Properties

Label 108.4.h.b.35.11
Level 108
Weight 4
Character 108.35
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.11
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.11

$q$-expansion

\(f(q)\) \(=\) \(q+(2.52436 - 1.27578i) q^{2} +(4.74478 - 6.44105i) q^{4} +(1.23846 - 0.715028i) q^{5} +(23.8818 + 13.7882i) q^{7} +(3.76017 - 22.3128i) q^{8} +O(q^{10})\) \(q+(2.52436 - 1.27578i) q^{2} +(4.74478 - 6.44105i) q^{4} +(1.23846 - 0.715028i) q^{5} +(23.8818 + 13.7882i) q^{7} +(3.76017 - 22.3128i) q^{8} +(2.21411 - 3.38499i) q^{10} +(11.1087 - 19.2409i) q^{11} +(-34.5965 - 59.9229i) q^{13} +(77.8769 + 4.33838i) q^{14} +(-18.9742 - 61.1227i) q^{16} +31.4507i q^{17} +11.4986i q^{19} +(1.27071 - 11.3697i) q^{20} +(3.49531 - 62.7433i) q^{22} +(72.6810 + 125.887i) q^{23} +(-61.4775 + 106.482i) q^{25} +(-163.782 - 107.129i) q^{26} +(202.124 - 88.4021i) q^{28} +(93.6986 + 54.0969i) q^{29} +(-102.800 + 59.3514i) q^{31} +(-125.877 - 130.089i) q^{32} +(40.1242 + 79.3929i) q^{34} +39.4357 q^{35} -300.439 q^{37} +(14.6696 + 29.0265i) q^{38} +(-11.2974 - 30.3222i) q^{40} +(-344.853 + 199.101i) q^{41} +(173.261 + 100.032i) q^{43} +(-71.2231 - 162.846i) q^{44} +(344.077 + 225.060i) q^{46} +(151.770 - 262.873i) q^{47} +(208.727 + 361.526i) q^{49} +(-19.3436 + 347.231i) q^{50} +(-550.119 - 61.4831i) q^{52} +243.342i q^{53} -31.7722i q^{55} +(397.452 - 481.024i) q^{56} +(305.545 + 17.0213i) q^{58} +(41.9197 + 72.6070i) q^{59} +(199.218 - 345.055i) q^{61} +(-183.784 + 280.974i) q^{62} +(-483.722 - 167.800i) q^{64} +(-85.6931 - 49.4749i) q^{65} +(-307.763 + 177.687i) q^{67} +(202.576 + 149.227i) q^{68} +(99.5499 - 50.3112i) q^{70} -866.235 q^{71} +64.6645 q^{73} +(-758.415 + 383.293i) q^{74} +(74.0629 + 54.5582i) q^{76} +(530.594 - 306.338i) q^{77} +(354.896 + 204.899i) q^{79} +(-67.2033 - 62.1312i) q^{80} +(-616.524 + 942.559i) q^{82} +(-79.8990 + 138.389i) q^{83} +(22.4881 + 38.9506i) q^{85} +(564.993 + 31.4747i) q^{86} +(-387.548 - 320.216i) q^{88} -1493.47i q^{89} -1908.09i q^{91} +(1155.70 + 129.165i) q^{92} +(47.7536 - 857.209i) q^{94} +(8.22181 + 14.2406i) q^{95} +(700.115 - 1212.63i) q^{97} +(988.129 + 646.332i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52436 1.27578i 0.892496 0.451056i
\(3\) 0 0
\(4\) 4.74478 6.44105i 0.593097 0.805131i
\(5\) 1.23846 0.715028i 0.110772 0.0639540i −0.443591 0.896230i \(-0.646296\pi\)
0.554362 + 0.832275i \(0.312962\pi\)
\(6\) 0 0
\(7\) 23.8818 + 13.7882i 1.28950 + 0.744491i 0.978564 0.205941i \(-0.0660255\pi\)
0.310932 + 0.950432i \(0.399359\pi\)
\(8\) 3.76017 22.3128i 0.166177 0.986096i
\(9\) 0 0
\(10\) 2.21411 3.38499i 0.0700164 0.107043i
\(11\) 11.1087 19.2409i 0.304492 0.527396i −0.672656 0.739955i \(-0.734847\pi\)
0.977148 + 0.212560i \(0.0681800\pi\)
\(12\) 0 0
\(13\) −34.5965 59.9229i −0.738103 1.27843i −0.953348 0.301872i \(-0.902388\pi\)
0.215245 0.976560i \(-0.430945\pi\)
\(14\) 77.8769 + 4.33838i 1.48668 + 0.0828201i
\(15\) 0 0
\(16\) −18.9742 61.1227i −0.296472 0.955042i
\(17\) 31.4507i 0.448701i 0.974509 + 0.224351i \(0.0720261\pi\)
−0.974509 + 0.224351i \(0.927974\pi\)
\(18\) 0 0
\(19\) 11.4986i 0.138840i 0.997588 + 0.0694199i \(0.0221148\pi\)
−0.997588 + 0.0694199i \(0.977885\pi\)
\(20\) 1.27071 11.3697i 0.0142070 0.127117i
\(21\) 0 0
\(22\) 3.49531 62.7433i 0.0338729 0.608041i
\(23\) 72.6810 + 125.887i 0.658914 + 1.14127i 0.980897 + 0.194528i \(0.0623174\pi\)
−0.321983 + 0.946746i \(0.604349\pi\)
\(24\) 0 0
\(25\) −61.4775 + 106.482i −0.491820 + 0.851857i
\(26\) −163.782 107.129i −1.23540 0.808070i
\(27\) 0 0
\(28\) 202.124 88.4021i 1.36421 0.596658i
\(29\) 93.6986 + 54.0969i 0.599979 + 0.346398i 0.769033 0.639209i \(-0.220738\pi\)
−0.169054 + 0.985607i \(0.554071\pi\)
\(30\) 0 0
\(31\) −102.800 + 59.3514i −0.595592 + 0.343865i −0.767306 0.641282i \(-0.778403\pi\)
0.171713 + 0.985147i \(0.445070\pi\)
\(32\) −125.877 130.089i −0.695377 0.718645i
\(33\) 0 0
\(34\) 40.1242 + 79.3929i 0.202389 + 0.400464i
\(35\) 39.4357 0.190453
\(36\) 0 0
\(37\) −300.439 −1.33491 −0.667457 0.744649i \(-0.732617\pi\)
−0.667457 + 0.744649i \(0.732617\pi\)
\(38\) 14.6696 + 29.0265i 0.0626245 + 0.123914i
\(39\) 0 0
\(40\) −11.2974 30.3222i −0.0446571 0.119859i
\(41\) −344.853 + 199.101i −1.31359 + 0.758399i −0.982688 0.185268i \(-0.940685\pi\)
−0.330897 + 0.943667i \(0.607351\pi\)
\(42\) 0 0
\(43\) 173.261 + 100.032i 0.614467 + 0.354763i 0.774712 0.632315i \(-0.217895\pi\)
−0.160245 + 0.987077i \(0.551228\pi\)
\(44\) −71.2231 162.846i −0.244029 0.557953i
\(45\) 0 0
\(46\) 344.077 + 225.060i 1.10286 + 0.721374i
\(47\) 151.770 262.873i 0.471018 0.815828i −0.528432 0.848976i \(-0.677220\pi\)
0.999450 + 0.0331478i \(0.0105532\pi\)
\(48\) 0 0
\(49\) 208.727 + 361.526i 0.608534 + 1.05401i
\(50\) −19.3436 + 347.231i −0.0547119 + 0.982117i
\(51\) 0 0
\(52\) −550.119 61.4831i −1.46707 0.163965i
\(53\) 243.342i 0.630673i 0.948980 + 0.315336i \(0.102117\pi\)
−0.948980 + 0.315336i \(0.897883\pi\)
\(54\) 0 0
\(55\) 31.7722i 0.0778940i
\(56\) 397.452 481.024i 0.948425 1.14785i
\(57\) 0 0
\(58\) 305.545 + 17.0213i 0.691724 + 0.0385347i
\(59\) 41.9197 + 72.6070i 0.0924996 + 0.160214i 0.908562 0.417749i \(-0.137181\pi\)
−0.816063 + 0.577963i \(0.803848\pi\)
\(60\) 0 0
\(61\) 199.218 345.055i 0.418151 0.724259i −0.577602 0.816318i \(-0.696012\pi\)
0.995754 + 0.0920592i \(0.0293449\pi\)
\(62\) −183.784 + 280.974i −0.376461 + 0.575544i
\(63\) 0 0
\(64\) −483.722 167.800i −0.944770 0.327734i
\(65\) −85.6931 49.4749i −0.163522 0.0944094i
\(66\) 0 0
\(67\) −307.763 + 177.687i −0.561183 + 0.323999i −0.753620 0.657310i \(-0.771694\pi\)
0.192437 + 0.981309i \(0.438361\pi\)
\(68\) 202.576 + 149.227i 0.361263 + 0.266123i
\(69\) 0 0
\(70\) 99.5499 50.3112i 0.169978 0.0859049i
\(71\) −866.235 −1.44793 −0.723966 0.689836i \(-0.757683\pi\)
−0.723966 + 0.689836i \(0.757683\pi\)
\(72\) 0 0
\(73\) 64.6645 0.103677 0.0518384 0.998655i \(-0.483492\pi\)
0.0518384 + 0.998655i \(0.483492\pi\)
\(74\) −758.415 + 383.293i −1.19140 + 0.602121i
\(75\) 0 0
\(76\) 74.0629 + 54.5582i 0.111784 + 0.0823455i
\(77\) 530.594 306.338i 0.785283 0.453383i
\(78\) 0 0
\(79\) 354.896 + 204.899i 0.505429 + 0.291809i 0.730953 0.682428i \(-0.239076\pi\)
−0.225524 + 0.974238i \(0.572409\pi\)
\(80\) −67.2033 62.1312i −0.0939194 0.0868310i
\(81\) 0 0
\(82\) −616.524 + 942.559i −0.830289 + 1.26937i
\(83\) −79.8990 + 138.389i −0.105663 + 0.183014i −0.914009 0.405694i \(-0.867030\pi\)
0.808346 + 0.588708i \(0.200363\pi\)
\(84\) 0 0
\(85\) 22.4881 + 38.9506i 0.0286962 + 0.0497034i
\(86\) 564.993 + 31.4747i 0.708427 + 0.0394652i
\(87\) 0 0
\(88\) −387.548 320.216i −0.469463 0.387900i
\(89\) 1493.47i 1.77873i −0.457195 0.889366i \(-0.651146\pi\)
0.457195 0.889366i \(-0.348854\pi\)
\(90\) 0 0
\(91\) 1908.09i 2.19805i
\(92\) 1155.70 + 129.165i 1.30967 + 0.146373i
\(93\) 0 0
\(94\) 47.7536 857.209i 0.0523979 0.940578i
\(95\) 8.22181 + 14.2406i 0.00887936 + 0.0153795i
\(96\) 0 0
\(97\) 700.115 1212.63i 0.732844 1.26932i −0.222819 0.974860i \(-0.571526\pi\)
0.955663 0.294463i \(-0.0951408\pi\)
\(98\) 988.129 + 646.332i 1.01853 + 0.666218i
\(99\) 0 0
\(100\) 394.159 + 901.213i 0.394159 + 0.901213i
\(101\) 207.342 + 119.709i 0.204270 + 0.117936i 0.598646 0.801014i \(-0.295706\pi\)
−0.394375 + 0.918949i \(0.629039\pi\)
\(102\) 0 0
\(103\) −504.070 + 291.025i −0.482208 + 0.278403i −0.721336 0.692585i \(-0.756472\pi\)
0.239128 + 0.970988i \(0.423138\pi\)
\(104\) −1467.14 + 546.625i −1.38331 + 0.515394i
\(105\) 0 0
\(106\) 310.451 + 614.284i 0.284469 + 0.562873i
\(107\) 1470.35 1.32845 0.664224 0.747533i \(-0.268762\pi\)
0.664224 + 0.747533i \(0.268762\pi\)
\(108\) 0 0
\(109\) −1.40399 −0.00123374 −0.000616870 1.00000i \(-0.500196\pi\)
−0.000616870 1.00000i \(0.500196\pi\)
\(110\) −40.5344 80.2045i −0.0351345 0.0695200i
\(111\) 0 0
\(112\) 389.632 1721.34i 0.328721 1.45224i
\(113\) 1174.77 678.256i 0.977996 0.564646i 0.0763312 0.997083i \(-0.475679\pi\)
0.901664 + 0.432436i \(0.142346\pi\)
\(114\) 0 0
\(115\) 180.026 + 103.938i 0.145978 + 0.0842805i
\(116\) 793.020 346.840i 0.634742 0.277614i
\(117\) 0 0
\(118\) 198.451 + 129.806i 0.154821 + 0.101268i
\(119\) −433.648 + 751.100i −0.334054 + 0.578598i
\(120\) 0 0
\(121\) 418.692 + 725.195i 0.314569 + 0.544850i
\(122\) 62.6829 1125.20i 0.0465168 0.835008i
\(123\) 0 0
\(124\) −105.476 + 943.747i −0.0763874 + 0.683475i
\(125\) 354.589i 0.253724i
\(126\) 0 0
\(127\) 547.847i 0.382784i 0.981514 + 0.191392i \(0.0613002\pi\)
−0.981514 + 0.191392i \(0.938700\pi\)
\(128\) −1435.16 + 193.536i −0.991030 + 0.133643i
\(129\) 0 0
\(130\) −279.439 15.5670i −0.188526 0.0105025i
\(131\) −931.609 1613.59i −0.621336 1.07619i −0.989237 0.146321i \(-0.953257\pi\)
0.367901 0.929865i \(1.61992\pi\)
\(132\) 0 0
\(133\) −158.544 + 274.607i −0.103365 + 0.179033i
\(134\) −550.216 + 841.185i −0.354712 + 0.542293i
\(135\) 0 0
\(136\) 701.754 + 118.260i 0.442462 + 0.0745640i
\(137\) −1253.96 723.973i −0.781992 0.451483i 0.0551439 0.998478i \(-0.482438\pi\)
−0.837136 + 0.546995i \(0.815772\pi\)
\(138\) 0 0
\(139\) 324.131 187.137i 0.197787 0.114193i −0.397836 0.917457i \(-0.630239\pi\)
0.595623 + 0.803264i \(0.296905\pi\)
\(140\) 187.114 254.007i 0.112957 0.153339i
\(141\) 0 0
\(142\) −2186.69 + 1105.12i −1.29227 + 0.653098i
\(143\) −1537.29 −0.898986
\(144\) 0 0
\(145\) 154.723 0.0886143
\(146\) 163.236 82.4976i 0.0925311 0.0467640i
\(147\) 0 0
\(148\) −1425.51 + 1935.14i −0.791733 + 1.07478i
\(149\) −2138.30 + 1234.55i −1.17568 + 0.678779i −0.955011 0.296570i \(-0.904157\pi\)
−0.220669 + 0.975349i \(0.570824\pi\)
\(150\) 0 0
\(151\) 525.453 + 303.370i 0.283184 + 0.163496i 0.634864 0.772624i \(-0.281056\pi\)
−0.351680 + 0.936120i \(0.614390\pi\)
\(152\) 256.566 + 43.2366i 0.136909 + 0.0230720i
\(153\) 0 0
\(154\) 948.589 1450.23i 0.496360 0.758849i
\(155\) −84.8758 + 147.009i −0.0439832 + 0.0761811i
\(156\) 0 0
\(157\) 37.1699 + 64.3801i 0.0188948 + 0.0327267i 0.875318 0.483547i \(-0.160652\pi\)
−0.856423 + 0.516274i \(0.827319\pi\)
\(158\) 1157.29 + 64.4705i 0.582715 + 0.0324620i
\(159\) 0 0
\(160\) −248.911 71.1049i −0.122988 0.0351333i
\(161\) 4008.55i 1.96222i
\(162\) 0 0
\(163\) 40.4850i 0.0194542i 0.999953 + 0.00972709i \(0.00309628\pi\)
−0.999953 + 0.00972709i \(0.996904\pi\)
\(164\) −353.832 + 3165.90i −0.168473 + 1.50741i
\(165\) 0 0
\(166\) −25.1398 + 451.277i −0.0117544 + 0.211000i
\(167\) 20.5614 + 35.6135i 0.00952750 + 0.0165021i 0.870750 0.491726i \(-0.163634\pi\)
−0.861222 + 0.508228i \(0.830301\pi\)
\(168\) 0 0
\(169\) −1295.34 + 2243.59i −0.589593 + 1.02121i
\(170\) 106.460 + 69.6354i 0.0480303 + 0.0314164i
\(171\) 0 0
\(172\) 1466.40 641.352i 0.650069 0.284318i
\(173\) 952.460 + 549.903i 0.418579 + 0.241667i 0.694469 0.719522i \(-0.255639\pi\)
−0.275890 + 0.961189i \(0.588973\pi\)
\(174\) 0 0
\(175\) −2936.39 + 1695.32i −1.26840 + 0.732311i
\(176\) −1386.83 313.915i −0.593958 0.134445i
\(177\) 0 0
\(178\) −1905.33 3770.05i −0.802308 1.58751i
\(179\) 3849.91 1.60757 0.803787 0.594917i \(-0.202815\pi\)
0.803787 + 0.594917i \(0.202815\pi\)
\(180\) 0 0
\(181\) −1091.65 −0.448296 −0.224148 0.974555i \(-0.571960\pi\)
−0.224148 + 0.974555i \(0.571960\pi\)
\(182\) −2434.30 4816.70i −0.991441 1.96175i
\(183\) 0 0
\(184\) 3082.19 1148.36i 1.23490 0.460099i
\(185\) −372.083 + 214.822i −0.147871 + 0.0853731i
\(186\) 0 0
\(187\) 605.140 + 349.378i 0.236643 + 0.136626i
\(188\) −973.062 2224.83i −0.377489 0.863097i
\(189\) 0 0
\(190\) 38.9226 + 25.4591i 0.0148618 + 0.00972105i
\(191\) −319.673 + 553.690i −0.121103 + 0.209757i −0.920203 0.391441i \(-0.871977\pi\)
0.799100 + 0.601199i \(0.205310\pi\)
\(192\) 0 0
\(193\) −874.103 1513.99i −0.326007 0.564660i 0.655709 0.755014i \(-0.272370\pi\)
−0.981716 + 0.190353i \(0.939037\pi\)
\(194\) 220.288 3954.31i 0.0815244 1.46342i
\(195\) 0 0
\(196\) 3318.97 + 370.939i 1.20954 + 0.135182i
\(197\) 2079.55i 0.752089i −0.926602 0.376044i \(-0.877284\pi\)
0.926602 0.376044i \(-0.122716\pi\)
\(198\) 0 0
\(199\) 1834.81i 0.653598i 0.945094 + 0.326799i \(0.105970\pi\)
−0.945094 + 0.326799i \(0.894030\pi\)
\(200\) 2144.75 + 1772.13i 0.758283 + 0.626541i
\(201\) 0 0
\(202\) 676.128 + 37.6659i 0.235506 + 0.0131196i
\(203\) 1491.80 + 2583.86i 0.515781 + 0.893358i
\(204\) 0 0
\(205\) −284.726 + 493.159i −0.0970053 + 0.168018i
\(206\) −901.169 + 1377.73i −0.304793 + 0.465976i
\(207\) 0 0
\(208\) −3006.21 + 3251.62i −1.00213 + 1.08394i
\(209\) 221.243 + 127.735i 0.0732235 + 0.0422756i
\(210\) 0 0
\(211\) 4307.35 2486.85i 1.40536 0.811383i 0.410421 0.911896i \(-0.365382\pi\)
0.994936 + 0.100513i \(0.0320483\pi\)
\(212\) 1567.38 + 1154.61i 0.507774 + 0.374050i
\(213\) 0 0
\(214\) 3711.69 1875.84i 1.18563 0.599205i
\(215\) 286.104 0.0907540
\(216\) 0 0
\(217\) −3273.39 −1.02402
\(218\) −3.54417 + 1.79118i −0.00110111 + 0.000556486i
\(219\) 0 0
\(220\) −204.647 150.752i −0.0627148 0.0461987i
\(221\) 1884.62 1088.08i 0.573634 0.331188i
\(222\) 0 0
\(223\) 611.995 + 353.335i 0.183777 + 0.106103i 0.589066 0.808085i \(-0.299496\pi\)
−0.405289 + 0.914189i \(0.632829\pi\)
\(224\) −1212.48 4842.36i −0.361661 1.44439i
\(225\) 0 0
\(226\) 2100.25 3210.92i 0.618170 0.945075i
\(227\) 1604.80 2779.60i 0.469227 0.812725i −0.530154 0.847901i \(-0.677866\pi\)
0.999381 + 0.0351765i \(0.0111994\pi\)
\(228\) 0 0
\(229\) −731.826 1267.56i −0.211181 0.365776i 0.740904 0.671611i \(-0.234398\pi\)
−0.952084 + 0.305836i \(0.901064\pi\)
\(230\) 587.051 + 32.7035i 0.168300 + 0.00937569i
\(231\) 0 0
\(232\) 1559.38 1887.27i 0.441285 0.534074i
\(233\) 1324.13i 0.372303i 0.982521 + 0.186152i \(0.0596015\pi\)
−0.982521 + 0.186152i \(0.940398\pi\)
\(234\) 0 0
\(235\) 434.078i 0.120494i
\(236\) 666.564 + 74.4974i 0.183854 + 0.0205482i
\(237\) 0 0
\(238\) −136.445 + 2449.28i −0.0371615 + 0.667074i
\(239\) −394.528 683.342i −0.106778 0.184944i 0.807685 0.589614i \(-0.200720\pi\)
−0.914463 + 0.404669i \(0.867387\pi\)
\(240\) 0 0
\(241\) 1170.39 2027.17i 0.312827 0.541832i −0.666146 0.745821i \(-0.732057\pi\)
0.978973 + 0.203989i \(0.0653907\pi\)
\(242\) 1982.12 + 1296.50i 0.526509 + 0.344388i
\(243\) 0 0
\(244\) −1277.27 2920.38i −0.335119 0.766222i
\(245\) 517.002 + 298.491i 0.134817 + 0.0778364i
\(246\) 0 0
\(247\) 689.028 397.811i 0.177497 0.102478i
\(248\) 937.752 + 2516.92i 0.240110 + 0.644454i
\(249\) 0 0
\(250\) 452.378 + 895.111i 0.114443 + 0.226447i
\(251\) −938.044 −0.235892 −0.117946 0.993020i \(-0.537631\pi\)
−0.117946 + 0.993020i \(0.537631\pi\)
\(252\) 0 0
\(253\) 3229.58 0.802537
\(254\) 698.932 + 1382.96i 0.172657 + 0.341633i
\(255\) 0 0
\(256\) −3375.96 + 2319.51i −0.824209 + 0.566286i
\(257\) −143.756 + 82.9975i −0.0348920 + 0.0201449i −0.517345 0.855777i \(-0.673079\pi\)
0.482453 + 0.875922i \(0.339746\pi\)
\(258\) 0 0
\(259\) −7175.02 4142.50i −1.72137 0.993831i
\(260\) −725.265 + 317.206i −0.172996 + 0.0756626i
\(261\) 0 0
\(262\) −4410.31 2884.76i −1.03996 0.680234i
\(263\) −2415.87 + 4184.41i −0.566422 + 0.981072i 0.430494 + 0.902594i \(0.358339\pi\)
−0.996916 + 0.0784782i \(0.974994\pi\)
\(264\) 0 0
\(265\) 173.997 + 301.371i 0.0403341 + 0.0698606i
\(266\) −49.8852 + 895.474i −0.0114987 + 0.206410i
\(267\) 0 0
\(268\) −315.776 + 2825.41i −0.0719743 + 0.643989i
\(269\) 5581.42i 1.26508i −0.774529 0.632538i \(-0.782013\pi\)
0.774529 0.632538i \(-0.217987\pi\)
\(270\) 0 0
\(271\) 8094.32i 1.81437i 0.420729 + 0.907186i \(0.361774\pi\)
−0.420729 + 0.907186i \(0.638226\pi\)
\(272\) 1922.35 596.752i 0.428528 0.133027i
\(273\) 0 0
\(274\) −4089.07 227.795i −0.901568 0.0502247i
\(275\) 1365.87 + 2365.76i 0.299510 + 0.518767i
\(276\) 0 0
\(277\) 922.842 1598.41i 0.200174 0.346712i −0.748410 0.663236i \(-0.769183\pi\)
0.948584 + 0.316524i \(0.102516\pi\)
\(278\) 579.477 885.921i 0.125017 0.191130i
\(279\) 0 0
\(280\) 148.285 879.921i 0.0316490 0.187805i
\(281\) 2195.00 + 1267.28i 0.465987 + 0.269038i 0.714558 0.699576i \(-0.246628\pi\)
−0.248571 + 0.968614i \(0.579961\pi\)
\(282\) 0 0
\(283\) 2691.52 1553.95i 0.565351 0.326405i −0.189940 0.981796i \(-0.560829\pi\)
0.755290 + 0.655390i \(0.227496\pi\)
\(284\) −4110.09 + 5579.46i −0.858764 + 1.16577i
\(285\) 0 0
\(286\) −3880.68 + 1961.25i −0.802341 + 0.405493i
\(287\) −10981.0 −2.25848
\(288\) 0 0
\(289\) 3923.85 0.798667
\(290\) 390.577 197.393i 0.0790878 0.0399700i
\(291\) 0 0
\(292\) 306.819 416.507i 0.0614904 0.0834734i
\(293\) −4824.35 + 2785.34i −0.961916 + 0.555363i −0.896762 0.442513i \(-0.854087\pi\)
−0.0651539 + 0.997875i \(0.520754\pi\)
\(294\) 0 0
\(295\) 103.832 + 59.9475i 0.0204927 + 0.0118314i
\(296\) −1129.70 + 6703.63i −0.221833 + 1.31635i
\(297\) 0 0
\(298\) −3822.83 + 5844.44i −0.743122 + 1.13610i
\(299\) 5029.02 8710.51i 0.972694 1.68476i
\(300\) 0 0
\(301\) 2758.53 + 4777.91i 0.528235 + 0.914930i
\(302\) 1713.47 + 95.4540i 0.326486 + 0.0181880i
\(303\) 0 0
\(304\) 702.824 218.176i 0.132598 0.0411621i
\(305\) 569.785i 0.106970i
\(306\) 0 0
\(307\) 7746.70i 1.44016i −0.693893 0.720078i \(-0.744106\pi\)
0.693893 0.720078i \(-0.255894\pi\)
\(308\) 544.408 4871.09i 0.100716 0.901156i
\(309\) 0 0
\(310\) −26.7058 + 479.387i −0.00489286 + 0.0878301i
\(311\) −2906.54 5034.28i −0.529951 0.917902i −0.999390 0.0349372i \(-0.988877\pi\)
0.469438 0.882965i \(1.65554\pi\)
\(312\) 0 0
\(313\) −1367.73 + 2368.98i −0.246993 + 0.427805i −0.962690 0.270606i \(-0.912776\pi\)
0.715697 + 0.698411i \(0.246109\pi\)
\(314\) 175.965 + 115.098i 0.0316251 + 0.0206858i
\(315\) 0 0
\(316\) 3003.67 1313.70i 0.534713 0.233865i
\(317\) −5434.46 3137.59i −0.962869 0.555913i −0.0658143 0.997832i \(-0.520965\pi\)
−0.897055 + 0.441919i \(0.854298\pi\)
\(318\) 0 0
\(319\) 2081.75 1201.90i 0.365378 0.210951i
\(320\) −719.054 + 138.061i −0.125614 + 0.0241182i
\(321\) 0 0
\(322\) 5114.02 + 10119.0i 0.885073 + 1.75128i
\(323\) −361.639 −0.0622976
\(324\) 0 0
\(325\) 8507.62 1.45206
\(326\) 51.6499 + 102.199i 0.00877492 + 0.0173628i
\(327\) 0 0
\(328\) 3145.80 + 8443.29i 0.529566 + 1.42135i
\(329\) 7249.06 4185.25i 1.21475 0.701338i
\(330\) 0 0
\(331\) 302.371 + 174.574i 0.0502110 + 0.0289893i 0.524895 0.851167i \(-0.324104\pi\)
−0.474684 + 0.880156i \(0.657438\pi\)
\(332\) 512.268 + 1171.26i 0.0846818 + 0.193618i
\(333\) 0 0
\(334\) 97.3394 + 63.6693i 0.0159466 + 0.0104306i
\(335\) −254.103 + 440.119i −0.0414421 + 0.0717799i
\(336\) 0 0
\(337\) −4663.04 8076.62i −0.753744 1.30552i −0.945996 0.324178i \(-0.894912\pi\)
0.192252 0.981346i \(-0.438421\pi\)
\(338\) −407.571 + 7316.18i −0.0655886 + 1.17736i
\(339\) 0 0
\(340\) 357.584 + 39.9647i 0.0570374 + 0.00637468i
\(341\) 2637.28i 0.418817i
\(342\) 0 0
\(343\) 2053.18i 0.323210i
\(344\) 2883.49 3489.80i 0.451941 0.546970i
\(345\) 0 0
\(346\) 3105.91 + 173.024i 0.482586 + 0.0268840i
\(347\) 2780.66 + 4816.24i 0.430183 + 0.745098i 0.996889 0.0788217i \(-0.0251158\pi\)
−0.566706 + 0.823920i \(0.691782\pi\)
\(348\) 0 0
\(349\) −5336.11 + 9242.41i −0.818439 + 1.41758i 0.0883931 + 0.996086i \(0.471827\pi\)
−0.906832 + 0.421492i \(0.861506\pi\)
\(350\) −5249.64 + 8025.78i −0.801728 + 1.22570i
\(351\) 0 0
\(352\) −3901.36 + 976.860i −0.590747 + 0.147917i
\(353\) −349.651 201.871i −0.0527196 0.0304377i 0.473409 0.880843i \(-0.343023\pi\)
−0.526128 + 0.850405i \(0.676357\pi\)
\(354\) 0 0
\(355\) −1072.80 + 619.382i −0.160390 + 0.0926011i
\(356\) −9619.50 7086.17i −1.43211 1.05496i
\(357\) 0 0
\(358\) 9718.55 4911.63i 1.43475 0.725106i
\(359\) 6398.10 0.940609 0.470305 0.882504i \(-0.344144\pi\)
0.470305 + 0.882504i \(0.344144\pi\)
\(360\) 0 0
\(361\) 6726.78 0.980724
\(362\) −2755.71 + 1392.70i −0.400102 + 0.202207i
\(363\) 0 0
\(364\) −12290.1 9053.46i −1.76971 1.30365i
\(365\) 80.0847 46.2369i 0.0114844 0.00663055i
\(366\) 0 0
\(367\) −9573.58 5527.31i −1.36168 0.786166i −0.371833 0.928300i \(-0.621270\pi\)
−0.989848 + 0.142133i \(0.954604\pi\)
\(368\) 6315.50 6831.06i 0.894614 0.967646i
\(369\) 0 0
\(370\) −665.205 + 1016.98i −0.0934658 + 0.142893i
\(371\) −3355.25 + 5811.46i −0.469530 + 0.813250i
\(372\) 0 0
\(373\) −1756.18 3041.80i −0.243785 0.422248i 0.718004 0.696039i \(-0.245056\pi\)
−0.961789 + 0.273791i \(0.911722\pi\)
\(374\) 1973.32 + 109.930i 0.272829 + 0.0151988i
\(375\) 0 0
\(376\) −5294.74 4374.85i −0.726212 0.600041i
\(377\) 7486.26i 1.02271i
\(378\) 0 0
\(379\) 1238.70i 0.167883i 0.996471 + 0.0839413i \(0.0267508\pi\)
−0.996471 + 0.0839413i \(0.973249\pi\)
\(380\) 130.735 + 14.6114i 0.0176488 + 0.00197249i
\(381\) 0 0
\(382\) −100.584 + 1805.55i −0.0134720 + 0.241832i
\(383\) 853.999 + 1479.17i 0.113936 + 0.197342i 0.917354 0.398073i \(-0.130321\pi\)
−0.803418 + 0.595415i \(0.796988\pi\)
\(384\) 0 0
\(385\) 438.081 758.779i 0.0579914 0.100444i
\(386\) −4138.07 2706.69i −0.545653 0.356910i
\(387\) 0 0
\(388\) −4488.75 10263.1i −0.587324 1.34287i
\(389\) 7751.80 + 4475.50i 1.01036 + 0.583334i 0.911298 0.411746i \(-0.135081\pi\)
0.0990663 + 0.995081i \(0.468414\pi\)
\(390\) 0 0
\(391\) −3959.24 + 2285.87i −0.512091 + 0.295656i
\(392\) 8851.51 3297.89i 1.14048 0.424920i
\(393\) 0 0
\(394\) −2653.04 5249.52i −0.339234 0.671236i
\(395\) 586.034 0.0746496
\(396\) 0 0
\(397\) −9391.26 −1.18724 −0.593619 0.804746i \(-0.702302\pi\)
−0.593619 + 0.804746i \(0.702302\pi\)
\(398\) 2340.81 + 4631.71i 0.294809 + 0.583334i
\(399\) 0 0
\(400\) 7674.95 + 1737.26i 0.959369 + 0.217157i
\(401\) −3528.74 + 2037.32i −0.439444 + 0.253713i −0.703362 0.710832i \(-0.748319\pi\)
0.263918 + 0.964545i \(0.414985\pi\)
\(402\) 0 0
\(403\) 7113.02 + 4106.70i 0.879217 + 0.507616i
\(404\) 1754.84 767.508i 0.216106 0.0945172i
\(405\) 0 0
\(406\) 7062.27 + 4619.40i 0.863287 + 0.564673i
\(407\) −3337.50 + 5780.71i −0.406471 + 0.704028i
\(408\) 0 0
\(409\) 335.715 + 581.476i 0.0405869 + 0.0702986i 0.885605 0.464439i \(-0.153744\pi\)
−0.845018 + 0.534737i \(0.820411\pi\)
\(410\) −89.5875 + 1608.16i −0.0107913 + 0.193710i
\(411\) 0 0
\(412\) −517.194 + 4627.58i −0.0618454 + 0.553361i
\(413\) 2311.98i 0.275460i
\(414\) 0 0
\(415\) 228.520i 0.0270304i
\(416\) −3440.40 + 12043.5i −0.405479 + 1.41943i
\(417\) 0 0
\(418\) 721.458 + 40.1911i 0.0844203 + 0.00470290i
\(419\) −4703.57 8146.83i −0.548412 0.949877i −0.998384 0.0568346i \(-0.981899\pi\)
0.449972 0.893043i \(1.64857\pi\)
\(420\) 0 0
\(421\) 6156.19 10662.8i 0.712671 1.23438i −0.251181 0.967940i \(-0.580819\pi\)
0.963851 0.266441i \(-0.0858479\pi\)
\(422\) 7700.63 11772.9i 0.888296 1.35805i
\(423\) 0 0
\(424\) 5429.65 + 915.008i 0.621904 + 0.104804i
\(425\) −3348.94 1933.51i −0.382229 0.220680i
\(426\) 0 0
\(427\) 9515.36 5493.70i 1.07841 0.622620i
\(428\) 6976.48 9470.59i 0.787899 1.06958i
\(429\) 0 0
\(430\) 722.229 365.005i 0.0809976 0.0409351i
\(431\) 7647.49 0.854679 0.427340 0.904091i \(-0.359451\pi\)
0.427340 + 0.904091i \(0.359451\pi\)
\(432\) 0 0
\(433\) −13985.2 −1.55216 −0.776082 0.630632i \(-0.782796\pi\)
−0.776082 + 0.630632i \(0.782796\pi\)
\(434\) −8263.21 + 4176.12i −0.913932 + 0.461890i
\(435\) 0 0
\(436\) −6.66161 + 9.04315i −0.000731727 + 0.000993322i
\(437\) −1447.52 + 835.728i −0.158454 + 0.0914835i
\(438\) 0 0
\(439\) 11706.7 + 6758.84i 1.27273 + 0.734811i 0.975501 0.219996i \(-0.0706044\pi\)
0.297228 + 0.954806i \(0.403938\pi\)
\(440\) −708.928 119.469i −0.0768109 0.0129442i
\(441\) 0 0
\(442\) 3369.30 5151.07i 0.362582 0.554325i
\(443\) 3270.50 5664.67i 0.350759 0.607532i −0.635624 0.771999i \(-0.719257\pi\)
0.986383 + 0.164467i \(0.0525904\pi\)
\(444\) 0 0
\(445\) −1067.87 1849.61i −0.113757 0.197033i
\(446\) 1995.67 + 111.175i 0.211878 + 0.0118034i
\(447\) 0 0
\(448\) −9238.51 10677.0i −0.974283 1.12598i
\(449\) 17599.7i 1.84984i 0.380158 + 0.924921i \(0.375870\pi\)
−0.380158 + 0.924921i \(0.624130\pi\)
\(450\) 0 0
\(451\) 8847.05i 0.923706i
\(452\) 1205.36 10785.0i 0.125432 1.12230i
\(453\) 0 0
\(454\) 504.943 9064.08i 0.0521986 0.937001i
\(455\) −1364.34 2363.10i −0.140574 0.243481i
\(456\) 0 0
\(457\) 1199.50 2077.59i 0.122779 0.212660i −0.798083 0.602547i \(-0.794153\pi\)
0.920863 + 0.389887i \(0.127486\pi\)
\(458\) −3464.52 2266.13i −0.353463 0.231199i
\(459\) 0 0
\(460\) 1523.65 666.392i 0.154436 0.0675450i
\(461\) 3237.72 + 1869.30i 0.327106 + 0.188855i 0.654555 0.756014i \(-0.272856\pi\)
−0.327450 + 0.944869i \(0.606189\pi\)
\(462\) 0 0
\(463\) −2167.70 + 1251.52i −0.217585 + 0.125623i −0.604831 0.796354i \(-0.706760\pi\)
0.387247 + 0.921976i \(0.373426\pi\)
\(464\) 1528.69 6753.56i 0.152948 0.675702i
\(465\) 0 0
\(466\) 1689.30 + 3342.58i 0.167930 + 0.332279i
\(467\) 5361.30 0.531245 0.265622 0.964077i \(-0.414423\pi\)
0.265622 + 0.964077i \(0.414423\pi\)
\(468\) 0 0
\(469\) −9799.93 −0.964859
\(470\) −553.787 1095.77i −0.0543496 0.107540i
\(471\) 0 0
\(472\) 1777.69 662.331i 0.173358 0.0645895i
\(473\) 3849.43 2222.47i 0.374201 0.216045i
\(474\) 0 0
\(475\) −1224.39 706.904i −0.118272 0.0682841i
\(476\) 2780.31 + 6356.95i 0.267721 + 0.612122i
\(477\) 0 0
\(478\) −1867.72 1221.67i −0.178719 0.116899i
\(479\) −609.925 + 1056.42i −0.0581799 + 0.100771i −0.893648 0.448768i \(-0.851863\pi\)
0.835468 + 0.549538i \(0.185196\pi\)
\(480\) 0 0
\(481\) 10394.1 + 18003.2i 0.985304 + 1.70660i
\(482\) 368.257 6610.46i 0.0348001 0.624685i
\(483\) 0 0
\(484\) 6657.62 + 744.076i 0.625246 + 0.0698795i
\(485\) 2002.41i 0.187473i
\(486\) 0 0
\(487\) 1483.03i 0.137993i 0.997617 + 0.0689964i \(0.0219797\pi\)
−0.997617 + 0.0689964i \(0.978020\pi\)
\(488\) −6950.06 5742.57i −0.644702 0.532693i
\(489\) 0 0
\(490\) 1685.91 + 93.9189i 0.155432 + 0.00865882i
\(491\) 6942.36 + 12024.5i 0.638094 + 1.10521i 0.985851 + 0.167627i \(0.0536103\pi\)
−0.347756 + 0.937585i \(0.613056\pi\)
\(492\) 0 0
\(493\) −1701.39 + 2946.89i −0.155429 + 0.269211i
\(494\) 1231.84 1883.26i 0.112192 0.171522i
\(495\) 0 0
\(496\) 5578.26 + 5157.24i 0.504982 + 0.466869i
\(497\) −20687.2 11943.8i −1.86710 1.07797i
\(498\) 0 0
\(499\) −17493.2 + 10099.7i −1.56935 + 0.906063i −0.573102 + 0.819484i \(0.694260\pi\)
−0.996245 + 0.0865784i \(0.972407\pi\)
\(500\) 2283.93 + 1682.45i 0.204281 + 0.150483i
\(501\) 0 0
\(502\) −2367.96 + 1196.74i −0.210532 + 0.106400i
\(503\) 388.562 0.0344436 0.0172218 0.999852i \(-0.494518\pi\)
0.0172218 + 0.999852i \(0.494518\pi\)
\(504\) 0 0
\(505\) 342.381 0.0301698
\(506\) 8152.61 4120.23i 0.716261 0.361989i
\(507\) 0 0
\(508\) 3528.71 + 2599.41i 0.308191 + 0.227028i
\(509\) −5854.78 + 3380.26i −0.509840 + 0.294356i −0.732768 0.680479i \(-0.761772\pi\)
0.222928 + 0.974835i \(0.428439\pi\)
\(510\) 0 0
\(511\) 1544.30 + 891.605i 0.133691 + 0.0771864i
\(512\) −5562.96 + 10162.2i −0.480177 + 0.877172i
\(513\) 0 0
\(514\) −257.005 + 392.916i −0.0220545 + 0.0337175i
\(515\) −416.182 + 720.848i −0.0356100 + 0.0616783i
\(516\) 0 0
\(517\) −3371.94 5840.37i −0.286843 0.496826i
\(518\) −23397.2 1303.42i −1.98459 0.110558i
\(519\) 0 0
\(520\) −1426.14 + 1726.02i −0.120270 + 0.145559i
\(521\) 17324.6i 1.45683i 0.685139 + 0.728413i \(0.259742\pi\)
−0.685139 + 0.728413i \(0.740258\pi\)
\(522\) 0 0
\(523\) 16119.4i 1.34771i −0.738864 0.673855i \(-0.764637\pi\)
0.738864 0.673855i \(-0.235363\pi\)
\(524\) −14813.5 1655.61i −1.23498 0.138026i
\(525\) 0 0
\(526\) −760.142 + 13645.1i −0.0630110 + 1.13109i
\(527\) −1866.64 3233.12i −0.154293 0.267243i
\(528\) 0 0
\(529\) −4481.55 + 7762.27i −0.368337 + 0.637978i
\(530\) 823.712 + 538.787i 0.0675090 + 0.0441574i
\(531\) 0 0
\(532\) 1016.50 + 2324.14i 0.0828398 + 0.189406i
\(533\) 23861.4 + 13776.4i 1.93912 + 1.11955i
\(534\) 0 0
\(535\) 1820.98 1051.34i 0.147154 0.0849597i
\(536\) 2807.46 + 7535.20i 0.226238 + 0.607222i
\(537\) 0 0
\(538\) −7120.66 14089.5i −0.570620 1.12907i
\(539\) 9274.78 0.741175
\(540\) 0 0
\(541\) −4412.42 −0.350655 −0.175328 0.984510i \(-0.556099\pi\)
−0.175328 + 0.984510i \(0.556099\pi\)
\(542\) 10326.6 + 20433.0i 0.818384 + 1.61932i
\(543\) 0 0
\(544\) 4091.38 3958.91i 0.322457 0.312016i
\(545\) −1.73879 + 1.00389i −0.000136663 + 7.89026e-5i
\(546\) 0 0
\(547\) −5985.94 3455.99i −0.467898 0.270141i 0.247461 0.968898i \(-0.420404\pi\)
−0.715360 + 0.698757i \(0.753737\pi\)
\(548\) −10612.9 + 4641.71i −0.827300 + 0.361832i
\(549\) 0 0
\(550\) 6466.15 + 4229.49i 0.501305 + 0.327902i
\(551\) −622.038 + 1077.40i −0.0480938 + 0.0833010i
\(552\) 0 0
\(553\) 5650.37 + 9786.72i 0.434499 + 0.752574i
\(554\) 290.368 5212.30i 0.0222681 0.399728i
\(555\) 0 0
\(556\) 332.570 2975.67i 0.0253671 0.226972i
\(557\) 17257.6i 1.31280i −0.754415 0.656398i \(-0.772079\pi\)
0.754415 0.656398i \(-0.227921\pi\)
\(558\) 0 0
\(559\) 13843.1i 1.04741i
\(560\) −748.260 2410.41i −0.0564639 0.181890i
\(561\) 0 0
\(562\) 7157.73 + 398.744i 0.537243 + 0.0299288i
\(563\) −12554.5 21745.1i −0.939805 1.62779i −0.765833 0.643039i \(-0.777673\pi\)
−0.173972 0.984751i \(1.44434\pi\)
\(564\) 0 0
\(565\) 969.945 1679.99i 0.0722228 0.125094i
\(566\) 4811.86 7356.51i 0.357346 0.546320i
\(567\) 0 0
\(568\) −3257.19 + 19328.1i −0.240614 + 1.42780i
\(569\) −14813.5 8552.60i −1.09142 0.630129i −0.157463 0.987525i \(-0.550331\pi\)
−0.933953 + 0.357396i \(0.883665\pi\)
\(570\) 0 0
\(571\) −4814.10 + 2779.42i −0.352827 + 0.203705i −0.665929 0.746015i \(-0.731965\pi\)
0.313103 + 0.949719i \(0.398632\pi\)
\(572\) −7294.12 + 9901.79i −0.533186 + 0.723802i
\(573\) 0 0
\(574\) −27719.9 + 14009.3i −2.01569 + 1.01870i
\(575\) −17873.0 −1.29627
\(576\) 0 0
\(577\) 19014.3 1.37188 0.685939 0.727659i \(-0.259392\pi\)
0.685939 + 0.727659i \(0.259392\pi\)
\(578\) 9905.21 5005.97i 0.712807 0.360244i
\(579\) 0 0
\(580\) 734.127 996.580i 0.0525569 0.0713461i
\(581\) −3816.27 + 2203.32i −0.272505 + 0.157331i
\(582\) 0 0
\(583\) 4682.13 + 2703.23i 0.332614 + 0.192035i
\(584\) 243.149 1442.85i 0.0172287 0.102235i
\(585\) 0 0
\(586\) −8624.91 + 13186.0i −0.608006 + 0.929537i
\(587\) −12597.2 + 21818.9i −0.885759 + 1.53418i −0.0409172 + 0.999163i \(0.513028\pi\)
−0.844842 + 0.535017i \(0.820305\pi\)
\(588\) 0 0
\(589\) −682.457 1182.05i −0.0477422 0.0826919i
\(590\) 338.589 + 18.8622i 0.0236263 + 0.00131618i
\(591\) 0 0
\(592\) 5700.58 + 18363.6i 0.395764 + 1.27490i
\(593\) 17307.5i 1.19854i −0.800548 0.599269i \(-0.795458\pi\)
0.800548 0.599269i \(-0.204542\pi\)
\(594\) 0 0
\(595\) 1240.28i 0.0854564i
\(596\) −2193.97 + 19630.5i −0.150786 + 1.34916i
\(597\) 0 0
\(598\) 1582.36 28404.4i 0.108206 1.94238i
\(599\) 10740.8 + 18603.5i 0.732647 + 1.26898i 0.955748 + 0.294186i \(0.0950487\pi\)
−0.223101 + 0.974795i \(0.571618\pi\)
\(600\) 0 0
\(601\) 2716.74 4705.53i 0.184390 0.319372i −0.758981 0.651113i \(-0.774303\pi\)
0.943371 + 0.331741i \(0.107636\pi\)
\(602\) 13059.1 + 8541.89i 0.884133 + 0.578308i
\(603\) 0 0
\(604\) 4447.18 1945.04i 0.299591 0.131031i
\(605\) 1037.07 + 598.752i 0.0696907 + 0.0402359i
\(606\) 0 0
\(607\) −11684.8 + 6746.19i −0.781333 + 0.451103i −0.836903 0.547352i \(-0.815636\pi\)
0.0555692 + 0.998455i \(0.482303\pi\)
\(608\) 1495.84 1447.40i 0.0997765 0.0965460i
\(609\) 0 0
\(610\) −726.920 1438.34i −0.0482494 0.0954701i
\(611\) −21002.8 −1.39064
\(612\) 0 0
\(613\) 8330.79 0.548903 0.274451 0.961601i \(-0.411504\pi\)
0.274451 + 0.961601i \(0.411504\pi\)
\(614\) −9883.08 19555.5i −0.649591 1.28533i
\(615\) 0 0
\(616\) −4840.15 12990.9i −0.316583 0.849706i
\(617\) 17147.1 9899.88i 1.11883 0.645955i 0.177726 0.984080i \(-0.443126\pi\)
0.941101 + 0.338125i \(0.109793\pi\)
\(618\) 0 0
\(619\) 22673.3 + 13090.4i 1.47224 + 0.849997i 0.999513 0.0312129i \(-0.00993698\pi\)
0.472725 + 0.881210i \(0.343270\pi\)
\(620\) 544.177 + 1244.22i 0.0352494 + 0.0805950i
\(621\) 0 0
\(622\) −13759.8 9000.22i −0.887005 0.580186i
\(623\) 20592.2 35666.7i 1.32425 2.29367i
\(624\) 0 0
\(625\) −7431.14 12871.1i −0.475593 0.823751i
\(626\) −430.351 + 7725.09i −0.0274765 + 0.493221i
\(627\) 0 0
\(628\) 591.038 + 66.0563i 0.0375557 + 0.00419735i
\(629\) 9449.01i 0.598977i
\(630\) 0 0
\(631\) 24489.4i 1.54502i −0.635004 0.772509i \(-0.719001\pi\)
0.635004 0.772509i \(-0.280999\pi\)
\(632\) 5906.34 7148.26i 0.371743 0.449909i
\(633\) 0 0
\(634\) −17721.4 987.226i −1.11010 0.0618419i
\(635\) 391.726 + 678.489i 0.0244806 + 0.0424016i
\(636\) 0 0
\(637\) 14442.5 25015.1i 0.898322 1.55594i
\(638\) 3721.72 5689.87i 0.230947 0.353079i
\(639\) 0 0
\(640\) −1639.02 + 1265.87i −0.101231 + 0.0781842i
\(641\) 20279.7 + 11708.5i 1.24961 + 0.721463i 0.971032 0.238951i \(-0.0768035\pi\)
0.278578 + 0.960414i \(0.410137\pi\)
\(642\) 0 0
\(643\) −1385.76 + 800.068i −0.0849907 + 0.0490694i −0.541893 0.840447i \(-0.682292\pi\)
0.456902 + 0.889517i \(0.348959\pi\)
\(644\) 25819.3 + 19019.7i 1.57985 + 1.16379i
\(645\) 0 0
\(646\) −912.906 + 461.371i −0.0556003 + 0.0280997i
\(647\) 19887.1 1.20841 0.604206 0.796828i \(-0.293491\pi\)
0.604206 + 0.796828i \(0.293491\pi\)
\(648\) 0 0
\(649\) 1862.70 0.112662
\(650\) 21476.3 10853.8i 1.29595 0.654958i
\(651\) 0 0
\(652\) 260.766 + 192.092i 0.0156632 + 0.0115382i
\(653\) −3929.91 + 2268.93i −0.235512 + 0.135973i −0.613112 0.789996i \(-0.710083\pi\)
0.377600 + 0.925969i \(0.376749\pi\)
\(654\) 0 0
\(655\) −2307.53 1332.25i −0.137653 0.0794739i
\(656\) 18712.9 + 17300.6i 1.11374 + 1.02968i
\(657\) 0 0
\(658\) 12959.8 19813.3i 0.767819 1.17386i
\(659\) −880.483 + 1525.04i −0.0520467 + 0.0901475i −0.890875 0.454249i \(-0.849908\pi\)
0.838828 + 0.544396i \(0.183241\pi\)
\(660\) 0 0
\(661\) 3948.96 + 6839.80i 0.232370 + 0.402477i 0.958505 0.285075i \(-0.0920185\pi\)
−0.726135 + 0.687552i \(0.758685\pi\)
\(662\) 986.012 + 54.9290i 0.0578889 + 0.00322489i
\(663\) 0 0
\(664\) 2787.42 + 2303.14i 0.162911 + 0.134607i
\(665\) 453.455i 0.0264424i
\(666\) 0 0
\(667\) 15727.3i 0.912987i
\(668\) 326.948 + 36.5407i 0.0189371 + 0.00211647i
\(669\) 0 0
\(670\) −79.9522 + 1435.20i −0.00461018 + 0.0827560i
\(671\) −4426.12 7666.26i −0.254647 0.441062i
\(672\) 0 0
\(673\) 8028.88 13906.4i 0.459867 0.796513i −0.539087 0.842250i \(-0.681230\pi\)
0.998953 + 0.0457375i \(0.0145638\pi\)
\(674\) −22075.2 14439.3i −1.26158 0.825193i
\(675\) 0 0
\(676\) 8304.98 + 18988.6i 0.472518 + 1.08037i
\(677\) −16512.7 9533.61i −0.937422 0.541221i −0.0482708 0.998834i \(-0.515371\pi\)
−0.889151 + 0.457613i \(0.848704\pi\)
\(678\) 0 0
\(679\) 33440.0 19306.6i 1.89000 1.09119i
\(680\) 953.656 355.313i 0.0537809 0.0200377i
\(681\) 0 0
\(682\) 3364.58 + 6657.44i 0.188910 + 0.373792i
\(683\) −15166.6 −0.849682 −0.424841 0.905268i \(-0.639670\pi\)
−0.424841 + 0.905268i \(0.639670\pi\)
\(684\) 0 0
\(685\) −2070.64 −0.115497
\(686\) 2619.40 + 5182.95i 0.145786 + 0.288464i
\(687\) 0 0
\(688\) 2826.76 12488.2i 0.156641 0.692019i
\(689\) 14581.8 8418.80i 0.806272 0.465502i
\(690\) 0 0
\(691\) −8692.79 5018.79i −0.478567 0.276301i 0.241252 0.970462i \(-0.422442\pi\)
−0.719819 + 0.694162i \(0.755775\pi\)
\(692\) 8061.16 3525.67i 0.442832 0.193679i
\(693\) 0 0
\(694\) 13163.8 + 8610.41i 0.720017 + 0.470961i
\(695\) 267.617 463.525i 0.0146061 0.0252986i
\(696\) 0 0
\(697\) −6261.87 10845.9i −0.340294 0.589407i
\(698\) −1678.98 + 30138.8i −0.0910463 + 1.63434i
\(699\) 0 0
\(700\) −3012.84 + 26957.3i −0.162678 + 1.45556i
\(701\) 13222.0i 0.712394i −0.934411 0.356197i \(-0.884073\pi\)
0.934411 0.356197i \(-0.115927\pi\)
\(702\) 0 0
\(703\) 3454.62i 0.185339i
\(704\) −8602.17 + 7443.21i −0.460520 + 0.398475i
\(705\) 0 0
\(706\) −1140.19 63.5177i −0.0607812 0.00338601i
\(707\) 3301.14 + 5717.74i 0.175604 + 0.304155i
\(708\) 0 0
\(709\) −11792.3 + 20424.8i −0.624636 + 1.08190i 0.363975 + 0.931409i \(0.381419\pi\)
−0.988611 + 0.150493i \(0.951914\pi\)
\(710\) −1917.94 + 2932.20i −0.101379 + 0.154991i
\(711\) 0 0
\(712\) −33323.4 5615.69i −1.75400 0.295585i
\(713\) −14943.2 8627.44i −0.784889 0.453156i
\(714\) 0 0
\(715\) −1903.89 + 1099.21i −0.0995822 + 0.0574938i
\(716\) 18267.0 24797.4i 0.953447 1.29431i
\(717\) 0 0
\(718\) 16151.1 8162.56i 0.839490 0.424267i
\(719\) −19376.4 −1.00503 −0.502517 0.864567i \(-0.667593\pi\)
−0.502517 + 0.864567i \(0.667593\pi\)
\(720\) 0 0
\(721\) −16050.8 −0.829074
\(722\) 16980.8 8581.89i 0.875292 0.442361i
\(723\) 0 0
\(724\) −5179.63 + 7031.36i −0.265883 + 0.360937i
\(725\) −11520.7 + 6651.48i −0.590163 + 0.340731i
\(726\) 0 0
\(727\) −19193.8 11081.5i −0.979172 0.565325i −0.0771518 0.997019i \(-0.524583\pi\)
−0.902020 + 0.431694i \(0.857916\pi\)
\(728\) −42574.8 7174.74i −2.16748 0.365266i
\(729\) 0 0
\(730\) 143.174 218.889i 0.00725907 0.0110979i
\(731\) −3146.09 + 5449.19i −0.159182 + 0.275712i
\(732\) 0 0
\(733\) 14834.2 + 25693.7i 0.747497 + 1.29470i 0.949019 + 0.315219i \(0.102078\pi\)
−0.201522 + 0.979484i \(0.564589\pi\)
\(734\) −31218.8 1739.14i −1.56990 0.0874562i
\(735\) 0 0
\(736\) 7227.65 25301.2i 0.361977 1.26714i
\(737\) 7895.53i 0.394621i
\(738\) 0 0
\(739\) 14616.0i 0.727549i 0.931487 + 0.363774i \(0.118512\pi\)
−0.931487 + 0.363774i \(0.881488\pi\)
\(740\) −381.770 + 3415.88i −0.0189651 + 0.169690i
\(741\) 0 0
\(742\) −1055.71 + 18950.8i −0.0522323 + 0.937606i
\(743\) 17948.9 + 31088.4i 0.886246 + 1.53502i 0.844278 + 0.535905i \(0.180029\pi\)
0.0419682 + 0.999119i \(0.486637\pi\)
\(744\) 0 0
\(745\) −1765.47 + 3057.89i −0.0868213 + 0.150379i
\(746\) −8313.90 5438.09i −0.408034 0.266894i
\(747\) 0 0
\(748\) 5121.62 2240.02i 0.250354 0.109496i
\(749\) 35114.6 + 20273.4i 1.71303 + 0.989018i
\(750\) 0 0
\(751\) −23192.8 + 13390.4i −1.12692 + 0.650627i −0.943158 0.332344i \(-0.892161\pi\)
−0.183761 + 0.982971i \(0.558827\pi\)
\(752\) −18947.2 4288.77i −0.918793 0.207972i
\(753\) 0 0
\(754\) −9550.81 18898.0i −0.461300 0.912765i
\(755\) 867.673 0.0418250
\(756\) 0 0
\(757\) 1805.80 0.0867016 0.0433508 0.999060i \(-0.486197\pi\)
0.0433508 + 0.999060i \(0.486197\pi\)
\(758\) 1580.30 + 3126.91i 0.0757244 + 0.149834i
\(759\) 0 0
\(760\) 348.663 129.905i 0.0166412 0.00620017i
\(761\) 3770.72 2177.03i 0.179617 0.103702i −0.407496 0.913207i \(-0.633598\pi\)
0.587113 + 0.809505i \(0.300265\pi\)
\(762\) 0 0
\(763\) −33.5298 19.3584i −0.00159090 0.000918508i
\(764\) 2049.57 + 4686.17i 0.0970560 + 0.221910i
\(765\) 0 0
\(766\) 4042.89 + 2644.44i 0.190699 + 0.124736i
\(767\) 2900.55 5023.90i 0.136549 0.236509i
\(768\) 0 0
\(769\) −1390.69 2408.74i −0.0652138 0.112954i 0.831575 0.555412i \(-0.187440\pi\)
−0.896789 + 0.442459i \(0.854106\pi\)
\(770\) 137.840 2474.32i 0.00645118 0.115803i
\(771\) 0 0
\(772\) −13899.1 1553.41i −0.647979 0.0724203i
\(773\) 7776.95i 0.361860i 0.983496 + 0.180930i \(0.0579107\pi\)
−0.983496 + 0.180930i \(0.942089\pi\)
\(774\) 0 0
\(775\) 14595.1i 0.676479i
\(776\) −24424.7 20181.2i −1.12989 0.933587i
\(777\) 0 0
\(778\) 25278.1 + 1408.20i 1.16486 + 0.0648924i
\(779\) −2289.38 3965.32i −0.105296 0.182378i
\(780\) 0 0
\(781\) −9622.78