LMFDB - Embedded newform 198.2.e.d.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(67,198)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.e (of order $3$, 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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	198.67
Dual form			198.2.e.d.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.04307 - 1.38276i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.71903 + 2.97746i) q^{5} +(-0.675970 + 1.59470i) q^{6} +(0.867095 + 1.50185i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.04307 - 1.38276i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.71903 + 2.97746i) q^{5} +(-0.675970 + 1.59470i) q^{6} +(0.867095 + 1.50185i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} +3.43807 q^{10} +(0.500000 + 0.866025i) q^{11} +(1.71903 - 0.211943i) q^{12} +(-0.543065 + 0.940616i) q^{13} +(0.867095 - 1.50185i) q^{14} +(5.91016 - 0.728674i) q^{15} +(-0.500000 - 0.866025i) q^{16} -4.61033 q^{17} +(2.91016 - 0.728674i) q^{18} +6.17226 q^{19} +(-1.71903 - 2.97746i) q^{20} +(1.17226 - 2.76551i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-3.67597 + 6.36697i) q^{23} +(-1.04307 - 1.38276i) q^{24} +(-3.41016 - 5.90657i) q^{25} +1.08613 q^{26} +(4.84823 - 1.86940i) q^{27} -1.73419 q^{28} +(0.895004 + 1.55019i) q^{29} +(-3.58613 - 4.75401i) q^{30} +(-3.91016 + 6.77260i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.675970 - 1.59470i) q^{33} +(2.30516 + 3.99266i) q^{34} -5.96227 q^{35} +(-2.08613 - 2.15594i) q^{36} -3.38225 q^{37} +(-3.08613 - 5.34533i) q^{38} +(1.86710 - 0.230197i) q^{39} +(-1.71903 + 2.97746i) q^{40} +(-1.86710 + 3.23390i) q^{41} +(-2.98113 + 0.367549i) q^{42} +(0.808874 + 1.40101i) q^{43} -1.00000 q^{44} +(-7.17226 - 7.41226i) q^{45} +7.35194 q^{46} +(-5.23419 - 9.06588i) q^{47} +(-0.675970 + 1.59470i) q^{48} +(1.99629 - 3.45768i) q^{49} +(-3.41016 + 5.90657i) q^{50} +(4.80887 + 6.37496i) q^{51} +(-0.543065 - 0.940616i) q^{52} +8.96227 q^{53} +(-4.04307 - 3.26399i) q^{54} -3.43807 q^{55} +(0.867095 + 1.50185i) q^{56} +(-6.43807 - 8.53473i) q^{57} +(0.895004 - 1.55019i) q^{58} +(6.12920 - 10.6161i) q^{59} +(-2.32403 + 5.48269i) q^{60} +(0.648061 + 1.12247i) q^{61} +7.82032 q^{62} +(-5.04677 + 1.26366i) q^{63} +1.00000 q^{64} +(-1.86710 - 3.23390i) q^{65} +(-1.71903 + 0.211943i) q^{66} +(2.30887 - 3.99909i) q^{67} +(2.30516 - 3.99266i) q^{68} +(12.6382 - 1.55819i) q^{69} +(2.98113 + 5.16348i) q^{70} +8.52420 q^{71} +(-0.824030 + 2.88461i) q^{72} -15.4865 q^{73} +(1.69113 + 2.92912i) q^{74} +(-4.61033 + 10.8764i) q^{75} +(-3.08613 + 5.34533i) q^{76} +(-0.867095 + 1.50185i) q^{77} +(-1.13290 - 1.50185i) q^{78} +(6.39130 + 11.0700i) q^{79} +3.43807 q^{80} +(-7.64195 - 4.75401i) q^{81} +3.73419 q^{82} +(2.08613 + 3.61328i) q^{83} +(1.80887 + 2.39796i) q^{84} +(7.92532 - 13.7271i) q^{85} +(0.808874 - 1.40101i) q^{86} +(1.20999 - 2.85453i) q^{87} +(0.500000 + 0.866025i) q^{88} +1.35194 q^{89} +(-2.83307 + 9.91749i) q^{90} -1.88356 q^{91} +(-3.67597 - 6.36697i) q^{92} +(13.4434 - 1.65746i) q^{93} +(-5.23419 + 9.06588i) q^{94} +(-10.6103 + 18.3776i) q^{95} +(1.71903 - 0.211943i) q^{96} +(-1.58613 - 2.74726i) q^{97} -3.99258 q^{98} +(-2.91016 + 0.728674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + q^{3} - 3 q^{4} - q^{5} - 2 q^{6} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + q^3 - 3 * q^4 - q^5 - 2 * q^6 + 6 * q^8 - 7 * q^9	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - q^{5} - 2 q^{6} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} + 4 q^{13} + 23 q^{15} - 3 q^{16} + 20 q^{17} + 5 q^{18} + 8 q^{19} - q^{20} - 22 q^{21} + 3 q^{22} - 20 q^{23} + q^{24} - 8 q^{25} - 8 q^{26} - 2 q^{27} - 6 q^{29} - 7 q^{30} - 11 q^{31} - 3 q^{32} + 2 q^{33} - 10 q^{34} + 16 q^{35} + 2 q^{36} - 14 q^{37} - 4 q^{38} + 6 q^{39} - q^{40} - 6 q^{41} + 8 q^{42} + 8 q^{43} - 6 q^{44} - 14 q^{45} + 40 q^{46} - 21 q^{47} - 2 q^{48} - 15 q^{49} - 8 q^{50} + 32 q^{51} + 4 q^{52} + 2 q^{53} - 17 q^{54} - 2 q^{55} - 20 q^{57} - 6 q^{58} + 15 q^{59} - 16 q^{60} + 8 q^{61} + 22 q^{62} - 50 q^{63} + 6 q^{64} - 6 q^{65} - q^{66} + 17 q^{67} - 10 q^{68} + 22 q^{69} - 8 q^{70} + 18 q^{71} - 7 q^{72} - 8 q^{73} + 7 q^{74} + 20 q^{75} - 4 q^{76} - 12 q^{78} + 2 q^{80} - 19 q^{81} + 12 q^{82} - 2 q^{83} + 14 q^{84} + 34 q^{85} + 8 q^{86} + 30 q^{87} + 3 q^{88} + 4 q^{89} + 13 q^{90} - 28 q^{91} - 20 q^{92} + 3 q^{93} - 21 q^{94} - 16 q^{95} + q^{96} + 5 q^{97} + 30 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - q^5 - 2 * q^6 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 3 * q^11 + q^12 + 4 * q^13 + 23 * q^15 - 3 * q^16 + 20 * q^17 + 5 * q^18 + 8 * q^19 - q^20 - 22 * q^21 + 3 * q^22 - 20 * q^23 + q^24 - 8 * q^25 - 8 * q^26 - 2 * q^27 - 6 * q^29 - 7 * q^30 - 11 * q^31 - 3 * q^32 + 2 * q^33 - 10 * q^34 + 16 * q^35 + 2 * q^36 - 14 * q^37 - 4 * q^38 + 6 * q^39 - q^40 - 6 * q^41 + 8 * q^42 + 8 * q^43 - 6 * q^44 - 14 * q^45 + 40 * q^46 - 21 * q^47 - 2 * q^48 - 15 * q^49 - 8 * q^50 + 32 * q^51 + 4 * q^52 + 2 * q^53 - 17 * q^54 - 2 * q^55 - 20 * q^57 - 6 * q^58 + 15 * q^59 - 16 * q^60 + 8 * q^61 + 22 * q^62 - 50 * q^63 + 6 * q^64 - 6 * q^65 - q^66 + 17 * q^67 - 10 * q^68 + 22 * q^69 - 8 * q^70 + 18 * q^71 - 7 * q^72 - 8 * q^73 + 7 * q^74 + 20 * q^75 - 4 * q^76 - 12 * q^78 + 2 * q^80 - 19 * q^81 + 12 * q^82 - 2 * q^83 + 14 * q^84 + 34 * q^85 + 8 * q^86 + 30 * q^87 + 3 * q^88 + 4 * q^89 + 13 * q^90 - 28 * q^91 - 20 * q^92 + 3 * q^93 - 21 * q^94 - 16 * q^95 + q^96 + 5 * q^97 + 30 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.04307	−	1.38276i	−0.602214	−	0.798335i
$3$	−1.04307	−	1.38276i	−0.602214	−	0.798335i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.71903	+	2.97746i	−0.768776	+	1.33156i	0.169451	+	0.985539i	$0.445800\pi$
$5$	−1.71903	+	2.97746i	−0.768776	+	1.33156i	−0.938227	+	0.346020i	$0.887533\pi$
$6$	−0.675970	+	1.59470i	−0.275963	+	0.651033i
$7$	0.867095	+	1.50185i	0.327731	+	0.567647i	0.982061	−	0.188562i	$-0.0603826\pi$
$7$	0.867095	+	1.50185i	0.327731	+	0.567647i	−0.654330	+	0.756209i	$0.727049\pi$
$8$	1.00000			0.353553
$9$	−0.824030	+	2.88461i	−0.274677	+	0.961537i
$10$	3.43807			1.08721
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.71903	−	0.211943i	0.496243	−	0.0611826i
$13$	−0.543065	+	0.940616i	−0.150619	+	0.260880i	−0.931455	−	0.363856i	$-0.881460\pi$
$13$	−0.543065	+	0.940616i	−0.150619	+	0.260880i	0.780836	+	0.624736i	$0.214793\pi$
$14$	0.867095	−	1.50185i	0.231741	−	0.401387i
$15$	5.91016	−	0.728674i	1.52600	−	0.188143i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.61033			−1.11817			−0.559085	−	0.829111i	$-0.688847\pi$
$17$	−4.61033			−1.11817			−0.559085	+	0.829111i	$0.688847\pi$
$18$	2.91016	−	0.728674i	0.685931	−	0.171750i
$19$	6.17226			1.41601			0.708007	−	0.706206i	$-0.249595\pi$
$19$	6.17226			1.41601			0.708007	+	0.706206i	$0.249595\pi$
$20$	−1.71903	−	2.97746i	−0.384388	−	0.665779i
$21$	1.17226	−	2.76551i	0.255808	−	0.603484i
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	−3.67597	+	6.36697i	−0.766493	+	1.32760i	0.172961	+	0.984929i	$0.444666\pi$
$23$	−3.67597	+	6.36697i	−0.766493	+	1.32760i	−0.939454	+	0.342676i	$0.888667\pi$
$24$	−1.04307	−	1.38276i	−0.212915	−	0.282254i
$25$	−3.41016	−	5.90657i	−0.682032	−	1.18131i
$26$	1.08613			0.213008
$27$	4.84823	−	1.86940i	0.933042	−	0.359767i
$28$	−1.73419			−0.327731
$29$	0.895004	+	1.55019i	0.166198	+	0.287864i	0.937080	−	0.349114i	$-0.113518\pi$
$29$	0.895004	+	1.55019i	0.166198	+	0.287864i	−0.770882	+	0.636978i	$0.780184\pi$
$30$	−3.58613	−	4.75401i	−0.654735	−	0.867960i
$31$	−3.91016	+	6.77260i	−0.702286	+	1.21639i	0.265377	+	0.964145i	$0.414504\pi$
$31$	−3.91016	+	6.77260i	−0.702286	+	1.21639i	−0.967662	+	0.252249i	$0.918830\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.675970	−	1.59470i	0.117671	−	0.277601i
$34$	2.30516	+	3.99266i	0.395333	+	0.684736i
$35$	−5.96227			−1.00781
$36$	−2.08613	−	2.15594i	−0.347688	−	0.359323i
$37$	−3.38225			−0.556039			−0.278019	−	0.960575i	$-0.589678\pi$
$37$	−3.38225			−0.556039			−0.278019	+	0.960575i	$0.589678\pi$
$38$	−3.08613	−	5.34533i	−0.500636	−	0.867128i
$39$	1.86710	−	0.230197i	0.298975	−	0.0368611i
$40$	−1.71903	+	2.97746i	−0.271803	+	0.470777i
$41$	−1.86710	+	3.23390i	−0.291591	+	0.505051i	−0.974186	−	0.225746i	$-0.927518\pi$
$41$	−1.86710	+	3.23390i	−0.291591	+	0.505051i	0.682595	+	0.730797i	$0.260851\pi$
$42$	−2.98113	+	0.367549i	−0.459999	+	0.0567141i
$43$	0.808874	+	1.40101i	0.123352	+	0.213652i	0.921088	−	0.389355i	$-0.127302\pi$
$43$	0.808874	+	1.40101i	0.123352	+	0.213652i	−0.797735	+	0.603008i	$0.793969\pi$
$44$	−1.00000			−0.150756
$45$	−7.17226	−	7.41226i	−1.06918	−	1.10495i
$46$	7.35194			1.08398
$47$	−5.23419	−	9.06588i	−0.763485	−	1.32240i	−0.941044	−	0.338285i	$-0.890153\pi$
$47$	−5.23419	−	9.06588i	−0.763485	−	1.32240i	0.177558	−	0.984110i	$-0.443180\pi$
$48$	−0.675970	+	1.59470i	−0.0975678	+	0.230175i
$49$	1.99629	−	3.45768i	0.285184	−	0.493954i
$50$	−3.41016	+	5.90657i	−0.482270	+	0.835315i
$51$	4.80887	+	6.37496i	0.673377	+	0.892673i
$52$	−0.543065	−	0.940616i	−0.0753096	−	0.130440i
$53$	8.96227			1.23106			0.615531	−	0.788113i	$-0.288942\pi$
$53$	8.96227			1.23106			0.615531	+	0.788113i	$0.288942\pi$
$54$	−4.04307	−	3.26399i	−0.550191	−	0.444173i
$55$	−3.43807			−0.463589
$56$	0.867095	+	1.50185i	0.115871	+	0.200694i
$57$	−6.43807	−	8.53473i	−0.852743	−	1.13045i
$58$	0.895004	−	1.55019i	0.117520	−	0.203550i
$59$	6.12920	−	10.6161i	0.797953	−	1.38210i	−0.122994	−	0.992407i	$-0.539249\pi$
$59$	6.12920	−	10.6161i	0.797953	−	1.38210i	0.920947	−	0.389688i	$-0.127417\pi$
$60$	−2.32403	+	5.48269i	−0.300031	+	0.707812i
$61$	0.648061	+	1.12247i	0.0829757	+	0.143718i	0.904527	−	0.426417i	$-0.140224\pi$
$61$	0.648061	+	1.12247i	0.0829757	+	0.143718i	−0.821551	+	0.570135i	$0.806891\pi$
$62$	7.82032			0.993182
$63$	−5.04677	+	1.26366i	−0.635834	+	0.159206i
$64$	1.00000			0.125000
$65$	−1.86710	−	3.23390i	−0.231585	−	0.401116i
$66$	−1.71903	+	0.211943i	−0.211599	+	0.0260883i
$67$	2.30887	−	3.99909i	0.282074	−	0.488566i	−0.689822	−	0.723979i	$-0.742311\pi$
$67$	2.30887	−	3.99909i	0.282074	−	0.488566i	0.971895	+	0.235413i	$0.0756443\pi$
$68$	2.30516	−	3.99266i	0.279542	−	0.484181i
$69$	12.6382	−	1.55819i	1.52147	−	0.187584i
$70$	2.98113	+	5.16348i	0.356314	+	0.617153i
$71$	8.52420			1.01164			0.505818	−	0.862640i	$-0.331191\pi$
$71$	8.52420			1.01164			0.505818	+	0.862640i	$0.331191\pi$
$72$	−0.824030	+	2.88461i	−0.0971129	+	0.339955i
$73$	−15.4865			−1.81255			−0.906277	−	0.422684i	$-0.861088\pi$
$73$	−15.4865			−1.81255			−0.906277	+	0.422684i	$0.861088\pi$
$74$	1.69113	+	2.92912i	0.196589	+	0.340503i
$75$	−4.61033	+	10.8764i	−0.532355	+	1.25589i
$76$	−3.08613	+	5.34533i	−0.354003	+	0.613152i
$77$	−0.867095	+	1.50185i	−0.0988147	+	0.171152i
$78$	−1.13290	−	1.50185i	−0.128276	−	0.170051i
$79$	6.39130	+	11.0700i	0.719077	+	1.24548i	0.961366	+	0.275274i	$0.0887684\pi$
$79$	6.39130	+	11.0700i	0.719077	+	1.24548i	−0.242289	+	0.970204i	$0.577898\pi$
$80$	3.43807			0.384388
$81$	−7.64195	−	4.75401i	−0.849105	−	0.528224i
$82$	3.73419			0.412372
$83$	2.08613	+	3.61328i	0.228983	+	0.396609i	0.957507	−	0.288411i	$-0.0931268\pi$
$83$	2.08613	+	3.61328i	0.228983	+	0.396609i	−0.728524	+	0.685020i	$0.759793\pi$
$84$	1.80887	+	2.39796i	0.197364	+	0.261639i
$85$	7.92532	−	13.7271i	0.859621	−	1.48891i
$86$	0.808874	−	1.40101i	0.0872231	−	0.151075i
$87$	1.20999	−	2.85453i	0.129725	−	0.306037i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	1.35194			0.143305			0.0716526	−	0.997430i	$-0.477173\pi$
$89$	1.35194			0.143305			0.0716526	+	0.997430i	$0.477173\pi$
$90$	−2.83307	+	9.91749i	−0.298632	+	1.04540i
$91$	−1.88356			−0.197450
$92$	−3.67597	−	6.36697i	−0.383246	−	0.663802i
$93$	13.4434	−	1.65746i	1.39402	−	0.171871i
$94$	−5.23419	+	9.06588i	−0.539866	+	0.935075i
$95$	−10.6103	+	18.3776i	−1.08860	+	1.88551i
$96$	1.71903	−	0.211943i	0.175448	−	0.0216313i
$97$	−1.58613	−	2.74726i	−0.161047	−	0.278942i	0.774197	−	0.632944i	$-0.218154\pi$
$97$	−1.58613	−	2.74726i	−0.161047	−	0.278942i	−0.935244	+	0.354002i	$0.884820\pi$
$98$	−3.99258			−0.403312
$99$	−2.91016	+	0.728674i	−0.292482	+	0.0732345i
$100$	6.82032			0.682032
$101$	7.17226	+	12.4227i	0.713667	+	1.23611i	0.963472	+	0.267811i	$0.0863002\pi$
$101$	7.17226	+	12.4227i	0.713667	+	1.23611i	−0.249805	+	0.968296i	$0.580367\pi$
$102$	3.11644	−	7.35209i	0.308574	−	0.727965i
$103$	−0.175970	+	0.304788i	−0.0173388	+	0.0300317i	−0.874565	−	0.484909i	$-0.838853\pi$
$103$	−0.175970	+	0.304788i	−0.0173388	+	0.0300317i	0.857226	+	0.514941i	$0.172186\pi$
$104$	−0.543065	+	0.940616i	−0.0532519	+	0.0922350i
$105$	6.21903	+	8.24437i	0.606916	+	0.804568i
$106$	−4.48113	−	7.76155i	−0.435246	−	0.753869i
$107$	16.1345			1.55978			0.779892	−	0.625914i	$-0.215274\pi$
$107$	16.1345			1.55978			0.779892	+	0.625914i	$0.215274\pi$
$108$	−0.805165	+	5.13339i	−0.0774770	+	0.493961i
$109$	−6.70388			−0.642115			−0.321058	−	0.947060i	$-0.604038\pi$
$109$	−6.70388			−0.642115			−0.321058	+	0.947060i	$0.604038\pi$
$110$	1.71903	+	2.97746i	0.163904	+	0.283889i
$111$	3.52791	+	4.67683i	0.334854	+	0.443905i
$112$	0.867095	−	1.50185i	0.0819328	−	0.141912i
$113$	7.46227	−	12.9250i	0.701991	−	1.21588i	−0.265775	−	0.964035i	$-0.585628\pi$
$113$	7.46227	−	12.9250i	0.701991	−	1.21588i	0.967766	−	0.251849i	$-0.0810388\pi$
$114$	−4.17226	+	9.84290i	−0.390768	+	0.921872i
$115$	−12.6382	−	21.8901i	−1.17852	−	2.04126i
$116$	−1.79001			−0.166198
$117$	−2.26581	−	2.34163i	−0.209474	−	0.216484i
$118$	−12.2584			−1.12848
$119$	−3.99760	−	6.92404i	−0.366459	−	0.634726i
$120$	5.91016	−	0.728674i	0.539521	−	0.0665185i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	0.648061	−	1.12247i	0.0586727	−	0.101624i
$123$	6.41920	−	0.791434i	0.578800	−	0.0713612i
$124$	−3.91016	−	6.77260i	−0.351143	−	0.608197i
$125$	6.25839			0.559767
$126$	3.61775	+	3.73881i	0.322295	+	0.333079i
$127$	16.3445			1.45034			0.725171	−	0.688569i	$-0.241761\pi$
$127$	16.3445			1.45034			0.725171	+	0.688569i	$0.241761\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.09355	−	2.57982i	0.0962816	−	0.227141i
$130$	−1.86710	+	3.23390i	−0.163755	+	0.283632i
$131$	−7.33307	+	12.7013i	−0.640694	+	1.10971i	0.344585	+	0.938755i	$0.388020\pi$
$131$	−7.33307	+	12.7013i	−0.640694	+	1.10971i	−0.985278	+	0.170959i	$0.945314\pi$
$132$	1.04307	+	1.38276i	0.0907872	+	0.120353i
$133$	5.35194	+	9.26983i	0.464072	+	0.803796i
$134$	−4.61775			−0.398913
$135$	−2.76821	+	17.6490i	−0.238250	+	1.51898i
$136$	−4.61033			−0.395333
$137$	6.96598	+	12.0654i	0.595144	+	1.03082i	0.993527	+	0.113600i	$0.0362382\pi$
$137$	6.96598	+	12.0654i	0.595144	+	1.03082i	−0.398383	+	0.917219i	$0.630428\pi$
$138$	−7.66855	−	10.1659i	−0.652790	−	0.865382i
$139$	6.15339	−	10.6580i	0.521924	−	0.903999i	−0.477751	−	0.878496i	$-0.658548\pi$
$139$	6.15339	−	10.6580i	0.521924	−	0.903999i	0.999675	−	0.0255036i	$-0.00811893\pi$
$140$	2.98113	−	5.16348i	0.251952	−	0.436393i
$141$	−7.07631	+	16.6939i	−0.595933	+	1.40588i
$142$	−4.26210	−	7.38217i	−0.357667	−	0.619498i
$143$	−1.08613			−0.0908268
$144$	2.91016	−	0.728674i	0.242513	−	0.0607228i
$145$	−6.15417			−0.511076
$146$	7.74323	+	13.4117i	0.640835	+	1.10996i
$147$	−6.86339	+	0.846198i	−0.566083	+	0.0697933i
$148$	1.69113	−	2.92912i	0.139010	−	0.240772i
$149$	−1.35194	+	2.34163i	−0.110755	+	0.191834i	−0.916075	−	0.401007i	$-0.868660\pi$
$149$	−1.35194	+	2.34163i	−0.110755	+	0.191834i	0.805320	+	0.592841i	$0.201994\pi$
$150$	11.7244	−	1.44552i	0.957291	−	0.118026i
$151$	2.51516	+	4.35638i	0.204681	+	0.354517i	0.950031	−	0.312156i	$-0.101051\pi$
$151$	2.51516	+	4.35638i	0.204681	+	0.354517i	−0.745350	+	0.666673i	$0.767718\pi$
$152$	6.17226			0.500636
$153$	3.79905	−	13.2990i	0.307135	−	1.07516i
$154$	1.73419			0.139745
$155$	−13.4434	−	23.2847i	−1.07980	−	1.87027i
$156$	−0.734191	+	1.73205i	−0.0587823	+	0.138675i
$157$	−0.632905	+	1.09622i	−0.0505113	+	0.0874881i	−0.890176	−	0.455618i	$-0.849418\pi$
$157$	−0.632905	+	1.09622i	−0.0505113	+	0.0874881i	0.839664	+	0.543106i	$0.182752\pi$
$158$	6.39130	−	11.0700i	0.508464	−	0.880686i
$159$	−9.34823	−	12.3926i	−0.741363	−	0.982800i
$160$	−1.71903	−	2.97746i	−0.135902	−	0.235389i
$161$	−12.7497			−1.00481
$162$	−0.296122	+	8.99513i	−0.0232655	+	0.706724i
$163$	−5.61033			−0.439435			−0.219717	−	0.975564i	$-0.570514\pi$
$163$	−5.61033			−0.439435			−0.219717	+	0.975564i	$0.570514\pi$
$164$	−1.86710	−	3.23390i	−0.145796	−	0.252525i
$165$	3.58613	+	4.75401i	0.279180	+	0.370099i
$166$	2.08613	−	3.61328i	0.161915	−	0.280445i
$167$	4.79001	−	8.29654i	0.370662	−	0.642005i	−0.619006	−	0.785387i	$-0.712464\pi$
$167$	4.79001	−	8.29654i	0.370662	−	0.642005i	0.989668	+	0.143381i	$0.0457975\pi$
$168$	1.17226	−	2.76551i	0.0904419	−	0.213364i
$169$	5.91016	+	10.2367i	0.454628	+	0.787438i
$170$	−15.8506			−1.21569
$171$	−5.08613	+	17.8046i	−0.388946	+	1.36155i
$172$	−1.61775			−0.123352
$173$	−10.1911	−	17.6515i	−0.774817	−	1.34202i	−0.934897	−	0.354918i	$-0.884509\pi$
$173$	−10.1911	−	17.6515i	−0.774817	−	1.34202i	0.160080	−	0.987104i	$-0.448825\pi$
$174$	−3.07709	+	0.379379i	−0.233273	+	0.0287607i
$175$	5.91387	−	10.2431i	0.447047	−	0.774307i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	−21.0726	+	2.59808i	−1.58391	+	0.195283i
$178$	−0.675970	−	1.17081i	−0.0506661	−	0.0877562i
$179$	−4.19777			−0.313756			−0.156878	−	0.987618i	$-0.550143\pi$
$179$	−4.19777			−0.313756			−0.156878	+	0.987618i	$0.550143\pi$
$180$	10.0053	−	2.50523i	0.745754	−	0.186729i
$181$	−13.7220			−1.01995			−0.509973	−	0.860191i	$-0.670345\pi$
$181$	−13.7220			−1.01995			−0.509973	+	0.860191i	$0.670345\pi$
$182$	0.941779	+	1.63121i	0.0698093	+	0.120913i
$183$	0.876139	−	2.06692i	0.0647660	−	0.152791i
$184$	−3.67597	+	6.36697i	−0.270996	+	0.469379i
$185$	5.81421	−	10.0705i	0.427469	−	0.740398i
$186$	−8.15710	−	10.8136i	−0.598108	−	0.792892i
$187$	−2.30516	−	3.99266i	−0.168570	−	0.291972i
$188$	10.4684			0.763485
$189$	7.01145	+	5.66038i	0.510008	+	0.411732i
$190$	21.2207			1.53951
$191$	−1.26210	−	2.18602i	−0.0913223	−	0.158175i	0.816745	−	0.576998i	$-0.195776\pi$
$191$	−1.26210	−	2.18602i	−0.0913223	−	0.158175i	−0.908068	+	0.418823i	$0.862443\pi$
$192$	−1.04307	−	1.38276i	−0.0752767	−	0.0997918i
$193$	−11.1345	+	19.2856i	−0.801481	+	1.38821i	0.117160	+	0.993113i	$0.462621\pi$
$193$	−11.1345	+	19.2856i	−0.801481	+	1.38821i	−0.918641	+	0.395093i	$0.870712\pi$
$194$	−1.58613	+	2.74726i	−0.113878	+	0.197242i
$195$	−2.52420	+	5.95491i	−0.180762	+	0.426440i
$196$	1.99629	+	3.45768i	0.142592	+	0.246977i
$197$	17.6029			1.25416			0.627078	−	0.778957i	$-0.284251\pi$
$197$	17.6029			1.25416			0.627078	+	0.778957i	$0.284251\pi$
$198$	2.08613	+	2.15594i	0.148255	+	0.153216i
$199$	−0.356747			−0.0252891			−0.0126446	−	0.999920i	$-0.504025\pi$
$199$	−0.356747			−0.0252891			−0.0126446	+	0.999920i	$0.504025\pi$
$200$	−3.41016	−	5.90657i	−0.241135	−	0.417658i
$201$	−7.93807	+	0.978698i	−0.559908	+	0.0690320i
$202$	7.17226	−	12.4227i	0.504638	−	0.874059i
$203$	−1.55211	+	2.68833i	−0.108937	+	0.188684i
$204$	−7.92532	+	0.977126i	−0.554883	+	0.0684125i
$205$	−6.41920	−	11.1184i	−0.448337	−	0.776542i
$206$	0.351939			0.0245208
$207$	−15.3371	−	15.8503i	−1.06600	−	1.10167i
$208$	1.08613			0.0753096
$209$	3.08613	+	5.34533i	0.213472	+	0.369745i
$210$	4.03031	−	9.50802i	0.278118	−	0.656116i
$211$	3.05582	−	5.29283i	0.210371	−	0.364374i	−0.741460	−	0.670998i	$-0.765866\pi$
$211$	3.05582	−	5.29283i	0.210371	−	0.364374i	0.951831	+	0.306624i	$0.0991994\pi$
$212$	−4.48113	+	7.76155i	−0.307766	+	0.533066i
$213$	−8.89130	−	11.7869i	−0.609222	−	0.807624i
$214$	−8.06726	−	13.9729i	−0.551467	−	0.955169i
$215$	−5.56193			−0.379321
$216$	4.84823	−	1.86940i	0.329880	−	0.127197i
$217$	−13.5619			−0.920644
$218$	3.35194	+	5.80573i	0.227022	+	0.393214i
$219$	16.1534	+	21.4140i	1.09155	+	1.44702i
$220$	1.71903	−	2.97746i	0.115897	−	0.200740i
$221$	2.50371	−	4.33655i	0.168418	−	0.291708i
$222$	2.28630	−	5.39367i	0.153446	−	0.362000i
$223$	2.37985	+	4.12202i	0.159366	+	0.276031i	0.934640	−	0.355594i	$-0.115722\pi$
$223$	2.37985	+	4.12202i	0.159366	+	0.276031i	−0.775274	+	0.631625i	$0.782388\pi$
$224$	−1.73419			−0.115871
$225$	19.8482	−	4.96979i	1.32322	−	0.331319i
$226$	−14.9245			−0.992765
$227$	3.16081	+	5.47469i	0.209791	+	0.363368i	0.951648	−	0.307189i	$-0.0993885\pi$
$227$	3.16081	+	5.47469i	0.209791	+	0.363368i	−0.741858	+	0.670557i	$0.766055\pi$
$228$	10.6103	−	1.30817i	0.702686	−	0.0866354i
$229$	5.23790	−	9.07231i	0.346130	−	0.599515i	−0.639428	−	0.768851i	$-0.720829\pi$
$229$	5.23790	−	9.07231i	0.346130	−	0.599515i	0.985558	+	0.169336i	$0.0541622\pi$
$230$	−12.6382	+	21.8901i	−0.833341	+	1.44339i
$231$	2.98113	−	0.367549i	0.196144	−	0.0241830i
$232$	0.895004	+	1.55019i	0.0587599	+	0.101775i
$233$	−10.9697			−0.718648			−0.359324	−	0.933213i	$-0.616993\pi$
$233$	−10.9697			−0.718648			−0.359324	+	0.933213i	$0.616993\pi$
$234$	−0.895004	+	3.13306i	−0.0585083	+	0.204815i
$235$	35.9910			2.34780
$236$	6.12920	+	10.6161i	0.398977	+	0.691048i
$237$	8.64064	−	20.3844i	0.561270	−	1.32411i
$238$	−3.99760	+	6.92404i	−0.259126	+	0.448819i
$239$	8.56356	−	14.8325i	0.553930	−	0.959436i	−0.444056	−	0.895999i	$-0.646461\pi$
$239$	8.56356	−	14.8325i	0.553930	−	0.959436i	0.997986	−	0.0634363i	$-0.0202060\pi$
$240$	−3.58613	−	4.75401i	−0.231484	−	0.306870i
$241$	11.4381	+	19.8113i	0.736791	+	1.27616i	0.953933	+	0.300019i	$0.0969931\pi$
$241$	11.4381	+	19.8113i	0.736791	+	1.27616i	−0.217142	+	0.976140i	$0.569674\pi$
$242$	1.00000			0.0642824
$243$	1.39741	+	15.5257i	0.0896438	+	0.995974i
$244$	−1.29612			−0.0829757
$245$	6.86339	+	11.8877i	0.438486	+	0.759479i
$246$	−3.89500	−	5.16348i	−0.248336	−	0.329211i
$247$	−3.35194	+	5.80573i	−0.213279	+	0.369410i
$248$	−3.91016	+	6.77260i	−0.248295	+	0.430060i
$249$	2.82032	−	6.65350i	0.178731	−	0.421648i
$250$	−3.12920	−	5.41993i	−0.197908	−	0.342786i
$251$	17.6406			1.11347			0.556734	−	0.830691i	$-0.312054\pi$
$251$	17.6406			1.11347			0.556734	+	0.830691i	$0.312054\pi$
$252$	1.42903	−	5.00246i	0.0900202	−	0.315126i
$253$	−7.35194			−0.462212
$254$	−8.17226	−	14.1548i	−0.512773	−	0.888149i
$255$	−27.2478	+	3.35943i	−1.70632	+	0.210375i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.55451	+	16.5489i	−0.595994	+	1.03229i	0.397412	+	0.917640i	$0.369909\pi$
$257$	−9.55451	+	16.5489i	−0.595994	+	1.03229i	−0.993406	+	0.114652i	$0.963425\pi$
$258$	−2.78097	+	0.342870i	−0.173135	+	0.0213461i
$259$	−2.93274	−	5.07965i	−0.182231	−	0.315634i
$260$	3.73419			0.231585
$261$	−5.20921	+	1.30433i	−0.322442	+	0.0807361i
$262$	14.6661			0.906078
$263$	−0.657104	−	1.13814i	−0.0405188	−	0.0701806i	0.845055	−	0.534680i	$-0.179568\pi$
$263$	−0.657104	−	1.13814i	−0.0405188	−	0.0701806i	−0.885574	+	0.464499i	$0.846234\pi$
$264$	0.675970	−	1.59470i	0.0416031	−	0.0981469i
$265$	−15.4065	+	26.6848i	−0.946411	+	1.63923i
$266$	5.35194	−	9.26983i	0.328148	−	0.568370i
$267$	−1.41016	−	1.86940i	−0.0863004	−	0.114406i
$268$	2.30887	+	3.99909i	0.141037	+	0.244283i
$269$	−2.56193			−0.156204			−0.0781018	−	0.996945i	$-0.524886\pi$
$269$	−2.56193			−0.156204			−0.0781018	+	0.996945i	$0.524886\pi$
$270$	16.6686	−	6.42714i	1.01442	−	0.391143i
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	2.30516	+	3.99266i	0.139771	+	0.242091i
$273$	1.96467	+	2.60450i	0.118907	+	0.157632i
$274$	6.96598	−	12.0654i	0.420830	−	0.728899i
$275$	3.41016	−	5.90657i	0.205640	−	0.356180i
$276$	−4.96969	+	11.7241i	−0.299140	+	0.705710i
$277$	15.3142	+	26.5250i	0.920142	+	1.59373i	0.799194	+	0.601073i	$0.205260\pi$
$277$	15.3142	+	26.5250i	0.920142	+	1.59373i	0.120948	+	0.992659i	$0.461407\pi$
$278$	−12.3068			−0.738112
$279$	−16.3142	−	16.8601i	−0.976706	−	1.00939i
$280$	−5.96227			−0.356314
$281$	4.17226	+	7.22657i	0.248896	+	0.431101i	0.963220	−	0.268715i	$-0.0865989\pi$
$281$	4.17226	+	7.22657i	0.248896	+	0.431101i	−0.714324	+	0.699816i	$0.753266\pi$
$282$	17.9955	−	2.21870i	1.07162	−	0.132121i
$283$	1.86469	−	3.22974i	0.110844	−	0.191988i	−0.805267	−	0.592913i	$-0.797978\pi$
$283$	1.86469	−	3.22974i	0.110844	−	0.191988i	0.916111	+	0.400925i	$0.131311\pi$
$284$	−4.26210	+	7.38217i	−0.252909	+	0.438051i
$285$	36.4791	−	4.49756i	2.16083	−	0.266413i
$286$	0.543065	+	0.940616i	0.0321121	+	0.0556198i
$287$	−6.47580			−0.382254
$288$	−2.08613	−	2.15594i	−0.122926	−	0.127040i
$289$	4.25514			0.250302
$290$	3.07709	+	5.32967i	0.180693	+	0.312969i
$291$	−2.14435	+	5.05880i	−0.125704	+	0.296552i
$292$	7.74323	−	13.4117i	0.453139	−	0.784859i
$293$	−12.1231	+	20.9978i	−0.708238	+	1.22670i	0.257272	+	0.966339i	$0.417176\pi$
$293$	−12.1231	+	20.9978i	−0.708238	+	1.22670i	−0.965510	+	0.260365i	$0.916157\pi$
$294$	4.16452	+	5.52077i	0.242880	+	0.321978i
$295$	21.0726	+	36.4988i	1.22689	+	2.12504i
$296$	−3.38225			−0.196589
$297$	4.04307	+	3.26399i	0.234602	+	0.189396i
$298$	2.70388			0.156631
$299$	−3.99258	−	6.91535i	−0.230897	−	0.399925i
$300$	−7.11404	−	9.43084i	−0.410729	−	0.544490i
$301$	−1.40274	+	2.42962i	−0.0808527	+	0.140041i
$302$	2.51516	−	4.35638i	0.144731	−	0.250681i
$303$	9.69646	−	22.8752i	0.557047	−	1.31415i
$304$	−3.08613	−	5.34533i	−0.177002	−	0.306576i
$305$	−4.45616			−0.255159
$306$	−13.4168	+	3.35943i	−0.766987	+	0.192046i
$307$	−23.1978			−1.32397			−0.661983	−	0.749519i	$-0.730285\pi$
$307$	−23.1978			−1.32397			−0.661983	+	0.749519i	$0.730285\pi$
$308$	−0.867095	−	1.50185i	−0.0494074	−	0.0855760i
$309$	0.604996	−	0.0745909i	0.0344170	−	0.00424333i
$310$	−13.4434	+	23.2847i	−0.763534	+	1.32248i
$311$	−1.85434	+	3.21182i	−0.105150	+	0.182125i	−0.913800	−	0.406165i	$-0.866866\pi$
$311$	−1.85434	+	3.21182i	−0.105150	+	0.182125i	0.808649	+	0.588291i	$0.200199\pi$
$312$	1.86710	−	0.230197i	0.105703	−	0.0130324i
$313$	3.55211	+	6.15243i	0.200777	+	0.347756i	0.948779	−	0.315940i	$-0.102320\pi$
$313$	3.55211	+	6.15243i	0.200777	+	0.347756i	−0.748002	+	0.663696i	$0.768987\pi$
$314$	1.26581			0.0714337
$315$	4.91309	−	17.1988i	0.276821	−	0.969044i
$316$	−12.7826			−0.719077
$317$	−10.3142	−	17.8647i	−0.579304	−	1.00338i	−0.995559	−	0.0941358i	$-0.969991\pi$
$317$	−10.3142	−	17.8647i	−0.579304	−	1.00338i	0.416256	−	0.909248i	$-0.363342\pi$
$318$	−6.05822	+	14.2921i	−0.339728	+	0.801462i
$319$	−0.895004	+	1.55019i	−0.0501106	+	0.0867941i
$320$	−1.71903	+	2.97746i	−0.0960970	+	0.166445i
$321$	−16.8294	−	22.3101i	−0.939324	−	1.24523i
$322$	6.37483	+	11.0415i	0.355256	+	0.615321i
$323$	−28.4562			−1.58334
$324$	7.93807	−	4.24111i	0.441004	−	0.235617i
$325$	7.40776			0.410908
$326$	2.80516	+	4.85869i	0.155364	+	0.269098i
$327$	6.99258	+	9.26983i	0.386691	+	0.512623i
$328$	−1.86710	+	3.23390i	−0.103093	+	0.178562i
$329$	9.07709	−	15.7220i	0.500436	−	0.866781i
$330$	2.32403	−	5.48269i	0.127934	−	0.301812i
$331$	−1.84290	−	3.19199i	−0.101295	−	0.175448i	0.810924	−	0.585152i	$-0.198965\pi$
$331$	−1.84290	−	3.19199i	−0.101295	−	0.175448i	−0.912218	+	0.409704i	$0.865632\pi$
$332$	−4.17226			−0.228983
$333$	2.78708	−	9.75648i	0.152731	−	0.534652i
$334$	−9.58002			−0.524195
$335$	7.93807	+	13.7491i	0.433703	+	0.751196i
$336$	−2.98113	+	0.367549i	−0.162634	+	0.0200514i
$337$	17.4774	−	30.2718i	0.952056	−	1.64901i	0.211090	−	0.977467i	$-0.432299\pi$
$337$	17.4774	−	30.2718i	0.952056	−	1.64901i	0.740966	−	0.671543i	$-0.234368\pi$
$338$	5.91016	−	10.2367i	0.321470	−	0.556803i
$339$	−25.6558	+	3.16315i	−1.39343	+	0.171799i
$340$	7.92532	+	13.7271i	0.429811	+	0.744454i
$341$	−7.82032			−0.423494
$342$	17.9623	−	4.49756i	0.971288	−	0.243200i
$343$	19.0632			1.02932
$344$	0.808874	+	1.40101i	0.0436116	+	0.0755375i
$345$	−17.0861	+	40.3084i	−0.919886	+	2.17013i
$346$	−10.1911	+	17.6515i	−0.547878	+	0.948953i
$347$	4.01145	−	6.94803i	0.215346	−	0.372990i	−0.738034	−	0.674764i	$-0.764245\pi$
$347$	4.01145	−	6.94803i	0.215346	−	0.372990i	0.953379	+	0.301774i	$0.0975788\pi$
$348$	1.86710	+	2.47515i	0.100087	+	0.132682i
$349$	7.24694	+	12.5521i	0.387920	+	0.671897i	0.992170	−	0.124898i	$-0.0398604\pi$
$349$	7.24694	+	12.5521i	0.387920	+	0.671897i	−0.604250	+	0.796795i	$0.706527\pi$
$350$	−11.8277			−0.632219
$351$	−0.874514	+	5.57553i	−0.0466781	+	0.297600i
$352$	−1.00000			−0.0533002
$353$	4.46838	+	7.73946i	0.237828	+	0.411930i	0.960091	−	0.279689i	$-0.0902312\pi$
$353$	4.46838	+	7.73946i	0.237828	+	0.411930i	−0.722263	+	0.691619i	$0.756898\pi$
$354$	12.7863	+	16.9504i	0.679584	+	0.900902i
$355$	−14.6534	+	25.3804i	−0.777721	+	1.34705i
$356$	−0.675970	+	1.17081i	−0.0358263	+	0.0620530i
$357$	−5.40451	+	12.7499i	−0.286037	+	0.674798i
$358$	2.09888	+	3.63537i	0.110929	+	0.192135i
$359$	−12.5168			−0.660610			−0.330305	−	0.943874i	$-0.607152\pi$
$359$	−12.5168			−0.660610			−0.330305	+	0.943874i	$0.607152\pi$
$360$	−7.17226	−	7.41226i	−0.378011	−	0.390660i
$361$	19.0968			1.00509
$362$	6.86098	+	11.8836i	0.360605	+	0.624587i
$363$	1.71903	−	0.211943i	0.0902259	−	0.0111241i
$364$	0.941779	−	1.63121i	0.0493626	−	0.0854986i
$365$	26.6218	−	46.1103i	1.39345	−	2.41352i
$366$	−2.22808	+	0.274703i	−0.116464	+	0.0143590i
$367$	−2.73790	−	4.74218i	−0.142917	−	0.247540i	0.785677	−	0.618637i	$-0.212315\pi$
$367$	−2.73790	−	4.74218i	−0.142917	−	0.247540i	−0.928594	+	0.371097i	$0.878982\pi$
$368$	7.35194			0.383246
$369$	−7.79001	−	8.05068i	−0.405532	−	0.419102i
$370$	−11.6284			−0.604533
$371$	7.77114	+	13.4600i	0.403458	+	0.698809i
$372$	−5.28630	+	12.4711i	−0.274082	+	0.646594i
$373$	2.11644	−	3.66579i	0.109585	−	0.189807i	−0.806017	−	0.591892i	$-0.798381\pi$
$373$	2.11644	−	3.66579i	0.109585	−	0.189807i	0.915602	+	0.402085i	$0.131714\pi$
$374$	−2.30516	+	3.99266i	−0.119197	+	0.206456i
$375$	−6.52791	−	8.65383i	−0.337100	−	0.446882i
$376$	−5.23419	−	9.06588i	−0.269933	−	0.467537i
$377$	−1.94418			−0.100130
$378$	1.39631	−	8.90228i	0.0718184	−	0.457884i
$379$	26.5168			1.36208			0.681038	−	0.732248i	$-0.261529\pi$
$379$	26.5168			1.36208			0.681038	+	0.732248i	$0.261529\pi$
$380$	−10.6103	−	18.3776i	−0.544298	−	0.942753i
$381$	−17.0484	−	22.6005i	−0.873416	−	1.15786i
$382$	−1.26210	+	2.18602i	−0.0645746	+	0.111847i
$383$	17.9307	−	31.0568i	0.916213	−	1.58693i	0.111099	−	0.993809i	$-0.464563\pi$
$383$	17.9307	−	31.0568i	0.916213	−	1.58693i	0.805115	−	0.593119i	$-0.202104\pi$
$384$	−0.675970	+	1.59470i	−0.0344954	+	0.0813791i
$385$	−2.98113	−	5.16348i	−0.151933	−	0.263155i
$386$	22.2691			1.13347
$387$	−4.70791	+	1.17881i	−0.239316	+	0.0599223i
$388$	3.17226			0.161047
$389$	5.87080	+	10.1685i	0.297662	+	0.515565i	0.975601	−	0.219553i	$-0.0704600\pi$
$389$	5.87080	+	10.1685i	0.297662	+	0.515565i	−0.677939	+	0.735118i	$0.737127\pi$
$390$	6.41920	−	0.791434i	0.325049	−	0.0400758i
$391$	16.9474	−	29.3538i	0.857068	−	1.48449i
$392$	1.99629	−	3.45768i	0.100828	−	0.174639i
$393$	25.2116	−	3.10838i	1.27176	−	0.156797i
$394$	−8.80146	−	15.2446i	−0.443411	−	0.768010i
$395$	−43.9474			−2.21124
$396$	0.824030	−	2.88461i	0.0414091	−	0.144957i
$397$	10.4865			0.526301			0.263150	−	0.964755i	$-0.415238\pi$
$397$	10.4865			0.526301			0.263150	+	0.964755i	$0.415238\pi$
$398$	0.178373	+	0.308952i	0.00894105	+	0.0154864i
$399$	7.23550	−	17.0695i	0.362228	−	0.854542i
$400$	−3.41016	+	5.90657i	−0.170508	+	0.295329i
$401$	−10.1406	+	17.5641i	−0.506400	+	0.877110i	0.493573	+	0.869704i	$0.335691\pi$
$401$	−10.1406	+	17.5641i	−0.506400	+	0.877110i	−0.999973	+	0.00740535i	$0.997643\pi$
$402$	4.81661	+	6.38522i	0.240231	+	0.318466i
$403$	−4.24694	−	7.35592i	−0.211555	−	0.366425i
$404$	−14.3445			−0.713667
$405$	27.2916	−	14.5812i	1.35613	−	0.724548i
$406$	3.10422			0.154060
$407$	−1.69113	−	2.92912i	−0.0838260	−	0.145191i
$408$	4.80887	+	6.37496i	0.238075	+	0.315608i
$409$	9.09517	−	15.7533i	0.449727	−	0.778951i	−0.548641	−	0.836058i	$-0.684854\pi$
$409$	9.09517	−	15.7533i	0.449727	−	0.778951i	0.998368	+	0.0571076i	$0.0181878\pi$
$410$	−6.41920	+	11.1184i	−0.317022	+	0.549098i
$411$	9.41758	−	22.2173i	0.464535	−	1.09590i
$412$	−0.175970	−	0.304788i	−0.00866940	−	0.0150158i
$413$	21.2584			1.04606
$414$	−6.05822	+	21.2075i	−0.297745	+	1.04229i
$415$	−14.3445			−0.704145
$416$	−0.543065	−	0.940616i	−0.0266260	−	0.0461175i
$417$	−21.1558	+	2.60833i	−1.03600	+	0.127731i
$418$	3.08613	−	5.34533i	0.150948	−	0.261449i
$419$	14.6739	−	25.4159i	0.716866	−	1.24165i	−0.245369	−	0.969430i	$-0.578909\pi$
$419$	14.6739	−	25.4159i	0.716866	−	1.24165i	0.962235	−	0.272219i	$-0.0877575\pi$
$420$	−10.2493	+	1.26366i	−0.500117	+	0.0616603i
$421$	−13.9471	−	24.1571i	−0.679741	−	1.17735i	−0.975059	−	0.221946i	$-0.928759\pi$
$421$	−13.9471	−	24.1571i	−0.679741	−	1.17735i	0.295318	−	0.955399i	$-0.404574\pi$
$422$	−6.11164			−0.297510
$423$	30.4647	−	7.62803i	1.48124	−	0.370888i
$424$	8.96227			0.435246
$425$	15.7220	+	27.2312i	0.762627	+	1.32091i
$426$	−5.76210	+	13.5935i	−0.279175	+	0.658609i
$427$	−1.12386	+	1.94658i	−0.0543875	+	0.0942018i
$428$	−8.06726	+	13.9729i	−0.389946	+	0.675406i
$429$	1.13290	+	1.50185i	0.0546971	+	0.0725102i
$430$	2.78097	+	4.81677i	0.134110	+	0.232285i
$431$	−18.7974			−0.905440			−0.452720	−	0.891653i	$-0.649546\pi$
$431$	−18.7974			−0.905440			−0.452720	+	0.891653i	$0.649546\pi$
$432$	−4.04307	−	3.26399i	−0.194522	−	0.157039i
$433$	−14.5726			−0.700314			−0.350157	−	0.936691i	$-0.613872\pi$
$433$	−14.5726			−0.700314			−0.350157	+	0.936691i	$0.613872\pi$
$434$	6.78097	+	11.7450i	0.325497	+	0.563777i
$435$	6.41920	+	8.50972i	0.307777	+	0.408010i
$436$	3.35194	−	5.80573i	0.160529	−	0.278044i
$437$	−22.6890	+	39.2986i	−1.08536	+	1.87991i
$438$	10.4684	−	24.6963i	0.500199	−	1.18003i
$439$	−9.66615	−	16.7423i	−0.461340	−	0.799064i	0.537688	−	0.843144i	$-0.319298\pi$
$439$	−9.66615	−	16.7423i	−0.461340	−	0.799064i	−0.999028	+	0.0440795i	$0.985965\pi$
$440$	−3.43807			−0.163904
$441$	8.32905	+	8.60775i	0.396621	+	0.409893i
$442$	−5.00742			−0.238179
$443$	−7.62308	−	13.2036i	−0.362184	−	0.627320i	0.626136	−	0.779714i	$-0.284635\pi$
$443$	−7.62308	−	13.2036i	−0.362184	−	0.627320i	−0.988320	+	0.152393i	$0.951302\pi$
$444$	−5.81421	+	0.716844i	−0.275930	+	0.0340199i
$445$	−2.32403	+	4.02534i	−0.110170	+	0.190819i
$446$	2.37985	−	4.12202i	0.112689	−	0.195183i
$447$	4.64806	−	0.573067i	0.219846	−	0.0271052i
$448$	0.867095	+	1.50185i	0.0409664	+	0.0709559i
$449$	−9.83516			−0.464150			−0.232075	−	0.972698i	$-0.574551\pi$
$449$	−9.83516			−0.464150			−0.232075	+	0.972698i	$0.574551\pi$
$450$	−14.2281	−	14.7042i	−0.670718	−	0.693162i
$451$	−3.73419			−0.175836
$452$	7.46227	+	12.9250i	0.350996	+	0.607942i
$453$	3.40034	−	8.02183i	0.159762	−	0.376899i
$454$	3.16081	−	5.47469i	0.148344	−	0.256940i
$455$	3.23790	−	5.60821i	0.151795	−	0.262917i
$456$	−6.43807	−	8.53473i	−0.301490	−	0.399675i
$457$	−11.8687	−	20.5572i	−0.555195	−	0.961627i	−0.997888	−	0.0649533i	$-0.979310\pi$
$457$	−11.8687	−	20.5572i	−0.555195	−	0.961627i	0.442693	−	0.896673i	$-0.354023\pi$
$458$	−10.4758			−0.489502
$459$	−22.3519	+	8.61856i	−1.04330	+	0.402280i
$460$	25.2765			1.17852
$461$	3.01887	+	5.22883i	0.140603	+	0.243531i	0.927724	−	0.373268i	$-0.121763\pi$
$461$	3.01887	+	5.22883i	0.140603	+	0.243531i	−0.787121	+	0.616798i	$0.788429\pi$
$462$	−1.80887	−	2.39796i	−0.0841564	−	0.111563i
$463$	−16.7802	+	29.0641i	−0.779841	+	1.35072i	0.152191	+	0.988351i	$0.451367\pi$
$463$	−16.7802	+	29.0641i	−0.779841	+	1.35072i	−0.932033	+	0.362374i	$0.881966\pi$
$464$	0.895004	−	1.55019i	0.0415495	−	0.0719659i
$465$	−18.1747	+	42.8764i	−0.842830	+	1.98834i
$466$	5.48484	+	9.50003i	0.254080	+	0.440080i
$467$	−28.1877			−1.30437			−0.652186	−	0.758059i	$-0.726148\pi$
$467$	−28.1877			−1.30437			−0.652186	+	0.758059i	$0.726148\pi$
$468$	3.16081	−	0.791434i	0.146109	−	0.0365841i
$469$	8.00806			0.369778
$470$	−17.9955	−	31.1691i	−0.830071	−	1.43773i
$471$	2.17597	−	0.268279i	0.100263	−	0.0123616i
$472$	6.12920	−	10.6161i	0.282119	−	0.488645i
$473$	−0.808874	+	1.40101i	−0.0371921	+	0.0644186i
$474$	−21.9737	+	2.70918i	−1.00929	+	0.124437i
$475$	−21.0484	−	36.4569i	−0.965767	−	1.67276i
$476$	7.99519			0.366459
$477$	−7.38518	+	25.8526i	−0.338144	+	1.18371i
$478$	−17.1271			−0.783376
$479$	−1.94418	−	3.36742i	−0.0888320	−	0.153861i	0.818186	−	0.574954i	$-0.194980\pi$
$479$	−1.94418	−	3.36742i	−0.0888320	−	0.153861i	−0.907018	+	0.421093i	$0.861647\pi$
$480$	−2.32403	+	5.48269i	−0.106077	+	0.250249i
$481$	1.83678	−	3.18140i	0.0837501	−	0.145059i
$482$	11.4381	−	19.8113i	0.520990	−	0.902381i
$483$	13.2987	+	17.6297i	0.605113	+	0.802178i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	10.9065			0.495236
$486$	12.7469	−	8.97304i	0.578213	−	0.407025i
$487$	−21.9777			−0.995907			−0.497953	−	0.867204i	$-0.665915\pi$
$487$	−21.9777			−0.995907			−0.497953	+	0.867204i	$0.665915\pi$
$488$	0.648061	+	1.12247i	0.0293363	+	0.0508120i
$489$	5.85194	+	7.75772i	0.264634	+	0.350816i
$490$	6.86339	−	11.8877i	0.310056	−	0.537033i
$491$	−10.1345	+	17.5535i	−0.457365	+	0.792179i	−0.998821	−	0.0485499i	$-0.984540\pi$
$491$	−10.1345	+	17.5535i	−0.457365	+	0.792179i	0.541456	+	0.840729i	$0.317873\pi$
$492$	−2.52420	+	5.95491i	−0.113800	+	0.268468i
$493$	−4.12626	−	7.14690i	−0.185838	−	0.321880i
$494$	6.70388			0.301622
$495$	2.83307	−	9.91749i	0.127337	−	0.445758i
$496$	7.82032			0.351143
$497$	7.39130	+	12.8021i	0.331545	+	0.574253i
$498$	−7.17226	+	0.884280i	−0.321397	+	0.0396255i
$499$	5.12920	−	8.88403i	0.229614	−	0.397704i	−0.728080	−	0.685493i	$-0.759587\pi$
$499$	5.12920	−	8.88403i	0.229614	−	0.397704i	0.957694	+	0.287789i	$0.0929202\pi$
$500$	−3.12920	+	5.41993i	−0.139942	+	0.242386i
$501$	−16.4684	+	2.03041i	−0.735753	+	0.0907122i
$502$	−8.82032	−	15.2772i	−0.393670	−	0.681857i
$503$	19.2355			0.857668			0.428834	−	0.903383i	$-0.358924\pi$
$503$	19.2355			0.857668			0.428834	+	0.903383i	$0.358924\pi$
$504$	−5.04677	+	1.26366i	−0.224801	+	0.0562879i
$505$	−49.3175			−2.19460
$506$	3.67597	+	6.36697i	0.163417	+	0.283046i
$507$	7.99018	−	18.8499i	0.354856	−	0.837151i
$508$	−8.17226	+	14.1548i	−0.362585	+	0.628016i
$509$	−4.35194	+	7.53778i	−0.192896	+	0.334106i	−0.946209	−	0.323556i	$-0.895121\pi$
$509$	−4.35194	+	7.53778i	−0.192896	+	0.334106i	0.753313	+	0.657663i	$0.228455\pi$
$510$	16.5332	+	21.9176i	0.732104	+	0.970526i
$511$	−13.4282	−	23.2584i	−0.594031	−	1.02889i
$512$	1.00000			0.0441942
$513$	29.9245	−	11.5384i	1.32120	−	0.509435i
$514$	19.1090			0.842863
$515$	−0.604996	−	1.04788i	−0.0266593	−	0.0461753i
$516$	1.68742	+	2.23695i	0.0742844	+	0.0984763i
$517$	5.23419	−	9.06588i	0.230199	−	0.398717i
$518$	−2.93274	+	5.07965i	−0.128857	+	0.223187i
$519$	−13.7778	+	32.5036i	−0.604778	+	1.42675i
$520$	−1.86710	−	3.23390i	−0.0818776	−	0.141816i
$521$	12.5800			0.551141			0.275570	−	0.961281i	$-0.411133\pi$
$521$	12.5800			0.551141			0.275570	+	0.961281i	$0.411133\pi$
$522$	3.73419	+	3.85914i	0.163441	+	0.168910i
$523$	1.67837			0.0733901			0.0366951	−	0.999327i	$-0.488317\pi$
$523$	1.67837			0.0733901			0.0366951	+	0.999327i	$0.488317\pi$
$524$	−7.33307	−	12.7013i	−0.320347	−	0.554857i
$525$	−20.3323	+	2.50680i	−0.887374	+	0.109406i
$526$	−0.657104	+	1.13814i	−0.0286511	+	0.0496252i
$527$	18.0271	−	31.2239i	0.785274	−	1.36013i
$528$	−1.71903	+	0.211943i	−0.0748114	+	0.00922362i
$529$	−15.5255	−	26.8910i	−0.675022	−	1.16917i
$530$	30.8129			1.33843
$531$	25.5726	+	26.4283i	1.10976	+	1.14689i
$532$	−10.7039			−0.464072
$533$	−2.02791	−	3.51244i	−0.0878385	−	0.152141i
$534$	−0.913870	+	2.15594i	−0.0395470	+	0.0932965i
$535$	−27.7358	+	48.0398i	−1.19912	+	2.07694i
$536$	2.30887	−	3.99909i	0.0997282	−	0.172734i
$537$	4.37854	+	5.80449i	0.188948	+	0.250482i
$538$	1.28097	+	2.21870i	0.0552263	+	0.0956548i
$539$	3.99258			0.171973
$540$	−13.9003	−	11.2218i	−0.598175	−	0.482910i
$541$	16.2558			0.698891			0.349445	−	0.936957i	$-0.386370\pi$
$541$	16.2558			0.698891			0.349445	+	0.936957i	$0.386370\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$	14.3129	+	18.9741i	0.614225	+	0.814258i
$544$	2.30516	−	3.99266i	0.0988331	−	0.171184i
$545$	11.5242	−	19.9605i	0.493642	−	0.855014i
$546$	1.27323	−	3.00371i	0.0544891	−	0.128547i
$547$	14.9926	+	25.9679i	0.641036	+	1.11031i	0.985202	+	0.171399i	$0.0548286\pi$
$547$	14.9926	+	25.9679i	0.641036	+	1.11031i	−0.344165	+	0.938909i	$0.611838\pi$
$548$	−13.9320			−0.595144
$549$	−3.77192	+	0.944450i	−0.160982	+	0.0403081i
$550$	−6.82032			−0.290819
$551$	5.52420	+	9.56819i	0.235339	+	0.407619i
$552$	12.6382	−	1.55819i	0.537919	−	0.0663210i
$553$	−11.0837	+	19.1976i	−0.471328	+	0.816364i
$554$	15.3142	−	26.5250i	0.650638	−	1.12694i
$555$	−19.9897	+	2.46456i	−0.848513	+	0.104615i
$556$	6.15339	+	10.6580i	0.260962	+	0.452000i
$557$	39.1452			1.65864			0.829318	−	0.558777i	$-0.188729\pi$
$557$	39.1452			1.65864			0.829318	+	0.558777i	$0.188729\pi$
$558$	−6.44418	+	22.5586i	−0.272804	+	0.954981i
$559$	−1.75709			−0.0743168
$560$	2.98113	+	5.16348i	0.125976	+	0.218197i
$561$	−3.11644	+	7.35209i	−0.131576	+	0.310405i
$562$	4.17226	−	7.22657i	0.175996	−	0.304834i
$563$	−16.2698	+	28.1802i	−0.685692	+	1.18765i	0.287527	+	0.957773i	$0.407167\pi$
$563$	−16.2698	+	28.1802i	−0.685692	+	1.18765i	−0.973219	+	0.229881i	$0.926166\pi$
$564$	−10.9192	−	14.4752i	−0.459781	−	0.609517i
$565$	25.6558	+	44.4371i	1.07935	+	1.86948i
$566$	−3.72938			−0.156758
$567$	0.513531	−	15.5993i	0.0215663	−	0.655108i
$568$	8.52420			0.357667
$569$	3.37321	+	5.84257i	0.141412	+	0.244933i	0.928029	−	0.372509i	$-0.121502\pi$
$569$	3.37321	+	5.84257i	0.141412	+	0.244933i	−0.786616	+	0.617442i	$0.788169\pi$
$570$	−22.1345	−	29.3430i	−0.927113	−	1.22904i
$571$	20.7940	−	36.0163i	0.870203	−	1.50724i	0.00841731	−	0.999965i	$-0.497321\pi$
$571$	20.7940	−	36.0163i	0.870203	−	1.50724i	0.861786	−	0.507272i	$-0.169346\pi$
$572$	0.543065	−	0.940616i	0.0227067	−	0.0393291i
$573$	−1.70628	+	4.02534i	−0.0712810	+	0.168161i
$574$	3.23790	+	5.60821i	0.135147	+	0.234082i
$575$	50.1426			2.09109
$576$	−0.824030	+	2.88461i	−0.0343346	+	0.120192i
$577$	5.95160			0.247768			0.123884	−	0.992297i	$-0.460465\pi$
$577$	5.95160			0.247768			0.123884	+	0.992297i	$0.460465\pi$
$578$	−2.12757	−	3.68506i	−0.0884953	−	0.153278i
$579$	38.2813	−	4.71976i	1.59092	−	0.196147i
$580$	3.07709	−	5.32967i	0.127769	−	0.221303i
$581$	−3.61775	+	6.26612i	−0.150089	+	0.259963i
$582$	5.45323	−	0.672337i	0.226043	−	0.0278693i
$583$	4.48113	+	7.76155i	0.185590	+	0.321451i
$584$	−15.4865			−0.640835
$585$	10.8671	−	2.72101i	0.449299	−	0.112500i
$586$	24.2462			1.00160
$587$	−3.34661	−	5.79649i	−0.138129	−	0.239247i	0.788659	−	0.614830i	$-0.210776\pi$
$587$	−3.34661	−	5.79649i	−0.138129	−	0.239247i	−0.926788	+	0.375584i	$0.877442\pi$
$588$	2.69886	−	6.36697i	0.111299	−	0.262569i
$589$	−24.1345	+	41.8022i	−0.994446	+	1.72243i
$590$	21.0726	−	36.4988i	0.867545	−	1.50263i
$591$	−18.3610	−	24.3405i	−0.755270	−	1.00124i
$592$	1.69113	+	2.92912i	0.0695048	+	0.120386i
$593$	1.62256			0.0666304			0.0333152	−	0.999445i	$-0.489393\pi$
$593$	1.62256			0.0666304			0.0333152	+	0.999445i	$0.489393\pi$
$594$	0.805165	−	5.13339i	0.0330363	−	0.210626i
$595$	27.4880			1.12690
$596$	−1.35194	−	2.34163i	−0.0553776	−	0.0959168i
$597$	0.372110	+	0.493294i	0.0152295	+	0.0201892i
$598$	−3.99258	+	6.91535i	−0.163269	+	0.282790i
$599$	3.71370	−	6.43232i	0.151738	−	0.262817i	−0.780129	−	0.625619i	$-0.784846\pi$
$599$	3.71370	−	6.43232i	0.151738	−	0.262817i	0.931866	+	0.362802i	$0.118180\pi$
$600$	−4.61033	+	10.8764i	−0.188216	+	0.444026i
$601$	−19.6587	−	34.0499i	−0.801896	−	1.38893i	−0.918367	−	0.395731i	$-0.870491\pi$
$601$	−19.6587	−	34.0499i	−0.801896	−	1.38893i	0.116470	−	0.993194i	$-0.462842\pi$
$602$	2.80548			0.114343
$603$	9.63322	+	9.95557i	0.392295	+	0.405422i
$604$	−5.03031			−0.204681
$605$	−1.71903	−	2.97746i	−0.0698887	−	0.121051i
$606$	−24.6587	+	3.04022i	−1.00169	+	0.123500i
$607$	−7.47743	+	12.9513i	−0.303499	+	0.525676i	−0.976926	−	0.213578i	$-0.931488\pi$
$607$	−7.47743	+	12.9513i	−0.303499	+	0.525676i	0.673427	+	0.739254i	$0.264822\pi$
$608$	−3.08613	+	5.34533i	−0.125159	+	0.216782i
$609$	5.33626	−	0.657916i	0.216236	−	0.0266601i
$610$	2.22808	+	3.85914i	0.0902122	+	0.156252i
$611$	11.3700			0.459982
$612$	9.61775	+	9.93958i	0.388774	+	0.401784i
$613$	36.9729			1.49332			0.746661	−	0.665204i	$-0.231656\pi$
$613$	36.9729			1.49332			0.746661	+	0.665204i	$0.231656\pi$
$614$	11.5989	+	20.0899i	0.468093	+	0.810761i
$615$	−8.67837	+	20.4734i	−0.349946	+	0.825567i
$616$	−0.867095	+	1.50185i	−0.0349363	+	0.0605114i
$617$	−0.0266034	+	0.0460784i	−0.00107101	+	0.00185505i	−0.866560	−	0.499072i	$-0.833674\pi$
$617$	−0.0266034	+	0.0460784i	−0.00107101	+	0.00185505i	0.865489	+	0.500927i	$0.167008\pi$
$618$	−0.367095	−	0.486646i	−0.0147667	−	0.0195758i
$619$	−0.157104	−	0.272112i	−0.00631455	−	0.0109371i	0.862851	−	0.505459i	$-0.168677\pi$
$619$	−0.157104	−	0.272112i	−0.00631455	−	0.0109371i	−0.869165	+	0.494521i	$0.835343\pi$
$620$	26.8868			1.07980
$621$	−5.91952	+	37.7404i	−0.237542	+	1.51447i
$622$	3.70869			0.148705
$623$	1.17226	+	2.03041i	0.0469656	+	0.0813468i
$624$	−1.13290	−	1.50185i	−0.0453525	−	0.0601223i
$625$	6.29241	−	10.8988i	0.251696	−	0.435951i
$626$	3.55211	−	6.15243i	0.141971	−	0.245901i
$627$	4.17226	−	9.84290i	0.166624	−	0.393087i
$628$	−0.632905	−	1.09622i	−0.0252556	−	0.0437441i
$629$	15.5933			0.621745
$630$	−17.3512	+	4.34455i	−0.691287	+	0.173091i
$631$	−7.35936			−0.292971			−0.146486	−	0.989213i	$-0.546796\pi$
$631$	−7.35936			−0.292971			−0.146486	+	0.989213i	$0.546796\pi$
$632$	6.39130	+	11.0700i	0.254232	+	0.440343i
$633$	−10.5061	+	1.29532i	−0.417581	+	0.0514842i
$634$	−10.3142	+	17.8647i	−0.409630	+	0.709499i
$635$	−28.0968	+	48.6651i	−1.11499	+	1.93121i
$636$	15.4065	−	1.89949i	0.610906	−	0.0753196i
$637$	2.16823	+	3.75549i	0.0859085	+	0.148798i
$638$	1.79001			0.0708671
$639$	−7.02420	+	24.5890i	−0.277873	+	0.972725i
$640$	3.43807			0.135902
$641$	−15.0205	−	26.0163i	−0.593274	−	1.02758i	−0.993788	−	0.111290i	$-0.964502\pi$
$641$	−15.0205	−	26.0163i	−0.593274	−	1.02758i	0.400514	−	0.916291i	$-0.368831\pi$
$642$	−10.9065	+	25.7297i	−0.430443	+	1.01547i
$643$	−23.0763	+	39.9693i	−0.910041	+	1.57624i	−0.0960366	+	0.995378i	$0.530617\pi$
$643$	−23.0763	+	39.9693i	−0.910041	+	1.57624i	−0.814004	+	0.580859i	$0.802717\pi$
$644$	6.37483	−	11.0415i	0.251204	−	0.435097i
$645$	5.80146	+	7.69080i	0.228432	+	0.302825i
$646$	14.2281	+	24.6438i	0.559796	+	0.969596i
$647$	10.1313			0.398302			0.199151	−	0.979969i	$-0.436182\pi$
$647$	10.1313			0.398302			0.199151	+	0.979969i	$0.436182\pi$
$648$	−7.64195	−	4.75401i	−0.300204	−	0.186755i
$649$	12.2584			0.481184
$650$	−3.70388	−	6.41531i	−0.145278	−	0.251629i
$651$	14.1460	+	18.7528i	0.554425	+	0.734982i
$652$	2.80516	−	4.85869i	0.109859	−	0.190281i
$653$	4.10129	−	7.10364i	0.160496	−	0.277987i	−0.774551	−	0.632512i	$-0.782024\pi$
$653$	4.10129	−	7.10364i	0.160496	−	0.277987i	0.935047	+	0.354525i	$0.115357\pi$
$654$	4.53162	−	10.6907i	0.177200	−	0.418038i
$655$	−25.2116	−	43.6678i	−0.985099	−	1.70624i
$656$	3.73419			0.145796
$657$	12.7613	−	44.6724i	0.497867	−	1.74284i
$658$	−18.1542			−0.707723
$659$	18.7752	+	32.5196i	0.731377	+	1.26678i	0.956295	+	0.292404i	$0.0944553\pi$
$659$	18.7752	+	32.5196i	0.731377	+	1.26678i	−0.224918	+	0.974378i	$0.572211\pi$
$660$	−5.91016	+	0.728674i	−0.230053	+	0.0283636i
$661$	19.4737	−	33.7295i	0.757440	−	1.31192i	−0.186712	−	0.982415i	$-0.559783\pi$
$661$	19.4737	−	33.7295i	0.757440	−	1.31192i	0.944152	−	0.329510i	$-0.106883\pi$
$662$	−1.84290	+	3.19199i	−0.0716262	+	0.124060i
$663$	−8.60793	+	1.06129i	−0.334304	+	0.0412169i
$664$	2.08613	+	3.61328i	0.0809576	+	0.140223i
$665$	−36.8007			−1.42707
$666$	−9.84290	+	2.46456i	−0.381404	+	0.0954997i
$667$	−13.1600			−0.509559
$668$	4.79001	+	8.29654i	0.185331	+	0.321003i
$669$	3.21741	−	7.59028i	0.124392	−	0.293457i
$670$	7.93807	−	13.7491i	0.306674	−	0.531176i
$671$	−0.648061	+	1.12247i	−0.0250181	+	0.0433326i
$672$	1.80887	+	2.39796i	0.0697788	+	0.0925035i
$673$	14.8384	+	25.7009i	0.571979	+	0.990696i	0.996363	+	0.0852137i	$0.0271573\pi$
$673$	14.8384	+	25.7009i	0.571979	+	0.990696i	−0.424384	+	0.905482i	$0.639509\pi$
$674$	−34.9549			−1.34641
$675$	−27.5750	−	22.2615i	−1.06136	−	0.856844i
$676$	−11.8203			−0.454628
$677$	−10.0181	−	17.3518i	−0.385026	−	0.666885i	0.606747	−	0.794895i	$-0.292474\pi$
$677$	−10.0181	−	17.3518i	−0.385026	−	0.666885i	−0.991773	+	0.128010i	$0.959141\pi$
$678$	15.5673	+	20.6370i	0.597857	+	0.792559i
$679$	2.75065	−	4.76427i	0.105560	−	0.182836i
$680$	7.92532	−	13.7271i	0.303922	−	0.526408i
$681$	4.27323	−	10.0811i	0.163750	−	0.386308i
$682$	3.91016	+	6.77260i	0.149728	+	0.259336i
$683$	−15.3626			−0.587834			−0.293917	−	0.955831i	$-0.594959\pi$
$683$	−15.3626			−0.587834			−0.293917	+	0.955831i	$0.594959\pi$
$684$	−12.8761	−	13.3070i	−0.492331	−	0.508806i
$685$	−47.8990			−1.83013
$686$	−9.53162	−	16.5092i	−0.363919	−	0.630326i
$687$	−18.0083	+	2.22027i	−0.687058	+	0.0847086i
$688$	0.808874	−	1.40101i	0.0308380	−	0.0534130i
$689$	−4.86710	+	8.43006i	−0.185422	+	0.321160i
$690$	43.4511	−	5.35716i	1.65416	−	0.203944i
$691$	−5.12679	−	8.87986i	−0.195032	−	0.337806i	0.751879	−	0.659301i	$-0.229148\pi$
$691$	−5.12679	−	8.87986i	−0.195032	−	0.337806i	−0.946911	+	0.321495i	$0.895815\pi$
$692$	20.3823			0.774817
$693$	−3.61775	−	3.73881i	−0.137427	−	0.142025i
$694$	−8.02289			−0.304545
$695$	21.1558	+	36.6429i	0.802485	+	1.38995i
$696$	1.20999	−	2.85453i	0.0458646	−	0.108200i
$697$	8.60793	−	14.9094i	0.326048	−	0.564732i
$698$	7.24694	−	12.5521i	0.274301	−	0.475103i
$699$	11.4421	+	15.1684i	0.432780	+	0.573722i
$700$	5.91387	+	10.2431i	0.223523	+	0.387154i
$701$	−7.98516			−0.301595			−0.150798	−	0.988565i	$-0.548184\pi$
$701$	−7.98516			−0.301595			−0.150798	+	0.988565i	$0.548184\pi$
$702$	5.26581	−	2.03041i	0.198745	−	0.0766331i
$703$	−20.8761			−0.787358
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−37.5410	−	49.7668i	−1.41388	−	1.87433i
$706$	4.46838	−	7.73946i	0.168170	−	0.291279i
$707$	−12.4381	+	21.5434i	−0.467782	+	0.810222i
$708$	8.28630	−	19.5484i	0.311418	−	0.734676i
$709$	−8.51887	−	14.7551i	−0.319933	−	0.554140i	0.660541	−	0.750790i	$-0.270327\pi$
$709$	−8.51887	−	14.7551i	−0.319933	−	0.554140i	−0.980474	+	0.196650i	$0.936994\pi$
$710$	29.3068			1.09986
$711$	−37.1994	+	9.31434i	−1.39509	+	0.349315i
$712$	1.35194			0.0506661
$713$	−28.7473	−	49.7917i	−1.07659	−	1.86471i
$714$	13.7440	−	1.69452i	0.514357	−	0.0634159i
$715$	1.86710	−	3.23390i	0.0698254	−	0.120941i
$716$	2.09888	−	3.63537i	0.0784389	−	0.135860i
$717$	−29.4421	+	3.62997i	−1.09954	+	0.135564i
$718$	6.25839	+	10.8399i	0.233561	+	0.404540i
$719$	22.1600			0.826430			0.413215	−	0.910634i	$-0.364406\pi$
$719$	22.1600			0.826430			0.413215	+	0.910634i	$0.364406\pi$
$720$	−2.83307	+	9.91749i	−0.105582	+	0.369603i
$721$	−0.610330			−0.0227299
$722$	−9.54840	−	16.5383i	−0.355355	−	0.615492i
$723$	15.4636	−	36.4806i	0.575097	−	1.35673i
$724$	6.86098	−	11.8836i	0.254986	−	0.441649i
$725$	6.10422	−	10.5728i	0.226705	−	0.392664i
$726$	−1.04307	−	1.38276i	−0.0387118	−	0.0513189i
$727$	−10.0848	−	17.4674i	−0.374025	−	0.647831i	0.616155	−	0.787625i	$-0.288689\pi$
$727$	−10.0848	−	17.4674i	−0.374025	−	0.647831i	−0.990181	+	0.139794i	$0.955356\pi$
$728$	−1.88356			−0.0698093
$729$	20.0107	−	18.1266i	0.741136	−	0.671355i
$730$	−53.2436			−1.97063
$731$	−3.72918	−	6.45912i	−0.137929	−	0.238899i
$732$	1.35194	+	1.79222i	0.0499691	+	0.0662424i
$733$	20.2650	−	35.1001i	0.748506	−	1.29645i	−0.200033	−	0.979789i	$-0.564105\pi$
$733$	20.2650	−	35.1001i	0.748506	−	1.29645i	0.948539	−	0.316661i	$-0.102562\pi$
$734$	−2.73790	+	4.74218i	−0.101058	+	0.175037i
$735$	9.27888	−	21.8901i	0.342257	−	0.807427i
$736$	−3.67597	−	6.36697i	−0.135498	−	0.234689i
$737$	4.61775			0.170097
$738$	−3.07709	+	10.7717i	−0.113269	+	0.396511i
$739$	14.5168			0.534008			0.267004	−	0.963695i	$-0.413966\pi$
$739$	14.5168			0.534008			0.267004	+	0.963695i	$0.413966\pi$
$740$	5.81421	+	10.0705i	0.213735	+	0.370199i
$741$	11.5242	−	1.42084i	0.423352	−	0.0521958i
$742$	7.77114	−	13.4600i	0.285288	−	0.494133i
$743$	−9.85063	+	17.0618i	−0.361385	+	0.625937i	−0.988189	−	0.153240i	$-0.951029\pi$
$743$	−9.85063	+	17.0618i	−0.361385	+	0.625937i	0.626804	+	0.779177i	$0.284363\pi$
$744$	13.4434	−	1.65746i	0.492859	−	0.0607654i
$745$	−4.64806	−	8.05068i	−0.170292	−	0.294954i
$746$	−4.23289			−0.154977
$747$	−12.1419	+	3.04022i	−0.444251	+	0.111236i
$748$	4.61033			0.168570
$749$	13.9902	+	24.2317i	0.511190	+	0.885407i
$750$	−4.23048	+	9.98025i	−0.154475	+	0.364427i
$751$	−10.0316	+	17.3753i	−0.366059	+	0.634033i	−0.988945	−	0.148279i	$-0.952626\pi$
$751$	−10.0316	+	17.3753i	−0.366059	+	0.634033i	0.622887	+	0.782312i	$0.285960\pi$
$752$	−5.23419	+	9.06588i	−0.190871	+	0.330599i
$753$	−18.4003	−	24.3927i	−0.670546	−	0.888920i
$754$	0.972091	+	1.68371i	0.0354015	+	0.0613172i
$755$	−17.2946			−0.629414
$756$	−8.40776	+	3.24190i	−0.305787	+	0.117907i
$757$	−47.2920			−1.71886			−0.859428	−	0.511257i	$-0.829180\pi$
$757$	−47.2920			−1.71886			−0.859428	+	0.511257i	$0.829180\pi$
$758$	−13.2584	−	22.9642i	−0.481566	−	0.834098i
$759$	7.66855	+	10.1659i	0.278351	+	0.369000i
$760$	−10.6103	+	18.3776i	−0.384877	+	0.666627i
$761$	−11.7687	+	20.3841i	−0.426616	+	0.738921i	−0.996570	−	0.0827556i	$-0.973628\pi$
$761$	−11.7687	+	20.3841i	−0.426616	+	0.738921i	0.569953	+	0.821677i	$0.306961\pi$
$762$	−11.0484	+	26.0646i	−0.400241	+	0.944221i
$763$	−5.81290	−	10.0682i	−0.210441	−	0.364495i
$764$	2.52420			0.0913223
$765$	33.0665	+	34.1730i	1.19552	+	1.23553i
$766$	−35.8613			−1.29572
$767$	6.65710	+	11.5304i	0.240374	+	0.416340i
$768$	1.71903	−	0.211943i	0.0620303	−	0.00764782i
$769$	−7.65873	+	13.2653i	−0.276181	+	0.478359i	−0.970432	−	0.241373i	$-0.922402\pi$
$769$	−7.65873	+	13.2653i	−0.276181	+	0.478359i	0.694252	+	0.719732i	$0.255736\pi$
$770$	−2.98113	+	5.16348i	−0.107433	+	0.186079i
$771$	32.8491	−	4.05002i	1.18303	−	0.145858i
$772$	−11.1345	−	19.2856i	−0.400740	−	0.694103i
$773$	3.06324			0.110177			0.0550885	−	0.998481i	$-0.482456\pi$
$773$	3.06324			0.110177			0.0550885	+	0.998481i	$0.482456\pi$
$774$	3.37483	+	3.48776i	0.121306	+	0.125365i
$775$	53.3371			1.91593
$776$	−1.58613	−	2.74726i	−0.0569388	−	0.0986208i
$777$	−3.96488	+	9.35366i	−0.142239	+	0.335561i
$778$	5.87080	−	10.1685i	0.210479	−	0.364560i
$779$	−11.5242	+	19.9605i	−0.412897	+	0.715159i
$780$	−3.89500	−	5.16348i	−0.139464	−	0.184882i
$781$	4.26210	+	7.38217i	0.152510	+	0.264155i
$782$	−33.8949			−1.21208
$783$	7.23712	+	5.84257i	0.258634	+	0.208796i
$784$	−3.99258			−0.142592
$785$	−2.17597	−	3.76889i	−0.0776637	−	0.134517i
$786$	−15.2977	−	20.2797i	−0.545653	−	0.723353i
$787$	9.49389	−	16.4439i	0.338421	−	0.586162i	−0.645715	−	0.763578i	$-0.723441\pi$
$787$	9.49389	−	16.4439i	0.338421	−	0.586162i	0.984136	+	0.177417i	$0.0567740\pi$
$788$	−8.80146	+	15.2446i	−0.313539	+	0.543065i
$789$	−0.888365	+	2.09577i	−0.0316266	+	0.0746113i
$790$	21.9737	+	38.0596i	0.781790	+	1.35410i
$791$	25.8820			0.920258
$792$	−2.91016	+	0.728674i	−0.103408	+	0.0258923i
$793$	−1.40776			−0.0499909
$794$	−5.24323	−	9.08155i	−0.186075	−	0.322292i
$795$	52.9684	−	6.53057i	1.87860	−	0.231615i
$796$	0.178373	−	0.308952i	0.00632228	−	0.0109505i
$797$	2.33177	−	4.03874i	0.0825955	−	0.143060i	−0.821769	−	0.569821i	$-0.807012\pi$
$797$	2.33177	−	4.03874i	0.0825955	−	0.143060i	0.904364	+	0.426762i	$0.140346\pi$
$798$	−18.4003	+	2.26861i	−0.651365	+	0.0803079i
$799$	24.1313	+	41.7967i	0.853706	+	1.47866i
$800$	6.82032			0.241135
$801$	−1.11404	+	3.89982i	−0.0393626	+	0.137793i
$802$	20.2813			0.716157
$803$	−7.74323	−	13.4117i	−0.273253	−	0.473288i
$804$	3.12146	−	7.36392i	0.110085	−	0.259705i
$805$	21.9171	−	37.9616i	0.772477	−	1.33797i
$806$	−4.24694	+	7.35592i	−0.149592	+	0.259101i
$807$	2.67226	+	3.54253i	0.0940680	+	0.124703i
$808$	7.17226	+	12.4227i	0.252319	+	0.437030i
$809$	−29.4865			−1.03669			−0.518345	−	0.855172i	$-0.673452\pi$
$809$	−29.4865			−1.03669			−0.518345	+	0.855172i	$0.673452\pi$
$810$	−26.2735	−	16.3446i	−0.923158	−	0.574292i
$811$	1.67837			0.0589357			0.0294678	−	0.999566i	$-0.490619\pi$
$811$	1.67837			0.0589357			0.0294678	+	0.999566i	$0.490619\pi$
$812$	−1.55211	−	2.68833i	−0.0544683	−	0.0943419i
$813$	−2.08613	−	2.76551i	−0.0731638	−	0.0969908i
$814$	−1.69113	+	2.92912i	−0.0592739	+	0.102665i
$815$	9.64435	−	16.7045i	0.337827	−	0.585133i
$816$	3.11644	−	7.35209i	0.109097	−	0.257375i
$817$	4.99258	+	8.64740i	0.174668	+	0.302534i
$818$	−18.1903			−0.636011
$819$	1.55211	−	5.43333i	0.0542351	−	0.189856i
$820$	12.8384			0.448337
$821$	−9.75306	−	16.8928i	−0.340384	−	0.589562i	0.644120	−	0.764924i	$-0.277224\pi$
$821$	−9.75306	−	16.8928i	−0.340384	−	0.589562i	−0.984504	+	0.175362i	$0.943890\pi$
$822$	−23.9495	+	2.95278i	−0.835335	+	0.102990i
$823$	−18.7826	+	32.5324i	−0.654720	+	1.13401i	0.327244	+	0.944940i	$0.393880\pi$
$823$	−18.7826	+	32.5324i	−0.654720	+	1.13401i	−0.981964	+	0.189068i	$0.939453\pi$
$824$	−0.175970	+	0.304788i	−0.00613019	+	0.0106178i
$825$	−11.7244	+	1.44552i	−0.408190	+	0.0503264i
$826$	−10.6292	−	18.4103i	−0.369837	−	0.640576i
$827$	−10.7645			−0.374318			−0.187159	−	0.982330i	$-0.559928\pi$
$827$	−10.7645			−0.374318			−0.187159	+	0.982330i	$0.559928\pi$
$828$	21.3953	−	5.35716i	0.743539	−	0.186174i
$829$	−8.98191			−0.311955			−0.155977	−	0.987761i	$-0.549853\pi$
$829$	−8.98191			−0.311955			−0.155977	+	0.987761i	$0.549853\pi$
$830$	7.17226	+	12.4227i	0.248953	+	0.431199i
$831$	20.7039	−	48.8431i	0.718210	−	1.69435i
$832$	−0.543065	+	0.940616i	−0.0188274	+	0.0326100i
$833$	−9.20356	+	15.9410i	−0.318884	+	0.552324i
$834$	12.8368	+	17.0173i	0.444501	+	0.589261i
$835$	16.4684	+	28.5241i	0.569912	+	0.987116i
$836$	−6.17226			−0.213472
$837$	−6.29665	+	40.1448i	−0.217644	+	1.38761i
$838$	−29.3478			−1.01380
$839$	−13.2937	−	23.0254i	−0.458950	−	0.794925i	0.539956	−	0.841693i	$-0.318441\pi$
$839$	−13.2937	−	23.0254i	−0.458950	−	0.794925i	−0.998906	+	0.0467686i	$0.985108\pi$
$840$	6.21903	+	8.24437i	0.214577	+	0.284458i
$841$	12.8979	−	22.3399i	0.444756	−	0.770341i
$842$	−13.9471	+	24.1571i	−0.480649	+	0.832509i
$843$	5.64064	−	13.3070i	0.194274	−	0.458317i
$844$	3.05582	+	5.29283i	0.105186	+	0.182187i
$845$	−40.6391			−1.39803
$846$	−21.8384	−	22.5692i	−0.750820	−	0.775944i
$847$	−1.73419			−0.0595875
$848$	−4.48113	−	7.76155i	−0.153883	−	0.266533i
$849$	−6.41094	+	0.790416i	−0.220023	+	0.0271270i
$850$	15.7220	−	27.2312i	0.539259	−	0.934024i
$851$	12.4331	−	21.5347i	0.426200	−	0.738199i
$852$	14.6534	−	1.80664i	0.502017	−	0.0618945i
$853$	11.5545	+	20.0130i	0.395619	+	0.685232i	0.993180	−	0.116591i	$-0.0371968\pi$
$853$	11.5545	+	20.0130i	0.395619	+	0.685232i	−0.597561	+	0.801823i	$0.703863\pi$
$854$	2.24772			0.0769155
$855$	−44.2691	−	45.7504i	−1.51397	−	1.56463i
$856$	16.1345			0.551467
$857$	−15.9532	−	27.6318i	−0.544952	−	0.943884i	−0.998610	−	0.0527084i	$-0.983215\pi$
$857$	−15.9532	−	27.6318i	−0.544952	−	0.943884i	0.453658	−	0.891176i	$-0.350119\pi$
$858$	0.734191	−	1.73205i	0.0250649	−	0.0591312i
$859$	8.11195	−	14.0503i	0.276776	−	0.479391i	−0.693805	−	0.720163i	$-0.744067\pi$
$859$	8.11195	−	14.0503i	0.276776	−	0.479391i	0.970582	+	0.240772i	$0.0774006\pi$
$860$	2.78097	−	4.81677i	0.0948301	−	0.164251i
$861$	6.75468	+	8.95445i	0.230199	+	0.305167i
$862$	9.39871	+	16.2790i	0.320121	+	0.554467i
$863$	32.6184			1.11034			0.555171	−	0.831736i	$-0.312653\pi$
$863$	32.6184			1.11034			0.555171	+	0.831736i	$0.312653\pi$
$864$	−0.805165	+	5.13339i	−0.0273923	+	0.174642i
$865$	70.0756			2.38264
$866$	7.28630	+	12.6202i	0.247599	+	0.428853i
$867$	−4.43839	−	5.88382i	−0.150736	−	0.199825i
$868$	6.78097	−	11.7450i	0.230161	−	0.398650i
$869$	−6.39130	+	11.0700i	−0.216810	+	0.375526i
$870$	4.16003	−	9.81406i	0.141038	−	0.332728i
$871$	2.50774	+	4.34353i	0.0849715	+	0.147175i
$872$	−6.70388			−0.227022
$873$	9.23179	−	2.31154i	0.312449	−	0.0782339i
$874$	45.3781			1.53494
$875$	5.42662	+	9.39919i	0.183453	+	0.317750i
$876$	−26.6218	+	3.28224i	−0.899466	+	0.110897i
$877$	−18.7449	+	32.4670i	−0.632969	+	1.09633i	0.353973	+	0.935256i	$0.384831\pi$
$877$	−18.7449	+	32.4670i	−0.632969	+	1.09633i	−0.986942	+	0.161079i	$0.948503\pi$
$878$	−9.66615	+	16.7423i	−0.326217	+	0.565024i
$879$	41.6800	−	5.13880i	1.40583	−	0.173327i
$880$	1.71903	+	2.97746i	0.0579486	+	0.100370i
$881$	2.75709			0.0928886			0.0464443	−	0.998921i	$-0.485211\pi$
$881$	2.75709			0.0928886			0.0464443	+	0.998921i	$0.485211\pi$
$882$	3.29001	−	11.5170i	0.110780	−	0.387799i
$883$	33.8432			1.13891			0.569457	−	0.822021i	$-0.307153\pi$
$883$	33.8432			1.13891			0.569457	+	0.822021i	$0.307153\pi$
$884$	2.50371	+	4.33655i	0.0842089	+	0.145854i
$885$	28.4889	−	67.2089i	0.957643	−	2.25920i
$886$	−7.62308	+	13.2036i	−0.256102	+	0.443582i
$887$	9.33548	−	16.1695i	0.313455	−	0.542919i	−0.665653	−	0.746261i	$-0.731847\pi$
$887$	9.33548	−	16.1695i	0.313455	−	0.542919i	0.979108	+	0.203342i	$0.0651803\pi$
$888$	3.52791	+	4.67683i	0.118389	+	0.156944i
$889$	14.1723	+	24.5471i	0.475322	+	0.823282i
$890$	4.64806			0.155803
$891$	0.296122	−	8.99513i	0.00992045	−	0.301348i
$892$	−4.75970			−0.159366
$893$	−32.3068	−	55.9570i	−1.08111	−	1.87253i
$894$	−2.82032	−	3.73881i	−0.0943257	−	0.125044i
$895$	7.21610	−	12.4987i	0.241208	−	0.417784i
$896$	0.867095	−	1.50185i	0.0289676	−	0.0501734i
$897$	−5.39773	+	12.7339i	−0.180225	+	0.425174i
$898$	4.91758	+	8.51750i	0.164102	+	0.284233i
$899$	−13.9984			−0.466874
$900$	−5.62015	+	19.6740i	−0.187338	+	0.655799i
$901$	−41.3190			−1.37654
$902$	1.86710	+	3.23390i	0.0621675	+	0.107677i
$903$	4.82272	−	0.594602i	0.160490	−	0.0197871i
$904$	7.46227	−	12.9250i	0.248191	−	0.429880i
$905$	23.5885	−	40.8565i	0.784109	−	1.35812i
$906$	−8.64728	+	1.06614i	−0.287287	+	0.0354201i
$907$	−8.33145	−	14.4305i	−0.276641	−	0.479157i	0.693907	−	0.720065i	$-0.255888\pi$
$907$	−8.33145	−	14.4305i	−0.276641	−	0.479157i	−0.970548	+	0.240908i	$0.922555\pi$
$908$	−6.32163			−0.209791
$909$	−41.7449	+	10.4525i	−1.38459	+	0.346687i
$910$	−6.47580			−0.214671
$911$	18.0931	+	31.3381i	0.599451	+	1.03828i	0.992902	+	0.118934i	$0.0379476\pi$
$911$	18.0931	+	31.3381i	0.599451	+	1.03828i	−0.393451	+	0.919345i	$0.628719\pi$
$912$	−4.17226	+	9.84290i	−0.138157	+	0.325931i
$913$	−2.08613	+	3.61328i	−0.0690408	+	0.119582i
$914$	−11.8687	+	20.5572i	−0.392582	+	0.679973i
$915$	4.64806	+	6.16178i	0.153660	+	0.203702i
$916$	5.23790	+	9.07231i	0.173065	+	0.299758i
$917$	−25.4339			−0.839901
$918$	18.6399	+	15.0481i	0.615207	+	0.496660i
$919$	−10.5168			−0.346917			−0.173458	−	0.984841i	$-0.555494\pi$
$919$	−10.5168			−0.346917			−0.173458	+	0.984841i	$0.555494\pi$
$920$	−12.6382	−	21.8901i	−0.416670	−	0.721694i
$921$	24.1968	+	32.0769i	0.797311	+	1.05697i
$922$	3.01887	−	5.22883i	0.0994210	−	0.172202i
$923$	−4.62920	+	8.01800i	−0.152372	+	0.263916i
$924$	−1.17226	+	2.76551i	−0.0385645	+	0.0909787i
$925$	11.5340	+	19.9775i	0.379236	+	0.656857i
$926$	33.5604			1.10286
$927$	−0.734191	−	0.758758i	−0.0241140	−	0.0249209i
$928$	−1.79001			−0.0587599
$929$	−7.75839	−	13.4379i	−0.254545	−	0.440884i	0.710227	−	0.703973i	$-0.248592\pi$
$929$	−7.75839	−	13.4379i	−0.254545	−	0.440884i	−0.964772	+	0.263088i	$0.915259\pi$
$930$	46.2194	−	5.69846i	1.51559	−	0.186860i
$931$	12.3216	−	21.3417i	0.403825	−	0.699445i
$932$	5.48484	−	9.50003i	0.179662	−	0.311184i
$933$	6.37536	−	0.786029i	0.208720	−	0.0257334i
$934$	14.0939	+	24.4113i	0.461165	+	0.798762i
$935$	15.8506			0.518371
$936$	−2.26581	−	2.34163i	−0.0740603	−	0.0765385i
$937$	−19.6587			−0.642223			−0.321111	−	0.947041i	$-0.604056\pi$
$937$	−19.6587			−0.642223			−0.321111	+	0.947041i	$0.604056\pi$
$938$	−4.00403	−	6.93518i	−0.130736	−	0.226442i
$939$	4.80223	−	11.3291i	0.156715	−	0.369711i
$940$	−17.9955	+	31.1691i	−0.586949	+	1.01663i
$941$	−20.2092	+	35.0034i	−0.658801	+	1.14108i	0.322125	+	0.946697i	$0.395603\pi$
$941$	−20.2092	+	35.0034i	−0.658801	+	1.14108i	−0.980926	+	0.194380i	$0.937730\pi$
$942$	−1.32032	−	1.75031i	−0.0430184	−	0.0570280i
$943$	−13.7268	−	23.7755i	−0.447005	−	0.774236i
$944$	−12.2584			−0.398977
$945$	−28.9065	+	11.1459i	−0.940327	+	0.362576i
$946$	1.61775			0.0525975
$947$	9.36710	+	16.2243i	0.304390	+	0.527218i	0.977125	−	0.212665i	$-0.0682142\pi$
$947$	9.36710	+	16.2243i	0.304390	+	0.527218i	−0.672736	+	0.739883i	$0.734881\pi$
$948$	13.3331	+	17.6752i	0.433038	+	0.574064i
$949$	8.41016	−	14.5668i	0.273005	−	0.472859i
$950$	−21.0484	+	36.4569i	−0.682900	+	1.18282i
$951$	−13.9442	+	32.8961i	−0.452171	+	1.06673i
$952$	−3.99760	−	6.92404i	−0.129563	−	0.224409i
$953$	22.4051			0.725774			0.362887	−	0.931833i	$-0.381791\pi$
$953$	22.4051			0.725774			0.362887	+	0.931833i	$0.381791\pi$
$954$	26.0816	−	6.53057i	0.844424	−	0.211435i
$955$	8.67837			0.280826
$956$	8.56356	+	14.8325i	0.276965	+	0.479718i
$957$	3.07709	−	0.379379i	0.0994681	−	0.0122636i
$958$	−1.94418	+	3.36742i	−0.0628137	+	0.108796i
$959$	−12.0803	+	20.9238i	−0.390094	+	0.675663i
$960$	5.91016	−	0.728674i	0.190750	−	0.0235178i
$961$	−15.0787	−	26.1171i	−0.486410	−	0.842487i
$962$	−3.67357			−0.118441
$963$	−13.2953	+	46.5418i	−0.428436	+	1.49979i
$964$	−22.8761			−0.736791
$965$	−38.2813	−	66.3051i	−1.23232	−	2.13444i
$966$	8.61839	−	20.3319i	0.277292	−	0.654168i
$967$	−16.1829	+	28.0297i	−0.520408	+	0.901373i	0.479311	+	0.877645i	$0.340887\pi$
$967$	−16.1829	+	28.0297i	−0.520408	+	0.901373i	−0.999718	+	0.0237276i	$0.992447\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	29.6816	+	39.3479i	0.953511	+	1.26404i
$970$	−5.45323	−	9.44526i	−0.175093	−	0.303269i
$971$	5.48322			0.175965			0.0879824	−	0.996122i	$-0.471958\pi$
$971$	5.48322			0.175965			0.0879824	+	0.996122i	$0.471958\pi$
$972$	−14.1444	−	6.55266i	−0.453680	−	0.210177i
$973$	21.3423			0.684203
$974$	10.9889	+	19.0333i	0.352106	+	0.609866i
$975$	−7.72677	−	10.2431i	−0.247455	−	0.328042i
$976$	0.648061	−	1.12247i	0.0207439	−	0.0359295i
$977$	−14.5824	+	25.2575i	−0.466533	+	0.808059i	−0.999269	−	0.0382225i	$-0.987830\pi$
$977$	−14.5824	+	25.2575i	−0.466533	+	0.808059i	0.532736	+	0.846281i	$0.321164\pi$
$978$	3.79241	−	8.94679i	0.121268	−	0.286087i
$979$	0.675970	+	1.17081i	0.0216041	+	0.0374194i
$980$	−13.7268			−0.438486
$981$	5.52420	−	19.3381i	0.176374	−	0.617417i
$982$	20.2691			0.646812
$983$	10.0874	+	17.4720i	0.321739	+	0.557269i	0.980847	−	0.194780i	$-0.0623992\pi$
$983$	10.0874	+	17.4720i	0.321739	+	0.557269i	−0.659108	+	0.752049i	$0.729066\pi$
$984$	6.41920	−	0.791434i	0.204637	−	0.0252300i
$985$	−30.2600	+	52.4119i	−0.964164	+	1.66998i
$986$	−4.12626	+	7.14690i	−0.131407	+	0.227604i
$987$	−31.2077	+	3.84764i	−0.993351	+	0.122472i
$988$	−3.35194	−	5.80573i	−0.106639	−	0.184705i
$989$	−11.8936			−0.378194
$990$	−10.0053	+	2.50523i	−0.317990	+	0.0796215i
$991$	38.5578			1.22483			0.612414	−	0.790537i	$-0.290199\pi$
$991$	38.5578			1.22483			0.612414	+	0.790537i	$0.290199\pi$
$992$	−3.91016	−	6.77260i	−0.124148	−	0.215030i
$993$	−2.49148	+	5.87773i	−0.0790648	+	0.186524i
$994$	7.39130	−	12.8021i	0.234438	−	0.406058i
$995$	0.613260	−	1.06220i	0.0194417	−	0.0336739i
$996$	4.35194	+	5.76922i	0.137896	+	0.182805i
$997$	29.6332	+	51.3262i	0.938494	+	1.62552i	0.768282	+	0.640111i	$0.221112\pi$
$997$	29.6332	+	51.3262i	0.938494	+	1.62552i	0.170211	+	0.985408i	$0.445555\pi$
$998$	−10.2584			−0.324724
$999$	−16.3979	+	6.32279i	−0.518808	+	0.200044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.e.d.67.1	✓	6
3.2	odd	2		594.2.e.e.199.3		6
9.2	odd	6		594.2.e.e.397.3		6
9.4	even	3		1782.2.a.s.1.3		3
9.5	odd	6		1782.2.a.r.1.1		3
9.7	even	3	inner	198.2.e.d.133.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.e.d.67.1	✓	6	1.1	even	1	trivial
198.2.e.d.133.1	yes	6	9.7	even	3	inner
594.2.e.e.199.3		6	3.2	odd	2
594.2.e.e.397.3		6	9.2	odd	6
1782.2.a.r.1.1		3	9.5	odd	6
1782.2.a.s.1.3		3	9.4	even	3

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.04307 - 1.38276i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.71903 + 2.97746i) q^{5} +(-0.675970 + 1.59470i) q^{6} +(0.867095 + 1.50185i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.04307 - 1.38276i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.71903 + 2.97746i) q^{5} +(-0.675970 + 1.59470i) q^{6} +(0.867095 + 1.50185i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} +3.43807 q^{10} +(0.500000 + 0.866025i) q^{11} +(1.71903 - 0.211943i) q^{12} +(-0.543065 + 0.940616i) q^{13} +(0.867095 - 1.50185i) q^{14} +(5.91016 - 0.728674i) q^{15} +(-0.500000 - 0.866025i) q^{16} -4.61033 q^{17} +(2.91016 - 0.728674i) q^{18} +6.17226 q^{19} +(-1.71903 - 2.97746i) q^{20} +(1.17226 - 2.76551i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-3.67597 + 6.36697i) q^{23} +(-1.04307 - 1.38276i) q^{24} +(-3.41016 - 5.90657i) q^{25} +1.08613 q^{26} +(4.84823 - 1.86940i) q^{27} -1.73419 q^{28} +(0.895004 + 1.55019i) q^{29} +(-3.58613 - 4.75401i) q^{30} +(-3.91016 + 6.77260i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.675970 - 1.59470i) q^{33} +(2.30516 + 3.99266i) q^{34} -5.96227 q^{35} +(-2.08613 - 2.15594i) q^{36} -3.38225 q^{37} +(-3.08613 - 5.34533i) q^{38} +(1.86710 - 0.230197i) q^{39} +(-1.71903 + 2.97746i) q^{40} +(-1.86710 + 3.23390i) q^{41} +(-2.98113 + 0.367549i) q^{42} +(0.808874 + 1.40101i) q^{43} -1.00000 q^{44} +(-7.17226 - 7.41226i) q^{45} +7.35194 q^{46} +(-5.23419 - 9.06588i) q^{47} +(-0.675970 + 1.59470i) q^{48} +(1.99629 - 3.45768i) q^{49} +(-3.41016 + 5.90657i) q^{50} +(4.80887 + 6.37496i) q^{51} +(-0.543065 - 0.940616i) q^{52} +8.96227 q^{53} +(-4.04307 - 3.26399i) q^{54} -3.43807 q^{55} +(0.867095 + 1.50185i) q^{56} +(-6.43807 - 8.53473i) q^{57} +(0.895004 - 1.55019i) q^{58} +(6.12920 - 10.6161i) q^{59} +(-2.32403 + 5.48269i) q^{60} +(0.648061 + 1.12247i) q^{61} +7.82032 q^{62} +(-5.04677 + 1.26366i) q^{63} +1.00000 q^{64} +(-1.86710 - 3.23390i) q^{65} +(-1.71903 + 0.211943i) q^{66} +(2.30887 - 3.99909i) q^{67} +(2.30516 - 3.99266i) q^{68} +(12.6382 - 1.55819i) q^{69} +(2.98113 + 5.16348i) q^{70} +8.52420 q^{71} +(-0.824030 + 2.88461i) q^{72} -15.4865 q^{73} +(1.69113 + 2.92912i) q^{74} +(-4.61033 + 10.8764i) q^{75} +(-3.08613 + 5.34533i) q^{76} +(-0.867095 + 1.50185i) q^{77} +(-1.13290 - 1.50185i) q^{78} +(6.39130 + 11.0700i) q^{79} +3.43807 q^{80} +(-7.64195 - 4.75401i) q^{81} +3.73419 q^{82} +(2.08613 + 3.61328i) q^{83} +(1.80887 + 2.39796i) q^{84} +(7.92532 - 13.7271i) q^{85} +(0.808874 - 1.40101i) q^{86} +(1.20999 - 2.85453i) q^{87} +(0.500000 + 0.866025i) q^{88} +1.35194 q^{89} +(-2.83307 + 9.91749i) q^{90} -1.88356 q^{91} +(-3.67597 - 6.36697i) q^{92} +(13.4434 - 1.65746i) q^{93} +(-5.23419 + 9.06588i) q^{94} +(-10.6103 + 18.3776i) q^{95} +(1.71903 - 0.211943i) q^{96} +(-1.58613 - 2.74726i) q^{97} -3.99258 q^{98} +(-2.91016 + 0.728674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - q^{5} - 2 q^{6} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - q^5 - 2 * q^6 + 6 * q^8 - 7 * q^9	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - q^{5} - 2 q^{6} + 6 q^{8} - 7 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} + 4 q^{13} + 23 q^{15} - 3 q^{16} + 20 q^{17} + 5 q^{18} + 8 q^{19} - q^{20} - 22 q^{21} + 3 q^{22} - 20 q^{23} + q^{24} - 8 q^{25} - 8 q^{26} - 2 q^{27} - 6 q^{29} - 7 q^{30} - 11 q^{31} - 3 q^{32} + 2 q^{33} - 10 q^{34} + 16 q^{35} + 2 q^{36} - 14 q^{37} - 4 q^{38} + 6 q^{39} - q^{40} - 6 q^{41} + 8 q^{42} + 8 q^{43} - 6 q^{44} - 14 q^{45} + 40 q^{46} - 21 q^{47} - 2 q^{48} - 15 q^{49} - 8 q^{50} + 32 q^{51} + 4 q^{52} + 2 q^{53} - 17 q^{54} - 2 q^{55} - 20 q^{57} - 6 q^{58} + 15 q^{59} - 16 q^{60} + 8 q^{61} + 22 q^{62} - 50 q^{63} + 6 q^{64} - 6 q^{65} - q^{66} + 17 q^{67} - 10 q^{68} + 22 q^{69} - 8 q^{70} + 18 q^{71} - 7 q^{72} - 8 q^{73} + 7 q^{74} + 20 q^{75} - 4 q^{76} - 12 q^{78} + 2 q^{80} - 19 q^{81} + 12 q^{82} - 2 q^{83} + 14 q^{84} + 34 q^{85} + 8 q^{86} + 30 q^{87} + 3 q^{88} + 4 q^{89} + 13 q^{90} - 28 q^{91} - 20 q^{92} + 3 q^{93} - 21 q^{94} - 16 q^{95} + q^{96} + 5 q^{97} + 30 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - q^5 - 2 * q^6 + 6 * q^8 - 7 * q^9 + 2 * q^10 + 3 * q^11 + q^12 + 4 * q^13 + 23 * q^15 - 3 * q^16 + 20 * q^17 + 5 * q^18 + 8 * q^19 - q^20 - 22 * q^21 + 3 * q^22 - 20 * q^23 + q^24 - 8 * q^25 - 8 * q^26 - 2 * q^27 - 6 * q^29 - 7 * q^30 - 11 * q^31 - 3 * q^32 + 2 * q^33 - 10 * q^34 + 16 * q^35 + 2 * q^36 - 14 * q^37 - 4 * q^38 + 6 * q^39 - q^40 - 6 * q^41 + 8 * q^42 + 8 * q^43 - 6 * q^44 - 14 * q^45 + 40 * q^46 - 21 * q^47 - 2 * q^48 - 15 * q^49 - 8 * q^50 + 32 * q^51 + 4 * q^52 + 2 * q^53 - 17 * q^54 - 2 * q^55 - 20 * q^57 - 6 * q^58 + 15 * q^59 - 16 * q^60 + 8 * q^61 + 22 * q^62 - 50 * q^63 + 6 * q^64 - 6 * q^65 - q^66 + 17 * q^67 - 10 * q^68 + 22 * q^69 - 8 * q^70 + 18 * q^71 - 7 * q^72 - 8 * q^73 + 7 * q^74 + 20 * q^75 - 4 * q^76 - 12 * q^78 + 2 * q^80 - 19 * q^81 + 12 * q^82 - 2 * q^83 + 14 * q^84 + 34 * q^85 + 8 * q^86 + 30 * q^87 + 3 * q^88 + 4 * q^89 + 13 * q^90 - 28 * q^91 - 20 * q^92 + 3 * q^93 - 21 * q^94 - 16 * q^95 + q^96 + 5 * q^97 + 30 * q^98 - 5 * q^99

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