Properties

Label 43.3.b.b.42.4
Level 43
Weight 3
Character 43.42
Analytic conductor 1.172
Analytic rank 0
Dimension 6
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.17166513675\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.4
Root \(1.77533i\) of \(x^{6} + 20 x^{4} + 121 x^{2} + 214\)
Character \(\chi\) \(=\) 43.42
Dual form 43.3.b.b.42.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.77533i q^{2} -5.61757i q^{3} +0.848217 q^{4} -2.98959i q^{5} +9.97302 q^{6} +6.83184i q^{7} +8.60717i q^{8} -22.5571 q^{9} +O(q^{10})\) \(q+1.77533i q^{2} -5.61757i q^{3} +0.848217 q^{4} -2.98959i q^{5} +9.97302 q^{6} +6.83184i q^{7} +8.60717i q^{8} -22.5571 q^{9} +5.30751 q^{10} +6.88766 q^{11} -4.76492i q^{12} +12.4014 q^{13} -12.1287 q^{14} -16.7943 q^{15} -11.8877 q^{16} -15.8212 q^{17} -40.0462i q^{18} +19.2112i q^{19} -2.53583i q^{20} +38.3784 q^{21} +12.2278i q^{22} -33.2226 q^{23} +48.3514 q^{24} +16.0623 q^{25} +22.0165i q^{26} +76.1581i q^{27} +5.79488i q^{28} -45.8411i q^{29} -29.8153i q^{30} +14.7278 q^{31} +13.3242i q^{32} -38.6919i q^{33} -28.0879i q^{34} +20.4244 q^{35} -19.1333 q^{36} -13.1726i q^{37} -34.1062 q^{38} -69.6657i q^{39} +25.7319 q^{40} -2.49085 q^{41} +68.1341i q^{42} +(-40.8836 - 13.3242i) q^{43} +5.84223 q^{44} +67.4366i q^{45} -58.9810i q^{46} -10.2595 q^{47} +66.7798i q^{48} +2.32596 q^{49} +28.5159i q^{50} +88.8770i q^{51} +10.5191 q^{52} -31.2780 q^{53} -135.205 q^{54} -20.5913i q^{55} -58.8028 q^{56} +107.920 q^{57} +81.3829 q^{58} +64.4112 q^{59} -14.2452 q^{60} -78.1922i q^{61} +26.1467i q^{62} -154.107i q^{63} -71.2054 q^{64} -37.0751i q^{65} +68.6908 q^{66} -89.3657 q^{67} -13.4198 q^{68} +186.631i q^{69} +36.2600i q^{70} +35.5065i q^{71} -194.153i q^{72} +35.9603i q^{73} +23.3857 q^{74} -90.2313i q^{75} +16.2953i q^{76} +47.0554i q^{77} +123.679 q^{78} +50.1103 q^{79} +35.5393i q^{80} +224.809 q^{81} -4.42207i q^{82} -10.3645 q^{83} +32.5532 q^{84} +47.2991i q^{85} +(23.6548 - 72.5817i) q^{86} -257.516 q^{87} +59.2832i q^{88} -13.4900i q^{89} -119.722 q^{90} +84.7243i q^{91} -28.1800 q^{92} -82.7347i q^{93} -18.2140i q^{94} +57.4338 q^{95} +74.8496 q^{96} +66.6322 q^{97} +4.12933i q^{98} -155.366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 16q^{4} + 6q^{6} - 36q^{9} + O(q^{10}) \) \( 6q - 16q^{4} + 6q^{6} - 36q^{9} - 2q^{10} + 38q^{11} + 30q^{13} + 36q^{14} + 28q^{15} - 68q^{16} - 20q^{17} + 56q^{21} - 80q^{23} + 62q^{24} - 84q^{25} - 112q^{31} + 208q^{35} - 122q^{36} + 170q^{38} + 206q^{40} - 172q^{41} + 10q^{43} - 36q^{44} + 30q^{47} - 6q^{49} - 120q^{52} - 110q^{53} - 284q^{54} - 264q^{56} + 420q^{57} + 430q^{58} - 12q^{59} - 232q^{60} + 100q^{64} - 144q^{66} - 70q^{67} - 50q^{68} - 50q^{74} + 620q^{78} + 178q^{79} + 382q^{81} + 10q^{83} + 172q^{84} - 372q^{86} - 510q^{87} - 796q^{90} + 150q^{92} - 130q^{95} + 362q^{96} - 380q^{97} - 466q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.77533i 0.887663i 0.896110 + 0.443832i \(0.146381\pi\)
−0.896110 + 0.443832i \(0.853619\pi\)
\(3\) 5.61757i 1.87252i −0.351302 0.936262i \(-0.614261\pi\)
0.351302 0.936262i \(-0.385739\pi\)
\(4\) 0.848217 0.212054
\(5\) 2.98959i 0.597919i −0.954266 0.298959i \(-0.903360\pi\)
0.954266 0.298959i \(-0.0966395\pi\)
\(6\) 9.97302 1.66217
\(7\) 6.83184i 0.975977i 0.872850 + 0.487989i \(0.162269\pi\)
−0.872850 + 0.487989i \(0.837731\pi\)
\(8\) 8.60717i 1.07590i
\(9\) −22.5571 −2.50635
\(10\) 5.30751 0.530751
\(11\) 6.88766 0.626151 0.313075 0.949728i \(-0.398641\pi\)
0.313075 + 0.949728i \(0.398641\pi\)
\(12\) 4.76492i 0.397077i
\(13\) 12.4014 0.953953 0.476977 0.878916i \(-0.341733\pi\)
0.476977 + 0.878916i \(0.341733\pi\)
\(14\) −12.1287 −0.866339
\(15\) −16.7943 −1.11962
\(16\) −11.8877 −0.742979
\(17\) −15.8212 −0.930661 −0.465331 0.885137i \(-0.654065\pi\)
−0.465331 + 0.885137i \(0.654065\pi\)
\(18\) 40.0462i 2.22479i
\(19\) 19.2112i 1.01112i 0.862792 + 0.505559i \(0.168714\pi\)
−0.862792 + 0.505559i \(0.831286\pi\)
\(20\) 2.53583i 0.126791i
\(21\) 38.3784 1.82754
\(22\) 12.2278i 0.555811i
\(23\) −33.2226 −1.44446 −0.722231 0.691652i \(-0.756883\pi\)
−0.722231 + 0.691652i \(0.756883\pi\)
\(24\) 48.3514 2.01464
\(25\) 16.0623 0.642493
\(26\) 22.0165i 0.846789i
\(27\) 76.1581i 2.82067i
\(28\) 5.79488i 0.206960i
\(29\) 45.8411i 1.58073i −0.612637 0.790364i \(-0.709891\pi\)
0.612637 0.790364i \(-0.290109\pi\)
\(30\) 29.8153i 0.993843i
\(31\) 14.7278 0.475092 0.237546 0.971376i \(-0.423657\pi\)
0.237546 + 0.971376i \(0.423657\pi\)
\(32\) 13.3242i 0.416381i
\(33\) 38.6919i 1.17248i
\(34\) 28.0879i 0.826114i
\(35\) 20.4244 0.583555
\(36\) −19.1333 −0.531481
\(37\) 13.1726i 0.356017i −0.984029 0.178009i \(-0.943034\pi\)
0.984029 0.178009i \(-0.0569655\pi\)
\(38\) −34.1062 −0.897532
\(39\) 69.6657i 1.78630i
\(40\) 25.7319 0.643298
\(41\) −2.49085 −0.0607525 −0.0303762 0.999539i \(-0.509671\pi\)
−0.0303762 + 0.999539i \(0.509671\pi\)
\(42\) 68.1341i 1.62224i
\(43\) −40.8836 13.3242i −0.950781 0.309865i
\(44\) 5.84223 0.132778
\(45\) 67.4366i 1.49859i
\(46\) 58.9810i 1.28220i
\(47\) −10.2595 −0.218288 −0.109144 0.994026i \(-0.534811\pi\)
−0.109144 + 0.994026i \(0.534811\pi\)
\(48\) 66.7798i 1.39125i
\(49\) 2.32596 0.0474685
\(50\) 28.5159i 0.570317i
\(51\) 88.8770i 1.74269i
\(52\) 10.5191 0.202290
\(53\) −31.2780 −0.590151 −0.295075 0.955474i \(-0.595345\pi\)
−0.295075 + 0.955474i \(0.595345\pi\)
\(54\) −135.205 −2.50380
\(55\) 20.5913i 0.374387i
\(56\) −58.8028 −1.05005
\(57\) 107.920 1.89334
\(58\) 81.3829 1.40315
\(59\) 64.4112 1.09171 0.545857 0.837878i \(-0.316204\pi\)
0.545857 + 0.837878i \(0.316204\pi\)
\(60\) −14.2452 −0.237420
\(61\) 78.1922i 1.28184i −0.767608 0.640920i \(-0.778553\pi\)
0.767608 0.640920i \(-0.221447\pi\)
\(62\) 26.1467i 0.421721i
\(63\) 154.107i 2.44614i
\(64\) −71.2054 −1.11258
\(65\) 37.0751i 0.570387i
\(66\) 68.6908 1.04077
\(67\) −89.3657 −1.33382 −0.666908 0.745140i \(-0.732383\pi\)
−0.666908 + 0.745140i \(0.732383\pi\)
\(68\) −13.4198 −0.197351
\(69\) 186.631i 2.70479i
\(70\) 36.2600i 0.518000i
\(71\) 35.5065i 0.500092i 0.968234 + 0.250046i \(0.0804457\pi\)
−0.968234 + 0.250046i \(0.919554\pi\)
\(72\) 194.153i 2.69657i
\(73\) 35.9603i 0.492607i 0.969193 + 0.246303i \(0.0792160\pi\)
−0.969193 + 0.246303i \(0.920784\pi\)
\(74\) 23.3857 0.316024
\(75\) 90.2313i 1.20308i
\(76\) 16.2953i 0.214412i
\(77\) 47.0554i 0.611109i
\(78\) 123.679 1.58563
\(79\) 50.1103 0.634308 0.317154 0.948374i \(-0.397273\pi\)
0.317154 + 0.948374i \(0.397273\pi\)
\(80\) 35.5393i 0.444241i
\(81\) 224.809 2.77543
\(82\) 4.42207i 0.0539277i
\(83\) −10.3645 −0.124873 −0.0624367 0.998049i \(-0.519887\pi\)
−0.0624367 + 0.998049i \(0.519887\pi\)
\(84\) 32.5532 0.387538
\(85\) 47.2991i 0.556460i
\(86\) 23.6548 72.5817i 0.275056 0.843973i
\(87\) −257.516 −2.95995
\(88\) 59.2832i 0.673673i
\(89\) 13.4900i 0.151573i −0.997124 0.0757865i \(-0.975853\pi\)
0.997124 0.0757865i \(-0.0241468\pi\)
\(90\) −119.722 −1.33024
\(91\) 84.7243i 0.931037i
\(92\) −28.1800 −0.306304
\(93\) 82.7347i 0.889621i
\(94\) 18.2140i 0.193766i
\(95\) 57.4338 0.604566
\(96\) 74.8496 0.779684
\(97\) 66.6322 0.686930 0.343465 0.939165i \(-0.388399\pi\)
0.343465 + 0.939165i \(0.388399\pi\)
\(98\) 4.12933i 0.0421360i
\(99\) −155.366 −1.56935
\(100\) 13.6243 0.136243
\(101\) 73.3449 0.726187 0.363094 0.931753i \(-0.381721\pi\)
0.363094 + 0.931753i \(0.381721\pi\)
\(102\) −157.786 −1.54692
\(103\) −34.7405 −0.337286 −0.168643 0.985677i \(-0.553939\pi\)
−0.168643 + 0.985677i \(0.553939\pi\)
\(104\) 106.741i 1.02635i
\(105\) 114.736i 1.09272i
\(106\) 55.5286i 0.523855i
\(107\) 120.519 1.12635 0.563173 0.826339i \(-0.309580\pi\)
0.563173 + 0.826339i \(0.309580\pi\)
\(108\) 64.5986i 0.598135i
\(109\) −81.5825 −0.748464 −0.374232 0.927335i \(-0.622094\pi\)
−0.374232 + 0.927335i \(0.622094\pi\)
\(110\) 36.5563 0.332330
\(111\) −73.9983 −0.666651
\(112\) 81.2146i 0.725130i
\(113\) 58.7443i 0.519861i 0.965627 + 0.259931i \(0.0836997\pi\)
−0.965627 + 0.259931i \(0.916300\pi\)
\(114\) 191.594i 1.68065i
\(115\) 99.3222i 0.863671i
\(116\) 38.8832i 0.335200i
\(117\) −279.740 −2.39094
\(118\) 114.351i 0.969075i
\(119\) 108.088i 0.908304i
\(120\) 144.551i 1.20459i
\(121\) −73.5601 −0.607935
\(122\) 138.817 1.13784
\(123\) 13.9925i 0.113760i
\(124\) 12.4924 0.100745
\(125\) 122.760i 0.982078i
\(126\) 273.590 2.17135
\(127\) −17.9828 −0.141597 −0.0707984 0.997491i \(-0.522555\pi\)
−0.0707984 + 0.997491i \(0.522555\pi\)
\(128\) 73.1161i 0.571219i
\(129\) −74.8496 + 229.666i −0.580230 + 1.78036i
\(130\) 65.8205 0.506311
\(131\) 103.364i 0.789039i 0.918887 + 0.394520i \(0.129089\pi\)
−0.918887 + 0.394520i \(0.870911\pi\)
\(132\) 32.8192i 0.248630i
\(133\) −131.248 −0.986827
\(134\) 158.653i 1.18398i
\(135\) 227.682 1.68653
\(136\) 136.176i 1.00129i
\(137\) 140.446i 1.02516i −0.858641 0.512578i \(-0.828691\pi\)
0.858641 0.512578i \(-0.171309\pi\)
\(138\) −331.330 −2.40094
\(139\) 248.580 1.78834 0.894172 0.447725i \(-0.147765\pi\)
0.894172 + 0.447725i \(0.147765\pi\)
\(140\) 17.3244 0.123745
\(141\) 57.6337i 0.408750i
\(142\) −63.0357 −0.443913
\(143\) 85.4166 0.597319
\(144\) 268.151 1.86216
\(145\) −137.046 −0.945147
\(146\) −63.8412 −0.437269
\(147\) 13.0662i 0.0888859i
\(148\) 11.1733i 0.0754950i
\(149\) 95.0589i 0.637979i 0.947758 + 0.318990i \(0.103344\pi\)
−0.947758 + 0.318990i \(0.896656\pi\)
\(150\) 160.190 1.06793
\(151\) 122.926i 0.814076i 0.913411 + 0.407038i \(0.133438\pi\)
−0.913411 + 0.407038i \(0.866562\pi\)
\(152\) −165.354 −1.08786
\(153\) 356.882 2.33256
\(154\) −83.5387 −0.542459
\(155\) 44.0303i 0.284066i
\(156\) 59.0917i 0.378793i
\(157\) 189.332i 1.20594i −0.797765 0.602969i \(-0.793984\pi\)
0.797765 0.602969i \(-0.206016\pi\)
\(158\) 88.9621i 0.563051i
\(159\) 175.706i 1.10507i
\(160\) 39.8339 0.248962
\(161\) 226.972i 1.40976i
\(162\) 399.110i 2.46364i
\(163\) 264.440i 1.62233i 0.584817 + 0.811165i \(0.301166\pi\)
−0.584817 + 0.811165i \(0.698834\pi\)
\(164\) −2.11278 −0.0128828
\(165\) −115.673 −0.701049
\(166\) 18.4004i 0.110845i
\(167\) 40.0299 0.239700 0.119850 0.992792i \(-0.461759\pi\)
0.119850 + 0.992792i \(0.461759\pi\)
\(168\) 330.329i 1.96624i
\(169\) −15.2054 −0.0899729
\(170\) −83.9713 −0.493949
\(171\) 433.350i 2.53421i
\(172\) −34.6781 11.3018i −0.201617 0.0657082i
\(173\) 181.497 1.04912 0.524559 0.851374i \(-0.324230\pi\)
0.524559 + 0.851374i \(0.324230\pi\)
\(174\) 457.175i 2.62744i
\(175\) 109.735i 0.627059i
\(176\) −81.8782 −0.465217
\(177\) 361.834i 2.04426i
\(178\) 23.9492 0.134546
\(179\) 62.5972i 0.349705i 0.984595 + 0.174852i \(0.0559448\pi\)
−0.984595 + 0.174852i \(0.944055\pi\)
\(180\) 57.2009i 0.317783i
\(181\) 16.7178 0.0923638 0.0461819 0.998933i \(-0.485295\pi\)
0.0461819 + 0.998933i \(0.485295\pi\)
\(182\) −150.413 −0.826447
\(183\) −439.251 −2.40028
\(184\) 285.953i 1.55409i
\(185\) −39.3809 −0.212870
\(186\) 146.881 0.789683
\(187\) −108.971 −0.582734
\(188\) −8.70231 −0.0462889
\(189\) −520.300 −2.75291
\(190\) 101.964i 0.536651i
\(191\) 44.7333i 0.234206i 0.993120 + 0.117103i \(0.0373607\pi\)
−0.993120 + 0.117103i \(0.962639\pi\)
\(192\) 400.002i 2.08334i
\(193\) 135.200 0.700516 0.350258 0.936653i \(-0.386094\pi\)
0.350258 + 0.936653i \(0.386094\pi\)
\(194\) 118.294i 0.609763i
\(195\) −208.272 −1.06806
\(196\) 1.97292 0.0100659
\(197\) 145.802 0.740109 0.370055 0.929010i \(-0.379339\pi\)
0.370055 + 0.929010i \(0.379339\pi\)
\(198\) 275.825i 1.39305i
\(199\) 280.657i 1.41034i −0.709039 0.705169i \(-0.750871\pi\)
0.709039 0.705169i \(-0.249129\pi\)
\(200\) 138.251i 0.691256i
\(201\) 502.018i 2.49760i
\(202\) 130.211i 0.644609i
\(203\) 313.179 1.54275
\(204\) 75.3870i 0.369544i
\(205\) 7.44664i 0.0363251i
\(206\) 61.6757i 0.299396i
\(207\) 749.407 3.62032
\(208\) −147.424 −0.708767
\(209\) 132.320i 0.633112i
\(210\) 203.693 0.969968
\(211\) 181.131i 0.858439i −0.903200 0.429219i \(-0.858789\pi\)
0.903200 0.429219i \(-0.141211\pi\)
\(212\) −26.5305 −0.125144
\(213\) 199.460 0.936434
\(214\) 213.961i 0.999816i
\(215\) −39.8339 + 122.225i −0.185274 + 0.568490i
\(216\) −655.505 −3.03475
\(217\) 100.618i 0.463679i
\(218\) 144.836i 0.664384i
\(219\) 202.010 0.922418
\(220\) 17.4659i 0.0793905i
\(221\) −196.205 −0.887807
\(222\) 131.371i 0.591762i
\(223\) 107.757i 0.483213i −0.970374 0.241607i \(-0.922326\pi\)
0.970374 0.241607i \(-0.0776744\pi\)
\(224\) −91.0288 −0.406378
\(225\) −362.320 −1.61031
\(226\) −104.290 −0.461461
\(227\) 139.742i 0.615603i 0.951451 + 0.307801i \(0.0995932\pi\)
−0.951451 + 0.307801i \(0.900407\pi\)
\(228\) 91.5400 0.401491
\(229\) 308.655 1.34784 0.673919 0.738805i \(-0.264610\pi\)
0.673919 + 0.738805i \(0.264610\pi\)
\(230\) −176.329 −0.766649
\(231\) 264.337 1.14432
\(232\) 394.562 1.70070
\(233\) 301.133i 1.29242i 0.763161 + 0.646209i \(0.223646\pi\)
−0.763161 + 0.646209i \(0.776354\pi\)
\(234\) 496.629i 2.12235i
\(235\) 30.6719i 0.130519i
\(236\) 54.6346 0.231503
\(237\) 281.498i 1.18776i
\(238\) 191.892 0.806268
\(239\) −122.039 −0.510625 −0.255312 0.966859i \(-0.582178\pi\)
−0.255312 + 0.966859i \(0.582178\pi\)
\(240\) 199.644 0.831852
\(241\) 475.092i 1.97133i −0.168701 0.985667i \(-0.553957\pi\)
0.168701 0.985667i \(-0.446043\pi\)
\(242\) 130.593i 0.539642i
\(243\) 577.461i 2.37638i
\(244\) 66.3240i 0.271820i
\(245\) 6.95367i 0.0283823i
\(246\) −24.8413 −0.100981
\(247\) 238.246i 0.964559i
\(248\) 126.765i 0.511149i
\(249\) 58.2233i 0.233828i
\(250\) 217.939 0.871754
\(251\) −35.9930 −0.143399 −0.0716993 0.997426i \(-0.522842\pi\)
−0.0716993 + 0.997426i \(0.522842\pi\)
\(252\) 130.716i 0.518714i
\(253\) −228.826 −0.904451
\(254\) 31.9253i 0.125690i
\(255\) 265.706 1.04198
\(256\) −155.017 −0.605534
\(257\) 62.7857i 0.244302i 0.992512 + 0.122151i \(0.0389793\pi\)
−0.992512 + 0.122151i \(0.961021\pi\)
\(258\) −407.733 132.882i −1.58036 0.515048i
\(259\) 89.9934 0.347465
\(260\) 31.4478i 0.120953i
\(261\) 1034.04i 3.96185i
\(262\) −183.505 −0.700401
\(263\) 17.1841i 0.0653386i 0.999466 + 0.0326693i \(0.0104008\pi\)
−0.999466 + 0.0326693i \(0.989599\pi\)
\(264\) 333.028 1.26147
\(265\) 93.5085i 0.352862i
\(266\) 233.008i 0.875970i
\(267\) −75.7811 −0.283824
\(268\) −75.8015 −0.282842
\(269\) −407.934 −1.51648 −0.758242 0.651974i \(-0.773941\pi\)
−0.758242 + 0.651974i \(0.773941\pi\)
\(270\) 404.209i 1.49707i
\(271\) −316.274 −1.16706 −0.583532 0.812090i \(-0.698330\pi\)
−0.583532 + 0.812090i \(0.698330\pi\)
\(272\) 188.078 0.691461
\(273\) 475.945 1.74339
\(274\) 249.338 0.909993
\(275\) 110.632 0.402298
\(276\) 158.303i 0.573562i
\(277\) 209.408i 0.755984i 0.925809 + 0.377992i \(0.123385\pi\)
−0.925809 + 0.377992i \(0.876615\pi\)
\(278\) 441.310i 1.58745i
\(279\) −332.218 −1.19074
\(280\) 175.796i 0.627845i
\(281\) 36.4182 0.129602 0.0648011 0.997898i \(-0.479359\pi\)
0.0648011 + 0.997898i \(0.479359\pi\)
\(282\) −102.319 −0.362832
\(283\) −15.3124 −0.0541074 −0.0270537 0.999634i \(-0.508613\pi\)
−0.0270537 + 0.999634i \(0.508613\pi\)
\(284\) 30.1172i 0.106047i
\(285\) 322.638i 1.13206i
\(286\) 151.642i 0.530218i
\(287\) 17.0171i 0.0592930i
\(288\) 300.555i 1.04360i
\(289\) −38.6884 −0.133870
\(290\) 243.302i 0.838972i
\(291\) 374.311i 1.28629i
\(292\) 30.5021i 0.104459i
\(293\) −421.851 −1.43976 −0.719882 0.694097i \(-0.755804\pi\)
−0.719882 + 0.694097i \(0.755804\pi\)
\(294\) 23.1968 0.0789008
\(295\) 192.563i 0.652757i
\(296\) 113.379 0.383038
\(297\) 524.551i 1.76616i
\(298\) −168.761 −0.566311
\(299\) −412.007 −1.37795
\(300\) 76.5357i 0.255119i
\(301\) 91.0288 279.310i 0.302421 0.927940i
\(302\) −218.233 −0.722625
\(303\) 412.020i 1.35980i
\(304\) 228.377i 0.751239i
\(305\) −233.763 −0.766436
\(306\) 633.581i 2.07053i
\(307\) −239.260 −0.779349 −0.389674 0.920953i \(-0.627412\pi\)
−0.389674 + 0.920953i \(0.627412\pi\)
\(308\) 39.9132i 0.129588i
\(309\) 195.157i 0.631576i
\(310\) 78.1681 0.252155
\(311\) 565.399 1.81800 0.909001 0.416793i \(-0.136846\pi\)
0.909001 + 0.416793i \(0.136846\pi\)
\(312\) 599.624 1.92187
\(313\) 340.149i 1.08674i −0.839493 0.543370i \(-0.817148\pi\)
0.839493 0.543370i \(-0.182852\pi\)
\(314\) 336.126 1.07047
\(315\) −460.716 −1.46259
\(316\) 42.5044 0.134508
\(317\) −470.259 −1.48347 −0.741733 0.670695i \(-0.765996\pi\)
−0.741733 + 0.670695i \(0.765996\pi\)
\(318\) −311.936 −0.980931
\(319\) 315.738i 0.989774i
\(320\) 212.875i 0.665235i
\(321\) 677.025i 2.10911i
\(322\) 402.949 1.25139
\(323\) 303.945i 0.941008i
\(324\) 190.687 0.588541
\(325\) 199.195 0.612908
\(326\) −469.467 −1.44008
\(327\) 458.296i 1.40152i
\(328\) 21.4392i 0.0653633i
\(329\) 70.0915i 0.213044i
\(330\) 205.358i 0.622296i
\(331\) 297.506i 0.898809i 0.893328 + 0.449405i \(0.148364\pi\)
−0.893328 + 0.449405i \(0.851636\pi\)
\(332\) −8.79134 −0.0264799
\(333\) 297.137i 0.892303i
\(334\) 71.0662i 0.212773i
\(335\) 267.167i 0.797514i
\(336\) −456.229 −1.35782
\(337\) 488.152 1.44852 0.724261 0.689526i \(-0.242181\pi\)
0.724261 + 0.689526i \(0.242181\pi\)
\(338\) 26.9946i 0.0798657i
\(339\) 330.000 0.973452
\(340\) 40.1199i 0.118000i
\(341\) 101.440 0.297479
\(342\) 769.337 2.24952
\(343\) 350.651i 1.02231i
\(344\) 114.684 351.892i 0.333382 1.02294i
\(345\) 557.950 1.61725
\(346\) 322.217i 0.931263i
\(347\) 620.235i 1.78742i −0.448646 0.893710i \(-0.648093\pi\)
0.448646 0.893710i \(-0.351907\pi\)
\(348\) −218.429 −0.627670
\(349\) 97.1065i 0.278242i −0.990275 0.139121i \(-0.955572\pi\)
0.990275 0.139121i \(-0.0444277\pi\)
\(350\) −194.816 −0.556617
\(351\) 944.466i 2.69079i
\(352\) 91.7725i 0.260717i
\(353\) 355.666 1.00755 0.503776 0.863834i \(-0.331944\pi\)
0.503776 + 0.863834i \(0.331944\pi\)
\(354\) 642.374 1.81462
\(355\) 106.150 0.299014
\(356\) 11.4425i 0.0321417i
\(357\) −607.193 −1.70082
\(358\) −111.130 −0.310420
\(359\) 185.120 0.515655 0.257827 0.966191i \(-0.416993\pi\)
0.257827 + 0.966191i \(0.416993\pi\)
\(360\) −580.438 −1.61233
\(361\) −8.07135 −0.0223583
\(362\) 29.6796i 0.0819879i
\(363\) 413.229i 1.13837i
\(364\) 71.8646i 0.197430i
\(365\) 107.507 0.294539
\(366\) 779.813i 2.13064i
\(367\) −379.616 −1.03438 −0.517188 0.855872i \(-0.673021\pi\)
−0.517188 + 0.855872i \(0.673021\pi\)
\(368\) 394.939 1.07320
\(369\) 56.1864 0.152267
\(370\) 69.9139i 0.188956i
\(371\) 213.686i 0.575974i
\(372\) 70.1770i 0.188648i
\(373\) 190.307i 0.510206i 0.966914 + 0.255103i \(0.0821094\pi\)
−0.966914 + 0.255103i \(0.917891\pi\)
\(374\) 193.460i 0.517272i
\(375\) −689.611 −1.83896
\(376\) 88.3055i 0.234855i
\(377\) 568.494i 1.50794i
\(378\) 923.702i 2.44366i
\(379\) −542.592 −1.43164 −0.715820 0.698285i \(-0.753947\pi\)
−0.715820 + 0.698285i \(0.753947\pi\)
\(380\) 48.7163 0.128201
\(381\) 101.020i 0.265143i
\(382\) −79.4161 −0.207896
\(383\) 126.903i 0.331340i −0.986181 0.165670i \(-0.947021\pi\)
0.986181 0.165670i \(-0.0529786\pi\)
\(384\) −410.735 −1.06962
\(385\) 140.677 0.365394
\(386\) 240.024i 0.621823i
\(387\) 922.215 + 300.555i 2.38299 + 0.776629i
\(388\) 56.5186 0.145667
\(389\) 689.167i 1.77164i 0.464031 + 0.885819i \(0.346403\pi\)
−0.464031 + 0.885819i \(0.653597\pi\)
\(390\) 369.751i 0.948080i
\(391\) 525.623 1.34430
\(392\) 20.0199i 0.0510712i
\(393\) 580.656 1.47750
\(394\) 258.845i 0.656968i
\(395\) 149.809i 0.379264i
\(396\) −131.784 −0.332788
\(397\) −422.076 −1.06316 −0.531582 0.847007i \(-0.678402\pi\)
−0.531582 + 0.847007i \(0.678402\pi\)
\(398\) 498.258 1.25191
\(399\) 737.295i 1.84786i
\(400\) −190.943 −0.477359
\(401\) −393.635 −0.981632 −0.490816 0.871263i \(-0.663301\pi\)
−0.490816 + 0.871263i \(0.663301\pi\)
\(402\) −891.247 −2.21703
\(403\) 182.646 0.453215
\(404\) 62.2124 0.153991
\(405\) 672.089i 1.65948i
\(406\) 555.995i 1.36945i
\(407\) 90.7287i 0.222921i
\(408\) −764.979 −1.87495
\(409\) 319.833i 0.781988i 0.920393 + 0.390994i \(0.127869\pi\)
−0.920393 + 0.390994i \(0.872131\pi\)
\(410\) −13.2202 −0.0322444
\(411\) −788.967 −1.91963
\(412\) −29.4675 −0.0715229
\(413\) 440.047i 1.06549i
\(414\) 1330.44i 3.21363i
\(415\) 30.9856i 0.0746642i
\(416\) 165.239i 0.397208i
\(417\) 1396.41i 3.34872i
\(418\) −234.912 −0.561990
\(419\) 334.413i 0.798121i 0.916925 + 0.399061i \(0.130664\pi\)
−0.916925 + 0.399061i \(0.869336\pi\)
\(420\) 97.3208i 0.231716i
\(421\) 332.902i 0.790740i −0.918522 0.395370i \(-0.870616\pi\)
0.918522 0.395370i \(-0.129384\pi\)
\(422\) 321.566 0.762005
\(423\) 231.426 0.547105
\(424\) 269.215i 0.634941i
\(425\) −254.126 −0.597943
\(426\) 354.107i 0.831238i
\(427\) 534.197 1.25105
\(428\) 102.226 0.238847
\(429\) 479.834i 1.11849i
\(430\) −216.990 70.7182i −0.504627 0.164461i
\(431\) −163.406 −0.379132 −0.189566 0.981868i \(-0.560708\pi\)
−0.189566 + 0.981868i \(0.560708\pi\)
\(432\) 905.341i 2.09570i
\(433\) 190.232i 0.439335i 0.975575 + 0.219668i \(0.0704973\pi\)
−0.975575 + 0.219668i \(0.929503\pi\)
\(434\) −178.630 −0.411590
\(435\) 769.868i 1.76981i
\(436\) −69.1997 −0.158715
\(437\) 638.248i 1.46052i
\(438\) 358.633i 0.818796i
\(439\) −343.705 −0.782927 −0.391463 0.920194i \(-0.628031\pi\)
−0.391463 + 0.920194i \(0.628031\pi\)
\(440\) 177.233 0.402802
\(441\) −52.4669 −0.118973
\(442\) 348.329i 0.788074i
\(443\) 515.530 1.16373 0.581863 0.813287i \(-0.302324\pi\)
0.581863 + 0.813287i \(0.302324\pi\)
\(444\) −62.7666 −0.141366
\(445\) −40.3296 −0.0906284
\(446\) 191.303 0.428931
\(447\) 534.000 1.19463
\(448\) 486.464i 1.08586i
\(449\) 598.611i 1.33321i 0.745411 + 0.666605i \(0.232253\pi\)
−0.745411 + 0.666605i \(0.767747\pi\)
\(450\) 643.236i 1.42941i
\(451\) −17.1561 −0.0380402
\(452\) 49.8279i 0.110239i
\(453\) 690.543 1.52438
\(454\) −248.087 −0.546448
\(455\) 253.291 0.556684
\(456\) 928.889i 2.03704i
\(457\) 459.459i 1.00538i 0.864467 + 0.502690i \(0.167656\pi\)
−0.864467 + 0.502690i \(0.832344\pi\)
\(458\) 547.963i 1.19643i
\(459\) 1204.92i 2.62509i
\(460\) 84.2468i 0.183145i
\(461\) 334.655 0.725933 0.362967 0.931802i \(-0.381764\pi\)
0.362967 + 0.931802i \(0.381764\pi\)
\(462\) 469.284i 1.01577i
\(463\) 696.646i 1.50464i −0.658801 0.752318i \(-0.728936\pi\)
0.658801 0.752318i \(-0.271064\pi\)
\(464\) 544.944i 1.17445i
\(465\) −247.343 −0.531921
\(466\) −534.610 −1.14723
\(467\) 123.292i 0.264009i 0.991249 + 0.132004i \(0.0421413\pi\)
−0.991249 + 0.132004i \(0.957859\pi\)
\(468\) −237.280 −0.507009
\(469\) 610.532i 1.30177i
\(470\) −54.4525 −0.115856
\(471\) −1063.59 −2.25815
\(472\) 554.398i 1.17457i
\(473\) −281.592 91.7725i −0.595332 0.194022i
\(474\) 499.751 1.05433
\(475\) 308.577i 0.649636i
\(476\) 91.6822i 0.192610i
\(477\) 705.541 1.47912
\(478\) 216.660i 0.453263i
\(479\) 201.938 0.421583 0.210791 0.977531i \(-0.432396\pi\)
0.210791 + 0.977531i \(0.432396\pi\)
\(480\) 223.770i 0.466188i
\(481\) 163.359i 0.339624i
\(482\) 843.443 1.74988
\(483\) −1275.03 −2.63981
\(484\) −62.3950 −0.128915
\(485\) 199.203i 0.410729i
\(486\) 1025.18 2.10943
\(487\) 151.294 0.310666 0.155333 0.987862i \(-0.450355\pi\)
0.155333 + 0.987862i \(0.450355\pi\)
\(488\) 673.014 1.37913
\(489\) 1485.51 3.03785
\(490\) 12.3450 0.0251939
\(491\) 56.4377i 0.114944i 0.998347 + 0.0574722i \(0.0183041\pi\)
−0.998347 + 0.0574722i \(0.981696\pi\)
\(492\) 11.8687i 0.0241234i
\(493\) 725.263i 1.47112i
\(494\) −422.964 −0.856203
\(495\) 464.481i 0.938345i
\(496\) −175.080 −0.352983
\(497\) −242.575 −0.488078
\(498\) −103.365 −0.207561
\(499\) 337.720i 0.676793i −0.941004 0.338396i \(-0.890116\pi\)
0.941004 0.338396i \(-0.109884\pi\)
\(500\) 104.127i 0.208254i
\(501\) 224.871i 0.448844i
\(502\) 63.8994i 0.127290i
\(503\) 124.026i 0.246573i −0.992371 0.123287i \(-0.960657\pi\)
0.992371 0.123287i \(-0.0393434\pi\)
\(504\) 1326.42 2.63179
\(505\) 219.272i 0.434201i
\(506\) 406.241i 0.802848i
\(507\) 85.4176i 0.168476i
\(508\) −15.2533 −0.0300262
\(509\) 229.831 0.451535 0.225767 0.974181i \(-0.427511\pi\)
0.225767 + 0.974181i \(0.427511\pi\)
\(510\) 471.715i 0.924931i
\(511\) −245.675 −0.480773
\(512\) 567.670i 1.10873i
\(513\) −1463.09 −2.85203
\(514\) −111.465 −0.216858
\(515\) 103.860i 0.201670i
\(516\) −63.4887 + 194.807i −0.123040 + 0.377533i
\(517\) −70.6642 −0.136681
\(518\) 159.768i 0.308432i
\(519\) 1019.57i 1.96450i
\(520\) 319.112 0.613677
\(521\) 335.813i 0.644555i −0.946645 0.322278i \(-0.895552\pi\)
0.946645 0.322278i \(-0.104448\pi\)
\(522\) −1835.76 −3.51679
\(523\) 630.020i 1.20463i 0.798259 + 0.602314i \(0.205754\pi\)
−0.798259 + 0.602314i \(0.794246\pi\)
\(524\) 87.6752i 0.167319i
\(525\) 616.446 1.17418
\(526\) −30.5073 −0.0579987
\(527\) −233.013 −0.442149
\(528\) 459.956i 0.871130i
\(529\) 574.743 1.08647
\(530\) −166.008 −0.313223
\(531\) −1452.93 −2.73621
\(532\) −111.327 −0.209261
\(533\) −30.8900 −0.0579550
\(534\) 134.536i 0.251940i
\(535\) 360.303i 0.673464i
\(536\) 769.186i 1.43505i
\(537\) 351.644 0.654831
\(538\) 724.216i 1.34613i
\(539\) 16.0204 0.0297224
\(540\) 193.124 0.357636
\(541\) 579.942 1.07198 0.535991 0.844224i \(-0.319938\pi\)
0.535991 + 0.844224i \(0.319938\pi\)
\(542\) 561.490i 1.03596i
\(543\) 93.9137i 0.172953i
\(544\) 210.805i 0.387510i
\(545\) 243.899i 0.447521i
\(546\) 844.958i 1.54754i
\(547\) 276.106 0.504764 0.252382 0.967628i \(-0.418786\pi\)
0.252382 + 0.967628i \(0.418786\pi\)
\(548\) 119.129i 0.217389i
\(549\) 1763.79i 3.21273i
\(550\) 196.408i 0.357105i
\(551\) 880.664 1.59830
\(552\) −1606.36 −2.91007
\(553\) 342.346i 0.619070i
\(554\) −371.767 −0.671059
\(555\) 221.225i 0.398603i
\(556\) 210.850 0.379226
\(557\) −1.44850 −0.00260054 −0.00130027 0.999999i \(-0.500414\pi\)
−0.00130027 + 0.999999i \(0.500414\pi\)
\(558\) 589.795i 1.05698i
\(559\) −507.013 165.239i −0.907000 0.295597i
\(560\) −242.799 −0.433569
\(561\) 612.154i 1.09118i
\(562\) 64.6542i 0.115043i
\(563\) −87.6035 −0.155601 −0.0778006 0.996969i \(-0.524790\pi\)
−0.0778006 + 0.996969i \(0.524790\pi\)
\(564\) 48.8859i 0.0866771i
\(565\) 175.622 0.310835
\(566\) 27.1845i 0.0480292i
\(567\) 1535.86i 2.70875i
\(568\) −305.611 −0.538047
\(569\) −657.323 −1.15522 −0.577612 0.816311i \(-0.696015\pi\)
−0.577612 + 0.816311i \(0.696015\pi\)
\(570\) 572.788 1.00489
\(571\) 321.145i 0.562426i −0.959645 0.281213i \(-0.909263\pi\)
0.959645 0.281213i \(-0.0907368\pi\)
\(572\) 72.4518 0.126664
\(573\) 251.292 0.438556
\(574\) 30.2109 0.0526322
\(575\) −533.633 −0.928057
\(576\) 1606.19 2.78852
\(577\) 440.527i 0.763479i 0.924270 + 0.381740i \(0.124675\pi\)
−0.924270 + 0.381740i \(0.875325\pi\)
\(578\) 68.6845i 0.118831i
\(579\) 759.494i 1.31173i
\(580\) −116.245 −0.200423
\(581\) 70.8085i 0.121874i
\(582\) 664.525 1.14180
\(583\) −215.432 −0.369523
\(584\) −309.516 −0.529994
\(585\) 836.308i 1.42959i
\(586\) 748.923i 1.27803i
\(587\) 975.567i 1.66195i 0.556307 + 0.830977i \(0.312218\pi\)
−0.556307 + 0.830977i \(0.687782\pi\)
\(588\) 11.0830i 0.0188486i
\(589\) 282.940i 0.480373i
\(590\) 341.863 0.579428
\(591\) 819.051i 1.38587i
\(592\) 156.592i 0.264513i
\(593\) 14.4319i 0.0243370i −0.999926 0.0121685i \(-0.996127\pi\)
0.999926 0.0121685i \(-0.00387345\pi\)
\(594\) −931.249 −1.56776
\(595\) −323.140 −0.543092
\(596\) 80.6306i 0.135286i
\(597\) −1576.61 −2.64089
\(598\) 731.447i 1.22316i
\(599\) −947.716 −1.58216 −0.791082 0.611710i \(-0.790482\pi\)
−0.791082 + 0.611710i \(0.790482\pi\)
\(600\) 776.636 1.29439
\(601\) 1115.25i 1.85565i 0.373016 + 0.927825i \(0.378324\pi\)
−0.373016 + 0.927825i \(0.621676\pi\)
\(602\) 495.866 + 161.606i 0.823698 + 0.268448i
\(603\) 2015.83 3.34301
\(604\) 104.268i 0.172628i
\(605\) 219.915i 0.363496i
\(606\) 731.470 1.20705
\(607\) 297.682i 0.490416i −0.969471 0.245208i \(-0.921144\pi\)
0.969471 0.245208i \(-0.0788562\pi\)
\(608\) −255.974 −0.421010
\(609\) 1759.31i 2.88885i
\(610\) 415.006i 0.680337i
\(611\) −127.233 −0.208237
\(612\) 302.713 0.494629
\(613\) 382.944 0.624705 0.312352 0.949966i \(-0.398883\pi\)
0.312352 + 0.949966i \(0.398883\pi\)
\(614\) 424.765i 0.691799i
\(615\) 41.8320 0.0680195
\(616\) −405.014 −0.657490
\(617\) −702.287 −1.13823 −0.569114 0.822258i \(-0.692714\pi\)
−0.569114 + 0.822258i \(0.692714\pi\)
\(618\) −346.467 −0.560627
\(619\) −680.743 −1.09975 −0.549873 0.835248i \(-0.685324\pi\)
−0.549873 + 0.835248i \(0.685324\pi\)
\(620\) 37.3472i 0.0602375i
\(621\) 2530.17i 4.07435i
\(622\) 1003.77i 1.61377i
\(623\) 92.1616 0.147932
\(624\) 828.162i 1.32718i
\(625\) 34.5564 0.0552903
\(626\) 603.876 0.964659
\(627\) 743.319 1.18552
\(628\) 160.595i 0.255724i
\(629\) 208.408i 0.331332i
\(630\) 817.922i 1.29829i
\(631\) 1019.35i 1.61546i −0.589555 0.807728i \(-0.700697\pi\)
0.589555 0.807728i \(-0.299303\pi\)
\(632\) 431.308i 0.682449i
\(633\) −1017.51 −1.60745
\(634\) 834.863i 1.31682i
\(635\) 53.7613i 0.0846634i
\(636\) 149.037i 0.234335i
\(637\) 28.8451 0.0452827
\(638\) 560.538 0.878586
\(639\) 800.925i 1.25340i
\(640\) −218.587 −0.341543
\(641\) 815.451i 1.27215i 0.771625 + 0.636077i \(0.219444\pi\)
−0.771625 + 0.636077i \(0.780556\pi\)
\(642\) 1201.94 1.87218
\(643\) 661.567 1.02888 0.514438 0.857528i \(-0.328001\pi\)
0.514438 + 0.857528i \(0.328001\pi\)
\(644\) 192.521i 0.298946i
\(645\) 686.609 + 223.770i 1.06451 + 0.346930i
\(646\) 539.602 0.835298
\(647\) 1013.73i 1.56681i −0.621512 0.783405i \(-0.713481\pi\)
0.621512 0.783405i \(-0.286519\pi\)
\(648\) 1934.97i 2.98607i
\(649\) 443.642 0.683578
\(650\) 353.636i 0.544056i
\(651\) 565.230 0.868249
\(652\) 224.302i 0.344022i
\(653\) 812.108i 1.24366i −0.783153 0.621829i \(-0.786390\pi\)
0.783153 0.621829i \(-0.213610\pi\)
\(654\) −813.624 −1.24407
\(655\) 309.017 0.471782
\(656\) 29.6104 0.0451378
\(657\) 811.160i 1.23464i
\(658\) 124.435 0.189111
\(659\) −1106.83 −1.67955 −0.839777 0.542932i \(-0.817314\pi\)
−0.839777 + 0.542932i \(0.817314\pi\)
\(660\) −98.1159 −0.148661
\(661\) 523.333 0.791729 0.395865 0.918309i \(-0.370445\pi\)
0.395865 + 0.918309i \(0.370445\pi\)
\(662\) −528.170 −0.797840
\(663\) 1102.20i 1.66244i
\(664\) 89.2089i 0.134351i
\(665\) 392.378i 0.590043i
\(666\) −527.515 −0.792064
\(667\) 1522.96i 2.28330i
\(668\) 33.9541 0.0508295
\(669\) −605.330 −0.904828
\(670\) −474.309 −0.707924
\(671\) 538.562i 0.802625i
\(672\) 511.361i 0.760953i
\(673\) 320.300i 0.475929i 0.971274 + 0.237965i \(0.0764803\pi\)
−0.971274 + 0.237965i \(0.923520\pi\)
\(674\) 866.629i 1.28580i
\(675\) 1223.28i 1.81226i
\(676\) −12.8975 −0.0190791
\(677\) 854.967i 1.26288i 0.775426 + 0.631438i \(0.217535\pi\)
−0.775426 + 0.631438i \(0.782465\pi\)
\(678\) 585.858i 0.864098i
\(679\) 455.221i 0.670428i
\(680\) −407.111 −0.598693
\(681\) 785.010 1.15273
\(682\) 180.090i 0.264061i
\(683\) 1331.16 1.94898 0.974492 0.224420i \(-0.0720488\pi\)
0.974492 + 0.224420i \(0.0720488\pi\)
\(684\) 367.575i 0.537390i
\(685\) −419.877 −0.612960
\(686\) −622.519 −0.907463
\(687\) 1733.89i 2.52386i
\(688\) 486.010 + 158.393i 0.706410 + 0.230223i
\(689\) −387.891 −0.562976
\(690\) 990.543i 1.43557i
\(691\) 568.600i 0.822866i 0.911440 + 0.411433i \(0.134972\pi\)
−0.911440 + 0.411433i \(0.865028\pi\)
\(692\) 153.949 0.222470
\(693\) 1061.43i 1.53165i
\(694\) 1101.12 1.58663
\(695\) 743.152i 1.06928i
\(696\) 2216.48i 3.18460i
\(697\) 39.4084 0.0565400
\(698\) 172.396 0.246985
\(699\) 1691.64 2.42008
\(700\) 93.0793i 0.132970i
\(701\) 369.079 0.526504 0.263252 0.964727i \(-0.415205\pi\)
0.263252 + 0.964727i \(0.415205\pi\)
\(702\) −1676.74 −2.38851
\(703\) 253.063 0.359975
\(704\) −490.439 −0.696646
\(705\) 172.301 0.244399
\(706\) 631.423i 0.894367i
\(707\) 501.081i 0.708742i
\(708\) 306.914i 0.433494i
\(709\) −656.495 −0.925945 −0.462972 0.886373i \(-0.653217\pi\)
−0.462972 + 0.886373i \(0.653217\pi\)
\(710\) 188.451i 0.265424i
\(711\) −1130.34 −1.58979
\(712\) 116.111 0.163077
\(713\) −489.298 −0.686252
\(714\) 1077.97i 1.50976i
\(715\) 255.361i 0.357148i
\(716\) 53.0960i 0.0741564i
\(717\) 685.564i 0.956157i
\(718\) 328.649i 0.457728i
\(719\) −497.631 −0.692115 −0.346057 0.938213i \(-0.612480\pi\)
−0.346057 + 0.938213i \(0.612480\pi\)
\(720\) 801.664i 1.11342i
\(721\) 237.341i 0.329183i
\(722\) 14.3293i 0.0198466i
\(723\) −2668.86 −3.69137
\(724\) 14.1804 0.0195861
\(725\) 736.315i 1.01561i
\(726\) −733.617 −1.01049
\(727\) 1020.14i 1.40322i −0.712559 0.701612i \(-0.752464\pi\)
0.712559 0.701612i \(-0.247536\pi\)
\(728\) −729.237 −1.00170
\(729\) −1220.64 −1.67441
\(730\) 190.859i 0.261451i
\(731\) 646.829 + 210.805i 0.884855 + 0.288379i
\(732\) −372.580 −0.508989
\(733\) 310.797i 0.424007i 0.977269 + 0.212003i \(0.0679987\pi\)
−0.977269 + 0.212003i \(0.932001\pi\)
\(734\) 673.942i 0.918177i
\(735\) −39.0627 −0.0531466
\(736\) 442.665i 0.601447i
\(737\) −615.521 −0.835171
\(738\) 99.7492i 0.135162i
\(739\) 1188.34i 1.60804i 0.594603 + 0.804020i \(0.297309\pi\)
−0.594603 + 0.804020i \(0.702691\pi\)
\(740\) −33.4035 −0.0451399
\(741\) 1338.36 1.80616
\(742\) 379.363 0.511271
\(743\) 258.515i 0.347934i −0.984752 0.173967i \(-0.944341\pi\)
0.984752 0.173967i \(-0.0556585\pi\)
\(744\) 712.111 0.957139
\(745\) 284.188 0.381460
\(746\) −337.857 −0.452891
\(747\) 233.793 0.312976
\(748\) −92.4313 −0.123571
\(749\) 823.367i 1.09929i
\(750\) 1224.29i 1.63238i
\(751\) 816.888i 1.08773i 0.839171 + 0.543867i \(0.183040\pi\)
−0.839171 + 0.543867i \(0.816960\pi\)
\(752\) 121.962 0.162183
\(753\) 202.193i 0.268517i
\(754\) 1009.26 1.33854
\(755\) 367.497 0.486752
\(756\) −441.327 −0.583766
\(757\) 807.752i 1.06704i −0.845786 0.533522i \(-0.820868\pi\)
0.845786 0.533522i \(-0.179132\pi\)
\(758\) 963.277i 1.27081i
\(759\) 1285.45i 1.69361i
\(760\) 494.342i 0.650450i
\(761\) 589.286i 0.774358i 0.922005 + 0.387179i \(0.126550\pi\)
−0.922005 + 0.387179i \(0.873450\pi\)
\(762\) −179.343 −0.235358
\(763\) 557.359i 0.730483i
\(764\) 37.9435i 0.0496643i
\(765\) 1066.93i 1.39468i
\(766\) 225.294 0.294118
\(767\) 798.788 1.04144
\(768\) 870.818i 1.13388i
\(769\) 1272.87 1.65522 0.827612 0.561300i \(-0.189699\pi\)
0.827612 + 0.561300i \(0.189699\pi\)
\(770\) 249.747i 0.324346i
\(771\) 352.703 0.457462
\(772\) 114.679 0.148547
\(773\) 176.192i 0.227933i 0.993485 + 0.113967i \(0.0363557\pi\)
−0.993485 + 0.113967i \(0.963644\pi\)
\(774\) −533.584 + 1637.23i −0.689385 + 2.11529i
\(775\) 236.563 0.305243
\(776\) 573.515i 0.739065i
\(777\) 505.544i 0.650636i
\(778\) −1223.50 −1.57262
\(779\) 47.8523i 0.0614279i
\(780\) −176.660 −0.226487
\(781\) 244.557i 0.313133i
\(782\) 933.153i 1.19329i
\(783\) 3491.17 4.45871
\(784\) −27.6502 −0.0352681
\(785\) −566.026 −0.721053
\(786\) 1030.85i 1.31152i
\(787\) −1120.38 −1.42361 −0.711804 0.702379i \(-0.752121\pi\)
−0.711804 + 0.702379i \(0.752121\pi\)
\(788\) 123.671 0.156943
\(789\) 96.5327 0.122348
\(790\) 265.961 0.336659
\(791\) −401.332 −0.507373
\(792\) 1337.26i 1.68846i
\(793\) 969.693i 1.22282i
\(794\) 749.323i 0.943732i
\(795\) 525.291 0.660743