LMFDB - Embedded newform 361.3.d.d.69.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(69,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("361.69");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.d (of order $6$, degree $2$, not 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:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.6
Root			$-1.89323i$ of defining polynomial
Character	$\chi$	$=$	361.69
Dual form			361.3.d.d.293.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23199 - 1.28864i) q^{2} +(-0.338180 + 0.195249i) q^{3} +(1.32117 - 2.28834i) q^{4} +(-1.13047 - 1.95804i) q^{5} +(-0.503209 + 0.871584i) q^{6} -11.4433 q^{7} +3.49905i q^{8} +(-4.42376 + 7.66217i) q^{9} +O(q^{10})$	\(q+(2.23199 - 1.28864i) q^{2} +(-0.338180 + 0.195249i) q^{3} +(1.32117 - 2.28834i) q^{4} +(-1.13047 - 1.95804i) q^{5} +(-0.503209 + 0.871584i) q^{6} -11.4433 q^{7} +3.49905i q^{8} +(-4.42376 + 7.66217i) q^{9} +(-5.04640 - 2.91354i) q^{10} -7.77344 q^{11} +1.03183i q^{12} +(-11.9459 - 6.89699i) q^{13} +(-25.5412 + 14.7462i) q^{14} +(0.764608 + 0.441446i) q^{15} +(9.79370 + 16.9632i) q^{16} +(1.48688 + 2.57535i) q^{17} +22.8025i q^{18} -5.97420 q^{20} +(3.86988 - 2.23428i) q^{21} +(-17.3502 + 10.0171i) q^{22} +(13.6817 - 23.6974i) q^{23} +(-0.683184 - 1.18331i) q^{24} +(9.94406 - 17.2236i) q^{25} -35.5509 q^{26} -6.96940i q^{27} +(-15.1185 + 26.1860i) q^{28} +(-16.4702 - 9.50907i) q^{29} +2.27546 q^{30} +33.2652i q^{31} +(31.5977 + 18.2429i) q^{32} +(2.62883 - 1.51775i) q^{33} +(6.63739 + 3.83210i) q^{34} +(12.9363 + 22.4063i) q^{35} +(11.6891 + 20.2461i) q^{36} +2.53007i q^{37} +5.38651 q^{39} +(6.85127 - 3.95558i) q^{40} +(-46.2518 + 26.7035i) q^{41} +(5.75835 - 9.97375i) q^{42} +(2.22386 + 3.85184i) q^{43} +(-10.2701 + 17.7883i) q^{44} +20.0037 q^{45} -70.5230i q^{46} +(10.6714 - 18.4834i) q^{47} +(-6.62407 - 3.82441i) q^{48} +81.9480 q^{49} -51.2572i q^{50} +(-1.00567 - 0.580623i) q^{51} +(-31.5653 + 18.2242i) q^{52} +(-64.2129 - 37.0733i) q^{53} +(-8.98103 - 15.5556i) q^{54} +(8.78767 + 15.2207i) q^{55} -40.0405i q^{56} -49.0150 q^{58} +(-47.0542 + 27.1667i) q^{59} +(2.02036 - 1.16645i) q^{60} +(-52.9120 + 91.6463i) q^{61} +(42.8668 + 74.2474i) q^{62} +(50.6222 - 87.6802i) q^{63} +15.6846 q^{64} +31.1875i q^{65} +(3.91167 - 6.77521i) q^{66} +(26.7323 + 15.4339i) q^{67} +7.85771 q^{68} +10.6853i q^{69} +(57.7472 + 33.3404i) q^{70} +(66.2688 - 38.2603i) q^{71} +(-26.8103 - 15.4789i) q^{72} +(-9.09782 - 15.7579i) q^{73} +(3.26035 + 5.64709i) q^{74} +7.76625i q^{75} +88.9535 q^{77} +(12.0226 - 6.94126i) q^{78} +(-26.4203 + 15.2537i) q^{79} +(22.1430 - 38.3528i) q^{80} +(-38.4530 - 66.6026i) q^{81} +(-68.8223 + 119.204i) q^{82} +82.5054 q^{83} -11.8075i q^{84} +(3.36176 - 5.82274i) q^{85} +(9.92725 + 5.73150i) q^{86} +7.42653 q^{87} -27.1997i q^{88} +(-76.0677 - 43.9177i) q^{89} +(44.6481 - 25.7776i) q^{90} +(136.700 + 78.9240i) q^{91} +(-36.1518 - 62.6167i) q^{92} +(-6.49498 - 11.2496i) q^{93} -55.0062i q^{94} -14.2476 q^{96} +(47.1033 - 27.1951i) q^{97} +(182.907 - 105.601i) q^{98} +(34.3878 - 59.5614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{3} - 3 q^{5} + 12 q^{6} - 12 q^{7} - 9 q^{9}+O(q^{10}) $ 12 * q - 9 * q^3 - 3 * q^5 + 12 * q^6 - 12 * q^7 - 9 * q^9	$ 12 q - 9 q^{3} - 3 q^{5} + 12 q^{6} - 12 q^{7} - 9 q^{9} - 36 q^{10} + 36 q^{11} - 18 q^{13} - 36 q^{14} + 81 q^{15} + 48 q^{16} + 33 q^{17} - 90 q^{20} + 135 q^{21} - 135 q^{22} - 60 q^{23} - 18 q^{24} + 33 q^{25} - 42 q^{26} - 105 q^{28} - 63 q^{29} - 48 q^{30} - 9 q^{32} - 126 q^{33} + 18 q^{34} + 135 q^{35} - 72 q^{36} - 108 q^{39} + 216 q^{40} - 108 q^{41} - 117 q^{42} - 51 q^{43} + 21 q^{44} + 6 q^{45} - 114 q^{47} - 306 q^{48} + 48 q^{49} - 117 q^{51} - 54 q^{53} - 144 q^{54} + 33 q^{55} - 132 q^{58} - 117 q^{59} - 51 q^{61} + 219 q^{62} - 21 q^{63} - 54 q^{64} + 138 q^{66} + 396 q^{67} + 60 q^{68} - 99 q^{70} - 72 q^{71} - 144 q^{72} - 18 q^{73} + 39 q^{74} + 246 q^{77} - 126 q^{78} + 495 q^{79} + 234 q^{80} - 102 q^{81} - 48 q^{82} + 312 q^{83} + 105 q^{85} + 216 q^{86} - 138 q^{87} + 450 q^{89} + 531 q^{90} + 243 q^{91} - 240 q^{92} + 120 q^{93} + 558 q^{96} - 729 q^{97} + 117 q^{98} + 159 q^{99}+O(q^{100}) $ 12 * q - 9 * q^3 - 3 * q^5 + 12 * q^6 - 12 * q^7 - 9 * q^9 - 36 * q^10 + 36 * q^11 - 18 * q^13 - 36 * q^14 + 81 * q^15 + 48 * q^16 + 33 * q^17 - 90 * q^20 + 135 * q^21 - 135 * q^22 - 60 * q^23 - 18 * q^24 + 33 * q^25 - 42 * q^26 - 105 * q^28 - 63 * q^29 - 48 * q^30 - 9 * q^32 - 126 * q^33 + 18 * q^34 + 135 * q^35 - 72 * q^36 - 108 * q^39 + 216 * q^40 - 108 * q^41 - 117 * q^42 - 51 * q^43 + 21 * q^44 + 6 * q^45 - 114 * q^47 - 306 * q^48 + 48 * q^49 - 117 * q^51 - 54 * q^53 - 144 * q^54 + 33 * q^55 - 132 * q^58 - 117 * q^59 - 51 * q^61 + 219 * q^62 - 21 * q^63 - 54 * q^64 + 138 * q^66 + 396 * q^67 + 60 * q^68 - 99 * q^70 - 72 * q^71 - 144 * q^72 - 18 * q^73 + 39 * q^74 + 246 * q^77 - 126 * q^78 + 495 * q^79 + 234 * q^80 - 102 * q^81 - 48 * q^82 + 312 * q^83 + 105 * q^85 + 216 * q^86 - 138 * q^87 + 450 * q^89 + 531 * q^90 + 243 * q^91 - 240 * q^92 + 120 * q^93 + 558 * q^96 - 729 * q^97 + 117 * q^98 + 159 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.23199	−	1.28864i	1.11599	−	0.644319i	0.175618	−	0.984458i	$-0.443808\pi$
$2$	2.23199	−	1.28864i	1.11599	−	0.644319i	0.940375	+	0.340140i	$0.110474\pi$
$3$	−0.338180	+	0.195249i	−0.112727	+	0.0650829i	−0.555303	−	0.831648i	$-0.687398\pi$
$3$	−0.338180	+	0.195249i	−0.112727	+	0.0650829i	0.442577	+	0.896731i	$0.354065\pi$
$4$	1.32117	−	2.28834i	0.330293	−	0.572084i
$5$	−1.13047	−	1.95804i	−0.226095	−	0.391607i	0.730553	−	0.682856i	$-0.239263\pi$
$5$	−1.13047	−	1.95804i	−0.226095	−	0.391607i	−0.956647	+	0.291249i	$0.905929\pi$
$6$	−0.503209	+	0.871584i	−0.0838682	+	0.145264i
$7$	−11.4433			−1.63475			−0.817375	−	0.576106i	$-0.804572\pi$
$7$	−11.4433			−1.63475			−0.817375	+	0.576106i	$0.804572\pi$
$8$			3.49905i			0.437381i
$9$	−4.42376	+	7.66217i	−0.491528	+	0.851352i
$10$	−5.04640	−	2.91354i	−0.504640	−	0.291354i
$11$	−7.77344			−0.706677			−0.353338	−	0.935496i	$-0.614954\pi$
$11$	−7.77344			−0.706677			−0.353338	+	0.935496i	$0.614954\pi$
$12$			1.03183i			0.0859857i
$13$	−11.9459	−	6.89699i	−0.918918	−	0.530538i	−0.0356285	−	0.999365i	$-0.511343\pi$
$13$	−11.9459	−	6.89699i	−0.918918	−	0.530538i	−0.883290	+	0.468827i	$0.844677\pi$
$14$	−25.5412	+	14.7462i	−1.82437	+	1.05330i
$15$	0.764608	+	0.441446i	0.0509739	+	0.0294298i
$16$	9.79370	+	16.9632i	0.612106	+	1.06020i
$17$	1.48688	+	2.57535i	0.0874636	+	0.151491i	0.906438	−	0.422338i	$-0.138791\pi$
$17$	1.48688	+	2.57535i	0.0874636	+	0.151491i	−0.818975	+	0.573830i	$0.805457\pi$
$18$			22.8025i			1.26680i
$19$		0			0
$19$		0			0
$20$	−5.97420			−0.298710
$21$	3.86988	−	2.23428i	0.184280	−	0.106394i
$22$	−17.3502	+	10.0171i	−0.788646	+	0.455325i
$23$	13.6817	−	23.6974i	0.594857	−	1.03032i	−0.398710	−	0.917077i	$-0.630542\pi$
$23$	13.6817	−	23.6974i	0.594857	−	1.03032i	0.993567	−	0.113245i	$-0.0361245\pi$
$24$	−0.683184	−	1.18331i	−0.0284660	−	0.0493046i
$25$	9.94406	−	17.2236i	0.397762	−	0.688945i
$26$	−35.5509			−1.36734
$27$		−	6.96940i		−	0.258126i
$28$	−15.1185	+	26.1860i	−0.539947	+	0.935215i
$29$	−16.4702	−	9.50907i	−0.567937	−	0.327899i	0.188388	−	0.982095i	$-0.439674\pi$
$29$	−16.4702	−	9.50907i	−0.567937	−	0.327899i	−0.756325	+	0.654196i	$0.773007\pi$
$30$	2.27546			0.0758486
$31$			33.2652i			1.07307i	0.843878	+	0.536535i	$0.180267\pi$
$31$			33.2652i			1.07307i	−0.843878	+	0.536535i	$0.819733\pi$
$32$	31.5977	+	18.2429i	0.987428	+	0.570092i
$33$	2.62883	−	1.51775i	0.0796614	−	0.0459925i
$34$	6.63739	+	3.83210i	0.195217	+	0.112709i
$35$	12.9363	+	22.4063i	0.369608	+	0.640180i
$36$	11.6891	+	20.2461i	0.324697	+	0.562392i
$37$			2.53007i			0.0683803i	0.999415	+	0.0341902i	$0.0108852\pi$
$37$			2.53007i			0.0683803i	−0.999415	+	0.0341902i	$0.989115\pi$
$38$		0			0
$39$	5.38651			0.138116
$40$	6.85127	−	3.95558i	0.171282	−	0.0988896i
$41$	−46.2518	+	26.7035i	−1.12809	+	0.651305i	−0.943455	−	0.331501i	$-0.892445\pi$
$41$	−46.2518	+	26.7035i	−1.12809	+	0.651305i	−0.184639	+	0.982806i	$0.559112\pi$
$42$	5.75835	−	9.97375i	0.137104	−	0.237470i
$43$	2.22386	+	3.85184i	0.0517177	+	0.0895777i	0.890725	−	0.454542i	$-0.150197\pi$
$43$	2.22386	+	3.85184i	0.0517177	+	0.0895777i	−0.839008	+	0.544120i	$0.816864\pi$
$44$	−10.2701	+	17.7883i	−0.233410	+	0.404279i
$45$	20.0037			0.444528
$46$		−	70.5230i		−	1.53311i
$47$	10.6714	−	18.4834i	0.227051	−	0.393263i	−0.729882	−	0.683573i	$-0.760425\pi$
$47$	10.6714	−	18.4834i	0.227051	−	0.393263i	0.956933	+	0.290310i	$0.0937584\pi$
$48$	−6.62407	−	3.82441i	−0.138002	−	0.0796752i
$49$	81.9480			1.67241
$50$		−	51.2572i		−	1.02514i
$51$	−1.00567	−	0.580623i	−0.0197190	−	0.0113848i
$52$	−31.5653	+	18.2242i	−0.607025	+	0.350466i
$53$	−64.2129	−	37.0733i	−1.21156	−	0.699497i	−0.248464	−	0.968641i	$-0.579926\pi$
$53$	−64.2129	−	37.0733i	−1.21156	−	0.699497i	−0.963100	+	0.269144i	$0.913259\pi$
$54$	−8.98103	−	15.5556i	−0.166315	−	0.288067i
$55$	8.78767	+	15.2207i	0.159776	+	0.276740i
$56$		−	40.0405i		−	0.715009i
$57$		0			0
$58$	−49.0150			−0.845085
$59$	−47.0542	+	27.1667i	−0.797528	+	0.460453i	−0.842606	−	0.538530i	$-0.818980\pi$
$59$	−47.0542	+	27.1667i	−0.797528	+	0.460453i	0.0450778	+	0.998983i	$0.485646\pi$
$60$	2.02036	−	1.16645i	0.0336726	−	0.0194409i
$61$	−52.9120	+	91.6463i	−0.867410	+	1.50240i	−0.00277651	+	0.999996i	$0.500884\pi$
$61$	−52.9120	+	91.6463i	−0.867410	+	1.50240i	−0.864634	+	0.502403i	$0.832450\pi$
$62$	42.8668	+	74.2474i	0.691399	+	1.19754i
$63$	50.6222	−	87.6802i	0.803526	−	1.39175i
$64$	15.6846			0.245072
$65$			31.1875i			0.479807i
$66$	3.91167	−	6.77521i	0.0592677	−	0.102655i
$67$	26.7323	+	15.4339i	0.398989	+	0.230357i	0.686048	−	0.727556i	$-0.259344\pi$
$67$	26.7323	+	15.4339i	0.398989	+	0.230357i	−0.287058	+	0.957913i	$0.592677\pi$
$68$	7.85771			0.115555
$69$			10.6853i			0.154860i
$70$	57.7472	+	33.3404i	0.824960	+	0.476291i
$71$	66.2688	−	38.2603i	0.933363	−	0.538877i	0.0454895	−	0.998965i	$-0.485515\pi$
$71$	66.2688	−	38.2603i	0.933363	−	0.538877i	0.887874	+	0.460087i	$0.152182\pi$
$72$	−26.8103	−	15.4789i	−0.372366	−	0.214985i
$73$	−9.09782	−	15.7579i	−0.124628	−	0.215861i	0.796960	−	0.604032i	$-0.206440\pi$
$73$	−9.09782	−	15.7579i	−0.124628	−	0.215861i	−0.921587	+	0.388171i	$0.873107\pi$
$74$	3.26035	+	5.64709i	0.0440587	+	0.0763120i
$75$			7.76625i			0.103550i
$76$		0			0
$77$	88.9535			1.15524
$78$	12.0226	−	6.94126i	0.154136	−	0.0889905i
$79$	−26.4203	+	15.2537i	−0.334434	+	0.193085i	−0.657808	−	0.753186i	$-0.728516\pi$
$79$	−26.4203	+	15.2537i	−0.334434	+	0.193085i	0.323374	+	0.946271i	$0.395183\pi$
$80$	22.1430	−	38.3528i	0.276788	−	0.479410i
$81$	−38.4530	−	66.6026i	−0.474729	−	0.822255i
$82$	−68.8223	+	119.204i	−0.839296	+	1.45370i
$83$	82.5054			0.994041			0.497020	−	0.867739i	$-0.334427\pi$
$83$	82.5054			0.994041			0.497020	+	0.867739i	$0.334427\pi$
$84$		−	11.8075i		−	0.140565i
$85$	3.36176	−	5.82274i	0.0395501	−	0.0685028i
$86$	9.92725	+	5.73150i	0.115433	+	0.0666454i
$87$	7.42653			0.0853624
$88$		−	27.1997i		−	0.309087i
$89$	−76.0677	−	43.9177i	−0.854693	−	0.493457i	0.00753850	−	0.999972i	$-0.497600\pi$
$89$	−76.0677	−	43.9177i	−0.854693	−	0.493457i	−0.862232	+	0.506514i	$0.830934\pi$
$90$	44.6481	−	25.7776i	0.496090	−	0.286418i
$91$	136.700	+	78.9240i	1.50220	+	0.867297i
$92$	−36.1518	−	62.6167i	−0.392954	−	0.680616i
$93$	−6.49498	−	11.2496i	−0.0698385	−	0.120964i
$94$		−	55.0062i		−	0.585172i
$95$		0			0
$96$	−14.2476			−0.148413
$97$	47.1033	−	27.1951i	0.485601	−	0.280362i	−0.237147	−	0.971474i	$-0.576212\pi$
$97$	47.1033	−	27.1951i	0.485601	−	0.280362i	0.722747	+	0.691112i	$0.242879\pi$
$98$	182.907	−	105.601i	1.86640	−	1.07756i
$99$	34.3878	−	59.5614i	0.347352	−	0.601631i
$100$	−26.2756	−	45.5107i	−0.262756	−	0.455107i
$101$	2.25552	−	3.90667i	0.0223318	−	0.0386799i	−0.854644	−	0.519215i	$-0.826224\pi$
$101$	2.25552	−	3.90667i	0.0223318	−	0.0386799i	0.876975	+	0.480535i	$0.159558\pi$
$102$	−2.99285			−0.0293417
$103$			37.2109i			0.361271i	0.983550	+	0.180636i	$0.0578154\pi$
$103$			37.2109i			0.361271i	−0.983550	+	0.180636i	$0.942185\pi$
$104$	24.1329	−	41.7994i	0.232047	−	0.401918i
$105$	−8.74960	−	5.05158i	−0.0833295	−	0.0481103i
$106$	−191.096			−1.80280
$107$			155.906i			1.45707i	0.685011	+	0.728533i	$0.259797\pi$
$107$			155.906i			1.45707i	−0.685011	+	0.728533i	$0.740203\pi$
$108$	−15.9483	−	9.20778i	−0.147670	−	0.0852572i
$109$	48.4569	−	27.9766i	0.444559	−	0.256666i	−0.260971	−	0.965347i	$-0.584043\pi$
$109$	48.4569	−	27.9766i	0.444559	−	0.256666i	0.705530	+	0.708681i	$0.250709\pi$
$110$	39.2279	+	22.6482i	0.356617	+	0.205893i
$111$	−0.493993	−	0.855621i	−0.00445039	−	0.00770830i
$112$	−112.072	−	194.114i	−1.00064	−	1.73316i
$113$			78.1077i			0.691219i	0.938378	+	0.345609i	$0.112328\pi$
$113$			78.1077i			0.691219i	−0.938378	+	0.345609i	$0.887672\pi$
$114$		0			0
$115$	−61.8672			−0.537976
$116$	−43.5199	+	25.1262i	−0.375172	+	0.216605i
$117$	105.692	−	61.0212i	0.903349	−	0.521549i
$118$	−70.0162	+	121.272i	−0.593357	+	1.02772i
$119$	−17.0148	−	29.4704i	−0.142981	−	0.247651i
$120$	−1.54464	+	2.67540i	−0.0128720	+	0.0222950i
$121$	−60.5736			−0.500608
$122$			272.738i			2.23555i
$123$	10.4276	−	18.0612i	0.0847776	−	0.146839i
$124$	76.1220	+	43.9490i	0.613887	+	0.354428i
$125$	−101.490			−0.811917
$126$		−	260.934i		−	2.07091i
$127$	−109.889	−	63.4442i	−0.865264	−	0.499560i	0.000507500	−	1.00000i	$-0.499838\pi$
$127$	−109.889	−	63.4442i	−0.865264	−	0.499560i	−0.865772	+	0.500439i	$0.833172\pi$
$128$	−91.3830	+	52.7600i	−0.713930	+	0.412188i
$129$	−1.50413	−	0.868411i	−0.0116599	−	0.00673187i
$130$	40.1893	+	69.6099i	0.309149	+	0.535461i
$131$	25.2965	+	43.8147i	0.193103	+	0.334464i	0.946277	−	0.323357i	$-0.104812\pi$
$131$	25.2965	+	43.8147i	0.193103	+	0.334464i	−0.753174	+	0.657821i	$0.771478\pi$
$132$		−	8.02086i		−	0.0607641i
$133$		0			0
$134$	79.5548			0.593692
$135$	−13.6463	+	7.87872i	−0.101084	+	0.0583609i
$136$	−9.01129	+	5.20267i	−0.0662595	+	0.0382549i
$137$	55.3221	−	95.8206i	0.403811	−	0.699421i	−0.590372	−	0.807132i	$-0.701019\pi$
$137$	55.3221	−	95.8206i	0.403811	−	0.699421i	0.994182	+	0.107711i	$0.0343521\pi$
$138$	13.7695	+	23.8495i	0.0997791	+	0.172822i
$139$	−37.8113	+	65.4911i	−0.272024	+	0.471159i	−0.969380	−	0.245566i	$-0.921026\pi$
$139$	−37.8113	+	65.4911i	−0.272024	+	0.471159i	0.697356	+	0.716725i	$0.254360\pi$
$140$	68.3643			0.488316
$141$			8.33429i			0.0591084i
$142$	98.6073	−	170.793i	0.694418	−	1.20277i
$143$	92.8611	+	53.6134i	0.649378	+	0.374919i
$144$	−173.300			−1.20347
$145$			42.9990i			0.296545i
$146$	−40.6124	−	23.4476i	−0.278167	−	0.160600i
$147$	−27.7132	+	16.0002i	−0.188525	+	0.108845i
$148$	5.78966	+	3.34266i	0.0391193	+	0.0225856i
$149$	−102.393	−	177.351i	−0.687204	−	1.19027i	−0.972739	−	0.231904i	$-0.925504\pi$
$149$	−102.393	−	177.351i	−0.687204	−	1.19027i	0.285534	−	0.958369i	$-0.407829\pi$
$150$	10.0079	+	17.3342i	0.0667192	+	0.115561i
$151$		−	45.8135i		−	0.303400i	−0.988427	−	0.151700i	$-0.951525\pi$
$151$		−	45.8135i		−	0.303400i	0.988427	−	0.151700i	$-0.0484748\pi$
$152$		0			0
$153$	−26.3104			−0.171963
$154$	198.543	−	114.629i	1.28924	−	0.744343i
$155$	65.1345	−	37.6054i	0.420222	−	0.242615i
$156$	7.11651	−	12.3262i	0.0456186	−	0.0790138i
$157$	5.14800	+	8.91660i	0.0327898	+	0.0567937i	0.881955	−	0.471334i	$-0.156227\pi$
$157$	5.14800	+	8.91660i	0.0327898	+	0.0567937i	−0.849165	+	0.528128i	$0.822894\pi$
$158$	−39.3131	+	68.0923i	−0.248817	+	0.430964i
$159$	28.9541			0.182101
$160$		−	82.4926i		−	0.515579i
$161$	−156.563	+	271.175i	−0.972442	+	1.68432i
$162$	−171.653	−	99.1040i	−1.05959	−	0.611753i
$163$	90.1530			0.553086			0.276543	−	0.961002i	$-0.410811\pi$
$163$	90.1530			0.553086			0.276543	+	0.961002i	$0.410811\pi$
$164$			141.120i			0.860486i
$165$	−5.94364	−	3.43156i	−0.0360220	−	0.0207973i
$166$	184.151	−	106.320i	1.10934	−	0.640479i
$167$	−61.8707	−	35.7211i	−0.370483	−	0.213899i	0.303186	−	0.952931i	$-0.401950\pi$
$167$	−61.8707	−	35.7211i	−0.370483	−	0.213899i	−0.673670	+	0.739033i	$0.735283\pi$
$168$	7.81785	+	13.5409i	0.0465348	+	0.0806007i
$169$	10.6370	+	18.4238i	0.0629407	+	0.109016i
$170$		−	17.3284i		−	0.101931i
$171$		0			0
$172$	11.7524			0.0683280
$173$	−141.201	+	81.5225i	−0.816191	+	0.471228i	−0.849101	−	0.528230i	$-0.822856\pi$
$173$	−141.201	+	81.5225i	−0.816191	+	0.471228i	0.0329100	+	0.999458i	$0.489523\pi$
$174$	16.5759	−	9.57010i	0.0952638	−	0.0550006i
$175$	−113.792	+	197.094i	−0.650242	+	1.12625i
$176$	−76.1307	−	131.862i	−0.432561	−	0.749218i
$177$	10.6085	−	18.3745i	0.0599352	−	0.103811i
$178$	−226.376			−1.27177
$179$		−	8.57953i		−	0.0479304i	−0.999713	−	0.0239652i	$-0.992371\pi$
$179$		−	8.57953i		−	0.0479304i	0.999713	−	0.0239652i	$-0.00762908\pi$
$180$	26.4284	−	45.7753i	0.146824	−	0.254307i
$181$	19.7379	+	11.3957i	0.109049	+	0.0629594i	0.553533	−	0.832828i	$-0.313279\pi$
$181$	19.7379	+	11.3957i	0.109049	+	0.0629594i	−0.444484	+	0.895787i	$0.646613\pi$
$182$	406.818			2.23526
$183$		−	41.3240i		−	0.225814i
$184$	82.9184	+	47.8730i	0.450643	+	0.260179i
$185$	4.95398	−	2.86018i	0.0267782	−	0.0154604i
$186$	−28.9934	−	16.7393i	−0.155878	−	0.0899965i
$187$	−11.5582	−	20.0194i	−0.0618085	−	0.107055i
$188$	−28.1975	−	48.8394i	−0.149987	−	0.259784i
$189$			79.7526i			0.421972i
$190$		0			0
$191$	84.5822			0.442839			0.221419	−	0.975179i	$-0.428931\pi$
$191$	84.5822			0.442839			0.221419	+	0.975179i	$0.428931\pi$
$192$	−5.30422	+	3.06239i	−0.0276262	+	0.0159500i
$193$	−262.819	+	151.739i	−1.36176	+	0.786211i	−0.989858	−	0.142061i	$-0.954627\pi$
$193$	−262.819	+	151.739i	−1.36176	+	0.786211i	−0.371900	+	0.928273i	$0.621294\pi$
$194$	70.0892	−	121.398i	0.361284	−	0.625763i
$195$	−6.08931	−	10.5470i	−0.0312272	−	0.0540871i
$196$	108.268	−	187.525i	0.552385	−	0.956759i
$197$	337.234			1.71185			0.855923	−	0.517103i	$-0.172990\pi$
$197$	337.234			1.71185			0.855923	+	0.517103i	$0.172990\pi$
$198$		−	177.254i		−	0.895221i
$199$	5.94748	−	10.3013i	0.0298869	−	0.0517656i	−0.850695	−	0.525659i	$-0.823819\pi$
$199$	5.94748	−	10.3013i	0.0298869	−	0.0517656i	0.880582	+	0.473894i	$0.157152\pi$
$200$	60.2663	+	34.7948i	0.301332	+	0.173974i
$201$	−12.0538			−0.0599691
$202$		−	11.6262i		−	0.0575553i
$203$	188.473	+	108.815i	0.928436	+	0.536033i
$204$	−2.65732	+	1.53421i	−0.0130261	+	0.00752062i
$205$	104.573	+	60.3752i	0.510112	+	0.294513i
$206$	47.9514	+	83.0542i	0.232774	+	0.403176i
$207$	121.049	+	209.663i	0.584778	+	1.01287i
$208$		−	270.188i		−	1.29898i
$209$		0			0
$210$	−26.0386			−0.123994
$211$	−95.6006	+	55.1951i	−0.453084	+	0.261588i	−0.709132	−	0.705076i	$-0.750913\pi$
$211$	−95.6006	+	55.1951i	−0.453084	+	0.261588i	0.256048	+	0.966664i	$0.417579\pi$
$212$	−169.673	+	97.9606i	−0.800343	+	0.462078i
$213$	−14.9405	+	25.8778i	−0.0701434	+	0.121492i
$214$	200.906	+	347.980i	0.938814	+	1.62607i
$215$	5.02803	−	8.70880i	0.0233862	−	0.0405061i
$216$	24.3863			0.112899
$217$		−	380.662i		−	1.75420i
$218$	72.1034	−	124.887i	0.330750	−	0.572875i
$219$	6.15341	+	3.55267i	0.0280978	+	0.0162222i
$220$	46.4401			0.211091
$221$		−	41.0200i		−	0.185611i
$222$	−2.20517	−	1.27316i	−0.00993320	−	0.00573494i
$223$	−231.112	+	133.433i	−1.03638	+	0.598352i	−0.918805	−	0.394712i	$-0.870844\pi$
$223$	−231.112	+	133.433i	−1.03638	+	0.598352i	−0.117572	+	0.993064i	$0.537511\pi$
$224$	−361.581	−	208.759i	−1.61420	−	0.931958i
$225$	87.9802	+	152.386i	0.391023	+	0.677272i
$226$	100.653	+	174.335i	0.445365	+	0.771395i
$227$			277.497i			1.22245i	0.791455	+	0.611227i	$0.209324\pi$
$227$			277.497i			1.22245i	−0.791455	+	0.611227i	$0.790676\pi$
$228$		0			0
$229$	−222.383			−0.971104			−0.485552	−	0.874208i	$-0.661381\pi$
$229$	−222.383			−0.971104			−0.485552	+	0.874208i	$0.661381\pi$
$230$	−138.087	+	79.7244i	−0.600377	+	0.346628i
$231$	−30.0823	+	17.3680i	−0.130227	+	0.0751863i
$232$	33.2727	−	57.6300i	0.143417	−	0.248405i
$233$	176.718	+	306.085i	0.758448	+	1.31367i	0.943642	+	0.330968i	$0.107375\pi$
$233$	176.718	+	306.085i	0.758448	+	1.31367i	−0.185194	+	0.982702i	$0.559291\pi$
$234$	157.268	−	272.397i	0.672087	−	1.16409i
$235$	−48.2548			−0.205340
$236$			143.568i			0.608338i
$237$	5.95654	−	10.3170i	0.0251331	−	0.0435318i
$238$	−75.9534	−	43.8517i	−0.319132	−	0.184251i
$239$	312.752			1.30858			0.654292	−	0.756242i	$-0.272967\pi$
$239$	312.752			1.30858			0.654292	+	0.756242i	$0.272967\pi$
$240$			17.2936i			0.0720566i
$241$	329.425	+	190.193i	1.36691	+	0.789184i	0.990532	−	0.137283i	$-0.0438370\pi$
$241$	329.425	+	190.193i	1.36691	+	0.789184i	0.376375	+	0.926467i	$0.377170\pi$
$242$	−135.199	+	78.0574i	−0.558675	+	0.322551i
$243$	80.3292	+	46.3781i	0.330573	+	0.190856i
$244$	139.812	+	242.161i	0.572999	+	0.992464i
$245$	−92.6401	−	160.457i	−0.378123	−	0.654928i
$246$		−	53.7498i		−	0.218495i
$247$		0			0
$248$	−116.397			−0.469341
$249$	−27.9017	+	16.1091i	−0.112055	+	0.0646950i
$250$	−226.523	+	130.783i	−0.906094	+	0.523133i
$251$	20.0045	−	34.6488i	0.0796991	−	0.138043i	−0.823421	−	0.567431i	$-0.807937\pi$
$251$	20.0045	−	34.6488i	0.0796991	−	0.138043i	0.903120	+	0.429388i	$0.141271\pi$
$252$	−133.761	−	231.681i	−0.530798	−	0.919370i
$253$	−106.354	+	184.210i	−0.420371	+	0.728104i
$254$	−327.026			−1.28750
$255$			2.62551i			0.0102961i
$256$	−167.346	+	289.852i	−0.653696	+	1.13224i
$257$	−313.933	−	181.250i	−1.22153	−	0.705251i	−0.256287	−	0.966601i	$-0.582499\pi$
$257$	−313.933	−	181.250i	−1.22153	−	0.705251i	−0.965244	+	0.261350i	$0.915832\pi$
$258$	−4.47627			−0.0173499
$259$		−	28.9523i		−	0.111785i
$260$	71.3674	+	41.2040i	0.274490	+	0.158477i
$261$	145.720	−	84.1316i	0.558315	−	0.322343i
$262$	112.923	+	65.1959i	0.431002	+	0.248839i
$263$	−28.1643	−	48.7820i	−0.107089	−	0.185483i	0.807501	−	0.589866i	$-0.200820\pi$
$263$	−28.1643	−	48.7820i	−0.107089	−	0.185483i	−0.914590	+	0.404383i	$0.867486\pi$
$264$	5.31070	+	9.19839i	0.0201163	+	0.0348424i
$265$			167.642i			0.632610i
$266$		0			0
$267$	34.2995			0.128462
$268$	70.6359	−	40.7817i	0.263567	−	0.152170i
$269$	135.723	−	78.3597i	0.504547	−	0.291300i	−0.226043	−	0.974117i	$-0.572579\pi$
$269$	135.723	−	78.3597i	0.504547	−	0.291300i	0.730589	+	0.682817i	$0.239246\pi$
$270$	−20.3056	+	35.1704i	−0.0752060	+	0.130261i
$271$	−197.381	−	341.874i	−0.728343	−	1.26153i	−0.957583	−	0.288157i	$-0.906958\pi$
$271$	−197.381	−	341.874i	−0.728343	−	1.26153i	0.229240	−	0.973370i	$-0.426376\pi$
$272$	−29.1241	+	50.4445i	−0.107074	+	0.185458i
$273$	−61.6392			−0.225785
$274$		−	285.160i		−	1.04073i
$275$	−77.2996	+	133.887i	−0.281089	+	0.486861i
$276$	24.4516	+	14.1172i	0.0885929	+	0.0511491i
$277$	−189.521			−0.684193			−0.342097	−	0.939665i	$-0.611137\pi$
$277$	−189.521			−0.684193			−0.342097	+	0.939665i	$0.611137\pi$
$278$			194.900i			0.701079i
$279$	−254.883	−	147.157i	−0.913561	−	0.527445i
$280$	−78.4008	+	45.2647i	−0.280003	+	0.161660i
$281$	−140.080	−	80.8754i	−0.498507	−	0.287813i	0.229590	−	0.973287i	$-0.426261\pi$
$281$	−140.080	−	80.8754i	−0.498507	−	0.287813i	−0.728097	+	0.685475i	$0.759595\pi$
$282$	10.7399	+	18.6020i	0.0380847	+	0.0659646i
$283$	118.975	+	206.070i	0.420405	+	0.728163i	0.995979	−	0.0895868i	$-0.0285546\pi$
$283$	118.975	+	206.070i	0.420405	+	0.728163i	−0.575574	+	0.817750i	$0.695221\pi$
$284$		−	202.194i		−	0.711950i
$285$		0			0
$286$	276.353			0.966268
$287$	529.272	−	305.575i	1.84415	−	1.06472i
$288$	−279.561	+	161.405i	−0.970698	+	0.560433i
$289$	140.078	−	242.623i	0.484700	−	0.839525i
$290$	55.4101	+	95.9731i	0.191069	+	0.330942i
$291$	−10.6196	+	18.3937i	−0.0364935	+	0.0632085i
$292$	−48.0791			−0.164655
$293$			159.143i			0.543150i	0.962417	+	0.271575i	$0.0875444\pi$
$293$			159.143i			0.543150i	−0.962417	+	0.271575i	$0.912456\pi$
$294$	−41.2370	+	71.4246i	−0.140262	+	0.242941i
$295$	106.387	+	61.4225i	0.360634	+	0.208212i
$296$	−8.85285			−0.0299083
$297$			54.1762i			0.182412i
$298$	−457.081	−	263.896i	−1.53383	−	0.885557i
$299$	−326.882	+	188.725i	−1.09325	+	0.631188i
$300$	17.7718	+	10.2606i	0.0592394	+	0.0342019i
$301$	−25.4482	−	44.0776i	−0.0845455	−	0.146437i
$302$	−59.0369	−	102.255i	−0.195487	−	0.338593i
$303$			1.76155i			0.00581368i
$304$		0			0
$305$	239.263			0.784467
$306$	−58.7244	+	33.9046i	−0.191910	+	0.110799i
$307$	34.3341	−	19.8228i	0.111837	−	0.0645694i	−0.443038	−	0.896503i	$-0.646099\pi$
$307$	34.3341	−	19.8228i	0.111837	−	0.0645694i	0.554875	+	0.831933i	$0.312766\pi$
$308$	117.523	−	203.556i	0.381568	−	0.660895i
$309$	−7.26538	−	12.5840i	−0.0235126	−	0.0407249i
$310$	96.9194	−	167.869i	0.312643	−	0.541514i
$311$	−582.541			−1.87312			−0.936561	−	0.350504i	$-0.886010\pi$
$311$	−582.541			−1.87312			−0.936561	+	0.350504i	$0.886010\pi$
$312$			18.8477i			0.0604092i
$313$	−62.0888	+	107.541i	−0.198367	+	0.343582i	−0.947999	−	0.318273i	$-0.896897\pi$
$313$	−62.0888	+	107.541i	−0.198367	+	0.343582i	0.749632	+	0.661855i	$0.230230\pi$
$314$	22.9805	+	13.2678i	0.0731864	+	0.0422542i
$315$	−228.908			−0.726692
$316$			80.6113i			0.255099i
$317$	15.9801	+	9.22614i	0.0504106	+	0.0291046i	0.524993	−	0.851106i	$-0.324068\pi$
$317$	15.9801	+	9.22614i	0.0504106	+	0.0291046i	−0.474583	+	0.880211i	$0.657401\pi$
$318$	64.6250	−	37.3113i	0.203223	−	0.117331i
$319$	128.030	+	73.9182i	0.401348	+	0.231718i
$320$	−17.7310	−	30.7110i	−0.0554094	−	0.0959719i
$321$	−30.4404	−	52.7244i	−0.0948300	−	0.164250i
$322$			807.013i			2.50625i
$323$		0			0
$324$	−203.212			−0.627199
$325$	−237.582	+	137.168i	−0.731022	+	0.422056i
$326$	201.220	−	116.174i	0.617240	−	0.356363i
$327$	−10.9248	+	18.9223i	−0.0334091	+	0.0578663i
$328$	−93.4369	−	161.837i	−0.284869	−	0.493407i
$329$	−122.115	+	211.510i	−0.371171	+	0.642887i
$330$	−17.6881			−0.0536004
$331$			499.179i			1.50809i	0.656821	+	0.754047i	$0.271901\pi$
$331$			499.179i			1.50809i	−0.656821	+	0.754047i	$0.728099\pi$
$332$	109.004	−	188.800i	0.328325	−	0.568675i
$333$	−19.3858	−	11.1924i	−0.0582158	−	0.0336109i
$334$	−184.126			−0.551275
$335$		−	69.7904i		−	0.208330i
$336$	75.8009	+	43.7637i	0.225598	+	0.130249i
$337$	−126.198	+	72.8602i	−0.374474	+	0.216203i	−0.675411	−	0.737441i	$-0.736034\pi$
$337$	−126.198	+	72.8602i	−0.374474	+	0.216203i	0.300937	+	0.953644i	$0.402700\pi$
$338$	47.4831	+	27.4144i	0.140483	+	0.0811077i
$339$	−15.2504	−	26.4145i	−0.0449865	−	0.0779189i
$340$	−8.88293	−	15.3857i	−0.0261263	−	0.0452520i
$341$		−	258.585i		−	0.758314i
$342$		0			0
$343$	−377.033			−1.09922
$344$	−13.4778	+	7.78140i	−0.0391796	+	0.0226203i
$345$	20.9223	−	12.0795i	0.0606443	−	0.0350130i
$346$	−210.106	+	363.914i	−0.607242	+	1.05177i
$347$	116.798	+	202.299i	0.336592	+	0.582995i	0.983789	−	0.179328i	$-0.0573922\pi$
$347$	116.798	+	202.299i	0.336592	+	0.582995i	−0.647197	+	0.762323i	$0.724059\pi$
$348$	9.81172	−	16.9944i	0.0281946	−	0.0488345i
$349$	146.532			0.419863			0.209932	−	0.977716i	$-0.432676\pi$
$349$	146.532			0.419863			0.209932	+	0.977716i	$0.432676\pi$
$350$			586.549i			1.67585i
$351$	−48.0679	+	83.2560i	−0.136946	+	0.237197i
$352$	−245.623	−	141.811i	−0.697793	−	0.402871i
$353$	−361.824			−1.02500			−0.512499	−	0.858688i	$-0.671280\pi$
$353$	−361.824			−1.02500			−0.512499	+	0.858688i	$0.671280\pi$
$354$		−	54.6822i		−	0.154470i
$355$	−149.830	−	86.5045i	−0.422057	−	0.243675i
$356$	−200.997	+	116.046i	−0.564598	+	0.325971i
$357$	11.5081	+	6.64421i	0.0322356	+	0.0186112i
$358$	−11.0559	−	19.1494i	−0.0308824	−	0.0534899i
$359$	−81.0010	−	140.298i	−0.225630	−	0.390802i	0.730879	−	0.682507i	$-0.239111\pi$
$359$	−81.0010	−	140.298i	−0.225630	−	0.390802i	−0.956508	+	0.291706i	$0.905777\pi$
$360$			69.9941i			0.194428i
$361$		0			0
$362$	58.7395			0.162264
$363$	20.4848	−	11.8269i	0.0564319	−	0.0325810i
$364$	361.210	−	208.544i	0.992334	−	0.572924i
$365$	−20.5697	+	35.6277i	−0.0563553	+	0.0976102i
$366$	−53.2516	−	92.2345i	−0.145496	−	0.252007i
$367$	180.445	−	312.540i	0.491676	−	0.851607i	−0.508278	−	0.861193i	$-0.669718\pi$
$367$	180.445	−	312.540i	0.491676	−	0.851607i	0.999954	+	0.00958565i	$0.00305125\pi$
$368$	535.978			1.45646
$369$		−	472.519i		−	1.28054i
$370$	7.37147	−	12.7678i	0.0199229	−	0.0345075i
$371$	734.805	+	424.240i	1.98061	+	1.14350i
$372$	−34.3239			−0.0922687
$373$		−	418.395i		−	1.12170i	−0.827917	−	0.560851i	$-0.810474\pi$
$373$		−	418.395i		−	1.12170i	0.827917	−	0.560851i	$-0.189526\pi$
$374$	−51.5954	−	29.7886i	−0.137956	−	0.0796487i
$375$	34.3218	−	19.8157i	0.0915248	−	0.0528419i
$376$	64.6742	+	37.3397i	0.172006	+	0.0993077i
$377$	131.168	+	227.189i	0.347925	+	0.602625i
$378$	102.772	+	178.007i	0.271884	+	0.470917i
$379$		−	653.197i		−	1.72347i	−0.507355	−	0.861737i	$-0.669377\pi$
$379$		−	653.197i		−	1.72347i	0.507355	−	0.861737i	$-0.330623\pi$
$380$		0			0
$381$	49.5495			0.130051
$382$	188.786	−	108.996i	0.494205	−	0.285329i
$383$	412.765	−	238.310i	1.07772	−	0.622219i	0.147436	−	0.989072i	$-0.452898\pi$
$383$	412.765	−	238.310i	1.07772	−	0.622219i	0.930279	+	0.366852i	$0.119564\pi$
$384$	20.6026	−	35.6848i	0.0536527	−	0.0929292i
$385$	−100.560	−	174.174i	−0.261194	−	0.452401i
$386$	−391.073	+	677.357i	−1.01314	+	1.75481i
$387$	−39.3513			−0.101683
$388$		−	143.718i		−	0.370406i
$389$	195.595	−	338.781i	0.502815	−	0.870902i	−0.497179	−	0.867648i	$-0.665631\pi$
$389$	195.595	−	338.781i	0.502815	−	0.870902i	0.999995	−	0.00325400i	$-0.00103578\pi$
$390$	−27.1825	−	15.6938i	−0.0696987	−	0.0402405i
$391$	81.3723			0.208113
$392$			286.740i			0.731480i
$393$	−17.1095	−	9.87819i	−0.0435357	−	0.0251353i
$394$	752.701	−	434.572i	1.91041	−	1.10297i
$395$	59.7348	+	34.4879i	0.151227	+	0.0873111i
$396$	−90.8645	−	157.382i	−0.229456	−	0.397429i
$397$	−237.817	−	411.912i	−0.599037	−	1.03756i	−0.992964	−	0.118420i	$-0.962217\pi$
$397$	−237.817	−	411.912i	−0.599037	−	1.03756i	0.393927	−	0.919142i	$-0.371116\pi$
$398$		−	30.6566i		−	0.0770266i
$399$		0			0
$400$	389.556			0.973891
$401$	−196.142	+	113.243i	−0.489132	+	0.282401i	−0.724214	−	0.689575i	$-0.757797\pi$
$401$	−196.142	+	113.243i	−0.489132	+	0.282401i	0.235082	+	0.971976i	$0.424464\pi$
$402$	−26.9039	+	15.5330i	−0.0669251	+	0.0386392i
$403$	229.430	−	397.384i	0.569304	−	0.986064i
$404$	−5.95985	−	10.3228i	−0.0147521	−	0.0255514i
$405$	−86.9403	+	150.585i	−0.214667	+	0.371815i
$406$	560.891			1.38150
$407$		−	19.6674i		−	0.0483228i
$408$	2.03163	−	3.51888i	0.00497948	−	0.00862471i
$409$	−664.607	−	383.711i	−1.62496	−	0.938169i	−0.985567	−	0.169287i	$-0.945854\pi$
$409$	−664.607	−	383.711i	−1.62496	−	0.938169i	−0.639390	−	0.768883i	$-0.720813\pi$
$410$	311.207			0.759041
$411$			43.2062i			0.105125i
$412$	85.1512	+	49.1620i	0.206678	+	0.119325i
$413$	538.453	−	310.876i	1.30376	−	0.752726i
$414$	540.359	+	311.977i	1.30522	+	0.753567i
$415$	−93.2701	−	161.549i	−0.224747	−	0.389274i
$416$	−251.643	−	435.858i	−0.604911	−	1.04774i
$417$		−	29.5304i		−	0.0708163i
$418$		0			0
$419$	−108.615			−0.259224			−0.129612	−	0.991565i	$-0.541373\pi$
$419$	−108.615			−0.259224			−0.129612	+	0.991565i	$0.541373\pi$
$420$	−23.1195	+	13.3480i	−0.0550463	+	0.0317810i
$421$	13.5394	−	7.81697i	0.0321601	−	0.0185676i	−0.483834	−	0.875160i	$-0.660756\pi$
$421$	13.5394	−	7.81697i	0.0321601	−	0.0185676i	0.515994	+	0.856592i	$0.327423\pi$
$422$	−142.253	+	246.389i	−0.337092	+	0.583860i
$423$	94.4152	+	163.532i	0.223204	+	0.386600i
$424$	129.721	−	224.684i	0.305947	−	0.529916i
$425$	59.1425			0.139159
$426$			77.0117i			0.180779i
$427$	605.486	−	1048.73i	1.41800	−	2.45605i
$428$	356.766	+	205.979i	0.833564	+	0.481259i
$429$	−41.8717			−0.0976031
$430$		−	25.9172i		−	0.0602726i
$431$	465.454	+	268.730i	1.07994	+	0.623503i	0.930880	−	0.365325i	$-0.119042\pi$
$431$	465.454	+	268.730i	1.07994	+	0.623503i	0.149059	+	0.988828i	$0.452376\pi$
$432$	118.223	−	68.2562i	0.273665	−	0.158000i
$433$	−572.206	−	330.363i	−1.32149	−	0.762964i	−0.337525	−	0.941316i	$-0.609590\pi$
$433$	−572.206	−	330.363i	−1.32149	−	0.762964i	−0.983967	+	0.178353i	$0.942923\pi$
$434$	−490.535	−	849.632i	−1.13027	−	1.95768i
$435$	−8.39549	−	14.5414i	−0.0193000	−	0.0334285i
$436$		−	147.848i		−	0.339100i
$437$		0			0
$438$	18.3124			0.0418092
$439$	−78.3124	+	45.2137i	−0.178388	+	0.102992i	−0.586535	−	0.809924i	$-0.699508\pi$
$439$	−78.3124	+	45.2137i	−0.178388	+	0.102992i	0.408147	+	0.912916i	$0.366175\pi$
$440$	−53.2580	+	30.7485i	−0.121041	+	0.0698829i
$441$	−362.518	+	627.900i	−0.822037	+	1.42381i
$442$	−52.8599	−	91.5561i	−0.119593	−	0.207140i
$443$	126.071	−	218.361i	0.284584	−	0.492915i	−0.687924	−	0.725783i	$-0.741478\pi$
$443$	126.071	−	218.361i	0.284584	−	0.492915i	0.972508	+	0.232868i	$0.0748111\pi$
$444$	−2.61060			−0.00587973
$445$			198.591i			0.446272i
$446$	−343.892	+	595.639i	−0.771059	+	1.33551i
$447$	69.2549	+	39.9843i	0.154933	+	0.0894504i
$448$	−179.483			−0.400631
$449$			30.8018i			0.0686009i	0.999412	+	0.0343005i	$0.0109203\pi$
$449$			30.8018i			0.0686009i	−0.999412	+	0.0343005i	$0.989080\pi$
$450$	392.741	+	226.749i	0.872758	+	0.503887i
$451$	359.536	−	207.578i	0.797197	−	0.460262i
$452$	178.737	+	103.194i	0.395436	+	0.228305i
$453$	8.94501	+	15.4932i	0.0197462	+	0.0342014i
$454$	357.593	+	619.370i	0.787650	+	1.36425i
$455$		−	356.886i		−	0.784365i
$456$		0			0
$457$	289.618			0.633738			0.316869	−	0.948469i	$-0.397368\pi$
$457$	289.618			0.633738			0.316869	+	0.948469i	$0.397368\pi$
$458$	−496.355	+	286.571i	−1.08375	+	0.625700i
$459$	17.9487	−	10.3627i	0.0391039	−	0.0225766i
$460$	−81.7372	+	141.573i	−0.177690	+	0.307767i
$461$	289.386	+	501.231i	0.627735	+	1.08727i	0.988005	+	0.154420i	$0.0493510\pi$
$461$	289.386	+	501.231i	0.627735	+	1.08727i	−0.360271	+	0.932848i	$0.617316\pi$
$462$	−44.7622	+	77.5304i	−0.0968879	+	0.167815i
$463$	306.466			0.661913			0.330957	−	0.943646i	$-0.392629\pi$
$463$	306.466			0.661913			0.330957	+	0.943646i	$0.392629\pi$
$464$		−	372.516i		−	0.802835i
$465$	−14.6848	+	25.4348i	−0.0315802	+	0.0546985i
$466$	788.866	+	455.452i	1.69284	+	0.977364i
$467$	577.984			1.23765			0.618827	−	0.785527i	$-0.287608\pi$
$467$	577.984			1.23765			0.618827	+	0.785527i	$0.287608\pi$
$468$		−	322.478i		−	0.689056i
$469$	−305.904	−	176.614i	−0.652248	−	0.376576i
$470$	−107.704	+	62.1830i	−0.229158	+	0.132304i
$471$	−3.48191	−	2.01028i	−0.00739259	−	0.00426811i
$472$	−95.0578	−	164.645i	−0.201394	−	0.348824i
$473$	−17.2871	−	29.9421i	−0.0365477	−	0.0633025i
$474$		−	30.7033i		−	0.0647749i
$475$		0			0
$476$	−89.9177			−0.188903
$477$	568.124	−	328.007i	1.19104	−	0.687645i
$478$	698.057	−	403.024i	1.46037	−	0.843145i
$479$	−89.8742	+	155.667i	−0.187629	+	0.324983i	−0.944459	−	0.328629i	$-0.893414\pi$
$479$	−89.8742	+	155.667i	−0.187629	+	0.324983i	0.756830	+	0.653611i	$0.226747\pi$
$480$	16.1066	+	27.8974i	0.0335554	+	0.0581196i
$481$	17.4499	−	30.2241i	0.0362784	−	0.0628360i
$482$	980.361			2.03394
$483$		−	122.275i		−	0.253157i
$484$	−80.0281	+	138.613i	−0.165347	+	0.286390i
$485$	−106.498	−	61.4866i	−0.219583	−	0.126777i
$486$	239.058			0.491889
$487$		−	689.497i		−	1.41580i	−0.706310	−	0.707902i	$-0.749642\pi$
$487$		−	689.497i		−	1.41580i	0.706310	−	0.707902i	$-0.250358\pi$
$488$	−320.675	−	185.142i	−0.657121	−	0.379389i
$489$	−30.4880	+	17.6022i	−0.0623476	+	0.0359964i
$490$	−413.543	−	238.759i	−0.843964	−	0.487263i
$491$	216.284	+	374.615i	0.440497	+	0.762963i	0.997726	−	0.0673957i	$-0.0214690\pi$
$491$	216.284	+	374.615i	0.440497	+	0.762963i	−0.557230	+	0.830358i	$0.688136\pi$
$492$	−27.5534	−	47.7239i	−0.0560029	−	0.0969999i
$493$		−	56.5554i		−	0.114717i
$494$		0			0
$495$	−155.498			−0.314137
$496$	−564.283	+	325.789i	−1.13767	+	0.656833i
$497$	−758.331	+	437.822i	−1.52582	+	0.880930i
$498$	−41.5175	+	71.9104i	−0.0833684	+	0.144398i
$499$	−142.938	−	247.576i	−0.286448	−	0.496143i	0.686511	−	0.727119i	$-0.259141\pi$
$499$	−142.938	−	247.576i	−0.286448	−	0.496143i	−0.972959	+	0.230976i	$0.925808\pi$
$500$	−134.085	+	232.243i	−0.268171	+	0.464485i
$501$	27.8979			0.0556845
$502$		−	103.114i		−	0.205406i
$503$	273.925	−	474.453i	0.544583	−	0.943246i	−0.454050	−	0.890976i	$-0.650021\pi$
$503$	273.925	−	474.453i	0.544583	−	0.943246i	0.998633	−	0.0522694i	$-0.0166454\pi$
$504$	306.797	+	177.129i	0.608725	+	0.351447i
$505$	−10.1992			−0.0201964
$506$			548.207i			1.08341i
$507$	−7.19443	−	4.15371i	−0.0141902	−	0.00819272i
$508$	−290.363	+	167.641i	−0.571582	+	0.330003i
$509$	−441.145	−	254.695i	−0.866690	−	0.500384i	−0.000443435	−	1.00000i	$-0.500141\pi$
$509$	−441.145	−	254.695i	−0.866690	−	0.500384i	−0.866247	+	0.499616i	$0.833474\pi$
$510$	3.38334	+	5.86011i	0.00663399	+	0.0114904i
$511$	104.109	+	180.321i	0.203735	+	0.352880i
$512$			440.514i			0.860380i
$513$		0			0
$514$	−934.260			−1.81763
$515$	72.8604	−	42.0659i	0.141476	−	0.0816814i
$516$	−3.97444	+	2.29464i	−0.00770240	+	0.00444698i
$517$	−82.9534	+	143.679i	−0.160451	+	0.277910i
$518$	−37.3090	−	64.6210i	−0.0720250	−	0.124751i
$519$	31.8343	−	55.1386i	0.0613378	−	0.106240i
$520$	−109.126			−0.209859
$521$			671.354i			1.28859i	0.764778	+	0.644294i	$0.222849\pi$
$521$			671.354i			1.28859i	−0.764778	+	0.644294i	$0.777151\pi$
$522$	216.830	−	375.561i	0.415383	−	0.719465i
$523$	−451.351	−	260.588i	−0.863005	−	0.498256i	0.00201266	−	0.999998i	$-0.499359\pi$
$523$	−451.351	−	260.588i	−0.863005	−	0.498256i	−0.865017	+	0.501742i	$0.832693\pi$
$524$	133.684			0.255122
$525$		−	88.8712i		−	0.169278i
$526$	−125.725	−	72.5871i	−0.239020	−	0.137998i
$527$	−85.6696	+	49.4614i	−0.162561	+	0.0938546i
$528$	51.4919	+	29.7288i	0.0975224	+	0.0563046i
$529$	−109.878	−	190.314i	−0.207709	−	0.359762i
$530$	216.029	+	374.174i	0.407602	+	0.705988i
$531$		−	480.716i		−	0.905303i
$532$		0			0
$533$	736.696			1.38217
$534$	76.5559	−	44.1996i	0.143363	−	0.0827707i
$535$	305.270	−	176.248i	0.570598	−	0.329435i
$536$	−54.0040	+	93.5376i	−0.100754	+	0.174511i
$537$	1.67514	+	2.90143i	0.00311944	+	0.00540304i
$538$	201.955	−	349.796i	0.375380	−	0.650178i
$539$	−637.019			−1.18185
$540$			41.6366i			0.0771048i
$541$	−321.366	+	556.622i	−0.594022	+	1.02888i	0.399663	+	0.916662i	$0.369127\pi$
$541$	−321.366	+	556.622i	−0.594022	+	1.02888i	−0.993684	+	0.112213i	$0.964206\pi$
$542$	−881.103	−	508.705i	−1.62565	−	0.938570i
$543$	−8.89994			−0.0163903
$544$			108.500i			0.199449i
$545$	−109.559	−	63.2536i	−0.201025	−	0.116062i
$546$	−137.578	+	79.4306i	−0.251974	+	0.145477i
$547$	337.812	+	195.036i	0.617573	+	0.356556i	0.775924	−	0.630827i	$-0.217284\pi$
$547$	337.812	+	195.036i	0.617573	+	0.356556i	−0.158350	+	0.987383i	$0.550618\pi$
$548$	−146.180	−	253.191i	−0.266752	−	0.462028i
$549$	−468.140	−	810.842i	−0.852714	−	1.47694i
$550$			398.445i			0.724445i
$551$		0			0
$552$	−37.3885			−0.0677328
$553$	302.334	−	174.552i	0.546716	−	0.315646i
$554$	−423.009	+	244.224i	−0.763554	+	0.440838i
$555$	−1.11689	+	1.93451i	−0.00201242	+	0.00348561i
$556$	99.9104	+	173.050i	0.179695	+	0.311241i
$557$	−112.230	+	194.388i	−0.201490	+	0.348990i	−0.949009	−	0.315250i	$-0.897912\pi$
$557$	−112.230	+	194.388i	−0.201490	+	0.348990i	0.747519	+	0.664240i	$0.231245\pi$
$558$	−758.528			−1.35937
$559$		−	61.3518i		−	0.109753i
$560$	−253.388	+	438.881i	−0.452479	+	0.783717i
$561$	7.81750	+	4.51344i	0.0139349	+	0.00804534i
$562$	−416.876			−0.741773
$563$			942.439i			1.67396i	0.547234	+	0.836980i	$0.315681\pi$
$563$			942.439i			1.67396i	−0.547234	+	0.836980i	$0.684319\pi$
$564$	19.0717	+	11.0110i	0.0338150	+	0.0195231i
$565$	152.938	−	88.2987i	0.270686	−	0.156281i
$566$	531.099	+	306.630i	0.938338	+	0.541750i
$567$	440.028	+	762.151i	0.776063	+	1.34418i
$568$	133.875	+	231.878i	0.235695	+	0.408236i
$569$		−	4.69641i		−	0.00825379i	−0.999991	−	0.00412690i	$-0.998686\pi$
$569$		−	4.69641i		−	0.00825379i	0.999991	−	0.00412690i	$-0.00131364\pi$
$570$		0			0
$571$	220.091			0.385449			0.192724	−	0.981253i	$-0.438268\pi$
$571$	220.091			0.385449			0.192724	+	0.981253i	$0.438268\pi$
$572$	245.371	−	141.665i	0.428970	−	0.247666i
$573$	−28.6040	+	16.5146i	−0.0499198	+	0.0288212i
$574$	787.551	−	1364.08i	1.37204	−	2.37644i
$575$	−272.103	−	471.297i	−0.473223	−	0.819647i
$576$	−69.3848	+	120.178i	−0.120460	+	0.208642i
$577$	−485.566			−0.841536			−0.420768	−	0.907168i	$-0.638239\pi$
$577$	−485.566			−0.841536			−0.420768	+	0.907168i	$0.638239\pi$
$578$		−	722.041i		−	1.24921i
$579$	59.2536	−	102.630i	0.102338	−	0.177254i
$580$	98.3962	+	56.8091i	0.169649	+	0.0979467i
$581$	−944.130			−1.62501
$582$			54.7392i			0.0940537i
$583$	499.155	+	288.188i	0.856184	+	0.494318i
$584$	55.1376	−	31.8337i	0.0944137	−	0.0545098i
$585$	−238.964	−	137.966i	−0.408485	−	0.235839i
$586$	205.077	+	355.204i	0.349961	+	0.606151i
$587$	−40.8719	−	70.7923i	−0.0696285	−	0.120600i	0.829109	−	0.559087i	$-0.188848\pi$
$587$	−40.8719	−	70.7923i	−0.0696285	−	0.120600i	−0.898738	+	0.438486i	$0.855515\pi$
$588$			84.5563i			0.143803i
$589$		0			0
$590$	316.606			0.536620
$591$	−114.046	+	65.8444i	−0.192971	+	0.111412i
$592$	−42.9181	+	24.7788i	−0.0724968	+	0.0418560i
$593$	264.264	−	457.719i	0.445640	−	0.771870i	−0.552457	−	0.833541i	$-0.686310\pi$
$593$	264.264	−	457.719i	0.445640	−	0.771870i	0.998097	+	0.0616711i	$0.0196430\pi$
$594$	69.8135	+	120.921i	0.117531	+	0.203570i
$595$	−38.4695	+	66.6311i	−0.0646545	+	0.111985i
$596$	−541.118			−0.907916
$597$			4.64495i			0.00778049i
$598$	−486.397	+	842.464i	−0.813372	+	1.40880i
$599$	780.668	+	450.719i	1.30329	+	0.752452i	0.980966	−	0.194179i	$-0.0622042\pi$
$599$	780.668	+	450.719i	1.30329	+	0.752452i	0.322319	+	0.946631i	$0.395538\pi$
$600$	−27.1745			−0.0452909
$601$		−	930.074i		−	1.54754i	−0.633465	−	0.773772i	$-0.718368\pi$
$601$		−	930.074i		−	1.54754i	0.633465	−	0.773772i	$-0.281632\pi$
$602$	−113.600	−	65.5870i	−0.188704	−	0.108949i
$603$	−236.514	+	136.552i	−0.392229	+	0.226454i
$604$	−104.837	−	60.5275i	−0.173571	−	0.100211i
$605$	68.4768	+	118.605i	0.113185	+	0.196042i
$606$	2.26999	+	3.93174i	0.00374586	+	0.00648803i
$607$			893.795i			1.47248i	0.676721	+	0.736240i	$0.263400\pi$
$607$			893.795i			1.47248i	−0.676721	+	0.736240i	$0.736600\pi$
$608$		0			0
$609$	−84.9836			−0.139546
$610$	534.030	−	308.323i	0.875460	−	0.505447i
$611$	−254.959	+	147.201i	−0.417282	+	0.240918i
$612$	−34.7606	+	60.2071i	−0.0567983	+	0.0983776i
$613$	−92.9202	−	160.943i	−0.151583	−	0.262549i	0.780227	−	0.625497i	$-0.215104\pi$
$613$	−92.9202	−	160.943i	−0.151583	−	0.262549i	−0.931809	+	0.362948i	$0.881770\pi$
$614$	51.0888	−	88.4884i	0.0832066	−	0.144118i
$615$	−47.1527			−0.0766710
$616$			311.253i			0.505280i
$617$	28.6795	−	49.6743i	0.0464821	−	0.0805094i	−0.841848	−	0.539714i	$-0.818532\pi$
$617$	28.6795	−	49.6743i	0.0464821	−	0.0805094i	0.888330	+	0.459205i	$0.151866\pi$
$618$	−32.4324	−	18.7249i	−0.0524797	−	0.0302992i
$619$	−129.182			−0.208695			−0.104347	−	0.994541i	$-0.533275\pi$
$619$	−129.182			−0.208695			−0.104347	+	0.994541i	$0.533275\pi$
$620$		−	198.733i		−	0.320537i
$621$	−165.157	−	95.3533i	−0.265953	−	0.153548i
$622$	−1300.22	+	750.684i	−2.09039	+	1.20689i
$623$	870.462	+	502.561i	1.39721	+	0.806680i
$624$	52.7538	+	91.3723i	0.0845414	+	0.146430i
$625$	−133.870	−	231.870i	−0.214192	−	0.370992i
$626$			320.040i			0.511246i
$627$		0			0
$628$	27.2056			0.0433210
$629$	−6.51583	+	3.76192i	−0.0103590	+	0.00598079i
$630$	−510.919	+	294.979i	−0.810983	+	0.468221i
$631$	342.136	−	592.597i	0.542212	−	0.939139i	−0.456564	−	0.889690i	$-0.650920\pi$
$631$	342.136	−	592.597i	0.542212	−	0.939139i	0.998777	−	0.0494490i	$-0.0157465\pi$
$632$	−53.3736	−	92.4458i	−0.0844519	−	0.146275i
$633$	21.5535	−	37.3318i	0.0340498	−	0.0589759i
$634$	47.5566			0.0750104
$635$			286.888i			0.451792i
$636$	38.2533	−	66.2567i	0.0601467	−	0.104177i
$637$	−978.946	−	565.195i	−1.53681	−	0.887276i
$638$	381.015			0.597202
$639$			677.017i			1.05949i
$640$	206.612	+	119.288i	0.322832	+	0.186387i
$641$	−556.792	+	321.464i	−0.868630	+	0.501504i	−0.866893	−	0.498494i	$-0.833886\pi$
$641$	−556.792	+	321.464i	−0.868630	+	0.501504i	−0.00173760	+	0.999998i	$0.500553\pi$
$642$	−135.885	−	78.4533i	−0.211659	−	0.122201i
$643$	73.5468	+	127.387i	0.114381	+	0.198113i	0.917532	−	0.397662i	$-0.130178\pi$
$643$	73.5468	+	127.387i	0.114381	+	0.198113i	−0.803151	+	0.595775i	$0.796845\pi$
$644$	413.694	+	716.539i	0.642382	+	1.11264i
$645$			3.92686i			0.00608816i
$646$		0			0
$647$	−854.914			−1.32135			−0.660675	−	0.750672i	$-0.729730\pi$
$647$	−854.914			−1.32135			−0.660675	+	0.750672i	$0.729730\pi$
$648$	233.046	−	134.549i	0.359639	−	0.207638i
$649$	365.773	−	211.179i	0.563595	−	0.325392i
$650$	−353.520	+	612.315i	−0.543877	+	0.942023i
$651$	74.3237	+	128.732i	0.114168	+	0.197746i
$652$	119.108	−	206.300i	0.182680	−	0.316412i
$653$	−763.603			−1.16938			−0.584688	−	0.811258i	$-0.698783\pi$
$653$	−763.603			−1.16938			−0.584688	+	0.811258i	$0.698783\pi$
$654$			56.3124i			0.0861045i
$655$	57.1939	−	99.0628i	0.0873190	−	0.151241i
$656$	−905.953	−	523.052i	−1.38103	−	0.797336i
$657$	160.986			0.245032
$658$			629.449i			0.956610i
$659$	−573.227	−	330.953i	−0.869844	−	0.502204i	−0.00254739	−	0.999997i	$-0.500811\pi$
$659$	−573.227	−	330.953i	−0.869844	−	0.502204i	−0.867296	+	0.497792i	$0.834144\pi$
$660$	−15.7051	+	9.06736i	−0.0237957	+	0.0137384i
$661$	−738.358	−	426.291i	−1.11703	−	0.644919i	−0.176390	−	0.984320i	$-0.556442\pi$
$661$	−738.358	−	426.291i	−1.11703	−	0.644919i	−0.940642	+	0.339402i	$0.889775\pi$
$662$	643.260	+	1114.16i	0.971693	+	1.68302i
$663$	8.00910	+	13.8722i	0.0120801	+	0.0209233i
$664$			288.690i			0.434775i
$665$		0			0
$666$	−57.6919			−0.0866245
$667$	−450.680	+	260.200i	−0.675683	+	0.390106i
$668$	−163.484	+	94.3874i	−0.244736	+	0.141298i
$669$	52.1050	−	90.2485i	0.0778849	−	0.134901i
$670$	−89.9346	−	155.771i	−0.134231	−	0.232494i
$671$	411.309	−	712.408i	0.612979	−	1.06171i
$672$	163.039			0.242618
$673$		−	512.608i		−	0.761676i	−0.924642	−	0.380838i	$-0.875635\pi$
$673$		−	512.608i		−	0.761676i	0.924642	−	0.380838i	$-0.124365\pi$
$674$	−187.781	+	325.246i	−0.278607	+	0.482561i
$675$	−120.038	−	69.3042i	−0.177835	−	0.102673i
$676$	56.2131			0.0831555
$677$			87.3684i			0.129052i	0.997916	+	0.0645261i	$0.0205536\pi$
$677$			87.3684i			0.129052i	−0.997916	+	0.0645261i	$0.979446\pi$
$678$	−68.0774	−	39.3045i	−0.100409	−	0.0579713i
$679$	−539.014	+	311.200i	−0.793836	+	0.458321i
$680$	20.3740	+	11.7630i	0.0299618	+	0.0172985i
$681$	−54.1809	−	93.8441i	−0.0795608	−	0.137803i
$682$	−333.222	−	577.158i	−0.488596	−	0.846273i
$683$		−	387.459i		−	0.567289i	−0.958929	−	0.283645i	$-0.908456\pi$
$683$		−	387.459i		−	0.567289i	0.958929	−	0.283645i	$-0.0915436\pi$
$684$		0			0
$685$	−250.160			−0.365198
$686$	−841.532	+	485.859i	−1.22672	+	0.708249i
$687$	75.2055	−	43.4199i	0.109469	−	0.0632022i
$688$	−43.5596	+	75.4475i	−0.0633134	+	0.109662i
$689$	511.389	+	885.752i	0.742219	+	1.28556i
$690$	31.1321	−	53.9224i	0.0451190	−	0.0781485i
$691$	−165.969			−0.240186			−0.120093	−	0.992763i	$-0.538319\pi$
$691$	−165.969			−0.240186			−0.120093	+	0.992763i	$0.538319\pi$
$692$			430.821i			0.622574i
$693$	−393.509	+	681.577i	−0.567833	+	0.983516i
$694$	521.381	+	301.019i	0.751269	+	0.433745i
$695$	170.979			0.246012
$696$			25.9858i			0.0373359i
$697$	−137.542	−	79.4099i	−0.197334	−	0.113931i
$698$	327.058	−	188.827i	0.468564	−	0.270526i
$699$	−119.525	−	69.0080i	−0.170995	−	0.0987239i
$700$	300.679	+	520.791i	0.429541	+	0.743987i
$701$	541.119	+	937.245i	0.771924	+	1.33701i	0.936507	+	0.350648i	$0.114039\pi$
$701$	541.119	+	937.245i	0.771924	+	1.33701i	−0.164584	+	0.986363i	$0.552628\pi$
$702$			247.768i			0.352946i
$703$		0			0
$704$	−121.923			−0.173187
$705$	16.3188	−	9.42169i	0.0231473	−	0.0133641i
$706$	−807.587	+	466.260i	−1.14389	+	0.660425i
$707$	−25.8104	+	44.7050i	−0.0365070	+	0.0632320i
$708$	−28.0314	−	48.5518i	−0.0395924	−	0.0685760i
$709$	−19.3334	+	33.4864i	−0.0272686	+	0.0472305i	−0.879338	−	0.476199i	$-0.842014\pi$
$709$	−19.3334	+	33.4864i	−0.0272686	+	0.0472305i	0.852069	+	0.523429i	$0.175348\pi$
$710$	−445.892			−0.628016
$711$		−	269.915i		−	0.379628i
$712$	153.670	−	266.165i	0.215829	−	0.373827i
$713$	788.298	+	455.124i	1.10561	+	0.638323i
$714$	34.2479			0.0479663
$715$		−	242.434i		−	0.339068i
$716$	−19.6329	−	11.3350i	−0.0274202	−	0.0158311i
$717$	−105.766	+	61.0643i	−0.147513	+	0.0851664i
$718$	−361.586	−	208.762i	−0.503602	−	0.290755i
$719$	−246.591	−	427.109i	−0.342964	−	0.594032i	0.642017	−	0.766690i	$-0.278098\pi$
$719$	−246.591	−	427.109i	−0.342964	−	0.594032i	−0.984982	+	0.172658i	$0.944764\pi$
$720$	195.911	+	339.327i	0.272098	+	0.471288i
$721$		−	425.814i		−	0.590588i
$722$		0			0
$723$	−148.540			−0.205449
$724$	52.1542	−	30.1113i	0.0720362	−	0.0415901i
$725$	−327.561	+	189.117i	−0.451808	+	0.260852i
$726$	30.4812	−	52.7950i	0.0419851	−	0.0727203i
$727$	−102.739	−	177.949i	−0.141319	−	0.244772i	0.786674	−	0.617368i	$-0.211801\pi$
$727$	−102.739	−	177.949i	−0.141319	−	0.244772i	−0.927994	+	0.372596i	$0.878468\pi$
$728$	−276.159	+	478.322i	−0.379339	+	0.657035i
$729$	655.934			0.899772
$730$			106.027i			0.145243i
$731$	−6.61323	+	11.4545i	−0.00904683	+	0.0156696i
$732$	−94.5632	−	54.5961i	−0.129185	−	0.0745849i
$733$	916.994			1.25101			0.625507	−	0.780218i	$-0.284892\pi$
$733$	916.994			1.25101			0.625507	+	0.780218i	$0.284892\pi$
$734$		−	930.112i		−	1.26718i
$735$	62.6581	+	36.1757i	0.0852491	+	0.0492186i
$736$	864.621	−	499.189i	1.17476	−	0.678246i
$737$	−207.802	−	119.975i	−0.281957	−	0.162788i
$738$	−608.906	−	1054.66i	−0.825076	−	1.42907i
$739$	543.551	+	941.458i	0.735522	+	1.27396i	0.954494	+	0.298230i	$0.0963964\pi$
$739$	543.551	+	941.458i	0.735522	+	1.27396i	−0.218972	+	0.975731i	$0.570270\pi$
$740$		−	15.1152i		−	0.0204259i
$741$		0			0
$742$	2186.76			2.94712
$743$	1123.96	−	648.921i	1.51274	−	0.873380i	0.512849	−	0.858479i	$-0.328590\pi$
$743$	1123.96	−	648.921i	1.51274	−	0.873380i	0.999889	−	0.0149010i	$-0.00474331\pi$
$744$	39.3630	−	22.7263i	0.0529073	−	0.0305460i
$745$	−231.506	+	400.980i	−0.310746	+	0.538229i
$746$	−539.159	−	933.850i	−0.722733	−	1.25181i
$747$	−364.984	+	632.170i	−0.488599	+	0.846279i
$748$	−61.0814			−0.0816597
$749$		−	1784.07i		−	2.38194i
$750$	51.0705	−	88.4567i	0.0680940	−	0.117942i
$751$	37.0344	+	21.3818i	0.0493135	+	0.0284711i	0.524454	−	0.851439i	$-0.324269\pi$
$751$	37.0344	+	21.3818i	0.0493135	+	0.0284711i	−0.475141	+	0.879910i	$0.657603\pi$
$752$	418.049			0.555916
$753$			15.6234i			0.0207482i
$754$	585.530	+	338.056i	0.776564	+	0.448350i
$755$	−89.7045	+	51.7909i	−0.118814	+	0.0685972i
$756$	182.501	+	105.367i	0.241403	+	0.139374i
$757$	−429.704	−	744.269i	−0.567641	−	0.983183i	−0.996799	−	0.0799531i	$-0.974523\pi$
$757$	−429.704	−	744.269i	−0.567641	−	0.983183i	0.429158	−	0.903229i	$-0.358810\pi$
$758$	−841.734	−	1457.93i	−1.11047	−	1.92338i
$759$		−	83.0618i		−	0.109436i
$760$		0			0
$761$	−296.354			−0.389427			−0.194713	−	0.980860i	$-0.562378\pi$
$761$	−296.354			−0.389427			−0.194713	+	0.980860i	$0.562378\pi$
$762$	110.594	−	63.8514i	0.145136	−	0.0837945i
$763$	−554.505	+	320.144i	−0.726743	+	0.419585i
$764$	111.748	−	193.553i	0.146267	−	0.253341i
$765$	29.7432	+	51.5167i	0.0388800	+	0.0673421i
$766$	614.190	−	1063.81i	0.801815	−	1.38878i
$767$	749.475			0.977151
$768$		−	130.696i		−	0.170178i
$769$	−181.103	+	313.680i	−0.235505	+	0.407907i	−0.959419	−	0.281983i	$-0.909008\pi$
$769$	−181.103	+	313.680i	−0.235505	+	0.407907i	0.723914	+	0.689890i	$0.242341\pi$
$770$	−448.895	−	259.170i	−0.582980	−	0.336584i
$771$	141.555			0.183599
$772$			801.892i			1.03872i
$773$	1320.52	+	762.404i	1.70831	+	0.986292i	0.936658	+	0.350245i	$0.113902\pi$
$773$	1320.52	+	762.404i	1.70831	+	0.986292i	0.771650	+	0.636047i	$0.219432\pi$
$774$	−87.8315	+	50.7095i	−0.113477	+	0.0655162i
$775$	572.947	+	330.791i	0.739286	+	0.426827i
$776$	95.1569	+	164.817i	0.122625	+	0.212393i
$777$	5.65289	+	9.79109i	0.00727527	+	0.0126011i
$778$		−	1008.21i		−	1.29589i
$779$		0			0
$780$	−32.1801			−0.0412565
$781$	−515.137	+	297.414i	−0.659586	+	0.380812i
$782$	181.622	−	104.859i	0.232253	−	0.134091i
$783$	−66.2725	+	114.787i	−0.0846392	+	0.146599i
$784$	802.574	+	1390.10i	1.02369	+	1.77309i
$785$	11.6394	−	20.1600i	0.0148272	−	0.0256815i
$786$	−50.9176			−0.0647807
$787$			1357.52i			1.72493i	0.506117	+	0.862465i	$0.331081\pi$
$787$			1357.52i			1.72493i	−0.506117	+	0.862465i	$0.668919\pi$
$788$	445.544	−	771.705i	0.565411	−	0.979321i
$789$	19.0492	+	10.9981i	0.0241435	+	0.0139393i
$790$	177.770			0.225025
$791$		−	893.807i		−	1.12997i
$792$	208.408	+	120.325i	0.263142	+	0.151925i
$793$	1264.17	−	729.868i	1.59416	−	0.920388i
$794$	−1061.61	−	612.921i	−1.33704	−	0.771941i
$795$	−32.7318	−	56.6931i	−0.0411721	−	0.0713121i
$796$	−15.7153	−	27.2197i	−0.0197428	−	0.0341956i
$797$			857.375i			1.07575i	0.843024	+	0.537876i	$0.180773\pi$
$797$			857.375i			1.07575i	−0.843024	+	0.537876i	$0.819227\pi$
$798$		0			0
$799$	63.4683			0.0794347
$800$	628.419	−	362.818i	0.785524	−	0.453522i
$801$	673.010	−	388.562i	0.840212	−	0.485097i
$802$	−291.857	+	505.512i	−0.363912	+	0.630314i
$803$	70.7214	+	122.493i	0.0880714	+	0.152544i
$804$	−15.9251	+	27.5831i	−0.0198074	+	0.0343074i
$805$	707.962			0.879456
$806$		−	1182.61i		−	1.46725i
$807$	−30.5992	+	52.9995i	−0.0379173	+	0.0656747i
$808$	13.6696	+	7.89217i	0.0169179	+	0.00976753i
$809$	−548.605			−0.678128			−0.339064	−	0.940763i	$-0.610110\pi$
$809$	−548.605			−0.678128			−0.339064	+	0.940763i	$0.610110\pi$
$810$			448.138i			0.553257i
$811$	−257.471	−	148.651i	−0.317473	−	0.183293i	0.332793	−	0.943000i	$-0.392009\pi$
$811$	−257.471	−	148.651i	−0.317473	−	0.183293i	−0.650266	+	0.759707i	$0.725342\pi$
$812$	498.009	−	287.526i	0.613312	−	0.354096i
$813$	133.501	+	77.0767i	0.164208	+	0.0948053i
$814$	−25.3441	−	43.8973i	−0.0311353	−	0.0539279i
$815$	−101.916	−	176.523i	−0.125050	−	0.216592i
$816$		−	22.7458i		−	0.0278747i
$817$		0			0
$818$	−1977.86			−2.41792
$819$	−1209.46	+	698.281i	−1.47675	+	0.852602i
$820$	276.318	−	159.532i	0.336973	−	0.194551i
$821$	−190.756	+	330.399i	−0.232346	+	0.402435i	−0.958498	−	0.285099i	$-0.907974\pi$
$821$	−190.756	+	330.399i	−0.232346	+	0.402435i	0.726152	+	0.687534i	$0.241307\pi$
$822$	55.6771	+	96.4356i	0.0677337	+	0.117318i
$823$	−345.190	+	597.887i	−0.419429	+	0.726472i	−0.995882	−	0.0906579i	$-0.971103\pi$
$823$	−345.190	+	597.887i	−0.419429	+	0.726472i	0.576453	+	0.817130i	$0.304436\pi$
$824$	−130.203			−0.158013
$825$		−	60.3705i		−	0.0731764i
$826$	801.213	−	1387.74i	0.969991	−	1.68007i
$827$	286.798	+	165.583i	0.346793	+	0.200221i	0.663272	−	0.748379i	$-0.269167\pi$
$827$	286.798	+	165.583i	0.346793	+	0.200221i	−0.316479	+	0.948600i	$0.602501\pi$
$828$	639.707			0.772592
$829$			860.677i			1.03821i	0.854710	+	0.519105i	$0.173735\pi$
$829$			860.677i			1.03821i	−0.854710	+	0.519105i	$0.826265\pi$
$830$	−416.355	−	240.383i	−0.501633	−	0.289618i
$831$	64.0924	−	37.0038i	0.0771269	−	0.0445292i
$832$	−187.367	−	108.177i	−0.225201	−	0.130020i
$833$	121.847	+	211.045i	0.146275	+	0.253356i
$834$	−38.0540	−	65.9114i	−0.0456283	−	0.0790304i
$835$			161.527i			0.193445i
$836$		0			0
$837$	231.838			0.276987
$838$	−242.427	+	139.965i	−0.289292	+	0.167023i
$839$	742.732	−	428.816i	0.885258	−	0.511104i	0.0128698	−	0.999917i	$-0.495903\pi$
$839$	742.732	−	428.816i	0.885258	−	0.511104i	0.872389	+	0.488813i	$0.162570\pi$
$840$	17.6757	−	30.6153i	0.0210426	−	0.0364468i
$841$	−239.655	−	415.095i	−0.284965	−	0.493573i
$842$	20.1465	−	34.8947i	0.0239269	−	0.0414427i
$843$	63.1632			0.0749267
$844$			291.689i			0.345603i
$845$	24.0496	−	41.6552i	0.0284611	−	0.0492961i
$846$	421.467	+	243.334i	0.498187	+	0.287629i
$847$	693.159			0.818369
$848$		−	1452.34i		−	1.71267i
$849$	−80.4698	−	46.4593i	−0.0947818	−	0.0547223i
$850$	132.005	−	76.2133i	0.155300	−	0.0896627i
$851$	59.9562	+	34.6157i	0.0704538	+	0.0406765i
$852$	39.4781	+	68.3780i	0.0463357	+	0.0802559i
$853$	−17.8180	−	30.8617i	−0.0208886	−	0.0361802i	0.855392	−	0.517981i	$-0.173316\pi$
$853$	−17.8180	−	30.8617i	−0.0208886	−	0.0361802i	−0.876281	+	0.481801i	$0.839983\pi$
$854$		−	3121.01i		−	3.65457i
$855$		0			0
$856$	−545.523			−0.637293
$857$	−785.762	+	453.660i	−0.916875	+	0.529358i	−0.882637	−	0.470056i	$-0.844234\pi$
$857$	−785.762	+	453.660i	−0.916875	+	0.529358i	−0.0342380	+	0.999414i	$0.510900\pi$
$858$	−93.4571	+	53.9575i	−0.108924	+	0.0628875i
$859$	−217.476	+	376.680i	−0.253174	+	0.438510i	−0.964398	−	0.264455i	$-0.914808\pi$
$859$	−217.476	+	376.680i	−0.253174	+	0.438510i	0.711224	+	0.702965i	$0.248141\pi$
$860$	−13.2858	−	23.0117i	−0.0154486	−	0.0267577i
$861$	−119.326	+	206.679i	−0.138590	+	0.240045i
$862$	1385.18			1.60694
$863$			260.819i			0.302224i	0.988517	+	0.151112i	$0.0482854\pi$
$863$			260.819i			0.302224i	−0.988517	+	0.151112i	$0.951715\pi$
$864$	127.142	−	220.217i	0.147156	−	0.254881i
$865$	319.248	+	184.318i	0.369073	+	0.213084i
$866$	−1702.87			−1.96637
$867$			109.400i			0.126183i
$868$	−871.083	−	502.920i	−1.00355	−	0.579401i
$869$	205.376	−	118.574i	0.236336	−	0.136449i
$870$	−37.4772	−	21.6375i	−0.0430773	−	0.0248707i
$871$	−212.895	−	368.745i	−0.244426	−	0.423358i
$872$	97.8916	+	169.553i	0.112261	+	0.194442i
$873$			481.217i			0.551223i
$874$		0			0
$875$	1161.37			1.32728
$876$	16.2594	−	9.38738i	0.0185610	−	0.0107162i
$877$	−350.496	+	202.359i	−0.399654	+	0.230740i	−0.686335	−	0.727286i	$-0.740781\pi$
$877$	−350.496	+	202.359i	−0.399654	+	0.230740i	0.286681	+	0.958026i	$0.407448\pi$
$878$	−116.528	+	201.833i	−0.132720	+	0.229878i
$879$	−31.0724	−	53.8190i	−0.0353497	−	0.0612275i
$880$	−172.128	+	298.134i	−0.195599	+	0.338788i
$881$	1651.36			1.87441			0.937205	−	0.348778i	$-0.113403\pi$
$881$	1651.36			1.87441			0.937205	+	0.348778i	$0.113403\pi$
$882$			1868.62i			2.11861i
$883$	−147.075	+	254.742i	−0.166563	+	0.288496i	−0.937209	−	0.348767i	$-0.886600\pi$
$883$	−147.075	+	254.742i	−0.166563	+	0.288496i	0.770646	+	0.637263i	$0.219934\pi$
$884$	−93.8677	−	54.1945i	−0.106185	−	0.0613060i
$885$	−47.9707			−0.0542041
$886$		−	649.839i		−	0.733452i
$887$	772.223	+	445.843i	0.870601	+	0.502642i	0.867548	−	0.497354i	$-0.165695\pi$
$887$	772.223	+	445.843i	0.870601	+	0.502642i	0.00305320	+	0.999995i	$0.499028\pi$
$888$	2.99386	−	1.72851i	0.00337146	−	0.00194652i
$889$	1257.48	+	726.008i	1.41449	+	0.816657i
$890$	255.912	+	443.252i	0.287541	+	0.498036i
$891$	298.913	+	517.732i	0.335480	+	0.581068i
$892$			705.150i			0.790526i
$893$		0			0
$894$	206.101			0.230538
$895$	−16.7990	+	9.69893i	−0.0187699	+	0.0108368i
$896$	1045.72	−	603.746i	1.16710	−	0.673824i
$897$	73.6966	−	127.646i	0.0821590	−	0.142304i
$898$	39.6924	+	68.7492i	0.0442008	+	0.0765581i
$899$	316.321	−	547.884i	0.351859	−	0.609437i
$900$	464.948			0.516609
$901$		−	220.495i		−	0.244722i
$902$	534.986	−	926.623i	0.593111	−	1.02730i
$903$	17.2122	+	9.93745i	0.0190611	+	0.0110049i
$904$	−273.303			−0.302326
$905$		−	51.5299i		−	0.0569392i
$906$	39.9303	+	23.0538i	0.0440732	+	0.0254456i
$907$	−924.439	+	533.725i	−1.01923	+	0.588451i	−0.913880	−	0.405985i	$-0.866929\pi$
$907$	−924.439	+	533.725i	−1.01923	+	0.588451i	−0.105347	+	0.994436i	$0.533595\pi$
$908$	635.007	+	366.622i	0.699347	+	0.403768i
$909$	19.9557	+	34.5643i	0.0219535	+	0.0380245i
$910$	−459.897	−	796.564i	−0.505381	−	0.875345i
$911$			1495.34i			1.64143i	0.571338	+	0.820715i	$0.306425\pi$
$911$			1495.34i			1.64143i	−0.571338	+	0.820715i	$0.693575\pi$
$912$		0			0
$913$	−641.351			−0.702465
$914$	646.424	−	373.213i	0.707247	−	0.408329i
$915$	−80.9139	+	46.7157i	−0.0884305	+	0.0510554i
$916$	−293.806	+	508.887i	−0.320749	+	0.555554i
$917$	−289.474	−	501.383i	−0.315675	−	0.546765i
$918$	26.7075	−	46.2587i	0.0290931	−	0.0503907i
$919$	−798.252			−0.868610			−0.434305	−	0.900766i	$-0.643006\pi$
$919$	−798.252			−0.868610			−0.434305	+	0.900766i	$0.643006\pi$
$920$		−	216.476i		−	0.235300i
$921$	−7.74075	+	13.4074i	−0.00840472	+	0.0145574i
$922$	1291.81	+	745.826i	1.40109	+	0.808922i
$923$	−1055.52			−1.14358
$924$			91.7847i			0.0993341i
$925$	43.5770	+	25.1592i	0.0471103	+	0.0271991i
$926$	684.027	−	394.923i	0.738691	−	0.426483i
$927$	−285.116	−	164.612i	−0.307569	−	0.177575i
$928$	−346.947	−	600.929i	−0.373865	−	0.647553i
$929$	−547.378	−	948.087i	−0.589212	−	1.02055i	−0.994336	−	0.106284i	$-0.966105\pi$
$929$	−547.378	−	948.087i	−0.589212	−	1.02055i	0.405123	−	0.914262i	$-0.367229\pi$
$930$			75.6935i			0.0813909i
$931$		0			0
$932$	933.902			1.00204
$933$	197.004	−	113.740i	0.211151	−	0.121908i
$934$	1290.05	−	744.812i	1.38121	−	0.797443i
$935$	−26.1324	+	45.2627i	−0.0279491	+	0.0484093i
$936$	213.516	+	369.821i	0.228116	+	0.395108i
$937$	−611.217	+	1058.66i	−0.652313	+	1.12984i	0.330248	+	0.943894i	$0.392868\pi$
$937$	−611.217	+	1058.66i	−0.652313	+	1.12984i	−0.982560	+	0.185944i	$0.940466\pi$
$938$	−910.366			−0.970539
$939$		−	48.4910i		−	0.0516411i
$940$	−63.7530	+	110.423i	−0.0678223	+	0.117472i
$941$	−810.101	−	467.712i	−0.860893	−	0.497037i	0.00341806	−	0.999994i	$-0.498912\pi$
$941$	−810.101	−	467.712i	−0.860893	−	0.497037i	−0.864311	+	0.502957i	$0.832245\pi$
$942$	−10.3621			−0.0110001
$943$			1461.40i			1.54973i
$944$	−921.669	−	532.126i	−0.976344	−	0.563692i
$945$	156.159	−	90.1582i	0.165247	−	0.0954055i
$946$	−77.1689	−	44.5535i	−0.0815739	−	0.0470967i
$947$	−617.329	−	1069.25i	−0.651879	−	1.12909i	−0.982667	−	0.185382i	$-0.940648\pi$
$947$	−617.329	−	1069.25i	−0.651879	−	1.12909i	0.330788	−	0.943705i	$-0.392686\pi$
$948$	−15.7392	−	27.2612i	−0.0166026	−	0.0287565i
$949$			250.990i			0.264479i
$950$		0			0
$951$	−7.20556			−0.00757683
$952$	103.118	−	59.5355i	0.108318	−	0.0625373i
$953$	652.496	−	376.719i	0.684676	−	0.395298i	−0.116939	−	0.993139i	$-0.537308\pi$
$953$	652.496	−	376.719i	0.684676	−	0.395298i	0.801614	+	0.597841i	$0.203975\pi$
$954$	845.364	−	1464.21i	0.886125	−	1.53481i
$955$	−95.6179	−	165.615i	−0.100123	−	0.173419i
$956$	413.199	−	715.682i	0.432216	−	0.748621i
$957$	−57.7297			−0.0603236
$958$			463.261i			0.483571i
$959$	−633.064	+	1096.50i	−0.660130	+	1.14338i
$960$	11.9926	+	6.92391i	0.0124923	+	0.00721241i
$961$	−145.572			−0.151480
$962$		−	89.9463i		−	0.0934993i
$963$	−1194.58	−	689.690i	−1.24048	−	0.716189i
$964$	870.453	−	502.557i	0.902960	−	0.521324i
$965$	594.220	+	343.073i	0.615772	+	0.355516i
$966$	−157.568	−	272.916i	−0.163114	−	0.282522i
$967$	−364.035	−	630.527i	−0.376458	−	0.652045i	0.614086	−	0.789239i	$-0.289525\pi$
$967$	−364.035	−	630.527i	−0.376458	−	0.652045i	−0.990544	+	0.137194i	$0.956191\pi$
$968$		−	211.950i		−	0.218957i
$969$		0			0
$970$	−316.936			−0.326738
$971$	1404.23	−	810.731i	1.44617	−	0.834945i	0.447916	−	0.894076i	$-0.352166\pi$
$971$	1404.23	−	810.731i	1.44617	−	0.834945i	0.998250	+	0.0591310i	$0.0188330\pi$
$972$	212.258	−	122.547i	0.218372	−	0.126077i
$973$	432.684	−	749.431i	0.444691	−	0.770227i
$974$	−888.511	−	1538.95i	−0.912229	−	1.58003i
$975$	53.5638	−	92.7752i	0.0549372	−	0.0951540i
$976$	−2072.82			−2.12379
$977$			1249.63i			1.27904i	0.768773	+	0.639522i	$0.220868\pi$
$977$			1249.63i			1.27904i	−0.768773	+	0.639522i	$0.779132\pi$
$978$	−45.3658	+	78.5759i	−0.0463863	+	0.0803434i
$979$	591.308	+	341.392i	0.603992	+	0.348715i
$980$	−489.574			−0.499565
$981$			495.047i			0.504635i
$982$	965.485	+	557.423i	0.983182	+	0.567641i
$983$	492.128	−	284.130i	0.500639	−	0.289044i	−0.228338	−	0.973582i	$-0.573329\pi$
$983$	492.128	−	284.130i	0.500639	−	0.289044i	0.728977	+	0.684538i	$0.239996\pi$
$984$	63.1971	+	36.4868i	0.0642247	+	0.0370801i
$985$	−381.234	−	660.316i	−0.387039	−	0.670372i
$986$	−72.8794	−	126.231i	−0.0739142	−	0.128023i
$987$		−	95.3713i		−	0.0966275i
$988$		0			0
$989$	121.705			0.123058
$990$	−347.069	+	200.381i	−0.350575	+	0.202405i
$991$	−221.145	+	127.678i	−0.223153	+	0.128838i	−0.607409	−	0.794389i	$-0.707791\pi$
$991$	−221.145	+	127.678i	−0.223153	+	0.128838i	0.384256	+	0.923226i	$0.374458\pi$
$992$	−606.855	+	1051.10i	−0.611749	+	1.05958i
$993$	−97.4639	−	168.812i	−0.0981510	−	0.170003i
$994$	−1128.39	+	1954.43i	−1.13520	+	1.96622i
$995$	−26.8939			−0.0270290
$996$			85.1314i			0.0854733i
$997$	−363.379	+	629.390i	−0.364472	+	0.631284i	−0.988691	−	0.149965i	$-0.952084\pi$
$997$	−363.379	+	629.390i	−0.364472	+	0.631284i	0.624219	+	0.781249i	$0.285417\pi$
$998$	−638.070	−	368.390i	−0.639349	−	0.369128i
$999$	17.6331			0.0176507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.d.d.69.6		12
19.2	odd	18		361.3.f.f.333.2		12
19.3	odd	18		361.3.f.e.127.1		12
19.4	even	9		361.3.f.f.116.2		12
19.5	even	9		361.3.f.g.262.2		12
19.6	even	9		19.3.f.a.14.1	✓	12
19.7	even	3		361.3.b.c.360.11		12
19.8	odd	6	inner	361.3.d.d.293.6		12
19.9	even	9		361.3.f.e.307.1		12
19.10	odd	18		361.3.f.c.307.2		12
19.11	even	3		361.3.d.f.293.1		12
19.12	odd	6		361.3.b.c.360.2		12
19.13	odd	18		361.3.f.g.299.2		12
19.14	odd	18		19.3.f.a.15.1	yes	12
19.15	odd	18		361.3.f.b.116.1		12
19.16	even	9		361.3.f.c.127.2		12
19.17	even	9		361.3.f.b.333.1		12
19.18	odd	2		361.3.d.f.69.1		12
57.14	even	18		171.3.ba.b.91.2		12
57.44	odd	18		171.3.ba.b.109.2		12
76.63	odd	18		304.3.z.a.33.1		12
76.71	even	18		304.3.z.a.129.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.1	✓	12	19.6	even	9
19.3.f.a.15.1	yes	12	19.14	odd	18
171.3.ba.b.91.2		12	57.14	even	18
171.3.ba.b.109.2		12	57.44	odd	18
304.3.z.a.33.1		12	76.63	odd	18
304.3.z.a.129.1		12	76.71	even	18
361.3.b.c.360.2		12	19.12	odd	6
361.3.b.c.360.11		12	19.7	even	3
361.3.d.d.69.6		12	1.1	even	1	trivial
361.3.d.d.293.6		12	19.8	odd	6	inner
361.3.d.f.69.1		12	19.18	odd	2
361.3.d.f.293.1		12	19.11	even	3
361.3.f.b.116.1		12	19.15	odd	18
361.3.f.b.333.1		12	19.17	even	9
361.3.f.c.127.2		12	19.16	even	9
361.3.f.c.307.2		12	19.10	odd	18
361.3.f.e.127.1		12	19.3	odd	18
361.3.f.e.307.1		12	19.9	even	9
361.3.f.f.116.2		12	19.4	even	9
361.3.f.f.333.2		12	19.2	odd	18
361.3.f.g.262.2		12	19.5	even	9
361.3.f.g.299.2		12	19.13	odd	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.23199 - 1.28864i) q^{2} +(-0.338180 + 0.195249i) q^{3} +(1.32117 - 2.28834i) q^{4} +(-1.13047 - 1.95804i) q^{5} +(-0.503209 + 0.871584i) q^{6} -11.4433 q^{7} +3.49905i q^{8} +(-4.42376 + 7.66217i) q^{9} +O(q^{10})\)	\(q+(2.23199 - 1.28864i) q^{2} +(-0.338180 + 0.195249i) q^{3} +(1.32117 - 2.28834i) q^{4} +(-1.13047 - 1.95804i) q^{5} +(-0.503209 + 0.871584i) q^{6} -11.4433 q^{7} +3.49905i q^{8} +(-4.42376 + 7.66217i) q^{9} +(-5.04640 - 2.91354i) q^{10} -7.77344 q^{11} +1.03183i q^{12} +(-11.9459 - 6.89699i) q^{13} +(-25.5412 + 14.7462i) q^{14} +(0.764608 + 0.441446i) q^{15} +(9.79370 + 16.9632i) q^{16} +(1.48688 + 2.57535i) q^{17} +22.8025i q^{18} -5.97420 q^{20} +(3.86988 - 2.23428i) q^{21} +(-17.3502 + 10.0171i) q^{22} +(13.6817 - 23.6974i) q^{23} +(-0.683184 - 1.18331i) q^{24} +(9.94406 - 17.2236i) q^{25} -35.5509 q^{26} -6.96940i q^{27} +(-15.1185 + 26.1860i) q^{28} +(-16.4702 - 9.50907i) q^{29} +2.27546 q^{30} +33.2652i q^{31} +(31.5977 + 18.2429i) q^{32} +(2.62883 - 1.51775i) q^{33} +(6.63739 + 3.83210i) q^{34} +(12.9363 + 22.4063i) q^{35} +(11.6891 + 20.2461i) q^{36} +2.53007i q^{37} +5.38651 q^{39} +(6.85127 - 3.95558i) q^{40} +(-46.2518 + 26.7035i) q^{41} +(5.75835 - 9.97375i) q^{42} +(2.22386 + 3.85184i) q^{43} +(-10.2701 + 17.7883i) q^{44} +20.0037 q^{45} -70.5230i q^{46} +(10.6714 - 18.4834i) q^{47} +(-6.62407 - 3.82441i) q^{48} +81.9480 q^{49} -51.2572i q^{50} +(-1.00567 - 0.580623i) q^{51} +(-31.5653 + 18.2242i) q^{52} +(-64.2129 - 37.0733i) q^{53} +(-8.98103 - 15.5556i) q^{54} +(8.78767 + 15.2207i) q^{55} -40.0405i q^{56} -49.0150 q^{58} +(-47.0542 + 27.1667i) q^{59} +(2.02036 - 1.16645i) q^{60} +(-52.9120 + 91.6463i) q^{61} +(42.8668 + 74.2474i) q^{62} +(50.6222 - 87.6802i) q^{63} +15.6846 q^{64} +31.1875i q^{65} +(3.91167 - 6.77521i) q^{66} +(26.7323 + 15.4339i) q^{67} +7.85771 q^{68} +10.6853i q^{69} +(57.7472 + 33.3404i) q^{70} +(66.2688 - 38.2603i) q^{71} +(-26.8103 - 15.4789i) q^{72} +(-9.09782 - 15.7579i) q^{73} +(3.26035 + 5.64709i) q^{74} +7.76625i q^{75} +88.9535 q^{77} +(12.0226 - 6.94126i) q^{78} +(-26.4203 + 15.2537i) q^{79} +(22.1430 - 38.3528i) q^{80} +(-38.4530 - 66.6026i) q^{81} +(-68.8223 + 119.204i) q^{82} +82.5054 q^{83} -11.8075i q^{84} +(3.36176 - 5.82274i) q^{85} +(9.92725 + 5.73150i) q^{86} +7.42653 q^{87} -27.1997i q^{88} +(-76.0677 - 43.9177i) q^{89} +(44.6481 - 25.7776i) q^{90} +(136.700 + 78.9240i) q^{91} +(-36.1518 - 62.6167i) q^{92} +(-6.49498 - 11.2496i) q^{93} -55.0062i q^{94} -14.2476 q^{96} +(47.1033 - 27.1951i) q^{97} +(182.907 - 105.601i) q^{98} +(34.3878 - 59.5614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{3} - 3 q^{5} + 12 q^{6} - 12 q^{7} - 9 q^{9}+O(q^{10}) \) 12 * q - 9 * q^3 - 3 * q^5 + 12 * q^6 - 12 * q^7 - 9 * q^9	\( 12 q - 9 q^{3} - 3 q^{5} + 12 q^{6} - 12 q^{7} - 9 q^{9} - 36 q^{10} + 36 q^{11} - 18 q^{13} - 36 q^{14} + 81 q^{15} + 48 q^{16} + 33 q^{17} - 90 q^{20} + 135 q^{21} - 135 q^{22} - 60 q^{23} - 18 q^{24} + 33 q^{25} - 42 q^{26} - 105 q^{28} - 63 q^{29} - 48 q^{30} - 9 q^{32} - 126 q^{33} + 18 q^{34} + 135 q^{35} - 72 q^{36} - 108 q^{39} + 216 q^{40} - 108 q^{41} - 117 q^{42} - 51 q^{43} + 21 q^{44} + 6 q^{45} - 114 q^{47} - 306 q^{48} + 48 q^{49} - 117 q^{51} - 54 q^{53} - 144 q^{54} + 33 q^{55} - 132 q^{58} - 117 q^{59} - 51 q^{61} + 219 q^{62} - 21 q^{63} - 54 q^{64} + 138 q^{66} + 396 q^{67} + 60 q^{68} - 99 q^{70} - 72 q^{71} - 144 q^{72} - 18 q^{73} + 39 q^{74} + 246 q^{77} - 126 q^{78} + 495 q^{79} + 234 q^{80} - 102 q^{81} - 48 q^{82} + 312 q^{83} + 105 q^{85} + 216 q^{86} - 138 q^{87} + 450 q^{89} + 531 q^{90} + 243 q^{91} - 240 q^{92} + 120 q^{93} + 558 q^{96} - 729 q^{97} + 117 q^{98} + 159 q^{99}+O(q^{100}) \) 12 * q - 9 * q^3 - 3 * q^5 + 12 * q^6 - 12 * q^7 - 9 * q^9 - 36 * q^10 + 36 * q^11 - 18 * q^13 - 36 * q^14 + 81 * q^15 + 48 * q^16 + 33 * q^17 - 90 * q^20 + 135 * q^21 - 135 * q^22 - 60 * q^23 - 18 * q^24 + 33 * q^25 - 42 * q^26 - 105 * q^28 - 63 * q^29 - 48 * q^30 - 9 * q^32 - 126 * q^33 + 18 * q^34 + 135 * q^35 - 72 * q^36 - 108 * q^39 + 216 * q^40 - 108 * q^41 - 117 * q^42 - 51 * q^43 + 21 * q^44 + 6 * q^45 - 114 * q^47 - 306 * q^48 + 48 * q^49 - 117 * q^51 - 54 * q^53 - 144 * q^54 + 33 * q^55 - 132 * q^58 - 117 * q^59 - 51 * q^61 + 219 * q^62 - 21 * q^63 - 54 * q^64 + 138 * q^66 + 396 * q^67 + 60 * q^68 - 99 * q^70 - 72 * q^71 - 144 * q^72 - 18 * q^73 + 39 * q^74 + 246 * q^77 - 126 * q^78 + 495 * q^79 + 234 * q^80 - 102 * q^81 - 48 * q^82 + 312 * q^83 + 105 * q^85 + 216 * q^86 - 138 * q^87 + 450 * q^89 + 531 * q^90 + 243 * q^91 - 240 * q^92 + 120 * q^93 + 558 * q^96 - 729 * q^97 + 117 * q^98 + 159 * q^99

Introduction

L-functions

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