Properties

Label 147.4.e.g.79.1
Level $147$
Weight $4$
Character 147.79
Analytic conductor $8.673$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.4.e.g.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-9.00000 + 15.5885i) q^{5} -9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-9.00000 + 15.5885i) q^{5} -9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(27.0000 + 46.7654i) q^{10} +(18.0000 + 31.1769i) q^{11} +(-1.50000 + 2.59808i) q^{12} +34.0000 q^{13} +54.0000 q^{15} +(35.5000 - 61.4878i) q^{16} +(21.0000 + 36.3731i) q^{17} +(13.5000 + 23.3827i) q^{18} +(-62.0000 + 107.387i) q^{19} +18.0000 q^{20} +108.000 q^{22} +(-31.5000 - 54.5596i) q^{24} +(-99.5000 - 172.339i) q^{25} +(51.0000 - 88.3346i) q^{26} +27.0000 q^{27} +102.000 q^{29} +(81.0000 - 140.296i) q^{30} +(-80.0000 - 138.564i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(54.0000 - 93.5307i) q^{33} +126.000 q^{34} +9.00000 q^{36} +(-199.000 + 344.678i) q^{37} +(186.000 + 322.161i) q^{38} +(-51.0000 - 88.3346i) q^{39} +(-189.000 + 327.358i) q^{40} +318.000 q^{41} -268.000 q^{43} +(18.0000 - 31.1769i) q^{44} +(-81.0000 - 140.296i) q^{45} +(120.000 - 207.846i) q^{47} -213.000 q^{48} -597.000 q^{50} +(63.0000 - 109.119i) q^{51} +(-17.0000 - 29.4449i) q^{52} +(249.000 + 431.281i) q^{53} +(40.5000 - 70.1481i) q^{54} -648.000 q^{55} +372.000 q^{57} +(153.000 - 265.004i) q^{58} +(-66.0000 - 114.315i) q^{59} +(-27.0000 - 46.7654i) q^{60} +(199.000 - 344.678i) q^{61} -480.000 q^{62} +433.000 q^{64} +(-306.000 + 530.008i) q^{65} +(-162.000 - 280.592i) q^{66} +(-46.0000 - 79.6743i) q^{67} +(21.0000 - 36.3731i) q^{68} -720.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(-251.000 - 434.745i) q^{73} +(597.000 + 1034.03i) q^{74} +(-298.500 + 517.017i) q^{75} +124.000 q^{76} -306.000 q^{78} +(512.000 - 886.810i) q^{79} +(639.000 + 1106.78i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(477.000 - 826.188i) q^{82} +204.000 q^{83} -756.000 q^{85} +(-402.000 + 696.284i) q^{86} +(-153.000 - 265.004i) q^{87} +(378.000 + 654.715i) q^{88} +(177.000 - 306.573i) q^{89} -486.000 q^{90} +(-240.000 + 415.692i) q^{93} +(-360.000 - 623.538i) q^{94} +(-1116.00 - 1932.97i) q^{95} +(-67.5000 + 116.913i) q^{96} +286.000 q^{97} -324.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} - 3q^{3} - q^{4} - 18q^{5} - 18q^{6} + 42q^{8} - 9q^{9} + O(q^{10}) \) \( 2q + 3q^{2} - 3q^{3} - q^{4} - 18q^{5} - 18q^{6} + 42q^{8} - 9q^{9} + 54q^{10} + 36q^{11} - 3q^{12} + 68q^{13} + 108q^{15} + 71q^{16} + 42q^{17} + 27q^{18} - 124q^{19} + 36q^{20} + 216q^{22} - 63q^{24} - 199q^{25} + 102q^{26} + 54q^{27} + 204q^{29} + 162q^{30} - 160q^{31} - 45q^{32} + 108q^{33} + 252q^{34} + 18q^{36} - 398q^{37} + 372q^{38} - 102q^{39} - 378q^{40} + 636q^{41} - 536q^{43} + 36q^{44} - 162q^{45} + 240q^{47} - 426q^{48} - 1194q^{50} + 126q^{51} - 34q^{52} + 498q^{53} + 81q^{54} - 1296q^{55} + 744q^{57} + 306q^{58} - 132q^{59} - 54q^{60} + 398q^{61} - 960q^{62} + 866q^{64} - 612q^{65} - 324q^{66} - 92q^{67} + 42q^{68} - 1440q^{71} - 189q^{72} - 502q^{73} + 1194q^{74} - 597q^{75} + 248q^{76} - 612q^{78} + 1024q^{79} + 1278q^{80} - 81q^{81} + 954q^{82} + 408q^{83} - 1512q^{85} - 804q^{86} - 306q^{87} + 756q^{88} + 354q^{89} - 972q^{90} - 480q^{93} - 720q^{94} - 2232q^{95} - 135q^{96} + 572q^{97} - 648q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 2.59808i 0.530330 0.918559i −0.469044 0.883175i \(-0.655401\pi\)
0.999374 0.0353837i \(-0.0112653\pi\)
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.0625000 0.108253i
\(5\) −9.00000 + 15.5885i −0.804984 + 1.39427i 0.111317 + 0.993785i \(0.464493\pi\)
−0.916302 + 0.400489i \(0.868840\pi\)
\(6\) −9.00000 −0.612372
\(7\) 0 0
\(8\) 21.0000 0.928078
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 27.0000 + 46.7654i 0.853815 + 1.47885i
\(11\) 18.0000 + 31.1769i 0.493382 + 0.854563i 0.999971 0.00762479i \(-0.00242707\pi\)
−0.506589 + 0.862188i \(0.669094\pi\)
\(12\) −1.50000 + 2.59808i −0.0360844 + 0.0625000i
\(13\) 34.0000 0.725377 0.362689 0.931910i \(-0.381859\pi\)
0.362689 + 0.931910i \(0.381859\pi\)
\(14\) 0 0
\(15\) 54.0000 0.929516
\(16\) 35.5000 61.4878i 0.554688 0.960747i
\(17\) 21.0000 + 36.3731i 0.299603 + 0.518927i 0.976045 0.217568i \(-0.0698125\pi\)
−0.676442 + 0.736496i \(0.736479\pi\)
\(18\) 13.5000 + 23.3827i 0.176777 + 0.306186i
\(19\) −62.0000 + 107.387i −0.748620 + 1.29665i 0.199865 + 0.979824i \(0.435950\pi\)
−0.948484 + 0.316824i \(0.897384\pi\)
\(20\) 18.0000 0.201246
\(21\) 0 0
\(22\) 108.000 1.04662
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −31.5000 54.5596i −0.267913 0.464039i
\(25\) −99.5000 172.339i −0.796000 1.37871i
\(26\) 51.0000 88.3346i 0.384689 0.666301i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 102.000 0.653135 0.326568 0.945174i \(-0.394108\pi\)
0.326568 + 0.945174i \(0.394108\pi\)
\(30\) 81.0000 140.296i 0.492950 0.853815i
\(31\) −80.0000 138.564i −0.463498 0.802801i 0.535635 0.844450i \(-0.320072\pi\)
−0.999132 + 0.0416484i \(0.986739\pi\)
\(32\) −22.5000 38.9711i −0.124296 0.215287i
\(33\) 54.0000 93.5307i 0.284854 0.493382i
\(34\) 126.000 0.635554
\(35\) 0 0
\(36\) 9.00000 0.0416667
\(37\) −199.000 + 344.678i −0.884200 + 1.53148i −0.0375721 + 0.999294i \(0.511962\pi\)
−0.846628 + 0.532185i \(0.821371\pi\)
\(38\) 186.000 + 322.161i 0.794031 + 1.37530i
\(39\) −51.0000 88.3346i −0.209398 0.362689i
\(40\) −189.000 + 327.358i −0.747088 + 1.29399i
\(41\) 318.000 1.21130 0.605649 0.795732i \(-0.292913\pi\)
0.605649 + 0.795732i \(0.292913\pi\)
\(42\) 0 0
\(43\) −268.000 −0.950456 −0.475228 0.879863i \(-0.657634\pi\)
−0.475228 + 0.879863i \(0.657634\pi\)
\(44\) 18.0000 31.1769i 0.0616728 0.106820i
\(45\) −81.0000 140.296i −0.268328 0.464758i
\(46\) 0 0
\(47\) 120.000 207.846i 0.372421 0.645053i −0.617516 0.786558i \(-0.711861\pi\)
0.989937 + 0.141506i \(0.0451943\pi\)
\(48\) −213.000 −0.640498
\(49\) 0 0
\(50\) −597.000 −1.68857
\(51\) 63.0000 109.119i 0.172976 0.299603i
\(52\) −17.0000 29.4449i −0.0453361 0.0785244i
\(53\) 249.000 + 431.281i 0.645335 + 1.11775i 0.984224 + 0.176927i \(0.0566157\pi\)
−0.338888 + 0.940827i \(0.610051\pi\)
\(54\) 40.5000 70.1481i 0.102062 0.176777i
\(55\) −648.000 −1.58866
\(56\) 0 0
\(57\) 372.000 0.864432
\(58\) 153.000 265.004i 0.346377 0.599943i
\(59\) −66.0000 114.315i −0.145635 0.252247i 0.783975 0.620793i \(-0.213189\pi\)
−0.929610 + 0.368546i \(0.879856\pi\)
\(60\) −27.0000 46.7654i −0.0580948 0.100623i
\(61\) 199.000 344.678i 0.417694 0.723467i −0.578013 0.816028i \(-0.696172\pi\)
0.995707 + 0.0925602i \(0.0295051\pi\)
\(62\) −480.000 −0.983227
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) −306.000 + 530.008i −0.583917 + 1.01137i
\(66\) −162.000 280.592i −0.302134 0.523311i
\(67\) −46.0000 79.6743i −0.0838775 0.145280i 0.821035 0.570878i \(-0.193397\pi\)
−0.904912 + 0.425598i \(0.860064\pi\)
\(68\) 21.0000 36.3731i 0.0374504 0.0648659i
\(69\) 0 0
\(70\) 0 0
\(71\) −720.000 −1.20350 −0.601748 0.798686i \(-0.705529\pi\)
−0.601748 + 0.798686i \(0.705529\pi\)
\(72\) −94.5000 + 163.679i −0.154680 + 0.267913i
\(73\) −251.000 434.745i −0.402429 0.697028i 0.591589 0.806239i \(-0.298501\pi\)
−0.994019 + 0.109212i \(0.965167\pi\)
\(74\) 597.000 + 1034.03i 0.937836 + 1.62438i
\(75\) −298.500 + 517.017i −0.459571 + 0.796000i
\(76\) 124.000 0.187155
\(77\) 0 0
\(78\) −306.000 −0.444201
\(79\) 512.000 886.810i 0.729171 1.26296i −0.228063 0.973646i \(-0.573239\pi\)
0.957234 0.289315i \(-0.0934274\pi\)
\(80\) 639.000 + 1106.78i 0.893030 + 1.54677i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 477.000 826.188i 0.642388 1.11265i
\(83\) 204.000 0.269782 0.134891 0.990860i \(-0.456932\pi\)
0.134891 + 0.990860i \(0.456932\pi\)
\(84\) 0 0
\(85\) −756.000 −0.964703
\(86\) −402.000 + 696.284i −0.504056 + 0.873050i
\(87\) −153.000 265.004i −0.188544 0.326568i
\(88\) 378.000 + 654.715i 0.457897 + 0.793101i
\(89\) 177.000 306.573i 0.210809 0.365131i −0.741159 0.671329i \(-0.765724\pi\)
0.951968 + 0.306198i \(0.0990570\pi\)
\(90\) −486.000 −0.569210
\(91\) 0 0
\(92\) 0 0
\(93\) −240.000 + 415.692i −0.267600 + 0.463498i
\(94\) −360.000 623.538i −0.395012 0.684182i
\(95\) −1116.00 1932.97i −1.20525 2.08756i
\(96\) −67.5000 + 116.913i −0.0717624 + 0.124296i
\(97\) 286.000 0.299370 0.149685 0.988734i \(-0.452174\pi\)
0.149685 + 0.988734i \(0.452174\pi\)
\(98\) 0 0
\(99\) −324.000 −0.328921
\(100\) −99.5000 + 172.339i −0.0995000 + 0.172339i
\(101\) 207.000 + 358.535i 0.203933 + 0.353223i 0.949792 0.312881i \(-0.101294\pi\)
−0.745859 + 0.666104i \(0.767961\pi\)
\(102\) −189.000 327.358i −0.183469 0.317777i
\(103\) 28.0000 48.4974i 0.0267857 0.0463941i −0.852322 0.523018i \(-0.824806\pi\)
0.879107 + 0.476624i \(0.158140\pi\)
\(104\) 714.000 0.673206
\(105\) 0 0
\(106\) 1494.00 1.36896
\(107\) −6.00000 + 10.3923i −0.00542095 + 0.00938936i −0.868723 0.495298i \(-0.835059\pi\)
0.863302 + 0.504687i \(0.168392\pi\)
\(108\) −13.5000 23.3827i −0.0120281 0.0208333i
\(109\) −739.000 1279.99i −0.649389 1.12477i −0.983269 0.182159i \(-0.941692\pi\)
0.333880 0.942615i \(-0.391642\pi\)
\(110\) −972.000 + 1683.55i −0.842514 + 1.45928i
\(111\) 1194.00 1.02099
\(112\) 0 0
\(113\) 402.000 0.334664 0.167332 0.985901i \(-0.446485\pi\)
0.167332 + 0.985901i \(0.446485\pi\)
\(114\) 558.000 966.484i 0.458434 0.794031i
\(115\) 0 0
\(116\) −51.0000 88.3346i −0.0408210 0.0707040i
\(117\) −153.000 + 265.004i −0.120896 + 0.209398i
\(118\) −396.000 −0.308939
\(119\) 0 0
\(120\) 1134.00 0.862663
\(121\) 17.5000 30.3109i 0.0131480 0.0227730i
\(122\) −597.000 1034.03i −0.443031 0.767353i
\(123\) −477.000 826.188i −0.349672 0.605649i
\(124\) −80.0000 + 138.564i −0.0579372 + 0.100350i
\(125\) 1332.00 0.953102
\(126\) 0 0
\(127\) 1280.00 0.894344 0.447172 0.894448i \(-0.352431\pi\)
0.447172 + 0.894448i \(0.352431\pi\)
\(128\) 829.500 1436.74i 0.572798 0.992115i
\(129\) 402.000 + 696.284i 0.274373 + 0.475228i
\(130\) 918.000 + 1590.02i 0.619338 + 1.07272i
\(131\) 882.000 1527.67i 0.588250 1.01888i −0.406212 0.913779i \(-0.633151\pi\)
0.994462 0.105099i \(-0.0335161\pi\)
\(132\) −108.000 −0.0712136
\(133\) 0 0
\(134\) −276.000 −0.177931
\(135\) −243.000 + 420.888i −0.154919 + 0.268328i
\(136\) 441.000 + 763.834i 0.278055 + 0.481605i
\(137\) 1179.00 + 2042.09i 0.735246 + 1.27348i 0.954615 + 0.297842i \(0.0962669\pi\)
−0.219369 + 0.975642i \(0.570400\pi\)
\(138\) 0 0
\(139\) 52.0000 0.0317308 0.0158654 0.999874i \(-0.494950\pi\)
0.0158654 + 0.999874i \(0.494950\pi\)
\(140\) 0 0
\(141\) −720.000 −0.430035
\(142\) −1080.00 + 1870.61i −0.638251 + 1.10548i
\(143\) 612.000 + 1060.02i 0.357888 + 0.619881i
\(144\) 319.500 + 553.390i 0.184896 + 0.320249i
\(145\) −918.000 + 1590.02i −0.525764 + 0.910650i
\(146\) −1506.00 −0.853681
\(147\) 0 0
\(148\) 398.000 0.221050
\(149\) 873.000 1512.08i 0.479993 0.831372i −0.519744 0.854322i \(-0.673973\pi\)
0.999737 + 0.0229501i \(0.00730589\pi\)
\(150\) 895.500 + 1551.05i 0.487448 + 0.844285i
\(151\) 116.000 + 200.918i 0.0625162 + 0.108281i 0.895590 0.444881i \(-0.146754\pi\)
−0.833073 + 0.553163i \(0.813421\pi\)
\(152\) −1302.00 + 2255.13i −0.694777 + 1.20339i
\(153\) −378.000 −0.199735
\(154\) 0 0
\(155\) 2880.00 1.49243
\(156\) −51.0000 + 88.3346i −0.0261748 + 0.0453361i
\(157\) 847.000 + 1467.05i 0.430560 + 0.745752i 0.996922 0.0784048i \(-0.0249827\pi\)
−0.566361 + 0.824157i \(0.691649\pi\)
\(158\) −1536.00 2660.43i −0.773403 1.33957i
\(159\) 747.000 1293.84i 0.372585 0.645335i
\(160\) 810.000 0.400226
\(161\) 0 0
\(162\) −243.000 −0.117851
\(163\) 1466.00 2539.19i 0.704454 1.22015i −0.262434 0.964950i \(-0.584525\pi\)
0.966888 0.255200i \(-0.0821413\pi\)
\(164\) −159.000 275.396i −0.0757062 0.131127i
\(165\) 972.000 + 1683.55i 0.458607 + 0.794330i
\(166\) 306.000 530.008i 0.143074 0.247811i
\(167\) −1176.00 −0.544920 −0.272460 0.962167i \(-0.587837\pi\)
−0.272460 + 0.962167i \(0.587837\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) −1134.00 + 1964.15i −0.511611 + 0.886136i
\(171\) −558.000 966.484i −0.249540 0.432216i
\(172\) 134.000 + 232.095i 0.0594035 + 0.102890i
\(173\) 435.000 753.442i 0.191170 0.331116i −0.754468 0.656337i \(-0.772105\pi\)
0.945638 + 0.325220i \(0.105438\pi\)
\(174\) −918.000 −0.399962
\(175\) 0 0
\(176\) 2556.00 1.09469
\(177\) −198.000 + 342.946i −0.0840824 + 0.145635i
\(178\) −531.000 919.719i −0.223596 0.387280i
\(179\) 1158.00 + 2005.71i 0.483536 + 0.837509i 0.999821 0.0189075i \(-0.00601881\pi\)
−0.516285 + 0.856417i \(0.672685\pi\)
\(180\) −81.0000 + 140.296i −0.0335410 + 0.0580948i
\(181\) 106.000 0.0435299 0.0217650 0.999763i \(-0.493071\pi\)
0.0217650 + 0.999763i \(0.493071\pi\)
\(182\) 0 0
\(183\) −1194.00 −0.482312
\(184\) 0 0
\(185\) −3582.00 6204.21i −1.42353 2.46563i
\(186\) 720.000 + 1247.08i 0.283833 + 0.491613i
\(187\) −756.000 + 1309.43i −0.295637 + 0.512059i
\(188\) −240.000 −0.0931053
\(189\) 0 0
\(190\) −6696.00 −2.55673
\(191\) 564.000 976.877i 0.213663 0.370075i −0.739195 0.673491i \(-0.764794\pi\)
0.952858 + 0.303416i \(0.0981273\pi\)
\(192\) −649.500 1124.97i −0.244133 0.422852i
\(193\) −2017.00 3493.55i −0.752263 1.30296i −0.946723 0.322048i \(-0.895629\pi\)
0.194460 0.980910i \(-0.437705\pi\)
\(194\) 429.000 743.050i 0.158765 0.274989i
\(195\) 1836.00 0.674250
\(196\) 0 0
\(197\) −1314.00 −0.475221 −0.237611 0.971360i \(-0.576364\pi\)
−0.237611 + 0.971360i \(0.576364\pi\)
\(198\) −486.000 + 841.777i −0.174437 + 0.302134i
\(199\) 2548.00 + 4413.27i 0.907653 + 1.57210i 0.817316 + 0.576190i \(0.195461\pi\)
0.0903369 + 0.995911i \(0.471206\pi\)
\(200\) −2089.50 3619.12i −0.738750 1.27955i
\(201\) −138.000 + 239.023i −0.0484267 + 0.0838775i
\(202\) 1242.00 0.432608
\(203\) 0 0
\(204\) −126.000 −0.0432439
\(205\) −2862.00 + 4957.13i −0.975077 + 1.68888i
\(206\) −84.0000 145.492i −0.0284105 0.0492084i
\(207\) 0 0
\(208\) 1207.00 2090.59i 0.402358 0.696904i
\(209\) −4464.00 −1.47742
\(210\) 0 0
\(211\) −3076.00 −1.00360 −0.501802 0.864982i \(-0.667330\pi\)
−0.501802 + 0.864982i \(0.667330\pi\)
\(212\) 249.000 431.281i 0.0806669 0.139719i
\(213\) 1080.00 + 1870.61i 0.347420 + 0.601748i
\(214\) 18.0000 + 31.1769i 0.00574979 + 0.00995893i
\(215\) 2412.00 4177.71i 0.765102 1.32520i
\(216\) 567.000 0.178609
\(217\) 0 0
\(218\) −4434.00 −1.37756
\(219\) −753.000 + 1304.23i −0.232343 + 0.402429i
\(220\) 324.000 + 561.184i 0.0992913 + 0.171977i
\(221\) 714.000 + 1236.68i 0.217325 + 0.376418i
\(222\) 1791.00 3102.10i 0.541460 0.937836i
\(223\) 1888.00 0.566950 0.283475 0.958980i \(-0.408513\pi\)
0.283475 + 0.958980i \(0.408513\pi\)
\(224\) 0 0
\(225\) 1791.00 0.530667
\(226\) 603.000 1044.43i 0.177482 0.307408i
\(227\) −2358.00 4084.18i −0.689454 1.19417i −0.972015 0.234919i \(-0.924517\pi\)
0.282561 0.959249i \(-0.408816\pi\)
\(228\) −186.000 322.161i −0.0540270 0.0935775i
\(229\) −845.000 + 1463.58i −0.243839 + 0.422342i −0.961805 0.273737i \(-0.911740\pi\)
0.717965 + 0.696079i \(0.245074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2142.00 0.606160
\(233\) −69.0000 + 119.512i −0.0194006 + 0.0336028i −0.875563 0.483104i \(-0.839509\pi\)
0.856162 + 0.516707i \(0.172842\pi\)
\(234\) 459.000 + 795.011i 0.128230 + 0.222100i
\(235\) 2160.00 + 3741.23i 0.599587 + 1.03851i
\(236\) −66.0000 + 114.315i −0.0182044 + 0.0315309i
\(237\) −3072.00 −0.841974
\(238\) 0 0
\(239\) 1896.00 0.513147 0.256573 0.966525i \(-0.417406\pi\)
0.256573 + 0.966525i \(0.417406\pi\)
\(240\) 1917.00 3320.34i 0.515591 0.893030i
\(241\) −1799.00 3115.96i −0.480846 0.832849i 0.518913 0.854827i \(-0.326337\pi\)
−0.999758 + 0.0219782i \(0.993004\pi\)
\(242\) −52.5000 90.9327i −0.0139456 0.0241544i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) −398.000 −0.104424
\(245\) 0 0
\(246\) −2862.00 −0.741766
\(247\) −2108.00 + 3651.16i −0.543032 + 0.940558i
\(248\) −1680.00 2909.85i −0.430162 0.745062i
\(249\) −306.000 530.008i −0.0778794 0.134891i
\(250\) 1998.00 3460.64i 0.505458 0.875480i
\(251\) 3060.00 0.769504 0.384752 0.923020i \(-0.374287\pi\)
0.384752 + 0.923020i \(0.374287\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1920.00 3325.54i 0.474297 0.821507i
\(255\) 1134.00 + 1964.15i 0.278486 + 0.482351i
\(256\) −756.500 1310.30i −0.184692 0.319897i
\(257\) −3411.00 + 5908.03i −0.827908 + 1.43398i 0.0717686 + 0.997421i \(0.477136\pi\)
−0.899676 + 0.436557i \(0.856198\pi\)
\(258\) 2412.00 0.582033
\(259\) 0 0
\(260\) 612.000 0.145979
\(261\) −459.000 + 795.011i −0.108856 + 0.188544i
\(262\) −2646.00 4583.01i −0.623933 1.08068i
\(263\) −1296.00 2244.74i −0.303858 0.526298i 0.673148 0.739508i \(-0.264942\pi\)
−0.977007 + 0.213209i \(0.931608\pi\)
\(264\) 1134.00 1964.15i 0.264367 0.457897i
\(265\) −8964.00 −2.07794
\(266\) 0 0
\(267\) −1062.00 −0.243421
\(268\) −46.0000 + 79.6743i −0.0104847 + 0.0181600i
\(269\) 4107.00 + 7113.53i 0.930886 + 1.61234i 0.781811 + 0.623515i \(0.214296\pi\)
0.149074 + 0.988826i \(0.452371\pi\)
\(270\) 729.000 + 1262.67i 0.164317 + 0.284605i
\(271\) −2672.00 + 4628.04i −0.598939 + 1.03739i 0.394039 + 0.919094i \(0.371077\pi\)
−0.992978 + 0.118299i \(0.962256\pi\)
\(272\) 2982.00 0.664744
\(273\) 0 0
\(274\) 7074.00 1.55969
\(275\) 3582.00 6204.21i 0.785464 1.36046i
\(276\) 0 0
\(277\) 3257.00 + 5641.29i 0.706477 + 1.22365i 0.966156 + 0.257959i \(0.0830500\pi\)
−0.259679 + 0.965695i \(0.583617\pi\)
\(278\) 78.0000 135.100i 0.0168278 0.0291466i
\(279\) 1440.00 0.308998
\(280\) 0 0
\(281\) 6618.00 1.40497 0.702485 0.711698i \(-0.252074\pi\)
0.702485 + 0.711698i \(0.252074\pi\)
\(282\) −1080.00 + 1870.61i −0.228061 + 0.395012i
\(283\) 1630.00 + 2823.24i 0.342380 + 0.593019i 0.984874 0.173271i \(-0.0554338\pi\)
−0.642494 + 0.766290i \(0.722100\pi\)
\(284\) 360.000 + 623.538i 0.0752186 + 0.130282i
\(285\) −3348.00 + 5798.91i −0.695854 + 1.20525i
\(286\) 3672.00 0.759195
\(287\) 0 0
\(288\) 405.000 0.0828641
\(289\) 1574.50 2727.11i 0.320476 0.555081i
\(290\) 2754.00 + 4770.07i 0.557657 + 0.965890i
\(291\) −429.000 743.050i −0.0864207 0.149685i
\(292\) −251.000 + 434.745i −0.0503036 + 0.0871285i
\(293\) −5118.00 −1.02047 −0.510233 0.860036i \(-0.670441\pi\)
−0.510233 + 0.860036i \(0.670441\pi\)
\(294\) 0 0
\(295\) 2376.00 0.468936
\(296\) −4179.00 + 7238.24i −0.820606 + 1.42133i
\(297\) 486.000 + 841.777i 0.0949514 + 0.164461i
\(298\) −2619.00 4536.24i −0.509109 0.881803i
\(299\) 0 0
\(300\) 597.000 0.114893
\(301\) 0 0
\(302\) 696.000 0.132617
\(303\) 621.000 1075.60i 0.117741 0.203933i
\(304\) 4402.00 + 7624.49i 0.830500 + 1.43847i
\(305\) 3582.00 + 6204.21i 0.672475 + 1.16476i
\(306\) −567.000 + 982.073i −0.105926 + 0.183469i
\(307\) −452.000 −0.0840293 −0.0420147 0.999117i \(-0.513378\pi\)
−0.0420147 + 0.999117i \(0.513378\pi\)
\(308\) 0 0
\(309\) −168.000 −0.0309294
\(310\) 4320.00 7482.46i 0.791482 1.37089i
\(311\) 2508.00 + 4343.98i 0.457285 + 0.792041i 0.998816 0.0486397i \(-0.0154886\pi\)
−0.541531 + 0.840681i \(0.682155\pi\)
\(312\) −1071.00 1855.03i −0.194338 0.336603i
\(313\) 2701.00 4678.27i 0.487762 0.844829i −0.512139 0.858903i \(-0.671147\pi\)
0.999901 + 0.0140739i \(0.00448001\pi\)
\(314\) 5082.00 0.913356
\(315\) 0 0
\(316\) −1024.00 −0.182293
\(317\) −5043.00 + 8734.73i −0.893511 + 1.54761i −0.0578751 + 0.998324i \(0.518433\pi\)
−0.835636 + 0.549283i \(0.814901\pi\)
\(318\) −2241.00 3881.53i −0.395186 0.684482i
\(319\) 1836.00 + 3180.05i 0.322245 + 0.558145i
\(320\) −3897.00 + 6749.80i −0.680778 + 1.17914i
\(321\) 36.0000 0.00625958
\(322\) 0 0
\(323\) −5208.00 −0.897154
\(324\) −40.5000 + 70.1481i −0.00694444 + 0.0120281i
\(325\) −3383.00 5859.53i −0.577400 1.00009i
\(326\) −4398.00 7617.56i −0.747186 1.29416i
\(327\) −2217.00 + 3839.96i −0.374925 + 0.649389i
\(328\) 6678.00 1.12418
\(329\) 0 0
\(330\) 5832.00 0.972852
\(331\) 4022.00 6966.31i 0.667883 1.15681i −0.310613 0.950537i \(-0.600534\pi\)
0.978495 0.206270i \(-0.0661325\pi\)
\(332\) −102.000 176.669i −0.0168614 0.0292048i
\(333\) −1791.00 3102.10i −0.294733 0.510493i
\(334\) −1764.00 + 3055.34i −0.288987 + 0.500541i
\(335\) 1656.00 0.270080
\(336\) 0 0
\(337\) 4178.00 0.675342 0.337671 0.941264i \(-0.390361\pi\)
0.337671 + 0.941264i \(0.390361\pi\)
\(338\) −1561.50 + 2704.60i −0.251285 + 0.435239i
\(339\) −603.000 1044.43i −0.0966090 0.167332i
\(340\) 378.000 + 654.715i 0.0602939 + 0.104432i
\(341\) 2880.00 4988.31i 0.457363 0.792176i
\(342\) −3348.00 −0.529354
\(343\) 0 0
\(344\) −5628.00 −0.882097
\(345\) 0 0
\(346\) −1305.00 2260.33i −0.202767 0.351202i
\(347\) −78.0000 135.100i −0.0120670 0.0209007i 0.859929 0.510414i \(-0.170508\pi\)
−0.871996 + 0.489513i \(0.837174\pi\)
\(348\) −153.000 + 265.004i −0.0235680 + 0.0408210i
\(349\) 12418.0 1.90464 0.952321 0.305097i \(-0.0986888\pi\)
0.952321 + 0.305097i \(0.0986888\pi\)
\(350\) 0 0
\(351\) 918.000 0.139599
\(352\) 810.000 1402.96i 0.122651 0.212438i
\(353\) −3915.00 6780.98i −0.590296 1.02242i −0.994192 0.107618i \(-0.965678\pi\)
0.403897 0.914805i \(-0.367656\pi\)
\(354\) 594.000 + 1028.84i 0.0891829 + 0.154469i
\(355\) 6480.00 11223.7i 0.968796 1.67800i
\(356\) −354.000 −0.0527021
\(357\) 0 0
\(358\) 6948.00 1.02574
\(359\) 4656.00 8064.43i 0.684497 1.18558i −0.289098 0.957299i \(-0.593355\pi\)
0.973595 0.228283i \(-0.0733113\pi\)
\(360\) −1701.00 2946.22i −0.249029 0.431332i
\(361\) −4258.50 7375.94i −0.620863 1.07537i
\(362\) 159.000 275.396i 0.0230852 0.0399848i
\(363\) −105.000 −0.0151820
\(364\) 0 0
\(365\) 9036.00 1.29580
\(366\) −1791.00 + 3102.10i −0.255784 + 0.443031i
\(367\) −1880.00 3256.26i −0.267398 0.463148i 0.700791 0.713367i \(-0.252831\pi\)
−0.968189 + 0.250219i \(0.919497\pi\)
\(368\) 0 0
\(369\) −1431.00 + 2478.56i −0.201883 + 0.349672i
\(370\) −21492.0 −3.01977
\(371\) 0 0
\(372\) 480.000 0.0669001
\(373\) −2935.00 + 5083.57i −0.407422 + 0.705676i −0.994600 0.103782i \(-0.966906\pi\)
0.587178 + 0.809458i \(0.300239\pi\)
\(374\) 2268.00 + 3928.29i 0.313571 + 0.543121i
\(375\) −1998.00 3460.64i −0.275137 0.476551i
\(376\) 2520.00 4364.77i 0.345636 0.598659i
\(377\) 3468.00 0.473769
\(378\) 0 0
\(379\) −1852.00 −0.251005 −0.125502 0.992093i \(-0.540054\pi\)
−0.125502 + 0.992093i \(0.540054\pi\)
\(380\) −1116.00 + 1932.97i −0.150657 + 0.260945i
\(381\) −1920.00 3325.54i −0.258175 0.447172i
\(382\) −1692.00 2930.63i −0.226624 0.392524i
\(383\) 1080.00 1870.61i 0.144087 0.249566i −0.784945 0.619566i \(-0.787309\pi\)
0.929032 + 0.369999i \(0.120642\pi\)
\(384\) −4977.00 −0.661410
\(385\) 0 0
\(386\) −12102.0 −1.59579
\(387\) 1206.00 2088.85i 0.158409 0.274373i
\(388\) −143.000 247.683i −0.0187106 0.0324078i
\(389\) 3393.00 + 5876.85i 0.442241 + 0.765985i 0.997855 0.0654557i \(-0.0208501\pi\)
−0.555614 + 0.831440i \(0.687517\pi\)
\(390\) 2754.00 4770.07i 0.357575 0.619338i
\(391\) 0 0
\(392\) 0 0
\(393\) −5292.00 −0.679252
\(394\) −1971.00 + 3413.87i −0.252024 + 0.436519i
\(395\) 9216.00 + 15962.6i 1.17394 + 2.03333i
\(396\) 162.000 + 280.592i 0.0205576 + 0.0356068i
\(397\) −3257.00 + 5641.29i −0.411748 + 0.713169i −0.995081 0.0990641i \(-0.968415\pi\)
0.583333 + 0.812233i \(0.301748\pi\)
\(398\) 15288.0 1.92542
\(399\) 0 0
\(400\) −14129.0 −1.76612
\(401\) −1665.00 + 2883.86i −0.207347 + 0.359135i −0.950878 0.309566i \(-0.899816\pi\)
0.743531 + 0.668701i \(0.233150\pi\)
\(402\) 414.000 + 717.069i 0.0513643 + 0.0889656i
\(403\) −2720.00 4711.18i −0.336211 0.582334i
\(404\) 207.000 358.535i 0.0254917 0.0441529i
\(405\) 1458.00 0.178885
\(406\) 0 0
\(407\) −14328.0 −1.74499
\(408\) 1323.00 2291.50i 0.160535 0.278055i
\(409\) −2699.00 4674.81i −0.326301 0.565169i 0.655474 0.755218i \(-0.272469\pi\)
−0.981775 + 0.190048i \(0.939136\pi\)
\(410\) 8586.00 + 14871.4i 1.03423 + 1.79133i
\(411\) 3537.00 6126.26i 0.424495 0.735246i
\(412\) −56.0000 −0.00669641
\(413\) 0 0
\(414\) 0 0
\(415\) −1836.00 + 3180.05i −0.217170 + 0.376150i
\(416\) −765.000 1325.02i −0.0901616 0.156164i
\(417\) −78.0000 135.100i −0.00915990 0.0158654i
\(418\) −6696.00 + 11597.8i −0.783522 + 1.35710i
\(419\) −13092.0 −1.52646 −0.763229 0.646128i \(-0.776387\pi\)
−0.763229 + 0.646128i \(0.776387\pi\)
\(420\) 0 0
\(421\) −322.000 −0.0372763 −0.0186381 0.999826i \(-0.505933\pi\)
−0.0186381 + 0.999826i \(0.505933\pi\)
\(422\) −4614.00 + 7991.68i −0.532242 + 0.921870i
\(423\) 1080.00 + 1870.61i 0.124140 + 0.215018i
\(424\) 5229.00 + 9056.89i 0.598921 + 1.03736i
\(425\) 4179.00 7238.24i 0.476968 0.826132i
\(426\) 6480.00 0.736988
\(427\) 0 0
\(428\) 12.0000 0.00135524
\(429\) 1836.00 3180.05i 0.206627 0.357888i
\(430\) −7236.00 12533.1i −0.811514 1.40558i
\(431\) −1308.00 2265.52i −0.146181 0.253193i 0.783632 0.621226i \(-0.213365\pi\)
−0.929813 + 0.368032i \(0.880032\pi\)
\(432\) 958.500 1660.17i 0.106750 0.184896i
\(433\) −4322.00 −0.479681 −0.239841 0.970812i \(-0.577095\pi\)
−0.239841 + 0.970812i \(0.577095\pi\)
\(434\) 0 0
\(435\) 5508.00 0.607100
\(436\) −739.000 + 1279.99i −0.0811736 + 0.140597i
\(437\) 0 0
\(438\) 2259.00 + 3912.70i 0.246437 + 0.426841i
\(439\) −4508.00 + 7808.09i −0.490103 + 0.848883i −0.999935 0.0113909i \(-0.996374\pi\)
0.509832 + 0.860274i \(0.329707\pi\)
\(440\) −13608.0 −1.47440
\(441\) 0 0
\(442\) 4284.00 0.461016
\(443\) 2634.00 4562.22i 0.282495 0.489295i −0.689504 0.724282i \(-0.742171\pi\)
0.971999 + 0.234987i \(0.0755047\pi\)
\(444\) −597.000 1034.03i −0.0638116 0.110525i
\(445\) 3186.00 + 5518.31i 0.339395 + 0.587850i
\(446\) 2832.00 4905.17i 0.300671 0.520777i
\(447\) −5238.00 −0.554248
\(448\) 0 0
\(449\) −5310.00 −0.558117 −0.279058 0.960274i \(-0.590022\pi\)
−0.279058 + 0.960274i \(0.590022\pi\)
\(450\) 2686.50 4653.15i 0.281428 0.487448i
\(451\) 5724.00 + 9914.26i 0.597633 + 1.03513i
\(452\) −201.000 348.142i −0.0209165 0.0362284i
\(453\) 348.000 602.754i 0.0360937 0.0625162i
\(454\) −14148.0 −1.46255
\(455\) 0 0
\(456\) 7812.00 0.802260
\(457\) −7885.00 + 13657.2i −0.807100 + 1.39794i 0.107764 + 0.994177i \(0.465631\pi\)
−0.914864 + 0.403762i \(0.867702\pi\)
\(458\) 2535.00 + 4390.75i 0.258631 + 0.447961i
\(459\) 567.000 + 982.073i 0.0576586 + 0.0998676i
\(460\) 0 0
\(461\) 5370.00 0.542529 0.271264 0.962505i \(-0.412558\pi\)
0.271264 + 0.962505i \(0.412558\pi\)
\(462\) 0 0
\(463\) −3328.00 −0.334050 −0.167025 0.985953i \(-0.553416\pi\)
−0.167025 + 0.985953i \(0.553416\pi\)
\(464\) 3621.00 6271.76i 0.362286 0.627498i
\(465\) −4320.00 7482.46i −0.430828 0.746217i
\(466\) 207.000 + 358.535i 0.0205774 + 0.0356412i
\(467\) 2274.00 3938.68i 0.225328 0.390280i −0.731090 0.682281i \(-0.760988\pi\)
0.956418 + 0.292002i \(0.0943213\pi\)
\(468\) 306.000 0.0302240
\(469\) 0 0
\(470\) 12960.0 1.27192
\(471\) 2541.00 4401.14i 0.248584 0.430560i
\(472\) −1386.00 2400.62i −0.135161 0.234105i
\(473\) −4824.00 8355.41i −0.468938 0.812225i
\(474\) −4608.00 + 7981.29i −0.446524 + 0.773403i
\(475\) 24676.0 2.38361
\(476\) 0 0
\(477\) −4482.00 −0.430224
\(478\) 2844.00 4925.95i 0.272137 0.471355i
\(479\) −4032.00 6983.63i −0.384607 0.666159i 0.607108 0.794620i \(-0.292330\pi\)
−0.991715 + 0.128461i \(0.958996\pi\)
\(480\) −1215.00 2104.44i −0.115535 0.200113i
\(481\) −6766.00 + 11719.1i −0.641378 + 1.11090i
\(482\) −10794.0 −1.02003
\(483\) 0 0
\(484\) −35.0000 −0.00328700
\(485\) −2574.00 + 4458.30i −0.240988 + 0.417404i
\(486\) 364.500 + 631.333i 0.0340207 + 0.0589256i
\(487\) −8308.00 14389.9i −0.773042 1.33895i −0.935888 0.352296i \(-0.885401\pi\)
0.162847 0.986651i \(-0.447932\pi\)
\(488\) 4179.00 7238.24i 0.387653 0.671434i
\(489\) −8796.00 −0.813433
\(490\) 0 0
\(491\) −7140.00 −0.656260 −0.328130 0.944633i \(-0.606418\pi\)
−0.328130 + 0.944633i \(0.606418\pi\)
\(492\) −477.000 + 826.188i −0.0437090 + 0.0757062i
\(493\) 2142.00 + 3710.05i 0.195681 + 0.338930i
\(494\) 6324.00 + 10953.5i 0.575972 + 0.997613i
\(495\) 2916.00 5050.66i 0.264777 0.458607i
\(496\) −11360.0 −1.02839
\(497\) 0 0
\(498\) −1836.00 −0.165207
\(499\) 4562.00 7901.62i 0.409265 0.708868i −0.585543 0.810642i \(-0.699119\pi\)
0.994808 + 0.101774i \(0.0324519\pi\)
\(500\) −666.000 1153.55i −0.0595689 0.103176i
\(501\) 1764.00 + 3055.34i 0.157305 + 0.272460i
\(502\) 4590.00 7950.11i 0.408091 0.706834i
\(503\) 6552.00 0.580794 0.290397 0.956906i \(-0.406213\pi\)
0.290397 + 0.956906i \(0.406213\pi\)
\(504\) 0 0
\(505\) −7452.00 −0.656653
\(506\) 0 0
\(507\) 1561.50 + 2704.60i 0.136782 + 0.236914i
\(508\) −640.000 1108.51i −0.0558965 0.0968155i
\(509\) 1395.00 2416.21i 0.121478 0.210406i −0.798873 0.601500i \(-0.794570\pi\)
0.920351 + 0.391094i \(0.127903\pi\)
\(510\) 6804.00 0.590757
\(511\) 0 0
\(512\) 8733.00 0.753804
\(513\) −1674.00 + 2899.45i −0.144072 + 0.249540i
\(514\) 10233.0 + 17724.1i 0.878129 + 1.52096i
\(515\) 504.000 + 872.954i 0.0431241 + 0.0746931i
\(516\) 402.000 696.284i 0.0342966 0.0594035i
\(517\) 8640.00 0.734984
\(518\) 0 0
\(519\) −2610.00 −0.220744
\(520\) −6426.00 + 11130.2i −0.541921 + 0.938634i
\(521\) −7431.00 12870.9i −0.624871 1.08231i −0.988566 0.150791i \(-0.951818\pi\)
0.363694 0.931518i \(-0.381515\pi\)
\(522\) 1377.00 + 2385.03i 0.115459 + 0.199981i
\(523\) 8830.00 15294.0i 0.738258 1.27870i −0.215021 0.976609i \(-0.568982\pi\)
0.953279 0.302091i \(-0.0976846\pi\)
\(524\) −1764.00 −0.147062
\(525\) 0 0
\(526\) −7776.00 −0.644581
\(527\) 3360.00 5819.69i 0.277730 0.481043i
\(528\) −3834.00 6640.68i −0.316010 0.547346i
\(529\) 6083.50 + 10536.9i 0.500000 + 0.866025i
\(530\) −13446.0 + 23289.2i −1.10199 + 1.90871i
\(531\) 1188.00 0.0970900
\(532\) 0 0
\(533\) 10812.0 0.878649
\(534\) −1593.00 + 2759.16i −0.129093 + 0.223596i
\(535\) −108.000 187.061i −0.00872756 0.0151166i
\(536\) −966.000 1673.16i −0.0778449 0.134831i
\(537\) 3474.00 6017.14i 0.279170 0.483536i
\(538\) 24642.0 1.97471
\(539\) 0 0
\(540\) 486.000 0.0387298
\(541\) 9917.00 17176.7i 0.788106 1.36504i −0.139021 0.990290i \(-0.544395\pi\)
0.927126 0.374749i \(-0.122271\pi\)
\(542\) 8016.00 + 13884.1i 0.635271 + 1.10032i
\(543\) −159.000 275.396i −0.0125660 0.0217650i
\(544\) 945.000 1636.79i 0.0744789 0.129001i
\(545\) 26604.0 2.09099
\(546\) 0 0
\(547\) 20972.0 1.63930 0.819651 0.572863i \(-0.194167\pi\)
0.819651 + 0.572863i \(0.194167\pi\)
\(548\) 1179.00 2042.09i 0.0919058 0.159186i
\(549\) 1791.00 + 3102.10i 0.139231 + 0.241156i
\(550\) −10746.0 18612.6i −0.833111 1.44299i
\(551\) −6324.00 + 10953.5i −0.488950 + 0.846886i
\(552\) 0 0
\(553\) 0 0
\(554\) 19542.0 1.49866
\(555\) −10746.0 + 18612.6i −0.821878 + 1.42353i
\(556\) −26.0000 45.0333i −0.00198318 0.00343496i
\(557\) −10587.0 18337.2i −0.805360 1.39492i −0.916048 0.401069i \(-0.868639\pi\)
0.110688 0.993855i \(-0.464695\pi\)
\(558\) 2160.00 3741.23i 0.163871 0.283833i
\(559\) −9112.00 −0.689439
\(560\) 0 0
\(561\) 4536.00 0.341373
\(562\) 9927.00 17194.1i 0.745098 1.29055i
\(563\) −8886.00 15391.0i −0.665187 1.15214i −0.979235 0.202730i \(-0.935019\pi\)
0.314048 0.949407i \(-0.398315\pi\)
\(564\) 360.000 + 623.538i 0.0268772 + 0.0465527i
\(565\) −3618.00 + 6266.56i −0.269399 + 0.466613i
\(566\) 9780.00 0.726297
\(567\) 0 0
\(568\) −15120.0 −1.11694
\(569\) −4125.00 + 7144.71i −0.303917 + 0.526400i −0.977020 0.213149i \(-0.931628\pi\)
0.673102 + 0.739549i \(0.264961\pi\)
\(570\) 10044.0 + 17396.7i 0.738065 + 1.27837i
\(571\) −10378.0 17975.2i −0.760606 1.31741i −0.942539 0.334097i \(-0.891569\pi\)
0.181933 0.983311i \(-0.441765\pi\)
\(572\) 612.000 1060.02i 0.0447360 0.0774851i
\(573\) −3384.00 −0.246717
\(574\) 0 0
\(575\) 0 0
\(576\) −1948.50 + 3374.90i −0.140951 + 0.244133i
\(577\) 1.00000 + 1.73205i 7.21500e−5 + 0.000124967i 0.866061 0.499938i \(-0.166644\pi\)
−0.865989 + 0.500062i \(0.833310\pi\)
\(578\) −4723.50 8181.34i −0.339916 0.588753i
\(579\) −6051.00 + 10480.6i −0.434319 + 0.752263i
\(580\) 1836.00 0.131441
\(581\) 0 0
\(582\) −2574.00 −0.183326
\(583\) −8964.00 + 15526.1i −0.636794 + 1.10296i
\(584\) −5271.00 9129.64i −0.373485 0.646896i
\(585\) −2754.00 4770.07i −0.194639 0.337125i
\(586\) −7677.00 + 13297.0i −0.541184 + 0.937359i
\(587\) −26364.0 −1.85376 −0.926881 0.375354i \(-0.877521\pi\)
−0.926881 + 0.375354i \(0.877521\pi\)
\(588\) 0 0
\(589\) 19840.0 1.38793
\(590\) 3564.00 6173.03i 0.248691 0.430745i
\(591\) 1971.00 + 3413.87i 0.137185 + 0.237611i
\(592\) 14129.0 + 24472.1i 0.980909 + 1.69898i
\(593\) 1149.00 1990.13i 0.0795679 0.137816i −0.823496 0.567323i \(-0.807979\pi\)
0.903064 + 0.429507i \(0.141313\pi\)
\(594\) 2916.00 0.201422
\(595\) 0 0
\(596\) −1746.00 −0.119998
\(597\) 7644.00 13239.8i 0.524034 0.907653i
\(598\) 0 0
\(599\) −1536.00 2660.43i −0.104773 0.181473i 0.808872 0.587984i \(-0.200078\pi\)
−0.913646 + 0.406512i \(0.866745\pi\)
\(600\) −6268.50 + 10857.4i −0.426517 + 0.738750i
\(601\) −24554.0 −1.66652 −0.833260 0.552881i \(-0.813528\pi\)
−0.833260 + 0.552881i \(0.813528\pi\)
\(602\) 0 0
\(603\) 828.000 0.0559184
\(604\) 116.000 200.918i 0.00781452 0.0135352i
\(605\) 315.000 + 545.596i 0.0211679 + 0.0366639i
\(606\) −1863.00 3226.81i −0.124883 0.216304i
\(607\) 8416.00 14576.9i 0.562759 0.974728i −0.434495 0.900674i \(-0.643073\pi\)
0.997254 0.0740535i \(-0.0235935\pi\)
\(608\) 5580.00 0.372202
\(609\) 0 0
\(610\) 21492.0 1.42653
\(611\) 4080.00 7066.77i 0.270146 0.467906i
\(612\) 189.000 + 327.358i 0.0124835 + 0.0216220i
\(613\) 1241.00 + 2149.48i 0.0817676 + 0.141626i 0.904009 0.427513i \(-0.140610\pi\)
−0.822242 + 0.569139i \(0.807277\pi\)
\(614\) −678.000 + 1174.33i −0.0445633 + 0.0771859i
\(615\) 17172.0 1.12592
\(616\) 0 0
\(617\) −15798.0 −1.03080 −0.515400 0.856950i \(-0.672357\pi\)
−0.515400 + 0.856950i \(0.672357\pi\)
\(618\) −252.000 + 436.477i −0.0164028 + 0.0284105i
\(619\) −7730.00 13388.8i −0.501930 0.869369i −0.999998 0.00223050i \(-0.999290\pi\)
0.498067 0.867138i \(-0.334043\pi\)
\(620\) −1440.00 2494.15i −0.0932771 0.161561i
\(621\) 0 0
\(622\) 15048.0 0.970048
\(623\) 0 0
\(624\) −7242.00 −0.464603
\(625\) 449.500 778.557i 0.0287680 0.0498276i
\(626\) −8103.00 14034.8i −0.517350 0.896076i
\(627\) 6696.00 + 11597.8i 0.426495 + 0.738711i
\(628\) 847.000 1467.05i 0.0538200 0.0932190i
\(629\) −16716.0 −1.05964
\(630\) 0 0
\(631\) −7720.00 −0.487050 −0.243525 0.969895i \(-0.578304\pi\)
−0.243525 + 0.969895i \(0.578304\pi\)
\(632\) 10752.0 18623.0i 0.676727 1.17213i
\(633\) 4614.00 + 7991.68i 0.289716 + 0.501802i
\(634\) 15129.0 + 26204.2i 0.947712 + 1.64149i
\(635\) −11520.0 + 19953.2i −0.719933 + 1.24696i
\(636\) −1494.00 −0.0931462
\(637\) 0 0
\(638\) 11016.0 0.683586
\(639\) 3240.00 5611.84i 0.200583 0.347420i
\(640\) 14931.0 + 25861.3i 0.922187 + 1.59727i
\(641\) 8631.00 + 14949.3i 0.531832 + 0.921159i 0.999310 + 0.0371545i \(0.0118294\pi\)
−0.467478 + 0.884005i \(0.654837\pi\)
\(642\) 54.0000 93.5307i 0.00331964 0.00574979i
\(643\) 12220.0 0.749471 0.374735 0.927132i \(-0.377734\pi\)
0.374735 + 0.927132i \(0.377734\pi\)
\(644\) 0 0
\(645\) −14472.0 −0.883464
\(646\) −7812.00 + 13530.8i −0.475788 + 0.824089i
\(647\) 6780.00 + 11743.3i 0.411977 + 0.713566i 0.995106 0.0988143i \(-0.0315050\pi\)
−0.583129 + 0.812380i \(0.698172\pi\)
\(648\) −850.500 1473.11i −0.0515599 0.0893043i
\(649\) 2376.00 4115.35i 0.143707 0.248909i
\(650\) −20298.0 −1.22485
\(651\) 0 0
\(652\) −2932.00 −0.176113
\(653\) −11547.0 + 20000.0i −0.691989 + 1.19856i 0.279196 + 0.960234i \(0.409932\pi\)
−0.971185 + 0.238326i \(0.923401\pi\)
\(654\) 6651.00 + 11519.9i 0.397668 + 0.688781i
\(655\) 15876.0 + 27498.0i 0.947064 + 1.64036i
\(656\) 11289.0 19553.1i 0.671892 1.16375i
\(657\) 4518.00 0.268286
\(658\) 0 0
\(659\) 22548.0 1.33285 0.666423 0.745574i \(-0.267825\pi\)
0.666423 + 0.745574i \(0.267825\pi\)
\(660\) 972.000 1683.55i 0.0573258 0.0992913i
\(661\) 8731.00 + 15122.5i 0.513762 + 0.889862i 0.999873 + 0.0159643i \(0.00508182\pi\)
−0.486111 + 0.873897i \(0.661585\pi\)
\(662\) −12066.0 20898.9i −0.708396 1.22698i
\(663\) 2142.00 3710.05i 0.125473 0.217325i
\(664\) 4284.00 0.250379
\(665\) 0 0
\(666\) −10746.0 −0.625224
\(667\) 0 0
\(668\) 588.000 + 1018.45i 0.0340575 + 0.0589893i
\(669\) −2832.00 4905.17i −0.163664 0.283475i
\(670\) 2484.00 4302.41i 0.143232 0.248085i
\(671\) 14328.0 0.824331
\(672\) 0 0
\(673\) −22462.0 −1.28655 −0.643274 0.765636i \(-0.722424\pi\)
−0.643274 + 0.765636i \(0.722424\pi\)
\(674\) 6267.00 10854.8i 0.358154 0.620341i
\(675\) −2686.50 4653.15i −0.153190 0.265333i
\(676\) 520.500 + 901.532i 0.0296142 + 0.0512934i
\(677\) −12777.0 + 22130.4i −0.725347 + 1.25634i 0.233484 + 0.972361i \(0.424987\pi\)
−0.958831 + 0.283977i \(0.908346\pi\)
\(678\) −3618.00 −0.204939
\(679\) 0 0
\(680\) −15876.0 −0.895319
\(681\) −7074.00 + 12252.5i −0.398056 + 0.689454i
\(682\) −8640.00 14964.9i −0.485107 0.840229i
\(683\) −4638.00 8033.25i −0.259836 0.450050i 0.706362 0.707851i \(-0.250335\pi\)
−0.966198 + 0.257802i \(0.917002\pi\)
\(684\) −558.000 + 966.484i −0.0311925 + 0.0540270i
\(685\) −42444.0 −2.36745
\(686\) 0 0
\(687\) 5070.00 0.281561
\(688\) −9514.00 + 16478.7i −0.527206 + 0.913148i
\(689\) 8466.00 + 14663.5i 0.468112 + 0.810793i
\(690\) 0 0
\(691\) 13690.0 23711.8i 0.753679 1.30541i −0.192349 0.981326i \(-0.561611\pi\)
0.946028 0.324084i \(-0.105056\pi\)
\(692\) −870.000 −0.0477925
\(693\) 0 0
\(694\) −468.000 −0.0255980
\(695\) −468.000 + 810.600i −0.0255428 + 0.0442414i
\(696\) −3213.00 5565.08i −0.174983 0.303080i
\(697\) 6678.00 + 11566.6i 0.362909 + 0.628576i
\(698\) 18627.0 32262.9i 1.01009 1.74953i
\(699\) 414.000 0.0224019
\(700\) 0 0
\(701\) 25830.0 1.39171 0.695853 0.718184i \(-0.255027\pi\)
0.695853 + 0.718184i \(0.255027\pi\)
\(702\) 1377.00 2385.03i 0.0740335 0.128230i
\(703\) −24676.0 42740.1i −1.32386 2.29299i
\(704\) 7794.00 + 13499.6i 0.417255 + 0.722707i
\(705\) 6480.00 11223.7i 0.346172 0.599587i
\(706\) −23490.0 −1.25221
\(707\) 0 0
\(708\) 396.000 0.0210206
\(709\) 3113.00 5391.87i 0.164896 0.285608i −0.771722 0.635959i \(-0.780605\pi\)
0.936618 + 0.350351i \(0.113938\pi\)
\(710\) −19440.0 33671.1i −1.02756 1.77979i
\(711\) 4608.00 + 7981.29i 0.243057 + 0.420987i
\(712\) 3717.00 6438.03i 0.195647 0.338870i
\(713\) 0 0
\(714\) 0 0
\(715\) −22032.0 −1.15238
\(716\) 1158.00 2005.71i 0.0604420 0.104689i
\(717\) −2844.00 4925.95i −0.148133 0.256573i
\(718\) −13968.0 24193.3i −0.726018 1.25750i
\(719\) −7536.00 + 13052.7i −0.390884 + 0.677030i −0.992566 0.121705i \(-0.961164\pi\)
0.601683 + 0.798735i \(0.294497\pi\)
\(720\) −11502.0 −0.595353
\(721\) 0 0
\(722\) −25551.0 −1.31705
\(723\) −5397.00 + 9347.88i −0.277616 + 0.480846i
\(724\) −53.0000 91.7987i −0.00272062 0.00471225i
\(725\) −10149.0 17578.6i −0.519896 0.900486i
\(726\) −157.500 + 272.798i −0.00805148 + 0.0139456i
\(727\) 32920.0 1.67942 0.839708 0.543038i \(-0.182726\pi\)
0.839708 + 0.543038i \(0.182726\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 13554.0 23476.2i 0.687200 1.19027i
\(731\) −5628.00 9747.98i −0.284759 0.493218i
\(732\) 597.000 + 1034.03i 0.0301445 + 0.0522118i
\(733\) −3473.00 + 6015.41i −0.175004 + 0.303116i −0.940163 0.340726i \(-0.889327\pi\)
0.765158 + 0.643842i \(0.222661\pi\)
\(734\) −11280.0 −0.567238
\(735\) 0 0
\(736\) 0 0
\(737\) 1656.00 2868.28i 0.0827674 0.143357i
\(738\) 4293.00 + 7435.69i 0.214129 + 0.370883i
\(739\) 1178.00 + 2040.36i 0.0586379 + 0.101564i 0.893854 0.448358i \(-0.147991\pi\)
−0.835216 + 0.549922i \(0.814658\pi\)
\(740\) −3582.00 + 6204.21i −0.177942 + 0.308204i
\(741\) 12648.0 0.627039
\(742\) 0 0
\(743\) −23520.0 −1.16133 −0.580663 0.814144i \(-0.697207\pi\)
−0.580663 + 0.814144i \(0.697207\pi\)
\(744\) −5040.00 + 8729.54i −0.248354 + 0.430162i
\(745\) 15714.0 + 27217.4i 0.772774 + 1.33848i
\(746\) 8805.00 + 15250.7i 0.432137 + 0.748483i
\(747\) −918.000 + 1590.02i −0.0449637 + 0.0778794i
\(748\) 1512.00 0.0739094
\(749\) 0 0
\(750\) −11988.0 −0.583653
\(751\) −1504.00 + 2605.00i −0.0730782 + 0.126575i −0.900249 0.435376i \(-0.856616\pi\)
0.827171 + 0.561951i \(0.189949\pi\)
\(752\) −8520.00 14757.1i −0.413155 0.715605i
\(753\) −4590.00 7950.11i −0.222137 0.384752i
\(754\) 5202.00 9010.13i 0.251254 0.435185i
\(755\) −4176.00 −0.201298
\(756\) 0 0
\(757\) −20770.0 −0.997224 −0.498612 0.866825i \(-0.666157\pi\)
−0.498612 + 0.866825i \(0.666157\pi\)
\(758\) −2778.00 + 4811.64i −0.133115 + 0.230563i
\(759\) 0 0
\(760\) −23436.0 40592.3i −1.11857 1.93742i
\(761\) 5769.00 9992.20i 0.274804 0.475975i −0.695281 0.718738i \(-0.744720\pi\)
0.970086 + 0.242763i \(0.0780536\pi\)
\(762\) −11520.0 −0.547671
\(763\) 0 0
\(764\) −1128.00 −0.0534157
\(765\) 3402.00 5892.44i 0.160784 0.278486i
\(766\) −3240.00 5611.84i −0.152828 0.264705i
\(767\) −2244.00 3886.72i −0.105640 0.182974i
\(768\) −2269.50 + 3930.89i −0.106632 + 0.184692i
\(769\) −8498.00 −0.398499 −0.199249 0.979949i \(-0.563850\pi\)
−0.199249 + 0.979949i \(0.563850\pi\)
\(770\) 0 0
\(771\) 20466.0 0.955986
\(772\) −2017.00 + 3493.55i −0.0940329 + 0.162870i
\(773\) −16161.0 27991.7i −0.751967 1.30245i −0.946868 0.321623i \(-0.895772\pi\)
0.194901 0.980823i \(-0.437562\pi\)
\(774\) −3618.00 6266.56i −0.168019 0.291017i
\(775\) −15920.0 + 27574.2i −0.737888 + 1.27806i
\(776\) 6006.00 0.277839
\(777\) 0 0
\(778\) 20358.0 0.938136
\(779\) −19716.0 + 34149.1i −0.906802 + 1.57063i
\(780\) −918.000 1590.02i −0.0421406 0.0729897i
\(781\) −12960.0 22447.4i −0.593784 1.02846i
\(782\) 0 0
\(783\) 2754.00 0.125696
\(784\) 0 0
\(785\) −30492.0 −1.38638
\(786\) −7938.00 + 13749.0i −0.360228 + 0.623933i
\(787\) 13114.0 + 22714.1i 0.593982 + 1.02881i 0.993690 + 0.112164i \(0.0357782\pi\)
−0.399708 + 0.916643i \(0.630888\pi\)
\(788\) 657.000 + 1137.96i 0.0297013 + 0.0514442i
\(789\) −3888.00 + 6734.21i −0.175433 + 0.303858i
\(790\) 55296.0 2.49031
\(791\) 0 0
\(792\) −6804.00 −0.305265
\(793\) 6766.00 11719.1i 0.302986 0.524787i
\(794\) 9771.00 + 16923.9i 0.436725 + 0.756430i
\(795\) 13446.0 + 23289.2i 0.599850 +