Properties

Label 108.4.i.a.49.2
Level 108
Weight 4
Character 108.49
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 49.2
Character \(\chi\) \(=\) 108.49
Dual form 108.4.i.a.97.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.14053 + 3.13943i) q^{3} +(-4.27250 + 1.55506i) q^{5} +(-4.69568 - 26.6305i) q^{7} +(7.28791 - 25.9978i) q^{9} +O(q^{10})\) \(q+(-4.14053 + 3.13943i) q^{3} +(-4.27250 + 1.55506i) q^{5} +(-4.69568 - 26.6305i) q^{7} +(7.28791 - 25.9978i) q^{9} +(50.9513 + 18.5448i) q^{11} +(42.8395 + 35.9466i) q^{13} +(12.8084 - 19.8520i) q^{15} +(49.3862 - 85.5394i) q^{17} +(-68.0936 - 117.942i) q^{19} +(103.047 + 95.5225i) q^{21} +(25.4482 - 144.324i) q^{23} +(-79.9195 + 67.0604i) q^{25} +(51.4427 + 130.525i) q^{27} +(-37.6146 + 31.5624i) q^{29} +(26.6026 - 150.871i) q^{31} +(-269.185 + 83.1733i) q^{33} +(61.4744 + 106.477i) q^{35} +(11.7745 - 20.3941i) q^{37} +(-290.230 - 14.3461i) q^{39} +(317.305 + 266.251i) q^{41} +(-269.878 - 98.2276i) q^{43} +(9.29066 + 122.409i) q^{45} +(-48.6186 - 275.730i) q^{47} +(-364.820 + 132.783i) q^{49} +(64.0605 + 509.223i) q^{51} +248.490 q^{53} -246.528 q^{55} +(652.213 + 274.565i) q^{57} +(243.543 - 88.6422i) q^{59} +(-57.5577 - 326.426i) q^{61} +(-726.556 - 72.0033i) q^{63} +(-238.931 - 86.9637i) q^{65} +(71.5526 + 60.0398i) q^{67} +(347.726 + 677.469i) q^{69} +(-333.619 + 577.845i) q^{71} +(-106.851 - 185.072i) q^{73} +(120.377 - 528.567i) q^{75} +(254.606 - 1443.94i) q^{77} +(-421.142 + 353.380i) q^{79} +(-622.773 - 378.939i) q^{81} +(310.120 - 260.222i) q^{83} +(-77.9834 + 442.266i) q^{85} +(56.6561 - 248.773i) q^{87} +(504.793 + 874.328i) q^{89} +(756.115 - 1309.63i) q^{91} +(363.501 + 708.203i) q^{93} +(474.337 + 398.016i) q^{95} +(-27.6645 - 10.0690i) q^{97} +(853.452 - 1189.47i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.14053 + 3.13943i −0.796845 + 0.604184i
\(4\) 0 0
\(5\) −4.27250 + 1.55506i −0.382144 + 0.139089i −0.525947 0.850517i \(-0.676289\pi\)
0.143803 + 0.989606i \(0.454067\pi\)
\(6\) 0 0
\(7\) −4.69568 26.6305i −0.253543 1.43791i −0.799786 0.600285i \(-0.795054\pi\)
0.546243 0.837627i \(-0.316057\pi\)
\(8\) 0 0
\(9\) 7.28791 25.9978i 0.269922 0.962882i
\(10\) 0 0
\(11\) 50.9513 + 18.5448i 1.39658 + 0.508315i 0.927162 0.374660i \(-0.122241\pi\)
0.469420 + 0.882975i \(0.344463\pi\)
\(12\) 0 0
\(13\) 42.8395 + 35.9466i 0.913964 + 0.766906i 0.972869 0.231357i \(-0.0743166\pi\)
−0.0589054 + 0.998264i \(0.518761\pi\)
\(14\) 0 0
\(15\) 12.8084 19.8520i 0.220474 0.341718i
\(16\) 0 0
\(17\) 49.3862 85.5394i 0.704583 1.22037i −0.262259 0.964998i \(-0.584467\pi\)
0.966842 0.255376i \(-0.0821993\pi\)
\(18\) 0 0
\(19\) −68.0936 117.942i −0.822197 1.42409i −0.904043 0.427442i \(-0.859415\pi\)
0.0818453 0.996645i \(-0.473919\pi\)
\(20\) 0 0
\(21\) 103.047 + 95.5225i 1.07080 + 0.992606i
\(22\) 0 0
\(23\) 25.4482 144.324i 0.230709 1.30842i −0.620756 0.784004i \(-0.713174\pi\)
0.851465 0.524412i \(-0.175715\pi\)
\(24\) 0 0
\(25\) −79.9195 + 67.0604i −0.639356 + 0.536483i
\(26\) 0 0
\(27\) 51.4427 + 130.525i 0.366672 + 0.930350i
\(28\) 0 0
\(29\) −37.6146 + 31.5624i −0.240857 + 0.202103i −0.755223 0.655468i \(-0.772472\pi\)
0.514366 + 0.857570i \(0.328027\pi\)
\(30\) 0 0
\(31\) 26.6026 150.871i 0.154128 0.874105i −0.805450 0.592663i \(-0.798076\pi\)
0.959578 0.281441i \(-0.0908125\pi\)
\(32\) 0 0
\(33\) −269.185 + 83.1733i −1.41997 + 0.438746i
\(34\) 0 0
\(35\) 61.4744 + 106.477i 0.296888 + 0.514225i
\(36\) 0 0
\(37\) 11.7745 20.3941i 0.0523168 0.0906154i −0.838681 0.544623i \(-0.816673\pi\)
0.890998 + 0.454008i \(0.150006\pi\)
\(38\) 0 0
\(39\) −290.230 14.3461i −1.19164 0.0589027i
\(40\) 0 0
\(41\) 317.305 + 266.251i 1.20865 + 1.01418i 0.999340 + 0.0363307i \(0.0115670\pi\)
0.209312 + 0.977849i \(0.432877\pi\)
\(42\) 0 0
\(43\) −269.878 98.2276i −0.957117 0.348362i −0.184214 0.982886i \(-0.558974\pi\)
−0.772903 + 0.634524i \(0.781196\pi\)
\(44\) 0 0
\(45\) 9.29066 + 122.409i 0.0307771 + 0.405503i
\(46\) 0 0
\(47\) −48.6186 275.730i −0.150888 0.855730i −0.962449 0.271462i \(-0.912493\pi\)
0.811561 0.584268i \(-0.198618\pi\)
\(48\) 0 0
\(49\) −364.820 + 132.783i −1.06361 + 0.387124i
\(50\) 0 0
\(51\) 64.0605 + 509.223i 0.175888 + 1.39815i
\(52\) 0 0
\(53\) 248.490 0.644015 0.322007 0.946737i \(-0.395642\pi\)
0.322007 + 0.946737i \(0.395642\pi\)
\(54\) 0 0
\(55\) −246.528 −0.604397
\(56\) 0 0
\(57\) 652.213 + 274.565i 1.51557 + 0.638018i
\(58\) 0 0
\(59\) 243.543 88.6422i 0.537399 0.195597i −0.0590401 0.998256i \(-0.518804\pi\)
0.596439 + 0.802658i \(0.296582\pi\)
\(60\) 0 0
\(61\) −57.5577 326.426i −0.120812 0.685156i −0.983708 0.179775i \(-0.942463\pi\)
0.862896 0.505381i \(-0.168648\pi\)
\(62\) 0 0
\(63\) −726.556 72.0033i −1.45298 0.143993i
\(64\) 0 0
\(65\) −238.931 86.9637i −0.455934 0.165946i
\(66\) 0 0
\(67\) 71.5526 + 60.0398i 0.130471 + 0.109478i 0.705688 0.708523i \(-0.250638\pi\)
−0.575217 + 0.818001i \(0.695082\pi\)
\(68\) 0 0
\(69\) 347.726 + 677.469i 0.606685 + 1.18199i
\(70\) 0 0
\(71\) −333.619 + 577.845i −0.557651 + 0.965881i 0.440040 + 0.897978i \(0.354964\pi\)
−0.997692 + 0.0679028i \(0.978369\pi\)
\(72\) 0 0
\(73\) −106.851 185.072i −0.171315 0.296726i 0.767565 0.640971i \(-0.221468\pi\)
−0.938880 + 0.344245i \(0.888135\pi\)
\(74\) 0 0
\(75\) 120.377 528.567i 0.185332 0.813783i
\(76\) 0 0
\(77\) 254.606 1443.94i 0.376818 2.13704i
\(78\) 0 0
\(79\) −421.142 + 353.380i −0.599775 + 0.503271i −0.891373 0.453270i \(-0.850257\pi\)
0.291598 + 0.956541i \(0.405813\pi\)
\(80\) 0 0
\(81\) −622.773 378.939i −0.854284 0.519807i
\(82\) 0 0
\(83\) 310.120 260.222i 0.410122 0.344133i −0.414268 0.910155i \(-0.635962\pi\)
0.824391 + 0.566021i \(0.191518\pi\)
\(84\) 0 0
\(85\) −77.9834 + 442.266i −0.0995116 + 0.564358i
\(86\) 0 0
\(87\) 56.6561 248.773i 0.0698180 0.306566i
\(88\) 0 0
\(89\) 504.793 + 874.328i 0.601213 + 1.04133i 0.992638 + 0.121122i \(0.0386492\pi\)
−0.391424 + 0.920210i \(0.628017\pi\)
\(90\) 0 0
\(91\) 756.115 1309.63i 0.871015 1.50864i
\(92\) 0 0
\(93\) 363.501 + 708.203i 0.405304 + 0.789647i
\(94\) 0 0
\(95\) 474.337 + 398.016i 0.512273 + 0.429848i
\(96\) 0 0
\(97\) −27.6645 10.0690i −0.0289578 0.0105398i 0.327501 0.944851i \(-0.393794\pi\)
−0.356458 + 0.934311i \(0.616016\pi\)
\(98\) 0 0
\(99\) 853.452 1189.47i 0.866416 1.20754i
\(100\) 0 0
\(101\) −16.0416 90.9764i −0.0158039 0.0896286i 0.975886 0.218283i \(-0.0700455\pi\)
−0.991690 + 0.128654i \(0.958934\pi\)
\(102\) 0 0
\(103\) 1917.18 697.795i 1.83403 0.667532i 0.842330 0.538963i \(-0.181184\pi\)
0.991701 0.128569i \(-0.0410385\pi\)
\(104\) 0 0
\(105\) −588.813 247.875i −0.547260 0.230382i
\(106\) 0 0
\(107\) −351.086 −0.317204 −0.158602 0.987343i \(-0.550699\pi\)
−0.158602 + 0.987343i \(0.550699\pi\)
\(108\) 0 0
\(109\) 656.929 0.577270 0.288635 0.957439i \(-0.406799\pi\)
0.288635 + 0.957439i \(0.406799\pi\)
\(110\) 0 0
\(111\) 15.2732 + 121.408i 0.0130600 + 0.103815i
\(112\) 0 0
\(113\) −119.983 + 43.6704i −0.0998857 + 0.0363554i −0.391480 0.920187i \(-0.628037\pi\)
0.291594 + 0.956542i \(0.405814\pi\)
\(114\) 0 0
\(115\) 115.705 + 656.196i 0.0938223 + 0.532092i
\(116\) 0 0
\(117\) 1246.74 851.757i 0.985140 0.673034i
\(118\) 0 0
\(119\) −2509.86 913.514i −1.93343 0.703711i
\(120\) 0 0
\(121\) 1232.53 + 1034.21i 0.926015 + 0.777019i
\(122\) 0 0
\(123\) −2149.69 106.259i −1.57586 0.0778947i
\(124\) 0 0
\(125\) 521.342 902.991i 0.373042 0.646127i
\(126\) 0 0
\(127\) −649.026 1124.15i −0.453478 0.785447i 0.545121 0.838357i \(-0.316484\pi\)
−0.998599 + 0.0529102i \(0.983150\pi\)
\(128\) 0 0
\(129\) 1425.82 440.551i 0.973148 0.300685i
\(130\) 0 0
\(131\) −196.126 + 1112.28i −0.130806 + 0.741837i 0.846883 + 0.531779i \(0.178476\pi\)
−0.977689 + 0.210058i \(0.932635\pi\)
\(132\) 0 0
\(133\) −2821.10 + 2367.18i −1.83925 + 1.54331i
\(134\) 0 0
\(135\) −422.763 477.670i −0.269523 0.304528i
\(136\) 0 0
\(137\) −1978.63 + 1660.27i −1.23391 + 1.03538i −0.235937 + 0.971768i \(0.575816\pi\)
−0.997975 + 0.0636072i \(0.979740\pi\)
\(138\) 0 0
\(139\) −487.444 + 2764.43i −0.297442 + 1.68688i 0.359666 + 0.933081i \(0.382891\pi\)
−0.657108 + 0.753797i \(0.728220\pi\)
\(140\) 0 0
\(141\) 1066.94 + 989.031i 0.637253 + 0.590720i
\(142\) 0 0
\(143\) 1516.11 + 2625.97i 0.886596 + 1.53563i
\(144\) 0 0
\(145\) 111.627 193.343i 0.0639317 0.110733i
\(146\) 0 0
\(147\) 1093.68 1695.12i 0.613641 0.951096i
\(148\) 0 0
\(149\) −2123.02 1781.43i −1.16728 0.979464i −0.167300 0.985906i \(-0.553505\pi\)
−0.999979 + 0.00644242i \(0.997949\pi\)
\(150\) 0 0
\(151\) −711.587 258.996i −0.383497 0.139582i 0.143075 0.989712i \(-0.454301\pi\)
−0.526573 + 0.850130i \(0.676523\pi\)
\(152\) 0 0
\(153\) −1863.92 1907.34i −0.984893 1.00784i
\(154\) 0 0
\(155\) 120.954 + 685.966i 0.0626792 + 0.355472i
\(156\) 0 0
\(157\) 1105.36 402.318i 0.561894 0.204513i −0.0454293 0.998968i \(-0.514466\pi\)
0.607323 + 0.794455i \(0.292243\pi\)
\(158\) 0 0
\(159\) −1028.88 + 780.119i −0.513179 + 0.389104i
\(160\) 0 0
\(161\) −3962.91 −1.93988
\(162\) 0 0
\(163\) 2323.45 1.11648 0.558240 0.829679i \(-0.311477\pi\)
0.558240 + 0.829679i \(0.311477\pi\)
\(164\) 0 0
\(165\) 1020.76 773.958i 0.481610 0.365167i
\(166\) 0 0
\(167\) 3377.16 1229.19i 1.56487 0.569565i 0.593022 0.805186i \(-0.297935\pi\)
0.971845 + 0.235621i \(0.0757126\pi\)
\(168\) 0 0
\(169\) 161.558 + 916.240i 0.0735356 + 0.417041i
\(170\) 0 0
\(171\) −3562.48 + 910.738i −1.59316 + 0.407286i
\(172\) 0 0
\(173\) −315.163 114.710i −0.138505 0.0504118i 0.271837 0.962343i \(-0.412369\pi\)
−0.410343 + 0.911931i \(0.634591\pi\)
\(174\) 0 0
\(175\) 2161.13 + 1813.40i 0.933520 + 0.783316i
\(176\) 0 0
\(177\) −730.108 + 1131.61i −0.310047 + 0.480549i
\(178\) 0 0
\(179\) −1838.52 + 3184.41i −0.767695 + 1.32969i 0.171115 + 0.985251i \(0.445263\pi\)
−0.938810 + 0.344436i \(0.888070\pi\)
\(180\) 0 0
\(181\) −208.366 360.900i −0.0855675 0.148207i 0.820065 0.572270i \(-0.193937\pi\)
−0.905633 + 0.424063i \(0.860604\pi\)
\(182\) 0 0
\(183\) 1263.11 + 1170.88i 0.510229 + 0.472971i
\(184\) 0 0
\(185\) −18.5926 + 105.444i −0.00738896 + 0.0419049i
\(186\) 0 0
\(187\) 4102.60 3442.49i 1.60434 1.34620i
\(188\) 0 0
\(189\) 3234.38 1982.84i 1.24479 0.763126i
\(190\) 0 0
\(191\) −1409.52 + 1182.73i −0.533977 + 0.448060i −0.869472 0.493982i \(-0.835541\pi\)
0.335495 + 0.942042i \(0.391096\pi\)
\(192\) 0 0
\(193\) 54.6854 310.136i 0.0203956 0.115669i −0.972910 0.231183i \(-0.925740\pi\)
0.993306 + 0.115514i \(0.0368515\pi\)
\(194\) 0 0
\(195\) 1262.32 390.032i 0.463571 0.143235i
\(196\) 0 0
\(197\) 839.214 + 1453.56i 0.303510 + 0.525695i 0.976929 0.213566i \(-0.0685079\pi\)
−0.673418 + 0.739262i \(0.735175\pi\)
\(198\) 0 0
\(199\) −255.716 + 442.913i −0.0910917 + 0.157775i −0.907971 0.419034i \(-0.862369\pi\)
0.816879 + 0.576809i \(0.195702\pi\)
\(200\) 0 0
\(201\) −484.756 23.9615i −0.170110 0.00840853i
\(202\) 0 0
\(203\) 1017.15 + 853.488i 0.351674 + 0.295089i
\(204\) 0 0
\(205\) −1769.72 644.127i −0.602941 0.219452i
\(206\) 0 0
\(207\) −3566.64 1713.41i −1.19758 0.575316i
\(208\) 0 0
\(209\) −1282.26 7272.07i −0.424382 2.40679i
\(210\) 0 0
\(211\) −2331.59 + 848.631i −0.760728 + 0.276882i −0.693113 0.720829i \(-0.743761\pi\)
−0.0676152 + 0.997711i \(0.521539\pi\)
\(212\) 0 0
\(213\) −432.748 3439.95i −0.139208 1.10658i
\(214\) 0 0
\(215\) 1305.81 0.414210
\(216\) 0 0
\(217\) −4142.69 −1.29596
\(218\) 0 0
\(219\) 1023.44 + 430.842i 0.315789 + 0.132939i
\(220\) 0 0
\(221\) 5190.53 1889.20i 1.57988 0.575028i
\(222\) 0 0
\(223\) −80.0661 454.077i −0.0240432 0.136355i 0.970423 0.241409i \(-0.0776096\pi\)
−0.994467 + 0.105054i \(0.966499\pi\)
\(224\) 0 0
\(225\) 1160.98 + 2566.46i 0.343994 + 0.760433i
\(226\) 0 0
\(227\) −1280.18 465.948i −0.374311 0.136238i 0.148012 0.988986i \(-0.452712\pi\)
−0.522324 + 0.852747i \(0.674935\pi\)
\(228\) 0 0
\(229\) 1253.28 + 1051.62i 0.361654 + 0.303464i 0.805450 0.592664i \(-0.201924\pi\)
−0.443796 + 0.896128i \(0.646368\pi\)
\(230\) 0 0
\(231\) 3478.95 + 6777.99i 0.990902 + 1.93056i
\(232\) 0 0
\(233\) 2293.06 3971.70i 0.644736 1.11672i −0.339627 0.940560i \(-0.610301\pi\)
0.984362 0.176155i \(-0.0563659\pi\)
\(234\) 0 0
\(235\) 636.500 + 1102.45i 0.176684 + 0.306025i
\(236\) 0 0
\(237\) 634.336 2785.33i 0.173859 0.763403i
\(238\) 0 0
\(239\) 285.319 1618.12i 0.0772206 0.437940i −0.921545 0.388271i \(-0.873072\pi\)
0.998766 0.0496686i \(-0.0158165\pi\)
\(240\) 0 0
\(241\) −4699.71 + 3943.52i −1.25616 + 1.05404i −0.260080 + 0.965587i \(0.583749\pi\)
−0.996080 + 0.0884567i \(0.971807\pi\)
\(242\) 0 0
\(243\) 3768.26 386.146i 0.994791 0.101940i
\(244\) 0 0
\(245\) 1352.21 1134.63i 0.352609 0.295874i
\(246\) 0 0
\(247\) 1322.50 7500.29i 0.340684 1.93211i
\(248\) 0 0
\(249\) −467.112 + 2051.06i −0.118884 + 0.522010i
\(250\) 0 0
\(251\) 2445.01 + 4234.88i 0.614851 + 1.06495i 0.990411 + 0.138154i \(0.0441170\pi\)
−0.375560 + 0.926798i \(0.622550\pi\)
\(252\) 0 0
\(253\) 3973.07 6881.55i 0.987291 1.71004i
\(254\) 0 0
\(255\) −1065.57 2076.04i −0.261681 0.509829i
\(256\) 0 0
\(257\) −904.386 758.870i −0.219510 0.184191i 0.526401 0.850236i \(-0.323541\pi\)
−0.745911 + 0.666046i \(0.767986\pi\)
\(258\) 0 0
\(259\) −598.395 217.798i −0.143562 0.0522521i
\(260\) 0 0
\(261\) 546.421 + 1207.92i 0.129589 + 0.286469i
\(262\) 0 0
\(263\) 1187.46 + 6734.40i 0.278410 + 1.57894i 0.727919 + 0.685664i \(0.240488\pi\)
−0.449509 + 0.893276i \(0.648401\pi\)
\(264\) 0 0
\(265\) −1061.68 + 386.418i −0.246106 + 0.0895754i
\(266\) 0 0
\(267\) −4835.01 2035.41i −1.10823 0.466536i
\(268\) 0 0
\(269\) 343.601 0.0778801 0.0389401 0.999242i \(-0.487602\pi\)
0.0389401 + 0.999242i \(0.487602\pi\)
\(270\) 0 0
\(271\) 2607.43 0.584466 0.292233 0.956347i \(-0.405602\pi\)
0.292233 + 0.956347i \(0.405602\pi\)
\(272\) 0 0
\(273\) 980.782 + 7796.33i 0.217435 + 1.72841i
\(274\) 0 0
\(275\) −5315.63 + 1934.73i −1.16562 + 0.424249i
\(276\) 0 0
\(277\) 0.0627023 + 0.355603i 1.36008e−5 + 7.71339e-5i 0.984815 0.173610i \(-0.0555431\pi\)
−0.984801 + 0.173687i \(0.944432\pi\)
\(278\) 0 0
\(279\) −3728.44 1791.14i −0.800057 0.384348i
\(280\) 0 0
\(281\) 4627.50 + 1684.27i 0.982396 + 0.357563i 0.782771 0.622310i \(-0.213806\pi\)
0.199625 + 0.979872i \(0.436028\pi\)
\(282\) 0 0
\(283\) −4317.90 3623.15i −0.906971 0.761039i 0.0645695 0.997913i \(-0.479433\pi\)
−0.971540 + 0.236874i \(0.923877\pi\)
\(284\) 0 0
\(285\) −3213.55 158.846i −0.667909 0.0330148i
\(286\) 0 0
\(287\) 5600.43 9700.22i 1.15186 1.99507i
\(288\) 0 0
\(289\) −2421.49 4194.15i −0.492874 0.853684i
\(290\) 0 0
\(291\) 146.157 45.1597i 0.0294428 0.00909727i
\(292\) 0 0
\(293\) −397.381 + 2253.66i −0.0792328 + 0.449352i 0.919220 + 0.393745i \(0.128821\pi\)
−0.998453 + 0.0556072i \(0.982291\pi\)
\(294\) 0 0
\(295\) −902.692 + 757.448i −0.178158 + 0.149493i
\(296\) 0 0
\(297\) 200.525 + 7604.39i 0.0391773 + 1.48570i
\(298\) 0 0
\(299\) 6278.12 5267.97i 1.21429 1.01891i
\(300\) 0 0
\(301\) −1348.59 + 7648.23i −0.258244 + 1.46457i
\(302\) 0 0
\(303\) 352.035 + 326.329i 0.0667455 + 0.0618716i
\(304\) 0 0
\(305\) 753.528 + 1305.15i 0.141465 + 0.245025i
\(306\) 0 0
\(307\) −3242.45 + 5616.10i −0.602790 + 1.04406i 0.389606 + 0.920982i \(0.372611\pi\)
−0.992397 + 0.123082i \(0.960722\pi\)
\(308\) 0 0
\(309\) −5747.44 + 8908.09i −1.05812 + 1.64001i
\(310\) 0 0
\(311\) 2064.12 + 1732.01i 0.376353 + 0.315797i 0.811269 0.584674i \(-0.198777\pi\)
−0.434916 + 0.900471i \(0.643222\pi\)
\(312\) 0 0
\(313\) −4366.05 1589.11i −0.788446 0.286971i −0.0837560 0.996486i \(-0.526692\pi\)
−0.704690 + 0.709515i \(0.748914\pi\)
\(314\) 0 0
\(315\) 3216.18 822.207i 0.575274 0.147067i
\(316\) 0 0
\(317\) 860.106 + 4877.90i 0.152392 + 0.864260i 0.961131 + 0.276092i \(0.0890394\pi\)
−0.808739 + 0.588168i \(0.799849\pi\)
\(318\) 0 0
\(319\) −2501.83 + 910.591i −0.439108 + 0.159822i
\(320\) 0 0
\(321\) 1453.68 1102.21i 0.252762 0.191650i
\(322\) 0 0
\(323\) −13451.5 −2.31723
\(324\) 0 0
\(325\) −5834.30 −0.995781
\(326\) 0 0
\(327\) −2720.03 + 2062.39i −0.459994 + 0.348777i
\(328\) 0 0
\(329\) −7114.53 + 2589.48i −1.19221 + 0.433928i
\(330\) 0 0
\(331\) −307.323 1742.92i −0.0510333 0.289424i 0.948601 0.316475i \(-0.102499\pi\)
−0.999634 + 0.0270512i \(0.991388\pi\)
\(332\) 0 0
\(333\) −444.391 454.743i −0.0731305 0.0748341i
\(334\) 0 0
\(335\) −399.074 145.251i −0.0650859 0.0236893i
\(336\) 0 0
\(337\) −625.914 525.204i −0.101174 0.0848952i 0.590797 0.806820i \(-0.298813\pi\)
−0.691972 + 0.721925i \(0.743258\pi\)
\(338\) 0 0
\(339\) 359.694 557.498i 0.0576280 0.0893190i
\(340\) 0 0
\(341\) 4153.31 7193.75i 0.659573 1.14241i
\(342\) 0 0
\(343\) 611.577 + 1059.28i 0.0962743 + 0.166752i
\(344\) 0 0
\(345\) −2539.17 2353.75i −0.396244 0.367309i
\(346\) 0 0
\(347\) 1301.07 7378.71i 0.201282 1.14153i −0.701902 0.712274i \(-0.747665\pi\)
0.903184 0.429254i \(-0.141223\pi\)
\(348\) 0 0
\(349\) 9295.98 7800.25i 1.42580 1.19638i 0.477648 0.878551i \(-0.341489\pi\)
0.948147 0.317833i \(-0.102955\pi\)
\(350\) 0 0
\(351\) −2488.13 + 7440.79i −0.378367 + 1.13151i
\(352\) 0 0
\(353\) −1902.32 + 1596.24i −0.286828 + 0.240678i −0.774837 0.632161i \(-0.782168\pi\)
0.488008 + 0.872839i \(0.337724\pi\)
\(354\) 0 0
\(355\) 526.802 2987.64i 0.0787598 0.446669i
\(356\) 0 0
\(357\) 13260.0 4097.11i 1.96582 0.607400i
\(358\) 0 0
\(359\) 5053.00 + 8752.06i 0.742862 + 1.28667i 0.951187 + 0.308614i \(0.0998653\pi\)
−0.208326 + 0.978060i \(0.566801\pi\)
\(360\) 0 0
\(361\) −5843.98 + 10122.1i −0.852017 + 1.47574i
\(362\) 0 0
\(363\) −8350.15 412.748i −1.20735 0.0596794i
\(364\) 0 0
\(365\) 744.320 + 624.559i 0.106738 + 0.0895641i
\(366\) 0 0
\(367\) 5169.49 + 1881.54i 0.735273 + 0.267618i 0.682395 0.730983i \(-0.260938\pi\)
0.0528780 + 0.998601i \(0.483161\pi\)
\(368\) 0 0
\(369\) 9234.43 6308.83i 1.30278 0.890040i
\(370\) 0 0
\(371\) −1166.83 6617.42i −0.163285 0.926036i
\(372\) 0 0
\(373\) 8111.81 2952.46i 1.12604 0.409845i 0.289188 0.957272i \(-0.406615\pi\)
0.836853 + 0.547427i \(0.184393\pi\)
\(374\) 0 0
\(375\) 676.250 + 5375.57i 0.0931237 + 0.740249i
\(376\) 0 0
\(377\) −2745.95 −0.375128
\(378\) 0 0
\(379\) 1742.39 0.236149 0.118075 0.993005i \(-0.462328\pi\)
0.118075 + 0.993005i \(0.462328\pi\)
\(380\) 0 0
\(381\) 6216.49 + 2616.98i 0.835906 + 0.351895i
\(382\) 0 0
\(383\) 2574.27 936.958i 0.343444 0.125003i −0.164539 0.986371i \(-0.552614\pi\)
0.507983 + 0.861367i \(0.330391\pi\)
\(384\) 0 0
\(385\) 1157.62 + 6565.16i 0.153240 + 0.869069i
\(386\) 0 0
\(387\) −4520.55 + 6300.37i −0.593779 + 0.827560i
\(388\) 0 0
\(389\) 6652.69 + 2421.38i 0.867108 + 0.315601i 0.736995 0.675898i \(-0.236244\pi\)
0.130112 + 0.991499i \(0.458466\pi\)
\(390\) 0 0
\(391\) −11088.6 9304.41i −1.43420 1.20344i
\(392\) 0 0
\(393\) −2679.88 5221.16i −0.343975 0.670160i
\(394\) 0 0
\(395\) 1249.80 2164.72i 0.159201 0.275744i
\(396\) 0 0
\(397\) 2624.35 + 4545.52i 0.331770 + 0.574642i 0.982859 0.184359i \(-0.0590210\pi\)
−0.651089 + 0.759001i \(0.725688\pi\)
\(398\) 0 0
\(399\) 4249.22 18658.0i 0.533150 2.34103i
\(400\) 0 0
\(401\) −949.429 + 5384.48i −0.118235 + 0.670544i 0.866863 + 0.498547i \(0.166133\pi\)
−0.985098 + 0.171997i \(0.944978\pi\)
\(402\) 0 0
\(403\) 6562.94 5506.96i 0.811224 0.680698i
\(404\) 0 0
\(405\) 3250.07 + 650.568i 0.398759 + 0.0798197i
\(406\) 0 0
\(407\) 978.133 820.751i 0.119126 0.0999585i
\(408\) 0 0
\(409\) 689.848 3912.32i 0.0834005 0.472987i −0.914290 0.405061i \(-0.867250\pi\)
0.997690 0.0679269i \(-0.0216385\pi\)
\(410\) 0 0
\(411\) 2980.27 13086.2i 0.357679 1.57054i
\(412\) 0 0
\(413\) −3504.18 6069.42i −0.417505 0.723140i
\(414\) 0 0
\(415\) −920.329 + 1594.06i −0.108861 + 0.188552i
\(416\) 0 0
\(417\) −6660.48 12976.5i −0.782170 1.52389i
\(418\) 0 0
\(419\) 11193.9 + 9392.79i 1.30515 + 1.09515i 0.989231 + 0.146363i \(0.0467566\pi\)
0.315917 + 0.948787i \(0.397688\pi\)
\(420\) 0 0
\(421\) 13068.9 + 4756.68i 1.51292 + 0.550657i 0.959367 0.282160i \(-0.0910509\pi\)
0.553549 + 0.832816i \(0.313273\pi\)
\(422\) 0 0
\(423\) −7522.70 745.516i −0.864696 0.0856932i
\(424\) 0 0
\(425\) 1789.39 + 10148.1i 0.204231 + 1.15825i
\(426\) 0 0
\(427\) −8422.61 + 3065.58i −0.954563 + 0.347433i
\(428\) 0 0
\(429\) −14521.6 6113.20i −1.63428 0.687990i
\(430\) 0 0
\(431\) −14619.4 −1.63385 −0.816927 0.576741i \(-0.804324\pi\)
−0.816927 + 0.576741i \(0.804324\pi\)
\(432\) 0 0
\(433\) 14257.6 1.58239 0.791197 0.611561i \(-0.209458\pi\)
0.791197 + 0.611561i \(0.209458\pi\)
\(434\) 0 0
\(435\) 144.795 + 1150.99i 0.0159595 + 0.126864i
\(436\) 0 0
\(437\) −18754.6 + 6826.12i −2.05299 + 0.747226i
\(438\) 0 0
\(439\) −2645.69 15004.5i −0.287635 1.63126i −0.695717 0.718316i \(-0.744913\pi\)
0.408081 0.912946i \(-0.366198\pi\)
\(440\) 0 0
\(441\) 793.309 + 10452.2i 0.0856613 + 1.12863i
\(442\) 0 0
\(443\) −4770.78 1736.42i −0.511663 0.186230i 0.0732692 0.997312i \(-0.476657\pi\)
−0.584932 + 0.811082i \(0.698879\pi\)
\(444\) 0 0
\(445\) −3516.37 2950.58i −0.374588 0.314317i
\(446\) 0 0
\(447\) 14383.1 + 710.956i 1.52192 + 0.0752283i
\(448\) 0 0
\(449\) 7046.08 12204.2i 0.740591 1.28274i −0.211636 0.977349i \(-0.567879\pi\)
0.952227 0.305392i \(-0.0987875\pi\)
\(450\) 0 0
\(451\) 11229.6 + 19450.2i 1.17246 + 2.03076i
\(452\) 0 0
\(453\) 3759.45 1161.60i 0.389921 0.120478i
\(454\) 0 0
\(455\) −1193.95 + 6771.20i −0.123018 + 0.697668i
\(456\) 0 0
\(457\) −949.074 + 796.368i −0.0971462 + 0.0815153i −0.690067 0.723745i \(-0.742419\pi\)
0.592921 + 0.805261i \(0.297975\pi\)
\(458\) 0 0
\(459\) 13705.5 + 2045.73i 1.39373 + 0.208032i
\(460\) 0 0
\(461\) −2354.96 + 1976.04i −0.237920 + 0.199639i −0.753950 0.656932i \(-0.771854\pi\)
0.516030 + 0.856571i \(0.327409\pi\)
\(462\) 0 0
\(463\) −1637.88 + 9288.87i −0.164403 + 0.932377i 0.785274 + 0.619148i \(0.212522\pi\)
−0.949678 + 0.313229i \(0.898589\pi\)
\(464\) 0 0
\(465\) −2654.36 2460.53i −0.264716 0.245386i
\(466\) 0 0
\(467\) −5454.27 9447.08i −0.540457 0.936100i −0.998878 0.0473641i \(-0.984918\pi\)
0.458420 0.888736i \(-0.348415\pi\)
\(468\) 0 0
\(469\) 1262.90 2187.41i 0.124340 0.215363i
\(470\) 0 0
\(471\) −3313.72 + 5136.01i −0.324179 + 0.502452i
\(472\) 0 0
\(473\) −11929.0 10009.7i −1.15962 0.973033i
\(474\) 0 0
\(475\) 13351.2 + 4859.45i 1.28968 + 0.469404i
\(476\) 0 0
\(477\) 1810.97 6460.21i 0.173834 0.620110i
\(478\) 0 0
\(479\) −2009.10 11394.2i −0.191645 1.08687i −0.917116 0.398621i \(-0.869489\pi\)
0.725470 0.688253i \(-0.241622\pi\)
\(480\) 0 0
\(481\) 1237.51 450.418i 0.117309 0.0426971i
\(482\) 0 0
\(483\) 16408.5 12441.3i 1.54578 1.17205i
\(484\) 0 0
\(485\) 133.855 0.0125320
\(486\) 0 0
\(487\) −15337.4 −1.42711 −0.713554 0.700600i \(-0.752916\pi\)
−0.713554 + 0.700600i \(0.752916\pi\)
\(488\) 0 0
\(489\) −9620.29 + 7294.31i −0.889661 + 0.674560i
\(490\) 0 0
\(491\) −6647.78 + 2419.59i −0.611018 + 0.222392i −0.628949 0.777447i \(-0.716514\pi\)
0.0179304 + 0.999839i \(0.494292\pi\)
\(492\) 0 0
\(493\) 842.185 + 4776.27i 0.0769374 + 0.436334i
\(494\) 0 0
\(495\) −1796.67 + 6409.19i −0.163140 + 0.581963i
\(496\) 0 0
\(497\) 16954.9 + 6171.06i 1.53024 + 0.556962i
\(498\) 0 0
\(499\) 10522.3 + 8829.24i 0.943972 + 0.792087i 0.978272 0.207325i \(-0.0664758\pi\)
−0.0343001 + 0.999412i \(0.510920\pi\)
\(500\) 0 0
\(501\) −10124.3 + 15691.9i −0.902833 + 1.39932i
\(502\) 0 0
\(503\) 1396.87 2419.45i 0.123824 0.214469i −0.797449 0.603387i \(-0.793818\pi\)
0.921273 + 0.388918i \(0.127151\pi\)
\(504\) 0 0
\(505\) 210.012 + 363.751i 0.0185057 + 0.0320529i
\(506\) 0 0
\(507\) −3545.41 3286.51i −0.310566 0.287888i
\(508\) 0 0
\(509\) −1433.78 + 8131.38i −0.124855 + 0.708089i 0.856539 + 0.516083i \(0.172610\pi\)
−0.981394 + 0.192006i \(0.938501\pi\)
\(510\) 0 0
\(511\) −4426.81 + 3714.54i −0.383230 + 0.321568i
\(512\) 0 0
\(513\) 11891.4 14955.1i 1.02342 1.28710i
\(514\) 0 0
\(515\) −7106.03 + 5962.66i −0.608017 + 0.510187i
\(516\) 0 0
\(517\) 2636.16 14950.4i 0.224252 1.27180i
\(518\) 0 0
\(519\) 1665.07 514.474i 0.140825 0.0435123i
\(520\) 0 0
\(521\) 10192.6 + 17654.1i 0.857094 + 1.48453i 0.874689 + 0.484685i \(0.161066\pi\)
−0.0175944 + 0.999845i \(0.505601\pi\)
\(522\) 0 0
\(523\) −7162.07 + 12405.1i −0.598806 + 1.03716i 0.394192 + 0.919028i \(0.371025\pi\)
−0.992998 + 0.118134i \(0.962309\pi\)
\(524\) 0 0
\(525\) −14641.3 723.718i −1.21714 0.0601631i
\(526\) 0 0
\(527\) −11591.6 9726.52i −0.958138 0.803973i
\(528\) 0 0
\(529\) −8748.46 3184.18i −0.719032 0.261706i
\(530\) 0 0
\(531\) −529.589 6977.59i −0.0432810 0.570248i
\(532\) 0 0
\(533\) 4022.38 + 22812.1i 0.326883 + 1.85385i
\(534\) 0 0
\(535\) 1500.02 545.962i 0.121218 0.0441196i
\(536\) 0 0
\(537\) −2384.81 18957.0i −0.191642 1.52338i
\(538\) 0 0
\(539\) −21050.5 −1.68221
\(540\) 0 0
\(541\) −9772.64 −0.776633 −0.388317 0.921526i \(-0.626943\pi\)
−0.388317 + 0.921526i \(0.626943\pi\)
\(542\) 0 0
\(543\) 1995.77 + 840.166i 0.157729 + 0.0663996i
\(544\) 0 0
\(545\) −2806.73 + 1021.57i −0.220600 + 0.0802919i
\(546\) 0 0
\(547\) 2487.70 + 14108.5i 0.194454 + 1.10280i 0.913194 + 0.407525i \(0.133608\pi\)
−0.718740 + 0.695279i \(0.755281\pi\)
\(548\) 0 0
\(549\) −8905.83 882.587i −0.692334 0.0686118i
\(550\) 0 0
\(551\) 6283.83 + 2287.13i 0.485844 + 0.176833i
\(552\) 0 0
\(553\) 11388.2 + 9555.87i 0.875728 + 0.734823i
\(554\) 0 0
\(555\) −254.051 494.964i −0.0194304 0.0378560i
\(556\) 0 0
\(557\) 7088.20 12277.1i 0.539204 0.933929i −0.459743 0.888052i \(-0.652058\pi\)
0.998947 0.0458770i \(-0.0146082\pi\)
\(558\) 0 0
\(559\) −8030.49 13909.2i −0.607609 1.05241i
\(560\) 0 0
\(561\) −6179.45 + 27133.6i −0.465056 + 2.04203i
\(562\) 0 0
\(563\) −2412.55 + 13682.2i −0.180598 + 1.02422i 0.750884 + 0.660435i \(0.229628\pi\)
−0.931482 + 0.363788i \(0.881483\pi\)
\(564\) 0 0
\(565\) 444.719 373.164i 0.0331141 0.0277860i
\(566\) 0 0
\(567\) −7167.00 + 18364.1i −0.530839 + 1.36018i
\(568\) 0 0
\(569\) 1899.81 1594.13i 0.139972 0.117451i −0.570113 0.821566i \(-0.693101\pi\)
0.710086 + 0.704115i \(0.248656\pi\)
\(570\) 0 0
\(571\) 680.576 3859.74i 0.0498795 0.282881i −0.949658 0.313288i \(-0.898569\pi\)
0.999538 + 0.0304075i \(0.00968049\pi\)
\(572\) 0 0
\(573\) 2123.06 9322.24i 0.154786 0.679654i
\(574\) 0 0
\(575\) 7644.60 + 13240.8i 0.554438 + 0.960315i
\(576\) 0 0
\(577\) 9634.98 16688.3i 0.695164 1.20406i −0.274962 0.961455i \(-0.588665\pi\)
0.970125 0.242604i \(-0.0780016\pi\)
\(578\) 0 0
\(579\) 747.227 + 1455.81i 0.0536333 + 0.104493i
\(580\) 0 0
\(581\) −8386.07 7036.74i −0.598817 0.502467i
\(582\) 0 0
\(583\) 12660.9 + 4608.20i 0.899420 + 0.327362i
\(584\) 0 0
\(585\) −4002.17 + 5577.90i −0.282854 + 0.394218i
\(586\) 0 0
\(587\) −2051.32 11633.6i −0.144237 0.818007i −0.967977 0.251040i \(-0.919228\pi\)
0.823740 0.566968i \(-0.191884\pi\)
\(588\) 0 0
\(589\) −19605.5 + 7135.80i −1.37153 + 0.499194i
\(590\) 0 0
\(591\) −8038.15 3383.85i −0.559468 0.235521i
\(592\) 0 0
\(593\) −13127.9 −0.909101 −0.454551 0.890721i \(-0.650200\pi\)
−0.454551 + 0.890721i \(0.650200\pi\)
\(594\) 0 0
\(595\) 12143.9 0.836728
\(596\) 0 0
\(597\) −331.698 2636.70i −0.0227395 0.180759i
\(598\) 0 0
\(599\) 26377.9 9600.77i 1.79928 0.654886i 0.800855 0.598858i \(-0.204378\pi\)
0.998429 0.0560284i \(-0.0178437\pi\)
\(600\) 0 0
\(601\) −2662.66 15100.7i −0.180719 1.02491i −0.931333 0.364167i \(-0.881354\pi\)
0.750615 0.660740i \(-0.229758\pi\)
\(602\) 0 0
\(603\) 2082.37 1422.65i 0.140631 0.0960774i
\(604\) 0 0
\(605\) −6874.24 2502.02i −0.461946 0.168135i
\(606\) 0 0
\(607\) −20854.2 17498.7i −1.39447 1.17010i −0.963491 0.267740i \(-0.913723\pi\)
−0.430981 0.902361i \(-0.641832\pi\)
\(608\) 0 0
\(609\) −6890.99 340.622i −0.458517 0.0226645i
\(610\) 0 0
\(611\) 7828.75 13559.8i 0.518359 0.897824i
\(612\) 0 0
\(613\) 2651.31 + 4592.20i 0.174690 + 0.302573i 0.940054 0.341025i \(-0.110774\pi\)
−0.765364 + 0.643598i \(0.777441\pi\)
\(614\) 0 0
\(615\) 9349.78 2888.91i 0.613040 0.189418i
\(616\) 0 0
\(617\) −1200.77 + 6809.92i −0.0783489 + 0.444339i 0.920246 + 0.391341i \(0.127989\pi\)
−0.998595 + 0.0529978i \(0.983122\pi\)
\(618\) 0 0
\(619\) 1564.51 1312.78i 0.101588 0.0852424i −0.590579 0.806980i \(-0.701101\pi\)
0.692167 + 0.721737i \(0.256656\pi\)
\(620\) 0 0
\(621\) 20146.9 4102.78i 1.30188 0.265119i
\(622\) 0 0
\(623\) 20913.4 17548.5i 1.34491 1.12851i
\(624\) 0 0
\(625\) 1441.31 8174.07i 0.0922438 0.523140i
\(626\) 0 0
\(627\) 28139.4 + 26084.6i 1.79231 + 1.66143i
\(628\) 0 0
\(629\) −1163.00 2014.38i −0.0737231 0.127692i
\(630\) 0 0
\(631\) −7978.31 + 13818.8i −0.503346 + 0.871821i 0.496646 + 0.867953i \(0.334565\pi\)
−0.999993 + 0.00386809i \(0.998769\pi\)
\(632\) 0 0
\(633\) 6989.81 10833.7i 0.438894 0.680252i
\(634\) 0 0
\(635\) 4521.08 + 3793.64i 0.282541 + 0.237080i
\(636\) 0 0
\(637\) −20401.8 7425.64i −1.26899 0.461875i
\(638\) 0 0
\(639\) 12591.3 + 12884.6i 0.779507 + 0.797666i
\(640\) 0 0
\(641\) 95.6010 + 542.180i 0.00589081 + 0.0334085i 0.987611 0.156919i \(-0.0501561\pi\)
−0.981721 + 0.190327i \(0.939045\pi\)
\(642\) 0 0
\(643\) −10646.4 + 3874.97i −0.652959 + 0.237658i −0.647194 0.762326i \(-0.724058\pi\)
−0.00576568 + 0.999983i \(0.501835\pi\)
\(644\) 0 0
\(645\) −5406.72 + 4099.49i −0.330061 + 0.250259i
\(646\) 0 0
\(647\) 21233.5 1.29022 0.645112 0.764088i \(-0.276811\pi\)
0.645112 + 0.764088i \(0.276811\pi\)
\(648\) 0 0
\(649\) 14052.7 0.849947
\(650\) 0 0
\(651\) 17152.9 13005.7i 1.03268 0.783001i
\(652\) 0 0
\(653\) 21181.2 7709.31i 1.26935 0.462004i 0.382451 0.923976i \(-0.375080\pi\)
0.886895 + 0.461971i \(0.152858\pi\)
\(654\) 0 0
\(655\) −891.725 5057.22i −0.0531948 0.301682i
\(656\) 0 0
\(657\) −5590.18 + 1429.11i −0.331954 + 0.0848630i
\(658\) 0 0
\(659\) −12762.0 4644.99i −0.754381 0.274572i −0.0639327 0.997954i \(-0.520364\pi\)
−0.690448 + 0.723382i \(0.742587\pi\)
\(660\) 0 0
\(661\) 1688.35 + 1416.69i 0.0993481 + 0.0833630i 0.691109 0.722751i \(-0.257123\pi\)
−0.591761 + 0.806114i \(0.701567\pi\)
\(662\) 0 0
\(663\) −15560.5 + 24117.6i −0.911492 + 1.41274i
\(664\) 0 0
\(665\) 8372.03 14500.8i 0.488201 0.845588i
\(666\) 0 0
\(667\) 3597.97 + 6231.87i 0.208867 + 0.361768i
\(668\) 0 0
\(669\) 1757.06 + 1628.76i 0.101543 + 0.0941276i
\(670\) 0 0
\(671\) 3120.85 17699.2i 0.179552 1.01829i
\(672\) 0 0
\(673\) −468.396 + 393.031i −0.0268281 + 0.0225115i −0.656103 0.754671i \(-0.727796\pi\)
0.629275 + 0.777183i \(0.283352\pi\)
\(674\) 0 0
\(675\) −12864.3 6981.69i −0.733551 0.398112i
\(676\) 0 0
\(677\) 10915.1 9158.89i 0.619650 0.519948i −0.278044 0.960568i \(-0.589686\pi\)
0.897693 + 0.440621i \(0.145242\pi\)
\(678\) 0 0
\(679\) −138.240 + 784.000i −0.00781322 + 0.0443110i
\(680\) 0 0
\(681\) 6763.44 2089.78i 0.380581 0.117592i
\(682\) 0 0
\(683\) 7351.56 + 12733.3i 0.411859 + 0.713360i 0.995093 0.0989436i \(-0.0315464\pi\)
−0.583234 + 0.812304i \(0.698213\pi\)
\(684\) 0 0
\(685\) 5871.89 10170.4i 0.327523 0.567286i
\(686\) 0 0
\(687\) −8490.72 419.696i −0.471530 0.0233077i
\(688\) 0 0
\(689\) 10645.2 + 8932.37i 0.588606 + 0.493899i
\(690\) 0 0
\(691\) −17454.4 6352.88i −0.960921 0.349747i −0.186527 0.982450i \(-0.559723\pi\)
−0.774394 + 0.632703i \(0.781945\pi\)
\(692\) 0 0
\(693\) −35683.7 17142.5i −1.95601 0.939667i
\(694\) 0 0
\(695\) −2216.26 12569.0i −0.120961 0.686002i
\(696\) 0 0
\(697\) 38445.4 13993.0i 2.08927 0.760433i
\(698\) 0 0
\(699\) 2974.41 + 23643.8i 0.160948 + 1.27939i
\(700\) 0 0
\(701\) 3749.76 0.202035 0.101017 0.994885i \(-0.467790\pi\)
0.101017 + 0.994885i \(0.467790\pi\)
\(702\) 0 0
\(703\) −3207.09 −0.172059
\(704\) 0 0
\(705\) −6096.52 2566.48i −0.325685 0.137105i
\(706\) 0 0
\(707\) −2347.42 + 854.391i −0.124871 + 0.0454494i
\(708\) 0 0
\(709\) 101.160 + 573.705i 0.00535843 + 0.0303892i 0.987370 0.158433i \(-0.0506442\pi\)
−0.982011 + 0.188822i \(0.939533\pi\)
\(710\) 0 0
\(711\) 6117.87 + 13524.2i 0.322698 + 0.713357i
\(712\) 0 0
\(713\) −21097.3 7678.78i −1.10813 0.403328i
\(714\) 0 0
\(715\) −10561.1 8861.84i −0.552397 0.463516i
\(716\) 0 0
\(717\) 3898.62 + 7595.61i 0.203064 + 0.395625i
\(718\) 0 0
\(719\) −13076.5 + 22649.2i −0.678264 + 1.17479i 0.297239 + 0.954803i \(0.403934\pi\)
−0.975503 + 0.219985i \(0.929399\pi\)
\(720\) 0 0
\(721\) −27585.1 47778.8i −1.42486 2.46793i
\(722\) 0 0
\(723\) 7078.83 31082.7i 0.364128 1.59886i
\(724\) 0 0
\(725\) 889.551 5044.90i 0.0455684 0.258431i
\(726\) 0 0
\(727\) 8156.67 6844.26i 0.416113 0.349160i −0.410569 0.911829i \(-0.634670\pi\)
0.826682 + 0.562669i \(0.190226\pi\)
\(728\) 0 0
\(729\) −14390.3 + 13429.1i −0.731103 + 0.682267i
\(730\) 0 0
\(731\) −21730.6 + 18234.1i −1.09950 + 0.922590i
\(732\) 0 0
\(733\) −3183.40 + 18053.9i −0.160411 + 0.909738i 0.793259 + 0.608884i \(0.208383\pi\)
−0.953670 + 0.300853i \(0.902729\pi\)
\(734\) 0 0
\(735\) −2036.73 + 8943.14i −0.102212 + 0.448807i
\(736\) 0 0
\(737\) 2532.28 + 4386.04i 0.126564 + 0.219215i
\(738\) 0 0
\(739\) −4580.62 + 7933.86i −0.228012 + 0.394928i −0.957219 0.289365i \(-0.906556\pi\)
0.729207 + 0.684293i \(0.239889\pi\)
\(740\) 0 0
\(741\) 18070.8 + 35207.0i 0.895880 + 1.74543i
\(742\) 0 0
\(743\) 19612.0 + 16456.4i 0.968362 + 0.812552i 0.982293 0.187351i \(-0.0599902\pi\)
−0.0139313 + 0.999903i \(0.504435\pi\)
\(744\) 0 0
\(745\) 11840.8 + 4309.71i 0.582302 + 0.211940i
\(746\) 0 0
\(747\) −4505.07 9958.93i −0.220659 0.487789i
\(748\) 0 0
\(749\) 1648.59 + 9349.61i 0.0804247 + 0.456111i
\(750\) 0 0
\(751\) −11820.2 + 4302.20i −0.574334 + 0.209040i −0.612825 0.790218i \(-0.709967\pi\)
0.0384913 + 0.999259i \(0.487745\pi\)
\(752\) 0 0
\(753\) −23418.7 9858.68i −1.13337 0.477118i
\(754\) 0 0
\(755\) 3443.01 0.165966
\(756\) 0 0
\(757\) −31497.3 −1.51227 −0.756134 0.654416i \(-0.772914\pi\)
−0.756134 + 0.654416i \(0.772914\pi\)
\(758\) 0 0
\(759\) 5153.60 + 40966.4i 0.246461 + 1.95914i
\(760\) 0 0
\(761\) 22625.0 8234.84i 1.07774 0.392264i 0.258672 0.965965i \(-0.416715\pi\)
0.819064 + 0.573702i \(0.194493\pi\)
\(762\) 0 0
\(763\) −3084.73 17494.4i −0.146362 0.830063i
\(764\) 0 0
\(765\) 10929.6 + 5250.59i 0.516550 + 0.248151i
\(766\) 0 0
\(767\) 13619.6 + 4957.13i 0.641168 + 0.233366i
\(768\) 0 0
\(769\) 17213.9 + 14444.1i 0.807214 + 0.677333i 0.949941 0.312429i \(-0.101143\pi\)
−0.142727 + 0.989762i \(0.545587\pi\)
\(770\) 0 0
\(771\) 6127.05 + 302.860i 0.286200 + 0.0141469i
\(772\) 0 0
\(773\) −16376.9 + 28365.5i −0.762011 + 1.31984i 0.179801 + 0.983703i \(0.442455\pi\)
−0.941812 + 0.336139i \(0.890879\pi\)
\(774\) 0 0
\(775\) 7991.41 + 13841.5i 0.370400 + 0.641551i
\(776\) 0 0
\(777\) 3161.43 976.823i 0.145966 0.0451008i
\(778\) 0 0
\(779\) 9795.57 55553.5i 0.450530 2.55508i
\(780\) 0 0
\(781\) −27714.3 + 23255.1i −1.26978 + 1.06547i
\(782\) 0 0