Properties

Label 483.3.f.a.22.15
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.15
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.16

$q$-expansion

\(f(q)\) \(=\) \(q-1.65091 q^{2} -1.73205 q^{3} -1.27448 q^{4} +4.21491i q^{5} +2.85947 q^{6} +2.64575i q^{7} +8.70772 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.65091 q^{2} -1.73205 q^{3} -1.27448 q^{4} +4.21491i q^{5} +2.85947 q^{6} +2.64575i q^{7} +8.70772 q^{8} +3.00000 q^{9} -6.95846i q^{10} -4.54772i q^{11} +2.20747 q^{12} +7.59356 q^{13} -4.36791i q^{14} -7.30044i q^{15} -9.27777 q^{16} +3.10823i q^{17} -4.95274 q^{18} -12.4447i q^{19} -5.37182i q^{20} -4.58258i q^{21} +7.50789i q^{22} +(22.5013 - 4.76355i) q^{23} -15.0822 q^{24} +7.23453 q^{25} -12.5363 q^{26} -5.19615 q^{27} -3.37196i q^{28} -6.35643 q^{29} +12.0524i q^{30} -30.1298 q^{31} -19.5141 q^{32} +7.87688i q^{33} -5.13142i q^{34} -11.1516 q^{35} -3.82344 q^{36} +62.2116i q^{37} +20.5452i q^{38} -13.1524 q^{39} +36.7022i q^{40} +58.9776 q^{41} +7.56544i q^{42} +46.9531i q^{43} +5.79598i q^{44} +12.6447i q^{45} +(-37.1477 + 7.86422i) q^{46} +7.95046 q^{47} +16.0696 q^{48} -7.00000 q^{49} -11.9436 q^{50} -5.38361i q^{51} -9.67785 q^{52} -24.5223i q^{53} +8.57840 q^{54} +19.1682 q^{55} +23.0385i q^{56} +21.5549i q^{57} +10.4939 q^{58} -32.6762 q^{59} +9.30427i q^{60} +81.8893i q^{61} +49.7417 q^{62} +7.93725i q^{63} +69.3271 q^{64} +32.0062i q^{65} -13.0041i q^{66} +100.648i q^{67} -3.96138i q^{68} +(-38.9734 + 8.25072i) q^{69} +18.4103 q^{70} -40.6975 q^{71} +26.1232 q^{72} -57.2966 q^{73} -102.706i q^{74} -12.5306 q^{75} +15.8606i q^{76} +12.0321 q^{77} +21.7135 q^{78} +116.054i q^{79} -39.1050i q^{80} +9.00000 q^{81} -97.3670 q^{82} -38.4315i q^{83} +5.84041i q^{84} -13.1009 q^{85} -77.5155i q^{86} +11.0097 q^{87} -39.6002i q^{88} -21.3831i q^{89} -20.8754i q^{90} +20.0907i q^{91} +(-28.6775 + 6.07106i) q^{92} +52.1864 q^{93} -13.1255 q^{94} +52.4534 q^{95} +33.7994 q^{96} +68.3863i q^{97} +11.5564 q^{98} -13.6432i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65091 −0.825457 −0.412729 0.910854i \(-0.635424\pi\)
−0.412729 + 0.910854i \(0.635424\pi\)
\(3\) −1.73205 −0.577350
\(4\) −1.27448 −0.318620
\(5\) 4.21491i 0.842982i 0.906833 + 0.421491i \(0.138493\pi\)
−0.906833 + 0.421491i \(0.861507\pi\)
\(6\) 2.85947 0.476578
\(7\) 2.64575i 0.377964i
\(8\) 8.70772 1.08846
\(9\) 3.00000 0.333333
\(10\) 6.95846i 0.695846i
\(11\) 4.54772i 0.413429i −0.978401 0.206714i \(-0.933723\pi\)
0.978401 0.206714i \(-0.0662771\pi\)
\(12\) 2.20747 0.183956
\(13\) 7.59356 0.584120 0.292060 0.956400i \(-0.405659\pi\)
0.292060 + 0.956400i \(0.405659\pi\)
\(14\) 4.36791i 0.311994i
\(15\) 7.30044i 0.486696i
\(16\) −9.27777 −0.579861
\(17\) 3.10823i 0.182837i 0.995813 + 0.0914186i \(0.0291401\pi\)
−0.995813 + 0.0914186i \(0.970860\pi\)
\(18\) −4.95274 −0.275152
\(19\) 12.4447i 0.654986i −0.944854 0.327493i \(-0.893796\pi\)
0.944854 0.327493i \(-0.106204\pi\)
\(20\) 5.37182i 0.268591i
\(21\) 4.58258i 0.218218i
\(22\) 7.50789i 0.341268i
\(23\) 22.5013 4.76355i 0.978317 0.207111i
\(24\) −15.0822 −0.628425
\(25\) 7.23453 0.289381
\(26\) −12.5363 −0.482166
\(27\) −5.19615 −0.192450
\(28\) 3.37196i 0.120427i
\(29\) −6.35643 −0.219187 −0.109594 0.993976i \(-0.534955\pi\)
−0.109594 + 0.993976i \(0.534955\pi\)
\(30\) 12.0524i 0.401747i
\(31\) −30.1298 −0.971929 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(32\) −19.5141 −0.609815
\(33\) 7.87688i 0.238693i
\(34\) 5.13142i 0.150924i
\(35\) −11.1516 −0.318617
\(36\) −3.82344 −0.106207
\(37\) 62.2116i 1.68140i 0.541505 + 0.840698i \(0.317855\pi\)
−0.541505 + 0.840698i \(0.682145\pi\)
\(38\) 20.5452i 0.540663i
\(39\) −13.1524 −0.337242
\(40\) 36.7022i 0.917556i
\(41\) 58.9776 1.43848 0.719239 0.694762i \(-0.244491\pi\)
0.719239 + 0.694762i \(0.244491\pi\)
\(42\) 7.56544i 0.180130i
\(43\) 46.9531i 1.09193i 0.837807 + 0.545966i \(0.183837\pi\)
−0.837807 + 0.545966i \(0.816163\pi\)
\(44\) 5.79598i 0.131727i
\(45\) 12.6447i 0.280994i
\(46\) −37.1477 + 7.86422i −0.807559 + 0.170961i
\(47\) 7.95046 0.169159 0.0845794 0.996417i \(-0.473045\pi\)
0.0845794 + 0.996417i \(0.473045\pi\)
\(48\) 16.0696 0.334783
\(49\) −7.00000 −0.142857
\(50\) −11.9436 −0.238872
\(51\) 5.38361i 0.105561i
\(52\) −9.67785 −0.186112
\(53\) 24.5223i 0.462684i −0.972872 0.231342i \(-0.925688\pi\)
0.972872 0.231342i \(-0.0743116\pi\)
\(54\) 8.57840 0.158859
\(55\) 19.1682 0.348513
\(56\) 23.0385i 0.411401i
\(57\) 21.5549i 0.378156i
\(58\) 10.4939 0.180930
\(59\) −32.6762 −0.553833 −0.276917 0.960894i \(-0.589313\pi\)
−0.276917 + 0.960894i \(0.589313\pi\)
\(60\) 9.30427i 0.155071i
\(61\) 81.8893i 1.34245i 0.741255 + 0.671224i \(0.234231\pi\)
−0.741255 + 0.671224i \(0.765769\pi\)
\(62\) 49.7417 0.802286
\(63\) 7.93725i 0.125988i
\(64\) 69.3271 1.08324
\(65\) 32.0062i 0.492402i
\(66\) 13.0041i 0.197031i
\(67\) 100.648i 1.50220i 0.660186 + 0.751102i \(0.270478\pi\)
−0.660186 + 0.751102i \(0.729522\pi\)
\(68\) 3.96138i 0.0582556i
\(69\) −38.9734 + 8.25072i −0.564832 + 0.119576i
\(70\) 18.4103 0.263005
\(71\) −40.6975 −0.573205 −0.286602 0.958050i \(-0.592526\pi\)
−0.286602 + 0.958050i \(0.592526\pi\)
\(72\) 26.1232 0.362822
\(73\) −57.2966 −0.784885 −0.392443 0.919777i \(-0.628370\pi\)
−0.392443 + 0.919777i \(0.628370\pi\)
\(74\) 102.706i 1.38792i
\(75\) −12.5306 −0.167074
\(76\) 15.8606i 0.208692i
\(77\) 12.0321 0.156261
\(78\) 21.7135 0.278379
\(79\) 116.054i 1.46904i 0.678587 + 0.734520i \(0.262592\pi\)
−0.678587 + 0.734520i \(0.737408\pi\)
\(80\) 39.1050i 0.488812i
\(81\) 9.00000 0.111111
\(82\) −97.3670 −1.18740
\(83\) 38.4315i 0.463031i −0.972831 0.231515i \(-0.925632\pi\)
0.972831 0.231515i \(-0.0743684\pi\)
\(84\) 5.84041i 0.0695287i
\(85\) −13.1009 −0.154128
\(86\) 77.5155i 0.901343i
\(87\) 11.0097 0.126548
\(88\) 39.6002i 0.450003i
\(89\) 21.3831i 0.240260i −0.992758 0.120130i \(-0.961669\pi\)
0.992758 0.120130i \(-0.0383311\pi\)
\(90\) 20.8754i 0.231949i
\(91\) 20.0907i 0.220777i
\(92\) −28.6775 + 6.07106i −0.311712 + 0.0659898i
\(93\) 52.1864 0.561144
\(94\) −13.1255 −0.139633
\(95\) 52.4534 0.552141
\(96\) 33.7994 0.352077
\(97\) 68.3863i 0.705013i 0.935809 + 0.352507i \(0.114671\pi\)
−0.935809 + 0.352507i \(0.885329\pi\)
\(98\) 11.5564 0.117922
\(99\) 13.6432i 0.137810i
\(100\) −9.22028 −0.0922028
\(101\) −172.128 −1.70423 −0.852117 0.523352i \(-0.824681\pi\)
−0.852117 + 0.523352i \(0.824681\pi\)
\(102\) 8.88789i 0.0871361i
\(103\) 109.279i 1.06096i −0.847697 0.530480i \(-0.822012\pi\)
0.847697 0.530480i \(-0.177988\pi\)
\(104\) 66.1226 0.635794
\(105\) 19.3151 0.183954
\(106\) 40.4841i 0.381926i
\(107\) 128.031i 1.19655i −0.801291 0.598274i \(-0.795853\pi\)
0.801291 0.598274i \(-0.204147\pi\)
\(108\) 6.62240 0.0613185
\(109\) 47.1808i 0.432852i 0.976299 + 0.216426i \(0.0694400\pi\)
−0.976299 + 0.216426i \(0.930560\pi\)
\(110\) −31.6451 −0.287683
\(111\) 107.754i 0.970754i
\(112\) 24.5467i 0.219167i
\(113\) 148.877i 1.31749i 0.752366 + 0.658746i \(0.228913\pi\)
−0.752366 + 0.658746i \(0.771087\pi\)
\(114\) 35.5853i 0.312152i
\(115\) 20.0780 + 94.8410i 0.174591 + 0.824704i
\(116\) 8.10115 0.0698375
\(117\) 22.7807 0.194707
\(118\) 53.9455 0.457166
\(119\) −8.22361 −0.0691059
\(120\) 63.5702i 0.529751i
\(121\) 100.318 0.829077
\(122\) 135.192i 1.10813i
\(123\) −102.152 −0.830506
\(124\) 38.3999 0.309677
\(125\) 135.866i 1.08693i
\(126\) 13.1037i 0.103998i
\(127\) −175.275 −1.38012 −0.690060 0.723752i \(-0.742416\pi\)
−0.690060 + 0.723752i \(0.742416\pi\)
\(128\) −36.3969 −0.284351
\(129\) 81.3251i 0.630427i
\(130\) 52.8394i 0.406457i
\(131\) 67.6253 0.516223 0.258112 0.966115i \(-0.416900\pi\)
0.258112 + 0.966115i \(0.416900\pi\)
\(132\) 10.0389i 0.0760525i
\(133\) 32.9257 0.247561
\(134\) 166.161i 1.24001i
\(135\) 21.9013i 0.162232i
\(136\) 27.0656i 0.199012i
\(137\) 46.4504i 0.339054i 0.985526 + 0.169527i \(0.0542240\pi\)
−0.985526 + 0.169527i \(0.945776\pi\)
\(138\) 64.3417 13.6212i 0.466245 0.0987046i
\(139\) 30.8658 0.222056 0.111028 0.993817i \(-0.464586\pi\)
0.111028 + 0.993817i \(0.464586\pi\)
\(140\) 14.2125 0.101518
\(141\) −13.7706 −0.0976639
\(142\) 67.1881 0.473156
\(143\) 34.5334i 0.241492i
\(144\) −27.8333 −0.193287
\(145\) 26.7918i 0.184771i
\(146\) 94.5918 0.647889
\(147\) 12.1244 0.0824786
\(148\) 79.2876i 0.535727i
\(149\) 31.6314i 0.212291i −0.994351 0.106146i \(-0.966149\pi\)
0.994351 0.106146i \(-0.0338510\pi\)
\(150\) 20.6869 0.137913
\(151\) −83.7183 −0.554426 −0.277213 0.960809i \(-0.589411\pi\)
−0.277213 + 0.960809i \(0.589411\pi\)
\(152\) 108.365i 0.712929i
\(153\) 9.32469i 0.0609457i
\(154\) −19.8640 −0.128987
\(155\) 126.994i 0.819319i
\(156\) 16.7625 0.107452
\(157\) 214.353i 1.36531i −0.730742 0.682654i \(-0.760826\pi\)
0.730742 0.682654i \(-0.239174\pi\)
\(158\) 191.595i 1.21263i
\(159\) 42.4738i 0.267131i
\(160\) 82.2500i 0.514063i
\(161\) 12.6032 + 59.5328i 0.0782806 + 0.369769i
\(162\) −14.8582 −0.0917175
\(163\) 61.9299 0.379938 0.189969 0.981790i \(-0.439161\pi\)
0.189969 + 0.981790i \(0.439161\pi\)
\(164\) −75.1659 −0.458329
\(165\) −33.2003 −0.201214
\(166\) 63.4472i 0.382212i
\(167\) 233.362 1.39738 0.698689 0.715425i \(-0.253767\pi\)
0.698689 + 0.715425i \(0.253767\pi\)
\(168\) 39.9038i 0.237522i
\(169\) −111.338 −0.658804
\(170\) 21.6285 0.127226
\(171\) 37.3342i 0.218329i
\(172\) 59.8408i 0.347912i
\(173\) 25.7071 0.148596 0.0742978 0.997236i \(-0.476328\pi\)
0.0742978 + 0.997236i \(0.476328\pi\)
\(174\) −18.1760 −0.104460
\(175\) 19.1408i 0.109376i
\(176\) 42.1927i 0.239731i
\(177\) 56.5968 0.319756
\(178\) 35.3017i 0.198324i
\(179\) 128.100 0.715642 0.357821 0.933790i \(-0.383520\pi\)
0.357821 + 0.933790i \(0.383520\pi\)
\(180\) 16.1155i 0.0895304i
\(181\) 227.238i 1.25546i 0.778433 + 0.627728i \(0.216015\pi\)
−0.778433 + 0.627728i \(0.783985\pi\)
\(182\) 33.1680i 0.182242i
\(183\) 141.836i 0.775063i
\(184\) 195.935 41.4797i 1.06486 0.225433i
\(185\) −262.216 −1.41739
\(186\) −86.1552 −0.463200
\(187\) 14.1354 0.0755901
\(188\) −10.1327 −0.0538974
\(189\) 13.7477i 0.0727393i
\(190\) −86.5961 −0.455769
\(191\) 81.2083i 0.425174i 0.977142 + 0.212587i \(0.0681889\pi\)
−0.977142 + 0.212587i \(0.931811\pi\)
\(192\) −120.078 −0.625407
\(193\) 6.86510 0.0355705 0.0177852 0.999842i \(-0.494338\pi\)
0.0177852 + 0.999842i \(0.494338\pi\)
\(194\) 112.900i 0.581958i
\(195\) 55.4363i 0.284289i
\(196\) 8.92137 0.0455172
\(197\) 163.498 0.829938 0.414969 0.909836i \(-0.363792\pi\)
0.414969 + 0.909836i \(0.363792\pi\)
\(198\) 22.5237i 0.113756i
\(199\) 129.255i 0.649521i −0.945796 0.324760i \(-0.894716\pi\)
0.945796 0.324760i \(-0.105284\pi\)
\(200\) 62.9963 0.314981
\(201\) 174.327i 0.867298i
\(202\) 284.168 1.40677
\(203\) 16.8175i 0.0828450i
\(204\) 6.86132i 0.0336339i
\(205\) 248.585i 1.21261i
\(206\) 180.410i 0.875778i
\(207\) 67.5039 14.2907i 0.326106 0.0690370i
\(208\) −70.4513 −0.338708
\(209\) −56.5951 −0.270790
\(210\) −31.8876 −0.151846
\(211\) −95.5511 −0.452849 −0.226424 0.974029i \(-0.572704\pi\)
−0.226424 + 0.974029i \(0.572704\pi\)
\(212\) 31.2532i 0.147421i
\(213\) 70.4902 0.330940
\(214\) 211.368i 0.987700i
\(215\) −197.903 −0.920479
\(216\) −45.2466 −0.209475
\(217\) 79.7160i 0.367355i
\(218\) 77.8915i 0.357301i
\(219\) 99.2407 0.453154
\(220\) −24.4295 −0.111043
\(221\) 23.6025i 0.106799i
\(222\) 177.892i 0.801316i
\(223\) −160.057 −0.717744 −0.358872 0.933387i \(-0.616839\pi\)
−0.358872 + 0.933387i \(0.616839\pi\)
\(224\) 51.6294i 0.230488i
\(225\) 21.7036 0.0964605
\(226\) 245.782i 1.08753i
\(227\) 58.2831i 0.256754i 0.991725 + 0.128377i \(0.0409767\pi\)
−0.991725 + 0.128377i \(0.959023\pi\)
\(228\) 27.4713i 0.120488i
\(229\) 94.5361i 0.412821i 0.978465 + 0.206411i \(0.0661783\pi\)
−0.978465 + 0.206411i \(0.933822\pi\)
\(230\) −33.1470 156.574i −0.144117 0.680758i
\(231\) −20.8403 −0.0902176
\(232\) −55.3500 −0.238578
\(233\) 436.615 1.87388 0.936942 0.349485i \(-0.113643\pi\)
0.936942 + 0.349485i \(0.113643\pi\)
\(234\) −37.6089 −0.160722
\(235\) 33.5105i 0.142598i
\(236\) 41.6452 0.176463
\(237\) 201.012i 0.848150i
\(238\) 13.5765 0.0570440
\(239\) 140.417 0.587518 0.293759 0.955879i \(-0.405094\pi\)
0.293759 + 0.955879i \(0.405094\pi\)
\(240\) 67.7318i 0.282216i
\(241\) 210.191i 0.872164i 0.899907 + 0.436082i \(0.143634\pi\)
−0.899907 + 0.436082i \(0.856366\pi\)
\(242\) −165.617 −0.684367
\(243\) −15.5885 −0.0641500
\(244\) 104.366i 0.427731i
\(245\) 29.5044i 0.120426i
\(246\) 168.645 0.685547
\(247\) 94.4998i 0.382590i
\(248\) −262.362 −1.05791
\(249\) 66.5654i 0.267331i
\(250\) 224.303i 0.897210i
\(251\) 495.849i 1.97549i 0.156066 + 0.987747i \(0.450119\pi\)
−0.156066 + 0.987747i \(0.549881\pi\)
\(252\) 10.1159i 0.0401424i
\(253\) −21.6633 102.330i −0.0856257 0.404465i
\(254\) 289.364 1.13923
\(255\) 22.6914 0.0889861
\(256\) −217.220 −0.848517
\(257\) −287.293 −1.11787 −0.558936 0.829211i \(-0.688790\pi\)
−0.558936 + 0.829211i \(0.688790\pi\)
\(258\) 134.261i 0.520391i
\(259\) −164.597 −0.635508
\(260\) 40.7913i 0.156889i
\(261\) −19.0693 −0.0730624
\(262\) −111.644 −0.426120
\(263\) 48.8657i 0.185801i 0.995675 + 0.0929005i \(0.0296139\pi\)
−0.995675 + 0.0929005i \(0.970386\pi\)
\(264\) 68.5896i 0.259809i
\(265\) 103.359 0.390034
\(266\) −54.3574 −0.204351
\(267\) 37.0366i 0.138714i
\(268\) 128.274i 0.478633i
\(269\) −253.706 −0.943147 −0.471573 0.881827i \(-0.656314\pi\)
−0.471573 + 0.881827i \(0.656314\pi\)
\(270\) 36.1572i 0.133916i
\(271\) −299.666 −1.10578 −0.552889 0.833255i \(-0.686475\pi\)
−0.552889 + 0.833255i \(0.686475\pi\)
\(272\) 28.8375i 0.106020i
\(273\) 34.7981i 0.127465i
\(274\) 76.6856i 0.279874i
\(275\) 32.9006i 0.119639i
\(276\) 49.6709 10.5154i 0.179967 0.0380992i
\(277\) 115.620 0.417402 0.208701 0.977980i \(-0.433077\pi\)
0.208701 + 0.977980i \(0.433077\pi\)
\(278\) −50.9568 −0.183298
\(279\) −90.3894 −0.323976
\(280\) −97.1050 −0.346804
\(281\) 497.545i 1.77062i 0.464999 + 0.885311i \(0.346055\pi\)
−0.464999 + 0.885311i \(0.653945\pi\)
\(282\) 22.7341 0.0806173
\(283\) 198.565i 0.701645i 0.936442 + 0.350822i \(0.114098\pi\)
−0.936442 + 0.350822i \(0.885902\pi\)
\(284\) 51.8683 0.182635
\(285\) −90.8520 −0.318779
\(286\) 57.0116i 0.199341i
\(287\) 156.040i 0.543694i
\(288\) −58.5422 −0.203272
\(289\) 279.339 0.966571
\(290\) 44.2309i 0.152520i
\(291\) 118.448i 0.407040i
\(292\) 73.0235 0.250080
\(293\) 72.3189i 0.246822i −0.992356 0.123411i \(-0.960617\pi\)
0.992356 0.123411i \(-0.0393834\pi\)
\(294\) −20.0163 −0.0680826
\(295\) 137.727i 0.466871i
\(296\) 541.721i 1.83014i
\(297\) 23.6306i 0.0795644i
\(298\) 52.2207i 0.175237i
\(299\) 170.865 36.1723i 0.571455 0.120978i
\(300\) 15.9700 0.0532333
\(301\) −124.226 −0.412712
\(302\) 138.212 0.457655
\(303\) 298.134 0.983940
\(304\) 115.459i 0.379800i
\(305\) −345.156 −1.13166
\(306\) 15.3943i 0.0503081i
\(307\) 168.067 0.547451 0.273725 0.961808i \(-0.411744\pi\)
0.273725 + 0.961808i \(0.411744\pi\)
\(308\) −15.3347 −0.0497881
\(309\) 189.277i 0.612546i
\(310\) 209.657i 0.676313i
\(311\) 98.4333 0.316506 0.158253 0.987399i \(-0.449414\pi\)
0.158253 + 0.987399i \(0.449414\pi\)
\(312\) −114.528 −0.367076
\(313\) 449.000i 1.43450i 0.696813 + 0.717252i \(0.254601\pi\)
−0.696813 + 0.717252i \(0.745399\pi\)
\(314\) 353.879i 1.12700i
\(315\) −33.4548 −0.106206
\(316\) 147.909i 0.468066i
\(317\) 64.7677 0.204314 0.102157 0.994768i \(-0.467426\pi\)
0.102157 + 0.994768i \(0.467426\pi\)
\(318\) 70.1206i 0.220505i
\(319\) 28.9072i 0.0906183i
\(320\) 292.208i 0.913149i
\(321\) 221.756i 0.690828i
\(322\) −20.8068 98.2836i −0.0646173 0.305229i
\(323\) 38.6811 0.119756
\(324\) −11.4703 −0.0354023
\(325\) 54.9358 0.169033
\(326\) −102.241 −0.313622
\(327\) 81.7196i 0.249907i
\(328\) 513.560 1.56573
\(329\) 21.0349i 0.0639360i
\(330\) 54.8109 0.166094
\(331\) 579.469 1.75066 0.875331 0.483524i \(-0.160643\pi\)
0.875331 + 0.483524i \(0.160643\pi\)
\(332\) 48.9803i 0.147531i
\(333\) 186.635i 0.560465i
\(334\) −385.261 −1.15348
\(335\) −424.221 −1.26633
\(336\) 42.5161i 0.126536i
\(337\) 60.8832i 0.180662i 0.995912 + 0.0903312i \(0.0287926\pi\)
−0.995912 + 0.0903312i \(0.971207\pi\)
\(338\) 183.809 0.543815
\(339\) 257.862i 0.760654i
\(340\) 16.6969 0.0491084
\(341\) 137.022i 0.401824i
\(342\) 61.6356i 0.180221i
\(343\) 18.5203i 0.0539949i
\(344\) 408.854i 1.18853i
\(345\) −34.7760 164.269i −0.100800 0.476143i
\(346\) −42.4401 −0.122659
\(347\) −88.2666 −0.254371 −0.127185 0.991879i \(-0.540594\pi\)
−0.127185 + 0.991879i \(0.540594\pi\)
\(348\) −14.0316 −0.0403207
\(349\) −18.0521 −0.0517253 −0.0258627 0.999666i \(-0.508233\pi\)
−0.0258627 + 0.999666i \(0.508233\pi\)
\(350\) 31.5998i 0.0902851i
\(351\) −39.4573 −0.112414
\(352\) 88.7445i 0.252115i
\(353\) −236.133 −0.668932 −0.334466 0.942408i \(-0.608556\pi\)
−0.334466 + 0.942408i \(0.608556\pi\)
\(354\) −93.4364 −0.263945
\(355\) 171.536i 0.483201i
\(356\) 27.2524i 0.0765516i
\(357\) 14.2437 0.0398983
\(358\) −211.482 −0.590732
\(359\) 56.2854i 0.156784i −0.996923 0.0783919i \(-0.975021\pi\)
0.996923 0.0783919i \(-0.0249785\pi\)
\(360\) 110.107i 0.305852i
\(361\) 206.129 0.570994
\(362\) 375.150i 1.03633i
\(363\) −173.756 −0.478668
\(364\) 25.6052i 0.0703439i
\(365\) 241.500i 0.661644i
\(366\) 234.160i 0.639781i
\(367\) 360.108i 0.981222i −0.871379 0.490611i \(-0.836774\pi\)
0.871379 0.490611i \(-0.163226\pi\)
\(368\) −208.762 + 44.1952i −0.567288 + 0.120096i
\(369\) 176.933 0.479493
\(370\) 432.897 1.16999
\(371\) 64.8798 0.174878
\(372\) −66.5106 −0.178792
\(373\) 61.6038i 0.165158i 0.996585 + 0.0825788i \(0.0263156\pi\)
−0.996585 + 0.0825788i \(0.973684\pi\)
\(374\) −23.3363 −0.0623964
\(375\) 235.326i 0.627537i
\(376\) 69.2304 0.184123
\(377\) −48.2679 −0.128032
\(378\) 22.6963i 0.0600432i
\(379\) 92.1888i 0.243242i −0.992577 0.121621i \(-0.961191\pi\)
0.992577 0.121621i \(-0.0388093\pi\)
\(380\) −66.8509 −0.175923
\(381\) 303.586 0.796813
\(382\) 134.068i 0.350963i
\(383\) 283.695i 0.740719i −0.928888 0.370360i \(-0.879234\pi\)
0.928888 0.370360i \(-0.120766\pi\)
\(384\) 63.0413 0.164170
\(385\) 50.7143i 0.131726i
\(386\) −11.3337 −0.0293619
\(387\) 140.859i 0.363977i
\(388\) 87.1570i 0.224632i
\(389\) 465.693i 1.19715i 0.801065 + 0.598577i \(0.204267\pi\)
−0.801065 + 0.598577i \(0.795733\pi\)
\(390\) 91.5206i 0.234668i
\(391\) 14.8062 + 69.9392i 0.0378676 + 0.178873i
\(392\) −60.9540 −0.155495
\(393\) −117.130 −0.298042
\(394\) −269.921 −0.685078
\(395\) −489.158 −1.23837
\(396\) 17.3879i 0.0439090i
\(397\) −478.271 −1.20471 −0.602356 0.798228i \(-0.705771\pi\)
−0.602356 + 0.798228i \(0.705771\pi\)
\(398\) 213.388i 0.536152i
\(399\) −57.0289 −0.142930
\(400\) −67.1203 −0.167801
\(401\) 88.2014i 0.219954i 0.993934 + 0.109977i \(0.0350776\pi\)
−0.993934 + 0.109977i \(0.964922\pi\)
\(402\) 287.799i 0.715918i
\(403\) −228.792 −0.567723
\(404\) 219.373 0.543003
\(405\) 37.9342i 0.0936647i
\(406\) 27.7643i 0.0683850i
\(407\) 282.921 0.695137
\(408\) 46.8790i 0.114899i
\(409\) 380.561 0.930467 0.465233 0.885188i \(-0.345970\pi\)
0.465233 + 0.885188i \(0.345970\pi\)
\(410\) 410.393i 1.00096i
\(411\) 80.4544i 0.195753i
\(412\) 139.274i 0.338044i
\(413\) 86.4530i 0.209329i
\(414\) −111.443 + 23.5927i −0.269186 + 0.0569871i
\(415\) 161.986 0.390327
\(416\) −148.181 −0.356205
\(417\) −53.4611 −0.128204
\(418\) 93.4337 0.223526
\(419\) 751.317i 1.79312i −0.442923 0.896560i \(-0.646058\pi\)
0.442923 0.896560i \(-0.353942\pi\)
\(420\) −24.6168 −0.0586114
\(421\) 734.354i 1.74431i 0.489231 + 0.872154i \(0.337278\pi\)
−0.489231 + 0.872154i \(0.662722\pi\)
\(422\) 157.747 0.373807
\(423\) 23.8514 0.0563863
\(424\) 213.533i 0.503615i
\(425\) 22.4866i 0.0529097i
\(426\) −116.373 −0.273177
\(427\) −216.659 −0.507398
\(428\) 163.173i 0.381245i
\(429\) 59.8135i 0.139425i
\(430\) 326.721 0.759816
\(431\) 291.967i 0.677417i −0.940891 0.338708i \(-0.890010\pi\)
0.940891 0.338708i \(-0.109990\pi\)
\(432\) 48.2087 0.111594
\(433\) 599.769i 1.38515i −0.721347 0.692573i \(-0.756477\pi\)
0.721347 0.692573i \(-0.243523\pi\)
\(434\) 131.604i 0.303236i
\(435\) 46.4047i 0.106678i
\(436\) 60.1311i 0.137915i
\(437\) −59.2811 280.023i −0.135655 0.640784i
\(438\) −163.838 −0.374059
\(439\) 43.1472 0.0982853 0.0491426 0.998792i \(-0.484351\pi\)
0.0491426 + 0.998792i \(0.484351\pi\)
\(440\) 166.911 0.379344
\(441\) −21.0000 −0.0476190
\(442\) 38.9658i 0.0881578i
\(443\) 159.701 0.360498 0.180249 0.983621i \(-0.442310\pi\)
0.180249 + 0.983621i \(0.442310\pi\)
\(444\) 137.330i 0.309302i
\(445\) 90.1279 0.202535
\(446\) 264.240 0.592467
\(447\) 54.7872i 0.122566i
\(448\) 183.422i 0.409425i
\(449\) 551.417 1.22810 0.614050 0.789267i \(-0.289539\pi\)
0.614050 + 0.789267i \(0.289539\pi\)
\(450\) −35.8308 −0.0796240
\(451\) 268.214i 0.594709i
\(452\) 189.740i 0.419780i
\(453\) 145.004 0.320098
\(454\) 96.2205i 0.211939i
\(455\) −84.6803 −0.186111
\(456\) 187.694i 0.411610i
\(457\) 447.366i 0.978918i −0.872026 0.489459i \(-0.837194\pi\)
0.872026 0.489459i \(-0.162806\pi\)
\(458\) 156.071i 0.340766i
\(459\) 16.1508i 0.0351870i
\(460\) −25.5890 120.873i −0.0556282 0.262768i
\(461\) −548.620 −1.19006 −0.595032 0.803702i \(-0.702861\pi\)
−0.595032 + 0.803702i \(0.702861\pi\)
\(462\) 34.4055 0.0744708
\(463\) −34.7666 −0.0750899 −0.0375450 0.999295i \(-0.511954\pi\)
−0.0375450 + 0.999295i \(0.511954\pi\)
\(464\) 58.9735 0.127098
\(465\) 219.961i 0.473034i
\(466\) −720.814 −1.54681
\(467\) 12.5545i 0.0268833i −0.999910 0.0134416i \(-0.995721\pi\)
0.999910 0.0134416i \(-0.00427874\pi\)
\(468\) −29.0335 −0.0620375
\(469\) −266.289 −0.567780
\(470\) 55.3229i 0.117708i
\(471\) 371.271i 0.788261i
\(472\) −284.535 −0.602828
\(473\) 213.529 0.451436
\(474\) 331.853i 0.700112i
\(475\) 90.0318i 0.189541i
\(476\) 10.4808 0.0220186
\(477\) 73.5668i 0.154228i
\(478\) −231.816 −0.484971
\(479\) 404.310i 0.844071i −0.906579 0.422036i \(-0.861316\pi\)
0.906579 0.422036i \(-0.138684\pi\)
\(480\) 142.461i 0.296794i
\(481\) 472.408i 0.982136i
\(482\) 347.008i 0.719934i
\(483\) −21.8293 103.114i −0.0451953 0.213486i
\(484\) −127.854 −0.264161
\(485\) −288.242 −0.594313
\(486\) 25.7352 0.0529531
\(487\) 694.784 1.42666 0.713331 0.700827i \(-0.247186\pi\)
0.713331 + 0.700827i \(0.247186\pi\)
\(488\) 713.069i 1.46121i
\(489\) −107.266 −0.219357
\(490\) 48.7092i 0.0994065i
\(491\) 646.833 1.31738 0.658689 0.752415i \(-0.271111\pi\)
0.658689 + 0.752415i \(0.271111\pi\)
\(492\) 130.191 0.264616
\(493\) 19.7573i 0.0400756i
\(494\) 156.011i 0.315812i
\(495\) 57.5047 0.116171
\(496\) 279.537 0.563584
\(497\) 107.676i 0.216651i
\(498\) 109.894i 0.220670i
\(499\) −909.018 −1.82168 −0.910839 0.412761i \(-0.864565\pi\)
−0.910839 + 0.412761i \(0.864565\pi\)
\(500\) 173.158i 0.346317i
\(501\) −404.195 −0.806777
\(502\) 818.604i 1.63069i
\(503\) 589.607i 1.17218i −0.810246 0.586090i \(-0.800666\pi\)
0.810246 0.586090i \(-0.199334\pi\)
\(504\) 69.1154i 0.137134i
\(505\) 725.502i 1.43664i
\(506\) 35.7643 + 168.937i 0.0706804 + 0.333868i
\(507\) 192.843 0.380361
\(508\) 223.385 0.439734
\(509\) −703.954 −1.38301 −0.691507 0.722370i \(-0.743053\pi\)
−0.691507 + 0.722370i \(0.743053\pi\)
\(510\) −37.4616 −0.0734542
\(511\) 151.593i 0.296659i
\(512\) 504.200 0.984765
\(513\) 64.6647i 0.126052i
\(514\) 474.296 0.922755
\(515\) 460.601 0.894371
\(516\) 103.647i 0.200867i
\(517\) 36.1565i 0.0699351i
\(518\) 271.735 0.524584
\(519\) −44.5259 −0.0857918
\(520\) 278.701i 0.535963i
\(521\) 201.467i 0.386694i 0.981130 + 0.193347i \(0.0619343\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(522\) 31.4818 0.0603099
\(523\) 875.330i 1.67367i −0.547455 0.836835i \(-0.684403\pi\)
0.547455 0.836835i \(-0.315597\pi\)
\(524\) −86.1872 −0.164479
\(525\) 33.1528i 0.0631482i
\(526\) 80.6730i 0.153371i
\(527\) 93.6504i 0.177705i
\(528\) 73.0799i 0.138409i
\(529\) 483.617 214.372i 0.914210 0.405241i
\(530\) −170.637 −0.321957
\(531\) −98.0285 −0.184611
\(532\) −41.9631 −0.0788781
\(533\) 447.850 0.840244
\(534\) 61.1443i 0.114502i
\(535\) 539.638 1.00867
\(536\) 876.412i 1.63510i
\(537\) −221.876 −0.413176
\(538\) 418.848 0.778527
\(539\) 31.8340i 0.0590613i
\(540\) 27.9128i 0.0516904i
\(541\) −276.743 −0.511539 −0.255770 0.966738i \(-0.582329\pi\)
−0.255770 + 0.966738i \(0.582329\pi\)
\(542\) 494.723 0.912772
\(543\) 393.587i 0.724838i
\(544\) 60.6542i 0.111497i
\(545\) −198.863 −0.364886
\(546\) 57.4486i 0.105217i
\(547\) 381.964 0.698289 0.349145 0.937069i \(-0.386472\pi\)
0.349145 + 0.937069i \(0.386472\pi\)
\(548\) 59.2001i 0.108029i
\(549\) 245.668i 0.447483i
\(550\) 54.3161i 0.0987566i
\(551\) 79.1040i 0.143565i
\(552\) −339.369 + 71.8449i −0.614800 + 0.130154i
\(553\) −307.050 −0.555245
\(554\) −190.879 −0.344547
\(555\) 454.172 0.818328
\(556\) −39.3379 −0.0707516
\(557\) 627.049i 1.12576i −0.826538 0.562880i \(-0.809693\pi\)
0.826538 0.562880i \(-0.190307\pi\)
\(558\) 149.225 0.267429
\(559\) 356.541i 0.637819i
\(560\) 103.462 0.184754
\(561\) −24.4832 −0.0436420
\(562\) 821.404i 1.46157i
\(563\) 6.12085i 0.0108718i 0.999985 + 0.00543592i \(0.00173032\pi\)
−0.999985 + 0.00543592i \(0.998270\pi\)
\(564\) 17.5504 0.0311177
\(565\) −627.501 −1.11062
\(566\) 327.815i 0.579178i
\(567\) 23.8118i 0.0419961i
\(568\) −354.383 −0.623913
\(569\) 933.547i 1.64068i −0.571876 0.820340i \(-0.693784\pi\)
0.571876 0.820340i \(-0.306216\pi\)
\(570\) 149.989 0.263138
\(571\) 123.163i 0.215698i −0.994167 0.107849i \(-0.965604\pi\)
0.994167 0.107849i \(-0.0343963\pi\)
\(572\) 44.0121i 0.0769443i
\(573\) 140.657i 0.245474i
\(574\) 257.609i 0.448796i
\(575\) 162.786 34.4621i 0.283107 0.0599341i
\(576\) 207.981 0.361079
\(577\) 686.069 1.18903 0.594514 0.804086i \(-0.297345\pi\)
0.594514 + 0.804086i \(0.297345\pi\)
\(578\) −461.165 −0.797863
\(579\) −11.8907 −0.0205366
\(580\) 34.1456i 0.0588718i
\(581\) 101.680 0.175009
\(582\) 195.548i 0.335994i
\(583\) −111.520 −0.191287
\(584\) −498.923 −0.854320
\(585\) 96.0185i 0.164134i
\(586\) 119.392i 0.203741i
\(587\) 424.082 0.722457 0.361228 0.932477i \(-0.382358\pi\)
0.361228 + 0.932477i \(0.382358\pi\)
\(588\) −15.4523 −0.0262794
\(589\) 374.957i 0.636600i
\(590\) 227.376i 0.385382i
\(591\) −283.186 −0.479165
\(592\) 577.185i 0.974975i
\(593\) 105.687 0.178224 0.0891118 0.996022i \(-0.471597\pi\)
0.0891118 + 0.996022i \(0.471597\pi\)
\(594\) 39.0122i 0.0656770i
\(595\) 34.6618i 0.0582551i
\(596\) 40.3136i 0.0676403i
\(597\) 223.876i 0.375001i
\(598\) −282.083 + 59.7174i −0.471711 + 0.0998619i
\(599\) 475.544 0.793897 0.396949 0.917841i \(-0.370069\pi\)
0.396949 + 0.917841i \(0.370069\pi\)
\(600\) −109.113 −0.181855
\(601\) 271.584 0.451887 0.225944 0.974140i \(-0.427453\pi\)
0.225944 + 0.974140i \(0.427453\pi\)
\(602\) 205.087 0.340676
\(603\) 301.943i 0.500735i
\(604\) 106.697 0.176651
\(605\) 422.832i 0.698897i
\(606\) −492.193 −0.812200
\(607\) −371.399 −0.611861 −0.305930 0.952054i \(-0.598967\pi\)
−0.305930 + 0.952054i \(0.598967\pi\)
\(608\) 242.847i 0.399420i
\(609\) 29.1288i 0.0478306i
\(610\) 569.823 0.934136
\(611\) 60.3723 0.0988090
\(612\) 11.8841i 0.0194185i
\(613\) 424.357i 0.692263i −0.938186 0.346131i \(-0.887495\pi\)
0.938186 0.346131i \(-0.112505\pi\)
\(614\) −277.465 −0.451897
\(615\) 430.562i 0.700102i
\(616\) 104.772 0.170085
\(617\) 721.025i 1.16860i −0.811539 0.584299i \(-0.801370\pi\)
0.811539 0.584299i \(-0.198630\pi\)
\(618\) 312.480i 0.505631i
\(619\) 1121.60i 1.81195i 0.423326 + 0.905977i \(0.360863\pi\)
−0.423326 + 0.905977i \(0.639137\pi\)
\(620\) 161.852i 0.261052i
\(621\) −116.920 + 24.7522i −0.188277 + 0.0398585i
\(622\) −162.505 −0.261262
\(623\) 56.5744 0.0908096
\(624\) 122.025 0.195553
\(625\) −391.798 −0.626877
\(626\) 741.261i 1.18412i
\(627\) 98.0256 0.156341
\(628\) 273.189i 0.435015i
\(629\) −193.368 −0.307421
\(630\) 55.2310 0.0876683
\(631\) 557.475i 0.883478i −0.897144 0.441739i \(-0.854362\pi\)
0.897144 0.441739i \(-0.145638\pi\)
\(632\) 1010.57i 1.59900i
\(633\) 165.499 0.261452
\(634\) −106.926 −0.168653
\(635\) 738.769i 1.16342i
\(636\) 54.1321i 0.0851133i
\(637\) −53.1549 −0.0834457
\(638\) 47.7234i 0.0748016i
\(639\) −122.093 −0.191068
\(640\) 153.410i 0.239703i
\(641\) 984.048i 1.53518i 0.640944 + 0.767588i \(0.278543\pi\)
−0.640944 + 0.767588i \(0.721457\pi\)
\(642\) 366.100i 0.570249i
\(643\) 514.028i 0.799422i 0.916641 + 0.399711i \(0.130889\pi\)
−0.916641 + 0.399711i \(0.869111\pi\)
\(644\) −16.0625 75.8735i −0.0249418 0.117816i
\(645\) 342.778 0.531439
\(646\) −63.8592 −0.0988532
\(647\) −590.304 −0.912371 −0.456186 0.889885i \(-0.650785\pi\)
−0.456186 + 0.889885i \(0.650785\pi\)
\(648\) 78.3695 0.120941
\(649\) 148.602i 0.228971i
\(650\) −90.6944 −0.139530
\(651\) 138.072i 0.212092i
\(652\) −78.9285 −0.121056
\(653\) −133.633 −0.204644 −0.102322 0.994751i \(-0.532627\pi\)
−0.102322 + 0.994751i \(0.532627\pi\)
\(654\) 134.912i 0.206288i
\(655\) 285.034i 0.435167i
\(656\) −547.181 −0.834117
\(657\) −171.890 −0.261628
\(658\) 34.7269i 0.0527764i
\(659\) 219.218i 0.332652i 0.986071 + 0.166326i \(0.0531904\pi\)
−0.986071 + 0.166326i \(0.946810\pi\)
\(660\) 42.3132 0.0641109
\(661\) 55.5775i 0.0840809i −0.999116 0.0420405i \(-0.986614\pi\)
0.999116 0.0420405i \(-0.0133858\pi\)
\(662\) −956.654 −1.44510
\(663\) 40.8808i 0.0616603i
\(664\) 334.651i 0.503993i
\(665\) 138.779i 0.208690i
\(666\) 308.118i 0.462640i
\(667\) −143.028 + 30.2792i −0.214435 + 0.0453961i
\(668\) −297.416 −0.445233
\(669\) 277.227 0.414390
\(670\) 700.353 1.04530
\(671\) 372.409 0.555007
\(672\) 89.4247i 0.133072i
\(673\) −163.832 −0.243435 −0.121718 0.992565i \(-0.538840\pi\)
−0.121718 + 0.992565i \(0.538840\pi\)
\(674\) 100.513i 0.149129i
\(675\) −37.5917 −0.0556915
\(676\) 141.898 0.209908
\(677\) 1154.10i 1.70473i 0.522949 + 0.852364i \(0.324832\pi\)
−0.522949 + 0.852364i \(0.675168\pi\)
\(678\) 425.708i 0.627887i
\(679\) −180.933 −0.266470
\(680\) −114.079 −0.167763
\(681\) 100.949i 0.148237i
\(682\) 226.211i 0.331688i
\(683\) 791.579 1.15897 0.579487 0.814982i \(-0.303253\pi\)
0.579487 + 0.814982i \(0.303253\pi\)
\(684\) 47.5817i 0.0695639i
\(685\) −195.784 −0.285816
\(686\) 30.5754i 0.0445705i
\(687\) 163.741i 0.238342i
\(688\) 435.620i 0.633168i
\(689\) 186.211i 0.270263i
\(690\) 57.4123 + 271.195i 0.0832062 + 0.393036i
\(691\) −637.514 −0.922597 −0.461298 0.887245i \(-0.652616\pi\)
−0.461298 + 0.887245i \(0.652616\pi\)
\(692\) −32.7632 −0.0473456
\(693\) 36.0964 0.0520871
\(694\) 145.721 0.209972
\(695\) 130.096i 0.187189i
\(696\) 95.8690 0.137743
\(697\) 183.316i 0.263007i
\(698\) 29.8025 0.0426971
\(699\) −756.239 −1.08189
\(700\) 24.3946i 0.0348494i
\(701\) 1124.94i 1.60476i 0.596811 + 0.802382i \(0.296434\pi\)
−0.596811 + 0.802382i \(0.703566\pi\)
\(702\) 65.1406 0.0927929
\(703\) 774.207 1.10129
\(704\) 315.280i 0.447841i
\(705\) 58.0419i 0.0823289i
\(706\) 389.835 0.552174
\(707\) 455.407i 0.644140i
\(708\) −72.1315 −0.101881
\(709\) 313.320i 0.441918i 0.975283 + 0.220959i \(0.0709187\pi\)
−0.975283 + 0.220959i \(0.929081\pi\)
\(710\) 283.192i 0.398862i
\(711\) 348.162i 0.489680i
\(712\) 186.198i 0.261514i
\(713\) −677.960 + 143.525i −0.950855 + 0.201297i
\(714\) −23.5151 −0.0329344
\(715\) 145.555 0.203573
\(716\) −163.261 −0.228018
\(717\) −243.209 −0.339204
\(718\) 92.9224i 0.129418i
\(719\) −739.371 −1.02833 −0.514166 0.857691i \(-0.671899\pi\)
−0.514166 + 0.857691i \(0.671899\pi\)
\(720\) 117.315i 0.162937i
\(721\) 289.125 0.401006
\(722\) −340.301 −0.471331
\(723\) 364.062i 0.503544i
\(724\) 289.610i 0.400014i
\(725\) −45.9858 −0.0634287
\(726\) 286.857 0.395120
\(727\) 314.072i 0.432010i 0.976392 + 0.216005i \(0.0693028\pi\)
−0.976392 + 0.216005i \(0.930697\pi\)
\(728\) 174.944i 0.240307i
\(729\) 27.0000 0.0370370
\(730\) 398.696i 0.546159i
\(731\) −145.941 −0.199646
\(732\) 180.768i 0.246951i
\(733\) 1294.12i 1.76552i −0.469828 0.882758i \(-0.655684\pi\)
0.469828 0.882758i \(-0.344316\pi\)
\(734\) 594.508i 0.809956i
\(735\) 51.1031i 0.0695280i
\(736\) −439.092 + 92.9563i −0.596592 + 0.126299i
\(737\) 457.717 0.621055
\(738\) −292.101 −0.395801
\(739\) 816.696 1.10514 0.552568 0.833468i \(-0.313648\pi\)
0.552568 + 0.833468i \(0.313648\pi\)
\(740\) 334.190 0.451608
\(741\) 163.678i 0.220889i
\(742\) −107.111 −0.144354
\(743\) 983.833i 1.32414i −0.749444 0.662068i \(-0.769679\pi\)
0.749444 0.662068i \(-0.230321\pi\)
\(744\) 454.424 0.610785
\(745\) 133.323 0.178958
\(746\) 101.703i 0.136331i
\(747\) 115.295i 0.154344i
\(748\) −18.0153 −0.0240846
\(749\) 338.737 0.452253
\(750\) 388.503i 0.518005i
\(751\) 209.234i 0.278608i 0.990250 + 0.139304i \(0.0444864\pi\)
−0.990250 + 0.139304i \(0.955514\pi\)
\(752\) −73.7626 −0.0980885
\(753\) 858.835i 1.14055i
\(754\) 79.6862 0.105685
\(755\) 352.865i 0.467371i
\(756\) 17.5212i 0.0231762i
\(757\) 780.239i 1.03070i 0.856980 + 0.515349i \(0.172338\pi\)
−0.856980 + 0.515349i \(0.827662\pi\)
\(758\) 152.196i 0.200786i
\(759\) 37.5219 + 177.240i 0.0494360 + 0.233518i
\(760\) 456.750 0.600986
\(761\) 79.2597 0.104152 0.0520760 0.998643i \(-0.483416\pi\)
0.0520760 + 0.998643i \(0.483416\pi\)
\(762\) −501.194 −0.657735
\(763\) −124.829 −0.163603
\(764\) 103.498i 0.135469i
\(765\) −39.3027 −0.0513761
\(766\) 468.357i 0.611432i
\(767\) −248.128 −0.323505
\(768\) 376.237 0.489892
\(769\) 648.022i 0.842681i 0.906902 + 0.421341i \(0.138440\pi\)
−0.906902 + 0.421341i \(0.861560\pi\)
\(770\) 83.7250i 0.108734i
\(771\) 497.606 0.645403
\(772\) −8.74944 −0.0113335
\(773\) 485.666i 0.628287i −0.949376 0.314143i \(-0.898283\pi\)
0.949376 0.314143i \(-0.101717\pi\)
\(774\) 232.547i 0.300448i
\(775\) −217.975 −0.281258
\(776\) 595.488i 0.767382i
\(777\) 285.090 0.366911
\(778\) 768.820i 0.988200i
\(779\) 733.961i 0.942183i
\(780\) 70.6525i 0.0905802i
\(781\) 185.081i 0.236979i
\(782\) −24.4438 115.464i −0.0312581 0.147652i
\(783\) 33.0290 0.0421826
\(784\) 64.9444 0.0828372
\(785\) 903.480 1.15093
\(786\) 193.372 0.246021
\(787\) 328.821i 0.417816i −0.977935 0.208908i \(-0.933009\pi\)
0.977935 0.208908i \(-0.0669910\pi\)
\(788\) −208.375 −0.264435
\(789\) 84.6378i 0.107272i
\(790\) 807.557 1.02222
\(791\) −393.890 −0.497965