LMFDB - Embedded newform 585.2.i.g.196.6

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			196.6
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0377835 + 0.0654430i) q^{2} +(-1.16946 + 1.27764i) q^{3} +(0.997145 + 1.72711i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0394262 - 0.124807i) q^{6} +(-0.0159135 + 0.0275629i) q^{7} -0.301837 q^{8} +(-0.264725 - 2.98830i) q^{9} +O(q^{10})$	\(q+(-0.0377835 + 0.0654430i) q^{2} +(-1.16946 + 1.27764i) q^{3} +(0.997145 + 1.72711i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0394262 - 0.124807i) q^{6} +(-0.0159135 + 0.0275629i) q^{7} -0.301837 q^{8} +(-0.264725 - 2.98830i) q^{9} +0.0755671 q^{10} +(-2.85952 + 4.95283i) q^{11} +(-3.37274 - 0.745790i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.00120253 - 0.00208285i) q^{14} +(1.69120 + 0.373963i) q^{15} +(-1.98289 + 3.43446i) q^{16} -3.52053 q^{17} +(0.205565 + 0.0955841i) q^{18} +2.66055 q^{19} +(0.997145 - 1.72711i) q^{20} +(-0.0166053 - 0.0525654i) q^{21} +(-0.216085 - 0.374271i) q^{22} +(-2.42047 - 4.19237i) q^{23} +(0.352986 - 0.385639i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.0755671 q^{26} +(4.12755 + 3.15647i) q^{27} -0.0634721 q^{28} +(-4.23440 + 7.33420i) q^{29} +(-0.0883727 + 0.0965475i) q^{30} +(-1.66335 - 2.88101i) q^{31} +(-0.451678 - 0.782329i) q^{32} +(-2.98384 - 9.44557i) q^{33} +(0.133018 - 0.230394i) q^{34} +0.0318269 q^{35} +(4.89714 - 3.43697i) q^{36} -7.25460 q^{37} +(-0.100525 + 0.174114i) q^{38} +(-1.69120 - 0.373963i) q^{39} +(0.150918 + 0.261398i) q^{40} +(-2.89535 - 5.01489i) q^{41} +(0.00406745 + 0.000899406i) q^{42} +(3.83587 - 6.64392i) q^{43} -11.4054 q^{44} +(-2.45558 + 1.72341i) q^{45} +0.365815 q^{46} +(1.12108 - 1.94177i) q^{47} +(-2.06909 - 6.54987i) q^{48} +(3.49949 + 6.06130i) q^{49} +(-0.0377835 - 0.0654430i) q^{50} +(4.11713 - 4.49797i) q^{51} +(-0.997145 + 1.72711i) q^{52} -9.14350 q^{53} +(-0.362523 + 0.150857i) q^{54} +5.71903 q^{55} +(0.00480327 - 0.00831951i) q^{56} +(-3.11140 + 3.39922i) q^{57} +(-0.319982 - 0.554224i) q^{58} +(4.02563 + 6.97259i) q^{59} +(1.04050 + 3.29377i) q^{60} +(-3.20298 + 5.54772i) q^{61} +0.251389 q^{62} +(0.0865789 + 0.0402576i) q^{63} -7.86328 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.730886 + 0.161616i) q^{66} +(4.46221 + 7.72878i) q^{67} +(-3.51048 - 6.08033i) q^{68} +(8.18698 + 1.81033i) q^{69} +(-0.00120253 + 0.00208285i) q^{70} +11.9463 q^{71} +(0.0799036 + 0.901978i) q^{72} +2.96399 q^{73} +(0.274105 - 0.474763i) q^{74} +(-0.521738 - 1.65160i) q^{75} +(2.65295 + 4.59505i) q^{76} +(-0.0910097 - 0.157633i) q^{77} +(0.0883727 - 0.0965475i) q^{78} +(-3.95547 + 6.85108i) q^{79} +3.96577 q^{80} +(-8.85984 + 1.58215i) q^{81} +0.437586 q^{82} +(1.12731 - 1.95255i) q^{83} +(0.0742281 - 0.0810945i) q^{84} +(1.76027 + 3.04887i) q^{85} +(0.289865 + 0.502062i) q^{86} +(-4.41850 - 13.9871i) q^{87} +(0.863107 - 1.49495i) q^{88} +12.5865 q^{89} +(-0.0200045 - 0.225817i) q^{90} -0.0318269 q^{91} +(4.82711 - 8.36081i) q^{92} +(5.62611 + 1.24406i) q^{93} +(0.0847167 + 0.146734i) q^{94} +(-1.33027 - 2.30410i) q^{95} +(1.52775 + 0.337821i) q^{96} +(-7.48069 + 12.9569i) q^{97} -0.528893 q^{98} +(15.5575 + 7.23395i) 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 $

$2$	−0.0377835	+	0.0654430i	−0.0267170	+	0.0462752i	−0.879075	−	0.476684i	$-0.841839\pi$
$2$	−0.0377835	+	0.0654430i	−0.0267170	+	0.0462752i	0.852358	+	0.522959i	$0.175172\pi$
$3$	−1.16946	+	1.27764i	−0.675188	+	0.737645i
$3$	−1.16946	+	1.27764i	−0.675188	+	0.737645i
$4$	0.997145	+	1.72711i	0.498572	+	0.863553i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.0394262	−	0.124807i	−0.0160957	−	0.0509521i
$7$	−0.0159135	+	0.0275629i	−0.00601473	+	0.0104178i	−0.869017	−	0.494782i	$-0.835248\pi$
$7$	−0.0159135	+	0.0275629i	−0.00601473	+	0.0104178i	0.863002	+	0.505200i	$0.168581\pi$
$8$	−0.301837			−0.106715
$9$	−0.264725	−	2.98830i	−0.0882415	−	0.996099i
$10$	0.0755671			0.0238964
$11$	−2.85952	+	4.95283i	−0.862177	+	1.49333i	0.00764667	+	0.999971i	$0.497566\pi$
$11$	−2.85952	+	4.95283i	−0.862177	+	1.49333i	−0.869823	+	0.493363i	$0.835767\pi$
$12$	−3.37274	−	0.745790i	−0.973626	−	0.215291i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−0.00120253	−	0.00208285i	−0.000321391	−	0.000556665i
$15$	1.69120	+	0.373963i	0.436666	+	0.0965568i
$16$	−1.98289	+	3.43446i	−0.495721	+	0.858614i
$17$	−3.52053			−0.853855			−0.426927	−	0.904286i	$-0.640404\pi$
$17$	−3.52053			−0.853855			−0.426927	+	0.904286i	$0.640404\pi$
$18$	0.205565	+	0.0955841i	0.0484522	+	0.0225294i
$19$	2.66055			0.610371			0.305186	−	0.952293i	$-0.401281\pi$
$19$	2.66055			0.610371			0.305186	+	0.952293i	$0.401281\pi$
$20$	0.997145	−	1.72711i	0.222968	−	0.386193i
$21$	−0.0166053	−	0.0525654i	−0.00362358	−	0.0114707i
$22$	−0.216085	−	0.374271i	−0.0460695	−	0.0797948i
$23$	−2.42047	−	4.19237i	−0.504702	−	0.874170i	−0.999985	−	0.00543851i	$-0.998269\pi$
$23$	−2.42047	−	4.19237i	−0.504702	−	0.874170i	0.495283	−	0.868732i	$-0.335064\pi$
$24$	0.352986	−	0.385639i	0.0720530	−	0.0787181i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.0755671			−0.0148199
$27$	4.12755	+	3.15647i	0.794348	+	0.607464i
$28$	−0.0634721			−0.0119951
$29$	−4.23440	+	7.33420i	−0.786309	+	1.36193i	0.141905	+	0.989880i	$0.454677\pi$
$29$	−4.23440	+	7.33420i	−0.786309	+	1.36193i	−0.928214	+	0.372047i	$0.878656\pi$
$30$	−0.0883727	+	0.0965475i	−0.0161346	+	0.0176271i
$31$	−1.66335	−	2.88101i	−0.298747	−	0.517444i	0.677103	−	0.735888i	$-0.263235\pi$
$31$	−1.66335	−	2.88101i	−0.298747	−	0.517444i	−0.975849	+	0.218444i	$0.929902\pi$
$32$	−0.451678	−	0.782329i	−0.0798461	−	0.138297i
$33$	−2.98384	−	9.44557i	−0.519419	−	1.64426i
$34$	0.133018	−	0.230394i	0.0228124	−	0.0395123i
$35$	0.0318269			0.00537973
$36$	4.89714	−	3.43697i	0.816189	−	0.572829i
$37$	−7.25460			−1.19265			−0.596325	−	0.802743i	$-0.703373\pi$
$37$	−7.25460			−1.19265			−0.596325	+	0.802743i	$0.703373\pi$
$38$	−0.100525	+	0.174114i	−0.0163073	+	0.0282451i
$39$	−1.69120	−	0.373963i	−0.270808	−	0.0598820i
$40$	0.150918	+	0.261398i	0.0238623	+	0.0413307i
$41$	−2.89535	−	5.01489i	−0.452178	−	0.783195i	0.546343	−	0.837561i	$-0.316019\pi$
$41$	−2.89535	−	5.01489i	−0.452178	−	0.783195i	−0.998521	+	0.0543666i	$0.982686\pi$
$42$	0.00406745		0.000899406i	0.000627621		0.000138781i
$43$	3.83587	−	6.64392i	0.584965	−	1.01319i	−0.409915	−	0.912124i	$-0.634442\pi$
$43$	3.83587	−	6.64392i	0.584965	−	1.01319i	0.994880	−	0.101065i	$-0.0322249\pi$
$44$	−11.4054			−1.71943
$45$	−2.45558	+	1.72341i	−0.366056	+	0.256910i
$46$	0.365815			0.0539365
$47$	1.12108	−	1.94177i	0.163526	−	0.283236i	−0.772605	−	0.634887i	$-0.781046\pi$
$47$	1.12108	−	1.94177i	0.163526	−	0.283236i	0.936131	+	0.351652i	$0.114380\pi$
$48$	−2.06909	−	6.54987i	−0.298648	−	0.945393i
$49$	3.49949	+	6.06130i	0.499928	+	0.865900i
$50$	−0.0377835	−	0.0654430i	−0.00534340	−	0.00925504i
$51$	4.11713	−	4.49797i	0.576513	−	0.629842i
$52$	−0.997145	+	1.72711i	−0.138279	+	0.239506i
$53$	−9.14350			−1.25596			−0.627978	−	0.778231i	$-0.716117\pi$
$53$	−9.14350			−1.25596			−0.627978	+	0.778231i	$0.716117\pi$
$54$	−0.362523	+	0.150857i	−0.0493331	+	0.0205290i
$55$	5.71903			0.771154
$56$	0.00480327	−	0.00831951i	0.000641864	−	0.00111174i
$57$	−3.11140	+	3.39922i	−0.412116	+	0.450238i
$58$	−0.319982	−	0.554224i	−0.0420156	−	0.0727732i
$59$	4.02563	+	6.97259i	0.524092	+	0.907754i	0.999607	+	0.0280462i	$0.00892857\pi$
$59$	4.02563	+	6.97259i	0.524092	+	0.907754i	−0.475515	+	0.879708i	$0.657738\pi$
$60$	1.04050	+	3.29377i	0.134328	+	0.425224i
$61$	−3.20298	+	5.54772i	−0.410099	+	0.710313i	−0.994900	−	0.100864i	$-0.967839\pi$
$61$	−3.20298	+	5.54772i	−0.410099	+	0.710313i	0.584801	+	0.811177i	$0.301173\pi$
$62$	0.251389			0.0319265
$63$	0.0865789	+	0.0402576i	0.0109079	+	0.00507198i
$64$	−7.86328			−0.982910
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	0.730886	+	0.161616i	0.0899659	+	0.0198935i
$67$	4.46221	+	7.72878i	0.545146	+	0.944221i	0.998598	+	0.0529400i	$0.0168592\pi$
$67$	4.46221	+	7.72878i	0.545146	+	0.944221i	−0.453451	+	0.891281i	$0.649807\pi$
$68$	−3.51048	−	6.08033i	−0.425709	−	0.737349i
$69$	8.18698	+	1.81033i	0.985597	+	0.217938i
$70$	−0.00120253	+	0.00208285i	−0.000143730	+	0.000248948i
$71$	11.9463			1.41776			0.708882	−	0.705327i	$-0.249200\pi$
$71$	11.9463			1.41776			0.708882	+	0.705327i	$0.249200\pi$
$72$	0.0799036	+	0.901978i	0.00941673	+	0.106299i
$73$	2.96399			0.346909			0.173455	−	0.984842i	$-0.444507\pi$
$73$	2.96399			0.346909			0.173455	+	0.984842i	$0.444507\pi$
$74$	0.274105	−	0.474763i	0.0318640	−	0.0551901i
$75$	−0.521738	−	1.65160i	−0.0602451	−	0.190711i
$76$	2.65295	+	4.59505i	0.304314	+	0.527088i
$77$	−0.0910097	−	0.157633i	−0.0103715	−	0.0179640i
$78$	0.0883727	−	0.0965475i	0.0100062	−	0.0109318i
$79$	−3.95547	+	6.85108i	−0.445026	+	0.770807i	−0.998054	−	0.0623554i	$-0.980139\pi$
$79$	−3.95547	+	6.85108i	−0.445026	+	0.770807i	0.553028	+	0.833162i	$0.313472\pi$
$80$	3.96577			0.443387
$81$	−8.85984	+	1.58215i	−0.984427	+	0.175795i
$82$	0.437586			0.0483233
$83$	1.12731	−	1.95255i	0.123738	−	0.214320i	−0.797501	−	0.603318i	$-0.793845\pi$
$83$	1.12731	−	1.95255i	0.123738	−	0.214320i	0.921239	+	0.388997i	$0.127178\pi$
$84$	0.0742281	−	0.0810945i	0.00809895	−	0.00884813i
$85$	1.76027	+	3.04887i	0.190928	+	0.330697i
$86$	0.289865	+	0.502062i	0.0312570	+	0.0541387i
$87$	−4.41850	−	13.9871i	−0.473713	−	1.49957i
$88$	0.863107	−	1.49495i	0.0920076	−	0.159362i
$89$	12.5865			1.33417			0.667086	−	0.744981i	$-0.267542\pi$
$89$	12.5865			1.33417			0.667086	+	0.744981i	$0.267542\pi$
$90$	−0.0200045	−	0.225817i	−0.00210866	−	0.0238032i
$91$	−0.0318269			−0.00333637
$92$	4.82711	−	8.36081i	0.503261	−	0.871674i
$93$	5.62611	+	1.24406i	0.583401	+	0.129003i
$94$	0.0847167	+	0.146734i	0.00873786	+	0.0151344i
$95$	−1.33027	−	2.30410i	−0.136483	−	0.236396i
$96$	1.52775	+	0.337821i	0.155926	+	0.0344787i
$97$	−7.48069	+	12.9569i	−0.759549	+	1.31558i	0.183533	+	0.983014i	$0.441247\pi$
$97$	−7.48069	+	12.9569i	−0.759549	+	1.31558i	−0.943081	+	0.332563i	$0.892087\pi$
$98$	−0.528893			−0.0534263
$99$	15.5575	+	7.23395i	1.56359	+	0.727039i
$100$	−1.99429			−0.199429
$101$	−3.53051	+	6.11503i	−0.351299	+	0.608468i	−0.986477	−	0.163898i	$-0.947593\pi$
$101$	−3.53051	+	6.11503i	−0.351299	+	0.608468i	0.635178	+	0.772366i	$0.280927\pi$
$102$	0.138801	+	0.439386i	0.0137434	+	0.0435057i
$103$	5.59797	+	9.69596i	0.551584	+	0.955371i	0.998161	+	0.0606260i	$0.0193097\pi$
$103$	5.59797	+	9.69596i	0.551584	+	0.955371i	−0.446577	+	0.894745i	$0.647357\pi$
$104$	−0.150918	−	0.261398i	−0.0147988	−	0.0256322i
$105$	−0.0372203	+	0.0406633i	−0.00363233	+	0.00396834i
$106$	0.345474	−	0.598378i	0.0335554	−	0.0581197i
$107$	1.42702			0.137955			0.0689776	−	0.997618i	$-0.478026\pi$
$107$	1.42702			0.137955			0.0689776	+	0.997618i	$0.478026\pi$
$108$	−1.33580	+	10.2762i	−0.128537	+	0.988826i
$109$	16.2397			1.55548			0.777741	−	0.628585i	$-0.216365\pi$
$109$	16.2397			1.55548			0.777741	+	0.628585i	$0.216365\pi$
$110$	−0.216085	+	0.374271i	−0.0206029	+	0.0356853i
$111$	8.48397	−	9.26876i	0.805263	−	0.879752i
$112$	−0.0631092	−	0.109308i	−0.00596325	−	0.0103287i
$113$	−6.07415	−	10.5207i	−0.571408	−	0.989708i	−0.996422	−	0.0845211i	$-0.973064\pi$
$113$	−6.07415	−	10.5207i	−0.571408	−	0.989708i	0.425013	−	0.905187i	$-0.360269\pi$
$114$	−0.104895	−	0.332054i	−0.00982434	−	0.0310997i
$115$	−2.42047	+	4.19237i	−0.225710	+	0.390941i
$116$	−16.8893			−1.56813
$117$	2.45558	−	1.72341i	0.227018	−	0.159329i
$118$	−0.608410			−0.0560087
$119$	0.0560239	−	0.0970363i	0.00513570	−	0.00889530i
$120$	−0.510466	−	0.112876i	−0.0465989	−	0.0103041i
$121$	−10.8537	−	18.7991i	−0.986697	−	1.70901i
$122$	−0.242040	−	0.419225i	−0.0219132	−	0.0379548i
$123$	9.79322	+	2.16551i	0.883025	+	0.195257i
$124$	3.31720	−	5.74557i	0.297894	−	0.515967i
$125$	1.00000			0.0894427
$126$	−0.00590584	+	0.00414491i	−0.000526134	+	0.000369258i
$127$	11.5704			1.02671			0.513353	−	0.858178i	$-0.328403\pi$
$127$	11.5704			1.02671			0.513353	+	0.858178i	$0.328403\pi$
$128$	1.20046	−	2.07925i	0.106106	−	0.183782i
$129$	4.00264	+	12.6707i	0.352413	+	1.11559i
$130$	0.0377835	+	0.0654430i	0.00331384	+	0.00573973i
$131$	6.40624	+	11.0959i	0.559715	+	0.969456i	0.997520	+	0.0703853i	$0.0224229\pi$
$131$	6.40624	+	11.0959i	0.559715	+	0.969456i	−0.437804	+	0.899070i	$0.644244\pi$
$132$	13.3382	−	14.5720i	1.16094	−	1.26833i
$133$	−0.0423385	+	0.0733325i	−0.00367122	+	0.00635873i
$134$	−0.674393			−0.0582587
$135$	0.669810	−	5.15280i	0.0576481	−	0.443482i
$136$	1.06263			0.0911195
$137$	4.32678	−	7.49421i	0.369662	−	0.640273i	−0.619851	−	0.784720i	$-0.712807\pi$
$137$	4.32678	−	7.49421i	0.369662	−	0.640273i	0.989513	+	0.144447i	$0.0461402\pi$
$138$	−0.427807	+	0.467380i	−0.0364173	+	0.0397860i
$139$	−7.09980	−	12.2972i	−0.602197	−	1.04304i	−0.992488	−	0.122344i	$-0.960959\pi$
$139$	−7.09980	−	12.2972i	−0.602197	−	1.04304i	0.390291	−	0.920692i	$-0.372375\pi$
$140$	0.0317361	+	0.0549685i	0.00268219	+	0.00464568i
$141$	1.16982	+	3.70316i	0.0985166	+	0.311862i
$142$	−0.451373	+	0.781802i	−0.0378784	+	0.0656073i
$143$	−5.71903			−0.478250
$144$	10.7881	+	5.01627i	0.899008	+	0.418022i
$145$	8.46881			0.703296
$146$	−0.111990	+	0.193973i	−0.00926838	+	0.0160533i
$147$	−11.8367	−	2.61736i	−0.976273	−	0.215876i
$148$	−7.23389	−	12.5295i	−0.594622	−	1.02992i
$149$	7.96865	+	13.8021i	0.652817	+	1.13071i	0.982436	+	0.186598i	$0.0597463\pi$
$149$	7.96865	+	13.8021i	0.652817	+	1.13071i	−0.329619	+	0.944114i	$0.606920\pi$
$150$	0.127799	+	0.0282593i	0.0104347	+	0.00230736i
$151$	−0.545154	+	0.944234i	−0.0443640	+	0.0768406i	−0.887355	−	0.461087i	$-0.847459\pi$
$151$	−0.545154	+	0.944234i	−0.0443640	+	0.0768406i	0.842991	+	0.537928i	$0.180793\pi$
$152$	−0.803051			−0.0651360
$153$	0.931972	+	10.5204i	0.0753455	+	0.850524i
$154$	0.0137547			0.00110838
$155$	−1.66335	+	2.88101i	−0.133604	+	0.231408i
$156$	−1.04050	−	3.29377i	−0.0833064	−	0.263713i
$157$	9.35306	+	16.2000i	0.746455	+	1.29290i	0.949512	+	0.313731i	$0.101579\pi$
$157$	9.35306	+	16.2000i	0.746455	+	1.29290i	−0.203057	+	0.979167i	$0.565088\pi$
$158$	−0.298904	−	0.517716i	−0.0237795	−	0.0411873i
$159$	10.6930	−	11.6821i	0.848007	−	0.926451i
$160$	−0.451678	+	0.782329i	−0.0357083	+	0.0618485i
$161$	0.154072			0.0121426
$162$	0.231215	−	0.639594i	0.0181660	−	0.0502513i
$163$	0.580285			0.0454515			0.0227257	−	0.999742i	$-0.492766\pi$
$163$	0.580285			0.0454515			0.0227257	+	0.999742i	$0.492766\pi$
$164$	5.77417	−	10.0011i	0.450887	−	0.780958i
$165$	−6.68818	+	7.30686i	−0.520674	+	0.568838i
$166$	0.0851872	+	0.147549i	0.00661181	+	0.0114520i
$167$	8.96210	+	15.5228i	0.693508	+	1.20119i	0.970681	+	0.240372i	$0.0772693\pi$
$167$	8.96210	+	15.5228i	0.693508	+	1.20119i	−0.277173	+	0.960820i	$0.589397\pi$
$168$	0.00501210	+	0.0158662i	0.000386692	+	0.00122410i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−0.266036			−0.0204041
$171$	−0.704312	−	7.95051i	−0.0538601	−	0.607990i
$172$	15.2997			1.16659
$173$	−2.37012	+	4.10518i	−0.180197	+	0.312111i	−0.941948	−	0.335760i	$-0.891007\pi$
$173$	−2.37012	+	4.10518i	−0.180197	+	0.312111i	0.761750	+	0.647871i	$0.224340\pi$
$174$	1.08230	+	0.239322i	0.0820493	+	0.0181430i
$175$	−0.0159135	−	0.0275629i	−0.00120295	−	0.00208356i
$176$	−11.3402	−	19.6418i	−0.854799	−	1.48055i
$177$	−13.6163	−	3.01087i	−1.02346	−	0.226311i
$178$	−0.475564	+	0.823701i	−0.0356450	+	0.0617390i
$179$	−22.6621			−1.69385			−0.846923	−	0.531715i	$-0.821548\pi$
$179$	−22.6621			−1.69385			−0.846923	+	0.531715i	$0.821548\pi$
$180$	−5.42507	−	2.52256i	−0.404361	−	0.188020i
$181$	3.50628			0.260620			0.130310	−	0.991473i	$-0.458403\pi$
$181$	3.50628			0.260620			0.130310	+	0.991473i	$0.458403\pi$
$182$	0.00120253	−	0.00208285i	8.91378e−5	−	0.000154391i
$183$	−3.34223	−	10.5801i	−0.247065	−	0.782103i
$184$	0.730586	+	1.26541i	0.0538595	+	0.0932875i
$185$	3.62730	+	6.28267i	0.266684	+	0.461911i
$186$	−0.293990	+	0.321185i	−0.0215564	+	0.0235504i
$187$	10.0670	−	17.4366i	0.736174	−	1.27509i
$188$	4.47152			0.326119
$189$	−0.152685	+	0.0635370i	−0.0111062	+	0.00462164i
$190$	0.201050			0.0145857
$191$	3.16943	−	5.48961i	0.229332	−	0.397214i	−0.728278	−	0.685281i	$-0.759679\pi$
$191$	3.16943	−	5.48961i	0.229332	−	0.397214i	0.957610	+	0.288067i	$0.0930126\pi$
$192$	9.19579	−	10.0464i	0.663649	−	0.725039i
$193$	−9.80814	−	16.9882i	−0.706006	−	1.22284i	−0.966327	−	0.257316i	$-0.917162\pi$
$193$	−9.80814	−	16.9882i	−0.706006	−	1.22284i	0.260322	−	0.965522i	$-0.416171\pi$
$194$	−0.565294	−	0.979117i	−0.0405857	−	0.0702965i
$195$	0.521738	+	1.65160i	0.0373624	+	0.118274i
$196$	−6.97900	+	12.0880i	−0.498500	+	0.863428i
$197$	8.10475			0.577439			0.288720	−	0.957414i	$-0.406770\pi$
$197$	8.10475			0.577439			0.288720	+	0.957414i	$0.406770\pi$
$198$	−1.06123	+	0.744806i	−0.0754183	+	0.0529310i
$199$	−0.612594			−0.0434257			−0.0217128	−	0.999764i	$-0.506912\pi$
$199$	−0.612594			−0.0434257			−0.0217128	+	0.999764i	$0.506912\pi$
$200$	0.150918	−	0.261398i	0.0106715	−	0.0184837i
$201$	−15.0930	−	3.33740i	−1.06458	−	0.235402i
$202$	−0.266791	−	0.462095i	−0.0187713	−	0.0325129i
$203$	−0.134768	−	0.233425i	−0.00945887	−	0.0163832i
$204$	11.8738	+	2.62558i	0.831335	+	0.183827i
$205$	−2.89535	+	5.01489i	−0.202220	+	0.350255i
$206$	−0.846044			−0.0589467
$207$	−11.8873	+	8.34290i	−0.826225	+	0.579872i
$208$	−3.96577			−0.274977
$209$	−7.60788	+	13.1772i	−0.526248	+	0.911488i
$210$	−0.00125482	−	0.00397222i	−8.65905e−5	−	0.000274109i
$211$	−6.76421	−	11.7160i	−0.465668	−	0.806560i	0.533564	−	0.845760i	$-0.320852\pi$
$211$	−6.76421	−	11.7160i	−0.465668	−	0.806560i	−0.999231	+	0.0391997i	$0.987519\pi$
$212$	−9.11740	−	15.7918i	−0.626185	−	1.08458i
$213$	−13.9707	+	15.2631i	−0.957258	+	1.04581i
$214$	−0.0539178	+	0.0933884i	−0.00368575	+	0.00638390i
$215$	−7.67174			−0.523208
$216$	−1.24585	−	0.952740i	−0.0847691	−	0.0648257i
$217$	0.105879			0.00718752
$218$	−0.613594	+	1.06278i	−0.0415578	+	0.0719802i
$219$	−3.46627	+	3.78692i	−0.234229	+	0.255896i
$220$	5.70270	+	9.87737i	0.384476	+	0.665932i
$221$	−1.76027	−	3.04887i	−0.118408	−	0.205089i
$222$	0.286021	+	0.905423i	0.0191965	+	0.0607680i
$223$	−5.48336	+	9.49745i	−0.367193	+	0.635997i	−0.989125	−	0.147074i	$-0.953014\pi$
$223$	−5.48336	+	9.49745i	−0.367193	+	0.635997i	0.621933	+	0.783071i	$0.286348\pi$
$224$	0.0287510			0.00192101
$225$	2.72030	+	1.26489i	0.181354	+	0.0843260i
$226$	0.918012			0.0610653
$227$	−7.36602	+	12.7583i	−0.488900	+	0.846799i	−0.999918	−	0.0127704i	$-0.995935\pi$
$227$	−7.36602	+	12.7583i	−0.488900	+	0.846799i	0.511019	+	0.859570i	$0.329268\pi$
$228$	−8.97333	−	1.98421i	−0.594273	−	0.131408i
$229$	0.603444	+	1.04520i	0.0398767	+	0.0690685i	0.885275	−	0.465068i	$-0.153970\pi$
$229$	0.603444	+	1.04520i	0.0398767	+	0.0690685i	−0.845398	+	0.534137i	$0.820637\pi$
$230$	−0.182908	−	0.316805i	−0.0120606	−	0.0208895i
$231$	0.307831	+	0.0680684i	0.0202538	+	0.00447858i
$232$	1.27810	−	2.21373i	0.0839113	−	0.145339i
$233$	11.7715			0.771178			0.385589	−	0.922671i	$-0.373998\pi$
$233$	11.7715			0.771178			0.385589	+	0.922671i	$0.373998\pi$
$234$	0.0200045	+	0.225817i	0.00130773	+	0.0147621i
$235$	−2.24216			−0.146262
$236$	−8.02827	+	13.9054i	−0.522596	+	0.905162i
$237$	−4.12744	−	13.0657i	−0.268106	−	0.848711i
$238$	0.00423356	+	0.00733275i	0.000274421	+	0.000475311i
$239$	7.11502	+	12.3236i	0.460232	+	0.797146i	0.998972	−	0.0453263i	$-0.0144328\pi$
$239$	7.11502	+	12.3236i	0.460232	+	0.797146i	−0.538740	+	0.842472i	$0.681099\pi$
$240$	−4.63781	+	5.06682i	−0.299369	+	0.327062i
$241$	−1.99897	+	3.46232i	−0.128765	+	0.223027i	−0.923198	−	0.384324i	$-0.874435\pi$
$241$	−1.99897	+	3.46232i	−0.128765	+	0.223027i	0.794433	+	0.607351i	$0.207768\pi$
$242$	1.64036			0.105446
$243$	8.33982	−	13.1699i	0.534999	−	0.844852i
$244$	−12.7753			−0.817857
$245$	3.49949	−	6.06130i	0.223574	−	0.387242i
$246$	−0.511740	+	0.559077i	−0.0326273	+	0.0356455i
$247$	1.33027	+	2.30410i	0.0846433	+	0.146606i
$248$	0.502061	+	0.869594i	0.0318809	+	0.0552193i
$249$	1.17632	+	3.72372i	0.0745460	+	0.235981i
$250$	−0.0377835	+	0.0654430i	−0.00238964	+	0.00413898i
$251$	23.3931			1.47656			0.738281	−	0.674493i	$-0.235638\pi$
$251$	23.3931			1.47656			0.738281	+	0.674493i	$0.235638\pi$
$252$	0.0168026	+	0.189674i	0.00105847	+	0.0119483i
$253$	27.6855			1.74057
$254$	−0.437170	+	0.757201i	−0.0274305	+	0.0475110i
$255$	−5.95392	−	1.31655i	−0.372849	−	0.0824455i
$256$	−7.77256	−	13.4625i	−0.485785	−	0.841404i
$257$	−3.89236	−	6.74177i	−0.242799	−	0.420540i	0.718712	−	0.695308i	$-0.244732\pi$
$257$	−3.89236	−	6.74177i	−0.242799	−	0.420540i	−0.961510	+	0.274768i	$0.911399\pi$
$258$	−0.980440	−	0.216798i	−0.0610395	−	0.0134972i
$259$	0.115446	−	0.199958i	0.00717346	−	0.0124248i
$260$	1.99429			0.123681
$261$	23.0377	+	10.7121i	1.42600	+	0.663063i
$262$	−0.968201			−0.0598157
$263$	−12.1895	+	21.1129i	−0.751640	+	1.30188i	0.195388	+	0.980726i	$0.437403\pi$
$263$	−12.1895	+	21.1129i	−0.751640	+	1.30188i	−0.947028	+	0.321152i	$0.895930\pi$
$264$	0.900632	+	2.85102i	0.0554300	+	0.175468i
$265$	4.57175	+	7.91851i	0.280840	+	0.486430i
$266$	−0.00319940	−	0.00554152i	−0.000196168	−	0.000339773i
$267$	−14.7195	+	16.0811i	−0.900817	+	0.984145i
$268$	−8.89895	+	15.4134i	−0.543590	+	0.941525i
$269$	−3.81148			−0.232390			−0.116195	−	0.993226i	$-0.537070\pi$
$269$	−3.81148			−0.232390			−0.116195	+	0.993226i	$0.537070\pi$
$270$	0.311907	+	0.238525i	0.0189821	+	0.0145162i
$271$	15.5942			0.947278			0.473639	−	0.880719i	$-0.342940\pi$
$271$	15.5942			0.947278			0.473639	+	0.880719i	$0.342940\pi$
$272$	6.98081	−	12.0911i	0.423274	−	0.733132i
$273$	0.0372203	−	0.0406633i	0.00225268	−	0.00246106i
$274$	0.326962	+	0.566315i	0.0197525	+	0.0342124i
$275$	−2.85952	−	4.95283i	−0.172435	−	0.298667i
$276$	5.03698	+	15.9449i	0.303190	+	0.959773i
$277$	−11.1688	+	19.3449i	−0.671067	+	1.16232i	0.306535	+	0.951859i	$0.400830\pi$
$277$	−11.1688	+	19.3449i	−0.671067	+	1.16232i	−0.977602	+	0.210462i	$0.932503\pi$
$278$	1.07302			0.0643556
$279$	−8.16898	+	5.73326i	−0.489064	+	0.343241i
$280$	−0.00960654			−0.000574101
$281$	1.16599	−	2.01955i	0.0695572	−	0.120477i	−0.829149	−	0.559027i	$-0.811175\pi$
$281$	1.16599	−	2.01955i	0.0695572	−	0.120477i	0.898706	+	0.438551i	$0.144508\pi$
$282$	−0.286546	−	0.0633618i	−0.0170635	−	0.00377314i
$283$	−11.4202	−	19.7803i	−0.678858	−	1.17582i	−0.975325	−	0.220773i	$-0.929142\pi$
$283$	−11.4202	−	19.7803i	−0.678858	−	1.17582i	0.296467	−	0.955043i	$-0.404191\pi$
$284$	11.9122	+	20.6325i	0.706858	+	1.22431i
$285$	4.49951	+	0.994946i	0.266528	+	0.0589355i
$286$	0.216085	−	0.374271i	0.0127774	−	0.0221311i
$287$	0.184300			0.0108789
$288$	−2.21826	+	1.55685i	−0.130712	+	0.0917382i
$289$	−4.60584			−0.270932
$290$	−0.319982	+	0.554224i	−0.0187900	+	0.0325452i
$291$	−7.80591	−	24.7102i	−0.457591	−	1.44854i
$292$	2.95553	+	5.11913i	0.172959	+	0.299575i
$293$	−1.93486	−	3.35128i	−0.113036	−	0.195784i	0.803957	−	0.594687i	$-0.202724\pi$
$293$	−1.93486	−	3.35128i	−0.113036	−	0.195784i	−0.916993	+	0.398903i	$0.869391\pi$
$294$	0.618519	−	0.675735i	0.0360728	−	0.0394096i
$295$	4.02563	−	6.97259i	0.234381	−	0.405960i
$296$	2.18971			0.127274
$297$	−27.4363	+	11.4171i	−1.59201	+	0.662485i
$298$	−1.20433			−0.0697652
$299$	2.42047	−	4.19237i	0.139979	−	0.242451i
$300$	2.33224	−	2.54798i	0.134652	−	0.147108i
$301$	0.122084	+	0.211456i	0.00703680	+	0.0121881i
$302$	−0.0411957	−	0.0713530i	−0.00237054	−	0.00410590i
$303$	−3.68400	−	11.6620i	−0.211641	−	0.669965i
$304$	−5.27556	+	9.13754i	−0.302574	+	0.524074i
$305$	6.40595			0.366804
$306$	−0.723700	−	0.336507i	−0.0413712	−	0.0192368i
$307$	3.56572			0.203506			0.101753	−	0.994810i	$-0.467555\pi$
$307$	3.56572			0.203506			0.101753	+	0.994810i	$0.467555\pi$
$308$	0.181500	−	0.314367i	0.0103419	−	0.0179127i
$309$	−18.9345	−	4.18686i	−1.07715	−	0.238182i
$310$	−0.125695	−	0.217709i	−0.00713897	−	0.0123651i
$311$	−15.0838	−	26.1258i	−0.855322	−	1.48146i	−0.876346	−	0.481682i	$-0.840026\pi$
$311$	−15.0838	−	26.1258i	−0.855322	−	1.48146i	0.0210247	−	0.999779i	$-0.493307\pi$
$312$	0.510466	+	0.112876i	0.0288994	+	0.00639033i
$313$	−2.80543	+	4.85915i	−0.158572	+	0.274655i	−0.934354	−	0.356346i	$-0.884022\pi$
$313$	−2.80543	+	4.85915i	−0.158572	+	0.274655i	0.775782	+	0.631001i	$0.217356\pi$
$314$	−1.41357			−0.0797722
$315$	−0.00842537	−	0.0951083i	−0.000474716	−	0.00535875i
$316$	−15.7767			−0.887510
$317$	11.9651	−	20.7242i	0.672028	−	1.16399i	−0.305300	−	0.952256i	$-0.598757\pi$
$317$	11.9651	−	20.7242i	0.672028	−	1.16399i	0.977328	−	0.211731i	$-0.0679101\pi$
$318$	0.360494	+	1.14117i	0.0202155	+	0.0639937i
$319$	−24.2167	−	41.9446i	−1.35588	−	2.34844i
$320$	3.93164	+	6.80980i	0.219785	+	0.380679i
$321$	−1.66884	+	1.82322i	−0.0931457	+	0.101762i
$322$	−0.00582139	+	0.0100829i	−0.000324413	+	0.000561901i
$323$	−9.36655			−0.521169
$324$	−11.5671	−	13.7242i	−0.642616	−	0.762458i
$325$	−1.00000			−0.0554700
$326$	−0.0219252	+	0.0379756i	−0.00121433	+	0.00210328i
$327$	−18.9917	+	20.7485i	−1.05024	+	1.14739i
$328$	0.873923	+	1.51368i	0.0482543	+	0.0835789i
$329$	0.0356805	+	0.0618005i	0.00196713	+	0.00340717i
$330$	−0.225480	−	0.713774i	−0.0124123	−	0.0392920i
$331$	17.0983	−	29.6150i	0.939805	−	1.62779i	0.173972	−	0.984751i	$-0.444340\pi$
$331$	17.0983	−	29.6150i	0.939805	−	1.62779i	0.765833	−	0.643040i	$-0.222327\pi$
$332$	4.49635			0.246769
$333$	1.92047	+	21.6789i	0.105241	+	1.18800i
$334$	−1.35448			−0.0741138
$335$	4.46221	−	7.72878i	0.243797	−	0.422268i
$336$	0.213460	+	0.0472010i	0.0116452	+	0.00257502i
$337$	−10.3985	−	18.0108i	−0.566443	−	0.981109i	−0.996914	−	0.0785040i	$-0.974986\pi$
$337$	−10.3985	−	18.0108i	−0.566443	−	0.981109i	0.430470	−	0.902605i	$-0.358348\pi$
$338$	−0.0377835	−	0.0654430i	−0.00205515	−	0.00355963i
$339$	20.5452	+	4.54301i	1.11586	+	0.246743i
$340$	−3.51048	+	6.08033i	−0.190383	+	0.329752i
$341$	19.0255			1.03029
$342$	0.546916	+	0.254306i	0.0295739	+	0.0137513i
$343$	−0.445545			−0.0240572
$344$	−1.15781	+	2.00538i	−0.0624247	+	0.108123i
$345$	−2.52570	−	7.99530i	−0.135979	−	0.430453i
$346$	−0.179103	−	0.310216i	−0.00962866	−	0.0166773i
$347$	4.97315	+	8.61375i	0.266973	+	0.462410i	0.968079	−	0.250647i	$-0.0806433\pi$
$347$	4.97315	+	8.61375i	0.266973	+	0.462410i	−0.701106	+	0.713057i	$0.747310\pi$
$348$	19.7513	−	21.5784i	1.05878	−	1.15672i
$349$	13.8961	−	24.0687i	0.743839	−	1.28837i	−0.206896	−	0.978363i	$-0.566336\pi$
$349$	13.8961	−	24.0687i	0.743839	−	1.28837i	0.950735	−	0.310004i	$-0.100331\pi$
$350$	0.00240507			0.000128556
$351$	−0.669810	+	5.15280i	−0.0357518	+	0.275036i
$352$	5.16632			0.275366
$353$	−13.0006	+	22.5177i	−0.691953	+	1.19850i	0.279245	+	0.960220i	$0.409916\pi$
$353$	−13.0006	+	22.5177i	−0.691953	+	1.19850i	−0.971197	+	0.238277i	$0.923417\pi$
$354$	0.711511	−	0.777328i	0.0378164	−	0.0413145i
$355$	−5.97315	−	10.3458i	−0.317022	−	0.549098i
$356$	12.5506	+	21.7383i	0.665181	+	1.15213i
$357$	0.0584596	+	0.185058i	0.00309401	+	0.00979433i
$358$	0.856255	−	1.48308i	0.0452545	−	0.0783831i
$359$	0.595595			0.0314343			0.0157171	−	0.999876i	$-0.494997\pi$
$359$	0.595595			0.0314343			0.0157171	+	0.999876i	$0.494997\pi$
$360$	0.741184	−	0.520188i	0.0390638	−	0.0274163i
$361$	−11.9215			−0.627447
$362$	−0.132480	+	0.229462i	−0.00696298	+	0.0120602i
$363$	36.7114	+	8.11774i	1.92685	+	0.426071i
$364$	−0.0317361	−	0.0549685i	−0.00166342	−	0.00288113i
$365$	−1.48200	−	2.56689i	−0.0775713	−	0.134357i
$366$	0.818674	+	0.181028i	0.0427928	+	0.00946247i
$367$	−3.46382	+	5.99952i	−0.180810	+	0.313172i	−0.942157	−	0.335173i	$-0.891205\pi$
$367$	−3.46382	+	5.99952i	−0.180810	+	0.313172i	0.761347	+	0.648345i	$0.224539\pi$
$368$	19.1980			1.00077
$369$	−14.2195	+	9.97973i	−0.740239	+	0.519524i
$370$	−0.548209			−0.0285000
$371$	0.145505	−	0.252022i	0.00755424	−	0.0130843i
$372$	3.46142	+	10.9574i	0.179466	+	0.568115i
$373$	−11.9682	−	20.7296i	−0.619691	−	1.07334i	−0.989542	−	0.144245i	$-0.953925\pi$
$373$	−11.9682	−	20.7296i	−0.619691	−	1.07334i	0.369851	−	0.929091i	$-0.379409\pi$
$374$	0.760736	+	1.31763i	0.0393367	+	0.0681332i
$375$	−1.16946	+	1.27764i	−0.0603907	+	0.0659770i
$376$	−0.338383	+	0.586097i	−0.0174508	+	0.0302256i
$377$	−8.46881			−0.436166
$378$	0.00161094	−	0.0123928i	8.28578e−5	−	0.000637419i
$379$	21.8501			1.12236			0.561181	−	0.827693i	$-0.310347\pi$
$379$	21.8501			1.12236			0.561181	+	0.827693i	$0.310347\pi$
$380$	2.65295	−	4.59505i	0.136094	−	0.235721i
$381$	−13.5311	+	14.7828i	−0.693220	+	0.757345i
$382$	0.239505	+	0.414834i	0.0122541	+	0.0212248i
$383$	12.3076	+	21.3174i	0.628888	+	1.08927i	0.987775	+	0.155886i	$0.0498231\pi$
$383$	12.3076	+	21.3174i	0.628888	+	1.08927i	−0.358887	+	0.933381i	$0.616844\pi$
$384$	1.25265	+	3.96536i	0.0639240	+	0.202356i
$385$	−0.0910097	+	0.157633i	−0.00463828	+	0.00803374i
$386$	1.48235			0.0754494
$387$	−20.8695	−	9.70391i	−1.06085	−	0.493277i
$388$	−29.8373			−1.51476
$389$	−4.27205	+	7.39940i	−0.216601	+	0.375164i	−0.953767	−	0.300548i	$-0.902830\pi$
$389$	−4.27205	+	7.39940i	−0.216601	+	0.375164i	0.737165	+	0.675712i	$0.236164\pi$
$390$	−0.127799	−	0.0282593i	−0.00647135	−	0.00143096i
$391$	8.52134	+	14.7594i	0.430943	+	0.746415i
$392$	−1.05628	−	1.82952i	−0.0533500	−	0.0924049i
$393$	−21.6684	−	4.79139i	−1.09303	−	0.241694i
$394$	−0.306226	+	0.530399i	−0.0154274	+	0.0267211i
$395$	7.91095			0.398043
$396$	3.01929	+	34.0828i	0.151725	+	1.71272i
$397$	−29.5865			−1.48490			−0.742452	−	0.669899i	$-0.766337\pi$
$397$	−29.5865			−1.48490			−0.742452	+	0.669899i	$0.766337\pi$
$398$	0.0231460	−	0.0400900i	0.00116020	−	0.00200953i
$399$	−0.0441792	−	0.139853i	−0.00221173	−	0.00700140i
$400$	−1.98289	−	3.43446i	−0.0991443	−	0.171723i
$401$	−2.27286	−	3.93670i	−0.113501	−	0.196590i	0.803679	−	0.595064i	$-0.202873\pi$
$401$	−2.27286	−	3.93670i	−0.113501	−	0.196590i	−0.917180	+	0.398474i	$0.869540\pi$
$402$	0.788676	−	0.861631i	0.0393356	−	0.0429742i
$403$	1.66335	−	2.88101i	0.0828574	−	0.143513i
$404$	−14.0817			−0.700592
$405$	5.80010	+	6.88177i	0.288209	+	0.341958i
$406$	0.0203681			0.00101085
$407$	20.7447	−	35.9308i	1.02827	−	1.78102i
$408$	−1.24270	+	1.35765i	−0.0615228	+	0.0672139i
$409$	−12.5979	−	21.8201i	−0.622924	−	1.07894i	−0.988938	−	0.148327i	$-0.952611\pi$
$409$	−12.5979	−	21.8201i	−0.622924	−	1.07894i	0.366014	−	0.930609i	$-0.380722\pi$
$410$	−0.218793	−	0.378961i	−0.0108054	−	0.0187155i
$411$	4.51489	+	14.2922i	0.222703	+	0.704984i
$412$	−11.1640	+	19.3366i	−0.550009	+	0.952644i
$413$	−0.256247			−0.0126091
$414$	−0.0968403	−	1.09317i	−0.00475944	−	0.0537261i
$415$	−2.25461			−0.110675
$416$	0.451678	−	0.782329i	0.0221453	−	0.0383568i
$417$	24.0143	+	5.31012i	1.17599	+	0.260038i
$418$	−0.574905	−	0.995765i	−0.0281195	−	0.0487045i
$419$	3.08048	+	5.33555i	0.150491	+	0.260659i	0.931408	−	0.363976i	$-0.118581\pi$
$419$	3.08048	+	5.33555i	0.150491	+	0.260659i	−0.780917	+	0.624635i	$0.785248\pi$
$420$	−0.107344	−	0.0237362i	−0.00523785	−	0.00115821i
$421$	−4.30443	+	7.45548i	−0.209785	+	0.363358i	−0.951647	−	0.307195i	$-0.900610\pi$
$421$	−4.30443	+	7.45548i	−0.209785	+	0.363358i	0.741862	+	0.670553i	$0.233943\pi$
$422$	1.02230			0.0497650
$423$	−6.09935	−	2.83609i	−0.296561	−	0.137895i
$424$	2.75985			0.134030
$425$	1.76027	−	3.04887i	0.0853855	−	0.147892i
$426$	−0.470997	−	1.49098i	−0.0228199	−	0.0722382i
$427$	−0.101941	−	0.176567i	−0.00493327	−	0.00854467i
$428$	1.42294	+	2.46461i	0.0687806	+	0.119132i
$429$	6.68818	−	7.30686i	0.322909	−	0.352779i
$430$	0.289865	−	0.502062i	0.0139786	−	0.0242116i
$431$	−19.4600			−0.937356			−0.468678	−	0.883369i	$-0.655269\pi$
$431$	−19.4600			−0.937356			−0.468678	+	0.883369i	$0.655269\pi$
$432$	−19.0252	+	7.91698i	−0.915352	+	0.380906i
$433$	−15.6118			−0.750255			−0.375127	−	0.926973i	$-0.622401\pi$
$433$	−15.6118			−0.750255			−0.375127	+	0.926973i	$0.622401\pi$
$434$	−0.00400047	+	0.00692902i	−0.000192029	+	0.000332604i
$435$	−9.90394	+	10.8201i	−0.474857	+	0.518783i
$436$	16.1933	+	28.0477i	0.775521	+	1.34324i
$437$	−6.43977	−	11.1540i	−0.308056	−	0.533569i
$438$	−0.116859	−	0.369927i	−0.00558374	−	0.0176758i
$439$	−14.6955	+	25.4534i	−0.701379	+	1.21482i	0.266604	+	0.963806i	$0.414099\pi$
$439$	−14.6955	+	25.4534i	−0.701379	+	1.21482i	−0.967983	+	0.251018i	$0.919235\pi$
$440$	−1.72621			−0.0822941
$441$	17.1866	−	12.0621i	0.818408	−	0.574386i
$442$	0.266036			0.0126541
$443$	8.81112	−	15.2613i	0.418629	−	0.725087i	−0.577173	−	0.816622i	$-0.695844\pi$
$443$	8.81112	−	15.2613i	0.418629	−	0.725087i	0.995802	+	0.0915353i	$0.0291774\pi$
$444$	24.4679	+	5.41041i	1.16119	+	0.256767i
$445$	−6.29327	−	10.9003i	−0.298330	−	0.516722i
$446$	−0.414361	−	0.717695i	−0.0196206	−	0.0339838i
$447$	−26.9531	−	5.95995i	−1.27484	−	0.281896i
$448$	0.125132	−	0.216735i	0.00591193	−	0.0102398i
$449$	−20.8212			−0.982612			−0.491306	−	0.870987i	$-0.663480\pi$
$449$	−20.8212			−0.982612			−0.491306	+	0.870987i	$0.663480\pi$
$450$	−0.185561	+	0.130233i	−0.00874743	+	0.00613923i
$451$	33.1172			1.55943
$452$	12.1136	−	20.9814i	0.569777	−	0.986882i
$453$	−0.568855	−	1.80075i	−0.0267271	−	0.0846068i
$454$	−0.556628	−	0.964109i	−0.0261239	−	0.0452479i
$455$	0.0159135	+	0.0275629i	0.000746035	+	0.00129217i
$456$	0.939136	−	1.02601i	0.0439791	−	0.0480473i
$457$	−14.8735	+	25.7616i	−0.695751	+	1.20508i	0.274175	+	0.961680i	$0.411595\pi$
$457$	−14.8735	+	25.7616i	−0.695751	+	1.20508i	−0.969927	+	0.243397i	$0.921738\pi$
$458$	−0.0912010			−0.00426154
$459$	−14.5312	−	11.1125i	−0.678258	−	0.518686i
$460$	−9.65423			−0.450131
$461$	1.73002	−	2.99647i	0.0805748	−	0.139560i	−0.822922	−	0.568154i	$-0.807658\pi$
$461$	1.73002	−	2.99647i	0.0805748	−	0.139560i	0.903497	+	0.428594i	$0.140991\pi$
$462$	−0.0160855	+	0.0175735i	−0.000748367	+	0.000817593i
$463$	−8.54741	−	14.8046i	−0.397232	−	0.688026i	0.596151	−	0.802872i	$-0.296696\pi$
$463$	−8.54741	−	14.8046i	−0.397232	−	0.688026i	−0.993383	+	0.114846i	$0.963362\pi$
$464$	−16.7927	−	29.0858i	−0.779580	−	1.35027i
$465$	−1.73567	−	5.49439i	−0.0804896	−	0.254796i
$466$	−0.444770	+	0.770364i	−0.0206036	+	0.0356864i
$467$	37.9426			1.75578			0.877888	−	0.478866i	$-0.158952\pi$
$467$	37.9426			1.75578			0.877888	+	0.478866i	$0.158952\pi$
$468$	5.42507	+	2.52256i	0.250774	+	0.116605i
$469$	−0.284037			−0.0131156
$470$	0.0847167	−	0.146734i	0.00390769	−	0.00676832i
$471$	−31.6357	−	6.99539i	−1.45770	−	0.322331i
$472$	−1.21508	−	2.10458i	−0.0559287	−	0.0968714i
$473$	21.9375	+	37.9968i	1.00869	+	1.74709i
$474$	1.01101	+	0.223558i	0.0464373	+	0.0102683i
$475$	−1.33027	+	2.30410i	−0.0610371	+	0.105719i
$476$	0.223456			0.0102421
$477$	2.42051	+	27.3235i	0.110828	+	1.25106i
$478$	−1.07532			−0.0491841
$479$	15.6590	−	27.1221i	0.715476	−	1.23924i	−0.247299	−	0.968939i	$-0.579543\pi$
$479$	15.6590	−	27.1221i	0.715476	−	1.23924i	0.962776	−	0.270302i	$-0.0871236\pi$
$480$	−0.471315	−	1.49198i	−0.0215125	−	0.0680994i
$481$	−3.62730	−	6.28267i	−0.165391	−	0.286465i
$482$	−0.151056	−	0.261637i	−0.00688043	−	0.0119172i
$483$	−0.180181	+	0.196849i	−0.00819853	+	0.00895692i
$484$	21.6454	−	37.4909i	0.983880	−	1.70413i
$485$	14.9614			0.679361
$486$	0.546773	+	1.04339i	0.0248021	+	0.0473291i
$487$	31.2277			1.41506			0.707531	−	0.706683i	$-0.249809\pi$
$487$	31.2277			1.41506			0.707531	+	0.706683i	$0.249809\pi$
$488$	0.966776	−	1.67451i	0.0437639	−	0.0758013i
$489$	−0.678621	+	0.741395i	−0.0306883	+	0.0335271i
$490$	0.264447	+	0.458035i	0.0119465	+	0.0206919i
$491$	4.46260	+	7.72946i	0.201395	+	0.348826i	0.948978	−	0.315342i	$-0.102119\pi$
$491$	4.46260	+	7.72946i	0.201395	+	0.348826i	−0.747583	+	0.664168i	$0.768786\pi$
$492$	6.02520	+	19.0732i	0.271637	+	0.859888i
$493$	14.9074	−	25.8203i	0.671394	−	1.16289i
$494$	−0.201050			−0.00904566
$495$	−1.51397	−	17.0902i	−0.0680478	−	0.768146i
$496$	13.1929			0.592380
$497$	−0.190107	+	0.329275i	−0.00852747	+	0.0147700i
$498$	−0.288137	−	0.0637137i	−0.0129117	−	0.00285508i
$499$	−12.0359	−	20.8468i	−0.538802	−	0.933233i	−0.998969	−	0.0454002i	$-0.985544\pi$
$499$	−12.0359	−	20.8468i	−0.538802	−	0.933233i	0.460167	−	0.887833i	$-0.347790\pi$
$500$	0.997145	+	1.72711i	0.0445937	+	0.0772385i
$501$	−30.3134	−	6.70299i	−1.35430	−	0.299467i
$502$	−0.883876	+	1.53092i	−0.0394493	+	0.0683282i
$503$	2.64303			0.117847			0.0589234	−	0.998263i	$-0.481233\pi$
$503$	2.64303			0.117847			0.0589234	+	0.998263i	$0.481233\pi$
$504$	−0.0261327	−	0.0121512i	−0.00116404	−	0.000541258i
$505$	7.06102			0.314211
$506$	−1.04606	+	1.81182i	−0.0465028	+	0.0805453i
$507$	−0.521738	−	1.65160i	−0.0231712	−	0.0733502i
$508$	11.5374	+	19.9833i	0.511887	+	0.886615i
$509$	12.3022	+	21.3081i	0.545286	+	0.944463i	0.998589	+	0.0531064i	$0.0169122\pi$
$509$	12.3022	+	21.3081i	0.545286	+	0.944463i	−0.453303	+	0.891357i	$0.649754\pi$
$510$	0.311119	−	0.339899i	0.0137766	−	0.0150510i
$511$	−0.0471674	+	0.0816964i	−0.00208656	+	0.00361404i
$512$	5.97653			0.264128
$513$	10.9815	+	8.39795i	0.484847	+	0.370778i
$514$	0.588269			0.0259474
$515$	5.59797	−	9.69596i	0.246676	−	0.427255i
$516$	−17.8924	+	19.5475i	−0.787667	+	0.860529i
$517$	6.41149	+	11.1050i	0.281977	+	0.488399i
$518$	0.00872391	+	0.0151103i	0.000383306	+	0.000663906i
$519$	−2.47317	−	7.82901i	−0.108560	−	0.343655i
$520$	−0.150918	+	0.261398i	−0.00661821	+	0.0114631i
$521$	39.4979			1.73043			0.865216	−	0.501399i	$-0.167181\pi$
$521$	39.4979			1.73043			0.865216	+	0.501399i	$0.167181\pi$
$522$	−1.57148	+	1.10292i	−0.0687818	+	0.0482734i
$523$	28.5620			1.24893			0.624465	−	0.781053i	$-0.285317\pi$
$523$	28.5620			1.24893			0.624465	+	0.781053i	$0.285317\pi$
$524$	−12.7759	+	22.1285i	−0.558117	+	0.966688i
$525$	0.0538257	+	0.0119021i	0.00234914	+	0.000519450i
$526$	−0.921128	−	1.59544i	−0.0401631	−	0.0695645i
$527$	5.85588	+	10.1427i	0.255086	+	0.441822i
$528$	38.3570	+	8.48162i	1.66927	+	0.369115i
$529$	−0.217332	+	0.376430i	−0.00944921	+	0.0163665i
$530$	−0.690948			−0.0300129
$531$	19.7705	−	13.8756i	0.857966	−	0.602149i
$532$	−0.168871			−0.00732147
$533$	2.89535	−	5.01489i	0.125412	−	0.217219i
$534$	−0.496240	−	1.57089i	−0.0214744	−	0.0679789i
$535$	−0.713509	−	1.23583i	−0.0308477	−	0.0534298i
$536$	−1.34686	−	2.33283i	−0.0581755	−	0.100763i
$537$	26.5024	−	28.9540i	1.14367	−	1.24946i
$538$	0.144011	−	0.249435i	0.00620877	−	0.0107539i
$539$	−40.0274			−1.72410
$540$	9.56733	−	3.98126i	0.411712	−	0.171326i
$541$	−37.1754			−1.59830			−0.799148	−	0.601135i	$-0.794716\pi$
$541$	−37.1754			−1.59830			−0.799148	+	0.601135i	$0.794716\pi$
$542$	−0.589203	+	1.02053i	−0.0253084	+	0.0438355i
$543$	−4.10046	+	4.47976i	−0.175968	+	0.192245i
$544$	1.59015	+	2.75421i	0.0681770	+	0.118086i
$545$	−8.11986	−	14.0640i	−0.347816	−	0.602436i
$546$	0.00125482	+	0.00397222i	5.37011e−5	+	0.000169995i
$547$	−4.15260	+	7.19251i	−0.177552	+	0.307529i	−0.941042	−	0.338291i	$-0.890151\pi$
$547$	−4.15260	+	7.19251i	−0.177552	+	0.307529i	0.763489	+	0.645820i	$0.223485\pi$
$548$	17.2577			0.737213
$549$	17.4261	+	8.10283i	0.743730	+	0.345820i
$550$	0.432171			0.0184278
$551$	−11.2658	+	19.5130i	−0.479941	+	0.831282i
$552$	−2.47113	−	0.546424i	−0.105178	−	0.0232574i
$553$	−0.125891	−	0.218049i	−0.00535341	−	0.00927239i
$554$	−0.843992	−	1.46184i	−0.0358578	−	0.0621075i
$555$	−12.2690	−	2.71295i	−0.520789	−	0.115158i
$556$	14.1591	−	24.5242i	0.600478	−	1.04006i
$557$	17.8722			0.757270			0.378635	−	0.925546i	$-0.376394\pi$
$557$	17.8722			0.757270			0.378635	+	0.925546i	$0.376394\pi$
$558$	−0.0665489	−	0.751226i	−0.00281724	−	0.0318019i
$559$	7.67174			0.324480
$560$	−0.0631092	+	0.109308i	−0.00266685	+	0.00461912i
$561$	10.5047	+	33.2534i	0.443509	+	1.40396i
$562$	0.0881105	+	0.152612i	0.00371672	+	0.00643754i
$563$	−11.6729	−	20.2181i	−0.491955	−	0.852090i	0.508003	−	0.861356i	$-0.330384\pi$
$563$	−11.6729	−	20.2181i	−0.491955	−	0.852090i	−0.999957	+	0.00926530i	$0.997051\pi$
$564$	−5.22926	+	5.71298i	−0.220192	+	0.240560i
$565$	−6.07415	+	10.5207i	−0.255542	+	0.442611i
$566$	1.72598			0.0725482
$567$	0.0973821	−	0.269381i	0.00408966	−	0.0113129i
$568$	−3.60583			−0.151297
$569$	2.29423	−	3.97372i	0.0961792	−	0.166587i	−0.813921	−	0.580976i	$-0.802671\pi$
$569$	2.29423	−	3.97372i	0.0961792	−	0.166587i	0.910100	+	0.414388i	$0.136004\pi$
$570$	−0.235120	+	0.256869i	−0.00984808	+	0.0107591i
$571$	17.3547	+	30.0593i	0.726273	+	1.25794i	0.958448	+	0.285268i	$0.0920826\pi$
$571$	17.3547	+	30.0593i	0.726273	+	1.25794i	−0.232174	+	0.972674i	$0.574584\pi$
$572$	−5.70270	−	9.87737i	−0.238442	−	0.412994i
$573$	3.30722	+	10.4693i	0.138161	+	0.437360i
$574$	−0.00696351	+	0.0120612i	−0.000290651	+	0.000503423i
$575$	4.84094			0.201881
$576$	2.08160	+	23.4978i	0.0867334	+	0.979075i
$577$	32.8992			1.36961			0.684806	−	0.728726i	$-0.259887\pi$
$577$	32.8992			1.36961			0.684806	+	0.728726i	$0.259887\pi$
$578$	0.174025	−	0.301420i	0.00723848	−	0.0125374i
$579$	33.1750	+	7.33576i	1.37871	+	0.304864i
$580$	8.44463	+	14.6265i	0.350644	+	0.607333i
$581$	0.0358787	+	0.0621437i	0.00148850	+	0.00257816i
$582$	1.91205	+	0.422797i	0.0792569	+	0.0175255i
$583$	26.1460	−	45.2862i	1.08286	−	1.87556i
$584$	−0.894643			−0.0370206
$585$	−2.72030	−	1.26489i	−0.112471	−	0.0522968i
$586$	0.292424			0.0120799
$587$	1.67419	−	2.89978i	0.0691011	−	0.119687i	−0.829405	−	0.558648i	$-0.811320\pi$
$587$	1.67419	−	2.89978i	0.0691011	−	0.119687i	0.898506	+	0.438962i	$0.144654\pi$
$588$	−7.28242	−	23.0531i	−0.300322	−	0.950693i
$589$	−4.42542	−	7.66506i	−0.182346	−	0.315833i
$590$	0.304205	+	0.526898i	0.0125239	+	0.0216921i
$591$	−9.47818	+	10.3549i	−0.389880	+	0.425945i
$592$	14.3850	−	24.9156i	0.591222	−	1.02403i
$593$	−13.8893			−0.570363			−0.285182	−	0.958473i	$-0.592054\pi$
$593$	−13.8893			−0.570363			−0.285182	+	0.958473i	$0.592054\pi$
$594$	0.289472	−	2.22689i	0.0118772	−	0.0913704i
$595$	−0.112048			−0.00459351
$596$	−15.8918	+	27.5254i	−0.650953	+	1.12748i
$597$	0.716405	−	0.782674i	0.0293205	−	0.0320327i
$598$	0.182908	+	0.316805i	0.00747965	+	0.0129551i
$599$	2.31924	+	4.01705i	0.0947617	+	0.164132i	0.909509	−	0.415684i	$-0.136458\pi$
$599$	2.31924	+	4.01705i	0.0947617	+	0.164132i	−0.814747	+	0.579816i	$0.803124\pi$
$600$	0.157480	+	0.498514i	0.00642908	+	0.0203518i
$601$	23.3259	−	40.4017i	0.951484	−	1.64802i	0.209267	−	0.977859i	$-0.432892\pi$
$601$	23.3259	−	40.4017i	0.951484	−	1.64802i	0.742217	−	0.670160i	$-0.233774\pi$
$602$	−0.0184511			−0.000752009
$603$	21.9146	−	15.3804i	0.892433	−	0.626339i
$604$	−2.17439			−0.0884746
$605$	−10.8537	+	18.7991i	−0.441265	+	0.764293i
$606$	0.902391	+	0.199539i	0.0366571	+	0.00810574i
$607$	11.3404	+	19.6421i	0.460291	+	0.797248i	0.998975	−	0.0452602i	$-0.0144117\pi$
$607$	11.3404	+	19.6421i	0.460291	+	0.797248i	−0.538684	+	0.842508i	$0.681078\pi$
$608$	−1.20171	−	2.08142i	−0.0487358	−	0.0844128i
$609$	0.455839	+	0.100797i	0.0184715	+	0.00408448i
$610$	−0.242040	+	0.419225i	−0.00979990	+	0.0169739i
$611$	2.24216			0.0907081
$612$	−17.2405	+	12.1000i	−0.696907	+	0.489113i
$613$	−13.3621			−0.539691			−0.269846	−	0.962904i	$-0.586973\pi$
$613$	−13.3621			−0.539691			−0.269846	+	0.962904i	$0.586973\pi$
$614$	−0.134725	+	0.233351i	−0.00543707	+	0.00941729i
$615$	−3.02123	−	9.56393i	−0.121828	−	0.385655i
$616$	0.0274701	+	0.0475795i	0.00110680	+	0.00191703i
$617$	11.9900	+	20.7672i	0.482697	+	0.836056i	0.999803	−	0.0198655i	$-0.00632381\pi$
$617$	11.9900	+	20.7672i	0.482697	+	0.836056i	−0.517105	+	0.855922i	$0.672990\pi$
$618$	0.989415	−	1.08094i	0.0398001	−	0.0434817i
$619$	−0.692598	+	1.19962i	−0.0278379	+	0.0482166i	−0.879609	−	0.475698i	$-0.842196\pi$
$619$	−0.692598	+	1.19962i	−0.0278379	+	0.0482166i	0.851771	+	0.523915i	$0.175529\pi$
$620$	−6.63441			−0.266444
$621$	3.24251	−	24.9444i	0.130117	−	1.00098i
$622$	2.27967			0.0914065
$623$	−0.200296	+	0.346922i	−0.00802467	+	0.0138991i
$624$	4.63781	−	5.06682i	0.185661	−	0.202835i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.211998	−	0.367192i	−0.00847315	−	0.0146759i
$627$	−7.93864	−	25.1304i	−0.317039	−	1.00361i
$628$	−18.6527	+	32.3074i	−0.744324	+	1.28921i
$629$	25.5401			1.01835
$630$	0.00654252	+	0.00304215i	0.000260660	+	0.000121202i
$631$	−18.7690			−0.747180			−0.373590	−	0.927594i	$-0.621873\pi$
$631$	−18.7690			−0.747180			−0.373590	+	0.927594i	$0.621873\pi$
$632$	1.19391	−	2.06791i	0.0474911	−	0.0822570i
$633$	22.8793	+	5.05913i	0.909369	+	0.201082i
$634$	0.904170	+	1.56607i	0.0359092	+	0.0621965i
$635$	−5.78520	−	10.0203i	−0.229578	−	0.397642i
$636$	30.8387	+	6.81913i	1.22283	+	0.270396i
$637$	−3.49949	+	6.06130i	−0.138655	+	0.240157i
$638$	3.65997			0.144900
$639$	−3.16248	−	35.6991i	−0.125106	−	1.41223i
$640$	−2.40092			−0.0949045
$641$	−0.295738	+	0.512233i	−0.0116809	+	0.0202320i	−0.871807	−	0.489850i	$-0.837052\pi$
$641$	−0.295738	+	0.512233i	−0.0116809	+	0.0202320i	0.860126	+	0.510082i	$0.170385\pi$
$642$	−0.0562619	−	0.178102i	−0.00222048	−	0.00702911i
$643$	−1.95409	−	3.38458i	−0.0770617	−	0.133475i	0.824919	−	0.565251i	$-0.191221\pi$
$643$	−1.95409	−	3.38458i	−0.0770617	−	0.133475i	−0.901981	+	0.431776i	$0.857887\pi$
$644$	0.153632	+	0.266099i	0.00605396	+	0.0104858i
$645$	8.97179	−	9.80171i	0.353264	−	0.385942i
$646$	0.353901	−	0.612975i	0.0139241	−	0.0241172i
$647$	−22.0401			−0.866486			−0.433243	−	0.901277i	$-0.642631\pi$
$647$	−22.0401			−0.866486			−0.433243	+	0.901277i	$0.642631\pi$
$648$	2.67423	−	0.477551i	0.105054	−	0.0187600i
$649$	−46.0454			−1.80744
$650$	0.0377835	−	0.0654430i	0.00148199	−	0.00256689i
$651$	−0.123821	+	0.135275i	−0.00485293	+	0.00530184i
$652$	0.578629	+	1.00221i	0.0226608	+	0.0392497i
$653$	14.7625	+	25.5694i	0.577702	+	1.00061i	0.995742	+	0.0921807i	$0.0293838\pi$
$653$	14.7625	+	25.5694i	0.577702	+	1.00061i	−0.418040	+	0.908428i	$0.637283\pi$
$654$	−0.640270	−	2.02683i	−0.0250365	−	0.0792552i
$655$	6.40624	−	11.0959i	0.250312	−	0.433554i
$656$	22.9646			0.896616
$657$	−0.784642	−	8.85730i	−0.0306118	−	0.345556i
$658$	−0.00539255			−0.000210223
$659$	−14.0894	+	24.4035i	−0.548843	+	0.950624i	0.449511	+	0.893275i	$0.351598\pi$
$659$	−14.0894	+	24.4035i	−0.548843	+	0.950624i	−0.998354	+	0.0573495i	$0.981735\pi$
$660$	−19.2888	−	4.26520i	−0.750816	−	0.166023i
$661$	6.93910	+	12.0189i	0.269900	+	0.467480i	0.968836	−	0.247704i	$-0.0796762\pi$
$661$	6.93910	+	12.0189i	0.269900	+	0.467480i	−0.698936	+	0.715184i	$0.746343\pi$
$662$	1.29207	+	2.23792i	0.0502175	+	0.0869793i
$663$	5.95392	+	1.31655i	0.231231	+	0.0511305i
$664$	−0.340262	+	0.589352i	−0.0132047	+	0.0228713i
$665$	0.0846771			0.00328364
$666$	−1.49130	−	0.693424i	−0.0577865	−	0.0268697i
$667$	40.9970			1.58741
$668$	−17.8730	+	30.9570i	−0.691528	+	1.19776i
$669$	−5.72175	−	18.1127i	−0.221216	−	0.700276i
$670$	0.337196	+	0.584041i	0.0130270	+	0.0225635i
$671$	−18.3179	−	31.7276i	−0.707156	−	1.22483i
$672$	−0.0336232	+	0.0367334i	−0.00129704	+	0.00141702i
$673$	−4.21021	+	7.29230i	−0.162292	+	0.281097i	−0.935690	−	0.352823i	$-0.885222\pi$
$673$	−4.21021	+	7.29230i	−0.162292	+	0.281097i	0.773399	+	0.633920i	$0.218555\pi$
$674$	1.57157			0.0605347
$675$	−4.79736	+	1.99633i	−0.184651	+	0.0768387i
$676$	−1.99429			−0.0767034
$677$	0.0207555	−	0.0359495i	0.000797697	−	0.00138165i	−0.865626	−	0.500691i	$-0.833079\pi$
$677$	0.0207555	−	0.0359495i	0.000797697	−	0.00138165i	0.866424	+	0.499309i	$0.166413\pi$
$678$	−1.07358	+	1.17289i	−0.0412305	+	0.0450445i
$679$	−0.238087	−	0.412379i	−0.00913695	−	0.0158257i
$680$	−0.531313	−	0.920262i	−0.0203749	−	0.0352904i
$681$	−7.68626	−	24.3315i	−0.294538	−	0.932384i
$682$	−0.718852	+	1.24509i	−0.0275262	+	0.0476769i
$683$	8.08761			0.309464			0.154732	−	0.987956i	$-0.450549\pi$
$683$	8.08761			0.309464			0.154732	+	0.987956i	$0.450549\pi$
$684$	13.0291	−	9.14423i	0.498179	−	0.349638i
$685$	−8.65356			−0.330636
$686$	0.0168343	−	0.0291578i	0.000642735	−	0.00111325i
$687$	−2.04109	−	0.451331i	−0.0778723	−	0.0172194i
$688$	15.2122	+	26.3483i	0.579959	+	1.00452i
$689$	−4.57175	−	7.91851i	−0.174170	−	0.301671i
$690$	0.618666	+	0.136801i	0.0235522	+	0.00520794i
$691$	−4.82694	+	8.36050i	−0.183625	+	0.318048i	−0.943112	−	0.332474i	$-0.892117\pi$
$691$	−4.82694	+	8.36050i	−0.183625	+	0.318048i	0.759487	+	0.650522i	$0.225450\pi$
$692$	−9.45343			−0.359365
$693$	−0.446963	+	0.313693i	−0.0169787	+	0.0119162i
$694$	−0.751613			−0.0285308
$695$	−7.09980	+	12.2972i	−0.269311	+	0.466460i
$696$	1.33367	+	4.22182i	0.0505525	+	0.160028i
$697$	10.1932	+	17.6551i	0.386094	+	0.668735i
$698$	1.05008	+	1.81880i	0.0397463	+	0.0688426i
$699$	−13.7663	+	15.0398i	−0.520691	+	0.568856i
$700$	0.0317361	−	0.0549685i	0.00119951	−	0.00207761i
$701$	−22.4892			−0.849405			−0.424703	−	0.905333i	$-0.639621\pi$
$701$	−22.4892			−0.849405			−0.424703	+	0.905333i	$0.639621\pi$
$702$	−0.311907	−	0.238525i	−0.0117722	−	0.00900256i
$703$	−19.3012			−0.727959
$704$	22.4852	−	38.9455i	0.847442	−	1.46781i
$705$	2.62212	−	2.86467i	0.0987546	−	0.107890i
$706$	−0.982418	−	1.70160i	−0.0369738	−	0.0640405i
$707$	−0.112365	−	0.194623i	−0.00422594	−	0.00731953i
$708$	−8.37730	−	26.5190i	−0.314838	−	0.996645i
$709$	13.4940	−	23.3723i	0.506778	−	0.877765i	−0.493191	−	0.869921i	$-0.664170\pi$
$709$	13.4940	−	23.3723i	0.506778	−	0.877765i	0.999969	−	0.00784418i	$-0.00249690\pi$
$710$	0.902747			0.0338795
$711$	21.5202	+	10.0065i	0.807070	+	0.375272i
$712$	−3.79908			−0.142377
$713$	−8.05218	+	13.9468i	−0.301556	+	0.522311i
$714$	−0.0143196	−	0.00316639i	−0.000535897	−	0.000118499i
$715$	2.85952	+	4.95283i	0.106940	+	0.185225i
$716$	−22.5974	−	39.1399i	−0.844505	−	1.46273i
$717$	−24.0658	−	5.32151i	−0.898754	−	0.198735i
$718$	−0.0225037	+	0.0389775i	−0.000839830	+	0.00145463i
$719$	−38.6330			−1.44077			−0.720384	−	0.693575i	$-0.756034\pi$
$719$	−38.6330			−1.44077			−0.720384	+	0.693575i	$0.756034\pi$
$720$	−1.04984	−	11.8509i	−0.0391251	−	0.441657i
$721$	−0.356332			−0.0132705
$722$	0.450436	−	0.780178i	0.0167635	−	0.0290352i
$723$	−2.08588	−	6.60301i	−0.0775746	−	0.245568i
$724$	3.49627	+	6.05572i	0.129938	+	0.225059i
$725$	−4.23440	−	7.33420i	−0.157262	−	0.272386i
$726$	−1.91834	+	2.09579i	−0.0711962	+	0.0777820i
$727$	−21.5738	+	37.3670i	−0.800129	+	1.38586i	0.119402	+	0.992846i	$0.461902\pi$
$727$	−21.5738	+	37.3670i	−0.800129	+	1.38586i	−0.919531	+	0.393018i	$0.871431\pi$
$728$	0.00960654			0.000356042
$729$	7.07336	+	26.0570i	0.261976	+	0.965074i
$730$	0.223980			0.00828989
$731$	−13.5043	+	23.3901i	−0.499475	+	0.865116i
$732$	14.9402	−	16.3223i	0.552207	−	0.603288i
$733$	15.0568	+	26.0791i	0.556135	+	0.963255i	0.997814	+	0.0660815i	$0.0210497\pi$
$733$	15.0568	+	26.0791i	0.556135	+	0.963255i	−0.441679	+	0.897173i	$0.645617\pi$
$734$	−0.261751	−	0.453366i	−0.00966141	−	0.0167340i
$735$	3.65164	+	11.5595i	0.134693	+	0.426380i
$736$	−2.18654	+	3.78720i	−0.0805970	+	0.139598i
$737$	−51.0391			−1.88005
$738$	−0.115840	−	1.30764i	−0.00426412	−	0.0481348i
$739$	−18.9795			−0.698171			−0.349085	−	0.937091i	$-0.613508\pi$
$739$	−18.9795			−0.698171			−0.349085	+	0.937091i	$0.613508\pi$
$740$	−7.23389	+	12.5295i	−0.265923	+	0.460592i
$741$	−4.49951	−	0.994946i	−0.165294	−	0.0365502i
$742$	0.0109954	+	0.0190446i	0.000403653	+	0.000699147i
$743$	−5.58335	−	9.67065i	−0.204833	−	0.354782i	0.745246	−	0.666789i	$-0.232332\pi$
$743$	−5.58335	−	9.67065i	−0.204833	−	0.354782i	−0.950080	+	0.312008i	$0.898999\pi$
$744$	−1.69817	−	0.375504i	−0.0622579	−	0.0137666i
$745$	7.96865	−	13.8021i	0.291949	−	0.505670i
$746$	1.80881			0.0662251
$747$	−6.13323	−	2.85184i	−0.224403	−	0.104343i
$748$	40.1531			1.46814
$749$	−0.0227088	+	0.0393328i	−0.000829762	+	0.00143719i
$750$	−0.0394262	−	0.124807i	−0.00143964	−	0.00455730i
$751$	9.78665	+	16.9510i	0.357120	+	0.618550i	0.987478	−	0.157754i	$-0.0504254\pi$
$751$	9.78665	+	16.9510i	0.357120	+	0.618550i	−0.630358	+	0.776304i	$0.717092\pi$
$752$	4.44594	+	7.70060i	0.162127	+	0.280812i
$753$	−27.3574	+	29.8880i	−0.996957	+	1.08918i
$754$	0.319982	−	0.554224i	0.0116530	−	0.0201837i
$755$	1.09031			0.0396803
$756$	−0.261984	−	0.200348i	−0.00952828	−	0.00728659i
$757$	−9.38250			−0.341013			−0.170506	−	0.985357i	$-0.554540\pi$
$757$	−9.38250			−0.341013			−0.170506	+	0.985357i	$0.554540\pi$
$758$	−0.825573	+	1.42993i	−0.0299862	+	0.0519375i
$759$	−32.3771	+	35.3721i	−1.17521	+	1.28392i
$760$	0.401526	+	0.695463i	0.0145649	+	0.0252271i
$761$	−1.47747	−	2.55906i	−0.0535584	−	0.0927658i	0.838003	−	0.545665i	$-0.183723\pi$
$761$	−1.47747	−	2.55906i	−0.0535584	−	0.0927658i	−0.891562	+	0.452899i	$0.850390\pi$
$762$	−0.456177	−	1.44406i	−0.0165255	−	0.0523129i
$763$	−0.258430	+	0.447614i	−0.00935580	+	0.0162047i
$764$	12.6415			0.457354
$765$	8.64495	−	6.06731i	0.312559	−	0.219364i
$766$	−1.86010			−0.0672080
$767$	−4.02563	+	6.97259i	−0.145357	+	0.251766i
$768$	26.2899	+	5.81330i	0.948655	+	0.209769i
$769$	5.71400	+	9.89694i	0.206052	+	0.356893i	0.950467	−	0.310824i	$-0.100605\pi$
$769$	5.71400	+	9.89694i	0.206052	+	0.356893i	−0.744415	+	0.667717i	$0.767272\pi$
$770$	−0.00687733	−	0.0119119i	−0.000247842	−	0.000429275i
$771$	13.1655	+	2.91120i	0.474144	+	0.104844i
$772$	19.5603	−	33.8794i	0.703990	−	1.21935i
$773$	33.0067			1.18717			0.593584	−	0.804772i	$-0.297713\pi$
$773$	33.0067			1.18717			0.593584	+	0.804772i	$0.297713\pi$
$774$	1.42358	−	0.999112i	0.0511693	−	0.0359123i
$775$	3.32670			0.119499
$776$	2.25795	−	3.91088i	0.0810555	−	0.140392i
$777$	0.120465	+	0.381341i	0.00432166	+	0.0136805i
$778$	−0.322826	−	0.559151i	−0.0115739	−	0.0200465i
$779$	−7.70321	−	13.3424i	−0.275996	−	0.478040i
$780$	−2.33224	+	2.54798i	−0.0835077	+	0.0912324i
$781$	−34.1606	+	59.1680i	−1.22236	+	2.11720i
$782$	−1.28787			−0.0460540
$783$	−40.6279	+	16.9065i	−1.45192	+	0.604190i
$784$	−27.7564			−0.991299
$785$	9.35306	−	16.2000i	0.333825	−	0.578202i
$786$	1.13227	−	1.23701i	0.0403868	−	0.0441227i
$787$	9.94736	+	17.2293i	0.354585	+	0.614160i	0.987047	−	0.160432i	$-0.0512888\pi$
$787$	9.94736	+	17.2293i	0.354585	+	0.614160i	−0.632462	+	0.774592i	$0.717955\pi$
$788$	8.08161	+	13.9978i	0.287895	+	0.498649i
$789$	−12.7195	−	40.2646i	−0.452826	−	1.43346i
$790$	−0.298904	+	0.517716i	−0.0106345	+	0.0184195i
$791$	0.386643			0.0137475
$792$	−4.69583	−	2.18347i	−0.166859	−	0.0775863i
$793$	−6.40595			−0.227482
$794$	1.11788	−	1.93623i	0.0396722	−	0.0687142i
$795$	−15.4635	−	3.41933i	−0.548433	−	0.121271i
$796$	−0.610845	−	1.05801i	−0.0216508	−	0.0375003i
$797$	−0.845505	−	1.46446i	−0.0299493	−	0.0518738i	0.850662	−	0.525713i	$-0.176201\pi$
$797$	−0.845505	−	1.46446i	−0.0299493	−	0.0518738i	−0.880612	+	0.473839i	$0.842868\pi$
$798$	0.0108216	+	0.00239291i	0.000383082	+	8.47082e-5i
$799$	−3.94680	+	6.83606i	−0.139628	+	0.241842i
$800$	0.903355			0.0319384
$801$	−3.33197	−	37.6123i	−0.117729	−	1.32897i
$802$	0.343506			0.0121296
$803$	−8.47559	+	14.6802i	−0.299097	+	0.518051i
$804$	−9.28584	−	29.3950i	−0.327486	−	1.03668i
$805$	−0.0770361	−	0.133430i	−0.00271517	−	0.00470280i
$806$	0.125695	+	0.217709i	0.00442740	+	0.00766849i
$807$	4.45738	−	4.86970i	0.156907	−	0.171422i
$808$	1.06564	−	1.84574i	0.0374890	−	0.0649329i
$809$	15.6187			0.549125			0.274563	−	0.961569i	$-0.411467\pi$
$809$	15.6187			0.549125			0.274563	+	0.961569i	$0.411467\pi$
$810$	−0.669512	+	0.119559i	−0.0235243	+	0.00420086i
$811$	−13.2705			−0.465991			−0.232995	−	0.972478i	$-0.574853\pi$
$811$	−13.2705			−0.465991			−0.232995	+	0.972478i	$0.574853\pi$
$812$	0.268767	−	0.465518i	0.00943186	−	0.0163365i
$813$	−18.2368	+	19.9237i	−0.639591	+	0.698756i
$814$	1.56761	+	2.71519i	0.0549448	+	0.0951672i
$815$	−0.290143	−	0.502542i	−0.0101633	−	0.0176033i
$816$	7.28431	+	23.0591i	0.255002	+	0.807228i
$817$	10.2055	−	17.6765i	0.357046	−	0.618421i
$818$	1.90397			0.0665707
$819$	0.00842537	+	0.0951083i	0.000294406	+	0.00332335i
$820$	−11.5483			−0.403285
$821$	1.24559	−	2.15743i	0.0434715	−	0.0752949i	−0.843471	−	0.537175i	$-0.819492\pi$
$821$	1.24559	−	2.15743i	0.0434715	−	0.0752949i	0.886942	+	0.461880i	$0.152825\pi$
$822$	−1.10592	−	0.244543i	−0.0385733	−	0.00852943i
$823$	14.7624	+	25.5693i	0.514586	+	0.891289i	0.999857	+	0.0169250i	$0.00538767\pi$
$823$	14.7624	+	25.5693i	0.514586	+	0.891289i	−0.485271	+	0.874364i	$0.661279\pi$
$824$	−1.68967	−	2.92660i	−0.0588625	−	0.101953i
$825$	9.67202	+	2.13871i	0.336737	+	0.0744602i
$826$	0.00968191	−	0.0167696i	0.000336877	−	0.000583488i
$827$	−28.5816			−0.993880			−0.496940	−	0.867785i	$-0.665543\pi$
$827$	−28.5816			−0.993880			−0.496940	+	0.867785i	$0.665543\pi$
$828$	−26.2624	−	12.2115i	−0.912683	−	0.424380i
$829$	−9.81060			−0.340736			−0.170368	−	0.985380i	$-0.554496\pi$
$829$	−9.81060			−0.340736			−0.170368	+	0.985380i	$0.554496\pi$
$830$	0.0851872	−	0.147549i	0.00295689	−	0.00512149i
$831$	−11.6543	−	36.8927i	−0.404285	−	1.27980i
$832$	−3.93164	−	6.80980i	−0.136305	−	0.236087i
$833$	−12.3201	−	21.3390i	−0.426866	−	0.739353i
$834$	−1.25486	+	1.37094i	−0.0434521	+	0.0474716i
$835$	8.96210	−	15.5228i	0.310146	−	0.537189i
$836$	−30.3446			−1.04949
$837$	2.22826	−	17.1418i	0.0770199	−	0.592508i
$838$	−0.465566			−0.0160827
$839$	−0.211729	+	0.366726i	−0.00730971	+	0.0126608i	−0.869657	−	0.493656i	$-0.835660\pi$
$839$	−0.211729	+	0.366726i	−0.00730971	+	0.0126608i	0.862347	+	0.506317i	$0.168993\pi$
$840$	0.0112345	−	0.0122737i	0.000387626	−	0.000423483i
$841$	−21.3604	−	36.9972i	−0.736564	−	1.27577i
$842$	−0.325273	−	0.563389i	−0.0112096	−	0.0194157i
$843$	1.21668	+	3.85150i	0.0419048	+	0.132653i
$844$	13.4898	−	23.3650i	0.464338	−	0.804257i
$845$	1.00000			0.0344010
$846$	0.416057	−	0.292003i	0.0143043	−	0.0100393i
$847$	0.690878			0.0237389
$848$	18.1305	−	31.4030i	0.622605	−	1.07838i
$849$	38.6275	+	8.54143i	1.32569	+	0.293141i
$850$	0.133018	+	0.230394i	0.00456249	+	0.00790246i
$851$	17.5595	+	30.4140i	0.601933	+	1.04258i
$852$	−40.2918	−	8.90943i	−1.38037	−	0.305232i
$853$	−27.0939	+	46.9280i	−0.927677	+	1.60678i	−0.140480	+	0.990084i	$0.544864\pi$
$853$	−27.0939	+	46.9280i	−0.927677	+	1.60678i	−0.787198	+	0.616701i	$0.788469\pi$
$854$	0.0154068			0.000527208
$855$	−6.53318	+	4.58521i	−0.223430	+	0.156811i
$856$	−0.430727			−0.0147219
$857$	15.7506	−	27.2809i	0.538032	−	0.931898i	−0.460978	−	0.887411i	$-0.652501\pi$
$857$	15.7506	−	27.2809i	0.538032	−	0.931898i	0.999010	−	0.0444868i	$-0.0141653\pi$
$858$	0.225480	+	0.713774i	0.00769775	+	0.0243678i
$859$	−10.4549	−	18.1084i	−0.356715	−	0.617849i	0.630695	−	0.776031i	$-0.282770\pi$
$859$	−10.4549	−	18.1084i	−0.356715	−	0.617849i	−0.987410	+	0.158182i	$0.949437\pi$
$860$	−7.64983	−	13.2499i	−0.260857	−	0.451818i
$861$	−0.215532	+	0.235469i	−0.00734530	+	0.00802477i
$862$	0.735268	−	1.27352i	0.0250433	−	0.0433763i
$863$	−42.7129			−1.45396			−0.726982	−	0.686657i	$-0.759078\pi$
$863$	−42.7129			−1.45396			−0.726982	+	0.686657i	$0.759078\pi$
$864$	0.605077	−	4.65481i	0.0205851	−	0.158360i
$865$	4.74025			0.161173
$866$	0.589869	−	1.02168i	0.0200446	−	0.0347182i
$867$	5.38635	−	5.88460i	0.182930	−	0.199852i
$868$	0.105576	+	0.182864i	0.00358350	+	0.00620680i
$869$	−22.6215	−	39.1816i	−0.767382	−	1.32914i
$870$	−0.333893	−	1.05696i	−0.0113200	−	0.0358345i
$871$	−4.46221	+	7.72878i	−0.151196	+	0.261880i
$872$	−4.90174			−0.165994
$873$	40.6995	+	18.9245i	1.37747	+	0.640497i
$874$	0.973269			0.0329213
$875$	−0.0159135	+	0.0275629i	−0.000537973	+	0.000931797i
$876$	−9.99678	−	2.21052i	−0.337760	−	0.0746865i
$877$	9.38024	+	16.2470i	0.316748	+	0.548624i	0.979808	−	0.199943i	$-0.0640757\pi$
$877$	9.38024	+	16.2470i	0.316748	+	0.548624i	−0.663059	+	0.748567i	$0.730742\pi$
$878$	−1.11050	−	1.92344i	−0.0374775	−	0.0649129i
$879$	6.54448	+	1.44713i	0.220740	+	0.0488106i
$880$	−11.3402	+	19.6418i	−0.382278	+	0.662124i
$881$	9.76165			0.328878			0.164439	−	0.986387i	$-0.447419\pi$
$881$	9.76165			0.328878			0.164439	+	0.986387i	$0.447419\pi$
$882$	0.140011	+	1.58049i	0.00471441	+	0.0532179i
$883$	−50.4642			−1.69826			−0.849128	−	0.528188i	$-0.822872\pi$
$883$	−50.4642			−1.69826			−0.849128	+	0.528188i	$0.822872\pi$
$884$	3.51048	−	6.08033i	0.118070	−	0.204504i
$885$	4.20064	+	13.2975i	0.141203	+	0.446990i
$886$	0.665831	+	1.15325i	0.0223690	+	0.0387443i
$887$	12.3082	+	21.3185i	0.413270	+	0.715804i	0.995245	−	0.0974021i	$-0.0310533\pi$
$887$	12.3082	+	21.3185i	0.413270	+	0.715804i	−0.581975	+	0.813207i	$0.697720\pi$
$888$	−2.56077	+	2.79765i	−0.0859340	+	0.0938831i
$889$	−0.184125	+	0.318914i	−0.00617536	+	0.0106960i
$890$	0.951128			0.0318819
$891$	17.4987	−	48.4055i	0.586230	−	1.62164i
$892$	−21.8708			−0.732289
$893$	2.98269	−	5.16616i	0.0998118	−	0.172879i
$894$	1.40842	−	1.53871i	0.0471047	−	0.0514620i
$895$	11.3311	+	19.6260i	0.378756	+	0.656024i
$896$	0.0382069	+	0.0661763i	0.00127640	+	0.00221079i
$897$	2.52570	+	7.99530i	0.0843307	+	0.266955i
$898$	0.786698	−	1.36260i	0.0262524	−	0.0454706i
$899$	28.1732			0.939629
$900$	0.527937	+	5.95953i	0.0175979	+	0.198651i
$901$	32.1900			1.07240
$902$	−1.25129	+	2.16729i	−0.0416632	+	0.0721628i
$903$	−0.412936	−	0.0913097i	−0.0137417	−	0.00303860i
$904$	1.83340	+	3.17555i	0.0609781	+	0.105617i
$905$	−1.75314	−	3.03653i	−0.0582764	−	0.100938i
$906$	0.139340	+	0.0308113i	0.00462926	+	0.00102364i
$907$	24.5065	−	42.4465i	0.813725	−	1.40941i	−0.0965140	−	0.995332i	$-0.530769\pi$
$907$	24.5065	−	42.4465i	0.813725	−	1.40941i	0.910239	−	0.414082i	$-0.135897\pi$
$908$	−29.3799			−0.975008
$909$	19.2081	+	8.93142i	0.637094	+	0.296237i
$910$	−0.00240507			−7.97272e−5
$911$	0.593675	−	1.02828i	0.0196693	−	0.0340683i	−0.856023	−	0.516937i	$-0.827072\pi$
$911$	0.593675	−	1.02828i	0.0196693	−	0.0340683i	0.875693	+	0.482869i	$0.160405\pi$
$912$	−5.50492	−	17.4263i	−0.182286	−	0.577041i
$913$	6.44710	+	11.1667i	0.213368	+	0.369564i
$914$	−1.12394	−	1.94673i	−0.0371768	−	0.0643921i
$915$	−7.49151	+	8.18450i	−0.247662	+	0.270571i
$916$	−1.20344	+	2.08442i	−0.0397628	+	0.0688713i
$917$	−0.407782			−0.0134661
$918$	1.27627	−	0.531096i	0.0421233	−	0.0175288i
$919$	16.8380			0.555436			0.277718	−	0.960663i	$-0.410422\pi$
$919$	16.8380			0.555436			0.277718	+	0.960663i	$0.410422\pi$
$920$	0.730586	−	1.26541i	0.0240867	−	0.0417194i
$921$	−4.16996	+	4.55570i	−0.137405	+	0.150115i
$922$	0.130732	+	0.226435i	0.00430544	+	0.00745723i
$923$	5.97315	+	10.3458i	0.196609	+	0.340536i
$924$	0.189390	+	0.599530i	0.00623049	+	0.0197231i
$925$	3.62730	−	6.28267i	0.119265	−	0.206573i
$926$	1.29181			0.0424514
$927$	27.4925	−	19.2951i	0.902972	−	0.633736i
$928$	7.65034			0.251135
$929$	8.70180	−	15.0720i	0.285497	−	0.494495i	−0.687233	−	0.726437i	$-0.741175\pi$
$929$	8.70180	−	15.0720i	0.285497	−	0.494495i	0.972729	+	0.231943i	$0.0745081\pi$
$930$	0.425149	+	0.0940102i	0.0139412	+	0.00308272i
$931$	9.31057	+	16.1264i	0.305142	+	0.528521i
$932$	11.7379	+	20.3307i	0.384488	+	0.665953i
$933$	51.0193	+	11.2815i	1.67030	+	0.369341i
$934$	−1.43361	+	2.48308i	−0.0469091	+	0.0812489i
$935$	−20.1341			−0.658454
$936$	−0.741184	+	0.520188i	−0.0242264	+	0.0170029i
$937$	−20.9053			−0.682947			−0.341473	−	0.939891i	$-0.610926\pi$
$937$	−20.9053			−0.682947			−0.341473	+	0.939891i	$0.610926\pi$
$938$	0.0107319	−	0.0185882i	0.000350410	−	0.000606928i
$939$	−2.92740	−	9.26691i	−0.0955321	−	0.302414i
$940$	−2.23576	−	3.87245i	−0.0729224	−	0.126305i
$941$	−14.0987	−	24.4196i	−0.459603	−	0.796056i	0.539337	−	0.842090i	$-0.318675\pi$
$941$	−14.0987	−	24.4196i	−0.459603	−	0.796056i	−0.998940	+	0.0460343i	$0.985342\pi$
$942$	1.65311	−	1.80603i	0.0538612	−	0.0588436i
$943$	−14.0162	+	24.2768i	−0.456430	+	0.790561i
$944$	−31.9294			−1.03921
$945$	0.131367	+	0.100461i	0.00427338	+	0.00326799i
$946$	−3.31550			−0.107796
$947$	−3.93771	+	6.82032i	−0.127958	+	0.221631i	−0.922886	−	0.385074i	$-0.874176\pi$
$947$	−3.93771	+	6.82032i	−0.127958	+	0.221631i	0.794927	+	0.606705i	$0.207509\pi$
$948$	18.4503	−	20.1570i	0.599236	−	0.654668i
$949$	1.48200	+	2.56689i	0.0481077	+	0.0833249i
$950$	−0.100525	−	0.174114i	−0.00326146	−	0.00564901i
$951$	12.4853	+	39.5233i	0.404864	+	1.28163i
$952$	−0.0169101	+	0.0292891i	−0.000548059	+	0.000949266i
$953$	−58.9456			−1.90943			−0.954717	−	0.297514i	$-0.903842\pi$
$953$	−58.9456			−1.90943			−0.954717	+	0.297514i	$0.903842\pi$
$954$	−1.87959	−	0.873973i	−0.0608539	−	0.0282959i
$955$	−6.33886			−0.205121
$956$	−14.1894	+	24.5768i	−0.458918	+	0.794870i
$957$	81.9105	+	18.1123i	2.64779	+	0.585487i
$958$	1.18330	+	2.04954i	0.0382308	+	0.0662176i
$959$	0.137708	+	0.238518i	0.00444683	+	0.00770214i
$960$	−13.2984	−	2.94057i	−0.429203	−	0.0949066i
$961$	9.96653	−	17.2625i	0.321501	−	0.556856i
$962$	0.548209			0.0176750
$963$	−0.377767	−	4.26436i	−0.0121734	−	0.137417i
$964$	−7.97305			−0.256795
$965$	−9.80814	+	16.9882i	−0.315735	+	0.546870i
$966$	−0.00607448	−	0.0192292i	−0.000195443	−	0.000618691i
$967$	−27.0449	−	46.8432i	−0.869707	−	1.50638i	−0.862296	−	0.506404i	$-0.830974\pi$
$967$	−27.0449	−	46.8432i	−0.869707	−	1.50638i	−0.00741044	−	0.999973i	$-0.502359\pi$
$968$	3.27604	+	5.67426i	0.105296	+	0.182378i
$969$	10.9538	−	11.9671i	0.351887	−	0.384438i
$970$	−0.565294	+	0.979117i	−0.0181505	+	0.0314376i
$971$	20.0513			0.643476			0.321738	−	0.946829i	$-0.395733\pi$
$971$	20.0513			0.643476			0.321738	+	0.946829i	$0.395733\pi$
$972$	31.0619	+	1.27140i	0.996311	+	0.0407801i
$973$	0.451930			0.0144882
$974$	−1.17989	+	2.04363i	−0.0378062	+	0.0654822i
$975$	1.16946	−	1.27764i	0.0374527	−	0.0409172i
$976$	−12.7023	−	22.0010i	−0.406590	−	0.704234i
$977$	22.5847	+	39.1179i	0.722549	+	1.25149i	0.959975	+	0.280086i	$0.0903631\pi$
$977$	22.5847	+	39.1179i	0.722549	+	1.25149i	−0.237425	+	0.971406i	$0.576304\pi$
$978$	−0.0228785	−	0.0724235i	−0.000731572	−	0.00231585i
$979$	−35.9914	+	62.3390i	−1.15029	+	1.99236i
$980$	13.9580			0.445872
$981$	−4.29905	−	48.5291i	−0.137258	−	1.54941i
$982$	−0.674452			−0.0215226
$983$	−3.38462	+	5.86233i	−0.107952	+	0.186979i	−0.914941	−	0.403588i	$-0.867763\pi$
$983$	−3.38462	+	5.86233i	−0.107952	+	0.186979i	0.806988	+	0.590568i	$0.201096\pi$
$984$	−2.95595	−	0.653629i	−0.0942324	−	0.0208369i
$985$	−4.05237	−	7.01892i	−0.129119	−	0.223641i
$986$	1.12651	+	1.95117i	0.0358753	+	0.0621378i
$987$	−0.120686	−	0.0266864i	−0.00384147	−	0.000849437i
$988$	−2.65295	+	4.59505i	−0.0844016	+	0.146188i
$989$	−37.1384			−1.18093
$990$	1.17564	+	0.546649i	0.0373641	+	0.0173736i
$991$	15.4853			0.491907			0.245954	−	0.969282i	$-0.420899\pi$
$991$	15.4853			0.491907			0.245954	+	0.969282i	$0.420899\pi$
$992$	−1.50260	+	2.60257i	−0.0477075	+	0.0826318i
$993$	17.8416	+	56.4790i	0.566187	+	1.79231i
$994$	−0.0143658	−	0.0248824i	−0.000455657	−	0.000789220i
$995$	0.306297	+	0.530522i	0.00971027	+	0.0168187i
$996$	−5.25830	+	5.74471i	−0.166616	+	0.182028i
$997$	−25.0092	+	43.3173i	−0.792051	+	1.37187i	0.132644	+	0.991164i	$0.457653\pi$
$997$	−25.0092	+	43.3173i	−0.792051	+	1.37187i	−0.924695	+	0.380709i	$0.875680\pi$
$998$	1.81904			0.0575807
$999$	−29.9437	−	22.8990i	−0.947378	−	0.724491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.6	✓	26
3.2	odd	2		1755.2.i.g.586.8		26
9.2	odd	6		5265.2.a.bh.1.6		13
9.4	even	3	inner	585.2.i.g.391.6	yes	26
9.5	odd	6		1755.2.i.g.1171.8		26
9.7	even	3		5265.2.a.bg.1.8		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.6	✓	26	1.1	even	1	trivial
585.2.i.g.391.6	yes	26	9.4	even	3	inner
1755.2.i.g.586.8		26	3.2	odd	2
1755.2.i.g.1171.8		26	9.5	odd	6
5265.2.a.bg.1.8		13	9.7	even	3
5265.2.a.bh.1.6		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)

\(f(q)\)	\(=\)	\(q+(-0.0377835 + 0.0654430i) q^{2} +(-1.16946 + 1.27764i) q^{3} +(0.997145 + 1.72711i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0394262 - 0.124807i) q^{6} +(-0.0159135 + 0.0275629i) q^{7} -0.301837 q^{8} +(-0.264725 - 2.98830i) q^{9} +O(q^{10})\)	\(q+(-0.0377835 + 0.0654430i) q^{2} +(-1.16946 + 1.27764i) q^{3} +(0.997145 + 1.72711i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0394262 - 0.124807i) q^{6} +(-0.0159135 + 0.0275629i) q^{7} -0.301837 q^{8} +(-0.264725 - 2.98830i) q^{9} +0.0755671 q^{10} +(-2.85952 + 4.95283i) q^{11} +(-3.37274 - 0.745790i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.00120253 - 0.00208285i) q^{14} +(1.69120 + 0.373963i) q^{15} +(-1.98289 + 3.43446i) q^{16} -3.52053 q^{17} +(0.205565 + 0.0955841i) q^{18} +2.66055 q^{19} +(0.997145 - 1.72711i) q^{20} +(-0.0166053 - 0.0525654i) q^{21} +(-0.216085 - 0.374271i) q^{22} +(-2.42047 - 4.19237i) q^{23} +(0.352986 - 0.385639i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.0755671 q^{26} +(4.12755 + 3.15647i) q^{27} -0.0634721 q^{28} +(-4.23440 + 7.33420i) q^{29} +(-0.0883727 + 0.0965475i) q^{30} +(-1.66335 - 2.88101i) q^{31} +(-0.451678 - 0.782329i) q^{32} +(-2.98384 - 9.44557i) q^{33} +(0.133018 - 0.230394i) q^{34} +0.0318269 q^{35} +(4.89714 - 3.43697i) q^{36} -7.25460 q^{37} +(-0.100525 + 0.174114i) q^{38} +(-1.69120 - 0.373963i) q^{39} +(0.150918 + 0.261398i) q^{40} +(-2.89535 - 5.01489i) q^{41} +(0.00406745 + 0.000899406i) q^{42} +(3.83587 - 6.64392i) q^{43} -11.4054 q^{44} +(-2.45558 + 1.72341i) q^{45} +0.365815 q^{46} +(1.12108 - 1.94177i) q^{47} +(-2.06909 - 6.54987i) q^{48} +(3.49949 + 6.06130i) q^{49} +(-0.0377835 - 0.0654430i) q^{50} +(4.11713 - 4.49797i) q^{51} +(-0.997145 + 1.72711i) q^{52} -9.14350 q^{53} +(-0.362523 + 0.150857i) q^{54} +5.71903 q^{55} +(0.00480327 - 0.00831951i) q^{56} +(-3.11140 + 3.39922i) q^{57} +(-0.319982 - 0.554224i) q^{58} +(4.02563 + 6.97259i) q^{59} +(1.04050 + 3.29377i) q^{60} +(-3.20298 + 5.54772i) q^{61} +0.251389 q^{62} +(0.0865789 + 0.0402576i) q^{63} -7.86328 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.730886 + 0.161616i) q^{66} +(4.46221 + 7.72878i) q^{67} +(-3.51048 - 6.08033i) q^{68} +(8.18698 + 1.81033i) q^{69} +(-0.00120253 + 0.00208285i) q^{70} +11.9463 q^{71} +(0.0799036 + 0.901978i) q^{72} +2.96399 q^{73} +(0.274105 - 0.474763i) q^{74} +(-0.521738 - 1.65160i) q^{75} +(2.65295 + 4.59505i) q^{76} +(-0.0910097 - 0.157633i) q^{77} +(0.0883727 - 0.0965475i) q^{78} +(-3.95547 + 6.85108i) q^{79} +3.96577 q^{80} +(-8.85984 + 1.58215i) q^{81} +0.437586 q^{82} +(1.12731 - 1.95255i) q^{83} +(0.0742281 - 0.0810945i) q^{84} +(1.76027 + 3.04887i) q^{85} +(0.289865 + 0.502062i) q^{86} +(-4.41850 - 13.9871i) q^{87} +(0.863107 - 1.49495i) q^{88} +12.5865 q^{89} +(-0.0200045 - 0.225817i) q^{90} -0.0318269 q^{91} +(4.82711 - 8.36081i) q^{92} +(5.62611 + 1.24406i) q^{93} +(0.0847167 + 0.146734i) q^{94} +(-1.33027 - 2.30410i) q^{95} +(1.52775 + 0.337821i) q^{96} +(-7.48069 + 12.9569i) q^{97} -0.528893 q^{98} +(15.5575 + 7.23395i) 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

Introduction

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