Properties

Label 432.6.i.d.289.3
Level 432
Weight 6
Character 432.289
Analytic conductor 69.286
Analytic rank 0
Dimension 10
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(69.2858101592\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{16} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.3
Root \(-7.64342i\) of defining polynomial
Character \(\chi\) \(=\) 432.289
Dual form 432.6.i.d.145.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.88422 - 8.45972i) q^{5} +(68.3340 - 118.358i) q^{7} +O(q^{10})\) \(q+(-4.88422 - 8.45972i) q^{5} +(68.3340 - 118.358i) q^{7} +(-326.660 + 565.792i) q^{11} +(-125.247 - 216.934i) q^{13} -249.768 q^{17} +1754.03 q^{19} +(827.440 + 1433.17i) q^{23} +(1514.79 - 2623.69i) q^{25} +(2123.96 - 3678.81i) q^{29} +(4493.72 + 7783.34i) q^{31} -1335.03 q^{35} -6000.33 q^{37} +(-5372.59 - 9305.61i) q^{41} +(5023.30 - 8700.62i) q^{43} +(-11743.3 + 20340.0i) q^{47} +(-935.582 - 1620.48i) q^{49} -9411.34 q^{53} +6381.93 q^{55} +(-22083.4 - 38249.5i) q^{59} +(11202.4 - 19403.2i) q^{61} +(-1223.47 + 2119.11i) q^{65} +(-18001.5 - 31179.5i) q^{67} +78538.5 q^{71} +61305.5 q^{73} +(44644.1 + 77325.8i) q^{77} +(13745.0 - 23807.1i) q^{79} +(32403.2 - 56124.0i) q^{83} +(1219.92 + 2112.97i) q^{85} +34652.4 q^{89} -34234.5 q^{91} +(-8567.06 - 14838.6i) q^{95} +(-8056.14 + 13953.6i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} - 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} - 29q^{7} + 177q^{11} - 181q^{13} - 2280q^{17} + 832q^{19} + 399q^{23} - 4778q^{25} + 6033q^{29} - 2759q^{31} + 37146q^{35} - 15172q^{37} + 18435q^{41} - 1469q^{43} - 25155q^{47} - 4056q^{49} - 116844q^{53} - 14778q^{55} - 90537q^{59} + 1403q^{61} + 148407q^{65} - 13907q^{67} + 229368q^{71} + 15200q^{73} + 211983q^{77} - 29993q^{79} - 228951q^{83} - 49662q^{85} - 598332q^{89} - 124930q^{91} - 394764q^{95} + 40541q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −4.88422 8.45972i −0.0873716 0.151332i 0.819028 0.573754i \(-0.194513\pi\)
−0.906399 + 0.422422i \(0.861180\pi\)
\(6\) 0 0
\(7\) 68.3340 118.358i 0.527099 0.912962i −0.472403 0.881383i \(-0.656613\pi\)
0.999501 0.0315789i \(-0.0100535\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −326.660 + 565.792i −0.813982 + 1.40986i 0.0960745 + 0.995374i \(0.469371\pi\)
−0.910057 + 0.414484i \(0.863962\pi\)
\(12\) 0 0
\(13\) −125.247 216.934i −0.205546 0.356016i 0.744761 0.667332i \(-0.232564\pi\)
−0.950307 + 0.311316i \(0.899230\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −249.768 −0.209611 −0.104806 0.994493i \(-0.533422\pi\)
−0.104806 + 0.994493i \(0.533422\pi\)
\(18\) 0 0
\(19\) 1754.03 1.11469 0.557343 0.830282i \(-0.311821\pi\)
0.557343 + 0.830282i \(0.311821\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 827.440 + 1433.17i 0.326150 + 0.564908i 0.981744 0.190205i \(-0.0609153\pi\)
−0.655595 + 0.755113i \(0.727582\pi\)
\(24\) 0 0
\(25\) 1514.79 2623.69i 0.484732 0.839581i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2123.96 3678.81i 0.468977 0.812292i −0.530394 0.847751i \(-0.677956\pi\)
0.999371 + 0.0354595i \(0.0112895\pi\)
\(30\) 0 0
\(31\) 4493.72 + 7783.34i 0.839849 + 1.45466i 0.890020 + 0.455921i \(0.150690\pi\)
−0.0501712 + 0.998741i \(0.515977\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1335.03 −0.184214
\(36\) 0 0
\(37\) −6000.33 −0.720561 −0.360280 0.932844i \(-0.617319\pi\)
−0.360280 + 0.932844i \(0.617319\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5372.59 9305.61i −0.499142 0.864540i 0.500857 0.865530i \(-0.333018\pi\)
−1.00000 0.000990010i \(0.999685\pi\)
\(42\) 0 0
\(43\) 5023.30 8700.62i 0.414303 0.717594i −0.581052 0.813867i \(-0.697359\pi\)
0.995355 + 0.0962724i \(0.0306920\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11743.3 + 20340.0i −0.775435 + 1.34309i 0.159114 + 0.987260i \(0.449136\pi\)
−0.934550 + 0.355833i \(0.884197\pi\)
\(48\) 0 0
\(49\) −935.582 1620.48i −0.0556662 0.0964167i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9411.34 −0.460216 −0.230108 0.973165i \(-0.573908\pi\)
−0.230108 + 0.973165i \(0.573908\pi\)
\(54\) 0 0
\(55\) 6381.93 0.284476
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −22083.4 38249.5i −0.825915 1.43053i −0.901218 0.433366i \(-0.857326\pi\)
0.0753026 0.997161i \(-0.476008\pi\)
\(60\) 0 0
\(61\) 11202.4 19403.2i 0.385467 0.667649i −0.606366 0.795185i \(-0.707374\pi\)
0.991834 + 0.127536i \(0.0407069\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1223.47 + 2119.11i −0.0359177 + 0.0622113i
\(66\) 0 0
\(67\) −18001.5 31179.5i −0.489916 0.848560i 0.510016 0.860165i \(-0.329639\pi\)
−0.999933 + 0.0116049i \(0.996306\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 78538.5 1.84900 0.924499 0.381184i \(-0.124483\pi\)
0.924499 + 0.381184i \(0.124483\pi\)
\(72\) 0 0
\(73\) 61305.5 1.34646 0.673229 0.739434i \(-0.264907\pi\)
0.673229 + 0.739434i \(0.264907\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 44644.1 + 77325.8i 0.858098 + 1.48627i
\(78\) 0 0
\(79\) 13745.0 23807.1i 0.247787 0.429180i −0.715125 0.698997i \(-0.753630\pi\)
0.962911 + 0.269817i \(0.0869634\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 32403.2 56124.0i 0.516289 0.894238i −0.483533 0.875326i \(-0.660647\pi\)
0.999821 0.0189117i \(-0.00602013\pi\)
\(84\) 0 0
\(85\) 1219.92 + 2112.97i 0.0183141 + 0.0317209i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 34652.4 0.463722 0.231861 0.972749i \(-0.425518\pi\)
0.231861 + 0.972749i \(0.425518\pi\)
\(90\) 0 0
\(91\) −34234.5 −0.433372
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8567.06 14838.6i −0.0973919 0.168688i
\(96\) 0 0
\(97\) −8056.14 + 13953.6i −0.0869356 + 0.150577i −0.906214 0.422819i \(-0.861041\pi\)
0.819279 + 0.573395i \(0.194374\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 93469.6 161894.i 0.911731 1.57916i 0.100113 0.994976i \(-0.468079\pi\)
0.811618 0.584189i \(-0.198587\pi\)
\(102\) 0 0
\(103\) −84293.8 146001.i −0.782893 1.35601i −0.930250 0.366927i \(-0.880410\pi\)
0.147357 0.989083i \(-0.452923\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 155131. 1.30991 0.654953 0.755669i \(-0.272688\pi\)
0.654953 + 0.755669i \(0.272688\pi\)
\(108\) 0 0
\(109\) −115289. −0.929439 −0.464720 0.885458i \(-0.653845\pi\)
−0.464720 + 0.885458i \(0.653845\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 62693.8 + 108589.i 0.461880 + 0.799999i 0.999055 0.0434719i \(-0.0138419\pi\)
−0.537175 + 0.843471i \(0.680509\pi\)
\(114\) 0 0
\(115\) 8082.80 13999.8i 0.0569924 0.0987138i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −17067.7 + 29562.1i −0.110486 + 0.191367i
\(120\) 0 0
\(121\) −132889. 230170.i −0.825134 1.42917i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −60120.6 −0.344151
\(126\) 0 0
\(127\) −17459.4 −0.0960548 −0.0480274 0.998846i \(-0.515293\pi\)
−0.0480274 + 0.998846i \(0.515293\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 14464.0 + 25052.4i 0.0736395 + 0.127547i 0.900494 0.434869i \(-0.143205\pi\)
−0.826854 + 0.562416i \(0.809872\pi\)
\(132\) 0 0
\(133\) 119860. 207603.i 0.587549 1.01767i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 204277. 353818.i 0.929862 1.61057i 0.146312 0.989239i \(-0.453260\pi\)
0.783550 0.621329i \(-0.213407\pi\)
\(138\) 0 0
\(139\) 144577. + 250415.i 0.634693 + 1.09932i 0.986580 + 0.163278i \(0.0522066\pi\)
−0.351888 + 0.936042i \(0.614460\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 163653. 0.669243
\(144\) 0 0
\(145\) −41495.6 −0.163901
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −169.673 293.882i −0.000626104 0.00108444i 0.865712 0.500542i \(-0.166866\pi\)
−0.866338 + 0.499458i \(0.833533\pi\)
\(150\) 0 0
\(151\) 178737. 309581.i 0.637928 1.10492i −0.347958 0.937510i \(-0.613125\pi\)
0.985887 0.167414i \(-0.0535417\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 43896.6 76031.1i 0.146758 0.254192i
\(156\) 0 0
\(157\) 376.310 + 651.789i 0.00121842 + 0.00211037i 0.866634 0.498944i \(-0.166279\pi\)
−0.865416 + 0.501055i \(0.832945\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 226169. 0.687653
\(162\) 0 0
\(163\) 358488. 1.05683 0.528416 0.848986i \(-0.322786\pi\)
0.528416 + 0.848986i \(0.322786\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 246875. + 427601.i 0.684994 + 1.18644i 0.973439 + 0.228948i \(0.0735284\pi\)
−0.288445 + 0.957496i \(0.593138\pi\)
\(168\) 0 0
\(169\) 154273. 267209.i 0.415502 0.719670i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 83924.6 145362.i 0.213193 0.369262i −0.739519 0.673136i \(-0.764947\pi\)
0.952712 + 0.303874i \(0.0982802\pi\)
\(174\) 0 0
\(175\) −207023. 358575.i −0.511004 0.885084i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −483862. −1.12873 −0.564364 0.825526i \(-0.690878\pi\)
−0.564364 + 0.825526i \(0.690878\pi\)
\(180\) 0 0
\(181\) 74732.3 0.169555 0.0847777 0.996400i \(-0.472982\pi\)
0.0847777 + 0.996400i \(0.472982\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 29306.9 + 50761.1i 0.0629565 + 0.109044i
\(186\) 0 0
\(187\) 81589.4 141317.i 0.170620 0.295522i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 297130. 514645.i 0.589337 1.02076i −0.404983 0.914324i \(-0.632723\pi\)
0.994319 0.106437i \(-0.0339441\pi\)
\(192\) 0 0
\(193\) 44949.8 + 77855.4i 0.0868630 + 0.150451i 0.906184 0.422885i \(-0.138982\pi\)
−0.819321 + 0.573336i \(0.805649\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −425161. −0.780527 −0.390263 0.920703i \(-0.627616\pi\)
−0.390263 + 0.920703i \(0.627616\pi\)
\(198\) 0 0
\(199\) −374339. −0.670089 −0.335044 0.942202i \(-0.608751\pi\)
−0.335044 + 0.942202i \(0.608751\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −290278. 502775.i −0.494394 0.856316i
\(204\) 0 0
\(205\) −52481.9 + 90901.3i −0.0872217 + 0.151072i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −572971. + 992416.i −0.907334 + 1.57155i
\(210\) 0 0
\(211\) −82302.7 142552.i −0.127265 0.220429i 0.795351 0.606149i \(-0.207286\pi\)
−0.922616 + 0.385720i \(0.873953\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −98139.7 −0.144793
\(216\) 0 0
\(217\) 1.22829e6 1.77073
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 31282.7 + 54183.2i 0.0430848 + 0.0746250i
\(222\) 0 0
\(223\) −162339. + 281179.i −0.218605 + 0.378635i −0.954382 0.298589i \(-0.903484\pi\)
0.735777 + 0.677224i \(0.236817\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 354884. 614677.i 0.457111 0.791739i −0.541696 0.840575i \(-0.682218\pi\)
0.998807 + 0.0488351i \(0.0155509\pi\)
\(228\) 0 0
\(229\) 126953. + 219889.i 0.159976 + 0.277086i 0.934860 0.355017i \(-0.115525\pi\)
−0.774884 + 0.632104i \(0.782192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 557666. 0.672952 0.336476 0.941692i \(-0.390765\pi\)
0.336476 + 0.941692i \(0.390765\pi\)
\(234\) 0 0
\(235\) 229427. 0.271004
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 266147. + 460981.i 0.301389 + 0.522021i 0.976451 0.215740i \(-0.0692164\pi\)
−0.675062 + 0.737761i \(0.735883\pi\)
\(240\) 0 0
\(241\) −332544. + 575984.i −0.368814 + 0.638804i −0.989380 0.145350i \(-0.953569\pi\)
0.620567 + 0.784154i \(0.286903\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9139.17 + 15829.5i −0.00972729 + 0.0168482i
\(246\) 0 0
\(247\) −219687. 380508.i −0.229119 0.396846i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −906446. −0.908150 −0.454075 0.890963i \(-0.650030\pi\)
−0.454075 + 0.890963i \(0.650030\pi\)
\(252\) 0 0
\(253\) −1.08117e6 −1.06192
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −362420. 627731.i −0.342279 0.592844i 0.642577 0.766221i \(-0.277865\pi\)
−0.984855 + 0.173377i \(0.944532\pi\)
\(258\) 0 0
\(259\) −410027. + 710187.i −0.379807 + 0.657844i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −126262. + 218692.i −0.112560 + 0.194959i −0.916802 0.399343i \(-0.869238\pi\)
0.804242 + 0.594302i \(0.202572\pi\)
\(264\) 0 0
\(265\) 45967.1 + 79617.3i 0.0402098 + 0.0696455i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 191107. 0.161026 0.0805131 0.996754i \(-0.474344\pi\)
0.0805131 + 0.996754i \(0.474344\pi\)
\(270\) 0 0
\(271\) −86694.8 −0.0717084 −0.0358542 0.999357i \(-0.511415\pi\)
−0.0358542 + 0.999357i \(0.511415\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 989643. + 1.71411e6i 0.789127 + 1.36681i
\(276\) 0 0
\(277\) −635239. + 1.10027e6i −0.497437 + 0.861586i −0.999996 0.00295734i \(-0.999059\pi\)
0.502559 + 0.864543i \(0.332392\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −28414.8 + 49215.9i −0.0214674 + 0.0371826i −0.876560 0.481293i \(-0.840167\pi\)
0.855092 + 0.518476i \(0.173500\pi\)
\(282\) 0 0
\(283\) 676798. + 1.17225e6i 0.502335 + 0.870069i 0.999996 + 0.00269796i \(0.000858787\pi\)
−0.497662 + 0.867371i \(0.665808\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.46852e6 −1.05239
\(288\) 0 0
\(289\) −1.35747e6 −0.956063
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −263851. 457003.i −0.179552 0.310993i 0.762175 0.647371i \(-0.224131\pi\)
−0.941727 + 0.336378i \(0.890798\pi\)
\(294\) 0 0
\(295\) −215720. + 373638.i −0.144323 + 0.249975i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 207269. 359000.i 0.134077 0.232229i
\(300\) 0 0
\(301\) −686525. 1.18910e6i −0.436757 0.756486i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −218861. −0.134716
\(306\) 0 0
\(307\) −1.15348e6 −0.698497 −0.349249 0.937030i \(-0.613563\pi\)
−0.349249 + 0.937030i \(0.613563\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 758833. + 1.31434e6i 0.444883 + 0.770559i 0.998044 0.0625148i \(-0.0199121\pi\)
−0.553161 + 0.833074i \(0.686579\pi\)
\(312\) 0 0
\(313\) 979958. 1.69734e6i 0.565388 0.979281i −0.431625 0.902053i \(-0.642060\pi\)
0.997013 0.0772280i \(-0.0246069\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 916140. 1.58680e6i 0.512052 0.886899i −0.487851 0.872927i \(-0.662219\pi\)
0.999902 0.0139724i \(-0.00444770\pi\)
\(318\) 0 0
\(319\) 1.38763e6 + 2.40344e6i 0.763477 + 1.32238i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −438100. −0.233651
\(324\) 0 0
\(325\) −758891. −0.398539
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.60493e6 + 2.77983e6i 0.817462 + 1.41589i
\(330\) 0 0
\(331\) −360056. + 623635.i −0.180634 + 0.312868i −0.942097 0.335341i \(-0.891148\pi\)
0.761462 + 0.648209i \(0.224482\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −175847. + 304575.i −0.0856095 + 0.148280i
\(336\) 0 0
\(337\) 1.55433e6 + 2.69218e6i 0.745537 + 1.29131i 0.949943 + 0.312422i \(0.101140\pi\)
−0.204406 + 0.978886i \(0.565526\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.87168e6 −2.73449
\(342\) 0 0
\(343\) 2.04125e6 0.936831
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −136034. 235618.i −0.0606490 0.105047i 0.834107 0.551603i \(-0.185984\pi\)
−0.894756 + 0.446556i \(0.852650\pi\)
\(348\) 0 0
\(349\) −1.51024e6 + 2.61582e6i −0.663718 + 1.14959i 0.315913 + 0.948788i \(0.397689\pi\)
−0.979631 + 0.200805i \(0.935644\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 526944. 912695.i 0.225075 0.389842i −0.731267 0.682092i \(-0.761070\pi\)
0.956342 + 0.292250i \(0.0944038\pi\)
\(354\) 0 0
\(355\) −383599. 664413.i −0.161550 0.279813i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.26085e6 −1.74486 −0.872430 0.488739i \(-0.837457\pi\)
−0.872430 + 0.488739i \(0.837457\pi\)
\(360\) 0 0
\(361\) 600514. 0.242524
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −299430. 518628.i −0.117642 0.203762i
\(366\) 0 0
\(367\) −155650. + 269594.i −0.0603231 + 0.104483i −0.894610 0.446848i \(-0.852546\pi\)
0.834287 + 0.551331i \(0.185880\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −643115. + 1.11391e6i −0.242579 + 0.420160i
\(372\) 0 0
\(373\) 1.13768e6 + 1.97052e6i 0.423397 + 0.733345i 0.996269 0.0862997i \(-0.0275043\pi\)
−0.572872 + 0.819645i \(0.694171\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.06408e6 −0.385585
\(378\) 0 0
\(379\) −3.28710e6 −1.17548 −0.587739 0.809050i \(-0.699982\pi\)
−0.587739 + 0.809050i \(0.699982\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.12336e6 1.94572e6i −0.391311 0.677770i 0.601312 0.799014i \(-0.294645\pi\)
−0.992623 + 0.121244i \(0.961312\pi\)
\(384\) 0 0
\(385\) 436103. 755352.i 0.149947 0.259715i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −683723. + 1.18424e6i −0.229090 + 0.396796i −0.957539 0.288305i \(-0.906908\pi\)
0.728449 + 0.685100i \(0.240242\pi\)
\(390\) 0 0
\(391\) −206668. 357960.i −0.0683647 0.118411i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −268535. −0.0865982
\(396\) 0 0
\(397\) 1.52652e6 0.486099 0.243050 0.970014i \(-0.421852\pi\)
0.243050 + 0.970014i \(0.421852\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.36998e6 + 4.10493e6i 0.736011 + 1.27481i 0.954278 + 0.298920i \(0.0966263\pi\)
−0.218267 + 0.975889i \(0.570040\pi\)
\(402\) 0 0
\(403\) 1.12565e6 1.94968e6i 0.345255 0.597999i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.96007e6 3.39494e6i 0.586523 1.01589i
\(408\) 0 0
\(409\) −478468. 828731.i −0.141431 0.244966i 0.786605 0.617457i \(-0.211837\pi\)
−0.928036 + 0.372491i \(0.878504\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6.03619e6 −1.74136
\(414\) 0 0
\(415\) −633057. −0.180436
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −885418. 1.53359e6i −0.246384 0.426750i 0.716135 0.697961i \(-0.245909\pi\)
−0.962520 + 0.271211i \(0.912576\pi\)
\(420\) 0 0
\(421\) −1.54265e6 + 2.67194e6i −0.424190 + 0.734719i −0.996344 0.0854269i \(-0.972775\pi\)
0.572154 + 0.820146i \(0.306108\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −378346. + 655315.i −0.101605 + 0.175986i
\(426\) 0 0
\(427\) −1.53101e6 2.65180e6i −0.406359 0.703834i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.16873e6 0.562356 0.281178 0.959656i \(-0.409275\pi\)
0.281178 + 0.959656i \(0.409275\pi\)
\(432\) 0 0
\(433\) 6.69677e6 1.71651 0.858253 0.513226i \(-0.171550\pi\)
0.858253 + 0.513226i \(0.171550\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.45135e6 + 2.51382e6i 0.363554 + 0.629695i
\(438\) 0 0
\(439\) −3.23130e6 + 5.59677e6i −0.800231 + 1.38604i 0.119232 + 0.992866i \(0.461957\pi\)
−0.919464 + 0.393175i \(0.871377\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −877362. + 1.51964e6i −0.212407 + 0.367900i −0.952467 0.304640i \(-0.901464\pi\)
0.740060 + 0.672541i \(0.234797\pi\)
\(444\) 0 0
\(445\) −169250. 293149.i −0.0405162 0.0701761i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 515131. 0.120587 0.0602937 0.998181i \(-0.480796\pi\)
0.0602937 + 0.998181i \(0.480796\pi\)
\(450\) 0 0
\(451\) 7.02006e6 1.62517
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 167209. + 289614.i 0.0378644 + 0.0655830i
\(456\) 0 0
\(457\) 2.46694e6 4.27287e6i 0.552546 0.957038i −0.445543 0.895260i \(-0.646990\pi\)
0.998090 0.0617782i \(-0.0196771\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.12932e6 7.15219e6i 0.904953 1.56742i 0.0839718 0.996468i \(-0.473239\pi\)
0.820981 0.570956i \(-0.193427\pi\)
\(462\) 0 0
\(463\) 1.09543e6 + 1.89734e6i 0.237482 + 0.411331i 0.959991 0.280030i \(-0.0903445\pi\)
−0.722509 + 0.691362i \(0.757011\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.29374e6 0.486691 0.243345 0.969940i \(-0.421755\pi\)
0.243345 + 0.969940i \(0.421755\pi\)
\(468\) 0 0
\(469\) −4.92046e6 −1.03294
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.28183e6 + 5.68429e6i 0.674471 + 1.16822i
\(474\) 0 0
\(475\) 2.65698e6 4.60203e6i 0.540324 0.935869i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −46443.2 + 80442.0i −0.00924876 + 0.0160193i −0.870613 0.491969i \(-0.836277\pi\)
0.861364 + 0.507988i \(0.169611\pi\)
\(480\) 0 0
\(481\) 751522. + 1.30168e6i 0.148108 + 0.256531i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 157392. 0.0303828
\(486\) 0 0
\(487\) 1.13899e6 0.217620 0.108810 0.994063i \(-0.465296\pi\)
0.108810 + 0.994063i \(0.465296\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.36473e6 + 7.55993e6i 0.817060 + 1.41519i 0.907840 + 0.419318i \(0.137731\pi\)
−0.0907800 + 0.995871i \(0.528936\pi\)
\(492\) 0 0
\(493\) −530498. + 918849.i −0.0983029 + 0.170266i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.36685e6 9.29566e6i 0.974605 1.68807i
\(498\) 0 0
\(499\) −738810. 1.27966e6i −0.132825 0.230061i 0.791939 0.610600i \(-0.209072\pi\)
−0.924765 + 0.380539i \(0.875738\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −743514. −0.131029 −0.0655147 0.997852i \(-0.520869\pi\)
−0.0655147 + 0.997852i \(0.520869\pi\)
\(504\) 0 0
\(505\) −1.82610e6 −0.318638
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.43560e6 7.68269e6i −0.758854 1.31437i −0.943435 0.331556i \(-0.892426\pi\)
0.184582 0.982817i \(-0.440907\pi\)
\(510\) 0 0
\(511\) 4.18926e6 7.25600e6i 0.709716 1.22926i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −823419. + 1.42620e6i −0.136805 + 0.236954i
\(516\) 0 0
\(517\) −7.67214e6 1.32885e7i −1.26238 2.18651i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00935e6 0.324311 0.162155 0.986765i \(-0.448155\pi\)
0.162155 + 0.986765i \(0.448155\pi\)
\(522\) 0 0
\(523\) −6.39895e6 −1.02295 −0.511475 0.859298i \(-0.670901\pi\)
−0.511475 + 0.859298i \(0.670901\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.12239e6 1.94403e6i −0.176042 0.304914i
\(528\) 0 0
\(529\) 1.84886e6 3.20231e6i 0.287253 0.497536i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.34580e6 + 2.33100e6i −0.205193 + 0.355405i
\(534\) 0 0
\(535\) −757696. 1.31237e6i −0.114449 0.198231i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.22247e6 0.181245
\(540\) 0 0
\(541\) −1.26335e7 −1.85580 −0.927899 0.372832i \(-0.878387\pi\)
−0.927899 + 0.372832i \(0.878387\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 563096. + 975311.i 0.0812066 + 0.140654i
\(546\) 0 0
\(547\) −5.51776e6 + 9.55704e6i −0.788487 + 1.36570i 0.138407 + 0.990375i \(0.455802\pi\)
−0.926894 + 0.375323i \(0.877532\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.72548e6 6.45273e6i 0.522762 0.905450i
\(552\) 0 0
\(553\) −1.87851e6 3.25367e6i −0.261216 0.452440i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.08374e7 1.48009 0.740046 0.672557i \(-0.234804\pi\)
0.740046 + 0.672557i \(0.234804\pi\)
\(558\) 0 0
\(559\) −2.51661e6 −0.340633
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.65688e6 + 2.86981e6i 0.220303 + 0.381577i 0.954900 0.296927i \(-0.0959619\pi\)
−0.734597 + 0.678504i \(0.762629\pi\)
\(564\) 0 0
\(565\) 612421. 1.06074e6i 0.0807103 0.139794i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −774757. + 1.34192e6i −0.100319 + 0.173758i −0.911816 0.410599i \(-0.865320\pi\)
0.811497 + 0.584357i \(0.198653\pi\)
\(570\) 0 0
\(571\) 1.59557e6 + 2.76361e6i 0.204798 + 0.354720i 0.950068 0.312042i \(-0.101013\pi\)
−0.745271 + 0.666762i \(0.767680\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.01359e6 0.632381
\(576\) 0 0
\(577\) 9.55234e6 1.19446 0.597228 0.802072i \(-0.296269\pi\)
0.597228 + 0.802072i \(0.296269\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.42848e6 7.67035e6i −0.544270 0.942704i
\(582\) 0 0
\(583\) 3.07431e6 5.32487e6i 0.374608 0.648840i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.64410e6 9.77587e6i 0.676083 1.17101i −0.300069 0.953918i \(-0.597010\pi\)
0.976151 0.217092i \(-0.0696571\pi\)
\(588\) 0 0
\(589\) 7.88210e6 + 1.36522e7i 0.936168 + 1.62149i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.91815e6 0.924671 0.462336 0.886705i \(-0.347012\pi\)
0.462336 + 0.886705i \(0.347012\pi\)
\(594\) 0 0
\(595\) 333449. 0.0386133
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.60914e6 + 2.78711e6i 0.183242 + 0.317385i 0.942983 0.332841i \(-0.108007\pi\)
−0.759740 + 0.650227i \(0.774674\pi\)
\(600\) 0 0
\(601\) 3.74304e6 6.48314e6i 0.422706 0.732149i −0.573497 0.819208i \(-0.694414\pi\)
0.996203 + 0.0870589i \(0.0277468\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.29811e6 + 2.24840e6i −0.144186 + 0.249738i
\(606\) 0 0
\(607\) −5.06061e6 8.76524e6i −0.557483 0.965588i −0.997706 0.0676999i \(-0.978434\pi\)
0.440223 0.897888i \(-0.354899\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.88325e6 0.637550
\(612\) 0 0
\(613\) −4.34715e6 −0.467254 −0.233627 0.972326i \(-0.575059\pi\)
−0.233627 + 0.972326i \(0.575059\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.29590e6 + 1.61010e7i 0.983056 + 1.70270i 0.650275 + 0.759699i \(0.274654\pi\)
0.332781 + 0.943004i \(0.392013\pi\)
\(618\) 0 0
\(619\) 6.83014e6 1.18301e7i 0.716478 1.24098i −0.245909 0.969293i \(-0.579086\pi\)
0.962387 0.271683i \(-0.0875802\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.36794e6 4.10139e6i 0.244428 0.423361i
\(624\) 0 0
\(625\) −4.44007e6 7.69043e6i −0.454663 0.787500i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.49869e6 0.151038
\(630\) 0 0
\(631\) 3.33121e6 0.333065 0.166532 0.986036i \(-0.446743\pi\)
0.166532 + 0.986036i \(0.446743\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 85275.4 + 147701.i 0.00839246 + 0.0145362i
\(636\) 0 0
\(637\) −234358. + 405919.i −0.0228839 + 0.0396361i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.14477e6 1.98280e6i 0.110046 0.190604i −0.805743 0.592266i \(-0.798234\pi\)
0.915788 + 0.401661i \(0.131567\pi\)
\(642\) 0 0
\(643\) −3.40519e6 5.89797e6i −0.324799 0.562568i 0.656673 0.754176i \(-0.271963\pi\)
−0.981472 + 0.191608i \(0.938630\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.48250e7 −1.39231 −0.696153 0.717894i \(-0.745106\pi\)
−0.696153 + 0.717894i \(0.745106\pi\)
\(648\) 0 0
\(649\) 2.88551e7 2.68912
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.06356e6 7.03829e6i −0.372927 0.645928i 0.617088 0.786894i \(-0.288312\pi\)
−0.990014 + 0.140966i \(0.954979\pi\)
\(654\) 0 0
\(655\) 141291. 244723.i 0.0128680 0.0222880i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.07616e6 7.06011e6i 0.365626 0.633283i −0.623250 0.782023i \(-0.714188\pi\)
0.988876 + 0.148739i \(0.0475215\pi\)
\(660\) 0 0
\(661\) 4.37958e6 + 7.58565e6i 0.389878 + 0.675288i 0.992433 0.122789i \(-0.0391839\pi\)
−0.602555 + 0.798077i \(0.705851\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.34169e6 −0.205341
\(666\) 0 0
\(667\) 7.02980e6 0.611827
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.31878e6 + 1.26765e7i 0.627527 + 1.08691i
\(672\) 0 0
\(673\) −4.26745e6 + 7.39143e6i −0.363187 + 0.629058i −0.988483 0.151329i \(-0.951645\pi\)
0.625296 + 0.780387i \(0.284978\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.58162e6 + 1.31317e7i −0.635755 + 1.10116i 0.350599 + 0.936526i \(0.385978\pi\)
−0.986355 + 0.164635i \(0.947355\pi\)
\(678\) 0 0
\(679\) 1.10102e6 + 1.90702e6i 0.0916473 + 0.158738i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.33221e7 −1.09275 −0.546376 0.837540i \(-0.683993\pi\)
−0.546376 + 0.837540i \(0.683993\pi\)
\(684\) 0 0
\(685\) −3.99094e6 −0.324974
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.17874e6 + 2.04164e6i 0.0945956 + 0.163844i
\(690\) 0 0
\(691\) −981739. + 1.70042e6i −0.0782169 + 0.135476i −0.902481 0.430730i \(-0.858256\pi\)
0.824264 + 0.566206i \(0.191589\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.41230e6 2.44617e6i 0.110908 0.192099i
\(696\) 0 0
\(697\) 1.34190e6 + 2.32425e6i 0.104626 + 0.181217i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.36605e7 −1.81856 −0.909282 0.416180i \(-0.863369\pi\)
−0.909282 + 0.416180i \(0.863369\pi\)
\(702\) 0 0
\(703\) −1.05247e7 −0.803199
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.27743e7 2.21257e7i −0.961145 1.66475i
\(708\) 0 0
\(709\) 8.39194e6 1.45353e7i 0.626970 1.08594i −0.361186 0.932494i \(-0.617628\pi\)
0.988156 0.153451i \(-0.0490386\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.43656e6 + 1.28805e7i −0.547833 + 0.948875i
\(714\) 0 0
\(715\) −799317. 1.38446e6i −0.0584728 0.101278i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5.89621e6 −0.425355 −0.212677 0.977123i \(-0.568218\pi\)
−0.212677 + 0.977123i \(0.568218\pi\)
\(720\) 0 0
\(721\) −2.30405e7 −1.65065
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.43470e6 1.11452e7i −0.454656 0.787488i
\(726\) 0 0
\(727\) −5.15459e6 + 8.92800e6i −0.361708 + 0.626496i −0.988242 0.152898i \(-0.951139\pi\)
0.626534 + 0.779394i \(0.284473\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.25466e6 + 2.17314e6i −0.0868427 + 0.150416i
\(732\) 0 0
\(733\) −7.66868e6 1.32825e7i −0.527182 0.913106i −0.999498 0.0316768i \(-0.989915\pi\)
0.472316 0.881429i \(-0.343418\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.35215e7 1.59513
\(738\) 0 0
\(739\) 1.97929e6 0.133321 0.0666606 0.997776i \(-0.478766\pi\)
0.0666606 + 0.997776i \(0.478766\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.44874e7 + 2.50929e7i 0.962758 + 1.66755i 0.715520 + 0.698592i \(0.246190\pi\)
0.247238 + 0.968955i \(0.420477\pi\)
\(744\) 0 0
\(745\) −1657.44 + 2870.77i −0.000109407 + 0.000189499i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.06008e7 1.83611e7i 0.690450 1.19589i
\(750\) 0 0
\(751\) 5.21827e6 + 9.03831e6i 0.337619 + 0.584773i 0.983984 0.178255i \(-0.0570452\pi\)
−0.646366 + 0.763028i \(0.723712\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.49196e6 −0.222947
\(756\) 0 0
\(757\) 1.51464e7 0.960661 0.480331 0.877087i \(-0.340517\pi\)
0.480331 + 0.877087i \(0.340517\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.10900e7 1.92084e7i −0.694176 1.20235i −0.970458 0.241271i \(-0.922436\pi\)
0.276282 0.961077i \(-0.410898\pi\)
\(762\) 0 0
\(763\) −7.87815e6 + 1.36454e7i −0.489906 + 0.848542i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.53175e6 + 9.58127e6i −0.339527 + 0.588078i
\(768\) 0 0
\(769\) 3.21191e6 + 5.56319e6i 0.195861 + 0.339241i 0.947182 0.320695i \(-0.103917\pi\)
−0.751322 + 0.659936i \(0.770583\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.34346e6 −0.141062 −0.0705308 0.997510i \(-0.522469\pi\)
−0.0705308 + 0.997510i \(0.522469\pi\)
\(774\) 0 0
\(775\) 2.72281e7 1.62841
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.42368e6 1.63223e7i −0.556387 0.963690i
\(780\) 0 0
\(781\) −2.56554e7 + 4.44365e7i −1.50505 + 2.60683i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3675.97 6366.96i 0.000212911 0.000368772i
\(786\) 0 0
\(787\) 1.42540e7 + 2.46887e7i 0.820354 + 1.42089i 0.905419 + 0.424519i \(0.139557\pi\)
−0.0850650 + 0.996375i \(0.527110\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.71365e7 0.973824
\(792\) 0 0
\(793\) −5.61228e6 −0.316925
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.77498e6 + 6.53845e6i 0.210508 + 0.364611i 0.951874 0.306491i \(-0.0991549\pi\)
−0.741366 + 0.671101i \(0.765822\pi\)
\(798\) 0 0
\(799\) 2.93310e6 5.08028e6i 0.162540 0.281528i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.00261e7 +