Properties

Label 80.6.c.a.49.2
Level $80$
Weight $6$
Character 80.49
Analytic conductor $12.831$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-11}) \)
Defining polynomial: \(x^{2} - x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.2
Root \(0.500000 - 1.65831i\) of defining polynomial
Character \(\chi\) \(=\) 80.49
Dual form 80.6.c.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+19.8997i q^{3} +(-45.0000 + 33.1662i) q^{5} +59.6992i q^{7} -153.000 q^{9} +O(q^{10})\) \(q+19.8997i q^{3} +(-45.0000 + 33.1662i) q^{5} +59.6992i q^{7} -153.000 q^{9} -252.000 q^{11} -119.398i q^{13} +(-660.000 - 895.489i) q^{15} -689.858i q^{17} +220.000 q^{19} -1188.00 q^{21} -2434.40i q^{23} +(925.000 - 2984.96i) q^{25} +1790.98i q^{27} -6930.00 q^{29} -6752.00 q^{31} -5014.74i q^{33} +(-1980.00 - 2686.47i) q^{35} +13969.6i q^{37} +2376.00 q^{39} -198.000 q^{41} +417.895i q^{43} +(6885.00 - 5074.44i) q^{45} +10540.2i q^{47} +13243.0 q^{49} +13728.0 q^{51} -5823.99i q^{53} +(11340.0 - 8357.89i) q^{55} +4377.94i q^{57} +24660.0 q^{59} -5698.00 q^{61} -9133.98i q^{63} +(3960.00 + 5372.93i) q^{65} +43640.1i q^{67} +48444.0 q^{69} -53352.0 q^{71} +70922.7i q^{73} +(59400.0 + 18407.3i) q^{75} -15044.2i q^{77} -51920.0 q^{79} -72819.0 q^{81} +61841.8i q^{83} +(22880.0 + 31043.6i) q^{85} -137905. i q^{87} -9990.00 q^{89} +7128.00 q^{91} -134363. i q^{93} +(-9900.00 + 7296.57i) q^{95} -101250. i q^{97} +38556.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 90q^{5} - 306q^{9} + O(q^{10}) \) \( 2q - 90q^{5} - 306q^{9} - 504q^{11} - 1320q^{15} + 440q^{19} - 2376q^{21} + 1850q^{25} - 13860q^{29} - 13504q^{31} - 3960q^{35} + 4752q^{39} - 396q^{41} + 13770q^{45} + 26486q^{49} + 27456q^{51} + 22680q^{55} + 49320q^{59} - 11396q^{61} + 7920q^{65} + 96888q^{69} - 106704q^{71} + 118800q^{75} - 103840q^{79} - 145638q^{81} + 45760q^{85} - 19980q^{89} + 14256q^{91} - 19800q^{95} + 77112q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 19.8997i 1.27657i 0.769800 + 0.638285i \(0.220356\pi\)
−0.769800 + 0.638285i \(0.779644\pi\)
\(4\) 0 0
\(5\) −45.0000 + 33.1662i −0.804984 + 0.593296i
\(6\) 0 0
\(7\) 59.6992i 0.460494i 0.973132 + 0.230247i \(0.0739534\pi\)
−0.973132 + 0.230247i \(0.926047\pi\)
\(8\) 0 0
\(9\) −153.000 −0.629630
\(10\) 0 0
\(11\) −252.000 −0.627941 −0.313970 0.949433i \(-0.601659\pi\)
−0.313970 + 0.949433i \(0.601659\pi\)
\(12\) 0 0
\(13\) 119.398i 0.195948i −0.995189 0.0979739i \(-0.968764\pi\)
0.995189 0.0979739i \(-0.0312362\pi\)
\(14\) 0 0
\(15\) −660.000 895.489i −0.757383 1.02762i
\(16\) 0 0
\(17\) 689.858i 0.578945i −0.957186 0.289473i \(-0.906520\pi\)
0.957186 0.289473i \(-0.0934799\pi\)
\(18\) 0 0
\(19\) 220.000 0.139810 0.0699051 0.997554i \(-0.477730\pi\)
0.0699051 + 0.997554i \(0.477730\pi\)
\(20\) 0 0
\(21\) −1188.00 −0.587852
\(22\) 0 0
\(23\) 2434.40i 0.959561i −0.877388 0.479781i \(-0.840716\pi\)
0.877388 0.479781i \(-0.159284\pi\)
\(24\) 0 0
\(25\) 925.000 2984.96i 0.296000 0.955188i
\(26\) 0 0
\(27\) 1790.98i 0.472804i
\(28\) 0 0
\(29\) −6930.00 −1.53016 −0.765082 0.643932i \(-0.777302\pi\)
−0.765082 + 0.643932i \(0.777302\pi\)
\(30\) 0 0
\(31\) −6752.00 −1.26191 −0.630955 0.775820i \(-0.717337\pi\)
−0.630955 + 0.775820i \(0.717337\pi\)
\(32\) 0 0
\(33\) 5014.74i 0.801610i
\(34\) 0 0
\(35\) −1980.00 2686.47i −0.273209 0.370690i
\(36\) 0 0
\(37\) 13969.6i 1.67757i 0.544464 + 0.838785i \(0.316733\pi\)
−0.544464 + 0.838785i \(0.683267\pi\)
\(38\) 0 0
\(39\) 2376.00 0.250141
\(40\) 0 0
\(41\) −198.000 −0.0183952 −0.00919762 0.999958i \(-0.502928\pi\)
−0.00919762 + 0.999958i \(0.502928\pi\)
\(42\) 0 0
\(43\) 417.895i 0.0344664i 0.999851 + 0.0172332i \(0.00548577\pi\)
−0.999851 + 0.0172332i \(0.994514\pi\)
\(44\) 0 0
\(45\) 6885.00 5074.44i 0.506842 0.373557i
\(46\) 0 0
\(47\) 10540.2i 0.695994i 0.937496 + 0.347997i \(0.113138\pi\)
−0.937496 + 0.347997i \(0.886862\pi\)
\(48\) 0 0
\(49\) 13243.0 0.787945
\(50\) 0 0
\(51\) 13728.0 0.739064
\(52\) 0 0
\(53\) 5823.99i 0.284794i −0.989810 0.142397i \(-0.954519\pi\)
0.989810 0.142397i \(-0.0454810\pi\)
\(54\) 0 0
\(55\) 11340.0 8357.89i 0.505483 0.372555i
\(56\) 0 0
\(57\) 4377.94i 0.178477i
\(58\) 0 0
\(59\) 24660.0 0.922281 0.461140 0.887327i \(-0.347440\pi\)
0.461140 + 0.887327i \(0.347440\pi\)
\(60\) 0 0
\(61\) −5698.00 −0.196064 −0.0980320 0.995183i \(-0.531255\pi\)
−0.0980320 + 0.995183i \(0.531255\pi\)
\(62\) 0 0
\(63\) 9133.98i 0.289941i
\(64\) 0 0
\(65\) 3960.00 + 5372.93i 0.116255 + 0.157735i
\(66\) 0 0
\(67\) 43640.1i 1.18768i 0.804583 + 0.593840i \(0.202389\pi\)
−0.804583 + 0.593840i \(0.797611\pi\)
\(68\) 0 0
\(69\) 48444.0 1.22495
\(70\) 0 0
\(71\) −53352.0 −1.25604 −0.628022 0.778196i \(-0.716135\pi\)
−0.628022 + 0.778196i \(0.716135\pi\)
\(72\) 0 0
\(73\) 70922.7i 1.55768i 0.627223 + 0.778840i \(0.284192\pi\)
−0.627223 + 0.778840i \(0.715808\pi\)
\(74\) 0 0
\(75\) 59400.0 + 18407.3i 1.21936 + 0.377865i
\(76\) 0 0
\(77\) 15044.2i 0.289163i
\(78\) 0 0
\(79\) −51920.0 −0.935981 −0.467990 0.883734i \(-0.655022\pi\)
−0.467990 + 0.883734i \(0.655022\pi\)
\(80\) 0 0
\(81\) −72819.0 −1.23320
\(82\) 0 0
\(83\) 61841.8i 0.985342i 0.870216 + 0.492671i \(0.163979\pi\)
−0.870216 + 0.492671i \(0.836021\pi\)
\(84\) 0 0
\(85\) 22880.0 + 31043.6i 0.343486 + 0.466042i
\(86\) 0 0
\(87\) 137905.i 1.95336i
\(88\) 0 0
\(89\) −9990.00 −0.133687 −0.0668437 0.997763i \(-0.521293\pi\)
−0.0668437 + 0.997763i \(0.521293\pi\)
\(90\) 0 0
\(91\) 7128.00 0.0902328
\(92\) 0 0
\(93\) 134363.i 1.61092i
\(94\) 0 0
\(95\) −9900.00 + 7296.57i −0.112545 + 0.0829488i
\(96\) 0 0
\(97\) 101250.i 1.09261i −0.837586 0.546305i \(-0.816034\pi\)
0.837586 0.546305i \(-0.183966\pi\)
\(98\) 0 0
\(99\) 38556.0 0.395370
\(100\) 0 0
\(101\) −109098. −1.06418 −0.532088 0.846689i \(-0.678592\pi\)
−0.532088 + 0.846689i \(0.678592\pi\)
\(102\) 0 0
\(103\) 70624.2i 0.655935i −0.944689 0.327967i \(-0.893636\pi\)
0.944689 0.327967i \(-0.106364\pi\)
\(104\) 0 0
\(105\) 53460.0 39401.5i 0.473212 0.348770i
\(106\) 0 0
\(107\) 97117.4i 0.820045i −0.912075 0.410022i \(-0.865521\pi\)
0.912075 0.410022i \(-0.134479\pi\)
\(108\) 0 0
\(109\) −21010.0 −0.169379 −0.0846895 0.996407i \(-0.526990\pi\)
−0.0846895 + 0.996407i \(0.526990\pi\)
\(110\) 0 0
\(111\) −277992. −2.14153
\(112\) 0 0
\(113\) 105018.i 0.773688i 0.922145 + 0.386844i \(0.126435\pi\)
−0.922145 + 0.386844i \(0.873565\pi\)
\(114\) 0 0
\(115\) 80740.0 + 109548.i 0.569304 + 0.772432i
\(116\) 0 0
\(117\) 18268.0i 0.123375i
\(118\) 0 0
\(119\) 41184.0 0.266601
\(120\) 0 0
\(121\) −97547.0 −0.605690
\(122\) 0 0
\(123\) 3940.15i 0.0234828i
\(124\) 0 0
\(125\) 57375.0 + 165002.i 0.328434 + 0.944527i
\(126\) 0 0
\(127\) 87220.6i 0.479855i 0.970791 + 0.239927i \(0.0771236\pi\)
−0.970791 + 0.239927i \(0.922876\pi\)
\(128\) 0 0
\(129\) −8316.00 −0.0439987
\(130\) 0 0
\(131\) −192852. −0.981852 −0.490926 0.871201i \(-0.663341\pi\)
−0.490926 + 0.871201i \(0.663341\pi\)
\(132\) 0 0
\(133\) 13133.8i 0.0643817i
\(134\) 0 0
\(135\) −59400.0 80594.0i −0.280512 0.380599i
\(136\) 0 0
\(137\) 143570.i 0.653525i −0.945106 0.326763i \(-0.894042\pi\)
0.945106 0.326763i \(-0.105958\pi\)
\(138\) 0 0
\(139\) 318340. 1.39751 0.698754 0.715362i \(-0.253738\pi\)
0.698754 + 0.715362i \(0.253738\pi\)
\(140\) 0 0
\(141\) −209748. −0.888485
\(142\) 0 0
\(143\) 30088.4i 0.123044i
\(144\) 0 0
\(145\) 311850. 229842.i 1.23176 0.907841i
\(146\) 0 0
\(147\) 263532.i 1.00587i
\(148\) 0 0
\(149\) 84150.0 0.310519 0.155260 0.987874i \(-0.450379\pi\)
0.155260 + 0.987874i \(0.450379\pi\)
\(150\) 0 0
\(151\) 155848. 0.556236 0.278118 0.960547i \(-0.410289\pi\)
0.278118 + 0.960547i \(0.410289\pi\)
\(152\) 0 0
\(153\) 105548.i 0.364521i
\(154\) 0 0
\(155\) 303840. 223939.i 1.01582 0.748686i
\(156\) 0 0
\(157\) 356643.i 1.15474i 0.816482 + 0.577371i \(0.195921\pi\)
−0.816482 + 0.577371i \(0.804079\pi\)
\(158\) 0 0
\(159\) 115896. 0.363560
\(160\) 0 0
\(161\) 145332. 0.441872
\(162\) 0 0
\(163\) 144890.i 0.427139i 0.976928 + 0.213570i \(0.0685090\pi\)
−0.976928 + 0.213570i \(0.931491\pi\)
\(164\) 0 0
\(165\) 166320. + 225663.i 0.475592 + 0.645284i
\(166\) 0 0
\(167\) 18102.1i 0.0502272i 0.999685 + 0.0251136i \(0.00799474\pi\)
−0.999685 + 0.0251136i \(0.992005\pi\)
\(168\) 0 0
\(169\) 357037. 0.961604
\(170\) 0 0
\(171\) −33660.0 −0.0880286
\(172\) 0 0
\(173\) 492572.i 1.25128i −0.780112 0.625640i \(-0.784838\pi\)
0.780112 0.625640i \(-0.215162\pi\)
\(174\) 0 0
\(175\) 178200. + 55221.8i 0.439858 + 0.136306i
\(176\) 0 0
\(177\) 490728.i 1.17736i
\(178\) 0 0
\(179\) −444420. −1.03672 −0.518359 0.855163i \(-0.673457\pi\)
−0.518359 + 0.855163i \(0.673457\pi\)
\(180\) 0 0
\(181\) 156902. 0.355985 0.177993 0.984032i \(-0.443040\pi\)
0.177993 + 0.984032i \(0.443040\pi\)
\(182\) 0 0
\(183\) 113389.i 0.250289i
\(184\) 0 0
\(185\) −463320. 628633.i −0.995295 1.35042i
\(186\) 0 0
\(187\) 173844.i 0.363543i
\(188\) 0 0
\(189\) −106920. −0.217723
\(190\) 0 0
\(191\) −332352. −0.659196 −0.329598 0.944121i \(-0.606913\pi\)
−0.329598 + 0.944121i \(0.606913\pi\)
\(192\) 0 0
\(193\) 786120.i 1.51913i 0.650430 + 0.759566i \(0.274589\pi\)
−0.650430 + 0.759566i \(0.725411\pi\)
\(194\) 0 0
\(195\) −106920. + 78803.0i −0.201360 + 0.148408i
\(196\) 0 0
\(197\) 59606.4i 0.109428i 0.998502 + 0.0547138i \(0.0174247\pi\)
−0.998502 + 0.0547138i \(0.982575\pi\)
\(198\) 0 0
\(199\) 395800. 0.708505 0.354253 0.935150i \(-0.384735\pi\)
0.354253 + 0.935150i \(0.384735\pi\)
\(200\) 0 0
\(201\) −868428. −1.51616
\(202\) 0 0
\(203\) 413716.i 0.704631i
\(204\) 0 0
\(205\) 8910.00 6566.92i 0.0148079 0.0109138i
\(206\) 0 0
\(207\) 372464.i 0.604168i
\(208\) 0 0
\(209\) −55440.0 −0.0877925
\(210\) 0 0
\(211\) 251548. 0.388969 0.194484 0.980906i \(-0.437697\pi\)
0.194484 + 0.980906i \(0.437697\pi\)
\(212\) 0 0
\(213\) 1.06169e6i 1.60343i
\(214\) 0 0
\(215\) −13860.0 18805.3i −0.0204488 0.0277449i
\(216\) 0 0
\(217\) 403089.i 0.581101i
\(218\) 0 0
\(219\) −1.41134e6 −1.98849
\(220\) 0 0
\(221\) −82368.0 −0.113443
\(222\) 0 0
\(223\) 288765.i 0.388851i 0.980917 + 0.194425i \(0.0622842\pi\)
−0.980917 + 0.194425i \(0.937716\pi\)
\(224\) 0 0
\(225\) −141525. + 456699.i −0.186370 + 0.601415i
\(226\) 0 0
\(227\) 1.16414e6i 1.49948i −0.661731 0.749741i \(-0.730178\pi\)
0.661731 0.749741i \(-0.269822\pi\)
\(228\) 0 0
\(229\) 547670. 0.690129 0.345064 0.938579i \(-0.387857\pi\)
0.345064 + 0.938579i \(0.387857\pi\)
\(230\) 0 0
\(231\) 299376. 0.369137
\(232\) 0 0
\(233\) 48104.3i 0.0580489i 0.999579 + 0.0290245i \(0.00924007\pi\)
−0.999579 + 0.0290245i \(0.990760\pi\)
\(234\) 0 0
\(235\) −349580. 474311.i −0.412930 0.560264i
\(236\) 0 0
\(237\) 1.03319e6i 1.19484i
\(238\) 0 0
\(239\) 1.00584e6 1.13903 0.569514 0.821982i \(-0.307132\pi\)
0.569514 + 0.821982i \(0.307132\pi\)
\(240\) 0 0
\(241\) 895202. 0.992838 0.496419 0.868083i \(-0.334648\pi\)
0.496419 + 0.868083i \(0.334648\pi\)
\(242\) 0 0
\(243\) 1.01387e6i 1.10146i
\(244\) 0 0
\(245\) −595935. + 439221.i −0.634284 + 0.467485i
\(246\) 0 0
\(247\) 26267.7i 0.0273955i
\(248\) 0 0
\(249\) −1.23064e6 −1.25786
\(250\) 0 0
\(251\) −558252. −0.559301 −0.279651 0.960102i \(-0.590219\pi\)
−0.279651 + 0.960102i \(0.590219\pi\)
\(252\) 0 0
\(253\) 613469.i 0.602548i
\(254\) 0 0
\(255\) −617760. + 455306.i −0.594935 + 0.438483i
\(256\) 0 0
\(257\) 787924.i 0.744135i −0.928206 0.372067i \(-0.878649\pi\)
0.928206 0.372067i \(-0.121351\pi\)
\(258\) 0 0
\(259\) −833976. −0.772510
\(260\) 0 0
\(261\) 1.06029e6 0.963437
\(262\) 0 0
\(263\) 1.63173e6i 1.45465i 0.686291 + 0.727327i \(0.259238\pi\)
−0.686291 + 0.727327i \(0.740762\pi\)
\(264\) 0 0
\(265\) 193160. + 262080.i 0.168967 + 0.229255i
\(266\) 0 0
\(267\) 198798.i 0.170661i
\(268\) 0 0
\(269\) −1.73637e6 −1.46306 −0.731529 0.681810i \(-0.761193\pi\)
−0.731529 + 0.681810i \(0.761193\pi\)
\(270\) 0 0
\(271\) 1.72005e6 1.42271 0.711357 0.702831i \(-0.248081\pi\)
0.711357 + 0.702831i \(0.248081\pi\)
\(272\) 0 0
\(273\) 141845.i 0.115188i
\(274\) 0 0
\(275\) −233100. + 752211.i −0.185871 + 0.599802i
\(276\) 0 0
\(277\) 1.27243e6i 0.996402i 0.867062 + 0.498201i \(0.166006\pi\)
−0.867062 + 0.498201i \(0.833994\pi\)
\(278\) 0 0
\(279\) 1.03306e6 0.794536
\(280\) 0 0
\(281\) 1.46500e6 1.10681 0.553404 0.832913i \(-0.313329\pi\)
0.553404 + 0.832913i \(0.313329\pi\)
\(282\) 0 0
\(283\) 1.65051e6i 1.22504i 0.790455 + 0.612521i \(0.209844\pi\)
−0.790455 + 0.612521i \(0.790156\pi\)
\(284\) 0 0
\(285\) −145200. 197008.i −0.105890 0.143672i
\(286\) 0 0
\(287\) 11820.5i 0.00847089i
\(288\) 0 0
\(289\) 943953. 0.664823
\(290\) 0 0
\(291\) 2.01485e6 1.39479
\(292\) 0 0
\(293\) 2.38772e6i 1.62485i 0.583064 + 0.812426i \(0.301854\pi\)
−0.583064 + 0.812426i \(0.698146\pi\)
\(294\) 0 0
\(295\) −1.10970e6 + 817880.i −0.742422 + 0.547185i
\(296\) 0 0
\(297\) 451326.i 0.296893i
\(298\) 0 0
\(299\) −290664. −0.188024
\(300\) 0 0
\(301\) −24948.0 −0.0158716
\(302\) 0 0
\(303\) 2.17102e6i 1.35849i
\(304\) 0 0
\(305\) 256410. 188981.i 0.157828 0.116324i
\(306\) 0 0
\(307\) 928264.i 0.562115i −0.959691 0.281058i \(-0.909315\pi\)
0.959691 0.281058i \(-0.0906852\pi\)
\(308\) 0 0
\(309\) 1.40540e6 0.837346
\(310\) 0 0
\(311\) −568152. −0.333092 −0.166546 0.986034i \(-0.553261\pi\)
−0.166546 + 0.986034i \(0.553261\pi\)
\(312\) 0 0
\(313\) 1.72244e6i 0.993766i −0.867818 0.496883i \(-0.834478\pi\)
0.867818 0.496883i \(-0.165522\pi\)
\(314\) 0 0
\(315\) 302940. + 411029.i 0.172021 + 0.233398i
\(316\) 0 0
\(317\) 131643.i 0.0735785i 0.999323 + 0.0367893i \(0.0117130\pi\)
−0.999323 + 0.0367893i \(0.988287\pi\)
\(318\) 0 0
\(319\) 1.74636e6 0.960853
\(320\) 0 0
\(321\) 1.93261e6 1.04684
\(322\) 0 0
\(323\) 151769.i 0.0809424i
\(324\) 0 0
\(325\) −356400. 110444.i −0.187167 0.0580006i
\(326\) 0 0
\(327\) 418094.i 0.216224i
\(328\) 0 0
\(329\) −629244. −0.320501
\(330\) 0 0
\(331\) 1.58055e6 0.792935 0.396468 0.918049i \(-0.370236\pi\)
0.396468 + 0.918049i \(0.370236\pi\)
\(332\) 0 0
\(333\) 2.13735e6i 1.05625i
\(334\) 0 0
\(335\) −1.44738e6 1.96381e6i −0.704645 0.956063i
\(336\) 0 0
\(337\) 1.22885e6i 0.589419i 0.955587 + 0.294709i \(0.0952228\pi\)
−0.955587 + 0.294709i \(0.904777\pi\)
\(338\) 0 0
\(339\) −2.08982e6 −0.987667
\(340\) 0 0
\(341\) 1.70150e6 0.792405
\(342\) 0 0
\(343\) 1.79396e6i 0.823338i
\(344\) 0 0
\(345\) −2.17998e6 + 1.60671e6i −0.986063 + 0.726756i
\(346\) 0 0
\(347\) 3.84224e6i 1.71301i 0.516137 + 0.856506i \(0.327370\pi\)
−0.516137 + 0.856506i \(0.672630\pi\)
\(348\) 0 0
\(349\) −1.59445e6 −0.700725 −0.350362 0.936614i \(-0.613942\pi\)
−0.350362 + 0.936614i \(0.613942\pi\)
\(350\) 0 0
\(351\) 213840. 0.0926448
\(352\) 0 0
\(353\) 295365.i 0.126160i −0.998008 0.0630802i \(-0.979908\pi\)
0.998008 0.0630802i \(-0.0200924\pi\)
\(354\) 0 0
\(355\) 2.40084e6 1.76949e6i 1.01110 0.745206i
\(356\) 0 0
\(357\) 819551.i 0.340334i
\(358\) 0 0
\(359\) −1.10484e6 −0.452442 −0.226221 0.974076i \(-0.572637\pi\)
−0.226221 + 0.974076i \(0.572637\pi\)
\(360\) 0 0
\(361\) −2.42770e6 −0.980453
\(362\) 0 0
\(363\) 1.94116e6i 0.773206i
\(364\) 0 0
\(365\) −2.35224e6 3.19152e6i −0.924165 1.25391i
\(366\) 0 0
\(367\) 1.83760e6i 0.712174i 0.934453 + 0.356087i \(0.115889\pi\)
−0.934453 + 0.356087i \(0.884111\pi\)
\(368\) 0 0
\(369\) 30294.0 0.0115822
\(370\) 0 0
\(371\) 347688. 0.131146
\(372\) 0 0
\(373\) 2.93350e6i 1.09173i 0.837874 + 0.545864i \(0.183798\pi\)
−0.837874 + 0.545864i \(0.816202\pi\)
\(374\) 0 0
\(375\) −3.28350e6 + 1.14175e6i −1.20575 + 0.419268i
\(376\) 0 0
\(377\) 827432.i 0.299832i
\(378\) 0 0
\(379\) −5.09342e6 −1.82143 −0.910713 0.413040i \(-0.864467\pi\)
−0.910713 + 0.413040i \(0.864467\pi\)
\(380\) 0 0
\(381\) −1.73567e6 −0.612568
\(382\) 0 0
\(383\) 3.17485e6i 1.10593i −0.833205 0.552964i \(-0.813497\pi\)
0.833205 0.552964i \(-0.186503\pi\)
\(384\) 0 0
\(385\) 498960. + 676989.i 0.171559 + 0.232772i
\(386\) 0 0
\(387\) 63937.9i 0.0217011i
\(388\) 0 0
\(389\) 1.79991e6 0.603083 0.301541 0.953453i \(-0.402499\pi\)
0.301541 + 0.953453i \(0.402499\pi\)
\(390\) 0 0
\(391\) −1.67939e6 −0.555533
\(392\) 0 0
\(393\) 3.83771e6i 1.25340i
\(394\) 0 0
\(395\) 2.33640e6 1.72199e6i 0.753450 0.555314i
\(396\) 0 0
\(397\) 4.90405e6i 1.56163i −0.624760 0.780817i \(-0.714803\pi\)
0.624760 0.780817i \(-0.285197\pi\)
\(398\) 0 0
\(399\) −261360. −0.0821877
\(400\) 0 0
\(401\) −642798. −0.199624 −0.0998122 0.995006i \(-0.531824\pi\)
−0.0998122 + 0.995006i \(0.531824\pi\)
\(402\) 0 0
\(403\) 806179.i 0.247268i
\(404\) 0 0
\(405\) 3.27686e6 2.41513e6i 0.992704 0.731650i
\(406\) 0 0
\(407\) 3.52035e6i 1.05341i
\(408\) 0 0
\(409\) −2.05711e6 −0.608064 −0.304032 0.952662i \(-0.598333\pi\)
−0.304032 + 0.952662i \(0.598333\pi\)
\(410\) 0 0
\(411\) 2.85701e6 0.834271
\(412\) 0 0
\(413\) 1.47218e6i 0.424704i
\(414\) 0 0
\(415\) −2.05106e6 2.78288e6i −0.584599 0.793185i
\(416\) 0 0
\(417\) 6.33489e6i 1.78402i
\(418\) 0 0
\(419\) 2.93742e6 0.817393 0.408697 0.912670i \(-0.365983\pi\)
0.408697 + 0.912670i \(0.365983\pi\)
\(420\) 0 0
\(421\) 2.71770e6 0.747303 0.373651 0.927569i \(-0.378106\pi\)
0.373651 + 0.927569i \(0.378106\pi\)
\(422\) 0 0
\(423\) 1.61266e6i 0.438219i
\(424\) 0 0
\(425\) −2.05920e6 638119.i −0.553001 0.171368i
\(426\) 0 0
\(427\) 340166.i 0.0902862i
\(428\) 0 0
\(429\) −598752. −0.157074
\(430\) 0 0
\(431\) −4.99435e6 −1.29505 −0.647524 0.762045i \(-0.724196\pi\)
−0.647524 + 0.762045i \(0.724196\pi\)
\(432\) 0 0
\(433\) 2.08183e6i 0.533612i −0.963750 0.266806i \(-0.914032\pi\)
0.963750 0.266806i \(-0.0859684\pi\)
\(434\) 0 0
\(435\) 4.57380e6 + 6.20574e6i 1.15892 + 1.57243i
\(436\) 0 0
\(437\) 535569.i 0.134156i
\(438\) 0 0
\(439\) 4.70404e6 1.16496 0.582478 0.812846i \(-0.302083\pi\)
0.582478 + 0.812846i \(0.302083\pi\)
\(440\) 0 0
\(441\) −2.02618e6 −0.496114
\(442\) 0 0
\(443\) 5.70103e6i 1.38021i 0.723711 + 0.690103i \(0.242435\pi\)
−0.723711 + 0.690103i \(0.757565\pi\)
\(444\) 0 0
\(445\) 449550. 331331.i 0.107616 0.0793162i
\(446\) 0 0
\(447\) 1.67456e6i 0.396399i
\(448\) 0 0
\(449\) 6.20325e6 1.45212 0.726062 0.687630i \(-0.241349\pi\)
0.726062 + 0.687630i \(0.241349\pi\)
\(450\) 0 0
\(451\) 49896.0 0.0115511
\(452\) 0 0
\(453\) 3.10134e6i 0.710074i
\(454\) 0 0
\(455\) −320760. + 236409.i −0.0726360 + 0.0535347i
\(456\) 0 0
\(457\) 2.15371e6i 0.482388i −0.970477 0.241194i \(-0.922461\pi\)
0.970477 0.241194i \(-0.0775391\pi\)
\(458\) 0 0
\(459\) 1.23552e6 0.273727
\(460\) 0 0
\(461\) −3.85130e6 −0.844024 −0.422012 0.906590i \(-0.638676\pi\)
−0.422012 + 0.906590i \(0.638676\pi\)
\(462\) 0 0
\(463\) 2.08213e6i 0.451394i 0.974198 + 0.225697i \(0.0724659\pi\)
−0.974198 + 0.225697i \(0.927534\pi\)
\(464\) 0 0
\(465\) 4.45632e6 + 6.04634e6i 0.955749 + 1.29676i
\(466\) 0 0
\(467\) 1.30822e6i 0.277579i −0.990322 0.138790i \(-0.955679\pi\)
0.990322 0.138790i \(-0.0443212\pi\)
\(468\) 0 0
\(469\) −2.60528e6 −0.546919
\(470\) 0 0
\(471\) −7.09711e6 −1.47411
\(472\) 0 0
\(473\) 105309.i 0.0216429i
\(474\) 0 0
\(475\) 203500. 656692.i 0.0413838 0.133545i
\(476\) 0 0
\(477\) 891071.i 0.179315i
\(478\) 0 0
\(479\) 6.76368e6 1.34693 0.673464 0.739220i \(-0.264806\pi\)
0.673464 + 0.739220i \(0.264806\pi\)
\(480\) 0 0
\(481\) 1.66795e6 0.328716
\(482\) 0 0
\(483\) 2.89207e6i 0.564080i
\(484\) 0 0
\(485\) 3.35808e6 + 4.55625e6i 0.648241 + 0.879534i
\(486\) 0 0
\(487\) 6.67193e6i 1.27476i −0.770549 0.637381i \(-0.780018\pi\)
0.770549 0.637381i \(-0.219982\pi\)
\(488\) 0 0
\(489\) −2.88328e6 −0.545273
\(490\) 0 0
\(491\) 6.87575e6 1.28711 0.643556 0.765399i \(-0.277458\pi\)
0.643556 + 0.765399i \(0.277458\pi\)
\(492\) 0 0
\(493\) 4.78072e6i 0.885881i
\(494\) 0 0
\(495\) −1.73502e6 + 1.27876e6i −0.318267 + 0.234572i
\(496\) 0 0
\(497\) 3.18507e6i 0.578400i
\(498\) 0 0
\(499\) −6.94010e6 −1.24771 −0.623856 0.781539i \(-0.714435\pi\)
−0.623856 + 0.781539i \(0.714435\pi\)
\(500\) 0 0
\(501\) −360228. −0.0641185
\(502\) 0 0
\(503\) 921007.i 0.162309i −0.996702 0.0811546i \(-0.974139\pi\)
0.996702 0.0811546i \(-0.0258607\pi\)
\(504\) 0 0
\(505\) 4.90941e6 3.61837e6i 0.856645 0.631371i
\(506\) 0 0
\(507\) 7.10495e6i 1.22755i
\(508\) 0 0
\(509\) 4.97979e6 0.851955 0.425977 0.904734i \(-0.359930\pi\)
0.425977 + 0.904734i \(0.359930\pi\)
\(510\) 0 0
\(511\) −4.23403e6 −0.717302
\(512\) 0 0
\(513\) 394015.i 0.0661027i
\(514\) 0 0
\(515\) 2.34234e6 + 3.17809e6i 0.389163 + 0.528017i
\(516\) 0 0
\(517\) 2.65614e6i 0.437043i
\(518\) 0 0
\(519\) 9.80206e6 1.59735
\(520\) 0 0
\(521\) −147798. −0.0238547 −0.0119274 0.999929i \(-0.503797\pi\)
−0.0119274 + 0.999929i \(0.503797\pi\)
\(522\) 0 0
\(523\) 1.23884e7i 1.98043i −0.139543 0.990216i \(-0.544563\pi\)
0.139543 0.990216i \(-0.455437\pi\)
\(524\) 0 0
\(525\) −1.09890e6 + 3.54614e6i −0.174004 + 0.561509i
\(526\) 0 0
\(527\) 4.65792e6i 0.730576i
\(528\) 0 0
\(529\) 510027. 0.0792417
\(530\) 0 0
\(531\) −3.77298e6 −0.580695
\(532\) 0 0
\(533\) 23640.9i 0.00360451i
\(534\) 0 0
\(535\) 3.22102e6 + 4.37028e6i 0.486529 + 0.660123i
\(536\) 0 0
\(537\) 8.84385e6i 1.32344i
\(538\) 0 0
\(539\) −3.33724e6 −0.494783
\(540\) 0 0
\(541\) −9.99810e6 −1.46867 −0.734335 0.678787i \(-0.762506\pi\)
−0.734335 + 0.678787i \(0.762506\pi\)
\(542\) 0 0
\(543\) 3.12231e6i 0.454440i
\(544\) 0 0
\(545\) 945450. 696823.i 0.136348 0.100492i
\(546\) 0 0
\(547\) 1.18580e7i 1.69451i −0.531189 0.847253i \(-0.678255\pi\)
0.531189 0.847253i \(-0.321745\pi\)
\(548\) 0 0
\(549\) 871794. 0.123448
\(550\) 0 0
\(551\) −1.52460e6 −0.213933
\(552\) 0 0
\(553\) 3.09958e6i 0.431013i
\(554\) 0 0
\(555\) 1.25096e7 9.21995e6i 1.72390 1.27056i
\(556\) 0 0
\(557\) 904550.i 0.123536i 0.998091 + 0.0617681i \(0.0196739\pi\)
−0.998091 + 0.0617681i \(0.980326\pi\)
\(558\) 0 0
\(559\) 49896.0 0.00675361
\(560\) 0 0
\(561\) −3.45946e6 −0.464088
\(562\) 0 0
\(563\) 8.68719e6i 1.15507i 0.816366 + 0.577535i \(0.195985\pi\)
−0.816366 + 0.577535i \(0.804015\pi\)
\(564\) 0 0
\(565\) −3.48304e6 4.72579e6i −0.459026 0.622807i
\(566\) 0 0
\(567\) 4.34724e6i 0.567879i
\(568\) 0 0
\(569\) −2.27007e6 −0.293940 −0.146970 0.989141i \(-0.546952\pi\)
−0.146970 + 0.989141i \(0.546952\pi\)
\(570\) 0 0
\(571\) −1.43807e7 −1.84582 −0.922908 0.385021i \(-0.874194\pi\)
−0.922908 + 0.385021i \(0.874194\pi\)
\(572\) 0 0
\(573\) 6.61372e6i 0.841510i
\(574\) 0 0
\(575\) −7.26660e6 2.25182e6i −0.916562 0.284030i
\(576\) 0 0
\(577\) 5.63943e6i 0.705173i 0.935779 + 0.352586i \(0.114698\pi\)
−0.935779 + 0.352586i \(0.885302\pi\)
\(578\) 0 0
\(579\) −1.56436e7 −1.93928
\(580\) 0 0
\(581\) −3.69191e6 −0.453744
\(582\) 0 0
\(583\) 1.46765e6i 0.178834i
\(584\) 0 0
\(585\) −605880. 822059.i −0.0731976 0.0993146i
\(586\) 0 0
\(587\) 1.28473e6i 0.153893i −0.997035 0.0769464i \(-0.975483\pi\)
0.997035 0.0769464i \(-0.0245170\pi\)
\(588\) 0 0
\(589\) −1.48544e6 −0.176428
\(590\) 0 0
\(591\) −1.18615e6 −0.139692
\(592\) 0 0
\(593\) 7.00943e6i 0.818552i 0.912411 + 0.409276i \(0.134219\pi\)
−0.912411 + 0.409276i \(0.865781\pi\)
\(594\) 0 0
\(595\) −1.85328e6 + 1.36592e6i −0.214609 + 0.158173i
\(596\) 0 0
\(597\) 7.87632e6i 0.904456i
\(598\) 0 0
\(599\) 8.80020e6 1.00213 0.501067 0.865409i \(-0.332941\pi\)
0.501067 + 0.865409i \(0.332941\pi\)
\(600\) 0 0
\(601\) −1.07670e7 −1.21593 −0.607965 0.793964i \(-0.708014\pi\)
−0.607965 + 0.793964i \(0.708014\pi\)
\(602\) 0 0
\(603\) 6.67694e6i 0.747798i
\(604\) 0 0
\(605\) 4.38962e6 3.23527e6i 0.487571 0.359353i
\(606\) 0 0
\(607\) 1.51219e7i 1.66584i 0.553391 + 0.832921i \(0.313333\pi\)
−0.553391 + 0.832921i \(0.686667\pi\)
\(608\) 0 0
\(609\) 8.23284e6 0.899511
\(610\) 0 0
\(611\) 1.25849e6 0.136379
\(612\) 0 0
\(613\) 8.31622e6i 0.893871i −0.894566 0.446936i \(-0.852515\pi\)
0.894566 0.446936i \(-0.147485\pi\)
\(614\) 0 0
\(615\) 130680. + 177307.i 0.0139323 + 0.0189033i
\(616\) 0 0
\(617\) 1.21083e7i 1.28047i 0.768178 + 0.640237i \(0.221164\pi\)
−0.768178 + 0.640237i \(0.778836\pi\)
\(618\) 0 0
\(619\) −9.73238e6 −1.02092 −0.510461 0.859901i \(-0.670525\pi\)
−0.510461 + 0.859901i \(0.670525\pi\)
\(620\) 0 0
\(621\) 4.35996e6 0.453684
\(622\) 0 0
\(623\) 596395.i 0.0615622i
\(624\) 0 0
\(625\) −8.05437e6 5.52218e6i −0.824768 0.565471i
\(626\) 0 0
\(627\) 1.10324e6i 0.112073i
\(628\) 0 0
\(629\) 9.63706e6 0.971220
\(630\) 0 0
\(631\) 8.60145e6 0.859999 0.430000 0.902829i \(-0.358514\pi\)
0.430000 + 0.902829i \(0.358514\pi\)
\(632\) 0 0
\(633\) 5.00574e6i 0.496546i
\(634\) 0 0
\(635\) −2.89278e6 3.92493e6i −0.284696 0.386276i
\(636\) 0 0
\(637\) 1.58119e6i 0.154396i
\(638\) 0 0
\(639\) 8.16286e6 0.790842
\(640\) 0 0
\(641\) −6.42440e6 −0.617572 −0.308786 0.951132i \(-0.599923\pi\)
−0.308786 + 0.951132i \(0.599923\pi\)
\(642\) 0 0
\(643\) 3.64721e6i 0.347883i −0.984756 0.173941i \(-0.944350\pi\)
0.984756 0.173941i \(-0.0556503\pi\)
\(644\) 0 0
\(645\) 374220. 275811.i 0.0354183 0.0261043i
\(646\) 0 0
\(647\) 3.78036e6i 0.355036i −0.984118 0.177518i \(-0.943193\pi\)
0.984118 0.177518i \(-0.0568068\pi\)
\(648\) 0 0
\(649\) −6.21432e6 −0.579138
\(650\) 0 0
\(651\) 8.02138e6 0.741816
\(652\) 0 0
\(653\) 1.66957e7i 1.53223i −0.642706 0.766113i \(-0.722188\pi\)
0.642706 0.766113i \(-0.277812\pi\)
\(654\) 0 0
\(655\) 8.67834e6 6.39618e6i 0.790375 0.582529i
\(656\) 0 0
\(657\) 1.08512e7i 0.980761i
\(658\) 0 0
\(659\) 1.22166e6 0.109581 0.0547907 0.998498i \(-0.482551\pi\)
0.0547907 + 0.998498i \(0.482551\pi\)
\(660\) 0 0
\(661\) 1.62789e7 1.44918 0.724589 0.689182i \(-0.242030\pi\)
0.724589 + 0.689182i \(0.242030\pi\)
\(662\) 0 0
\(663\) 1.63910e6i 0.144818i
\(664\) 0 0
\(665\) −435600. 591023.i −0.0381974 0.0518263i
\(666\) 0 0
\(667\) 1.68704e7i 1.46829i
\(668\) 0 0
\(669\) −5.74636e6 −0.496395
\(670\) 0 0
\(671\) 1.43590e6 0.123117
\(672\) 0 0
\(673\) 1.43928e7i 1.22492i 0.790503 + 0.612459i \(0.209819\pi\)
−0.790503 + 0.612459i \(0.790181\pi\)
\(674\) 0 0
\(675\) 5.34600e6 + 1.65665e6i 0.451616 + 0.139950i
\(676\) 0 0
\(677\) 2.62429e6i 0.220059i 0.993928 + 0.110030i \(0.0350946\pi\)
−0.993928 + 0.110030i \(0.964905\pi\)
\(678\) 0 0
\(679\) 6.04454e6 0.503140
\(680\) 0 0
\(681\) 2.31661e7 1.91419
\(682\) 0 0
\(683\) 1.03039e7i 0.845184i −0.906320 0.422592i \(-0.861120\pi\)
0.906320 0.422592i \(-0.138880\pi\)
\(684\) 0 0
\(685\) 4.76168e6 + 6.46065e6i 0.387734 + 0.526078i
\(686\) 0 0
\(687\) 1.08985e7i 0.880998i
\(688\) 0 0
\(689\) −695376. −0.0558048
\(690\) 0 0
\(691\) −4.50285e6 −0.358751 −0.179375 0.983781i \(-0.557408\pi\)
−0.179375 + 0.983781i \(0.557408\pi\)
\(692\) 0 0
\(693\) 2.30176e6i 0.182066i
\(694\) 0 0
\(695\) −1.43253e7 + 1.05581e7i −1.12497 + 0.829136i
\(696\) 0 0
\(697\) 136592.i 0.0106498i
\(698\) 0 0
\(699\) −957264. −0.0741035
\(700\) 0 0
\(701\) −4.88090e6 −0.375150 −0.187575 0.982250i \(-0.560063\pi\)
−0.187575 + 0.982250i \(0.560063\pi\)
\(702\) 0 0
\(703\) 3.07332e6i 0.234541i
\(704\) 0 0
\(705\) 9.43866e6 6.95655e6i 0.715217 0.527134i
\(706\) 0 0
\(707\) 6.51307e6i 0.490046i
\(708\) 0 0
\(709\) −9.96961e6 −0.744839 −0.372420 0.928064i \(-0.621472\pi\)
−0.372420 + 0.928064i \(0.621472\pi\)
\(710\) 0 0
\(711\) 7.94376e6 0.589321
\(712\) 0 0
\(713\) 1.64371e7i 1.21088i
\(714\) 0 0
\(715\) −997920. 1.35398e6i −0.0730013 0.0990482i
\(716\) 0 0
\(717\) 2.00160e7i 1.45405i
\(718\) 0 0
\(719\) 1.19167e7 0.859675 0.429838 0.902906i \(-0.358571\pi\)
0.429838 + 0.902906i \(0.358571\pi\)
\(720\) 0 0
\(721\) 4.21621e6 0.302054
\(722\) 0 0
\(723\) 1.78143e7i 1.26743i
\(724\) 0 0
\(725\) −6.41025e6 + 2.06858e7i −0.452929 + 1.46160i
\(726\) 0 0
\(727\) 1.38269e6i 0.0970264i 0.998823 + 0.0485132i \(0.0154483\pi\)
−0.998823 + 0.0485132i \(0.984552\pi\)
\(728\) 0 0
\(729\) 2.48079e6 0.172890
\(730\) 0 0
\(731\) 288288. 0.0199541
\(732\) 0 0
\(733\) 6.09661e6i 0.419110i −0.977797 0.209555i \(-0.932798\pi\)
0.977797 0.209555i \(-0.0672016\pi\)
\(734\) 0 0
\(735\) −8.74038e6 1.18590e7i −0.596777 0.809707i
\(736\) 0 0
\(737\) 1.09973e7i 0.745793i
\(738\) 0 0
\(739\) −6.16946e6 −0.415562 −0.207781 0.978175i \(-0.566624\pi\)
−0.207781 + 0.978175i \(0.566624\pi\)
\(740\) 0 0
\(741\) 522720. 0.0349723
\(742\) 0 0
\(743\) 1.57574e7i 1.04716i 0.851978 + 0.523578i \(0.175403\pi\)
−0.851978 + 0.523578i \(0.824597\pi\)
\(744\) 0 0
\(745\) −3.78675e6 + 2.79094e6i −0.249963 + 0.184230i
\(746\) 0 0
\(747\) 9.46179e6i 0.620400i
\(748\) 0 0
\(749\) 5.79784e6 0.377626
\(750\) 0 0
\(751\) 1.51816e7 0.982243 0.491122 0.871091i \(-0.336587\pi\)
0.491122 + 0.871091i \(0.336587\pi\)
\(752\) 0 0
\(753\) 1.11091e7i 0.713987i
\(754\) 0 0
\(755\) −7.01316e6 + 5.16889e6i −0.447761 + 0.330012i
\(756\) 0 0
\(757\) 652274.i 0.0413705i −0.999786 0.0206852i \(-0.993415\pi\)
0.999786 0.0206852i \(-0.00658478\pi\)
\(758\) 0 0
\(759\) −1.22079e7 −0.769194
\(760\) 0 0
\(761\) 4.51420e6 0.282566 0.141283 0.989969i \(-0.454877\pi\)
0.141283 + 0.989969i \(0.454877\pi\)
\(762\) 0 0
\(763\) 1.25428e6i 0.0779980i
\(764\) 0 0
\(765\) −3.50064e6 4.74967e6i −0.216269 0.293434i
\(766\) 0 0
\(767\) 2.94437e6i 0.180719i
\(768\) 0 0
\(769\) −1.20799e7 −0.736625 −0.368312 0.929702i \(-0.620064\pi\)
−0.368312 + 0.929702i \(0.620064\pi\)
\(770\) 0 0
\(771\) 1.56795e7 0.949939
\(772\) 0 0
\(773\) 1.04245e7i 0.627492i −0.949507 0.313746i \(-0.898416\pi\)
0.949507 0.313746i \(-0.101584\pi\)
\(774\) 0 0
\(775\) −6.24560e6 + 2.01545e7i −0.373525 + 1.20536i
\(776\) 0 0
\(777\) 1.65959e7i 0.986163i
\(778\) 0 0
\(779\) −43560.0 −0.00257184
\(780\) 0 0
\(781\) 1.34447e7 0.788721
\(782\) 0 0
\(783\) 1.24115e7i 0.723467i
\(784\) 0 0
\(785\) −1.18285e7 1.60489e7i −0.685104 0.929549i
\(786\) 0 0
\(787\) 3.45366e7i 1.98766i −0.110913 0.993830i \(-0.535378\pi\)
0.110913 0.993830i \(-0.464622\pi\)
\(788\) 0 0
\(789\) −3.24711e7 −1.85697
\(790\) 0 0
\(791\) −6.26947e6 −0.356279
\(792\) 0 0
\(793\) 680333.i 0.0384183i
\(794\) 0 0
\(795\) −5.21532e6 + 3.84384e6i −0.292660 + 0.215698i
\(796\) 0 0
\(797\) 2.09287e7i 1.16707i −0.812089 0.583533i \(-0.801670\pi\)
0.812089 0.583533i \(-0.198330\pi\)
\(798\) 0 0
\(799\) 7.27126e6 0.402942
\(800\) 0 0
\(801\) 1.52847e6 0.0841735
\(802\) 0 0
\(803\) 1.78725e7i 0.978131i
\(804\) 0 0
\(805\) −6.53994e6 + 4.82012e6i −0.355700 + 0.262161i
\(806\) 0 0
\(807\) 3.45533e7i 1.86770i
\(808\) 0 0
\(809\) 2.48797e7 1.33651