LMFDB - Embedded newform 1110.2.ba.b.529.2

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			529.2
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.b.619.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16062 + 0.575954i) q^{5} -1.00000i q^{6} +(-1.29297 - 0.746494i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16062 + 0.575954i) 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} +(2.15913 + 0.581519i) 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} +(0.581519 - 2.15913i) q^{20} +(0.746494 + 1.29297i) q^{21} +(-2.49619 - 4.32353i) q^{22} +7.83788 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.33655 - 2.48883i) q^{25} +7.11776 q^{26} -1.00000i q^{27} +(1.29297 - 0.746494i) q^{28} +8.24378i q^{29} +(0.575954 + 2.16062i) q^{30} -0.925166i q^{31} +(0.500000 - 0.866025i) q^{32} +(4.32353 + 2.49619i) q^{33} +(-2.24427 + 3.88718i) q^{34} +(3.22355 + 0.868201i) q^{35} -1.00000 q^{36} +(4.87320 + 3.64031i) q^{37} +3.10196i q^{38} +(-6.16416 + 3.55888i) q^{39} +(2.16062 - 0.575954i) 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} +(4.32367 + 2.51115i) q^{50} -4.48853i q^{51} +(3.55888 + 6.16416i) q^{52} +(3.66104 - 2.11370i) q^{53} +(0.866025 - 0.500000i) q^{54} +(10.7866 - 2.87538i) 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} +(-4.13911 + 15.3682i) q^{65} +4.99238i q^{66} +(11.5321 + 6.65806i) q^{67} -4.48853 q^{68} +(-6.78780 - 3.91894i) q^{69} +(0.859892 + 3.22578i) 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} +(0.581519 - 2.15913i) 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} +(-6.69752 - 1.80385i) 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} + 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$5$	−2.16062	+	0.575954i	−0.966258	+	0.257574i
$5$	−2.16062	+	0.575954i	−0.966258	+	0.257574i
$6$		−	1.00000i		−	0.408248i
$7$	−1.29297	−	0.746494i	−0.488695	−	0.282148i	0.235338	−	0.971914i	$-0.424380\pi$
$7$	−1.29297	−	0.746494i	−0.488695	−	0.282148i	−0.724033	+	0.689765i	$0.757714\pi$
$8$	−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	$-0.384605\pi$
$13$	3.55888	−	6.16416i	0.987055	−	1.70963i	0.632421	−	0.774625i	$-0.282061\pi$
$14$		−	1.49299i		−	0.399018i
$15$	2.15913	+	0.581519i	0.557485	+	0.150148i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.24427	+	3.88718i	0.544314	+	0.942780i	0.998650	+	0.0519493i	$0.0165434\pi$
$17$	2.24427	+	3.88718i	0.544314	+	0.942780i	−0.454335	+	0.890831i	$0.650123\pi$
$18$	−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	$0.550869\pi$
$20$	0.581519	−	2.15913i	0.130032	−	0.482796i
$21$	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	$-0.195550\pi$
$23$	7.83788			1.63431			0.817155	+	0.576417i	$0.195550\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	4.33655	−	2.48883i	0.867311	−	0.497767i
$26$	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	$0.722534\pi$
$30$	0.575954	+	2.16062i	0.105154	+	0.394473i
$31$		−	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
$35$	3.22355	+	0.868201i	0.544880	+	0.146753i
$36$	−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
$40$	2.16062	−	0.575954i	0.341624	−	0.0910663i
$41$	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	$-0.710153\pi$
$43$	−8.04319			−1.22657			−0.613287	+	0.789860i	$0.710153\pi$
$44$	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	$-0.893099\pi$
$47$		−	4.51871i		−	0.659121i	0.944134	−	0.329560i	$-0.106901\pi$
$48$			1.00000i			0.144338i
$49$	−2.38549	−	4.13180i	−0.340785	−	0.590257i
$50$	4.32367	+	2.51115i	0.611459	+	0.355130i
$51$		−	4.48853i		−	0.628520i
$52$	3.55888	+	6.16416i	0.493528	+	0.854815i
$53$	3.66104	−	2.11370i	0.502882	−	0.290339i	−0.227021	−	0.973890i	$-0.572899\pi$
$53$	3.66104	−	2.11370i	0.502882	−	0.290339i	0.729903	+	0.683551i	$0.239565\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	10.7866	−	2.87538i	1.45447	−	0.387717i
$56$	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
$65$	−4.13911	+	15.3682i	−0.513394	+	1.90618i
$66$			4.99238i			0.614520i
$67$	11.5321	+	6.65806i	1.40887	+	0.813412i	0.995279	−	0.0970505i	$-0.0309408\pi$
$67$	11.5321	+	6.65806i	1.40887	+	0.813412i	0.413592	+	0.910463i	$0.364274\pi$
$68$	−4.48853			−0.544314
$69$	−6.78780	−	3.91894i	−0.817155	−	0.471785i
$70$	0.859892	+	3.22578i	0.102777	+	0.385554i
$71$	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	$-0.700157\pi$
$73$		−	13.8195i		−	1.61745i	0.588185	−	0.808726i	$-0.299843\pi$
$74$	−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	−0.00366573	−	0.999993i	$-0.501167\pi$
$83$	7.83972	−	4.52626i	0.860521	−	0.496822i	0.864187	+	0.503171i	$0.167834\pi$
$84$	−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	$0.196886\pi$
$90$	0.581519	−	2.15913i	0.0612975	−	0.227592i
$91$	−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
$95$	−6.69752	−	1.80385i	−0.687151	−	0.185071i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	9.48892			0.963454			0.481727	−	0.876321i	$-0.340010\pi$
$97$	9.48892			0.963454			0.481727	+	0.876321i	$0.340010\pi$
$98$	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	$-0.584558\pi$
$103$	−5.32885			−0.525068			−0.262534	+	0.964923i	$0.584558\pi$
$104$	−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	0.724394	−	0.689386i	$-0.242120\pi$
$107$	5.06411	+	2.92376i	0.489566	+	0.282651i	−0.234829	+	0.972037i	$0.575453\pi$
$108$	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	0.819524	−	0.573045i	$-0.194238\pi$
$113$	−0.919606	−	1.59280i	−0.0865092	−	0.149838i	−0.906033	+	0.423206i	$0.860905\pi$
$114$	1.55098	−	2.68637i	0.145262	−	0.251602i
$115$	−16.9347	+	4.51426i	−1.57917	+	0.420957i
$116$	−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
$120$	−2.15913	−	0.581519i	−0.197101	−	0.0530852i
$121$	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	−0.103263	−	0.994654i	$-0.532928\pi$
$127$	7.96186	−	4.59678i	0.706501	−	0.407899i	0.809764	+	0.586755i	$0.199595\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.96561	+	4.02159i	0.613287	+	0.354082i
$130$	−15.3788	+	4.09950i	−1.34881	+	0.359550i
$131$	−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
$135$	0.575954	+	2.16062i	0.0495702	+	0.185957i
$136$	−2.24427	−	3.88718i	−0.192444	−	0.333323i
$137$		−	5.30952i		−	0.453623i	−0.973939	−	0.226812i	$-0.927170\pi$
$137$		−	5.30952i		−	0.453623i	0.973939	−	0.226812i	$-0.0728301\pi$
$138$		−	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
$145$	−4.74803	−	17.8117i	−0.394303	−	1.47918i
$146$	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	$0.381493\pi$
$150$	−2.48883	−	4.33655i	−0.203212	−	0.354078i
$151$	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
$155$	0.532853	+	1.99893i	0.0427998	+	0.160558i
$156$		−	7.11776i		−	0.569877i
$157$	−5.76364	+	3.32764i	−0.459988	+	0.265574i	−0.712039	−	0.702140i	$-0.752228\pi$
$157$	−5.76364	+	3.32764i	−0.459988	+	0.265574i	0.252051	+	0.967714i	$0.418895\pi$
$158$		−	0.965634i		−	0.0768217i
$159$	−4.22740			−0.335255
$160$	−0.581519	+	2.15913i	−0.0459731	+	0.170694i
$161$	−10.1341	−	5.85093i	−0.798679	−	0.461118i
$162$	−1.00000			−0.0785674
$163$	−1.39135	−	2.40989i	−0.108979	−	0.188757i	0.806378	−	0.591401i	$-0.201425\pi$
$163$	−1.39135	−	2.40989i	−0.108979	−	0.188757i	−0.915357	+	0.402644i	$0.868091\pi$
$164$	3.23677	+	5.60626i	0.252750	+	0.437775i
$165$	−10.7792	−	2.90317i	−0.839160	−	0.226011i
$166$	7.83972	+	4.52626i	0.608480	+	0.351306i
$167$	7.54017	−	13.0600i	0.583476	−	1.01061i	−0.411588	−	0.911370i	$-0.635026\pi$
$167$	7.54017	−	13.0600i	0.583476	−	1.01061i	0.995064	−	0.0992397i	$-0.0316411\pi$
$168$	−0.746494	−	1.29297i	−0.0575933	−	0.0997544i
$169$	−18.8312	−	32.6167i	−1.44856	−	2.50897i
$170$	2.61017	−	9.69131i	0.200191	−	0.743290i
$171$			3.10196i			0.237213i
$172$	4.02159	−	6.96561i	0.306644	−	0.531123i
$173$	−15.2577	+	8.80902i	−1.16002	+	0.669737i	−0.951309	−	0.308240i	$-0.900260\pi$
$173$	−15.2577	+	8.80902i	−1.16002	+	0.669737i	−0.208711	+	0.977977i	$0.566927\pi$
$174$	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	$0.925918\pi$
$180$	2.16062	−	0.575954i	0.161043	−	0.0429291i
$181$	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
$185$	−12.6258	−	5.05859i	−0.928267	−	0.371915i
$186$	−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
$190$	−1.78658	−	6.70215i	−0.129612	−	0.486225i
$191$		−	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	$-0.301402\pi$
$193$	16.2324			1.16843			0.584217	+	0.811597i	$0.301402\pi$
$194$	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	−0.686936	−	0.726718i	$-0.741045\pi$
$197$	−5.62897	+	3.24989i	−0.401047	+	0.231545i	0.285888	+	0.958263i	$0.407711\pi$
$198$	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	$0.749350\pi$
$200$	−4.33655	+	2.48883i	−0.306641	+	0.175987i
$201$	−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
$205$	−3.76449	+	13.9772i	−0.262923	+	0.976211i
$206$	−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
$210$	0.868201	−	3.22355i	0.0599116	−	0.222446i
$211$	−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
$215$	17.3783	−	4.63251i	1.18519	−	0.315934i
$216$			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
$220$	−2.90317	+	10.7792i	−0.195731	+	0.726733i
$221$	31.9483			2.14907
$222$	3.64031	−	4.87320i	0.244322	−	0.327068i
$223$			27.7499i			1.85827i	0.369741	+	0.929135i	$0.379446\pi$
$223$			27.7499i			1.85827i	−0.369741	+	0.929135i	$0.620554\pi$
$224$	−1.29297	+	0.746494i	−0.0863899	+	0.0498772i
$225$	4.32367	+	2.51115i	0.288245	+	0.167410i
$226$	0.919606	−	1.59280i	0.0611713	−	0.105952i
$227$	−9.89438	+	17.1376i	−0.656713	+	1.13746i	0.324748	+	0.945800i	$0.394720\pi$
$227$	−9.89438	+	17.1376i	−0.656713	+	1.13746i	−0.981461	+	0.191660i	$0.938613\pi$
$228$	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	$0.0223036\pi$
$233$			2.13736i			0.140023i	−0.997546	+	0.0700115i	$0.977696\pi$
$234$	3.55888	+	6.16416i	0.232651	+	0.402964i
$235$	2.60257	+	9.76320i	0.169773	+	0.636881i
$236$		−	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	$0.309526\pi$
$240$	−0.575954	−	2.16062i	−0.0371777	−	0.139467i
$241$	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
$250$	−10.7881	−	2.93540i	−0.682300	−	0.185651i
$251$			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
$255$	2.58519	+	9.69801i	0.161891	+	0.607313i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.45518	+	4.25250i	0.153150	+	0.265263i	0.932384	−	0.361470i	$-0.117725\pi$
$257$	2.45518	+	4.25250i	0.153150	+	0.265263i	−0.779234	+	0.626733i	$0.784392\pi$
$258$			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	−0.0952619	−	0.995452i	$-0.530369\pi$
$263$	−16.2980	−	9.40967i	−1.00498	−	0.580225i	−0.909718	+	0.415227i	$0.863702\pi$
$264$	−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
$275$	−21.6497	+	12.4252i	−1.30553	+	0.749269i
$276$	6.78780	−	3.91894i	0.408578	−	0.235892i
$277$	−12.6092	+	21.8397i	−0.757611	+	1.31222i	0.186454	+	0.982464i	$0.440300\pi$
$277$	−12.6092	+	21.8397i	−0.757611	+	1.31222i	−0.944066	+	0.329758i	$0.893033\pi$
$278$	3.98426	−	6.90094i	0.238960	−	0.413891i
$279$	0.801217	−	0.462583i	0.0479676	−	0.0276941i
$280$	−3.22355	−	0.868201i	−0.192644	−	0.0518849i
$281$	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	$-0.479202\pi$
$283$	15.0869	−	26.1313i	0.896824	−	1.55334i	0.831531	−	0.555478i	$-0.187465\pi$
$284$	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	0.996448	−	0.0842159i	$-0.0268385\pi$
$293$	24.3362	+	14.0505i	1.42174	+	0.820841i	0.425291	+	0.905057i	$0.360172\pi$
$294$	−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
$300$	2.51115	−	4.32367i	0.144981	−	0.249627i
$301$	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
$305$	−20.8926	−	5.62702i	−1.19631	−	0.322202i
$306$	−4.48853			−0.256592
$307$		−	13.0437i		−	0.744446i	−0.928143	−	0.372223i	$-0.878596\pi$
$307$		−	13.0437i		−	0.744446i	0.928143	−	0.372223i	$-0.121404\pi$
$308$	−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	0.998164	−	0.0605646i	$-0.0192901\pi$
$313$	7.90172	+	13.6862i	0.446632	+	0.773589i	−0.551533	+	0.834153i	$0.685957\pi$
$314$	−5.76364	−	3.32764i	−0.325261	−	0.187789i
$315$	0.859892	+	3.22578i	0.0484494	+	0.181752i
$316$	0.836264	−	0.482817i	0.0470435	−	0.0271606i
$317$	16.8545	−	9.73093i	0.946641	−	0.546543i	0.0546048	−	0.998508i	$-0.482610\pi$
$317$	16.8545	−	9.73093i	0.946641	−	0.546543i	0.892036	+	0.451965i	$0.149277\pi$
$318$	−2.11370	−	3.66104i	−0.118530	−	0.205301i
$319$		−	41.1561i		−	2.30430i
$320$	−2.16062	+	0.575954i	−0.120782	+	0.0321968i
$321$	−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
$330$	−2.87538	−	10.7866i	−0.158285	−	0.593785i
$331$	−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
$335$	−28.7512	−	7.74358i	−1.57085	−	0.423077i
$336$	0.746494	−	1.29297i	0.0407246	−	0.0705370i
$337$	11.0981	+	6.40748i	0.604551	+	0.349038i	0.770830	−	0.637041i	$-0.219842\pi$
$337$	11.0981	+	6.40748i	0.604551	+	0.349038i	−0.166279	+	0.986079i	$0.553175\pi$
$338$	18.8312	−	32.6167i	1.02428	−	1.77411i
$339$			1.83921i			0.0998923i
$340$	9.69801	−	2.58519i	0.525948	−	0.140201i
$341$			4.61878i			0.250121i
$342$	−2.68637	+	1.55098i	−0.145262	+	0.0838673i
$343$			17.5739i			0.948904i
$344$	8.04319			0.433660
$345$	16.9230	+	4.55788i	0.911103	+	0.245388i
$346$	−15.2577	−	8.80902i	−0.820257	−	0.473576i
$347$	−12.0755			−0.648247			−0.324123	−	0.946015i	$-0.605069\pi$
$347$	−12.0755			−0.648247			−0.324123	+	0.946015i	$0.605069\pi$
$348$	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	$0.771973\pi$
$350$	−3.71580	−	6.47442i	−0.198618	−	0.346072i
$351$	−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	$0.169574\pi$
$353$	16.3563	+	28.3299i	0.870556	+	1.50785i	0.00913392	+	0.999958i	$0.497093\pi$
$354$	2.63046	+	4.55609i	0.139808	+	0.242154i
$355$	−0.301318	+	1.11877i	−0.0159923	+	0.0593779i
$356$			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
$365$	7.95941	+	29.8587i	0.416614	+	1.56288i
$366$	4.83821	−	8.38002i	0.252897	−	0.438031i
$367$	−1.34639	−	0.777339i	−0.0702810	−	0.0405768i	0.464448	−	0.885601i	$-0.346253\pi$
$367$	−1.34639	−	0.777339i	−0.0702810	−	0.0405768i	−0.534729	+	0.845024i	$0.679586\pi$
$368$	−3.91894	−	6.78780i	−0.204289	−	0.353839i
$369$	6.47355			0.336999
$370$	−1.93203	−	13.4636i	−0.100441	−	0.699937i
$371$	−6.31146			−0.327675
$372$	−0.462583	−	0.801217i	−0.0239838	−	0.0415412i
$373$	−23.6846	−	13.6743i	−1.22634	−	0.708028i	−0.260078	−	0.965588i	$-0.583748\pi$
$373$	−23.6846	−	13.6743i	−1.22634	−	0.708028i	−0.966262	+	0.257560i	$0.917082\pi$
$374$	11.2042	−	19.4063i	0.579357	−	1.00348i
$375$	10.8105	−	2.85192i	0.558251	−	0.147273i
$376$			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	$-0.481511\pi$
$383$	17.4879	−	30.2900i	0.893591	−	1.54774i	0.835539	−	0.549431i	$-0.185155\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−16.0932	−	4.33439i	−0.820186	−	0.220901i
$386$	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	$0.826714\pi$
$390$	15.3682	+	4.13911i	0.778197	+	0.209592i
$391$	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
$395$	2.08493	+	0.561535i	0.104904	+	0.0282539i
$396$	4.99238			0.250877
$397$		−	15.0132i		−	0.753492i	−0.926317	−	0.376746i	$-0.877043\pi$
$397$		−	15.0132i		−	0.753492i	0.926317	−	0.376746i	$-0.122957\pi$
$398$	−17.3124	+	9.99533i	−0.867793	+	0.501021i
$399$			4.63118i			0.231849i
$400$	−4.32367	−	2.51115i	−0.216184	−	0.125557i
$401$		−	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
$405$	0.581519	−	2.15913i	0.0288959	−	0.107288i
$406$	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	$0.217779\pi$
$410$	−13.9869	+	3.72846i	−0.690762	+	0.184136i
$411$	−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	$0.823326\pi$
$420$	3.22578	−	0.859892i	0.157402	−	0.0419584i
$421$			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
$425$	19.4069	+	11.2714i	0.941374	+	0.546742i
$426$	−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	$0.0586345\pi$
$433$			7.62286i			0.366332i	−0.983082	+	0.183166i	$0.941365\pi$
$434$	−1.38126			−0.0663026
$435$	−4.79391	+	17.7994i	−0.229851	+	0.853415i
$436$		−	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	$0.463672\pi$
$440$	−10.7866	+	2.87538i	−0.514233	+	0.137079i
$441$	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	$-0.856198\pi$
$443$		−	18.3769i		−	0.873111i	0.899677	−	0.436555i	$-0.143802\pi$
$444$	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	$-0.648106\pi$
$457$	11.7495	−	20.3508i	0.549619	−	0.951968i	0.998300	−	0.0582764i	$-0.0185605\pi$
$458$	8.67189			0.405211
$459$	3.88718	−	2.24427i	0.181438	−	0.104753i
$460$	4.55788	−	16.9230i	0.212512	−	0.789038i
$461$	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	−0.691124	−	0.722736i	$-0.742884\pi$
$463$	6.03232	−	10.4483i	0.280346	−	0.485573i	0.971470	+	0.237163i	$0.0762175\pi$
$464$	7.13932	−	4.12189i	0.331435	−	0.191354i
$465$	0.538002	−	1.99755i	0.0249492	−	0.0926342i
$466$	−1.85101	+	1.06868i	−0.0857462	+	0.0495056i
$467$	−8.08233			−0.374005			−0.187003	−	0.982359i	$-0.559877\pi$
$467$	−8.08233			−0.374005			−0.187003	+	0.982359i	$0.559877\pi$
$468$	−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
$485$	−20.5020	+	5.46518i	−0.930946	+	0.248161i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−33.2218			−1.50542			−0.752711	−	0.658351i	$-0.771254\pi$
$487$	−33.2218			−1.50542			−0.752711	+	0.658351i	$0.771254\pi$
$488$	−8.38002	−	4.83821i	−0.379346	−	0.219015i
$489$			2.78270i			0.125838i
$490$	−2.77442	+	10.3012i	−0.125336	+	0.465360i
$491$	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	$0.787480\pi$
$500$	−2.85192	−	10.8105i	−0.127542	−	0.483459i
$501$	−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	$-0.990522\pi$
$503$	−11.7871	−	20.4159i	−0.525562	−	0.910299i	0.473995	−	0.880527i	$-0.342811\pi$
$504$			1.49299i			0.0665030i
$505$	−18.3529	+	4.89231i	−0.816693	+	0.217705i
$506$	−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
$515$	11.5136	−	3.06917i	0.507351	−	0.135244i
$516$	−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
$520$	4.13911	−	15.3682i	0.181512	−	0.673938i
$521$	−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	$-0.570934\pi$
$523$	16.7885	−	29.0785i	0.734108	−	1.27151i	0.955113	−	0.296240i	$-0.0957329\pi$
$524$		−	7.70903i		−	0.336771i
$525$	6.45519	+	3.74911i	0.281727	+	0.163625i
$526$		−	18.8193i		−	0.820563i
$527$	3.59629	−	2.07632i	0.156657	−	0.0904458i
$528$		−	4.99238i		−	0.217266i
$529$	38.4323			1.67097
$530$	−9.12750	−	2.45832i	−0.396473	−	0.106782i
$531$	−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
$535$	−12.6256	−	3.40045i	−0.545851	−	0.147014i
$536$	−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
$540$	−2.15913	−	0.581519i	−0.0929141	−	0.0250246i
$541$		−	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	$-0.361539\pi$
$547$	19.7115			0.842802			0.421401	+	0.906874i	$0.361539\pi$
$548$	4.59818	+	2.65476i	0.196425	+	0.113406i
$549$			9.67642i			0.412979i
$550$	−21.5854	−	12.5366i	−0.920406	−	0.534563i
$551$	−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
$555$	8.40496	+	10.6938i	0.356771	+	0.453925i
$556$	7.96852			0.337941
$557$	−6.44022	−	11.1548i	−0.272881	−	0.472643i	0.696717	−	0.717346i	$-0.254643\pi$
$557$	−6.44022	−	11.1548i	−0.272881	−	0.472643i	−0.969598	+	0.244702i	$0.921310\pi$
$558$	0.801217	+	0.462583i	0.0339182	+	0.0195827i
$559$	−28.6247	+	49.5795i	−1.21070	+	2.09699i
$560$	−0.859892	−	3.22578i	−0.0363371	−	0.136314i
$561$			22.4085i			0.946086i
$562$	3.24794	+	1.87520i	0.137006	+	0.0791004i
$563$	4.71733			0.198812			0.0994059	−	0.995047i	$-0.468306\pi$
$563$	4.71733			0.198812			0.0994059	+	0.995047i	$0.468306\pi$
$564$	−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	$0.675273\pi$
$570$	−1.80385	+	6.69752i	−0.0755548	+	0.280528i
$571$	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
$575$	33.9894	−	19.5072i	1.41746	−	0.813506i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	18.0545	+	31.2713i	0.751619	+	1.30184i	0.947038	+	0.321122i	$0.104060\pi$
$577$	18.0545	+	31.2713i	0.751619	+	1.30184i	−0.195419	+	0.980720i	$0.562607\pi$
$578$	−3.14690			−0.130894
$579$	−14.0577	−	8.11621i	−0.584217	−	0.337298i
$580$	17.7994	+	4.79391i	0.739079	+	0.199056i
$581$	−13.5153			−0.560710
$582$		−	9.48892i		−	0.393329i
$583$	−18.2773	+	10.5524i	−0.756969	+	0.437036i
$584$			13.8195i			0.571856i
$585$	−15.3788	+	4.09950i	−0.635834	+	0.169493i
$586$			28.1011i			1.16084i
$587$	15.0657	−	26.0945i	0.621827	−	1.07704i	−0.367318	−	0.930095i	$-0.619724\pi$
$587$	15.0657	−	26.0945i	0.621827	−	1.07704i	0.989145	−	0.146941i	$-0.0469427\pi$
$588$	−4.13180	−	2.38549i	−0.170392	−	0.0983761i
$589$	1.43491	−	2.48534i	0.0591245	−	0.102407i
$590$	11.3590	+	3.05933i	0.467643	+	0.125951i
$591$	6.49977			0.267365
$592$	0.716002	−	6.04048i	0.0294275	−	0.248262i
$593$			20.9906i			0.861981i	0.902356	+	0.430991i	$0.141836\pi$
$593$			20.9906i			0.861981i	−0.902356	+	0.430991i	$0.858164\pi$
$594$	−4.32353	+	2.49619i	−0.177397	+	0.102420i
$595$	3.85965	+	14.4790i	0.158230	+	0.593581i
$596$	−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
$605$	−30.0843	+	8.01952i	−1.22310	+	0.326040i
$606$		−	8.49427i		−	0.345056i
$607$	20.3935	+	35.3226i	0.827746	+	1.43370i	0.899802	+	0.436298i	$0.143711\pi$
$607$	20.3935	+	35.3226i	0.827746	+	1.43370i	−0.0720560	+	0.997401i	$0.522956\pi$
$608$	2.68637	−	1.55098i	0.108947	−	0.0629005i
$609$	−10.6589	+	6.15393i	−0.431921	+	0.249370i
$610$	−5.57317	−	20.9071i	−0.225651	−	0.846502i
$611$	−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	−0.835652	−	0.549260i	$-0.814910\pi$
$613$	−19.2575	+	11.1183i	−0.777805	+	0.449066i	0.0578469	+	0.998325i	$0.481576\pi$
$614$	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	−0.296011	−	0.955184i	$-0.595657\pi$
$617$	9.51843	−	5.49547i	0.383197	−	0.221239i	0.679208	+	0.733945i	$0.262323\pi$
$618$			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	$0.155458\pi$
$620$	−1.99755	−	0.538002i	−0.0802236	−	0.0216067i
$621$		−	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
$625$	12.6114	−	21.5859i	0.504456	−	0.863437i
$626$	−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	$-0.300199\pi$
$643$	29.7837			1.17456			0.587278	+	0.809385i	$0.300199\pi$
$644$	10.1341	−	5.85093i	0.399340	−	0.230559i
$645$	−17.3663	−	4.67727i	−0.683797	−	0.184167i
$646$	−12.0579	+	6.96161i	−0.474410	+	0.273901i
$647$	9.75527	−	16.8966i	0.383519	−	0.664275i	−0.608043	−	0.793904i	$-0.708045\pi$
$647$	9.75527	−	16.8966i	0.383519	−	0.664275i	0.991563	+	0.129629i	$0.0413787\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	22.7458	−	13.1323i	0.892850	−	0.515487i
$650$	30.8665	−	17.7149i	1.21069	−	0.694836i
$651$	1.19621	−	0.690630i	0.0468830	−	0.0270679i
$652$	2.78270			0.108979
$653$	−6.40287	+	11.0901i	−0.250563	+	0.433989i	−0.963681	−	0.267056i	$-0.913949\pi$
$653$	−6.40287	+	11.0901i	−0.250563	+	0.433989i	0.713118	+	0.701044i	$0.247283\pi$
$654$	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
$670$	−7.66948	−	28.7711i	−0.296298	−	1.11152i
$671$	−41.8363	−	24.1542i	−1.61507	−	0.932462i
$672$	1.49299			0.0575933
$673$	9.21745	+	5.32170i	0.355307	+	0.205136i	0.667020	−	0.745040i	$-0.267570\pi$
$673$	9.21745	+	5.32170i	0.355307	+	0.205136i	−0.311713	+	0.950176i	$0.600903\pi$
$674$			12.8150i			0.493614i
$675$	−2.48883	−	4.33655i	−0.0957953	−	0.166914i
$676$	37.6625			1.44856
$677$		−	21.2505i		−	0.816725i	−0.912820	−	0.408362i	$-0.866100\pi$
$677$		−	21.2505i		−	0.816725i	0.912820	−	0.408362i	$-0.133900\pi$
$678$	−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	$-0.974039\pi$
$683$	−14.8676	−	25.7514i	−0.568893	−	0.985351i	0.427783	−	0.903881i	$-0.359295\pi$
$684$	−2.68637	−	1.55098i	−0.102716	−	0.0593031i
$685$	3.05804	+	11.4719i	0.116842	+	0.438317i
$686$	−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
$690$	4.51426	+	16.9347i	0.171855	+	0.644692i
$691$	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
$700$	3.74911	−	6.45519i	0.141703	−	0.243983i
$701$	−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
$705$	2.62771	−	9.75647i	0.0989654	−	0.367450i
$706$	−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	$-0.238920\pi$
$710$	−1.11954	+	0.298434i	−0.0420155	+	0.0112000i
$711$		−	0.965634i		−	0.0362141i
$712$	−6.79186	+	3.92128i	−0.254536	+	0.146956i
$713$		−	7.25134i		−	0.271565i
$714$	−6.70132			−0.250791
$715$	20.6640	−	76.7237i	0.772791	−	2.86930i
$716$	−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	$0.862033\pi$
$720$	−0.581519	+	2.15913i	−0.0216719	+	0.0804660i
$721$	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
$725$	20.5174	+	35.7496i	0.761997	+	1.32771i
$726$		−	13.9239i		−	0.516764i
$727$	−1.93804	+	3.35679i	−0.0718780	+	0.124496i	−0.899724	−	0.436459i	$-0.856233\pi$
$727$	−1.93804	+	3.35679i	−0.0718780	+	0.124496i	0.827846	+	0.560955i	$0.189566\pi$
$728$	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	−0.0160613	−	0.999871i	$-0.505113\pi$
$733$	−24.0960	−	13.9118i	−0.890006	−	0.513845i	−0.873944	+	0.486026i	$0.838446\pi$
$734$		−	1.55468i		−	0.0573842i
$735$	−2.74787	−	10.3083i	−0.101357	−	0.380227i
$736$	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	$0.815905\pi$
$740$	10.6938	−	8.40496i	0.393111	−	0.308973i
$741$	−22.0790			−0.811091
$742$	−3.15573	−	5.46588i	−0.115850	−	0.200659i
$743$	24.4648	+	14.1248i	0.897527	+	0.518188i	0.876397	−	0.481589i	$-0.159940\pi$
$743$	24.4648	+	14.1248i	0.897527	+	0.518188i	0.0211303	+	0.999777i	$0.493274\pi$
$744$	0.462583	−	0.801217i	0.0169591	−	0.0293740i
$745$	−19.1874	+	5.11477i	−0.702973	+	0.187391i
$746$		−	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
$755$	−6.22837	+	23.1254i	−0.226674	+	0.841619i
$756$	−0.746494	−	1.29297i	−0.0271497	−	0.0470247i
$757$	−20.2892	−	35.1419i	−0.737423	−	1.27725i	−0.953652	−	0.300911i	$-0.902709\pi$
$757$	−20.2892	−	35.1419i	−0.737423	−	1.27725i	0.216230	−	0.976343i	$-0.430624\pi$
$758$	−3.06678	+	5.31181i	−0.111390	+	0.192934i
$759$	33.8873	+	19.5649i	1.23003	+	0.710159i
$760$	6.69752	+	1.80385i	0.242945	+	0.0654324i
$761$	−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
$765$	2.61017	−	9.69131i	0.0943708	−	0.350390i
$766$	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	$-0.0148412\pi$
$770$	−4.29291	−	16.1043i	−0.154706	−	0.580360i
$771$		−	4.91036i		−	0.176842i
$772$	−8.11621	+	14.0577i	−0.292109	+	0.505947i
$773$	−39.0202	−	22.5283i	−1.40346	−	0.810288i	−0.408715	−	0.912662i	$-0.634023\pi$
$773$	−39.0202	−	22.5283i	−1.40346	−	0.810288i	−0.994746	+	0.102374i	$0.967356\pi$
$774$	4.02159	−	6.96561i	0.144553	−	0.250374i
$775$	−2.30258	−	4.01203i	−0.0827113	−	0.144116i
$776$	−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
$780$	4.09950	+	15.3788i	0.146786	+	0.550648i
$781$	−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	$0.105708\pi$
$787$			18.2922i			0.652045i	−0.945362	+	0.326022i	$0.894292\pi$
$788$		−	6.49977i		−	0.231545i
$789$	9.40967	+	16.2980i	0.334993	+	0.580225i
$790$	0.556161	+	2.08637i	0.0197873	+	0.0742297i
$791$			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
$795$	9.13381	−	2.43479i	0.323943	−	0.0863530i
$796$	−17.3124	−	9.99533i	−0.613623	−	0.354275i
$797$	−27.5893	−	47.7861i	−0.977264	−	1.69267i	−0.672254	−	0.740321i	$-0.734674\pi$
$797$	−27.5893	−	47.7861i	−0.977264	−	1.69267i	−0.305010	−	0.952349i	$-0.598660\pi$
$798$	−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
$805$	25.2658	+	6.80485i	0.890503	+	0.239840i
$806$		−	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	$0.853508\pi$
$810$	2.16062	−	0.575954i	0.0759164	−	0.0202370i
$811$	−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	−0.311724	−	0.950173i	$-0.600906\pi$
$823$	10.1925	−	5.88464i	0.355288	−	0.205126i	0.667012	+	0.745047i	$0.267573\pi$
$824$	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	−0.602523	−	0.798102i	$-0.705838\pi$
$827$	11.2130	−	19.4215i	0.389915	−	0.675352i	0.992438	+	0.122749i	$0.0391711\pi$
$828$	−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	$0.252062\pi$
$830$	−19.5456	−	5.26422i	−0.678437	−	0.182724i
$831$	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
$835$	−8.76951	+	32.5604i	−0.303481	+	1.12680i
$836$	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	0.984821	−	0.173573i	$-0.0555314\pi$
$853$	9.99118	+	17.3052i	0.342092	+	0.592520i	−0.642729	+	0.766093i	$0.722198\pi$
$854$	7.22339	−	12.5113i	0.247179	−	0.428127i
$855$	−1.78658	−	6.70215i	−0.0610999	−	0.229209i
$856$	−5.06411	−	2.92376i	−0.173088	−	0.0999322i
$857$	0.870779			0.0297453			0.0148726	−	0.999889i	$-0.495266\pi$
$857$	0.870779			0.0297453			0.0148726	+	0.999889i	$0.495266\pi$
$858$	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	$-0.265743\pi$
$860$	−4.67727	+	17.3663i	−0.159494	+	0.592185i
$861$	9.66493			0.329380
$862$			7.31830i			0.249262i
$863$	−11.6269	+	6.71281i	−0.395785	+	0.228507i	−0.684664	−	0.728859i	$-0.740051\pi$
$863$	−11.6269	+	6.71281i	−0.395785	+	0.228507i	0.288879	+	0.957366i	$0.406718\pi$
$864$	−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
$870$	−17.8117	+	4.74803i	−0.603872	+	0.160973i
$871$	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
$875$	16.1399	−	4.25789i	0.545629	−	0.143943i
$876$	−6.90976	−	11.9681i	−0.233459	−	0.404363i
$877$		−	37.0309i		−	1.25044i	−0.780447	−	0.625222i	$-0.785008\pi$
$877$		−	37.0309i		−	1.25044i	0.780447	−	0.625222i	$-0.214992\pi$
$878$			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	−0.831346	−	0.555755i	$-0.812429\pi$
$883$	1.95007	−	3.37762i	0.0656250	−	0.113666i	0.896971	+	0.442089i	$0.145763\pi$
$884$	−15.9741	+	27.6680i	−0.537268	+	0.930576i
$885$	−11.3669	+	3.03005i	−0.382093	+	0.101854i
$886$	15.9148	−	9.18843i	0.534669	−	0.308691i
$887$		−	2.91300i		−	0.0978089i	−0.998803	−	0.0489045i	$-0.984427\pi$
$887$		−	2.91300i		−	0.0978089i	0.998803	−	0.0489045i	$-0.0155730\pi$
$888$	2.40016	+	5.58921i	0.0805442	+	0.187561i
$889$	−13.7259			−0.460351
$890$	−16.9331	−	4.56060i	−0.567599	−	0.152872i
$891$	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
$895$	−3.55451	−	13.3343i	−0.118814	−	0.445716i
$896$		−	1.49299i		−	0.0498772i
$897$	−48.3139	+	27.8941i	−1.61316	+	0.931356i
$898$			6.57988i			0.219573i
$899$	7.62686			0.254370
$900$	−4.33655	+	2.48883i	−0.144552	+	0.0829611i
$901$	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
$905$	−5.77652	+	21.4477i	−0.192018	+	0.712946i
$906$	−9.27558	−	5.35526i	−0.308160	−	0.177917i
$907$	−6.42331	+	11.1255i	−0.213283	+	0.369416i	−0.952740	−	0.303787i	$-0.901749\pi$
$907$	−6.42331	+	11.1255i	−0.213283	+	0.369416i	0.739457	+	0.673203i	$0.235082\pi$
$908$	−9.89438	−	17.1376i	−0.328356	−	0.568730i
$909$	4.24713	+	7.35625i	0.140869	+	0.243992i
$910$	22.9445	+	6.17964i	0.760602	+	0.204853i
$911$			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	$0.849975\pi$
$920$	16.9347	−	4.51426i	0.558320	−	0.148831i
$921$	−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
$925$	30.1931	+	3.65782i	0.992741	+	0.120268i
$926$	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	$-0.0127186\pi$
$930$	1.99893	−	0.532853i	0.0655475	−	0.0174729i
$931$		−	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	−0.130539	−	0.991443i	$-0.541671\pi$
$937$	20.2888	−	11.7137i	0.662806	−	0.382671i	0.793345	+	0.608772i	$0.208337\pi$
$938$	9.94041	−	17.2173i	0.324566	−	0.562165i
$939$		−	15.8034i		−	0.515726i
$940$	−9.75647	−	2.62771i	−0.318221	−	0.0857066i
$941$	−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
$945$	0.868201	−	3.22355i	0.0282426	−	0.104862i
$946$	20.0773	+	34.7750i	0.652771	+	1.13063i
$947$	12.4533	+	21.5698i	0.404679	+	0.700925i	0.994284	−	0.106767i	$-0.0340498\pi$
$947$	12.4533	+	21.5698i	0.404679	+	0.700925i	−0.589605	+	0.807692i	$0.700716\pi$
$948$	−0.965634			−0.0313623
$949$	−85.1857	−	49.1820i	−2.76525	−	1.59652i
$950$	7.72026	+	13.4518i	0.250478	+	0.436434i
$951$	−19.4619			−0.631094
$952$			6.70132i			0.217191i
$953$	16.8347	−	9.71953i	0.545330	−	0.314846i	−0.201906	−	0.979405i	$-0.564714\pi$
$953$	16.8347	−	9.71953i	0.545330	−	0.314846i	0.747236	+	0.664558i	$0.231380\pi$
$954$			4.22740i			0.136867i
$955$	5.71042	+	21.4220i	0.184785	+	0.693198i
$956$			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
$960$	2.15913	+	0.581519i	0.0696856	+	0.0187685i
$961$	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
$965$	−35.0721	+	9.34912i	−1.12901	+	0.300959i
$966$	−5.85093	+	10.1341i	−0.188251	+	0.326060i
$967$	18.3367	−	31.7601i	0.589669	−	1.02134i	−0.404607	−	0.914491i	$-0.632592\pi$
$967$	18.3367	−	31.7601i	0.589669	−	1.02134i	0.994276	−	0.106846i	$-0.0340751\pi$
$968$	−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
$975$	−17.8737	+	30.7748i	−0.572418	+	0.985584i
$976$		−	9.67642i		−	0.309735i
$977$	−5.87311	−	10.1725i	−0.187898	−	0.325448i	0.756652	−	0.653818i	$-0.226834\pi$
$977$	−5.87311	−	10.1725i	−0.187898	−	0.325448i	−0.944549	+	0.328370i	$0.893501\pi$
$978$	−2.40989	+	1.39135i	−0.0770597	+	0.0444904i
$979$	−33.9076	+	19.5765i	−1.08369	+	0.625669i
$980$	−10.3083	+	2.74787i	−0.329286	+	0.0877774i
$981$	−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	0.157439	−	0.987529i	$-0.449676\pi$
$983$	34.2180	−	19.7558i	1.09138	−	0.630111i	0.933945	+	0.357418i	$0.116343\pi$
$984$	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
$990$	−2.90317	+	10.7792i	−0.0922687	+	0.342585i
$991$			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
$995$	−11.5137	−	43.1922i	−0.365009	−	1.36929i
$996$	4.52626	−	7.83972i	0.143420	−	0.248411i
$997$	11.9343	+	20.6708i	0.377962	+	0.654650i	0.990766	−	0.135586i	$-0.0432916\pi$
$997$	11.9343	+	20.6708i	0.377962	+	0.654650i	−0.612804	+	0.790235i	$0.709958\pi$
$998$		−	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.b.529.2	yes	36
5.4	even	2		1110.2.ba.a.529.17	✓	36
37.27	even	6		1110.2.ba.a.619.17	yes	36
185.64	even	6	inner	1110.2.ba.b.619.2	yes	36

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16062 + 0.575954i) q^{5} -1.00000i q^{6} +(-1.29297 - 0.746494i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16062 + 0.575954i) 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} +(2.15913 + 0.581519i) 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} +(0.581519 - 2.15913i) q^{20} +(0.746494 + 1.29297i) q^{21} +(-2.49619 - 4.32353i) q^{22} +7.83788 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.33655 - 2.48883i) q^{25} +7.11776 q^{26} -1.00000i q^{27} +(1.29297 - 0.746494i) q^{28} +8.24378i q^{29} +(0.575954 + 2.16062i) q^{30} -0.925166i q^{31} +(0.500000 - 0.866025i) q^{32} +(4.32353 + 2.49619i) q^{33} +(-2.24427 + 3.88718i) q^{34} +(3.22355 + 0.868201i) q^{35} -1.00000 q^{36} +(4.87320 + 3.64031i) q^{37} +3.10196i q^{38} +(-6.16416 + 3.55888i) q^{39} +(2.16062 - 0.575954i) 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} +(4.32367 + 2.51115i) q^{50} -4.48853i q^{51} +(3.55888 + 6.16416i) q^{52} +(3.66104 - 2.11370i) q^{53} +(0.866025 - 0.500000i) q^{54} +(10.7866 - 2.87538i) 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} +(-4.13911 + 15.3682i) q^{65} +4.99238i q^{66} +(11.5321 + 6.65806i) q^{67} -4.48853 q^{68} +(-6.78780 - 3.91894i) q^{69} +(0.859892 + 3.22578i) 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} +(0.581519 - 2.15913i) 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} +(-6.69752 - 1.80385i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 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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