Properties

Label 80.6.c.b.49.1
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: \(\Q(\sqrt{-31}) \)
Defining polynomial: \(x^{2} - x + 8\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 + 2.78388i\) of defining polynomial
Character \(\chi\) \(=\) 80.49
Dual form 80.6.c.b.49.2

$q$-expansion

\(f(q)\) \(=\) \(q-11.1355i q^{3} +(-5.00000 + 55.6776i) q^{5} -122.491i q^{7} +119.000 q^{9} +O(q^{10})\) \(q-11.1355i q^{3} +(-5.00000 + 55.6776i) q^{5} -122.491i q^{7} +119.000 q^{9} +100.000 q^{11} -734.945i q^{13} +(620.000 + 55.6776i) q^{15} -979.927i q^{17} -2244.00 q^{19} -1364.00 q^{21} -3418.61i q^{23} +(-3075.00 - 556.776i) q^{25} -4031.06i q^{27} +7854.00 q^{29} +2144.00 q^{31} -1113.55i q^{33} +(6820.00 + 612.454i) q^{35} -10400.6i q^{37} -8184.00 q^{39} -7414.00 q^{41} +17761.2i q^{43} +(-595.000 + 6625.64i) q^{45} -9431.79i q^{47} +1803.00 q^{49} -10912.0 q^{51} +24253.2i q^{53} +(-500.000 + 5567.76i) q^{55} +24988.1i q^{57} +25972.0 q^{59} -3058.00 q^{61} -14576.4i q^{63} +(40920.0 + 3674.72i) q^{65} +58784.5i q^{67} -38068.0 q^{69} -37608.0 q^{71} -24008.2i q^{73} +(-6200.00 + 34241.8i) q^{75} -12249.1i q^{77} +79728.0 q^{79} -15971.0 q^{81} +16291.3i q^{83} +(54560.0 + 4899.63i) q^{85} -87458.4i q^{87} +826.000 q^{89} -90024.0 q^{91} -23874.6i q^{93} +(11220.0 - 124941. i) q^{95} +37593.5i q^{97} +11900.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 10q^{5} + 238q^{9} + O(q^{10}) \) \( 2q - 10q^{5} + 238q^{9} + 200q^{11} + 1240q^{15} - 4488q^{19} - 2728q^{21} - 6150q^{25} + 15708q^{29} + 4288q^{31} + 13640q^{35} - 16368q^{39} - 14828q^{41} - 1190q^{45} + 3606q^{49} - 21824q^{51} - 1000q^{55} + 51944q^{59} - 6116q^{61} + 81840q^{65} - 76136q^{69} - 75216q^{71} - 12400q^{75} + 159456q^{79} - 31942q^{81} + 109120q^{85} + 1652q^{89} - 180048q^{91} + 22440q^{95} + 23800q^{99} + O(q^{100}) \)

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
\(3\) 11.1355i 0.714345i −0.934039 0.357172i \(-0.883741\pi\)
0.934039 0.357172i \(-0.116259\pi\)
\(4\) 0 0
\(5\) −5.00000 + 55.6776i −0.0894427 + 0.995992i
\(6\) 0 0
\(7\) 122.491i 0.944840i −0.881373 0.472420i \(-0.843380\pi\)
0.881373 0.472420i \(-0.156620\pi\)
\(8\) 0 0
\(9\) 119.000 0.489712
\(10\) 0 0
\(11\) 100.000 0.249183 0.124591 0.992208i \(-0.460238\pi\)
0.124591 + 0.992208i \(0.460238\pi\)
\(12\) 0 0
\(13\) 734.945i 1.20614i −0.797690 0.603068i \(-0.793945\pi\)
0.797690 0.603068i \(-0.206055\pi\)
\(14\) 0 0
\(15\) 620.000 + 55.6776i 0.711481 + 0.0638929i
\(16\) 0 0
\(17\) 979.927i 0.822377i −0.911550 0.411189i \(-0.865114\pi\)
0.911550 0.411189i \(-0.134886\pi\)
\(18\) 0 0
\(19\) −2244.00 −1.42606 −0.713032 0.701132i \(-0.752678\pi\)
−0.713032 + 0.701132i \(0.752678\pi\)
\(20\) 0 0
\(21\) −1364.00 −0.674942
\(22\) 0 0
\(23\) 3418.61i 1.34750i −0.738958 0.673751i \(-0.764682\pi\)
0.738958 0.673751i \(-0.235318\pi\)
\(24\) 0 0
\(25\) −3075.00 556.776i −0.984000 0.178168i
\(26\) 0 0
\(27\) 4031.06i 1.06417i
\(28\) 0 0
\(29\) 7854.00 1.73419 0.867093 0.498146i \(-0.165985\pi\)
0.867093 + 0.498146i \(0.165985\pi\)
\(30\) 0 0
\(31\) 2144.00 0.400701 0.200351 0.979724i \(-0.435792\pi\)
0.200351 + 0.979724i \(0.435792\pi\)
\(32\) 0 0
\(33\) 1113.55i 0.178002i
\(34\) 0 0
\(35\) 6820.00 + 612.454i 0.941053 + 0.0845091i
\(36\) 0 0
\(37\) 10400.6i 1.24897i −0.781035 0.624487i \(-0.785308\pi\)
0.781035 0.624487i \(-0.214692\pi\)
\(38\) 0 0
\(39\) −8184.00 −0.861597
\(40\) 0 0
\(41\) −7414.00 −0.688800 −0.344400 0.938823i \(-0.611918\pi\)
−0.344400 + 0.938823i \(0.611918\pi\)
\(42\) 0 0
\(43\) 17761.2i 1.46487i 0.680835 + 0.732437i \(0.261617\pi\)
−0.680835 + 0.732437i \(0.738383\pi\)
\(44\) 0 0
\(45\) −595.000 + 6625.64i −0.0438012 + 0.487749i
\(46\) 0 0
\(47\) 9431.79i 0.622801i −0.950279 0.311401i \(-0.899202\pi\)
0.950279 0.311401i \(-0.100798\pi\)
\(48\) 0 0
\(49\) 1803.00 0.107277
\(50\) 0 0
\(51\) −10912.0 −0.587461
\(52\) 0 0
\(53\) 24253.2i 1.18598i 0.805208 + 0.592992i \(0.202054\pi\)
−0.805208 + 0.592992i \(0.797946\pi\)
\(54\) 0 0
\(55\) −500.000 + 5567.76i −0.0222876 + 0.248184i
\(56\) 0 0
\(57\) 24988.1i 1.01870i
\(58\) 0 0
\(59\) 25972.0 0.971349 0.485675 0.874140i \(-0.338574\pi\)
0.485675 + 0.874140i \(0.338574\pi\)
\(60\) 0 0
\(61\) −3058.00 −0.105224 −0.0526118 0.998615i \(-0.516755\pi\)
−0.0526118 + 0.998615i \(0.516755\pi\)
\(62\) 0 0
\(63\) 14576.4i 0.462700i
\(64\) 0 0
\(65\) 40920.0 + 3674.72i 1.20130 + 0.107880i
\(66\) 0 0
\(67\) 58784.5i 1.59984i 0.600109 + 0.799918i \(0.295124\pi\)
−0.600109 + 0.799918i \(0.704876\pi\)
\(68\) 0 0
\(69\) −38068.0 −0.962581
\(70\) 0 0
\(71\) −37608.0 −0.885389 −0.442695 0.896672i \(-0.645977\pi\)
−0.442695 + 0.896672i \(0.645977\pi\)
\(72\) 0 0
\(73\) 24008.2i 0.527294i −0.964619 0.263647i \(-0.915075\pi\)
0.964619 0.263647i \(-0.0849253\pi\)
\(74\) 0 0
\(75\) −6200.00 + 34241.8i −0.127274 + 0.702915i
\(76\) 0 0
\(77\) 12249.1i 0.235438i
\(78\) 0 0
\(79\) 79728.0 1.43729 0.718643 0.695379i \(-0.244764\pi\)
0.718643 + 0.695379i \(0.244764\pi\)
\(80\) 0 0
\(81\) −15971.0 −0.270470
\(82\) 0 0
\(83\) 16291.3i 0.259573i 0.991542 + 0.129787i \(0.0414292\pi\)
−0.991542 + 0.129787i \(0.958571\pi\)
\(84\) 0 0
\(85\) 54560.0 + 4899.63i 0.819081 + 0.0735557i
\(86\) 0 0
\(87\) 87458.4i 1.23881i
\(88\) 0 0
\(89\) 826.000 0.0110536 0.00552682 0.999985i \(-0.498241\pi\)
0.00552682 + 0.999985i \(0.498241\pi\)
\(90\) 0 0
\(91\) −90024.0 −1.13961
\(92\) 0 0
\(93\) 23874.6i 0.286239i
\(94\) 0 0
\(95\) 11220.0 124941.i 0.127551 1.42035i
\(96\) 0 0
\(97\) 37593.5i 0.405680i 0.979212 + 0.202840i \(0.0650172\pi\)
−0.979212 + 0.202840i \(0.934983\pi\)
\(98\) 0 0
\(99\) 11900.0 0.122028
\(100\) 0 0
\(101\) −143594. −1.40066 −0.700330 0.713819i \(-0.746964\pi\)
−0.700330 + 0.713819i \(0.746964\pi\)
\(102\) 0 0
\(103\) 111834.i 1.03868i −0.854568 0.519339i \(-0.826178\pi\)
0.854568 0.519339i \(-0.173822\pi\)
\(104\) 0 0
\(105\) 6820.00 75944.3i 0.0603686 0.672236i
\(106\) 0 0
\(107\) 92235.6i 0.778824i 0.921064 + 0.389412i \(0.127322\pi\)
−0.921064 + 0.389412i \(0.872678\pi\)
\(108\) 0 0
\(109\) 106238. 0.856473 0.428236 0.903667i \(-0.359135\pi\)
0.428236 + 0.903667i \(0.359135\pi\)
\(110\) 0 0
\(111\) −115816. −0.892198
\(112\) 0 0
\(113\) 113048.i 0.832849i −0.909170 0.416425i \(-0.863283\pi\)
0.909170 0.416425i \(-0.136717\pi\)
\(114\) 0 0
\(115\) 190340. + 17093.0i 1.34210 + 0.120524i
\(116\) 0 0
\(117\) 87458.4i 0.590659i
\(118\) 0 0
\(119\) −120032. −0.777015
\(120\) 0 0
\(121\) −151051. −0.937908
\(122\) 0 0
\(123\) 82558.8i 0.492040i
\(124\) 0 0
\(125\) 46375.0 168425.i 0.265466 0.964120i
\(126\) 0 0
\(127\) 51568.6i 0.283711i −0.989887 0.141856i \(-0.954693\pi\)
0.989887 0.141856i \(-0.0453069\pi\)
\(128\) 0 0
\(129\) 197780. 1.04642
\(130\) 0 0
\(131\) 89100.0 0.453628 0.226814 0.973938i \(-0.427169\pi\)
0.226814 + 0.973938i \(0.427169\pi\)
\(132\) 0 0
\(133\) 274869.i 1.34740i
\(134\) 0 0
\(135\) 224440. + 20155.3i 1.05990 + 0.0951820i
\(136\) 0 0
\(137\) 38350.8i 0.174571i 0.996183 + 0.0872856i \(0.0278193\pi\)
−0.996183 + 0.0872856i \(0.972181\pi\)
\(138\) 0 0
\(139\) −134684. −0.591261 −0.295630 0.955302i \(-0.595530\pi\)
−0.295630 + 0.955302i \(0.595530\pi\)
\(140\) 0 0
\(141\) −105028. −0.444895
\(142\) 0 0
\(143\) 73494.5i 0.300549i
\(144\) 0 0
\(145\) −39270.0 + 437292.i −0.155110 + 1.72724i
\(146\) 0 0
\(147\) 20077.4i 0.0766325i
\(148\) 0 0
\(149\) 248006. 0.915159 0.457579 0.889169i \(-0.348717\pi\)
0.457579 + 0.889169i \(0.348717\pi\)
\(150\) 0 0
\(151\) −313720. −1.11970 −0.559848 0.828596i \(-0.689140\pi\)
−0.559848 + 0.828596i \(0.689140\pi\)
\(152\) 0 0
\(153\) 116611.i 0.402728i
\(154\) 0 0
\(155\) −10720.0 + 119373.i −0.0358398 + 0.399095i
\(156\) 0 0
\(157\) 245583.i 0.795150i 0.917570 + 0.397575i \(0.130148\pi\)
−0.917570 + 0.397575i \(0.869852\pi\)
\(158\) 0 0
\(159\) 270072. 0.847202
\(160\) 0 0
\(161\) −418748. −1.27317
\(162\) 0 0
\(163\) 397483.i 1.17179i 0.810388 + 0.585894i \(0.199257\pi\)
−0.810388 + 0.585894i \(0.800743\pi\)
\(164\) 0 0
\(165\) 62000.0 + 5567.76i 0.177289 + 0.0159210i
\(166\) 0 0
\(167\) 189983.i 0.527138i 0.964641 + 0.263569i \(0.0848996\pi\)
−0.964641 + 0.263569i \(0.915100\pi\)
\(168\) 0 0
\(169\) −168851. −0.454765
\(170\) 0 0
\(171\) −267036. −0.698360
\(172\) 0 0
\(173\) 81088.9i 0.205990i −0.994682 0.102995i \(-0.967157\pi\)
0.994682 0.102995i \(-0.0328426\pi\)
\(174\) 0 0
\(175\) −68200.0 + 376659.i −0.168341 + 0.929723i
\(176\) 0 0
\(177\) 289212.i 0.693878i
\(178\) 0 0
\(179\) 142108. 0.331502 0.165751 0.986168i \(-0.446995\pi\)
0.165751 + 0.986168i \(0.446995\pi\)
\(180\) 0 0
\(181\) 250790. 0.569002 0.284501 0.958676i \(-0.408172\pi\)
0.284501 + 0.958676i \(0.408172\pi\)
\(182\) 0 0
\(183\) 34052.4i 0.0751659i
\(184\) 0 0
\(185\) 579080. + 52002.9i 1.24397 + 0.111712i
\(186\) 0 0
\(187\) 97992.7i 0.204922i
\(188\) 0 0
\(189\) −493768. −1.00547
\(190\) 0 0
\(191\) 209472. 0.415473 0.207736 0.978185i \(-0.433390\pi\)
0.207736 + 0.978185i \(0.433390\pi\)
\(192\) 0 0
\(193\) 356693.i 0.689289i 0.938733 + 0.344645i \(0.112001\pi\)
−0.938733 + 0.344645i \(0.887999\pi\)
\(194\) 0 0
\(195\) 40920.0 455666.i 0.0770636 0.858144i
\(196\) 0 0
\(197\) 86478.5i 0.158761i −0.996844 0.0793803i \(-0.974706\pi\)
0.996844 0.0793803i \(-0.0252941\pi\)
\(198\) 0 0
\(199\) 749208. 1.34113 0.670563 0.741852i \(-0.266053\pi\)
0.670563 + 0.741852i \(0.266053\pi\)
\(200\) 0 0
\(201\) 654596. 1.14283
\(202\) 0 0
\(203\) 962043.i 1.63853i
\(204\) 0 0
\(205\) 37070.0 412794.i 0.0616081 0.686039i
\(206\) 0 0
\(207\) 406814.i 0.659888i
\(208\) 0 0
\(209\) −224400. −0.355351
\(210\) 0 0
\(211\) −287364. −0.444351 −0.222176 0.975007i \(-0.571316\pi\)
−0.222176 + 0.975007i \(0.571316\pi\)
\(212\) 0 0
\(213\) 418785.i 0.632473i
\(214\) 0 0
\(215\) −988900. 88805.8i −1.45900 0.131022i
\(216\) 0 0
\(217\) 262620.i 0.378599i
\(218\) 0 0
\(219\) −267344. −0.376669
\(220\) 0 0
\(221\) −720192. −0.991899
\(222\) 0 0
\(223\) 1.18866e6i 1.60065i 0.599567 + 0.800325i \(0.295340\pi\)
−0.599567 + 0.800325i \(0.704660\pi\)
\(224\) 0 0
\(225\) −365925. 66256.4i −0.481877 0.0872512i
\(226\) 0 0
\(227\) 978334.i 1.26015i −0.776534 0.630075i \(-0.783024\pi\)
0.776534 0.630075i \(-0.216976\pi\)
\(228\) 0 0
\(229\) −506474. −0.638217 −0.319109 0.947718i \(-0.603383\pi\)
−0.319109 + 0.947718i \(0.603383\pi\)
\(230\) 0 0
\(231\) −136400. −0.168184
\(232\) 0 0
\(233\) 1.55465e6i 1.87605i −0.346571 0.938024i \(-0.612654\pi\)
0.346571 0.938024i \(-0.387346\pi\)
\(234\) 0 0
\(235\) 525140. + 47159.0i 0.620305 + 0.0557051i
\(236\) 0 0
\(237\) 887813.i 1.02672i
\(238\) 0 0
\(239\) −374704. −0.424320 −0.212160 0.977235i \(-0.568050\pi\)
−0.212160 + 0.977235i \(0.568050\pi\)
\(240\) 0 0
\(241\) 843634. 0.935646 0.467823 0.883822i \(-0.345039\pi\)
0.467823 + 0.883822i \(0.345039\pi\)
\(242\) 0 0
\(243\) 801702.i 0.870959i
\(244\) 0 0
\(245\) −9015.00 + 100387.i −0.00959512 + 0.106847i
\(246\) 0 0
\(247\) 1.64922e6i 1.72003i
\(248\) 0 0
\(249\) 181412. 0.185425
\(250\) 0 0
\(251\) 1.72050e6 1.72373 0.861867 0.507134i \(-0.169295\pi\)
0.861867 + 0.507134i \(0.169295\pi\)
\(252\) 0 0
\(253\) 341861.i 0.335775i
\(254\) 0 0
\(255\) 54560.0 607554.i 0.0525441 0.585106i
\(256\) 0 0
\(257\) 1.55220e6i 1.46594i 0.680262 + 0.732969i \(0.261866\pi\)
−0.680262 + 0.732969i \(0.738134\pi\)
\(258\) 0 0
\(259\) −1.27398e6 −1.18008
\(260\) 0 0
\(261\) 934626. 0.849252
\(262\) 0 0
\(263\) 407772.i 0.363520i −0.983343 0.181760i \(-0.941821\pi\)
0.983343 0.181760i \(-0.0581793\pi\)
\(264\) 0 0
\(265\) −1.35036e6 121266.i −1.18123 0.106078i
\(266\) 0 0
\(267\) 9197.95i 0.00789610i
\(268\) 0 0
\(269\) 1.82710e6 1.53951 0.769754 0.638340i \(-0.220379\pi\)
0.769754 + 0.638340i \(0.220379\pi\)
\(270\) 0 0
\(271\) 616880. 0.510243 0.255122 0.966909i \(-0.417884\pi\)
0.255122 + 0.966909i \(0.417884\pi\)
\(272\) 0 0
\(273\) 1.00246e6i 0.814071i
\(274\) 0 0
\(275\) −307500. 55677.6i −0.245196 0.0443965i
\(276\) 0 0
\(277\) 1.83712e6i 1.43859i 0.694704 + 0.719296i \(0.255535\pi\)
−0.694704 + 0.719296i \(0.744465\pi\)
\(278\) 0 0
\(279\) 255136. 0.196228
\(280\) 0 0
\(281\) −1.22093e6 −0.922415 −0.461208 0.887292i \(-0.652584\pi\)
−0.461208 + 0.887292i \(0.652584\pi\)
\(282\) 0 0
\(283\) 688766.i 0.511217i −0.966780 0.255609i \(-0.917724\pi\)
0.966780 0.255609i \(-0.0822758\pi\)
\(284\) 0 0
\(285\) −1.39128e6 124941.i −1.01462 0.0911154i
\(286\) 0 0
\(287\) 908147.i 0.650806i
\(288\) 0 0
\(289\) 459601. 0.323695
\(290\) 0 0
\(291\) 418624. 0.289796
\(292\) 0 0
\(293\) 856211.i 0.582655i 0.956623 + 0.291328i \(0.0940970\pi\)
−0.956623 + 0.291328i \(0.905903\pi\)
\(294\) 0 0
\(295\) −129860. + 1.44606e6i −0.0868801 + 0.967456i
\(296\) 0 0
\(297\) 403106.i 0.265172i
\(298\) 0 0
\(299\) −2.51249e6 −1.62527
\(300\) 0 0
\(301\) 2.17558e6 1.38407
\(302\) 0 0
\(303\) 1.59900e6i 1.00055i
\(304\) 0 0
\(305\) 15290.0 170262.i 0.00941148 0.104802i
\(306\) 0 0
\(307\) 1.09617e6i 0.663792i 0.943316 + 0.331896i \(0.107688\pi\)
−0.943316 + 0.331896i \(0.892312\pi\)
\(308\) 0 0
\(309\) −1.24533e6 −0.741974
\(310\) 0 0
\(311\) 2.12465e6 1.24562 0.622811 0.782373i \(-0.285991\pi\)
0.622811 + 0.782373i \(0.285991\pi\)
\(312\) 0 0
\(313\) 294824.i 0.170099i 0.996377 + 0.0850496i \(0.0271049\pi\)
−0.996377 + 0.0850496i \(0.972895\pi\)
\(314\) 0 0
\(315\) 811580. + 72882.0i 0.460845 + 0.0413851i
\(316\) 0 0
\(317\) 2.53153e6i 1.41493i −0.706749 0.707465i \(-0.749839\pi\)
0.706749 0.707465i \(-0.250161\pi\)
\(318\) 0 0
\(319\) 785400. 0.432130
\(320\) 0 0
\(321\) 1.02709e6 0.556348
\(322\) 0 0
\(323\) 2.19896e6i 1.17276i
\(324\) 0 0
\(325\) −409200. + 2.25996e6i −0.214895 + 1.18684i
\(326\) 0 0
\(327\) 1.18302e6i 0.611817i
\(328\) 0 0
\(329\) −1.15531e6 −0.588448
\(330\) 0 0
\(331\) 1.17021e6 0.587076 0.293538 0.955947i \(-0.405167\pi\)
0.293538 + 0.955947i \(0.405167\pi\)
\(332\) 0 0
\(333\) 1.23767e6i 0.611637i
\(334\) 0 0
\(335\) −3.27298e6 293922.i −1.59342 0.143094i
\(336\) 0 0
\(337\) 1.86872e6i 0.896333i 0.893950 + 0.448167i \(0.147923\pi\)
−0.893950 + 0.448167i \(0.852077\pi\)
\(338\) 0 0
\(339\) −1.25885e6 −0.594941
\(340\) 0 0
\(341\) 214400. 0.0998479
\(342\) 0 0
\(343\) 2.27955e6i 1.04620i
\(344\) 0 0
\(345\) 190340. 2.11954e6i 0.0860959 0.958723i
\(346\) 0 0
\(347\) 1.63342e6i 0.728237i −0.931353 0.364119i \(-0.881370\pi\)
0.931353 0.364119i \(-0.118630\pi\)
\(348\) 0 0
\(349\) −2.00629e6 −0.881719 −0.440859 0.897576i \(-0.645326\pi\)
−0.440859 + 0.897576i \(0.645326\pi\)
\(350\) 0 0
\(351\) −2.96261e6 −1.28353
\(352\) 0 0
\(353\) 1.80859e6i 0.772508i 0.922392 + 0.386254i \(0.126231\pi\)
−0.922392 + 0.386254i \(0.873769\pi\)
\(354\) 0 0
\(355\) 188040. 2.09392e6i 0.0791916 0.881841i
\(356\) 0 0
\(357\) 1.33662e6i 0.555057i
\(358\) 0 0
\(359\) 4.50674e6 1.84555 0.922777 0.385334i \(-0.125914\pi\)
0.922777 + 0.385334i \(0.125914\pi\)
\(360\) 0 0
\(361\) 2.55944e6 1.03366
\(362\) 0 0
\(363\) 1.68203e6i 0.669989i
\(364\) 0 0
\(365\) 1.33672e6 + 120041.i 0.525180 + 0.0471626i
\(366\) 0 0
\(367\) 3.02796e6i 1.17351i −0.809766 0.586753i \(-0.800406\pi\)
0.809766 0.586753i \(-0.199594\pi\)
\(368\) 0 0
\(369\) −882266. −0.337313
\(370\) 0 0
\(371\) 2.97079e6 1.12057
\(372\) 0 0
\(373\) 1.16342e6i 0.432976i −0.976285 0.216488i \(-0.930540\pi\)
0.976285 0.216488i \(-0.0694602\pi\)
\(374\) 0 0
\(375\) −1.87550e6 516410.i −0.688714 0.189634i
\(376\) 0 0
\(377\) 5.77226e6i 2.09167i
\(378\) 0 0
\(379\) 832052. 0.297545 0.148772 0.988871i \(-0.452468\pi\)
0.148772 + 0.988871i \(0.452468\pi\)
\(380\) 0 0
\(381\) −574244. −0.202667
\(382\) 0 0
\(383\) 2.86948e6i 0.999554i −0.866154 0.499777i \(-0.833415\pi\)
0.866154 0.499777i \(-0.166585\pi\)
\(384\) 0 0
\(385\) 682000. + 61245.4i 0.234494 + 0.0210582i
\(386\) 0 0
\(387\) 2.11358e6i 0.717366i
\(388\) 0 0
\(389\) 311926. 0.104515 0.0522574 0.998634i \(-0.483358\pi\)
0.0522574 + 0.998634i \(0.483358\pi\)
\(390\) 0 0
\(391\) −3.34998e6 −1.10816
\(392\) 0 0
\(393\) 992176.i 0.324046i
\(394\) 0 0
\(395\) −398640. + 4.43907e6i −0.128555 + 1.43153i
\(396\) 0 0
\(397\) 2.95619e6i 0.941362i −0.882304 0.470681i \(-0.844008\pi\)
0.882304 0.470681i \(-0.155992\pi\)
\(398\) 0 0
\(399\) 3.06082e6 0.962509
\(400\) 0 0
\(401\) 2770.00 0.000860238 0.000430119 1.00000i \(-0.499863\pi\)
0.000430119 1.00000i \(0.499863\pi\)
\(402\) 0 0
\(403\) 1.57572e6i 0.483300i
\(404\) 0 0
\(405\) 79855.0 889228.i 0.0241916 0.269386i
\(406\) 0 0
\(407\) 1.04006e6i 0.311223i
\(408\) 0 0
\(409\) −1.97985e6 −0.585225 −0.292613 0.956231i \(-0.594525\pi\)
−0.292613 + 0.956231i \(0.594525\pi\)
\(410\) 0 0
\(411\) 427056. 0.124704
\(412\) 0 0
\(413\) 3.18133e6i 0.917770i
\(414\) 0 0
\(415\) −907060. 81456.4i −0.258533 0.0232169i
\(416\) 0 0
\(417\) 1.49978e6i 0.422364i
\(418\) 0 0
\(419\) −5.10120e6 −1.41951 −0.709754 0.704450i \(-0.751194\pi\)
−0.709754 + 0.704450i \(0.751194\pi\)
\(420\) 0 0
\(421\) −2.43223e6 −0.668806 −0.334403 0.942430i \(-0.608535\pi\)
−0.334403 + 0.942430i \(0.608535\pi\)
\(422\) 0 0
\(423\) 1.12238e6i 0.304993i
\(424\) 0 0
\(425\) −545600. + 3.01327e6i −0.146522 + 0.809219i
\(426\) 0 0
\(427\) 374577.i 0.0994194i
\(428\) 0 0
\(429\) −818400. −0.214695
\(430\) 0 0
\(431\) −918896. −0.238272 −0.119136 0.992878i \(-0.538012\pi\)
−0.119136 + 0.992878i \(0.538012\pi\)
\(432\) 0 0
\(433\) 2.05455e6i 0.526619i 0.964711 + 0.263310i \(0.0848141\pi\)
−0.964711 + 0.263310i \(0.915186\pi\)
\(434\) 0 0
\(435\) 4.86948e6 + 437292.i 1.23384 + 0.110802i
\(436\) 0 0
\(437\) 7.67135e6i 1.92162i
\(438\) 0 0
\(439\) −676632. −0.167568 −0.0837840 0.996484i \(-0.526701\pi\)
−0.0837840 + 0.996484i \(0.526701\pi\)
\(440\) 0 0
\(441\) 214557. 0.0525347
\(442\) 0 0
\(443\) 2.53092e6i 0.612729i 0.951914 + 0.306365i \(0.0991126\pi\)
−0.951914 + 0.306365i \(0.900887\pi\)
\(444\) 0 0
\(445\) −4130.00 + 45989.7i −0.000988667 + 0.0110093i
\(446\) 0 0
\(447\) 2.76168e6i 0.653739i
\(448\) 0 0
\(449\) 5.17619e6 1.21170 0.605849 0.795579i \(-0.292833\pi\)
0.605849 + 0.795579i \(0.292833\pi\)
\(450\) 0 0
\(451\) −741400. −0.171637
\(452\) 0 0
\(453\) 3.49344e6i 0.799848i
\(454\) 0 0
\(455\) 450120. 5.01232e6i 0.101929 1.13504i
\(456\) 0 0
\(457\) 3.11274e6i 0.697191i −0.937273 0.348596i \(-0.886659\pi\)
0.937273 0.348596i \(-0.113341\pi\)
\(458\) 0 0
\(459\) −3.95014e6 −0.875147
\(460\) 0 0
\(461\) −2.64957e6 −0.580662 −0.290331 0.956926i \(-0.593765\pi\)
−0.290331 + 0.956926i \(0.593765\pi\)
\(462\) 0 0
\(463\) 2.59165e6i 0.561854i 0.959729 + 0.280927i \(0.0906420\pi\)
−0.959729 + 0.280927i \(0.909358\pi\)
\(464\) 0 0
\(465\) 1.32928e6 + 119373.i 0.285091 + 0.0256020i
\(466\) 0 0
\(467\) 6.62135e6i 1.40493i 0.711719 + 0.702465i \(0.247917\pi\)
−0.711719 + 0.702465i \(0.752083\pi\)
\(468\) 0 0
\(469\) 7.20056e6 1.51159
\(470\) 0 0
\(471\) 2.73470e6 0.568011
\(472\) 0 0
\(473\) 1.77612e6i 0.365022i
\(474\) 0 0
\(475\) 6.90030e6 + 1.24941e6i 1.40325 + 0.254080i
\(476\) 0 0
\(477\) 2.88613e6i 0.580791i
\(478\) 0 0
\(479\) 6.89322e6 1.37272 0.686362 0.727260i \(-0.259207\pi\)
0.686362 + 0.727260i \(0.259207\pi\)
\(480\) 0 0
\(481\) −7.64386e6 −1.50643
\(482\) 0 0
\(483\) 4.66298e6i 0.909485i
\(484\) 0 0
\(485\) −2.09312e6 187968.i −0.404054 0.0362852i
\(486\) 0 0
\(487\) 5.65370e6i 1.08021i 0.841596 + 0.540107i \(0.181616\pi\)
−0.841596 + 0.540107i \(0.818384\pi\)
\(488\) 0 0
\(489\) 4.42618e6 0.837061
\(490\) 0 0
\(491\) −5.88390e6 −1.10144 −0.550721 0.834689i \(-0.685647\pi\)
−0.550721 + 0.834689i \(0.685647\pi\)
\(492\) 0 0
\(493\) 7.69634e6i 1.42616i
\(494\) 0 0
\(495\) −59500.0 + 662564.i −0.0109145 + 0.121539i
\(496\) 0 0
\(497\) 4.60663e6i 0.836552i
\(498\) 0 0
\(499\) −6.72080e6 −1.20829 −0.604143 0.796876i \(-0.706485\pi\)
−0.604143 + 0.796876i \(0.706485\pi\)
\(500\) 0 0
\(501\) 2.11556e6 0.376558
\(502\) 0 0
\(503\) 469262.i 0.0826981i 0.999145 + 0.0413491i \(0.0131656\pi\)
−0.999145 + 0.0413491i \(0.986834\pi\)
\(504\) 0 0
\(505\) 717970. 7.99498e6i 0.125279 1.39505i
\(506\) 0 0
\(507\) 1.88025e6i 0.324859i
\(508\) 0 0
\(509\) 294414. 0.0503691 0.0251845 0.999683i \(-0.491983\pi\)
0.0251845 + 0.999683i \(0.491983\pi\)
\(510\) 0 0
\(511\) −2.94078e6 −0.498208
\(512\) 0 0
\(513\) 9.04570e6i 1.51757i
\(514\) 0 0
\(515\) 6.22666e6 + 559171.i 1.03452 + 0.0929023i
\(516\) 0 0
\(517\) 943179.i 0.155191i
\(518\) 0 0
\(519\) −902968. −0.147148
\(520\) 0 0
\(521\) −7.10025e6 −1.14599 −0.572993 0.819560i \(-0.694218\pi\)
−0.572993 + 0.819560i \(0.694218\pi\)
\(522\) 0 0
\(523\) 5.96567e6i 0.953685i −0.878989 0.476843i \(-0.841781\pi\)
0.878989 0.476843i \(-0.158219\pi\)
\(524\) 0 0
\(525\) 4.19430e6 + 759443.i 0.664142 + 0.120253i
\(526\) 0 0
\(527\) 2.10096e6i 0.329528i
\(528\) 0 0
\(529\) −5.25053e6 −0.815763
\(530\) 0 0
\(531\) 3.09067e6 0.475681
\(532\) 0 0
\(533\) 5.44888e6i 0.830786i
\(534\) 0 0
\(535\) −5.13546e6 461178.i −0.775702 0.0696601i
\(536\) 0 0
\(537\) 1.58245e6i 0.236807i
\(538\) 0 0
\(539\) 180300. 0.0267315
\(540\) 0 0
\(541\) −2.72367e6 −0.400093 −0.200046 0.979786i \(-0.564109\pi\)
−0.200046 + 0.979786i \(0.564109\pi\)
\(542\) 0 0
\(543\) 2.79268e6i 0.406463i
\(544\) 0 0
\(545\) −531190. + 5.91508e6i −0.0766053 + 0.853040i
\(546\) 0 0
\(547\) 9.22148e6i 1.31775i −0.752254 0.658874i \(-0.771033\pi\)
0.752254 0.658874i \(-0.228967\pi\)
\(548\) 0 0
\(549\) −363902. −0.0515292
\(550\) 0 0
\(551\) −1.76244e7 −2.47306
\(552\) 0 0
\(553\) 9.76595e6i 1.35801i
\(554\) 0 0
\(555\) 579080. 6.44836e6i 0.0798006 0.888622i
\(556\) 0 0
\(557\) 3.42852e6i 0.468240i −0.972208 0.234120i \(-0.924779\pi\)
0.972208 0.234120i \(-0.0752209\pi\)
\(558\) 0 0
\(559\) 1.30535e7 1.76684
\(560\) 0 0
\(561\) −1.09120e6 −0.146385
\(562\) 0 0
\(563\) 5.77899e6i 0.768389i −0.923252 0.384195i \(-0.874479\pi\)
0.923252 0.384195i \(-0.125521\pi\)
\(564\) 0 0
\(565\) 6.29424e6 + 565239.i 0.829511 + 0.0744923i
\(566\) 0 0
\(567\) 1.95630e6i 0.255551i
\(568\) 0 0
\(569\) 3.89257e6 0.504029 0.252015 0.967723i \(-0.418907\pi\)
0.252015 + 0.967723i \(0.418907\pi\)
\(570\) 0 0
\(571\) 5.06277e6 0.649828 0.324914 0.945744i \(-0.394665\pi\)
0.324914 + 0.945744i \(0.394665\pi\)
\(572\) 0 0
\(573\) 2.33258e6i 0.296791i
\(574\) 0 0
\(575\) −1.90340e6 + 1.05122e7i −0.240082 + 1.32594i
\(576\) 0 0
\(577\) 3.30075e6i 0.412737i −0.978474 0.206368i \(-0.933836\pi\)
0.978474 0.206368i \(-0.0661645\pi\)
\(578\) 0 0
\(579\) 3.97197e6 0.492390
\(580\) 0 0
\(581\) 1.99553e6 0.245255
\(582\) 0 0
\(583\) 2.42532e6i 0.295527i
\(584\) 0 0
\(585\) 4.86948e6 + 437292.i 0.588292 + 0.0528302i
\(586\) 0 0
\(587\) 5.16997e6i 0.619288i −0.950853 0.309644i \(-0.899790\pi\)
0.950853 0.309644i \(-0.100210\pi\)
\(588\) 0 0
\(589\) −4.81114e6 −0.571425
\(590\) 0 0
\(591\) −962984. −0.113410
\(592\) 0 0
\(593\) 1.58484e7i 1.85075i −0.379055 0.925374i \(-0.623751\pi\)
0.379055 0.925374i \(-0.376249\pi\)
\(594\) 0 0
\(595\) 600160. 6.68310e6i 0.0694984 0.773901i
\(596\) 0 0
\(597\) 8.34283e6i 0.958026i
\(598\) 0 0
\(599\) 1.66146e7 1.89201 0.946004 0.324156i \(-0.105080\pi\)
0.946004 + 0.324156i \(0.105080\pi\)
\(600\) 0 0
\(601\) 7.88249e6 0.890179 0.445089 0.895486i \(-0.353172\pi\)
0.445089 + 0.895486i \(0.353172\pi\)
\(602\) 0 0
\(603\) 6.99535e6i 0.783459i
\(604\) 0 0
\(605\) 755255. 8.41016e6i 0.0838890 0.934149i
\(606\) 0 0
\(607\) 782594.i 0.0862114i −0.999071 0.0431057i \(-0.986275\pi\)
0.999071 0.0431057i \(-0.0137252\pi\)
\(608\) 0 0
\(609\) −1.07129e7 −1.17047
\(610\) 0 0
\(611\) −6.93185e6 −0.751183
\(612\) 0 0
\(613\) 2.41233e6i 0.259290i 0.991560 + 0.129645i \(0.0413838\pi\)
−0.991560 + 0.129645i \(0.958616\pi\)
\(614\) 0 0
\(615\) −4.59668e6 412794.i −0.490068 0.0440094i
\(616\) 0 0
\(617\) 9.66355e6i 1.02194i 0.859600 + 0.510968i \(0.170713\pi\)
−0.859600 + 0.510968i \(0.829287\pi\)
\(618\) 0 0
\(619\) −1.80036e7 −1.88857 −0.944283 0.329134i \(-0.893243\pi\)
−0.944283 + 0.329134i \(0.893243\pi\)
\(620\) 0 0
\(621\) −1.37806e7 −1.43397
\(622\) 0 0
\(623\) 101177.i 0.0104439i
\(624\) 0 0
\(625\) 9.14562e6 + 3.42418e6i 0.936512 + 0.350636i
\(626\) 0 0
\(627\) 2.49881e6i 0.253843i
\(628\) 0 0
\(629\) −1.01918e7 −1.02713
\(630\) 0 0
\(631\) 4.80081e6 0.480000 0.240000 0.970773i \(-0.422853\pi\)
0.240000 + 0.970773i \(0.422853\pi\)
\(632\) 0 0
\(633\) 3.19995e6i 0.317420i
\(634\) 0 0
\(635\) 2.87122e6 + 257843.i 0.282574 + 0.0253759i
\(636\) 0 0
\(637\) 1.32511e6i 0.129390i
\(638\) 0 0
\(639\) −4.47535e6 −0.433586
\(640\) 0 0
\(641\) 1.44950e7 1.39340 0.696698 0.717365i \(-0.254652\pi\)
0.696698 + 0.717365i \(0.254652\pi\)
\(642\) 0 0
\(643\) 1.82430e7i 1.74008i −0.492979 0.870041i \(-0.664092\pi\)
0.492979 0.870041i \(-0.335908\pi\)
\(644\) 0 0
\(645\) −988900. + 1.10119e7i −0.0935951 + 1.04223i
\(646\) 0 0
\(647\) 9.64592e6i 0.905905i 0.891535 + 0.452953i \(0.149629\pi\)
−0.891535 + 0.452953i \(0.850371\pi\)
\(648\) 0 0
\(649\) 2.59720e6 0.242044
\(650\) 0 0
\(651\) −2.92442e6 −0.270450
\(652\) 0 0
\(653\) 1.92807e7i 1.76945i 0.466111 + 0.884726i \(0.345655\pi\)
−0.466111 + 0.884726i \(0.654345\pi\)
\(654\) 0 0
\(655\) −445500. + 4.96088e6i −0.0405737 + 0.451809i
\(656\) 0 0
\(657\) 2.85698e6i 0.258222i
\(658\) 0 0
\(659\) 9.70592e6 0.870609 0.435304 0.900283i \(-0.356641\pi\)
0.435304 + 0.900283i \(0.356641\pi\)
\(660\) 0 0
\(661\) −4.28396e6 −0.381366 −0.190683 0.981652i \(-0.561070\pi\)
−0.190683 + 0.981652i \(0.561070\pi\)
\(662\) 0 0
\(663\) 8.01972e6i 0.708558i
\(664\) 0 0
\(665\) −1.53041e7 1.37435e6i −1.34200 0.120515i
\(666\) 0 0
\(667\) 2.68497e7i 2.33682i
\(668\) 0 0
\(669\) 1.32364e7 1.14342
\(670\) 0 0
\(671\) −305800. −0.0262199
\(672\) 0 0
\(673\) 1.30585e7i 1.11136i 0.831395 + 0.555681i \(0.187542\pi\)
−0.831395 + 0.555681i \(0.812458\pi\)
\(674\) 0 0
\(675\) −2.24440e6 + 1.23955e7i −0.189601 + 1.04714i
\(676\) 0 0
\(677\) 8.42565e6i 0.706532i −0.935523 0.353266i \(-0.885071\pi\)
0.935523 0.353266i \(-0.114929\pi\)
\(678\) 0 0
\(679\) 4.60486e6 0.383303
\(680\) 0 0
\(681\) −1.08943e7 −0.900182
\(682\) 0 0
\(683\) 1.64100e7i 1.34603i 0.739627 + 0.673017i \(0.235002\pi\)
−0.739627 + 0.673017i \(0.764998\pi\)
\(684\) 0 0
\(685\) −2.13528e6 191754.i −0.173872 0.0156141i
\(686\) 0 0
\(687\) 5.63986e6i 0.455907i
\(688\) 0 0
\(689\) 1.78248e7 1.43046
\(690\) 0 0
\(691\) 1.12139e7 0.893428 0.446714 0.894677i \(-0.352594\pi\)
0.446714 + 0.894677i \(0.352594\pi\)
\(692\) 0 0
\(693\) 1.45764e6i 0.115297i
\(694\) 0 0
\(695\) 673420. 7.49889e6i 0.0528840 0.588891i
\(696\) 0 0
\(697\) 7.26518e6i 0.566453i
\(698\) 0 0
\(699\) −1.73119e7 −1.34014
\(700\) 0 0
\(701\) 2.04707e7 1.57339 0.786696 0.617340i \(-0.211790\pi\)
0.786696 + 0.617340i \(0.211790\pi\)
\(702\) 0 0
\(703\) 2.33389e7i 1.78112i
\(704\) 0 0
\(705\) 525140. 5.84771e6i 0.0397926 0.443112i
\(706\) 0 0
\(707\) 1.75889e7i 1.32340i
\(708\) 0 0
\(709\) 81654.0 0.00610045 0.00305023 0.999995i \(-0.499029\pi\)
0.00305023 + 0.999995i \(0.499029\pi\)
\(710\) 0 0
\(711\) 9.48763e6 0.703856
\(712\) 0 0
\(713\) 7.32949e6i 0.539946i
\(714\) 0 0
\(715\) 4.09200e6 + 367472.i 0.299344 + 0.0268819i
\(716\) 0 0
\(717\) 4.17253e6i 0.303111i
\(718\) 0 0
\(719\) −8.61006e6 −0.621132 −0.310566 0.950552i \(-0.600519\pi\)
−0.310566 + 0.950552i \(0.600519\pi\)
\(720\) 0 0
\(721\) −1.36987e7 −0.981386
\(722\) 0 0
\(723\) 9.39431e6i 0.668373i
\(724\) 0 0
\(725\) −2.41510e7 4.37292e6i −1.70644 0.308977i
\(726\) 0 0
\(727\) 1.17682e7i 0.825796i 0.910777 + 0.412898i \(0.135483\pi\)
−0.910777 + 0.412898i \(0.864517\pi\)
\(728\) 0 0
\(729\) −1.28083e7 −0.892635
\(730\) 0 0
\(731\) 1.74046e7 1.20468
\(732\) 0 0
\(733\) 3.93759e6i 0.270689i 0.990799 + 0.135344i \(0.0432141\pi\)
−0.990799 + 0.135344i \(0.956786\pi\)
\(734\) 0 0
\(735\) 1.11786e6 + 100387.i 0.0763254 + 0.00685422i
\(736\) 0 0
\(737\) 5.87845e6i 0.398652i
\(738\) 0 0
\(739\) −2.30602e7 −1.55329 −0.776643 0.629941i \(-0.783079\pi\)
−0.776643 + 0.629941i \(0.783079\pi\)
\(740\) 0 0
\(741\) 1.83649e7 1.22869
\(742\) 0 0
\(743\) 1.72675e6i 0.114751i −0.998353 0.0573757i \(-0.981727\pi\)
0.998353 0.0573757i \(-0.0182733\pi\)
\(744\) 0 0
\(745\) −1.24003e6 + 1.38084e7i −0.0818543 + 0.911491i
\(746\) 0 0
\(747\) 1.93866e6i 0.127116i
\(748\) 0 0
\(749\) 1.12980e7 0.735864
\(750\) 0 0
\(751\) 2.58030e6 0.166944 0.0834720 0.996510i \(-0.473399\pi\)
0.0834720 + 0.996510i \(0.473399\pi\)
\(752\) 0 0
\(753\) 1.91587e7i 1.23134i
\(754\) 0 0
\(755\) 1.56860e6 1.74672e7i 0.100149 1.11521i
\(756\) 0 0
\(757\) 5.75878e6i 0.365251i 0.983183 + 0.182625i \(0.0584595\pi\)
−0.983183 + 0.182625i \(0.941540\pi\)
\(758\) 0 0
\(759\) −3.80680e6 −0.239859
\(760\) 0 0
\(761\) 1.40499e7 0.879450 0.439725 0.898133i \(-0.355076\pi\)
0.439725 + 0.898133i \(0.355076\pi\)
\(762\) 0 0
\(763\) 1.30132e7i 0.809230i
\(764\) 0 0
\(765\) 6.49264e6 + 583056.i 0.401114 + 0.0360211i
\(766\) 0 0
\(767\) 1.90880e7i 1.17158i
\(768\) 0 0
\(769\) 5.59898e6 0.341423 0.170712 0.985321i \(-0.445393\pi\)
0.170712 + 0.985321i \(0.445393\pi\)
\(770\) 0 0
\(771\) 1.72846e7 1.04719
\(772\) 0 0
\(773\) 6.34625e6i 0.382004i −0.981590 0.191002i \(-0.938826\pi\)
0.981590 0.191002i \(-0.0611738\pi\)
\(774\) 0 0
\(775\) −6.59280e6 1.19373e6i −0.394290 0.0713923i
\(776\) 0 0
\(777\) 1.41864e7i 0.842984i
\(778\) 0 0
\(779\) 1.66370e7 0.982272
\(780\) 0 0
\(781\) −3.76080e6 −0.220624
\(782\) 0 0
\(783\) 3.16600e7i 1.84547i
\(784\) 0 0
\(785\) −1.36735e7 1.22791e6i −0.791963 0.0711204i
\(786\) 0 0
\(787\) 1.73688e7i 0.999617i 0.866136 + 0.499809i \(0.166596\pi\)
−0.866136 + 0.499809i \(0.833404\pi\)
\(788\) 0 0
\(789\) −4.54076e6 −0.259678
\(790\) 0 0
\(791\) −1.38473e7 −0.786909
\(792\) 0 0
\(793\) 2.24746e6i 0.126914i
\(794\) 0 0
\(795\) −1.35036e6 + 1.50370e7i −0.0757760 + 0.843806i
\(796\) 0 0
\(797\) 8.06932e6i 0.449978i 0.974361 + 0.224989i \(0.0722346\pi\)
−0.974361 + 0.224989i \(0.927765\pi\)
\(798\) 0 0
\(799\) −9.24246e6 −0.512178
\(800\) 0 0
\(801\) 98294.0 0.00541310
\(802\) 0 0
\(803\) 2.40082e6i 0.131393i
\(804\) 0 0
\(805\) 2.09374e6 2.33149e7i 0.113876 1.26807i
\(806\) 0 0
\(807\) 2.03457e7i 1.09974i
\(808\) 0 0
\(809\) −1.94554e7 −1.04513 −0.522564 0.852600i \(-0.675024\pi\)
−0.522564 + 0.852600i \(0.675024\pi\)
\(810\) 0 0
\(811\) 2.85204e6 0.152266