0.196926i
$729$	−1.00000			−0.0370370
$730$	−21.8787	−	21.8224i	−0.809768	−	0.807684i
$731$	−18.0511	−	31.2653i	−0.667642	−	1.15639i
$732$	−9.67642			−0.357651
$733$	24.0960	+	13.9118i	0.890006	+	0.513845i	0.873944	−	0.486026i	$-0.161554\pi$
$733$	24.0960	+	13.9118i	0.890006	+	0.513845i	0.0160613	+	0.999871i	$0.494887\pi$
$734$		−	1.55468i		−	0.0573842i
$735$	−10.3012	+	2.77442i	−0.379965	+	0.102336i
$736$	3.91894	−	6.78780i	0.144454	−	0.250202i
$737$	57.5727	+	33.2396i	2.12072	+	1.22440i
$738$	−3.23677	−	5.60626i	−0.119147	−	0.206369i
$739$	−45.5267			−1.67473			−0.837364	−	0.546646i	$-0.815905\pi$
$739$	−45.5267			−1.67473			−0.837364	+	0.546646i	$0.815905\pi$
$740$	−8.43249	−	10.6721i	−0.309984	−	0.392313i
$741$	−22.0790			−0.811091
$742$	3.15573	+	5.46588i	0.115850	+	0.200659i
$743$	−24.4648	−	14.1248i	−0.897527	−	0.518188i	−0.0211303	−	0.999777i	$-0.506726\pi$
$743$	−24.4648	−	14.1248i	−0.897527	−	0.518188i	−0.876397	+	0.481589i	$0.840060\pi$
$744$	0.462583	−	0.801217i	0.0169591	−	0.0293740i
$745$	−5.16420	−	19.1742i	−0.189201	−	0.702488i
$746$		−	27.3486i		−	1.00130i
$747$	−7.83972	−	4.52626i	−0.286840	−	0.165607i
$748$	−22.4085			−0.819335
$749$	−4.36514	−	7.56065i	−0.159499	−	0.276260i
$750$	7.87508	−	7.93619i	0.287557	−	0.289789i
$751$	14.1263			0.515474			0.257737	−	0.966215i	$-0.417023\pi$
$751$	14.1263			0.515474			0.257737	+	0.966215i	$0.417023\pi$
$752$	3.91331	−	2.25935i	0.142704	−	0.0823901i
$753$	−8.66600	+	15.0099i	−0.315806	+	0.546993i
$754$			58.6772i			2.13690i
$755$	−23.1413	−	6.16876i	−0.842200	−	0.224504i
$756$	−0.746494	−	1.29297i	−0.0271497	−	0.0470247i
$757$	20.2892	+	35.1419i	0.737423	+	1.27725i	0.953652	+	0.300911i	$0.0972907\pi$
$757$	20.2892	+	35.1419i	0.737423	+	1.27725i	−0.216230	+	0.976343i	$0.569376\pi$
$758$	3.06678	−	5.31181i	0.111390	−	0.192934i
$759$	33.8873	+	19.5649i	1.23003	+	0.710159i
$760$	1.78658	−	6.70215i	0.0648062	−	0.243112i
$761$	−0.220861	−	0.382543i	−0.00800622	−	0.0138672i	0.861995	−	0.506918i	$-0.169215\pi$
$761$	−0.220861	−	0.382543i	−0.00800622	−	0.0138672i	−0.870001	+	0.493050i	$0.835882\pi$
$762$	4.59678	+	7.96186i	0.166524	+	0.288428i
$763$	−11.6290			−0.420998
$764$	8.58641	+	4.95736i	0.310645	+	0.179351i
$765$	−9.69801	−	2.58519i	−0.350632	−	0.0934676i
$766$	34.9758			1.26373
$767$		−	37.4460i		−	1.35210i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$		−	2.58497i		−	0.0932163i	−0.998913	−	0.0466082i	$-0.985159\pi$
$769$		−	2.58497i		−	0.0932163i	0.998913	−	0.0466082i	$-0.0148412\pi$
$770$	16.0932	−	4.33439i	0.579959	−	0.156201i
$771$		−	4.91036i		−	0.176842i
$772$	8.11621	−	14.0577i	0.292109	−	0.505947i
$773$	39.0202	+	22.5283i	1.40346	+	0.810288i	0.994746	−	0.102374i	$-0.0326438\pi$
$773$	39.0202	+	22.5283i	1.40346	+	0.810288i	0.408715	+	0.912662i	$0.365977\pi$
$774$	4.02159	−	6.96561i	0.144553	−	0.250374i
$775$	2.32323	+	4.00011i	0.0834528	+	0.143688i
$776$	−9.48892			−0.340633
$777$	1.06898	−	9.01836i	0.0383495	−	0.323532i
$778$			19.0085i			0.681487i
$779$	17.3904	−	10.0403i	0.623074	−	0.359732i
$780$	−15.3682	+	4.13911i	−0.550268	+	0.148204i
$781$	−1.29342	+	2.24026i	−0.0462821	+	0.0801629i
$782$	17.5903	−	30.4673i	0.629027	−	1.08951i
$783$	−8.24378			−0.294609
$784$	−2.38549	+	4.13180i	−0.0851962	+	0.147564i
$785$	−10.5365	−	10.5094i	−0.376063	−	0.375095i
$786$	3.85452	+	6.67622i	0.137486	+	0.238133i
$787$		−	18.2922i		−	0.652045i	−0.945362	−	0.326022i	$-0.894292\pi$
$787$		−	18.2922i		−	0.652045i	0.945362	−	0.326022i	$-0.105708\pi$
$788$			6.49977i			0.231545i
$789$	9.40967	+	16.2980i	0.334993	+	0.580225i
$790$	2.08493	−	0.561535i	0.0741784	−	0.0199785i
$791$			2.74592i			0.0976337i
$792$	−2.49619	−	4.32353i	−0.0886983	−	0.153630i
$793$	−59.6470	+	34.4372i	−2.11813	+	1.22290i
$794$	13.0018	−	7.50661i	0.461418	−	0.266400i
$795$	2.45832	+	9.12750i	0.0871874	+	0.323719i
$796$	−17.3124	−	9.99533i	−0.613623	−	0.354275i
$797$	27.5893	+	47.7861i	0.977264	+	1.69267i	0.672254	+	0.740321i	$0.265326\pi$
$797$	27.5893	+	47.7861i	0.977264	+	1.69267i	0.305010	+	0.952349i	$0.401340\pi$
$798$	4.01072	−	2.31559i	0.141978	−	0.0819711i
$799$	17.5650	−	10.1412i	0.621406	−	0.358769i
$800$	−0.0128835	−	4.99998i	−0.000455500	−	0.176776i
$801$	6.79186	+	3.92128i	0.239978	+	0.138552i
$802$	−2.46478	+	1.42304i	−0.0870345	+	0.0502494i
$803$		−	68.9924i		−	2.43469i
$804$	13.3161			0.469624
$805$	−6.73973	+	25.2833i	−0.237544	+	0.891118i
$806$		−	6.58510i		−	0.231950i
$807$	10.8315	+	6.25354i	0.381285	+	0.220135i
$808$	8.49427			0.298827
$809$	−27.2852	−	15.7531i	−0.959295	−	0.553849i	−0.0633389	−	0.997992i	$-0.520175\pi$
$809$	−27.2852	−	15.7531i	−0.959295	−	0.553849i	−0.895956	+	0.444143i	$0.853508\pi$
$810$	−0.581519	−	2.15913i	−0.0204325	−	0.0758640i
$811$	−16.2893	+	28.2139i	−0.571995	+	0.990725i	0.424366	+	0.905491i	$0.360497\pi$
$811$	−16.2893	+	28.2139i	−0.571995	+	0.990725i	−0.996361	+	0.0852340i	$0.972836\pi$
$812$	−6.15393	−	10.6589i	−0.215961	−	0.374055i
$813$		−	24.2092i		−	0.849053i
$814$	3.57456	−	30.1564i	0.125288	−	1.05698i
$815$	4.39416	−	4.40550i	0.153921	−	0.154318i
$816$	−3.88718	+	2.24427i	−0.136079	+	0.0785650i
$817$	21.6070	+	12.4748i	0.755934	+	0.436438i
$818$	−12.4387	−	7.18152i	−0.434911	−	0.251096i
$819$	−9.20301	−	5.31336i	−0.321579	−	0.185664i
$820$	10.2224	−	10.2488i	0.356981	−	0.357902i
$821$	14.7980	−	25.6308i	0.516453	−	0.894522i	−0.483365	−	0.875419i	$-0.660586\pi$
$821$	14.7980	−	25.6308i	0.516453	−	0.894522i	0.999818	−	0.0191031i	$-0.00608107\pi$
$822$	5.30952			0.185191
$823$	−10.1925	+	5.88464i	−0.355288	+	0.205126i	−0.667012	−	0.745047i	$-0.732427\pi$
$823$	−10.1925	+	5.88464i	−0.355288	+	0.205126i	0.311724	+	0.950173i	$0.399094\pi$
$824$	5.32885			0.185639
$825$	24.9618	−	0.0643192i	0.869060	−	0.00223931i
$826$	3.92725	+	6.80219i	0.136646	+	0.236679i
$827$	−11.2130	+	19.4215i	−0.389915	+	0.675352i	−0.992438	−	0.122749i	$-0.960829\pi$
$827$	−11.2130	+	19.4215i	−0.389915	+	0.675352i	0.602523	+	0.798102i	$0.294162\pi$
$828$	7.83788			0.272385
$829$	12.5950	−	7.27171i	0.437441	−	0.252557i	−0.265070	−	0.964229i	$-0.585395\pi$
$829$	12.5950	−	7.27171i	0.437441	−	0.252557i	0.702512	+	0.711672i	$0.252062\pi$
$830$	5.21384	−	19.5591i	0.180975	−	0.678905i
$831$	21.8397	−	12.6092i	0.757611	−	0.437407i
$832$	−3.55888	+	6.16416i	−0.123382	+	0.213704i
$833$	−10.7074	+	18.5457i	−0.370988	+	0.642570i
$834$	−6.90094	+	3.98426i	−0.238960	+	0.137964i
$835$	32.5829	+	8.68558i	1.12758	+	0.300577i
$836$	13.4114	−	7.74308i	0.463843	−	0.267800i
$837$	0.925166			0.0319784
$838$	0.643425	−	1.11444i	0.0222267	−	0.0384978i
$839$	−24.6097	−	42.6252i	−0.849620	−	1.47158i	−0.881548	−	0.472094i	$-0.843498\pi$
$839$	−24.6097	−	42.6252i	−0.849620	−	1.47158i	0.0319284	−	0.999490i	$-0.489835\pi$
$840$	2.35758	−	2.36366i	0.0813442	−	0.0815540i
$841$	−38.9598			−1.34344
$842$	34.6721	−	20.0180i	1.19488	−	0.689865i
$843$	3.75039			0.129170
$844$	1.56399	−	2.70892i	0.0538349	−	0.0932447i
$845$	−59.4728	+	59.6263i	−2.04593	+	2.05121i
$846$	3.91331	+	2.25935i	0.134543	+	0.0776782i
$847$	18.0031	+	10.3941i	0.618595	+	0.357146i
$848$	3.66104	+	2.11370i	0.125721	+	0.0725848i
$849$	−26.1313	+	15.0869i	−0.896824	+	0.517782i
$850$	−0.0578279	−	22.4426i	−0.00198348	−	0.769774i
$851$	38.1956	+	28.5323i	1.30933	+	0.978076i
$852$			0.518156i			0.0177517i
$853$	−9.99118	−	17.3052i	−0.342092	−	0.592520i	0.642729	−	0.766093i	$-0.277802\pi$
$853$	−9.99118	−	17.3052i	−0.342092	−	0.592520i	−0.984821	+	0.173573i	$0.944469\pi$
$854$	7.22339	−	12.5113i	0.247179	−	0.428127i
$855$	6.69752	−	1.80385i	0.229050	−	0.0616903i
$856$	−5.06411	−	2.92376i	−0.173088	−	0.0999322i
$857$	−0.870779			−0.0297453			−0.0148726	−	0.999889i	$-0.504734\pi$
$857$	−0.870779			−0.0297453			−0.0148726	+	0.999889i	$0.504734\pi$
$858$	−30.7738	−	17.7673i	−1.05060	−	0.606565i
$859$		−	43.4472i		−	1.48240i	−0.671284	−	0.741200i	$-0.734257\pi$
$859$		−	43.4472i		−	1.48240i	0.671284	−	0.741200i	$-0.265743\pi$
$860$	17.3783	+	4.63251i	0.592594	+	0.157967i
$861$	9.66493			0.329380
$862$		−	7.31830i		−	0.249262i
$863$	11.6269	−	6.71281i	0.395785	−	0.228507i	−0.288879	−	0.957366i	$-0.593282\pi$
$863$	11.6269	−	6.71281i	0.395785	−	0.228507i	0.684664	+	0.728859i	$0.259949\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−27.8924	−	27.8207i	−0.948371	−	0.945931i
$866$	−6.60159	+	3.81143i	−0.224331	+	0.129518i
$867$	−2.72530	+	1.57345i	−0.0925560	+	0.0534372i
$868$	0.690630	+	1.19621i	0.0234415	+	0.0406019i
$869$	4.17495	+	2.41041i	0.141626	+	0.0817675i
$870$	−4.79391	−	17.7994i	−0.162529	−	0.603455i
$871$	82.0827	−	47.3905i	2.78127	−	1.60577i
$872$	−6.74554	+	3.89454i	−0.228433	+	0.131886i
$873$	−4.74446	−	8.21765i	−0.160576	−	0.278125i
$874$			24.3128i			0.822391i
$875$	4.38252	+	16.1065i	0.148156	+	0.544500i
$876$	−6.90976	−	11.9681i	−0.233459	−	0.404363i
$877$			37.0309i			1.25044i	0.780447	+	0.625222i	$0.214992\pi$
$877$			37.0309i			1.25044i	−0.780447	+	0.625222i	$0.785008\pi$
$878$		−	24.9488i		−	0.841980i
$879$	−14.0505	−	24.3362i	−0.473913	−	0.820841i
$880$	7.88348	−	7.90382i	0.265752	−	0.266438i
$881$	−10.6602	+	18.4639i	−0.359150	+	0.622066i	−0.987819	−	0.155607i	$-0.950267\pi$
$881$	−10.6602	+	18.4639i	−0.359150	+	0.622066i	0.628669	+	0.777673i	$0.283600\pi$
$882$	−4.77099			−0.160648
$883$	−1.95007	+	3.37762i	−0.0656250	+	0.113666i	−0.896971	−	0.442089i	$-0.854237\pi$
$883$	−1.95007	+	3.37762i	−0.0656250	+	0.113666i	0.831346	+	0.555755i	$0.187571\pi$
$884$	−15.9741	+	27.6680i	−0.537268	+	0.930576i
$885$	3.05933	+	11.3590i	0.102838	+	0.381829i
$886$	15.9148	−	9.18843i	0.534669	−	0.308691i
$887$			2.91300i			0.0978089i	0.998803	+	0.0489045i	$0.0155730\pi$
$887$			2.91300i			0.0978089i	−0.998803	+	0.0489045i	$0.984427\pi$
$888$	−2.40016	−	5.58921i	−0.0805442	−	0.187561i
$889$	−13.7259			−0.460351
$890$	−4.51695	+	16.9448i	−0.151409	+	0.567991i
$891$	2.49619	−	4.32353i	0.0836256	−	0.144844i
$892$	24.0321	+	13.8749i	0.804654	+	0.464567i
$893$	−7.00841	+	12.1389i	−0.234528	+	0.406214i
$894$		−	8.88053i		−	0.297009i
$895$	13.3251	−	3.58885i	0.445408	−	0.119962i
$896$		−	1.49299i		−	0.0498772i
$897$	48.3139	−	27.8941i	1.61316	−	0.931356i
$898$		−	6.57988i		−	0.219573i
$899$	7.62686			0.254370
$900$	4.32367	−	2.51115i	0.144122	−	0.0837050i
$901$	16.4327	+	9.48741i	0.547452	+	0.316071i
$902$	32.3184			1.07609
$903$	6.00419	+	10.3996i	0.199807	+	0.346076i
$904$	0.919606	+	1.59280i	0.0305856	+	0.0529759i
$905$	−21.4625	−	5.72124i	−0.713438	−	0.190180i
$906$	−9.27558	−	5.35526i	−0.308160	−	0.177917i
$907$	6.42331	−	11.1255i	0.213283	−	0.369416i	−0.739457	−	0.673203i	$-0.764918\pi$
$907$	6.42331	−	11.1255i	0.213283	−	0.369416i	0.952740	+	0.303787i	$0.0982512\pi$
$908$	9.89438	+	17.1376i	0.328356	+	0.568730i
$909$	4.24713	+	7.35625i	0.140869	+	0.243992i
$910$	6.12050	−	22.9603i	0.202893	−	0.761127i
$911$			51.8090i			1.71651i	0.513226	+	0.858254i	$0.328450\pi$
$911$			51.8090i			1.71651i	−0.513226	+	0.858254i	$0.671550\pi$
$912$	1.55098	−	2.68637i	0.0513580	−	0.0889547i
$913$	39.1389	−	22.5969i	1.29531	−	0.747847i
$914$	23.4990			0.777279
$915$	15.2800	−	15.3195i	0.505142	−	0.506446i
$916$	4.33595	+	7.51008i	0.143264	+	0.248140i
$917$	−11.5095			−0.380077
$918$	−3.88718	−	2.24427i	−0.128296	−	0.0740718i
$919$			27.5296i			0.908118i	0.890972	+	0.454059i	$0.150025\pi$
$919$			27.5296i			0.908118i	−0.890972	+	0.454059i	$0.849975\pi$
$920$	4.55788	+	16.9230i	0.150269	+	0.557934i
$921$	−6.52187	+	11.2962i	−0.214903	+	0.372223i
$922$	−9.55328	−	5.51559i	−0.314621	−	0.181646i
$923$	1.84405	+	3.19399i	0.0606978	+	0.105132i
$924$	7.45357			0.245204
$925$	30.2115	+	3.50218i	0.993348	+	0.115151i
$926$	12.0646			0.396469
$927$	2.66443	+	4.61492i	0.0875113	+	0.151574i
$928$	−7.13932	−	4.12189i	−0.234360	−	0.135308i
$929$	16.2820	−	28.2013i	0.534195	−	0.925253i	−0.465007	−	0.885307i	$-0.653948\pi$
$929$	16.2820	−	28.2013i	0.534195	−	0.925253i	0.999202	−	0.0399460i	$-0.0127186\pi$
$930$	0.538002	+	1.99755i	0.0176418	+	0.0655023i
$931$		−	14.7994i		−	0.485031i
$932$	1.85101	+	1.06868i	0.0606317	+	0.0350057i
$933$	−20.9396			−0.685531
$934$	−4.04116	−	6.99950i	−0.132231	−	0.229031i
$935$	35.3852	−	35.4765i	1.15722	−	1.16021i
$936$	−7.11776			−0.232651
$937$	−20.2888	+	11.7137i	−0.662806	+	0.382671i	−0.793345	−	0.608772i	$-0.791663\pi$
$937$	−20.2888	+	11.7137i	−0.662806	+	0.382671i	0.130539	+	0.991443i	$0.458329\pi$
$938$	−9.94041	+	17.2173i	−0.324566	+	0.562165i
$939$		−	15.8034i		−	0.515726i
$940$	−2.60257	+	9.76320i	−0.0848863	+	0.318441i
$941$	−15.7366	−	27.2565i	−0.512997	−	0.888538i	−0.999886	−	0.0150737i	$-0.995202\pi$
$941$	−15.7366	−	27.2565i	−0.512997	−	0.888538i	0.486889	−	0.873464i	$-0.338132\pi$
$942$	−3.32764	−	5.76364i	−0.108420	−	0.187789i
$943$	−25.3694	+	43.9412i	−0.826143	+	1.43092i
$944$	4.55609	+	2.63046i	0.148288	+	0.0856143i
$945$	3.22578	+	0.859892i	0.104935	+	0.0279723i
$946$	20.0773	+	34.7750i	0.652771	+	1.13063i
$947$	−12.4533	−	21.5698i	−0.404679	−	0.700925i	0.589605	−	0.807692i	$-0.299284\pi$
$947$	−12.4533	−	21.5698i	−0.404679	−	0.700925i	−0.994284	+	0.106767i	$0.965950\pi$
$948$	0.965634			0.0313623
$949$	−85.1857	−	49.1820i	−2.76525	−	1.59652i
$950$	7.78948	+	13.4118i	0.252724	+	0.435138i
$951$	−19.4619			−0.631094
$952$		−	6.70132i		−	0.217191i
$953$	−16.8347	+	9.71953i	−0.545330	+	0.314846i	−0.747236	−	0.664558i	$-0.768620\pi$
$953$	−16.8347	+	9.71953i	−0.545330	+	0.314846i	0.201906	+	0.979405i	$0.435286\pi$
$954$			4.22740i			0.136867i
$955$	−21.4072	+	5.76560i	−0.692720	+	0.186571i
$956$			2.31041i			0.0747241i
$957$	20.5780	−	35.6422i	0.665194	−	1.15215i
$958$	14.6391	+	8.45188i	0.472968	+	0.273068i
$959$	−3.96353	+	6.86503i	−0.127989	+	0.221683i
$960$	0.575954	−	2.16062i	0.0185888	−	0.0697337i
$961$	30.1441			0.972389
$962$	−34.6863	−	25.9109i	−1.11833	−	0.835400i
$963$		−	5.84753i		−	0.188434i
$964$	−18.1405	+	10.4734i	−0.584266	+	0.337326i
$965$	9.43946	+	35.0479i	0.303867	+	1.12823i
$966$	−5.85093	+	10.1341i	−0.188251	+	0.326060i
$967$	−18.3367	+	31.7601i	−0.589669	+	1.02134i	0.404607	+	0.914491i	$0.367408\pi$
$967$	−18.3367	+	31.7601i	−0.589669	+	1.02134i	−0.994276	+	0.106846i	$0.965925\pi$
$968$	13.9239			0.447531
$969$	6.96161	−	12.0579i	0.223639	−	0.387355i
$970$	14.9840	−	15.0226i	0.481106	−	0.482347i
$971$	−29.1049	−	50.4111i	−0.934020	−	1.61777i	−0.776372	−	0.630274i	$-0.782942\pi$
$971$	−29.1049	−	50.4111i	−0.934020	−	1.61777i	−0.157647	−	0.987495i	$-0.550391\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	11.8969i		−	0.381397i
$974$	−16.6109	−	28.7709i	−0.532247	−	0.921879i
$975$	17.7149	−	30.8665i	0.567331	−	0.988520i
$976$		−	9.67642i		−	0.309735i
$977$	5.87311	+	10.1725i	0.187898	+	0.325448i	0.944549	−	0.328370i	$-0.106499\pi$
$977$	5.87311	+	10.1725i	0.187898	+	0.325448i	−0.756652	+	0.653818i	$0.773166\pi$
$978$	2.40989	−	1.39135i	0.0770597	−	0.0444904i
$979$	−33.9076	+	19.5765i	−1.08369	+	0.625669i
$980$	−2.77442	−	10.3012i	−0.0886256	−	0.329059i
$981$	−6.74554	−	3.89454i	−0.215368	−	0.124343i
$982$	−1.20331	−	2.08419i	−0.0383992	−	0.0665093i
$983$	−34.2180	+	19.7558i	−1.09138	+	0.630111i	−0.933945	−	0.357418i	$-0.883657\pi$
$983$	−34.2180	+	19.7558i	−1.09138	+	0.630111i	−0.157439	+	0.987529i	$0.550324\pi$
$984$	5.60626	−	3.23677i	0.178721	−	0.103185i
$985$	−10.2903	−	10.2638i	−0.327875	−	0.327032i
$986$	−32.0451	−	18.5012i	−1.02052	−	0.589199i
$987$	−5.84253	+	3.37319i	−0.185970	+	0.107370i
$988$		−	22.0790i		−	0.702426i
$989$	−63.0415			−2.00460
$990$	10.7866	+	2.87538i	0.342822	+	0.0913857i
$991$			10.4417i			0.331692i	0.986152	+	0.165846i	$0.0530355\pi$
$991$			10.4417i			0.331692i	−0.986152	+	0.165846i	$0.946965\pi$
$992$	0.801217	+	0.462583i	0.0254387	+	0.0146870i
$993$	−4.18458			−0.132794
$994$	−0.669958	−	0.386800i	−0.0212498	−	0.0122686i
$995$	43.1624	−	11.6250i	1.36834	−	0.368536i
$996$	4.52626	−	7.83972i	0.143420	−	0.248411i
$997$	−11.9343	−	20.6708i	−0.377962	−	0.654650i	0.612804	−	0.790235i	$-0.290042\pi$
$997$	−11.9343	−	20.6708i	−0.377962	−	0.654650i	−0.990766	+	0.135586i	$0.956708\pi$
$998$			16.5526i			0.523965i
$999$	3.64031	−	4.87320i	0.115174	−	0.154181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.529.17	✓	36
5.4	even	2		1110.2.ba.b.529.2	yes	36
37.27	even	6		1110.2.ba.b.619.2	yes	36
185.64	even	6	inner	1110.2.ba.a.619.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.17	✓	36	1.1	even	1	trivial
1110.2.ba.a.619.17	yes	36	185.64	even	6	inner
1110.2.ba.b.529.2	yes	36	5.4	even	2
1110.2.ba.b.619.2	yes	36	37.27	even	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.581519 - 2.15913i) q^{5} -1.00000i q^{6} +(1.29297 + 0.746494i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.581519 - 2.15913i) q^{5} -1.00000i q^{6} +(1.29297 + 0.746494i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.57910 + 1.58317i) q^{10} -4.99238 q^{11} +(-0.866025 + 0.500000i) q^{12} +(-3.55888 + 6.16416i) q^{13} -1.49299i q^{14} +(0.575954 - 2.16062i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.24427 - 3.88718i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.68637 + 1.55098i) q^{19} +(2.16062 + 0.575954i) q^{20} +(0.746494 + 1.29297i) q^{21} +(2.49619 + 4.32353i) q^{22} -7.83788 q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.32367 + 2.51115i) q^{25} +7.11776 q^{26} +1.00000i q^{27} +(-1.29297 + 0.746494i) q^{28} +8.24378i q^{29} +(-2.15913 + 0.581519i) q^{30} -0.925166i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.32353 - 2.49619i) q^{33} +(-2.24427 + 3.88718i) q^{34} +(0.859892 - 3.22578i) q^{35} -1.00000 q^{36} +(-4.87320 - 3.64031i) q^{37} -3.10196i q^{38} +(-6.16416 + 3.55888i) q^{39} +(-0.581519 - 2.15913i) q^{40} +(3.23677 - 5.60626i) q^{41} +(0.746494 - 1.29297i) q^{42} +8.04319 q^{43} +(2.49619 - 4.32353i) q^{44} +(1.57910 - 1.58317i) q^{45} +(3.91894 + 6.78780i) q^{46} +4.51871i q^{47} -1.00000i q^{48} +(-2.38549 - 4.13180i) q^{49} +(4.33655 + 2.48883i) q^{50} -4.48853i q^{51} +(-3.55888 - 6.16416i) q^{52} +(-3.66104 + 2.11370i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.90317 + 10.7792i) q^{55} +(1.29297 + 0.746494i) q^{56} +(1.55098 + 2.68637i) q^{57} +(7.13932 - 4.12189i) q^{58} +(-4.55609 + 2.63046i) q^{59} +(1.58317 + 1.57910i) q^{60} +(8.38002 + 4.83821i) q^{61} +(-0.801217 + 0.462583i) q^{62} +1.49299i q^{63} +1.00000 q^{64} +(15.3788 + 4.09950i) q^{65} +4.99238i q^{66} +(-11.5321 - 6.65806i) q^{67} +4.48853 q^{68} +(-6.78780 - 3.91894i) q^{69} +(-3.22355 + 0.868201i) q^{70} +(0.259078 - 0.448736i) q^{71} +(0.500000 + 0.866025i) q^{72} +13.8195i q^{73} +(-0.716002 + 6.04048i) q^{74} +(-4.99998 + 0.0128835i) q^{75} +(-2.68637 + 1.55098i) q^{76} +(-6.45498 - 3.72678i) q^{77} +(6.16416 + 3.55888i) q^{78} +(-0.836264 - 0.482817i) q^{79} +(-1.57910 + 1.58317i) q^{80} +(-0.500000 + 0.866025i) q^{81} -6.47355 q^{82} +(-7.83972 + 4.52626i) q^{83} -1.49299 q^{84} +(-7.08784 + 7.10613i) q^{85} +(-4.02159 - 6.96561i) q^{86} +(-4.12189 + 7.13932i) q^{87} -4.99238 q^{88} +(6.79186 - 3.92128i) q^{89} +(-2.16062 - 0.575954i) q^{90} +(-9.20301 + 5.31336i) q^{91} +(3.91894 - 6.78780i) q^{92} +(0.462583 - 0.801217i) q^{93} +(3.91331 - 2.25935i) q^{94} +(1.78658 - 6.70215i) q^{95} +(-0.866025 + 0.500000i) q^{96} -9.48892 q^{97} +(-2.38549 + 4.13180i) q^{98} +(-2.49619 - 4.32353i) 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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