LMFDB - Embedded newform 105.3.o.a.44.2

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			44.2
Root			$1.51479 - 1.11371i$ of defining polynomial
Character	$\chi$	$=$	105.44
Dual form			105.3.o.a.74.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48938 + 2.57968i) q^{2} +(1.79802 + 2.40148i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(-4.91811 - 0.901243i) q^{5} +(-8.87298 + 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} +2.60040 q^{8} +(-2.53422 + 8.63584i) q^{9} +O(q^{10})$	\(q+(-1.48938 + 2.57968i) q^{2} +(1.79802 + 2.40148i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(-4.91811 - 0.901243i) q^{5} +(-8.87298 + 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} +2.60040 q^{8} +(-2.53422 + 8.63584i) q^{9} +(9.64983 - 11.3448i) q^{10} +(-3.56075 + 2.05580i) q^{11} +(5.75368 - 13.4391i) 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} +(-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} +(23.3755 + 8.86482i) q^{25} +(-55.1481 - 31.8397i) q^{26} +(-25.2954 + 9.44157i) q^{27} +(-7.32910 + 33.3142i) q^{28} +28.1241i q^{29} +(44.5950 + 2.77560i) q^{30} +(17.6270 + 30.5309i) q^{31} +(22.6950 + 39.3089i) q^{32} +(-11.3393 - 4.85469i) q^{33} +6.61895 q^{34} +(21.1650 + 27.8755i) q^{35} +(42.6190 - 10.3464i) q^{36} +(-43.1613 - 24.9192i) q^{37} +(14.7046 + 25.4691i) q^{38} +(-51.3386 + 38.4380i) q^{39} +(-12.7891 - 2.34360i) q^{40} -27.4670i q^{41} +(50.8724 + 36.4004i) q^{42} +41.9977i q^{43} +(17.3515 + 10.0179i) q^{44} +(20.2466 - 40.1880i) 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} +(-40.4091 + 60.9093i) q^{60} +(-34.1825 + 59.2058i) q^{61} -105.013 q^{62} +(53.8662 - 32.6715i) q^{63} -88.2218 q^{64} +(19.2667 - 105.139i) 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} +(-103.432 + 13.0819i) q^{70} +11.9474i q^{71} +(-6.59000 + 22.4567i) q^{72} +(88.6742 - 51.1961i) q^{73} +(128.567 - 74.2282i) q^{74} +(20.7411 + 72.0750i) q^{75} -48.1109 q^{76} +(28.1090 + 6.18396i) q^{77} +(-22.6950 - 189.686i) q^{78} +(32.1905 - 55.7556i) q^{79} +(-38.0517 + 44.7355i) q^{80} +(-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} +(73.5174 + 112.085i) q^{90} +(100.920 - 110.493i) q^{91} +94.2332 q^{92} +(-41.6255 + 97.2262i) q^{93} +(57.1109 + 98.9190i) q^{94} +(-31.9840 + 37.6021i) 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	$0.434069\pi$
$2$	−1.48938	+	2.57968i	−0.744689	+	1.28984i	−0.950340	+	0.311214i	$0.899265\pi$
$3$	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
$5$	−4.91811	−	0.901243i	−0.983621	−	0.180249i
$5$	−4.91811	−	0.901243i	−0.983621	−	0.180249i
$6$	−8.87298	+	1.06161i	−1.47883	+	0.176935i
$7$	−5.16858	−	4.72078i	−0.738368	−	0.674398i
$7$	−5.16858	−	4.72078i	−0.738368	−	0.674398i
$8$	2.60040			0.325050
$9$	−2.53422	+	8.63584i	−0.281580	+	0.959538i
$10$	9.64983	−	11.3448i	0.964983	−	1.13448i
$11$	−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	$0.307268\pi$
$13$			21.3779i			1.64445i	−0.569160	+	0.822226i	$0.692732\pi$
$14$	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	$0.854151\pi$
$18$	−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	−0.995977	−	0.0896047i	$-0.971440\pi$
$23$	−9.66894	+	16.7471i	−0.420389	+	0.728135i	0.575589	+	0.817739i	$0.304773\pi$
$24$	4.67559	+	6.24482i	0.194816	+	0.260201i
$25$	23.3755	+	8.86482i	0.935021	+	0.354593i
$26$	−55.1481	−	31.8397i	−2.12108	−	1.22461i
$27$	−25.2954	+	9.44157i	−0.936866	+	0.349688i
$28$	−7.32910	+	33.3142i	−0.261754	+	1.18979i
$29$			28.1241i			0.969797i	0.874570	+	0.484898i	$0.161143\pi$
$29$			28.1241i			0.969797i	−0.874570	+	0.484898i	$0.838857\pi$
$30$	44.5950	+	2.77560i	1.48650	+	0.0925201i
$31$	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
$35$	21.1650	+	27.8755i	0.604716	+	0.796441i
$36$	42.6190	−	10.3464i	1.18386	−	0.287401i
$37$	−43.1613	−	24.9192i	−1.16652	−	0.673492i	−0.213664	−	0.976907i	$-0.568540\pi$
$37$	−43.1613	−	24.9192i	−1.16652	−	0.673492i	−0.952858	+	0.303416i	$0.901873\pi$
$38$	14.7046	+	25.4691i	0.386963	+	0.670240i
$39$	−51.3386	+	38.4380i	−1.31637	+	0.985589i
$40$	−12.7891	−	2.34360i	−0.319727	−	0.0585899i
$41$		−	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	$0.162399\pi$
$43$			41.9977i			0.976691i	−0.872650	+	0.488346i	$0.837601\pi$
$44$	17.3515	+	10.0179i	0.394352	+	0.227679i
$45$	20.2466	−	40.1880i	0.449923	−	0.893067i
$46$	−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
$51$	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	0.515429	−	0.856932i	$-0.327632\pi$
$53$	−25.6737	−	44.4682i	−0.484410	−	0.839023i	−0.999840	+	0.0179089i	$0.994299\pi$
$54$	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	$0.264105\pi$
$60$	−40.4091	+	60.9093i	−0.673485	+	1.01516i
$61$	−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
$65$	19.2667	−	105.139i	0.296410	−	1.61752i
$66$	29.4120	−	22.0212i	0.445637	−	0.333655i
$67$	−59.1667	+	34.1599i	−0.883086	+	0.509850i	−0.871675	−	0.490085i	$-0.836966\pi$
$67$	−59.1667	+	34.1599i	−0.883086	+	0.509850i	−0.0114110	+	0.999935i	$0.503632\pi$
$68$	−5.41401	+	9.37734i	−0.0796178	+	0.137902i
$69$	−57.6028	+	6.89190i	−0.834823	+	0.0998827i
$70$	−103.432	+	13.0819i	−1.47761	+	0.186885i
$71$			11.9474i			0.168273i	0.996454	+	0.0841366i	$0.0268132\pi$
$71$			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	0.250932	−	0.968005i	$-0.419263\pi$
$73$	88.6742	−	51.1961i	1.21471	−	0.701316i	0.963783	+	0.266689i	$0.0859296\pi$
$74$	128.567	−	74.2282i	1.73739	−	1.00308i
$75$	20.7411	+	72.0750i	0.276548	+	0.961000i
$76$	−48.1109			−0.633038
$77$	28.1090	+	6.18396i	0.365052	+	0.0803112i
$78$	−22.6950	−	189.686i	−0.290961	−	2.43187i
$79$	32.1905	−	55.7556i	0.407475	−	0.705767i	−0.587131	−	0.809492i	$-0.699743\pi$
$79$	32.1905	−	55.7556i	0.407475	−	0.705767i	0.994606	+	0.103724i	$0.0330760\pi$
$80$	−38.0517	+	44.7355i	−0.475646	+	0.559194i
$81$	−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	$-0.234969\pi$
$83$	122.790			1.47939			0.739696	+	0.672941i	$0.234969\pi$
$84$	−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	$0.394268\pi$
$90$	73.5174	+	112.085i	0.816860	+	1.24539i
$91$	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
$95$	−31.9840	+	37.6021i	−0.336674	+	0.395811i
$96$	−53.5934	+	125.180i	−0.558264	+	1.30396i
$97$			13.6730i			0.140959i	0.997513	+	0.0704795i	$0.0224529\pi$
$97$			13.6730i			0.140959i	−0.997513	+	0.0704795i	$0.977547\pi$
$98$	−132.483	−	61.2569i	−1.35186	−	0.625071i
$99$	−8.72983	−	35.9599i	−0.0881801	−	0.363231i
$100$	−19.5436	−	120.247i	−0.195436	−	1.20247i
$101$	−79.2855	+	45.7755i	−0.785005	+	0.453223i	−0.838201	−	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	0.489643	−	0.871923i	$-0.337127\pi$
$103$	−2.12630	−	1.22762i	−0.0206437	−	0.0119186i	−0.510286	+	0.860005i	$0.670461\pi$
$104$			55.5911i			0.534530i
$105$	−28.8871	+	100.948i	−0.275115	+	0.961411i
$106$	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	$0.190316\pi$
$108$	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	$0.868960\pi$
$110$	−11.0379	+	60.2342i	−0.100345	+	0.547584i
$111$	−17.7621	−	148.456i	−0.160019	−	1.33744i
$112$	−78.3762	+	24.8513i	−0.699788	+	0.221887i
$113$	17.8725			0.158164			0.0790820	−	0.996868i	$-0.474801\pi$
$113$	17.8725			0.158164			0.0790820	+	0.996868i	$0.474801\pi$
$114$	−34.7244	+	81.1069i	−0.304600	+	0.711464i
$115$	62.6461	−	73.6499i	0.544748	−	0.640434i
$116$	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
$120$	−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
$123$	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	$0.0956576\pi$
$127$			75.1876i			0.592029i	−0.955184	+	0.296014i	$0.904342\pi$
$128$	40.6156	−	70.3482i	0.317309	−	0.549596i
$129$	−100.857	+	75.5129i	−0.781835	+	0.585371i
$130$	242.529	+	206.293i	1.86560	+	1.58687i
$131$	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
$135$	132.915	−	23.6373i	0.984552	−	0.175091i
$136$	−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	$0.929367\pi$
$138$	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	$0.345316\pi$
$140$	66.0695	−	157.237i	0.471925	−	1.12312i
$141$	114.222	−	13.6661i	0.810083	−	0.0969226i
$142$	−30.8204	−	17.7942i	−0.217045	−	0.125311i
$143$	−43.9487	−	76.1213i	−0.307333	−	0.532317i
$144$	72.9630	+	76.4970i	0.506687	+	0.531229i
$145$	25.3467	−	138.317i	0.174805	−	0.953913i
$146$			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	$0.898110\pi$
$150$	−216.822	−	53.8417i	−1.44548	−	0.358944i
$151$	−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	−0.0858070	−	0.996312i	$-0.527347\pi$
$157$	115.257	−	66.5436i	0.734121	−	0.423845i	0.819928	+	0.572467i	$0.194014\pi$
$158$	95.8877	+	166.082i	0.606884	+	1.05115i
$159$	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	0.632417	−	0.774628i	$-0.282063\pi$
$163$	45.2776	+	26.1411i	0.277777	+	0.160375i	−0.354640	+	0.935003i	$0.615396\pi$
$164$	−115.914	+	66.9232i	−0.706795	+	0.408068i
$165$	51.3925	+	34.0953i	0.311470	+	0.206638i
$166$	−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	$0.428939\pi$
$168$	5.31429	−	54.3493i	0.0316327	−	0.323508i
$169$	−288.014			−1.70423
$170$	−32.5527	−	5.96528i	−0.191486	−	0.0350899i
$171$	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	$0.391464\pi$
$173$	−112.271	+	194.459i	−0.648964	+	1.12404i	−0.983371	+	0.181610i	$0.941869\pi$
$174$	−29.8569	−	249.545i	−0.171591	−	1.43417i
$175$	−78.9694	−	156.169i	−0.451254	−	0.892396i
$176$			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	$0.601161\pi$
$180$	−218.929	+	12.4748i	−1.21627	+	0.0693042i
$181$	−236.792			−1.30824			−0.654122	−	0.756389i	$-0.726962\pi$
$181$	−236.792			−1.30824			−0.654122	+	0.756389i	$0.726962\pi$
$182$	134.729	+	424.908i	0.740267	+	2.33466i
$183$	−203.642	+	24.3648i	−1.11280	+	0.133141i
$184$	−25.1431	+	43.5492i	−0.136648	+	0.236681i
$185$	189.814	+	161.454i	1.02602	+	0.872725i
$186$	−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	−0.967792	−	0.251751i	$-0.918994\pi$
$193$	−238.098	+	137.466i	−1.23367	+	0.712257i	−0.265874	+	0.964008i	$0.585660\pi$
$194$	−35.2720	−	20.3643i	−0.181814	−	0.104971i
$195$	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	$0.474457\pi$
$198$	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	$0.958575\pi$
$200$	60.7858	+	23.0521i	0.303929	+	0.115261i
$201$	−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
$205$	−24.7545	+	135.086i	−0.120753	+	0.658955i
$206$	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
$210$	−217.390	−	224.869i	−1.03519	−	1.07081i
$211$	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
$215$	37.8501	−	206.549i	0.176047	−	0.960694i
$216$	−65.7782	+	24.5519i	−0.304529	+	0.113666i
$217$	53.0230	−	241.015i	0.244346	−	1.11067i
$218$	72.5291			0.332702
$219$	282.385	+	120.898i	1.28943	+	0.552044i
$220$	−76.3078	−	64.9069i	−0.346854	−	0.295031i
$221$	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	$-0.959460\pi$
$223$		−	56.6494i		−	0.254033i	0.991901	−	0.127017i	$-0.0405401\pi$
$224$	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	$0.825842\pi$
$228$	−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	−0.607246	−	0.794514i	$-0.707726\pi$
$233$	89.5759	−	155.150i	0.384446	−	0.665880i	0.991692	+	0.128634i	$0.0410592\pi$
$234$	414.720	−	395.561i	1.77231	−	1.69043i
$235$	−124.222	+	146.042i	−0.528605	+	0.621455i
$236$	−107.451	−	62.0368i	−0.455300	−	0.262868i
$237$	191.775	−	22.9450i	0.809179	−	0.0968144i
$238$	−34.2106	−	31.2466i	−0.143742	−	0.131288i
$239$			375.016i			1.56910i	0.620063	+	0.784552i	$0.287107\pi$
$239$			375.016i			1.56910i	−0.620063	+	0.784552i	$0.712893\pi$
$240$	−175.849	−	10.9449i	−0.732705	−	0.0456037i
$241$	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
$245$	22.2007	−	243.992i	0.0906152	−	0.995886i
$246$	29.1593	+	243.714i	0.118534	+	0.990709i
$247$	182.786	+	105.532i	0.740026	+	0.427254i
$248$	45.8374	+	79.3926i	0.184828	+	0.320132i
$249$	220.779	+	294.877i	0.886661	+	1.18424i
$250$	326.140	−	179.647i	1.30456	−	0.718590i
$251$		−	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
$255$	−18.4263	+	27.7743i	−0.0722601	+	0.108919i
$256$	−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
$261$	−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	$0.0123198\pi$
$263$	140.215	+	242.859i	0.533136	+	0.923418i	−0.466115	+	0.884724i	$0.654347\pi$
$264$	−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	$0.409480\pi$
$270$	−136.983	+	378.082i	−0.507346	+	1.40030i
$271$	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
$275$	−101.459	+	16.4900i	−0.368941	+	0.0599636i
$276$	169.433	+	226.299i	0.613889	+	0.819924i
$277$	175.222	−	101.165i	0.632571	−	0.365215i	−0.149176	−	0.988811i	$-0.547662\pi$
$277$	175.222	−	101.165i	0.632571	−	0.365215i	0.781747	+	0.623596i	$0.214329\pi$
$278$	−193.382	+	334.947i	−0.695618	+	1.20485i
$279$	−308.331	+	74.8521i	−1.10513	+	0.268287i
$280$	55.0377	+	72.4874i	0.196563	+	0.258884i
$281$			311.623i			1.10898i	0.832190	+	0.554490i	$0.187087\pi$
$281$			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	−0.373564	−	0.927604i	$-0.621864\pi$
$283$	68.7640	−	39.7009i	0.242982	−	0.140286i	0.616547	+	0.787318i	$0.288531\pi$
$284$	50.4195	−	29.1097i	0.177534	−	0.102499i
$285$	−147.809	−	9.19964i	−0.518627	−	0.0322794i
$286$	261.825			0.915471
$287$	−129.666	+	141.966i	−0.451797	+	0.494653i
$288$	−396.979	+	96.3729i	−1.37840	+	0.334628i
$289$	142.031	−	246.005i	0.491458	−	0.851230i
$290$	319.063	+	271.393i	1.10022	+	0.935838i
$291$	−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	$-0.588697\pi$
$293$	−161.183			−0.550113			−0.275056	+	0.961428i	$0.588697\pi$
$294$	−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
$300$	253.630	−	263.140i	0.845434	−	0.877134i
$301$	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
$305$	221.472	−	260.373i	0.726137	−	0.853683i
$306$	−16.7739	+	57.1602i	−0.0548166	+	0.186798i
$307$			214.316i			0.698099i	0.937104	+	0.349049i	$0.113495\pi$
$307$			214.316i			0.698099i	−0.937104	+	0.349049i	$0.886505\pi$
$308$	−42.3902	−	133.691i	−0.137631	−	0.434061i
$309$	−0.875033	−	7.31356i	−0.00283182	−	0.0236685i
$310$	516.466	+	94.6424i	1.66602	+	0.305298i
$311$	355.712	−	205.370i	1.14377	−	0.660354i	0.196407	−	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	−0.295711	−	0.955277i	$-0.595557\pi$
$313$	−397.780	−	229.658i	−1.27086	−	0.733732i	−0.975150	+	0.221545i	$0.928890\pi$
$314$			396.434i			1.26253i
$315$	−294.365	+	112.135i	−0.934491	+	0.355985i
$316$	−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	$0.279722\pi$
$318$	275.011	+	367.310i	0.864813	+	1.15506i
$319$	−57.8175	−	100.143i	−0.181246	−	0.313928i
$320$	433.884	+	79.5092i	1.35589	+	0.248466i
$321$	−47.3165	+	5.66120i	−0.147403	+	0.0176361i
$322$	−86.6362	+	393.802i	−0.269057	+	1.22299i
$323$	−21.9383			−0.0679204
$324$	−18.6558	+	394.271i	−0.0575796	+	1.21688i
$325$	−189.511	+	499.719i	−0.583111	+	1.53760i
$326$	−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
$330$	−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
$333$	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	$-0.884901\pi$
$337$		−	238.438i		−	0.707530i	0.935334	−	0.353765i	$-0.115099\pi$
$338$	428.962	−	742.984i	1.26912	−	2.19818i
$339$	32.1352	+	42.9205i	0.0947942	+	0.126609i
$340$	35.0779	−	41.2394i	0.103170	−	0.121292i
$341$	−125.531	−	72.4752i	−0.368125	−	0.212537i
$342$	−257.212	+	62.4422i	−0.752082	+	0.182580i
$343$	207.483	−	273.130i	0.604907	−	0.796296i
$344$			109.211i			0.317474i
$345$	289.508	+	18.0190i	0.839154	+	0.0522290i
$346$	−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	$0.724025\pi$
$348$	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	$0.540633\pi$
$350$	520.482	+	28.8795i	1.48709	+	0.0825128i
$351$	−201.841	−	540.762i	−0.575045	−	1.54063i
$352$	−161.622	−	93.3127i	−0.459154	−	0.265093i
$353$	−264.349	−	457.867i	−0.748865	−	1.29707i	−0.948367	−	0.317175i	$-0.897266\pi$
$353$	−264.349	−	457.867i	−0.748865	−	1.29707i	0.199502	−	0.979898i	$-0.436068\pi$
$354$	−182.137	+	136.369i	−0.514511	+	0.385222i
$355$	10.7675	−	58.7586i	0.0303310	−	0.165517i
$356$		−	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	$0.629040\pi$
$360$	52.6492	−	104.505i	0.146248	−	0.290292i
$361$	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	−0.130694	−	0.991423i	$-0.541720\pi$
$367$	243.158	−	140.388i	0.662557	−	0.382528i	0.793251	+	0.608895i	$0.208387\pi$
$368$	113.571	+	196.711i	0.308617	+	0.534540i
$369$	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	0.792183	−	0.610284i	$-0.208944\pi$
$373$	246.088	+	142.079i	0.659754	+	0.380909i	−0.132429	+	0.991192i	$0.542278\pi$
$374$	−23.5684	+	13.6072i	−0.0630172	+	0.0363830i
$375$	−37.0496	−	373.165i	−0.0987990	−	0.995107i
$376$	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	$0.370163\pi$
$380$	236.614	+	43.3596i	0.622669	+	0.114104i
$381$	−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	$0.525619\pi$
$383$	−346.010	+	599.307i	−0.903421	+	1.56477i	−0.823023	+	0.568007i	$0.807714\pi$
$384$	241.968	−	28.9503i	0.630124	−	0.0753914i
$385$	−132.670	−	55.7464i	−0.344597	−	0.144796i
$386$		−	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	$0.0120600\pi$
$390$	−59.3365	+	953.348i	−0.152145	+	2.44448i
$391$	42.9698			0.109897
$392$	11.5157	+	126.898i	0.0293768	+	0.323720i
$393$	78.4385	+	655.592i	0.199589	+	1.66817i
$394$	−47.0393	+	81.4745i	−0.119389	+	0.206788i
$395$	−208.566	+	245.201i	−0.528015	+	0.620761i
$396$	−130.485	+	124.457i	−0.329508	+	0.314285i
$397$	384.288	+	221.869i	0.967979	+	0.558863i	0.898619	−	0.438729i	$-0.144571\pi$
$397$	384.288	+	221.869i	0.967979	+	0.558863i	0.0693593	+	0.997592i	$0.477905\pi$
$398$	454.518			1.14201
$399$	−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
$405$	295.748	+	276.691i	0.730242	+	0.683188i
$406$	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	$0.937146\pi$
$410$	−311.609	−	265.052i	−0.760022	−	0.646469i
$411$	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
$415$	−603.892	−	110.663i	−1.45516	−	0.266658i
$416$	−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	$-0.0356627\pi$
$420$	496.397	−	124.052i	1.18190	−	0.295362i
$421$	−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
$425$	−8.91178	−	54.8318i	−0.0209689	−	0.129016i
$426$	−12.6835	−	106.009i	−0.0297734	−	0.248848i
$427$	456.172	−	144.642i	1.06832	−	0.338739i
$428$	77.4057			0.180854
$429$	103.783	−	242.410i	0.241919	−	0.565058i
$430$	476.457	+	405.271i	1.10804	+	0.942491i
$431$	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	$0.133643\pi$
$433$			353.004i			0.815251i	−0.913149	+	0.407626i	$0.866357\pi$
$434$	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
$438$	−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	−0.891978	−	0.452079i	$-0.850682\pi$
$443$	−24.1333	+	41.8000i	−0.0544769	+	0.0943567i	0.837501	+	0.546436i	$0.184016\pi$
$444$	−583.228	+	436.671i	−1.31358	+	0.983493i
$445$	−511.884	−	435.405i	−1.15030	−	0.978438i
$446$	146.137	+	84.3723i	0.327662	+	0.189176i
$447$	−70.5954	−	590.039i	−0.157931	−	1.32000i
$448$	455.981	+	416.476i	1.01782	+	0.929633i
$449$		−	633.019i		−	1.40984i	−0.709285	−	0.704921i	$-0.750982\pi$
$449$		−	633.019i		−	1.40984i	0.709285	−	0.704921i	$-0.249018\pi$
$450$	−260.551	−	617.502i	−0.579002	−	1.37223i
$451$	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
$455$	−595.918	+	452.464i	−1.30971	+	0.994426i
$456$	76.4758	−	9.14997i	0.167710	−	0.0200657i
$457$	446.482	+	257.776i	0.976984	+	0.564062i	0.901358	−	0.433074i	$-0.142571\pi$
$457$	446.482	+	257.776i	0.976984	+	0.564062i	0.0756257	+	0.997136i	$0.475905\pi$
$458$	−240.354	−	416.306i	−0.524791	−	0.908965i
$459$	46.2728	+	38.1875i	0.100812	+	0.0831971i
$460$	−463.449	−	84.9270i	−1.00750	−	0.184624i
$461$			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	$-0.993390\pi$
$463$		−	19.2280i		−	0.0415292i	0.999784	−	0.0207646i	$-0.00661005\pi$
$464$	286.087	+	165.172i	0.616567	+	0.355975i
$465$	292.343	−	440.654i	0.628695	−	0.947643i
$466$	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
$471$	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	$0.210930\pi$
$480$	376.395	−	567.347i	0.784157	−	1.18197i
$481$	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
$485$	12.3227	−	67.2454i	0.0254077	−	0.138650i
$486$	651.209	+	316.018i	1.33994	+	0.650243i
$487$	−287.133	+	165.776i	−0.589596	+	0.340403i	−0.764938	−	0.644104i	$-0.777230\pi$
$487$	−287.133	+	165.776i	−0.589596	+	0.340403i	0.175342	+	0.984508i	$0.443897\pi$
$488$	−88.8882	+	153.959i	−0.182148	+	0.315489i
$489$	18.6330	+	155.736i	0.0381044	+	0.318478i
$490$	596.356	+	420.667i	1.21705	+	0.858504i
$491$			102.807i			0.209383i	0.994505	+	0.104692i	$0.0333855\pi$
$491$			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
$495$	10.5256	+	184.722i	0.0212639	+	0.373176i
$496$	414.093			0.834864
$497$	56.4011	−	61.7511i	0.113483	−	0.124248i
$498$	−1089.51	+	130.355i	−2.18777	+	0.261756i
$499$	463.720	−	803.186i	0.929298	−	1.60959i	0.144799	−	0.989461i	$-0.453746\pi$
$499$	463.720	−	803.186i	0.929298	−	1.60959i	0.784499	−	0.620130i	$-0.212920\pi$
$500$	−12.2540	+	609.000i	−0.0245079	+	1.21800i
$501$	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	$-0.350394\pi$
$503$	455.605			0.905776			0.452888	+	0.891567i	$0.350394\pi$
$504$	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	$0.573922\pi$
$510$	−44.2050	−	88.9004i	−0.0866765	−	0.174314i
$511$	−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
$515$	9.35098	+	7.95388i	0.0181572	+	0.0154444i
$516$	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
$520$	50.1011	−	273.403i	0.0963483	−	0.525775i
$521$	−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	0.827727	−	0.561131i	$-0.189634\pi$
$523$	395.198	+	228.168i	0.755636	+	0.436267i	−0.0720905	+	0.997398i	$0.522967\pi$
$524$		−	1072.49i		−	2.04674i
$525$	233.049	−	470.439i	0.443902	−	0.896075i
$526$	−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
$530$	−752.232	−	137.847i	−1.41931	−	0.260088i
$531$	54.0604	+	222.686i	0.101809	+	0.419370i
$532$	248.665	+	227.121i	0.467415	+	0.426919i
$533$	587.187			1.10166
$534$	−1104.12	−	472.710i	−2.06765	−	0.885224i
$535$	51.4592	−	60.4980i	0.0961854	−	0.113080i
$536$	−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
$540$	−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
$543$	−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	$-0.980216\pi$
$547$		−	67.9520i		−	0.124227i	0.998069	−	0.0621133i	$-0.0197840\pi$
$548$	−198.373	+	343.591i	−0.361994	+	0.626991i
$549$	−424.666	−	445.235i	−0.773526	−	0.810992i
$550$	108.571	−	286.291i	0.197403	−	0.520528i
$551$	240.468	+	138.834i	0.436422	+	0.251968i
$552$	−149.791	+	17.9217i	−0.271360	+	0.0324669i
$553$	−429.589	+	136.213i	−0.776834	+	0.246316i
$554$			602.689i			1.08789i
$555$	−46.4394	+	746.132i	−0.0836745	+	1.34438i
$556$	−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	$0.799155\pi$
$558$	266.126	−	906.877i	0.476929	−	1.62523i
$559$	−897.823			−1.60612
$560$	407.860	−	51.5853i	0.728321	−	0.0921165i
$561$	3.25608	+	27.2145i	0.00580407	+	0.0485106i
$562$	−803.888	−	464.125i	−1.43041	−	0.825845i
$563$	461.941	+	800.106i	0.820500	+	1.42115i	0.905311	+	0.424750i	$0.139638\pi$
$563$	461.941	+	800.106i	0.820500	+	1.42115i	−0.0848112	+	0.996397i	$0.527029\pi$
$564$	−335.973	−	448.733i	−0.595697	−	0.795626i
$565$	−87.8990	−	16.1075i	−0.155573	−	0.0285088i
$566$			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	$0.569522\pi$
$570$	243.875	−	367.597i	0.427851	−	0.644907i
$571$	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	−0.0838807	−	0.996476i	$-0.526731\pi$
$577$	425.337	−	245.568i	0.737152	−	0.425595i	0.821033	+	0.570881i	$0.193398\pi$
$578$	423.076	+	732.790i	0.731966	+	1.26780i
$579$	−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
$585$	859.135	+	432.829i	1.46861	+	0.739878i
$586$	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	$0.590167\pi$
$588$	681.300	+	221.263i	1.15867	+	0.376297i
$589$	348.062			0.590938
$590$	68.3536	−	373.007i	0.115853	−	0.632215i
$591$	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	−0.980762	−	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
$595$	30.1273	−	71.6994i	0.0506341	−	0.120503i
$596$			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	$0.378838\pi$
$600$	53.9351	+	187.424i	0.0898919	+	0.312374i
$601$	40.5746			0.0675119			0.0337559	−	0.999430i	$-0.489253\pi$
$601$	40.5746			0.0675119			0.0337559	+	0.999430i	$0.489253\pi$
$602$	264.680	+	834.749i	0.439667	+	1.38663i
$603$	−145.058	−	597.523i	−0.240561	−	0.990917i
$604$	−405.425	+	702.217i	−0.671234	+	1.16261i
$605$	337.220	−	396.453i	0.557389	−	0.655295i
$606$	654.903	−	490.336i	1.08070	−	0.809135i
$607$	−88.2380	−	50.9442i	−0.145367	−	0.0839279i	0.425552	−	0.904934i	$-0.360080\pi$
$607$	−88.2380	−	50.9442i	−0.145367	−	0.0839279i	−0.570920	+	0.821006i	$0.693413\pi$
$608$	448.134			0.737063
$609$	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	0.453107	−	0.891456i	$-0.350316\pi$
$613$	889.882	−	513.774i	1.45168	−	0.838130i	0.998577	+	0.0533259i	$0.0169822\pi$
$614$	−552.867	−	319.198i	−0.900435	−	0.519866i
$615$	−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	$0.788407\pi$
$618$	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	$0.684238\pi$
$620$	−556.530	+	654.285i	−0.897629	+	1.05530i
$621$	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
$625$	467.830	+	414.439i	0.748528	+	0.663103i
$626$	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
$630$	149.147	−	926.378i	0.236742	−	1.47044i
$631$	−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
$635$	67.7623	−	369.781i	0.106712	−	0.582332i
$636$	−745.331	+	89.1753i	−1.17190	+	0.140213i
$637$	−1043.23	+	94.6704i	−1.63772	+	0.148619i
$638$	344.449			0.539888
$639$	−103.176	−	30.2773i	−0.161465	−	0.0473824i
$640$	−263.153	+	309.376i	−0.411176	+	0.483399i
$641$	−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	$-0.804524\pi$
$643$		−	741.031i		−	1.15246i	0.817288	−	0.576229i	$-0.195476\pi$
$644$	−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	$0.772126\pi$
$648$	−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	−0.995081	−	0.0990692i	$-0.968413\pi$
$653$	−268.869	+	465.694i	−0.411744	+	0.713161i	0.583337	+	0.812230i	$0.301747\pi$
$654$	130.409	+	174.177i	0.199402	+	0.266326i
$655$	−838.229	−	712.991i	−1.27974	−	1.08854i
$656$	−279.403	−	161.313i	−0.425919	−	0.245905i
$657$	217.401	+	895.518i	0.330900	+	1.36304i
$658$	171.793	−	780.879i	0.261083	−	1.18675i
$659$		−	257.346i		−	0.390510i	−0.980752	−	0.195255i	$-0.937446\pi$
$659$		−	257.346i		−	0.390510i	0.980752	−	0.195255i	$-0.0625535\pi$
$660$	18.6693	−	299.956i	0.0282868	−	0.454479i
$661$	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
$665$	342.823	−	43.3596i	0.515524	−	0.0652024i
$666$	315.206	+	1298.39i	0.473282	+	1.94954i
$667$	−470.997	−	271.930i	−0.706143	−	0.407692i
$668$	−180.170	−	312.063i	−0.269715	−	0.467160i
$669$	136.042	−	101.857i	0.203352	−	0.152253i
$670$	−183.410	+	1000.87i	−0.273747	+	1.49384i
$671$		−	281.089i		−	0.418911i
$672$	867.949	−	393.999i	1.29159	−	0.586309i
$673$		−	714.374i		−	1.06148i	−0.847535	−	0.530739i	$-0.821915\pi$
$673$		−	714.374i		−	1.06148i	0.847535	−	0.530739i	$-0.178085\pi$
$674$	615.092	+	355.124i	0.912600	+	0.526890i
$675$	−674.991	−	3.53747i	−0.999986	−	0.00524070i
$676$	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
$681$	−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	$-0.838424\pi$
$683$	−585.959	−	1014.91i	−0.857919	−	1.48596i	0.0159906	−	0.999872i	$-0.494910\pi$
$684$	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
$690$	−477.670	+	720.000i	−0.692275	+	1.04348i
$691$	−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
$695$	−638.570	−	117.018i	−0.918806	−	0.168371i
$696$	−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
$700$	−466.646	+	713.766i	−0.666637	+	1.01967i
$701$			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
$705$	−574.071	−	35.7303i	−0.814285	−	0.0506812i
$706$	1574.86			2.23069
$707$	625.890	+	137.695i	0.885276	+	0.194760i
$708$	−44.2191	−	369.585i	−0.0624563	−	0.522012i
$709$	−50.1663	+	86.8906i	−0.0707565	+	0.122554i	−0.899233	−	0.437470i	$-0.855875\pi$
$709$	−50.1663	+	86.8906i	−0.0707565	+	0.122554i	0.828477	+	0.560024i	$0.189208\pi$
$710$	135.541	+	115.290i	0.190903	+	0.162381i
$711$	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	$0.703148\pi$
$720$	−289.897	−	441.978i	−0.402635	−	0.613858i
$721$	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
$725$	−249.315	+	657.416i	−0.343883	+	0.906780i
$726$	366.113	−	855.142i	0.504287	−	1.17788i
$727$		−	1029.30i		−	1.41581i	−0.706307	−	0.707906i	$-0.749640\pi$
$727$		−	1029.30i		−	1.41581i	0.706307	−	0.707906i	$-0.250360\pi$
$728$	262.434	−	287.327i	0.360486	−	0.394680i
$729$	550.714	−	477.656i	0.755437	−	0.655221i
$730$	274.880	−	1500.03i	0.376548	−	2.05483i
$731$	80.8185	−	46.6606i	0.110559	−	0.0638311i
$732$	598.996	+	800.032i	0.818300	+	1.09294i
$733$	405.750	+	234.260i	0.553547	+	0.319591i	0.750552	−	0.660812i	$-0.229788\pi$
$733$	405.750	+	234.260i	0.553547	+	0.319591i	−0.197004	+	0.980403i	$0.563121\pi$
$734$			836.361i			1.13946i
$735$	625.860	−	385.389i	0.851510	−	0.524339i
$736$	−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	$0.806329\pi$
$740$	218.877	−	1194.42i	0.295780	−	1.61408i
$741$	75.2218	+	628.707i	0.101514	+	0.848457i
$742$	−790.542	−	722.051i	−1.06542	−	0.973115i
$743$	1032.44			1.38956			0.694781	−	0.719221i	$-0.255501\pi$
$743$	1032.44			1.38956			0.694781	+	0.719221i	$0.255501\pi$
$744$	−108.243	+	252.827i	−0.145488	+	0.339822i
$745$	754.413	+	641.698i	1.01264	+	0.861340i
$746$	−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
$750$	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
$753$	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	$0.126654\pi$
$757$			586.645i			0.774960i	−0.921878	+	0.387480i	$0.873346\pi$
$758$	−447.828	+	775.661i	−0.590802	+	1.02330i
$759$	190.941	−	142.960i	0.251569	−	0.188353i
$760$	−83.1714	+	97.7806i	−0.109436	+	0.128659i
$761$	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
$765$	−99.8304	+	5.68842i	−0.130497	+	0.00743584i
$766$	−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	$0.697687\pi$
$770$	341.403	−	259.218i	0.443381	−	0.336647i
$771$	478.300	−	57.2264i	0.620364	−	0.0742236i
$772$	1160.25	+	669.868i	1.50291	+	0.867705i
$773$	181.254	+	313.941i	0.234481	+	0.406133i	0.959122	−	0.282994i	$-0.0913277\pi$
$773$	181.254	+	313.941i	0.234481	+	0.406133i	−0.724641	+	0.689127i	$0.757994\pi$
$774$	814.735	−	777.095i	1.05263	−	1.00400i
$775$	141.390	+	869.936i	0.182439	+	1.12250i
$776$			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
$780$	−1302.11	−	863.861i	−1.66938	−	1.10751i
$781$	−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	−0.842310	−	0.538993i	$-0.818805\pi$
$787$	−626.990	+	361.993i	−0.796683	+	0.459965i	0.0456267	+	0.998959i	$0.485472\pi$
$788$	−76.9522	−	133.285i	−0.0976551	−	0.169144i
$789$	−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
$795$	−425.798	+	641.812i	−0.535595	+	0.807311i
$796$	−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	$0.282972\pi$
$798$	562.364	−	255.281i	0.704716	−	0.319901i
$799$	−85.2056			−0.106640
$800$	182.041	+	1120.05i	0.227552	+	1.40007i
$801$	−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
$805$	−671.476	+	84.9270i	−0.834132	+	0.105499i
$806$		−	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	$0.392500\pi$
$810$	−1154.25	+	350.837i	−1.42501	+	0.433132i
$811$	1055.66			1.30168			0.650840	−	0.759215i	$-0.274417\pi$
$811$	1055.66			1.30168			0.650840	+	0.759215i	$0.274417\pi$
$812$	−936.933	−	206.125i	−1.15386	−	0.253848i
$813$	342.647	−	40.9961i	0.421460	−	0.0504257i
$814$	−305.197	+	528.616i	−0.374934	+	0.649405i
$815$	−199.121	−	169.371i	−0.244320	−	0.207817i
$816$	−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	−0.401162	−	0.916007i	$-0.631394\pi$
$823$	157.639	−	91.0130i	0.191542	−	0.110587i	0.592704	+	0.805420i	$0.298060\pi$
$824$	−5.52924	−	3.19231i	−0.00671024	−	0.00387416i
$825$	−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	$0.465585\pi$
$828$	−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	$0.983562\pi$
$830$	1184.90	−	1393.03i	1.42759	−	1.67835i
$831$	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
$835$	−363.676	−	66.6436i	−0.435540	−	0.0798127i
$836$	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	$-0.212467\pi$
$840$	−75.1181	+	262.506i	−0.0894264	+	0.312507i
$841$	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
$845$	1416.48	+	259.571i	1.67631	+	0.307184i
$846$	−998.980	+	242.518i	−1.18083	+	0.286664i
$847$	694.583	−	220.236i	0.820051	−	0.260019i
$848$	−603.126			−0.711233
$849$	218.980	+	93.7522i	0.257927	+	0.110427i
$850$	154.721	+	58.6758i	0.182025	+	0.0690303i
$851$	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	$0.0324006\pi$
$853$			173.353i			0.203228i	−0.994824	+	0.101614i	$0.967599\pi$
$854$	−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	$0.999071\pi$
$858$	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	$-0.525304\pi$
$863$	710.754	−	1231.06i	0.823585	−	1.42649i	0.902996	−	0.429650i	$-0.141363\pi$
$864$	−945.216	−	780.057i	−1.09400	−	0.902844i
$865$	727.415	−	855.186i	0.840942	−	0.988654i
$866$	−910.636	−	525.756i	−1.05154	−	0.607109i
$867$	846.153	−	101.238i	0.975955	−	0.116768i
$868$	−1146.30	+	363.466i	−1.32063	+	0.418740i
$869$			264.709i			0.304613i
$870$	−78.0613	+	1254.20i	−0.0897257	+	1.44160i
$871$	−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
$875$	247.633	+	839.227i	0.283009	+	0.959117i
$876$	−177.825	−	1486.27i	−0.202996	−	1.69665i
$877$	9.68130	+	5.58950i	0.0110391	+	0.00637343i	0.505509	−	0.862821i	$-0.331305\pi$
$877$	9.68130	+	5.58950i	0.0110391	+	0.00637343i	−0.494470	+	0.869195i	$0.664638\pi$
$878$	−988.067	−	1711.38i	−1.12536	−	1.94918i
$879$	−289.811	−	387.078i	−0.329705	−	0.440362i
$880$	43.5253	−	237.518i	0.0494605	−	0.269907i
$881$		−	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	$0.365486\pi$
$883$			1610.65i			1.82406i	−0.410123	+	0.912030i	$0.634514\pi$
$884$	−200.468	−	115.740i	−0.226774	−	0.130928i
$885$	−318.254	−	211.139i	−0.359609	−	0.238575i
$886$	−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
$891$	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
$900$	1087.96	+	135.956i	1.20884	+	0.151062i
$901$	−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
$905$	1164.57	+	213.407i	1.28682	+	0.235809i
$906$	891.202	+	1190.31i	0.983667	+	1.31381i
$907$	265.679	−	153.390i	0.292921	−	0.169118i	−0.346338	−	0.938110i	$-0.612575\pi$
$907$	265.679	−	153.390i	0.292921	−	0.169118i	0.639258	+	0.768992i	$0.279241\pi$
$908$	26.0311	−	45.0872i	0.0286686	−	0.0496555i
$909$	−194.383	−	800.702i	−0.213843	−	0.880861i
$910$	−279.664	−	2211.17i	−0.307323	−	2.42985i
$911$			722.972i			0.793602i	0.917905	+	0.396801i	$0.129880\pi$
$911$			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
$915$	1023.49	+	63.7024i	1.11857	+	0.0696201i
$916$	786.397			0.858512
$917$	−465.650	−	1468.57i	−0.507797	−	1.60149i
$918$	−167.429	+	62.4932i	−0.182384	+	0.0680754i
$919$	755.087	−	1307.85i	0.821639	−	1.42312i	−0.0828212	−	0.996564i	$-0.526393\pi$
$919$	755.087	−	1307.85i	0.821639	−	1.42312i	0.904461	−	0.426557i	$-0.140274\pi$
$920$	162.905	−	191.520i	0.177071	−	0.208173i
$921$	−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	$0.546784\pi$
$930$	701.336	+	1410.45i	0.754125	+	1.51661i
$931$	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
$935$	−34.7959	−	29.5972i	−0.0372149	−	0.0316547i
$936$	−480.076	−	140.880i	−0.512902	−	0.150513i
$937$			1295.06i			1.38214i	0.722789	+	0.691069i	$0.242860\pi$
$937$			1295.06i			1.38214i	−0.722789	+	0.691069i	$0.757140\pi$
$938$	−960.718	+	1051.85i	−1.02422	+	1.12137i
$939$	−163.698	−	1368.19i	−0.174332	−	1.45707i
$940$	918.982	+	168.403i	0.977640	+	0.179153i
$941$	−520.118	+	300.290i	−0.552729	+	0.319118i	−0.750222	−	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
$945$	−798.566	−	505.289i	−0.845043	−	0.534698i
$946$	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	$0.154854\pi$
$948$	−564.090	−	753.411i	−0.595032	−	0.794738i
$949$	1094.46	+	1895.67i	1.15328	+	1.99754i
$950$	117.949	+	725.707i	0.124157	+	0.763903i
$951$	−656.744	+	78.5763i	−0.690582	+	0.0826249i
$952$	−8.69062	+	39.5030i	−0.00912881	+	0.0414947i
$953$	751.223			0.788272			0.394136	−	0.919052i	$-0.371044\pi$
$953$	751.223			0.788272			0.394136	+	0.919052i	$0.371044\pi$
$954$	−387.613	+	1320.87i	−0.406303	+	1.38456i
$955$	−358.625	−	305.044i	−0.375523	−	0.319417i
$956$	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
$960$	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
$963$	−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	$-0.789802\pi$
$967$		−	1186.31i		−	1.22680i	0.789774	−	0.613398i	$-0.210198\pi$
$968$	−135.344	+	234.423i	−0.139818	+	0.242173i
$969$	−39.4456	−	52.6844i	−0.0407075	−	0.0543698i
$970$	155.118	+	131.942i	0.159916	+	0.136023i
$971$	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
$975$	−1540.81	+	443.400i	−1.58032	+	0.454769i
$976$	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	$0.645065\pi$
$978$	−429.499	−	183.882i	−0.439161	−	0.188018i
$979$	−552.611			−0.564465
$980$	−1083.77	+	500.795i	−1.10589	+	0.511015i
$981$	212.954	−	51.6978i	0.217078	−	0.0526991i
$982$	−265.209	−	153.119i	−0.270070	−	0.155925i
$983$	49.3566	+	85.4881i	0.0502101	+	0.0869665i	0.890038	−	0.455886i	$-0.150678\pi$
$983$	49.3566	+	85.4881i	0.0502101	+	0.0869665i	−0.839828	+	0.542853i	$0.817344\pi$
$984$	171.527	−	128.425i	0.174316	−	0.130513i
$985$	−155.329	−	28.4641i	−0.157695	−	0.0288976i
$986$			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
$990$	−492.201	−	247.969i	−0.497172	−	0.250473i
$991$	−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	−0.476054	−	0.879416i	$-0.657933\pi$
$997$	47.3741	−	27.3514i	0.0475166	−	0.0274337i	0.523570	+	0.851983i	$0.324600\pi$
$998$	1381.31	+	2392.49i	1.38408	+	2.39729i
$999$	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.44.2	yes	16
3.2	odd	2	inner	105.3.o.a.44.8	yes	16
5.4	even	2	inner	105.3.o.a.44.7	yes	16
7.4	even	3	inner	105.3.o.a.74.1	yes	16
15.14	odd	2	inner	105.3.o.a.44.1	✓	16
21.11	odd	6	inner	105.3.o.a.74.7	yes	16
35.4	even	6	inner	105.3.o.a.74.8	yes	16
105.74	odd	6	inner	105.3.o.a.74.2	yes	16

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

\(f(q)\)	\(=\)	\(q+(-1.48938 + 2.57968i) q^{2} +(1.79802 + 2.40148i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(-4.91811 - 0.901243i) q^{5} +(-8.87298 + 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} +2.60040 q^{8} +(-2.53422 + 8.63584i) q^{9} +O(q^{10})\)	\(q+(-1.48938 + 2.57968i) q^{2} +(1.79802 + 2.40148i) q^{3} +(-2.43649 - 4.22013i) q^{4} +(-4.91811 - 0.901243i) q^{5} +(-8.87298 + 1.06161i) q^{6} +(-5.16858 - 4.72078i) q^{7} +2.60040 q^{8} +(-2.53422 + 8.63584i) q^{9} +(9.64983 - 11.3448i) q^{10} +(-3.56075 + 2.05580i) q^{11} +(5.75368 - 13.4391i) 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} +(-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} +(23.3755 + 8.86482i) q^{25} +(-55.1481 - 31.8397i) q^{26} +(-25.2954 + 9.44157i) q^{27} +(-7.32910 + 33.3142i) q^{28} +28.1241i q^{29} +(44.5950 + 2.77560i) q^{30} +(17.6270 + 30.5309i) q^{31} +(22.6950 + 39.3089i) q^{32} +(-11.3393 - 4.85469i) q^{33} +6.61895 q^{34} +(21.1650 + 27.8755i) q^{35} +(42.6190 - 10.3464i) q^{36} +(-43.1613 - 24.9192i) q^{37} +(14.7046 + 25.4691i) q^{38} +(-51.3386 + 38.4380i) q^{39} +(-12.7891 - 2.34360i) q^{40} -27.4670i q^{41} +(50.8724 + 36.4004i) q^{42} +41.9977i q^{43} +(17.3515 + 10.0179i) q^{44} +(20.2466 - 40.1880i) 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} +(-40.4091 + 60.9093i) q^{60} +(-34.1825 + 59.2058i) q^{61} -105.013 q^{62} +(53.8662 - 32.6715i) q^{63} -88.2218 q^{64} +(19.2667 - 105.139i) 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} +(-103.432 + 13.0819i) q^{70} +11.9474i q^{71} +(-6.59000 + 22.4567i) q^{72} +(88.6742 - 51.1961i) q^{73} +(128.567 - 74.2282i) q^{74} +(20.7411 + 72.0750i) q^{75} -48.1109 q^{76} +(28.1090 + 6.18396i) q^{77} +(-22.6950 - 189.686i) q^{78} +(32.1905 - 55.7556i) q^{79} +(-38.0517 + 44.7355i) q^{80} +(-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} +(73.5174 + 112.085i) q^{90} +(100.920 - 110.493i) q^{91} +94.2332 q^{92} +(-41.6255 + 97.2262i) q^{93} +(57.1109 + 98.9190i) q^{94} +(-31.9840 + 37.6021i) 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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