Properties

Label 320.6.f.c.289.14
Level 320
Weight 6
Character 320.289
Analytic conductor 51.323
Analytic rank 0
Dimension 16
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 39122 x^{12} + 391243971 x^{8} + 75462898750 x^{4} + 18538406640625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{42}\cdot 5^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.14
Root \(-11.8760 + 0.526271i\) of defining polynomial
Character \(\chi\) \(=\) 320.289
Dual form 320.6.f.c.289.13

$q$-expansion

\(f(q)\) \(=\) \(q+24.8046 q^{3} +(-53.4447 + 16.3911i) q^{5} +100.281i q^{7} +372.267 q^{9} +O(q^{10})\) \(q+24.8046 q^{3} +(-53.4447 + 16.3911i) q^{5} +100.281i q^{7} +372.267 q^{9} +5.36667i q^{11} -506.854 q^{13} +(-1325.67 + 406.573i) q^{15} +1454.37i q^{17} -722.433i q^{19} +2487.43i q^{21} -3086.22i q^{23} +(2587.67 - 1752.03i) q^{25} +3206.40 q^{27} +7298.39i q^{29} -8609.68 q^{31} +133.118i q^{33} +(-1643.72 - 5359.50i) q^{35} -5276.52 q^{37} -12572.3 q^{39} -18175.5 q^{41} -8340.95 q^{43} +(-19895.7 + 6101.84i) q^{45} +22120.2i q^{47} +6750.67 q^{49} +36075.1i q^{51} -13363.7 q^{53} +(-87.9654 - 286.820i) q^{55} -17919.6i q^{57} -10958.8i q^{59} -10982.0i q^{61} +37331.4i q^{63} +(27088.7 - 8307.88i) q^{65} -13007.5 q^{67} -76552.4i q^{69} +36009.0 q^{71} +64286.0i q^{73} +(64186.0 - 43458.3i) q^{75} -538.177 q^{77} +48638.8 q^{79} -10927.3 q^{81} -49784.4 q^{83} +(-23838.7 - 77728.6i) q^{85} +181033. i q^{87} +7764.40 q^{89} -50828.0i q^{91} -213559. q^{93} +(11841.4 + 38610.2i) q^{95} -36848.8i q^{97} +1997.83i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 1904q^{9} + O(q^{10}) \) \( 16q + 1904q^{9} + 880q^{25} - 100352q^{41} + 128272q^{49} + 149760q^{65} - 154576q^{81} - 459296q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 24.8046 1.59121 0.795607 0.605813i \(-0.207152\pi\)
0.795607 + 0.605813i \(0.207152\pi\)
\(4\) 0 0
\(5\) −53.4447 + 16.3911i −0.956047 + 0.293212i
\(6\) 0 0
\(7\) 100.281i 0.773526i 0.922179 + 0.386763i \(0.126407\pi\)
−0.922179 + 0.386763i \(0.873593\pi\)
\(8\) 0 0
\(9\) 372.267 1.53196
\(10\) 0 0
\(11\) 5.36667i 0.0133728i 0.999978 + 0.00668641i \(0.00212837\pi\)
−0.999978 + 0.00668641i \(0.997872\pi\)
\(12\) 0 0
\(13\) −506.854 −0.831811 −0.415906 0.909408i \(-0.636535\pi\)
−0.415906 + 0.909408i \(0.636535\pi\)
\(14\) 0 0
\(15\) −1325.67 + 406.573i −1.52128 + 0.466563i
\(16\) 0 0
\(17\) 1454.37i 1.22055i 0.792191 + 0.610273i \(0.208940\pi\)
−0.792191 + 0.610273i \(0.791060\pi\)
\(18\) 0 0
\(19\) 722.433i 0.459107i −0.973296 0.229553i \(-0.926273\pi\)
0.973296 0.229553i \(-0.0737266\pi\)
\(20\) 0 0
\(21\) 2487.43i 1.23084i
\(22\) 0 0
\(23\) 3086.22i 1.21649i −0.793750 0.608244i \(-0.791874\pi\)
0.793750 0.608244i \(-0.208126\pi\)
\(24\) 0 0
\(25\) 2587.67 1752.03i 0.828053 0.560649i
\(26\) 0 0
\(27\) 3206.40 0.846465
\(28\) 0 0
\(29\) 7298.39i 1.61151i 0.592251 + 0.805753i \(0.298239\pi\)
−0.592251 + 0.805753i \(0.701761\pi\)
\(30\) 0 0
\(31\) −8609.68 −1.60910 −0.804549 0.593886i \(-0.797593\pi\)
−0.804549 + 0.593886i \(0.797593\pi\)
\(32\) 0 0
\(33\) 133.118i 0.0212790i
\(34\) 0 0
\(35\) −1643.72 5359.50i −0.226807 0.739527i
\(36\) 0 0
\(37\) −5276.52 −0.633641 −0.316821 0.948485i \(-0.602615\pi\)
−0.316821 + 0.948485i \(0.602615\pi\)
\(38\) 0 0
\(39\) −12572.3 −1.32359
\(40\) 0 0
\(41\) −18175.5 −1.68860 −0.844301 0.535869i \(-0.819984\pi\)
−0.844301 + 0.535869i \(0.819984\pi\)
\(42\) 0 0
\(43\) −8340.95 −0.687930 −0.343965 0.938982i \(-0.611770\pi\)
−0.343965 + 0.938982i \(0.611770\pi\)
\(44\) 0 0
\(45\) −19895.7 + 6101.84i −1.46463 + 0.449190i
\(46\) 0 0
\(47\) 22120.2i 1.46064i 0.683103 + 0.730322i \(0.260630\pi\)
−0.683103 + 0.730322i \(0.739370\pi\)
\(48\) 0 0
\(49\) 6750.67 0.401658
\(50\) 0 0
\(51\) 36075.1i 1.94215i
\(52\) 0 0
\(53\) −13363.7 −0.653489 −0.326745 0.945113i \(-0.605952\pi\)
−0.326745 + 0.945113i \(0.605952\pi\)
\(54\) 0 0
\(55\) −87.9654 286.820i −0.00392108 0.0127851i
\(56\) 0 0
\(57\) 17919.6i 0.730537i
\(58\) 0 0
\(59\) 10958.8i 0.409859i −0.978777 0.204929i \(-0.934304\pi\)
0.978777 0.204929i \(-0.0656965\pi\)
\(60\) 0 0
\(61\) 10982.0i 0.377883i −0.981988 0.188941i \(-0.939494\pi\)
0.981988 0.188941i \(-0.0605056\pi\)
\(62\) 0 0
\(63\) 37331.4i 1.18501i
\(64\) 0 0
\(65\) 27088.7 8307.88i 0.795251 0.243897i
\(66\) 0 0
\(67\) −13007.5 −0.354003 −0.177002 0.984211i \(-0.556640\pi\)
−0.177002 + 0.984211i \(0.556640\pi\)
\(68\) 0 0
\(69\) 76552.4i 1.93569i
\(70\) 0 0
\(71\) 36009.0 0.847744 0.423872 0.905722i \(-0.360671\pi\)
0.423872 + 0.905722i \(0.360671\pi\)
\(72\) 0 0
\(73\) 64286.0i 1.41192i 0.708253 + 0.705959i \(0.249484\pi\)
−0.708253 + 0.705959i \(0.750516\pi\)
\(74\) 0 0
\(75\) 64186.0 43458.3i 1.31761 0.892113i
\(76\) 0 0
\(77\) −538.177 −0.0103442
\(78\) 0 0
\(79\) 48638.8 0.876830 0.438415 0.898773i \(-0.355540\pi\)
0.438415 + 0.898773i \(0.355540\pi\)
\(80\) 0 0
\(81\) −10927.3 −0.185055
\(82\) 0 0
\(83\) −49784.4 −0.793228 −0.396614 0.917985i \(-0.629815\pi\)
−0.396614 + 0.917985i \(0.629815\pi\)
\(84\) 0 0
\(85\) −23838.7 77728.6i −0.357879 1.16690i
\(86\) 0 0
\(87\) 181033.i 2.56425i
\(88\) 0 0
\(89\) 7764.40 0.103904 0.0519521 0.998650i \(-0.483456\pi\)
0.0519521 + 0.998650i \(0.483456\pi\)
\(90\) 0 0
\(91\) 50828.0i 0.643427i
\(92\) 0 0
\(93\) −213559. −2.56042
\(94\) 0 0
\(95\) 11841.4 + 38610.2i 0.134616 + 0.438928i
\(96\) 0 0
\(97\) 36848.8i 0.397644i −0.980036 0.198822i \(-0.936288\pi\)
0.980036 0.198822i \(-0.0637116\pi\)
\(98\) 0 0
\(99\) 1997.83i 0.0204867i
\(100\) 0 0
\(101\) 174557.i 1.70268i −0.524611 0.851342i \(-0.675789\pi\)
0.524611 0.851342i \(-0.324211\pi\)
\(102\) 0 0
\(103\) 172505.i 1.60217i 0.598551 + 0.801085i \(0.295743\pi\)
−0.598551 + 0.801085i \(0.704257\pi\)
\(104\) 0 0
\(105\) −40771.7 132940.i −0.360899 1.17675i
\(106\) 0 0
\(107\) 155176. 1.31028 0.655140 0.755507i \(-0.272609\pi\)
0.655140 + 0.755507i \(0.272609\pi\)
\(108\) 0 0
\(109\) 111055.i 0.895306i 0.894207 + 0.447653i \(0.147740\pi\)
−0.894207 + 0.447653i \(0.852260\pi\)
\(110\) 0 0
\(111\) −130882. −1.00826
\(112\) 0 0
\(113\) 199647.i 1.47084i 0.677609 + 0.735422i \(0.263016\pi\)
−0.677609 + 0.735422i \(0.736984\pi\)
\(114\) 0 0
\(115\) 50586.4 + 164942.i 0.356689 + 1.16302i
\(116\) 0 0
\(117\) −188685. −1.27430
\(118\) 0 0
\(119\) −145847. −0.944123
\(120\) 0 0
\(121\) 161022. 0.999821
\(122\) 0 0
\(123\) −450836. −2.68693
\(124\) 0 0
\(125\) −109579. + 136051.i −0.627269 + 0.778803i
\(126\) 0 0
\(127\) 93300.5i 0.513304i −0.966504 0.256652i \(-0.917381\pi\)
0.966504 0.256652i \(-0.0826194\pi\)
\(128\) 0 0
\(129\) −206894. −1.09464
\(130\) 0 0
\(131\) 174939.i 0.890655i −0.895368 0.445328i \(-0.853087\pi\)
0.895368 0.445328i \(-0.146913\pi\)
\(132\) 0 0
\(133\) 72446.5 0.355131
\(134\) 0 0
\(135\) −171365. + 52556.3i −0.809260 + 0.248194i
\(136\) 0 0
\(137\) 127441.i 0.580106i −0.957011 0.290053i \(-0.906327\pi\)
0.957011 0.290053i \(-0.0936730\pi\)
\(138\) 0 0
\(139\) 393660.i 1.72816i 0.503352 + 0.864082i \(0.332100\pi\)
−0.503352 + 0.864082i \(0.667900\pi\)
\(140\) 0 0
\(141\) 548682.i 2.32420i
\(142\) 0 0
\(143\) 2720.12i 0.0111237i
\(144\) 0 0
\(145\) −119628. 390060.i −0.472513 1.54068i
\(146\) 0 0
\(147\) 167447. 0.639124
\(148\) 0 0
\(149\) 167112.i 0.616656i −0.951280 0.308328i \(-0.900231\pi\)
0.951280 0.308328i \(-0.0997694\pi\)
\(150\) 0 0
\(151\) −184305. −0.657803 −0.328901 0.944364i \(-0.606678\pi\)
−0.328901 + 0.944364i \(0.606678\pi\)
\(152\) 0 0
\(153\) 541415.i 1.86983i
\(154\) 0 0
\(155\) 460141. 141122.i 1.53837 0.471807i
\(156\) 0 0
\(157\) −403676. −1.30702 −0.653512 0.756916i \(-0.726705\pi\)
−0.653512 + 0.756916i \(0.726705\pi\)
\(158\) 0 0
\(159\) −331482. −1.03984
\(160\) 0 0
\(161\) 309490. 0.940984
\(162\) 0 0
\(163\) −357436. −1.05373 −0.526864 0.849949i \(-0.676632\pi\)
−0.526864 + 0.849949i \(0.676632\pi\)
\(164\) 0 0
\(165\) −2181.94 7114.45i −0.00623927 0.0203438i
\(166\) 0 0
\(167\) 38221.8i 0.106052i 0.998593 + 0.0530262i \(0.0168867\pi\)
−0.998593 + 0.0530262i \(0.983113\pi\)
\(168\) 0 0
\(169\) −114392. −0.308090
\(170\) 0 0
\(171\) 268938.i 0.703334i
\(172\) 0 0
\(173\) 134258. 0.341056 0.170528 0.985353i \(-0.445453\pi\)
0.170528 + 0.985353i \(0.445453\pi\)
\(174\) 0 0
\(175\) 175696. + 259494.i 0.433677 + 0.640520i
\(176\) 0 0
\(177\) 271829.i 0.652173i
\(178\) 0 0
\(179\) 566014.i 1.32037i −0.751105 0.660183i \(-0.770479\pi\)
0.751105 0.660183i \(-0.229521\pi\)
\(180\) 0 0
\(181\) 572156.i 1.29813i −0.760733 0.649065i \(-0.775160\pi\)
0.760733 0.649065i \(-0.224840\pi\)
\(182\) 0 0
\(183\) 272404.i 0.601292i
\(184\) 0 0
\(185\) 282002. 86487.8i 0.605791 0.185791i
\(186\) 0 0
\(187\) −7805.15 −0.0163221
\(188\) 0 0
\(189\) 321542.i 0.654762i
\(190\) 0 0
\(191\) 685564. 1.35977 0.679883 0.733320i \(-0.262030\pi\)
0.679883 + 0.733320i \(0.262030\pi\)
\(192\) 0 0
\(193\) 931503.i 1.80008i 0.435810 + 0.900039i \(0.356462\pi\)
−0.435810 + 0.900039i \(0.643538\pi\)
\(194\) 0 0
\(195\) 671923. 206073.i 1.26541 0.388093i
\(196\) 0 0
\(197\) 692118. 1.27062 0.635308 0.772259i \(-0.280873\pi\)
0.635308 + 0.772259i \(0.280873\pi\)
\(198\) 0 0
\(199\) 969167. 1.73487 0.867433 0.497554i \(-0.165768\pi\)
0.867433 + 0.497554i \(0.165768\pi\)
\(200\) 0 0
\(201\) −322646. −0.563295
\(202\) 0 0
\(203\) −731892. −1.24654
\(204\) 0 0
\(205\) 971385. 297916.i 1.61438 0.495119i
\(206\) 0 0
\(207\) 1.14890e6i 1.86361i
\(208\) 0 0
\(209\) 3877.06 0.00613956
\(210\) 0 0
\(211\) 800177.i 1.23731i 0.785661 + 0.618657i \(0.212323\pi\)
−0.785661 + 0.618657i \(0.787677\pi\)
\(212\) 0 0
\(213\) 893187. 1.34894
\(214\) 0 0
\(215\) 445779. 136717.i 0.657694 0.201709i
\(216\) 0 0
\(217\) 863389.i 1.24468i
\(218\) 0 0
\(219\) 1.59459e6i 2.24666i
\(220\) 0 0
\(221\) 737156.i 1.01526i
\(222\) 0 0
\(223\) 619923.i 0.834787i −0.908726 0.417394i \(-0.862944\pi\)
0.908726 0.417394i \(-0.137056\pi\)
\(224\) 0 0
\(225\) 963302. 652222.i 1.26855 0.858893i
\(226\) 0 0
\(227\) 547541. 0.705264 0.352632 0.935762i \(-0.385287\pi\)
0.352632 + 0.935762i \(0.385287\pi\)
\(228\) 0 0
\(229\) 368527.i 0.464387i −0.972670 0.232194i \(-0.925410\pi\)
0.972670 0.232194i \(-0.0745903\pi\)
\(230\) 0 0
\(231\) −13349.2 −0.0164599
\(232\) 0 0
\(233\) 347048.i 0.418794i 0.977831 + 0.209397i \(0.0671500\pi\)
−0.977831 + 0.209397i \(0.932850\pi\)
\(234\) 0 0
\(235\) −362573. 1.18221e6i −0.428278 1.39644i
\(236\) 0 0
\(237\) 1.20646e6 1.39522
\(238\) 0 0
\(239\) 1.17224e6 1.32746 0.663731 0.747971i \(-0.268972\pi\)
0.663731 + 0.747971i \(0.268972\pi\)
\(240\) 0 0
\(241\) −1.10163e6 −1.22178 −0.610889 0.791716i \(-0.709188\pi\)
−0.610889 + 0.791716i \(0.709188\pi\)
\(242\) 0 0
\(243\) −1.05020e6 −1.14093
\(244\) 0 0
\(245\) −360787. + 110651.i −0.384004 + 0.117771i
\(246\) 0 0
\(247\) 366168.i 0.381890i
\(248\) 0 0
\(249\) −1.23488e6 −1.26220
\(250\) 0 0
\(251\) 97443.4i 0.0976265i 0.998808 + 0.0488133i \(0.0155439\pi\)
−0.998808 + 0.0488133i \(0.984456\pi\)
\(252\) 0 0
\(253\) 16562.7 0.0162679
\(254\) 0 0
\(255\) −591310. 1.92802e6i −0.569462 1.85679i
\(256\) 0 0
\(257\) 1.35298e6i 1.27779i 0.769296 + 0.638893i \(0.220607\pi\)
−0.769296 + 0.638893i \(0.779393\pi\)
\(258\) 0 0
\(259\) 529136.i 0.490138i
\(260\) 0 0
\(261\) 2.71695e6i 2.46877i
\(262\) 0 0
\(263\) 892943.i 0.796039i 0.917377 + 0.398019i \(0.130302\pi\)
−0.917377 + 0.398019i \(0.869698\pi\)
\(264\) 0 0
\(265\) 714221. 219046.i 0.624766 0.191611i
\(266\) 0 0
\(267\) 192593. 0.165334
\(268\) 0 0
\(269\) 395573.i 0.333308i −0.986015 0.166654i \(-0.946704\pi\)
0.986015 0.166654i \(-0.0532963\pi\)
\(270\) 0 0
\(271\) 548411. 0.453610 0.226805 0.973940i \(-0.427172\pi\)
0.226805 + 0.973940i \(0.427172\pi\)
\(272\) 0 0
\(273\) 1.26077e6i 1.02383i
\(274\) 0 0
\(275\) 9402.56 + 13887.2i 0.00749747 + 0.0110734i
\(276\) 0 0
\(277\) 84078.7 0.0658395 0.0329198 0.999458i \(-0.489519\pi\)
0.0329198 + 0.999458i \(0.489519\pi\)
\(278\) 0 0
\(279\) −3.20509e6 −2.46508
\(280\) 0 0
\(281\) 869957. 0.657252 0.328626 0.944460i \(-0.393414\pi\)
0.328626 + 0.944460i \(0.393414\pi\)
\(282\) 0 0
\(283\) 1.80499e6 1.33970 0.669852 0.742495i \(-0.266358\pi\)
0.669852 + 0.742495i \(0.266358\pi\)
\(284\) 0 0
\(285\) 293722. + 957710.i 0.214202 + 0.698428i
\(286\) 0 0
\(287\) 1.82267e6i 1.30618i
\(288\) 0 0
\(289\) −695348. −0.489731
\(290\) 0 0
\(291\) 914020.i 0.632737i
\(292\) 0 0
\(293\) 734707. 0.499972 0.249986 0.968250i \(-0.419574\pi\)
0.249986 + 0.968250i \(0.419574\pi\)
\(294\) 0 0
\(295\) 179627. + 585691.i 0.120176 + 0.391844i
\(296\) 0 0
\(297\) 17207.7i 0.0113196i
\(298\) 0 0
\(299\) 1.56427e6i 1.01189i
\(300\) 0 0
\(301\) 836441.i 0.532132i
\(302\) 0 0
\(303\) 4.32981e6i 2.70933i
\(304\) 0 0
\(305\) 180007. + 586930.i 0.110800 + 0.361274i
\(306\) 0 0
\(307\) −568071. −0.343999 −0.171999 0.985097i \(-0.555023\pi\)
−0.171999 + 0.985097i \(0.555023\pi\)
\(308\) 0 0
\(309\) 4.27891e6i 2.54939i
\(310\) 0 0
\(311\) −1.69667e6 −0.994712 −0.497356 0.867547i \(-0.665696\pi\)
−0.497356 + 0.867547i \(0.665696\pi\)
\(312\) 0 0
\(313\) 349961.i 0.201910i 0.994891 + 0.100955i \(0.0321899\pi\)
−0.994891 + 0.100955i \(0.967810\pi\)
\(314\) 0 0
\(315\) −611901. 1.99516e6i −0.347460 1.13293i
\(316\) 0 0
\(317\) 2.16674e6 1.21104 0.605520 0.795830i \(-0.292965\pi\)
0.605520 + 0.795830i \(0.292965\pi\)
\(318\) 0 0
\(319\) −39168.1 −0.0215504
\(320\) 0 0
\(321\) 3.84907e6 2.08494
\(322\) 0 0
\(323\) 1.05069e6 0.560361
\(324\) 0 0
\(325\) −1.31157e6 + 888024.i −0.688784 + 0.466354i
\(326\) 0 0
\(327\) 2.75467e6i 1.42462i
\(328\) 0 0
\(329\) −2.21824e6 −1.12985
\(330\) 0 0
\(331\) 3.09909e6i 1.55476i −0.629031 0.777380i \(-0.716548\pi\)
0.629031 0.777380i \(-0.283452\pi\)
\(332\) 0 0
\(333\) −1.96427e6 −0.970714
\(334\) 0 0
\(335\) 695182. 213207.i 0.338444 0.103798i
\(336\) 0 0
\(337\) 913351.i 0.438089i 0.975715 + 0.219045i \(0.0702941\pi\)
−0.975715 + 0.219045i \(0.929706\pi\)
\(338\) 0 0
\(339\) 4.95216e6i 2.34043i
\(340\) 0 0
\(341\) 46205.3i 0.0215182i
\(342\) 0 0
\(343\) 2.36239e6i 1.08422i
\(344\) 0 0
\(345\) 1.25478e6 + 4.09132e6i 0.567568 + 1.85061i
\(346\) 0 0
\(347\) −1.81927e6 −0.811100 −0.405550 0.914073i \(-0.632920\pi\)
−0.405550 + 0.914073i \(0.632920\pi\)
\(348\) 0 0
\(349\) 3.66132e6i 1.60907i −0.593908 0.804533i \(-0.702416\pi\)
0.593908 0.804533i \(-0.297584\pi\)
\(350\) 0 0
\(351\) −1.62518e6 −0.704099
\(352\) 0 0
\(353\) 4.00606e6i 1.71112i −0.517703 0.855560i \(-0.673213\pi\)
0.517703 0.855560i \(-0.326787\pi\)
\(354\) 0 0
\(355\) −1.92449e6 + 590225.i −0.810483 + 0.248569i
\(356\) 0 0
\(357\) −3.61766e6 −1.50230
\(358\) 0 0
\(359\) 3.37100e6 1.38046 0.690228 0.723592i \(-0.257510\pi\)
0.690228 + 0.723592i \(0.257510\pi\)
\(360\) 0 0
\(361\) 1.95419e6 0.789221
\(362\) 0 0
\(363\) 3.99409e6 1.59093
\(364\) 0 0
\(365\) −1.05372e6 3.43574e6i −0.413991 1.34986i
\(366\) 0 0
\(367\) 3.30503e6i 1.28089i 0.768005 + 0.640444i \(0.221249\pi\)
−0.768005 + 0.640444i \(0.778751\pi\)
\(368\) 0 0
\(369\) −6.76614e6 −2.58687
\(370\) 0 0
\(371\) 1.34013e6i 0.505491i
\(372\) 0 0
\(373\) −582132. −0.216646 −0.108323 0.994116i \(-0.534548\pi\)
−0.108323 + 0.994116i \(0.534548\pi\)
\(374\) 0 0
\(375\) −2.71807e6 + 3.37469e6i −0.998119 + 1.23924i
\(376\) 0 0
\(377\) 3.69922e6i 1.34047i
\(378\) 0 0
\(379\) 2.24404e6i 0.802478i 0.915973 + 0.401239i \(0.131420\pi\)
−0.915973 + 0.401239i \(0.868580\pi\)
\(380\) 0 0
\(381\) 2.31428e6i 0.816776i
\(382\) 0 0
\(383\) 2.03163e6i 0.707696i 0.935303 + 0.353848i \(0.115127\pi\)
−0.935303 + 0.353848i \(0.884873\pi\)
\(384\) 0 0
\(385\) 28762.7 8821.28i 0.00988957 0.00303305i
\(386\) 0 0
\(387\) −3.10506e6 −1.05388
\(388\) 0 0
\(389\) 3.29458e6i 1.10389i −0.833881 0.551945i \(-0.813886\pi\)
0.833881 0.551945i \(-0.186114\pi\)
\(390\) 0 0
\(391\) 4.48852e6 1.48478
\(392\) 0 0
\(393\) 4.33930e6i 1.41722i
\(394\) 0 0
\(395\) −2.59949e6 + 797242.i −0.838291 + 0.257097i
\(396\) 0 0
\(397\) −2.66575e6 −0.848875 −0.424438 0.905457i \(-0.639528\pi\)
−0.424438 + 0.905457i \(0.639528\pi\)
\(398\) 0 0
\(399\) 1.79700e6 0.565089
\(400\) 0 0
\(401\) −1.41349e6 −0.438965 −0.219483 0.975616i \(-0.570437\pi\)
−0.219483 + 0.975616i \(0.570437\pi\)
\(402\) 0 0
\(403\) 4.36385e6 1.33847
\(404\) 0 0
\(405\) 584008. 179111.i 0.176922 0.0542605i
\(406\) 0 0
\(407\) 28317.4i 0.00847358i
\(408\) 0 0
\(409\) −1.65117e6 −0.488072 −0.244036 0.969766i \(-0.578472\pi\)
−0.244036 + 0.969766i \(0.578472\pi\)
\(410\) 0 0
\(411\) 3.16112e6i 0.923073i
\(412\) 0 0
\(413\) 1.09897e6 0.317036
\(414\) 0 0
\(415\) 2.66071e6 816019.i 0.758364 0.232584i
\(416\) 0 0
\(417\) 9.76458e6i 2.74988i
\(418\) 0 0
\(419\) 4.58123e6i 1.27482i 0.770527 + 0.637408i \(0.219993\pi\)
−0.770527 + 0.637408i \(0.780007\pi\)
\(420\) 0 0
\(421\) 3.54620e6i 0.975120i −0.873089 0.487560i \(-0.837887\pi\)
0.873089 0.487560i \(-0.162113\pi\)
\(422\) 0 0
\(423\) 8.23461e6i 2.23765i
\(424\) 0 0
\(425\) 2.54811e6 + 3.76344e6i 0.684298 + 1.01068i
\(426\) 0 0
\(427\) 1.10129e6 0.292302
\(428\) 0 0
\(429\) 67471.4i 0.0177001i
\(430\) 0 0
\(431\) 3.24667e6 0.841871 0.420935 0.907091i \(-0.361702\pi\)
0.420935 + 0.907091i \(0.361702\pi\)
\(432\) 0 0
\(433\) 4.93639e6i 1.26529i −0.774443 0.632644i \(-0.781970\pi\)
0.774443 0.632644i \(-0.218030\pi\)
\(434\) 0 0
\(435\) −2.96733e6 9.67527e6i −0.751870 2.45155i
\(436\) 0 0
\(437\) −2.22959e6 −0.558498
\(438\) 0 0
\(439\) −5.91592e6 −1.46508 −0.732539 0.680725i \(-0.761665\pi\)
−0.732539 + 0.680725i \(0.761665\pi\)
\(440\) 0 0
\(441\) 2.51305e6 0.615325
\(442\) 0 0
\(443\) 723323. 0.175115 0.0875574 0.996159i \(-0.472094\pi\)
0.0875574 + 0.996159i \(0.472094\pi\)
\(444\) 0 0
\(445\) −414966. + 127267.i −0.0993373 + 0.0304660i
\(446\) 0 0
\(447\) 4.14515e6i 0.981231i
\(448\) 0 0
\(449\) −1.61902e6 −0.378999 −0.189499 0.981881i \(-0.560686\pi\)
−0.189499 + 0.981881i \(0.560686\pi\)
\(450\) 0 0
\(451\) 97542.1i 0.0225814i
\(452\) 0 0
\(453\) −4.57162e6 −1.04670
\(454\) 0 0
\(455\) 833125. + 2.71649e6i 0.188661 + 0.615147i
\(456\) 0 0
\(457\) 419909.i 0.0940512i −0.998894 0.0470256i \(-0.985026\pi\)
0.998894 0.0470256i \(-0.0149742\pi\)
\(458\) 0 0
\(459\) 4.66331e6i 1.03315i
\(460\) 0 0
\(461\) 3.17942e6i 0.696780i 0.937350 + 0.348390i \(0.113272\pi\)
−0.937350 + 0.348390i \(0.886728\pi\)
\(462\) 0 0
\(463\) 620530.i 0.134527i 0.997735 + 0.0672636i \(0.0214269\pi\)
−0.997735 + 0.0672636i \(0.978573\pi\)
\(464\) 0 0
\(465\) 1.14136e7 3.50046e6i 2.44788 0.750746i
\(466\) 0 0
\(467\) 1.96565e6 0.417075 0.208538 0.978014i \(-0.433130\pi\)
0.208538 + 0.978014i \(0.433130\pi\)
\(468\) 0 0
\(469\) 1.30441e6i 0.273831i
\(470\) 0 0
\(471\) −1.00130e7 −2.07975
\(472\) 0 0
\(473\) 44763.1i 0.00919957i
\(474\) 0 0
\(475\) −1.26572e6 1.86942e6i −0.257398 0.380165i
\(476\) 0 0
\(477\) −4.97487e6 −1.00112
\(478\) 0 0
\(479\) −4.57977e6 −0.912022 −0.456011 0.889974i \(-0.650722\pi\)
−0.456011 + 0.889974i \(0.650722\pi\)
\(480\) 0 0
\(481\) 2.67443e6 0.527070
\(482\) 0 0
\(483\) 7.67677e6 1.49731
\(484\) 0 0
\(485\) 603991. + 1.96937e6i 0.116594 + 0.380167i
\(486\) 0 0
\(487\) 9.22794e6i 1.76312i 0.472070 + 0.881561i \(0.343507\pi\)
−0.472070 + 0.881561i \(0.656493\pi\)
\(488\) 0 0
\(489\) −8.86603e6 −1.67671
\(490\) 0 0
\(491\) 6.77438e6i 1.26814i 0.773277 + 0.634068i \(0.218616\pi\)
−0.773277 + 0.634068i \(0.781384\pi\)
\(492\) 0 0
\(493\) −1.06146e7 −1.96692
\(494\) 0 0
\(495\) −32746.6 106774.i −0.00600694 0.0195862i
\(496\) 0 0
\(497\) 3.61102e6i 0.655752i
\(498\) 0 0
\(499\) 3.54380e6i 0.637115i 0.947903 + 0.318558i \(0.103198\pi\)
−0.947903 + 0.318558i \(0.896802\pi\)
\(500\) 0 0
\(501\) 948077.i 0.168752i
\(502\) 0 0
\(503\) 582992.i 0.102741i 0.998680 + 0.0513704i \(0.0163589\pi\)
−0.998680 + 0.0513704i \(0.983641\pi\)
\(504\) 0 0
\(505\) 2.86118e6 + 9.32915e6i 0.499248 + 1.62785i
\(506\) 0 0
\(507\) −2.83744e6 −0.490237
\(508\) 0 0
\(509\) 1.00694e7i 1.72270i 0.508013 + 0.861349i \(0.330380\pi\)
−0.508013 + 0.861349i \(0.669620\pi\)
\(510\) 0 0
\(511\) −6.44668e6 −1.09215
\(512\) 0 0
\(513\) 2.31641e6i 0.388618i
\(514\) 0 0
\(515\) −2.82754e6 9.21947e6i −0.469775 1.53175i
\(516\) 0 0
\(517\) −118712. −0.0195329
\(518\) 0 0
\(519\) 3.33022e6 0.542693
\(520\) 0 0
\(521\) −6.76200e6 −1.09139 −0.545696 0.837983i \(-0.683735\pi\)
−0.545696 + 0.837983i \(0.683735\pi\)
\(522\) 0 0
\(523\) −6.39905e6 −1.02297 −0.511483 0.859293i \(-0.670904\pi\)
−0.511483 + 0.859293i \(0.670904\pi\)
\(524\) 0 0
\(525\) 4.35806e6 + 6.43665e6i 0.690072 + 1.01921i
\(526\) 0 0
\(527\) 1.25217e7i 1.96398i
\(528\) 0 0
\(529\) −3.08843e6 −0.479842
\(530\) 0 0
\(531\) 4.07961e6i 0.627888i
\(532\) 0 0
\(533\) 9.21235e6 1.40460
\(534\) 0 0
\(535\) −8.29332e6 + 2.54349e6i −1.25269 + 0.384190i
\(536\) 0 0
\(537\) 1.40397e7i 2.10098i
\(538\) 0 0
\(539\) 36228.6i 0.00537130i
\(540\) 0 0
\(541\) 9.42388e6i 1.38432i 0.721744 + 0.692160i \(0.243341\pi\)
−0.721744 + 0.692160i \(0.756659\pi\)
\(542\) 0 0
\(543\) 1.41921e7i 2.06560i
\(544\) 0 0
\(545\) −1.82031e6 5.93529e6i −0.262514 0.855955i
\(546\) 0 0
\(547\) −1.39418e6 −0.199228 −0.0996138 0.995026i \(-0.531761\pi\)
−0.0996138 + 0.995026i \(0.531761\pi\)
\(548\) 0 0
\(549\) 4.08824e6i 0.578902i
\(550\) 0 0
\(551\) 5.27260e6 0.739854
\(552\) 0 0
\(553\) 4.87756e6i 0.678250i
\(554\) 0 0
\(555\) 6.99494e6 2.14529e6i 0.963943 0.295634i
\(556\) 0 0
\(557\) 1.27617e6 0.174289 0.0871445 0.996196i \(-0.472226\pi\)
0.0871445 + 0.996196i \(0.472226\pi\)
\(558\) 0 0
\(559\) 4.22765e6 0.572228
\(560\) 0 0
\(561\) −193603. −0.0259720
\(562\) 0 0
\(563\) −1.87381e6 −0.249146 −0.124573 0.992210i \(-0.539756\pi\)
−0.124573 + 0.992210i \(0.539756\pi\)
\(564\) 0 0
\(565\) −3.27243e6 1.06701e7i −0.431269 1.40620i
\(566\) 0 0
\(567\) 1.09581e6i 0.143145i
\(568\) 0 0
\(569\) −6.96458e6 −0.901808 −0.450904 0.892572i \(-0.648898\pi\)
−0.450904 + 0.892572i \(0.648898\pi\)
\(570\) 0 0
\(571\) 344717.i 0.0442458i 0.999755 + 0.0221229i \(0.00704251\pi\)
−0.999755 + 0.0221229i \(0.992957\pi\)
\(572\) 0 0
\(573\) 1.70051e7 2.16368
\(574\) 0 0
\(575\) −5.40715e6 7.98612e6i −0.682023 1.00732i
\(576\) 0 0
\(577\) 5.35769e6i 0.669944i 0.942228 + 0.334972i \(0.108727\pi\)
−0.942228 + 0.334972i \(0.891273\pi\)
\(578\) 0 0
\(579\) 2.31055e7i 2.86431i
\(580\) 0 0
\(581\) 4.99245e6i 0.613583i
\(582\) 0 0
\(583\) 71718.8i 0.00873900i
\(584\) 0 0
\(585\) 1.00842e7 3.09275e6i 1.21829 0.373641i
\(586\) 0 0
\(587\) −1.33004e6 −0.159320 −0.0796599 0.996822i \(-0.525383\pi\)
−0.0796599 + 0.996822i \(0.525383\pi\)
\(588\) 0 0
\(589\) 6.21992e6i 0.738748i
\(590\) 0 0
\(591\) 1.71677e7 2.02182
\(592\) 0 0
\(593\) 4.87875e6i 0.569734i 0.958567 + 0.284867i \(0.0919494\pi\)
−0.958567 + 0.284867i \(0.908051\pi\)
\(594\) 0 0
\(595\) 7.79472e6 2.39058e6i 0.902627 0.276828i
\(596\) 0 0
\(597\) 2.40398e7 2.76054
\(598\) 0 0
\(599\) −2.71017e6 −0.308624 −0.154312 0.988022i \(-0.549316\pi\)
−0.154312 + 0.988022i \(0.549316\pi\)
\(600\) 0 0
\(601\) 1.02295e7 1.15523 0.577615 0.816309i \(-0.303983\pi\)
0.577615 + 0.816309i \(0.303983\pi\)
\(602\) 0 0
\(603\) −4.84226e6 −0.542319
\(604\) 0 0
\(605\) −8.60578e6 + 2.63932e6i −0.955876 + 0.293160i
\(606\) 0 0
\(607\) 6.63212e6i 0.730602i 0.930890 + 0.365301i \(0.119034\pi\)
−0.930890 + 0.365301i \(0.880966\pi\)
\(608\) 0 0
\(609\) −1.81543e7 −1.98351
\(610\) 0 0
\(611\) 1.12117e7i 1.21498i
\(612\) 0 0
\(613\) −7.17868e6 −0.771602 −0.385801 0.922582i \(-0.626075\pi\)
−0.385801 + 0.922582i \(0.626075\pi\)
\(614\) 0 0
\(615\) 2.40948e7 7.38968e6i 2.56883 0.787840i
\(616\) 0 0
\(617\) 1.22481e7i 1.29526i −0.761956 0.647629i \(-0.775761\pi\)
0.761956 0.647629i \(-0.224239\pi\)
\(618\) 0 0
\(619\) 2.10012e6i 0.220302i 0.993915 + 0.110151i \(0.0351334\pi\)
−0.993915 + 0.110151i \(0.964867\pi\)
\(620\) 0 0
\(621\) 9.89568e6i 1.02971i
\(622\) 0 0
\(623\) 778624.i 0.0803725i
\(624\) 0 0
\(625\) 3.62641e6 9.06734e6i 0.371345 0.928495i
\(626\) 0 0
\(627\) 96168.9 0.00976935
\(628\) 0 0
\(629\) 7.67404e6i 0.773388i
\(630\) 0 0
\(631\) −5.94323e6 −0.594223 −0.297111 0.954843i \(-0.596023\pi\)
−0.297111 + 0.954843i \(0.596023\pi\)
\(632\) 0 0
\(633\) 1.98481e7i 1.96883i
\(634\) 0 0
\(635\) 1.52929e6 + 4.98641e6i 0.150507 + 0.490743i
\(636\) 0 0
\(637\) −3.42160e6 −0.334104
\(638\) 0 0
\(639\) 1.34049e7 1.29871
\(640\) 0 0
\(641\) 1.73665e7 1.66943 0.834713 0.550686i \(-0.185634\pi\)
0.834713 + 0.550686i \(0.185634\pi\)
\(642\) 0 0
\(643\) −1.88563e7 −1.79858 −0.899290 0.437353i \(-0.855916\pi\)
−0.899290 + 0.437353i \(0.855916\pi\)
\(644\) 0 0
\(645\) 1.10574e7 3.39121e6i 1.04653 0.320963i
\(646\) 0 0
\(647\) 2.16987e6i 0.203785i −0.994795 0.101893i \(-0.967510\pi\)
0.994795 0.101893i \(-0.0324898\pi\)
\(648\) 0 0
\(649\) 58812.5 0.00548097
\(650\) 0 0
\(651\) 2.14160e7i 1.98055i
\(652\) 0 0
\(653\) 1.97704e7 1.81440 0.907198 0.420703i \(-0.138217\pi\)
0.907198 + 0.420703i \(0.138217\pi\)
\(654\) 0 0
\(655\) 2.86744e6 + 9.34958e6i 0.261151 + 0.851509i
\(656\) 0 0
\(657\) 2.39315e7i 2.16300i
\(658\) 0 0
\(659\) 3.61872e6i 0.324595i 0.986742 + 0.162297i \(0.0518904\pi\)
−0.986742 + 0.162297i \(0.948110\pi\)
\(660\) 0 0
\(661\) 3.75269e6i 0.334071i −0.985951 0.167036i \(-0.946580\pi\)
0.985951 0.167036i \(-0.0534195\pi\)
\(662\) 0 0
\(663\) 1.82848e7i 1.61550i
\(664\) 0 0
\(665\) −3.87188e6 + 1.18748e6i −0.339522 + 0.104129i
\(666\) 0 0
\(667\) 2.25245e7 1.96038
\(668\) 0 0
\(669\) 1.53769e7i 1.32833i
\(670\) 0 0
\(671\) 58936.8 0.00505336
\(672\) 0 0
\(673\) 1.93077e6i 0.164321i −0.996619 0.0821606i \(-0.973818\pi\)
0.996619 0.0821606i \(-0.0261820\pi\)
\(674\) 0 0
\(675\) 8.29710e6 5.61771e6i 0.700918 0.474570i
\(676\) 0 0
\(677\) 7.53721e6 0.632032 0.316016 0.948754i \(-0.397655\pi\)
0.316016 + 0.948754i \(0.397655\pi\)
\(678\) 0 0
\(679\) 3.69525e6 0.307588
\(680\) 0 0
\(681\) 1.35815e7 1.12223
\(682\) 0 0
\(683\) −2.28279e6 −0.187247 −0.0936234 0.995608i \(-0.529845\pi\)
−0.0936234 + 0.995608i \(0.529845\pi\)
\(684\) 0 0
\(685\) 2.08889e6 + 6.81104e6i 0.170094 + 0.554609i
\(686\) 0 0
\(687\) 9.14114e6i 0.738939i
\(688\) 0 0
\(689\) 6.77347e6 0.543580
\(690\) 0 0
\(691\) 4.89825e6i 0.390252i 0.980778 + 0.195126i \(0.0625116\pi\)
−0.980778 + 0.195126i \(0.937488\pi\)
\(692\) 0 0
\(693\) −200345. −0.0158470
\(694\) 0 0
\(695\) −6.45251e6 2.10391e7i −0.506718 1.65221i
\(696\) 0 0
\(697\) 2.64340e7i 2.06102i
\(698\) 0 0
\(699\) 8.60838e6i 0.666390i
\(700\) 0 0
\(701\) 1.36266e7i 1.04735i 0.851917 + 0.523676i \(0.175440\pi\)
−0.851917 + 0.523676i \(0.824560\pi\)
\(702\) 0 0
\(703\) 3.81194e6i 0.290909i
\(704\) 0 0
\(705\) −8.99347e6 2.93241e7i −0.681483 2.22204i
\(706\) 0 0
\(707\) 1.75048e7 1.31707
\(708\) 0 0
\(709\) 1.03111e7i 0.770350i 0.922843 + 0.385175i \(0.125859\pi\)
−0.922843 + 0.385175i \(0.874141\pi\)
\(710\) 0 0
\(711\) 1.81066e7 1.34327
\(712\) 0 0
\(713\) 2.65714e7i 1.95745i
\(714\) 0 0
\(715\) 44585.6 + 145376.i 0.00326159 + 0.0106348i
\(716\) 0 0
\(717\) 2.90769e7 2.11228
\(718\) 0 0
\(719\) −9.38661e6 −0.677153 −0.338576 0.940939i \(-0.609945\pi\)
−0.338576 + 0.940939i \(0.609945\pi\)
\(720\) 0 0
\(721\) −1.72990e7 −1.23932
\(722\) 0 0
\(723\) −2.73254e7 −1.94411
\(724\) 0 0
\(725\) 1.27870e7 + 1.88858e7i 0.903490 + 1.33441i
\(726\) 0 0
\(727\) 4.62442e6i 0.324505i −0.986749 0.162252i \(-0.948124\pi\)
0.986749 0.162252i \(-0.0518759\pi\)
\(728\) 0 0
\(729\) −2.33945e7 −1.63040
\(730\) 0 0
\(731\) 1.21309e7i 0.839650i
\(732\) 0 0
\(733\) −2.68859e7 −1.84827 −0.924134 0.382068i \(-0.875212\pi\)
−0.924134 + 0.382068i \(0.875212\pi\)
\(734\) 0 0
\(735\) −8.94917e6 + 2.74464e6i −0.611033 + 0.187399i
\(736\) 0 0
\(737\) 69807.0i 0.00473403i
\(738\) 0 0
\(739\) 686127.i 0.0462161i −0.999733 0.0231081i \(-0.992644\pi\)
0.999733 0.0231081i \(-0.00735618\pi\)
\(740\) 0 0
\(741\) 9.08265e6i 0.607669i
\(742\) 0 0
\(743\) 1.09400e7i 0.727017i −0.931591 0.363508i \(-0.881579\pi\)
0.931591 0.363508i \(-0.118421\pi\)
\(744\) 0 0
\(745\) 2.73915e6 + 8.93126e6i 0.180811 + 0.589552i
\(746\) 0 0
\(747\) −1.85331e7 −1.21520
\(748\) 0 0
\(749\) 1.55612e7i 1.01354i
\(750\) 0 0
\(751\) −2.37534e7 −1.53683 −0.768416 0.639951i \(-0.778955\pi\)
−0.768416 + 0.639951i \(0.778955\pi\)
\(752\) 0 0
\(753\) 2.41704e6i 0.155345i
\(754\) 0 0
\(755\) 9.85014e6 3.02096e6i 0.628891 0.192876i
\(756\) 0 0
\(757\) −2.95506e7 −1.87424 −0.937122 0.349003i \(-0.886520\pi\)
−0.937122 + 0.349003i \(0.886520\pi\)
\(758\) 0 0
\(759\) 410832. 0.0258857
\(760\) 0 0
\(761\) 2.38225e6 0.149116 0.0745582 0.997217i \(-0.476245\pi\)
0.0745582 + 0.997217i \(0.476245\pi\)
\(762\) 0 0
\(763\) −1.11367e7 −0.692542
\(764\) 0 0
\(765\) −8.87437e6 2.89358e7i −0.548256 1.78764i
\(766\) 0 0
\(767\) 5.55453e6i 0.340925i
\(768\) 0 0
\(769\) −1.58003e7 −0.963495 −0.481747 0.876310i \(-0.659998\pi\)
−0.481747 + 0.876310i \(0.659998\pi\)
\(770\) 0 0
\(771\) 3.35600e7i 2.03323i
\(772\) 0 0
\(773\) −8.84834e6 −0.532615 −0.266307 0.963888i \(-0.585804\pi\)
−0.266307 + 0.963888i \(0.585804\pi\)
\(774\) 0 0
\(775\) −2.22790e7 + 1.50844e7i −1.33242 + 0.902140i
\(776\) 0 0
\(777\) 1.31250e7i 0.779914i
\(778\) 0 0
\(779\) 1.31306e7i 0.775249i
\(780\) 0 0
\(781\) 193248.i 0.0113367i
\(782\) 0 0
\(783\) 2.34016e7i 1.36408i
\(784\) 0 0
\(785\) 2.15743e7 6.61667e6i 1.24958 0.383235i
\(786\) 0 0
\(787\) −5.30753e6 −0.305461 −0.152730 0.988268i \(-0.548807\pi\)
−0.152730 + 0.988268i \(0.548807\pi\)
\(788\) 0 0
\(789\) 2.21491e7i 1.26667i
\(790\) 0 0
\(791\) −2.00209e7 −1.13774
\(792\) 0 0
\(793\) 5.56628e6i 0.314327i
\(794\) 0 0
\(795\) 1.77159e7 5.43334e6i 0.994137 0.304894i
\(796\) 0 0
\(797\) −1.99099e7 −1.11026 −0.555128 0.831765i \(-0.687331\pi\)