LMFDB - Embedded newform 546.4.s.d.43.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(43,546)] 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("546.43"); 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, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,36] 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	546.43
Dual form			546.4.s.d.127.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} -3.23892i q^{5} +(5.19615 - 3.00000i) q^{6} +(-6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 - 7.79423i) q^{9} +(3.23892 - 5.60997i) q^{10} +(0.0746475 + 0.0430977i) q^{11} +12.0000 q^{12} +(43.1998 - 18.1872i) q^{13} -14.0000 q^{14} +(-8.41495 - 4.85838i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(53.3702 + 92.4400i) q^{17} -18.0000i q^{18} +(-27.0793 + 15.6342i) q^{19} +(11.2199 - 6.47783i) q^{20} +21.0000i q^{21} +(0.0861955 + 0.149295i) q^{22} +(82.7370 - 143.305i) q^{23} +(20.7846 + 12.0000i) q^{24} +114.509 q^{25} +(93.0115 + 11.6987i) q^{26} -27.0000 q^{27} +(-24.2487 - 14.0000i) q^{28} +(67.1563 - 116.318i) q^{29} +(-9.71675 - 16.8299i) q^{30} -222.063i q^{31} +(-27.7128 + 16.0000i) q^{32} +(0.223942 - 0.129293i) q^{33} +213.481i q^{34} +(11.3362 + 19.6349i) q^{35} +(18.0000 - 31.1769i) q^{36} +(234.621 + 135.458i) q^{37} -62.5370 q^{38} +(17.5481 - 139.517i) q^{39} +25.9113 q^{40} +(313.273 + 180.868i) q^{41} +(-21.0000 + 36.3731i) q^{42} +(97.5880 + 169.027i) q^{43} +0.344782i q^{44} +(-25.2449 + 14.5751i) q^{45} +(286.609 - 165.474i) q^{46} -252.226i q^{47} +(24.0000 + 41.5692i) q^{48} +(24.5000 - 42.4352i) q^{49} +(198.336 + 114.509i) q^{50} +320.221 q^{51} +(149.402 + 113.274i) q^{52} -414.710 q^{53} +(-46.7654 - 27.0000i) q^{54} +(0.139590 - 0.241777i) q^{55} +(-28.0000 - 48.4974i) q^{56} +93.8055i q^{57} +(232.636 - 134.313i) q^{58} +(-214.760 + 123.992i) q^{59} -38.8670i q^{60} +(-445.652 - 771.891i) q^{61} +(222.063 - 384.624i) q^{62} +(54.5596 + 31.5000i) q^{63} -64.0000 q^{64} +(-58.9068 - 139.921i) q^{65} +0.517173 q^{66} +(485.822 + 280.490i) q^{67} +(-213.481 + 369.760i) q^{68} +(-248.211 - 429.914i) q^{69} +45.3448i q^{70} +(87.4851 - 50.5096i) q^{71} +(62.3538 - 36.0000i) q^{72} +234.703i q^{73} +(270.917 + 469.242i) q^{74} +(171.764 - 297.504i) q^{75} +(-108.317 - 62.5370i) q^{76} -0.603368 q^{77} +(169.911 - 224.103i) q^{78} +610.972 q^{79} +(44.8798 + 25.9113i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(361.736 + 626.545i) q^{82} -949.997i q^{83} +(-72.7461 + 42.0000i) q^{84} +(299.405 - 172.862i) q^{85} +390.352i q^{86} +(-201.469 - 348.955i) q^{87} +(-0.344782 + 0.597180i) q^{88} +(1263.02 + 729.202i) q^{89} -58.3005 q^{90} +(-198.230 + 261.453i) q^{91} +661.896 q^{92} +(-576.937 - 333.095i) q^{93} +(252.226 - 436.868i) q^{94} +(50.6380 + 87.7076i) q^{95} +96.0000i q^{96} +(-331.431 + 191.352i) q^{97} +(84.8705 - 49.0000i) q^{98} -0.775759i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{3} + 48 q^{4} - 108 q^{9} - 24 q^{10} - 174 q^{11} + 288 q^{12} - 96 q^{13} - 336 q^{14} - 90 q^{15} - 192 q^{16} + 140 q^{17} - 60 q^{19} + 120 q^{20} - 128 q^{22} + 34 q^{23} - 1004 q^{25}+ \cdots - 3936 q^{97}+O(q^{100}) $ 24 * q + 36 * q^3 + 48 * q^4 - 108 * q^9 - 24 * q^10 - 174 * q^11 + 288 * q^12 - 96 * q^13 - 336 * q^14 - 90 * q^15 - 192 * q^16 + 140 * q^17 - 60 * q^19 + 120 * q^20 - 128 * q^22 + 34 * q^23 - 1004 * q^25 - 144 * q^26 - 648 * q^27 + 54 * q^29 + 72 * q^30 - 522 * q^33 - 84 * q^35 + 432 * q^36 + 1416 * q^37 + 1056 * q^38 + 108 * q^39 - 192 * q^40 - 942 * q^41 - 504 * q^42 + 762 * q^43 - 270 * q^45 + 636 * q^46 + 576 * q^48 + 588 * q^49 + 720 * q^50 + 840 * q^51 - 528 * q^52 + 184 * q^53 - 256 * q^55 - 672 * q^56 - 2088 * q^58 + 2322 * q^59 - 1274 * q^61 - 232 * q^62 - 1536 * q^64 - 1298 * q^65 - 768 * q^66 - 2472 * q^67 - 560 * q^68 - 102 * q^69 - 2196 * q^71 - 348 * q^74 - 1506 * q^75 - 240 * q^76 + 896 * q^77 - 468 * q^78 - 520 * q^79 + 480 * q^80 - 972 * q^81 - 244 * q^82 + 7974 * q^85 - 162 * q^87 + 512 * q^88 + 1032 * q^89 + 432 * q^90 + 546 * q^91 + 272 * q^92 - 2880 * q^93 - 1104 * q^94 - 2574 * q^95 - 3936 * q^97

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	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
$5$		−	3.23892i		−	0.289698i	−0.989454	−	0.144849i	$-0.953730\pi$
$5$		−	3.23892i		−	0.289698i	0.989454	−	0.144849i	$-0.0462696\pi$
$6$	5.19615	−	3.00000i	0.353553	−	0.204124i
$7$	−6.06218	+	3.50000i	−0.327327	+	0.188982i
$7$	−6.06218	+	3.50000i	−0.327327	+	0.188982i
$8$			8.00000i			0.353553i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	3.23892	−	5.60997i	0.102424	−	0.177403i
$11$	0.0746475	+	0.0430977i	0.00204610	+	0.00118131i	0.501023	−	0.865434i	$-0.332957\pi$
$11$	0.0746475	+	0.0430977i	0.00204610	+	0.00118131i	−0.498977	+	0.866615i	$0.666291\pi$
$12$	12.0000			0.288675
$13$	43.1998	−	18.1872i	0.921652	−	0.388017i
$13$	43.1998	−	18.1872i	0.921652	−	0.388017i
$14$	−14.0000			−0.267261
$15$	−8.41495	−	4.85838i	−0.144849	−	0.0836285i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	53.3702	+	92.4400i	0.761423	+	1.31882i	0.942117	+	0.335284i	$0.108832\pi$
$17$	53.3702	+	92.4400i	0.761423	+	1.31882i	−0.180695	+	0.983539i	$0.557835\pi$
$18$		−	18.0000i		−	0.235702i
$19$	−27.0793	+	15.6342i	−0.326969	+	0.188776i	−0.654495	−	0.756067i	$-0.727119\pi$
$19$	−27.0793	+	15.6342i	−0.326969	+	0.188776i	0.327525	+	0.944842i	$0.393785\pi$
$20$	11.2199	−	6.47783i	0.125443	−	0.0724244i
$21$			21.0000i			0.218218i
$22$	0.0861955	+	0.149295i	0.000835315	+	0.00144681i
$23$	82.7370	−	143.305i	0.750081	−	1.29918i	−0.197702	−	0.980262i	$-0.563348\pi$
$23$	82.7370	−	143.305i	0.750081	−	1.29918i	0.947783	−	0.318916i	$-0.103319\pi$
$24$	20.7846	+	12.0000i	0.176777	+	0.102062i
$25$	114.509			0.916075
$26$	93.0115	+	11.6987i	0.701579	+	0.0882425i
$27$	−27.0000			−0.192450
$28$	−24.2487	−	14.0000i	−0.163663	−	0.0944911i
$29$	67.1563	−	116.318i	0.430021	−	0.744819i	−0.566853	−	0.823819i	$-0.691839\pi$
$29$	67.1563	−	116.318i	0.430021	−	0.744819i	0.996875	+	0.0790000i	$0.0251727\pi$
$30$	−9.71675	−	16.8299i	−0.0591343	−	0.102424i
$31$		−	222.063i		−	1.28657i	−0.765626	−	0.643285i	$-0.777571\pi$
$31$		−	222.063i		−	1.28657i	0.765626	−	0.643285i	$-0.222429\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	0.223942	−	0.129293i	0.00118131	−	0.000682032i
$34$			213.481i			1.07681i
$35$	11.3362	+	19.6349i	0.0547477	+	0.0948258i
$36$	18.0000	−	31.1769i	0.0833333	−	0.144338i
$37$	234.621	+	135.458i	1.04247	+	0.601871i	0.920532	−	0.390666i	$-0.127755\pi$
$37$	234.621	+	135.458i	1.04247	+	0.601871i	0.121939	+	0.992538i	$0.461089\pi$
$38$	−62.5370			−0.266969
$39$	17.5481	−	139.517i	0.0720497	−	0.572837i
$40$	25.9113			0.102424
$41$	313.273	+	180.868i	1.19329	+	0.688947i	0.959052	−	0.283232i	$-0.0914066\pi$
$41$	313.273	+	180.868i	1.19329	+	0.688947i	0.234240	+	0.972179i	$0.424740\pi$
$42$	−21.0000	+	36.3731i	−0.0771517	+	0.133631i
$43$	97.5880	+	169.027i	0.346094	+	0.599452i	0.985552	−	0.169374i	$-0.0541745\pi$
$43$	97.5880	+	169.027i	0.346094	+	0.599452i	−0.639458	+	0.768826i	$0.720841\pi$
$44$			0.344782i			0.00118131i
$45$	−25.2449	+	14.5751i	−0.0836285	+	0.0482829i
$46$	286.609	−	165.474i	0.918658	−	0.530387i
$47$		−	252.226i		−	0.782786i	−0.920224	−	0.391393i	$-0.871993\pi$
$47$		−	252.226i		−	0.782786i	0.920224	−	0.391393i	$-0.128007\pi$
$48$	24.0000	+	41.5692i	0.0721688	+	0.125000i
$49$	24.5000	−	42.4352i	0.0714286	−	0.123718i
$50$	198.336	+	114.509i	0.560979	+	0.323882i
$51$	320.221			0.879215
$52$	149.402	+	113.274i	0.398429	+	0.302083i
$53$	−414.710			−1.07481			−0.537404	−	0.843325i	$-0.680595\pi$
$53$	−414.710			−1.07481			−0.537404	+	0.843325i	$0.680595\pi$
$54$	−46.7654	−	27.0000i	−0.117851	−	0.0680414i
$55$	0.139590	−	0.241777i	0.000342224	−	0.000592749i
$56$	−28.0000	−	48.4974i	−0.0668153	−	0.115728i
$57$			93.8055i			0.217980i
$58$	232.636	−	134.313i	0.526666	−	0.304071i
$59$	−214.760	+	123.992i	−0.473888	+	0.273599i	−0.717866	−	0.696182i	$-0.754881\pi$
$59$	−214.760	+	123.992i	−0.473888	+	0.273599i	0.243978	+	0.969781i	$0.421547\pi$
$60$		−	38.8670i		−	0.0836285i
$61$	−445.652	−	771.891i	−0.935407	−	1.62017i	−0.773906	−	0.633301i	$-0.781700\pi$
$61$	−445.652	−	771.891i	−0.935407	−	1.62017i	−0.161502	−	0.986872i	$-0.551634\pi$
$62$	222.063	−	384.624i	0.454872	−	0.787861i
$63$	54.5596	+	31.5000i	0.109109	+	0.0629941i
$64$	−64.0000			−0.125000
$65$	−58.9068	−	139.921i	−0.112408	−	0.267000i
$66$	0.517173			0.000964539
$67$	485.822	+	280.490i	0.885860	+	0.511452i	0.872586	−	0.488460i	$-0.162441\pi$
$67$	485.822	+	280.490i	0.885860	+	0.511452i	0.0132742	+	0.999912i	$0.495775\pi$
$68$	−213.481	+	369.760i	−0.380711	+	0.659411i
$69$	−248.211	−	429.914i	−0.433059	−	0.750081i
$70$			45.3448i			0.0774249i
$71$	87.4851	−	50.5096i	0.146233	−	0.0844279i	−0.425098	−	0.905147i	$-0.639760\pi$
$71$	87.4851	−	50.5096i	0.146233	−	0.0844279i	0.571332	+	0.820719i	$0.306427\pi$
$72$	62.3538	−	36.0000i	0.102062	−	0.0589256i
$73$			234.703i			0.376300i	0.982140	+	0.188150i	$0.0602490\pi$
$73$			234.703i			0.376300i	−0.982140	+	0.188150i	$0.939751\pi$
$74$	270.917	+	469.242i	0.425587	+	0.737139i
$75$	171.764	−	297.504i	0.264448	−	0.458038i
$76$	−108.317	−	62.5370i	−0.163485	−	0.0943879i
$77$	−0.603368			−0.000892990
$78$	169.911	−	224.103i	0.246650	−	0.325316i
$79$	610.972			0.870123			0.435062	−	0.900401i	$-0.356727\pi$
$79$	610.972			0.870123			0.435062	+	0.900401i	$0.356727\pi$
$80$	44.8798	+	25.9113i	0.0627214	+	0.0362122i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	361.736	+	626.545i	0.487159	+	0.843784i
$83$		−	949.997i		−	1.25633i	−0.778078	−	0.628167i	$-0.783805\pi$
$83$		−	949.997i		−	1.25633i	0.778078	−	0.628167i	$-0.216195\pi$
$84$	−72.7461	+	42.0000i	−0.0944911	+	0.0545545i
$85$	299.405	−	172.862i	0.382060	−	0.220582i
$86$			390.352i			0.489451i
$87$	−201.469	−	348.955i	−0.248273	−	0.430021i
$88$	−0.344782	+	0.597180i	−0.000417658	+	0.000723404i
$89$	1263.02	+	729.202i	1.50426	+	0.868486i	0.999988	+	0.00494289i	$0.00157338\pi$
$89$	1263.02	+	729.202i	1.50426	+	0.868486i	0.504275	+	0.863543i	$0.331760\pi$
$90$	−58.3005			−0.0682824
$91$	−198.230	+	261.453i	−0.228353	+	0.301184i
$92$	661.896			0.750081
$93$	−576.937	−	333.095i	−0.643285	−	0.371401i
$94$	252.226	−	436.868i	0.276756	−	0.479356i
$95$	50.6380	+	87.7076i	0.0546879	+	0.0947222i
$96$			96.0000i			0.102062i
$97$	−331.431	+	191.352i	−0.346925	+	0.200297i	−0.663330	−	0.748327i	$-0.730857\pi$
$97$	−331.431	+	191.352i	−0.346925	+	0.200297i	0.316405	+	0.948624i	$0.397524\pi$
$98$	84.8705	−	49.0000i	0.0874818	−	0.0505076i
$99$		−	0.775759i		−	0.000787543i
$100$	229.019	+	396.672i	0.229019	+	0.396672i
$101$	314.927	−	545.469i	0.310261	−	0.537388i	−0.668158	−	0.744020i	$-0.732917\pi$
$101$	314.927	−	545.469i	0.310261	−	0.537388i	0.978419	+	0.206632i	$0.0662502\pi$
$102$	554.640	+	320.221i	0.538407	+	0.310850i
$103$	−492.646			−0.471280			−0.235640	−	0.971840i	$-0.575719\pi$
$103$	−492.646			−0.471280			−0.235640	+	0.971840i	$0.575719\pi$
$104$	145.498	+	345.599i	0.137185	+	0.325853i
$105$	68.0173			0.0632172
$106$	−718.299	−	414.710i	−0.658183	−	0.380002i
$107$	−418.538	+	724.930i	−0.378146	+	0.654968i	−0.990793	−	0.135389i	$-0.956772\pi$
$107$	−418.538	+	724.930i	−0.378146	+	0.654968i	0.612646	+	0.790357i	$0.290105\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$			2011.23i			1.76735i	0.468101	+	0.883675i	$0.344938\pi$
$109$			2011.23i			1.76735i	−0.468101	+	0.883675i	$0.655062\pi$
$110$	0.483554	−	0.279180i	0.000419137	−	0.000241989i
$111$	703.863	−	406.375i	0.601871	−	0.347490i
$112$		−	112.000i		−	0.0944911i
$113$	151.151	+	261.801i	0.125832	+	0.217948i	0.922058	−	0.387052i	$-0.126507\pi$
$113$	151.151	+	261.801i	0.125832	+	0.217948i	−0.796226	+	0.605000i	$0.793173\pi$
$114$	−93.8055	+	162.476i	−0.0770674	+	0.133485i
$115$	−464.152	−	267.978i	−0.376369	−	0.217297i
$116$	537.251			0.430021
$117$	−336.154	−	254.867i	−0.265620	−	0.201389i
$118$	−495.967			−0.386928
$119$	−647.080	−	373.592i	−0.498468	−	0.287791i
$120$	38.8670	−	67.3196i	0.0295671	−	0.0512118i
$121$	−665.496	−	1152.67i	−0.499997	−	0.866021i
$122$		−	1782.61i		−	1.32287i
$123$	939.818	−	542.604i	0.688947	−	0.397764i
$124$	769.249	−	444.126i	0.557102	−	0.321643i
$125$		−	775.751i		−	0.555082i
$126$	63.0000	+	109.119i	0.0445435	+	0.0771517i
$127$	−899.424	+	1557.85i	−0.628433	+	1.08848i	0.359433	+	0.933171i	$0.382970\pi$
$127$	−899.424	+	1557.85i	−0.628433	+	1.08848i	−0.987866	+	0.155307i	$0.950363\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	585.528			0.399635
$130$	37.8911	−	301.257i	0.0255636	−	0.203246i
$131$	996.229			0.664435			0.332217	−	0.943203i	$-0.392203\pi$
$131$	996.229			0.664435			0.332217	+	0.943203i	$0.392203\pi$
$132$	0.895770	+	0.517173i	0.000590657	+	0.000341016i
$133$	109.440	−	189.555i	0.0713506	−	0.123583i
$134$	560.979	+	971.645i	0.361651	+	0.626398i
$135$			87.4508i			0.0557523i
$136$	−739.520	+	426.962i	−0.466274	+	0.269204i
$137$	−1030.04	+	594.696i	−0.642355	+	0.370864i	−0.785521	−	0.618835i	$-0.787605\pi$
$137$	−1030.04	+	594.696i	−0.642355	+	0.370864i	0.143166	+	0.989699i	$0.454272\pi$
$138$		−	992.844i		−	0.612438i
$139$	867.513	+	1502.58i	0.529363	+	0.916884i	0.999413	+	0.0342442i	$0.0109024\pi$
$139$	867.513	+	1502.58i	0.529363	+	0.916884i	−0.470050	+	0.882640i	$0.655764\pi$
$140$	−45.3448	+	78.5396i	−0.0273738	+	0.0474129i
$141$	−655.302	−	378.339i	−0.391393	−	0.225971i
$142$	202.038			0.119399
$143$	4.00859	+	0.504188i	0.00234416	+	0.000294841i
$144$	144.000			0.0833333
$145$	−376.745	−	217.514i	−0.215772	−	0.124576i
$146$	−234.703	+	406.517i	−0.133042	+	0.230435i
$147$	−73.5000	−	127.306i	−0.0412393	−	0.0714286i
$148$			1083.67i			0.601871i
$149$	−1275.61	+	736.472i	−0.701354	+	0.404927i	−0.807852	−	0.589386i	$-0.799370\pi$
$149$	−1275.61	+	736.472i	−0.701354	+	0.404927i	0.106497	+	0.994313i	$0.466036\pi$
$150$	595.008	−	343.528i	0.323882	−	0.186993i
$151$		−	489.295i		−	0.263697i	−0.991270	−	0.131849i	$-0.957909\pi$
$151$		−	489.295i		−	0.263697i	0.991270	−	0.131849i	$-0.0420913\pi$
$152$	−125.074	−	216.634i	−0.0667423	−	0.115601i
$153$	480.332	−	831.960i	0.253808	−	0.439608i
$154$	−1.04506	−	0.603368i	−0.000546842	−	0.000315720i
$155$	−719.244			−0.372716
$156$	518.398	−	218.246i	0.266058	−	0.112011i
$157$	−1429.98			−0.726911			−0.363455	−	0.931612i	$-0.618403\pi$
$157$	−1429.98			−0.726911			−0.363455	+	0.931612i	$0.618403\pi$
$158$	1058.23	+	610.972i	0.532840	+	0.307635i
$159$	−622.066	+	1077.45i	−0.310270	+	0.537404i
$160$	51.8227	+	89.7595i	0.0256059	+	0.0443507i
$161$			1158.32i			0.567008i
$162$	−140.296	+	81.0000i	−0.0680414	+	0.0392837i
$163$	−2365.24	+	1365.57i	−1.13657	+	0.656197i	−0.945578	−	0.325396i	$-0.894503\pi$
$163$	−2365.24	+	1365.57i	−1.13657	+	0.656197i	−0.190988	+	0.981592i	$0.561169\pi$
$164$			1446.94i			0.688947i
$165$	−0.418770	−	0.725331i	−0.000197583	−	0.000342224i
$166$	949.997	−	1645.44i	0.444181	−	0.769344i
$167$	−446.437	−	257.750i	−0.206864	−	0.119433i	0.392989	−	0.919543i	$-0.371441\pi$
$167$	−446.437	−	257.750i	−0.206864	−	0.119433i	−0.599853	+	0.800110i	$0.704774\pi$
$168$	−168.000			−0.0771517
$169$	1535.45	−	1571.37i	0.698886	−	0.715233i
$170$	691.447			0.311950
$171$	243.714	+	140.708i	0.108990	+	0.0629253i
$172$	−390.352	+	676.110i	−0.173047	+	0.299726i
$173$	248.006	+	429.559i	0.108992	+	0.188779i	0.915362	−	0.402632i	$-0.131905\pi$
$173$	248.006	+	429.559i	0.108992	+	0.188779i	−0.806370	+	0.591411i	$0.798571\pi$
$174$		−	805.876i		−	0.351111i
$175$	−694.176	+	400.783i	−0.299856	+	0.173122i
$176$	−1.19436	+	0.689564i	−0.000511524	+	0.000295329i
$177$			743.950i			0.315925i
$178$	1458.40	+	2526.03i	0.614113	+	1.06367i
$179$	1640.46	−	2841.36i	0.684993	−	1.18644i	−0.288445	−	0.957496i	$-0.593138\pi$
$179$	1640.46	−	2841.36i	0.684993	−	1.18644i	0.973439	−	0.228947i	$-0.0735283\pi$
$180$	−100.979	−	58.3005i	−0.0418142	−	0.0241415i
$181$	133.871			0.0549755			0.0274878	−	0.999622i	$-0.491249\pi$
$181$	133.871			0.0549755			0.0274878	+	0.999622i	$0.491249\pi$
$182$	−604.798	+	254.621i	−0.246322	+	0.103702i
$183$	−2673.91			−1.08012
$184$	1146.44	+	661.896i	0.459329	+	0.265194i
$185$	438.739	−	759.918i	0.174361	−	0.302001i
$186$	−666.189	−	1153.87i	−0.262620	−	0.454872i
$187$			9.20055i			0.00359792i
$188$	873.736	−	504.452i	0.338956	−	0.195696i
$189$	163.679	−	94.5000i	0.0629941	−	0.0363696i
$190$			202.552i			0.0773404i
$191$	316.332	+	547.903i	0.119838	+	0.207565i	0.919703	−	0.392614i	$-0.128429\pi$
$191$	316.332	+	547.903i	0.119838	+	0.207565i	−0.799866	+	0.600179i	$0.795096\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	−3342.94	−	1930.04i	−1.24679	−	0.719833i	−0.276319	−	0.961066i	$-0.589115\pi$
$193$	−3342.94	−	1930.04i	−1.24679	−	0.719833i	−0.970467	+	0.241233i	$0.922448\pi$
$194$	−765.407			−0.283263
$195$	−451.885	−	56.8367i	−0.165949	−	0.0208726i
$196$	196.000			0.0714286
$197$	2214.95	+	1278.80i	0.801061	+	0.462493i	0.843842	−	0.536592i	$-0.180289\pi$
$197$	2214.95	+	1278.80i	0.801061	+	0.462493i	−0.0427813	+	0.999084i	$0.513622\pi$
$198$	0.775759	−	1.34365i	0.000278438	−	0.000482270i
$199$	−1603.76	−	2777.80i	−0.571295	−	0.989513i	−0.996433	−	0.0843840i	$-0.973108\pi$
$199$	−1603.76	−	2777.80i	−0.571295	−	0.989513i	0.425138	−	0.905129i	$-0.360226\pi$
$200$			916.075i			0.323882i
$201$	1457.47	−	841.469i	0.511452	−	0.295287i
$202$	1090.94	−	629.853i	0.379991	−	0.219388i
$203$			940.189i			0.325066i
$204$	640.443	+	1109.28i	0.219804	+	0.380711i
$205$	585.816	−	1014.66i	0.199586	−	0.345694i
$206$	−853.288	−	492.646i	−0.288599	−	0.166623i
$207$	−1489.27			−0.500054
$208$	−93.5896	+	744.092i	−0.0311984	+	0.248046i
$209$	−2.69520			−0.000892014
$210$	117.809	+	68.0173i	0.0387125	+	0.0223507i
$211$	−1884.74	+	3264.47i	−0.614934	+	1.06510i	0.375463	+	0.926838i	$0.377484\pi$
$211$	−1884.74	+	3264.47i	−0.614934	+	1.06510i	−0.990396	+	0.138259i	$0.955849\pi$
$212$	−829.421	−	1436.60i	−0.268702	−	0.465406i
$213$		−	303.057i		−	0.0974889i
$214$	−1449.86	+	837.077i	−0.463133	+	0.267390i
$215$	547.466	−	316.080i	0.173660	−	0.100263i
$216$		−	216.000i		−	0.0680414i
$217$	777.221	+	1346.19i	0.243139	+	0.421129i
$218$	−2011.23	+	3483.56i	−0.624853	+	1.08228i
$219$	609.775	+	352.054i	0.188150	+	0.108628i
$220$	1.11672			0.000342224
$221$	3986.81	+	3022.74i	1.21349	+	0.920051i
$222$	1625.50			0.491426
$223$	−4187.19	−	2417.47i	−1.25738	−	0.725947i	−0.284813	−	0.958583i	$-0.591931\pi$
$223$	−4187.19	−	2417.47i	−1.25738	−	0.725947i	−0.972564	+	0.232637i	$0.925265\pi$
$224$	112.000	−	193.990i	0.0334077	−	0.0578638i
$225$	−515.292	−	892.513i	−0.152679	−	0.264448i
$226$			604.603i			0.177954i
$227$	−3724.49	+	2150.33i	−1.08900	+	0.628734i	−0.933310	−	0.359072i	$-0.883093\pi$
$227$	−3724.49	+	2150.33i	−1.08900	+	0.628734i	−0.155689	+	0.987806i	$0.549760\pi$
$228$	−324.952	+	187.611i	−0.0943879	+	0.0544949i
$229$			5310.28i			1.53237i	0.642619	+	0.766186i	$0.277848\pi$
$229$			5310.28i			1.53237i	−0.642619	+	0.766186i	$0.722152\pi$
$230$	−535.957	−	928.304i	−0.153652	−	0.266133i
$231$	−0.905052	+	1.56760i	−0.000257784	+	0.000446495i
$232$	930.545	+	537.251i	0.263333	+	0.152035i
$233$	−1219.98			−0.343021			−0.171510	−	0.985182i	$-0.554865\pi$
$233$	−1219.98			−0.343021			−0.171510	+	0.985182i	$0.554865\pi$
$234$	−327.369	−	777.597i	−0.0914564	−	0.217236i
$235$	−816.939			−0.226771
$236$	−859.040	−	495.967i	−0.236944	−	0.136800i
$237$	916.458	−	1587.35i	0.251183	−	0.435062i
$238$	−747.183	−	1294.16i	−0.203499	−	0.352470i
$239$		−	4515.53i		−	1.22211i	−0.791587	−	0.611057i	$-0.790745\pi$
$239$		−	4515.53i		−	1.22211i	0.791587	−	0.611057i	$-0.209255\pi$
$240$	134.639	−	77.7340i	0.0362122	−	0.0209071i
$241$	−5248.65	+	3030.31i	−1.40289	+	0.809956i	−0.994688	−	0.102938i	$-0.967176\pi$
$241$	−5248.65	+	3030.31i	−1.40289	+	0.809956i	−0.408197	+	0.912894i	$0.633842\pi$
$242$		−	2661.99i		−	0.707103i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	1782.61	−	3087.57i	0.467704	−	0.810087i
$245$	−137.444	−	79.3535i	−0.0358408	−	0.0206927i
$246$	2170.42			0.562523
$247$	−885.479	+	1167.89i	−0.228104	+	0.300855i
$248$	1776.50			0.454872
$249$	−2468.17	−	1425.00i	−0.628167	−	0.362672i
$250$	775.751	−	1343.64i	0.196251	−	0.339917i
$251$	−2291.82	−	3969.55i	−0.576329	−	0.998231i	−0.995896	−	0.0905068i	$-0.971151\pi$
$251$	−2291.82	−	3969.55i	−0.576329	−	0.998231i	0.419567	−	0.907724i	$-0.362182\pi$
$252$			252.000i			0.0629941i
$253$	12.3522	−	7.13156i	0.00306948	−	0.00177216i
$254$	−3115.70	+	1798.85i	−0.769670	+	0.444369i
$255$		−	1037.17i		−	0.254707i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1706.16	−	2955.16i	0.414114	−	0.717267i	−0.581221	−	0.813746i	$-0.697425\pi$
$257$	1706.16	−	2955.16i	0.414114	−	0.717267i	0.995335	+	0.0964790i	$0.0307581\pi$
$258$	1014.16	+	585.528i	0.244725	+	0.141292i
$259$	−1896.42			−0.454972
$260$	366.886	−	483.901i	0.0875127	−	0.115424i
$261$	−1208.81			−0.286681
$262$	1725.52	+	996.229i	0.406882	+	0.234913i
$263$	2166.60	−	3752.66i	0.507978	−	0.879845i	−0.491979	−	0.870607i	$-0.663726\pi$
$263$	2166.60	−	3752.66i	0.507978	−	0.879845i	0.999957	−	0.00923739i	$-0.00294039\pi$
$264$	1.03435	+	1.79154i	0.000241135	+	0.000417658i
$265$			1343.21i			0.311369i
$266$	379.110	−	218.879i	0.0873862	−	0.0504525i
$267$	3789.05	−	2187.61i	0.868486	−	0.501421i
$268$			2243.92i			0.511452i
$269$	−4290.22	−	7430.88i	−0.972414	−	1.68427i	−0.688218	−	0.725504i	$-0.741607\pi$
$269$	−4290.22	−	7430.88i	−0.972414	−	1.68427i	−0.284196	−	0.958766i	$-0.591727\pi$
$270$	−87.4508	+	151.469i	−0.0197114	+	0.0341412i
$271$	2724.81	+	1573.17i	0.610777	+	0.352632i	0.773270	−	0.634077i	$-0.218620\pi$
$271$	2724.81	+	1573.17i	0.610777	+	0.352632i	−0.162492	+	0.986710i	$0.551953\pi$
$272$	−1707.85			−0.380711
$273$	381.931	+	907.197i	0.0846722	+	0.201121i
$274$	−2378.78			−0.524480
$275$	8.54784	+	4.93510i	0.00187438	+	0.00108217i
$276$	992.844	−	1719.66i	0.216530	−	0.375040i
$277$	3231.03	+	5596.31i	0.700845	+	1.21390i	0.968170	+	0.250292i	$0.0805267\pi$
$277$	3231.03	+	5596.31i	0.700845	+	1.21390i	−0.267326	+	0.963606i	$0.586140\pi$
$278$			3470.05i			0.748632i
$279$	−1730.81	+	999.284i	−0.371401	+	0.214428i
$280$	−157.079	+	90.6897i	−0.0335260	+	0.0193562i
$281$		−	6217.83i		−	1.32002i	−0.751258	−	0.660008i	$-0.770553\pi$
$281$		−	6217.83i		−	1.32002i	0.751258	−	0.660008i	$-0.229447\pi$
$282$	−756.678	−	1310.60i	−0.159785	−	0.276756i
$283$	597.723	−	1035.29i	0.125551	−	0.217461i	−0.796397	−	0.604774i	$-0.793263\pi$
$283$	597.723	−	1035.29i	0.125551	−	0.217461i	0.921948	+	0.387313i	$0.126597\pi$
$284$	349.940	+	202.038i	0.0731167	+	0.0422139i
$285$	303.828			0.0631482
$286$	6.43889	+	4.88186i	0.00133126	+	0.00100934i
$287$	−2532.15			−0.520795
$288$	249.415	+	144.000i	0.0510310	+	0.0294628i
$289$	−3240.27	+	5612.31i	−0.659529	+	1.14234i
$290$	−435.028	−	753.490i	−0.0880886	−	0.152574i
$291$			1148.11i			0.231283i
$292$	−813.034	+	469.405i	−0.162942	+	0.0940749i
$293$	2758.61	−	1592.68i	0.550032	−	0.317561i	−0.199103	−	0.979979i	$-0.563803\pi$
$293$	2758.61	−	1592.68i	0.550032	−	0.317561i	0.749135	+	0.662417i	$0.230469\pi$
$294$		−	294.000i		−	0.0583212i
$295$	401.599	+	695.590i	0.0792610	+	0.137284i
$296$	−1083.67	+	1876.97i	−0.212794	+	0.368569i
$297$	−2.01548	−	1.16364i	−0.000393771	−	0.000227344i
$298$	−2945.89			−0.572653
$299$	967.915	−	7695.49i	0.187211	−	1.48843i
$300$	1374.11			0.264448
$301$	−1183.19	−	683.116i	−0.226572	−	0.130811i
$302$	489.295	−	847.484i	0.0932311	−	0.161481i
$303$	−944.780	−	1636.41i	−0.179129	−	0.310261i
$304$		−	500.296i		−	0.0943879i
$305$	−2500.09	+	1443.43i	−0.469360	+	0.270985i
$306$	1663.92	−	960.664i	0.310850	−	0.179469i
$307$		−	5382.59i		−	1.00065i	−0.865837	−	0.500327i	$-0.833213\pi$
$307$		−	5382.59i		−	1.00065i	0.865837	−	0.500327i	$-0.166787\pi$
$308$	−1.20674	−	2.09013i	−0.000223247	−	0.000386676i
$309$	−738.969	+	1279.93i	−0.136047	+	0.235640i
$310$	−1245.77	−	719.244i	−0.228241	−	0.131775i
$311$	−5997.76			−1.09358			−0.546788	−	0.837271i	$-0.684149\pi$
$311$	−5997.76			−1.09358			−0.546788	+	0.837271i	$0.684149\pi$
$312$	1116.14	+	140.384i	0.202528	+	0.0254734i
$313$	−3205.16			−0.578807			−0.289403	−	0.957207i	$-0.593457\pi$
$313$	−3205.16			−0.578807			−0.289403	+	0.957207i	$0.593457\pi$
$314$	−2476.80	−	1429.98i	−0.445140	−	0.257002i
$315$	102.026	−	176.714i	0.0182492	−	0.0316086i
$316$	1221.94	+	2116.47i	0.217531	+	0.376774i
$317$		−	3043.35i		−	0.539217i	−0.962970	−	0.269609i	$-0.913106\pi$
$317$		−	3043.35i		−	0.539217i	0.962970	−	0.269609i	$-0.0868943\pi$
$318$	−2154.90	+	1244.13i	−0.380002	+	0.219394i
$319$	10.0261	−	5.78857i	0.00175973	−	0.00101598i
$320$			207.291i			0.0362122i
$321$	1255.62	+	2174.79i	0.218323	+	0.378146i
$322$	−1158.32	+	2006.27i	−0.200468	+	0.347220i
$323$	−2890.46	−	1668.81i	−0.497924	−	0.287476i
$324$	−324.000			−0.0555556
$325$	4946.79	−	2082.60i	0.844303	−	0.355453i
$326$	−5462.30			−0.928002
$327$	5225.34	+	3016.85i	0.883675	+	0.510190i
$328$	−1446.94	+	2506.18i	−0.243580	+	0.421892i
$329$	882.790	+	1529.04i	0.147933	+	0.256227i
$330$		−	1.67508i		−	0.000279425i
$331$	−4221.00	+	2436.99i	−0.700927	+	0.404681i	−0.807693	−	0.589604i	$-0.799284\pi$
$331$	−4221.00	+	2436.99i	−0.700927	+	0.404681i	0.106765	+	0.994284i	$0.465951\pi$
$332$	3290.89	−	1899.99i	0.544009	−	0.314084i
$333$		−	2438.25i		−	0.401247i
$334$	−515.500	−	892.873i	−0.0844519	−	0.146275i
$335$	908.483	−	1573.54i	0.148166	−	0.256632i
$336$	−290.985	−	168.000i	−0.0472456	−	0.0272772i
$337$	−7925.57			−1.28111			−0.640554	−	0.767913i	$-0.721295\pi$
$337$	−7925.57			−1.28111			−0.640554	+	0.767913i	$0.721295\pi$
$338$	4230.85	−	1186.24i	0.680852	−	0.190896i
$339$	906.904			0.145299
$340$	1197.62	+	691.447i	0.191030	+	0.110291i
$341$	9.57041	−	16.5764i	0.00151984	−	0.00263245i
$342$	281.416	+	487.427i	0.0444949	+	0.0770674i
$343$			343.000i			0.0539949i
$344$	−1352.22	+	780.704i	−0.211938	+	0.122363i
$345$	−1392.46	+	803.935i	−0.217297	+	0.125456i
$346$			992.023i			0.154137i
$347$	5093.24	+	8821.76i	0.787953	+	1.36477i	0.927219	+	0.374520i	$0.122192\pi$
$347$	5093.24	+	8821.76i	0.787953	+	1.36477i	−0.139266	+	0.990255i	$0.544474\pi$
$348$	805.876	−	1395.82i	0.124136	−	0.215011i
$349$	5680.33	+	3279.54i	0.871235	+	0.503008i	0.867759	−	0.496986i	$-0.165560\pi$
$349$	5680.33	+	3279.54i	0.871235	+	0.503008i	0.00347677	+	0.999994i	$0.498893\pi$
$350$	−1603.13			−0.244831
$351$	−1166.40	+	491.054i	−0.177372	+	0.0746739i
$352$	−2.75826			−0.000417658
$353$	10838.8	+	6257.76i	1.63425	+	0.943532i	0.982763	+	0.184869i	$0.0591859\pi$
$353$	10838.8	+	6257.76i	1.63425	+	0.943532i	0.651483	+	0.758664i	$0.274147\pi$
$354$	−743.950	+	1288.56i	−0.111696	+	0.193464i
$355$	−163.596	−	283.357i	−0.0244586	−	0.0423635i
$356$			5833.62i			0.868486i
$357$	−1941.24	+	1120.78i	−0.287791	+	0.166156i
$358$	5682.72	−	3280.92i	0.838942	−	0.484363i
$359$			10170.3i			1.49518i	0.664161	+	0.747589i	$0.268789\pi$
$359$			10170.3i			1.49518i	−0.664161	+	0.747589i	$0.731211\pi$
$360$	−116.601	−	201.959i	−0.0170706	−	0.0295671i
$361$	−2940.64	+	5093.34i	−0.428727	+	0.742578i
$362$	231.872	+	133.871i	0.0336655	+	0.0194368i
$363$	−3992.98			−0.577347
$364$	−1302.16	−	163.782i	−0.187505	−	0.0235838i
$365$	760.182			0.109013
$366$	−4631.35	−	2673.91i	−0.661433	−	0.381878i
$367$	−4302.58	+	7452.29i	−0.611970	+	1.05996i	0.378938	+	0.925422i	$0.376289\pi$
$367$	−4302.58	+	7452.29i	−0.611970	+	1.05996i	−0.990908	+	0.134541i	$0.957044\pi$
$368$	1323.79	+	2292.88i	0.187520	+	0.324795i
$369$		−	3255.62i		−	0.459298i
$370$	1519.84	−	877.477i	0.213547	−	0.123292i
$371$	2514.05	−	1451.49i	0.351814	−	0.203120i
$372$		−	2664.76i		−	0.371401i
$373$	4780.26	+	8279.65i	0.663572	+	1.14934i	0.979670	+	0.200615i	$0.0642939\pi$
$373$	4780.26	+	8279.65i	0.663572	+	1.14934i	−0.316098	+	0.948727i	$0.602373\pi$
$374$	−9.20055	+	15.9358i	−0.00127206	+	0.00220327i
$375$	−2015.46	−	1163.63i	−0.277541	−	0.160238i
$376$	2017.81			0.276756
$377$	785.642	−	6246.31i	0.107328	−	0.853319i
$378$	378.000			0.0514344
$379$	4338.44	+	2504.80i	0.587997	+	0.339480i	0.764305	−	0.644855i	$-0.223082\pi$
$379$	4338.44	+	2504.80i	0.587997	+	0.339480i	−0.176308	+	0.984335i	$0.556416\pi$
$380$	−202.552	+	350.831i	−0.0273440	+	0.0473611i
$381$	2698.27	+	4673.54i	0.362826	+	0.628433i
$382$			1265.33i			0.169476i
$383$	4783.16	−	2761.56i	0.638141	−	0.368431i	−0.145757	−	0.989320i	$-0.546562\pi$
$383$	4783.16	−	2761.56i	0.638141	−	0.368431i	0.783898	+	0.620890i	$0.213228\pi$
$384$	−332.554	+	192.000i	−0.0441942	+	0.0255155i
$385$			1.95426i			0.000258697i
$386$	−3860.09	−	6685.87i	−0.508998	−	0.881611i
$387$	878.292	−	1521.25i	0.115365	−	0.199817i
$388$	−1325.72	−	765.407i	−0.173462	−	0.100149i
$389$	−2600.21			−0.338910			−0.169455	−	0.985538i	$-0.554201\pi$
$389$	−2600.21			−0.338910			−0.169455	+	0.985538i	$0.554201\pi$
$390$	−725.851	−	550.329i	−0.0942433	−	0.0714538i
$391$	17662.8			2.28451
$392$	339.482	+	196.000i	0.0437409	+	0.0252538i
$393$	1494.34	−	2588.28i	0.191806	−	0.332217i
$394$	2557.61	+	4429.91i	0.327032	+	0.566435i
$395$		−	1978.89i		−	0.252073i
$396$	2.68731	−	1.55152i	0.000341016	−	0.000196886i
$397$	−928.473	+	536.054i	−0.117377	+	0.0677677i	−0.557539	−	0.830151i	$-0.688254\pi$
$397$	−928.473	+	536.054i	−0.117377	+	0.0677677i	0.440162	+	0.897918i	$0.354921\pi$
$398$		−	6415.05i		−	0.807934i
$399$	−328.319	−	568.665i	−0.0411943	−	0.0713506i
$400$	−916.075	+	1586.69i	−0.114509	+	0.198336i
$401$	−5904.89	−	3409.19i	−0.735352	−	0.424556i	0.0850251	−	0.996379i	$-0.472903\pi$
$401$	−5904.89	−	3409.19i	−0.735352	−	0.424556i	−0.820377	+	0.571823i	$0.806236\pi$
$402$	3365.88			0.417599
$403$	−4038.70	−	9593.09i	−0.499211	−	1.18577i
$404$	2519.41			0.310261
$405$	227.204	+	131.176i	0.0278762	+	0.0160943i
$406$	−940.189	+	1628.45i	−0.114928	+	0.199061i
$407$	11.6759	+	20.2233i	0.00142200	+	0.00246297i
$408$			2561.77i			0.310850i
$409$	−11508.8	+	6644.60i	−1.39138	+	0.803312i	−0.993468	−	0.114113i	$-0.963597\pi$
$409$	−11508.8	+	6644.60i	−1.39138	+	0.803312i	−0.397909	+	0.917425i	$0.630264\pi$
$410$	2029.33	−	1171.63i	0.244442	−	0.141129i
$411$			3568.18i			0.428236i
$412$	−985.292	−	1706.58i	−0.117820	−	0.204070i
$413$	867.942	−	1503.32i	0.103411	−	0.179113i
$414$	−2579.48	−	1489.27i	−0.306219	−	0.176796i
$415$	−3076.96			−0.363957
$416$	−906.194	+	1195.22i	−0.106802	+	0.140866i
$417$	5205.08			0.611256
$418$	−4.66823	−	2.69520i	−0.000546245	−	0.000315375i
$419$	3170.05	−	5490.69i	0.369611	−	0.640186i	−0.619893	−	0.784686i	$-0.712824\pi$
$419$	3170.05	−	5490.69i	0.369611	−	0.640186i	0.989505	+	0.144500i	$0.0461575\pi$
$420$	136.035	+	235.619i	0.0158043	+	0.0273738i
$421$			8723.80i			1.00991i	0.863146	+	0.504955i	$0.168491\pi$
$421$			8723.80i			1.00991i	−0.863146	+	0.504955i	$0.831509\pi$
$422$	−6528.94	+	3769.48i	−0.753137	+	0.434824i
$423$	−1965.91	+	1135.02i	−0.225971	+	0.130464i
$424$		−	3317.68i		−	0.380002i
$425$	6111.40	+	10585.2i	0.697521	+	1.20814i
$426$	303.057	−	524.911i	0.0344675	−	0.0596995i
$427$	5403.24	+	3119.56i	0.612368	+	0.353551i
$428$	−3348.31			−0.378146
$429$	7.32280	−	9.65833i	0.000824121	−	0.00108697i
$430$	1264.32			0.141793
$431$	−3342.63	−	1929.87i	−0.373571	−	0.215681i	0.301447	−	0.953483i	$-0.402530\pi$
$431$	−3342.63	−	1929.87i	−0.373571	−	0.215681i	−0.675017	+	0.737802i	$0.735864\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	−10.0728	−	17.4466i	−0.00111794	−	0.00193633i	0.865466	−	0.500968i	$-0.167023\pi$
$433$	−10.0728	−	17.4466i	−0.00111794	−	0.00193633i	−0.866584	+	0.499032i	$0.833689\pi$
$434$			3108.88i			0.343851i
$435$	−1130.23	+	652.541i	−0.124576	+	0.0719241i
$436$	−6967.11	+	4022.47i	−0.765285	+	0.441838i
$437$			5174.12i			0.566389i
$438$	704.108	+	1219.55i	0.0768118	+	0.133042i
$439$	8141.77	−	14102.0i	0.885161	−	1.53314i	0.0396317	−	0.999214i	$-0.487382\pi$
$439$	8141.77	−	14102.0i	0.885161	−	1.53314i	0.845529	−	0.533929i	$-0.179285\pi$
$440$	1.93422	+	1.11672i	0.000209568	+	0.000120994i
$441$	−441.000			−0.0476190
$442$	3882.62	+	9222.34i	0.417822	+	0.992448i
$443$	−6883.48			−0.738248			−0.369124	−	0.929380i	$-0.620342\pi$
$443$	−6883.48			−0.738248			−0.369124	+	0.929380i	$0.620342\pi$
$444$	2815.45	+	1625.50i	0.300936	+	0.173745i
$445$	2361.83	−	4090.80i	0.251598	−	0.435781i
$446$	−4834.95	−	8374.38i	−0.513322	−	0.889099i
$447$			4418.83i			0.467570i
$448$	387.979	−	224.000i	0.0409159	−	0.0236228i
$449$	13607.4	−	7856.21i	1.43023	−	0.825741i	0.433088	−	0.901352i	$-0.357424\pi$
$449$	13607.4	−	7856.21i	1.43023	−	0.825741i	0.997137	+	0.0756109i	$0.0240907\pi$
$450$		−	2061.17i		−	0.215921i
$451$	15.5900	+	27.0027i	0.00162773	+	0.00281930i
$452$	−604.603	+	1047.20i	−0.0629162	+	0.108974i
$453$	−1271.23	−	733.943i	−0.131849	−	0.0761229i
$454$	−8601.33			−0.889164
$455$	846.826	+	642.050i	0.0872523	+	0.0661534i
$456$	−750.444			−0.0770674
$457$	2706.48	+	1562.59i	0.277033	+	0.159945i	0.632079	−	0.774904i	$-0.282202\pi$
$457$	2706.48	+	1562.59i	0.277033	+	0.159945i	−0.355047	+	0.934849i	$0.615535\pi$
$458$	−5310.28	+	9197.68i	−0.541775	+	0.938383i
$459$	−1441.00	−	2495.88i	−0.146536	−	0.253808i
$460$		−	2143.83i		−	0.217297i
$461$	12528.1	−	7233.11i	1.26571	−	0.730758i	0.291536	−	0.956560i	$-0.405834\pi$
$461$	12528.1	−	7233.11i	1.26571	−	0.730758i	0.974173	+	0.225802i	$0.0725002\pi$
$462$	−3.13519	+	1.81010i	−0.000315720	+	0.000182281i
$463$		−	560.830i		−	0.0562937i	−0.999604	−	0.0281468i	$-0.991039\pi$
$463$		−	560.830i		−	0.0562937i	0.999604	−	0.0281468i	$-0.00896060\pi$
$464$	1074.50	+	1861.09i	0.107505	+	0.186205i
$465$	−1078.87	+	1868.65i	−0.107594	+	0.186358i
$466$	−2113.07	−	1219.98i	−0.210056	−	0.121276i
$467$	13077.2			1.29580			0.647901	−	0.761725i	$-0.275647\pi$
$467$	13077.2			1.29580			0.647901	+	0.761725i	$0.275647\pi$
$468$	210.577	−	1674.21i	0.0207989	−	0.165364i
$469$	−3926.86			−0.386621
$470$	−1414.98	−	816.939i	−0.138868	−	0.0801757i
$471$	−2144.97	+	3715.20i	−0.209841	+	0.363455i
$472$	−991.934	−	1718.08i	−0.0967319	−	0.167545i
$473$			16.8233i			0.00163538i
$474$	3174.70	−	1832.92i	0.307635	−	0.177613i
$475$	−3100.84	+	1790.27i	−0.299529	+	0.172933i
$476$		−	2988.73i		−	0.287791i
$477$	1866.20	+	3232.35i	0.179135	+	0.310270i
$478$	4515.53	−	7821.12i	0.432083	−	0.748389i
$479$	−5275.03	−	3045.54i	−0.503178	−	0.290510i	0.226847	−	0.973930i	$-0.427158\pi$
$479$	−5275.03	−	3045.54i	−0.503178	−	0.290510i	−0.730025	+	0.683420i	$0.760492\pi$
$480$	310.936			0.0295671
$481$	12599.2	+	1584.69i	1.19433	+	0.150219i
$482$	−12121.2			−1.14545
$483$	3009.40	+	1737.48i	0.283504	+	0.163681i
$484$	2661.99	−	4610.69i	0.249999	−	0.433010i
$485$	619.772	+	1073.48i	0.0580256	+	0.100503i
$486$			486.000i			0.0453609i
$487$	−6483.11	+	3743.03i	−0.603240	+	0.348281i	−0.770315	−	0.637664i	$-0.779901\pi$
$487$	−6483.11	+	3743.03i	−0.603240	+	0.348281i	0.167075	+	0.985944i	$0.446568\pi$
$488$	6175.13	−	3565.21i	0.572818	−	0.330716i
$489$			8193.45i			0.757711i
$490$	−158.707	−	274.889i	−0.0146319	−	0.0253433i
$491$	5272.17	−	9131.66i	0.484582	−	0.839320i	−0.515262	−	0.857033i	$-0.672305\pi$
$491$	5272.17	−	9131.66i	0.484582	−	0.839320i	0.999843	+	0.0177131i	$0.00563855\pi$
$492$	3759.27	+	2170.42i	0.344474	+	0.198882i
$493$	14336.6			1.30971
$494$	−2701.59	+	1137.37i	−0.246053	+	0.103589i
$495$	−2.51262			−0.000228149
$496$	3077.00	+	1776.50i	0.278551	+	0.160821i
$497$	−353.567	+	612.396i	−0.0319107	+	0.0552710i
$498$	−2849.99	−	4936.33i	−0.256448	−	0.444181i
$499$			10451.5i			0.937622i	0.883299	+	0.468811i	$0.155317\pi$
$499$			10451.5i			0.937622i	−0.883299	+	0.468811i	$0.844683\pi$
$500$	2687.28	−	1551.50i	0.240358	−	0.138771i
$501$	−1339.31	+	773.251i	−0.119433	+	0.0689547i
$502$		−	9167.29i		−	0.815052i
$503$	468.555	+	811.561i	0.0415344	+	0.0719398i	0.886045	−	0.463599i	$-0.153442\pi$
$503$	468.555	+	811.561i	0.0415344	+	0.0719398i	−0.844511	+	0.535538i	$0.820109\pi$
$504$	−252.000	+	436.477i	−0.0222718	+	0.0385758i
$505$	−1766.73	−	1020.02i	−0.155680	−	0.0898819i
$506$	28.5262			0.00250622
$507$	−1779.35	−	6346.27i	−0.155866	−	0.555913i
$508$	−7195.39			−0.628433
$509$	1954.98	+	1128.71i	0.170242	+	0.0982890i	0.582700	−	0.812688i	$-0.301996\pi$
$509$	1954.98	+	1128.71i	0.170242	+	0.0982890i	−0.412458	+	0.910977i	$0.635330\pi$
$510$	1037.17	−	1796.43i	0.0900523	−	0.155975i
$511$	−821.459	−	1422.81i	−0.0711139	−	0.123173i
$512$		−	512.000i		−	0.0441942i
$513$	731.141	−	422.125i	0.0629253	−	0.0363299i
$514$	5910.31	−	3412.32i	0.507184	−	0.292823i
$515$			1595.64i			0.136529i
$516$	1171.06	+	2028.33i	0.0999087	+	0.173047i
$517$	10.8704	−	18.8280i	0.000924716	−	0.00160165i
$518$	−3284.69	−	1896.42i	−0.278612	−	0.160857i
$519$	1488.04			0.125853
$520$	1119.37	−	471.254i	0.0943989	−	0.0397421i
$521$	1535.77			0.129142			0.0645712	−	0.997913i	$-0.479432\pi$
$521$	1535.77			0.129142			0.0645712	+	0.997913i	$0.479432\pi$
$522$	−2093.73	−	1208.81i	−0.175555	−	0.101357i
$523$	10678.9	−	18496.4i	0.892841	−	1.54645i	0.0563872	−	0.998409i	$-0.482042\pi$
$523$	10678.9	−	18496.4i	0.892841	−	1.54645i	0.836454	−	0.548037i	$-0.184625\pi$
$524$	1992.46	+	3451.04i	0.166109	+	0.287709i
$525$			2404.70i			0.199904i
$526$	7505.33	−	4333.20i	0.622144	−	0.359195i
$527$	20527.5	−	11851.6i	1.69676	−	0.979624i
$528$			4.13738i			0.000341016i
$529$	−7607.32	−	13176.3i	−0.625242	−	1.08295i
$530$	−1343.21	+	2326.51i	−0.110086	+	0.190674i
$531$	1932.84	+	1115.93i	0.157963	+	0.0911997i
$532$	875.518			0.0713506
$533$	16822.8	+	2115.92i	1.36712	+	0.171952i
$534$	8750.43			0.709116
$535$	2347.99	+	1355.61i	0.189743	+	0.109548i
$536$	−2243.92	+	3886.58i	−0.180826	+	0.313199i
$537$	−4921.38	−	8524.09i	−0.395481	−	0.684993i
$538$		−	17160.9i		−	1.37520i
$539$	3.65773	−	2.11179i	0.000292299	−	0.000168759i
$540$	−302.938	+	174.902i	−0.0241415	+	0.0139381i
$541$		−	4804.77i		−	0.381836i	−0.981606	−	0.190918i	$-0.938854\pi$
$541$		−	4804.77i		−	0.381836i	0.981606	−	0.190918i	$-0.0611465\pi$
$542$	3146.34	+	5449.63i	0.249349	+	0.431885i
$543$	200.807	−	347.808i	0.0158701	−	0.0274878i
$544$	−2958.08	−	1707.85i	−0.233137	−	0.134602i
$545$	6514.22			0.511997
$546$	−245.673	+	1953.24i	−0.0192561	+	0.153097i
$547$	18909.2			1.47806			0.739032	−	0.673671i	$-0.235283\pi$
$547$	18909.2			1.47806			0.739032	+	0.673671i	$0.235283\pi$
$548$	−4120.18	−	2378.78i	−0.321177	−	0.185432i
$549$	−4010.87	+	6947.02i	−0.311802	+	0.540058i
$550$	9.87019	+	17.0957i	0.000765212	+	0.00132539i
$551$			4199.75i			0.324711i
$552$	3439.31	−	1985.69i	0.265194	−	0.153110i
$553$	−3703.82	+	2138.40i	−0.284815	+	0.164438i
$554$			12924.1i			0.991144i
$555$	−1316.22	−	2279.75i	−0.100667	−	0.174361i
$556$	−3470.05	+	6010.30i	−0.264682	+	0.458442i
$557$	−1261.21	−	728.159i	−0.0959409	−	0.0553915i	0.451262	−	0.892392i	$-0.350974\pi$
$557$	−1261.21	−	728.159i	−0.0959409	−	0.0553915i	−0.547203	+	0.837000i	$0.684307\pi$
$558$	−3997.13			−0.303248
$559$	7289.92	+	5527.11i	0.551576	+	0.418196i
$560$	−362.759			−0.0273738
$561$	23.9037	+	13.8008i	0.00179896	+	0.00103863i
$562$	6217.83	−	10769.6i	0.466696	−	0.808342i
$563$	−9784.62	−	16947.5i	−0.732456	−	1.26865i	−0.955831	−	0.293918i	$-0.905041\pi$
$563$	−9784.62	−	16947.5i	−0.732456	−	1.26865i	0.223375	−	0.974733i	$-0.428293\pi$
$564$		−	3026.71i		−	0.225971i
$565$	847.951	−	489.565i	0.0631390	−	0.0364533i
$566$	2070.57	−	1195.45i	0.153768	−	0.0887780i
$567$		−	567.000i		−	0.0419961i
$568$	404.076	+	699.881i	0.0298498	+	0.0517013i
$569$	−12507.9	+	21664.4i	−0.921546	+	1.59616i	−0.124522	+	0.992217i	$0.539740\pi$
$569$	−12507.9	+	21664.4i	−0.921546	+	1.59616i	−0.797024	+	0.603947i	$0.793594\pi$
$570$	526.246	+	303.828i	0.0386702	+	0.0223262i
$571$	−17411.5			−1.27609			−0.638045	−	0.769999i	$-0.720257\pi$
$571$	−17411.5			−1.27609			−0.638045	+	0.769999i	$0.720257\pi$
$572$	6.27061	+	14.8945i	0.000458370	+	0.00108876i
$573$	1897.99			0.138377
$574$	−4385.82	−	2532.15i	−0.318921	−	0.184129i
$575$	9474.17	−	16409.7i	0.687131	−	1.19014i
$576$	288.000	+	498.831i	0.0208333	+	0.0360844i
$577$			14027.6i			1.01209i	0.862507	+	0.506044i	$0.168893\pi$
$577$			14027.6i			1.01209i	−0.862507	+	0.506044i	$0.831107\pi$
$578$	−11224.6	+	6480.53i	−0.807755	+	0.466357i
$579$	−10028.8	+	5790.13i	−0.719833	+	0.415595i
$580$		−	1740.11i		−	0.124576i
$581$	3324.99	+	5759.05i	0.237425	+	0.411232i
$582$	−1148.11	+	1988.59i	−0.0817710	+	0.141631i
$583$	−30.9571	−	17.8731i	−0.00219916	−	0.00126969i
$584$	−1877.62			−0.133042
$585$	−825.493	+	1088.78i	−0.0583418	+	0.0769493i
$586$	6370.73			0.449099
$587$	14086.6	+	8132.92i	0.990490	+	0.571860i	0.905421	−	0.424515i	$-0.139556\pi$
$587$	14086.6	+	8132.92i	0.990490	+	0.571860i	0.0850692	+	0.996375i	$0.472889\pi$
$588$	294.000	−	509.223i	0.0206197	−	0.0357143i
$589$	3471.79	+	6013.31i	0.242874	+	0.420669i
$590$			1606.40i			0.112092i
$591$	6644.86	−	3836.41i	0.462493	−	0.267020i
$592$	−3753.93	+	2167.34i	−0.260618	+	0.150468i
$593$			7773.50i			0.538312i	0.963097	+	0.269156i	$0.0867448\pi$
$593$			7773.50i			0.538312i	−0.963097	+	0.269156i	$0.913255\pi$
$594$	−2.32728	−	4.03096i	−0.000160757	−	0.000278438i
$595$	−1210.03	+	2095.84i	−0.0833723	+	0.144405i
$596$	−5102.43	−	2945.89i	−0.350677	−	0.202464i
$597$	−9622.58			−0.659675
$598$	9371.97	−	12361.1i	0.640884	−	0.845287i
$599$	8946.27			0.610242			0.305121	−	0.952314i	$-0.401303\pi$
$599$	8946.27			0.610242			0.305121	+	0.952314i	$0.401303\pi$
$600$	2380.03	+	1374.11i	0.161941	+	0.0934965i
$601$	11878.3	−	20573.8i	0.806199	−	1.39638i	−0.109280	−	0.994011i	$-0.534854\pi$
$601$	11878.3	−	20573.8i	0.806199	−	1.39638i	0.915479	−	0.402367i	$-0.131812\pi$
$602$	−1366.23	−	2366.38i	−0.0924975	−	0.160210i
$603$		−	5048.81i		−	0.340968i
$604$	1694.97	−	978.591i	0.114184	−	0.0659243i
$605$	−3733.41	+	2155.49i	−0.250884	+	0.144848i
$606$		−	3779.12i		−	0.253327i
$607$	−10669.9	−	18480.8i	−0.713473	−	1.23577i	−0.963546	−	0.267544i	$-0.913788\pi$
$607$	−10669.9	−	18480.8i	−0.713473	−	1.23577i	0.250073	−	0.968227i	$-0.419545\pi$
$608$	500.296	−	866.538i	0.0333712	−	0.0578006i
$609$	2442.68	+	1410.28i	0.162533	+	0.0938383i
$610$	−5773.72			−0.383231
$611$	−4587.28	−	10896.1i	−0.303734	−	0.721456i
$612$	3842.66			0.253808
$613$	5723.15	+	3304.26i	0.377089	+	0.217713i	0.676551	−	0.736396i	$-0.263474\pi$
$613$	5723.15	+	3304.26i	0.377089	+	0.217713i	−0.299462	+	0.954108i	$0.596807\pi$
$614$	5382.59	−	9322.92i	0.353784	−	0.612773i
$615$	−1757.45	−	3043.99i	−0.115231	−	0.199586i
$616$		−	4.82695i		−	0.000315720i
$617$	−8246.51	+	4761.13i	−0.538075	+	0.310658i	−0.744298	−	0.667847i	$-0.767216\pi$
$617$	−8246.51	+	4761.13i	−0.538075	+	0.310658i	0.206224	+	0.978505i	$0.433883\pi$
$618$	−2559.86	+	1477.94i	−0.166623	+	0.0961997i
$619$			17222.4i			1.11830i	0.829067	+	0.559149i	$0.188872\pi$
$619$			17222.4i			1.11830i	−0.829067	+	0.559149i	$0.811128\pi$
$620$	−1438.49	−	2491.53i	−0.0931791	−	0.161391i
$621$	−2233.90	+	3869.23i	−0.144353	+	0.250027i
$622$	−10388.4	−	5997.76i	−0.669675	−	0.386637i
$623$	−10208.8			−0.656514
$624$	1792.82	+	1359.29i	0.115017	+	0.0872038i
$625$	11801.1			0.755269
$626$	−5551.50	−	3205.16i	−0.354445	−	0.204639i
$627$	−4.04280	+	7.00234i	−0.000257502	+	0.000446007i
$628$	−2859.96	−	4953.60i	−0.181728	−	0.314762i
$629$			28917.8i			1.83311i
$630$	353.428	−	204.052i	0.0223507	−	0.0129042i
$631$	13664.8	−	7889.40i	0.862106	−	0.497737i	−0.00261113	−	0.999997i	$-0.500831\pi$
$631$	13664.8	−	7889.40i	0.862106	−	0.497737i	0.864717	+	0.502260i	$0.167498\pi$
$632$			4887.78i			0.307635i
$633$	5654.23	+	9793.41i	0.355032	+	0.614934i
$634$	3043.35	−	5271.24i	0.190642	−	0.330202i
$635$	5045.74	+	2913.16i	0.315329	+	0.182056i
$636$	−4976.52			−0.310270
$637$	286.618	−	2278.78i	0.0178277	−	0.141740i
$638$	23.1543			0.00143681
$639$	−787.366	−	454.586i	−0.0487445	−	0.0281426i
$640$	−207.291	+	359.038i	−0.0128029	+	0.0221754i
$641$	10285.1	+	17814.3i	0.633756	+	1.09770i	0.986777	+	0.162082i	$0.0518209\pi$
$641$	10285.1	+	17814.3i	0.633756	+	1.09770i	−0.353022	+	0.935615i	$0.614846\pi$
$642$			5022.46i			0.308755i
$643$	7343.47	−	4239.75i	0.450386	−	0.260030i	−0.257607	−	0.966250i	$-0.582934\pi$
$643$	7343.47	−	4239.75i	0.450386	−	0.260030i	0.707993	+	0.706219i	$0.249601\pi$
$644$	−4012.53	+	2316.64i	−0.245522	+	0.141752i
$645$		−	1896.48i		−	0.115773i
$646$	−3337.61	−	5780.92i	−0.203277	−	0.352085i
$647$	7405.15	−	12826.1i	0.449963	−	0.779359i	−0.548420	−	0.836203i	$-0.684770\pi$
$647$	7405.15	−	12826.1i	0.449963	−	0.779359i	0.998383	+	0.0568438i	$0.0181037\pi$
$648$	−561.184	−	324.000i	−0.0340207	−	0.0196419i
$649$	−21.3751			−0.00129283
$650$	10650.7	+	1339.61i	0.642699	+	0.0808367i
$651$	4663.32			0.280753
$652$	−9460.98	−	5462.30i	−0.568283	−	0.328098i
$653$	−12758.9	+	22099.1i	−0.764619	+	1.32436i	0.175829	+	0.984421i	$0.443739\pi$
$653$	−12758.9	+	22099.1i	−0.764619	+	1.32436i	−0.940448	+	0.339938i	$0.889594\pi$
$654$	6033.70	+	10450.7i	0.360759	+	0.624853i
$655$		−	3226.70i		−	0.192485i
$656$	−5012.36	+	2893.89i	−0.298323	+	0.172237i
$657$	1829.33	−	1056.16i	0.108628	−	0.0627166i
$658$			3531.16i			0.209208i
$659$	1000.04	+	1732.12i	0.0591137	+	0.102388i	0.894068	−	0.447932i	$-0.147839\pi$
$659$	1000.04	+	1732.12i	0.0591137	+	0.102388i	−0.834954	+	0.550320i	$0.814506\pi$
$660$	1.67508	−	2.90132i	9.87915e−5	−	0.000171112i
$661$	−26051.3	−	15040.7i	−1.53295	−	0.885047i	−0.999224	−	0.0393871i	$-0.987459\pi$
$661$	−26051.3	−	15040.7i	−1.53295	−	0.885047i	−0.533722	−	0.845660i	$-0.679207\pi$
$662$	−9747.97			−0.572305
$663$	13833.5	−	5823.93i	0.810331	−	0.341150i
$664$	7599.98			0.444181
$665$	−613.953	−	354.466i	−0.0358016	−	0.0206701i
$666$	2438.25	−	4223.18i	0.141862	−	0.245713i
$667$	−11112.6	−	19247.6i	−0.645101	−	1.11735i
$668$		−	2062.00i		−	0.119433i
$669$	−12561.6	+	7252.42i	−0.725947	+	0.419125i
$670$	3147.08	−	1816.97i	0.181466	−	0.104769i
$671$		−	76.8263i		−	0.00442004i
$672$	−336.000	−	581.969i	−0.0192879	−	0.0334077i
$673$	13053.6	−	22609.5i	0.747665	−	1.29499i	−0.201275	−	0.979535i	$-0.564508\pi$
$673$	13053.6	−	22609.5i	0.747665	−	1.29499i	0.948939	−	0.315459i	$-0.102158\pi$
$674$	−13727.5	−	7925.57i	−0.784515	−	0.452940i
$675$	−3091.75			−0.176299
$676$	8514.28	+	2176.23i	0.484427	+	0.123818i
$677$	26493.2			1.50401			0.752006	−	0.659156i	$-0.229086\pi$
$677$	26493.2			1.50401			0.752006	+	0.659156i	$0.229086\pi$
$678$	1570.80	+	906.904i	0.0889769	+	0.0513709i
$679$	1339.46	−	2320.02i	0.0757052	−	0.131125i
$680$	1382.89	+	2395.24i	0.0779876	+	0.135079i
$681$			12902.0i			0.725999i
$682$	33.1529	−	19.1408i	0.00186142	−	0.00107469i
$683$	−25693.8	+	14834.3i	−1.43945	+	0.831068i	−0.997811	−	0.0661236i	$-0.978937\pi$
$683$	−25693.8	+	14834.3i	−1.43945	+	0.831068i	−0.441641	+	0.897192i	$0.645604\pi$
$684$			1125.67i			0.0629253i
$685$	1926.17	+	3336.23i	0.107438	+	0.186089i
$686$	−343.000	+	594.093i	−0.0190901	+	0.0330650i
$687$	13796.5	+	7965.42i	0.766186	+	0.442358i
$688$	−3122.82			−0.173047
$689$	−17915.4	+	7542.42i	−0.990600	+	0.417044i
$690$	−3215.74			−0.177422
$691$	−15906.7	−	9183.73i	−0.875715	−	0.505594i	−0.00647174	−	0.999979i	$-0.502060\pi$
$691$	−15906.7	−	9183.73i	−0.875715	−	0.505594i	−0.869243	+	0.494385i	$0.835393\pi$
$692$	−992.023	+	1718.24i	−0.0544958	+	0.0943894i
$693$	2.71516	+	4.70279i	0.000148832	+	0.000257784i
$694$			20373.0i			1.11433i
$695$	4866.72	−	2809.80i	0.265619	−	0.153355i
$696$	2791.64	−	1611.75i	0.152035	−	0.0877777i
$697$			38611.9i			2.09832i
$698$	6559.08	+	11360.7i	0.355680	+	0.616056i
$699$	−1829.98	+	3169.61i	−0.0990215	+	0.171510i
$700$	−2776.71	−	1603.13i	−0.149928	−	0.0865610i
$701$	−6406.48			−0.345178			−0.172589	−	0.984994i	$-0.555213\pi$
$701$	−6406.48			−0.345178			−0.172589	+	0.984994i	$0.555213\pi$
$702$	−2511.31	−	315.865i	−0.135019	−	0.0169823i
$703$	−8471.16			−0.454475
$704$	−4.77744	−	2.75826i	−0.000255762	−	0.000147664i
$705$	−1225.41	+	2122.47i	−0.0654632	+	0.113386i
$706$	12515.5	+	21677.5i	0.667178	+	1.15559i
$707$			4408.97i			0.234535i
$708$	−2577.12	+	1487.90i	−0.136800	+	0.0789813i
$709$	−12383.6	+	7149.67i	−0.655960	+	0.378718i	−0.790736	−	0.612158i	$-0.790302\pi$
$709$	−12383.6	+	7149.67i	−0.655960	+	0.378718i	0.134776	+	0.990876i	$0.456968\pi$
$710$		−	654.385i		−	0.0345896i
$711$	−2749.37	−	4762.06i	−0.145021	−	0.251183i
$712$	−5833.62	+	10104.1i	−0.307056	+	0.531837i
$713$	−31822.7	−	18372.8i	−1.67148	−	0.965032i
$714$	−4483.10			−0.234980
$715$	1.63302	−	12.9835i	8.54148e−5	−	0.000679097i
$716$	13123.7			0.684993
$717$	−11731.7	−	6773.29i	−0.611057	−	0.352794i
$718$	−10170.3	+	17615.5i	−0.528626	+	0.915606i
$719$	−8351.42	−	14465.1i	−0.433178	−	0.750287i	0.563967	−	0.825798i	$-0.309275\pi$
$719$	−8351.42	−	14465.1i	−0.433178	−	0.750287i	−0.997145	+	0.0755105i	$0.975941\pi$
$720$		−	466.404i		−	0.0241415i
$721$	2986.51	−	1724.26i	0.154263	−	0.0890636i
$722$	−10186.7	+	5881.28i	−0.525082	+	0.303156i
$723$			18181.9i			0.935257i
$724$	267.742	+	463.743i	0.0137439	+	0.0238051i
$725$	7690.03	−	13319.5i	0.393932	−	0.682310i
$726$	−6916.04	−	3992.98i	−0.353551	−	0.204123i
$727$	−10806.6			−0.551301			−0.275651	−	0.961258i	$-0.588893\pi$
$727$	−10806.6			−0.551301			−0.275651	+	0.961258i	$0.588893\pi$
$728$	−2091.63	−	1585.84i	−0.106485	−	0.0807351i
$729$	729.000			0.0370370
$730$	1316.67	+	760.182i	0.0667566	+	0.0385419i
$731$	−10416.6	+	18042.1i	−0.527047	+	0.912873i
$732$	−5347.82	−	9262.70i	−0.270029	−	0.467704i
$733$			81.0613i			0.00408468i	0.999998	+	0.00204234i	$0.000650097\pi$
$733$			81.0613i			0.00408468i	−0.999998	+	0.00204234i	$0.999350\pi$
$734$	−14904.6	+	8605.16i	−0.749507	+	0.432728i
$735$	−412.333	+	238.060i	−0.0206927	+	0.0119469i
$736$			5295.17i			0.265194i
$737$	24.1769	+	41.8757i	0.00120837	+	0.00209296i
$738$	3255.62	−	5638.91i	0.162386	−	0.281261i
$739$	3833.13	+	2213.06i	0.190804	+	0.110161i	0.592359	−	0.805674i	$-0.298197\pi$
$739$	3833.13	+	2213.06i	0.190804	+	0.110161i	−0.401555	+	0.915835i	$0.631530\pi$
$740$	3509.91			0.174361
$741$	1706.06	+	4052.38i	0.0845798	+	0.200901i
$742$	5805.94			0.287255
$743$	−3181.14	−	1836.63i	−0.157072	−	0.0906857i	0.419404	−	0.907800i	$-0.362239\pi$
$743$	−3181.14	−	1836.63i	−0.157072	−	0.0906857i	−0.576476	+	0.817114i	$0.695573\pi$
$744$	2664.76	−	4615.49i	0.131310	−	0.227436i
$745$	2385.37	+	4131.59i	0.117306	+	0.203181i
$746$			19121.0i			0.938433i
$747$	−7404.50	+	4274.99i	−0.362672	+	0.209389i
$748$	−31.8716	+	18.4011i	−0.00155794	+	0.000899479i
$749$		−	5859.54i		−	0.285852i
$750$	−2327.25	−	4030.92i	−0.113306	−	0.196251i
$751$	9044.52	−	15665.6i	0.439466	−	0.761178i	−0.558182	−	0.829719i	$-0.688501\pi$
$751$	9044.52	−	15665.6i	0.439466	−	0.761178i	0.997648	+	0.0685405i	$0.0218342\pi$
$752$	3494.94	+	2017.81i	0.169478	+	0.0978482i
$753$	−13750.9			−0.665488
$754$	7607.08	−	10033.3i	0.367419	−	0.484603i
$755$	−1584.79			−0.0763925
$756$	654.715	+	378.000i	0.0314970	+	0.0181848i
$757$	−8206.88	+	14214.7i	−0.394035	+	0.682488i	−0.992977	−	0.118304i	$-0.962254\pi$
$757$	−8206.88	+	14214.7i	−0.394035	+	0.682488i	0.598943	+	0.800792i	$0.295588\pi$
$758$	5009.60	+	8676.88i	0.240049	+	0.415776i
$759$		−	42.7893i		−	0.00204632i
$760$	−701.661	+	405.104i	−0.0334894	+	0.0193351i
$761$	16532.6	−	9545.10i	0.787524	−	0.454677i	−0.0515659	−	0.998670i	$-0.516421\pi$
$761$	16532.6	−	9545.10i	0.787524	−	0.454677i	0.839090	+	0.543992i	$0.183088\pi$
$762$			10793.1i			0.513113i
$763$	−7039.31	−	12192.5i	−0.333998	−	0.578501i
$764$	−1265.33	+	2191.61i	−0.0599188	+	0.103782i
$765$	−2694.65	−	1555.76i	−0.127353	−	0.0735274i
$766$	11046.2			0.521040
$767$	−7022.53	+	9262.30i	−0.330598	+	0.436040i
$768$	−768.000			−0.0360844
$769$	−13341.2	−	7702.54i	−0.625612	−	0.361197i	0.153439	−	0.988158i	$-0.450965\pi$
$769$	−13341.2	−	7702.54i	−0.625612	−	0.361197i	−0.779051	+	0.626961i	$0.784299\pi$
$770$	−1.95426	+	3.38488i	−9.14632e−5	+	0.000158419i
$771$	−5118.48	−	8865.47i	−0.239089	−	0.414114i
$772$		−	15440.4i		−	0.719833i
$773$	−8775.76	+	5066.68i	−0.408334	+	0.235752i	−0.690074	−	0.723739i	$-0.742422\pi$
$773$	−8775.76	+	5066.68i	−0.408334	+	0.235752i	0.281740	+	0.959491i	$0.409089\pi$
$774$	3042.49	−	1756.58i	0.141292	−	0.0815751i
$775$		−	25428.3i		−	1.17860i
$776$	−1530.81	−	2651.45i	−0.0708157	−	0.122656i
$777$	−2844.63	+	4927.04i	−0.131339	+	0.227486i
$778$	−4503.70	−	2600.21i	−0.207539	−	0.119823i
$779$	−11310.9			−0.520226
$780$	−706.882	−	1679.05i	−0.0324493	−	0.0770764i
$781$	8.70739			0.000398944
$782$	30592.8	+	17662.8i	1.39897	+	0.807698i
$783$	−1813.22	+	3140.59i	−0.0827576	+	0.143340i
$784$	392.000	+	678.964i	0.0178571	+	0.0309295i
$785$			4631.59i			0.210584i
$786$	5176.56	−	2988.69i	0.234913	−	0.135627i
$787$	−25306.4	+	14610.7i	−1.14622	+	0.661771i	−0.947963	−	0.318380i	$-0.896861\pi$
$787$	−25306.4	+	14610.7i	−1.14622	+	0.661771i	−0.198257	+	0.980150i	$0.563528\pi$
$788$			10230.4i			0.462493i
$789$	−6499.80	−	11258.0i	−0.293282	−	0.507978i
$790$	1978.89	−	3427.54i	0.0891211	−	0.154362i
$791$	−1832.60	−	1058.05i	−0.0823766	−	0.0475602i
$792$	6.20607			0.000278438
$793$	−33290.6	−	25240.4i	−1.49077	−	1.13028i
$794$	−2144.22			−0.0958380
$795$	3489.77	+	2014.82i	0.155685	+	0.0898846i
$796$	6415.05	−	11111.2i	0.285648	−	0.494756i
$797$	−1826.05	−	3162.81i	−0.0811568	−	0.140568i	0.822590	−	0.568635i	$-0.192528\pi$
$797$	−1826.05	−	3162.81i	−0.0811568	−	0.140568i	−0.903747	+	0.428067i	$0.859195\pi$
$798$		−	1313.28i		−	0.0582575i
$799$	23315.8	−	13461.4i	1.03236	−	0.596031i
$800$	−3173.38	+	1832.15i	−0.140245	+	0.0809704i
$801$		−	13125.6i		−	0.578991i
$802$	−6818.38	−	11809.8i	−0.300206	−	0.519972i
$803$	−10.1152	+	17.5200i	−0.000444528	+	0.000769945i
$804$	5829.87	+	3365.88i	0.255726	+	0.147643i
$805$	3751.70			0.164261
$806$	2597.85	−	20654.4i	0.113530	−	0.902631i
$807$	−25741.3			−1.12285
$808$	4363.75	+	2519.41i	0.189995	+	0.109694i
$809$	−13182.1	+	22832.1i	−0.572878	+	0.992253i	0.423391	+	0.905947i	$0.360840\pi$
$809$	−13182.1	+	22832.1i	−0.572878	+	0.992253i	−0.996269	+	0.0863062i	$0.972494\pi$
$810$	262.352	+	454.408i	0.0113804	+	0.0197114i
$811$			7061.62i			0.305755i	0.988245	+	0.152877i	$0.0488540\pi$
$811$			7061.62i			0.305755i	−0.988245	+	0.152877i	$0.951146\pi$
$812$	−3256.91	+	1880.38i	−0.140758	+	0.0812664i
$813$	8174.44	−	4719.52i	0.352632	−	0.203592i
$814$			46.7036i			0.00201101i
$815$	4422.98	+	7660.83i	0.190099	+	0.329260i
$816$	−2561.77	+	4437.12i	−0.109902	+	0.190356i
$817$	−5285.23	−	3051.43i	−0.226324	−	0.130668i
$818$	−26578.4			−1.13605
$819$	2929.86	+	368.509i	0.125003	+	0.0157225i
$820$	4686.53			0.199586
$821$	16830.0	+	9716.79i	0.715433	+	0.413055i	0.813069	−	0.582167i	$-0.197795\pi$
$821$	16830.0	+	9716.79i	0.715433	+	0.413055i	−0.0976366	+	0.995222i	$0.531128\pi$
$822$	−3568.18	+	6180.26i	−0.151404	+	0.262240i
$823$	−17443.6	−	30213.2i	−0.738815	−	1.27967i	−0.953029	−	0.302879i	$-0.902052\pi$
$823$	−17443.6	−	30213.2i	−0.738815	−	1.27967i	0.214214	−	0.976787i	$-0.431281\pi$
$824$		−	3941.17i		−	0.166623i
$825$	25.6435	−	14.8053i	0.00108217	−	0.000624793i
$826$	3006.64	−	1735.88i	0.126652	−	0.0731224i
$827$			2233.43i			0.0939104i	0.998897	+	0.0469552i	$0.0149518\pi$
$827$			2233.43i			0.0939104i	−0.998897	+	0.0469552i	$0.985048\pi$
$828$	−2978.53	−	5158.97i	−0.125013	−	0.216530i
$829$	6735.94	−	11667.0i	0.282206	−	0.488795i	−0.689722	−	0.724075i	$-0.742267\pi$
$829$	6735.94	−	11667.0i	0.282206	−	0.488795i	0.971928	+	0.235279i	$0.0756005\pi$
$830$	−5329.46	−	3076.96i	−0.222877	−	0.128678i
$831$	19386.2			0.809266
$832$	−2764.79	+	1163.98i	−0.115207	+	0.0485021i
$833$	5230.28			0.217549
$834$	9015.46	+	5205.08i	0.374316	+	0.216112i
$835$	−834.832	+	1445.97i	−0.0345995	+	0.0599280i
$836$	−5.39040	−	9.33645i	−0.000223004	−	0.000386254i
$837$			5995.70i			0.247601i
$838$	10981.4	−	6340.10i	0.452680	−	0.261355i
$839$	−13636.5	+	7873.02i	−0.561124	+	0.323965i	−0.753597	−	0.657337i	$-0.771683\pi$
$839$	−13636.5	+	7873.02i	−0.561124	+	0.323965i	0.192472	+	0.981302i	$0.438349\pi$
$840$			544.138i			0.0223507i
$841$	3174.55	+	5498.49i	0.130163	+	0.225450i
$842$	−8723.80	+	15110.1i	−0.357057	+	0.618441i
$843$	−16154.4	−	9326.75i	−0.660008	−	0.381056i
$844$	−15077.9			−0.614934
$845$	−5089.53	−	4973.20i	−0.207201	−	0.202466i
$846$	−4540.07			−0.184504
$847$	8068.71	+	4658.47i	0.327325	+	0.188981i
$848$	3317.68	−	5746.40i	0.134351	−	0.232703i
$849$	−1793.17	−	3105.86i	−0.0724869	−	0.125551i
$850$			24445.6i			0.986443i
$851$	38823.7	−	22414.9i	1.56388	−	0.902904i
$852$	1049.82	−	606.115i	0.0422139	−	0.0243722i
$853$			31908.8i			1.28082i	0.768034	+	0.640409i	$0.221235\pi$
$853$			31908.8i			1.28082i	−0.768034	+	0.640409i	$0.778765\pi$
$854$	6239.12	+	10806.5i	0.249998	+	0.433010i
$855$	455.742	−	789.369i	0.0182293	−	0.0315741i
$856$	−5799.44	−	3348.31i	−0.231566	−	0.133695i
$857$	−42805.0			−1.70618			−0.853088	−	0.521767i	$-0.825273\pi$
$857$	−42805.0			−1.70618			−0.853088	+	0.521767i	$0.825273\pi$
$858$	22.3418	−	9.40592i	0.000888970	−	0.000374257i
$859$	7069.97			0.280820			0.140410	−	0.990093i	$-0.455158\pi$
$859$	7069.97			0.280820			0.140410	+	0.990093i	$0.455158\pi$
$860$	2189.86	+	1264.32i	0.0868299	+	0.0501313i
$861$	−3798.23	+	6578.72i	−0.150341	+	0.260398i
$862$	−3859.74	−	6685.27i	−0.152510	−	0.264154i
$863$		−	9206.42i		−	0.363141i	−0.983378	−	0.181570i	$-0.941882\pi$
$863$		−	9206.42i		−	0.363141i	0.983378	−	0.181570i	$-0.0581180\pi$
$864$	748.246	−	432.000i	0.0294628	−	0.0170103i
$865$	1391.31	−	803.270i	0.0546888	−	0.0315746i
$866$		−	40.2913i		−	0.00158101i
$867$	9720.80	+	16836.9i	0.380779	+	0.659529i
$868$	−3108.88	+	5384.74i	−0.121570	+	0.210565i
$869$	45.6075	+	26.3315i	0.00178036	+	0.00102789i
$870$	−2610.17			−0.101716
$871$	26088.8	+	3281.36i	1.01491	+	0.127652i
$872$	−16089.9			−0.624853
$873$	2982.88	+	1722.17i	0.115642	+	0.0667657i
$874$	−5174.12	+	8961.84i	−0.200249	+	0.346841i
$875$	2715.13	+	4702.74i	0.104901	+	0.181693i
$876$			2816.43i			0.108628i
$877$	−10958.3	+	6326.75i	−0.421932	+	0.243602i	−0.695903	−	0.718135i	$-0.744996\pi$
$877$	−10958.3	+	6326.75i	−0.421932	+	0.243602i	0.273972	+	0.961738i	$0.411663\pi$
$878$	28203.9	−	16283.5i	1.08410	−	0.625903i
$879$		−	9556.09i		−	0.366688i
$880$	2.23344	+	3.86843i	8.55560e−5	+	0.000148187i
$881$	−2379.64	+	4121.67i	−0.0910014	+	0.157619i	−0.907933	−	0.419116i	$-0.862340\pi$
$881$	−2379.64	+	4121.67i	−0.0910014	+	0.157619i	0.816931	+	0.576735i	$0.195673\pi$
$882$	−763.834	−	441.000i	−0.0291606	−	0.0168359i
$883$	−15282.8			−0.582453			−0.291226	−	0.956654i	$-0.594063\pi$
$883$	−15282.8			−0.582453			−0.291226	+	0.956654i	$0.594063\pi$
$884$	−2497.45	+	19856.2i	−0.0950207	+	0.755470i
$885$	2409.59			0.0915227
$886$	−11922.5	−	6883.48i	−0.452083	−	0.261010i
$887$	−15897.6	+	27535.5i	−0.601792	+	1.04234i	0.390757	+	0.920494i	$0.372213\pi$
$887$	−15897.6	+	27535.5i	−0.601792	+	1.04234i	−0.992550	+	0.121841i	$0.961120\pi$
$888$	3251.00	+	5630.90i	0.122856	+	0.212794i
$889$		−	12591.9i		−	0.475051i
$890$	8181.60	−	4723.65i	0.308144	−	0.177907i
$891$	−6.04645	+	3.49092i	−0.000227344	+	0.000131257i
$892$		−	19339.8i		−	0.725947i
$893$	3943.36	+	6830.10i	0.147771	+	0.255947i
$894$	−4418.83	+	7653.64i	−0.165311	+	0.286327i
$895$	−9202.94	−	5313.32i	−0.343710	−	0.198441i
$896$	896.000			0.0334077
$897$	−18541.6	−	14058.0i	−0.690174	−	0.523279i
$898$	31424.9			1.16777
$899$	−25830.0	−	14912.9i	−0.958262	−	0.553253i
$900$	2061.17	−	3570.05i	0.0763396	−	0.132224i
$901$	−22133.2	−	38335.8i	−0.818384	−	1.41748i
$902$			62.3600i			0.00230195i
$903$	−3549.58	+	2049.35i	−0.130811	+	0.0755239i
$904$	−2094.41	+	1209.21i	−0.0770563	+	0.0444885i
$905$		−	433.598i		−	0.0159263i
$906$	−1467.89	−	2542.45i	−0.0538270	−	0.0932311i
$907$	11125.9	−	19270.6i	0.407309	−	0.705480i	−0.587278	−	0.809385i	$-0.699801\pi$
$907$	11125.9	−	19270.6i	0.407309	−	0.705480i	0.994587	+	0.103905i	$0.0331339\pi$
$908$	−14897.9	−	8601.33i	−0.544500	−	0.314367i
$909$	−5668.68			−0.206841
$910$	824.695	+	1958.89i	0.0300422	+	0.0713589i
$911$	−53788.0			−1.95618			−0.978089	−	0.208189i	$-0.933243\pi$
$911$	−53788.0			−1.95618			−0.978089	+	0.208189i	$0.933243\pi$
$912$	−1299.81	−	750.444i	−0.0471940	−	0.0272474i
$913$	40.9427	−	70.9149i	0.00148413	−	0.00257058i
$914$	3125.18	+	5412.97i	0.113098	+	0.195892i
$915$			8660.57i			0.312907i
$916$	−18395.4	+	10620.6i	−0.663537	+	0.383093i
$917$	−6039.32	+	3486.80i	−0.217487	+	0.125566i
$918$		−	5763.99i		−	0.207233i
$919$	−2540.12	−	4399.62i	−0.0911761	−	0.157922i	0.816830	−	0.576878i	$-0.195729\pi$
$919$	−2540.12	−	4399.62i	−0.0911761	−	0.157922i	−0.908006	+	0.418957i	$0.862396\pi$
$920$	2143.83	−	3713.22i	0.0768259	−	0.133066i
$921$	−13984.4	−	8073.89i	−0.500327	−	0.288864i
$922$	28932.4			1.03345
$923$	2860.72	−	3773.11i	0.102017	−	0.134554i
$924$	−7.24042			−0.000257784
$925$	26866.3	+	15511.3i	0.954982	+	0.551359i
$926$	560.830	−	971.385i	0.0199028	−	0.0344727i
$927$	2216.91	+	3839.80i	0.0785467	+	0.136047i
$928$			4298.01i			0.152035i
$929$	16297.9	−	9409.59i	0.575583	−	0.332313i	−0.183793	−	0.982965i	$-0.558838\pi$
$929$	16297.9	−	9409.59i	0.575583	−	0.332313i	0.759376	+	0.650652i	$0.225504\pi$
$930$	−3737.30	+	2157.73i	−0.131775	+	0.0760804i
$931$			1532.16i			0.0539360i
$932$	−2439.97	−	4226.15i	−0.0857551	−	0.148532i
$933$	−8996.64	+	15582.6i	−0.315688	+	0.546788i
$934$	22650.3	+	13077.2i	0.793513	+	0.458135i
$935$	29.7998			0.00104231
$936$	2038.94	−	2689.24i	0.0712016	−	0.0939107i
$937$	523.079			0.0182372			0.00911860	−	0.999958i	$-0.497097\pi$
$937$	523.079			0.0182372			0.00911860	+	0.999958i	$0.497097\pi$
$938$	−6801.51	−	3926.86i	−0.236756	−	0.136691i
$939$	−4807.74	+	8327.26i	−0.167087	+	0.289403i
$940$	−1633.88	−	2829.96i	−0.0566928	−	0.0981948i
$941$		−	3622.06i		−	0.125479i	−0.998030	−	0.0627395i	$-0.980016\pi$
$941$		−	3622.06i		−	0.125479i	0.998030	−	0.0627395i	$-0.0199837\pi$
$942$	−7430.40	+	4289.95i	−0.257002	+	0.148380i
$943$	51838.5	−	29928.9i	1.79013	−	1.03353i
$944$		−	3967.74i		−	0.136800i
$945$	−306.078	−	530.142i	−0.0105362	−	0.0182492i
$946$	−16.8233	+	29.1388i	−0.000578195	+	0.00100146i
$947$	−46752.8	−	26992.7i	−1.60429	−	0.926237i	−0.990616	−	0.136677i	$-0.956358\pi$
$947$	−46752.8	−	26992.7i	−1.60429	−	0.926237i	−0.613674	−	0.789560i	$-0.710309\pi$
$948$	7331.67			0.251183
$949$	4268.58	+	10139.1i	0.146011	+	0.346817i
$950$	−7161.07			−0.244564
$951$	−7906.87	−	4565.03i	−0.269609	−	0.155659i
$952$	2988.73	−	5176.64i	0.101749	−	0.176235i
$953$	6523.63	+	11299.3i	0.221743	+	0.384070i	0.955337	−	0.295517i	$-0.0954920\pi$
$953$	6523.63	+	11299.3i	0.221743	+	0.384070i	−0.733594	+	0.679588i	$0.762159\pi$
$954$			7464.79i			0.253335i
$955$	1774.61	−	1024.57i	0.0601310	−	0.0347167i
$956$	15642.2	−	9031.06i	0.529191	−	0.305529i
$957$		−	34.7314i		−	0.00117315i
$958$	−6091.08	−	10550.1i	−0.205422	−	0.355801i
$959$	4162.87	−	7210.31i	0.140173	−	0.242787i
$960$	538.557	+	310.936i	0.0181061	+	0.0104536i
$961$	−19521.0			−0.655265
$962$	20237.8	+	15344.0i	0.678266	+	0.514250i
$963$	7533.69			0.252097
$964$	−20994.6	−	12121.2i	−0.701443	−	0.404978i
$965$	−6251.26	+	10827.5i	−0.208534	+	0.361191i
$966$	3474.95	+	6018.80i	0.115740	+	0.200468i
$967$			15621.2i			0.519488i	0.965678	+	0.259744i	$0.0836382\pi$
$967$			15621.2i			0.519488i	−0.965678	+	0.259744i	$0.916362\pi$
$968$	9221.39	−	5323.97i	0.306185	−	0.176776i
$969$	−8671.37	+	5006.42i	−0.287476	+	0.165975i
$970$			2479.09i			0.0820606i
$971$	−4486.77	−	7771.31i	−0.148288	−	0.256841i	0.782307	−	0.622893i	$-0.214043\pi$
$971$	−4486.77	−	7771.31i	−0.148288	−	0.256841i	−0.930595	+	0.366051i	$0.880709\pi$
$972$	−486.000	+	841.777i	−0.0160375	+	0.0277778i
$973$	−10518.0	−	6072.59i	−0.346549	−	0.200080i
$974$	−14972.1			−0.492543
$975$	2009.42	−	15976.0i	0.0660029	−	0.524762i
$976$	14260.9			0.467704
$977$	44613.5	+	25757.6i	1.46091	+	0.843459i	0.999054	−	0.0434932i	$-0.0138487\pi$
$977$	44613.5	+	25757.6i	1.46091	+	0.843459i	0.461861	+	0.886952i	$0.347182\pi$
$978$	−8193.45	+	14191.5i	−0.267891	+	0.464001i
$979$	62.8539	+	108.866i	0.00205191	+	0.00355401i
$980$		−	634.828i		−	0.0206927i
$981$	15676.0	−	9050.55i	0.510190	−	0.294558i
$982$	18263.3	−	10544.3i	0.593489	−	0.342651i
$983$		−	19445.3i		−	0.630934i	−0.948937	−	0.315467i	$-0.897839\pi$
$983$		−	19445.3i		−	0.630934i	0.948937	−	0.315467i	$-0.102161\pi$
$984$	4340.83	+	7518.54i	0.140631	+	0.243580i
$985$	4141.94	−	7174.05i	0.133983	−	0.232065i
$986$	24831.7	+	14336.6i	0.802031	+	0.463053i
$987$	5296.74			0.170818
$988$	−5816.66	−	731.601i	−0.187300	−	0.0235580i
$989$	32296.6			1.03839
$990$	−4.35199	−	2.51262i	−0.000139712	−	8.06629e-5i
$991$	−16986.7	+	29421.9i	−0.544502	+	0.943105i	0.454136	+	0.890932i	$0.349948\pi$
$991$	−16986.7	+	29421.9i	−0.544502	+	0.943105i	−0.998638	+	0.0521725i	$0.983385\pi$
$992$	3553.01	+	6153.99i	0.113718	+	0.196965i
$993$			14622.0i			0.467285i
$994$	−1224.79	+	707.134i	−0.0390825	+	0.0225643i
$995$	−8997.06	+	5194.46i	−0.286659	+	0.165503i
$996$		−	11400.0i		−	0.362672i
$997$	2290.32	+	3966.96i	0.0727536	+	0.126013i	0.900107	−	0.435669i	$-0.143488\pi$
$997$	2290.32	+	3966.96i	0.0727536	+	0.126013i	−0.827354	+	0.561681i	$0.810155\pi$
$998$	−10451.5	+	18102.5i	−0.331499	+	0.574174i
$999$	−6334.76	−	3657.38i	−0.200624	−	0.115830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.s.d.43.8	✓	24
13.10	even	6	inner	546.4.s.d.127.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.s.d.43.8	✓	24	1.1	even	1	trivial
546.4.s.d.127.8	yes	24	13.10	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} -3.23892i q^{5} +(5.19615 - 3.00000i) q^{6} +(-6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 - 7.79423i) q^{9} +(3.23892 - 5.60997i) q^{10} +(0.0746475 + 0.0430977i) q^{11} +12.0000 q^{12} +(43.1998 - 18.1872i) q^{13} -14.0000 q^{14} +(-8.41495 - 4.85838i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(53.3702 + 92.4400i) q^{17} -18.0000i q^{18} +(-27.0793 + 15.6342i) q^{19} +(11.2199 - 6.47783i) q^{20} +21.0000i q^{21} +(0.0861955 + 0.149295i) q^{22} +(82.7370 - 143.305i) q^{23} +(20.7846 + 12.0000i) q^{24} +114.509 q^{25} +(93.0115 + 11.6987i) q^{26} -27.0000 q^{27} +(-24.2487 - 14.0000i) q^{28} +(67.1563 - 116.318i) q^{29} +(-9.71675 - 16.8299i) q^{30} -222.063i q^{31} +(-27.7128 + 16.0000i) q^{32} +(0.223942 - 0.129293i) q^{33} +213.481i q^{34} +(11.3362 + 19.6349i) q^{35} +(18.0000 - 31.1769i) q^{36} +(234.621 + 135.458i) q^{37} -62.5370 q^{38} +(17.5481 - 139.517i) q^{39} +25.9113 q^{40} +(313.273 + 180.868i) q^{41} +(-21.0000 + 36.3731i) q^{42} +(97.5880 + 169.027i) q^{43} +0.344782i q^{44} +(-25.2449 + 14.5751i) q^{45} +(286.609 - 165.474i) q^{46} -252.226i q^{47} +(24.0000 + 41.5692i) q^{48} +(24.5000 - 42.4352i) q^{49} +(198.336 + 114.509i) q^{50} +320.221 q^{51} +(149.402 + 113.274i) q^{52} -414.710 q^{53} +(-46.7654 - 27.0000i) q^{54} +(0.139590 - 0.241777i) q^{55} +(-28.0000 - 48.4974i) q^{56} +93.8055i q^{57} +(232.636 - 134.313i) q^{58} +(-214.760 + 123.992i) q^{59} -38.8670i q^{60} +(-445.652 - 771.891i) q^{61} +(222.063 - 384.624i) q^{62} +(54.5596 + 31.5000i) q^{63} -64.0000 q^{64} +(-58.9068 - 139.921i) q^{65} +0.517173 q^{66} +(485.822 + 280.490i) q^{67} +(-213.481 + 369.760i) q^{68} +(-248.211 - 429.914i) q^{69} +45.3448i q^{70} +(87.4851 - 50.5096i) q^{71} +(62.3538 - 36.0000i) q^{72} +234.703i q^{73} +(270.917 + 469.242i) q^{74} +(171.764 - 297.504i) q^{75} +(-108.317 - 62.5370i) q^{76} -0.603368 q^{77} +(169.911 - 224.103i) q^{78} +610.972 q^{79} +(44.8798 + 25.9113i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(361.736 + 626.545i) q^{82} -949.997i q^{83} +(-72.7461 + 42.0000i) q^{84} +(299.405 - 172.862i) q^{85} +390.352i q^{86} +(-201.469 - 348.955i) q^{87} +(-0.344782 + 0.597180i) q^{88} +(1263.02 + 729.202i) q^{89} -58.3005 q^{90} +(-198.230 + 261.453i) q^{91} +661.896 q^{92} +(-576.937 - 333.095i) q^{93} +(252.226 - 436.868i) q^{94} +(50.6380 + 87.7076i) q^{95} +96.0000i q^{96} +(-331.431 + 191.352i) q^{97} +(84.8705 - 49.0000i) q^{98} -0.775759i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{3} + 48 q^{4} - 108 q^{9} - 24 q^{10} - 174 q^{11} + 288 q^{12} - 96 q^{13} - 336 q^{14} - 90 q^{15} - 192 q^{16} + 140 q^{17} - 60 q^{19} + 120 q^{20} - 128 q^{22} + 34 q^{23} - 1004 q^{25}+ \cdots - 3936 q^{97}+O(q^{100}) \) 24 * q + 36 * q^3 + 48 * q^4 - 108 * q^9 - 24 * q^10 - 174 * q^11 + 288 * q^12 - 96 * q^13 - 336 * q^14 - 90 * q^15 - 192 * q^16 + 140 * q^17 - 60 * q^19 + 120 * q^20 - 128 * q^22 + 34 * q^23 - 1004 * q^25 - 144 * q^26 - 648 * q^27 + 54 * q^29 + 72 * q^30 - 522 * q^33 - 84 * q^35 + 432 * q^36 + 1416 * q^37 + 1056 * q^38 + 108 * q^39 - 192 * q^40 - 942 * q^41 - 504 * q^42 + 762 * q^43 - 270 * q^45 + 636 * q^46 + 576 * q^48 + 588 * q^49 + 720 * q^50 + 840 * q^51 - 528 * q^52 + 184 * q^53 - 256 * q^55 - 672 * q^56 - 2088 * q^58 + 2322 * q^59 - 1274 * q^61 - 232 * q^62 - 1536 * q^64 - 1298 * q^65 - 768 * q^66 - 2472 * q^67 - 560 * q^68 - 102 * q^69 - 2196 * q^71 - 348 * q^74 - 1506 * q^75 - 240 * q^76 + 896 * q^77 - 468 * q^78 - 520 * q^79 + 480 * q^80 - 972 * q^81 - 244 * q^82 + 7974 * q^85 - 162 * q^87 + 512 * q^88 + 1032 * q^89 + 432 * q^90 + 546 * q^91 + 272 * q^92 - 2880 * q^93 - 1104 * q^94 - 2574 * q^95 - 3936 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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