Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −71.6191 | −1.58257 | −0.791287 | − | 0.611445i | \(-0.790589\pi\) | ||||
−0.791287 | + | 0.611445i | \(0.790589\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 3081.30 | 1.50454 | ||||||||
\(5\) | −9710.01 | −1.38958 | −0.694792 | − | 0.719211i | \(-0.744503\pi\) | ||||
−0.694792 | + | 0.719211i | \(0.744503\pi\) | |||||||
\(6\) | −17403.4 | −0.913699 | ||||||||
\(7\) | 37645.0 | 0.846579 | 0.423290 | − | 0.905994i | \(-0.360875\pi\) | ||||
0.423290 | + | 0.905994i | \(0.360875\pi\) | |||||||
\(8\) | −74003.9 | −0.798472 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 695422. | 2.19912 | ||||||||
\(11\) | 60655.0 | 0.113555 | 0.0567776 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567776 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(12\) | 748755. | 0.868647 | ||||||||
\(13\) | 624964. | 0.466838 | 0.233419 | − | 0.972376i | \(-0.425009\pi\) | ||||
0.233419 | + | 0.972376i | \(0.425009\pi\) | |||||||
\(14\) | −2.69610e6 | −1.33977 | ||||||||
\(15\) | −2.35953e6 | −0.802276 | ||||||||
\(16\) | −1.01041e6 | −0.240899 | ||||||||
\(17\) | 2.49028e6 | 0.425382 | 0.212691 | − | 0.977120i | \(-0.431777\pi\) | ||||
0.212691 | + | 0.977120i | \(0.431777\pi\) | |||||||
\(18\) | −4.22904e6 | −0.527525 | ||||||||
\(19\) | −1.44054e7 | −1.33469 | −0.667346 | − | 0.744748i | \(-0.732570\pi\) | ||||
−0.667346 | + | 0.744748i | \(0.732570\pi\) | |||||||
\(20\) | −2.99194e7 | −2.09068 | ||||||||
\(21\) | 9.14772e6 | 0.488773 | ||||||||
\(22\) | −4.34406e6 | −0.179709 | ||||||||
\(23\) | 1.14743e7 | 0.371727 | 0.185863 | − | 0.982576i | \(-0.440492\pi\) | ||||
0.185863 | + | 0.982576i | \(0.440492\pi\) | |||||||
\(24\) | −1.79829e7 | −0.460998 | ||||||||
\(25\) | 4.54562e7 | 0.930942 | ||||||||
\(26\) | −4.47593e7 | −0.738806 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 1.15995e8 | 1.27371 | ||||||||
\(29\) | −1.23449e8 | −1.11763 | −0.558815 | − | 0.829292i | \(-0.688744\pi\) | ||||
−0.558815 | + | 0.829292i | \(0.688744\pi\) | |||||||
\(30\) | 1.68988e8 | 1.26966 | ||||||||
\(31\) | 2.37452e8 | 1.48966 | 0.744828 | − | 0.667256i | \(-0.232531\pi\) | ||||
0.744828 | + | 0.667256i | \(0.232531\pi\) | |||||||
\(32\) | 2.23924e8 | 1.17971 | ||||||||
\(33\) | 1.47392e7 | 0.0655611 | ||||||||
\(34\) | −1.78352e8 | −0.673198 | ||||||||
\(35\) | −3.65533e8 | −1.17639 | ||||||||
\(36\) | 1.81948e8 | 0.501513 | ||||||||
\(37\) | −4.08733e8 | −0.969015 | −0.484507 | − | 0.874787i | \(-0.661001\pi\) | ||||
−0.484507 | + | 0.874787i | \(0.661001\pi\) | |||||||
\(38\) | 1.03170e9 | 2.11225 | ||||||||
\(39\) | 1.51866e8 | 0.269529 | ||||||||
\(40\) | 7.18578e8 | 1.10954 | ||||||||
\(41\) | −2.82822e8 | −0.381243 | −0.190621 | − | 0.981664i | \(-0.561050\pi\) | ||||
−0.190621 | + | 0.981664i | \(0.561050\pi\) | |||||||
\(42\) | −6.55152e8 | −0.773519 | ||||||||
\(43\) | 1.04999e9 | 1.08920 | 0.544601 | − | 0.838695i | \(-0.316681\pi\) | ||||
0.544601 | + | 0.838695i | \(0.316681\pi\) | |||||||
\(44\) | 1.86896e8 | 0.170848 | ||||||||
\(45\) | −5.73366e8 | −0.463195 | ||||||||
\(46\) | −8.21780e8 | −0.588285 | ||||||||
\(47\) | −2.58355e9 | −1.64315 | −0.821577 | − | 0.570098i | \(-0.806905\pi\) | ||||
−0.821577 | + | 0.570098i | \(0.806905\pi\) | |||||||
\(48\) | −2.45529e8 | −0.139083 | ||||||||
\(49\) | −5.60184e8 | −0.283304 | ||||||||
\(50\) | −3.25553e9 | −1.47329 | ||||||||
\(51\) | 6.05138e8 | 0.245594 | ||||||||
\(52\) | 1.92570e9 | 0.702376 | ||||||||
\(53\) | −1.74096e9 | −0.571835 | −0.285918 | − | 0.958254i | \(-0.592298\pi\) | ||||
−0.285918 | + | 0.958254i | \(0.592298\pi\) | |||||||
\(54\) | −1.02766e9 | −0.304566 | ||||||||
\(55\) | −5.88961e8 | −0.157794 | ||||||||
\(56\) | −2.78587e9 | −0.675969 | ||||||||
\(57\) | −3.50052e9 | −0.770585 | ||||||||
\(58\) | 8.84130e9 | 1.76873 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −7.27042e9 | −1.20706 | ||||||||
\(61\) | 1.03848e10 | 1.57429 | 0.787146 | − | 0.616766i | \(-0.211558\pi\) | ||||
0.787146 | + | 0.616766i | \(0.211558\pi\) | |||||||
\(62\) | −1.70061e10 | −2.35749 | ||||||||
\(63\) | 2.22290e9 | 0.282193 | ||||||||
\(64\) | −1.39679e10 | −1.62608 | ||||||||
\(65\) | −6.06840e9 | −0.648710 | ||||||||
\(66\) | −1.05561e9 | −0.103755 | ||||||||
\(67\) | 1.41202e10 | 1.27770 | 0.638850 | − | 0.769331i | \(-0.279410\pi\) | ||||
0.638850 | + | 0.769331i | \(0.279410\pi\) | |||||||
\(68\) | 7.67329e9 | 0.640004 | ||||||||
\(69\) | 2.78826e9 | 0.214616 | ||||||||
\(70\) | 2.61791e10 | 1.86173 | ||||||||
\(71\) | −1.38159e10 | −0.908778 | −0.454389 | − | 0.890803i | \(-0.650142\pi\) | ||||
−0.454389 | + | 0.890803i | \(0.650142\pi\) | |||||||
\(72\) | −4.36986e9 | −0.266157 | ||||||||
\(73\) | 1.71356e10 | 0.967442 | 0.483721 | − | 0.875222i | \(-0.339285\pi\) | ||||
0.483721 | + | 0.875222i | \(0.339285\pi\) | |||||||
\(74\) | 2.92731e10 | 1.53354 | ||||||||
\(75\) | 1.10459e10 | 0.537480 | ||||||||
\(76\) | −4.43874e10 | −2.00810 | ||||||||
\(77\) | 2.28336e9 | 0.0961334 | ||||||||
\(78\) | −1.08765e10 | −0.426550 | ||||||||
\(79\) | 1.65750e10 | 0.606044 | 0.303022 | − | 0.952984i | \(-0.402004\pi\) | ||||
0.303022 | + | 0.952984i | \(0.402004\pi\) | |||||||
\(80\) | 9.81105e9 | 0.334750 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 2.02554e10 | 0.603345 | ||||||||
\(83\) | 1.81884e10 | 0.506834 | 0.253417 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253417 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(84\) | 2.81869e10 | 0.735378 | ||||||||
\(85\) | −2.41806e10 | −0.591104 | ||||||||
\(86\) | −7.51994e10 | −1.72374 | ||||||||
\(87\) | −2.99981e10 | −0.645264 | ||||||||
\(88\) | −4.48871e9 | −0.0906706 | ||||||||
\(89\) | −9.62794e10 | −1.82763 | −0.913815 | − | 0.406131i | \(-0.866878\pi\) | ||||
−0.913815 | + | 0.406131i | \(0.866878\pi\) | |||||||
\(90\) | 4.10640e10 | 0.733040 | ||||||||
\(91\) | 2.35267e10 | 0.395215 | ||||||||
\(92\) | 3.53558e10 | 0.559278 | ||||||||
\(93\) | 5.77008e10 | 0.860053 | ||||||||
\(94\) | 1.85031e11 | 2.60041 | ||||||||
\(95\) | 1.39877e11 | 1.85467 | ||||||||
\(96\) | 5.44136e10 | 0.681108 | ||||||||
\(97\) | 6.76303e10 | 0.799644 | 0.399822 | − | 0.916593i | \(-0.369072\pi\) | ||||
0.399822 | + | 0.916593i | \(0.369072\pi\) | |||||||
\(98\) | 4.01199e10 | 0.448349 | ||||||||
\(99\) | 3.58162e9 | 0.0378517 | ||||||||
\(100\) | 1.40064e11 | 1.40064 | ||||||||
\(101\) | 9.72443e10 | 0.920654 | 0.460327 | − | 0.887749i | \(-0.347732\pi\) | ||||
0.460327 | + | 0.887749i | \(0.347732\pi\) | |||||||
\(102\) | −4.33395e10 | −0.388671 | ||||||||
\(103\) | 1.68362e11 | 1.43100 | 0.715500 | − | 0.698613i | \(-0.246199\pi\) | ||||
0.715500 | + | 0.698613i | \(0.246199\pi\) | |||||||
\(104\) | −4.62497e10 | −0.372757 | ||||||||
\(105\) | −8.88245e10 | −0.679190 | ||||||||
\(106\) | 1.24686e11 | 0.904971 | ||||||||
\(107\) | 2.85563e10 | 0.196830 | 0.0984151 | − | 0.995145i | \(-0.468623\pi\) | ||||
0.0984151 | + | 0.995145i | \(0.468623\pi\) | |||||||
\(108\) | 4.42133e10 | 0.289549 | ||||||||
\(109\) | 1.07166e11 | 0.667134 | 0.333567 | − | 0.942726i | \(-0.391748\pi\) | ||||
0.333567 | + | 0.942726i | \(0.391748\pi\) | |||||||
\(110\) | 4.21809e10 | 0.249721 | ||||||||
\(111\) | −9.93222e10 | −0.559461 | ||||||||
\(112\) | −3.80367e10 | −0.203940 | ||||||||
\(113\) | 2.67933e11 | 1.36803 | 0.684015 | − | 0.729468i | \(-0.260232\pi\) | ||||
0.684015 | + | 0.729468i | \(0.260232\pi\) | |||||||
\(114\) | 2.50704e11 | 1.21951 | ||||||||
\(115\) | −1.11416e11 | −0.516545 | ||||||||
\(116\) | −3.80383e11 | −1.68152 | ||||||||
\(117\) | 3.69035e10 | 0.155613 | ||||||||
\(118\) | 5.12022e10 | 0.206034 | ||||||||
\(119\) | 9.37465e10 | 0.360120 | ||||||||
\(120\) | 1.74615e11 | 0.640595 | ||||||||
\(121\) | −2.81633e11 | −0.987105 | ||||||||
\(122\) | −7.43753e11 | −2.49143 | ||||||||
\(123\) | −6.87257e10 | −0.220111 | ||||||||
\(124\) | 7.31659e11 | 2.24125 | ||||||||
\(125\) | 3.27417e10 | 0.0959613 | ||||||||
\(126\) | −1.59202e11 | −0.446591 | ||||||||
\(127\) | −4.93391e11 | −1.32517 | −0.662583 | − | 0.748988i | \(-0.730540\pi\) | ||||
−0.662583 | + | 0.748988i | \(0.730540\pi\) | |||||||
\(128\) | 5.41775e11 | 1.39368 | ||||||||
\(129\) | 2.55148e11 | 0.628851 | ||||||||
\(130\) | 4.34614e11 | 1.02663 | ||||||||
\(131\) | −3.92825e11 | −0.889625 | −0.444813 | − | 0.895624i | \(-0.646730\pi\) | ||||
−0.444813 | + | 0.895624i | \(0.646730\pi\) | |||||||
\(132\) | 4.54158e10 | 0.0986393 | ||||||||
\(133\) | −5.42292e11 | −1.12992 | ||||||||
\(134\) | −1.01127e12 | −2.02205 | ||||||||
\(135\) | −1.39328e11 | −0.267425 | ||||||||
\(136\) | −1.84290e11 | −0.339656 | ||||||||
\(137\) | 1.35467e11 | 0.239811 | 0.119906 | − | 0.992785i | \(-0.461741\pi\) | ||||
0.119906 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(138\) | −1.99693e11 | −0.339646 | ||||||||
\(139\) | −3.25168e11 | −0.531529 | −0.265764 | − | 0.964038i | \(-0.585624\pi\) | ||||
−0.265764 | + | 0.964038i | \(0.585624\pi\) | |||||||
\(140\) | −1.12632e12 | −1.76993 | ||||||||
\(141\) | −6.27802e11 | −0.948675 | ||||||||
\(142\) | 9.89481e11 | 1.43821 | ||||||||
\(143\) | 3.79072e10 | 0.0530119 | ||||||||
\(144\) | −5.96634e10 | −0.0802998 | ||||||||
\(145\) | 1.19869e12 | 1.55304 | ||||||||
\(146\) | −1.22724e12 | −1.53105 | ||||||||
\(147\) | −1.36125e11 | −0.163566 | ||||||||
\(148\) | −1.25943e12 | −1.45792 | ||||||||
\(149\) | −8.60761e11 | −0.960192 | −0.480096 | − | 0.877216i | \(-0.659398\pi\) | ||||
−0.480096 | + | 0.877216i | \(0.659398\pi\) | |||||||
\(150\) | −7.91094e11 | −0.850602 | ||||||||
\(151\) | −2.95852e11 | −0.306691 | −0.153346 | − | 0.988173i | \(-0.549005\pi\) | ||||
−0.153346 | + | 0.988173i | \(0.549005\pi\) | |||||||
\(152\) | 1.06606e12 | 1.06571 | ||||||||
\(153\) | 1.47049e11 | 0.141794 | ||||||||
\(154\) | −1.63532e11 | −0.152138 | ||||||||
\(155\) | −2.30566e12 | −2.07000 | ||||||||
\(156\) | 4.67945e11 | 0.405517 | ||||||||
\(157\) | 8.60052e11 | 0.719576 | 0.359788 | − | 0.933034i | \(-0.382849\pi\) | ||||
0.359788 | + | 0.933034i | \(0.382849\pi\) | |||||||
\(158\) | −1.18709e12 | −0.959109 | ||||||||
\(159\) | −4.23053e11 | −0.330149 | ||||||||
\(160\) | −2.17431e12 | −1.63931 | ||||||||
\(161\) | 4.31950e11 | 0.314696 | ||||||||
\(162\) | −2.49720e11 | −0.175842 | ||||||||
\(163\) | −4.52373e11 | −0.307939 | −0.153970 | − | 0.988076i | \(-0.549206\pi\) | ||||
−0.153970 | + | 0.988076i | \(0.549206\pi\) | |||||||
\(164\) | −8.71458e11 | −0.573595 | ||||||||
\(165\) | −1.43117e11 | −0.0911027 | ||||||||
\(166\) | −1.30264e12 | −0.802102 | ||||||||
\(167\) | −3.57279e11 | −0.212846 | −0.106423 | − | 0.994321i | \(-0.533940\pi\) | ||||
−0.106423 | + | 0.994321i | \(0.533940\pi\) | |||||||
\(168\) | −6.76967e11 | −0.390271 | ||||||||
\(169\) | −1.40158e12 | −0.782062 | ||||||||
\(170\) | 1.73180e12 | 0.935466 | ||||||||
\(171\) | −8.50626e11 | −0.444898 | ||||||||
\(172\) | 3.23533e12 | 1.63875 | ||||||||
\(173\) | 1.16482e12 | 0.571486 | 0.285743 | − | 0.958306i | \(-0.407760\pi\) | ||||
0.285743 | + | 0.958306i | \(0.407760\pi\) | |||||||
\(174\) | 2.14844e12 | 1.02118 | ||||||||
\(175\) | 1.71120e12 | 0.788116 | ||||||||
\(176\) | −6.12862e10 | −0.0273554 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | 6.89544e12 | 2.89236 | ||||||||
\(179\) | −5.99613e11 | −0.243882 | −0.121941 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121941 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(180\) | −1.76671e12 | −0.696895 | ||||||||
\(181\) | 2.40799e11 | 0.0921347 | 0.0460673 | − | 0.998938i | \(-0.485331\pi\) | ||||
0.0460673 | + | 0.998938i | \(0.485331\pi\) | |||||||
\(182\) | −1.68496e12 | −0.625457 | ||||||||
\(183\) | 2.52351e12 | 0.908918 | ||||||||
\(184\) | −8.49144e11 | −0.296813 | ||||||||
\(185\) | 3.96880e12 | 1.34653 | ||||||||
\(186\) | −4.13248e12 | −1.36110 | ||||||||
\(187\) | 1.51048e11 | 0.0483043 | ||||||||
\(188\) | −7.96068e12 | −2.47219 | ||||||||
\(189\) | 5.40164e11 | 0.162924 | ||||||||
\(190\) | −1.00179e13 | −2.93515 | ||||||||
\(191\) | −1.64656e12 | −0.468699 | −0.234350 | − | 0.972152i | \(-0.575296\pi\) | ||||
−0.234350 | + | 0.972152i | \(0.575296\pi\) | |||||||
\(192\) | −3.39421e12 | −0.938820 | ||||||||
\(193\) | 1.54565e12 | 0.415476 | 0.207738 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207738 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(194\) | −4.84362e12 | −1.26550 | ||||||||
\(195\) | −1.47462e12 | −0.374533 | ||||||||
\(196\) | −1.72609e12 | −0.426242 | ||||||||
\(197\) | 1.38427e12 | 0.332397 | 0.166199 | − | 0.986092i | \(-0.446851\pi\) | ||||
0.166199 | + | 0.986092i | \(0.446851\pi\) | |||||||
\(198\) | −2.56512e11 | −0.0599032 | ||||||||
\(199\) | −1.07613e12 | −0.244441 | −0.122221 | − | 0.992503i | \(-0.539002\pi\) | ||||
−0.122221 | + | 0.992503i | \(0.539002\pi\) | |||||||
\(200\) | −3.36393e12 | −0.743331 | ||||||||
\(201\) | 3.43120e12 | 0.737680 | ||||||||
\(202\) | −6.96455e12 | −1.45700 | ||||||||
\(203\) | −4.64723e12 | −0.946163 | ||||||||
\(204\) | 1.86461e12 | 0.369507 | ||||||||
\(205\) | 2.74620e12 | 0.529769 | ||||||||
\(206\) | −1.20579e13 | −2.26466 | ||||||||
\(207\) | 6.77547e11 | 0.123909 | ||||||||
\(208\) | −6.31467e11 | −0.112461 | ||||||||
\(209\) | −8.73761e11 | −0.151561 | ||||||||
\(210\) | 6.36153e12 | 1.07487 | ||||||||
\(211\) | −9.00351e12 | −1.48204 | −0.741018 | − | 0.671486i | \(-0.765657\pi\) | ||||
−0.741018 | + | 0.671486i | \(0.765657\pi\) | |||||||
\(212\) | −5.36441e12 | −0.860349 | ||||||||
\(213\) | −3.35726e12 | −0.524683 | ||||||||
\(214\) | −2.04518e12 | −0.311498 | ||||||||
\(215\) | −1.01954e13 | −1.51354 | ||||||||
\(216\) | −1.06187e12 | −0.153666 | ||||||||
\(217\) | 8.93886e12 | 1.26111 | ||||||||
\(218\) | −7.67517e12 | −1.05579 | ||||||||
\(219\) | 4.16396e12 | 0.558553 | ||||||||
\(220\) | −1.81476e12 | −0.237408 | ||||||||
\(221\) | 1.55633e12 | 0.198585 | ||||||||
\(222\) | 7.11337e12 | 0.885388 | ||||||||
\(223\) | 2.56413e12 | 0.311360 | 0.155680 | − | 0.987808i | \(-0.450243\pi\) | ||||
0.155680 | + | 0.987808i | \(0.450243\pi\) | |||||||
\(224\) | 8.42962e12 | 0.998720 | ||||||||
\(225\) | 2.68414e12 | 0.310314 | ||||||||
\(226\) | −1.91892e13 | −2.16501 | ||||||||
\(227\) | 4.72205e12 | 0.519982 | 0.259991 | − | 0.965611i | \(-0.416280\pi\) | ||||
0.259991 | + | 0.965611i | \(0.416280\pi\) | |||||||
\(228\) | −1.07861e13 | −1.15938 | ||||||||
\(229\) | −1.74449e13 | −1.83051 | −0.915256 | − | 0.402873i | \(-0.868012\pi\) | ||||
−0.915256 | + | 0.402873i | \(0.868012\pi\) | |||||||
\(230\) | 7.97949e12 | 0.817471 | ||||||||
\(231\) | 5.54855e11 | 0.0555027 | ||||||||
\(232\) | 9.13570e12 | 0.892396 | ||||||||
\(233\) | 6.59376e11 | 0.0629036 | 0.0314518 | − | 0.999505i | \(-0.489987\pi\) | ||||
0.0314518 | + | 0.999505i | \(0.489987\pi\) | |||||||
\(234\) | −2.64299e12 | −0.246269 | ||||||||
\(235\) | 2.50863e13 | 2.28330 | ||||||||
\(236\) | −2.20289e12 | −0.195874 | ||||||||
\(237\) | 4.02772e12 | 0.349899 | ||||||||
\(238\) | −6.71404e12 | −0.569916 | ||||||||
\(239\) | −9.06209e12 | −0.751692 | −0.375846 | − | 0.926682i | \(-0.622648\pi\) | ||||
−0.375846 | + | 0.926682i | \(0.622648\pi\) | |||||||
\(240\) | 2.38408e12 | 0.193268 | ||||||||
\(241\) | −2.24055e13 | −1.77525 | −0.887626 | − | 0.460565i | \(-0.847647\pi\) | ||||
−0.887626 | + | 0.460565i | \(0.847647\pi\) | |||||||
\(242\) | 2.01703e13 | 1.56217 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 3.19988e13 | 2.36859 | ||||||||
\(245\) | 5.43940e12 | 0.393674 | ||||||||
\(246\) | 4.92207e12 | 0.348341 | ||||||||
\(247\) | −9.00287e12 | −0.623085 | ||||||||
\(248\) | −1.75723e13 | −1.18945 | ||||||||
\(249\) | 4.41979e12 | 0.292621 | ||||||||
\(250\) | −2.34493e12 | −0.151866 | ||||||||
\(251\) | 1.13619e13 | 0.719857 | 0.359929 | − | 0.932980i | \(-0.382801\pi\) | ||||
0.359929 | + | 0.932980i | \(0.382801\pi\) | |||||||
\(252\) | 6.84941e12 | 0.424571 | ||||||||
\(253\) | 6.95975e11 | 0.0422115 | ||||||||
\(254\) | 3.53362e13 | 2.09717 | ||||||||
\(255\) | −5.87590e12 | −0.341274 | ||||||||
\(256\) | −1.01951e13 | −0.579525 | ||||||||
\(257\) | 1.61056e12 | 0.0896074 | 0.0448037 | − | 0.998996i | \(-0.485734\pi\) | ||||
0.0448037 | + | 0.998996i | \(0.485734\pi\) | |||||||
\(258\) | −1.82734e13 | −0.995204 | ||||||||
\(259\) | −1.53867e13 | −0.820348 | ||||||||
\(260\) | −1.86986e13 | −0.976011 | ||||||||
\(261\) | −7.28953e12 | −0.372544 | ||||||||
\(262\) | 2.81338e13 | 1.40790 | ||||||||
\(263\) | −1.14324e13 | −0.560251 | −0.280125 | − | 0.959963i | \(-0.590376\pi\) | ||||
−0.280125 | + | 0.959963i | \(0.590376\pi\) | |||||||
\(264\) | −1.09076e12 | −0.0523487 | ||||||||
\(265\) | 1.69047e13 | 0.794613 | ||||||||
\(266\) | 3.88384e13 | 1.78819 | ||||||||
\(267\) | −2.33959e13 | −1.05518 | ||||||||
\(268\) | 4.35085e13 | 1.92235 | ||||||||
\(269\) | −3.96300e13 | −1.71548 | −0.857742 | − | 0.514081i | \(-0.828133\pi\) | ||||
−0.857742 | + | 0.514081i | \(0.828133\pi\) | |||||||
\(270\) | 9.97855e12 | 0.423221 | ||||||||
\(271\) | 6.17718e12 | 0.256720 | 0.128360 | − | 0.991728i | \(-0.459029\pi\) | ||||
0.128360 | + | 0.991728i | \(0.459029\pi\) | |||||||
\(272\) | −2.51619e12 | −0.102474 | ||||||||
\(273\) | 5.71699e12 | 0.228178 | ||||||||
\(274\) | −9.70201e12 | −0.379519 | ||||||||
\(275\) | 2.75715e12 | 0.105713 | ||||||||
\(276\) | 8.59145e12 | 0.322899 | ||||||||
\(277\) | −5.13723e13 | −1.89274 | −0.946368 | − | 0.323090i | \(-0.895278\pi\) | ||||
−0.946368 | + | 0.323090i | \(0.895278\pi\) | |||||||
\(278\) | 2.32883e13 | 0.841184 | ||||||||
\(279\) | 1.40213e13 | 0.496552 | ||||||||
\(280\) | 2.70508e13 | 0.939316 | ||||||||
\(281\) | 1.65407e13 | 0.563210 | 0.281605 | − | 0.959530i | \(-0.409133\pi\) | ||||
0.281605 | + | 0.959530i | \(0.409133\pi\) | |||||||
\(282\) | 4.49626e13 | 1.50135 | ||||||||
\(283\) | 9.14231e12 | 0.299385 | 0.149693 | − | 0.988733i | \(-0.452172\pi\) | ||||
0.149693 | + | 0.988733i | \(0.452172\pi\) | |||||||
\(284\) | −4.25708e13 | −1.36729 | ||||||||
\(285\) | 3.39901e13 | 1.07079 | ||||||||
\(286\) | −2.71488e12 | −0.0838952 | ||||||||
\(287\) | −1.06468e13 | −0.322752 | ||||||||
\(288\) | 1.32225e13 | 0.393238 | ||||||||
\(289\) | −2.80704e13 | −0.819050 | ||||||||
\(290\) | −8.58491e13 | −2.45780 | ||||||||
\(291\) | 1.64342e13 | 0.461675 | ||||||||
\(292\) | 5.28000e13 | 1.45555 | ||||||||
\(293\) | −1.46326e13 | −0.395866 | −0.197933 | − | 0.980216i | \(-0.563423\pi\) | ||||
−0.197933 | + | 0.980216i | \(0.563423\pi\) | |||||||
\(294\) | 9.74914e12 | 0.258855 | ||||||||
\(295\) | 6.94192e12 | 0.180908 | ||||||||
\(296\) | 3.02478e13 | 0.773731 | ||||||||
\(297\) | 8.70333e11 | 0.0218537 | ||||||||
\(298\) | 6.16470e13 | 1.51958 | ||||||||
\(299\) | 7.17103e12 | 0.173536 | ||||||||
\(300\) | 3.40356e13 | 0.808660 | ||||||||
\(301\) | 3.95268e13 | 0.922096 | ||||||||
\(302\) | 2.11887e13 | 0.485362 | ||||||||
\(303\) | 2.36304e13 | 0.531540 | ||||||||
\(304\) | 1.45553e13 | 0.321527 | ||||||||
\(305\) | −1.00837e14 | −2.18761 | ||||||||
\(306\) | −1.05315e13 | −0.224399 | ||||||||
\(307\) | 9.77088e12 | 0.204490 | 0.102245 | − | 0.994759i | \(-0.467397\pi\) | ||||
0.102245 | + | 0.994759i | \(0.467397\pi\) | |||||||
\(308\) | 7.03570e12 | 0.144637 | ||||||||
\(309\) | 4.09120e13 | 0.826188 | ||||||||
\(310\) | 1.65129e14 | 3.27593 | ||||||||
\(311\) | −3.39024e13 | −0.660767 | −0.330383 | − | 0.943847i | \(-0.607178\pi\) | ||||
−0.330383 | + | 0.943847i | \(0.607178\pi\) | |||||||
\(312\) | −1.12387e13 | −0.215211 | ||||||||
\(313\) | −6.89569e13 | −1.29743 | −0.648714 | − | 0.761032i | \(-0.724693\pi\) | ||||
−0.648714 | + | 0.761032i | \(0.724693\pi\) | |||||||
\(314\) | −6.15962e13 | −1.13878 | ||||||||
\(315\) | −2.15843e13 | −0.392131 | ||||||||
\(316\) | 5.10724e13 | 0.911817 | ||||||||
\(317\) | −6.46132e13 | −1.13369 | −0.566847 | − | 0.823823i | \(-0.691837\pi\) | ||||
−0.566847 | + | 0.823823i | \(0.691837\pi\) | |||||||
\(318\) | 3.02987e13 | 0.522485 | ||||||||
\(319\) | −7.48780e12 | −0.126913 | ||||||||
\(320\) | 1.35629e14 | 2.25958 | ||||||||
\(321\) | 6.93919e12 | 0.113640 | ||||||||
\(322\) | −3.09359e13 | −0.498030 | ||||||||
\(323\) | −3.58735e13 | −0.567754 | ||||||||
\(324\) | 1.07438e13 | 0.167171 | ||||||||
\(325\) | 2.84085e13 | 0.434599 | ||||||||
\(326\) | 3.23986e13 | 0.487337 | ||||||||
\(327\) | 2.60415e13 | 0.385170 | ||||||||
\(328\) | 2.09299e13 | 0.304412 | ||||||||
\(329\) | −9.72575e13 | −1.39106 | ||||||||
\(330\) | 1.02499e13 | 0.144177 | ||||||||
\(331\) | −9.99966e13 | −1.38335 | −0.691674 | − | 0.722210i | \(-0.743126\pi\) | ||||
−0.691674 | + | 0.722210i | \(0.743126\pi\) | |||||||
\(332\) | 5.60439e13 | 0.762552 | ||||||||
\(333\) | −2.41353e13 | −0.323005 | ||||||||
\(334\) | 2.55880e13 | 0.336845 | ||||||||
\(335\) | −1.37107e14 | −1.77547 | ||||||||
\(336\) | −9.24291e12 | −0.117745 | ||||||||
\(337\) | −1.23806e14 | −1.55159 | −0.775795 | − | 0.630985i | \(-0.782651\pi\) | ||||
−0.775795 | + | 0.630985i | \(0.782651\pi\) | |||||||
\(338\) | 1.00380e14 | 1.23767 | ||||||||
\(339\) | 6.51078e13 | 0.789832 | ||||||||
\(340\) | −7.45078e13 | −0.889339 | ||||||||
\(341\) | 1.44026e13 | 0.169158 | ||||||||
\(342\) | 6.09211e13 | 0.704083 | ||||||||
\(343\) | −9.55245e13 | −1.08642 | ||||||||
\(344\) | −7.77033e13 | −0.869698 | ||||||||
\(345\) | −2.70740e13 | −0.298227 | ||||||||
\(346\) | −8.34234e13 | −0.904418 | ||||||||
\(347\) | 9.04500e13 | 0.965154 | 0.482577 | − | 0.875854i | \(-0.339701\pi\) | ||||
0.482577 | + | 0.875854i | \(0.339701\pi\) | |||||||
\(348\) | −9.24330e13 | −0.970826 | ||||||||
\(349\) | −4.98058e12 | −0.0514920 | −0.0257460 | − | 0.999669i | \(-0.508196\pi\) | ||||
−0.0257460 | + | 0.999669i | \(0.508196\pi\) | |||||||
\(350\) | −1.22554e14 | −1.24725 | ||||||||
\(351\) | 8.96754e12 | 0.0898430 | ||||||||
\(352\) | 1.35821e13 | 0.133963 | ||||||||
\(353\) | −9.99494e13 | −0.970554 | −0.485277 | − | 0.874361i | \(-0.661281\pi\) | ||||
−0.485277 | + | 0.874361i | \(0.661281\pi\) | |||||||
\(354\) | 1.24421e13 | 0.118954 | ||||||||
\(355\) | 1.34152e14 | 1.26282 | ||||||||
\(356\) | −2.96665e14 | −2.74974 | ||||||||
\(357\) | 2.27804e13 | 0.207915 | ||||||||
\(358\) | 4.29437e13 | 0.385961 | ||||||||
\(359\) | 7.76199e13 | 0.686995 | 0.343498 | − | 0.939154i | \(-0.388388\pi\) | ||||
0.343498 | + | 0.939154i | \(0.388388\pi\) | |||||||
\(360\) | 4.24313e13 | 0.369848 | ||||||||
\(361\) | 9.10260e13 | 0.781404 | ||||||||
\(362\) | −1.72458e13 | −0.145810 | ||||||||
\(363\) | −6.84367e13 | −0.569905 | ||||||||
\(364\) | 7.24928e13 | 0.594617 | ||||||||
\(365\) | −1.66387e14 | −1.34434 | ||||||||
\(366\) | −1.80732e14 | −1.43843 | ||||||||
\(367\) | 1.26252e14 | 0.989861 | 0.494930 | − | 0.868933i | \(-0.335194\pi\) | ||||
0.494930 | + | 0.868933i | \(0.335194\pi\) | |||||||
\(368\) | −1.15937e13 | −0.0895487 | ||||||||
\(369\) | −1.67003e13 | −0.127081 | ||||||||
\(370\) | −2.84242e14 | −2.13098 | ||||||||
\(371\) | −6.55383e13 | −0.484104 | ||||||||
\(372\) | 1.77793e14 | 1.29398 | ||||||||
\(373\) | 2.49748e14 | 1.79103 | 0.895515 | − | 0.445031i | \(-0.146807\pi\) | ||||
0.895515 | + | 0.445031i | \(0.146807\pi\) | |||||||
\(374\) | −1.08179e13 | −0.0764452 | ||||||||
\(375\) | 7.95623e12 | 0.0554033 | ||||||||
\(376\) | 1.91193e14 | 1.31201 | ||||||||
\(377\) | −7.71511e13 | −0.521752 | ||||||||
\(378\) | −3.86861e13 | −0.257840 | ||||||||
\(379\) | 5.89118e13 | 0.386978 | 0.193489 | − | 0.981102i | \(-0.438020\pi\) | ||||
0.193489 | + | 0.981102i | \(0.438020\pi\) | |||||||
\(380\) | 4.31002e14 | 2.79042 | ||||||||
\(381\) | −1.19894e14 | −0.765085 | ||||||||
\(382\) | 1.17925e14 | 0.741752 | ||||||||
\(383\) | −1.30460e14 | −0.808881 | −0.404440 | − | 0.914564i | \(-0.632534\pi\) | ||||
−0.404440 | + | 0.914564i | \(0.632534\pi\) | |||||||
\(384\) | 1.31651e14 | 0.804644 | ||||||||
\(385\) | −2.21714e13 | −0.133585 | ||||||||
\(386\) | −1.10698e14 | −0.657521 | ||||||||
\(387\) | 6.20009e13 | 0.363068 | ||||||||
\(388\) | 2.08389e14 | 1.20310 | ||||||||
\(389\) | 1.05199e14 | 0.598807 | 0.299403 | − | 0.954127i | \(-0.403212\pi\) | ||||
0.299403 | + | 0.954127i | \(0.403212\pi\) | |||||||
\(390\) | 1.05611e14 | 0.592726 | ||||||||
\(391\) | 2.85743e13 | 0.158126 | ||||||||
\(392\) | 4.14558e13 | 0.226210 | ||||||||
\(393\) | −9.54565e13 | −0.513625 | ||||||||
\(394\) | −9.91404e13 | −0.526043 | ||||||||
\(395\) | −1.60943e14 | −0.842148 | ||||||||
\(396\) | 1.10360e13 | 0.0569494 | ||||||||
\(397\) | −2.32327e14 | −1.18237 | −0.591184 | − | 0.806537i | \(-0.701339\pi\) | ||||
−0.591184 | + | 0.806537i | \(0.701339\pi\) | |||||||
\(398\) | 7.70718e13 | 0.386846 | ||||||||
\(399\) | −1.31777e14 | −0.652361 | ||||||||
\(400\) | −4.59292e13 | −0.224264 | ||||||||
\(401\) | −3.00084e14 | −1.44527 | −0.722635 | − | 0.691230i | \(-0.757069\pi\) | ||||
−0.722635 | + | 0.691230i | \(0.757069\pi\) | |||||||
\(402\) | −2.45740e14 | −1.16743 | ||||||||
\(403\) | 1.48399e14 | 0.695428 | ||||||||
\(404\) | 2.99639e14 | 1.38516 | ||||||||
\(405\) | −3.38567e13 | −0.154398 | ||||||||
\(406\) | 3.32830e14 | 1.49737 | ||||||||
\(407\) | −2.47917e13 | −0.110037 | ||||||||
\(408\) | −4.47826e13 | −0.196100 | ||||||||
\(409\) | 3.69758e14 | 1.59749 | 0.798747 | − | 0.601667i | \(-0.205497\pi\) | ||||
0.798747 | + | 0.601667i | \(0.205497\pi\) | |||||||
\(410\) | −1.96681e14 | −0.838398 | ||||||||
\(411\) | 3.29184e13 | 0.138455 | ||||||||
\(412\) | 5.18774e14 | 2.15300 | ||||||||
\(413\) | −2.69133e13 | −0.110215 | ||||||||
\(414\) | −4.85253e13 | −0.196095 | ||||||||
\(415\) | −1.76610e14 | −0.704288 | ||||||||
\(416\) | 1.39945e14 | 0.550735 | ||||||||
\(417\) | −7.90159e13 | −0.306878 | ||||||||
\(418\) | 6.25780e13 | 0.239857 | ||||||||
\(419\) | 1.12710e14 | 0.426370 | 0.213185 | − | 0.977012i | \(-0.431616\pi\) | ||||
0.213185 | + | 0.977012i | \(0.431616\pi\) | |||||||
\(420\) | −2.73695e14 | −1.02187 | ||||||||
\(421\) | 4.47083e14 | 1.64754 | 0.823772 | − | 0.566922i | \(-0.191866\pi\) | ||||
0.823772 | + | 0.566922i | \(0.191866\pi\) | |||||||
\(422\) | 6.44824e14 | 2.34543 | ||||||||
\(423\) | −1.52556e14 | −0.547718 | ||||||||
\(424\) | 1.28838e14 | 0.456594 | ||||||||
\(425\) | 1.13199e14 | 0.396006 | ||||||||
\(426\) | 2.40444e14 | 0.830350 | ||||||||
\(427\) | 3.90937e14 | 1.33276 | ||||||||
\(428\) | 8.79906e13 | 0.296139 | ||||||||
\(429\) | 9.21144e12 | 0.0306064 | ||||||||
\(430\) | 7.30187e14 | 2.39529 | ||||||||
\(431\) | 2.16562e14 | 0.701386 | 0.350693 | − | 0.936490i | \(-0.385946\pi\) | ||||
0.350693 | + | 0.936490i | \(0.385946\pi\) | |||||||
\(432\) | −1.44982e13 | −0.0463611 | ||||||||
\(433\) | −4.32371e14 | −1.36513 | −0.682563 | − | 0.730827i | \(-0.739135\pi\) | ||||
−0.682563 | + | 0.730827i | \(0.739135\pi\) | |||||||
\(434\) | −6.40193e14 | −1.99580 | ||||||||
\(435\) | 2.91282e14 | 0.896649 | ||||||||
\(436\) | 3.30212e14 | 1.00373 | ||||||||
\(437\) | −1.65292e14 | −0.496141 | ||||||||
\(438\) | −2.98219e14 | −0.883951 | ||||||||
\(439\) | −3.18492e14 | −0.932275 | −0.466137 | − | 0.884712i | \(-0.654355\pi\) | ||||
−0.466137 | + | 0.884712i | \(0.654355\pi\) | |||||||
\(440\) | 4.35854e13 | 0.125994 | ||||||||
\(441\) | −3.30783e13 | −0.0944346 | ||||||||
\(442\) | −1.11463e14 | −0.314275 | ||||||||
\(443\) | 4.44114e14 | 1.23673 | 0.618364 | − | 0.785892i | \(-0.287796\pi\) | ||||
0.618364 | + | 0.785892i | \(0.287796\pi\) | |||||||
\(444\) | −3.06041e14 | −0.841731 | ||||||||
\(445\) | 9.34874e14 | 2.53964 | ||||||||
\(446\) | −1.83641e14 | −0.492751 | ||||||||
\(447\) | −2.09165e14 | −0.554367 | ||||||||
\(448\) | −5.25823e14 | −1.37661 | ||||||||
\(449\) | −1.82168e14 | −0.471105 | −0.235552 | − | 0.971862i | \(-0.575690\pi\) | ||||
−0.235552 | + | 0.971862i | \(0.575690\pi\) | |||||||
\(450\) | −1.92236e14 | −0.491095 | ||||||||
\(451\) | −1.71546e13 | −0.0432921 | ||||||||
\(452\) | 8.25583e14 | 2.05825 | ||||||||
\(453\) | −7.18921e13 | −0.177068 | ||||||||
\(454\) | −3.38189e14 | −0.822910 | ||||||||
\(455\) | −2.28445e14 | −0.549185 | ||||||||
\(456\) | 2.59052e14 | 0.615290 | ||||||||
\(457\) | 1.57071e14 | 0.368602 | 0.184301 | − | 0.982870i | \(-0.440998\pi\) | ||||
0.184301 | + | 0.982870i | \(0.440998\pi\) | |||||||
\(458\) | 1.24939e15 | 2.89692 | ||||||||
\(459\) | 3.57328e13 | 0.0818648 | ||||||||
\(460\) | −3.43305e14 | −0.777163 | ||||||||
\(461\) | −6.23903e14 | −1.39560 | −0.697801 | − | 0.716292i | \(-0.745838\pi\) | ||||
−0.697801 | + | 0.716292i | \(0.745838\pi\) | |||||||
\(462\) | −3.97382e13 | −0.0878371 | ||||||||
\(463\) | −3.29305e14 | −0.719288 | −0.359644 | − | 0.933090i | \(-0.617102\pi\) | ||||
−0.359644 | + | 0.933090i | \(0.617102\pi\) | |||||||
\(464\) | 1.24733e14 | 0.269237 | ||||||||
\(465\) | −5.60275e14 | −1.19512 | ||||||||
\(466\) | −4.72240e13 | −0.0995497 | ||||||||
\(467\) | 7.60322e14 | 1.58400 | 0.791999 | − | 0.610522i | \(-0.209040\pi\) | ||||
0.791999 | + | 0.610522i | \(0.209040\pi\) | |||||||
\(468\) | 1.13711e14 | 0.234125 | ||||||||
\(469\) | 5.31554e14 | 1.08167 | ||||||||
\(470\) | −1.79666e15 | −3.61349 | ||||||||
\(471\) | 2.08993e14 | 0.415447 | ||||||||
\(472\) | 5.29072e13 | 0.103952 | ||||||||
\(473\) | 6.36872e13 | 0.123685 | ||||||||
\(474\) | −2.88462e14 | −0.553742 | ||||||||
\(475\) | −6.54815e14 | −1.24252 | ||||||||
\(476\) | 2.88861e14 | 0.541814 | ||||||||
\(477\) | −1.02802e14 | −0.190612 | ||||||||
\(478\) | 6.49019e14 | 1.18961 | ||||||||
\(479\) | −5.26864e13 | −0.0954669 | −0.0477335 | − | 0.998860i | \(-0.515200\pi\) | ||||
−0.0477335 | + | 0.998860i | \(0.515200\pi\) | |||||||
\(480\) | −5.28357e14 | −0.946456 | ||||||||
\(481\) | −2.55443e14 | −0.452373 | ||||||||
\(482\) | 1.60466e15 | 2.80947 | ||||||||
\(483\) | 1.04964e14 | 0.181690 | ||||||||
\(484\) | −8.67794e14 | −1.48514 | ||||||||
\(485\) | −6.56691e14 | −1.11117 | ||||||||
\(486\) | −6.06821e13 | −0.101522 | ||||||||
\(487\) | −3.58994e14 | −0.593851 | −0.296926 | − | 0.954901i | \(-0.595961\pi\) | ||||
−0.296926 | + | 0.954901i | \(0.595961\pi\) | |||||||
\(488\) | −7.68518e14 | −1.25703 | ||||||||
\(489\) | −1.09927e14 | −0.177789 | ||||||||
\(490\) | −3.89565e14 | −0.623019 | ||||||||
\(491\) | 8.18417e14 | 1.29427 | 0.647137 | − | 0.762373i | \(-0.275966\pi\) | ||||
0.647137 | + | 0.762373i | \(0.275966\pi\) | |||||||
\(492\) | −2.11764e14 | −0.331165 | ||||||||
\(493\) | −3.07422e14 | −0.475420 | ||||||||
\(494\) | 6.44777e14 | 0.986078 | ||||||||
\(495\) | −3.47775e13 | −0.0525981 | ||||||||
\(496\) | −2.39923e14 | −0.358857 | ||||||||
\(497\) | −5.20098e14 | −0.769352 | ||||||||
\(498\) | −3.16541e14 | −0.463094 | ||||||||
\(499\) | 1.37376e13 | 0.0198774 | 0.00993869 | − | 0.999951i | \(-0.496836\pi\) | ||||
0.00993869 | + | 0.999951i | \(0.496836\pi\) | |||||||
\(500\) | 1.00887e14 | 0.144378 | ||||||||
\(501\) | −8.68187e13 | −0.122887 | ||||||||
\(502\) | −8.13731e14 | −1.13923 | ||||||||
\(503\) | 5.86134e14 | 0.811658 | 0.405829 | − | 0.913949i | \(-0.366983\pi\) | ||||
0.405829 | + | 0.913949i | \(0.366983\pi\) | |||||||
\(504\) | −1.64503e14 | −0.225323 | ||||||||
\(505\) | −9.44243e14 | −1.27933 | ||||||||
\(506\) | −4.98451e13 | −0.0668028 | ||||||||
\(507\) | −3.40584e14 | −0.451524 | ||||||||
\(508\) | −1.52028e15 | −1.99377 | ||||||||
\(509\) | −9.93752e14 | −1.28923 | −0.644615 | − | 0.764507i | \(-0.722982\pi\) | ||||
−0.644615 | + | 0.764507i | \(0.722982\pi\) | |||||||
\(510\) | 4.20827e14 | 0.540091 | ||||||||
\(511\) | 6.45071e14 | 0.819016 | ||||||||
\(512\) | −3.79391e14 | −0.476544 | ||||||||
\(513\) | −2.06702e14 | −0.256862 | ||||||||
\(514\) | −1.15347e14 | −0.141810 | ||||||||
\(515\) | −1.63480e15 | −1.98849 | ||||||||
\(516\) | 7.86186e14 | 0.946132 | ||||||||
\(517\) | −1.56705e14 | −0.186589 | ||||||||
\(518\) | 1.10198e15 | 1.29826 | ||||||||
\(519\) | 2.83051e14 | 0.329947 | ||||||||
\(520\) | 4.49085e14 | 0.517977 | ||||||||
\(521\) | 8.59337e14 | 0.980745 | 0.490372 | − | 0.871513i | \(-0.336861\pi\) | ||||
0.490372 | + | 0.871513i | \(0.336861\pi\) | |||||||
\(522\) | 5.22070e14 | 0.589578 | ||||||||
\(523\) | 4.92525e13 | 0.0550388 | 0.0275194 | − | 0.999621i | \(-0.491239\pi\) | ||||
0.0275194 | + | 0.999621i | \(0.491239\pi\) | |||||||
\(524\) | −1.21041e15 | −1.33848 | ||||||||
\(525\) | 4.15820e14 | 0.455019 | ||||||||
\(526\) | 8.18781e14 | 0.886638 | ||||||||
\(527\) | 5.91321e14 | 0.633673 | ||||||||
\(528\) | −1.48925e13 | −0.0157936 | ||||||||
\(529\) | −8.21150e14 | −0.861819 | ||||||||
\(530\) | −1.21070e15 | −1.25753 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −1.67096e15 | −1.70001 | ||||||||
\(533\) | −1.76753e14 | −0.177979 | ||||||||
\(534\) | 1.67559e15 | 1.66990 | ||||||||
\(535\) | −2.77282e14 | −0.273512 | ||||||||
\(536\) | −1.04495e15 | −1.02021 | ||||||||
\(537\) | −1.45706e14 | −0.140805 | ||||||||
\(538\) | 2.83827e15 | 2.71488 | ||||||||
\(539\) | −3.39780e13 | −0.0321706 | ||||||||
\(540\) | −4.29311e14 | −0.402352 | ||||||||
\(541\) | 4.94069e14 | 0.458356 | 0.229178 | − | 0.973385i | \(-0.426396\pi\) | ||||
0.229178 | + | 0.973385i | \(0.426396\pi\) | |||||||
\(542\) | −4.42404e14 | −0.406278 | ||||||||
\(543\) | 5.85142e13 | 0.0531940 | ||||||||
\(544\) | 5.57634e14 | 0.501829 | ||||||||
\(545\) | −1.04059e15 | −0.927039 | ||||||||
\(546\) | −4.09446e14 | −0.361108 | ||||||||
\(547\) | 5.68865e12 | 0.00496682 | 0.00248341 | − | 0.999997i | \(-0.499210\pi\) | ||||
0.00248341 | + | 0.999997i | \(0.499210\pi\) | |||||||
\(548\) | 4.17413e14 | 0.360806 | ||||||||
\(549\) | 6.13214e14 | 0.524764 | ||||||||
\(550\) | −1.97464e14 | −0.167299 | ||||||||
\(551\) | 1.77833e15 | 1.49169 | ||||||||
\(552\) | −2.06342e14 | −0.171365 | ||||||||
\(553\) | 6.23964e14 | 0.513064 | ||||||||
\(554\) | 3.67924e15 | 2.99540 | ||||||||
\(555\) | 9.64419e14 | 0.777418 | ||||||||
\(556\) | −1.00194e15 | −0.799706 | ||||||||
\(557\) | 2.04927e15 | 1.61956 | 0.809778 | − | 0.586737i | \(-0.199588\pi\) | ||||
0.809778 | + | 0.586737i | \(0.199588\pi\) | |||||||
\(558\) | −1.00419e15 | −0.785830 | ||||||||
\(559\) | 6.56205e14 | 0.508481 | ||||||||
\(560\) | 3.69336e14 | 0.283392 | ||||||||
\(561\) | 3.67047e13 | 0.0278885 | ||||||||
\(562\) | −1.18463e15 | −0.891321 | ||||||||
\(563\) | −1.25655e15 | −0.936234 | −0.468117 | − | 0.883667i | \(-0.655067\pi\) | ||||
−0.468117 | + | 0.883667i | \(0.655067\pi\) | |||||||
\(564\) | −1.93444e15 | −1.42732 | ||||||||
\(565\) | −2.60164e15 | −1.90099 | ||||||||
\(566\) | −6.54764e14 | −0.473800 | ||||||||
\(567\) | 1.31260e14 | 0.0940643 | ||||||||
\(568\) | 1.02243e15 | 0.725633 | ||||||||
\(569\) | −2.63511e15 | −1.85217 | −0.926085 | − | 0.377316i | \(-0.876847\pi\) | ||||
−0.926085 | + | 0.377316i | \(0.876847\pi\) | |||||||
\(570\) | −2.43434e15 | −1.69461 | ||||||||
\(571\) | 1.17266e15 | 0.808485 | 0.404242 | − | 0.914652i | \(-0.367535\pi\) | ||||
0.404242 | + | 0.914652i | \(0.367535\pi\) | |||||||
\(572\) | 1.16803e14 | 0.0797585 | ||||||||
\(573\) | −4.00114e14 | −0.270604 | ||||||||
\(574\) | 7.62515e14 | 0.510779 | ||||||||
\(575\) | 5.21578e14 | 0.346056 | ||||||||
\(576\) | −8.24793e14 | −0.542028 | ||||||||
\(577\) | −1.41481e15 | −0.920938 | −0.460469 | − | 0.887676i | \(-0.652319\pi\) | ||||
−0.460469 | + | 0.887676i | \(0.652319\pi\) | |||||||
\(578\) | 2.01038e15 | 1.29621 | ||||||||
\(579\) | 3.75593e14 | 0.239875 | ||||||||
\(580\) | 3.69352e15 | 2.33661 | ||||||||
\(581\) | 6.84702e14 | 0.429075 | ||||||||
\(582\) | −1.17700e15 | −0.730635 | ||||||||
\(583\) | −1.05598e14 | −0.0649349 | ||||||||
\(584\) | −1.26810e15 | −0.772475 | ||||||||
\(585\) | −3.58333e14 | −0.216237 | ||||||||
\(586\) | 1.04797e15 | 0.626487 | ||||||||
\(587\) | −7.67307e14 | −0.454422 | −0.227211 | − | 0.973846i | \(-0.572961\pi\) | ||||
−0.227211 | + | 0.973846i | \(0.572961\pi\) | |||||||
\(588\) | −4.19441e14 | −0.246091 | ||||||||
\(589\) | −3.42059e15 | −1.98823 | ||||||||
\(590\) | −4.97174e14 | −0.286301 | ||||||||
\(591\) | 3.36378e14 | 0.191910 | ||||||||
\(592\) | 4.12986e14 | 0.233435 | ||||||||
\(593\) | 7.93935e14 | 0.444615 | 0.222307 | − | 0.974977i | \(-0.428641\pi\) | ||||
0.222307 | + | 0.974977i | \(0.428641\pi\) | |||||||
\(594\) | −6.23325e13 | −0.0345851 | ||||||||
\(595\) | −9.10279e14 | −0.500416 | ||||||||
\(596\) | −2.65226e15 | −1.44465 | ||||||||
\(597\) | −2.61501e14 | −0.141128 | ||||||||
\(598\) | −5.13583e14 | −0.274634 | ||||||||
\(599\) | −7.13533e14 | −0.378065 | −0.189033 | − | 0.981971i | \(-0.560535\pi\) | ||||
−0.189033 | + | 0.981971i | \(0.560535\pi\) | |||||||
\(600\) | −8.17436e14 | −0.429162 | ||||||||
\(601\) | 1.02257e15 | 0.531967 | 0.265984 | − | 0.963978i | \(-0.414303\pi\) | ||||
0.265984 | + | 0.963978i | \(0.414303\pi\) | |||||||
\(602\) | −2.83088e15 | −1.45929 | ||||||||
\(603\) | 8.33783e14 | 0.425900 | ||||||||
\(604\) | −9.11608e14 | −0.461429 | ||||||||
\(605\) | 2.73466e15 | 1.37167 | ||||||||
\(606\) | −1.69239e15 | −0.841201 | ||||||||
\(607\) | −2.89132e14 | −0.142416 | −0.0712078 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712078 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(608\) | −3.22572e15 | −1.57455 | ||||||||
\(609\) | −1.12928e15 | −0.546267 | ||||||||
\(610\) | 7.22185e15 | 3.46206 | ||||||||
\(611\) | −1.61462e15 | −0.767087 | ||||||||
\(612\) | 4.53100e14 | 0.213335 | ||||||||
\(613\) | 1.49684e15 | 0.698463 | 0.349232 | − | 0.937036i | \(-0.386443\pi\) | ||||
0.349232 | + | 0.937036i | \(0.386443\pi\) | |||||||
\(614\) | −6.99782e14 | −0.323621 | ||||||||
\(615\) | 6.67327e14 | 0.305862 | ||||||||
\(616\) | −1.68977e14 | −0.0767598 | ||||||||
\(617\) | −3.99373e15 | −1.79808 | −0.899042 | − | 0.437863i | \(-0.855736\pi\) | ||||
−0.899042 | + | 0.437863i | \(0.855736\pi\) | |||||||
\(618\) | −2.93008e15 | −1.30750 | ||||||||
\(619\) | −2.08009e15 | −0.919989 | −0.459995 | − | 0.887922i | \(-0.652149\pi\) | ||||
−0.459995 | + | 0.887922i | \(0.652149\pi\) | |||||||
\(620\) | −7.10442e15 | −3.11440 | ||||||||
\(621\) | 1.64644e14 | 0.0715388 | ||||||||
\(622\) | 2.42806e15 | 1.04571 | ||||||||
\(623\) | −3.62443e15 | −1.54723 | ||||||||
\(624\) | −1.53446e14 | −0.0649294 | ||||||||
\(625\) | −2.53746e15 | −1.06429 | ||||||||
\(626\) | 4.93863e15 | 2.05328 | ||||||||
\(627\) | −2.12324e14 | −0.0875039 | ||||||||
\(628\) | 2.65008e15 | 1.08263 | ||||||||
\(629\) | −1.01786e15 | −0.412202 | ||||||||
\(630\) | 1.54585e15 | 0.620576 | ||||||||
\(631\) | −3.76713e15 | −1.49916 | −0.749581 | − | 0.661912i | \(-0.769745\pi\) | ||||
−0.749581 | + | 0.661912i | \(0.769745\pi\) | |||||||
\(632\) | −1.22661e15 | −0.483909 | ||||||||
\(633\) | −2.18785e15 | −0.855653 | ||||||||
\(634\) | 4.62754e15 | 1.79415 | ||||||||
\(635\) | 4.79083e15 | 1.84143 | ||||||||
\(636\) | −1.30355e15 | −0.496723 | ||||||||
\(637\) | −3.50095e14 | −0.132257 | ||||||||
\(638\) | 5.36269e14 | 0.200849 | ||||||||
\(639\) | −8.15814e14 | −0.302926 | ||||||||
\(640\) | −5.26064e15 | −1.93664 | ||||||||
\(641\) | 3.19313e15 | 1.16546 | 0.582731 | − | 0.812665i | \(-0.301984\pi\) | ||||
0.582731 | + | 0.812665i | \(0.301984\pi\) | |||||||
\(642\) | −4.96979e14 | −0.179844 | ||||||||
\(643\) | −1.62229e15 | −0.582061 | −0.291030 | − | 0.956714i | \(-0.593998\pi\) | ||||
−0.291030 | + | 0.956714i | \(0.593998\pi\) | |||||||
\(644\) | 1.33097e15 | 0.473473 | ||||||||
\(645\) | −2.47749e15 | −0.873842 | ||||||||
\(646\) | 2.56923e15 | 0.898513 | ||||||||
\(647\) | 1.56046e15 | 0.541102 | 0.270551 | − | 0.962706i | \(-0.412794\pi\) | ||||
0.270551 | + | 0.962706i | \(0.412794\pi\) | |||||||
\(648\) | −2.58036e14 | −0.0887191 | ||||||||
\(649\) | −4.33637e13 | −0.0147836 | ||||||||
\(650\) | −2.03459e15 | −0.687786 | ||||||||
\(651\) | 2.17214e15 | 0.728103 | ||||||||
\(652\) | −1.39390e15 | −0.463307 | ||||||||
\(653\) | −3.73978e15 | −1.23260 | −0.616301 | − | 0.787511i | \(-0.711370\pi\) | ||||
−0.616301 | + | 0.787511i | \(0.711370\pi\) | |||||||
\(654\) | −1.86507e15 | −0.609560 | ||||||||
\(655\) | 3.81434e15 | 1.23621 | ||||||||
\(656\) | 2.85765e14 | 0.0918412 | ||||||||
\(657\) | 1.01184e15 | 0.322481 | ||||||||
\(658\) | 6.96550e15 | 2.20145 | ||||||||
\(659\) | −8.52327e14 | −0.267139 | −0.133569 | − | 0.991039i | \(-0.542644\pi\) | ||||
−0.133569 | + | 0.991039i | \(0.542644\pi\) | |||||||
\(660\) | −4.40988e14 | −0.137068 | ||||||||
\(661\) | 6.46071e14 | 0.199146 | 0.0995732 | − | 0.995030i | \(-0.468252\pi\) | ||||
0.0995732 | + | 0.995030i | \(0.468252\pi\) | |||||||
\(662\) | 7.16167e15 | 2.18925 | ||||||||
\(663\) | 3.78189e14 | 0.114653 | ||||||||
\(664\) | −1.34601e15 | −0.404692 | ||||||||
\(665\) | 5.26566e15 | 1.57012 | ||||||||
\(666\) | 1.72855e15 | 0.511179 | ||||||||
\(667\) | −1.41649e15 | −0.415453 | ||||||||
\(668\) | −1.10088e15 | −0.320236 | ||||||||
\(669\) | 6.23084e14 | 0.179764 | ||||||||
\(670\) | 9.81949e15 | 2.80981 | ||||||||
\(671\) | 6.29892e14 | 0.178769 | ||||||||
\(672\) | 2.04840e15 | 0.576611 | ||||||||
\(673\) | −5.08949e15 | −1.42099 | −0.710495 | − | 0.703702i | \(-0.751529\pi\) | ||||
−0.710495 | + | 0.703702i | \(0.751529\pi\) | |||||||
\(674\) | 8.86687e15 | 2.45551 | ||||||||
\(675\) | 6.52246e14 | 0.179160 | ||||||||
\(676\) | −4.31869e15 | −1.17664 | ||||||||
\(677\) | −3.90992e14 | −0.105665 | −0.0528324 | − | 0.998603i | \(-0.516825\pi\) | ||||
−0.0528324 | + | 0.998603i | \(0.516825\pi\) | |||||||
\(678\) | −4.66296e15 | −1.24997 | ||||||||
\(679\) | 2.54594e15 | 0.676962 | ||||||||
\(680\) | 1.78946e15 | 0.471980 | ||||||||
\(681\) | 1.14746e15 | 0.300212 | ||||||||
\(682\) | −1.03150e15 | −0.267705 | ||||||||
\(683\) | −1.81796e15 | −0.468026 | −0.234013 | − | 0.972233i | \(-0.575186\pi\) | ||||
−0.234013 | + | 0.972233i | \(0.575186\pi\) | |||||||
\(684\) | −2.62103e15 | −0.669366 | ||||||||
\(685\) | −1.31538e15 | −0.333238 | ||||||||
\(686\) | 6.84138e15 | 1.71934 | ||||||||
\(687\) | −4.23910e15 | −1.05685 | ||||||||
\(688\) | −1.06092e15 | −0.262388 | ||||||||
\(689\) | −1.08803e15 | −0.266954 | ||||||||
\(690\) | 1.93902e15 | 0.471967 | ||||||||
\(691\) | 4.28858e15 | 1.03558 | 0.517791 | − | 0.855507i | \(-0.326754\pi\) | ||||
0.517791 | + | 0.855507i | \(0.326754\pi\) | |||||||
\(692\) | 3.58916e15 | 0.859823 | ||||||||
\(693\) | 1.34830e14 | 0.0320445 | ||||||||
\(694\) | −6.47795e15 | −1.52743 | ||||||||
\(695\) | 3.15739e15 | 0.738604 | ||||||||
\(696\) | 2.21997e15 | 0.515225 | ||||||||
\(697\) | −7.04306e14 | −0.162174 | ||||||||
\(698\) | 3.56705e14 | 0.0814899 | ||||||||
\(699\) | 1.60228e14 | 0.0363174 | ||||||||
\(700\) | 5.27270e15 | 1.18575 | ||||||||
\(701\) | 4.36940e15 | 0.974929 | 0.487464 | − | 0.873143i | \(-0.337922\pi\) | ||||
0.487464 | + | 0.873143i | \(0.337922\pi\) | |||||||
\(702\) | −6.42248e14 | −0.142183 | ||||||||
\(703\) | 5.88798e15 | 1.29334 | ||||||||
\(704\) | −8.47226e14 | −0.184650 | ||||||||
\(705\) | 6.09596e15 | 1.31826 | ||||||||
\(706\) | 7.15829e15 | 1.53597 | ||||||||
\(707\) | 3.66076e15 | 0.779407 | ||||||||
\(708\) | −5.35303e14 | −0.113088 | ||||||||
\(709\) | −5.54169e14 | −0.116168 | −0.0580842 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580842 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(710\) | −9.60787e15 | −1.99851 | ||||||||
\(711\) | 9.78736e14 | 0.202015 | ||||||||
\(712\) | 7.12505e15 | 1.45931 | ||||||||
\(713\) | 2.72460e15 | 0.553745 | ||||||||
\(714\) | −1.63151e15 | −0.329041 | ||||||||
\(715\) | −3.68079e14 | −0.0736644 | ||||||||
\(716\) | −1.84759e15 | −0.366930 | ||||||||
\(717\) | −2.20209e15 | −0.433990 | ||||||||
\(718\) | −5.55907e15 | −1.08722 | ||||||||
\(719\) | −1.11509e15 | −0.216422 | −0.108211 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108211 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(720\) | 5.79333e14 | 0.111583 | ||||||||
\(721\) | 6.33798e15 | 1.21145 | ||||||||
\(722\) | −6.51920e15 | −1.23663 | ||||||||
\(723\) | −5.44453e15 | −1.02494 | ||||||||
\(724\) | 7.41974e14 | 0.138620 | ||||||||
\(725\) | −5.61151e15 | −1.04045 | ||||||||
\(726\) | 4.90138e15 | 0.901917 | ||||||||
\(727\) | 8.02340e15 | 1.46528 | 0.732638 | − | 0.680619i | \(-0.238289\pi\) | ||||
0.732638 | + | 0.680619i | \(0.238289\pi\) | |||||||
\(728\) | −1.74107e15 | −0.315568 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 1.19165e16 | 2.12752 | ||||||||
\(731\) | 2.61477e15 | 0.463327 | ||||||||
\(732\) | 7.77570e15 | 1.36750 | ||||||||
\(733\) | −9.57279e14 | −0.167096 | −0.0835481 | − | 0.996504i | \(-0.526625\pi\) | ||||
−0.0835481 | + | 0.996504i | \(0.526625\pi\) | |||||||
\(734\) | −9.04204e15 | −1.56653 | ||||||||
\(735\) | 1.32177e15 | 0.227288 | ||||||||
\(736\) | 2.56938e15 | 0.438531 | ||||||||
\(737\) | 8.56460e14 | 0.145089 | ||||||||
\(738\) | 1.19606e15 | 0.201115 | ||||||||
\(739\) | −9.01924e14 | −0.150531 | −0.0752654 | − | 0.997164i | \(-0.523980\pi\) | ||||
−0.0752654 | + | 0.997164i | \(0.523980\pi\) | |||||||
\(740\) | 1.22291e16 | 2.02590 | ||||||||
\(741\) | −2.18770e15 | −0.359738 | ||||||||
\(742\) | 4.69379e15 | 0.766130 | ||||||||
\(743\) | 2.27033e15 | 0.367833 | 0.183916 | − | 0.982942i | \(-0.441122\pi\) | ||||
0.183916 | + | 0.982942i | \(0.441122\pi\) | |||||||
\(744\) | −4.27008e15 | −0.686728 | ||||||||
\(745\) | 8.35800e15 | 1.33427 | ||||||||
\(746\) | −1.78867e16 | −2.83444 | ||||||||
\(747\) | 1.07401e15 | 0.168945 | ||||||||
\(748\) | 4.65424e14 | 0.0726758 | ||||||||
\(749\) | 1.07500e15 | 0.166632 | ||||||||
\(750\) | −5.69818e14 | −0.0876798 | ||||||||
\(751\) | −3.58007e15 | −0.546855 | −0.273427 | − | 0.961893i | \(-0.588157\pi\) | ||||
−0.273427 | + | 0.961893i | \(0.588157\pi\) | |||||||
\(752\) | 2.61043e15 | 0.395835 | ||||||||
\(753\) | 2.76095e15 | 0.415610 | ||||||||
\(754\) | 5.52549e15 | 0.825712 | ||||||||
\(755\) | 2.87273e15 | 0.426173 | ||||||||
\(756\) | 1.66441e15 | 0.245126 | ||||||||
\(757\) | −9.09591e15 | −1.32990 | −0.664950 | − | 0.746888i | \(-0.731547\pi\) | ||||
−0.664950 | + | 0.746888i | \(0.731547\pi\) | |||||||
\(758\) | −4.21921e15 | −0.612422 | ||||||||
\(759\) | 1.69122e14 | 0.0243708 | ||||||||
\(760\) | −1.03514e16 | −1.48090 | ||||||||
\(761\) | −6.24456e15 | −0.886924 | −0.443462 | − | 0.896293i | \(-0.646250\pi\) | ||||
−0.443462 | + | 0.896293i | \(0.646250\pi\) | |||||||
\(762\) | 8.58670e15 | 1.21080 | ||||||||
\(763\) | 4.03428e15 | 0.564782 | ||||||||
\(764\) | −5.07355e15 | −0.705177 | ||||||||
\(765\) | −1.42784e15 | −0.197035 | ||||||||
\(766\) | 9.34344e15 | 1.28011 | ||||||||
\(767\) | −4.46802e14 | −0.0607771 | ||||||||
\(768\) | −2.47741e15 | −0.334589 | ||||||||
\(769\) | 9.24521e15 | 1.23972 | 0.619858 | − | 0.784714i | \(-0.287190\pi\) | ||||
0.619858 | + | 0.784714i | \(0.287190\pi\) | |||||||
\(770\) | 1.58790e15 | 0.211409 | ||||||||
\(771\) | 3.91365e14 | 0.0517349 | ||||||||
\(772\) | 4.76261e15 | 0.625100 | ||||||||
\(773\) | −1.06718e15 | −0.139075 | −0.0695376 | − | 0.997579i | \(-0.522152\pi\) | ||||
−0.0695376 | + | 0.997579i | \(0.522152\pi\) | |||||||
\(774\) | −4.44045e15 | −0.574581 | ||||||||
\(775\) | 1.07936e16 | 1.38678 | ||||||||
\(776\) | −5.00491e15 | −0.638493 | ||||||||
\(777\) | −3.73898e15 | −0.473628 | ||||||||
\(778\) | −7.53422e15 | −0.947656 | ||||||||
\(779\) | 4.07417e15 | 0.508842 | ||||||||
\(780\) | −4.54375e15 | −0.563500 | ||||||||
\(781\) | −8.38002e14 | −0.103196 | ||||||||
\(782\) | −2.04646e15 | −0.250246 | ||||||||
\(783\) | −1.77136e15 | −0.215088 | ||||||||
\(784\) | 5.66013e14 | 0.0682478 | ||||||||
\(785\) | −8.35111e15 | −0.999911 | ||||||||
\(786\) | 6.83651e15 | 0.812850 | ||||||||
\(787\) | 1.31820e16 | 1.55640 | 0.778201 | − | 0.628016i | \(-0.216133\pi\) | ||||
0.778201 | + | 0.628016i | \(0.216133\pi\) | |||||||
\(788\) | 4.26536e15 | 0.500105 | ||||||||
\(789\) | −2.77808e15 | −0.323461 | ||||||||
\(790\) | 1.15266e16 | 1.33276 | ||||||||
\(791\) | 1.00863e16 | 1.15815 | ||||||||
\(792\) | −2.65054e14 | −0.0302235 | ||||||||
\(793\) | 6.49014e15 | 0.734940 | ||||||||
\(794\) | 1.66391e16 | 1.87119 | ||||||||
\(795\) | 4.10785e15 | 0.458770 | ||||||||
\(796\) | −3.31589e15 | −0.367772 | ||||||||
\(797\) | 8.00193e14 | 0.0881401 | 0.0440701 | − | 0.999028i | \(-0.485968\pi\) | ||||
0.0440701 | + | 0.999028i | \(0.485968\pi\) | |||||||
\(798\) | 9.43774e15 | 1.03241 | ||||||||
\(799\) | −6.43376e15 | −0.698968 | ||||||||
\(800\) | 1.01787e16 | 1.09824 | ||||||||
\(801\) | −5.68520e15 | −0.609210 | ||||||||
\(802\) | 2.14918e16 | 2.28725 | ||||||||
\(803\) | 1.03936e15 | 0.109858 | ||||||||
\(804\) | 1.05726e16 | 1.10987 | ||||||||
\(805\) | −4.19424e15 | −0.437296 | ||||||||
\(806\) | −1.06282e16 | −1.10057 | ||||||||
\(807\) | −9.63009e15 | −0.990435 | ||||||||
\(808\) | −7.19646e15 | −0.735116 | ||||||||
\(809\) | −6.00294e15 | −0.609042 | −0.304521 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304521 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(810\) | 2.42479e15 | 0.244347 | ||||||||
\(811\) | −2.41855e15 | −0.242070 | −0.121035 | − | 0.992648i | \(-0.538621\pi\) | ||||
−0.121035 | + | 0.992648i | \(0.538621\pi\) | |||||||
\(812\) | −1.43195e16 | −1.42354 | ||||||||
\(813\) | 1.50105e15 | 0.148217 | ||||||||
\(814\) | 1.77556e15 | 0.174141 | ||||||||
\(815\) | 4.39255e15 | 0.427907 | ||||||||
\(816\) | −6.11435e14 | −0.0591636 | ||||||||
\(817\) | −1.51256e16 | −1.45375 | ||||||||
\(818\) | −2.64817e16 | −2.52815 | ||||||||
\(819\) | 1.38923e15 | 0.131738 | ||||||||
\(820\) | 8.46187e15 | 0.797058 | ||||||||
\(821\) | −1.95856e16 | −1.83252 | −0.916260 | − | 0.400584i | \(-0.868807\pi\) | ||||
−0.916260 | + | 0.400584i | \(0.868807\pi\) | |||||||
\(822\) | −2.35759e15 | −0.219115 | ||||||||
\(823\) | −8.60498e15 | −0.794421 | −0.397211 | − | 0.917727i | \(-0.630022\pi\) | ||||
−0.397211 | + | 0.917727i | \(0.630022\pi\) | |||||||
\(824\) | −1.24595e16 | −1.14261 | ||||||||
\(825\) | 6.69986e14 | 0.0610336 | ||||||||
\(826\) | 1.92751e15 | 0.174424 | ||||||||
\(827\) | −9.60942e15 | −0.863807 | −0.431904 | − | 0.901920i | \(-0.642158\pi\) | ||||
−0.431904 | + | 0.901920i | \(0.642158\pi\) | |||||||
\(828\) | 2.08772e15 | 0.186426 | ||||||||
\(829\) | −1.43126e16 | −1.26960 | −0.634800 | − | 0.772676i | \(-0.718918\pi\) | ||||
−0.634800 | + | 0.772676i | \(0.718918\pi\) | |||||||
\(830\) | 1.26486e16 | 1.11459 | ||||||||
\(831\) | −1.24835e16 | −1.09277 | ||||||||
\(832\) | −8.72946e15 | −0.759118 | ||||||||
\(833\) | −1.39502e15 | −0.120512 | ||||||||
\(834\) | 5.65905e15 | 0.485658 | ||||||||
\(835\) | 3.46918e15 | 0.295768 | ||||||||
\(836\) | −2.69232e15 | −0.228030 | ||||||||
\(837\) | 3.40717e15 | 0.286684 | ||||||||
\(838\) | −8.07222e15 | −0.674763 | ||||||||
\(839\) | −4.75190e15 | −0.394618 | −0.197309 | − | 0.980341i | \(-0.563220\pi\) | ||||
−0.197309 | + | 0.980341i | \(0.563220\pi\) | |||||||
\(840\) | 6.57336e15 | 0.542314 | ||||||||
\(841\) | 3.03912e15 | 0.249098 | ||||||||
\(842\) | −3.20197e16 | −2.60736 | ||||||||
\(843\) | 4.01940e15 | 0.325169 | ||||||||
\(844\) | −2.77425e16 | −2.22978 | ||||||||
\(845\) | 1.36094e16 | 1.08674 | ||||||||
\(846\) | 1.09259e16 | 0.866804 | ||||||||
\(847\) | −1.06020e16 | −0.835663 | ||||||||
\(848\) | 1.75907e15 | 0.137755 | ||||||||
\(849\) | 2.22158e15 | 0.172850 | ||||||||
\(850\) | −8.10718e15 | −0.626709 | ||||||||
\(851\) | −4.68993e15 | −0.360209 | ||||||||
\(852\) | −1.03447e16 | −0.789406 | ||||||||
\(853\) | 3.78608e15 | 0.287058 | 0.143529 | − | 0.989646i | \(-0.454155\pi\) | ||||
0.143529 | + | 0.989646i | \(0.454155\pi\) | |||||||
\(854\) | −2.79985e16 | −2.10920 | ||||||||
\(855\) | 8.25959e15 | 0.618222 | ||||||||
\(856\) | −2.11328e15 | −0.157163 | ||||||||
\(857\) | 4.05160e15 | 0.299386 | 0.149693 | − | 0.988733i | \(-0.452171\pi\) | ||||
0.149693 | + | 0.988733i | \(0.452171\pi\) | |||||||
\(858\) | −6.59715e14 | −0.0484369 | ||||||||
\(859\) | −1.59860e16 | −1.16621 | −0.583107 | − | 0.812395i | \(-0.698163\pi\) | ||||
−0.583107 | + | 0.812395i | \(0.698163\pi\) | |||||||
\(860\) | −3.14151e16 | −2.27718 | ||||||||
\(861\) | −2.58718e15 | −0.186341 | ||||||||
\(862\) | −1.55100e16 | −1.11000 | ||||||||
\(863\) | 1.06600e16 | 0.758052 | 0.379026 | − | 0.925386i | \(-0.376259\pi\) | ||||
0.379026 | + | 0.925386i | \(0.376259\pi\) | |||||||
\(864\) | 3.21307e15 | 0.227036 | ||||||||
\(865\) | −1.13104e16 | −0.794127 | ||||||||
\(866\) | 3.09660e16 | 2.16041 | ||||||||
\(867\) | −6.82111e15 | −0.472879 | ||||||||
\(868\) | 2.75433e16 | 1.89739 | ||||||||
\(869\) | 1.00536e15 | 0.0688194 | ||||||||
\(870\) | −2.08613e16 | −1.41901 | ||||||||
\(871\) | 8.82460e15 | 0.596479 | ||||||||
\(872\) | −7.93074e15 | −0.532688 | ||||||||
\(873\) | 3.99350e15 | 0.266548 | ||||||||
\(874\) | 1.18381e16 | 0.785179 | ||||||||
\(875\) | 1.23256e15 | 0.0812388 | ||||||||
\(876\) | 1.28304e16 | 0.840365 | ||||||||
\(877\) | 5.94643e15 | 0.387043 | 0.193521 | − | 0.981096i | \(-0.438009\pi\) | ||||
0.193521 | + | 0.981096i | \(0.438009\pi\) | |||||||
\(878\) | 2.28101e16 | 1.47539 | ||||||||
\(879\) | −3.55571e15 | −0.228553 | ||||||||
\(880\) | 5.95089e14 | 0.0380126 | ||||||||
\(881\) | 2.84161e16 | 1.80384 | 0.901918 | − | 0.431907i | \(-0.142159\pi\) | ||||
0.901918 | + | 0.431907i | \(0.142159\pi\) | |||||||
\(882\) | 2.36904e15 | 0.149450 | ||||||||
\(883\) | −8.18053e15 | −0.512858 | −0.256429 | − | 0.966563i | \(-0.582546\pi\) | ||||
−0.256429 | + | 0.966563i | \(0.582546\pi\) | |||||||
\(884\) | 4.79553e15 | 0.298778 | ||||||||
\(885\) | 1.68689e15 | 0.104447 | ||||||||
\(886\) | −3.18071e16 | −1.95721 | ||||||||
\(887\) | −1.99589e16 | −1.22055 | −0.610277 | − | 0.792188i | \(-0.708942\pi\) | ||||
−0.610277 | + | 0.792188i | \(0.708942\pi\) | |||||||
\(888\) | 7.35023e15 | 0.446714 | ||||||||
\(889\) | −1.85737e16 | −1.12186 | ||||||||
\(890\) | −6.69548e16 | −4.01918 | ||||||||
\(891\) | 2.11491e14 | 0.0126172 | ||||||||
\(892\) | 7.90085e15 | 0.468454 | ||||||||
\(893\) | 3.72171e16 | 2.19311 | ||||||||
\(894\) | 1.49802e16 | 0.877327 | ||||||||
\(895\) | 5.82224e15 | 0.338894 | ||||||||
\(896\) | 2.03951e16 | 1.17986 | ||||||||
\(897\) | 1.74256e15 | 0.100191 | ||||||||
\(898\) | 1.30467e16 | 0.745558 | ||||||||
\(899\) | −2.93132e16 | −1.66489 | ||||||||
\(900\) | 8.27064e15 | 0.466880 | ||||||||
\(901\) | −4.33547e15 | −0.243248 | ||||||||
\(902\) | 1.22859e15 | 0.0685130 | ||||||||
\(903\) | 9.60502e15 | 0.532372 | ||||||||
\(904\) | −1.98281e16 | −1.09233 | ||||||||
\(905\) | −2.33816e15 | −0.128029 | ||||||||
\(906\) | 5.14885e15 | 0.280224 | ||||||||
\(907\) | −2.33057e16 | −1.26073 | −0.630366 | − | 0.776298i | \(-0.717095\pi\) | ||||
−0.630366 | + | 0.776298i | \(0.717095\pi\) | |||||||
\(908\) | 1.45500e16 | 0.782334 | ||||||||
\(909\) | 5.74218e15 | 0.306885 | ||||||||
\(910\) | 1.63610e16 | 0.869125 | ||||||||
\(911\) | −1.41043e16 | −0.744731 | −0.372366 | − | 0.928086i | \(-0.621453\pi\) | ||||
−0.372366 | + | 0.928086i | \(0.621453\pi\) | |||||||
\(912\) | 3.53694e15 | 0.185634 | ||||||||
\(913\) | 1.10322e15 | 0.0575536 | ||||||||
\(914\) | −1.12493e16 | −0.583340 | ||||||||
\(915\) | −2.45034e16 | −1.26302 | ||||||||
\(916\) | −5.37528e16 | −2.75408 | ||||||||
\(917\) | −1.47879e16 | −0.753138 | ||||||||
\(918\) | −2.55915e15 | −0.129557 | ||||||||
\(919\) | −2.24983e16 | −1.13218 | −0.566088 | − | 0.824345i | \(-0.691544\pi\) | ||||
−0.566088 | + | 0.824345i | \(0.691544\pi\) | |||||||
\(920\) | 8.24519e15 | 0.412447 | ||||||||
\(921\) | 2.37432e15 | 0.118062 | ||||||||
\(922\) | 4.46833e16 | 2.20864 | ||||||||
\(923\) | −8.63442e15 | −0.424252 | ||||||||
\(924\) | 1.70967e15 | 0.0835060 | ||||||||
\(925\) | −1.85794e16 | −0.902097 | ||||||||
\(926\) | 2.35845e16 | 1.13833 | ||||||||
\(927\) | 9.94162e15 | 0.477000 | ||||||||
\(928\) | −2.76432e16 | −1.31848 | ||||||||
\(929\) | −1.50141e16 | −0.711888 | −0.355944 | − | 0.934507i | \(-0.615841\pi\) | ||||
−0.355944 | + | 0.934507i | \(0.615841\pi\) | |||||||
\(930\) | 4.01264e16 | 1.89136 | ||||||||
\(931\) | 8.06969e15 | 0.378124 | ||||||||
\(932\) | 2.03173e15 | 0.0946410 | ||||||||
\(933\) | −8.23828e15 | −0.381494 | ||||||||
\(934\) | −5.44536e16 | −2.50679 | ||||||||
\(935\) | −1.46668e15 | −0.0671229 | ||||||||
\(936\) | −2.73100e15 | −0.124252 | ||||||||
\(937\) | −3.18844e15 | −0.144215 | −0.0721075 | − | 0.997397i | \(-0.522972\pi\) | ||||
−0.0721075 | + | 0.997397i | \(0.522972\pi\) | |||||||
\(938\) | −3.80694e16 | −1.71183 | ||||||||
\(939\) | −1.67565e16 | −0.749071 | ||||||||
\(940\) | 7.72983e16 | 3.43532 | ||||||||
\(941\) | 5.16849e15 | 0.228360 | 0.114180 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114180 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(942\) | −1.49679e16 | −0.657476 | ||||||||
\(943\) | −3.24519e15 | −0.141718 | ||||||||
\(944\) | 7.22363e14 | 0.0313624 | ||||||||
\(945\) | −5.24500e15 | −0.226397 | ||||||||
\(946\) | −4.56122e15 | −0.195740 | ||||||||
\(947\) | 3.76798e16 | 1.60762 | 0.803811 | − | 0.594885i | \(-0.202802\pi\) | ||||
0.803811 | + | 0.594885i | \(0.202802\pi\) | |||||||
\(948\) | 1.24106e16 | 0.526438 | ||||||||
\(949\) | 1.07092e16 | 0.451639 | ||||||||
\(950\) | 4.68973e16 | 1.96638 | ||||||||
\(951\) | −1.57010e16 | −0.654538 | ||||||||
\(952\) | −6.93760e15 | −0.287545 | ||||||||
\(953\) | 2.04664e15 | 0.0843396 | 0.0421698 | − | 0.999110i | \(-0.486573\pi\) | ||||
0.0421698 | + | 0.999110i | \(0.486573\pi\) | |||||||
\(954\) | 7.36257e15 | 0.301657 | ||||||||
\(955\) | 1.59881e16 | 0.651297 | ||||||||
\(956\) | −2.79230e16 | −1.13095 | ||||||||
\(957\) | −1.81953e15 | −0.0732731 | ||||||||
\(958\) | 3.77335e15 | 0.151083 | ||||||||
\(959\) | 5.09964e15 | 0.203019 | ||||||||
\(960\) | 3.29578e16 | 1.30457 | ||||||||
\(961\) | 3.09748e16 | 1.21908 | ||||||||
\(962\) | 1.82946e16 | 0.715914 | ||||||||
\(963\) | 1.68622e15 | 0.0656101 | ||||||||
\(964\) | −6.90379e16 | −2.67094 | ||||||||
\(965\) | −1.50083e16 | −0.577339 | ||||||||
\(966\) | −7.51742e15 | −0.287538 | ||||||||
\(967\) | −2.18214e16 | −0.829923 | −0.414961 | − | 0.909839i | \(-0.636205\pi\) | ||||
−0.414961 | + | 0.909839i | \(0.636205\pi\) | |||||||
\(968\) | 2.08419e16 | 0.788176 | ||||||||
\(969\) | −8.71727e15 | −0.327793 | ||||||||
\(970\) | 4.70316e16 | 1.75851 | ||||||||
\(971\) | −7.42026e15 | −0.275876 | −0.137938 | − | 0.990441i | \(-0.544047\pi\) | ||||
−0.137938 | + | 0.990441i | \(0.544047\pi\) | |||||||
\(972\) | 2.61075e15 | 0.0965163 | ||||||||
\(973\) | −1.22409e16 | −0.449981 | ||||||||
\(974\) | 2.57108e16 | 0.939813 | ||||||||
\(975\) | 6.90325e15 | 0.250916 | ||||||||
\(976\) | −1.04929e16 | −0.379246 | ||||||||
\(977\) | −3.89311e16 | −1.39919 | −0.699595 | − | 0.714540i | \(-0.746636\pi\) | ||||
−0.699595 | + | 0.714540i | \(0.746636\pi\) | |||||||
\(978\) | 7.87285e15 | 0.281364 | ||||||||
\(979\) | −5.83983e15 | −0.207537 | ||||||||
\(980\) | 1.67604e16 | 0.592299 | ||||||||
\(981\) | 6.32807e15 | 0.222378 | ||||||||
\(982\) | −5.86143e16 | −2.04829 | ||||||||
\(983\) | 2.02760e16 | 0.704591 | 0.352295 | − | 0.935889i | \(-0.385401\pi\) | ||||
0.352295 | + | 0.935889i | \(0.385401\pi\) | |||||||
\(984\) | 5.08597e15 | 0.175752 | ||||||||
\(985\) | −1.34413e16 | −0.461894 | ||||||||
\(986\) | 2.20173e16 | 0.752387 | ||||||||
\(987\) | −2.36336e16 | −0.803129 | ||||||||
\(988\) | −2.77405e16 | −0.937457 | ||||||||
\(989\) | 1.20479e16 | 0.404886 | ||||||||
\(990\) | 2.49074e15 | 0.0832404 | ||||||||
\(991\) | −1.25418e16 | −0.416827 | −0.208414 | − | 0.978041i | \(-0.566830\pi\) | ||||
−0.208414 | + | 0.978041i | \(0.566830\pi\) | |||||||
\(992\) | 5.31712e16 | 1.75737 | ||||||||
\(993\) | −2.42992e16 | −0.798676 | ||||||||
\(994\) | 3.72490e16 | 1.21756 | ||||||||
\(995\) | 1.04493e16 | 0.339672 | ||||||||
\(996\) | 1.36187e16 | 0.440259 | ||||||||
\(997\) | 8.28428e15 | 0.266337 | 0.133169 | − | 0.991093i | \(-0.457485\pi\) | ||||
0.133169 | + | 0.991093i | \(0.457485\pi\) | |||||||
\(998\) | −9.83877e14 | −0.0314574 | ||||||||
\(999\) | −5.86487e15 | −0.186487 |
(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 | 177.12.a.b.1.4 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.4 | ✓ | 27 | 1.1 | even | 1 | trivial |