LMFDB - Embedded newform 546.4.i.b.235.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(79,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.79"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,12] 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:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 149x^{6} + 684x^{5} + 20666x^{4} + 28425x^{3} + 33734x^{2} + 6895x + 1225 $ x^8 - 2x^7 + 149x^6 + 684x^5 + 20666x^4 + 28425x^3 + 33734x^2 + 6895*x + 1225
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.2
Root			$-5.13830 - 8.89979i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.4.i.b.79.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-9.83247 - 17.0303i) q^{5} -6.00000 q^{6} +(-0.135629 - 18.5198i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-19.6649 + 34.0607i) q^{10} +(15.5257 - 26.8912i) q^{11} +(6.00000 + 10.3923i) q^{12} +13.0000 q^{13} +(-31.9415 + 18.7547i) q^{14} -58.9948 q^{15} +(-8.00000 - 13.8564i) q^{16} +(26.7092 - 46.2618i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-65.3015 - 113.106i) q^{19} +78.6598 q^{20} +(-48.3192 - 27.4273i) q^{21} -62.1027 q^{22} +(-108.358 - 187.682i) q^{23} +(12.0000 - 20.7846i) q^{24} +(-130.855 + 226.648i) q^{25} +(-13.0000 - 22.5167i) q^{26} -27.0000 q^{27} +(64.4256 + 36.5697i) q^{28} +164.282 q^{29} +(58.9948 + 102.182i) q^{30} +(126.620 - 219.312i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-46.5770 - 80.6737i) q^{33} -106.837 q^{34} +(-314.064 + 184.405i) q^{35} +36.0000 q^{36} +(96.0195 + 166.311i) q^{37} +(-130.603 + 226.211i) q^{38} +(19.5000 - 33.7750i) q^{39} +(-78.6598 - 136.243i) q^{40} +404.967 q^{41} +(0.813773 + 111.119i) q^{42} +60.2339 q^{43} +(62.1027 + 107.565i) q^{44} +(-88.4922 + 153.273i) q^{45} +(-216.717 + 375.364i) q^{46} +(296.521 + 513.590i) q^{47} -48.0000 q^{48} +(-342.963 + 5.02363i) q^{49} +523.420 q^{50} +(-80.1277 - 138.785i) q^{51} +(-26.0000 + 45.0333i) q^{52} +(263.801 - 456.916i) q^{53} +(27.0000 + 46.7654i) q^{54} -610.623 q^{55} +(-1.08503 - 148.158i) q^{56} -391.809 q^{57} +(-164.282 - 284.545i) q^{58} +(-180.310 + 312.306i) q^{59} +(117.990 - 204.364i) q^{60} +(131.485 + 227.739i) q^{61} -506.480 q^{62} +(-143.737 + 84.3961i) q^{63} +64.0000 q^{64} +(-127.822 - 221.394i) q^{65} +(-93.1540 + 161.347i) q^{66} +(-246.018 + 426.116i) q^{67} +(106.837 + 185.047i) q^{68} -650.150 q^{69} +(633.463 + 359.570i) q^{70} +121.549 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-393.198 + 681.039i) q^{73} +(192.039 - 332.621i) q^{74} +(392.565 + 679.943i) q^{75} +522.412 q^{76} +(-500.125 - 283.884i) q^{77} -78.0000 q^{78} +(-140.968 - 244.164i) q^{79} +(-157.320 + 272.485i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-404.967 - 701.424i) q^{82} +1116.60 q^{83} +(191.649 - 112.528i) q^{84} -1050.47 q^{85} +(-60.2339 - 104.328i) q^{86} +(246.423 - 426.817i) q^{87} +(124.205 - 215.130i) q^{88} +(104.485 + 180.973i) q^{89} +353.969 q^{90} +(-1.76318 - 240.757i) q^{91} +866.866 q^{92} +(-379.860 - 657.937i) q^{93} +(593.043 - 1027.18i) q^{94} +(-1284.15 + 2224.21i) q^{95} +(48.0000 + 83.1384i) q^{96} +585.034 q^{97} +(351.664 + 589.006i) q^{98} -279.462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 12 q^{3} - 16 q^{4} - 34 q^{5} - 48 q^{6} + 35 q^{7} + 64 q^{8} - 36 q^{9} - 68 q^{10} + 74 q^{11} + 48 q^{12} + 104 q^{13} - 80 q^{14} - 204 q^{15} - 64 q^{16} + 49 q^{17} - 72 q^{18} + 41 q^{19}+ \cdots - 1332 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 12 * q^3 - 16 * q^4 - 34 * q^5 - 48 * q^6 + 35 * q^7 + 64 * q^8 - 36 * q^9 - 68 * q^10 + 74 * q^11 + 48 * q^12 + 104 * q^13 - 80 * q^14 - 204 * q^15 - 64 * q^16 + 49 * q^17 - 72 * q^18 + 41 * q^19 + 272 * q^20 - 15 * q^21 - 296 * q^22 - 48 * q^23 + 96 * q^24 - 330 * q^25 - 104 * q^26 - 216 * q^27 + 20 * q^28 + 330 * q^29 + 204 * q^30 - 349 * q^31 - 128 * q^32 - 222 * q^33 - 196 * q^34 - 827 * q^35 + 288 * q^36 + 563 * q^37 + 82 * q^38 + 156 * q^39 - 272 * q^40 - 548 * q^41 - 210 * q^42 + 1136 * q^43 + 296 * q^44 - 306 * q^45 - 96 * q^46 + 186 * q^47 - 384 * q^48 + 275 * q^49 + 1320 * q^50 - 147 * q^51 - 208 * q^52 + 236 * q^53 + 216 * q^54 + 1034 * q^55 + 280 * q^56 + 246 * q^57 - 330 * q^58 + 204 * q^59 + 408 * q^60 - 659 * q^61 + 1396 * q^62 - 360 * q^63 + 512 * q^64 - 442 * q^65 - 444 * q^66 + 297 * q^67 + 196 * q^68 - 288 * q^69 + 704 * q^70 - 1554 * q^71 - 288 * q^72 - 1778 * q^73 + 1126 * q^74 + 990 * q^75 - 328 * q^76 - 3320 * q^77 - 624 * q^78 - 1295 * q^79 - 544 * q^80 - 324 * q^81 + 548 * q^82 + 8778 * q^83 + 480 * q^84 - 2236 * q^85 - 1136 * q^86 + 495 * q^87 + 592 * q^88 + 1151 * q^89 + 1224 * q^90 + 455 * q^91 + 384 * q^92 + 1047 * q^93 + 372 * q^94 - 1355 * q^95 + 384 * q^96 + 1260 * q^97 + 2686 * q^98 - 1332 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−9.83247	−	17.0303i	−0.879443	−	1.52324i	−0.851953	−	0.523618i	$-0.824582\pi$
$5$	−9.83247	−	17.0303i	−0.879443	−	1.52324i	−0.0274898	−	0.999622i	$-0.508751\pi$
$6$	−6.00000			−0.408248
$7$	−0.135629	−	18.5198i	−0.00732327	−	0.999973i
$7$	−0.135629	−	18.5198i	−0.00732327	−	0.999973i
$8$	8.00000			0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−19.6649	+	34.0607i	−0.621860	+	1.07709i
$11$	15.5257	−	26.8912i	0.425560	−	0.737092i	−0.570912	−	0.821011i	$-0.693410\pi$
$11$	15.5257	−	26.8912i	0.425560	−	0.737092i	0.996473	+	0.0839190i	$0.0267437\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	13.0000			0.277350
$13$	13.0000			0.277350
$14$	−31.9415	+	18.7547i	−0.609767	+	0.358028i
$15$	−58.9948			−1.01549
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	26.7092	−	46.2618i	0.381055	−	0.660007i	−0.610158	−	0.792280i	$-0.708894\pi$
$17$	26.7092	−	46.2618i	0.381055	−	0.660007i	0.991213	+	0.132272i	$0.0422274\pi$
$18$	−9.00000	+	15.5885i	−0.117851	+	0.204124i
$19$	−65.3015	−	113.106i	−0.788484	−	1.36569i	−0.926895	−	0.375320i	$-0.877533\pi$
$19$	−65.3015	−	113.106i	−0.788484	−	1.36569i	0.138411	−	0.990375i	$-0.455800\pi$
$20$	78.6598			0.879443
$21$	−48.3192	−	27.4273i	−0.502101	−	0.285006i
$22$	−62.1027			−0.601833
$23$	−108.358	−	187.682i	−0.982359	−	1.70150i	−0.653129	−	0.757247i	$-0.726544\pi$
$23$	−108.358	−	187.682i	−0.982359	−	1.70150i	−0.329230	−	0.944250i	$-0.606789\pi$
$24$	12.0000	−	20.7846i	0.102062	−	0.176777i
$25$	−130.855	+	226.648i	−1.04684	+	1.81318i
$26$	−13.0000	−	22.5167i	−0.0980581	−	0.169842i
$27$	−27.0000			−0.192450
$28$	64.4256	+	36.5697i	0.434832	+	0.246822i
$29$	164.282			1.05194			0.525972	−	0.850502i	$-0.323702\pi$
$29$	164.282			1.05194			0.525972	+	0.850502i	$0.323702\pi$
$30$	58.9948	+	102.182i	0.359031	+	0.621860i
$31$	126.620	−	219.312i	0.733601	−	1.27063i	−0.221734	−	0.975107i	$-0.571172\pi$
$31$	126.620	−	219.312i	0.733601	−	1.27063i	0.955335	−	0.295527i	$-0.0954951\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−46.5770	−	80.6737i	−0.245697	−	0.425560i
$34$	−106.837			−0.538894
$35$	−314.064	+	184.405i	−1.51676	+	0.890575i
$36$	36.0000			0.166667
$37$	96.0195	+	166.311i	0.426635	+	0.738954i	0.996572	−	0.0827349i	$-0.0263655\pi$
$37$	96.0195	+	166.311i	0.426635	+	0.738954i	−0.569936	+	0.821689i	$0.693032\pi$
$38$	−130.603	+	226.211i	−0.557543	+	0.965692i
$39$	19.5000	−	33.7750i	0.0800641	−	0.138675i
$40$	−78.6598	−	136.243i	−0.310930	−	0.538547i
$41$	404.967			1.54257			0.771284	−	0.636491i	$-0.219615\pi$
$41$	404.967			1.54257			0.771284	+	0.636491i	$0.219615\pi$
$42$	0.813773	+	111.119i	0.00298971	+	0.408237i
$43$	60.2339			0.213618			0.106809	−	0.994280i	$-0.465937\pi$
$43$	60.2339			0.213618			0.106809	+	0.994280i	$0.465937\pi$
$44$	62.1027	+	107.565i	0.212780	+	0.368546i
$45$	−88.4922	+	153.273i	−0.293148	+	0.507747i
$46$	−216.717	+	375.364i	−0.694633	+	1.20314i
$47$	296.521	+	513.590i	0.920257	+	1.59393i	0.799017	+	0.601309i	$0.205354\pi$
$47$	296.521	+	513.590i	0.920257	+	1.59393i	0.121240	+	0.992623i	$0.461313\pi$
$48$	−48.0000			−0.144338
$49$	−342.963	+	5.02363i	−0.999893	+	0.0146461i
$50$	523.420			1.48046
$51$	−80.1277	−	138.785i	−0.220002	−	0.381055i
$52$	−26.0000	+	45.0333i	−0.0693375	+	0.120096i
$53$	263.801	−	456.916i	0.683695	−	1.18419i	−0.290150	−	0.956981i	$-0.593705\pi$
$53$	263.801	−	456.916i	0.683695	−	1.18419i	0.973845	−	0.227213i	$-0.0729613\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−610.623			−1.49702
$56$	−1.08503	−	148.158i	−0.00258917	−	0.353544i
$57$	−391.809			−0.910463
$58$	−164.282	−	284.545i	−0.371918	−	0.644182i
$59$	−180.310	+	312.306i	−0.397870	+	0.689131i	−0.993463	−	0.114155i	$-0.963584\pi$
$59$	−180.310	+	312.306i	−0.397870	+	0.689131i	0.595593	+	0.803286i	$0.296917\pi$
$60$	117.990	−	204.364i	0.253873	−	0.439722i
$61$	131.485	+	227.739i	0.275983	+	0.478016i	0.970383	−	0.241573i	$-0.0776634\pi$
$61$	131.485	+	227.739i	0.275983	+	0.478016i	−0.694400	+	0.719589i	$0.744330\pi$
$62$	−506.480			−1.03747
$63$	−143.737	+	84.3961i	−0.287447	+	0.168776i
$64$	64.0000			0.125000
$65$	−127.822	−	221.394i	−0.243914	−	0.422471i
$66$	−93.1540	+	161.347i	−0.173734	+	0.300917i
$67$	−246.018	+	426.116i	−0.448595	+	0.776990i	−0.998295	−	0.0583727i	$-0.981409\pi$
$67$	−246.018	+	426.116i	−0.448595	+	0.776990i	0.549700	+	0.835362i	$0.314742\pi$
$68$	106.837	+	185.047i	0.190528	+	0.330004i
$69$	−650.150			−1.13433
$70$	633.463	+	359.570i	1.08162	+	0.613956i
$71$	121.549			0.203172			0.101586	−	0.994827i	$-0.467608\pi$
$71$	121.549			0.203172			0.101586	+	0.994827i	$0.467608\pi$
$72$	−36.0000	−	62.3538i	−0.0589256	−	0.102062i
$73$	−393.198	+	681.039i	−0.630416	+	1.09191i	0.357051	+	0.934085i	$0.383782\pi$
$73$	−393.198	+	681.039i	−0.630416	+	1.09191i	−0.987467	+	0.157827i	$0.949551\pi$
$74$	192.039	−	332.621i	0.301677	−	0.522519i
$75$	392.565	+	679.943i	0.604393	+	1.04684i
$76$	522.412			0.788484
$77$	−500.125	−	283.884i	−0.740189	−	0.420151i
$78$	−78.0000			−0.113228
$79$	−140.968	−	244.164i	−0.200761	−	0.347729i	0.748013	−	0.663685i	$-0.231008\pi$
$79$	−140.968	−	244.164i	−0.200761	−	0.347729i	−0.948774	+	0.315956i	$0.897675\pi$
$80$	−157.320	+	272.485i	−0.219861	+	0.380810i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−404.967	−	701.424i	−0.545380	−	0.944626i
$83$	1116.60			1.47666			0.738328	−	0.674441i	$-0.235616\pi$
$83$	1116.60			1.47666			0.738328	+	0.674441i	$0.235616\pi$
$84$	191.649	−	112.528i	0.248936	−	0.146165i
$85$	−1050.47			−1.34047
$86$	−60.2339	−	104.328i	−0.0755255	−	0.130814i
$87$	246.423	−	426.817i	0.303670	−	0.525972i
$88$	124.205	−	215.130i	0.150458	−	0.260601i
$89$	104.485	+	180.973i	0.124442	+	0.215541i	0.921515	−	0.388343i	$-0.126952\pi$
$89$	104.485	+	180.973i	0.124442	+	0.215541i	−0.797072	+	0.603884i	$0.793619\pi$
$90$	353.969			0.414573
$91$	−1.76318	−	240.757i	−0.00203111	−	0.277343i
$92$	866.866			0.982359
$93$	−379.860	−	657.937i	−0.423545	−	0.733601i
$94$	593.043	−	1027.18i	0.650720	−	1.12708i
$95$	−1284.15	+	2224.21i	−1.38685	+	2.40210i
$96$	48.0000	+	83.1384i	0.0510310	+	0.0883883i
$97$	585.034			0.612384			0.306192	−	0.951970i	$-0.400945\pi$
$97$	585.034			0.612384			0.306192	+	0.951970i	$0.400945\pi$
$98$	351.664	+	589.006i	0.362484	+	0.607129i
$99$	−279.462			−0.283707
$100$	−523.420	−	906.590i	−0.523420	−	0.906590i
$101$	47.4010	−	82.1009i	0.0466988	−	0.0808846i	−0.841731	−	0.539897i	$-0.818463\pi$
$101$	47.4010	−	82.1009i	0.0466988	−	0.0808846i	0.888430	+	0.459012i	$0.151797\pi$
$102$	−160.255	+	277.571i	−0.155565	+	0.269447i
$103$	−215.430	−	373.136i	−0.206087	−	0.356953i	0.744391	−	0.667744i	$-0.232740\pi$
$103$	−215.430	−	373.136i	−0.206087	−	0.356953i	−0.950479	+	0.310790i	$0.899406\pi$
$104$	104.000			0.0980581
$105$	8.00140	+	1092.57i	0.00743673	+	1.01547i
$106$	−1055.20			−0.966890
$107$	190.997	+	330.816i	0.172564	+	0.298889i	0.939316	−	0.343054i	$-0.111462\pi$
$107$	190.997	+	330.816i	0.172564	+	0.298889i	−0.766752	+	0.641944i	$0.778128\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	606.665	−	1050.77i	0.533100	−	0.923357i	−0.466152	−	0.884704i	$-0.654360\pi$
$109$	606.665	−	1050.77i	0.533100	−	0.923357i	0.999253	−	0.0386523i	$-0.0123065\pi$
$110$	610.623	+	1057.63i	0.529278	+	0.916736i
$111$	576.117			0.492636
$112$	−255.532	+	150.037i	−0.215585	+	0.126582i
$113$	−607.588			−0.505815			−0.252908	−	0.967490i	$-0.581387\pi$
$113$	−607.588			−0.505815			−0.252908	+	0.967490i	$0.581387\pi$
$114$	391.809	+	678.633i	0.321897	+	0.557543i
$115$	−2130.86	+	3690.76i	−1.72786	+	2.99274i
$116$	−328.564	+	569.089i	−0.262986	+	0.455505i
$117$	−58.5000	−	101.325i	−0.0462250	−	0.0800641i
$118$	721.239			0.562673
$119$	−860.379	−	488.374i	−0.662780	−	0.376212i
$120$	−471.959			−0.359031
$121$	183.408	+	317.671i	0.137797	+	0.238671i
$122$	262.970	−	455.478i	0.195149	−	0.338009i
$123$	607.451	−	1052.14i	0.445301	−	0.771284i
$124$	506.480	+	877.249i	0.366800	+	0.635317i
$125$	2688.39			1.92366
$126$	289.915	+	164.564i	0.204982	+	0.116353i
$127$	212.566			0.148521			0.0742604	−	0.997239i	$-0.476340\pi$
$127$	212.566			0.148521			0.0742604	+	0.997239i	$0.476340\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	90.3509	−	156.492i	0.0616663	−	0.106809i
$130$	−255.644	+	442.789i	−0.172473	+	0.298732i
$131$	−267.703	−	463.676i	−0.178545	−	0.309248i	0.762838	−	0.646590i	$-0.223806\pi$
$131$	−267.703	−	463.676i	−0.178545	−	0.309248i	−0.941382	+	0.337342i	$0.890472\pi$
$132$	372.616			0.245697
$133$	−2085.83	+	1224.71i	−1.35988	+	0.798464i
$134$	984.072			0.634409
$135$	265.477	+	459.819i	0.169249	+	0.293148i
$136$	213.674	−	370.094i	0.134723	−	0.233348i
$137$	714.835	−	1238.13i	0.445785	−	0.772122i	−0.552322	−	0.833631i	$-0.686258\pi$
$137$	714.835	−	1238.13i	0.445785	−	0.772122i	0.998107	+	0.0615092i	$0.0195913\pi$
$138$	650.150	+	1126.09i	0.401047	+	0.694633i
$139$	2787.49			1.70095			0.850474	−	0.526016i	$-0.176315\pi$
$139$	2787.49			1.70095			0.850474	+	0.526016i	$0.176315\pi$
$140$	−10.6685	−	1456.76i	−0.00644040	−	0.879419i
$141$	1779.13			1.06262
$142$	−121.549	−	210.529i	−0.0718321	−	0.124417i
$143$	201.834	−	349.586i	0.118029	−	0.204433i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	−1615.30	−	2797.78i	−0.925125	−	1.60236i
$146$	1572.79			0.891542
$147$	−501.393	+	898.580i	−0.281321	+	0.504174i
$148$	−768.156			−0.426635
$149$	1734.73	+	3004.63i	0.953787	+	1.65201i	0.737120	+	0.675762i	$0.236185\pi$
$149$	1734.73	+	3004.63i	0.953787	+	1.65201i	0.216667	+	0.976246i	$0.430481\pi$
$150$	785.130	−	1359.89i	0.427371	−	0.740228i
$151$	−1560.59	+	2703.02i	−0.841053	+	1.45675i	0.0479515	+	0.998850i	$0.484731\pi$
$151$	−1560.59	+	2703.02i	−0.841053	+	1.45675i	−0.889005	+	0.457898i	$0.848603\pi$
$152$	−522.412	−	904.845i	−0.278771	−	0.482846i
$153$	−480.766			−0.254037
$154$	8.42291	+	1150.13i	0.00440739	+	0.601817i
$155$	−4979.95			−2.58064
$156$	78.0000	+	135.100i	0.0400320	+	0.0693375i
$157$	−505.706	+	875.908i	−0.257068	+	0.445255i	−0.965455	−	0.260569i	$-0.916090\pi$
$157$	−505.706	+	875.908i	−0.257068	+	0.445255i	0.708387	+	0.705824i	$0.249423\pi$
$158$	−281.936	+	488.328i	−0.141960	+	0.245882i
$159$	−791.402	−	1370.75i	−0.394731	−	0.683695i
$160$	629.278			0.310930
$161$	−3461.13	+	2032.22i	−1.69426	+	0.994793i
$162$	162.000			0.0785674
$163$	−1247.47	−	2160.69i	−0.599446	−	1.03827i	−0.992903	−	0.118927i	$-0.962054\pi$
$163$	−1247.47	−	2160.69i	−0.599446	−	1.03827i	0.393457	−	0.919343i	$-0.371279\pi$
$164$	−809.935	+	1402.85i	−0.385642	+	0.667952i
$165$	−915.934	+	1586.44i	−0.432154	+	0.748512i
$166$	−1116.60	−	1934.00i	−0.522077	−	0.904264i
$167$	3350.23			1.55239			0.776193	−	0.630495i	$-0.217148\pi$
$167$	3350.23			1.55239			0.776193	+	0.630495i	$0.217148\pi$
$168$	−386.554	−	219.418i	−0.177519	−	0.100765i
$169$	169.000			0.0769231
$170$	1050.47	+	1819.47i	0.473926	+	0.820865i
$171$	−587.714	+	1017.95i	−0.262828	+	0.455232i
$172$	−120.468	+	208.656i	−0.0534046	+	0.0924995i
$173$	−203.432	−	352.354i	−0.0894024	−	0.154850i	0.817856	−	0.575423i	$-0.195162\pi$
$173$	−203.432	−	352.354i	−0.0894024	−	0.154850i	−0.907259	+	0.420573i	$0.861829\pi$
$174$	−985.691			−0.429454
$175$	4215.21	+	2392.66i	1.82080	+	1.03353i
$176$	−496.821			−0.212780
$177$	540.929	+	936.917i	0.229710	+	0.397870i
$178$	208.970	−	361.946i	0.0879941	−	0.152410i
$179$	−924.047	+	1600.50i	−0.385847	+	0.668306i	−0.991886	−	0.127129i	$-0.959424\pi$
$179$	−924.047	+	1600.50i	−0.385847	+	0.668306i	0.606040	+	0.795434i	$0.292757\pi$
$180$	−353.969	−	613.092i	−0.146574	−	0.253873i
$181$	358.058			0.147040			0.0735201	−	0.997294i	$-0.476577\pi$
$181$	358.058			0.147040			0.0735201	+	0.997294i	$0.476577\pi$
$182$	−415.240	+	243.811i	−0.169119	+	0.0992992i
$183$	788.911			0.318678
$184$	−866.866	−	1501.46i	−0.347316	−	0.601570i
$185$	1888.22	−	3270.49i	0.750403	−	1.29974i
$186$	−759.720	+	1315.87i	−0.299491	+	0.518734i
$187$	−829.357	−	1436.49i	−0.324324	−	0.561746i
$188$	−2372.17			−0.920257
$189$	3.66198	+	500.034i	0.00140936	+	0.192445i
$190$	5136.60			1.96131
$191$	−1440.17	−	2494.45i	−0.545587	−	0.944984i	−0.998570	−	0.0534651i	$-0.982973\pi$
$191$	−1440.17	−	2494.45i	−0.545587	−	0.944984i	0.452983	−	0.891519i	$-0.350360\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	2574.36	−	4458.93i	0.960139	−	1.66301i	0.237995	−	0.971266i	$-0.423510\pi$
$193$	2574.36	−	4458.93i	0.960139	−	1.66301i	0.722144	−	0.691743i	$-0.243157\pi$
$194$	−585.034	−	1013.31i	−0.216510	−	0.375007i
$195$	−766.933			−0.281647
$196$	668.524	−	1198.11i	0.243631	−	0.436628i
$197$	1308.33			0.473172			0.236586	−	0.971611i	$-0.423971\pi$
$197$	1308.33			0.473172			0.236586	+	0.971611i	$0.423971\pi$
$198$	279.462	+	484.042i	0.100306	+	0.173734i
$199$	2387.80	−	4135.79i	0.850586	−	1.47326i	−0.0300938	−	0.999547i	$-0.509581\pi$
$199$	2387.80	−	4135.79i	0.850586	−	1.47326i	0.880680	−	0.473712i	$-0.157086\pi$
$200$	−1046.84	+	1813.18i	−0.370114	+	0.641056i
$201$	738.054	+	1278.35i	0.258997	+	0.448595i
$202$	−189.604			−0.0660420
$203$	−22.2814	−	3042.46i	−0.00770367	−	1.05192i
$204$	641.022			0.220002
$205$	−3981.83	−	6896.73i	−1.35660	−	2.34970i
$206$	−430.861	+	746.272i	−0.145726	+	0.252404i
$207$	−975.225	+	1689.14i	−0.327453	+	0.567165i
$208$	−104.000	−	180.133i	−0.0346688	−	0.0600481i
$209$	−4055.40			−1.34219
$210$	1884.39	−	1106.43i	0.619214	−	0.363576i
$211$	−4875.17			−1.59062			−0.795310	−	0.606203i	$-0.792692\pi$
$211$	−4875.17			−1.59062			−0.795310	+	0.606203i	$0.792692\pi$
$212$	1055.20	+	1827.67i	0.341847	+	0.592097i
$213$	182.323	−	315.793i	0.0586507	−	0.101586i
$214$	381.993	−	661.632i	0.122021	−	0.211347i
$215$	−592.249	−	1025.80i	−0.187865	−	0.325392i
$216$	−216.000			−0.0680414
$217$	−4078.78	−	2315.23i	−1.27597	−	0.724276i
$218$	−2426.66			−0.753918
$219$	1179.59	+	2043.12i	0.363971	+	0.630416i
$220$	1221.25	−	2115.26i	0.374256	−	0.648230i
$221$	347.220	−	601.403i	0.105686	−	0.183053i
$222$	−576.117	−	997.864i	−0.174173	−	0.301677i
$223$	1580.06			0.474479			0.237240	−	0.971451i	$-0.423757\pi$
$223$	1580.06			0.474479			0.237240	+	0.971451i	$0.423757\pi$
$224$	515.405	+	292.558i	0.153736	+	0.0872648i
$225$	2355.39			0.697893
$226$	607.588	+	1052.37i	0.178833	+	0.309747i
$227$	1794.75	−	3108.61i	0.524767	−	0.908922i	−0.474817	−	0.880084i	$-0.657486\pi$
$227$	1794.75	−	3108.61i	0.524767	−	0.908922i	0.999584	−	0.0288382i	$-0.00918075\pi$
$228$	783.618	−	1357.27i	0.227616	−	0.394242i
$229$	1111.09	+	1924.46i	0.320624	+	0.555337i	0.980617	−	0.195935i	$-0.0627741\pi$
$229$	1111.09	+	1924.46i	0.320624	+	0.555337i	−0.659993	+	0.751272i	$0.729441\pi$
$230$	8523.44			2.44356
$231$	−1487.74	+	873.536i	−0.423750	+	0.248807i
$232$	1314.26			0.371918
$233$	−161.094	−	279.023i	−0.0452944	−	0.0784523i	0.842489	−	0.538713i	$-0.181089\pi$
$233$	−161.094	−	279.023i	−0.0452944	−	0.0784523i	−0.887784	+	0.460261i	$0.847756\pi$
$234$	−117.000	+	202.650i	−0.0326860	+	0.0566139i
$235$	5831.08	−	10099.7i	1.61863	−	2.80354i
$236$	−721.239	−	1249.22i	−0.198935	−	0.344565i
$237$	−845.809			−0.231819
$238$	14.4902	+	1978.60i	0.00394646	+	0.538879i
$239$	−785.968			−0.212720			−0.106360	−	0.994328i	$-0.533920\pi$
$239$	−785.968			−0.212720			−0.106360	+	0.994328i	$0.533920\pi$
$240$	471.959	+	817.456i	0.126937	+	0.219861i
$241$	1246.37	−	2158.77i	0.333135	−	0.577006i	−0.649990	−	0.759943i	$-0.725227\pi$
$241$	1246.37	−	2158.77i	0.333135	−	0.577006i	0.983125	+	0.182936i	$0.0585602\pi$
$242$	366.815	−	635.343i	0.0974371	−	0.168766i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−1051.88			−0.275983
$245$	3457.73	+	5791.39i	0.901658	+	1.51020i
$246$	−2429.80			−0.629751
$247$	−848.920	−	1470.37i	−0.218686	−	0.378776i
$248$	1012.96	−	1754.50i	0.259367	−	0.449237i
$249$	1674.90	−	2901.01i	0.426274	−	0.738328i
$250$	−2688.39	−	4656.44i	−0.680116	−	1.17800i
$251$	3934.48			0.989410			0.494705	−	0.869061i	$-0.335276\pi$
$251$	3934.48			0.989410			0.494705	+	0.869061i	$0.335276\pi$
$252$	−4.88264	−	666.711i	−0.00122055	−	0.166662i
$253$	−6729.34			−1.67221
$254$	−212.566	−	368.174i	−0.0525100	−	0.0909501i
$255$	−1575.71	+	2729.21i	−0.386959	+	0.670233i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	370.144	+	641.109i	0.0898403	+	0.155608i	0.907444	−	0.420174i	$-0.138031\pi$
$257$	370.144	+	641.109i	0.0898403	+	0.155608i	−0.817603	+	0.575782i	$0.804698\pi$
$258$	−361.404			−0.0872093
$259$	3067.01	−	1800.81i	0.735810	−	0.432035i
$260$	1022.58			0.243914
$261$	−739.269	−	1280.45i	−0.175324	−	0.303670i
$262$	−535.406	+	927.351i	−0.126250	+	0.218672i
$263$	3133.17	−	5426.81i	0.734600	−	1.27236i	−0.220299	−	0.975432i	$-0.570703\pi$
$263$	3133.17	−	5426.81i	0.734600	−	1.27236i	0.954899	−	0.296931i	$-0.0959633\pi$
$264$	−372.616	−	645.390i	−0.0868671	−	0.150458i
$265$	−10375.3			−2.40508
$266$	4207.09	+	2388.06i	0.969749	+	0.550456i
$267$	626.909			0.143694
$268$	−984.072	−	1704.46i	−0.224298	−	0.388495i
$269$	−2745.07	+	4754.61i	−0.622194	+	1.07767i	0.366883	+	0.930267i	$0.380425\pi$
$269$	−2745.07	+	4754.61i	−0.622194	+	1.07767i	−0.989076	+	0.147404i	$0.952908\pi$
$270$	530.953	−	919.638i	0.119677	−	0.207287i
$271$	−26.3127	−	45.5749i	−0.00589809	−	0.0102158i	0.863061	−	0.505099i	$-0.168544\pi$
$271$	−26.3127	−	45.5749i	−0.00589809	−	0.0102158i	−0.868959	+	0.494883i	$0.835211\pi$
$272$	−854.696			−0.190528
$273$	−628.150	−	356.555i	−0.139258	−	0.0790464i
$274$	−2859.34			−0.630435
$275$	4063.22	+	7037.71i	0.890987	+	1.54324i
$276$	1300.30	−	2252.18i	0.283583	−	0.491180i
$277$	−2402.14	+	4160.64i	−0.521050	+	0.902485i	0.478650	+	0.878006i	$0.341126\pi$
$277$	−2402.14	+	4160.64i	−0.521050	+	0.902485i	−0.999700	+	0.0244795i	$0.992207\pi$
$278$	−2787.49	−	4828.08i	−0.601376	−	1.04161i
$279$	−2279.16			−0.489067
$280$	−2512.51	+	1475.24i	−0.536255	+	0.314866i
$281$	1913.01			0.406123			0.203062	−	0.979166i	$-0.434911\pi$
$281$	1913.01			0.406123			0.203062	+	0.979166i	$0.434911\pi$
$282$	−1779.13	−	3081.54i	−0.375693	−	0.650720i
$283$	−580.859	+	1006.08i	−0.122009	+	0.211326i	−0.920560	−	0.390602i	$-0.872267\pi$
$283$	−580.859	+	1006.08i	−0.122009	+	0.211326i	0.798551	+	0.601927i	$0.205600\pi$
$284$	−243.098	+	421.058i	−0.0507930	+	0.0879760i
$285$	3852.45	+	6672.64i	0.800700	+	1.38685i
$286$	−807.334			−0.166918
$287$	−54.9253	−	7499.90i	−0.0112966	−	1.54253i
$288$	288.000			0.0589256
$289$	1029.73	+	1783.55i	0.209593	+	0.363027i
$290$	−3230.59	+	5595.55i	−0.654162	+	1.13304i
$291$	877.551	−	1519.96i	0.176780	−	0.306192i
$292$	−1572.79	−	2724.15i	−0.315208	−	0.545956i
$293$	4962.42			0.989446			0.494723	−	0.869051i	$-0.335269\pi$
$293$	4962.42			0.989446			0.494723	+	0.869051i	$0.335269\pi$
$294$	2057.78	−	30.1418i	0.408205	−	0.00597926i
$295$	7091.56			1.39962
$296$	768.156	+	1330.48i	0.150838	+	0.261260i
$297$	−419.193	+	726.063i	−0.0818991	+	0.141853i
$298$	3469.45	−	6009.27i	0.674429	−	1.16815i
$299$	−1408.66	−	2439.87i	−0.272457	−	0.471910i
$300$	−3140.52			−0.604393
$301$	−8.16946	−	1115.52i	−0.00156439	−	0.213613i
$302$	6242.36			1.18943
$303$	−142.203	−	246.303i	−0.0269615	−	0.0466988i
$304$	−1044.82	+	1809.69i	−0.197121	+	0.341424i
$305$	2585.65	−	4478.48i	0.485422	−	0.840776i
$306$	480.766	+	832.712i	0.0898156	+	0.155565i
$307$	−6773.86			−1.25930			−0.629650	−	0.776879i	$-0.716802\pi$
$307$	−6773.86			−1.25930			−0.629650	+	0.776879i	$0.716802\pi$
$308$	1983.65	−	1164.72i	0.366978	−	0.215473i
$309$	−1292.58			−0.237969
$310$	4979.95	+	8625.53i	0.912394	+	1.58031i
$311$	−4721.58	+	8178.01i	−0.860888	+	1.49110i	0.0101852	+	0.999948i	$0.496758\pi$
$311$	−4721.58	+	8178.01i	−0.860888	+	1.49110i	−0.871073	+	0.491153i	$0.836575\pi$
$312$	156.000	−	270.200i	0.0283069	−	0.0490290i
$313$	−356.880	−	618.134i	−0.0644474	−	0.111626i	0.832001	−	0.554774i	$-0.187195\pi$
$313$	−356.880	−	618.134i	−0.0644474	−	0.111626i	−0.896449	+	0.443147i	$0.853862\pi$
$314$	2022.82			0.363550
$315$	2850.58	+	1618.07i	0.509880	+	0.289421i
$316$	1127.74			0.200761
$317$	−2422.90	−	4196.58i	−0.429286	−	0.743544i	0.567524	−	0.823357i	$-0.307901\pi$
$317$	−2422.90	−	4196.58i	−0.429286	−	0.743544i	−0.996810	+	0.0798122i	$0.974568\pi$
$318$	−1582.80	+	2741.50i	−0.279117	+	0.483445i
$319$	2550.59	−	4417.74i	0.447666	−	0.775380i
$320$	−629.278	−	1089.94i	−0.109930	−	0.190405i
$321$	1145.98			0.199260
$322$	6981.05	+	3962.63i	1.20819	+	0.685803i
$323$	−6976.62			−1.20182
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	−1701.12	+	2946.42i	−0.290341	+	0.502886i
$326$	−2494.95	+	4321.37i	−0.423872	+	0.734168i
$327$	−1819.99	−	3152.32i	−0.307786	−	0.533100i
$328$	3239.74			0.545380
$329$	9471.35	−	5561.16i	1.58715	−	0.931905i
$330$	3663.74			0.611158
$331$	−3369.63	−	5836.37i	−0.559551	−	0.969171i	−0.997534	−	0.0701878i	$-0.977640\pi$
$331$	−3369.63	−	5836.37i	−0.559551	−	0.969171i	0.437982	−	0.898984i	$-0.355693\pi$
$332$	−2233.20	+	3868.01i	−0.369164	+	0.639411i
$333$	864.175	−	1496.80i	0.142212	−	0.246318i
$334$	−3350.23	−	5802.77i	−0.548852	−	0.950639i
$335$	9675.86			1.57806
$336$	6.51019	+	888.949i	0.00105702	+	0.144334i
$337$	7205.69			1.16475			0.582373	−	0.812922i	$-0.302125\pi$
$337$	7205.69			1.16475			0.582373	+	0.812922i	$0.302125\pi$
$338$	−169.000	−	292.717i	−0.0271964	−	0.0471056i
$339$	−911.383	+	1578.56i	−0.146016	+	0.252908i
$340$	2100.94	−	3638.94i	0.335117	−	0.580439i
$341$	−3931.72	−	6809.94i	−0.624383	−	1.08146i
$342$	2350.86			0.371695
$343$	139.552	+	6350.92i	0.0219682	+	0.999759i
$344$	481.872			0.0755255
$345$	6392.58	+	11072.3i	0.997579	+	1.72786i
$346$	−406.863	+	704.708i	−0.0632171	+	0.109495i
$347$	−493.545	+	854.844i	−0.0763541	+	0.132249i	−0.901674	−	0.432416i	$-0.857661\pi$
$347$	−493.545	+	854.844i	−0.0763541	+	0.132249i	0.825320	+	0.564665i	$0.190995\pi$
$348$	985.691	+	1707.27i	0.151835	+	0.262986i
$349$	−21.6864			−0.00332621			−0.00166311	−	0.999999i	$-0.500529\pi$
$349$	−21.6864			−0.00332621			−0.00166311	+	0.999999i	$0.500529\pi$
$350$	−70.9909	−	9693.61i	−0.0108418	−	1.48042i
$351$	−351.000			−0.0533761
$352$	496.821	+	860.520i	0.0752291	+	0.130301i
$353$	−3174.40	+	5498.22i	−0.478629	+	0.829010i	−0.999700	−	0.0245033i	$-0.992200\pi$
$353$	−3174.40	+	5498.22i	−0.478629	+	0.829010i	0.521070	+	0.853514i	$0.325533\pi$
$354$	1081.86	−	1873.83i	0.162430	−	0.281337i
$355$	−1195.13	−	2070.02i	−0.178678	−	0.309480i
$356$	−835.879			−0.124442
$357$	−2559.40	+	1502.77i	−0.379434	+	0.222787i
$358$	3696.19			0.545669
$359$	1485.05	+	2572.18i	0.218323	+	0.378146i	0.954295	−	0.298865i	$-0.0966082\pi$
$359$	1485.05	+	2572.18i	0.218323	+	0.378146i	−0.735973	+	0.677011i	$0.763275\pi$
$360$	−707.938	+	1226.18i	−0.103643	+	0.179516i
$361$	−5099.08	+	8831.87i	−0.743415	+	1.28763i
$362$	−358.058	−	620.175i	−0.0519866	−	0.0900434i
$363$	1100.45			0.159114
$364$	837.533	+	475.406i	0.120601	+	0.0684562i
$365$	15464.4			2.21766
$366$	−788.911	−	1366.43i	−0.112670	−	0.195149i
$367$	−5620.56	+	9735.09i	−0.799430	+	1.38465i	0.120558	+	0.992706i	$0.461531\pi$
$367$	−5620.56	+	9735.09i	−0.799430	+	1.38465i	−0.919988	+	0.391946i	$0.871802\pi$
$368$	−1733.73	+	3002.91i	−0.245590	+	0.425374i
$369$	−1822.35	−	3156.41i	−0.257095	−	0.445301i
$370$	−7552.87			−1.06123
$371$	−8497.76	−	4823.56i	−1.18917	−	0.675004i
$372$	3038.88			0.423545
$373$	−16.5017	−	28.5818i	−0.00229069	−	0.00396759i	0.864878	−	0.501982i	$-0.167396\pi$
$373$	−16.5017	−	28.5818i	−0.00229069	−	0.00396759i	−0.867168	+	0.498015i	$0.834062\pi$
$374$	−1658.71	+	2872.98i	−0.229332	+	0.397214i
$375$	4032.59	−	6984.65i	0.555312	−	0.961829i
$376$	2372.17	+	4108.72i	0.325360	+	0.563540i
$377$	2135.66			0.291757
$378$	862.422	−	506.376i	0.117350	−	0.0689026i
$379$	−2358.47			−0.319647			−0.159824	−	0.987146i	$-0.551093\pi$
$379$	−2358.47			−0.319647			−0.159824	+	0.987146i	$0.551093\pi$
$380$	−5136.60	−	8896.86i	−0.693427	−	1.20105i
$381$	318.848	−	552.262i	0.0428743	−	0.0742604i
$382$	−2880.34	+	4988.90i	−0.385788	+	0.668205i
$383$	1403.51	+	2430.95i	0.187248	+	0.324323i	0.944332	−	0.328995i	$-0.106710\pi$
$383$	1403.51	+	2430.95i	0.187248	+	0.324323i	−0.757084	+	0.653318i	$0.773377\pi$
$384$	−384.000			−0.0510310
$385$	82.8180	+	11308.6i	0.0109631	+	1.49698i
$386$	−10297.5			−1.35784
$387$	−271.053	−	469.477i	−0.0356031	−	0.0616663i
$388$	−1170.07	+	2026.62i	−0.153096	+	0.265170i
$389$	−261.422	+	452.796i	−0.0340736	+	0.0590171i	−0.882559	−	0.470201i	$-0.844181\pi$
$389$	−261.422	+	452.796i	−0.0340736	+	0.0590171i	0.848486	+	0.529218i	$0.177515\pi$
$390$	766.933	+	1328.37i	0.0995773	+	0.172473i
$391$	−11576.7			−1.49733
$392$	−2743.71	+	40.1890i	−0.353515	+	0.00517820i
$393$	−1606.22			−0.206166
$394$	−1308.33	−	2266.10i	−0.167292	−	0.289758i
$395$	−2772.13	+	4801.47i	−0.353116	+	0.611616i
$396$	558.924	−	968.085i	0.0709267	−	0.122849i
$397$	−93.1336	−	161.312i	−0.0117739	−	0.0203930i	0.860078	−	0.510162i	$-0.170415\pi$
$397$	−93.1336	−	161.312i	−0.0117739	−	0.0203930i	−0.871852	+	0.489769i	$0.837081\pi$
$398$	−9551.20			−1.20291
$399$	53.1406	+	7256.21i	0.00666757	+	0.910439i
$400$	4187.36			0.523420
$401$	−2313.30	−	4006.76i	−0.288082	−	0.498973i	0.685270	−	0.728289i	$-0.259684\pi$
$401$	−2313.30	−	4006.76i	−0.288082	−	0.498973i	−0.973352	+	0.229317i	$0.926351\pi$
$402$	1476.11	−	2556.69i	0.183138	−	0.317205i
$403$	1646.06	−	2851.06i	0.203464	−	0.352410i
$404$	189.604	+	328.404i	0.0233494	+	0.0404423i
$405$	1592.86			0.195432
$406$	−5247.42	+	3081.05i	−0.641441	+	0.376626i
$407$	5963.06			0.726236
$408$	−641.022	−	1110.28i	−0.0777826	−	0.134723i
$409$	1442.52	−	2498.52i	0.174396	−	0.302063i	−0.765556	−	0.643369i	$-0.777536\pi$
$409$	1442.52	−	2498.52i	0.174396	−	0.302063i	0.939952	+	0.341306i	$0.110869\pi$
$410$	−7963.66	+	13793.5i	−0.959262	+	1.66149i
$411$	−2144.51	−	3714.39i	−0.257374	−	0.445785i
$412$	1723.44			0.206087
$413$	5808.28	+	3296.94i	0.692026	+	0.392813i
$414$	3900.90			0.463089
$415$	−10978.9	−	19016.0i	−1.29864	−	2.24930i
$416$	−208.000	+	360.267i	−0.0245145	+	0.0424604i
$417$	4181.24	−	7242.11i	0.491022	−	0.850474i
$418$	4055.40	+	7024.16i	0.474536	+	0.821920i
$419$	−7848.56			−0.915101			−0.457550	−	0.889184i	$-0.651273\pi$
$419$	−7848.56			−0.915101			−0.457550	+	0.889184i	$0.651273\pi$
$420$	−3800.78	−	2157.42i	−0.441569	−	0.250646i
$421$	−9943.46			−1.15110			−0.575552	−	0.817765i	$-0.695213\pi$
$421$	−9943.46			−1.15110			−0.575552	+	0.817765i	$0.695213\pi$
$422$	4875.17	+	8444.04i	0.562369	+	0.974051i
$423$	2668.69	−	4622.31i	0.306752	−	0.531311i
$424$	2110.41	−	3655.33i	0.241723	−	0.418676i
$425$	6990.08	+	12107.2i	0.797808	+	1.38184i
$426$	−729.294			−0.0829446
$427$	4199.84	−	2465.96i	0.475982	−	0.279476i
$428$	−1527.97			−0.172564
$429$	−605.501	−	1048.76i	−0.0681442	−	0.118029i
$430$	−1184.50	+	2051.61i	−0.132841	+	0.230087i
$431$	2287.05	−	3961.29i	0.255600	−	0.442712i	−0.709459	−	0.704747i	$-0.751060\pi$
$431$	2287.05	−	3961.29i	0.255600	−	0.442712i	0.965058	+	0.262036i	$0.0843938\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−2902.15			−0.322098			−0.161049	−	0.986946i	$-0.551488\pi$
$433$	−2902.15			−0.322098			−0.161049	+	0.986946i	$0.551488\pi$
$434$	68.6933	+	9379.89i	0.00759766	+	1.03744i
$435$	−9691.78			−1.06824
$436$	2426.66	+	4203.10i	0.266550	+	0.461678i
$437$	−14151.9	+	24511.9i	−1.54915	+	2.68321i
$438$	2359.19	−	4086.23i	0.257366	−	0.445771i
$439$	3487.17	+	6039.95i	0.379119	+	0.656654i	0.990934	−	0.134347i	$-0.0428937\pi$
$439$	3487.17	+	6039.95i	0.379119	+	0.656654i	−0.611815	+	0.791001i	$0.709560\pi$
$440$	−4884.98			−0.529278
$441$	1582.49	+	2650.53i	0.170877	+	0.286203i
$442$	−1388.88			−0.149462
$443$	−5997.71	−	10388.3i	−0.643250	−	1.11414i	−0.984703	−	0.174242i	$-0.944252\pi$
$443$	−5997.71	−	10388.3i	−0.643250	−	1.11414i	0.341453	−	0.939899i	$-0.389081\pi$
$444$	−1152.23	+	1995.73i	−0.123159	+	0.213318i
$445$	2054.69	−	3558.83i	0.218880	−	0.379111i
$446$	−1580.06	−	2736.75i	−0.167754	−	0.290558i
$447$	10408.4			1.10134
$448$	−8.68025	−	1185.26i	−0.000915409	−	0.124997i
$449$	−6096.37			−0.640769			−0.320385	−	0.947288i	$-0.603812\pi$
$449$	−6096.37			−0.640769			−0.320385	+	0.947288i	$0.603812\pi$
$450$	−2355.39	−	4079.66i	−0.246743	−	0.427371i
$451$	6287.39	−	10890.1i	0.656456	−	1.13701i
$452$	1215.18	−	2104.75i	0.126454	−	0.219024i
$453$	4681.77	+	8109.07i	0.485582	+	0.841053i
$454$	−7179.02			−0.742132
$455$	−4082.84	+	2397.26i	−0.420673	+	0.247001i
$456$	−3134.47			−0.321897
$457$	5425.28	+	9396.87i	0.555326	+	0.961853i	0.997878	+	0.0651103i	$0.0207399\pi$
$457$	5425.28	+	9396.87i	0.555326	+	0.961853i	−0.442552	+	0.896743i	$0.645927\pi$
$458$	2222.18	−	3848.93i	0.226715	−	0.392682i
$459$	−721.150	+	1249.07i	−0.0733342	+	0.127018i
$460$	−8523.44	−	14763.0i	−0.863929	−	1.49637i
$461$	10257.0			1.03626			0.518131	−	0.855301i	$-0.326628\pi$
$461$	10257.0			1.03626			0.518131	+	0.855301i	$0.326628\pi$
$462$	3000.75	+	1703.31i	0.302181	+	0.171526i
$463$	9954.33			0.999172			0.499586	−	0.866264i	$-0.333485\pi$
$463$	9954.33			0.999172			0.499586	+	0.866264i	$0.333485\pi$
$464$	−1314.26	−	2276.36i	−0.131493	−	0.227753i
$465$	−7469.93	+	12938.3i	−0.744967	+	1.29032i
$466$	−322.188	+	558.045i	−0.0320280	+	0.0554741i
$467$	−9153.52	−	15854.4i	−0.907012	−	1.57099i	−0.818194	−	0.574942i	$-0.805024\pi$
$467$	−9153.52	−	15854.4i	−0.907012	−	1.57099i	−0.0888178	−	0.996048i	$-0.528309\pi$
$468$	468.000			0.0462250
$469$	7924.93	+	4498.40i	0.780254	+	0.442893i
$470$	−23324.3			−2.28908
$471$	1517.12	+	2627.73i	0.148418	+	0.257068i
$472$	−1442.48	+	2498.44i	−0.140668	+	0.243645i
$473$	935.172	−	1619.77i	0.0909075	−	0.157456i
$474$	845.809	+	1464.98i	0.0819605	+	0.141960i
$475$	34180.1			3.30167
$476$	3412.54	−	2003.69i	0.328600	−	0.192939i
$477$	−4748.41			−0.455796
$478$	785.968	+	1361.34i	0.0752079	+	0.130264i
$479$	−3403.95	+	5895.81i	−0.324698	+	0.562394i	−0.981451	−	0.191712i	$-0.938596\pi$
$479$	−3403.95	+	5895.81i	−0.324698	+	0.562394i	0.656753	+	0.754106i	$0.271929\pi$
$480$	943.917	−	1634.91i	0.0897578	−	0.155465i
$481$	1248.25	+	2162.04i	0.118327	+	0.204949i
$482$	−4985.46			−0.471124
$483$	88.1791	+	12040.6i	0.00830701	+	1.13430i
$484$	−1467.26			−0.137797
$485$	−5752.33	−	9963.33i	−0.538556	−	0.932807i
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	2698.13	−	4673.31i	0.251056	−	0.434841i	−0.712761	−	0.701407i	$-0.752556\pi$
$487$	2698.13	−	4673.31i	0.251056	−	0.434841i	0.963817	+	0.266566i	$0.0858889\pi$
$488$	1051.88	+	1821.91i	0.0975747	+	0.169004i
$489$	−7484.84			−0.692180
$490$	6573.24	−	11780.4i	0.606018	−	1.08609i
$491$	−12396.8			−1.13943			−0.569715	−	0.821843i	$-0.692946\pi$
$491$	−12396.8			−1.13943			−0.569715	+	0.821843i	$0.692946\pi$
$492$	2429.80	+	4208.55i	0.222651	+	0.385642i
$493$	4387.84	−	7599.97i	0.400849	−	0.694291i
$494$	−1697.84	+	2940.74i	−0.154634	+	0.267835i
$495$	2747.80	+	4759.33i	0.249504	+	0.432154i
$496$	−4051.84			−0.366800
$497$	−16.4855	−	2251.06i	−0.00148788	−	0.203166i
$498$	−6699.59			−0.602843
$499$	4744.08	+	8216.98i	0.425599	+	0.737160i	0.996476	−	0.0838759i	$-0.0267299\pi$
$499$	4744.08	+	8216.98i	0.425599	+	0.737160i	−0.570877	+	0.821036i	$0.693397\pi$
$500$	−5376.79	+	9312.87i	−0.480915	+	0.832969i
$501$	5025.35	−	8704.15i	0.448136	−	0.776193i
$502$	−3934.48	−	6814.71i	−0.349809	−	0.605888i
$503$	18924.9			1.67758			0.838789	−	0.544457i	$-0.183264\pi$
$503$	18924.9			1.67758			0.838789	+	0.544457i	$0.183264\pi$
$504$	−1149.90	+	675.168i	−0.101628	+	0.0596714i
$505$	−1864.28			−0.164276
$506$	6729.34	+	11655.6i	0.591216	+	1.02402i
$507$	253.500	−	439.075i	0.0222058	−	0.0384615i
$508$	−425.131	+	736.349i	−0.0371302	+	0.0643114i
$509$	2243.28	+	3885.47i	0.195347	+	0.338351i	0.947014	−	0.321192i	$-0.104083\pi$
$509$	2243.28	+	3885.47i	0.195347	+	0.338351i	−0.751667	+	0.659542i	$0.770750\pi$
$510$	6302.83			0.547243
$511$	12666.0	+	7189.56i	1.09650	+	0.622402i
$512$	512.000			0.0441942
$513$	1763.14	+	3053.85i	0.151744	+	0.262828i
$514$	740.288	−	1282.22i	0.0635267	−	0.110031i
$515$	−4236.42	+	7337.70i	−0.362484	+	0.627840i
$516$	361.404	+	625.969i	0.0308332	+	0.0534046i
$517$	18414.8			1.56650
$518$	−6186.11	−	3511.40i	−0.524715	−	0.297842i
$519$	−1220.59			−0.103233
$520$	−1022.58	−	1771.16i	−0.0862365	−	0.149366i
$521$	−4609.12	+	7983.24i	−0.387580	+	0.671309i	−0.992124	−	0.125263i	$-0.960022\pi$
$521$	−4609.12	+	7983.24i	−0.387580	+	0.671309i	0.604543	+	0.796572i	$0.293356\pi$
$522$	−1478.54	+	2560.90i	−0.123973	+	0.214727i
$523$	6019.15	+	10425.5i	0.503249	+	0.871652i	0.999993	+	0.00375546i	$0.00119540\pi$
$523$	6019.15	+	10425.5i	0.503249	+	0.871652i	−0.496744	+	0.867897i	$0.665471\pi$
$524$	2141.63			0.178545
$525$	12539.1	−	7362.43i	1.04239	−	0.612043i
$526$	−12532.7			−1.03888
$527$	−6763.85	−	11715.3i	−0.559085	−	0.968364i
$528$	−745.232	+	1290.78i	−0.0614243	+	0.106390i
$529$	−17399.5	+	30136.9i	−1.43006	+	2.47694i
$530$	10375.3	+	17970.5i	0.850325	+	1.47281i
$531$	3245.57			0.265247
$532$	−70.8542	−	9674.95i	−0.00577428	−	0.788463i
$533$	5264.58			0.427831
$534$	−626.909	−	1085.84i	−0.0508034	−	0.0879941i
$535$	3755.94	−	6505.47i	0.303520	−	0.525713i
$536$	−1968.14	+	3408.93i	−0.158602	+	0.274707i
$537$	2772.14	+	4801.49i	0.222769	+	0.385847i
$538$	10980.3			0.879915
$539$	−5189.64	+	9300.70i	−0.414719	+	0.743246i
$540$	−2123.81			−0.169249
$541$	4502.99	+	7799.41i	0.357853	+	0.619820i	0.987602	−	0.156979i	$-0.0501754\pi$
$541$	4502.99	+	7799.41i	0.357853	+	0.619820i	−0.629749	+	0.776799i	$0.716842\pi$
$542$	−52.6254	+	91.1499i	−0.00417058	+	0.00722366i
$543$	537.088	−	930.263i	0.0424468	−	0.0735201i
$544$	854.696	+	1480.38i	0.0673617	+	0.116674i
$545$	−23860.0			−1.87533
$546$	10.5791	+	1444.54i	0.000829197	+	0.113225i
$547$	10995.6			0.859482			0.429741	−	0.902952i	$-0.358605\pi$
$547$	10995.6			0.859482			0.429741	+	0.902952i	$0.358605\pi$
$548$	2859.34	+	4952.53i	0.222892	+	0.386061i
$549$	1183.37	−	2049.65i	0.0919943	−	0.159339i
$550$	8126.44	−	14075.4i	0.630023	−	1.09123i
$551$	−10727.9	−	18581.2i	−0.829441	−	1.43663i
$552$	−5201.20			−0.401047
$553$	−4502.74	+	2643.81i	−0.346249	+	0.203303i
$554$	9608.58			0.736876
$555$	−5664.65	−	9811.47i	−0.433245	−	0.750403i
$556$	−5574.98	+	9656.15i	−0.425237	+	0.736533i
$557$	5096.73	−	8827.80i	0.387712	−	0.671536i	−0.604430	−	0.796659i	$-0.706599\pi$
$557$	5096.73	−	8827.80i	0.387712	−	0.671536i	0.992141	+	0.125122i	$0.0399323\pi$
$558$	2279.16	+	3947.62i	0.172911	+	0.299491i
$559$	783.041			0.0592471
$560$	5067.70	+	2876.56i	0.382410	+	0.217066i
$561$	−4976.14			−0.374497
$562$	−1913.01	−	3313.43i	−0.143586	−	0.248699i
$563$	3098.52	−	5366.79i	0.231948	−	0.401746i	−0.726433	−	0.687237i	$-0.758823\pi$
$563$	3098.52	−	5366.79i	0.231948	−	0.401746i	0.958381	+	0.285491i	$0.0921566\pi$
$564$	−3558.26	+	6163.08i	−0.265655	+	0.460129i
$565$	5974.10	+	10347.4i	0.444836	+	0.770478i
$566$	2323.44			0.172547
$567$	1304.62	+	740.536i	0.0966293	+	0.0548494i
$568$	972.391			0.0718321
$569$	6364.66	+	11023.9i	0.468928	+	0.812208i	0.999369	−	0.0355142i	$-0.0113069\pi$
$569$	6364.66	+	11023.9i	0.468928	+	0.812208i	−0.530441	+	0.847722i	$0.677974\pi$
$570$	7704.91	−	13345.3i	0.566181	−	0.980654i
$571$	−8022.24	+	13894.9i	−0.587952	+	1.01836i	0.406549	+	0.913629i	$0.366732\pi$
$571$	−8022.24	+	13894.9i	−0.587952	+	1.01836i	−0.994500	+	0.104733i	$0.966601\pi$
$572$	807.334	+	1398.34i	0.0590146	+	0.102216i
$573$	−8641.03			−0.629990
$574$	−12935.3	+	7595.03i	−0.940607	+	0.552283i
$575$	56716.9			4.11349
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−8169.70	+	14150.3i	−0.589444	+	1.02095i	0.404862	+	0.914378i	$0.367320\pi$
$577$	−8169.70	+	14150.3i	−0.589444	+	1.02095i	−0.994305	+	0.106568i	$0.966014\pi$
$578$	2059.47	−	3567.10i	0.148205	−	0.256699i
$579$	−7723.09	−	13376.8i	−0.554336	−	0.960139i
$580$	12922.4			0.925125
$581$	−151.443	−	20679.1i	−0.0108140	−	1.47662i
$582$	−3510.20			−0.250005
$583$	−8191.36	−	14187.9i	−0.581907	−	1.00789i
$584$	−3145.58	+	5448.31i	−0.222886	+	0.386049i
$585$	−1150.40	+	1992.55i	−0.0813045	+	0.140824i
$586$	−4962.42	−	8595.17i	−0.349822	−	0.605910i
$587$	−11035.7			−0.775966			−0.387983	−	0.921667i	$-0.626828\pi$
$587$	−11035.7			−0.775966			−0.387983	+	0.921667i	$0.626828\pi$
$588$	−2109.99	−	3534.04i	−0.147984	−	0.247859i
$589$	−33073.9			−2.31373
$590$	−7091.56	−	12282.9i	−0.494839	−	0.857086i
$591$	1962.50	−	3399.15i	0.136593	−	0.236586i
$592$	1536.31	−	2660.97i	0.106659	−	0.184738i
$593$	−10943.0	−	18953.9i	−0.757803	−	1.31255i	−0.943969	−	0.330035i	$-0.892940\pi$
$593$	−10943.0	−	18953.9i	−0.757803	−	1.31255i	0.186166	−	0.982518i	$-0.440394\pi$
$594$	1676.77			0.115823
$595$	142.474	+	19454.5i	0.00981660	+	1.34043i
$596$	−13877.8			−0.953787
$597$	−7163.40	−	12407.4i	−0.491086	−	0.850586i
$598$	−2817.32	+	4879.73i	−0.192657	+	0.333691i
$599$	7716.67	−	13365.7i	0.526368	−	0.911696i	−0.473160	−	0.880977i	$-0.656887\pi$
$599$	7716.67	−	13365.7i	0.526368	−	0.911696i	0.999528	−	0.0307197i	$-0.00977993\pi$
$600$	3140.52	+	5439.54i	0.213685	+	0.370114i
$601$	6146.03			0.417141			0.208571	−	0.978007i	$-0.433119\pi$
$601$	6146.03			0.417141			0.208571	+	0.978007i	$0.433119\pi$
$602$	−1923.96	+	1129.67i	−0.130257	+	0.0764815i
$603$	4428.32			0.299063
$604$	−6242.36	−	10812.1i	−0.420527	−	0.728374i
$605$	3606.70	−	6246.99i	0.242369	−	0.419795i
$606$	−284.406	+	492.606i	−0.0190647	+	0.0330210i
$607$	5516.99	+	9555.72i	0.368909	+	0.638970i	0.989395	−	0.145248i	$-0.0463980\pi$
$607$	5516.99	+	9555.72i	0.368909	+	0.638970i	−0.620486	+	0.784217i	$0.713065\pi$
$608$	4179.30			0.278771
$609$	−7937.97	−	4505.80i	−0.528182	−	0.299810i
$610$	−10342.6			−0.686491
$611$	3854.78	+	6676.67i	0.255233	+	0.442077i
$612$	961.533	−	1665.42i	0.0635092	−	0.110001i
$613$	−2166.84	+	3753.08i	−0.142770	+	0.247285i	−0.928539	−	0.371236i	$-0.878934\pi$
$613$	−2166.84	+	3753.08i	−0.142770	+	0.247285i	0.785769	+	0.618520i	$0.212268\pi$
$614$	6773.86	+	11732.7i	0.445229	+	0.771160i
$615$	−23891.0			−1.56647
$616$	−4001.00	−	2271.07i	−0.261696	−	0.148546i
$617$	12879.6			0.840375			0.420187	−	0.907437i	$-0.361964\pi$
$617$	12879.6			0.840375			0.420187	+	0.907437i	$0.361964\pi$
$618$	1292.58	+	2238.82i	0.0841347	+	0.145726i
$619$	2520.76	−	4366.08i	0.163680	−	0.283502i	−0.772506	−	0.635008i	$-0.780997\pi$
$619$	2520.76	−	4366.08i	0.163680	−	0.283502i	0.936186	+	0.351506i	$0.114330\pi$
$620$	9959.90	−	17251.1i	0.645160	−	1.11745i
$621$	2925.67	+	5067.42i	0.189055	+	0.327453i
$622$	18886.3			1.21748
$623$	3337.41	−	1959.58i	0.214623	−	0.126018i
$624$	−624.000			−0.0400320
$625$	−10076.7	−	17453.3i	−0.644908	−	1.11701i
$626$	−713.760	+	1236.27i	−0.0455712	+	0.0789317i
$627$	−6083.10	+	10536.2i	−0.387457	+	0.671095i
$628$	−2022.82	−	3503.63i	−0.128534	−	0.222628i
$629$	10258.4			0.650287
$630$	−48.0084	−	6555.42i	−0.00303603	−	0.414562i
$631$	19603.2			1.23675			0.618377	−	0.785882i	$-0.287791\pi$
$631$	19603.2			1.23675			0.618377	+	0.785882i	$0.287791\pi$
$632$	−1127.74	−	1953.31i	−0.0709799	−	0.122941i
$633$	−7312.76	+	12666.1i	−0.459172	+	0.795310i
$634$	−4845.80	+	8393.17i	−0.303551	+	0.525765i
$635$	−2090.05	−	3620.06i	−0.130616	−	0.226233i
$636$	6331.22			0.394731
$637$	−4458.52	+	65.3072i	−0.277320	+	0.00406211i
$638$	−10202.3			−0.633095
$639$	−546.970	−	947.380i	−0.0338620	−	0.0586507i
$640$	−1258.56	+	2179.88i	−0.0777325	+	0.134637i
$641$	2478.32	−	4292.58i	0.152711	−	0.264504i	−0.779512	−	0.626387i	$-0.784533\pi$
$641$	2478.32	−	4292.58i	0.152711	−	0.264504i	0.932223	+	0.361884i	$0.117866\pi$
$642$	−1145.98	−	1984.90i	−0.0704489	−	0.122021i
$643$	−14895.1			−0.913536			−0.456768	−	0.889586i	$-0.650993\pi$
$643$	−14895.1			−0.913536			−0.456768	+	0.889586i	$0.650993\pi$
$644$	−117.572	−	16054.2i	−0.00719408	−	0.982333i
$645$	−3553.49			−0.216928
$646$	6976.62	+	12083.9i	0.424909	+	0.735964i
$647$	6736.99	−	11668.8i	0.409364	−	0.709039i	−0.585455	−	0.810705i	$-0.699084\pi$
$647$	6736.99	−	11668.8i	0.409364	−	0.709039i	0.994819	+	0.101666i	$0.0324174\pi$
$648$	−324.000	+	561.184i	−0.0196419	+	0.0340207i
$649$	5598.86	+	9697.50i	0.338635	+	0.586534i
$650$	6804.46			0.410604
$651$	−12133.3	+	7124.15i	−0.730479	+	0.428906i
$652$	9979.79			0.599446
$653$	6518.40	+	11290.2i	0.390635	+	0.676599i	0.992533	−	0.121973i	$-0.0389222\pi$
$653$	6518.40	+	11290.2i	0.390635	+	0.676599i	−0.601899	+	0.798573i	$0.705589\pi$
$654$	−3639.99	+	6304.64i	−0.217637	+	0.376959i
$655$	−5264.37	+	9118.15i	−0.314040	+	0.543932i
$656$	−3239.74	−	5611.39i	−0.192821	−	0.333976i
$657$	7077.56			0.420277
$658$	−19103.6	−	10843.7i	−1.13182	−	0.642449i
$659$	−11913.0			−0.704194			−0.352097	−	0.935964i	$-0.614531\pi$
$659$	−11913.0			−0.704194			−0.352097	+	0.935964i	$0.614531\pi$
$660$	−3663.74	−	6345.78i	−0.216077	−	0.374256i
$661$	−13884.3	+	24048.3i	−0.816998	+	1.41508i	0.0908870	+	0.995861i	$0.471030\pi$
$661$	−13884.3	+	24048.3i	−0.816998	+	1.41508i	−0.907885	+	0.419220i	$0.862304\pi$
$662$	−6739.26	+	11672.7i	−0.395663	+	0.685308i
$663$	−1041.66	−	1804.21i	−0.0610177	−	0.105686i
$664$	8932.78			0.522077
$665$	41366.1	+	23480.5i	2.41219	+	1.36923i
$666$	−3456.70			−0.201118
$667$	−17801.3	−	30832.8i	−1.03339	−	1.78988i
$668$	−6700.46	+	11605.5i	−0.388097	+	0.672203i
$669$	2370.09	−	4105.12i	0.136970	−	0.237240i
$670$	−9675.86	−	16759.1i	−0.557927	−	0.966358i
$671$	8165.58			0.469789
$672$	1533.19	−	900.225i	0.0880123	−	0.0516770i
$673$	−1533.24			−0.0878189			−0.0439095	−	0.999036i	$-0.513981\pi$
$673$	−1533.24			−0.0878189			−0.0439095	+	0.999036i	$0.513981\pi$
$674$	−7205.69	−	12480.6i	−0.411800	−	0.713258i
$675$	3533.09	−	6119.48i	0.201464	−	0.348947i
$676$	−338.000	+	585.433i	−0.0192308	+	0.0333087i
$677$	7410.48	+	12835.3i	0.420691	+	0.728659i	0.996007	−	0.0892726i	$-0.0284542\pi$
$677$	7410.48	+	12835.3i	0.420691	+	0.728659i	−0.575316	+	0.817931i	$0.695121\pi$
$678$	3645.53			0.206498
$679$	−79.3475	−	10834.7i	−0.00448465	−	0.612367i
$680$	−8403.77			−0.473926
$681$	−5384.26	−	9325.82i	−0.302974	−	0.524767i
$682$	−7863.44	+	13619.9i	−0.441505	+	0.764710i
$683$	10562.6	−	18295.0i	0.591754	−	1.02495i	−0.402243	−	0.915533i	$-0.631769\pi$
$683$	10562.6	−	18295.0i	0.591754	−	1.02495i	0.993996	−	0.109414i	$-0.0348975\pi$
$684$	−2350.86	−	4071.80i	−0.131414	−	0.227616i
$685$	−28114.4			−1.56817
$686$	10860.6	−	6592.63i	0.604458	−	0.366921i
$687$	6666.54			0.370225
$688$	−481.872	−	834.626i	−0.0267023	−	0.0462497i
$689$	3429.41	−	5939.91i	0.189623	−	0.328436i
$690$	12785.2	−	22144.5i	0.705395	−	1.22178i
$691$	17607.1	+	30496.5i	0.969330	+	1.67893i	0.697501	+	0.716584i	$0.254295\pi$
$691$	17607.1	+	30496.5i	0.969330	+	1.67893i	0.271829	+	0.962346i	$0.412372\pi$
$692$	1627.45			0.0894024
$693$	37.9031	+	5175.57i	0.00207766	+	0.283699i
$694$	1974.18			0.107981
$695$	−27407.9	−	47471.9i	−1.49589	−	2.59095i
$696$	1971.38	−	3414.54i	0.107364	−	0.185959i
$697$	10816.4	−	18734.5i	0.587804	−	1.01811i
$698$	21.6864	+	37.5620i	0.00117599	+	0.00203688i
$699$	−966.563			−0.0523015
$700$	−16718.8	+	9816.57i	−0.902733	+	0.530045i
$701$	−31415.1			−1.69263			−0.846314	−	0.532685i	$-0.821183\pi$
$701$	−31415.1			−1.69263			−0.846314	+	0.532685i	$0.821183\pi$
$702$	351.000	+	607.950i	0.0188713	+	0.0326860i
$703$	12540.4	−	21720.7i	0.672790	−	1.16531i
$704$	993.642	−	1721.04i	0.0531950	−	0.0921365i
$705$	−17493.2	−	30299.2i	−0.934515	−	1.61863i
$706$	12697.6			0.676884
$707$	−1526.92	−	866.720i	−0.0812245	−	0.0461052i
$708$	−4327.43			−0.229710
$709$	3629.69	+	6286.81i	0.192265	+	0.333013i	0.946000	−	0.324165i	$-0.105083\pi$
$709$	3629.69	+	6286.81i	0.192265	+	0.333013i	−0.753736	+	0.657178i	$0.771750\pi$
$710$	−2390.25	+	4140.04i	−0.126344	+	0.218835i
$711$	−1268.71	+	2197.48i	−0.0669205	+	0.115910i
$712$	835.879	+	1447.78i	0.0439970	+	0.0762051i
$713$	−54881.3			−2.88264
$714$	5162.28	+	2930.25i	0.270579	+	0.153588i
$715$	−7938.09			−0.415200
$716$	−3696.19	−	6401.99i	−0.192923	−	0.334153i
$717$	−1178.95	+	2042.01i	−0.0614070	+	0.106360i
$718$	2970.09	−	5144.36i	0.154377	−	0.267389i
$719$	−2314.36	−	4008.58i	−0.120043	−	0.207921i	0.799741	−	0.600345i	$-0.204970\pi$
$719$	−2314.36	−	4008.58i	−0.120043	−	0.207921i	−0.919784	+	0.392424i	$0.871637\pi$
$720$	2831.75			0.146574
$721$	−6881.18	+	4040.33i	−0.355435	+	0.208696i
$722$	20396.3			1.05135
$723$	−3739.10	−	6476.31i	−0.192335	−	0.333135i
$724$	−716.117	+	1240.35i	−0.0367600	+	0.0636703i
$725$	−21497.1	+	37234.1i	−1.10122	+	1.90736i
$726$	−1100.45	−	1906.03i	−0.0562553	−	0.0974371i
$727$	22366.5			1.14103			0.570515	−	0.821287i	$-0.306744\pi$
$727$	22366.5			1.14103			0.570515	+	0.821287i	$0.306744\pi$
$728$	−14.1054	−	1926.06i	−0.000718106	−	0.0980554i
$729$	729.000			0.0370370
$730$	−15464.4	−	26785.2i	−0.784061	−	1.35803i
$731$	1608.80	−	2786.53i	0.0814004	−	0.140990i
$732$	−1577.82	+	2732.87i	−0.0796694	+	0.137991i
$733$	210.821	+	365.153i	0.0106233	+	0.0184000i	0.871288	−	0.490772i	$-0.163285\pi$
$733$	210.821	+	365.153i	0.0106233	+	0.0184000i	−0.860665	+	0.509172i	$0.829952\pi$
$734$	22482.2			1.13056
$735$	20233.1	−	296.368i	1.01538	−	0.0148731i
$736$	6934.93			0.347316
$737$	7639.18	+	13231.5i	0.381809	+	0.661312i
$738$	−3644.71	+	6312.82i	−0.181793	+	0.314875i
$739$	−6733.14	+	11662.1i	−0.335159	+	0.580512i	−0.983515	−	0.180825i	$-0.942123\pi$
$739$	−6733.14	+	11662.1i	−0.335159	+	0.580512i	0.648356	+	0.761337i	$0.275457\pi$
$740$	7552.87	+	13082.0i	0.375201	+	0.649868i
$741$	−5093.52			−0.252517
$742$	143.116	+	19542.1i	0.00708080	+	0.966864i
$743$	15819.2			0.781090			0.390545	−	0.920584i	$-0.372287\pi$
$743$	15819.2			0.781090			0.390545	+	0.920584i	$0.372287\pi$
$744$	−3038.88	−	5263.49i	−0.149746	−	0.259367i
$745$	34113.3	−	59085.9i	1.67760	−	2.90569i
$746$	−33.0034	+	57.1636i	−0.00161976	+	0.00280551i
$747$	−5024.69	−	8703.02i	−0.246109	−	0.426274i
$748$	6634.86			0.324324
$749$	6100.73	−	3582.08i	0.297618	−	0.174748i
$750$	−16130.4			−0.785330
$751$	3326.19	+	5761.13i	0.161617	+	0.279929i	0.935449	−	0.353462i	$-0.114996\pi$
$751$	3326.19	+	5761.13i	0.161617	+	0.279929i	−0.773832	+	0.633391i	$0.781662\pi$
$752$	4744.34	−	8217.44i	0.230064	−	0.398483i
$753$	5901.72	−	10222.1i	0.285618	−	0.494705i
$754$	−2135.66	−	3699.08i	−0.103152	−	0.178664i
$755$	61377.9			2.95863
$756$	−1739.49	−	987.382i	−0.0836834	−	0.0475010i
$757$	−21520.9			−1.03328			−0.516638	−	0.856204i	$-0.672817\pi$
$757$	−21520.9			−1.03328			−0.516638	+	0.856204i	$0.672817\pi$
$758$	2358.47	+	4084.98i	0.113012	+	0.195743i
$759$	−10094.0	+	17483.3i	−0.482726	+	0.836106i
$760$	−10273.2	+	17793.7i	−0.490327	+	0.849271i
$761$	−4846.09	−	8393.67i	−0.230842	−	0.399829i	0.727214	−	0.686410i	$-0.240815\pi$
$761$	−4846.09	−	8393.67i	−0.230842	−	0.399829i	−0.958056	+	0.286581i	$0.907481\pi$
$762$	−1275.39			−0.0606334
$763$	−19542.4	−	11092.8i	−0.927236	−	0.526324i
$764$	11521.4			0.545587
$765$	4727.12	+	8187.62i	0.223411	+	0.386959i
$766$	2807.02	−	4861.90i	0.132404	−	0.229331i
$767$	−2344.03	+	4059.97i	−0.110349	+	0.191131i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	−7187.85			−0.337062			−0.168531	−	0.985696i	$-0.553902\pi$
$769$	−7187.85			−0.337062			−0.168531	+	0.985696i	$0.553902\pi$
$770$	19504.2	−	11452.0i	0.912836	−	0.535977i
$771$	2220.87			0.103739
$772$	10297.5	+	17835.7i	0.480069	+	0.831505i
$773$	8802.32	−	15246.1i	0.409570	−	0.709396i	−0.585272	−	0.810837i	$-0.699012\pi$
$773$	8802.32	−	15246.1i	0.409570	−	0.709396i	0.994841	+	0.101442i	$0.0323455\pi$
$774$	−542.105	+	938.954i	−0.0251752	+	0.0436047i
$775$	33137.7	+	57396.2i	1.53593	+	2.66030i
$776$	4680.27			0.216510
$777$	−78.1381	−	10669.5i	−0.00360771	−	0.492623i
$778$	1045.69			0.0481873
$779$	−26445.0	−	45804.1i	−1.21629	−	2.10668i
$780$	1533.87	−	2656.73i	0.0704118	−	0.121957i
$781$	1887.13	−	3268.60i	0.0864619	−	0.149756i
$782$	11576.7	+	20051.4i	0.529387	+	0.916926i
$783$	−4435.61			−0.202447
$784$	2813.32	+	4712.05i	0.128158	+	0.214652i
$785$	19889.4			0.904308
$786$	1606.22	+	2782.05i	0.0728905	+	0.126250i
$787$	−10258.7	+	17768.5i	−0.464653	+	0.804803i	−0.999186	−	0.0403447i	$-0.987154\pi$
$787$	−10258.7	+	17768.5i	−0.464653	+	0.804803i	0.534532	+	0.845148i	$0.320488\pi$
$788$	−2616.67	+	4532.20i	−0.118293	+	0.204889i
$789$	−9399.52	−	16280.4i	−0.424121	−	0.734600i
$790$	11088.5			0.499382
$791$	82.4065	+	11252.4i	0.00370422	+	0.505802i
$792$	−2235.70			−0.100306
$793$	1709.31	+	2960.61i	0.0765439	+	0.132578i
$794$	−186.267	+	322.624i	−0.00832541	+	0.0144200i
$795$	−15562.9	+	26955.7i	−0.694287	+	1.20254i
$796$	9551.20	+	16543.2i	0.425293	+	0.736629i
$797$	5895.31			0.262011			0.131005	−	0.991382i	$-0.458180\pi$
$797$	5895.31			0.262011			0.131005	+	0.991382i	$0.458180\pi$
$798$	12515.0	−	7348.26i	0.555170	−	0.325972i
$799$	31679.4			1.40268
$800$	−4187.36	−	7252.72i	−0.185057	−	0.320528i
$801$	940.364	−	1628.76i	0.0414808	−	0.0718469i
$802$	−4626.61	+	8013.52i	−0.203705	+	0.352827i
$803$	12209.3	+	21147.2i	0.536560	+	0.929349i
$804$	−5904.43			−0.258997
$805$	68640.9	+	38962.4i	3.00531	+	1.70590i
$806$	−6584.24			−0.287742
$807$	8235.22	+	14263.8i	0.359224	+	0.622194i
$808$	379.208	−	656.807i	0.0165105	−	0.0285970i
$809$	19864.0	−	34405.5i	0.863266	−	1.49522i	−0.00549214	−	0.999985i	$-0.501748\pi$
$809$	19864.0	−	34405.5i	0.863266	−	1.49522i	0.868758	−	0.495236i	$-0.164918\pi$
$810$	−1592.86	−	2758.92i	−0.0690956	−	0.119677i
$811$	11067.1			0.479185			0.239593	−	0.970873i	$-0.422986\pi$
$811$	11067.1			0.479185			0.239593	+	0.970873i	$0.422986\pi$
$812$	10584.0	+	6007.74i	0.457419	+	0.259643i
$813$	−157.876			−0.00681053
$814$	−5963.06	−	10328.3i	−0.256763	−	0.444727i
$815$	−24531.5	+	42489.8i	−1.05436	+	1.82620i
$816$	−1282.04	+	2220.56i	−0.0550006	+	0.0952639i
$817$	−3933.37	−	6812.79i	−0.168435	−	0.291737i
$818$	−5770.08			−0.246633
$819$	−1868.58	+	1097.15i	−0.0797234	+	0.0468101i
$820$	31854.6			1.35660
$821$	−11602.9	−	20096.9i	−0.493234	−	0.854306i	0.506736	−	0.862101i	$-0.330852\pi$
$821$	−11602.9	−	20096.9i	−0.493234	−	0.854306i	−0.999970	+	0.00779550i	$0.997519\pi$
$822$	−4289.01	+	7428.79i	−0.181991	+	0.315217i
$823$	−3149.03	+	5454.29i	−0.133376	+	0.231014i	−0.924976	−	0.380026i	$-0.875915\pi$
$823$	−3149.03	+	5454.29i	−0.133376	+	0.231014i	0.791600	+	0.611040i	$0.209248\pi$
$824$	−1723.44	−	2985.09i	−0.0728628	−	0.126202i
$825$	24379.3			1.02882
$826$	−97.8208	−	13357.2i	−0.00412061	−	0.562658i
$827$	−10330.2			−0.434359			−0.217180	−	0.976132i	$-0.569686\pi$
$827$	−10330.2			−0.434359			−0.217180	+	0.976132i	$0.569686\pi$
$828$	−3900.90	−	6756.55i	−0.163727	−	0.283583i
$829$	−22635.6	+	39206.0i	−0.948331	+	1.64256i	−0.199392	+	0.979920i	$0.563897\pi$
$829$	−22635.6	+	39206.0i	−0.948331	+	1.64256i	−0.748940	+	0.662638i	$0.769437\pi$
$830$	−21957.8	+	38032.1i	−0.918274	+	1.59050i
$831$	7206.43	+	12481.9i	0.300828	+	0.521050i
$832$	832.000			0.0346688
$833$	−8927.89	+	16000.3i	−0.371348	+	0.665518i
$834$	−16724.9			−0.694410
$835$	−32941.0	−	57055.6i	−1.36524	−	2.36466i
$836$	8110.80	−	14048.3i	0.335548	−	0.581185i
$837$	−3418.74	+	5921.43i	−0.141182	+	0.244534i
$838$	7848.56	+	13594.1i	0.323537	+	0.560382i
$839$	9449.07			0.388818			0.194409	−	0.980921i	$-0.437721\pi$
$839$	9449.07			0.388818			0.194409	+	0.980921i	$0.437721\pi$
$840$	64.0112	+	8740.56i	0.00262928	+	0.359021i
$841$	2599.54			0.106587
$842$	9943.46	+	17222.6i	0.406977	+	0.704904i
$843$	2869.52	−	4970.15i	0.117238	−	0.203062i
$844$	9750.34	−	16888.1i	0.397655	−	0.688758i
$845$	−1661.69	−	2878.13i	−0.0676495	−	0.117172i
$846$	−10674.8			−0.433813
$847$	5858.32	−	3439.75i	0.237656	−	0.139541i
$848$	−8441.62			−0.341847
$849$	1742.58	+	3018.23i	0.0704418	+	0.122009i
$850$	13980.2	−	24214.3i	0.564136	−	0.977112i
$851$	20809.0	−	36042.3i	0.838218	−	1.45184i
$852$	729.294	+	1263.17i	0.0293253	+	0.0507930i
$853$	−16239.5			−0.651851			−0.325926	−	0.945395i	$-0.605676\pi$
$853$	−16239.5			−0.651851			−0.325926	+	0.945395i	$0.605676\pi$
$854$	−8471.01	−	4808.37i	−0.339429	−	0.192669i
$855$	23114.7			0.924569
$856$	1527.97	+	2646.53i	0.0610106	+	0.105673i
$857$	7365.83	−	12758.0i	0.293596	−	0.508524i	−0.681061	−	0.732227i	$-0.738481\pi$
$857$	7365.83	−	12758.0i	0.293596	−	0.508524i	0.974657	+	0.223703i	$0.0718145\pi$
$858$	−1211.00	+	2097.52i	−0.0481852	+	0.0834592i
$859$	−3928.67	−	6804.66i	−0.156047	−	0.270282i	0.777393	−	0.629016i	$-0.216542\pi$
$859$	−3928.67	−	6804.66i	−0.156047	−	0.270282i	−0.933440	+	0.358734i	$0.883209\pi$
$860$	4737.99			0.187865
$861$	−19567.7	−	11107.2i	−0.774524	−	0.439641i
$862$	−9148.21			−0.361473
$863$	4165.18	+	7214.31i	0.164293	+	0.284563i	0.936404	−	0.350924i	$-0.114133\pi$
$863$	4165.18	+	7214.31i	0.164293	+	0.284563i	−0.772111	+	0.635487i	$0.780799\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−4000.47	+	6929.02i	−0.157249	+	0.272363i
$866$	2902.15	+	5026.67i	0.113879	+	0.197244i
$867$	6178.40			0.242018
$868$	16177.8	−	9498.87i	0.632614	−	0.371443i
$869$	−8754.49			−0.341744
$870$	9691.78	+	16786.7i	0.377681	+	0.654162i
$871$	−3198.23	+	5539.50i	−0.124418	+	0.215498i
$872$	4853.32	−	8406.19i	0.188479	−	0.326456i
$873$	−2632.65	−	4559.89i	−0.102064	−	0.176780i
$874$	56607.7			2.19083
$875$	−364.624	−	49788.4i	−0.0140875	−	1.92361i
$876$	−9436.75			−0.363971
$877$	5701.68	+	9875.61i	0.219535	+	0.380246i	0.954666	−	0.297679i	$-0.0962127\pi$
$877$	5701.68	+	9875.61i	0.219535	+	0.380246i	−0.735131	+	0.677925i	$0.762879\pi$
$878$	6974.33	−	12079.9i	0.268078	−	0.464324i
$879$	7443.63	−	12892.8i	0.285629	−	0.494723i
$880$	4884.98	+	8461.03i	0.187128	+	0.324115i
$881$	−14562.7			−0.556901			−0.278451	−	0.960451i	$-0.589821\pi$
$881$	−14562.7			−0.556901			−0.278451	+	0.960451i	$0.589821\pi$
$882$	3008.36	−	5391.48i	0.114849	−	0.205828i
$883$	18102.6			0.689923			0.344961	−	0.938617i	$-0.387892\pi$
$883$	18102.6			0.689923			0.344961	+	0.938617i	$0.387892\pi$
$884$	1388.88	+	2405.61i	0.0528429	+	0.0915266i
$885$	10637.3	−	18424.4i	0.404034	−	0.699808i
$886$	−11995.4	+	20776.7i	−0.454846	+	0.787817i
$887$	25780.7	+	44653.4i	0.975908	+	1.69032i	0.676905	+	0.736070i	$0.263321\pi$
$887$	25780.7	+	44653.4i	0.975908	+	1.69032i	0.299003	+	0.954252i	$0.403346\pi$
$888$	4608.93			0.174173
$889$	−28.8300	−	3936.66i	−0.00108766	−	0.148517i
$890$	−8218.76			−0.309543
$891$	1257.58	+	2178.19i	0.0472845	+	0.0818991i
$892$	−3160.13	+	5473.50i	−0.118620	+	0.205456i
$893$	38726.6	−	67076.4i	1.45122	−	2.51358i
$894$	−10408.4	−	18027.8i	−0.389382	−	0.674429i
$895$	36342.7			1.35732
$896$	−2044.26	+	1200.30i	−0.0762209	+	0.0447536i
$897$	−8451.95			−0.314607
$898$	6096.37	+	10559.2i	0.226546	+	0.392389i
$899$	20801.4	−	36029.0i	0.771707	−	1.33664i
$900$	−4710.78	+	8159.31i	−0.174473	+	0.302197i
$901$	−14091.8	−	24407.8i	−0.521051	−	0.902487i
$902$	−25149.6			−0.928369
$903$	−2910.46	−	1652.05i	−0.107258	−	0.0608825i
$904$	−4860.71			−0.178833
$905$	−3520.60	−	6097.86i	−0.129313	−	0.223977i
$906$	9363.54	−	16218.1i	0.343359	−	0.594715i
$907$	−5098.55	+	8830.94i	−0.186653	+	0.323293i	−0.944132	−	0.329567i	$-0.893097\pi$
$907$	−5098.55	+	8830.94i	−0.186653	+	0.323293i	0.757479	+	0.652859i	$0.226431\pi$
$908$	7179.02	+	12434.4i	0.262383	+	0.454461i
$909$	−853.218			−0.0311325
$910$	8235.02	+	4674.42i	0.299987	+	0.170281i
$911$	20351.5			0.740149			0.370074	−	0.929002i	$-0.379332\pi$
$911$	20351.5			0.740149			0.370074	+	0.929002i	$0.379332\pi$
$912$	3134.47	+	5429.07i	0.113808	+	0.197121i
$913$	17335.9	−	30026.7i	0.628406	−	1.08843i
$914$	10850.6	−	18793.7i	0.392675	−	0.680133i
$915$	−7756.95	−	13435.4i	−0.280259	−	0.485422i
$916$	−8888.72			−0.320624
$917$	−8550.85	+	5020.69i	−0.307932	+	0.180805i
$918$	2884.60			0.103710
$919$	−9053.29	−	15680.8i	−0.324962	−	0.562851i	0.656542	−	0.754289i	$-0.272018\pi$
$919$	−9053.29	−	15680.8i	−0.324962	−	0.562851i	−0.981505	+	0.191438i	$0.938685\pi$
$920$	−17046.9	+	29526.1i	−0.610890	+	1.05809i
$921$	−10160.8	+	17599.0i	−0.363528	+	0.629650i
$922$	−10257.0	−	17765.7i	−0.366374	−	0.634578i
$923$	1580.14			0.0563497
$924$	−50.5375	−	6900.76i	−0.00179931	−	0.245691i
$925$	−50258.5			−1.78648
$926$	−9954.33	−	17241.4i	−0.353261	−	0.611866i
$927$	−1938.87	+	3358.23i	−0.0686957	+	0.118984i
$928$	−2628.51	+	4552.71i	−0.0929796	+	0.161045i
$929$	22554.7	+	39065.9i	0.796551	+	1.37967i	0.921849	+	0.387548i	$0.126678\pi$
$929$	22554.7	+	39065.9i	0.796551	+	1.37967i	−0.125298	+	0.992119i	$0.539989\pi$
$930$	29879.7			1.05354
$931$	22964.2	+	38463.0i	0.808402	+	1.35400i
$932$	1288.75			0.0452944
$933$	14164.7	+	24534.0i	0.497034	+	0.860888i
$934$	−18307.0	+	31708.7i	−0.641354	+	1.11086i
$935$	−16309.3	+	28248.5i	−0.570449	+	0.988047i
$936$	−468.000	−	810.600i	−0.0163430	−	0.0283069i
$937$	22136.4			0.771788			0.385894	−	0.922543i	$-0.373893\pi$
$937$	22136.4			0.771788			0.385894	+	0.922543i	$0.373893\pi$
$938$	−133.469	−	18224.8i	−0.00464595	−	0.634392i
$939$	−2141.28			−0.0744175
$940$	23324.3	+	40398.9i	0.809314	+	1.40177i
$941$	−25431.9	+	44049.3i	−0.881038	+	1.52600i	−0.0308486	+	0.999524i	$0.509821\pi$
$941$	−25431.9	+	44049.3i	−0.881038	+	1.52600i	−0.850189	+	0.526478i	$0.823512\pi$
$942$	3034.24	−	5255.45i	0.104948	−	0.181775i
$943$	−43881.6	−	76005.1i	−1.51536	−	2.62467i
$944$	5769.91			0.198935
$945$	8479.74	−	4978.93i	0.291900	−	0.171391i
$946$	−3740.69			−0.128563
$947$	3197.77	+	5538.70i	0.109729	+	0.190057i	0.915661	−	0.401952i	$-0.131668\pi$
$947$	3197.77	+	5538.70i	0.109729	+	0.190057i	−0.805931	+	0.592009i	$0.798335\pi$
$948$	1691.62	−	2929.97i	0.0579548	−	0.100381i
$949$	−5111.57	+	8853.50i	−0.174846	+	0.302842i
$950$	−34180.1	−	59201.7i	−1.16732	−	2.02185i
$951$	−14537.4			−0.495696
$952$	−6883.04	−	3907.00i	−0.234328	−	0.133011i
$953$	−17669.2			−0.600590			−0.300295	−	0.953846i	$-0.597085\pi$
$953$	−17669.2			−0.600590			−0.300295	+	0.953846i	$0.597085\pi$
$954$	4748.41	+	8224.49i	0.161148	+	0.279117i
$955$	−28320.9	+	49053.2i	−0.959625	+	1.66212i
$956$	1571.94	−	2722.67i	0.0531800	−	0.0921104i
$957$	−7651.76	−	13253.2i	−0.258460	−	0.447666i
$958$	13615.8			0.459193
$959$	−23026.9	−	13070.7i	−0.775366	−	0.440118i
$960$	−3775.67			−0.126937
$961$	−17169.8	−	29738.9i	−0.576340	−	0.998251i
$962$	2496.51	−	4324.08i	0.0836701	−	0.144921i
$963$	1718.97	−	2977.34i	0.0575213	−	0.0996298i
$964$	4985.46	+	8635.08i	0.166567	+	0.288503i
$965$	−101249.			−3.37755
$966$	20766.8	−	12193.3i	0.691677	−	0.406123i
$967$	1252.94			0.0416669			0.0208334	−	0.999783i	$-0.493368\pi$
$967$	1252.94			0.0416669			0.0208334	+	0.999783i	$0.493368\pi$
$968$	1467.26	+	2541.37i	0.0487185	+	0.0843830i
$969$	−10464.9	+	18125.8i	−0.346937	+	0.600912i
$970$	−11504.7	+	19926.7i	−0.380817	+	0.659594i
$971$	−26772.1	−	46370.6i	−0.884817	−	1.53255i	−0.845923	−	0.533304i	$-0.820950\pi$
$971$	−26772.1	−	46370.6i	−0.884817	−	1.53255i	−0.0388934	−	0.999243i	$-0.512383\pi$
$972$	−972.000			−0.0320750
$973$	−378.064	−	51623.7i	−0.0124565	−	1.70090i
$974$	−10792.5			−0.355046
$975$	5103.35	+	8839.25i	0.167629	+	0.290341i
$976$	2103.76	−	3643.82i	0.0689957	−	0.119504i
$977$	−23303.1	+	40362.2i	−0.763084	+	1.32170i	0.178170	+	0.984000i	$0.442982\pi$
$977$	−23303.1	+	40362.2i	−0.763084	+	1.32170i	−0.941254	+	0.337700i	$0.890351\pi$
$978$	7484.84	+	12964.1i	0.244723	+	0.423872i
$979$	6488.79			0.211831
$980$	−26977.4	+	395.157i	−0.879349	+	0.0128805i
$981$	−10920.0			−0.355400
$982$	12396.8	+	21471.9i	0.402849	+	0.697755i
$983$	17988.9	−	31157.7i	0.583679	−	1.01096i	−0.411360	−	0.911473i	$-0.634946\pi$
$983$	17988.9	−	31157.7i	0.583679	−	1.01096i	0.995039	−	0.0994887i	$-0.0317207\pi$
$984$	4859.61	−	8417.09i	0.157438	−	0.272690i
$985$	−12864.2	−	22281.4i	−0.416128	−	0.720755i
$986$	−17551.4			−0.566886
$987$	−241.301	−	32949.0i	−0.00778186	−	1.06259i
$988$	6791.36			0.218686
$989$	−6526.85	−	11304.8i	−0.209850	−	0.363471i
$990$	5495.60	−	9518.66i	0.176426	−	0.305579i
$991$	5302.67	−	9184.49i	0.169975	−	0.294405i	−0.768436	−	0.639927i	$-0.778965\pi$
$991$	5302.67	−	9184.49i	0.169975	−	0.294405i	0.938411	+	0.345522i	$0.112298\pi$
$992$	4051.84	+	7017.99i	0.129684	+	0.224618i
$993$	−20217.8			−0.646114
$994$	−3882.46	+	2279.61i	−0.123887	+	0.0727413i
$995$	−93911.9			−2.99217
$996$	6699.59	+	11604.0i	0.213137	+	0.369164i
$997$	2077.64	−	3598.58i	0.0659975	−	0.114311i	−0.831139	−	0.556065i	$-0.812310\pi$
$997$	2077.64	−	3598.58i	0.0659975	−	0.114311i	0.897136	+	0.441754i	$0.145644\pi$
$998$	9488.16	−	16434.0i	0.300944	−	0.521251i
$999$	−2592.53	−	4490.39i	−0.0821060	−	0.142212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.i.b.235.2	yes	8
7.2	even	3	inner	546.4.i.b.79.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.i.b.79.2	✓	8	7.2	even	3	inner
546.4.i.b.235.2	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-9.83247 - 17.0303i) q^{5} -6.00000 q^{6} +(-0.135629 - 18.5198i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-19.6649 + 34.0607i) q^{10} +(15.5257 - 26.8912i) q^{11} +(6.00000 + 10.3923i) q^{12} +13.0000 q^{13} +(-31.9415 + 18.7547i) q^{14} -58.9948 q^{15} +(-8.00000 - 13.8564i) q^{16} +(26.7092 - 46.2618i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-65.3015 - 113.106i) q^{19} +78.6598 q^{20} +(-48.3192 - 27.4273i) q^{21} -62.1027 q^{22} +(-108.358 - 187.682i) q^{23} +(12.0000 - 20.7846i) q^{24} +(-130.855 + 226.648i) q^{25} +(-13.0000 - 22.5167i) q^{26} -27.0000 q^{27} +(64.4256 + 36.5697i) q^{28} +164.282 q^{29} +(58.9948 + 102.182i) q^{30} +(126.620 - 219.312i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-46.5770 - 80.6737i) q^{33} -106.837 q^{34} +(-314.064 + 184.405i) q^{35} +36.0000 q^{36} +(96.0195 + 166.311i) q^{37} +(-130.603 + 226.211i) q^{38} +(19.5000 - 33.7750i) q^{39} +(-78.6598 - 136.243i) q^{40} +404.967 q^{41} +(0.813773 + 111.119i) q^{42} +60.2339 q^{43} +(62.1027 + 107.565i) q^{44} +(-88.4922 + 153.273i) q^{45} +(-216.717 + 375.364i) q^{46} +(296.521 + 513.590i) q^{47} -48.0000 q^{48} +(-342.963 + 5.02363i) q^{49} +523.420 q^{50} +(-80.1277 - 138.785i) q^{51} +(-26.0000 + 45.0333i) q^{52} +(263.801 - 456.916i) q^{53} +(27.0000 + 46.7654i) q^{54} -610.623 q^{55} +(-1.08503 - 148.158i) q^{56} -391.809 q^{57} +(-164.282 - 284.545i) q^{58} +(-180.310 + 312.306i) q^{59} +(117.990 - 204.364i) q^{60} +(131.485 + 227.739i) q^{61} -506.480 q^{62} +(-143.737 + 84.3961i) q^{63} +64.0000 q^{64} +(-127.822 - 221.394i) q^{65} +(-93.1540 + 161.347i) q^{66} +(-246.018 + 426.116i) q^{67} +(106.837 + 185.047i) q^{68} -650.150 q^{69} +(633.463 + 359.570i) q^{70} +121.549 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-393.198 + 681.039i) q^{73} +(192.039 - 332.621i) q^{74} +(392.565 + 679.943i) q^{75} +522.412 q^{76} +(-500.125 - 283.884i) q^{77} -78.0000 q^{78} +(-140.968 - 244.164i) q^{79} +(-157.320 + 272.485i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-404.967 - 701.424i) q^{82} +1116.60 q^{83} +(191.649 - 112.528i) q^{84} -1050.47 q^{85} +(-60.2339 - 104.328i) q^{86} +(246.423 - 426.817i) q^{87} +(124.205 - 215.130i) q^{88} +(104.485 + 180.973i) q^{89} +353.969 q^{90} +(-1.76318 - 240.757i) q^{91} +866.866 q^{92} +(-379.860 - 657.937i) q^{93} +(593.043 - 1027.18i) q^{94} +(-1284.15 + 2224.21i) q^{95} +(48.0000 + 83.1384i) q^{96} +585.034 q^{97} +(351.664 + 589.006i) q^{98} -279.462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 12 q^{3} - 16 q^{4} - 34 q^{5} - 48 q^{6} + 35 q^{7} + 64 q^{8} - 36 q^{9} - 68 q^{10} + 74 q^{11} + 48 q^{12} + 104 q^{13} - 80 q^{14} - 204 q^{15} - 64 q^{16} + 49 q^{17} - 72 q^{18} + 41 q^{19}+ \cdots - 1332 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 12 * q^3 - 16 * q^4 - 34 * q^5 - 48 * q^6 + 35 * q^7 + 64 * q^8 - 36 * q^9 - 68 * q^10 + 74 * q^11 + 48 * q^12 + 104 * q^13 - 80 * q^14 - 204 * q^15 - 64 * q^16 + 49 * q^17 - 72 * q^18 + 41 * q^19 + 272 * q^20 - 15 * q^21 - 296 * q^22 - 48 * q^23 + 96 * q^24 - 330 * q^25 - 104 * q^26 - 216 * q^27 + 20 * q^28 + 330 * q^29 + 204 * q^30 - 349 * q^31 - 128 * q^32 - 222 * q^33 - 196 * q^34 - 827 * q^35 + 288 * q^36 + 563 * q^37 + 82 * q^38 + 156 * q^39 - 272 * q^40 - 548 * q^41 - 210 * q^42 + 1136 * q^43 + 296 * q^44 - 306 * q^45 - 96 * q^46 + 186 * q^47 - 384 * q^48 + 275 * q^49 + 1320 * q^50 - 147 * q^51 - 208 * q^52 + 236 * q^53 + 216 * q^54 + 1034 * q^55 + 280 * q^56 + 246 * q^57 - 330 * q^58 + 204 * q^59 + 408 * q^60 - 659 * q^61 + 1396 * q^62 - 360 * q^63 + 512 * q^64 - 442 * q^65 - 444 * q^66 + 297 * q^67 + 196 * q^68 - 288 * q^69 + 704 * q^70 - 1554 * q^71 - 288 * q^72 - 1778 * q^73 + 1126 * q^74 + 990 * q^75 - 328 * q^76 - 3320 * q^77 - 624 * q^78 - 1295 * q^79 - 544 * q^80 - 324 * q^81 + 548 * q^82 + 8778 * q^83 + 480 * q^84 - 2236 * q^85 - 1136 * q^86 + 495 * q^87 + 592 * q^88 + 1151 * q^89 + 1224 * q^90 + 455 * q^91 + 384 * q^92 + 1047 * q^93 + 372 * q^94 - 1355 * q^95 + 384 * q^96 + 1260 * q^97 + 2686 * q^98 - 1332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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