Properties

Label 432.6.i.d.289.4
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 289.4
Root \(2.13639i\) of defining polynomial
Character \(\chi\) \(=\) 432.289
Dual form 432.6.i.d.145.4

$q$-expansion

\(f(q)\) \(=\) \(q+(14.0718 + 24.3731i) q^{5} +(-75.7039 + 131.123i) q^{7} +O(q^{10})\) \(q+(14.0718 + 24.3731i) q^{5} +(-75.7039 + 131.123i) q^{7} +(138.873 - 240.536i) q^{11} +(-291.929 - 505.636i) q^{13} +1612.01 q^{17} -1368.76 q^{19} +(-428.014 - 741.342i) q^{23} +(1166.47 - 2020.38i) q^{25} +(4267.49 - 7391.50i) q^{29} +(1469.19 + 2544.71i) q^{31} -4261.17 q^{35} +4036.80 q^{37} +(9449.81 + 16367.5i) q^{41} +(-10158.6 + 17595.1i) q^{43} +(147.890 - 256.152i) q^{47} +(-3058.67 - 5297.78i) q^{49} -3039.13 q^{53} +7816.81 q^{55} +(8618.31 + 14927.4i) q^{59} +(-12826.2 + 22215.7i) q^{61} +(8215.95 - 14230.4i) q^{65} +(-13140.1 - 22759.4i) q^{67} +76665.7 q^{71} +1496.33 q^{73} +(21026.5 + 36419.0i) q^{77} +(49637.1 - 85974.0i) q^{79} +(-25025.7 + 43345.7i) q^{83} +(22683.8 + 39289.6i) q^{85} -136635. q^{89} +88400.8 q^{91} +(-19261.0 - 33361.0i) q^{95} +(33325.0 - 57720.5i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} - 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} - 29q^{7} + 177q^{11} - 181q^{13} - 2280q^{17} + 832q^{19} + 399q^{23} - 4778q^{25} + 6033q^{29} - 2759q^{31} + 37146q^{35} - 15172q^{37} + 18435q^{41} - 1469q^{43} - 25155q^{47} - 4056q^{49} - 116844q^{53} - 14778q^{55} - 90537q^{59} + 1403q^{61} + 148407q^{65} - 13907q^{67} + 229368q^{71} + 15200q^{73} + 211983q^{77} - 29993q^{79} - 228951q^{83} - 49662q^{85} - 598332q^{89} - 124930q^{91} - 394764q^{95} + 40541q^{97} + O(q^{100}) \)

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
\(5\) 14.0718 + 24.3731i 0.251724 + 0.435999i 0.964001 0.265900i \(-0.0856690\pi\)
−0.712276 + 0.701899i \(0.752336\pi\)
\(6\) 0 0
\(7\) −75.7039 + 131.123i −0.583947 + 1.01143i 0.411059 + 0.911609i \(0.365159\pi\)
−0.995006 + 0.0998170i \(0.968174\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 138.873 240.536i 0.346049 0.599374i −0.639495 0.768795i \(-0.720856\pi\)
0.985544 + 0.169421i \(0.0541898\pi\)
\(12\) 0 0
\(13\) −291.929 505.636i −0.479092 0.829812i 0.520620 0.853788i \(-0.325701\pi\)
−0.999713 + 0.0239762i \(0.992367\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1612.01 1.35283 0.676417 0.736519i \(-0.263532\pi\)
0.676417 + 0.736519i \(0.263532\pi\)
\(18\) 0 0
\(19\) −1368.76 −0.869851 −0.434925 0.900467i \(-0.643225\pi\)
−0.434925 + 0.900467i \(0.643225\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −428.014 741.342i −0.168709 0.292213i 0.769257 0.638939i \(-0.220627\pi\)
−0.937966 + 0.346727i \(0.887293\pi\)
\(24\) 0 0
\(25\) 1166.47 2020.38i 0.373270 0.646522i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4267.49 7391.50i 0.942274 1.63207i 0.181154 0.983455i \(-0.442017\pi\)
0.761120 0.648611i \(-0.224650\pi\)
\(30\) 0 0
\(31\) 1469.19 + 2544.71i 0.274583 + 0.475591i 0.970030 0.242986i \(-0.0781269\pi\)
−0.695447 + 0.718577i \(0.744794\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4261.17 −0.587975
\(36\) 0 0
\(37\) 4036.80 0.484767 0.242383 0.970181i \(-0.422071\pi\)
0.242383 + 0.970181i \(0.422071\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9449.81 + 16367.5i 0.877937 + 1.52063i 0.853601 + 0.520928i \(0.174414\pi\)
0.0243361 + 0.999704i \(0.492253\pi\)
\(42\) 0 0
\(43\) −10158.6 + 17595.1i −0.837840 + 1.45118i 0.0538576 + 0.998549i \(0.482848\pi\)
−0.891697 + 0.452632i \(0.850485\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 147.890 256.152i 0.00976546 0.0169143i −0.861101 0.508433i \(-0.830225\pi\)
0.870867 + 0.491519i \(0.163558\pi\)
\(48\) 0 0
\(49\) −3058.67 5297.78i −0.181988 0.315213i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3039.13 −0.148614 −0.0743069 0.997235i \(-0.523674\pi\)
−0.0743069 + 0.997235i \(0.523674\pi\)
\(54\) 0 0
\(55\) 7816.81 0.348436
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8618.31 + 14927.4i 0.322324 + 0.558281i 0.980967 0.194174i \(-0.0622027\pi\)
−0.658643 + 0.752455i \(0.728869\pi\)
\(60\) 0 0
\(61\) −12826.2 + 22215.7i −0.441342 + 0.764426i −0.997789 0.0664565i \(-0.978831\pi\)
0.556448 + 0.830883i \(0.312164\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 8215.95 14230.4i 0.241198 0.417768i
\(66\) 0 0
\(67\) −13140.1 22759.4i −0.357613 0.619403i 0.629949 0.776637i \(-0.283076\pi\)
−0.987561 + 0.157233i \(0.949743\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 76665.7 1.80491 0.902454 0.430786i \(-0.141764\pi\)
0.902454 + 0.430786i \(0.141764\pi\)
\(72\) 0 0
\(73\) 1496.33 0.0328640 0.0164320 0.999865i \(-0.494769\pi\)
0.0164320 + 0.999865i \(0.494769\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 21026.5 + 36419.0i 0.404148 + 0.700006i
\(78\) 0 0
\(79\) 49637.1 85974.0i 0.894826 1.54988i 0.0608070 0.998150i \(-0.480633\pi\)
0.834019 0.551735i \(-0.186034\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −25025.7 + 43345.7i −0.398740 + 0.690639i −0.993571 0.113213i \(-0.963886\pi\)
0.594830 + 0.803851i \(0.297219\pi\)
\(84\) 0 0
\(85\) 22683.8 + 39289.6i 0.340541 + 0.589834i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −136635. −1.82847 −0.914235 0.405185i \(-0.867207\pi\)
−0.914235 + 0.405185i \(0.867207\pi\)
\(90\) 0 0
\(91\) 88400.8 1.11906
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −19261.0 33361.0i −0.218963 0.379254i
\(96\) 0 0
\(97\) 33325.0 57720.5i 0.359617 0.622875i −0.628280 0.777987i \(-0.716241\pi\)
0.987897 + 0.155113i \(0.0495740\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12338.7 + 21371.2i −0.120355 + 0.208462i −0.919908 0.392135i \(-0.871737\pi\)
0.799552 + 0.600596i \(0.205070\pi\)
\(102\) 0 0
\(103\) 57883.5 + 100257.i 0.537603 + 0.931155i 0.999032 + 0.0439785i \(0.0140033\pi\)
−0.461430 + 0.887177i \(0.652663\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 84364.3 0.712360 0.356180 0.934417i \(-0.384079\pi\)
0.356180 + 0.934417i \(0.384079\pi\)
\(108\) 0 0
\(109\) 198400. 1.59947 0.799735 0.600354i \(-0.204973\pi\)
0.799735 + 0.600354i \(0.204973\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 114453. + 198238.i 0.843199 + 1.46046i 0.887176 + 0.461430i \(0.152664\pi\)
−0.0439777 + 0.999033i \(0.514003\pi\)
\(114\) 0 0
\(115\) 12045.9 20864.1i 0.0849364 0.147114i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −122035. + 211371.i −0.789983 + 1.36829i
\(120\) 0 0
\(121\) 41953.8 + 72666.2i 0.260500 + 0.451200i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 153606. 0.879293
\(126\) 0 0
\(127\) 246629. 1.35686 0.678430 0.734665i \(-0.262661\pi\)
0.678430 + 0.734665i \(0.262661\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 84612.6 + 146553.i 0.430781 + 0.746135i 0.996941 0.0781606i \(-0.0249047\pi\)
−0.566159 + 0.824296i \(0.691571\pi\)
\(132\) 0 0
\(133\) 103621. 179477.i 0.507947 0.879789i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 49985.3 86577.0i 0.227531 0.394095i −0.729545 0.683933i \(-0.760268\pi\)
0.957076 + 0.289838i \(0.0936013\pi\)
\(138\) 0 0
\(139\) −18699.4 32388.2i −0.0820899 0.142184i 0.822058 0.569404i \(-0.192826\pi\)
−0.904147 + 0.427221i \(0.859493\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −162165. −0.663158
\(144\) 0 0
\(145\) 240205. 0.948773
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 127267. + 220433.i 0.469623 + 0.813411i 0.999397 0.0347281i \(-0.0110565\pi\)
−0.529774 + 0.848139i \(0.677723\pi\)
\(150\) 0 0
\(151\) −118363. + 205010.i −0.422448 + 0.731701i −0.996178 0.0873434i \(-0.972162\pi\)
0.573731 + 0.819044i \(0.305496\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −41348.3 + 71617.4i −0.138238 + 0.239436i
\(156\) 0 0
\(157\) −127406. 220673.i −0.412515 0.714497i 0.582649 0.812724i \(-0.302016\pi\)
−0.995164 + 0.0982266i \(0.968683\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 129609. 0.394069
\(162\) 0 0
\(163\) −215050. −0.633973 −0.316987 0.948430i \(-0.602671\pi\)
−0.316987 + 0.948430i \(0.602671\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −96168.5 166569.i −0.266834 0.462171i 0.701208 0.712956i \(-0.252644\pi\)
−0.968043 + 0.250786i \(0.919311\pi\)
\(168\) 0 0
\(169\) 15201.2 26329.2i 0.0409411 0.0709121i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4150.57 + 7189.00i −0.0105437 + 0.0182622i −0.871249 0.490841i \(-0.836690\pi\)
0.860705 + 0.509103i \(0.170023\pi\)
\(174\) 0 0
\(175\) 176612. + 305902.i 0.435939 + 0.755069i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 574496. 1.34015 0.670077 0.742292i \(-0.266261\pi\)
0.670077 + 0.742292i \(0.266261\pi\)
\(180\) 0 0
\(181\) −224707. −0.509823 −0.254912 0.966964i \(-0.582046\pi\)
−0.254912 + 0.966964i \(0.582046\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 56805.1 + 98389.3i 0.122028 + 0.211358i
\(186\) 0 0
\(187\) 223865. 387745.i 0.468147 0.810854i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 239041. 414031.i 0.474121 0.821201i −0.525440 0.850830i \(-0.676099\pi\)
0.999561 + 0.0296294i \(0.00943271\pi\)
\(192\) 0 0
\(193\) 263025. + 455572.i 0.508281 + 0.880368i 0.999954 + 0.00958824i \(0.00305208\pi\)
−0.491673 + 0.870780i \(0.663615\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 222278. 0.408067 0.204034 0.978964i \(-0.434595\pi\)
0.204034 + 0.978964i \(0.434595\pi\)
\(198\) 0 0
\(199\) 109696. 0.196363 0.0981813 0.995169i \(-0.468697\pi\)
0.0981813 + 0.995169i \(0.468697\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 646131. + 1.11913e6i 1.10048 + 1.90608i
\(204\) 0 0
\(205\) −265952. + 460642.i −0.441996 + 0.765560i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −190085. + 329237.i −0.301011 + 0.521366i
\(210\) 0 0
\(211\) −309436. 535959.i −0.478482 0.828754i 0.521214 0.853426i \(-0.325479\pi\)
−0.999696 + 0.0246717i \(0.992146\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −571797. −0.843618
\(216\) 0 0
\(217\) −444893. −0.641367
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −470592. 815089.i −0.648132 1.12260i
\(222\) 0 0
\(223\) 231653. 401234.i 0.311943 0.540301i −0.666840 0.745201i \(-0.732354\pi\)
0.978783 + 0.204900i \(0.0656868\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 573326. 993029.i 0.738477 1.27908i −0.214704 0.976679i \(-0.568879\pi\)
0.953181 0.302400i \(-0.0977878\pi\)
\(228\) 0 0
\(229\) 175527. + 304022.i 0.221185 + 0.383104i 0.955168 0.296064i \(-0.0956741\pi\)
−0.733983 + 0.679168i \(0.762341\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −814275. −0.982610 −0.491305 0.870988i \(-0.663480\pi\)
−0.491305 + 0.870988i \(0.663480\pi\)
\(234\) 0 0
\(235\) 8324.30 0.00983281
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 357452. + 619124.i 0.404783 + 0.701105i 0.994296 0.106654i \(-0.0340137\pi\)
−0.589513 + 0.807759i \(0.700680\pi\)
\(240\) 0 0
\(241\) −22648.5 + 39228.3i −0.0251186 + 0.0435068i −0.878311 0.478089i \(-0.841330\pi\)
0.853193 + 0.521596i \(0.174663\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 86082.2 149099.i 0.0916216 0.158693i
\(246\) 0 0
\(247\) 399582. + 692097.i 0.416739 + 0.721813i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.35110e6 −1.35364 −0.676822 0.736147i \(-0.736643\pi\)
−0.676822 + 0.736147i \(0.736643\pi\)
\(252\) 0 0
\(253\) −237759. −0.233526
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 600097. + 1.03940e6i 0.566747 + 0.981634i 0.996885 + 0.0788708i \(0.0251315\pi\)
−0.430138 + 0.902763i \(0.641535\pi\)
\(258\) 0 0
\(259\) −305602. + 529318.i −0.283078 + 0.490306i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 656802. 1.13761e6i 0.585525 1.01416i −0.409285 0.912407i \(-0.634222\pi\)
0.994810 0.101752i \(-0.0324449\pi\)
\(264\) 0 0
\(265\) −42766.1 74073.0i −0.0374097 0.0647956i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −321363. −0.270779 −0.135389 0.990792i \(-0.543229\pi\)
−0.135389 + 0.990792i \(0.543229\pi\)
\(270\) 0 0
\(271\) −384928. −0.318388 −0.159194 0.987247i \(-0.550890\pi\)
−0.159194 + 0.987247i \(0.550890\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −323983. 561155.i −0.258339 0.447457i
\(276\) 0 0
\(277\) 847964. 1.46872e6i 0.664015 1.15011i −0.315536 0.948913i \(-0.602184\pi\)
0.979551 0.201194i \(-0.0644822\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 530669. 919146.i 0.400920 0.694415i −0.592917 0.805264i \(-0.702024\pi\)
0.993837 + 0.110849i \(0.0353570\pi\)
\(282\) 0 0
\(283\) −192313. 333096.i −0.142739 0.247231i 0.785788 0.618496i \(-0.212258\pi\)
−0.928527 + 0.371265i \(0.878924\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.86155e6 −2.05067
\(288\) 0 0
\(289\) 1.17871e6 0.830158
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −667643. 1.15639e6i −0.454334 0.786929i 0.544316 0.838880i \(-0.316789\pi\)
−0.998650 + 0.0519513i \(0.983456\pi\)
\(294\) 0 0
\(295\) −242551. + 420110.i −0.162273 + 0.281066i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −249900. + 432839.i −0.161655 + 0.279994i
\(300\) 0 0
\(301\) −1.53809e6 2.66404e6i −0.978508 1.69483i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −721954. −0.444386
\(306\) 0 0
\(307\) −636269. −0.385296 −0.192648 0.981268i \(-0.561708\pi\)
−0.192648 + 0.981268i \(0.561708\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 269890. + 467464.i 0.158229 + 0.274061i 0.934230 0.356671i \(-0.116088\pi\)
−0.776001 + 0.630732i \(0.782755\pi\)
\(312\) 0 0
\(313\) −976605. + 1.69153e6i −0.563454 + 0.975931i 0.433738 + 0.901039i \(0.357194\pi\)
−0.997192 + 0.0748915i \(0.976139\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 781983. 1.35443e6i 0.437068 0.757024i −0.560394 0.828226i \(-0.689350\pi\)
0.997462 + 0.0712021i \(0.0226835\pi\)
\(318\) 0 0
\(319\) −1.18528e6 2.05297e6i −0.652146 1.12955i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.20646e6 −1.17676
\(324\) 0 0
\(325\) −1.36210e6 −0.715323
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 22391.6 + 38783.5i 0.0114050 + 0.0197541i
\(330\) 0 0
\(331\) −1.28000e6 + 2.21702e6i −0.642154 + 1.11224i 0.342796 + 0.939410i \(0.388626\pi\)
−0.984951 + 0.172834i \(0.944707\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 369811. 640532.i 0.180040 0.311838i
\(336\) 0 0
\(337\) 299646. + 519002.i 0.143725 + 0.248940i 0.928897 0.370339i \(-0.120758\pi\)
−0.785171 + 0.619279i \(0.787425\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 816125. 0.380076
\(342\) 0 0
\(343\) −1.61850e6 −0.742808
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.34386e6 2.32764e6i −0.599144 1.03775i −0.992948 0.118553i \(-0.962174\pi\)
0.393804 0.919195i \(-0.371159\pi\)
\(348\) 0 0
\(349\) −335807. + 581635.i −0.147580 + 0.255615i −0.930332 0.366717i \(-0.880482\pi\)
0.782753 + 0.622333i \(0.213815\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −764881. + 1.32481e6i −0.326706 + 0.565871i −0.981856 0.189627i \(-0.939272\pi\)
0.655150 + 0.755499i \(0.272605\pi\)
\(354\) 0 0
\(355\) 1.07883e6 + 1.86858e6i 0.454339 + 0.786939i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.27210e6 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(360\) 0 0
\(361\) −602583. −0.243360
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 21056.1 + 36470.2i 0.00827267 + 0.0143287i
\(366\) 0 0
\(367\) 313571. 543121.i 0.121526 0.210490i −0.798843 0.601539i \(-0.794554\pi\)
0.920370 + 0.391049i \(0.127888\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 230074. 398500.i 0.0867826 0.150312i
\(372\) 0 0
\(373\) −66186.8 114639.i −0.0246320 0.0426638i 0.853447 0.521180i \(-0.174508\pi\)
−0.878079 + 0.478516i \(0.841175\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.98322e6 −1.80574
\(378\) 0 0
\(379\) 163225. 0.0583700 0.0291850 0.999574i \(-0.490709\pi\)
0.0291850 + 0.999574i \(0.490709\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 398301. + 689877.i 0.138744 + 0.240312i 0.927021 0.375008i \(-0.122360\pi\)
−0.788277 + 0.615320i \(0.789027\pi\)
\(384\) 0 0
\(385\) −591763. + 1.02496e6i −0.203468 + 0.352417i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.04745e6 3.54629e6i 0.686024 1.18823i −0.287089 0.957904i \(-0.592688\pi\)
0.973114 0.230325i \(-0.0739790\pi\)
\(390\) 0 0
\(391\) −689961. 1.19505e6i −0.228235 0.395315i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.79394e6 0.900998
\(396\) 0 0
\(397\) −5.58867e6 −1.77964 −0.889820 0.456312i \(-0.849170\pi\)
−0.889820 + 0.456312i \(0.849170\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.11676e6 + 1.93429e6i 0.346817 + 0.600705i 0.985682 0.168614i \(-0.0539291\pi\)
−0.638865 + 0.769319i \(0.720596\pi\)
\(402\) 0 0
\(403\) 857798. 1.48575e6i 0.263101 0.455704i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 560604. 970995.i 0.167753 0.290557i
\(408\) 0 0
\(409\) 2.30256e6 + 3.98815e6i 0.680617 + 1.17886i 0.974793 + 0.223111i \(0.0716214\pi\)
−0.294176 + 0.955751i \(0.595045\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.60976e6 −0.752880
\(414\) 0 0
\(415\) −1.40863e6 −0.401491
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −571064. 989112.i −0.158909 0.275239i 0.775566 0.631266i \(-0.217464\pi\)
−0.934476 + 0.356027i \(0.884131\pi\)
\(420\) 0 0
\(421\) −962383. + 1.66690e6i −0.264632 + 0.458356i −0.967467 0.252996i \(-0.918584\pi\)
0.702835 + 0.711353i \(0.251917\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.88035e6 3.25687e6i 0.504972 0.874637i
\(426\) 0 0
\(427\) −1.94199e6 3.36363e6i −0.515440 0.892769i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.21303e6 0.573843 0.286922 0.957954i \(-0.407368\pi\)
0.286922 + 0.957954i \(0.407368\pi\)
\(432\) 0 0
\(433\) 3.00235e6 0.769558 0.384779 0.923009i \(-0.374278\pi\)
0.384779 + 0.923009i \(0.374278\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 585851. + 1.01472e6i 0.146752 + 0.254181i
\(438\) 0 0
\(439\) 960857. 1.66425e6i 0.237956 0.412153i −0.722171 0.691714i \(-0.756856\pi\)
0.960128 + 0.279562i \(0.0901891\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 924258. 1.60086e6i 0.223761 0.387565i −0.732186 0.681105i \(-0.761500\pi\)
0.955947 + 0.293540i \(0.0948332\pi\)
\(444\) 0 0
\(445\) −1.92271e6 3.33022e6i −0.460270 0.797211i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.45640e6 −0.809110 −0.404555 0.914514i \(-0.632574\pi\)
−0.404555 + 0.914514i \(0.632574\pi\)
\(450\) 0 0
\(451\) 5.24931e6 1.21524
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.24396e6 + 2.15460e6i 0.281694 + 0.487908i
\(456\) 0 0
\(457\) −1.79319e6 + 3.10589e6i −0.401638 + 0.695658i −0.993924 0.110070i \(-0.964892\pi\)
0.592286 + 0.805728i \(0.298226\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.21775e6 7.30536e6i 0.924333 1.60099i 0.131703 0.991289i \(-0.457955\pi\)
0.792630 0.609703i \(-0.208711\pi\)
\(462\) 0 0
\(463\) 2.47237e6 + 4.28227e6i 0.535995 + 0.928370i 0.999114 + 0.0420745i \(0.0133967\pi\)
−0.463120 + 0.886296i \(0.653270\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.12589e6 −0.875438 −0.437719 0.899112i \(-0.644213\pi\)
−0.437719 + 0.899112i \(0.644213\pi\)
\(468\) 0 0
\(469\) 3.97904e6 0.835307
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.82151e6 + 4.88700e6i 0.579867 + 1.00436i
\(474\) 0 0
\(475\) −1.59662e6 + 2.76543e6i −0.324689 + 0.562378i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 561301. 972203.i 0.111778 0.193606i −0.804709 0.593669i \(-0.797679\pi\)
0.916487 + 0.400064i \(0.131012\pi\)
\(480\) 0 0
\(481\) −1.17846e6 2.04115e6i −0.232248 0.402265i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.87577e6 0.362097
\(486\) 0 0
\(487\) −8.11380e6 −1.55025 −0.775126 0.631807i \(-0.782313\pi\)
−0.775126 + 0.631807i \(0.782313\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.66481e6 + 2.88353e6i 0.311645 + 0.539786i 0.978719 0.205207i \(-0.0657866\pi\)
−0.667073 + 0.744992i \(0.732453\pi\)
\(492\) 0 0
\(493\) 6.87921e6 1.19151e7i 1.27474 2.20791i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.80389e6 + 1.00526e7i −1.05397 + 1.82553i
\(498\) 0 0
\(499\) 940630. + 1.62922e6i 0.169109 + 0.292906i 0.938107 0.346346i \(-0.112578\pi\)
−0.768998 + 0.639252i \(0.779244\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.96749e6 −1.40411 −0.702056 0.712122i \(-0.747734\pi\)
−0.702056 + 0.712122i \(0.747734\pi\)
\(504\) 0 0
\(505\) −694511. −0.121186
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.40561e6 + 9.36279e6i 0.924805 + 1.60181i 0.791874 + 0.610684i \(0.209106\pi\)
0.132931 + 0.991125i \(0.457561\pi\)
\(510\) 0 0
\(511\) −113278. + 196204.i −0.0191908 + 0.0332395i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.62905e6 + 2.82160e6i −0.270655 + 0.468789i
\(516\) 0 0
\(517\) −41075.9 71145.5i −0.00675865 0.0117063i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.19670e6 0.193148 0.0965740 0.995326i \(-0.469212\pi\)
0.0965740 + 0.995326i \(0.469212\pi\)
\(522\) 0 0
\(523\) 6.43371e6 1.02851 0.514254 0.857638i \(-0.328069\pi\)
0.514254 + 0.857638i \(0.328069\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.36834e6 + 4.10209e6i 0.371465 + 0.643396i
\(528\) 0 0
\(529\) 2.85178e6 4.93943e6i 0.443074 0.767427i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.51735e6 9.55633e6i 0.841226 1.45705i
\(534\) 0 0
\(535\) 1.18716e6 + 2.05622e6i 0.179318 + 0.310588i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.69907e6 −0.251907
\(540\) 0 0
\(541\) 5.85989e6 0.860788 0.430394 0.902641i \(-0.358375\pi\)
0.430394 + 0.902641i \(0.358375\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.79185e6 + 4.83563e6i 0.402625 + 0.697368i
\(546\) 0 0
\(547\) 2.59436e6 4.49357e6i 0.370734 0.642130i −0.618945 0.785434i \(-0.712440\pi\)
0.989679 + 0.143305i \(0.0457729\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.84118e6 + 1.01172e7i −0.819637 + 1.41965i
\(552\) 0 0
\(553\) 7.51545e6 + 1.30171e7i 1.04506 + 1.81010i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.07405e6 −0.692973 −0.346487 0.938055i \(-0.612625\pi\)
−0.346487 + 0.938055i \(0.612625\pi\)
\(558\) 0 0
\(559\) 1.18623e7 1.60561
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.05439e6 + 5.29036e6i 0.406119 + 0.703419i 0.994451 0.105200i \(-0.0335484\pi\)
−0.588332 + 0.808620i \(0.700215\pi\)
\(564\) 0 0
\(565\) −3.22111e6 + 5.57913e6i −0.424507 + 0.735268i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.40483e6 + 9.36143e6i −0.699844 + 1.21216i 0.268677 + 0.963230i \(0.413414\pi\)
−0.968520 + 0.248934i \(0.919920\pi\)
\(570\) 0 0
\(571\) 6.02796e6 + 1.04407e7i 0.773714 + 1.34011i 0.935515 + 0.353288i \(0.114937\pi\)
−0.161801 + 0.986823i \(0.551730\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.99706e6 −0.251896
\(576\) 0 0
\(577\) 1.22323e7 1.52957 0.764786 0.644285i \(-0.222845\pi\)
0.764786 + 0.644285i \(0.222845\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.78908e6 6.56288e6i −0.465686 0.806593i
\(582\) 0 0
\(583\) −422054. + 731019.i −0.0514277 + 0.0890754i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.29817e6 7.44465e6i 0.514859 0.891762i −0.484992 0.874519i \(-0.661177\pi\)
0.999851 0.0172439i \(-0.00548917\pi\)
\(588\) 0 0
\(589\) −2.01097e6 3.48311e6i −0.238846 0.413693i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.78455e6 0.675511 0.337756 0.941234i \(-0.390332\pi\)
0.337756 + 0.941234i \(0.390332\pi\)
\(594\) 0 0
\(595\) −6.86903e6 −0.795432
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.62557e6 + 4.54761e6i 0.298989 + 0.517865i 0.975905 0.218196i \(-0.0700172\pi\)
−0.676916 + 0.736061i \(0.736684\pi\)
\(600\) 0 0
\(601\) 3.11169e6 5.38960e6i 0.351407 0.608654i −0.635090 0.772439i \(-0.719037\pi\)
0.986496 + 0.163784i \(0.0523701\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.18073e6 + 2.04509e6i −0.131148 + 0.227156i
\(606\) 0 0
\(607\) −7.94049e6 1.37533e7i −0.874733 1.51508i −0.857046 0.515239i \(-0.827703\pi\)
−0.0176871 0.999844i \(-0.505630\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −172693. −0.0187142
\(612\) 0 0
\(613\) −1.28661e7 −1.38292 −0.691458 0.722417i \(-0.743031\pi\)
−0.691458 + 0.722417i \(0.743031\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.43797e6 5.95473e6i −0.363571 0.629723i 0.624975 0.780645i \(-0.285109\pi\)
−0.988546 + 0.150922i \(0.951776\pi\)
\(618\) 0 0
\(619\) 6.52408e6 1.13000e7i 0.684373 1.18537i −0.289261 0.957250i \(-0.593409\pi\)
0.973633 0.228118i \(-0.0732572\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.03438e7 1.79160e7i 1.06773 1.84936i
\(624\) 0 0
\(625\) −1.48369e6 2.56983e6i −0.151930 0.263151i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.50734e6 0.655809
\(630\) 0 0
\(631\) 1.52784e7 1.52758 0.763790 0.645464i \(-0.223336\pi\)
0.763790 + 0.645464i \(0.223336\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.47052e6 + 6.01111e6i 0.341554 + 0.591590i
\(636\) 0 0
\(637\) −1.78583e6 + 3.09315e6i −0.174378 + 0.302032i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.96157e6 + 1.03257e7i −0.573080 + 0.992604i 0.423167 + 0.906052i \(0.360918\pi\)
−0.996247 + 0.0865524i \(0.972415\pi\)
\(642\) 0 0
\(643\) −3.00302e6 5.20137e6i −0.286438 0.496125i 0.686519 0.727112i \(-0.259138\pi\)
−0.972957 + 0.230987i \(0.925804\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.19440e7 1.12173 0.560864 0.827908i \(-0.310469\pi\)
0.560864 + 0.827908i \(0.310469\pi\)
\(648\) 0 0
\(649\) 4.78742e6 0.446159
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.53297e6 2.65518e6i −0.140686 0.243675i 0.787069 0.616864i \(-0.211597\pi\)
−0.927755 + 0.373190i \(0.878264\pi\)
\(654\) 0 0
\(655\) −2.38131e6 + 4.12454e6i −0.216876 + 0.375641i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.55065e6 2.68581e6i 0.139092 0.240914i −0.788061 0.615597i \(-0.788915\pi\)
0.927153 + 0.374683i \(0.122248\pi\)
\(660\) 0 0
\(661\) −6.48853e6 1.12385e7i −0.577621 1.00047i −0.995751 0.0920819i \(-0.970648\pi\)
0.418130 0.908387i \(-0.362685\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.83253e6 0.511450
\(666\) 0 0
\(667\) −7.30618e6 −0.635881
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.56245e6 + 6.17034e6i 0.305452 + 0.529058i
\(672\) 0 0
\(673\) −1.10703e7 + 1.91743e7i −0.942154 + 1.63186i −0.180801 + 0.983520i \(0.557869\pi\)
−0.761352 + 0.648338i \(0.775464\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 799850. 1.38538e6i 0.0670713 0.116171i −0.830540 0.556960i \(-0.811968\pi\)
0.897611 + 0.440789i \(0.145301\pi\)
\(678\) 0 0
\(679\) 5.04566e6 + 8.73934e6i 0.419994 + 0.727452i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.36986e7 1.12363 0.561816 0.827262i \(-0.310103\pi\)
0.561816 + 0.827262i \(0.310103\pi\)
\(684\) 0 0
\(685\) 2.81353e6 0.229100
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 887210. + 1.53669e6i 0.0711998 + 0.123322i
\(690\) 0 0
\(691\) −2.09107e6 + 3.62183e6i −0.166599 + 0.288558i −0.937222 0.348733i \(-0.886612\pi\)
0.770623 + 0.637291i \(0.219945\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 526268. 911522.i 0.0413280 0.0715822i
\(696\) 0 0
\(697\) 1.52331e7 + 2.63846e7i 1.18770 + 2.05716i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.47134e7 1.13089 0.565443 0.824788i \(-0.308705\pi\)
0.565443 + 0.824788i \(0.308705\pi\)
\(702\) 0 0
\(703\) −5.52543e6 −0.421675
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.86818e6 3.23577e6i −0.140562 0.243461i
\(708\) 0 0
\(709\) 4.25908e6 7.37694e6i 0.318200 0.551139i −0.661913 0.749581i \(-0.730255\pi\)
0.980113 + 0.198442i \(0.0635883\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.25767e6 2.17834e6i 0.0926493 0.160473i
\(714\) 0 0
\(715\) −2.28195e6 3.95246e6i −0.166933 0.289136i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.20183e7 −0.867003 −0.433502 0.901153i \(-0.642722\pi\)
−0.433502 + 0.901153i \(0.642722\pi\)
\(720\) 0 0
\(721\) −1.75280e7 −1.25573
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9.95577e6 1.72439e7i −0.703445 1.21840i
\(726\) 0 0
\(727\) 1.49257e6 2.58521e6i 0.104737 0.181409i −0.808894 0.587955i \(-0.799933\pi\)
0.913631 + 0.406545i \(0.133267\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.63757e7 + 2.83635e7i −1.13346 + 1.96321i
\(732\) 0 0
\(733\) −1.05675e7 1.83035e7i −0.726464 1.25827i −0.958369 0.285534i \(-0.907829\pi\)
0.231905 0.972739i \(-0.425504\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.29926e6 −0.495006
\(738\) 0 0
\(739\) −1.33961e7 −0.902337 −0.451168 0.892439i \(-0.648993\pi\)
−0.451168 + 0.892439i \(0.648993\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.95418e6 1.03129e7i −0.395685 0.685347i 0.597503 0.801867i \(-0.296160\pi\)
−0.993188 + 0.116519i \(0.962826\pi\)
\(744\) 0 0
\(745\) −3.58175e6 + 6.20377e6i −0.236431 + 0.409511i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.38671e6 + 1.10621e7i −0.415980 + 0.720499i
\(750\) 0 0
\(751\) 2.33184e6 + 4.03886e6i 0.150868 + 0.261312i 0.931547 0.363621i \(-0.118460\pi\)
−0.780679 + 0.624933i \(0.785126\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6.66232e6 −0.425361
\(756\) 0 0
\(757\) 138599. 0.00879065 0.00439532 0.999990i \(-0.498601\pi\)
0.00439532 + 0.999990i \(0.498601\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.19856e6 + 2.07597e6i 0.0750237 + 0.129945i 0.901097 0.433618i \(-0.142763\pi\)
−0.826073 + 0.563563i \(0.809430\pi\)
\(762\) 0 0
\(763\) −1.50197e7 + 2.60148e7i −0.934005 + 1.61774i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.03188e6 8.71546e6i 0.308846 0.534936i
\(768\) 0 0
\(769\) −399739. 692369.i −0.0243759 0.0422203i 0.853580 0.520962i \(-0.174427\pi\)
−0.877956 + 0.478741i \(0.841093\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.07743e6 −0.0648546 −0.0324273 0.999474i \(-0.510324\pi\)
−0.0324273 + 0.999474i \(0.510324\pi\)
\(774\) 0 0
\(775\) 6.85505e6 0.409974
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.29346e7 2.24033e7i −0.763674 1.32272i
\(780\) 0 0
\(781\) 1.06468e7 1.84408e7i 0.624586 1.08182i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.58566e6 6.21055e6i 0.207680 0.359713i
\(786\) 0 0
\(787\) 1.53546e6 + 2.65949e6i 0.0883692 + 0.153060i 0.906822 0.421514i \(-0.138501\pi\)
−0.818453 + 0.574574i \(0.805168\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.46581e7 −1.96953
\(792\) 0 0
\(793\) 1.49774e7 0.845774
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.49242e6 + 1.29772e7i 0.417808 + 0.723664i 0.995719 0.0924359i \(-0.0294653\pi\)
−0.577911 + 0.816100i \(0.696132\pi\)
\(798\) 0 0
\(799\) 238399. 412919.i 0.0132110 0.0228822i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 207801. 359921.i 0.0113726