LMFDB - Embedded newform 105.3.o.a.44.1

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			44.1
Root			$2.22190 + 0.111032i$ of defining polynomial
Character	$\chi$	$=$	105.44
Dual form			105.3.o.a.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48938 + 2.57968i) q^{2} +(1.18073 + 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(3.23955 + 3.80858i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(5.16858 + 4.72078i) q^{7} +2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +O(q^{10})$	\(q+(-1.48938 + 2.57968i) q^{2} +(1.18073 + 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(3.23955 + 3.80858i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(5.16858 + 4.72078i) q^{7} +2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +(-14.6498 + 2.68458i) q^{10} +(3.56075 - 2.05580i) q^{11} +(8.76174 - 11.7024i) q^{12} -21.3779i q^{13} +(-19.8761 + 6.30224i) q^{14} +(-6.67855 + 13.4312i) 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} +(-4.01061 + 24.6762i) q^{25} +(55.1481 + 31.8397i) q^{26} +(-25.2954 - 9.44157i) q^{27} +(7.32910 - 33.3142i) q^{28} -28.1241i q^{29} +(-24.7013 - 37.2326i) q^{30} +(17.6270 + 30.5309i) q^{31} +(22.6950 + 39.3089i) q^{32} +(9.87393 + 7.39275i) q^{33} +6.61895 q^{34} +(-1.23561 + 34.9782i) 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} +(8.42414 + 9.90385i) q^{40} +27.4670i q^{41} +(-40.8491 - 47.3744i) q^{42} -41.9977i q^{43} +(-17.3515 - 10.0179i) q^{44} +(-44.9271 - 2.55998i) 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} +(72.9536 - 4.54064i) q^{60} +(-34.1825 + 59.2058i) q^{61} -105.013 q^{62} +(-62.8506 + 4.33668i) q^{63} -88.2218 q^{64} +(81.4195 - 69.2548i) 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} +(-88.3922 - 55.2832i) q^{70} -11.9474i q^{71} +(-16.1530 + 16.9354i) q^{72} +(-88.6742 + 51.1961i) q^{73} +(-128.567 + 74.2282i) q^{74} +(-72.7893 + 18.0752i) q^{75} -48.1109 q^{76} +(28.1090 + 6.18396i) q^{77} +(-22.6950 + 189.686i) q^{78} +(32.1905 - 55.7556i) q^{79} +(57.7679 - 10.5860i) 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} +(73.5174 - 112.085i) q^{90} +(100.920 - 110.493i) q^{91} +94.2332 q^{92} +(-63.3876 + 84.6619i) q^{93} +(57.1109 + 98.9190i) q^{94} +(48.5564 - 8.89796i) 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	$0.434069\pi$
$2$	−1.48938	+	2.57968i	−0.744689	+	1.28984i	−0.950340	+	0.311214i	$0.899265\pi$
$3$	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
$5$	3.23955	+	3.80858i	0.647910	+	0.761717i
$5$	3.23955	+	3.80858i	0.647910	+	0.761717i
$6$	−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
$10$	−14.6498	+	2.68458i	−1.46498	+	0.268458i
$11$	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	$-0.692732\pi$
$13$		−	21.3779i		−	1.64445i	0.569160	−	0.822226i	$-0.307268\pi$
$14$	−19.8761	+	6.30224i	−1.41972	+	0.450160i
$15$	−6.67855	+	13.4312i	−0.445237	+	0.895413i
$16$	5.87298	−	10.1723i	0.367061	−	0.635769i
$17$	−1.11103	−	1.92435i	−0.0653545	−	0.113197i	0.831497	−	0.555530i	$-0.187484\pi$
$17$	−1.11103	−	1.92435i	−0.0653545	−	0.113197i	−0.896851	+	0.442332i	$0.854151\pi$
$18$	−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	−0.995977	−	0.0896047i	$-0.971440\pi$
$23$	−9.66894	+	16.7471i	−0.420389	+	0.728135i	0.575589	+	0.817739i	$0.304773\pi$
$24$	3.07038	+	7.17159i	0.127932	+	0.298816i
$25$	−4.01061	+	24.6762i	−0.160424	+	0.987048i
$26$	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	$-0.161143\pi$
$30$	−24.7013	−	37.2326i	−0.823375	−	1.24109i
$31$	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
$35$	−1.23561	+	34.9782i	−0.0353031	+	0.999377i
$36$	42.6190	+	10.3464i	1.18386	+	0.287401i
$37$	43.1613	+	24.9192i	1.16652	+	0.673492i	0.952858	−	0.303416i	$-0.0981270\pi$
$37$	43.1613	+	24.9192i	1.16652	+	0.673492i	0.213664	+	0.976907i	$0.431460\pi$
$38$	14.7046	+	25.4691i	0.386963	+	0.670240i
$39$	58.9575	−	25.2415i	1.51173	−	0.647219i
$40$	8.42414	+	9.90385i	0.210604	+	0.247596i
$41$			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	$-0.837601\pi$
$43$		−	41.9977i		−	0.976691i	0.872650	−	0.488346i	$-0.162399\pi$
$44$	−17.3515	−	10.0179i	−0.394352	−	0.227679i
$45$	−44.9271	−	2.55998i	−0.998381	−	0.0568885i
$46$	−28.8014	−	49.8855i	−0.626118	−	1.08447i
$47$	19.1727	−	33.2081i	0.407931	−	0.706556i	−0.586727	−	0.809785i	$-0.699584\pi$
$47$	19.1727	−	33.2081i	0.407931	−	0.706556i	0.994658	+	0.103228i	$0.0329172\pi$
$48$	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	0.515429	−	0.856932i	$-0.327632\pi$
$53$	−25.6737	−	44.4682i	−0.484410	−	0.839023i	−0.999840	+	0.0179089i	$0.994299\pi$
$54$	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	$0.402561\pi$
$60$	72.9536	−	4.54064i	1.21589	−	0.0756774i
$61$	−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
$65$	81.4195	−	69.2548i	1.25261	−	1.06546i
$66$	−33.7769	+	14.4609i	−0.511772	+	0.219105i
$67$	59.1667	−	34.1599i	0.883086	−	0.509850i	0.0114110	−	0.999935i	$-0.496368\pi$
$67$	59.1667	−	34.1599i	0.883086	−	0.509850i	0.871675	+	0.490085i	$0.163034\pi$
$68$	−5.41401	+	9.37734i	−0.0796178	+	0.137902i
$69$	−57.6028	−	6.89190i	−0.834823	−	0.0998827i
$70$	−88.3922	−	55.2832i	−1.26275	−	0.789760i
$71$		−	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	−0.963783	−	0.266689i	$-0.914070\pi$
$73$	−88.6742	+	51.1961i	−1.21471	+	0.701316i	−0.250932	+	0.968005i	$0.580737\pi$
$74$	−128.567	+	74.2282i	−1.73739	+	1.00308i
$75$	−72.7893	+	18.0752i	−0.970524	+	0.241003i
$76$	−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	$0.0330760\pi$
$80$	57.7679	−	10.5860i	0.722099	−	0.132325i
$81$	−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	$-0.234969\pi$
$83$	122.790			1.47939			0.739696	+	0.672941i	$0.234969\pi$
$84$	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	$0.939065\pi$
$90$	73.5174	−	112.085i	0.816860	−	1.24539i
$91$	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
$95$	48.5564	−	8.89796i	0.511120	−	0.0936627i
$96$	−81.6123	+	109.003i	−0.850128	+	1.13545i
$97$		−	13.6730i		−	0.140959i	−0.997513	−	0.0704795i	$-0.977547\pi$
$97$		−	13.6730i		−	0.140959i	0.997513	−	0.0704795i	$-0.0224529\pi$
$98$	−132.483	−	61.2569i	−1.35186	−	0.625071i
$99$	−8.72983	+	35.9599i	−0.0881801	+	0.363231i
$100$	113.909	−	43.1981i	1.13909	−	0.431981i
$101$	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	0.510286	−	0.860005i	$-0.329539\pi$
$103$	2.12630	+	1.22762i	0.0206437	+	0.0119186i	−0.489643	+	0.871923i	$0.662873\pi$
$104$		−	55.5911i		−	0.534530i
$105$	−97.9244	+	37.8922i	−0.932613	+	0.360878i
$106$	152.952			1.44294
$107$	−7.94233	+	13.7565i	−0.0742274	+	0.128566i	−0.900750	−	0.434338i	$-0.856982\pi$
$107$	−7.94233	+	13.7565i	−0.0742274	+	0.128566i	0.826523	+	0.562903i	$0.190316\pi$
$108$	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	$0.868960\pi$
$110$	−46.6454	+	39.6762i	−0.424049	+	0.360693i
$111$	−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	$-0.474801\pi$
$113$	17.8725			0.158164			0.0790820	+	0.996868i	$0.474801\pi$
$114$	−52.8784	+	70.6256i	−0.463846	+	0.619523i
$115$	−95.1057	+	17.4281i	−0.827006	+	0.151549i
$116$	−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
$120$	−17.3669	+	34.9265i	−0.144724	+	0.291054i
$121$	−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	$-0.904342\pi$
$127$		−	75.1876i		−	0.592029i	0.955184	−	0.296014i	$-0.0956576\pi$
$128$	40.6156	−	70.3482i	0.317309	−	0.549596i
$129$	115.824	−	49.5880i	0.897864	−	0.384403i
$130$	57.3907	+	313.182i	0.441467	+	2.40910i
$131$	−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
$135$	−45.9868	−	126.926i	−0.340643	−	0.940193i
$136$	−2.88912	−	5.00410i	−0.0212435	−	0.0367948i
$137$	−40.7086	−	70.5094i	−0.297143	−	0.514667i	0.678338	−	0.734750i	$-0.262701\pi$
$137$	−40.7086	−	70.5094i	−0.297143	−	0.514667i	−0.975481	+	0.220083i	$0.929367\pi$
$138$	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	$0.345316\pi$
$140$	150.623	−	80.0096i	1.07588	−	0.571497i
$141$	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
$145$	107.113	−	91.1095i	0.738710	−	0.628342i
$146$		−	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	$0.435224\pi$
$150$	61.7826	−	214.694i	0.411884	−	1.43129i
$151$	−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	−0.819928	−	0.572467i	$-0.805986\pi$
$157$	−115.257	+	66.5436i	−0.734121	+	0.423845i	0.0858070	+	0.996312i	$0.472653\pi$
$158$	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	0.354640	−	0.935003i	$-0.384604\pi$
$163$	−45.2776	−	26.1411i	−0.277777	−	0.160375i	−0.632417	+	0.774628i	$0.717937\pi$
$164$	115.914	−	66.9232i	0.706795	−	0.408068i
$165$	3.83118	+	61.5549i	0.0232193	+	0.373060i
$166$	−182.880	+	316.757i	−1.10169	+	1.90818i
$167$	73.9464			0.442793			0.221396	−	0.975184i	$-0.428939\pi$
$167$	73.9464			0.442793			0.221396	+	0.975184i	$0.428939\pi$
$168$	−17.9860	+	51.5615i	−0.107060	+	0.306914i
$169$	−288.014			−1.70423
$170$	21.4424	+	25.2088i	0.126132	+	0.148287i
$171$	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	$0.391464\pi$
$173$	−112.271	+	194.459i	−0.648964	+	1.12404i	−0.983371	+	0.181610i	$0.941869\pi$
$174$	−29.8569	+	249.545i	−0.171591	+	1.43417i
$175$	−137.220	+	108.608i	−0.784115	+	0.620616i
$176$		−	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	$0.0655055\pi$
$180$	98.6611	+	195.836i	0.548117	+	1.08798i
$181$	−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
$185$	44.9165	+	245.110i	0.242792	+	1.32492i
$186$	−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	0.265874	−	0.964008i	$-0.414340\pi$
$193$	238.098	−	137.466i	1.23367	−	0.712257i	0.967792	+	0.251751i	$0.0810062\pi$
$194$	35.2720	+	20.3643i	0.181814	+	0.104971i
$195$	287.131	+	142.773i	1.47246	+	0.732171i
$196$	195.150	−	137.588i	0.995664	−	0.701980i
$197$	31.5832			0.160321			0.0801604	−	0.996782i	$-0.474457\pi$
$197$	31.5832			0.160321			0.0801604	+	0.996782i	$0.474457\pi$
$198$	−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	$0.958575\pi$
$200$	−10.4292	+	64.1681i	−0.0521460	+	0.320840i
$201$	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
$205$	−104.610	+	88.9809i	−0.510295	+	0.434053i
$206$	−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
$210$	48.0967	−	309.049i	0.229032	−	1.47166i
$211$	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
$215$	159.952	−	136.054i	0.743962	−	0.632808i
$216$	−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
$220$	−18.0571	−	98.5380i	−0.0820777	−	0.447900i
$221$	−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	$0.0405401\pi$
$223$			56.6494i			0.254033i	−0.991901	+	0.127017i	$0.959460\pi$
$224$	−68.2678	+	310.309i	−0.304767	+	1.38531i
$225$	−135.794	−	179.402i	−0.603528	−	0.797342i
$226$	−26.6190	+	46.1054i	−0.117783	+	0.204006i
$227$	5.34193	+	9.25249i	0.0235327	+	0.0407599i	0.877552	−	0.479482i	$-0.159175\pi$
$227$	5.34193	+	9.25249i	0.0235327	+	0.0407599i	−0.854019	+	0.520241i	$0.825842\pi$
$228$	−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	−0.607246	−	0.794514i	$-0.707726\pi$
$233$	89.5759	−	155.150i	0.384446	−	0.665880i	0.991692	+	0.128634i	$0.0410592\pi$
$234$	−549.926	+	161.378i	−2.35011	+	0.689649i
$235$	188.587	−	34.5586i	0.802498	−	0.147058i
$236$	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	$-0.287107\pi$
$240$	97.4032	+	146.817i	0.405846	+	0.611739i
$241$	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
$245$	−171.511	+	174.954i	−0.700044	+	0.714100i
$246$	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
$250$	−7.49060	−	372.269i	−0.0299624	−	1.48908i
$251$			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
$255$	33.2664	−	2.07051i	0.130457	−	0.00811963i
$256$	−55.4597	−	96.0590i	−0.216639	−	0.375230i
$257$	80.2853	−	139.058i	0.312394	−	0.541082i	−0.666486	−	0.745517i	$-0.732202\pi$
$257$	80.2853	−	139.058i	0.312394	−	0.541082i	0.978880	+	0.204435i	$0.0655357\pi$
$258$	−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	$0.0123198\pi$
$263$	140.215	+	242.859i	0.533136	+	0.923418i	−0.466115	+	0.884724i	$0.654347\pi$
$264$	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	$0.257187\pi$
$270$	395.920	+	70.4098i	1.46637	+	0.260777i
$271$	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
$275$	36.4486	+	96.1108i	0.132540	+	0.349494i
$276$	111.264	+	259.883i	0.403131	+	0.941606i
$277$	−175.222	+	101.165i	−0.632571	+	0.365215i	−0.781747	−	0.623596i	$-0.785671\pi$
$277$	−175.222	+	101.165i	−0.632571	+	0.365215i	0.149176	+	0.988811i	$0.452338\pi$
$278$	−193.382	+	334.947i	−0.695618	+	1.20485i
$279$	−308.331	−	74.8521i	−1.10513	−	0.268287i
$280$	−3.21308	+	90.9574i	−0.0114753	+	0.324848i
$281$		−	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	−0.616547	−	0.787318i	$-0.711469\pi$
$283$	−68.7640	+	39.7009i	−0.242982	+	0.140286i	0.373564	+	0.927604i	$0.378136\pi$
$284$	−50.4195	+	29.1097i	−0.177534	+	0.102499i
$285$	81.8715	+	123.406i	0.287268	+	0.433005i
$286$	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
$290$	75.5015	+	412.014i	0.260350	+	1.42074i
$291$	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	$-0.588697\pi$
$293$	−161.183			−0.550113			−0.275056	+	0.961428i	$0.588697\pi$
$294$	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
$300$	253.630	+	263.140i	0.845434	+	0.877134i
$301$	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
$305$	−336.226	+	61.6134i	−1.10238	+	0.202011i
$306$	−41.1152	+	43.1067i	−0.134364	+	0.140872i
$307$		−	214.316i		−	0.698099i	−0.937104	−	0.349049i	$-0.886505\pi$
$307$		−	214.316i		−	0.698099i	0.937104	−	0.349049i	$-0.113495\pi$
$308$	−42.3902	−	133.691i	−0.137631	−	0.434061i
$309$	−0.875033	+	7.31356i	−0.00283182	+	0.0236685i
$310$	−340.196	−	399.951i	−1.09740	−	1.29017i
$311$	−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	0.975150	−	0.221545i	$-0.0711100\pi$
$313$	397.780	+	229.658i	1.27086	+	0.733732i	0.295711	+	0.955277i	$0.404443\pi$
$314$		−	396.434i		−	1.26253i
$315$	−220.124	−	225.323i	−0.698807	−	0.715310i
$316$	−313.728			−0.992809
$317$	−110.238	+	190.938i	−0.347754	+	0.602327i	−0.985850	−	0.167629i	$-0.946389\pi$
$317$	−110.238	+	190.938i	−0.347754	+	0.602327i	0.638096	+	0.769957i	$0.279722\pi$
$318$	180.595	+	421.821i	0.567908	+	1.32648i
$319$	−57.8175	−	100.143i	−0.181246	−	0.313928i
$320$	−285.799	−	336.000i	−0.893122	−	1.05000i
$321$	−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
$325$	527.525	+	85.7383i	1.62315	+	0.263810i
$326$	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
$330$	−164.498	−	81.7952i	−0.498478	−	0.247864i
$331$	−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	$0.115099\pi$
$337$			238.438i			0.707530i	−0.935334	+	0.353765i	$0.884901\pi$
$338$	428.962	−	742.984i	1.26912	−	2.19818i
$339$	21.1027	+	49.2902i	0.0622497	+	0.145399i
$340$	−53.2534	+	9.75868i	−0.156628	+	0.0287020i
$341$	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
$345$	−160.359	−	241.712i	−0.464809	−	0.700614i
$346$	−334.427	−	579.245i	−0.966553	−	1.67412i
$347$	116.832	+	202.359i	0.336692	+	0.583167i	0.983808	−	0.179224i	$-0.0573586\pi$
$347$	116.832	+	202.359i	0.336692	+	0.583167i	−0.647117	+	0.762391i	$0.724025\pi$
$348$	−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	$0.540633\pi$
$350$	−75.8003	−	515.742i	−0.216572	−	1.47355i
$351$	−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	$-0.897266\pi$
$353$	−264.349	−	457.867i	−0.748865	−	1.29707i	0.199502	−	0.979898i	$-0.436068\pi$
$354$	209.167	−	89.5510i	0.590868	−	0.252969i
$355$	45.5027	−	38.7042i	0.128177	−	0.109026i
$356$			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	$0.704294\pi$
$360$	−116.829	−	6.65699i	−0.324524	−	0.0184916i
$361$	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	−0.793251	−	0.608895i	$-0.791613\pi$
$367$	−243.158	+	140.388i	−0.662557	+	0.382528i	0.130694	+	0.991423i	$0.458280\pi$
$368$	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	0.132429	−	0.991192i	$-0.457722\pi$
$373$	−246.088	−	142.079i	−0.659754	−	0.380909i	−0.792183	+	0.610284i	$0.791056\pi$
$374$	23.5684	−	13.6072i	0.0630172	−	0.0363830i
$375$	−304.646	−	218.669i	−0.812389	−	0.583116i
$376$	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	$0.370163\pi$
$380$	−155.858	−	183.234i	−0.410152	−	0.482195i
$381$	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	$0.525619\pi$
$383$	−346.010	+	599.307i	−0.903421	+	1.56477i	−0.823023	+	0.568007i	$0.807714\pi$
$384$	241.968	+	28.9503i	0.630124	+	0.0753914i
$385$	67.5084	+	127.089i	0.175347	+	0.330101i
$386$			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	$0.654607\pi$
$390$	−795.955	+	528.061i	−2.04091	+	1.35400i
$391$	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
$395$	316.633	−	58.0230i	0.801602	−	0.146894i
$396$	173.026	−	50.7750i	0.436933	−	0.128220i
$397$	−384.288	−	221.869i	−0.967979	−	0.558863i	−0.0693593	−	0.997592i	$-0.522095\pi$
$397$	−384.288	−	221.869i	−0.967979	−	0.558863i	−0.898619	+	0.438729i	$0.855429\pi$
$398$	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
$405$	295.748	−	276.691i	0.730242	−	0.683188i
$406$	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	$0.937146\pi$
$410$	−73.7375	−	402.387i	−0.179848	−	0.981433i
$411$	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
$415$	397.783	+	467.654i	0.958514	+	1.12688i
$416$	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	$0.964337\pi$
$420$	398.502	+	320.929i	0.948814	+	0.764117i
$421$	−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
$425$	51.9416	−	19.6981i	0.122216	−	0.0463484i
$426$	−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
$430$	112.746	+	615.260i	0.262201	+	1.43084i
$431$	−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	$-0.866357\pi$
$433$		−	353.004i		−	0.815251i	0.913149	−	0.407626i	$-0.133643\pi$
$434$	−542.769	−	495.744i	−1.25062	−	1.14227i
$435$	377.740	+	187.828i	0.868369	+	0.431789i
$436$	−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	−0.891978	−	0.452079i	$-0.850682\pi$
$443$	−24.1333	+	41.8000i	−0.0544769	+	0.0943567i	0.837501	+	0.546436i	$0.184016\pi$
$444$	669.782	−	286.754i	1.50852	−	0.645843i
$445$	−121.130	−	661.007i	−0.272201	−	1.48541i
$446$	−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	$0.750982\pi$
$450$	665.047	−	83.1072i	1.47788	−	0.184683i
$451$	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
$455$	747.760	+	26.4147i	1.64343	+	0.0580543i
$456$	76.4758	+	9.14997i	0.167710	+	0.0200657i
$457$	−446.482	−	257.776i	−0.976984	−	0.564062i	−0.0756257	−	0.997136i	$-0.524095\pi$
$457$	−446.482	−	257.776i	−0.976984	−	0.564062i	−0.901358	+	0.433074i	$0.857429\pi$
$458$	−240.354	−	416.306i	−0.524791	−	0.908965i
$459$	9.93493	+	59.1671i	0.0216447	+	0.128904i
$460$	305.273	+	358.895i	0.663638	+	0.780206i
$461$		−	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	$0.00661005\pi$
$463$			19.2280i			0.0415292i	−0.999784	+	0.0207646i	$0.993390\pi$
$464$	−286.087	−	165.172i	−0.616567	−	0.355975i
$465$	−527.789	+	32.8497i	−1.13503	+	0.0706445i
$466$	266.825	+	462.154i	0.572585	+	0.991746i
$467$	234.139	−	405.540i	0.501367	−	0.868394i	−0.498631	−	0.866814i	$-0.666164\pi$
$467$	234.139	−	405.540i	0.501367	−	0.868394i	0.999999	−	0.00157962i	$-0.000502808\pi$
$468$	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	$0.455737\pi$
$480$	−679.535	+	42.2943i	−1.41570	+	0.0881132i
$481$	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
$485$	52.0748	−	44.2945i	0.107371	−	0.0913288i
$486$	−51.9249	+	721.973i	−0.106841	+	1.48554i
$487$	287.133	−	165.776i	0.589596	−	0.340403i	−0.175342	−	0.984508i	$-0.556103\pi$
$487$	287.133	−	165.776i	0.589596	−	0.340403i	0.764938	+	0.644104i	$0.222770\pi$
$488$	−88.8882	+	153.959i	−0.182148	+	0.315489i
$489$	18.6330	−	155.736i	0.0381044	−	0.318478i
$490$	−195.882	−	703.016i	−0.399759	−	1.43473i
$491$		−	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
$495$	−165.237	+	83.2457i	−0.333812	+	0.168173i
$496$	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	$-0.212920\pi$
$500$	533.536	+	293.888i	1.06707	+	0.587775i
$501$	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	$-0.350394\pi$
$503$	455.605			0.905776			0.452888	+	0.891567i	$0.350394\pi$
$504$	−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	$0.759411\pi$
$510$	−44.2050	+	88.9004i	−0.0866765	+	0.174314i
$511$	−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
$515$	2.21277	+	12.0751i	0.00429664	+	0.0234468i
$516$	−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
$520$	211.723	−	180.090i	0.407161	−	0.346328i
$521$	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	0.0720905	−	0.997398i	$-0.477033\pi$
$523$	−395.198	−	228.168i	−0.755636	−	0.436267i	−0.827727	+	0.561131i	$0.810366\pi$
$524$			1072.49i			2.04674i
$525$	−461.547	−	250.199i	−0.879136	−	0.476570i
$526$	−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
$530$	495.495	+	582.529i	0.934896	+	1.09911i
$531$	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
$535$	−78.1224	+	14.3159i	−0.146023	+	0.0267588i
$536$	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
$540$	−423.598	+	503.324i	−0.784440	+	0.932082i
$541$	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	$0.0197840\pi$
$547$			67.9520i			0.124227i	−0.998069	+	0.0621133i	$0.980216\pi$
$548$	−198.373	+	343.591i	−0.361994	+	0.626991i
$549$	−173.252	−	590.388i	−0.315577	−	1.07539i
$550$	−302.221	−	49.1197i	−0.549492	−	0.0893085i
$551$	−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
$555$	−622.950	+	413.284i	−1.12243	+	0.744655i
$556$	−316.356	−	547.944i	−0.568985	−	0.985511i
$557$	59.6922	+	103.390i	0.107167	+	0.185619i	0.914622	−	0.404311i	$-0.132489\pi$
$557$	59.6922	+	103.390i	0.107167	+	0.185619i	−0.807454	+	0.589930i	$0.799155\pi$
$558$	652.315	−	683.911i	1.16902	−	1.22565i
$559$	−897.823			−1.60612
$560$	348.552	+	217.995i	0.622414	+	0.389277i
$561$	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	$0.139638\pi$
$563$	461.941	+	800.106i	0.820500	+	1.42115i	−0.0848112	+	0.996397i	$0.527029\pi$
$564$	−220.628	−	515.328i	−0.391184	−	0.913702i
$565$	57.8990	+	68.0690i	0.102476	+	0.120476i
$566$		−	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	$0.763811\pi$
$570$	−440.286	+	27.4035i	−0.772432	+	0.0480763i
$571$	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	−0.821033	−	0.570881i	$-0.806602\pi$
$577$	−425.337	+	245.568i	−0.737152	+	0.425595i	0.0838807	+	0.996476i	$0.473269\pi$
$578$	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
$585$	−54.7270	+	960.447i	−0.0935505	+	1.64179i
$586$	240.062	−	415.800i	0.409663	−	0.709557i
$587$	−328.125			−0.558987			−0.279493	−	0.960148i	$-0.590167\pi$
$587$	−328.125			−0.558987			−0.279493	+	0.960148i	$0.590167\pi$
$588$	609.871	+	375.745i	1.03719	+	0.639023i
$589$	348.062			0.590938
$590$	288.857	−	245.699i	0.489588	−	0.416440i
$591$	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	−0.980762	−	0.195206i	$-0.937462\pi$
$593$	−190.547	+	330.038i	−0.321328	+	0.556556i	0.659435	+	0.751762i	$0.270796\pi$
$594$	115.635	−	309.804i	0.194672	−	0.521556i
$595$	68.6832	−	36.4839i	0.115434	−	0.0613175i
$596$		−	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	$0.287828\pi$
$600$	−189.282	+	47.0029i	−0.315469	+	0.0783381i
$601$	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
$605$	−511.949	+	93.8147i	−0.846197	+	0.155066i
$606$	−752.095	+	321.995i	−1.24108	+	0.531345i
$607$	88.2380	+	50.9442i	0.145367	+	0.0839279i	0.570920	−	0.821006i	$-0.306587\pi$
$607$	88.2380	+	50.9442i	0.145367	+	0.0839279i	−0.425552	+	0.904934i	$0.639920\pi$
$608$	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	−0.998577	−	0.0533259i	$-0.983018\pi$
$613$	−889.882	+	513.774i	−1.45168	+	0.838130i	−0.453107	+	0.891456i	$0.649684\pi$
$614$	552.867	+	319.198i	0.900435	+	0.519866i
$615$	−368.915	−	183.440i	−0.599862	−	0.298276i
$616$	73.0948	+	16.0808i	0.118660	+	0.0261052i
$617$	−971.254			−1.57416			−0.787078	−	0.616853i	$-0.788407\pi$
$617$	−971.254			−1.57416			−0.787078	+	0.616853i	$0.788407\pi$
$618$	−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	$0.684238\pi$
$620$	844.893	−	154.827i	1.36273	−	0.249720i
$621$	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
$625$	−592.830	−	197.933i	−0.948528	−	0.316693i
$626$	−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
$630$	909.108	−	232.259i	1.44303	−	0.368665i
$631$	−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
$635$	286.358	−	243.574i	0.450958	−	0.383581i
$636$	−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
$640$	399.503	−	73.2090i	0.624224	−	0.114389i
$641$	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	$0.195476\pi$
$643$			741.031i			1.15246i	−0.817288	+	0.576229i	$0.804524\pi$
$644$	487.052	+	444.854i	0.756291	+	0.690768i
$645$	564.079	+	280.484i	0.874542	+	0.434859i
$646$	32.6744	−	56.5937i	0.0505796	−	0.0876064i
$647$	123.645	+	214.160i	0.191106	+	0.331005i	0.945617	−	0.325282i	$-0.105459\pi$
$647$	123.645	+	214.160i	0.191106	+	0.331005i	−0.754511	+	0.656287i	$0.772126\pi$
$648$	−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	−0.995081	−	0.0990692i	$-0.968413\pi$
$653$	−268.869	+	465.694i	−0.411744	+	0.713161i	0.583337	+	0.812230i	$0.301747\pi$
$654$	85.6374	+	200.026i	0.130944	+	0.305850i
$655$	−198.354	−	1082.42i	−0.302831	−	1.65255i
$656$	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	$0.937446\pi$
$660$	250.435	−	166.146i	0.379447	−	0.251736i
$661$	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
$665$	292.973	+	183.234i	0.440561	+	0.275540i
$666$	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
$670$	−775.078	+	659.275i	−1.15683	+	0.983993i
$671$			281.089i			0.418911i
$672$	−936.400	+	178.118i	−1.39345	+	0.265056i
$673$			714.374i			1.06148i	0.847535	+	0.530739i	$0.178085\pi$
$673$			714.374i			1.06148i	−0.847535	+	0.530739i	$0.821915\pi$
$674$	−615.092	−	355.124i	−0.912600	−	0.526890i
$675$	334.432	−	586.328i	0.495455	−	0.868634i
$676$	701.744	+	1215.46i	1.03808	+	1.79801i
$677$	104.239	−	180.546i	0.153971	−	0.266686i	−0.778713	−	0.627381i	$-0.784127\pi$
$677$	104.239	−	180.546i	0.153971	−	0.266686i	0.932684	+	0.360695i	$0.117460\pi$
$678$	−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	$-0.838424\pi$
$683$	−585.959	−	1014.91i	−0.857919	−	1.48596i	0.0159906	−	0.999872i	$-0.494910\pi$
$684$	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
$690$	862.374	−	53.6743i	1.24982	−	0.0777888i
$691$	−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
$695$	420.626	+	494.509i	0.605217	+	0.711524i
$696$	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
$700$	792.674	+	314.465i	1.13239	+	0.449235i
$701$		−	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
$705$	317.979	+	479.295i	0.451034	+	0.679851i
$706$	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	$0.189208\pi$
$710$	32.0738	+	175.027i	0.0451743	+	0.246517i
$711$	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	$0.630185\pi$
$720$	−289.897	+	441.978i	−0.402635	+	0.613858i
$721$	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
$725$	693.996	+	112.795i	0.957236	+	0.155579i
$726$	557.518	−	744.634i	0.767932	−	1.02567i
$727$			1029.30i			1.41581i	0.706307	+	0.707906i	$0.250360\pi$
$727$			1029.30i			1.41581i	−0.706307	+	0.707906i	$0.749640\pi$
$728$	262.434	−	287.327i	0.360486	−	0.394680i
$729$	550.714	+	477.656i	0.755437	+	0.655221i
$730$	1161.62	−	988.067i	1.59126	−	1.35352i
$731$	−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	0.197004	−	0.980403i	$-0.436879\pi$
$733$	−405.750	−	234.260i	−0.553547	−	0.319591i	−0.750552	+	0.660812i	$0.770212\pi$
$734$		−	836.361i		−	1.13946i
$735$	−685.011	−	266.431i	−0.931987	−	0.362491i
$736$	−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	$0.806329\pi$
$740$	924.959	−	786.763i	1.24994	−	1.06319i
$741$	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	$-0.255501\pi$
$743$	1032.44			1.38956			0.694781	+	0.719221i	$0.255501\pi$
$744$	−164.833	+	220.155i	−0.221550	+	0.295907i
$745$	178.520	+	974.190i	0.239625	+	1.30764i
$746$	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
$750$	1017.83	−	460.208i	1.35710	−	0.613611i
$751$	−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	$-0.873346\pi$
$757$		−	586.645i		−	0.774960i	0.921878	−	0.387480i	$-0.126654\pi$
$758$	−447.828	+	775.661i	−0.590802	+	1.02330i
$759$	−219.278	+	93.8795i	−0.288903	+	0.123688i
$760$	126.266	−	23.1383i	0.166140	−	0.0304451i
$761$	−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
$765$	44.9889	+	89.2999i	0.0588090	+	0.116732i
$766$	−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	$0.697687\pi$
$770$	−428.393	−	15.1331i	−0.556355	−	0.0196533i
$771$	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	0.959122	−	0.282994i	$-0.0913277\pi$
$773$	181.254	+	313.941i	0.234481	+	0.406133i	−0.724641	+	0.689127i	$0.757994\pi$
$774$	−1080.35	+	317.033i	−1.39580	+	0.409604i
$775$	−824.081	+	312.521i	−1.06333	+	0.403252i
$776$		−	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
$780$	−97.0693	−	1559.59i	−0.124448	−	1.99948i
$781$	−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	−0.0456267	−	0.998959i	$-0.514528\pi$
$787$	626.990	−	361.993i	0.796683	−	0.459965i	0.842310	+	0.538993i	$0.181195\pi$
$788$	−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
$795$	768.725	−	47.8455i	0.966949	−	0.0601831i
$796$	−371.776	+	643.935i	−0.467056	+	0.808964i
$797$	1004.54			1.26041			0.630203	−	0.776431i	$-0.282972\pi$
$797$	1004.54			1.26041			0.630203	+	0.776431i	$0.282972\pi$
$798$	−606.715	+	115.407i	−0.760294	+	0.144620i
$799$	−85.2056			−0.106640
$800$	−1061.01	+	402.374i	−1.32627	+	0.502967i
$801$	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
$805$	−573.836	−	358.895i	−0.712840	−	0.445832i
$806$			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	$0.274167\pi$
$810$	273.294	+	1175.03i	0.337400	+	1.45066i
$811$	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
$815$	−47.1189	−	257.129i	−0.0578146	−	0.315496i
$816$	−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	−0.592704	−	0.805420i	$-0.701940\pi$
$823$	−157.639	+	91.0130i	−0.191542	+	0.110587i	0.401162	+	0.916007i	$0.368606\pi$
$824$	5.52924	+	3.19231i	0.00671024	+	0.00387416i
$825$	−222.026	+	214.002i	−0.269122	+	0.259396i
$826$	358.041	−	392.004i	0.433464	−	0.474581i
$827$	178.479			0.215815			0.107907	−	0.994161i	$-0.465585\pi$
$827$	178.479			0.215815			0.107907	+	0.994161i	$0.465585\pi$
$828$	−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	$0.983562\pi$
$830$	−1798.85	+	329.639i	−2.16728	+	0.397155i
$831$	−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
$835$	239.553	+	281.631i	0.286890	+	0.337282i
$836$	−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	$0.787533\pi$
$840$	−254.643	+	98.5350i	−0.303146	+	0.117304i
$841$	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
$845$	−933.037	−	1096.93i	−1.10419	−	1.29814i
$846$	−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
$850$	−26.5460	+	163.331i	−0.0312306	+	0.192154i
$851$	−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	$-0.967599\pi$
$853$		−	173.353i		−	0.203228i	0.994824	−	0.101614i	$-0.0324006\pi$
$854$	306.284	−	1392.20i	0.358646	−	1.63021i
$855$	−243.671	+	371.501i	−0.284995	+	0.434504i
$856$	−20.6533	+	35.7725i	−0.0241276	+	0.0417903i
$857$	−426.331	−	738.427i	−0.497469	−	0.861642i	0.502526	−	0.864562i	$-0.332404\pi$
$857$	−426.331	−	738.427i	−0.497469	−	0.861642i	−0.999996	+	0.00291972i	$0.999071\pi$
$858$	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	$-0.525304\pi$
$863$	710.754	−	1231.06i	0.823585	−	1.42649i	0.902996	−	0.429650i	$-0.141363\pi$
$864$	−202.941	−	1208.61i	−0.234886	−	1.39885i
$865$	−1104.32	+	202.367i	−1.27667	+	0.233950i
$866$	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
$870$	−1047.13	+	694.701i	−1.20360	+	0.798507i
$871$	−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
$875$	−858.173	−	170.774i	−0.980769	−	0.195170i
$876$	−177.825	+	1486.27i	−0.202996	+	1.69665i
$877$	−9.68130	−	5.58950i	−0.0110391	−	0.00637343i	0.494470	−	0.869195i	$-0.335362\pi$
$877$	−9.68130	−	5.58950i	−0.0110391	−	0.00637343i	−0.505509	+	0.862821i	$0.668695\pi$
$878$	−988.067	−	1711.38i	−1.12536	−	1.94918i
$879$	−190.314	−	444.523i	−0.216512	−	0.505714i
$880$	183.934	−	156.453i	0.209016	−	0.177788i
$881$			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	$-0.634514\pi$
$883$		−	1610.65i		−	1.82406i	0.410123	−	0.912030i	$-0.365486\pi$
$884$	200.468	+	115.740i	0.226774	+	0.130928i
$885$	−23.7250	−	381.185i	−0.0268079	−	0.430718i
$886$	−71.8871	−	124.512i	−0.0811366	−	0.140533i
$887$	−15.0891	+	26.1350i	−0.0170113	+	0.0294645i	−0.874406	−	0.485195i	$-0.838748\pi$
$887$	−15.0891	+	26.1350i	−0.0170113	+	0.0294645i	0.857394	+	0.514660i	$0.172082\pi$
$888$	−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
$900$	−426.238	+	1010.18i	−0.473598	+	1.12242i
$901$	−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
$905$	−767.101	−	901.843i	−0.847625	−	0.996512i
$906$	585.237	+	1366.96i	0.645957	+	1.50878i
$907$	−265.679	+	153.390i	−0.292921	+	0.169118i	−0.639258	−	0.768992i	$-0.720759\pi$
$907$	−265.679	+	153.390i	−0.292921	+	0.169118i	0.346338	+	0.938110i	$0.387425\pi$
$908$	26.0311	−	45.0872i	0.0286686	−	0.0496555i
$909$	−194.383	+	800.702i	−0.213843	+	0.880861i
$910$	−1181.84	+	1889.64i	−1.29872	+	2.07652i
$911$		−	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
$915$	−566.914	−	854.520i	−0.619579	−	0.933902i
$916$	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	$-0.140274\pi$
$920$	−247.313	+	45.3202i	−0.268819	+	0.0492611i
$921$	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	$0.786549\pi$
$930$	701.336	−	1410.45i	0.754125	−	1.51661i
$931$	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
$935$	−8.23393	−	44.9327i	−0.00880634	−	0.0480564i
$936$	362.044	+	345.318i	0.386799	+	0.368930i
$937$		−	1295.06i		−	1.38214i	−0.722789	−	0.691069i	$-0.757140\pi$
$937$		−	1295.06i		−	1.38214i	0.722789	−	0.691069i	$-0.242860\pi$
$938$	−960.718	+	1051.85i	−1.02422	+	1.12137i
$939$	−163.698	+	1368.19i	−0.174332	+	1.45707i
$940$	−605.332	−	711.660i	−0.643971	−	0.757085i
$941$	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
$945$	361.504	−	873.121i	0.382544	−	0.923937i
$946$	514.365			0.543726
$947$	35.1356	−	60.8566i	0.0371020	−	0.0642625i	−0.846878	−	0.531787i	$-0.821521\pi$
$947$	35.1356	−	60.8566i	0.0371020	−	0.0642625i	0.883980	+	0.467524i	$0.154854\pi$
$948$	−370.428	−	865.222i	−0.390747	−	0.912681i
$949$	1094.46	+	1895.67i	1.15328	+	1.99754i
$950$	−687.455	+	260.707i	−0.723637	+	0.274429i
$951$	−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	$-0.371044\pi$
$953$	751.223			0.788272			0.394136	+	0.919052i	$0.371044\pi$
$954$	−950.097	+	996.115i	−0.995908	+	1.04415i
$955$	−84.8631	−	463.100i	−0.0888619	−	0.484921i
$956$	−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
$960$	589.194	−	1184.92i	0.613744	−	1.23430i
$961$	−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	$0.210198\pi$
$967$			1186.31i			1.22680i	−0.789774	+	0.613398i	$0.789802\pi$
$968$	−135.344	+	234.423i	−0.139818	+	0.242173i
$969$	−25.9032	−	60.5030i	−0.0267319	−	0.0624386i
$970$	36.7064	+	200.308i	0.0378416	+	0.206503i
$971$	−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
$975$	386.410	+	1556.08i	0.396318	+	1.59598i
$976$	401.506	+	695.429i	0.411379	+	0.712530i
$977$	544.752	+	943.538i	0.557576	+	0.965750i	0.997698	+	0.0678121i	$0.0216018\pi$
$977$	544.752	+	943.538i	0.557576	+	0.965750i	−0.440122	+	0.897938i	$0.645065\pi$
$978$	373.996	+	280.016i	0.382409	+	0.286315i
$979$	−552.611			−0.564465
$980$	1156.21	+	297.522i	1.17981	+	0.303594i
$981$	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	0.890038	−	0.455886i	$-0.150678\pi$
$983$	49.3566	+	85.4881i	0.0502101	+	0.0869665i	−0.839828	+	0.542853i	$0.817344\pi$
$984$	−196.982	+	84.3342i	−0.200185	+	0.0857055i
$985$	102.315	+	120.287i	0.103874	+	0.122119i
$986$		−	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
$990$	31.3533	−	550.243i	0.0316700	−	0.555801i
$991$	−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	−0.523570	−	0.851983i	$-0.675400\pi$
$997$	−47.3741	+	27.3514i	−0.0475166	+	0.0274337i	0.476054	+	0.879416i	$0.342067\pi$
$998$	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.44.1	✓	16
3.2	odd	2	inner	105.3.o.a.44.7	yes	16
5.4	even	2	inner	105.3.o.a.44.8	yes	16
7.4	even	3	inner	105.3.o.a.74.2	yes	16
15.14	odd	2	inner	105.3.o.a.44.2	yes	16
21.11	odd	6	inner	105.3.o.a.74.8	yes	16
35.4	even	6	inner	105.3.o.a.74.7	yes	16
105.74	odd	6	inner	105.3.o.a.74.1	yes	16

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

\(f(q)\)	\(=\)	\(q+(-1.48938 + 2.57968i) q^{2} +(1.18073 + 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(3.23955 + 3.80858i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(5.16858 + 4.72078i) q^{7} +2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +O(q^{10})\)	\(q+(-1.48938 + 2.57968i) q^{2} +(1.18073 + 2.75787i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(3.23955 + 3.80858i) q^{5} +(-8.87298 - 1.06161i) q^{6} +(5.16858 + 4.72078i) q^{7} +2.60040 q^{8} +(-6.21175 + 6.51262i) q^{9} +(-14.6498 + 2.68458i) q^{10} +(3.56075 - 2.05580i) q^{11} +(8.76174 - 11.7024i) q^{12} -21.3779i q^{13} +(-19.8761 + 6.30224i) q^{14} +(-6.67855 + 13.4312i) 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} +(-4.01061 + 24.6762i) q^{25} +(55.1481 + 31.8397i) q^{26} +(-25.2954 - 9.44157i) q^{27} +(7.32910 - 33.3142i) q^{28} -28.1241i q^{29} +(-24.7013 - 37.2326i) q^{30} +(17.6270 + 30.5309i) q^{31} +(22.6950 + 39.3089i) q^{32} +(9.87393 + 7.39275i) q^{33} +6.61895 q^{34} +(-1.23561 + 34.9782i) 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} +(8.42414 + 9.90385i) q^{40} +27.4670i q^{41} +(-40.8491 - 47.3744i) q^{42} -41.9977i q^{43} +(-17.3515 - 10.0179i) q^{44} +(-44.9271 - 2.55998i) 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} +(72.9536 - 4.54064i) q^{60} +(-34.1825 + 59.2058i) q^{61} -105.013 q^{62} +(-62.8506 + 4.33668i) q^{63} -88.2218 q^{64} +(81.4195 - 69.2548i) 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} +(-88.3922 - 55.2832i) q^{70} -11.9474i q^{71} +(-16.1530 + 16.9354i) q^{72} +(-88.6742 + 51.1961i) q^{73} +(-128.567 + 74.2282i) q^{74} +(-72.7893 + 18.0752i) q^{75} -48.1109 q^{76} +(28.1090 + 6.18396i) q^{77} +(-22.6950 + 189.686i) q^{78} +(32.1905 - 55.7556i) q^{79} +(57.7679 - 10.5860i) 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} +(73.5174 - 112.085i) q^{90} +(100.920 - 110.493i) q^{91} +94.2332 q^{92} +(-63.3876 + 84.6619i) q^{93} +(57.1109 + 98.9190i) q^{94} +(48.5564 - 8.89796i) 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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