Properties

Label 108.4.i.a.49.7
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 49.7
Character \(\chi\) \(=\) 108.49
Dual form 108.4.i.a.97.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.27095 - 4.67363i) q^{3} +(-10.0092 + 3.64305i) q^{5} +(-2.90933 - 16.4997i) q^{7} +(-16.6855 - 21.2272i) q^{9} +O(q^{10})\) \(q+(2.27095 - 4.67363i) q^{3} +(-10.0092 + 3.64305i) q^{5} +(-2.90933 - 16.4997i) q^{7} +(-16.6855 - 21.2272i) q^{9} +(3.53602 + 1.28701i) q^{11} +(-55.0460 - 46.1890i) q^{13} +(-5.70417 + 55.0525i) q^{15} +(-14.0443 + 24.3254i) q^{17} +(4.34509 + 7.52591i) q^{19} +(-83.7201 - 23.8728i) q^{21} +(4.21963 - 23.9307i) q^{23} +(-8.84313 + 7.42027i) q^{25} +(-137.100 + 29.7761i) q^{27} +(183.135 - 153.668i) q^{29} +(45.3635 - 257.269i) q^{31} +(14.0451 - 13.6033i) q^{33} +(89.2293 + 154.550i) q^{35} +(50.0527 - 86.6937i) q^{37} +(-340.877 + 152.371i) q^{39} +(177.609 + 149.031i) q^{41} +(220.317 + 80.1887i) q^{43} +(244.341 + 151.681i) q^{45} +(98.9672 + 561.271i) q^{47} +(58.5403 - 21.3069i) q^{49} +(81.7939 + 120.879i) q^{51} +368.316 q^{53} -40.0814 q^{55} +(45.0408 - 3.21632i) q^{57} +(-485.116 + 176.568i) q^{59} +(-106.741 - 605.358i) q^{61} +(-301.697 + 337.063i) q^{63} +(719.236 + 261.780i) q^{65} +(-264.013 - 221.533i) q^{67} +(-102.261 - 74.0665i) q^{69} +(496.578 - 860.098i) q^{71} +(-180.607 - 312.820i) q^{73} +(14.5972 + 58.1806i) q^{75} +(10.9477 - 62.0874i) q^{77} +(127.623 - 107.088i) q^{79} +(-172.185 + 708.374i) q^{81} +(-718.475 + 602.872i) q^{83} +(51.9533 - 294.642i) q^{85} +(-302.298 - 1204.88i) q^{87} +(-404.414 - 700.465i) q^{89} +(-601.956 + 1042.62i) q^{91} +(-1099.36 - 796.258i) q^{93} +(-70.9082 - 59.4990i) q^{95} +(1723.85 + 627.431i) q^{97} +(-31.6809 - 96.5340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

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
\(3\) 2.27095 4.67363i 0.437045 0.899440i
\(4\) 0 0
\(5\) −10.0092 + 3.64305i −0.895251 + 0.325845i −0.748348 0.663306i \(-0.769153\pi\)
−0.146903 + 0.989151i \(0.546930\pi\)
\(6\) 0 0
\(7\) −2.90933 16.4997i −0.157089 0.890897i −0.956851 0.290580i \(-0.906152\pi\)
0.799762 0.600318i \(-0.204959\pi\)
\(8\) 0 0
\(9\) −16.6855 21.2272i −0.617983 0.786191i
\(10\) 0 0
\(11\) 3.53602 + 1.28701i 0.0969227 + 0.0352770i 0.390026 0.920804i \(-0.372466\pi\)
−0.293104 + 0.956081i \(0.594688\pi\)
\(12\) 0 0
\(13\) −55.0460 46.1890i −1.17438 0.985426i −1.00000 0.000748193i \(-0.999762\pi\)
−0.174385 0.984678i \(-0.555794\pi\)
\(14\) 0 0
\(15\) −5.70417 + 55.0525i −0.0981874 + 0.947633i
\(16\) 0 0
\(17\) −14.0443 + 24.3254i −0.200367 + 0.347046i −0.948647 0.316338i \(-0.897547\pi\)
0.748280 + 0.663383i \(0.230880\pi\)
\(18\) 0 0
\(19\) 4.34509 + 7.52591i 0.0524648 + 0.0908717i 0.891065 0.453876i \(-0.149959\pi\)
−0.838600 + 0.544747i \(0.816626\pi\)
\(20\) 0 0
\(21\) −83.7201 23.8728i −0.869964 0.248070i
\(22\) 0 0
\(23\) 4.21963 23.9307i 0.0382545 0.216952i −0.959688 0.281068i \(-0.909312\pi\)
0.997942 + 0.0641155i \(0.0204226\pi\)
\(24\) 0 0
\(25\) −8.84313 + 7.42027i −0.0707451 + 0.0593622i
\(26\) 0 0
\(27\) −137.100 + 29.7761i −0.977218 + 0.212238i
\(28\) 0 0
\(29\) 183.135 153.668i 1.17267 0.983983i 0.172666 0.984980i \(-0.444762\pi\)
1.00000 0.000996932i \(0.000317333\pi\)
\(30\) 0 0
\(31\) 45.3635 257.269i 0.262823 1.49055i −0.512339 0.858783i \(-0.671221\pi\)
0.775162 0.631762i \(-0.217668\pi\)
\(32\) 0 0
\(33\) 14.0451 13.6033i 0.0740891 0.0717585i
\(34\) 0 0
\(35\) 89.2293 + 154.550i 0.430928 + 0.746390i
\(36\) 0 0
\(37\) 50.0527 86.6937i 0.222395 0.385199i −0.733140 0.680078i \(-0.761946\pi\)
0.955535 + 0.294879i \(0.0952793\pi\)
\(38\) 0 0
\(39\) −340.877 + 152.371i −1.39959 + 0.625613i
\(40\) 0 0
\(41\) 177.609 + 149.031i 0.676531 + 0.567677i 0.914991 0.403475i \(-0.132198\pi\)
−0.238459 + 0.971153i \(0.576642\pi\)
\(42\) 0 0
\(43\) 220.317 + 80.1887i 0.781348 + 0.284387i 0.701735 0.712438i \(-0.252409\pi\)
0.0796135 + 0.996826i \(0.474631\pi\)
\(44\) 0 0
\(45\) 244.341 + 151.681i 0.809426 + 0.502472i
\(46\) 0 0
\(47\) 98.9672 + 561.271i 0.307146 + 1.74191i 0.613229 + 0.789905i \(0.289870\pi\)
−0.306083 + 0.952005i \(0.599019\pi\)
\(48\) 0 0
\(49\) 58.5403 21.3069i 0.170671 0.0621193i
\(50\) 0 0
\(51\) 81.7939 + 120.879i 0.224577 + 0.331892i
\(52\) 0 0
\(53\) 368.316 0.954567 0.477283 0.878749i \(-0.341622\pi\)
0.477283 + 0.878749i \(0.341622\pi\)
\(54\) 0 0
\(55\) −40.0814 −0.0982649
\(56\) 0 0
\(57\) 45.0408 3.21632i 0.104663 0.00747389i
\(58\) 0 0
\(59\) −485.116 + 176.568i −1.07045 + 0.389613i −0.816346 0.577563i \(-0.804004\pi\)
−0.254107 + 0.967176i \(0.581782\pi\)
\(60\) 0 0
\(61\) −106.741 605.358i −0.224046 1.27063i −0.864501 0.502631i \(-0.832366\pi\)
0.640456 0.767995i \(-0.278746\pi\)
\(62\) 0 0
\(63\) −301.697 + 337.063i −0.603337 + 0.674062i
\(64\) 0 0
\(65\) 719.236 + 261.780i 1.37246 + 0.499536i
\(66\) 0 0
\(67\) −264.013 221.533i −0.481407 0.403949i 0.369528 0.929220i \(-0.379520\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(68\) 0 0
\(69\) −102.261 74.0665i −0.178416 0.129225i
\(70\) 0 0
\(71\) 496.578 860.098i 0.830041 1.43767i −0.0679634 0.997688i \(-0.521650\pi\)
0.898005 0.439986i \(-0.145017\pi\)
\(72\) 0 0
\(73\) −180.607 312.820i −0.289568 0.501546i 0.684139 0.729352i \(-0.260178\pi\)
−0.973707 + 0.227806i \(0.926845\pi\)
\(74\) 0 0
\(75\) 14.5972 + 58.1806i 0.0224739 + 0.0895748i
\(76\) 0 0
\(77\) 10.9477 62.0874i 0.0162027 0.0918898i
\(78\) 0 0
\(79\) 127.623 107.088i 0.181756 0.152511i −0.547371 0.836890i \(-0.684371\pi\)
0.729126 + 0.684379i \(0.239927\pi\)
\(80\) 0 0
\(81\) −172.185 + 708.374i −0.236193 + 0.971706i
\(82\) 0 0
\(83\) −718.475 + 602.872i −0.950156 + 0.797275i −0.979324 0.202299i \(-0.935159\pi\)
0.0291680 + 0.999575i \(0.490714\pi\)
\(84\) 0 0
\(85\) 51.9533 294.642i 0.0662956 0.375981i
\(86\) 0 0
\(87\) −302.298 1204.88i −0.372526 1.48479i
\(88\) 0 0
\(89\) −404.414 700.465i −0.481660 0.834260i 0.518118 0.855309i \(-0.326633\pi\)
−0.999778 + 0.0210490i \(0.993299\pi\)
\(90\) 0 0
\(91\) −601.956 + 1042.62i −0.693430 + 1.20106i
\(92\) 0 0
\(93\) −1099.36 796.258i −1.22579 0.887829i
\(94\) 0 0
\(95\) −70.9082 59.4990i −0.0765792 0.0642576i
\(96\) 0 0
\(97\) 1723.85 + 627.431i 1.80444 + 0.656762i 0.997842 + 0.0656621i \(0.0209160\pi\)
0.806598 + 0.591100i \(0.201306\pi\)
\(98\) 0 0
\(99\) −31.6809 96.5340i −0.0321622 0.0980004i
\(100\) 0 0
\(101\) −104.411 592.143i −0.102864 0.583370i −0.992052 0.125829i \(-0.959841\pi\)
0.889188 0.457542i \(-0.151270\pi\)
\(102\) 0 0
\(103\) 61.8832 22.5237i 0.0591994 0.0215468i −0.312251 0.950000i \(-0.601083\pi\)
0.371450 + 0.928453i \(0.378861\pi\)
\(104\) 0 0
\(105\) 924.942 66.0493i 0.859668 0.0613881i
\(106\) 0 0
\(107\) −1123.65 −1.01520 −0.507602 0.861591i \(-0.669468\pi\)
−0.507602 + 0.861591i \(0.669468\pi\)
\(108\) 0 0
\(109\) −1790.18 −1.57310 −0.786550 0.617527i \(-0.788135\pi\)
−0.786550 + 0.617527i \(0.788135\pi\)
\(110\) 0 0
\(111\) −291.507 430.805i −0.249267 0.368380i
\(112\) 0 0
\(113\) −1032.17 + 375.680i −0.859281 + 0.312753i −0.733818 0.679346i \(-0.762264\pi\)
−0.125462 + 0.992098i \(0.540041\pi\)
\(114\) 0 0
\(115\) 44.9457 + 254.900i 0.0364453 + 0.206692i
\(116\) 0 0
\(117\) −61.9904 + 1939.16i −0.0489831 + 1.53227i
\(118\) 0 0
\(119\) 442.220 + 160.955i 0.340657 + 0.123989i
\(120\) 0 0
\(121\) −1008.76 846.449i −0.757895 0.635949i
\(122\) 0 0
\(123\) 1099.86 491.633i 0.806266 0.360399i
\(124\) 0 0
\(125\) 727.204 1259.55i 0.520345 0.901264i
\(126\) 0 0
\(127\) 1048.77 + 1816.52i 0.732782 + 1.26922i 0.955690 + 0.294376i \(0.0951118\pi\)
−0.222908 + 0.974840i \(0.571555\pi\)
\(128\) 0 0
\(129\) 875.101 847.573i 0.597274 0.578485i
\(130\) 0 0
\(131\) −157.676 + 894.228i −0.105162 + 0.596405i 0.885993 + 0.463698i \(0.153478\pi\)
−0.991155 + 0.132707i \(0.957633\pi\)
\(132\) 0 0
\(133\) 111.534 93.5878i 0.0727157 0.0610157i
\(134\) 0 0
\(135\) 1263.79 797.498i 0.805699 0.508427i
\(136\) 0 0
\(137\) 603.157 506.109i 0.376140 0.315619i −0.435045 0.900409i \(-0.643267\pi\)
0.811185 + 0.584790i \(0.198823\pi\)
\(138\) 0 0
\(139\) 175.366 994.552i 0.107010 0.606883i −0.883389 0.468641i \(-0.844744\pi\)
0.990398 0.138242i \(-0.0441452\pi\)
\(140\) 0 0
\(141\) 2847.92 + 812.084i 1.70098 + 0.485034i
\(142\) 0 0
\(143\) −135.198 234.170i −0.0790617 0.136939i
\(144\) 0 0
\(145\) −1273.21 + 2205.27i −0.729204 + 1.26302i
\(146\) 0 0
\(147\) 33.3617 321.982i 0.0187185 0.180658i
\(148\) 0 0
\(149\) −2624.88 2202.54i −1.44321 1.21100i −0.937352 0.348383i \(-0.886731\pi\)
−0.505859 0.862616i \(-0.668825\pi\)
\(150\) 0 0
\(151\) 2253.91 + 820.356i 1.21471 + 0.442117i 0.868334 0.495980i \(-0.165191\pi\)
0.346372 + 0.938097i \(0.387413\pi\)
\(152\) 0 0
\(153\) 750.695 107.762i 0.396667 0.0569417i
\(154\) 0 0
\(155\) 483.193 + 2740.32i 0.250393 + 1.42005i
\(156\) 0 0
\(157\) −1595.55 + 580.732i −0.811073 + 0.295207i −0.714067 0.700077i \(-0.753149\pi\)
−0.0970061 + 0.995284i \(0.530927\pi\)
\(158\) 0 0
\(159\) 836.427 1721.37i 0.417189 0.858575i
\(160\) 0 0
\(161\) −407.125 −0.199291
\(162\) 0 0
\(163\) 1962.35 0.942966 0.471483 0.881875i \(-0.343719\pi\)
0.471483 + 0.881875i \(0.343719\pi\)
\(164\) 0 0
\(165\) −91.0229 + 187.325i −0.0429462 + 0.0883834i
\(166\) 0 0
\(167\) −2348.59 + 854.817i −1.08826 + 0.396094i −0.822976 0.568076i \(-0.807688\pi\)
−0.265284 + 0.964170i \(0.585466\pi\)
\(168\) 0 0
\(169\) 515.125 + 2921.42i 0.234467 + 1.32973i
\(170\) 0 0
\(171\) 87.2536 217.808i 0.0390202 0.0974046i
\(172\) 0 0
\(173\) 1234.35 + 449.268i 0.542463 + 0.197440i 0.598695 0.800977i \(-0.295686\pi\)
−0.0562317 + 0.998418i \(0.517909\pi\)
\(174\) 0 0
\(175\) 148.159 + 124.321i 0.0639989 + 0.0537014i
\(176\) 0 0
\(177\) −276.464 + 2668.23i −0.117403 + 1.13309i
\(178\) 0 0
\(179\) 1735.29 3005.61i 0.724589 1.25503i −0.234554 0.972103i \(-0.575363\pi\)
0.959143 0.282922i \(-0.0913038\pi\)
\(180\) 0 0
\(181\) 1010.33 + 1749.94i 0.414901 + 0.718630i 0.995418 0.0956180i \(-0.0304827\pi\)
−0.580517 + 0.814248i \(0.697149\pi\)
\(182\) 0 0
\(183\) −3071.62 875.872i −1.24077 0.353805i
\(184\) 0 0
\(185\) −185.157 + 1050.08i −0.0735841 + 0.417316i
\(186\) 0 0
\(187\) −80.9677 + 67.9400i −0.0316628 + 0.0265683i
\(188\) 0 0
\(189\) 890.165 + 2175.47i 0.342592 + 0.837261i
\(190\) 0 0
\(191\) 1101.83 924.547i 0.417412 0.350251i −0.409765 0.912191i \(-0.634389\pi\)
0.827178 + 0.561940i \(0.189945\pi\)
\(192\) 0 0
\(193\) 165.021 935.881i 0.0615465 0.349048i −0.938447 0.345423i \(-0.887735\pi\)
0.999993 0.00362415i \(-0.00115361\pi\)
\(194\) 0 0
\(195\) 2856.81 2766.95i 1.04913 1.01613i
\(196\) 0 0
\(197\) 630.410 + 1091.90i 0.227994 + 0.394898i 0.957214 0.289382i \(-0.0934499\pi\)
−0.729219 + 0.684280i \(0.760117\pi\)
\(198\) 0 0
\(199\) 45.3986 78.6327i 0.0161720 0.0280107i −0.857826 0.513940i \(-0.828185\pi\)
0.873998 + 0.485929i \(0.161519\pi\)
\(200\) 0 0
\(201\) −1634.92 + 730.806i −0.573724 + 0.256453i
\(202\) 0 0
\(203\) −3068.28 2574.59i −1.06084 0.890152i
\(204\) 0 0
\(205\) −2320.65 844.647i −0.790640 0.287769i
\(206\) 0 0
\(207\) −578.388 + 309.726i −0.194206 + 0.103997i
\(208\) 0 0
\(209\) 5.67842 + 32.2039i 0.00187935 + 0.0106583i
\(210\) 0 0
\(211\) 3332.78 1213.03i 1.08739 0.395776i 0.264734 0.964322i \(-0.414716\pi\)
0.822652 + 0.568546i \(0.192494\pi\)
\(212\) 0 0
\(213\) −2892.07 4274.06i −0.930335 1.37490i
\(214\) 0 0
\(215\) −2497.33 −0.792169
\(216\) 0 0
\(217\) −4376.83 −1.36921
\(218\) 0 0
\(219\) −1872.15 + 133.689i −0.577664 + 0.0412505i
\(220\) 0 0
\(221\) 1896.65 690.323i 0.577295 0.210118i
\(222\) 0 0
\(223\) 168.174 + 953.762i 0.0505012 + 0.286406i 0.999591 0.0285993i \(-0.00910469\pi\)
−0.949090 + 0.315006i \(0.897994\pi\)
\(224\) 0 0
\(225\) 305.064 + 63.9034i 0.0903893 + 0.0189343i
\(226\) 0 0
\(227\) −1558.12 567.109i −0.455577 0.165816i 0.104031 0.994574i \(-0.466826\pi\)
−0.559608 + 0.828758i \(0.689048\pi\)
\(228\) 0 0
\(229\) −3824.88 3209.45i −1.10373 0.926142i −0.106063 0.994359i \(-0.533825\pi\)
−0.997671 + 0.0682170i \(0.978269\pi\)
\(230\) 0 0
\(231\) −265.312 192.163i −0.0755680 0.0547333i
\(232\) 0 0
\(233\) 1892.72 3278.28i 0.532171 0.921748i −0.467123 0.884192i \(-0.654710\pi\)
0.999295 0.0375555i \(-0.0119571\pi\)
\(234\) 0 0
\(235\) −3035.32 5257.33i −0.842565 1.45936i
\(236\) 0 0
\(237\) −210.665 839.654i −0.0577391 0.230133i
\(238\) 0 0
\(239\) −280.643 + 1591.60i −0.0759551 + 0.430763i 0.922989 + 0.384826i \(0.125738\pi\)
−0.998944 + 0.0459369i \(0.985373\pi\)
\(240\) 0 0
\(241\) 4034.39 3385.25i 1.07833 0.904826i 0.0825491 0.996587i \(-0.473694\pi\)
0.995781 + 0.0917605i \(0.0292494\pi\)
\(242\) 0 0
\(243\) 2919.65 + 2413.41i 0.770764 + 0.637121i
\(244\) 0 0
\(245\) −508.320 + 426.531i −0.132553 + 0.111225i
\(246\) 0 0
\(247\) 108.435 614.966i 0.0279335 0.158418i
\(248\) 0 0
\(249\) 1185.98 + 4726.98i 0.301840 + 1.20305i
\(250\) 0 0
\(251\) 2000.32 + 3464.66i 0.503025 + 0.871264i 0.999994 + 0.00349620i \(0.00111288\pi\)
−0.496969 + 0.867768i \(0.665554\pi\)
\(252\) 0 0
\(253\) 45.7196 79.1887i 0.0113611 0.0196781i
\(254\) 0 0
\(255\) −1259.06 911.928i −0.309198 0.223950i
\(256\) 0 0
\(257\) 5312.76 + 4457.93i 1.28950 + 1.08202i 0.991859 + 0.127338i \(0.0406432\pi\)
0.297638 + 0.954679i \(0.403801\pi\)
\(258\) 0 0
\(259\) −1576.04 573.630i −0.378109 0.137620i
\(260\) 0 0
\(261\) −6317.65 1323.39i −1.49829 0.313854i
\(262\) 0 0
\(263\) 902.671 + 5119.30i 0.211639 + 1.20027i 0.886644 + 0.462452i \(0.153030\pi\)
−0.675005 + 0.737813i \(0.735859\pi\)
\(264\) 0 0
\(265\) −3686.55 + 1341.79i −0.854577 + 0.311041i
\(266\) 0 0
\(267\) −4192.12 + 299.355i −0.960874 + 0.0686151i
\(268\) 0 0
\(269\) −3202.65 −0.725907 −0.362953 0.931807i \(-0.618232\pi\)
−0.362953 + 0.931807i \(0.618232\pi\)
\(270\) 0 0
\(271\) 2563.49 0.574616 0.287308 0.957838i \(-0.407240\pi\)
0.287308 + 0.957838i \(0.407240\pi\)
\(272\) 0 0
\(273\) 3505.79 + 5181.05i 0.777217 + 1.14861i
\(274\) 0 0
\(275\) −40.8194 + 14.8570i −0.00895092 + 0.00325787i
\(276\) 0 0
\(277\) −934.933 5302.27i −0.202797 1.15012i −0.900869 0.434090i \(-0.857070\pi\)
0.698073 0.716027i \(-0.254041\pi\)
\(278\) 0 0
\(279\) −6218.01 + 3329.74i −1.33427 + 0.714503i
\(280\) 0 0
\(281\) 3415.67 + 1243.20i 0.725131 + 0.263926i 0.678102 0.734967i \(-0.262803\pi\)
0.0470287 + 0.998894i \(0.485025\pi\)
\(282\) 0 0
\(283\) 5021.18 + 4213.27i 1.05469 + 0.884993i 0.993579 0.113138i \(-0.0360902\pi\)
0.0611141 + 0.998131i \(0.480535\pi\)
\(284\) 0 0
\(285\) −439.105 + 196.279i −0.0912644 + 0.0407949i
\(286\) 0 0
\(287\) 1942.24 3364.06i 0.399466 0.691896i
\(288\) 0 0
\(289\) 2062.02 + 3571.52i 0.419706 + 0.726953i
\(290\) 0 0
\(291\) 6847.16 6631.77i 1.37934 1.33595i
\(292\) 0 0
\(293\) 88.6969 503.025i 0.0176851 0.100297i −0.974688 0.223571i \(-0.928228\pi\)
0.992373 + 0.123274i \(0.0393395\pi\)
\(294\) 0 0
\(295\) 4212.38 3534.61i 0.831371 0.697603i
\(296\) 0 0
\(297\) −523.110 71.1594i −0.102202 0.0139027i
\(298\) 0 0
\(299\) −1337.61 + 1122.39i −0.258716 + 0.217088i
\(300\) 0 0
\(301\) 682.111 3868.44i 0.130619 0.740775i
\(302\) 0 0
\(303\) −3004.57 856.752i −0.569663 0.162439i
\(304\) 0 0
\(305\) 3273.75 + 5670.29i 0.614604 + 1.06452i
\(306\) 0 0
\(307\) 975.162 1689.03i 0.181288 0.314000i −0.761031 0.648715i \(-0.775307\pi\)
0.942319 + 0.334715i \(0.108640\pi\)
\(308\) 0 0
\(309\) 35.2668 340.369i 0.00649274 0.0626632i
\(310\) 0 0
\(311\) 4843.13 + 4063.87i 0.883051 + 0.740968i 0.966804 0.255518i \(-0.0822462\pi\)
−0.0837528 + 0.996487i \(0.526691\pi\)
\(312\) 0 0
\(313\) 472.116 + 171.836i 0.0852575 + 0.0310312i 0.384297 0.923210i \(-0.374444\pi\)
−0.299039 + 0.954241i \(0.596666\pi\)
\(314\) 0 0
\(315\) 1791.81 4472.83i 0.320499 0.800049i
\(316\) 0 0
\(317\) −1665.94 9448.01i −0.295169 1.67398i −0.666517 0.745490i \(-0.732215\pi\)
0.371348 0.928494i \(-0.378896\pi\)
\(318\) 0 0
\(319\) 845.341 307.679i 0.148370 0.0540022i
\(320\) 0 0
\(321\) −2551.75 + 5251.50i −0.443690 + 0.913116i
\(322\) 0 0
\(323\) −244.094 −0.0420488
\(324\) 0 0
\(325\) 829.514 0.141579
\(326\) 0 0
\(327\) −4065.41 + 8366.62i −0.687515 + 1.41491i
\(328\) 0 0
\(329\) 8972.84 3265.85i 1.50361 0.547271i
\(330\) 0 0
\(331\) 862.280 + 4890.23i 0.143188 + 0.812059i 0.968804 + 0.247827i \(0.0797165\pi\)
−0.825616 + 0.564232i \(0.809172\pi\)
\(332\) 0 0
\(333\) −2675.42 + 384.057i −0.440276 + 0.0632017i
\(334\) 0 0
\(335\) 3449.62 + 1255.56i 0.562605 + 0.204771i
\(336\) 0 0
\(337\) −350.546 294.143i −0.0566632 0.0475460i 0.614016 0.789293i \(-0.289553\pi\)
−0.670679 + 0.741747i \(0.733997\pi\)
\(338\) 0 0
\(339\) −588.228 + 5677.14i −0.0942423 + 0.909558i
\(340\) 0 0
\(341\) 491.513 851.326i 0.0780555 0.135196i
\(342\) 0 0
\(343\) −3395.21 5880.68i −0.534473 0.925735i
\(344\) 0 0
\(345\) 1293.38 + 368.806i 0.201835 + 0.0575532i
\(346\) 0 0
\(347\) 645.039 3658.20i 0.0997911 0.565943i −0.893382 0.449297i \(-0.851675\pi\)
0.993174 0.116646i \(-0.0372144\pi\)
\(348\) 0 0
\(349\) −2640.17 + 2215.37i −0.404943 + 0.339788i −0.822401 0.568909i \(-0.807366\pi\)
0.417457 + 0.908696i \(0.362921\pi\)
\(350\) 0 0
\(351\) 8922.13 + 4693.46i 1.35677 + 0.713727i
\(352\) 0 0
\(353\) −2239.14 + 1878.86i −0.337613 + 0.283291i −0.795793 0.605569i \(-0.792946\pi\)
0.458181 + 0.888859i \(0.348501\pi\)
\(354\) 0 0
\(355\) −1836.97 + 10418.0i −0.274637 + 1.55754i
\(356\) 0 0
\(357\) 1756.50 1701.25i 0.260403 0.252212i
\(358\) 0 0
\(359\) 6470.47 + 11207.2i 0.951249 + 1.64761i 0.742727 + 0.669594i \(0.233532\pi\)
0.208522 + 0.978018i \(0.433135\pi\)
\(360\) 0 0
\(361\) 3391.74 5874.67i 0.494495 0.856490i
\(362\) 0 0
\(363\) −6246.83 + 2792.31i −0.903232 + 0.403742i
\(364\) 0 0
\(365\) 2947.35 + 2473.12i 0.422662 + 0.354655i
\(366\) 0 0
\(367\) −12298.8 4476.41i −1.74930 0.636694i −0.749620 0.661869i \(-0.769764\pi\)
−0.999683 + 0.0251747i \(0.991986\pi\)
\(368\) 0 0
\(369\) 200.015 6256.79i 0.0282178 0.882698i
\(370\) 0 0
\(371\) −1071.55 6077.08i −0.149952 0.850421i
\(372\) 0 0
\(373\) 8627.89 3140.29i 1.19768 0.435920i 0.335267 0.942123i \(-0.391174\pi\)
0.862414 + 0.506203i \(0.168951\pi\)
\(374\) 0 0
\(375\) −4235.24 6259.07i −0.583218 0.861911i
\(376\) 0 0
\(377\) −17178.6 −2.34680
\(378\) 0 0
\(379\) 2260.05 0.306308 0.153154 0.988202i \(-0.451057\pi\)
0.153154 + 0.988202i \(0.451057\pi\)
\(380\) 0 0
\(381\) 10871.5 776.320i 1.46184 0.104389i
\(382\) 0 0
\(383\) −9927.52 + 3613.32i −1.32447 + 0.482068i −0.904888 0.425649i \(-0.860046\pi\)
−0.419583 + 0.907717i \(0.637824\pi\)
\(384\) 0 0
\(385\) 116.610 + 661.329i 0.0154364 + 0.0875440i
\(386\) 0 0
\(387\) −1973.93 6014.69i −0.259277 0.790036i
\(388\) 0 0
\(389\) −9659.45 3515.75i −1.25901 0.458241i −0.375571 0.926793i \(-0.622554\pi\)
−0.883436 + 0.468552i \(0.844776\pi\)
\(390\) 0 0
\(391\) 522.862 + 438.733i 0.0676273 + 0.0567460i
\(392\) 0 0
\(393\) 3821.21 + 2767.67i 0.490470 + 0.355243i
\(394\) 0 0
\(395\) −887.276 + 1536.81i −0.113022 + 0.195760i
\(396\) 0 0
\(397\) 1494.01 + 2587.71i 0.188873 + 0.327137i 0.944875 0.327432i \(-0.106183\pi\)
−0.756002 + 0.654569i \(0.772850\pi\)
\(398\) 0 0
\(399\) −184.107 733.800i −0.0230999 0.0920700i
\(400\) 0 0
\(401\) 1287.47 7301.59i 0.160332 0.909287i −0.793416 0.608680i \(-0.791700\pi\)
0.953748 0.300607i \(-0.0971894\pi\)
\(402\) 0 0
\(403\) −14380.1 + 12066.3i −1.77748 + 1.49148i
\(404\) 0 0
\(405\) −857.208 7717.54i −0.105173 0.946883i
\(406\) 0 0
\(407\) 288.562 242.133i 0.0351438 0.0294891i
\(408\) 0 0
\(409\) −136.025 + 771.437i −0.0164450 + 0.0932643i −0.991926 0.126821i \(-0.959523\pi\)
0.975481 + 0.220086i \(0.0706337\pi\)
\(410\) 0 0
\(411\) −995.622 3968.28i −0.119490 0.476255i
\(412\) 0 0
\(413\) 4324.67 + 7490.55i 0.515262 + 0.892460i
\(414\) 0 0
\(415\) 4995.07 8651.72i 0.590840 1.02336i
\(416\) 0 0
\(417\) −4249.92 3078.18i −0.499087 0.361484i
\(418\) 0 0
\(419\) −7526.09 6315.14i −0.877502 0.736312i 0.0881616 0.996106i \(-0.471901\pi\)
−0.965664 + 0.259794i \(0.916345\pi\)
\(420\) 0 0
\(421\) 1020.41 + 371.400i 0.118128 + 0.0429951i 0.400408 0.916337i \(-0.368868\pi\)
−0.282280 + 0.959332i \(0.591091\pi\)
\(422\) 0 0
\(423\) 10262.9 11465.9i 1.17966 1.31795i
\(424\) 0 0
\(425\) −56.3056 319.325i −0.00642641 0.0364460i
\(426\) 0 0
\(427\) −9677.65 + 3522.38i −1.09680 + 0.399203i
\(428\) 0 0
\(429\) −1401.45 + 100.076i −0.157722 + 0.0112628i
\(430\) 0 0
\(431\) −4258.28 −0.475903 −0.237951 0.971277i \(-0.576476\pi\)
−0.237951 + 0.971277i \(0.576476\pi\)
\(432\) 0 0
\(433\) 7152.99 0.793882 0.396941 0.917844i \(-0.370072\pi\)
0.396941 + 0.917844i \(0.370072\pi\)
\(434\) 0 0
\(435\) 7415.20 + 10958.6i 0.817314 + 1.20787i
\(436\) 0 0
\(437\) 198.435 72.2244i 0.0217218 0.00790609i
\(438\) 0 0
\(439\) −1804.32 10232.8i −0.196162 1.11249i −0.910754 0.412950i \(-0.864498\pi\)
0.714591 0.699542i \(-0.246613\pi\)
\(440\) 0 0
\(441\) −1429.06 887.127i −0.154310 0.0957917i
\(442\) 0 0
\(443\) −12028.7 4378.09i −1.29007 0.469548i −0.396321 0.918112i \(-0.629713\pi\)
−0.893750 + 0.448565i \(0.851935\pi\)
\(444\) 0 0
\(445\) 6599.69 + 5537.80i 0.703046 + 0.589926i
\(446\) 0 0
\(447\) −16254.8 + 7265.85i −1.71997 + 0.768821i
\(448\) 0 0
\(449\) 3046.78 5277.17i 0.320237 0.554666i −0.660300 0.751002i \(-0.729571\pi\)
0.980537 + 0.196336i \(0.0629043\pi\)
\(450\) 0 0
\(451\) 436.223 + 755.560i 0.0455453 + 0.0788868i
\(452\) 0 0
\(453\) 8952.56 8670.94i 0.928539 0.899330i
\(454\) 0 0
\(455\) 2226.79 12628.7i 0.229436 1.30120i
\(456\) 0 0
\(457\) −5464.80 + 4585.51i −0.559371 + 0.469368i −0.878099 0.478478i \(-0.841189\pi\)
0.318729 + 0.947846i \(0.396744\pi\)
\(458\) 0 0
\(459\) 1201.15 3753.19i 0.122146 0.381665i
\(460\) 0 0
\(461\) 9715.80 8152.53i 0.981583 0.823646i −0.00274406 0.999996i \(-0.500873\pi\)
0.984328 + 0.176350i \(0.0564290\pi\)
\(462\) 0 0
\(463\) −2328.16 + 13203.7i −0.233691 + 1.32533i 0.611663 + 0.791119i \(0.290501\pi\)
−0.845353 + 0.534208i \(0.820610\pi\)
\(464\) 0 0
\(465\) 13904.6 + 3964.88i 1.38668 + 0.395413i
\(466\) 0 0
\(467\) −68.4431 118.547i −0.00678195 0.0117467i 0.862615 0.505862i \(-0.168825\pi\)
−0.869396 + 0.494115i \(0.835492\pi\)
\(468\) 0 0
\(469\) −2887.12 + 5000.63i −0.284253 + 0.492341i
\(470\) 0 0
\(471\) −909.290 + 8775.80i −0.0889551 + 0.858530i
\(472\) 0 0
\(473\) 675.840 + 567.097i 0.0656980 + 0.0551272i
\(474\) 0 0
\(475\) −94.2685 34.3109i −0.00910597 0.00331430i
\(476\) 0 0
\(477\) −6145.55 7818.30i −0.589906 0.750472i
\(478\) 0 0
\(479\) 599.222 + 3398.35i 0.0571589 + 0.324164i 0.999958 0.00919797i \(-0.00292785\pi\)
−0.942799 + 0.333362i \(0.891817\pi\)
\(480\) 0 0
\(481\) −6759.50 + 2460.26i −0.640762 + 0.233218i
\(482\) 0 0
\(483\) −924.561 + 1902.75i −0.0870993 + 0.179251i
\(484\) 0 0
\(485\) −19540.2 −1.82943
\(486\) 0 0
\(487\) 8808.83 0.819643 0.409821 0.912166i \(-0.365591\pi\)
0.409821 + 0.912166i \(0.365591\pi\)
\(488\) 0 0
\(489\) 4456.41 9171.31i 0.412119 0.848141i
\(490\) 0 0
\(491\) 11912.6 4335.83i 1.09493 0.398520i 0.269482 0.963005i \(-0.413147\pi\)
0.825443 + 0.564485i \(0.190925\pi\)
\(492\) 0 0
\(493\) 1166.05 + 6612.99i 0.106524 + 0.604126i
\(494\) 0 0
\(495\) 668.780 + 850.814i 0.0607261 + 0.0772550i
\(496\) 0 0
\(497\) −15636.0 5691.05i −1.41121 0.513639i
\(498\) 0 0
\(499\) 13503.0 + 11330.4i 1.21138 + 1.01647i 0.999230 + 0.0392306i \(0.0124907\pi\)
0.212149 + 0.977237i \(0.431954\pi\)
\(500\) 0 0
\(501\) −1338.44 + 12917.7i −0.119356 + 1.15194i
\(502\) 0 0
\(503\) 3751.33 6497.50i 0.332532 0.575962i −0.650476 0.759527i \(-0.725430\pi\)
0.983008 + 0.183565i \(0.0587637\pi\)
\(504\) 0 0
\(505\) 3202.28 + 5546.51i 0.282177 + 0.488745i
\(506\) 0 0
\(507\) 14823.4 + 4226.90i 1.29848 + 0.370263i
\(508\) 0 0
\(509\) −3912.83 + 22190.7i −0.340733 + 1.93239i 0.0201923 + 0.999796i \(0.493572\pi\)
−0.360925 + 0.932595i \(0.617539\pi\)
\(510\) 0 0
\(511\) −4635.98 + 3890.05i −0.401338 + 0.336762i
\(512\) 0 0
\(513\) −819.803 902.422i −0.0705559 0.0776665i
\(514\) 0 0
\(515\) −537.347 + 450.888i −0.0459774 + 0.0385796i
\(516\) 0 0
\(517\) −372.409 + 2112.04i −0.0316799 + 0.179666i
\(518\) 0 0
\(519\) 4902.86 4748.64i 0.414666 0.401622i
\(520\) 0 0
\(521\) 10309.3 + 17856.2i 0.866906 + 1.50153i 0.865142 + 0.501527i \(0.167228\pi\)
0.00176401 + 0.999998i \(0.499438\pi\)
\(522\) 0 0
\(523\) −3362.40 + 5823.85i −0.281123 + 0.486920i −0.971662 0.236376i \(-0.924040\pi\)
0.690538 + 0.723296i \(0.257374\pi\)
\(524\) 0 0
\(525\) 917.491 410.116i 0.0762716 0.0340932i
\(526\) 0 0
\(527\) 5621.08 + 4716.64i 0.464626 + 0.389868i
\(528\) 0 0
\(529\) 10878.4 + 3959.40i 0.894088 + 0.325421i
\(530\) 0 0
\(531\) 11842.5 + 7351.51i 0.967833 + 0.600807i
\(532\) 0 0
\(533\) −2893.02 16407.1i −0.235104 1.33334i
\(534\) 0 0
\(535\) 11246.8 4093.50i 0.908863 0.330799i
\(536\) 0 0
\(537\) −10106.3 14935.7i −0.812141 1.20023i
\(538\) 0 0
\(539\) 234.422 0.0187333
\(540\) 0 0
\(541\) −9213.40 −0.732190 −0.366095 0.930577i \(-0.619306\pi\)
−0.366095 + 0.930577i \(0.619306\pi\)
\(542\) 0 0
\(543\) 10473.0 747.866i 0.827695 0.0591049i
\(544\) 0 0
\(545\) 17918.3 6521.71i 1.40832 0.512586i
\(546\) 0 0
\(547\) −1180.97 6697.60i −0.0923117 0.523526i −0.995538 0.0943612i \(-0.969919\pi\)
0.903226 0.429165i \(-0.141192\pi\)
\(548\) 0 0
\(549\) −11069.0 + 12366.5i −0.860498 + 0.961368i
\(550\) 0 0
\(551\) 1952.23 + 710.554i 0.150940 + 0.0549376i
\(552\) 0 0
\(553\) −2138.22 1794.18i −0.164424 0.137968i
\(554\) 0 0
\(555\) 4487.20 + 3250.04i 0.343191 + 0.248570i
\(556\) 0 0
\(557\) −8957.05 + 15514.1i −0.681369 + 1.18017i 0.293194 + 0.956053i \(0.405282\pi\)
−0.974563 + 0.224113i \(0.928052\pi\)
\(558\) 0 0
\(559\) −8423.70 14590.3i −0.637361 1.10394i
\(560\) 0 0
\(561\) 133.652 + 532.701i 0.0100585 + 0.0400903i
\(562\) 0 0
\(563\) 1738.41 9859.03i 0.130134 0.738026i −0.847992 0.530010i \(-0.822188\pi\)
0.978125 0.208016i \(-0.0667007\pi\)
\(564\) 0 0
\(565\) 8962.62 7520.53i 0.667363 0.559984i
\(566\) 0 0
\(567\) 12188.9 + 780.097i 0.902794 + 0.0577795i
\(568\) 0 0
\(569\) −11756.4 + 9864.81i −0.866177 + 0.726809i −0.963290 0.268464i \(-0.913484\pi\)
0.0971124 + 0.995273i \(0.469039\pi\)
\(570\) 0 0
\(571\) 661.504 3751.58i 0.0484818 0.274954i −0.950924 0.309425i \(-0.899864\pi\)
0.999406 + 0.0344710i \(0.0109746\pi\)
\(572\) 0 0
\(573\) −1818.78 7249.15i −0.132601 0.528513i
\(574\) 0 0
\(575\) 140.258 + 242.933i 0.0101724 + 0.0176192i
\(576\) 0 0
\(577\) 3496.19 6055.58i 0.252250 0.436910i −0.711895 0.702286i \(-0.752163\pi\)
0.964145 + 0.265376i \(0.0854961\pi\)
\(578\) 0 0
\(579\) −3999.20 2896.59i −0.287049 0.207907i
\(580\) 0 0
\(581\) 12037.5 + 10100.6i 0.859550 + 0.721248i
\(582\) 0 0
\(583\) 1302.37 + 474.024i 0.0925192 + 0.0336742i
\(584\) 0 0
\(585\) −6443.99 19635.3i −0.455429 1.38772i
\(586\) 0 0
\(587\) 314.256 + 1782.23i 0.0220966 + 0.125316i 0.993861 0.110638i \(-0.0352895\pi\)
−0.971764 + 0.235954i \(0.924178\pi\)
\(588\) 0 0
\(589\) 2133.29 776.455i 0.149237 0.0543180i
\(590\) 0 0
\(591\) 6534.78 466.642i 0.454830 0.0324790i
\(592\) 0 0
\(593\) −23574.5 −1.63253 −0.816265 0.577677i \(-0.803959\pi\)
−0.816265 + 0.577677i \(0.803959\pi\)
\(594\) 0 0
\(595\) −5012.64 −0.345375
\(596\) 0 0
\(597\) −264.402 390.747i −0.0181260 0.0267876i
\(598\) 0 0
\(599\) −1293.63 + 470.845i −0.0882412 + 0.0321172i −0.385764 0.922598i \(-0.626062\pi\)
0.297522 + 0.954715i \(0.403840\pi\)
\(600\) 0 0
\(601\) −2569.25 14571.0i −0.174379 0.988955i −0.938858 0.344305i \(-0.888114\pi\)
0.764478 0.644649i \(-0.222997\pi\)
\(602\) 0 0
\(603\) −297.320 + 9300.64i −0.0200793 + 0.628112i
\(604\) 0 0
\(605\) 13180.5 + 4797.32i 0.885727 + 0.322378i
\(606\) 0 0
\(607\) −9051.09 7594.77i −0.605226 0.507845i 0.287894 0.957662i \(-0.407045\pi\)
−0.893121 + 0.449817i \(0.851489\pi\)
\(608\) 0 0
\(609\) −19000.6 + 8493.20i −1.26427 + 0.565126i
\(610\) 0 0
\(611\) 20476.8 35466.9i 1.35582 2.34834i
\(612\) 0 0
\(613\) 3225.23 + 5586.27i 0.212506 + 0.368071i 0.952498 0.304545i \(-0.0985042\pi\)
−0.739992 + 0.672615i \(0.765171\pi\)
\(614\) 0 0
\(615\) −9217.65 + 8927.69i −0.604376 + 0.585365i
\(616\) 0 0
\(617\) −2856.84 + 16201.9i −0.186405 + 1.05716i 0.737732 + 0.675094i \(0.235897\pi\)
−0.924137 + 0.382061i \(0.875214\pi\)
\(618\) 0 0
\(619\) −13064.5 + 10962.4i −0.848316 + 0.711822i −0.959418 0.281987i \(-0.909006\pi\)
0.111102 + 0.993809i \(0.464562\pi\)
\(620\) 0 0
\(621\) 134.053 + 3406.54i 0.00866240 + 0.220128i
\(622\) 0 0
\(623\) −10380.9 + 8710.57i −0.667576 + 0.560163i
\(624\) 0 0
\(625\) −2439.54 + 13835.3i −0.156131 + 0.885460i
\(626\) 0 0
\(627\) 163.404 + 46.5948i 0.0104079 + 0.00296781i
\(628\) 0 0
\(629\) 1405.91 + 2435.10i 0.0891211 + 0.154362i
\(630\) 0 0
\(631\) 7321.24 12680.8i 0.461892 0.800021i −0.537163 0.843479i \(-0.680504\pi\)
0.999055 + 0.0434573i \(0.0138373\pi\)
\(632\) 0 0
\(633\) 1899.33 18330.9i 0.119260 1.15101i
\(634\) 0 0
\(635\) −17115.1 14361.2i −1.06959 0.897493i
\(636\) 0 0
\(637\) −4206.55 1531.06i −0.261648 0.0952321i
\(638\) 0 0
\(639\) −26543.1 + 3810.27i −1.64324 + 0.235887i
\(640\) 0 0
\(641\) 792.456 + 4494.24i 0.0488301 + 0.276929i 0.999440 0.0334585i \(-0.0106522\pi\)
−0.950610 + 0.310388i \(0.899541\pi\)
\(642\) 0 0
\(643\) −4259.61 + 1550.37i −0.261248 + 0.0950865i −0.469324 0.883026i \(-0.655502\pi\)
0.208076 + 0.978113i \(0.433280\pi\)
\(644\) 0 0
\(645\) −5671.31 + 11671.6i −0.346213 + 0.712508i
\(646\) 0 0
\(647\) 24993.3 1.51868 0.759342 0.650692i \(-0.225521\pi\)
0.759342 + 0.650692i \(0.225521\pi\)
\(648\) 0 0
\(649\) −1942.62 −0.117496
\(650\) 0 0
\(651\) −9939.57 + 20455.7i −0.598407 + 1.23152i
\(652\) 0 0
\(653\) −2358.00 + 858.241i −0.141310 + 0.0514327i −0.411707 0.911316i \(-0.635067\pi\)
0.270397 + 0.962749i \(0.412845\pi\)
\(654\) 0 0
\(655\) −1679.50 9524.94i −0.100189 0.568199i
\(656\) 0 0
\(657\) −3626.76 + 9053.35i −0.215363 + 0.537602i
\(658\) 0 0
\(659\) 24430.9 + 8892.11i 1.44415 + 0.525626i 0.940950 0.338546i \(-0.109935\pi\)
0.503196 + 0.864172i \(0.332157\pi\)
\(660\) 0 0
\(661\) −4539.92 3809.44i −0.267144 0.224161i 0.499369 0.866390i \(-0.333565\pi\)
−0.766513 + 0.642229i \(0.778010\pi\)
\(662\) 0 0
\(663\) 1080.88 10431.9i 0.0633153 0.611073i
\(664\) 0 0
\(665\) −775.418 + 1343.06i −0.0452171 + 0.0783184i
\(666\) 0 0
\(667\) −2904.63 5030.97i −0.168617 0.292054i
\(668\) 0 0
\(669\) 4839.44 + 1379.97i 0.279677 + 0.0797497i
\(670\) 0 0
\(671\) 401.661 2277.93i 0.0231087 0.131056i
\(672\) 0 0
\(673\) 22589.1 18954.5i 1.29383 1.08565i 0.302649 0.953102i \(-0.402129\pi\)
0.991177 0.132547i \(-0.0423156\pi\)
\(674\) 0 0
\(675\) 991.446 1280.63i 0.0565345 0.0730245i
\(676\) 0 0
\(677\) 16020.1 13442.5i 0.909459 0.763127i −0.0625569 0.998041i \(-0.519925\pi\)
0.972016 + 0.234915i \(0.0754811\pi\)
\(678\) 0 0
\(679\) 5337.13 30268.4i 0.301650 1.71074i
\(680\) 0 0
\(681\) −6188.87 + 5994.18i −0.348249 + 0.337295i
\(682\) 0 0
\(683\) 4479.23 + 7758.25i 0.250941 + 0.434643i 0.963785 0.266680i \(-0.0859265\pi\)
−0.712844 + 0.701323i \(0.752593\pi\)
\(684\) 0 0
\(685\) −4193.34 + 7263.08i −0.233897 + 0.405121i
\(686\) 0 0
\(687\) −23685.9 + 10587.5i −1.31539 + 0.587976i
\(688\) 0 0
\(689\) −20274.3 17012.1i −1.12103 0.940655i
\(690\) 0 0
\(691\) −23144.5 8423.91i −1.27418 0.463764i −0.385677 0.922634i \(-0.626032\pi\)
−0.888503 + 0.458870i \(0.848254\pi\)
\(692\) 0 0
\(693\) −1500.61 + 803.574i −0.0822559 + 0.0440480i
\(694\) 0 0
\(695\) 1867.93 + 10593.5i 0.101949 + 0.578182i
\(696\) 0 0
\(697\) −6119.62 + 2227.36i −0.332564 + 0.121044i
\(698\) 0 0
\(699\) −11023.2 16290.7i −0.596474 0.881501i
\(700\) 0 0
\(701\) 13936.1 0.750869 0.375435 0.926849i \(-0.377493\pi\)
0.375435 + 0.926849i \(0.377493\pi\)
\(702\) 0 0
\(703\) 869.932 0.0466716
\(704\) 0 0
\(705\) −31463.9 + 2246.81i −1.68085 + 0.120028i
\(706\) 0 0
\(707\) −9466.38 + 3445.48i −0.503564 + 0.183282i
\(708\) 0 0
\(709\) 2364.96 + 13412.3i 0.125272 + 0.710453i 0.981146 + 0.193268i \(0.0619088\pi\)
−0.855874 + 0.517185i \(0.826980\pi\)
\(710\) 0 0
\(711\) −4402.64 922.245i −0.232225 0.0486454i
\(712\) 0 0
\(713\) −5965.22 2171.16i −0.313323 0.114040i
\(714\) 0 0
\(715\) 2206.32 + 1851.32i 0.115401 + 0.0968328i
\(716\) 0 0
\(717\) 6801.23 + 4926.07i 0.354249 + 0.256580i
\(718\) 0 0
\(719\) 7771.31 13460.3i 0.403089 0.698171i −0.591008 0.806666i \(-0.701270\pi\)
0.994097 + 0.108495i \(0.0346032\pi\)
\(720\) 0 0
\(721\) −551.671 955.523i −0.0284956 0.0493558i
\(722\) 0 0
\(723\) −6659.50 26542.9i −0.342558 1.36534i
\(724\) 0 0
\(725\) −479.225 + 2717.82i −0.0245489 + 0.139224i
\(726\) 0 0
\(727\) 323.352 271.325i 0.0164958 0.0138417i −0.634502 0.772921i \(-0.718795\pi\)
0.650998 + 0.759079i \(0.274351\pi\)
\(728\) 0 0
\(729\) 17909.8 8164.60i 0.909910 0.414805i
\(730\) 0 0
\(731\) −5044.81 + 4233.10i −0.255252 + 0.214182i
\(732\) 0 0
\(733\) 4836.28 27427.9i 0.243700 1.38209i −0.579793 0.814764i \(-0.696867\pi\)
0.823493 0.567326i \(-0.192022\pi\)
\(734\) 0 0
\(735\) 839.076 + 3344.33i 0.0421085 + 0.167833i
\(736\) 0 0
\(737\) −648.440 1123.13i −0.0324092 0.0561344i
\(738\) 0 0
\(739\) 6838.48 11844.6i 0.340403 0.589595i −0.644105 0.764937i \(-0.722770\pi\)
0.984507 + 0.175343i \(0.0561033\pi\)
\(740\) 0 0
\(741\) −2627.87 1903.34i −0.130280 0.0943605i
\(742\) 0 0
\(743\) 25241.3 + 21180.0i 1.24632 + 1.04578i 0.997003 + 0.0773619i \(0.0246497\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(744\) 0 0
\(745\) 34296.9 + 12483.1i 1.68663 + 0.613885i
\(746\) 0 0
\(747\) 24785.4 + 5191.94i 1.21399 + 0.254301i
\(748\) 0 0
\(749\) 3269.06 + 18539.8i 0.159478 + 0.904443i
\(750\) 0 0
\(751\) 16216.5 5902.33i 0.787948 0.286790i 0.0834654 0.996511i \(-0.473401\pi\)
0.704483 + 0.709721i \(0.251179\pi\)
\(752\) 0 0
\(753\) 20735.2 1480.68i 1.00349 0.0716586i
\(754\) 0 0
\(755\) −25548.5 −1.23153
\(756\) 0 0
\(757\) 11119.9 0.533897 0.266949 0.963711i \(-0.413985\pi\)
0.266949 + 0.963711i \(0.413985\pi\)
\(758\) 0 0
\(759\) −266.271 393.510i −0.0127339 0.0188189i
\(760\) 0 0
\(761\) −15727.2 + 5724.22i −0.749158 + 0.272671i −0.688251 0.725472i \(-0.741621\pi\)
−0.0609065 + 0.998143i \(0.519399\pi\)
\(762\) 0 0
\(763\) 5208.22 + 29537.3i 0.247117 + 1.40147i
\(764\) 0 0
\(765\) −7121.28 + 3813.44i −0.336563 + 0.180229i
\(766\) 0 0
\(767\) 34859.2 + 12687.7i 1.64106 + 0.597297i
\(768\) 0 0
\(769\) −29314.2 24597.6i −1.37464 1.15346i −0.971148 0.238477i \(-0.923352\pi\)
−0.403492 0.914983i \(-0.632204\pi\)
\(770\) 0 0
\(771\) 32899.7 14706.1i 1.53678 0.686935i
\(772\) 0 0
\(773\) −9959.54 + 17250.4i −0.463415 + 0.802658i −0.999128 0.0417417i \(-0.986709\pi\)
0.535714 + 0.844400i \(0.320043\pi\)
\(774\) 0 0
\(775\) 1507.85 + 2611.68i 0.0698886 + 0.121051i
\(776\) 0 0
\(777\) −6260.04 + 6063.12i −0.289032 + 0.279940i
\(778\) 0 0
\(779\) −349.871 + 1984.22i −0.0160917 + 0.0912606i
\(780\) 0 0
\(781\) 2862.86 2402.22i 0.131167 0.110062i
\(782\) 0 0
\(783\) −20532.1 + 26521.0i −0.937112 + 1.21045i