Properties

Label 108.4.h.b.71.7
Level 108
Weight 4
Character 108.71
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 71.7
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.157323 - 2.82405i) q^{2} +(-7.95050 - 0.888573i) q^{4} +(1.23846 + 0.715028i) q^{5} +(-23.8818 + 13.7882i) q^{7} +(-3.76017 + 22.3128i) q^{8} +O(q^{10})\) \(q+(0.157323 - 2.82405i) q^{2} +(-7.95050 - 0.888573i) q^{4} +(1.23846 + 0.715028i) q^{5} +(-23.8818 + 13.7882i) q^{7} +(-3.76017 + 22.3128i) q^{8} +(2.21411 - 3.38499i) q^{10} +(-11.1087 - 19.2409i) q^{11} +(-34.5965 + 59.9229i) q^{13} +(35.1813 + 69.6126i) q^{14} +(62.4209 + 14.1292i) q^{16} -31.4507i q^{17} +11.4986i q^{19} +(-9.21106 - 6.78529i) q^{20} +(-56.0849 + 28.3446i) q^{22} +(-72.6810 + 125.887i) q^{23} +(-61.4775 - 106.482i) q^{25} +(163.782 + 107.129i) q^{26} +(202.124 - 88.4021i) q^{28} +(93.6986 - 54.0969i) q^{29} +(102.800 + 59.3514i) q^{31} +(49.7218 - 174.057i) q^{32} +(-88.8183 - 4.94791i) q^{34} -39.4357 q^{35} -300.439 q^{37} +(32.4725 + 1.80899i) q^{38} +(-20.6111 + 24.9450i) q^{40} +(-344.853 - 199.101i) q^{41} +(-173.261 + 100.032i) q^{43} +(71.2231 + 162.846i) q^{44} +(344.077 + 225.060i) q^{46} +(-151.770 - 262.873i) q^{47} +(208.727 - 361.526i) q^{49} +(-310.382 + 156.863i) q^{50} +(328.305 - 445.675i) q^{52} -243.342i q^{53} -31.7722i q^{55} +(-217.853 - 584.716i) q^{56} +(-138.031 - 273.120i) q^{58} +(-41.9197 + 72.6070i) q^{59} +(199.218 + 345.055i) q^{61} +(183.784 - 280.974i) q^{62} +(-483.722 - 167.800i) q^{64} +(-85.6931 + 49.4749i) q^{65} +(307.763 + 177.687i) q^{67} +(-27.9463 + 250.049i) q^{68} +(-6.20413 + 111.368i) q^{70} +866.235 q^{71} +64.6645 q^{73} +(-47.2658 + 848.453i) q^{74} +(10.2173 - 91.4195i) q^{76} +(530.594 + 306.338i) q^{77} +(-354.896 + 204.899i) q^{79} +(67.2033 + 62.1312i) q^{80} +(-616.524 + 942.559i) q^{82} +(79.8990 + 138.389i) q^{83} +(22.4881 - 38.9506i) q^{85} +(255.238 + 505.035i) q^{86} +(471.089 - 175.518i) q^{88} +1493.47i q^{89} -1908.09i q^{91} +(689.710 - 936.283i) q^{92} +(-766.242 + 387.249i) q^{94} +(-8.22181 + 14.2406i) q^{95} +(700.115 + 1212.63i) q^{97} +(-988.129 - 646.332i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.157323 2.82405i 0.0556219 0.998452i
\(3\) 0 0
\(4\) −7.95050 0.888573i −0.993812 0.111072i
\(5\) 1.23846 + 0.715028i 0.110772 + 0.0639540i 0.554362 0.832275i \(-0.312962\pi\)
−0.443591 + 0.896230i \(0.646296\pi\)
\(6\) 0 0
\(7\) −23.8818 + 13.7882i −1.28950 + 0.744491i −0.978564 0.205941i \(-0.933974\pi\)
−0.310932 + 0.950432i \(0.600641\pi\)
\(8\) −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 \(-0.265153\pi\)
−0.977148 + 0.212560i \(0.931820\pi\)
\(12\) 0 0
\(13\) −34.5965 + 59.9229i −0.738103 + 1.27843i 0.215245 + 0.976560i \(0.430945\pi\)
−0.953348 + 0.301872i \(0.902388\pi\)
\(14\) 35.1813 + 69.6126i 0.671614 + 1.32891i
\(15\) 0 0
\(16\) 62.4209 + 14.1292i 0.975326 + 0.220769i
\(17\) 31.4507i 0.448701i −0.974509 0.224351i \(-0.927974\pi\)
0.974509 0.224351i \(-0.0720261\pi\)
\(18\) 0 0
\(19\) 11.4986i 0.138840i 0.997588 + 0.0694199i \(0.0221148\pi\)
−0.997588 + 0.0694199i \(0.977885\pi\)
\(20\) −9.21106 6.78529i −0.102983 0.0758619i
\(21\) 0 0
\(22\) −56.0849 + 28.3446i −0.543516 + 0.274686i
\(23\) −72.6810 + 125.887i −0.658914 + 1.14127i 0.321983 + 0.946746i \(0.395651\pi\)
−0.980897 + 0.194528i \(0.937683\pi\)
\(24\) 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 −0.169054 0.985607i \(-0.554071\pi\)
0.769033 + 0.639209i \(0.220738\pi\)
\(30\) 0 0
\(31\) 102.800 + 59.3514i 0.595592 + 0.343865i 0.767306 0.641282i \(-0.221597\pi\)
−0.171713 + 0.985147i \(0.554930\pi\)
\(32\) 49.7218 174.057i 0.274677 0.961537i
\(33\) 0 0
\(34\) −88.8183 4.94791i −0.448006 0.0249576i
\(35\) −39.4357 −0.190453
\(36\) 0 0
\(37\) −300.439 −1.33491 −0.667457 0.744649i \(-0.732617\pi\)
−0.667457 + 0.744649i \(0.732617\pi\)
\(38\) 32.4725 + 1.80899i 0.138625 + 0.00772254i
\(39\) 0 0
\(40\) −20.6111 + 24.9450i −0.0814726 + 0.0986037i
\(41\) −344.853 199.101i −1.31359 0.758399i −0.330897 0.943667i \(-0.607351\pi\)
−0.982688 + 0.185268i \(0.940685\pi\)
\(42\) 0 0
\(43\) −173.261 + 100.032i −0.614467 + 0.354763i −0.774712 0.632315i \(-0.782105\pi\)
0.160245 + 0.987077i \(0.448772\pi\)
\(44\) 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 \(-0.322780\pi\)
−0.999450 + 0.0331478i \(0.989447\pi\)
\(48\) 0 0
\(49\) 208.727 361.526i 0.608534 1.05401i
\(50\) −310.382 + 156.863i −0.877894 + 0.443676i
\(51\) 0 0
\(52\) 328.305 445.675i 0.875534 1.18854i
\(53\) 243.342i 0.630673i −0.948980 0.315336i \(-0.897883\pi\)
0.948980 0.315336i \(-0.102117\pi\)
\(54\) 0 0
\(55\) 31.7722i 0.0778940i
\(56\) −217.853 584.716i −0.519854 1.39528i
\(57\) 0 0
\(58\) −138.031 273.120i −0.312490 0.618318i
\(59\) −41.9197 + 72.6070i −0.0924996 + 0.160214i −0.908562 0.417749i \(-0.862819\pi\)
0.816063 + 0.577963i \(0.196152\pi\)
\(60\) 0 0
\(61\) 199.218 + 345.055i 0.418151 + 0.724259i 0.995754 0.0920592i \(-0.0293449\pi\)
−0.577602 + 0.816318i \(0.696012\pi\)
\(62\) 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 \(-0.228306\pi\)
−0.192437 + 0.981309i \(0.561639\pi\)
\(68\) −27.9463 + 250.049i −0.0498380 + 0.445925i
\(69\) 0 0
\(70\) −6.20413 + 111.368i −0.0105934 + 0.190158i
\(71\) 866.235 1.44793 0.723966 0.689836i \(-0.242317\pi\)
0.723966 + 0.689836i \(0.242317\pi\)
\(72\) 0 0
\(73\) 64.6645 0.103677 0.0518384 0.998655i \(-0.483492\pi\)
0.0518384 + 0.998655i \(0.483492\pi\)
\(74\) −47.2658 + 848.453i −0.0742505 + 1.33285i
\(75\) 0 0
\(76\) 10.2173 91.4195i 0.0154212 0.137981i
\(77\) 530.594 + 306.338i 0.785283 + 0.453383i
\(78\) 0 0
\(79\) −354.896 + 204.899i −0.505429 + 0.291809i −0.730953 0.682428i \(-0.760924\pi\)
0.225524 + 0.974238i \(0.427591\pi\)
\(80\) 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 \(-0.132970\pi\)
−0.808346 + 0.588708i \(0.799637\pi\)
\(84\) 0 0
\(85\) 22.4881 38.9506i 0.0286962 0.0497034i
\(86\) 255.238 + 505.035i 0.320036 + 0.633248i
\(87\) 0 0
\(88\) 471.089 175.518i 0.570662 0.212617i
\(89\) 1493.47i 1.77873i 0.457195 + 0.889366i \(0.348854\pi\)
−0.457195 + 0.889366i \(0.651146\pi\)
\(90\) 0 0
\(91\) 1908.09i 2.19805i
\(92\) 689.710 936.283i 0.781600 1.06102i
\(93\) 0 0
\(94\) −766.242 + 387.249i −0.840764 + 0.424911i
\(95\) −8.22181 + 14.2406i −0.00887936 + 0.0153795i
\(96\) 0 0
\(97\) 700.115 + 1212.63i 0.732844 + 1.26932i 0.955663 + 0.294463i \(0.0951408\pi\)
−0.222819 + 0.974860i \(0.571526\pi\)
\(98\) −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 −0.394375 0.918949i \(-0.629039\pi\)
0.598646 + 0.801014i \(0.295706\pi\)
\(102\) 0 0
\(103\) 504.070 + 291.025i 0.482208 + 0.278403i 0.721336 0.692585i \(-0.243528\pi\)
−0.239128 + 0.970988i \(0.576862\pi\)
\(104\) −1206.96 997.265i −1.13800 0.940287i
\(105\) 0 0
\(106\) −687.211 38.2833i −0.629696 0.0350792i
\(107\) −1470.35 −1.32845 −0.664224 0.747533i \(-0.731238\pi\)
−0.664224 + 0.747533i \(0.731238\pi\)
\(108\) 0 0
\(109\) −1.40399 −0.00123374 −0.000616870 1.00000i \(-0.500196\pi\)
−0.000616870 1.00000i \(0.500196\pi\)
\(110\) −89.7264 4.99849i −0.0777734 0.00433261i
\(111\) 0 0
\(112\) −1685.54 + 523.239i −1.42204 + 0.441441i
\(113\) 1174.77 + 678.256i 0.977996 + 0.564646i 0.901664 0.432436i \(-0.142346\pi\)
0.0763312 + 0.997083i \(0.475679\pi\)
\(114\) 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
\(122\) 1005.79 508.316i 0.746396 0.377219i
\(123\) 0 0
\(124\) −764.570 563.218i −0.553713 0.407891i
\(125\) 354.589i 0.253724i
\(126\) 0 0
\(127\) 547.847i 0.382784i 0.981514 + 0.191392i \(0.0613002\pi\)
−0.981514 + 0.191392i \(0.938700\pi\)
\(128\) −549.975 + 1339.66i −0.379776 + 0.925078i
\(129\) 0 0
\(130\) 126.238 + 249.785i 0.0851678 + 0.168520i
\(131\) 931.609 1613.59i 0.621336 1.07619i −0.367901 0.929865i \(-0.619923\pi\)
0.989237 0.146321i \(-0.0467433\pi\)
\(132\) 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 −0.837136 0.546995i \(-0.815772\pi\)
0.0551439 + 0.998478i \(0.482438\pi\)
\(138\) 0 0
\(139\) −324.131 187.137i −0.197787 0.114193i 0.397836 0.917457i \(-0.369761\pi\)
−0.595623 + 0.803264i \(0.703095\pi\)
\(140\) 313.533 + 35.0415i 0.189274 + 0.0211539i
\(141\) 0 0
\(142\) 136.278 2446.29i 0.0805368 1.44569i
\(143\) 1537.29 0.898986
\(144\) 0 0
\(145\) 154.723 0.0886143
\(146\) 10.1732 182.616i 0.00576670 0.103516i
\(147\) 0 0
\(148\) 2388.64 + 266.962i 1.32665 + 0.148271i
\(149\) −2138.30 1234.55i −1.17568 0.678779i −0.220669 0.975349i \(-0.570824\pi\)
−0.955011 + 0.296570i \(0.904157\pi\)
\(150\) 0 0
\(151\) −525.453 + 303.370i −0.283184 + 0.163496i −0.634864 0.772624i \(-0.718944\pi\)
0.351680 + 0.936120i \(0.385610\pi\)
\(152\) −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 −0.856423 0.516274i \(-0.827319\pi\)
0.875318 + 0.483547i \(0.160652\pi\)
\(158\) 522.812 + 1034.48i 0.263245 + 0.520877i
\(159\) 0 0
\(160\) 186.034 180.011i 0.0919205 0.0889443i
\(161\) 4008.55i 1.96222i
\(162\) 0 0
\(163\) 40.4850i 0.0194542i 0.999953 + 0.00972709i \(0.00309628\pi\)
−0.999953 + 0.00972709i \(0.996904\pi\)
\(164\) 2564.84 + 1889.38i 1.22122 + 0.899608i
\(165\) 0 0
\(166\) 403.388 203.867i 0.188608 0.0953201i
\(167\) −20.5614 + 35.6135i −0.00952750 + 0.0165021i −0.870750 0.491726i \(-0.836366\pi\)
0.861222 + 0.508228i \(0.169699\pi\)
\(168\) 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 −0.275890 0.961189i \(-0.588973\pi\)
0.694469 + 0.719522i \(0.255639\pi\)
\(174\) 0 0
\(175\) 2936.39 + 1695.32i 1.26840 + 0.732311i
\(176\) −421.559 1357.99i −0.180547 0.581605i
\(177\) 0 0
\(178\) 4217.62 + 234.956i 1.77598 + 0.0989366i
\(179\) −3849.91 −1.60757 −0.803787 0.594917i \(-0.797185\pi\)
−0.803787 + 0.594917i \(0.797185\pi\)
\(180\) 0 0
\(181\) −1091.65 −0.448296 −0.224148 0.974555i \(-0.571960\pi\)
−0.224148 + 0.974555i \(0.571960\pi\)
\(182\) −5388.54 300.186i −2.19464 0.122260i
\(183\) 0 0
\(184\) −2535.60 2095.07i −1.01591 0.839407i
\(185\) −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 \(-0.128023\pi\)
−0.799100 + 0.601199i \(0.794690\pi\)
\(192\) 0 0
\(193\) −874.103 + 1513.99i −0.326007 + 0.564660i −0.981716 0.190353i \(-0.939037\pi\)
0.655709 + 0.755014i \(0.272370\pi\)
\(194\) 3534.68 1786.38i 1.30812 0.661107i
\(195\) 0 0
\(196\) −1980.73 + 2688.84i −0.721839 + 0.979899i
\(197\) 2079.55i 0.752089i 0.926602 + 0.376044i \(0.122716\pi\)
−0.926602 + 0.376044i \(0.877284\pi\)
\(198\) 0 0
\(199\) 1834.81i 0.653598i 0.945094 + 0.326799i \(0.105970\pi\)
−0.945094 + 0.326799i \(0.894030\pi\)
\(200\) 2607.08 971.344i 0.921742 0.343422i
\(201\) 0 0
\(202\) −305.444 604.377i −0.106391 0.210514i
\(203\) −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 \(-0.634618\pi\)
−0.994936 + 0.100513i \(0.967952\pi\)
\(212\) −216.228 + 1934.69i −0.0700498 + 0.626770i
\(213\) 0 0
\(214\) −231.319 + 4152.34i −0.0738909 + 1.32639i
\(215\) −286.104 −0.0907540
\(216\) 0 0
\(217\) −3273.39 −1.02402
\(218\) −0.220879 + 3.96493i −6.86230e−5 + 0.00123183i
\(219\) 0 0
\(220\) −28.2320 + 252.605i −0.00865181 + 0.0774120i
\(221\) 1884.62 + 1088.08i 0.573634 + 0.331188i
\(222\) 0 0
\(223\) −611.995 + 353.335i −0.183777 + 0.106103i −0.589066 0.808085i \(-0.700504\pi\)
0.405289 + 0.914189i \(0.367171\pi\)
\(224\) 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 \(-0.322134\pi\)
−0.999381 + 0.0351765i \(0.988801\pi\)
\(228\) 0 0
\(229\) −731.826 + 1267.56i −0.211181 + 0.365776i −0.952084 0.305836i \(-0.901064\pi\)
0.740904 + 0.671611i \(0.234398\pi\)
\(230\) 265.203 + 524.753i 0.0760304 + 0.150440i
\(231\) 0 0
\(232\) 854.732 + 2294.09i 0.241879 + 0.649201i
\(233\) 1324.13i 0.372303i −0.982521 0.186152i \(-0.940398\pi\)
0.982521 0.186152i \(-0.0596015\pi\)
\(234\) 0 0
\(235\) 434.078i 0.120494i
\(236\) 397.799 540.013i 0.109722 0.148949i
\(237\) 0 0
\(238\) 2189.37 1106.48i 0.596283 0.301354i
\(239\) 394.528 683.342i 0.106778 0.184944i −0.807685 0.589614i \(-0.799280\pi\)
0.914463 + 0.404669i \(0.132613\pi\)
\(240\) 0 0
\(241\) 1170.39 + 2027.17i 0.312827 + 0.541832i 0.978973 0.203989i \(-0.0653907\pi\)
−0.666146 + 0.745821i \(0.732057\pi\)
\(242\) −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
\(248\) −1710.84 + 2070.58i −0.438058 + 0.530168i
\(249\) 0 0
\(250\) −1001.38 55.7849i −0.253331 0.0141126i
\(251\) 938.044 0.235892 0.117946 0.993020i \(-0.462369\pi\)
0.117946 + 0.993020i \(0.462369\pi\)
\(252\) 0 0
\(253\) 3229.58 0.802537
\(254\) 1547.15 + 86.1887i 0.382191 + 0.0212912i
\(255\) 0 0
\(256\) 3696.73 + 1763.91i 0.902522 + 0.430643i
\(257\) −143.756 82.9975i −0.0348920 0.0201449i 0.482453 0.875922i \(-0.339746\pi\)
−0.517345 + 0.855777i \(0.673079\pi\)
\(258\) 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 0.996916 + 0.0784782i \(0.0250061\pi\)
−0.430494 + 0.902594i \(0.641661\pi\)
\(264\) 0 0
\(265\) 173.997 301.371i 0.0403341 0.0698606i
\(266\) −800.446 + 404.535i −0.184506 + 0.0932468i
\(267\) 0 0
\(268\) −2288.98 1686.17i −0.521724 0.384326i
\(269\) 5581.42i 1.26508i 0.774529 + 0.632538i \(0.217987\pi\)
−0.774529 + 0.632538i \(0.782013\pi\)
\(270\) 0 0
\(271\) 8094.32i 1.81437i 0.420729 + 0.907186i \(0.361774\pi\)
−0.420729 + 0.907186i \(0.638226\pi\)
\(272\) 444.374 1963.18i 0.0990592 0.437630i
\(273\) 0 0
\(274\) 1847.26 + 3655.14i 0.407288 + 0.805894i
\(275\) −1365.87 + 2365.76i −0.299510 + 0.518767i
\(276\) 0 0
\(277\) 922.842 + 1598.41i 0.200174 + 0.346712i 0.948584 0.316524i \(-0.102516\pi\)
−0.748410 + 0.663236i \(0.769183\pi\)
\(278\) −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 −0.248571 0.968614i \(-0.579961\pi\)
0.714558 + 0.699576i \(0.246628\pi\)
\(282\) 0 0
\(283\) −2691.52 1553.95i −0.565351 0.326405i 0.189940 0.981796i \(-0.439171\pi\)
−0.755290 + 0.655390i \(0.772504\pi\)
\(284\) −6887.00 769.713i −1.43897 0.160824i
\(285\) 0 0
\(286\) 241.851 4341.39i 0.0500034 0.897595i
\(287\) 10981.0 2.25848
\(288\) 0 0
\(289\) 3923.85 0.798667
\(290\) 24.3415 436.946i 0.00492890 0.0884771i
\(291\) 0 0
\(292\) −514.115 57.4591i −0.103035 0.0115156i
\(293\) −4824.35 2785.34i −0.961916 0.555363i −0.0651539 0.997875i \(-0.520754\pi\)
−0.896762 + 0.442513i \(0.854087\pi\)
\(294\) 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
\(302\) 774.067 + 1531.63i 0.147492 + 0.291839i
\(303\) 0 0
\(304\) −162.466 + 717.751i −0.0306515 + 0.135414i
\(305\) 569.785i 0.106970i
\(306\) 0 0
\(307\) 7746.70i 1.44016i −0.693893 0.720078i \(-0.744106\pi\)
0.693893 0.720078i \(-0.255894\pi\)
\(308\) −3946.28 2907.01i −0.730066 0.537800i
\(309\) 0 0
\(310\) 428.514 216.566i 0.0785096 0.0396777i
\(311\) 2906.54 5034.28i 0.529951 0.917902i −0.469438 0.882965i \(-0.655544\pi\)
0.999390 0.0349372i \(-0.0111231\pi\)
\(312\) 0 0
\(313\) −1367.73 2368.98i −0.246993 0.427805i 0.715697 0.698411i \(-0.246109\pi\)
−0.962690 + 0.270606i \(0.912776\pi\)
\(314\) −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 −0.897055 0.441919i \(-0.854298\pi\)
−0.0658143 + 0.997832i \(0.520965\pi\)
\(318\) 0 0
\(319\) −2081.75 1201.90i −0.365378 0.210951i
\(320\) −479.091 553.689i −0.0836938 0.0967255i
\(321\) 0 0
\(322\) −11320.3 630.636i −1.95919 0.109143i
\(323\) 361.639 0.0622976
\(324\) 0 0
\(325\) 8507.62 1.45206
\(326\) 114.332 + 6.36921i 0.0194241 + 0.00108208i
\(327\) 0 0
\(328\) 5739.21 6945.99i 0.966142 1.16929i
\(329\) 7249.06 + 4185.25i 1.21475 + 0.701338i
\(330\) 0 0
\(331\) −302.371 + 174.574i −0.0502110 + 0.0289893i −0.524895 0.851167i \(-0.675896\pi\)
0.474684 + 0.880156i \(0.342562\pi\)
\(332\) −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 0.192252 + 0.981346i \(0.438421\pi\)
−0.945996 + 0.324178i \(0.894912\pi\)
\(338\) −6539.79 + 3305.13i −1.05242 + 0.531879i
\(339\) 0 0
\(340\) −213.402 + 289.694i −0.0340393 + 0.0462085i
\(341\) 2637.28i 0.418817i
\(342\) 0 0
\(343\) 2053.18i 0.323210i
\(344\) −1580.51 4242.08i −0.247719 0.664877i
\(345\) 0 0
\(346\) −1403.11 2776.31i −0.218011 0.431373i
\(347\) −2780.66 + 4816.24i −0.430183 + 0.745098i −0.996889 0.0788217i \(-0.974884\pi\)
0.566706 + 0.823920i \(0.308218\pi\)
\(348\) 0 0
\(349\) −5336.11 9242.41i −0.818439 1.41758i −0.906832 0.421492i \(-0.861506\pi\)
0.0883931 0.996086i \(-0.471827\pi\)
\(350\) 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 −0.526128 0.850405i \(-0.676357\pi\)
0.473409 + 0.880843i \(0.343023\pi\)
\(354\) 0 0
\(355\) 1072.80 + 619.382i 0.160390 + 0.0926011i
\(356\) 1327.06 11873.8i 0.197567 1.76773i
\(357\) 0 0
\(358\) −605.678 + 10872.3i −0.0894164 + 1.60509i
\(359\) −6398.10 −0.940609 −0.470305 0.882504i \(-0.655856\pi\)
−0.470305 + 0.882504i \(0.655856\pi\)
\(360\) 0 0
\(361\) 6726.78 0.980724
\(362\) −171.741 + 3082.87i −0.0249351 + 0.447602i
\(363\) 0 0
\(364\) −1695.48 + 15170.3i −0.244141 + 2.18444i
\(365\) 80.0847 + 46.2369i 0.0114844 + 0.00663055i
\(366\) 0 0
\(367\) 9573.58 5527.31i 1.36168 0.786166i 0.371833 0.928300i \(-0.378730\pi\)
0.989848 + 0.142133i \(0.0453962\pi\)
\(368\) −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 −0.961789 0.273791i \(-0.911722\pi\)
0.718004 + 0.696039i \(0.245056\pi\)
\(374\) 891.458 + 1763.91i 0.123252 + 0.243876i
\(375\) 0 0
\(376\) 6436.10 2397.96i 0.882757 0.328897i
\(377\) 7486.26i 1.02271i
\(378\) 0 0
\(379\) 1238.70i 0.167883i 0.996471 + 0.0839413i \(0.0267508\pi\)
−0.996471 + 0.0839413i \(0.973249\pi\)
\(380\) 78.0213 105.914i 0.0105326 0.0142981i
\(381\) 0 0
\(382\) 1613.94 815.665i 0.216169 0.109249i
\(383\) −853.999 + 1479.17i −0.113936 + 0.197342i −0.917354 0.398073i \(-0.869679\pi\)
0.803418 + 0.595415i \(0.203012\pi\)
\(384\) 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 0.0990663 0.995081i \(-0.468414\pi\)
0.911298 + 0.411746i \(0.135081\pi\)
\(390\) 0 0
\(391\) 3959.24 + 2285.87i 0.512091 + 0.295656i
\(392\) 7281.81 + 6016.69i 0.938232 + 0.775226i
\(393\) 0 0
\(394\) 5872.74 + 327.159i 0.750924 + 0.0418326i
\(395\) −586.034 −0.0746496
\(396\) 0 0
\(397\) −9391.26 −1.18724 −0.593619 0.804746i \(-0.702302\pi\)
−0.593619 + 0.804746i \(0.702302\pi\)
\(398\) 5181.59 + 288.657i 0.652586 + 0.0363544i
\(399\) 0 0
\(400\) −2332.97 7515.33i −0.291621 0.939417i
\(401\) −3528.74 2037.32i −0.439444 0.253713i 0.263918 0.964545i \(-0.414985\pi\)
−0.703362 + 0.710832i \(0.748319\pi\)
\(402\) 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 −0.845018 0.534737i \(-0.820411\pi\)
0.885605 + 0.464439i \(0.153744\pi\)
\(410\) −1437.50 + 726.494i −0.173154 + 0.0875097i
\(411\) 0 0
\(412\) −3749.01 2761.69i −0.448302 0.330240i
\(413\) 2311.98i 0.275460i
\(414\) 0 0
\(415\) 228.520i 0.0270304i
\(416\) 8709.79 + 9001.23i 1.02652 + 1.06087i
\(417\) 0 0
\(418\) −325.923 644.897i −0.0381373 0.0754616i
\(419\) 4703.57 8146.83i 0.548412 0.949877i −0.449972 0.893043i \(-0.648566\pi\)
0.998384 0.0568346i \(-0.0181008\pi\)
\(420\) 0 0
\(421\) 6156.19 + 10662.8i 0.712671 + 1.23438i 0.963851 + 0.266441i \(0.0858479\pi\)
−0.251181 + 0.967940i \(0.580819\pi\)
\(422\) −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
\(428\) 11690.0 + 1306.51i 1.32023 + 0.147553i
\(429\) 0 0
\(430\) −45.0106 + 807.971i −0.00504791 + 0.0906135i
\(431\) −7647.49 −0.854679 −0.427340 0.904091i \(-0.640549\pi\)
−0.427340 + 0.904091i \(0.640549\pi\)
\(432\) 0 0
\(433\) −13985.2 −1.55216 −0.776082 0.630632i \(-0.782796\pi\)
−0.776082 + 0.630632i \(0.782796\pi\)
\(434\) −514.978 + 9244.21i −0.0569579 + 1.02243i
\(435\) 0 0
\(436\) 11.1624 + 1.24755i 0.00122611 + 0.000137034i
\(437\) −1447.52 835.728i −0.158454 0.0914835i
\(438\) 0 0
\(439\) −11706.7 + 6758.84i −1.27273 + 0.734811i −0.975501 0.219996i \(-0.929396\pi\)
−0.297228 + 0.954806i \(0.596062\pi\)
\(440\) 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 \(-0.280743\pi\)
−0.986383 + 0.164467i \(0.947410\pi\)
\(444\) 0 0
\(445\) −1067.87 + 1849.61i −0.113757 + 0.197033i
\(446\) 901.555 + 1783.89i 0.0957172 + 0.189394i
\(447\) 0 0
\(448\) 13865.8 2662.28i 1.46227 0.280761i
\(449\) 17599.7i 1.84984i −0.380158 0.924921i \(-0.624130\pi\)
0.380158 0.924921i \(-0.375870\pi\)
\(450\) 0 0
\(451\) 8847.05i 0.923706i
\(452\) −8737.36 6436.35i −0.909228 0.669780i
\(453\) 0 0
\(454\) −8102.19 + 4094.75i −0.837566 + 0.423295i
\(455\) 1364.34 2363.10i 0.140574 0.243481i
\(456\) 0 0
\(457\) 1199.50 + 2077.59i 0.122779 + 0.212660i 0.920863 0.389887i \(-0.127486\pi\)
−0.798083 + 0.602547i \(0.794153\pi\)
\(458\) 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 −0.327450 0.944869i \(-0.606189\pi\)
0.654555 + 0.756014i \(0.272856\pi\)
\(462\) 0 0
\(463\) 2167.70 + 1251.52i 0.217585 + 0.125623i 0.604831 0.796354i \(-0.293240\pi\)
−0.387247 + 0.921976i \(0.626574\pi\)
\(464\) 6613.10 2052.89i 0.661649 0.205395i
\(465\) 0 0
\(466\) −3739.41 208.316i −0.371727 0.0207082i
\(467\) −5361.30 −0.531245 −0.265622 0.964077i \(-0.585577\pi\)
−0.265622 + 0.964077i \(0.585577\pi\)
\(468\) 0 0
\(469\) −9799.93 −0.964859
\(470\) −1225.86 68.2902i −0.120308 0.00670212i
\(471\) 0 0
\(472\) −1462.44 1208.36i −0.142615 0.117837i
\(473\) 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 \(-0.148137\pi\)
−0.835468 + 0.549538i \(0.814804\pi\)
\(480\) 0 0
\(481\) 10394.1 18003.2i 0.985304 1.70660i
\(482\) 5908.96 2986.31i 0.558393 0.282205i
\(483\) 0 0
\(484\) −3973.20 + 5393.63i −0.373140 + 0.506539i
\(485\) 2002.41i 0.187473i
\(486\) 0 0
\(487\) 1483.03i 0.137993i 0.997617 + 0.0689964i \(0.0219797\pi\)
−0.997617 + 0.0689964i \(0.978020\pi\)
\(488\) −8448.24 + 3147.64i −0.783676 + 0.291982i
\(489\) 0 0
\(490\) −761.618 1507.00i −0.0702171 0.138937i
\(491\) −6942.36 + 12024.5i −0.638094 + 1.10521i 0.347756 + 0.937585i \(0.386944\pi\)
−0.985851 + 0.167627i \(0.946390\pi\)
\(492\) 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 0.996245 + 0.0865784i \(0.0275933\pi\)
0.573102 + 0.819484i \(0.305740\pi\)
\(500\) −315.079 + 2819.16i −0.0281815 + 0.252154i
\(501\) 0 0
\(502\) 147.575 2649.08i 0.0131207 0.235526i
\(503\) −388.562 −0.0344436 −0.0172218 0.999852i \(-0.505482\pi\)
−0.0172218 + 0.999852i \(0.505482\pi\)
\(504\) 0 0
\(505\) 342.381 0.0301698
\(506\) 508.086 9120.48i 0.0446387 0.801294i
\(507\) 0 0
\(508\) 486.802 4355.66i 0.0425165 0.380416i
\(509\) −5854.78 3380.26i −0.509840 0.294356i 0.222928 0.974835i \(-0.428439\pi\)
−0.732768 + 0.680479i \(0.761772\pi\)
\(510\) 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
\(518\) −10569.8 20914.3i −0.896547 1.77398i
\(519\) 0 0
\(520\) −781.704 2098.09i −0.0659230 0.176937i
\(521\) 17324.6i 1.45683i −0.685139 0.728413i \(-0.740258\pi\)
0.685139 0.728413i \(-0.259742\pi\)
\(522\) 0 0
\(523\) 16119.4i 1.34771i −0.738864 0.673855i \(-0.764637\pi\)
0.738864 0.673855i \(-0.235363\pi\)
\(524\) −8840.55 + 12001.1i −0.737026 + 1.00051i
\(525\) 0 0
\(526\) 12197.1 6164.23i 1.01106 0.510976i
\(527\) 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
\(536\) −5121.94 + 6198.93i −0.412750 + 0.499539i
\(537\) 0 0
\(538\) 15762.2 + 878.084i 1.26312 + 0.0703660i
\(539\) −9274.78 −0.741175
\(540\) 0 0
\(541\) −4412.42 −0.350655 −0.175328 0.984510i \(-0.556099\pi\)
−0.175328 + 0.984510i \(0.556099\pi\)
\(542\) 22858.8 + 1273.42i 1.81156 + 0.100919i
\(543\) 0 0
\(544\) −5474.21 1563.79i −0.431443 0.123248i
\(545\) −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 \(-0.579596\pi\)
0.715360 + 0.698757i \(0.246263\pi\)
\(548\) 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
\(554\) 4659.17 2354.69i 0.357309 0.180579i
\(555\) 0 0
\(556\) 2410.72 + 1775.85i 0.183880 + 0.135455i
\(557\) 17257.6i 1.31280i 0.754415 + 0.656398i \(0.227921\pi\)
−0.754415 + 0.656398i \(0.772079\pi\)
\(558\) 0 0
\(559\) 13843.1i 1.04741i
\(560\) −2461.61 557.195i −0.185754 0.0420460i
\(561\) 0 0
\(562\) −3233.54 6398.15i −0.242702 0.480230i
\(563\) 12554.5 21745.1i 0.939805 1.62779i 0.173972 0.984751i \(-0.444340\pi\)
0.765833 0.643039i \(-0.222327\pi\)
\(564\) 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 −0.933953 0.357396i \(-0.883665\pi\)
−0.157463 + 0.987525i \(0.550331\pi\)
\(570\) 0 0
\(571\) 4814.10 + 2779.42i 0.352827 + 0.203705i 0.665929 0.746015i \(-0.268035\pi\)
−0.313103 + 0.949719i \(0.601368\pi\)
\(572\) −12222.3 1366.00i −0.893424 0.0998519i
\(573\) 0 0
\(574\) 1727.55 31010.7i 0.125621 2.25499i
\(575\) 17873.0 1.29627
\(576\) 0 0
\(577\) 19014.3 1.37188 0.685939 0.727659i \(-0.259392\pi\)
0.685939 + 0.727659i \(0.259392\pi\)
\(578\) 617.311 11081.1i 0.0444234 0.797431i
\(579\) 0 0
\(580\) −1230.13 137.483i −0.0880659 0.00984253i
\(581\) −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 0.844842 + 0.535017i \(0.179695\pi\)
0.0409172 + 0.999163i \(0.486972\pi\)
\(588\) 0 0
\(589\) −682.457 + 1182.05i −0.0477422 + 0.0826919i
\(590\) 152.959 + 302.658i 0.0106733 + 0.0211190i
\(591\) 0 0
\(592\) −18753.6 4244.96i −1.30198 0.294707i
\(593\) 17307.5i 1.19854i 0.800548 + 0.599269i \(0.204542\pi\)
−0.800548 + 0.599269i \(0.795458\pi\)
\(594\) 0 0
\(595\) 1240.28i 0.0854564i
\(596\) 15903.6 + 11715.3i 1.09301 + 0.805164i
\(597\) 0 0
\(598\) −25390.1 + 12831.8i −1.73625 + 0.877479i
\(599\) −10740.8 + 18603.5i −0.732647 + 1.26898i 0.223101 + 0.974795i \(0.428382\pi\)
−0.955748 + 0.294186i \(0.904951\pi\)
\(600\) 0 0
\(601\) 2716.74 + 4705.53i 0.184390 + 0.319372i 0.943371 0.331741i \(-0.107636\pi\)
−0.758981 + 0.651113i \(0.774303\pi\)
\(602\) −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 \(-0.184364\pi\)
−0.0555692 + 0.998455i \(0.517697\pi\)
\(608\) 2001.41 + 571.730i 0.133500 + 0.0381360i
\(609\) 0 0
\(610\) 1609.10 + 89.6401i 0.106804 + 0.00594987i
\(611\) 21002.8 1.39064
\(612\) 0 0
\(613\) 8330.79 0.548903 0.274451 0.961601i \(-0.411504\pi\)
0.274451 + 0.961601i \(0.411504\pi\)
\(614\) −21877.1 1218.73i −1.43793 0.0801042i
\(615\) 0 0
\(616\) −8830.39 + 10687.1i −0.577576 + 0.699022i
\(617\) 17147.1 + 9899.88i 1.11883 + 0.645955i 0.941101 0.338125i \(-0.109793\pi\)
0.177726 + 0.984080i \(0.443126\pi\)
\(618\) 0 0
\(619\) −22673.3 + 13090.4i −1.47224 + 0.849997i −0.999513 0.0312129i \(-0.990063\pi\)
−0.472725 + 0.881210i \(0.656730\pi\)
\(620\) −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
\(626\) −6905.30 + 3489.85i −0.440880 + 0.222815i
\(627\) 0 0
\(628\) −352.726 + 478.826i −0.0224129 + 0.0304255i
\(629\) 9449.01i 0.598977i
\(630\) 0 0
\(631\) 24489.4i 1.54502i −0.635004 0.772509i \(-0.719001\pi\)
0.635004 0.772509i \(-0.280999\pi\)
\(632\) −3237.41 8689.17i −0.203761 0.546893i
\(633\) 0 0
\(634\) 8005.73 + 15840.8i 0.501496 + 0.992300i
\(635\) −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 0.278578 0.960414i \(-0.410137\pi\)
0.971032 + 0.238951i \(0.0768035\pi\)
\(642\) 0 0
\(643\) 1385.76 + 800.068i 0.0849907 + 0.0490694i 0.541893 0.840447i \(-0.317708\pi\)
−0.456902 + 0.889517i \(0.651041\pi\)
\(644\) −3561.89 + 31870.0i −0.217947 + 1.95008i
\(645\) 0 0
\(646\) 56.8939 1021.28i 0.00346511 0.0622011i
\(647\) −19887.1 −1.20841 −0.604206 0.796828i \(-0.706509\pi\)
−0.604206 + 0.796828i \(0.706509\pi\)
\(648\) 0 0
\(649\) 1862.70 0.112662
\(650\) 1338.44 24025.9i 0.0807661 1.44981i
\(651\) 0 0
\(652\) 35.9739 321.876i 0.00216081 0.0193338i
\(653\) −3929.91 2268.93i −0.235512 0.135973i 0.377600 0.925969i \(-0.376749\pi\)
−0.613112 + 0.789996i \(0.710083\pi\)
\(654\) 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 \(-0.150092\pi\)
−0.838828 + 0.544396i \(0.816759\pi\)
\(660\) 0 0
\(661\) 3948.96 6839.80i 0.232370 0.402477i −0.726135 0.687552i \(-0.758685\pi\)
0.958505 + 0.285075i \(0.0920185\pi\)
\(662\) 445.436 + 881.376i 0.0261516 + 0.0517457i
\(663\) 0 0
\(664\) −3388.28 + 1262.40i −0.198028 + 0.0737813i
\(665\) 453.455i 0.0264424i
\(666\) 0 0
\(667\) 15727.3i 0.912987i
\(668\) 195.119 264.874i 0.0113015 0.0153418i
\(669\) 0 0
\(670\) 1282.89 648.358i 0.0739739 0.0373854i
\(671\) 4426.12 7666.26i 0.254647 0.441062i
\(672\) 0 0
\(673\) 8028.88 + 13906.4i 0.459867 + 0.796513i 0.998953 0.0457375i \(-0.0145638\pi\)
−0.539087 + 0.842250i \(0.681230\pi\)
\(674\) 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 −0.889151 0.457613i \(-0.848704\pi\)
−0.0482708 + 0.998834i \(0.515371\pi\)
\(678\) 0 0
\(679\) −33440.0 19306.6i −1.89000 1.09119i
\(680\) 784.538 + 648.234i 0.0442436 + 0.0365568i
\(681\) 0 0
\(682\) −7447.80 414.903i −0.418169 0.0232954i
\(683\) 15166.6 0.849682 0.424841 0.905268i \(-0.360330\pi\)
0.424841 + 0.905268i \(0.360330\pi\)
\(684\) 0 0
\(685\) −2070.64 −0.115497
\(686\) 5798.27 + 323.011i 0.322710 + 0.0179776i
\(687\) 0 0
\(688\) −12228.5 + 3796.07i −0.677626 + 0.210354i
\(689\) 14581.8 + 8418.80i 0.806272 + 0.465502i
\(690\) 0 0
\(691\) 8692.79 5018.79i 0.478567 0.276301i −0.241252 0.970462i \(-0.577558\pi\)
0.719819 + 0.694162i \(0.244225\pi\)
\(692\) −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
\(698\) −26940.5 + 13615.4i −1.46091 + 0.738324i
\(699\) 0 0
\(700\) −21839.3 16087.9i −1.17921 0.868663i
\(701\) 13222.0i 0.712394i 0.934411 + 0.356197i \(0.115927\pi\)
−0.934411 + 0.356197i \(0.884073\pi\)
\(702\) 0 0
\(703\) 3454.62i 0.185339i
\(704\) 2144.93 + 11171.3i 0.114830 + 0.598060i
\(705\) 0 0
\(706\) 515.085 + 1019.19i 0.0274582 + 0.0543310i
\(707\) −3301.14 + 5717.74i −0.175604 + 0.304155i
\(708\) 0 0
\(709\) −11792.3 20424.8i −0.624636 1.08190i −0.988611 0.150493i \(-0.951914\pi\)
0.363975 0.931409i \(-0.381419\pi\)
\(710\) 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
\(716\) 30608.7 + 3420.93i 1.59763 + 0.178556i
\(717\) 0 0
\(718\) −1006.57 + 18068.5i −0.0523185 + 0.939153i
\(719\) 19376.4 1.00503 0.502517 0.864567i \(-0.332407\pi\)
0.502517 + 0.864567i \(0.332407\pi\)
\(720\) 0 0
\(721\) −16050.8 −0.829074
\(722\) 1058.27 18996.8i 0.0545497 0.979205i
\(723\) 0 0
\(724\) 8679.15 + 970.010i 0.445522 + 0.0497930i
\(725\) −11520.7 6651.48i −0.590163 0.340731i
\(726\) 0 0
\(727\) 19193.8 11081.5i 0.979172 0.565325i 0.0771518 0.997019i \(-0.475417\pi\)
0.902020 + 0.431694i \(0.142084\pi\)
\(728\) 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 −0.201522 0.979484i \(-0.564589\pi\)
0.949019 0.315219i \(-0.102078\pi\)
\(734\) −14103.2 27905.8i −0.709210 1.40330i
\(735\) 0 0
\(736\) 18297.7 + 18909.9i 0.916388 + 0.947051i
\(737\) 7895.53i 0.394621i
\(738\) 0 0
\(739\) 14616.0i 0.727549i 0.931487 + 0.363774i \(0.118512\pi\)
−0.931487 + 0.363774i \(0.881488\pi\)
\(740\) 2767.36 + 2038.56i 0.137473 + 0.101269i
\(741\) 0 0
\(742\) 16939.7 8561.10i 0.838107 0.423569i
\(743\) −17948.9 + 31088.4i −0.886246 + 1.53502i −0.0419682 + 0.999119i \(0.513363\pi\)
−0.844278 + 0.535905i \(0.819971\pi\)
\(744\) 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 \(-0.107839\pi\)
0.183761 + 0.982971i \(0.441173\pi\)
\(752\) −5759.41 18553.1i −0.279287 0.899684i
\(753\) 0 0
\(754\) 21141.6 + 1177.76i 1.02113 + 0.0568852i
\(755\) −867.673 −0.0418250
\(756\) 0 0
\(757\) 1805.80 0.0867016 0.0433508 0.999060i \(-0.486197\pi\)
0.0433508 + 0.999060i \(0.486197\pi\)
\(758\) 3498.14 + 194.875i 0.167623 + 0.00933795i
\(759\) 0 0
\(760\) −286.832 236.998i −0.0136901 0.0113116i
\(761\) 3770.72 + 2177.03i 0.179617 + 0.103702i 0.587113 0.809505i \(-0.300265\pi\)
−0.407496 + 0.913207i \(0.633598\pi\)
\(762\) 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 −0.896789 0.442459i \(-0.854106\pi\)
0.831575 + 0.555412i \(0.187440\pi\)
\(770\) 2211.75 1117.79i 0.103514 0.0523147i
\(771\) 0 0
\(772\) 8294.85 11260.3i 0.386707 0.524956i
\(773\) 7776.95i 0.361860i −0.983496 0.180930i \(-0.942089\pi\)
0.983496 0.180930i \(-0.0579107\pi\)
\(774\) 0 0
\(775\) 14595.1i 0.676479i
\(776\) −29689.8 + 11061.8i −1.37346 + 0.511721i
\(777\) 0 0
\(778\) −11419.5 22595.6i −0.526233 1.04125i
\(779\) 2289.38 3965.32i 0.105296 0.182378i
\(780\) 0 0