Properties

Label 80.10.c.c.49.2
Level 80
Weight 10
Character 80.49
Analytic conductor 41.203
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 80.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.2028668931\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.49740556.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{7}\cdot 3^{2}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 49.2
Root \(2.87724i\)
Character \(\chi\) = 80.49
Dual form 80.10.c.c.49.3

$q$-expansion

\(f(q)\) \(=\) \(q-37.6407i q^{3} +(1138.29 - 810.818i) q^{5} +5315.22i q^{7} +18266.2 q^{9} +O(q^{10})\) \(q-37.6407i q^{3} +(1138.29 - 810.818i) q^{5} +5315.22i q^{7} +18266.2 q^{9} -10426.2 q^{11} +79655.1i q^{13} +(-30519.7 - 42845.9i) q^{15} +313750. i q^{17} -246945. q^{19} +200068. q^{21} +721761. i q^{23} +(638273. - 1.84589e6i) q^{25} -1.42843e6i q^{27} -2.56903e6 q^{29} +3.29543e6 q^{31} +392451. i q^{33} +(4.30967e6 + 6.05025e6i) q^{35} +1.40463e7i q^{37} +2.99827e6 q^{39} +1.70412e7 q^{41} +2.92261e7i q^{43} +(2.07922e7 - 1.48105e7i) q^{45} -4.10316e7i q^{47} +1.21021e7 q^{49} +1.18098e7 q^{51} +5.67230e7i q^{53} +(-1.18681e7 + 8.45379e6i) q^{55} +9.29518e6i q^{57} +1.60408e8 q^{59} +5.33033e7 q^{61} +9.70887e7i q^{63} +(6.45858e7 + 9.06705e7i) q^{65} +2.80916e8i q^{67} +2.71676e7 q^{69} +8.97228e7 q^{71} +7.60225e7i q^{73} +(-6.94805e7 - 2.40250e7i) q^{75} -5.54178e7i q^{77} +4.10672e8 q^{79} +3.05766e8 q^{81} -5.21969e8i q^{83} +(2.54394e8 + 3.57138e8i) q^{85} +9.66999e7i q^{87} -2.37312e8 q^{89} -4.23384e8 q^{91} -1.24042e8i q^{93} +(-2.81094e8 + 2.00227e8i) q^{95} -6.03778e8i q^{97} -1.90448e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1140q^{5} + 11628q^{9} + O(q^{10}) \) \( 4q + 1140q^{5} + 11628q^{9} - 109968q^{11} + 396720q^{15} + 636880q^{19} + 3523968q^{21} - 1337900q^{25} - 3531720q^{29} + 10587712q^{31} - 13629840q^{35} - 1686816q^{39} - 16788552q^{41} + 55737180q^{45} - 46921028q^{49} - 84017088q^{51} + 26907120q^{55} + 460829040q^{59} + 360490568q^{61} + 183895680q^{65} - 286524864q^{69} + 47611872q^{71} - 659239200q^{75} + 728043520q^{79} - 343387836q^{81} + 1275419840q^{85} - 1582700760q^{89} - 473322528q^{91} - 1204791600q^{95} + 728787024q^{99} + O(q^{100}) \)

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
\(3\) 37.6407i 0.268294i −0.990961 0.134147i \(-0.957170\pi\)
0.990961 0.134147i \(-0.0428295\pi\)
\(4\) 0 0
\(5\) 1138.29 810.818i 0.814492 0.580174i
\(6\) 0 0
\(7\) 5315.22i 0.836719i 0.908281 + 0.418360i \(0.137395\pi\)
−0.908281 + 0.418360i \(0.862605\pi\)
\(8\) 0 0
\(9\) 18266.2 0.928018
\(10\) 0 0
\(11\) −10426.2 −0.214714 −0.107357 0.994221i \(-0.534239\pi\)
−0.107357 + 0.994221i \(0.534239\pi\)
\(12\) 0 0
\(13\) 79655.1i 0.773515i 0.922181 + 0.386758i \(0.126405\pi\)
−0.922181 + 0.386758i \(0.873595\pi\)
\(14\) 0 0
\(15\) −30519.7 42845.9i −0.155658 0.218524i
\(16\) 0 0
\(17\) 313750.i 0.911095i 0.890212 + 0.455547i \(0.150556\pi\)
−0.890212 + 0.455547i \(0.849444\pi\)
\(18\) 0 0
\(19\) −246945. −0.434719 −0.217360 0.976092i \(-0.569744\pi\)
−0.217360 + 0.976092i \(0.569744\pi\)
\(20\) 0 0
\(21\) 200068. 0.224487
\(22\) 0 0
\(23\) 721761.i 0.537797i 0.963169 + 0.268898i \(0.0866595\pi\)
−0.963169 + 0.268898i \(0.913340\pi\)
\(24\) 0 0
\(25\) 638273. 1.84589e6i 0.326796 0.945095i
\(26\) 0 0
\(27\) 1.42843e6i 0.517277i
\(28\) 0 0
\(29\) −2.56903e6 −0.674493 −0.337247 0.941416i \(-0.609496\pi\)
−0.337247 + 0.941416i \(0.609496\pi\)
\(30\) 0 0
\(31\) 3.29543e6 0.640891 0.320445 0.947267i \(-0.396167\pi\)
0.320445 + 0.947267i \(0.396167\pi\)
\(32\) 0 0
\(33\) 392451.i 0.0576066i
\(34\) 0 0
\(35\) 4.30967e6 + 6.05025e6i 0.485443 + 0.681502i
\(36\) 0 0
\(37\) 1.40463e7i 1.23212i 0.787699 + 0.616060i \(0.211272\pi\)
−0.787699 + 0.616060i \(0.788728\pi\)
\(38\) 0 0
\(39\) 2.99827e6 0.207530
\(40\) 0 0
\(41\) 1.70412e7 0.941830 0.470915 0.882178i \(-0.343924\pi\)
0.470915 + 0.882178i \(0.343924\pi\)
\(42\) 0 0
\(43\) 2.92261e7i 1.30365i 0.758368 + 0.651827i \(0.225997\pi\)
−0.758368 + 0.651827i \(0.774003\pi\)
\(44\) 0 0
\(45\) 2.07922e7 1.48105e7i 0.755864 0.538412i
\(46\) 0 0
\(47\) 4.10316e7i 1.22653i −0.789878 0.613264i \(-0.789856\pi\)
0.789878 0.613264i \(-0.210144\pi\)
\(48\) 0 0
\(49\) 1.21021e7 0.299901
\(50\) 0 0
\(51\) 1.18098e7 0.244442
\(52\) 0 0
\(53\) 5.67230e7i 0.987456i 0.869616 + 0.493728i \(0.164366\pi\)
−0.869616 + 0.493728i \(0.835634\pi\)
\(54\) 0 0
\(55\) −1.18681e7 + 8.45379e6i −0.174883 + 0.124572i
\(56\) 0 0
\(57\) 9.29518e6i 0.116633i
\(58\) 0 0
\(59\) 1.60408e8 1.72342 0.861710 0.507402i \(-0.169394\pi\)
0.861710 + 0.507402i \(0.169394\pi\)
\(60\) 0 0
\(61\) 5.33033e7 0.492912 0.246456 0.969154i \(-0.420734\pi\)
0.246456 + 0.969154i \(0.420734\pi\)
\(62\) 0 0
\(63\) 9.70887e7i 0.776491i
\(64\) 0 0
\(65\) 6.45858e7 + 9.06705e7i 0.448773 + 0.630022i
\(66\) 0 0
\(67\) 2.80916e8i 1.70310i 0.524276 + 0.851548i \(0.324336\pi\)
−0.524276 + 0.851548i \(0.675664\pi\)
\(68\) 0 0
\(69\) 2.71676e7 0.144288
\(70\) 0 0
\(71\) 8.97228e7 0.419025 0.209513 0.977806i \(-0.432812\pi\)
0.209513 + 0.977806i \(0.432812\pi\)
\(72\) 0 0
\(73\) 7.60225e7i 0.313321i 0.987653 + 0.156660i \(0.0500728\pi\)
−0.987653 + 0.156660i \(0.949927\pi\)
\(74\) 0 0
\(75\) −6.94805e7 2.40250e7i −0.253564 0.0876775i
\(76\) 0 0
\(77\) 5.54178e7i 0.179656i
\(78\) 0 0
\(79\) 4.10672e8 1.18624 0.593120 0.805114i \(-0.297896\pi\)
0.593120 + 0.805114i \(0.297896\pi\)
\(80\) 0 0
\(81\) 3.05766e8 0.789236
\(82\) 0 0
\(83\) 5.21969e8i 1.20724i −0.797272 0.603620i \(-0.793724\pi\)
0.797272 0.603620i \(-0.206276\pi\)
\(84\) 0 0
\(85\) 2.54394e8 + 3.57138e8i 0.528594 + 0.742080i
\(86\) 0 0
\(87\) 9.66999e7i 0.180963i
\(88\) 0 0
\(89\) −2.37312e8 −0.400926 −0.200463 0.979701i \(-0.564245\pi\)
−0.200463 + 0.979701i \(0.564245\pi\)
\(90\) 0 0
\(91\) −4.23384e8 −0.647215
\(92\) 0 0
\(93\) 1.24042e8i 0.171947i
\(94\) 0 0
\(95\) −2.81094e8 + 2.00227e8i −0.354076 + 0.252213i
\(96\) 0 0
\(97\) 6.03778e8i 0.692476i −0.938147 0.346238i \(-0.887459\pi\)
0.938147 0.346238i \(-0.112541\pi\)
\(98\) 0 0
\(99\) −1.90448e8 −0.199259
\(100\) 0 0
\(101\) −2.03606e8 −0.194690 −0.0973451 0.995251i \(-0.531035\pi\)
−0.0973451 + 0.995251i \(0.531035\pi\)
\(102\) 0 0
\(103\) 9.15893e8i 0.801821i 0.916117 + 0.400910i \(0.131306\pi\)
−0.916117 + 0.400910i \(0.868694\pi\)
\(104\) 0 0
\(105\) 2.27735e8 1.62219e8i 0.182843 0.130242i
\(106\) 0 0
\(107\) 1.66237e9i 1.22603i −0.790072 0.613014i \(-0.789957\pi\)
0.790072 0.613014i \(-0.210043\pi\)
\(108\) 0 0
\(109\) −1.73161e9 −1.17498 −0.587491 0.809231i \(-0.699884\pi\)
−0.587491 + 0.809231i \(0.699884\pi\)
\(110\) 0 0
\(111\) 5.28711e8 0.330571
\(112\) 0 0
\(113\) 6.30956e8i 0.364038i −0.983295 0.182019i \(-0.941737\pi\)
0.983295 0.182019i \(-0.0582632\pi\)
\(114\) 0 0
\(115\) 5.85217e8 + 8.21571e8i 0.312016 + 0.438031i
\(116\) 0 0
\(117\) 1.45500e9i 0.717836i
\(118\) 0 0
\(119\) −1.66765e9 −0.762331
\(120\) 0 0
\(121\) −2.24924e9 −0.953898
\(122\) 0 0
\(123\) 6.41442e8i 0.252688i
\(124\) 0 0
\(125\) −7.70141e8 2.61868e9i −0.282147 0.959371i
\(126\) 0 0
\(127\) 2.12104e9i 0.723490i −0.932277 0.361745i \(-0.882181\pi\)
0.932277 0.361745i \(-0.117819\pi\)
\(128\) 0 0
\(129\) 1.10009e9 0.349763
\(130\) 0 0
\(131\) −5.57686e9 −1.65451 −0.827254 0.561828i \(-0.810098\pi\)
−0.827254 + 0.561828i \(0.810098\pi\)
\(132\) 0 0
\(133\) 1.31257e9i 0.363738i
\(134\) 0 0
\(135\) −1.15820e9 1.62597e9i −0.300111 0.421318i
\(136\) 0 0
\(137\) 2.57317e9i 0.624059i −0.950072 0.312029i \(-0.898991\pi\)
0.950072 0.312029i \(-0.101009\pi\)
\(138\) 0 0
\(139\) −1.62297e9 −0.368761 −0.184380 0.982855i \(-0.559028\pi\)
−0.184380 + 0.982855i \(0.559028\pi\)
\(140\) 0 0
\(141\) −1.54446e9 −0.329071
\(142\) 0 0
\(143\) 8.30504e8i 0.166085i
\(144\) 0 0
\(145\) −2.92429e9 + 2.08301e9i −0.549370 + 0.391324i
\(146\) 0 0
\(147\) 4.55530e8i 0.0804617i
\(148\) 0 0
\(149\) 5.98422e9 0.994647 0.497324 0.867565i \(-0.334316\pi\)
0.497324 + 0.867565i \(0.334316\pi\)
\(150\) 0 0
\(151\) 5.95089e9 0.931505 0.465753 0.884915i \(-0.345784\pi\)
0.465753 + 0.884915i \(0.345784\pi\)
\(152\) 0 0
\(153\) 5.73101e9i 0.845513i
\(154\) 0 0
\(155\) 3.75114e9 2.67199e9i 0.522001 0.371828i
\(156\) 0 0
\(157\) 2.94325e9i 0.386615i −0.981138 0.193308i \(-0.938078\pi\)
0.981138 0.193308i \(-0.0619215\pi\)
\(158\) 0 0
\(159\) 2.13509e9 0.264929
\(160\) 0 0
\(161\) −3.83632e9 −0.449985
\(162\) 0 0
\(163\) 2.69823e9i 0.299389i 0.988732 + 0.149694i \(0.0478290\pi\)
−0.988732 + 0.149694i \(0.952171\pi\)
\(164\) 0 0
\(165\) 3.18206e8 + 4.46722e8i 0.0334219 + 0.0469202i
\(166\) 0 0
\(167\) 1.47132e10i 1.46380i 0.681410 + 0.731902i \(0.261367\pi\)
−0.681410 + 0.731902i \(0.738633\pi\)
\(168\) 0 0
\(169\) 4.25956e9 0.401675
\(170\) 0 0
\(171\) −4.51074e9 −0.403427
\(172\) 0 0
\(173\) 1.56605e8i 0.0132923i 0.999978 + 0.00664613i \(0.00211555\pi\)
−0.999978 + 0.00664613i \(0.997884\pi\)
\(174\) 0 0
\(175\) 9.81130e9 + 3.39256e9i 0.790779 + 0.273436i
\(176\) 0 0
\(177\) 6.03785e9i 0.462384i
\(178\) 0 0
\(179\) −5.35516e9 −0.389883 −0.194941 0.980815i \(-0.562452\pi\)
−0.194941 + 0.980815i \(0.562452\pi\)
\(180\) 0 0
\(181\) −1.52107e9 −0.105341 −0.0526704 0.998612i \(-0.516773\pi\)
−0.0526704 + 0.998612i \(0.516773\pi\)
\(182\) 0 0
\(183\) 2.00637e9i 0.132246i
\(184\) 0 0
\(185\) 1.13890e10 + 1.59887e10i 0.714845 + 1.00355i
\(186\) 0 0
\(187\) 3.27123e9i 0.195625i
\(188\) 0 0
\(189\) 7.59243e9 0.432815
\(190\) 0 0
\(191\) 9.28266e9 0.504687 0.252344 0.967638i \(-0.418799\pi\)
0.252344 + 0.967638i \(0.418799\pi\)
\(192\) 0 0
\(193\) 6.94351e9i 0.360223i −0.983646 0.180111i \(-0.942354\pi\)
0.983646 0.180111i \(-0.0576458\pi\)
\(194\) 0 0
\(195\) 3.41290e9 2.43105e9i 0.169031 0.120403i
\(196\) 0 0
\(197\) 3.60722e10i 1.70637i 0.521606 + 0.853187i \(0.325333\pi\)
−0.521606 + 0.853187i \(0.674667\pi\)
\(198\) 0 0
\(199\) 2.25173e10 1.01784 0.508918 0.860815i \(-0.330045\pi\)
0.508918 + 0.860815i \(0.330045\pi\)
\(200\) 0 0
\(201\) 1.05739e10 0.456931
\(202\) 0 0
\(203\) 1.36549e10i 0.564362i
\(204\) 0 0
\(205\) 1.93978e10 1.38173e10i 0.767114 0.546426i
\(206\) 0 0
\(207\) 1.31838e10i 0.499085i
\(208\) 0 0
\(209\) 2.57471e9 0.0933404
\(210\) 0 0
\(211\) −3.62300e10 −1.25834 −0.629169 0.777268i \(-0.716605\pi\)
−0.629169 + 0.777268i \(0.716605\pi\)
\(212\) 0 0
\(213\) 3.37723e9i 0.112422i
\(214\) 0 0
\(215\) 2.36970e10 + 3.32677e10i 0.756346 + 1.06182i
\(216\) 0 0
\(217\) 1.75159e10i 0.536246i
\(218\) 0 0
\(219\) 2.86154e9 0.0840623
\(220\) 0 0
\(221\) −2.49918e10 −0.704746
\(222\) 0 0
\(223\) 4.93834e10i 1.33724i 0.743605 + 0.668619i \(0.233114\pi\)
−0.743605 + 0.668619i \(0.766886\pi\)
\(224\) 0 0
\(225\) 1.16588e10 3.37173e10i 0.303272 0.877065i
\(226\) 0 0
\(227\) 3.27710e10i 0.819169i −0.912272 0.409585i \(-0.865674\pi\)
0.912272 0.409585i \(-0.134326\pi\)
\(228\) 0 0
\(229\) −1.35586e10 −0.325803 −0.162902 0.986642i \(-0.552085\pi\)
−0.162902 + 0.986642i \(0.552085\pi\)
\(230\) 0 0
\(231\) −2.08596e9 −0.0482006
\(232\) 0 0
\(233\) 7.99837e9i 0.177787i 0.996041 + 0.0888935i \(0.0283331\pi\)
−0.996041 + 0.0888935i \(0.971667\pi\)
\(234\) 0 0
\(235\) −3.32691e10 4.67057e10i −0.711600 0.998998i
\(236\) 0 0
\(237\) 1.54580e10i 0.318262i
\(238\) 0 0
\(239\) 8.30208e10 1.64587 0.822937 0.568133i \(-0.192334\pi\)
0.822937 + 0.568133i \(0.192334\pi\)
\(240\) 0 0
\(241\) −6.04789e10 −1.15485 −0.577427 0.816442i \(-0.695943\pi\)
−0.577427 + 0.816442i \(0.695943\pi\)
\(242\) 0 0
\(243\) 3.96251e10i 0.729024i
\(244\) 0 0
\(245\) 1.37756e10 9.81258e9i 0.244267 0.173995i
\(246\) 0 0
\(247\) 1.96704e10i 0.336262i
\(248\) 0 0
\(249\) −1.96473e10 −0.323896
\(250\) 0 0
\(251\) −1.04682e11 −1.66471 −0.832354 0.554244i \(-0.813007\pi\)
−0.832354 + 0.554244i \(0.813007\pi\)
\(252\) 0 0
\(253\) 7.52525e9i 0.115473i
\(254\) 0 0
\(255\) 1.34429e10 9.57557e9i 0.199096 0.141819i
\(256\) 0 0
\(257\) 7.92751e10i 1.13354i −0.823875 0.566771i \(-0.808192\pi\)
0.823875 0.566771i \(-0.191808\pi\)
\(258\) 0 0
\(259\) −7.46590e10 −1.03094
\(260\) 0 0
\(261\) −4.69263e10 −0.625942
\(262\) 0 0
\(263\) 1.04629e8i 0.00134850i −1.00000 0.000674250i \(-0.999785\pi\)
1.00000 0.000674250i \(-0.000214620\pi\)
\(264\) 0 0
\(265\) 4.59920e10 + 6.45671e10i 0.572897 + 0.804275i
\(266\) 0 0
\(267\) 8.93258e9i 0.107566i
\(268\) 0 0
\(269\) 7.38735e9 0.0860208 0.0430104 0.999075i \(-0.486305\pi\)
0.0430104 + 0.999075i \(0.486305\pi\)
\(270\) 0 0
\(271\) −1.27706e11 −1.43831 −0.719153 0.694852i \(-0.755470\pi\)
−0.719153 + 0.694852i \(0.755470\pi\)
\(272\) 0 0
\(273\) 1.59365e10i 0.173644i
\(274\) 0 0
\(275\) −6.65479e9 + 1.92457e10i −0.0701677 + 0.202925i
\(276\) 0 0
\(277\) 3.16563e10i 0.323074i −0.986867 0.161537i \(-0.948355\pi\)
0.986867 0.161537i \(-0.0516451\pi\)
\(278\) 0 0
\(279\) 6.01949e10 0.594758
\(280\) 0 0
\(281\) −9.50309e10 −0.909257 −0.454628 0.890681i \(-0.650228\pi\)
−0.454628 + 0.890681i \(0.650228\pi\)
\(282\) 0 0
\(283\) 4.91862e10i 0.455832i −0.973681 0.227916i \(-0.926809\pi\)
0.973681 0.227916i \(-0.0731911\pi\)
\(284\) 0 0
\(285\) 7.53670e9 + 1.05806e10i 0.0676673 + 0.0949965i
\(286\) 0 0
\(287\) 9.05777e10i 0.788048i
\(288\) 0 0
\(289\) 2.01488e10 0.169906
\(290\) 0 0
\(291\) −2.27266e10 −0.185787
\(292\) 0 0
\(293\) 3.53889e10i 0.280519i 0.990115 + 0.140260i \(0.0447937\pi\)
−0.990115 + 0.140260i \(0.955206\pi\)
\(294\) 0 0
\(295\) 1.82590e11 1.30061e11i 1.40371 0.999883i
\(296\) 0 0
\(297\) 1.48932e10i 0.111067i
\(298\) 0 0
\(299\) −5.74920e10 −0.415994
\(300\) 0 0
\(301\) −1.55343e11 −1.09079
\(302\) 0 0
\(303\) 7.66386e9i 0.0522343i
\(304\) 0 0
\(305\) 6.06745e10 4.32193e10i 0.401473 0.285975i
\(306\) 0 0
\(307\) 8.30301e10i 0.533474i −0.963769 0.266737i \(-0.914055\pi\)
0.963769 0.266737i \(-0.0859455\pi\)
\(308\) 0 0
\(309\) 3.44748e10 0.215124
\(310\) 0 0
\(311\) −2.13935e10 −0.129676 −0.0648382 0.997896i \(-0.520653\pi\)
−0.0648382 + 0.997896i \(0.520653\pi\)
\(312\) 0 0
\(313\) 2.56558e11i 1.51090i −0.655204 0.755452i \(-0.727418\pi\)
0.655204 0.755452i \(-0.272582\pi\)
\(314\) 0 0
\(315\) 7.87213e10 + 1.10515e11i 0.450500 + 0.632446i
\(316\) 0 0
\(317\) 1.26112e11i 0.701436i −0.936481 0.350718i \(-0.885938\pi\)
0.936481 0.350718i \(-0.114062\pi\)
\(318\) 0 0
\(319\) 2.67853e10 0.144823
\(320\) 0 0
\(321\) −6.25727e10 −0.328936
\(322\) 0 0
\(323\) 7.74790e10i 0.396071i
\(324\) 0 0
\(325\) 1.47035e11 + 5.08417e10i 0.731045 + 0.252781i
\(326\) 0 0
\(327\) 6.51790e10i 0.315241i
\(328\) 0 0
\(329\) 2.18092e11 1.02626
\(330\) 0 0
\(331\) −1.71300e11 −0.784389 −0.392194 0.919882i \(-0.628284\pi\)
−0.392194 + 0.919882i \(0.628284\pi\)
\(332\) 0 0
\(333\) 2.56572e11i 1.14343i
\(334\) 0 0
\(335\) 2.27771e11 + 3.19763e11i 0.988093 + 1.38716i
\(336\) 0 0
\(337\) 4.70320e11i 1.98637i 0.116569 + 0.993183i \(0.462810\pi\)
−0.116569 + 0.993183i \(0.537190\pi\)
\(338\) 0 0
\(339\) −2.37496e10 −0.0976693
\(340\) 0 0
\(341\) −3.43589e10 −0.137608
\(342\) 0 0
\(343\) 2.78813e11i 1.08765i
\(344\) 0 0
\(345\) 3.09245e10 2.20279e10i 0.117521 0.0837121i
\(346\) 0 0
\(347\) 2.86642e11i 1.06135i −0.847576 0.530674i \(-0.821939\pi\)
0.847576 0.530674i \(-0.178061\pi\)
\(348\) 0 0
\(349\) 3.54310e11 1.27841 0.639203 0.769038i \(-0.279264\pi\)
0.639203 + 0.769038i \(0.279264\pi\)
\(350\) 0 0
\(351\) 1.13782e11 0.400121
\(352\) 0 0
\(353\) 2.09491e11i 0.718092i 0.933320 + 0.359046i \(0.116898\pi\)
−0.933320 + 0.359046i \(0.883102\pi\)
\(354\) 0 0
\(355\) 1.02130e11 7.27489e10i 0.341293 0.243108i
\(356\) 0 0
\(357\) 6.27715e10i 0.204529i
\(358\) 0 0
\(359\) 2.88081e11 0.915355 0.457678 0.889118i \(-0.348681\pi\)
0.457678 + 0.889118i \(0.348681\pi\)
\(360\) 0 0
\(361\) −2.61706e11 −0.811019
\(362\) 0 0
\(363\) 8.46630e10i 0.255926i
\(364\) 0 0
\(365\) 6.16404e10 + 8.65355e10i 0.181781 + 0.255197i
\(366\) 0 0
\(367\) 1.33587e10i 0.0384387i −0.999815 0.0192193i \(-0.993882\pi\)
0.999815 0.0192193i \(-0.00611808\pi\)
\(368\) 0 0
\(369\) 3.11278e11 0.874036
\(370\) 0 0
\(371\) −3.01495e11 −0.826224
\(372\) 0 0
\(373\) 4.17763e11i 1.11748i −0.829342 0.558741i \(-0.811284\pi\)
0.829342 0.558741i \(-0.188716\pi\)
\(374\) 0 0
\(375\) −9.85687e10 + 2.89886e10i −0.257394 + 0.0756985i
\(376\) 0 0
\(377\) 2.04636e11i 0.521731i
\(378\) 0 0
\(379\) 2.63110e11 0.655031 0.327515 0.944846i \(-0.393789\pi\)
0.327515 + 0.944846i \(0.393789\pi\)
\(380\) 0 0
\(381\) −7.98374e10 −0.194108
\(382\) 0 0
\(383\) 7.84146e10i 0.186210i −0.995656 0.0931049i \(-0.970321\pi\)
0.995656 0.0931049i \(-0.0296792\pi\)
\(384\) 0 0
\(385\) −4.49337e10 6.30814e10i −0.104232 0.146328i
\(386\) 0 0
\(387\) 5.33849e11i 1.20981i
\(388\) 0 0
\(389\) −1.66007e11 −0.367581 −0.183791 0.982965i \(-0.558837\pi\)
−0.183791 + 0.982965i \(0.558837\pi\)
\(390\) 0 0
\(391\) −2.26452e11 −0.489984
\(392\) 0 0
\(393\) 2.09917e11i 0.443896i
\(394\) 0 0
\(395\) 4.67462e11 3.32980e11i 0.966184 0.688226i
\(396\) 0 0
\(397\) 4.09536e11i 0.827437i −0.910405 0.413719i \(-0.864230\pi\)
0.910405 0.413719i \(-0.135770\pi\)
\(398\) 0 0
\(399\) −4.94059e10 −0.0975889
\(400\) 0 0
\(401\) −7.92645e10 −0.153084 −0.0765419 0.997066i \(-0.524388\pi\)
−0.0765419 + 0.997066i \(0.524388\pi\)
\(402\) 0 0
\(403\) 2.62498e11i 0.495739i
\(404\) 0 0
\(405\) 3.48050e11 2.47921e11i 0.642826 0.457894i
\(406\) 0 0
\(407\) 1.46450e11i 0.264554i
\(408\) 0 0
\(409\) −6.85827e11 −1.21188 −0.605940 0.795510i \(-0.707203\pi\)
−0.605940 + 0.795510i \(0.707203\pi\)
\(410\) 0 0
\(411\) −9.68557e10 −0.167431
\(412\) 0 0
\(413\) 8.52601e11i 1.44202i
\(414\) 0 0
\(415\) −4.23222e11 5.94151e11i −0.700410 0.983288i
\(416\) 0 0
\(417\) 6.10898e10i 0.0989365i
\(418\) 0 0
\(419\) 3.31879e11 0.526037 0.263018 0.964791i \(-0.415282\pi\)
0.263018 + 0.964791i \(0.415282\pi\)
\(420\) 0 0
\(421\) −6.30694e11 −0.978475 −0.489237 0.872151i \(-0.662725\pi\)
−0.489237 + 0.872151i \(0.662725\pi\)
\(422\) 0 0
\(423\) 7.49490e11i 1.13824i
\(424\) 0 0
\(425\) 5.79148e11 + 2.00258e11i 0.861071 + 0.297742i
\(426\) 0 0
\(427\) 2.83319e11i 0.412429i
\(428\) 0 0
\(429\) −3.12607e10 −0.0445596
\(430\) 0 0
\(431\) −7.70903e11 −1.07610 −0.538049 0.842913i \(-0.680839\pi\)
−0.538049 + 0.842913i \(0.680839\pi\)
\(432\) 0 0
\(433\) 1.07829e12i 1.47415i −0.675811 0.737075i \(-0.736206\pi\)
0.675811 0.737075i \(-0.263794\pi\)
\(434\) 0 0
\(435\) 7.84060e10 + 1.10072e11i 0.104990 + 0.147393i
\(436\) 0 0
\(437\) 1.78235e11i 0.233791i
\(438\) 0 0
\(439\) −9.56419e11 −1.22902 −0.614508 0.788910i \(-0.710646\pi\)
−0.614508 + 0.788910i \(0.710646\pi\)
\(440\) 0 0
\(441\) 2.21059e11 0.278313
\(442\) 0 0
\(443\) 2.06392e11i 0.254611i 0.991864 + 0.127305i \(0.0406328\pi\)
−0.991864 + 0.127305i \(0.959367\pi\)
\(444\) 0 0
\(445\) −2.70129e11 + 1.92417e11i −0.326551 + 0.232607i
\(446\) 0 0
\(447\) 2.25250e11i 0.266858i
\(448\) 0 0
\(449\) −1.75939e11 −0.204293 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(450\) 0 0
\(451\) −1.77676e11 −0.202224
\(452\) 0 0
\(453\) 2.23995e11i 0.249918i
\(454\) 0 0
\(455\) −4.81933e11 + 3.43288e11i −0.527152 + 0.375497i
\(456\) 0 0
\(457\) 2.98819e11i 0.320469i −0.987079 0.160234i \(-0.948775\pi\)
0.987079 0.160234i \(-0.0512250\pi\)
\(458\) 0 0
\(459\) 4.48171e11 0.471288
\(460\) 0 0
\(461\) 4.39422e11 0.453135 0.226567 0.973995i \(-0.427250\pi\)
0.226567 + 0.973995i \(0.427250\pi\)
\(462\) 0 0
\(463\) 1.16254e12i 1.17569i −0.808973 0.587846i \(-0.799976\pi\)
0.808973 0.587846i \(-0.200024\pi\)
\(464\) 0 0
\(465\) −1.00576e11 1.41196e11i −0.0997595 0.140050i
\(466\) 0 0
\(467\) 1.65923e11i 0.161429i 0.996737 + 0.0807144i \(0.0257202\pi\)
−0.996737 + 0.0807144i \(0.974280\pi\)
\(468\) 0 0
\(469\) −1.49313e12 −1.42501
\(470\) 0 0
\(471\) −1.10786e11 −0.103727
\(472\) 0 0
\(473\) 3.04718e11i 0.279913i
\(474\) 0 0
\(475\) −1.57618e11 + 4.55833e11i −0.142064 + 0.410851i
\(476\) 0 0
\(477\) 1.03611e12i 0.916377i
\(478\) 0 0
\(479\) 1.33180e11 0.115592 0.0577960 0.998328i \(-0.481593\pi\)
0.0577960 + 0.998328i \(0.481593\pi\)
\(480\) 0 0
\(481\) −1.11886e12 −0.953064
\(482\) 0 0
\(483\) 1.44401e11i 0.120728i
\(484\) 0 0
\(485\) −4.89554e11 6.87273e11i −0.401756 0.564016i
\(486\) 0 0
\(487\) 1.43276e12i 1.15423i −0.816662 0.577116i \(-0.804178\pi\)
0.816662 0.577116i \(-0.195822\pi\)
\(488\) 0 0
\(489\) 1.01563e11 0.0803243
\(490\) 0 0
\(491\) 1.05688e12 0.820655 0.410327 0.911938i \(-0.365414\pi\)
0.410327 + 0.911938i \(0.365414\pi\)
\(492\) 0 0
\(493\) 8.06032e11i 0.614527i
\(494\) 0 0
\(495\) −2.16784e11 + 1.54418e11i −0.162295 + 0.115605i
\(496\) 0 0
\(497\) 4.76896e11i 0.350607i
\(498\) 0 0
\(499\) 1.77897e11 0.128445 0.0642223 0.997936i \(-0.479543\pi\)
0.0642223 + 0.997936i \(0.479543\pi\)
\(500\) 0 0
\(501\) 5.53814e11 0.392730
\(502\) 0 0
\(503\) 1.58467e12i 1.10378i 0.833917 + 0.551889i \(0.186093\pi\)
−0.833917 + 0.551889i \(0.813907\pi\)
\(504\) 0 0
\(505\) −2.31762e11 + 1.65087e11i −0.158574 + 0.112954i
\(506\) 0 0
\(507\) 1.60333e11i 0.107767i
\(508\) 0 0
\(509\) 1.93674e12 1.27891 0.639456 0.768827i \(-0.279159\pi\)
0.639456 + 0.768827i \(0.279159\pi\)
\(510\) 0 0
\(511\) −4.04076e11 −0.262162
\(512\) 0 0
\(513\) 3.52744e11i 0.224870i
\(514\) 0 0
\(515\) 7.42623e11 + 1.04255e12i 0.465196 + 0.653077i
\(516\) 0 0
\(517\) 4.27805e11i 0.263353i
\(518\) 0 0
\(519\) 5.89473e9 0.00356624
\(520\) 0 0
\(521\) 2.72419e12 1.61982 0.809912 0.586552i \(-0.199515\pi\)
0.809912 + 0.586552i \(0.199515\pi\)
\(522\) 0 0
\(523\) 4.86784e11i 0.284497i 0.989831 + 0.142249i \(0.0454333\pi\)
−0.989831 + 0.142249i \(0.954567\pi\)
\(524\) 0 0
\(525\) 1.27698e11 3.69304e11i 0.0733615 0.212162i
\(526\) 0 0
\(527\) 1.03394e12i 0.583912i
\(528\) 0 0
\(529\) 1.28021e12 0.710775
\(530\) 0 0
\(531\) 2.93003e12 1.59936
\(532\) 0 0
\(533\) 1.35742e12i 0.728520i
\(534\) 0 0
\(535\) −1.34788e12 1.89225e12i −0.711309 0.998590i
\(536\) 0 0
\(537\) 2.01572e11i 0.104603i
\(538\) 0 0
\(539\) −1.26179e11 −0.0643929
\(540\) 0 0
\(541\) 1.98233e11 0.0994920 0.0497460 0.998762i \(-0.484159\pi\)
0.0497460 + 0.998762i \(0.484159\pi\)
\(542\) 0 0
\(543\) 5.72543e10i 0.0282624i
\(544\) 0 0
\(545\) −1.97107e12 + 1.40402e12i −0.957014 + 0.681694i
\(546\) 0 0
\(547\) 4.79532e11i 0.229021i 0.993422 + 0.114510i \(0.0365299\pi\)
−0.993422 + 0.114510i \(0.963470\pi\)
\(548\) 0 0
\(549\) 9.73647e11 0.457432
\(550\) 0 0
\(551\) 6.34408e11 0.293215
\(552\) 0 0
\(553\) 2.18281e12i 0.992550i
\(554\) 0 0
\(555\) 6.01825e11 4.28688e11i 0.269248 0.191789i
\(556\) 0 0
\(557\) 1.20856e11i 0.0532011i 0.999646 + 0.0266006i \(0.00846822\pi\)
−0.999646 + 0.0266006i \(0.991532\pi\)
\(558\) 0 0
\(559\) −2.32801e12 −1.00840
\(560\) 0 0
\(561\) −1.23131e11 −0.0524851
\(562\) 0 0
\(563\) 1.01468e12i 0.425637i −0.977092 0.212818i \(-0.931736\pi\)
0.977092 0.212818i \(-0.0682643\pi\)
\(564\) 0 0
\(565\) −5.11591e11 7.18210e11i −0.211205 0.296506i
\(566\) 0 0
\(567\) 1.62521e12i 0.660369i
\(568\) 0 0
\(569\) −1.12630e12 −0.450454 −0.225227 0.974306i \(-0.572312\pi\)
−0.225227 + 0.974306i \(0.572312\pi\)
\(570\) 0 0
\(571\) 2.75478e12 1.08449 0.542243 0.840221i \(-0.317575\pi\)
0.542243 + 0.840221i \(0.317575\pi\)
\(572\) 0 0
\(573\) 3.49405e11i 0.135405i
\(574\) 0 0
\(575\) 1.33229e12 + 4.60680e11i 0.508269 + 0.175750i
\(576\) 0 0
\(577\) 4.14763e12i 1.55779i −0.627155 0.778895i \(-0.715781\pi\)
0.627155 0.778895i \(-0.284219\pi\)
\(578\) 0 0
\(579\) −2.61358e11 −0.0966458
\(580\) 0 0
\(581\) 2.77438e12 1.01012
\(582\) 0 0
\(583\) 5.91408e11i 0.212021i
\(584\) 0 0
\(585\) 1.17974e12 + 1.65620e12i 0.416470 + 0.584672i
\(586\) 0 0
\(587\) 1.38017e12i 0.479800i 0.970798 + 0.239900i \(0.0771147\pi\)
−0.970798 + 0.239900i \(0.922885\pi\)
\(588\) 0 0
\(589\) −8.13789e11 −0.278608
\(590\) 0 0
\(591\) 1.35778e12 0.457811
\(592\) 0 0
\(593\) 6.90406e11i 0.229276i −0.993407 0.114638i \(-0.963429\pi\)
0.993407 0.114638i \(-0.0365708\pi\)
\(594\) 0 0
\(595\) −1.89827e12 + 1.35216e12i −0.620913 + 0.442285i
\(596\) 0 0
\(597\) 8.47568e11i 0.273080i
\(598\) 0 0
\(599\) 1.24239e12 0.394309 0.197155 0.980372i \(-0.436830\pi\)
0.197155 + 0.980372i \(0.436830\pi\)
\(600\) 0 0
\(601\) 2.01140e12 0.628873 0.314437 0.949278i \(-0.398184\pi\)
0.314437 + 0.949278i \(0.398184\pi\)
\(602\) 0 0
\(603\) 5.13126e12i 1.58050i
\(604\) 0 0
\(605\) −2.56028e12 + 1.82373e12i −0.776943 + 0.553427i
\(606\) 0 0
\(607\) 2.73579e12i 0.817963i −0.912543 0.408981i \(-0.865884\pi\)
0.912543 0.408981i \(-0.134116\pi\)
\(608\) 0 0
\(609\) −5.13981e11 −0.151415
\(610\) 0 0
\(611\) 3.26838e12 0.948738
\(612\) 0 0
\(613\) 1.63707e12i 0.468269i 0.972204 + 0.234135i \(0.0752257\pi\)
−0.972204 + 0.234135i \(0.924774\pi\)
\(614\) 0 0
\(615\) −5.20093e11 7.30146e11i −0.146603 0.205812i
\(616\) 0 0
\(617\) 1.22267e12i 0.339646i 0.985475 + 0.169823i \(0.0543197\pi\)
−0.985475 + 0.169823i \(0.945680\pi\)
\(618\) 0 0
\(619\) −5.78784e12 −1.58456 −0.792280 0.610158i \(-0.791106\pi\)
−0.792280 + 0.610158i \(0.791106\pi\)
\(620\) 0 0
\(621\) 1.03099e12 0.278190
\(622\) 0 0
\(623\) 1.26136e12i 0.335463i
\(624\) 0 0
\(625\) −2.99991e12 2.35636e12i −0.786409 0.617706i
\(626\) 0 0
\(627\) 9.69138e10i 0.0250427i
\(628\) 0 0
\(629\) −4.40702e12 −1.12258
\(630\) 0 0
\(631\) −2.00341e12 −0.503081 −0.251540 0.967847i \(-0.580937\pi\)
−0.251540 + 0.967847i \(0.580937\pi\)
\(632\) 0 0
\(633\) 1.36372e12i 0.337605i
\(634\) 0 0
\(635\) −1.71978e12 2.41435e12i −0.419750 0.589277i
\(636\) 0 0
\(637\) 9.63992e11i 0.231978i
\(638\) 0 0
\(639\) 1.63889e12 0.388863
\(640\) 0 0
\(641\) 2.75478e12 0.644505 0.322253 0.946654i \(-0.395560\pi\)
0.322253 + 0.946654i \(0.395560\pi\)
\(642\) 0 0
\(643\) 7.38857e12i 1.70455i −0.523091 0.852277i \(-0.675221\pi\)
0.523091 0.852277i \(-0.324779\pi\)
\(644\) 0 0
\(645\) 1.25222e12 8.91972e11i 0.284879 0.202924i
\(646\) 0 0
\(647\) 4.12045e12i 0.924432i −0.886767 0.462216i \(-0.847054\pi\)
0.886767 0.462216i \(-0.152946\pi\)
\(648\) 0 0
\(649\) −1.67245e12 −0.370043
\(650\) 0 0
\(651\) 6.59311e11 0.143872
\(652\) 0 0
\(653\) 6.51407e12i 1.40198i −0.713170 0.700992i \(-0.752741\pi\)
0.713170 0.700992i \(-0.247259\pi\)
\(654\) 0 0
\(655\) −6.34807e12 + 4.52182e12i −1.34758 + 0.959903i
\(656\) 0 0
\(657\) 1.38864e12i 0.290767i
\(658\) 0 0
\(659\) −1.74145e12 −0.359688 −0.179844 0.983695i \(-0.557559\pi\)
−0.179844 + 0.983695i \(0.557559\pi\)
\(660\) 0 0
\(661\) −1.39849e12 −0.284939 −0.142469 0.989799i \(-0.545504\pi\)
−0.142469 + 0.989799i \(0.545504\pi\)
\(662\) 0 0
\(663\) 9.40708e11i 0.189079i
\(664\) 0 0
\(665\) −1.06425e12 1.49408e12i −0.211031 0.296262i
\(666\) 0 0
\(667\) 1.85422e12i 0.362740i
\(668\) 0 0
\(669\) 1.85882e12 0.358774
\(670\) 0 0
\(671\) −5.55753e11 −0.105835
\(672\) 0 0
\(673\) 7.23077e12i 1.35868i −0.733824 0.679340i \(-0.762266\pi\)
0.733824 0.679340i \(-0.237734\pi\)
\(674\) 0 0
\(675\) −2.63673e12 9.11730e11i −0.488876 0.169044i
\(676\) 0 0
\(677\) 1.09854e12i 0.200986i 0.994938 + 0.100493i \(0.0320419\pi\)
−0.994938 + 0.100493i \(0.967958\pi\)
\(678\) 0 0
\(679\) 3.20921e12 0.579408
\(680\) 0 0
\(681\) −1.23352e12 −0.219779
\(682\) 0 0
\(683\) 1.51781e12i 0.266885i 0.991057 + 0.133442i \(0.0426031\pi\)
−0.991057 + 0.133442i \(0.957397\pi\)
\(684\) 0 0
\(685\) −2.08637e12 2.92900e12i −0.362063 0.508291i
\(686\) 0 0
\(687\) 5.10355e11i 0.0874112i
\(688\) 0 0
\(689\) −4.51828e12 −0.763812
\(690\) 0 0
\(691\) −1.51489e12 −0.252772 −0.126386 0.991981i \(-0.540338\pi\)
−0.126386 + 0.991981i \(0.540338\pi\)
\(692\) 0 0
\(693\) 1.01227e12i 0.166724i
\(694\) 0 0
\(695\) −1.84741e12 + 1.31594e12i −0.300353 + 0.213946i
\(696\) 0 0
\(697\) 5.34668e12i 0.858097i
\(698\) 0 0
\(699\) 3.01064e11 0.0476993
\(700\) 0 0
\(701\) 7.62368e12 1.19243 0.596216 0.802824i \(-0.296670\pi\)
0.596216 + 0.802824i \(0.296670\pi\)
\(702\) 0 0
\(703\) 3.46866e12i 0.535627i
\(704\) 0 0
\(705\) −1.75804e12 + 1.25227e12i −0.268026 + 0.190918i
\(706\) 0 0
\(707\) 1.08221e12i 0.162901i
\(708\) 0 0
\(709\) −1.00657e13 −1.49602 −0.748010 0.663687i \(-0.768991\pi\)
−0.748010 + 0.663687i \(0.768991\pi\)
\(710\) 0 0
\(711\) 7.50140e12 1.10085
\(712\) 0 0
\(713\) 2.37851e12i 0.344669i
\(714\) 0 0
\(715\) −6.73388e11 9.45353e11i −0.0963580 0.135275i
\(716\) 0 0
\(717\) 3.12496e12i 0.441579i
\(718\) 0 0
\(719\) 8.94464e12 1.24820 0.624098 0.781346i \(-0.285466\pi\)
0.624098 + 0.781346i \(0.285466\pi\)
\(720\) 0 0
\(721\) −4.86817e12 −0.670899
\(722\) 0 0
\(723\) 2.27647e12i 0.309841i
\(724\) 0 0
\(725\) −1.63974e12 + 4.74214e12i −0.220422 + 0.637460i
\(726\) 0 0
\(727\) 1.22168e13i 1.62201i 0.585038 + 0.811006i \(0.301079\pi\)
−0.585038 + 0.811006i \(0.698921\pi\)
\(728\) 0 0
\(729\) 4.52688e12 0.593642
\(730\) 0 0
\(731\) −9.16968e12 −1.18775
\(732\) 0 0
\(733\) 1.44452e13i 1.84823i 0.382118 + 0.924114i \(0.375195\pi\)
−0.382118 + 0.924114i \(0.624805\pi\)
\(734\) 0 0
\(735\) −3.69352e11 5.18524e11i −0.0466818 0.0655354i
\(736\) 0 0
\(737\) 2.92889e12i 0.365679i
\(738\) 0 0
\(739\) −1.11591e13 −1.37635 −0.688175 0.725545i \(-0.741588\pi\)
−0.688175 + 0.725545i \(0.741588\pi\)
\(740\) 0 0
\(741\) −7.40409e11 −0.0902172
\(742\) 0 0
\(743\) 9.35882e12i 1.12660i 0.826251 + 0.563302i \(0.190469\pi\)
−0.826251 + 0.563302i \(0.809531\pi\)
\(744\) 0 0
\(745\) 6.81176e12 4.85211e12i 0.810133 0.577069i
\(746\) 0 0
\(747\) 9.53439e12i 1.12034i
\(748\) 0 0
\(749\) 8.83585e12 1.02584
\(750\) 0 0
\(751\) 1.28609e13 1.47533 0.737667 0.675165i \(-0.235928\pi\)
0.737667 + 0.675165i \(0.235928\pi\)
\(752\) 0 0
\(753\) 3.94028e12i 0.446632i
\(754\) 0 0
\(755\) 6.77382e12 4.82509e12i 0.758704 0.540435i
\(756\) 0 0
\(757\) 1.42250e13i 1.57442i −0.616684 0.787211i \(-0.711524\pi\)
0.616684 0.787211i \(-0.288476\pi\)
\(758\) 0 0
\(759\) −2.83256e11 −0.0309807
\(760\) 0 0
\(761\) 1.65722e13 1.79122 0.895610 0.444841i \(-0.146740\pi\)
0.895610 + 0.444841i \(0.146740\pi\)
\(762\) 0 0
\(763\) 9.20389e12i 0.983130i
\(764\) 0 0
\(765\) 4.64681e12 + 6.52354e12i 0.490545 + 0.688664i
\(766\) 0 0
\(767\) 1.27773e13i 1.33309i
\(768\) 0 0
\(769\) −2.81269e12 −0.290037 −0.145019 0.989429i \(-0.546324\pi\)
−0.145019 + 0.989429i \(0.546324\pi\)
\(770\) 0 0
\(771\) −2.98397e12 −0.304123
\(772\) 0 0
\(773\) 8.57982e12i 0.864311i −0.901799 0.432156i \(-0.857753\pi\)
0.901799 0.432156i \(-0.142247\pi\)
\(774\) 0 0
\(775\) 2.10338e12 6.08299e12i 0.209440 0.605703i
\(776\) 0 0
\(777\) 2.81021e12i 0.276595i
\(778\) 0 0
\(779\) −4.20824e12 −0.409432
\(780\) 0 0
\(781\) −9.35472e11 −0.0899707
\(782\) 0 0
\(783\) 3.66968e12i 0.348900i
\(784\) 0 0
\(785\) −2.38644e12 3.35027e12i −0.224304 0.314895i
\(786\) 0 0
\(787\) 1.75771e12i 0.163328i −0.996660 0.0816642i \(-0.973976\pi\)
0.996660 0.0816642i \(-0.0260235\pi\)
\(788\) 0 0
\(789\) −3.93830e9 −0.000361795
\(790\) 0 0
\(791\) 3.35367e12 0.304597
\(792\) 0 0
\(793\) 4.24588e12i 0.381275i
\(794\) 0 0
\(795\) 2.43035e12 1.73117e12i 0.215783 0.153705i
\(796\) 0 0
\(797\) 2.27115e13i 1.99381i 0.0786130 + 0.996905i \(0.474951\pi\)
−0.0786130 + 0.996905i \(0.525049\pi\)
\(798\) 0 0
\(799\) 1.28737e13 1.11748
\(800\) 0 0
\(801\) −4.33478e12 −0.372067