Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(274,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.274");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Character | \(\chi\) | \(=\) | 325.274 |
Dual form | 325.6.b.i.274.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 9.27946i | − 1.64039i | −0.572083 | − | 0.820196i | \(-0.693864\pi\) | ||||
0.572083 | − | 0.820196i | \(-0.306136\pi\) | |||||||
\(3\) | − 5.85765i | − 0.375768i | −0.982191 | − | 0.187884i | \(-0.939837\pi\) | ||||
0.982191 | − | 0.187884i | \(-0.0601630\pi\) | |||||||
\(4\) | −54.1083 | −1.69089 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −54.3558 | −0.616408 | ||||||||
\(7\) | 90.4001i | 0.697307i | 0.937252 | + | 0.348653i | \(0.113361\pi\) | ||||
−0.937252 | + | 0.348653i | \(0.886639\pi\) | |||||||
\(8\) | 205.153i | 1.13332i | ||||||||
\(9\) | 208.688 | 0.858798 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 597.487 | 1.48884 | 0.744418 | − | 0.667714i | \(-0.232727\pi\) | ||||
0.744418 | + | 0.667714i | \(0.232727\pi\) | |||||||
\(12\) | 316.948i | 0.635382i | ||||||||
\(13\) | 169.000i | 0.277350i | ||||||||
\(14\) | 838.864 | 1.14386 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 172.246 | 0.168209 | ||||||||
\(17\) | − 1347.74i | − 1.13106i | −0.824729 | − | 0.565528i | \(-0.808673\pi\) | ||||
0.824729 | − | 0.565528i | \(-0.191327\pi\) | |||||||
\(18\) | − 1936.51i | − 1.40877i | ||||||||
\(19\) | −2986.90 | −1.89818 | −0.949089 | − | 0.315008i | \(-0.897993\pi\) | ||||
−0.949089 | + | 0.315008i | \(0.897993\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 529.532 | 0.262026 | ||||||||
\(22\) | − 5544.36i | − 2.44227i | ||||||||
\(23\) | − 1354.91i | − 0.534061i | −0.963688 | − | 0.267031i | \(-0.913957\pi\) | ||||
0.963688 | − | 0.267031i | \(-0.0860425\pi\) | |||||||
\(24\) | 1201.72 | 0.425867 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1568.23 | 0.454963 | ||||||||
\(27\) | − 2645.83i | − 0.698478i | ||||||||
\(28\) | − 4891.40i | − 1.17907i | ||||||||
\(29\) | −6786.00 | −1.49837 | −0.749184 | − | 0.662362i | \(-0.769554\pi\) | ||||
−0.749184 | + | 0.662362i | \(0.769554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 661.963 | 0.123717 | 0.0618585 | − | 0.998085i | \(-0.480297\pi\) | ||||
0.0618585 | + | 0.998085i | \(0.480297\pi\) | |||||||
\(32\) | 4966.56i | 0.857395i | ||||||||
\(33\) | − 3499.87i | − 0.559458i | ||||||||
\(34\) | −12506.3 | −1.85537 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11291.8 | −1.45213 | ||||||||
\(37\) | − 9682.46i | − 1.16274i | −0.813640 | − | 0.581368i | \(-0.802518\pi\) | ||||
0.813640 | − | 0.581368i | \(-0.197482\pi\) | |||||||
\(38\) | 27716.8i | 3.11376i | ||||||||
\(39\) | 989.943 | 0.104219 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6933.76 | 0.644183 | 0.322091 | − | 0.946709i | \(-0.395614\pi\) | ||||
0.322091 | + | 0.946709i | \(0.395614\pi\) | |||||||
\(42\) | − 4913.77i | − 0.429825i | ||||||||
\(43\) | − 2511.55i | − 0.207143i | −0.994622 | − | 0.103572i | \(-0.966973\pi\) | ||||
0.994622 | − | 0.103572i | \(-0.0330271\pi\) | |||||||
\(44\) | −32329.0 | −2.51745 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12572.8 | −0.876070 | ||||||||
\(47\) | − 10294.9i | − 0.679797i | −0.940462 | − | 0.339899i | \(-0.889607\pi\) | ||||
0.940462 | − | 0.339899i | \(-0.110393\pi\) | |||||||
\(48\) | − 1008.96i | − 0.0632076i | ||||||||
\(49\) | 8634.82 | 0.513763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7894.59 | −0.425015 | ||||||||
\(52\) | − 9144.31i | − 0.468967i | ||||||||
\(53\) | − 1060.19i | − 0.0518436i | −0.999664 | − | 0.0259218i | \(-0.991748\pi\) | ||||
0.999664 | − | 0.0259218i | \(-0.00825209\pi\) | |||||||
\(54\) | −24551.9 | −1.14578 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −18545.9 | −0.790274 | ||||||||
\(57\) | 17496.2i | 0.713275i | ||||||||
\(58\) | 62970.4i | 2.45791i | ||||||||
\(59\) | 7026.83 | 0.262802 | 0.131401 | − | 0.991329i | \(-0.458052\pi\) | ||||
0.131401 | + | 0.991329i | \(0.458052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31222.1 | −1.07433 | −0.537164 | − | 0.843478i | \(-0.680505\pi\) | ||||
−0.537164 | + | 0.843478i | \(0.680505\pi\) | |||||||
\(62\) | − 6142.65i | − 0.202944i | ||||||||
\(63\) | 18865.4i | 0.598846i | ||||||||
\(64\) | 51598.9 | 1.57467 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −32476.9 | −0.917730 | ||||||||
\(67\) | − 27843.5i | − 0.757768i | −0.925444 | − | 0.378884i | \(-0.876308\pi\) | ||||
0.925444 | − | 0.378884i | \(-0.123692\pi\) | |||||||
\(68\) | 72924.0i | 1.91249i | ||||||||
\(69\) | −7936.60 | −0.200683 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −59047.0 | −1.39012 | −0.695060 | − | 0.718952i | \(-0.744622\pi\) | ||||
−0.695060 | + | 0.718952i | \(0.744622\pi\) | |||||||
\(72\) | 42813.1i | 0.973296i | ||||||||
\(73\) | − 69099.5i | − 1.51764i | −0.651302 | − | 0.758818i | \(-0.725777\pi\) | ||||
0.651302 | − | 0.758818i | \(-0.274223\pi\) | |||||||
\(74\) | −89848.0 | −1.90734 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 161616. | 3.20960 | ||||||||
\(77\) | 54012.9i | 1.03817i | ||||||||
\(78\) | − 9186.13i | − 0.170961i | ||||||||
\(79\) | −59896.7 | −1.07978 | −0.539890 | − | 0.841736i | \(-0.681534\pi\) | ||||
−0.539890 | + | 0.841736i | \(0.681534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35212.8 | 0.596332 | ||||||||
\(82\) | − 64341.5i | − 1.05671i | ||||||||
\(83\) | − 35435.2i | − 0.564599i | −0.959326 | − | 0.282300i | \(-0.908903\pi\) | ||||
0.959326 | − | 0.282300i | \(-0.0910972\pi\) | |||||||
\(84\) | −28652.1 | −0.443056 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −23305.8 | −0.339796 | ||||||||
\(87\) | 39750.0i | 0.563040i | ||||||||
\(88\) | 122577.i | 1.68733i | ||||||||
\(89\) | −79177.3 | −1.05956 | −0.529780 | − | 0.848135i | \(-0.677726\pi\) | ||||
−0.529780 | + | 0.848135i | \(0.677726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15277.6 | −0.193398 | ||||||||
\(92\) | 73312.0i | 0.903037i | ||||||||
\(93\) | − 3877.55i | − 0.0464889i | ||||||||
\(94\) | −95531.5 | −1.11513 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 29092.4 | 0.322182 | ||||||||
\(97\) | − 59235.2i | − 0.639221i | −0.947549 | − | 0.319610i | \(-0.896448\pi\) | ||||
0.947549 | − | 0.319610i | \(-0.103552\pi\) | |||||||
\(98\) | − 80126.5i | − 0.842773i | ||||||||
\(99\) | 124688. | 1.27861 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 190448. | 1.85769 | 0.928844 | − | 0.370471i | \(-0.120804\pi\) | ||||
0.928844 | + | 0.370471i | \(0.120804\pi\) | |||||||
\(102\) | 73257.5i | 0.697191i | ||||||||
\(103\) | 60755.7i | 0.564279i | 0.959373 | + | 0.282140i | \(0.0910441\pi\) | ||||
−0.959373 | + | 0.282140i | \(0.908956\pi\) | |||||||
\(104\) | −34670.9 | −0.314327 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9838.01 | −0.0850438 | ||||||||
\(107\) | 131827.i | 1.11313i | 0.830805 | + | 0.556563i | \(0.187880\pi\) | ||||
−0.830805 | + | 0.556563i | \(0.812120\pi\) | |||||||
\(108\) | 143161.i | 1.18105i | ||||||||
\(109\) | −148041. | −1.19348 | −0.596742 | − | 0.802433i | \(-0.703539\pi\) | ||||
−0.596742 | + | 0.802433i | \(0.703539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −56716.5 | −0.436920 | ||||||||
\(112\) | 15571.1i | 0.117293i | ||||||||
\(113\) | 47163.1i | 0.347461i | 0.984793 | + | 0.173731i | \(0.0555822\pi\) | ||||
−0.984793 | + | 0.173731i | \(0.944418\pi\) | |||||||
\(114\) | 162356. | 1.17005 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 367179. | 2.53357 | ||||||||
\(117\) | 35268.3i | 0.238188i | ||||||||
\(118\) | − 65205.1i | − 0.431099i | ||||||||
\(119\) | 121836. | 0.788692 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 195940. | 1.21663 | ||||||||
\(122\) | 289724.i | 1.76232i | ||||||||
\(123\) | − 40615.5i | − 0.242064i | ||||||||
\(124\) | −35817.7 | −0.209191 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 175061. | 0.982341 | ||||||||
\(127\) | − 130485.i | − 0.717881i | −0.933360 | − | 0.358941i | \(-0.883138\pi\) | ||||
0.933360 | − | 0.358941i | \(-0.116862\pi\) | |||||||
\(128\) | − 319880.i | − 1.72569i | ||||||||
\(129\) | −14711.8 | −0.0778379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 39838.7 | 0.202828 | 0.101414 | − | 0.994844i | \(-0.467663\pi\) | ||||
0.101414 | + | 0.994844i | \(0.467663\pi\) | |||||||
\(132\) | 189372.i | 0.945979i | ||||||||
\(133\) | − 270016.i | − 1.32361i | ||||||||
\(134\) | −258372. | −1.24304 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 276494. | 1.28185 | ||||||||
\(137\) | 405016.i | 1.84362i | 0.387644 | + | 0.921809i | \(0.373289\pi\) | ||||
−0.387644 | + | 0.921809i | \(0.626711\pi\) | |||||||
\(138\) | 73647.3i | 0.329199i | ||||||||
\(139\) | −146603. | −0.643584 | −0.321792 | − | 0.946810i | \(-0.604285\pi\) | ||||
−0.321792 | + | 0.946810i | \(0.604285\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −60304.2 | −0.255446 | ||||||||
\(142\) | 547924.i | 2.28034i | ||||||||
\(143\) | 100975.i | 0.412929i | ||||||||
\(144\) | 35945.7 | 0.144458 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −641206. | −2.48952 | ||||||||
\(147\) | − 50579.8i | − 0.193056i | ||||||||
\(148\) | 523902.i | 1.96606i | ||||||||
\(149\) | −45802.9 | −0.169016 | −0.0845079 | − | 0.996423i | \(-0.526932\pi\) | ||||
−0.0845079 | + | 0.996423i | \(0.526932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −299685. | −1.06960 | −0.534802 | − | 0.844977i | \(-0.679614\pi\) | ||||
−0.534802 | + | 0.844977i | \(0.679614\pi\) | |||||||
\(152\) | − 612773.i | − 2.15125i | ||||||||
\(153\) | − 281257.i | − 0.971348i | ||||||||
\(154\) | 501210. | 1.70301 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −53564.2 | −0.176223 | ||||||||
\(157\) | 248510.i | 0.804626i | 0.915502 | + | 0.402313i | \(0.131794\pi\) | ||||
−0.915502 | + | 0.402313i | \(0.868206\pi\) | |||||||
\(158\) | 555809.i | 1.77126i | ||||||||
\(159\) | −6210.24 | −0.0194812 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 122484. | 0.372405 | ||||||||
\(162\) | − 326756.i | − 0.978218i | ||||||||
\(163\) | − 610706.i | − 1.80038i | −0.435501 | − | 0.900188i | \(-0.643429\pi\) | ||||
0.435501 | − | 0.900188i | \(-0.356571\pi\) | |||||||
\(164\) | −375174. | −1.08924 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −328820. | −0.926164 | ||||||||
\(167\) | 383764.i | 1.06481i | 0.846489 | + | 0.532406i | \(0.178712\pi\) | ||||
−0.846489 | + | 0.532406i | \(0.821288\pi\) | |||||||
\(168\) | 108635.i | 0.296960i | ||||||||
\(169\) | −28561.0 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −623330. | −1.63015 | ||||||||
\(172\) | 135896.i | 0.350255i | ||||||||
\(173\) | − 544383.i | − 1.38290i | −0.722426 | − | 0.691448i | \(-0.756973\pi\) | ||||
0.722426 | − | 0.691448i | \(-0.243027\pi\) | |||||||
\(174\) | 368858. | 0.923606 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 102915. | 0.250435 | ||||||||
\(177\) | − 41160.7i | − 0.0987528i | ||||||||
\(178\) | 734723.i | 1.73809i | ||||||||
\(179\) | 459644. | 1.07223 | 0.536117 | − | 0.844144i | \(-0.319891\pi\) | ||||
0.536117 | + | 0.844144i | \(0.319891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −209506. | −0.475334 | −0.237667 | − | 0.971347i | \(-0.576383\pi\) | ||||
−0.237667 | + | 0.971347i | \(0.576383\pi\) | |||||||
\(182\) | 141768.i | 0.317249i | ||||||||
\(183\) | 182888.i | 0.403699i | ||||||||
\(184\) | 277965. | 0.605264 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −35981.5 | −0.0762601 | ||||||||
\(187\) | − 805257.i | − 1.68396i | ||||||||
\(188\) | 557042.i | 1.14946i | ||||||||
\(189\) | 239183. | 0.487053 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 311387. | 0.617614 | 0.308807 | − | 0.951125i | \(-0.400070\pi\) | ||||
0.308807 | + | 0.951125i | \(0.400070\pi\) | |||||||
\(192\) | − 302248.i | − 0.591712i | ||||||||
\(193\) | 775484.i | 1.49858i | 0.662243 | + | 0.749289i | \(0.269605\pi\) | ||||
−0.662243 | + | 0.749289i | \(0.730395\pi\) | |||||||
\(194\) | −549671. | −1.04857 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −467216. | −0.868715 | ||||||||
\(197\) | − 492489.i | − 0.904130i | −0.891985 | − | 0.452065i | \(-0.850687\pi\) | ||||
0.891985 | − | 0.452065i | \(-0.149313\pi\) | |||||||
\(198\) | − 1.15704e6i | − 2.09742i | ||||||||
\(199\) | −805242. | −1.44143 | −0.720716 | − | 0.693231i | \(-0.756187\pi\) | ||||
−0.720716 | + | 0.693231i | \(0.756187\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −163097. | −0.284745 | ||||||||
\(202\) | − 1.76725e6i | − 3.04734i | ||||||||
\(203\) | − 613455.i | − 1.04482i | ||||||||
\(204\) | 427163. | 0.718652 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 563780. | 0.925639 | ||||||||
\(207\) | − 282754.i | − 0.458651i | ||||||||
\(208\) | 29109.6i | 0.0466528i | ||||||||
\(209\) | −1.78463e6 | −2.82607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 112124. | 0.173377 | 0.0866885 | − | 0.996235i | \(-0.472372\pi\) | ||||
0.0866885 | + | 0.996235i | \(0.472372\pi\) | |||||||
\(212\) | 57365.2i | 0.0876616i | ||||||||
\(213\) | 345877.i | 0.522363i | ||||||||
\(214\) | 1.22328e6 | 1.82596 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 542801. | 0.791601 | ||||||||
\(217\) | 59841.5i | 0.0862686i | ||||||||
\(218\) | 1.37374e6i | 1.95778i | ||||||||
\(219\) | −404761. | −0.570280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 227768. | 0.313698 | ||||||||
\(222\) | 526298.i | 0.716720i | ||||||||
\(223\) | − 309032.i | − 0.416142i | −0.978114 | − | 0.208071i | \(-0.933281\pi\) | ||||
0.978114 | − | 0.208071i | \(-0.0667186\pi\) | |||||||
\(224\) | −448978. | −0.597867 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 437648. | 0.569973 | ||||||||
\(227\) | − 229817.i | − 0.296018i | −0.988986 | − | 0.148009i | \(-0.952714\pi\) | ||||
0.988986 | − | 0.148009i | \(-0.0472865\pi\) | |||||||
\(228\) | − 946692.i | − 1.20607i | ||||||||
\(229\) | 1.48633e6 | 1.87295 | 0.936475 | − | 0.350735i | \(-0.114068\pi\) | ||||
0.936475 | + | 0.350735i | \(0.114068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 316389. | 0.390113 | ||||||||
\(232\) | − 1.39217e6i | − 1.69814i | ||||||||
\(233\) | − 706867.i | − 0.852997i | −0.904488 | − | 0.426499i | \(-0.859747\pi\) | ||||
0.904488 | − | 0.426499i | \(-0.140253\pi\) | |||||||
\(234\) | 327270. | 0.390721 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −380210. | −0.444369 | ||||||||
\(237\) | 350854.i | 0.405747i | ||||||||
\(238\) | − 1.13057e6i | − 1.29376i | ||||||||
\(239\) | −657958. | −0.745080 | −0.372540 | − | 0.928016i | \(-0.621513\pi\) | ||||
−0.372540 | + | 0.928016i | \(0.621513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −790694. | −0.876932 | −0.438466 | − | 0.898748i | \(-0.644478\pi\) | ||||
−0.438466 | + | 0.898748i | \(0.644478\pi\) | |||||||
\(242\) | − 1.81821e6i | − 1.99575i | ||||||||
\(243\) | − 849201.i | − 0.922561i | ||||||||
\(244\) | 1.68938e6 | 1.81657 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −376890. | −0.397079 | ||||||||
\(247\) | − 504786.i | − 0.526460i | ||||||||
\(248\) | 135804.i | 0.140211i | ||||||||
\(249\) | −207567. | −0.212159 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −129798. | −0.130042 | −0.0650212 | − | 0.997884i | \(-0.520711\pi\) | ||||
−0.0650212 | + | 0.997884i | \(0.520711\pi\) | |||||||
\(252\) | − 1.02078e6i | − 1.01258i | ||||||||
\(253\) | − 809542.i | − 0.795130i | ||||||||
\(254\) | −1.21083e6 | −1.17761 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.31715e6 | −1.25613 | ||||||||
\(257\) | 475029.i | 0.448629i | 0.974517 | + | 0.224314i | \(0.0720142\pi\) | ||||
−0.974517 | + | 0.224314i | \(0.927986\pi\) | |||||||
\(258\) | 136517.i | 0.127685i | ||||||||
\(259\) | 875295. | 0.810784 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41616e6 | −1.28680 | ||||||||
\(262\) | − 369682.i | − 0.332717i | ||||||||
\(263\) | − 1.81430e6i | − 1.61741i | −0.588214 | − | 0.808705i | \(-0.700169\pi\) | ||||
0.588214 | − | 0.808705i | \(-0.299831\pi\) | |||||||
\(264\) | 718011. | 0.634046 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.50560e6 | −2.17124 | ||||||||
\(267\) | 463793.i | 0.398149i | ||||||||
\(268\) | 1.50656e6i | 1.28130i | ||||||||
\(269\) | −1.77036e6 | −1.49170 | −0.745849 | − | 0.666115i | \(-0.767956\pi\) | ||||
−0.745849 | + | 0.666115i | \(0.767956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.11442e6 | 0.921777 | 0.460888 | − | 0.887458i | \(-0.347531\pi\) | ||||
0.460888 | + | 0.887458i | \(0.347531\pi\) | |||||||
\(272\) | − 232143.i | − 0.190254i | ||||||||
\(273\) | 89490.9i | 0.0726729i | ||||||||
\(274\) | 3.75833e6 | 3.02426 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 429436. | 0.339333 | ||||||||
\(277\) | − 508146.i | − 0.397914i | −0.980008 | − | 0.198957i | \(-0.936245\pi\) | ||||
0.980008 | − | 0.198957i | \(-0.0637554\pi\) | |||||||
\(278\) | 1.36039e6i | 1.05573i | ||||||||
\(279\) | 138144. | 0.106248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60415e6 | 1.21193 | 0.605966 | − | 0.795491i | \(-0.292787\pi\) | ||||
0.605966 | + | 0.795491i | \(0.292787\pi\) | |||||||
\(282\) | 559590.i | 0.419032i | ||||||||
\(283\) | 1.80648e6i | 1.34081i | 0.741997 | + | 0.670403i | \(0.233879\pi\) | ||||
−0.741997 | + | 0.670403i | \(0.766121\pi\) | |||||||
\(284\) | 3.19494e6 | 2.35053 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 936996. | 0.677365 | ||||||||
\(287\) | 626812.i | 0.449193i | ||||||||
\(288\) | 1.03646e6i | 0.736329i | ||||||||
\(289\) | −396546. | −0.279286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −346979. | −0.240199 | ||||||||
\(292\) | 3.73886e6i | 2.56615i | ||||||||
\(293\) | − 2.20331e6i | − 1.49936i | −0.661798 | − | 0.749682i | \(-0.730206\pi\) | ||||
0.661798 | − | 0.749682i | \(-0.269794\pi\) | |||||||
\(294\) | −469353. | −0.316688 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.98639e6 | 1.31776 | ||||||||
\(297\) | − 1.58085e6i | − 1.03992i | ||||||||
\(298\) | 425026.i | 0.277252i | ||||||||
\(299\) | 228980. | 0.148122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 227044. | 0.144442 | ||||||||
\(302\) | 2.78092e6i | 1.75457i | ||||||||
\(303\) | − 1.11558e6i | − 0.698061i | ||||||||
\(304\) | −514482. | −0.319290 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.60991e6 | −1.59339 | ||||||||
\(307\) | 2.20792e6i | 1.33702i | 0.743704 | + | 0.668509i | \(0.233067\pi\) | ||||
−0.743704 | + | 0.668509i | \(0.766933\pi\) | |||||||
\(308\) | − 2.92255e6i | − 1.75544i | ||||||||
\(309\) | 355886. | 0.212038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.09149e6 | −0.639910 | −0.319955 | − | 0.947433i | \(-0.603668\pi\) | ||||
−0.319955 | + | 0.947433i | \(0.603668\pi\) | |||||||
\(312\) | 203090.i | 0.118114i | ||||||||
\(313\) | − 1.38817e6i | − 0.800905i | −0.916318 | − | 0.400452i | \(-0.868853\pi\) | ||||
0.916318 | − | 0.400452i | \(-0.131147\pi\) | |||||||
\(314\) | 2.30604e6 | 1.31990 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.24091e6 | 1.82578 | ||||||||
\(317\) | 1.04832e6i | 0.585931i | 0.956123 | + | 0.292965i | \(0.0946421\pi\) | ||||
−0.956123 | + | 0.292965i | \(0.905358\pi\) | |||||||
\(318\) | 57627.6i | 0.0319568i | ||||||||
\(319\) | −4.05454e6 | −2.23082 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 772196. | 0.418278 | ||||||||
\(322\) | − 1.13659e6i | − 0.610889i | ||||||||
\(323\) | 4.02557e6i | 2.14694i | ||||||||
\(324\) | −1.90531e6 | −1.00833 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.66702e6 | −2.95332 | ||||||||
\(327\) | 867175.i | 0.448474i | ||||||||
\(328\) | 1.42248e6i | 0.730067i | ||||||||
\(329\) | 930664. | 0.474027 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.48155e6 | 1.74664 | 0.873320 | − | 0.487148i | \(-0.161963\pi\) | ||||
0.873320 | + | 0.487148i | \(0.161963\pi\) | |||||||
\(332\) | 1.91734e6i | 0.954673i | ||||||||
\(333\) | − 2.02061e6i | − 0.998556i | ||||||||
\(334\) | 3.56112e6 | 1.74671 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 91209.8 | 0.0440751 | ||||||||
\(337\) | − 1.92271e6i | − 0.922231i | −0.887340 | − | 0.461115i | \(-0.847449\pi\) | ||||
0.887340 | − | 0.461115i | \(-0.152551\pi\) | |||||||
\(338\) | 265031.i | 0.126184i | ||||||||
\(339\) | 276265. | 0.130565 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 395514. | 0.184194 | ||||||||
\(342\) | 5.78417e6i | 2.67409i | ||||||||
\(343\) | 2.29994e6i | 1.05556i | ||||||||
\(344\) | 515253. | 0.234760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.05158e6 | −2.26849 | ||||||||
\(347\) | − 3.52602e6i | − 1.57203i | −0.618207 | − | 0.786016i | \(-0.712140\pi\) | ||||
0.618207 | − | 0.786016i | \(-0.287860\pi\) | |||||||
\(348\) | − 2.15081e6i | − 0.952036i | ||||||||
\(349\) | 1.36701e6 | 0.600771 | 0.300385 | − | 0.953818i | \(-0.402885\pi\) | ||||
0.300385 | + | 0.953818i | \(0.402885\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 447145. | 0.193723 | ||||||||
\(352\) | 2.96746e6i | 1.27652i | ||||||||
\(353\) | 829000.i | 0.354094i | 0.984202 | + | 0.177047i | \(0.0566544\pi\) | ||||
−0.984202 | + | 0.177047i | \(0.943346\pi\) | |||||||
\(354\) | −381949. | −0.161993 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.28415e6 | 1.79160 | ||||||||
\(357\) | − 713672.i | − 0.296366i | ||||||||
\(358\) | − 4.26525e6i | − 1.75888i | ||||||||
\(359\) | −663764. | −0.271818 | −0.135909 | − | 0.990721i | \(-0.543395\pi\) | ||||
−0.135909 | + | 0.990721i | \(0.543395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.44548e6 | 2.60308 | ||||||||
\(362\) | 1.94410e6i | 0.779734i | ||||||||
\(363\) | − 1.14775e6i | − 0.457172i | ||||||||
\(364\) | 826647. | 0.327014 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.69710e6 | 0.662224 | ||||||||
\(367\) | 193910.i | 0.0751511i | 0.999294 | + | 0.0375755i | \(0.0119635\pi\) | ||||
−0.999294 | + | 0.0375755i | \(0.988037\pi\) | |||||||
\(368\) | − 233378.i | − 0.0898339i | ||||||||
\(369\) | 1.44699e6 | 0.553223 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 95841.5 | 0.0361509 | ||||||||
\(372\) | 209808.i | 0.0786075i | ||||||||
\(373\) | − 1.83984e6i | − 0.684712i | −0.939570 | − | 0.342356i | \(-0.888775\pi\) | ||||
0.939570 | − | 0.342356i | \(-0.111225\pi\) | |||||||
\(374\) | −7.47235e6 | −2.76235 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.11204e6 | 0.770430 | ||||||||
\(377\) | − 1.14683e6i | − 0.415573i | ||||||||
\(378\) | − 2.21949e6i | − 0.798958i | ||||||||
\(379\) | 1.64249e6 | 0.587359 | 0.293680 | − | 0.955904i | \(-0.405120\pi\) | ||||
0.293680 | + | 0.955904i | \(0.405120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −764338. | −0.269757 | ||||||||
\(382\) | − 2.88951e6i | − 1.01313i | ||||||||
\(383\) | 126562.i | 0.0440865i | 0.999757 | + | 0.0220432i | \(0.00701715\pi\) | ||||
−0.999757 | + | 0.0220432i | \(0.992983\pi\) | |||||||
\(384\) | −1.87374e6 | −0.648458 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.19607e6 | 2.45826 | ||||||||
\(387\) | − 524130.i | − 0.177894i | ||||||||
\(388\) | 3.20512e6i | 1.08085i | ||||||||
\(389\) | 5.20026e6 | 1.74241 | 0.871206 | − | 0.490917i | \(-0.163338\pi\) | ||||
0.871206 | + | 0.490917i | \(0.163338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.82607e6 | −0.604053 | ||||||||
\(392\) | 1.77146e6i | 0.582260i | ||||||||
\(393\) | − 233361.i | − 0.0762163i | ||||||||
\(394\) | −4.57003e6 | −1.48313 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.74668e6 | −2.16198 | ||||||||
\(397\) | − 2.24899e6i | − 0.716163i | −0.933690 | − | 0.358081i | \(-0.883431\pi\) | ||||
0.933690 | − | 0.358081i | \(-0.116569\pi\) | |||||||
\(398\) | 7.47221e6i | 2.36451i | ||||||||
\(399\) | −1.58166e6 | −0.497372 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.11199e6 | 0.655889 | 0.327945 | − | 0.944697i | \(-0.393644\pi\) | ||||
0.327945 | + | 0.944697i | \(0.393644\pi\) | |||||||
\(402\) | 1.51345e6i | 0.467094i | ||||||||
\(403\) | 111872.i | 0.0343129i | ||||||||
\(404\) | −1.03048e7 | −3.14114 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.69253e6 | −1.71392 | ||||||||
\(407\) | − 5.78514e6i | − 1.73112i | ||||||||
\(408\) | − 1.61960e6i | − 0.481679i | ||||||||
\(409\) | −1.01144e6 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.37244e6 | 0.692774 | ||||||||
\(412\) | − 3.28739e6i | − 0.954132i | ||||||||
\(413\) | 635226.i | 0.183254i | ||||||||
\(414\) | −2.62380e6 | −0.752367 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −839349. | −0.237799 | ||||||||
\(417\) | 858748.i | 0.241839i | ||||||||
\(418\) | 1.65604e7i | 4.63587i | ||||||||
\(419\) | 84677.5 | 0.0235631 | 0.0117816 | − | 0.999931i | \(-0.496250\pi\) | ||||
0.0117816 | + | 0.999931i | \(0.496250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.58658e6 | −0.711247 | −0.355624 | − | 0.934629i | \(-0.615731\pi\) | ||||
−0.355624 | + | 0.934629i | \(0.615731\pi\) | |||||||
\(422\) | − 1.04045e6i | − 0.284406i | ||||||||
\(423\) | − 2.14843e6i | − 0.583808i | ||||||||
\(424\) | 217502. | 0.0587555 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.20955e6 | 0.856880 | ||||||||
\(427\) | − 2.82248e6i | − 0.749137i | ||||||||
\(428\) | − 7.13294e6i | − 1.88217i | ||||||||
\(429\) | 591478. | 0.155166 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 63405.6 | 0.0164412 | 0.00822062 | − | 0.999966i | \(-0.497383\pi\) | ||||
0.00822062 | + | 0.999966i | \(0.497383\pi\) | |||||||
\(432\) | − 455734.i | − 0.117490i | ||||||||
\(433\) | 916925.i | 0.235025i | 0.993071 | + | 0.117512i | \(0.0374920\pi\) | ||||
−0.993071 | + | 0.117512i | \(0.962508\pi\) | |||||||
\(434\) | 555296. | 0.141514 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.01027e6 | 2.01805 | ||||||||
\(437\) | 4.04699e6i | 1.01374i | ||||||||
\(438\) | 3.75596e6i | 0.935483i | ||||||||
\(439\) | −1.74762e6 | −0.432799 | −0.216399 | − | 0.976305i | \(-0.569431\pi\) | ||||
−0.216399 | + | 0.976305i | \(0.569431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.80198e6 | 0.441219 | ||||||||
\(442\) | − 2.11356e6i | − 0.514588i | ||||||||
\(443\) | 3.55036e6i | 0.859533i | 0.902940 | + | 0.429766i | \(0.141404\pi\) | ||||
−0.902940 | + | 0.429766i | \(0.858596\pi\) | |||||||
\(444\) | 3.06883e6 | 0.738782 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.86765e6 | −0.682637 | ||||||||
\(447\) | 268297.i | 0.0635108i | ||||||||
\(448\) | 4.66454e6i | 1.09803i | ||||||||
\(449\) | −7.03537e6 | −1.64691 | −0.823457 | − | 0.567378i | \(-0.807958\pi\) | ||||
−0.823457 | + | 0.567378i | \(0.807958\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.14283e6 | 0.959082 | ||||||||
\(452\) | − 2.55192e6i | − 0.587517i | ||||||||
\(453\) | 1.75545e6i | 0.401924i | ||||||||
\(454\) | −2.13258e6 | −0.485586 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.58941e6 | −0.808372 | ||||||||
\(457\) | 1.68083e6i | 0.376472i | 0.982124 | + | 0.188236i | \(0.0602770\pi\) | ||||
−0.982124 | + | 0.188236i | \(0.939723\pi\) | |||||||
\(458\) | − 1.37923e7i | − 3.07237i | ||||||||
\(459\) | −3.56589e6 | −0.790017 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.85997e6 | −1.94169 | −0.970845 | − | 0.239709i | \(-0.922948\pi\) | ||||
−0.970845 | + | 0.239709i | \(0.922948\pi\) | |||||||
\(462\) | − 2.93592e6i | − 0.639939i | ||||||||
\(463\) | 7.32234e6i | 1.58744i | 0.608284 | + | 0.793720i | \(0.291858\pi\) | ||||
−0.608284 | + | 0.793720i | \(0.708142\pi\) | |||||||
\(464\) | −1.16886e6 | −0.252039 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.55934e6 | −1.39925 | ||||||||
\(467\) | 840696.i | 0.178380i | 0.996015 | + | 0.0891901i | \(0.0284279\pi\) | ||||
−0.996015 | + | 0.0891901i | \(0.971572\pi\) | |||||||
\(468\) | − 1.90831e6i | − 0.402748i | ||||||||
\(469\) | 2.51705e6 | 0.528396 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.45568e6 | 0.302353 | ||||||||
\(472\) | 1.44158e6i | 0.297840i | ||||||||
\(473\) | − 1.50062e6i | − 0.308402i | ||||||||
\(474\) | 3.25574e6 | 0.665585 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.59233e6 | −1.33359 | ||||||||
\(477\) | − 221249.i | − 0.0445232i | ||||||||
\(478\) | 6.10549e6i | 1.22222i | ||||||||
\(479\) | 4.72739e6 | 0.941418 | 0.470709 | − | 0.882288i | \(-0.343998\pi\) | ||||
0.470709 | + | 0.882288i | \(0.343998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.63634e6 | 0.322485 | ||||||||
\(482\) | 7.33722e6i | 1.43851i | ||||||||
\(483\) | − 717469.i | − 0.139938i | ||||||||
\(484\) | −1.06020e7 | −2.05718 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.88013e6 | −1.51336 | ||||||||
\(487\) | 5.60717e6i | 1.07133i | 0.844432 | + | 0.535663i | \(0.179938\pi\) | ||||
−0.844432 | + | 0.535663i | \(0.820062\pi\) | |||||||
\(488\) | − 6.40532e6i | − 1.21756i | ||||||||
\(489\) | −3.57730e6 | −0.676525 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 117889. | 0.0220683 | 0.0110341 | − | 0.999939i | \(-0.496488\pi\) | ||||
0.0110341 | + | 0.999939i | \(0.496488\pi\) | |||||||
\(492\) | 2.19764e6i | 0.409302i | ||||||||
\(493\) | 9.14576e6i | 1.69474i | ||||||||
\(494\) | −4.68414e6 | −0.863600 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 114020. | 0.0208103 | ||||||||
\(497\) | − 5.33786e6i | − 0.969340i | ||||||||
\(498\) | 1.92611e6i | 0.348023i | ||||||||
\(499\) | 314105. | 0.0564707 | 0.0282354 | − | 0.999601i | \(-0.491011\pi\) | ||||
0.0282354 | + | 0.999601i | \(0.491011\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.24796e6 | 0.400123 | ||||||||
\(502\) | 1.20446e6i | 0.213320i | ||||||||
\(503\) | − 8.44792e6i | − 1.48878i | −0.667747 | − | 0.744389i | \(-0.732741\pi\) | ||||
0.667747 | − | 0.744389i | \(-0.267259\pi\) | |||||||
\(504\) | −3.87030e6 | −0.678686 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.51211e6 | −1.30432 | ||||||||
\(507\) | 167300.i | 0.0289053i | ||||||||
\(508\) | 7.06035e6i | 1.21385i | ||||||||
\(509\) | 4.29988e6 | 0.735635 | 0.367817 | − | 0.929898i | \(-0.380105\pi\) | ||||
0.367817 | + | 0.929898i | \(0.380105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.24660e6 | 1.05826 | ||||||||
\(512\) | 1.98625e6i | 0.334857i | ||||||||
\(513\) | 7.90283e6i | 1.32583i | ||||||||
\(514\) | 4.40801e6 | 0.735927 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 796030. | 0.131615 | ||||||||
\(517\) | − 6.15110e6i | − 1.01211i | ||||||||
\(518\) | − 8.12227e6i | − 1.33000i | ||||||||
\(519\) | −3.18881e6 | −0.519649 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.31158e6 | −1.18009 | −0.590047 | − | 0.807369i | \(-0.700891\pi\) | ||||
−0.590047 | + | 0.807369i | \(0.700891\pi\) | |||||||
\(522\) | 1.31412e7i | 2.11085i | ||||||||
\(523\) | 3.72278e6i | 0.595131i | 0.954701 | + | 0.297566i | \(0.0961747\pi\) | ||||
−0.954701 | + | 0.297566i | \(0.903825\pi\) | |||||||
\(524\) | −2.15561e6 | −0.342959 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.68357e7 | −2.65319 | ||||||||
\(527\) | − 892153.i | − 0.139931i | ||||||||
\(528\) | − 602839.i | − 0.0941058i | ||||||||
\(529\) | 4.60056e6 | 0.714778 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.46641e6 | 0.225694 | ||||||||
\(532\) | 1.46101e7i | 2.23808i | ||||||||
\(533\) | 1.17181e6i | 0.178664i | ||||||||
\(534\) | 4.30375e6 | 0.653121 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.71218e6 | 0.858796 | ||||||||
\(537\) | − 2.69244e6i | − 0.402912i | ||||||||
\(538\) | 1.64280e7i | 2.44697i | ||||||||
\(539\) | 5.15919e6 | 0.764909 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 612758. | 0.0900111 | 0.0450056 | − | 0.998987i | \(-0.485669\pi\) | ||||
0.0450056 | + | 0.998987i | \(0.485669\pi\) | |||||||
\(542\) | − 1.03412e7i | − 1.51208i | ||||||||
\(543\) | 1.22721e6i | 0.178616i | ||||||||
\(544\) | 6.69363e6 | 0.969761 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 830428. | 0.119212 | ||||||||
\(547\) | − 1.31870e7i | − 1.88442i | −0.335020 | − | 0.942211i | \(-0.608743\pi\) | ||||
0.335020 | − | 0.942211i | \(-0.391257\pi\) | |||||||
\(548\) | − 2.19148e7i | − 3.11735i | ||||||||
\(549\) | −6.51567e6 | −0.922632 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.02691e7 | 2.84417 | ||||||||
\(552\) | − 1.62822e6i | − 0.227439i | ||||||||
\(553\) | − 5.41467e6i | − 0.752938i | ||||||||
\(554\) | −4.71532e6 | −0.652735 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.93244e6 | 1.08823 | ||||||||
\(557\) | − 2.49720e6i | − 0.341048i | −0.985354 | − | 0.170524i | \(-0.945454\pi\) | ||||
0.985354 | − | 0.170524i | \(-0.0545460\pi\) | |||||||
\(558\) | − 1.28190e6i | − 0.174288i | ||||||||
\(559\) | 424452. | 0.0574512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.71692e6 | −0.632777 | ||||||||
\(562\) | − 1.48856e7i | − 1.98804i | ||||||||
\(563\) | − 8.39064e6i | − 1.11564i | −0.829962 | − | 0.557820i | \(-0.811638\pi\) | ||||
0.829962 | − | 0.557820i | \(-0.188362\pi\) | |||||||
\(564\) | 3.26296e6 | 0.431931 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.67631e7 | 2.19945 | ||||||||
\(567\) | 3.18324e6i | 0.415826i | ||||||||
\(568\) | − 1.21137e7i | − 1.57546i | ||||||||
\(569\) | 2.18516e6 | 0.282945 | 0.141473 | − | 0.989942i | \(-0.454816\pi\) | ||||
0.141473 | + | 0.989942i | \(0.454816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.46108e7 | 1.87535 | 0.937676 | − | 0.347510i | \(-0.112973\pi\) | ||||
0.937676 | + | 0.347510i | \(0.112973\pi\) | |||||||
\(572\) | − 5.46361e6i | − 0.698215i | ||||||||
\(573\) | − 1.82400e6i | − 0.232080i | ||||||||
\(574\) | 5.81648e6 | 0.736852 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.07681e7 | 1.35233 | ||||||||
\(577\) | 756371.i | 0.0945791i | 0.998881 | + | 0.0472896i | \(0.0150583\pi\) | ||||
−0.998881 | + | 0.0472896i | \(0.984942\pi\) | |||||||
\(578\) | 3.67973e6i | 0.458138i | ||||||||
\(579\) | 4.54252e6 | 0.563119 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.20335e6 | 0.393699 | ||||||||
\(582\) | 3.21978e6i | 0.394020i | ||||||||
\(583\) | − 633451.i | − 0.0771866i | ||||||||
\(584\) | 1.41760e7 | 1.71997 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.04456e7 | −2.45955 | ||||||||
\(587\) | 797341.i | 0.0955100i | 0.998859 | + | 0.0477550i | \(0.0152067\pi\) | ||||
−0.998859 | + | 0.0477550i | \(0.984793\pi\) | |||||||
\(588\) | 2.73679e6i | 0.326436i | ||||||||
\(589\) | −1.97722e6 | −0.234837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.88483e6 | −0.339744 | ||||||||
\(592\) | − 1.66776e6i | − 0.195583i | ||||||||
\(593\) | − 9.00116e6i | − 1.05114i | −0.850750 | − | 0.525571i | \(-0.823852\pi\) | ||||
0.850750 | − | 0.525571i | \(-0.176148\pi\) | |||||||
\(594\) | −1.46694e7 | −1.70587 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.47832e6 | 0.285786 | ||||||||
\(597\) | 4.71683e6i | 0.541644i | ||||||||
\(598\) | − 2.12481e6i | − 0.242978i | ||||||||
\(599\) | 1.40266e7 | 1.59730 | 0.798648 | − | 0.601799i | \(-0.205549\pi\) | ||||
0.798648 | + | 0.601799i | \(0.205549\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.55864e7 | 1.76019 | 0.880094 | − | 0.474800i | \(-0.157480\pi\) | ||||
0.880094 | + | 0.474800i | \(0.157480\pi\) | |||||||
\(602\) | − 2.10685e6i | − 0.236942i | ||||||||
\(603\) | − 5.81059e6i | − 0.650769i | ||||||||
\(604\) | 1.62155e7 | 1.80858 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.03520e7 | −1.14509 | ||||||||
\(607\) | 6.45850e6i | 0.711475i | 0.934586 | + | 0.355738i | \(0.115770\pi\) | ||||
−0.934586 | + | 0.355738i | \(0.884230\pi\) | |||||||
\(608\) | − 1.48346e7i | − 1.62749i | ||||||||
\(609\) | −3.59340e6 | −0.392611 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.73985e6 | 0.188542 | ||||||||
\(612\) | 1.52184e7i | 1.64244i | ||||||||
\(613\) | − 8.15464e6i | − 0.876503i | −0.898852 | − | 0.438252i | \(-0.855598\pi\) | ||||
0.898852 | − | 0.438252i | \(-0.144402\pi\) | |||||||
\(614\) | 2.04883e7 | 2.19323 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.10809e7 | −1.17659 | ||||||||
\(617\) | 1.30591e7i | 1.38102i | 0.723323 | + | 0.690510i | \(0.242614\pi\) | ||||
−0.723323 | + | 0.690510i | \(0.757386\pi\) | |||||||
\(618\) | − 3.30243e6i | − 0.347826i | ||||||||
\(619\) | 1.16624e7 | 1.22338 | 0.611690 | − | 0.791098i | \(-0.290490\pi\) | ||||
0.611690 | + | 0.791098i | \(0.290490\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.58486e6 | −0.373030 | ||||||||
\(622\) | 1.01284e7i | 1.04970i | ||||||||
\(623\) | − 7.15764e6i | − 0.738839i | ||||||||
\(624\) | 170514. | 0.0175306 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.28814e7 | −1.31380 | ||||||||
\(627\) | 1.04538e7i | 1.06195i | ||||||||
\(628\) | − 1.34465e7i | − 1.36053i | ||||||||
\(629\) | −1.30494e7 | −1.31512 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.56162e6 | 0.656051 | 0.328026 | − | 0.944669i | \(-0.393617\pi\) | ||||
0.328026 | + | 0.944669i | \(0.393617\pi\) | |||||||
\(632\) | − 1.22880e7i | − 1.22374i | ||||||||
\(633\) | − 656782.i | − 0.0651496i | ||||||||
\(634\) | 9.72786e6 | 0.961156 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 336026. | 0.0329405 | ||||||||
\(637\) | 1.45928e6i | 0.142492i | ||||||||
\(638\) | 3.76240e7i | 3.65943i | ||||||||
\(639\) | −1.23224e7 | −1.19383 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.91450e6 | 0.856943 | 0.428472 | − | 0.903555i | \(-0.359052\pi\) | ||||
0.428472 | + | 0.903555i | \(0.359052\pi\) | |||||||
\(642\) | − 7.16556e6i | − 0.686140i | ||||||||
\(643\) | 1.65259e7i | 1.57629i | 0.615489 | + | 0.788146i | \(0.288959\pi\) | ||||
−0.615489 | + | 0.788146i | \(0.711041\pi\) | |||||||
\(644\) | −6.62741e6 | −0.629694 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.73551e7 | 3.52183 | ||||||||
\(647\) | − 1.36339e7i | − 1.28044i | −0.768192 | − | 0.640220i | \(-0.778843\pi\) | ||||
0.768192 | − | 0.640220i | \(-0.221157\pi\) | |||||||
\(648\) | 7.22403e6i | 0.675837i | ||||||||
\(649\) | 4.19844e6 | 0.391269 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 350530. | 0.0324170 | ||||||||
\(652\) | 3.30443e7i | 3.04423i | ||||||||
\(653\) | 9.93610e6i | 0.911870i | 0.890013 | + | 0.455935i | \(0.150695\pi\) | ||||
−0.890013 | + | 0.455935i | \(0.849305\pi\) | |||||||
\(654\) | 8.04691e6 | 0.735673 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.19431e6 | 0.108357 | ||||||||
\(657\) | − 1.44202e7i | − 1.30334i | ||||||||
\(658\) | − 8.63606e6i | − 0.777590i | ||||||||
\(659\) | 1.18157e6 | 0.105985 | 0.0529926 | − | 0.998595i | \(-0.483124\pi\) | ||||
0.0529926 | + | 0.998595i | \(0.483124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.40076e7 | −1.24698 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(662\) | − 3.23069e7i | − 2.86517i | ||||||||
\(663\) | − 1.33419e6i | − 0.117878i | ||||||||
\(664\) | 7.26966e6 | 0.639873 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.87502e7 | −1.63802 | ||||||||
\(667\) | 9.19442e6i | 0.800221i | ||||||||
\(668\) | − 2.07648e7i | − 1.80048i | ||||||||
\(669\) | −1.81020e6 | −0.156373 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.86548e7 | −1.59950 | ||||||||
\(672\) | 2.62995e6i | 0.224660i | ||||||||
\(673\) | − 1.45325e7i | − 1.23681i | −0.785860 | − | 0.618404i | \(-0.787779\pi\) | ||||
0.785860 | − | 0.618404i | \(-0.212221\pi\) | |||||||
\(674\) | −1.78417e7 | −1.51282 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.54539e6 | 0.130068 | ||||||||
\(677\) | 6.27094e6i | 0.525849i | 0.964816 | + | 0.262925i | \(0.0846870\pi\) | ||||
−0.964816 | + | 0.262925i | \(0.915313\pi\) | |||||||
\(678\) | − 2.56359e6i | − 0.214178i | ||||||||
\(679\) | 5.35487e6 | 0.445733 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.34619e6 | −0.111234 | ||||||||
\(682\) | − 3.67016e6i | − 0.302151i | ||||||||
\(683\) | − 188702.i | − 0.0154784i | −0.999970 | − | 0.00773919i | \(-0.997537\pi\) | ||||
0.999970 | − | 0.00773919i | \(-0.00246348\pi\) | |||||||
\(684\) | 3.37274e7 | 2.75640 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.13422e7 | 1.73153 | ||||||||
\(687\) | − 8.70639e6i | − 0.703796i | ||||||||
\(688\) | − 432604.i | − 0.0348433i | ||||||||
\(689\) | 179172. | 0.0143788 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49501e7 | −1.98782 | −0.993910 | − | 0.110195i | \(-0.964852\pi\) | ||||
−0.993910 | + | 0.110195i | \(0.964852\pi\) | |||||||
\(692\) | 2.94557e7i | 2.33832i | ||||||||
\(693\) | 1.12718e7i | 0.891583i | ||||||||
\(694\) | −3.27196e7 | −2.57875 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.15485e6 | −0.638106 | ||||||||
\(697\) | − 9.34490e6i | − 0.728606i | ||||||||
\(698\) | − 1.26851e7i | − 0.985500i | ||||||||
\(699\) | −4.14058e6 | −0.320530 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.11757e7 | 0.858975 | 0.429488 | − | 0.903073i | \(-0.358694\pi\) | ||||
0.429488 | + | 0.903073i | \(0.358694\pi\) | |||||||
\(702\) | − 4.14927e6i | − 0.317781i | ||||||||
\(703\) | 2.89206e7i | 2.20708i | ||||||||
\(704\) | 3.08297e7 | 2.34443 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.69267e6 | 0.580852 | ||||||||
\(707\) | 1.72165e7i | 1.29538i | ||||||||
\(708\) | 2.22714e6i | 0.166980i | ||||||||
\(709\) | 1.91144e7 | 1.42806 | 0.714028 | − | 0.700117i | \(-0.246869\pi\) | ||||
0.714028 | + | 0.700117i | \(0.246869\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.24997e7 | −0.927313 | ||||||||
\(712\) | − 1.62435e7i | − 1.20082i | ||||||||
\(713\) | − 896900.i | − 0.0660724i | ||||||||
\(714\) | −6.62249e6 | −0.486156 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.48706e7 | −1.81302 | ||||||||
\(717\) | 3.85409e6i | 0.279978i | ||||||||
\(718\) | 6.15937e6i | 0.445887i | ||||||||
\(719\) | 9.47384e6 | 0.683446 | 0.341723 | − | 0.939801i | \(-0.388990\pi\) | ||||
0.341723 | + | 0.939801i | \(0.388990\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.49232e6 | −0.393476 | ||||||||
\(722\) | − 5.98106e7i | − 4.27007i | ||||||||
\(723\) | 4.63161e6i | 0.329524i | ||||||||
\(724\) | 1.13360e7 | 0.803736 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.06505e7 | −0.749941 | ||||||||
\(727\) | 2.00091e7i | 1.40408i | 0.712139 | + | 0.702039i | \(0.247727\pi\) | ||||
−0.712139 | + | 0.702039i | \(0.752273\pi\) | |||||||
\(728\) | − 3.13426e6i | − 0.219183i | ||||||||
\(729\) | 3.58239e6 | 0.249663 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.38492e6 | −0.234290 | ||||||||
\(732\) | − 9.89577e6i | − 0.682609i | ||||||||
\(733\) | − 8.14639e6i | − 0.560023i | −0.959997 | − | 0.280011i | \(-0.909662\pi\) | ||||
0.959997 | − | 0.280011i | \(-0.0903382\pi\) | |||||||
\(734\) | 1.79938e6 | 0.123277 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.72925e6 | 0.457901 | ||||||||
\(737\) | − 1.66361e7i | − 1.12819i | ||||||||
\(738\) | − 1.34273e7i | − 0.907502i | ||||||||
\(739\) | −9.22447e6 | −0.621342 | −0.310671 | − | 0.950518i | \(-0.600554\pi\) | ||||
−0.310671 | + | 0.950518i | \(0.600554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.95686e6 | −0.197827 | ||||||||
\(742\) | − 889357.i | − 0.0593016i | ||||||||
\(743\) | 1.27277e7i | 0.845820i | 0.906172 | + | 0.422910i | \(0.138991\pi\) | ||||
−0.906172 | + | 0.422910i | \(0.861009\pi\) | |||||||
\(744\) | 795492. | 0.0526870 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.70727e7 | −1.12320 | ||||||||
\(747\) | − 7.39491e6i | − 0.484877i | ||||||||
\(748\) | 4.35711e7i | 2.84738i | ||||||||
\(749\) | −1.19172e7 | −0.776191 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45313e7 | −0.940169 | −0.470084 | − | 0.882622i | \(-0.655776\pi\) | ||||
−0.470084 | + | 0.882622i | \(0.655776\pi\) | |||||||
\(752\) | − 1.77326e6i | − 0.114348i | ||||||||
\(753\) | 760313.i | 0.0488658i | ||||||||
\(754\) | −1.06420e7 | −0.681702 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.29418e7 | −0.823551 | ||||||||
\(757\) | − 9.46969e6i | − 0.600615i | −0.953842 | − | 0.300307i | \(-0.902911\pi\) | ||||
0.953842 | − | 0.300307i | \(-0.0970893\pi\) | |||||||
\(758\) | − 1.52414e7i | − 0.963499i | ||||||||
\(759\) | −4.74201e6 | −0.298785 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.61063e7 | 1.63412 | 0.817059 | − | 0.576554i | \(-0.195603\pi\) | ||||
0.817059 | + | 0.576554i | \(0.195603\pi\) | |||||||
\(762\) | 7.09264e6i | 0.442507i | ||||||||
\(763\) | − 1.33830e7i | − 0.832225i | ||||||||
\(764\) | −1.68486e7 | −1.04432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.17442e6 | 0.0723191 | ||||||||
\(767\) | 1.18753e6i | 0.0728883i | ||||||||
\(768\) | 7.71538e6i | 0.472013i | ||||||||
\(769\) | 5.26481e6 | 0.321045 | 0.160523 | − | 0.987032i | \(-0.448682\pi\) | ||||
0.160523 | + | 0.987032i | \(0.448682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78255e6 | 0.168580 | ||||||||
\(772\) | − 4.19602e7i | − 2.53393i | ||||||||
\(773\) | − 6.66639e6i | − 0.401275i | −0.979666 | − | 0.200638i | \(-0.935699\pi\) | ||||
0.979666 | − | 0.200638i | \(-0.0643014\pi\) | |||||||
\(774\) | −4.86364e6 | −0.291816 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.21523e7 | 0.724444 | ||||||||
\(777\) | − 5.12717e6i | − 0.304667i | ||||||||
\(778\) | − 4.82556e7i | − 2.85824i | ||||||||
\(779\) | −2.07105e7 | −1.22277 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.52798e7 | −2.06966 | ||||||||
\(782\) | 1.69449e7i | 0.990883i | ||||||||
\(783\) | 1.79546e7i | 1.04658i | ||||||||
\(784\) | 1.48731e6 | 0.0864196 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.16547e6 | −0.125025 | ||||||||
\(787\) | − 1.01573e7i | − 0.584577i | −0.956330 | − | 0.292288i | \(-0.905583\pi\) | ||||
0.956330 | − | 0.292288i | \(-0.0944167\pi\) | |||||||
\(788\) | 2.66478e7i | 1.52878i | ||||||||
\(789\) | −1.06275e7 | −0.607772 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.26355e6 | −0.242287 | ||||||||
\(792\) | 2.55802e7i | 1.44908i | ||||||||
\(793\) | − 5.27653e6i | − 0.297965i | ||||||||
\(794\) | −2.08694e7 | −1.17479 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.35703e7 | 2.43730 | ||||||||
\(797\) | 9.12058e6i | 0.508600i | 0.967125 | + | 0.254300i | \(0.0818451\pi\) | ||||
−0.967125 | + | 0.254300i | \(0.918155\pi\) | |||||||
\(798\) | 1.46770e7i | 0.815885i | ||||||||
\(799\) | −1.38749e7 | −0.768888 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.65233e7 | −0.909948 | ||||||||
\(802\) | − 1.95981e7i | − 1.07592i | ||||||||
\(803\) | − 4.12861e7i | − 2.25951i | ||||||||
\(804\) | 8.82492e6 | 0.481472 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.03811e6 | 0.0562866 | ||||||||
\(807\) | 1.03702e7i | 0.560533i | ||||||||
\(808\) | 3.90710e7i | 2.10536i | ||||||||
\(809\) | 1.59436e7 | 0.856475 | 0.428238 | − | 0.903666i | \(-0.359135\pi\) | ||||
0.428238 | + | 0.903666i | \(0.359135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.92860e7 | −1.02965 | −0.514825 | − | 0.857295i | \(-0.672143\pi\) | ||||
−0.514825 | + | 0.857295i | \(0.672143\pi\) | |||||||
\(812\) | 3.31930e7i | 1.76668i | ||||||||
\(813\) | − 6.52789e6i | − 0.346375i | ||||||||
\(814\) | −5.36830e7 | −2.83972 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.35981e6 | −0.0714913 | ||||||||
\(817\) | 7.50175e6i | 0.393195i | ||||||||
\(818\) | 9.38565e6i | 0.490435i | ||||||||
\(819\) | −3.18825e6 | −0.166090 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.67112e6 | −0.190082 | −0.0950408 | − | 0.995473i | \(-0.530298\pi\) | ||||
−0.0950408 | + | 0.995473i | \(0.530298\pi\) | |||||||
\(822\) | − 2.20150e7i | − 1.13642i | ||||||||
\(823\) | − 7.63657e6i | − 0.393006i | −0.980503 | − | 0.196503i | \(-0.937042\pi\) | ||||
0.980503 | − | 0.196503i | \(-0.0629585\pi\) | |||||||
\(824\) | −1.24642e7 | −0.639511 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.89455e6 | 0.300608 | ||||||||
\(827\) | − 1.92879e7i | − 0.980667i | −0.871535 | − | 0.490334i | \(-0.836875\pi\) | ||||
0.871535 | − | 0.490334i | \(-0.163125\pi\) | |||||||
\(828\) | 1.52993e7i | 0.775526i | ||||||||
\(829\) | −1.14847e7 | −0.580407 | −0.290203 | − | 0.956965i | \(-0.593723\pi\) | ||||
−0.290203 | + | 0.956965i | \(0.593723\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.97654e6 | −0.149524 | ||||||||
\(832\) | 8.72021e6i | 0.436736i | ||||||||
\(833\) | − 1.16375e7i | − 0.581095i | ||||||||
\(834\) | 7.96872e6 | 0.396710 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.65636e7 | 4.77857 | ||||||||
\(837\) | − 1.75144e6i | − 0.0864135i | ||||||||
\(838\) | − 785761.i | − 0.0386528i | ||||||||
\(839\) | −3.21966e7 | −1.57908 | −0.789541 | − | 0.613698i | \(-0.789681\pi\) | ||||
−0.789541 | + | 0.613698i | \(0.789681\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.55386e7 | 1.24511 | ||||||||
\(842\) | 2.40020e7i | 1.16672i | ||||||||
\(843\) | − 9.39653e6i | − 0.455406i | ||||||||
\(844\) | −6.06683e6 | −0.293161 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.99363e7 | −0.957675 | ||||||||
\(847\) | 1.77130e7i | 0.848365i | ||||||||
\(848\) | − 182614.i | − 0.00872055i | ||||||||
\(849\) | 1.05817e7 | 0.503833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.31189e7 | −0.620973 | ||||||||
\(852\) | − 1.87148e7i | − 0.883256i | ||||||||
\(853\) | − 3.91351e7i | − 1.84160i | −0.390040 | − | 0.920798i | \(-0.627539\pi\) | ||||
0.390040 | − | 0.920798i | \(-0.372461\pi\) | |||||||
\(854\) | −2.61911e7 | −1.22888 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.70448e7 | −1.26153 | ||||||||
\(857\) | − 2.45430e7i | − 1.14150i | −0.821124 | − | 0.570750i | \(-0.806653\pi\) | ||||
0.821124 | − | 0.570750i | \(-0.193347\pi\) | |||||||
\(858\) | − 5.48860e6i | − 0.254532i | ||||||||
\(859\) | 3.17559e7 | 1.46839 | 0.734196 | − | 0.678937i | \(-0.237559\pi\) | ||||
0.734196 | + | 0.678937i | \(0.237559\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.67165e6 | 0.168793 | ||||||||
\(862\) | − 588370.i | − 0.0269701i | ||||||||
\(863\) | 2.85461e7i | 1.30473i | 0.757906 | + | 0.652363i | \(0.226222\pi\) | ||||
−0.757906 | + | 0.652363i | \(0.773778\pi\) | |||||||
\(864\) | 1.31407e7 | 0.598871 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.50857e6 | 0.385533 | ||||||||
\(867\) | 2.32283e6i | 0.104947i | ||||||||
\(868\) | − 3.23792e6i | − 0.145870i | ||||||||
\(869\) | −3.57875e7 | −1.60761 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.70554e6 | 0.210167 | ||||||||
\(872\) | − 3.03712e7i | − 1.35260i | ||||||||
\(873\) | − 1.23617e7i | − 0.548961i | ||||||||
\(874\) | 3.75538e7 | 1.66294 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.19009e7 | 0.964278 | ||||||||
\(877\) | 3.56134e7i | 1.56356i | 0.623556 | + | 0.781779i | \(0.285688\pi\) | ||||
−0.623556 | + | 0.781779i | \(0.714312\pi\) | |||||||
\(878\) | 1.62170e7i | 0.709959i | ||||||||
\(879\) | −1.29062e7 | −0.563414 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.79621e7 | −1.21375 | −0.606877 | − | 0.794796i | \(-0.707578\pi\) | ||||
−0.606877 | + | 0.794796i | \(0.707578\pi\) | |||||||
\(882\) | − 1.67214e7i | − 0.723772i | ||||||||
\(883\) | 1.65853e7i | 0.715849i | 0.933751 | + | 0.357924i | \(0.116515\pi\) | ||||
−0.933751 | + | 0.357924i | \(0.883485\pi\) | |||||||
\(884\) | −1.23242e7 | −0.530428 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.29454e7 | 1.40997 | ||||||||
\(887\) | 376818.i | 0.0160813i | 0.999968 | + | 0.00804067i | \(0.00255945\pi\) | ||||
−0.999968 | + | 0.00804067i | \(0.997441\pi\) | |||||||
\(888\) | − 1.16356e7i | − 0.495172i | ||||||||
\(889\) | 1.17959e7 | 0.500583 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.10392e7 | 0.887840 | ||||||||
\(892\) | 1.67212e7i | 0.703649i | ||||||||
\(893\) | 3.07500e7i | 1.29038i | ||||||||
\(894\) | 2.48966e6 | 0.104183 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.89171e7 | 1.20333 | ||||||||
\(897\) | − 1.34128e6i | − 0.0556596i | ||||||||
\(898\) | 6.52844e7i | 2.70159i | ||||||||
\(899\) | −4.49208e6 | −0.185374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.42886e6 | −0.0586379 | ||||||||
\(902\) | − 3.84432e7i | − 1.57327i | ||||||||
\(903\) | − 1.32995e6i | − 0.0542769i | ||||||||
\(904\) | −9.67568e6 | −0.393786 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.62896e7 | 0.659312 | ||||||||
\(907\) | 2.16129e7i | 0.872360i | 0.899860 | + | 0.436180i | \(0.143669\pi\) | ||||
−0.899860 | + | 0.436180i | \(0.856331\pi\) | |||||||
\(908\) | 1.24350e7i | 0.500533i | ||||||||
\(909\) | 3.97442e7 | 1.59538 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.44743e7 | 0.977043 | 0.488521 | − | 0.872552i | \(-0.337536\pi\) | ||||
0.488521 | + | 0.872552i | \(0.337536\pi\) | |||||||
\(912\) | 3.01365e6i | 0.119979i | ||||||||
\(913\) | − 2.11721e7i | − 0.840595i | ||||||||
\(914\) | 1.55972e7 | 0.617561 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.04228e7 | −3.16694 | ||||||||
\(917\) | 3.60143e6i | 0.141433i | ||||||||
\(918\) | 3.30895e7i | 1.29594i | ||||||||
\(919\) | −3.34269e7 | −1.30559 | −0.652796 | − | 0.757534i | \(-0.726404\pi\) | ||||
−0.652796 | + | 0.757534i | \(0.726404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.29332e7 | 0.502409 | ||||||||
\(922\) | 8.22157e7i | 3.18513i | ||||||||
\(923\) | − 9.97895e6i | − 0.385550i | ||||||||
\(924\) | −1.71193e7 | −0.659637 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.79473e7 | 2.60402 | ||||||||
\(927\) | 1.26790e7i | 0.484602i | ||||||||
\(928\) | − 3.37031e7i | − 1.28469i | ||||||||
\(929\) | 2.68705e7 | 1.02149 | 0.510747 | − | 0.859731i | \(-0.329369\pi\) | ||||
0.510747 | + | 0.859731i | \(0.329369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.57914e7 | −0.975214 | ||||||||
\(932\) | 3.82474e7i | 1.44232i | ||||||||
\(933\) | 6.39357e6i | 0.240458i | ||||||||
\(934\) | 7.80120e6 | 0.292613 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.23541e6 | −0.269944 | ||||||||
\(937\) | 1.17808e7i | 0.438353i | 0.975685 | + | 0.219177i | \(0.0703371\pi\) | ||||
−0.975685 | + | 0.219177i | \(0.929663\pi\) | |||||||
\(938\) | − 2.33569e7i | − 0.866777i | ||||||||
\(939\) | −8.13140e6 | −0.300955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.37398e7 | −1.61029 | −0.805143 | − | 0.593081i | \(-0.797911\pi\) | ||||
−0.805143 | + | 0.593081i | \(0.797911\pi\) | |||||||
\(942\) | − 1.35080e7i | − 0.495978i | ||||||||
\(943\) | − 9.39463e6i | − 0.344033i | ||||||||
\(944\) | 1.21034e6 | 0.0442057 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.39249e7 | −0.505900 | ||||||||
\(947\) | 5.14429e7i | 1.86402i | 0.362435 | + | 0.932009i | \(0.381946\pi\) | ||||
−0.362435 | + | 0.932009i | \(0.618054\pi\) | |||||||
\(948\) | − 1.89841e7i | − 0.686072i | ||||||||
\(949\) | 1.16778e7 | 0.420917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.14070e6 | 0.220174 | ||||||||
\(952\) | 2.49950e7i | 0.893843i | ||||||||
\(953\) | 5.27803e7i | 1.88252i | 0.337682 | + | 0.941260i | \(0.390357\pi\) | ||||
−0.337682 | + | 0.941260i | \(0.609643\pi\) | |||||||
\(954\) | −2.05307e6 | −0.0730354 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.56010e7 | 1.25985 | ||||||||
\(957\) | 2.37501e7i | 0.838274i | ||||||||
\(958\) | − 4.38676e7i | − 1.54429i | ||||||||
\(959\) | −3.66135e7 | −1.28557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.81910e7 | −0.984694 | ||||||||
\(962\) | − 1.51843e7i | − 0.529002i | ||||||||
\(963\) | 2.75107e7i | 0.955951i | ||||||||
\(964\) | 4.27832e7 | 1.48279 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.65772e6 | −0.229553 | ||||||||
\(967\) | − 2.62374e6i | − 0.0902307i | −0.998982 | − | 0.0451154i | \(-0.985634\pi\) | ||||
0.998982 | − | 0.0451154i | \(-0.0143655\pi\) | |||||||
\(968\) | 4.01977e7i | 1.37884i | ||||||||
\(969\) | 2.35804e7 | 0.806754 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.08316e6 | 0.104942 | 0.0524708 | − | 0.998622i | \(-0.483290\pi\) | ||||
0.0524708 | + | 0.998622i | \(0.483290\pi\) | |||||||
\(972\) | 4.59489e7i | 1.55994i | ||||||||
\(973\) | − 1.32529e7i | − 0.448775i | ||||||||
\(974\) | 5.20315e7 | 1.75739 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.37788e6 | −0.180712 | ||||||||
\(977\) | 3.86878e7i | 1.29669i | 0.761345 | + | 0.648347i | \(0.224539\pi\) | ||||
−0.761345 | + | 0.648347i | \(0.775461\pi\) | |||||||
\(978\) | 3.31954e7i | 1.10977i | ||||||||
\(979\) | −4.73074e7 | −1.57751 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.08944e7 | −1.02496 | ||||||||
\(982\) | − 1.09394e6i | − 0.0362006i | ||||||||
\(983\) | 4.32293e7i | 1.42690i | 0.700705 | + | 0.713451i | \(0.252869\pi\) | ||||
−0.700705 | + | 0.713451i | \(0.747131\pi\) | |||||||
\(984\) | 8.33242e6 | 0.274336 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.48677e7 | 2.78003 | ||||||||
\(987\) | − 5.45150e6i | − 0.178124i | ||||||||
\(988\) | 2.73132e7i | 0.890183i | ||||||||
\(989\) | −3.40293e6 | −0.110627 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.44224e7 | −0.466501 | −0.233251 | − | 0.972417i | \(-0.574936\pi\) | ||||
−0.233251 | + | 0.972417i | \(0.574936\pi\) | |||||||
\(992\) | 3.28768e6i | 0.106074i | ||||||||
\(993\) | − 2.03937e7i | − 0.656332i | ||||||||
\(994\) | −4.95324e7 | −1.59010 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.12311e7 | 0.358736 | ||||||||
\(997\) | − 4.29304e7i | − 1.36781i | −0.729569 | − | 0.683907i | \(-0.760279\pi\) | ||||
0.729569 | − | 0.683907i | \(-0.239721\pi\) | |||||||
\(998\) | − 2.91472e6i | − 0.0926341i | ||||||||
\(999\) | −2.56181e7 | −0.812146 |
(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 | 325.6.b.i.274.4 | 22 | ||
5.2 | odd | 4 | 325.6.a.k.1.10 | yes | 11 | ||
5.3 | odd | 4 | 325.6.a.j.1.2 | ✓ | 11 | ||
5.4 | even | 2 | inner | 325.6.b.i.274.19 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.2 | ✓ | 11 | 5.3 | odd | 4 | ||
325.6.a.k.1.10 | yes | 11 | 5.2 | odd | 4 | ||
325.6.b.i.274.4 | 22 | 1.1 | even | 1 | trivial | ||
325.6.b.i.274.19 | 22 | 5.4 | even | 2 | inner |