Properties

Label 108.4.i.a.25.9
Level 108
Weight 4
Character 108.25
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 25.9
Character \(\chi\) \(=\) 108.25
Dual form 108.4.i.a.13.9

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

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 0.445122 0.895470i \(-0.353160\pi\)
0.959160 0.282863i \(-0.0912840\pi\)
\(6\) 0 0
\(7\) −8.81657 + 3.20897i −0.476050 + 0.173268i −0.568891 0.822413i \(-0.692627\pi\)
0.0928410 + 0.995681i \(0.470405\pi\)
\(8\) 0 0
\(9\) 26.8782 + 2.56145i 0.995490 + 0.0948684i
\(10\) 0 0
\(11\) −45.7414 38.3816i −1.25378 1.05204i −0.996316 0.0857561i \(-0.972669\pi\)
−0.257462 0.966288i \(-0.582886\pi\)
\(12\) 0 0
\(13\) 2.61377 + 14.8234i 0.0557638 + 0.316252i 0.999912 0.0132689i \(-0.00422374\pi\)
−0.944148 + 0.329521i \(0.893113\pi\)
\(14\) 0 0
\(15\) 84.7402 64.5036i 1.45865 1.11032i
\(16\) 0 0
\(17\) 44.8278 + 77.6441i 0.639550 + 1.10773i 0.985532 + 0.169491i \(0.0542124\pi\)
−0.345982 + 0.938241i \(0.612454\pi\)
\(18\) 0 0
\(19\) −3.79866 + 6.57947i −0.0458669 + 0.0794439i −0.888047 0.459752i \(-0.847938\pi\)
0.842180 + 0.539196i \(0.181272\pi\)
\(20\) 0 0
\(21\) −46.5524 + 14.4800i −0.483741 + 0.150466i
\(22\) 0 0
\(23\) 126.350 + 45.9876i 1.14547 + 0.416917i 0.843886 0.536523i \(-0.180262\pi\)
0.301584 + 0.953440i \(0.402485\pi\)
\(24\) 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 0.793151 + 0.609026i \(0.208439\pi\)
−0.953617 + 0.301023i \(0.902672\pi\)
\(30\) 0 0
\(31\) −243.712 88.7037i −1.41200 0.513925i −0.480281 0.877115i \(-0.659465\pi\)
−0.931715 + 0.363190i \(0.881688\pi\)
\(32\) 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 0.999996 + 0.00267179i \(0.000850458\pi\)
−0.497684 + 0.867358i \(0.665816\pi\)
\(38\) 0 0
\(39\) 9.90850 + 77.5829i 0.0406828 + 0.318544i
\(40\) 0 0
\(41\) 32.6776 + 185.324i 0.124473 + 0.705921i 0.981620 + 0.190848i \(0.0611238\pi\)
−0.857147 + 0.515072i \(0.827765\pi\)
\(42\) 0 0
\(43\) −45.0211 37.7772i −0.159667 0.133976i 0.559454 0.828861i \(-0.311011\pi\)
−0.719121 + 0.694885i \(0.755455\pi\)
\(44\) 0 0
\(45\) 455.743 313.882i 1.50974 1.03980i
\(46\) 0 0
\(47\) −298.842 + 108.770i −0.927459 + 0.337568i −0.761202 0.648515i \(-0.775390\pi\)
−0.166257 + 0.986082i \(0.553168\pi\)
\(48\) 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 −0.729350 0.684140i \(-0.760178\pi\)
0.547096 + 0.837070i \(0.315733\pi\)
\(60\) 0 0
\(61\) −324.349 + 118.053i −0.680797 + 0.247790i −0.659190 0.751977i \(-0.729101\pi\)
−0.0216072 + 0.999767i \(0.506878\pi\)
\(62\) 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 0.985727 0.168351i \(-0.0538441\pi\)
−0.983860 + 0.178941i \(0.942733\pi\)
\(68\) 0 0
\(69\) 644.446 + 269.867i 1.12438 + 0.470842i
\(70\) 0 0
\(71\) −205.653 356.202i −0.343754 0.595400i 0.641372 0.767230i \(-0.278365\pi\)
−0.985127 + 0.171830i \(0.945032\pi\)
\(72\) 0 0
\(73\) 602.689 1043.89i 0.966294 1.67367i 0.260196 0.965556i \(-0.416213\pi\)
0.706098 0.708115i \(-0.250454\pi\)
\(74\) 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 −0.967448 0.253071i \(-0.918559\pi\)
0.995659 + 0.0930777i \(0.0296705\pi\)
\(80\) 0 0
\(81\) 715.878 + 137.694i 0.982000 + 0.188881i
\(82\) 0 0
\(83\) −245.975 + 1394.99i −0.325292 + 1.84482i 0.182324 + 0.983238i \(0.441638\pi\)
−0.507616 + 0.861583i \(0.669473\pi\)
\(84\) 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 −0.0962172 0.995360i \(-0.530674\pi\)
0.910116 0.414354i \(-0.135992\pi\)
\(90\) 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 0.475574 0.879676i \(-0.342240\pi\)
−0.783729 + 0.621103i \(0.786685\pi\)
\(98\) 0 0
\(99\) −1131.14 1148.79i −1.14832 1.16624i
\(100\) 0 0
\(101\) 586.611 213.509i 0.577920 0.210346i −0.0364880 0.999334i \(-0.511617\pi\)
0.614408 + 0.788988i \(0.289395\pi\)
\(102\) 0 0
\(103\) 801.072 672.179i 0.766330 0.643027i −0.173436 0.984845i \(-0.555487\pi\)
0.939766 + 0.341818i \(0.111043\pi\)
\(104\) 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 −0.693932 0.720041i \(-0.744123\pi\)
0.588601 + 0.808423i \(0.299679\pi\)
\(114\) 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 0.437413 + 0.899261i \(0.355895\pi\)
−0.997489 + 0.0708201i \(0.977438\pi\)
\(128\) 0 0
\(129\) −224.351 207.184i −0.153124 0.141407i
\(130\) 0 0
\(131\) 1986.87 + 723.162i 1.32514 + 0.482313i 0.905103 0.425193i \(-0.139794\pi\)
0.420040 + 0.907505i \(0.362016\pi\)
\(132\) 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 −0.880960 0.473191i \(-0.843102\pi\)
0.989672 0.143348i \(-0.0457868\pi\)
\(138\) 0 0
\(139\) −141.218 51.3992i −0.0861724 0.0313642i 0.298574 0.954386i \(-0.403489\pi\)
−0.384747 + 0.923022i \(0.625711\pi\)
\(140\) 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 −0.913677 0.406441i \(-0.866770\pi\)
0.719565 0.694426i \(-0.244341\pi\)
\(150\) 0 0
\(151\) −998.407 837.763i −0.538074 0.451498i 0.332804 0.942996i \(-0.392005\pi\)
−0.870879 + 0.491498i \(0.836450\pi\)
\(152\) 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 −0.938482 0.345328i \(-0.887768\pi\)
0.177116 + 0.984190i \(0.443323\pi\)
\(158\) 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 −0.0756896 0.997131i \(-0.524116\pi\)
0.968839 + 0.247690i \(0.0796714\pi\)
\(168\) 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 0.546627 0.837376i \(-0.315912\pi\)
−0.729734 + 0.683731i \(0.760356\pi\)
\(174\) 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 0.989255 + 0.146197i \(0.0467034\pi\)
−0.368017 + 0.929819i \(0.619963\pi\)
\(180\) 0 0
\(181\) −6.47319 + 11.2119i −0.00265828 + 0.00460427i −0.867351 0.497696i \(-0.834179\pi\)
0.864693 + 0.502300i \(0.167513\pi\)
\(182\) 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 −0.957751 0.287599i \(-0.907143\pi\)
0.998356 + 0.0573151i \(0.0182540\pi\)
\(192\) 0 0
\(193\) 1940.91 + 706.433i 0.723884 + 0.263472i 0.677574 0.735455i \(-0.263032\pi\)
0.0463102 + 0.998927i \(0.485254\pi\)
\(194\) 0 0
\(195\) 1177.66 + 1087.54i 0.432481 + 0.399387i
\(196\) 0 0
\(197\) −300.362 + 520.241i −0.108629 + 0.188151i −0.915215 0.402966i \(-0.867979\pi\)
0.806586 + 0.591116i \(0.201313\pi\)
\(198\) 0 0
\(199\) −1860.07 3221.74i −0.662597 1.14765i −0.979931 0.199338i \(-0.936121\pi\)
0.317333 0.948314i \(-0.397213\pi\)
\(200\) 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 −0.418355 0.908284i \(-0.637393\pi\)
0.821838 + 0.569721i \(0.192949\pi\)
\(212\) 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 −0.782299 0.622902i \(-0.785953\pi\)
−0.198882 + 0.980023i \(0.563731\pi\)
\(224\) 0 0
\(225\) 2121.45 7678.95i 0.628576 2.27524i
\(226\) 0 0
\(227\) 573.716 + 481.405i 0.167748 + 0.140758i 0.722797 0.691060i \(-0.242856\pi\)
−0.555049 + 0.831818i \(0.687300\pi\)
\(228\) 0 0
\(229\) −628.614 3565.05i −0.181397 1.02875i −0.930498 0.366298i \(-0.880625\pi\)
0.749100 0.662457i \(-0.230486\pi\)
\(230\) 0 0
\(231\) 2685.14 + 1124.42i 0.764801 + 0.320266i
\(232\) 0 0
\(233\) −2041.89 3536.65i −0.574113 0.994393i −0.996137 0.0878086i \(-0.972014\pi\)
0.422024 0.906585i \(-0.361320\pi\)
\(234\) 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 0.688421 0.725312i \(-0.258304\pi\)
0.0611393 + 0.998129i \(0.480527\pi\)
\(240\) 0 0
\(241\) −17.3695 + 98.5075i −0.00464261 + 0.0263296i −0.987041 0.160468i \(-0.948700\pi\)
0.982398 + 0.186797i \(0.0598108\pi\)
\(242\) 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 −0.432570 0.901600i \(-0.642393\pi\)
0.997094 0.0761832i \(-0.0242734\pi\)
\(252\) 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 −0.977932 0.208922i \(-0.933005\pi\)
0.847500 0.530795i \(-0.178107\pi\)
\(258\) 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 0.326125 0.945327i \(-0.394257\pi\)
0.857471 + 0.514533i \(0.172035\pi\)
\(264\) 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 −0.606523 0.795066i \(-0.707436\pi\)
0.0464347 + 0.998921i \(0.485214\pi\)
\(278\) 0 0
\(279\) −6323.32 3008.45i −1.35687 0.645561i
\(280\) 0 0
\(281\) 3848.57 + 3229.33i 0.817034 + 0.685573i 0.952275 0.305240i \(-0.0987367\pi\)
−0.135242 + 0.990813i \(0.543181\pi\)
\(282\) 0 0
\(283\) 63.6653 + 361.064i 0.0133728 + 0.0758411i 0.990764 0.135599i \(-0.0432958\pi\)
−0.977391 + 0.211440i \(0.932185\pi\)
\(284\) 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 0.229913 0.973211i \(-0.426156\pi\)
−0.449445 + 0.893308i \(0.648378\pi\)
\(294\) 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 −0.930166 0.367139i \(-0.880337\pi\)
0.147132 0.989117i \(-0.452996\pi\)
\(308\) 0 0
\(309\) 4323.66 3291.14i 0.796001 0.605910i
\(310\) 0 0
\(311\) 1088.82 + 6175.03i 0.198526 + 1.12590i 0.907307 + 0.420468i \(0.138134\pi\)
−0.708781 + 0.705428i \(0.750755\pi\)
\(312\) 0 0
\(313\) −1561.71 1310.43i −0.282022 0.236645i 0.490792 0.871277i \(-0.336707\pi\)
−0.772815 + 0.634632i \(0.781152\pi\)
\(314\) 0 0
\(315\) −3010.85 + 4229.83i −0.538546 + 0.756584i
\(316\) 0 0
\(317\) −4935.72 + 1796.45i −0.874503 + 0.318293i −0.739989 0.672619i \(-0.765170\pi\)
−0.134514 + 0.990912i \(0.542947\pi\)
\(318\) 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 −0.739914 0.672702i \(-0.765134\pi\)
−0.134403 + 0.990927i \(0.542912\pi\)
\(332\) 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 −0.903777 0.428004i \(-0.859217\pi\)
0.702886 0.711302i \(-0.251894\pi\)
\(338\) 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 0.798237 0.602343i \(-0.205766\pi\)
0.224307 + 0.974519i \(0.427988\pi\)
\(348\) 0 0
\(349\) −2117.69 + 12010.0i −0.324806 + 1.84207i 0.186226 + 0.982507i \(0.440374\pi\)
−0.511032 + 0.859562i \(0.670737\pi\)
\(350\) 0 0
\(351\) 67.5982 + 2110.67i 0.0102796 + 0.320967i
\(352\) 0 0
\(353\) 1121.15 6358.37i 0.169045 0.958702i −0.775750 0.631040i \(-0.782628\pi\)
0.944795 0.327662i \(-0.106261\pi\)
\(354\) 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 −0.995664 0.0930261i \(-0.970346\pi\)
0.578395 + 0.815757i \(0.303679\pi\)
\(360\) 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 0.196457 0.980512i \(-0.437056\pi\)
−0.931502 + 0.363737i \(0.881501\pi\)
\(368\) 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 −0.972506 0.232879i \(-0.925185\pi\)
0.0604669 + 0.998170i \(0.480741\pi\)
\(374\) 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 −0.999532 0.0305975i \(-0.990259\pi\)
−0.143434 + 0.989660i \(0.545815\pi\)
\(384\) 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 −0.00824146 0.999966i \(-0.502623\pi\)
−0.986205 + 0.165526i \(0.947068\pi\)
\(390\) 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 −0.738610 0.674133i \(-0.764517\pi\)
0.953121 + 0.302588i \(0.0978508\pi\)
\(398\) 0 0
\(399\) 81.5662 361.294i 0.0102341 0.0453317i
\(400\) 0 0
\(401\) 4357.03 + 1585.83i 0.542593 + 0.197488i 0.598752 0.800934i \(-0.295663\pi\)
−0.0561597 + 0.998422i \(0.517886\pi\)
\(402\) 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 −0.591495 0.806309i \(-0.701462\pi\)
−0.971397 + 0.237463i \(0.923684\pi\)
\(410\) 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 −0.778722 0.627369i \(-0.784132\pi\)
0.517186 0.855873i \(-0.326979\pi\)
\(420\) 0 0
\(421\) 9277.02 + 7784.35i 1.07395 + 0.901154i 0.995405 0.0957563i \(-0.0305270\pi\)
0.0785486 + 0.996910i \(0.474971\pi\)
\(422\) 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 −0.0640794 0.997945i \(-0.520411\pi\)
0.592379 + 0.805659i \(0.298189\pi\)
\(440\) 0 0
\(441\) −5669.62 + 3904.83i −0.612204 + 0.421642i
\(442\) 0 0
\(443\) −4319.54 3624.52i −0.463267 0.388728i 0.381064 0.924549i \(-0.375558\pi\)
−0.844332 + 0.535821i \(0.820002\pi\)
\(444\) 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 0.944570 0.328309i \(-0.106479\pi\)
−0.756609 + 0.653867i \(0.773146\pi\)
\(450\) 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 0.888750 + 0.458391i \(0.151574\pi\)
−0.991931 + 0.126776i \(0.959537\pi\)
\(458\) 0 0
\(459\) 4678.20 + 11676.0i 0.475729 + 1.18734i
\(460\) 0 0
\(461\) −1782.29 + 10107.9i −0.180065 + 1.02120i 0.752070 + 0.659084i \(0.229056\pi\)
−0.932134 + 0.362113i \(0.882055\pi\)
\(462\) 0 0
\(463\) 4506.47 + 1640.22i 0.452340 + 0.164638i 0.558136 0.829750i \(-0.311517\pi\)
−0.105796 + 0.994388i \(0.533739\pi\)
\(464\) 0 0
\(465\) −26373.9 + 8203.50i −2.63023 + 0.818125i
\(466\) 0 0
\(467\) −517.986 + 897.177i −0.0513266 + 0.0889003i −0.890547 0.454891i \(-0.849678\pi\)
0.839221 + 0.543791i \(0.183012\pi\)
\(468\) 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 −0.665963 0.745985i \(-0.731979\pi\)
−0.0306475 + 0.999530i \(0.509757\pi\)
\(480\) 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 −0.710796 0.703398i \(-0.751665\pi\)
0.569283 + 0.822141i \(0.307221\pi\)
\(492\) 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 0.959592 + 0.281395i \(0.0907972\pi\)
−0.805479 + 0.592625i \(0.798092\pi\)
\(500\) 0 0
\(501\) 10403.5 7919.06i 0.927731 0.706182i
\(502\) 0 0
\(503\) 3388.43 + 5868.93i 0.300363 + 0.520244i 0.976218 0.216791i \(-0.0695589\pi\)
−0.675855 + 0.737034i \(0.736226\pi\)
\(504\) 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 0.281076 0.959686i \(-0.409309\pi\)
−0.401557 + 0.915834i \(0.631531\pi\)
\(510\) 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 0.418605 + 0.908168i \(0.362519\pi\)
−0.995799 + 0.0915615i \(0.970814\pi\)
\(522\) 0 0
\(523\) 2877.17 + 4983.40i 0.240554 + 0.416652i 0.960872 0.276992i \(-0.0893376\pi\)
−0.720318 + 0.693644i \(0.756004\pi\)
\(524\) 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 −0.937154 0.348916i \(-0.886550\pi\)
−0.493623 + 0.869676i \(0.664328\pi\)
\(548\) 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 0.734469 0.678642i \(-0.237431\pi\)
−0.954956 + 0.296748i \(0.904098\pi\)
\(558\) 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 0.633321 0.773889i \(-0.281691\pi\)
−0.0122940 + 0.999924i \(0.503913\pi\)
\(564\) 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 −0.918561 0.395279i \(-0.870648\pi\)
0.998358 0.0572742i \(-0.0182409\pi\)
\(570\) 0 0
\(571\) 4348.11 + 1582.58i 0.318674 + 0.115988i 0.496404 0.868091i \(-0.334653\pi\)
−0.177730 + 0.984079i \(0.556876\pi\)
\(572\) 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 0.725546 0.688174i \(-0.241587\pi\)
−0.958749 + 0.284254i \(0.908254\pi\)
\(578\) 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 −0.407560 0.913178i \(-0.633620\pi\)
0.274771 + 0.961510i \(0.411398\pi\)
\(588\) 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 −0.625136 0.780516i \(-0.714957\pi\)
0.660104 + 0.751174i \(0.270512\pi\)
\(600\) 0 0
\(601\) −25139.4 + 9150.01i −1.70626 + 0.621026i −0.996513 0.0834358i \(-0.973411\pi\)
−0.709742 + 0.704462i \(0.751188\pi\)
\(602\) 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 0.948257 0.317504i \(-0.102845\pi\)
−0.999663 + 0.0259666i \(0.991734\pi\)
\(608\) 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 −0.0628026 0.998026i \(-0.520004\pi\)
0.895717 0.444624i \(-0.146663\pi\)
\(614\) 0 0
\(615\) 14723.2 + 13596.6i 0.965359 + 0.891490i
\(616\) 0 0
\(617\) −5179.38 1885.14i −0.337948 0.123003i 0.167471 0.985877i \(-0.446440\pi\)
−0.505419 + 0.862874i \(0.668662\pi\)
\(618\) 0 0
\(619\) 2252.52 12774.7i 0.146263 0.829497i −0.820082 0.572246i \(-0.806072\pi\)
0.966345 0.257251i \(-0.0828166\pi\)
\(620\) 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 0.999600 0.0282687i \(-0.00899939\pi\)
−0.524282 + 0.851545i \(0.675666\pi\)
\(632\) 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 −0.315414 0.948954i \(-0.602143\pi\)
0.368355 + 0.929685i \(0.379921\pi\)
\(642\) 0 0
\(643\) 15011.2 12595.9i 0.920657 0.772523i −0.0534597 0.998570i \(-0.517025\pi\)
0.974116 + 0.226047i \(0.0725804\pi\)
\(644\) 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 −0.503078 0.864241i \(-0.667799\pi\)
0.763753 + 0.645509i \(0.223355\pi\)
\(654\) 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 0.320720 0.947174i \(-0.396075\pi\)
−0.877092 + 0.480322i \(0.840520\pi\)
\(660\) 0 0
\(661\) 1355.06 + 7684.91i 0.0797362 + 0.452206i 0.998369 + 0.0570936i \(0.0181833\pi\)
−0.918633 + 0.395113i \(0.870706\pi\)
\(662\) 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 −0.545333 0.838220i \(-0.683597\pi\)
0.799133 0.601154i \(-0.205292\pi\)
\(674\) 0 0
\(675\) 12905.7 39332.5i 0.735914 2.24283i
\(676\) 0 0
\(677\) −4224.47 + 23958.2i −0.239822 + 1.36010i 0.592394 + 0.805648i \(0.298183\pi\)
−0.832216 + 0.554451i \(0.812928\pi\)
\(678\) 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 0.244438 + 0.969665i \(0.421397\pi\)
−0.961973 + 0.273143i \(0.911937\pi\)
\(684\) 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 0.406967 0.913443i \(-0.366586\pi\)
−0.828897 + 0.559402i \(0.811031\pi\)
\(692\) 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 −0.101824 0.994802i \(-0.532468\pi\)
0.561445 + 0.827514i \(0.310246\pi\)
\(710\) 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 0.999107 0.0422449i \(-0.0134510\pi\)
−0.536139 + 0.844130i \(0.680118\pi\)
\(720\) 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 −0.999980 0.00625749i \(-0.998008\pi\)
0.941814 + 0.336133i \(0.109119\pi\)
\(728\) 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 0.0315647 0.999502i \(-0.489951\pi\)
−0.618287 + 0.785952i \(0.712173\pi\)
\(734\) 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 −0.967843 0.251554i \(-0.919059\pi\)
0.266070 0.963954i \(-0.414275\pi\)
\(740\) 0 0
\(741\) −548.093 229.518i −0.0271723 0.0113786i
\(742\) 0 0
\(743\) −4020.09 22799.1i −0.198497 1.12573i −0.907351 0.420375i \(-0.861899\pi\)
0.708854 0.705355i \(-0.249213\pi\)
\(744\) 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 −0.953872 0.300212i \(-0.902942\pi\)
0.130013 + 0.991512i \(0.458498\pi\)
\(752\) 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 0.432417 0.901674i \(-0.357661\pi\)
0.963064 0.269274i \(-0.0867837\pi\)
\(762\) 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 0.406563 + 0.913623i \(0.366727\pi\)
−0.0695665 + 0.997577i \(0.522162\pi\)
\(770\) 0 0
\(771\) −2037.15 15950.8i −0.0951573 0.745076i
\(772\) 0 0
\(773\) −11033.1 19110.0i −0.513370 0.889182i −0.999880 0.0155073i \(-0.995064\pi\)
0.486510 0.873675i \(-0.338270\pi\)
\(774\) 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