LMFDB - Embedded newform 585.2.bt.b.376.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.6
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03176 - 1.17304i) q^{2} +(0.447750 + 1.67318i) q^{3} +(1.75203 + 3.03461i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.05298 - 3.92472i) q^{6} +(-2.60767 - 1.50554i) q^{7} -3.52864i q^{8} +(-2.59904 + 1.49833i) q^{9} +O(q^{10})$	\(q+(-2.03176 - 1.17304i) q^{2} +(0.447750 + 1.67318i) q^{3} +(1.75203 + 3.03461i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.05298 - 3.92472i) q^{6} +(-2.60767 - 1.50554i) q^{7} -3.52864i q^{8} +(-2.59904 + 1.49833i) q^{9} -2.34607 q^{10} +(4.21397 + 2.43294i) q^{11} +(-4.29296 + 4.29020i) q^{12} +(-3.56763 + 0.521530i) q^{13} +(3.53211 + 6.11780i) q^{14} +(1.22435 + 1.22514i) q^{15} +(-0.635160 + 1.10013i) q^{16} +3.52537 q^{17} +(7.03822 + 0.00452088i) q^{18} +1.76684i q^{19} +(3.03461 + 1.75203i) q^{20} +(1.35145 - 5.03721i) q^{21} +(-5.70785 - 9.88629i) q^{22} +(0.803384 + 1.39150i) q^{23} +(5.90403 - 1.57995i) q^{24} +(0.500000 - 0.866025i) q^{25} +(7.86035 + 3.12534i) q^{26} +(-3.67069 - 3.67777i) q^{27} -10.5510i q^{28} +(-4.11800 + 7.13259i) q^{29} +(-1.05046 - 3.92539i) q^{30} +(-3.57912 + 2.06641i) q^{31} +(-3.53079 + 2.03850i) q^{32} +(-2.18393 + 8.14007i) q^{33} +(-7.16270 - 4.13539i) q^{34} -3.01108 q^{35} +(-9.10044 - 5.26194i) q^{36} +4.97866i q^{37} +(2.07257 - 3.58980i) q^{38} +(-2.47002 - 5.73576i) q^{39} +(-1.76432 - 3.05589i) q^{40} +(-1.46032 + 0.843116i) q^{41} +(-8.65465 + 8.64909i) q^{42} +(-2.47744 + 4.29105i) q^{43} +17.0503i q^{44} +(-1.50167 + 2.59711i) q^{45} -3.76959i q^{46} +(-1.99000 - 1.14893i) q^{47} +(-2.12510 - 0.570152i) q^{48} +(1.03331 + 1.78975i) q^{49} +(-2.03176 + 1.17304i) q^{50} +(1.57848 + 5.89856i) q^{51} +(-7.83324 - 9.91262i) q^{52} +0.0235717 q^{53} +(3.14380 + 11.7782i) q^{54} +4.86588 q^{55} +(-5.31251 + 9.20154i) q^{56} +(-2.95624 + 0.791104i) q^{57} +(16.7336 - 9.66114i) q^{58} +(12.0954 - 6.98331i) q^{59} +(-1.57271 + 5.86190i) q^{60} +(-7.41416 + 12.8417i) q^{61} +9.69588 q^{62} +(9.03325 + 0.00580235i) q^{63} +12.1056 q^{64} +(-2.82890 + 2.23547i) q^{65} +(13.9858 - 13.9768i) q^{66} +(-12.2089 + 7.04883i) q^{67} +(6.17655 + 10.6981i) q^{68} +(-1.96851 + 1.96725i) q^{69} +(6.11780 + 3.53211i) q^{70} +10.4870i q^{71} +(5.28707 + 9.17107i) q^{72} -0.0924209i q^{73} +(5.84015 - 10.1154i) q^{74} +(1.67289 + 0.448825i) q^{75} +(-5.36167 + 3.09556i) q^{76} +(-7.32578 - 12.6886i) q^{77} +(-1.70977 + 14.5511i) q^{78} +(4.65227 - 8.05796i) q^{79} +1.27032i q^{80} +(4.51001 - 7.78844i) q^{81} +3.95603 q^{82} +(-4.07164 - 2.35076i) q^{83} +(17.6537 - 4.72422i) q^{84} +(3.05306 - 1.76268i) q^{85} +(10.0671 - 5.81226i) q^{86} +(-13.7779 - 3.69653i) q^{87} +(8.58496 - 14.8696i) q^{88} +16.2397i q^{89} +(6.09754 - 3.51519i) q^{90} +(10.0884 + 4.01124i) q^{91} +(-2.81511 + 4.87591i) q^{92} +(-5.06002 - 5.06327i) q^{93} +(2.69547 + 4.66869i) q^{94} +(0.883421 + 1.53013i) q^{95} +(-4.99169 - 4.99490i) q^{96} +(11.3656 + 6.56194i) q^{97} -4.84845i q^{98} +(-14.5976 - 0.00937653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−2.03176	−	1.17304i	−1.43667	−	0.829462i	−0.439054	−	0.898461i	$-0.644686\pi$
$2$	−2.03176	−	1.17304i	−1.43667	−	0.829462i	−0.997617	+	0.0689985i	$0.978020\pi$
$3$	0.447750	+	1.67318i	0.258509	+	0.966009i
$3$	0.447750	+	1.67318i	0.258509	+	0.966009i
$4$	1.75203	+	3.03461i	0.876015	+	1.51730i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.05298	−	3.92472i	0.429876	−	1.60226i
$7$	−2.60767	−	1.50554i	−0.985608	−	0.569041i	−0.0816498	−	0.996661i	$-0.526019\pi$
$7$	−2.60767	−	1.50554i	−0.985608	−	0.569041i	−0.903959	+	0.427620i	$0.859352\pi$
$8$		−	3.52864i		−	1.24756i
$9$	−2.59904	+	1.49833i	−0.866346	+	0.499444i
$10$	−2.34607			−0.741894
$11$	4.21397	+	2.43294i	1.27056	+	0.733559i	0.975094	−	0.221794i	$-0.0711913\pi$
$11$	4.21397	+	2.43294i	1.27056	+	0.733559i	0.295467	+	0.955353i	$0.404525\pi$
$12$	−4.29296	+	4.29020i	−1.23927	+	1.23847i
$13$	−3.56763	+	0.521530i	−0.989483	+	0.144646i
$13$	−3.56763	+	0.521530i	−0.989483	+	0.144646i
$14$	3.53211	+	6.11780i	0.943997	+	1.63505i
$15$	1.22435	+	1.22514i	0.316126	+	0.316329i
$16$	−0.635160	+	1.10013i	−0.158790	+	0.275032i
$17$	3.52537			0.855027			0.427514	−	0.904009i	$-0.359390\pi$
$17$	3.52537			0.855027			0.427514	+	0.904009i	$0.359390\pi$
$18$	7.03822	+	0.00452088i	1.65892	+	0.00106558i
$19$			1.76684i			0.405341i	0.979247	+	0.202671i	$0.0649621\pi$
$19$			1.76684i			0.405341i	−0.979247	+	0.202671i	$0.935038\pi$
$20$	3.03461	+	1.75203i	0.678558	+	0.391766i
$21$	1.35145	−	5.03721i	0.294911	−	1.09921i
$22$	−5.70785	−	9.88629i	−1.21692	−	2.10776i
$23$	0.803384	+	1.39150i	0.167517	+	0.290148i	0.937546	−	0.347861i	$-0.113092\pi$
$23$	0.803384	+	1.39150i	0.167517	+	0.290148i	−0.770029	+	0.638009i	$0.779758\pi$
$24$	5.90403	−	1.57995i	1.20516	−	0.322506i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	7.86035	+	3.12534i	1.54154	+	0.612930i
$27$	−3.67069	−	3.67777i	−0.706425	−	0.707788i
$28$		−	10.5510i		−	1.99396i
$29$	−4.11800	+	7.13259i	−0.764694	+	1.32449i	0.175714	+	0.984441i	$0.443777\pi$
$29$	−4.11800	+	7.13259i	−0.764694	+	1.32449i	−0.940408	+	0.340048i	$0.889557\pi$
$30$	−1.05046	−	3.92539i	−0.191786	−	0.716676i
$31$	−3.57912	+	2.06641i	−0.642829	+	0.371138i	−0.785703	−	0.618603i	$-0.787699\pi$
$31$	−3.57912	+	2.06641i	−0.642829	+	0.371138i	0.142874	+	0.989741i	$0.454365\pi$
$32$	−3.53079	+	2.03850i	−0.624162	+	0.360360i
$33$	−2.18393	+	8.14007i	−0.380173	+	1.41700i
$34$	−7.16270	−	4.13539i	−1.22839	−	0.709213i
$35$	−3.01108			−0.508966
$36$	−9.10044	−	5.26194i	−1.51674	−	0.876990i
$37$			4.97866i			0.818486i	0.912425	+	0.409243i	$0.134207\pi$
$37$			4.97866i			0.818486i	−0.912425	+	0.409243i	$0.865793\pi$
$38$	2.07257	−	3.58980i	0.336215	−	0.582342i
$39$	−2.47002	−	5.73576i	−0.395520	−	0.918457i
$40$	−1.76432	−	3.05589i	−0.278963	−	0.483179i
$41$	−1.46032	+	0.843116i	−0.228064	+	0.131673i	−0.609678	−	0.792649i	$-0.708701\pi$
$41$	−1.46032	+	0.843116i	−0.228064	+	0.131673i	0.381615	+	0.924321i	$0.375368\pi$
$42$	−8.65465	+	8.64909i	−1.33544	+	1.33458i
$43$	−2.47744	+	4.29105i	−0.377806	+	0.654380i	−0.990743	−	0.135753i	$-0.956655\pi$
$43$	−2.47744	+	4.29105i	−0.377806	+	0.654380i	0.612937	+	0.790132i	$0.289988\pi$
$44$			17.0503i			2.57043i
$45$	−1.50167	+	2.59711i	−0.223856	+	0.387155i
$46$		−	3.76959i		−	0.555796i
$47$	−1.99000	−	1.14893i	−0.290271	−	0.167588i	0.347793	−	0.937571i	$-0.386931\pi$
$47$	−1.99000	−	1.14893i	−0.290271	−	0.167588i	−0.638064	+	0.769983i	$0.720265\pi$
$48$	−2.12510	−	0.570152i	−0.306732	−	0.0822943i
$49$	1.03331	+	1.78975i	0.147616	+	0.255679i
$50$	−2.03176	+	1.17304i	−0.287334	+	0.165892i
$51$	1.57848	+	5.89856i	0.221032	+	0.825964i
$52$	−7.83324	−	9.91262i	−1.08627	−	1.37463i
$53$	0.0235717			0.00323782			0.00161891	−	0.999999i	$-0.499485\pi$
$53$	0.0235717			0.00323782			0.00161891	+	0.999999i	$0.499485\pi$
$54$	3.14380	+	11.7782i	0.427817	+	1.60281i
$55$	4.86588			0.656115
$56$	−5.31251	+	9.20154i	−0.709914	+	1.22961i
$57$	−2.95624	+	0.791104i	−0.391563	+	0.104784i
$58$	16.7336	−	9.66114i	2.19723	−	1.26857i
$59$	12.0954	−	6.98331i	1.57469	−	0.909149i	0.579111	−	0.815248i	$-0.303400\pi$
$59$	12.0954	−	6.98331i	1.57469	−	0.909149i	0.995582	−	0.0939009i	$-0.0299337\pi$
$60$	−1.57271	+	5.86190i	−0.203036	+	0.756768i
$61$	−7.41416	+	12.8417i	−0.949285	+	1.64421i	−0.202351	+	0.979313i	$0.564858\pi$
$61$	−7.41416	+	12.8417i	−0.949285	+	1.64421i	−0.746935	+	0.664897i	$0.768475\pi$
$62$	9.69588			1.23138
$63$	9.03325	+	0.00580235i	1.13808	+	0.000731027i
$64$	12.1056			1.51320
$65$	−2.82890	+	2.23547i	−0.350881	+	0.277277i
$66$	13.9858	−	13.9768i	1.72154	−	1.72043i
$67$	−12.2089	+	7.04883i	−1.49156	+	0.861151i	−0.999953	−	0.00966753i	$-0.996923\pi$
$67$	−12.2089	+	7.04883i	−1.49156	+	0.861151i	−0.491604	+	0.870819i	$0.663589\pi$
$68$	6.17655	+	10.6981i	0.749017	+	1.29734i
$69$	−1.96851	+	1.96725i	−0.236981	+	0.236829i
$70$	6.11780	+	3.53211i	0.731217	+	0.422168i
$71$			10.4870i			1.24458i	0.782788	+	0.622289i	$0.213797\pi$
$71$			10.4870i			1.24458i	−0.782788	+	0.622289i	$0.786203\pi$
$72$	5.28707	+	9.17107i	0.623087	+	1.08082i
$73$		−	0.0924209i		−	0.0108171i	−0.999985	−	0.00540853i	$-0.998278\pi$
$73$		−	0.0924209i		−	0.0108171i	0.999985	−	0.00540853i	$-0.00172160\pi$
$74$	5.84015	−	10.1154i	0.678903	−	1.17589i
$75$	1.67289	+	0.448825i	0.193169	+	0.0518259i
$76$	−5.36167	+	3.09556i	−0.615025	+	0.355085i
$77$	−7.32578	−	12.6886i	−0.834850	−	1.44600i
$78$	−1.70977	+	14.5511i	−0.193594	+	1.64759i
$79$	4.65227	−	8.05796i	0.523421	−	0.906592i	−0.476208	−	0.879333i	$-0.657989\pi$
$79$	4.65227	−	8.05796i	0.523421	−	0.906592i	0.999628	−	0.0272587i	$-0.00867778\pi$
$80$			1.27032i			0.142026i
$81$	4.51001	−	7.78844i	0.501112	−	0.865382i
$82$	3.95603			0.436870
$83$	−4.07164	−	2.35076i	−0.446921	−	0.258030i	0.259608	−	0.965714i	$-0.416407\pi$
$83$	−4.07164	−	2.35076i	−0.446921	−	0.258030i	−0.706529	+	0.707684i	$0.749740\pi$
$84$	17.6537	−	4.72422i	1.92618	−	0.515455i
$85$	3.05306	−	1.76268i	0.331151	−	0.191190i
$86$	10.0671	−	5.81226i	1.08557	−	0.626752i
$87$	−13.7779	−	3.69653i	−1.47715	−	0.396309i
$88$	8.58496	−	14.8696i	0.915160	−	1.58510i
$89$			16.2397i			1.72141i	0.509108	+	0.860703i	$0.329975\pi$
$89$			16.2397i			1.72141i	−0.509108	+	0.860703i	$0.670025\pi$
$90$	6.09754	−	3.51519i	0.642737	−	0.370534i
$91$	10.0884	+	4.01124i	1.05755	+	0.420492i
$92$	−2.81511	+	4.87591i	−0.293495	+	0.508348i
$93$	−5.06002	−	5.06327i	−0.524699	−	0.525036i
$94$	2.69547	+	4.66869i	0.278016	+	0.481538i
$95$	0.883421	+	1.53013i	0.0906370	+	0.156988i
$96$	−4.99169	−	4.99490i	−0.509462	−	0.509790i
$97$	11.3656	+	6.56194i	1.15400	+	0.666264i	0.949859	−	0.312677i	$-0.101226\pi$
$97$	11.3656	+	6.56194i	1.15400	+	0.666264i	0.204143	+	0.978941i	$0.434559\pi$
$98$		−	4.84845i		−	0.489768i
$99$	−14.5976	−	0.00937653i	−1.46712	−	0.000942377i
$100$	3.50406			0.350406
$101$	−2.32210	+	4.02200i	−0.231058	+	0.400204i	−0.958120	−	0.286368i	$-0.907552\pi$
$101$	−2.32210	+	4.02200i	−0.231058	+	0.400204i	0.727062	+	0.686572i	$0.240885\pi$
$102$	3.71213	−	13.8361i	0.367556	−	1.36998i
$103$	4.82912	+	8.36428i	0.475827	+	0.824157i	0.999617	−	0.0276912i	$-0.00881549\pi$
$103$	4.82912	+	8.36428i	0.475827	+	0.824157i	−0.523790	+	0.851848i	$0.675482\pi$
$104$	1.84029	+	12.5889i	0.180455	+	1.23444i
$105$	−1.34821	−	5.03807i	−0.131572	−	0.491666i
$106$	−0.0478920	−	0.0276505i	−0.00465169	−	0.00268565i
$107$	−0.627574			−0.0606699			−0.0303349	−	0.999540i	$-0.509657\pi$
$107$	−0.627574			−0.0606699			−0.0303349	+	0.999540i	$0.509657\pi$
$108$	4.72943	−	17.5827i	0.455089	−	1.69189i
$109$		−	8.19251i		−	0.784700i	−0.919816	−	0.392350i	$-0.871662\pi$
$109$		−	8.19251i		−	0.784700i	0.919816	−	0.392350i	$-0.128338\pi$
$110$	−9.88629	−	5.70785i	−0.942621	−	0.544222i
$111$	−8.33017	+	2.22920i	−0.790665	+	0.211586i
$112$	3.31258	−	1.91252i	0.313010	−	0.180716i
$113$	1.20432	+	2.08595i	0.113293	+	0.196229i	0.917096	−	0.398666i	$-0.130527\pi$
$113$	1.20432	+	2.08595i	0.113293	+	0.196229i	−0.803803	+	0.594896i	$0.797193\pi$
$114$	6.93436	+	1.86044i	0.649462	+	0.174246i
$115$	1.39150	+	0.803384i	0.129758	+	0.0749159i
$116$	−28.8595			−2.67953
$117$	8.49099	−	6.70097i	0.784993	−	0.619505i
$118$	−32.7667			−3.01642
$119$	−9.19301	−	5.30759i	−0.842722	−	0.486546i
$120$	4.32307	−	4.32029i	0.394640	−	0.394387i
$121$	6.33838	+	10.9784i	0.576217	+	0.998037i
$122$	30.1276	−	17.3942i	2.72762	−	1.57479i
$123$	−2.06454	−	2.06587i	−0.186153	−	0.186273i
$124$	−12.5415	−	7.24081i	−1.12626	−	0.650244i
$125$		−	1.00000i		−	0.0894427i
$126$	−18.3466	−	10.6081i	−1.63444	−	0.945047i
$127$	0.104062			0.00923399			0.00461700	−	0.999989i	$-0.498530\pi$
$127$	0.104062			0.00923399			0.00461700	+	0.999989i	$0.498530\pi$
$128$	−17.5341	−	10.1233i	−1.54981	−	0.894783i
$129$	−8.28896	−	2.22387i	−0.729803	−	0.195801i
$130$	8.36993	−	1.22355i	0.734091	−	0.107312i
$131$	−7.41509	−	12.8433i	−0.647859	−	1.12213i	−0.983633	−	0.180183i	$-0.942331\pi$
$131$	−7.41509	−	12.8433i	−0.647859	−	1.12213i	0.335774	−	0.941943i	$-0.391002\pi$
$132$	−28.5282	+	7.63429i	−2.48306	+	0.664480i
$133$	2.66005	−	4.60735i	0.230656	−	0.399508i
$134$	33.0741			2.85717
$135$	−5.01780	−	1.34970i	−0.431863	−	0.116164i
$136$		−	12.4397i		−	1.06670i
$137$	7.09830	+	4.09820i	0.606448	+	0.350133i	0.771574	−	0.636139i	$-0.219470\pi$
$137$	7.09830	+	4.09820i	0.606448	+	0.350133i	−0.165126	+	0.986273i	$0.552803\pi$
$138$	6.30720	−	1.68784i	0.536904	−	0.143678i
$139$	−3.89026	−	6.73812i	−0.329967	−	0.571520i	0.652538	−	0.757756i	$-0.273704\pi$
$139$	−3.89026	−	6.73812i	−0.329967	−	0.571520i	−0.982505	+	0.186236i	$0.940371\pi$
$140$	−5.27551	−	9.13745i	−0.445862	−	0.772256i
$141$	1.03133	−	3.84405i	0.0868540	−	0.323728i
$142$	12.3016	−	21.3071i	1.03233	−	1.78805i
$143$	−16.3028	−	6.48212i	−1.36331	−	0.542062i
$144$	0.00244790	−	3.81096i	0.000203992	−	0.317580i
$145$			8.23601i			0.683963i
$146$	−0.108413	+	0.187777i	−0.00897234	+	0.0155405i
$147$	−2.53190	+	2.53028i	−0.208828	+	0.208694i
$148$	−15.1083	+	8.72276i	−1.24189	+	0.717006i
$149$	12.7430	−	7.35717i	1.04395	−	0.602723i	0.122998	−	0.992407i	$-0.460749\pi$
$149$	12.7430	−	7.35717i	1.04395	−	0.602723i	0.920949	+	0.389684i	$0.127416\pi$
$150$	−2.87242	−	2.87426i	−0.234532	−	0.234683i
$151$	−14.2369	−	8.21969i	−1.15858	−	0.668909i	−0.207620	−	0.978209i	$-0.566572\pi$
$151$	−14.2369	−	8.21969i	−1.15858	−	0.668909i	−0.950964	+	0.309300i	$0.899905\pi$
$152$	6.23454			0.505688
$153$	−9.16257	+	5.28217i	−0.740750	+	0.427038i
$154$			34.3736i			2.76991i
$155$	−2.06641	+	3.57912i	−0.165978	+	0.287482i
$156$	13.0782	−	17.5448i	1.04710	−	1.40471i
$157$	−9.94956	−	17.2331i	−0.794062	−	1.37536i	−0.923433	−	0.383759i	$-0.874629\pi$
$157$	−9.94956	−	17.2331i	−0.794062	−	1.37536i	0.129372	−	0.991596i	$-0.458704\pi$
$158$	−18.9046	+	10.9146i	−1.50397	+	0.868316i
$159$	0.0105542	+	0.0394396i	0.000837006	+	0.00312777i
$160$	−2.03850	+	3.53079i	−0.161158	+	0.279134i
$161$		−	4.83811i		−	0.381297i
$162$	−18.2994	+	10.5338i	−1.43774	+	0.827616i
$163$		−	6.57929i		−	0.515330i	−0.966234	−	0.257665i	$-0.917047\pi$
$163$		−	6.57929i		−	0.515330i	0.966234	−	0.257665i	$-0.0829531\pi$
$164$	−5.11705	−	2.95433i	−0.399575	−	0.230694i
$165$	2.17870	+	8.14147i	0.169611	+	0.633813i
$166$	5.51506	+	9.55237i	0.428052	+	0.741408i
$167$	6.20266	−	3.58110i	0.479976	−	0.277114i	−0.240431	−	0.970666i	$-0.577289\pi$
$167$	6.20266	−	3.58110i	0.479976	−	0.277114i	0.720406	+	0.693552i	$0.243955\pi$
$168$	−17.7745	−	4.76878i	−1.37133	−	0.367919i
$169$	12.4560	−	3.72126i	0.958155	−	0.286250i
$170$	−8.27077			−0.634339
$171$	−2.64731	−	4.59209i	−0.202445	−	0.351166i
$172$	−17.3622			−1.32386
$173$	−7.43076	+	12.8705i	−0.564950	+	0.978523i	0.432104	+	0.901824i	$0.357771\pi$
$173$	−7.43076	+	12.8705i	−0.564950	+	0.978523i	−0.997054	+	0.0766991i	$0.975562\pi$
$174$	23.6573	+	23.6725i	1.79345	+	1.79460i
$175$	−2.60767	+	1.50554i	−0.197122	+	0.113808i
$176$	−5.35310	+	3.09061i	−0.403505	+	0.232964i
$177$	17.1000	+	17.1110i	1.28532	+	1.28614i
$178$	19.0498	−	32.9952i	1.42784	−	2.47309i
$179$	22.8325			1.70658			0.853290	−	0.521436i	$-0.174603\pi$
$179$	22.8325			1.70658			0.853290	+	0.521436i	$0.174603\pi$
$180$	−10.5122	−	0.00675231i	−0.783532	−	0.000503288i
$181$	15.2979			1.13709			0.568544	−	0.822653i	$-0.307507\pi$
$181$	15.2979			1.13709			0.568544	+	0.822653i	$0.307507\pi$
$182$	−15.7919	−	19.9840i	−1.17057	−	1.48131i
$183$	−24.8061	−	6.65532i	−1.83372	−	0.491975i
$184$	4.91010	−	2.83485i	0.361978	−	0.208988i
$185$	2.48933	+	4.31164i	0.183019	+	0.316998i
$186$	4.34133	+	16.2229i	0.318322	+	1.18952i
$187$	14.8558	+	8.57700i	1.08636	+	0.627213i
$188$		−	8.05182i		−	0.587239i
$189$	4.03493	+	15.1168i	0.293498	+	1.09959i
$190$		−	4.14514i		−	0.300720i
$191$	5.09701	−	8.82828i	0.368807	−	0.638792i	−0.620573	−	0.784149i	$-0.713100\pi$
$191$	5.09701	−	8.82828i	0.368807	−	0.638792i	0.989379	+	0.145357i	$0.0464332\pi$
$192$	5.42029	+	20.2548i	0.391176	+	1.46177i
$193$	16.0902	−	9.28971i	1.15820	−	0.668688i	0.207329	−	0.978271i	$-0.433523\pi$
$193$	16.0902	−	9.28971i	1.15820	−	0.668688i	0.950872	+	0.309584i	$0.100190\pi$
$194$	−15.3948	−	26.6646i	−1.10528	−	1.91440i
$195$	−5.00698	−	3.73231i	−0.358558	−	0.267276i
$196$	−3.62079	+	6.27139i	−0.258628	+	0.447957i
$197$		−	10.6841i		−	0.761212i	−0.924737	−	0.380606i	$-0.875715\pi$
$197$		−	10.6841i		−	0.761212i	0.924737	−	0.380606i	$-0.124285\pi$
$198$	29.6479	+	17.1426i	2.10698	+	1.21827i
$199$	−14.8783			−1.05470			−0.527348	−	0.849650i	$-0.676813\pi$
$199$	−14.8783			−1.05470			−0.527348	+	0.849650i	$0.676813\pi$
$200$	−3.05589	−	1.76432i	−0.216084	−	0.124756i
$201$	−17.2605	−	17.2716i	−1.21746	−	1.21824i
$202$	9.43591	−	5.44783i	0.663908	−	0.383308i
$203$	21.4768	−	12.3997i	1.50738	−	0.870285i
$204$	−15.1343	+	15.1245i	−1.05961	+	1.05893i
$205$	−0.843116	+	1.46032i	−0.0588858	+	0.101993i
$206$		−	22.6589i		−	1.57872i
$207$	−4.17296	−	2.41283i	−0.290040	−	0.167703i
$208$	1.69227	−	4.25611i	0.117338	−	0.295108i
$209$	−4.29862	+	7.44542i	−0.297342	+	0.515011i
$210$	−3.17060	+	11.8177i	−0.218792	+	0.815496i
$211$	−6.61701	−	11.4610i	−0.455534	−	0.789007i	0.543185	−	0.839613i	$-0.317218\pi$
$211$	−6.61701	−	11.4610i	−0.455534	−	0.789007i	−0.998719	+	0.0506056i	$0.983885\pi$
$212$	0.0412984	+	0.0715309i	0.00283638	+	0.00491276i
$213$	−17.5466	+	4.69556i	−1.20227	+	0.321734i
$214$	1.27508	+	0.736167i	0.0871626	+	0.0503234i
$215$			4.95488i			0.337920i
$216$	−12.9775	+	12.9525i	−0.883009	+	0.881309i
$217$	12.4442			0.844770
$218$	−9.61012	+	16.6452i	−0.650879	+	1.12736i
$219$	0.154637	−	0.0413815i	0.0104494	−	0.00279630i
$220$	8.52517	+	14.7660i	0.574767	+	0.995525i
$221$	−12.5772	+	1.83859i	−0.846035	+	0.123677i
$222$	19.5398	+	5.24241i	1.31143	+	0.351847i
$223$	14.7263	+	8.50221i	0.986144	+	0.569350i	0.904119	−	0.427280i	$-0.140528\pi$
$223$	14.7263	+	8.50221i	0.986144	+	0.569350i	0.0820242	+	0.996630i	$0.473862\pi$
$224$	12.2762			0.820239
$225$	−0.00192700	+	3.00000i	−0.000128466	+	0.200000i
$226$		−	5.65086i		−	0.375890i
$227$	0.928183	+	0.535886i	0.0616056	+	0.0355680i	0.530486	−	0.847693i	$-0.322009\pi$
$227$	0.928183	+	0.535886i	0.0616056	+	0.0355680i	−0.468881	+	0.883261i	$0.655343\pi$
$228$	−7.58011	−	7.58498i	−0.502005	−	0.502327i
$229$	−2.90717	+	1.67846i	−0.192111	+	0.110915i	−0.592971	−	0.805224i	$-0.702045\pi$
$229$	−2.90717	+	1.67846i	−0.192111	+	0.110915i	0.400859	+	0.916140i	$0.368712\pi$
$230$	−1.88480	−	3.26456i	−0.124280	−	0.215259i
$231$	17.9502	−	17.9387i	1.18104	−	1.18028i
$232$	25.1683	+	14.5309i	1.65238	+	0.954003i
$233$	11.1489			0.730385			0.365193	−	0.930932i	$-0.381003\pi$
$233$	11.1489			0.730385			0.365193	+	0.930932i	$0.381003\pi$
$234$	−25.1121	+	3.65451i	−1.64163	+	0.238903i
$235$	−2.29785			−0.149895
$236$	42.3832	+	24.4699i	2.75891	+	1.59286i
$237$	15.5654	+	4.17611i	1.01108	+	0.271267i
$238$	12.4520	+	21.5675i	0.807143	+	1.39801i
$239$	15.4693	−	8.93120i	1.00063	−	0.577711i	0.0921923	−	0.995741i	$-0.470613\pi$
$239$	15.4693	−	8.93120i	1.00063	−	0.577711i	0.908433	+	0.418030i	$0.137279\pi$
$240$	−2.12547	+	0.568786i	−0.137198	+	0.0367150i
$241$	6.50757	+	3.75715i	0.419189	+	0.242019i	0.694730	−	0.719270i	$-0.255524\pi$
$241$	6.50757	+	3.75715i	0.419189	+	0.242019i	−0.275541	+	0.961289i	$0.588857\pi$
$242$		−	29.7406i		−	1.91180i
$243$	15.0508	+	4.05876i	0.965509	+	0.260370i
$244$	−51.9593			−3.32635
$245$	1.78975	+	1.03331i	0.114343	+	0.0660159i
$246$	1.77131	+	6.61913i	0.112935	+	0.422020i
$247$	−0.921461	−	6.30344i	−0.0586312	−	0.401078i
$248$	7.29160	+	12.6294i	0.463017	+	0.801969i
$249$	2.11016	−	7.86513i	0.133726	−	0.498432i
$250$	−1.17304	+	2.03176i	−0.0741894	+	0.128500i
$251$	−17.3950			−1.09796			−0.548982	−	0.835834i	$-0.684984\pi$
$251$	−17.3950			−1.09796			−0.548982	+	0.835834i	$0.684984\pi$
$252$	15.8089	+	27.4225i	0.995868	+	1.72746i
$253$			7.81833i			0.491534i
$254$	−0.211429	−	0.122068i	−0.0132662	−	0.00765925i
$255$	4.31629	+	4.31906i	0.270296	+	0.270470i
$256$	11.6444	+	20.1687i	0.727776	+	1.26055i
$257$	13.6866	+	23.7059i	0.853746	+	1.47873i	0.877803	+	0.479021i	$0.159008\pi$
$257$	13.6866	+	23.7059i	0.853746	+	1.47873i	−0.0240569	+	0.999711i	$0.507658\pi$
$258$	14.2325	+	14.2416i	0.886076	+	0.886646i
$259$	7.49557	−	12.9827i	0.465752	−	0.806707i
$260$	−11.7401	−	4.66796i	−0.728090	−	0.289495i
$261$	0.0158708	−	24.7080i	0.000982375	−	1.52939i
$262$			34.7927i			2.14950i
$263$	9.79031	−	16.9573i	0.603696	−	1.04563i	−0.388560	−	0.921424i	$-0.627027\pi$
$263$	9.79031	−	16.9573i	0.603696	−	1.04563i	0.992256	−	0.124209i	$-0.0396394\pi$
$264$	28.7234	+	7.70629i	1.76780	+	0.474289i
$265$	0.0204137	−	0.0117859i	0.00125400	−	0.000723999i
$266$	−10.8092	+	6.24068i	−0.662753	+	0.382641i
$267$	−27.1719	+	7.27133i	−1.66289	+	0.444998i
$268$	−42.7808	−	24.6995i	−2.61325	−	1.50876i
$269$	−24.7562			−1.50941			−0.754705	−	0.656064i	$-0.772220\pi$
$269$	−24.7562			−1.50941			−0.754705	+	0.656064i	$0.772220\pi$
$270$	8.61171	+	8.62833i	0.524092	+	0.525103i
$271$			3.20359i			0.194604i	0.995255	+	0.0973020i	$0.0310213\pi$
$271$			3.20359i			0.194604i	−0.995255	+	0.0973020i	$0.968979\pi$
$272$	−2.23917	+	3.87836i	−0.135770	+	0.235160i
$273$	−2.19442	+	18.6757i	−0.132812	+	1.13031i
$274$	−9.61469	−	16.6531i	−0.580844	−	1.00605i
$275$	4.21397	−	2.43294i	0.254112	−	0.146712i
$276$	−9.41872	−	2.52698i	−0.566940	−	0.152106i
$277$	−0.198774	+	0.344286i	−0.0119432	+	0.0206861i	−0.871935	−	0.489621i	$-0.837135\pi$
$277$	−0.198774	+	0.344286i	−0.0119432	+	0.0206861i	0.859992	+	0.510307i	$0.170468\pi$
$278$			18.2537i			1.09478i
$279$	6.20611	−	10.7334i	0.371550	−	0.642591i
$280$			10.6250i			0.634966i
$281$	−3.75638	−	2.16875i	−0.224087	−	0.129377i	0.383754	−	0.923435i	$-0.374631\pi$
$281$	−3.75638	−	2.16875i	−0.224087	−	0.129377i	−0.607841	+	0.794059i	$0.707964\pi$
$282$	−6.60464	+	6.60040i	−0.393301	+	0.393048i
$283$	−0.628989	−	1.08944i	−0.0373895	−	0.0647605i	0.846725	−	0.532031i	$-0.178571\pi$
$283$	−0.628989	−	1.08944i	−0.0373895	−	0.0647605i	−0.884115	+	0.467270i	$0.845238\pi$
$284$	−31.8239	+	18.3735i	−1.88840	+	1.09027i
$285$	−2.16462	+	2.16323i	−0.128221	+	0.128139i
$286$	25.5195	+	32.2938i	1.50900	+	1.90958i
$287$	5.07739			0.299709
$288$	6.12232	−	10.5885i	0.360761	−	0.623930i
$289$	−4.57178			−0.268929
$290$	9.66114	−	16.7336i	0.567322	−	0.982630i
$291$	−5.89032	+	21.9548i	−0.345297	+	1.28701i
$292$	0.280461	−	0.161924i	0.0164127	−	0.00947590i
$293$	3.65963	−	2.11289i	0.213798	−	0.123436i	−0.389277	−	0.921121i	$-0.627275\pi$
$293$	3.65963	−	2.11289i	0.213798	−	0.123436i	0.603075	+	0.797684i	$0.293942\pi$
$294$	8.11232	−	2.17090i	0.473120	−	0.126609i
$295$	6.98331	−	12.0954i	0.406584	−	0.704224i
$296$	17.5679			1.02111
$297$	−6.52041	−	24.4286i	−0.378352	−	1.41749i
$298$	−34.5209			−1.99974
$299$	−3.59189	−	4.54538i	−0.207724	−	0.262866i
$300$	1.56894	+	5.86291i	0.0905831	+	0.338495i
$301$	12.9207	−	7.45978i	0.744738	−	0.429975i
$302$	19.2840	+	33.4009i	1.10967	+	1.92200i
$303$	−7.76924	−	2.08444i	−0.446331	−	0.119748i
$304$	−1.94375	−	1.12223i	−0.111482	−	0.0643641i
$305$			14.8283i			0.849067i
$306$	24.8123	+	0.0159378i	1.41843	+	0.000911101i
$307$		−	11.9594i		−	0.682560i	−0.939962	−	0.341280i	$-0.889140\pi$
$307$		−	11.9594i		−	0.682560i	0.939962	−	0.341280i	$-0.110860\pi$
$308$	25.6700	−	44.4617i	1.46268	−	2.53344i
$309$	−11.8327	+	11.8251i	−0.673137	+	0.672705i
$310$	8.39688	−	4.84794i	0.476911	−	0.275345i
$311$	−7.69401	−	13.3264i	−0.436287	−	0.755672i	0.561112	−	0.827740i	$-0.310374\pi$
$311$	−7.69401	−	13.3264i	−0.436287	−	0.755672i	−0.997400	+	0.0720679i	$0.977040\pi$
$312$	−20.2394	+	8.71581i	−1.14583	+	0.493435i
$313$	−15.6183	+	27.0516i	−0.882797	+	1.52905i	−0.0345782	+	0.999402i	$0.511009\pi$
$313$	−15.6183	+	27.0516i	−0.882797	+	1.52905i	−0.848218	+	0.529647i	$0.822325\pi$
$314$			46.6848i			2.63458i
$315$	7.82592	−	4.51160i	0.440941	−	0.254200i
$316$	32.6037			1.83410
$317$	6.94765	+	4.01123i	0.390219	+	0.225293i	0.682255	−	0.731114i	$-0.260999\pi$
$317$	6.94765	+	4.01123i	0.390219	+	0.225293i	−0.292036	+	0.956407i	$0.594333\pi$
$318$	0.0248205	−	0.0925124i	0.00139186	−	0.00518784i
$319$	−34.7063	+	20.0377i	−1.94318	+	1.12190i
$320$	10.4838	−	6.05280i	0.586060	−	0.338362i
$321$	−0.280997	−	1.05004i	−0.0156837	−	0.0586076i
$322$	−5.67528	+	9.82988i	−0.316271	+	0.547798i
$323$			6.22876i			0.346578i
$324$	31.5365	+	0.0405139i	1.75203	+	0.00225077i
$325$	−1.33216	+	3.35043i	−0.0738948	+	0.185848i
$326$	−7.71775	+	13.3675i	−0.427447	+	0.740359i
$327$	13.7075	−	3.66820i	0.758028	−	0.202852i
$328$	2.97505	+	5.15294i	0.164270	+	0.284524i
$329$	3.45952	+	5.99206i	0.190729	+	0.330353i
$330$	5.12365	−	19.0972i	0.282048	−	1.05127i
$331$	1.57712	+	0.910548i	0.0866861	+	0.0500483i	0.542716	−	0.839916i	$-0.317396\pi$
$331$	1.57712	+	0.910548i	0.0866861	+	0.0500483i	−0.456030	+	0.889964i	$0.650729\pi$
$332$		−	16.4744i		−	0.904152i
$333$	−7.45967	−	12.9397i	−0.408788	−	0.709092i
$334$	−16.8031			−0.919423
$335$	−7.04883	+	12.2089i	−0.385119	+	0.667045i
$336$	4.68319	+	4.68620i	0.255489	+	0.255653i
$337$	15.6482	+	27.1036i	0.852414	+	1.47642i	0.879023	+	0.476779i	$0.158196\pi$
$337$	15.6482	+	27.1036i	0.852414	+	1.47642i	−0.0266088	+	0.999646i	$0.508471\pi$
$338$	−29.6728	−	7.05066i	−1.61399	−	0.383506i
$339$	−2.95092	+	2.94903i	−0.160272	+	0.160169i
$340$	10.6981	+	6.17655i	0.580186	+	0.334970i
$341$	−20.1098			−1.08900
$342$	−0.00798767	+	12.4354i	−0.000431924	+	0.672430i
$343$			14.8548i			0.802084i
$344$	15.1416	+	8.74199i	0.816379	+	0.471336i
$345$	−0.721157	+	2.68794i	−0.0388258	+	0.144714i
$346$	30.1950	−	17.4331i	1.62330	−	0.937210i
$347$	−8.63907	−	14.9633i	−0.463770	−	0.803273i	0.535375	−	0.844614i	$-0.320170\pi$
$347$	−8.63907	−	14.9633i	−0.463770	−	0.803273i	−0.999145	+	0.0413416i	$0.986837\pi$
$348$	−12.9218	−	48.2870i	−0.692683	−	2.58845i
$349$	−27.3293	−	15.7786i	−1.46291	−	0.844609i	−0.463761	−	0.885961i	$-0.653500\pi$
$349$	−27.3293	−	15.7786i	−1.46291	−	0.844609i	−0.999145	+	0.0413518i	$0.986834\pi$
$350$	7.06422			0.377599
$351$	15.0138	+	11.2066i	0.801375	+	0.598162i
$352$	−19.8382			−1.05738
$353$	26.8225	+	15.4860i	1.42762	+	0.824236i	0.996933	−	0.0782651i	$-0.0249380\pi$
$353$	26.8225	+	15.4860i	1.42762	+	0.824236i	0.430687	+	0.902501i	$0.358271\pi$
$354$	−14.6713	−	54.8245i	−0.779771	−	2.91389i
$355$	5.24350	+	9.08201i	0.278296	+	0.482023i
$356$	−49.2811	+	28.4525i	−2.61189	+	1.50798i
$357$	4.76436	−	17.7580i	0.252157	−	0.939853i
$358$	−46.3901	−	26.7834i	−2.45179	−	1.41554i
$359$			16.7231i			0.882613i	0.897356	+	0.441307i	$0.145485\pi$
$359$			16.7231i			0.882613i	−0.897356	+	0.441307i	$0.854515\pi$
$360$	9.16427	+	5.29884i	0.482999	+	0.279274i
$361$	15.8783			0.835699
$362$	−31.0817	−	17.9451i	−1.63362	−	0.943171i
$363$	−15.5308	+	15.5208i	−0.815155	+	0.814632i
$364$	5.50267	+	37.6422i	0.288419	+	1.97299i
$365$	−0.0462105	−	0.0800389i	−0.00241877	−	0.00418943i
$366$	42.5931	+	42.6205i	2.22638	+	2.22781i
$367$	8.33456	−	14.4359i	0.435060	−	0.753547i	−0.562240	−	0.826974i	$-0.690060\pi$
$367$	8.33456	−	14.4359i	0.435060	−	0.753547i	0.997301	+	0.0734272i	$0.0233937\pi$
$368$	−2.04111			−0.106400
$369$	2.53216	−	4.37934i	0.131819	−	0.227979i
$370$		−	11.6803i		−	0.607229i
$371$	−0.0614674	−	0.0354882i	−0.00319123	−	0.00184246i
$372$	6.49972	−	24.2261i	0.336995	−	1.25607i
$373$	18.2792	+	31.6605i	0.946460	+	1.63932i	0.752802	+	0.658247i	$0.228702\pi$
$373$	18.2792	+	31.6605i	0.946460	+	1.63932i	0.193658	+	0.981069i	$0.437965\pi$
$374$	−20.1223	−	34.8528i	−1.04050	−	1.80220i
$375$	1.67318	−	0.447750i	0.0864025	−	0.0231217i
$376$	−4.05415	+	7.02199i	−0.209077	+	0.362131i
$377$	10.9717	−	27.5941i	0.565069	−	1.42117i
$378$	9.53457	−	35.4469i	0.490405	−	1.82319i
$379$		−	30.4260i		−	1.56288i	−0.623980	−	0.781440i	$-0.714485\pi$
$379$		−	30.4260i		−	1.56288i	0.623980	−	0.781440i	$-0.285515\pi$
$380$	−3.09556	+	5.36167i	−0.158799	+	0.275048i
$381$	0.0465937	+	0.174114i	0.00238707	+	0.00892012i
$382$	−20.7118	+	11.9580i	−1.05971	+	0.611822i
$383$	2.09473	−	1.20939i	0.107036	−	0.0617971i	−0.445526	−	0.895269i	$-0.646983\pi$
$383$	2.09473	−	1.20939i	0.107036	−	0.0617971i	0.552562	+	0.833472i	$0.313650\pi$
$384$	9.08719	−	33.8703i	0.463729	−	1.72844i
$385$	−12.6886	−	7.32578i	−0.646672	−	0.373356i
$386$	−43.5887			−2.21860
$387$	0.00954804	−	14.8646i	0.000485354	−	0.755612i
$388$			45.9869i			2.33463i
$389$	0.948414	−	1.64270i	0.0480865	−	0.0832883i	−0.840980	−	0.541066i	$-0.818021\pi$
$389$	0.948414	−	1.64270i	0.0480865	−	0.0832883i	0.889067	+	0.457777i	$0.151354\pi$
$390$	5.79485	+	13.4565i	0.293434	+	0.681398i
$391$	2.83222	+	4.90555i	0.143232	+	0.248085i
$392$	6.31538	−	3.64618i	0.318975	−	0.184160i
$393$	18.1690	−	18.1573i	0.916506	−	0.915917i
$394$	−12.5329	+	21.7076i	−0.631396	+	1.09361i
$395$		−	9.30453i		−	0.468162i
$396$	−25.5470	−	44.3145i	−1.28379	−	2.22689i
$397$		−	9.29366i		−	0.466435i	−0.972425	−	0.233218i	$-0.925075\pi$
$397$		−	9.29366i		−	0.466435i	0.972425	−	0.233218i	$-0.0749255\pi$
$398$	30.2291	+	17.4528i	1.51525	+	0.874830i
$399$	8.89995	+	2.38780i	0.445555	+	0.119539i
$400$	0.635160	+	1.10013i	0.0317580	+	0.0550065i
$401$	−16.7032	+	9.64361i	−0.834119	+	0.481579i	−0.855261	−	0.518198i	$-0.826603\pi$
$401$	−16.7032	+	9.64361i	−0.834119	+	0.481579i	0.0211418	+	0.999776i	$0.493270\pi$
$402$	14.8090	+	55.3389i	0.738603	+	2.76005i
$403$	11.6913	−	9.23880i	0.582385	−	0.460217i
$404$	−16.2736			−0.809641
$405$	0.0115620	−	8.99999i	0.000574519	−	0.447213i
$406$	−58.1810			−2.88747
$407$	−12.1128	+	20.9799i	−0.600407	+	1.03994i
$408$	20.8139	−	5.56990i	1.03044	−	0.275751i
$409$	24.5831	−	14.1930i	1.21555	−	0.701801i	0.251590	−	0.967834i	$-0.419046\pi$
$409$	24.5831	−	14.1930i	1.21555	−	0.701801i	0.963964	+	0.266033i	$0.0857131\pi$
$410$	3.42602	−	1.97801i	0.169199	−	0.0976871i
$411$	−3.67875	+	13.7117i	−0.181459	+	0.676347i
$412$	−16.9215	+	29.3089i	−0.833663	+	1.44395i
$413$	−42.0547			−2.06937
$414$	5.64810	+	9.79732i	0.277589	+	0.481512i
$415$	−4.70153			−0.230789
$416$	11.5334	−	9.11405i	0.565473	−	0.446853i
$417$	9.53220	−	9.52608i	0.466794	−	0.466494i
$418$	17.4675	−	10.0849i	0.854364	−	0.493267i
$419$	17.7608	+	30.7626i	0.867672	+	1.50285i	0.864370	+	0.502857i	$0.167718\pi$
$419$	17.7608	+	30.7626i	0.867672	+	1.50285i	0.00330191	+	0.999995i	$0.498949\pi$
$420$	12.9265	−	12.9182i	0.630747	−	0.630342i
$421$	4.44999	+	2.56920i	0.216879	+	0.125215i	0.604504	−	0.796602i	$-0.293371\pi$
$421$	4.44999	+	2.56920i	0.216879	+	0.125215i	−0.387625	+	0.921817i	$0.626705\pi$
$422$			31.0480i			1.51139i
$423$	6.89356	+	0.00442796i	0.335176	+	0.000215295i
$424$		−	0.0831760i		−	0.00403938i
$425$	1.76268	−	3.05306i	0.0855027	−	0.148095i
$426$	41.1585	+	11.0426i	1.99414	+	0.535014i
$427$	38.6674	−	22.3246i	1.87125	−	1.08037i
$428$	−1.09953	−	1.90444i	−0.0531477	−	0.0920546i
$429$	3.54616	−	30.1798i	0.171210	−	1.45709i
$430$	5.81226	−	10.0671i	0.280292	−	0.485480i
$431$			10.2617i			0.494290i	0.968979	+	0.247145i	$0.0794924\pi$
$431$			10.2617i			0.494290i	−0.968979	+	0.247145i	$0.920508\pi$
$432$	6.37750	−	1.70226i	0.306838	−	0.0819002i
$433$	24.3491			1.17014			0.585071	−	0.810982i	$-0.301067\pi$
$433$	24.3491			1.17014			0.585071	+	0.810982i	$0.301067\pi$
$434$	−25.2837	−	14.5976i	−1.21366	−	0.700705i
$435$	−13.7803	+	3.68768i	−0.660714	+	0.176810i
$436$	24.8610	−	14.3535i	1.19063	−	0.687409i
$437$	−2.45856	+	1.41945i	−0.117609	+	0.0679016i
$438$	−0.362726	−	0.0973171i	−0.0173317	−	0.00464999i
$439$	−1.83478	+	3.17793i	−0.0875692	+	0.151674i	−0.906483	−	0.422242i	$-0.861243\pi$
$439$	−1.83478	+	3.17793i	−0.0875692	+	0.151674i	0.818914	+	0.573916i	$0.194577\pi$
$440$		−	17.1699i		−	0.818544i
$441$	−5.36726	−	3.10339i	−0.255584	−	0.147780i
$442$	27.7106	+	11.0180i	1.31806	+	0.524072i
$443$	−4.99424	+	8.65028i	−0.237284	+	0.410987i	−0.959934	−	0.280227i	$-0.909590\pi$
$443$	−4.99424	+	8.65028i	−0.237284	+	0.410987i	0.722650	+	0.691214i	$0.242924\pi$
$444$	−21.3594	−	21.3732i	−1.01367	−	1.01433i
$445$	8.11985	+	14.0640i	0.384918	+	0.666697i
$446$	−19.9468	−	34.5489i	−0.944509	−	1.63594i
$447$	18.0155	+	18.0271i	0.852105	+	0.852653i
$448$	−31.5675	−	18.2255i	−1.49142	−	0.861074i
$449$		−	13.8617i		−	0.654175i	−0.944994	−	0.327087i	$-0.893933\pi$
$449$		−	13.8617i		−	0.654175i	0.944994	−	0.327087i	$-0.106067\pi$
$450$	3.52302	−	6.09302i	0.166077	−	0.287228i
$451$	−8.20500			−0.386358
$452$	−4.22002	+	7.30929i	−0.198493	+	0.343800i
$453$	7.37841	−	27.5013i	0.346668	−	1.29212i
$454$	−1.25723	−	2.17758i	−0.0590047	−	0.102199i
$455$	10.7424	−	1.57037i	0.503613	−	0.0736201i
$456$	2.79152	+	10.4315i	0.130725	+	0.488499i
$457$	−29.5725	−	17.0737i	−1.38334	−	0.798675i	−0.390791	−	0.920480i	$-0.627798\pi$
$457$	−29.5725	−	17.0737i	−1.38334	−	0.798675i	−0.992554	+	0.121805i	$0.961132\pi$
$458$	7.87556			0.368001
$459$	−12.9405	−	12.9655i	−0.604013	−	0.605178i
$460$			5.63021i			0.262510i
$461$	−27.2654	−	15.7417i	−1.26988	−	0.733163i	−0.294912	−	0.955525i	$-0.595290\pi$
$461$	−27.2654	−	15.7417i	−1.26988	−	0.733163i	−0.974964	+	0.222361i	$0.928624\pi$
$462$	−57.5132	+	15.3908i	−2.67576	+	0.716045i
$463$	−11.8594	+	6.84700i	−0.551151	+	0.318207i	−0.749586	−	0.661907i	$-0.769747\pi$
$463$	−11.8594	+	6.84700i	−0.551151	+	0.318207i	0.198435	+	0.980114i	$0.436414\pi$
$464$	−5.23118	−	9.06067i	−0.242852	−	0.420631i
$465$	−6.91373	−	1.85491i	−0.320617	−	0.0860194i
$466$	−22.6518	−	13.0780i	−1.04932	−	0.605827i
$467$	2.38157			0.110206			0.0551029	−	0.998481i	$-0.482451\pi$
$467$	2.38157			0.110206			0.0551029	+	0.998481i	$0.482451\pi$
$468$	35.2113	+	14.0265i	1.62764	+	0.648376i
$469$	42.4492			1.96012
$470$	4.66869	+	2.69547i	0.215350	+	0.124333i
$471$	24.3792	−	24.3635i	1.12333	−	1.12261i
$472$	−24.6416	−	42.6804i	−1.13422	−	1.96453i
$473$	−20.8797	+	12.0549i	−0.960052	+	0.554286i
$474$	−26.7265	−	26.7437i	−1.22759	−	1.22838i
$475$	1.53013	+	0.883421i	0.0702072	+	0.0405341i
$476$		−	37.1962i		−	1.70489i
$477$	−0.0612638	+	0.0353182i	−0.00280508	+	0.00161711i
$478$	−41.9065			−1.91676
$479$	−15.8023	−	9.12347i	−0.722026	−	0.416862i	0.0934721	−	0.995622i	$-0.470203\pi$
$479$	−15.8023	−	9.12347i	−0.722026	−	0.416862i	−0.815498	+	0.578760i	$0.803537\pi$
$480$	−6.82038	−	1.82986i	−0.311306	−	0.0835215i
$481$	−2.59652	−	17.7620i	−0.118391	−	0.809878i
$482$	−8.81454	−	15.2672i	−0.401491	−	0.695404i
$483$	8.09501	−	2.16627i	0.368336	−	0.0985685i
$484$	−22.2101	+	38.4690i	−1.00955	+	1.74859i
$485$	13.1239			0.595924
$486$	−25.8185	−	25.9016i	−1.17115	−	1.17492i
$487$		−	1.00591i		−	0.0455820i	−0.999740	−	0.0227910i	$-0.992745\pi$
$487$		−	1.00591i		−	0.0455820i	0.999740	−	0.0227910i	$-0.00725522\pi$
$488$	45.3137	+	26.1619i	2.05125	+	1.18429i
$489$	11.0083	−	2.94588i	0.497813	−	0.133217i
$490$	−2.42423	−	4.19888i	−0.109515	−	0.189686i
$491$	14.7045	+	25.4689i	0.663604	+	1.14940i	0.979662	+	0.200656i	$0.0643075\pi$
$491$	14.7045	+	25.4689i	0.663604	+	1.14940i	−0.316057	+	0.948740i	$0.602359\pi$
$492$	2.65196	−	9.88453i	0.119559	−	0.445629i
$493$	−14.5175	+	25.1450i	−0.653834	+	1.13247i
$494$	−5.52198	+	13.8880i	−0.248446	+	0.624850i
$495$	−12.6466	+	7.29069i	−0.568423	+	0.327692i
$496$		−	5.25000i		−	0.235732i
$497$	15.7886	−	27.3467i	0.708216	−	1.22667i
$498$	−13.5134	+	13.5048i	−0.605551	+	0.605162i
$499$	−10.6843	+	6.16857i	−0.478294	+	0.276143i	−0.719705	−	0.694280i	$-0.755723\pi$
$499$	−10.6843	+	6.16857i	−0.478294	+	0.276143i	0.241411	+	0.970423i	$0.422390\pi$
$500$	3.03461	−	1.75203i	0.135712	−	0.0783532i
$501$	8.76906	+	8.77470i	0.391773	+	0.392025i
$502$	35.3425	+	20.4050i	1.57741	+	0.910719i
$503$	18.8762			0.841650			0.420825	−	0.907142i	$-0.361741\pi$
$503$	18.8762			0.841650			0.420825	+	0.907142i	$0.361741\pi$
$504$	0.0204744	−	31.8751i	0.000912002	−	1.41983i
$505$			4.64421i			0.206665i
$506$	9.17119	−	15.8850i	0.407709	−	0.706173i
$507$	11.8035	+	19.1749i	0.524212	+	0.851588i
$508$	0.182319	+	0.315787i	0.00808912	+	0.0140108i
$509$	0.488382	−	0.281968i	0.0216472	−	0.0124980i	−0.489137	−	0.872207i	$-0.662688\pi$
$509$	0.488382	−	0.281968i	0.0216472	−	0.0124980i	0.510785	+	0.859709i	$0.329355\pi$
$510$	−3.70324	−	13.8385i	−0.163982	−	0.612777i
$511$	−0.139144	+	0.241004i	−0.00615535	+	0.0106614i
$512$		−	14.1441i		−	0.625087i
$513$	6.49804	−	6.48553i	0.286896	−	0.286343i
$514$		−	64.2195i		−	2.83260i
$515$	8.36428	+	4.82912i	0.368574	+	0.212796i
$516$	−7.77393	−	29.0500i	−0.342228	−	1.27886i
$517$	−5.59054	−	9.68310i	−0.245872	−	0.425862i
$518$	−30.4584	+	17.5852i	−1.33827	+	0.772648i
$519$	−24.8617	−	6.67023i	−1.09131	−	0.292790i
$520$	7.88818	+	9.98215i	0.345920	+	0.437746i
$521$	40.6199			1.77959			0.889796	−	0.456358i	$-0.150847\pi$
$521$	40.6199			1.77959			0.889796	+	0.456358i	$0.150847\pi$
$522$	−29.0157	+	50.1821i	−1.26998	+	2.19641i
$523$	−32.7623			−1.43260			−0.716298	−	0.697795i	$-0.754165\pi$
$523$	−32.7623			−1.43260			−0.716298	+	0.697795i	$0.754165\pi$
$524$	25.9829	−	45.0037i	1.13507	−	1.96600i
$525$	−3.68662	−	3.68899i	−0.160897	−	0.161001i
$526$	−39.7831	+	22.9688i	−1.73463	+	1.00149i
$527$	−12.6177	+	7.28484i	−0.549636	+	0.317333i
$528$	−7.56799	−	7.57285i	−0.329354	−	0.329566i
$529$	10.2091	−	17.6828i	0.443876	−	0.768816i
$530$	−0.0553010			−0.00240212
$531$	−20.9732	+	36.2729i	−0.910161	+	1.57411i
$532$	18.6420			0.808232
$533$	4.77018	−	3.76953i	0.206619	−	0.163276i
$534$	63.7363	+	17.1000i	2.75814	+	0.739991i
$535$	−0.543495	+	0.313787i	−0.0234973	+	0.0135662i
$536$	24.8727	+	43.0809i	1.07434	+	1.86081i
$537$	10.2233	+	38.2028i	0.441166	+	1.64857i
$538$	50.2986	+	29.0399i	2.16853	+	1.25200i
$539$			10.0559i			0.433140i
$540$	−4.69553	−	17.5918i	−0.202064	−	0.757029i
$541$		−	9.70325i		−	0.417175i	−0.978004	−	0.208588i	$-0.933113\pi$
$541$		−	9.70325i		−	0.417175i	0.978004	−	0.208588i	$-0.0668867\pi$
$542$	3.75793	−	6.50892i	0.161417	−	0.279582i
$543$	6.84966	+	25.5962i	0.293947	+	1.09844i
$544$	−12.4473	+	7.18648i	−0.533676	+	0.308118i
$545$	−4.09626	−	7.09492i	−0.175464	−	0.303913i
$546$	26.3659	−	35.3704i	1.12835	−	1.51372i
$547$	2.34181	−	4.05613i	0.100128	−	0.173428i	−0.811609	−	0.584201i	$-0.801408\pi$
$547$	2.34181	−	4.05613i	0.100128	−	0.173428i	0.911737	+	0.410773i	$0.134741\pi$
$548$			28.7207i			1.22689i
$549$	0.0285741	−	44.4849i	0.00121951	−	1.89857i
$550$	−11.4157			−0.486767
$551$	−12.6022	−	7.27586i	−0.536870	−	0.309962i
$552$	6.94170	+	6.94616i	0.295459	+	0.295648i
$553$	−24.2632	+	14.0084i	−1.03178	+	0.595696i
$554$	0.807720	−	0.466338i	0.0343168	−	0.0198128i
$555$	−6.09954	+	6.09562i	−0.258911	+	0.258745i
$556$	13.6317	−	23.6108i	0.578113	−	1.00132i
$557$			34.9144i			1.47937i	0.672952	+	0.739686i	$0.265026\pi$
$557$			34.9144i			1.47937i	−0.672952	+	0.739686i	$0.734974\pi$
$558$	−25.2000	+	14.5276i	−1.06680	+	0.615004i
$559$	6.60069	−	16.6010i	0.279179	−	0.702146i
$560$	1.91252	−	3.31258i	0.0808187	−	0.139982i
$561$	−7.69915	+	28.6967i	−0.325058	+	1.21158i
$562$	5.08804	+	8.81274i	0.214626	+	0.371743i
$563$	−18.8875	−	32.7140i	−0.796011	−	1.37873i	−0.922195	−	0.386725i	$-0.873606\pi$
$563$	−18.8875	−	32.7140i	−0.796011	−	1.37873i	0.126184	−	0.992007i	$-0.459727\pi$
$564$	13.4721	−	3.60521i	0.567278	−	0.151807i
$565$	2.08595	+	1.20432i	0.0877565	+	0.0506662i
$566$			2.95131i			0.124053i
$567$	−23.4865	+	13.5197i	−0.986339	+	0.567775i
$568$	37.0048			1.55269
$569$	−17.5536	+	30.4038i	−0.735886	+	1.27459i	0.218447	+	0.975849i	$0.429901\pi$
$569$	−17.5536	+	30.4038i	−0.735886	+	1.27459i	−0.954333	+	0.298744i	$0.903432\pi$
$570$	6.93555	−	1.85599i	0.290498	−	0.0777388i
$571$	−8.10439	−	14.0372i	−0.339158	−	0.587439i	0.645117	−	0.764084i	$-0.276809\pi$
$571$	−8.10439	−	14.0372i	−0.339158	−	0.587439i	−0.984275	+	0.176645i	$0.943475\pi$
$572$	−8.89226	−	60.8293i	−0.371804	−	2.54340i
$573$	17.0535	+	4.57533i	0.712418	+	0.191137i
$574$	−10.3160	−	5.95596i	−0.430583	−	0.248597i
$575$	1.60677			0.0670068
$576$	−31.4629	+	18.1382i	−1.31096	+	0.755758i
$577$		−	25.8038i		−	1.07423i	−0.843510	−	0.537113i	$-0.819515\pi$
$577$		−	25.8038i		−	1.07423i	0.843510	−	0.537113i	$-0.180485\pi$
$578$	9.28877	+	5.36287i	0.386362	+	0.223066i
$579$	22.7477	+	22.7623i	0.945363	+	0.945971i
$580$	−24.9930	+	14.4297i	−1.03778	+	0.599162i
$581$	7.07835	+	12.2601i	0.293659	+	0.508633i
$582$	37.7215	−	37.6973i	1.56361	−	1.56260i
$583$	0.0993306	+	0.0573485i	0.00411385	+	0.00237513i
$584$	−0.326120			−0.0134949
$585$	4.00293	−	10.0487i	0.165501	−	0.415463i
$586$	−9.91399			−0.409543
$587$	−9.45716	−	5.46009i	−0.390339	−	0.225362i	0.291968	−	0.956428i	$-0.405690\pi$
$587$	−9.45716	−	5.46009i	−0.390339	−	0.225362i	−0.682307	+	0.731066i	$0.739023\pi$
$588$	−12.1144	−	3.25020i	−0.499588	−	0.134036i
$589$	−3.65101	−	6.32374i	−0.150437	−	0.260565i
$590$	−28.3768	+	16.3834i	−1.16825	+	0.674492i
$591$	17.8764	−	4.78382i	0.735337	−	0.196780i
$592$	−5.47717	−	3.16224i	−0.225110	−	0.129967i
$593$			18.9202i			0.776961i	0.921457	+	0.388481i	$0.127000\pi$
$593$			18.9202i			0.776961i	−0.921457	+	0.388481i	$0.873000\pi$
$594$	−15.4078	+	57.2817i	−0.632188	+	2.35030i
$595$	−10.6152			−0.435180
$596$	44.6522	+	25.7800i	1.82903	+	1.05599i
$597$	−6.66177	−	24.8940i	−0.272648	−	1.01884i
$598$	1.96596	+	13.4485i	0.0803940	+	0.549951i
$599$	6.45037	+	11.1724i	0.263555	+	0.456491i	0.967184	−	0.254077i	$-0.0817716\pi$
$599$	6.45037	+	11.1724i	0.263555	+	0.456491i	−0.703629	+	0.710568i	$0.748438\pi$
$600$	1.58374	−	5.90302i	0.0646559	−	0.240990i
$601$	−20.0298	+	34.6926i	−0.817032	+	1.41514i	0.0908272	+	0.995867i	$0.471049\pi$
$601$	−20.0298	+	34.6926i	−0.817032	+	1.41514i	−0.907859	+	0.419275i	$0.862284\pi$
$602$	−35.0024			−1.42659
$603$	21.1700	−	36.6132i	0.862109	−	1.49100i
$604$		−	57.6046i		−	2.34390i
$605$	10.9784	+	6.33838i	0.446335	+	0.257692i
$606$	13.3401	+	13.3487i	0.541905	+	0.542253i
$607$	−2.47822	−	4.29241i	−0.100588	−	0.174223i	0.811339	−	0.584576i	$-0.198739\pi$
$607$	−2.47822	−	4.29241i	−0.100588	−	0.174223i	−0.911927	+	0.410352i	$0.865406\pi$
$608$	−3.60171	−	6.23835i	−0.146069	−	0.252999i
$609$	30.3631	+	30.3826i	1.23037	+	1.23116i
$610$	17.3942	−	30.1276i	0.704269	−	1.21983i
$611$	7.69879	+	3.06111i	0.311460	+	0.123839i
$612$	−32.0824	−	18.5503i	−1.29685	−	0.749850i
$613$			42.4885i			1.71609i	0.513572	+	0.858047i	$0.328322\pi$
$613$			42.4885i			1.71609i	−0.513572	+	0.858047i	$0.671678\pi$
$614$	−14.0288	+	24.2986i	−0.566157	+	0.980613i
$615$	−2.82088	−	0.756823i	−0.113749	−	0.0305181i
$616$	−44.7736	+	25.8500i	−1.80398	+	1.04153i
$617$	10.8234	−	6.24890i	0.435734	−	0.251571i	−0.266052	−	0.963959i	$-0.585719\pi$
$617$	10.8234	−	6.24890i	0.435734	−	0.251571i	0.701786	+	0.712387i	$0.252386\pi$
$618$	37.9124	−	10.1455i	1.52506	−	0.408114i
$619$	9.13994	+	5.27695i	0.367365	+	0.212098i	0.672307	−	0.740273i	$-0.265304\pi$
$619$	9.13994	+	5.27695i	0.367365	+	0.212098i	−0.304942	+	0.952371i	$0.598637\pi$
$620$	−14.4816			−0.581596
$621$	2.16865	−	8.06244i	0.0870250	−	0.323534i
$622$			36.1014i			1.44754i
$623$	24.4496	−	42.3479i	0.979551	−	1.69663i
$624$	7.87894	+	0.925786i	0.315410	+	0.0370611i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	63.4651	−	36.6416i	2.53658	−	1.46449i
$627$	−14.3822	−	3.85865i	−0.574370	−	0.154100i
$628$	34.8639	−	60.3860i	1.39122	−	2.40966i
$629$			17.5516i			0.699828i
$630$	−21.1927	−	0.0136127i	−0.844336	−	0.000542344i
$631$			2.24202i			0.0892534i	0.999004	+	0.0446267i	$0.0142098\pi$
$631$			2.24202i			0.0892534i	−0.999004	+	0.0446267i	$0.985790\pi$
$632$	−28.4336	−	16.4162i	−1.13103	−	0.653000i
$633$	16.2135	−	16.2031i	0.644429	−	0.644015i
$634$	−9.41063	−	16.2997i	−0.373744	−	0.647343i
$635$	0.0901202	−	0.0520309i	0.00357631	−	0.00206478i
$636$	−0.101192	+	0.101127i	−0.00401254	+	0.00400996i
$637$	−4.61989	−	5.84627i	−0.183047	−	0.231638i
$638$	94.0198			3.72228
$639$	−15.7130	−	27.2561i	−0.621597	−	1.07824i
$640$	−20.2466			−0.800318
$641$	−4.20443	+	7.28228i	−0.166065	+	0.287633i	−0.937033	−	0.349241i	$-0.886439\pi$
$641$	−4.20443	+	7.28228i	−0.166065	+	0.287633i	0.770968	+	0.636874i	$0.219773\pi$
$642$	−0.660821	+	2.46305i	−0.0260805	+	0.0972089i
$643$	7.96450	−	4.59830i	0.314089	−	0.181339i	−0.334666	−	0.942337i	$-0.608623\pi$
$643$	7.96450	−	4.59830i	0.314089	−	0.181339i	0.648755	+	0.760997i	$0.275290\pi$
$644$	14.6818	−	8.47652i	0.578542	−	0.334022i
$645$	−8.29039	+	2.21855i	−0.326434	+	0.0873553i
$646$	7.30657	−	12.6553i	0.287473	−	0.497918i
$647$	26.6157			1.04637			0.523185	−	0.852219i	$-0.324744\pi$
$647$	26.6157			1.04637			0.523185	+	0.852219i	$0.324744\pi$
$648$	−27.4826	−	15.9142i	−1.07962	−	0.625168i
$649$	67.9599			2.66766
$650$	6.63680	−	5.24459i	0.260317	−	0.205710i
$651$	5.57192	+	20.8214i	0.218381	+	0.816056i
$652$	19.9656	−	11.5271i	0.781911	−	0.451437i
$653$	3.30181	+	5.71890i	0.129210	+	0.223798i	0.923371	−	0.383910i	$-0.125423\pi$
$653$	3.30181	+	5.71890i	0.129210	+	0.223798i	−0.794161	+	0.607708i	$0.792089\pi$
$654$	−32.1533	−	8.62652i	−1.25729	−	0.337324i
$655$	−12.8433	−	7.41509i	−0.501830	−	0.289731i
$656$		−	2.14206i		−	0.0836332i
$657$	0.138477	+	0.240206i	0.00540251	+	0.00937132i
$658$		−	16.2326i		−	0.632811i
$659$	−10.8053	+	18.7153i	−0.420913	+	0.729043i	−0.996029	−	0.0890287i	$-0.971624\pi$
$659$	−10.8053	+	18.7153i	−0.420913	+	0.729043i	0.575116	+	0.818072i	$0.304957\pi$
$660$	−20.8890	+	20.8756i	−0.813104	+	0.812582i
$661$	−27.0882	+	15.6394i	−1.05361	+	0.608302i	−0.923658	−	0.383218i	$-0.874816\pi$
$661$	−27.0882	+	15.6394i	−1.05361	+	0.608302i	−0.129953	+	0.991520i	$0.541483\pi$
$662$	−2.13621	−	3.70003i	−0.0830263	−	0.143806i
$663$	−8.70773	−	20.2207i	−0.338180	−	0.785306i
$664$	−8.29499	+	14.3673i	−0.321908	+	0.557561i
$665$		−	5.32011i		−	0.206305i
$666$	−0.0225079	+	35.0409i	−0.000872163	+	1.35781i
$667$	−13.2333			−0.512397
$668$	21.7345	+	12.5484i	0.840932	+	0.485512i
$669$	−7.63201	+	28.4465i	−0.295071	+	1.09981i
$670$	28.6430	−	16.5371i	1.10658	−	0.638883i
$671$	−62.4861	+	36.0764i	−2.41225	+	1.39271i
$672$	5.49668	+	20.5403i	0.212039	+	0.792358i
$673$	−1.57667	+	2.73088i	−0.0607763	+	0.105268i	−0.894813	−	0.446442i	$-0.852691\pi$
$673$	−1.57667	+	2.73088i	−0.0607763	+	0.105268i	0.834036	+	0.551709i	$0.186024\pi$
$674$		−	73.4239i		−	2.82818i
$675$	−5.02039	+	1.34003i	−0.193235	+	0.0515777i
$676$	33.1159	+	31.2793i	1.27369	+	1.20305i
$677$	6.10021	−	10.5659i	0.234450	−	0.406080i	−0.724663	−	0.689104i	$-0.758004\pi$
$677$	6.10021	−	10.5659i	0.234450	−	0.406080i	0.959113	+	0.283024i	$0.0913377\pi$
$678$	9.45488	−	2.53017i	0.363113	−	0.0971707i
$679$	−19.7585	−	34.2228i	−0.758263	−	1.31335i
$680$	−6.21987	−	10.7731i	−0.238521	−	0.413131i
$681$	−0.481039	+	1.79296i	−0.0184334	+	0.0687063i
$682$	40.8582	+	23.5895i	1.56454	+	0.903288i
$683$		−	4.23880i		−	0.162193i	−0.996706	−	0.0810966i	$-0.974158\pi$
$683$		−	4.23880i		−	0.162193i	0.996706	−	0.0810966i	$-0.0258422\pi$
$684$	9.29701	−	16.0790i	0.355480	−	0.614797i
$685$	8.19641			0.313169
$686$	17.4252	−	30.1814i	0.665298	−	1.15233i
$687$	−4.11004	−	4.11268i	−0.156808	−	0.156909i
$688$	−3.14714	−	5.45101i	−0.119984	−	0.207818i
$689$	−0.0840952	+	0.0122934i	−0.00320377	+	0.000468340i
$690$	4.61827	−	4.61531i	0.175815	−	0.175702i
$691$	−22.4820	−	12.9800i	−0.855255	−	0.493782i	0.00716545	−	0.999974i	$-0.497719\pi$
$691$	−22.4820	−	12.9800i	−0.855255	−	0.493782i	−0.862420	+	0.506193i	$0.831052\pi$
$692$	−52.0757			−1.97962
$693$	38.0518	+	22.0018i	1.44547	+	0.835779i
$694$			40.5358i			1.53872i
$695$	−6.73812	−	3.89026i	−0.255591	−	0.147566i
$696$	−13.0437	+	48.6173i	−0.494420	+	1.84283i
$697$	−5.14817	+	2.97229i	−0.195001	+	0.112584i
$698$	37.0177	+	64.1166i	1.40114	+	2.42685i
$699$	4.99190	+	18.6540i	0.188811	+	0.705559i
$700$	−9.13745	−	5.27551i	−0.345363	−	0.199396i
$701$	47.5126			1.79453			0.897263	−	0.441497i	$-0.145553\pi$
$701$	47.5126			1.79453			0.897263	+	0.441497i	$0.145553\pi$
$702$	−17.3586	−	40.3807i	−0.655159	−	1.52407i
$703$	−8.79649			−0.331766
$704$	51.0127	+	29.4522i	1.92261	+	1.11002i
$705$	−1.02887	−	3.84472i	−0.0387493	−	0.144800i
$706$	−36.3313	−	62.9276i	−1.36735	−	2.36831i
$707$	12.1106	−	6.99205i	0.455465	−	0.262963i
$708$	−21.9654	+	81.8710i	−0.825512	+	3.07690i
$709$	23.8962	+	13.7965i	0.897441	+	0.518138i	0.876369	−	0.481640i	$-0.159959\pi$
$709$	23.8962	+	13.7965i	0.897441	+	0.518138i	0.0210722	+	0.999778i	$0.493292\pi$
$710$		−	24.6033i		−	0.923345i
$711$	−0.0179298	+	27.9136i	−0.000672420	+	1.04684i
$712$	57.3040			2.14756
$713$	−5.75081	−	3.32023i	−0.215370	−	0.124344i
$714$	−30.5108	+	30.4912i	−1.14184	+	1.14111i
$715$	−17.3597	+	2.53770i	−0.649215	+	0.0949047i
$716$	40.0032	+	69.2876i	1.49499	+	2.58940i
$717$	21.8699	+	21.8839i	0.816745	+	0.817270i
$718$	19.6168	−	33.9774i	0.732094	−	1.26802i
$719$	26.3274			0.981848			0.490924	−	0.871202i	$-0.336659\pi$
$719$	26.3274			0.981848			0.490924	+	0.871202i	$0.336659\pi$
$720$	−1.90336	−	3.30161i	−0.0709340	−	0.123044i
$721$		−	29.0817i		−	1.08306i
$722$	−32.2608	−	18.6258i	−1.20062	−	0.693180i
$723$	−3.37260	+	12.5706i	−0.125428	+	0.467505i
$724$	26.8025	+	46.4232i	0.996106	+	1.72531i
$725$	4.11800	+	7.13259i	0.152939	+	0.264898i
$726$	49.7613	−	13.3164i	1.84682	−	0.494217i
$727$	−4.40426	+	7.62840i	−0.163345	+	0.282922i	−0.936066	−	0.351824i	$-0.885562\pi$
$727$	−4.40426	+	7.62840i	−0.163345	+	0.282922i	0.772721	+	0.634745i	$0.218895\pi$
$728$	14.1542	−	35.5983i	0.524590	−	1.31936i
$729$	−0.0520289	+	26.9999i	−0.00192700	+	0.999998i
$730$			0.216826i			0.00802510i
$731$	−8.73389	+	15.1275i	−0.323035	+	0.559512i
$732$	−23.2648	−	86.9371i	−0.859892	−	3.21329i
$733$	−21.3136	+	12.3054i	−0.787236	+	0.454511i	−0.838988	−	0.544149i	$-0.816853\pi$
$733$	−21.3136	+	12.3054i	−0.787236	+	0.454511i	0.0517529	+	0.998660i	$0.483519\pi$
$734$	−33.8676	+	19.5535i	−1.25008	+	0.721732i
$735$	−0.927553	+	3.45723i	−0.0342133	+	0.127522i
$736$	−5.67316	−	3.27540i	−0.209116	−	0.120733i
$737$	−68.5975			−2.52682
$738$	−10.2819	+	5.92743i	−0.378481	+	0.218192i
$739$			28.4527i			1.04665i	0.852133	+	0.523325i	$0.175309\pi$
$739$			28.4527i			1.04665i	−0.852133	+	0.523325i	$0.824691\pi$
$740$	−8.72276	+	15.1083i	−0.320655	+	0.555391i
$741$	10.1342	−	4.36413i	0.372289	−	0.160321i
$742$	0.0832579	+	0.144207i	0.00305649	+	0.00529400i
$743$	−26.8082	+	15.4777i	−0.983496	+	0.567822i	−0.903324	−	0.428959i	$-0.858880\pi$
$743$	−26.8082	+	15.4777i	−0.983496	+	0.567822i	−0.0801725	+	0.996781i	$0.525547\pi$
$744$	−17.8664	+	17.8550i	−0.655015	+	0.654594i
$745$	7.35717	−	12.7430i	0.269546	−	0.466867i
$746$		−	85.7686i		−	3.14021i
$747$	14.1046	+	0.00905983i	0.516060	+	0.000331482i
$748$			60.1087i			2.19779i
$749$	1.63651	+	0.944839i	0.0597967	+	0.0345237i
$750$	−3.92472	−	1.05298i	−0.143310	−	0.0384493i
$751$	−8.22543	−	14.2469i	−0.300150	−	0.519876i	0.676020	−	0.736884i	$-0.263703\pi$
$751$	−8.22543	−	14.2469i	−0.300150	−	0.519876i	−0.976170	+	0.217008i	$0.930370\pi$
$752$	2.52794	−	1.45951i	0.0921844	−	0.0532227i
$753$	−7.78862	−	29.1049i	−0.283833	−	1.06064i
$754$	−54.6607	+	43.1945i	−1.99063	+	1.57305i
$755$	−16.4394			−0.598291
$756$	−38.8043	+	38.7296i	−1.41130	+	1.40858i
$757$	−21.7306			−0.789814			−0.394907	−	0.918721i	$-0.629223\pi$
$757$	−21.7306			−0.789814			−0.394907	+	0.918721i	$0.629223\pi$
$758$	−35.6909	+	61.8184i	−1.29635	+	2.24534i
$759$	−13.0815	+	3.50066i	−0.474827	+	0.127066i
$760$	5.39927	−	3.11727i	0.195852	−	0.113075i
$761$	20.0415	−	11.5709i	0.726503	−	0.419446i	−0.0906388	−	0.995884i	$-0.528891\pi$
$761$	20.0415	−	11.5709i	0.726503	−	0.419446i	0.817141	+	0.576437i	$0.195558\pi$
$762$	0.109575	−	0.408413i	0.00396947	−	0.0147953i
$763$	−12.3342	+	21.3634i	−0.446527	+	0.773407i
$764$	35.7204			1.29232
$765$	−5.29393	+	9.15577i	−0.191403	+	0.331028i
$766$	−5.67465			−0.205034
$767$	−39.5101	+	31.2220i	−1.42663	+	1.12736i
$768$	−28.5321	+	28.5137i	−1.02956	+	1.02890i
$769$	26.3323	−	15.2030i	0.949567	−	0.548233i	0.0566204	−	0.998396i	$-0.481968\pi$
$769$	26.3323	−	15.2030i	0.949567	−	0.548233i	0.892946	+	0.450163i	$0.148634\pi$
$770$	17.1868	+	29.7685i	0.619370	+	1.07278i
$771$	−33.5359	+	33.5144i	−1.20777	+	1.20699i
$772$	56.3812	+	32.5517i	2.02920	+	1.17156i
$773$		−	33.3792i		−	1.20056i	−0.799788	−	0.600282i	$-0.795055\pi$
$773$		−	33.3792i		−	1.20056i	0.799788	−	0.600282i	$-0.204945\pi$
$774$	−17.4562	+	30.1902i	−0.627449	+	1.08516i
$775$			4.13281i			0.148455i
$776$	23.1547	−	40.1051i	0.831205	−	1.43969i
$777$	25.0785	+	6.72840i	0.899687	+	0.241380i
$778$	−3.85390	+	2.22505i	−0.138169	+	0.0797719i
$779$	−1.48965	−	2.58015i	−0.0533723	−	0.0924436i
$780$	2.55369	−	21.7333i	0.0914369	−	0.778178i
$781$	−25.5142	+	44.1920i	−0.912971	+	1.58131i
$782$		−	13.2892i		−	0.475221i
$783$	41.3480	−	11.0365i	1.47766	−	0.394411i
$784$	−2.62528			−0.0937598
$785$	−17.2331	−	9.94956i	−0.615077	−	0.355115i
$786$	−58.2143	+	15.5784i	−2.07644	+	0.555664i
$787$	1.44425	−	0.833837i	0.0514819	−	0.0297231i	−0.474038	−	0.880504i	$-0.657204\pi$
$787$	1.44425	−	0.833837i	0.0514819	−	0.0297231i	0.525520	+	0.850781i	$0.323871\pi$
$788$	32.4221	−	18.7189i	1.15499	−	0.666833i
$789$	32.7562	+	8.78827i	1.16615	+	0.312871i
$790$	−10.9146	+	18.9046i	−0.388323	+	0.672594i
$791$		−	7.25263i		−	0.257874i
$792$	−0.0330864	+	51.5097i	−0.00117567	+	1.83032i
$793$	19.7537	−	49.6812i	0.701473	−	1.76423i
$794$	−10.9018	+	18.8825i	−0.386891	+	0.670114i
$795$	0.0288601	+	0.0288786i	0.00102356	+	0.00102422i
$796$	−26.0672	−	45.1498i	−0.923929	−	1.60029i
$797$	−21.5369	−	37.3029i	−0.762875	−	1.32134i	−0.941363	−	0.337396i	$-0.890454\pi$
$797$	−21.5369	−	37.3029i	−0.762875	−	1.32134i	0.178488	−	0.983942i	$-0.442879\pi$
$798$	−15.2816	−	15.2914i	−0.540962	−	0.541309i
$799$	−7.01548	−	4.05039i	−0.248190	−	0.143293i
$800$			4.07701i			0.144144i
$801$	−24.3325	−	42.2076i	−0.859745	−	1.49133i
$802$	45.2492			1.59781
$803$	0.224855	−	0.389459i	0.00793494	−	0.0137437i
$804$	22.1715	−	82.6391i	0.781929	−	2.91446i
$805$	−2.41906	−	4.18993i	−0.0852605	−	0.147676i
$806$	−34.5913	+	5.05669i	−1.21843	+	0.178114i
$807$	−11.0846	−	41.4214i	−0.390196	−	1.45810i
$808$	14.1922	+	8.19386i	0.499279	+	0.288259i
$809$	27.6262			0.971286			0.485643	−	0.874157i	$-0.338586\pi$
$809$	27.6262			0.971286			0.485643	+	0.874157i	$0.338586\pi$
$810$	−10.5808	+	18.2723i	−0.371772	+	0.642022i
$811$		−	13.4600i		−	0.472644i	−0.971675	−	0.236322i	$-0.924058\pi$
$811$		−	13.4600i		−	0.472644i	0.971675	−	0.236322i	$-0.0759420\pi$
$812$	75.2561	+	43.4491i	2.64097	+	1.52477i
$813$	−5.36017	+	1.43441i	−0.187989	+	0.0503069i
$814$	49.2204	−	28.4174i	1.72518	−	0.996031i
$815$	−3.28965	−	5.69783i	−0.115231	−	0.199586i
$816$	−7.49177	−	2.00999i	−0.262265	−	0.0703638i
$817$	−7.58161	−	4.37724i	−0.265247	−	0.153140i
$818$	−66.5958			−2.32847
$819$	−32.2303	+	4.69041i	−1.12622	+	0.163896i
$820$	−5.90866			−0.206339
$821$	6.69766	+	3.86690i	0.233750	+	0.134956i	0.612301	−	0.790625i	$-0.290244\pi$
$821$	6.69766	+	3.86690i	0.233750	+	0.134956i	−0.378551	+	0.925581i	$0.623577\pi$
$822$	23.5586	−	23.5435i	0.821702	−	0.821174i
$823$	−7.20646	−	12.4820i	−0.251201	−	0.435093i	0.712656	−	0.701514i	$-0.247492\pi$
$823$	−7.20646	−	12.4820i	−0.251201	−	0.435093i	−0.963857	+	0.266421i	$0.914159\pi$
$824$	29.5145	−	17.0402i	1.02819	−	0.593624i
$825$	5.95754	+	5.96137i	0.207415	+	0.207548i
$826$	85.4449	+	49.3317i	2.97301	+	1.71647i
$827$			10.1684i			0.353589i	0.984248	+	0.176795i	$0.0565729\pi$
$827$			10.1684i			0.353589i	−0.984248	+	0.176795i	$0.943427\pi$
$828$	0.0108494	−	16.8906i	0.000377043	−	0.586990i
$829$	−2.99485			−0.104015			−0.0520076	−	0.998647i	$-0.516562\pi$
$829$	−2.99485			−0.104015			−0.0520076	+	0.998647i	$0.516562\pi$
$830$	9.55237	+	5.51506i	0.331568	+	0.191431i
$831$	−0.665052	−	0.178429i	−0.0230704	−	0.00618964i
$832$	−43.1884	+	6.31344i	−1.49729	+	0.218879i
$833$	3.64281	+	6.30953i	0.126216	+	0.218612i
$834$	−30.5416	+	8.17308i	−1.05757	+	0.283011i
$835$	3.58110	−	6.20266i	0.123929	−	0.214652i
$836$	−30.1252			−1.04190
$837$	20.7376	+	5.57805i	0.716797	+	0.192806i
$838$		−	83.3363i		−	2.87880i
$839$	−40.0412	−	23.1178i	−1.38238	−	0.798116i	−0.389936	−	0.920842i	$-0.627503\pi$
$839$	−40.0412	−	23.1178i	−1.38238	−	0.798116i	−0.992441	+	0.122726i	$0.960836\pi$
$840$	−17.7775	+	4.75736i	−0.613383	+	0.164144i
$841$	−19.4159	−	33.6293i	−0.669514	−	1.15963i
$842$	−6.02753	−	10.4400i	−0.207723	−	0.359786i
$843$	1.94678	−	7.25615i	0.0670505	−	0.249915i
$844$	23.1864	−	40.1600i	0.798109	−	1.38236i
$845$	8.92660	−	9.45071i	0.307084	−	0.325114i
$846$	−14.0009	−	8.09540i	−0.481360	−	0.278325i
$847$		−	38.1708i		−	1.31156i
$848$	−0.0149718	+	0.0259319i	−0.000514134	+	0.000890506i
$849$	1.54120	−	1.54021i	0.0528937	−	0.0528598i
$850$	−7.16270	+	4.13539i	−0.245679	+	0.141843i
$851$	−6.92781	+	3.99977i	−0.237482	+	0.137110i
$852$	−44.9914	−	45.0203i	−1.54138	−	1.54237i
$853$	19.2796	+	11.1311i	0.660120	+	0.381121i	0.792323	−	0.610102i	$-0.208872\pi$
$853$	19.2796	+	11.1311i	0.660120	+	0.381121i	−0.132203	+	0.991223i	$0.542205\pi$
$854$	−104.751			−3.58449
$855$	−4.58868	−	2.65321i	−0.156930	−	0.0907379i
$856$			2.21448i			0.0756894i
$857$	−2.14476	+	3.71483i	−0.0732635	+	0.126896i	−0.900330	−	0.435208i	$-0.856675\pi$
$857$	−2.14476	+	3.71483i	−0.0732635	+	0.126896i	0.827066	+	0.562104i	$0.190008\pi$
$858$	−42.6069	+	57.1583i	−1.45458	+	1.95135i
$859$	−9.97833	−	17.2830i	−0.340456	−	0.589688i	0.644061	−	0.764974i	$-0.277248\pi$
$859$	−9.97833	−	17.2830i	−0.340456	−	0.589688i	−0.984517	+	0.175286i	$0.943915\pi$
$860$	−15.0361	+	8.68110i	−0.512727	+	0.296023i
$861$	2.27340	+	8.49536i	0.0774773	+	0.289521i
$862$	12.0374	−	20.8494i	0.409995	−	0.710132i
$863$			4.74227i			0.161429i	0.996737	+	0.0807143i	$0.0257201\pi$
$863$			4.74227i			0.161429i	−0.996737	+	0.0807143i	$0.974280\pi$
$864$	20.4576	+	5.50273i	0.695982	+	0.187207i
$865$			14.8615i			0.505307i
$866$	−49.4714	−	28.5623i	−1.68111	−	0.970588i
$867$	−2.04702	−	7.64940i	−0.0695204	−	0.259787i
$868$	21.8027	+	37.7634i	0.740032	+	1.28177i
$869$	39.2091	−	22.6374i	1.33008	−	0.767920i
$870$	32.3240	+	8.67232i	1.09589	+	0.294019i
$871$	39.8808	−	31.5149i	1.35131	−	1.06784i
$872$	−28.9084			−0.978962
$873$	−39.3716	−	0.0252897i	−1.33253	−	0.000855926i
$874$	6.66027			0.225287
$875$	−1.50554	+	2.60767i	−0.0508966	+	0.0881555i
$876$	0.396505	+	0.396759i	0.0133966	+	0.0134053i
$877$	41.2569	−	23.8197i	1.39315	−	0.804334i	0.399485	−	0.916740i	$-0.369189\pi$
$877$	41.2569	−	23.8197i	1.39315	−	0.804334i	0.993662	+	0.112406i	$0.0358556\pi$
$878$	7.45566	−	4.30453i	0.251616	−	0.145271i
$879$	5.17384	+	5.17717i	0.174509	+	0.174621i
$880$	−3.09061	+	5.35310i	−0.104184	+	0.180453i
$881$	−42.8991			−1.44531			−0.722653	−	0.691211i	$-0.757078\pi$
$881$	−42.8991			−1.44531			−0.722653	+	0.691211i	$0.757078\pi$
$882$	7.26459	+	12.6013i	0.244611	+	0.424309i
$883$	36.0410			1.21288			0.606439	−	0.795130i	$-0.292598\pi$
$883$	36.0410			1.21288			0.606439	+	0.795130i	$0.292598\pi$
$884$	−27.6150	−	34.9456i	−0.928795	−	1.17535i
$885$	23.3646	+	6.26857i	0.785392	+	0.210716i
$886$	20.2942	−	11.7169i	0.681797	−	0.393636i
$887$	−7.80410	−	13.5171i	−0.262036	−	0.453860i	0.704747	−	0.709459i	$-0.251061\pi$
$887$	−7.80410	−	13.5171i	−0.262036	−	0.453860i	−0.966783	+	0.255599i	$0.917727\pi$
$888$	7.86602	+	29.3941i	0.263966	+	0.986403i
$889$	−0.271359	−	0.156669i	−0.00910110	−	0.00525452i
$890$		−	38.0995i		−	1.27710i
$891$	37.9539	−	21.8477i	1.27150	−	0.731926i
$892$			59.5845i			1.99504i
$893$	2.02997	−	3.51601i	0.0679304	−	0.117659i
$894$	−15.4568	−	57.7596i	−0.516951	−	1.93177i
$895$	19.7735	−	11.4162i	0.660956	−	0.381603i
$896$	30.4821	+	52.7966i	1.01834	+	1.76381i
$897$	5.99695	−	8.04506i	0.200232	−	0.268617i
$898$	−16.2603	+	28.1637i	−0.542613	+	0.939834i
$899$		−	34.0379i		−	1.13523i
$900$	−9.10719	+	5.25024i	−0.303573	+	0.175008i
$901$	0.0830990			0.00276843
$902$	16.6706	+	9.62477i	0.555070	+	0.320470i
$903$	18.2668	+	18.2785i	0.607881	+	0.608271i
$904$	7.36055	−	4.24962i	0.244808	−	0.141340i
$905$	13.2484	−	7.64897i	0.440392	−	0.254260i
$906$	−47.2511	+	47.2208i	−1.56981	+	1.56881i
$907$	−2.27286	+	3.93671i	−0.0754691	+	0.130716i	−0.901290	−	0.433216i	$-0.857379\pi$
$907$	−2.27286	+	3.93671i	−0.0754691	+	0.130716i	0.825821	+	0.563932i	$0.190712\pi$
$908$			3.75556i			0.124633i
$909$	0.00894937	−	13.9326i	0.000296832	−	0.462116i
$910$	−23.6682	−	9.41066i	−0.784592	−	0.311960i
$911$	−4.90140	+	8.48947i	−0.162391	+	0.281269i	−0.935726	−	0.352729i	$-0.885254\pi$
$911$	−4.90140	+	8.48947i	−0.162391	+	0.281269i	0.773335	+	0.633998i	$0.218587\pi$
$912$	1.00737	−	3.75472i	0.0333573	−	0.124331i
$913$	−11.4385	−	19.8121i	−0.378560	−	0.655685i
$914$	40.0562	+	69.3793i	1.32494	+	2.29486i
$915$	−24.8104	+	6.63938i	−0.820206	+	0.219491i
$916$	−10.1869	−	5.88141i	−0.336585	−	0.194327i
$917$			44.6549i			1.47463i
$918$	11.0831	+	41.5225i	0.365795	+	1.37045i
$919$	12.1859			0.401976			0.200988	−	0.979594i	$-0.435585\pi$
$919$	12.1859			0.401976			0.200988	+	0.979594i	$0.435585\pi$
$920$	2.83485	−	4.91010i	0.0934622	−	0.161881i
$921$	20.0102	−	5.35483i	0.659359	−	0.176448i
$922$	36.9311	+	63.9666i	1.21626	+	2.10663i
$923$	−5.46929	−	37.4138i	−0.180024	−	1.23149i
$924$	85.8861	+	23.0427i	2.82544	+	0.758048i
$925$	4.31164	+	2.48933i	0.141766	+	0.0818486i
$926$	32.1271			1.05576
$927$	−25.0835	−	14.5035i	−0.823851	−	0.476356i
$928$		−	33.5783i		−	1.10226i
$929$	23.9448	+	13.8245i	0.785604	+	0.453569i	0.838413	−	0.545036i	$-0.183484\pi$
$929$	23.9448	+	13.8245i	0.785604	+	0.453569i	−0.0528086	+	0.998605i	$0.516817\pi$
$930$	11.8712	+	11.8788i	0.389271	+	0.389521i
$931$	−3.16220	+	1.82570i	−0.103637	+	0.0598349i
$932$	19.5331	+	33.8324i	0.639829	+	1.10822i
$933$	18.8524	−	18.8403i	0.617201	−	0.616805i
$934$	−4.83877	−	2.79367i	−0.158329	−	0.0914115i
$935$	17.1540			0.560996
$936$	−23.6453	−	29.9616i	−0.772871	−	0.979327i
$937$	−0.645852			−0.0210991			−0.0105495	−	0.999944i	$-0.503358\pi$
$937$	−0.645852			−0.0210991			−0.0105495	+	0.999944i	$0.503358\pi$
$938$	−86.2466	−	49.7945i	−2.81605	−	1.62585i
$939$	−52.2552	−	14.0197i	−1.70529	−	0.457517i
$940$	−4.02591	−	6.97308i	−0.131311	−	0.227437i
$941$	−6.73759	+	3.88995i	−0.219639	+	0.126809i	−0.605783	−	0.795630i	$-0.707140\pi$
$941$	−6.73759	+	3.88995i	−0.219639	+	0.126809i	0.386144	+	0.922438i	$0.373807\pi$
$942$	−78.1119	+	20.9031i	−2.54502	+	0.681061i
$943$	−2.34639	−	1.35469i	−0.0764091	−	0.0441148i
$944$			17.7421i			0.577455i
$945$	11.0528	+	11.0741i	0.359546	+	0.360240i
$946$	56.5635			1.83904
$947$	−16.6191	−	9.59505i	−0.540049	−	0.311797i	0.205050	−	0.978751i	$-0.434264\pi$
$947$	−16.6191	−	9.59505i	−0.540049	−	0.311797i	−0.745099	+	0.666954i	$0.767598\pi$
$948$	14.5983	+	54.5517i	0.474131	+	1.77176i
$949$	0.0482003	+	0.329724i	0.00156465	+	0.0107033i
$950$	−2.07257	−	3.58980i	−0.0672430	−	0.116468i
$951$	−3.60068	+	13.4207i	−0.116760	+	0.435195i
$952$	−18.7286	+	32.4388i	−0.606996	+	1.05135i
$953$	−30.1995			−0.978257			−0.489128	−	0.872212i	$-0.662685\pi$
$953$	−30.1995			−0.978257			−0.489128	+	0.872212i	$0.662685\pi$
$954$	0.165903		0.000106565i	0.00537130		3.45016e-6i
$955$		−	10.1940i		−	0.329871i
$956$	54.2054	+	31.2955i	1.75313	+	1.01217i
$957$	−49.0664	−	49.0979i	−1.58609	−	1.58711i
$958$	21.4043	+	37.0734i	0.691542	+	1.19779i
$959$	−12.3400	−	21.3736i	−0.398480	−	0.690188i
$960$	14.8215	+	14.8310i	0.478362	+	0.478670i
$961$	−6.95993	+	12.0550i	−0.224514	+	0.388869i
$962$	−15.5600	+	39.1340i	−0.501674	+	1.26173i
$963$	1.63109	−	0.940314i	0.0525611	−	0.0303012i
$964$			26.3305i			0.848050i
$965$	9.28971	−	16.0902i	0.299046	−	0.517963i
$966$	−18.9882	−	5.09442i	−0.610936	−	0.163910i
$967$	−11.6501	+	6.72617i	−0.374641	+	0.216299i	−0.675484	−	0.737375i	$-0.736065\pi$
$967$	−11.6501	+	6.72617i	−0.374641	+	0.216299i	0.300843	+	0.953674i	$0.402732\pi$
$968$	38.7388	−	22.3659i	1.24511	−	0.718866i
$969$	−10.4218	+	2.78893i	−0.334797	+	0.0895934i
$970$	−26.6646	−	15.3948i	−0.856147	−	0.494297i
$971$	28.6086			0.918094			0.459047	−	0.888412i	$-0.348191\pi$
$971$	28.6086			0.918094			0.459047	+	0.888412i	$0.348191\pi$
$972$	14.0527	+	52.7843i	0.450741	+	1.69306i
$973$			23.4278i			0.751060i
$974$	−1.17997	+	2.04376i	−0.0378085	+	0.0654863i
$975$	−6.20233	−	0.728781i	−0.198633	−	0.0233397i
$976$	−9.41835	−	16.3131i	−0.301474	−	0.522168i
$977$	−7.14287	+	4.12394i	−0.228521	+	0.131936i	−0.609889	−	0.792487i	$-0.708786\pi$
$977$	−7.14287	+	4.12394i	−0.228521	+	0.131936i	0.381369	+	0.924423i	$0.375453\pi$
$978$	−25.8219	−	6.92784i	−0.825692	−	0.221528i
$979$	−39.5102	+	68.4337i	−1.26275	+	2.18715i
$980$			7.24158i			0.231324i
$981$	12.2751	+	21.2927i	0.391914	+	0.679822i
$982$		−	68.9956i		−	2.20174i
$983$	1.32806	+	0.766756i	0.0423586	+	0.0244557i	0.521030	−	0.853539i	$-0.325548\pi$
$983$	1.32806	+	0.766756i	0.0423586	+	0.0244557i	−0.478671	+	0.877994i	$0.658881\pi$
$984$	−7.28970	+	7.28502i	−0.232387	+	0.232238i
$985$	−5.34206	−	9.25272i	−0.170212	−	0.294816i
$986$	58.9920	−	34.0591i	1.87869	−	1.08466i
$987$	−8.47677	+	8.47133i	−0.269819	+	0.269645i
$988$	17.5140	−	13.8401i	0.557196	−	0.440312i
$989$	−7.96134			−0.253156
$990$	34.2471	+	0.0219980i	1.08844	+	0.000699143i
$991$	36.0620			1.14555			0.572773	−	0.819714i	$-0.305868\pi$
$991$	36.0620			1.14555			0.572773	+	0.819714i	$0.305868\pi$
$992$	8.42476	−	14.5921i	0.267486	−	0.463300i
$993$	−0.817354	+	3.04649i	−0.0259379	+	0.0966775i
$994$	−64.1573	+	37.0413i	−2.03495	+	1.17488i
$995$	−12.8850	+	7.43915i	−0.408482	+	0.235837i
$996$	27.5646	−	7.37644i	0.873419	−	0.233731i
$997$	−8.40749	+	14.5622i	−0.266268	+	0.461189i	−0.967895	−	0.251355i	$-0.919124\pi$
$997$	−8.40749	+	14.5622i	−0.266268	+	0.461189i	0.701627	+	0.712544i	$0.252457\pi$
$998$	28.9438			0.916201
$999$	18.3104	−	18.2751i	0.579314	−	0.578199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.6	✓	108
9.4	even	3	inner	585.2.bt.b.571.49	yes	108
13.12	even	2	inner	585.2.bt.b.376.49	yes	108
117.103	even	6	inner	585.2.bt.b.571.6	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.6	✓	108	1.1	even	1	trivial
585.2.bt.b.376.49	yes	108	13.12	even	2	inner
585.2.bt.b.571.6	yes	108	117.103	even	6	inner
585.2.bt.b.571.49	yes	108	9.4	even	3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03176 - 1.17304i) q^{2} +(0.447750 + 1.67318i) q^{3} +(1.75203 + 3.03461i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.05298 - 3.92472i) q^{6} +(-2.60767 - 1.50554i) q^{7} -3.52864i q^{8} +(-2.59904 + 1.49833i) q^{9} +O(q^{10})\)	\(q+(-2.03176 - 1.17304i) q^{2} +(0.447750 + 1.67318i) q^{3} +(1.75203 + 3.03461i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.05298 - 3.92472i) q^{6} +(-2.60767 - 1.50554i) q^{7} -3.52864i q^{8} +(-2.59904 + 1.49833i) q^{9} -2.34607 q^{10} +(4.21397 + 2.43294i) q^{11} +(-4.29296 + 4.29020i) q^{12} +(-3.56763 + 0.521530i) q^{13} +(3.53211 + 6.11780i) q^{14} +(1.22435 + 1.22514i) q^{15} +(-0.635160 + 1.10013i) q^{16} +3.52537 q^{17} +(7.03822 + 0.00452088i) q^{18} +1.76684i q^{19} +(3.03461 + 1.75203i) q^{20} +(1.35145 - 5.03721i) q^{21} +(-5.70785 - 9.88629i) q^{22} +(0.803384 + 1.39150i) q^{23} +(5.90403 - 1.57995i) q^{24} +(0.500000 - 0.866025i) q^{25} +(7.86035 + 3.12534i) q^{26} +(-3.67069 - 3.67777i) q^{27} -10.5510i q^{28} +(-4.11800 + 7.13259i) q^{29} +(-1.05046 - 3.92539i) q^{30} +(-3.57912 + 2.06641i) q^{31} +(-3.53079 + 2.03850i) q^{32} +(-2.18393 + 8.14007i) q^{33} +(-7.16270 - 4.13539i) q^{34} -3.01108 q^{35} +(-9.10044 - 5.26194i) q^{36} +4.97866i q^{37} +(2.07257 - 3.58980i) q^{38} +(-2.47002 - 5.73576i) q^{39} +(-1.76432 - 3.05589i) q^{40} +(-1.46032 + 0.843116i) q^{41} +(-8.65465 + 8.64909i) q^{42} +(-2.47744 + 4.29105i) q^{43} +17.0503i q^{44} +(-1.50167 + 2.59711i) q^{45} -3.76959i q^{46} +(-1.99000 - 1.14893i) q^{47} +(-2.12510 - 0.570152i) q^{48} +(1.03331 + 1.78975i) q^{49} +(-2.03176 + 1.17304i) q^{50} +(1.57848 + 5.89856i) q^{51} +(-7.83324 - 9.91262i) q^{52} +0.0235717 q^{53} +(3.14380 + 11.7782i) q^{54} +4.86588 q^{55} +(-5.31251 + 9.20154i) q^{56} +(-2.95624 + 0.791104i) q^{57} +(16.7336 - 9.66114i) q^{58} +(12.0954 - 6.98331i) q^{59} +(-1.57271 + 5.86190i) q^{60} +(-7.41416 + 12.8417i) q^{61} +9.69588 q^{62} +(9.03325 + 0.00580235i) q^{63} +12.1056 q^{64} +(-2.82890 + 2.23547i) q^{65} +(13.9858 - 13.9768i) q^{66} +(-12.2089 + 7.04883i) q^{67} +(6.17655 + 10.6981i) q^{68} +(-1.96851 + 1.96725i) q^{69} +(6.11780 + 3.53211i) q^{70} +10.4870i q^{71} +(5.28707 + 9.17107i) q^{72} -0.0924209i q^{73} +(5.84015 - 10.1154i) q^{74} +(1.67289 + 0.448825i) q^{75} +(-5.36167 + 3.09556i) q^{76} +(-7.32578 - 12.6886i) q^{77} +(-1.70977 + 14.5511i) q^{78} +(4.65227 - 8.05796i) q^{79} +1.27032i q^{80} +(4.51001 - 7.78844i) q^{81} +3.95603 q^{82} +(-4.07164 - 2.35076i) q^{83} +(17.6537 - 4.72422i) q^{84} +(3.05306 - 1.76268i) q^{85} +(10.0671 - 5.81226i) q^{86} +(-13.7779 - 3.69653i) q^{87} +(8.58496 - 14.8696i) q^{88} +16.2397i q^{89} +(6.09754 - 3.51519i) q^{90} +(10.0884 + 4.01124i) q^{91} +(-2.81511 + 4.87591i) q^{92} +(-5.06002 - 5.06327i) q^{93} +(2.69547 + 4.66869i) q^{94} +(0.883421 + 1.53013i) q^{95} +(-4.99169 - 4.99490i) q^{96} +(11.3656 + 6.56194i) q^{97} -4.84845i q^{98} +(-14.5976 - 0.00937653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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