Properties

Label 336.4.h.a.239.1
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 152 x^{10} + 8222 x^{8} + 194132 x^{6} + 1882697 x^{4} + 5152508 x^{2} + 4008004\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7}\cdot 3^{2}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.1
Root \(4.19902i\) of defining polynomial
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.a.239.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.90731 - 1.70829i) q^{3} -20.5781i q^{5} +7.00000i q^{7} +(21.1635 + 16.7663i) q^{9} +O(q^{10})\) \(q+(-4.90731 - 1.70829i) q^{3} -20.5781i q^{5} +7.00000i q^{7} +(21.1635 + 16.7663i) q^{9} +63.9252 q^{11} +56.5700 q^{13} +(-35.1534 + 100.983i) q^{15} -81.6568i q^{17} +22.4109i q^{19} +(11.9580 - 34.3512i) q^{21} +114.603 q^{23} -298.458 q^{25} +(-75.2141 - 118.431i) q^{27} -62.7161i q^{29} -88.6606i q^{31} +(-313.701 - 109.203i) q^{33} +144.047 q^{35} -51.3374 q^{37} +(-277.607 - 96.6381i) q^{39} -165.933i q^{41} +393.078i q^{43} +(345.018 - 435.504i) q^{45} -164.421 q^{47} -49.0000 q^{49} +(-139.494 + 400.716i) q^{51} -231.927i q^{53} -1315.46i q^{55} +(38.2843 - 109.977i) q^{57} +13.4719 q^{59} +665.952 q^{61} +(-117.364 + 148.144i) q^{63} -1164.10i q^{65} -837.255i q^{67} +(-562.392 - 195.775i) q^{69} -175.804 q^{71} +301.790 q^{73} +(1464.63 + 509.854i) q^{75} +447.477i q^{77} +1049.12i q^{79} +(166.785 + 709.664i) q^{81} -1263.02 q^{83} -1680.34 q^{85} +(-107.137 + 307.768i) q^{87} -780.001i q^{89} +395.990i q^{91} +(-151.458 + 435.085i) q^{93} +461.173 q^{95} -780.280 q^{97} +(1352.88 + 1071.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 76q^{9} + O(q^{10}) \) \( 12q + 76q^{9} - 96q^{13} + 112q^{21} - 1068q^{25} - 832q^{33} - 720q^{37} + 392q^{45} - 588q^{49} - 2336q^{57} + 432q^{61} - 424q^{69} + 1656q^{73} - 868q^{81} - 1464q^{85} + 696q^{93} - 6264q^{97} + O(q^{100}) \)

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
\(3\) −4.90731 1.70829i −0.944413 0.328761i
\(4\) 0 0
\(5\) 20.5781i 1.84056i −0.391259 0.920281i \(-0.627960\pi\)
0.391259 0.920281i \(-0.372040\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) 21.1635 + 16.7663i 0.783832 + 0.620973i
\(10\) 0 0
\(11\) 63.9252 1.75220 0.876099 0.482131i \(-0.160137\pi\)
0.876099 + 0.482131i \(0.160137\pi\)
\(12\) 0 0
\(13\) 56.5700 1.20690 0.603450 0.797401i \(-0.293792\pi\)
0.603450 + 0.797401i \(0.293792\pi\)
\(14\) 0 0
\(15\) −35.1534 + 100.983i −0.605105 + 1.73825i
\(16\) 0 0
\(17\) 81.6568i 1.16498i −0.812837 0.582491i \(-0.802078\pi\)
0.812837 0.582491i \(-0.197922\pi\)
\(18\) 0 0
\(19\) 22.4109i 0.270600i 0.990805 + 0.135300i \(0.0431998\pi\)
−0.990805 + 0.135300i \(0.956800\pi\)
\(20\) 0 0
\(21\) 11.9580 34.3512i 0.124260 0.356955i
\(22\) 0 0
\(23\) 114.603 1.03897 0.519486 0.854479i \(-0.326124\pi\)
0.519486 + 0.854479i \(0.326124\pi\)
\(24\) 0 0
\(25\) −298.458 −2.38767
\(26\) 0 0
\(27\) −75.2141 118.431i −0.536110 0.844148i
\(28\) 0 0
\(29\) 62.7161i 0.401589i −0.979633 0.200795i \(-0.935648\pi\)
0.979633 0.200795i \(-0.0643524\pi\)
\(30\) 0 0
\(31\) 88.6606i 0.513675i −0.966455 0.256837i \(-0.917320\pi\)
0.966455 0.256837i \(-0.0826805\pi\)
\(32\) 0 0
\(33\) −313.701 109.203i −1.65480 0.576055i
\(34\) 0 0
\(35\) 144.047 0.695667
\(36\) 0 0
\(37\) −51.3374 −0.228103 −0.114052 0.993475i \(-0.536383\pi\)
−0.114052 + 0.993475i \(0.536383\pi\)
\(38\) 0 0
\(39\) −277.607 96.6381i −1.13981 0.396782i
\(40\) 0 0
\(41\) 165.933i 0.632057i −0.948750 0.316029i \(-0.897650\pi\)
0.948750 0.316029i \(-0.102350\pi\)
\(42\) 0 0
\(43\) 393.078i 1.39404i 0.717051 + 0.697021i \(0.245491\pi\)
−0.717051 + 0.697021i \(0.754509\pi\)
\(44\) 0 0
\(45\) 345.018 435.504i 1.14294 1.44269i
\(46\) 0 0
\(47\) −164.421 −0.510282 −0.255141 0.966904i \(-0.582122\pi\)
−0.255141 + 0.966904i \(0.582122\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) −139.494 + 400.716i −0.383001 + 1.10022i
\(52\) 0 0
\(53\) 231.927i 0.601087i −0.953768 0.300543i \(-0.902832\pi\)
0.953768 0.300543i \(-0.0971680\pi\)
\(54\) 0 0
\(55\) 1315.46i 3.22503i
\(56\) 0 0
\(57\) 38.2843 109.977i 0.0889628 0.255558i
\(58\) 0 0
\(59\) 13.4719 0.0297269 0.0148634 0.999890i \(-0.495269\pi\)
0.0148634 + 0.999890i \(0.495269\pi\)
\(60\) 0 0
\(61\) 665.952 1.39781 0.698905 0.715215i \(-0.253671\pi\)
0.698905 + 0.715215i \(0.253671\pi\)
\(62\) 0 0
\(63\) −117.364 + 148.144i −0.234706 + 0.296261i
\(64\) 0 0
\(65\) 1164.10i 2.22137i
\(66\) 0 0
\(67\) 837.255i 1.52667i −0.646002 0.763336i \(-0.723560\pi\)
0.646002 0.763336i \(-0.276440\pi\)
\(68\) 0 0
\(69\) −562.392 195.775i −0.981218 0.341573i
\(70\) 0 0
\(71\) −175.804 −0.293860 −0.146930 0.989147i \(-0.546939\pi\)
−0.146930 + 0.989147i \(0.546939\pi\)
\(72\) 0 0
\(73\) 301.790 0.483861 0.241931 0.970294i \(-0.422219\pi\)
0.241931 + 0.970294i \(0.422219\pi\)
\(74\) 0 0
\(75\) 1464.63 + 509.854i 2.25494 + 0.784972i
\(76\) 0 0
\(77\) 447.477i 0.662269i
\(78\) 0 0
\(79\) 1049.12i 1.49411i 0.664762 + 0.747055i \(0.268533\pi\)
−0.664762 + 0.747055i \(0.731467\pi\)
\(80\) 0 0
\(81\) 166.785 + 709.664i 0.228786 + 0.973477i
\(82\) 0 0
\(83\) −1263.02 −1.67030 −0.835149 0.550023i \(-0.814619\pi\)
−0.835149 + 0.550023i \(0.814619\pi\)
\(84\) 0 0
\(85\) −1680.34 −2.14422
\(86\) 0 0
\(87\) −107.137 + 307.768i −0.132027 + 0.379266i
\(88\) 0 0
\(89\) 780.001i 0.928988i −0.885576 0.464494i \(-0.846236\pi\)
0.885576 0.464494i \(-0.153764\pi\)
\(90\) 0 0
\(91\) 395.990i 0.456165i
\(92\) 0 0
\(93\) −151.458 + 435.085i −0.168876 + 0.485121i
\(94\) 0 0
\(95\) 461.173 0.498056
\(96\) 0 0
\(97\) −780.280 −0.816757 −0.408378 0.912813i \(-0.633906\pi\)
−0.408378 + 0.912813i \(0.633906\pi\)
\(98\) 0 0
\(99\) 1352.88 + 1071.79i 1.37343 + 1.08807i
\(100\) 0 0
\(101\) 47.4348i 0.0467321i 0.999727 + 0.0233661i \(0.00743832\pi\)
−0.999727 + 0.0233661i \(0.992562\pi\)
\(102\) 0 0
\(103\) 24.0000i 0.0229591i 0.999934 + 0.0114796i \(0.00365414\pi\)
−0.999934 + 0.0114796i \(0.996346\pi\)
\(104\) 0 0
\(105\) −706.883 246.074i −0.656997 0.228708i
\(106\) 0 0
\(107\) −432.110 −0.390408 −0.195204 0.980763i \(-0.562537\pi\)
−0.195204 + 0.980763i \(0.562537\pi\)
\(108\) 0 0
\(109\) 323.801 0.284537 0.142268 0.989828i \(-0.454560\pi\)
0.142268 + 0.989828i \(0.454560\pi\)
\(110\) 0 0
\(111\) 251.929 + 87.6994i 0.215424 + 0.0749915i
\(112\) 0 0
\(113\) 1972.82i 1.64236i 0.570667 + 0.821181i \(0.306685\pi\)
−0.570667 + 0.821181i \(0.693315\pi\)
\(114\) 0 0
\(115\) 2358.31i 1.91229i
\(116\) 0 0
\(117\) 1197.22 + 948.467i 0.946007 + 0.749451i
\(118\) 0 0
\(119\) 571.598 0.440322
\(120\) 0 0
\(121\) 2755.44 2.07020
\(122\) 0 0
\(123\) −283.462 + 814.284i −0.207796 + 0.596923i
\(124\) 0 0
\(125\) 3569.44i 2.55408i
\(126\) 0 0
\(127\) 1694.77i 1.18415i −0.805883 0.592074i \(-0.798309\pi\)
0.805883 0.592074i \(-0.201691\pi\)
\(128\) 0 0
\(129\) 671.492 1928.96i 0.458306 1.31655i
\(130\) 0 0
\(131\) −1240.10 −0.827084 −0.413542 0.910485i \(-0.635709\pi\)
−0.413542 + 0.910485i \(0.635709\pi\)
\(132\) 0 0
\(133\) −156.876 −0.102277
\(134\) 0 0
\(135\) −2437.08 + 1547.76i −1.55371 + 0.986743i
\(136\) 0 0
\(137\) 1698.55i 1.05925i −0.848233 0.529623i \(-0.822334\pi\)
0.848233 0.529623i \(-0.177666\pi\)
\(138\) 0 0
\(139\) 1234.84i 0.753508i 0.926313 + 0.376754i \(0.122960\pi\)
−0.926313 + 0.376754i \(0.877040\pi\)
\(140\) 0 0
\(141\) 806.864 + 280.879i 0.481917 + 0.167761i
\(142\) 0 0
\(143\) 3616.25 2.11473
\(144\) 0 0
\(145\) −1290.58 −0.739149
\(146\) 0 0
\(147\) 240.458 + 83.7063i 0.134916 + 0.0469659i
\(148\) 0 0
\(149\) 2080.66i 1.14399i 0.820257 + 0.571995i \(0.193830\pi\)
−0.820257 + 0.571995i \(0.806170\pi\)
\(150\) 0 0
\(151\) 1209.99i 0.652102i −0.945352 0.326051i \(-0.894282\pi\)
0.945352 0.326051i \(-0.105718\pi\)
\(152\) 0 0
\(153\) 1369.08 1728.14i 0.723422 0.913150i
\(154\) 0 0
\(155\) −1824.47 −0.945450
\(156\) 0 0
\(157\) 3193.69 1.62347 0.811734 0.584027i \(-0.198524\pi\)
0.811734 + 0.584027i \(0.198524\pi\)
\(158\) 0 0
\(159\) −396.199 + 1138.14i −0.197614 + 0.567674i
\(160\) 0 0
\(161\) 802.220i 0.392694i
\(162\) 0 0
\(163\) 3417.95i 1.64242i −0.570624 0.821211i \(-0.693299\pi\)
0.570624 0.821211i \(-0.306701\pi\)
\(164\) 0 0
\(165\) −2247.19 + 6455.38i −1.06026 + 3.04576i
\(166\) 0 0
\(167\) −626.793 −0.290435 −0.145218 0.989400i \(-0.546388\pi\)
−0.145218 + 0.989400i \(0.546388\pi\)
\(168\) 0 0
\(169\) 1003.16 0.456606
\(170\) 0 0
\(171\) −375.746 + 474.291i −0.168035 + 0.212105i
\(172\) 0 0
\(173\) 1310.07i 0.575740i −0.957669 0.287870i \(-0.907053\pi\)
0.957669 0.287870i \(-0.0929472\pi\)
\(174\) 0 0
\(175\) 2089.21i 0.902453i
\(176\) 0 0
\(177\) −66.1106 23.0139i −0.0280745 0.00977304i
\(178\) 0 0
\(179\) 3826.17 1.59766 0.798830 0.601557i \(-0.205453\pi\)
0.798830 + 0.601557i \(0.205453\pi\)
\(180\) 0 0
\(181\) 305.944 0.125639 0.0628195 0.998025i \(-0.479991\pi\)
0.0628195 + 0.998025i \(0.479991\pi\)
\(182\) 0 0
\(183\) −3268.03 1137.64i −1.32011 0.459545i
\(184\) 0 0
\(185\) 1056.43i 0.419838i
\(186\) 0 0
\(187\) 5219.93i 2.04128i
\(188\) 0 0
\(189\) 829.015 526.499i 0.319058 0.202631i
\(190\) 0 0
\(191\) −4263.10 −1.61501 −0.807505 0.589861i \(-0.799183\pi\)
−0.807505 + 0.589861i \(0.799183\pi\)
\(192\) 0 0
\(193\) −3859.28 −1.43936 −0.719681 0.694305i \(-0.755712\pi\)
−0.719681 + 0.694305i \(0.755712\pi\)
\(194\) 0 0
\(195\) −1988.63 + 5712.62i −0.730301 + 2.09789i
\(196\) 0 0
\(197\) 2956.09i 1.06910i 0.845137 + 0.534550i \(0.179519\pi\)
−0.845137 + 0.534550i \(0.820481\pi\)
\(198\) 0 0
\(199\) 3601.86i 1.28306i 0.767098 + 0.641530i \(0.221700\pi\)
−0.767098 + 0.641530i \(0.778300\pi\)
\(200\) 0 0
\(201\) −1430.28 + 4108.67i −0.501910 + 1.44181i
\(202\) 0 0
\(203\) 439.013 0.151786
\(204\) 0 0
\(205\) −3414.58 −1.16334
\(206\) 0 0
\(207\) 2425.39 + 1921.46i 0.814379 + 0.645173i
\(208\) 0 0
\(209\) 1432.62i 0.474145i
\(210\) 0 0
\(211\) 1210.52i 0.394957i −0.980307 0.197478i \(-0.936725\pi\)
0.980307 0.197478i \(-0.0632752\pi\)
\(212\) 0 0
\(213\) 862.724 + 300.324i 0.277525 + 0.0966097i
\(214\) 0 0
\(215\) 8088.79 2.56582
\(216\) 0 0
\(217\) 620.624 0.194151
\(218\) 0 0
\(219\) −1480.98 515.546i −0.456965 0.159075i
\(220\) 0 0
\(221\) 4619.33i 1.40602i
\(222\) 0 0
\(223\) 4434.61i 1.33168i 0.746096 + 0.665838i \(0.231926\pi\)
−0.746096 + 0.665838i \(0.768074\pi\)
\(224\) 0 0
\(225\) −6316.41 5004.03i −1.87153 1.48267i
\(226\) 0 0
\(227\) 1003.61 0.293444 0.146722 0.989178i \(-0.453128\pi\)
0.146722 + 0.989178i \(0.453128\pi\)
\(228\) 0 0
\(229\) 3572.10 1.03079 0.515396 0.856952i \(-0.327645\pi\)
0.515396 + 0.856952i \(0.327645\pi\)
\(230\) 0 0
\(231\) 764.421 2195.91i 0.217728 0.625455i
\(232\) 0 0
\(233\) 5058.93i 1.42241i −0.702985 0.711204i \(-0.748150\pi\)
0.702985 0.711204i \(-0.251850\pi\)
\(234\) 0 0
\(235\) 3383.47i 0.939205i
\(236\) 0 0
\(237\) 1792.20 5148.34i 0.491205 1.41106i
\(238\) 0 0
\(239\) −859.569 −0.232640 −0.116320 0.993212i \(-0.537110\pi\)
−0.116320 + 0.993212i \(0.537110\pi\)
\(240\) 0 0
\(241\) −1789.17 −0.478218 −0.239109 0.970993i \(-0.576855\pi\)
−0.239109 + 0.970993i \(0.576855\pi\)
\(242\) 0 0
\(243\) 393.847 3767.46i 0.103972 0.994580i
\(244\) 0 0
\(245\) 1008.33i 0.262937i
\(246\) 0 0
\(247\) 1267.78i 0.326587i
\(248\) 0 0
\(249\) 6198.05 + 2157.61i 1.57745 + 0.549129i
\(250\) 0 0
\(251\) 3442.21 0.865618 0.432809 0.901486i \(-0.357522\pi\)
0.432809 + 0.901486i \(0.357522\pi\)
\(252\) 0 0
\(253\) 7326.01 1.82048
\(254\) 0 0
\(255\) 8245.97 + 2870.52i 2.02503 + 0.704936i
\(256\) 0 0
\(257\) 3520.64i 0.854519i −0.904129 0.427259i \(-0.859479\pi\)
0.904129 0.427259i \(-0.140521\pi\)
\(258\) 0 0
\(259\) 359.362i 0.0862149i
\(260\) 0 0
\(261\) 1051.51 1327.29i 0.249376 0.314779i
\(262\) 0 0
\(263\) −5073.74 −1.18958 −0.594792 0.803880i \(-0.702765\pi\)
−0.594792 + 0.803880i \(0.702765\pi\)
\(264\) 0 0
\(265\) −4772.61 −1.10634
\(266\) 0 0
\(267\) −1332.47 + 3827.71i −0.305415 + 0.877349i
\(268\) 0 0
\(269\) 4866.95i 1.10313i 0.834130 + 0.551567i \(0.185970\pi\)
−0.834130 + 0.551567i \(0.814030\pi\)
\(270\) 0 0
\(271\) 1174.35i 0.263234i −0.991301 0.131617i \(-0.957983\pi\)
0.991301 0.131617i \(-0.0420169\pi\)
\(272\) 0 0
\(273\) 676.467 1943.25i 0.149969 0.430808i
\(274\) 0 0
\(275\) −19079.0 −4.18367
\(276\) 0 0
\(277\) 4246.00 0.921001 0.460501 0.887659i \(-0.347670\pi\)
0.460501 + 0.887659i \(0.347670\pi\)
\(278\) 0 0
\(279\) 1486.51 1876.37i 0.318978 0.402635i
\(280\) 0 0
\(281\) 3654.37i 0.775806i −0.921700 0.387903i \(-0.873200\pi\)
0.921700 0.387903i \(-0.126800\pi\)
\(282\) 0 0
\(283\) 9256.48i 1.94431i −0.234331 0.972157i \(-0.575290\pi\)
0.234331 0.972157i \(-0.424710\pi\)
\(284\) 0 0
\(285\) −2263.12 787.818i −0.470371 0.163741i
\(286\) 0 0
\(287\) 1161.53 0.238895
\(288\) 0 0
\(289\) −1754.84 −0.357182
\(290\) 0 0
\(291\) 3829.08 + 1332.95i 0.771356 + 0.268518i
\(292\) 0 0
\(293\) 310.759i 0.0619615i 0.999520 + 0.0309807i \(0.00986305\pi\)
−0.999520 + 0.0309807i \(0.990137\pi\)
\(294\) 0 0
\(295\) 277.225i 0.0547142i
\(296\) 0 0
\(297\) −4808.08 7570.71i −0.939371 1.47912i
\(298\) 0 0
\(299\) 6483.08 1.25393
\(300\) 0 0
\(301\) −2751.54 −0.526898
\(302\) 0 0
\(303\) 81.0326 232.778i 0.0153637 0.0441344i
\(304\) 0 0
\(305\) 13704.0i 2.57275i
\(306\) 0 0
\(307\) 2309.44i 0.429338i 0.976687 + 0.214669i \(0.0688673\pi\)
−0.976687 + 0.214669i \(0.931133\pi\)
\(308\) 0 0
\(309\) 40.9990 117.775i 0.00754806 0.0216829i
\(310\) 0 0
\(311\) −1750.76 −0.319216 −0.159608 0.987180i \(-0.551023\pi\)
−0.159608 + 0.987180i \(0.551023\pi\)
\(312\) 0 0
\(313\) −4130.16 −0.745847 −0.372924 0.927862i \(-0.621645\pi\)
−0.372924 + 0.927862i \(0.621645\pi\)
\(314\) 0 0
\(315\) 3048.53 + 2415.12i 0.545286 + 0.431990i
\(316\) 0 0
\(317\) 3470.62i 0.614919i 0.951561 + 0.307460i \(0.0994789\pi\)
−0.951561 + 0.307460i \(0.900521\pi\)
\(318\) 0 0
\(319\) 4009.14i 0.703664i
\(320\) 0 0
\(321\) 2120.50 + 738.171i 0.368707 + 0.128351i
\(322\) 0 0
\(323\) 1830.00 0.315244
\(324\) 0 0
\(325\) −16883.8 −2.88167
\(326\) 0 0
\(327\) −1588.99 553.147i −0.268720 0.0935447i
\(328\) 0 0
\(329\) 1150.95i 0.192868i
\(330\) 0 0
\(331\) 6625.10i 1.10015i 0.835116 + 0.550073i \(0.185400\pi\)
−0.835116 + 0.550073i \(0.814600\pi\)
\(332\) 0 0
\(333\) −1086.48 860.737i −0.178795 0.141646i
\(334\) 0 0
\(335\) −17229.1 −2.80993
\(336\) 0 0
\(337\) −1193.87 −0.192979 −0.0964897 0.995334i \(-0.530761\pi\)
−0.0964897 + 0.995334i \(0.530761\pi\)
\(338\) 0 0
\(339\) 3370.15 9681.23i 0.539945 1.55107i
\(340\) 0 0
\(341\) 5667.65i 0.900060i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) −4028.68 + 11573.0i −0.628687 + 1.80599i
\(346\) 0 0
\(347\) 9431.38 1.45909 0.729543 0.683935i \(-0.239733\pi\)
0.729543 + 0.683935i \(0.239733\pi\)
\(348\) 0 0
\(349\) −4294.01 −0.658604 −0.329302 0.944225i \(-0.606813\pi\)
−0.329302 + 0.944225i \(0.606813\pi\)
\(350\) 0 0
\(351\) −4254.86 6699.62i −0.647031 1.01880i
\(352\) 0 0
\(353\) 5205.64i 0.784896i 0.919774 + 0.392448i \(0.128372\pi\)
−0.919774 + 0.392448i \(0.871628\pi\)
\(354\) 0 0
\(355\) 3617.71i 0.540867i
\(356\) 0 0
\(357\) −2805.01 976.456i −0.415846 0.144761i
\(358\) 0 0
\(359\) −1696.11 −0.249352 −0.124676 0.992197i \(-0.539789\pi\)
−0.124676 + 0.992197i \(0.539789\pi\)
\(360\) 0 0
\(361\) 6356.75 0.926776
\(362\) 0 0
\(363\) −13521.8 4707.09i −1.95512 0.680601i
\(364\) 0 0
\(365\) 6210.27i 0.890576i
\(366\) 0 0
\(367\) 6924.96i 0.984959i 0.870324 + 0.492479i \(0.163909\pi\)
−0.870324 + 0.492479i \(0.836091\pi\)
\(368\) 0 0
\(369\) 2782.07 3511.71i 0.392490 0.495427i
\(370\) 0 0
\(371\) 1623.49 0.227189
\(372\) 0 0
\(373\) 10377.2 1.44052 0.720258 0.693707i \(-0.244024\pi\)
0.720258 + 0.693707i \(0.244024\pi\)
\(374\) 0 0
\(375\) 6097.65 17516.4i 0.839683 2.41211i
\(376\) 0 0
\(377\) 3547.85i 0.484678i
\(378\) 0 0
\(379\) 10635.6i 1.44146i 0.693215 + 0.720730i \(0.256193\pi\)
−0.693215 + 0.720730i \(0.743807\pi\)
\(380\) 0 0
\(381\) −2895.17 + 8316.79i −0.389302 + 1.11833i
\(382\) 0 0
\(383\) 8069.79 1.07662 0.538312 0.842745i \(-0.319062\pi\)
0.538312 + 0.842745i \(0.319062\pi\)
\(384\) 0 0
\(385\) 9208.22 1.21895
\(386\) 0 0
\(387\) −6590.44 + 8318.89i −0.865661 + 1.09269i
\(388\) 0 0
\(389\) 6771.67i 0.882615i 0.897356 + 0.441307i \(0.145485\pi\)
−0.897356 + 0.441307i \(0.854515\pi\)
\(390\) 0 0
\(391\) 9358.10i 1.21038i
\(392\) 0 0
\(393\) 6085.56 + 2118.45i 0.781109 + 0.271913i
\(394\) 0 0
\(395\) 21588.8 2.75000
\(396\) 0 0
\(397\) −357.176 −0.0451541 −0.0225770 0.999745i \(-0.507187\pi\)
−0.0225770 + 0.999745i \(0.507187\pi\)
\(398\) 0 0
\(399\) 769.840 + 267.990i 0.0965920 + 0.0336248i
\(400\) 0 0
\(401\) 7785.56i 0.969557i −0.874637 0.484779i \(-0.838900\pi\)
0.874637 0.484779i \(-0.161100\pi\)
\(402\) 0 0
\(403\) 5015.53i 0.619954i
\(404\) 0 0
\(405\) 14603.5 3432.12i 1.79174 0.421095i
\(406\) 0 0
\(407\) −3281.76 −0.399682
\(408\) 0 0
\(409\) 11301.2 1.36628 0.683139 0.730288i \(-0.260614\pi\)
0.683139 + 0.730288i \(0.260614\pi\)
\(410\) 0 0
\(411\) −2901.61 + 8335.30i −0.348239 + 1.00037i
\(412\) 0 0
\(413\) 94.3030i 0.0112357i
\(414\) 0 0
\(415\) 25990.6i 3.07429i
\(416\) 0 0
\(417\) 2109.46 6059.74i 0.247724 0.711623i
\(418\) 0 0
\(419\) 1022.70 0.119241 0.0596207 0.998221i \(-0.481011\pi\)
0.0596207 + 0.998221i \(0.481011\pi\)
\(420\) 0 0
\(421\) 4810.60 0.556898 0.278449 0.960451i \(-0.410180\pi\)
0.278449 + 0.960451i \(0.410180\pi\)
\(422\) 0 0
\(423\) −3479.71 2756.72i −0.399975 0.316871i
\(424\) 0 0
\(425\) 24371.2i 2.78159i
\(426\) 0 0
\(427\) 4661.66i 0.528322i
\(428\) 0 0
\(429\) −17746.1 6177.61i −1.99718 0.695240i
\(430\) 0 0
\(431\) −189.365 −0.0211633 −0.0105816 0.999944i \(-0.503368\pi\)
−0.0105816 + 0.999944i \(0.503368\pi\)
\(432\) 0 0
\(433\) 6284.67 0.697510 0.348755 0.937214i \(-0.386604\pi\)
0.348755 + 0.937214i \(0.386604\pi\)
\(434\) 0 0
\(435\) 6333.27 + 2204.68i 0.698062 + 0.243004i
\(436\) 0 0
\(437\) 2568.35i 0.281146i
\(438\) 0 0
\(439\) 14240.9i 1.54825i 0.633035 + 0.774123i \(0.281809\pi\)
−0.633035 + 0.774123i \(0.718191\pi\)
\(440\) 0 0
\(441\) −1037.01 821.547i −0.111976 0.0887104i
\(442\) 0 0
\(443\) −4560.34 −0.489093 −0.244547 0.969638i \(-0.578639\pi\)
−0.244547 + 0.969638i \(0.578639\pi\)
\(444\) 0 0
\(445\) −16050.9 −1.70986
\(446\) 0 0
\(447\) 3554.38 10210.5i 0.376099 1.08040i
\(448\) 0 0
\(449\) 7453.68i 0.783432i 0.920086 + 0.391716i \(0.128118\pi\)
−0.920086 + 0.391716i \(0.871882\pi\)
\(450\) 0 0
\(451\) 10607.3i 1.10749i
\(452\) 0 0
\(453\) −2067.01 + 5937.79i −0.214386 + 0.615854i
\(454\) 0 0
\(455\) 8148.72 0.839600
\(456\) 0 0
\(457\) −5124.39 −0.524527 −0.262264 0.964996i \(-0.584469\pi\)
−0.262264 + 0.964996i \(0.584469\pi\)
\(458\) 0 0
\(459\) −9670.67 + 6141.75i −0.983417 + 0.624558i
\(460\) 0 0
\(461\) 2810.43i 0.283936i −0.989871 0.141968i \(-0.954657\pi\)
0.989871 0.141968i \(-0.0453431\pi\)
\(462\) 0 0
\(463\) 9716.28i 0.975278i 0.873045 + 0.487639i \(0.162142\pi\)
−0.873045 + 0.487639i \(0.837858\pi\)
\(464\) 0 0
\(465\) 8953.23 + 3116.72i 0.892895 + 0.310827i
\(466\) 0 0
\(467\) 1200.36 0.118942 0.0594709 0.998230i \(-0.481059\pi\)
0.0594709 + 0.998230i \(0.481059\pi\)
\(468\) 0 0
\(469\) 5860.78 0.577027
\(470\) 0 0
\(471\) −15672.5 5455.76i −1.53322 0.533733i
\(472\) 0 0
\(473\) 25127.6i 2.44264i
\(474\) 0 0
\(475\) 6688.70i 0.646103i
\(476\) 0 0
\(477\) 3888.54 4908.38i 0.373258 0.471151i
\(478\) 0 0
\(479\) 8213.87 0.783510 0.391755 0.920070i \(-0.371868\pi\)
0.391755 + 0.920070i \(0.371868\pi\)
\(480\) 0 0
\(481\) −2904.16 −0.275298
\(482\) 0 0
\(483\) 1370.43 3936.74i 0.129103 0.370866i
\(484\) 0 0
\(485\) 16056.7i 1.50329i
\(486\) 0 0
\(487\) 1756.97i 0.163482i 0.996654 + 0.0817411i \(0.0260481\pi\)
−0.996654 + 0.0817411i \(0.973952\pi\)
\(488\) 0 0
\(489\) −5838.87 + 16773.0i −0.539965 + 1.55113i
\(490\) 0 0
\(491\) 3491.44 0.320910 0.160455 0.987043i \(-0.448704\pi\)
0.160455 + 0.987043i \(0.448704\pi\)
\(492\) 0 0
\(493\) −5121.20 −0.467844
\(494\) 0 0
\(495\) 22055.3 27839.7i 2.00265 2.52788i
\(496\) 0 0
\(497\) 1230.63i 0.111069i
\(498\) 0 0
\(499\) 2052.58i 0.184140i −0.995753 0.0920702i \(-0.970652\pi\)
0.995753 0.0920702i \(-0.0293484\pi\)
\(500\) 0 0
\(501\) 3075.87 + 1070.75i 0.274291 + 0.0954838i
\(502\) 0 0
\(503\) −11456.0 −1.01550 −0.507752 0.861503i \(-0.669523\pi\)
−0.507752 + 0.861503i \(0.669523\pi\)
\(504\) 0 0
\(505\) 976.119 0.0860133
\(506\) 0 0
\(507\) −4922.84 1713.70i −0.431225 0.150114i
\(508\) 0 0
\(509\) 8286.73i 0.721616i −0.932640 0.360808i \(-0.882501\pi\)
0.932640 0.360808i \(-0.117499\pi\)
\(510\) 0 0
\(511\) 2112.53i 0.182882i
\(512\) 0 0
\(513\) 2654.13 1685.61i 0.228427 0.145071i
\(514\) 0 0
\(515\) 493.874 0.0422576
\(516\) 0 0
\(517\) −10510.6 −0.894115
\(518\) 0 0
\(519\) −2237.99 + 6428.94i −0.189281 + 0.543737i
\(520\) 0 0
\(521\) 4530.21i 0.380944i 0.981693 + 0.190472i \(0.0610019\pi\)
−0.981693 + 0.190472i \(0.938998\pi\)
\(522\) 0 0
\(523\) 6344.62i 0.530460i −0.964185 0.265230i \(-0.914552\pi\)
0.964185 0.265230i \(-0.0854480\pi\)
\(524\) 0 0
\(525\) −3568.98 + 10252.4i −0.296691 + 0.852288i
\(526\) 0 0
\(527\) −7239.74 −0.598422
\(528\) 0 0
\(529\) 966.807 0.0794614
\(530\) 0 0
\(531\) 285.111 + 225.873i 0.0233009 + 0.0184596i
\(532\) 0 0
\(533\) 9386.82i 0.762830i
\(534\) 0 0
\(535\) 8892.01i 0.718570i
\(536\) 0 0
\(537\) −18776.2 6536.21i −1.50885 0.525248i
\(538\) 0 0
\(539\) −3132.34 −0.250314
\(540\) 0 0
\(541\) 11240.5 0.893285 0.446643 0.894713i \(-0.352620\pi\)
0.446643 + 0.894713i \(0.352620\pi\)
\(542\) 0 0
\(543\) −1501.37 522.642i −0.118655 0.0413052i
\(544\) 0 0
\(545\) 6663.21i 0.523708i
\(546\) 0 0
\(547\) 910.522i 0.0711721i −0.999367 0.0355860i \(-0.988670\pi\)
0.999367 0.0355860i \(-0.0113298\pi\)
\(548\) 0 0
\(549\) 14093.8 + 11165.5i 1.09565 + 0.868001i
\(550\) 0 0
\(551\) 1405.52 0.108670
\(552\) 0 0
\(553\) −7343.81 −0.564721
\(554\) 0 0
\(555\) 1804.69 5184.22i 0.138026 0.396501i
\(556\) 0 0
\(557\) 1315.08i 0.100039i −0.998748 0.0500194i \(-0.984072\pi\)
0.998748 0.0500194i \(-0.0159283\pi\)
\(558\) 0 0
\(559\) 22236.4i 1.68247i
\(560\) 0 0
\(561\) −8917.17 + 25615.8i −0.671093 + 1.92781i
\(562\) 0 0
\(563\) −18890.6 −1.41411 −0.707055 0.707159i \(-0.749977\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(564\) 0 0
\(565\) 40596.8 3.02287
\(566\) 0 0
\(567\) −4967.65 + 1167.50i −0.367940 + 0.0864731i
\(568\) 0 0
\(569\) 10534.7i 0.776166i 0.921624 + 0.388083i \(0.126863\pi\)
−0.921624 + 0.388083i \(0.873137\pi\)
\(570\) 0 0
\(571\) 5473.47i 0.401151i 0.979678 + 0.200576i \(0.0642813\pi\)
−0.979678 + 0.200576i \(0.935719\pi\)
\(572\) 0 0
\(573\) 20920.4 + 7282.62i 1.52524 + 0.530952i
\(574\) 0 0
\(575\) −34204.2 −2.48072
\(576\) 0 0
\(577\) −10941.0 −0.789390 −0.394695 0.918812i \(-0.629150\pi\)
−0.394695 + 0.918812i \(0.629150\pi\)
\(578\) 0 0
\(579\) 18938.7 + 6592.77i 1.35935 + 0.473206i
\(580\) 0 0
\(581\) 8841.16i 0.631313i
\(582\) 0 0
\(583\) 14826.0i 1.05322i
\(584\) 0 0
\(585\) 19517.7 24636.5i 1.37941 1.74118i
\(586\) 0 0
\(587\) −7729.23 −0.543474 −0.271737 0.962372i \(-0.587598\pi\)
−0.271737 + 0.962372i \(0.587598\pi\)
\(588\) 0 0
\(589\) 1986.96 0.139000
\(590\) 0 0
\(591\) 5049.87 14506.5i 0.351478 1.00967i
\(592\) 0 0
\(593\) 5216.63i 0.361250i 0.983552 + 0.180625i \(0.0578121\pi\)
−0.983552 + 0.180625i \(0.942188\pi\)
\(594\) 0 0
\(595\) 11762.4i 0.810439i
\(596\) 0 0
\(597\) 6153.03 17675.5i 0.421820 1.21174i
\(598\) 0 0
\(599\) 24351.3 1.66105 0.830525 0.556982i \(-0.188041\pi\)
0.830525 + 0.556982i \(0.188041\pi\)
\(600\) 0 0
\(601\) −22958.3 −1.55822 −0.779109 0.626889i \(-0.784328\pi\)
−0.779109 + 0.626889i \(0.784328\pi\)
\(602\) 0 0
\(603\) 14037.6 17719.2i 0.948021 1.19665i
\(604\) 0 0
\(605\) 56701.7i 3.81033i
\(606\) 0 0
\(607\) 27664.8i 1.84988i −0.380111 0.924941i \(-0.624114\pi\)
0.380111 0.924941i \(-0.375886\pi\)
\(608\) 0 0
\(609\) −2154.37 749.962i −0.143349 0.0499015i
\(610\) 0 0
\(611\) −9301.28 −0.615859
\(612\) 0 0
\(613\) −14975.3 −0.986697 −0.493349 0.869832i \(-0.664227\pi\)
−0.493349 + 0.869832i \(0.664227\pi\)
\(614\) 0 0
\(615\) 16756.4 + 5833.10i 1.09867 + 0.382461i
\(616\) 0 0
\(617\) 10894.6i 0.710862i 0.934702 + 0.355431i \(0.115666\pi\)
−0.934702 + 0.355431i \(0.884334\pi\)
\(618\) 0 0
\(619\) 14213.8i 0.922942i 0.887155 + 0.461471i \(0.152678\pi\)
−0.887155 + 0.461471i \(0.847322\pi\)
\(620\) 0 0
\(621\) −8619.75 13572.5i −0.557003 0.877046i
\(622\) 0 0
\(623\) 5460.01 0.351125
\(624\) 0 0
\(625\) 36145.0 2.31328
\(626\) 0 0
\(627\) 2447.33 7030.31i 0.155880 0.447789i
\(628\) 0 0
\(629\) 4192.05i 0.265736i
\(630\) 0 0
\(631\) 12822.4i 0.808957i 0.914548 + 0.404478i \(0.132547\pi\)
−0.914548 + 0.404478i \(0.867453\pi\)
\(632\) 0 0
\(633\) −2067.93 + 5940.42i −0.129846 + 0.373002i
\(634\) 0 0
\(635\) −34875.2 −2.17950
\(636\) 0 0
\(637\) −2771.93 −0.172414
\(638\) 0 0
\(639\) −3720.62 2947.57i −0.230337 0.182479i
\(640\) 0 0
\(641\) 18120.3i 1.11655i 0.829657 + 0.558274i \(0.188536\pi\)
−0.829657 + 0.558274i \(0.811464\pi\)
\(642\) 0 0
\(643\) 15848.0i 0.971982i 0.873964 + 0.485991i \(0.161541\pi\)
−0.873964 + 0.485991i \(0.838459\pi\)
\(644\) 0 0
\(645\) −39694.2 13818.0i −2.42319 0.843541i
\(646\) 0 0
\(647\) 7882.76 0.478985 0.239493 0.970898i \(-0.423019\pi\)
0.239493 + 0.970898i \(0.423019\pi\)
\(648\) 0 0
\(649\) 861.192 0.0520874
\(650\) 0 0
\(651\) −3045.60 1060.21i −0.183359 0.0638292i
\(652\) 0 0
\(653\) 5732.96i 0.343565i 0.985135 + 0.171782i \(0.0549526\pi\)
−0.985135 + 0.171782i \(0.945047\pi\)
\(654\) 0 0
\(655\) 25518.9i 1.52230i
\(656\) 0 0
\(657\) 6386.93 + 5059.89i 0.379266 + 0.300465i
\(658\) 0 0
\(659\) 8321.00 0.491867 0.245933 0.969287i \(-0.420906\pi\)
0.245933 + 0.969287i \(0.420906\pi\)
\(660\) 0 0
\(661\) −658.617 −0.0387553 −0.0193776 0.999812i \(-0.506168\pi\)
−0.0193776 + 0.999812i \(0.506168\pi\)
\(662\) 0 0
\(663\) −7891.16 + 22668.5i −0.462243 + 1.32786i
\(664\) 0 0
\(665\) 3228.21i 0.188248i
\(666\) 0 0
\(667\) 7187.44i 0.417240i
\(668\) 0 0
\(669\) 7575.62 21762.0i 0.437803 1.25765i
\(670\) 0 0
\(671\) 42571.1 2.44924
\(672\) 0 0
\(673\) 433.488 0.0248287 0.0124144 0.999923i \(-0.496048\pi\)
0.0124144 + 0.999923i \(0.496048\pi\)
\(674\) 0 0
\(675\) 22448.3 + 35346.6i 1.28005 + 2.01554i
\(676\) 0 0
\(677\) 15477.7i 0.878663i −0.898325 0.439332i \(-0.855215\pi\)
0.898325 0.439332i \(-0.144785\pi\)
\(678\) 0 0
\(679\) 5461.96i 0.308705i
\(680\) 0 0
\(681\) −4925.02 1714.45i −0.277132 0.0964729i
\(682\) 0 0
\(683\) −8246.35 −0.461988 −0.230994 0.972955i \(-0.574198\pi\)
−0.230994 + 0.972955i \(0.574198\pi\)
\(684\) 0 0
\(685\) −34952.9 −1.94961
\(686\) 0 0
\(687\) −17529.4 6102.20i −0.973493 0.338884i
\(688\) 0 0
\(689\) 13120.1i 0.725451i
\(690\) 0 0
\(691\) 9543.79i 0.525417i 0.964875 + 0.262708i \(0.0846157\pi\)
−0.964875 + 0.262708i \(0.915384\pi\)
\(692\) 0 0
\(693\) −7502.51 + 9470.16i −0.411251 + 0.519108i
\(694\) 0 0
\(695\) 25410.6 1.38688
\(696\) 0 0
\(697\) −13549.5 −0.736335
\(698\) 0 0
\(699\) −8642.12 + 24825.7i −0.467633 + 1.34334i
\(700\) 0 0
\(701\) 468.446i 0.0252396i −0.999920 0.0126198i \(-0.995983\pi\)
0.999920 0.0126198i \(-0.00401712\pi\)
\(702\) 0 0
\(703\) 1150.52i 0.0617248i
\(704\) 0 0
\(705\) 5779.95 16603.7i 0.308774 0.886997i
\(706\) 0 0
\(707\) −332.044 −0.0176631
\(708\) 0 0
\(709\) −29596.7 −1.56774 −0.783869 0.620926i \(-0.786757\pi\)
−0.783869 + 0.620926i \(0.786757\pi\)
\(710\) 0 0
\(711\) −17589.7 + 22202.9i −0.927802 + 1.17113i
\(712\) 0 0
\(713\) 10160.8i 0.533693i
\(714\) 0 0
\(715\) 74415.6i 3.89229i
\(716\) 0 0
\(717\) 4218.18 + 1468.40i 0.219708 + 0.0764829i
\(718\) 0 0
\(719\) −9175.10 −0.475902 −0.237951 0.971277i \(-0.576476\pi\)
−0.237951 + 0.971277i \(0.576476\pi\)
\(720\) 0 0
\(721\) −168.000 −0.00867773
\(722\) 0 0
\(723\) 8780.03 + 3056.43i 0.451636 + 0.157220i
\(724\) 0 0
\(725\) 18718.1i 0.958861i
\(726\) 0 0
\(727\) 28785.0i 1.46847i 0.678897 + 0.734233i \(0.262458\pi\)
−0.678897 + 0.734233i \(0.737542\pi\)
\(728\) 0 0
\(729\) −8368.66 + 17815.3i −0.425172 + 0.905112i
\(730\) 0 0
\(731\) 32097.5 1.62403
\(732\) 0 0
\(733\) −16765.7 −0.844822 −0.422411 0.906404i \(-0.638816\pi\)
−0.422411 + 0.906404i \(0.638816\pi\)
\(734\) 0 0
\(735\) 1722.52 4948.18i 0.0864436 0.248321i
\(736\) 0 0
\(737\) 53521.7i 2.67503i
\(738\) 0 0
\(739\) 20608.6i 1.02585i −0.858434 0.512924i \(-0.828562\pi\)
0.858434 0.512924i \(-0.171438\pi\)
\(740\) 0 0
\(741\) 2165.74 6221.40i 0.107369 0.308433i
\(742\) 0 0
\(743\) 28519.6 1.40818 0.704092 0.710108i \(-0.251354\pi\)
0.704092 + 0.710108i \(0.251354\pi\)
\(744\) 0 0
\(745\) 42816.1 2.10558
\(746\) 0 0
\(747\) −26729.9 21176.2i −1.30923 1.03721i
\(748\) 0 0
\(749\) 3024.77i 0.147560i
\(750\) 0 0
\(751\) 27316.0i 1.32726i −0.748059 0.663632i \(-0.769014\pi\)
0.748059 0.663632i \(-0.230986\pi\)
\(752\) 0 0
\(753\) −16892.0 5880.29i −0.817501 0.284581i
\(754\) 0 0
\(755\) −24899.2 −1.20023
\(756\) 0 0
\(757\) 17115.2 0.821749 0.410874 0.911692i \(-0.365223\pi\)
0.410874 + 0.911692i \(0.365223\pi\)
\(758\) 0 0
\(759\) −35951.1 12515.0i −1.71929 0.598504i
\(760\) 0 0
\(761\) 28590.3i 1.36189i 0.732336 + 0.680944i \(0.238430\pi\)
−0.732336 + 0.680944i \(0.761570\pi\)
\(762\) 0 0
\(763\) 2266.61i 0.107545i
\(764\) 0 0
\(765\) −35561.9 28173.1i −1.68071 1.33150i
\(766\) 0 0
\(767\) 762.103 0.0358774
\(768\) 0 0
\(769\) −25114.9 −1.17772 −0.588860 0.808235i \(-0.700423\pi\)
−0.588860 + 0.808235i \(0.700423\pi\)
\(770\) 0 0
\(771\) −6014.28 + 17276.9i −0.280932 + 0.807019i
\(772\) 0 0
\(773\) 3680.65i 0.171260i 0.996327 + 0.0856298i \(0.0272902\pi\)
−0.996327 + 0.0856298i \(0.972710\pi\)
\(774\) 0 0
\(775\) 26461.5i 1.22648i
\(776\) 0 0
\(777\) −613.896 + 1763.50i −0.0283441 + 0.0814225i
\(778\) 0 0
\(779\) 3718.70 0.171035
\(780\) 0 0
\(781\) −11238.3 −0.514901
\(782\) 0 0
\(783\) −7427.51 + 4717.14i −0.339001 + 0.215296i
\(784\) 0 0
\(785\) 65720.2i 2.98809i
\(786\) 0 0
\(787\) 16721.5i 0.757377i −0.925524 0.378689i \(-0.876375\pi\)
0.925524 0.378689i \(-0.123625\pi\)
\(788\) 0 0
\(789\) 24898.4 + 8667.44i 1.12346 + 0.391089i
\(790\) 0 0
\(791\) −13809.7 −0.620755
\(792\) 0 0
\(793\) 37672.9 1.68702
\(794\) 0 0
\(795\) 23420.7 + 8153.02i 1.04484 + 0.363721i
\(796\) 0 0
\(797\) 44061.5i 1.95827i −0.203219 0.979133i \(-0.565140\pi\)
0.203219 0.979133i \(-0.434860\pi\)
\(798\)