Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,4,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(47.2015280046\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.4.c.i.449.2 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.898979i | 0.173009i | 0.996251 | + | 0.0865043i | \(0.0275696\pi\) | ||||
−0.996251 | + | 0.0865043i | \(0.972430\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.4949i | 1.53858i | 0.638900 | + | 0.769290i | \(0.279390\pi\) | ||||
−0.638900 | + | 0.769290i | \(0.720610\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.1918 | 0.970068 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60612 | −0.0714342 | −0.0357171 | − | 0.999362i | \(-0.511372\pi\) | ||||
−0.0357171 | + | 0.999362i | \(0.511372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 33.1918i | − 0.708135i | −0.935220 | − | 0.354068i | \(-0.884798\pi\) | ||||
0.935220 | − | 0.354068i | \(-0.115202\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 119.576i | − 1.70596i | −0.521944 | − | 0.852980i | \(-0.674793\pi\) | ||||
0.521944 | − | 0.852980i | \(-0.325207\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 143.192 | 1.72897 | 0.864486 | − | 0.502657i | \(-0.167644\pi\) | ||||
0.864486 | + | 0.502657i | \(0.167644\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −25.6163 | −0.266188 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 113.889i | − 1.03250i | −0.856439 | − | 0.516249i | \(-0.827328\pi\) | ||||
0.856439 | − | 0.516249i | \(-0.172672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 47.8184i | 0.340839i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 67.6163 | 0.432967 | 0.216483 | − | 0.976286i | \(-0.430541\pi\) | ||||
0.216483 | + | 0.976286i | \(0.430541\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −117.394 | −0.680147 | −0.340074 | − | 0.940399i | \(-0.610452\pi\) | ||||
−0.340074 | + | 0.940399i | \(0.610452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.34285i | − 0.0123587i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 256.384i | 1.13917i | 0.821933 | + | 0.569584i | \(0.192896\pi\) | ||||
−0.821933 | + | 0.569584i | \(0.807104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 29.8388 | 0.122514 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 245.959 | 0.936887 | 0.468444 | − | 0.883493i | \(-0.344815\pi\) | ||||
0.468444 | + | 0.883493i | \(0.344815\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 369.262i | 1.30958i | 0.755811 | + | 0.654790i | \(0.227243\pi\) | ||||
−0.755811 | + | 0.654790i | \(0.772757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 76.3133i | − 0.236839i | −0.992964 | − | 0.118420i | \(-0.962217\pi\) | ||||
0.992964 | − | 0.118420i | \(-0.0377828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −468.959 | −1.36723 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 107.496 | 0.295146 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.4245i | 0.104769i | 0.998627 | + | 0.0523843i | \(0.0166821\pi\) | ||||
−0.998627 | + | 0.0523843i | \(0.983318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 128.727i | 0.299127i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 457.980 | 1.01057 | 0.505287 | − | 0.862951i | \(-0.331387\pi\) | ||||
0.505287 | + | 0.862951i | \(0.331387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −477.233 | −1.00169 | −0.500847 | − | 0.865536i | \(-0.666978\pi\) | ||||
−0.500847 | + | 0.865536i | \(0.666978\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 746.334i | 1.49253i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 602.252i | − 1.09816i | −0.835769 | − | 0.549081i | \(-0.814978\pi\) | ||||
0.835769 | − | 0.549081i | \(-0.185022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 102.384 | 0.178631 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1091.98 | 1.82527 | 0.912633 | − | 0.408780i | \(-0.134046\pi\) | ||||
0.912633 | + | 0.408780i | \(0.134046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 117.878i | 0.188993i | 0.995525 | + | 0.0944967i | \(0.0301242\pi\) | ||||
−0.995525 | + | 0.0944967i | \(0.969876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 74.2612i | − 0.109907i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 858.624 | 1.22282 | 0.611410 | − | 0.791314i | \(-0.290603\pi\) | ||||
0.611410 | + | 0.791314i | \(0.290603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 664.192 | 0.911100 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 565.748i | 0.748180i | 0.927392 | + | 0.374090i | \(0.122045\pi\) | ||||
−0.927392 | + | 0.374090i | \(0.877955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 60.7857i | 0.0749070i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 625.151 | 0.744560 | 0.372280 | − | 0.928120i | \(-0.378576\pi\) | ||||
0.372280 | + | 0.928120i | \(0.378576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 945.798 | 1.08952 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 105.535i | − 0.117671i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 805.959i | − 0.843637i | −0.906680 | − | 0.421818i | \(-0.861392\pi\) | ||||
0.906680 | − | 0.421818i | \(-0.138608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −68.2591 | −0.0692960 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −260.988 | −0.257121 | −0.128561 | − | 0.991702i | \(-0.541036\pi\) | ||||
−0.128561 | + | 0.991702i | \(0.541036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1640.01i | 1.56888i | 0.620203 | + | 0.784441i | \(0.287050\pi\) | ||||
−0.620203 | + | 0.784441i | \(0.712950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 679.001i | 0.613472i | 0.951795 | + | 0.306736i | \(0.0992369\pi\) | ||||
−0.951795 | + | 0.306736i | \(0.900763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 840.220 | 0.738335 | 0.369168 | − | 0.929363i | \(-0.379643\pi\) | ||||
0.369168 | + | 0.929363i | \(0.379643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −230.484 | −0.197086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1609.15i | − 1.33961i | −0.742536 | − | 0.669806i | \(-0.766377\pi\) | ||||
0.742536 | − | 0.669806i | \(-0.233623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 869.355i | − 0.686939i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3407.29 | 2.62476 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1324.21 | −0.994897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 221.112i | 0.162090i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1149.60i | − 0.803234i | −0.915808 | − | 0.401617i | \(-0.868448\pi\) | ||||
0.915808 | − | 0.401617i | \(-0.131552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −331.959 | −0.226569 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2436.99 | −1.62535 | −0.812673 | − | 0.582719i | \(-0.801989\pi\) | ||||
−0.812673 | + | 0.582719i | \(0.801989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4080.24i | 2.66016i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 764.465i | 0.476735i | 0.971175 | + | 0.238367i | \(0.0766123\pi\) | ||||
−0.971175 | + | 0.238367i | \(0.923388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2547.35 | 1.55441 | 0.777207 | − | 0.629245i | \(-0.216636\pi\) | ||||
0.777207 | + | 0.629245i | \(0.216636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 68.6041 | 0.0409752 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 86.5020i | 0.0505850i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 421.585i | − 0.236542i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2565.76 | −1.41070 | −0.705352 | − | 0.708857i | \(-0.749211\pi\) | ||||
−0.705352 | + | 0.708857i | \(0.749211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 524.949 | 0.282912 | 0.141456 | − | 0.989945i | \(-0.454822\pi\) | ||||
0.141456 | + | 0.989945i | \(0.454822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 3131.90i | − 1.65490i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3569.59i | 1.81455i | 0.420537 | + | 0.907275i | \(0.361842\pi\) | ||||
−0.420537 | + | 0.907275i | \(0.638158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −36.3408 | −0.0181259 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3245.25 | 1.58858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1450.96i | 0.697227i | 0.937267 | + | 0.348613i | \(0.113347\pi\) | ||||
−0.937267 | + | 0.348613i | \(0.886653\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3281.38i | 1.52048i | 0.649640 | + | 0.760242i | \(0.274920\pi\) | ||||
−0.649640 | + | 0.760242i | \(0.725080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1095.30 | 0.498544 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3750.46 | 1.67722 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1387.01i | 0.609553i | 0.952424 | + | 0.304776i | \(0.0985817\pi\) | ||||
−0.952424 | + | 0.304776i | \(0.901418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 411.714i | 0.174838i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3009.90 | 1.25682 | 0.628409 | − | 0.777883i | \(-0.283707\pi\) | ||||
0.628409 | + | 0.777883i | \(0.283707\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2304.14 | −0.946217 | −0.473109 | − | 0.881004i | \(-0.656868\pi\) | ||||
−0.473109 | + | 0.881004i | \(0.656868\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 429.022i | − 0.173302i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 311.628i | 0.121864i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1362.58 | −0.524408 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −166.647 | −0.0631317 | −0.0315658 | − | 0.999502i | \(-0.510049\pi\) | ||||
−0.0315658 | + | 0.999502i | \(0.510049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 484.669i | 0.180763i | 0.995907 | + | 0.0903815i | \(0.0288086\pi\) | ||||
−0.995907 | + | 0.0903815i | \(0.971191\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2088.10i | − 0.755182i | −0.925973 | − | 0.377591i | \(-0.876753\pi\) | ||||
0.925973 | − | 0.377591i | \(-0.123247\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3401.93 | −1.21184 | −0.605921 | − | 0.795524i | \(-0.707195\pi\) | ||||
−0.605921 | + | 0.795524i | \(0.707195\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 541.412 | 0.189991 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1926.72i | 0.666154i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2982.96i | − 1.00159i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −373.176 | −0.123508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2246.24 | 0.732879 | 0.366439 | − | 0.930442i | \(-0.380577\pi\) | ||||
0.366439 | + | 0.930442i | \(0.380577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 981.665i | 0.315787i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 3345.13i | − 1.04646i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −105.969 | −0.0326975 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3968.93 | −1.20805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1129.63i | 0.339217i | 0.985512 | + | 0.169608i | \(0.0542503\pi\) | ||||
−0.985512 | + | 0.169608i | \(0.945750\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1693.88i | − 0.495273i | −0.968853 | − | 0.247637i | \(-0.920346\pi\) | ||||
0.968853 | − | 0.247637i | \(-0.0796539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5250.72 | 1.51518 | 0.757592 | − | 0.652728i | \(-0.226376\pi\) | ||||
0.757592 | + | 0.652728i | \(0.226376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 66.7593 | 0.0190149 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 6042.60i | − 1.69899i | −0.527600 | − | 0.849493i | \(-0.676908\pi\) | ||||
0.527600 | − | 0.849493i | \(-0.323092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 771.886i | 0.211559i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −385.416 | −0.104312 | −0.0521559 | − | 0.998639i | \(-0.516609\pi\) | ||||
−0.0521559 | + | 0.998639i | \(0.516609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4858.73 | 1.29866 | 0.649332 | − | 0.760505i | \(-0.275049\pi\) | ||||
0.649332 | + | 0.760505i | \(0.275049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1888.19i | 0.498467i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4752.80i | − 1.22435i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −508.596 | −0.129442 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3784.74 | −0.951757 | −0.475878 | − | 0.879511i | \(-0.657870\pi\) | ||||
−0.475878 | + | 0.879511i | \(0.657870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 296.808i | 0.0737556i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3702.36i | − 0.898626i | −0.893374 | − | 0.449313i | \(-0.851669\pi\) | ||||
0.893374 | − | 0.449313i | \(-0.148331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7305.63 | −1.75270 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1771.00 | 0.420007 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 3517.77i | − 0.824771i | −0.911009 | − | 0.412385i | \(-0.864696\pi\) | ||||
0.911009 | − | 0.412385i | \(-0.135304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 561.998i | 0.128815i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5564.09 | 1.26115 | 0.630573 | − | 0.776130i | \(-0.282820\pi\) | ||||
0.630573 | + | 0.776130i | \(0.282820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2585.39 | −0.579525 | −0.289762 | − | 0.957099i | \(-0.593576\pi\) | ||||
−0.289762 | + | 0.957099i | \(0.593576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 850.253i | 0.188497i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 884.433i | 0.191843i | 0.995389 | + | 0.0959213i | \(0.0305797\pi\) | ||||
−0.995389 | + | 0.0959213i | \(0.969420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3074.76 | −0.659789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3165.55 | 0.672032 | 0.336016 | − | 0.941856i | \(-0.390920\pi\) | ||||
0.336016 | + | 0.941856i | \(0.390920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4425.40i | − 0.929550i | −0.885429 | − | 0.464775i | \(-0.846135\pi\) | ||||
0.885429 | − | 0.464775i | \(-0.153865\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7008.58i | 1.44148i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9385.30 | −1.91030 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 724.541 | 0.145956 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2871.70i | 0.572582i | 0.958143 | + | 0.286291i | \(0.0924223\pi\) | ||||
−0.958143 | + | 0.286291i | \(0.907578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 124.621i | − 0.0243475i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3780.18 | −0.731148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10522.1 | −2.01489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 234.623i | − 0.0444842i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3145.45i | 0.584757i | 0.956303 | + | 0.292379i | \(0.0944468\pi\) | ||||
−0.956303 | + | 0.292379i | \(0.905553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1474.33 | −0.271430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −306.614 | −0.0559052 | −0.0279526 | − | 0.999609i | \(-0.508899\pi\) | ||||
−0.0279526 | + | 0.999609i | \(0.508899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3120.66i | − 0.563547i | −0.959481 | − | 0.281773i | \(-0.909077\pi\) | ||||
0.959481 | − | 0.281773i | \(-0.0909227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8131.12i | 1.44066i | 0.693632 | + | 0.720330i | \(0.256010\pi\) | ||||
−0.693632 | + | 0.720330i | \(0.743990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −176.216 | −0.0309286 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −610.408 | −0.106136 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 17122.2i | − 2.94956i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 755.341i | 0.127738i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2174.54 | 0.364396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7877.80 | −1.30817 | −0.654083 | − | 0.756423i | \(-0.726945\pi\) | ||||
−0.654083 | + | 0.756423i | \(0.726945\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6715.16i | 1.10507i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2169.15i | 0.350627i | 0.984513 | + | 0.175313i | \(0.0560938\pi\) | ||||
−0.984513 | + | 0.175313i | \(0.943906\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1446.59 | 0.231765 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 305.943 | 0.0485857 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3589.19i | − 0.565009i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 325.475i | 0.0503527i | 0.999683 | + | 0.0251764i | \(0.00801473\pi\) | ||||
−0.999683 | + | 0.0251764i | \(0.991985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9311.11 | −1.42812 | −0.714058 | − | 0.700087i | \(-0.753145\pi\) | ||||
−0.714058 | + | 0.700087i | \(0.753145\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1587.18 | 0.241360 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3144.94i | 0.474188i | 0.971487 | + | 0.237094i | \(0.0761949\pi\) | ||||
−0.971487 | + | 0.237094i | \(0.923805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3063.09i | 0.454106i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 570.424 | 0.0838603 | 0.0419302 | − | 0.999121i | \(-0.486649\pi\) | ||||
0.0419302 | + | 0.999121i | \(0.486649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13644.9 | 1.98934 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1190.44i | − 0.172126i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1629.17i | 0.231722i | 0.993265 | + | 0.115861i | \(0.0369627\pi\) | ||||
−0.993265 | + | 0.115861i | \(0.963037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6442.12 | 0.908844 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1151.89 | −0.161195 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6985.76i | − 0.969728i | −0.874589 | − | 0.484864i | \(-0.838869\pi\) | ||||
0.874589 | − | 0.484864i | \(-0.161131\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2244.31i | − 0.306599i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11101.3 | −1.50458 | −0.752291 | − | 0.658831i | \(-0.771051\pi\) | ||||
−0.752291 | + | 0.658831i | \(0.771051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1033.47 | 0.138967 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 6608.71i | − 0.881695i | −0.897582 | − | 0.440848i | \(-0.854678\pi\) | ||||
0.897582 | − | 0.440848i | \(-0.145322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9671.66i | 1.27038i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −503.208 | −0.0655878 | −0.0327939 | − | 0.999462i | \(-0.510440\pi\) | ||||
−0.0327939 | + | 0.999462i | \(0.510440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13618.3 | −1.76140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 2190.80i | − 0.281199i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1885.18i | − 0.238323i | −0.992875 | − | 0.119162i | \(-0.961979\pi\) | ||||
0.992875 | − | 0.119162i | \(-0.0380206\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3668.05 | −0.460231 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13212.7 | −1.64541 | −0.822706 | − | 0.568467i | \(-0.807537\pi\) | ||||
−0.822706 | + | 0.568467i | \(0.807537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3896.52i | 0.481636i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 668.167i | − 0.0813755i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8441.37 | 1.02054 | 0.510268 | − | 0.860016i | \(-0.329546\pi\) | ||||
0.510268 | + | 0.860016i | \(0.329546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −687.239 | −0.0824793 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13050.1i | 1.55485i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2290.02i | 0.268927i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12823.2 | −1.49512 | −0.747559 | − | 0.664195i | \(-0.768774\pi\) | ||||
−0.747559 | + | 0.664195i | \(0.768774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2474.24 | −0.286431 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1998.78i | − 0.229750i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 13598.7i | − 1.54119i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −77.7635 | −0.00875165 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12461.3 | 1.39267 | 0.696334 | − | 0.717718i | \(-0.254813\pi\) | ||||
0.696334 | + | 0.717718i | \(0.254813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 12063.0i | − 1.33883i | −0.742890 | − | 0.669414i | \(-0.766545\pi\) | ||||
0.742890 | − | 0.669414i | \(-0.233455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 16307.9i | − 1.78516i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16480.7 | −1.79176 | −0.895879 | − | 0.444299i | \(-0.853453\pi\) | ||||
−0.895879 | + | 0.444299i | \(0.853453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12282.9 | −1.32630 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2159.19i | 0.231572i | 0.993274 | + | 0.115786i | \(0.0369387\pi\) | ||||
−0.993274 | + | 0.115786i | \(0.963061\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2306.56i | − 0.244064i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5552.38 | −0.583592 | −0.291796 | − | 0.956481i | \(-0.594253\pi\) | ||||
−0.291796 | + | 0.956481i | \(0.594253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −641.000 | −0.0669257 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 471.918i | 0.0489463i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 16667.9i | − 1.70611i | −0.521820 | − | 0.853055i | \(-0.674747\pi\) | ||||
0.521820 | − | 0.853055i | \(-0.325253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5717.91 | 0.581457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15255.5 | 1.54126 | 0.770629 | − | 0.637284i | \(-0.219942\pi\) | ||||
0.770629 | + | 0.637284i | \(0.219942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6806.85i | − 0.683242i | −0.939838 | − | 0.341621i | \(-0.889024\pi\) | ||||
0.939838 | − | 0.341621i | \(-0.110976\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6455.78i | − 0.639696i | −0.947469 | − | 0.319848i | \(-0.896368\pi\) | ||||
0.947469 | − | 0.319848i | \(-0.103632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17161.1 | 1.68961 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3208.99 | −0.313933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 962.343i | − 0.0935488i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1058.79i | 0.101633i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8481.34 | −0.809024 | −0.404512 | − | 0.914533i | \(-0.632559\pi\) | ||||
−0.404512 | + | 0.914533i | \(0.632559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8509.84 | 0.806685 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2917.41i | 0.274838i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 10966.2i | − 1.02038i | −0.860061 | − | 0.510191i | \(-0.829575\pi\) | ||||
0.860061 | − | 0.510191i | \(-0.170425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1304.38 | −0.120626 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6784.15 | 0.623553 | 0.311777 | − | 0.950155i | \(-0.399076\pi\) | ||||
0.311777 | + | 0.950155i | \(0.399076\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8085.26i | − 0.738624i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31115.8i | 2.80832i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17785.8 | 1.59560 | 0.797799 | − | 0.602924i | \(-0.205998\pi\) | ||||
0.797799 | + | 0.602924i | \(0.205998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2949.89 | −0.263057 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8440.25i | 0.748175i | 0.927393 | + | 0.374087i | \(0.122044\pi\) | ||||
−0.927393 | + | 0.374087i | \(0.877956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 984.654i | 0.0862525i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10923.4 | −0.951222 | −0.475611 | − | 0.879656i | \(-0.657773\pi\) | ||||
−0.475611 | + | 0.879656i | \(0.657773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3358.91 | −0.290782 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6847.20i | 0.589301i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 198.882i | 0.0169184i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1246.90 | −0.105458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9879.76 | −0.830787 | −0.415394 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415394 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 105.197i | 0.00879531i | 0.999990 | + | 0.00439766i | \(0.00139982\pi\) | ||||
−0.999990 | + | 0.00439766i | \(0.998600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14037.4i | 1.16030i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −803.653 | −0.0660519 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11995.3 | 0.980325 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8163.84i | − 0.663443i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2705.84i | 0.217440i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1222.17 | 0.0976668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19055.6 | 1.51435 | 0.757175 | − | 0.653212i | \(-0.226579\pi\) | ||||
0.757175 | + | 0.653212i | \(0.226579\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 2071.37i | − 0.163704i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3910.22i | 0.305647i | 0.988253 | + | 0.152824i | \(0.0488366\pi\) | ||||
−0.988253 | + | 0.152824i | \(0.951163\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12499.6 | −0.971712 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9682.11 | 0.748587 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24466.4i | 1.88141i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1727.52i | − 0.131413i | −0.997839 | − | 0.0657067i | \(-0.979070\pi\) | ||||
0.997839 | − | 0.0657067i | \(-0.0209302\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12256.5 | 0.927360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −280.148 | −0.0210835 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20905.0i | 1.56491i | 0.622709 | + | 0.782453i | \(0.286032\pi\) | ||||
−0.622709 | + | 0.782453i | \(0.713968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18926.1i | 1.40180i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 256.523 | 0.0188998 | 0.00944990 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00944990 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15793.4 | −1.15750 | −0.578749 | − | 0.815506i | \(-0.696459\pi\) | ||||
−0.578749 | + | 0.815506i | \(0.696459\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 149.812i | − 0.0109223i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5923.65i | 0.427391i | 0.976900 | + | 0.213696i | \(0.0685501\pi\) | ||||
−0.976900 | + | 0.213696i | \(0.931450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −435.708 | −0.0312736 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16120.9 | −1.15113 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 105.351i | − 0.00748405i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11730.7i | 0.824832i | 0.910996 | + | 0.412416i | \(0.135315\pi\) | ||||
−0.910996 | + | 0.412416i | \(0.864685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16809.8 | −1.17596 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1877.16 | 0.130653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2781.00i | 0.192584i | 0.995353 | + | 0.0962919i | \(0.0306982\pi\) | ||||
−0.995353 | + | 0.0962919i | \(0.969302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3058.27i | − 0.209659i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22999.7 | 1.56885 | 0.784425 | − | 0.620224i | \(-0.212958\pi\) | ||||
0.784425 | + | 0.620224i | \(0.212958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2680.42 | −0.181925 | −0.0909624 | − | 0.995854i | \(-0.528994\pi\) | ||||
−0.0909624 | + | 0.995854i | \(0.528994\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 15774.1i | − 1.06529i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16977.3i | − 1.13523i | −0.823293 | − | 0.567617i | \(-0.807865\pi\) | ||||
0.823293 | − | 0.567617i | \(-0.192135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1732.08 | −0.115250 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2532.98 | −0.167714 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 24124.3i | − 1.58951i | −0.606930 | − | 0.794755i | \(-0.707599\pi\) | ||||
0.606930 | − | 0.794755i | \(-0.292401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12286.0i | − 0.801644i | −0.916156 | − | 0.400822i | \(-0.868725\pi\) | ||||
0.916156 | − | 0.400822i | \(-0.131275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6240.17 | 0.405192 | 0.202596 | − | 0.979262i | \(-0.435062\pi\) | ||||
0.202596 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5445.98 | 0.351915 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17813.6i | 1.14557i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 335.477i | − 0.0213679i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30657.2 | 1.94338 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8142.22 | −0.513687 | −0.256844 | − | 0.966453i | \(-0.582683\pi\) | ||||
−0.256844 | + | 0.966453i | \(0.582683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2019.32i | 0.126794i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15565.6i | 0.968182i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28600.9 | 1.77063 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6380.36 | 0.393150 | 0.196575 | − | 0.980489i | \(-0.437018\pi\) | ||||
0.196575 | + | 0.980489i | \(0.437018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 18308.0i | − 1.12286i | −0.827524 | − | 0.561430i | \(-0.810251\pi\) | ||||
0.827524 | − | 0.561430i | \(-0.189749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 21497.9i | − 1.30629i | −0.757233 | − | 0.653145i | \(-0.773449\pi\) | ||||
0.757233 | − | 0.653145i | \(-0.226551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1193.55 | −0.0721895 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3007.20 | 0.181047 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 16035.4i | − 0.960972i | −0.877002 | − | 0.480486i | \(-0.840460\pi\) | ||||
0.877002 | − | 0.480486i | \(-0.159540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3087.43i | 0.183337i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12259.7 | 0.724688 | 0.362344 | − | 0.932044i | \(-0.381977\pi\) | ||||
0.362344 | + | 0.932044i | \(0.381977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7515.22 | 0.442221 | 0.221111 | − | 0.975249i | \(-0.429032\pi\) | ||||
0.221111 | + | 0.975249i | \(0.429032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3567.99i | − 0.209003i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7700.74i | − 0.447037i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1015.51 | −0.0586874 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1243.73 | 0.0715552 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17438.7i | 0.998829i | 0.866363 | + | 0.499415i | \(0.166452\pi\) | ||||
−0.866363 | + | 0.499415i | \(0.833548\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 14679.1i | − 0.833331i | −0.909060 | − | 0.416665i | \(-0.863199\pi\) | ||||
0.909060 | − | 0.416665i | \(-0.136801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22965.7 | 1.29800 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1522.77 | 0.0856866 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30494.6i | 1.70841i | 0.519937 | + | 0.854204i | \(0.325955\pi\) | ||||
−0.519937 | + | 0.854204i | \(0.674045\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4720.29i | 0.262140i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1341.76 | 0.0741903 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13887.9 | −0.764576 | −0.382288 | − | 0.924043i | \(-0.624864\pi\) | ||||
−0.382288 | + | 0.924043i | \(0.624864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1945.04i | − 0.106617i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 29410.7i | − 1.59829i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5432.17 | 0.293939 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11296.0 | 0.608622 | 0.304311 | − | 0.952573i | \(-0.401574\pi\) | ||||
0.304311 | + | 0.952573i | \(0.401574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36712.0i | 1.96959i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7436.82i | − 0.395602i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24405.6 | 1.29277 | 0.646384 | − | 0.763013i | \(-0.276281\pi\) | ||||
0.646384 | + | 0.763013i | \(0.276281\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22489.0 | 1.18622 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13369.8i | 0.702251i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 346.481i | − 0.0180468i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11883.4 | −0.616379 | −0.308189 | − | 0.951325i | \(-0.599723\pi\) | ||||
−0.308189 | + | 0.951325i | \(0.599723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46731.9 | −2.41385 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4367.90i | 0.224680i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21154.5i | 1.07920i | 0.841922 | + | 0.539599i | \(0.181424\pi\) | ||||
−0.841922 | + | 0.539599i | \(0.818576\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16235.7 | 0.824861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44154.7 | 2.23409 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5806.54i | − 0.292591i | −0.989241 | − | 0.146296i | \(-0.953265\pi\) | ||||
0.989241 | − | 0.146296i | \(-0.0467351\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1569.54i | 0.0784462i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14389.0 | −0.716248 | −0.358124 | − | 0.933674i | \(-0.616584\pi\) | ||||
−0.358124 | + | 0.933674i | \(0.616584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4272.67 | 0.211822 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18366.0i | 0.906839i | 0.891297 | + | 0.453420i | \(0.149796\pi\) | ||||
−0.891297 | + | 0.453420i | \(0.850204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14818.0i | 0.725785i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19348.1 | −0.943876 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19355.0 | −0.940444 | −0.470222 | − | 0.882548i | \(-0.655826\pi\) | ||||
−0.470222 | + | 0.882548i | \(0.655826\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 3402.41i | − 0.164662i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 494.408i | 0.0237379i | 0.999930 | + | 0.0118689i | \(0.00377809\pi\) | ||||
−0.999930 | + | 0.0118689i | \(0.996222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −266.824 | −0.0127604 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2310.20 | −0.110045 | −0.0550227 | − | 0.998485i | \(-0.517523\pi\) | ||||
−0.0550227 | + | 0.998485i | \(0.517523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23942.0i | 1.13599i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 15201.2i | − 0.715623i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24590.9 | −1.15315 | −0.576573 | − | 0.817045i | \(-0.695611\pi\) | ||||
−0.576573 | + | 0.817045i | \(0.695611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3328.34 | 0.155470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 22102.6i | − 1.02843i | −0.857662 | − | 0.514214i | \(-0.828084\pi\) | ||||
0.857662 | − | 0.514214i | \(-0.171916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 6567.61i | − 0.303232i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35219.3 | 1.61985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2845.83 | −0.130386 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3233.30i | 0.147572i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 29715.0i | − 1.34590i | −0.739686 | − | 0.672952i | \(-0.765026\pi\) | ||||
0.739686 | − | 0.672952i | \(-0.234974\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3162.40 | 0.142693 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45852.6 | 2.06110 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15840.2i | 0.709335i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1237.06i | 0.0549799i | 0.999622 | + | 0.0274899i | \(0.00875142\pi\) | ||||
−0.999622 | + | 0.0274899i | \(0.991249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9125.20 | −0.404038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16373.9 | 0.722274 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 307.203i | − 0.0135006i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5002.00i | 0.218189i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4675.39 | 0.203186 | 0.101593 | − | 0.994826i | \(-0.467606\pi\) | ||||
0.101593 | + | 0.994826i | \(0.467606\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3243.36 | −0.140431 | −0.0702156 | − | 0.997532i | \(-0.522369\pi\) | ||||
−0.0702156 | + | 0.997532i | \(0.522369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2324.21i | − 0.100263i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 52875.3i | 2.26423i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24772.2 | 1.05691 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33551.4 | 1.42625 | 0.713126 | − | 0.701036i | \(-0.247279\pi\) | ||||
0.713126 | + | 0.701036i | \(0.247279\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6365.66i | 0.269615i | 0.990872 | + | 0.134807i | \(0.0430416\pi\) | ||||
−0.990872 | + | 0.134807i | \(0.956958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18980.7i | 0.798094i | 0.916930 | + | 0.399047i | \(0.130659\pi\) | ||||
−0.916930 | + | 0.399047i | \(0.869341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33674.2 | −1.41080 | −0.705400 | − | 0.708809i | \(-0.749233\pi\) | ||||
−0.705400 | + | 0.708809i | \(0.749233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −795.087 | −0.0331904 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 56076.0i | 2.33244i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 5613.58i | − 0.231821i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4639.47 | 0.190909 | 0.0954544 | − | 0.995434i | \(-0.469570\pi\) | ||||
0.0954544 | + | 0.995434i | \(0.469570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19817.0 | −0.812540 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2845.77i | 0.116267i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 37733.2i | − 1.53073i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3978.34 | 0.160820 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29199.2 | 1.17619 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1646.37i | − 0.0660850i | −0.999454 | − | 0.0330425i | \(-0.989480\pi\) | ||||
0.999454 | − | 0.0330425i | \(-0.0105197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46767.8i | 1.86413i | 0.362295 | + | 0.932064i | \(0.381993\pi\) | ||||
−0.362295 | + | 0.932064i | \(0.618007\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11466.7 | −0.455460 | −0.227730 | − | 0.973724i | \(-0.573130\pi\) | ||||
−0.227730 | + | 0.973724i | \(0.573130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6300.57 | −0.249388 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 42704.1i | − 1.68443i | −0.539140 | − | 0.842216i | \(-0.681250\pi\) | ||||
0.539140 | − | 0.842216i | \(-0.318750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 8437.19i | − 0.330498i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2237.68 | −0.0873511 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19989.9 | −0.777647 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 21109.6i | − 0.818385i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18376.9i | 0.707574i | 0.935326 | + | 0.353787i | \(0.115106\pi\) | ||||
−0.935326 | + | 0.353787i | \(0.884894\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2581.60 | −0.0990616 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7024.26 | −0.268619 | −0.134310 | − | 0.990939i | \(-0.542882\pi\) | ||||
−0.134310 | + | 0.990939i | \(0.542882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41747.1i | 1.59106i | 0.605917 | + | 0.795528i | \(0.292806\pi\) | ||||
−0.605917 | + | 0.795528i | \(0.707194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 5863.18i | − 0.221946i | −0.993823 | − | 0.110973i | \(-0.964603\pi\) | ||||
0.993823 | − | 0.110973i | \(-0.0353967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32757.8 | 1.23584 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1730.97 | −0.0650836 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 10927.4i | − 0.409488i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3398.30i | − 0.126495i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7937.74 | −0.294481 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4833.78 | 0.178731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 9459.14i | − 0.348594i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 13945.6i | − 0.510536i | −0.966870 | − | 0.255268i | \(-0.917836\pi\) | ||||
0.966870 | − | 0.255268i | \(-0.0821638\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6835.75 | −0.249425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38202.8 | −1.38937 | −0.694685 | − | 0.719314i | \(-0.744456\pi\) | ||||
−0.694685 | + | 0.719314i | \(0.744456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1474.41i | − 0.0534456i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 69441.7i | − 2.50073i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8586.98 | −0.308225 | −0.154112 | − | 0.988053i | \(-0.549252\pi\) | ||||
−0.154112 | + | 0.988053i | \(0.549252\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2827.70 | −0.101168 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 36244.7i | − 1.29254i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42954.9i | 1.52192i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50645.2 | −1.78861 | −0.894303 | − | 0.447461i | \(-0.852328\pi\) | ||||
−0.894303 | + | 0.447461i | \(0.852328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −67151.1 | −2.36390 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 275.640i | − 0.00967208i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 26068.7i | − 0.908887i | −0.890775 | − | 0.454444i | \(-0.849838\pi\) | ||||
0.890775 | − | 0.454444i | \(-0.150162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2805.41 | 0.0974985 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4036.78 | −0.139846 | −0.0699230 | − | 0.997552i | \(-0.522275\pi\) | ||||
−0.0699230 | + | 0.997552i | \(0.522275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 28012.0i | − 0.967334i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47790.1i | 1.63988i | 0.572446 | + | 0.819942i | \(0.305995\pi\) | ||||
−0.572446 | + | 0.819942i | \(0.694005\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3912.57 | 0.133833 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7309.71 | −0.249247 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 49284.8i | − 1.67523i | −0.546264 | − | 0.837613i | \(-0.683950\pi\) | ||||
0.546264 | − | 0.837613i | \(-0.316050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 158.415i | − 0.00535092i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21783.4 | −0.733495 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16009.7 | −0.537400 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17784.3i | 0.595110i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19830.2i | 0.659459i | 0.944076 | + | 0.329729i | \(0.106957\pi\) | ||||
−0.944076 | + | 0.329729i | \(0.893043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15392.5 | 0.510299 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24538.6 | 0.811000 | 0.405500 | − | 0.914095i | \(-0.367097\pi\) | ||||
0.405500 | + | 0.914095i | \(0.367097\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 72586.5i | 2.39159i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15113.6i | 0.494909i | 0.968900 | + | 0.247454i | \(0.0795940\pi\) | ||||
−0.968900 | + | 0.247454i | \(0.920406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1629.22 | −0.0531870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22006.9 | 0.716235 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13262.7i | 0.430330i | 0.976578 | + | 0.215165i | \(0.0690289\pi\) | ||||
−0.976578 | + | 0.215165i | \(0.930971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1954.87i | 0.0630436i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42054.8 | 1.35214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7053.73 | −0.226104 | −0.113052 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113052 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 7081.98i | − 0.226324i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38686.1i | − 1.22889i | −0.788961 | − | 0.614443i | \(-0.789381\pi\) | ||||
0.788961 | − | 0.614443i | \(-0.210619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12259.8 | −0.388273 |
(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 | 800.4.c.i.449.3 | 4 | ||
4.3 | odd | 2 | 800.4.c.k.449.2 | 4 | |||
5.2 | odd | 4 | 160.4.a.c.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 800.4.a.s.1.1 | 2 | |||
5.4 | even | 2 | inner | 800.4.c.i.449.2 | 4 | ||
15.2 | even | 4 | 1440.4.a.t.1.1 | 2 | |||
20.3 | even | 4 | 800.4.a.m.1.2 | 2 | |||
20.7 | even | 4 | 160.4.a.g.1.1 | yes | 2 | ||
20.19 | odd | 2 | 800.4.c.k.449.3 | 4 | |||
40.3 | even | 4 | 1600.4.a.cn.1.1 | 2 | |||
40.13 | odd | 4 | 1600.4.a.cd.1.2 | 2 | |||
40.27 | even | 4 | 320.4.a.o.1.2 | 2 | |||
40.37 | odd | 4 | 320.4.a.s.1.1 | 2 | |||
60.47 | odd | 4 | 1440.4.a.x.1.2 | 2 | |||
80.27 | even | 4 | 1280.4.d.q.641.3 | 4 | |||
80.37 | odd | 4 | 1280.4.d.x.641.2 | 4 | |||
80.67 | even | 4 | 1280.4.d.q.641.2 | 4 | |||
80.77 | odd | 4 | 1280.4.d.x.641.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.c.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
160.4.a.g.1.1 | yes | 2 | 20.7 | even | 4 | ||
320.4.a.o.1.2 | 2 | 40.27 | even | 4 | |||
320.4.a.s.1.1 | 2 | 40.37 | odd | 4 | |||
800.4.a.m.1.2 | 2 | 20.3 | even | 4 | |||
800.4.a.s.1.1 | 2 | 5.3 | odd | 4 | |||
800.4.c.i.449.2 | 4 | 5.4 | even | 2 | inner | ||
800.4.c.i.449.3 | 4 | 1.1 | even | 1 | trivial | ||
800.4.c.k.449.2 | 4 | 4.3 | odd | 2 | |||
800.4.c.k.449.3 | 4 | 20.19 | odd | 2 | |||
1280.4.d.q.641.2 | 4 | 80.67 | even | 4 | |||
1280.4.d.q.641.3 | 4 | 80.27 | even | 4 | |||
1280.4.d.x.641.2 | 4 | 80.37 | odd | 4 | |||
1280.4.d.x.641.3 | 4 | 80.77 | odd | 4 | |||
1440.4.a.t.1.1 | 2 | 15.2 | even | 4 | |||
1440.4.a.x.1.2 | 2 | 60.47 | odd | 4 | |||
1600.4.a.cd.1.2 | 2 | 40.13 | odd | 4 | |||
1600.4.a.cn.1.1 | 2 | 40.3 | even | 4 |