Properties

Label 483.3.f.a.22.17
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 22.17
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.18

$q$-expansion

\(f(q)\) \(=\) \(q-0.984102 q^{2} +1.73205 q^{3} -3.03154 q^{4} -2.95865i q^{5} -1.70451 q^{6} +2.64575i q^{7} +6.91976 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-0.984102 q^{2} +1.73205 q^{3} -3.03154 q^{4} -2.95865i q^{5} -1.70451 q^{6} +2.64575i q^{7} +6.91976 q^{8} +3.00000 q^{9} +2.91162i q^{10} +1.64161i q^{11} -5.25079 q^{12} -20.6451 q^{13} -2.60369i q^{14} -5.12454i q^{15} +5.31643 q^{16} +1.80914i q^{17} -2.95231 q^{18} -30.5833i q^{19} +8.96928i q^{20} +4.58258i q^{21} -1.61551i q^{22} +(-4.61202 + 22.5328i) q^{23} +11.9854 q^{24} +16.2464 q^{25} +20.3169 q^{26} +5.19615 q^{27} -8.02071i q^{28} -23.0792 q^{29} +5.04307i q^{30} -46.3849 q^{31} -32.9109 q^{32} +2.84335i q^{33} -1.78038i q^{34} +7.82786 q^{35} -9.09463 q^{36} +61.7024i q^{37} +30.0971i q^{38} -35.7583 q^{39} -20.4732i q^{40} -46.0087 q^{41} -4.50972i q^{42} +47.1312i q^{43} -4.97660i q^{44} -8.87596i q^{45} +(4.53870 - 22.1746i) q^{46} -77.1309 q^{47} +9.20832 q^{48} -7.00000 q^{49} -15.9881 q^{50} +3.13352i q^{51} +62.5864 q^{52} -75.2969i q^{53} -5.11354 q^{54} +4.85694 q^{55} +18.3080i q^{56} -52.9719i q^{57} +22.7123 q^{58} -59.3394 q^{59} +15.5353i q^{60} -13.6900i q^{61} +45.6475 q^{62} +7.93725i q^{63} +11.1220 q^{64} +61.0816i q^{65} -2.79814i q^{66} -24.4518i q^{67} -5.48449i q^{68} +(-7.98826 + 39.0280i) q^{69} -7.70341 q^{70} -24.4667 q^{71} +20.7593 q^{72} -5.03409 q^{73} -60.7214i q^{74} +28.1395 q^{75} +92.7147i q^{76} -4.34328 q^{77} +35.1898 q^{78} -120.358i q^{79} -15.7295i q^{80} +9.00000 q^{81} +45.2773 q^{82} +84.7183i q^{83} -13.8923i q^{84} +5.35262 q^{85} -46.3819i q^{86} -39.9744 q^{87} +11.3595i q^{88} +62.8049i q^{89} +8.73485i q^{90} -54.6217i q^{91} +(13.9815 - 68.3093i) q^{92} -80.3410 q^{93} +75.9047 q^{94} -90.4855 q^{95} -57.0034 q^{96} -49.7308i q^{97} +6.88871 q^{98} +4.92482i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984102 −0.492051 −0.246025 0.969263i \(-0.579125\pi\)
−0.246025 + 0.969263i \(0.579125\pi\)
\(3\) 1.73205 0.577350
\(4\) −3.03154 −0.757886
\(5\) 2.95865i 0.591731i −0.955230 0.295865i \(-0.904392\pi\)
0.955230 0.295865i \(-0.0956079\pi\)
\(6\) −1.70451 −0.284086
\(7\) 2.64575i 0.377964i
\(8\) 6.91976 0.864969
\(9\) 3.00000 0.333333
\(10\) 2.91162i 0.291162i
\(11\) 1.64161i 0.149237i 0.997212 + 0.0746185i \(0.0237739\pi\)
−0.997212 + 0.0746185i \(0.976226\pi\)
\(12\) −5.25079 −0.437566
\(13\) −20.6451 −1.58808 −0.794041 0.607864i \(-0.792027\pi\)
−0.794041 + 0.607864i \(0.792027\pi\)
\(14\) 2.60369i 0.185978i
\(15\) 5.12454i 0.341636i
\(16\) 5.31643 0.332277
\(17\) 1.80914i 0.106420i 0.998583 + 0.0532100i \(0.0169453\pi\)
−0.998583 + 0.0532100i \(0.983055\pi\)
\(18\) −2.95231 −0.164017
\(19\) 30.5833i 1.60965i −0.593513 0.804825i \(-0.702259\pi\)
0.593513 0.804825i \(-0.297741\pi\)
\(20\) 8.96928i 0.448464i
\(21\) 4.58258i 0.218218i
\(22\) 1.61551i 0.0734322i
\(23\) −4.61202 + 22.5328i −0.200523 + 0.979689i
\(24\) 11.9854 0.499390
\(25\) 16.2464 0.649855
\(26\) 20.3169 0.781417
\(27\) 5.19615 0.192450
\(28\) 8.02071i 0.286454i
\(29\) −23.0792 −0.795835 −0.397918 0.917421i \(-0.630267\pi\)
−0.397918 + 0.917421i \(0.630267\pi\)
\(30\) 5.04307i 0.168102i
\(31\) −46.3849 −1.49629 −0.748144 0.663537i \(-0.769055\pi\)
−0.748144 + 0.663537i \(0.769055\pi\)
\(32\) −32.9109 −1.02847
\(33\) 2.84335i 0.0861620i
\(34\) 1.78038i 0.0523641i
\(35\) 7.82786 0.223653
\(36\) −9.09463 −0.252629
\(37\) 61.7024i 1.66763i 0.552042 + 0.833816i \(0.313849\pi\)
−0.552042 + 0.833816i \(0.686151\pi\)
\(38\) 30.0971i 0.792029i
\(39\) −35.7583 −0.916880
\(40\) 20.4732i 0.511829i
\(41\) −46.0087 −1.12216 −0.561082 0.827760i \(-0.689615\pi\)
−0.561082 + 0.827760i \(0.689615\pi\)
\(42\) 4.50972i 0.107374i
\(43\) 47.1312i 1.09608i 0.836454 + 0.548038i \(0.184625\pi\)
−0.836454 + 0.548038i \(0.815375\pi\)
\(44\) 4.97660i 0.113105i
\(45\) 8.87596i 0.197244i
\(46\) 4.53870 22.1746i 0.0986674 0.482057i
\(47\) −77.1309 −1.64108 −0.820541 0.571587i \(-0.806328\pi\)
−0.820541 + 0.571587i \(0.806328\pi\)
\(48\) 9.20832 0.191840
\(49\) −7.00000 −0.142857
\(50\) −15.9881 −0.319762
\(51\) 3.13352i 0.0614417i
\(52\) 62.5864 1.20359
\(53\) 75.2969i 1.42070i −0.703851 0.710348i \(-0.748538\pi\)
0.703851 0.710348i \(-0.251462\pi\)
\(54\) −5.11354 −0.0946953
\(55\) 4.85694 0.0883081
\(56\) 18.3080i 0.326928i
\(57\) 52.9719i 0.929331i
\(58\) 22.7123 0.391592
\(59\) −59.3394 −1.00575 −0.502876 0.864359i \(-0.667725\pi\)
−0.502876 + 0.864359i \(0.667725\pi\)
\(60\) 15.5353i 0.258921i
\(61\) 13.6900i 0.224426i −0.993684 0.112213i \(-0.964206\pi\)
0.993684 0.112213i \(-0.0357939\pi\)
\(62\) 45.6475 0.736250
\(63\) 7.93725i 0.125988i
\(64\) 11.1220 0.173781
\(65\) 61.0816i 0.939717i
\(66\) 2.79814i 0.0423961i
\(67\) 24.4518i 0.364953i −0.983210 0.182476i \(-0.941589\pi\)
0.983210 0.182476i \(-0.0584113\pi\)
\(68\) 5.48449i 0.0806543i
\(69\) −7.98826 + 39.0280i −0.115772 + 0.565624i
\(70\) −7.70341 −0.110049
\(71\) −24.4667 −0.344601 −0.172301 0.985044i \(-0.555120\pi\)
−0.172301 + 0.985044i \(0.555120\pi\)
\(72\) 20.7593 0.288323
\(73\) −5.03409 −0.0689602 −0.0344801 0.999405i \(-0.510978\pi\)
−0.0344801 + 0.999405i \(0.510978\pi\)
\(74\) 60.7214i 0.820560i
\(75\) 28.1395 0.375194
\(76\) 92.7147i 1.21993i
\(77\) −4.34328 −0.0564063
\(78\) 35.1898 0.451152
\(79\) 120.358i 1.52352i −0.647862 0.761758i \(-0.724337\pi\)
0.647862 0.761758i \(-0.275663\pi\)
\(80\) 15.7295i 0.196618i
\(81\) 9.00000 0.111111
\(82\) 45.2773 0.552162
\(83\) 84.7183i 1.02070i 0.859966 + 0.510351i \(0.170485\pi\)
−0.859966 + 0.510351i \(0.829515\pi\)
\(84\) 13.8923i 0.165384i
\(85\) 5.35262 0.0629720
\(86\) 46.3819i 0.539325i
\(87\) −39.9744 −0.459476
\(88\) 11.3595i 0.129085i
\(89\) 62.8049i 0.705673i 0.935685 + 0.352837i \(0.114783\pi\)
−0.935685 + 0.352837i \(0.885217\pi\)
\(90\) 8.73485i 0.0970539i
\(91\) 54.6217i 0.600239i
\(92\) 13.9815 68.3093i 0.151973 0.742492i
\(93\) −80.3410 −0.863882
\(94\) 75.9047 0.807496
\(95\) −90.4855 −0.952479
\(96\) −57.0034 −0.593785
\(97\) 49.7308i 0.512689i −0.966586 0.256344i \(-0.917482\pi\)
0.966586 0.256344i \(-0.0825181\pi\)
\(98\) 6.88871 0.0702930
\(99\) 4.92482i 0.0497456i
\(100\) −49.2516 −0.492516
\(101\) −94.1838 −0.932513 −0.466257 0.884650i \(-0.654398\pi\)
−0.466257 + 0.884650i \(0.654398\pi\)
\(102\) 3.08371i 0.0302324i
\(103\) 124.143i 1.20527i 0.798015 + 0.602637i \(0.205883\pi\)
−0.798015 + 0.602637i \(0.794117\pi\)
\(104\) −142.859 −1.37364
\(105\) 13.5582 0.129126
\(106\) 74.0998i 0.699055i
\(107\) 209.537i 1.95829i 0.203156 + 0.979146i \(0.434880\pi\)
−0.203156 + 0.979146i \(0.565120\pi\)
\(108\) −15.7524 −0.145855
\(109\) 98.4084i 0.902829i −0.892314 0.451415i \(-0.850920\pi\)
0.892314 0.451415i \(-0.149080\pi\)
\(110\) −4.77973 −0.0434521
\(111\) 106.872i 0.962808i
\(112\) 14.0659i 0.125589i
\(113\) 163.527i 1.44714i −0.690251 0.723570i \(-0.742500\pi\)
0.690251 0.723570i \(-0.257500\pi\)
\(114\) 52.1297i 0.457278i
\(115\) 66.6669 + 13.6454i 0.579712 + 0.118655i
\(116\) 69.9657 0.603152
\(117\) −61.9352 −0.529361
\(118\) 58.3960 0.494881
\(119\) −4.78654 −0.0402230
\(120\) 35.4605i 0.295505i
\(121\) 118.305 0.977728
\(122\) 13.4723i 0.110429i
\(123\) −79.6894 −0.647882
\(124\) 140.618 1.13402
\(125\) 122.034i 0.976270i
\(126\) 7.81107i 0.0619926i
\(127\) 132.335 1.04201 0.521003 0.853555i \(-0.325558\pi\)
0.521003 + 0.853555i \(0.325558\pi\)
\(128\) 120.699 0.942957
\(129\) 81.6337i 0.632819i
\(130\) 60.1105i 0.462389i
\(131\) 112.519 0.858923 0.429462 0.903085i \(-0.358703\pi\)
0.429462 + 0.903085i \(0.358703\pi\)
\(132\) 8.61972i 0.0653009i
\(133\) 80.9159 0.608390
\(134\) 24.0631i 0.179575i
\(135\) 15.3736i 0.113879i
\(136\) 12.5188i 0.0920501i
\(137\) 88.6187i 0.646851i −0.946254 0.323426i \(-0.895165\pi\)
0.946254 0.323426i \(-0.104835\pi\)
\(138\) 7.86126 38.4076i 0.0569656 0.278316i
\(139\) 158.393 1.13952 0.569760 0.821811i \(-0.307036\pi\)
0.569760 + 0.821811i \(0.307036\pi\)
\(140\) −23.7305 −0.169504
\(141\) −133.595 −0.947480
\(142\) 24.0777 0.169561
\(143\) 33.8911i 0.237001i
\(144\) 15.9493 0.110759
\(145\) 68.2834i 0.470920i
\(146\) 4.95406 0.0339319
\(147\) −12.1244 −0.0824786
\(148\) 187.053i 1.26387i
\(149\) 241.254i 1.61915i 0.587015 + 0.809576i \(0.300303\pi\)
−0.587015 + 0.809576i \(0.699697\pi\)
\(150\) −27.6922 −0.184615
\(151\) −39.1314 −0.259148 −0.129574 0.991570i \(-0.541361\pi\)
−0.129574 + 0.991570i \(0.541361\pi\)
\(152\) 211.629i 1.39230i
\(153\) 5.42742i 0.0354734i
\(154\) 4.27423 0.0277548
\(155\) 137.237i 0.885399i
\(156\) 108.403 0.694890
\(157\) 33.6563i 0.214371i −0.994239 0.107186i \(-0.965816\pi\)
0.994239 0.107186i \(-0.0341839\pi\)
\(158\) 118.444i 0.749647i
\(159\) 130.418i 0.820239i
\(160\) 97.3720i 0.608575i
\(161\) −59.6163 12.2023i −0.370288 0.0757905i
\(162\) −8.85692 −0.0546723
\(163\) 24.0778 0.147717 0.0738583 0.997269i \(-0.476469\pi\)
0.0738583 + 0.997269i \(0.476469\pi\)
\(164\) 139.477 0.850472
\(165\) 8.41247 0.0509847
\(166\) 83.3715i 0.502238i
\(167\) −118.883 −0.711876 −0.355938 0.934510i \(-0.615839\pi\)
−0.355938 + 0.934510i \(0.615839\pi\)
\(168\) 31.7103i 0.188752i
\(169\) 257.219 1.52201
\(170\) −5.26752 −0.0309854
\(171\) 91.7500i 0.536550i
\(172\) 142.880i 0.830700i
\(173\) −74.7281 −0.431955 −0.215977 0.976398i \(-0.569294\pi\)
−0.215977 + 0.976398i \(0.569294\pi\)
\(174\) 39.3389 0.226085
\(175\) 42.9839i 0.245622i
\(176\) 8.72748i 0.0495880i
\(177\) −102.779 −0.580671
\(178\) 61.8065i 0.347227i
\(179\) 277.617 1.55093 0.775466 0.631390i \(-0.217515\pi\)
0.775466 + 0.631390i \(0.217515\pi\)
\(180\) 26.9079i 0.149488i
\(181\) 53.3247i 0.294611i −0.989091 0.147306i \(-0.952940\pi\)
0.989091 0.147306i \(-0.0470601\pi\)
\(182\) 53.7533i 0.295348i
\(183\) 23.7117i 0.129572i
\(184\) −31.9141 + 155.922i −0.173446 + 0.847401i
\(185\) 182.556 0.986789
\(186\) 79.0638 0.425074
\(187\) −2.96990 −0.0158818
\(188\) 233.826 1.24375
\(189\) 13.7477i 0.0727393i
\(190\) 89.0469 0.468668
\(191\) 262.168i 1.37261i −0.727316 0.686303i \(-0.759232\pi\)
0.727316 0.686303i \(-0.240768\pi\)
\(192\) 19.2639 0.100333
\(193\) 64.1974 0.332629 0.166314 0.986073i \(-0.446813\pi\)
0.166314 + 0.986073i \(0.446813\pi\)
\(194\) 48.9402i 0.252269i
\(195\) 105.796i 0.542546i
\(196\) 21.2208 0.108269
\(197\) −328.623 −1.66814 −0.834068 0.551662i \(-0.813994\pi\)
−0.834068 + 0.551662i \(0.813994\pi\)
\(198\) 4.84652i 0.0244774i
\(199\) 354.709i 1.78246i −0.453556 0.891228i \(-0.649845\pi\)
0.453556 0.891228i \(-0.350155\pi\)
\(200\) 112.421 0.562105
\(201\) 42.3518i 0.210706i
\(202\) 92.6865 0.458844
\(203\) 61.0619i 0.300797i
\(204\) 9.49941i 0.0465658i
\(205\) 136.124i 0.664019i
\(206\) 122.170i 0.593056i
\(207\) −13.8361 + 67.5985i −0.0668409 + 0.326563i
\(208\) −109.758 −0.527683
\(209\) 50.2058 0.240219
\(210\) −13.3427 −0.0635367
\(211\) −285.944 −1.35519 −0.677593 0.735437i \(-0.736977\pi\)
−0.677593 + 0.735437i \(0.736977\pi\)
\(212\) 228.266i 1.07673i
\(213\) −42.3775 −0.198955
\(214\) 206.206i 0.963580i
\(215\) 139.445 0.648581
\(216\) 35.9561 0.166463
\(217\) 122.723i 0.565544i
\(218\) 96.8439i 0.444238i
\(219\) −8.71931 −0.0398142
\(220\) −14.7240 −0.0669274
\(221\) 37.3498i 0.169004i
\(222\) 105.173i 0.473751i
\(223\) 396.446 1.77779 0.888893 0.458115i \(-0.151475\pi\)
0.888893 + 0.458115i \(0.151475\pi\)
\(224\) 87.0741i 0.388724i
\(225\) 48.7391 0.216618
\(226\) 160.927i 0.712067i
\(227\) 168.217i 0.741042i 0.928824 + 0.370521i \(0.120821\pi\)
−0.928824 + 0.370521i \(0.879179\pi\)
\(228\) 160.587i 0.704327i
\(229\) 182.998i 0.799118i 0.916708 + 0.399559i \(0.130837\pi\)
−0.916708 + 0.399559i \(0.869163\pi\)
\(230\) −65.6070 13.4284i −0.285248 0.0583845i
\(231\) −7.52278 −0.0325662
\(232\) −159.703 −0.688373
\(233\) 146.908 0.630505 0.315253 0.949008i \(-0.397911\pi\)
0.315253 + 0.949008i \(0.397911\pi\)
\(234\) 60.9506 0.260472
\(235\) 228.203i 0.971079i
\(236\) 179.890 0.762245
\(237\) 208.466i 0.879602i
\(238\) 4.71044 0.0197918
\(239\) 279.831 1.17084 0.585421 0.810729i \(-0.300929\pi\)
0.585421 + 0.810729i \(0.300929\pi\)
\(240\) 27.2442i 0.113518i
\(241\) 274.634i 1.13956i −0.821797 0.569780i \(-0.807028\pi\)
0.821797 0.569780i \(-0.192972\pi\)
\(242\) −116.424 −0.481092
\(243\) 15.5885 0.0641500
\(244\) 41.5018i 0.170089i
\(245\) 20.7106i 0.0845329i
\(246\) 78.4225 0.318791
\(247\) 631.395i 2.55626i
\(248\) −320.972 −1.29424
\(249\) 146.736i 0.589303i
\(250\) 120.094i 0.480374i
\(251\) 176.637i 0.703731i 0.936051 + 0.351866i \(0.114453\pi\)
−0.936051 + 0.351866i \(0.885547\pi\)
\(252\) 24.0621i 0.0954846i
\(253\) −36.9901 7.57113i −0.146206 0.0299254i
\(254\) −130.231 −0.512720
\(255\) 9.27101 0.0363569
\(256\) −163.268 −0.637764
\(257\) −322.584 −1.25519 −0.627595 0.778540i \(-0.715961\pi\)
−0.627595 + 0.778540i \(0.715961\pi\)
\(258\) 80.3359i 0.311379i
\(259\) −163.249 −0.630306
\(260\) 185.171i 0.712198i
\(261\) −69.2377 −0.265278
\(262\) −110.730 −0.422634
\(263\) 177.102i 0.673393i −0.941613 0.336696i \(-0.890690\pi\)
0.941613 0.336696i \(-0.109310\pi\)
\(264\) 19.6753i 0.0745275i
\(265\) −222.777 −0.840669
\(266\) −79.6295 −0.299359
\(267\) 108.781i 0.407421i
\(268\) 74.1268i 0.276593i
\(269\) −55.4512 −0.206138 −0.103069 0.994674i \(-0.532866\pi\)
−0.103069 + 0.994674i \(0.532866\pi\)
\(270\) 15.1292i 0.0560341i
\(271\) −180.846 −0.667327 −0.333663 0.942692i \(-0.608285\pi\)
−0.333663 + 0.942692i \(0.608285\pi\)
\(272\) 9.61817i 0.0353609i
\(273\) 94.6076i 0.346548i
\(274\) 87.2098i 0.318284i
\(275\) 26.6701i 0.0969824i
\(276\) 24.2167 118.315i 0.0877418 0.428678i
\(277\) −152.629 −0.551007 −0.275503 0.961300i \(-0.588845\pi\)
−0.275503 + 0.961300i \(0.588845\pi\)
\(278\) −155.875 −0.560702
\(279\) −139.155 −0.498763
\(280\) 54.1669 0.193453
\(281\) 211.984i 0.754391i −0.926134 0.377196i \(-0.876888\pi\)
0.926134 0.377196i \(-0.123112\pi\)
\(282\) 131.471 0.466208
\(283\) 496.918i 1.75589i −0.478757 0.877947i \(-0.658913\pi\)
0.478757 0.877947i \(-0.341087\pi\)
\(284\) 74.1718 0.261168
\(285\) −156.725 −0.549914
\(286\) 33.3523i 0.116616i
\(287\) 121.728i 0.424138i
\(288\) −98.7328 −0.342822
\(289\) 285.727 0.988675
\(290\) 67.1978i 0.231717i
\(291\) 86.1363i 0.296001i
\(292\) 15.2611 0.0522640
\(293\) 584.701i 1.99557i 0.0665528 + 0.997783i \(0.478800\pi\)
−0.0665528 + 0.997783i \(0.521200\pi\)
\(294\) 11.9316 0.0405837
\(295\) 175.565i 0.595134i
\(296\) 426.965i 1.44245i
\(297\) 8.53004i 0.0287207i
\(298\) 237.418i 0.796706i
\(299\) 95.2155 465.192i 0.318447 1.55583i
\(300\) −85.3063 −0.284354
\(301\) −124.698 −0.414278
\(302\) 38.5093 0.127514
\(303\) −163.131 −0.538387
\(304\) 162.594i 0.534849i
\(305\) −40.5039 −0.132800
\(306\) 5.34114i 0.0174547i
\(307\) −536.733 −1.74832 −0.874158 0.485641i \(-0.838586\pi\)
−0.874158 + 0.485641i \(0.838586\pi\)
\(308\) 13.1668 0.0427495
\(309\) 215.022i 0.695866i
\(310\) 135.055i 0.435662i
\(311\) −171.080 −0.550096 −0.275048 0.961431i \(-0.588694\pi\)
−0.275048 + 0.961431i \(0.588694\pi\)
\(312\) −247.439 −0.793073
\(313\) 132.047i 0.421875i 0.977500 + 0.210937i \(0.0676516\pi\)
−0.977500 + 0.210937i \(0.932348\pi\)
\(314\) 33.1212i 0.105482i
\(315\) 23.4836 0.0745510
\(316\) 364.870i 1.15465i
\(317\) 41.3975 0.130591 0.0652957 0.997866i \(-0.479201\pi\)
0.0652957 + 0.997866i \(0.479201\pi\)
\(318\) 128.345i 0.403599i
\(319\) 37.8870i 0.118768i
\(320\) 32.9061i 0.102832i
\(321\) 362.929i 1.13062i
\(322\) 58.6685 + 12.0083i 0.182200 + 0.0372928i
\(323\) 55.3296 0.171299
\(324\) −27.2839 −0.0842095
\(325\) −335.408 −1.03202
\(326\) −23.6950 −0.0726841
\(327\) 170.448i 0.521249i
\(328\) −318.369 −0.970637
\(329\) 204.069i 0.620271i
\(330\) −8.27873 −0.0250871
\(331\) −529.880 −1.60085 −0.800423 0.599436i \(-0.795392\pi\)
−0.800423 + 0.599436i \(0.795392\pi\)
\(332\) 256.827i 0.773576i
\(333\) 185.107i 0.555877i
\(334\) 116.993 0.350279
\(335\) −72.3445 −0.215954
\(336\) 24.3629i 0.0725087i
\(337\) 107.305i 0.318412i −0.987245 0.159206i \(-0.949107\pi\)
0.987245 0.159206i \(-0.0508933\pi\)
\(338\) −253.130 −0.748904
\(339\) 283.237i 0.835507i
\(340\) −16.2267 −0.0477256
\(341\) 76.1458i 0.223301i
\(342\) 90.2914i 0.264010i
\(343\) 18.5203i 0.0539949i
\(344\) 326.137i 0.948072i
\(345\) 115.470 + 23.6345i 0.334697 + 0.0685057i
\(346\) 73.5401 0.212544
\(347\) −205.554 −0.592373 −0.296187 0.955130i \(-0.595715\pi\)
−0.296187 + 0.955130i \(0.595715\pi\)
\(348\) 121.184 0.348230
\(349\) 257.695 0.738382 0.369191 0.929354i \(-0.379635\pi\)
0.369191 + 0.929354i \(0.379635\pi\)
\(350\) 42.3005i 0.120859i
\(351\) −107.275 −0.305627
\(352\) 54.0268i 0.153485i
\(353\) −219.135 −0.620779 −0.310390 0.950609i \(-0.600460\pi\)
−0.310390 + 0.950609i \(0.600460\pi\)
\(354\) 101.145 0.285720
\(355\) 72.3884i 0.203911i
\(356\) 190.396i 0.534820i
\(357\) −8.29053 −0.0232228
\(358\) −273.203 −0.763137
\(359\) 188.537i 0.525173i 0.964908 + 0.262587i \(0.0845756\pi\)
−0.964908 + 0.262587i \(0.915424\pi\)
\(360\) 61.4195i 0.170610i
\(361\) −574.340 −1.59097
\(362\) 52.4769i 0.144964i
\(363\) 204.910 0.564492
\(364\) 165.588i 0.454912i
\(365\) 14.8941i 0.0408059i
\(366\) 23.3348i 0.0637562i
\(367\) 262.250i 0.714577i −0.933994 0.357288i \(-0.883701\pi\)
0.933994 0.357288i \(-0.116299\pi\)
\(368\) −24.5195 + 119.794i −0.0666290 + 0.325528i
\(369\) −138.026 −0.374055
\(370\) −179.654 −0.485550
\(371\) 199.217 0.536973
\(372\) 243.557 0.654724
\(373\) 65.3990i 0.175333i −0.996150 0.0876663i \(-0.972059\pi\)
0.996150 0.0876663i \(-0.0279409\pi\)
\(374\) 2.92268 0.00781466
\(375\) 211.369i 0.563649i
\(376\) −533.727 −1.41949
\(377\) 476.472 1.26385
\(378\) 13.5292i 0.0357914i
\(379\) 296.488i 0.782291i 0.920329 + 0.391145i \(0.127921\pi\)
−0.920329 + 0.391145i \(0.872079\pi\)
\(380\) 274.311 0.721870
\(381\) 229.210 0.601602
\(382\) 258.000i 0.675392i
\(383\) 479.187i 1.25114i −0.780168 0.625570i \(-0.784866\pi\)
0.780168 0.625570i \(-0.215134\pi\)
\(384\) 209.056 0.544417
\(385\) 12.8503i 0.0333773i
\(386\) −63.1767 −0.163670
\(387\) 141.394i 0.365358i
\(388\) 150.761i 0.388560i
\(389\) 101.204i 0.260164i 0.991503 + 0.130082i \(0.0415241\pi\)
−0.991503 + 0.130082i \(0.958476\pi\)
\(390\) 104.114i 0.266960i
\(391\) −40.7651 8.34380i −0.104259 0.0213396i
\(392\) −48.4383 −0.123567
\(393\) 194.889 0.495900
\(394\) 323.398 0.820808
\(395\) −356.097 −0.901510
\(396\) 14.9298i 0.0377015i
\(397\) 376.793 0.949102 0.474551 0.880228i \(-0.342611\pi\)
0.474551 + 0.880228i \(0.342611\pi\)
\(398\) 349.069i 0.877059i
\(399\) 140.150 0.351254
\(400\) 86.3727 0.215932
\(401\) 5.99307i 0.0149453i 0.999972 + 0.00747265i \(0.00237864\pi\)
−0.999972 + 0.00747265i \(0.997621\pi\)
\(402\) 41.6785i 0.103678i
\(403\) 957.620 2.37623
\(404\) 285.522 0.706738
\(405\) 26.6279i 0.0657478i
\(406\) 60.0911i 0.148008i
\(407\) −101.291 −0.248872
\(408\) 21.6832i 0.0531452i
\(409\) −392.937 −0.960726 −0.480363 0.877070i \(-0.659495\pi\)
−0.480363 + 0.877070i \(0.659495\pi\)
\(410\) 133.960i 0.326731i
\(411\) 153.492i 0.373460i
\(412\) 376.346i 0.913460i
\(413\) 156.997i 0.380139i
\(414\) 13.6161 66.5239i 0.0328891 0.160686i
\(415\) 250.652 0.603981
\(416\) 679.448 1.63329
\(417\) 274.345 0.657902
\(418\) −49.4076 −0.118200
\(419\) 337.328i 0.805080i −0.915402 0.402540i \(-0.868127\pi\)
0.915402 0.402540i \(-0.131873\pi\)
\(420\) −41.1024 −0.0978629
\(421\) 715.484i 1.69949i 0.527197 + 0.849743i \(0.323243\pi\)
−0.527197 + 0.849743i \(0.676757\pi\)
\(422\) 281.398 0.666821
\(423\) −231.393 −0.547028
\(424\) 521.036i 1.22886i
\(425\) 29.3920i 0.0691576i
\(426\) 41.7038 0.0978962
\(427\) 36.2203 0.0848250
\(428\) 635.221i 1.48416i
\(429\) 58.7011i 0.136832i
\(430\) −137.228 −0.319135
\(431\) 795.766i 1.84632i 0.384410 + 0.923162i \(0.374405\pi\)
−0.384410 + 0.923162i \(0.625595\pi\)
\(432\) 27.6250 0.0639467
\(433\) 217.649i 0.502654i 0.967902 + 0.251327i \(0.0808669\pi\)
−0.967902 + 0.251327i \(0.919133\pi\)
\(434\) 120.772i 0.278276i
\(435\) 118.270i 0.271886i
\(436\) 298.329i 0.684241i
\(437\) 689.130 + 141.051i 1.57696 + 0.322771i
\(438\) 8.58069 0.0195906
\(439\) 431.228 0.982297 0.491148 0.871076i \(-0.336577\pi\)
0.491148 + 0.871076i \(0.336577\pi\)
\(440\) 33.6089 0.0763838
\(441\) −21.0000 −0.0476190
\(442\) 36.7561i 0.0831585i
\(443\) −239.193 −0.539940 −0.269970 0.962869i \(-0.587014\pi\)
−0.269970 + 0.962869i \(0.587014\pi\)
\(444\) 323.986i 0.729698i
\(445\) 185.818 0.417569
\(446\) −390.143 −0.874761
\(447\) 417.864i 0.934818i
\(448\) 29.4260i 0.0656831i
\(449\) −97.7033 −0.217602 −0.108801 0.994064i \(-0.534701\pi\)
−0.108801 + 0.994064i \(0.534701\pi\)
\(450\) −47.9643 −0.106587
\(451\) 75.5282i 0.167468i
\(452\) 495.739i 1.09677i
\(453\) −67.7776 −0.149619
\(454\) 165.542i 0.364630i
\(455\) −161.607 −0.355180
\(456\) 366.553i 0.803843i
\(457\) 196.469i 0.429911i 0.976624 + 0.214956i \(0.0689607\pi\)
−0.976624 + 0.214956i \(0.931039\pi\)
\(458\) 180.089i 0.393207i
\(459\) 9.40057i 0.0204806i
\(460\) −202.104 41.3665i −0.439355 0.0899273i
\(461\) −217.422 −0.471632 −0.235816 0.971798i \(-0.575776\pi\)
−0.235816 + 0.971798i \(0.575776\pi\)
\(462\) 7.40319 0.0160242
\(463\) 838.394 1.81079 0.905393 0.424574i \(-0.139576\pi\)
0.905393 + 0.424574i \(0.139576\pi\)
\(464\) −122.699 −0.264438
\(465\) 237.701i 0.511185i
\(466\) −144.572 −0.310241
\(467\) 392.675i 0.840845i −0.907328 0.420423i \(-0.861882\pi\)
0.907328 0.420423i \(-0.138118\pi\)
\(468\) 187.759 0.401195
\(469\) 64.6935 0.137939
\(470\) 224.576i 0.477820i
\(471\) 58.2944i 0.123767i
\(472\) −410.614 −0.869945
\(473\) −77.3709 −0.163575
\(474\) 205.151i 0.432809i
\(475\) 496.868i 1.04604i
\(476\) 14.5106 0.0304844
\(477\) 225.891i 0.473565i
\(478\) −275.383 −0.576114
\(479\) 285.575i 0.596190i 0.954536 + 0.298095i \(0.0963512\pi\)
−0.954536 + 0.298095i \(0.903649\pi\)
\(480\) 168.653i 0.351361i
\(481\) 1273.85i 2.64834i
\(482\) 270.268i 0.560721i
\(483\) −103.258 21.1349i −0.213786 0.0437576i
\(484\) −358.647 −0.741006
\(485\) −147.136 −0.303374
\(486\) −15.3406 −0.0315651
\(487\) 199.314 0.409269 0.204635 0.978838i \(-0.434399\pi\)
0.204635 + 0.978838i \(0.434399\pi\)
\(488\) 94.7313i 0.194122i
\(489\) 41.7040 0.0852842
\(490\) 20.3813i 0.0415945i
\(491\) −178.193 −0.362918 −0.181459 0.983398i \(-0.558082\pi\)
−0.181459 + 0.983398i \(0.558082\pi\)
\(492\) 241.582 0.491020
\(493\) 41.7536i 0.0846928i
\(494\) 621.357i 1.25781i
\(495\) 14.5708 0.0294360
\(496\) −246.602 −0.497182
\(497\) 64.7327i 0.130247i
\(498\) 144.404i 0.289967i
\(499\) 623.881 1.25026 0.625131 0.780520i \(-0.285046\pi\)
0.625131 + 0.780520i \(0.285046\pi\)
\(500\) 369.950i 0.739901i
\(501\) −205.912 −0.411002
\(502\) 173.828i 0.346272i
\(503\) 259.558i 0.516021i 0.966142 + 0.258010i \(0.0830669\pi\)
−0.966142 + 0.258010i \(0.916933\pi\)
\(504\) 54.9239i 0.108976i
\(505\) 278.657i 0.551796i
\(506\) 36.4020 + 7.45076i 0.0719407 + 0.0147248i
\(507\) 445.516 0.878730
\(508\) −401.178 −0.789721
\(509\) −590.340 −1.15980 −0.579902 0.814686i \(-0.696909\pi\)
−0.579902 + 0.814686i \(0.696909\pi\)
\(510\) −9.12362 −0.0178894
\(511\) 13.3190i 0.0260645i
\(512\) −322.122 −0.629145
\(513\) 158.916i 0.309777i
\(514\) 317.456 0.617618
\(515\) 367.297 0.713198
\(516\) 247.476i 0.479605i
\(517\) 126.619i 0.244910i
\(518\) 160.654 0.310143
\(519\) −129.433 −0.249389
\(520\) 422.670i 0.812826i
\(521\) 597.731i 1.14728i 0.819109 + 0.573638i \(0.194468\pi\)
−0.819109 + 0.573638i \(0.805532\pi\)
\(522\) 68.1369 0.130531
\(523\) 976.357i 1.86684i 0.358786 + 0.933420i \(0.383191\pi\)
−0.358786 + 0.933420i \(0.616809\pi\)
\(524\) −341.106 −0.650966
\(525\) 74.4502i 0.141810i
\(526\) 174.287i 0.331344i
\(527\) 83.9169i 0.159235i
\(528\) 15.1164i 0.0286296i
\(529\) −486.458 207.844i −0.919581 0.392900i
\(530\) 219.236 0.413652
\(531\) −178.018 −0.335251
\(532\) −245.300 −0.461090
\(533\) 949.853 1.78209
\(534\) 107.052i 0.200472i
\(535\) 619.948 1.15878
\(536\) 169.201i 0.315673i
\(537\) 480.846 0.895431
\(538\) 54.5696 0.101430
\(539\) 11.4912i 0.0213196i
\(540\) 46.6058i 0.0863070i
\(541\) −978.363 −1.80843 −0.904217 0.427074i \(-0.859545\pi\)
−0.904217 + 0.427074i \(0.859545\pi\)
\(542\) 177.970 0.328359
\(543\) 92.3610i 0.170094i
\(544\) 59.5405i 0.109449i
\(545\) −291.156 −0.534232
\(546\) 93.1035i 0.170519i
\(547\) 682.278 1.24731 0.623654 0.781700i \(-0.285647\pi\)
0.623654 + 0.781700i \(0.285647\pi\)
\(548\) 268.651i 0.490240i
\(549\) 41.0699i 0.0748086i
\(550\) 26.2461i 0.0477203i
\(551\) 705.840i 1.28102i
\(552\) −55.2768 + 270.064i −0.100139 + 0.489247i
\(553\) 318.437 0.575835
\(554\) 150.202 0.271123
\(555\) 316.196 0.569723
\(556\) −480.176 −0.863626
\(557\) 896.298i 1.60915i −0.593850 0.804576i \(-0.702393\pi\)
0.593850 0.804576i \(-0.297607\pi\)
\(558\) 136.942 0.245417
\(559\) 973.028i 1.74066i
\(560\) 41.6163 0.0743147
\(561\) −5.14401 −0.00916936
\(562\) 208.614i 0.371199i
\(563\) 311.938i 0.554064i −0.960861 0.277032i \(-0.910649\pi\)
0.960861 0.277032i \(-0.0893508\pi\)
\(564\) 404.998 0.718081
\(565\) −483.819 −0.856317
\(566\) 489.018i 0.863990i
\(567\) 23.8118i 0.0419961i
\(568\) −169.303 −0.298069
\(569\) 685.321i 1.20443i −0.798334 0.602216i \(-0.794285\pi\)
0.798334 0.602216i \(-0.205715\pi\)
\(570\) 154.234 0.270586
\(571\) 284.733i 0.498656i −0.968419 0.249328i \(-0.919790\pi\)
0.968419 0.249328i \(-0.0802097\pi\)
\(572\) 102.742i 0.179619i
\(573\) 454.088i 0.792475i
\(574\) 119.792i 0.208698i
\(575\) −74.9286 + 366.077i −0.130311 + 0.636656i
\(576\) 33.3660 0.0579271
\(577\) −427.106 −0.740219 −0.370109 0.928988i \(-0.620680\pi\)
−0.370109 + 0.928988i \(0.620680\pi\)
\(578\) −281.185 −0.486478
\(579\) 111.193 0.192043
\(580\) 207.004i 0.356904i
\(581\) −224.144 −0.385789
\(582\) 84.7669i 0.145648i
\(583\) 123.608 0.212020
\(584\) −34.8347 −0.0596485
\(585\) 183.245i 0.313239i
\(586\) 575.405i 0.981920i
\(587\) 936.975 1.59621 0.798105 0.602519i \(-0.205836\pi\)
0.798105 + 0.602519i \(0.205836\pi\)
\(588\) 36.7555 0.0625094
\(589\) 1418.61i 2.40850i
\(590\) 172.773i 0.292836i
\(591\) −569.191 −0.963099
\(592\) 328.036i 0.554115i
\(593\) 967.284 1.63117 0.815585 0.578637i \(-0.196415\pi\)
0.815585 + 0.578637i \(0.196415\pi\)
\(594\) 8.39443i 0.0141320i
\(595\) 14.1617i 0.0238012i
\(596\) 731.371i 1.22713i
\(597\) 614.373i 1.02910i
\(598\) −93.7018 + 457.797i −0.156692 + 0.765546i
\(599\) −695.902 −1.16177 −0.580887 0.813985i \(-0.697294\pi\)
−0.580887 + 0.813985i \(0.697294\pi\)
\(600\) 194.719 0.324531
\(601\) −482.402 −0.802665 −0.401333 0.915932i \(-0.631453\pi\)
−0.401333 + 0.915932i \(0.631453\pi\)
\(602\) 122.715 0.203846
\(603\) 73.3555i 0.121651i
\(604\) 118.629 0.196405
\(605\) 350.024i 0.578552i
\(606\) 160.538 0.264914
\(607\) −534.976 −0.881344 −0.440672 0.897668i \(-0.645260\pi\)
−0.440672 + 0.897668i \(0.645260\pi\)
\(608\) 1006.53i 1.65547i
\(609\) 105.762i 0.173666i
\(610\) 39.8600 0.0653442
\(611\) 1592.37 2.60617
\(612\) 16.4535i 0.0268848i
\(613\) 7.13100i 0.0116329i −0.999983 0.00581647i \(-0.998149\pi\)
0.999983 0.00581647i \(-0.00185145\pi\)
\(614\) 528.200 0.860261
\(615\) 235.773i 0.383371i
\(616\) −30.0544 −0.0487897
\(617\) 675.408i 1.09466i 0.836916 + 0.547332i \(0.184357\pi\)
−0.836916 + 0.547332i \(0.815643\pi\)
\(618\) 211.604i 0.342401i
\(619\) 201.503i 0.325529i −0.986665 0.162765i \(-0.947959\pi\)
0.986665 0.162765i \(-0.0520411\pi\)
\(620\) 416.039i 0.671031i
\(621\) −23.9648 + 117.084i −0.0385906 + 0.188541i
\(622\) 168.360 0.270675
\(623\) −166.166 −0.266719
\(624\) −190.106 −0.304658
\(625\) 45.1040 0.0721665
\(626\) 129.947i 0.207584i
\(627\) 86.9590 0.138691
\(628\) 102.031i 0.162469i
\(629\) −111.628 −0.177470
\(630\) −23.1102 −0.0366829
\(631\) 804.427i 1.27485i 0.770514 + 0.637423i \(0.219999\pi\)
−0.770514 + 0.637423i \(0.780001\pi\)
\(632\) 832.846i 1.31779i
\(633\) −495.270 −0.782418
\(634\) −40.7394 −0.0642577
\(635\) 391.532i 0.616587i
\(636\) 395.368i 0.621648i
\(637\) 144.515 0.226869
\(638\) 37.2847i 0.0584399i
\(639\) −73.4000 −0.114867
\(640\) 357.105i 0.557977i
\(641\) 184.130i 0.287255i 0.989632 + 0.143627i \(0.0458767\pi\)
−0.989632 + 0.143627i \(0.954123\pi\)
\(642\) 357.159i 0.556323i
\(643\) 778.840i 1.21126i −0.795747 0.605630i \(-0.792921\pi\)
0.795747 0.605630i \(-0.207079\pi\)
\(644\) 180.729 + 36.9917i 0.280636 + 0.0574405i
\(645\) 241.526 0.374459
\(646\) −54.4499 −0.0842878
\(647\) 143.648 0.222022 0.111011 0.993819i \(-0.464591\pi\)
0.111011 + 0.993819i \(0.464591\pi\)
\(648\) 62.2778 0.0961077
\(649\) 97.4119i 0.150095i
\(650\) 330.075 0.507808
\(651\) 212.562i 0.326517i
\(652\) −72.9929 −0.111952
\(653\) −533.097 −0.816382 −0.408191 0.912897i \(-0.633840\pi\)
−0.408191 + 0.912897i \(0.633840\pi\)
\(654\) 167.739i 0.256481i
\(655\) 332.904i 0.508251i
\(656\) −244.602 −0.372869
\(657\) −15.1023 −0.0229867
\(658\) 200.825i 0.305205i
\(659\) 129.534i 0.196562i 0.995159 + 0.0982809i \(0.0313344\pi\)
−0.995159 + 0.0982809i \(0.968666\pi\)
\(660\) −25.5028 −0.0386406
\(661\) 613.199i 0.927684i 0.885918 + 0.463842i \(0.153530\pi\)
−0.885918 + 0.463842i \(0.846470\pi\)
\(662\) 521.456 0.787697
\(663\) 64.6918i 0.0975744i
\(664\) 586.230i 0.882877i
\(665\) 239.402i 0.360003i
\(666\) 182.164i 0.273520i
\(667\) 106.442 520.041i 0.159583 0.779671i
\(668\) 360.400 0.539520
\(669\) 686.665 1.02641
\(670\) 71.1944 0.106260
\(671\) 22.4736 0.0334926
\(672\) 150.817i 0.224430i
\(673\) −1086.59 −1.61455 −0.807275 0.590175i \(-0.799059\pi\)
−0.807275 + 0.590175i \(0.799059\pi\)
\(674\) 105.599i 0.156675i
\(675\) 84.4186 0.125065
\(676\) −779.770 −1.15351
\(677\) 591.555i 0.873788i 0.899513 + 0.436894i \(0.143922\pi\)
−0.899513 + 0.436894i \(0.856078\pi\)
\(678\) 278.734i 0.411112i
\(679\) 131.575 0.193778
\(680\) 37.0388 0.0544689
\(681\) 291.360i 0.427841i
\(682\) 74.9352i 0.109876i
\(683\) −213.493 −0.312581 −0.156290 0.987711i \(-0.549954\pi\)
−0.156290 + 0.987711i \(0.549954\pi\)
\(684\) 278.144i 0.406643i
\(685\) −262.192 −0.382762
\(686\) 18.2258i 0.0265683i
\(687\) 316.962i 0.461371i
\(688\) 250.570i 0.364200i
\(689\) 1554.51i 2.25618i
\(690\) −113.635 23.2587i −0.164688 0.0337083i
\(691\) 1199.99 1.73660 0.868298 0.496044i \(-0.165214\pi\)
0.868298 + 0.496044i \(0.165214\pi\)
\(692\) 226.542 0.327372
\(693\) −13.0298 −0.0188021
\(694\) 202.286 0.291478
\(695\) 468.630i 0.674288i
\(696\) −276.613 −0.397432
\(697\) 83.2363i 0.119421i
\(698\) −253.598 −0.363321
\(699\) 254.452 0.364022
\(700\) 130.307i 0.186154i
\(701\) 974.622i 1.39033i −0.718850 0.695165i \(-0.755331\pi\)
0.718850 0.695165i \(-0.244669\pi\)
\(702\) 105.569 0.150384
\(703\) 1887.06 2.68430
\(704\) 18.2579i 0.0259346i
\(705\) 395.260i 0.560653i
\(706\) 215.651 0.305455
\(707\) 249.187i 0.352457i
\(708\) 311.578 0.440083
\(709\) 688.631i 0.971271i 0.874162 + 0.485635i \(0.161412\pi\)
−0.874162 + 0.485635i \(0.838588\pi\)
\(710\) 71.2376i 0.100335i
\(711\) 361.073i 0.507838i
\(712\) 434.595i 0.610386i
\(713\) 213.928 1045.18i 0.300040 1.46590i
\(714\) 8.15872 0.0114268
\(715\) −100.272 −0.140240
\(716\) −841.607 −1.17543
\(717\) 484.682 0.675986
\(718\) 185.540i 0.258412i
\(719\) 57.7261 0.0802866 0.0401433 0.999194i \(-0.487219\pi\)
0.0401433 + 0.999194i \(0.487219\pi\)
\(720\) 47.1884i 0.0655394i
\(721\) −328.452 −0.455551
\(722\) 565.210 0.782839
\(723\) 475.680i 0.657925i
\(724\) 161.656i 0.223282i
\(725\) −374.954 −0.517178
\(726\) −201.653 −0.277759
\(727\) 734.127i 1.00980i −0.863177 0.504902i \(-0.831529\pi\)
0.863177 0.504902i \(-0.168471\pi\)
\(728\) 377.969i 0.519188i
\(729\) 27.0000 0.0370370
\(730\) 14.6574i 0.0200786i
\(731\) −85.2671 −0.116644
\(732\) 71.8832i 0.0982010i
\(733\) 692.573i 0.944847i −0.881372 0.472423i \(-0.843379\pi\)
0.881372 0.472423i \(-0.156621\pi\)
\(734\) 258.080i 0.351608i
\(735\) 35.8718i 0.0488051i
\(736\) 151.786 741.577i 0.206231 1.00758i
\(737\) 40.1403 0.0544645
\(738\) 135.832 0.184054
\(739\) 639.157 0.864895 0.432447 0.901659i \(-0.357650\pi\)
0.432447 + 0.901659i \(0.357650\pi\)
\(740\) −553.426 −0.747873
\(741\) 1093.61i 1.47585i
\(742\) −196.050 −0.264218
\(743\) 745.887i 1.00389i −0.864901 0.501943i \(-0.832619\pi\)
0.864901 0.501943i \(-0.167381\pi\)
\(744\) −555.940 −0.747232
\(745\) 713.786 0.958102
\(746\) 64.3593i 0.0862725i
\(747\) 254.155i 0.340234i
\(748\) 9.00337 0.0120366
\(749\) −554.384 −0.740165
\(750\) 208.008i 0.277344i
\(751\) 1.32171i 0.00175993i 1.00000 0.000879967i \(0.000280102\pi\)
−1.00000 0.000879967i \(0.999720\pi\)
\(752\) −410.061 −0.545294
\(753\) 305.943i 0.406299i
\(754\) −468.897 −0.621880
\(755\) 115.776i 0.153346i
\(756\) 41.6768i 0.0551281i
\(757\) 464.771i 0.613964i −0.951715 0.306982i \(-0.900681\pi\)
0.951715 0.306982i \(-0.0993192\pi\)
\(758\) 291.775i 0.384927i
\(759\) −64.0687 13.1136i −0.0844120 0.0172774i
\(760\) −626.137 −0.823865
\(761\) −1046.21 −1.37479 −0.687394 0.726285i \(-0.741245\pi\)
−0.687394 + 0.726285i \(0.741245\pi\)
\(762\) −225.566 −0.296019
\(763\) 260.364 0.341237
\(764\) 794.773i 1.04028i
\(765\) 16.0579 0.0209907
\(766\) 471.569i 0.615625i
\(767\) 1225.07 1.59722
\(768\) −282.788 −0.368213
\(769\) 1061.61i 1.38051i −0.723566 0.690255i \(-0.757498\pi\)
0.723566 0.690255i \(-0.242502\pi\)
\(770\) 12.6460i 0.0164233i
\(771\) −558.732 −0.724685
\(772\) −194.617 −0.252095
\(773\) 384.077i 0.496866i 0.968649 + 0.248433i \(0.0799155\pi\)
−0.968649 + 0.248433i \(0.920084\pi\)
\(774\) 139.146i 0.179775i
\(775\) −753.587 −0.972370
\(776\) 344.125i 0.443460i
\(777\) −282.756 −0.363907
\(778\) 99.5950i 0.128014i
\(779\) 1407.10i 1.80629i
\(780\) 320.726i 0.411188i
\(781\) 40.1646i 0.0514272i
\(782\) 40.1170 + 8.21115i 0.0513005 + 0.0105002i
\(783\) −119.923 −0.153159
\(784\) −37.2150 −0.0474681
\(785\) −99.5773 −0.126850
\(786\) −191.790 −0.244008
\(787\) 493.710i 0.627332i −0.949533 0.313666i \(-0.898443\pi\)
0.949533 0.313666i \(-0.101557\pi\)
\(788\) 996.234 1.26426
\(789\) 306.750i 0.388783i
\(790\) 350.435 0.443589
\(791\) 432.651