Properties

Label 336.4.q.m.289.2
Level $336$
Weight $4$
Character 336.289
Analytic conductor $19.825$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.2
Root \(8.34231i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.4.q.m.193.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(18.1420 - 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{3} +(-0.363171 + 0.629031i) q^{5} +(18.1420 - 3.72380i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-32.2447 - 55.8495i) q^{11} +71.8475 q^{13} -2.17903 q^{15} +(-24.4517 - 42.3515i) q^{17} +(17.1984 - 29.7885i) q^{19} +(36.8878 + 41.5487i) q^{21} +(-0.451675 + 0.782324i) q^{23} +(62.2362 + 107.796i) q^{25} -27.0000 q^{27} +226.686 q^{29} +(-137.898 - 238.846i) q^{31} +(96.7342 - 167.549i) q^{33} +(-4.24627 + 12.7643i) q^{35} +(-147.605 + 255.658i) q^{37} +(107.771 + 186.665i) q^{39} +186.604 q^{41} +455.317 q^{43} +(-3.26854 - 5.66128i) q^{45} +(141.167 - 244.509i) q^{47} +(315.267 - 135.115i) q^{49} +(73.3550 - 127.055i) q^{51} +(-178.107 - 308.491i) q^{53} +46.8414 q^{55} +103.191 q^{57} +(364.685 + 631.653i) q^{59} +(-137.176 + 237.596i) q^{61} +(-52.6150 + 158.160i) q^{63} +(-26.0929 + 45.1943i) q^{65} +(96.6361 + 167.379i) q^{67} -2.71005 q^{69} -40.5277 q^{71} +(103.236 + 178.810i) q^{73} +(-186.709 + 323.389i) q^{75} +(-792.958 - 893.151i) q^{77} +(468.870 - 812.107i) q^{79} +(-40.5000 - 70.1481i) q^{81} -911.607 q^{83} +35.5206 q^{85} +(340.029 + 588.948i) q^{87} +(474.988 - 822.703i) q^{89} +(1303.46 - 267.546i) q^{91} +(413.693 - 716.537i) q^{93} +(12.4919 + 21.6367i) q^{95} +39.4687 q^{97} +580.405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 4q^{5} - 18q^{7} - 36q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 4q^{5} - 18q^{7} - 36q^{9} + 14q^{11} + 44q^{13} - 24q^{15} - 96q^{17} - 26q^{19} - 36q^{21} + 96q^{23} - 110q^{25} - 216q^{27} - 152q^{29} + 238q^{31} - 42q^{33} - 152q^{35} - 562q^{37} + 66q^{39} + 856q^{41} + 516q^{43} - 36q^{45} - 80q^{47} + 156q^{49} + 288q^{51} - 2952q^{55} - 156q^{57} + 262q^{59} + 276q^{61} + 54q^{63} - 2196q^{65} + 150q^{67} + 576q^{69} + 1696q^{71} + 218q^{73} + 330q^{75} - 764q^{77} + 1762q^{79} - 324q^{81} - 6900q^{83} + 2904q^{85} - 228q^{87} + 344q^{89} + 2806q^{91} - 714q^{93} + 2004q^{95} - 1244q^{97} - 252q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.363171 + 0.629031i −0.0324830 + 0.0562622i −0.881810 0.471605i \(-0.843675\pi\)
0.849327 + 0.527867i \(0.177008\pi\)
\(6\) 0 0
\(7\) 18.1420 3.72380i 0.979578 0.201066i
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −32.2447 55.8495i −0.883832 1.53084i −0.847046 0.531519i \(-0.821621\pi\)
−0.0367856 0.999323i \(-0.511712\pi\)
\(12\) 0 0
\(13\) 71.8475 1.53284 0.766420 0.642340i \(-0.222036\pi\)
0.766420 + 0.642340i \(0.222036\pi\)
\(14\) 0 0
\(15\) −2.17903 −0.0375081
\(16\) 0 0
\(17\) −24.4517 42.3515i −0.348847 0.604221i 0.637198 0.770700i \(-0.280093\pi\)
−0.986045 + 0.166479i \(0.946760\pi\)
\(18\) 0 0
\(19\) 17.1984 29.7885i 0.207663 0.359682i −0.743315 0.668941i \(-0.766748\pi\)
0.950978 + 0.309259i \(0.100081\pi\)
\(20\) 0 0
\(21\) 36.8878 + 41.5487i 0.383313 + 0.431746i
\(22\) 0 0
\(23\) −0.451675 + 0.782324i −0.00409482 + 0.00709243i −0.868066 0.496450i \(-0.834637\pi\)
0.863971 + 0.503542i \(0.167970\pi\)
\(24\) 0 0
\(25\) 62.2362 + 107.796i 0.497890 + 0.862370i
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 226.686 1.45154 0.725769 0.687939i \(-0.241484\pi\)
0.725769 + 0.687939i \(0.241484\pi\)
\(30\) 0 0
\(31\) −137.898 238.846i −0.798940 1.38380i −0.920307 0.391197i \(-0.872061\pi\)
0.121367 0.992608i \(-0.461272\pi\)
\(32\) 0 0
\(33\) 96.7342 167.549i 0.510281 0.883832i
\(34\) 0 0
\(35\) −4.24627 + 12.7643i −0.0205072 + 0.0616444i
\(36\) 0 0
\(37\) −147.605 + 255.658i −0.655839 + 1.13595i 0.325844 + 0.945423i \(0.394352\pi\)
−0.981683 + 0.190522i \(0.938982\pi\)
\(38\) 0 0
\(39\) 107.771 + 186.665i 0.442493 + 0.766420i
\(40\) 0 0
\(41\) 186.604 0.710798 0.355399 0.934715i \(-0.384345\pi\)
0.355399 + 0.934715i \(0.384345\pi\)
\(42\) 0 0
\(43\) 455.317 1.61477 0.807386 0.590023i \(-0.200881\pi\)
0.807386 + 0.590023i \(0.200881\pi\)
\(44\) 0 0
\(45\) −3.26854 5.66128i −0.0108277 0.0187541i
\(46\) 0 0
\(47\) 141.167 244.509i 0.438114 0.758835i −0.559430 0.828877i \(-0.688980\pi\)
0.997544 + 0.0700420i \(0.0223133\pi\)
\(48\) 0 0
\(49\) 315.267 135.115i 0.919145 0.393920i
\(50\) 0 0
\(51\) 73.3550 127.055i 0.201407 0.348847i
\(52\) 0 0
\(53\) −178.107 308.491i −0.461602 0.799518i 0.537439 0.843303i \(-0.319392\pi\)
−0.999041 + 0.0437844i \(0.986059\pi\)
\(54\) 0 0
\(55\) 46.8414 0.114838
\(56\) 0 0
\(57\) 103.191 0.239788
\(58\) 0 0
\(59\) 364.685 + 631.653i 0.804711 + 1.39380i 0.916486 + 0.400066i \(0.131013\pi\)
−0.111776 + 0.993733i \(0.535654\pi\)
\(60\) 0 0
\(61\) −137.176 + 237.596i −0.287928 + 0.498706i −0.973315 0.229473i \(-0.926300\pi\)
0.685387 + 0.728179i \(0.259633\pi\)
\(62\) 0 0
\(63\) −52.6150 + 158.160i −0.105220 + 0.316291i
\(64\) 0 0
\(65\) −26.0929 + 45.1943i −0.0497912 + 0.0862409i
\(66\) 0 0
\(67\) 96.6361 + 167.379i 0.176209 + 0.305202i 0.940579 0.339575i \(-0.110283\pi\)
−0.764370 + 0.644778i \(0.776950\pi\)
\(68\) 0 0
\(69\) −2.71005 −0.00472829
\(70\) 0 0
\(71\) −40.5277 −0.0677429 −0.0338715 0.999426i \(-0.510784\pi\)
−0.0338715 + 0.999426i \(0.510784\pi\)
\(72\) 0 0
\(73\) 103.236 + 178.810i 0.165519 + 0.286687i 0.936839 0.349760i \(-0.113737\pi\)
−0.771320 + 0.636447i \(0.780403\pi\)
\(74\) 0 0
\(75\) −186.709 + 323.389i −0.287457 + 0.497890i
\(76\) 0 0
\(77\) −792.958 893.151i −1.17358 1.32187i
\(78\) 0 0
\(79\) 468.870 812.107i 0.667747 1.15657i −0.310785 0.950480i \(-0.600592\pi\)
0.978533 0.206092i \(-0.0660746\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −911.607 −1.20556 −0.602782 0.797906i \(-0.705941\pi\)
−0.602782 + 0.797906i \(0.705941\pi\)
\(84\) 0 0
\(85\) 35.5206 0.0453264
\(86\) 0 0
\(87\) 340.029 + 588.948i 0.419023 + 0.725769i
\(88\) 0 0
\(89\) 474.988 822.703i 0.565715 0.979846i −0.431268 0.902224i \(-0.641934\pi\)
0.996983 0.0776226i \(-0.0247329\pi\)
\(90\) 0 0
\(91\) 1303.46 267.546i 1.50154 0.308203i
\(92\) 0 0
\(93\) 413.693 716.537i 0.461268 0.798940i
\(94\) 0 0
\(95\) 12.4919 + 21.6367i 0.0134910 + 0.0233671i
\(96\) 0 0
\(97\) 39.4687 0.0413138 0.0206569 0.999787i \(-0.493424\pi\)
0.0206569 + 0.999787i \(0.493424\pi\)
\(98\) 0 0
\(99\) 580.405 0.589221
\(100\) 0 0
\(101\) 158.437 + 274.421i 0.156090 + 0.270356i 0.933455 0.358694i \(-0.116778\pi\)
−0.777365 + 0.629049i \(0.783444\pi\)
\(102\) 0 0
\(103\) −161.317 + 279.409i −0.154321 + 0.267291i −0.932811 0.360365i \(-0.882652\pi\)
0.778491 + 0.627656i \(0.215986\pi\)
\(104\) 0 0
\(105\) −39.5320 + 8.11426i −0.0367421 + 0.00754163i
\(106\) 0 0
\(107\) 340.726 590.154i 0.307843 0.533200i −0.670047 0.742318i \(-0.733726\pi\)
0.977890 + 0.209119i \(0.0670595\pi\)
\(108\) 0 0
\(109\) 227.984 + 394.879i 0.200338 + 0.346996i 0.948637 0.316365i \(-0.102463\pi\)
−0.748299 + 0.663361i \(0.769129\pi\)
\(110\) 0 0
\(111\) −885.627 −0.757297
\(112\) 0 0
\(113\) −796.025 −0.662688 −0.331344 0.943510i \(-0.607502\pi\)
−0.331344 + 0.943510i \(0.607502\pi\)
\(114\) 0 0
\(115\) −0.328071 0.568235i −0.000266024 0.000460767i
\(116\) 0 0
\(117\) −323.314 + 559.996i −0.255473 + 0.442493i
\(118\) 0 0
\(119\) −601.312 677.290i −0.463212 0.521740i
\(120\) 0 0
\(121\) −1413.95 + 2449.03i −1.06232 + 1.83999i
\(122\) 0 0
\(123\) 279.907 + 484.813i 0.205190 + 0.355399i
\(124\) 0 0
\(125\) −181.202 −0.129658
\(126\) 0 0
\(127\) −2333.92 −1.63072 −0.815362 0.578952i \(-0.803462\pi\)
−0.815362 + 0.578952i \(0.803462\pi\)
\(128\) 0 0
\(129\) 682.976 + 1182.95i 0.466145 + 0.807386i
\(130\) 0 0
\(131\) −943.489 + 1634.17i −0.629259 + 1.08991i 0.358441 + 0.933552i \(0.383308\pi\)
−0.987701 + 0.156357i \(0.950025\pi\)
\(132\) 0 0
\(133\) 201.088 604.468i 0.131102 0.394091i
\(134\) 0 0
\(135\) 9.80562 16.9838i 0.00625136 0.0108277i
\(136\) 0 0
\(137\) −1473.63 2552.40i −0.918983 1.59173i −0.800963 0.598714i \(-0.795678\pi\)
−0.118021 0.993011i \(-0.537655\pi\)
\(138\) 0 0
\(139\) −955.433 −0.583013 −0.291506 0.956569i \(-0.594156\pi\)
−0.291506 + 0.956569i \(0.594156\pi\)
\(140\) 0 0
\(141\) 847.003 0.505890
\(142\) 0 0
\(143\) −2316.70 4012.65i −1.35477 2.34654i
\(144\) 0 0
\(145\) −82.3259 + 142.593i −0.0471503 + 0.0816667i
\(146\) 0 0
\(147\) 823.938 + 616.415i 0.462294 + 0.345857i
\(148\) 0 0
\(149\) −1091.87 + 1891.17i −0.600332 + 1.03981i 0.392439 + 0.919778i \(0.371631\pi\)
−0.992771 + 0.120027i \(0.961702\pi\)
\(150\) 0 0
\(151\) 202.360 + 350.497i 0.109058 + 0.188894i 0.915389 0.402570i \(-0.131883\pi\)
−0.806331 + 0.591465i \(0.798550\pi\)
\(152\) 0 0
\(153\) 440.130 0.232565
\(154\) 0 0
\(155\) 200.322 0.103808
\(156\) 0 0
\(157\) 464.791 + 805.042i 0.236270 + 0.409231i 0.959641 0.281228i \(-0.0907418\pi\)
−0.723371 + 0.690459i \(0.757408\pi\)
\(158\) 0 0
\(159\) 534.322 925.472i 0.266506 0.461602i
\(160\) 0 0
\(161\) −5.28108 + 15.8749i −0.00258514 + 0.00777092i
\(162\) 0 0
\(163\) −712.840 + 1234.68i −0.342540 + 0.593296i −0.984904 0.173104i \(-0.944620\pi\)
0.642364 + 0.766400i \(0.277954\pi\)
\(164\) 0 0
\(165\) 70.2621 + 121.698i 0.0331509 + 0.0574190i
\(166\) 0 0
\(167\) −4185.15 −1.93926 −0.969631 0.244572i \(-0.921353\pi\)
−0.969631 + 0.244572i \(0.921353\pi\)
\(168\) 0 0
\(169\) 2965.07 1.34960
\(170\) 0 0
\(171\) 154.786 + 268.097i 0.0692209 + 0.119894i
\(172\) 0 0
\(173\) −1117.78 + 1936.05i −0.491231 + 0.850837i −0.999949 0.0100961i \(-0.996786\pi\)
0.508718 + 0.860933i \(0.330120\pi\)
\(174\) 0 0
\(175\) 1530.50 + 1723.89i 0.661115 + 0.744650i
\(176\) 0 0
\(177\) −1094.05 + 1894.96i −0.464600 + 0.804711i
\(178\) 0 0
\(179\) −470.740 815.345i −0.196563 0.340457i 0.750849 0.660474i \(-0.229645\pi\)
−0.947412 + 0.320017i \(0.896311\pi\)
\(180\) 0 0
\(181\) −467.540 −0.192000 −0.0960000 0.995381i \(-0.530605\pi\)
−0.0960000 + 0.995381i \(0.530605\pi\)
\(182\) 0 0
\(183\) −823.058 −0.332471
\(184\) 0 0
\(185\) −107.211 185.696i −0.0426072 0.0737979i
\(186\) 0 0
\(187\) −1576.88 + 2731.23i −0.616645 + 1.06806i
\(188\) 0 0
\(189\) −489.835 + 100.543i −0.188520 + 0.0386953i
\(190\) 0 0
\(191\) 137.701 238.506i 0.0521660 0.0903542i −0.838763 0.544496i \(-0.816721\pi\)
0.890929 + 0.454142i \(0.150054\pi\)
\(192\) 0 0
\(193\) −820.148 1420.54i −0.305884 0.529806i 0.671574 0.740937i \(-0.265619\pi\)
−0.977458 + 0.211131i \(0.932285\pi\)
\(194\) 0 0
\(195\) −156.558 −0.0574940
\(196\) 0 0
\(197\) 1303.88 0.471560 0.235780 0.971806i \(-0.424236\pi\)
0.235780 + 0.971806i \(0.424236\pi\)
\(198\) 0 0
\(199\) −663.678 1149.52i −0.236417 0.409485i 0.723267 0.690569i \(-0.242640\pi\)
−0.959683 + 0.281083i \(0.909306\pi\)
\(200\) 0 0
\(201\) −289.908 + 502.136i −0.101734 + 0.176209i
\(202\) 0 0
\(203\) 4112.55 844.135i 1.42189 0.291855i
\(204\) 0 0
\(205\) −67.7693 + 117.380i −0.0230889 + 0.0399911i
\(206\) 0 0
\(207\) −4.06508 7.04092i −0.00136494 0.00236414i
\(208\) 0 0
\(209\) −2218.23 −0.734155
\(210\) 0 0
\(211\) 4753.28 1.55085 0.775426 0.631439i \(-0.217535\pi\)
0.775426 + 0.631439i \(0.217535\pi\)
\(212\) 0 0
\(213\) −60.7915 105.294i −0.0195557 0.0338715i
\(214\) 0 0
\(215\) −165.358 + 286.408i −0.0524527 + 0.0908507i
\(216\) 0 0
\(217\) −3391.16 3819.64i −1.06086 1.19490i
\(218\) 0 0
\(219\) −309.709 + 536.431i −0.0955624 + 0.165519i
\(220\) 0 0
\(221\) −1756.79 3042.85i −0.534727 0.926174i
\(222\) 0 0
\(223\) −513.149 −0.154094 −0.0770470 0.997027i \(-0.524549\pi\)
−0.0770470 + 0.997027i \(0.524549\pi\)
\(224\) 0 0
\(225\) −1120.25 −0.331926
\(226\) 0 0
\(227\) 1654.67 + 2865.97i 0.483808 + 0.837980i 0.999827 0.0185972i \(-0.00592001\pi\)
−0.516019 + 0.856577i \(0.672587\pi\)
\(228\) 0 0
\(229\) 2954.73 5117.75i 0.852639 1.47681i −0.0261800 0.999657i \(-0.508334\pi\)
0.878819 0.477156i \(-0.158332\pi\)
\(230\) 0 0
\(231\) 1131.04 3399.89i 0.322151 0.968382i
\(232\) 0 0
\(233\) 176.786 306.202i 0.0497065 0.0860943i −0.840102 0.542429i \(-0.817505\pi\)
0.889808 + 0.456335i \(0.150838\pi\)
\(234\) 0 0
\(235\) 102.536 + 177.597i 0.0284625 + 0.0492985i
\(236\) 0 0
\(237\) 2813.22 0.771048
\(238\) 0 0
\(239\) 1652.55 0.447259 0.223629 0.974674i \(-0.428209\pi\)
0.223629 + 0.974674i \(0.428209\pi\)
\(240\) 0 0
\(241\) 1553.47 + 2690.69i 0.415220 + 0.719182i 0.995452 0.0952696i \(-0.0303713\pi\)
−0.580232 + 0.814451i \(0.697038\pi\)
\(242\) 0 0
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −29.5044 + 247.382i −0.00769374 + 0.0645088i
\(246\) 0 0
\(247\) 1235.66 2140.23i 0.318313 0.551335i
\(248\) 0 0
\(249\) −1367.41 2368.42i −0.348016 0.602782i
\(250\) 0 0
\(251\) −1771.77 −0.445551 −0.222776 0.974870i \(-0.571512\pi\)
−0.222776 + 0.974870i \(0.571512\pi\)
\(252\) 0 0
\(253\) 58.2566 0.0144765
\(254\) 0 0
\(255\) 53.2808 + 92.2851i 0.0130846 + 0.0226632i
\(256\) 0 0
\(257\) −739.063 + 1280.09i −0.179383 + 0.310701i −0.941669 0.336539i \(-0.890743\pi\)
0.762286 + 0.647240i \(0.224077\pi\)
\(258\) 0 0
\(259\) −1725.82 + 5187.81i −0.414044 + 1.24461i
\(260\) 0 0
\(261\) −1020.09 + 1766.84i −0.241923 + 0.419023i
\(262\) 0 0
\(263\) −715.987 1240.13i −0.167869 0.290758i 0.769801 0.638284i \(-0.220355\pi\)
−0.937671 + 0.347525i \(0.887022\pi\)
\(264\) 0 0
\(265\) 258.734 0.0599769
\(266\) 0 0
\(267\) 2849.93 0.653231
\(268\) 0 0
\(269\) −142.699 247.162i −0.0323439 0.0560213i 0.849400 0.527749i \(-0.176964\pi\)
−0.881744 + 0.471728i \(0.843631\pi\)
\(270\) 0 0
\(271\) −2624.66 + 4546.05i −0.588328 + 1.01901i 0.406123 + 0.913818i \(0.366880\pi\)
−0.994452 + 0.105196i \(0.966453\pi\)
\(272\) 0 0
\(273\) 2650.29 + 2985.17i 0.587557 + 0.661797i
\(274\) 0 0
\(275\) 4013.58 6951.72i 0.880102 1.52438i
\(276\) 0 0
\(277\) −3573.93 6190.24i −0.775224 1.34273i −0.934669 0.355520i \(-0.884304\pi\)
0.159445 0.987207i \(-0.449029\pi\)
\(278\) 0 0
\(279\) 2482.16 0.532627
\(280\) 0 0
\(281\) 4228.36 0.897661 0.448831 0.893617i \(-0.351841\pi\)
0.448831 + 0.893617i \(0.351841\pi\)
\(282\) 0 0
\(283\) 4171.19 + 7224.71i 0.876154 + 1.51754i 0.855528 + 0.517756i \(0.173232\pi\)
0.0206255 + 0.999787i \(0.493434\pi\)
\(284\) 0 0
\(285\) −37.4758 + 64.9100i −0.00778904 + 0.0134910i
\(286\) 0 0
\(287\) 3385.38 694.878i 0.696282 0.142918i
\(288\) 0 0
\(289\) 1260.73 2183.65i 0.256611 0.444464i
\(290\) 0 0
\(291\) 59.2030 + 102.543i 0.0119263 + 0.0206569i
\(292\) 0 0
\(293\) 5038.84 1.00468 0.502342 0.864669i \(-0.332472\pi\)
0.502342 + 0.864669i \(0.332472\pi\)
\(294\) 0 0
\(295\) −529.772 −0.104558
\(296\) 0 0
\(297\) 870.608 + 1507.94i 0.170094 + 0.294611i
\(298\) 0 0
\(299\) −32.4517 + 56.2081i −0.00627670 + 0.0108716i
\(300\) 0 0
\(301\) 8260.38 1695.51i 1.58180 0.324677i
\(302\) 0 0
\(303\) −475.311 + 823.263i −0.0901186 + 0.156090i
\(304\) 0 0
\(305\) −99.6369 172.576i −0.0187055 0.0323990i
\(306\) 0 0
\(307\) 4869.67 0.905300 0.452650 0.891688i \(-0.350479\pi\)
0.452650 + 0.891688i \(0.350479\pi\)
\(308\) 0 0
\(309\) −967.901 −0.178194
\(310\) 0 0
\(311\) −726.421 1258.20i −0.132449 0.229408i 0.792171 0.610299i \(-0.208951\pi\)
−0.924620 + 0.380891i \(0.875617\pi\)
\(312\) 0 0
\(313\) −2848.14 + 4933.12i −0.514333 + 0.890850i 0.485529 + 0.874221i \(0.338627\pi\)
−0.999862 + 0.0166299i \(0.994706\pi\)
\(314\) 0 0
\(315\) −80.3794 90.5356i −0.0143774 0.0161940i
\(316\) 0 0
\(317\) 1735.73 3006.38i 0.307535 0.532666i −0.670288 0.742101i \(-0.733829\pi\)
0.977822 + 0.209435i \(0.0671626\pi\)
\(318\) 0 0
\(319\) −7309.44 12660.3i −1.28291 2.22207i
\(320\) 0 0
\(321\) 2044.35 0.355466
\(322\) 0 0
\(323\) −1682.12 −0.289770
\(324\) 0 0
\(325\) 4471.52 + 7744.90i 0.763185 + 1.32188i
\(326\) 0 0
\(327\) −683.951 + 1184.64i −0.115665 + 0.200338i
\(328\) 0 0
\(329\) 1650.56 4961.56i 0.276590 0.831428i
\(330\) 0 0
\(331\) 3127.19 5416.45i 0.519293 0.899441i −0.480456 0.877019i \(-0.659529\pi\)
0.999749 0.0224223i \(-0.00713785\pi\)
\(332\) 0 0
\(333\) −1328.44 2300.93i −0.218613 0.378649i
\(334\) 0 0
\(335\) −140.382 −0.0228951
\(336\) 0 0
\(337\) 8006.96 1.29426 0.647132 0.762378i \(-0.275968\pi\)
0.647132 + 0.762378i \(0.275968\pi\)
\(338\) 0 0
\(339\) −1194.04 2068.13i −0.191302 0.331344i
\(340\) 0 0
\(341\) −8892.94 + 15403.0i −1.41226 + 2.44610i
\(342\) 0 0
\(343\) 5216.44 3625.25i 0.821169 0.570685i
\(344\) 0 0
\(345\) 0.984212 1.70471i 0.000153589 0.000266024i
\(346\) 0 0
\(347\) 3817.80 + 6612.62i 0.590634 + 1.02301i 0.994147 + 0.108034i \(0.0344556\pi\)
−0.403513 + 0.914974i \(0.632211\pi\)
\(348\) 0 0
\(349\) −10358.0 −1.58869 −0.794345 0.607468i \(-0.792185\pi\)
−0.794345 + 0.607468i \(0.792185\pi\)
\(350\) 0 0
\(351\) −1939.88 −0.294995
\(352\) 0 0
\(353\) −1692.12 2930.83i −0.255134 0.441905i 0.709798 0.704405i \(-0.248786\pi\)
−0.964932 + 0.262500i \(0.915453\pi\)
\(354\) 0 0
\(355\) 14.7185 25.4931i 0.00220049 0.00381137i
\(356\) 0 0
\(357\) 857.683 2578.19i 0.127152 0.382219i
\(358\) 0 0
\(359\) −4097.31 + 7096.74i −0.602361 + 1.04332i 0.390102 + 0.920772i \(0.372440\pi\)
−0.992463 + 0.122548i \(0.960894\pi\)
\(360\) 0 0
\(361\) 2837.93 + 4915.44i 0.413752 + 0.716640i
\(362\) 0 0
\(363\) −8483.67 −1.22666
\(364\) 0 0
\(365\) −149.970 −0.0215062
\(366\) 0 0
\(367\) 402.755 + 697.592i 0.0572851 + 0.0992208i 0.893246 0.449569i \(-0.148422\pi\)
−0.835961 + 0.548789i \(0.815089\pi\)
\(368\) 0 0
\(369\) −839.720 + 1454.44i −0.118466 + 0.205190i
\(370\) 0 0
\(371\) −4379.99 4933.41i −0.612931 0.690377i
\(372\) 0 0
\(373\) −3952.86 + 6846.55i −0.548716 + 0.950404i 0.449647 + 0.893206i \(0.351550\pi\)
−0.998363 + 0.0571977i \(0.981783\pi\)
\(374\) 0 0
\(375\) −271.803 470.777i −0.0374290 0.0648289i
\(376\) 0 0
\(377\) 16286.8 2.22497
\(378\) 0 0
\(379\) −3324.24 −0.450540 −0.225270 0.974296i \(-0.572326\pi\)
−0.225270 + 0.974296i \(0.572326\pi\)
\(380\) 0 0
\(381\) −3500.88 6063.70i −0.470749 0.815362i
\(382\) 0 0
\(383\) −4235.38 + 7335.90i −0.565060 + 0.978712i 0.431984 + 0.901881i \(0.357814\pi\)
−0.997044 + 0.0768310i \(0.975520\pi\)
\(384\) 0 0
\(385\) 849.798 174.428i 0.112493 0.0230901i
\(386\) 0 0
\(387\) −2048.93 + 3548.85i −0.269129 + 0.466145i
\(388\) 0 0
\(389\) 3954.20 + 6848.88i 0.515388 + 0.892678i 0.999840 + 0.0178606i \(0.00568551\pi\)
−0.484452 + 0.874818i \(0.660981\pi\)
\(390\) 0 0
\(391\) 44.1769 0.00571386
\(392\) 0 0
\(393\) −5660.93 −0.726606
\(394\) 0 0
\(395\) 340.560 + 589.868i 0.0433809 + 0.0751379i
\(396\) 0 0
\(397\) 4890.79 8471.10i 0.618292 1.07091i −0.371506 0.928431i \(-0.621158\pi\)
0.989797 0.142482i \(-0.0455083\pi\)
\(398\) 0 0
\(399\) 1872.09 384.261i 0.234891 0.0482134i
\(400\) 0 0
\(401\) 397.827 689.056i 0.0495424 0.0858100i −0.840191 0.542291i \(-0.817557\pi\)
0.889733 + 0.456481i \(0.150890\pi\)
\(402\) 0 0
\(403\) −9907.60 17160.5i −1.22465 2.12115i
\(404\) 0 0
\(405\) 58.8337 0.00721844
\(406\) 0 0
\(407\) 19037.9 2.31860
\(408\) 0 0
\(409\) −4292.36 7434.59i −0.518933 0.898818i −0.999758 0.0220017i \(-0.992996\pi\)
0.480825 0.876817i \(-0.340337\pi\)
\(410\) 0 0
\(411\) 4420.89 7657.21i 0.530575 0.918983i
\(412\) 0 0
\(413\) 8968.27 + 10101.4i 1.06852 + 1.20353i
\(414\) 0 0
\(415\) 331.069 573.428i 0.0391603 0.0678277i
\(416\) 0 0
\(417\) −1433.15 2482.29i −0.168301 0.291506i
\(418\) 0 0
\(419\) 7447.09 0.868292 0.434146 0.900843i \(-0.357050\pi\)
0.434146 + 0.900843i \(0.357050\pi\)
\(420\) 0 0
\(421\) −4446.76 −0.514779 −0.257390 0.966308i \(-0.582862\pi\)
−0.257390 + 0.966308i \(0.582862\pi\)
\(422\) 0 0
\(423\) 1270.50 + 2200.58i 0.146038 + 0.252945i
\(424\) 0 0
\(425\) 3043.56 5271.60i 0.347375 0.601671i
\(426\) 0 0
\(427\) −1603.89 + 4821.30i −0.181775 + 0.546414i
\(428\) 0 0
\(429\) 6950.11 12037.9i 0.782178 1.35477i
\(430\) 0 0
\(431\) −4481.85 7762.79i −0.500889 0.867565i −0.999999 0.00102683i \(-0.999673\pi\)
0.499110 0.866538i \(-0.333660\pi\)
\(432\) 0 0
\(433\) −16173.6 −1.79504 −0.897520 0.440973i \(-0.854633\pi\)
−0.897520 + 0.440973i \(0.854633\pi\)
\(434\) 0 0
\(435\) −493.955 −0.0544445
\(436\) 0 0
\(437\) 15.5362 + 26.9095i 0.00170068 + 0.00294567i
\(438\) 0 0
\(439\) −3149.21 + 5454.60i −0.342378 + 0.593015i −0.984874 0.173274i \(-0.944566\pi\)
0.642496 + 0.766289i \(0.277899\pi\)
\(440\) 0 0
\(441\) −365.585 + 3065.28i −0.0394757 + 0.330988i
\(442\) 0 0
\(443\) −8392.35 + 14536.0i −0.900074 + 1.55897i −0.0726770 + 0.997356i \(0.523154\pi\)
−0.827397 + 0.561618i \(0.810179\pi\)
\(444\) 0 0
\(445\) 345.004 + 597.564i 0.0367522 + 0.0636567i
\(446\) 0 0
\(447\) −6551.22 −0.693203
\(448\) 0 0
\(449\) 2733.88 0.287349 0.143674 0.989625i \(-0.454108\pi\)
0.143674 + 0.989625i \(0.454108\pi\)
\(450\) 0 0
\(451\) −6017.01 10421.8i −0.628226 1.08812i
\(452\) 0 0
\(453\) −607.079 + 1051.49i −0.0629648 + 0.109058i
\(454\) 0 0
\(455\) −305.084 + 917.081i −0.0314342 + 0.0944910i
\(456\) 0 0
\(457\) −4614.60 + 7992.72i −0.472345 + 0.818126i −0.999499 0.0316437i \(-0.989926\pi\)
0.527154 + 0.849770i \(0.323259\pi\)
\(458\) 0 0
\(459\) 660.195 + 1143.49i 0.0671357 + 0.116282i
\(460\) 0 0
\(461\) −19726.7 −1.99298 −0.996491 0.0837048i \(-0.973325\pi\)
−0.996491 + 0.0837048i \(0.973325\pi\)
\(462\) 0 0
\(463\) −368.924 −0.0370310 −0.0185155 0.999829i \(-0.505894\pi\)
−0.0185155 + 0.999829i \(0.505894\pi\)
\(464\) 0 0
\(465\) 300.482 + 520.451i 0.0299667 + 0.0519039i
\(466\) 0 0
\(467\) −6654.78 + 11526.4i −0.659414 + 1.14214i 0.321353 + 0.946959i \(0.395862\pi\)
−0.980768 + 0.195179i \(0.937471\pi\)
\(468\) 0 0
\(469\) 2376.46 + 2676.73i 0.233976 + 0.263540i
\(470\) 0 0
\(471\) −1394.37 + 2415.12i −0.136410 + 0.236270i
\(472\) 0 0
\(473\) −14681.6 25429.2i −1.42719 2.47196i
\(474\) 0 0
\(475\) 4281.46 0.413572
\(476\) 0 0
\(477\) 3205.93 0.307735
\(478\) 0 0
\(479\) 5781.39 + 10013.7i 0.551479 + 0.955189i 0.998168 + 0.0605002i \(0.0192696\pi\)
−0.446689 + 0.894689i \(0.647397\pi\)
\(480\) 0 0
\(481\) −10605.0 + 18368.4i −1.00530 + 1.74122i
\(482\) 0 0
\(483\) −49.1658 + 10.0917i −0.00463172 + 0.000950700i
\(484\) 0 0
\(485\) −14.3339 + 24.8270i −0.00134200 + 0.00232440i
\(486\) 0 0
\(487\) 1314.06 + 2276.02i 0.122271 + 0.211779i 0.920663 0.390359i \(-0.127649\pi\)
−0.798392 + 0.602138i \(0.794316\pi\)
\(488\) 0 0
\(489\) −4277.04 −0.395531
\(490\) 0 0
\(491\) 12319.9 1.13236 0.566181 0.824281i \(-0.308420\pi\)
0.566181 + 0.824281i \(0.308420\pi\)
\(492\) 0 0
\(493\) −5542.86 9600.51i −0.506365 0.877049i
\(494\) 0 0
\(495\) −210.786 + 365.093i −0.0191397 + 0.0331509i
\(496\) 0 0
\(497\) −735.254 + 150.917i −0.0663595 + 0.0136208i
\(498\) 0 0
\(499\) −1652.90 + 2862.91i −0.148285 + 0.256837i −0.930594 0.366054i \(-0.880709\pi\)
0.782309 + 0.622891i \(0.214042\pi\)
\(500\) 0 0
\(501\) −6277.73 10873.3i −0.559817 0.969631i
\(502\) 0 0
\(503\) 3072.72 0.272377 0.136189 0.990683i \(-0.456515\pi\)
0.136189 + 0.990683i \(0.456515\pi\)
\(504\) 0 0
\(505\) −230.159 −0.0202811
\(506\) 0 0
\(507\) 4447.60 + 7703.47i 0.389595 + 0.674799i
\(508\) 0 0
\(509\) −6784.91 + 11751.8i −0.590836 + 1.02336i 0.403284 + 0.915075i \(0.367869\pi\)
−0.994120 + 0.108284i \(0.965465\pi\)
\(510\) 0 0
\(511\) 2538.77 + 2859.55i 0.219782 + 0.247552i
\(512\) 0 0
\(513\) −464.357 + 804.291i −0.0399647 + 0.0692209i
\(514\) 0 0
\(515\) −117.171 202.947i −0.0100256 0.0173648i
\(516\) 0 0
\(517\) −18207.6 −1.54888
\(518\) 0 0
\(519\) −6706.66 −0.567225
\(520\) 0 0
\(521\) 5366.68 + 9295.36i 0.451283 + 0.781645i 0.998466 0.0553681i \(-0.0176332\pi\)
−0.547183 + 0.837013i \(0.684300\pi\)
\(522\) 0 0
\(523\) 4174.07 7229.71i 0.348986 0.604461i −0.637084 0.770794i \(-0.719860\pi\)
0.986070 + 0.166334i \(0.0531928\pi\)
\(524\) 0 0
\(525\) −2183.04 + 6562.20i −0.181477 + 0.545520i
\(526\) 0 0
\(527\) −6743.65 + 11680.3i −0.557416 + 0.965473i
\(528\) 0 0
\(529\) 6083.09 + 10536.2i 0.499966 + 0.865967i
\(530\) 0 0
\(531\) −6564.33 −0.536474
\(532\) 0 0
\(533\) 13407.1 1.08954
\(534\) 0 0
\(535\) 247.483 + 428.654i 0.0199993 + 0.0346399i
\(536\) 0 0
\(537\) 1412.22 2446.04i 0.113486 0.196563i
\(538\) 0 0
\(539\) −17711.8 13250.7i −1.41540 1.05891i
\(540\) 0 0
\(541\) 11553.6 20011.5i 0.918170 1.59032i 0.115978 0.993252i \(-0.463000\pi\)
0.802192 0.597066i \(-0.203667\pi\)
\(542\) 0 0
\(543\) −701.310 1214.71i −0.0554256 0.0960000i
\(544\) 0 0
\(545\) −331.188 −0.0260304
\(546\) 0 0
\(547\) −13935.2 −1.08926 −0.544630 0.838676i \(-0.683330\pi\)
−0.544630 + 0.838676i \(0.683330\pi\)
\(548\) 0 0
\(549\) −1234.59 2138.37i −0.0959761 0.166235i
\(550\) 0 0
\(551\) 3898.65 6752.65i 0.301430 0.522092i
\(552\) 0 0
\(553\) 5482.13 16479.3i 0.421562 1.26721i
\(554\) 0 0
\(555\) 321.634 557.087i 0.0245993 0.0426072i
\(556\) 0 0
\(557\) 7523.76 + 13031.5i 0.572337 + 0.991317i 0.996325 + 0.0856492i \(0.0272964\pi\)
−0.423988 + 0.905668i \(0.639370\pi\)
\(558\) 0 0
\(559\) 32713.4 2.47519
\(560\) 0 0
\(561\) −9461.25 −0.712040
\(562\) 0 0
\(563\) 7721.08 + 13373.3i 0.577983 + 1.00110i 0.995710 + 0.0925239i \(0.0294934\pi\)
−0.417727 + 0.908572i \(0.637173\pi\)
\(564\) 0 0
\(565\) 289.093 500.724i 0.0215261 0.0372843i
\(566\) 0 0
\(567\) −995.970 1121.81i −0.0737686 0.0830895i
\(568\) 0 0
\(569\) 6681.06 11571.9i 0.492240 0.852585i −0.507720 0.861522i \(-0.669511\pi\)
0.999960 + 0.00893696i \(0.00284476\pi\)
\(570\) 0 0
\(571\) −11092.6 19213.0i −0.812981 1.40812i −0.910769 0.412917i \(-0.864510\pi\)
0.0977876 0.995207i \(-0.468823\pi\)
\(572\) 0 0
\(573\) 826.208 0.0602362
\(574\) 0 0
\(575\) −112.442 −0.00815507
\(576\) 0 0
\(577\) 9475.68 + 16412.4i 0.683671 + 1.18415i 0.973853 + 0.227181i \(0.0729508\pi\)
−0.290182 + 0.956971i \(0.593716\pi\)
\(578\) 0 0
\(579\) 2460.44 4261.61i 0.176602 0.305884i
\(580\) 0 0
\(581\) −16538.4 + 3394.64i −1.18094 + 0.242399i
\(582\) 0 0
\(583\) −11486.0 + 19894.4i −0.815957 + 1.41328i
\(584\) 0 0
\(585\) −234.836 406.749i −0.0165971 0.0287470i
\(586\) 0 0
\(587\) −19579.5 −1.37672 −0.688359 0.725371i \(-0.741668\pi\)
−0.688359 + 0.725371i \(0.741668\pi\)
\(588\) 0 0
\(589\) −9486.48 −0.663640
\(590\) 0 0
\(591\) 1955.81 + 3387.57i 0.136128 + 0.235780i
\(592\) 0 0
\(593\) −2806.51 + 4861.01i −0.194350 + 0.336624i −0.946687 0.322154i \(-0.895593\pi\)
0.752337 + 0.658778i \(0.228926\pi\)
\(594\) 0 0
\(595\) 644.415 132.272i 0.0444007 0.00911362i
\(596\) 0 0
\(597\) 1991.03 3448.57i 0.136495 0.236417i
\(598\) 0 0
\(599\) 10962.8 + 18988.0i 0.747790 + 1.29521i 0.948880 + 0.315637i \(0.102218\pi\)
−0.201090 + 0.979573i \(0.564448\pi\)
\(600\) 0 0
\(601\) −2067.51 −0.140326 −0.0701628 0.997536i \(-0.522352\pi\)
−0.0701628 + 0.997536i \(0.522352\pi\)
\(602\) 0 0
\(603\) −1739.45 −0.117472
\(604\) 0 0
\(605\) −1027.01 1778.83i −0.0690146 0.119537i
\(606\) 0 0
\(607\) −5083.61 + 8805.07i −0.339930 + 0.588775i −0.984419 0.175838i \(-0.943737\pi\)
0.644490 + 0.764613i \(0.277070\pi\)
\(608\) 0 0
\(609\) 8361.95 + 9418.51i 0.556393 + 0.626695i
\(610\) 0 0
\(611\) 10142.5 17567.3i 0.671558 1.16317i
\(612\) 0 0
\(613\) 9093.05 + 15749.6i 0.599127 + 1.03772i 0.992950 + 0.118532i \(0.0378188\pi\)
−0.393824 + 0.919186i \(0.628848\pi\)
\(614\) 0 0
\(615\) −406.616 −0.0266607
\(616\) 0 0
\(617\) 6584.41 0.429625 0.214812 0.976655i \(-0.431086\pi\)
0.214812 + 0.976655i \(0.431086\pi\)
\(618\) 0 0
\(619\) −3889.86 6737.43i −0.252579 0.437480i 0.711656 0.702528i \(-0.247946\pi\)
−0.964235 + 0.265048i \(0.914612\pi\)
\(620\) 0 0
\(621\) 12.1952 21.1228i 0.000788048 0.00136494i
\(622\) 0 0
\(623\) 5553.66 16694.3i 0.357147 1.07358i
\(624\) 0 0
\(625\) −7713.72 + 13360.6i −0.493678 + 0.855075i
\(626\) 0 0
\(627\) −3327.35 5763.14i −0.211932 0.367078i
\(628\) 0 0
\(629\) 14436.7 0.915150
\(630\) 0 0
\(631\) −3787.78 −0.238969 −0.119484 0.992836i \(-0.538124\pi\)
−0.119484 + 0.992836i \(0.538124\pi\)
\(632\) 0 0
\(633\) 7129.93 + 12349.4i 0.447692 + 0.775426i
\(634\) 0 0
\(635\) 847.612 1468.11i 0.0529708 0.0917481i
\(636\) 0 0
\(637\) 22651.1 9707.66i 1.40890 0.603817i
\(638\) 0 0
\(639\) 182.374 315.882i 0.0112905 0.0195557i
\(640\) 0 0
\(641\) 9965.44 + 17260.6i 0.614058 + 1.06358i 0.990549 + 0.137159i \(0.0437973\pi\)
−0.376491 + 0.926420i \(0.622869\pi\)
\(642\) 0 0
\(643\) −3185.18 −0.195352 −0.0976759 0.995218i \(-0.531141\pi\)
−0.0976759 + 0.995218i \(0.531141\pi\)
\(644\) 0 0
\(645\) −992.148 −0.0605671
\(646\) 0 0
\(647\) −8471.50 14673.1i −0.514759 0.891589i −0.999853 0.0171270i \(-0.994548\pi\)
0.485094 0.874462i \(-0.338785\pi\)
\(648\) 0 0
\(649\) 23518.3 40734.9i 1.42246 2.46377i
\(650\) 0 0
\(651\) 4836.98 14539.9i 0.291208 0.875369i
\(652\) 0 0
\(653\) 10039.4 17388.7i 0.601640 1.04207i −0.390932 0.920419i \(-0.627847\pi\)
0.992573 0.121652i \(-0.0388193\pi\)
\(654\) 0 0
\(655\) −685.295 1186.97i −0.0408805 0.0708070i
\(656\) 0 0
\(657\) −1858.25 −0.110346
\(658\) 0 0
\(659\) 9442.46 0.558158 0.279079 0.960268i \(-0.409971\pi\)
0.279079 + 0.960268i \(0.409971\pi\)
\(660\) 0 0
\(661\) −380.995 659.902i −0.0224190 0.0388309i 0.854598 0.519290i \(-0.173803\pi\)
−0.877017 + 0.480459i \(0.840470\pi\)
\(662\) 0 0
\(663\) 5270.38 9128.56i 0.308725 0.534727i
\(664\) 0 0
\(665\) 307.200 + 346.016i 0.0179138 + 0.0201773i
\(666\) 0 0
\(667\) −102.389 + 177.342i −0.00594378 + 0.0102949i
\(668\) 0 0
\(669\) −769.723 1333.20i −0.0444831 0.0770470i
\(670\) 0 0
\(671\) 17692.8 1.01792
\(672\) 0 0
\(673\) −16111.6 −0.922818 −0.461409 0.887188i \(-0.652656\pi\)
−0.461409 + 0.887188i \(0.652656\pi\)
\(674\) 0 0
\(675\) −1680.38 2910.50i −0.0958189 0.165963i
\(676\) 0 0
\(677\) −15620.7 + 27055.9i −0.886786 + 1.53596i −0.0431329 + 0.999069i \(0.513734\pi\)
−0.843653 + 0.536889i \(0.819599\pi\)
\(678\) 0 0
\(679\) 716.042 146.974i 0.0404700 0.00830682i
\(680\) 0 0
\(681\) −4964.01 + 8597.92i −0.279327 + 0.483808i
\(682\) 0 0
\(683\) −15056.8 26079.1i −0.843530 1.46104i −0.886892 0.461978i \(-0.847140\pi\)
0.0433614 0.999059i \(-0.486193\pi\)
\(684\) 0 0
\(685\) 2140.72 0.119405
\(686\) 0 0
\(687\) 17728.4 0.984542
\(688\) 0 0
\(689\) −12796.6 22164.3i −0.707562 1.22553i
\(690\) 0 0
\(691\) −4875.43 + 8444.49i −0.268408 + 0.464896i −0.968451 0.249204i \(-0.919831\pi\)
0.700043 + 0.714101i \(0.253164\pi\)
\(692\) 0 0
\(693\) 10529.7 2161.31i 0.577188 0.118473i
\(694\) 0 0
\(695\) 346.986 600.997i 0.0189380 0.0328016i
\(696\) 0 0
\(697\) −4562.79 7902.99i −0.247960 0.429479i
\(698\) 0 0
\(699\) 1060.71 0.0573962
\(700\) 0 0
\(701\) 11851.6 0.638559 0.319280 0.947661i \(-0.396559\pi\)
0.319280 + 0.947661i \(0.396559\pi\)
\(702\) 0 0
\(703\) 5077.13 + 8793.85i 0.272386 + 0.471787i
\(704\) 0 0
\(705\) −307.607 + 532.791i −0.0164328 + 0.0284625i
\(706\) 0 0
\(707\) 3896.26 + 4388.57i 0.207262 + 0.233450i
\(708\) 0 0
\(709\) −661.196 + 1145.22i −0.0350236 + 0.0606627i −0.883006 0.469362i \(-0.844484\pi\)
0.847982 + 0.530025i \(0.177817\pi\)
\(710\) 0 0
\(711\) 4219.83 + 7308.96i 0.222582 + 0.385524i
\(712\) 0 0
\(713\) 249.140 0.0130861
\(714\) 0 0
\(715\) 3365.44 0.176028
\(716\) 0 0
\(717\) 2478.83 + 4293.46i 0.129112 + 0.223629i
\(718\) 0 0
\(719\) 3650.78 6323.33i 0.189362 0.327984i −0.755676 0.654946i \(-0.772691\pi\)
0.945038 + 0.326962i \(0.106025\pi\)
\(720\) 0 0
\(721\) −1886.15 + 5669.76i −0.0974257 + 0.292861i
\(722\) 0 0
\(723\) −4660.42 + 8072.08i −0.239727 + 0.415220i
\(724\) 0 0
\(725\) 14108.1 + 24435.9i 0.722705 + 1.25176i
\(726\) 0 0
\(727\) 6088.72 0.310616 0.155308 0.987866i \(-0.450363\pi\)
0.155308 + 0.987866i \(0.450363\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −11133.3 19283.4i −0.563309 0.975680i
\(732\) 0 0
\(733\) 13289.2 23017.6i 0.669644 1.15986i −0.308360 0.951270i \(-0.599780\pi\)
0.978004 0.208587i \(-0.0668865\pi\)
\(734\) 0 0
\(735\) −686.974 + 294.418i −0.0344754 + 0.0147752i
\(736\) 0 0
\(737\) 6232.01 10794.2i 0.311478 0.539495i
\(738\) 0 0
\(739\) 12609.9 + 21841.0i 0.627689 + 1.08719i 0.988014 + 0.154363i \(0.0493324\pi\)
−0.360325 + 0.932827i \(0.617334\pi\)
\(740\) 0 0
\(741\) 7413.98 0.367557
\(742\) 0 0
\(743\) −2634.28 −0.130071 −0.0650353 0.997883i \(-0.520716\pi\)
−0.0650353 + 0.997883i \(0.520716\pi\)
\(744\) 0 0
\(745\) −793.071 1373.64i −0.0390012 0.0675520i
\(746\) 0 0
\(747\) 4102.23 7105.27i 0.200927 0.348016i
\(748\) 0 0
\(749\) 3983.84 11975.4i 0.194347 0.584207i
\(750\) 0 0
\(751\) 2883.64 4994.62i 0.140114 0.242685i −0.787425 0.616410i \(-0.788586\pi\)
0.927539 + 0.373725i \(0.121920\pi\)
\(752\) 0 0
\(753\) −2657.66 4603.20i −0.128619 0.222776i
\(754\) 0 0
\(755\) −293.965 −0.0141702
\(756\) 0 0
\(757\) 33378.7 1.60260 0.801302 0.598260i \(-0.204141\pi\)
0.801302 + 0.598260i \(0.204141\pi\)
\(758\) 0 0
\(759\) 87.3849 + 151.355i 0.00417901 + 0.00723826i
\(760\) 0 0
\(761\) −1813.04 + 3140.28i −0.0863637 + 0.149586i −0.905971 0.423339i \(-0.860858\pi\)
0.819608 + 0.572925i \(0.194191\pi\)
\(762\) 0 0
\(763\) 5606.54 + 6314.95i 0.266016 + 0.299628i
\(764\) 0 0
\(765\) −159.843 + 276.855i −0.00755440 + 0.0130846i
\(766\) 0 0
\(767\) 26201.7 + 45382.7i 1.23349 + 2.13647i
\(768\) 0 0
\(769\) 3426.15 0.160663 0.0803316 0.996768i \(-0.474402\pi\)
0.0803316 + 0.996768i \(0.474402\pi\)
\(770\) 0 0
\(771\) −4434.38 −0.207134
\(772\) 0 0
\(773\) −6554.09 11352.0i −0.304960 0.528207i 0.672292 0.740286i \(-0.265310\pi\)
−0.977252 + 0.212079i \(0.931976\pi\)
\(774\) 0 0
\(775\) 17164.4 29729.7i 0.795568 1.37796i
\(776\) 0 0
\(777\) −16067.1 + 3297.90i −0.741831 + 0.152267i
\(778\) 0 0
\(779\) 3209.30 5558.67i 0.147606 0.255661i
\(780\) 0 0
\(781\) 1306.80 + 2263.45i 0.0598734 + 0.103704i
\(782\) 0 0
\(783\) −6120.53 −0.279348
\(784\) 0 0
\(785\) −675.194 −0.0306990
\(786\) 0 0
\(787\) 19659.9 + 34051.9i 0.890468 + 1.54234i 0.839315 + 0.543646i \(0.182957\pi\)
0.0511538 + 0.998691i \(0.483710\pi\)
\(788\) 0 0
\(789\) 2147.96 3720.38i 0.0969195 0.167869i
\(790\) 0 0
\(791\) −14441.5 + 2964.24i −0.649154 + 0.133244i
\(792\) 0 0
\(793\) −9855.77 + 17070.7i −0.441348 + 0.764437i
\(794\) 0 0