LMFDB - Embedded newform 105.3.o.a.44.7

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			44.7
Root			$0.921698 + 0.861704i$ of defining polynomial
Character	$\chi$	$=$	105.44
Dual form			105.3.o.a.74.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48938 - 2.57968i) q^{2} +(-1.79802 - 2.40148i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(-3.23955 - 3.80858i) q^{5} +(-8.87298 + 1.06161i) q^{6} +(5.16858 + 4.72078i) q^{7} -2.60040 q^{8} +(-2.53422 + 8.63584i) q^{9} +O(q^{10})$	\(q+(1.48938 - 2.57968i) q^{2} +(-1.79802 - 2.40148i) 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} +(-2.53422 + 8.63584i) q^{9} +(-14.6498 + 2.68458i) q^{10} +(-3.56075 + 2.05580i) q^{11} +(-5.75368 + 13.4391i) 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} +(18.5033 + 19.3995i) q^{18} +(4.93649 - 8.55025i) q^{19} +(-8.17956 + 22.9509i) q^{20} +(2.04364 - 20.9003i) q^{21} +12.2474i q^{22} +(9.66894 - 16.7471i) q^{23} +(4.67559 + 6.24482i) 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} +(32.7877 + 30.3543i) q^{30} +(17.6270 + 30.5309i) q^{31} +(-22.6950 - 39.3089i) q^{32} +(11.3393 + 4.85469i) 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} +(-51.3386 + 38.4380i) q^{39} +(8.42414 + 9.90385i) q^{40} -27.4670i q^{41} +(-50.8724 - 36.4004i) q^{42} -41.9977i q^{43} +(17.3515 + 10.0179i) q^{44} +(41.1000 - 18.3245i) 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} +(2.62365 - 6.12814i) q^{51} +(-90.2174 + 52.0870i) q^{52} +(25.6737 + 44.4682i) q^{53} +(13.3182 - 79.3160i) 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} +(69.8232 - 21.6232i) q^{60} +(-34.1825 + 59.2058i) q^{61} +105.013 q^{62} +(-53.8662 + 32.6715i) q^{63} -88.2218 q^{64} +(-81.4195 + 69.2548i) q^{65} +(29.4120 - 22.0212i) 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} +(6.59000 - 22.4567i) q^{72} +(-88.6742 + 51.1961i) q^{73} +(128.567 - 74.2282i) q^{74} +(66.4706 - 34.7370i) 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} +(-68.1555 - 43.7702i) q^{81} +(-70.8561 - 40.9088i) q^{82} -122.790 q^{83} +(-93.1813 + 42.2990i) q^{84} +(3.72983 - 10.4655i) q^{85} +(-108.341 - 62.5505i) q^{86} +(67.5395 - 50.5678i) 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} +(41.6255 - 97.2262i) q^{93} +(57.1109 + 98.9190i) q^{94} +(-48.5564 + 8.89796i) q^{95} +(-53.5934 + 125.180i) 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	$-0.100735\pi$
$3$	−1.79802	−	2.40148i	−0.599341	−	0.800494i
$3$	−1.79802	−	2.40148i	−0.599341	−	0.800494i
$4$	−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
$9$	−2.53422	+	8.63584i	−0.281580	+	0.959538i
$10$	−14.6498	+	2.68458i	−1.46498	+	0.268458i
$11$	−3.56075	+	2.05580i	−0.323705	+	0.186891i	−0.653043	−	0.757321i	$-0.726508\pi$
$11$	−3.56075	+	2.05580i	−0.323705	+	0.186891i	0.329338	+	0.944212i	$0.393174\pi$
$12$	−5.75368	+	13.4391i	−0.479474	+	1.11992i
$13$		−	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
$15$	−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	$0.812516\pi$
$18$	18.5033	+	19.3995i	1.02796	+	1.07775i
$19$	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
$21$	2.04364	−	20.9003i	0.0973162	−	0.995254i
$22$			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	$0.0285604\pi$
$24$	4.67559	+	6.24482i	0.194816	+	0.260201i
$25$	−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	$0.161143\pi$
$29$			28.1241i			0.969797i	−0.874570	+	0.484898i	$0.838857\pi$
$30$	32.7877	+	30.3543i	1.09292	+	1.01181i
$31$	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
$33$	11.3393	+	4.85469i	0.343614	+	0.147112i
$34$	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
$39$	−51.3386	+	38.4380i	−1.31637	+	0.985589i
$40$	8.42414	+	9.90385i	0.210604	+	0.247596i
$41$		−	27.4670i		−	0.669928i	−0.942231	−	0.334964i	$-0.891276\pi$
$41$		−	27.4670i		−	0.669928i	0.942231	−	0.334964i	$-0.108724\pi$
$42$	−50.8724	−	36.4004i	−1.21125	−	0.866676i
$43$		−	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
$45$	41.1000	−	18.3245i	0.913334	−	0.407210i
$46$	−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
$51$	2.62365	−	6.12814i	0.0514441	−	0.120160i
$52$	−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	$0.672368\pi$
$54$	13.3182	−	79.3160i	0.246633	−	1.46882i
$55$	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	−0.301354	−	0.953512i	$-0.597439\pi$
$59$	22.0503	−	12.7308i	0.373734	−	0.215776i	0.675089	+	0.737737i	$0.264105\pi$
$60$	69.8232	−	21.6232i	1.16372	−	0.360387i
$61$	−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
$63$	−53.8662	+	32.6715i	−0.855020	+	0.518596i
$64$	−88.2218			−1.37847
$65$	−81.4195	+	69.2548i	−1.25261	+	1.06546i
$66$	29.4120	−	22.0212i	0.445637	−	0.333655i
$67$	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	$0.0268132\pi$
$71$			11.9474i			0.168273i	−0.996454	+	0.0841366i	$0.973187\pi$
$72$	6.59000	−	22.4567i	0.0915277	−	0.311898i
$73$	−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
$75$	66.4706	−	34.7370i	0.886275	−	0.463160i
$76$	−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
$81$	−68.1555	−	43.7702i	−0.841425	−	0.540373i
$82$	−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	$0.765031\pi$
$84$	−93.1813	+	42.2990i	−1.10930	+	0.503560i
$85$	3.72983	−	10.4655i	0.0438804	−	0.123123i
$86$	−108.341	−	62.5505i	−1.25977	−	0.727331i
$87$	67.5395	−	50.5678i	0.776316	−	0.581239i
$88$	9.25939	−	5.34591i	0.105220	−	0.0607490i
$89$	116.396	+	67.2014i	1.30782	+	0.755072i	0.981733	−	0.190266i	$-0.0609351\pi$
$89$	116.396	+	67.2014i	1.30782	+	0.755072i	0.326091	+	0.945338i	$0.394268\pi$
$90$	13.9423	−	133.317i	0.154914	−	1.48130i
$91$	100.920	−	110.493i	1.10901	−	1.21421i
$92$	−94.2332			−1.02427
$93$	41.6255	−	97.2262i	0.447587	−	1.04544i
$94$	57.1109	+	98.9190i	0.607563	+	1.05233i
$95$	−48.5564	+	8.89796i	−0.511120	+	0.0936627i
$96$	−53.5934	+	125.180i	−0.558264	+	1.30396i
$97$		−	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	−0.838201	−	0.545361i	$-0.816393\pi$
$101$	−79.2855	+	45.7755i	−0.785005	+	0.453223i	0.0531959	+	0.998584i	$0.483059\pi$
$102$	−11.9010	−	15.8953i	−0.116677	−	0.155836i
$103$	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
$105$	−86.2211	+	59.9243i	−0.821153	+	0.570708i
$106$	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	$0.143018\pi$
$108$	−101.477	−	83.7455i	−0.939598	−	0.775421i
$109$	−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	$-0.525199\pi$
$113$	−17.8725			−0.158164			−0.0790820	+	0.996868i	$0.525199\pi$
$114$	−34.7244	+	81.1069i	−0.304600	+	0.711464i
$115$	−95.1057	+	17.4281i	−0.827006	+	0.151549i
$116$	118.687	−	68.5242i	1.02317	−	0.590726i
$117$	184.616	+	54.1763i	1.57791	+	0.463045i
$118$		−	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
$123$	−65.9615	+	49.3864i	−0.536273	+	0.401515i
$124$	85.8962	−	148.777i	0.692711	−	1.19981i
$125$	106.974	−	64.6651i	0.855791	−	0.517321i
$126$	4.05482	+	187.618i	0.0321811	+	1.48903i
$127$		−	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
$129$	−100.857	+	75.5129i	−0.781835	+	0.585371i
$130$	57.3907	+	313.182i	0.441467	+	2.40910i
$131$	190.603	+	110.045i	1.45498	+	0.840036i	0.998758	−	0.0498278i	$-0.0158672\pi$
$131$	190.603	+	110.045i	1.45498	+	0.840036i	0.456227	+	0.889864i	$0.349201\pi$
$132$	−7.14062	−	59.6816i	−0.0540956	−	0.452133i
$133$	65.8785	−	20.8886i	0.495327	−	0.157057i
$134$		−	203.508i		−	1.51872i
$135$	−117.905	−	65.7532i	−0.873368	−	0.487060i
$136$	−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	$0.737299\pi$
$138$	−68.0135	+	158.861i	−0.492851	+	1.15117i
$139$	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
$144$	72.9630	+	76.4970i	0.506687	+	0.531229i
$145$	107.113	−	91.1095i	0.738710	−	0.628342i
$146$			305.001i			2.08905i
$147$	109.229	−	98.3774i	0.743052	−	0.669234i
$148$		−	242.862i		−	1.64096i
$149$	−171.544	−	99.0412i	−1.15130	−	0.664706i	−0.202100	−	0.979365i	$-0.564776\pi$
$149$	−171.544	−	99.0412i	−1.15130	−	0.664706i	−0.949205	+	0.314659i	$0.898110\pi$
$150$	9.38952	−	223.209i	0.0625968	−	1.48806i
$151$	−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
$156$	287.299	+	123.002i	1.84166	+	0.788472i
$157$	−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
$159$	60.6276	−	141.610i	0.381306	−	0.890629i
$160$	−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
$165$	−18.2447	−	58.9136i	−0.110574	−	0.357052i
$166$	−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	$0.571061\pi$
$168$	−5.31429	+	54.3493i	−0.0316327	+	0.323508i
$169$	−288.014			−1.70423
$170$	−21.4424	−	25.2088i	−0.126132	−	0.148287i
$171$	61.3285	+	64.2990i	0.358646	+	0.376017i
$172$	−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
$175$	−137.220	+	108.608i	−0.784115	+	0.620616i
$176$			48.2947i			0.274402i
$177$	−70.2197	−	30.0632i	−0.396721	−	0.169849i
$178$	346.716	−	200.177i	1.94784	−	1.12459i
$179$	−231.158	+	133.459i	−1.29138	+	0.745581i	−0.978900	−	0.204342i	$-0.934495\pi$
$179$	−231.158	+	133.459i	−1.29138	+	0.745581i	−0.312484	+	0.949923i	$0.601161\pi$
$180$	−177.472	−	128.800i	−0.985953	−	0.715556i
$181$	−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
$186$	−188.816	−	252.187i	−1.01514	−	1.35584i
$187$	−7.91217	−	4.56809i	−0.0423111	−	0.0244283i
$188$	186.857			0.993919
$189$	175.313	+	70.6146i	0.927581	+	0.373622i
$190$	−49.3649	+	138.512i	−0.259815	+	0.729012i
$191$	81.5469	+	47.0811i	0.426947	+	0.246498i	0.698045	−	0.716054i	$-0.254053\pi$
$191$	81.5469	+	47.0811i	0.426947	+	0.246498i	−0.271098	+	0.962552i	$0.587387\pi$
$192$	158.625	+	211.863i	0.826171	+	1.10345i
$193$	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
$195$	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	$0.525543\pi$
$198$	−105.767	−	31.0377i	−0.534177	−	0.156756i
$199$	−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
$201$	−188.418	−	80.6674i	−0.937401	−	0.401330i
$202$			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
$207$	120.122	+	125.940i	0.580300	+	0.608407i
$208$	−217.462	−	125.552i	−1.04549	−	0.603615i
$209$			40.5938i			0.194228i
$210$	26.1697	+	311.673i	0.124617	+	1.48416i
$211$	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
$213$	28.6914	−	21.4817i	0.134702	−	0.100853i
$214$	−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
$219$	282.385	+	120.898i	1.28943	+	0.552044i
$220$	−18.0571	−	98.5380i	−0.0820777	−	0.447900i
$221$	41.1386	−	23.7514i	0.186148	−	0.107472i
$222$	−409.424	−	175.287i	−1.84425	−	0.789581i
$223$			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
$225$	−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	$0.840825\pi$
$228$	86.5045	+	115.537i	0.379406	+	0.506743i
$229$	−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
$231$	35.6900	+	78.6221i	0.154502	+	0.340356i
$232$		−	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	$0.292274\pi$
$234$	414.720	−	395.561i	1.77231	−	1.69043i
$235$	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	$0.287107\pi$
$239$			375.016i			1.56910i	−0.620063	+	0.784552i	$0.712893\pi$
$240$	129.290	+	119.695i	0.538709	+	0.498728i
$241$	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
$243$	17.4317	+	242.374i	0.0717356	+	0.997424i
$244$	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
$249$	220.779	+	294.877i	0.886661	+	1.18424i
$250$	−7.49060	−	372.269i	−0.0299624	−	1.48908i
$251$		−	55.3043i		−	0.220336i	−0.993913	−	0.110168i	$-0.964861\pi$
$251$		−	55.3043i		−	0.220336i	0.993913	−	0.110168i	$-0.0351389\pi$
$252$	269.123	+	147.719i	1.06795	+	0.586185i
$253$			79.5096i			0.314267i
$254$	−193.960	−	111.983i	−0.763621	−	0.440877i
$255$	−31.8390	+	9.86006i	−0.124859	+	0.0386669i
$256$	−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
$261$	−242.875	−	71.2727i	−0.930557	−	0.273075i
$262$	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	$-0.345653\pi$
$264$	−29.4867	−	12.6242i	−0.111692	−	0.0478188i
$265$	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	−0.690962	−	0.722891i	$-0.742813\pi$
$269$	−110.398	+	63.7384i	−0.410402	+	0.236946i	0.280561	+	0.959836i	$0.409480\pi$
$270$	−345.227	+	206.225i	−1.27862	+	0.763796i
$271$	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
$273$	−446.805	−	43.6887i	−1.63665	−	0.160032i
$274$	242.522			0.885117
$275$	−36.4486	−	96.1108i	−0.132540	−	0.349494i
$276$	169.433	+	226.299i	0.613889	+	0.819924i
$277$	−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	$0.187087\pi$
$281$			311.623i			1.10898i	−0.832190	+	0.554490i	$0.812913\pi$
$282$	134.865	−	315.009i	0.478246	−	1.11705i
$283$	−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
$285$	108.674	+	100.608i	0.381312	+	0.353012i
$286$	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
$291$	−32.8355	+	24.5844i	−0.112837	+	0.0844826i
$292$	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	$0.411303\pi$
$294$	−91.0994	−	428.296i	−0.309862	−	1.45679i
$295$	−119.919	−	42.7385i	−0.406506	−	0.144876i
$296$	−112.237	−	64.8000i	−0.379178	−	0.218919i
$297$	−70.6606	+	85.6213i	−0.237914	+	0.288287i
$298$	−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
$303$	252.486	+	108.097i	0.833288	+	0.356756i
$304$	−57.9839	−	100.431i	−0.190736	−	0.330365i
$305$	336.226	−	61.6134i	1.10238	−	0.202011i
$306$	−16.7739	+	57.1602i	−0.0548166	+	0.186798i
$307$		−	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	0.196407	−	0.980523i	$-0.437073\pi$
$311$	355.712	−	205.370i	1.14377	−	0.660354i	0.947361	+	0.320168i	$0.103739\pi$
$312$	133.501	−	99.9542i	0.427888	−	0.320366i
$313$	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
$315$	298.935	+	99.3129i	0.948999	+	0.315279i
$316$	−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	$0.0536112\pi$
$318$	−275.011	−	367.310i	−0.864813	−	1.15506i
$319$	−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
$324$	−18.6558	+	394.271i	−0.0575796	+	1.21688i
$325$	527.525	+	85.7383i	1.62315	+	0.263810i
$326$	−134.871	+	77.8678i	−0.413715	+	0.238858i
$327$	−28.7494	+	67.1509i	−0.0879186	+	0.205354i
$328$			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
$333$	−324.578	+	309.583i	−0.974710	+	0.929680i
$334$	−110.134	+	190.758i	−0.329743	+	0.571131i
$335$	−321.775	−	114.679i	−0.960521	−	0.342324i
$336$	−200.602	−	143.536i	−0.597030	−	0.427190i
$337$			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
$339$	32.1352	+	42.9205i	0.0947942	+	0.126609i
$340$	−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
$345$	212.856	+	197.058i	0.616973	+	0.571184i
$346$	−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	$0.942641\pi$
$348$	−377.962	−	161.817i	−1.08610	−	0.464992i
$349$	−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	$0.102734\pi$
$353$	264.349	+	457.867i	0.748865	+	1.29707i	−0.199502	+	0.979898i	$0.563932\pi$
$354$	−182.137	+	136.369i	−0.514511	+	0.385222i
$355$	45.5027	−	38.7042i	0.128177	−	0.109026i
$356$		−	654.943i		−	1.83973i
$357$	42.4902	−	19.2881i	0.119020	−	0.0540283i
$358$			795.083i			2.22090i
$359$	73.3318	+	42.3381i	0.204267	+	0.117934i	0.598644	−	0.801015i	$-0.295706\pi$
$359$	73.3318	+	42.3381i	0.204267	+	0.117934i	−0.394377	+	0.918949i	$0.629040\pi$
$360$	−106.877	+	47.6510i	−0.296880	+	0.132364i
$361$	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
$366$	240.447	−	561.620i	0.656959	−	1.53448i
$367$	−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
$369$	237.201	+	69.6075i	0.642821	+	0.188638i
$370$	−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
$375$	−347.634	−	140.626i	−0.927023	−	0.375004i
$376$	49.8569	−	86.3546i	0.132598	−	0.229666i
$377$	601.234			1.59479
$378$	443.270	−	347.079i	1.17267	−	0.918198i
$379$	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
$381$	−180.562	+	135.189i	−0.473915	+	0.354827i
$382$	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
$385$	67.5084	+	127.089i	0.175347	+	0.330101i
$386$		−	818.953i		−	2.12164i
$387$	362.686	+	106.431i	0.937172	+	0.275017i
$388$	−57.7019	+	33.3142i	−0.148716	+	0.0858614i
$389$	570.321	−	329.275i	1.46612	−	0.846465i	0.466837	−	0.884343i	$-0.345393\pi$
$389$	570.321	−	329.275i	1.46612	−	0.846465i	0.999282	+	0.0378787i	$0.0120600\pi$
$390$	648.912	−	700.932i	1.66388	−	1.79726i
$391$	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
$396$	−130.485	+	124.457i	−0.329508	+	0.314285i
$397$	−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
$399$	−168.615	−	120.648i	−0.422593	−	0.302376i
$400$	227.460	+	185.720i	0.568649	+	0.464300i
$401$	−433.596	−	250.337i	−1.08129	−	0.624281i	−0.150043	−	0.988679i	$-0.547941\pi$
$401$	−433.596	−	250.337i	−1.08129	−	0.624281i	−0.931243	+	0.364398i	$0.881275\pi$
$402$	−488.721	+	365.912i	−1.21572	+	0.910230i
$403$	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
$408$	−6.82254	+	15.9356i	−0.0167219	+	0.0390579i
$409$	−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
$411$	96.1319	−	224.539i	0.233898	−	0.546323i
$412$		−	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
$417$	−233.457	−	311.810i	−0.559848	−	0.747746i
$418$	104.719	+	60.4594i	0.250523	+	0.144640i
$419$		−	93.6914i		−	0.223607i	−0.993730	−	0.111804i	$-0.964337\pi$
$419$		−	93.6914i		−	0.223607i	0.993730	−	0.111804i	$-0.0356627\pi$
$420$	462.965	+	217.859i	1.10230	+	0.518712i
$421$	−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
$423$	−238.192	−	249.729i	−0.563102	−	0.590377i
$424$	−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
$429$	103.783	−	242.410i	0.241919	−	0.565058i
$430$	112.746	+	615.260i	0.262201	+	1.43084i
$431$	395.347	−	228.254i	0.917278	−	0.529591i	0.0345127	−	0.999404i	$-0.489012\pi$
$431$	395.347	−	228.254i	0.917278	−	0.529591i	0.882766	+	0.469813i	$0.155679\pi$
$432$	52.5169	−	312.763i	0.121567	−	0.723988i
$433$		−	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
$435$	−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
$438$	732.454	−	548.399i	1.67227	−	1.25205i
$439$	−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
$441$	−432.647	−	85.4255i	−0.981059	−	0.193709i
$442$		−	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	$0.149318\pi$
$444$	−583.228	+	436.671i	−1.31358	+	0.983493i
$445$	−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	$-0.750982\pi$
$449$		−	633.019i		−	1.40984i	0.709285	−	0.704921i	$-0.249018\pi$
$450$	−552.915	+	378.787i	−1.22870	+	0.841748i
$451$	56.4667	+	97.8032i	0.125203	+	0.216859i
$452$	43.5463	+	75.4244i	0.0963413	+	0.166868i
$453$	−196.470	+	458.903i	−0.433709	+	1.01303i
$454$	−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
$459$	46.2728	+	38.1875i	0.100812	+	0.0831971i
$460$	305.273	+	358.895i	0.663638	+	0.780206i
$461$			579.029i			1.25603i	0.778202	+	0.628014i	$0.216132\pi$
$461$			579.029i			1.25603i	−0.778202	+	0.628014i	$0.783868\pi$
$462$	255.976	+	25.0294i	0.554060	+	0.0541761i
$463$			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
$465$	−505.142	+	156.435i	−1.08633	+	0.336419i
$466$	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
$471$	367.038	+	157.140i	0.779274	+	0.333631i
$472$	−57.3397	+	33.1051i	−0.121483	+	0.0701380i
$473$	86.3389	+	149.543i	0.182535	+	0.316159i
$474$	−226.435	+	528.893i	−0.477711	+	1.11581i
$475$	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	−0.138609	−	0.990347i	$-0.544263\pi$
$479$	311.231	−	179.689i	0.649752	−	0.375134i	0.788361	+	0.615213i	$0.210930\pi$
$480$	650.376	−	201.412i	1.35495	−	0.419608i
$481$	532.720	−	922.698i	1.10753	−	1.91829i
$482$	254.894			0.528825
$483$	−330.260	−	236.309i	−0.683768	−	0.489253i
$484$	507.252			1.04804
$485$	−52.0748	+	44.2945i	−0.107371	+	0.0913288i
$486$	651.209	+	316.018i	1.33994	+	0.650243i
$487$	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	$0.0333855\pi$
$491$			102.807i			0.209383i	−0.994505	+	0.104692i	$0.966614\pi$
$492$	369.132	+	158.037i	0.750267	+	0.321213i
$493$	−54.1207	+	31.2466i	−0.109778	+	0.0633806i
$494$	−544.476	+	314.353i	−1.10218	+	0.636343i
$495$	−108.676	+	149.742i	−0.219547	+	0.302510i
$496$	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
$501$	132.957	+	177.581i	0.265384	+	0.354453i
$502$	−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	$0.649606\pi$
$504$	140.074	−	84.9591i	0.277925	−	0.168570i
$505$	431.190	+	153.673i	0.853841	+	0.304304i
$506$	205.109	+	118.420i	0.405354	+	0.234031i
$507$	517.856	+	691.660i	1.02141	+	1.36422i
$508$	−317.301	+	183.194i	−0.624609	+	0.360618i
$509$	253.253	+	146.215i	0.497549	+	0.287260i	0.727701	−	0.685895i	$-0.240589\pi$
$509$	253.253	+	146.215i	0.497549	+	0.287260i	−0.230152	+	0.973155i	$0.573922\pi$
$510$	−21.9845	+	96.8197i	−0.0431068	+	0.189842i
$511$	−700.005	−	154.001i	−1.36987	−	0.301371i
$512$	−655.326			−1.27993
$513$	44.1427	−	262.890i	0.0860482	−	0.512457i
$514$	239.150	+	414.220i	0.465273	+	0.805876i
$515$	−2.21277	−	12.0751i	−0.00429664	−	0.0234468i
$516$	564.411	+	241.642i	1.09382	+	0.468298i
$517$		−	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	−0.504866	−	0.863198i	$-0.668458\pi$
$521$	−5.07885	+	2.93227i	−0.00974827	+	0.00562817i	0.495118	+	0.868826i	$0.335125\pi$
$522$	−545.594	+	520.388i	−1.04520	+	0.996912i
$523$	−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
$525$	507.544	+	134.252i	0.966751	+	0.255719i
$526$	−835.331			−1.58808
$527$	−39.1682	+	67.8412i	−0.0743229	+	0.128731i
$528$	115.979	−	86.8350i	0.219657	−	0.164460i
$529$	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
$534$	−1104.12	−	472.710i	−2.06765	−	0.885224i
$535$	−78.1224	+	14.3159i	−0.146023	+	0.0267588i
$536$	−153.857	+	88.8296i	−0.287047	+	0.165727i
$537$	736.126	+	315.158i	1.37081	+	0.586887i
$538$			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
$543$	425.758	+	568.652i	0.784085	+	1.04724i
$544$	50.4294	−	87.3464i	0.0927012	−	0.160563i
$545$	−40.8707	+	114.679i	−0.0749922	+	0.210419i
$546$	−778.164	+	1087.54i	−1.42521	+	1.99184i
$547$			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
$549$	−424.666	−	445.235i	−0.773526	−	0.810992i
$550$	−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
$555$	−507.867	+	548.581i	−0.915076	+	0.988433i
$556$	−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	$0.867511\pi$
$558$	−266.126	+	906.877i	−0.476929	+	1.62523i
$559$	−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	$-0.860362\pi$
$563$	−461.941	−	800.106i	−0.820500	−	1.42115i	0.0848112	−	0.996397i	$-0.472971\pi$
$564$	−335.973	−	448.733i	−0.595697	−	0.795626i
$565$	57.8990	+	68.0690i	0.102476	+	0.120476i
$566$			236.519i			0.417877i
$567$	−145.637	−	547.977i	−0.256856	−	0.966450i
$568$		−	31.0681i		−	0.0546973i
$569$	296.128	+	170.970i	0.520436	+	0.300474i	0.737113	−	0.675770i	$-0.236189\pi$
$569$	296.128	+	170.970i	0.520436	+	0.300474i	−0.216677	+	0.976243i	$0.569522\pi$
$570$	421.394	−	130.499i	0.739287	−	0.228946i
$571$	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
$576$	223.573	−	761.869i	0.388148	−	1.32269i
$577$	−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
$579$	−758.226	−	324.620i	−1.30954	−	0.560656i
$580$	−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
$585$	−391.738	−	878.632i	−0.669638	−	1.50194i
$586$	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	$0.409833\pi$
$588$	−681.300	−	221.263i	−1.15867	−	0.376297i
$589$	348.062			0.590938
$590$	−288.857	+	245.699i	−0.489588	+	0.416440i
$591$	56.7873	+	75.8464i	0.0960869	+	0.128336i
$592$	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
$595$	68.6832	−	36.4839i	0.115434	−	0.0613175i
$596$			965.252i			1.61955i
$597$	−180.164	+	420.815i	−0.301782	+	0.704883i
$598$	−1066.45	+	615.713i	−1.78336	+	1.02962i
$599$	−147.815	+	85.3408i	−0.246769	+	0.142472i	−0.618284	−	0.785955i	$-0.712172\pi$
$599$	−147.815	+	85.3408i	−0.246769	+	0.142472i	0.371515	+	0.928427i	$0.378838\pi$
$600$	−172.850	+	90.3303i	−0.288084	+	0.150550i
$601$	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
$606$	654.903	−	490.336i	1.08070	−	0.809135i
$607$	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
$609$	587.803	+	57.4755i	0.965194	+	0.0943769i
$610$	341.825	−	959.120i	0.560368	−	1.57233i
$611$	709.920	+	409.873i	1.16190	+	0.670823i
$612$	67.2609	+	70.5188i	0.109903	+	0.115227i
$613$	−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
$615$	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	$0.211593\pi$
$618$	−20.1699	−	8.63535i	−0.0326373	−	0.0139731i
$619$	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
$621$	86.4608	−	514.914i	0.139228	−	0.829170i
$622$		−	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
$627$	97.4851	−	72.9885i	0.155479	−	0.116409i
$628$	561.645	+	324.266i	0.894340	+	0.516347i
$629$			110.743i			0.176063i
$630$	701.422	−	623.241i	1.11337	−	0.989271i
$631$	−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
$633$	−367.279	−	490.546i	−0.580220	−	0.774954i
$634$	−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
$639$	−103.176	−	30.2773i	−0.161465	−	0.0473824i
$640$	399.503	−	73.2090i	0.624224	−	0.114389i
$641$	−1106.38	+	638.767i	−1.72602	+	0.996517i	−0.821313	+	0.570478i	$0.806758\pi$
$641$	−1106.38	+	638.767i	−1.72602	+	0.996517i	−0.904705	+	0.426039i	$0.859909\pi$
$642$	−55.8681	+	130.493i	−0.0870220	+	0.203260i
$643$			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
$645$	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	$0.894541\pi$
$648$	177.232	+	113.820i	0.273506	+	0.175649i
$649$	−52.3438	+	90.6621i	−0.0806530	+	0.139695i
$650$	1006.86	−	1233.15i	1.54902	−	1.89715i
$651$	674.129	−	306.016i	1.03553	−	0.470071i
$652$			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	$0.0315865\pi$
$654$	130.409	+	174.177i	0.199402	+	0.266326i
$655$	−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	$-0.937446\pi$
$659$		−	257.346i		−	0.390510i	0.980752	−	0.195255i	$-0.0625535\pi$
$660$	−204.170	+	220.537i	−0.309348	+	0.334147i
$661$	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
$663$	−131.007	−	56.0880i	−0.197597	−	0.0845973i
$664$	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
$669$	136.042	−	101.857i	0.203352	−	0.152253i
$670$	−775.078	+	659.275i	−1.15683	+	0.983993i
$671$		−	281.089i		−	0.418911i
$672$	−867.949	+	393.999i	−1.29159	+	0.586309i
$673$			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
$675$	131.532	+	662.061i	0.194862	+	0.980831i
$676$	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
$681$	−12.6148	+	29.4647i	−0.0185239	+	0.0432669i
$682$	−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	$0.505090\pi$
$684$	121.924	−	415.478i	0.178251	−	0.607424i
$685$	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
$690$	825.370	−	255.605i	1.19619	−	0.370442i
$691$	−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
$693$	124.638	−	227.073i	0.179853	−	0.327667i
$694$	−696.028			−1.00292
$695$	−420.626	−	494.509i	−0.605217	−	0.711524i
$696$	−175.630	+	131.497i	−0.252342	+	0.188932i
$697$	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	$0.0291707\pi$
$701$			128.303i			0.183028i	−0.995804	+	0.0915142i	$0.970829\pi$
$702$	−1695.61	−	284.715i	−2.41540	−	0.405577i
$703$	426.131	−	246.027i	0.606161	−	0.349967i
$704$	314.136	−	181.366i	0.446215	−	0.257623i
$705$	−422.076	−	390.751i	−0.598689	−	0.554257i
$706$	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
$711$	399.919	+	419.289i	0.562474	+	0.589718i
$712$	−302.677	−	174.751i	−0.425109	−	0.245437i
$713$	681.738			0.956155
$714$	13.5267	−	138.338i	0.0189450	−	0.193751i
$715$	147.540	−	413.981i	0.206350	−	0.578994i
$716$	1126.43	+	650.343i	1.57322	+	0.908301i
$717$	900.594	−	674.288i	1.25606	−	0.940429i
$718$	218.438	−	126.115i	0.304231	−	0.175648i
$719$	−142.417	−	82.2245i	−0.198077	−	0.114360i	0.397681	−	0.917524i	$-0.369815\pi$
$719$	−142.417	−	82.2245i	−0.198077	−	0.114360i	−0.595758	+	0.803164i	$0.703148\pi$
$720$	54.9778	−	525.702i	0.0763581	−	0.730141i
$721$	5.19462	+	16.3828i	0.00720475	+	0.0227224i
$722$	784.974			1.08722
$723$	101.036	−	235.993i	0.139745	−	0.326408i
$724$	576.943	+	999.294i	0.796882	+	1.38024i
$725$	−693.996	−	112.795i	−0.957236	−	0.155579i
$726$	366.113	−	855.142i	0.504287	−	1.17788i
$727$			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
$732$	−598.996	−	800.032i	−0.818300	−	1.09294i
$733$	−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
$735$	−728.530	−	97.3074i	−0.991198	−	0.132391i
$736$	−877.746			−1.19259
$737$	−140.452	+	243.270i	−0.190573	+	0.330081i
$738$	532.847	−	508.230i	0.722014	−	0.688658i
$739$	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	$-0.744499\pi$
$743$	−1032.44			−1.38956			−0.694781	+	0.719221i	$0.744499\pi$
$744$	−108.243	+	252.827i	−0.145488	+	0.339822i
$745$	178.520	+	974.190i	0.239625	+	1.30764i
$746$	−733.036	+	423.219i	−0.982622	+	0.567317i
$747$	311.176	−	1060.39i	0.416567	−	1.41953i
$748$			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
$753$	−132.812	+	99.4385i	−0.176378	+	0.132056i
$754$	895.465	−	1550.99i	1.18762	−	2.05702i
$755$	−279.307	+	783.702i	−0.369942	+	1.03802i
$756$	−129.146	−	911.894i	−0.170828	−	1.20621i
$757$		−	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
$759$	190.941	−	142.960i	0.251569	−	0.188353i
$760$	126.266	−	23.1383i	0.166140	−	0.0304451i
$761$	144.343	+	83.3364i	0.189675	+	0.109509i	0.591831	−	0.806062i	$-0.298405\pi$
$761$	144.343	+	83.3364i	0.189675	+	0.109509i	−0.402155	+	0.915571i	$0.631739\pi$
$762$	79.8200	+	667.139i	0.104751	+	0.875510i
$763$	36.6212	−	166.461i	0.0479964	−	0.218166i
$764$		−	458.851i		−	0.600590i
$765$	80.9260	+	58.7321i	0.105786	+	0.0767740i
$766$	−1030.68	−	1785.19i	−1.34553	−	2.33053i
$767$	−272.157	−	471.389i	−0.354833	−	0.614589i
$768$	−130.966	+	305.902i	−0.170529	+	0.398309i
$769$	−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	0.724641	−	0.689127i	$-0.242006\pi$
$773$	−181.254	−	313.941i	−0.234481	−	0.406133i	−0.959122	+	0.282994i	$0.908672\pi$
$774$	814.735	−	777.095i	1.05263	−	1.00400i
$775$	−824.081	+	312.521i	−1.06333	+	0.403252i
$776$			35.5554i			0.0458188i
$777$	609.025	−	851.159i	0.783816	−	1.09544i
$778$		−	1961.66i		−	2.52141i
$779$	−234.850	−	135.591i	−0.301476	−	0.174057i
$780$	−462.258	−	1492.67i	−0.592639	−	1.91368i
$781$	−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
$786$	−1808.04	−	774.079i	−2.30031	−	0.984833i
$787$	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
$789$	−331.112	+	773.389i	−0.419660	+	0.980214i
$790$	−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
$795$	−735.739	+	227.848i	−0.925458	+	0.286601i
$796$	−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	$0.717028\pi$
$798$	−562.364	+	255.281i	−0.704716	+	0.319901i
$799$	−85.2056			−0.106640
$800$	1061.01	−	402.374i	1.32627	−	0.502967i
$801$	−875.315	+	834.877i	−1.09278	+	1.04229i
$802$	−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
$807$	351.565	+	150.516i	0.435644	+	0.186513i
$808$	206.174	−	119.035i	0.255166	−	0.147320i
$809$	−258.960	+	149.510i	−0.320099	+	0.184809i	−0.651437	−	0.758703i	$-0.725833\pi$
$809$	−258.960	+	149.510i	−0.320099	+	0.184809i	0.331338	+	0.943512i	$0.392500\pi$
$810$	1115.97	+	458.258i	1.37774	+	0.565750i
$811$	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
$816$	−46.9287	−	62.6790i	−0.0575107	−	0.0768125i
$817$	−359.091	−	207.321i	−0.439524	−	0.253759i
$818$	−780.662			−0.954354
$819$	698.448	+	1151.55i	0.852806	+	1.40604i
$820$	630.393	+	224.668i	0.768772	+	0.273986i
$821$	−362.090	−	209.053i	−0.441035	−	0.254632i	0.263001	−	0.964795i	$-0.415288\pi$
$821$	−362.090	−	209.053i	−0.441035	−	0.254632i	−0.704037	+	0.710164i	$0.748621\pi$
$822$	−436.061	−	582.412i	−0.530487	−	0.708531i
$823$	−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
$825$	−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	$0.534415\pi$
$828$	238.808	−	813.783i	0.288415	−	0.982829i
$829$	−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
$831$	557.998	+	238.896i	0.671478	+	0.287480i
$832$			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
$837$	734.142	+	605.864i	0.877111	+	0.723852i
$838$	−241.694	−	139.542i	−0.288417	−	0.166518i
$839$		−	1038.70i		−	1.23803i	−0.785380	−	0.619013i	$-0.787533\pi$
$839$		−	1038.70i		−	1.23803i	0.785380	−	0.619013i	$-0.212467\pi$
$840$	224.210	−	155.827i	0.266916	−	0.185509i
$841$	50.0343			0.0594938
$842$	−7.56398	+	13.1012i	−0.00898335	+	0.0155596i
$843$	748.357	−	560.306i	0.887731	−	0.664657i
$844$	−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
$849$	218.980	+	93.7522i	0.257927	+	0.110427i
$850$	−26.5460	+	163.331i	−0.0312306	+	0.192154i
$851$	834.648	−	481.884i	0.980785	−	0.566257i
$852$	−160.562	−	68.7416i	−0.188453	−	0.0806826i
$853$		−	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
$855$	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	$0.667596\pi$
$858$	−470.767	−	628.767i	−0.548679	−	0.732828i
$859$	−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
$861$	−574.070	−	56.1327i	−0.666748	−	0.0651948i
$862$		−	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	$0.858637\pi$
$864$	−945.216	−	780.057i	−1.09400	−	0.902844i
$865$	−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
$870$	−853.689	+	922.126i	−0.981252	+	1.05991i
$871$	−730.267	−	1264.86i	−0.838424	−	1.45219i
$872$	31.6583	+	54.8338i	0.0363054	+	0.0628828i
$873$	118.078	+	34.6505i	0.135255	+	0.0396912i
$874$	−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
$879$	−289.811	−	387.078i	−0.329705	−	0.440362i
$880$	183.934	−	156.453i	0.209016	−	0.177788i
$881$		−	1653.70i		−	1.87707i	−0.345189	−	0.938533i	$-0.612185\pi$
$881$		−	1653.70i		−	1.87707i	0.345189	−	0.938533i	$-0.387815\pi$
$882$	−864.745	+	988.859i	−0.980437	+	1.12116i
$883$		−	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
$885$	112.982	+	364.829i	0.127663	+	0.412236i
$886$	−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
$891$	332.667	+	15.7409i	0.373364	+	0.0176665i
$892$	239.068	−	138.026i	0.268013	−	0.154737i
$893$	189.292	+	327.864i	0.211973	+	0.367148i
$894$	1627.25	+	696.677i	1.82019	+	0.779281i
$895$	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
$900$	84.3826	+	1093.17i	0.0937584	+	1.21463i
$901$	−57.0484	+	98.8107i	−0.0633168	+	0.109668i
$902$	336.401			0.372950
$903$	−877.766	−	85.8282i	−0.972055	−	0.0950478i
$904$	46.4758			0.0514113
$905$	767.101	+	901.843i	0.847625	+	0.996512i
$906$	891.202	+	1190.31i	0.983667	+	1.31381i
$907$	−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	$0.129880\pi$
$911$			722.972i			0.793602i	−0.917905	+	0.396801i	$0.870120\pi$
$912$	−136.927	+	319.824i	−0.150139	+	0.350685i
$913$	437.223	−	252.431i	0.478886	−	0.276485i
$914$	−1329.96	+	767.852i	−1.45510	+	0.840101i
$915$	−752.506	−	696.658i	−0.822410	−	0.761374i
$916$	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
$921$	−514.677	+	385.346i	−0.558824	+	0.418399i
$922$	1493.71	+	862.393i	1.62007	+	0.935351i
$923$	255.410			0.276717
$924$	244.837	−	342.178i	0.264975	−	0.370323i
$925$	−788.014	+	965.116i	−0.851907	+	1.04337i
$926$	49.6021	+	28.6378i	0.0535660	+	0.0309263i
$927$	−15.9900	+	15.2513i	−0.0172492	+	0.0164523i
$928$	1105.53	−	638.276i	1.19130	−	0.687798i
$929$	591.787	+	341.668i	0.637015	+	0.367781i	0.783464	−	0.621437i	$-0.213451\pi$
$929$	591.787	+	341.668i	0.637015	+	0.367781i	−0.146449	+	0.989218i	$0.546784\pi$
$930$	−348.796	+	1536.09i	−0.375049	+	1.65171i
$931$	439.109	+	203.034i	0.471653	+	0.218082i
$932$	873.003			0.936699
$933$	−1132.77	−	484.974i	−1.21412	−	0.519801i
$934$	697.441	+	1208.00i	0.746725	+	1.29337i
$935$	8.23393	+	44.9327i	0.00880634	+	0.0480564i
$936$	−480.076	−	140.880i	−0.512902	−	0.150513i
$937$		−	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	−0.750222	−	0.661186i	$-0.770053\pi$
$941$	−520.118	+	300.290i	−0.552729	+	0.319118i	0.197493	+	0.980304i	$0.436720\pi$
$942$	952.030	−	712.799i	1.01065	−	0.756686i
$943$	−459.993	−	265.577i	−0.487797	−	0.281630i
$944$		−	299.070i		−	0.316812i
$945$	−298.994	−	896.453i	−0.316395	−	0.948627i
$946$	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	$0.178479\pi$
$948$	564.090	+	753.411i	0.595032	+	0.794738i
$949$	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	$-0.628956\pi$
$953$	−751.223			−0.788272			−0.394136	+	0.919052i	$0.628956\pi$
$954$	−387.613	+	1320.87i	−0.406303	+	1.38456i
$955$	−84.8631	−	463.100i	−0.0888619	−	0.484921i
$956$	1582.62	−	913.723i	1.65546	−	0.955778i
$957$	−136.534	+	318.907i	−0.142669	+	0.333236i
$958$		−	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
$963$	98.6715	+	103.451i	0.102463	+	0.107425i
$964$	208.492	−	361.119i	0.216278	−	0.374604i
$965$	−1294.88	−	461.487i	−1.34184	−	0.478225i
$966$	−1101.48	+	500.011i	−1.14025	+	0.517610i
$967$			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
$969$	−39.4456	−	52.6844i	−0.0407075	−	0.0543698i
$970$	36.7064	+	200.308i	0.0378416	+	0.206503i
$971$	288.814	+	166.747i	0.297439	+	0.171727i	0.641292	−	0.767297i	$-0.278399\pi$
$971$	288.814	+	166.747i	0.297439	+	0.171727i	−0.343853	+	0.939024i	$0.611732\pi$
$972$	980.377	−	664.106i	1.00862	−	0.683237i
$973$	671.092	+	612.950i	0.689714	+	0.629959i
$974$		−	987.614i		−	1.01398i
$975$	−742.604	−	1421.00i	−0.761645	−	1.45744i
$976$	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	$-0.354935\pi$
$978$	429.499	+	183.882i	0.439161	+	0.188018i
$979$	−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	0.839828	−	0.542853i	$-0.182656\pi$
$983$	−49.3566	−	85.4881i	−0.0502101	−	0.0869665i	−0.890038	+	0.455886i	$0.849322\pi$
$984$	171.527	−	128.425i	0.174316	−	0.130513i
$985$	102.315	+	120.287i	0.103874	+	0.122119i
$986$			186.152i			0.188795i
$987$	654.879	+	468.582i	0.663504	+	0.474754i
$988$			1028.51i			1.04100i
$989$	−703.340	−	406.073i	−0.711163	−	0.410590i
$990$	224.428	+	503.371i	0.226695	+	0.508455i
$991$	−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
$996$	706.492	−	1650.18i	0.709330	−	1.65681i
$997$	−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
$999$	1327.06	+	222.830i	1.32839	+	0.223054i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.48938 - 2.57968i) q^{2} +(-1.79802 - 2.40148i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(-3.23955 - 3.80858i) q^{5} +(-8.87298 + 1.06161i) q^{6} +(5.16858 + 4.72078i) q^{7} -2.60040 q^{8} +(-2.53422 + 8.63584i) q^{9} +O(q^{10})\)	\(q+(1.48938 - 2.57968i) q^{2} +(-1.79802 - 2.40148i) 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} +(-2.53422 + 8.63584i) q^{9} +(-14.6498 + 2.68458i) q^{10} +(-3.56075 + 2.05580i) q^{11} +(-5.75368 + 13.4391i) 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} +(18.5033 + 19.3995i) q^{18} +(4.93649 - 8.55025i) q^{19} +(-8.17956 + 22.9509i) q^{20} +(2.04364 - 20.9003i) q^{21} +12.2474i q^{22} +(9.66894 - 16.7471i) q^{23} +(4.67559 + 6.24482i) 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} +(32.7877 + 30.3543i) q^{30} +(17.6270 + 30.5309i) q^{31} +(-22.6950 - 39.3089i) q^{32} +(11.3393 + 4.85469i) 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} +(-51.3386 + 38.4380i) q^{39} +(8.42414 + 9.90385i) q^{40} -27.4670i q^{41} +(-50.8724 - 36.4004i) q^{42} -41.9977i q^{43} +(17.3515 + 10.0179i) q^{44} +(41.1000 - 18.3245i) 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} +(2.62365 - 6.12814i) q^{51} +(-90.2174 + 52.0870i) q^{52} +(25.6737 + 44.4682i) q^{53} +(13.3182 - 79.3160i) 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} +(69.8232 - 21.6232i) q^{60} +(-34.1825 + 59.2058i) q^{61} +105.013 q^{62} +(-53.8662 + 32.6715i) q^{63} -88.2218 q^{64} +(-81.4195 + 69.2548i) q^{65} +(29.4120 - 22.0212i) 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} +(6.59000 - 22.4567i) q^{72} +(-88.6742 + 51.1961i) q^{73} +(128.567 - 74.2282i) q^{74} +(66.4706 - 34.7370i) 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} +(-68.1555 - 43.7702i) q^{81} +(-70.8561 - 40.9088i) q^{82} -122.790 q^{83} +(-93.1813 + 42.2990i) q^{84} +(3.72983 - 10.4655i) q^{85} +(-108.341 - 62.5505i) q^{86} +(67.5395 - 50.5678i) 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} +(41.6255 - 97.2262i) q^{93} +(57.1109 + 98.9190i) q^{94} +(-48.5564 + 8.89796i) q^{95} +(-53.5934 + 125.180i) 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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