Properties

Label 108.4.h.b.35.7
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 35.7
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.7

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.443591 0.896230i \(-0.646296\pi\)
0.554362 + 0.832275i \(0.312962\pi\)
\(6\) 0 0
\(7\) −23.8818 13.7882i −1.28950 0.744491i −0.310932 0.950432i \(-0.600641\pi\)
−0.978564 + 0.205941i \(0.933974\pi\)
\(8\) −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 −0.977148 0.212560i \(-0.931820\pi\)
0.672656 + 0.739955i \(0.265153\pi\)
\(12\) 0 0
\(13\) −34.5965 59.9229i −0.738103 1.27843i −0.953348 0.301872i \(-0.902388\pi\)
0.215245 0.976560i \(-0.430945\pi\)
\(14\) 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 \(0.0720261\pi\)
−0.974509 + 0.224351i \(0.927974\pi\)
\(18\) 0 0
\(19\) 11.4986i 0.138840i −0.997588 0.0694199i \(-0.977885\pi\)
0.997588 0.0694199i \(-0.0221148\pi\)
\(20\) −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 −0.980897 0.194528i \(-0.937683\pi\)
0.321983 0.946746i \(1.60435\pi\)
\(24\) 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 −0.171713 0.985147i \(-0.554930\pi\)
0.767306 + 0.641282i \(0.221597\pi\)
\(32\) 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 −0.982688 0.185268i \(-0.940685\pi\)
−0.330897 + 0.943667i \(0.607351\pi\)
\(42\) 0 0
\(43\) −173.261 100.032i −0.614467 0.354763i 0.160245 0.987077i \(-0.448772\pi\)
−0.774712 + 0.632315i \(0.782105\pi\)
\(44\) 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 −0.999450 0.0331478i \(-0.989447\pi\)
0.528432 + 0.848976i \(0.322780\pi\)
\(48\) 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 \(0.102117\pi\)
−0.948980 + 0.315336i \(0.897883\pi\)
\(54\) 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 0.816063 0.577963i \(-0.196152\pi\)
−0.908562 + 0.417749i \(0.862819\pi\)
\(60\) 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 −0.192437 0.981309i \(-0.561639\pi\)
0.753620 + 0.657310i \(0.228306\pi\)
\(68\) −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 0.225524 0.974238i \(-0.427591\pi\)
−0.730953 + 0.682428i \(0.760924\pi\)
\(80\) 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 −0.808346 0.588708i \(-0.799637\pi\)
0.914009 + 0.405694i \(0.132970\pi\)
\(84\) 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 \(-0.651146\pi\)
0.457195 0.889366i \(-0.348854\pi\)
\(90\) 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 −0.222819 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 −0.239128 0.970988i \(-0.576862\pi\)
0.721336 + 0.692585i \(0.243528\pi\)
\(104\) −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 0.0763312 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
\(122\) 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 \(-0.938700\pi\)
0.981514 0.191392i \(-0.0613002\pi\)
\(128\) −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 0.989237 + 0.146321i \(0.0467433\pi\)
−0.367901 + 0.929865i \(0.619923\pi\)
\(132\) 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 −0.595623 0.803264i \(-0.703095\pi\)
0.397836 + 0.917457i \(0.369761\pi\)
\(140\) 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 −0.955011 0.296570i \(-0.904157\pi\)
−0.220669 + 0.975349i \(0.570824\pi\)
\(150\) 0 0
\(151\) −525.453 303.370i −0.283184 0.163496i 0.351680 0.936120i \(-0.385610\pi\)
−0.634864 + 0.772624i \(0.718944\pi\)
\(152\) −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 \(0.827319\pi\)
\(158\) 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 \(-0.996904\pi\)
0.999953 0.00972709i \(-0.00309628\pi\)
\(164\) 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 0.861222 0.508228i \(-0.169699\pi\)
−0.870750 + 0.491726i \(0.836366\pi\)
\(168\) 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
\(176\) −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 −0.799100 0.601199i \(-0.794690\pi\)
0.920203 + 0.391441i \(0.128023\pi\)
\(192\) 0 0
\(193\) −874.103 1513.99i −0.326007 0.564660i 0.655709 0.755014i \(-0.272370\pi\)
−0.981716 + 0.190353i \(0.939037\pi\)
\(194\) 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 \(-0.877284\pi\)
0.926602 0.376044i \(-0.122716\pi\)
\(198\) 0 0
\(199\) 1834.81i 0.653598i −0.945094 0.326799i \(-0.894030\pi\)
0.945094 0.326799i \(-0.105970\pi\)
\(200\) 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 −0.994936 0.100513i \(-0.967952\pi\)
−0.410421 + 0.911896i \(0.634618\pi\)
\(212\) −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 0.405289 0.914189i \(-0.367171\pi\)
−0.589066 + 0.808085i \(0.700504\pi\)
\(224\) 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 −0.999381 0.0351765i \(-0.988801\pi\)
0.530154 + 0.847901i \(0.322134\pi\)
\(228\) 0 0
\(229\) −731.826 1267.56i −0.211181 0.365776i 0.740904 0.671611i \(-0.234398\pi\)
−0.952084 + 0.305836i \(0.901064\pi\)
\(230\) 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 \(0.0596015\pi\)
−0.982521 + 0.186152i \(0.940398\pi\)
\(234\) 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 0.914463 0.404669i \(-0.132613\pi\)
−0.807685 + 0.589614i \(0.799280\pi\)
\(240\) 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
\(248\) −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 −0.517345 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 \(-0.641661\pi\)
0.996916 0.0784782i \(-0.0250061\pi\)
\(264\) 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 \(-0.782013\pi\)
0.774529 0.632538i \(-0.217987\pi\)
\(270\) 0 0
\(271\) 8094.32i 1.81437i −0.420729 0.907186i \(-0.638226\pi\)
0.420729 0.907186i \(-0.361774\pi\)
\(272\) 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 −0.748410 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 −0.755290 0.655390i \(-0.772504\pi\)
0.189940 + 0.981796i \(0.439171\pi\)
\(284\) −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 −0.896762 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
\(302\) 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 \(0.255894\pi\)
−0.693893 + 0.720078i \(0.744106\pi\)
\(308\) −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 0.999390 + 0.0349372i \(0.0111231\pi\)
−0.469438 + 0.882965i \(0.655544\pi\)
\(312\) 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
\(320\) −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 0.474684 0.880156i \(-0.342562\pi\)
−0.524895 + 0.851167i \(0.675896\pi\)
\(332\) −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 \(-0.438421\pi\)
\(338\) −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 0.566706 0.823920i \(-0.308218\pi\)
−0.996889 + 0.0788217i \(0.974884\pi\)
\(348\) 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
\(356\) 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 0.989848 0.142133i \(-0.0453962\pi\)
0.371833 + 0.928300i \(0.378730\pi\)
\(368\) −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 \(0.911722\pi\)
\(374\) 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 \(-0.973249\pi\)
0.996471 0.0839413i \(-0.0267508\pi\)
\(380\) 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 0.803418 0.595415i \(-0.203012\pi\)
−0.917354 + 0.398073i \(0.869679\pi\)
\(384\) 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
\(392\) 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 −0.703362 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 \(0.820411\pi\)
\(410\) −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 0.998384 + 0.0568346i \(0.0181008\pi\)
−0.449972 + 0.893043i \(0.648566\pi\)
\(420\) 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
\(428\) 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 −0.297228 0.954806i \(-0.596062\pi\)
−0.975501 + 0.219996i \(0.929396\pi\)
\(440\) 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 −0.986383 0.164467i \(-0.947410\pi\)
0.635624 + 0.771999i \(0.280743\pi\)
\(444\) 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 \(0.375870\pi\)
−0.380158 + 0.924921i \(0.624130\pi\)
\(450\) 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 −0.798083 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 −0.387247 0.921976i \(-0.626574\pi\)
0.604831 + 0.796354i \(0.293240\pi\)
\(464\) 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 −0.835468 0.549538i \(-0.814804\pi\)
0.893648 + 0.448768i \(0.148137\pi\)
\(480\) 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 \(-0.978020\pi\)
0.997617 0.0689964i \(-0.0219797\pi\)
\(488\) −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 −0.985851 0.167627i \(-0.946390\pi\)
0.347756 0.937585i \(1.61306\pi\)
\(492\) 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 \(-0.305740\pi\)
0.996245 0.0865784i \(-0.0275933\pi\)
\(500\) −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 −0.732768 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
\(518\) −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 \(0.259742\pi\)
−0.685139 + 0.728413i \(0.740258\pi\)
\(522\) 0 0
\(523\) 16119.4i 1.34771i 0.738864 + 0.673855i \(0.235363\pi\)
−0.738864 + 0.673855i \(0.764637\pi\)
\(524\) −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 0.715360 0.698757i \(-0.246263\pi\)
−0.247461 + 0.968898i \(0.579596\pi\)
\(548\) 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 \(-0.772079\pi\)
0.754415 0.656398i \(-0.227921\pi\)
\(558\) 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 0.765833 + 0.643039i \(0.222327\pi\)
0.173972 + 0.984751i \(0.444340\pi\)
\(564\) 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 −0.313103 0.949719i \(-0.601368\pi\)
0.665929 + 0.746015i \(0.268035\pi\)
\(572\) −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 0.0409172 0.999163i \(-0.486972\pi\)
0.844842 0.535017i \(-0.179695\pi\)
\(588\) 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 \(-0.795458\pi\)
0.800548 0.599269i \(-0.204542\pi\)
\(594\) 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 −0.955748 0.294186i \(-0.904951\pi\)
0.223101 0.974795i \(1.57162\pi\)
\(600\) 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 −0.0555692 0.998455i \(-0.517697\pi\)
0.836903 + 0.547352i \(0.184364\pi\)
\(608\) 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 0.177726 0.984080i \(-0.443126\pi\)
0.941101 + 0.338125i \(0.109793\pi\)
\(618\) 0 0
\(619\) −22673.3 13090.4i −1.47224 0.849997i −0.472725 0.881210i \(-0.656730\pi\)
−0.999513 + 0.0312129i \(0.990063\pi\)
\(620\) −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 \(0.280999\pi\)
−0.635004 + 0.772509i \(0.719001\pi\)
\(632\) −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 0.971032 0.238951i \(-0.0768035\pi\)
0.278578 + 0.960414i \(0.410137\pi\)
\(642\) 0 0
\(643\) 1385.76 800.068i 0.0849907 0.0490694i −0.456902 0.889517i \(-0.651041\pi\)
0.541893 + 0.840447i \(0.317708\pi\)
\(644\) −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 −0.613112 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 −0.838828 0.544396i \(-0.816759\pi\)
0.890875 + 0.454249i \(0.150092\pi\)
\(660\) 0 0
\(661\) 3948.96 + 6839.80i 0.232370 + 0.402477i 0.958505 0.285075i \(-0.0920185\pi\)
−0.726135 + 0.687552i \(0.758685\pi\)
\(662\) 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 −0.539087 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
\(680\) 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 0.719819 0.694162i \(-0.244225\pi\)
−0.241252 + 0.970462i \(0.577558\pi\)
\(692\) −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 \(-0.884073\pi\)
0.934411 0.356197i \(-0.115927\pi\)
\(702\) 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 0.363975 + 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
\(716\) 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 0.902020 0.431694i \(-0.142084\pi\)
0.0771518 + 0.997019i \(0.475417\pi\)
\(728\) 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 \(0.564589\pi\)
\(734\) −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 \(-0.881488\pi\)
0.931487 0.363774i \(-0.118512\pi\)
\(740\) 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 −0.844278 0.535905i \(-0.819971\pi\)
−0.0419682 0.999119i \(1.48664\pi\)
\(744\) 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 0.183761 0.982971i \(-0.441173\pi\)
0.943158 + 0.332344i \(0.107839\pi\)
\(752\) −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 −0.407496 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 \(0.854106\pi\)
\(770\) 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 \(0.0579107\pi\)
−0.983496 + 0.180930i \(0.942089\pi\)
\(774\) 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