LMFDB - Embedded newform 70.4.e.c.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,4,Mod(11,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.11"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	70.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.13013370040$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	70.51
Dual form			70.4.e.c.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +2.00000 q^{6} +(8.50000 - 16.4545i) q^{7} -8.00000 q^{8} +(13.0000 - 22.5167i) q^{9} +(-5.00000 - 8.66025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.00000 - 3.46410i) q^{12} -8.00000 q^{13} +(-20.0000 - 31.1769i) q^{14} +5.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(26.0000 + 45.0333i) q^{17} +(-26.0000 - 45.0333i) q^{18} +(-13.0000 + 22.5167i) q^{19} -20.0000 q^{20} +(18.5000 - 0.866025i) q^{21} +4.00000 q^{22} +(-33.5000 + 58.0237i) q^{23} +(-4.00000 - 6.92820i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-8.00000 + 13.8564i) q^{26} +53.0000 q^{27} +(-74.0000 + 3.46410i) q^{28} +69.0000 q^{29} +(5.00000 - 8.66025i) q^{30} +(166.000 + 287.520i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-1.00000 + 1.73205i) q^{33} +104.000 q^{34} +(-50.0000 - 77.9423i) q^{35} -104.000 q^{36} +(-98.0000 + 169.741i) q^{37} +(26.0000 + 45.0333i) q^{38} +(-4.00000 - 6.92820i) q^{39} +(-20.0000 + 34.6410i) q^{40} +353.000 q^{41} +(17.0000 - 32.9090i) q^{42} -369.000 q^{43} +(4.00000 - 6.92820i) q^{44} +(-65.0000 - 112.583i) q^{45} +(67.0000 + 116.047i) q^{46} +(-44.0000 + 76.2102i) q^{47} -16.0000 q^{48} +(-198.500 - 279.726i) q^{49} -50.0000 q^{50} +(-26.0000 + 45.0333i) q^{51} +(16.0000 + 27.7128i) q^{52} +(-291.000 - 504.027i) q^{53} +(53.0000 - 91.7987i) q^{54} +10.0000 q^{55} +(-68.0000 + 131.636i) q^{56} -26.0000 q^{57} +(69.0000 - 119.512i) q^{58} +(175.000 + 303.109i) q^{59} +(-10.0000 - 17.3205i) q^{60} +(233.500 - 404.434i) q^{61} +664.000 q^{62} +(-260.000 - 405.300i) q^{63} +64.0000 q^{64} +(-20.0000 + 34.6410i) q^{65} +(2.00000 + 3.46410i) q^{66} +(-145.500 - 252.013i) q^{67} +(104.000 - 180.133i) q^{68} -67.0000 q^{69} +(-185.000 + 8.66025i) q^{70} +770.000 q^{71} +(-104.000 + 180.133i) q^{72} +(-314.000 - 543.864i) q^{73} +(196.000 + 339.482i) q^{74} +(12.5000 - 21.6506i) q^{75} +104.000 q^{76} +(37.0000 - 1.73205i) q^{77} -16.0000 q^{78} +(-585.000 + 1013.25i) q^{79} +(40.0000 + 69.2820i) q^{80} +(-324.500 - 562.050i) q^{81} +(353.000 - 611.414i) q^{82} +525.000 q^{83} +(-40.0000 - 62.3538i) q^{84} +260.000 q^{85} +(-369.000 + 639.127i) q^{86} +(34.5000 + 59.7558i) q^{87} +(-8.00000 - 13.8564i) q^{88} +(-44.5000 + 77.0763i) q^{89} -260.000 q^{90} +(-68.0000 + 131.636i) q^{91} +268.000 q^{92} +(-166.000 + 287.520i) q^{93} +(88.0000 + 152.420i) q^{94} +(65.0000 + 112.583i) q^{95} +(-16.0000 + 27.7128i) q^{96} -290.000 q^{97} +(-683.000 + 64.0859i) q^{98} +52.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} - 4 q^{4} + 5 q^{5} + 4 q^{6} + 17 q^{7} - 16 q^{8} + 26 q^{9} - 10 q^{10} + 2 q^{11} + 4 q^{12} - 16 q^{13} - 40 q^{14} + 10 q^{15} - 16 q^{16} + 52 q^{17} - 52 q^{18} - 26 q^{19}+ \cdots + 104 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 - 4 * q^4 + 5 * q^5 + 4 * q^6 + 17 * q^7 - 16 * q^8 + 26 * q^9 - 10 * q^10 + 2 * q^11 + 4 * q^12 - 16 * q^13 - 40 * q^14 + 10 * q^15 - 16 * q^16 + 52 * q^17 - 52 * q^18 - 26 * q^19 - 40 * q^20 + 37 * q^21 + 8 * q^22 - 67 * q^23 - 8 * q^24 - 25 * q^25 - 16 * q^26 + 106 * q^27 - 148 * q^28 + 138 * q^29 + 10 * q^30 + 332 * q^31 + 32 * q^32 - 2 * q^33 + 208 * q^34 - 100 * q^35 - 208 * q^36 - 196 * q^37 + 52 * q^38 - 8 * q^39 - 40 * q^40 + 706 * q^41 + 34 * q^42 - 738 * q^43 + 8 * q^44 - 130 * q^45 + 134 * q^46 - 88 * q^47 - 32 * q^48 - 397 * q^49 - 100 * q^50 - 52 * q^51 + 32 * q^52 - 582 * q^53 + 106 * q^54 + 20 * q^55 - 136 * q^56 - 52 * q^57 + 138 * q^58 + 350 * q^59 - 20 * q^60 + 467 * q^61 + 1328 * q^62 - 520 * q^63 + 128 * q^64 - 40 * q^65 + 4 * q^66 - 291 * q^67 + 208 * q^68 - 134 * q^69 - 370 * q^70 + 1540 * q^71 - 208 * q^72 - 628 * q^73 + 392 * q^74 + 25 * q^75 + 208 * q^76 + 74 * q^77 - 32 * q^78 - 1170 * q^79 + 80 * q^80 - 649 * q^81 + 706 * q^82 + 1050 * q^83 - 80 * q^84 + 520 * q^85 - 738 * q^86 + 69 * q^87 - 16 * q^88 - 89 * q^89 - 520 * q^90 - 136 * q^91 + 536 * q^92 - 332 * q^93 + 176 * q^94 + 130 * q^95 - 32 * q^96 - 580 * q^97 - 1366 * q^98 + 104 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.0962250	+	0.166667i	0.910119	−	0.414346i	$-0.135990\pi$
$3$	0.500000	+	0.866025i	0.0962250	+	0.166667i	−0.813894	+	0.581013i	$0.802656\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	2.00000			0.136083
$7$	8.50000	−	16.4545i	0.458957	−	0.888459i
$7$	8.50000	−	16.4545i	0.458957	−	0.888459i
$8$	−8.00000			−0.353553
$9$	13.0000	−	22.5167i	0.481481	−	0.833950i
$10$	−5.00000	−	8.66025i	−0.158114	−	0.273861i
$11$	1.00000	+	1.73205i	0.0274101	+	0.0474757i	0.879405	−	0.476074i	$-0.157941\pi$
$11$	1.00000	+	1.73205i	0.0274101	+	0.0474757i	−0.851995	+	0.523550i	$0.824607\pi$
$12$	2.00000	−	3.46410i	0.0481125	−	0.0833333i
$13$	−8.00000			−0.170677			−0.0853385	−	0.996352i	$-0.527197\pi$
$13$	−8.00000			−0.170677			−0.0853385	+	0.996352i	$0.527197\pi$
$14$	−20.0000	−	31.1769i	−0.381802	−	0.595170i
$15$	5.00000			0.0860663
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	26.0000	+	45.0333i	0.370937	+	0.642481i	0.989710	−	0.143088i	$-0.0457033\pi$
$17$	26.0000	+	45.0333i	0.370937	+	0.642481i	−0.618773	+	0.785570i	$0.712370\pi$
$18$	−26.0000	−	45.0333i	−0.340459	−	0.589692i
$19$	−13.0000	+	22.5167i	−0.156969	+	0.271878i	−0.933774	−	0.357863i	$-0.883505\pi$
$19$	−13.0000	+	22.5167i	−0.156969	+	0.271878i	0.776805	+	0.629741i	$0.216839\pi$
$20$	−20.0000			−0.223607
$21$	18.5000	−	0.866025i	0.192240	−	0.00899915i
$22$	4.00000			0.0387638
$23$	−33.5000	+	58.0237i	−0.303706	+	0.526034i	−0.976972	−	0.213366i	$-0.931557\pi$
$23$	−33.5000	+	58.0237i	−0.303706	+	0.526034i	0.673267	+	0.739400i	$0.264891\pi$
$24$	−4.00000	−	6.92820i	−0.0340207	−	0.0589256i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−8.00000	+	13.8564i	−0.0603434	+	0.104518i
$27$	53.0000			0.377772
$28$	−74.0000	+	3.46410i	−0.499453	+	0.0233805i
$29$	69.0000			0.441827			0.220913	−	0.975293i	$-0.429096\pi$
$29$	69.0000			0.441827			0.220913	+	0.975293i	$0.429096\pi$
$30$	5.00000	−	8.66025i	0.0304290	−	0.0527046i
$31$	166.000	+	287.520i	0.961757	+	1.66581i	0.718085	+	0.695955i	$0.245019\pi$
$31$	166.000	+	287.520i	0.961757	+	1.66581i	0.243672	+	0.969858i	$0.421648\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−1.00000	+	1.73205i	−0.00527508	+	0.00913671i
$34$	104.000			0.524584
$35$	−50.0000	−	77.9423i	−0.241473	−	0.376419i
$36$	−104.000			−0.481481
$37$	−98.0000	+	169.741i	−0.435435	+	0.754196i	−0.997331	−	0.0730121i	$-0.976739\pi$
$37$	−98.0000	+	169.741i	−0.435435	+	0.754196i	0.561896	+	0.827208i	$0.310072\pi$
$38$	26.0000	+	45.0333i	0.110994	+	0.192247i
$39$	−4.00000	−	6.92820i	−0.0164234	−	0.0284462i
$40$	−20.0000	+	34.6410i	−0.0790569	+	0.136931i
$41$	353.000			1.34462			0.672309	−	0.740271i	$-0.265303\pi$
$41$	353.000			1.34462			0.672309	+	0.740271i	$0.265303\pi$
$42$	17.0000	−	32.9090i	0.0624561	−	0.120904i
$43$	−369.000			−1.30865			−0.654325	−	0.756213i	$-0.727047\pi$
$43$	−369.000			−1.30865			−0.654325	+	0.756213i	$0.727047\pi$
$44$	4.00000	−	6.92820i	0.0137051	−	0.0237379i
$45$	−65.0000	−	112.583i	−0.215325	−	0.372954i
$46$	67.0000	+	116.047i	0.214752	+	0.371962i
$47$	−44.0000	+	76.2102i	−0.136554	+	0.236519i	−0.926190	−	0.377057i	$-0.876936\pi$
$47$	−44.0000	+	76.2102i	−0.136554	+	0.236519i	0.789636	+	0.613576i	$0.210270\pi$
$48$	−16.0000			−0.0481125
$49$	−198.500	−	279.726i	−0.578717	−	0.815528i
$50$	−50.0000			−0.141421
$51$	−26.0000	+	45.0333i	−0.0713868	+	0.123646i
$52$	16.0000	+	27.7128i	0.0426692	+	0.0739053i
$53$	−291.000	−	504.027i	−0.754187	−	1.30629i	−0.945777	−	0.324816i	$-0.894698\pi$
$53$	−291.000	−	504.027i	−0.754187	−	1.30629i	0.191590	−	0.981475i	$-0.438636\pi$
$54$	53.0000	−	91.7987i	0.133563	−	0.231337i
$55$	10.0000			0.0245164
$56$	−68.0000	+	131.636i	−0.162266	+	0.314118i
$57$	−26.0000			−0.0604173
$58$	69.0000	−	119.512i	0.156209	−	0.270563i
$59$	175.000	+	303.109i	0.386154	+	0.668838i	0.991928	−	0.126798i	$-0.0404702\pi$
$59$	175.000	+	303.109i	0.386154	+	0.668838i	−0.605775	+	0.795636i	$0.707137\pi$
$60$	−10.0000	−	17.3205i	−0.0215166	−	0.0372678i
$61$	233.500	−	404.434i	0.490108	−	0.848893i	−0.509827	−	0.860277i	$-0.670291\pi$
$61$	233.500	−	404.434i	0.490108	−	0.848893i	0.999935	+	0.0113844i	$0.00362386\pi$
$62$	664.000			1.36013
$63$	−260.000	−	405.300i	−0.519951	−	0.810524i
$64$	64.0000			0.125000
$65$	−20.0000	+	34.6410i	−0.0381645	+	0.0661029i
$66$	2.00000	+	3.46410i	0.00373005	+	0.00646063i
$67$	−145.500	−	252.013i	−0.265308	−	0.459527i	0.702336	−	0.711846i	$-0.252140\pi$
$67$	−145.500	−	252.013i	−0.265308	−	0.459527i	−0.967644	+	0.252318i	$0.918807\pi$
$68$	104.000	−	180.133i	0.185468	−	0.321241i
$69$	−67.0000			−0.116896
$70$	−185.000	+	8.66025i	−0.315882	+	0.0147871i
$71$	770.000			1.28707			0.643537	−	0.765415i	$-0.277466\pi$
$71$	770.000			1.28707			0.643537	+	0.765415i	$0.277466\pi$
$72$	−104.000	+	180.133i	−0.170229	+	0.294846i
$73$	−314.000	−	543.864i	−0.503437	−	0.871979i	−0.999992	−	0.00397357i	$-0.998735\pi$
$73$	−314.000	−	543.864i	−0.503437	−	0.871979i	0.496555	−	0.868005i	$-0.334598\pi$
$74$	196.000	+	339.482i	0.307899	+	0.533297i
$75$	12.5000	−	21.6506i	0.0192450	−	0.0333333i
$76$	104.000			0.156969
$77$	37.0000	−	1.73205i	0.0547603	−	0.00256345i
$78$	−16.0000			−0.0232262
$79$	−585.000	+	1013.25i	−0.833135	+	1.44303i	0.0624054	+	0.998051i	$0.480123\pi$
$79$	−585.000	+	1013.25i	−0.833135	+	1.44303i	−0.895540	+	0.444981i	$0.853211\pi$
$80$	40.0000	+	69.2820i	0.0559017	+	0.0968246i
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$	353.000	−	611.414i	0.475394	−	0.823407i
$83$	525.000			0.694292			0.347146	−	0.937811i	$-0.387151\pi$
$83$	525.000			0.694292			0.347146	+	0.937811i	$0.387151\pi$
$84$	−40.0000	−	62.3538i	−0.0519566	−	0.0809924i
$85$	260.000			0.331776
$86$	−369.000	+	639.127i	−0.462678	+	0.801382i
$87$	34.5000	+	59.7558i	0.0425148	+	0.0736378i
$88$	−8.00000	−	13.8564i	−0.00969094	−	0.0167852i
$89$	−44.5000	+	77.0763i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−44.5000	+	77.0763i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$	−260.000			−0.304516
$91$	−68.0000	+	131.636i	−0.0783334	+	0.151639i
$92$	268.000			0.303706
$93$	−166.000	+	287.520i	−0.185090	+	0.320586i
$94$	88.0000	+	152.420i	0.0965586	+	0.167244i
$95$	65.0000	+	112.583i	0.0701985	+	0.121587i
$96$	−16.0000	+	27.7128i	−0.0170103	+	0.0294628i
$97$	−290.000			−0.303557			−0.151779	−	0.988415i	$-0.548500\pi$
$97$	−290.000			−0.303557			−0.151779	+	0.988415i	$0.548500\pi$
$98$	−683.000	+	64.0859i	−0.704014	+	0.0660577i
$99$	52.0000			0.0527899
$100$	−50.0000	+	86.6025i	−0.0500000	+	0.0866025i
$101$	616.500	+	1067.81i	0.607367	+	1.05199i	0.991673	+	0.128784i	$0.0411075\pi$
$101$	616.500	+	1067.81i	0.607367	+	1.05199i	−0.384306	+	0.923206i	$0.625559\pi$
$102$	52.0000	+	90.0666i	0.0504781	+	0.0874307i
$103$	−776.500	+	1344.94i	−0.742823	+	1.28661i	0.208381	+	0.978048i	$0.433181\pi$
$103$	−776.500	+	1344.94i	−0.742823	+	1.28661i	−0.951205	+	0.308560i	$0.900153\pi$
$104$	64.0000			0.0603434
$105$	42.5000	−	82.2724i	0.0395007	−	0.0764663i
$106$	−1164.00			−1.06658
$107$	−915.500	+	1585.69i	−0.827147	+	1.43266i	0.0731204	+	0.997323i	$0.476704\pi$
$107$	−915.500	+	1585.69i	−0.827147	+	1.43266i	−0.900267	+	0.435337i	$0.856629\pi$
$108$	−106.000	−	183.597i	−0.0944431	−	0.163580i
$109$	−405.500	−	702.347i	−0.356329	−	0.617180i	0.631016	−	0.775770i	$-0.282638\pi$
$109$	−405.500	−	702.347i	−0.356329	−	0.617180i	−0.987344	+	0.158590i	$0.949305\pi$
$110$	10.0000	−	17.3205i	0.00866784	−	0.0150131i
$111$	−196.000			−0.167599
$112$	160.000	+	249.415i	0.134987	+	0.210424i
$113$	2170.00			1.80652			0.903259	−	0.429097i	$-0.141168\pi$
$113$	2170.00			1.80652			0.903259	+	0.429097i	$0.141168\pi$
$114$	−26.0000	+	45.0333i	−0.0213607	+	0.0369979i
$115$	167.500	+	290.119i	0.135821	+	0.235249i
$116$	−138.000	−	239.023i	−0.110457	−	0.191317i
$117$	−104.000	+	180.133i	−0.0821778	+	0.142336i
$118$	700.000			0.546104
$119$	962.000	−	45.0333i	0.741062	−	0.0346907i
$120$	−40.0000			−0.0304290
$121$	663.500	−	1149.22i	0.498497	−	0.863423i
$122$	−467.000	−	808.868i	−0.346559	−	0.600258i
$123$	176.500	+	305.707i	0.129386	+	0.224103i
$124$	664.000	−	1150.08i	0.480879	−	0.832906i
$125$	−125.000			−0.0894427
$126$	−962.000	+	45.0333i	−0.680173	+	0.0318404i
$127$	48.0000			0.0335379			0.0167689	−	0.999859i	$-0.494662\pi$
$127$	48.0000			0.0335379			0.0167689	+	0.999859i	$0.494662\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−184.500	−	319.563i	−0.125925	−	0.218108i
$130$	40.0000	+	69.2820i	0.0269864	+	0.0467418i
$131$	396.000	−	685.892i	0.264112	−	0.457456i	−0.703219	−	0.710974i	$-0.748254\pi$
$131$	396.000	−	685.892i	0.264112	−	0.457456i	0.967331	+	0.253518i	$0.0815878\pi$
$132$	8.00000			0.00527508
$133$	260.000	+	405.300i	0.169510	+	0.264240i
$134$	−582.000			−0.375203
$135$	132.500	−	229.497i	0.0844725	−	0.146311i
$136$	−208.000	−	360.267i	−0.131146	−	0.227151i
$137$	−542.000	−	938.772i	−0.338001	−	0.585436i	0.646055	−	0.763291i	$-0.276418\pi$
$137$	−542.000	−	938.772i	−0.338001	−	0.585436i	−0.984057	+	0.177855i	$0.943084\pi$
$138$	−67.0000	+	116.047i	−0.0413291	+	0.0715841i
$139$	−46.0000			−0.0280696			−0.0140348	−	0.999902i	$-0.504468\pi$
$139$	−46.0000			−0.0280696			−0.0140348	+	0.999902i	$0.504468\pi$
$140$	−170.000	+	329.090i	−0.102626	+	0.198665i
$141$	−88.0000			−0.0525598
$142$	770.000	−	1333.68i	0.455049	−	0.788168i
$143$	−8.00000	−	13.8564i	−0.00467828	−	0.00810301i
$144$	208.000	+	360.267i	0.120370	+	0.208488i
$145$	172.500	−	298.779i	0.0987955	−	0.171119i
$146$	−1256.00			−0.711968
$147$	143.000	−	311.769i	0.0802343	−	0.174927i
$148$	784.000			0.435435
$149$	184.500	−	319.563i	0.101442	−	0.175702i	−0.810837	−	0.585272i	$-0.800988\pi$
$149$	184.500	−	319.563i	0.101442	−	0.175702i	0.912279	+	0.409570i	$0.134321\pi$
$150$	−25.0000	−	43.3013i	−0.0136083	−	0.0235702i
$151$	−1240.00	−	2147.74i	−0.668277	−	1.15749i	−0.978386	−	0.206788i	$-0.933699\pi$
$151$	−1240.00	−	2147.74i	−0.668277	−	1.15749i	0.310109	−	0.950701i	$-0.399634\pi$
$152$	104.000	−	180.133i	0.0554968	−	0.0961233i
$153$	1352.00			0.714397
$154$	34.0000	−	65.8179i	0.0177909	−	0.0344400i
$155$	1660.00			0.860222
$156$	−16.0000	+	27.7128i	−0.00821170	+	0.0142231i
$157$	−613.000	−	1061.75i	−0.311610	−	0.539724i	0.667101	−	0.744967i	$-0.267535\pi$
$157$	−613.000	−	1061.75i	−0.311610	−	0.539724i	−0.978711	+	0.205243i	$0.934201\pi$
$158$	1170.00	+	2026.50i	0.589115	+	1.02038i
$159$	291.000	−	504.027i	0.145143	−	0.251396i
$160$	160.000			0.0790569
$161$	670.000	+	1044.43i	0.327971	+	0.511257i
$162$	−1298.00			−0.629509
$163$	330.000	−	571.577i	0.158574	−	0.274659i	−0.775781	−	0.631003i	$-0.782644\pi$
$163$	330.000	−	571.577i	0.158574	−	0.274659i	0.934355	+	0.356344i	$0.115977\pi$
$164$	−706.000	−	1222.83i	−0.336154	−	0.582237i
$165$	5.00000	+	8.66025i	0.00235909	+	0.00408606i
$166$	525.000	−	909.327i	0.245469	−	0.425165i
$167$	−949.000			−0.439735			−0.219868	−	0.975530i	$-0.570563\pi$
$167$	−949.000			−0.439735			−0.219868	+	0.975530i	$0.570563\pi$
$168$	−148.000	+	6.92820i	−0.0679670	+	0.00318168i
$169$	−2133.00			−0.970869
$170$	260.000	−	450.333i	0.117301	−	0.203170i
$171$	338.000	+	585.433i	0.151155	+	0.261808i
$172$	738.000	+	1278.25i	0.327163	+	0.566662i
$173$	−1696.00	+	2937.56i	−0.745344	+	1.29097i	0.204690	+	0.978827i	$0.434381\pi$
$173$	−1696.00	+	2937.56i	−0.745344	+	1.29097i	−0.950034	+	0.312147i	$0.898952\pi$
$174$	138.000			0.0601250
$175$	−462.500	+	21.6506i	−0.199781	+	0.00935220i
$176$	−32.0000			−0.0137051
$177$	−175.000	+	303.109i	−0.0743153	+	0.128718i
$178$	89.0000	+	154.153i	0.0374766	+	0.0649113i
$179$	−134.000	−	232.095i	−0.0559532	−	0.0969139i	0.836692	−	0.547674i	$-0.184486\pi$
$179$	−134.000	−	232.095i	−0.0559532	−	0.0969139i	−0.892645	+	0.450760i	$0.851153\pi$
$180$	−260.000	+	450.333i	−0.107663	+	0.186477i
$181$	−4093.00			−1.68083			−0.840415	−	0.541943i	$-0.817689\pi$
$181$	−4093.00			−1.68083			−0.840415	+	0.541943i	$0.817689\pi$
$182$	160.000	+	249.415i	0.0651648	+	0.101582i
$183$	467.000			0.188643
$184$	268.000	−	464.190i	0.107376	−	0.185981i
$185$	490.000	+	848.705i	0.194733	+	0.337287i
$186$	332.000	+	575.041i	0.130879	+	0.226688i
$187$	−52.0000	+	90.0666i	−0.0203348	+	0.0352210i
$188$	352.000			0.136554
$189$	450.500	−	872.088i	0.173381	−	0.335635i
$190$	260.000			0.0992757
$191$	989.000	−	1713.00i	0.374668	−	0.648943i	−0.615610	−	0.788051i	$-0.711090\pi$
$191$	989.000	−	1713.00i	0.374668	−	0.648943i	0.990277	+	0.139108i	$0.0444235\pi$
$192$	32.0000	+	55.4256i	0.0120281	+	0.0208333i
$193$	1999.00	+	3462.37i	0.745550	+	1.29133i	0.949937	+	0.312441i	$0.101146\pi$
$193$	1999.00	+	3462.37i	0.745550	+	1.29133i	−0.204387	+	0.978890i	$0.565520\pi$
$194$	−290.000	+	502.295i	−0.107324	+	0.185890i
$195$	−40.0000			−0.0146895
$196$	−572.000	+	1247.08i	−0.208455	+	0.454474i
$197$	−3030.00			−1.09583			−0.547915	−	0.836534i	$-0.684578\pi$
$197$	−3030.00			−1.09583			−0.547915	+	0.836534i	$0.684578\pi$
$198$	52.0000	−	90.0666i	0.0186640	−	0.0323271i
$199$	−178.000	−	308.305i	−0.0634075	−	0.109825i	0.832579	−	0.553906i	$-0.186863\pi$
$199$	−178.000	−	308.305i	−0.0634075	−	0.109825i	−0.895986	+	0.444081i	$0.853530\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$	145.500	−	252.013i	0.0510586	−	0.0884361i
$202$	2466.00			0.858946
$203$	586.500	−	1135.36i	0.202779	−	0.392545i
$204$	208.000			0.0713868
$205$	882.500	−	1528.53i	0.300666	−	0.520768i
$206$	1553.00	+	2689.87i	0.525256	+	0.909769i
$207$	871.000	+	1508.62i	0.292457	+	0.506551i
$208$	64.0000	−	110.851i	0.0213346	−	0.0369527i
$209$	−52.0000			−0.0172101
$210$	−100.000	−	155.885i	−0.0328603	−	0.0512241i
$211$	−2602.00			−0.848953			−0.424476	−	0.905439i	$-0.639542\pi$
$211$	−2602.00			−0.848953			−0.424476	+	0.905439i	$0.639542\pi$
$212$	−1164.00	+	2016.11i	−0.377094	+	0.653145i
$213$	385.000	+	666.840i	0.123849	+	0.214512i
$214$	1831.00	+	3171.39i	0.584881	+	1.01304i
$215$	−922.500	+	1597.82i	−0.292623	+	0.506838i
$216$	−424.000			−0.133563
$217$	6142.00	−	287.520i	1.92141	−	0.0899454i
$218$	−1622.00			−0.503925
$219$	314.000	−	543.864i	0.0968865	−	0.167812i
$220$	−20.0000	−	34.6410i	−0.00612909	−	0.0106159i
$221$	−208.000	−	360.267i	−0.0633104	−	0.109657i
$222$	−196.000	+	339.482i	−0.0592552	+	0.102633i
$223$	−3156.00			−0.947719			−0.473860	−	0.880600i	$-0.657140\pi$
$223$	−3156.00			−0.947719			−0.473860	+	0.880600i	$0.657140\pi$
$224$	592.000	−	27.7128i	0.176583	−	0.00826625i
$225$	−650.000			−0.192593
$226$	2170.00	−	3758.55i	0.638700	−	1.10626i
$227$	−2118.00	−	3668.48i	−0.619280	−	1.07262i	−0.989617	−	0.143727i	$-0.954091\pi$
$227$	−2118.00	−	3668.48i	−0.619280	−	1.07262i	0.370337	−	0.928897i	$-0.379242\pi$
$228$	52.0000	+	90.0666i	0.0151043	+	0.0261614i
$229$	−3167.00	+	5485.40i	−0.913892	+	1.58291i	−0.105376	+	0.994432i	$0.533605\pi$
$229$	−3167.00	+	5485.40i	−0.913892	+	1.58291i	−0.808516	+	0.588475i	$0.799729\pi$
$230$	670.000			0.192080
$231$	20.0000	+	31.1769i	0.00569655	+	0.00888004i
$232$	−552.000			−0.156209
$233$	2344.00	−	4059.93i	0.659058	−	1.14152i	−0.321802	−	0.946807i	$-0.604288\pi$
$233$	2344.00	−	4059.93i	0.659058	−	1.14152i	0.980860	−	0.194715i	$-0.0623782\pi$
$234$	208.000	+	360.267i	0.0581085	+	0.100647i
$235$	220.000	+	381.051i	0.0610690	+	0.105775i
$236$	700.000	−	1212.44i	0.193077	−	0.334419i
$237$	−1170.00			−0.320674
$238$	884.000	−	1711.27i	0.240761	−	0.466071i
$239$	1856.00			0.502321			0.251160	−	0.967945i	$-0.419188\pi$
$239$	1856.00			0.502321			0.251160	+	0.967945i	$0.419188\pi$
$240$	−40.0000	+	69.2820i	−0.0107583	+	0.0186339i
$241$	2403.00	+	4162.12i	0.642286	+	1.11247i	0.984921	+	0.173003i	$0.0553470\pi$
$241$	2403.00	+	4162.12i	0.642286	+	1.11247i	−0.342636	+	0.939468i	$0.611320\pi$
$242$	−1327.00	−	2298.43i	−0.352491	−	0.610532i
$243$	1040.00	−	1801.33i	0.274552	−	0.475537i
$244$	−1868.00			−0.490108
$245$	−1707.50	+	160.215i	−0.445258	+	0.0417785i
$246$	706.000			0.182979
$247$	104.000	−	180.133i	0.0267909	−	0.0464033i
$248$	−1328.00	−	2300.16i	−0.340033	−	0.588954i
$249$	262.500	+	454.663i	0.0668083	+	0.115715i
$250$	−125.000	+	216.506i	−0.0316228	+	0.0547723i
$251$	−3200.00			−0.804710			−0.402355	−	0.915484i	$-0.631808\pi$
$251$	−3200.00			−0.804710			−0.402355	+	0.915484i	$0.631808\pi$
$252$	−884.000	+	1711.27i	−0.220979	+	0.427776i
$253$	−134.000			−0.0332984
$254$	48.0000	−	83.1384i	0.0118574	−	0.0205377i
$255$	130.000	+	225.167i	0.0319252	+	0.0552960i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	560.000	−	969.948i	0.135922	−	0.235423i	−0.790028	−	0.613071i	$-0.789934\pi$
$257$	560.000	−	969.948i	0.135922	−	0.235423i	0.925949	+	0.377648i	$0.123267\pi$
$258$	−738.000			−0.178085
$259$	1960.00	+	3055.34i	0.470226	+	0.733009i
$260$	160.000			0.0381645
$261$	897.000	−	1553.65i	0.212731	−	0.368462i
$262$	−792.000	−	1371.78i	−0.186755	−	0.323470i
$263$	−3202.50	−	5546.89i	−0.750854	−	1.30052i	−0.947409	−	0.320025i	$-0.896309\pi$
$263$	−3202.50	−	5546.89i	−0.750854	−	1.30052i	0.196555	−	0.980493i	$-0.437025\pi$
$264$	8.00000	−	13.8564i	0.00186502	−	0.00323031i
$265$	−2910.00			−0.674566
$266$	962.000	−	45.0333i	0.221744	−	0.0103803i
$267$	−89.0000			−0.0203997
$268$	−582.000	+	1008.05i	−0.132654	+	0.229764i
$269$	−2467.50	−	4273.84i	−0.559279	−	0.968700i	−0.997557	−	0.0698604i	$-0.977745\pi$
$269$	−2467.50	−	4273.84i	−0.559279	−	0.968700i	0.438277	−	0.898840i	$-0.355589\pi$
$270$	−265.000	−	458.993i	−0.0597311	−	0.103457i
$271$	723.000	−	1252.27i	0.162063	−	0.280702i	−0.773545	−	0.633741i	$-0.781518\pi$
$271$	723.000	−	1252.27i	0.162063	−	0.280702i	0.935608	+	0.353039i	$0.114852\pi$
$272$	−832.000			−0.185468
$273$	−148.000	+	6.92820i	−0.0328109	+	0.00153595i
$274$	−2168.00			−0.478006
$275$	25.0000	−	43.3013i	0.00548202	−	0.00949514i
$276$	134.000	+	232.095i	0.0292241	+	0.0506176i
$277$	4010.00	+	6945.52i	0.869811	+	1.50656i	0.862190	+	0.506585i	$0.169092\pi$
$277$	4010.00	+	6945.52i	0.869811	+	1.50656i	0.00762078	+	0.999971i	$0.497574\pi$
$278$	−46.0000	+	79.6743i	−0.00992409	+	0.0171890i
$279$	8632.00			1.85227
$280$	400.000	+	623.538i	0.0853735	+	0.133084i
$281$	4978.00			1.05681			0.528403	−	0.848994i	$-0.322791\pi$
$281$	4978.00			1.05681			0.528403	+	0.848994i	$0.322791\pi$
$282$	−88.0000	+	152.420i	−0.0185827	+	0.0321862i
$283$	−2926.00	−	5067.98i	−0.614603	−	1.06452i	−0.990454	−	0.137844i	$-0.955983\pi$
$283$	−2926.00	−	5067.98i	−0.614603	−	1.06452i	0.375851	−	0.926680i	$-0.377350\pi$
$284$	−1540.00	−	2667.36i	−0.321768	−	0.557319i
$285$	−65.0000	+	112.583i	−0.0135097	+	0.0233995i
$286$	−32.0000			−0.00661608
$287$	3000.50	−	5808.43i	0.617122	−	1.19464i
$288$	832.000			0.170229
$289$	1104.50	−	1913.05i	0.224812	−	0.389385i
$290$	−345.000	−	597.558i	−0.0698590	−	0.120999i
$291$	−145.000	−	251.147i	−0.0292098	−	0.0505929i
$292$	−1256.00	+	2175.46i	−0.251719	+	0.435989i
$293$	−3012.00			−0.600556			−0.300278	−	0.953852i	$-0.597079\pi$
$293$	−3012.00			−0.600556			−0.300278	+	0.953852i	$0.597079\pi$
$294$	−397.000	−	559.452i	−0.0787534	−	0.110979i
$295$	1750.00			0.345386
$296$	784.000	−	1357.93i	0.153950	−	0.266648i
$297$	53.0000	+	91.7987i	0.0103548	+	0.0179350i
$298$	−369.000	−	639.127i	−0.0717302	−	0.124240i
$299$	268.000	−	464.190i	0.0518356	−	0.0897819i
$300$	−100.000			−0.0192450
$301$	−3136.50	+	6071.70i	−0.600614	+	1.16268i
$302$	−4960.00			−0.945086
$303$	−616.500	+	1067.81i	−0.116888	+	0.202456i
$304$	−208.000	−	360.267i	−0.0392422	−	0.0679694i
$305$	−1167.50	−	2022.17i	−0.219183	−	0.379636i
$306$	1352.00	−	2341.73i	0.252577	−	0.437477i
$307$	9443.00			1.75551			0.877753	−	0.479113i	$-0.159042\pi$
$307$	9443.00			1.75551			0.877753	+	0.479113i	$0.159042\pi$
$308$	−80.0000	−	124.708i	−0.0148001	−	0.0230710i
$309$	−1553.00			−0.285913
$310$	1660.00	−	2875.20i	0.304134	−	0.526776i
$311$	4997.00	+	8655.06i	0.911106	+	1.57808i	0.812505	+	0.582954i	$0.198103\pi$
$311$	4997.00	+	8655.06i	0.911106	+	1.57808i	0.0986008	+	0.995127i	$0.468563\pi$
$312$	32.0000	+	55.4256i	0.00580655	+	0.0100572i
$313$	−728.000	+	1260.93i	−0.131466	+	0.227707i	−0.924242	−	0.381807i	$-0.875302\pi$
$313$	−728.000	+	1260.93i	−0.131466	+	0.227707i	0.792776	+	0.609514i	$0.208635\pi$
$314$	−2452.00			−0.440683
$315$	−2405.00	+	112.583i	−0.430179	+	0.0201376i
$316$	4680.00			0.833135
$317$	−3436.00	+	5951.33i	−0.608785	+	1.05445i	0.382655	+	0.923891i	$0.375010\pi$
$317$	−3436.00	+	5951.33i	−0.608785	+	1.05445i	−0.991441	+	0.130556i	$0.958324\pi$
$318$	−582.000	−	1008.05i	−0.102632	−	0.177764i
$319$	69.0000	+	119.512i	0.0121105	+	0.0209760i
$320$	160.000	−	277.128i	0.0279508	−	0.0484123i
$321$	−1831.00			−0.318369
$322$	2479.00	−	116.047i	0.429035	−	0.0200841i
$323$	−1352.00			−0.232902
$324$	−1298.00	+	2248.20i	−0.222565	+	0.385494i
$325$	100.000	+	173.205i	0.0170677	+	0.0295621i
$326$	−660.000	−	1143.15i	−0.112129	−	0.194213i
$327$	405.500	−	702.347i	0.0685755	−	0.118776i
$328$	−2824.00			−0.475394
$329$	880.000	+	1371.78i	0.147465	+	0.229875i
$330$	20.0000			0.00333625
$331$	196.000	−	339.482i	0.0325472	−	0.0563735i	−0.849293	−	0.527922i	$-0.822971\pi$
$331$	196.000	−	339.482i	0.0325472	−	0.0563735i	0.881840	+	0.471548i	$0.156305\pi$
$332$	−1050.00	−	1818.65i	−0.173573	−	0.300637i
$333$	2548.00	+	4413.27i	0.419308	+	0.726263i
$334$	−949.000	+	1643.72i	−0.155470	+	0.269282i
$335$	−1455.00			−0.237299
$336$	−136.000	+	263.272i	−0.0220816	+	0.0427460i
$337$	3926.00			0.634608			0.317304	−	0.948324i	$-0.397222\pi$
$337$	3926.00			0.634608			0.317304	+	0.948324i	$0.397222\pi$
$338$	−2133.00	+	3694.46i	−0.343254	+	0.594534i
$339$	1085.00	+	1879.28i	0.173832	+	0.301086i
$340$	−520.000	−	900.666i	−0.0829440	−	0.143663i
$341$	−332.000	+	575.041i	−0.0527238	+	0.0913203i
$342$	1352.00			0.213765
$343$	−6290.00	+	888.542i	−0.990169	+	0.139874i
$344$	2952.00			0.462678
$345$	−167.500	+	290.119i	−0.0261388	+	0.0452738i
$346$	3392.00	+	5875.12i	0.527038	+	0.912856i
$347$	892.500	+	1545.86i	0.138075	+	0.239152i	0.926768	−	0.375635i	$-0.122575\pi$
$347$	892.500	+	1545.86i	0.138075	+	0.239152i	−0.788693	+	0.614787i	$0.789242\pi$
$348$	138.000	−	239.023i	0.0212574	−	0.0368189i
$349$	−1591.00			−0.244024			−0.122012	−	0.992529i	$-0.538935\pi$
$349$	−1591.00			−0.244024			−0.122012	+	0.992529i	$0.538935\pi$
$350$	−425.000	+	822.724i	−0.0649063	+	0.125647i
$351$	−424.000			−0.0644771
$352$	−32.0000	+	55.4256i	−0.00484547	+	0.00839260i
$353$	−843.000	−	1460.12i	−0.127106	−	0.220154i	0.795448	−	0.606021i	$-0.207235\pi$
$353$	−843.000	−	1460.12i	−0.127106	−	0.220154i	−0.922554	+	0.385868i	$0.873902\pi$
$354$	350.000	+	606.218i	0.0525488	+	0.0910173i
$355$	1925.00	−	3334.20i	0.287798	−	0.498481i
$356$	356.000			0.0529999
$357$	520.000	+	810.600i	0.0770905	+	0.120172i
$358$	−536.000			−0.0791298
$359$	−3686.00	+	6384.34i	−0.541893	+	0.938586i	0.456902	+	0.889517i	$0.348959\pi$
$359$	−3686.00	+	6384.34i	−0.541893	+	0.938586i	−0.998795	+	0.0490695i	$0.984374\pi$
$360$	520.000	+	900.666i	0.0761289	+	0.131859i
$361$	3091.50	+	5354.64i	0.450722	+	0.780673i
$362$	−4093.00	+	7089.28i	−0.594263	+	1.02929i
$363$	1327.00			0.191872
$364$	592.000	−	27.7128i	0.0852451	−	0.00399051i
$365$	−3140.00			−0.450288
$366$	467.000	−	808.868i	0.0666953	−	0.115520i
$367$	−3318.50	−	5747.81i	−0.472001	−	0.817529i	0.527486	−	0.849564i	$-0.323135\pi$
$367$	−3318.50	−	5747.81i	−0.472001	−	0.817529i	−0.999487	+	0.0320344i	$0.989801\pi$
$368$	−536.000	−	928.379i	−0.0759264	−	0.131508i
$369$	4589.00	−	7948.38i	0.647409	−	1.12134i
$370$	1960.00			0.275393
$371$	−10767.0	+	504.027i	−1.50672	+	0.0705331i
$372$	1328.00			0.185090
$373$	−1738.00	+	3010.30i	−0.241261	+	0.417876i	−0.961074	−	0.276292i	$-0.910894\pi$
$373$	−1738.00	+	3010.30i	−0.241261	+	0.417876i	0.719813	+	0.694168i	$0.244228\pi$
$374$	104.000	+	180.133i	0.0143789	+	0.0249050i
$375$	−62.5000	−	108.253i	−0.00860663	−	0.0149071i
$376$	352.000	−	609.682i	0.0482793	−	0.0836222i
$377$	−552.000			−0.0754097
$378$	−1060.00	−	1652.38i	−0.144234	−	0.224839i
$379$	−2378.00			−0.322295			−0.161147	−	0.986930i	$-0.551519\pi$
$379$	−2378.00			−0.322295			−0.161147	+	0.986930i	$0.551519\pi$
$380$	260.000	−	450.333i	0.0350993	−	0.0607937i
$381$	24.0000	+	41.5692i	0.00322718	+	0.00558965i
$382$	−1978.00	−	3426.00i	−0.264930	−	0.458872i
$383$	1228.50	−	2127.82i	0.163899	−	0.283882i	−0.772365	−	0.635179i	$-0.780926\pi$
$383$	1228.50	−	2127.82i	0.163899	−	0.283882i	0.936264	+	0.351298i	$0.114259\pi$
$384$	128.000			0.0170103
$385$	85.0000	−	164.545i	0.0112520	−	0.0217818i
$386$	7996.00			1.05437
$387$	−4797.00	+	8308.65i	−0.630091	+	1.09135i
$388$	580.000	+	1004.59i	0.0758893	+	0.131444i
$389$	−4281.00	−	7414.91i	−0.557983	−	0.966455i	−0.997665	−	0.0683010i	$-0.978242\pi$
$389$	−4281.00	−	7414.91i	−0.557983	−	0.966455i	0.439682	−	0.898154i	$-0.355091\pi$
$390$	−40.0000	+	69.2820i	−0.00519354	+	0.00899547i
$391$	−3484.00			−0.450623
$392$	1588.00	+	2237.81i	0.204607	+	0.288333i
$393$	792.000			0.101657
$394$	−3030.00	+	5248.11i	−0.387435	+	0.671056i
$395$	2925.00	+	5066.25i	0.372589	+	0.645343i
$396$	−104.000	−	180.133i	−0.0131975	−	0.0228587i
$397$	4921.00	−	8523.42i	0.622111	−	1.07753i	−0.366981	−	0.930228i	$-0.619609\pi$
$397$	4921.00	−	8523.42i	0.622111	−	1.07753i	0.989092	−	0.147299i	$-0.0470579\pi$
$398$	−712.000			−0.0896717
$399$	−221.000	+	427.817i	−0.0277289	+	0.0536782i
$400$	400.000			0.0500000
$401$	4048.50	−	7012.21i	0.504171	−	0.873249i	−0.495818	−	0.868427i	$-0.665132\pi$
$401$	4048.50	−	7012.21i	0.504171	−	0.873249i	0.999988	−	0.00482260i	$-0.00153509\pi$
$402$	−291.000	−	504.027i	−0.0361039	−	0.0625338i
$403$	−1328.00	−	2300.16i	−0.164150	−	0.284316i
$404$	2466.00	−	4271.24i	0.303683	−	0.525995i
$405$	−3245.00			−0.398137
$406$	−1380.00	−	2151.21i	−0.168690	−	0.262962i
$407$	−392.000			−0.0477413
$408$	208.000	−	360.267i	0.0252391	−	0.0437153i
$409$	−7629.50	−	13214.7i	−0.922383	−	1.59761i	−0.795717	−	0.605668i	$-0.792906\pi$
$409$	−7629.50	−	13214.7i	−0.922383	−	1.59761i	−0.126665	−	0.991946i	$-0.540427\pi$
$410$	−1765.00	−	3057.07i	−0.212603	−	0.368239i
$411$	542.000	−	938.772i	0.0650484	−	0.112667i
$412$	6212.00			0.742823
$413$	6475.00	−	303.109i	0.771462	−	0.0361138i
$414$	3484.00			0.413597
$415$	1312.50	−	2273.32i	0.155248	−	0.268898i
$416$	−128.000	−	221.703i	−0.0150859	−	0.0261295i
$417$	−23.0000	−	39.8372i	−0.00270099	−	0.00467826i
$418$	−52.0000	+	90.0666i	−0.00608470	+	0.0105390i
$419$	16224.0			1.89163			0.945817	−	0.324701i	$-0.105264\pi$
$419$	16224.0			1.89163			0.945817	+	0.324701i	$0.105264\pi$
$420$	−370.000	+	17.3205i	−0.0429861	+	0.00201227i
$421$	2977.00			0.344632			0.172316	−	0.985042i	$-0.444875\pi$
$421$	2977.00			0.344632			0.172316	+	0.985042i	$0.444875\pi$
$422$	−2602.00	+	4506.80i	−0.300150	+	0.519875i
$423$	1144.00	+	1981.47i	0.131497	+	0.227759i
$424$	2328.00	+	4032.21i	0.266645	+	0.461843i
$425$	650.000	−	1125.83i	0.0741874	−	0.128496i
$426$	1540.00			0.175148
$427$	−4670.00	−	7279.81i	−0.529267	−	0.825046i
$428$	7324.00			0.827147
$429$	8.00000	−	13.8564i	0.000900335	−	0.00155943i
$430$	1845.00	+	3195.63i	0.206916	+	0.358389i
$431$	−7101.00	−	12299.3i	−0.793604	−	1.37456i	−0.923722	−	0.383063i	$-0.874869\pi$
$431$	−7101.00	−	12299.3i	−0.793604	−	1.37456i	0.130119	−	0.991498i	$-0.458464\pi$
$432$	−424.000	+	734.390i	−0.0472215	+	0.0817901i
$433$	14310.0			1.58821			0.794105	−	0.607781i	$-0.207940\pi$
$433$	14310.0			1.58821			0.794105	+	0.607781i	$0.207940\pi$
$434$	5644.00	−	10925.8i	0.624241	−	1.20842i
$435$	345.000			0.0380264
$436$	−1622.00	+	2809.39i	−0.178164	+	0.308590i
$437$	−871.000	−	1508.62i	−0.0953446	−	0.165142i
$438$	−628.000	−	1087.73i	−0.0685091	−	0.118661i
$439$	1178.00	−	2040.36i	0.128070	−	0.221824i	−0.794859	−	0.606795i	$-0.792455\pi$
$439$	1178.00	−	2040.36i	0.128070	−	0.221824i	0.922929	+	0.384970i	$0.125788\pi$
$440$	−80.0000			−0.00866784
$441$	−8879.00	+	833.116i	−0.958752	+	0.0899597i
$442$	−832.000			−0.0895344
$443$	−4145.50	+	7180.22i	−0.444602	+	0.770073i	−0.998024	−	0.0628276i	$-0.979988\pi$
$443$	−4145.50	+	7180.22i	−0.444602	+	0.770073i	0.553422	+	0.832901i	$0.313322\pi$
$444$	392.000	+	678.964i	0.0418998	+	0.0725725i
$445$	222.500	+	385.381i	0.0237023	+	0.0410535i
$446$	−3156.00	+	5466.35i	−0.335069	+	0.580357i
$447$	369.000			0.0390450
$448$	544.000	−	1053.09i	0.0573696	−	0.111057i
$449$	−3521.00			−0.370081			−0.185040	−	0.982731i	$-0.559242\pi$
$449$	−3521.00			−0.370081			−0.185040	+	0.982731i	$0.559242\pi$
$450$	−650.000	+	1125.83i	−0.0680918	+	0.117938i
$451$	353.000	+	611.414i	0.0368561	+	0.0638367i
$452$	−4340.00	−	7517.10i	−0.451629	−	0.782245i
$453$	1240.00	−	2147.74i	0.128610	−	0.222759i
$454$	−8472.00			−0.875794
$455$	400.000	+	623.538i	0.0412138	+	0.0642460i
$456$	208.000			0.0213607
$457$	2716.00	−	4704.25i	0.278007	−	0.481522i	−0.692882	−	0.721051i	$-0.743660\pi$
$457$	2716.00	−	4704.25i	0.278007	−	0.481522i	0.970889	+	0.239529i	$0.0769929\pi$
$458$	6334.00	+	10970.8i	0.646219	+	1.11928i
$459$	1378.00	+	2386.77i	0.140130	+	0.242712i
$460$	670.000	−	1160.47i	0.0679107	−	0.117625i
$461$	−5350.00			−0.540508			−0.270254	−	0.962789i	$-0.587108\pi$
$461$	−5350.00			−0.540508			−0.270254	+	0.962789i	$0.587108\pi$
$462$	74.0000	−	3.46410i	0.00745193	−	0.000348841i
$463$	−10123.0			−1.01610			−0.508052	−	0.861327i	$-0.669634\pi$
$463$	−10123.0			−1.01610			−0.508052	+	0.861327i	$0.669634\pi$
$464$	−552.000	+	956.092i	−0.0552284	+	0.0956583i
$465$	830.000	+	1437.60i	0.0827749	+	0.143370i
$466$	−4688.00	−	8119.85i	−0.466024	−	0.807178i
$467$	−3231.50	+	5597.12i	−0.320206	+	0.554612i	−0.980530	−	0.196368i	$-0.937085\pi$
$467$	−3231.50	+	5597.12i	−0.320206	+	0.554612i	0.660325	+	0.750980i	$0.270419\pi$
$468$	832.000			0.0821778
$469$	−5383.50	+	252.013i	−0.530036	+	0.0248121i
$470$	880.000			0.0863646
$471$	613.000	−	1061.75i	0.0599693	−	0.103870i
$472$	−1400.00	−	2424.87i	−0.136526	−	0.236470i
$473$	−369.000	−	639.127i	−0.0358703	−	0.0621291i
$474$	−1170.00	+	2026.50i	−0.113375	+	0.196372i
$475$	650.000			0.0627875
$476$	−2080.00	−	3242.40i	−0.200287	−	0.312217i
$477$	−15132.0			−1.45251
$478$	1856.00	−	3214.69i	0.177597	−	0.307607i
$479$	8820.00	+	15276.7i	0.841328	+	1.45722i	0.888772	+	0.458349i	$0.151559\pi$
$479$	8820.00	+	15276.7i	0.841328	+	1.45722i	−0.0474444	+	0.998874i	$0.515108\pi$
$480$	80.0000	+	138.564i	0.00760726	+	0.0131762i
$481$	784.000	−	1357.93i	0.0743188	−	0.128724i
$482$	9612.00			0.908329
$483$	−569.500	+	1102.45i	−0.0536504	+	0.103858i
$484$	−5308.00			−0.498497
$485$	−725.000	+	1255.74i	−0.0678774	+	0.117567i
$486$	−2080.00	−	3602.67i	−0.194137	−	0.336256i
$487$	5016.00	+	8687.97i	0.466728	+	0.808397i	0.999278	−	0.0380019i	$-0.0120993\pi$
$487$	5016.00	+	8687.97i	0.466728	+	0.808397i	−0.532549	+	0.846399i	$0.678766\pi$
$488$	−1868.00	+	3235.47i	−0.173279	+	0.300129i
$489$	660.000			0.0610352
$490$	−1430.00	+	3117.69i	−0.131838	+	0.287435i
$491$	5916.00			0.543758			0.271879	−	0.962331i	$-0.412355\pi$
$491$	5916.00			0.543758			0.271879	+	0.962331i	$0.412355\pi$
$492$	706.000	−	1222.83i	0.0646930	−	0.112051i
$493$	1794.00	+	3107.30i	0.163890	+	0.283866i
$494$	−208.000	−	360.267i	−0.0189441	−	0.0328121i
$495$	130.000	−	225.167i	0.0118042	−	0.0204454i
$496$	−5312.00			−0.480879
$497$	6545.00	−	12670.0i	0.590711	−	1.14351i
$498$	1050.00			0.0944812
$499$	−6947.00	+	12032.6i	−0.623227	+	1.07946i	0.365653	+	0.930751i	$0.380846\pi$
$499$	−6947.00	+	12032.6i	−0.623227	+	1.07946i	−0.988881	+	0.148710i	$0.952488\pi$
$500$	250.000	+	433.013i	0.0223607	+	0.0387298i
$501$	−474.500	−	821.858i	−0.0423136	−	0.0732892i
$502$	−3200.00	+	5542.56i	−0.284508	+	0.492782i
$503$	18427.0			1.63344			0.816719	−	0.577036i	$-0.195791\pi$
$503$	18427.0			1.63344			0.816719	+	0.577036i	$0.195791\pi$
$504$	2080.00	+	3242.40i	0.183830	+	0.286563i
$505$	6165.00			0.543245
$506$	−134.000	+	232.095i	−0.0117728	+	0.0203911i
$507$	−1066.50	−	1847.23i	−0.0934219	−	0.161812i
$508$	−96.0000	−	166.277i	−0.00838447	−	0.0145223i
$509$	−9278.50	+	16070.8i	−0.807981	+	1.39946i	0.106279	+	0.994336i	$0.466106\pi$
$509$	−9278.50	+	16070.8i	−0.807981	+	1.39946i	−0.914260	+	0.405128i	$0.867227\pi$
$510$	520.000			0.0451490
$511$	−11618.0	+	543.864i	−1.00577	+	0.0470824i
$512$	−512.000			−0.0441942
$513$	−689.000	+	1193.38i	−0.0592984	+	0.102708i
$514$	−1120.00	−	1939.90i	−0.0961111	−	0.166469i
$515$	3882.50	+	6724.69i	0.332201	+	0.575389i
$516$	−738.000	+	1278.25i	−0.0629625	+	0.109054i
$517$	−176.000			−0.0149719
$518$	7252.00	−	339.482i	0.615125	−	0.0287953i
$519$	−3392.00			−0.286883
$520$	160.000	−	277.128i	0.0134932	−	0.0233709i
$521$	4965.00	+	8599.63i	0.417506	+	0.723142i	0.995688	−	0.0927663i	$-0.0295710\pi$
$521$	4965.00	+	8599.63i	0.417506	+	0.723142i	−0.578182	+	0.815908i	$0.696238\pi$
$522$	−1794.00	−	3107.30i	−0.150424	−	0.260542i
$523$	3962.00	−	6862.39i	0.331255	−	0.573750i	−0.651504	−	0.758646i	$-0.725861\pi$
$523$	3962.00	−	6862.39i	0.331255	−	0.573750i	0.982758	+	0.184896i	$0.0591948\pi$
$524$	−3168.00			−0.264112
$525$	−250.000	−	389.711i	−0.0207827	−	0.0323970i
$526$	−12810.0			−1.06187
$527$	−8632.00	+	14951.1i	−0.713503	+	1.23582i
$528$	−16.0000	−	27.7128i	−0.00131877	−	0.00228418i
$529$	3839.00	+	6649.34i	0.315526	+	0.546506i
$530$	−2910.00	+	5040.27i	−0.238495	+	0.413085i
$531$	9100.00			0.743703
$532$	884.000	−	1711.27i	0.0720418	−	0.139460i
$533$	−2824.00			−0.229495
$534$	−89.0000	+	154.153i	−0.00721237	+	0.0124922i
$535$	4577.50	+	7928.46i	0.369911	+	0.640705i
$536$	1164.00	+	2016.11i	0.0938006	+	0.162467i
$537$	134.000	−	232.095i	0.0107682	−	0.0186511i
$538$	−9870.00			−0.790940
$539$	286.000	−	623.538i	0.0228551	−	0.0498287i
$540$	−1060.00			−0.0844725
$541$	11748.5	−	20349.0i	0.933655	−	1.61714i	0.156641	−	0.987656i	$-0.449934\pi$
$541$	11748.5	−	20349.0i	0.933655	−	1.61714i	0.777015	−	0.629483i	$-0.216733\pi$
$542$	−1446.00	−	2504.55i	−0.114596	−	0.198486i
$543$	−2046.50	−	3544.64i	−0.161738	−	0.280138i
$544$	−832.000	+	1441.07i	−0.0655730	+	0.113576i
$545$	−4055.00			−0.318710
$546$	−136.000	+	263.272i	−0.0106598	+	0.0206355i
$547$	11131.0			0.870068			0.435034	−	0.900414i	$-0.356736\pi$
$547$	11131.0			0.870068			0.435034	+	0.900414i	$0.356736\pi$
$548$	−2168.00	+	3755.09i	−0.169001	+	0.292718i
$549$	−6071.00	−	10515.3i	−0.471956	−	0.817452i
$550$	−50.0000	−	86.6025i	−0.00387638	−	0.00671408i
$551$	−897.000	+	1553.65i	−0.0693530	+	0.120123i
$552$	536.000			0.0413291
$553$	11700.0	+	18238.5i	0.899701	+	1.40249i
$554$	16040.0			1.23010
$555$	−490.000	+	848.705i	−0.0374763	+	0.0649108i
$556$	92.0000	+	159.349i	0.00701739	+	0.0121545i
$557$	5989.00	+	10373.3i	0.455587	+	0.789100i	0.998722	−	0.0505455i	$-0.0160960\pi$
$557$	5989.00	+	10373.3i	0.455587	+	0.789100i	−0.543135	+	0.839646i	$0.682763\pi$
$558$	8632.00	−	14951.1i	0.654878	−	1.13428i
$559$	2952.00			0.223357
$560$	1480.00	−	69.2820i	0.111681	−	0.00522804i
$561$	−104.000			−0.00782689
$562$	4978.00	−	8622.15i	0.373637	−	0.647159i
$563$	5029.50	+	8711.35i	0.376498	+	0.652113i	0.990550	−	0.137152i	$-0.0437950\pi$
$563$	5029.50	+	8711.35i	0.376498	+	0.652113i	−0.614052	+	0.789265i	$0.710462\pi$
$564$	176.000	+	304.841i	0.0131400	+	0.0227591i
$565$	5425.00	−	9396.38i	0.403949	−	0.699661i
$566$	−11704.0			−0.869180
$567$	−12006.5	+	562.050i	−0.889287	+	0.0416295i
$568$	−6160.00			−0.455049
$569$	7833.00	−	13567.2i	0.577111	−	0.999586i	−0.418697	−	0.908126i	$-0.637513\pi$
$569$	7833.00	−	13567.2i	0.577111	−	0.999586i	0.995809	−	0.0914605i	$-0.0291535\pi$
$570$	130.000	+	225.167i	0.00955281	+	0.0165459i
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	0.815939	−	0.578138i	$-0.196220\pi$
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	−0.908651	+	0.417555i	$0.862887\pi$
$572$	−32.0000	+	55.4256i	−0.00233914	+	0.00405151i
$573$	1978.00			0.144210
$574$	−7060.00	−	11005.5i	−0.513378	−	0.800276i
$575$	1675.00			0.121482
$576$	832.000	−	1441.07i	0.0601852	−	0.104244i
$577$	−6409.00	−	11100.7i	−0.462409	−	0.800916i	0.536671	−	0.843791i	$-0.319682\pi$
$577$	−6409.00	−	11100.7i	−0.462409	−	0.800916i	−0.999080	+	0.0428751i	$0.986348\pi$
$578$	−2209.00	−	3826.10i	−0.158966	−	0.275337i
$579$	−1999.00	+	3462.37i	−0.143481	+	0.248517i
$580$	−1380.00			−0.0987955
$581$	4462.50	−	8638.60i	0.318650	−	0.616850i
$582$	−580.000			−0.0413089
$583$	582.000	−	1008.05i	0.0413447	−	0.0716112i
$584$	2512.00	+	4350.91i	0.177992	+	0.308291i
$585$	520.000	+	900.666i	0.0367510	+	0.0636547i
$586$	−3012.00	+	5216.94i	−0.212329	+	0.367764i
$587$	−15228.0			−1.07074			−0.535372	−	0.844616i	$-0.679829\pi$
$587$	−15228.0			−1.07074			−0.535372	+	0.844616i	$0.679829\pi$
$588$	−1366.00	+	128.172i	−0.0958042	+	0.00898931i
$589$	−8632.00			−0.603863
$590$	1750.00	−	3031.09i	0.122112	−	0.211505i
$591$	−1515.00	−	2624.06i	−0.105446	−	0.182638i
$592$	−1568.00	−	2715.86i	−0.108859	−	0.188549i
$593$	1299.00	−	2249.93i	0.0899554	−	0.155807i	−0.817537	−	0.575877i	$-0.804661\pi$
$593$	1299.00	−	2249.93i	0.0899554	−	0.155807i	0.907492	+	0.420069i	$0.137994\pi$
$594$	212.000			0.0146439
$595$	2210.00	−	4278.17i	0.152271	−	0.294769i
$596$	−1476.00			−0.101442
$597$	178.000	−	308.305i	0.0122028	−	0.0211358i
$598$	−536.000	−	928.379i	−0.0366533	−	0.0634854i
$599$	1274.00	+	2206.63i	0.0869019	+	0.150518i	0.906200	−	0.422849i	$-0.138970\pi$
$599$	1274.00	+	2206.63i	0.0869019	+	0.150518i	−0.819298	+	0.573368i	$0.805637\pi$
$600$	−100.000	+	173.205i	−0.00680414	+	0.0117851i
$601$	1706.00			0.115789			0.0578945	−	0.998323i	$-0.481561\pi$
$601$	1706.00			0.115789			0.0578945	+	0.998323i	$0.481561\pi$
$602$	7380.00	+	11504.3i	0.499645	+	0.778870i
$603$	−7566.00			−0.510964
$604$	−4960.00	+	8590.97i	−0.334138	+	0.578745i
$605$	−3317.50	−	5746.08i	−0.222935	−	0.386134i
$606$	1233.00	+	2135.62i	0.0826521	+	0.143158i
$607$	6283.50	−	10883.3i	0.420164	−	0.727745i	−0.575791	−	0.817597i	$-0.695306\pi$
$607$	6283.50	−	10883.3i	0.420164	−	0.727745i	0.995955	+	0.0898517i	$0.0286393\pi$
$608$	−832.000			−0.0554968
$609$	1276.50	−	59.7558i	0.0849366	−	0.00397607i
$610$	−4670.00			−0.309972
$611$	352.000	−	609.682i	0.0233067	−	0.0403684i
$612$	−2704.00	−	4683.47i	−0.178599	−	0.309343i
$613$	4814.00	+	8338.09i	0.317187	+	0.549384i	0.979900	−	0.199490i	$-0.0639284\pi$
$613$	4814.00	+	8338.09i	0.317187	+	0.549384i	−0.662713	+	0.748874i	$0.730595\pi$
$614$	9443.00	−	16355.8i	0.620665	−	1.07502i
$615$	1765.00			0.115726
$616$	−296.000	+	13.8564i	−0.0193607	+	0.000906316i
$617$	−4316.00			−0.281614			−0.140807	−	0.990037i	$-0.544970\pi$
$617$	−4316.00			−0.281614			−0.140807	+	0.990037i	$0.544970\pi$
$618$	−1553.00	+	2689.87i	−0.101085	+	0.175085i
$619$	−8201.00	−	14204.5i	−0.532514	−	0.922341i	−0.999279	−	0.0379598i	$-0.987914\pi$
$619$	−8201.00	−	14204.5i	−0.532514	−	0.922341i	0.466766	−	0.884381i	$-0.345419\pi$
$620$	−3320.00	−	5750.41i	−0.215055	−	0.372487i
$621$	−1775.50	+	3075.26i	−0.114732	+	0.198721i
$622$	19988.0			1.28850
$623$	890.000	+	1387.37i	0.0572345	+	0.0892198i
$624$	128.000			0.00821170
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	1456.00	+	2521.87i	0.0929608	+	0.161013i
$627$	−26.0000	−	45.0333i	−0.00165604	−	0.00286835i
$628$	−2452.00	+	4246.99i	−0.155805	+	0.269862i
$629$	−10192.0			−0.646076
$630$	−2210.00	+	4278.17i	−0.139760	+	0.270550i
$631$	8490.00			0.535628			0.267814	−	0.963471i	$-0.413699\pi$
$631$	8490.00			0.535628			0.267814	+	0.963471i	$0.413699\pi$
$632$	4680.00	−	8106.00i	0.294558	−	0.510189i
$633$	−1301.00	−	2253.40i	−0.0816905	−	0.141492i
$634$	6872.00	+	11902.7i	0.430476	+	0.745607i
$635$	120.000	−	207.846i	0.00749930	−	0.0129892i
$636$	−2328.00			−0.145143
$637$	1588.00	+	2237.81i	0.0987737	+	0.139192i
$638$	276.000			0.0171269
$639$	10010.0	−	17337.8i	0.619702	−	1.07336i
$640$	−320.000	−	554.256i	−0.0197642	−	0.0342327i
$641$	61.5000	+	106.521i	0.00378955	+	0.00656370i	0.867914	−	0.496715i	$-0.165460\pi$
$641$	61.5000	+	106.521i	0.00378955	+	0.00656370i	−0.864124	+	0.503278i	$0.832127\pi$
$642$	−1831.00	+	3171.39i	−0.112560	+	0.194960i
$643$	−23924.0			−1.46729			−0.733647	−	0.679530i	$-0.762184\pi$
$643$	−23924.0			−1.46729			−0.733647	+	0.679530i	$0.762184\pi$
$644$	2278.00	−	4409.80i	0.139388	−	0.269830i
$645$	−1845.00			−0.112631
$646$	−1352.00	+	2341.73i	−0.0823432	+	0.142623i
$647$	−90.5000	−	156.751i	−0.00549911	−	0.00952473i	0.863263	−	0.504755i	$-0.168417\pi$
$647$	−90.5000	−	156.751i	−0.00549911	−	0.00952473i	−0.868762	+	0.495230i	$0.835084\pi$
$648$	2596.00	+	4496.40i	0.157377	+	0.272586i
$649$	−350.000	+	606.218i	−0.0211690	+	0.0366658i
$650$	400.000			0.0241374
$651$	3320.00	+	5175.37i	0.199879	+	0.311580i
$652$	−2640.00			−0.158574
$653$	8906.00	−	15425.6i	0.533719	−	0.924429i	−0.465505	−	0.885045i	$-0.654127\pi$
$653$	8906.00	−	15425.6i	0.533719	−	0.924429i	0.999224	−	0.0393836i	$-0.0125394\pi$
$654$	−811.000	−	1404.69i	−0.0484902	−	0.0839875i
$655$	−1980.00	−	3429.46i	−0.118115	−	0.204580i
$656$	−2824.00	+	4891.31i	−0.168077	+	0.291118i
$657$	−16328.0			−0.969583
$658$	3256.00	−	152.420i	0.192906	−	0.00903035i
$659$	15334.0			0.906416			0.453208	−	0.891405i	$-0.350280\pi$
$659$	15334.0			0.906416			0.453208	+	0.891405i	$0.350280\pi$
$660$	20.0000	−	34.6410i	0.00117954	−	0.00204303i
$661$	−668.500	−	1157.88i	−0.0393368	−	0.0681334i	0.845687	−	0.533680i	$-0.179191\pi$
$661$	−668.500	−	1157.88i	−0.0393368	−	0.0681334i	−0.885024	+	0.465546i	$0.845858\pi$
$662$	−392.000	−	678.964i	−0.0230144	−	0.0398621i
$663$	208.000	−	360.267i	0.0121841	−	0.0211035i
$664$	−4200.00			−0.245469
$665$	2405.00	−	112.583i	0.140243	−	0.00656510i
$666$	10192.0			0.592991
$667$	−2311.50	+	4003.64i	−0.134185	+	0.232416i
$668$	1898.00	+	3287.43i	0.109934	+	0.190411i
$669$	−1578.00	−	2733.18i	−0.0911943	−	0.157953i
$670$	−1455.00	+	2520.13i	−0.0838978	+	0.145315i
$671$	934.000			0.0537357
$672$	320.000	+	498.831i	0.0183694	+	0.0286351i
$673$	−15112.0			−0.865564			−0.432782	−	0.901499i	$-0.642468\pi$
$673$	−15112.0			−0.865564			−0.432782	+	0.901499i	$0.642468\pi$
$674$	3926.00	−	6800.03i	0.224368	−	0.388616i
$675$	−662.500	−	1147.48i	−0.0377772	−	0.0654321i
$676$	4266.00	+	7388.93i	0.242717	+	0.420399i
$677$	−12696.0	+	21990.1i	−0.720749	+	1.24837i	0.239951	+	0.970785i	$0.422869\pi$
$677$	−12696.0	+	21990.1i	−0.720749	+	1.24837i	−0.960700	+	0.277589i	$0.910465\pi$
$678$	4340.00			0.245836
$679$	−2465.00	+	4771.80i	−0.139320	+	0.269698i
$680$	−2080.00			−0.117301
$681$	2118.00	−	3668.48i	0.119181	−	0.206427i
$682$	664.000	+	1150.08i	0.0372813	+	0.0645732i
$683$	−14615.5	−	25314.8i	−0.818809	−	1.41822i	−0.906560	−	0.422076i	$-0.861301\pi$
$683$	−14615.5	−	25314.8i	−0.818809	−	1.41822i	0.0877512	−	0.996142i	$-0.472032\pi$
$684$	1352.00	−	2341.73i	0.0755775	−	0.130904i
$685$	−5420.00			−0.302318
$686$	−4751.00	+	11783.1i	−0.264423	+	0.655805i
$687$	−6334.00			−0.351757
$688$	2952.00	−	5113.01i	0.163581	−	0.283331i
$689$	2328.00	+	4032.21i	0.128722	+	0.222954i
$690$	335.000	+	580.237i	0.0184829	+	0.0320134i
$691$	3769.00	−	6528.10i	0.207496	−	0.359393i	−0.743429	−	0.668814i	$-0.766802\pi$
$691$	3769.00	−	6528.10i	0.207496	−	0.359393i	0.950925	+	0.309421i	$0.100135\pi$
$692$	13568.0			0.745344
$693$	442.000	−	855.633i	0.0242283	−	0.0469016i
$694$	3570.00			0.195267
$695$	−115.000	+	199.186i	−0.00627654	+	0.0108713i
$696$	−276.000	−	478.046i	−0.0150313	−	0.0260349i
$697$	9178.00	+	15896.8i	0.498768	+	0.863892i
$698$	−1591.00	+	2755.69i	−0.0862754	+	0.149433i
$699$	4688.00			0.253672
$700$	1000.00	+	1558.85i	0.0539949	+	0.0841698i
$701$	22125.0			1.19208			0.596041	−	0.802954i	$-0.296739\pi$
$701$	22125.0			1.19208			0.596041	+	0.802954i	$0.296739\pi$
$702$	−424.000	+	734.390i	−0.0227961	+	0.0394840i
$703$	−2548.00	−	4413.27i	−0.136699	−	0.236770i
$704$	64.0000	+	110.851i	0.00342627	+	0.00593447i
$705$	−220.000	+	381.051i	−0.0117527	+	0.0203563i
$706$	−3372.00			−0.179755
$707$	22810.5	−	1067.81i	1.21340	−	0.0568021i
$708$	1400.00			0.0743153
$709$	2219.50	−	3844.29i	0.117567	−	0.203632i	−0.801236	−	0.598349i	$-0.795824\pi$
$709$	2219.50	−	3844.29i	0.117567	−	0.203632i	0.918803	+	0.394716i	$0.129157\pi$
$710$	−3850.00	−	6668.40i	−0.203504	−	0.352479i
$711$	15210.0	+	26344.5i	0.802278	+	1.38959i
$712$	356.000	−	616.610i	0.0187383	−	0.0324557i
$713$	−22244.0			−1.16837
$714$	1924.00	−	90.0666i	0.100846	−	0.00472081i
$715$	−80.0000			−0.00418438
$716$	−536.000	+	928.379i	−0.0279766	+	0.0484569i
$717$	928.000	+	1607.34i	0.0483358	+	0.0837201i
$718$	7372.00	+	12768.7i	0.383176	+	0.663681i
$719$	−6825.00	+	11821.2i	−0.354005	+	0.613155i	−0.986947	−	0.161045i	$-0.948514\pi$
$719$	−6825.00	+	11821.2i	−0.354005	+	0.613155i	0.632942	+	0.774199i	$0.281847\pi$
$720$	2080.00			0.107663
$721$	15530.0	+	24208.9i	0.802174	+	1.25047i
$722$	12366.0			0.637417
$723$	−2403.00	+	4162.12i	−0.123608	+	0.214095i
$724$	8186.00	+	14178.6i	0.420208	+	0.727821i
$725$	−862.500	−	1493.89i	−0.0441827	−	0.0765267i
$726$	1327.00	−	2298.43i	0.0678369	−	0.117497i
$727$	−11397.0			−0.581419			−0.290709	−	0.956811i	$-0.593891\pi$
$727$	−11397.0			−0.581419			−0.290709	+	0.956811i	$0.593891\pi$
$728$	544.000	−	1053.09i	0.0276950	−	0.0536126i
$729$	−15443.0			−0.784586
$730$	−3140.00	+	5438.64i	−0.159201	+	0.275744i
$731$	−9594.00	−	16617.3i	−0.485427	−	0.840784i
$732$	−934.000	−	1617.74i	−0.0471607	−	0.0816847i
$733$	−8343.00	+	14450.5i	−0.420403	+	0.728160i	−0.995979	−	0.0895886i	$-0.971445\pi$
$733$	−8343.00	+	14450.5i	−0.420403	+	0.728160i	0.575575	+	0.817749i	$0.304778\pi$
$734$	−13274.0			−0.667510
$735$	−992.500	−	1398.63i	−0.0498080	−	0.0701895i
$736$	−2144.00			−0.107376
$737$	291.000	−	504.027i	0.0145443	−	0.0251914i
$738$	−9178.00	−	15896.8i	−0.457787	−	0.792910i
$739$	−11235.0	−	19459.6i	−0.559251	−	0.968650i	−0.997559	−	0.0698258i	$-0.977756\pi$
$739$	−11235.0	−	19459.6i	−0.559251	−	0.968650i	0.438309	−	0.898825i	$-0.355578\pi$
$740$	1960.00	−	3394.82i	0.0973663	−	0.168643i
$741$	208.000			0.0103118
$742$	−9894.00	+	19153.0i	−0.489515	+	0.947614i
$743$	5625.00			0.277741			0.138870	−	0.990311i	$-0.455653\pi$
$743$	5625.00			0.277741			0.138870	+	0.990311i	$0.455653\pi$
$744$	1328.00	−	2300.16i	0.0654393	−	0.113344i
$745$	−922.500	−	1597.82i	−0.0453662	−	0.0785765i
$746$	3476.00	+	6020.61i	0.170597	+	0.295483i
$747$	6825.00	−	11821.2i	0.334289	−	0.579005i
$748$	416.000			0.0203348
$749$	18310.0	+	28542.5i	0.893235	+	1.39242i
$750$	−250.000			−0.0121716
$751$	−8810.00	+	15259.4i	−0.428071	+	0.741441i	−0.996702	−	0.0811520i	$-0.974140\pi$
$751$	−8810.00	+	15259.4i	−0.428071	+	0.741441i	0.568631	+	0.822593i	$0.307473\pi$
$752$	−704.000	−	1219.36i	−0.0341386	−	0.0591298i
$753$	−1600.00	−	2771.28i	−0.0774333	−	0.134118i
$754$	−552.000	+	956.092i	−0.0266613	+	0.0461788i
$755$	−12400.0			−0.597725
$756$	−3922.00	+	183.597i	−0.188680	+	0.00883250i
$757$	39056.0			1.87518			0.937592	−	0.347737i	$-0.113050\pi$
$757$	39056.0			1.87518			0.937592	+	0.347737i	$0.113050\pi$
$758$	−2378.00	+	4118.82i	−0.113948	+	0.197364i
$759$	−67.0000	−	116.047i	−0.00320414	−	0.00554974i
$760$	−520.000	−	900.666i	−0.0248189	−	0.0429876i
$761$	−14869.0	+	25753.9i	−0.708280	+	1.22678i	0.257215	+	0.966354i	$0.417195\pi$
$761$	−14869.0	+	25753.9i	−0.708280	+	1.22678i	−0.965495	+	0.260422i	$0.916138\pi$
$762$	96.0000			0.00456393
$763$	−15003.5	+	702.347i	−0.711878	+	0.0333246i
$764$	−7912.00			−0.374668
$765$	3380.00	−	5854.33i	0.159744	−	0.276685i
$766$	−2457.00	−	4255.65i	−0.115894	−	0.200735i
$767$	−1400.00	−	2424.87i	−0.0659075	−	0.114155i
$768$	128.000	−	221.703i	0.00601407	−	0.0104167i
$769$	−1118.00			−0.0524267			−0.0262133	−	0.999656i	$-0.508345\pi$
$769$	−1118.00			−0.0524267			−0.0262133	+	0.999656i	$0.508345\pi$
$770$	−200.000	−	311.769i	−0.00936039	−	0.0145914i
$771$	1120.00			0.0523162
$772$	7996.00	−	13849.5i	0.372775	−	0.645665i
$773$	−6716.00	−	11632.5i	−0.312494	−	0.541255i	0.666408	−	0.745587i	$-0.267831\pi$
$773$	−6716.00	−	11632.5i	−0.312494	−	0.541255i	−0.978902	+	0.204332i	$0.934498\pi$
$774$	9594.00	+	16617.3i	0.445542	+	0.771701i
$775$	4150.00	−	7188.01i	0.192351	−	0.333163i
$776$	2320.00			0.107324
$777$	−1666.00	+	3225.08i	−0.0769207	+	0.148905i
$778$	−17124.0			−0.789107
$779$	−4589.00	+	7948.38i	−0.211063	+	0.365572i
$780$	80.0000	+	138.564i	0.00367238	+	0.00636076i
$781$	770.000	+	1333.68i	0.0352788	+	0.0611047i
$782$	−3484.00	+	6034.47i	−0.159319	+	0.275949i
$783$	3657.00			0.166910
$784$	5464.00	−	512.687i	0.248907	−	0.0233549i
$785$	−6130.00			−0.278712
$786$	792.000	−	1371.78i	0.0359411	−	0.0622518i
$787$	4674.50	+	8096.47i	0.211725	+	0.366719i	0.952255	−	0.305305i	$-0.0987584\pi$
$787$	4674.50	+	8096.47i	0.211725	+	0.366719i	−0.740529	+	0.672024i	$0.765425\pi$
$788$	6060.00	+	10496.2i	0.273958	+	0.474508i
$789$	3202.50	−	5546.89i	0.144502	−	0.250285i
$790$	11700.0			0.526921
$791$	18445.0	−	35706.2i	0.829113	−	1.60502i
$792$	−416.000			−0.0186640
$793$	−1868.00	+	3235.47i	−0.0836502	+	0.144886i
$794$	−9842.00	−	17046.8i	−0.439899	−	0.761927i
$795$	−1455.00	−	2520.13i	−0.0649101	−	0.112428i
$796$	−712.000	+	1233.22i	−0.0317037	+	0.0549125i
$797$	−28008.0			−1.24479			−0.622393	−	0.782705i	$-0.713839\pi$
$797$	−28008.0			−1.24479			−0.622393	+	0.782705i	$0.713839\pi$
$798$	520.000	+	810.600i	0.0230674	+	0.0359585i
$799$	−4576.00			−0.202612
$800$	400.000	−	692.820i	0.0176777	−	0.0306186i
$801$	1157.00	+	2003.98i	0.0510369	+	0.0883986i
$802$	−8097.00	−	14024.4i	−0.356503	−	0.617480i
$803$	628.000	−	1087.73i	0.0275986	−	0.0478021i
$804$	−1164.00			−0.0510586
$805$	6197.50	−	290.119i	0.271346	−	0.0127023i
$806$	−5312.00			−0.232143
$807$	2467.50	−	4273.84i	0.107633	−	0.186426i
$808$	−4932.00	−	8542.47i	−0.214737	−	0.371935i
$809$	−9834.50	−	17033.9i	−0.427395	−	0.740270i	0.569246	−	0.822167i	$-0.307235\pi$
$809$	−9834.50	−	17033.9i	−0.427395	−	0.740270i	−0.996641	+	0.0818975i	$0.973902\pi$
$810$	−3245.00	+	5620.50i	−0.140763	+	0.243808i
$811$	31860.0			1.37948			0.689739	−	0.724059i	$-0.257725\pi$
$811$	31860.0			1.37948			0.689739	+	0.724059i	$0.257725\pi$
$812$	−5106.00	+	239.023i	−0.220672	+	0.0103301i
$813$	1446.00			0.0623781
$814$	−392.000	+	678.964i	−0.0168791	+	0.0292355i
$815$	−1650.00	−	2857.88i	−0.0709165	−	0.122831i
$816$	−416.000	−	720.533i	−0.0178467	−	0.0309114i
$817$	4797.00	−	8308.65i	0.205417	−	0.355793i
$818$	−30518.0			−1.30445
$819$	2080.00	+	3242.40i	0.0887437	+	0.138338i
$820$	−7060.00			−0.300666
$821$	−1115.00	+	1931.24i	−0.0473980	+	0.0820958i	−0.888751	−	0.458390i	$-0.848426\pi$
$821$	−1115.00	+	1931.24i	−0.0473980	+	0.0820958i	0.841353	+	0.540486i	$0.181760\pi$
$822$	−1084.00	−	1877.54i	−0.0459962	−	0.0796677i
$823$	−7401.50	−	12819.8i	−0.313487	−	0.542976i	0.665627	−	0.746284i	$-0.268164\pi$
$823$	−7401.50	−	12819.8i	−0.313487	−	0.542976i	−0.979115	+	0.203308i	$0.934831\pi$
$824$	6212.00	−	10759.5i	0.262628	−	0.454885i
$825$	50.0000			0.00211003
$826$	5950.00	−	11518.1i	0.250638	−	0.485190i
$827$	13257.0			0.557426			0.278713	−	0.960374i	$-0.410092\pi$
$827$	13257.0			0.557426			0.278713	+	0.960374i	$0.410092\pi$
$828$	3484.00	−	6034.47i	0.146229	−	0.253276i
$829$	10787.0	+	18683.6i	0.451928	+	0.782762i	0.998506	−	0.0546465i	$-0.0174032\pi$
$829$	10787.0	+	18683.6i	0.451928	+	0.782762i	−0.546578	+	0.837408i	$0.684070\pi$
$830$	−2625.00	−	4546.63i	−0.109777	−	0.190140i
$831$	−4010.00	+	6945.52i	−0.167395	+	0.289937i
$832$	−512.000			−0.0213346
$833$	7436.00	−	16212.0i	0.309294	−	0.674325i
$834$	−92.0000			−0.00381978
$835$	−2372.50	+	4109.29i	−0.0983278	+	0.170309i
$836$	104.000	+	180.133i	0.00430253	+	0.00745220i
$837$	8798.00	+	15238.6i	0.363325	+	0.629298i
$838$	16224.0	−	28100.8i	0.668793	−	1.15838i
$839$	12990.0			0.534523			0.267261	−	0.963624i	$-0.413881\pi$
$839$	12990.0			0.534523			0.267261	+	0.963624i	$0.413881\pi$
$840$	−340.000	+	658.179i	−0.0139656	+	0.0270349i
$841$	−19628.0			−0.804789
$842$	2977.00	−	5156.32i	0.121846	−	0.211043i
$843$	2489.00	+	4311.07i	0.101691	+	0.176134i
$844$	5204.00	+	9013.59i	0.212238	+	0.367607i
$845$	−5332.50	+	9236.16i	−0.217093	+	0.376016i
$846$	4576.00			0.185965
$847$	−13270.0	−	20685.9i	−0.538327	−	0.839168i
$848$	9312.00			0.377094
$849$	2926.00	−	5067.98i	0.118280	−	0.204868i
$850$	−1300.00	−	2251.67i	−0.0524584	−	0.0908606i
$851$	−6566.00	−	11372.6i	−0.264488	−	0.458107i
$852$	1540.00	−	2667.36i	0.0619243	−	0.107256i
$853$	24838.0			0.996995			0.498498	−	0.866891i	$-0.333885\pi$
$853$	24838.0			0.996995			0.498498	+	0.866891i	$0.333885\pi$
$854$	−17279.0	+	808.868i	−0.692360	+	0.0324109i
$855$	3380.00			0.135197
$856$	7324.00	−	12685.5i	0.292441	−	0.506522i
$857$	8513.00	+	14744.9i	0.339322	+	0.587722i	0.984305	−	0.176474i	$-0.0564692\pi$
$857$	8513.00	+	14744.9i	0.339322	+	0.587722i	−0.644984	+	0.764196i	$0.723136\pi$
$858$	−16.0000	−	27.7128i	−0.000636633	−	0.00110268i
$859$	−3364.00	+	5826.62i	−0.133618	+	0.231434i	−0.925069	−	0.379800i	$-0.875993\pi$
$859$	−3364.00	+	5826.62i	−0.133618	+	0.231434i	0.791450	+	0.611233i	$0.209326\pi$
$860$	7380.00			0.292623
$861$	6530.50	−	305.707i	0.258489	−	0.0121004i
$862$	−28404.0			−1.12232
$863$	15049.5	−	26066.5i	0.593616	−	1.02817i	−0.400124	−	0.916461i	$-0.631033\pi$
$863$	15049.5	−	26066.5i	0.593616	−	1.02817i	0.993741	−	0.111713i	$-0.0356337\pi$
$864$	848.000	+	1468.78i	0.0333907	+	0.0578344i
$865$	8480.00	+	14687.8i	0.333328	+	0.577341i
$866$	14310.0	−	24785.6i	0.561517	−	0.972576i
$867$	2209.00			0.0865301
$868$	−13280.0	−	20701.5i	−0.519300	−	0.809509i
$869$	−2340.00			−0.0913453
$870$	345.000	−	597.558i	0.0134444	−	0.0232863i
$871$	1164.00	+	2016.11i	0.0452820	+	0.0784308i
$872$	3244.00	+	5618.77i	0.125981	+	0.218206i
$873$	−3770.00	+	6529.83i	−0.146157	+	0.253152i
$874$	−3484.00			−0.134838
$875$	−1062.50	+	2056.81i	−0.0410503	+	0.0794661i
$876$	−2512.00			−0.0968865
$877$	2813.00	−	4872.26i	0.108310	−	0.187599i	−0.806775	−	0.590858i	$-0.798789\pi$
$877$	2813.00	−	4872.26i	0.108310	−	0.187599i	0.915086	+	0.403259i	$0.132123\pi$
$878$	−2356.00	−	4080.71i	−0.0905594	−	0.156853i
$879$	−1506.00	−	2608.47i	−0.0577885	−	0.100093i
$880$	−80.0000	+	138.564i	−0.00306454	+	0.00530795i
$881$	−15927.0			−0.609074			−0.304537	−	0.952500i	$-0.598502\pi$
$881$	−15927.0			−0.609074			−0.304537	+	0.952500i	$0.598502\pi$
$882$	−7436.00	+	16212.0i	−0.283881	+	0.618919i
$883$	39124.0			1.49108			0.745542	−	0.666458i	$-0.232191\pi$
$883$	39124.0			1.49108			0.745542	+	0.666458i	$0.232191\pi$
$884$	−832.000	+	1441.07i	−0.0316552	+	0.0548284i
$885$	875.000	+	1515.54i	0.0332348	+	0.0575644i
$886$	8291.00	+	14360.4i	0.314381	+	0.544524i
$887$	12665.5	−	21937.3i	0.479443	−	0.830419i	−0.520279	−	0.853996i	$-0.674172\pi$
$887$	12665.5	−	21937.3i	0.479443	−	0.830419i	0.999722	+	0.0235768i	$0.00750542\pi$
$888$	1568.00			0.0592552
$889$	408.000	−	789.815i	0.0153924	−	0.0297970i
$890$	890.000			0.0335201
$891$	649.000	−	1124.10i	0.0244022	−	0.0422658i
$892$	6312.00	+	10932.7i	0.236930	+	0.410374i
$893$	−1144.00	−	1981.47i	−0.0428695	−	0.0742522i
$894$	369.000	−	639.127i	0.0138045	−	0.0239101i
$895$	−1340.00			−0.0500461
$896$	−1280.00	−	1995.32i	−0.0477252	−	0.0743963i
$897$	536.000			0.0199515
$898$	−3521.00	+	6098.55i	−0.130843	+	0.226627i
$899$	11454.0	+	19838.9i	0.424930	+	0.736001i
$900$	1300.00	+	2251.67i	0.0481481	+	0.0833950i
$901$	15132.0	−	26209.4i	0.559512	−	0.969103i
$902$	1412.00			0.0521225
$903$	−6826.50	+	319.563i	−0.251574	+	0.0117767i
$904$	−17360.0			−0.638700
$905$	−10232.5	+	17723.2i	−0.375845	+	0.650983i
$906$	−2480.00	−	4295.49i	−0.0909409	−	0.157514i
$907$	−13192.5	−	22850.1i	−0.482966	−	0.836521i	0.516843	−	0.856080i	$-0.327107\pi$
$907$	−13192.5	−	22850.1i	−0.482966	−	0.836521i	−0.999809	+	0.0195592i	$0.993774\pi$
$908$	−8472.00	+	14673.9i	−0.309640	+	0.536312i
$909$	32058.0			1.16974
$910$	1480.00	−	69.2820i	0.0539138	−	0.00252382i
$911$	−40770.0			−1.48273			−0.741367	−	0.671100i	$-0.765822\pi$
$911$	−40770.0			−1.48273			−0.741367	+	0.671100i	$0.765822\pi$
$912$	208.000	−	360.267i	0.00755216	−	0.0130807i
$913$	525.000	+	909.327i	0.0190306	+	0.0329620i
$914$	−5432.00	−	9408.50i	−0.196581	−	0.340487i
$915$	1167.50	−	2022.17i	0.0421818	−	0.0730610i
$916$	25336.0			0.913892
$917$	−7920.00	−	12346.1i	−0.285214	−	0.444605i
$918$	5512.00			0.198173
$919$	7309.00	−	12659.6i	0.262352	−	0.454407i	−0.704514	−	0.709690i	$-0.748835\pi$
$919$	7309.00	−	12659.6i	0.262352	−	0.454407i	0.966867	+	0.255282i	$0.0821685\pi$
$920$	−1340.00	−	2320.95i	−0.0480201	−	0.0831733i
$921$	4721.50	+	8177.88i	0.168924	+	0.292584i
$922$	−5350.00	+	9266.47i	−0.191099	+	0.330992i
$923$	−6160.00			−0.219674
$924$	68.0000	−	131.636i	0.00242103	−	0.00468669i
$925$	4900.00			0.174174
$926$	−10123.0	+	17533.6i	−0.359247	+	0.622233i
$927$	20189.0	+	34968.4i	0.715311	+	1.23896i
$928$	1104.00	+	1912.18i	0.0390523	+	0.0676406i
$929$	−20661.5	+	35786.8i	−0.729690	+	1.26386i	0.227324	+	0.973819i	$0.427002\pi$
$929$	−20661.5	+	35786.8i	−0.729690	+	1.26386i	−0.957014	+	0.290041i	$0.906331\pi$
$930$	3320.00			0.117061
$931$	8879.00	−	833.116i	0.312564	−	0.0293279i
$932$	−18752.0			−0.659058
$933$	−4997.00	+	8655.06i	−0.175342	+	0.303702i
$934$	6463.00	+	11194.2i	0.226420	+	0.392170i
$935$	260.000	+	450.333i	0.00909402	+	0.0157513i
$936$	832.000	−	1441.07i	0.0290542	−	0.0503234i
$937$	−22620.0			−0.788648			−0.394324	−	0.918971i	$-0.629021\pi$
$937$	−22620.0			−0.788648			−0.394324	+	0.918971i	$0.629021\pi$
$938$	−4947.00	+	9576.51i	−0.172202	+	0.333352i
$939$	−1456.00			−0.0506015
$940$	880.000	−	1524.20i	0.0305345	−	0.0528873i
$941$	−25989.0	−	45014.3i	−0.900337	−	1.55943i	−0.827057	−	0.562118i	$-0.809987\pi$
$941$	−25989.0	−	45014.3i	−0.900337	−	1.55943i	−0.0732801	−	0.997311i	$-0.523347\pi$
$942$	−1226.00	−	2123.49i	−0.0424047	−	0.0734471i
$943$	−11825.5	+	20482.4i	−0.408368	+	0.707315i
$944$	−5600.00			−0.193077
$945$	−2650.00	−	4130.94i	−0.0912217	−	0.142201i
$946$	−1476.00			−0.0507282
$947$	−4993.50	+	8649.00i	−0.171348	+	0.296784i	−0.938892	−	0.344213i	$-0.888146\pi$
$947$	−4993.50	+	8649.00i	−0.171348	+	0.296784i	0.767543	+	0.640997i	$0.221479\pi$
$948$	2340.00	+	4053.00i	0.0801684	+	0.138856i
$949$	2512.00	+	4350.91i	0.0859252	+	0.148827i
$950$	650.000	−	1125.83i	0.0221987	−	0.0384493i
$951$	−6872.00			−0.234322
$952$	−7696.00	+	360.267i	−0.262005	+	0.0122650i
$953$	6588.00			0.223931			0.111966	−	0.993712i	$-0.464285\pi$
$953$	6588.00			0.223931			0.111966	+	0.993712i	$0.464285\pi$
$954$	−15132.0	+	26209.4i	−0.513539	+	0.889476i
$955$	−4945.00	−	8564.99i	−0.167556	−	0.290216i
$956$	−3712.00	−	6429.37i	−0.125580	−	0.217511i
$957$	−69.0000	+	119.512i	−0.00233067	+	0.00403684i
$958$	35280.0			1.18982
$959$	−20054.0	+	938.772i	−0.675263	+	0.0316105i
$960$	320.000			0.0107583
$961$	−40216.5	+	69657.0i	−1.34995	+	2.33819i
$962$	−1568.00	−	2715.86i	−0.0525513	−	0.0910215i
$963$	23803.0	+	41228.0i	0.796512	+	1.37960i
$964$	9612.00	−	16648.5i	0.321143	−	0.556236i
$965$	19990.0			0.666840
$966$	1340.00	+	2088.85i	0.0446313	+	0.0695732i
$967$	−4091.00			−0.136047			−0.0680236	−	0.997684i	$-0.521669\pi$
$967$	−4091.00			−0.136047			−0.0680236	+	0.997684i	$0.521669\pi$
$968$	−5308.00	+	9193.73i	−0.176245	+	0.305266i
$969$	−676.000	−	1170.87i	−0.0224110	−	0.0388170i
$970$	1450.00	+	2511.47i	0.0479966	+	0.0831325i
$971$	−11820.0	+	20472.8i	−0.390651	+	0.676627i	−0.992536	−	0.121956i	$-0.961083\pi$
$971$	−11820.0	+	20472.8i	−0.390651	+	0.676627i	0.601885	+	0.798583i	$0.294417\pi$
$972$	−8320.00			−0.274552
$973$	−391.000	+	756.906i	−0.0128827	+	0.0249386i
$974$	20064.0			0.660053
$975$	−100.000	+	173.205i	−0.00328468	+	0.00568923i
$976$	3736.00	+	6470.94i	0.122527	+	0.212223i
$977$	−18333.0	−	31753.7i	−0.600332	−	1.03981i	−0.992771	−	0.120028i	$-0.961702\pi$
$977$	−18333.0	−	31753.7i	−0.600332	−	1.03981i	0.392438	−	0.919778i	$-0.371632\pi$
$978$	660.000	−	1143.15i	0.0215792	−	0.0373763i
$979$	−178.000			−0.00581093
$980$	3970.00	+	5594.52i	0.129405	+	0.182358i
$981$	−21086.0			−0.686263
$982$	5916.00	−	10246.8i	0.192248	−	0.332983i
$983$	20535.5	+	35568.5i	0.666308	+	1.15408i	0.978929	+	0.204201i	$0.0654597\pi$
$983$	20535.5	+	35568.5i	0.666308	+	1.15408i	−0.312621	+	0.949878i	$0.601207\pi$
$984$	−1412.00	−	2445.66i	−0.0457448	−	0.0792324i
$985$	−7575.00	+	13120.3i	−0.245035	+	0.424413i
$986$	7176.00			0.231775
$987$	−748.000	+	1447.99i	−0.0241227	+	0.0466972i
$988$	−832.000			−0.0267909
$989$	12361.5	−	21410.7i	0.397445	−	0.688394i
$990$	−260.000	−	450.333i	−0.00834681	−	0.0144571i
$991$	−15992.0	−	27699.0i	−0.512616	−	0.887877i	−0.999893	−	0.0146297i	$-0.995343\pi$
$991$	−15992.0	−	27699.0i	−0.512616	−	0.887877i	0.487277	−	0.873248i	$-0.337990\pi$
$992$	−5312.00	+	9200.65i	−0.170016	+	0.294477i
$993$	392.000			0.0125274
$994$	−15400.0	−	24006.2i	−0.491407	−	0.766027i
$995$	−1780.00			−0.0567134
$996$	1050.00	−	1818.65i	0.0334041	−	0.0578577i
$997$	21947.0	+	38013.3i	0.697160	+	1.20752i	0.969447	+	0.245300i	$0.0788866\pi$
$997$	21947.0	+	38013.3i	0.697160	+	1.20752i	−0.272287	+	0.962216i	$0.587780\pi$
$998$	13894.0	+	24065.1i	0.440688	+	0.763294i
$999$	−5194.00	+	8996.27i	−0.164495	+	0.284914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.4.e.c.51.1	yes	2
3.2	odd	2		630.4.k.b.541.1		2
4.3	odd	2		560.4.q.d.401.1		2
5.2	odd	4		350.4.j.e.149.2		4
5.3	odd	4		350.4.j.e.149.1		4
5.4	even	2		350.4.e.a.51.1		2
7.2	even	3		490.4.a.c.1.1		1
7.3	odd	6		490.4.e.m.361.1		2
7.4	even	3	inner	70.4.e.c.11.1	✓	2
7.5	odd	6		490.4.a.e.1.1		1
7.6	odd	2		490.4.e.m.471.1		2
21.11	odd	6		630.4.k.b.361.1		2
28.11	odd	6		560.4.q.d.81.1		2
35.4	even	6		350.4.e.a.151.1		2
35.9	even	6		2450.4.a.bg.1.1		1
35.18	odd	12		350.4.j.e.249.2		4
35.19	odd	6		2450.4.a.be.1.1		1
35.32	odd	12		350.4.j.e.249.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.c.11.1	✓	2	7.4	even	3	inner
70.4.e.c.51.1	yes	2	1.1	even	1	trivial
350.4.e.a.51.1		2	5.4	even	2
350.4.e.a.151.1		2	35.4	even	6
350.4.j.e.149.1		4	5.3	odd	4
350.4.j.e.149.2		4	5.2	odd	4
350.4.j.e.249.1		4	35.32	odd	12
350.4.j.e.249.2		4	35.18	odd	12
490.4.a.c.1.1		1	7.2	even	3
490.4.a.e.1.1		1	7.5	odd	6
490.4.e.m.361.1		2	7.3	odd	6
490.4.e.m.471.1		2	7.6	odd	2
560.4.q.d.81.1		2	28.11	odd	6
560.4.q.d.401.1		2	4.3	odd	2
630.4.k.b.361.1		2	21.11	odd	6
630.4.k.b.541.1		2	3.2	odd	2
2450.4.a.be.1.1		1	35.19	odd	6
2450.4.a.bg.1.1		1	35.9	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	70.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +2.00000 q^{6} +(8.50000 - 16.4545i) q^{7} -8.00000 q^{8} +(13.0000 - 22.5167i) q^{9} +(-5.00000 - 8.66025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.00000 - 3.46410i) q^{12} -8.00000 q^{13} +(-20.0000 - 31.1769i) q^{14} +5.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(26.0000 + 45.0333i) q^{17} +(-26.0000 - 45.0333i) q^{18} +(-13.0000 + 22.5167i) q^{19} -20.0000 q^{20} +(18.5000 - 0.866025i) q^{21} +4.00000 q^{22} +(-33.5000 + 58.0237i) q^{23} +(-4.00000 - 6.92820i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-8.00000 + 13.8564i) q^{26} +53.0000 q^{27} +(-74.0000 + 3.46410i) q^{28} +69.0000 q^{29} +(5.00000 - 8.66025i) q^{30} +(166.000 + 287.520i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-1.00000 + 1.73205i) q^{33} +104.000 q^{34} +(-50.0000 - 77.9423i) q^{35} -104.000 q^{36} +(-98.0000 + 169.741i) q^{37} +(26.0000 + 45.0333i) q^{38} +(-4.00000 - 6.92820i) q^{39} +(-20.0000 + 34.6410i) q^{40} +353.000 q^{41} +(17.0000 - 32.9090i) q^{42} -369.000 q^{43} +(4.00000 - 6.92820i) q^{44} +(-65.0000 - 112.583i) q^{45} +(67.0000 + 116.047i) q^{46} +(-44.0000 + 76.2102i) q^{47} -16.0000 q^{48} +(-198.500 - 279.726i) q^{49} -50.0000 q^{50} +(-26.0000 + 45.0333i) q^{51} +(16.0000 + 27.7128i) q^{52} +(-291.000 - 504.027i) q^{53} +(53.0000 - 91.7987i) q^{54} +10.0000 q^{55} +(-68.0000 + 131.636i) q^{56} -26.0000 q^{57} +(69.0000 - 119.512i) q^{58} +(175.000 + 303.109i) q^{59} +(-10.0000 - 17.3205i) q^{60} +(233.500 - 404.434i) q^{61} +664.000 q^{62} +(-260.000 - 405.300i) q^{63} +64.0000 q^{64} +(-20.0000 + 34.6410i) q^{65} +(2.00000 + 3.46410i) q^{66} +(-145.500 - 252.013i) q^{67} +(104.000 - 180.133i) q^{68} -67.0000 q^{69} +(-185.000 + 8.66025i) q^{70} +770.000 q^{71} +(-104.000 + 180.133i) q^{72} +(-314.000 - 543.864i) q^{73} +(196.000 + 339.482i) q^{74} +(12.5000 - 21.6506i) q^{75} +104.000 q^{76} +(37.0000 - 1.73205i) q^{77} -16.0000 q^{78} +(-585.000 + 1013.25i) q^{79} +(40.0000 + 69.2820i) q^{80} +(-324.500 - 562.050i) q^{81} +(353.000 - 611.414i) q^{82} +525.000 q^{83} +(-40.0000 - 62.3538i) q^{84} +260.000 q^{85} +(-369.000 + 639.127i) q^{86} +(34.5000 + 59.7558i) q^{87} +(-8.00000 - 13.8564i) q^{88} +(-44.5000 + 77.0763i) q^{89} -260.000 q^{90} +(-68.0000 + 131.636i) q^{91} +268.000 q^{92} +(-166.000 + 287.520i) q^{93} +(88.0000 + 152.420i) q^{94} +(65.0000 + 112.583i) q^{95} +(-16.0000 + 27.7128i) q^{96} -290.000 q^{97} +(-683.000 + 64.0859i) q^{98} +52.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} - 4 q^{4} + 5 q^{5} + 4 q^{6} + 17 q^{7} - 16 q^{8} + 26 q^{9} - 10 q^{10} + 2 q^{11} + 4 q^{12} - 16 q^{13} - 40 q^{14} + 10 q^{15} - 16 q^{16} + 52 q^{17} - 52 q^{18} - 26 q^{19}+ \cdots + 104 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 - 4 * q^4 + 5 * q^5 + 4 * q^6 + 17 * q^7 - 16 * q^8 + 26 * q^9 - 10 * q^10 + 2 * q^11 + 4 * q^12 - 16 * q^13 - 40 * q^14 + 10 * q^15 - 16 * q^16 + 52 * q^17 - 52 * q^18 - 26 * q^19 - 40 * q^20 + 37 * q^21 + 8 * q^22 - 67 * q^23 - 8 * q^24 - 25 * q^25 - 16 * q^26 + 106 * q^27 - 148 * q^28 + 138 * q^29 + 10 * q^30 + 332 * q^31 + 32 * q^32 - 2 * q^33 + 208 * q^34 - 100 * q^35 - 208 * q^36 - 196 * q^37 + 52 * q^38 - 8 * q^39 - 40 * q^40 + 706 * q^41 + 34 * q^42 - 738 * q^43 + 8 * q^44 - 130 * q^45 + 134 * q^46 - 88 * q^47 - 32 * q^48 - 397 * q^49 - 100 * q^50 - 52 * q^51 + 32 * q^52 - 582 * q^53 + 106 * q^54 + 20 * q^55 - 136 * q^56 - 52 * q^57 + 138 * q^58 + 350 * q^59 - 20 * q^60 + 467 * q^61 + 1328 * q^62 - 520 * q^63 + 128 * q^64 - 40 * q^65 + 4 * q^66 - 291 * q^67 + 208 * q^68 - 134 * q^69 - 370 * q^70 + 1540 * q^71 - 208 * q^72 - 628 * q^73 + 392 * q^74 + 25 * q^75 + 208 * q^76 + 74 * q^77 - 32 * q^78 - 1170 * q^79 + 80 * q^80 - 649 * q^81 + 706 * q^82 + 1050 * q^83 - 80 * q^84 + 520 * q^85 - 738 * q^86 + 69 * q^87 - 16 * q^88 - 89 * q^89 - 520 * q^90 - 136 * q^91 + 536 * q^92 - 332 * q^93 + 176 * q^94 + 130 * q^95 - 32 * q^96 - 580 * q^97 - 1366 * q^98 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more