LMFDB - Embedded newform 105.3.o.a.44.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(44,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("105.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 4 x^{14} + 12 x^{13} + 162 x^{12} - 524 x^{11} - 88 x^{10} + 1492 x^{9} + \cdots + 1521 $ x^16 - 4x^15 - 4x^14 + 12x^13 + 162x^12 - 524x^11 - 88x^10 + 1492x^9 + 6266x^8 - 41348x^7 + 103092x^6 - 152724x^5 + 148342x^4 - 96348x^3 + 41016x^2 - 10764*x + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.8
Root			$0.214591 - 0.363041i$ of defining polynomial
Character	$\chi$	$=$	105.44
Dual form			105.3.o.a.74.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48938 - 2.57968i) q^{2} +(-1.18073 - 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(4.91811 + 0.901243i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} -2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +O(q^{10})$	\(q+(1.48938 - 2.57968i) q^{2} +(-1.18073 - 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(4.91811 + 0.901243i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} -2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +(9.64983 - 11.3448i) q^{10} +(3.56075 - 2.05580i) q^{11} +(-8.76174 + 11.7024i) q^{12} +21.3779i q^{13} +(-19.8761 + 6.30224i) q^{14} +(-3.32145 - 14.6276i) q^{15} +(5.87298 - 10.1723i) q^{16} +(1.11103 + 1.92435i) q^{17} +(7.54882 + 25.7241i) q^{18} +(4.93649 - 8.55025i) q^{19} +(-8.17956 - 22.9509i) q^{20} +(-6.91662 + 19.8283i) q^{21} -12.2474i q^{22} +(9.66894 - 16.7471i) q^{23} +(3.07038 + 7.17159i) q^{24} +(23.3755 + 8.86482i) q^{25} +(55.1481 + 31.8397i) q^{26} +(25.2954 + 9.44157i) q^{27} +(-7.32910 + 33.3142i) q^{28} -28.1241i q^{29} +(-42.6815 - 13.2178i) q^{30} +(17.6270 + 30.5309i) q^{31} +(-22.6950 - 39.3089i) q^{32} +(-9.87393 - 7.39275i) q^{33} +6.61895 q^{34} +(-21.1650 - 27.8755i) q^{35} +(42.6190 + 10.3464i) q^{36} +(-43.1613 - 24.9192i) q^{37} +(-14.7046 - 25.4691i) q^{38} +(58.9575 - 25.2415i) q^{39} +(-12.7891 - 2.34360i) q^{40} +27.4670i q^{41} +(40.8491 + 47.3744i) q^{42} +41.9977i q^{43} +(-17.3515 - 10.0179i) q^{44} +(-36.4195 + 26.4315i) q^{45} +(-28.8014 - 49.8855i) q^{46} +(-19.1727 + 33.2081i) q^{47} +(-34.9884 - 4.18619i) q^{48} +(4.42843 + 48.7995i) q^{49} +(57.6833 - 47.0983i) q^{50} +(3.99530 - 5.33622i) q^{51} +(90.2174 - 52.0870i) q^{52} +(25.6737 + 44.4682i) q^{53} +(62.0306 - 51.1919i) q^{54} +(19.3649 - 6.90154i) q^{55} +(13.4404 + 12.2759i) q^{56} +(-29.4092 - 3.51867i) q^{57} +(-72.5511 - 41.8874i) q^{58} +(-22.0503 + 12.7308i) q^{59} +(-53.6378 + 49.6571i) q^{60} +(-34.1825 + 59.2058i) q^{61} +105.013 q^{62} +(62.8506 - 4.33668i) q^{63} -88.2218 q^{64} +(-19.2667 + 105.139i) q^{65} +(-33.7769 + 14.4609i) q^{66} +(-59.1667 + 34.1599i) q^{67} +(5.41401 - 9.37734i) q^{68} +(-57.6028 - 6.89190i) q^{69} +(-103.432 + 13.0819i) q^{70} -11.9474i q^{71} +(16.1530 - 16.9354i) q^{72} +(88.6742 - 51.1961i) q^{73} +(-128.567 + 74.2282i) q^{74} +(-3.15216 - 74.9337i) q^{75} -48.1109 q^{76} +(-28.1090 - 6.18396i) q^{77} +(22.6950 - 189.686i) q^{78} +(32.1905 - 55.7556i) q^{79} +(38.0517 - 44.7355i) q^{80} +(-3.82841 - 80.9095i) q^{81} +(70.8561 + 40.9088i) q^{82} -122.790 q^{83} +(100.530 - 19.1224i) q^{84} +(3.72983 + 10.4655i) q^{85} +(108.341 + 62.5505i) q^{86} +(-77.5628 + 33.2070i) q^{87} +(-9.25939 + 5.34591i) q^{88} +(-116.396 - 67.2014i) q^{89} +(13.9423 + 133.317i) q^{90} +(100.920 - 110.493i) q^{91} -94.2332 q^{92} +(63.3876 - 84.6619i) q^{93} +(57.1109 + 98.9190i) q^{94} +(31.9840 - 37.6021i) q^{95} +(-81.6123 + 109.003i) q^{96} +13.6730i q^{97} +(132.483 + 61.2569i) q^{98} +(-8.72983 + 35.9599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9	$ 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9} - 40 q^{10} - 80 q^{15} + 32 q^{16} + 48 q^{19} - 8 q^{21} + 40 q^{30} + 344 q^{31} - 80 q^{34} + 496 q^{36} - 32 q^{39} + 120 q^{40} - 80 q^{45} - 120 q^{46} - 208 q^{49} - 40 q^{51} + 200 q^{54} + 40 q^{60} - 392 q^{61} - 544 q^{64} + 120 q^{66} - 240 q^{69} - 760 q^{70} + 200 q^{75} - 336 q^{76} + 608 q^{79} - 328 q^{81} - 344 q^{84} - 560 q^{85} + 80 q^{90} + 1088 q^{91} + 480 q^{94} - 400 q^{96} + 480 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9 - 40 * q^10 - 80 * q^15 + 32 * q^16 + 48 * q^19 - 8 * q^21 + 40 * q^30 + 344 * q^31 - 80 * q^34 + 496 * q^36 - 32 * q^39 + 120 * q^40 - 80 * q^45 - 120 * q^46 - 208 * q^49 - 40 * q^51 + 200 * q^54 + 40 * q^60 - 392 * q^61 - 544 * q^64 + 120 * q^66 - 240 * q^69 - 760 * q^70 + 200 * q^75 - 336 * q^76 + 608 * q^79 - 328 * q^81 - 344 * q^84 - 560 * q^85 + 80 * q^90 + 1088 * q^91 + 480 * q^94 - 400 * q^96 + 480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.48938	−	2.57968i	0.744689	−	1.28984i	−0.205651	−	0.978625i	$-0.565931\pi$
$2$	1.48938	−	2.57968i	0.744689	−	1.28984i	0.950340	−	0.311214i	$-0.100735\pi$
$3$	−1.18073	−	2.75787i	−0.393577	−	0.919292i
$3$	−1.18073	−	2.75787i	−0.393577	−	0.919292i
$4$	−2.43649	−	4.22013i	−0.609123	−	1.05503i
$5$	4.91811	+	0.901243i	0.983621	+	0.180249i
$5$	4.91811	+	0.901243i	0.983621	+	0.180249i
$6$	−8.87298	−	1.06161i	−1.47883	−	0.176935i
$7$	−5.16858	−	4.72078i	−0.738368	−	0.674398i
$7$	−5.16858	−	4.72078i	−0.738368	−	0.674398i
$8$	−2.60040			−0.325050
$9$	−6.21175	+	6.51262i	−0.690194	+	0.723624i
$10$	9.64983	−	11.3448i	0.964983	−	1.13448i
$11$	3.56075	−	2.05580i	0.323705	−	0.186891i	−0.329338	−	0.944212i	$-0.606826\pi$
$11$	3.56075	−	2.05580i	0.323705	−	0.186891i	0.653043	+	0.757321i	$0.273492\pi$
$12$	−8.76174	+	11.7024i	−0.730145	+	0.975198i
$13$			21.3779i			1.64445i	0.569160	+	0.822226i	$0.307268\pi$
$13$			21.3779i			1.64445i	−0.569160	+	0.822226i	$0.692732\pi$
$14$	−19.8761	+	6.30224i	−1.41972	+	0.450160i
$15$	−3.32145	−	14.6276i	−0.221430	−	0.975176i
$16$	5.87298	−	10.1723i	0.367061	−	0.635769i
$17$	1.11103	+	1.92435i	0.0653545	+	0.113197i	0.896851	−	0.442332i	$-0.145849\pi$
$17$	1.11103	+	1.92435i	0.0653545	+	0.113197i	−0.831497	+	0.555530i	$0.812516\pi$
$18$	7.54882	+	25.7241i	0.419379	+	1.42911i
$19$	4.93649	−	8.55025i	0.259815	−	0.450013i	−0.706377	−	0.707836i	$-0.749672\pi$
$19$	4.93649	−	8.55025i	0.259815	−	0.450013i	0.966192	+	0.257822i	$0.0830050\pi$
$20$	−8.17956	−	22.9509i	−0.408978	−	1.14755i
$21$	−6.91662	+	19.8283i	−0.329363	+	0.944203i
$22$		−	12.2474i		−	0.556702i
$23$	9.66894	−	16.7471i	0.420389	−	0.728135i	−0.575589	−	0.817739i	$-0.695227\pi$
$23$	9.66894	−	16.7471i	0.420389	−	0.728135i	0.995977	+	0.0896047i	$0.0285604\pi$
$24$	3.07038	+	7.17159i	0.127932	+	0.298816i
$25$	23.3755	+	8.86482i	0.935021	+	0.354593i
$26$	55.1481	+	31.8397i	2.12108	+	1.22461i
$27$	25.2954	+	9.44157i	0.936866	+	0.349688i
$28$	−7.32910	+	33.3142i	−0.261754	+	1.18979i
$29$		−	28.1241i		−	0.969797i	−0.874570	−	0.484898i	$-0.838857\pi$
$29$		−	28.1241i		−	0.969797i	0.874570	−	0.484898i	$-0.161143\pi$
$30$	−42.6815	−	13.2178i	−1.42272	−	0.440594i
$31$	17.6270	+	30.5309i	0.568613	+	0.984867i	0.996703	+	0.0811313i	$0.0258533\pi$
$31$	17.6270	+	30.5309i	0.568613	+	0.984867i	−0.428090	+	0.903736i	$0.640813\pi$
$32$	−22.6950	−	39.3089i	−0.709218	−	1.22840i
$33$	−9.87393	−	7.39275i	−0.299210	−	0.224023i
$34$	6.61895			0.194675
$35$	−21.1650	−	27.8755i	−0.604716	−	0.796441i
$36$	42.6190	+	10.3464i	1.18386	+	0.287401i
$37$	−43.1613	−	24.9192i	−1.16652	−	0.673492i	−0.213664	−	0.976907i	$-0.568540\pi$
$37$	−43.1613	−	24.9192i	−1.16652	−	0.673492i	−0.952858	+	0.303416i	$0.901873\pi$
$38$	−14.7046	−	25.4691i	−0.386963	−	0.670240i
$39$	58.9575	−	25.2415i	1.51173	−	0.647219i
$40$	−12.7891	−	2.34360i	−0.319727	−	0.0585899i
$41$			27.4670i			0.669928i	0.942231	+	0.334964i	$0.108724\pi$
$41$			27.4670i			0.669928i	−0.942231	+	0.334964i	$0.891276\pi$
$42$	40.8491	+	47.3744i	0.972597	+	1.12796i
$43$			41.9977i			0.976691i	0.872650	+	0.488346i	$0.162399\pi$
$43$			41.9977i			0.976691i	−0.872650	+	0.488346i	$0.837601\pi$
$44$	−17.3515	−	10.0179i	−0.394352	−	0.227679i
$45$	−36.4195	+	26.4315i	−0.809322	+	0.587366i
$46$	−28.8014	−	49.8855i	−0.626118	−	1.08447i
$47$	−19.1727	+	33.2081i	−0.407931	+	0.706556i	−0.994658	−	0.103228i	$-0.967083\pi$
$47$	−19.1727	+	33.2081i	−0.407931	+	0.706556i	0.586727	+	0.809785i	$0.300416\pi$
$48$	−34.9884	−	4.18619i	−0.728924	−	0.0872123i
$49$	4.42843	+	48.7995i	0.0903760	+	0.995908i
$50$	57.6833	−	47.0983i	1.15367	−	0.941965i
$51$	3.99530	−	5.33622i	0.0783393	−	0.104632i
$52$	90.2174	−	52.0870i	1.73495	−	1.00167i
$53$	25.6737	+	44.4682i	0.484410	+	0.839023i	0.999840	−	0.0179089i	$-0.00570088\pi$
$53$	25.6737	+	44.4682i	0.484410	+	0.839023i	−0.515429	+	0.856932i	$0.672368\pi$
$54$	62.0306	−	51.1919i	1.14871	−	0.947998i
$55$	19.3649	−	6.90154i	0.352089	−	0.125483i
$56$	13.4404	+	12.2759i	0.240007	+	0.219213i
$57$	−29.4092	−	3.51867i	−0.515951	−	0.0617311i
$58$	−72.5511	−	41.8874i	−1.25088	−	0.722197i
$59$	−22.0503	+	12.7308i	−0.373734	+	0.215776i	−0.675089	−	0.737737i	$-0.735895\pi$
$59$	−22.0503	+	12.7308i	−0.373734	+	0.215776i	0.301354	+	0.953512i	$0.402561\pi$
$60$	−53.6378	+	49.6571i	−0.893964	+	0.827618i
$61$	−34.1825	+	59.2058i	−0.560368	+	0.970586i	0.437096	+	0.899415i	$0.356007\pi$
$61$	−34.1825	+	59.2058i	−0.560368	+	0.970586i	−0.997464	+	0.0711713i	$0.977326\pi$
$62$	105.013			1.69376
$63$	62.8506	−	4.33668i	0.997628	−	0.0688362i
$64$	−88.2218			−1.37847
$65$	−19.2667	+	105.139i	−0.296410	+	1.61752i
$66$	−33.7769	+	14.4609i	−0.511772	+	0.219105i
$67$	−59.1667	+	34.1599i	−0.883086	+	0.509850i	−0.871675	−	0.490085i	$-0.836966\pi$
$67$	−59.1667	+	34.1599i	−0.883086	+	0.509850i	−0.0114110	+	0.999935i	$0.503632\pi$
$68$	5.41401	−	9.37734i	0.0796178	−	0.137902i
$69$	−57.6028	−	6.89190i	−0.834823	−	0.0998827i
$70$	−103.432	+	13.0819i	−1.47761	+	0.186885i
$71$		−	11.9474i		−	0.168273i	−0.996454	−	0.0841366i	$-0.973187\pi$
$71$		−	11.9474i		−	0.168273i	0.996454	−	0.0841366i	$-0.0268132\pi$
$72$	16.1530	−	16.9354i	0.224348	−	0.235214i
$73$	88.6742	−	51.1961i	1.21471	−	0.701316i	0.250932	−	0.968005i	$-0.419263\pi$
$73$	88.6742	−	51.1961i	1.21471	−	0.701316i	0.963783	+	0.266689i	$0.0859296\pi$
$74$	−128.567	+	74.2282i	−1.73739	+	1.00308i
$75$	−3.15216	−	74.9337i	−0.0420288	−	0.999116i
$76$	−48.1109			−0.633038
$77$	−28.1090	−	6.18396i	−0.365052	−	0.0803112i
$78$	22.6950	−	189.686i	0.290961	−	2.43187i
$79$	32.1905	−	55.7556i	0.407475	−	0.705767i	−0.587131	−	0.809492i	$-0.699743\pi$
$79$	32.1905	−	55.7556i	0.407475	−	0.705767i	0.994606	+	0.103724i	$0.0330760\pi$
$80$	38.0517	−	44.7355i	0.475646	−	0.559194i
$81$	−3.82841	−	80.9095i	−0.0472643	−	0.998882i
$82$	70.8561	+	40.9088i	0.864099	+	0.498888i
$83$	−122.790			−1.47939			−0.739696	−	0.672941i	$-0.765031\pi$
$83$	−122.790			−1.47939			−0.739696	+	0.672941i	$0.765031\pi$
$84$	100.530	−	19.1224i	1.19679	−	0.227647i
$85$	3.72983	+	10.4655i	0.0438804	+	0.123123i
$86$	108.341	+	62.5505i	1.25977	+	0.727331i
$87$	−77.5628	+	33.2070i	−0.891526	+	0.381690i
$88$	−9.25939	+	5.34591i	−0.105220	+	0.0607490i
$89$	−116.396	−	67.2014i	−1.30782	−	0.755072i	−0.326091	−	0.945338i	$-0.605732\pi$
$89$	−116.396	−	67.2014i	−1.30782	−	0.755072i	−0.981733	+	0.190266i	$0.939065\pi$
$90$	13.9423	+	133.317i	0.154914	+	1.48130i
$91$	100.920	−	110.493i	1.10901	−	1.21421i
$92$	−94.2332			−1.02427
$93$	63.3876	−	84.6619i	0.681587	−	0.910343i
$94$	57.1109	+	98.9190i	0.607563	+	1.05233i
$95$	31.9840	−	37.6021i	0.336674	−	0.395811i
$96$	−81.6123	+	109.003i	−0.850128	+	1.13545i
$97$			13.6730i			0.140959i	0.997513	+	0.0704795i	$0.0224529\pi$
$97$			13.6730i			0.140959i	−0.997513	+	0.0704795i	$0.977547\pi$
$98$	132.483	+	61.2569i	1.35186	+	0.625071i
$99$	−8.72983	+	35.9599i	−0.0881801	+	0.363231i
$100$	−19.5436	−	120.247i	−0.195436	−	1.20247i
$101$	79.2855	−	45.7755i	0.785005	−	0.453223i	−0.0531959	−	0.998584i	$-0.516941\pi$
$101$	79.2855	−	45.7755i	0.785005	−	0.453223i	0.838201	+	0.545361i	$0.183607\pi$
$102$	−7.81520	−	18.2542i	−0.0766196	−	0.178963i
$103$	−2.12630	−	1.22762i	−0.0206437	−	0.0119186i	0.489643	−	0.871923i	$-0.337127\pi$
$103$	−2.12630	−	1.22762i	−0.0206437	−	0.0119186i	−0.510286	+	0.860005i	$0.670461\pi$
$104$		−	55.5911i		−	0.534530i
$105$	−51.8868	+	91.2840i	−0.494160	+	0.869371i
$106$	152.952			1.44294
$107$	7.94233	−	13.7565i	0.0742274	−	0.128566i	−0.826523	−	0.562903i	$-0.809684\pi$
$107$	7.94233	−	13.7565i	0.0742274	−	0.128566i	0.900750	+	0.434338i	$0.143018\pi$
$108$	−21.7874	−	129.754i	−0.201735	−	1.20143i
$109$	−12.1744	−	21.0867i	−0.111692	−	0.193456i	0.804761	−	0.593599i	$-0.202294\pi$
$109$	−12.1744	−	21.0867i	−0.111692	−	0.193456i	−0.916452	+	0.400144i	$0.868960\pi$
$110$	11.0379	−	60.2342i	0.100345	−	0.547584i
$111$	−17.7621	+	148.456i	−0.160019	+	1.33744i
$112$	−78.3762	+	24.8513i	−0.699788	+	0.221887i
$113$	−17.8725			−0.158164			−0.0790820	−	0.996868i	$-0.525199\pi$
$113$	−17.8725			−0.158164			−0.0790820	+	0.996868i	$0.525199\pi$
$114$	−52.8784	+	70.6256i	−0.463846	+	0.619523i
$115$	62.6461	−	73.6499i	0.544748	−	0.640434i
$116$	−118.687	+	68.5242i	−1.02317	+	0.590726i
$117$	−139.226	−	132.794i	−1.18997	−	1.13499i
$118$			75.8436i			0.642743i
$119$	3.34203	−	15.1911i	0.0280843	−	0.127656i
$120$	8.63710	+	38.0378i	0.0719759	+	0.316982i
$121$	−52.0474	+	90.1487i	−0.430144	+	0.745031i
$122$	101.821	+	176.359i	0.834600	+	1.44557i
$123$	75.7506	−	32.4312i	0.615859	−	0.263668i
$124$	85.8962	−	148.777i	0.692711	−	1.19981i
$125$	106.974	+	64.6651i	0.855791	+	0.517321i
$126$	82.4210	−	168.593i	0.654135	−	1.33804i
$127$			75.1876i			0.592029i	0.955184	+	0.296014i	$0.0956576\pi$
$127$			75.1876i			0.592029i	−0.955184	+	0.296014i	$0.904342\pi$
$128$	−40.6156	+	70.3482i	−0.317309	+	0.549596i
$129$	115.824	−	49.5880i	0.897864	−	0.384403i
$130$	242.529	+	206.293i	1.86560	+	1.58687i
$131$	−190.603	−	110.045i	−1.45498	−	0.840036i	−0.456227	−	0.889864i	$-0.650799\pi$
$131$	−190.603	−	110.045i	−1.45498	−	0.840036i	−0.998758	+	0.0498278i	$0.984133\pi$
$132$	−7.14062	+	59.6816i	−0.0540956	+	0.452133i
$133$	−65.8785	+	20.8886i	−0.495327	+	0.157057i
$134$			203.508i			1.51872i
$135$	115.896	+	69.2319i	0.858491	+	0.512829i
$136$	−2.88912	−	5.00410i	−0.0212435	−	0.0367948i
$137$	40.7086	+	70.5094i	0.297143	+	0.514667i	0.975481	−	0.220083i	$-0.0706327\pi$
$137$	40.7086	+	70.5094i	0.297143	+	0.514667i	−0.678338	+	0.734750i	$0.737299\pi$
$138$	−103.571	+	138.332i	−0.750516	+	1.00241i
$139$	129.841			0.934106			0.467053	−	0.884229i	$-0.345316\pi$
$139$	129.841			0.934106			0.467053	+	0.884229i	$0.345316\pi$
$140$	−66.0695	+	157.237i	−0.471925	+	1.12312i
$141$	114.222	+	13.6661i	0.810083	+	0.0969226i
$142$	−30.8204	−	17.7942i	−0.217045	−	0.125311i
$143$	43.9487	+	76.1213i	0.307333	+	0.532317i
$144$	29.7669	+	101.436i	0.206714	+	0.704419i
$145$	25.3467	−	138.317i	0.174805	−	0.953913i
$146$		−	305.001i		−	2.08905i
$147$	129.354	−	69.8321i	0.879960	−	0.475048i
$148$			242.862i			1.64096i
$149$	171.544	+	99.0412i	1.15130	+	0.664706i	0.949205	−	0.314659i	$-0.101890\pi$
$149$	171.544	+	99.0412i	1.15130	+	0.664706i	0.202100	+	0.979365i	$0.435224\pi$
$150$	−198.000	−	103.473i	−1.32000	−	0.689820i
$151$	−83.1986	−	144.104i	−0.550984	−	0.954332i	−0.998204	−	0.0599083i	$-0.980919\pi$
$151$	−83.1986	−	144.104i	−0.550984	−	0.954332i	0.447220	−	0.894424i	$-0.352414\pi$
$152$	−12.8369	+	22.2341i	−0.0844531	+	0.146277i
$153$	−19.4340	−	4.71791i	−0.127020	−	0.0308360i
$154$	−57.8175	+	63.3019i	−0.375439	+	0.411051i
$155$	59.1758	+	166.040i	0.381779	+	1.07123i
$156$	−250.172	−	187.308i	−1.60367	−	1.20069i
$157$	115.257	−	66.5436i	0.734121	−	0.423845i	−0.0858070	−	0.996312i	$-0.527347\pi$
$157$	115.257	−	66.5436i	0.734121	−	0.423845i	0.819928	+	0.572467i	$0.194014\pi$
$158$	−95.8877	−	166.082i	−0.606884	−	1.05115i
$159$	92.3240	−	123.310i	0.580654	−	0.775535i
$160$	−76.1895	−	213.779i	−0.476184	−	1.33612i
$161$	−129.034	+	40.9137i	−0.801454	+	0.254123i
$162$	−214.422	−	110.629i	−1.32359	−	0.682893i
$163$	45.2776	+	26.1411i	0.277777	+	0.160375i	0.632417	−	0.774628i	$-0.282063\pi$
$163$	45.2776	+	26.1411i	0.277777	+	0.160375i	−0.354640	+	0.935003i	$0.615396\pi$
$164$	115.914	−	66.9232i	0.706795	−	0.408068i
$165$	−41.8983	−	45.2572i	−0.253929	−	0.274286i
$166$	−182.880	+	316.757i	−1.10169	+	1.90818i
$167$	−73.9464			−0.442793			−0.221396	−	0.975184i	$-0.571061\pi$
$167$	−73.9464			−0.442793			−0.221396	+	0.975184i	$0.571061\pi$
$168$	17.9860	−	51.5615i	0.107060	−	0.306914i
$169$	−288.014			−1.70423
$170$	32.5527	+	5.96528i	0.191486	+	0.0350899i
$171$	25.0203	+	85.2615i	0.146318	+	0.498605i
$172$	177.236	−	102.327i	1.03044	−	0.594925i
$173$	112.271	−	194.459i	0.648964	−	1.12404i	−0.334406	−	0.942429i	$-0.608536\pi$
$173$	112.271	−	194.459i	0.648964	−	1.12404i	0.983371	−	0.181610i	$-0.0581310\pi$
$174$	−29.8569	+	249.545i	−0.171591	+	1.43417i
$175$	−78.9694	−	156.169i	−0.451254	−	0.892396i
$176$		−	48.2947i		−	0.274402i
$177$	61.1454	+	45.7804i	0.345454	+	0.258646i
$178$	−346.716	+	200.177i	−1.94784	+	1.12459i
$179$	231.158	−	133.459i	1.29138	−	0.745581i	0.312484	−	0.949923i	$-0.398839\pi$
$179$	231.158	−	133.459i	1.29138	−	0.745581i	0.978900	+	0.204342i	$0.0655055\pi$
$180$	200.280	+	89.2948i	1.11267	+	0.496082i
$181$	−236.792			−1.30824			−0.654122	−	0.756389i	$-0.726962\pi$
$181$	−236.792			−1.30824			−0.654122	+	0.756389i	$0.726962\pi$
$182$	−134.729	−	424.908i	−0.740267	−	2.33466i
$183$	203.642	+	24.3648i	1.11280	+	0.133141i
$184$	−25.1431	+	43.5492i	−0.136648	+	0.236681i
$185$	−189.814	−	161.454i	−1.02602	−	0.872725i
$186$	−123.992	−	289.613i	−0.666625	−	1.55706i
$187$	7.91217	+	4.56809i	0.0423111	+	0.0244283i
$188$	186.857			0.993919
$189$	−86.1697	−	168.214i	−0.455924	−	0.890019i
$190$	−49.3649	−	138.512i	−0.259815	−	0.729012i
$191$	−81.5469	−	47.0811i	−0.426947	−	0.246498i	0.271098	−	0.962552i	$-0.412613\pi$
$191$	−81.5469	−	47.0811i	−0.426947	−	0.246498i	−0.698045	+	0.716054i	$0.745947\pi$
$192$	104.166	+	243.305i	0.542532	+	1.26721i
$193$	−238.098	+	137.466i	−1.23367	+	0.712257i	−0.967792	−	0.251751i	$-0.918994\pi$
$193$	−238.098	+	137.466i	−1.23367	+	0.712257i	−0.265874	+	0.964008i	$0.585660\pi$
$194$	35.2720	+	20.3643i	0.181814	+	0.104971i
$195$	312.708	−	71.0055i	1.60363	−	0.364131i
$196$	195.150	−	137.588i	0.995664	−	0.701980i
$197$	−31.5832			−0.160321			−0.0801604	−	0.996782i	$-0.525543\pi$
$197$	−31.5832			−0.160321			−0.0801604	+	0.996782i	$0.525543\pi$
$198$	79.7630	+	76.0780i	0.402843	+	0.384233i
$199$	−76.2933	−	132.144i	−0.383384	−	0.664040i	0.608160	−	0.793815i	$-0.291908\pi$
$199$	−76.2933	−	132.144i	−0.383384	−	0.664040i	−0.991544	+	0.129775i	$0.958575\pi$
$200$	−60.7858	−	23.0521i	−0.303929	−	0.115261i
$201$	164.069	+	122.841i	0.816263	+	0.611148i
$202$		−	272.708i		−	1.35004i
$203$	−132.768	+	145.362i	−0.654029	+	0.716068i
$204$	−32.2540	−	3.85904i	−0.158108	−	0.0189169i
$205$	−24.7545	+	135.086i	−0.120753	+	0.658955i
$206$	−6.33373	+	3.65678i	−0.0307462	+	0.0177514i
$207$	49.0064	+	166.999i	0.236746	+	0.806758i
$208$	217.462	+	125.552i	1.04549	+	0.603615i
$209$		−	40.5938i		−	0.194228i
$210$	158.204	+	269.807i	0.753353	+	1.28480i
$211$	204.268			0.968095			0.484048	−	0.875042i	$-0.339166\pi$
$211$	204.268			0.968095			0.484048	+	0.875042i	$0.339166\pi$
$212$	125.108	−	216.693i	0.590131	−	1.02214i
$213$	−32.9494	+	14.1067i	−0.154692	+	0.0662285i
$214$	−23.6583	−	40.9773i	−0.110553	−	0.191483i
$215$	−37.8501	+	206.549i	−0.176047	+	0.960694i
$216$	−65.7782	−	24.5519i	−0.304529	−	0.113666i
$217$	53.0230	−	241.015i	0.244346	−	1.11067i
$218$	−72.5291			−0.332702
$219$	−245.893	−	184.103i	−1.12280	−	0.840655i
$220$	−76.3078	−	64.9069i	−0.346854	−	0.295031i
$221$	−41.1386	+	23.7514i	−0.186148	+	0.107472i
$222$	356.515	+	266.928i	1.60592	+	1.20238i
$223$		−	56.6494i		−	0.254033i	−0.991901	−	0.127017i	$-0.959460\pi$
$223$		−	56.6494i		−	0.254033i	0.991901	−	0.127017i	$-0.0405401\pi$
$224$	−68.2678	+	310.309i	−0.304767	+	1.38531i
$225$	−202.936	+	97.1699i	−0.901938	+	0.431866i
$226$	−26.6190	+	46.1054i	−0.117783	+	0.204006i
$227$	−5.34193	−	9.25249i	−0.0235327	−	0.0407599i	0.854019	−	0.520241i	$-0.174158\pi$
$227$	−5.34193	−	9.25249i	−0.0235327	−	0.0407599i	−0.877552	+	0.479482i	$0.840825\pi$
$228$	56.8060	+	132.684i	0.249149	+	0.581946i
$229$	−80.6895	+	139.758i	−0.352356	+	0.610298i	−0.986662	−	0.162784i	$-0.947953\pi$
$229$	−80.6895	+	139.758i	−0.352356	+	0.610298i	0.634306	+	0.773082i	$0.281286\pi$
$230$	−96.6894	−	271.299i	−0.420389	−	1.17956i
$231$	16.1346	+	84.8227i	0.0698467	+	0.367198i
$232$			73.1340i			0.315233i
$233$	−89.5759	+	155.150i	−0.384446	+	0.665880i	−0.991692	−	0.128634i	$-0.958941\pi$
$233$	−89.5759	+	155.150i	−0.384446	+	0.665880i	0.607246	+	0.794514i	$0.292274\pi$
$234$	−549.926	+	161.378i	−2.35011	+	0.689649i
$235$	−124.222	+	146.042i	−0.528605	+	0.621455i
$236$	107.451	+	62.0368i	0.455300	+	0.262868i
$237$	−191.775	−	22.9450i	−0.809179	−	0.0968144i
$238$	−34.2106	−	31.2466i	−0.143742	−	0.131288i
$239$		−	375.016i		−	1.56910i	−0.620063	−	0.784552i	$-0.712893\pi$
$239$		−	375.016i		−	1.56910i	0.620063	−	0.784552i	$-0.287107\pi$
$240$	−168.304	−	52.1211i	−0.701265	−	0.217171i
$241$	42.7853	+	74.1063i	0.177532	+	0.307495i	0.941035	−	0.338310i	$-0.109855\pi$
$241$	42.7853	+	74.1063i	0.177532	+	0.307495i	−0.763502	+	0.645805i	$0.776522\pi$
$242$	155.036	+	268.531i	0.640646	+	1.10963i
$243$	−218.618	+	106.091i	−0.899662	+	0.436587i
$244$	333.141			1.36533
$245$	−22.2007	+	243.992i	−0.0906152	+	0.995886i
$246$	29.1593	−	243.714i	0.118534	−	0.990709i
$247$	182.786	+	105.532i	0.740026	+	0.427254i
$248$	−45.8374	−	79.3926i	−0.184828	−	0.320132i
$249$	144.981	+	338.638i	0.582255	+	1.35999i
$250$	326.140	−	179.647i	1.30456	−	0.718590i
$251$			55.3043i			0.220336i	0.993913	+	0.110168i	$0.0351389\pi$
$251$			55.3043i			0.220336i	−0.993913	+	0.110168i	$0.964861\pi$
$252$	−171.436	−	254.671i	−0.680302	−	1.01060i
$253$		−	79.5096i		−	0.314267i
$254$	193.960	+	111.983i	0.763621	+	0.440877i
$255$	24.4585	−	22.6433i	0.0959159	−	0.0887974i
$256$	−55.4597	−	96.0590i	−0.216639	−	0.375230i
$257$	−80.2853	+	139.058i	−0.312394	+	0.541082i	−0.978880	−	0.204435i	$-0.934464\pi$
$257$	−80.2853	+	139.058i	−0.312394	+	0.541082i	0.666486	+	0.745517i	$0.267798\pi$
$258$	44.5852	−	372.645i	0.172811	−	1.44436i
$259$	105.445	+	332.552i	0.407122	+	1.28398i
$260$	490.642	−	174.862i	1.88708	−	0.672545i
$261$	183.162	+	174.700i	0.701769	+	0.669348i
$262$	−567.760	+	327.796i	−2.16702	+	1.25113i
$263$	−140.215	−	242.859i	−0.533136	−	0.923418i	−0.999251	−	0.0386943i	$-0.987680\pi$
$263$	−140.215	−	242.859i	−0.533136	−	0.923418i	0.466115	−	0.884724i	$-0.345653\pi$
$264$	25.6762	+	19.2241i	0.0972583	+	0.0728187i
$265$	86.1895	+	241.838i	0.325243	+	0.912595i
$266$	−44.2323	+	201.056i	−0.166287	+	0.755851i
$267$	−47.9004	+	400.353i	−0.179402	+	1.49945i
$268$	288.318	+	166.461i	1.07582	+	0.621122i
$269$	110.398	−	63.7384i	0.410402	−	0.236946i	−0.280561	−	0.959836i	$-0.590520\pi$
$269$	110.398	−	63.7384i	0.410402	−	0.236946i	0.690962	+	0.722891i	$0.257187\pi$
$270$	351.209	−	195.863i	1.30078	−	0.725417i
$271$	57.5151	−	99.6191i	0.212233	−	0.367598i	−0.740180	−	0.672409i	$-0.765260\pi$
$271$	57.5151	−	99.6191i	0.212233	−	0.367598i	0.952413	+	0.304811i	$0.0985931\pi$
$272$	26.1002			0.0959564
$273$	−423.887	−	147.863i	−1.55270	−	0.541622i
$274$	242.522			0.885117
$275$	101.459	−	16.4900i	0.368941	−	0.0599636i
$276$	111.264	+	259.883i	0.403131	+	0.941606i
$277$	175.222	−	101.165i	0.632571	−	0.365215i	−0.149176	−	0.988811i	$-0.547662\pi$
$277$	175.222	−	101.165i	0.632571	−	0.365215i	0.781747	+	0.623596i	$0.214329\pi$
$278$	193.382	−	334.947i	0.695618	−	1.20485i
$279$	−308.331	−	74.8521i	−1.10513	−	0.268287i
$280$	55.0377	+	72.4874i	0.196563	+	0.258884i
$281$		−	311.623i		−	1.10898i	−0.832190	−	0.554490i	$-0.812913\pi$
$281$		−	311.623i		−	1.10898i	0.832190	−	0.554490i	$-0.187087\pi$
$282$	205.373	−	274.301i	0.728275	−	0.972700i
$283$	68.7640	−	39.7009i	0.242982	−	0.140286i	−0.373564	−	0.927604i	$-0.621864\pi$
$283$	68.7640	−	39.7009i	0.242982	−	0.140286i	0.616547	+	0.787318i	$0.288531\pi$
$284$	−50.4195	+	29.1097i	−0.177534	+	0.102499i
$285$	−141.466	−	43.8100i	−0.496373	−	0.153719i
$286$	261.825			0.915471
$287$	129.666	−	141.966i	0.451797	−	0.494653i
$288$	396.979	+	96.3729i	1.37840	+	0.334628i
$289$	142.031	−	246.005i	0.491458	−	0.851230i
$290$	−319.063	−	271.393i	−1.10022	−	0.935838i
$291$	37.7085	−	16.1442i	0.129582	−	0.0554782i
$292$	−432.108	−	249.478i	−1.47982	−	0.854375i
$293$	161.183			0.550113			0.275056	−	0.961428i	$-0.411303\pi$
$293$	161.183			0.550113			0.275056	+	0.961428i	$0.411303\pi$
$294$	12.5127	−	437.698i	0.0425602	−	1.48877i
$295$	−119.919	+	42.7385i	−0.406506	+	0.144876i
$296$	112.237	+	64.8000i	0.379178	+	0.218919i
$297$	109.481	−	18.3832i	0.368621	−	0.0618963i
$298$	510.989	−	295.019i	1.71473	−	0.989998i
$299$	358.018	+	206.702i	1.19738	+	0.691309i
$300$	−308.550	+	195.878i	−1.02850	+	0.652926i
$301$	198.262	−	217.069i	0.658678	−	0.721158i
$302$	−495.656			−1.64125
$303$	−219.858	−	164.611i	−0.725604	−	0.543271i
$304$	−57.9839	−	100.431i	−0.190736	−	0.330365i
$305$	−221.472	+	260.373i	−0.726137	+	0.853683i
$306$	−41.1152	+	43.1067i	−0.134364	+	0.140872i
$307$			214.316i			0.698099i	0.937104	+	0.349049i	$0.113495\pi$
$307$			214.316i			0.698099i	−0.937104	+	0.349049i	$0.886505\pi$
$308$	42.3902	+	133.691i	0.137631	+	0.434061i
$309$	−0.875033	+	7.31356i	−0.00283182	+	0.0236685i
$310$	516.466	+	94.6424i	1.66602	+	0.305298i
$311$	−355.712	+	205.370i	−1.14377	+	0.660354i	−0.947361	−	0.320168i	$-0.896261\pi$
$311$	−355.712	+	205.370i	−1.14377	+	0.660354i	−0.196407	+	0.980523i	$0.562927\pi$
$312$	−153.313	+	65.6382i	−0.491389	+	0.210379i
$313$	−397.780	−	229.658i	−1.27086	−	0.733732i	−0.295711	−	0.955277i	$-0.595557\pi$
$313$	−397.780	−	229.658i	−1.27086	−	0.733732i	−0.975150	+	0.221545i	$0.928890\pi$
$314$		−	396.434i		−	1.26253i
$315$	313.014	+	35.3154i	0.993696	+	0.112112i
$316$	−313.728			−0.992809
$317$	110.238	−	190.938i	0.347754	−	0.602327i	−0.638096	−	0.769957i	$-0.720278\pi$
$317$	110.238	−	190.938i	0.347754	−	0.602327i	0.985850	+	0.167629i	$0.0536112\pi$
$318$	−180.595	−	421.821i	−0.567908	−	1.32648i
$319$	−57.8175	−	100.143i	−0.181246	−	0.313928i
$320$	−433.884	−	79.5092i	−1.35589	−	0.248466i
$321$	−47.3165	−	5.66120i	−0.147403	−	0.0176361i
$322$	−86.6362	+	393.802i	−0.269057	+	1.22299i
$323$	21.9383			0.0679204
$324$	−332.120	+	213.292i	−1.02506	+	0.658308i
$325$	−189.511	+	499.719i	−0.583111	+	1.53760i
$326$	134.871	−	77.8678i	0.413715	−	0.238858i
$327$	−43.7797	+	58.4731i	−0.133883	+	0.178817i
$328$		−	71.4254i		−	0.217760i
$329$	255.864	−	81.1286i	0.777703	−	0.246592i
$330$	−179.151	+	40.6792i	−0.542883	+	0.123270i
$331$	−232.881	+	403.362i	−0.703568	+	1.21862i	0.263638	+	0.964622i	$0.415078\pi$
$331$	−232.881	+	403.362i	−0.703568	+	1.21862i	−0.967206	+	0.253994i	$0.918256\pi$
$332$	299.176	+	518.188i	0.901132	+	1.56081i
$333$	430.396	−	126.301i	1.29248	−	0.379284i
$334$	−110.134	+	190.758i	−0.329743	+	0.571131i
$335$	−321.775	+	114.679i	−0.960521	+	0.342324i
$336$	161.078	+	186.809i	0.479399	+	0.555979i
$337$		−	238.438i		−	0.707530i	−0.935334	−	0.353765i	$-0.884901\pi$
$337$		−	238.438i		−	0.707530i	0.935334	−	0.353765i	$-0.115099\pi$
$338$	−428.962	+	742.984i	−1.26912	+	2.19818i
$339$	21.1027	+	49.2902i	0.0622497	+	0.145399i
$340$	35.0779	−	41.2394i	0.103170	−	0.121292i
$341$	125.531	+	72.4752i	0.368125	+	0.212537i
$342$	257.212	+	62.4422i	0.752082	+	0.182580i
$343$	207.483	−	273.130i	0.604907	−	0.796296i
$344$		−	109.211i		−	0.317474i
$345$	−277.085	−	85.8092i	−0.803146	−	0.248722i
$346$	−334.427	−	579.245i	−0.966553	−	1.67412i
$347$	−116.832	−	202.359i	−0.336692	−	0.583167i	0.647117	−	0.762391i	$-0.275975\pi$
$347$	−116.832	−	202.359i	−0.336692	−	0.583167i	−0.983808	+	0.179224i	$0.942641\pi$
$348$	329.119	+	246.416i	0.945744	+	0.708092i
$349$	−88.8589			−0.254610			−0.127305	−	0.991864i	$-0.540633\pi$
$349$	−88.8589			−0.254610			−0.127305	+	0.991864i	$0.540633\pi$
$350$	−520.482	−	28.8795i	−1.48709	−	0.0825128i
$351$	−201.841	+	540.762i	−0.575045	+	1.54063i
$352$	−161.622	−	93.3127i	−0.459154	−	0.265093i
$353$	264.349	+	457.867i	0.748865	+	1.29707i	0.948367	+	0.317175i	$0.102734\pi$
$353$	264.349	+	457.867i	0.748865	+	1.29707i	−0.199502	+	0.979898i	$0.563932\pi$
$354$	209.167	−	89.5510i	0.590868	−	0.252969i
$355$	10.7675	−	58.7586i	0.0303310	−	0.165517i
$356$			654.943i			1.83973i
$357$	−45.8412	+	8.71970i	−0.128407	+	0.0244249i
$358$		−	795.083i		−	2.22090i
$359$	−73.3318	−	42.3381i	−0.204267	−	0.117934i	0.394377	−	0.918949i	$-0.370960\pi$
$359$	−73.3318	−	42.3381i	−0.204267	−	0.117934i	−0.598644	+	0.801015i	$0.704294\pi$
$360$	94.7053	−	68.7325i	0.263070	−	0.190923i
$361$	131.762	+	228.219i	0.364992	+	0.632185i
$362$	−352.673	+	610.848i	−0.974235	+	1.68743i
$363$	310.073	+	37.0987i	0.854195	+	0.102200i
$364$	−712.187	−	156.681i	−1.95656	−	0.430442i
$365$	482.249	−	171.871i	1.32123	−	0.470878i
$366$	366.154	−	489.043i	1.00042	−	1.33618i
$367$	243.158	−	140.388i	0.662557	−	0.382528i	−0.130694	−	0.991423i	$-0.541720\pi$
$367$	243.158	−	140.388i	0.662557	−	0.382528i	0.793251	+	0.608895i	$0.208387\pi$
$368$	−113.571	−	196.711i	−0.308617	−	0.534540i
$369$	−178.882	−	170.618i	−0.484776	−	0.462380i
$370$	−699.204	+	249.192i	−1.88974	+	0.673492i
$371$	77.2281	−	351.038i	0.208162	−	0.946193i
$372$	−511.727	−	61.2257i	−1.37561	−	0.164585i
$373$	246.088	+	142.079i	0.659754	+	0.380909i	0.792183	−	0.610284i	$-0.208944\pi$
$373$	246.088	+	142.079i	0.659754	+	0.380909i	−0.132429	+	0.991192i	$0.542278\pi$
$374$	23.5684	−	13.6072i	0.0630172	−	0.0363830i
$375$	52.0308	−	371.373i	0.138749	−	0.990328i
$376$	49.8569	−	86.3546i	0.132598	−	0.229666i
$377$	601.234			1.59479
$378$	−562.276	−	28.2435i	−1.48750	−	0.0747182i
$379$	300.681			0.793355			0.396677	−	0.917958i	$-0.370163\pi$
$379$	300.681			0.793355			0.396677	+	0.917958i	$0.370163\pi$
$380$	−236.614	−	43.3596i	−0.622669	−	0.114104i
$381$	207.358	−	88.7764i	0.544247	−	0.233009i
$382$	−242.908	+	140.243i	−0.635886	+	0.367129i
$383$	346.010	−	599.307i	0.903421	−	1.56477i	0.0803972	−	0.996763i	$-0.474381\pi$
$383$	346.010	−	599.307i	0.903421	−	1.56477i	0.823023	−	0.568007i	$-0.192286\pi$
$384$	241.968	+	28.9503i	0.630124	+	0.0753914i
$385$	−132.670	−	55.7464i	−0.344597	−	0.144796i
$386$			818.953i			2.12164i
$387$	−273.515	−	260.879i	−0.706757	−	0.674106i
$388$	57.7019	−	33.3142i	0.148716	−	0.0858614i
$389$	−570.321	+	329.275i	−1.46612	+	0.846465i	−0.999282	−	0.0378787i	$-0.987940\pi$
$389$	−570.321	+	329.275i	−1.46612	+	0.846465i	−0.466837	+	0.884343i	$0.654607\pi$
$390$	282.569	−	912.440i	0.724536	−	2.33959i
$391$	42.9698			0.109897
$392$	−11.5157	−	126.898i	−0.0293768	−	0.323720i
$393$	−78.4385	+	655.592i	−0.199589	+	1.66817i
$394$	−47.0393	+	81.4745i	−0.119389	+	0.206788i
$395$	208.566	−	245.201i	0.528015	−	0.620761i
$396$	173.026	−	50.7750i	0.436933	−	0.128220i
$397$	384.288	+	221.869i	0.967979	+	0.558863i	0.898619	−	0.438729i	$-0.144571\pi$
$397$	384.288	+	221.869i	0.967979	+	0.558863i	0.0693593	+	0.997592i	$0.477905\pi$
$398$	−454.518			−1.14201
$399$	135.393	+	157.021i	0.339331	+	0.393536i
$400$	227.460	−	185.720i	0.568649	−	0.464300i
$401$	433.596	+	250.337i	1.08129	+	0.624281i	0.931243	−	0.364398i	$-0.118725\pi$
$401$	433.596	+	250.337i	1.08129	+	0.624281i	0.150043	+	0.988679i	$0.452059\pi$
$402$	561.250	−	240.288i	1.39614	−	0.597732i
$403$	−652.686	+	376.828i	−1.61957	+	0.935058i
$404$	−386.357	−	223.063i	−0.956329	−	0.552137i
$405$	54.0906	−	401.372i	0.133557	−	0.991041i
$406$	177.245	+	558.997i	0.436564	+	1.37684i
$407$	−204.915			−0.503478
$408$	−10.3894	+	13.8763i	−0.0254642	+	0.0340106i
$409$	−131.038	−	226.965i	−0.320387	−	0.554927i	0.660181	−	0.751107i	$-0.270480\pi$
$409$	−131.038	−	226.965i	−0.320387	−	0.554927i	−0.980568	+	0.196180i	$0.937146\pi$
$410$	311.609	+	265.052i	0.760022	+	0.646469i
$411$	146.390	−	195.522i	0.356181	−	0.475723i
$412$			11.9643i			0.0290397i
$413$	174.068	+	38.2948i	0.421472	+	0.0927236i
$414$	503.792	+	122.303i	1.21689	+	0.295419i
$415$	−603.892	−	110.663i	−1.45516	−	0.266658i
$416$	840.341	−	485.171i	2.02005	−	1.16628i
$417$	−153.307	−	358.084i	−0.367643	−	0.858716i
$418$	−104.719	−	60.4594i	−0.250523	−	0.144640i
$419$			93.6914i			0.223607i	0.993730	+	0.111804i	$0.0356627\pi$
$419$			93.6914i			0.223607i	−0.993730	+	0.111804i	$0.964337\pi$
$420$	511.652	−	3.44386i	1.21822	−	0.00819966i
$421$	−5.07862			−0.0120632			−0.00603161	−	0.999982i	$-0.501920\pi$
$421$	−5.07862			−0.0120632			−0.00603161	+	0.999982i	$0.501920\pi$
$422$	304.232	−	526.946i	0.720930	−	1.24869i
$423$	−97.1759	−	331.145i	−0.229730	−	0.782849i
$424$	−66.7621	−	115.635i	−0.157458	−	0.272725i
$425$	8.91178	+	54.8318i	0.0209689	+	0.129016i
$426$	−12.6835	+	106.009i	−0.0297734	+	0.248848i
$427$	456.172	−	144.642i	1.06832	−	0.338739i
$428$	−77.4057			−0.180854
$429$	158.041	−	211.084i	0.368395	−	0.492037i
$430$	476.457	+	405.271i	1.10804	+	0.942491i
$431$	−395.347	+	228.254i	−0.917278	+	0.529591i	−0.882766	−	0.469813i	$-0.844321\pi$
$431$	−395.347	+	228.254i	−0.917278	+	0.529591i	−0.0345127	+	0.999404i	$0.510988\pi$
$432$	244.602	−	201.862i	0.566208	−	0.467274i
$433$			353.004i			0.815251i	0.913149	+	0.407626i	$0.133643\pi$
$433$			353.004i			0.815251i	−0.913149	+	0.407626i	$0.866357\pi$
$434$	−542.769	−	495.744i	−1.25062	−	1.14227i
$435$	−411.390	+	93.4127i	−0.945723	+	0.214742i
$436$	−59.3256	+	102.755i	−0.136068	+	0.235677i
$437$	−95.4613	−	165.344i	−0.218447	−	0.378361i
$438$	−841.155	+	360.124i	−1.92044	+	0.822202i
$439$	−331.705	+	574.529i	−0.755591	+	1.30872i	0.189488	+	0.981883i	$0.439317\pi$
$439$	−331.705	+	574.529i	−0.755591	+	1.30872i	−0.945080	+	0.326840i	$0.894016\pi$
$440$	−50.3566	+	17.9468i	−0.114447	+	0.0407882i
$441$	−345.321	−	274.289i	−0.783040	−	0.621971i
$442$			141.499i			0.320134i
$443$	24.1333	−	41.8000i	0.0544769	−	0.0943567i	−0.837501	−	0.546436i	$-0.815984\pi$
$443$	24.1333	−	41.8000i	0.0544769	−	0.0943567i	0.891978	+	0.452079i	$0.149318\pi$
$444$	669.782	−	286.754i	1.50852	−	0.645843i
$445$	−511.884	−	435.405i	−1.15030	−	0.978438i
$446$	−146.137	−	84.3723i	−0.327662	−	0.189176i
$447$	70.5954	−	590.039i	0.157931	−	1.32000i
$448$	455.981	+	416.476i	1.01782	+	0.929633i
$449$			633.019i			1.40984i	0.709285	+	0.704921i	$0.249018\pi$
$449$			633.019i			1.40984i	−0.709285	+	0.704921i	$0.750982\pi$
$450$	−51.5813	+	668.232i	−0.114625	+	1.48496i
$451$	56.4667	+	97.8032i	0.125203	+	0.216859i
$452$	43.5463	+	75.4244i	0.0963413	+	0.166868i
$453$	−299.186	+	399.600i	−0.660455	+	0.882118i
$454$	−31.8246			−0.0700982
$455$	595.918	−	452.464i	1.30971	−	0.994426i
$456$	76.4758	+	9.14997i	0.167710	+	0.0200657i
$457$	446.482	+	257.776i	0.976984	+	0.564062i	0.901358	−	0.433074i	$-0.142571\pi$
$457$	446.482	+	257.776i	0.976984	+	0.564062i	0.0756257	+	0.997136i	$0.475905\pi$
$458$	240.354	+	416.306i	0.524791	+	0.908965i
$459$	9.93493	+	59.1671i	0.0216447	+	0.128904i
$460$	−463.449	−	84.9270i	−1.00750	−	0.184624i
$461$		−	579.029i		−	1.25603i	−0.778202	−	0.628014i	$-0.783868\pi$
$461$		−	579.029i		−	1.25603i	0.778202	−	0.628014i	$-0.216132\pi$
$462$	242.846	+	84.7110i	0.525640	+	0.183357i
$463$		−	19.2280i		−	0.0415292i	−0.999784	−	0.0207646i	$-0.993390\pi$
$463$		−	19.2280i		−	0.0415292i	0.999784	−	0.0207646i	$-0.00661005\pi$
$464$	−286.087	−	165.172i	−0.616567	−	0.355975i
$465$	388.048	−	359.248i	0.834511	−	0.772577i
$466$	266.825	+	462.154i	0.572585	+	0.991746i
$467$	−234.139	+	405.540i	−0.501367	+	0.868394i	0.498631	+	0.866814i	$0.333836\pi$
$467$	−234.139	+	405.540i	−0.501367	+	0.868394i	−0.999999	+	0.00157962i	$0.999497\pi$
$468$	−221.185	+	911.103i	−0.472617	+	1.94680i
$469$	467.070	+	102.755i	0.995884	+	0.219094i
$470$	191.727	+	537.965i	0.407931	+	1.14461i
$471$	−319.607	−	239.294i	−0.678570	−	0.508055i
$472$	57.3397	−	33.1051i	0.121483	−	0.0701380i
$473$	86.3389	+	149.543i	0.182535	+	0.316159i
$474$	−344.817	+	460.545i	−0.727461	+	0.971614i
$475$	191.190	−	156.106i	0.402504	−	0.328643i
$476$	−72.2511	+	22.9092i	−0.151788	+	0.0481285i
$477$	−449.083	−	109.022i	−0.941475	−	0.228558i
$478$	−967.420	−	558.540i	−2.02389	−	1.16849i
$479$	−311.231	+	179.689i	−0.649752	+	0.375134i	−0.788361	−	0.615213i	$-0.789070\pi$
$479$	−311.231	+	179.689i	−0.649752	+	0.375134i	0.138609	+	0.990347i	$0.455737\pi$
$480$	−499.616	+	462.537i	−1.04087	+	0.963618i
$481$	532.720	−	922.698i	1.10753	−	1.91829i
$482$	254.894			0.528825
$483$	265.190	+	307.552i	0.549047	+	0.636753i
$484$	507.252			1.04804
$485$	−12.3227	+	67.2454i	−0.0254077	+	0.138650i
$486$	−51.9249	+	721.973i	−0.106841	+	1.48554i
$487$	−287.133	+	165.776i	−0.589596	+	0.340403i	−0.764938	−	0.644104i	$-0.777230\pi$
$487$	−287.133	+	165.776i	−0.589596	+	0.340403i	0.175342	+	0.984508i	$0.443897\pi$
$488$	88.8882	−	153.959i	0.182148	−	0.315489i
$489$	18.6330	−	155.736i	0.0381044	−	0.318478i
$490$	596.356	+	420.667i	1.21705	+	0.858504i
$491$		−	102.807i		−	0.209383i	−0.994505	−	0.104692i	$-0.966614\pi$
$491$		−	102.807i		−	0.209383i	0.994505	−	0.104692i	$-0.0333855\pi$
$492$	−321.429	−	240.659i	−0.653312	−	0.489144i
$493$	54.1207	−	31.2466i	0.109778	−	0.0633806i
$494$	544.476	−	314.353i	1.10218	−	0.636343i
$495$	−75.3429	+	168.987i	−0.152208	+	0.341388i
$496$	414.093			0.834864
$497$	−56.4011	+	61.7511i	−0.113483	+	0.124248i
$498$	1089.51	+	130.355i	2.18777	+	0.261756i
$499$	463.720	−	803.186i	0.929298	−	1.60959i	0.144799	−	0.989461i	$-0.453746\pi$
$499$	463.720	−	803.186i	0.929298	−	1.60959i	0.784499	−	0.620130i	$-0.212920\pi$
$500$	12.2540	−	609.000i	0.0245079	−	1.21800i
$501$	87.3108	+	203.935i	0.174273	+	0.407055i
$502$	142.667	+	82.3690i	0.284198	+	0.164082i
$503$	−455.605			−0.905776			−0.452888	−	0.891567i	$-0.649606\pi$
$503$	−455.605			−0.905776			−0.452888	+	0.891567i	$0.649606\pi$
$504$	−163.437	+	11.2771i	−0.324279	+	0.0223753i
$505$	431.190	−	153.673i	0.853841	−	0.304304i
$506$	−205.109	−	118.420i	−0.405354	−	0.234031i
$507$	340.067	+	794.307i	0.670744	+	1.56668i
$508$	317.301	−	183.194i	0.624609	−	0.360618i
$509$	−253.253	−	146.215i	−0.497549	−	0.287260i	0.230152	−	0.973155i	$-0.426078\pi$
$509$	−253.253	−	146.215i	−0.497549	−	0.287260i	−0.727701	+	0.685895i	$0.759411\pi$
$510$	−21.9845	−	96.8197i	−0.0431068	−	0.189842i
$511$	−700.005	−	154.001i	−1.36987	−	0.301371i
$512$	−655.326			−1.27993
$513$	205.598	−	169.674i	0.400776	−	0.330748i
$514$	239.150	+	414.220i	0.465273	+	0.805876i
$515$	−9.35098	−	7.95388i	−0.0181572	−	0.0154444i
$516$	−491.473	−	367.973i	−0.952467	−	0.713126i
$517$			157.661i			0.304954i
$518$	1014.92	+	223.283i	1.95931	+	0.431047i
$519$	−668.855	−	80.0253i	−1.28874	−	0.154191i
$520$	50.1011	−	273.403i	0.0963483	−	0.525775i
$521$	5.07885	−	2.93227i	0.00974827	−	0.00562817i	−0.495118	−	0.868826i	$-0.664875\pi$
$521$	5.07885	−	2.93227i	0.00974827	−	0.00562817i	0.504866	+	0.863198i	$0.331542\pi$
$522$	723.466	−	212.304i	1.38595	−	0.406712i
$523$	395.198	+	228.168i	0.755636	+	0.436267i	0.827727	−	0.561131i	$-0.189634\pi$
$523$	395.198	+	228.168i	0.755636	+	0.436267i	−0.0720905	+	0.997398i	$0.522967\pi$
$524$			1072.49i			2.04674i
$525$	−337.454	+	402.182i	−0.642769	+	0.766060i
$526$	−835.331			−1.58808
$527$	−39.1682	+	67.8412i	−0.0743229	+	0.128731i
$528$	−133.191	+	57.0231i	−0.252255	+	0.107998i
$529$	77.5232	+	134.274i	0.146547	+	0.253826i
$530$	752.232	+	137.847i	1.41931	+	0.260088i
$531$	54.0604	−	222.686i	0.101809	−	0.419370i
$532$	248.665	+	227.121i	0.467415	+	0.426919i
$533$	−587.187			−1.10166
$534$	961.441	+	719.845i	1.80045	+	1.34802i
$535$	51.4592	−	60.4980i	0.0961854	−	0.113080i
$536$	153.857	−	88.8296i	0.287047	−	0.165727i
$537$	−640.998	−	479.925i	−1.19367	−	0.893715i
$538$		−	379.722i		−	0.705803i
$539$	116.090	+	164.659i	0.215381	+	0.305489i
$540$	9.78719	−	657.780i	0.0181244	−	1.21811i
$541$	30.2944	−	52.4714i	0.0559970	−	0.0969896i	−0.836668	−	0.547710i	$-0.815500\pi$
$541$	30.2944	−	52.4714i	0.0559970	−	0.0969896i	0.892665	+	0.450721i	$0.148833\pi$
$542$	−171.323	−	296.741i	−0.316095	−	0.547492i
$543$	279.588	+	653.044i	0.514895	+	1.20266i
$544$	50.4294	−	87.3464i	0.0927012	−	0.160563i
$545$	−40.8707	−	114.679i	−0.0749922	−	0.210419i
$546$	−1012.77	+	873.267i	−1.85488	+	1.59939i
$547$		−	67.9520i		−	0.124227i	−0.998069	−	0.0621133i	$-0.980216\pi$
$547$		−	67.9520i		−	0.124227i	0.998069	−	0.0621133i	$-0.0197840\pi$
$548$	198.373	−	343.591i	0.361994	−	0.626991i
$549$	−173.252	−	590.388i	−0.315577	−	1.07539i
$550$	108.571	−	286.291i	0.197403	−	0.520528i
$551$	−240.468	−	138.834i	−0.436422	−	0.251968i
$552$	149.791	+	17.9217i	0.271360	+	0.0324669i
$553$	−429.589	+	136.213i	−0.776834	+	0.246316i
$554$		−	602.689i		−	1.08789i
$555$	−221.151	+	714.116i	−0.398471	+	1.28670i
$556$	−316.356	−	547.944i	−0.568985	−	0.985511i
$557$	−59.6922	−	103.390i	−0.107167	−	0.185619i	0.807454	−	0.589930i	$-0.200845\pi$
$557$	−59.6922	−	103.390i	−0.107167	−	0.185619i	−0.914622	+	0.404311i	$0.867511\pi$
$558$	−652.315	+	683.911i	−1.16902	+	1.22565i
$559$	−897.823			−1.60612
$560$	−407.860	+	51.5853i	−0.728321	+	0.0921165i
$561$	3.25608	−	27.2145i	0.00580407	−	0.0485106i
$562$	−803.888	−	464.125i	−1.43041	−	0.825845i
$563$	−461.941	−	800.106i	−0.820500	−	1.42115i	−0.905311	−	0.424750i	$-0.860362\pi$
$563$	−461.941	−	800.106i	−0.820500	−	1.42115i	0.0848112	−	0.996397i	$-0.472971\pi$
$564$	−220.628	−	515.328i	−0.391184	−	0.913702i
$565$	−87.8990	−	16.1075i	−0.155573	−	0.0285088i
$566$		−	236.519i		−	0.417877i
$567$	−362.169	+	436.260i	−0.638745	+	0.769418i
$568$			31.0681i			0.0546973i
$569$	−296.128	−	170.970i	−0.520436	−	0.300474i	0.216677	−	0.976243i	$-0.430478\pi$
$569$	−296.128	−	170.970i	−0.520436	−	0.300474i	−0.737113	+	0.675770i	$0.763811\pi$
$570$	−323.713	+	299.688i	−0.567917	+	0.525768i
$571$	318.648	+	551.915i	0.558053	+	0.966576i	0.997659	+	0.0683852i	$0.0217847\pi$
$571$	318.648	+	551.915i	0.558053	+	0.966576i	−0.439606	+	0.898191i	$0.644882\pi$
$572$	214.161	−	370.938i	0.374407	−	0.648493i
$573$	−33.5589	+	280.486i	−0.0585669	+	0.489505i
$574$	−173.104	−	545.936i	−0.301575	−	0.951109i
$575$	374.476	−	305.759i	0.651263	−	0.531754i
$576$	548.011	−	574.555i	0.951408	−	0.997491i
$577$	425.337	−	245.568i	0.737152	−	0.425595i	−0.0838807	−	0.996476i	$-0.526731\pi$
$577$	425.337	−	245.568i	0.737152	−	0.425595i	0.821033	+	0.570881i	$0.193398\pi$
$578$	−423.076	−	732.790i	−0.731966	−	1.26780i
$579$	660.242	+	494.333i	1.14031	+	0.853770i
$580$	−645.474	+	230.043i	−1.11289	+	0.396626i
$581$	634.648	+	579.663i	1.09234	+	0.997698i
$582$	14.5154	−	121.321i	0.0249406	−	0.208455i
$583$	182.836	+	105.560i	0.313612	+	0.181064i
$584$	−230.589	+	133.130i	−0.394844	+	0.227963i
$585$	−565.049	−	778.571i	−0.965895	−	1.33089i
$586$	240.062	−	415.800i	0.409663	−	0.709557i
$587$	328.125			0.558987			0.279493	−	0.960148i	$-0.409833\pi$
$587$	328.125			0.558987			0.279493	+	0.960148i	$0.409833\pi$
$588$	−609.871	−	375.745i	−1.03719	−	0.639023i
$589$	348.062			0.590938
$590$	−68.3536	+	373.007i	−0.115853	+	0.632215i
$591$	37.2913	+	87.1025i	0.0630986	+	0.147382i
$592$	−506.971	+	292.700i	−0.856370	+	0.494426i
$593$	190.547	−	330.038i	0.321328	−	0.556556i	−0.659435	−	0.751762i	$-0.729204\pi$
$593$	190.547	−	330.038i	0.321328	−	0.556556i	0.980762	+	0.195206i	$0.0625376\pi$
$594$	115.635	−	309.804i	0.194672	−	0.521556i
$595$	30.1273	−	71.6994i	0.0506341	−	0.120503i
$596$		−	965.252i		−	1.61955i
$597$	−274.355	+	366.434i	−0.459555	+	0.613792i
$598$	1066.45	−	615.713i	1.78336	−	1.02962i
$599$	147.815	−	85.3408i	0.246769	−	0.142472i	−0.371515	−	0.928427i	$-0.621162\pi$
$599$	147.815	−	85.3408i	0.246769	−	0.142472i	0.618284	+	0.785955i	$0.287828\pi$
$600$	8.19690	+	194.858i	0.0136615	+	0.324763i
$601$	40.5746			0.0675119			0.0337559	−	0.999430i	$-0.489253\pi$
$601$	40.5746			0.0675119			0.0337559	+	0.999430i	$0.489253\pi$
$602$	−264.680	−	834.749i	−0.439667	−	1.38663i
$603$	145.058	−	597.523i	0.240561	−	0.990917i
$604$	−405.425	+	702.217i	−0.671234	+	1.16261i
$605$	−337.220	+	396.453i	−0.557389	+	0.655295i
$606$	−752.095	+	321.995i	−1.24108	+	0.531345i
$607$	−88.2380	−	50.9442i	−0.145367	−	0.0839279i	0.425552	−	0.904934i	$-0.360080\pi$
$607$	−88.2380	−	50.9442i	−0.145367	−	0.0839279i	−0.570920	+	0.821006i	$0.693413\pi$
$608$	−448.134			−0.737063
$609$	557.653	+	194.524i	0.915686	+	0.319415i
$610$	341.825	+	959.120i	0.560368	+	1.57233i
$611$	−709.920	−	409.873i	−1.16190	−	0.670823i
$612$	27.4406	+	93.5091i	0.0448376	+	0.152793i
$613$	889.882	−	513.774i	1.45168	−	0.838130i	0.453107	−	0.891456i	$-0.350316\pi$
$613$	889.882	−	513.774i	1.45168	−	0.838130i	0.998577	+	0.0533259i	$0.0169822\pi$
$614$	552.867	+	319.198i	0.900435	+	0.519866i
$615$	401.778	−	91.2303i	0.653297	−	0.148342i
$616$	73.0948	+	16.0808i	0.118660	+	0.0261052i
$617$	971.254			1.57416			0.787078	−	0.616853i	$-0.211593\pi$
$617$	971.254			1.57416			0.787078	+	0.616853i	$0.211593\pi$
$618$	17.5634	+	13.1500i	0.0284197	+	0.0212782i
$619$	279.452	+	484.024i	0.451457	+	0.781946i	0.998477	−	0.0551737i	$-0.0175713\pi$
$619$	279.452	+	484.024i	0.451457	+	0.781946i	−0.547020	+	0.837119i	$0.684238\pi$
$620$	556.530	−	654.285i	0.897629	−	1.05530i
$621$	402.698	−	332.334i	0.648468	−	0.535160i
$622$			1223.50i			1.96703i
$623$	284.360	+	896.818i	0.456437	+	1.43951i
$624$	89.4919	−	747.977i	0.143417	−	1.19868i
$625$	467.830	+	414.439i	0.748528	+	0.663103i
$626$	−1184.89	+	684.095i	−1.89279	+	1.09280i
$627$	−111.952	+	47.9303i	−0.178553	+	0.0764439i
$628$	−561.645	−	324.266i	−0.894340	−	0.516347i
$629$		−	110.743i		−	0.176063i
$630$	557.298	−	754.878i	0.884601	−	1.19822i
$631$	−778.827			−1.23427			−0.617137	−	0.786856i	$-0.711707\pi$
$631$	−778.827			−1.23427			−0.617137	+	0.786856i	$0.711707\pi$
$632$	−83.7084	+	144.987i	−0.132450	+	0.229410i
$633$	−241.186	−	563.346i	−0.381020	−	0.889962i
$634$	−328.372	−	568.757i	−0.517937	−	0.897093i
$635$	−67.7623	+	369.781i	−0.106712	+	0.582332i
$636$	−745.331	−	89.1753i	−1.17190	−	0.140213i
$637$	−1043.23	+	94.6704i	−1.63772	+	0.148619i
$638$	−344.449			−0.539888
$639$	77.8089	+	74.2142i	0.121767	+	0.116141i
$640$	−263.153	+	309.376i	−0.411176	+	0.483399i
$641$	1106.38	−	638.767i	1.72602	−	0.996517i	0.821313	−	0.570478i	$-0.193242\pi$
$641$	1106.38	−	638.767i	1.72602	−	0.996517i	0.904705	−	0.426039i	$-0.140091\pi$
$642$	−85.0762	+	113.630i	−0.132517	+	0.176993i
$643$		−	741.031i		−	1.15246i	−0.817288	−	0.576229i	$-0.804524\pi$
$643$		−	741.031i		−	1.15246i	0.817288	−	0.576229i	$-0.195476\pi$
$644$	487.052	+	444.854i	0.756291	+	0.690768i
$645$	614.328	−	139.493i	0.952446	−	0.216268i
$646$	32.6744	−	56.5937i	0.0505796	−	0.0876064i
$647$	−123.645	−	214.160i	−0.191106	−	0.331005i	0.754511	−	0.656287i	$-0.227874\pi$
$647$	−123.645	−	214.160i	−0.191106	−	0.331005i	−0.945617	+	0.325282i	$0.894541\pi$
$648$	9.95541	+	210.397i	0.0153633	+	0.324687i
$649$	−52.3438	+	90.6621i	−0.0806530	+	0.139695i
$650$	1006.86	+	1233.15i	1.54902	+	1.89715i
$651$	−727.294	+	138.343i	−1.11720	+	0.212508i
$652$		−	254.770i		−	0.390751i
$653$	268.869	−	465.694i	0.411744	−	0.713161i	−0.583337	−	0.812230i	$-0.698253\pi$
$653$	268.869	−	465.694i	0.411744	−	0.713161i	0.995081	+	0.0990692i	$0.0315865\pi$
$654$	85.6374	+	200.026i	0.130944	+	0.305850i
$655$	−838.229	−	712.991i	−1.27974	−	1.08854i
$656$	279.403	+	161.313i	0.425919	+	0.245905i
$657$	−217.401	+	895.518i	−0.330900	+	1.36304i
$658$	171.793	−	780.879i	0.261083	−	1.18675i
$659$			257.346i			0.390510i	0.980752	+	0.195255i	$0.0625535\pi$
$659$			257.346i			0.390510i	−0.980752	+	0.195255i	$0.937446\pi$
$660$	−88.9060	+	287.085i	−0.134706	+	0.434977i
$661$	7.45864	+	12.9187i	0.0112839	+	0.0195442i	0.871612	−	0.490196i	$-0.163075\pi$
$661$	7.45864	+	12.9187i	0.0112839	+	0.0195442i	−0.860328	+	0.509740i	$0.829741\pi$
$662$	693.696	+	1201.52i	1.04788	+	1.81498i
$663$	114.077	+	85.4111i	0.172062	+	0.128825i
$664$	319.302			0.480877
$665$	−342.823	+	43.3596i	−0.515524	+	0.0652024i
$666$	315.206	−	1298.39i	0.473282	−	1.94954i
$667$	−470.997	−	271.930i	−0.706143	−	0.407692i
$668$	180.170	+	312.063i	0.269715	+	0.467160i
$669$	−156.232	+	66.8877i	−0.233531	+	0.0999816i
$670$	−183.410	+	1000.87i	−0.273747	+	1.49384i
$671$			281.089i			0.418911i
$672$	936.400	−	178.118i	1.39345	−	0.265056i
$673$		−	714.374i		−	1.06148i	−0.847535	−	0.530739i	$-0.821915\pi$
$673$		−	714.374i		−	1.06148i	0.847535	−	0.530739i	$-0.178085\pi$
$674$	−615.092	−	355.124i	−0.912600	−	0.526890i
$675$	507.595	+	444.941i	0.751993	+	0.659171i
$676$	701.744	+	1215.46i	1.03808	+	1.79801i
$677$	−104.239	+	180.546i	−0.153971	+	0.266686i	−0.932684	−	0.360695i	$-0.882540\pi$
$677$	−104.239	+	180.546i	−0.153971	+	0.266686i	0.778713	+	0.627381i	$0.215873\pi$
$678$	158.583	+	18.9737i	0.233898	+	0.0279848i
$679$	64.5474	−	70.6701i	0.0950624	−	0.104080i
$680$	−9.69907	−	27.2145i	−0.0142633	−	0.0400213i
$681$	−19.2098	+	25.6571i	−0.0282083	+	0.0376756i
$682$	373.925	−	215.886i	0.548278	−	0.316548i
$683$	585.959	+	1014.91i	0.857919	+	1.48596i	0.873910	+	0.486088i	$0.161576\pi$
$683$	585.959	+	1014.91i	0.857919	+	1.48596i	−0.0159906	+	0.999872i	$0.505090\pi$
$684$	298.853	−	313.328i	0.436919	−	0.458082i
$685$	136.663	+	383.461i	0.199508	+	0.559797i
$686$	−395.566	−	942.033i	−0.576626	−	1.37323i
$687$	480.709	+	57.5145i	0.699721	+	0.0837183i
$688$	427.214	+	246.652i	0.620950	+	0.358506i
$689$	−950.637	+	548.850i	−1.37973	+	0.796590i
$690$	−634.045	+	586.989i	−0.918906	+	0.850708i
$691$	−345.958	+	599.216i	−0.500662	+	0.867172i	0.499337	+	0.866408i	$0.333577\pi$
$691$	−345.958	+	599.216i	−0.500662	+	0.867172i	−1.00000		0.000764874i	$0.999757\pi$
$692$	−1094.19			−1.58120
$693$	214.880	−	144.650i	0.310072	−	0.208730i
$694$	−696.028			−1.00292
$695$	638.570	+	117.018i	0.918806	+	0.168371i
$696$	201.695	−	86.3517i	0.289791	−	0.124068i
$697$	−52.8563	+	30.5166i	−0.0758340	+	0.0437828i
$698$	−132.344	+	229.227i	−0.189605	+	0.328406i
$699$	533.649	+	63.8486i	0.763447	+	0.0913428i
$700$	−466.646	+	713.766i	−0.666637	+	1.01967i
$701$		−	128.303i		−	0.183028i	−0.995804	−	0.0915142i	$-0.970829\pi$
$701$		−	128.303i		−	0.183028i	0.995804	−	0.0915142i	$-0.0291707\pi$
$702$	1094.37	+	1326.08i	1.55894	+	1.88901i
$703$	−426.131	+	246.027i	−0.606161	+	0.349967i
$704$	−314.136	+	181.366i	−0.446215	+	0.257623i
$705$	549.438	+	170.153i	0.779345	+	0.241352i
$706$	1574.86			2.23069
$707$	−625.890	−	137.695i	−0.885276	−	0.194760i
$708$	44.2191	−	369.585i	0.0624563	−	0.522012i
$709$	−50.1663	+	86.8906i	−0.0707565	+	0.122554i	−0.899233	−	0.437470i	$-0.855875\pi$
$709$	−50.1663	+	86.8906i	−0.0707565	+	0.122554i	0.828477	+	0.560024i	$0.189208\pi$
$710$	−135.541	−	115.290i	−0.190903	−	0.162381i
$711$	163.156	+	555.984i	0.229474	+	0.781975i
$712$	302.677	+	174.751i	0.425109	+	0.245437i
$713$	681.738			0.956155
$714$	−45.7808	+	131.242i	−0.0641187	+	0.183813i
$715$	147.540	+	413.981i	0.206350	+	0.578994i
$716$	−1126.43	−	650.343i	−1.57322	−	0.908301i
$717$	−1034.25	+	442.793i	−1.44246	+	0.617564i
$718$	−218.438	+	126.115i	−0.304231	+	0.175648i
$719$	142.417	+	82.2245i	0.198077	+	0.114360i	0.595758	−	0.803164i	$-0.296852\pi$
$719$	142.417	+	82.2245i	0.198077	+	0.114360i	−0.397681	+	0.917524i	$0.630185\pi$
$720$	54.9778	+	525.702i	0.0763581	+	0.730141i
$721$	5.19462	+	16.3828i	0.00720475	+	0.0227224i
$722$	784.974			1.08722
$723$	153.858	−	205.496i	0.212805	−	0.284227i
$724$	576.943	+	999.294i	0.796882	+	1.38024i
$725$	249.315	−	657.416i	0.343883	−	0.906780i
$726$	557.518	−	744.634i	0.767932	−	1.02567i
$727$		−	1029.30i		−	1.41581i	−0.706307	−	0.707906i	$-0.749640\pi$
$727$		−	1029.30i		−	1.41581i	0.706307	−	0.707906i	$-0.250360\pi$
$728$	−262.434	+	287.327i	−0.360486	+	0.394680i
$729$	550.714	+	477.656i	0.755437	+	0.655221i
$730$	274.880	−	1500.03i	0.376548	−	2.05483i
$731$	−80.8185	+	46.6606i	−0.110559	+	0.0638311i
$732$	−393.350	−	918.761i	−0.537364	−	1.25514i
$733$	405.750	+	234.260i	0.553547	+	0.319591i	0.750552	−	0.660812i	$-0.229788\pi$
$733$	405.750	+	234.260i	0.553547	+	0.319591i	−0.197004	+	0.980403i	$0.563121\pi$
$734$		−	836.361i		−	1.13946i
$735$	699.113	−	226.862i	0.951174	−	0.308656i
$736$	−877.746			−1.19259
$737$	−140.452	+	243.270i	−0.190573	+	0.330081i
$738$	−706.563	+	207.344i	−0.957403	+	0.280954i
$739$	62.6200	+	108.461i	0.0847361	+	0.146767i	0.905279	−	0.424818i	$-0.139662\pi$
$739$	62.6200	+	108.461i	0.0847361	+	0.146767i	−0.820543	+	0.571585i	$0.806329\pi$
$740$	−218.877	+	1194.42i	−0.295780	+	1.61408i
$741$	75.2218	−	628.707i	0.101514	−	0.848457i
$742$	−790.542	−	722.051i	−1.06542	−	0.973115i
$743$	−1032.44			−1.38956			−0.694781	−	0.719221i	$-0.744499\pi$
$743$	−1032.44			−1.38956			−0.694781	+	0.719221i	$0.744499\pi$
$744$	−164.833	+	220.155i	−0.221550	+	0.295907i
$745$	754.413	+	641.698i	1.01264	+	0.861340i
$746$	733.036	−	423.219i	0.982622	−	0.567317i
$747$	762.738	−	799.682i	1.02107	−	1.07052i
$748$		−	44.5205i		−	0.0595194i
$749$	−105.992	+	33.6076i	−0.141511	+	0.0448700i
$750$	−880.529	−	687.337i	−1.17404	−	0.916450i
$751$	−302.532	+	524.001i	−0.402839	+	0.697738i	−0.994067	−	0.108766i	$-0.965310\pi$
$751$	−302.532	+	524.001i	−0.402839	+	0.697738i	0.591228	+	0.806504i	$0.298643\pi$
$752$	225.202	+	390.062i	0.299471	+	0.518699i
$753$	152.522	−	65.2996i	0.202553	−	0.0867192i
$754$	895.465	−	1550.99i	1.18762	−	2.05702i
$755$	−279.307	−	783.702i	−0.369942	−	1.03802i
$756$	−499.931	+	773.498i	−0.661284	+	1.02315i
$757$			586.645i			0.774960i	0.921878	+	0.387480i	$0.126654\pi$
$757$			586.645i			0.774960i	−0.921878	+	0.387480i	$0.873346\pi$
$758$	447.828	−	775.661i	0.590802	−	1.02330i
$759$	−219.278	+	93.8795i	−0.288903	+	0.123688i
$760$	−83.1714	+	97.7806i	−0.109436	+	0.128659i
$761$	−144.343	−	83.3364i	−0.189675	−	0.109509i	0.402155	−	0.915571i	$-0.368261\pi$
$761$	−144.343	−	83.3364i	−0.189675	−	0.109509i	−0.591831	+	0.806062i	$0.701595\pi$
$762$	79.8200	−	667.139i	0.104751	−	0.875510i
$763$	−36.6212	+	166.461i	−0.0479964	+	0.218166i
$764$			458.851i			0.600590i
$765$	−91.3265	−	40.7179i	−0.119381	−	0.0532260i
$766$	−1030.68	−	1785.19i	−1.34553	−	2.33053i
$767$	−272.157	−	471.389i	−0.354833	−	0.614589i
$768$	−199.436	+	266.371i	−0.259682	+	0.346837i
$769$	−894.950			−1.16378			−0.581892	−	0.813266i	$-0.697687\pi$
$769$	−894.950			−1.16378			−0.581892	+	0.813266i	$0.697687\pi$
$770$	−341.403	+	259.218i	−0.443381	+	0.336647i
$771$	478.300	+	57.2264i	0.620364	+	0.0742236i
$772$	1160.25	+	669.868i	1.50291	+	0.867705i
$773$	−181.254	−	313.941i	−0.234481	−	0.406133i	0.724641	−	0.689127i	$-0.242006\pi$
$773$	−181.254	−	313.941i	−0.234481	−	0.406133i	−0.959122	+	0.282994i	$0.908672\pi$
$774$	−1080.35	+	317.033i	−1.39580	+	0.409604i
$775$	141.390	+	869.936i	0.182439	+	1.12250i
$776$		−	35.5554i		−	0.0458188i
$777$	792.635	−	683.457i	1.02012	−	0.879611i
$778$			1961.66i			2.52141i
$779$	234.850	+	135.591i	0.301476	+	0.174057i
$780$	−1061.56	−	1146.66i	−1.36098	−	1.47008i
$781$	−24.5615	−	42.5417i	−0.0314487	−	0.0544708i
$782$	63.9982	−	110.848i	0.0818392	−	0.141750i
$783$	265.536	−	711.410i	0.339126	−	0.908570i
$784$	522.411	+	241.551i	0.666341	+	0.308101i
$785$	626.818	−	223.394i	0.798494	−	0.284578i
$786$	1574.39	+	1178.77i	2.00304	+	1.49971i
$787$	−626.990	+	361.993i	−0.796683	+	0.459965i	−0.842310	−	0.538993i	$-0.818805\pi$
$787$	−626.990	+	361.993i	−0.796683	+	0.459965i	0.0456267	+	0.998959i	$0.485472\pi$
$788$	76.9522	+	133.285i	0.0976551	+	0.169144i
$789$	−504.219	+	673.446i	−0.639061	+	0.853544i
$790$	−321.905	−	903.229i	−0.407475	−	1.14333i
$791$	92.3756	+	84.3723i	0.116783	+	0.106665i
$792$	22.7011	−	93.5103i	0.0286630	−	0.118069i
$793$	−1265.69	−	730.749i	−1.59608	−	0.921499i
$794$	1144.70	−	660.892i	1.44169	−	0.832358i
$795$	565.191	−	523.245i	0.710933	−	0.658170i
$796$	−371.776	+	643.935i	−0.467056	+	0.808964i
$797$	−1004.54			−1.26041			−0.630203	−	0.776431i	$-0.717028\pi$
$797$	−1004.54			−1.26041			−0.630203	+	0.776431i	$0.717028\pi$
$798$	606.715	−	115.407i	0.760294	−	0.144620i
$799$	−85.2056			−0.106640
$800$	−182.041	−	1120.05i	−0.227552	−	1.40007i
$801$	1160.68	−	340.606i	1.44904	−	0.425227i
$802$	1291.58	−	745.692i	1.61044	−	0.929790i
$803$	210.498	−	364.593i	0.262139	−	0.454038i
$804$	118.651	−	991.692i	0.147576	−	1.23345i
$805$	−671.476	+	84.9270i	−0.834132	+	0.105499i
$806$			2244.96i			2.78531i
$807$	−306.133	−	229.206i	−0.379347	−	0.284023i
$808$	−206.174	+	119.035i	−0.255166	+	0.147320i
$809$	258.960	−	149.510i	0.320099	−	0.184809i	−0.331338	−	0.943512i	$-0.607500\pi$
$809$	258.960	−	149.510i	0.320099	−	0.184809i	0.651437	+	0.758703i	$0.274167\pi$
$810$	−954.848	−	737.330i	−1.17883	−	0.910284i
$811$	1055.66			1.30168			0.650840	−	0.759215i	$-0.274417\pi$
$811$	1055.66			1.30168			0.650840	+	0.759215i	$0.274417\pi$
$812$	936.933	+	206.125i	1.15386	+	0.253848i
$813$	−342.647	−	40.9961i	−0.421460	−	0.0504257i
$814$	−305.197	+	528.616i	−0.374934	+	0.649405i
$815$	199.121	+	169.371i	0.244320	+	0.207817i
$816$	−30.8173	−	71.9810i	−0.0377663	−	0.0882119i
$817$	359.091	+	207.321i	0.439524	+	0.253759i
$818$	−780.662			−0.954354
$819$	92.7091	+	1343.61i	0.113198	+	1.64055i
$820$	630.393	−	224.668i	0.768772	−	0.273986i
$821$	362.090	+	209.053i	0.441035	+	0.254632i	0.704037	−	0.710164i	$-0.251379\pi$
$821$	362.090	+	209.053i	0.441035	+	0.254632i	−0.263001	+	0.964795i	$0.584712\pi$
$822$	−286.354	−	668.846i	−0.348362	−	0.813681i
$823$	157.639	−	91.0130i	0.191542	−	0.110587i	−0.401162	−	0.916007i	$-0.631394\pi$
$823$	157.639	−	91.0130i	0.191542	−	0.110587i	0.592704	+	0.805420i	$0.298060\pi$
$824$	5.52924	+	3.19231i	0.00671024	+	0.00387416i
$825$	−165.273	−	260.340i	−0.200331	−	0.315564i
$826$	358.041	−	392.004i	0.433464	−	0.474581i
$827$	−178.479			−0.215815			−0.107907	−	0.994161i	$-0.534415\pi$
$827$	−178.479			−0.215815			−0.107907	+	0.994161i	$0.534415\pi$
$828$	585.353	−	613.705i	0.706948	−	0.741189i
$829$	−376.888	−	652.789i	−0.454630	−	0.787442i	0.544037	−	0.839061i	$-0.316895\pi$
$829$	−376.888	−	652.789i	−0.454630	−	0.787442i	−0.998667	+	0.0516193i	$0.983562\pi$
$830$	−1184.90	+	1393.03i	−1.42759	+	1.67835i
$831$	−485.889	−	363.792i	−0.584704	−	0.437777i
$832$		−	1886.00i		−	2.26682i
$833$	−88.9874	+	62.7394i	−0.106828	+	0.0753173i
$834$	−1152.07	−	137.840i	−1.38138	−	0.165276i
$835$	−363.676	−	66.6436i	−0.435540	−	0.0798127i
$836$	−171.311	+	98.9063i	−0.204917	+	0.118309i
$837$	157.623	+	938.717i	0.188319	+	1.12153i
$838$	241.694	+	139.542i	0.288417	+	0.166518i
$839$			1038.70i			1.23803i	0.785380	+	0.619013i	$0.212467\pi$
$839$			1038.70i			1.23803i	−0.785380	+	0.619013i	$0.787533\pi$
$840$	134.927	−	237.375i	0.160627	−	0.282590i
$841$	50.0343			0.0594938
$842$	−7.56398	+	13.1012i	−0.00898335	+	0.0155596i
$843$	−859.418	+	367.943i	−1.01948	+	0.436469i
$844$	−497.698	−	862.037i	−0.589689	−	1.02137i
$845$	−1416.48	−	259.571i	−1.67631	−	0.307184i
$846$	−998.980	−	242.518i	−1.18083	−	0.286664i
$847$	694.583	−	220.236i	0.820051	−	0.260019i
$848$	603.126			0.711233
$849$	−190.682	−	142.766i	−0.224596	−	0.168158i
$850$	154.721	+	58.6758i	0.182025	+	0.0690303i
$851$	−834.648	+	481.884i	−0.980785	+	0.566257i
$852$	139.813	+	104.680i	0.164100	+	0.122864i
$853$			173.353i			0.203228i	0.994824	+	0.101614i	$0.0324006\pi$
$853$			173.353i			0.203228i	−0.994824	+	0.101614i	$0.967599\pi$
$854$	306.284	−	1392.20i	0.358646	−	1.63021i
$855$	46.2112	+	441.874i	0.0540482	+	0.516812i
$856$	−20.6533	+	35.7725i	−0.0241276	+	0.0417903i
$857$	426.331	+	738.427i	0.497469	+	0.861642i	0.999996	−	0.00291972i	$-0.000929376\pi$
$857$	426.331	+	738.427i	0.497469	+	0.861642i	−0.502526	+	0.864562i	$0.667596\pi$
$858$	−309.145	−	722.079i	−0.360308	−	0.841584i
$859$	−73.2006	+	126.787i	−0.0852161	+	0.147599i	−0.905483	−	0.424382i	$-0.860491\pi$
$859$	−73.2006	+	126.787i	−0.0852161	+	0.147599i	0.820267	+	0.571981i	$0.193825\pi$
$860$	963.886	−	343.523i	1.12080	−	0.399445i
$861$	−544.624	−	189.979i	−0.632548	−	0.220649i
$862$			1359.82i			1.57752i
$863$	−710.754	+	1231.06i	−0.823585	+	1.42649i	0.0794101	+	0.996842i	$0.474696\pi$
$863$	−710.754	+	1231.06i	−0.823585	+	1.42649i	−0.902996	+	0.429650i	$0.858637\pi$
$864$	−202.941	−	1208.61i	−0.234886	−	1.39885i
$865$	727.415	−	855.186i	0.840942	−	0.988654i
$866$	910.636	+	525.756i	1.05154	+	0.607109i
$867$	−846.153	−	101.238i	−0.975955	−	0.116768i
$868$	−1146.30	+	363.466i	−1.32063	+	0.418740i
$869$		−	264.709i		−	0.304613i
$870$	−371.740	+	1200.38i	−0.427287	+	1.37975i
$871$	−730.267	−	1264.86i	−0.838424	−	1.45219i
$872$	31.6583	+	54.8338i	0.0363054	+	0.0628828i
$873$	−89.0472	−	84.9334i	−0.102001	−	0.0972891i
$874$	−568.712			−0.650700
$875$	−247.633	−	839.227i	−0.283009	−	0.959117i
$876$	−177.825	+	1486.27i	−0.202996	+	1.69665i
$877$	9.68130	+	5.58950i	0.0110391	+	0.00637343i	0.505509	−	0.862821i	$-0.331305\pi$
$877$	9.68130	+	5.58950i	0.0110391	+	0.00637343i	−0.494470	+	0.869195i	$0.664638\pi$
$878$	988.067	+	1711.38i	1.12536	+	1.94918i
$879$	−190.314	−	444.523i	−0.216512	−	0.505714i
$880$	43.5253	−	237.518i	0.0494605	−	0.269907i
$881$			1653.70i			1.87707i	0.345189	+	0.938533i	$0.387815\pi$
$881$			1653.70i			1.87707i	−0.345189	+	0.938533i	$0.612185\pi$
$882$	−1221.89	+	482.296i	−1.38536	+	0.546820i
$883$			1610.65i			1.82406i	0.410123	+	0.912030i	$0.365486\pi$
$883$			1610.65i			1.82406i	−0.410123	+	0.912030i	$0.634514\pi$
$884$	200.468	+	115.740i	0.226774	+	0.130928i
$885$	259.460	+	280.260i	0.293175	+	0.316678i
$886$	−71.8871	−	124.512i	−0.0811366	−	0.140533i
$887$	15.0891	−	26.1350i	0.0170113	−	0.0294645i	−0.857394	−	0.514660i	$-0.827918\pi$
$887$	15.0891	−	26.1350i	0.0170113	−	0.0294645i	0.874406	+	0.485195i	$0.161252\pi$
$888$	46.1886	−	386.046i	0.0520142	−	0.434737i
$889$	354.944	−	388.613i	0.399263	−	0.437135i
$890$	−1885.59	+	672.014i	−2.11865	+	0.755072i
$891$	−179.966	−	280.228i	−0.201982	−	0.314509i
$892$	−239.068	+	138.026i	−0.268013	+	0.154737i
$893$	189.292	+	327.864i	0.211973	+	0.367148i
$894$	−1416.97	−	1060.90i	−1.58497	−	1.18669i
$895$	1257.14	−	448.036i	1.40462	−	0.500599i
$896$	542.024	−	171.863i	0.604937	−	0.191812i
$897$	147.334	−	1231.43i	0.164252	−	1.37283i
$898$	1632.99	+	942.805i	1.81847	+	1.04989i
$899$	858.654	−	495.744i	0.955121	−	0.551440i
$900$	904.521	+	619.662i	1.00502	+	0.688513i
$901$	−57.0484	+	98.8107i	−0.0633168	+	0.109668i
$902$	336.401			0.372950
$903$	−832.742	−	290.482i	−0.922195	−	0.321686i
$904$	46.4758			0.0514113
$905$	−1164.57	−	213.407i	−1.28682	−	0.235809i
$906$	585.237	+	1366.96i	0.645957	+	1.50878i
$907$	265.679	−	153.390i	0.292921	−	0.169118i	−0.346338	−	0.938110i	$-0.612575\pi$
$907$	265.679	−	153.390i	0.292921	−	0.169118i	0.639258	+	0.768992i	$0.279241\pi$
$908$	−26.0311	+	45.0872i	−0.0286686	+	0.0496555i
$909$	−194.383	+	800.702i	−0.213843	+	0.880861i
$910$	−279.664	−	2211.17i	−0.307323	−	2.42985i
$911$		−	722.972i		−	0.793602i	−0.917905	−	0.396801i	$-0.870120\pi$
$911$		−	722.972i		−	0.793602i	0.917905	−	0.396801i	$-0.129880\pi$
$912$	−208.513	+	278.494i	−0.228632	+	0.305367i
$913$	−437.223	+	252.431i	−0.478886	+	0.276485i
$914$	1329.96	−	767.852i	1.45510	−	0.840101i
$915$	979.576	+	303.360i	1.07057	+	0.331541i
$916$	786.397			0.858512
$917$	465.650	+	1468.57i	0.507797	+	1.60149i
$918$	167.429	+	62.4932i	0.182384	+	0.0680754i
$919$	755.087	−	1307.85i	0.821639	−	1.42312i	−0.0828212	−	0.996564i	$-0.526393\pi$
$919$	755.087	−	1307.85i	0.821639	−	1.42312i	0.904461	−	0.426557i	$-0.140274\pi$
$920$	−162.905	+	191.520i	−0.177071	+	0.208173i
$921$	591.058	−	253.050i	0.641756	−	0.274756i
$922$	−1493.71	−	862.393i	−1.62007	−	0.935351i
$923$	255.410			0.276717
$924$	318.651	−	274.760i	0.344860	−	0.297359i
$925$	−788.014	−	965.116i	−0.851907	−	1.04337i
$926$	−49.6021	−	28.6378i	−0.0535660	−	0.0309263i
$927$	21.2031	−	6.22212i	0.0228728	−	0.00671210i
$928$	−1105.53	+	638.276i	−1.19130	+	0.687798i
$929$	−591.787	−	341.668i	−0.637015	−	0.367781i	0.146449	−	0.989218i	$-0.453216\pi$
$929$	−591.787	−	341.668i	−0.637015	−	0.367781i	−0.783464	+	0.621437i	$0.786549\pi$
$930$	−348.796	−	1536.09i	−0.375049	−	1.65171i
$931$	439.109	+	203.034i	0.471653	+	0.218082i
$932$	873.003			0.936699
$933$	986.385	+	738.521i	1.05722	+	0.791555i
$934$	697.441	+	1208.00i	0.746725	+	1.29337i
$935$	34.7959	+	29.5972i	0.0372149	+	0.0316547i
$936$	362.044	+	345.318i	0.386799	+	0.368930i
$937$			1295.06i			1.38214i	0.722789	+	0.691069i	$0.242860\pi$
$937$			1295.06i			1.38214i	−0.722789	+	0.691069i	$0.757140\pi$
$938$	960.718	−	1051.85i	1.02422	−	1.12137i
$939$	−163.698	+	1368.19i	−0.174332	+	1.45707i
$940$	918.982	+	168.403i	0.977640	+	0.179153i
$941$	520.118	−	300.290i	0.552729	−	0.319118i	−0.197493	−	0.980304i	$-0.563280\pi$
$941$	520.118	−	300.290i	0.552729	−	0.319118i	0.750222	+	0.661186i	$0.229947\pi$
$942$	−1093.32	+	468.083i	−1.16063	+	0.496903i
$943$	459.993	+	265.577i	0.487797	+	0.281630i
$944$			299.070i			0.316812i
$945$	−272.190	−	904.952i	−0.288032	−	0.957621i
$946$	514.365			0.543726
$947$	−35.1356	+	60.8566i	−0.0371020	+	0.0642625i	−0.883980	−	0.467524i	$-0.845146\pi$
$947$	−35.1356	+	60.8566i	−0.0371020	+	0.0642625i	0.846878	+	0.531787i	$0.178479\pi$
$948$	370.428	+	865.222i	0.390747	+	0.912681i
$949$	1094.46	+	1895.67i	1.15328	+	1.99754i
$950$	−117.949	−	725.707i	−0.124157	−	0.763903i
$951$	−656.744	−	78.5763i	−0.690582	−	0.0826249i
$952$	−8.69062	+	39.5030i	−0.00912881	+	0.0414947i
$953$	−751.223			−0.788272			−0.394136	−	0.919052i	$-0.628956\pi$
$953$	−751.223			−0.788272			−0.394136	+	0.919052i	$0.628956\pi$
$954$	−950.097	+	996.115i	−0.995908	+	1.04415i
$955$	−358.625	−	305.044i	−0.375523	−	0.319417i
$956$	−1582.62	+	913.723i	−1.65546	+	0.955778i
$957$	−207.915	+	277.695i	−0.217257	+	0.290173i
$958$			1070.50i			1.11743i
$959$	122.454	−	556.610i	0.127689	−	0.580407i
$960$	293.024	+	1290.48i	0.305233	+	1.34425i
$961$	−140.923	+	244.087i	−0.146642	+	0.253992i
$962$	−1586.84	−	2748.49i	−1.64952	−	2.85706i
$963$	40.2552	+	137.177i	0.0418019	+	0.142448i
$964$	208.492	−	361.119i	0.216278	−	0.374604i
$965$	−1294.88	+	461.487i	−1.34184	+	0.478225i
$966$	1188.35	−	226.043i	1.23018	−	0.233999i
$967$		−	1186.31i		−	1.22680i	−0.789774	−	0.613398i	$-0.789802\pi$
$967$		−	1186.31i		−	1.22680i	0.789774	−	0.613398i	$-0.210198\pi$
$968$	135.344	−	234.423i	0.139818	−	0.242173i
$969$	−25.9032	−	60.5030i	−0.0267319	−	0.0624386i
$970$	155.118	+	131.942i	0.159916	+	0.136023i
$971$	−288.814	−	166.747i	−0.297439	−	0.171727i	0.343853	−	0.939024i	$-0.388268\pi$
$971$	−288.814	−	166.747i	−0.297439	−	0.171727i	−0.641292	+	0.767297i	$0.721601\pi$
$972$	980.377	+	664.106i	1.00862	+	0.683237i
$973$	−671.092	−	612.950i	−0.689714	−	0.629959i
$974$			987.614i			1.01398i
$975$	1601.92	−	67.3866i	1.64300	−	0.0691144i
$976$	401.506	+	695.429i	0.411379	+	0.712530i
$977$	−544.752	−	943.538i	−0.557576	−	0.965750i	−0.997698	−	0.0678121i	$-0.978398\pi$
$977$	−544.752	−	943.538i	−0.557576	−	0.965750i	0.440122	−	0.897938i	$-0.354935\pi$
$978$	−373.996	−	280.016i	−0.382409	−	0.286315i
$979$	−552.611			−0.564465
$980$	1083.77	−	500.795i	1.10589	−	0.511015i
$981$	212.954	+	51.6978i	0.217078	+	0.0526991i
$982$	−265.209	−	153.119i	−0.270070	−	0.155925i
$983$	−49.3566	−	85.4881i	−0.0502101	−	0.0869665i	0.839828	−	0.542853i	$-0.182656\pi$
$983$	−49.3566	−	85.4881i	−0.0502101	−	0.0869665i	−0.890038	+	0.455886i	$0.849322\pi$
$984$	−196.982	+	84.3342i	−0.200185	+	0.0857055i
$985$	−155.329	−	28.4641i	−0.157695	−	0.0288976i
$986$		−	186.152i		−	0.188795i
$987$	−525.850	−	609.850i	−0.532776	−	0.617883i
$988$		−	1028.51i		−	1.04100i
$989$	703.340	+	406.073i	0.711163	+	0.410590i
$990$	323.718	+	446.046i	0.326988	+	0.450551i
$991$	−405.029	−	701.531i	−0.408708	−	0.707902i	0.586038	−	0.810284i	$-0.300687\pi$
$991$	−405.029	−	701.531i	−0.408708	−	0.707902i	−0.994745	+	0.102382i	$0.967354\pi$
$992$	800.090	−	1385.80i	0.806542	−	1.39697i
$993$	1387.39	+	165.995i	1.39717	+	0.167165i
$994$	75.2954	+	237.467i	0.0757499	+	0.238901i
$995$	−256.125	−	718.657i	−0.257412	−	0.722268i
$996$	1075.85	−	1436.93i	1.08017	−	1.44270i
$997$	47.3741	−	27.3514i	0.0475166	−	0.0274337i	−0.476054	−	0.879416i	$-0.657933\pi$
$997$	47.3741	−	27.3514i	0.0475166	−	0.0274337i	0.523570	+	0.851983i	$0.324600\pi$
$998$	−1381.31	−	2392.49i	−1.38408	−	2.39729i
$999$	−856.506	−	1037.85i	−0.857363	−	1.03889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.o.a.44.8	yes	16
3.2	odd	2	inner	105.3.o.a.44.2	yes	16
5.4	even	2	inner	105.3.o.a.44.1	✓	16
7.4	even	3	inner	105.3.o.a.74.7	yes	16
15.14	odd	2	inner	105.3.o.a.44.7	yes	16
21.11	odd	6	inner	105.3.o.a.74.1	yes	16
35.4	even	6	inner	105.3.o.a.74.2	yes	16
105.74	odd	6	inner	105.3.o.a.74.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.a.44.1	✓	16	5.4	even	2	inner
105.3.o.a.44.2	yes	16	3.2	odd	2	inner
105.3.o.a.44.7	yes	16	15.14	odd	2	inner
105.3.o.a.44.8	yes	16	1.1	even	1	trivial
105.3.o.a.74.1	yes	16	21.11	odd	6	inner
105.3.o.a.74.2	yes	16	35.4	even	6	inner
105.3.o.a.74.7	yes	16	7.4	even	3	inner
105.3.o.a.74.8	yes	16	105.74	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48938 - 2.57968i) q^{2} +(-1.18073 - 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(4.91811 + 0.901243i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} -2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +O(q^{10})\)	\(q+(1.48938 - 2.57968i) q^{2} +(-1.18073 - 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(4.91811 + 0.901243i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} -2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +(9.64983 - 11.3448i) q^{10} +(3.56075 - 2.05580i) q^{11} +(-8.76174 + 11.7024i) q^{12} +21.3779i q^{13} +(-19.8761 + 6.30224i) q^{14} +(-3.32145 - 14.6276i) q^{15} +(5.87298 - 10.1723i) q^{16} +(1.11103 + 1.92435i) q^{17} +(7.54882 + 25.7241i) q^{18} +(4.93649 - 8.55025i) q^{19} +(-8.17956 - 22.9509i) q^{20} +(-6.91662 + 19.8283i) q^{21} -12.2474i q^{22} +(9.66894 - 16.7471i) q^{23} +(3.07038 + 7.17159i) q^{24} +(23.3755 + 8.86482i) q^{25} +(55.1481 + 31.8397i) q^{26} +(25.2954 + 9.44157i) q^{27} +(-7.32910 + 33.3142i) q^{28} -28.1241i q^{29} +(-42.6815 - 13.2178i) q^{30} +(17.6270 + 30.5309i) q^{31} +(-22.6950 - 39.3089i) q^{32} +(-9.87393 - 7.39275i) q^{33} +6.61895 q^{34} +(-21.1650 - 27.8755i) q^{35} +(42.6190 + 10.3464i) q^{36} +(-43.1613 - 24.9192i) q^{37} +(-14.7046 - 25.4691i) q^{38} +(58.9575 - 25.2415i) q^{39} +(-12.7891 - 2.34360i) q^{40} +27.4670i q^{41} +(40.8491 + 47.3744i) q^{42} +41.9977i q^{43} +(-17.3515 - 10.0179i) q^{44} +(-36.4195 + 26.4315i) q^{45} +(-28.8014 - 49.8855i) q^{46} +(-19.1727 + 33.2081i) q^{47} +(-34.9884 - 4.18619i) q^{48} +(4.42843 + 48.7995i) q^{49} +(57.6833 - 47.0983i) q^{50} +(3.99530 - 5.33622i) q^{51} +(90.2174 - 52.0870i) q^{52} +(25.6737 + 44.4682i) q^{53} +(62.0306 - 51.1919i) q^{54} +(19.3649 - 6.90154i) q^{55} +(13.4404 + 12.2759i) q^{56} +(-29.4092 - 3.51867i) q^{57} +(-72.5511 - 41.8874i) q^{58} +(-22.0503 + 12.7308i) q^{59} +(-53.6378 + 49.6571i) q^{60} +(-34.1825 + 59.2058i) q^{61} +105.013 q^{62} +(62.8506 - 4.33668i) q^{63} -88.2218 q^{64} +(-19.2667 + 105.139i) q^{65} +(-33.7769 + 14.4609i) q^{66} +(-59.1667 + 34.1599i) q^{67} +(5.41401 - 9.37734i) q^{68} +(-57.6028 - 6.89190i) q^{69} +(-103.432 + 13.0819i) q^{70} -11.9474i q^{71} +(16.1530 - 16.9354i) q^{72} +(88.6742 - 51.1961i) q^{73} +(-128.567 + 74.2282i) q^{74} +(-3.15216 - 74.9337i) q^{75} -48.1109 q^{76} +(-28.1090 - 6.18396i) q^{77} +(22.6950 - 189.686i) q^{78} +(32.1905 - 55.7556i) q^{79} +(38.0517 - 44.7355i) q^{80} +(-3.82841 - 80.9095i) q^{81} +(70.8561 + 40.9088i) q^{82} -122.790 q^{83} +(100.530 - 19.1224i) q^{84} +(3.72983 + 10.4655i) q^{85} +(108.341 + 62.5505i) q^{86} +(-77.5628 + 33.2070i) q^{87} +(-9.25939 + 5.34591i) q^{88} +(-116.396 - 67.2014i) q^{89} +(13.9423 + 133.317i) q^{90} +(100.920 - 110.493i) q^{91} -94.2332 q^{92} +(63.3876 - 84.6619i) q^{93} +(57.1109 + 98.9190i) q^{94} +(31.9840 - 37.6021i) q^{95} +(-81.6123 + 109.003i) q^{96} +13.6730i q^{97} +(132.483 + 61.2569i) q^{98} +(-8.72983 + 35.9599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9	\( 16 q - 8 q^{4} - 80 q^{6} - 8 q^{9} - 40 q^{10} - 80 q^{15} + 32 q^{16} + 48 q^{19} - 8 q^{21} + 40 q^{30} + 344 q^{31} - 80 q^{34} + 496 q^{36} - 32 q^{39} + 120 q^{40} - 80 q^{45} - 120 q^{46} - 208 q^{49} - 40 q^{51} + 200 q^{54} + 40 q^{60} - 392 q^{61} - 544 q^{64} + 120 q^{66} - 240 q^{69} - 760 q^{70} + 200 q^{75} - 336 q^{76} + 608 q^{79} - 328 q^{81} - 344 q^{84} - 560 q^{85} + 80 q^{90} + 1088 q^{91} + 480 q^{94} - 400 q^{96} + 480 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 - 80 * q^6 - 8 * q^9 - 40 * q^10 - 80 * q^15 + 32 * q^16 + 48 * q^19 - 8 * q^21 + 40 * q^30 + 344 * q^31 - 80 * q^34 + 496 * q^36 - 32 * q^39 + 120 * q^40 - 80 * q^45 - 120 * q^46 - 208 * q^49 - 40 * q^51 + 200 * q^54 + 40 * q^60 - 392 * q^61 - 544 * q^64 + 120 * q^66 - 240 * q^69 - 760 * q^70 + 200 * q^75 - 336 * q^76 + 608 * q^79 - 328 * q^81 - 344 * q^84 - 560 * q^85 + 80 * q^90 + 1088 * q^91 + 480 * q^94 - 400 * q^96 + 480 * q^99

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