LMFDB - Embedded newform 585.2.i.e.196.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.2
Root			$-0.628312 + 0.590424i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.e.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12831 + 1.95429i) q^{2} +(-0.604199 - 1.62325i) q^{3} +(-1.54617 - 2.67805i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.85403 + 0.650751i) q^{6} +(-0.353285 + 0.611908i) q^{7} +2.46502 q^{8} +(-2.26989 + 1.96153i) q^{9} +O(q^{10})$	\(q+(-1.12831 + 1.95429i) q^{2} +(-0.604199 - 1.62325i) q^{3} +(-1.54617 - 2.67805i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.85403 + 0.650751i) q^{6} +(-0.353285 + 0.611908i) q^{7} +2.46502 q^{8} +(-2.26989 + 1.96153i) q^{9} -2.25662 q^{10} +(1.16510 - 2.01802i) q^{11} +(-3.41295 + 4.12791i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.797232 - 1.38085i) q^{14} +(1.10368 - 1.33488i) q^{15} +(0.311036 - 0.538731i) q^{16} +6.04736 q^{17} +(-1.27227 - 6.64925i) q^{18} -7.91884 q^{19} +(1.54617 - 2.67805i) q^{20} +(1.20674 + 0.203756i) q^{21} +(2.62920 + 4.55391i) q^{22} +(4.47799 + 7.75611i) q^{23} +(-1.48936 - 4.00135i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.25662 q^{26} +(4.55552 + 2.49944i) q^{27} +2.18496 q^{28} +(1.20340 - 2.08435i) q^{29} +(1.36345 + 3.66307i) q^{30} +(1.53216 + 2.65378i) q^{31} +(3.16691 + 5.48526i) q^{32} +(-3.97971 - 0.671971i) q^{33} +(-6.82331 + 11.8183i) q^{34} -0.706571 q^{35} +(8.76273 + 3.04600i) q^{36} -2.38079 q^{37} +(8.93492 - 15.4757i) q^{38} +(1.10368 - 1.33488i) q^{39} +(1.23251 + 2.13477i) q^{40} +(4.72945 + 8.19164i) q^{41} +(-1.75977 + 2.12841i) q^{42} +(-5.96795 + 10.3368i) q^{43} -7.20582 q^{44} +(-2.83368 - 0.985013i) q^{45} -20.2103 q^{46} +(-4.86433 + 8.42527i) q^{47} +(-1.06242 - 0.179389i) q^{48} +(3.25038 + 5.62982i) q^{49} +(-1.12831 - 1.95429i) q^{50} +(-3.65381 - 9.81639i) q^{51} +(1.54617 - 2.67805i) q^{52} +5.90968 q^{53} +(-10.0247 + 6.08269i) q^{54} +2.33021 q^{55} +(-0.870856 + 1.50837i) q^{56} +(4.78456 + 12.8543i) q^{57} +(2.71562 + 4.70359i) q^{58} +(-1.48719 - 2.57588i) q^{59} +(-5.28135 - 0.891752i) q^{60} +(4.62078 - 8.00343i) q^{61} -6.91501 q^{62} +(-0.398361 - 2.08194i) q^{63} -13.0489 q^{64} +(-0.500000 + 0.866025i) q^{65} +(5.80358 - 7.01933i) q^{66} +(0.847241 + 1.46746i) q^{67} +(-9.35028 - 16.1952i) q^{68} +(9.88452 - 11.9551i) q^{69} +(0.797232 - 1.38085i) q^{70} -12.4439 q^{71} +(-5.59532 + 4.83522i) q^{72} +4.88899 q^{73} +(2.68628 - 4.65277i) q^{74} +(1.70788 + 0.288374i) q^{75} +(12.2439 + 21.2071i) q^{76} +(0.823229 + 1.42587i) q^{77} +(1.36345 + 3.66307i) q^{78} +(5.51270 - 9.54827i) q^{79} +0.622073 q^{80} +(1.30477 - 8.90492i) q^{81} -21.3452 q^{82} +(0.260845 - 0.451797i) q^{83} +(-1.32015 - 3.54674i) q^{84} +(3.02368 + 5.23717i) q^{85} +(-13.4674 - 23.3262i) q^{86} +(-4.11051 - 0.694057i) q^{87} +(2.87201 - 4.97447i) q^{88} +10.7608 q^{89} +(5.12228 - 4.42644i) q^{90} -0.706571 q^{91} +(13.8475 - 23.9846i) q^{92} +(3.38201 - 4.09049i) q^{93} +(-10.9770 - 19.0127i) q^{94} +(-3.95942 - 6.85792i) q^{95} +(6.99050 - 8.45488i) q^{96} +(1.48153 - 2.56609i) q^{97} -14.6698 q^{98} +(1.31376 + 6.86607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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 $

$2$	−1.12831	+	1.95429i	−0.797837	+	1.38189i	0.123185	+	0.992384i	$0.460689\pi$
$2$	−1.12831	+	1.95429i	−0.797837	+	1.38189i	−0.921022	+	0.389510i	$0.872644\pi$
$3$	−0.604199	−	1.62325i	−0.348835	−	0.937184i
$3$	−0.604199	−	1.62325i	−0.348835	−	0.937184i
$4$	−1.54617	−	2.67805i	−0.773087	−	1.33903i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	3.85403	+	0.650751i	1.57340	+	0.265668i
$7$	−0.353285	+	0.611908i	−0.133529	+	0.231280i	−0.925035	−	0.379883i	$-0.875964\pi$
$7$	−0.353285	+	0.611908i	−0.133529	+	0.231280i	0.791505	+	0.611162i	$0.209298\pi$
$8$	2.46502			0.871517
$9$	−2.26989	+	1.96153i	−0.756629	+	0.653845i
$10$	−2.25662			−0.713607
$11$	1.16510	−	2.01802i	0.351292	−	0.608456i	−0.635184	−	0.772361i	$-0.719076\pi$
$11$	1.16510	−	2.01802i	0.351292	−	0.608456i	0.986476	+	0.163905i	$0.0524090\pi$
$12$	−3.41295	+	4.12791i	−0.985235	+	1.19162i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−0.797232	−	1.38085i	−0.213069	−	0.369047i
$15$	1.10368	−	1.33488i	0.284968	−	0.344664i
$16$	0.311036	−	0.538731i	0.0777591	−	0.134683i
$17$	6.04736			1.46670			0.733351	−	0.679851i	$-0.237955\pi$
$17$	6.04736			1.46670			0.733351	+	0.679851i	$0.237955\pi$
$18$	−1.27227	−	6.64925i	−0.299877	−	1.56724i
$19$	−7.91884			−1.81671			−0.908353	−	0.418204i	$-0.862660\pi$
$19$	−7.91884			−1.81671			−0.908353	+	0.418204i	$0.862660\pi$
$20$	1.54617	−	2.67805i	0.345735	−	0.598831i
$21$	1.20674	+	0.203756i	0.263331	+	0.0444633i
$22$	2.62920	+	4.55391i	0.560548	+	0.970898i
$23$	4.47799	+	7.75611i	0.933726	+	1.61726i	0.776890	+	0.629637i	$0.216796\pi$
$23$	4.47799	+	7.75611i	0.933726	+	1.61726i	0.156837	+	0.987625i	$0.449870\pi$
$24$	−1.48936	−	4.00135i	−0.304015	−	0.816772i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.25662			−0.442560
$27$	4.55552	+	2.49944i	0.876711	+	0.481017i
$28$	2.18496			0.412919
$29$	1.20340	−	2.08435i	0.223465	−	0.387054i	−0.732392	−	0.680883i	$-0.761596\pi$
$29$	1.20340	−	2.08435i	0.223465	−	0.387054i	0.955858	+	0.293829i	$0.0949297\pi$
$30$	1.36345	+	3.66307i	0.248931	+	0.668781i
$31$	1.53216	+	2.65378i	0.275184	+	0.476632i	0.970181	−	0.242380i	$-0.0779280\pi$
$31$	1.53216	+	2.65378i	0.275184	+	0.476632i	−0.694998	+	0.719012i	$0.744595\pi$
$32$	3.16691	+	5.48526i	0.559837	+	0.969665i
$33$	−3.97971	−	0.671971i	−0.692779	−	0.116975i
$34$	−6.82331	+	11.8183i	−1.17019	+	2.02683i
$35$	−0.706571			−0.119432
$36$	8.76273	+	3.04600i	1.46046	+	0.507667i
$37$	−2.38079			−0.391400			−0.195700	−	0.980664i	$-0.562698\pi$
$37$	−2.38079			−0.391400			−0.195700	+	0.980664i	$0.562698\pi$
$38$	8.93492	−	15.4757i	1.44944	−	2.51050i
$39$	1.10368	−	1.33488i	0.176730	−	0.213751i
$40$	1.23251	+	2.13477i	0.194877	+	0.337537i
$41$	4.72945	+	8.19164i	0.738616	+	1.27932i	0.953119	+	0.302596i	$0.0978534\pi$
$41$	4.72945	+	8.19164i	0.738616	+	1.27932i	−0.214503	+	0.976723i	$0.568813\pi$
$42$	−1.75977	+	2.12841i	−0.271539	+	0.328421i
$43$	−5.96795	+	10.3368i	−0.910103	+	1.57635i	−0.0961869	+	0.995363i	$0.530665\pi$
$43$	−5.96795	+	10.3368i	−0.910103	+	1.57635i	−0.813916	+	0.580982i	$0.802669\pi$
$44$	−7.20582			−1.08632
$45$	−2.83368	−	0.985013i	−0.422420	−	0.146837i
$46$	−20.2103			−2.97985
$47$	−4.86433	+	8.42527i	−0.709536	+	1.22895i	0.255493	+	0.966811i	$0.417762\pi$
$47$	−4.86433	+	8.42527i	−0.709536	+	1.22895i	−0.965029	+	0.262142i	$0.915571\pi$
$48$	−1.06242	−	0.179389i	−0.153348	−	0.0258926i
$49$	3.25038	+	5.62982i	0.464340	+	0.804260i
$50$	−1.12831	−	1.95429i	−0.159567	−	0.276379i
$51$	−3.65381	−	9.81639i	−0.511636	−	1.37457i
$52$	1.54617	−	2.67805i	0.214416	−	0.371379i
$53$	5.90968			0.811756			0.405878	−	0.913927i	$-0.366966\pi$
$53$	5.90968			0.811756			0.405878	+	0.913927i	$0.366966\pi$
$54$	−10.0247	+	6.08269i	−1.36419	+	0.827749i
$55$	2.33021			0.314205
$56$	−0.870856	+	1.50837i	−0.116373	+	0.201564i
$57$	4.78456	+	12.8543i	0.633730	+	1.70259i
$58$	2.71562	+	4.70359i	0.356578	+	0.617611i
$59$	−1.48719	−	2.57588i	−0.193615	−	0.335351i	0.752831	−	0.658214i	$-0.228688\pi$
$59$	−1.48719	−	2.57588i	−0.193615	−	0.335351i	−0.946446	+	0.322863i	$0.895355\pi$
$60$	−5.28135	−	0.891752i	−0.681819	−	0.115125i
$61$	4.62078	−	8.00343i	0.591630	−	1.02473i	−0.402383	−	0.915472i	$-0.631818\pi$
$61$	4.62078	−	8.00343i	0.591630	−	1.02473i	0.994013	−	0.109262i	$-0.0348488\pi$
$62$	−6.91501			−0.878207
$63$	−0.398361	−	2.08194i	−0.0501887	−	0.262300i
$64$	−13.0489			−1.63111
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	5.80358	−	7.01933i	0.714371	−	0.864019i
$67$	0.847241	+	1.46746i	0.103507	+	0.179279i	0.913127	−	0.407675i	$-0.133660\pi$
$67$	0.847241	+	1.46746i	0.103507	+	0.179279i	−0.809620	+	0.586954i	$0.800327\pi$
$68$	−9.35028	−	16.1952i	−1.13389	−	1.96395i
$69$	9.88452	−	11.9551i	1.18996	−	1.43923i
$70$	0.797232	−	1.38085i	0.0952875	−	0.165043i
$71$	−12.4439			−1.47682			−0.738410	−	0.674352i	$-0.764423\pi$
$71$	−12.4439			−1.47682			−0.738410	+	0.674352i	$0.764423\pi$
$72$	−5.59532	+	4.83522i	−0.659415	+	0.569837i
$73$	4.88899			0.572213			0.286106	−	0.958198i	$-0.407639\pi$
$73$	4.88899			0.572213			0.286106	+	0.958198i	$0.407639\pi$
$74$	2.68628	−	4.65277i	0.312273	−	0.540873i
$75$	1.70788	+	0.288374i	0.197209	+	0.0332985i
$76$	12.2439	+	21.2071i	1.40447	+	2.43262i
$77$	0.823229	+	1.42587i	0.0938157	+	0.162493i
$78$	1.36345	+	3.66307i	0.154380	+	0.414761i
$79$	5.51270	−	9.54827i	0.620227	−	1.07426i	−0.369217	−	0.929343i	$-0.620374\pi$
$79$	5.51270	−	9.54827i	0.620227	−	1.07426i	0.989443	−	0.144921i	$-0.0462927\pi$
$80$	0.622073			0.0695499
$81$	1.30477	−	8.90492i	0.144975	−	0.989435i
$82$	−21.3452			−2.35718
$83$	0.260845	−	0.451797i	0.0286315	−	0.0495912i	−0.851355	−	0.524591i	$-0.824218\pi$
$83$	0.260845	−	0.451797i	0.0286315	−	0.0495912i	0.879986	+	0.474999i	$0.157552\pi$
$84$	−1.32015	−	3.54674i	−0.144041	−	0.386982i
$85$	3.02368	+	5.23717i	0.327964	+	0.568051i
$86$	−13.4674	−	23.3262i	−1.45223	−	2.51533i
$87$	−4.11051	−	0.694057i	−0.440693	−	0.0744107i
$88$	2.87201	−	4.97447i	0.306157	−	0.530280i
$89$	10.7608			1.14065			0.570323	−	0.821420i	$-0.306818\pi$
$89$	10.7608			1.14065			0.570323	+	0.821420i	$0.306818\pi$
$90$	5.12228	−	4.42644i	0.539936	−	0.466588i
$91$	−0.706571			−0.0740687
$92$	13.8475	−	23.9846i	1.44370	−	2.50057i
$93$	3.38201	−	4.09049i	0.350699	−	0.424164i
$94$	−10.9770	−	19.0127i	−1.13219	−	1.96101i
$95$	−3.95942	−	6.85792i	−0.406228	−	0.703607i
$96$	6.99050	−	8.45488i	0.713465	−	0.862923i
$97$	1.48153	−	2.56609i	0.150427	−	0.260547i	−0.780958	−	0.624584i	$-0.785269\pi$
$97$	1.48153	−	2.56609i	0.150427	−	0.260547i	0.931384	+	0.364037i	$0.118602\pi$
$98$	−14.6698			−1.48187
$99$	1.31376	+	6.86607i	0.132038	+	0.690066i
$100$	3.09235			0.309235
$101$	−6.83573	+	11.8398i	−0.680181	+	1.17811i	0.294745	+	0.955576i	$0.404765\pi$
$101$	−6.83573	+	11.8398i	−0.680181	+	1.17811i	−0.974925	+	0.222532i	$0.928568\pi$
$102$	23.3067	+	3.93533i	2.30771	+	0.389655i
$103$	3.56535	+	6.17537i	0.351305	+	0.608478i	0.986478	−	0.163892i	$-0.0524048\pi$
$103$	3.56535	+	6.17537i	0.351305	+	0.608478i	−0.635174	+	0.772369i	$0.719071\pi$
$104$	1.23251	+	2.13477i	0.120858	+	0.209332i
$105$	0.426909	+	1.14694i	0.0416621	+	0.111930i
$106$	−6.66796	+	11.5492i	−0.647649	+	1.12176i
$107$	−1.70776			−0.165095			−0.0825477	−	0.996587i	$-0.526306\pi$
$107$	−1.70776			−0.165095			−0.0825477	+	0.996587i	$0.526306\pi$
$108$	−0.350008	−	16.0645i	−0.0336796	−	1.54581i
$109$	−3.23628			−0.309979			−0.154989	−	0.987916i	$-0.549534\pi$
$109$	−3.23628			−0.309979			−0.154989	+	0.987916i	$0.549534\pi$
$110$	−2.62920	+	4.55391i	−0.250685	+	0.434199i
$111$	1.43847	+	3.86462i	0.136534	+	0.366814i
$112$	0.219769	+	0.380652i	0.0207662	+	0.0359682i
$113$	0.339220	+	0.587547i	0.0319112	+	0.0552717i	0.881540	−	0.472109i	$-0.156507\pi$
$113$	0.339220	+	0.587547i	0.0319112	+	0.0552717i	−0.849629	+	0.527381i	$0.823174\pi$
$114$	−30.5195	−	5.15319i	−2.85841	−	0.482641i
$115$	−4.47799	+	7.75611i	−0.417575	+	0.723261i
$116$	−7.44266			−0.691033
$117$	−2.83368	−	0.985013i	−0.261974	−	0.0910645i
$118$	6.71204			0.617893
$119$	−2.13645	+	3.70043i	−0.195848	+	0.339218i
$120$	2.72059	−	3.29050i	0.248355	−	0.300380i
$121$	2.78506	+	4.82387i	0.253187	+	0.438533i
$122$	10.4274	+	18.0607i	0.944049	+	1.63514i
$123$	10.4396	−	12.6265i	0.941304	−	1.13849i
$124$	4.73797	−	8.20640i	0.425482	−	0.736957i
$125$	−1.00000			−0.0894427
$126$	4.51820	+	1.57057i	0.402514	+	0.139917i
$127$	14.6889			1.30343			0.651714	−	0.758465i	$-0.274050\pi$
$127$	14.6889			1.30343			0.651714	+	0.758465i	$0.274050\pi$
$128$	8.38942	−	14.5309i	0.741527	−	1.28436i
$129$	20.3850	+	3.44200i	1.79480	+	0.303051i
$130$	−1.12831	−	1.95429i	−0.0989595	−	0.171403i
$131$	4.53194	+	7.84955i	0.395957	+	0.685818i	0.993223	−	0.116225i	$-0.0370795\pi$
$131$	4.53194	+	7.84955i	0.395957	+	0.685818i	−0.597266	+	0.802044i	$0.703746\pi$
$132$	4.35375	+	11.6969i	0.378946	+	1.01808i
$133$	2.79761	−	4.84560i	0.242584	−	0.420167i
$134$	−3.82381			−0.330327
$135$	0.113185	+	5.19492i	0.00974144	+	0.447107i
$136$	14.9069			1.27825
$137$	1.01492	−	1.75789i	0.0867104	−	0.150187i	−0.819408	−	0.573210i	$-0.805698\pi$
$137$	1.01492	−	1.75789i	0.0867104	−	0.150187i	0.906119	+	0.423023i	$0.139031\pi$
$138$	12.2110	+	32.8064i	1.03947	+	2.79266i
$139$	1.42659	+	2.47092i	0.121002	+	0.209581i	0.920163	−	0.391536i	$-0.128056\pi$
$139$	1.42659	+	2.47092i	0.121002	+	0.209581i	−0.799161	+	0.601117i	$0.794723\pi$
$140$	1.09248	+	1.89223i	0.0923316	+	0.159923i
$141$	16.6154	+	2.80549i	1.39927	+	0.236265i
$142$	14.0406	−	24.3190i	1.17826	−	2.04081i
$143$	2.33021			0.194862
$144$	0.350721	+	1.83297i	0.0292268	+	0.152747i
$145$	2.40680			0.199874
$146$	−5.51630	+	9.55452i	−0.456532	+	0.790737i
$147$	7.17474	−	8.67771i	0.591762	−	0.715726i
$148$	3.68112	+	6.37589i	0.302586	+	0.524095i
$149$	−4.49112	−	7.77885i	−0.367927	−	0.637269i	0.621314	−	0.783562i	$-0.286599\pi$
$149$	−4.49112	−	7.77885i	−0.367927	−	0.637269i	−0.989241	+	0.146293i	$0.953266\pi$
$150$	−2.49058	+	3.01232i	−0.203355	+	0.245955i
$151$	1.37741	−	2.38575i	0.112092	−	0.194150i	−0.804521	−	0.593924i	$-0.797578\pi$
$151$	1.37741	−	2.38575i	0.112092	−	0.194150i	0.916614	+	0.399774i	$0.130911\pi$
$152$	−19.5201			−1.58329
$153$	−13.7268	+	11.8621i	−1.10975	+	0.958995i
$154$	−3.71544			−0.299398
$155$	−1.53216	+	2.65378i	−0.123066	+	0.213156i
$156$	−5.28135	−	0.891752i	−0.422846	−	0.0713973i
$157$	−12.2493	−	21.2164i	−0.977601	−	1.69325i	−0.671071	−	0.741393i	$-0.734166\pi$
$157$	−12.2493	−	21.2164i	−0.977601	−	1.69325i	−0.306529	−	0.951861i	$-0.599168\pi$
$158$	12.4401	+	21.5468i	0.989679	+	1.71418i
$159$	−3.57062	−	9.59289i	−0.283169	−	0.760765i
$160$	−3.16691	+	5.48526i	−0.250367	+	0.433648i
$161$	−6.32804			−0.498719
$162$	15.9306	+	12.5974i	1.25163	+	0.989748i
$163$	−18.2489			−1.42937			−0.714684	−	0.699448i	$-0.753429\pi$
$163$	−18.2489			−1.42937			−0.714684	+	0.699448i	$0.753429\pi$
$164$	14.6251	−	25.3314i	1.14203	−	1.97805i
$165$	−1.40791	−	3.78252i	−0.109606	−	0.294468i
$166$	0.588630	+	1.01954i	0.0456865	+	0.0791314i
$167$	−2.80066	−	4.85088i	−0.216721	−	0.375372i	0.737082	−	0.675803i	$-0.236203\pi$
$167$	−2.80066	−	4.85088i	−0.216721	−	0.375372i	−0.953804	+	0.300431i	$0.902870\pi$
$168$	2.97463	+	0.502264i	0.229498	+	0.0387505i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−13.6466			−1.04665
$171$	17.9749	−	15.5331i	1.37457	−	1.18784i
$172$	36.9100			2.81436
$173$	1.80130	−	3.11994i	0.136950	−	0.237205i	−0.789391	−	0.613891i	$-0.789603\pi$
$173$	1.80130	−	3.11994i	0.136950	−	0.237205i	0.926341	+	0.376687i	$0.122937\pi$
$174$	5.99433	−	7.25003i	0.454429	−	0.549624i
$175$	−0.353285	−	0.611908i	−0.0267059	−	0.0462559i
$176$	−0.724780	−	1.25536i	−0.0546324	−	0.0946260i
$177$	−3.28274	+	3.97042i	−0.246746	+	0.298435i
$178$	−12.1416	+	21.0298i	−0.910050	+	1.57625i
$179$	15.3123			1.14449			0.572246	−	0.820082i	$-0.306072\pi$
$179$	15.3123			1.14449			0.572246	+	0.820082i	$0.306072\pi$
$180$	1.74345	+	9.11175i	0.129949	+	0.679150i
$181$	−7.23734			−0.537947			−0.268974	−	0.963148i	$-0.586684\pi$
$181$	−7.23734			−0.537947			−0.268974	+	0.963148i	$0.586684\pi$
$182$	0.797232	−	1.38085i	0.0590948	−	0.102355i
$183$	−15.7834	−	2.66502i	−1.16675	−	0.197004i
$184$	11.0384	+	19.1190i	0.813758	+	1.40947i
$185$	−1.19040	−	2.06183i	−0.0875197	−	0.151589i
$186$	4.17804	+	11.2248i	0.306349	+	0.823042i
$187$	7.04581	−	12.2037i	0.515241	−	0.892423i
$188$	30.0844			2.19413
$189$	−3.13883	+	1.90455i	−0.228316	+	0.138535i
$190$	17.8698			1.29641
$191$	9.68393	−	16.7731i	0.700705	−	1.21366i	−0.267515	−	0.963554i	$-0.586202\pi$
$191$	9.68393	−	16.7731i	0.700705	−	1.21366i	0.968219	−	0.250102i	$-0.0804642\pi$
$192$	7.88415	+	21.1817i	0.568989	+	1.52866i
$193$	−2.52773	−	4.37816i	−0.181950	−	0.315147i	0.760595	−	0.649227i	$-0.224908\pi$
$193$	−2.52773	−	4.37816i	−0.181950	−	0.315147i	−0.942545	+	0.334081i	$0.891574\pi$
$194$	3.34326	+	5.79069i	0.240032	+	0.415747i
$195$	1.70788	+	0.288374i	0.122304	+	0.0206509i
$196$	10.0513	−	17.4094i	0.717951	−	1.24353i
$197$	6.35430			0.452725			0.226363	−	0.974043i	$-0.427317\pi$
$197$	6.35430			0.452725			0.226363	+	0.974043i	$0.427317\pi$
$198$	−14.9006	−	5.17960i	−1.05894	−	0.368098i
$199$	−16.7816			−1.18961			−0.594807	−	0.803868i	$-0.702772\pi$
$199$	−16.7816			−1.18961			−0.594807	+	0.803868i	$0.702772\pi$
$200$	−1.23251	+	2.13477i	−0.0871517	+	0.150951i
$201$	1.87016	−	2.26193i	0.131911	−	0.159544i
$202$	−15.4257	−	26.7181i	−1.08535	−	1.87988i
$203$	0.850286	+	1.47274i	0.0596784	+	0.103366i
$204$	−20.6394	+	24.9630i	−1.44505	+	1.74776i
$205$	−4.72945	+	8.19164i	−0.330319	+	0.572129i
$206$	−16.0913			−1.12114
$207$	−25.3784	−	8.82176i	−1.76392	−	0.613155i
$208$	0.622073			0.0431330
$209$	−9.22628	+	15.9804i	−0.638195	+	1.10539i
$210$	−2.72315	−	0.459801i	−0.187915	−	0.0317293i
$211$	5.68155	+	9.84073i	0.391134	+	0.677464i	0.992599	−	0.121435i	$-0.0387495\pi$
$211$	5.68155	+	9.84073i	0.391134	+	0.677464i	−0.601465	+	0.798899i	$0.705416\pi$
$212$	−9.13739	−	15.8264i	−0.627559	−	1.08696i
$213$	7.51860	+	20.1996i	0.515166	+	1.38405i
$214$	1.92689	−	3.33747i	0.131719	−	0.228144i
$215$	−11.9359			−0.814021
$216$	11.2295	+	6.16117i	0.764069	+	0.419215i
$217$	−2.16516			−0.146980
$218$	3.65153	−	6.32463i	0.247313	−	0.428358i
$219$	−2.95392	−	7.93605i	−0.199608	−	0.536269i
$220$	−3.60291	−	6.24043i	−0.242908	−	0.420729i
$221$	3.02368	+	5.23717i	0.203395	+	0.352290i
$222$	−9.17565	−	1.54930i	−0.615829	−	0.103982i
$223$	10.0428	−	17.3947i	0.672518	−	1.16484i	−0.304669	−	0.952458i	$-0.598546\pi$
$223$	10.0428	−	17.3947i	0.672518	−	1.16484i	0.977188	−	0.212378i	$-0.0681207\pi$
$224$	−4.47530			−0.299018
$225$	−0.563795	−	2.94655i	−0.0375863	−	0.196436i
$226$	−1.53098			−0.101840
$227$	5.67412	−	9.82787i	0.376605	−	0.652299i	−0.613961	−	0.789336i	$-0.710425\pi$
$227$	5.67412	−	9.82787i	0.376605	−	0.652299i	0.990566	+	0.137038i	$0.0437582\pi$
$228$	27.0266	−	32.6882i	1.78988	−	2.16483i
$229$	1.84068	+	3.18815i	0.121635	+	0.210679i	0.920413	−	0.390948i	$-0.127853\pi$
$229$	1.84068	+	3.18815i	0.121635	+	0.210679i	−0.798777	+	0.601627i	$0.794519\pi$
$230$	−10.1051	−	17.5026i	−0.666314	−	1.15409i
$231$	1.81716	−	2.19782i	0.119560	−	0.144606i
$232$	2.96640	−	5.13796i	0.194754	−	0.337324i
$233$	12.5286			0.820778			0.410389	−	0.911911i	$-0.365393\pi$
$233$	12.5286			0.820778			0.410389	+	0.911911i	$0.365393\pi$
$234$	5.12228	−	4.42644i	0.334854	−	0.289366i
$235$	−9.72867			−0.634628
$236$	−4.59890	+	7.96552i	−0.299363	+	0.518511i
$237$	−18.8300	−	3.17943i	−1.22314	−	0.206526i
$238$	−4.82115	−	8.35048i	−0.312509	−	0.541281i
$239$	−1.66443	−	2.88288i	−0.107663	−	0.186478i	0.807160	−	0.590333i	$-0.201004\pi$
$239$	−1.66443	−	2.88288i	−0.107663	−	0.186478i	−0.914823	+	0.403855i	$0.867670\pi$
$240$	−0.375856	−	1.00978i	−0.0242614	−	0.0651811i
$241$	13.3919	−	23.1955i	0.862649	−	1.49415i	−0.00671442	−	0.999977i	$-0.502137\pi$
$241$	13.3919	−	23.1955i	0.862649	−	1.49415i	0.869363	−	0.494174i	$-0.164529\pi$
$242$	−12.5697			−0.808009
$243$	−15.2433	+	3.26237i	−0.977855	+	0.209281i
$244$	−28.5781			−1.82953
$245$	−3.25038	+	5.62982i	−0.207659	+	0.359676i
$246$	12.8967	+	34.6486i	0.822265	+	2.20911i
$247$	−3.95942	−	6.85792i	−0.251932	−	0.436359i
$248$	3.77680	+	6.54161i	0.239827	+	0.415393i
$249$	−0.890983	−	0.150442i	−0.0564637	−	0.00953386i
$250$	1.12831	−	1.95429i	0.0713607	−	0.123600i
$251$	−6.05718			−0.382326			−0.191163	−	0.981558i	$-0.561226\pi$
$251$	−6.05718			−0.382326			−0.191163	+	0.981558i	$0.561226\pi$
$252$	−4.95962	+	4.28588i	−0.312427	+	0.269985i
$253$	20.8693			1.31204
$254$	−16.5737	+	28.7064i	−1.03992	+	1.80120i
$255$	6.67434	−	8.07249i	0.417963	−	0.505519i
$256$	5.88285	+	10.1894i	0.367678	+	0.636837i
$257$	1.97635	+	3.42314i	0.123281	+	0.213529i	0.921060	−	0.389421i	$-0.127325\pi$
$257$	1.97635	+	3.42314i	0.123281	+	0.213529i	−0.797779	+	0.602951i	$0.793992\pi$
$258$	−29.7273	+	35.9547i	−1.85074	+	2.23844i
$259$	0.841099	−	1.45683i	0.0522634	−	0.0905228i
$260$	3.09235			0.191779
$261$	1.35694	+	7.09174i	0.0839924	+	0.438968i
$262$	−20.4538			−1.26364
$263$	−5.65057	+	9.78708i	−0.348429	+	0.603497i	−0.985971	−	0.166919i	$-0.946618\pi$
$263$	−5.65057	+	9.78708i	−0.348429	+	0.603497i	0.637541	+	0.770416i	$0.279952\pi$
$264$	−9.81007	−	1.65642i	−0.603768	−	0.101946i
$265$	2.95484	+	5.11793i	0.181514	+	0.314392i
$266$	6.31315	+	10.9347i	0.387084	+	0.670450i
$267$	−6.50169	−	17.4675i	−0.397897	−	1.06900i
$268$	2.61997	−	4.53791i	0.160040	−	0.277197i
$269$	−20.7773			−1.26681			−0.633407	−	0.773819i	$-0.718344\pi$
$269$	−20.7773			−1.26681			−0.633407	+	0.773819i	$0.718344\pi$
$270$	−10.2801	−	5.64029i	−0.625627	−	0.343257i
$271$	−1.72567			−0.104827			−0.0524136	−	0.998625i	$-0.516691\pi$
$271$	−1.72567			−0.104827			−0.0524136	+	0.998625i	$0.516691\pi$
$272$	1.88095	−	3.25790i	0.114049	−	0.197539i
$273$	0.426909	+	1.14694i	0.0258377	+	0.0694161i
$274$	2.29029	+	3.96690i	0.138361	+	0.239649i
$275$	1.16510	+	2.01802i	0.0702585	+	0.121691i
$276$	−47.2997	−	7.98652i	−2.84711	−	0.480732i
$277$	1.73361	−	3.00270i	0.104163	−	0.180415i	−0.809233	−	0.587488i	$-0.800117\pi$
$277$	1.73361	−	3.00270i	0.104163	−	0.180415i	0.913396	+	0.407073i	$0.133450\pi$
$278$	−6.43855			−0.386158
$279$	−8.68329	−	3.01839i	−0.519855	−	0.180706i
$280$	−1.74171			−0.104087
$281$	−0.586316	+	1.01553i	−0.0349767	+	0.0605814i	−0.882984	−	0.469403i	$-0.844469\pi$
$281$	−0.586316	+	1.01553i	−0.0349767	+	0.0605814i	0.848007	+	0.529985i	$0.177802\pi$
$282$	−24.2301	+	29.3058i	−1.44288	+	1.74514i
$283$	−10.9061	−	18.8899i	−0.648301	−	1.12289i	−0.983529	−	0.180753i	$-0.942147\pi$
$283$	−10.9061	−	18.8899i	−0.648301	−	1.12289i	0.335228	−	0.942137i	$-0.391187\pi$
$284$	19.2405	+	33.3255i	1.14171	+	1.97750i
$285$	−8.73984	+	10.5707i	−0.517704	+	0.626153i
$286$	−2.62920	+	4.55391i	−0.155468	+	0.269279i
$287$	−6.68338			−0.394507
$288$	−17.9481	−	6.23890i	−1.05760	−	0.367631i
$289$	19.5706			1.15121
$290$	−2.71562	+	4.70359i	−0.159467	+	0.276204i
$291$	−5.06054	−	0.854468i	−0.296654	−	0.0500898i
$292$	−7.55923	−	13.0930i	−0.442371	−	0.766208i
$293$	13.9460	+	24.1551i	0.814732	+	1.41116i	0.909520	+	0.415659i	$0.136449\pi$
$293$	13.9460	+	24.1551i	0.814732	+	1.41116i	−0.0947888	+	0.995497i	$0.530218\pi$
$294$	8.86346	+	23.8127i	0.516927	+	1.38879i
$295$	1.48719	−	2.57588i	0.0865873	−	0.149974i
$296$	−5.86870			−0.341112
$297$	10.3516	−	6.28104i	0.600660	−	0.364463i
$298$	20.2695			1.17418
$299$	−4.47799	+	7.75611i	−0.258969	+	0.448548i
$300$	−1.86840	−	5.01966i	−0.107872	−	0.289810i
$301$	−4.21678	−	7.30367i	−0.243051	−	0.420977i
$302$	3.10831	+	5.38374i	0.178863	+	0.309800i
$303$	23.3492	+	3.94249i	1.34137	+	0.226490i
$304$	−2.46305	+	4.26613i	−0.141266	+	0.244679i
$305$	9.24156			0.529170
$306$	−7.69389	−	40.2104i	−0.439831	−	2.29868i
$307$	−0.574330			−0.0327787			−0.0163894	−	0.999866i	$-0.505217\pi$
$307$	−0.574330			−0.0327787			−0.0163894	+	0.999866i	$0.505217\pi$
$308$	2.54571	−	4.40930i	0.145055	−	0.251243i
$309$	7.87000	−	9.51862i	0.447709	−	0.541495i
$310$	−3.45750	−	5.98857i	−0.196373	−	0.340128i
$311$	−11.5536	−	20.0114i	−0.655143	−	1.13474i	−0.981858	−	0.189618i	$-0.939275\pi$
$311$	−11.5536	−	20.0114i	−0.655143	−	1.13474i	0.326715	−	0.945123i	$-0.394058\pi$
$312$	2.72059	−	3.29050i	0.154023	−	0.186288i
$313$	−12.7427	+	22.0710i	−0.720260	+	1.24753i	0.240635	+	0.970616i	$0.422644\pi$
$313$	−12.7427	+	22.0710i	−0.720260	+	1.24753i	−0.960895	+	0.276912i	$0.910689\pi$
$314$	55.2841			3.11986
$315$	1.60384	−	1.38596i	0.0903659	−	0.0780901i
$316$	−34.0944			−1.91796
$317$	−16.1778	+	28.0208i	−0.908638	+	1.57381i	−0.0926799	+	0.995696i	$0.529543\pi$
$317$	−16.1778	+	28.0208i	−0.908638	+	1.57381i	−0.815958	+	0.578111i	$0.803790\pi$
$318$	22.7761	+	3.84573i	1.27722	+	0.215658i
$319$	−2.80417	−	4.85697i	−0.157003	−	0.271938i
$320$	−6.52446	−	11.3007i	−0.364728	−	0.631728i
$321$	1.03183	+	2.77212i	0.0575910	+	0.154725i
$322$	7.14000	−	12.3668i	0.397897	−	0.689177i
$323$	−47.8881			−2.66457
$324$	−25.8653	+	10.2743i	−1.43696	+	0.570795i
$325$	−1.00000			−0.0554700
$326$	20.5905	−	35.6638i	1.14040	−	1.97523i
$327$	1.95535	+	5.25329i	0.108131	+	0.290507i
$328$	11.6582	+	20.1926i	0.643716	+	1.11495i
$329$	−3.43700	−	5.95305i	−0.189488	−	0.328202i
$330$	8.98071	+	1.51639i	0.494372	+	0.0834743i
$331$	−15.0848	+	26.1276i	−0.829135	+	1.43610i	0.0695818	+	0.997576i	$0.477834\pi$
$331$	−15.0848	+	26.1276i	−0.829135	+	1.43610i	−0.898717	+	0.438529i	$0.855500\pi$
$332$	−1.61325			−0.0885386
$333$	5.40413	−	4.67000i	0.296144	−	0.255915i
$334$	12.6400			0.691633
$335$	−0.847241	+	1.46746i	−0.0462897	+	0.0801762i
$336$	0.485109	−	0.586730i	0.0264648	−	0.0320087i
$337$	−3.28919	−	5.69705i	−0.179174	−	0.310338i	0.762424	−	0.647078i	$-0.224009\pi$
$337$	−3.28919	−	5.69705i	−0.179174	−	0.310338i	−0.941598	+	0.336740i	$0.890676\pi$
$338$	−1.12831	−	1.95429i	−0.0613721	−	0.106300i
$339$	0.748779	−	0.905635i	0.0406681	−	0.0491873i
$340$	9.35028	−	16.1952i	0.507090	−	0.878306i
$341$	7.14050			0.386680
$342$	10.0749	+	52.6543i	0.544789	+	2.84722i
$343$	−9.53924			−0.515071
$344$	−14.7111	+	25.4804i	−0.793170	+	1.37381i
$345$	15.2957	+	2.58267i	0.823494	+	0.139046i
$346$	4.06485	+	7.04053i	0.218528	+	0.378501i
$347$	1.00532	+	1.74126i	0.0539682	+	0.0934756i	0.891747	−	0.452534i	$-0.149480\pi$
$347$	1.00532	+	1.74126i	0.0539682	+	0.0934756i	−0.837779	+	0.546009i	$0.816146\pi$
$348$	4.49685	+	12.0813i	0.241056	+	0.647626i
$349$	−7.00194	+	12.1277i	−0.374805	+	0.649182i	−0.990298	−	0.138961i	$-0.955624\pi$
$349$	−7.00194	+	12.1277i	−0.374805	+	0.649182i	0.615493	+	0.788143i	$0.288957\pi$
$350$	1.59446			0.0852277
$351$	0.113185	+	5.19492i	0.00604138	+	0.277284i
$352$	14.7591			0.786665
$353$	−17.2999	+	29.9643i	−0.920780	+	1.59484i	−0.122570	+	0.992460i	$0.539114\pi$
$353$	−17.2999	+	29.9643i	−0.920780	+	1.59484i	−0.798211	+	0.602379i	$0.794220\pi$
$354$	−4.05541	−	10.8953i	−0.215542	−	0.579080i
$355$	−6.22195	−	10.7767i	−0.330227	−	0.571970i
$356$	−16.6381	−	28.8181i	−0.881820	−	1.52736i
$357$	7.29757	+	1.23219i	0.386228	+	0.0652143i
$358$	−17.2770	+	29.9247i	−0.913118	+	1.58157i
$359$	22.7679			1.20164			0.600822	−	0.799382i	$-0.294840\pi$
$359$	22.7679			1.20164			0.600822	+	0.799382i	$0.294840\pi$
$360$	−6.98509	−	2.42808i	−0.368146	−	0.127971i
$361$	43.7080			2.30042
$362$	8.16597	−	14.1439i	0.429194	−	0.743386i
$363$	6.14762	−	7.43543i	0.322666	−	0.390259i
$364$	1.09248	+	1.89223i	0.0572616	+	0.0991800i
$365$	2.44449	+	4.23399i	0.127951	+	0.221617i
$366$	23.0169	−	27.8385i	1.20311	−	1.45514i
$367$	5.69696	−	9.86742i	0.297379	−	0.515075i	−0.678157	−	0.734917i	$-0.737221\pi$
$367$	5.69696	−	9.86742i	0.297379	−	0.515075i	0.975535	+	0.219842i	$0.0705543\pi$
$368$	5.57128			0.290423
$369$	−26.8035	−	9.31713i	−1.39533	−	0.485030i
$370$	5.37255			0.279306
$371$	−2.08780	+	3.61618i	−0.108393	+	0.187743i
$372$	−16.1837	−	2.73261i	−0.839087	−	0.141679i
$373$	−1.29760	−	2.24750i	−0.0671870	−	0.116371i	0.830475	−	0.557056i	$-0.188069\pi$
$373$	−1.29760	−	2.24750i	−0.0671870	−	0.116371i	−0.897662	+	0.440685i	$0.854736\pi$
$374$	15.8997	+	27.5392i	0.822156	+	1.42402i
$375$	0.604199	+	1.62325i	0.0312007	+	0.0838243i
$376$	−11.9907	+	20.7685i	−0.618373	+	1.07105i
$377$	2.40680			0.123956
$378$	−0.180470	−	8.28311i	−0.00928237	−	0.426037i
$379$	2.38710			0.122617			0.0613084	−	0.998119i	$-0.480473\pi$
$379$	2.38710			0.122617			0.0613084	+	0.998119i	$0.480473\pi$
$380$	−12.2439	+	21.2071i	−0.628099	+	1.08790i
$381$	−8.87502	−	23.8438i	−0.454681	−	1.22155i
$382$	21.8530	+	37.8505i	1.11810	+	1.93660i
$383$	16.1363	+	27.9488i	0.824525	+	1.42812i	0.902282	+	0.431147i	$0.141891\pi$
$383$	16.1363	+	27.9488i	0.824525	+	1.42812i	−0.0777565	+	0.996972i	$0.524776\pi$
$384$	−28.6562	−	4.83857i	−1.46235	−	0.246917i
$385$	−0.823229	+	1.42587i	−0.0419556	+	0.0726693i
$386$	11.4083			0.580666
$387$	−6.72939	−	35.1697i	−0.342074	−	1.78777i
$388$	−9.16282			−0.465172
$389$	−3.75052	+	6.49610i	−0.190159	+	0.329365i	−0.945303	−	0.326194i	$-0.894234\pi$
$389$	−3.75052	+	6.49610i	−0.190159	+	0.329365i	0.755144	+	0.655559i	$0.227567\pi$
$390$	−2.49058	+	3.01232i	−0.126116	+	0.152535i
$391$	27.0801	+	46.9040i	1.36950	+	2.37204i
$392$	8.01226	+	13.8776i	0.404680	+	0.700926i
$393$	10.0036	−	12.0992i	0.504614	−	0.610322i
$394$	−7.16963	+	12.4182i	−0.361201	+	0.625618i
$395$	11.0254			0.554748
$396$	16.3564	−	14.1345i	0.821940	−	0.710284i
$397$	−22.5214			−1.13032			−0.565158	−	0.824983i	$-0.691185\pi$
$397$	−22.5214			−1.13032			−0.565158	+	0.824983i	$0.691185\pi$
$398$	18.9349	−	32.7961i	0.949119	−	1.64392i
$399$	−9.55594	−	1.61351i	−0.478396	−	0.0807767i
$400$	0.311036	+	0.538731i	0.0155518	+	0.0269366i
$401$	−1.26630	−	2.19330i	−0.0632362	−	0.109528i	0.832674	−	0.553763i	$-0.186809\pi$
$401$	−1.26630	−	2.19330i	−0.0632362	−	0.109528i	−0.895910	+	0.444235i	$0.853475\pi$
$402$	2.31034	+	6.20700i	0.115229	+	0.309577i
$403$	−1.53216	+	2.65378i	−0.0763222	+	0.132194i
$404$	42.2770			2.10336
$405$	8.36427	−	3.32249i	0.415624	−	0.165096i
$406$	−3.83755			−0.190454
$407$	−2.77387	+	4.80449i	−0.137496	+	0.238150i
$408$	−9.00673	−	24.1976i	−0.445899	−	1.19796i
$409$	3.18542	+	5.51731i	0.157509	+	0.272814i	0.933970	−	0.357352i	$-0.116320\pi$
$409$	3.18542	+	5.51731i	0.157509	+	0.272814i	−0.776461	+	0.630166i	$0.782987\pi$
$410$	−10.6726	−	18.4855i	−0.527081	−	0.912931i
$411$	−3.46671	−	0.585352i	−0.171000	−	0.0288733i
$412$	11.0253	−	19.0964i	0.543179	−	0.940813i
$413$	2.10160			0.103413
$414$	45.8751	−	39.6432i	2.25464	−	1.94836i
$415$	0.521691			0.0256088
$416$	−3.16691	+	5.48526i	−0.155271	+	0.268937i
$417$	3.14899	−	3.80864i	0.154207	−	0.186510i
$418$	−20.8202	−	36.0617i	−1.01835	−	1.76384i
$419$	−15.4679	−	26.7912i	−0.755657	−	1.30884i	−0.945047	−	0.326934i	$-0.893984\pi$
$419$	−15.4679	−	26.7912i	−0.755657	−	1.30884i	0.189390	−	0.981902i	$-0.439349\pi$
$420$	2.41149	−	2.91666i	0.117669	−	0.142318i
$421$	6.98221	−	12.0935i	0.340292	−	0.589403i	−0.644195	−	0.764861i	$-0.722807\pi$
$421$	6.98221	−	12.0935i	0.340292	−	0.589403i	0.984487	+	0.175459i	$0.0561408\pi$
$422$	−25.6422			−1.24824
$423$	−5.48497	−	28.6660i	−0.266688	−	1.39379i
$424$	14.5675			0.707459
$425$	−3.02368	+	5.23717i	−0.146670	+	0.254040i
$426$	−47.9592	−	8.09788i	−2.32363	−	0.392344i
$427$	3.26491	+	5.65499i	0.158000	+	0.273664i
$428$	2.64050	+	4.57348i	0.127633	+	0.221067i
$429$	−1.40791	−	3.78252i	−0.0679746	−	0.182622i
$430$	13.4674	−	23.3262i	0.649456	−	1.12489i
$431$	20.2027			0.973131			0.486566	−	0.873644i	$-0.338249\pi$
$431$	20.2027			0.973131			0.486566	+	0.873644i	$0.338249\pi$
$432$	2.76346	−	1.67679i	0.132957	−	0.0806744i
$433$	−13.7657			−0.661537			−0.330768	−	0.943712i	$-0.607308\pi$
$433$	−13.7657			−0.661537			−0.330768	+	0.943712i	$0.607308\pi$
$434$	2.44297	−	4.23135i	0.117266	−	0.203111i
$435$	−1.45418	−	3.90684i	−0.0697228	−	0.187318i
$436$	5.00385	+	8.66692i	0.239641	+	0.415070i
$437$	−35.4605	−	61.4194i	−1.69631	−	2.93809i
$438$	18.8423	+	3.18151i	0.900321	+	0.152019i
$439$	−3.88378	+	6.72690i	−0.185363	+	0.321058i	−0.943699	−	0.330806i	$-0.892679\pi$
$439$	−3.88378	+	6.72690i	−0.185363	+	0.321058i	0.758336	+	0.651864i	$0.226013\pi$
$440$	5.74402			0.273835
$441$	−18.4211	−	6.40333i	−0.877194	−	0.304920i
$442$	−13.6466			−0.649104
$443$	−8.21573	+	14.2301i	−0.390341	+	0.676090i	−0.992494	−	0.122290i	$-0.960976\pi$
$443$	−8.21573	+	14.2301i	−0.390341	+	0.676090i	0.602153	+	0.798380i	$0.294310\pi$
$444$	8.12554	−	9.82769i	0.385621	−	0.466401i
$445$	5.38042	+	9.31916i	0.255056	+	0.441771i
$446$	22.6629	+	39.2533i	1.07312	+	1.85870i
$447$	−9.91350	+	11.9902i	−0.468892	+	0.567117i
$448$	4.60999	−	7.98474i	0.217802	−	0.377244i
$449$	9.97715			0.470851			0.235425	−	0.971892i	$-0.424352\pi$
$449$	9.97715			0.470851			0.235425	+	0.971892i	$0.424352\pi$
$450$	6.39455	+	2.22280i	0.301442	+	0.104784i
$451$	22.0412			1.03788
$452$	1.04899	−	1.81690i	0.0493402	−	0.0854598i
$453$	−4.70491	−	0.794420i	−0.221056	−	0.0373251i
$454$	12.8044	+	22.1778i	0.600938	+	1.04086i
$455$	−0.353285	−	0.611908i	−0.0165623	−	0.0286867i
$456$	11.7940	+	31.6860i	0.552306	+	1.48384i
$457$	8.67799	−	15.0307i	0.405939	−	0.703108i	−0.588491	−	0.808504i	$-0.700278\pi$
$457$	8.67799	−	15.0307i	0.405939	−	0.703108i	0.994430	+	0.105396i	$0.0336111\pi$
$458$	−8.30743			−0.388181
$459$	27.5489	+	15.1150i	1.28587	+	0.705508i
$460$	27.6950			1.29129
$461$	5.29646	−	9.17373i	0.246681	−	0.427263i	−0.715922	−	0.698180i	$-0.753994\pi$
$461$	5.29646	−	9.17373i	0.246681	−	0.427263i	0.962603	+	0.270917i	$0.0873268\pi$
$462$	2.24486	+	6.03108i	0.104440	+	0.280591i
$463$	1.80372	+	3.12414i	0.0838260	+	0.145191i	0.904890	−	0.425645i	$-0.139953\pi$
$463$	1.80372	+	3.12414i	0.0838260	+	0.145191i	−0.821064	+	0.570836i	$0.806619\pi$
$464$	−0.748602	−	1.29662i	−0.0347530	−	0.0601939i
$465$	5.23347	+	0.883668i	0.242696	+	0.0409791i
$466$	−14.1362	+	24.4846i	−0.654847	+	1.13423i
$467$	6.96611			0.322353			0.161177	−	0.986926i	$-0.448471\pi$
$467$	6.96611			0.322353			0.161177	+	0.986926i	$0.448471\pi$
$468$	1.74345	+	9.11175i	0.0805910	+	0.421191i
$469$	−1.19727			−0.0552849
$470$	10.9770	−	19.0127i	0.506330	−	0.876989i
$471$	−27.0385	+	32.7026i	−1.24587	+	1.50686i
$472$	−3.66594	−	6.34960i	−0.168739	−	0.292264i
$473$	13.9066	+	24.0869i	0.639425	+	1.10752i
$474$	27.4597	−	33.2120i	1.26126	−	1.52548i
$475$	3.95942	−	6.85792i	0.181671	−	0.314663i
$476$	13.2133			0.605629
$477$	−13.4143	+	11.5920i	−0.614198	+	0.530763i
$478$	7.51200			0.343591
$479$	11.0303	−	19.1050i	0.503987	−	0.872932i	−0.496002	−	0.868321i	$-0.665199\pi$
$479$	11.0303	−	19.1050i	0.503987	−	0.872932i	0.999989	−	0.00461038i	$-0.00146754\pi$
$480$	10.8174	+	1.82651i	0.493744	+	0.0833683i
$481$	−1.19040	−	2.06183i	−0.0542774	−	0.0940112i
$482$	30.2205	+	52.3434i	1.37651	+	2.38418i
$483$	3.82340	+	10.2720i	0.173971	+	0.467392i
$484$	8.61238	−	14.9171i	0.391472	−	0.678049i
$485$	2.96306			0.134546
$486$	10.8235	−	33.4708i	0.490965	−	1.51827i
$487$	−5.19759			−0.235525			−0.117763	−	0.993042i	$-0.537572\pi$
$487$	−5.19759			−0.235525			−0.117763	+	0.993042i	$0.537572\pi$
$488$	11.3903	−	19.7286i	0.515616	−	0.893073i
$489$	11.0260	+	29.6226i	0.498613	+	1.33958i
$490$	−7.33488	−	12.7044i	−0.331356	−	0.573926i
$491$	1.11828	+	1.93692i	0.0504675	+	0.0874122i	0.890156	−	0.455657i	$-0.150596\pi$
$491$	1.11828	+	1.93692i	0.0504675	+	0.0874122i	−0.839688	+	0.543069i	$0.817262\pi$
$492$	−49.9557	−	8.43499i	−2.25218	−	0.380279i
$493$	7.27739	−	12.6048i	0.327757	−	0.567692i
$494$	17.8698			0.804002
$495$	−5.28931	+	4.57079i	−0.237737	+	0.205442i
$496$	1.90623			0.0855922
$497$	4.39625	−	7.61453i	0.197199	−	0.341558i
$498$	1.29931	−	1.57150i	0.0582236	−	0.0704205i
$499$	10.6446	+	18.4370i	0.476519	+	0.825356i	0.999638	−	0.0269043i	$-0.00856493\pi$
$499$	10.6446	+	18.4370i	0.476519	+	0.825356i	−0.523119	+	0.852260i	$0.675232\pi$
$500$	1.54617	+	2.67805i	0.0691470	+	0.119766i
$501$	−6.18204	+	7.47706i	−0.276193	+	0.334051i
$502$	6.83439	−	11.8375i	0.305034	−	0.528334i
$503$	−33.5371			−1.49534			−0.747672	−	0.664068i	$-0.768829\pi$
$503$	−33.5371			−1.49534			−0.747672	+	0.664068i	$0.768829\pi$
$504$	−0.981968	−	5.13204i	−0.0437403	−	0.228599i
$505$	−13.6715			−0.608372
$506$	−23.5471	+	40.7848i	−1.04680	+	1.81311i
$507$	1.70788	+	0.288374i	0.0758494	+	0.0128071i
$508$	−22.7116	−	39.3376i	−1.00766	−	1.74533i
$509$	1.53741	+	2.66287i	0.0681444	+	0.118030i	0.898085	−	0.439823i	$-0.144959\pi$
$509$	1.53741	+	2.66287i	0.0681444	+	0.118030i	−0.829940	+	0.557853i	$0.811625\pi$
$510$	8.24528	+	22.1519i	0.365107	+	0.980902i
$511$	−1.72721	+	2.99161i	−0.0764072	+	0.132341i
$512$	7.00695			0.309666
$513$	−36.0745	−	19.7927i	−1.59273	−	0.873867i
$514$	−8.91975			−0.393433
$515$	−3.56535	+	6.17537i	−0.157108	+	0.272119i
$516$	−22.3010	−	59.9141i	−0.981745	−	2.63757i
$517$	11.3349	+	19.6327i	0.498509	+	0.863443i
$518$	1.89804	+	3.28751i	0.0833953	+	0.144445i
$519$	−6.15279	−	1.03889i	−0.270077	−	0.0456024i
$520$	−1.23251	+	2.13477i	−0.0540492	+	0.0936159i
$521$	32.8855			1.44074			0.720371	−	0.693589i	$-0.243972\pi$
$521$	32.8855			1.44074			0.720371	+	0.693589i	$0.243972\pi$
$522$	−15.3904	−	5.34984i	−0.673619	−	0.234156i
$523$	19.0090			0.831206			0.415603	−	0.909546i	$-0.363571\pi$
$523$	19.0090			0.831206			0.415603	+	0.909546i	$0.363571\pi$
$524$	14.0143	−	24.2735i	0.612219	−	1.06039i
$525$	−0.779826	+	0.943185i	−0.0340344	+	0.0411640i
$526$	−12.7512	−	22.0858i	−0.555979	−	0.962985i
$527$	9.26552	+	16.0483i	0.403612	+	0.699077i
$528$	−1.59985	+	1.93499i	−0.0696244	+	0.0842094i
$529$	−28.6049	+	49.5451i	−1.24369	+	2.15413i
$530$	−13.3359			−0.579275
$531$	8.42842	+	2.92979i	0.365762	+	0.127142i
$532$	−17.3024			−0.750153
$533$	−4.72945	+	8.19164i	−0.204855	+	0.354819i
$534$	41.4726	+	7.00262i	1.79470	+	0.303033i
$535$	−0.853881	−	1.47896i	−0.0369165	−	0.0639412i
$536$	2.08847	+	3.61733i	0.0902081	+	0.156245i
$537$	−9.25166	−	24.8556i	−0.399238	−	1.07260i
$538$	23.4433	−	40.6049i	1.01071	−	1.75060i
$539$	15.1481			0.652476
$540$	13.7373	−	8.33537i	0.591158	−	0.358697i
$541$	−13.4399			−0.577825			−0.288912	−	0.957356i	$-0.593294\pi$
$541$	−13.4399			−0.577825			−0.288912	+	0.957356i	$0.593294\pi$
$542$	1.94710	−	3.37247i	0.0836351	−	0.144860i
$543$	4.37279	+	11.7480i	0.187655	+	0.504156i
$544$	19.1515	+	33.1713i	0.821113	+	1.42221i
$545$	−1.61814	−	2.80270i	−0.0693134	−	0.120054i
$546$	−2.72315	−	0.459801i	−0.116540	−	0.0196777i
$547$	−5.66269	+	9.80807i	−0.242119	+	0.419363i	−0.961318	−	0.275442i	$-0.911176\pi$
$547$	−5.66269	+	9.80807i	−0.242119	+	0.419363i	0.719198	+	0.694805i	$0.244509\pi$
$548$	−6.27697			−0.268139
$549$	5.21034	+	27.2307i	0.222372	+	1.16218i
$550$	−5.25841			−0.224219
$551$	−9.52952	+	16.5056i	−0.405971	+	0.703163i
$552$	24.3656	−	29.4697i	1.03707	−	1.25431i
$553$	3.89511	+	6.74653i	0.165637	+	0.286892i
$554$	3.91210	+	6.77596i	0.166209	+	0.287883i
$555$	−2.62763	+	3.17807i	−0.111536	+	0.134901i
$556$	4.41151	−	7.64096i	0.187090	−	0.324049i
$557$	4.71355			0.199720			0.0998598	−	0.995002i	$-0.468161\pi$
$557$	4.71355			0.199720			0.0998598	+	0.995002i	$0.468161\pi$
$558$	15.6963	−	13.5640i	0.664477	−	0.574211i
$559$	−11.9359			−0.504835
$560$	−0.219769	+	0.380652i	−0.00928695	+	0.0160855i
$561$	−24.0668	−	4.06365i	−1.01610	−	0.171568i
$562$	−1.32309	−	2.29167i	−0.0558114	−	0.0966681i
$563$	−17.6579	−	30.5844i	−0.744193	−	1.28898i	−0.950571	−	0.310508i	$-0.899501\pi$
$563$	−17.6579	−	30.5844i	−0.744193	−	1.28898i	0.206377	−	0.978473i	$-0.433833\pi$
$564$	−18.1770	−	48.8346i	−0.765390	−	2.05631i
$565$	−0.339220	+	0.587547i	−0.0142711	+	0.0247183i
$566$	49.2220			2.06895
$567$	4.98804	+	3.94438i	0.209478	+	0.165648i
$568$	−30.6745			−1.28707
$569$	13.2680	−	22.9808i	0.556222	−	0.963404i	−0.441586	−	0.897219i	$-0.645584\pi$
$569$	13.2680	−	22.9808i	0.556222	−	0.963404i	0.997807	−	0.0661850i	$-0.0210827\pi$
$570$	−10.7969	−	29.0072i	−0.452234	−	1.21498i
$571$	16.8771	+	29.2320i	0.706284	+	1.22332i	0.966226	+	0.257696i	$0.0829632\pi$
$571$	16.8771	+	29.2320i	0.706284	+	1.22332i	−0.259942	+	0.965624i	$0.583703\pi$
$572$	−3.60291	−	6.24043i	−0.150645	−	0.260925i
$573$	−33.0779	−	5.58518i	−1.38185	−	0.233324i
$574$	7.54093	−	13.0613i	0.314752	−	0.545167i
$575$	−8.95599			−0.373491
$576$	29.6196	−	25.5959i	1.23415	−	1.06650i
$577$	−30.7531			−1.28027			−0.640133	−	0.768264i	$-0.721121\pi$
$577$	−30.7531			−1.28027			−0.640133	+	0.768264i	$0.721121\pi$
$578$	−22.0817	+	38.2467i	−0.918480	+	1.59085i
$579$	−5.57959	+	6.74842i	−0.231880	+	0.280455i
$580$	−3.72133	−	6.44553i	−0.154520	−	0.267636i
$581$	0.184306	+	0.319227i	0.00764629	+	0.0132438i
$582$	7.37975	−	8.92567i	0.305900	−	0.369981i
$583$	6.88539	−	11.9259i	0.285164	−	0.493918i
$584$	12.0515			0.498693
$585$	−0.563795	−	2.94655i	−0.0233100	−	0.121825i
$586$	−62.9416			−2.60009
$587$	−2.61862	+	4.53559i	−0.108082	+	0.187204i	−0.914993	−	0.403469i	$-0.867804\pi$
$587$	−2.61862	+	4.53559i	−0.108082	+	0.187204i	0.806911	+	0.590673i	$0.201138\pi$
$588$	−34.3328	−	5.79706i	−1.41586	−	0.239067i
$589$	−12.1329	−	21.0148i	−0.499928	−	0.865901i
$590$	3.35602	+	5.81279i	0.138165	+	0.239309i
$591$	−3.83926	−	10.3146i	−0.157926	−	0.424287i
$592$	−0.740513	+	1.28261i	−0.0304349	+	0.0527148i
$593$	15.8490			0.650839			0.325420	−	0.945570i	$-0.394494\pi$
$593$	15.8490			0.650839			0.325420	+	0.945570i	$0.394494\pi$
$594$	0.595174	+	27.3170i	0.0244203	+	1.12083i
$595$	−4.27289			−0.175171
$596$	−13.8881	+	24.0549i	−0.568880	+	0.985329i
$597$	10.1394	+	27.2407i	0.414979	+	1.11489i
$598$	−10.1051	−	17.5026i	−0.413230	−	0.715736i
$599$	−13.1618	−	22.7969i	−0.537775	−	0.931454i	−0.999023	−	0.0441829i	$-0.985932\pi$
$599$	−13.1618	−	22.7969i	−0.537775	−	0.931454i	0.461248	−	0.887271i	$-0.347402\pi$
$600$	4.20995	+	0.710847i	0.171871	+	0.0290202i
$601$	−0.901862	+	1.56207i	−0.0367877	+	0.0637182i	−0.883833	−	0.467802i	$-0.845046\pi$
$601$	−0.901862	+	1.56207i	−0.0367877	+	0.0637182i	0.847045	+	0.531521i	$0.178379\pi$
$602$	19.0314			0.775660
$603$	−4.80162	−	1.66909i	−0.195537	−	0.0679705i
$604$	−8.51889			−0.346629
$605$	−2.78506	+	4.82387i	−0.113229	+	0.196118i
$606$	−34.0499	+	41.1828i	−1.38318	+	1.67294i
$607$	−6.26933	−	10.8588i	−0.254464	−	0.440745i	0.710286	−	0.703914i	$-0.248566\pi$
$607$	−6.26933	−	10.8588i	−0.254464	−	0.440745i	−0.964750	+	0.263168i	$0.915232\pi$
$608$	−25.0783	−	43.4369i	−1.01706	−	1.76160i
$609$	1.87688	−	2.27006i	0.0760551	−	0.0919873i
$610$	−10.4274	+	18.0607i	−0.422192	+	0.731257i
$611$	−9.72867			−0.393580
$612$	52.9914	+	18.4203i	2.14205	+	0.744596i
$613$	9.01785			0.364228			0.182114	−	0.983277i	$-0.441706\pi$
$613$	9.01785			0.364228			0.182114	+	0.983277i	$0.441706\pi$
$614$	0.648023	−	1.12241i	0.0261521	−	0.0452968i
$615$	16.1546	+	2.72770i	0.651417	+	0.109991i
$616$	2.02928	+	3.51481i	0.0817619	+	0.141616i
$617$	−7.34095	−	12.7149i	−0.295536	−	0.511883i	0.679574	−	0.733607i	$-0.262165\pi$
$617$	−7.34095	−	12.7149i	−0.295536	−	0.511883i	−0.975109	+	0.221725i	$0.928831\pi$
$618$	9.72236	+	26.1203i	0.391091	+	1.05071i
$619$	20.8355	−	36.0881i	0.837448	−	1.45050i	−0.0545741	−	0.998510i	$-0.517380\pi$
$619$	20.8355	−	36.0881i	0.837448	−	1.45050i	0.892022	−	0.451992i	$-0.149287\pi$
$620$	9.47594			0.380563
$621$	1.01369	+	46.5256i	0.0406778	+	1.86701i
$622$	52.1441			2.09079
$623$	−3.80165	+	6.58465i	−0.152310	+	0.263808i
$624$	−0.375856	−	1.00978i	−0.0150463	−	0.0404236i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−28.7555	−	49.8060i	−1.14930	−	1.99065i
$627$	31.5147	+	5.32123i	1.25858	+	0.212510i
$628$	−37.8791	+	65.6086i	−1.51154	+	2.61807i
$629$	−14.3975			−0.574067
$630$	0.898950	+	4.69816i	0.0358150	+	0.187179i
$631$	−19.8681			−0.790936			−0.395468	−	0.918480i	$-0.629418\pi$
$631$	−19.8681			−0.790936			−0.395468	+	0.918480i	$0.629418\pi$
$632$	13.5889	−	23.5367i	0.540538	−	0.936239i
$633$	12.5412	−	15.1683i	0.498468	−	0.602888i
$634$	−36.5073	−	63.2325i	−1.44989	−	2.51128i
$635$	7.34445	+	12.7210i	0.291456	+	0.504816i
$636$	−20.1695	+	24.3946i	−0.799771	+	0.967309i
$637$	−3.25038	+	5.62982i	−0.128785	+	0.223062i
$638$	12.6559			0.501053
$639$	28.2463	−	24.4091i	1.11740	−	0.965611i
$640$	16.7788			0.663242
$641$	−11.1576	+	19.3256i	−0.440700	+	0.763315i	−0.997742	−	0.0671694i	$-0.978603\pi$
$641$	−11.1576	+	19.3256i	−0.440700	+	0.763315i	0.557041	+	0.830485i	$0.311937\pi$
$642$	−6.58177	−	1.11133i	−0.259762	−	0.0438606i
$643$	−7.72222	−	13.3753i	−0.304535	−	0.527470i	0.672623	−	0.739985i	$-0.265168\pi$
$643$	−7.72222	−	13.3753i	−0.304535	−	0.527470i	−0.977158	+	0.212516i	$0.931834\pi$
$644$	9.78426	+	16.9468i	0.385554	+	0.667799i
$645$	7.21166	+	19.3749i	0.283959	+	0.762888i
$646$	54.0327	−	93.5874i	2.12589	−	3.68215i
$647$	−25.0635			−0.985349			−0.492675	−	0.870214i	$-0.663981\pi$
$647$	−25.0635			−0.985349			−0.492675	+	0.870214i	$0.663981\pi$
$648$	3.21629	−	21.9508i	0.126348	−	0.862310i
$649$	−6.93091			−0.272062
$650$	1.12831	−	1.95429i	0.0442560	−	0.0766537i
$651$	1.30819	+	3.51459i	0.0512718	+	0.137748i
$652$	28.2161	+	48.8716i	1.10503	+	1.91396i
$653$	1.49244	+	2.58498i	0.0584036	+	0.101158i	0.893749	−	0.448568i	$-0.148066\pi$
$653$	1.49244	+	2.58498i	0.0584036	+	0.101158i	−0.835345	+	0.549726i	$0.814732\pi$
$654$	−12.4727	−	2.10601i	−0.487722	−	0.0823514i
$655$	−4.53194	+	7.84955i	−0.177077	+	0.306707i
$656$	5.88412			0.229736
$657$	−11.0974	+	9.58992i	−0.432953	+	0.374138i
$658$	15.5120			0.604721
$659$	18.7165	−	32.4180i	0.729092	−	1.26282i	−0.228175	−	0.973620i	$-0.573276\pi$
$659$	18.7165	−	32.4180i	0.729092	−	1.26282i	0.957267	−	0.289204i	$-0.0933907\pi$
$660$	−7.95290	+	9.61889i	−0.309566	+	0.374415i
$661$	−7.68631	−	13.3131i	−0.298963	−	0.517819i	0.676936	−	0.736042i	$-0.263307\pi$
$661$	−7.68631	−	13.3131i	−0.298963	−	0.517819i	−0.975899	+	0.218223i	$0.929974\pi$
$662$	−34.0407	−	58.9602i	−1.32303	−	2.29155i
$663$	6.67434	−	8.07249i	0.259210	−	0.313509i
$664$	0.642989	−	1.11369i	0.0249528	−	0.0432196i
$665$	5.59522			0.216973
$666$	3.02902	+	15.8305i	0.117372	+	0.613418i
$667$	21.5552			0.834622
$668$	−8.66061	+	15.0006i	−0.335089	+	0.580391i
$669$	−34.3039	−	5.79218i	−1.32626	−	0.223939i
$670$	−1.91190	−	3.31152i	−0.0738633	−	0.127935i
$671$	−10.7674	−	18.6497i	−0.415670	−	0.719962i
$672$	2.70397	+	7.26453i	0.104308	+	0.280235i
$673$	0.271779	−	0.470734i	0.0104763	−	0.0181455i	−0.860740	−	0.509045i	$-0.829999\pi$
$673$	0.271779	−	0.470734i	0.0104763	−	0.0181455i	0.871216	+	0.490900i	$0.163332\pi$
$674$	14.8449			0.571805
$675$	−4.44234	+	2.69548i	−0.170986	+	0.103749i
$676$	3.09235			0.118937
$677$	10.0293	−	17.3713i	0.385458	−	0.667633i	−0.606374	−	0.795179i	$-0.707377\pi$
$677$	10.0293	−	17.3713i	0.385458	−	0.667633i	0.991833	+	0.127546i	$0.0407100\pi$
$678$	0.925020	+	2.48517i	0.0355252	+	0.0954425i
$679$	1.04681	+	1.81312i	0.0401727	+	0.0695812i
$680$	7.45344	+	12.9097i	0.285826	+	0.495066i
$681$	−19.3814	−	3.27253i	−0.742697	−	0.125404i
$682$	−8.05671	+	13.9546i	−0.308507	+	0.534350i
$683$	35.5213			1.35919			0.679593	−	0.733589i	$-0.262156\pi$
$683$	35.5213			1.35919			0.679593	+	0.733589i	$0.262156\pi$
$684$	−69.3907	−	24.1208i	−2.65322	−	0.922283i
$685$	2.02984			0.0775561
$686$	10.7632	−	18.6425i	0.410942	−	0.711773i
$687$	4.06303	−	4.91416i	0.155014	−	0.187487i
$688$	3.71250	+	6.43024i	0.141538	+	0.245150i
$689$	2.95484	+	5.11793i	0.112570	+	0.194978i
$690$	−22.3056	+	26.9783i	−0.849161	+	1.02704i
$691$	25.6756	−	44.4714i	0.976746	−	1.69177i	0.302697	−	0.953087i	$-0.402113\pi$
$691$	25.6756	−	44.4714i	0.976746	−	1.69177i	0.674049	−	0.738686i	$-0.264554\pi$
$692$	−11.1405			−0.423498
$693$	−4.66554	−	1.62178i	−0.177229	−	0.0616064i
$694$	−4.53724			−0.172231
$695$	−1.42659	+	2.47092i	−0.0541136	+	0.0937275i
$696$	−10.1325	−	1.71086i	−0.384071	−	0.0648502i
$697$	28.6007	+	49.5378i	1.08333	+	1.87638i
$698$	−15.8007	−	27.3677i	−0.598067	−	1.03588i
$699$	−7.56979	−	20.3371i	−0.286316	−	0.769220i
$700$	−1.09248	+	1.89223i	−0.0412919	+	0.0715197i
$701$	26.2661			0.992057			0.496029	−	0.868306i	$-0.334791\pi$
$701$	26.2661			0.992057			0.496029	+	0.868306i	$0.334791\pi$
$702$	−10.2801	−	5.64029i	−0.387998	−	0.212879i
$703$	18.8531			0.711059
$704$	−15.2034	+	26.3330i	−0.572998	+	0.992462i
$705$	5.87805	+	15.7921i	0.221380	+	0.594764i
$706$	−39.0393	−	67.6181i	−1.46927	−	2.54484i
$707$	−4.82993	−	8.36568i	−0.181648	−	0.314624i
$708$	15.7087	+	2.65240i	0.590369	+	0.0996833i
$709$	12.8681	−	22.2882i	0.483273	−	0.837053i	−0.516543	−	0.856261i	$-0.672781\pi$
$709$	12.8681	−	22.2882i	0.483273	−	0.837053i	0.999815	+	0.0192087i	$0.00611468\pi$
$710$	28.0812			1.05387
$711$	6.21606	+	32.4868i	0.233120	+	1.21835i
$712$	26.5257			0.994093
$713$	−13.7220	+	23.7672i	−0.513892	+	0.890088i
$714$	−10.6420	+	12.8713i	−0.398266	+	0.481696i
$715$	1.16510	+	2.01802i	0.0435725	+	0.0754697i
$716$	−23.6754	−	41.0071i	−0.884793	−	1.53251i
$717$	−3.67400	+	4.44363i	−0.137208	+	0.165950i
$718$	−25.6893	+	44.4952i	−0.958717	+	1.66055i
$719$	−21.6829			−0.808634			−0.404317	−	0.914619i	$-0.632491\pi$
$719$	−21.6829			−0.808634			−0.404317	+	0.914619i	$0.632491\pi$
$720$	−1.41204	+	1.22022i	−0.0526234	+	0.0454748i
$721$	−5.03835			−0.187638
$722$	−49.3163	+	85.4183i	−1.83536	+	3.17894i
$723$	−45.7434	−	7.72375i	−1.70122	−	0.287249i
$724$	11.1902	+	19.3820i	0.415880	+	0.720326i
$725$	1.20340	+	2.08435i	0.0446931	+	0.0774107i
$726$	7.59458	+	20.4037i	0.281861	+	0.757253i
$727$	24.6644	−	42.7200i	0.914752	−	1.58440i	0.107488	−	0.994206i	$-0.465719\pi$
$727$	24.6644	−	42.7200i	0.914752	−	1.58440i	0.807264	−	0.590190i	$-0.200947\pi$
$728$	−1.74171			−0.0645522
$729$	14.5056	+	22.7725i	0.537245	+	0.843426i
$730$	−11.0326			−0.408335
$731$	−36.0903	+	62.5103i	−1.33485	+	2.31203i
$732$	17.2669	+	46.3895i	0.638203	+	1.71460i
$733$	−13.0583	−	22.6176i	−0.482318	−	0.835399i	0.517476	−	0.855698i	$-0.326872\pi$
$733$	−13.0583	−	22.6176i	−0.482318	−	0.835399i	−0.999794	+	0.0202985i	$0.993538\pi$
$734$	12.8559	+	22.2671i	0.474520	+	0.821892i
$735$	11.1025	+	1.87465i	0.409521	+	0.0691474i
$736$	−28.3628	+	49.1259i	−1.04547	+	1.81080i
$737$	3.94850			0.145445
$738$	48.4511	−	41.8693i	1.78351	−	1.54123i
$739$	−20.3143			−0.747275			−0.373637	−	0.927575i	$-0.621890\pi$
$739$	−20.3143			−0.747275			−0.373637	+	0.927575i	$0.621890\pi$
$740$	−3.68112	+	6.37589i	−0.135321	+	0.234382i
$741$	−8.73984	+	10.5707i	−0.321066	+	0.388324i
$742$	−4.71138	−	8.16036i	−0.172960	−	0.299576i
$743$	−4.73644	−	8.20375i	−0.173763	−	0.300966i	0.765969	−	0.642877i	$-0.222259\pi$
$743$	−4.73644	−	8.20375i	−0.173763	−	0.300966i	−0.939733	+	0.341911i	$0.888926\pi$
$744$	8.33674	−	10.0831i	0.305640	−	0.369666i
$745$	4.49112	−	7.77885i	0.164542	−	0.284995i
$746$	5.85637			0.214417
$747$	0.294126	+	1.53719i	0.0107615	+	0.0562427i
$748$	−43.5762			−1.59330
$749$	0.603327	−	1.04499i	0.0220451	−	0.0381832i
$750$	−3.85403	−	0.650751i	−0.140729	−	0.0237621i
$751$	3.02922	+	5.24676i	0.110538	+	0.191457i	0.915987	−	0.401207i	$-0.131409\pi$
$751$	3.02922	+	5.24676i	0.110538	+	0.191457i	−0.805449	+	0.592664i	$0.798076\pi$
$752$	3.02597	+	5.24114i	0.110346	+	0.191125i
$753$	3.65975	+	9.83233i	0.133369	+	0.358310i
$754$	−2.71562	+	4.70359i	−0.0988970	+	0.171295i
$755$	2.75483			0.100258
$756$	9.95366	+	5.46118i	0.362011	+	0.198621i
$757$	19.3009			0.701503			0.350752	−	0.936469i	$-0.385926\pi$
$757$	19.3009			0.701503			0.350752	+	0.936469i	$0.385926\pi$
$758$	−2.69339	+	4.66509i	−0.0978283	+	0.169444i
$759$	−12.6092	−	33.8762i	−0.457686	−	1.22963i
$760$	−9.76006	−	16.9049i	−0.354035	−	0.613206i
$761$	15.7544	+	27.2873i	0.571095	+	0.989165i	0.996454	+	0.0841405i	$0.0268145\pi$
$761$	15.7544	+	27.2873i	0.571095	+	0.989165i	−0.425359	+	0.905025i	$0.639852\pi$
$762$	56.6115	+	9.55881i	2.05082	+	0.346279i
$763$	1.14333	−	1.98030i	0.0413913	−	0.0716918i
$764$	−59.8922			−2.16682
$765$	−17.1363	−	5.95673i	−0.619564	−	0.215366i
$766$	−72.8270			−2.63135
$767$	1.48719	−	2.57588i	0.0536992	−	0.0930097i
$768$	12.9855	−	15.7058i	0.468575	−	0.566733i
$769$	−4.65962	−	8.07070i	−0.168030	−	0.291037i	0.769697	−	0.638409i	$-0.220407\pi$
$769$	−4.65962	−	8.07070i	−0.168030	−	0.291037i	−0.937727	+	0.347373i	$0.887074\pi$
$770$	−1.85772	−	3.21766i	−0.0669475	−	0.115956i
$771$	4.36250	−	5.27637i	0.157112	−	0.190024i
$772$	−7.81662	+	13.5388i	−0.281326	+	0.487272i
$773$	24.3144			0.874529			0.437265	−	0.899333i	$-0.355947\pi$
$773$	24.3144			0.874529			0.437265	+	0.899333i	$0.355947\pi$
$774$	76.3247	+	26.5311i	2.74343	+	0.953642i
$775$	−3.06432			−0.110073
$776$	3.65200	−	6.32546i	0.131099	−	0.227071i
$777$	−2.87299	−	0.485101i	−0.103068	−	0.0174029i
$778$	−8.46352	−	14.6592i	−0.303432	−	0.525560i
$779$	−37.4517	−	64.8683i	−1.34185	−	2.32415i
$780$	−1.86840	−	5.01966i	−0.0668993	−	0.179733i
$781$	−14.4985	+	25.1121i	−0.518796	+	0.898580i
$782$	−122.219			−4.37054
$783$	10.6918	−	6.48748i	0.382094	−	0.231843i
$784$	4.04395			0.144427
$785$	12.2493	−	21.2164i	0.437196	−	0.757246i
$786$	12.3581	+	33.2016i	0.440800	+	1.18426i
$787$	21.4150	+	37.0919i	0.763362	+	1.32218i	0.941108	+	0.338106i	$0.109786\pi$
$787$	21.4150	+	37.0919i	0.763362	+	1.32218i	−0.177746	+	0.984076i	$0.556880\pi$
$788$	−9.82486	−	17.0172i	−0.349996	−	0.606211i
$789$	19.3010	+	3.25895i	0.687132	+	0.116022i
$790$	−12.4401	+	21.5468i	−0.442598	+	0.766602i
$791$	−0.479366			−0.0170443
$792$	3.23845	+	16.9250i	0.115073	+	0.601404i
$793$	9.24156			0.328177
$794$	25.4112	−	44.0134i	0.901808	−	1.56198i
$795$	6.52237	−	7.88869i	0.231325	−	0.279783i
$796$	25.9473	+	44.9420i	0.919676	+	1.59293i
$797$	15.4198	+	26.7079i	0.546199	+	0.946044i	0.998530	+	0.0541940i	$0.0172589\pi$
$797$	15.4198	+	26.7079i	0.546199	+	0.946044i	−0.452332	+	0.891850i	$0.649408\pi$
$798$	13.9354	−	16.8546i	0.493307	−	0.596645i
$799$	−29.4164	+	50.9507i	−1.04068	+	1.80251i
$800$	−6.33383			−0.223935
$801$	−24.4259	+	21.1078i	−0.863046	+	0.745806i
$802$	5.71514			0.201809
$803$	5.69618	−	9.86608i	0.201014	−	0.348166i
$804$	−8.94915	−	1.51106i	−0.315612	−	0.0532909i
$805$	−3.16402	−	5.48024i	−0.111517	−	0.193153i
$806$	−3.45750	−	5.98857i	−0.121785	−	0.210938i
$807$	12.5536	+	33.7267i	0.441908	+	1.18724i
$808$	−16.8502	+	29.1855i	−0.592789	+	1.02674i
$809$	−14.4671			−0.508636			−0.254318	−	0.967121i	$-0.581851\pi$
$809$	−14.4671			−0.508636			−0.254318	+	0.967121i	$0.581851\pi$
$810$	−2.94438	+	20.0950i	−0.103455	+	0.706068i
$811$	40.9902			1.43936			0.719681	−	0.694305i	$-0.244288\pi$
$811$	40.9902			1.43936			0.719681	+	0.694305i	$0.244288\pi$
$812$	2.62938	−	4.55422i	0.0922732	−	0.159822i
$813$	1.04265	+	2.80120i	0.0365674	+	0.0982425i
$814$	−6.25959	−	10.8419i	−0.219398	−	0.380009i
$815$	−9.12447	−	15.8040i	−0.319616	−	0.553592i
$816$	−6.42486	−	1.08483i	−0.224915	−	0.0379768i
$817$	47.2592	−	81.8554i	1.65339	−	2.86376i
$818$	−14.3766			−0.502666
$819$	1.60384	−	1.38596i	0.0560425	−	0.0484294i
$820$	29.2502			1.02146
$821$	23.6408	−	40.9470i	0.825068	−	1.42906i	−0.0767992	−	0.997047i	$-0.524470\pi$
$821$	23.6408	−	40.9470i	0.825068	−	1.42906i	0.901867	−	0.432013i	$-0.142197\pi$
$822$	5.05548	−	6.11451i	0.176330	−	0.213268i
$823$	−14.9104	−	25.8256i	−0.519744	−	0.900223i	−0.999737	−	0.0229503i	$-0.992694\pi$
$823$	−14.9104	−	25.8256i	−0.519744	−	0.900223i	0.479993	−	0.877272i	$-0.340639\pi$
$824$	8.78868	+	15.2224i	0.306168	+	0.530299i
$825$	2.57180	−	3.11054i	0.0895385	−	0.108295i
$826$	−2.37126	+	4.10715i	−0.0825068	+	0.142906i
$827$	3.90807			0.135897			0.0679484	−	0.997689i	$-0.478355\pi$
$827$	3.90807			0.135897			0.0679484	+	0.997689i	$0.478355\pi$
$828$	15.6143	+	81.6047i	0.542635	+	2.83596i
$829$	−7.76600			−0.269724			−0.134862	−	0.990864i	$-0.543059\pi$
$829$	−7.76600			−0.269724			−0.134862	+	0.990864i	$0.543059\pi$
$830$	−0.588630	+	1.01954i	−0.0204316	+	0.0353886i
$831$	−5.92158	−	0.999854i	−0.205417	−	0.0346846i
$832$	−6.52446	−	11.3007i	−0.226195	−	0.391781i
$833$	19.6562	+	34.0456i	0.681048	+	1.17961i
$834$	3.89016	+	10.4514i	0.134705	+	0.361902i
$835$	2.80066	−	4.85088i	0.0969207	−	0.167872i
$836$	57.0618			1.97352
$837$	0.346835	+	15.9189i	0.0119884	+	0.550237i
$838$	69.8105			2.41156
$839$	−7.80495	+	13.5186i	−0.269457	+	0.466713i	−0.968722	−	0.248150i	$-0.920177\pi$
$839$	−7.80495	+	13.5186i	−0.269457	+	0.466713i	0.699265	+	0.714863i	$0.253511\pi$
$840$	1.05234	+	2.82724i	0.0363092	+	0.0975489i
$841$	11.6037	+	20.0981i	0.400126	+	0.693039i
$842$	15.7562	+	27.2906i	0.542995	+	0.940495i
$843$	2.00271	+	0.338156i	0.0689770	+	0.0116467i
$844$	17.5693	−	30.4310i	0.604762	−	1.04748i
$845$	−1.00000			−0.0344010
$846$	62.2105	+	21.6249i	2.13884	+	0.743480i
$847$	−3.93569			−0.135232
$848$	1.83813	−	3.18373i	0.0631215	−	0.109330i
$849$	−24.0736	+	29.1166i	−0.826205	+	0.999280i
$850$	−6.82331	−	11.8183i	−0.234038	−	0.405365i
$851$	−10.6612	−	18.4657i	−0.365460	−	0.632996i
$852$	42.4705	−	51.3673i	1.45502	−	1.75981i
$853$	6.17301	−	10.6920i	0.211360	−	0.366086i	−0.740781	−	0.671747i	$-0.765544\pi$
$853$	6.17301	−	10.6920i	0.211360	−	0.366086i	0.952140	+	0.305661i	$0.0988775\pi$
$854$	−14.7353			−0.504233
$855$	22.4395	+	7.80016i	0.767414	+	0.266760i
$856$	−4.20967			−0.143884
$857$	18.4503	−	31.9569i	0.630251	−	1.09163i	−0.357250	−	0.934009i	$-0.616286\pi$
$857$	18.4503	−	31.9569i	0.630251	−	1.09163i	0.987500	−	0.157617i	$-0.0503811\pi$
$858$	8.98071	+	1.51639i	0.306596	+	0.0517685i
$859$	14.1989	+	24.5932i	0.484460	+	0.839109i	0.999841	−	0.0178523i	$-0.00568287\pi$
$859$	14.1989	+	24.5932i	0.484460	+	0.839109i	−0.515381	+	0.856961i	$0.672350\pi$
$860$	18.4550	+	31.9650i	0.629310	+	1.09000i
$861$	4.03809	+	10.8488i	0.137618	+	0.369726i
$862$	−22.7950	+	39.4821i	−0.776400	+	1.34476i
$863$	−26.6238			−0.906283			−0.453142	−	0.891438i	$-0.649697\pi$
$863$	−26.6238			−0.906283			−0.453142	+	0.891438i	$0.649697\pi$
$864$	0.716896	+	32.9037i	0.0243893	+	1.11941i
$865$	3.60260			0.122492
$866$	15.5320	−	26.9022i	0.527798	−	0.914173i
$867$	−11.8245	−	31.7680i	−0.401583	−	1.07890i
$868$	3.34771	+	5.79840i	0.113629	+	0.196811i
$869$	−12.8457	−	22.2495i	−0.435762	−	0.754762i
$870$	9.27588	+	1.56622i	0.314482	+	0.0531000i
$871$	−0.847241	+	1.46746i	−0.0287077	+	0.0497231i
$872$	−7.97749			−0.270152
$873$	1.67056	+	8.73079i	0.0565398	+	0.295493i
$874$	160.042			5.41350
$875$	0.353285	−	0.611908i	0.0119432	−	0.0206863i
$876$	−16.6859	+	20.1813i	−0.563764	+	0.681863i
$877$	25.6019	+	44.3439i	0.864516	+	1.49739i	0.867527	+	0.497390i	$0.165708\pi$
$877$	25.6019	+	44.3439i	0.864516	+	1.49739i	−0.00301066	+	0.999995i	$0.500958\pi$
$878$	−8.76423	−	15.1801i	−0.295778	−	0.512303i
$879$	30.7837	−	37.2323i	1.03831	−	1.25581i
$880$	0.724780	−	1.25536i	0.0244323	−	0.0423181i
$881$	−29.0213			−0.977751			−0.488876	−	0.872354i	$-0.662593\pi$
$881$	−29.0213			−0.977751			−0.488876	+	0.872354i	$0.662593\pi$
$882$	33.2987	−	28.7752i	1.12123	−	0.968913i
$883$	21.5185			0.724154			0.362077	−	0.932148i	$-0.382068\pi$
$883$	21.5185			0.724154			0.362077	+	0.932148i	$0.382068\pi$
$884$	9.35028	−	16.1952i	0.314484	−	0.544702i
$885$	−5.07986	−	0.857730i	−0.170758	−	0.0288323i
$886$	−18.5398	−	32.1119i	−0.622857	−	1.07882i
$887$	−9.60108	−	16.6296i	−0.322373	−	0.558366i	0.658604	−	0.752489i	$-0.271147\pi$
$887$	−9.60108	−	16.6296i	−0.322373	−	0.558366i	−0.980977	+	0.194124i	$0.937814\pi$
$888$	3.54587	+	9.52638i	0.118991	+	0.319684i
$889$	−5.18937	+	8.98826i	−0.174046	+	0.301456i
$890$	−24.2832			−0.813974
$891$	−16.4501	−	13.0082i	−0.551100	−	0.435792i
$892$	−62.1120			−2.07966
$893$	38.5199	−	66.7184i	1.28902	−	2.23265i
$894$	−12.2468	−	32.9026i	−0.409596	−	1.10043i
$895$	7.65613	+	13.2608i	0.255916	+	0.443260i
$896$	5.92772	+	10.2671i	0.198031	+	0.343000i
$897$	15.2957	+	2.58267i	0.510709	+	0.0862329i
$898$	−11.2573	+	19.4983i	−0.375662	+	0.650666i
$899$	7.37519			0.245976
$900$	−7.01928	+	6.06575i	−0.233976	+	0.202192i
$901$	35.7380			1.19060
$902$	−24.8694	+	43.0750i	−0.828059	+	1.43424i
$903$	−9.30792	+	11.2578i	−0.309748	+	0.374635i
$904$	0.836185	+	1.44832i	0.0278111	+	0.0481702i
$905$	−3.61867	−	6.26772i	−0.120289	−	0.208346i
$906$	6.86113	−	8.29841i	0.227946	−	0.275696i
$907$	−23.7416	+	41.1216i	−0.788326	+	1.36542i	0.138666	+	0.990339i	$0.455719\pi$
$907$	−23.7416	+	41.1216i	−0.788326	+	1.36542i	−0.926992	+	0.375081i	$0.877615\pi$
$908$	−35.0927			−1.16459
$909$	−7.70790	−	40.2836i	−0.255655	−	1.33612i
$910$	1.59446			0.0528560
$911$	7.00522	−	12.1334i	0.232093	−	0.401997i	−0.726331	−	0.687345i	$-0.758776\pi$
$911$	7.00522	−	12.1334i	0.232093	−	0.401997i	0.958424	+	0.285348i	$0.0921092\pi$
$912$	8.41316	+	1.42056i	0.278588	+	0.0470393i
$913$	−0.607824	−	1.05278i	−0.0201160	−	0.0348420i
$914$	19.5830	+	33.9187i	0.647747	+	1.12193i
$915$	−5.58374	−	15.0014i	−0.184593	−	0.495930i
$916$	5.69202	−	9.85886i	0.188070	−	0.325746i
$917$	−6.40427			−0.211488
$918$	−60.6229	+	36.7842i	−2.00086	+	1.21406i
$919$	47.7699			1.57579			0.787893	−	0.615813i	$-0.211172\pi$
$919$	47.7699			1.57579			0.787893	+	0.615813i	$0.211172\pi$
$920$	−11.0384	+	19.1190i	−0.363924	+	0.630334i
$921$	0.347010	+	0.932282i	0.0114344	+	0.0307197i
$922$	11.9521	+	20.7017i	0.393622	+	0.681773i
$923$	−6.22195	−	10.7767i	−0.204798	−	0.354721i
$924$	−8.69552	−	1.46823i	−0.286062	−	0.0483013i
$925$	1.19040	−	2.06183i	0.0391400	−	0.0677924i
$926$	−8.14064			−0.267518
$927$	−20.2062	−	7.02384i	−0.663657	−	0.230693i
$928$	15.2442			0.500417
$929$	−18.1478	+	31.4329i	−0.595409	+	1.03128i	0.398080	+	0.917351i	$0.369677\pi$
$929$	−18.1478	+	31.4329i	−0.595409	+	1.03128i	−0.993489	+	0.113928i	$0.963657\pi$
$930$	−7.63193	+	9.23069i	−0.250261	+	0.302686i
$931$	−25.7392	−	44.5817i	−0.843569	−	1.46110i
$932$	−19.3715	−	33.5524i	−0.634533	−	1.09904i
$933$	−25.5028	+	30.8452i	−0.834925	+	1.00983i
$934$	−7.85995	+	13.6138i	−0.257185	+	0.445458i
$935$	14.0916			0.460845
$936$	−6.98509	−	2.42808i	−0.228315	−	0.0793642i
$937$	−16.6768			−0.544808			−0.272404	−	0.962183i	$-0.587819\pi$
$937$	−16.6768			−0.544808			−0.272404	+	0.962183i	$0.587819\pi$
$938$	1.35090	−	2.33982i	0.0441083	−	0.0763978i
$939$	43.5259	+	7.34932i	1.42041	+	0.239836i
$940$	15.0422	+	26.0539i	0.490623	+	0.849784i
$941$	−24.4145	−	42.2872i	−0.795890	−	1.37852i	−0.922273	−	0.386540i	$-0.873670\pi$
$941$	−24.4145	−	42.2872i	−0.795890	−	1.37852i	0.126383	−	0.991982i	$-0.459663\pi$
$942$	−33.4026	−	89.7400i	−1.08832	−	2.92389i
$943$	−42.3569	+	73.3643i	−1.37933	+	2.38907i
$944$	−1.85028			−0.0602213
$945$	−3.21880	−	1.76603i	−0.104708	−	0.0574490i
$946$	−62.7638			−2.04063
$947$	5.03571	−	8.72210i	0.163639	−	0.283430i	−0.772532	−	0.634975i	$-0.781010\pi$
$947$	5.03571	−	8.72210i	0.163639	−	0.283430i	0.936171	+	0.351545i	$0.114344\pi$
$948$	20.5998	+	55.3437i	0.669050	+	1.79748i
$949$	2.44449	+	4.23399i	0.0793516	+	0.137441i
$950$	8.93492	+	15.4757i	0.289887	+	0.502099i
$951$	55.2595	+	9.33052i	1.79191	+	0.302563i
$952$	−5.26638	+	9.12164i	−0.170684	+	0.295634i
$953$	19.2233			0.622703			0.311351	−	0.950295i	$-0.399218\pi$
$953$	19.2233			0.622703			0.311351	+	0.950295i	$0.399218\pi$
$954$	−7.51872	−	39.2949i	−0.243427	−	1.27222i
$955$	19.3679			0.626729
$956$	−5.14701	+	8.91489i	−0.166466	+	0.288328i
$957$	−6.18980	+	7.48645i	−0.200088	+	0.242003i
$958$	24.8912	+	43.1129i	0.804199	+	1.39291i
$959$	0.717112	+	1.24207i	0.0231568	+	0.0401087i
$960$	−14.4018	+	17.4187i	−0.464816	+	0.562186i
$961$	10.8050	−	18.7148i	0.348548	−	0.603703i
$962$	5.37255			0.173218
$963$	3.87642	−	3.34983i	0.124916	−	0.107947i
$964$	−82.8249			−2.66761
$965$	2.52773	−	4.37816i	0.0813705	−	0.140938i
$966$	−24.3885	−	4.11798i	−0.784686	−	0.132494i
$967$	11.9833	+	20.7558i	0.385358	+	0.667460i	0.991819	−	0.127653i	$-0.0407445\pi$
$967$	11.9833	+	20.7558i	0.385358	+	0.667460i	−0.606460	+	0.795114i	$0.707411\pi$
$968$	6.86524	+	11.8909i	0.220657	+	0.382189i
$969$	28.9340	+	77.7344i	0.929493	+	2.49719i
$970$	−3.34326	+	5.79069i	−0.107345	+	0.185928i
$971$	22.5951			0.725111			0.362556	−	0.931962i	$-0.381904\pi$
$971$	22.5951			0.725111			0.362556	+	0.931962i	$0.381904\pi$
$972$	32.3056	+	35.7781i	1.03620	+	1.14758i
$973$	−2.01597			−0.0646291
$974$	5.86450	−	10.1576i	0.187911	−	0.325471i
$975$	0.604199	+	1.62325i	0.0193499	+	0.0519856i
$976$	−2.87446	−	4.97872i	−0.0920093	−	0.159365i
$977$	4.77325	+	8.26751i	0.152710	+	0.264501i	0.932223	−	0.361885i	$-0.117867\pi$
$977$	4.77325	+	8.26751i	0.152710	+	0.264501i	−0.779513	+	0.626386i	$0.784533\pi$
$978$	−70.3320	−	11.8755i	−2.24897	−	0.379737i
$979$	12.5375	−	21.7156i	0.400701	−	0.694034i
$980$	20.1026			0.642155
$981$	7.34598	−	6.34806i	0.234539	−	0.202678i
$982$	−5.04709			−0.161059
$983$	−14.9234	+	25.8480i	−0.475981	+	0.824424i	−0.999621	−	0.0275157i	$-0.991240\pi$
$983$	−14.9234	+	25.8480i	−0.475981	+	0.824424i	0.523640	+	0.851940i	$0.324574\pi$
$984$	25.7338	−	31.1245i	0.820362	−	0.992213i
$985$	3.17715	+	5.50299i	0.101232	+	0.175340i
$986$	16.4223	+	28.4443i	0.522993	+	0.905851i
$987$	−7.58667	+	9.17594i	−0.241486	+	0.292073i
$988$	−12.2439	+	21.2071i	−0.389531	+	0.674687i
$989$	−106.898			−3.39915
$990$	−2.96466	−	15.4941i	−0.0942231	−	0.492436i
$991$	−24.1499			−0.767146			−0.383573	−	0.923511i	$-0.625307\pi$
$991$	−24.1499			−0.767146			−0.383573	+	0.923511i	$0.625307\pi$
$992$	−9.70442	+	16.8086i	−0.308116	+	0.533672i
$993$	51.5259	+	8.70011i	1.63513	+	0.276090i
$994$	9.92068	+	17.1831i	0.314665	+	0.545016i
$995$	−8.39079	−	14.5333i	−0.266006	−	0.460736i
$996$	0.974724	+	2.61871i	0.0308853	+	0.0829770i
$997$	−15.9893	+	27.6943i	−0.506387	+	0.877088i	0.493586	+	0.869697i	$0.335686\pi$
$997$	−15.9893	+	27.6943i	−0.506387	+	0.877088i	−0.999973	+	0.00739074i	$0.997647\pi$
$998$	−48.0419			−1.52074
$999$	−10.8458	−	5.95064i	−0.343145	−	0.188270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.196.2	✓	16
3.2	odd	2		1755.2.i.f.586.7		16
9.2	odd	6		5265.2.a.ba.1.2		8
9.4	even	3	inner	585.2.i.e.391.2	yes	16
9.5	odd	6		1755.2.i.f.1171.7		16
9.7	even	3		5265.2.a.bf.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.2	✓	16	1.1	even	1	trivial
585.2.i.e.391.2	yes	16	9.4	even	3	inner
1755.2.i.f.586.7		16	3.2	odd	2
1755.2.i.f.1171.7		16	9.5	odd	6
5265.2.a.ba.1.2		8	9.2	odd	6
5265.2.a.bf.1.7		8	9.7	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12831 + 1.95429i) q^{2} +(-0.604199 - 1.62325i) q^{3} +(-1.54617 - 2.67805i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.85403 + 0.650751i) q^{6} +(-0.353285 + 0.611908i) q^{7} +2.46502 q^{8} +(-2.26989 + 1.96153i) q^{9} +O(q^{10})\)	\(q+(-1.12831 + 1.95429i) q^{2} +(-0.604199 - 1.62325i) q^{3} +(-1.54617 - 2.67805i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.85403 + 0.650751i) q^{6} +(-0.353285 + 0.611908i) q^{7} +2.46502 q^{8} +(-2.26989 + 1.96153i) q^{9} -2.25662 q^{10} +(1.16510 - 2.01802i) q^{11} +(-3.41295 + 4.12791i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.797232 - 1.38085i) q^{14} +(1.10368 - 1.33488i) q^{15} +(0.311036 - 0.538731i) q^{16} +6.04736 q^{17} +(-1.27227 - 6.64925i) q^{18} -7.91884 q^{19} +(1.54617 - 2.67805i) q^{20} +(1.20674 + 0.203756i) q^{21} +(2.62920 + 4.55391i) q^{22} +(4.47799 + 7.75611i) q^{23} +(-1.48936 - 4.00135i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.25662 q^{26} +(4.55552 + 2.49944i) q^{27} +2.18496 q^{28} +(1.20340 - 2.08435i) q^{29} +(1.36345 + 3.66307i) q^{30} +(1.53216 + 2.65378i) q^{31} +(3.16691 + 5.48526i) q^{32} +(-3.97971 - 0.671971i) q^{33} +(-6.82331 + 11.8183i) q^{34} -0.706571 q^{35} +(8.76273 + 3.04600i) q^{36} -2.38079 q^{37} +(8.93492 - 15.4757i) q^{38} +(1.10368 - 1.33488i) q^{39} +(1.23251 + 2.13477i) q^{40} +(4.72945 + 8.19164i) q^{41} +(-1.75977 + 2.12841i) q^{42} +(-5.96795 + 10.3368i) q^{43} -7.20582 q^{44} +(-2.83368 - 0.985013i) q^{45} -20.2103 q^{46} +(-4.86433 + 8.42527i) q^{47} +(-1.06242 - 0.179389i) q^{48} +(3.25038 + 5.62982i) q^{49} +(-1.12831 - 1.95429i) q^{50} +(-3.65381 - 9.81639i) q^{51} +(1.54617 - 2.67805i) q^{52} +5.90968 q^{53} +(-10.0247 + 6.08269i) q^{54} +2.33021 q^{55} +(-0.870856 + 1.50837i) q^{56} +(4.78456 + 12.8543i) q^{57} +(2.71562 + 4.70359i) q^{58} +(-1.48719 - 2.57588i) q^{59} +(-5.28135 - 0.891752i) q^{60} +(4.62078 - 8.00343i) q^{61} -6.91501 q^{62} +(-0.398361 - 2.08194i) q^{63} -13.0489 q^{64} +(-0.500000 + 0.866025i) q^{65} +(5.80358 - 7.01933i) q^{66} +(0.847241 + 1.46746i) q^{67} +(-9.35028 - 16.1952i) q^{68} +(9.88452 - 11.9551i) q^{69} +(0.797232 - 1.38085i) q^{70} -12.4439 q^{71} +(-5.59532 + 4.83522i) q^{72} +4.88899 q^{73} +(2.68628 - 4.65277i) q^{74} +(1.70788 + 0.288374i) q^{75} +(12.2439 + 21.2071i) q^{76} +(0.823229 + 1.42587i) q^{77} +(1.36345 + 3.66307i) q^{78} +(5.51270 - 9.54827i) q^{79} +0.622073 q^{80} +(1.30477 - 8.90492i) q^{81} -21.3452 q^{82} +(0.260845 - 0.451797i) q^{83} +(-1.32015 - 3.54674i) q^{84} +(3.02368 + 5.23717i) q^{85} +(-13.4674 - 23.3262i) q^{86} +(-4.11051 - 0.694057i) q^{87} +(2.87201 - 4.97447i) q^{88} +10.7608 q^{89} +(5.12228 - 4.42644i) q^{90} -0.706571 q^{91} +(13.8475 - 23.9846i) q^{92} +(3.38201 - 4.09049i) q^{93} +(-10.9770 - 19.0127i) q^{94} +(-3.95942 - 6.85792i) q^{95} +(6.99050 - 8.45488i) q^{96} +(1.48153 - 2.56609i) q^{97} -14.6698 q^{98} +(1.31376 + 6.86607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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