Properties

Label 336.4.q.m.193.4
Level $336$
Weight $4$
Character 336.193
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 193.4
Root \(-4.63878i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.m.289.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(7.90648 + 13.6944i) q^{5} +(-15.2050 - 10.5739i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(7.90648 + 13.6944i) q^{5} +(-15.2050 - 10.5739i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-15.1240 + 26.1955i) q^{11} -61.6298 q^{13} +47.4389 q^{15} +(-28.0724 + 48.6228i) q^{17} +(-69.7002 - 120.724i) q^{19} +(-50.2793 + 23.6429i) q^{21} +(-4.07240 - 7.05360i) q^{23} +(-62.5247 + 108.296i) q^{25} -27.0000 q^{27} -0.217857 q^{29} +(88.2903 - 152.923i) q^{31} +(45.3719 + 78.5864i) q^{33} +(24.5855 - 291.826i) q^{35} +(-105.540 - 182.801i) q^{37} +(-92.4447 + 160.119i) q^{39} -293.305 q^{41} -434.591 q^{43} +(71.1583 - 123.250i) q^{45} +(241.698 + 418.633i) q^{47} +(119.385 + 321.553i) q^{49} +(84.2172 + 145.868i) q^{51} +(-10.2536 + 17.7598i) q^{53} -478.309 q^{55} -418.201 q^{57} +(-115.674 + 200.353i) q^{59} +(419.351 + 726.337i) q^{61} +(-13.9930 + 166.094i) q^{63} +(-487.274 - 843.984i) q^{65} +(-312.020 + 540.435i) q^{67} -24.4344 q^{69} -227.106 q^{71} +(-21.5247 + 37.2819i) q^{73} +(187.574 + 324.888i) q^{75} +(506.949 - 238.383i) q^{77} +(-154.530 - 267.654i) q^{79} +(-40.5000 + 70.1481i) q^{81} -1233.99 q^{83} -887.815 q^{85} +(-0.326785 + 0.566009i) q^{87} +(-572.179 - 991.042i) q^{89} +(937.082 + 651.668i) q^{91} +(-264.871 - 458.770i) q^{93} +(1102.17 - 1909.01i) q^{95} +1688.12 q^{97} +272.231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 4q^{5} - 18q^{7} - 36q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 4q^{5} - 18q^{7} - 36q^{9} + 14q^{11} + 44q^{13} - 24q^{15} - 96q^{17} - 26q^{19} - 36q^{21} + 96q^{23} - 110q^{25} - 216q^{27} - 152q^{29} + 238q^{31} - 42q^{33} - 152q^{35} - 562q^{37} + 66q^{39} + 856q^{41} + 516q^{43} - 36q^{45} - 80q^{47} + 156q^{49} + 288q^{51} - 2952q^{55} - 156q^{57} + 262q^{59} + 276q^{61} + 54q^{63} - 2196q^{65} + 150q^{67} + 576q^{69} + 1696q^{71} + 218q^{73} + 330q^{75} - 764q^{77} + 1762q^{79} - 324q^{81} - 6900q^{83} + 2904q^{85} - 228q^{87} + 344q^{89} + 2806q^{91} - 714q^{93} + 2004q^{95} - 1244q^{97} - 252q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 7.90648 + 13.6944i 0.707177 + 1.22487i 0.965900 + 0.258915i \(0.0833648\pi\)
−0.258724 + 0.965951i \(0.583302\pi\)
\(6\) 0 0
\(7\) −15.2050 10.5739i −0.820993 0.570938i
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) −15.1240 + 26.1955i −0.414550 + 0.718021i −0.995381 0.0960028i \(-0.969394\pi\)
0.580831 + 0.814024i \(0.302728\pi\)
\(12\) 0 0
\(13\) −61.6298 −1.31485 −0.657424 0.753521i \(-0.728354\pi\)
−0.657424 + 0.753521i \(0.728354\pi\)
\(14\) 0 0
\(15\) 47.4389 0.816577
\(16\) 0 0
\(17\) −28.0724 + 48.6228i −0.400503 + 0.693692i −0.993787 0.111302i \(-0.964498\pi\)
0.593283 + 0.804994i \(0.297831\pi\)
\(18\) 0 0
\(19\) −69.7002 120.724i −0.841596 1.45769i −0.888544 0.458790i \(-0.848283\pi\)
0.0469481 0.998897i \(-0.485050\pi\)
\(20\) 0 0
\(21\) −50.2793 + 23.6429i −0.522469 + 0.245681i
\(22\) 0 0
\(23\) −4.07240 7.05360i −0.0369197 0.0639469i 0.846975 0.531633i \(-0.178421\pi\)
−0.883895 + 0.467686i \(0.845088\pi\)
\(24\) 0 0
\(25\) −62.5247 + 108.296i −0.500198 + 0.866368i
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −0.217857 −0.00139500 −0.000697500 1.00000i \(-0.500222\pi\)
−0.000697500 1.00000i \(0.500222\pi\)
\(30\) 0 0
\(31\) 88.2903 152.923i 0.511529 0.885994i −0.488382 0.872630i \(-0.662413\pi\)
0.999911 0.0133642i \(-0.00425408\pi\)
\(32\) 0 0
\(33\) 45.3719 + 78.5864i 0.239340 + 0.414550i
\(34\) 0 0
\(35\) 24.5855 291.826i 0.118735 1.40936i
\(36\) 0 0
\(37\) −105.540 182.801i −0.468937 0.812223i 0.530432 0.847727i \(-0.322030\pi\)
−0.999370 + 0.0355042i \(0.988696\pi\)
\(38\) 0 0
\(39\) −92.4447 + 160.119i −0.379564 + 0.657424i
\(40\) 0 0
\(41\) −293.305 −1.11723 −0.558616 0.829427i \(-0.688667\pi\)
−0.558616 + 0.829427i \(0.688667\pi\)
\(42\) 0 0
\(43\) −434.591 −1.54127 −0.770634 0.637278i \(-0.780060\pi\)
−0.770634 + 0.637278i \(0.780060\pi\)
\(44\) 0 0
\(45\) 71.1583 123.250i 0.235726 0.408289i
\(46\) 0 0
\(47\) 241.698 + 418.633i 0.750112 + 1.29923i 0.947768 + 0.318960i \(0.103334\pi\)
−0.197657 + 0.980271i \(0.563333\pi\)
\(48\) 0 0
\(49\) 119.385 + 321.553i 0.348060 + 0.937472i
\(50\) 0 0
\(51\) 84.2172 + 145.868i 0.231231 + 0.400503i
\(52\) 0 0
\(53\) −10.2536 + 17.7598i −0.0265745 + 0.0460283i −0.879007 0.476809i \(-0.841793\pi\)
0.852432 + 0.522838i \(0.175127\pi\)
\(54\) 0 0
\(55\) −478.309 −1.17264
\(56\) 0 0
\(57\) −418.201 −0.971792
\(58\) 0 0
\(59\) −115.674 + 200.353i −0.255245 + 0.442097i −0.964962 0.262390i \(-0.915489\pi\)
0.709717 + 0.704487i \(0.248823\pi\)
\(60\) 0 0
\(61\) 419.351 + 726.337i 0.880203 + 1.52456i 0.851115 + 0.524979i \(0.175927\pi\)
0.0290872 + 0.999577i \(0.490740\pi\)
\(62\) 0 0
\(63\) −13.9930 + 166.094i −0.0279833 + 0.332157i
\(64\) 0 0
\(65\) −487.274 843.984i −0.929830 1.61051i
\(66\) 0 0
\(67\) −312.020 + 540.435i −0.568945 + 0.985442i 0.427726 + 0.903909i \(0.359315\pi\)
−0.996671 + 0.0815332i \(0.974018\pi\)
\(68\) 0 0
\(69\) −24.4344 −0.0426312
\(70\) 0 0
\(71\) −227.106 −0.379613 −0.189806 0.981822i \(-0.560786\pi\)
−0.189806 + 0.981822i \(0.560786\pi\)
\(72\) 0 0
\(73\) −21.5247 + 37.2819i −0.0345107 + 0.0597742i −0.882765 0.469815i \(-0.844321\pi\)
0.848254 + 0.529589i \(0.177654\pi\)
\(74\) 0 0
\(75\) 187.574 + 324.888i 0.288789 + 0.500198i
\(76\) 0 0
\(77\) 506.949 238.383i 0.750288 0.352809i
\(78\) 0 0
\(79\) −154.530 267.654i −0.220076 0.381183i 0.734755 0.678333i \(-0.237297\pi\)
−0.954831 + 0.297150i \(0.903964\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −1233.99 −1.63190 −0.815951 0.578122i \(-0.803786\pi\)
−0.815951 + 0.578122i \(0.803786\pi\)
\(84\) 0 0
\(85\) −887.815 −1.13291
\(86\) 0 0
\(87\) −0.326785 + 0.566009i −0.000402702 + 0.000697500i
\(88\) 0 0
\(89\) −572.179 991.042i −0.681470 1.18034i −0.974532 0.224247i \(-0.928008\pi\)
0.293063 0.956093i \(-0.405326\pi\)
\(90\) 0 0
\(91\) 937.082 + 651.668i 1.07948 + 0.750696i
\(92\) 0 0
\(93\) −264.871 458.770i −0.295331 0.511529i
\(94\) 0 0
\(95\) 1102.17 1909.01i 1.19031 2.06169i
\(96\) 0 0
\(97\) 1688.12 1.76704 0.883520 0.468394i \(-0.155167\pi\)
0.883520 + 0.468394i \(0.155167\pi\)
\(98\) 0 0
\(99\) 272.231 0.276366
\(100\) 0 0
\(101\) 743.930 1288.52i 0.732909 1.26944i −0.222726 0.974881i \(-0.571496\pi\)
0.955635 0.294554i \(-0.0951712\pi\)
\(102\) 0 0
\(103\) −389.204 674.121i −0.372324 0.644884i 0.617598 0.786494i \(-0.288106\pi\)
−0.989923 + 0.141609i \(0.954772\pi\)
\(104\) 0 0
\(105\) −721.308 501.614i −0.670405 0.466215i
\(106\) 0 0
\(107\) 651.040 + 1127.63i 0.588209 + 1.01881i 0.994467 + 0.105050i \(0.0335001\pi\)
−0.406258 + 0.913758i \(0.633167\pi\)
\(108\) 0 0
\(109\) −234.541 + 406.237i −0.206100 + 0.356976i −0.950483 0.310777i \(-0.899411\pi\)
0.744382 + 0.667754i \(0.232744\pi\)
\(110\) 0 0
\(111\) −633.240 −0.541482
\(112\) 0 0
\(113\) 1653.86 1.37684 0.688418 0.725314i \(-0.258306\pi\)
0.688418 + 0.725314i \(0.258306\pi\)
\(114\) 0 0
\(115\) 64.3966 111.538i 0.0522175 0.0904434i
\(116\) 0 0
\(117\) 277.334 + 480.357i 0.219141 + 0.379564i
\(118\) 0 0
\(119\) 940.975 442.475i 0.724866 0.340854i
\(120\) 0 0
\(121\) 208.032 + 360.321i 0.156297 + 0.270715i
\(122\) 0 0
\(123\) −439.957 + 762.028i −0.322517 + 0.558616i
\(124\) 0 0
\(125\) −0.781685 −0.000559328
\(126\) 0 0
\(127\) −163.760 −0.114420 −0.0572100 0.998362i \(-0.518220\pi\)
−0.0572100 + 0.998362i \(0.518220\pi\)
\(128\) 0 0
\(129\) −651.887 + 1129.10i −0.444926 + 0.770634i
\(130\) 0 0
\(131\) −260.947 451.973i −0.174038 0.301443i 0.765790 0.643091i \(-0.222348\pi\)
−0.939828 + 0.341648i \(0.889015\pi\)
\(132\) 0 0
\(133\) −216.736 + 2572.62i −0.141304 + 1.67725i
\(134\) 0 0
\(135\) −213.475 369.749i −0.136096 0.235726i
\(136\) 0 0
\(137\) −1338.44 + 2318.25i −0.834679 + 1.44571i 0.0596120 + 0.998222i \(0.481014\pi\)
−0.894291 + 0.447485i \(0.852320\pi\)
\(138\) 0 0
\(139\) −853.692 −0.520930 −0.260465 0.965483i \(-0.583876\pi\)
−0.260465 + 0.965483i \(0.583876\pi\)
\(140\) 0 0
\(141\) 1450.19 0.866154
\(142\) 0 0
\(143\) 932.087 1614.42i 0.545070 0.944089i
\(144\) 0 0
\(145\) −1.72248 2.98342i −0.000986512 0.00170869i
\(146\) 0 0
\(147\) 1014.50 + 172.159i 0.569212 + 0.0965947i
\(148\) 0 0
\(149\) −278.843 482.970i −0.153313 0.265547i 0.779130 0.626862i \(-0.215661\pi\)
−0.932444 + 0.361316i \(0.882328\pi\)
\(150\) 0 0
\(151\) 884.674 1532.30i 0.476780 0.825807i −0.522866 0.852415i \(-0.675137\pi\)
0.999646 + 0.0266077i \(0.00847049\pi\)
\(152\) 0 0
\(153\) 505.303 0.267002
\(154\) 0 0
\(155\) 2792.26 1.44697
\(156\) 0 0
\(157\) 1202.45 2082.70i 0.611247 1.05871i −0.379784 0.925075i \(-0.624002\pi\)
0.991031 0.133635i \(-0.0426651\pi\)
\(158\) 0 0
\(159\) 30.7609 + 53.2795i 0.0153428 + 0.0265745i
\(160\) 0 0
\(161\) −12.6633 + 150.311i −0.00619881 + 0.0735788i
\(162\) 0 0
\(163\) 1689.40 + 2926.12i 0.811802 + 1.40608i 0.911601 + 0.411075i \(0.134847\pi\)
−0.0997991 + 0.995008i \(0.531820\pi\)
\(164\) 0 0
\(165\) −717.463 + 1242.68i −0.338512 + 0.586320i
\(166\) 0 0
\(167\) 805.900 0.373428 0.186714 0.982414i \(-0.440216\pi\)
0.186714 + 0.982414i \(0.440216\pi\)
\(168\) 0 0
\(169\) 1601.23 0.728826
\(170\) 0 0
\(171\) −627.302 + 1086.52i −0.280532 + 0.485896i
\(172\) 0 0
\(173\) 420.252 + 727.898i 0.184689 + 0.319890i 0.943472 0.331453i \(-0.107539\pi\)
−0.758783 + 0.651344i \(0.774206\pi\)
\(174\) 0 0
\(175\) 2095.80 985.511i 0.905301 0.425701i
\(176\) 0 0
\(177\) 347.021 + 601.059i 0.147366 + 0.255245i
\(178\) 0 0
\(179\) 802.305 1389.63i 0.335012 0.580258i −0.648475 0.761236i \(-0.724593\pi\)
0.983487 + 0.180978i \(0.0579263\pi\)
\(180\) 0 0
\(181\) −3779.43 −1.55206 −0.776029 0.630697i \(-0.782769\pi\)
−0.776029 + 0.630697i \(0.782769\pi\)
\(182\) 0 0
\(183\) 2516.10 1.01637
\(184\) 0 0
\(185\) 1668.90 2890.62i 0.663243 1.14877i
\(186\) 0 0
\(187\) −849.132 1470.74i −0.332057 0.575140i
\(188\) 0 0
\(189\) 410.535 + 285.496i 0.158000 + 0.109877i
\(190\) 0 0
\(191\) −924.798 1601.80i −0.350346 0.606816i 0.635964 0.771718i \(-0.280603\pi\)
−0.986310 + 0.164902i \(0.947269\pi\)
\(192\) 0 0
\(193\) 176.501 305.709i 0.0658282 0.114018i −0.831233 0.555924i \(-0.812364\pi\)
0.897061 + 0.441907i \(0.145698\pi\)
\(194\) 0 0
\(195\) −2923.65 −1.07368
\(196\) 0 0
\(197\) 4448.22 1.60874 0.804372 0.594125i \(-0.202502\pi\)
0.804372 + 0.594125i \(0.202502\pi\)
\(198\) 0 0
\(199\) −1120.08 + 1940.03i −0.398995 + 0.691080i −0.993602 0.112936i \(-0.963974\pi\)
0.594607 + 0.804017i \(0.297308\pi\)
\(200\) 0 0
\(201\) 936.060 + 1621.30i 0.328481 + 0.568945i
\(202\) 0 0
\(203\) 3.31252 + 2.30360i 0.00114529 + 0.000796458i
\(204\) 0 0
\(205\) −2319.01 4016.64i −0.790080 1.36846i
\(206\) 0 0
\(207\) −36.6516 + 63.4824i −0.0123066 + 0.0213156i
\(208\) 0 0
\(209\) 4216.58 1.39553
\(210\) 0 0
\(211\) −1224.34 −0.399463 −0.199732 0.979851i \(-0.564007\pi\)
−0.199732 + 0.979851i \(0.564007\pi\)
\(212\) 0 0
\(213\) −340.659 + 590.039i −0.109585 + 0.189806i
\(214\) 0 0
\(215\) −3436.08 5951.47i −1.08995 1.88785i
\(216\) 0 0
\(217\) −2959.45 + 1391.63i −0.925810 + 0.435344i
\(218\) 0 0
\(219\) 64.5741 + 111.846i 0.0199247 + 0.0345107i
\(220\) 0 0
\(221\) 1730.10 2996.61i 0.526601 0.912100i
\(222\) 0 0
\(223\) 3457.37 1.03822 0.519108 0.854708i \(-0.326264\pi\)
0.519108 + 0.854708i \(0.326264\pi\)
\(224\) 0 0
\(225\) 1125.44 0.333465
\(226\) 0 0
\(227\) −2589.11 + 4484.47i −0.757027 + 1.31121i 0.187333 + 0.982296i \(0.440016\pi\)
−0.944360 + 0.328913i \(0.893318\pi\)
\(228\) 0 0
\(229\) −1155.94 2002.15i −0.333567 0.577755i 0.649642 0.760241i \(-0.274919\pi\)
−0.983208 + 0.182486i \(0.941586\pi\)
\(230\) 0 0
\(231\) 141.086 1674.67i 0.0401852 0.476991i
\(232\) 0 0
\(233\) −2371.49 4107.54i −0.666787 1.15491i −0.978798 0.204830i \(-0.934336\pi\)
0.312011 0.950078i \(-0.398997\pi\)
\(234\) 0 0
\(235\) −3821.95 + 6619.82i −1.06092 + 1.83757i
\(236\) 0 0
\(237\) −927.181 −0.254122
\(238\) 0 0
\(239\) 1412.59 0.382313 0.191157 0.981560i \(-0.438776\pi\)
0.191157 + 0.981560i \(0.438776\pi\)
\(240\) 0 0
\(241\) 940.577 1629.13i 0.251402 0.435441i −0.712510 0.701662i \(-0.752442\pi\)
0.963912 + 0.266221i \(0.0857750\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −3459.57 + 4177.25i −0.902138 + 1.08929i
\(246\) 0 0
\(247\) 4295.61 + 7440.22i 1.10657 + 1.91664i
\(248\) 0 0
\(249\) −1850.98 + 3206.00i −0.471089 + 0.815951i
\(250\) 0 0
\(251\) −4519.64 −1.13656 −0.568281 0.822834i \(-0.692391\pi\)
−0.568281 + 0.822834i \(0.692391\pi\)
\(252\) 0 0
\(253\) 246.363 0.0612202
\(254\) 0 0
\(255\) −1331.72 + 2306.61i −0.327042 + 0.566453i
\(256\) 0 0
\(257\) −3956.33 6852.56i −0.960268 1.66323i −0.721824 0.692077i \(-0.756696\pi\)
−0.238445 0.971156i \(-0.576638\pi\)
\(258\) 0 0
\(259\) −328.182 + 3895.46i −0.0787344 + 0.934564i
\(260\) 0 0
\(261\) 0.980356 + 1.69803i 0.000232500 + 0.000402702i
\(262\) 0 0
\(263\) −1715.58 + 2971.47i −0.402233 + 0.696688i −0.993995 0.109425i \(-0.965099\pi\)
0.591762 + 0.806113i \(0.298432\pi\)
\(264\) 0 0
\(265\) −324.281 −0.0751714
\(266\) 0 0
\(267\) −3433.07 −0.786894
\(268\) 0 0
\(269\) −4149.60 + 7187.31i −0.940540 + 1.62906i −0.176097 + 0.984373i \(0.556347\pi\)
−0.764443 + 0.644691i \(0.776986\pi\)
\(270\) 0 0
\(271\) −2962.24 5130.75i −0.663998 1.15008i −0.979556 0.201172i \(-0.935525\pi\)
0.315558 0.948906i \(-0.397808\pi\)
\(272\) 0 0
\(273\) 3098.71 1457.11i 0.686968 0.323033i
\(274\) 0 0
\(275\) −1891.24 3275.73i −0.414714 0.718305i
\(276\) 0 0
\(277\) −760.300 + 1316.88i −0.164917 + 0.285645i −0.936626 0.350331i \(-0.886069\pi\)
0.771709 + 0.635976i \(0.219402\pi\)
\(278\) 0 0
\(279\) −1589.22 −0.341019
\(280\) 0 0
\(281\) −352.333 −0.0747986 −0.0373993 0.999300i \(-0.511907\pi\)
−0.0373993 + 0.999300i \(0.511907\pi\)
\(282\) 0 0
\(283\) 2144.24 3713.94i 0.450396 0.780109i −0.548014 0.836469i \(-0.684616\pi\)
0.998411 + 0.0563599i \(0.0179494\pi\)
\(284\) 0 0
\(285\) −3306.50 5727.03i −0.687229 1.19031i
\(286\) 0 0
\(287\) 4459.70 + 3101.38i 0.917239 + 0.637869i
\(288\) 0 0
\(289\) 880.381 + 1524.86i 0.179194 + 0.310373i
\(290\) 0 0
\(291\) 2532.18 4385.87i 0.510100 0.883520i
\(292\) 0 0
\(293\) 2661.99 0.530767 0.265384 0.964143i \(-0.414501\pi\)
0.265384 + 0.964143i \(0.414501\pi\)
\(294\) 0 0
\(295\) −3658.29 −0.722013
\(296\) 0 0
\(297\) 408.347 707.278i 0.0797801 0.138183i
\(298\) 0 0
\(299\) 250.981 + 434.712i 0.0485438 + 0.0840804i
\(300\) 0 0
\(301\) 6607.96 + 4595.33i 1.26537 + 0.879968i
\(302\) 0 0
\(303\) −2231.79 3865.57i −0.423145 0.732909i
\(304\) 0 0
\(305\) −6631.17 + 11485.5i −1.24492 + 2.15626i
\(306\) 0 0
\(307\) −145.970 −0.0271366 −0.0135683 0.999908i \(-0.504319\pi\)
−0.0135683 + 0.999908i \(0.504319\pi\)
\(308\) 0 0
\(309\) −2335.22 −0.429923
\(310\) 0 0
\(311\) 1708.26 2958.79i 0.311467 0.539477i −0.667213 0.744867i \(-0.732513\pi\)
0.978680 + 0.205390i \(0.0658462\pi\)
\(312\) 0 0
\(313\) −1841.18 3189.01i −0.332490 0.575890i 0.650509 0.759498i \(-0.274555\pi\)
−0.982999 + 0.183608i \(0.941222\pi\)
\(314\) 0 0
\(315\) −2385.19 + 1121.59i −0.426637 + 0.200618i
\(316\) 0 0
\(317\) 688.389 + 1192.32i 0.121968 + 0.211254i 0.920544 0.390640i \(-0.127746\pi\)
−0.798576 + 0.601894i \(0.794413\pi\)
\(318\) 0 0
\(319\) 3.29486 5.70686i 0.000578297 0.00100164i
\(320\) 0 0
\(321\) 3906.24 0.679205
\(322\) 0 0
\(323\) 7826.61 1.34825
\(324\) 0 0
\(325\) 3853.38 6674.26i 0.657684 1.13914i
\(326\) 0 0
\(327\) 703.622 + 1218.71i 0.118992 + 0.206100i
\(328\) 0 0
\(329\) 751.570 8921.01i 0.125943 1.49493i
\(330\) 0 0
\(331\) 1087.46 + 1883.54i 0.180581 + 0.312776i 0.942079 0.335392i \(-0.108869\pi\)
−0.761497 + 0.648168i \(0.775535\pi\)
\(332\) 0 0
\(333\) −949.860 + 1645.21i −0.156312 + 0.270741i
\(334\) 0 0
\(335\) −9867.92 −1.60938
\(336\) 0 0
\(337\) −6321.14 −1.02176 −0.510882 0.859651i \(-0.670681\pi\)
−0.510882 + 0.859651i \(0.670681\pi\)
\(338\) 0 0
\(339\) 2480.80 4296.86i 0.397458 0.688418i
\(340\) 0 0
\(341\) 2670.60 + 4625.61i 0.424108 + 0.734577i
\(342\) 0 0
\(343\) 1584.83 6151.58i 0.249483 0.968379i
\(344\) 0 0
\(345\) −193.190 334.615i −0.0301478 0.0522175i
\(346\) 0 0
\(347\) −5812.21 + 10067.0i −0.899181 + 1.55743i −0.0706381 + 0.997502i \(0.522504\pi\)
−0.828543 + 0.559925i \(0.810830\pi\)
\(348\) 0 0
\(349\) −9841.79 −1.50951 −0.754755 0.656007i \(-0.772244\pi\)
−0.754755 + 0.656007i \(0.772244\pi\)
\(350\) 0 0
\(351\) 1664.00 0.253043
\(352\) 0 0
\(353\) −2265.94 + 3924.73i −0.341654 + 0.591762i −0.984740 0.174032i \(-0.944320\pi\)
0.643086 + 0.765794i \(0.277654\pi\)
\(354\) 0 0
\(355\) −1795.61 3110.08i −0.268453 0.464975i
\(356\) 0 0
\(357\) 261.877 3108.44i 0.0388236 0.460829i
\(358\) 0 0
\(359\) −1140.05 1974.63i −0.167603 0.290298i 0.769973 0.638076i \(-0.220269\pi\)
−0.937577 + 0.347779i \(0.886936\pi\)
\(360\) 0 0
\(361\) −6286.75 + 10889.0i −0.916569 + 1.58754i
\(362\) 0 0
\(363\) 1248.19 0.180476
\(364\) 0 0
\(365\) −680.739 −0.0976205
\(366\) 0 0
\(367\) 3168.76 5488.45i 0.450702 0.780639i −0.547728 0.836657i \(-0.684507\pi\)
0.998430 + 0.0560176i \(0.0178403\pi\)
\(368\) 0 0
\(369\) 1319.87 + 2286.08i 0.186205 + 0.322517i
\(370\) 0 0
\(371\) 343.698 161.617i 0.0480968 0.0226166i
\(372\) 0 0
\(373\) 1812.48 + 3139.31i 0.251600 + 0.435783i 0.963966 0.266024i \(-0.0857100\pi\)
−0.712367 + 0.701807i \(0.752377\pi\)
\(374\) 0 0
\(375\) −1.17253 + 2.03088i −0.000161464 + 0.000279664i
\(376\) 0 0
\(377\) 13.4265 0.00183421
\(378\) 0 0
\(379\) −268.622 −0.0364068 −0.0182034 0.999834i \(-0.505795\pi\)
−0.0182034 + 0.999834i \(0.505795\pi\)
\(380\) 0 0
\(381\) −245.640 + 425.461i −0.0330302 + 0.0572100i
\(382\) 0 0
\(383\) −1068.70 1851.03i −0.142579 0.246954i 0.785888 0.618369i \(-0.212206\pi\)
−0.928467 + 0.371415i \(0.878873\pi\)
\(384\) 0 0
\(385\) 7272.69 + 5057.60i 0.962729 + 0.669504i
\(386\) 0 0
\(387\) 1955.66 + 3387.30i 0.256878 + 0.444926i
\(388\) 0 0
\(389\) −731.615 + 1267.19i −0.0953583 + 0.165165i −0.909758 0.415139i \(-0.863733\pi\)
0.814400 + 0.580304i \(0.197066\pi\)
\(390\) 0 0
\(391\) 457.288 0.0591459
\(392\) 0 0
\(393\) −1565.68 −0.200962
\(394\) 0 0
\(395\) 2443.58 4232.40i 0.311265 0.539127i
\(396\) 0 0
\(397\) 618.718 + 1071.65i 0.0782180 + 0.135478i 0.902481 0.430729i \(-0.141744\pi\)
−0.824263 + 0.566207i \(0.808410\pi\)
\(398\) 0 0
\(399\) 6358.76 + 4422.03i 0.797835 + 0.554833i
\(400\) 0 0
\(401\) 3089.94 + 5351.94i 0.384799 + 0.666492i 0.991741 0.128254i \(-0.0409374\pi\)
−0.606942 + 0.794746i \(0.707604\pi\)
\(402\) 0 0
\(403\) −5441.31 + 9424.63i −0.672583 + 1.16495i
\(404\) 0 0
\(405\) −1280.85 −0.157150
\(406\) 0 0
\(407\) 6384.73 0.777591
\(408\) 0 0
\(409\) 1127.49 1952.87i 0.136310 0.236096i −0.789787 0.613381i \(-0.789809\pi\)
0.926097 + 0.377285i \(0.123142\pi\)
\(410\) 0 0
\(411\) 4015.33 + 6954.76i 0.481902 + 0.834679i
\(412\) 0 0
\(413\) 3877.34 1823.24i 0.461964 0.217230i
\(414\) 0 0
\(415\) −9756.50 16898.7i −1.15404 1.99886i
\(416\) 0 0
\(417\) −1280.54 + 2217.96i −0.150379 + 0.260465i
\(418\) 0 0
\(419\) 1404.53 0.163761 0.0818806 0.996642i \(-0.473907\pi\)
0.0818806 + 0.996642i \(0.473907\pi\)
\(420\) 0 0
\(421\) 13068.1 1.51283 0.756414 0.654094i \(-0.226950\pi\)
0.756414 + 0.654094i \(0.226950\pi\)
\(422\) 0 0
\(423\) 2175.28 3767.70i 0.250037 0.433077i
\(424\) 0 0
\(425\) −3510.44 6080.26i −0.400662 0.693966i
\(426\) 0 0
\(427\) 1303.99 15478.1i 0.147786 1.75419i
\(428\) 0 0
\(429\) −2796.26 4843.26i −0.314696 0.545070i
\(430\) 0 0
\(431\) −2681.39 + 4644.31i −0.299671 + 0.519046i −0.976061 0.217499i \(-0.930210\pi\)
0.676390 + 0.736544i \(0.263544\pi\)
\(432\) 0 0
\(433\) −2495.82 −0.277001 −0.138501 0.990362i \(-0.544228\pi\)
−0.138501 + 0.990362i \(0.544228\pi\)
\(434\) 0 0
\(435\) −10.3349 −0.00113913
\(436\) 0 0
\(437\) −567.694 + 983.275i −0.0621430 + 0.107635i
\(438\) 0 0
\(439\) 1881.06 + 3258.09i 0.204506 + 0.354215i 0.949975 0.312325i \(-0.101108\pi\)
−0.745469 + 0.666540i \(0.767775\pi\)
\(440\) 0 0
\(441\) 1969.03 2377.50i 0.212615 0.256722i
\(442\) 0 0
\(443\) 5722.63 + 9911.88i 0.613748 + 1.06304i 0.990603 + 0.136770i \(0.0436721\pi\)
−0.376855 + 0.926272i \(0.622995\pi\)
\(444\) 0 0
\(445\) 9047.83 15671.3i 0.963839 1.66942i
\(446\) 0 0
\(447\) −1673.06 −0.177031
\(448\) 0 0
\(449\) −9420.02 −0.990107 −0.495054 0.868862i \(-0.664852\pi\)
−0.495054 + 0.868862i \(0.664852\pi\)
\(450\) 0 0
\(451\) 4435.93 7683.25i 0.463148 0.802196i
\(452\) 0 0
\(453\) −2654.02 4596.90i −0.275269 0.476780i
\(454\) 0 0
\(455\) −1515.20 + 17985.2i −0.156118 + 1.85310i
\(456\) 0 0
\(457\) −5731.98 9928.08i −0.586719 1.01623i −0.994659 0.103219i \(-0.967086\pi\)
0.407939 0.913009i \(-0.366247\pi\)
\(458\) 0 0
\(459\) 757.955 1312.82i 0.0770769 0.133501i
\(460\) 0 0
\(461\) −9751.10 −0.985149 −0.492575 0.870270i \(-0.663944\pi\)
−0.492575 + 0.870270i \(0.663944\pi\)
\(462\) 0 0
\(463\) −2182.03 −0.219023 −0.109512 0.993986i \(-0.534929\pi\)
−0.109512 + 0.993986i \(0.534929\pi\)
\(464\) 0 0
\(465\) 4188.39 7254.50i 0.417703 0.723483i
\(466\) 0 0
\(467\) 1598.17 + 2768.11i 0.158361 + 0.274289i 0.934278 0.356546i \(-0.116046\pi\)
−0.775917 + 0.630835i \(0.782712\pi\)
\(468\) 0 0
\(469\) 10458.8 4918.04i 1.02973 0.484209i
\(470\) 0 0
\(471\) −3607.34 6248.10i −0.352904 0.611247i
\(472\) 0 0
\(473\) 6572.74 11384.3i 0.638932 1.10666i
\(474\) 0 0
\(475\) 17432.0 1.68386
\(476\) 0 0
\(477\) 184.566 0.0177163
\(478\) 0 0
\(479\) −6071.79 + 10516.7i −0.579180 + 1.00317i 0.416394 + 0.909184i \(0.363294\pi\)
−0.995574 + 0.0939849i \(0.970039\pi\)
\(480\) 0 0
\(481\) 6504.41 + 11266.0i 0.616581 + 1.06795i
\(482\) 0 0
\(483\) 371.525 + 258.367i 0.0350000 + 0.0243398i
\(484\) 0 0
\(485\) 13347.1 + 23117.9i 1.24961 + 2.16439i
\(486\) 0 0
\(487\) −10151.2 + 17582.5i −0.944551 + 1.63601i −0.187905 + 0.982187i \(0.560170\pi\)
−0.756647 + 0.653824i \(0.773164\pi\)
\(488\) 0 0
\(489\) 10136.4 0.937389
\(490\) 0 0
\(491\) −2562.41 −0.235519 −0.117760 0.993042i \(-0.537571\pi\)
−0.117760 + 0.993042i \(0.537571\pi\)
\(492\) 0 0
\(493\) 6.11577 10.5928i 0.000558702 0.000967701i
\(494\) 0 0
\(495\) 2152.39 + 3728.05i 0.195440 + 0.338512i
\(496\) 0 0
\(497\) 3453.15 + 2401.40i 0.311660 + 0.216735i
\(498\) 0 0
\(499\) −5828.05 10094.5i −0.522844 0.905592i −0.999647 0.0265820i \(-0.991538\pi\)
0.476803 0.879010i \(-0.341796\pi\)
\(500\) 0 0
\(501\) 1208.85 2093.79i 0.107799 0.186714i
\(502\) 0 0
\(503\) 18532.8 1.64281 0.821407 0.570342i \(-0.193189\pi\)
0.821407 + 0.570342i \(0.193189\pi\)
\(504\) 0 0
\(505\) 23527.5 2.07318
\(506\) 0 0
\(507\) 2401.85 4160.12i 0.210394 0.364413i
\(508\) 0 0
\(509\) −9366.05 16222.5i −0.815605 1.41267i −0.908893 0.417030i \(-0.863071\pi\)
0.0932881 0.995639i \(-0.470262\pi\)
\(510\) 0 0
\(511\) 721.499 339.271i 0.0624604 0.0293708i
\(512\) 0 0
\(513\) 1881.91 + 3259.56i 0.161965 + 0.280532i
\(514\) 0 0
\(515\) 6154.46 10659.8i 0.526598 0.912094i
\(516\) 0 0
\(517\) −14621.7 −1.24383
\(518\) 0 0
\(519\) 2521.51 0.213260
\(520\) 0 0
\(521\) 1661.63 2878.02i 0.139726 0.242012i −0.787667 0.616101i \(-0.788711\pi\)
0.927393 + 0.374089i \(0.122045\pi\)
\(522\) 0 0
\(523\) −11648.7 20176.2i −0.973925 1.68689i −0.683437 0.730010i \(-0.739516\pi\)
−0.290489 0.956878i \(-0.593818\pi\)
\(524\) 0 0
\(525\) 583.270 6923.32i 0.0484876 0.575540i
\(526\) 0 0
\(527\) 4957.04 + 8585.84i 0.409738 + 0.709687i
\(528\) 0 0
\(529\) 6050.33 10479.5i 0.497274 0.861304i
\(530\) 0 0
\(531\) 2082.13 0.170163
\(532\) 0 0
\(533\) 18076.3 1.46899
\(534\) 0 0
\(535\) −10294.9 + 17831.2i −0.831936 + 1.44095i
\(536\) 0 0
\(537\) −2406.92 4168.90i −0.193419 0.335012i
\(538\) 0 0
\(539\) −10228.8 1735.82i −0.817413 0.138714i
\(540\) 0 0
\(541\) −4525.01 7837.54i −0.359603 0.622851i 0.628292 0.777978i \(-0.283755\pi\)
−0.987894 + 0.155127i \(0.950421\pi\)
\(542\) 0 0
\(543\) −5669.14 + 9819.24i −0.448041 + 0.776029i
\(544\) 0 0
\(545\) −7417.56 −0.582997
\(546\) 0 0
\(547\) 12316.7 0.962749 0.481374 0.876515i \(-0.340138\pi\)
0.481374 + 0.876515i \(0.340138\pi\)
\(548\) 0 0
\(549\) 3774.16 6537.03i 0.293401 0.508185i
\(550\) 0 0
\(551\) 15.1847 + 26.3006i 0.00117403 + 0.00203347i
\(552\) 0 0
\(553\) −480.518 + 5703.67i −0.0369507 + 0.438598i
\(554\) 0 0
\(555\) −5006.70 8671.86i −0.382923 0.663243i
\(556\) 0 0
\(557\) −12452.0 + 21567.6i −0.947236 + 1.64066i −0.196024 + 0.980599i \(0.562803\pi\)
−0.751212 + 0.660061i \(0.770530\pi\)
\(558\) 0 0
\(559\) 26783.8 2.02653
\(560\) 0 0
\(561\) −5094.79 −0.383426
\(562\) 0 0
\(563\) −2073.30 + 3591.06i −0.155203 + 0.268819i −0.933133 0.359532i \(-0.882936\pi\)
0.777930 + 0.628351i \(0.216270\pi\)
\(564\) 0 0
\(565\) 13076.2 + 22648.7i 0.973666 + 1.68644i
\(566\) 0 0
\(567\) 1357.54 638.358i 0.100549 0.0472814i
\(568\) 0 0
\(569\) −3648.74 6319.80i −0.268828 0.465624i 0.699731 0.714406i \(-0.253303\pi\)
−0.968559 + 0.248782i \(0.919970\pi\)
\(570\) 0 0
\(571\) −5782.45 + 10015.5i −0.423797 + 0.734037i −0.996307 0.0858600i \(-0.972636\pi\)
0.572511 + 0.819897i \(0.305970\pi\)
\(572\) 0 0
\(573\) −5548.79 −0.404544
\(574\) 0 0
\(575\) 1018.50 0.0738687
\(576\) 0 0
\(577\) −4736.72 + 8204.25i −0.341755 + 0.591936i −0.984759 0.173926i \(-0.944354\pi\)
0.643004 + 0.765863i \(0.277688\pi\)
\(578\) 0 0
\(579\) −529.504 917.128i −0.0380059 0.0658282i
\(580\) 0 0
\(581\) 18762.8 + 13048.1i 1.33978 + 0.931714i
\(582\) 0 0
\(583\) −310.152 537.198i −0.0220329 0.0381620i
\(584\) 0 0
\(585\) −4385.47 + 7595.86i −0.309943 + 0.536838i
\(586\) 0 0
\(587\) −7336.02 −0.515826 −0.257913 0.966168i \(-0.583035\pi\)
−0.257913 + 0.966168i \(0.583035\pi\)
\(588\) 0 0
\(589\) −24615.4 −1.72200
\(590\) 0 0
\(591\) 6672.33 11556.8i 0.464405 0.804372i
\(592\) 0 0
\(593\) −9040.73 15659.0i −0.626068 1.08438i −0.988333 0.152307i \(-0.951330\pi\)
0.362265 0.932075i \(-0.382004\pi\)
\(594\) 0 0
\(595\) 13499.2 + 9387.68i 0.930109 + 0.646819i
\(596\) 0 0
\(597\) 3360.23 + 5820.08i 0.230360 + 0.398995i
\(598\) 0 0
\(599\) −96.2165 + 166.652i −0.00656310 + 0.0113676i −0.869288 0.494305i \(-0.835422\pi\)
0.862725 + 0.505673i \(0.168756\pi\)
\(600\) 0 0
\(601\) −5055.76 −0.343143 −0.171571 0.985172i \(-0.554884\pi\)
−0.171571 + 0.985172i \(0.554884\pi\)
\(602\) 0 0
\(603\) 5616.36 0.379297
\(604\) 0 0
\(605\) −3289.59 + 5697.74i −0.221059 + 0.382886i
\(606\) 0 0
\(607\) 10117.9 + 17524.7i 0.676560 + 1.17184i 0.976010 + 0.217724i \(0.0698633\pi\)
−0.299451 + 0.954112i \(0.596803\pi\)
\(608\) 0 0
\(609\) 10.9537 5.15077i 0.000728845 0.000342725i
\(610\) 0 0
\(611\) −14895.8 25800.2i −0.986283 1.70829i
\(612\) 0 0
\(613\) 1920.25 3325.98i 0.126523 0.219143i −0.795805 0.605554i \(-0.792952\pi\)
0.922327 + 0.386410i \(0.126285\pi\)
\(614\) 0 0
\(615\) −13914.0 −0.912306
\(616\) 0 0
\(617\) −5720.89 −0.373281 −0.186641 0.982428i \(-0.559760\pi\)
−0.186641 + 0.982428i \(0.559760\pi\)
\(618\) 0 0
\(619\) 11470.1 19866.8i 0.744787 1.29001i −0.205507 0.978656i \(-0.565884\pi\)
0.950294 0.311354i \(-0.100782\pi\)
\(620\) 0 0
\(621\) 109.955 + 190.447i 0.00710521 + 0.0123066i
\(622\) 0 0
\(623\) −1779.22 + 21119.0i −0.114419 + 1.35813i
\(624\) 0 0
\(625\) 7809.41 + 13526.3i 0.499802 + 0.865683i
\(626\) 0 0
\(627\) 6324.86 10955.0i 0.402856 0.697767i
\(628\) 0 0
\(629\) 11851.0 0.751244
\(630\) 0 0
\(631\) −7634.81 −0.481675 −0.240837 0.970565i \(-0.577422\pi\)
−0.240837 + 0.970565i \(0.577422\pi\)
\(632\) 0 0
\(633\) −1836.50 + 3180.92i −0.115315 + 0.199732i
\(634\) 0 0
\(635\) −1294.76 2242.60i −0.0809152 0.140149i
\(636\) 0 0
\(637\) −7357.65 19817.2i −0.457646 1.23263i
\(638\) 0 0
\(639\) 1021.98 + 1770.12i 0.0632688 + 0.109585i
\(640\) 0 0
\(641\) 1389.80 2407.20i 0.0856376 0.148329i −0.820025 0.572328i \(-0.806041\pi\)
0.905663 + 0.423999i \(0.139374\pi\)
\(642\) 0 0
\(643\) −18304.5 −1.12264 −0.561322 0.827598i \(-0.689707\pi\)
−0.561322 + 0.827598i \(0.689707\pi\)
\(644\) 0 0
\(645\) −20616.5 −1.25856
\(646\) 0 0
\(647\) 3276.27 5674.66i 0.199078 0.344813i −0.749152 0.662398i \(-0.769539\pi\)
0.948230 + 0.317585i \(0.102872\pi\)
\(648\) 0 0
\(649\) −3498.89 6060.26i −0.211623 0.366542i
\(650\) 0 0
\(651\) −823.628 + 9776.32i −0.0495861 + 0.588578i
\(652\) 0 0
\(653\) 15993.0 + 27700.8i 0.958432 + 1.66005i 0.726312 + 0.687365i \(0.241233\pi\)
0.232120 + 0.972687i \(0.425434\pi\)
\(654\) 0 0
\(655\) 4126.34 7147.03i 0.246152 0.426348i
\(656\) 0 0
\(657\) 387.445 0.0230071
\(658\) 0 0
\(659\) −517.327 −0.0305799 −0.0152900 0.999883i \(-0.504867\pi\)
−0.0152900 + 0.999883i \(0.504867\pi\)
\(660\) 0 0
\(661\) −9828.40 + 17023.3i −0.578336 + 1.00171i 0.417334 + 0.908753i \(0.362965\pi\)
−0.995670 + 0.0929549i \(0.970369\pi\)
\(662\) 0 0
\(663\) −5190.29 8989.84i −0.304033 0.526601i
\(664\) 0 0
\(665\) −36944.1 + 17372.3i −2.15433 + 1.01303i
\(666\) 0 0
\(667\) 0.887200 + 1.53668i 5.15030e−5 + 8.92059e-5i
\(668\) 0 0
\(669\) 5186.05 8982.50i 0.299707 0.519108i
\(670\) 0 0
\(671\) −25369.0 −1.45955
\(672\) 0 0
\(673\) 25836.1 1.47981 0.739904 0.672713i \(-0.234871\pi\)
0.739904 + 0.672713i \(0.234871\pi\)
\(674\) 0 0
\(675\) 1688.17 2923.99i 0.0962631 0.166733i
\(676\) 0 0
\(677\) −13263.1 22972.4i −0.752944 1.30414i −0.946390 0.323026i \(-0.895300\pi\)
0.193447 0.981111i \(-0.438033\pi\)
\(678\) 0 0
\(679\) −25667.9 17850.1i −1.45073 1.00887i
\(680\) 0 0
\(681\) 7767.33 + 13453.4i 0.437070 + 0.757027i
\(682\) 0 0
\(683\) 16939.4 29339.9i 0.949002 1.64372i 0.201470 0.979495i \(-0.435428\pi\)
0.747532 0.664225i \(-0.231239\pi\)
\(684\) 0 0
\(685\) −42329.5 −2.36106
\(686\) 0 0
\(687\) −6935.65 −0.385170
\(688\) 0 0
\(689\) 631.930 1094.53i 0.0349414 0.0605203i
\(690\) 0 0
\(691\) −500.631 867.119i −0.0275614 0.0477377i 0.851916 0.523679i \(-0.175441\pi\)
−0.879477 + 0.475941i \(0.842108\pi\)
\(692\) 0 0
\(693\) −4139.28 2878.55i −0.226895 0.157788i
\(694\) 0 0
\(695\) −6749.70 11690.8i −0.368389 0.638069i
\(696\) 0 0
\(697\) 8233.76 14261.3i 0.447455 0.775015i
\(698\) 0 0
\(699\) −14228.9 −0.769939
\(700\) 0 0
\(701\) 7713.38 0.415592 0.207796 0.978172i \(-0.433371\pi\)
0.207796 + 0.978172i \(0.433371\pi\)
\(702\) 0 0
\(703\) −14712.3 + 25482.5i −0.789312 + 1.36713i
\(704\) 0 0
\(705\) 11465.9 + 19859.5i 0.612524 + 1.06092i
\(706\) 0 0
\(707\) −24936.2 + 11725.8i −1.32648 + 0.623753i
\(708\) 0 0
\(709\) −5017.56 8690.67i −0.265781 0.460346i 0.701987 0.712190i \(-0.252296\pi\)
−0.967768 + 0.251844i \(0.918963\pi\)
\(710\) 0 0
\(711\) −1390.77 + 2408.89i −0.0733586 + 0.127061i
\(712\) 0 0
\(713\) −1438.21 −0.0755421
\(714\) 0 0
\(715\) 29478.1 1.54184
\(716\) 0 0
\(717\) 2118.89 3670.02i 0.110364 0.191157i
\(718\) 0 0
\(719\) −10059.7 17423.9i −0.521785 0.903758i −0.999679 0.0253401i \(-0.991933\pi\)
0.477894 0.878417i \(-0.341400\pi\)
\(720\) 0 0
\(721\) −1210.25 + 14365.4i −0.0625131 + 0.742020i
\(722\) 0 0
\(723\) −2821.73 4887.38i −0.145147 0.251402i
\(724\) 0 0
\(725\) 13.6214 23.5930i 0.000697776 0.00120858i
\(726\) 0 0
\(727\) 7567.09 0.386035 0.193018 0.981195i \(-0.438173\pi\)
0.193018 + 0.981195i \(0.438173\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 12200.0 21131.0i 0.617283 1.06917i
\(732\) 0 0
\(733\) −15400.0 26673.6i −0.776006 1.34408i −0.934228 0.356678i \(-0.883909\pi\)
0.158222 0.987404i \(-0.449424\pi\)
\(734\) 0 0
\(735\) 5663.47 + 15254.1i 0.284218 + 0.765518i
\(736\) 0 0
\(737\) −9437.96 16347.0i −0.471712 0.817029i
\(738\) 0 0
\(739\) −6659.66 + 11534.9i −0.331501 + 0.574177i −0.982806 0.184639i \(-0.940889\pi\)
0.651305 + 0.758816i \(0.274222\pi\)
\(740\) 0 0
\(741\) 25773.7 1.27776
\(742\) 0 0
\(743\) 10747.7 0.530682 0.265341 0.964155i \(-0.414516\pi\)
0.265341 + 0.964155i \(0.414516\pi\)
\(744\) 0 0
\(745\) 4409.33 7637.18i 0.216839 0.375577i
\(746\) 0 0
\(747\) 5552.95 + 9617.99i 0.271984 + 0.471089i
\(748\) 0 0
\(749\) 2024.44 24029.7i 0.0987601 1.17227i
\(750\) 0 0
\(751\) 6106.70 + 10577.1i 0.296720 + 0.513934i 0.975383 0.220515i \(-0.0707739\pi\)
−0.678664 + 0.734449i \(0.737441\pi\)
\(752\) 0 0
\(753\) −6779.46 + 11742.4i −0.328097 + 0.568281i
\(754\) 0 0
\(755\) 27978.6 1.34867
\(756\) 0 0
\(757\) −30173.2 −1.44870 −0.724349 0.689434i \(-0.757860\pi\)
−0.724349 + 0.689434i \(0.757860\pi\)
\(758\) 0 0
\(759\) 369.545 640.070i 0.0176728 0.0306101i
\(760\) 0 0
\(761\) −7603.67 13169.9i −0.362198 0.627346i 0.626124 0.779723i \(-0.284640\pi\)
−0.988322 + 0.152378i \(0.951307\pi\)
\(762\) 0 0
\(763\) 7861.71 3696.82i 0.373018 0.175405i
\(764\) 0 0
\(765\) 3995.17 + 6919.83i 0.188818 + 0.327042i
\(766\) 0 0
\(767\) 7128.95 12347.7i 0.335608 0.581290i
\(768\) 0 0
\(769\) −9368.65 −0.439327 −0.219663 0.975576i \(-0.570496\pi\)
−0.219663 + 0.975576i \(0.570496\pi\)
\(770\) 0 0
\(771\) −23738.0 −1.10882
\(772\) 0 0
\(773\) −16258.2 + 28159.9i −0.756488 + 1.31028i 0.188143 + 0.982142i \(0.439753\pi\)
−0.944631 + 0.328134i \(0.893580\pi\)
\(774\) 0 0
\(775\) 11040.6 + 19123.0i 0.511731 + 0.886345i
\(776\) 0 0
\(777\) 9628.42 + 6695.83i 0.444553 + 0.309152i
\(778\) 0 0
\(779\) 20443.4 + 35409.0i 0.940258 + 1.62857i
\(780\) 0 0
\(781\) 3434.74 5949.15i 0.157368 0.272570i
\(782\) 0 0
\(783\) 5.88214 0.000268468
\(784\) 0 0
\(785\) 38028.5 1.72904
\(786\) 0 0
\(787\) −20125.1 + 34857.8i −0.911542 + 1.57884i −0.0996552 + 0.995022i \(0.531774\pi\)
−0.811887 + 0.583815i \(0.801559\pi\)
\(788\) 0 0
\(789\) 5146.74 + 8914.42i 0.232229 + 0.402233i
\(790\) 0 0
\(791\) −25147.0 17487.8i −1.13037 0.786087i
\(792\) 0 0
\(793\) −25844.5 44764.0i −1.15733 2.00456i
\(794\) 0 0