Properties

Label 147.4.e.i.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.i.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 \(-0.535507\pi\)
0.916302 0.400489i \(-0.131160\pi\)
\(6\) 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 \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 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 0.676442 0.736496i \(-0.263521\pi\)
−0.976045 + 0.217568i \(0.930187\pi\)
\(18\) 13.5000 + 23.3827i 0.176777 + 0.306186i
\(19\) 62.0000 107.387i 0.748620 1.29665i −0.199865 0.979824i \(-0.564050\pi\)
0.948484 0.316824i \(-0.102616\pi\)
\(20\) −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 0.999132 0.0416484i \(-0.0132609\pi\)
−0.535635 + 0.844450i \(0.679928\pi\)
\(32\) −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 \(-0.707087\pi\)
−0.605649 + 0.795732i \(0.707087\pi\)
\(42\) 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 −0.989937 0.141506i \(-0.954806\pi\)
0.617516 + 0.786558i \(0.288139\pi\)
\(48\) 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 0.929610 0.368546i \(-0.120144\pi\)
−0.783975 + 0.620793i \(0.786811\pi\)
\(60\) −27.0000 46.7654i −0.0580948 0.100623i
\(61\) −199.000 + 344.678i −0.417694 + 0.723467i −0.995707 0.0925602i \(-0.970495\pi\)
0.578013 + 0.816028i \(0.303828\pi\)
\(62\) 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 0.994019 0.109212i \(-0.0348326\pi\)
−0.591589 + 0.806239i \(0.701499\pi\)
\(74\) 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 \(-0.543068\pi\)
−0.134891 + 0.990860i \(0.543068\pi\)
\(84\) 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 −0.951968 0.306198i \(-0.900943\pi\)
0.741159 + 0.671329i \(0.234276\pi\)
\(90\) 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 \(-0.547826\pi\)
−0.149685 + 0.988734i \(0.547826\pi\)
\(98\) 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 0.745859 0.666104i \(-0.232039\pi\)
−0.949792 + 0.312881i \(0.898706\pi\)
\(102\) −189.000 327.358i −0.183469 0.317777i
\(103\) −28.0000 + 48.4974i −0.0267857 + 0.0463941i −0.879107 0.476624i \(-0.841860\pi\)
0.852322 + 0.523018i \(0.175194\pi\)
\(104\) −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 \(0.366849\pi\)
−0.994462 + 0.105099i \(0.966484\pi\)
\(132\) 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 \(-0.505050\pi\)
−0.0158654 + 0.999874i \(0.505050\pi\)
\(140\) 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 0.566361 0.824157i \(-0.308351\pi\)
−0.996922 + 0.0784048i \(0.975017\pi\)
\(158\) −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 \(-0.412163\pi\)
0.272460 + 0.962167i \(0.412163\pi\)
\(168\) 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 −0.945638 0.325220i \(-0.894562\pi\)
0.754468 + 0.656337i \(0.227895\pi\)
\(174\) 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 \(-0.506929\pi\)
−0.0217650 + 0.999763i \(0.506929\pi\)
\(182\) 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 \(-0.804539\pi\)
−0.0903369 0.995911i \(-0.528794\pi\)
\(200\) −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 \(-0.591487\pi\)
−0.283475 + 0.958980i \(0.591487\pi\)
\(224\) 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 \(0.0754826\pi\)
−0.282561 + 0.959249i \(0.591184\pi\)
\(228\) −186.000 322.161i −0.0540270 0.0935775i
\(229\) 845.000 1463.58i 0.243839 0.422342i −0.717965 0.696079i \(-0.754926\pi\)
0.961805 + 0.273737i \(0.0882598\pi\)
\(230\) 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 0.999758 0.0219782i \(-0.00699644\pi\)
−0.518913 + 0.854827i \(0.673663\pi\)
\(242\) −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 \(-0.625713\pi\)
−0.384752 + 0.923020i \(0.625713\pi\)
\(252\) 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 \(-0.522864\pi\)
0.899676 0.436557i \(-0.143802\pi\)
\(258\) −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 \(-0.785704\pi\)
−0.149074 0.988826i \(-0.547629\pi\)
\(270\) 729.000 + 1262.67i 0.164317 + 0.284605i
\(271\) 2672.00 4628.04i 0.598939 1.03739i −0.394039 0.919094i \(-0.628923\pi\)
0.992978 0.118299i \(-0.0377441\pi\)
\(272\) −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 0.642494 0.766290i \(-0.277900\pi\)
−0.984874 + 0.173271i \(0.944566\pi\)
\(284\) 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 \(-0.329559\pi\)
0.510233 + 0.860036i \(0.329559\pi\)
\(294\) 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 \(-0.486622\pi\)
0.0420147 + 0.999117i \(0.486622\pi\)
\(308\) 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 0.541531 0.840681i \(-0.317845\pi\)
−0.998816 + 0.0486397i \(0.984511\pi\)
\(312\) −1071.00 1855.03i −0.194338 0.336603i
\(313\) −2701.00 + 4678.27i −0.487762 + 0.844829i −0.999901 0.0140739i \(-0.995520\pi\)
0.512139 + 0.858903i \(0.328853\pi\)
\(314\) −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 \(-0.901311\pi\)
−0.952321 + 0.305097i \(0.901311\pi\)
\(350\) 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 \(0.0343222\pi\)
−0.403897 + 0.914805i \(0.632344\pi\)
\(354\) 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 0.968189 0.250219i \(-0.0805027\pi\)
−0.700791 + 0.713367i \(0.747169\pi\)
\(368\) 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 −0.929032 0.369999i \(-0.879358\pi\)
0.784945 + 0.619566i \(0.212691\pi\)
\(384\) 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 −0.583333 0.812233i \(-0.698252\pi\)
0.995081 + 0.0990641i \(0.0315849\pi\)
\(398\) −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 0.981775 0.190048i \(-0.0608645\pi\)
−0.655474 + 0.755218i \(0.727531\pi\)
\(410\) 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 \(-0.223613\pi\)
0.763229 + 0.646128i \(0.223613\pi\)
\(420\) 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 \(-0.422905\pi\)
0.239841 + 0.970812i \(0.422905\pi\)
\(434\) 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 −0.509832 0.860274i \(-0.670293\pi\)
0.999935 + 0.0113909i \(0.00362592\pi\)
\(440\) 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 \(-0.587442\pi\)
−0.271264 + 0.962505i \(0.587442\pi\)
\(462\) 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 −0.956418 0.292002i \(-0.905679\pi\)
0.731090 + 0.682281i \(0.239012\pi\)
\(468\) −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 0.991715 0.128461i \(-0.0410036\pi\)
−0.607108 + 0.794620i \(0.707670\pi\)
\(480\) −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 \(-0.593787\pi\)
−0.290397 + 0.956906i \(0.593787\pi\)
\(504\) 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 −0.920351 0.391094i \(-0.872097\pi\)
0.798873 + 0.601500i \(0.205430\pi\)
\(510\) −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 \(0.0481820\pi\)
−0.363694 + 0.931518i \(0.618485\pi\)
\(522\) 1377.00 + 2385.03i 0.115459 + 0.199981i
\(523\) −8830.00 + 15294.0i −0.738258 + 1.27870i 0.215021 + 0.976609i \(0.431018\pi\)
−0.953279 + 0.302091i \(0.902315\pi\)
\(524\) 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 \(0.0649815\pi\)
−0.314048 + 0.949407i \(0.601685\pi\)
\(564\) 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 0.865989 0.500062i \(-0.166690\pi\)
−0.866061 + 0.499938i \(0.833356\pi\)
\(578\) −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 \(-0.122479\pi\)
0.926881 + 0.375354i \(0.122479\pi\)
\(588\) 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 −0.903064 0.429507i \(-0.858687\pi\)
0.823496 + 0.567323i \(0.192021\pi\)
\(594\) −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 \(-0.186472\pi\)
0.833260 + 0.552881i \(0.186472\pi\)
\(602\) 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 \(0.356927\pi\)
−0.997254 + 0.0740535i \(0.976406\pi\)
\(608\) −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 \(0.000709990\pi\)
−0.498067 + 0.867138i \(0.665957\pi\)
\(620\) −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 \(-0.622266\pi\)
−0.374735 + 0.927132i \(0.622266\pi\)
\(644\) 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 0.583129 0.812380i \(-0.301828\pi\)
−0.995106 + 0.0988143i \(0.968495\pi\)
\(648\) −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 \(-0.994918\pi\)
0.486111 0.873897i \(-0.338415\pi\)
\(662\) −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 \(-0.575013\pi\)
0.958831 0.283977i \(-0.0916541\pi\)
\(678\) 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 \(0.438389\pi\)
−0.946028 + 0.324084i \(0.894944\pi\)
\(692\) 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 −0.601683 0.798735i \(-0.705503\pi\)
0.992566 + 0.121705i \(0.0388361\pi\)
\(720\) 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 \(-0.817274\pi\)
−0.839708 + 0.543038i \(0.817274\pi\)
\(728\) 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 −0.765158 0.643842i \(-0.777339\pi\)
0.940163 + 0.340726i \(0.110673\pi\)
\(734\) 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 −0.970086 0.242763i \(-0.921946\pi\)
0.695281 + 0.718738i \(0.255280\pi\)
\(762\) 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 \(-0.436150\pi\)
0.199249 + 0.979949i \(0.436150\pi\)
\(770\) 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 \(0.104228\pi\)
−0.194901 + 0.980823i \(0.562438\pi\)
\(774\) −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 \(-0.964222\pi\)
0.399708 0.916643i \(-0.369112\pi\)
\(788\) 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 + 1.03897i
\(796\) −2548.00 +