Properties

Label 108.5.f.a.91.17
Level 108
Weight 5
Character 108.91
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 91.17
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.17

$q$-expansion

\(f(q)\) \(=\) \(q+(2.73046 - 2.92312i) q^{2} +(-1.08921 - 15.9629i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(-10.5700 + 6.10260i) q^{7} +(-49.6354 - 40.4021i) q^{8} +O(q^{10})\) \(q+(2.73046 - 2.92312i) q^{2} +(-1.08921 - 15.9629i) q^{4} +(-19.5394 + 33.8433i) q^{5} +(-10.5700 + 6.10260i) q^{7} +(-49.6354 - 40.4021i) q^{8} +(45.5763 + 149.524i) q^{10} +(-96.1446 + 55.5091i) q^{11} +(-104.491 + 180.984i) q^{13} +(-11.0224 + 47.5603i) q^{14} +(-253.627 + 34.7739i) q^{16} -93.3790 q^{17} -26.8894i q^{19} +(561.519 + 275.043i) q^{20} +(-100.259 + 432.607i) q^{22} +(757.577 + 437.387i) q^{23} +(-451.080 - 781.293i) q^{25} +(243.728 + 799.608i) q^{26} +(108.928 + 162.081i) q^{28} +(-650.809 - 1127.23i) q^{29} +(593.492 + 342.653i) q^{31} +(-590.870 + 836.330i) q^{32} +(-254.967 + 272.958i) q^{34} -476.966i q^{35} -1760.25 q^{37} +(-78.6008 - 73.4203i) q^{38} +(2337.19 - 890.392i) q^{40} +(39.0421 - 67.6229i) q^{41} +(-1405.46 + 811.442i) q^{43} +(990.807 + 1474.28i) q^{44} +(3347.06 - 1020.22i) q^{46} +(1999.54 - 1154.43i) q^{47} +(-1126.02 + 1950.32i) q^{49} +(-3515.46 - 814.729i) q^{50} +(3002.84 + 1470.85i) q^{52} +1313.48 q^{53} -4338.47i q^{55} +(771.205 + 124.146i) q^{56} +(-5072.04 - 1175.47i) q^{58} +(-4818.38 - 2781.89i) q^{59} +(-1090.13 - 1888.16i) q^{61} +(2622.12 - 799.247i) q^{62} +(831.345 + 4010.75i) q^{64} +(-4083.39 - 7072.65i) q^{65} +(-213.077 - 123.020i) q^{67} +(101.709 + 1490.60i) q^{68} +(-1394.23 - 1302.33i) q^{70} +4608.15i q^{71} +2564.79 q^{73} +(-4806.29 + 5145.42i) q^{74} +(-429.232 + 29.2882i) q^{76} +(677.500 - 1173.46i) q^{77} +(4486.29 - 2590.16i) q^{79} +(3778.87 - 9263.05i) q^{80} +(-91.0669 - 298.766i) q^{82} +(1622.37 - 936.677i) q^{83} +(1824.57 - 3160.25i) q^{85} +(-1465.61 + 6323.93i) q^{86} +(7014.86 + 1129.22i) q^{88} +1167.17 q^{89} -2550.67i q^{91} +(6156.80 - 12569.5i) q^{92} +(2085.11 - 8997.00i) q^{94} +(910.026 + 525.404i) q^{95} +(2869.58 + 4970.26i) q^{97} +(2626.47 + 8616.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.73046 2.92312i 0.682614 0.730779i
\(3\) 0 0
\(4\) −1.08921 15.9629i −0.0680757 0.997680i
\(5\) −19.5394 + 33.8433i −0.781578 + 1.35373i 0.149444 + 0.988770i \(0.452251\pi\)
−0.931022 + 0.364962i \(0.881082\pi\)
\(6\) 0 0
\(7\) −10.5700 + 6.10260i −0.215715 + 0.124543i −0.603964 0.797011i \(-0.706413\pi\)
0.388250 + 0.921554i \(0.373080\pi\)
\(8\) −49.6354 40.4021i −0.775553 0.631282i
\(9\) 0 0
\(10\) 45.5763 + 149.524i 0.455763 + 1.49524i
\(11\) −96.1446 + 55.5091i −0.794583 + 0.458753i −0.841574 0.540142i \(-0.818370\pi\)
0.0469902 + 0.998895i \(0.485037\pi\)
\(12\) 0 0
\(13\) −104.491 + 180.984i −0.618290 + 1.07091i 0.371507 + 0.928430i \(0.378841\pi\)
−0.989798 + 0.142480i \(0.954492\pi\)
\(14\) −11.0224 + 47.5603i −0.0562366 + 0.242654i
\(15\) 0 0
\(16\) −253.627 + 34.7739i −0.990731 + 0.135835i
\(17\) −93.3790 −0.323111 −0.161555 0.986864i \(-0.551651\pi\)
−0.161555 + 0.986864i \(0.551651\pi\)
\(18\) 0 0
\(19\) 26.8894i 0.0744859i −0.999306 0.0372429i \(-0.988142\pi\)
0.999306 0.0372429i \(-0.0118575\pi\)
\(20\) 561.519 + 275.043i 1.40380 + 0.687608i
\(21\) 0 0
\(22\) −100.259 + 432.607i −0.207147 + 0.893816i
\(23\) 757.577 + 437.387i 1.43209 + 0.826819i 0.997280 0.0737029i \(-0.0234816\pi\)
0.434812 + 0.900521i \(0.356815\pi\)
\(24\) 0 0
\(25\) −451.080 781.293i −0.721728 1.25007i
\(26\) 243.728 + 799.608i 0.360545 + 1.18285i
\(27\) 0 0
\(28\) 108.928 + 162.081i 0.138939 + 0.206736i
\(29\) −650.809 1127.23i −0.773851 1.34035i −0.935438 0.353491i \(-0.884995\pi\)
0.161587 0.986858i \(-0.448339\pi\)
\(30\) 0 0
\(31\) 593.492 + 342.653i 0.617577 + 0.356558i 0.775925 0.630825i \(-0.217283\pi\)
−0.158348 + 0.987383i \(0.550617\pi\)
\(32\) −590.870 + 836.330i −0.577022 + 0.816729i
\(33\) 0 0
\(34\) −254.967 + 272.958i −0.220560 + 0.236122i
\(35\) 476.966i 0.389360i
\(36\) 0 0
\(37\) −1760.25 −1.28579 −0.642897 0.765953i \(-0.722268\pi\)
−0.642897 + 0.765953i \(0.722268\pi\)
\(38\) −78.6008 73.4203i −0.0544327 0.0508451i
\(39\) 0 0
\(40\) 2337.19 890.392i 1.46074 0.556495i
\(41\) 39.0421 67.6229i 0.0232255 0.0402278i −0.854179 0.519979i \(-0.825940\pi\)
0.877405 + 0.479751i \(0.159273\pi\)
\(42\) 0 0
\(43\) −1405.46 + 811.442i −0.760118 + 0.438855i −0.829338 0.558747i \(-0.811282\pi\)
0.0692198 + 0.997601i \(0.477949\pi\)
\(44\) 990.807 + 1474.28i 0.511780 + 0.761510i
\(45\) 0 0
\(46\) 3347.06 1020.22i 1.58179 0.482144i
\(47\) 1999.54 1154.43i 0.905177 0.522604i 0.0263007 0.999654i \(-0.491627\pi\)
0.878876 + 0.477050i \(0.158294\pi\)
\(48\) 0 0
\(49\) −1126.02 + 1950.32i −0.468978 + 0.812294i
\(50\) −3515.46 814.729i −1.40619 0.325892i
\(51\) 0 0
\(52\) 3002.84 + 1470.85i 1.11052 + 0.543953i
\(53\) 1313.48 0.467598 0.233799 0.972285i \(-0.424884\pi\)
0.233799 + 0.972285i \(0.424884\pi\)
\(54\) 0 0
\(55\) 4338.47i 1.43420i
\(56\) 771.205 + 124.146i 0.245920 + 0.0395872i
\(57\) 0 0
\(58\) −5072.04 1175.47i −1.50774 0.349427i
\(59\) −4818.38 2781.89i −1.38419 0.799164i −0.391540 0.920161i \(-0.628058\pi\)
−0.992653 + 0.120997i \(0.961391\pi\)
\(60\) 0 0
\(61\) −1090.13 1888.16i −0.292967 0.507433i 0.681543 0.731778i \(-0.261309\pi\)
−0.974510 + 0.224345i \(0.927976\pi\)
\(62\) 2622.12 799.247i 0.682132 0.207921i
\(63\) 0 0
\(64\) 831.345 + 4010.75i 0.202965 + 0.979186i
\(65\) −4083.39 7072.65i −0.966484 1.67400i
\(66\) 0 0
\(67\) −213.077 123.020i −0.0474665 0.0274048i 0.476079 0.879403i \(-0.342058\pi\)
−0.523545 + 0.851998i \(0.675391\pi\)
\(68\) 101.709 + 1490.60i 0.0219960 + 0.322361i
\(69\) 0 0
\(70\) −1394.23 1302.33i −0.284536 0.265783i
\(71\) 4608.15i 0.914134i 0.889432 + 0.457067i \(0.151100\pi\)
−0.889432 + 0.457067i \(0.848900\pi\)
\(72\) 0 0
\(73\) 2564.79 0.481290 0.240645 0.970613i \(-0.422641\pi\)
0.240645 + 0.970613i \(0.422641\pi\)
\(74\) −4806.29 + 5145.42i −0.877701 + 0.939631i
\(75\) 0 0
\(76\) −429.232 + 29.2882i −0.0743131 + 0.00507067i
\(77\) 677.500 1173.46i 0.114269 0.197919i
\(78\) 0 0
\(79\) 4486.29 2590.16i 0.718842 0.415023i −0.0954846 0.995431i \(-0.530440\pi\)
0.814326 + 0.580408i \(0.197107\pi\)
\(80\) 3778.87 9263.05i 0.590449 1.44735i
\(81\) 0 0
\(82\) −91.0669 298.766i −0.0135436 0.0444328i
\(83\) 1622.37 936.677i 0.235502 0.135967i −0.377606 0.925966i \(-0.623253\pi\)
0.613108 + 0.789999i \(0.289919\pi\)
\(84\) 0 0
\(85\) 1824.57 3160.25i 0.252536 0.437405i
\(86\) −1465.61 + 6323.93i −0.198162 + 0.855047i
\(87\) 0 0
\(88\) 7014.86 + 1129.22i 0.905844 + 0.145819i
\(89\) 1167.17 0.147352 0.0736759 0.997282i \(-0.476527\pi\)
0.0736759 + 0.997282i \(0.476527\pi\)
\(90\) 0 0
\(91\) 2550.67i 0.308015i
\(92\) 6156.80 12569.5i 0.727410 1.48506i
\(93\) 0 0
\(94\) 2085.11 8997.00i 0.235979 1.01822i
\(95\) 910.026 + 525.404i 0.100834 + 0.0582165i
\(96\) 0 0
\(97\) 2869.58 + 4970.26i 0.304983 + 0.528245i 0.977257 0.212056i \(-0.0680160\pi\)
−0.672275 + 0.740302i \(0.734683\pi\)
\(98\) 2626.47 + 8616.73i 0.273476 + 0.897203i
\(99\) 0 0
\(100\) −11980.4 + 8051.53i −1.19804 + 0.805153i
\(101\) 7793.37 + 13498.5i 0.763981 + 1.32325i 0.940783 + 0.339008i \(0.110091\pi\)
−0.176802 + 0.984246i \(0.556575\pi\)
\(102\) 0 0
\(103\) 9636.52 + 5563.65i 0.908334 + 0.524427i 0.879895 0.475168i \(-0.157613\pi\)
0.0284395 + 0.999596i \(0.490946\pi\)
\(104\) 12498.6 4761.55i 1.15556 0.440232i
\(105\) 0 0
\(106\) 3586.41 3839.46i 0.319189 0.341711i
\(107\) 4464.91i 0.389983i 0.980805 + 0.194991i \(0.0624679\pi\)
−0.980805 + 0.194991i \(0.937532\pi\)
\(108\) 0 0
\(109\) −4736.05 −0.398624 −0.199312 0.979936i \(-0.563871\pi\)
−0.199312 + 0.979936i \(0.563871\pi\)
\(110\) −12681.8 11846.0i −1.04809 0.979008i
\(111\) 0 0
\(112\) 2468.63 1915.35i 0.196798 0.152690i
\(113\) −9173.06 + 15888.2i −0.718385 + 1.24428i 0.243254 + 0.969963i \(0.421785\pi\)
−0.961639 + 0.274317i \(0.911548\pi\)
\(114\) 0 0
\(115\) −29605.3 + 17092.6i −2.23858 + 1.29245i
\(116\) −17285.0 + 11616.6i −1.28456 + 0.863301i
\(117\) 0 0
\(118\) −21288.2 + 6488.84i −1.52888 + 0.466018i
\(119\) 987.017 569.855i 0.0696997 0.0402411i
\(120\) 0 0
\(121\) −1157.98 + 2005.68i −0.0790915 + 0.136990i
\(122\) −8495.85 1968.96i −0.570804 0.132287i
\(123\) 0 0
\(124\) 4823.29 9847.06i 0.313689 0.640417i
\(125\) 10831.1 0.693190
\(126\) 0 0
\(127\) 8169.42i 0.506505i 0.967400 + 0.253252i \(0.0815003\pi\)
−0.967400 + 0.253252i \(0.918500\pi\)
\(128\) 13993.8 + 8521.05i 0.854115 + 0.520084i
\(129\) 0 0
\(130\) −31823.7 7375.32i −1.88306 0.436410i
\(131\) 9131.01 + 5271.79i 0.532079 + 0.307196i 0.741863 0.670552i \(-0.233943\pi\)
−0.209784 + 0.977748i \(0.567276\pi\)
\(132\) 0 0
\(133\) 164.095 + 284.221i 0.00927669 + 0.0160677i
\(134\) −941.399 + 286.948i −0.0524281 + 0.0159806i
\(135\) 0 0
\(136\) 4634.90 + 3772.70i 0.250589 + 0.203974i
\(137\) 1612.85 + 2793.54i 0.0859318 + 0.148838i 0.905788 0.423731i \(-0.139280\pi\)
−0.819856 + 0.572570i \(0.805947\pi\)
\(138\) 0 0
\(139\) 16276.4 + 9397.17i 0.842419 + 0.486371i 0.858086 0.513506i \(-0.171654\pi\)
−0.0156666 + 0.999877i \(0.504987\pi\)
\(140\) −7613.75 + 519.516i −0.388457 + 0.0265059i
\(141\) 0 0
\(142\) 13470.2 + 12582.4i 0.668030 + 0.624001i
\(143\) 23200.8i 1.13457i
\(144\) 0 0
\(145\) 50865.8 2.41930
\(146\) 7003.05 7497.18i 0.328535 0.351716i
\(147\) 0 0
\(148\) 1917.28 + 28098.7i 0.0875313 + 1.28281i
\(149\) −3825.13 + 6625.31i −0.172295 + 0.298424i −0.939222 0.343311i \(-0.888452\pi\)
0.766927 + 0.641735i \(0.221785\pi\)
\(150\) 0 0
\(151\) −974.974 + 562.901i −0.0427601 + 0.0246876i −0.521228 0.853418i \(-0.674526\pi\)
0.478468 + 0.878105i \(0.341192\pi\)
\(152\) −1086.39 + 1334.67i −0.0470216 + 0.0577677i
\(153\) 0 0
\(154\) −1580.29 5184.51i −0.0666338 0.218608i
\(155\) −23193.0 + 13390.5i −0.965369 + 0.557356i
\(156\) 0 0
\(157\) 1755.81 3041.15i 0.0712326 0.123378i −0.828209 0.560419i \(-0.810640\pi\)
0.899442 + 0.437041i \(0.143973\pi\)
\(158\) 4678.28 20186.3i 0.187401 0.808615i
\(159\) 0 0
\(160\) −16758.9 36338.4i −0.654645 1.41947i
\(161\) −10676.8 −0.411898
\(162\) 0 0
\(163\) 41947.9i 1.57883i −0.613861 0.789414i \(-0.710385\pi\)
0.613861 0.789414i \(-0.289615\pi\)
\(164\) −1121.98 549.569i −0.0417156 0.0204331i
\(165\) 0 0
\(166\) 1691.80 7299.94i 0.0613951 0.264913i
\(167\) −5900.58 3406.70i −0.211574 0.122152i 0.390469 0.920616i \(-0.372313\pi\)
−0.602043 + 0.798464i \(0.705646\pi\)
\(168\) 0 0
\(169\) −7556.26 13087.8i −0.264566 0.458241i
\(170\) −4255.87 13962.4i −0.147262 0.483127i
\(171\) 0 0
\(172\) 14483.8 + 21551.3i 0.489582 + 0.728480i
\(173\) 7874.16 + 13638.4i 0.263095 + 0.455693i 0.967063 0.254539i \(-0.0819236\pi\)
−0.703968 + 0.710232i \(0.748590\pi\)
\(174\) 0 0
\(175\) 9535.85 + 5505.52i 0.311375 + 0.179772i
\(176\) 22454.6 17421.9i 0.724904 0.562434i
\(177\) 0 0
\(178\) 3186.92 3411.79i 0.100584 0.107682i
\(179\) 22497.6i 0.702151i 0.936347 + 0.351075i \(0.114184\pi\)
−0.936347 + 0.351075i \(0.885816\pi\)
\(180\) 0 0
\(181\) −21847.2 −0.666867 −0.333434 0.942774i \(-0.608207\pi\)
−0.333434 + 0.942774i \(0.608207\pi\)
\(182\) −7455.90 6964.49i −0.225091 0.210255i
\(183\) 0 0
\(184\) −19931.3 52317.5i −0.588707 1.54530i
\(185\) 34394.3 59572.7i 1.00495 1.74062i
\(186\) 0 0
\(187\) 8977.88 5183.38i 0.256738 0.148228i
\(188\) −20606.0 30660.9i −0.583012 0.867500i
\(189\) 0 0
\(190\) 4020.60 1225.52i 0.111374 0.0339479i
\(191\) −16182.1 + 9342.76i −0.443577 + 0.256099i −0.705114 0.709094i \(-0.749104\pi\)
0.261537 + 0.965194i \(0.415771\pi\)
\(192\) 0 0
\(193\) −23049.7 + 39923.2i −0.618800 + 1.07179i 0.370905 + 0.928671i \(0.379048\pi\)
−0.989705 + 0.143123i \(0.954286\pi\)
\(194\) 22363.9 + 5182.96i 0.594216 + 0.137713i
\(195\) 0 0
\(196\) 32359.2 + 15850.2i 0.842336 + 0.412593i
\(197\) −15934.7 −0.410592 −0.205296 0.978700i \(-0.565816\pi\)
−0.205296 + 0.978700i \(0.565816\pi\)
\(198\) 0 0
\(199\) 73733.8i 1.86192i −0.365124 0.930959i \(-0.618974\pi\)
0.365124 0.930959i \(-0.381026\pi\)
\(200\) −9176.34 + 57004.4i −0.229408 + 1.42511i
\(201\) 0 0
\(202\) 60737.2 + 14076.2i 1.48851 + 0.344971i
\(203\) 13758.1 + 7943.25i 0.333862 + 0.192755i
\(204\) 0 0
\(205\) 1525.72 + 2642.63i 0.0363051 + 0.0628823i
\(206\) 42575.3 12977.4i 1.00328 0.305810i
\(207\) 0 0
\(208\) 20208.3 49536.0i 0.467092 1.14497i
\(209\) 1492.61 + 2585.27i 0.0341706 + 0.0591852i
\(210\) 0 0
\(211\) 15431.2 + 8909.20i 0.346605 + 0.200112i 0.663189 0.748452i \(-0.269203\pi\)
−0.316584 + 0.948564i \(0.602536\pi\)
\(212\) −1430.66 20967.0i −0.0318321 0.466513i
\(213\) 0 0
\(214\) 13051.4 + 12191.2i 0.284991 + 0.266208i
\(215\) 63420.5i 1.37200i
\(216\) 0 0
\(217\) −8364.29 −0.177627
\(218\) −12931.6 + 13844.0i −0.272106 + 0.291306i
\(219\) 0 0
\(220\) −69254.5 + 4725.51i −1.43088 + 0.0976344i
\(221\) 9757.27 16900.1i 0.199776 0.346022i
\(222\) 0 0
\(223\) −58353.8 + 33690.6i −1.17344 + 0.677483i −0.954487 0.298253i \(-0.903596\pi\)
−0.218949 + 0.975736i \(0.570263\pi\)
\(224\) 1141.72 12445.9i 0.0227542 0.248044i
\(225\) 0 0
\(226\) 21396.4 + 70196.0i 0.418914 + 1.37434i
\(227\) 54381.5 31397.2i 1.05536 0.609310i 0.131212 0.991354i \(-0.458113\pi\)
0.924144 + 0.382044i \(0.124780\pi\)
\(228\) 0 0
\(229\) 20463.2 35443.2i 0.390213 0.675868i −0.602265 0.798297i \(-0.705735\pi\)
0.992477 + 0.122428i \(0.0390681\pi\)
\(230\) −30872.2 + 133210.i −0.583596 + 2.51815i
\(231\) 0 0
\(232\) −13239.4 + 82244.7i −0.245976 + 1.52803i
\(233\) −79254.5 −1.45986 −0.729932 0.683520i \(-0.760448\pi\)
−0.729932 + 0.683520i \(0.760448\pi\)
\(234\) 0 0
\(235\) 90227.9i 1.63382i
\(236\) −39158.8 + 79945.2i −0.703080 + 1.43539i
\(237\) 0 0
\(238\) 1029.26 4441.13i 0.0181706 0.0784042i
\(239\) −39084.7 22565.5i −0.684243 0.395048i 0.117209 0.993107i \(-0.462605\pi\)
−0.801452 + 0.598059i \(0.795939\pi\)
\(240\) 0 0
\(241\) −37826.8 65517.9i −0.651276 1.12804i −0.982814 0.184601i \(-0.940901\pi\)
0.331537 0.943442i \(-0.392433\pi\)
\(242\) 2701.02 + 8861.32i 0.0461208 + 0.151310i
\(243\) 0 0
\(244\) −28953.1 + 19458.2i −0.486312 + 0.326831i
\(245\) −44003.5 76216.3i −0.733086 1.26974i
\(246\) 0 0
\(247\) 4866.55 + 2809.70i 0.0797677 + 0.0460539i
\(248\) −15614.3 40986.0i −0.253875 0.666395i
\(249\) 0 0
\(250\) 29573.8 31660.6i 0.473182 0.506569i
\(251\) 78270.9i 1.24238i 0.783662 + 0.621188i \(0.213350\pi\)
−0.783662 + 0.621188i \(0.786650\pi\)
\(252\) 0 0
\(253\) −97115.9 −1.51722
\(254\) 23880.2 + 22306.2i 0.370143 + 0.345747i
\(255\) 0 0
\(256\) 63117.6 17639.2i 0.963097 0.269153i
\(257\) −11506.3 + 19929.5i −0.174209 + 0.301739i −0.939887 0.341485i \(-0.889070\pi\)
0.765678 + 0.643224i \(0.222403\pi\)
\(258\) 0 0
\(259\) 18605.9 10742.1i 0.277365 0.160136i
\(260\) −108452. + 72886.4i −1.60432 + 1.07820i
\(261\) 0 0
\(262\) 40341.9 12296.6i 0.587697 0.179136i
\(263\) 75237.8 43438.5i 1.08774 0.628006i 0.154765 0.987951i \(-0.450538\pi\)
0.932973 + 0.359945i \(0.117205\pi\)
\(264\) 0 0
\(265\) −25664.7 + 44452.6i −0.365464 + 0.633003i
\(266\) 1278.87 + 296.385i 0.0180743 + 0.00418883i
\(267\) 0 0
\(268\) −1731.67 + 3535.32i −0.0241099 + 0.0492220i
\(269\) 54083.3 0.747409 0.373705 0.927548i \(-0.378087\pi\)
0.373705 + 0.927548i \(0.378087\pi\)
\(270\) 0 0
\(271\) 47957.3i 0.653004i 0.945197 + 0.326502i \(0.105870\pi\)
−0.945197 + 0.326502i \(0.894130\pi\)
\(272\) 23683.5 3247.15i 0.320116 0.0438899i
\(273\) 0 0
\(274\) 12569.7 + 2913.09i 0.167426 + 0.0388019i
\(275\) 86737.8 + 50078.1i 1.14695 + 0.662190i
\(276\) 0 0
\(277\) 36861.8 + 63846.5i 0.480415 + 0.832103i 0.999748 0.0224689i \(-0.00715269\pi\)
−0.519332 + 0.854572i \(0.673819\pi\)
\(278\) 71911.0 21919.2i 0.930477 0.283618i
\(279\) 0 0
\(280\) −19270.4 + 23674.4i −0.245796 + 0.301969i
\(281\) 28062.0 + 48604.7i 0.355390 + 0.615554i 0.987185 0.159582i \(-0.0510147\pi\)
−0.631795 + 0.775136i \(0.717681\pi\)
\(282\) 0 0
\(283\) −132300. 76383.2i −1.65191 0.953730i −0.976287 0.216481i \(-0.930542\pi\)
−0.675621 0.737249i \(1.26388\pi\)
\(284\) 73559.3 5019.25i 0.912013 0.0622303i
\(285\) 0 0
\(286\) −67818.7 63348.8i −0.829120 0.774474i
\(287\) 953.034i 0.0115703i
\(288\) 0 0
\(289\) −74801.4 −0.895600
\(290\) 138887. 148687.i 1.65145 1.76797i
\(291\) 0 0
\(292\) −2793.60 40941.5i −0.0327641 0.480173i
\(293\) −19420.1 + 33636.7i −0.226213 + 0.391812i −0.956683 0.291133i \(-0.905968\pi\)
0.730470 + 0.682945i \(0.239301\pi\)
\(294\) 0 0
\(295\) 188297. 108713.i 2.16371 1.24922i
\(296\) 87370.8 + 71117.8i 0.997201 + 0.811699i
\(297\) 0 0
\(298\) 8922.21 + 29271.4i 0.100471 + 0.329618i
\(299\) −158320. + 91406.1i −1.77090 + 1.02243i
\(300\) 0 0
\(301\) 9903.82 17153.9i 0.109312 0.189335i
\(302\) −1016.70 + 4386.94i −0.0111475 + 0.0481003i
\(303\) 0 0
\(304\) 935.049 + 6819.88i 0.0101178 + 0.0737955i
\(305\) 85202.0 0.915905
\(306\) 0 0
\(307\) 457.528i 0.00485446i 0.999997 + 0.00242723i \(0.000772612\pi\)
−0.999997 + 0.00242723i \(0.999227\pi\)
\(308\) −19469.8 9536.70i −0.205239 0.100530i
\(309\) 0 0
\(310\) −24185.5 + 104358.i −0.251671 + 1.08593i
\(311\) 9285.82 + 5361.17i 0.0960062 + 0.0554292i 0.547234 0.836979i \(-0.315681\pi\)
−0.451228 + 0.892409i \(0.649014\pi\)
\(312\) 0 0
\(313\) −8976.10 15547.1i −0.0916218 0.158694i 0.816572 0.577244i \(-0.195872\pi\)
−0.908194 + 0.418550i \(0.862538\pi\)
\(314\) −4095.48 13436.2i −0.0415380 0.136275i
\(315\) 0 0
\(316\) −46232.9 68792.9i −0.462996 0.688921i
\(317\) −30685.9 53149.6i −0.305366 0.528909i 0.671977 0.740572i \(-0.265445\pi\)
−0.977343 + 0.211663i \(0.932112\pi\)
\(318\) 0 0
\(319\) 125143. + 72251.6i 1.22978 + 0.710013i
\(320\) −151981. 50232.3i −1.48419 0.490550i
\(321\) 0 0
\(322\) −29152.5 + 31209.5i −0.281167 + 0.301006i
\(323\) 2510.90i 0.0240672i
\(324\) 0 0
\(325\) 188535. 1.78495
\(326\) −122619. 114537.i −1.15377 1.07773i
\(327\) 0 0
\(328\) −4669.98 + 1779.11i −0.0434077 + 0.0165369i
\(329\) −14090.1 + 24404.7i −0.130173 + 0.225467i
\(330\) 0 0
\(331\) −160993. + 92949.3i −1.46944 + 0.848379i −0.999412 0.0342747i \(-0.989088\pi\)
−0.470023 + 0.882654i \(0.655755\pi\)
\(332\) −16719.2 24877.5i −0.151684 0.225700i
\(333\) 0 0
\(334\) −26069.4 + 7946.22i −0.233689 + 0.0712308i
\(335\) 8326.81 4807.49i 0.0741975 0.0428379i
\(336\) 0 0
\(337\) 73998.8 128170.i 0.651576 1.12856i −0.331165 0.943573i \(-0.607442\pi\)
0.982741 0.184989i \(-0.0592251\pi\)
\(338\) −58889.3 13647.9i −0.515469 0.119463i
\(339\) 0 0
\(340\) −52434.1 25683.3i −0.453582 0.222174i
\(341\) −76081.3 −0.654289
\(342\) 0 0
\(343\) 56791.2i 0.482717i
\(344\) 102544. + 16507.2i 0.866553 + 0.139494i
\(345\) 0 0
\(346\) 61366.8 + 14222.1i 0.512603 + 0.118799i
\(347\) −125556. 72490.0i −1.04275 0.602031i −0.122138 0.992513i \(-0.538975\pi\)
−0.920611 + 0.390482i \(0.872308\pi\)
\(348\) 0 0
\(349\) 89475.8 + 154977.i 0.734606 + 1.27238i 0.954896 + 0.296941i \(0.0959664\pi\)
−0.220290 + 0.975435i \(0.570700\pi\)
\(350\) 42130.5 12841.8i 0.343922 0.104831i
\(351\) 0 0
\(352\) 10385.0 113207.i 0.0838150 0.913670i
\(353\) 13197.7 + 22859.1i 0.105913 + 0.183446i 0.914111 0.405465i \(-0.132890\pi\)
−0.808198 + 0.588911i \(0.799557\pi\)
\(354\) 0 0
\(355\) −155955. 90040.7i −1.23749 0.714467i
\(356\) −1271.30 18631.5i −0.0100311 0.147010i
\(357\) 0 0
\(358\) 65763.1 + 61428.8i 0.513117 + 0.479298i
\(359\) 181364.i 1.40722i −0.710587 0.703609i \(-0.751571\pi\)
0.710587 0.703609i \(-0.248429\pi\)
\(360\) 0 0
\(361\) 129598. 0.994452
\(362\) −59652.9 + 63862.0i −0.455213 + 0.487333i
\(363\) 0 0
\(364\) −40716.0 + 2778.22i −0.307300 + 0.0209683i
\(365\) −50114.6 + 86801.1i −0.376165 + 0.651537i
\(366\) 0 0
\(367\) 181000. 104500.i 1.34383 0.775863i 0.356467 0.934308i \(-0.383981\pi\)
0.987368 + 0.158445i \(0.0506481\pi\)
\(368\) −207352. 84589.4i −1.53113 0.624626i
\(369\) 0 0
\(370\) −80225.8 263199.i −0.586017 1.92257i
\(371\) −13883.5 + 8015.67i −0.100868 + 0.0582360i
\(372\) 0 0
\(373\) 38298.0 66334.0i 0.275269 0.476781i −0.694934 0.719074i \(-0.744566\pi\)
0.970203 + 0.242293i \(0.0778996\pi\)
\(374\) 9362.09 40396.4i 0.0669314 0.288801i
\(375\) 0 0
\(376\) −145889. 23484.7i −1.03192 0.166115i
\(377\) 272015. 1.91386
\(378\) 0 0
\(379\) 232118.i 1.61596i 0.589211 + 0.807979i \(0.299439\pi\)
−0.589211 + 0.807979i \(0.700561\pi\)
\(380\) 7395.75 15098.9i 0.0512171 0.104563i
\(381\) 0 0
\(382\) −16874.7 + 72812.3i −0.115640 + 0.498974i
\(383\) −74119.1 42792.7i −0.505280 0.291724i 0.225611 0.974217i \(-0.427562\pi\)
−0.730891 + 0.682494i \(0.760895\pi\)
\(384\) 0 0
\(385\) 26476.0 + 45857.7i 0.178620 + 0.309379i
\(386\) 53764.1 + 176386.i 0.360842 + 1.18383i
\(387\) 0 0
\(388\) 76214.1 51220.4i 0.506258 0.340236i
\(389\) 60869.2 + 105429.i 0.402252 + 0.696721i 0.993997 0.109404i \(-0.0348942\pi\)
−0.591745 + 0.806125i \(0.701561\pi\)
\(390\) 0 0
\(391\) −70741.7 40842.8i −0.462724 0.267154i
\(392\) 134687. 51311.4i 0.876504 0.333919i
\(393\) 0 0
\(394\) −43508.9 + 46578.9i −0.280276 + 0.300052i
\(395\) 202441.i 1.29749i
\(396\) 0 0
\(397\) −71690.8 −0.454865 −0.227432 0.973794i \(-0.573033\pi\)
−0.227432 + 0.973794i \(0.573033\pi\)
\(398\) −215532. 201327.i −1.36065 1.27097i
\(399\) 0 0
\(400\) 141575. + 182471.i 0.884842 + 1.14045i
\(401\) −43140.3 + 74721.1i −0.268283 + 0.464681i −0.968419 0.249330i \(-0.919790\pi\)
0.700135 + 0.714010i \(0.253123\pi\)
\(402\) 0 0
\(403\) −124029. + 71608.3i −0.763684 + 0.440913i
\(404\) 206987. 139107.i 1.26818 0.852291i
\(405\) 0 0
\(406\) 60785.0 18527.9i 0.368761 0.112402i
\(407\) 169239. 97710.0i 1.02167 0.589862i
\(408\) 0 0
\(409\) −115231. + 199585.i −0.688844 + 1.19311i 0.283368 + 0.959011i \(0.408548\pi\)
−0.972212 + 0.234102i \(0.924785\pi\)
\(410\) 11890.6 + 2755.72i 0.0707355 + 0.0163933i
\(411\) 0 0
\(412\) 78315.6 159887.i 0.461375 0.941928i
\(413\) 67907.1 0.398121
\(414\) 0 0
\(415\) 73208.6i 0.425075i
\(416\) −89621.6 194327.i −0.517876 1.12291i
\(417\) 0 0
\(418\) 11632.5 + 2695.91i 0.0665767 + 0.0154295i
\(419\) −48172.3 27812.3i −0.274391 0.158420i 0.356491 0.934299i \(-0.383973\pi\)
−0.630881 + 0.775879i \(0.717307\pi\)
\(420\) 0 0
\(421\) −70485.7 122085.i −0.397683 0.688807i 0.595757 0.803165i \(-0.296852\pi\)
−0.993440 + 0.114358i \(0.963519\pi\)
\(422\) 68176.8 20781.0i 0.382835 0.116692i
\(423\) 0 0
\(424\) −65195.3 53067.4i −0.362647 0.295186i
\(425\) 42121.4 + 72956.4i 0.233198 + 0.403911i
\(426\) 0 0
\(427\) 23045.4 + 13305.2i 0.126394 + 0.0729738i
\(428\) 71272.8 4863.23i 0.389078 0.0265483i
\(429\) 0 0
\(430\) −185386. 173167.i −1.00263 0.936544i
\(431\) 191015.i 1.02828i 0.857705 + 0.514142i \(0.171889\pi\)
−0.857705 + 0.514142i \(0.828111\pi\)
\(432\) 0 0
\(433\) 48243.4 0.257313 0.128657 0.991689i \(-0.458933\pi\)
0.128657 + 0.991689i \(0.458933\pi\)
\(434\) −22838.3 + 24449.8i −0.121251 + 0.129806i
\(435\) 0 0
\(436\) 5158.56 + 75601.0i 0.0271366 + 0.397699i
\(437\) 11761.1 20370.8i 0.0615863 0.106671i
\(438\) 0 0
\(439\) 227081. 131105.i 1.17829 0.680285i 0.222670 0.974894i \(-0.428523\pi\)
0.955618 + 0.294609i \(0.0951893\pi\)
\(440\) −175283. + 215342.i −0.905388 + 1.11230i
\(441\) 0 0
\(442\) −22759.1 74666.6i −0.116496 0.382192i
\(443\) 78793.6 45491.5i 0.401498 0.231805i −0.285632 0.958339i \(-0.592204\pi\)
0.687130 + 0.726534i \(0.258870\pi\)
\(444\) 0 0
\(445\) −22805.9 + 39501.0i −0.115167 + 0.199475i
\(446\) −60851.0 + 262566.i −0.305913 + 1.31998i
\(447\) 0 0
\(448\) −33263.3 37320.3i −0.165733 0.185947i
\(449\) −283350. −1.40550 −0.702748 0.711438i \(-0.748044\pi\)
−0.702748 + 0.711438i \(0.748044\pi\)
\(450\) 0 0
\(451\) 8668.77i 0.0426191i
\(452\) 263613. + 129123.i 1.29030 + 0.632014i
\(453\) 0 0
\(454\) 56708.7 244692.i 0.275130 1.18716i
\(455\) 86323.1 + 49838.7i 0.416970 + 0.240737i
\(456\) 0 0
\(457\) −99226.7 171866.i −0.475112 0.822918i 0.524482 0.851422i \(-0.324259\pi\)
−0.999594 + 0.0285035i \(0.990926\pi\)
\(458\) −47730.9 156592.i −0.227546 0.746517i
\(459\) 0 0
\(460\) 305094. + 453968.i 1.44184 + 2.14541i
\(461\) −104347. 180735.i −0.490998 0.850433i 0.508949 0.860797i \(-0.330034\pi\)
−0.999946 + 0.0103639i \(0.996701\pi\)
\(462\) 0 0
\(463\) −22687.9 13098.9i −0.105836 0.0611044i 0.446148 0.894959i \(-0.352796\pi\)
−0.551984 + 0.833855i \(0.686129\pi\)
\(464\) 204261. + 263266.i 0.948746 + 1.22281i
\(465\) 0 0
\(466\) −216401. + 231670.i −0.996524 + 1.06684i
\(467\) 96607.8i 0.442974i 0.975163 + 0.221487i \(0.0710911\pi\)
−0.975163 + 0.221487i \(0.928909\pi\)
\(468\) 0 0
\(469\) 3002.97 0.0136523
\(470\) 263747. + 246363.i 1.19396 + 1.11527i
\(471\) 0 0
\(472\) 126768. + 332753.i 0.569017 + 1.49361i
\(473\) 90084.9 156032.i 0.402652 0.697413i
\(474\) 0 0
\(475\) −21008.5 + 12129.3i −0.0931125 + 0.0537585i
\(476\) −10171.6 15135.0i −0.0448926 0.0667986i
\(477\) 0 0
\(478\) −172681. + 52634.7i −0.755767 + 0.230365i
\(479\) 29664.3 17126.7i 0.129289 0.0746453i −0.433960 0.900932i \(-0.642884\pi\)
0.563250 + 0.826287i \(0.309551\pi\)
\(480\) 0 0
\(481\) 183931. 318577.i 0.794994 1.37697i
\(482\) −294801. 68321.7i −1.26892 0.294080i
\(483\) 0 0
\(484\) 33277.7 + 16300.1i 0.142057 + 0.0695823i
\(485\) −224280. −0.953470
\(486\) 0 0
\(487\) 69521.4i 0.293130i 0.989201 + 0.146565i \(0.0468218\pi\)
−0.989201 + 0.146565i \(0.953178\pi\)
\(488\) −22176.5 + 137763.i −0.0931224 + 0.578486i
\(489\) 0 0
\(490\) −342939. 79477.9i −1.42832 0.331020i
\(491\) 174305. + 100635.i 0.723016 + 0.417433i 0.815862 0.578247i \(-0.196263\pi\)
−0.0928458 + 0.995681i \(0.529596\pi\)
\(492\) 0 0
\(493\) 60771.9 + 105260.i 0.250040 + 0.433081i
\(494\) 21501.0 6553.71i 0.0881057 0.0268555i
\(495\) 0 0
\(496\) −162441. 66268.0i −0.660286 0.269365i
\(497\) −28121.7 48708.2i −0.113849 0.197192i
\(498\) 0 0
\(499\) 46850.8 + 27049.3i 0.188155 + 0.108631i 0.591119 0.806585i \(-0.298687\pi\)
−0.402964 + 0.915216i \(0.632020\pi\)
\(500\) −11797.3 172896.i −0.0471894 0.691582i
\(501\) 0 0
\(502\) 228795. + 213715.i 0.907902 + 0.848064i
\(503\) 239548.i 0.946795i −0.880849 0.473397i \(-0.843027\pi\)
0.880849 0.473397i \(-0.156973\pi\)
\(504\) 0 0
\(505\) −609113. −2.38844
\(506\) −265171. + 283881.i −1.03568 + 1.10875i
\(507\) 0 0
\(508\) 130407. 8898.22i 0.505330 0.0344807i
\(509\) 57738.0 100005.i 0.222857 0.386000i −0.732817 0.680425i \(-0.761795\pi\)
0.955674 + 0.294426i \(0.0951284\pi\)
\(510\) 0 0
\(511\) −27109.9 + 15651.9i −0.103821 + 0.0599412i
\(512\) 120778. 232663.i 0.460733 0.887539i
\(513\) 0 0
\(514\) 26838.8 + 88051.1i 0.101587 + 0.333279i
\(515\) −376584. + 217421.i −1.41987 + 0.819761i
\(516\) 0 0
\(517\) −128163. + 221985.i −0.479492 + 0.830505i
\(518\) 19402.1 83718.1i 0.0723086 0.312004i
\(519\) 0 0
\(520\) −83068.7 + 516031.i −0.307207 + 1.90840i
\(521\) −217267. −0.800420 −0.400210 0.916424i \(-0.631063\pi\)
−0.400210 + 0.916424i \(0.631063\pi\)
\(522\) 0 0
\(523\) 39683.4i 0.145079i −0.997366 0.0725397i \(-0.976890\pi\)
0.997366 0.0725397i \(-0.0231104\pi\)
\(524\) 74207.4 151499.i 0.270262 0.551757i
\(525\) 0 0
\(526\) 78457.6 338536.i 0.283572 1.22358i
\(527\) −55419.6 31996.5i −0.199546 0.115208i
\(528\) 0 0
\(529\) 242694. + 420359.i 0.867258 + 1.50213i
\(530\) 59863.7 + 196397.i 0.213114 + 0.699170i
\(531\) 0 0
\(532\) 4358.26 2929.01i 0.0153989 0.0103490i
\(533\) 8159.11 + 14132.0i 0.0287202 + 0.0497449i
\(534\) 0 0
\(535\) −151107. 87241.9i −0.527932 0.304802i
\(536\) 5605.90 + 14714.9i 0.0195126 + 0.0512186i
\(537\) 0 0
\(538\) 147672. 158092.i 0.510192 0.546191i
\(539\) 250017.i 0.860580i
\(540\) 0 0
\(541\) −194992. −0.666228 −0.333114 0.942887i \(-0.608099\pi\)
−0.333114 + 0.942887i \(0.608099\pi\)
\(542\) 140185. + 130945.i 0.477201 + 0.445750i
\(543\) 0 0
\(544\) 55174.8 78095.7i 0.186442 0.263894i
\(545\) 92539.8 160284.i 0.311556 0.539630i
\(546\) 0 0
\(547\) 81637.9 47133.6i 0.272846 0.157527i −0.357335 0.933976i \(-0.616314\pi\)
0.630180 + 0.776449i \(0.282981\pi\)
\(548\) 42836.3 28788.5i 0.142643 0.0958647i
\(549\) 0 0
\(550\) 383218. 116809.i 1.26684 0.386144i
\(551\) −30310.6 + 17499.9i −0.0998371 + 0.0576410i
\(552\) 0 0
\(553\) −31613.4 + 54756.1i −0.103376 + 0.179053i
\(554\) 287280. + 66578.8i 0.936022 + 0.216928i
\(555\) 0 0
\(556\) 132278. 270053.i 0.427894 0.873575i
\(557\) 563587. 1.81656 0.908282 0.418358i \(-0.137394\pi\)
0.908282 + 0.418358i \(0.137394\pi\)
\(558\) 0 0
\(559\) 339154.i 1.08536i
\(560\) 16586.0 + 120972.i 0.0528889 + 0.385751i
\(561\) 0 0
\(562\) 218699. + 50684.8i 0.692428 + 0.160474i
\(563\) 543509. + 313795.i 1.71471 + 0.989986i 0.927935 + 0.372741i \(0.121582\pi\)
0.786771 + 0.617245i \(0.211751\pi\)
\(564\) 0 0
\(565\) −358473. 620894.i −1.12295 1.94500i
\(566\) −584516. + 178166.i −1.82458 + 0.556150i
\(567\) 0 0
\(568\) 186179. 228727.i 0.577077 0.708959i
\(569\) −38859.9 67307.3i −0.120026 0.207892i 0.799751 0.600331i \(-0.204965\pi\)
−0.919778 + 0.392439i \(0.871631\pi\)
\(570\) 0 0
\(571\) −276094. 159403.i −0.846809 0.488905i 0.0127640 0.999919i \(-0.495937\pi\)
−0.859573 + 0.511013i \(0.829270\pi\)
\(572\) −370352. + 25270.6i −1.13194 + 0.0772366i
\(573\) 0 0
\(574\) 2785.83 + 2602.22i 0.00845533 + 0.00789805i
\(575\) 789186.i 2.38695i
\(576\) 0 0
\(577\) 40053.7 0.120307 0.0601534 0.998189i \(-0.480841\pi\)
0.0601534 + 0.998189i \(0.480841\pi\)
\(578\) −204242. + 218653.i −0.611349 + 0.654485i
\(579\) 0 0
\(580\) −55403.5 811964.i −0.164695 2.41369i
\(581\) −11432.3 + 19801.4i −0.0338675 + 0.0586602i
\(582\) 0 0
\(583\) −126284. + 72910.3i −0.371546 + 0.214512i
\(584\) −127304. 103623.i −0.373266 0.303830i
\(585\) 0 0
\(586\) 45298.0 + 148611.i 0.131912 + 0.432768i
\(587\) 11894.5 6867.28i 0.0345199 0.0199301i −0.482641 0.875818i \(-0.660322\pi\)
0.517161 + 0.855888i \(0.326989\pi\)
\(588\) 0 0
\(589\) 9213.72 15958.6i 0.0265586 0.0460008i
\(590\) 196355. 847250.i 0.564076 2.43393i
\(591\) 0 0
\(592\) 446448. 61210.8i 1.27388 0.174656i
\(593\) −537582. −1.52875 −0.764373 0.644775i \(-0.776951\pi\)
−0.764373 + 0.644775i \(0.776951\pi\)
\(594\) 0 0
\(595\) 44538.6i 0.125806i
\(596\) 109925. + 53843.7i 0.309461 + 0.151580i
\(597\) 0 0
\(598\) −165095. + 712368.i −0.461671 + 1.99206i
\(599\) −394401. 227708.i −1.09922 0.634635i −0.163204 0.986592i \(-0.552183\pi\)
−0.936016 + 0.351958i \(0.885516\pi\)
\(600\) 0 0
\(601\) 118996. + 206108.i 0.329446 + 0.570618i 0.982402 0.186778i \(-0.0598046\pi\)
−0.652956 + 0.757396i \(0.726471\pi\)
\(602\) −23100.9 75788.0i −0.0637436 0.209126i
\(603\) 0 0
\(604\) 10047.5 + 14950.3i 0.0275412 + 0.0409803i
\(605\) −45252.5 78379.7i −0.123632 0.214137i
\(606\) 0 0
\(607\) 516142. + 297995.i 1.40085 + 0.808781i 0.994480 0.104927i \(-0.0334608\pi\)
0.406371 + 0.913708i \(0.366794\pi\)
\(608\) 22488.4 + 15888.1i 0.0608347 + 0.0429799i
\(609\) 0 0
\(610\) 232640. 249055.i 0.625209 0.669324i
\(611\) 482511.i 1.29248i
\(612\) 0 0
\(613\) 547275. 1.45641 0.728206 0.685358i \(-0.240354\pi\)
0.728206 + 0.685358i \(0.240354\pi\)
\(614\) 1337.41 + 1249.26i 0.00354754 + 0.00331372i
\(615\) 0 0
\(616\) −81038.4 + 30873.0i −0.213565 + 0.0813611i
\(617\) 259077. 448735.i 0.680549 1.17874i −0.294265 0.955724i \(-0.595075\pi\)
0.974814 0.223021i \(-0.0715919\pi\)
\(618\) 0 0
\(619\) 176869. 102115.i 0.461605 0.266508i −0.251114 0.967958i \(-0.580797\pi\)
0.712719 + 0.701450i \(0.247463\pi\)
\(620\) 239013. + 355642.i 0.621781 + 0.925187i
\(621\) 0 0
\(622\) 41025.8 12505.1i 0.106042 0.0323226i
\(623\) −12337.1 + 7122.80i −0.0317860 + 0.0183516i
\(624\) 0 0
\(625\) 70291.3 121748.i 0.179946 0.311675i
\(626\) −69954.7 16212.4i −0.178512 0.0413712i
\(627\) 0 0
\(628\) −50458.0 24715.4i −0.127941 0.0626683i
\(629\) 164370. 0.415454
\(630\) 0 0
\(631\) 177036.i 0.444633i 0.974975 + 0.222317i \(0.0713618\pi\)
−0.974975 + 0.222317i \(0.928638\pi\)
\(632\) −327327. 52691.8i −0.819497 0.131919i
\(633\) 0 0
\(634\) −239149. 55424.1i −0.594963 0.137886i
\(635\) −276480. 159626.i −0.685672 0.395873i
\(636\) 0 0
\(637\) −235317. 407582.i −0.579929 1.00447i
\(638\) 552899. 168529.i 1.35833 0.414031i
\(639\) 0 0
\(640\) −561812. + 307101.i −1.37161 + 0.749758i
\(641\) 109444. + 189562.i 0.266364 + 0.461356i 0.967920 0.251258i \(-0.0808444\pi\)
−0.701556 + 0.712614i \(0.747511\pi\)
\(642\) 0 0
\(643\) 298938. + 172592.i 0.723035 + 0.417445i 0.815869 0.578237i \(-0.196259\pi\)
−0.0928336 + 0.995682i \(0.529592\pi\)
\(644\) 11629.3 + 170432.i 0.0280402 + 0.410942i
\(645\) 0 0
\(646\) 7339.66 + 6855.91i 0.0175878 + 0.0164286i
\(647\) 398251.i 0.951366i 0.879617 + 0.475683i \(0.157799\pi\)
−0.879617 + 0.475683i \(0.842201\pi\)
\(648\) 0 0
\(649\) 617681. 1.46648
\(650\) 514787. 551110.i 1.21843 1.30440i
\(651\) 0 0
\(652\) −669609. + 45690.1i −1.57517 + 0.107480i
\(653\) −171144. + 296430.i −0.401361 + 0.695178i −0.993890 0.110371i \(-0.964796\pi\)
0.592529 + 0.805549i \(0.298129\pi\)
\(654\) 0 0
\(655\) −356830. + 206016.i −0.831722 + 0.480195i
\(656\) −7550.63 + 18508.7i −0.0175459 + 0.0430098i
\(657\) 0 0
\(658\) 32865.5 + 107823.i 0.0759082 + 0.249035i
\(659\) 452868. 261464.i 1.04280 0.602061i 0.122175 0.992509i \(-0.461013\pi\)
0.920625 + 0.390447i \(0.127680\pi\)
\(660\) 0 0
\(661\) −154294. + 267245.i −0.353140 + 0.611656i −0.986798 0.161957i \(-0.948219\pi\)
0.633658 + 0.773613i \(0.281553\pi\)
\(662\) −167883. + 724395.i −0.383080 + 1.65295i
\(663\) 0 0
\(664\) −118371. 19054.9i −0.268478 0.0432185i
\(665\) −12825.3 −0.0290018
\(666\) 0 0
\(667\) 1.13862e6i 2.55934i
\(668\) −47953.8 + 97900.8i −0.107466 + 0.219398i
\(669\) 0 0
\(670\) 8683.16 37466.9i 0.0193432 0.0834637i
\(671\) 209620. + 121024.i 0.465573 + 0.268798i
\(672\) 0 0
\(673\) 124260. + 215225.i 0.274348 + 0.475184i 0.969970 0.243223i \(-0.0782047\pi\)
−0.695623 + 0.718407i \(0.744871\pi\)
\(674\) −172604. 566269.i −0.379955 1.24653i
\(675\) 0 0
\(676\) −200689. + 134875.i −0.439168 + 0.295147i
\(677\) 134761. + 233413.i 0.294027 + 0.509270i 0.974758 0.223264i \(-0.0716711\pi\)
−0.680731 + 0.732533i \(0.738338\pi\)
\(678\) 0 0
\(679\) −60663.0 35023.8i −0.131578 0.0759668i
\(680\) −218244. + 83143.9i −0.471981 + 0.179809i
\(681\) 0 0
\(682\) −207737. + 222395.i −0.446627 + 0.478140i
\(683\) 124482.i 0.266848i 0.991059 + 0.133424i \(0.0425972\pi\)
−0.991059 + 0.133424i \(0.957403\pi\)
\(684\) 0 0
\(685\) −126057. −0.268649
\(686\) −166007. 155066.i −0.352760 0.329510i
\(687\) 0 0
\(688\) 328246. 254677.i 0.693461 0.538038i
\(689\) −137247. + 237719.i −0.289111 + 0.500756i
\(690\) 0 0
\(691\) −771402. + 445369.i −1.61557 + 0.932747i −0.627518 + 0.778602i \(0.715929\pi\)
−0.988048 + 0.154145i \(0.950738\pi\)
\(692\) 209132. 140549.i 0.436726 0.293506i
\(693\) 0 0
\(694\) −554723. + 169085.i −1.15175 + 0.351064i
\(695\) −636063. + 367231.i −1.31683 + 0.760274i
\(696\) 0 0
\(697\) −3645.71 + 6314.56i −0.00750442 + 0.0129980i
\(698\) 697324. + 161609.i 1.43128 + 0.331707i
\(699\) 0 0
\(700\) 77497.5 158216.i 0.158158 0.322890i
\(701\) 170934. 0.347851 0.173925 0.984759i \(-0.444355\pi\)
0.173925 + 0.984759i \(0.444355\pi\)
\(702\) 0 0
\(703\) 47332.1i 0.0957734i
\(704\) −302562. 339464.i −0.610477 0.684934i
\(705\) 0 0
\(706\) 102855. + 23837.3i 0.206356 + 0.0478242i
\(707\) −164752. 95119.7i −0.329604 0.190297i
\(708\) 0 0
\(709\) 350963. + 607886.i 0.698183 + 1.20929i 0.969096 + 0.246684i \(0.0793410\pi\)
−0.270913 + 0.962604i \(0.587326\pi\)
\(710\) −689028. + 210022.i −1.36685 + 0.416628i
\(711\) 0 0
\(712\) −57933.2 47156.3i −0.114279 0.0930206i
\(713\) 299744. + 519171.i 0.589618 + 1.02125i
\(714\) 0 0
\(715\) 785193. + 453331.i 1.53590 + 0.886755i
\(716\) 359127. 24504.6i 0.700522 0.0477994i
\(717\) 0 0
\(718\) −530147. 495206.i −1.02837 0.960587i
\(719\) 768366.i 1.48631i 0.669117 + 0.743157i \(0.266672\pi\)
−0.669117 + 0.743157i \(0.733328\pi\)
\(720\) 0 0
\(721\) −135811. −0.261255
\(722\) 353862. 378830.i 0.678827 0.726724i
\(723\) 0 0
\(724\) 23796.2 + 348745.i 0.0453974 + 0.665320i
\(725\) −587133. + 1.01695e6i −1.11702 + 1.93473i
\(726\) 0 0
\(727\) −221493. + 127879.i −0.419074 + 0.241952i −0.694681 0.719318i \(-0.744454\pi\)
0.275607 + 0.961270i \(0.411121\pi\)
\(728\) −103052. + 126604.i −0.194444 + 0.238882i
\(729\) 0 0
\(730\) 116894. + 383497.i 0.219354 + 0.719642i
\(731\) 131240. 75771.6i 0.245602 0.141799i
\(732\) 0 0
\(733\) −184829. + 320133.i −0.344003 + 0.595831i −0.985172 0.171569i \(-0.945116\pi\)
0.641169 + 0.767400i \(0.278450\pi\)
\(734\) 188746. 814416.i 0.350336 1.51166i
\(735\) 0 0
\(736\) −813429. + 375145.i −1.50163 + 0.692539i
\(737\) 27314.9 0.0502881
\(738\) 0 0
\(739\) 1.03557e6i 1.89623i 0.317932 + 0.948114i \(0.397012\pi\)
−0.317932 + 0.948114i \(0.602988\pi\)
\(740\) −988415. 484146.i −1.80500 0.884123i
\(741\) 0 0
\(742\) −14477.7 + 62469.6i −0.0262961 + 0.113465i
\(743\) −486002. 280593.i −0.880360 0.508276i −0.00958322 0.999954i \(-0.503050\pi\)
−0.870777 + 0.491678i \(0.836384\pi\)
\(744\) 0 0
\(745\) −149482. 258910.i −0.269324 0.466483i
\(746\) −89331.1 293072.i −0.160518 0.526618i
\(747\) 0 0
\(748\) −92520.5 137667.i −0.165362 0.246052i
\(749\) −27247.6 47194.2i −0.0485696 0.0841250i
\(750\) 0 0
\(751\) −164898. 95204.1i −0.292372 0.168801i 0.346639 0.937999i \(-0.387323\pi\)
−0.639011 + 0.769197i \(0.720656\pi\)
\(752\) −466993. + 362327.i −0.825799 + 0.640715i
\(753\) 0 0
\(754\) 742725. 795131.i 1.30643 1.39861i
\(755\) 43995.1i 0.0771810i
\(756\) 0 0
\(757\) 523077. 0.912797 0.456398 0.889776i \(-0.349139\pi\)
0.456398 + 0.889776i \(0.349139\pi\)
\(758\) 678508. + 633788.i 1.18091 + 1.10308i
\(759\) 0 0
\(760\) −23942.1 62845.6i −0.0414510 0.108805i
\(761\) −80448.7 + 139341.i −0.138915 + 0.240608i −0.927086 0.374848i \(-0.877695\pi\)
0.788171 + 0.615456i \(0.211028\pi\)
\(762\) 0 0
\(763\) 50060.1 28902.2i 0.0859890 0.0496458i
\(764\) 166763. + 248137.i 0.285702 + 0.425114i
\(765\) 0 0
\(766\) −327467. + 99815.1i −0.558097 + 0.170113i
\(767\) 1.00695e6 581365.i 1.71167 0.988231i
\(768\) 0 0
\(769\) 297804. 515812.i 0.503591 0.872246i −0.496400 0.868094i \(-0.665345\pi\)
0.999991 0.00415186i \(-0.00132158\pi\)
\(770\) 206339. + 47820.2i 0.348016 + 0.0806547i
\(771\) 0 0
\(772\) 662396. + 324455.i 1.11143 + 0.544402i
\(773\) 583394. 0.976345 0.488172 0.872747i \(-0.337664\pi\)
0.488172 + 0.872747i \(0.337664\pi\)
\(774\) 0 0
\(775\) 618255.i 1.02935i
\(776\) 58376.0 362638.i 0.0969418 0.602212i
\(777\) 0 0
\(778\) 474381. + 109940.i 0.78373