Properties

Label 108.4.i.a.13.9
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.9
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.9

$q$-expansion

\(f(q)\) \(=\) \(q+(5.19029 - 0.246754i) q^{3} +(15.7004 + 13.1742i) q^{5} +(-8.81657 - 3.20897i) q^{7} +(26.8782 - 2.56145i) q^{9} +O(q^{10})\) \(q+(5.19029 - 0.246754i) q^{3} +(15.7004 + 13.1742i) q^{5} +(-8.81657 - 3.20897i) q^{7} +(26.8782 - 2.56145i) q^{9} +(-45.7414 + 38.3816i) q^{11} +(2.61377 - 14.8234i) q^{13} +(84.7402 + 64.5036i) q^{15} +(44.8278 - 77.6441i) q^{17} +(-3.79866 - 6.57947i) q^{19} +(-46.5524 - 14.4800i) q^{21} +(126.350 - 45.9876i) q^{23} +(51.2365 + 290.577i) q^{25} +(138.874 - 19.9270i) q^{27} +(-25.0600 - 142.122i) q^{29} +(-243.712 + 88.7037i) q^{31} +(-227.940 + 210.499i) q^{33} +(-96.1478 - 166.533i) q^{35} +(113.051 - 195.811i) q^{37} +(9.90850 - 77.5829i) q^{39} +(32.6776 - 185.324i) q^{41} +(-45.0211 + 37.7772i) q^{43} +(455.743 + 313.882i) q^{45} +(-298.842 - 108.770i) q^{47} +(-195.319 - 163.892i) q^{49} +(213.510 - 414.057i) q^{51} -170.290 q^{53} -1223.80 q^{55} +(-21.3396 - 33.2120i) q^{57} +(-82.5952 - 69.3056i) q^{59} +(-324.349 - 118.053i) q^{61} +(-245.193 - 63.6682i) q^{63} +(236.323 - 198.299i) q^{65} +(1.02407 - 5.80776i) q^{67} +(644.446 - 269.867i) q^{69} +(-205.653 + 356.202i) q^{71} +(602.689 + 1043.89i) q^{73} +(337.634 + 1495.54i) q^{75} +(526.448 - 191.611i) q^{77} +(19.8089 + 112.342i) q^{79} +(715.878 - 137.694i) q^{81} +(-245.975 - 1394.99i) q^{83} +(1726.71 - 628.470i) q^{85} +(-165.138 - 731.472i) q^{87} +(683.369 + 1183.63i) q^{89} +(-70.6125 + 122.304i) q^{91} +(-1243.05 + 520.535i) q^{93} +(27.0387 - 153.344i) q^{95} +(-294.392 + 247.025i) q^{97} +(-1131.14 + 1148.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 5.19029 0.246754i 0.998872 0.0474878i
\(4\) 0 0
\(5\) 15.7004 + 13.1742i 1.40428 + 1.17833i 0.959160 + 0.282863i \(0.0912840\pi\)
0.445122 + 0.895470i \(0.353160\pi\)
\(6\) 0 0
\(7\) −8.81657 3.20897i −0.476050 0.173268i 0.0928410 0.995681i \(-0.470405\pi\)
−0.568891 + 0.822413i \(0.692627\pi\)
\(8\) 0 0
\(9\) 26.8782 2.56145i 0.995490 0.0948684i
\(10\) 0 0
\(11\) −45.7414 + 38.3816i −1.25378 + 1.05204i −0.257462 + 0.966288i \(0.582886\pi\)
−0.996316 + 0.0857561i \(0.972669\pi\)
\(12\) 0 0
\(13\) 2.61377 14.8234i 0.0557638 0.316252i −0.944148 0.329521i \(-0.893113\pi\)
0.999912 + 0.0132689i \(0.00422374\pi\)
\(14\) 0 0
\(15\) 84.7402 + 64.5036i 1.45865 + 1.11032i
\(16\) 0 0
\(17\) 44.8278 77.6441i 0.639550 1.10773i −0.345982 0.938241i \(-0.612454\pi\)
0.985532 0.169491i \(-0.0542124\pi\)
\(18\) 0 0
\(19\) −3.79866 6.57947i −0.0458669 0.0794439i 0.842180 0.539196i \(-0.181272\pi\)
−0.888047 + 0.459752i \(0.847938\pi\)
\(20\) 0 0
\(21\) −46.5524 14.4800i −0.483741 0.150466i
\(22\) 0 0
\(23\) 126.350 45.9876i 1.14547 0.416917i 0.301584 0.953440i \(-0.402485\pi\)
0.843886 + 0.536523i \(0.180262\pi\)
\(24\) 0 0
\(25\) 51.2365 + 290.577i 0.409892 + 2.32462i
\(26\) 0 0
\(27\) 138.874 19.9270i 0.989862 0.142035i
\(28\) 0 0
\(29\) −25.0600 142.122i −0.160466 0.910049i −0.953617 0.301023i \(-0.902672\pi\)
0.793151 0.609026i \(-0.208439\pi\)
\(30\) 0 0
\(31\) −243.712 + 88.7037i −1.41200 + 0.513925i −0.931715 0.363190i \(-0.881688\pi\)
−0.480281 + 0.877115i \(0.659465\pi\)
\(32\) 0 0
\(33\) −227.940 + 210.499i −1.20240 + 1.11040i
\(34\) 0 0
\(35\) −96.1478 166.533i −0.464341 0.804263i
\(36\) 0 0
\(37\) 113.051 195.811i 0.502312 0.870030i −0.497684 0.867358i \(-0.665816\pi\)
0.999996 0.00267179i \(-0.000850458\pi\)
\(38\) 0 0
\(39\) 9.90850 77.5829i 0.0406828 0.318544i
\(40\) 0 0
\(41\) 32.6776 185.324i 0.124473 0.705921i −0.857147 0.515072i \(-0.827765\pi\)
0.981620 0.190848i \(-0.0611238\pi\)
\(42\) 0 0
\(43\) −45.0211 + 37.7772i −0.159667 + 0.133976i −0.719121 0.694885i \(-0.755455\pi\)
0.559454 + 0.828861i \(0.311011\pi\)
\(44\) 0 0
\(45\) 455.743 + 313.882i 1.50974 + 1.03980i
\(46\) 0 0
\(47\) −298.842 108.770i −0.927459 0.337568i −0.166257 0.986082i \(-0.553168\pi\)
−0.761202 + 0.648515i \(0.775390\pi\)
\(48\) 0 0
\(49\) −195.319 163.892i −0.569443 0.477819i
\(50\) 0 0
\(51\) 213.510 414.057i 0.586224 1.13685i
\(52\) 0 0
\(53\) −170.290 −0.441341 −0.220671 0.975348i \(-0.570825\pi\)
−0.220671 + 0.975348i \(0.570825\pi\)
\(54\) 0 0
\(55\) −1223.80 −3.00032
\(56\) 0 0
\(57\) −21.3396 33.2120i −0.0495878 0.0771761i
\(58\) 0 0
\(59\) −82.5952 69.3056i −0.182254 0.152929i 0.547096 0.837070i \(-0.315733\pi\)
−0.729350 + 0.684140i \(0.760178\pi\)
\(60\) 0 0
\(61\) −324.349 118.053i −0.680797 0.247790i −0.0216072 0.999767i \(-0.506878\pi\)
−0.659190 + 0.751977i \(0.729101\pi\)
\(62\) 0 0
\(63\) −245.193 63.6682i −0.490341 0.127324i
\(64\) 0 0
\(65\) 236.323 198.299i 0.450959 0.378399i
\(66\) 0 0
\(67\) 1.02407 5.80776i 0.00186731 0.0105900i −0.983860 0.178941i \(-0.942733\pi\)
0.985727 + 0.168351i \(0.0538441\pi\)
\(68\) 0 0
\(69\) 644.446 269.867i 1.12438 0.470842i
\(70\) 0 0
\(71\) −205.653 + 356.202i −0.343754 + 0.595400i −0.985127 0.171830i \(-0.945032\pi\)
0.641372 + 0.767230i \(0.278365\pi\)
\(72\) 0 0
\(73\) 602.689 + 1043.89i 0.966294 + 1.67367i 0.706098 + 0.708115i \(0.250454\pi\)
0.260196 + 0.965556i \(0.416213\pi\)
\(74\) 0 0
\(75\) 337.634 + 1495.54i 0.519821 + 2.30253i
\(76\) 0 0
\(77\) 526.448 191.611i 0.779147 0.283586i
\(78\) 0 0
\(79\) 19.8089 + 112.342i 0.0282111 + 0.159993i 0.995659 0.0930777i \(-0.0296705\pi\)
−0.967448 + 0.253071i \(0.918559\pi\)
\(80\) 0 0
\(81\) 715.878 137.694i 0.982000 0.188881i
\(82\) 0 0
\(83\) −245.975 1394.99i −0.325292 1.84482i −0.507616 0.861583i \(-0.669473\pi\)
0.182324 0.983238i \(-0.441638\pi\)
\(84\) 0 0
\(85\) 1726.71 628.470i 2.20339 0.801967i
\(86\) 0 0
\(87\) −165.138 731.472i −0.203501 0.901402i
\(88\) 0 0
\(89\) 683.369 + 1183.63i 0.813899 + 1.40971i 0.910116 + 0.414354i \(0.135992\pi\)
−0.0962172 + 0.995360i \(0.530674\pi\)
\(90\) 0 0
\(91\) −70.6125 + 122.304i −0.0813428 + 0.140890i
\(92\) 0 0
\(93\) −1243.05 + 520.535i −1.38600 + 0.580397i
\(94\) 0 0
\(95\) 27.0387 153.344i 0.0292012 0.165608i
\(96\) 0 0
\(97\) −294.392 + 247.025i −0.308155 + 0.258573i −0.783729 0.621103i \(-0.786685\pi\)
0.475574 + 0.879676i \(0.342240\pi\)
\(98\) 0 0
\(99\) −1131.14 + 1148.79i −1.14832 + 1.16624i
\(100\) 0 0
\(101\) 586.611 + 213.509i 0.577920 + 0.210346i 0.614408 0.788988i \(-0.289395\pi\)
−0.0364880 + 0.999334i \(0.511617\pi\)
\(102\) 0 0
\(103\) 801.072 + 672.179i 0.766330 + 0.643027i 0.939766 0.341818i \(-0.111043\pi\)
−0.173436 + 0.984845i \(0.555487\pi\)
\(104\) 0 0
\(105\) −540.128 840.629i −0.502010 0.781305i
\(106\) 0 0
\(107\) 219.340 0.198172 0.0990860 0.995079i \(-0.468408\pi\)
0.0990860 + 0.995079i \(0.468408\pi\)
\(108\) 0 0
\(109\) −2066.92 −1.81628 −0.908142 0.418663i \(-0.862499\pi\)
−0.908142 + 0.418663i \(0.862499\pi\)
\(110\) 0 0
\(111\) 538.453 1044.21i 0.460430 0.892902i
\(112\) 0 0
\(113\) −126.524 106.166i −0.105331 0.0883828i 0.588601 0.808423i \(-0.299679\pi\)
−0.693932 + 0.720041i \(0.744123\pi\)
\(114\) 0 0
\(115\) 2589.59 + 942.533i 2.09983 + 0.764275i
\(116\) 0 0
\(117\) 32.2841 405.123i 0.0255100 0.320116i
\(118\) 0 0
\(119\) −644.385 + 540.703i −0.496392 + 0.416523i
\(120\) 0 0
\(121\) 388.004 2200.48i 0.291513 1.65325i
\(122\) 0 0
\(123\) 123.877 969.949i 0.0908098 0.711035i
\(124\) 0 0
\(125\) −1742.72 + 3018.47i −1.24699 + 2.15984i
\(126\) 0 0
\(127\) −801.591 1388.40i −0.560077 0.970081i −0.997489 0.0708201i \(-0.977438\pi\)
0.437413 0.899261i \(-0.355895\pi\)
\(128\) 0 0
\(129\) −224.351 + 207.184i −0.153124 + 0.141407i
\(130\) 0 0
\(131\) 1986.87 723.162i 1.32514 0.482313i 0.420040 0.907505i \(-0.362016\pi\)
0.905103 + 0.425193i \(0.139794\pi\)
\(132\) 0 0
\(133\) 12.3778 + 70.1981i 0.00806988 + 0.0457665i
\(134\) 0 0
\(135\) 2442.89 + 1516.68i 1.55741 + 0.966929i
\(136\) 0 0
\(137\) 174.325 + 988.647i 0.108712 + 0.616539i 0.989672 + 0.143348i \(0.0457868\pi\)
−0.880960 + 0.473191i \(0.843102\pi\)
\(138\) 0 0
\(139\) −141.218 + 51.3992i −0.0861724 + 0.0313642i −0.384747 0.923022i \(-0.625711\pi\)
0.298574 + 0.954386i \(0.403489\pi\)
\(140\) 0 0
\(141\) −1577.92 490.805i −0.942443 0.293144i
\(142\) 0 0
\(143\) 449.390 + 778.366i 0.262796 + 0.455176i
\(144\) 0 0
\(145\) 1478.89 2561.51i 0.847001 1.46705i
\(146\) 0 0
\(147\) −1054.20 802.451i −0.591491 0.450238i
\(148\) 0 0
\(149\) −353.047 + 2002.23i −0.194112 + 1.10087i 0.719565 + 0.694426i \(0.244341\pi\)
−0.913677 + 0.406441i \(0.866770\pi\)
\(150\) 0 0
\(151\) −998.407 + 837.763i −0.538074 + 0.451498i −0.870879 0.491498i \(-0.836450\pi\)
0.332804 + 0.942996i \(0.392005\pi\)
\(152\) 0 0
\(153\) 1006.01 2201.76i 0.531576 1.16341i
\(154\) 0 0
\(155\) −4994.95 1818.01i −2.58842 0.942106i
\(156\) 0 0
\(157\) −1497.76 1256.77i −0.761366 0.638862i 0.177116 0.984190i \(-0.443323\pi\)
−0.938482 + 0.345328i \(0.887768\pi\)
\(158\) 0 0
\(159\) −883.853 + 42.0196i −0.440844 + 0.0209583i
\(160\) 0 0
\(161\) −1261.55 −0.617539
\(162\) 0 0
\(163\) 304.483 0.146312 0.0731562 0.997320i \(-0.476693\pi\)
0.0731562 + 0.997320i \(0.476693\pi\)
\(164\) 0 0
\(165\) −6351.89 + 301.978i −2.99693 + 0.142478i
\(166\) 0 0
\(167\) 1927.52 + 1617.38i 0.893150 + 0.749442i 0.968839 0.247690i \(-0.0796714\pi\)
−0.0756896 + 0.997131i \(0.524116\pi\)
\(168\) 0 0
\(169\) 1851.60 + 673.928i 0.842787 + 0.306749i
\(170\) 0 0
\(171\) −118.954 167.114i −0.0531968 0.0747342i
\(172\) 0 0
\(173\) −416.652 + 349.613i −0.183107 + 0.153645i −0.729734 0.683731i \(-0.760356\pi\)
0.546627 + 0.837376i \(0.315912\pi\)
\(174\) 0 0
\(175\) 480.722 2726.31i 0.207652 1.17765i
\(176\) 0 0
\(177\) −445.795 339.336i −0.189311 0.144102i
\(178\) 0 0
\(179\) 1487.78 2576.91i 0.621238 1.07602i −0.368017 0.929819i \(-0.619963\pi\)
0.989255 0.146197i \(-0.0467034\pi\)
\(180\) 0 0
\(181\) −6.47319 11.2119i −0.00265828 0.00460427i 0.864693 0.502300i \(-0.167513\pi\)
−0.867351 + 0.497696i \(0.834179\pi\)
\(182\) 0 0
\(183\) −1712.59 532.697i −0.691796 0.215181i
\(184\) 0 0
\(185\) 4354.59 1584.94i 1.73057 0.629877i
\(186\) 0 0
\(187\) 929.616 + 5272.11i 0.363531 + 2.06168i
\(188\) 0 0
\(189\) −1288.34 269.954i −0.495834 0.103896i
\(190\) 0 0
\(191\) 107.185 + 607.875i 0.0406053 + 0.230284i 0.998356 0.0573151i \(-0.0182540\pi\)
−0.957751 + 0.287599i \(0.907143\pi\)
\(192\) 0 0
\(193\) 1940.91 706.433i 0.723884 0.263472i 0.0463102 0.998927i \(-0.485254\pi\)
0.677574 + 0.735455i \(0.263032\pi\)
\(194\) 0 0
\(195\) 1177.66 1087.54i 0.432481 0.399387i
\(196\) 0 0
\(197\) −300.362 520.241i −0.108629 0.188151i 0.806586 0.591116i \(-0.201313\pi\)
−0.915215 + 0.402966i \(0.867979\pi\)
\(198\) 0 0
\(199\) −1860.07 + 3221.74i −0.662597 + 1.14765i 0.317333 + 0.948314i \(0.397213\pi\)
−0.979931 + 0.199338i \(0.936121\pi\)
\(200\) 0 0
\(201\) 3.88211 30.3967i 0.00136230 0.0106667i
\(202\) 0 0
\(203\) −235.123 + 1333.45i −0.0812925 + 0.461033i
\(204\) 0 0
\(205\) 2954.54 2479.15i 1.00660 0.844641i
\(206\) 0 0
\(207\) 3278.27 1559.71i 1.10075 0.523705i
\(208\) 0 0
\(209\) 426.287 + 155.156i 0.141085 + 0.0513509i
\(210\) 0 0
\(211\) 1236.66 + 1037.68i 0.403484 + 0.338563i 0.821838 0.569721i \(-0.192949\pi\)
−0.418355 + 0.908284i \(0.637393\pi\)
\(212\) 0 0
\(213\) −979.506 + 1899.54i −0.315092 + 0.611052i
\(214\) 0 0
\(215\) −1204.53 −0.382085
\(216\) 0 0
\(217\) 2433.35 0.761228
\(218\) 0 0
\(219\) 3385.72 + 5269.37i 1.04468 + 1.62589i
\(220\) 0 0
\(221\) −1033.78 867.446i −0.314659 0.264031i
\(222\) 0 0
\(223\) −3267.43 1189.25i −0.981182 0.357121i −0.198882 0.980023i \(-0.563731\pi\)
−0.782299 + 0.622902i \(0.785953\pi\)
\(224\) 0 0
\(225\) 2121.45 + 7678.95i 0.628576 + 2.27524i
\(226\) 0 0
\(227\) 573.716 481.405i 0.167748 0.140758i −0.555049 0.831818i \(-0.687300\pi\)
0.722797 + 0.691060i \(0.242856\pi\)
\(228\) 0 0
\(229\) −628.614 + 3565.05i −0.181397 + 1.02875i 0.749100 + 0.662457i \(0.230486\pi\)
−0.930498 + 0.366298i \(0.880625\pi\)
\(230\) 0 0
\(231\) 2685.14 1124.42i 0.764801 0.320266i
\(232\) 0 0
\(233\) −2041.89 + 3536.65i −0.574113 + 0.994393i 0.422024 + 0.906585i \(0.361320\pi\)
−0.996137 + 0.0878086i \(0.972014\pi\)
\(234\) 0 0
\(235\) −3258.98 5644.71i −0.904648 1.56690i
\(236\) 0 0
\(237\) 130.535 + 578.200i 0.0357770 + 0.158473i
\(238\) 0 0
\(239\) 2769.51 1008.02i 0.749560 0.272817i 0.0611393 0.998129i \(-0.480527\pi\)
0.688421 + 0.725312i \(0.258304\pi\)
\(240\) 0 0
\(241\) −17.3695 98.5075i −0.00464261 0.0263296i 0.982398 0.186797i \(-0.0598108\pi\)
−0.987041 + 0.160468i \(0.948700\pi\)
\(242\) 0 0
\(243\) 3681.64 891.319i 0.971923 0.235301i
\(244\) 0 0
\(245\) −907.435 5146.32i −0.236628 1.34199i
\(246\) 0 0
\(247\) −107.459 + 39.1119i −0.0276820 + 0.0100754i
\(248\) 0 0
\(249\) −1620.90 7179.72i −0.412531 1.82729i
\(250\) 0 0
\(251\) 2244.88 + 3888.24i 0.564524 + 0.977783i 0.997094 + 0.0761832i \(0.0242734\pi\)
−0.432570 + 0.901600i \(0.642393\pi\)
\(252\) 0 0
\(253\) −4014.35 + 6953.06i −0.997549 + 1.72781i
\(254\) 0 0
\(255\) 8807.04 3688.01i 2.16282 0.905696i
\(256\) 0 0
\(257\) −537.383 + 3047.65i −0.130432 + 0.739717i 0.847500 + 0.530795i \(0.178107\pi\)
−0.977932 + 0.208922i \(0.933005\pi\)
\(258\) 0 0
\(259\) −1625.08 + 1363.60i −0.389874 + 0.327143i
\(260\) 0 0
\(261\) −1037.61 3755.80i −0.246077 0.890721i
\(262\) 0 0
\(263\) 5048.21 + 1837.40i 1.18360 + 0.430794i 0.857471 0.514533i \(-0.172035\pi\)
0.326125 + 0.945327i \(0.394257\pi\)
\(264\) 0 0
\(265\) −2673.61 2243.42i −0.619768 0.520047i
\(266\) 0 0
\(267\) 3838.95 + 5974.76i 0.879925 + 1.36947i
\(268\) 0 0
\(269\) 3518.17 0.797422 0.398711 0.917077i \(-0.369458\pi\)
0.398711 + 0.917077i \(0.369458\pi\)
\(270\) 0 0
\(271\) 168.611 0.0377948 0.0188974 0.999821i \(-0.493984\pi\)
0.0188974 + 0.999821i \(0.493984\pi\)
\(272\) 0 0
\(273\) −336.320 + 652.219i −0.0745605 + 0.144594i
\(274\) 0 0
\(275\) −13496.4 11324.9i −2.95951 2.48333i
\(276\) 0 0
\(277\) −2582.12 939.815i −0.560088 0.203856i 0.0464347 0.998921i \(-0.485214\pi\)
−0.606523 + 0.795066i \(0.707436\pi\)
\(278\) 0 0
\(279\) −6323.32 + 3008.45i −1.35687 + 0.645561i
\(280\) 0 0
\(281\) 3848.57 3229.33i 0.817034 0.685573i −0.135242 0.990813i \(-0.543181\pi\)
0.952275 + 0.305240i \(0.0987367\pi\)
\(282\) 0 0
\(283\) 63.6653 361.064i 0.0133728 0.0758411i −0.977391 0.211440i \(-0.932185\pi\)
0.990764 + 0.135599i \(0.0432958\pi\)
\(284\) 0 0
\(285\) 102.500 802.572i 0.0213039 0.166808i
\(286\) 0 0
\(287\) −882.804 + 1529.06i −0.181569 + 0.314486i
\(288\) 0 0
\(289\) −1562.57 2706.44i −0.318047 0.550874i
\(290\) 0 0
\(291\) −1467.03 + 1354.77i −0.295528 + 0.272914i
\(292\) 0 0
\(293\) −1101.03 + 400.741i −0.219532 + 0.0799029i −0.449445 0.893308i \(-0.648378\pi\)
0.229913 + 0.973211i \(0.426156\pi\)
\(294\) 0 0
\(295\) −383.731 2176.25i −0.0757345 0.429511i
\(296\) 0 0
\(297\) −5587.45 + 6241.69i −1.09164 + 1.21946i
\(298\) 0 0
\(299\) −351.445 1993.14i −0.0679752 0.385506i
\(300\) 0 0
\(301\) 518.158 188.594i 0.0992230 0.0361142i
\(302\) 0 0
\(303\) 3097.36 + 963.424i 0.587257 + 0.182664i
\(304\) 0 0
\(305\) −3537.14 6126.50i −0.664052 1.15017i
\(306\) 0 0
\(307\) −4212.00 + 7295.40i −0.783034 + 1.35626i 0.147132 + 0.989117i \(0.452996\pi\)
−0.930166 + 0.367139i \(0.880337\pi\)
\(308\) 0 0
\(309\) 4323.66 + 3291.14i 0.796001 + 0.605910i
\(310\) 0 0
\(311\) 1088.82 6175.03i 0.198526 1.12590i −0.708781 0.705428i \(-0.750755\pi\)
0.907307 0.420468i \(-0.138134\pi\)
\(312\) 0 0
\(313\) −1561.71 + 1310.43i −0.282022 + 0.236645i −0.772815 0.634632i \(-0.781152\pi\)
0.490792 + 0.871277i \(0.336707\pi\)
\(314\) 0 0
\(315\) −3010.85 4229.83i −0.538546 0.756584i
\(316\) 0 0
\(317\) −4935.72 1796.45i −0.874503 0.318293i −0.134514 0.990912i \(-0.542947\pi\)
−0.739989 + 0.672619i \(0.765170\pi\)
\(318\) 0 0
\(319\) 6601.16 + 5539.03i 1.15860 + 0.972182i
\(320\) 0 0
\(321\) 1138.44 54.1230i 0.197948 0.00941075i
\(322\) 0 0
\(323\) −681.142 −0.117337
\(324\) 0 0
\(325\) 4441.27 0.758023
\(326\) 0 0
\(327\) −10727.9 + 510.020i −1.81423 + 0.0862513i
\(328\) 0 0
\(329\) 2285.72 + 1917.95i 0.383027 + 0.321398i
\(330\) 0 0
\(331\) −5265.15 1916.36i −0.874317 0.318225i −0.134403 0.990927i \(-0.542912\pi\)
−0.739914 + 0.672702i \(0.765134\pi\)
\(332\) 0 0
\(333\) 2537.06 5552.62i 0.417508 0.913760i
\(334\) 0 0
\(335\) 92.5906 77.6927i 0.0151008 0.0126711i
\(336\) 0 0
\(337\) −1242.81 + 7048.32i −0.200890 + 1.13931i 0.702886 + 0.711302i \(0.251894\pi\)
−0.903777 + 0.428004i \(0.859217\pi\)
\(338\) 0 0
\(339\) −682.891 519.812i −0.109409 0.0832812i
\(340\) 0 0
\(341\) 7743.12 13411.5i 1.22966 2.12983i
\(342\) 0 0
\(343\) 2805.20 + 4858.75i 0.441593 + 0.764862i
\(344\) 0 0
\(345\) 13673.3 + 4253.03i 2.13375 + 0.663697i
\(346\) 0 0
\(347\) 6609.62 2405.70i 1.02254 0.372176i 0.224307 0.974519i \(-0.427988\pi\)
0.798237 + 0.602343i \(0.205766\pi\)
\(348\) 0 0
\(349\) −2117.69 12010.0i −0.324806 1.84207i −0.511032 0.859562i \(-0.670737\pi\)
0.186226 0.982507i \(-0.440374\pi\)
\(350\) 0 0
\(351\) 67.5982 2110.67i 0.0102796 0.320967i
\(352\) 0 0
\(353\) 1121.15 + 6358.37i 0.169045 + 0.958702i 0.944795 + 0.327662i \(0.106261\pi\)
−0.775750 + 0.631040i \(0.782628\pi\)
\(354\) 0 0
\(355\) −7921.49 + 2883.19i −1.18431 + 0.431053i
\(356\) 0 0
\(357\) −3211.12 + 2965.41i −0.476053 + 0.439625i
\(358\) 0 0
\(359\) −2838.30 4916.07i −0.417269 0.722731i 0.578395 0.815757i \(-0.303679\pi\)
−0.995664 + 0.0930261i \(0.970346\pi\)
\(360\) 0 0
\(361\) 3400.64 5890.08i 0.495792 0.858738i
\(362\) 0 0
\(363\) 1470.88 11516.9i 0.212675 1.66523i
\(364\) 0 0
\(365\) −4289.92 + 24329.3i −0.615191 + 3.48892i
\(366\) 0 0
\(367\) −5167.88 + 4336.37i −0.735045 + 0.616776i −0.931502 0.363737i \(-0.881501\pi\)
0.196457 + 0.980512i \(0.437056\pi\)
\(368\) 0 0
\(369\) 403.619 5064.88i 0.0569419 0.714545i
\(370\) 0 0
\(371\) 1501.37 + 546.455i 0.210101 + 0.0764704i
\(372\) 0 0
\(373\) −6570.17 5513.03i −0.912039 0.765292i 0.0604669 0.998170i \(-0.480741\pi\)
−0.972506 + 0.232879i \(0.925185\pi\)
\(374\) 0 0
\(375\) −8300.38 + 16096.8i −1.14301 + 2.21662i
\(376\) 0 0
\(377\) −2172.24 −0.296754
\(378\) 0 0
\(379\) 2072.06 0.280830 0.140415 0.990093i \(-0.455156\pi\)
0.140415 + 0.990093i \(0.455156\pi\)
\(380\) 0 0
\(381\) −4503.08 7008.39i −0.605512 0.942390i
\(382\) 0 0
\(383\) −8567.05 7188.61i −1.14297 0.959062i −0.143434 0.989660i \(-0.545815\pi\)
−0.999532 + 0.0305975i \(0.990259\pi\)
\(384\) 0 0
\(385\) 10789.7 + 3927.14i 1.42830 + 0.519859i
\(386\) 0 0
\(387\) −1113.32 + 1130.70i −0.146236 + 0.148519i
\(388\) 0 0
\(389\) −7629.67 + 6402.06i −0.994447 + 0.834440i −0.986205 0.165526i \(-0.947068\pi\)
−0.00824146 + 0.999966i \(0.502623\pi\)
\(390\) 0 0
\(391\) 2093.33 11871.9i 0.270752 1.53551i
\(392\) 0 0
\(393\) 10134.0 4243.69i 1.30074 0.544697i
\(394\) 0 0
\(395\) −1169.00 + 2024.78i −0.148909 + 0.257918i
\(396\) 0 0
\(397\) 1696.82 + 2938.98i 0.214511 + 0.371545i 0.953121 0.302588i \(-0.0978508\pi\)
−0.738610 + 0.674133i \(0.764517\pi\)
\(398\) 0 0
\(399\) 81.5662 + 361.294i 0.0102341 + 0.0453317i
\(400\) 0 0
\(401\) 4357.03 1585.83i 0.542593 0.197488i −0.0561597 0.998422i \(-0.517886\pi\)
0.598752 + 0.800934i \(0.295663\pi\)
\(402\) 0 0
\(403\) 677.888 + 3844.49i 0.0837916 + 0.475206i
\(404\) 0 0
\(405\) 13053.5 + 7269.24i 1.60157 + 0.891880i
\(406\) 0 0
\(407\) 2344.40 + 13295.8i 0.285523 + 1.61928i
\(408\) 0 0
\(409\) −12927.5 + 4705.22i −1.56289 + 0.568846i −0.971397 0.237463i \(-0.923684\pi\)
−0.591495 + 0.806309i \(0.701462\pi\)
\(410\) 0 0
\(411\) 1148.75 + 5088.35i 0.137868 + 0.610681i
\(412\) 0 0
\(413\) 505.807 + 876.083i 0.0602643 + 0.104381i
\(414\) 0 0
\(415\) 14516.0 25142.4i 1.71701 2.97395i
\(416\) 0 0
\(417\) −720.280 + 301.623i −0.0845858 + 0.0354209i
\(418\) 0 0
\(419\) −2243.12 + 12721.3i −0.261536 + 1.48324i 0.517186 + 0.855873i \(0.326979\pi\)
−0.778722 + 0.627369i \(0.784132\pi\)
\(420\) 0 0
\(421\) 9277.02 7784.35i 1.07395 0.901154i 0.0785486 0.996910i \(-0.474971\pi\)
0.995405 + 0.0957563i \(0.0305270\pi\)
\(422\) 0 0
\(423\) −8310.95 2158.07i −0.955301 0.248058i
\(424\) 0 0
\(425\) 24858.4 + 9047.71i 2.83720 + 1.03266i
\(426\) 0 0
\(427\) 2480.81 + 2081.65i 0.281159 + 0.235921i
\(428\) 0 0
\(429\) 2524.53 + 3929.06i 0.284115 + 0.442183i
\(430\) 0 0
\(431\) 8454.10 0.944826 0.472413 0.881377i \(-0.343383\pi\)
0.472413 + 0.881377i \(0.343383\pi\)
\(432\) 0 0
\(433\) 16108.8 1.78785 0.893926 0.448214i \(-0.147940\pi\)
0.893926 + 0.448214i \(0.147940\pi\)
\(434\) 0 0
\(435\) 7043.80 13659.9i 0.776378 1.50562i
\(436\) 0 0
\(437\) −782.535 656.625i −0.0856607 0.0718778i
\(438\) 0 0
\(439\) 4859.34 + 1768.65i 0.528300 + 0.192285i 0.592379 0.805659i \(-0.298189\pi\)
−0.0640794 + 0.997945i \(0.520411\pi\)
\(440\) 0 0
\(441\) −5669.62 3904.83i −0.612204 0.421642i
\(442\) 0 0
\(443\) −4319.54 + 3624.52i −0.463267 + 0.388728i −0.844332 0.535821i \(-0.820002\pi\)
0.381064 + 0.924549i \(0.375558\pi\)
\(444\) 0 0
\(445\) −4864.20 + 27586.2i −0.518169 + 2.93868i
\(446\) 0 0
\(447\) −1338.36 + 10479.3i −0.141616 + 1.10884i
\(448\) 0 0
\(449\) 1788.29 3097.40i 0.187961 0.325558i −0.756609 0.653867i \(-0.773146\pi\)
0.944570 + 0.328309i \(0.106479\pi\)
\(450\) 0 0
\(451\) 5618.31 + 9731.20i 0.586599 + 1.01602i
\(452\) 0 0
\(453\) −4975.30 + 4594.59i −0.516027 + 0.476541i
\(454\) 0 0
\(455\) −2719.90 + 989.962i −0.280244 + 0.102000i
\(456\) 0 0
\(457\) −1008.03 5716.82i −0.103181 0.585168i −0.991931 0.126776i \(-0.959537\pi\)
0.888750 0.458391i \(-0.151574\pi\)
\(458\) 0 0
\(459\) 4678.20 11676.0i 0.475729 1.18734i
\(460\) 0 0
\(461\) −1782.29 10107.9i −0.180065 1.02120i −0.932134 0.362113i \(-0.882055\pi\)
0.752070 0.659084i \(-0.229056\pi\)
\(462\) 0 0
\(463\) 4506.47 1640.22i 0.452340 0.164638i −0.105796 0.994388i \(-0.533739\pi\)
0.558136 + 0.829750i \(0.311517\pi\)
\(464\) 0 0
\(465\) −26373.9 8203.50i −2.63023 0.818125i
\(466\) 0 0
\(467\) −517.986 897.177i −0.0513266 0.0889003i 0.839221 0.543791i \(-0.183012\pi\)
−0.890547 + 0.454891i \(0.849678\pi\)
\(468\) 0 0
\(469\) −27.6657 + 47.9184i −0.00272384 + 0.00471783i
\(470\) 0 0
\(471\) −8083.94 6153.44i −0.790846 0.601986i
\(472\) 0 0
\(473\) 609.380 3455.97i 0.0592375 0.335953i
\(474\) 0 0
\(475\) 1717.21 1440.91i 0.165876 0.139186i
\(476\) 0 0
\(477\) −4577.09 + 436.188i −0.439351 + 0.0418694i
\(478\) 0 0
\(479\) −7302.87 2658.03i −0.696611 0.253546i −0.0306475 0.999530i \(-0.509757\pi\)
−0.665963 + 0.745985i \(0.731979\pi\)
\(480\) 0 0
\(481\) −2607.10 2187.62i −0.247138 0.207374i
\(482\) 0 0
\(483\) −6547.79 + 311.292i −0.616843 + 0.0293256i
\(484\) 0 0
\(485\) −7876.40 −0.737421
\(486\) 0 0
\(487\) −6402.34 −0.595724 −0.297862 0.954609i \(-0.596274\pi\)
−0.297862 + 0.954609i \(0.596274\pi\)
\(488\) 0 0
\(489\) 1580.35 75.1323i 0.146147 0.00694806i
\(490\) 0 0
\(491\) −1539.64 1291.91i −0.141513 0.118743i 0.569283 0.822141i \(-0.307221\pi\)
−0.710796 + 0.703398i \(0.751665\pi\)
\(492\) 0 0
\(493\) −12158.3 4425.27i −1.11072 0.404268i
\(494\) 0 0
\(495\) −32893.6 + 3134.70i −2.98678 + 0.284635i
\(496\) 0 0
\(497\) 2956.20 2480.55i 0.266808 0.223879i
\(498\) 0 0
\(499\) 1717.87 9742.54i 0.154113 0.874020i −0.805479 0.592625i \(-0.798092\pi\)
0.959592 0.281395i \(-0.0907972\pi\)
\(500\) 0 0
\(501\) 10403.5 + 7919.06i 0.927731 + 0.706182i
\(502\) 0 0
\(503\) 3388.43 5868.93i 0.300363 0.520244i −0.675855 0.737034i \(-0.736226\pi\)
0.976218 + 0.216791i \(0.0695589\pi\)
\(504\) 0 0
\(505\) 6397.19 + 11080.3i 0.563706 + 0.976367i
\(506\) 0 0
\(507\) 9776.65 + 3040.99i 0.856403 + 0.266381i
\(508\) 0 0
\(509\) −1383.55 + 503.573i −0.120481 + 0.0438516i −0.401557 0.915834i \(-0.631531\pi\)
0.281076 + 0.959686i \(0.409309\pi\)
\(510\) 0 0
\(511\) −1963.85 11137.5i −0.170011 0.964179i
\(512\) 0 0
\(513\) −658.643 838.020i −0.0566857 0.0721237i
\(514\) 0 0
\(515\) 3721.72 + 21106.9i 0.318444 + 1.80598i
\(516\) 0 0
\(517\) 17844.2 6494.76i 1.51796 0.552494i
\(518\) 0 0
\(519\) −2076.28 + 1917.40i −0.175604 + 0.162167i
\(520\) 0 0
\(521\) −6864.02 11888.8i −0.577194 0.999730i −0.995799 0.0915615i \(-0.970814\pi\)
0.418605 0.908168i \(-0.362519\pi\)
\(522\) 0 0
\(523\) 2877.17 4983.40i 0.240554 0.416652i −0.720318 0.693644i \(-0.756004\pi\)
0.960872 + 0.276992i \(0.0893376\pi\)
\(524\) 0 0
\(525\) 1822.36 14269.0i 0.151494 1.18619i
\(526\) 0 0
\(527\) −4037.74 + 22899.1i −0.333751 + 1.89279i
\(528\) 0 0
\(529\) 4529.00 3800.28i 0.372236 0.312343i
\(530\) 0 0
\(531\) −2397.54 1651.25i −0.195940 0.134949i
\(532\) 0 0
\(533\) −2661.73 968.789i −0.216308 0.0787297i
\(534\) 0 0
\(535\) 3443.72 + 2889.62i 0.278289 + 0.233513i
\(536\) 0 0
\(537\) 7086.13 13742.0i 0.569440 1.10430i
\(538\) 0 0
\(539\) 15224.6 1.21664
\(540\) 0 0
\(541\) −17020.2 −1.35260 −0.676298 0.736628i \(-0.736417\pi\)
−0.676298 + 0.736628i \(0.736417\pi\)
\(542\) 0 0
\(543\) −36.3643 56.5957i −0.00287393 0.00447284i
\(544\) 0 0
\(545\) −32451.3 27229.9i −2.55057 2.14019i
\(546\) 0 0
\(547\) −18304.3 6662.21i −1.43078 0.520760i −0.493623 0.869676i \(-0.664328\pi\)
−0.937154 + 0.348916i \(0.886550\pi\)
\(548\) 0 0
\(549\) −9020.31 2342.26i −0.701234 0.182086i
\(550\) 0 0
\(551\) −839.894 + 704.755i −0.0649377 + 0.0544892i
\(552\) 0 0
\(553\) 185.855 1054.04i 0.0142918 0.0810529i
\(554\) 0 0
\(555\) 22210.5 9300.82i 1.69871 0.711347i
\(556\) 0 0
\(557\) −2898.44 + 5020.24i −0.220486 + 0.381893i −0.954956 0.296748i \(-0.904098\pi\)
0.734469 + 0.678642i \(0.237431\pi\)
\(558\) 0 0
\(559\) 442.313 + 766.109i 0.0334667 + 0.0579660i
\(560\) 0 0
\(561\) 6125.89 + 27134.4i 0.461025 + 2.04210i
\(562\) 0 0
\(563\) 8296.09 3019.53i 0.621027 0.226035i −0.0122940 0.999924i \(-0.503913\pi\)
0.633321 + 0.773889i \(0.281691\pi\)
\(564\) 0 0
\(565\) −587.819 3333.69i −0.0437694 0.248229i
\(566\) 0 0
\(567\) −6753.45 1083.24i −0.500208 0.0802324i
\(568\) 0 0
\(569\) 1083.07 + 6142.40i 0.0797973 + 0.452553i 0.998358 + 0.0572742i \(0.0182409\pi\)
−0.918561 + 0.395279i \(0.870648\pi\)
\(570\) 0 0
\(571\) 4348.11 1582.58i 0.318674 0.115988i −0.177730 0.984079i \(-0.556876\pi\)
0.496404 + 0.868091i \(0.334653\pi\)
\(572\) 0 0
\(573\) 706.316 + 3128.60i 0.0514952 + 0.228096i
\(574\) 0 0
\(575\) 19836.7 + 34358.1i 1.43869 + 2.49188i
\(576\) 0 0
\(577\) −3232.20 + 5598.33i −0.233203 + 0.403920i −0.958749 0.284254i \(-0.908254\pi\)
0.725546 + 0.688174i \(0.241587\pi\)
\(578\) 0 0
\(579\) 9899.56 4145.52i 0.710555 0.297551i
\(580\) 0 0
\(581\) −2307.83 + 13088.4i −0.164793 + 0.934590i
\(582\) 0 0
\(583\) 7789.30 6536.00i 0.553344 0.464311i
\(584\) 0 0
\(585\) 5844.02 5935.25i 0.413027 0.419474i
\(586\) 0 0
\(587\) −1888.52 687.365i −0.132790 0.0483315i 0.274771 0.961510i \(-0.411398\pi\)
−0.407560 + 0.913178i \(0.633620\pi\)
\(588\) 0 0
\(589\) 1509.40 + 1266.54i 0.105592 + 0.0886023i
\(590\) 0 0
\(591\) −1687.34 2626.09i −0.117441 0.182780i
\(592\) 0 0
\(593\) −22078.4 −1.52892 −0.764460 0.644671i \(-0.776994\pi\)
−0.764460 + 0.644671i \(0.776994\pi\)
\(594\) 0 0
\(595\) −17240.4 −1.18788
\(596\) 0 0
\(597\) −8859.33 + 17180.7i −0.607350 + 1.17782i
\(598\) 0 0
\(599\) 512.637 + 430.153i 0.0349679 + 0.0293415i 0.660104 0.751174i \(-0.270512\pi\)
−0.625136 + 0.780516i \(0.714957\pi\)
\(600\) 0 0
\(601\) −25139.4 9150.01i −1.70626 0.621026i −0.709742 0.704462i \(-0.751188\pi\)
−0.996513 + 0.0834358i \(0.973411\pi\)
\(602\) 0 0
\(603\) 12.6488 158.725i 0.000854225 0.0107194i
\(604\) 0 0
\(605\) 35081.3 29436.7i 2.35745 1.97813i
\(606\) 0 0
\(607\) −768.770 + 4359.91i −0.0514059 + 0.291538i −0.999663 0.0259666i \(-0.991734\pi\)
0.948257 + 0.317504i \(0.102845\pi\)
\(608\) 0 0
\(609\) −891.322 + 6978.99i −0.0593074 + 0.464373i
\(610\) 0 0
\(611\) −2393.44 + 4145.57i −0.158475 + 0.274487i
\(612\) 0 0
\(613\) 12641.3 + 21895.3i 0.832915 + 1.44265i 0.895717 + 0.444624i \(0.146663\pi\)
−0.0628026 + 0.998026i \(0.520004\pi\)
\(614\) 0 0
\(615\) 14723.2 13596.6i 0.965359 0.891490i
\(616\) 0 0
\(617\) −5179.38 + 1885.14i −0.337948 + 0.123003i −0.505419 0.862874i \(-0.668662\pi\)
0.167471 + 0.985877i \(0.446440\pi\)
\(618\) 0 0
\(619\) 2252.52 + 12774.7i 0.146263 + 0.829497i 0.966345 + 0.257251i \(0.0828166\pi\)
−0.820082 + 0.572246i \(0.806072\pi\)
\(620\) 0 0
\(621\) 16630.3 8904.25i 1.07464 0.575387i
\(622\) 0 0
\(623\) −2226.74 12628.5i −0.143198 0.812117i
\(624\) 0 0
\(625\) −32468.9 + 11817.7i −2.07801 + 0.756334i
\(626\) 0 0
\(627\) 2250.84 + 700.115i 0.143365 + 0.0445931i
\(628\) 0 0
\(629\) −10135.7 17555.5i −0.642507 1.11285i
\(630\) 0 0
\(631\) 7534.06 13049.4i 0.475319 0.823276i −0.524282 0.851545i \(-0.675666\pi\)
0.999600 + 0.0282687i \(0.00899939\pi\)
\(632\) 0 0
\(633\) 6674.67 + 5080.71i 0.419106 + 0.319021i
\(634\) 0 0
\(635\) 5705.70 32358.6i 0.356573 2.02222i
\(636\) 0 0
\(637\) −2939.96 + 2466.92i −0.182866 + 0.153443i
\(638\) 0 0
\(639\) −4615.20 + 10100.8i −0.285719 + 0.625326i
\(640\) 0 0
\(641\) 859.168 + 312.712i 0.0529409 + 0.0192689i 0.368355 0.929685i \(-0.379921\pi\)
−0.315414 + 0.948954i \(0.602143\pi\)
\(642\) 0 0
\(643\) 15011.2 + 12595.9i 0.920657 + 0.772523i 0.974116 0.226047i \(-0.0725804\pi\)
−0.0534597 + 0.998570i \(0.517025\pi\)
\(644\) 0 0
\(645\) −6251.87 + 297.223i −0.381654 + 0.0181444i
\(646\) 0 0
\(647\) 13286.6 0.807339 0.403670 0.914905i \(-0.367735\pi\)
0.403670 + 0.914905i \(0.367735\pi\)
\(648\) 0 0
\(649\) 6438.08 0.389394
\(650\) 0 0
\(651\) 12629.8 600.438i 0.760369 0.0361490i
\(652\) 0 0
\(653\) 4349.80 + 3649.92i 0.260675 + 0.218733i 0.763753 0.645509i \(-0.223355\pi\)
−0.503078 + 0.864241i \(0.667799\pi\)
\(654\) 0 0
\(655\) 40721.6 + 14821.5i 2.42920 + 0.884156i
\(656\) 0 0
\(657\) 18873.1 + 26514.1i 1.12071 + 1.57445i
\(658\) 0 0
\(659\) −9412.25 + 7897.82i −0.556372 + 0.466852i −0.877092 0.480322i \(-0.840520\pi\)
0.320720 + 0.947174i \(0.396075\pi\)
\(660\) 0 0
\(661\) 1355.06 7684.91i 0.0797362 0.452206i −0.918633 0.395113i \(-0.870706\pi\)
0.998369 0.0570936i \(-0.0181833\pi\)
\(662\) 0 0
\(663\) −5579.68 4247.21i −0.326843 0.248790i
\(664\) 0 0
\(665\) −730.465 + 1265.20i −0.0425958 + 0.0737781i
\(666\) 0 0
\(667\) −9702.19 16804.7i −0.563224 0.975533i
\(668\) 0 0
\(669\) −17252.4 5366.29i −0.997034 0.310124i
\(670\) 0 0
\(671\) 19367.3 7049.10i 1.11425 0.405555i
\(672\) 0 0
\(673\) 4431.14 + 25130.2i 0.253800 + 1.43937i 0.799133 + 0.601154i \(0.205292\pi\)
−0.545333 + 0.838220i \(0.683597\pi\)
\(674\) 0 0
\(675\) 12905.7 + 39332.5i 0.735914 + 2.24283i
\(676\) 0 0
\(677\) −4224.47 23958.2i −0.239822 1.36010i −0.832216 0.554451i \(-0.812928\pi\)
0.592394 0.805648i \(-0.298183\pi\)
\(678\) 0 0
\(679\) 3388.23 1233.21i 0.191499 0.0697001i
\(680\) 0 0
\(681\) 2858.97 2640.20i 0.160875 0.148565i
\(682\) 0 0
\(683\) −12807.8 22183.8i −0.717535 1.24281i −0.961973 0.273143i \(-0.911937\pi\)
0.244438 0.969665i \(-0.421397\pi\)
\(684\) 0 0
\(685\) −10287.6 + 17818.7i −0.573825 + 0.993894i
\(686\) 0 0
\(687\) −2383.00 + 18658.7i −0.132339 + 1.03621i
\(688\) 0 0
\(689\) −445.099 + 2524.28i −0.0246109 + 0.139575i
\(690\) 0 0
\(691\) −7664.03 + 6430.89i −0.421930 + 0.354041i −0.828897 0.559402i \(-0.811031\pi\)
0.406967 + 0.913443i \(0.366586\pi\)
\(692\) 0 0
\(693\) 13659.2 6498.64i 0.748729 0.356224i
\(694\) 0 0
\(695\) −2894.31 1053.44i −0.157968 0.0574956i
\(696\) 0 0
\(697\) −12924.4 10844.9i −0.702365 0.589354i
\(698\) 0 0
\(699\) −9725.30 + 18860.1i −0.526244 + 1.02053i
\(700\) 0 0
\(701\) 18295.6 0.985758 0.492879 0.870098i \(-0.335945\pi\)
0.492879 + 0.870098i \(0.335945\pi\)
\(702\) 0 0
\(703\) −1717.78 −0.0921581
\(704\) 0 0
\(705\) −18307.9 28493.5i −0.978035 1.52217i
\(706\) 0 0
\(707\) −4486.75 3764.83i −0.238673 0.200270i
\(708\) 0 0
\(709\) 8676.97 + 3158.16i 0.459620 + 0.167288i 0.561445 0.827514i \(-0.310246\pi\)
−0.101824 + 0.994802i \(0.532468\pi\)
\(710\) 0 0
\(711\) 820.187 + 2968.81i 0.0432622 + 0.156595i
\(712\) 0 0
\(713\) −26713.7 + 22415.4i −1.40313 + 1.17737i
\(714\) 0 0
\(715\) −3198.74 + 18141.0i −0.167309 + 0.948858i
\(716\) 0 0
\(717\) 14125.8 5915.30i 0.735759 0.308105i
\(718\) 0 0
\(719\) 8925.75 15459.9i 0.462968 0.801885i −0.536139 0.844130i \(-0.680118\pi\)
0.999107 + 0.0422449i \(0.0134510\pi\)
\(720\) 0 0
\(721\) −4905.71 8496.93i −0.253395 0.438894i
\(722\) 0 0
\(723\) −114.460 506.997i −0.00588771 0.0260794i
\(724\) 0 0
\(725\) 40013.4 14563.7i 2.04974 0.746044i
\(726\) 0 0
\(727\) −1140.17 6466.24i −0.0581660 0.329876i 0.941814 0.336133i \(-0.109119\pi\)
−0.999980 + 0.00625749i \(0.998008\pi\)
\(728\) 0 0
\(729\) 18888.8 5534.66i 0.959652 0.281190i
\(730\) 0 0
\(731\) 914.977 + 5189.09i 0.0462950 + 0.262552i
\(732\) 0 0
\(733\) −11643.6 + 4237.94i −0.586723 + 0.213550i −0.618287 0.785952i \(-0.712173\pi\)
0.0315647 + 0.999502i \(0.489951\pi\)
\(734\) 0 0
\(735\) −5979.73 26487.0i −0.300089 1.32923i
\(736\) 0 0
\(737\) 176.069 + 304.961i 0.00879998 + 0.0152420i
\(738\) 0 0
\(739\) −14098.2 + 24418.8i −0.701773 + 1.21551i 0.266070 + 0.963954i \(0.414275\pi\)
−0.967843 + 0.251554i \(0.919059\pi\)
\(740\) 0 0
\(741\) −548.093 + 229.518i −0.0271723 + 0.0113786i
\(742\) 0 0
\(743\) −4020.09 + 22799.1i −0.198497 + 1.12573i 0.708854 + 0.705355i \(0.249213\pi\)
−0.907351 + 0.420375i \(0.861899\pi\)
\(744\) 0 0
\(745\) −31920.7 + 26784.6i −1.56978 + 1.31720i
\(746\) 0 0
\(747\) −10184.6 36864.8i −0.498840 1.80564i
\(748\) 0 0
\(749\) −1933.83 703.855i −0.0943398 0.0343369i
\(750\) 0 0
\(751\) −16955.6 14227.4i −0.823859 0.691300i 0.130013 0.991512i \(-0.458498\pi\)
−0.953872 + 0.300212i \(0.902942\pi\)
\(752\) 0 0
\(753\) 12611.0 + 19627.2i 0.610319 + 0.949872i
\(754\) 0 0
\(755\) −26712.2 −1.28762
\(756\) 0 0
\(757\) 22131.8 1.06261 0.531303 0.847182i \(-0.321703\pi\)
0.531303 + 0.847182i \(0.321703\pi\)
\(758\) 0 0
\(759\) −19119.9 + 37078.9i −0.914374 + 1.77323i
\(760\) 0 0
\(761\) 29295.5 + 24581.8i 1.39548 + 1.17095i 0.963064 + 0.269274i \(0.0867837\pi\)
0.432417 + 0.901674i \(0.357661\pi\)
\(762\) 0 0
\(763\) 18223.1 + 6632.68i 0.864642 + 0.314704i
\(764\) 0 0
\(765\) 44801.0 21315.0i 2.11737 1.00738i
\(766\) 0 0
\(767\) −1243.23 + 1043.20i −0.0585274 + 0.0491103i
\(768\) 0 0
\(769\) 7186.45 40756.4i 0.336996 1.91120i −0.0695665 0.997577i \(-0.522162\pi\)
0.406563 0.913623i \(-0.366727\pi\)
\(770\) 0 0
\(771\) −2037.15 + 15950.8i −0.0951573 + 0.745076i
\(772\) 0 0
\(773\) −11033.1 + 19110.0i −0.513370 + 0.889182i 0.486510 + 0.873675i \(0.338270\pi\)
−0.999880 + 0.0155073i \(0.995064\pi\)
\(774\) 0 0
\(775\) −38262.2 66272.1i −1.77344 3.07169i
\(776\) 0 0
\(777\) −8098.15 + 7478.48i −0.373899 + 0.345288i
\(778\) 0 0
\(779\) −1343.46 + 488.981i −0.0617903 + 0.0224898i
\(780\) 0 0
\(781\) −4264.73 24186.5i −0.195396 1.10814i
\(782\) 0