Properties

Label 483.3.f.a.22.13
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 22.13
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.14

$q$-expansion

\(f(q)\) \(=\) \(q-1.75802 q^{2} -1.73205 q^{3} -0.909354 q^{4} +0.711109i q^{5} +3.04499 q^{6} -2.64575i q^{7} +8.63076 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.75802 q^{2} -1.73205 q^{3} -0.909354 q^{4} +0.711109i q^{5} +3.04499 q^{6} -2.64575i q^{7} +8.63076 q^{8} +3.00000 q^{9} -1.25015i q^{10} +8.01603i q^{11} +1.57505 q^{12} -19.1112 q^{13} +4.65129i q^{14} -1.23168i q^{15} -11.5357 q^{16} -25.4247i q^{17} -5.27407 q^{18} -5.80334i q^{19} -0.646650i q^{20} +4.58258i q^{21} -14.0924i q^{22} +(-19.3326 - 12.4600i) q^{23} -14.9489 q^{24} +24.4943 q^{25} +33.5979 q^{26} -5.19615 q^{27} +2.40593i q^{28} -13.4076 q^{29} +2.16532i q^{30} +49.8044 q^{31} -14.2431 q^{32} -13.8842i q^{33} +44.6973i q^{34} +1.88142 q^{35} -2.72806 q^{36} +61.8720i q^{37} +10.2024i q^{38} +33.1016 q^{39} +6.13741i q^{40} +11.2387 q^{41} -8.05627i q^{42} +69.0959i q^{43} -7.28941i q^{44} +2.13333i q^{45} +(33.9871 + 21.9050i) q^{46} -8.79613 q^{47} +19.9803 q^{48} -7.00000 q^{49} -43.0616 q^{50} +44.0369i q^{51} +17.3789 q^{52} +63.7575i q^{53} +9.13496 q^{54} -5.70027 q^{55} -22.8348i q^{56} +10.0517i q^{57} +23.5709 q^{58} +54.3128 q^{59} +1.12003i q^{60} +65.2892i q^{61} -87.5573 q^{62} -7.93725i q^{63} +71.1823 q^{64} -13.5902i q^{65} +24.4087i q^{66} -102.088i q^{67} +23.1201i q^{68} +(33.4850 + 21.5813i) q^{69} -3.30758 q^{70} +14.5341 q^{71} +25.8923 q^{72} +74.1461 q^{73} -108.772i q^{74} -42.4254 q^{75} +5.27729i q^{76} +21.2084 q^{77} -58.1934 q^{78} +70.0342i q^{79} -8.20311i q^{80} +9.00000 q^{81} -19.7579 q^{82} +68.9881i q^{83} -4.16719i q^{84} +18.0798 q^{85} -121.472i q^{86} +23.2227 q^{87} +69.1844i q^{88} -12.2196i q^{89} -3.75044i q^{90} +50.5635i q^{91} +(17.5802 + 11.3306i) q^{92} -86.2638 q^{93} +15.4638 q^{94} +4.12681 q^{95} +24.6697 q^{96} +135.825i q^{97} +12.3062 q^{98} +24.0481i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.75802 −0.879012 −0.439506 0.898240i \(-0.644846\pi\)
−0.439506 + 0.898240i \(0.644846\pi\)
\(3\) −1.73205 −0.577350
\(4\) −0.909354 −0.227339
\(5\) 0.711109i 0.142222i 0.997468 + 0.0711109i \(0.0226544\pi\)
−0.997468 + 0.0711109i \(0.977346\pi\)
\(6\) 3.04499 0.507498
\(7\) 2.64575i 0.377964i
\(8\) 8.63076 1.07884
\(9\) 3.00000 0.333333
\(10\) 1.25015i 0.125015i
\(11\) 8.01603i 0.728730i 0.931256 + 0.364365i \(0.118714\pi\)
−0.931256 + 0.364365i \(0.881286\pi\)
\(12\) 1.57505 0.131254
\(13\) −19.1112 −1.47009 −0.735047 0.678017i \(-0.762840\pi\)
−0.735047 + 0.678017i \(0.762840\pi\)
\(14\) 4.65129i 0.332235i
\(15\) 1.23168i 0.0821118i
\(16\) −11.5357 −0.720979
\(17\) 25.4247i 1.49557i −0.663940 0.747786i \(-0.731117\pi\)
0.663940 0.747786i \(-0.268883\pi\)
\(18\) −5.27407 −0.293004
\(19\) 5.80334i 0.305439i −0.988270 0.152719i \(-0.951197\pi\)
0.988270 0.152719i \(-0.0488031\pi\)
\(20\) 0.646650i 0.0323325i
\(21\) 4.58258i 0.218218i
\(22\) 14.0924i 0.640562i
\(23\) −19.3326 12.4600i −0.840547 0.541739i
\(24\) −14.9489 −0.622871
\(25\) 24.4943 0.979773
\(26\) 33.5979 1.29223
\(27\) −5.19615 −0.192450
\(28\) 2.40593i 0.0859259i
\(29\) −13.4076 −0.462332 −0.231166 0.972914i \(-0.574254\pi\)
−0.231166 + 0.972914i \(0.574254\pi\)
\(30\) 2.16532i 0.0721772i
\(31\) 49.8044 1.60659 0.803297 0.595579i \(-0.203077\pi\)
0.803297 + 0.595579i \(0.203077\pi\)
\(32\) −14.2431 −0.445096
\(33\) 13.8842i 0.420733i
\(34\) 44.6973i 1.31463i
\(35\) 1.88142 0.0537548
\(36\) −2.72806 −0.0757795
\(37\) 61.8720i 1.67222i 0.548566 + 0.836108i \(0.315174\pi\)
−0.548566 + 0.836108i \(0.684826\pi\)
\(38\) 10.2024i 0.268484i
\(39\) 33.1016 0.848759
\(40\) 6.13741i 0.153435i
\(41\) 11.2387 0.274115 0.137057 0.990563i \(-0.456236\pi\)
0.137057 + 0.990563i \(0.456236\pi\)
\(42\) 8.05627i 0.191816i
\(43\) 69.0959i 1.60688i 0.595385 + 0.803441i \(0.297000\pi\)
−0.595385 + 0.803441i \(0.703000\pi\)
\(44\) 7.28941i 0.165669i
\(45\) 2.13333i 0.0474073i
\(46\) 33.9871 + 21.9050i 0.738850 + 0.476195i
\(47\) −8.79613 −0.187152 −0.0935758 0.995612i \(-0.529830\pi\)
−0.0935758 + 0.995612i \(0.529830\pi\)
\(48\) 19.9803 0.416257
\(49\) −7.00000 −0.142857
\(50\) −43.0616 −0.861232
\(51\) 44.0369i 0.863469i
\(52\) 17.3789 0.334209
\(53\) 63.7575i 1.20297i 0.798884 + 0.601485i \(0.205424\pi\)
−0.798884 + 0.601485i \(0.794576\pi\)
\(54\) 9.13496 0.169166
\(55\) −5.70027 −0.103641
\(56\) 22.8348i 0.407765i
\(57\) 10.0517i 0.176345i
\(58\) 23.5709 0.406395
\(59\) 54.3128 0.920556 0.460278 0.887775i \(-0.347750\pi\)
0.460278 + 0.887775i \(0.347750\pi\)
\(60\) 1.12003i 0.0186672i
\(61\) 65.2892i 1.07031i 0.844753 + 0.535157i \(0.179748\pi\)
−0.844753 + 0.535157i \(0.820252\pi\)
\(62\) −87.5573 −1.41221
\(63\) 7.93725i 0.125988i
\(64\) 71.1823 1.11222
\(65\) 13.5902i 0.209079i
\(66\) 24.4087i 0.369829i
\(67\) 102.088i 1.52370i −0.647751 0.761852i \(-0.724290\pi\)
0.647751 0.761852i \(-0.275710\pi\)
\(68\) 23.1201i 0.340001i
\(69\) 33.4850 + 21.5813i 0.485290 + 0.312773i
\(70\) −3.30758 −0.0472511
\(71\) 14.5341 0.204705 0.102353 0.994748i \(-0.467363\pi\)
0.102353 + 0.994748i \(0.467363\pi\)
\(72\) 25.8923 0.359615
\(73\) 74.1461 1.01570 0.507850 0.861446i \(-0.330441\pi\)
0.507850 + 0.861446i \(0.330441\pi\)
\(74\) 108.772i 1.46990i
\(75\) −42.4254 −0.565672
\(76\) 5.27729i 0.0694380i
\(77\) 21.2084 0.275434
\(78\) −58.1934 −0.746069
\(79\) 70.0342i 0.886509i 0.896396 + 0.443255i \(0.146176\pi\)
−0.896396 + 0.443255i \(0.853824\pi\)
\(80\) 8.20311i 0.102539i
\(81\) 9.00000 0.111111
\(82\) −19.7579 −0.240950
\(83\) 68.9881i 0.831181i 0.909552 + 0.415591i \(0.136425\pi\)
−0.909552 + 0.415591i \(0.863575\pi\)
\(84\) 4.16719i 0.0496093i
\(85\) 18.0798 0.212703
\(86\) 121.472i 1.41247i
\(87\) 23.2227 0.266928
\(88\) 69.1844i 0.786187i
\(89\) 12.2196i 0.137299i −0.997641 0.0686497i \(-0.978131\pi\)
0.997641 0.0686497i \(-0.0218691\pi\)
\(90\) 3.75044i 0.0416715i
\(91\) 50.5635i 0.555643i
\(92\) 17.5802 + 11.3306i 0.191089 + 0.123158i
\(93\) −86.2638 −0.927568
\(94\) 15.4638 0.164508
\(95\) 4.12681 0.0434401
\(96\) 24.6697 0.256976
\(97\) 135.825i 1.40026i 0.714016 + 0.700130i \(0.246875\pi\)
−0.714016 + 0.700130i \(0.753125\pi\)
\(98\) 12.3062 0.125573
\(99\) 24.0481i 0.242910i
\(100\) −22.2740 −0.222740
\(101\) 86.7443 0.858854 0.429427 0.903102i \(-0.358716\pi\)
0.429427 + 0.903102i \(0.358716\pi\)
\(102\) 77.4179i 0.758999i
\(103\) 15.5070i 0.150554i 0.997163 + 0.0752769i \(0.0239841\pi\)
−0.997163 + 0.0752769i \(0.976016\pi\)
\(104\) −164.944 −1.58600
\(105\) −3.25871 −0.0310353
\(106\) 112.087i 1.05743i
\(107\) 39.3116i 0.367398i 0.982982 + 0.183699i \(0.0588072\pi\)
−0.982982 + 0.183699i \(0.941193\pi\)
\(108\) 4.72514 0.0437513
\(109\) 119.619i 1.09742i 0.836012 + 0.548711i \(0.184881\pi\)
−0.836012 + 0.548711i \(0.815119\pi\)
\(110\) 10.0212 0.0911020
\(111\) 107.165i 0.965454i
\(112\) 30.5205i 0.272504i
\(113\) 188.364i 1.66694i −0.552565 0.833470i \(-0.686351\pi\)
0.552565 0.833470i \(-0.313649\pi\)
\(114\) 17.6711i 0.155009i
\(115\) 8.86042 13.7476i 0.0770471 0.119544i
\(116\) 12.1923 0.105106
\(117\) −57.3336 −0.490031
\(118\) −95.4832 −0.809180
\(119\) −67.2675 −0.565273
\(120\) 10.6303i 0.0885859i
\(121\) 56.7432 0.468952
\(122\) 114.780i 0.940818i
\(123\) −19.4660 −0.158260
\(124\) −45.2899 −0.365241
\(125\) 35.1959i 0.281567i
\(126\) 13.9539i 0.110745i
\(127\) 77.7836 0.612469 0.306235 0.951956i \(-0.400931\pi\)
0.306235 + 0.951956i \(0.400931\pi\)
\(128\) −68.1678 −0.532561
\(129\) 119.678i 0.927733i
\(130\) 23.8918i 0.183783i
\(131\) −79.4552 −0.606528 −0.303264 0.952907i \(-0.598076\pi\)
−0.303264 + 0.952907i \(0.598076\pi\)
\(132\) 12.6256i 0.0956488i
\(133\) −15.3542 −0.115445
\(134\) 179.473i 1.33935i
\(135\) 3.69503i 0.0273706i
\(136\) 219.435i 1.61349i
\(137\) 113.187i 0.826184i −0.910689 0.413092i \(-0.864449\pi\)
0.910689 0.413092i \(-0.135551\pi\)
\(138\) −58.8674 37.9405i −0.426575 0.274931i
\(139\) 121.495 0.874067 0.437033 0.899445i \(-0.356029\pi\)
0.437033 + 0.899445i \(0.356029\pi\)
\(140\) −1.71088 −0.0122205
\(141\) 15.2353 0.108052
\(142\) −25.5512 −0.179938
\(143\) 153.196i 1.07130i
\(144\) −34.6070 −0.240326
\(145\) 9.53429i 0.0657537i
\(146\) −130.350 −0.892812
\(147\) 12.1244 0.0824786
\(148\) 56.2635i 0.380159i
\(149\) 21.8043i 0.146338i 0.997320 + 0.0731688i \(0.0233112\pi\)
−0.997320 + 0.0731688i \(0.976689\pi\)
\(150\) 74.5849 0.497232
\(151\) 44.0474 0.291704 0.145852 0.989306i \(-0.453408\pi\)
0.145852 + 0.989306i \(0.453408\pi\)
\(152\) 50.0872i 0.329521i
\(153\) 76.2742i 0.498524i
\(154\) −37.2849 −0.242110
\(155\) 35.4164i 0.228493i
\(156\) −30.1011 −0.192956
\(157\) 282.497i 1.79934i 0.436569 + 0.899671i \(0.356193\pi\)
−0.436569 + 0.899671i \(0.643807\pi\)
\(158\) 123.122i 0.779252i
\(159\) 110.431i 0.694536i
\(160\) 10.1284i 0.0633024i
\(161\) −32.9660 + 51.1492i −0.204758 + 0.317697i
\(162\) −15.8222 −0.0976680
\(163\) −318.274 −1.95260 −0.976299 0.216426i \(-0.930560\pi\)
−0.976299 + 0.216426i \(0.930560\pi\)
\(164\) −10.2200 −0.0623169
\(165\) 9.87316 0.0598374
\(166\) 121.283i 0.730618i
\(167\) −40.9876 −0.245435 −0.122717 0.992442i \(-0.539161\pi\)
−0.122717 + 0.992442i \(0.539161\pi\)
\(168\) 39.5511i 0.235423i
\(169\) 196.238 1.16117
\(170\) −31.7846 −0.186968
\(171\) 17.4100i 0.101813i
\(172\) 62.8327i 0.365306i
\(173\) 205.900 1.19017 0.595086 0.803662i \(-0.297118\pi\)
0.595086 + 0.803662i \(0.297118\pi\)
\(174\) −40.8260 −0.234632
\(175\) 64.8059i 0.370319i
\(176\) 92.4702i 0.525399i
\(177\) −94.0726 −0.531484
\(178\) 21.4824i 0.120688i
\(179\) −250.038 −1.39686 −0.698430 0.715678i \(-0.746118\pi\)
−0.698430 + 0.715678i \(0.746118\pi\)
\(180\) 1.93995i 0.0107775i
\(181\) 31.4840i 0.173945i −0.996211 0.0869724i \(-0.972281\pi\)
0.996211 0.0869724i \(-0.0277192\pi\)
\(182\) 88.8918i 0.488417i
\(183\) 113.084i 0.617946i
\(184\) −166.855 107.539i −0.906820 0.584452i
\(185\) −43.9977 −0.237825
\(186\) 151.654 0.815343
\(187\) 203.805 1.08987
\(188\) 7.99880 0.0425468
\(189\) 13.7477i 0.0727393i
\(190\) −7.25502 −0.0381843
\(191\) 356.198i 1.86491i 0.361288 + 0.932454i \(0.382337\pi\)
−0.361288 + 0.932454i \(0.617663\pi\)
\(192\) −123.291 −0.642142
\(193\) −17.4493 −0.0904107 −0.0452053 0.998978i \(-0.514394\pi\)
−0.0452053 + 0.998978i \(0.514394\pi\)
\(194\) 238.784i 1.23084i
\(195\) 23.5388i 0.120712i
\(196\) 6.36548 0.0324769
\(197\) 216.442 1.09869 0.549346 0.835595i \(-0.314877\pi\)
0.549346 + 0.835595i \(0.314877\pi\)
\(198\) 42.2771i 0.213521i
\(199\) 79.5233i 0.399615i −0.979835 0.199807i \(-0.935968\pi\)
0.979835 0.199807i \(-0.0640316\pi\)
\(200\) 211.405 1.05702
\(201\) 176.822i 0.879711i
\(202\) −152.498 −0.754943
\(203\) 35.4733i 0.174745i
\(204\) 40.0452i 0.196300i
\(205\) 7.99195i 0.0389851i
\(206\) 27.2617i 0.132338i
\(207\) −57.9977 37.3800i −0.280182 0.180580i
\(208\) 220.460 1.05991
\(209\) 46.5197 0.222582
\(210\) 5.72889 0.0272804
\(211\) −137.441 −0.651378 −0.325689 0.945477i \(-0.605596\pi\)
−0.325689 + 0.945477i \(0.605596\pi\)
\(212\) 57.9781i 0.273482i
\(213\) −25.1737 −0.118187
\(214\) 69.1108i 0.322948i
\(215\) −49.1347 −0.228534
\(216\) −44.8467 −0.207624
\(217\) 131.770i 0.607236i
\(218\) 210.293i 0.964646i
\(219\) −128.425 −0.586414
\(220\) 5.18357 0.0235617
\(221\) 485.897i 2.19863i
\(222\) 188.399i 0.848645i
\(223\) −206.967 −0.928105 −0.464052 0.885808i \(-0.653605\pi\)
−0.464052 + 0.885808i \(0.653605\pi\)
\(224\) 37.6837i 0.168231i
\(225\) 73.4830 0.326591
\(226\) 331.149i 1.46526i
\(227\) 332.026i 1.46267i −0.682019 0.731335i \(-0.738898\pi\)
0.682019 0.731335i \(-0.261102\pi\)
\(228\) 9.14053i 0.0400901i
\(229\) 1.54210i 0.00673406i 0.999994 + 0.00336703i \(0.00107176\pi\)
−0.999994 + 0.00336703i \(0.998928\pi\)
\(230\) −15.5768 + 24.1685i −0.0677253 + 0.105081i
\(231\) −36.7341 −0.159022
\(232\) −115.718 −0.498785
\(233\) 78.1284 0.335315 0.167658 0.985845i \(-0.446380\pi\)
0.167658 + 0.985845i \(0.446380\pi\)
\(234\) 100.794 0.430743
\(235\) 6.25501i 0.0266170i
\(236\) −49.3896 −0.209278
\(237\) 121.303i 0.511826i
\(238\) 118.258 0.496882
\(239\) −292.092 −1.22214 −0.611072 0.791575i \(-0.709261\pi\)
−0.611072 + 0.791575i \(0.709261\pi\)
\(240\) 14.2082i 0.0592009i
\(241\) 394.307i 1.63613i 0.575126 + 0.818065i \(0.304953\pi\)
−0.575126 + 0.818065i \(0.695047\pi\)
\(242\) −99.7559 −0.412214
\(243\) −15.5885 −0.0641500
\(244\) 59.3710i 0.243324i
\(245\) 4.97776i 0.0203174i
\(246\) 34.2217 0.139113
\(247\) 110.909i 0.449023i
\(248\) 429.850 1.73327
\(249\) 119.491i 0.479883i
\(250\) 61.8751i 0.247501i
\(251\) 107.173i 0.426984i −0.976945 0.213492i \(-0.931516\pi\)
0.976945 0.213492i \(-0.0684838\pi\)
\(252\) 7.21778i 0.0286420i
\(253\) 99.8797 154.971i 0.394782 0.612532i
\(254\) −136.745 −0.538368
\(255\) −31.3151 −0.122804
\(256\) −164.889 −0.644096
\(257\) −42.3722 −0.164872 −0.0824362 0.996596i \(-0.526270\pi\)
−0.0824362 + 0.996596i \(0.526270\pi\)
\(258\) 210.396i 0.815488i
\(259\) 163.698 0.632038
\(260\) 12.3583i 0.0475318i
\(261\) −40.2229 −0.154111
\(262\) 139.684 0.533145
\(263\) 40.5143i 0.154047i −0.997029 0.0770234i \(-0.975458\pi\)
0.997029 0.0770234i \(-0.0245416\pi\)
\(264\) 119.831i 0.453905i
\(265\) −45.3385 −0.171089
\(266\) 26.9930 0.101478
\(267\) 21.1651i 0.0792699i
\(268\) 92.8343i 0.346397i
\(269\) 517.952 1.92547 0.962737 0.270440i \(-0.0871690\pi\)
0.962737 + 0.270440i \(0.0871690\pi\)
\(270\) 6.49595i 0.0240591i
\(271\) 265.958 0.981395 0.490697 0.871330i \(-0.336742\pi\)
0.490697 + 0.871330i \(0.336742\pi\)
\(272\) 293.291i 1.07828i
\(273\) 87.5786i 0.320801i
\(274\) 198.986i 0.726225i
\(275\) 196.347i 0.713990i
\(276\) −30.4497 19.6251i −0.110325 0.0711054i
\(277\) 426.483 1.53965 0.769824 0.638256i \(-0.220344\pi\)
0.769824 + 0.638256i \(0.220344\pi\)
\(278\) −213.591 −0.768315
\(279\) 149.413 0.535531
\(280\) 16.2381 0.0579931
\(281\) 365.313i 1.30005i 0.759914 + 0.650024i \(0.225241\pi\)
−0.759914 + 0.650024i \(0.774759\pi\)
\(282\) −26.7841 −0.0949790
\(283\) 517.783i 1.82962i −0.403882 0.914811i \(-0.632340\pi\)
0.403882 0.914811i \(-0.367660\pi\)
\(284\) −13.2166 −0.0465374
\(285\) −7.14784 −0.0250801
\(286\) 269.322i 0.941686i
\(287\) 29.7348i 0.103606i
\(288\) −42.7292 −0.148365
\(289\) −357.417 −1.23674
\(290\) 16.7615i 0.0577983i
\(291\) 235.256i 0.808440i
\(292\) −67.4250 −0.230908
\(293\) 478.496i 1.63309i 0.577280 + 0.816546i \(0.304114\pi\)
−0.577280 + 0.816546i \(0.695886\pi\)
\(294\) −21.3149 −0.0724997
\(295\) 38.6223i 0.130923i
\(296\) 534.002i 1.80406i
\(297\) 41.6525i 0.140244i
\(298\) 38.3325i 0.128632i
\(299\) 369.469 + 238.126i 1.23568 + 0.796407i
\(300\) 38.5797 0.128599
\(301\) 182.811 0.607344
\(302\) −77.4363 −0.256411
\(303\) −150.245 −0.495860
\(304\) 66.9453i 0.220215i
\(305\) −46.4277 −0.152222
\(306\) 134.092i 0.438208i
\(307\) −395.306 −1.28764 −0.643821 0.765176i \(-0.722652\pi\)
−0.643821 + 0.765176i \(0.722652\pi\)
\(308\) −19.2860 −0.0626168
\(309\) 26.8590i 0.0869222i
\(310\) 62.2628i 0.200848i
\(311\) 584.020 1.87788 0.938939 0.344084i \(-0.111810\pi\)
0.938939 + 0.344084i \(0.111810\pi\)
\(312\) 285.692 0.915679
\(313\) 121.168i 0.387118i −0.981089 0.193559i \(-0.937997\pi\)
0.981089 0.193559i \(-0.0620031\pi\)
\(314\) 496.636i 1.58164i
\(315\) 5.64425 0.0179183
\(316\) 63.6859i 0.201538i
\(317\) −557.796 −1.75961 −0.879805 0.475335i \(-0.842327\pi\)
−0.879805 + 0.475335i \(0.842327\pi\)
\(318\) 194.141i 0.610505i
\(319\) 107.476i 0.336915i
\(320\) 50.6184i 0.158182i
\(321\) 68.0898i 0.212118i
\(322\) 57.9551 89.9215i 0.179985 0.279259i
\(323\) −147.548 −0.456806
\(324\) −8.18419 −0.0252598
\(325\) −468.116 −1.44036
\(326\) 559.532 1.71636
\(327\) 207.186i 0.633596i
\(328\) 96.9986 0.295727
\(329\) 23.2724i 0.0707367i
\(330\) −17.3573 −0.0525977
\(331\) 511.085 1.54406 0.772031 0.635585i \(-0.219241\pi\)
0.772031 + 0.635585i \(0.219241\pi\)
\(332\) 62.7346i 0.188960i
\(333\) 185.616i 0.557405i
\(334\) 72.0572 0.215740
\(335\) 72.5958 0.216704
\(336\) 52.8630i 0.157330i
\(337\) 486.160i 1.44261i 0.692617 + 0.721305i \(0.256458\pi\)
−0.692617 + 0.721305i \(0.743542\pi\)
\(338\) −344.992 −1.02069
\(339\) 326.256i 0.962408i
\(340\) −16.4409 −0.0483556
\(341\) 399.234i 1.17077i
\(342\) 30.6072i 0.0894947i
\(343\) 18.5203i 0.0539949i
\(344\) 596.350i 1.73358i
\(345\) −15.3467 + 23.8115i −0.0444832 + 0.0690188i
\(346\) −361.976 −1.04617
\(347\) 237.184 0.683528 0.341764 0.939786i \(-0.388976\pi\)
0.341764 + 0.939786i \(0.388976\pi\)
\(348\) −21.1177 −0.0606829
\(349\) 132.541 0.379775 0.189887 0.981806i \(-0.439188\pi\)
0.189887 + 0.981806i \(0.439188\pi\)
\(350\) 113.930i 0.325515i
\(351\) 99.3048 0.282920
\(352\) 114.173i 0.324355i
\(353\) 183.098 0.518691 0.259346 0.965785i \(-0.416493\pi\)
0.259346 + 0.965785i \(0.416493\pi\)
\(354\) 165.382 0.467180
\(355\) 10.3353i 0.0291135i
\(356\) 11.1120i 0.0312135i
\(357\) 116.511 0.326361
\(358\) 439.573 1.22786
\(359\) 299.975i 0.835584i −0.908543 0.417792i \(-0.862804\pi\)
0.908543 0.417792i \(-0.137196\pi\)
\(360\) 18.4122i 0.0511451i
\(361\) 327.321 0.906707
\(362\) 55.3496i 0.152899i
\(363\) −98.2821 −0.270750
\(364\) 45.9801i 0.126319i
\(365\) 52.7259i 0.144455i
\(366\) 198.805i 0.543182i
\(367\) 135.980i 0.370517i 0.982690 + 0.185259i \(0.0593123\pi\)
−0.982690 + 0.185259i \(0.940688\pi\)
\(368\) 223.014 + 143.734i 0.606016 + 0.390582i
\(369\) 33.7161 0.0913716
\(370\) 77.3490 0.209051
\(371\) 168.686 0.454680
\(372\) 78.4444 0.210872
\(373\) 4.36491i 0.0117022i −0.999983 0.00585109i \(-0.998138\pi\)
0.999983 0.00585109i \(-0.00186247\pi\)
\(374\) −358.295 −0.958007
\(375\) 60.9610i 0.162563i
\(376\) −75.9172 −0.201908
\(377\) 256.236 0.679671
\(378\) 24.1688i 0.0639387i
\(379\) 152.822i 0.403225i −0.979465 0.201612i \(-0.935382\pi\)
0.979465 0.201612i \(-0.0646182\pi\)
\(380\) −3.75273 −0.00987560
\(381\) −134.725 −0.353609
\(382\) 626.204i 1.63928i
\(383\) 408.302i 1.06606i −0.846096 0.533031i \(-0.821053\pi\)
0.846096 0.533031i \(-0.178947\pi\)
\(384\) 118.070 0.307474
\(385\) 15.0815i 0.0391727i
\(386\) 30.6762 0.0794720
\(387\) 207.288i 0.535627i
\(388\) 123.513i 0.318333i
\(389\) 653.238i 1.67928i −0.543146 0.839638i \(-0.682767\pi\)
0.543146 0.839638i \(-0.317233\pi\)
\(390\) 41.3818i 0.106107i
\(391\) −316.792 + 491.525i −0.810210 + 1.25710i
\(392\) −60.4153 −0.154121
\(393\) 137.620 0.350179
\(394\) −380.510 −0.965762
\(395\) −49.8020 −0.126081
\(396\) 21.8682i 0.0552228i
\(397\) −347.048 −0.874176 −0.437088 0.899419i \(-0.643990\pi\)
−0.437088 + 0.899419i \(0.643990\pi\)
\(398\) 139.804i 0.351266i
\(399\) 26.5942 0.0666522
\(400\) −282.558 −0.706395
\(401\) 75.2554i 0.187669i −0.995588 0.0938347i \(-0.970087\pi\)
0.995588 0.0938347i \(-0.0299125\pi\)
\(402\) 310.857i 0.773276i
\(403\) −951.823 −2.36184
\(404\) −78.8813 −0.195251
\(405\) 6.39998i 0.0158024i
\(406\) 62.3628i 0.153603i
\(407\) −495.968 −1.21859
\(408\) 380.072i 0.931549i
\(409\) −120.274 −0.294068 −0.147034 0.989131i \(-0.546973\pi\)
−0.147034 + 0.989131i \(0.546973\pi\)
\(410\) 14.0500i 0.0342684i
\(411\) 196.046i 0.476998i
\(412\) 14.1014i 0.0342267i
\(413\) 143.698i 0.347938i
\(414\) 101.961 + 65.7149i 0.246283 + 0.158732i
\(415\) −49.0580 −0.118212
\(416\) 272.203 0.654333
\(417\) −210.436 −0.504643
\(418\) −81.7828 −0.195653
\(419\) 223.088i 0.532430i −0.963914 0.266215i \(-0.914227\pi\)
0.963914 0.266215i \(-0.0857731\pi\)
\(420\) 2.96332 0.00705553
\(421\) 475.998i 1.13064i −0.824873 0.565318i \(-0.808753\pi\)
0.824873 0.565318i \(-0.191247\pi\)
\(422\) 241.624 0.572569
\(423\) −26.3884 −0.0623839
\(424\) 550.275i 1.29782i
\(425\) 622.761i 1.46532i
\(426\) 44.2560 0.103887
\(427\) 172.739 0.404541
\(428\) 35.7482i 0.0835239i
\(429\) 265.343i 0.618516i
\(430\) 86.3800 0.200884
\(431\) 589.612i 1.36801i 0.729477 + 0.684005i \(0.239763\pi\)
−0.729477 + 0.684005i \(0.760237\pi\)
\(432\) 59.9410 0.138752
\(433\) 28.3248i 0.0654153i 0.999465 + 0.0327077i \(0.0104130\pi\)
−0.999465 + 0.0327077i \(0.989587\pi\)
\(434\) 231.655i 0.533767i
\(435\) 16.5139i 0.0379629i
\(436\) 108.776i 0.249486i
\(437\) −72.3095 + 112.193i −0.165468 + 0.256736i
\(438\) 225.774 0.515465
\(439\) 770.570 1.75528 0.877642 0.479316i \(-0.159115\pi\)
0.877642 + 0.479316i \(0.159115\pi\)
\(440\) −49.1977 −0.111813
\(441\) −21.0000 −0.0476190
\(442\) 854.219i 1.93262i
\(443\) −192.079 −0.433588 −0.216794 0.976217i \(-0.569560\pi\)
−0.216794 + 0.976217i \(0.569560\pi\)
\(444\) 97.4513i 0.219485i
\(445\) 8.68950 0.0195270
\(446\) 363.853 0.815815
\(447\) 37.7662i 0.0844880i
\(448\) 188.331i 0.420381i
\(449\) −810.000 −1.80401 −0.902004 0.431727i \(-0.857904\pi\)
−0.902004 + 0.431727i \(0.857904\pi\)
\(450\) −129.185 −0.287077
\(451\) 90.0899i 0.199756i
\(452\) 171.290i 0.378960i
\(453\) −76.2923 −0.168416
\(454\) 583.709i 1.28570i
\(455\) −35.9562 −0.0790246
\(456\) 86.7536i 0.190249i
\(457\) 84.0185i 0.183848i 0.995766 + 0.0919239i \(0.0293017\pi\)
−0.995766 + 0.0919239i \(0.970698\pi\)
\(458\) 2.71105i 0.00591931i
\(459\) 132.111i 0.287823i
\(460\) −8.05726 + 12.5014i −0.0175158 + 0.0271770i
\(461\) 156.389 0.339240 0.169620 0.985510i \(-0.445746\pi\)
0.169620 + 0.985510i \(0.445746\pi\)
\(462\) 64.5794 0.139782
\(463\) 729.911 1.57648 0.788241 0.615366i \(-0.210992\pi\)
0.788241 + 0.615366i \(0.210992\pi\)
\(464\) 154.666 0.333332
\(465\) 61.3430i 0.131920i
\(466\) −137.352 −0.294746
\(467\) 278.356i 0.596051i −0.954558 0.298026i \(-0.903672\pi\)
0.954558 0.298026i \(-0.0963281\pi\)
\(468\) 52.1366 0.111403
\(469\) −270.100 −0.575906
\(470\) 10.9964i 0.0233967i
\(471\) 489.298i 1.03885i
\(472\) 468.761 0.993138
\(473\) −553.875 −1.17098
\(474\) 213.253i 0.449901i
\(475\) 142.149i 0.299261i
\(476\) 61.1700 0.128508
\(477\) 191.272i 0.400990i
\(478\) 513.505 1.07428
\(479\) 195.302i 0.407728i −0.978999 0.203864i \(-0.934650\pi\)
0.978999 0.203864i \(-0.0653501\pi\)
\(480\) 17.5429i 0.0365477i
\(481\) 1182.45i 2.45831i
\(482\) 693.201i 1.43818i
\(483\) 57.0989 88.5930i 0.118217 0.183422i
\(484\) −51.5997 −0.106611
\(485\) −96.5865 −0.199147
\(486\) 27.4049 0.0563886
\(487\) −356.792 −0.732632 −0.366316 0.930491i \(-0.619381\pi\)
−0.366316 + 0.930491i \(0.619381\pi\)
\(488\) 563.495i 1.15470i
\(489\) 551.266 1.12733
\(490\) 8.75102i 0.0178592i
\(491\) −336.651 −0.685644 −0.342822 0.939400i \(-0.611383\pi\)
−0.342822 + 0.939400i \(0.611383\pi\)
\(492\) 17.7015 0.0359787
\(493\) 340.885i 0.691451i
\(494\) 194.980i 0.394697i
\(495\) −17.1008 −0.0345471
\(496\) −574.527 −1.15832
\(497\) 38.4535i 0.0773713i
\(498\) 210.068i 0.421823i
\(499\) −168.599 −0.337873 −0.168936 0.985627i \(-0.554033\pi\)
−0.168936 + 0.985627i \(0.554033\pi\)
\(500\) 32.0055i 0.0640110i
\(501\) 70.9927 0.141702
\(502\) 188.413i 0.375324i
\(503\) 804.464i 1.59933i −0.600445 0.799666i \(-0.705010\pi\)
0.600445 0.799666i \(-0.294990\pi\)
\(504\) 68.5045i 0.135922i
\(505\) 61.6846i 0.122148i
\(506\) −175.591 + 272.442i −0.347018 + 0.538423i
\(507\) −339.895 −0.670404
\(508\) −70.7329 −0.139238
\(509\) 62.7242 0.123230 0.0616152 0.998100i \(-0.480375\pi\)
0.0616152 + 0.998100i \(0.480375\pi\)
\(510\) 55.0526 0.107946
\(511\) 196.172i 0.383898i
\(512\) 562.549 1.09873
\(513\) 30.1550i 0.0587817i
\(514\) 74.4913 0.144925
\(515\) −11.0272 −0.0214120
\(516\) 108.829i 0.210910i
\(517\) 70.5100i 0.136383i
\(518\) −287.785 −0.555569
\(519\) −356.629 −0.687146
\(520\) 117.293i 0.225564i
\(521\) 497.634i 0.955152i 0.878590 + 0.477576i \(0.158485\pi\)
−0.878590 + 0.477576i \(0.841515\pi\)
\(522\) 70.7128 0.135465
\(523\) 84.1903i 0.160976i −0.996756 0.0804878i \(-0.974352\pi\)
0.996756 0.0804878i \(-0.0256478\pi\)
\(524\) 72.2529 0.137887
\(525\) 112.247i 0.213804i
\(526\) 71.2251i 0.135409i
\(527\) 1266.26i 2.40278i
\(528\) 160.163i 0.303339i
\(529\) 218.497 + 481.768i 0.413038 + 0.910714i
\(530\) 79.7062 0.150389
\(531\) 162.938 0.306852
\(532\) 13.9624 0.0262451
\(533\) −214.785 −0.402974
\(534\) 37.2087i 0.0696791i
\(535\) −27.9549 −0.0522521
\(536\) 881.098i 1.64384i
\(537\) 433.079 0.806478
\(538\) −910.572 −1.69251
\(539\) 56.1122i 0.104104i
\(540\) 3.36009i 0.00622239i
\(541\) 71.2344 0.131672 0.0658359 0.997830i \(-0.479029\pi\)
0.0658359 + 0.997830i \(0.479029\pi\)
\(542\) −467.560 −0.862657
\(543\) 54.5319i 0.100427i
\(544\) 362.126i 0.665674i
\(545\) −85.0621 −0.156077
\(546\) 153.965i 0.281987i
\(547\) −504.297 −0.921933 −0.460966 0.887418i \(-0.652497\pi\)
−0.460966 + 0.887418i \(0.652497\pi\)
\(548\) 102.927i 0.187823i
\(549\) 195.867i 0.356771i
\(550\) 345.183i 0.627606i
\(551\) 77.8090i 0.141214i
\(552\) 289.001 + 186.263i 0.523553 + 0.337434i
\(553\) 185.293 0.335069
\(554\) −749.766 −1.35337
\(555\) 76.2063 0.137309
\(556\) −110.482 −0.198709
\(557\) 243.692i 0.437507i −0.975780 0.218754i \(-0.929801\pi\)
0.975780 0.218754i \(-0.0701991\pi\)
\(558\) −262.672 −0.470738
\(559\) 1320.51i 2.36227i
\(560\) −21.7034 −0.0387561
\(561\) −353.001 −0.629236
\(562\) 642.230i 1.14276i
\(563\) 790.151i 1.40346i −0.712441 0.701732i \(-0.752410\pi\)
0.712441 0.701732i \(-0.247590\pi\)
\(564\) −13.8543 −0.0245644
\(565\) 133.948 0.237075
\(566\) 910.274i 1.60826i
\(567\) 23.8118i 0.0419961i
\(568\) 125.440 0.220845
\(569\) 739.643i 1.29990i 0.759977 + 0.649950i \(0.225210\pi\)
−0.759977 + 0.649950i \(0.774790\pi\)
\(570\) 12.5661 0.0220457
\(571\) 692.965i 1.21360i 0.794855 + 0.606799i \(0.207547\pi\)
−0.794855 + 0.606799i \(0.792453\pi\)
\(572\) 139.310i 0.243548i
\(573\) 616.952i 1.07671i
\(574\) 52.2745i 0.0910706i
\(575\) −473.538 305.199i −0.823545 0.530781i
\(576\) 213.547 0.370741
\(577\) −932.406 −1.61596 −0.807978 0.589213i \(-0.799438\pi\)
−0.807978 + 0.589213i \(0.799438\pi\)
\(578\) 628.347 1.08711
\(579\) 30.2230 0.0521986
\(580\) 8.67005i 0.0149484i
\(581\) 182.525 0.314157
\(582\) 413.586i 0.710628i
\(583\) −511.082 −0.876641
\(584\) 639.937 1.09578
\(585\) 40.7705i 0.0696931i
\(586\) 841.207i 1.43551i
\(587\) 253.018 0.431035 0.215518 0.976500i \(-0.430856\pi\)
0.215518 + 0.976500i \(0.430856\pi\)
\(588\) −11.0253 −0.0187506
\(589\) 289.032i 0.490716i
\(590\) 67.8990i 0.115083i
\(591\) −374.889 −0.634330
\(592\) 713.734i 1.20563i
\(593\) 91.0966 0.153620 0.0768100 0.997046i \(-0.475527\pi\)
0.0768100 + 0.997046i \(0.475527\pi\)
\(594\) 73.2261i 0.123276i
\(595\) 47.8345i 0.0803942i
\(596\) 19.8278i 0.0332682i
\(597\) 137.738i 0.230718i
\(598\) −649.535 418.630i −1.08618 0.700051i
\(599\) −426.693 −0.712342 −0.356171 0.934421i \(-0.615918\pi\)
−0.356171 + 0.934421i \(0.615918\pi\)
\(600\) −366.164 −0.610273
\(601\) 243.004 0.404332 0.202166 0.979351i \(-0.435202\pi\)
0.202166 + 0.979351i \(0.435202\pi\)
\(602\) −321.385 −0.533862
\(603\) 306.265i 0.507901i
\(604\) −40.0547 −0.0663156
\(605\) 40.3506i 0.0666952i
\(606\) 264.135 0.435866
\(607\) 242.034 0.398738 0.199369 0.979924i \(-0.436111\pi\)
0.199369 + 0.979924i \(0.436111\pi\)
\(608\) 82.6574i 0.135950i
\(609\) 61.4415i 0.100889i
\(610\) 81.6210 0.133805
\(611\) 168.105 0.275130
\(612\) 69.3603i 0.113334i
\(613\) 118.345i 0.193058i 0.995330 + 0.0965291i \(0.0307741\pi\)
−0.995330 + 0.0965291i \(0.969226\pi\)
\(614\) 694.957 1.13185
\(615\) 13.8425i 0.0225081i
\(616\) 183.045 0.297151
\(617\) 1152.80i 1.86840i 0.356749 + 0.934200i \(0.383885\pi\)
−0.356749 + 0.934200i \(0.616115\pi\)
\(618\) 47.2187i 0.0764057i
\(619\) 12.3379i 0.0199319i 0.999950 + 0.00996596i \(0.00317232\pi\)
−0.999950 + 0.00996596i \(0.996828\pi\)
\(620\) 32.2060i 0.0519452i
\(621\) 100.455 + 64.7440i 0.161763 + 0.104258i
\(622\) −1026.72 −1.65068
\(623\) −32.3302 −0.0518943
\(624\) −381.849 −0.611937
\(625\) 587.330 0.939728
\(626\) 213.016i 0.340281i
\(627\) −80.5746 −0.128508
\(628\) 256.890i 0.409060i
\(629\) 1573.08 2.50092
\(630\) −9.92273 −0.0157504
\(631\) 51.6407i 0.0818395i 0.999162 + 0.0409198i \(0.0130288\pi\)
−0.999162 + 0.0409198i \(0.986971\pi\)
\(632\) 604.448i 0.956406i
\(633\) 238.054 0.376073
\(634\) 980.619 1.54672
\(635\) 55.3126i 0.0871065i
\(636\) 100.421i 0.157895i
\(637\) 133.778 0.210013
\(638\) 188.945i 0.296153i
\(639\) 43.6022 0.0682350
\(640\) 48.4747i 0.0757418i
\(641\) 700.130i 1.09225i 0.837705 + 0.546123i \(0.183897\pi\)
−0.837705 + 0.546123i \(0.816103\pi\)
\(642\) 119.703i 0.186454i
\(643\) 839.673i 1.30587i 0.757415 + 0.652934i \(0.226462\pi\)
−0.757415 + 0.652934i \(0.773538\pi\)
\(644\) 29.9778 46.5127i 0.0465494 0.0722248i
\(645\) 85.1038 0.131944
\(646\) 259.393 0.401538
\(647\) −790.982 −1.22254 −0.611269 0.791423i \(-0.709341\pi\)
−0.611269 + 0.791423i \(0.709341\pi\)
\(648\) 77.6768 0.119872
\(649\) 435.373i 0.670837i
\(650\) 822.959 1.26609
\(651\) 228.233i 0.350588i
\(652\) 289.423 0.443901
\(653\) 341.232 0.522561 0.261280 0.965263i \(-0.415855\pi\)
0.261280 + 0.965263i \(0.415855\pi\)
\(654\) 364.238i 0.556939i
\(655\) 56.5013i 0.0862615i
\(656\) −129.646 −0.197631
\(657\) 222.438 0.338566
\(658\) 40.9134i 0.0621783i
\(659\) 682.936i 1.03632i 0.855283 + 0.518161i \(0.173383\pi\)
−0.855283 + 0.518161i \(0.826617\pi\)
\(660\) −8.97821 −0.0136033
\(661\) 562.849i 0.851511i 0.904838 + 0.425755i \(0.139992\pi\)
−0.904838 + 0.425755i \(0.860008\pi\)
\(662\) −898.499 −1.35725
\(663\) 841.599i 1.26938i
\(664\) 595.419i 0.896716i
\(665\) 10.9185i 0.0164188i
\(666\) 326.317i 0.489965i
\(667\) 259.204 + 167.059i 0.388612 + 0.250463i
\(668\) 37.2723 0.0557968
\(669\) 358.478 0.535842
\(670\) −127.625 −0.190485
\(671\) −523.360 −0.779970
\(672\) 65.2700i 0.0971280i
\(673\) 28.5552 0.0424297 0.0212149 0.999775i \(-0.493247\pi\)
0.0212149 + 0.999775i \(0.493247\pi\)
\(674\) 854.680i 1.26807i
\(675\) −127.276 −0.188557
\(676\) −178.450 −0.263980
\(677\) 663.295i 0.979757i −0.871791 0.489878i \(-0.837041\pi\)
0.871791 0.489878i \(-0.162959\pi\)
\(678\) 573.566i 0.845968i
\(679\) 359.360 0.529248
\(680\) 156.042 0.229474
\(681\) 575.086i 0.844473i
\(682\) 701.862i 1.02912i
\(683\) −24.5205 −0.0359012 −0.0179506 0.999839i \(-0.505714\pi\)
−0.0179506 + 0.999839i \(0.505714\pi\)
\(684\) 15.8319i 0.0231460i
\(685\) 80.4885 0.117501
\(686\) 32.5590i 0.0474622i
\(687\) 2.67099i 0.00388791i
\(688\) 797.067i 1.15853i
\(689\) 1218.48i 1.76848i
\(690\) 26.9798 41.8612i 0.0391012 0.0606683i
\(691\) −421.109 −0.609419 −0.304710 0.952445i \(-0.598559\pi\)
−0.304710 + 0.952445i \(0.598559\pi\)
\(692\) −187.236 −0.270572
\(693\) 63.6253 0.0918114
\(694\) −416.976 −0.600829
\(695\) 86.3964i 0.124311i
\(696\) 200.430 0.287973
\(697\) 285.741i 0.409959i
\(698\) −233.011 −0.333826
\(699\) −135.322 −0.193594
\(700\) 58.9315i 0.0841879i
\(701\) 1159.54i 1.65413i 0.562109 + 0.827063i \(0.309990\pi\)
−0.562109 + 0.827063i \(0.690010\pi\)
\(702\) −174.580 −0.248690
\(703\) 359.064 0.510759
\(704\) 570.600i 0.810511i
\(705\) 10.8340i 0.0153674i
\(706\) −321.891 −0.455936
\(707\) 229.504i 0.324616i
\(708\) 85.5453 0.120827
\(709\) 156.174i 0.220273i 0.993916 + 0.110137i \(0.0351289\pi\)
−0.993916 + 0.110137i \(0.964871\pi\)
\(710\) 18.1697i 0.0255911i
\(711\) 210.103i 0.295503i
\(712\) 105.465i 0.148125i
\(713\) −962.848 620.563i −1.35042 0.870355i
\(714\) −204.829 −0.286875
\(715\) 108.939 0.152362
\(716\) 227.373 0.317560
\(717\) 505.919 0.705605
\(718\) 527.362i 0.734488i
\(719\) −498.495 −0.693317 −0.346659 0.937991i \(-0.612684\pi\)
−0.346659 + 0.937991i \(0.612684\pi\)
\(720\) 24.6093i 0.0341796i
\(721\) 41.0278 0.0569040
\(722\) −575.438 −0.797006
\(723\) 682.960i 0.944620i
\(724\) 28.6301i 0.0395444i
\(725\) −328.411 −0.452980
\(726\) 172.782 0.237992
\(727\) 1060.14i 1.45824i 0.684385 + 0.729121i \(0.260071\pi\)
−0.684385 + 0.729121i \(0.739929\pi\)
\(728\) 436.401i 0.599453i
\(729\) 27.0000 0.0370370
\(730\) 92.6934i 0.126977i
\(731\) 1756.74 2.40321
\(732\) 102.834i 0.140483i
\(733\) 807.046i 1.10102i 0.834829 + 0.550509i \(0.185566\pi\)
−0.834829 + 0.550509i \(0.814434\pi\)
\(734\) 239.056i 0.325689i
\(735\) 8.62174i 0.0117303i
\(736\) 275.355 + 177.469i 0.374124 + 0.241126i
\(737\) 818.342 1.11037
\(738\) −59.2737 −0.0803167
\(739\) −603.367 −0.816463 −0.408232 0.912878i \(-0.633854\pi\)
−0.408232 + 0.912878i \(0.633854\pi\)
\(740\) 40.0095 0.0540669
\(741\) 192.100i 0.259244i
\(742\) −296.555 −0.399669
\(743\) 578.041i 0.777982i −0.921241 0.388991i \(-0.872824\pi\)
0.921241 0.388991i \(-0.127176\pi\)
\(744\) −744.522 −1.00070
\(745\) −15.5052 −0.0208124
\(746\) 7.67362i 0.0102864i
\(747\) 206.964i 0.277060i
\(748\) −185.331 −0.247769
\(749\) 104.009 0.138864
\(750\) 107.171i 0.142895i
\(751\) 138.968i 0.185044i 0.995711 + 0.0925222i \(0.0294929\pi\)
−0.995711 + 0.0925222i \(0.970507\pi\)
\(752\) 101.469 0.134932
\(753\) 185.629i 0.246519i
\(754\) −450.469 −0.597439
\(755\) 31.3225i 0.0414867i
\(756\) 12.5016i 0.0165364i
\(757\) 804.571i 1.06284i −0.847108 0.531421i \(-0.821658\pi\)
0.847108 0.531421i \(-0.178342\pi\)
\(758\) 268.665i 0.354439i
\(759\) −172.997 + 268.417i −0.227927 + 0.353645i
\(760\) 35.6175 0.0468651
\(761\) 142.923 0.187810 0.0939049 0.995581i \(-0.470065\pi\)
0.0939049 + 0.995581i \(0.470065\pi\)
\(762\) 236.850 0.310827
\(763\) 316.482 0.414786
\(764\) 323.910i 0.423966i
\(765\) 54.2393 0.0709010
\(766\) 717.804i 0.937080i
\(767\) −1037.98 −1.35330
\(768\) 285.595 0.371869
\(769\) 544.852i 0.708520i −0.935147 0.354260i \(-0.884733\pi\)
0.935147 0.354260i \(-0.115267\pi\)
\(770\) 26.5136i 0.0344333i
\(771\) 73.3908 0.0951891
\(772\) 15.8676 0.0205538
\(773\) 221.017i 0.285921i 0.989728 + 0.142961i \(0.0456622\pi\)
−0.989728 + 0.142961i \(0.954338\pi\)
\(774\) 364.417i 0.470822i
\(775\) 1219.93 1.57410
\(776\) 1172.27i 1.51066i
\(777\) −283.533 −0.364907
\(778\) 1148.41i 1.47610i
\(779\) 65.2220i 0.0837253i
\(780\) 21.4051i 0.0274425i
\(781\) 116.506i 0.149175i
\(782\) 556.928 864.113i 0.712184 1.10500i
\(783\) 69.6681 0.0889759
\(784\) 80.7496 0.102997
\(785\) −200.886 −0.255906
\(786\) −241.940 −0.307812
\(787\) 533.056i 0.677327i −0.940908 0.338663i \(-0.890025\pi\)
0.940908 0.338663i \(-0.109975\pi\)
\(788\) −196.823 −0.249775
\(789\) 70.1729i 0.0889390i
\(790\) 87.5530 0.110827
\(791\) −498.365 −0.630044