Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −44.2174 | −0.488538 | −0.244269 | − | 0.969708i | \(-0.578548\pi\) | ||||
−0.244269 | + | 0.969708i | \(0.578548\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −6236.82 | −0.761331 | ||||||||
\(5\) | 14897.9 | 0.426402 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(6\) | −32234.5 | −0.282057 | ||||||||
\(7\) | 473501. | 1.52119 | 0.760595 | − | 0.649227i | \(-0.224907\pi\) | ||||
0.760595 | + | 0.649227i | \(0.224907\pi\) | |||||||
\(8\) | 638005. | 0.860477 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −658745. | −0.208313 | ||||||||
\(11\) | −5.62449e6 | −0.957262 | −0.478631 | − | 0.878016i | \(-0.658867\pi\) | ||||
−0.478631 | + | 0.878016i | \(0.658867\pi\) | |||||||
\(12\) | −4.54664e6 | −0.439555 | ||||||||
\(13\) | −1.37488e7 | −0.790014 | −0.395007 | − | 0.918678i | \(-0.629258\pi\) | ||||
−0.395007 | + | 0.918678i | \(0.629258\pi\) | |||||||
\(14\) | −2.09370e7 | −0.743159 | ||||||||
\(15\) | 1.08605e7 | 0.246183 | ||||||||
\(16\) | 2.28811e7 | 0.340956 | ||||||||
\(17\) | 1.90754e8 | 1.91670 | 0.958352 | − | 0.285588i | \(-0.0921890\pi\) | ||||
0.958352 | + | 0.285588i | \(0.0921890\pi\) | |||||||
\(18\) | −2.34989e7 | −0.162846 | ||||||||
\(19\) | −2.39269e8 | −1.16678 | −0.583388 | − | 0.812194i | \(-0.698273\pi\) | ||||
−0.583388 | + | 0.812194i | \(0.698273\pi\) | |||||||
\(20\) | −9.29153e7 | −0.324633 | ||||||||
\(21\) | 3.45182e8 | 0.878259 | ||||||||
\(22\) | 2.48700e8 | 0.467659 | ||||||||
\(23\) | 8.48230e8 | 1.19477 | 0.597383 | − | 0.801956i | \(-0.296207\pi\) | ||||
0.597383 | + | 0.801956i | \(0.296207\pi\) | |||||||
\(24\) | 4.65106e8 | 0.496796 | ||||||||
\(25\) | −9.98757e8 | −0.818182 | ||||||||
\(26\) | 6.07938e8 | 0.385951 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −2.95314e9 | −1.15813 | ||||||||
\(29\) | −2.26512e9 | −0.707137 | −0.353568 | − | 0.935409i | \(-0.615032\pi\) | ||||
−0.353568 | + | 0.935409i | \(0.615032\pi\) | |||||||
\(30\) | −4.80225e8 | −0.120270 | ||||||||
\(31\) | 6.87064e8 | 0.139042 | 0.0695210 | − | 0.997580i | \(-0.477853\pi\) | ||||
0.0695210 | + | 0.997580i | \(0.477853\pi\) | |||||||
\(32\) | −6.23828e9 | −1.02705 | ||||||||
\(33\) | −4.10025e9 | −0.552676 | ||||||||
\(34\) | −8.43464e9 | −0.936383 | ||||||||
\(35\) | 7.05415e9 | 0.648638 | ||||||||
\(36\) | −3.31450e9 | −0.253777 | ||||||||
\(37\) | −1.85095e10 | −1.18599 | −0.592997 | − | 0.805205i | \(-0.702055\pi\) | ||||
−0.592997 | + | 0.805205i | \(0.702055\pi\) | |||||||
\(38\) | 1.05798e10 | 0.570014 | ||||||||
\(39\) | −1.00229e10 | −0.456115 | ||||||||
\(40\) | 9.50491e9 | 0.366909 | ||||||||
\(41\) | −2.65666e10 | −0.873456 | −0.436728 | − | 0.899593i | \(-0.643863\pi\) | ||||
−0.436728 | + | 0.899593i | \(0.643863\pi\) | |||||||
\(42\) | −1.52630e10 | −0.429063 | ||||||||
\(43\) | −8.00165e10 | −1.93034 | −0.965172 | − | 0.261617i | \(-0.915744\pi\) | ||||
−0.965172 | + | 0.261617i | \(0.915744\pi\) | |||||||
\(44\) | 3.50790e10 | 0.728793 | ||||||||
\(45\) | 7.91734e9 | 0.142134 | ||||||||
\(46\) | −3.75065e10 | −0.583688 | ||||||||
\(47\) | −1.28932e11 | −1.74471 | −0.872357 | − | 0.488869i | \(-0.837410\pi\) | ||||
−0.872357 | + | 0.488869i | \(0.837410\pi\) | |||||||
\(48\) | 1.66804e10 | 0.196851 | ||||||||
\(49\) | 1.27314e11 | 1.31402 | ||||||||
\(50\) | 4.41624e10 | 0.399713 | ||||||||
\(51\) | 1.39060e11 | 1.10661 | ||||||||
\(52\) | 8.57491e10 | 0.601462 | ||||||||
\(53\) | 2.46479e11 | 1.52752 | 0.763760 | − | 0.645500i | \(-0.223351\pi\) | ||||
0.763760 | + | 0.645500i | \(0.223351\pi\) | |||||||
\(54\) | −1.71307e10 | −0.0940191 | ||||||||
\(55\) | −8.37929e10 | −0.408178 | ||||||||
\(56\) | 3.02096e11 | 1.30895 | ||||||||
\(57\) | −1.74427e11 | −0.673638 | ||||||||
\(58\) | 1.00157e11 | 0.345463 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | −6.77353e10 | −0.187427 | ||||||||
\(61\) | 6.06790e11 | 1.50798 | 0.753989 | − | 0.656888i | \(-0.228127\pi\) | ||||
0.753989 | + | 0.656888i | \(0.228127\pi\) | |||||||
\(62\) | −3.03802e10 | −0.0679272 | ||||||||
\(63\) | 2.51638e11 | 0.507063 | ||||||||
\(64\) | 8.83981e10 | 0.160795 | ||||||||
\(65\) | −2.04828e11 | −0.336863 | ||||||||
\(66\) | 1.81303e11 | 0.270003 | ||||||||
\(67\) | 1.30921e11 | 0.176817 | 0.0884086 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884086 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(68\) | −1.18970e12 | −1.45925 | ||||||||
\(69\) | 6.18360e11 | 0.689798 | ||||||||
\(70\) | −3.11916e11 | −0.316884 | ||||||||
\(71\) | −1.05368e12 | −0.976175 | −0.488088 | − | 0.872795i | \(-0.662305\pi\) | ||||
−0.488088 | + | 0.872795i | \(0.662305\pi\) | |||||||
\(72\) | 3.39062e11 | 0.286826 | ||||||||
\(73\) | −1.45214e12 | −1.12308 | −0.561538 | − | 0.827451i | \(-0.689790\pi\) | ||||
−0.561538 | + | 0.827451i | \(0.689790\pi\) | |||||||
\(74\) | 8.18440e11 | 0.579403 | ||||||||
\(75\) | −7.28094e11 | −0.472377 | ||||||||
\(76\) | 1.49228e12 | 0.888303 | ||||||||
\(77\) | −2.66320e12 | −1.45618 | ||||||||
\(78\) | 4.43187e11 | 0.222829 | ||||||||
\(79\) | 9.47431e10 | 0.0438502 | 0.0219251 | − | 0.999760i | \(-0.493020\pi\) | ||||
0.0219251 | + | 0.999760i | \(0.493020\pi\) | |||||||
\(80\) | 3.40880e11 | 0.145384 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 1.17471e12 | 0.426716 | ||||||||
\(83\) | 4.49947e12 | 1.51062 | 0.755308 | − | 0.655370i | \(-0.227487\pi\) | ||||
0.755308 | + | 0.655370i | \(0.227487\pi\) | |||||||
\(84\) | −2.15284e12 | −0.668646 | ||||||||
\(85\) | 2.84182e12 | 0.817286 | ||||||||
\(86\) | 3.53812e12 | 0.943046 | ||||||||
\(87\) | −1.65127e12 | −0.408265 | ||||||||
\(88\) | −3.58845e12 | −0.823702 | ||||||||
\(89\) | 4.97158e11 | 0.106038 | 0.0530188 | − | 0.998594i | \(-0.483116\pi\) | ||||
0.0530188 | + | 0.998594i | \(0.483116\pi\) | |||||||
\(90\) | −3.50084e11 | −0.0694378 | ||||||||
\(91\) | −6.51009e12 | −1.20176 | ||||||||
\(92\) | −5.29026e12 | −0.909612 | ||||||||
\(93\) | 5.00869e11 | 0.0802759 | ||||||||
\(94\) | 5.70103e12 | 0.852359 | ||||||||
\(95\) | −3.56459e12 | −0.497515 | ||||||||
\(96\) | −4.54771e12 | −0.592965 | ||||||||
\(97\) | −1.63570e12 | −0.199382 | −0.0996911 | − | 0.995018i | \(-0.531785\pi\) | ||||
−0.0996911 | + | 0.995018i | \(0.531785\pi\) | |||||||
\(98\) | −5.62949e12 | −0.641947 | ||||||||
\(99\) | −2.98909e12 | −0.319087 | ||||||||
\(100\) | 6.22907e12 | 0.622907 | ||||||||
\(101\) | 7.02588e12 | 0.658585 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(102\) | −6.14885e12 | −0.540621 | ||||||||
\(103\) | −6.28234e12 | −0.518417 | −0.259209 | − | 0.965821i | \(-0.583462\pi\) | ||||
−0.259209 | + | 0.965821i | \(0.583462\pi\) | |||||||
\(104\) | −8.77183e12 | −0.679788 | ||||||||
\(105\) | 5.14247e12 | 0.374491 | ||||||||
\(106\) | −1.08987e13 | −0.746251 | ||||||||
\(107\) | −2.66456e12 | −0.171645 | −0.0858223 | − | 0.996310i | \(-0.527352\pi\) | ||||
−0.0858223 | + | 0.996310i | \(0.527352\pi\) | |||||||
\(108\) | −2.41627e12 | −0.146518 | ||||||||
\(109\) | 2.75266e13 | 1.57210 | 0.786050 | − | 0.618163i | \(-0.212123\pi\) | ||||
0.786050 | + | 0.618163i | \(0.212123\pi\) | |||||||
\(110\) | 3.70510e12 | 0.199410 | ||||||||
\(111\) | −1.34934e13 | −0.684734 | ||||||||
\(112\) | 1.08342e13 | 0.518658 | ||||||||
\(113\) | 5.68272e12 | 0.256771 | 0.128386 | − | 0.991724i | \(-0.459021\pi\) | ||||
0.128386 | + | 0.991724i | \(0.459021\pi\) | |||||||
\(114\) | 7.71270e12 | 0.329098 | ||||||||
\(115\) | 1.26368e13 | 0.509450 | ||||||||
\(116\) | 1.41271e13 | 0.538365 | ||||||||
\(117\) | −7.30670e12 | −0.263338 | ||||||||
\(118\) | −1.86511e12 | −0.0636022 | ||||||||
\(119\) | 9.03221e13 | 2.91567 | ||||||||
\(120\) | 6.92908e12 | 0.211835 | ||||||||
\(121\) | −2.88780e12 | −0.0836492 | ||||||||
\(122\) | −2.68307e13 | −0.736704 | ||||||||
\(123\) | −1.93671e13 | −0.504290 | ||||||||
\(124\) | −4.28509e12 | −0.105857 | ||||||||
\(125\) | −3.30652e13 | −0.775276 | ||||||||
\(126\) | −1.11268e13 | −0.247720 | ||||||||
\(127\) | −3.37035e13 | −0.712773 | −0.356386 | − | 0.934339i | \(-0.615991\pi\) | ||||
−0.356386 | + | 0.934339i | \(0.615991\pi\) | |||||||
\(128\) | 4.71953e13 | 0.948492 | ||||||||
\(129\) | −5.83320e13 | −1.11448 | ||||||||
\(130\) | 9.05698e12 | 0.164570 | ||||||||
\(131\) | 4.65155e13 | 0.804144 | 0.402072 | − | 0.915608i | \(-0.368290\pi\) | ||||
0.402072 | + | 0.915608i | \(0.368290\pi\) | |||||||
\(132\) | 2.55726e13 | 0.420769 | ||||||||
\(133\) | −1.13294e14 | −1.77489 | ||||||||
\(134\) | −5.78900e12 | −0.0863818 | ||||||||
\(135\) | 5.77174e12 | 0.0820611 | ||||||||
\(136\) | 1.21702e14 | 1.64928 | ||||||||
\(137\) | −1.23746e14 | −1.59900 | −0.799498 | − | 0.600669i | \(-0.794901\pi\) | ||||
−0.799498 | + | 0.600669i | \(0.794901\pi\) | |||||||
\(138\) | −2.73423e13 | −0.336993 | ||||||||
\(139\) | 1.38699e13 | 0.163108 | 0.0815541 | − | 0.996669i | \(-0.474012\pi\) | ||||
0.0815541 | + | 0.996669i | \(0.474012\pi\) | |||||||
\(140\) | −4.39955e13 | −0.493828 | ||||||||
\(141\) | −9.39914e13 | −1.00731 | ||||||||
\(142\) | 4.65908e13 | 0.476899 | ||||||||
\(143\) | 7.73303e13 | 0.756250 | ||||||||
\(144\) | 1.21600e13 | 0.113652 | ||||||||
\(145\) | −3.37454e13 | −0.301524 | ||||||||
\(146\) | 6.42098e13 | 0.548665 | ||||||||
\(147\) | 9.28118e13 | 0.758649 | ||||||||
\(148\) | 1.15440e14 | 0.902934 | ||||||||
\(149\) | −8.35651e13 | −0.625625 | −0.312813 | − | 0.949815i | \(-0.601271\pi\) | ||||
−0.312813 | + | 0.949815i | \(0.601271\pi\) | |||||||
\(150\) | 3.21944e13 | 0.230774 | ||||||||
\(151\) | −5.63763e13 | −0.387032 | −0.193516 | − | 0.981097i | \(-0.561989\pi\) | ||||
−0.193516 | + | 0.981097i | \(0.561989\pi\) | |||||||
\(152\) | −1.52655e14 | −1.00398 | ||||||||
\(153\) | 1.01374e14 | 0.638902 | ||||||||
\(154\) | 1.17760e14 | 0.711398 | ||||||||
\(155\) | 1.02358e13 | 0.0592877 | ||||||||
\(156\) | 6.25111e13 | 0.347254 | ||||||||
\(157\) | 7.91560e12 | 0.0421829 | 0.0210914 | − | 0.999778i | \(-0.493286\pi\) | ||||
0.0210914 | + | 0.999778i | \(0.493286\pi\) | |||||||
\(158\) | −4.18929e12 | −0.0214225 | ||||||||
\(159\) | 1.79683e14 | 0.881914 | ||||||||
\(160\) | −9.29370e13 | −0.437934 | ||||||||
\(161\) | 4.01638e14 | 1.81747 | ||||||||
\(162\) | −1.24883e13 | −0.0542820 | ||||||||
\(163\) | −1.46318e13 | −0.0611053 | −0.0305526 | − | 0.999533i | \(-0.509727\pi\) | ||||
−0.0305526 | + | 0.999533i | \(0.509727\pi\) | |||||||
\(164\) | 1.65691e14 | 0.664989 | ||||||||
\(165\) | −6.10850e13 | −0.235662 | ||||||||
\(166\) | −1.98955e14 | −0.737993 | ||||||||
\(167\) | −2.35885e14 | −0.841479 | −0.420739 | − | 0.907182i | \(-0.638229\pi\) | ||||
−0.420739 | + | 0.907182i | \(0.638229\pi\) | |||||||
\(168\) | 2.20228e14 | 0.755722 | ||||||||
\(169\) | −1.13844e14 | −0.375879 | ||||||||
\(170\) | −1.25658e14 | −0.399275 | ||||||||
\(171\) | −1.27157e14 | −0.388925 | ||||||||
\(172\) | 4.99049e14 | 1.46963 | ||||||||
\(173\) | −9.02605e13 | −0.255975 | −0.127988 | − | 0.991776i | \(-0.540852\pi\) | ||||
−0.127988 | + | 0.991776i | \(0.540852\pi\) | |||||||
\(174\) | 7.30148e13 | 0.199453 | ||||||||
\(175\) | −4.72912e14 | −1.24461 | ||||||||
\(176\) | −1.28695e14 | −0.326384 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −2.19830e13 | −0.0518033 | ||||||||
\(179\) | −4.73759e14 | −1.07650 | −0.538248 | − | 0.842787i | \(-0.680914\pi\) | ||||
−0.538248 | + | 0.842787i | \(0.680914\pi\) | |||||||
\(180\) | −4.93790e13 | −0.108211 | ||||||||
\(181\) | −3.94362e14 | −0.833652 | −0.416826 | − | 0.908986i | \(-0.636858\pi\) | ||||
−0.416826 | + | 0.908986i | \(0.636858\pi\) | |||||||
\(182\) | 2.87859e14 | 0.587105 | ||||||||
\(183\) | 4.42350e14 | 0.870631 | ||||||||
\(184\) | 5.41175e14 | 1.02807 | ||||||||
\(185\) | −2.75751e14 | −0.505710 | ||||||||
\(186\) | −2.21471e13 | −0.0392178 | ||||||||
\(187\) | −1.07289e15 | −1.83479 | ||||||||
\(188\) | 8.04126e14 | 1.32831 | ||||||||
\(189\) | 1.83444e14 | 0.292753 | ||||||||
\(190\) | 1.57617e14 | 0.243055 | ||||||||
\(191\) | 1.12171e15 | 1.67172 | 0.835860 | − | 0.548943i | \(-0.184969\pi\) | ||||
0.835860 | + | 0.548943i | \(0.184969\pi\) | |||||||
\(192\) | 6.44422e13 | 0.0928352 | ||||||||
\(193\) | −9.55941e14 | −1.33140 | −0.665700 | − | 0.746219i | \(-0.731867\pi\) | ||||
−0.665700 | + | 0.746219i | \(0.731867\pi\) | |||||||
\(194\) | 7.23262e13 | 0.0974058 | ||||||||
\(195\) | −1.49320e14 | −0.194488 | ||||||||
\(196\) | −7.94034e14 | −1.00040 | ||||||||
\(197\) | 1.29129e15 | 1.57395 | 0.786976 | − | 0.616983i | \(-0.211645\pi\) | ||||
0.786976 | + | 0.616983i | \(0.211645\pi\) | |||||||
\(198\) | 1.32170e14 | 0.155886 | ||||||||
\(199\) | −2.34104e14 | −0.267217 | −0.133609 | − | 0.991034i | \(-0.542657\pi\) | ||||
−0.133609 | + | 0.991034i | \(0.542657\pi\) | |||||||
\(200\) | −6.37212e14 | −0.704026 | ||||||||
\(201\) | 9.54417e13 | 0.102085 | ||||||||
\(202\) | −3.10666e14 | −0.321744 | ||||||||
\(203\) | −1.07253e15 | −1.07569 | ||||||||
\(204\) | −8.67290e14 | −0.842496 | ||||||||
\(205\) | −3.95786e14 | −0.372443 | ||||||||
\(206\) | 2.77789e14 | 0.253266 | ||||||||
\(207\) | 4.50784e14 | 0.398255 | ||||||||
\(208\) | −3.14589e14 | −0.269360 | ||||||||
\(209\) | 1.34576e15 | 1.11691 | ||||||||
\(210\) | −2.27387e14 | −0.182953 | ||||||||
\(211\) | −2.23736e15 | −1.74542 | −0.872709 | − | 0.488241i | \(-0.837639\pi\) | ||||
−0.872709 | + | 0.488241i | \(0.837639\pi\) | |||||||
\(212\) | −1.53725e15 | −1.16295 | ||||||||
\(213\) | −7.68130e14 | −0.563595 | ||||||||
\(214\) | 1.17820e14 | 0.0838549 | ||||||||
\(215\) | −1.19208e15 | −0.823102 | ||||||||
\(216\) | 2.47176e14 | 0.165599 | ||||||||
\(217\) | 3.25325e14 | 0.211509 | ||||||||
\(218\) | −1.21715e15 | −0.768030 | ||||||||
\(219\) | −1.05861e15 | −0.648409 | ||||||||
\(220\) | 5.22602e14 | 0.310759 | ||||||||
\(221\) | −2.62265e15 | −1.51422 | ||||||||
\(222\) | 5.96643e14 | 0.334518 | ||||||||
\(223\) | −3.19039e15 | −1.73725 | −0.868626 | − | 0.495468i | \(-0.834996\pi\) | ||||
−0.868626 | + | 0.495468i | \(0.834996\pi\) | |||||||
\(224\) | −2.95383e15 | −1.56233 | ||||||||
\(225\) | −5.30780e14 | −0.272727 | ||||||||
\(226\) | −2.51275e14 | −0.125442 | ||||||||
\(227\) | −6.78365e14 | −0.329075 | −0.164538 | − | 0.986371i | \(-0.552613\pi\) | ||||
−0.164538 | + | 0.986371i | \(0.552613\pi\) | |||||||
\(228\) | 1.08787e15 | 0.512862 | ||||||||
\(229\) | 2.07816e15 | 0.952245 | 0.476123 | − | 0.879379i | \(-0.342042\pi\) | ||||
0.476123 | + | 0.879379i | \(0.342042\pi\) | |||||||
\(230\) | −5.58767e14 | −0.248886 | ||||||||
\(231\) | −1.94147e15 | −0.840724 | ||||||||
\(232\) | −1.44515e15 | −0.608474 | ||||||||
\(233\) | 8.65199e13 | 0.0354244 | 0.0177122 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177122 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(234\) | 3.23083e14 | 0.128650 | ||||||||
\(235\) | −1.92081e15 | −0.743949 | ||||||||
\(236\) | −2.63073e14 | −0.0991168 | ||||||||
\(237\) | 6.90677e13 | 0.0253169 | ||||||||
\(238\) | −3.99381e15 | −1.42442 | ||||||||
\(239\) | −2.97537e15 | −1.03265 | −0.516326 | − | 0.856392i | \(-0.672701\pi\) | ||||
−0.516326 | + | 0.856392i | \(0.672701\pi\) | |||||||
\(240\) | 2.48502e14 | 0.0839375 | ||||||||
\(241\) | 1.38612e15 | 0.455710 | 0.227855 | − | 0.973695i | \(-0.426829\pi\) | ||||
0.227855 | + | 0.973695i | \(0.426829\pi\) | |||||||
\(242\) | 1.27691e14 | 0.0408658 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −3.78444e15 | −1.14807 | ||||||||
\(245\) | 1.89671e15 | 0.560300 | ||||||||
\(246\) | 8.56361e14 | 0.246365 | ||||||||
\(247\) | 3.28967e15 | 0.921769 | ||||||||
\(248\) | 4.38350e14 | 0.119642 | ||||||||
\(249\) | 3.28012e15 | 0.872154 | ||||||||
\(250\) | 1.46206e15 | 0.378751 | ||||||||
\(251\) | −4.33970e15 | −1.09542 | −0.547710 | − | 0.836668i | \(-0.684500\pi\) | ||||
−0.547710 | + | 0.836668i | \(0.684500\pi\) | |||||||
\(252\) | −1.56942e15 | −0.386043 | ||||||||
\(253\) | −4.77087e15 | −1.14370 | ||||||||
\(254\) | 1.49028e15 | 0.348216 | ||||||||
\(255\) | 2.07169e15 | 0.471860 | ||||||||
\(256\) | −2.81101e15 | −0.624169 | ||||||||
\(257\) | 6.59104e14 | 0.142688 | 0.0713442 | − | 0.997452i | \(-0.477271\pi\) | ||||
0.0713442 | + | 0.997452i | \(0.477271\pi\) | |||||||
\(258\) | 2.57929e15 | 0.544468 | ||||||||
\(259\) | −8.76424e15 | −1.80412 | ||||||||
\(260\) | 1.27748e15 | 0.256464 | ||||||||
\(261\) | −1.20378e15 | −0.235712 | ||||||||
\(262\) | −2.05679e15 | −0.392855 | ||||||||
\(263\) | −3.76994e15 | −0.702461 | −0.351231 | − | 0.936289i | \(-0.614237\pi\) | ||||
−0.351231 | + | 0.936289i | \(0.614237\pi\) | |||||||
\(264\) | −2.61598e15 | −0.475564 | ||||||||
\(265\) | 3.67201e15 | 0.651337 | ||||||||
\(266\) | 5.00956e15 | 0.867099 | ||||||||
\(267\) | 3.62428e14 | 0.0612208 | ||||||||
\(268\) | −8.16533e14 | −0.134616 | ||||||||
\(269\) | −9.46874e14 | −0.152371 | −0.0761855 | − | 0.997094i | \(-0.524274\pi\) | ||||
−0.0761855 | + | 0.997094i | \(0.524274\pi\) | |||||||
\(270\) | −2.55211e14 | −0.0400899 | ||||||||
\(271\) | 1.35782e15 | 0.208230 | 0.104115 | − | 0.994565i | \(-0.466799\pi\) | ||||
0.104115 | + | 0.994565i | \(0.466799\pi\) | |||||||
\(272\) | 4.36467e15 | 0.653511 | ||||||||
\(273\) | −4.74586e15 | −0.693837 | ||||||||
\(274\) | 5.47172e15 | 0.781169 | ||||||||
\(275\) | 5.61750e15 | 0.783214 | ||||||||
\(276\) | −3.85660e15 | −0.525165 | ||||||||
\(277\) | 1.45446e16 | 1.93456 | 0.967280 | − | 0.253712i | \(-0.0816517\pi\) | ||||
0.967280 | + | 0.253712i | \(0.0816517\pi\) | |||||||
\(278\) | −6.13289e14 | −0.0796845 | ||||||||
\(279\) | 3.65134e14 | 0.0463473 | ||||||||
\(280\) | 4.50058e15 | 0.558138 | ||||||||
\(281\) | −1.08921e16 | −1.31984 | −0.659918 | − | 0.751337i | \(-0.729409\pi\) | ||||
−0.659918 | + | 0.751337i | \(0.729409\pi\) | |||||||
\(282\) | 4.15605e15 | 0.492110 | ||||||||
\(283\) | 1.28425e15 | 0.148607 | 0.0743034 | − | 0.997236i | \(-0.476327\pi\) | ||||
0.0743034 | + | 0.997236i | \(0.476327\pi\) | |||||||
\(284\) | 6.57159e15 | 0.743193 | ||||||||
\(285\) | −2.59859e15 | −0.287241 | ||||||||
\(286\) | −3.41934e15 | −0.369457 | ||||||||
\(287\) | −1.25793e16 | −1.32869 | ||||||||
\(288\) | −3.31528e15 | −0.342349 | ||||||||
\(289\) | 2.64824e16 | 2.67376 | ||||||||
\(290\) | 1.49213e15 | 0.147306 | ||||||||
\(291\) | −1.19242e15 | −0.115113 | ||||||||
\(292\) | 9.05673e15 | 0.855033 | ||||||||
\(293\) | −1.63989e16 | −1.51417 | −0.757085 | − | 0.653316i | \(-0.773377\pi\) | ||||
−0.757085 | + | 0.653316i | \(0.773377\pi\) | |||||||
\(294\) | −4.10390e15 | −0.370628 | ||||||||
\(295\) | 6.28400e14 | 0.0555128 | ||||||||
\(296\) | −1.18091e16 | −1.02052 | ||||||||
\(297\) | −2.17904e15 | −0.184225 | ||||||||
\(298\) | 3.69503e15 | 0.305642 | ||||||||
\(299\) | −1.16622e16 | −0.943881 | ||||||||
\(300\) | 4.54099e15 | 0.359635 | ||||||||
\(301\) | −3.78879e16 | −2.93642 | ||||||||
\(302\) | 2.49281e15 | 0.189080 | ||||||||
\(303\) | 5.12187e15 | 0.380234 | ||||||||
\(304\) | −5.47474e15 | −0.397819 | ||||||||
\(305\) | 9.03988e15 | 0.643004 | ||||||||
\(306\) | −4.48251e15 | −0.312128 | ||||||||
\(307\) | 1.15451e16 | 0.787043 | 0.393522 | − | 0.919315i | \(-0.371257\pi\) | ||||
0.393522 | + | 0.919315i | \(0.371257\pi\) | |||||||
\(308\) | 1.66099e16 | 1.10863 | ||||||||
\(309\) | −4.57983e15 | −0.299308 | ||||||||
\(310\) | −4.52599e14 | −0.0289643 | ||||||||
\(311\) | −2.58262e15 | −0.161852 | −0.0809260 | − | 0.996720i | \(-0.525788\pi\) | ||||
−0.0809260 | + | 0.996720i | \(0.525788\pi\) | |||||||
\(312\) | −6.39467e15 | −0.392476 | ||||||||
\(313\) | 1.58178e16 | 0.950839 | 0.475420 | − | 0.879759i | \(-0.342296\pi\) | ||||
0.475420 | + | 0.879759i | \(0.342296\pi\) | |||||||
\(314\) | −3.50007e14 | −0.0206079 | ||||||||
\(315\) | 3.74886e15 | 0.216213 | ||||||||
\(316\) | −5.90896e14 | −0.0333845 | ||||||||
\(317\) | 1.23606e15 | 0.0684157 | 0.0342079 | − | 0.999415i | \(-0.489109\pi\) | ||||
0.0342079 | + | 0.999415i | \(0.489109\pi\) | |||||||
\(318\) | −7.94513e15 | −0.430848 | ||||||||
\(319\) | 1.27401e16 | 0.676915 | ||||||||
\(320\) | 1.31694e15 | 0.0685634 | ||||||||
\(321\) | −1.94246e15 | −0.0990991 | ||||||||
\(322\) | −1.77594e16 | −0.887901 | ||||||||
\(323\) | −4.56414e16 | −2.23636 | ||||||||
\(324\) | −1.76146e15 | −0.0845923 | ||||||||
\(325\) | 1.37318e16 | 0.646375 | ||||||||
\(326\) | 6.46980e14 | 0.0298522 | ||||||||
\(327\) | 2.00669e16 | 0.907653 | ||||||||
\(328\) | −1.69496e16 | −0.751589 | ||||||||
\(329\) | −6.10494e16 | −2.65404 | ||||||||
\(330\) | 2.70102e15 | 0.115130 | ||||||||
\(331\) | 2.43886e15 | 0.101931 | 0.0509654 | − | 0.998700i | \(-0.483770\pi\) | ||||
0.0509654 | + | 0.998700i | \(0.483770\pi\) | |||||||
\(332\) | −2.80624e16 | −1.15008 | ||||||||
\(333\) | −9.83668e15 | −0.395331 | ||||||||
\(334\) | 1.04302e16 | 0.411094 | ||||||||
\(335\) | 1.95045e15 | 0.0753951 | ||||||||
\(336\) | 7.89816e15 | 0.299447 | ||||||||
\(337\) | −3.73870e16 | −1.39036 | −0.695179 | − | 0.718837i | \(-0.744675\pi\) | ||||
−0.695179 | + | 0.718837i | \(0.744675\pi\) | |||||||
\(338\) | 5.03390e15 | 0.183631 | ||||||||
\(339\) | 4.14270e15 | 0.148247 | ||||||||
\(340\) | −1.77240e16 | −0.622225 | ||||||||
\(341\) | −3.86438e15 | −0.133100 | ||||||||
\(342\) | 5.62256e15 | 0.190005 | ||||||||
\(343\) | 1.44062e16 | 0.477681 | ||||||||
\(344\) | −5.10509e16 | −1.66102 | ||||||||
\(345\) | 9.21224e15 | 0.294131 | ||||||||
\(346\) | 3.99108e15 | 0.125054 | ||||||||
\(347\) | 6.97870e15 | 0.214602 | 0.107301 | − | 0.994227i | \(-0.465779\pi\) | ||||
0.107301 | + | 0.994227i | \(0.465779\pi\) | |||||||
\(348\) | 1.02987e16 | 0.310825 | ||||||||
\(349\) | 3.93172e16 | 1.16471 | 0.582354 | − | 0.812935i | \(-0.302132\pi\) | ||||
0.582354 | + | 0.812935i | \(0.302132\pi\) | |||||||
\(350\) | 2.09109e16 | 0.608039 | ||||||||
\(351\) | −5.32659e15 | −0.152038 | ||||||||
\(352\) | 3.50872e16 | 0.983152 | ||||||||
\(353\) | 2.99842e15 | 0.0824817 | 0.0412408 | − | 0.999149i | \(-0.486869\pi\) | ||||
0.0412408 | + | 0.999149i | \(0.486869\pi\) | |||||||
\(354\) | −1.35967e15 | −0.0367207 | ||||||||
\(355\) | −1.56975e16 | −0.416243 | ||||||||
\(356\) | −3.10069e15 | −0.0807296 | ||||||||
\(357\) | 6.58448e16 | 1.68336 | ||||||||
\(358\) | 2.09484e16 | 0.525909 | ||||||||
\(359\) | −2.98048e16 | −0.734806 | −0.367403 | − | 0.930062i | \(-0.619753\pi\) | ||||
−0.367403 | + | 0.930062i | \(0.619753\pi\) | |||||||
\(360\) | 5.05130e15 | 0.122303 | ||||||||
\(361\) | 1.51965e16 | 0.361366 | ||||||||
\(362\) | 1.74377e16 | 0.407270 | ||||||||
\(363\) | −2.10520e15 | −0.0482949 | ||||||||
\(364\) | 4.06023e16 | 0.914937 | ||||||||
\(365\) | −2.16338e16 | −0.478882 | ||||||||
\(366\) | −1.95596e16 | −0.425336 | ||||||||
\(367\) | −2.33299e16 | −0.498406 | −0.249203 | − | 0.968451i | \(-0.580169\pi\) | ||||
−0.249203 | + | 0.968451i | \(0.580169\pi\) | |||||||
\(368\) | 1.94085e16 | 0.407362 | ||||||||
\(369\) | −1.41186e16 | −0.291152 | ||||||||
\(370\) | 1.21930e16 | 0.247058 | ||||||||
\(371\) | 1.16708e17 | 2.32365 | ||||||||
\(372\) | −3.12383e15 | −0.0611165 | ||||||||
\(373\) | −8.12135e16 | −1.56142 | −0.780712 | − | 0.624892i | \(-0.785143\pi\) | ||||
−0.780712 | + | 0.624892i | \(0.785143\pi\) | |||||||
\(374\) | 4.74405e16 | 0.896364 | ||||||||
\(375\) | −2.41045e16 | −0.447606 | ||||||||
\(376\) | −8.22592e16 | −1.50129 | ||||||||
\(377\) | 3.11427e16 | 0.558648 | ||||||||
\(378\) | −8.11141e15 | −0.143021 | ||||||||
\(379\) | −1.05622e17 | −1.83062 | −0.915309 | − | 0.402752i | \(-0.868054\pi\) | ||||
−0.915309 | + | 0.402752i | \(0.868054\pi\) | |||||||
\(380\) | 2.22317e16 | 0.378774 | ||||||||
\(381\) | −2.45699e16 | −0.411520 | ||||||||
\(382\) | −4.95991e16 | −0.816698 | ||||||||
\(383\) | 7.65692e14 | 0.0123955 | 0.00619773 | − | 0.999981i | \(-0.498027\pi\) | ||||
0.00619773 | + | 0.999981i | \(0.498027\pi\) | |||||||
\(384\) | 3.44053e16 | 0.547612 | ||||||||
\(385\) | −3.96760e16 | −0.620917 | ||||||||
\(386\) | 4.22692e16 | 0.650439 | ||||||||
\(387\) | −4.25241e16 | −0.643448 | ||||||||
\(388\) | 1.02016e16 | 0.151796 | ||||||||
\(389\) | −6.70250e16 | −0.980764 | −0.490382 | − | 0.871507i | \(-0.663143\pi\) | ||||
−0.490382 | + | 0.871507i | \(0.663143\pi\) | |||||||
\(390\) | 6.60254e15 | 0.0950147 | ||||||||
\(391\) | 1.61803e17 | 2.29001 | ||||||||
\(392\) | 8.12269e16 | 1.13068 | ||||||||
\(393\) | 3.39098e16 | 0.464273 | ||||||||
\(394\) | −5.70973e16 | −0.768935 | ||||||||
\(395\) | 1.41147e15 | 0.0186978 | ||||||||
\(396\) | 1.86424e16 | 0.242931 | ||||||||
\(397\) | 1.20104e17 | 1.53964 | 0.769820 | − | 0.638262i | \(-0.220346\pi\) | ||||
0.769820 | + | 0.638262i | \(0.220346\pi\) | |||||||
\(398\) | 1.03515e16 | 0.130546 | ||||||||
\(399\) | −8.25912e16 | −1.02473 | ||||||||
\(400\) | −2.28527e16 | −0.278964 | ||||||||
\(401\) | −6.36394e16 | −0.764342 | −0.382171 | − | 0.924092i | \(-0.624823\pi\) | ||||
−0.382171 | + | 0.924092i | \(0.624823\pi\) | |||||||
\(402\) | −4.22018e15 | −0.0498726 | ||||||||
\(403\) | −9.44633e15 | −0.109845 | ||||||||
\(404\) | −4.38192e16 | −0.501401 | ||||||||
\(405\) | 4.20760e15 | 0.0473780 | ||||||||
\(406\) | 4.74246e16 | 0.525515 | ||||||||
\(407\) | 1.04106e17 | 1.13531 | ||||||||
\(408\) | 8.87207e16 | 0.952212 | ||||||||
\(409\) | 6.97030e16 | 0.736292 | 0.368146 | − | 0.929768i | \(-0.379993\pi\) | ||||
0.368146 | + | 0.929768i | \(0.379993\pi\) | |||||||
\(410\) | 1.75006e16 | 0.181953 | ||||||||
\(411\) | −9.02108e16 | −0.923180 | ||||||||
\(412\) | 3.91819e16 | 0.394687 | ||||||||
\(413\) | 1.99725e16 | 0.198042 | ||||||||
\(414\) | −1.99325e16 | −0.194563 | ||||||||
\(415\) | 6.70325e16 | 0.644129 | ||||||||
\(416\) | 8.57692e16 | 0.811381 | ||||||||
\(417\) | 1.01111e16 | 0.0941706 | ||||||||
\(418\) | −5.95062e16 | −0.545653 | ||||||||
\(419\) | 4.45589e16 | 0.402294 | 0.201147 | − | 0.979561i | \(-0.435533\pi\) | ||||
0.201147 | + | 0.979561i | \(0.435533\pi\) | |||||||
\(420\) | −3.20727e16 | −0.285112 | ||||||||
\(421\) | −9.19806e16 | −0.805123 | −0.402562 | − | 0.915393i | \(-0.631880\pi\) | ||||
−0.402562 | + | 0.915393i | \(0.631880\pi\) | |||||||
\(422\) | 9.89301e16 | 0.852702 | ||||||||
\(423\) | −6.85197e16 | −0.581572 | ||||||||
\(424\) | 1.57255e17 | 1.31440 | ||||||||
\(425\) | −1.90517e17 | −1.56821 | ||||||||
\(426\) | 3.39647e16 | 0.275337 | ||||||||
\(427\) | 2.87316e17 | 2.29392 | ||||||||
\(428\) | 1.66184e16 | 0.130678 | ||||||||
\(429\) | 5.63738e16 | 0.436621 | ||||||||
\(430\) | 5.27104e16 | 0.402116 | ||||||||
\(431\) | −3.66494e16 | −0.275400 | −0.137700 | − | 0.990474i | \(-0.543971\pi\) | ||||
−0.137700 | + | 0.990474i | \(0.543971\pi\) | |||||||
\(432\) | 8.86462e15 | 0.0656169 | ||||||||
\(433\) | −4.93879e16 | −0.360122 | −0.180061 | − | 0.983655i | \(-0.557630\pi\) | ||||
−0.180061 | + | 0.983655i | \(0.557630\pi\) | |||||||
\(434\) | −1.43850e16 | −0.103330 | ||||||||
\(435\) | −2.46004e16 | −0.174085 | ||||||||
\(436\) | −1.71678e17 | −1.19689 | ||||||||
\(437\) | −2.02955e17 | −1.39402 | ||||||||
\(438\) | 4.68089e16 | 0.316772 | ||||||||
\(439\) | −5.19055e16 | −0.346094 | −0.173047 | − | 0.984914i | \(-0.555361\pi\) | ||||
−0.173047 | + | 0.984914i | \(0.555361\pi\) | |||||||
\(440\) | −5.34603e16 | −0.351228 | ||||||||
\(441\) | 6.76598e16 | 0.438006 | ||||||||
\(442\) | 1.15967e17 | 0.739755 | ||||||||
\(443\) | −1.57657e17 | −0.991033 | −0.495517 | − | 0.868598i | \(-0.665021\pi\) | ||||
−0.495517 | + | 0.868598i | \(0.665021\pi\) | |||||||
\(444\) | 8.41559e16 | 0.521309 | ||||||||
\(445\) | 7.40660e15 | 0.0452146 | ||||||||
\(446\) | 1.41071e17 | 0.848713 | ||||||||
\(447\) | −6.09190e16 | −0.361205 | ||||||||
\(448\) | 4.18566e16 | 0.244600 | ||||||||
\(449\) | −1.00305e17 | −0.577724 | −0.288862 | − | 0.957371i | \(-0.593277\pi\) | ||||
−0.288862 | + | 0.957371i | \(0.593277\pi\) | |||||||
\(450\) | 2.34697e16 | 0.133238 | ||||||||
\(451\) | 1.49424e17 | 0.836127 | ||||||||
\(452\) | −3.54421e16 | −0.195488 | ||||||||
\(453\) | −4.10983e16 | −0.223453 | ||||||||
\(454\) | 2.99955e16 | 0.160766 | ||||||||
\(455\) | −9.69864e16 | −0.512433 | ||||||||
\(456\) | −1.11285e17 | −0.579650 | ||||||||
\(457\) | −5.63806e16 | −0.289517 | −0.144759 | − | 0.989467i | \(-0.546241\pi\) | ||||
−0.144759 | + | 0.989467i | \(0.546241\pi\) | |||||||
\(458\) | −9.18909e16 | −0.465208 | ||||||||
\(459\) | 7.39019e16 | 0.368870 | ||||||||
\(460\) | −7.88136e16 | −0.387860 | ||||||||
\(461\) | −1.20880e17 | −0.586541 | −0.293270 | − | 0.956030i | \(-0.594744\pi\) | ||||
−0.293270 | + | 0.956030i | \(0.594744\pi\) | |||||||
\(462\) | 8.58469e16 | 0.410726 | ||||||||
\(463\) | 1.67790e17 | 0.791572 | 0.395786 | − | 0.918343i | \(-0.370472\pi\) | ||||
0.395786 | + | 0.918343i | \(0.370472\pi\) | |||||||
\(464\) | −5.18284e16 | −0.241102 | ||||||||
\(465\) | 7.46188e15 | 0.0342298 | ||||||||
\(466\) | −3.82569e15 | −0.0173062 | ||||||||
\(467\) | 3.70336e17 | 1.65210 | 0.826049 | − | 0.563598i | \(-0.190583\pi\) | ||||
0.826049 | + | 0.563598i | \(0.190583\pi\) | |||||||
\(468\) | 4.55706e16 | 0.200487 | ||||||||
\(469\) | 6.19914e16 | 0.268972 | ||||||||
\(470\) | 8.49332e16 | 0.363447 | ||||||||
\(471\) | 5.77048e15 | 0.0243543 | ||||||||
\(472\) | 2.69114e16 | 0.112025 | ||||||||
\(473\) | 4.50052e17 | 1.84784 | ||||||||
\(474\) | −3.05399e15 | −0.0123683 | ||||||||
\(475\) | 2.38971e17 | 0.954634 | ||||||||
\(476\) | −5.63323e17 | −2.21979 | ||||||||
\(477\) | 1.30989e17 | 0.509173 | ||||||||
\(478\) | 1.31563e17 | 0.504489 | ||||||||
\(479\) | 6.66464e16 | 0.252114 | 0.126057 | − | 0.992023i | \(-0.459768\pi\) | ||||
0.126057 | + | 0.992023i | \(0.459768\pi\) | |||||||
\(480\) | −6.77511e16 | −0.252842 | ||||||||
\(481\) | 2.54484e17 | 0.936951 | ||||||||
\(482\) | −6.12904e16 | −0.222632 | ||||||||
\(483\) | 2.92794e17 | 1.04931 | ||||||||
\(484\) | 1.80107e16 | 0.0636847 | ||||||||
\(485\) | −2.43684e16 | −0.0850169 | ||||||||
\(486\) | −9.10397e15 | −0.0313397 | ||||||||
\(487\) | 3.56614e16 | 0.121132 | 0.0605662 | − | 0.998164i | \(-0.480709\pi\) | ||||
0.0605662 | + | 0.998164i | \(0.480709\pi\) | |||||||
\(488\) | 3.87135e17 | 1.29758 | ||||||||
\(489\) | −1.06666e16 | −0.0352791 | ||||||||
\(490\) | −8.38674e16 | −0.273727 | ||||||||
\(491\) | 2.91939e16 | 0.0940293 | 0.0470146 | − | 0.998894i | \(-0.485029\pi\) | ||||
0.0470146 | + | 0.998894i | \(0.485029\pi\) | |||||||
\(492\) | 1.20789e17 | 0.383932 | ||||||||
\(493\) | −4.32079e17 | −1.35537 | ||||||||
\(494\) | −1.45461e17 | −0.450319 | ||||||||
\(495\) | −4.45310e16 | −0.136059 | ||||||||
\(496\) | 1.57208e16 | 0.0474071 | ||||||||
\(497\) | −4.98916e17 | −1.48495 | ||||||||
\(498\) | −1.45038e17 | −0.426080 | ||||||||
\(499\) | 6.02093e17 | 1.74586 | 0.872932 | − | 0.487842i | \(-0.162216\pi\) | ||||
0.872932 | + | 0.487842i | \(0.162216\pi\) | |||||||
\(500\) | 2.06222e17 | 0.590241 | ||||||||
\(501\) | −1.71960e17 | −0.485828 | ||||||||
\(502\) | 1.91890e17 | 0.535154 | ||||||||
\(503\) | −2.10322e17 | −0.579020 | −0.289510 | − | 0.957175i | \(-0.593492\pi\) | ||||
−0.289510 | + | 0.957175i | \(0.593492\pi\) | |||||||
\(504\) | 1.60546e17 | 0.436316 | ||||||||
\(505\) | 1.04671e17 | 0.280822 | ||||||||
\(506\) | 2.10955e17 | 0.558743 | ||||||||
\(507\) | −8.29925e16 | −0.217014 | ||||||||
\(508\) | 2.10203e17 | 0.542656 | ||||||||
\(509\) | 4.81081e17 | 1.22618 | 0.613088 | − | 0.790015i | \(-0.289927\pi\) | ||||
0.613088 | + | 0.790015i | \(0.289927\pi\) | |||||||
\(510\) | −9.16047e16 | −0.230522 | ||||||||
\(511\) | −6.87589e17 | −1.70841 | ||||||||
\(512\) | −2.62328e17 | −0.643562 | ||||||||
\(513\) | −9.26976e16 | −0.224546 | ||||||||
\(514\) | −2.91438e16 | −0.0697086 | ||||||||
\(515\) | −9.35935e16 | −0.221054 | ||||||||
\(516\) | 3.63807e17 | 0.848491 | ||||||||
\(517\) | 7.25177e17 | 1.67015 | ||||||||
\(518\) | 3.87532e17 | 0.881381 | ||||||||
\(519\) | −6.57999e16 | −0.147787 | ||||||||
\(520\) | −1.30682e17 | −0.289863 | ||||||||
\(521\) | 5.80316e16 | 0.127122 | 0.0635608 | − | 0.997978i | \(-0.479754\pi\) | ||||
0.0635608 | + | 0.997978i | \(0.479754\pi\) | |||||||
\(522\) | 5.32278e16 | 0.115154 | ||||||||
\(523\) | −2.89417e17 | −0.618391 | −0.309195 | − | 0.950999i | \(-0.600060\pi\) | ||||
−0.309195 | + | 0.950999i | \(0.600060\pi\) | |||||||
\(524\) | −2.90109e17 | −0.612220 | ||||||||
\(525\) | −3.44753e17 | −0.718576 | ||||||||
\(526\) | 1.66697e17 | 0.343179 | ||||||||
\(527\) | 1.31060e17 | 0.266502 | ||||||||
\(528\) | −9.38185e16 | −0.188438 | ||||||||
\(529\) | 2.15458e17 | 0.427466 | ||||||||
\(530\) | −1.62367e17 | −0.318203 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | 7.06594e17 | 1.35128 | ||||||||
\(533\) | 3.65260e17 | 0.690042 | ||||||||
\(534\) | −1.60256e16 | −0.0299087 | ||||||||
\(535\) | −3.96962e16 | −0.0731896 | ||||||||
\(536\) | 8.35285e16 | 0.152147 | ||||||||
\(537\) | −3.45370e17 | −0.621515 | ||||||||
\(538\) | 4.18683e16 | 0.0744390 | ||||||||
\(539\) | −7.16076e17 | −1.25786 | ||||||||
\(540\) | −3.59973e16 | −0.0624756 | ||||||||
\(541\) | −2.95677e17 | −0.507032 | −0.253516 | − | 0.967331i | \(-0.581587\pi\) | ||||
−0.253516 | + | 0.967331i | \(0.581587\pi\) | |||||||
\(542\) | −6.00395e16 | −0.101728 | ||||||||
\(543\) | −2.87490e17 | −0.481309 | ||||||||
\(544\) | −1.18998e18 | −1.96854 | ||||||||
\(545\) | 4.10087e17 | 0.670346 | ||||||||
\(546\) | 2.09849e17 | 0.338965 | ||||||||
\(547\) | −9.39910e17 | −1.50027 | −0.750134 | − | 0.661286i | \(-0.770011\pi\) | ||||
−0.750134 | + | 0.661286i | \(0.770011\pi\) | |||||||
\(548\) | 7.71781e17 | 1.21736 | ||||||||
\(549\) | 3.22473e17 | 0.502659 | ||||||||
\(550\) | −2.48391e17 | −0.382630 | ||||||||
\(551\) | 5.41971e17 | 0.825070 | ||||||||
\(552\) | 3.94517e17 | 0.593555 | ||||||||
\(553\) | 4.48609e16 | 0.0667044 | ||||||||
\(554\) | −6.43122e17 | −0.945105 | ||||||||
\(555\) | −2.01023e17 | −0.291972 | ||||||||
\(556\) | −8.65039e16 | −0.124179 | ||||||||
\(557\) | 6.16218e17 | 0.874330 | 0.437165 | − | 0.899381i | \(-0.355983\pi\) | ||||
0.437165 | + | 0.899381i | \(0.355983\pi\) | |||||||
\(558\) | −1.61453e16 | −0.0226424 | ||||||||
\(559\) | 1.10013e18 | 1.52500 | ||||||||
\(560\) | 1.61407e17 | 0.221157 | ||||||||
\(561\) | −7.82139e17 | −1.05932 | ||||||||
\(562\) | 4.81620e17 | 0.644790 | ||||||||
\(563\) | −6.77170e17 | −0.896175 | −0.448088 | − | 0.893990i | \(-0.647895\pi\) | ||||
−0.448088 | + | 0.893990i | \(0.647895\pi\) | |||||||
\(564\) | 5.86208e17 | 0.766897 | ||||||||
\(565\) | 8.46603e16 | 0.109488 | ||||||||
\(566\) | −5.67863e16 | −0.0726001 | ||||||||
\(567\) | 1.33731e17 | 0.169021 | ||||||||
\(568\) | −6.72250e17 | −0.839976 | ||||||||
\(569\) | −4.29749e17 | −0.530866 | −0.265433 | − | 0.964129i | \(-0.585515\pi\) | ||||
−0.265433 | + | 0.964129i | \(0.585515\pi\) | |||||||
\(570\) | 1.14903e17 | 0.140328 | ||||||||
\(571\) | 1.18834e18 | 1.43485 | 0.717423 | − | 0.696637i | \(-0.245321\pi\) | ||||
0.717423 | + | 0.696637i | \(0.245321\pi\) | |||||||
\(572\) | −4.82295e17 | −0.575757 | ||||||||
\(573\) | 8.17726e17 | 0.965168 | ||||||||
\(574\) | 5.56224e17 | 0.649117 | ||||||||
\(575\) | −8.47176e17 | −0.977536 | ||||||||
\(576\) | 4.69784e16 | 0.0535984 | ||||||||
\(577\) | −2.62221e17 | −0.295818 | −0.147909 | − | 0.989001i | \(-0.547254\pi\) | ||||
−0.147909 | + | 0.989001i | \(0.547254\pi\) | |||||||
\(578\) | −1.17098e18 | −1.30623 | ||||||||
\(579\) | −6.96881e17 | −0.768685 | ||||||||
\(580\) | 2.10464e17 | 0.229560 | ||||||||
\(581\) | 2.13050e18 | 2.29793 | ||||||||
\(582\) | 5.27258e16 | 0.0562372 | ||||||||
\(583\) | −1.38632e18 | −1.46224 | ||||||||
\(584\) | −9.26471e17 | −0.966381 | ||||||||
\(585\) | −1.08854e17 | −0.112288 | ||||||||
\(586\) | 7.25116e17 | 0.739729 | ||||||||
\(587\) | −1.57347e18 | −1.58749 | −0.793745 | − | 0.608250i | \(-0.791872\pi\) | ||||
−0.793745 | + | 0.608250i | \(0.791872\pi\) | |||||||
\(588\) | −5.78851e17 | −0.577583 | ||||||||
\(589\) | −1.64393e17 | −0.162231 | ||||||||
\(590\) | −2.77862e16 | −0.0271201 | ||||||||
\(591\) | 9.41347e17 | 0.908722 | ||||||||
\(592\) | −4.23518e17 | −0.404371 | ||||||||
\(593\) | −8.97746e17 | −0.847809 | −0.423904 | − | 0.905707i | \(-0.639341\pi\) | ||||
−0.423904 | + | 0.905707i | \(0.639341\pi\) | |||||||
\(594\) | 9.63516e16 | 0.0900010 | ||||||||
\(595\) | 1.34561e18 | 1.24325 | ||||||||
\(596\) | 5.21181e17 | 0.476308 | ||||||||
\(597\) | −1.70662e17 | −0.154278 | ||||||||
\(598\) | 5.15672e17 | 0.461122 | ||||||||
\(599\) | 9.76390e17 | 0.863673 | 0.431836 | − | 0.901952i | \(-0.357866\pi\) | ||||
0.431836 | + | 0.901952i | \(0.357866\pi\) | |||||||
\(600\) | −4.64527e17 | −0.406470 | ||||||||
\(601\) | 1.28535e18 | 1.11260 | 0.556299 | − | 0.830982i | \(-0.312221\pi\) | ||||
0.556299 | + | 0.830982i | \(0.312221\pi\) | |||||||
\(602\) | 1.67530e18 | 1.43455 | ||||||||
\(603\) | 6.95770e16 | 0.0589390 | ||||||||
\(604\) | 3.51609e17 | 0.294659 | ||||||||
\(605\) | −4.30220e16 | −0.0356682 | ||||||||
\(606\) | −2.26476e17 | −0.185759 | ||||||||
\(607\) | −2.35015e18 | −1.90708 | −0.953539 | − | 0.301269i | \(-0.902590\pi\) | ||||
−0.953539 | + | 0.301269i | \(0.902590\pi\) | |||||||
\(608\) | 1.49262e18 | 1.19833 | ||||||||
\(609\) | −7.81877e17 | −0.621049 | ||||||||
\(610\) | −3.99720e17 | −0.314132 | ||||||||
\(611\) | 1.77267e18 | 1.37835 | ||||||||
\(612\) | −6.32254e17 | −0.486416 | ||||||||
\(613\) | 1.19210e18 | 0.907444 | 0.453722 | − | 0.891143i | \(-0.350096\pi\) | ||||
0.453722 | + | 0.891143i | \(0.350096\pi\) | |||||||
\(614\) | −5.10495e17 | −0.384500 | ||||||||
\(615\) | −2.88528e17 | −0.215030 | ||||||||
\(616\) | −1.69914e18 | −1.25301 | ||||||||
\(617\) | −1.32168e18 | −0.964435 | −0.482218 | − | 0.876051i | \(-0.660169\pi\) | ||||
−0.482218 | + | 0.876051i | \(0.660169\pi\) | |||||||
\(618\) | 2.02508e17 | 0.146223 | ||||||||
\(619\) | −1.31387e18 | −0.938780 | −0.469390 | − | 0.882991i | \(-0.655526\pi\) | ||||
−0.469390 | + | 0.882991i | \(0.655526\pi\) | |||||||
\(620\) | −6.38387e16 | −0.0451376 | ||||||||
\(621\) | 3.28622e17 | 0.229933 | ||||||||
\(622\) | 1.14197e17 | 0.0790708 | ||||||||
\(623\) | 2.35405e17 | 0.161303 | ||||||||
\(624\) | −2.29336e17 | −0.155515 | ||||||||
\(625\) | 7.26584e17 | 0.487603 | ||||||||
\(626\) | −6.99421e17 | −0.464521 | ||||||||
\(627\) | 9.81063e17 | 0.644848 | ||||||||
\(628\) | −4.93682e16 | −0.0321151 | ||||||||
\(629\) | −3.53075e18 | −2.27320 | ||||||||
\(630\) | −1.65765e17 | −0.105628 | ||||||||
\(631\) | 2.19393e17 | 0.138367 | 0.0691834 | − | 0.997604i | \(-0.477961\pi\) | ||||
0.0691834 | + | 0.997604i | \(0.477961\pi\) | |||||||
\(632\) | 6.04465e16 | 0.0377320 | ||||||||
\(633\) | −1.63103e18 | −1.00772 | ||||||||
\(634\) | −5.46555e16 | −0.0334237 | ||||||||
\(635\) | −5.02110e17 | −0.303928 | ||||||||
\(636\) | −1.12065e18 | −0.671429 | ||||||||
\(637\) | −1.75042e18 | −1.03809 | ||||||||
\(638\) | −5.63335e17 | −0.330699 | ||||||||
\(639\) | −5.59967e17 | −0.325392 | ||||||||
\(640\) | 7.03109e17 | 0.404439 | ||||||||
\(641\) | 9.07607e17 | 0.516798 | 0.258399 | − | 0.966038i | \(-0.416805\pi\) | ||||
0.258399 | + | 0.966038i | \(0.416805\pi\) | |||||||
\(642\) | 8.58906e16 | 0.0484136 | ||||||||
\(643\) | 1.88340e18 | 1.05092 | 0.525462 | − | 0.850817i | \(-0.323893\pi\) | ||||
0.525462 | + | 0.850817i | \(0.323893\pi\) | |||||||
\(644\) | −2.50494e18 | −1.38369 | ||||||||
\(645\) | −8.69023e17 | −0.475218 | ||||||||
\(646\) | 2.01814e18 | 1.09255 | ||||||||
\(647\) | 1.34923e18 | 0.723118 | 0.361559 | − | 0.932349i | \(-0.382245\pi\) | ||||
0.361559 | + | 0.932349i | \(0.382245\pi\) | |||||||
\(648\) | 1.80191e17 | 0.0956085 | ||||||||
\(649\) | −2.37244e17 | −0.124625 | ||||||||
\(650\) | −6.07182e17 | −0.315778 | ||||||||
\(651\) | 2.37162e17 | 0.122115 | ||||||||
\(652\) | 9.12560e16 | 0.0465213 | ||||||||
\(653\) | 1.71614e18 | 0.866199 | 0.433100 | − | 0.901346i | \(-0.357420\pi\) | ||||
0.433100 | + | 0.901346i | \(0.357420\pi\) | |||||||
\(654\) | −8.87305e17 | −0.443422 | ||||||||
\(655\) | 6.92981e17 | 0.342889 | ||||||||
\(656\) | −6.07875e17 | −0.297810 | ||||||||
\(657\) | −7.71726e17 | −0.374359 | ||||||||
\(658\) | 2.69944e18 | 1.29660 | ||||||||
\(659\) | −1.28135e18 | −0.609415 | −0.304708 | − | 0.952446i | \(-0.598559\pi\) | ||||
−0.304708 | + | 0.952446i | \(0.598559\pi\) | |||||||
\(660\) | 3.80977e17 | 0.179417 | ||||||||
\(661\) | −1.79244e18 | −0.835864 | −0.417932 | − | 0.908478i | \(-0.637245\pi\) | ||||
−0.417932 | + | 0.908478i | \(0.637245\pi\) | |||||||
\(662\) | −1.07840e17 | −0.0497971 | ||||||||
\(663\) | −1.91191e18 | −0.874237 | ||||||||
\(664\) | 2.87069e18 | 1.29985 | ||||||||
\(665\) | −1.68784e18 | −0.756815 | ||||||||
\(666\) | 4.34952e17 | 0.193134 | ||||||||
\(667\) | −1.92134e18 | −0.844863 | ||||||||
\(668\) | 1.47117e18 | 0.640644 | ||||||||
\(669\) | −2.32580e18 | −1.00300 | ||||||||
\(670\) | −8.62438e16 | −0.0368334 | ||||||||
\(671\) | −3.41289e18 | −1.44353 | ||||||||
\(672\) | −2.15334e18 | −0.902013 | ||||||||
\(673\) | 6.34042e16 | 0.0263039 | 0.0131519 | − | 0.999914i | \(-0.495813\pi\) | ||||
0.0131519 | + | 0.999914i | \(0.495813\pi\) | |||||||
\(674\) | 1.65316e18 | 0.679242 | ||||||||
\(675\) | −3.86939e17 | −0.157459 | ||||||||
\(676\) | 7.10026e17 | 0.286168 | ||||||||
\(677\) | −9.29177e17 | −0.370913 | −0.185457 | − | 0.982652i | \(-0.559376\pi\) | ||||
−0.185457 | + | 0.982652i | \(0.559376\pi\) | |||||||
\(678\) | −1.83179e17 | −0.0724242 | ||||||||
\(679\) | −7.74504e17 | −0.303298 | ||||||||
\(680\) | 1.81310e18 | 0.703256 | ||||||||
\(681\) | −4.94528e17 | −0.189992 | ||||||||
\(682\) | 1.70873e17 | 0.0650242 | ||||||||
\(683\) | −3.07516e18 | −1.15913 | −0.579566 | − | 0.814925i | \(-0.696778\pi\) | ||||
−0.579566 | + | 0.814925i | \(0.696778\pi\) | |||||||
\(684\) | 7.93057e17 | 0.296101 | ||||||||
\(685\) | −1.84355e18 | −0.681814 | ||||||||
\(686\) | −6.37005e17 | −0.233365 | ||||||||
\(687\) | 1.51498e18 | 0.549779 | ||||||||
\(688\) | −1.83087e18 | −0.658162 | ||||||||
\(689\) | −3.38880e18 | −1.20676 | ||||||||
\(690\) | −4.07341e17 | −0.143694 | ||||||||
\(691\) | −2.73730e18 | −0.956565 | −0.478283 | − | 0.878206i | \(-0.658741\pi\) | ||||
−0.478283 | + | 0.878206i | \(0.658741\pi\) | |||||||
\(692\) | 5.62939e17 | 0.194882 | ||||||||
\(693\) | −1.41533e18 | −0.485392 | ||||||||
\(694\) | −3.08580e17 | −0.104841 | ||||||||
\(695\) | 2.06631e17 | 0.0695497 | ||||||||
\(696\) | −1.05352e18 | −0.351303 | ||||||||
\(697\) | −5.06768e18 | −1.67416 | ||||||||
\(698\) | −1.73850e18 | −0.569004 | ||||||||
\(699\) | 6.30730e16 | 0.0204523 | ||||||||
\(700\) | 2.94947e18 | 0.947560 | ||||||||
\(701\) | −4.73652e17 | −0.150762 | −0.0753811 | − | 0.997155i | \(-0.524017\pi\) | ||||
−0.0753811 | + | 0.997155i | \(0.524017\pi\) | |||||||
\(702\) | 2.35528e17 | 0.0742764 | ||||||||
\(703\) | 4.42873e18 | 1.38379 | ||||||||
\(704\) | −4.97194e17 | −0.153923 | ||||||||
\(705\) | −1.40027e18 | −0.429519 | ||||||||
\(706\) | −1.32582e17 | −0.0402954 | ||||||||
\(707\) | 3.32676e18 | 1.00183 | ||||||||
\(708\) | −1.91780e17 | −0.0572251 | ||||||||
\(709\) | 2.44513e18 | 0.722938 | 0.361469 | − | 0.932384i | \(-0.382275\pi\) | ||||
0.361469 | + | 0.932384i | \(0.382275\pi\) | |||||||
\(710\) | 6.94103e17 | 0.203350 | ||||||||
\(711\) | 5.03503e16 | 0.0146167 | ||||||||
\(712\) | 3.17189e17 | 0.0912428 | ||||||||
\(713\) | 5.82788e17 | 0.166123 | ||||||||
\(714\) | −2.91148e18 | −0.822387 | ||||||||
\(715\) | 1.15206e18 | 0.322466 | ||||||||
\(716\) | 2.95475e18 | 0.819570 | ||||||||
\(717\) | −2.16904e18 | −0.596202 | ||||||||
\(718\) | 1.31789e18 | 0.358981 | ||||||||
\(719\) | 4.08649e18 | 1.10309 | 0.551547 | − | 0.834144i | \(-0.314038\pi\) | ||||
0.551547 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(720\) | 1.81158e17 | 0.0484614 | ||||||||
\(721\) | −2.97469e18 | −0.788611 | ||||||||
\(722\) | −6.71950e17 | −0.176541 | ||||||||
\(723\) | 1.01048e18 | 0.263104 | ||||||||
\(724\) | 2.45957e18 | 0.634685 | ||||||||
\(725\) | 2.26230e18 | 0.578566 | ||||||||
\(726\) | 9.30866e16 | 0.0235939 | ||||||||
\(727\) | 7.13650e18 | 1.79272 | 0.896358 | − | 0.443331i | \(-0.146203\pi\) | ||||
0.896358 | + | 0.443331i | \(0.146203\pi\) | |||||||
\(728\) | −4.15347e18 | −1.03409 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 9.56589e17 | 0.233952 | ||||||||
\(731\) | −1.52635e19 | −3.69990 | ||||||||
\(732\) | −2.75886e18 | −0.662838 | ||||||||
\(733\) | 2.80764e18 | 0.668598 | 0.334299 | − | 0.942467i | \(-0.391501\pi\) | ||||
0.334299 | + | 0.942467i | \(0.391501\pi\) | |||||||
\(734\) | 1.03159e18 | 0.243490 | ||||||||
\(735\) | 1.38270e18 | 0.323489 | ||||||||
\(736\) | −5.29150e18 | −1.22708 | ||||||||
\(737\) | −7.36366e17 | −0.169260 | ||||||||
\(738\) | 6.24287e17 | 0.142239 | ||||||||
\(739\) | 4.67894e18 | 1.05672 | 0.528359 | − | 0.849021i | \(-0.322808\pi\) | ||||
0.528359 | + | 0.849021i | \(0.322808\pi\) | |||||||
\(740\) | 1.71981e18 | 0.385013 | ||||||||
\(741\) | 2.39817e18 | 0.532183 | ||||||||
\(742\) | −5.16053e18 | −1.13519 | ||||||||
\(743\) | 7.01746e18 | 1.53022 | 0.765108 | − | 0.643902i | \(-0.222686\pi\) | ||||
0.765108 | + | 0.643902i | \(0.222686\pi\) | |||||||
\(744\) | 3.19557e17 | 0.0690755 | ||||||||
\(745\) | −1.24494e18 | −0.266768 | ||||||||
\(746\) | 3.59105e18 | 0.762814 | ||||||||
\(747\) | 2.39120e18 | 0.503539 | ||||||||
\(748\) | 6.69145e18 | 1.39688 | ||||||||
\(749\) | −1.26167e18 | −0.261104 | ||||||||
\(750\) | 1.06584e18 | 0.218672 | ||||||||
\(751\) | 6.91693e18 | 1.40687 | 0.703434 | − | 0.710760i | \(-0.251649\pi\) | ||||
0.703434 | + | 0.710760i | \(0.251649\pi\) | |||||||
\(752\) | −2.95011e18 | −0.594870 | ||||||||
\(753\) | −3.16364e18 | −0.632441 | ||||||||
\(754\) | −1.37705e18 | −0.272920 | ||||||||
\(755\) | −8.39887e17 | −0.165031 | ||||||||
\(756\) | −1.14411e18 | −0.222882 | ||||||||
\(757\) | −4.84887e18 | −0.936520 | −0.468260 | − | 0.883591i | \(-0.655119\pi\) | ||||
−0.468260 | + | 0.883591i | \(0.655119\pi\) | |||||||
\(758\) | 4.67031e18 | 0.894326 | ||||||||
\(759\) | −3.47796e18 | −0.660318 | ||||||||
\(760\) | −2.27423e18 | −0.428100 | ||||||||
\(761\) | −9.04988e18 | −1.68905 | −0.844525 | − | 0.535517i | \(-0.820117\pi\) | ||||
−0.844525 | + | 0.535517i | \(0.820117\pi\) | |||||||
\(762\) | 1.08642e18 | 0.201043 | ||||||||
\(763\) | 1.30339e19 | 2.39146 | ||||||||
\(764\) | −6.99590e18 | −1.27273 | ||||||||
\(765\) | 1.51026e18 | 0.272429 | ||||||||
\(766\) | −3.38569e16 | −0.00605565 | ||||||||
\(767\) | −5.79934e17 | −0.102851 | ||||||||
\(768\) | −2.04922e18 | −0.360364 | ||||||||
\(769\) | −2.90761e18 | −0.507007 | −0.253504 | − | 0.967334i | \(-0.581583\pi\) | ||||
−0.253504 | + | 0.967334i | \(0.581583\pi\) | |||||||
\(770\) | 1.75437e18 | 0.303341 | ||||||||
\(771\) | 4.80487e17 | 0.0823811 | ||||||||
\(772\) | 5.96204e18 | 1.01364 | ||||||||
\(773\) | 1.55467e18 | 0.262103 | 0.131052 | − | 0.991376i | \(-0.458165\pi\) | ||||
0.131052 | + | 0.991376i | \(0.458165\pi\) | |||||||
\(774\) | 1.88030e18 | 0.314349 | ||||||||
\(775\) | −6.86209e17 | −0.113762 | ||||||||
\(776\) | −1.04358e18 | −0.171564 | ||||||||
\(777\) | −6.38913e18 | −1.04161 | ||||||||
\(778\) | 2.96367e18 | 0.479140 | ||||||||
\(779\) | 6.35656e18 | 1.01913 | ||||||||
\(780\) | 9.31282e17 | 0.148070 | ||||||||
\(781\) | 5.92639e18 | 0.934456 | ||||||||
\(782\) | −7.15451e18 | −1.11876 | ||||||||
\(783\) | −8.77552e17 | −0.136088 | ||||||||
\(784\) | 2.91309e18 | 0.448022 | ||||||||
\(785\) | 1.17926e17 | 0.0179869 | ||||||||
\(786\) | −1.49940e18 | −0.226815 | ||||||||
\(787\) | 5.65108e18 | 0.847805 | 0.423902 | − | 0.905708i | \(-0.360660\pi\) | ||||
0.423902 | + | 0.905708i | \(0.360660\pi\) | |||||||
\(788\) | −8.05352e18 | −1.19830 | ||||||||
\(789\) | −2.74829e18 | −0.405566 | ||||||||
\(790\) | −6.24115e16 | −0.00913458 | ||||||||
\(791\) | 2.69077e18 | 0.390597 | ||||||||
\(792\) | −1.90705e18 | −0.274567 | ||||||||
\(793\) | −8.34267e18 | −1.19132 | ||||||||
\(794\) | −5.31068e18 | −0.752172 | ||||||||
\(795\) | 2.67690e18 | 0.376050 | ||||||||
\(796\) | 1.46007e18 | 0.203441 | ||||||||
\(797\) | −2.10870e18 | −0.291430 | −0.145715 | − | 0.989327i | \(-0.546548\pi\) | ||||
−0.145715 | + | 0.989327i | \(0.546548\pi\) | |||||||
\(798\) | 3.65197e18 | 0.500620 | ||||||||
\(799\) | −2.45943e19 | −3.34410 | ||||||||
\(800\) | 6.23052e18 | 0.840310 | ||||||||
\(801\) | 2.64210e17 | 0.0353458 | ||||||||
\(802\) | 2.81397e18 | 0.373410 | ||||||||
\(803\) | 8.16754e18 | 1.07508 | ||||||||
\(804\) | −5.95253e17 | −0.0777208 | ||||||||
\(805\) | 5.98354e18 | 0.774971 | ||||||||
\(806\) | 4.17692e17 | 0.0536634 | ||||||||
\(807\) | −6.90271e17 | −0.0879714 | ||||||||
\(808\) | 4.48255e18 | 0.566697 | ||||||||
\(809\) | 4.06041e18 | 0.509219 | 0.254609 | − | 0.967044i | \(-0.418053\pi\) | ||||
0.254609 | + | 0.967044i | \(0.418053\pi\) | |||||||
\(810\) | −1.86049e17 | −0.0231459 | ||||||||
\(811\) | 7.82447e17 | 0.0965650 | 0.0482825 | − | 0.998834i | \(-0.484625\pi\) | ||||
0.0482825 | + | 0.998834i | \(0.484625\pi\) | |||||||
\(812\) | 6.68920e18 | 0.818955 | ||||||||
\(813\) | 9.89854e17 | 0.120222 | ||||||||
\(814\) | −4.60331e18 | −0.554640 | ||||||||
\(815\) | −2.17983e17 | −0.0260554 | ||||||||
\(816\) | 3.18184e18 | 0.377305 | ||||||||
\(817\) | 1.91454e19 | 2.25228 | ||||||||
\(818\) | −3.08208e18 | −0.359706 | ||||||||
\(819\) | −3.45973e18 | −0.400587 | ||||||||
\(820\) | 2.46845e18 | 0.283553 | ||||||||
\(821\) | 8.67478e18 | 0.988617 | 0.494308 | − | 0.869287i | \(-0.335421\pi\) | ||||
0.494308 | + | 0.869287i | \(0.335421\pi\) | |||||||
\(822\) | 3.98888e18 | 0.451008 | ||||||||
\(823\) | −2.87394e18 | −0.322388 | −0.161194 | − | 0.986923i | \(-0.551534\pi\) | ||||
−0.161194 | + | 0.986923i | \(0.551534\pi\) | |||||||
\(824\) | −4.00816e18 | −0.446086 | ||||||||
\(825\) | 4.09516e18 | 0.452189 | ||||||||
\(826\) | −8.83132e17 | −0.0967510 | ||||||||
\(827\) | −8.01024e18 | −0.870682 | −0.435341 | − | 0.900266i | \(-0.643372\pi\) | ||||
−0.435341 | + | 0.900266i | \(0.643372\pi\) | |||||||
\(828\) | −2.81146e18 | −0.303204 | ||||||||
\(829\) | −9.97891e18 | −1.06777 | −0.533886 | − | 0.845556i | \(-0.679269\pi\) | ||||
−0.533886 | + | 0.845556i | \(0.679269\pi\) | |||||||
\(830\) | −2.96400e18 | −0.314681 | ||||||||
\(831\) | 1.06030e19 | 1.11692 | ||||||||
\(832\) | −1.21537e18 | −0.127030 | ||||||||
\(833\) | 2.42856e19 | 2.51858 | ||||||||
\(834\) | −4.47088e17 | −0.0460059 | ||||||||
\(835\) | −3.51418e18 | −0.358808 | ||||||||
\(836\) | −8.39330e18 | −0.850338 | ||||||||
\(837\) | 2.66183e17 | 0.0267586 | ||||||||
\(838\) | −1.97028e18 | −0.196536 | ||||||||
\(839\) | 1.57978e19 | 1.56366 | 0.781831 | − | 0.623491i | \(-0.214286\pi\) | ||||
0.781831 | + | 0.623491i | \(0.214286\pi\) | |||||||
\(840\) | 3.28092e18 | 0.322241 | ||||||||
\(841\) | −5.12988e18 | −0.499958 | ||||||||
\(842\) | 4.06714e18 | 0.393333 | ||||||||
\(843\) | −7.94033e18 | −0.762008 | ||||||||
\(844\) | 1.39540e19 | 1.32884 | ||||||||
\(845\) | −1.69604e18 | −0.160275 | ||||||||
\(846\) | 3.02976e18 | 0.284120 | ||||||||
\(847\) | −1.36737e18 | −0.127246 | ||||||||
\(848\) | 5.63973e18 | 0.520817 | ||||||||
\(849\) | 9.36221e17 | 0.0857982 | ||||||||
\(850\) | 8.42415e18 | 0.766131 | ||||||||
\(851\) | −1.57003e19 | −1.41699 | ||||||||
\(852\) | 4.79069e18 | 0.429082 | ||||||||
\(853\) | 7.10936e17 | 0.0631919 | 0.0315960 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315960 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(854\) | −1.27043e19 | −1.12067 | ||||||||
\(855\) | −1.89437e18 | −0.165838 | ||||||||
\(856\) | −1.70000e18 | −0.147696 | ||||||||
\(857\) | 1.28817e19 | 1.11070 | 0.555350 | − | 0.831617i | \(-0.312584\pi\) | ||||
0.555350 | + | 0.831617i | \(0.312584\pi\) | |||||||
\(858\) | −2.49270e18 | −0.213306 | ||||||||
\(859\) | 2.25964e19 | 1.91904 | 0.959519 | − | 0.281645i | \(-0.0908800\pi\) | ||||
0.959519 | + | 0.281645i | \(0.0908800\pi\) | |||||||
\(860\) | 7.43476e18 | 0.626653 | ||||||||
\(861\) | −9.17032e18 | −0.767121 | ||||||||
\(862\) | 1.62054e18 | 0.134543 | ||||||||
\(863\) | −1.69103e19 | −1.39341 | −0.696707 | − | 0.717356i | \(-0.745352\pi\) | ||||
−0.696707 | + | 0.717356i | \(0.745352\pi\) | |||||||
\(864\) | −2.41684e18 | −0.197655 | ||||||||
\(865\) | −1.34469e18 | −0.109148 | ||||||||
\(866\) | 2.18381e18 | 0.175933 | ||||||||
\(867\) | 1.93057e19 | 1.54369 | ||||||||
\(868\) | −2.02899e18 | −0.161029 | ||||||||
\(869\) | −5.32882e17 | −0.0419761 | ||||||||
\(870\) | 1.08776e18 | 0.0850471 | ||||||||
\(871\) | −1.80002e18 | −0.139688 | ||||||||
\(872\) | 1.75621e19 | 1.35276 | ||||||||
\(873\) | −8.69276e17 | −0.0664608 | ||||||||
\(874\) | 8.97414e18 | 0.681033 | ||||||||
\(875\) | −1.56564e19 | −1.17934 | ||||||||
\(876\) | 6.60236e18 | 0.493654 | ||||||||
\(877\) | −2.01142e19 | −1.49281 | −0.746405 | − | 0.665491i | \(-0.768222\pi\) | ||||
−0.746405 | + | 0.665491i | \(0.768222\pi\) | |||||||
\(878\) | 2.29513e18 | 0.169080 | ||||||||
\(879\) | −1.19548e19 | −0.874207 | ||||||||
\(880\) | −1.91728e18 | −0.139171 | ||||||||
\(881\) | −1.66197e19 | −1.19751 | −0.598754 | − | 0.800933i | \(-0.704337\pi\) | ||||
−0.598754 | + | 0.800933i | \(0.704337\pi\) | |||||||
\(882\) | −2.99174e18 | −0.213982 | ||||||||
\(883\) | 1.56643e19 | 1.11216 | 0.556079 | − | 0.831129i | \(-0.312305\pi\) | ||||
0.556079 | + | 0.831129i | \(0.312305\pi\) | |||||||
\(884\) | 1.63570e19 | 1.15282 | ||||||||
\(885\) | 4.58104e17 | 0.0320503 | ||||||||
\(886\) | 6.97117e18 | 0.484157 | ||||||||
\(887\) | 1.06391e19 | 0.733504 | 0.366752 | − | 0.930319i | \(-0.380470\pi\) | ||||
0.366752 | + | 0.930319i | \(0.380470\pi\) | |||||||
\(888\) | −8.60885e18 | −0.589197 | ||||||||
\(889\) | −1.59586e19 | −1.08426 | ||||||||
\(890\) | −3.27500e17 | −0.0220890 | ||||||||
\(891\) | −1.58852e18 | −0.106362 | ||||||||
\(892\) | 1.98979e19 | 1.32262 | ||||||||
\(893\) | 3.08494e19 | 2.03569 | ||||||||
\(894\) | 2.69368e18 | 0.176462 | ||||||||
\(895\) | −7.05799e18 | −0.459020 | ||||||||
\(896\) | 2.23470e19 | 1.44284 | ||||||||
\(897\) | −8.50174e18 | −0.544950 | ||||||||
\(898\) | 4.43521e18 | 0.282240 | ||||||||
\(899\) | −1.55628e18 | −0.0983217 | ||||||||
\(900\) | 3.31038e18 | 0.207636 | ||||||||
\(901\) | 4.70168e19 | 2.92781 | ||||||||
\(902\) | −6.60713e18 | −0.408479 | ||||||||
\(903\) | −2.76203e19 | −1.69534 | ||||||||
\(904\) | 3.62560e18 | 0.220945 | ||||||||
\(905\) | −5.87516e18 | −0.355471 | ||||||||
\(906\) | 1.81726e18 | 0.109165 | ||||||||
\(907\) | 8.52215e18 | 0.508278 | 0.254139 | − | 0.967168i | \(-0.418208\pi\) | ||||
0.254139 | + | 0.967168i | \(0.418208\pi\) | |||||||
\(908\) | 4.23084e18 | 0.250535 | ||||||||
\(909\) | 3.73384e18 | 0.219528 | ||||||||
\(910\) | 4.28849e18 | 0.250343 | ||||||||
\(911\) | −1.45978e19 | −0.846092 | −0.423046 | − | 0.906108i | \(-0.639039\pi\) | ||||
−0.423046 | + | 0.906108i | \(0.639039\pi\) | |||||||
\(912\) | −3.99109e18 | −0.229681 | ||||||||
\(913\) | −2.53073e19 | −1.44606 | ||||||||
\(914\) | 2.49300e18 | 0.141440 | ||||||||
\(915\) | 6.59007e18 | 0.371239 | ||||||||
\(916\) | −1.29611e19 | −0.724974 | ||||||||
\(917\) | 2.20251e19 | 1.22326 | ||||||||
\(918\) | −3.26775e18 | −0.180207 | ||||||||
\(919\) | 3.06603e19 | 1.67890 | 0.839450 | − | 0.543437i | \(-0.182877\pi\) | ||||
0.839450 | + | 0.543437i | \(0.182877\pi\) | |||||||
\(920\) | 8.06235e18 | 0.438370 | ||||||||
\(921\) | 8.41639e18 | 0.454400 | ||||||||
\(922\) | 5.34499e18 | 0.286547 | ||||||||
\(923\) | 1.44868e19 | 0.771192 | ||||||||
\(924\) | 1.21086e19 | 0.640069 | ||||||||
\(925\) | 1.84864e19 | 0.970358 | ||||||||
\(926\) | −7.41925e18 | −0.386713 | ||||||||
\(927\) | −3.33869e18 | −0.172806 | ||||||||
\(928\) | 1.41304e19 | 0.726262 | ||||||||
\(929\) | −3.57344e19 | −1.82383 | −0.911916 | − | 0.410378i | \(-0.865397\pi\) | ||||
−0.911916 | + | 0.410378i | \(0.865397\pi\) | |||||||
\(930\) | −3.29945e17 | −0.0167225 | ||||||||
\(931\) | −3.04622e19 | −1.53316 | ||||||||
\(932\) | −5.39609e17 | −0.0269697 | ||||||||
\(933\) | −1.88273e18 | −0.0934453 | ||||||||
\(934\) | −1.63753e19 | −0.807112 | ||||||||
\(935\) | −1.59838e19 | −0.782357 | ||||||||
\(936\) | −4.66171e18 | −0.226596 | ||||||||
\(937\) | 3.54595e19 | 1.71169 | 0.855844 | − | 0.517233i | \(-0.173038\pi\) | ||||
0.855844 | + | 0.517233i | \(0.173038\pi\) | |||||||
\(938\) | −2.74110e18 | −0.131403 | ||||||||
\(939\) | 1.15312e19 | 0.548967 | ||||||||
\(940\) | 1.19798e19 | 0.566392 | ||||||||
\(941\) | −3.26670e19 | −1.53383 | −0.766915 | − | 0.641749i | \(-0.778209\pi\) | ||||
−0.766915 | + | 0.641749i | \(0.778209\pi\) | |||||||
\(942\) | −2.55155e17 | −0.0118980 | ||||||||
\(943\) | −2.25346e19 | −1.04358 | ||||||||
\(944\) | 9.65139e17 | 0.0443886 | ||||||||
\(945\) | 2.73292e18 | 0.124830 | ||||||||
\(946\) | −1.99001e19 | −0.902742 | ||||||||
\(947\) | −1.43139e19 | −0.644886 | −0.322443 | − | 0.946589i | \(-0.604504\pi\) | ||||
−0.322443 | + | 0.946589i | \(0.604504\pi\) | |||||||
\(948\) | −4.30763e17 | −0.0192745 | ||||||||
\(949\) | 1.99652e19 | 0.887246 | ||||||||
\(950\) | −1.05667e19 | −0.466375 | ||||||||
\(951\) | 9.01091e17 | 0.0394998 | ||||||||
\(952\) | 5.76259e19 | 2.50887 | ||||||||
\(953\) | 5.17993e18 | 0.223986 | 0.111993 | − | 0.993709i | \(-0.464277\pi\) | ||||
0.111993 | + | 0.993709i | \(0.464277\pi\) | |||||||
\(954\) | −5.79200e18 | −0.248750 | ||||||||
\(955\) | 1.67111e19 | 0.712824 | ||||||||
\(956\) | 1.85568e19 | 0.786190 | ||||||||
\(957\) | 9.28755e18 | 0.390817 | ||||||||
\(958\) | −2.94693e18 | −0.123167 | ||||||||
\(959\) | −5.85938e19 | −2.43238 | ||||||||
\(960\) | 9.60051e17 | 0.0395851 | ||||||||
\(961\) | −2.39455e19 | −0.980667 | ||||||||
\(962\) | −1.12526e19 | −0.457736 | ||||||||
\(963\) | −1.41605e18 | −0.0572149 | ||||||||
\(964\) | −8.64496e18 | −0.346946 | ||||||||
\(965\) | −1.42415e19 | −0.567712 | ||||||||
\(966\) | −1.29466e19 | −0.512630 | ||||||||
\(967\) | 7.35443e18 | 0.289252 | 0.144626 | − | 0.989486i | \(-0.453802\pi\) | ||||
0.144626 | + | 0.989486i | \(0.453802\pi\) | |||||||
\(968\) | −1.84243e18 | −0.0719782 | ||||||||
\(969\) | −3.32726e19 | −1.29117 | ||||||||
\(970\) | 1.07751e18 | 0.0415340 | ||||||||
\(971\) | 4.34657e18 | 0.166426 | 0.0832131 | − | 0.996532i | \(-0.473482\pi\) | ||||
0.0832131 | + | 0.996532i | \(0.473482\pi\) | |||||||
\(972\) | −1.28411e18 | −0.0488394 | ||||||||
\(973\) | 6.56739e18 | 0.248119 | ||||||||
\(974\) | −1.57685e18 | −0.0591777 | ||||||||
\(975\) | 1.00105e19 | 0.373185 | ||||||||
\(976\) | 1.38841e19 | 0.514153 | ||||||||
\(977\) | 1.39032e19 | 0.511445 | 0.255722 | − | 0.966750i | \(-0.417687\pi\) | ||||
0.255722 | + | 0.966750i | \(0.417687\pi\) | |||||||
\(978\) | 4.71649e17 | 0.0172352 | ||||||||
\(979\) | −2.79626e18 | −0.101506 | ||||||||
\(980\) | −1.18294e19 | −0.426573 | ||||||||
\(981\) | 1.46288e19 | 0.524033 | ||||||||
\(982\) | −1.29088e18 | −0.0459369 | ||||||||
\(983\) | −5.29076e19 | −1.87034 | −0.935170 | − | 0.354199i | \(-0.884753\pi\) | ||||
−0.935170 | + | 0.354199i | \(0.884753\pi\) | |||||||
\(984\) | −1.23563e19 | −0.433930 | ||||||||
\(985\) | 1.92374e19 | 0.671136 | ||||||||
\(986\) | 1.91054e19 | 0.662150 | ||||||||
\(987\) | −4.45050e19 | −1.53231 | ||||||||
\(988\) | −2.05171e19 | −0.701771 | ||||||||
\(989\) | −6.78724e19 | −2.30631 | ||||||||
\(990\) | 1.96904e18 | 0.0664702 | ||||||||
\(991\) | −7.55353e18 | −0.253321 | −0.126660 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126660 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(992\) | −4.28610e18 | −0.142803 | ||||||||
\(993\) | 1.77793e18 | 0.0588498 | ||||||||
\(994\) | 2.20608e19 | 0.725453 | ||||||||
\(995\) | −3.48765e18 | −0.113942 | ||||||||
\(996\) | −2.04575e19 | −0.663998 | ||||||||
\(997\) | 3.67023e19 | 1.18352 | 0.591759 | − | 0.806115i | \(-0.298434\pi\) | ||||
0.591759 | + | 0.806115i | \(0.298434\pi\) | |||||||
\(998\) | −2.66230e19 | −0.852920 | ||||||||
\(999\) | −7.17094e18 | −0.228245 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.14.a.a.1.12 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.12 | ✓ | 30 | 1.1 | even | 1 | trivial |