Properties

Label 108.5.f.a.19.17
Level 108
Weight 5
Character 108.19
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 19.17
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.17

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 −0.931022 0.364962i \(-0.881082\pi\)
0.149444 0.988770i \(-0.452251\pi\)
\(6\) 0 0
\(7\) −10.5700 6.10260i −0.215715 0.124543i 0.388250 0.921554i \(-0.373080\pi\)
−0.603964 + 0.797011i \(0.706413\pi\)
\(8\) −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 0.0469902 0.998895i \(-0.485037\pi\)
−0.841574 + 0.540142i \(0.818370\pi\)
\(12\) 0 0
\(13\) −104.491 180.984i −0.618290 1.07091i −0.989798 0.142480i \(-0.954492\pi\)
0.371507 0.928430i \(-0.378841\pi\)
\(14\) −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 \(0.0118575\pi\)
−0.999306 + 0.0372429i \(0.988142\pi\)
\(20\) 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 0.434812 0.900521i \(-0.356815\pi\)
0.997280 + 0.0737029i \(0.0234816\pi\)
\(24\) 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 0.161587 + 0.986858i \(0.448339\pi\)
−0.935438 + 0.353491i \(0.884995\pi\)
\(30\) 0 0
\(31\) 593.492 342.653i 0.617577 0.356558i −0.158348 0.987383i \(-0.550617\pi\)
0.775925 + 0.630825i \(0.217283\pi\)
\(32\) −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 0.877405 0.479751i \(-0.159273\pi\)
−0.854179 + 0.519979i \(0.825940\pi\)
\(42\) 0 0
\(43\) −1405.46 811.442i −0.760118 0.438855i 0.0692198 0.997601i \(-0.477949\pi\)
−0.829338 + 0.558747i \(0.811282\pi\)
\(44\) 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 0.878876 0.477050i \(-0.158294\pi\)
0.0263007 + 0.999654i \(0.491627\pi\)
\(48\) 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 −0.992653 0.120997i \(-0.961391\pi\)
−0.391540 + 0.920161i \(0.628058\pi\)
\(60\) 0 0
\(61\) −1090.13 + 1888.16i −0.292967 + 0.507433i −0.974510 0.224345i \(-0.927976\pi\)
0.681543 + 0.731778i \(0.261309\pi\)
\(62\) 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 −0.523545 0.851998i \(-0.675391\pi\)
0.476079 + 0.879403i \(0.342058\pi\)
\(68\) 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 \(-0.848900\pi\)
0.889432 0.457067i \(-0.151100\pi\)
\(72\) 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 0.814326 0.580408i \(-0.197107\pi\)
−0.0954846 + 0.995431i \(0.530440\pi\)
\(80\) 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 0.613108 0.789999i \(-0.289919\pi\)
−0.377606 + 0.925966i \(0.623253\pi\)
\(84\) 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 −0.672275 0.740302i \(-0.734683\pi\)
0.977257 + 0.212056i \(0.0680160\pi\)
\(98\) 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 −0.176802 0.984246i \(-0.556575\pi\)
0.940783 0.339008i \(-0.110091\pi\)
\(102\) 0 0
\(103\) 9636.52 5563.65i 0.908334 0.524427i 0.0284395 0.999596i \(-0.490946\pi\)
0.879895 + 0.475168i \(0.157613\pi\)
\(104\) 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 \(-0.937532\pi\)
0.980805 0.194991i \(-0.0624679\pi\)
\(108\) 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 −0.961639 0.274317i \(-0.911548\pi\)
0.243254 0.969963i \(-0.421785\pi\)
\(114\) 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 \(-0.918500\pi\)
0.967400 0.253252i \(-0.0815003\pi\)
\(128\) 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 −0.209784 0.977748i \(-0.567276\pi\)
0.741863 + 0.670552i \(0.233943\pi\)
\(132\) 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 −0.819856 0.572570i \(-0.805947\pi\)
0.905788 + 0.423731i \(0.139280\pi\)
\(138\) 0 0
\(139\) 16276.4 9397.17i 0.842419 0.486371i −0.0156666 0.999877i \(-0.504987\pi\)
0.858086 + 0.513506i \(0.171654\pi\)
\(140\) −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 0.766927 0.641735i \(-0.221785\pi\)
−0.939222 + 0.343311i \(0.888452\pi\)
\(150\) 0 0
\(151\) −974.974 562.901i −0.0427601 0.0246876i 0.478468 0.878105i \(-0.341192\pi\)
−0.521228 + 0.853418i \(0.674526\pi\)
\(152\) −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 0.899442 0.437041i \(-0.143973\pi\)
−0.828209 + 0.560419i \(0.810640\pi\)
\(158\) 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 \(0.289615\pi\)
−0.613861 + 0.789414i \(0.710385\pi\)
\(164\) −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 −0.602043 0.798464i \(-0.705646\pi\)
0.390469 + 0.920616i \(0.372313\pi\)
\(168\) 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 −0.703968 0.710232i \(-0.748590\pi\)
0.967063 + 0.254539i \(0.0819236\pi\)
\(174\) 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 \(-0.885816\pi\)
0.936347 0.351075i \(-0.114184\pi\)
\(180\) 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 0.261537 0.965194i \(-0.415771\pi\)
−0.705114 + 0.709094i \(0.749104\pi\)
\(192\) 0 0
\(193\) −23049.7 39923.2i −0.618800 1.07179i −0.989705 0.143123i \(-0.954286\pi\)
0.370905 0.928671i \(-0.379048\pi\)
\(194\) 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 \(0.381026\pi\)
−0.365124 + 0.930959i \(0.618974\pi\)
\(200\) −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 −0.316584 0.948564i \(-0.602536\pi\)
0.663189 + 0.748452i \(0.269203\pi\)
\(212\) −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 −0.218949 0.975736i \(-0.570263\pi\)
−0.954487 + 0.298253i \(0.903596\pi\)
\(224\) 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 0.924144 0.382044i \(-0.124780\pi\)
0.131212 + 0.991354i \(0.458113\pi\)
\(228\) 0 0
\(229\) 20463.2 + 35443.2i 0.390213 + 0.675868i 0.992477 0.122428i \(-0.0390681\pi\)
−0.602265 + 0.798297i \(0.705735\pi\)
\(230\) −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 −0.801452 0.598059i \(-0.795939\pi\)
0.117209 + 0.993107i \(0.462605\pi\)
\(240\) 0 0
\(241\) −37826.8 + 65517.9i −0.651276 + 1.12804i 0.331537 + 0.943442i \(0.392433\pi\)
−0.982814 + 0.184601i \(0.940901\pi\)
\(242\) 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 \(-0.786650\pi\)
0.783662 0.621188i \(-0.213350\pi\)
\(252\) 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 0.765678 0.643224i \(-0.222403\pi\)
−0.939887 + 0.341485i \(0.889070\pi\)
\(258\) 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 0.932973 0.359945i \(-0.117205\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(264\) 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 \(-0.894130\pi\)
0.945197 0.326502i \(-0.105870\pi\)
\(272\) 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 −0.519332 0.854572i \(-0.673819\pi\)
0.999748 + 0.0224689i \(0.00715269\pi\)
\(278\) 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 −0.631795 0.775136i \(-0.717681\pi\)
0.987185 + 0.159582i \(0.0510147\pi\)
\(282\) 0 0
\(283\) −132300. + 76383.2i −1.65191 + 0.953730i −0.675621 + 0.737249i \(0.736124\pi\)
−0.976287 + 0.216481i \(0.930542\pi\)
\(284\) 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 0.730470 0.682945i \(-0.239301\pi\)
−0.956683 + 0.291133i \(0.905968\pi\)
\(294\) 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 \(-0.999227\pi\)
0.999997 0.00242723i \(-0.000772612\pi\)
\(308\) −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 −0.451228 0.892409i \(-0.649014\pi\)
0.547234 + 0.836979i \(0.315681\pi\)
\(312\) 0 0
\(313\) −8976.10 + 15547.1i −0.0916218 + 0.158694i −0.908194 0.418550i \(-0.862538\pi\)
0.816572 + 0.577244i \(0.195872\pi\)
\(314\) −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 −0.977343 0.211663i \(-0.932112\pi\)
0.671977 + 0.740572i \(0.265445\pi\)
\(318\) 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 −0.470023 0.882654i \(-0.655755\pi\)
−0.999412 + 0.0342747i \(0.989088\pi\)
\(332\) −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 0.982741 + 0.184989i \(0.0592251\pi\)
−0.331165 + 0.943573i \(0.607442\pi\)
\(338\) −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 −0.920611 0.390482i \(-0.872308\pi\)
−0.122138 + 0.992513i \(0.538975\pi\)
\(348\) 0 0
\(349\) 89475.8 154977.i 0.734606 1.27238i −0.220290 0.975435i \(-0.570700\pi\)
0.954896 0.296941i \(-0.0959664\pi\)
\(350\) 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 −0.808198 0.588911i \(-0.799557\pi\)
0.914111 + 0.405465i \(0.132890\pi\)
\(354\) 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 \(0.248429\pi\)
−0.710587 + 0.703609i \(0.751571\pi\)
\(360\) 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 0.987368 0.158445i \(-0.0506481\pi\)
0.356467 + 0.934308i \(0.383981\pi\)
\(368\) −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 0.970203 0.242293i \(-0.0778996\pi\)
−0.694934 + 0.719074i \(0.744566\pi\)
\(374\) 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 \(-0.700561\pi\)
0.589211 0.807979i \(-0.299439\pi\)
\(380\) 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 −0.730891 0.682494i \(-0.760895\pi\)
0.225611 + 0.974217i \(0.427562\pi\)
\(384\) 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 −0.591745 0.806125i \(-0.701561\pi\)
0.993997 + 0.109404i \(0.0348942\pi\)
\(390\) 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 0.700135 0.714010i \(-0.253123\pi\)
−0.968419 + 0.249330i \(0.919790\pi\)
\(402\) 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 −0.972212 0.234102i \(-0.924785\pi\)
0.283368 0.959011i \(-0.408548\pi\)
\(410\) 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 −0.630881 0.775879i \(-0.717307\pi\)
0.356491 + 0.934299i \(0.383973\pi\)
\(420\) 0 0
\(421\) −70485.7 + 122085.i −0.397683 + 0.688807i −0.993440 0.114358i \(-0.963519\pi\)
0.595757 + 0.803165i \(0.296852\pi\)
\(422\) 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 \(-0.828111\pi\)
0.857705 0.514142i \(-0.171889\pi\)
\(432\) 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 0.955618 0.294609i \(-0.0951893\pi\)
0.222670 + 0.974894i \(0.428523\pi\)
\(440\) −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 0.687130 0.726534i \(-0.258870\pi\)
−0.285632 + 0.958339i \(0.592204\pi\)
\(444\) 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 −0.999594 0.0285035i \(-0.990926\pi\)
0.524482 + 0.851422i \(0.324259\pi\)
\(458\) −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 −0.999946 0.0103639i \(-0.996701\pi\)
0.508949 + 0.860797i \(0.330034\pi\)
\(462\) 0 0
\(463\) −22687.9 + 13098.9i −0.105836 + 0.0611044i −0.551984 0.833855i \(-0.686129\pi\)
0.446148 + 0.894959i \(0.352796\pi\)
\(464\) 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 \(-0.928909\pi\)
0.975163 0.221487i \(-0.0710911\pi\)
\(468\) 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 0.563250 0.826287i \(-0.309551\pi\)
−0.433960 + 0.900932i \(0.642884\pi\)
\(480\) 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 \(-0.953178\pi\)
0.989201 0.146565i \(-0.0468218\pi\)
\(488\) −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 −0.0928458 0.995681i \(-0.529596\pi\)
0.815862 + 0.578247i \(0.196263\pi\)
\(492\) 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 −0.402964 0.915216i \(-0.632020\pi\)
0.591119 + 0.806585i \(0.298687\pi\)
\(500\) −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 \(0.156973\pi\)
−0.880849 + 0.473397i \(0.843027\pi\)
\(504\) 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 0.955674 0.294426i \(-0.0951284\pi\)
−0.732817 + 0.680425i \(0.761795\pi\)
\(510\) 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 \(0.0231104\pi\)
−0.997366 + 0.0725397i \(0.976890\pi\)
\(524\) 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 0.630180 0.776449i \(-0.282981\pi\)
−0.357335 + 0.933976i \(0.616314\pi\)
\(548\) 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 0.786771 0.617245i \(-0.211751\pi\)
0.927935 0.372741i \(-0.121582\pi\)
\(564\) 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 −0.919778 0.392439i \(-0.871631\pi\)
0.799751 + 0.600331i \(0.204965\pi\)
\(570\) 0 0
\(571\) −276094. + 159403.i −0.846809 + 0.488905i −0.859573 0.511013i \(-0.829270\pi\)
0.0127640 + 0.999919i \(0.495937\pi\)
\(572\) −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 0.517161 0.855888i \(-0.326989\pi\)
−0.482641 + 0.875818i \(0.660322\pi\)
\(588\) 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 −0.936016 0.351958i \(-0.885516\pi\)
−0.163204 + 0.986592i \(0.552183\pi\)
\(600\) 0 0
\(601\) 118996. 206108.i 0.329446 0.570618i −0.652956 0.757396i \(-0.726471\pi\)
0.982402 + 0.186778i \(0.0598046\pi\)
\(602\) −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 0.406371 0.913708i \(-0.366794\pi\)
0.994480 + 0.104927i \(0.0334608\pi\)
\(608\) 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 0.974814 + 0.223021i \(0.0715919\pi\)
−0.294265 + 0.955724i \(0.595075\pi\)
\(618\) 0 0
\(619\) 176869. + 102115.i 0.461605 + 0.266508i 0.712719 0.701450i \(-0.247463\pi\)
−0.251114 + 0.967958i \(0.580797\pi\)
\(620\) 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 \(-0.928638\pi\)
0.974975 0.222317i \(-0.0713618\pi\)
\(632\) −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 −0.701556 0.712614i \(-0.747511\pi\)
0.967920 + 0.251258i \(0.0808444\pi\)
\(642\) 0 0
\(643\) 298938. 172592.i 0.723035 0.417445i −0.0928336 0.995682i \(-0.529592\pi\)
0.815869 + 0.578237i \(0.196259\pi\)
\(644\) 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 \(-0.842201\pi\)
0.879617 0.475683i \(-0.157799\pi\)
\(648\) 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 0.592529 0.805549i \(-0.298129\pi\)
−0.993890 + 0.110371i \(0.964796\pi\)
\(654\) 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 0.920625 0.390447i \(-0.127680\pi\)
0.122175 + 0.992509i \(0.461013\pi\)
\(660\) 0 0
\(661\) −154294. 267245.i −0.353140 0.611656i 0.633658 0.773613i \(-0.281553\pi\)
−0.986798 + 0.161957i \(0.948219\pi\)
\(662\) −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 −0.695623 0.718407i \(-0.744871\pi\)
0.969970 + 0.243223i \(0.0782047\pi\)
\(674\) −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 −0.680731 0.732533i \(-0.738338\pi\)
0.974758 + 0.223264i \(0.0716711\pi\)
\(678\) 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 \(-0.957403\pi\)
0.991059 0.133424i \(-0.0425972\pi\)
\(684\) 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 −0.988048 0.154145i \(-0.950738\pi\)
−0.627518 0.778602i \(1.28407\pi\)
\(692\) 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 −0.270913 0.962604i \(-0.587326\pi\)
0.969096 0.246684i \(-0.0793410\pi\)
\(710\) −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 \(-0.733328\pi\)
0.669117 0.743157i \(-0.266672\pi\)
\(720\) 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 0.275607 0.961270i \(-0.411121\pi\)
−0.694681 + 0.719318i \(0.744454\pi\)
\(728\) −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 0.641169 0.767400i \(-0.278450\pi\)
−0.985172 + 0.171569i \(0.945116\pi\)
\(734\) 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 \(-0.602988\pi\)
0.317932 0.948114i \(-0.397012\pi\)
\(740\) −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 −0.870777 0.491678i \(-0.836384\pi\)
−0.00958322 + 0.999954i \(0.503050\pi\)
\(744\) 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 −0.639011 0.769197i \(-0.720656\pi\)
0.346639 + 0.937999i \(0.387323\pi\)
\(752\) −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 0.788171 0.615456i \(-0.211028\pi\)
−0.927086 + 0.374848i \(0.877695\pi\)
\(762\) 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 0.999991 + 0.00415186i \(0.00132158\pi\)
−0.496400 + 0.868094i \(0.665345\pi\)
\(770\) 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