Properties

Label 336.4.h.b.239.20
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.20
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.b.239.19

$q$-expansion

\(f(q)\) \(=\) \(q+(3.03558 + 4.21726i) q^{3} -3.22455i q^{5} -7.00000i q^{7} +(-8.57055 + 25.6036i) q^{9} +O(q^{10})\) \(q+(3.03558 + 4.21726i) q^{3} -3.22455i q^{5} -7.00000i q^{7} +(-8.57055 + 25.6036i) q^{9} -9.66135 q^{11} +34.8726 q^{13} +(13.5988 - 9.78836i) q^{15} +129.486i q^{17} +67.0042i q^{19} +(29.5208 - 21.2490i) q^{21} +15.6037 q^{23} +114.602 q^{25} +(-133.994 + 41.5775i) q^{27} +87.6664i q^{29} +143.597i q^{31} +(-29.3278 - 40.7444i) q^{33} -22.5718 q^{35} +104.519 q^{37} +(105.858 + 147.067i) q^{39} -257.630i q^{41} +267.467i q^{43} +(82.5601 + 27.6362i) q^{45} -430.734 q^{47} -49.0000 q^{49} +(-546.076 + 393.065i) q^{51} +121.797i q^{53} +31.1535i q^{55} +(-282.574 + 203.396i) q^{57} -861.356 q^{59} +502.028 q^{61} +(179.225 + 59.9939i) q^{63} -112.448i q^{65} -162.918i q^{67} +(47.3661 + 65.8047i) q^{69} +616.070 q^{71} +719.577 q^{73} +(347.884 + 483.308i) q^{75} +67.6295i q^{77} +250.539i q^{79} +(-582.091 - 438.874i) q^{81} +376.936 q^{83} +417.534 q^{85} +(-369.712 + 266.118i) q^{87} +870.360i q^{89} -244.108i q^{91} +(-605.586 + 435.900i) q^{93} +216.058 q^{95} +44.3227 q^{97} +(82.8031 - 247.366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 136 q^{9} + O(q^{10}) \) \( 24 q - 136 q^{9} + 96 q^{13} - 112 q^{21} + 168 q^{25} - 320 q^{33} - 864 q^{37} + 592 q^{45} - 1176 q^{49} - 1120 q^{57} - 2304 q^{61} + 1168 q^{69} + 3312 q^{73} - 968 q^{81} - 5808 q^{85} + 1776 q^{93} + 6480 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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 0
\(3\) 3.03558 + 4.21726i 0.584197 + 0.811612i
\(4\) 0 0
\(5\) 3.22455i 0.288412i −0.989548 0.144206i \(-0.953937\pi\)
0.989548 0.144206i \(-0.0460628\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) −8.57055 + 25.6036i −0.317428 + 0.948282i
\(10\) 0 0
\(11\) −9.66135 −0.264819 −0.132409 0.991195i \(-0.542271\pi\)
−0.132409 + 0.991195i \(0.542271\pi\)
\(12\) 0 0
\(13\) 34.8726 0.743993 0.371997 0.928234i \(-0.378673\pi\)
0.371997 + 0.928234i \(0.378673\pi\)
\(14\) 0 0
\(15\) 13.5988 9.78836i 0.234079 0.168490i
\(16\) 0 0
\(17\) 129.486i 1.84735i 0.383175 + 0.923676i \(0.374831\pi\)
−0.383175 + 0.923676i \(0.625169\pi\)
\(18\) 0 0
\(19\) 67.0042i 0.809043i 0.914528 + 0.404522i \(0.132562\pi\)
−0.914528 + 0.404522i \(0.867438\pi\)
\(20\) 0 0
\(21\) 29.5208 21.2490i 0.306760 0.220806i
\(22\) 0 0
\(23\) 15.6037 0.141460 0.0707302 0.997495i \(-0.477467\pi\)
0.0707302 + 0.997495i \(0.477467\pi\)
\(24\) 0 0
\(25\) 114.602 0.916818
\(26\) 0 0
\(27\) −133.994 + 41.5775i −0.955078 + 0.296355i
\(28\) 0 0
\(29\) 87.6664i 0.561353i 0.959802 + 0.280677i \(0.0905589\pi\)
−0.959802 + 0.280677i \(0.909441\pi\)
\(30\) 0 0
\(31\) 143.597i 0.831960i 0.909374 + 0.415980i \(0.136561\pi\)
−0.909374 + 0.415980i \(0.863439\pi\)
\(32\) 0 0
\(33\) −29.3278 40.7444i −0.154706 0.214930i
\(34\) 0 0
\(35\) −22.5718 −0.109010
\(36\) 0 0
\(37\) 104.519 0.464400 0.232200 0.972668i \(-0.425408\pi\)
0.232200 + 0.972668i \(0.425408\pi\)
\(38\) 0 0
\(39\) 105.858 + 147.067i 0.434639 + 0.603834i
\(40\) 0 0
\(41\) 257.630i 0.981344i −0.871344 0.490672i \(-0.836751\pi\)
0.871344 0.490672i \(-0.163249\pi\)
\(42\) 0 0
\(43\) 267.467i 0.948567i 0.880372 + 0.474284i \(0.157293\pi\)
−0.880372 + 0.474284i \(0.842707\pi\)
\(44\) 0 0
\(45\) 82.5601 + 27.6362i 0.273496 + 0.0915501i
\(46\) 0 0
\(47\) −430.734 −1.33679 −0.668394 0.743807i \(-0.733018\pi\)
−0.668394 + 0.743807i \(0.733018\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) −546.076 + 393.065i −1.49933 + 1.07922i
\(52\) 0 0
\(53\) 121.797i 0.315662i 0.987466 + 0.157831i \(0.0504501\pi\)
−0.987466 + 0.157831i \(0.949550\pi\)
\(54\) 0 0
\(55\) 31.1535i 0.0763770i
\(56\) 0 0
\(57\) −282.574 + 203.396i −0.656629 + 0.472641i
\(58\) 0 0
\(59\) −861.356 −1.90066 −0.950331 0.311243i \(-0.899255\pi\)
−0.950331 + 0.311243i \(0.899255\pi\)
\(60\) 0 0
\(61\) 502.028 1.05374 0.526870 0.849946i \(-0.323366\pi\)
0.526870 + 0.849946i \(0.323366\pi\)
\(62\) 0 0
\(63\) 179.225 + 59.9939i 0.358417 + 0.119976i
\(64\) 0 0
\(65\) 112.448i 0.214577i
\(66\) 0 0
\(67\) 162.918i 0.297069i −0.988907 0.148534i \(-0.952544\pi\)
0.988907 0.148534i \(-0.0474555\pi\)
\(68\) 0 0
\(69\) 47.3661 + 65.8047i 0.0826407 + 0.114811i
\(70\) 0 0
\(71\) 616.070 1.02978 0.514888 0.857258i \(-0.327834\pi\)
0.514888 + 0.857258i \(0.327834\pi\)
\(72\) 0 0
\(73\) 719.577 1.15370 0.576850 0.816850i \(-0.304282\pi\)
0.576850 + 0.816850i \(0.304282\pi\)
\(74\) 0 0
\(75\) 347.884 + 483.308i 0.535602 + 0.744101i
\(76\) 0 0
\(77\) 67.6295i 0.100092i
\(78\) 0 0
\(79\) 250.539i 0.356807i 0.983957 + 0.178404i \(0.0570933\pi\)
−0.983957 + 0.178404i \(0.942907\pi\)
\(80\) 0 0
\(81\) −582.091 438.874i −0.798479 0.602023i
\(82\) 0 0
\(83\) 376.936 0.498484 0.249242 0.968441i \(-0.419819\pi\)
0.249242 + 0.968441i \(0.419819\pi\)
\(84\) 0 0
\(85\) 417.534 0.532799
\(86\) 0 0
\(87\) −369.712 + 266.118i −0.455601 + 0.327941i
\(88\) 0 0
\(89\) 870.360i 1.03661i 0.855197 + 0.518303i \(0.173436\pi\)
−0.855197 + 0.518303i \(0.826564\pi\)
\(90\) 0 0
\(91\) 244.108i 0.281203i
\(92\) 0 0
\(93\) −605.586 + 435.900i −0.675229 + 0.486029i
\(94\) 0 0
\(95\) 216.058 0.233338
\(96\) 0 0
\(97\) 44.3227 0.0463947 0.0231974 0.999731i \(-0.492615\pi\)
0.0231974 + 0.999731i \(0.492615\pi\)
\(98\) 0 0
\(99\) 82.8031 247.366i 0.0840609 0.251123i
\(100\) 0 0
\(101\) 1280.12i 1.26116i 0.776124 + 0.630580i \(0.217183\pi\)
−0.776124 + 0.630580i \(0.782817\pi\)
\(102\) 0 0
\(103\) 1178.72i 1.12760i −0.825912 0.563799i \(-0.809339\pi\)
0.825912 0.563799i \(-0.190661\pi\)
\(104\) 0 0
\(105\) −68.5185 95.1913i −0.0636831 0.0884735i
\(106\) 0 0
\(107\) −447.212 −0.404052 −0.202026 0.979380i \(-0.564753\pi\)
−0.202026 + 0.979380i \(0.564753\pi\)
\(108\) 0 0
\(109\) 1220.46 1.07247 0.536235 0.844069i \(-0.319846\pi\)
0.536235 + 0.844069i \(0.319846\pi\)
\(110\) 0 0
\(111\) 317.275 + 440.784i 0.271301 + 0.376913i
\(112\) 0 0
\(113\) 2045.19i 1.70262i −0.524666 0.851308i \(-0.675810\pi\)
0.524666 0.851308i \(-0.324190\pi\)
\(114\) 0 0
\(115\) 50.3147i 0.0407989i
\(116\) 0 0
\(117\) −298.877 + 892.865i −0.236164 + 0.705516i
\(118\) 0 0
\(119\) 906.402 0.698233
\(120\) 0 0
\(121\) −1237.66 −0.929871
\(122\) 0 0
\(123\) 1086.49 782.056i 0.796470 0.573298i
\(124\) 0 0
\(125\) 772.609i 0.552834i
\(126\) 0 0
\(127\) 1565.99i 1.09416i −0.837079 0.547082i \(-0.815739\pi\)
0.837079 0.547082i \(-0.184261\pi\)
\(128\) 0 0
\(129\) −1127.98 + 811.918i −0.769869 + 0.554150i
\(130\) 0 0
\(131\) 723.018 0.482217 0.241108 0.970498i \(-0.422489\pi\)
0.241108 + 0.970498i \(0.422489\pi\)
\(132\) 0 0
\(133\) 469.030 0.305790
\(134\) 0 0
\(135\) 134.069 + 432.069i 0.0854726 + 0.275456i
\(136\) 0 0
\(137\) 938.113i 0.585025i −0.956262 0.292513i \(-0.905509\pi\)
0.956262 0.292513i \(-0.0944913\pi\)
\(138\) 0 0
\(139\) 1335.12i 0.814703i −0.913271 0.407352i \(-0.866452\pi\)
0.913271 0.407352i \(-0.133548\pi\)
\(140\) 0 0
\(141\) −1307.53 1816.52i −0.780947 1.08495i
\(142\) 0 0
\(143\) −336.916 −0.197023
\(144\) 0 0
\(145\) 282.685 0.161901
\(146\) 0 0
\(147\) −148.743 206.646i −0.0834567 0.115945i
\(148\) 0 0
\(149\) 57.1263i 0.0314092i 0.999877 + 0.0157046i \(0.00499914\pi\)
−0.999877 + 0.0157046i \(0.995001\pi\)
\(150\) 0 0
\(151\) 1891.83i 1.01957i −0.860302 0.509785i \(-0.829725\pi\)
0.860302 0.509785i \(-0.170275\pi\)
\(152\) 0 0
\(153\) −3315.31 1109.77i −1.75181 0.586401i
\(154\) 0 0
\(155\) 463.035 0.239948
\(156\) 0 0
\(157\) 3169.39 1.61112 0.805558 0.592517i \(-0.201866\pi\)
0.805558 + 0.592517i \(0.201866\pi\)
\(158\) 0 0
\(159\) −513.649 + 369.723i −0.256195 + 0.184409i
\(160\) 0 0
\(161\) 109.226i 0.0534670i
\(162\) 0 0
\(163\) 21.6682i 0.0104122i −0.999986 0.00520609i \(-0.998343\pi\)
0.999986 0.00520609i \(-0.00165716\pi\)
\(164\) 0 0
\(165\) −131.382 + 94.5688i −0.0619885 + 0.0446192i
\(166\) 0 0
\(167\) 1060.81 0.491544 0.245772 0.969328i \(-0.420958\pi\)
0.245772 + 0.969328i \(0.420958\pi\)
\(168\) 0 0
\(169\) −980.903 −0.446474
\(170\) 0 0
\(171\) −1715.55 574.263i −0.767202 0.256813i
\(172\) 0 0
\(173\) 1286.23i 0.565260i −0.959229 0.282630i \(-0.908793\pi\)
0.959229 0.282630i \(-0.0912069\pi\)
\(174\) 0 0
\(175\) 802.216i 0.346525i
\(176\) 0 0
\(177\) −2614.71 3632.56i −1.11036 1.54260i
\(178\) 0 0
\(179\) 3303.96 1.37961 0.689804 0.723996i \(-0.257697\pi\)
0.689804 + 0.723996i \(0.257697\pi\)
\(180\) 0 0
\(181\) −435.130 −0.178690 −0.0893452 0.996001i \(-0.528477\pi\)
−0.0893452 + 0.996001i \(0.528477\pi\)
\(182\) 0 0
\(183\) 1523.94 + 2117.18i 0.615591 + 0.855228i
\(184\) 0 0
\(185\) 337.026i 0.133939i
\(186\) 0 0
\(187\) 1251.01i 0.489214i
\(188\) 0 0
\(189\) 291.043 + 937.956i 0.112012 + 0.360985i
\(190\) 0 0
\(191\) −5111.52 −1.93642 −0.968212 0.250132i \(-0.919526\pi\)
−0.968212 + 0.250132i \(0.919526\pi\)
\(192\) 0 0
\(193\) −799.596 −0.298219 −0.149109 0.988821i \(-0.547641\pi\)
−0.149109 + 0.988821i \(0.547641\pi\)
\(194\) 0 0
\(195\) 474.224 341.345i 0.174153 0.125355i
\(196\) 0 0
\(197\) 1801.06i 0.651372i 0.945478 + 0.325686i \(0.105595\pi\)
−0.945478 + 0.325686i \(0.894405\pi\)
\(198\) 0 0
\(199\) 3923.64i 1.39769i −0.715274 0.698844i \(-0.753698\pi\)
0.715274 0.698844i \(-0.246302\pi\)
\(200\) 0 0
\(201\) 687.067 494.550i 0.241104 0.173547i
\(202\) 0 0
\(203\) 613.665 0.212172
\(204\) 0 0
\(205\) −830.741 −0.283032
\(206\) 0 0
\(207\) −133.732 + 399.510i −0.0449035 + 0.134144i
\(208\) 0 0
\(209\) 647.351i 0.214250i
\(210\) 0 0
\(211\) 1152.54i 0.376040i −0.982165 0.188020i \(-0.939793\pi\)
0.982165 0.188020i \(-0.0602070\pi\)
\(212\) 0 0
\(213\) 1870.13 + 2598.13i 0.601592 + 0.835778i
\(214\) 0 0
\(215\) 862.461 0.273579
\(216\) 0 0
\(217\) 1005.18 0.314452
\(218\) 0 0
\(219\) 2184.33 + 3034.64i 0.673988 + 0.936356i
\(220\) 0 0
\(221\) 4515.51i 1.37442i
\(222\) 0 0
\(223\) 3981.61i 1.19564i 0.801629 + 0.597822i \(0.203967\pi\)
−0.801629 + 0.597822i \(0.796033\pi\)
\(224\) 0 0
\(225\) −982.205 + 2934.23i −0.291024 + 0.869403i
\(226\) 0 0
\(227\) 4563.49 1.33432 0.667158 0.744917i \(-0.267511\pi\)
0.667158 + 0.744917i \(0.267511\pi\)
\(228\) 0 0
\(229\) 6076.65 1.75352 0.876760 0.480928i \(-0.159700\pi\)
0.876760 + 0.480928i \(0.159700\pi\)
\(230\) 0 0
\(231\) −285.211 + 205.294i −0.0812360 + 0.0584735i
\(232\) 0 0
\(233\) 5496.46i 1.54543i −0.634753 0.772715i \(-0.718898\pi\)
0.634753 0.772715i \(-0.281102\pi\)
\(234\) 0 0
\(235\) 1388.92i 0.385546i
\(236\) 0 0
\(237\) −1056.59 + 760.529i −0.289589 + 0.208446i
\(238\) 0 0
\(239\) 136.634 0.0369796 0.0184898 0.999829i \(-0.494114\pi\)
0.0184898 + 0.999829i \(0.494114\pi\)
\(240\) 0 0
\(241\) 1063.48 0.284251 0.142126 0.989849i \(-0.454606\pi\)
0.142126 + 0.989849i \(0.454606\pi\)
\(242\) 0 0
\(243\) 83.8647 3787.07i 0.0221396 0.999755i
\(244\) 0 0
\(245\) 158.003i 0.0412018i
\(246\) 0 0
\(247\) 2336.61i 0.601923i
\(248\) 0 0
\(249\) 1144.22 + 1589.64i 0.291213 + 0.404575i
\(250\) 0 0
\(251\) −4726.05 −1.18847 −0.594235 0.804292i \(-0.702545\pi\)
−0.594235 + 0.804292i \(0.702545\pi\)
\(252\) 0 0
\(253\) −150.752 −0.0374614
\(254\) 0 0
\(255\) 1267.46 + 1760.85i 0.311260 + 0.432426i
\(256\) 0 0
\(257\) 6394.09i 1.55196i 0.630760 + 0.775978i \(0.282743\pi\)
−0.630760 + 0.775978i \(0.717257\pi\)
\(258\) 0 0
\(259\) 731.633i 0.175527i
\(260\) 0 0
\(261\) −2244.58 751.350i −0.532321 0.178189i
\(262\) 0 0
\(263\) −4276.02 −1.00255 −0.501275 0.865288i \(-0.667135\pi\)
−0.501275 + 0.865288i \(0.667135\pi\)
\(264\) 0 0
\(265\) 392.740 0.0910407
\(266\) 0 0
\(267\) −3670.53 + 2642.04i −0.841322 + 0.605582i
\(268\) 0 0
\(269\) 5377.74i 1.21891i 0.792821 + 0.609455i \(0.208612\pi\)
−0.792821 + 0.609455i \(0.791388\pi\)
\(270\) 0 0
\(271\) 383.121i 0.0858780i −0.999078 0.0429390i \(-0.986328\pi\)
0.999078 0.0429390i \(-0.0136721\pi\)
\(272\) 0 0
\(273\) 1029.47 741.009i 0.228228 0.164278i
\(274\) 0 0
\(275\) −1107.21 −0.242791
\(276\) 0 0
\(277\) 7849.35 1.70260 0.851302 0.524675i \(-0.175813\pi\)
0.851302 + 0.524675i \(0.175813\pi\)
\(278\) 0 0
\(279\) −3676.60 1230.71i −0.788933 0.264087i
\(280\) 0 0
\(281\) 823.141i 0.174749i −0.996176 0.0873745i \(-0.972152\pi\)
0.996176 0.0873745i \(-0.0278477\pi\)
\(282\) 0 0
\(283\) 2493.25i 0.523704i 0.965108 + 0.261852i \(0.0843332\pi\)
−0.965108 + 0.261852i \(0.915667\pi\)
\(284\) 0 0
\(285\) 655.862 + 911.174i 0.136315 + 0.189380i
\(286\) 0 0
\(287\) −1803.41 −0.370913
\(288\) 0 0
\(289\) −11853.6 −2.41271
\(290\) 0 0
\(291\) 134.545 + 186.920i 0.0271036 + 0.0376545i
\(292\) 0 0
\(293\) 3055.99i 0.609327i −0.952460 0.304663i \(-0.901456\pi\)
0.952460 0.304663i \(-0.0985440\pi\)
\(294\) 0 0
\(295\) 2777.48i 0.548174i
\(296\) 0 0
\(297\) 1294.56 401.695i 0.252923 0.0784805i
\(298\) 0 0
\(299\) 544.140 0.105246
\(300\) 0 0
\(301\) 1872.27 0.358525
\(302\) 0 0
\(303\) −5398.62 + 3885.92i −1.02357 + 0.736766i
\(304\) 0 0
\(305\) 1618.81i 0.303911i
\(306\) 0 0
\(307\) 10524.4i 1.95654i 0.207324 + 0.978272i \(0.433525\pi\)
−0.207324 + 0.978272i \(0.566475\pi\)
\(308\) 0 0
\(309\) 4970.96 3578.09i 0.915173 0.658740i
\(310\) 0 0
\(311\) 4222.89 0.769962 0.384981 0.922925i \(-0.374208\pi\)
0.384981 + 0.922925i \(0.374208\pi\)
\(312\) 0 0
\(313\) 4384.59 0.791795 0.395897 0.918295i \(-0.370434\pi\)
0.395897 + 0.918295i \(0.370434\pi\)
\(314\) 0 0
\(315\) 193.453 577.921i 0.0346027 0.103372i
\(316\) 0 0
\(317\) 5473.01i 0.969701i −0.874597 0.484850i \(-0.838874\pi\)
0.874597 0.484850i \(-0.161126\pi\)
\(318\) 0 0
\(319\) 846.976i 0.148657i
\(320\) 0 0
\(321\) −1357.54 1886.01i −0.236046 0.327933i
\(322\) 0 0
\(323\) −8676.11 −1.49459
\(324\) 0 0
\(325\) 3996.48 0.682107
\(326\) 0 0
\(327\) 3704.81 + 5147.02i 0.626534 + 0.870430i
\(328\) 0 0
\(329\) 3015.14i 0.505258i
\(330\) 0 0
\(331\) 6909.33i 1.14735i 0.819085 + 0.573673i \(0.194482\pi\)
−0.819085 + 0.573673i \(0.805518\pi\)
\(332\) 0 0
\(333\) −895.785 + 2676.06i −0.147414 + 0.440383i
\(334\) 0 0
\(335\) −525.337 −0.0856783
\(336\) 0 0
\(337\) −4014.83 −0.648967 −0.324483 0.945891i \(-0.605190\pi\)
−0.324483 + 0.945891i \(0.605190\pi\)
\(338\) 0 0
\(339\) 8625.11 6208.34i 1.38186 0.994663i
\(340\) 0 0
\(341\) 1387.34i 0.220319i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) 212.190 152.734i 0.0331129 0.0238346i
\(346\) 0 0
\(347\) −11080.9 −1.71428 −0.857142 0.515081i \(-0.827762\pi\)
−0.857142 + 0.515081i \(0.827762\pi\)
\(348\) 0 0
\(349\) −4933.75 −0.756726 −0.378363 0.925657i \(-0.623513\pi\)
−0.378363 + 0.925657i \(0.623513\pi\)
\(350\) 0 0
\(351\) −4672.71 + 1449.92i −0.710572 + 0.220486i
\(352\) 0 0
\(353\) 5003.24i 0.754378i −0.926136 0.377189i \(-0.876891\pi\)
0.926136 0.377189i \(-0.123109\pi\)
\(354\) 0 0
\(355\) 1986.55i 0.297000i
\(356\) 0 0
\(357\) 2751.45 + 3822.53i 0.407906 + 0.566694i
\(358\) 0 0
\(359\) 7436.01 1.09320 0.546599 0.837395i \(-0.315922\pi\)
0.546599 + 0.837395i \(0.315922\pi\)
\(360\) 0 0
\(361\) 2369.43 0.345449
\(362\) 0 0
\(363\) −3757.01 5219.53i −0.543228 0.754694i
\(364\) 0 0
\(365\) 2320.31i 0.332741i
\(366\) 0 0
\(367\) 7661.86i 1.08977i −0.838511 0.544885i \(-0.816573\pi\)
0.838511 0.544885i \(-0.183427\pi\)
\(368\) 0 0
\(369\) 6596.27 + 2208.03i 0.930591 + 0.311506i
\(370\) 0 0
\(371\) 852.577 0.119309
\(372\) 0 0
\(373\) −10560.6 −1.46597 −0.732986 0.680243i \(-0.761874\pi\)
−0.732986 + 0.680243i \(0.761874\pi\)
\(374\) 0 0
\(375\) 3258.29 2345.31i 0.448687 0.322964i
\(376\) 0 0
\(377\) 3057.15i 0.417643i
\(378\) 0 0
\(379\) 6155.60i 0.834280i 0.908842 + 0.417140i \(0.136968\pi\)
−0.908842 + 0.417140i \(0.863032\pi\)
\(380\) 0 0
\(381\) 6604.17 4753.67i 0.888036 0.639207i
\(382\) 0 0
\(383\) 1370.99 0.182909 0.0914545 0.995809i \(-0.470848\pi\)
0.0914545 + 0.995809i \(0.470848\pi\)
\(384\) 0 0
\(385\) 218.074 0.0288678
\(386\) 0 0
\(387\) −6848.14 2292.34i −0.899510 0.301102i
\(388\) 0 0
\(389\) 12583.7i 1.64015i 0.572259 + 0.820073i \(0.306067\pi\)
−0.572259 + 0.820073i \(0.693933\pi\)
\(390\) 0 0
\(391\) 2020.46i 0.261327i
\(392\) 0 0
\(393\) 2194.78 + 3049.15i 0.281710 + 0.391373i
\(394\) 0 0
\(395\) 807.874 0.102908
\(396\) 0 0
\(397\) −10127.6 −1.28033 −0.640164 0.768238i \(-0.721134\pi\)
−0.640164 + 0.768238i \(0.721134\pi\)
\(398\) 0 0
\(399\) 1423.78 + 1978.02i 0.178641 + 0.248183i
\(400\) 0 0
\(401\) 12873.2i 1.60314i −0.597902 0.801569i \(-0.703999\pi\)
0.597902 0.801569i \(-0.296001\pi\)
\(402\) 0 0
\(403\) 5007.60i 0.618973i
\(404\) 0 0
\(405\) −1415.17 + 1876.98i −0.173631 + 0.230291i
\(406\) 0 0
\(407\) −1009.79 −0.122982
\(408\) 0 0
\(409\) 8017.83 0.969331 0.484665 0.874700i \(-0.338941\pi\)
0.484665 + 0.874700i \(0.338941\pi\)
\(410\) 0 0
\(411\) 3956.27 2847.71i 0.474813 0.341770i
\(412\) 0 0
\(413\) 6029.49i 0.718382i
\(414\) 0 0
\(415\) 1215.45i 0.143769i
\(416\) 0 0
\(417\) 5630.56 4052.87i 0.661223 0.475947i
\(418\) 0 0
\(419\) 2005.37 0.233816 0.116908 0.993143i \(-0.462702\pi\)
0.116908 + 0.993143i \(0.462702\pi\)
\(420\) 0 0
\(421\) −12564.8 −1.45456 −0.727282 0.686338i \(-0.759217\pi\)
−0.727282 + 0.686338i \(0.759217\pi\)
\(422\) 0 0
\(423\) 3691.63 11028.4i 0.424334 1.26765i
\(424\) 0 0
\(425\) 14839.4i 1.69369i
\(426\) 0 0
\(427\) 3514.20i 0.398276i
\(428\) 0 0
\(429\) −1022.74 1420.86i −0.115101 0.159907i
\(430\) 0 0
\(431\) 16505.8 1.84468 0.922339 0.386381i \(-0.126275\pi\)
0.922339 + 0.386381i \(0.126275\pi\)
\(432\) 0 0
\(433\) −7420.32 −0.823551 −0.411776 0.911285i \(-0.635091\pi\)
−0.411776 + 0.911285i \(0.635091\pi\)
\(434\) 0 0
\(435\) 858.111 + 1192.15i 0.0945822 + 0.131401i
\(436\) 0 0
\(437\) 1045.51i 0.114448i
\(438\) 0 0
\(439\) 13783.5i 1.49852i −0.662275 0.749261i \(-0.730409\pi\)
0.662275 0.749261i \(-0.269591\pi\)
\(440\) 0 0
\(441\) 419.957 1254.58i 0.0453468 0.135469i
\(442\) 0 0
\(443\) 3398.98 0.364538 0.182269 0.983249i \(-0.441656\pi\)
0.182269 + 0.983249i \(0.441656\pi\)
\(444\) 0 0
\(445\) 2806.52 0.298970
\(446\) 0 0
\(447\) −240.917 + 173.411i −0.0254921 + 0.0183492i
\(448\) 0 0
\(449\) 3161.50i 0.332295i 0.986101 + 0.166148i \(0.0531328\pi\)
−0.986101 + 0.166148i \(0.946867\pi\)
\(450\) 0 0
\(451\) 2489.06i 0.259878i
\(452\) 0 0
\(453\) 7978.35 5742.80i 0.827496 0.595630i
\(454\) 0 0
\(455\) −787.138 −0.0811024
\(456\) 0 0
\(457\) −12742.8 −1.30434 −0.652169 0.758074i \(-0.726141\pi\)
−0.652169 + 0.758074i \(0.726141\pi\)
\(458\) 0 0
\(459\) −5383.71 17350.3i −0.547473 1.76436i
\(460\) 0 0
\(461\) 11859.1i 1.19812i −0.800705 0.599058i \(-0.795542\pi\)
0.800705 0.599058i \(-0.204458\pi\)
\(462\) 0 0
\(463\) 14654.9i 1.47100i −0.677527 0.735498i \(-0.736948\pi\)
0.677527 0.735498i \(-0.263052\pi\)
\(464\) 0 0
\(465\) 1405.58 + 1952.74i 0.140177 + 0.194744i
\(466\) 0 0
\(467\) 11520.9 1.14159 0.570795 0.821093i \(-0.306635\pi\)
0.570795 + 0.821093i \(0.306635\pi\)
\(468\) 0 0
\(469\) −1140.43 −0.112281
\(470\) 0 0
\(471\) 9620.94 + 13366.2i 0.941209 + 1.30760i
\(472\) 0 0
\(473\) 2584.10i 0.251199i
\(474\) 0 0
\(475\) 7678.84i 0.741746i
\(476\) 0 0
\(477\) −3118.44 1043.87i −0.299337 0.100200i
\(478\) 0 0
\(479\) 11359.8 1.08360 0.541799 0.840508i \(-0.317744\pi\)
0.541799 + 0.840508i \(0.317744\pi\)
\(480\) 0 0
\(481\) 3644.85 0.345511
\(482\) 0 0
\(483\) 460.633 331.563i 0.0433944 0.0312352i
\(484\) 0 0
\(485\) 142.921i 0.0133808i
\(486\) 0 0
\(487\) 3608.22i 0.335737i 0.985809 + 0.167869i \(0.0536884\pi\)
−0.985809 + 0.167869i \(0.946312\pi\)
\(488\) 0 0
\(489\) 91.3805 65.7755i 0.00845065 0.00608276i
\(490\) 0 0
\(491\) 6484.43 0.596004 0.298002 0.954565i \(-0.403680\pi\)
0.298002 + 0.954565i \(0.403680\pi\)
\(492\) 0 0
\(493\) −11351.6 −1.03702
\(494\) 0 0
\(495\) −797.642 267.003i −0.0724270 0.0242442i
\(496\) 0 0
\(497\) 4312.49i 0.389219i
\(498\) 0 0
\(499\) 6222.23i 0.558207i −0.960261 0.279104i \(-0.909963\pi\)
0.960261 0.279104i \(-0.0900373\pi\)
\(500\) 0 0
\(501\) 3220.17 + 4473.71i 0.287159 + 0.398943i
\(502\) 0 0
\(503\) −14360.8 −1.27300 −0.636498 0.771279i \(-0.719617\pi\)
−0.636498 + 0.771279i \(0.719617\pi\)
\(504\) 0 0
\(505\) 4127.82 0.363734
\(506\) 0 0
\(507\) −2977.61 4136.72i −0.260829 0.362364i
\(508\) 0 0
\(509\) 16261.1i 1.41603i −0.706196 0.708016i \(-0.749590\pi\)
0.706196 0.708016i \(-0.250410\pi\)
\(510\) 0 0
\(511\) 5037.04i 0.436057i
\(512\) 0 0
\(513\) −2785.87 8978.14i −0.239764 0.772699i
\(514\) 0 0
\(515\) −3800.84 −0.325213
\(516\) 0 0
\(517\) 4161.47 0.354007
\(518\) 0 0
\(519\) 5424.35 3904.44i 0.458772 0.330223i
\(520\) 0 0
\(521\) 11086.3i 0.932245i 0.884720 + 0.466122i \(0.154349\pi\)
−0.884720 + 0.466122i \(0.845651\pi\)
\(522\) 0 0
\(523\) 2411.61i 0.201630i −0.994905 0.100815i \(-0.967855\pi\)
0.994905 0.100815i \(-0.0321450\pi\)
\(524\) 0 0
\(525\) 3383.15 2435.19i 0.281244 0.202439i
\(526\) 0 0
\(527\) −18593.8 −1.53692
\(528\) 0 0
\(529\) −11923.5 −0.979989
\(530\) 0 0
\(531\) 7382.30 22053.8i 0.603323 1.80236i
\(532\) 0 0
\(533\) 8984.23i 0.730113i
\(534\) 0 0
\(535\) 1442.05i 0.116534i
\(536\) 0 0
\(537\) 10029.4 + 13933.7i 0.805963 + 1.11971i
\(538\) 0 0
\(539\) 473.406 0.0378313
\(540\) 0 0
\(541\) −24027.6 −1.90948 −0.954738 0.297449i \(-0.903864\pi\)
−0.954738 + 0.297449i \(0.903864\pi\)
\(542\) 0 0
\(543\) −1320.87 1835.06i −0.104390 0.145027i
\(544\) 0 0
\(545\) 3935.45i 0.309314i
\(546\) 0 0
\(547\) 15384.7i 1.20256i 0.799038 + 0.601281i \(0.205343\pi\)
−0.799038 + 0.601281i \(0.794657\pi\)
\(548\) 0 0
\(549\) −4302.66 + 12853.7i −0.334486 + 0.999243i
\(550\) 0 0
\(551\) −5874.02 −0.454159
\(552\) 0 0
\(553\) 1753.77 0.134861
\(554\) 0 0
\(555\) 1421.33 1023.07i 0.108706 0.0782466i
\(556\) 0 0
\(557\) 19292.2i 1.46757i −0.679381 0.733785i \(-0.737752\pi\)
0.679381 0.733785i \(-0.262248\pi\)
\(558\) 0 0
\(559\) 9327.28i 0.705728i
\(560\) 0 0
\(561\) 5275.84 3797.54i 0.397052 0.285797i
\(562\) 0 0
\(563\) 2682.90 0.200836 0.100418 0.994945i \(-0.467982\pi\)
0.100418 + 0.994945i \(0.467982\pi\)
\(564\) 0 0
\(565\) −6594.82 −0.491055
\(566\) 0 0
\(567\) −3072.12 + 4074.64i −0.227543 + 0.301797i
\(568\) 0 0
\(569\) 264.723i 0.0195040i −0.999952 0.00975200i \(-0.996896\pi\)
0.999952 0.00975200i \(-0.00310421\pi\)
\(570\) 0 0
\(571\) 3749.99i 0.274838i 0.990513 + 0.137419i \(0.0438807\pi\)
−0.990513 + 0.137419i \(0.956119\pi\)
\(572\) 0 0
\(573\) −15516.4 21556.6i −1.13125 1.57162i
\(574\) 0 0
\(575\) 1788.22 0.129693
\(576\) 0 0
\(577\) 5633.19 0.406435 0.203217 0.979134i \(-0.434860\pi\)
0.203217 + 0.979134i \(0.434860\pi\)
\(578\) 0 0
\(579\) −2427.23 3372.10i −0.174218 0.242038i
\(580\) 0 0
\(581\) 2638.55i 0.188409i
\(582\) 0 0
\(583\) 1176.72i 0.0835932i
\(584\) 0 0
\(585\) 2879.08 + 963.744i 0.203479 + 0.0681127i
\(586\) 0 0
\(587\) 13846.9 0.973632 0.486816 0.873505i \(-0.338158\pi\)
0.486816 + 0.873505i \(0.338158\pi\)
\(588\) 0 0
\(589\) −9621.60 −0.673092
\(590\) 0 0
\(591\) −7595.55 + 5467.26i −0.528662 + 0.380530i
\(592\) 0 0
\(593\) 960.169i 0.0664914i −0.999447 0.0332457i \(-0.989416\pi\)
0.999447 0.0332457i \(-0.0105844\pi\)
\(594\) 0 0
\(595\) 2922.74i 0.201379i
\(596\) 0 0
\(597\) 16547.0 11910.5i 1.13438 0.816525i
\(598\) 0 0
\(599\) 10833.3 0.738961 0.369480 0.929239i \(-0.379536\pi\)
0.369480 + 0.929239i \(0.379536\pi\)
\(600\) 0 0
\(601\) 12910.5 0.876255 0.438127 0.898913i \(-0.355642\pi\)
0.438127 + 0.898913i \(0.355642\pi\)
\(602\) 0 0
\(603\) 4171.29 + 1396.30i 0.281705 + 0.0942979i
\(604\) 0 0
\(605\) 3990.89i 0.268186i
\(606\) 0 0
\(607\) 8211.17i 0.549063i 0.961578 + 0.274531i \(0.0885228\pi\)
−0.961578 + 0.274531i \(0.911477\pi\)
\(608\) 0 0
\(609\) 1862.83 + 2587.98i 0.123950 + 0.172201i
\(610\) 0 0
\(611\) −15020.8 −0.994561
\(612\) 0 0
\(613\) −1109.90 −0.0731295 −0.0365647 0.999331i \(-0.511642\pi\)
−0.0365647 + 0.999331i \(0.511642\pi\)
\(614\) 0 0
\(615\) −2521.78 3503.45i −0.165346 0.229712i
\(616\) 0 0
\(617\) 19329.7i 1.26124i 0.776092 + 0.630620i \(0.217199\pi\)
−0.776092 + 0.630620i \(0.782801\pi\)
\(618\) 0 0
\(619\) 9754.29i 0.633373i 0.948530 + 0.316687i \(0.102570\pi\)
−0.948530 + 0.316687i \(0.897430\pi\)
\(620\) 0 0
\(621\) −2090.79 + 648.761i −0.135106 + 0.0419225i
\(622\) 0 0
\(623\) 6092.52 0.391800
\(624\) 0 0
\(625\) 11834.0 0.757374
\(626\) 0 0
\(627\) 2730.05 1965.08i 0.173888 0.125164i
\(628\) 0 0
\(629\) 13533.7i 0.857911i
\(630\) 0 0
\(631\) 22206.3i 1.40098i −0.713663 0.700489i \(-0.752965\pi\)
0.713663 0.700489i \(-0.247035\pi\)
\(632\) 0 0
\(633\) 4860.58 3498.64i 0.305198 0.219681i
\(634\) 0 0
\(635\) −5049.59 −0.315570
\(636\) 0 0
\(637\) −1708.76 −0.106285
\(638\) 0 0
\(639\) −5280.06 + 15773.6i −0.326879 + 0.976518i
\(640\) 0 0
\(641\) 13749.7i 0.847237i 0.905841 + 0.423618i \(0.139240\pi\)
−0.905841 + 0.423618i \(0.860760\pi\)
\(642\) 0 0
\(643\) 12621.8i 0.774116i 0.922055 + 0.387058i \(0.126509\pi\)
−0.922055 + 0.387058i \(0.873491\pi\)
\(644\) 0 0
\(645\) 2618.07 + 3637.22i 0.159824 + 0.222040i
\(646\) 0 0
\(647\) −25525.1 −1.55100 −0.775499 0.631349i \(-0.782502\pi\)
−0.775499 + 0.631349i \(0.782502\pi\)
\(648\) 0 0
\(649\) 8321.86 0.503331
\(650\) 0 0
\(651\) 3051.30 + 4239.10i 0.183702 + 0.255213i
\(652\) 0 0
\(653\) 17846.3i 1.06950i 0.845012 + 0.534748i \(0.179593\pi\)
−0.845012 + 0.534748i \(0.820407\pi\)
\(654\) 0 0
\(655\) 2331.41i 0.139077i
\(656\) 0 0
\(657\) −6167.17 + 18423.8i −0.366216 + 1.09403i
\(658\) 0 0
\(659\) −6650.82 −0.393140 −0.196570 0.980490i \(-0.562980\pi\)
−0.196570 + 0.980490i \(0.562980\pi\)
\(660\) 0 0
\(661\) 24355.4 1.43315 0.716577 0.697508i \(-0.245708\pi\)
0.716577 + 0.697508i \(0.245708\pi\)
\(662\) 0 0
\(663\) −19043.1 + 13707.2i −1.11549 + 0.802930i
\(664\) 0 0
\(665\) 1512.41i 0.0881935i
\(666\) 0 0
\(667\) 1367.92i 0.0794092i
\(668\) 0 0
\(669\) −16791.5 + 12086.5i −0.970398 + 0.698491i
\(670\) 0 0
\(671\) −4850.27 −0.279050
\(672\) 0 0
\(673\) −7268.47 −0.416313 −0.208157 0.978095i \(-0.566746\pi\)
−0.208157 + 0.978095i \(0.566746\pi\)
\(674\) 0 0
\(675\) −15356.0 + 4764.88i −0.875633 + 0.271704i
\(676\) 0 0
\(677\) 1498.86i 0.0850898i −0.999095 0.0425449i \(-0.986453\pi\)
0.999095 0.0425449i \(-0.0135466\pi\)
\(678\) 0 0
\(679\) 310.259i 0.0175355i
\(680\) 0 0
\(681\) 13852.8 + 19245.4i 0.779503 + 1.08295i
\(682\) 0 0
\(683\) 26696.0 1.49560 0.747799 0.663925i \(-0.231110\pi\)
0.747799 + 0.663925i \(0.231110\pi\)
\(684\) 0 0
\(685\) −3024.99 −0.168728
\(686\) 0 0
\(687\) 18446.1 + 25626.8i 1.02440 + 1.42318i
\(688\) 0 0
\(689\) 4247.37i 0.234850i
\(690\) 0 0
\(691\) 7008.81i 0.385858i −0.981213 0.192929i \(-0.938201\pi\)
0.981213 0.192929i \(-0.0617987\pi\)
\(692\) 0 0
\(693\) −1731.56 579.622i −0.0949156 0.0317720i
\(694\) 0 0
\(695\) −4305.17 −0.234970
\(696\) 0 0
\(697\) 33359.5 1.81289
\(698\) 0 0
\(699\) 23180.0 16684.9i 1.25429 0.902836i
\(700\) 0 0
\(701\) 26041.0i 1.40308i −0.712632 0.701538i \(-0.752497\pi\)
0.712632 0.701538i \(-0.247503\pi\)
\(702\) 0 0
\(703\) 7003.21i 0.375720i
\(704\) 0 0
\(705\) −5857.45 + 4216.18i −0.312914 + 0.225235i
\(706\) 0 0
\(707\) 8960.87 0.476674
\(708\) 0 0
\(709\) 14314.4 0.758236 0.379118 0.925348i \(-0.376227\pi\)
0.379118 + 0.925348i \(0.376227\pi\)
\(710\) 0 0
\(711\) −6414.70 2147.25i −0.338354 0.113261i
\(712\) 0 0
\(713\) 2240.64i 0.117689i
\(714\) 0 0
\(715\) 1086.40i 0.0568240i
\(716\) 0 0
\(717\) 414.763 + 576.221i 0.0216034 + 0.0300131i
\(718\) 0 0
\(719\) 2775.39 0.143956 0.0719781 0.997406i \(-0.477069\pi\)
0.0719781 + 0.997406i \(0.477069\pi\)
\(720\) 0 0
\(721\) −8251.04 −0.426192
\(722\) 0 0
\(723\) 3228.26 + 4484.95i 0.166059 + 0.230702i
\(724\) 0 0
\(725\) 10046.8i 0.514659i
\(726\) 0 0
\(727\) 37751.6i 1.92590i 0.269684 + 0.962949i \(0.413081\pi\)
−0.269684 + 0.962949i \(0.586919\pi\)
\(728\) 0 0
\(729\) 16225.6 11142.3i 0.824347 0.566085i
\(730\) 0 0
\(731\) −34633.3 −1.75234
\(732\) 0 0
\(733\) 3282.13 0.165387 0.0826933 0.996575i \(-0.473648\pi\)
0.0826933 + 0.996575i \(0.473648\pi\)
\(734\) 0 0
\(735\) −666.339 + 479.630i −0.0334398 + 0.0240699i
\(736\) 0 0
\(737\) 1574.01i 0.0786694i
\(738\) 0 0
\(739\) 23720.7i 1.18076i 0.807125 + 0.590380i \(0.201022\pi\)
−0.807125 + 0.590380i \(0.798978\pi\)
\(740\) 0 0
\(741\) −9854.09 + 7092.96i −0.488528 + 0.351642i
\(742\) 0 0
\(743\) 16992.0 0.838998 0.419499 0.907756i \(-0.362206\pi\)
0.419499 + 0.907756i \(0.362206\pi\)
\(744\) 0 0
\(745\) 184.207 0.00905880
\(746\) 0 0
\(747\) −3230.55 + 9650.94i −0.158233 + 0.472703i
\(748\) 0 0
\(749\) 3130.48i 0.152717i
\(750\) 0 0
\(751\) 30346.4i 1.47451i −0.675615 0.737255i \(-0.736122\pi\)
0.675615 0.737255i \(-0.263878\pi\)
\(752\) 0 0
\(753\) −14346.3 19931.0i −0.694300 0.964576i
\(754\) 0 0
\(755\) −6100.31 −0.294057
\(756\) 0 0
\(757\) 2235.09 0.107313 0.0536565 0.998559i \(-0.482912\pi\)
0.0536565 + 0.998559i \(0.482912\pi\)
\(758\) 0 0
\(759\) −457.621 635.762i −0.0218848 0.0304041i
\(760\) 0 0
\(761\) 15663.8i 0.746138i 0.927804 + 0.373069i \(0.121695\pi\)
−0.927804 + 0.373069i \(0.878305\pi\)
\(762\) 0 0
\(763\) 8543.25i 0.405356i
\(764\) 0 0
\(765\) −3578.50 + 10690.4i −0.169125 + 0.505244i
\(766\) 0 0
\(767\) −30037.7 −1.41408
\(768\) 0 0
\(769\) 28687.6 1.34525 0.672627 0.739982i \(-0.265166\pi\)
0.672627 + 0.739982i \(0.265166\pi\)
\(770\) 0 0
\(771\) −26965.5 + 19409.8i −1.25959 + 0.906647i
\(772\) 0 0
\(773\) 874.384i 0.0406849i −0.999793 0.0203424i \(-0.993524\pi\)
0.999793 0.0203424i \(-0.00647564\pi\)
\(774\) 0 0
\(775\) 16456.5i 0.762757i
\(776\) 0 0
\(777\) 3085.48 2220.93i 0.142460 0.102542i
\(778\) 0 0
\(779\) 17262.3 0.793949
\(780\) 0 0
\(781\) −5952.07 −0.272704
\(782\) 0 0
\(783\) −3644.95 11746.7i −0.166360 0.536136i
\(784\) 0 0
\(785\) 10219.9i 0.464666i
\(786\) 0 0
\(787\) 25149.6i 1.13912i 0.821951 + 0.569559i \(0.192886\pi\)
−0.821951 + 0.569559i \(0.807114\pi\)
\(788\) 0 0
\(789\) −12980.2 18033.1i −0.585686 0.813681i
\(790\) 0 0
\(791\) −14316.4 −0.643528
\(792\) 0 0
\(793\) 17507.0 0.783975
\(794\) 0 0
\(795\) 1192.19 + 1656.28i 0.0531857 + 0.0738898i
\(796\) 0 0
\(797\) 11126.2i 0.494491i 0.968953 + 0.247246i \(0.0795255\pi\)
−0.968953 + 0.247246i \(0.920475\pi\)
\(798\) 0 0
\(799\) 55774.1i 2.46952i