Properties

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

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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: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 10)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 80.49
Dual form 80.6.c.c.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+14.0000i q^{3} +(55.0000 - 10.0000i) q^{5} -158.000i q^{7} +47.0000 q^{9} +O(q^{10})\) \(q+14.0000i q^{3} +(55.0000 - 10.0000i) q^{5} -158.000i q^{7} +47.0000 q^{9} +148.000 q^{11} -684.000i q^{13} +(140.000 + 770.000i) q^{15} +2048.00i q^{17} +2220.00 q^{19} +2212.00 q^{21} -1246.00i q^{23} +(2925.00 - 1100.00i) q^{25} +4060.00i q^{27} +270.000 q^{29} +2048.00 q^{31} +2072.00i q^{33} +(-1580.00 - 8690.00i) q^{35} -4372.00i q^{37} +9576.00 q^{39} -2398.00 q^{41} +2294.00i q^{43} +(2585.00 - 470.000i) q^{45} +10682.0i q^{47} -8157.00 q^{49} -28672.0 q^{51} -2964.00i q^{53} +(8140.00 - 1480.00i) q^{55} +31080.0i q^{57} -39740.0 q^{59} -42298.0 q^{61} -7426.00i q^{63} +(-6840.00 - 37620.0i) q^{65} -32098.0i q^{67} +17444.0 q^{69} +4248.00 q^{71} -30104.0i q^{73} +(15400.0 + 40950.0i) q^{75} -23384.0i q^{77} +35280.0 q^{79} -45419.0 q^{81} -27826.0i q^{83} +(20480.0 + 112640. i) q^{85} +3780.00i q^{87} +85210.0 q^{89} -108072. q^{91} +28672.0i q^{93} +(122100. - 22200.0i) q^{95} -97232.0i q^{97} +6956.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 110q^{5} + 94q^{9} + O(q^{10}) \) \( 2q + 110q^{5} + 94q^{9} + 296q^{11} + 280q^{15} + 4440q^{19} + 4424q^{21} + 5850q^{25} + 540q^{29} + 4096q^{31} - 3160q^{35} + 19152q^{39} - 4796q^{41} + 5170q^{45} - 16314q^{49} - 57344q^{51} + 16280q^{55} - 79480q^{59} - 84596q^{61} - 13680q^{65} + 34888q^{69} + 8496q^{71} + 30800q^{75} + 70560q^{79} - 90838q^{81} + 40960q^{85} + 170420q^{89} - 216144q^{91} + 244200q^{95} + 13912q^{99} + O(q^{100}) \)

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
\(3\) 14.0000i 0.898100i 0.893507 + 0.449050i \(0.148238\pi\)
−0.893507 + 0.449050i \(0.851762\pi\)
\(4\) 0 0
\(5\) 55.0000 10.0000i 0.983870 0.178885i
\(6\) 0 0
\(7\) 158.000i 1.21874i −0.792885 0.609371i \(-0.791422\pi\)
0.792885 0.609371i \(-0.208578\pi\)
\(8\) 0 0
\(9\) 47.0000 0.193416
\(10\) 0 0
\(11\) 148.000 0.368791 0.184395 0.982852i \(-0.440967\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(12\) 0 0
\(13\) 684.000i 1.12253i −0.827636 0.561265i \(-0.810315\pi\)
0.827636 0.561265i \(-0.189685\pi\)
\(14\) 0 0
\(15\) 140.000 + 770.000i 0.160657 + 0.883614i
\(16\) 0 0
\(17\) 2048.00i 1.71873i 0.511363 + 0.859365i \(0.329141\pi\)
−0.511363 + 0.859365i \(0.670859\pi\)
\(18\) 0 0
\(19\) 2220.00 1.41081 0.705406 0.708804i \(-0.250765\pi\)
0.705406 + 0.708804i \(0.250765\pi\)
\(20\) 0 0
\(21\) 2212.00 1.09455
\(22\) 0 0
\(23\) 1246.00i 0.491132i −0.969380 0.245566i \(-0.921026\pi\)
0.969380 0.245566i \(-0.0789738\pi\)
\(24\) 0 0
\(25\) 2925.00 1100.00i 0.936000 0.352000i
\(26\) 0 0
\(27\) 4060.00i 1.07181i
\(28\) 0 0
\(29\) 270.000 0.0596168 0.0298084 0.999556i \(-0.490510\pi\)
0.0298084 + 0.999556i \(0.490510\pi\)
\(30\) 0 0
\(31\) 2048.00 0.382759 0.191380 0.981516i \(-0.438704\pi\)
0.191380 + 0.981516i \(0.438704\pi\)
\(32\) 0 0
\(33\) 2072.00i 0.331211i
\(34\) 0 0
\(35\) −1580.00 8690.00i −0.218015 1.19908i
\(36\) 0 0
\(37\) 4372.00i 0.525020i −0.964929 0.262510i \(-0.915450\pi\)
0.964929 0.262510i \(-0.0845503\pi\)
\(38\) 0 0
\(39\) 9576.00 1.00814
\(40\) 0 0
\(41\) −2398.00 −0.222787 −0.111393 0.993776i \(-0.535531\pi\)
−0.111393 + 0.993776i \(0.535531\pi\)
\(42\) 0 0
\(43\) 2294.00i 0.189200i 0.995515 + 0.0946002i \(0.0301573\pi\)
−0.995515 + 0.0946002i \(0.969843\pi\)
\(44\) 0 0
\(45\) 2585.00 470.000i 0.190296 0.0345992i
\(46\) 0 0
\(47\) 10682.0i 0.705355i 0.935745 + 0.352678i \(0.114729\pi\)
−0.935745 + 0.352678i \(0.885271\pi\)
\(48\) 0 0
\(49\) −8157.00 −0.485333
\(50\) 0 0
\(51\) −28672.0 −1.54359
\(52\) 0 0
\(53\) 2964.00i 0.144940i −0.997371 0.0724700i \(-0.976912\pi\)
0.997371 0.0724700i \(-0.0230882\pi\)
\(54\) 0 0
\(55\) 8140.00 1480.00i 0.362842 0.0659713i
\(56\) 0 0
\(57\) 31080.0i 1.26705i
\(58\) 0 0
\(59\) −39740.0 −1.48627 −0.743135 0.669141i \(-0.766662\pi\)
−0.743135 + 0.669141i \(0.766662\pi\)
\(60\) 0 0
\(61\) −42298.0 −1.45544 −0.727722 0.685873i \(-0.759421\pi\)
−0.727722 + 0.685873i \(0.759421\pi\)
\(62\) 0 0
\(63\) 7426.00i 0.235724i
\(64\) 0 0
\(65\) −6840.00 37620.0i −0.200804 1.10442i
\(66\) 0 0
\(67\) 32098.0i 0.873556i −0.899569 0.436778i \(-0.856119\pi\)
0.899569 0.436778i \(-0.143881\pi\)
\(68\) 0 0
\(69\) 17444.0 0.441086
\(70\) 0 0
\(71\) 4248.00 0.100009 0.0500044 0.998749i \(-0.484076\pi\)
0.0500044 + 0.998749i \(0.484076\pi\)
\(72\) 0 0
\(73\) 30104.0i 0.661176i −0.943775 0.330588i \(-0.892753\pi\)
0.943775 0.330588i \(-0.107247\pi\)
\(74\) 0 0
\(75\) 15400.0 + 40950.0i 0.316131 + 0.840622i
\(76\) 0 0
\(77\) 23384.0i 0.449461i
\(78\) 0 0
\(79\) 35280.0 0.636005 0.318003 0.948090i \(-0.396988\pi\)
0.318003 + 0.948090i \(0.396988\pi\)
\(80\) 0 0
\(81\) −45419.0 −0.769175
\(82\) 0 0
\(83\) 27826.0i 0.443359i −0.975120 0.221680i \(-0.928846\pi\)
0.975120 0.221680i \(-0.0711539\pi\)
\(84\) 0 0
\(85\) 20480.0 + 112640.i 0.307456 + 1.69101i
\(86\) 0 0
\(87\) 3780.00i 0.0535419i
\(88\) 0 0
\(89\) 85210.0 1.14029 0.570145 0.821544i \(-0.306887\pi\)
0.570145 + 0.821544i \(0.306887\pi\)
\(90\) 0 0
\(91\) −108072. −1.36807
\(92\) 0 0
\(93\) 28672.0i 0.343756i
\(94\) 0 0
\(95\) 122100. 22200.0i 1.38805 0.252374i
\(96\) 0 0
\(97\) 97232.0i 1.04925i −0.851333 0.524626i \(-0.824205\pi\)
0.851333 0.524626i \(-0.175795\pi\)
\(98\) 0 0
\(99\) 6956.00 0.0713299
\(100\) 0 0
\(101\) −4298.00 −0.0419240 −0.0209620 0.999780i \(-0.506673\pi\)
−0.0209620 + 0.999780i \(0.506673\pi\)
\(102\) 0 0
\(103\) 124114.i 1.15273i 0.817192 + 0.576365i \(0.195529\pi\)
−0.817192 + 0.576365i \(0.804471\pi\)
\(104\) 0 0
\(105\) 121660. 22120.0i 1.07690 0.195800i
\(106\) 0 0
\(107\) 42342.0i 0.357530i 0.983892 + 0.178765i \(0.0572101\pi\)
−0.983892 + 0.178765i \(0.942790\pi\)
\(108\) 0 0
\(109\) 35990.0 0.290145 0.145073 0.989421i \(-0.453658\pi\)
0.145073 + 0.989421i \(0.453658\pi\)
\(110\) 0 0
\(111\) 61208.0 0.471521
\(112\) 0 0
\(113\) 228816.i 1.68574i 0.538118 + 0.842869i \(0.319135\pi\)
−0.538118 + 0.842869i \(0.680865\pi\)
\(114\) 0 0
\(115\) −12460.0 68530.0i −0.0878564 0.483210i
\(116\) 0 0
\(117\) 32148.0i 0.217115i
\(118\) 0 0
\(119\) 323584. 2.09469
\(120\) 0 0
\(121\) −139147. −0.863993
\(122\) 0 0
\(123\) 33572.0i 0.200085i
\(124\) 0 0
\(125\) 149875. 89750.0i 0.857935 0.513759i
\(126\) 0 0
\(127\) 175238.i 0.964093i −0.876146 0.482047i \(-0.839894\pi\)
0.876146 0.482047i \(-0.160106\pi\)
\(128\) 0 0
\(129\) −32116.0 −0.169921
\(130\) 0 0
\(131\) −299652. −1.52559 −0.762797 0.646638i \(-0.776174\pi\)
−0.762797 + 0.646638i \(0.776174\pi\)
\(132\) 0 0
\(133\) 350760.i 1.71942i
\(134\) 0 0
\(135\) 40600.0 + 223300.i 0.191731 + 1.05452i
\(136\) 0 0
\(137\) 107928.i 0.491284i 0.969361 + 0.245642i \(0.0789988\pi\)
−0.969361 + 0.245642i \(0.921001\pi\)
\(138\) 0 0
\(139\) −196460. −0.862456 −0.431228 0.902243i \(-0.641920\pi\)
−0.431228 + 0.902243i \(0.641920\pi\)
\(140\) 0 0
\(141\) −149548. −0.633480
\(142\) 0 0
\(143\) 101232.i 0.413978i
\(144\) 0 0
\(145\) 14850.0 2700.00i 0.0586552 0.0106646i
\(146\) 0 0
\(147\) 114198.i 0.435878i
\(148\) 0 0
\(149\) −138850. −0.512366 −0.256183 0.966628i \(-0.582465\pi\)
−0.256183 + 0.966628i \(0.582465\pi\)
\(150\) 0 0
\(151\) −416152. −1.48528 −0.742642 0.669688i \(-0.766428\pi\)
−0.742642 + 0.669688i \(0.766428\pi\)
\(152\) 0 0
\(153\) 96256.0i 0.332429i
\(154\) 0 0
\(155\) 112640. 20480.0i 0.376585 0.0684701i
\(156\) 0 0
\(157\) 433108.i 1.40232i 0.713004 + 0.701160i \(0.247334\pi\)
−0.713004 + 0.701160i \(0.752666\pi\)
\(158\) 0 0
\(159\) 41496.0 0.130171
\(160\) 0 0
\(161\) −196868. −0.598564
\(162\) 0 0
\(163\) 149134.i 0.439651i 0.975539 + 0.219825i \(0.0705487\pi\)
−0.975539 + 0.219825i \(0.929451\pi\)
\(164\) 0 0
\(165\) 20720.0 + 113960.i 0.0592488 + 0.325869i
\(166\) 0 0
\(167\) 559602.i 1.55270i 0.630301 + 0.776351i \(0.282932\pi\)
−0.630301 + 0.776351i \(0.717068\pi\)
\(168\) 0 0
\(169\) −96563.0 −0.260072
\(170\) 0 0
\(171\) 104340. 0.272873
\(172\) 0 0
\(173\) 343804.i 0.873365i −0.899616 0.436682i \(-0.856153\pi\)
0.899616 0.436682i \(-0.143847\pi\)
\(174\) 0 0
\(175\) −173800. 462150.i −0.428997 1.14074i
\(176\) 0 0
\(177\) 556360.i 1.33482i
\(178\) 0 0
\(179\) 23980.0 0.0559392 0.0279696 0.999609i \(-0.491096\pi\)
0.0279696 + 0.999609i \(0.491096\pi\)
\(180\) 0 0
\(181\) −651898. −1.47905 −0.739526 0.673128i \(-0.764950\pi\)
−0.739526 + 0.673128i \(0.764950\pi\)
\(182\) 0 0
\(183\) 592172.i 1.30713i
\(184\) 0 0
\(185\) −43720.0 240460.i −0.0939184 0.516551i
\(186\) 0 0
\(187\) 303104.i 0.633852i
\(188\) 0 0
\(189\) 641480. 1.30626
\(190\) 0 0
\(191\) −202752. −0.402144 −0.201072 0.979576i \(-0.564443\pi\)
−0.201072 + 0.979576i \(0.564443\pi\)
\(192\) 0 0
\(193\) 452656.i 0.874732i 0.899284 + 0.437366i \(0.144089\pi\)
−0.899284 + 0.437366i \(0.855911\pi\)
\(194\) 0 0
\(195\) 526680. 95760.0i 0.991883 0.180342i
\(196\) 0 0
\(197\) 337468.i 0.619537i 0.950812 + 0.309768i \(0.100252\pi\)
−0.950812 + 0.309768i \(0.899748\pi\)
\(198\) 0 0
\(199\) −561000. −1.00422 −0.502112 0.864803i \(-0.667443\pi\)
−0.502112 + 0.864803i \(0.667443\pi\)
\(200\) 0 0
\(201\) 449372. 0.784541
\(202\) 0 0
\(203\) 42660.0i 0.0726576i
\(204\) 0 0
\(205\) −131890. + 23980.0i −0.219193 + 0.0398533i
\(206\) 0 0
\(207\) 58562.0i 0.0949927i
\(208\) 0 0
\(209\) 328560. 0.520294
\(210\) 0 0
\(211\) 805548. 1.24562 0.622810 0.782373i \(-0.285991\pi\)
0.622810 + 0.782373i \(0.285991\pi\)
\(212\) 0 0
\(213\) 59472.0i 0.0898180i
\(214\) 0 0
\(215\) 22940.0 + 126170.i 0.0338452 + 0.186149i
\(216\) 0 0
\(217\) 323584.i 0.466485i
\(218\) 0 0
\(219\) 421456. 0.593802
\(220\) 0 0
\(221\) 1.40083e6 1.92932
\(222\) 0 0
\(223\) 1.21855e6i 1.64090i 0.571717 + 0.820451i \(0.306278\pi\)
−0.571717 + 0.820451i \(0.693722\pi\)
\(224\) 0 0
\(225\) 137475. 51700.0i 0.181037 0.0680823i
\(226\) 0 0
\(227\) 564338.i 0.726900i −0.931614 0.363450i \(-0.881599\pi\)
0.931614 0.363450i \(-0.118401\pi\)
\(228\) 0 0
\(229\) −560330. −0.706082 −0.353041 0.935608i \(-0.614852\pi\)
−0.353041 + 0.935608i \(0.614852\pi\)
\(230\) 0 0
\(231\) 327376. 0.403661
\(232\) 0 0
\(233\) 293576.i 0.354267i 0.984187 + 0.177134i \(0.0566824\pi\)
−0.984187 + 0.177134i \(0.943318\pi\)
\(234\) 0 0
\(235\) 106820. + 587510.i 0.126178 + 0.693978i
\(236\) 0 0
\(237\) 493920.i 0.571197i
\(238\) 0 0
\(239\) 584240. 0.661602 0.330801 0.943701i \(-0.392681\pi\)
0.330801 + 0.943701i \(0.392681\pi\)
\(240\) 0 0
\(241\) −563798. −0.625289 −0.312645 0.949870i \(-0.601215\pi\)
−0.312645 + 0.949870i \(0.601215\pi\)
\(242\) 0 0
\(243\) 350714.i 0.381011i
\(244\) 0 0
\(245\) −448635. + 81570.0i −0.477505 + 0.0868191i
\(246\) 0 0
\(247\) 1.51848e6i 1.58368i
\(248\) 0 0
\(249\) 389564. 0.398181
\(250\) 0 0
\(251\) 1.01975e6 1.02167 0.510833 0.859680i \(-0.329337\pi\)
0.510833 + 0.859680i \(0.329337\pi\)
\(252\) 0 0
\(253\) 184408.i 0.181125i
\(254\) 0 0
\(255\) −1.57696e6 + 286720.i −1.51869 + 0.276126i
\(256\) 0 0
\(257\) 657408.i 0.620872i 0.950594 + 0.310436i \(0.100475\pi\)
−0.950594 + 0.310436i \(0.899525\pi\)
\(258\) 0 0
\(259\) −690776. −0.639864
\(260\) 0 0
\(261\) 12690.0 0.0115308
\(262\) 0 0
\(263\) 562366.i 0.501337i −0.968073 0.250668i \(-0.919350\pi\)
0.968073 0.250668i \(-0.0806504\pi\)
\(264\) 0 0
\(265\) −29640.0 163020.i −0.0259277 0.142602i
\(266\) 0 0
\(267\) 1.19294e6i 1.02410i
\(268\) 0 0
\(269\) −366570. −0.308870 −0.154435 0.988003i \(-0.549356\pi\)
−0.154435 + 0.988003i \(0.549356\pi\)
\(270\) 0 0
\(271\) −1.16075e6 −0.960099 −0.480050 0.877241i \(-0.659381\pi\)
−0.480050 + 0.877241i \(0.659381\pi\)
\(272\) 0 0
\(273\) 1.51301e6i 1.22867i
\(274\) 0 0
\(275\) 432900. 162800.i 0.345188 0.129814i
\(276\) 0 0
\(277\) 2.51501e6i 1.96943i −0.174172 0.984715i \(-0.555725\pi\)
0.174172 0.984715i \(-0.444275\pi\)
\(278\) 0 0
\(279\) 96256.0 0.0740316
\(280\) 0 0
\(281\) 2.08600e6 1.57597 0.787987 0.615692i \(-0.211124\pi\)
0.787987 + 0.615692i \(0.211124\pi\)
\(282\) 0 0
\(283\) 2.23803e6i 1.66111i −0.556935 0.830556i \(-0.688023\pi\)
0.556935 0.830556i \(-0.311977\pi\)
\(284\) 0 0
\(285\) 310800. + 1.70940e6i 0.226657 + 1.24661i
\(286\) 0 0
\(287\) 378884.i 0.271520i
\(288\) 0 0
\(289\) −2.77445e6 −1.95403
\(290\) 0 0
\(291\) 1.36125e6 0.942334
\(292\) 0 0
\(293\) 975756.i 0.664006i 0.943278 + 0.332003i \(0.107724\pi\)
−0.943278 + 0.332003i \(0.892276\pi\)
\(294\) 0 0
\(295\) −2.18570e6 + 397400.i −1.46230 + 0.265872i
\(296\) 0 0
\(297\) 600880.i 0.395273i
\(298\) 0 0
\(299\) −852264. −0.551310
\(300\) 0 0
\(301\) 362452. 0.230587
\(302\) 0 0
\(303\) 60172.0i 0.0376520i
\(304\) 0 0
\(305\) −2.32639e6 + 422980.i −1.43197 + 0.260358i
\(306\) 0 0
\(307\) 87858.0i 0.0532029i −0.999646 0.0266015i \(-0.991531\pi\)
0.999646 0.0266015i \(-0.00846850\pi\)
\(308\) 0 0
\(309\) −1.73760e6 −1.03527
\(310\) 0 0
\(311\) −599352. −0.351383 −0.175692 0.984445i \(-0.556216\pi\)
−0.175692 + 0.984445i \(0.556216\pi\)
\(312\) 0 0
\(313\) 2.09342e6i 1.20780i 0.797060 + 0.603900i \(0.206387\pi\)
−0.797060 + 0.603900i \(0.793613\pi\)
\(314\) 0 0
\(315\) −74260.0 408430.i −0.0421676 0.231922i
\(316\) 0 0
\(317\) 2.41625e6i 1.35050i −0.737590 0.675249i \(-0.764036\pi\)
0.737590 0.675249i \(-0.235964\pi\)
\(318\) 0 0
\(319\) 39960.0 0.0219861
\(320\) 0 0
\(321\) −592788. −0.321097
\(322\) 0 0
\(323\) 4.54656e6i 2.42480i
\(324\) 0 0
\(325\) −752400. 2.00070e6i −0.395130 1.05069i
\(326\) 0 0
\(327\) 503860.i 0.260580i
\(328\) 0 0
\(329\) 1.68776e6 0.859647
\(330\) 0 0
\(331\) 1.64095e6 0.823237 0.411618 0.911356i \(-0.364964\pi\)
0.411618 + 0.911356i \(0.364964\pi\)
\(332\) 0 0
\(333\) 205484.i 0.101547i
\(334\) 0 0
\(335\) −320980. 1.76539e6i −0.156267 0.859466i
\(336\) 0 0
\(337\) 2.18773e6i 1.04935i 0.851304 + 0.524673i \(0.175812\pi\)
−0.851304 + 0.524673i \(0.824188\pi\)
\(338\) 0 0
\(339\) −3.20342e6 −1.51396
\(340\) 0 0
\(341\) 303104. 0.141158
\(342\) 0 0
\(343\) 1.36670e6i 0.627246i
\(344\) 0 0
\(345\) 959420. 174440.i 0.433971 0.0789039i
\(346\) 0 0
\(347\) 2.74502e6i 1.22383i −0.790923 0.611916i \(-0.790399\pi\)
0.790923 0.611916i \(-0.209601\pi\)
\(348\) 0 0
\(349\) 2.65115e6 1.16512 0.582560 0.812788i \(-0.302051\pi\)
0.582560 + 0.812788i \(0.302051\pi\)
\(350\) 0 0
\(351\) 2.77704e6 1.20313
\(352\) 0 0
\(353\) 3.05766e6i 1.30603i −0.757345 0.653015i \(-0.773504\pi\)
0.757345 0.653015i \(-0.226496\pi\)
\(354\) 0 0
\(355\) 233640. 42480.0i 0.0983957 0.0178901i
\(356\) 0 0
\(357\) 4.53018e6i 1.88124i
\(358\) 0 0
\(359\) 3.79356e6 1.55350 0.776749 0.629810i \(-0.216867\pi\)
0.776749 + 0.629810i \(0.216867\pi\)
\(360\) 0 0
\(361\) 2.45230e6 0.990389
\(362\) 0 0
\(363\) 1.94806e6i 0.775953i
\(364\) 0 0
\(365\) −301040. 1.65572e6i −0.118275 0.650511i
\(366\) 0 0
\(367\) 3.11060e6i 1.20553i 0.797917 + 0.602767i \(0.205935\pi\)
−0.797917 + 0.602767i \(0.794065\pi\)
\(368\) 0 0
\(369\) −112706. −0.0430905
\(370\) 0 0
\(371\) −468312. −0.176645
\(372\) 0 0
\(373\) 1.41520e6i 0.526677i 0.964703 + 0.263339i \(0.0848236\pi\)
−0.964703 + 0.263339i \(0.915176\pi\)
\(374\) 0 0
\(375\) 1.25650e6 + 2.09825e6i 0.461407 + 0.770511i
\(376\) 0 0
\(377\) 184680.i 0.0669216i
\(378\) 0 0
\(379\) −3.90262e6 −1.39559 −0.697796 0.716297i \(-0.745836\pi\)
−0.697796 + 0.716297i \(0.745836\pi\)
\(380\) 0 0
\(381\) 2.45333e6 0.865852
\(382\) 0 0
\(383\) 695674.i 0.242331i 0.992632 + 0.121165i \(0.0386632\pi\)
−0.992632 + 0.121165i \(0.961337\pi\)
\(384\) 0 0
\(385\) −233840. 1.28612e6i −0.0804020 0.442211i
\(386\) 0 0
\(387\) 107818.i 0.0365943i
\(388\) 0 0
\(389\) −498290. −0.166958 −0.0834792 0.996510i \(-0.526603\pi\)
−0.0834792 + 0.996510i \(0.526603\pi\)
\(390\) 0 0
\(391\) 2.55181e6 0.844124
\(392\) 0 0
\(393\) 4.19513e6i 1.37014i
\(394\) 0 0
\(395\) 1.94040e6 352800.i 0.625747 0.113772i
\(396\) 0 0
\(397\) 1.09567e6i 0.348901i 0.984666 + 0.174451i \(0.0558150\pi\)
−0.984666 + 0.174451i \(0.944185\pi\)
\(398\) 0 0
\(399\) 4.91064e6 1.54421
\(400\) 0 0
\(401\) −2.49160e6 −0.773779 −0.386890 0.922126i \(-0.626451\pi\)
−0.386890 + 0.922126i \(0.626451\pi\)
\(402\) 0 0
\(403\) 1.40083e6i 0.429659i
\(404\) 0 0
\(405\) −2.49805e6 + 454190.i −0.756768 + 0.137594i
\(406\) 0 0
\(407\) 647056.i 0.193623i
\(408\) 0 0
\(409\) 3.63349e6 1.07403 0.537014 0.843573i \(-0.319552\pi\)
0.537014 + 0.843573i \(0.319552\pi\)
\(410\) 0 0
\(411\) −1.51099e6 −0.441222
\(412\) 0 0
\(413\) 6.27892e6i 1.81138i
\(414\) 0 0
\(415\) −278260. 1.53043e6i −0.0793105 0.436208i
\(416\) 0 0
\(417\) 2.75044e6i 0.774572i
\(418\) 0 0
\(419\) −3.64378e6 −1.01395 −0.506976 0.861960i \(-0.669237\pi\)
−0.506976 + 0.861960i \(0.669237\pi\)
\(420\) 0 0
\(421\) −1.82530e6 −0.501913 −0.250957 0.967998i \(-0.580745\pi\)
−0.250957 + 0.967998i \(0.580745\pi\)
\(422\) 0 0
\(423\) 502054.i 0.136427i
\(424\) 0 0
\(425\) 2.25280e6 + 5.99040e6i 0.604993 + 1.60873i
\(426\) 0 0
\(427\) 6.68308e6i 1.77381i
\(428\) 0 0
\(429\) 1.41725e6 0.371794
\(430\) 0 0
\(431\) −2.85435e6 −0.740141 −0.370070 0.929004i \(-0.620666\pi\)
−0.370070 + 0.929004i \(0.620666\pi\)
\(432\) 0 0
\(433\) 587776.i 0.150658i 0.997159 + 0.0753290i \(0.0240007\pi\)
−0.997159 + 0.0753290i \(0.975999\pi\)
\(434\) 0 0
\(435\) 37800.0 + 207900.i 0.00957786 + 0.0526783i
\(436\) 0 0
\(437\) 2.76612e6i 0.692895i
\(438\) 0 0
\(439\) 6.11604e6 1.51464 0.757319 0.653045i \(-0.226509\pi\)
0.757319 + 0.653045i \(0.226509\pi\)
\(440\) 0 0
\(441\) −383379. −0.0938711
\(442\) 0 0
\(443\) 2.35771e6i 0.570795i −0.958409 0.285398i \(-0.907874\pi\)
0.958409 0.285398i \(-0.0921257\pi\)
\(444\) 0 0
\(445\) 4.68655e6 852100.i 1.12190 0.203981i
\(446\) 0 0
\(447\) 1.94390e6i 0.460156i
\(448\) 0 0
\(449\) −5.49735e6 −1.28688 −0.643439 0.765497i \(-0.722493\pi\)
−0.643439 + 0.765497i \(0.722493\pi\)
\(450\) 0 0
\(451\) −354904. −0.0821617
\(452\) 0 0
\(453\) 5.82613e6i 1.33393i
\(454\) 0 0
\(455\) −5.94396e6 + 1.08072e6i −1.34601 + 0.244729i
\(456\) 0 0
\(457\) 1.16039e6i 0.259905i −0.991520 0.129952i \(-0.958518\pi\)
0.991520 0.129952i \(-0.0414824\pi\)
\(458\) 0 0
\(459\) −8.31488e6 −1.84215
\(460\) 0 0
\(461\) −2.30330e6 −0.504775 −0.252387 0.967626i \(-0.581216\pi\)
−0.252387 + 0.967626i \(0.581216\pi\)
\(462\) 0 0
\(463\) 2.71343e6i 0.588257i 0.955766 + 0.294128i \(0.0950293\pi\)
−0.955766 + 0.294128i \(0.904971\pi\)
\(464\) 0 0
\(465\) 286720. + 1.57696e6i 0.0614930 + 0.338211i
\(466\) 0 0
\(467\) 4.05050e6i 0.859441i −0.902962 0.429721i \(-0.858612\pi\)
0.902962 0.429721i \(-0.141388\pi\)
\(468\) 0 0
\(469\) −5.07148e6 −1.06464
\(470\) 0 0
\(471\) −6.06351e6 −1.25942
\(472\) 0 0
\(473\) 339512.i 0.0697754i
\(474\) 0 0
\(475\) 6.49350e6 2.44200e6i 1.32052 0.496606i
\(476\) 0 0
\(477\) 139308.i 0.0280337i
\(478\) 0 0
\(479\) 5.60528e6 1.11624 0.558121 0.829759i \(-0.311522\pi\)
0.558121 + 0.829759i \(0.311522\pi\)
\(480\) 0 0
\(481\) −2.99045e6 −0.589350
\(482\) 0 0
\(483\) 2.75615e6i 0.537570i
\(484\) 0 0
\(485\) −972320. 5.34776e6i −0.187696 1.03233i
\(486\) 0 0
\(487\) 7.13168e6i 1.36260i −0.732003 0.681301i \(-0.761414\pi\)
0.732003 0.681301i \(-0.238586\pi\)
\(488\) 0 0
\(489\) −2.08788e6 −0.394850
\(490\) 0 0
\(491\) −5.88145e6 −1.10098 −0.550492 0.834841i \(-0.685560\pi\)
−0.550492 + 0.834841i \(0.685560\pi\)
\(492\) 0 0
\(493\) 552960.i 0.102465i
\(494\) 0 0
\(495\) 382580. 69560.0i 0.0701793 0.0127599i
\(496\) 0 0
\(497\) 671184.i 0.121885i
\(498\) 0 0
\(499\) 1.75710e6 0.315897 0.157948 0.987447i \(-0.449512\pi\)
0.157948 + 0.987447i \(0.449512\pi\)
\(500\) 0 0
\(501\) −7.83443e6 −1.39448
\(502\) 0 0
\(503\) 4.91411e6i 0.866015i 0.901390 + 0.433007i \(0.142548\pi\)
−0.901390 + 0.433007i \(0.857452\pi\)
\(504\) 0 0
\(505\) −236390. + 42980.0i −0.0412478 + 0.00749960i
\(506\) 0 0
\(507\) 1.35188e6i 0.233571i
\(508\) 0 0
\(509\) 5.75499e6 0.984578 0.492289 0.870432i \(-0.336160\pi\)
0.492289 + 0.870432i \(0.336160\pi\)
\(510\) 0 0
\(511\) −4.75643e6 −0.805803
\(512\) 0 0
\(513\) 9.01320e6i 1.51212i
\(514\) 0 0
\(515\) 1.24114e6 + 6.82627e6i 0.206207 + 1.13414i
\(516\) 0 0
\(517\) 1.58094e6i 0.260128i
\(518\) 0 0
\(519\) 4.81326e6 0.784369
\(520\) 0 0
\(521\) −1.61980e6 −0.261437 −0.130718 0.991420i \(-0.541728\pi\)
−0.130718 + 0.991420i \(0.541728\pi\)
\(522\) 0 0
\(523\) 1.19117e7i 1.90422i 0.305751 + 0.952112i \(0.401093\pi\)
−0.305751 + 0.952112i \(0.598907\pi\)
\(524\) 0 0
\(525\) 6.47010e6 2.43320e6i 1.02450 0.385283i
\(526\) 0 0
\(527\) 4.19430e6i 0.657860i
\(528\) 0 0
\(529\) 4.88383e6 0.758789
\(530\) 0 0
\(531\) −1.86778e6 −0.287468
\(532\) 0 0
\(533\) 1.64023e6i 0.250085i
\(534\) 0 0
\(535\) 423420. + 2.32881e6i 0.0639568 + 0.351763i
\(536\) 0 0
\(537\) 335720.i 0.0502391i
\(538\) 0 0
\(539\) −1.20724e6 −0.178986
\(540\) 0 0
\(541\) 4.07630e6 0.598788 0.299394 0.954130i \(-0.403215\pi\)
0.299394 + 0.954130i \(0.403215\pi\)
\(542\) 0 0
\(543\) 9.12657e6i 1.32834i
\(544\) 0 0
\(545\) 1.97945e6 359900.i 0.285465 0.0519028i
\(546\) 0 0
\(547\) 1.23680e7i 1.76739i −0.468065 0.883694i \(-0.655049\pi\)
0.468065 0.883694i \(-0.344951\pi\)
\(548\) 0 0
\(549\) −1.98801e6 −0.281505
\(550\) 0 0
\(551\) 599400. 0.0841081
\(552\) 0 0
\(553\) 5.57424e6i 0.775127i
\(554\) 0 0
\(555\) 3.36644e6 612080.i 0.463915 0.0843482i
\(556\) 0 0
\(557\) 130308.i 0.0177964i 0.999960 + 0.00889822i \(0.00283243\pi\)
−0.999960 + 0.00889822i \(0.997168\pi\)
\(558\) 0 0
\(559\) 1.56910e6 0.212383
\(560\) 0 0
\(561\) −4.24346e6 −0.569262
\(562\) 0 0
\(563\) 5.91687e6i 0.786721i −0.919384 0.393361i \(-0.871312\pi\)
0.919384 0.393361i \(-0.128688\pi\)
\(564\) 0 0
\(565\) 2.28816e6 + 1.25849e7i 0.301554 + 1.65855i
\(566\) 0 0
\(567\) 7.17620e6i 0.937426i
\(568\) 0 0
\(569\) 9.03013e6 1.16927 0.584633 0.811298i \(-0.301239\pi\)
0.584633 + 0.811298i \(0.301239\pi\)
\(570\) 0 0
\(571\) 1.07093e7 1.37459 0.687294 0.726379i \(-0.258798\pi\)
0.687294 + 0.726379i \(0.258798\pi\)
\(572\) 0 0
\(573\) 2.83853e6i 0.361166i
\(574\) 0 0
\(575\) −1.37060e6 3.64455e6i −0.172879 0.459700i
\(576\) 0 0
\(577\) 1.22051e6i 0.152617i −0.997084 0.0763084i \(-0.975687\pi\)
0.997084 0.0763084i \(-0.0243134\pi\)
\(578\) 0 0
\(579\) −6.33718e6 −0.785597
\(580\) 0 0
\(581\) −4.39651e6 −0.540341
\(582\) 0 0
\(583\) 438672.i 0.0534526i
\(584\) 0 0
\(585\) −321480. 1.76814e6i −0.0388387 0.213613i
\(586\) 0 0
\(587\) 1.47104e7i 1.76210i 0.473026 + 0.881049i \(0.343162\pi\)
−0.473026 + 0.881049i \(0.656838\pi\)
\(588\) 0 0
\(589\) 4.54656e6 0.540001
\(590\) 0 0
\(591\) −4.72455e6 −0.556406
\(592\) 0 0
\(593\) 8.52014e6i 0.994970i −0.867472 0.497485i \(-0.834257\pi\)
0.867472 0.497485i \(-0.165743\pi\)
\(594\) 0 0
\(595\) 1.77971e7 3.23584e6i 2.06090 0.374709i
\(596\) 0 0
\(597\) 7.85400e6i 0.901893i
\(598\) 0 0
\(599\) 2.90100e6 0.330355 0.165177 0.986264i \(-0.447180\pi\)
0.165177 + 0.986264i \(0.447180\pi\)
\(600\) 0 0
\(601\) 5.72760e6 0.646825 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(602\) 0 0
\(603\) 1.50861e6i 0.168959i
\(604\) 0 0
\(605\) −7.65308e6 + 1.39147e6i −0.850057 + 0.154556i
\(606\) 0 0
\(607\) 8.79924e6i 0.969334i 0.874699 + 0.484667i \(0.161059\pi\)
−0.874699 + 0.484667i \(0.838941\pi\)
\(608\) 0 0
\(609\) 597240. 0.0652538
\(610\) 0 0
\(611\) 7.30649e6 0.791782
\(612\) 0 0
\(613\) 1.03408e6i 0.111149i −0.998455 0.0555744i \(-0.982301\pi\)
0.998455 0.0555744i \(-0.0176990\pi\)
\(614\) 0 0
\(615\) −335720. 1.84646e6i −0.0357923 0.196858i
\(616\) 0 0
\(617\) 1.29854e7i 1.37323i 0.727020 + 0.686616i \(0.240905\pi\)
−0.727020 + 0.686616i \(0.759095\pi\)
\(618\) 0 0
\(619\) 7.92002e6 0.830806 0.415403 0.909637i \(-0.363641\pi\)
0.415403 + 0.909637i \(0.363641\pi\)
\(620\) 0 0
\(621\) 5.05876e6 0.526399
\(622\) 0 0
\(623\) 1.34632e7i 1.38972i
\(624\) 0 0
\(625\) 7.34562e6 6.43500e6i 0.752192 0.658944i
\(626\) 0 0
\(627\) 4.59984e6i 0.467276i
\(628\) 0 0
\(629\) 8.95386e6 0.902368
\(630\) 0 0
\(631\) −1.68218e7 −1.68189 −0.840945 0.541120i \(-0.818001\pi\)
−0.840945 + 0.541120i \(0.818001\pi\)
\(632\) 0 0
\(633\) 1.12777e7i 1.11869i
\(634\) 0 0
\(635\) −1.75238e6 9.63809e6i −0.172462 0.948542i
\(636\) 0 0
\(637\) 5.57939e6i 0.544801i
\(638\) 0 0
\(639\) 199656. 0.0193433
\(640\) 0 0
\(641\) −1.55154e7 −1.49148 −0.745741 0.666236i \(-0.767904\pi\)
−0.745741 + 0.666236i \(0.767904\pi\)
\(642\) 0 0
\(643\) 1.05801e7i 1.00916i 0.863364 + 0.504582i \(0.168354\pi\)
−0.863364 + 0.504582i \(0.831646\pi\)
\(644\) 0 0
\(645\) −1.76638e6 + 321160.i −0.167180 + 0.0303964i
\(646\) 0 0
\(647\) 1.37883e7i 1.29494i −0.762090 0.647471i \(-0.775827\pi\)
0.762090 0.647471i \(-0.224173\pi\)
\(648\) 0 0
\(649\) −5.88152e6 −0.548123
\(650\) 0 0
\(651\) 4.53018e6 0.418950
\(652\) 0 0
\(653\) 1.58924e6i 0.145850i 0.997337 + 0.0729248i \(0.0232333\pi\)
−0.997337 + 0.0729248i \(0.976767\pi\)
\(654\) 0 0
\(655\) −1.64809e7 + 2.99652e6i −1.50099 + 0.272907i
\(656\) 0 0
\(657\) 1.41489e6i 0.127882i
\(658\) 0 0
\(659\) −9.12434e6 −0.818442 −0.409221 0.912435i \(-0.634199\pi\)
−0.409221 + 0.912435i \(0.634199\pi\)
\(660\) 0 0
\(661\) 6.50310e6 0.578918 0.289459 0.957190i \(-0.406525\pi\)
0.289459 + 0.957190i \(0.406525\pi\)
\(662\) 0 0
\(663\) 1.96116e7i 1.73273i
\(664\) 0 0
\(665\) −3.50760e6 1.92918e7i −0.307578 1.69168i
\(666\) 0 0
\(667\) 336420.i 0.0292797i
\(668\) 0 0
\(669\) −1.70598e7 −1.47369
\(670\) 0 0
\(671\) −6.26010e6 −0.536754
\(672\) 0 0
\(673\) 2.17810e6i 0.185370i 0.995695 + 0.0926850i \(0.0295449\pi\)
−0.995695 + 0.0926850i \(0.970455\pi\)
\(674\) 0 0
\(675\) 4.46600e6 + 1.18755e7i 0.377276 + 1.00321i
\(676\) 0 0
\(677\) 3.98419e6i 0.334094i 0.985949 + 0.167047i \(0.0534231\pi\)
−0.985949 + 0.167047i \(0.946577\pi\)
\(678\) 0 0
\(679\) −1.53627e7 −1.27877
\(680\) 0 0
\(681\) 7.90073e6 0.652829
\(682\) 0 0
\(683\) 5.91563e6i 0.485231i −0.970122 0.242616i \(-0.921995\pi\)
0.970122 0.242616i \(-0.0780054\pi\)
\(684\) 0 0
\(685\) 1.07928e6 + 5.93604e6i 0.0878836 + 0.483360i
\(686\) 0 0
\(687\) 7.84462e6i 0.634133i
\(688\) 0 0
\(689\) −2.02738e6 −0.162700
\(690\) 0 0
\(691\) 1.55471e7 1.23867 0.619335 0.785127i \(-0.287402\pi\)
0.619335 + 0.785127i \(0.287402\pi\)
\(692\) 0 0
\(693\) 1.09905e6i 0.0869328i
\(694\) 0 0
\(695\) −1.08053e7 + 1.96460e6i −0.848545 + 0.154281i
\(696\) 0 0
\(697\) 4.91110e6i 0.382910i
\(698\) 0 0
\(699\) −4.11006e6 −0.318167
\(700\) 0 0
\(701\) −2.27103e7 −1.74553 −0.872766 0.488139i \(-0.837676\pi\)
−0.872766 + 0.488139i \(0.837676\pi\)
\(702\) 0 0
\(703\) 9.70584e6i 0.740704i
\(704\) 0 0
\(705\) −8.22514e6 + 1.49548e6i −0.623262 + 0.113320i
\(706\) 0 0
\(707\) 679084.i 0.0510946i
\(708\) 0 0
\(709\) −6.29841e6 −0.470560 −0.235280 0.971928i \(-0.575601\pi\)
−0.235280 + 0.971928i \(0.575601\pi\)
\(710\) 0 0
\(711\) 1.65816e6 0.123013
\(712\) 0 0
\(713\) 2.55181e6i 0.187985i
\(714\) 0 0
\(715\) −1.01232e6 5.56776e6i −0.0740547 0.407301i
\(716\) 0 0
\(717\) 8.17936e6i 0.594185i
\(718\) 0 0
\(719\) 2.11911e7 1.52873 0.764367 0.644782i \(-0.223052\pi\)
0.764367 + 0.644782i \(0.223052\pi\)
\(720\) 0 0
\(721\) 1.96100e7 1.40488
\(722\) 0 0
\(723\) 7.89317e6i 0.561572i
\(724\) 0 0
\(725\) 789750. 297000.i 0.0558013 0.0209851i
\(726\) 0 0
\(727\) 1.35610e7i 0.951605i −0.879552 0.475803i \(-0.842158\pi\)
0.879552 0.475803i \(-0.157842\pi\)
\(728\) 0 0
\(729\) −1.59468e7 −1.11136
\(730\) 0 0
\(731\) −4.69811e6 −0.325185
\(732\) 0 0
\(733\) 2.69413e7i 1.85208i −0.377429 0.926038i \(-0.623192\pi\)
0.377429 0.926038i \(-0.376808\pi\)
\(734\) 0 0
\(735\) −1.14198e6 6.28089e6i −0.0779723 0.428847i
\(736\) 0 0
\(737\) 4.75050e6i 0.322160i
\(738\) 0 0
\(739\) 2.77414e6 0.186860 0.0934302 0.995626i \(-0.470217\pi\)
0.0934302 + 0.995626i \(0.470217\pi\)
\(740\) 0 0
\(741\) 2.12587e7 1.42230
\(742\) 0 0
\(743\) 1.85538e7i 1.23299i 0.787358 + 0.616497i \(0.211449\pi\)
−0.787358 + 0.616497i \(0.788551\pi\)
\(744\) 0 0
\(745\) −7.63675e6 + 1.38850e6i −0.504101 + 0.0916548i
\(746\) 0 0
\(747\) 1.30782e6i 0.0857526i
\(748\) 0 0
\(749\) 6.69004e6 0.435736
\(750\) 0 0
\(751\) 2.19285e6 0.141876 0.0709380 0.997481i \(-0.477401\pi\)
0.0709380 + 0.997481i \(0.477401\pi\)
\(752\) 0 0
\(753\) 1.42765e7i 0.917558i
\(754\) 0 0
\(755\) −2.28884e7 + 4.16152e6i −1.46133 + 0.265696i
\(756\) 0 0
\(757\) 9.48749e6i 0.601744i −0.953665 0.300872i \(-0.902722\pi\)
0.953665 0.300872i \(-0.0972777\pi\)
\(758\) 0 0
\(759\) 2.58171e6 0.162668
\(760\) 0 0
\(761\) 9.69580e6 0.606907 0.303453 0.952846i \(-0.401860\pi\)
0.303453 + 0.952846i \(0.401860\pi\)
\(762\) 0 0
\(763\) 5.68642e6i 0.353612i
\(764\) 0 0
\(765\) 962560. + 5.29408e6i 0.0594668 + 0.327067i
\(766\) 0 0
\(767\) 2.71822e7i 1.66838i
\(768\) 0 0
\(769\) −9.32787e6 −0.568809 −0.284405 0.958704i \(-0.591796\pi\)
−0.284405 + 0.958704i \(0.591796\pi\)
\(770\) 0 0
\(771\) −9.20371e6 −0.557606
\(772\) 0 0
\(773\) 9.68080e6i 0.582723i 0.956613 + 0.291362i \(0.0941083\pi\)
−0.956613 + 0.291362i \(0.905892\pi\)
\(774\) 0 0
\(775\) 5.99040e6 2.25280e6i 0.358263 0.134731i
\(776\) 0 0
\(777\) 9.67086e6i 0.574662i
\(778\) 0 0
\(779\) −5.32356e6 −0.314310
\(780\) 0 0
\(781\) 628704. 0.0368824
\(782\) 0 0
\(783\) 1.09620e6i 0.0638977i
\(784\) 0 0
\(785\) 4.33108e6 + 2.38209e7i 0.250855 + 1.37970i
\(786\) 0 0
\(787\) 5.52302e6i 0.317863i 0.987290 + 0.158931i \(0.0508049\pi\)
−0.987290 + 0.158931i \(0.949195\pi\)
\(788\) 0 0
\(789\) 7.87312e6 0.450251
\(790\) 0 0
\(791\) 3.61529e7 2.05448
\(792\) 0 0
\(793\) 2.89318e7i 1.63378i
\(794\) 0 0
\(795\) 2.28228e6 414960.i 0.128071 0.0232857i
\(796\) 0 0
\(797\) 1.71119e7i 0.954230i −0.878841 0.477115i \(-0.841682\pi\)
0.878841 0.477115i \(-0.158318\pi\)
\(798\) 0 0
\(799\) −2.18767e7 −1.21232
\(800\) 0 0
\(801\) 4.00487e6 0.220550
\(802\) 0 0
\(803\) 4.45539e6i 0.243836i
\(804\) 0 0
\(805\) −1.08277e7 + 1.96868e6i −0.588909 + 0.107074i
\(806\) 0 0
\(807\) 5.13198e6i 0.277397i
\(808\) 0 0
\(809\) 1.45309e7