LMFDB - Embedded newform 546.4.i.b.79.3

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			79.3
Root			$-0.593002 + 1.02711i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.4.i.b.235.3

$q$-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} +(-0.502223 + 0.869875i) q^{5} -6.00000 q^{6} +(-14.8884 + 11.0152i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-1.00445 - 1.73975i) q^{10} +(30.3056 + 52.4908i) q^{11} +(6.00000 - 10.3923i) q^{12} +13.0000 q^{13} +(-4.19045 - 36.8027i) q^{14} -3.01334 q^{15} +(-8.00000 + 13.8564i) q^{16} +(66.6078 + 115.368i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(41.9805 - 72.7124i) q^{19} +4.01778 q^{20} +(-50.9510 - 22.1585i) q^{21} -121.222 q^{22} +(55.2490 - 95.6941i) q^{23} +(12.0000 + 20.7846i) q^{24} +(61.9955 + 107.379i) q^{25} +(-13.0000 + 22.5167i) q^{26} -27.0000 q^{27} +(67.9346 + 29.5446i) q^{28} -32.3634 q^{29} +(3.01334 - 5.21925i) q^{30} +(-91.0017 - 157.620i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-90.9168 + 157.472i) q^{33} -266.431 q^{34} +(-2.10454 - 18.4832i) q^{35} +36.0000 q^{36} +(-47.8639 + 82.9027i) q^{37} +(83.9611 + 145.425i) q^{38} +(19.5000 + 33.7750i) q^{39} +(-4.01778 + 6.95900i) q^{40} -380.302 q^{41} +(89.3306 - 66.0912i) q^{42} -186.493 q^{43} +(121.222 - 209.963i) q^{44} +(-4.52001 - 7.82888i) q^{45} +(110.498 + 191.388i) q^{46} +(-240.309 + 416.227i) q^{47} -48.0000 q^{48} +(100.331 - 327.998i) q^{49} -247.982 q^{50} +(-199.823 + 346.104i) q^{51} +(-26.0000 - 45.0333i) q^{52} +(-105.411 - 182.578i) q^{53} +(27.0000 - 46.7654i) q^{54} -60.8806 q^{55} +(-119.107 + 88.1216i) q^{56} +251.883 q^{57} +(32.3634 - 56.0551i) q^{58} +(59.5863 + 103.207i) q^{59} +(6.02667 + 10.4385i) q^{60} +(-377.530 + 653.902i) q^{61} +364.007 q^{62} +(-18.8570 - 165.612i) q^{63} +64.0000 q^{64} +(-6.52890 + 11.3084i) q^{65} +(-181.834 - 314.945i) q^{66} +(230.168 + 398.663i) q^{67} +(266.431 - 461.472i) q^{68} +331.494 q^{69} +(34.1183 + 14.8380i) q^{70} -236.828 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-238.310 - 412.764i) q^{73} +(-95.7278 - 165.805i) q^{74} +(-185.987 + 322.138i) q^{75} -335.844 q^{76} +(-1029.40 - 447.684i) q^{77} -78.0000 q^{78} +(-611.151 + 1058.54i) q^{79} +(-8.03556 - 13.9180i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(380.302 - 658.703i) q^{82} +846.533 q^{83} +(25.1427 + 220.816i) q^{84} -133.808 q^{85} +(186.493 - 323.016i) q^{86} +(-48.5451 - 84.0826i) q^{87} +(242.445 + 419.927i) q^{88} +(586.350 - 1015.59i) q^{89} +18.0800 q^{90} +(-193.550 + 143.198i) q^{91} -441.992 q^{92} +(273.005 - 472.859i) q^{93} +(-480.618 - 832.455i) q^{94} +(42.1672 + 73.0357i) q^{95} +(48.0000 - 83.1384i) q^{96} -423.744 q^{97} +(467.778 + 501.776i) q^{98} -545.501 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$	−0.502223	+	0.869875i	−0.0449202	+	0.0778040i	−0.887611	−	0.460593i	$-0.847637\pi$
$5$	−0.502223	+	0.869875i	−0.0449202	+	0.0778040i	0.842691	+	0.538397i	$0.180970\pi$
$6$	−6.00000			−0.408248
$7$	−14.8884	+	11.0152i	−0.803900	+	0.594765i
$7$	−14.8884	+	11.0152i	−0.803900	+	0.594765i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−1.00445	−	1.73975i	−0.0317634	−	0.0550158i
$11$	30.3056	+	52.4908i	0.830680	+	1.43878i	0.897500	+	0.441015i	$0.145381\pi$
$11$	30.3056	+	52.4908i	0.830680	+	1.43878i	−0.0668200	+	0.997765i	$0.521285\pi$
$12$	6.00000	−	10.3923i	0.144338	−	0.250000i
$13$	13.0000			0.277350
$13$	13.0000			0.277350
$14$	−4.19045	−	36.8027i	−0.0799961	−	0.702567i
$15$	−3.01334			−0.0518693
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	66.6078	+	115.368i	0.950280	+	1.64593i	0.744818	+	0.667268i	$0.232536\pi$
$17$	66.6078	+	115.368i	0.950280	+	1.64593i	0.205462	+	0.978665i	$0.434130\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	41.9805	−	72.7124i	0.506895	−	0.877967i	−0.493074	−	0.869988i	$-0.664127\pi$
$19$	41.9805	−	72.7124i	0.506895	−	0.877967i	0.999968	−	0.00797964i	$-0.00254002\pi$
$20$	4.01778			0.0449202
$21$	−50.9510	−	22.1585i	−0.529448	−	0.230256i
$22$	−121.222			−1.17476
$23$	55.2490	−	95.6941i	0.500879	−	0.867547i	−0.499121	−	0.866532i	$-0.666344\pi$
$23$	55.2490	−	95.6941i	0.500879	−	0.867547i	0.999999	−	0.00101501i	$-0.000323089\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	61.9955	+	107.379i	0.495964	+	0.859035i
$26$	−13.0000	+	22.5167i	−0.0980581	+	0.169842i
$27$	−27.0000			−0.192450
$28$	67.9346	+	29.5446i	0.458516	+	0.199408i
$29$	−32.3634			−0.207232			−0.103616	−	0.994617i	$-0.533041\pi$
$29$	−32.3634			−0.207232			−0.103616	+	0.994617i	$0.533041\pi$
$30$	3.01334	−	5.21925i	0.0183386	−	0.0317634i
$31$	−91.0017	−	157.620i	−0.527238	−	0.913204i	−0.999496	−	0.0317432i	$-0.989894\pi$
$31$	−91.0017	−	157.620i	−0.527238	−	0.913204i	0.472258	−	0.881461i	$-0.343439\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−90.9168	+	157.472i	−0.479593	+	0.830680i
$34$	−266.431			−1.34390
$35$	−2.10454	−	18.4832i	−0.0101638	−	0.0892636i
$36$	36.0000			0.166667
$37$	−47.8639	+	82.9027i	−0.212670	+	0.368355i	−0.952549	−	0.304385i	$-0.901549\pi$
$37$	−47.8639	+	82.9027i	−0.212670	+	0.368355i	0.739879	+	0.672739i	$0.234883\pi$
$38$	83.9611	+	145.425i	0.358429	+	0.620817i
$39$	19.5000	+	33.7750i	0.0800641	+	0.138675i
$40$	−4.01778	+	6.95900i	−0.0158817	+	0.0275079i
$41$	−380.302			−1.44861			−0.724307	−	0.689477i	$-0.757840\pi$
$41$	−380.302			−1.44861			−0.724307	+	0.689477i	$0.757840\pi$
$42$	89.3306	−	66.0912i	0.328191	−	0.242812i
$43$	−186.493			−0.661394			−0.330697	−	0.943737i	$-0.607284\pi$
$43$	−186.493			−0.661394			−0.330697	+	0.943737i	$0.607284\pi$
$44$	121.222	−	209.963i	0.415340	−	0.719390i
$45$	−4.52001	−	7.82888i	−0.0149734	−	0.0259347i
$46$	110.498	+	191.388i	0.354175	+	0.613449i
$47$	−240.309	+	416.227i	−0.745801	+	1.29177i	0.204018	+	0.978967i	$0.434600\pi$
$47$	−240.309	+	416.227i	−0.745801	+	1.29177i	−0.949819	+	0.312799i	$0.898733\pi$
$48$	−48.0000			−0.144338
$49$	100.331	−	327.998i	0.292510	−	0.956263i
$50$	−247.982			−0.701400
$51$	−199.823	+	346.104i	−0.548644	+	0.950280i
$52$	−26.0000	−	45.0333i	−0.0693375	−	0.120096i
$53$	−105.411	−	182.578i	−0.273195	−	0.473188i	0.696483	−	0.717573i	$-0.254747\pi$
$53$	−105.411	−	182.578i	−0.273195	−	0.473188i	−0.969678	+	0.244385i	$0.921414\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−60.8806			−0.149257
$56$	−119.107	+	88.1216i	−0.284221	+	0.210281i
$57$	251.883			0.585312
$58$	32.3634	−	56.0551i	0.0732677	−	0.126903i
$59$	59.5863	+	103.207i	0.131483	+	0.227735i	0.924248	−	0.381792i	$-0.124693\pi$
$59$	59.5863	+	103.207i	0.131483	+	0.227735i	−0.792766	+	0.609527i	$0.791360\pi$
$60$	6.02667	+	10.4385i	0.0129673	+	0.0224601i
$61$	−377.530	+	653.902i	−0.792423	+	1.37252i	0.132039	+	0.991244i	$0.457848\pi$
$61$	−377.530	+	653.902i	−0.792423	+	1.37252i	−0.924463	+	0.381273i	$0.875486\pi$
$62$	364.007			0.745628
$63$	−18.8570	−	165.612i	−0.0377105	−	0.331193i
$64$	64.0000			0.125000
$65$	−6.52890	+	11.3084i	−0.0124586	+	0.0215790i
$66$	−181.834	−	314.945i	−0.339124	−	0.587379i
$67$	230.168	+	398.663i	0.419695	+	0.726933i	0.995909	−	0.0903663i	$-0.0288038\pi$
$67$	230.168	+	398.663i	0.419695	+	0.726933i	−0.576214	+	0.817299i	$0.695470\pi$
$68$	266.431	−	461.472i	0.475140	−	0.822966i
$69$	331.494			0.578365
$70$	34.1183	+	14.8380i	0.0582560	+	0.0253354i
$71$	−236.828			−0.395863			−0.197931	−	0.980216i	$-0.563422\pi$
$71$	−236.828			−0.395863			−0.197931	+	0.980216i	$0.563422\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−238.310	−	412.764i	−0.382083	−	0.661787i	0.609277	−	0.792957i	$-0.291460\pi$
$73$	−238.310	−	412.764i	−0.382083	−	0.661787i	−0.991360	+	0.131171i	$0.958126\pi$
$74$	−95.7278	−	165.805i	−0.150380	−	0.260466i
$75$	−185.987	+	322.138i	−0.286345	+	0.495964i
$76$	−335.844			−0.506895
$77$	−1029.40	−	447.684i	−1.52352	−	0.662576i
$78$	−78.0000			−0.113228
$79$	−611.151	+	1058.54i	−0.870377	+	1.50754i	−0.00877076	+	0.999962i	$0.502792\pi$
$79$	−611.151	+	1058.54i	−0.870377	+	1.50754i	−0.861607	+	0.507576i	$0.830541\pi$
$80$	−8.03556	−	13.9180i	−0.0112300	−	0.0194510i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	380.302	−	658.703i	0.512163	−	0.887092i
$83$	846.533			1.11951			0.559753	−	0.828659i	$-0.310896\pi$
$83$	846.533			1.11951			0.559753	+	0.828659i	$0.310896\pi$
$84$	25.1427	+	220.816i	0.0326583	+	0.286822i
$85$	−133.808			−0.170747
$86$	186.493	−	323.016i	0.233838	−	0.405020i
$87$	−48.5451	−	84.0826i	−0.0598228	−	0.103616i
$88$	242.445	+	419.927i	0.293690	+	0.508685i
$89$	586.350	−	1015.59i	0.698348	−	1.20957i	−0.270692	−	0.962666i	$-0.587252\pi$
$89$	586.350	−	1015.59i	0.698348	−	1.20957i	0.969039	−	0.246907i	$-0.0794143\pi$
$90$	18.0800			0.0211756
$91$	−193.550	+	143.198i	−0.222962	+	0.164958i
$92$	−441.992			−0.500879
$93$	273.005	−	472.859i	0.304401	−	0.527238i
$94$	−480.618	−	832.455i	−0.527361	−	0.913416i
$95$	42.1672	+	73.0357i	0.0455396	+	0.0788769i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	−423.744			−0.443553			−0.221777	−	0.975097i	$-0.571186\pi$
$97$	−423.744			−0.443553			−0.221777	+	0.975097i	$0.571186\pi$
$98$	467.778	+	501.776i	0.482171	+	0.517215i
$99$	−545.501			−0.553787
$100$	247.982	−	429.518i	0.247982	−	0.429518i
$101$	−767.300	−	1329.00i	−0.755932	−	1.30931i	−0.944910	−	0.327332i	$-0.893851\pi$
$101$	−767.300	−	1329.00i	−0.755932	−	1.30931i	0.188977	−	0.981981i	$-0.439483\pi$
$102$	−399.647	−	692.208i	−0.387950	−	0.671949i
$103$	−729.947	+	1264.31i	−0.698289	+	1.20947i	0.270770	+	0.962644i	$0.412722\pi$
$103$	−729.947	+	1264.31i	−0.698289	+	1.20947i	−0.969059	+	0.246829i	$0.920612\pi$
$104$	104.000			0.0980581
$105$	44.8639	−	33.1925i	0.0416978	−	0.0308501i
$106$	421.645			0.386356
$107$	219.760	−	380.635i	0.198551	−	0.343901i	−0.749508	−	0.661996i	$-0.769710\pi$
$107$	219.760	−	380.635i	0.198551	−	0.343901i	0.948059	+	0.318095i	$0.103043\pi$
$108$	54.0000	+	93.5307i	0.0481125	+	0.0833333i
$109$	−330.055	−	571.672i	−0.290033	−	0.502351i	0.683784	−	0.729684i	$-0.260333\pi$
$109$	−330.055	−	571.672i	−0.290033	−	0.502351i	−0.973817	+	0.227333i	$0.927000\pi$
$110$	60.8806	−	105.448i	0.0527704	−	0.0914010i
$111$	−287.183			−0.245570
$112$	−33.5236	−	294.422i	−0.0282829	−	0.248395i
$113$	857.977			0.714263			0.357131	−	0.934054i	$-0.383755\pi$
$113$	857.977			0.714263			0.357131	+	0.934054i	$0.383755\pi$
$114$	−251.883	+	436.275i	−0.206939	+	0.358429i
$115$	55.4946	+	96.1195i	0.0449991	+	0.0779408i
$116$	64.7268	+	112.110i	0.0518081	+	0.0897342i
$117$	−58.5000	+	101.325i	−0.0462250	+	0.0800641i
$118$	−238.345			−0.185945
$119$	−2262.49	−	983.952i	−1.74287	−	0.757972i
$120$	−24.1067			−0.0183386
$121$	−1171.36	+	2028.85i	−0.880058	+	1.52431i
$122$	−755.061	−	1307.80i	−0.560328	−	0.970516i
$123$	−570.453	−	988.054i	−0.418179	−	0.724307i
$124$	−364.007	+	630.478i	−0.263619	+	0.456602i
$125$	−250.098			−0.178956
$126$	305.706	+	132.951i	0.216146	+	0.0940017i
$127$	−1044.46			−0.729770			−0.364885	−	0.931053i	$-0.618892\pi$
$127$	−1044.46			−0.729770			−0.364885	+	0.931053i	$0.618892\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−279.740	−	484.524i	−0.190928	−	0.330697i
$130$	−13.0578	−	22.6168i	−0.00880957	−	0.0152586i
$131$	335.920	−	581.830i	0.224042	−	0.388052i	−0.731990	−	0.681316i	$-0.761408\pi$
$131$	335.920	−	581.830i	0.224042	−	0.388052i	0.956032	+	0.293264i	$0.0947415\pi$
$132$	727.334			0.479593
$133$	175.917	+	1545.00i	0.114692	+	1.00728i
$134$	−920.674			−0.593538
$135$	13.5600	−	23.4866i	0.00864489	−	0.0149734i
$136$	532.862	+	922.944i	0.335975	+	0.581925i
$137$	−62.4513	−	108.169i	−0.0389458	−	0.0674561i	0.845895	−	0.533349i	$-0.179067\pi$
$137$	−62.4513	−	108.169i	−0.0389458	−	0.0674561i	−0.884841	+	0.465893i	$0.845733\pi$
$138$	−331.494	+	574.164i	−0.204483	+	0.354175i
$139$	2729.13			1.66534			0.832670	−	0.553770i	$-0.186811\pi$
$139$	2729.13			1.66534			0.832670	+	0.553770i	$0.186811\pi$
$140$	−59.8185	+	44.2567i	−0.0361113	+	0.0267169i
$141$	−1441.85			−0.861177
$142$	236.828	−	410.197i	0.139959	−	0.242416i
$143$	393.973	+	682.381i	0.230389	+	0.399046i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	16.2536	−	28.1521i	0.00930891	−	0.0161235i
$146$	953.239			0.540347
$147$	1002.66	−	231.330i	0.562572	−	0.129794i
$148$	382.911			0.212670
$149$	1441.68	−	2497.06i	0.792664	−	1.37293i	−0.131649	−	0.991296i	$-0.542027\pi$
$149$	1441.68	−	2497.06i	0.792664	−	1.37293i	0.924312	−	0.381637i	$-0.124640\pi$
$150$	−371.973	−	644.277i	−0.202477	−	0.350700i
$151$	−588.345	−	1019.04i	−0.317078	−	0.549196i	0.662799	−	0.748798i	$-0.269369\pi$
$151$	−588.345	−	1019.04i	−0.317078	−	0.549196i	−0.979877	+	0.199602i	$0.936035\pi$
$152$	335.844	−	581.700i	0.179214	−	0.310408i
$153$	−1198.94			−0.633520
$154$	1804.81	−	1335.29i	0.944388	−	0.698705i
$155$	182.813			0.0947346
$156$	78.0000	−	135.100i	0.0400320	−	0.0693375i
$157$	156.263	+	270.656i	0.0794342	+	0.137584i	0.903006	−	0.429628i	$-0.141355\pi$
$157$	156.263	+	270.656i	0.0794342	+	0.137584i	−0.823572	+	0.567212i	$0.808022\pi$
$158$	−1222.30	−	2117.09i	−0.615450	−	1.06599i
$159$	316.234	−	547.733i	0.157729	−	0.273195i
$160$	32.1423			0.0158817
$161$	231.518	+	2033.31i	0.113330	+	0.995326i
$162$	162.000			0.0785674
$163$	1383.64	−	2396.54i	0.664878	−	1.15160i	−0.314441	−	0.949277i	$-0.601817\pi$
$163$	1383.64	−	2396.54i	0.664878	−	1.15160i	0.979318	−	0.202325i	$-0.0648497\pi$
$164$	760.604	+	1317.41i	0.362154	+	0.627269i
$165$	−91.3209	−	158.173i	−0.0430868	−	0.0746286i
$166$	−846.533	+	1466.24i	−0.395805	+	0.685555i
$167$	206.667			0.0957628			0.0478814	−	0.998853i	$-0.484753\pi$
$167$	206.667			0.0957628			0.0478814	+	0.998853i	$0.484753\pi$
$168$	−407.608	−	177.268i	−0.187188	−	0.0814078i
$169$	169.000			0.0769231
$170$	133.808	−	231.762i	0.0603682	−	0.104561i
$171$	377.825	+	654.412i	0.168965	+	0.292656i
$172$	372.987	+	646.032i	0.165349	+	0.286392i
$173$	−1033.52	+	1790.10i	−0.454201	+	0.786699i	−0.998642	−	0.0521001i	$-0.983408\pi$
$173$	−1033.52	+	1790.10i	−0.454201	+	0.786699i	0.544441	+	0.838799i	$0.316742\pi$
$174$	194.181			0.0846022
$175$	−2105.82	−	915.818i	−0.909630	−	0.395596i
$176$	−969.779			−0.415340
$177$	−178.759	+	309.620i	−0.0759115	+	0.131483i
$178$	1172.70	+	2031.17i	0.493806	+	0.855298i
$179$	2014.77	+	3489.69i	0.841292	+	1.45716i	0.888803	+	0.458289i	$0.151538\pi$
$179$	2014.77	+	3489.69i	0.841292	+	1.45716i	−0.0475114	+	0.998871i	$0.515129\pi$
$180$	−18.0800	+	31.3155i	−0.00748670	+	0.0129673i
$181$	−1314.37			−0.539757			−0.269879	−	0.962894i	$-0.586984\pi$
$181$	−1314.37			−0.539757			−0.269879	+	0.962894i	$0.586984\pi$
$182$	−54.4758	−	478.435i	−0.0221869	−	0.194857i
$183$	−2265.18			−0.915012
$184$	441.992	−	765.553i	0.177087	−	0.306724i
$185$	−48.0767	−	83.2713i	−0.0191063	−	0.0330931i
$186$	546.010	+	945.718i	0.215244	+	0.372814i
$187$	−4037.18	+	6992.59i	−1.57876	+	2.73449i
$188$	1922.47			0.745801
$189$	401.988	−	297.410i	0.154711	−	0.114463i
$190$	−168.669			−0.0644027
$191$	271.428	−	470.127i	0.102826	−	0.178100i	−0.810022	−	0.586400i	$-0.800545\pi$
$191$	271.428	−	470.127i	0.102826	−	0.178100i	0.912848	+	0.408299i	$0.133878\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	548.387	+	949.835i	0.204527	+	0.354252i	0.949982	−	0.312305i	$-0.101101\pi$
$193$	548.387	+	949.835i	0.204527	+	0.354252i	−0.745455	+	0.666556i	$0.767768\pi$
$194$	423.744	−	733.946i	0.156820	−	0.271620i
$195$	−39.1734			−0.0143860
$196$	−1336.88	+	308.440i	−0.487201	+	0.112405i
$197$	−4003.89			−1.44805			−0.724023	−	0.689776i	$-0.757709\pi$
$197$	−4003.89			−1.44805			−0.724023	+	0.689776i	$0.757709\pi$
$198$	545.501	−	944.835i	0.195793	−	0.339124i
$199$	1265.76	+	2192.36i	0.450890	+	0.780965i	0.998442	−	0.0558071i	$-0.0177732\pi$
$199$	1265.76	+	2192.36i	0.450890	+	0.780965i	−0.547551	+	0.836772i	$0.684440\pi$
$200$	495.964	+	859.035i	0.175350	+	0.303715i
$201$	−690.505	+	1195.99i	−0.242311	+	0.419695i
$202$	3069.20			1.06905
$203$	481.841	−	356.489i	0.166594	−	0.123254i
$204$	1598.59			0.548644
$205$	190.996	−	330.815i	0.0650720	−	0.112708i
$206$	−1459.89	−	2528.61i	−0.493765	−	0.855226i
$207$	497.241	+	861.247i	0.166960	+	0.289182i
$208$	−104.000	+	180.133i	−0.0346688	+	0.0600481i
$209$	5088.98			1.68427
$210$	12.6272	+	110.899i	0.00414934	+	0.0364417i
$211$	2649.23			0.864363			0.432181	−	0.901787i	$-0.357744\pi$
$211$	2649.23			0.864363			0.432181	+	0.901787i	$0.357744\pi$
$212$	−421.645	+	730.311i	−0.136598	+	0.236594i
$213$	−355.241	−	615.296i	−0.114276	−	0.197931i
$214$	439.519	+	761.270i	0.140397	+	0.243174i
$215$	93.6612	−	162.226i	0.0297100	−	0.0514591i
$216$	−216.000			−0.0680414
$217$	3091.08	+	1344.31i	0.966988	+	0.420541i
$218$	1320.22			0.410168
$219$	714.929	−	1238.29i	0.220596	−	0.382083i
$220$	121.761	+	210.897i	0.0373143	+	0.0646302i
$221$	865.901	+	1499.78i	0.263560	+	0.456500i
$222$	287.183	−	497.416i	0.0868220	−	0.150380i
$223$	6044.14			1.81500			0.907501	−	0.420049i	$-0.137987\pi$
$223$	6044.14			1.81500			0.907501	+	0.420049i	$0.137987\pi$
$224$	543.477	+	236.357i	0.162110	+	0.0705012i
$225$	−1115.92			−0.330643
$226$	−857.977	+	1486.06i	−0.252530	+	0.437395i
$227$	−1257.69	−	2178.39i	−0.367736	−	0.636938i	0.621475	−	0.783434i	$-0.286534\pi$
$227$	−1257.69	−	2178.39i	−0.367736	−	0.636938i	−0.989211	+	0.146496i	$0.953200\pi$
$228$	−503.767	−	872.549i	−0.146328	−	0.253447i
$229$	192.868	−	334.057i	0.0556553	−	0.0963978i	−0.836855	−	0.547424i	$-0.815609\pi$
$229$	192.868	−	334.057i	0.0556553	−	0.0963978i	0.892511	+	0.451026i	$0.148942\pi$
$230$	−221.978			−0.0636384
$231$	−380.982	−	3345.98i	−0.108514	−	0.953029i
$232$	−258.907			−0.0732677
$233$	−731.632	+	1267.22i	−0.205712	+	0.356303i	−0.950359	−	0.311155i	$-0.899284\pi$
$233$	−731.632	+	1267.22i	−0.205712	+	0.356303i	0.744648	+	0.667458i	$0.232618\pi$
$234$	−117.000	−	202.650i	−0.0326860	−	0.0566139i
$235$	−241.377	−	418.078i	−0.0670031	−	0.116053i
$236$	238.345	−	412.826i	0.0657413	−	0.113867i
$237$	−3666.90			−1.00503
$238$	3966.74	−	2934.79i	1.08036	−	0.799304i
$239$	−1848.06			−0.500172			−0.250086	−	0.968224i	$-0.580459\pi$
$239$	−1848.06			−0.500172			−0.250086	+	0.968224i	$0.580459\pi$
$240$	24.1067	−	41.7540i	0.00648367	−	0.0112300i
$241$	1766.95	+	3060.44i	0.472278	+	0.818010i	0.999497	−	0.0317198i	$-0.0100984\pi$
$241$	1766.95	+	3060.44i	0.472278	+	0.818010i	−0.527219	+	0.849730i	$0.676765\pi$
$242$	−2342.71	−	4057.70i	−0.622295	−	1.07785i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	3020.24			0.792423
$245$	234.929	+	252.003i	0.0612615	+	0.0657139i
$246$	2281.81			0.591395
$247$	545.747	−	945.262i	0.140587	−	0.243504i
$248$	−728.014	−	1260.96i	−0.186407	−	0.322866i
$249$	1269.80	+	2199.36i	0.323174	+	0.559753i
$250$	250.098	−	433.182i	0.0632703	−	0.109587i
$251$	920.080			0.231374			0.115687	−	0.993286i	$-0.463093\pi$
$251$	920.080			0.231374			0.115687	+	0.993286i	$0.463093\pi$
$252$	−535.984	+	396.547i	−0.133983	+	0.0991275i
$253$	6697.41			1.66428
$254$	1044.46	−	1809.06i	0.258013	−	0.446891i
$255$	−200.712	−	347.643i	−0.0492904	−	0.0853735i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	666.894	−	1155.09i	0.161867	−	0.280361i	−0.773672	−	0.633587i	$-0.781582\pi$
$257$	666.894	−	1155.09i	0.161867	−	0.280361i	0.935538	+	0.353226i	$0.114915\pi$
$258$	1118.96			0.270013
$259$	−200.571	−	1761.52i	−0.0481193	−	0.422609i
$260$	52.2312			0.0124586
$261$	145.635	−	252.248i	0.0345387	−	0.0598228i
$262$	671.840	+	1163.66i	0.158421	+	0.274394i
$263$	3027.09	+	5243.07i	0.709727	+	1.22928i	0.964958	+	0.262403i	$0.0845148\pi$
$263$	3027.09	+	5243.07i	0.709727	+	1.22928i	−0.255232	+	0.966880i	$0.582152\pi$
$264$	−727.334	+	1259.78i	−0.169562	+	0.293690i
$265$	211.760			0.0490879
$266$	−2851.93	−	1240.30i	−0.657381	−	0.285894i
$267$	3518.10			0.806382
$268$	920.674	−	1594.65i	0.209847	−	0.363466i
$269$	−3477.64	−	6023.46i	−0.788237	−	1.36527i	−0.927046	−	0.374947i	$-0.877661\pi$
$269$	−3477.64	−	6023.46i	−0.788237	−	1.36527i	0.138809	−	0.990319i	$-0.455672\pi$
$270$	27.1200	+	46.9733i	0.00611286	+	0.0105878i
$271$	−1927.23	+	3338.05i	−0.431995	+	0.748237i	−0.997045	−	0.0768192i	$-0.975524\pi$
$271$	−1927.23	+	3338.05i	−0.431995	+	0.748237i	0.565050	+	0.825057i	$0.308857\pi$
$272$	−2131.45			−0.475140
$273$	−662.363	−	288.060i	−0.146843	−	0.0638616i
$274$	249.805			0.0550777
$275$	−3757.62	+	6508.39i	−0.823975	+	1.42717i
$276$	−662.988	−	1148.33i	−0.144591	−	0.250439i
$277$	1550.13	+	2684.91i	0.336239	+	0.582384i	0.983722	−	0.179696i	$-0.0575115\pi$
$277$	1550.13	+	2684.91i	0.336239	+	0.582384i	−0.647483	+	0.762080i	$0.724178\pi$
$278$	−2729.13	+	4727.00i	−0.588786	+	1.01981i
$279$	1638.03			0.351492
$280$	−16.8363	−	147.865i	−0.00359344	−	0.0315594i
$281$	4956.53			1.05225			0.526125	−	0.850408i	$-0.323645\pi$
$281$	4956.53			1.05225			0.526125	+	0.850408i	$0.323645\pi$
$282$	1441.85	−	2497.36i	0.304472	−	0.527361i
$283$	−2010.67	−	3482.58i	−0.422339	−	0.731512i	0.573829	−	0.818975i	$-0.305457\pi$
$283$	−2010.67	−	3482.58i	−0.422339	−	0.731512i	−0.996168	+	0.0874632i	$0.972124\pi$
$284$	473.655	+	820.395i	0.0989657	+	0.171414i
$285$	−126.502	+	219.107i	−0.0262923	+	0.0455396i
$286$	−1575.89			−0.325819
$287$	5662.10	−	4189.10i	1.16454	−	0.861585i
$288$	288.000			0.0589256
$289$	−6416.69	+	11114.0i	−1.30606	+	2.26217i
$290$	32.5073	+	56.3043i	0.00658239	+	0.0114010i
$291$	−635.616	−	1100.92i	−0.128043	−	0.221777i
$292$	−953.239	+	1651.06i	−0.191041	+	0.330893i
$293$	717.001			0.142961			0.0714807	−	0.997442i	$-0.477228\pi$
$293$	717.001			0.142961			0.0714807	+	0.997442i	$0.477228\pi$
$294$	−601.985	+	1967.99i	−0.119417	+	0.390393i
$295$	−119.702			−0.0236249
$296$	−382.911	+	663.222i	−0.0751901	+	0.130233i
$297$	−818.251	−	1417.25i	−0.159864	−	0.276893i
$298$	2883.36	+	4994.12i	0.560498	+	0.970811i
$299$	718.237	−	1244.02i	0.138919	−	0.240614i
$300$	1487.89			0.286345
$301$	2776.59	−	2054.26i	0.531695	−	0.393374i
$302$	2353.38			0.448417
$303$	2301.90	−	3987.01i	0.436438	−	0.755932i
$304$	671.689	+	1163.40i	0.126724	+	0.219492i
$305$	−379.209	−	656.809i	−0.0711916	−	0.123307i
$306$	1198.94	−	2076.62i	0.223983	−	0.387950i
$307$	−1005.80			−0.186984			−0.0934918	−	0.995620i	$-0.529803\pi$
$307$	−1005.80			−0.186984			−0.0934918	+	0.995620i	$0.529803\pi$
$308$	507.976	+	4461.31i	0.0939761	+	0.825347i
$309$	−4379.68			−0.806315
$310$	−182.813	+	316.641i	−0.0334937	+	0.0580128i
$311$	3333.35	+	5773.54i	0.607772	+	1.05269i	0.991607	+	0.129291i	$0.0412700\pi$
$311$	3333.35	+	5773.54i	0.607772	+	1.05269i	−0.383834	+	0.923402i	$0.625397\pi$
$312$	156.000	+	270.200i	0.0283069	+	0.0490290i
$313$	3170.20	−	5490.95i	0.572494	−	0.991588i	−0.423815	−	0.905749i	$-0.639309\pi$
$313$	3170.20	−	5490.95i	0.572494	−	0.991588i	0.996309	−	0.0858395i	$-0.0273572\pi$
$314$	−625.053			−0.112337
$315$	153.532	+	66.7710i	0.0274621	+	0.0119432i
$316$	4889.21			0.870377
$317$	764.652	−	1324.42i	0.135480	−	0.234658i	−0.790301	−	0.612719i	$-0.790076\pi$
$317$	764.652	−	1324.42i	0.135480	−	0.234658i	0.925781	+	0.378061i	$0.123409\pi$
$318$	632.468	+	1095.47i	0.111532	+	0.193178i
$319$	−980.792	−	1698.78i	−0.172144	−	0.298162i
$320$	−32.1423	+	55.6720i	−0.00561502	+	0.00972550i
$321$	1318.56			0.229267
$322$	−3753.32	−	1632.31i	−0.649579	−	0.282501i
$323$	11184.9			1.92677
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	805.942	+	1395.93i	0.137556	+	0.238254i
$326$	2767.28	+	4793.07i	0.470140	+	0.814306i
$327$	990.166	−	1715.02i	0.167450	−	0.290033i
$328$	−3042.42			−0.512163
$329$	−1007.00	−	8844.02i	−0.168747	−	1.48203i
$330$	365.284			0.0609340
$331$	−4489.77	+	7776.51i	−0.745559	+	1.29135i	0.204373	+	0.978893i	$0.434484\pi$
$331$	−4489.77	+	7776.51i	−0.745559	+	1.29135i	−0.949933	+	0.312454i	$0.898849\pi$
$332$	−1693.07	−	2932.47i	−0.279877	−	0.484760i
$333$	−430.775	−	746.125i	−0.0708899	−	0.122785i
$334$	−206.667	+	357.958i	−0.0338573	+	0.0586425i
$335$	−462.383			−0.0754110
$336$	714.645	−	528.729i	0.116033	−	0.0858469i
$337$	3160.02			0.510793			0.255396	−	0.966836i	$-0.417794\pi$
$337$	3160.02			0.510793			0.255396	+	0.966836i	$0.417794\pi$
$338$	−169.000	+	292.717i	−0.0271964	+	0.0471056i
$339$	1286.97	+	2229.09i	0.206190	+	0.357131i
$340$	267.616	+	463.524i	0.0426867	+	0.0739356i
$341$	5515.72	−	9553.51i	0.875933	−	1.51716i
$342$	−1511.30			−0.238952
$343$	2119.19	+	5988.54i	0.333603	+	0.942714i
$344$	−1491.95			−0.233838
$345$	−166.484	+	288.358i	−0.0259803	+	0.0449991i
$346$	−2067.03	−	3580.20i	−0.321169	−	0.556280i
$347$	−1193.00	−	2066.34i	−0.184564	−	0.319675i	0.758865	−	0.651248i	$-0.225754\pi$
$347$	−1193.00	−	2066.34i	−0.184564	−	0.319675i	−0.943430	+	0.331573i	$0.892421\pi$
$348$	−194.181	+	336.331i	−0.0299114	+	0.0518081i
$349$	−8247.11			−1.26492			−0.632461	−	0.774592i	$-0.717955\pi$
$349$	−8247.11			−1.26492			−0.632461	+	0.774592i	$0.717955\pi$
$350$	3692.07	−	2731.57i	0.563855	−	0.417168i
$351$	−351.000			−0.0533761
$352$	969.779	−	1679.71i	0.146845	−	0.254343i
$353$	−2708.62	−	4691.47i	−0.408401	−	0.707371i	0.586310	−	0.810087i	$-0.300580\pi$
$353$	−2708.62	−	4691.47i	−0.408401	−	0.707371i	−0.994711	+	0.102716i	$0.967247\pi$
$354$	−357.518	−	619.239i	−0.0536776	−	0.0929723i
$355$	118.940	−	206.010i	0.0177822	−	0.0307997i
$356$	−4690.80			−0.698348
$357$	−837.350	−	7354.04i	−0.124138	−	1.09024i
$358$	−8059.09			−1.18977
$359$	−3397.05	+	5883.86i	−0.499413	+	0.865009i	−1.00000		0.000677483i	$-0.999784\pi$
$359$	−3397.05	+	5883.86i	−0.499413	+	0.865009i	0.500587	+	0.865686i	$0.333118\pi$
$360$	−36.1600	−	62.6310i	−0.00529389	−	0.00916929i
$361$	−95.2329	−	164.948i	−0.0138844	−	0.0240484i
$362$	1314.37	−	2276.55i	0.190833	−	0.330532i
$363$	−7028.14			−1.01620
$364$	883.150	+	384.080i	0.127169	+	0.0553057i
$365$	478.738			0.0686529
$366$	2265.18	−	3923.41i	0.323505	−	0.560328i
$367$	1603.30	+	2777.00i	0.228043	+	0.394982i	0.957228	−	0.289335i	$-0.0934340\pi$
$367$	1603.30	+	2777.00i	0.228043	+	0.394982i	−0.729185	+	0.684316i	$0.760101\pi$
$368$	883.984	+	1531.11i	0.125220	+	0.216887i
$369$	1711.36	−	2964.16i	0.241436	−	0.418179i
$370$	192.307			0.0270204
$371$	3580.54	+	1557.17i	0.501057	+	0.217909i
$372$	−2184.04			−0.304401
$373$	305.547	−	529.224i	0.0424146	−	0.0734642i	−0.844039	−	0.536282i	$-0.819828\pi$
$373$	305.547	−	529.224i	0.0424146	−	0.0734642i	0.886453	+	0.462818i	$0.153162\pi$
$374$	−8074.35	−	13985.2i	−1.11635	−	1.93357i
$375$	−375.147	−	649.774i	−0.0516600	−	0.0894778i
$376$	−1922.47	+	3329.82i	−0.263681	+	0.456708i
$377$	−420.724			−0.0574759
$378$	113.142	+	993.673i	0.0153952	+	0.135209i
$379$	−12040.3			−1.63185			−0.815925	−	0.578158i	$-0.803772\pi$
$379$	−12040.3			−1.63185			−0.815925	+	0.578158i	$0.803772\pi$
$380$	168.669	−	292.143i	0.0227698	−	0.0394384i
$381$	−1566.69	−	2713.58i	−0.210666	−	0.364885i
$382$	542.856	+	940.254i	0.0727092	+	0.125936i
$383$	−6344.65	+	10989.3i	−0.846466	+	1.46612i	0.0378752	+	0.999282i	$0.487941\pi$
$383$	−6344.65	+	10989.3i	−0.846466	+	1.46612i	−0.884342	+	0.466840i	$0.845392\pi$
$384$	−384.000			−0.0510310
$385$	906.417	−	670.612i	0.119988	−	0.0887729i
$386$	−2193.55			−0.289245
$387$	839.220	−	1453.57i	0.110232	−	0.190928i
$388$	847.488	+	1467.89i	0.110888	+	0.192064i
$389$	4314.67	+	7473.24i	0.562372	+	0.974057i	0.997289	+	0.0735862i	$0.0234444\pi$
$389$	4314.67	+	7473.24i	0.562372	+	0.974057i	−0.434917	+	0.900471i	$0.643222\pi$
$390$	39.1734	−	67.8503i	0.00508621	−	0.00880957i
$391$	14720.0			1.90390
$392$	802.647	−	2623.98i	0.103418	−	0.338090i
$393$	2015.52			0.258701
$394$	4003.89	−	6934.93i	0.511962	−	0.886743i
$395$	−613.868	−	1063.25i	−0.0781950	−	0.135438i
$396$	1091.00	+	1889.67i	0.138447	+	0.239797i
$397$	−1181.81	+	2046.96i	−0.149404	+	0.258775i	−0.931007	−	0.365000i	$-0.881069\pi$
$397$	−1181.81	+	2046.96i	−0.149404	+	0.258775i	0.781603	+	0.623776i	$0.214402\pi$
$398$	−5063.03			−0.637655
$399$	−3750.15	+	2774.54i	−0.470532	+	0.348123i
$400$	−1983.86			−0.247982
$401$	−3952.59	+	6846.08i	−0.492226	+	0.852561i	−0.999960	−	0.00895317i	$-0.997150\pi$
$401$	−3952.59	+	6846.08i	−0.492226	+	0.852561i	0.507734	+	0.861514i	$0.330483\pi$
$402$	−1381.01	−	2391.98i	−0.171340	−	0.296769i
$403$	−1183.02	−	2049.05i	−0.146230	−	0.253277i
$404$	−3069.20	+	5316.01i	−0.377966	+	0.654657i
$405$	81.3601			0.00998226
$406$	135.617	+	1191.06i	0.0165778	+	0.145595i
$407$	−5802.18			−0.706642
$408$	−1598.59	+	2768.83i	−0.193975	+	0.335975i
$409$	−3779.30	−	6545.93i	−0.456905	−	0.791383i	0.541891	−	0.840449i	$-0.317709\pi$
$409$	−3779.30	−	6545.93i	−0.456905	−	0.791383i	−0.998796	+	0.0490664i	$0.984375\pi$
$410$	381.993	+	661.631i	0.0460129	+	0.0796966i
$411$	187.354	−	324.507i	0.0224854	−	0.0389458i
$412$	5839.58			0.698289
$413$	−2023.99	−	880.228i	−0.241147	−	0.104875i
$414$	−1988.96			−0.236117
$415$	−425.148	+	736.378i	−0.0502884	+	0.0871021i
$416$	−208.000	−	360.267i	−0.0245145	−	0.0424604i
$417$	4093.70	+	7090.50i	0.480742	+	0.832670i
$418$	−5088.98	+	8814.37i	−0.595479	+	1.03140i
$419$	2184.13			0.254658			0.127329	−	0.991861i	$-0.459360\pi$
$419$	2184.13			0.254658			0.127329	+	0.991861i	$0.459360\pi$
$420$	−204.710	−	89.0280i	−0.0237829	−	0.0103431i
$421$	−4511.31			−0.522251			−0.261125	−	0.965305i	$-0.584094\pi$
$421$	−4511.31			−0.522251			−0.261125	+	0.965305i	$0.584094\pi$
$422$	−2649.23	+	4588.60i	−0.305598	+	0.529312i
$423$	−2162.78	−	3746.05i	−0.248600	−	0.430589i
$424$	−843.290	−	1460.62i	−0.0965891	−	0.167297i
$425$	−8258.77	+	14304.6i	−0.942610	+	1.63265i
$426$	1420.97			0.161610
$427$	−1582.02	−	13894.1i	−0.179296	−	1.57467i
$428$	−1758.08			−0.198551
$429$	−1181.92	+	2047.14i	−0.133015	+	0.230389i
$430$	187.322	+	324.452i	0.0210081	+	0.0363871i
$431$	−6765.02	−	11717.4i	−0.756055	−	1.30953i	−0.944848	−	0.327509i	$-0.893791\pi$
$431$	−6765.02	−	11717.4i	−0.756055	−	1.30953i	0.188793	−	0.982017i	$-0.439542\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	−4680.48			−0.519467			−0.259734	−	0.965680i	$-0.583635\pi$
$433$	−4680.48			−0.519467			−0.259734	+	0.965680i	$0.583635\pi$
$434$	−5419.49	+	4009.61i	−0.599410	+	0.443473i
$435$	97.5219			0.0107490
$436$	−1320.22	+	2286.69i	−0.145016	+	0.251176i
$437$	−4638.77	−	8034.58i	−0.507786	−	0.879510i
$438$	1429.86	+	2476.59i	0.155985	+	0.270173i
$439$	4131.53	−	7156.01i	0.449173	−	0.777991i	−0.549159	−	0.835718i	$-0.685052\pi$
$439$	4131.53	−	7156.01i	0.449173	−	0.777991i	0.998332	+	0.0577270i	$0.0183853\pi$
$440$	−487.045			−0.0527704
$441$	2105.00	+	2257.99i	0.227298	+	0.243817i
$442$	−3463.60			−0.372730
$443$	−2251.32	+	3899.39i	−0.241452	+	0.418207i	−0.961128	−	0.276103i	$-0.910957\pi$
$443$	−2251.32	+	3899.39i	−0.241452	+	0.418207i	0.719676	+	0.694310i	$0.244290\pi$
$444$	574.367	+	994.833i	0.0613925	+	0.106335i
$445$	588.956	+	1020.10i	0.0627398	+	0.108668i
$446$	−6044.14	+	10468.8i	−0.641700	+	1.11146i
$447$	8650.07			0.915289
$448$	−952.860	+	704.973i	−0.100487	+	0.0743456i
$449$	−9976.69			−1.04862			−0.524308	−	0.851528i	$-0.675676\pi$
$449$	−9976.69			−1.04862			−0.524308	+	0.851528i	$0.675676\pi$
$450$	1115.92	−	1932.83i	0.116900	−	0.202477i
$451$	−11525.3	−	19962.4i	−1.20334	−	2.08424i
$452$	−1715.95	−	2972.12i	−0.178566	−	0.309285i
$453$	1765.04	−	3057.13i	0.183065	−	0.317078i
$454$	5030.78			0.520058
$455$	−27.3590	−	240.281i	−0.00281892	−	0.0247573i
$456$	2015.07			0.206939
$457$	3925.50	−	6799.16i	0.401810	−	0.695955i	−0.592135	−	0.805839i	$-0.701715\pi$
$457$	3925.50	−	6799.16i	0.401810	−	0.695955i	0.993944	+	0.109884i	$0.0350480\pi$
$458$	385.736	+	668.114i	0.0393542	+	0.0681635i
$459$	−1798.41	−	3114.94i	−0.182881	−	0.316760i
$460$	221.978	−	384.478i	0.0224996	−	0.0389704i
$461$	126.771			0.0128076			0.00640380	−	0.999979i	$-0.497962\pi$
$461$	126.771			0.0128076			0.00640380	+	0.999979i	$0.497962\pi$
$462$	6176.40	+	2686.10i	0.621974	+	0.270495i
$463$	2512.79			0.252223			0.126112	−	0.992016i	$-0.459750\pi$
$463$	2512.79			0.252223			0.126112	+	0.992016i	$0.459750\pi$
$464$	258.907	−	448.441i	0.0259040	−	0.0448671i
$465$	274.219	+	474.961i	0.0273475	+	0.0473673i
$466$	−1463.26	−	2534.45i	−0.145460	−	0.251944i
$467$	−306.247	+	530.435i	−0.0303456	+	0.0525601i	−0.880799	−	0.473490i	$-0.842994\pi$
$467$	−306.247	+	530.435i	−0.0303456	+	0.0525601i	0.850454	+	0.526050i	$0.176327\pi$
$468$	468.000			0.0462250
$469$	−7818.20	−	3400.12i	−0.769746	−	0.334761i
$470$	965.509			0.0947566
$471$	−468.790	+	811.968i	−0.0458613	+	0.0794342i
$472$	476.690	+	825.652i	0.0464861	+	0.0805163i
$473$	−5651.79	−	9789.19i	−0.549407	−	0.951601i
$474$	3666.90	−	6351.26i	0.355330	−	0.615450i
$475$	10410.4			1.00561
$476$	1116.47	+	9805.39i	0.107507	+	0.944179i
$477$	1897.40			0.182130
$478$	1848.06	−	3200.93i	0.176837	−	0.306291i
$479$	−7457.37	−	12916.5i	−0.711348	−	1.23209i	−0.964351	−	0.264626i	$-0.914752\pi$
$479$	−7457.37	−	12916.5i	−0.711348	−	1.23209i	0.253003	−	0.967466i	$-0.418582\pi$
$480$	48.2134	+	83.5080i	0.00458465	+	0.00794084i
$481$	−622.231	+	1077.74i	−0.0589840	+	0.102163i
$482$	−7067.79			−0.667902
$483$	−4935.43	+	3651.47i	−0.464947	+	0.343991i
$484$	9370.86			0.880058
$485$	212.814	−	368.604i	0.0199245	−	0.0345102i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	8016.34	+	13884.7i	0.745904	+	1.29194i	0.949771	+	0.312945i	$0.101316\pi$
$487$	8016.34	+	13884.7i	0.745904	+	1.29194i	−0.203867	+	0.978999i	$0.565351\pi$
$488$	−3020.24	+	5231.22i	−0.280164	+	0.485258i
$489$	8301.84			0.767735
$490$	−671.412	+	154.906i	−0.0619006	+	0.0142815i
$491$	5579.29			0.512810			0.256405	−	0.966569i	$-0.417462\pi$
$491$	5579.29			0.512810			0.256405	+	0.966569i	$0.417462\pi$
$492$	−2281.81	+	3952.22i	−0.209090	+	0.362154i
$493$	−2155.66	−	3733.70i	−0.196929	−	0.341090i
$494$	1091.49	+	1890.52i	0.0994102	+	0.172184i
$495$	273.963	−	474.518i	0.0248762	−	0.0430868i
$496$	2912.05			0.263619
$497$	3525.99	−	2608.70i	0.318234	−	0.235445i
$498$	−5079.20			−0.457037
$499$	−7157.29	+	12396.8i	−0.642092	+	1.11214i	0.342872	+	0.939382i	$0.388600\pi$
$499$	−7157.29	+	12396.8i	−0.642092	+	1.11214i	−0.984965	+	0.172755i	$0.944733\pi$
$500$	500.196	+	866.365i	0.0447389	+	0.0774900i
$501$	310.001	+	536.937i	0.0276443	+	0.0478814i
$502$	−920.080	+	1593.63i	−0.0818032	+	0.141687i
$503$	16735.2			1.48347			0.741735	−	0.670693i	$-0.234003\pi$
$503$	16735.2			1.48347			0.741735	+	0.670693i	$0.234003\pi$
$504$	−150.856	−	1324.90i	−0.0133327	−	0.117095i
$505$	1541.42			0.135826
$506$	−6697.41	+	11600.3i	−0.588412	+	1.01916i
$507$	253.500	+	439.075i	0.0222058	+	0.0384615i
$508$	2088.92	+	3618.11i	0.182442	+	0.316000i
$509$	7005.82	−	12134.4i	0.610074	−	1.05668i	−0.381154	−	0.924512i	$-0.624473\pi$
$509$	7005.82	−	12134.4i	0.610074	−	1.05668i	0.991227	−	0.132167i	$-0.0421935\pi$
$510$	802.847			0.0697071
$511$	8094.74	+	3520.39i	0.700764	+	0.304761i
$512$	512.000			0.0441942
$513$	−1133.47	+	1963.24i	−0.0975519	+	0.168965i
$514$	1333.79	+	2310.19i	0.114457	+	0.198245i
$515$	−733.192	−	1269.93i	−0.0627346	−	0.108659i
$516$	−1118.96	+	1938.10i	−0.0954641	+	0.165349i
$517$	−29130.8			−2.47809
$518$	3251.62	+	1414.12i	0.275807	+	0.119948i
$519$	−6201.09			−0.524466
$520$	−52.2312	+	90.4670i	−0.00440479	+	0.00762931i
$521$	3356.08	+	5812.90i	0.282212	+	0.488806i	0.971929	−	0.235273i	$-0.0755984\pi$
$521$	3356.08	+	5812.90i	0.282212	+	0.488806i	−0.689717	+	0.724079i	$0.742265\pi$
$522$	291.271	+	504.496i	0.0244226	+	0.0423011i
$523$	5930.12	−	10271.3i	0.495805	−	0.858759i	−0.504183	−	0.863597i	$-0.668206\pi$
$523$	5930.12	−	10271.3i	0.495805	−	0.858759i	0.999988	+	0.00483742i	$0.00153980\pi$
$524$	−2687.36			−0.224042
$525$	−779.368	−	6844.81i	−0.0647893	−	0.569014i
$526$	−12108.3			−1.00370
$527$	12122.8	−	20997.4i	1.00205	−	1.73560i
$528$	−1454.67	−	2519.56i	−0.119898	−	0.207670i
$529$	−21.4028	−	37.0708i	−0.00175909	−	0.00304683i
$530$	−211.760	+	366.779i	−0.0173552	+	0.0300601i
$531$	−1072.55			−0.0876551
$532$	5000.20	−	3699.39i	0.407493	−	0.301483i
$533$	−4943.93			−0.401773
$534$	−3518.10	+	6093.52i	−0.285099	+	0.493806i
$535$	220.737	+	382.327i	0.0178379	+	0.0308961i
$536$	1841.35	+	3189.31i	0.148385	+	0.257009i
$537$	−6044.32	+	10469.1i	−0.485720	+	0.841292i
$538$	13910.6			1.11474
$539$	20257.5	−	4673.73i	1.61883	−	0.373491i
$540$	−108.480			−0.00864489
$541$	−9346.58	+	16188.7i	−0.742774	+	1.28652i	0.208453	+	0.978032i	$0.433157\pi$
$541$	−9346.58	+	16188.7i	−0.742774	+	1.28652i	−0.951228	+	0.308490i	$0.900176\pi$
$542$	−3854.45	−	6676.11i	−0.305467	−	0.529084i
$543$	−1971.55	−	3414.82i	−0.155814	−	0.269879i
$544$	2131.45	−	3691.78i	0.167987	−	0.290963i
$545$	663.045			0.0521133
$546$	1161.30	−	859.185i	0.0910237	−	0.0673438i
$547$	15847.3			1.23872			0.619360	−	0.785107i	$-0.287392\pi$
$547$	15847.3			1.23872			0.619360	+	0.785107i	$0.287392\pi$
$548$	−249.805	+	432.675i	−0.0194729	+	0.0337281i
$549$	−3397.77	−	5885.12i	−0.264141	−	0.457506i
$550$	−7515.25	−	13016.8i	−0.582638	−	1.00916i
$551$	−1358.63	+	2353.22i	−0.105045	+	0.181943i
$552$	2651.95			0.204483
$553$	−2561.00	−	22492.0i	−0.196934	−	1.72958i
$554$	−6200.52			−0.475514
$555$	144.230	−	249.814i	0.0110310	−	0.0191063i
$556$	−5458.27	−	9454.00i	−0.416335	−	0.721113i
$557$	3759.89	+	6512.33i	0.286018	+	0.495397i	0.972855	−	0.231414i	$-0.0743351\pi$
$557$	3759.89	+	6512.33i	0.286018	+	0.495397i	−0.686838	+	0.726811i	$0.741002\pi$
$558$	−1638.03	+	2837.15i	−0.124271	+	0.215244i
$559$	−2424.41			−0.183438
$560$	272.947	+	118.704i	0.0205966	+	0.00895743i
$561$	−24223.1			−1.82299
$562$	−4956.53	+	8584.97i	−0.372026	+	0.644368i
$563$	11700.3	+	20265.5i	0.875861	+	1.51704i	0.855843	+	0.517235i	$0.173039\pi$
$563$	11700.3	+	20265.5i	0.875861	+	1.51704i	0.0200174	+	0.999800i	$0.493628\pi$
$564$	2883.71	+	4994.73i	0.215294	+	0.372901i
$565$	−430.895	+	746.333i	−0.0320848	+	0.0555725i
$566$	8042.67			0.597277
$567$	1375.68	+	598.279i	0.101892	+	0.0443128i
$568$	−1894.62			−0.139959
$569$	−4688.90	+	8121.42i	−0.345464	+	0.598361i	−0.985438	−	0.170035i	$-0.945612\pi$
$569$	−4688.90	+	8121.42i	−0.345464	+	0.598361i	0.639974	+	0.768397i	$0.278945\pi$
$570$	−253.003	−	438.214i	−0.0185915	−	0.0322014i
$571$	3926.57	+	6801.03i	0.287779	+	0.498448i	0.973279	−	0.229624i	$-0.0737497\pi$
$571$	3926.57	+	6801.03i	0.287779	+	0.498448i	−0.685500	+	0.728073i	$0.740416\pi$
$572$	1575.89	−	2729.52i	0.115195	−	0.199523i
$573$	1628.57			0.118734
$574$	1593.64	+	13996.2i	0.115883	+	1.01775i
$575$	13700.8			0.993672
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−3242.00	−	5615.31i	−0.233910	−	0.405145i	0.725045	−	0.688701i	$-0.241819\pi$
$577$	−3242.00	−	5615.31i	−0.233910	−	0.405145i	−0.958955	+	0.283557i	$0.908486\pi$
$578$	−12833.4	−	22228.1i	−0.923526	−	1.59959i
$579$	−1645.16	+	2849.50i	−0.118084	+	0.204527i
$580$	−130.029			−0.00930891
$581$	−12603.5	+	9324.72i	−0.899971	+	0.665843i
$582$	2542.46			0.181080
$583$	6389.10	−	11066.2i	0.453876	−	0.786136i
$584$	−1906.48	−	3302.12i	−0.135087	−	0.233977i
$585$	−58.7601	−	101.775i	−0.00415287	−	0.00719298i
$586$	−717.001	+	1241.88i	−0.0505445	+	0.0875456i
$587$	16216.7			1.14027			0.570134	−	0.821552i	$-0.306891\pi$
$587$	16216.7			1.14027			0.570134	+	0.821552i	$0.306891\pi$
$588$	−2806.67	−	3010.66i	−0.196845	−	0.211152i
$589$	−15281.2			−1.06902
$590$	119.702	−	207.331i	0.00835266	−	0.0144672i
$591$	−6005.83	−	10402.4i	−0.418015	−	0.724023i
$592$	−765.823	−	1326.44i	−0.0531674	−	0.0920887i
$593$	7586.09	−	13139.5i	0.525335	−	0.909906i	−0.474230	−	0.880401i	$-0.657273\pi$
$593$	7586.09	−	13139.5i	0.525335	−	0.909906i	0.999565	−	0.0295053i	$-0.00939318\pi$
$594$	3273.00			0.226082
$595$	1992.19	−	1473.92i	0.137263	−	0.101554i
$596$	−11533.4			−0.792664
$597$	−3797.27	+	6577.07i	−0.260322	+	0.450890i
$598$	1436.47	+	2488.05i	0.0982304	+	0.170140i
$599$	4667.79	+	8084.85i	0.318398	+	0.551482i	0.980154	−	0.198237i	$-0.0635217\pi$
$599$	4667.79	+	8084.85i	0.318398	+	0.551482i	−0.661756	+	0.749720i	$0.730188\pi$
$600$	−1487.89	+	2577.11i	−0.101238	+	0.175350i
$601$	−3830.87			−0.260008			−0.130004	−	0.991514i	$-0.541499\pi$
$601$	−3830.87			−0.260008			−0.130004	+	0.991514i	$0.541499\pi$
$602$	781.491	+	6863.46i	0.0529089	+	0.464674i
$603$	−4143.03			−0.279796
$604$	−2353.38	+	4076.18i	−0.158539	+	0.274598i
$605$	−1176.56	−	2037.87i	−0.0790647	−	0.136944i
$606$	4603.80	+	7974.01i	0.308608	+	0.534525i
$607$	8081.66	−	13997.8i	0.540402	−	0.936005i	−0.458478	−	0.888706i	$-0.651605\pi$
$607$	8081.66	−	13997.8i	0.540402	−	0.936005i	0.998881	−	0.0472990i	$-0.0150613\pi$
$608$	−2686.76			−0.179214
$609$	1648.95	+	717.124i	0.109719	+	0.0477165i
$610$	1516.84			0.100680
$611$	−3124.02	+	5410.96i	−0.206848	+	0.358271i
$612$	2397.88	+	4153.25i	0.158380	+	0.274322i
$613$	−3180.26	−	5508.38i	−0.209543	−	0.362938i	0.742028	−	0.670369i	$-0.233864\pi$
$613$	−3180.26	−	5508.38i	−0.209543	−	0.362938i	−0.951571	+	0.307431i	$0.900531\pi$
$614$	1005.80	−	1742.09i	0.0661087	−	0.114504i
$615$	1145.98			0.0751387
$616$	−8235.20	−	3581.47i	−0.538645	−	0.234256i
$617$	14724.5			0.960756			0.480378	−	0.877062i	$-0.340499\pi$
$617$	14724.5			0.960756			0.480378	+	0.877062i	$0.340499\pi$
$618$	4379.68	−	7585.83i	0.285075	−	0.493765i
$619$	−14311.0	−	24787.3i	−0.929250	−	1.60951i	−0.784579	−	0.620029i	$-0.787121\pi$
$619$	−14311.0	−	24787.3i	−0.929250	−	1.60951i	−0.144672	−	0.989480i	$-0.546213\pi$
$620$	−365.625	−	633.281i	−0.0236836	−	0.0410213i
$621$	−1491.72	+	2583.74i	−0.0963942	+	0.166960i
$622$	−13333.4			−0.859520
$623$	2457.07	+	21579.3i	0.158010	+	1.38773i
$624$	−624.000			−0.0400320
$625$	−7623.84	+	13204.9i	−0.487926	+	0.845112i
$626$	6340.41	+	10981.9i	0.404814	+	0.701159i
$627$	7633.47	+	13221.6i	0.486207	+	0.842134i
$628$	625.053	−	1082.62i	0.0397171	−	0.0687920i
$629$	−12752.4			−0.808383
$630$	−269.183	+	199.155i	−0.0170230	+	0.0125945i
$631$	16883.8			1.06519			0.532593	−	0.846372i	$-0.321218\pi$
$631$	16883.8			1.06519			0.532593	+	0.846372i	$0.321218\pi$
$632$	−4889.21	+	8468.35i	−0.307725	+	0.532995i
$633$	3973.85	+	6882.90i	0.249520	+	0.432181i
$634$	1529.30	+	2648.83i	0.0957988	+	0.165928i
$635$	524.551	−	908.549i	0.0327814	−	0.0567790i
$636$	−2529.87			−0.157729
$637$	1304.30	−	4263.97i	0.0811276	−	0.265220i
$638$	3923.17			0.243448
$639$	1065.72	−	1845.89i	0.0659771	−	0.114276i
$640$	−64.2845	−	111.344i	−0.00397042	−	0.00687697i
$641$	12030.9	+	20838.2i	0.741331	+	1.28402i	0.951890	+	0.306441i	$0.0991383\pi$
$641$	12030.9	+	20838.2i	0.741331	+	1.28402i	−0.210559	+	0.977581i	$0.567528\pi$
$642$	−1318.56	+	2283.81i	−0.0810581	+	0.140397i
$643$	19275.4			1.18219			0.591095	−	0.806602i	$-0.298696\pi$
$643$	19275.4			1.18219			0.591095	+	0.806602i	$0.298696\pi$
$644$	6580.57	−	4868.63i	0.402656	−	0.297905i
$645$	561.967			0.0343061
$646$	−11184.9	+	19372.9i	−0.681215	+	1.17990i
$647$	−11068.7	−	19171.6i	−0.672575	−	1.16493i	−0.977171	−	0.212453i	$-0.931855\pi$
$647$	−11068.7	−	19171.6i	−0.672575	−	1.16493i	0.304596	−	0.952482i	$-0.401478\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−3611.60	+	6255.47i	−0.218440	+	0.378349i
$650$	−3223.77			−0.194533
$651$	1144.01	+	10047.3i	0.0688747	+	0.604894i
$652$	−11069.1			−0.664878
$653$	280.679	−	486.151i	0.0168206	−	0.0291341i	−0.857493	−	0.514496i	$-0.827979\pi$
$653$	280.679	−	486.151i	0.0168206	−	0.0291341i	0.874313	+	0.485362i	$0.161312\pi$
$654$	1980.33	+	3430.03i	0.118405	+	0.205084i
$655$	337.413	+	584.417i	0.0201280	+	0.0348627i
$656$	3042.42	−	5269.62i	0.181077	−	0.313634i
$657$	4289.57			0.254722
$658$	16325.3	+	7099.84i	0.967214	+	0.420639i
$659$	15208.5			0.898995			0.449498	−	0.893282i	$-0.351603\pi$
$659$	15208.5			0.898995			0.449498	+	0.893282i	$0.351603\pi$
$660$	−365.284	+	632.690i	−0.0215434	+	0.0373143i
$661$	7382.25	+	12786.4i	0.434397	+	0.752398i	0.997246	−	0.0741619i	$-0.0236282\pi$
$661$	7382.25	+	12786.4i	0.434397	+	0.752398i	−0.562849	+	0.826560i	$0.690295\pi$
$662$	−8979.54	−	15553.0i	−0.527190	−	0.913120i
$663$	−2597.70	+	4499.35i	−0.152167	+	0.263560i
$664$	6772.26			0.395805
$665$	−1432.31	−	622.907i	−0.0835225	−	0.0363238i
$666$	1723.10			0.100253
$667$	−1788.05	+	3096.99i	−0.103798	+	0.179784i
$668$	−413.335	−	715.916i	−0.0239407	−	0.0414665i
$669$	9066.21	+	15703.1i	0.523946	+	0.907501i
$670$	462.383	−	800.871i	0.0266618	−	0.0461796i
$671$	−45765.1			−2.63300
$672$	201.142	+	1766.53i	0.0115464	+	0.101407i
$673$	−19244.3			−1.10225			−0.551123	−	0.834424i	$-0.685801\pi$
$673$	−19244.3			−1.10225			−0.551123	+	0.834424i	$0.685801\pi$
$674$	−3160.02	+	5473.31i	−0.180592	+	0.312795i
$675$	−1673.88	−	2899.24i	−0.0954484	−	0.165321i
$676$	−338.000	−	585.433i	−0.0192308	−	0.0333087i
$677$	4052.63	−	7019.37i	0.230067	−	0.398488i	−0.727761	−	0.685831i	$-0.759439\pi$
$677$	4052.63	−	7019.37i	0.230067	−	0.398488i	0.957828	+	0.287343i	$0.0927721\pi$
$678$	−5147.86			−0.291596
$679$	6308.88	−	4667.62i	0.356572	−	0.263810i
$680$	−1070.46			−0.0603682
$681$	3773.08	−	6535.17i	0.212313	−	0.367736i
$682$	11031.4	+	19107.0i	0.619378	+	1.07279i
$683$	17509.9	+	30328.1i	0.980964	+	1.69908i	0.658654	+	0.752446i	$0.271126\pi$
$683$	17509.9	+	30328.1i	0.980964	+	1.69908i	0.322311	+	0.946634i	$0.395540\pi$
$684$	1511.30	−	2617.65i	0.0844824	−	0.146328i
$685$	125.458			0.00699781
$686$	−12491.7	−	2317.99i	−0.695238	−	0.129011i
$687$	1157.21			0.0642652
$688$	1491.95	−	2584.13i	0.0826743	−	0.143196i
$689$	−1370.35	−	2373.51i	−0.0757707	−	0.131239i
$690$	−332.968	−	576.717i	−0.0183708	−	0.0318192i
$691$	−5978.84	+	10355.7i	−0.329155	+	0.570113i	−0.982344	−	0.187082i	$-0.940097\pi$
$691$	−5978.84	+	10355.7i	−0.329155	+	0.570113i	0.653190	+	0.757194i	$0.273430\pi$
$692$	8268.13			0.454201
$693$	8121.65	−	6008.80i	0.445189	−	0.329373i
$694$	4772.01			0.261013
$695$	−1370.63	+	2374.01i	−0.0748073	+	0.129570i
$696$	−388.361	−	672.661i	−0.0211506	−	0.0366338i
$697$	−25331.1	−	43874.7i	−1.37659	−	2.38432i
$698$	8247.11	−	14284.4i	0.447218	−	0.774603i
$699$	−4389.79			−0.237535
$700$	1039.16	+	9126.42i	0.0561092	+	0.492780i
$701$	29109.6			1.56841			0.784205	−	0.620501i	$-0.213071\pi$
$701$	29109.6			1.56841			0.784205	+	0.620501i	$0.213071\pi$
$702$	351.000	−	607.950i	0.0188713	−	0.0326860i
$703$	4018.71	+	6960.60i	0.215602	+	0.373434i
$704$	1939.56	+	3359.41i	0.103835	+	0.179847i
$705$	724.132	−	1254.23i	0.0386842	−	0.0670031i
$706$	10834.5			0.577566
$707$	26063.1	+	11334.8i	1.38643	+	0.602955i
$708$	1430.07			0.0759115
$709$	−4981.53	+	8628.27i	−0.263872	+	0.457040i	−0.967268	−	0.253759i	$-0.918333\pi$
$709$	−4981.53	+	8628.27i	−0.263872	+	0.457040i	0.703395	+	0.710799i	$0.251666\pi$
$710$	237.880	+	412.021i	0.0125739	+	0.0217787i
$711$	−5500.36	−	9526.90i	−0.290126	−	0.502513i
$712$	4690.80	−	8124.70i	0.246903	−	0.427649i
$713$	−20111.0			−1.05633
$714$	13574.9	+	5903.71i	0.711525	+	0.309441i
$715$	−791.448			−0.0413965
$716$	8059.09	−	13958.8i	0.420646	−	0.728580i
$717$	−2772.09	−	4801.40i	−0.144387	−	0.250086i
$718$	−6794.10	−	11767.7i	−0.353138	−	0.611654i
$719$	15597.6	−	27015.8i	0.809028	−	1.40128i	−0.104510	−	0.994524i	$-0.533327\pi$
$719$	15597.6	−	27015.8i	0.809028	−	1.40128i	0.913538	−	0.406754i	$-0.133339\pi$
$720$	144.640			0.00748670
$721$	−3058.81	−	26864.0i	−0.157997	−	1.38761i
$722$	380.932			0.0196355
$723$	−5300.84	+	9181.33i	−0.272670	+	0.472278i
$724$	2628.73	+	4553.10i	0.134939	+	0.233722i
$725$	−2006.39	−	3475.17i	−0.102780	−	0.178020i
$726$	7028.14	−	12173.1i	0.359282	−	0.622295i
$727$	30763.8			1.56942			0.784708	−	0.619866i	$-0.212813\pi$
$727$	30763.8			1.56942			0.784708	+	0.619866i	$0.212813\pi$
$728$	−1548.40	+	1145.58i	−0.0788289	+	0.0583215i
$729$	729.000			0.0370370
$730$	−478.738	+	829.199i	−0.0242725	+	0.0420411i
$731$	−12421.9	−	21515.4i	−0.628510	−	1.08861i
$732$	4530.37	+	7846.82i	0.228753	+	0.396212i
$733$	−3281.44	+	5683.62i	−0.165352	+	0.286397i	−0.936780	−	0.349919i	$-0.886209\pi$
$733$	−3281.44	+	5683.62i	−0.165352	+	0.286397i	0.771428	+	0.636316i	$0.219543\pi$
$734$	−6413.21			−0.322501
$735$	−302.331	+	988.369i	−0.0151723	+	0.0496007i
$736$	−3535.94			−0.177087
$737$	−13950.8	+	24163.5i	−0.697264	+	1.20770i
$738$	3422.72	+	5928.32i	0.170721	+	0.295697i
$739$	4949.29	+	8572.43i	0.246364	+	0.426714i	0.962514	−	0.271232i	$-0.0874310\pi$
$739$	4949.29	+	8572.43i	0.246364	+	0.426714i	−0.716151	+	0.697946i	$0.754098\pi$
$740$	−192.307	+	333.085i	−0.00955316	+	0.0165466i
$741$	3274.48			0.162336
$742$	−6277.63	+	4644.50i	−0.310592	+	0.229791i
$743$	316.378			0.0156215			0.00781075	−	0.999969i	$-0.497514\pi$
$743$	316.378			0.0156215			0.00781075	+	0.999969i	$0.497514\pi$
$744$	2184.04	−	3782.87i	0.107622	−	0.186407i
$745$	1448.09	+	2508.16i	0.0712132	+	0.123345i
$746$	611.095	+	1058.45i	0.0299916	+	0.0519471i
$747$	−3809.40	+	6598.07i	−0.186584	+	0.323174i
$748$	32297.4			1.57876
$749$	920.892	+	8087.75i	0.0449248	+	0.394553i
$750$	1500.59			0.0730583
$751$	−12052.4	+	20875.3i	−0.585615	+	1.01432i	0.409183	+	0.912452i	$0.365814\pi$
$751$	−12052.4	+	20875.3i	−0.585615	+	1.01432i	−0.994798	+	0.101863i	$0.967520\pi$
$752$	−3844.94	−	6659.64i	−0.186450	−	0.322941i
$753$	1380.12	+	2390.44i	0.0667920	+	0.115687i
$754$	420.724	−	728.716i	0.0203208	−	0.0351967i
$755$	1181.92			0.0569729
$756$	−1834.23	−	797.705i	−0.0882414	−	0.0383760i
$757$	39844.8			1.91306			0.956529	−	0.291637i	$-0.0941999\pi$
$757$	39844.8			1.91306			0.956529	+	0.291637i	$0.0941999\pi$
$758$	12040.3	−	20854.5i	0.576946	−	0.999299i
$759$	10046.1	+	17400.4i	0.480436	+	0.832140i
$760$	337.337	+	584.286i	0.0161007	+	0.0278872i
$761$	3155.53	−	5465.55i	0.150313	−	0.260349i	−0.781030	−	0.624494i	$-0.785305\pi$
$761$	3155.53	−	5465.55i	0.150313	−	0.260349i	0.931342	+	0.364145i	$0.118639\pi$
$762$	6266.75			0.297927
$763$	11211.1	+	4875.68i	0.531938	+	0.231339i
$764$	−2171.42			−0.102826
$765$	602.135	−	1042.93i	0.0284578	−	0.0492904i
$766$	−12689.3	−	21978.5i	−0.598542	−	1.03671i
$767$	774.622	+	1341.68i	0.0364667	+	0.0631622i
$768$	384.000	−	665.108i	0.0180422	−	0.0312500i
$769$	2683.79			0.125852			0.0629259	−	0.998018i	$-0.479957\pi$
$769$	2683.79			0.125852			0.0629259	+	0.998018i	$0.479957\pi$
$770$	255.117	+	2240.57i	0.0119400	+	0.104863i
$771$	4001.36			0.186907
$772$	2193.55	−	3799.34i	0.102264	−	0.177126i
$773$	−8647.57	−	14978.0i	−0.402369	−	0.696924i	0.591642	−	0.806201i	$-0.298480\pi$
$773$	−8647.57	−	14978.0i	−0.402369	−	0.696924i	−0.994011	+	0.109277i	$0.965147\pi$
$774$	1678.44	+	2907.14i	0.0779461	+	0.135007i
$775$	11283.4	−	19543.4i	0.522983	−	0.905833i
$776$	−3389.95			−0.156820
$777$	4275.71	−	3163.38i	0.197414	−	0.146056i
$778$	−17258.7			−0.795314
$779$	−15965.3	+	27652.7i	−0.734295	+	1.27184i
$780$	78.3468	+	135.701i	0.00359649	+	0.00622931i
$781$	−7177.20	−	12431.3i	−0.328835	−	0.569559i
$782$	−14720.0	+	25495.9i	−0.673130	+	1.16590i
$783$	873.812			0.0398819
$784$	3742.23	+	4014.21i	0.170473	+	0.182863i
$785$	−313.916			−0.0142728
$786$	−2015.52	+	3490.98i	−0.0914646	+	0.158421i
$787$	10711.0	+	18552.0i	0.485140	+	0.840287i	0.999854	−	0.0170746i	$-0.00543527\pi$
$787$	10711.0	+	18552.0i	0.485140	+	0.840287i	−0.514714	+	0.857362i	$0.672102\pi$
$788$	8007.77	+	13869.9i	0.362011	+	0.627022i
$789$	−9081.26	+	15729.2i	−0.409761	+	0.709727i
$790$	2455.47			0.110584
$791$	−12773.9	+	9450.78i	−0.574195	+	0.424818i
$792$	−4364.00			−0.195793
$793$	−4907.90	+	8500.72i	−0.219779	+	0.380668i
$794$	−2363.62	−	4093.91i	−0.105645	−	0.182982i
$795$	317.640	+	550.168i	0.0141705	+	0.0245440i
$796$	5063.03	−	8769.43i	0.225445	−	0.390483i
$797$	13873.1			0.616575			0.308287	−	0.951293i	$-0.400244\pi$
$797$	13873.1			0.616575			0.308287	+	0.951293i	$0.400244\pi$
$798$	−1055.50	−	9269.99i	−0.0468226	−	0.411221i
$799$	−64025.8			−2.83488
$800$	1983.86	−	3436.14i	0.0876749	−	0.151857i
$801$	5277.15	+	9140.29i	0.232783	+	0.403191i
$802$	−7905.17	−	13692.2i	−0.348057	−	0.602852i
$803$	14444.2	−	25018.1i	0.634777	−	1.09947i
$804$	5524.04			0.242311
$805$	−1885.00	−	819.784i	−0.0825312	−	0.0358927i
$806$	4732.09			0.206800
$807$	10432.9	−	18070.4i	0.455089	−	0.788237i
$808$	−6138.40	−	10632.0i	−0.267262	−	0.462912i
$809$	11263.5	+	19508.9i	0.489496	+	0.847832i	0.999927	−	0.0120865i	$-0.00384735\pi$
$809$	11263.5	+	19508.9i	0.489496	+	0.847832i	−0.510431	+	0.859919i	$0.670514\pi$
$810$	−81.3601	+	140.920i	−0.00352926	+	0.00611286i
$811$	−45345.0			−1.96335			−0.981676	−	0.190556i	$-0.938971\pi$
$811$	−45345.0			−1.96335			−0.981676	+	0.190556i	$0.938971\pi$
$812$	−2198.60	−	956.166i	−0.0950192	−	0.0413237i
$813$	−11563.4			−0.498825
$814$	5802.18	−	10049.7i	0.249836	−	0.432728i
$815$	1389.79	+	2407.19i	0.0597329	+	0.103460i
$816$	−3197.17	−	5537.67i	−0.137161	−	0.237570i
$817$	−7829.09	+	13560.4i	−0.335257	+	0.580683i
$818$	15117.2			0.646161
$819$	−245.141	−	2152.96i	−0.0104590	−	0.0918565i
$820$	−1527.97			−0.0650720
$821$	15347.0	−	26581.8i	0.652394	−	1.12998i	−0.330147	−	0.943930i	$-0.607098\pi$
$821$	15347.0	−	26581.8i	0.652394	−	1.12998i	0.982540	−	0.186049i	$-0.0595684\pi$
$822$	374.708	+	649.013i	0.0158996	+	0.0275389i
$823$	2831.41	+	4904.14i	0.119923	+	0.207713i	0.919737	−	0.392535i	$-0.128402\pi$
$823$	2831.41	+	4904.14i	0.119923	+	0.207713i	−0.799814	+	0.600248i	$0.795069\pi$
$824$	−5839.58	+	10114.4i	−0.246883	+	0.427613i
$825$	−22545.7			−0.951445
$826$	3548.59	−	2625.42i	0.149481	−	0.110593i
$827$	38550.7			1.62097			0.810483	−	0.585762i	$-0.199205\pi$
$827$	38550.7			1.62097			0.810483	+	0.585762i	$0.199205\pi$
$828$	1988.96	−	3444.99i	0.0834798	−	0.144591i
$829$	−1271.05	−	2201.52i	−0.0532513	−	0.0922340i	0.838171	−	0.545408i	$-0.183625\pi$
$829$	−1271.05	−	2201.52i	−0.0532513	−	0.0922340i	−0.891422	+	0.453174i	$0.850292\pi$
$830$	−850.296	−	1472.76i	−0.0355593	−	0.0615905i
$831$	−4650.39	+	8054.72i	−0.194128	+	0.336239i
$832$	832.000			0.0346688
$833$	44523.3	−	10272.2i	1.85191	−	0.427266i
$834$	−16374.8			−0.679872
$835$	−103.793	+	179.775i	−0.00430168	+	0.00745073i
$836$	−10178.0	−	17628.7i	−0.421067	−	0.729310i
$837$	2457.05	+	4255.73i	0.101467	+	0.175746i
$838$	−2184.13	+	3783.03i	−0.0900353	+	0.155946i
$839$	38507.2			1.58452			0.792262	−	0.610181i	$-0.208903\pi$
$839$	38507.2			1.58452			0.792262	+	0.610181i	$0.208903\pi$
$840$	358.911	−	265.540i	0.0147424	−	0.0109071i
$841$	−23341.6			−0.957055
$842$	4511.31	−	7813.81i	0.184644	−	0.319812i
$843$	7434.80	+	12877.5i	0.303758	+	0.526125i
$844$	−5298.46	−	9177.20i	−0.216091	−	0.374280i
$845$	−84.8757	+	147.009i	−0.00345540	+	0.00598492i
$846$	8651.12			0.351574
$847$	−4908.51	−	43109.1i	−0.199125	−	1.74882i
$848$	3373.16			0.136598
$849$	6032.00	−	10447.7i	0.243837	−	0.422339i
$850$	−16517.5	−	28609.2i	−0.666526	−	1.15446i
$851$	5288.87	+	9160.59i	0.213043	+	0.369002i
$852$	−1420.97	+	2461.18i	−0.0571379	+	0.0989657i
$853$	29753.1			1.19429			0.597143	−	0.802135i	$-0.296302\pi$
$853$	29753.1			1.19429			0.597143	+	0.802135i	$0.296302\pi$
$854$	25647.4	+	11154.0i	1.02768	+	0.446935i
$855$	−759.009			−0.0303597
$856$	1758.08	−	3045.08i	0.0701984	−	0.121587i
$857$	−8420.46	−	14584.7i	−0.335633	−	0.581333i	0.647973	−	0.761663i	$-0.275617\pi$
$857$	−8420.46	−	14584.7i	−0.335633	−	0.581333i	−0.983606	+	0.180330i	$0.942284\pi$
$858$	−2363.84	−	4094.28i	−0.0940560	−	0.162910i
$859$	13578.3	−	23518.2i	0.539330	−	0.934147i	−0.459610	−	0.888121i	$-0.652011\pi$
$859$	13578.3	−	23518.2i	0.539330	−	0.934147i	0.998940	−	0.0460261i	$-0.0146557\pi$
$860$	−749.289			−0.0297100
$861$	19376.8	+	8426.92i	0.766967	+	0.333552i
$862$	27060.1			1.06922
$863$	14476.6	−	25074.2i	0.571019	−	0.989034i	−0.425443	−	0.904985i	$-0.639882\pi$
$863$	14476.6	−	25074.2i	0.571019	−	0.989034i	0.996462	−	0.0840485i	$-0.0267851\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	−1038.11	−	1798.06i	−0.0408056	−	0.0706773i
$866$	4680.48	−	8106.82i	0.183659	−	0.318107i
$867$	−38500.1			−1.50811
$868$	−1525.35	−	13396.4i	−0.0596473	−	0.523854i
$869$	−74085.1			−2.89202
$870$	−97.5219	+	168.913i	−0.00380035	+	0.00658239i
$871$	2992.19	+	5182.62i	0.116402	+	0.201615i
$872$	−2640.44	−	4573.38i	−0.102542	−	0.177608i
$873$	1906.85	−	3302.76i	0.0739256	−	0.128043i
$874$	18555.1			0.718117
$875$	3723.57	−	2754.88i	0.143862	−	0.106436i
$876$	−5719.43			−0.220596
$877$	16675.8	−	28883.3i	0.642077	−	1.11211i	−0.342892	−	0.939375i	$-0.611406\pi$
$877$	16675.8	−	28883.3i	0.642077	−	1.11211i	0.984968	−	0.172735i	$-0.0552603\pi$
$878$	8263.05	+	14312.0i	0.317613	+	0.550122i
$879$	1075.50	+	1862.82i	0.0412694	+	0.0714807i
$880$	487.045	−	843.587i	0.0186571	−	0.0323151i
$881$	28373.0			1.08503			0.542515	−	0.840046i	$-0.317472\pi$
$881$	28373.0			1.08503			0.542515	+	0.840046i	$0.317472\pi$
$882$	−6015.96	+	1387.98i	−0.229669	+	0.0529883i
$883$	12504.2			0.476555			0.238278	−	0.971197i	$-0.423417\pi$
$883$	12504.2			0.476555			0.238278	+	0.971197i	$0.423417\pi$
$884$	3463.60	−	5999.14i	0.131780	−	0.228250i
$885$	−179.554	−	310.996i	−0.00681992	−	0.0118124i
$886$	−4502.63	−	7798.79i	−0.170732	−	0.295717i
$887$	−8226.19	+	14248.2i	−0.311396	+	0.539354i	−0.978665	−	0.205463i	$-0.934130\pi$
$887$	−8226.19	+	14248.2i	−0.311396	+	0.539354i	0.667269	+	0.744817i	$0.267463\pi$
$888$	−2297.47			−0.0868220
$889$	15550.4	−	11504.9i	0.586662	−	0.434041i
$890$	−2355.82			−0.0887275
$891$	2454.75	−	4251.76i	0.0922978	−	0.159864i
$892$	−12088.3	−	20937.5i	−0.453751	−	0.785919i
$893$	20176.6	+	34946.9i	0.756085	+	1.30958i
$894$	−8650.07	+	14982.4i	−0.323604	+	0.560498i
$895$	−4047.46			−0.151164
$896$	−268.189	−	2355.37i	−0.00999951	−	0.0878209i
$897$	4309.42			0.160410
$898$	9976.69	−	17280.1i	0.370742	−	0.642144i
$899$	2945.13	+	5101.11i	0.109261	+	0.189245i
$900$	2231.84	+	3865.66i	0.0826607	+	0.143173i
$901$	14042.4	−	24322.2i	0.519224	−	0.899322i
$902$	46101.1			1.70177
$903$	9502.01	+	4132.41i	0.350174	+	0.152290i
$904$	6863.81			0.252530
$905$	660.105	−	1143.33i	0.0242460	−	0.0419953i
$906$	3530.07	+	6114.26i	0.129447	+	0.224208i
$907$	−12820.8	−	22206.3i	−0.469359	−	0.812954i	0.530027	−	0.847981i	$-0.322182\pi$
$907$	−12820.8	−	22206.3i	−0.469359	−	0.812954i	−0.999386	+	0.0350267i	$0.988848\pi$
$908$	−5030.78	+	8713.57i	−0.183868	+	0.318469i
$909$	13811.4			0.503955
$910$	443.538	+	192.894i	0.0161573	+	0.00702678i
$911$	35083.4			1.27592			0.637961	−	0.770068i	$-0.279778\pi$
$911$	35083.4			1.27592			0.637961	+	0.770068i	$0.279778\pi$
$912$	−2015.07	+	3490.20i	−0.0731639	+	0.126724i
$913$	25654.7	+	44435.2i	0.929951	+	1.61072i
$914$	7850.99	+	13598.3i	0.284122	+	0.492114i
$915$	1137.63	−	1970.43i	0.0411025	−	0.0711916i
$916$	−1542.94			−0.0556553
$917$	1407.66	+	12362.8i	0.0506924	+	0.445207i
$918$	7193.64			0.258633
$919$	−13391.8	+	23195.3i	−0.480691	+	0.832581i	−0.999755	−	0.0221543i	$-0.992947\pi$
$919$	−13391.8	+	23195.3i	−0.480691	+	0.832581i	0.519063	+	0.854736i	$0.326281\pi$
$920$	443.957	+	768.956i	0.0159096	+	0.0275562i
$921$	−1508.70	−	2613.14i	−0.0539775	−	0.0934918i
$922$	−126.771	+	219.573i	−0.00452817	+	0.00784302i
$923$	−3078.76			−0.109793
$924$	−10828.9	+	8011.73i	−0.385545	+	0.285245i
$925$	−11869.4			−0.421906
$926$	−2512.79	+	4352.28i	−0.0891744	+	0.154455i
$927$	−6569.52	−	11378.7i	−0.232763	−	0.403158i
$928$	517.815	+	896.881i	0.0183169	+	0.0317258i
$929$	−24691.6	+	42767.2i	−0.872020	+	1.51038i	−0.0121156	+	0.999927i	$0.503857\pi$
$929$	−24691.6	+	42767.2i	−0.872020	+	1.51038i	−0.859904	+	0.510456i	$0.829477\pi$
$930$	−1096.88			−0.0386752
$931$	−19637.6	−	21064.8i	−0.691296	−	0.741538i
$932$	5853.06			0.205712
$933$	−10000.1	+	17320.6i	−0.350898	+	0.607772i
$934$	−612.493	−	1060.87i	−0.0214576	−	0.0371656i
$935$	−4055.12	−	7023.68i	−0.141836	−	0.245667i
$936$	−468.000	+	810.600i	−0.0163430	+	0.0283069i
$937$	−22484.4			−0.783920			−0.391960	−	0.919982i	$-0.628203\pi$
$937$	−22484.4			−0.783920			−0.391960	+	0.919982i	$0.628203\pi$
$938$	13707.4	−	10141.4i	0.477145	−	0.353015i
$939$	19021.2			0.661059
$940$	−965.509	+	1672.31i	−0.0335015	+	0.0580263i
$941$	9317.94	+	16139.1i	0.322801	+	0.559108i	0.981065	−	0.193679i	$-0.0620421\pi$
$941$	9317.94	+	16139.1i	0.322801	+	0.559108i	−0.658264	+	0.752788i	$0.728709\pi$
$942$	−937.579	−	1623.94i	−0.0324289	−	0.0561684i
$943$	−21011.3	+	36392.7i	−0.725580	+	1.25674i
$944$	−1906.76			−0.0657413
$945$	56.8226	+	499.045i	0.00195602	+	0.0171788i
$946$	22607.2			0.776979
$947$	−28734.7	+	49769.9i	−0.986010	+	1.70782i	−0.348650	+	0.937253i	$0.613360\pi$
$947$	−28734.7	+	49769.9i	−0.986010	+	1.70782i	−0.637360	+	0.770567i	$0.719973\pi$
$948$	7333.81	+	12702.5i	0.251256	+	0.435189i
$949$	−3098.03	−	5365.94i	−0.105971	−	0.183547i
$950$	−10410.4	+	18031.4i	−0.355536	+	0.615806i
$951$	4587.91			0.156439
$952$	−18099.9	−	7871.61i	−0.616199	−	0.267984i
$953$	−39938.2			−1.35753			−0.678765	−	0.734356i	$-0.737484\pi$
$953$	−39938.2			−1.35753			−0.678765	+	0.734356i	$0.737484\pi$
$954$	−1897.40	+	3286.40i	−0.0643927	+	0.111532i
$955$	272.635	+	472.217i	0.00923795	+	0.0160006i
$956$	3696.12	+	6401.87i	0.125043	+	0.216581i
$957$	2942.38	−	5096.35i	0.0993872	−	0.172144i
$958$	29829.5			1.00600
$959$	2121.30	+	922.551i	0.0714291	+	0.0310644i
$960$	−192.854			−0.00648367
$961$	−1667.13	+	2887.55i	−0.0559607	+	0.0969268i
$962$	−1244.46	−	2155.47i	−0.0417080	−	0.0722403i
$963$	1977.84	+	3425.71i	0.0661837	+	0.114634i
$964$	7067.79	−	12241.8i	0.236139	−	0.409005i
$965$	−1101.65			−0.0367496
$966$	−1389.11	−	12199.9i	−0.0462669	−	0.406340i
$967$	−46252.5			−1.53814			−0.769070	−	0.639165i	$-0.779280\pi$
$967$	−46252.5			−1.53814			−0.769070	+	0.639165i	$0.779280\pi$
$968$	−9370.86	+	16230.8i	−0.311148	+	0.538923i
$969$	16777.4	+	29059.3i	0.556210	+	0.963384i
$970$	425.628	+	737.209i	0.0140887	+	0.0244024i
$971$	16447.1	−	28487.1i	0.543575	−	0.941499i	−0.455120	−	0.890430i	$-0.650404\pi$
$971$	16447.1	−	28487.1i	0.543575	−	0.941499i	0.998695	−	0.0510693i	$-0.0162630\pi$
$972$	−972.000			−0.0320750
$973$	−40632.5	+	30062.0i	−1.33877	+	0.990485i
$974$	−32065.4			−1.05487
$975$	−2417.83	+	4187.80i	−0.0794179	+	0.137556i
$976$	−6040.49	−	10462.4i	−0.198106	−	0.343129i
$977$	−25359.3	−	43923.6i	−0.830415	−	1.43832i	−0.897709	−	0.440588i	$-0.854770\pi$
$977$	−25359.3	−	43923.6i	−0.830415	−	1.43832i	0.0672940	−	0.997733i	$-0.478563\pi$
$978$	−8301.84	+	14379.2i	−0.271435	+	0.470140i
$979$	71078.7			2.32041
$980$	403.107	−	1317.82i	0.0131396	−	0.0429555i
$981$	5940.99			0.193355
$982$	−5579.29	+	9663.61i	−0.181306	+	0.314031i
$983$	−379.985	−	658.154i	−0.0123292	−	0.0213549i	0.859795	−	0.510639i	$-0.170591\pi$
$983$	−379.985	−	658.154i	−0.0123292	−	0.0213549i	−0.872124	+	0.489285i	$0.837258\pi$
$984$	−4563.63	−	7904.43i	−0.147849	−	0.256081i
$985$	2010.84	−	3482.88i	0.0650465	−	0.112664i
$986$	8622.62			0.278499
$987$	21466.9	−	15882.3i	0.692300	−	0.512198i
$988$	−4365.98			−0.140587
$989$	−10303.6	+	17846.3i	−0.331278	+	0.573791i
$990$	547.926	+	949.035i	0.0175901	+	0.0304670i
$991$	−6467.63	−	11202.3i	−0.207317	−	0.359083i	0.743552	−	0.668679i	$-0.233140\pi$
$991$	−6467.63	−	11202.3i	−0.207317	−	0.359083i	−0.950868	+	0.309595i	$0.899806\pi$
$992$	−2912.05	+	5043.83i	−0.0932035	+	0.161433i
$993$	−26938.6			−0.860898
$994$	992.414	+	8715.90i	0.0316675	+	0.278120i
$995$	−2542.77			−0.0810163
$996$	5079.20	−	8797.42i	0.161587	−	0.279877i
$997$	17033.5	+	29502.9i	0.541081	+	0.937179i	0.998842	+	0.0481043i	$0.0153180\pi$
$997$	17033.5	+	29502.9i	0.541081	+	0.937179i	−0.457762	+	0.889075i	$0.651349\pi$
$998$	−14314.6	−	24793.6i	−0.454028	−	0.786399i
$999$	1292.33	−	2238.37i	0.0409283	−	0.0708899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.i.b.79.3	✓	8
7.4	even	3	inner	546.4.i.b.235.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.i.b.79.3	✓	8	1.1	even	1	trivial
546.4.i.b.235.3	yes	8	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-0.502223 + 0.869875i) q^{5} -6.00000 q^{6} +(-14.8884 + 11.0152i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-1.00445 - 1.73975i) q^{10} +(30.3056 + 52.4908i) q^{11} +(6.00000 - 10.3923i) q^{12} +13.0000 q^{13} +(-4.19045 - 36.8027i) q^{14} -3.01334 q^{15} +(-8.00000 + 13.8564i) q^{16} +(66.6078 + 115.368i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(41.9805 - 72.7124i) q^{19} +4.01778 q^{20} +(-50.9510 - 22.1585i) q^{21} -121.222 q^{22} +(55.2490 - 95.6941i) q^{23} +(12.0000 + 20.7846i) q^{24} +(61.9955 + 107.379i) q^{25} +(-13.0000 + 22.5167i) q^{26} -27.0000 q^{27} +(67.9346 + 29.5446i) q^{28} -32.3634 q^{29} +(3.01334 - 5.21925i) q^{30} +(-91.0017 - 157.620i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-90.9168 + 157.472i) q^{33} -266.431 q^{34} +(-2.10454 - 18.4832i) q^{35} +36.0000 q^{36} +(-47.8639 + 82.9027i) q^{37} +(83.9611 + 145.425i) q^{38} +(19.5000 + 33.7750i) q^{39} +(-4.01778 + 6.95900i) q^{40} -380.302 q^{41} +(89.3306 - 66.0912i) q^{42} -186.493 q^{43} +(121.222 - 209.963i) q^{44} +(-4.52001 - 7.82888i) q^{45} +(110.498 + 191.388i) q^{46} +(-240.309 + 416.227i) q^{47} -48.0000 q^{48} +(100.331 - 327.998i) q^{49} -247.982 q^{50} +(-199.823 + 346.104i) q^{51} +(-26.0000 - 45.0333i) q^{52} +(-105.411 - 182.578i) q^{53} +(27.0000 - 46.7654i) q^{54} -60.8806 q^{55} +(-119.107 + 88.1216i) q^{56} +251.883 q^{57} +(32.3634 - 56.0551i) q^{58} +(59.5863 + 103.207i) q^{59} +(6.02667 + 10.4385i) q^{60} +(-377.530 + 653.902i) q^{61} +364.007 q^{62} +(-18.8570 - 165.612i) q^{63} +64.0000 q^{64} +(-6.52890 + 11.3084i) q^{65} +(-181.834 - 314.945i) q^{66} +(230.168 + 398.663i) q^{67} +(266.431 - 461.472i) q^{68} +331.494 q^{69} +(34.1183 + 14.8380i) q^{70} -236.828 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-238.310 - 412.764i) q^{73} +(-95.7278 - 165.805i) q^{74} +(-185.987 + 322.138i) q^{75} -335.844 q^{76} +(-1029.40 - 447.684i) q^{77} -78.0000 q^{78} +(-611.151 + 1058.54i) q^{79} +(-8.03556 - 13.9180i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(380.302 - 658.703i) q^{82} +846.533 q^{83} +(25.1427 + 220.816i) q^{84} -133.808 q^{85} +(186.493 - 323.016i) q^{86} +(-48.5451 - 84.0826i) q^{87} +(242.445 + 419.927i) q^{88} +(586.350 - 1015.59i) q^{89} +18.0800 q^{90} +(-193.550 + 143.198i) q^{91} -441.992 q^{92} +(273.005 - 472.859i) q^{93} +(-480.618 - 832.455i) q^{94} +(42.1672 + 73.0357i) q^{95} +(48.0000 - 83.1384i) q^{96} -423.744 q^{97} +(467.778 + 501.776i) q^{98} -545.501 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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