LMFDB - Embedded newform 585.2.i.g.196.12

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:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.12
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34334 - 2.32674i) q^{2} +(-1.55252 + 0.767915i) q^{3} +(-2.60914 - 4.51916i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.298825 + 4.64387i) q^{6} +(1.78091 - 3.08463i) q^{7} -8.64648 q^{8} +(1.82061 - 2.38440i) q^{9} +O(q^{10})$	\(q+(1.34334 - 2.32674i) q^{2} +(-1.55252 + 0.767915i) q^{3} +(-2.60914 - 4.51916i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.298825 + 4.64387i) q^{6} +(1.78091 - 3.08463i) q^{7} -8.64648 q^{8} +(1.82061 - 2.38440i) q^{9} -2.68668 q^{10} +(-0.198432 + 0.343695i) q^{11} +(7.52105 + 5.01247i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-4.78475 - 8.28744i) q^{14} +(1.44129 + 0.960561i) q^{15} +(-6.39691 + 11.0798i) q^{16} -6.55451 q^{17} +(-3.10217 - 7.43915i) q^{18} -0.842552 q^{19} +(-2.60914 + 4.51916i) q^{20} +(-0.396162 + 6.15654i) q^{21} +(0.533125 + 0.923399i) q^{22} +(3.60683 + 6.24721i) q^{23} +(13.4238 - 6.63976i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.68668 q^{26} +(-0.995515 + 5.09990i) q^{27} -18.5866 q^{28} +(1.75757 - 3.04421i) q^{29} +(4.17112 - 2.06314i) q^{30} +(-4.68120 - 8.10808i) q^{31} +(8.54000 + 14.7917i) q^{32} +(0.0441410 - 0.685970i) q^{33} +(-8.80495 + 15.2506i) q^{34} -3.56183 q^{35} +(-15.5257 - 2.00641i) q^{36} -0.0513329 q^{37} +(-1.13184 + 1.96040i) q^{38} +(-1.44129 - 0.960561i) q^{39} +(4.32324 + 7.48807i) q^{40} +(1.03774 + 1.79742i) q^{41} +(13.7925 + 9.19210i) q^{42} +(1.94256 - 3.36462i) q^{43} +2.07095 q^{44} +(-2.97526 - 0.384497i) q^{45} +19.3808 q^{46} +(1.90984 - 3.30794i) q^{47} +(1.42298 - 22.1138i) q^{48} +(-2.84331 - 4.92476i) q^{49} +(1.34334 + 2.32674i) q^{50} +(10.1760 - 5.03330i) q^{51} +(2.60914 - 4.51916i) q^{52} +7.12862 q^{53} +(10.5288 + 9.16721i) q^{54} +0.396864 q^{55} +(-15.3986 + 26.6712i) q^{56} +(1.30808 - 0.647009i) q^{57} +(-4.72204 - 8.17882i) q^{58} +(0.329135 + 0.570079i) q^{59} +(0.580399 - 9.01966i) q^{60} +(6.12603 - 10.6106i) q^{61} -25.1538 q^{62} +(-4.11265 - 9.86234i) q^{63} +20.3009 q^{64} +(0.500000 - 0.866025i) q^{65} +(-1.53678 - 1.02420i) q^{66} +(-3.49456 - 6.05276i) q^{67} +(17.1016 + 29.6208i) q^{68} +(-10.3970 - 6.92916i) q^{69} +(-4.78475 + 8.28744i) q^{70} -6.39870 q^{71} +(-15.7419 + 20.6167i) q^{72} -0.841345 q^{73} +(-0.0689576 + 0.119438i) q^{74} +(0.111224 - 1.72848i) q^{75} +(2.19833 + 3.80763i) q^{76} +(0.706781 + 1.22418i) q^{77} +(-4.17112 + 2.06314i) q^{78} +(6.87775 - 11.9126i) q^{79} +12.7938 q^{80} +(-2.37073 - 8.68214i) q^{81} +5.57615 q^{82} +(2.20902 - 3.82614i) q^{83} +(28.8560 - 14.2729i) q^{84} +(3.27725 + 5.67637i) q^{85} +(-5.21905 - 9.03966i) q^{86} +(-0.390970 + 6.07585i) q^{87} +(1.71574 - 2.97175i) q^{88} -11.3850 q^{89} +(-4.89141 + 6.40613i) q^{90} +3.56183 q^{91} +(18.8214 - 32.5997i) q^{92} +(13.4940 + 8.99316i) q^{93} +(-5.13114 - 8.88739i) q^{94} +(0.421276 + 0.729672i) q^{95} +(-24.6173 - 16.4064i) q^{96} +(-8.64012 + 14.9651i) q^{97} -15.2782 q^{98} +(0.458237 + 1.09888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * 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 $

$2$	1.34334	−	2.32674i	0.949886	−	1.64525i	0.204228	−	0.978923i	$-0.434532\pi$
$2$	1.34334	−	2.32674i	0.949886	−	1.64525i	0.745659	−	0.666328i	$-0.232135\pi$
$3$	−1.55252	+	0.767915i	−0.896346	+	0.443356i
$3$	−1.55252	+	0.767915i	−0.896346	+	0.443356i
$4$	−2.60914	−	4.51916i	−1.30457	−	2.25958i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.298825	+	4.64387i	−0.121995	+	1.89585i
$7$	1.78091	−	3.08463i	0.673122	−	1.16588i	−0.303892	−	0.952707i	$-0.598286\pi$
$7$	1.78091	−	3.08463i	0.673122	−	1.16588i	0.977014	−	0.213175i	$-0.0683806\pi$
$8$	−8.64648			−3.05699
$9$	1.82061	−	2.38440i	0.606871	−	0.794800i
$10$	−2.68668			−0.849604
$11$	−0.198432	+	0.343695i	−0.0598295	+	0.103628i	−0.894389	−	0.447290i	$-0.852389\pi$
$11$	−0.198432	+	0.343695i	−0.0598295	+	0.103628i	0.834559	+	0.550918i	$0.185722\pi$
$12$	7.52105	+	5.01247i	2.17114	+	1.44698i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−4.78475	−	8.28744i	−1.27878	−	2.21491i
$15$	1.44129	+	0.960561i	0.372140	+	0.248016i
$16$	−6.39691	+	11.0798i	−1.59923	+	2.76994i
$17$	−6.55451			−1.58970			−0.794851	−	0.606805i	$-0.792451\pi$
$17$	−6.55451			−1.58970			−0.794851	+	0.606805i	$0.792451\pi$
$18$	−3.10217	−	7.43915i	−0.731188	−	1.75343i
$19$	−0.842552			−0.193295			−0.0966474	−	0.995319i	$-0.530812\pi$
$19$	−0.842552			−0.193295			−0.0966474	+	0.995319i	$0.530812\pi$
$20$	−2.60914	+	4.51916i	−0.583421	+	1.01051i
$21$	−0.396162	+	6.15654i	−0.0864496	+	1.34347i
$22$	0.533125	+	0.923399i	0.113663	+	0.196869i
$23$	3.60683	+	6.24721i	0.752076	+	1.30263i	0.946815	+	0.321779i	$0.104281\pi$
$23$	3.60683	+	6.24721i	0.752076	+	1.30263i	−0.194739	+	0.980855i	$0.562386\pi$
$24$	13.4238	−	6.63976i	2.74012	−	1.35534i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.68668			0.526902
$27$	−0.995515	+	5.09990i	−0.191587	+	0.981476i
$28$	−18.5866			−3.51254
$29$	1.75757	−	3.04421i	0.326373	−	0.565295i	−0.655416	−	0.755268i	$-0.727507\pi$
$29$	1.75757	−	3.04421i	0.326373	−	0.565295i	0.981789	+	0.189973i	$0.0608401\pi$
$30$	4.17112	−	2.06314i	0.761539	−	0.376677i
$31$	−4.68120	−	8.10808i	−0.840769	−	1.45625i	−0.889246	−	0.457430i	$-0.848770\pi$
$31$	−4.68120	−	8.10808i	−0.840769	−	1.45625i	0.0484771	−	0.998824i	$-0.484563\pi$
$32$	8.54000	+	14.7917i	1.50967	+	2.61483i
$33$	0.0441410	−	0.685970i	0.00768395	−	0.119412i
$34$	−8.80495	+	15.2506i	−1.51004	+	2.61546i
$35$	−3.56183			−0.602059
$36$	−15.5257	−	2.00641i	−2.58762	−	0.334402i
$37$	−0.0513329			−0.00843907			−0.00421954	−	0.999991i	$-0.501343\pi$
$37$	−0.0513329			−0.00843907			−0.00421954	+	0.999991i	$0.501343\pi$
$38$	−1.13184	+	1.96040i	−0.183608	+	0.318018i
$39$	−1.44129	−	0.960561i	−0.230791	−	0.153813i
$40$	4.32324	+	7.48807i	0.683564	+	1.18397i
$41$	1.03774	+	1.79742i	0.162068	+	0.280709i	0.935610	−	0.353035i	$-0.114850\pi$
$41$	1.03774	+	1.79742i	0.162068	+	0.280709i	−0.773542	+	0.633745i	$0.781517\pi$
$42$	13.7925	+	9.19210i	2.12822	+	1.41837i
$43$	1.94256	−	3.36462i	0.296238	−	0.513099i	−0.679034	−	0.734107i	$-0.737601\pi$
$43$	1.94256	−	3.36462i	0.296238	−	0.513099i	0.975272	+	0.221008i	$0.0709345\pi$
$44$	2.07095			0.312207
$45$	−2.97526	−	0.384497i	−0.443525	−	0.0573174i
$46$	19.3808			2.85755
$47$	1.90984	−	3.30794i	0.278579	−	0.482513i	−0.692453	−	0.721463i	$-0.743470\pi$
$47$	1.90984	−	3.30794i	0.278579	−	0.482513i	0.971032	+	0.238950i	$0.0768033\pi$
$48$	1.42298	−	22.1138i	0.205390	−	3.19185i
$49$	−2.84331	−	4.92476i	−0.406187	−	0.703537i
$50$	1.34334	+	2.32674i	0.189977	+	0.329050i
$51$	10.1760	−	5.03330i	1.42492	−	0.704804i
$52$	2.60914	−	4.51916i	0.361822	−	0.626694i
$53$	7.12862			0.979191			0.489596	−	0.871950i	$-0.337144\pi$
$53$	7.12862			0.979191			0.489596	+	0.871950i	$0.337144\pi$
$54$	10.5288	+	9.16721i	1.43279	+	1.24750i
$55$	0.396864			0.0535132
$56$	−15.3986	+	26.6712i	−2.05773	+	3.56409i
$57$	1.30808	−	0.647009i	0.173259	−	0.0856984i
$58$	−4.72204	−	8.17882i	−0.620035	−	1.07393i
$59$	0.329135	+	0.570079i	0.0428497	+	0.0742179i	0.886655	−	0.462432i	$-0.153023\pi$
$59$	0.329135	+	0.570079i	0.0428497	+	0.0742179i	−0.843805	+	0.536650i	$0.819690\pi$
$60$	0.580399	−	9.01966i	0.0749292	−	1.16443i
$61$	6.12603	−	10.6106i	0.784358	−	1.35855i	−0.145024	−	0.989428i	$-0.546326\pi$
$61$	6.12603	−	10.6106i	0.784358	−	1.35855i	0.929382	−	0.369120i	$-0.120341\pi$
$62$	−25.1538			−3.19454
$63$	−4.11265	−	9.86234i	−0.518145	−	1.24254i
$64$	20.3009			2.53761
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	−1.53678	−	1.02420i	−0.189164	−	0.126070i
$67$	−3.49456	−	6.05276i	−0.426929	−	0.739462i	0.569670	−	0.821874i	$-0.307071\pi$
$67$	−3.49456	−	6.05276i	−0.426929	−	0.739462i	−0.996598	+	0.0824114i	$0.973738\pi$
$68$	17.1016	+	29.6208i	2.07387	+	3.59206i
$69$	−10.3970	−	6.92916i	−1.25165	−	0.834173i
$70$	−4.78475	+	8.28744i	−0.571888	+	0.990538i
$71$	−6.39870			−0.759386			−0.379693	−	0.925112i	$-0.623970\pi$
$71$	−6.39870			−0.759386			−0.379693	+	0.925112i	$0.623970\pi$
$72$	−15.7419	+	20.6167i	−1.85520	+	2.42970i
$73$	−0.841345			−0.0984720			−0.0492360	−	0.998787i	$-0.515679\pi$
$73$	−0.841345			−0.0984720			−0.0492360	+	0.998787i	$0.515679\pi$
$74$	−0.0689576	+	0.119438i	−0.00801616	+	0.0138844i
$75$	0.111224	−	1.72848i	0.0128431	−	0.199587i
$76$	2.19833	+	3.80763i	0.252166	+	0.436765i
$77$	0.706781	+	1.22418i	0.0805452	+	0.139508i
$78$	−4.17112	+	2.06314i	−0.472286	+	0.233605i
$79$	6.87775	−	11.9126i	0.773807	−	1.34027i	−0.161656	−	0.986847i	$-0.551683\pi$
$79$	6.87775	−	11.9126i	0.773807	−	1.34027i	0.935463	−	0.353425i	$-0.114983\pi$
$80$	12.7938			1.43039
$81$	−2.37073	−	8.68214i	−0.263415	−	0.964683i
$82$	5.57615			0.615783
$83$	2.20902	−	3.82614i	0.242472	−	0.419974i	−0.718946	−	0.695066i	$-0.755375\pi$
$83$	2.20902	−	3.82614i	0.242472	−	0.419974i	0.961418	+	0.275092i	$0.0887084\pi$
$84$	28.8560	−	14.2729i	3.14845	−	1.55730i
$85$	3.27725	+	5.67637i	0.355468	+	0.615689i
$86$	−5.21905	−	9.03966i	−0.562785	−	0.974772i
$87$	−0.390970	+	6.07585i	−0.0419164	+	0.651399i
$88$	1.71574	−	2.97175i	0.182898	−	0.316789i
$89$	−11.3850			−1.20681			−0.603404	−	0.797435i	$-0.706189\pi$
$89$	−11.3850			−1.20681			−0.603404	+	0.797435i	$0.706189\pi$
$90$	−4.89141	+	6.40613i	−0.515600	+	0.675266i
$91$	3.56183			0.373381
$92$	18.8214	−	32.5997i	1.96227	−	3.39875i
$93$	13.4940	+	8.99316i	1.39926	+	0.932547i
$94$	−5.13114	−	8.88739i	−0.529236	−	0.916664i
$95$	0.421276	+	0.729672i	0.0432220	+	0.0748627i
$96$	−24.6173	−	16.4064i	−2.51249	−	1.67447i
$97$	−8.64012	+	14.9651i	−0.877271	+	1.51948i	−0.0229474	+	0.999737i	$0.507305\pi$
$97$	−8.64012	+	14.9651i	−0.877271	+	1.51948i	−0.854324	+	0.519741i	$0.826028\pi$
$98$	−15.2782			−1.54333
$99$	0.458237	+	1.09888i	0.0460546	+	0.110441i
$100$	5.21827			0.521827
$101$	4.37858	−	7.58392i	0.435685	−	0.754628i	−0.561666	−	0.827364i	$-0.689840\pi$
$101$	4.37858	−	7.58392i	0.435685	−	0.754628i	0.997351	+	0.0727355i	$0.0231729\pi$
$102$	1.95865	−	30.4383i	0.193935	−	3.01384i
$103$	−10.0184	−	17.3524i	−0.987144	−	1.70978i	−0.631990	−	0.774976i	$-0.717762\pi$
$103$	−10.0184	−	17.3524i	−0.987144	−	1.70978i	−0.355154	−	0.934808i	$-0.615572\pi$
$104$	−4.32324	−	7.48807i	−0.423929	−	0.734266i
$105$	5.52980	−	2.73518i	0.539653	−	0.266926i
$106$	9.57618	−	16.5864i	0.930120	−	1.61102i
$107$	14.0578			1.35902			0.679508	−	0.733669i	$-0.262193\pi$
$107$	14.0578			1.35902			0.679508	+	0.733669i	$0.262193\pi$
$108$	25.6447	−	8.80744i	2.46766	−	0.847496i
$109$	20.5480			1.96814			0.984071	−	0.177777i	$-0.0568905\pi$
$109$	20.5480			1.96814			0.984071	+	0.177777i	$0.0568905\pi$
$110$	0.533125	−	0.923399i	0.0508314	−	0.0880426i
$111$	0.0796951	−	0.0394193i	0.00756433	−	0.00374151i
$112$	22.7847	+	39.4643i	2.15295	+	3.72902i
$113$	4.75111	+	8.22917i	0.446947	+	0.774135i	0.998186	−	0.0602127i	$-0.0191779\pi$
$113$	4.75111	+	8.22917i	0.446947	+	0.774135i	−0.551239	+	0.834348i	$0.685845\pi$
$114$	0.251775	−	3.91270i	0.0235809	−	0.366458i
$115$	3.60683	−	6.24721i	0.336339	−	0.582555i
$116$	−18.3430			−1.70310
$117$	2.97526	+	0.384497i	0.275063	+	0.0355468i
$118$	1.76856			0.162809
$119$	−11.6730	+	20.2183i	−1.07006	+	1.85340i
$120$	−12.4621	−	8.30547i	−1.13763	−	0.758183i
$121$	5.42125	+	9.38988i	0.492841	+	0.853625i
$122$	−16.4587	−	28.5073i	−1.49010	−	2.58093i
$123$	−2.99137	−	1.99362i	−0.269723	−	0.179759i
$124$	−24.4278	+	42.3102i	−2.19368	+	3.79957i
$125$	1.00000			0.0894427
$126$	−28.4718	−	3.67945i	−2.53647	−	0.327791i
$127$	9.46555			0.839932			0.419966	−	0.907540i	$-0.362042\pi$
$127$	9.46555			0.839932			0.419966	+	0.907540i	$0.362042\pi$
$128$	10.1911	−	17.6515i	0.900773	−	1.56018i
$129$	−0.432120	+	6.71534i	−0.0380461	+	0.591253i
$130$	−1.34334	−	2.32674i	−0.117819	−	0.204068i
$131$	−0.769116	−	1.33215i	−0.0671980	−	0.116390i	0.830469	−	0.557065i	$-0.188073\pi$
$131$	−0.769116	−	1.33215i	−0.0671980	−	0.116390i	−0.897667	+	0.440675i	$0.854739\pi$
$132$	−3.21518	+	1.59031i	−0.279845	+	0.138419i
$133$	−1.50051	+	2.59897i	−0.130111	+	0.225359i
$134$	−18.7776			−1.62214
$135$	4.91440	−	1.68781i	0.422964	−	0.145263i
$136$	56.6734			4.85971
$137$	−10.3559	+	17.9369i	−0.884760	+	1.53245i	−0.0387718	+	0.999248i	$0.512345\pi$
$137$	−10.3559	+	17.9369i	−0.884760	+	1.53245i	−0.845988	+	0.533201i	$0.820989\pi$
$138$	−30.0890	+	14.8828i	−2.56135	+	1.26691i
$139$	−1.35377	−	2.34480i	−0.114825	−	0.198883i	0.802885	−	0.596134i	$-0.203297\pi$
$139$	−1.35377	−	2.34480i	−0.114825	−	0.198883i	−0.917710	+	0.397251i	$0.869964\pi$
$140$	9.29330	+	16.0965i	0.785427	+	1.36040i
$141$	−0.424841	+	6.60222i	−0.0357781	+	0.556008i
$142$	−8.59565	+	14.8881i	−0.721331	+	1.24938i
$143$	−0.396864			−0.0331875
$144$	14.7723	+	35.4248i	1.23103	+	2.95207i
$145$	−3.51515			−0.291917
$146$	−1.13021	+	1.95759i	−0.0935372	+	0.162011i
$147$	8.19608	+	5.46235i	0.676002	+	0.450527i
$148$	0.133934	+	0.231981i	0.0110093	+	0.0190687i
$149$	−4.32561	−	7.49218i	−0.354368	−	0.613783i	0.632642	−	0.774445i	$-0.281971\pi$
$149$	−4.32561	−	7.49218i	−0.354368	−	0.613783i	−0.987010	+	0.160661i	$0.948637\pi$
$150$	−3.87230	−	2.58072i	−0.316172	−	0.210715i
$151$	6.48951	−	11.2402i	0.528109	−	0.914711i	−0.471354	−	0.881944i	$-0.656235\pi$
$151$	6.48951	−	11.2402i	0.528109	−	0.914711i	0.999463	−	0.0327673i	$-0.0104320\pi$
$152$	7.28511			0.590901
$153$	−11.9332	+	15.6286i	−0.964744	+	1.26350i
$154$	3.79780			0.306035
$155$	−4.68120	+	8.10808i	−0.376003	+	0.651257i
$156$	−0.580399	+	9.01966i	−0.0464691	+	0.722151i
$157$	7.64375	+	13.2394i	0.610038	+	1.05662i	0.991233	+	0.132122i	$0.0421791\pi$
$157$	7.64375	+	13.2394i	0.610038	+	1.05662i	−0.381196	+	0.924494i	$0.624488\pi$
$158$	−18.4783	−	32.0054i	−1.47006	−	2.54621i
$159$	−11.0673	+	5.47417i	−0.877694	+	0.434130i
$160$	8.54000	−	14.7917i	0.675146	−	1.16939i
$161$	25.6938			2.02496
$162$	−23.3858	−	6.14702i	−1.83736	−	0.482955i
$163$	−20.7390			−1.62441			−0.812203	−	0.583375i	$-0.801732\pi$
$163$	−20.7390			−1.62441			−0.812203	+	0.583375i	$0.801732\pi$
$164$	5.41521	−	9.37941i	0.422857	−	0.732409i
$165$	−0.616138	+	0.304758i	−0.0479663	+	0.0237254i
$166$	−5.93495	−	10.2796i	−0.460641	−	0.797854i
$167$	−3.97695	−	6.88828i	−0.307746	−	0.533031i	0.670123	−	0.742250i	$-0.266241\pi$
$167$	−3.97695	−	6.88828i	−0.307746	−	0.533031i	−0.977869	+	0.209219i	$0.932908\pi$
$168$	3.42541	−	53.2324i	0.264276	−	4.10697i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	17.6099			1.35062
$171$	−1.53396	+	2.00898i	−0.117305	+	0.153631i
$172$	−20.2736			−1.54585
$173$	−10.0147	+	17.3460i	−0.761406	+	1.31879i	0.180720	+	0.983535i	$0.442157\pi$
$173$	−10.0147	+	17.3460i	−0.761406	+	1.31879i	−0.942126	+	0.335259i	$0.891176\pi$
$174$	13.6117	+	9.07162i	1.03190	+	0.687718i
$175$	1.78091	+	3.08463i	0.134624	+	0.233176i
$176$	−2.53871	−	4.39717i	−0.191362	−	0.331449i
$177$	−0.948759	−	0.632309i	−0.0713131	−	0.0475272i
$178$	−15.2940	+	26.4899i	−1.14633	+	1.98550i
$179$	19.1000			1.42760			0.713801	−	0.700348i	$-0.246972\pi$
$179$	19.1000			1.42760			0.713801	+	0.700348i	$0.246972\pi$
$180$	6.02525	+	14.4489i	0.449096	+	1.07695i
$181$	−0.0807001			−0.00599839			−0.00299920	−	0.999996i	$-0.500955\pi$
$181$	−0.0807001			−0.00599839			−0.00299920	+	0.999996i	$0.500955\pi$
$182$	4.78475	−	8.28744i	0.354670	−	0.614306i
$183$	−1.36273	+	21.1774i	−0.100736	+	1.56548i
$184$	−31.1864	−	54.0164i	−2.29909	−	3.98214i
$185$	0.0256664	+	0.0444556i	0.00188703	+	0.00326844i
$186$	39.0517	−	19.3160i	2.86341	−	1.41632i
$187$	1.30063	−	2.25275i	0.0951111	−	0.164737i
$188$	−19.9321			−1.45370
$189$	13.9584	+	12.1533i	1.01532	+	0.884021i
$190$	2.26367			0.164224
$191$	7.27850	−	12.6067i	0.526654	−	0.912191i	−0.472864	−	0.881136i	$-0.656780\pi$
$191$	7.27850	−	12.6067i	0.526654	−	0.912191i	0.999518	−	0.0310558i	$-0.00988694\pi$
$192$	−31.5175	+	15.5894i	−2.27458	+	1.12507i
$193$	−2.56732	−	4.44672i	−0.184799	−	0.320082i	0.758709	−	0.651429i	$-0.225830\pi$
$193$	−2.56732	−	4.44672i	−0.184799	−	0.320082i	−0.943509	+	0.331347i	$0.892497\pi$
$194$	23.2133	+	40.2066i	1.66662	+	2.88666i
$195$	−0.111224	+	1.72848i	−0.00796494	+	0.123779i
$196$	−14.8372	+	25.6987i	−1.05980	+	1.83562i
$197$	−2.44266			−0.174033			−0.0870163	−	0.996207i	$-0.527733\pi$
$197$	−2.44266			−0.174033			−0.0870163	+	0.996207i	$0.527733\pi$
$198$	3.17237	+	0.409970i	0.225450	+	0.0291353i
$199$	12.3837			0.877854			0.438927	−	0.898523i	$-0.355359\pi$
$199$	12.3837			0.877854			0.438927	+	0.898523i	$0.355359\pi$
$200$	4.32324	−	7.48807i	0.305699	−	0.529487i
$201$	10.0734	+	6.71348i	0.710521	+	0.473533i
$202$	−11.7639	−	20.3756i	−0.827702	−	1.43362i
$203$	−6.26017	−	10.8429i	−0.439378	−	0.761025i
$204$	−49.2968	−	32.8543i	−3.45147	−	2.30026i
$205$	1.03774	−	1.79742i	0.0724788	−	0.125537i
$206$	−53.8327			−3.75070
$207$	21.4625	+	2.77363i	1.49175	+	0.192781i
$208$	−12.7938			−0.887092
$209$	0.167189	−	0.289581i	0.0115647	−	0.0200307i
$210$	1.06436	−	16.5407i	0.0734480	−	1.14141i
$211$	1.66296	+	2.88033i	0.114483	+	0.198290i	0.917573	−	0.397568i	$-0.130146\pi$
$211$	1.66296	+	2.88033i	0.114483	+	0.198290i	−0.803090	+	0.595858i	$0.796812\pi$
$212$	−18.5995	−	32.2154i	−1.27742	−	2.21256i
$213$	9.93409	−	4.91366i	0.680673	−	0.336678i
$214$	18.8844	−	32.7087i	1.29091	−	2.23592i
$215$	−3.88512			−0.264963
$216$	8.60770	−	44.0962i	0.585680	−	3.00036i
$217$	−33.3473			−2.26376
$218$	27.6030	−	47.8098i	1.86951	−	3.23809i
$219$	1.30620	−	0.646081i	0.0882649	−	0.0436581i
$220$	−1.03547	−	1.79349i	−0.0698116	−	0.120917i
$221$	−3.27725	−	5.67637i	−0.220452	−	0.381834i
$222$	0.0153395	−	0.238383i	0.00102952	−	0.0159992i
$223$	−5.00891	+	8.67569i	−0.335422	+	0.580967i	−0.983566	−	0.180551i	$-0.942212\pi$
$223$	−5.00891	+	8.67569i	−0.335422	+	0.580967i	0.648144	+	0.761518i	$0.275545\pi$
$224$	60.8360			4.06478
$225$	1.15464	+	2.76890i	0.0769763	+	0.184593i
$226$	25.5295			1.69820
$227$	−0.739868	+	1.28149i	−0.0491068	+	0.0850554i	−0.889534	−	0.456869i	$-0.848971\pi$
$227$	−0.739868	+	1.28149i	−0.0491068	+	0.0850554i	0.840427	+	0.541924i	$0.182304\pi$
$228$	−6.33688	−	4.22327i	−0.419670	−	0.279693i
$229$	4.10619	+	7.11214i	0.271345	+	0.469983i	0.969206	−	0.246249i	$-0.0791983\pi$
$229$	4.10619	+	7.11214i	0.271345	+	0.469983i	−0.697862	+	0.716233i	$0.745865\pi$
$230$	−9.69041	−	16.7843i	−0.638967	−	1.10672i
$231$	−2.03736	−	1.35781i	−0.134048	−	0.0893375i
$232$	−15.1968	+	26.3217i	−0.997720	+	1.72810i
$233$	−9.30808			−0.609793			−0.304896	−	0.952386i	$-0.598622\pi$
$233$	−9.30808			−0.609793			−0.304896	+	0.952386i	$0.598622\pi$
$234$	4.89141	−	6.40613i	0.319762	−	0.418782i
$235$	−3.81968			−0.249168
$236$	1.71752	−	2.97483i	0.111801	−	0.193645i
$237$	−1.52995	+	23.7760i	−0.0993806	+	1.54442i
$238$	31.3617	+	54.3201i	2.03288	+	3.52105i
$239$	−10.4405	−	18.0835i	−0.675340	−	1.16972i	−0.976370	−	0.216108i	$-0.930664\pi$
$239$	−10.4405	−	18.0835i	−0.675340	−	1.16972i	0.301030	−	0.953615i	$-0.402670\pi$
$240$	−19.8626	+	9.82457i	−1.28213	+	0.634173i
$241$	4.04458	−	7.00541i	0.260534	−	0.451258i	−0.705850	−	0.708361i	$-0.749435\pi$
$241$	4.04458	−	7.00541i	0.260534	−	0.451258i	0.966384	+	0.257103i	$0.0827680\pi$
$242$	29.1304			1.87257
$243$	10.3477	+	11.6586i	0.663808	+	0.747903i
$244$	−63.9346			−4.09299
$245$	−2.84331	+	4.92476i	−0.181653	+	0.314631i
$246$	−8.65707	+	4.28201i	−0.551955	+	0.273011i
$247$	−0.421276	−	0.729672i	−0.0268052	−	0.0464279i
$248$	40.4759	+	70.1064i	2.57022	+	4.45176i
$249$	−0.491394	+	7.63649i	−0.0311409	+	0.483943i
$250$	1.34334	−	2.32674i	0.0849604	−	0.147156i
$251$	0.448016			0.0282785			0.0141393	−	0.999900i	$-0.495499\pi$
$251$	0.448016			0.0282785			0.0141393	+	0.999900i	$0.495499\pi$
$252$	−33.8390	+	44.3179i	−2.13166	+	2.79176i
$253$	−2.86284			−0.179985
$254$	12.7155	−	22.0238i	0.797840	−	1.38190i
$255$	−9.44696	−	6.29601i	−0.591592	−	0.394271i
$256$	−7.07929	−	12.2617i	−0.442456	−	0.766356i
$257$	6.17551	+	10.6963i	0.385218	+	0.667217i	0.991799	−	0.127804i	$-0.0407929\pi$
$257$	6.17551	+	10.6963i	0.385218	+	0.667217i	−0.606581	+	0.795021i	$0.707460\pi$
$258$	15.0444	+	10.0264i	0.936620	+	0.624218i
$259$	−0.0914195	+	0.158343i	−0.00568053	+	0.00983897i
$260$	−5.21827			−0.323624
$261$	−4.05875	−	9.73308i	−0.251230	−	0.602463i
$262$	−4.13274			−0.255322
$263$	−3.17187	+	5.49383i	−0.195586	+	0.338764i	−0.947092	−	0.320961i	$-0.895994\pi$
$263$	−3.17187	+	5.49383i	−0.195586	+	0.338764i	0.751507	+	0.659725i	$0.229327\pi$
$264$	−0.381664	+	5.93123i	−0.0234898	+	0.365042i
$265$	−3.56431	−	6.17357i	−0.218954	−	0.379239i
$266$	4.03141	+	6.98260i	0.247181	+	0.428131i
$267$	17.6754	−	8.74272i	1.08172	−	0.535046i
$268$	−18.2356	+	31.5850i	−1.11392	+	1.92936i
$269$	15.4273			0.940622			0.470311	−	0.882501i	$-0.344142\pi$
$269$	15.4273			0.940622			0.470311	+	0.882501i	$0.344142\pi$
$270$	2.67463	−	13.7018i	0.162773	−	0.833866i
$271$	6.48692			0.394052			0.197026	−	0.980398i	$-0.436872\pi$
$271$	6.48692			0.394052			0.197026	+	0.980398i	$0.436872\pi$
$272$	41.9286	−	72.6225i	2.54230	−	4.40338i
$273$	−5.52980	+	2.73518i	−0.334679	+	0.165541i
$274$	27.8229	+	48.1907i	1.68084	+	2.91131i
$275$	−0.198432	−	0.343695i	−0.0119659	−	0.0207256i
$276$	−4.18680	+	65.0647i	−0.252016	+	3.91644i
$277$	9.69734	−	16.7963i	0.582657	−	1.00919i	−0.412507	−	0.910955i	$-0.635347\pi$
$277$	9.69734	−	16.7963i	0.582657	−	1.00919i	0.995163	−	0.0982362i	$-0.0313201\pi$
$278$	−7.27430			−0.436283
$279$	−27.8556	−	3.59982i	−1.66767	−	0.215515i
$280$	30.7973			1.84049
$281$	−8.88187	+	15.3838i	−0.529848	+	0.917723i	0.469546	+	0.882908i	$0.344418\pi$
$281$	−8.88187	+	15.3838i	−0.529848	+	0.917723i	−0.999394	+	0.0348153i	$0.988916\pi$
$282$	14.7909	+	9.85754i	0.880787	+	0.587008i
$283$	4.21502	+	7.30063i	0.250557	+	0.433977i	0.963679	−	0.267062i	$-0.0860529\pi$
$283$	4.21502	+	7.30063i	0.250557	+	0.433977i	−0.713122	+	0.701040i	$0.752720\pi$
$284$	16.6951	+	28.9167i	0.990671	+	1.71589i
$285$	−1.21436	−	0.809323i	−0.0719327	−	0.0479402i
$286$	−0.533125	+	0.923399i	−0.0315243	+	0.0546017i
$287$	7.39250			0.436365
$288$	50.8174	+	6.56721i	2.99444	+	0.386977i
$289$	25.9616			1.52715
$290$	−4.72204	+	8.17882i	−0.277288	+	0.480277i
$291$	1.92198	−	29.8685i	0.112669	−	1.75092i
$292$	2.19518	+	3.80217i	0.128463	+	0.222505i
$293$	−1.33518	−	2.31260i	−0.0780022	−	0.135104i	0.824386	−	0.566028i	$-0.191521\pi$
$293$	−1.33518	−	2.31260i	−0.0780022	−	0.135104i	−0.902388	+	0.430925i	$0.858187\pi$
$294$	23.7196	−	11.7323i	1.38335	−	0.684243i
$295$	0.329135	−	0.570079i	0.0191630	−	0.0331913i
$296$	0.443849			0.0257982
$297$	−1.55526	−	1.35414i	−0.0902456	−	0.0785750i
$298$	−23.2431			−1.34644
$299$	−3.60683	+	6.24721i	−0.208588	+	0.361286i
$300$	−8.10145	+	4.00719i	−0.467738	+	0.231355i
$301$	−6.91907	−	11.9842i	−0.398809	−	0.690757i
$302$	−17.4353	−	30.1988i	−1.00329	−	1.73774i
$303$	−0.974009	+	15.1365i	−0.0559553	+	0.869571i
$304$	5.38973	−	9.33529i	0.309122	−	0.535416i
$305$	−12.2521			−0.701551
$306$	20.3332	+	48.7600i	1.16237	+	2.78742i
$307$	24.1596			1.37886			0.689431	−	0.724352i	$-0.257861\pi$
$307$	24.1596			1.37886			0.689431	+	0.724352i	$0.257861\pi$
$308$	3.68818	−	6.38811i	0.210153	−	0.363996i
$309$	28.8789	+	19.2466i	1.64287	+	1.09490i
$310$	12.5769	+	21.7838i	0.714321	+	1.23724i
$311$	10.1721	+	17.6185i	0.576805	+	0.999056i	0.995843	+	0.0910872i	$0.0290342\pi$
$311$	10.1721	+	17.6185i	0.576805	+	0.999056i	−0.419038	+	0.907969i	$0.637632\pi$
$312$	12.4621	+	8.30547i	0.705528	+	0.470205i
$313$	16.0856	−	27.8611i	0.909212	−	1.57480i	0.0940500	−	0.995567i	$-0.470019\pi$
$313$	16.0856	−	27.8611i	0.909212	−	1.57480i	0.815162	−	0.579233i	$-0.196648\pi$
$314$	41.0727			2.31787
$315$	−6.48471	+	8.49283i	−0.365372	+	0.478517i
$316$	−71.7799			−4.03793
$317$	3.81597	−	6.60945i	0.214326	−	0.371224i	−0.738738	−	0.673993i	$-0.764578\pi$
$317$	3.81597	−	6.60945i	0.214326	−	0.371224i	0.953064	+	0.302769i	$0.0979112\pi$
$318$	−2.13021	+	33.1044i	−0.119456	+	1.85640i
$319$	0.697518	+	1.20814i	0.0390535	+	0.0676427i
$320$	−10.1505	−	17.5811i	−0.567428	−	0.982814i
$321$	−21.8249	+	10.7952i	−1.21815	+	0.602527i
$322$	34.5156	−	59.7827i	1.92348	−	3.33156i
$323$	5.52252			0.307281
$324$	−33.0504	+	33.3666i	−1.83613	+	1.85370i
$325$	−1.00000			−0.0554700
$326$	−27.8596	+	48.2542i	−1.54300	+	2.67256i
$327$	−31.9011	+	15.7791i	−1.76414	+	0.872587i
$328$	−8.97279	−	15.5413i	−0.495440	−	0.858127i
$329$	−6.80252	−	11.7823i	−0.375035	−	0.649580i
$330$	−0.118593	+	1.84299i	−0.00652832	+	0.101453i
$331$	5.41283	−	9.37530i	0.297516	−	0.515313i	−0.678051	−	0.735015i	$-0.737175\pi$
$331$	5.41283	−	9.37530i	0.297516	−	0.515313i	0.975567	+	0.219702i	$0.0705084\pi$
$332$	−23.0546			−1.26528
$333$	−0.0934573	+	0.122398i	−0.00512143	+	0.00670738i
$334$	−21.3696			−1.16929
$335$	−3.49456	+	6.05276i	−0.190928	+	0.330698i
$336$	−65.6788	−	43.7722i	−3.58307	−	2.38797i
$337$	−2.80391	−	4.85651i	−0.152739	−	0.264551i	0.779495	−	0.626409i	$-0.215476\pi$
$337$	−2.80391	−	4.85651i	−0.152739	−	0.264551i	−0.932233	+	0.361858i	$0.882143\pi$
$338$	1.34334	+	2.32674i	0.0730682	+	0.126558i
$339$	−13.6955	−	9.12747i	−0.743836	−	0.495736i
$340$	17.1016	−	29.6208i	0.927465	−	1.60642i
$341$	3.71560			0.201211
$342$	2.61374	+	6.26788i	0.141335	+	0.338928i
$343$	4.67802			0.252590
$344$	−16.7963	+	29.0921i	−0.905597	+	1.56854i
$345$	−0.802334	+	12.4686i	−0.0431962	+	0.671289i
$346$	26.9064	+	46.6033i	1.44650	+	2.50541i
$347$	−2.15653	−	3.73522i	−0.115769	−	0.200517i	0.802318	−	0.596897i	$-0.203600\pi$
$347$	−2.15653	−	3.73522i	−0.115769	−	0.200517i	−0.918087	+	0.396379i	$0.870266\pi$
$348$	28.4778	−	14.0859i	1.52657	−	0.755081i
$349$	−3.01890	+	5.22889i	−0.161598	+	0.279896i	−0.935442	−	0.353480i	$-0.884998\pi$
$349$	−3.01890	+	5.22889i	−0.161598	+	0.279896i	0.773844	+	0.633376i	$0.218331\pi$
$350$	9.56951			0.511512
$351$	−4.91440	+	1.68781i	−0.262311	+	0.0900885i
$352$	−6.77844			−0.361292
$353$	−2.79366	+	4.83876i	−0.148691	+	0.257541i	−0.930744	−	0.365671i	$-0.880839\pi$
$353$	−2.79366	+	4.83876i	−0.148691	+	0.257541i	0.782053	+	0.623212i	$0.214173\pi$
$354$	−2.74572	+	1.35811i	−0.145934	+	0.0721825i
$355$	3.19935	+	5.54144i	0.169804	+	0.294109i
$356$	29.7050	+	51.4506i	1.57436	+	2.72688i
$357$	2.59665	−	40.3531i	0.137429	−	2.13571i
$358$	25.6579	−	44.4407i	1.35606	−	2.34877i
$359$	−2.02322			−0.106781			−0.0533907	−	0.998574i	$-0.517003\pi$
$359$	−2.02322			−0.106781			−0.0533907	+	0.998574i	$0.517003\pi$
$360$	25.7255	+	3.32455i	1.35585	+	0.175219i
$361$	−18.2901			−0.962637
$362$	−0.108408	+	0.187768i	−0.00569779	+	0.00986886i
$363$	−15.6272	−	10.4149i	−0.820216	−	0.546640i
$364$	−9.29330	−	16.0965i	−0.487101	−	0.843684i
$365$	0.420672	+	0.728626i	0.0220190	+	0.0381380i
$366$	47.4436	+	31.6192i	2.47992	+	1.65276i
$367$	−1.17444	+	2.03418i	−0.0613051	+	0.106184i	−0.895049	−	0.445968i	$-0.852860\pi$
$367$	−1.17444	+	2.03418i	−0.0613051	+	0.106184i	0.833744	+	0.552151i	$0.186193\pi$
$368$	−92.2903			−4.81096
$369$	6.17508	+	0.798015i	0.321462	+	0.0415430i
$370$	0.137915			0.00716987
$371$	12.6955	−	21.9892i	0.659116	−	1.14162i
$372$	5.43393	−	84.4457i	0.281736	−	4.37830i
$373$	13.9026	+	24.0799i	0.719848	+	1.24681i	0.961060	+	0.276340i	$0.0891216\pi$
$373$	13.9026	+	24.0799i	0.719848	+	1.24681i	−0.241212	+	0.970472i	$0.577545\pi$
$374$	−3.49437	−	6.05242i	−0.180690	−	0.312963i
$375$	−1.55252	+	0.767915i	−0.0801716	+	0.0396550i
$376$	−16.5134	+	28.6020i	−0.851613	+	1.47504i
$377$	3.51515			0.181039
$378$	47.0284	−	16.1515i	2.41888	−	0.830743i
$379$	−0.286636			−0.0147235			−0.00736176	−	0.999973i	$-0.502343\pi$
$379$	−0.286636			−0.0147235			−0.00736176	+	0.999973i	$0.502343\pi$
$380$	2.19833	−	3.80763i	0.112772	−	0.195327i
$381$	−14.6954	+	7.26874i	−0.752869	+	0.372389i
$382$	−19.5550	−	33.8703i	−1.00052	−	1.73296i
$383$	17.1374	+	29.6828i	0.875678	+	1.51672i	0.856039	+	0.516912i	$0.172918\pi$
$383$	17.1374	+	29.6828i	0.875678	+	1.51672i	0.0196394	+	0.999807i	$0.493748\pi$
$384$	−2.26699	+	35.2301i	−0.115687	+	1.79783i
$385$	0.706781	−	1.22418i	0.0360209	−	0.0623900i
$386$	−13.7951			−0.702154
$387$	−4.48594	−	10.7575i	−0.228033	−	0.546835i
$388$	90.1730			4.57784
$389$	−17.0633	+	29.5546i	−0.865146	+	1.49848i	0.00175708	+	0.999998i	$0.499441\pi$
$389$	−17.0633	+	29.5546i	−0.865146	+	1.49848i	−0.866903	+	0.498478i	$0.833893\pi$
$390$	3.87230	+	2.58072i	0.196081	+	0.130680i
$391$	−23.6410	−	40.9474i	−1.19558	−	2.07080i
$392$	24.5846	+	42.5818i	1.24171	+	2.15071i
$393$	2.21704	+	1.47757i	0.111835	+	0.0745333i
$394$	−3.28133	+	5.68344i	−0.165311	+	0.286327i
$395$	−13.7555			−0.692114
$396$	3.77039	−	4.93796i	0.189469	−	0.248142i
$397$	17.1397			0.860216			0.430108	−	0.902777i	$-0.358475\pi$
$397$	17.1397			0.860216			0.430108	+	0.902777i	$0.358475\pi$
$398$	16.6355	−	28.8135i	0.833861	−	1.44429i
$399$	0.333787	−	5.18720i	0.0167103	−	0.259685i
$400$	−6.39691	−	11.0798i	−0.319846	−	0.553989i
$401$	−3.02121	−	5.23289i	−0.150872	−	0.261318i	0.780676	−	0.624936i	$-0.214875\pi$
$401$	−3.02121	−	5.23289i	−0.150872	−	0.261318i	−0.931548	+	0.363618i	$0.881541\pi$
$402$	29.1525	−	14.4196i	1.45399	−	0.719183i
$403$	4.68120	−	8.10808i	0.233187	−	0.403892i
$404$	−45.6972			−2.27352
$405$	−6.33359	+	6.39419i	−0.314719	+	0.317730i
$406$	−33.6382			−1.66944
$407$	0.0101861	−	0.0176428i	0.000504906	−	0.000874523i
$408$	−87.9864	+	43.5204i	−4.35598	+	2.15458i
$409$	7.07795	+	12.2594i	0.349982	+	0.606187i	0.986246	−	0.165285i	$-0.0528544\pi$
$409$	7.07795	+	12.2594i	0.349982	+	0.606187i	−0.636264	+	0.771471i	$0.719521\pi$
$410$	−2.78808	−	4.82909i	−0.137693	−	0.238492i
$411$	2.30365	−	35.7997i	0.113630	−	1.76587i
$412$	−52.2788	+	90.5496i	−2.57559	+	4.46106i
$413$	2.34464			0.115372
$414$	35.2850	−	46.2116i	1.73416	−	2.27118i
$415$	−4.41805			−0.216873
$416$	−8.54000	+	14.7917i	−0.418708	+	0.725223i
$417$	3.90235	+	2.60075i	0.191099	+	0.127360i
$418$	−0.449185	−	0.778012i	−0.0219704	−	0.0380538i
$419$	−18.9353	−	32.7968i	−0.925048	−	1.60223i	−0.791484	−	0.611190i	$-0.790691\pi$
$419$	−18.9353	−	32.7968i	−0.925048	−	1.60223i	−0.133564	−	0.991040i	$-0.542642\pi$
$420$	−26.7887	−	17.8536i	−1.30715	−	0.871164i
$421$	−6.83407	+	11.8370i	−0.333072	+	0.576898i	−0.983113	−	0.183002i	$-0.941419\pi$
$421$	−6.83407	+	11.8370i	−0.333072	+	0.576898i	0.650040	+	0.759900i	$0.274752\pi$
$422$	8.93568			0.434982
$423$	−4.41037	−	10.5763i	−0.214440	−	0.514237i
$424$	−61.6375			−2.99338
$425$	3.27725	−	5.67637i	0.158970	−	0.275344i
$426$	1.91209	−	29.7147i	0.0926411	−	1.43968i
$427$	−21.8199	−	37.7931i	−1.05594	−	1.82894i
$428$	−36.6786	−	63.5292i	−1.77293	−	3.07080i
$429$	0.616138	−	0.304758i	0.0297474	−	0.0147139i
$430$	−5.21905	+	9.03966i	−0.251685	+	0.435931i
$431$	−18.4437			−0.888404			−0.444202	−	0.895927i	$-0.646513\pi$
$431$	−18.4437			−0.888404			−0.444202	+	0.895927i	$0.646513\pi$
$432$	−50.1375	−	43.6537i	−2.41224	−	2.10029i
$433$	−9.10699			−0.437654			−0.218827	−	0.975764i	$-0.570223\pi$
$433$	−9.10699			−0.437654			−0.218827	+	0.975764i	$0.570223\pi$
$434$	−44.7968	+	77.5903i	−2.15032	+	3.72446i
$435$	5.45732	−	2.69933i	0.261659	−	0.129423i
$436$	−53.6125	−	92.8596i	−2.56757	−	4.44717i
$437$	−3.03894	−	5.26360i	−0.145372	−	0.251792i
$438$	0.251415	−	3.90710i	0.0120131	−	0.186688i
$439$	−5.64994	+	9.78598i	−0.269657	+	0.467060i	−0.968773	−	0.247948i	$-0.920244\pi$
$439$	−5.64994	+	9.78598i	−0.269657	+	0.467060i	0.699116	+	0.715008i	$0.253577\pi$
$440$	−3.43148			−0.163589
$441$	−16.9192	−	2.18649i	−0.805675	−	0.104119i
$442$	−17.6099			−0.837617
$443$	6.58551	−	11.4064i	0.312887	−	0.541936i	−0.666099	−	0.745863i	$-0.732037\pi$
$443$	6.58551	−	11.4064i	0.312887	−	0.541936i	0.978986	+	0.203927i	$0.0653705\pi$
$444$	−0.386077	−	0.257305i	−0.0183224	−	0.0122111i
$445$	5.69251	+	9.85971i	0.269851	+	0.467395i
$446$	13.4574	+	23.3088i	0.637225	+	1.10371i
$447$	12.4689	+	8.31003i	0.589761	+	0.393051i
$448$	36.1542	−	62.6209i	1.70812	−	2.95856i
$449$	−0.262177			−0.0123729			−0.00618644	−	0.999981i	$-0.501969\pi$
$449$	−0.262177			−0.0123729			−0.00618644	+	0.999981i	$0.501969\pi$
$450$	7.99358	+	1.03302i	0.376821	+	0.0486971i
$451$	−0.823683			−0.0387857
$452$	24.7926	−	42.9420i	1.16615	−	2.01982i
$453$	−1.44358	+	22.4339i	−0.0678254	+	1.05404i
$454$	1.98779	+	3.44296i	0.0932917	+	0.161586i
$455$	−1.78091	−	3.08463i	−0.0834905	−	0.144610i
$456$	−11.3103	+	5.59435i	−0.529651	+	0.261979i
$457$	−7.28899	+	12.6249i	−0.340965	+	0.590568i	−0.984612	−	0.174754i	$-0.944087\pi$
$457$	−7.28899	+	12.6249i	−0.340965	+	0.590568i	0.643648	+	0.765322i	$0.277420\pi$
$458$	22.0641			1.03099
$459$	6.52511	−	33.4273i	0.304566	−	1.56025i
$460$	−37.6428			−1.75511
$461$	2.27082	−	3.93317i	0.105763	−	0.183186i	−0.808287	−	0.588789i	$-0.799605\pi$
$461$	2.27082	−	3.93317i	0.105763	−	0.183186i	0.914050	+	0.405603i	$0.132938\pi$
$462$	−5.89614	+	2.91638i	−0.274313	+	0.135682i
$463$	−6.58595	−	11.4072i	−0.306075	−	0.530137i	0.671425	−	0.741072i	$-0.265682\pi$
$463$	−6.58595	−	11.4072i	−0.306075	−	0.530137i	−0.977500	+	0.210935i	$0.932349\pi$
$464$	22.4861	+	38.9470i	1.04389	+	1.80807i
$465$	1.04133	−	16.1827i	0.0482904	−	0.750454i
$466$	−12.5039	+	21.6575i	−0.579234	+	1.00326i
$467$	23.3465			1.08035			0.540173	−	0.841554i	$-0.318359\pi$
$467$	23.3465			1.08035			0.540173	+	0.841554i	$0.318359\pi$
$468$	−6.02525	−	14.4489i	−0.278517	−	0.667899i
$469$	−24.8941			−1.14950
$470$	−5.13114	+	8.88739i	−0.236682	+	0.409945i
$471$	−22.0338	−	14.6846i	−1.01526	−	0.676630i
$472$	−2.84586	−	4.92917i	−0.130991	−	0.226884i
$473$	0.770933	+	1.33530i	0.0354476	+	0.0613970i
$474$	53.2653	+	35.4991i	2.44656	+	1.63053i
$475$	0.421276	−	0.729672i	0.0193295	−	0.0334796i
$476$	121.826			5.58388
$477$	12.9785	−	16.9975i	0.594243	−	0.778261i
$478$	−56.1006			−2.56598
$479$	−12.4266	+	21.5235i	−0.567786	+	0.983435i	0.428998	+	0.903305i	$0.358867\pi$
$479$	−12.4266	+	21.5235i	−0.567786	+	0.983435i	−0.996784	+	0.0801296i	$0.974467\pi$
$480$	−1.89971	+	29.5224i	−0.0867095	+	1.34751i
$481$	−0.0256664	−	0.0444556i	−0.00117029	−	0.00202700i
$482$	−10.8665	−	18.8213i	−0.494956	−	0.857288i
$483$	−39.8901	+	19.7307i	−1.81506	+	0.897776i
$484$	28.2896	−	48.9989i	1.28589	−	2.22722i
$485$	17.2802			0.784655
$486$	41.0272	−	8.41494i	1.86103	−	0.381709i
$487$	34.4404			1.56064			0.780322	−	0.625378i	$-0.215055\pi$
$487$	34.4404			1.56064			0.780322	+	0.625378i	$0.215055\pi$
$488$	−52.9686	+	91.7444i	−2.39778	+	4.15307i
$489$	32.1977	−	15.9258i	1.45603	−	0.720190i
$490$	7.63908	+	13.2313i	0.345098	+	0.597728i
$491$	8.46426	+	14.6605i	0.381987	+	0.661620i	0.991346	−	0.131274i	$-0.0419067\pi$
$491$	8.46426	+	14.6605i	0.381987	+	0.661620i	−0.609359	+	0.792894i	$0.708573\pi$
$492$	−1.20461	+	18.7201i	−0.0543078	+	0.843968i
$493$	−11.5200	+	19.9533i	−0.518836	+	0.898650i
$494$	−2.26367			−0.101847
$495$	0.722536	−	0.946283i	0.0324756	−	0.0425323i
$496$	119.781			5.37832
$497$	−11.3955	+	19.7377i	−0.511160	+	0.885355i
$498$	17.1080	+	11.4018i	0.766627	+	0.510925i
$499$	2.02247	+	3.50303i	0.0905384	+	0.156817i	0.907738	−	0.419538i	$-0.137808\pi$
$499$	2.02247	+	3.50303i	0.0905384	+	0.156817i	−0.817199	+	0.576355i	$0.804475\pi$
$500$	−2.60914	−	4.51916i	−0.116684	−	0.202103i
$501$	11.4639	+	7.64021i	0.512169	+	0.341339i
$502$	0.601838	−	1.04241i	0.0268614	−	0.0465252i
$503$	12.7729			0.569517			0.284758	−	0.958599i	$-0.408087\pi$
$503$	12.7729			0.569517			0.284758	+	0.958599i	$0.408087\pi$
$504$	35.5599	+	85.2745i	1.58397	+	3.79843i
$505$	−8.75716			−0.389688
$506$	−3.84578	+	6.66108i	−0.170966	+	0.296121i
$507$	0.111224	−	1.72848i	0.00493965	−	0.0767643i
$508$	−24.6969	−	42.7763i	−1.09575	−	1.89789i
$509$	−5.47740	−	9.48714i	−0.242782	−	0.420510i	0.718724	−	0.695296i	$-0.244727\pi$
$509$	−5.47740	−	9.48714i	−0.242782	−	0.420510i	−0.961506	+	0.274785i	$0.911393\pi$
$510$	−27.3396	+	13.5229i	−1.21062	+	0.598804i
$511$	−1.49836	+	2.59524i	−0.0662837	+	0.114807i
$512$	2.72466			0.120414
$513$	0.838774	−	4.29693i	0.0370328	−	0.189714i
$514$	33.1833			1.46365
$515$	−10.0184	+	17.3524i	−0.441464	+	0.764639i
$516$	31.4751	−	15.5684i	1.38562	−	0.685362i
$517$	0.757947	+	1.31280i	0.0333345	+	0.0577370i
$518$	0.245615	+	0.425418i	0.0107917	+	0.0186918i
$519$	2.22776	−	34.6204i	0.0977880	−	1.51967i
$520$	−4.32324	+	7.48807i	−0.189587	+	0.328374i
$521$	23.6682			1.03692			0.518461	−	0.855101i	$-0.326505\pi$
$521$	23.6682			1.03692			0.518461	+	0.855101i	$0.326505\pi$
$522$	−28.0986	−	3.63122i	−1.22984	−	0.158934i
$523$	−10.6015			−0.463573			−0.231786	−	0.972767i	$-0.574457\pi$
$523$	−10.6015			−0.463573			−0.231786	+	0.972767i	$0.574457\pi$
$524$	−4.01346	+	6.95151i	−0.175329	+	0.303678i
$525$	−5.13363	−	3.42135i	−0.224050	−	0.149320i
$526$	8.52180	+	14.7602i	0.371568	+	0.643575i
$527$	30.6830	+	53.1445i	1.33657	+	2.31501i
$528$	7.31803	+	4.87716i	0.318476	+	0.212251i
$529$	−14.5184	+	25.1467i	−0.631236	+	1.09333i
$530$	−19.1524			−0.831925
$531$	1.95852	+	0.253103i	0.0849927	+	0.0109837i
$532$	15.6602			0.678955
$533$	−1.03774	+	1.79742i	−0.0449495	+	0.0778548i
$534$	3.40212	−	52.8705i	0.147224	−	2.28793i
$535$	−7.02888	−	12.1744i	−0.303885	−	0.526344i
$536$	30.2157	+	52.3351i	1.30512	+	2.26053i
$537$	−29.6531	+	14.6672i	−1.27963	+	0.632936i
$538$	20.7242	−	35.8954i	0.893484	−	1.54756i
$539$	2.25682			0.0972080
$540$	−20.4498	−	17.8052i	−0.880019	−	0.766214i
$541$	25.1160			1.07982			0.539910	−	0.841723i	$-0.318458\pi$
$541$	25.1160			1.07982			0.539910	+	0.841723i	$0.318458\pi$
$542$	8.71416	−	15.0934i	0.374305	−	0.648315i
$543$	0.125288	−	0.0619708i	0.00537663	−	0.00265942i
$544$	−55.9755	−	96.9524i	−2.39993	−	4.15680i
$545$	−10.2740	−	17.7951i	−0.440090	−	0.762258i
$546$	−1.06436	+	16.5407i	−0.0455505	+	0.707875i
$547$	−5.76015	+	9.97688i	−0.246286	+	0.426581i	−0.962493	−	0.271308i	$-0.912544\pi$
$547$	−5.76015	+	9.97688i	−0.246286	+	0.426581i	0.716206	+	0.697889i	$0.245877\pi$
$548$	108.079			4.61692
$549$	−14.1468	−	33.9247i	−0.603770	−	1.44787i
$550$	−1.06625			−0.0454650
$551$	−1.48085	+	2.56490i	−0.0630862	+	0.109269i
$552$	89.8974	+	59.9129i	3.82629	+	2.55006i
$553$	−24.4973	−	42.4307i	−1.04173	−	1.80433i
$554$	−26.0537	−	45.1263i	−1.10692	−	1.91723i
$555$	−0.0739857	−	0.0493084i	−0.00314052	−	0.00209302i
$556$	−7.06433	+	12.2358i	−0.299594	+	0.518913i
$557$	12.2095			0.517333			0.258667	−	0.965967i	$-0.416717\pi$
$557$	12.2095			0.517333			0.258667	+	0.965967i	$0.416717\pi$
$558$	−45.7954	+	59.9768i	−1.93867	+	2.53902i
$559$	3.88512			0.164323
$560$	22.7847	−	39.4643i	0.962829	−	1.66767i
$561$	−0.289322	+	4.49620i	−0.0122152	+	0.189830i
$562$	23.8628	+	41.3315i	1.00659	+	1.74347i
$563$	−16.7285	−	28.9746i	−0.705021	−	1.22113i	−0.966684	−	0.255973i	$-0.917604\pi$
$563$	−16.7285	−	28.9746i	−0.705021	−	1.22113i	0.261663	−	0.965159i	$-0.415729\pi$
$564$	30.9450	−	15.3062i	1.30302	−	0.644506i
$565$	4.75111	−	8.22917i	0.199881	−	0.346204i
$566$	22.6489			0.952003
$567$	−31.0033	−	8.14931i	−1.30202	−	0.342239i
$568$	55.3263			2.32144
$569$	1.43598	−	2.48719i	0.0601994	−	0.104268i	−0.834355	−	0.551227i	$-0.814160\pi$
$569$	1.43598	−	2.48719i	0.0601994	−	0.104268i	0.894554	+	0.446959i	$0.147493\pi$
$570$	−3.51439	+	1.73831i	−0.147202	+	0.0728097i
$571$	7.60401	+	13.1705i	0.318218	+	0.551170i	0.980116	−	0.198424i	$-0.0635823\pi$
$571$	7.60401	+	13.1705i	0.318218	+	0.551170i	−0.661898	+	0.749594i	$0.730249\pi$
$572$	1.03547	+	1.79349i	0.0432953	+	0.0749897i
$573$	−1.61909	+	25.1614i	−0.0676386	+	1.05113i
$574$	9.93065	−	17.2004i	0.414497	−	0.717931i
$575$	−7.21366			−0.300830
$576$	36.9601	−	48.4055i	1.54000	−	2.01690i
$577$	−13.5901			−0.565763			−0.282882	−	0.959155i	$-0.591290\pi$
$577$	−13.5901			−0.565763			−0.282882	+	0.959155i	$0.591290\pi$
$578$	34.8753	−	60.4058i	1.45062	−	2.51255i
$579$	7.40050	+	4.93213i	0.307554	+	0.204972i
$580$	9.17150	+	15.8855i	0.380826	+	0.659609i
$581$	−7.86817	−	13.6281i	−0.326426	−	0.565387i
$582$	−66.9142	−	44.5955i	−2.77368	−	1.84854i
$583$	−1.41455	+	2.45007i	−0.0585846	+	0.101471i
$584$	7.27467			0.301028
$585$	−1.15464	−	2.76890i	−0.0477387	−	0.114480i
$586$	−7.17443			−0.296373
$587$	2.68073	−	4.64316i	0.110645	−	0.191644i	−0.805385	−	0.592752i	$-0.798042\pi$
$587$	2.68073	−	4.64316i	0.110645	−	0.191644i	0.916031	+	0.401108i	$0.131375\pi$
$588$	3.30051	−	51.2914i	0.136111	−	2.11522i
$589$	3.94416	+	6.83148i	0.162516	+	0.281486i
$590$	−0.884282	−	1.53162i	−0.0364053	−	0.0630558i
$591$	3.79228	−	1.87576i	0.155993	−	0.0771584i
$592$	0.328372	−	0.568757i	0.0134960	−	0.0233758i
$593$	−10.6709			−0.438201			−0.219100	−	0.975702i	$-0.570312\pi$
$593$	−10.6709			−0.438201			−0.219100	+	0.975702i	$0.570312\pi$
$594$	−5.23997	+	1.79962i	−0.214999	+	0.0738394i
$595$	23.3460			0.957094
$596$	−22.5722	+	39.0962i	−0.924594	+	1.60144i
$597$	−19.2258	+	9.50959i	−0.786861	+	0.389202i
$598$	9.69041	+	16.7843i	0.396270	+	0.686360i
$599$	−2.51891	−	4.36288i	−0.102920	−	0.178262i	0.809967	−	0.586476i	$-0.199485\pi$
$599$	−2.51891	−	4.36288i	−0.102920	−	0.178262i	−0.912886	+	0.408214i	$0.866152\pi$
$600$	−0.961699	+	14.9452i	−0.0392612	+	0.610137i
$601$	0.836962	−	1.44966i	0.0341404	−	0.0591329i	−0.848450	−	0.529275i	$-0.822464\pi$
$601$	0.836962	−	1.44966i	0.0341404	−	0.0591329i	0.882591	+	0.470142i	$0.155797\pi$
$602$	−37.1787			−1.51529
$603$	−20.7945	−	2.68730i	−0.846816	−	0.109435i
$604$	−67.7281			−2.75582
$605$	5.42125	−	9.38988i	0.220405	−	0.381753i
$606$	33.9103	+	22.5998i	1.37751	+	0.918054i
$607$	−13.8566	−	24.0003i	−0.562422	−	0.974144i	−0.997284	−	0.0736469i	$-0.976536\pi$
$607$	−13.8566	−	24.0003i	−0.562422	−	0.974144i	0.434862	−	0.900497i	$-0.356797\pi$
$608$	−7.19540	−	12.4628i	−0.291812	−	0.505433i
$609$	18.0455	+	12.0266i	0.731240	+	0.487341i
$610$	−16.4587	+	28.5073i	−0.666394	+	1.15423i
$611$	3.81968			0.154528
$612$	101.763	+	13.1510i	4.11354	+	0.531599i
$613$	5.58132			0.225427			0.112714	−	0.993628i	$-0.464046\pi$
$613$	5.58132			0.225427			0.112714	+	0.993628i	$0.464046\pi$
$614$	32.4546	−	56.2130i	1.30976	−	2.26857i
$615$	−0.230844	+	3.58741i	−0.00930851	+	0.144659i
$616$	−6.11117	−	10.5849i	−0.246226	−	0.426476i
$617$	8.31358	+	14.3995i	0.334692	+	0.579704i	0.983426	−	0.181312i	$-0.0580343\pi$
$617$	8.31358	+	14.3995i	0.334692	+	0.579704i	−0.648733	+	0.761016i	$0.724701\pi$
$618$	83.5761	−	41.3389i	3.36192	−	1.66289i
$619$	−11.1936	+	19.3879i	−0.449908	+	0.779263i	−0.998380	−	0.0569057i	$-0.981877\pi$
$619$	−11.1936	+	19.3879i	−0.449908	+	0.779263i	0.548472	+	0.836169i	$0.315210\pi$
$620$	48.8556			1.96209
$621$	−35.4508	+	12.1753i	−1.42259	+	0.488577i
$622$	54.6583			2.19160
$623$	−20.2757	+	35.1186i	−0.812330	+	1.40700i
$624$	19.8626	−	9.82457i	0.795141	−	0.393297i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−43.2169	−	74.8539i	−1.72730	−	2.99176i
$627$	−0.0371911	+	0.577966i	−0.00148527	+	0.0230817i
$628$	39.8872	−	69.0866i	1.59167	−	2.75686i
$629$	0.336462			0.0134156
$630$	11.0494	+	26.4970i	0.440218	+	1.05567i
$631$	−29.8320			−1.18759			−0.593796	−	0.804616i	$-0.702371\pi$
$631$	−29.8320			−1.18759			−0.593796	+	0.804616i	$0.702371\pi$
$632$	−59.4683	+	103.002i	−2.36552	+	4.09720i
$633$	−4.79361	−	3.19474i	−0.190529	−	0.126980i
$634$	−10.2523	−	17.7575i	−0.407171	−	0.705240i
$635$	−4.73277	−	8.19741i	−0.187814	−	0.325304i
$636$	53.6147	+	35.7320i	2.12596	+	1.41687i
$637$	2.84331	−	4.92476i	0.112656	−	0.195126i
$638$	3.74802			0.148386
$639$	−11.6496	+	15.2571i	−0.460850	+	0.603560i
$640$	−20.3822			−0.805675
$641$	12.5008	−	21.6519i	0.493750	−	0.855200i	−0.506224	−	0.862402i	$-0.668959\pi$
$641$	12.5008	−	21.6519i	0.493750	−	0.855200i	0.999974	+	0.00720178i	$0.00229242\pi$
$642$	−4.20081	+	65.2824i	−0.165793	+	2.57649i
$643$	−4.76626	−	8.25540i	−0.187963	−	0.325561i	0.756608	−	0.653869i	$-0.226855\pi$
$643$	−4.76626	−	8.25540i	−0.187963	−	0.325561i	−0.944571	+	0.328307i	$0.893522\pi$
$644$	−67.0387	−	116.114i	−2.64169	−	4.57555i
$645$	6.03172	−	2.98344i	0.237499	−	0.117473i
$646$	7.41863	−	12.8494i	0.291882	−	0.505555i
$647$	−2.13351			−0.0838771			−0.0419386	−	0.999120i	$-0.513353\pi$
$647$	−2.13351			−0.0838771			−0.0419386	+	0.999120i	$0.513353\pi$
$648$	20.4985	+	75.0700i	0.805257	+	2.94903i
$649$	−0.261244			−0.0102547
$650$	−1.34334	+	2.32674i	−0.0526902	+	0.0912621i
$651$	51.7722	−	25.6079i	2.02911	−	1.00365i
$652$	54.1109	+	93.7229i	2.11915	+	3.67047i
$653$	−0.136064	−	0.235670i	−0.00532460	−	0.00922247i	0.863351	−	0.504604i	$-0.168362\pi$
$653$	−0.136064	−	0.235670i	−0.00532460	−	0.00922247i	−0.868675	+	0.495382i	$0.835028\pi$
$654$	−6.14025	+	95.4222i	−0.240103	+	3.73130i
$655$	−0.769116	+	1.33215i	−0.0300518	+	0.0520513i
$656$	−26.5533			−1.03673
$657$	−1.53176	+	2.00610i	−0.0597598	+	0.0782655i
$658$	−36.5525			−1.42496
$659$	−16.6585	+	28.8534i	−0.648925	+	1.12397i	0.334455	+	0.942412i	$0.391448\pi$
$659$	−16.6585	+	28.8534i	−0.648925	+	1.12397i	−0.983380	+	0.181559i	$0.941886\pi$
$660$	2.98484	+	1.98927i	0.116185	+	0.0774322i
$661$	3.03652	+	5.25941i	0.118107	+	0.204567i	0.919018	−	0.394217i	$-0.128984\pi$
$661$	3.03652	+	5.25941i	0.118107	+	0.204567i	−0.800910	+	0.598784i	$0.795651\pi$
$662$	−14.5426	−	25.1885i	−0.565213	−	0.978978i
$663$	9.44696	+	6.29601i	0.366890	+	0.244517i
$664$	−19.1003	+	33.0827i	−0.741235	+	1.28386i
$665$	3.00103			0.116375
$666$	0.159243	+	0.381873i	0.00617055	+	0.0147973i
$667$	25.3571			0.981830
$668$	−20.7528	+	35.9449i	−0.802950	+	1.39075i
$669$	1.11423	−	17.3156i	0.0430784	−	0.669458i
$670$	9.38879	+	16.2619i	0.362721	+	0.628250i
$671$	2.43120	+	4.21097i	0.0938556	+	0.162563i
$672$	−94.4489	+	46.7169i	−3.64345	+	1.80214i
$673$	−3.83202	+	6.63726i	−0.147714	+	0.255847i	−0.930382	−	0.366591i	$-0.880525\pi$
$673$	−3.83202	+	6.63726i	−0.147714	+	0.255847i	0.782668	+	0.622439i	$0.213858\pi$
$674$	−15.0664			−0.580337
$675$	−3.91888	−	3.41209i	−0.150838	−	0.131331i
$676$	5.21827			0.200703
$677$	14.4768	−	25.0746i	0.556390	−	0.963696i	−0.441404	−	0.897309i	$-0.645519\pi$
$677$	14.4768	−	25.0746i	0.556390	−	0.963696i	0.997794	−	0.0663876i	$-0.0211474\pi$
$678$	−39.6349	+	19.6045i	−1.52217	+	0.752905i
$679$	30.7746	+	53.3032i	1.18102	+	2.04559i
$680$	−28.3367	−	49.0806i	−1.08666	−	1.88216i
$681$	0.164583	−	2.55769i	0.00630682	−	0.0980108i
$682$	4.99133	−	8.64523i	0.191128	−	0.331043i
$683$	−18.7519			−0.717520			−0.358760	−	0.933430i	$-0.616800\pi$
$683$	−18.7519			−0.717520			−0.358760	+	0.933430i	$0.616800\pi$
$684$	13.0812	+	1.69051i	0.500173	+	0.0646381i
$685$	20.7117			0.791354
$686$	6.28419	−	10.8845i	0.239931	−	0.415573i
$687$	−11.8364	−	7.88850i	−0.451589	−	0.300965i
$688$	24.8528	+	43.0463i	0.947504	+	1.64112i
$689$	3.56431	+	6.17357i	0.135789	+	0.235194i
$690$	27.9334	+	18.6165i	1.06341	+	0.708717i
$691$	−19.2548	+	33.3503i	−0.732488	+	1.26871i	0.223329	+	0.974743i	$0.428307\pi$
$691$	−19.2548	+	33.3503i	−0.732488	+	1.26871i	−0.955817	+	0.293963i	$0.905026\pi$
$692$	104.519			3.97322
$693$	4.20571	+	0.543511i	0.159762	+	0.0206463i
$694$	−11.5878			−0.439868
$695$	−1.35377	+	2.34480i	−0.0513514	+	0.0889432i
$696$	3.38051	−	52.5347i	0.128138	−	1.99132i
$697$	−6.80187	−	11.7812i	−0.257639	−	0.446244i
$698$	8.11083	+	14.0484i	0.306999	+	0.531739i
$699$	14.4509	−	7.14781i	0.546585	−	0.270355i
$700$	9.29330	−	16.0965i	0.351254	−	0.608389i
$701$	22.0767			0.833827			0.416913	−	0.908946i	$-0.363112\pi$
$701$	22.0767			0.833827			0.416913	+	0.908946i	$0.363112\pi$
$702$	−2.67463	+	13.7018i	−0.100948	+	0.517142i
$703$	0.0432506			0.00163123
$704$	−4.02835	+	6.97731i	−0.151824	+	0.262967i
$705$	5.93011	−	2.93319i	0.223341	−	0.110470i
$706$	7.50568	+	13.0002i	0.282480	+	0.489270i
$707$	−15.5957	−	27.0126i	−0.586538	−	1.01591i
$708$	−0.382059	+	5.93737i	−0.0143587	+	0.223140i
$709$	5.67777	−	9.83419i	0.213233	−	0.369331i	−0.739491	−	0.673166i	$-0.764934\pi$
$709$	5.67777	−	9.83419i	0.213233	−	0.369331i	0.952725	+	0.303835i	$0.0982673\pi$
$710$	17.1913			0.645178
$711$	−15.8827	−	38.0875i	−0.595648	−	1.42839i
$712$	98.4403			3.68921
$713$	33.7686	−	58.4889i	1.26464	−	2.19043i
$714$	−90.4028	−	60.2497i	−3.38324	−	2.25479i
$715$	0.198432	+	0.343695i	0.00742094	+	0.0128534i
$716$	−49.8346	−	86.3160i	−1.86241	−	3.22578i
$717$	30.0956	+	20.0575i	1.12394	+	0.749060i
$718$	−2.71788	+	4.70750i	−0.101430	+	0.175682i
$719$	−11.1182			−0.414641			−0.207320	−	0.978273i	$-0.566474\pi$
$719$	−11.1182			−0.414641			−0.207320	+	0.978273i	$0.566474\pi$
$720$	23.2926	−	30.5056i	0.868064	−	1.13688i
$721$	−71.3678			−2.65788
$722$	−24.5699	+	42.5563i	−0.914396	+	1.58378i
$723$	−0.899710	+	13.9819i	−0.0334606	+	0.519993i
$724$	0.210558	+	0.364696i	0.00782531	+	0.0135538i
$725$	1.75757	+	3.04421i	0.0652746	+	0.113059i
$726$	−45.2254	+	22.3696i	−1.67847	+	0.830215i
$727$	−25.1800	+	43.6131i	−0.933875	+	1.61752i	−0.157247	+	0.987559i	$0.550262\pi$
$727$	−25.1800	+	43.6131i	−0.933875	+	1.61752i	−0.776628	+	0.629960i	$0.783071\pi$
$728$	−30.7973			−1.14142
$729$	−25.0179	−	10.1540i	−0.926589	−	0.376076i
$730$	2.26043			0.0836622
$731$	−12.7325	+	22.0534i	−0.470930	+	0.815675i
$732$	99.2595	−	49.0963i	3.66874	−	1.81465i
$733$	−5.64330	−	9.77448i	−0.208440	−	0.361029i	0.742783	−	0.669532i	$-0.233505\pi$
$733$	−5.64330	−	9.77448i	−0.208440	−	0.361029i	−0.951223	+	0.308503i	$0.900172\pi$
$734$	3.15534	+	5.46521i	0.116466	+	0.201725i
$735$	0.632491	−	9.82919i	0.0233298	−	0.362555i
$736$	−61.6046	+	106.702i	−2.27078	+	3.93310i
$737$	2.77373			0.102172
$738$	10.1520	−	13.2958i	0.373701	−	0.489425i
$739$	13.4378			0.494319			0.247159	−	0.968975i	$-0.420503\pi$
$739$	13.4378			0.494319			0.247159	+	0.968975i	$0.420503\pi$
$740$	0.133934	−	0.231981i	0.00492353	−	0.00852780i
$741$	1.21436	+	0.809323i	0.0446108	+	0.0297312i
$742$	−34.1087	−	59.0780i	−1.25217	−	2.16882i
$743$	−12.5115	−	21.6706i	−0.459003	−	0.795017i	0.539905	−	0.841726i	$-0.318460\pi$
$743$	−12.5115	−	21.6706i	−0.459003	−	0.795017i	−0.998909	+	0.0467087i	$0.985127\pi$
$744$	−116.675	−	77.7592i	−4.27752	−	2.85079i
$745$	−4.32561	+	7.49218i	−0.158478	+	0.274492i
$746$	74.7036			2.73509
$747$	−5.10128	−	12.2331i	−0.186646	−	0.447587i
$748$	−13.5740			−0.496316
$749$	25.0357	−	43.3630i	0.914783	−	1.58445i
$750$	−0.298825	+	4.64387i	−0.0109115	+	0.169570i
$751$	−6.35228	−	11.0025i	−0.231798	−	0.401486i	0.726539	−	0.687125i	$-0.241128\pi$
$751$	−6.35228	−	11.0025i	−0.231798	−	0.401486i	−0.958337	+	0.285639i	$0.907794\pi$
$752$	24.4341	+	42.3212i	0.891022	+	1.54329i
$753$	−0.695552	+	0.344038i	−0.0253473	+	0.0125374i
$754$	4.72204	−	8.17882i	0.171967	−	0.297855i
$755$	−12.9790			−0.472355
$756$	18.5032	−	94.7897i	0.672956	−	3.44747i
$757$	−28.8779			−1.04959			−0.524793	−	0.851230i	$-0.675857\pi$
$757$	−28.8779			−1.04959			−0.524793	+	0.851230i	$0.675857\pi$
$758$	−0.385051	+	0.666927i	−0.0139857	+	0.0242239i
$759$	4.44461	−	2.19842i	0.161329	−	0.0797976i
$760$	−3.64256	−	6.30909i	−0.132129	−	0.228855i
$761$	−15.6488	−	27.1045i	−0.567269	−	0.982538i	−0.996835	−	0.0795028i	$-0.974667\pi$
$761$	−15.6488	−	27.1045i	−0.567269	−	0.982538i	0.429566	−	0.903036i	$-0.358667\pi$
$762$	−2.82854	+	43.9568i	−0.102467	+	1.59239i
$763$	36.5942	−	63.3831i	1.32480	−	2.29462i
$764$	−75.9624			−2.74822
$765$	19.5014	+	2.52019i	0.705073	+	0.0911176i
$766$	92.0853			3.32718
$767$	−0.329135	+	0.570079i	−0.0118844	+	0.0205843i
$768$	20.4067	+	13.6002i	0.736362	+	0.490755i
$769$	24.4072	+	42.2745i	0.880146	+	1.52446i	0.851178	+	0.524876i	$0.175888\pi$
$769$	24.4072	+	42.2745i	0.880146	+	1.52446i	0.0289672	+	0.999580i	$0.490778\pi$
$770$	−1.89890	−	3.28899i	−0.0684315	−	0.118527i
$771$	−17.8014	−	11.8639i	−0.641103	−	0.427269i
$772$	−13.3970	+	23.2042i	−0.482167	+	0.835138i
$773$	21.9516			0.789544			0.394772	−	0.918779i	$-0.370824\pi$
$773$	21.9516			0.789544			0.394772	+	0.918779i	$0.370824\pi$
$774$	−31.0560	−	4.01342i	−1.11629	−	0.144259i
$775$	9.36240			0.336307
$776$	74.7066	−	129.396i	2.68181	−	4.64503i
$777$	0.0203361	−	0.316033i	0.000729555	−	0.0113376i
$778$	45.8438	+	79.4038i	1.64358	+	2.84676i
$779$	−0.874350	−	1.51442i	−0.0313268	−	0.0542597i
$780$	8.10145	−	4.00719i	0.290079	−	0.143480i
$781$	1.26971	−	2.19920i	0.0454337	−	0.0786935i
$782$	−127.032			−4.54265
$783$	13.7754	+	11.9940i	0.492294	+	0.428630i
$784$	72.7536			2.59834
$785$	7.64375	−	13.2394i	0.272817	−	0.472533i
$786$	6.41615	−	3.17360i	0.228857	−	0.113198i
$787$	0.995183	+	1.72371i	0.0354744	+	0.0614435i	0.883218	−	0.468964i	$-0.155372\pi$
$787$	0.995183	+	1.72371i	0.0354744	+	0.0614435i	−0.847743	+	0.530407i	$0.822039\pi$
$788$	6.37324	+	11.0388i	0.227037	+	0.393240i
$789$	0.705577	−	10.9650i	0.0251192	−	0.390364i
$790$	−18.4783	+	32.0054i	−0.657429	+	1.13870i
$791$	33.8453			1.20340
$792$	−3.96214	−	9.50142i	−0.140789	−	0.337618i
$793$	12.2521			0.435084
$794$	23.0245	−	39.8795i	0.817107	−	1.41527i
$795$	10.2744	+	6.84748i	0.364396	+	0.242855i
$796$	−32.3106	−	55.9637i	−1.14522	−	1.98358i
$797$	19.7535	+	34.2140i	0.699704	+	1.21192i	0.968569	+	0.248745i	$0.0800183\pi$
$797$	19.7535	+	34.2140i	0.699704	+	1.21192i	−0.268865	+	0.963178i	$0.586648\pi$
$798$	−11.6209	−	7.74482i	−0.411374	−	0.274164i
$799$	−12.5181	+	21.6819i	−0.442857	+	0.767051i
$800$	−17.0800			−0.603869
$801$	−20.7277	+	27.1464i	−0.732377	+	0.959172i
$802$	−16.2341			−0.573245
$803$	0.166950	−	0.289166i	0.00589153	−	0.0102044i
$804$	4.05648	−	63.0395i	0.143061	−	2.22323i
$805$	−12.8469	−	22.2515i	−0.452794	−	0.784262i
$806$	−12.5769	−	21.7838i	−0.443003	−	0.767303i
$807$	−23.9512	+	11.8469i	−0.843122	+	0.417030i
$808$	−37.8593	+	65.5742i	−1.33189	+	2.30689i
$809$	14.2336			0.500425			0.250213	−	0.968191i	$-0.419499\pi$
$809$	14.2336			0.500425			0.250213	+	0.968191i	$0.419499\pi$
$810$	6.36941	+	23.3262i	0.223798	+	0.819598i
$811$	25.6732			0.901509			0.450754	−	0.892648i	$-0.351155\pi$
$811$	25.6732			0.901509			0.450754	+	0.892648i	$0.351155\pi$
$812$	−32.6673	+	56.5814i	−1.14640	+	1.98562i
$813$	−10.0711	+	4.98140i	−0.353207	+	0.174705i
$814$	−0.0273668	−	0.0474007i	−0.000959207	−	0.00166139i
$815$	10.3695	+	17.9605i	0.363228	+	0.629130i
$816$	−9.32696	+	144.945i	−0.326509	+	5.07410i
$817$	−1.63671	+	2.83486i	−0.0572612	+	0.0991794i
$818$	38.0324			1.32977
$819$	6.48471	−	8.49283i	0.226594	−	0.296763i
$820$	−10.8304			−0.378214
$821$	21.1639	−	36.6570i	0.738626	−	1.27934i	−0.214489	−	0.976726i	$-0.568808\pi$
$821$	21.1639	−	36.6570i	0.738626	−	1.27934i	0.953114	−	0.302611i	$-0.0978582\pi$
$822$	−80.2019	−	53.4512i	−2.79736	−	1.86432i
$823$	−5.39353	−	9.34187i	−0.188007	−	0.325637i	0.756579	−	0.653902i	$-0.226869\pi$
$823$	−5.39353	−	9.34187i	−0.188007	−	0.325637i	−0.944586	+	0.328265i	$0.893536\pi$
$824$	86.6241	+	150.037i	3.01769	+	5.22680i
$825$	0.571997	+	0.381212i	0.0199144	+	0.0132721i
$826$	3.14966	−	5.45537i	0.109591	−	0.189817i
$827$	−2.57600			−0.0895763			−0.0447882	−	0.998997i	$-0.514261\pi$
$827$	−2.57600			−0.0895763			−0.0447882	+	0.998997i	$0.514261\pi$
$828$	−43.4641	−	104.229i	−1.51048	−	3.62221i
$829$	−15.7511			−0.547058			−0.273529	−	0.961864i	$-0.588191\pi$
$829$	−15.7511			−0.547058			−0.273529	+	0.961864i	$0.588191\pi$
$830$	−5.93495	+	10.2796i	−0.206005	+	0.356811i
$831$	−2.15716	+	33.5232i	−0.0748310	+	1.16291i
$832$	10.1505	+	17.5811i	0.351904	+	0.609515i
$833$	18.6365	+	32.2794i	0.645717	+	1.11841i
$834$	11.2935	−	5.58604i	0.391061	−	0.193429i
$835$	−3.97695	+	6.88828i	−0.137628	+	0.238379i
$836$	−1.74488			−0.0603479
$837$	46.0106	−	15.8019i	1.59036	−	0.546195i
$838$	−101.746			−3.51476
$839$	12.0471	−	20.8663i	0.415914	−	0.720383i	−0.579610	−	0.814894i	$-0.696795\pi$
$839$	12.0471	−	20.8663i	0.415914	−	0.720383i	0.995524	+	0.0945104i	$0.0301286\pi$
$840$	−47.8133	+	23.6497i	−1.64972	+	0.815992i
$841$	8.32187	+	14.4139i	0.286961	+	0.497031i
$842$	18.3610	+	31.8022i	0.632762	+	1.09598i
$843$	1.97576	−	30.7042i	0.0680488	−	1.05751i
$844$	8.67776	−	15.0303i	0.298701	−	0.517365i
$845$	1.00000			0.0344010
$846$	−30.5329	−	3.94581i	−1.04974	−	0.135660i
$847$	38.6191			1.32697
$848$	−45.6012	+	78.9835i	−1.56595	+	2.71230i
$849$	−12.1502	−	8.09757i	−0.416992	−	0.277908i
$850$	−8.80495	−	15.2506i	−0.302007	−	0.523092i
$851$	−0.185149	−	0.320687i	−0.00634682	−	0.0109930i
$852$	−48.1250	−	32.0733i	−1.64873	−	1.09881i
$853$	−3.91585	+	6.78244i	−0.134076	+	0.232226i	−0.925244	−	0.379372i	$-0.876140\pi$
$853$	−3.91585	+	6.78244i	−0.134076	+	0.232226i	0.791168	+	0.611599i	$0.209473\pi$
$854$	−117.246			−4.01208
$855$	2.50681	+	0.323959i	0.0857311	+	0.0110792i
$856$	−121.550			−4.15450
$857$	21.1176	−	36.5768i	0.721364	−	1.24944i	−0.239090	−	0.970998i	$-0.576849\pi$
$857$	21.1176	−	36.5768i	0.721364	−	1.24944i	0.960453	−	0.278441i	$-0.0898177\pi$
$858$	0.118593	−	1.84299i	0.00404869	−	0.0629185i
$859$	5.92757	+	10.2669i	0.202246	+	0.350300i	0.949252	−	0.314517i	$-0.101843\pi$
$859$	5.92757	+	10.2669i	0.202246	+	0.350300i	−0.747006	+	0.664818i	$0.768509\pi$
$860$	10.1368	+	17.5575i	0.345663	+	0.598705i
$861$	−11.4770	+	5.67681i	−0.391134	+	0.193465i
$862$	−24.7762	+	42.9137i	−0.843882	+	1.46165i
$863$	17.8343			0.607087			0.303543	−	0.952818i	$-0.401830\pi$
$863$	17.8343			0.607087			0.303543	+	0.952818i	$0.401830\pi$
$864$	−83.9379	+	28.8277i	−2.85563	+	0.980740i
$865$	20.0295			0.681022
$866$	−12.2338	+	21.1896i	−0.415722	+	0.720051i
$867$	−40.3058	+	19.9363i	−1.36886	+	0.677072i
$868$	87.0076	+	150.702i	2.95323	+	5.11514i
$869$	2.72953	+	4.72769i	0.0925930	+	0.160376i
$870$	1.05041	−	16.3239i	0.0356123	−	0.553431i
$871$	3.49456	−	6.05276i	0.118409	−	0.205090i
$872$	−177.668			−6.01660
$873$	19.9525	+	47.8472i	0.675291	+	1.61938i
$874$	−16.3294			−0.552349
$875$	1.78091	−	3.08463i	0.0602059	−	0.104280i
$876$	−6.32780	−	4.21721i	−0.213797	−	0.142486i
$877$	−19.6714	−	34.0719i	−0.664256	−	1.15053i	−0.979486	−	0.201510i	$-0.935415\pi$
$877$	−19.6714	−	34.0719i	−0.664256	−	1.15053i	0.315230	−	0.949015i	$-0.397918\pi$
$878$	15.1796	+	26.2919i	0.512287	+	0.887307i
$879$	3.84878	+	2.56505i	0.129816	+	0.0865170i
$880$	−2.53871	+	4.39717i	−0.0855797	+	0.148228i
$881$	7.90169			0.266215			0.133107	−	0.991102i	$-0.457504\pi$
$881$	7.90169			0.266215			0.133107	+	0.991102i	$0.457504\pi$
$882$	−27.8156	+	36.4293i	−0.936601	+	1.22664i
$883$	21.7549			0.732109			0.366055	−	0.930593i	$-0.380708\pi$
$883$	21.7549			0.732109			0.366055	+	0.930593i	$0.380708\pi$
$884$	−17.1016	+	29.6208i	−0.575189	+	0.996257i
$885$	−0.0732156	+	1.13780i	−0.00246112	+	0.0382469i
$886$	−17.6932	−	30.6455i	−0.594415	−	1.02956i
$887$	−9.23661	−	15.9983i	−0.310135	−	0.537170i	0.668256	−	0.743931i	$-0.267041\pi$
$887$	−9.23661	−	15.9983i	−0.310135	−	0.537170i	−0.978391	+	0.206761i	$0.933708\pi$
$888$	−0.689083	+	0.340838i	−0.0231241	+	0.0114378i
$889$	16.8573	−	29.1978i	0.565377	−	0.979261i
$890$	30.5879			1.02531
$891$	3.45444	+	0.908008i	0.115728	+	0.0304194i
$892$	52.2757			1.75032
$893$	−1.60914	+	2.78711i	−0.0538478	+	0.0932671i
$894$	36.0853	−	17.8487i	1.20687	−	0.596951i
$895$	−9.55001	−	16.5411i	−0.319222	−	0.552908i
$896$	−36.2989	−	62.8715i	−1.21266	−	2.10039i
$897$	0.802334	−	12.4686i	0.0267892	−	0.416316i
$898$	−0.352193	+	0.610016i	−0.0117528	+	0.0203565i
$899$	−32.9102			−1.09762
$900$	9.50046	−	12.4425i	0.316682	−	0.414748i
$901$	−46.7246			−1.55662
$902$	−1.10649	+	1.91649i	−0.0368420	+	0.0638123i
$903$	19.9448	+	13.2924i	0.663722	+	0.442343i
$904$	−41.0804	−	71.1534i	−1.36631	−	2.36653i
$905$	0.0403501	+	0.0698883i	0.00134128	+	0.00232317i
$906$	50.2586	+	33.4953i	1.66973	+	1.11281i
$907$	−22.5179	+	39.0021i	−0.747694	+	1.29504i	0.201231	+	0.979544i	$0.435506\pi$
$907$	−22.5179	+	39.0021i	−0.747694	+	1.29504i	−0.948925	+	0.315501i	$0.897828\pi$
$908$	7.72166			0.256252
$909$	−10.1114	−	24.2477i	−0.335374	−	0.804245i
$910$	−9.56951			−0.317226
$911$	−8.50918	+	14.7383i	−0.281922	+	0.488303i	−0.971858	−	0.235567i	$-0.924305\pi$
$911$	−8.50918	+	14.7383i	−0.281922	+	0.488303i	0.689936	+	0.723870i	$0.257639\pi$
$912$	−1.19894	+	18.6320i	−0.0397008	+	0.616969i
$913$	0.876683	+	1.51846i	0.0290140	+	0.0502537i
$914$	19.5832	+	33.9191i	0.647755	+	1.12194i
$915$	19.0215	−	9.40854i	0.628832	−	0.311037i
$916$	21.4272	−	37.1131i	0.707976	−	1.22625i
$917$	−5.47892			−0.180930
$918$	−69.0111	−	60.0865i	−2.27771	−	1.98315i
$919$	−5.01669			−0.165485			−0.0827426	−	0.996571i	$-0.526368\pi$
$919$	−5.01669			−0.165485			−0.0827426	+	0.996571i	$0.526368\pi$
$920$	−31.1864	+	54.0164i	−1.02818	+	1.78087i
$921$	−37.5082	+	18.5525i	−1.23594	+	0.611326i
$922$	−6.10097	−	10.5672i	−0.200925	−	0.348012i
$923$	−3.19935	−	5.54144i	−0.105308	−	0.182399i
$924$	−0.820430	+	12.7499i	−0.0269902	+	0.419439i
$925$	0.0256664	−	0.0444556i	0.000843907	−	0.00146169i
$926$	−35.3887			−1.16295
$927$	−59.6148	−	7.70411i	−1.95801	−	0.253036i
$928$	60.0387			1.97087
$929$	3.27540	−	5.67316i	0.107462	−	0.186130i	−0.807279	−	0.590170i	$-0.799061\pi$
$929$	3.27540	−	5.67316i	0.107462	−	0.186130i	0.914742	+	0.404039i	$0.132394\pi$
$930$	−36.2540	−	24.1618i	−1.18882	−	0.792296i
$931$	2.39564	+	4.14937i	0.0785139	+	0.135990i
$932$	24.2861	+	42.0647i	0.795516	+	1.37787i
$933$	−29.3219	−	19.5418i	−0.959954	−	0.639770i
$934$	31.3623	−	54.3211i	1.02621	−	1.77744i
$935$	−2.60125			−0.0850700
$936$	−25.7255	−	3.32455i	−0.840865	−	0.108666i
$937$	28.3589			0.926446			0.463223	−	0.886242i	$-0.346693\pi$
$937$	28.3589			0.926446			0.463223	+	0.886242i	$0.346693\pi$
$938$	−33.4413	+	57.9219i	−1.09190	+	1.89122i
$939$	−3.57822	+	55.6071i	−0.116771	+	1.81467i
$940$	9.96606	+	17.2617i	0.325057	+	0.563016i
$941$	−19.7573	−	34.2206i	−0.644068	−	1.11556i	−0.984516	−	0.175295i	$-0.943912\pi$
$941$	−19.7573	−	34.2206i	−0.644068	−	1.11556i	0.340448	−	0.940263i	$-0.389421\pi$
$942$	−63.7660	+	31.5403i	−2.07761	+	1.02764i
$943$	−7.48590	+	12.9660i	−0.243774	+	0.422229i
$944$	−8.42179			−0.274106
$945$	3.54585	−	18.1650i	0.115347	−	0.590906i
$946$	4.14251			0.134685
$947$	−7.27826	+	12.6063i	−0.236512	+	0.409650i	−0.959711	−	0.280989i	$-0.909337\pi$
$947$	−7.27826	+	12.6063i	−0.236512	+	0.409650i	0.723199	+	0.690639i	$0.242671\pi$
$948$	111.439	−	55.1209i	3.61939	−	1.79024i
$949$	−0.420672	−	0.728626i	−0.0136556	−	0.0236522i
$950$	−1.13184	−	1.96040i	−0.0367216	−	0.0636037i
$951$	−0.848856	+	13.1916i	−0.0275261	+	0.427767i
$952$	100.931	−	174.817i	3.27118	−	5.66585i
$953$	28.0021			0.907078			0.453539	−	0.891236i	$-0.350161\pi$
$953$	28.0021			0.907078			0.453539	+	0.891236i	$0.350161\pi$
$954$	−22.1142	−	53.0309i	−0.715973	−	1.71694i
$955$	−14.5570			−0.471054
$956$	−54.4814	+	94.3645i	−1.76205	+	3.05197i
$957$	−2.01065	−	1.34002i	−0.0649952	−	0.0433166i
$958$	33.3864	+	57.8269i	1.07867	+	1.86830i
$959$	36.8858	+	63.8880i	1.19110	+	2.06305i
$960$	29.2595	+	19.5003i	0.944348	+	0.629368i
$961$	−28.3273	+	49.0643i	−0.913784	+	1.58272i
$962$	−0.137915			−0.00444657
$963$	25.5937	−	33.5193i	0.824747	−	1.08015i
$964$	−42.2114			−1.35954
$965$	−2.56732	+	4.44672i	−0.0826448	+	0.143145i
$966$	−7.67794	+	119.319i	−0.247034	+	3.83902i
$967$	22.1985	+	38.4490i	0.713857	+	1.23644i	0.963399	+	0.268072i	$0.0863865\pi$
$967$	22.1985	+	38.4490i	0.713857	+	1.23644i	−0.249542	+	0.968364i	$0.580280\pi$
$968$	−46.8747	−	81.1894i	−1.50661	−	2.60953i
$969$	−8.57380	+	4.24082i	−0.275430	+	0.136235i
$970$	23.2133	−	40.2066i	0.745333	−	1.29095i
$971$	35.2407			1.13093			0.565464	−	0.824773i	$-0.308697\pi$
$971$	35.2407			1.13093			0.565464	+	0.824773i	$0.308697\pi$
$972$	25.6886	−	77.1821i	0.823961	−	2.47562i
$973$	−9.64378			−0.309165
$974$	46.2652	−	80.1337i	1.48243	−	2.56765i
$975$	1.55252	−	0.767915i	0.0497203	−	0.0245930i
$976$	78.3754	+	135.750i	2.50873	+	4.34526i
$977$	13.6068	+	23.5676i	0.435319	+	0.753995i	0.997322	−	0.0731408i	$-0.0233023\pi$
$977$	13.6068	+	23.5676i	0.435319	+	0.753995i	−0.562003	+	0.827135i	$0.689969\pi$
$978$	6.19733	−	96.3093i	0.198169	−	3.07963i
$979$	2.25915	−	3.91297i	0.0722028	−	0.125059i
$980$	29.6743			0.947912
$981$	37.4100	−	48.9947i	1.19441	−	1.56428i
$982$	45.4816			1.45138
$983$	20.8660	−	36.1409i	0.665521	−	1.15272i	−0.313623	−	0.949548i	$-0.601543\pi$
$983$	20.8660	−	36.1409i	0.665521	−	1.15272i	0.979144	−	0.203168i	$-0.0651239\pi$
$984$	25.8648	+	17.2378i	0.824541	+	0.549522i
$985$	1.22133	+	2.11541i	0.0389149	+	0.0674025i
$986$	30.9507	+	53.6081i	0.985670	+	1.70723i
$987$	19.6088	+	13.0685i	0.624156	+	0.415974i
$988$	−2.19833	+	3.80763i	−0.0699383	+	0.121137i
$989$	28.0260			0.891174
$990$	−1.23114	−	2.95233i	−0.0391282	−	0.0938314i
$991$	46.7192			1.48409			0.742043	−	0.670352i	$-0.233857\pi$
$991$	46.7192			1.48409			0.742043	+	0.670352i	$0.233857\pi$
$992$	79.9549	−	138.486i	2.53857	−	4.39693i
$993$	−1.20408	+	18.7119i	−0.0382102	+	0.593804i
$994$	30.6162	+	53.0288i	0.971088	+	1.68197i
$995$	−6.19183	−	10.7246i	−0.196294	−	0.339991i
$996$	35.7926	−	17.7040i	1.13413	−	0.560971i
$997$	−27.4895	+	47.6132i	−0.870601	+	1.50793i	−0.00922514	+	0.999957i	$0.502936\pi$
$997$	−27.4895	+	47.6132i	−0.870601	+	1.50793i	−0.861376	+	0.507968i	$0.830397\pi$
$998$	10.8675			0.344005
$999$	0.0511027	−	0.261792i	0.00161682	−	0.00828275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.12	✓	26
3.2	odd	2		1755.2.i.g.586.2		26
9.2	odd	6		5265.2.a.bh.1.12		13
9.4	even	3	inner	585.2.i.g.391.12	yes	26
9.5	odd	6		1755.2.i.g.1171.2		26
9.7	even	3		5265.2.a.bg.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.12	✓	26	1.1	even	1	trivial
585.2.i.g.391.12	yes	26	9.4	even	3	inner
1755.2.i.g.586.2		26	3.2	odd	2
1755.2.i.g.1171.2		26	9.5	odd	6
5265.2.a.bg.1.2		13	9.7	even	3
5265.2.a.bh.1.12		13	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34334 - 2.32674i) q^{2} +(-1.55252 + 0.767915i) q^{3} +(-2.60914 - 4.51916i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.298825 + 4.64387i) q^{6} +(1.78091 - 3.08463i) q^{7} -8.64648 q^{8} +(1.82061 - 2.38440i) q^{9} +O(q^{10})\)	\(q+(1.34334 - 2.32674i) q^{2} +(-1.55252 + 0.767915i) q^{3} +(-2.60914 - 4.51916i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.298825 + 4.64387i) q^{6} +(1.78091 - 3.08463i) q^{7} -8.64648 q^{8} +(1.82061 - 2.38440i) q^{9} -2.68668 q^{10} +(-0.198432 + 0.343695i) q^{11} +(7.52105 + 5.01247i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-4.78475 - 8.28744i) q^{14} +(1.44129 + 0.960561i) q^{15} +(-6.39691 + 11.0798i) q^{16} -6.55451 q^{17} +(-3.10217 - 7.43915i) q^{18} -0.842552 q^{19} +(-2.60914 + 4.51916i) q^{20} +(-0.396162 + 6.15654i) q^{21} +(0.533125 + 0.923399i) q^{22} +(3.60683 + 6.24721i) q^{23} +(13.4238 - 6.63976i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.68668 q^{26} +(-0.995515 + 5.09990i) q^{27} -18.5866 q^{28} +(1.75757 - 3.04421i) q^{29} +(4.17112 - 2.06314i) q^{30} +(-4.68120 - 8.10808i) q^{31} +(8.54000 + 14.7917i) q^{32} +(0.0441410 - 0.685970i) q^{33} +(-8.80495 + 15.2506i) q^{34} -3.56183 q^{35} +(-15.5257 - 2.00641i) q^{36} -0.0513329 q^{37} +(-1.13184 + 1.96040i) q^{38} +(-1.44129 - 0.960561i) q^{39} +(4.32324 + 7.48807i) q^{40} +(1.03774 + 1.79742i) q^{41} +(13.7925 + 9.19210i) q^{42} +(1.94256 - 3.36462i) q^{43} +2.07095 q^{44} +(-2.97526 - 0.384497i) q^{45} +19.3808 q^{46} +(1.90984 - 3.30794i) q^{47} +(1.42298 - 22.1138i) q^{48} +(-2.84331 - 4.92476i) q^{49} +(1.34334 + 2.32674i) q^{50} +(10.1760 - 5.03330i) q^{51} +(2.60914 - 4.51916i) q^{52} +7.12862 q^{53} +(10.5288 + 9.16721i) q^{54} +0.396864 q^{55} +(-15.3986 + 26.6712i) q^{56} +(1.30808 - 0.647009i) q^{57} +(-4.72204 - 8.17882i) q^{58} +(0.329135 + 0.570079i) q^{59} +(0.580399 - 9.01966i) q^{60} +(6.12603 - 10.6106i) q^{61} -25.1538 q^{62} +(-4.11265 - 9.86234i) q^{63} +20.3009 q^{64} +(0.500000 - 0.866025i) q^{65} +(-1.53678 - 1.02420i) q^{66} +(-3.49456 - 6.05276i) q^{67} +(17.1016 + 29.6208i) q^{68} +(-10.3970 - 6.92916i) q^{69} +(-4.78475 + 8.28744i) q^{70} -6.39870 q^{71} +(-15.7419 + 20.6167i) q^{72} -0.841345 q^{73} +(-0.0689576 + 0.119438i) q^{74} +(0.111224 - 1.72848i) q^{75} +(2.19833 + 3.80763i) q^{76} +(0.706781 + 1.22418i) q^{77} +(-4.17112 + 2.06314i) q^{78} +(6.87775 - 11.9126i) q^{79} +12.7938 q^{80} +(-2.37073 - 8.68214i) q^{81} +5.57615 q^{82} +(2.20902 - 3.82614i) q^{83} +(28.8560 - 14.2729i) q^{84} +(3.27725 + 5.67637i) q^{85} +(-5.21905 - 9.03966i) q^{86} +(-0.390970 + 6.07585i) q^{87} +(1.71574 - 2.97175i) q^{88} -11.3850 q^{89} +(-4.89141 + 6.40613i) q^{90} +3.56183 q^{91} +(18.8214 - 32.5997i) q^{92} +(13.4940 + 8.99316i) q^{93} +(-5.13114 - 8.88739i) q^{94} +(0.421276 + 0.729672i) q^{95} +(-24.6173 - 16.4064i) q^{96} +(-8.64012 + 14.9651i) q^{97} -15.2782 q^{98} +(0.458237 + 1.09888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

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