Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (of order \(2\), degree \(1\), 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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.5 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.80 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.63886i | − 1.81943i | −0.415233 | − | 0.909715i | \(-0.636300\pi\) | ||||
0.415233 | − | 0.909715i | \(-0.363700\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.24130 | −2.31033 | ||||||||
\(5\) | − 3.49336i | − 0.698671i | −0.936998 | − | 0.349336i | \(-0.886407\pi\) | ||||
0.936998 | − | 0.349336i | \(-0.113593\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.62828 | −1.37547 | −0.687734 | − | 0.725962i | \(-0.741395\pi\) | ||||
−0.687734 | + | 0.725962i | \(0.741395\pi\) | |||||||
\(8\) | 19.0724i | 2.38405i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −12.7118 | −1.27118 | ||||||||
\(11\) | 19.0515i | 1.73196i | 0.500083 | + | 0.865978i | \(0.333303\pi\) | ||||
−0.500083 | + | 0.865978i | \(0.666697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.1962 | 1.55355 | 0.776776 | − | 0.629777i | \(-0.216854\pi\) | ||||
0.776776 | + | 0.629777i | \(0.216854\pi\) | |||||||
\(14\) | 35.0360i | 2.50257i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 32.4365 | 2.02728 | ||||||||
\(17\) | − 0.819801i | − 0.0482236i | −0.999709 | − | 0.0241118i | \(-0.992324\pi\) | ||||
0.999709 | − | 0.0241118i | \(-0.00767577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.28753 | 0.383554 | 0.191777 | − | 0.981438i | \(-0.438575\pi\) | ||||
0.191777 | + | 0.981438i | \(0.438575\pi\) | |||||||
\(20\) | 32.2832i | 1.61416i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 69.3258 | 3.15117 | ||||||||
\(23\) | 0.446991i | 0.0194344i | 0.999953 | + | 0.00971719i | \(0.00309313\pi\) | ||||
−0.999953 | + | 0.00971719i | \(0.996907\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.7965 | 0.511858 | ||||||||
\(26\) | − 73.4911i | − 2.82658i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 88.9779 | 3.17778 | ||||||||
\(29\) | − 43.3692i | − 1.49549i | −0.663986 | − | 0.747745i | \(-0.731137\pi\) | ||||
0.663986 | − | 0.747745i | \(-0.268863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.5475 | −0.404757 | −0.202379 | − | 0.979307i | \(-0.564867\pi\) | ||||
−0.202379 | + | 0.979307i | \(0.564867\pi\) | |||||||
\(32\) | − 41.7423i | − 1.30445i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.98314 | −0.0877395 | ||||||||
\(35\) | 33.6350i | 0.961001i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −31.1753 | −0.842576 | −0.421288 | − | 0.906927i | \(-0.638422\pi\) | ||||
−0.421288 | + | 0.906927i | \(0.638422\pi\) | |||||||
\(38\) | − 26.5183i | − 0.697850i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 66.6266 | 1.66566 | ||||||||
\(41\) | − 17.5224i | − 0.427375i | −0.976902 | − | 0.213688i | \(-0.931453\pi\) | ||||
0.976902 | − | 0.213688i | \(-0.0685474\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21.4646 | 0.499177 | 0.249588 | − | 0.968352i | \(-0.419705\pi\) | ||||
0.249588 | + | 0.968352i | \(0.419705\pi\) | |||||||
\(44\) | − 176.061i | − 4.00138i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.62654 | 0.0353595 | ||||||||
\(47\) | 61.7080i | 1.31294i | 0.754354 | + | 0.656468i | \(0.227950\pi\) | ||||
−0.754354 | + | 0.656468i | \(0.772050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 43.7038 | 0.891915 | ||||||||
\(50\) | − 46.5645i | − 0.931290i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −186.639 | −3.58921 | ||||||||
\(53\) | 65.6615i | 1.23890i | 0.785038 | + | 0.619448i | \(0.212644\pi\) | ||||
−0.785038 | + | 0.619448i | \(0.787356\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 66.5537 | 1.21007 | ||||||||
\(56\) | − 183.634i | − 3.27918i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −157.814 | −2.72094 | ||||||||
\(59\) | 15.3487i | 0.260147i | 0.991504 | + | 0.130073i | \(0.0415213\pi\) | ||||
−0.991504 | + | 0.130073i | \(0.958479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 59.7978 | 0.980292 | 0.490146 | − | 0.871640i | \(-0.336943\pi\) | ||||
0.490146 | + | 0.871640i | \(0.336943\pi\) | |||||||
\(62\) | 45.6585i | 0.736427i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −22.1485 | −0.346070 | ||||||||
\(65\) | − 70.5525i | − 1.08542i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −51.8217 | −0.773458 | −0.386729 | − | 0.922193i | \(-0.626395\pi\) | ||||
−0.386729 | + | 0.922193i | \(0.626395\pi\) | |||||||
\(68\) | 7.57603i | 0.111412i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 122.393 | 1.74847 | ||||||||
\(71\) | 11.6672i | 0.164327i | 0.996619 | + | 0.0821635i | \(0.0261830\pi\) | ||||
−0.996619 | + | 0.0821635i | \(0.973817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 123.785 | 1.69568 | 0.847842 | − | 0.530248i | \(-0.177901\pi\) | ||||
0.847842 | + | 0.530248i | \(0.177901\pi\) | |||||||
\(74\) | 113.443i | 1.53301i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −67.3463 | −0.886136 | ||||||||
\(77\) | − 183.433i | − 2.38225i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.3561 | 0.662736 | 0.331368 | − | 0.943502i | \(-0.392490\pi\) | ||||
0.331368 | + | 0.943502i | \(0.392490\pi\) | |||||||
\(80\) | − 113.312i | − 1.41640i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −63.7615 | −0.777579 | ||||||||
\(83\) | − 92.4955i | − 1.11440i | −0.830377 | − | 0.557202i | \(-0.811875\pi\) | ||||
0.830377 | − | 0.557202i | \(-0.188125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.86386 | −0.0336925 | ||||||||
\(86\) | − 78.1067i | − 0.908217i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −363.357 | −4.12906 | ||||||||
\(89\) | 1.56409i | 0.0175740i | 0.999961 | + | 0.00878700i | \(0.00279703\pi\) | ||||
−0.999961 | + | 0.00878700i | \(0.997203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −194.455 | −2.13686 | ||||||||
\(92\) | − 4.13078i | − 0.0448998i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 224.547 | 2.38880 | ||||||||
\(95\) | − 25.4580i | − 0.267978i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −40.8492 | −0.421125 | −0.210563 | − | 0.977580i | \(-0.567530\pi\) | ||||
−0.210563 | + | 0.977580i | \(0.567530\pi\) | |||||||
\(98\) | − 159.032i | − 1.62278i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −118.256 | −1.18256 | ||||||||
\(101\) | 95.6674i | 0.947202i | 0.880739 | + | 0.473601i | \(0.157046\pi\) | ||||
−0.880739 | + | 0.473601i | \(0.842954\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.6832 | −0.200808 | −0.100404 | − | 0.994947i | \(-0.532013\pi\) | ||||
−0.100404 | + | 0.994947i | \(0.532013\pi\) | |||||||
\(104\) | 385.189i | 3.70374i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 238.933 | 2.25409 | ||||||||
\(107\) | 102.522i | 0.958152i | 0.877773 | + | 0.479076i | \(0.159028\pi\) | ||||
−0.877773 | + | 0.479076i | \(0.840972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.438 | 0.921450 | 0.460725 | − | 0.887543i | \(-0.347589\pi\) | ||||
0.460725 | + | 0.887543i | \(0.347589\pi\) | |||||||
\(110\) | − 242.180i | − 2.20163i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −312.307 | −2.78846 | ||||||||
\(113\) | − 117.964i | − 1.04393i | −0.852967 | − | 0.521964i | \(-0.825199\pi\) | ||||
0.852967 | − | 0.521964i | \(-0.174801\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.56150 | 0.0135782 | ||||||||
\(116\) | 400.788i | 3.45507i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 55.8517 | 0.473319 | ||||||||
\(119\) | 7.89328i | 0.0663301i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −241.960 | −1.99967 | ||||||||
\(122\) | − 217.596i | − 1.78357i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 115.955 | 0.935121 | ||||||||
\(125\) | − 132.037i | − 1.05629i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2694 | −0.0887357 | ||||||||
\(128\) | − 86.3740i | − 0.674797i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −256.731 | −1.97485 | ||||||||
\(131\) | − 180.115i | − 1.37493i | −0.726219 | − | 0.687463i | \(-0.758724\pi\) | ||||
0.726219 | − | 0.687463i | \(-0.241276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −70.1664 | −0.527567 | ||||||||
\(134\) | 188.572i | 1.40725i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.6355 | 0.114967 | ||||||||
\(137\) | − 179.632i | − 1.31118i | −0.755116 | − | 0.655591i | \(-0.772419\pi\) | ||||
0.755116 | − | 0.655591i | \(-0.227581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 238.348 | 1.71474 | 0.857369 | − | 0.514703i | \(-0.172098\pi\) | ||||
0.857369 | + | 0.514703i | \(0.172098\pi\) | |||||||
\(140\) | − 310.831i | − 2.22022i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 42.4554 | 0.298981 | ||||||||
\(143\) | 384.768i | 2.69068i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −151.504 | −1.04486 | ||||||||
\(146\) | − 450.436i | − 3.08518i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 288.100 | 1.94662 | ||||||||
\(149\) | − 152.663i | − 1.02458i | −0.858812 | − | 0.512292i | \(-0.828797\pi\) | ||||
0.858812 | − | 0.512292i | \(-0.171203\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 298.056 | 1.97388 | 0.986939 | − | 0.161092i | \(-0.0515015\pi\) | ||||
0.986939 | + | 0.161092i | \(0.0515015\pi\) | |||||||
\(152\) | 138.991i | 0.914411i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −667.488 | −4.33434 | ||||||||
\(155\) | 43.8328i | 0.282792i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 90.2523 | 0.574855 | 0.287428 | − | 0.957802i | \(-0.407200\pi\) | ||||
0.287428 | + | 0.957802i | \(0.407200\pi\) | |||||||
\(158\) | − 190.517i | − 1.20580i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −145.821 | −0.911379 | ||||||||
\(161\) | − 4.30375i | − 0.0267314i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 307.712 | 1.88780 | 0.943901 | − | 0.330229i | \(-0.107126\pi\) | ||||
0.943901 | + | 0.330229i | \(0.107126\pi\) | |||||||
\(164\) | 161.930i | 0.987376i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −336.578 | −2.02758 | ||||||||
\(167\) | 40.6463i | 0.243391i | 0.992567 | + | 0.121696i | \(0.0388331\pi\) | ||||
−0.992567 | + | 0.121696i | \(0.961167\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 238.886 | 1.41352 | ||||||||
\(170\) | 10.4212i | 0.0613011i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −198.361 | −1.15326 | ||||||||
\(173\) | − 234.964i | − 1.35818i | −0.734057 | − | 0.679088i | \(-0.762376\pi\) | ||||
0.734057 | − | 0.679088i | \(-0.237624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −123.208 | −0.704045 | ||||||||
\(176\) | 617.963i | 3.51116i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.69149 | 0.0319747 | ||||||||
\(179\) | 254.540i | 1.42201i | 0.703186 | + | 0.711006i | \(0.251760\pi\) | ||||
−0.703186 | + | 0.711006i | \(0.748240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −160.679 | −0.887731 | −0.443865 | − | 0.896094i | \(-0.646393\pi\) | ||||
−0.443865 | + | 0.896094i | \(0.646393\pi\) | |||||||
\(182\) | 707.593i | 3.88787i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.52517 | −0.0463325 | ||||||||
\(185\) | 108.906i | 0.588684i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.6184 | 0.0835211 | ||||||||
\(188\) | − 570.262i | − 3.03331i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −92.6379 | −0.487568 | ||||||||
\(191\) | 168.426i | 0.881814i | 0.897553 | + | 0.440907i | \(0.145343\pi\) | ||||
−0.897553 | + | 0.440907i | \(0.854657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 325.539 | 1.68673 | 0.843364 | − | 0.537343i | \(-0.180572\pi\) | ||||
0.843364 | + | 0.537343i | \(0.180572\pi\) | |||||||
\(194\) | 148.644i | 0.766208i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −403.880 | −2.06061 | ||||||||
\(197\) | 154.639i | 0.784968i | 0.919759 | + | 0.392484i | \(0.128384\pi\) | ||||
−0.919759 | + | 0.392484i | \(0.871616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −310.045 | −1.55801 | −0.779007 | − | 0.627016i | \(-0.784276\pi\) | ||||
−0.779007 | + | 0.627016i | \(0.784276\pi\) | |||||||
\(200\) | 244.059i | 1.22029i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 348.120 | 1.72337 | ||||||||
\(203\) | 417.571i | 2.05700i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −61.2119 | −0.298595 | ||||||||
\(206\) | 75.2632i | 0.365355i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 655.092 | 3.14948 | ||||||||
\(209\) | 138.838i | 0.664299i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 212.697 | 1.00804 | 0.504021 | − | 0.863691i | \(-0.331853\pi\) | ||||
0.504021 | + | 0.863691i | \(0.331853\pi\) | |||||||
\(212\) | − 606.798i | − 2.86225i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 373.064 | 1.74329 | ||||||||
\(215\) | − 74.9835i | − 0.348761i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 120.811 | 0.556731 | ||||||||
\(218\) | − 365.480i | − 1.67651i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −615.043 | −2.79565 | ||||||||
\(221\) | − 16.5569i | − 0.0749179i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −259.955 | −1.16572 | −0.582859 | − | 0.812573i | \(-0.698066\pi\) | ||||
−0.582859 | + | 0.812573i | \(0.698066\pi\) | |||||||
\(224\) | 401.906i | 1.79423i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −429.254 | −1.89936 | ||||||||
\(227\) | − 213.321i | − 0.939742i | −0.882735 | − | 0.469871i | \(-0.844300\pi\) | ||||
0.882735 | − | 0.469871i | \(-0.155700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −72.3915 | −0.316120 | −0.158060 | − | 0.987430i | \(-0.550524\pi\) | ||||
−0.158060 | + | 0.987430i | \(0.550524\pi\) | |||||||
\(230\) | − 5.68208i | − 0.0247047i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 827.153 | 3.56532 | ||||||||
\(233\) | 254.852i | 1.09378i | 0.837203 | + | 0.546892i | \(0.184189\pi\) | ||||
−0.837203 | + | 0.546892i | \(0.815811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 215.568 | 0.917311 | ||||||||
\(236\) | − 141.842i | − 0.601024i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28.7225 | 0.120683 | ||||||||
\(239\) | 99.5547i | 0.416547i | 0.978071 | + | 0.208273i | \(0.0667844\pi\) | ||||
−0.978071 | + | 0.208273i | \(0.933216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 280.958 | 1.16580 | 0.582900 | − | 0.812544i | \(-0.301918\pi\) | ||||
0.582900 | + | 0.812544i | \(0.301918\pi\) | |||||||
\(242\) | 880.458i | 3.63826i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −552.610 | −2.26479 | ||||||||
\(245\) | − 152.673i | − 0.623155i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 147.180 | 0.595872 | ||||||||
\(248\) | − 239.310i | − 0.964960i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −480.462 | −1.92185 | ||||||||
\(251\) | 394.884i | 1.57324i | 0.617436 | + | 0.786621i | \(0.288172\pi\) | ||||
−0.617436 | + | 0.786621i | \(0.711828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.51585 | −0.0336595 | ||||||||
\(254\) | 41.0079i | 0.161448i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −402.897 | −1.57381 | ||||||||
\(257\) | − 21.2709i | − 0.0827660i | −0.999143 | − | 0.0413830i | \(-0.986824\pi\) | ||||
0.999143 | − | 0.0413830i | \(-0.0131764\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 300.165 | 1.15894 | ||||||||
\(260\) | 651.997i | 2.50768i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −655.415 | −2.50158 | ||||||||
\(263\) | − 380.580i | − 1.44707i | −0.690287 | − | 0.723536i | \(-0.742516\pi\) | ||||
0.690287 | − | 0.723536i | \(-0.257484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 229.379 | 0.865581 | ||||||||
\(266\) | 255.326i | 0.959872i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 478.900 | 1.78694 | ||||||||
\(269\) | 184.288i | 0.685087i | 0.939502 | + | 0.342543i | \(0.111288\pi\) | ||||
−0.939502 | + | 0.342543i | \(0.888712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −509.810 | −1.88122 | −0.940608 | − | 0.339494i | \(-0.889744\pi\) | ||||
−0.940608 | + | 0.339494i | \(0.889744\pi\) | |||||||
\(272\) | − 26.5915i | − 0.0977627i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −653.656 | −2.38561 | ||||||||
\(275\) | 243.792i | 0.886515i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 78.0363 | 0.281720 | 0.140860 | − | 0.990030i | \(-0.455013\pi\) | ||||
0.140860 | + | 0.990030i | \(0.455013\pi\) | |||||||
\(278\) | − 867.317i | − 3.11984i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −641.500 | −2.29107 | ||||||||
\(281\) | − 143.781i | − 0.511676i | −0.966720 | − | 0.255838i | \(-0.917649\pi\) | ||||
0.966720 | − | 0.255838i | \(-0.0823514\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 275.281 | 0.972724 | 0.486362 | − | 0.873757i | \(-0.338324\pi\) | ||||
0.486362 | + | 0.873757i | \(0.338324\pi\) | |||||||
\(284\) | − 107.820i | − 0.379649i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1400.12 | 4.89551 | ||||||||
\(287\) | 168.710i | 0.587841i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 288.328 | 0.997674 | ||||||||
\(290\) | 551.302i | 1.90104i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1143.93 | −3.91758 | ||||||||
\(293\) | 267.650i | 0.913480i | 0.889600 | + | 0.456740i | \(0.150983\pi\) | ||||
−0.889600 | + | 0.456740i | \(0.849017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53.6184 | 0.181757 | ||||||||
\(296\) | − 594.587i | − 2.00874i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −555.519 | −1.86416 | ||||||||
\(299\) | 9.02751i | 0.0301923i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −206.667 | −0.686602 | ||||||||
\(302\) | − 1084.58i | − 3.59133i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 236.382 | 0.777572 | ||||||||
\(305\) | − 208.895i | − 0.684902i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 151.145 | 0.492329 | 0.246164 | − | 0.969228i | \(-0.420830\pi\) | ||||
0.246164 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(308\) | 1695.16i | 5.50377i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 159.501 | 0.514521 | ||||||||
\(311\) | − 493.265i | − 1.58606i | −0.609182 | − | 0.793030i | \(-0.708502\pi\) | ||||
0.609182 | − | 0.793030i | \(-0.291498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99.1298 | 0.316708 | 0.158354 | − | 0.987382i | \(-0.449381\pi\) | ||||
0.158354 | + | 0.987382i | \(0.449381\pi\) | |||||||
\(314\) | − 328.415i | − 1.04591i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −483.839 | −1.53114 | ||||||||
\(317\) | 195.074i | 0.615375i | 0.951487 | + | 0.307687i | \(0.0995551\pi\) | ||||
−0.951487 | + | 0.307687i | \(0.900445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 826.249 | 2.59012 | ||||||||
\(320\) | 77.3725i | 0.241789i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.6608 | −0.0486359 | ||||||||
\(323\) | − 5.97433i | − 0.0184964i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 258.439 | 0.795198 | ||||||||
\(326\) | − 1119.72i | − 3.43472i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 334.193 | 1.01888 | ||||||||
\(329\) | − 594.142i | − 1.80590i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 116.566 | 0.352163 | 0.176082 | − | 0.984376i | \(-0.443658\pi\) | ||||
0.176082 | + | 0.984376i | \(0.443658\pi\) | |||||||
\(332\) | 854.778i | 2.57463i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 147.906 | 0.442833 | ||||||||
\(335\) | 181.032i | 0.540393i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −193.848 | −0.575216 | −0.287608 | − | 0.957748i | \(-0.592860\pi\) | ||||
−0.287608 | + | 0.957748i | \(0.592860\pi\) | |||||||
\(338\) | − 869.271i | − 2.57181i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26.4658 | 0.0778405 | ||||||||
\(341\) | − 239.048i | − 0.701021i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 50.9930 | 0.148668 | ||||||||
\(344\) | 409.381i | 1.19006i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −855.003 | −2.47111 | ||||||||
\(347\) | 365.092i | 1.05214i | 0.850442 | + | 0.526069i | \(0.176335\pi\) | ||||
−0.850442 | + | 0.526069i | \(0.823665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 619.739 | 1.77576 | 0.887879 | − | 0.460078i | \(-0.152179\pi\) | ||||
0.887879 | + | 0.460078i | \(0.152179\pi\) | |||||||
\(350\) | 448.336i | 1.28096i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 795.253 | 2.25924 | ||||||||
\(353\) | − 553.745i | − 1.56868i | −0.620330 | − | 0.784341i | \(-0.713001\pi\) | ||||
0.620330 | − | 0.784341i | \(-0.286999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.7577 | 0.114811 | ||||||||
\(356\) | − 14.4542i | − 0.0406017i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 926.235 | 2.58725 | ||||||||
\(359\) | − 97.3629i | − 0.271206i | −0.990763 | − | 0.135603i | \(-0.956703\pi\) | ||||
0.990763 | − | 0.135603i | \(-0.0432972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −307.892 | −0.852886 | ||||||||
\(362\) | 584.689i | 1.61516i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1797.01 | 4.93685 | ||||||||
\(365\) | − 432.425i | − 1.18473i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −491.906 | −1.34034 | −0.670172 | − | 0.742206i | \(-0.733780\pi\) | ||||
−0.670172 | + | 0.742206i | \(0.733780\pi\) | |||||||
\(368\) | 14.4988i | 0.0393989i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 396.295 | 1.07107 | ||||||||
\(371\) | − 632.208i | − 1.70406i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 379.909 | 1.01852 | 0.509261 | − | 0.860612i | \(-0.329919\pi\) | ||||
0.509261 | + | 0.860612i | \(0.329919\pi\) | |||||||
\(374\) | − 56.8333i | − 0.151961i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1176.92 | −3.13010 | ||||||||
\(377\) | − 875.892i | − 2.32332i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 646.240 | 1.70512 | 0.852559 | − | 0.522631i | \(-0.175049\pi\) | ||||
0.852559 | + | 0.522631i | \(0.175049\pi\) | |||||||
\(380\) | 235.265i | 0.619118i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 612.880 | 1.60440 | ||||||||
\(383\) | − 363.219i | − 0.948354i | −0.880430 | − | 0.474177i | \(-0.842746\pi\) | ||||
0.880430 | − | 0.474177i | \(-0.157254\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −640.798 | −1.66441 | ||||||||
\(386\) | − 1184.59i | − 3.06888i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 377.499 | 0.972937 | ||||||||
\(389\) | 662.872i | 1.70404i | 0.523509 | + | 0.852020i | \(0.324623\pi\) | ||||
−0.523509 | + | 0.852020i | \(0.675377\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.366444 | 0.000937196 0 | ||||||||
\(392\) | 833.535i | 2.12637i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 562.708 | 1.42819 | ||||||||
\(395\) | − 182.899i | − 0.463035i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6407 | 0.0620674 | 0.0310337 | − | 0.999518i | \(-0.490120\pi\) | ||||
0.0310337 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(398\) | 1128.21i | 2.83470i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 415.072 | 1.03768 | ||||||||
\(401\) | 273.425i | 0.681858i | 0.940089 | + | 0.340929i | \(0.110742\pi\) | ||||
−0.940089 | + | 0.340929i | \(0.889258\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −253.411 | −0.628811 | ||||||||
\(404\) | − 884.092i | − 2.18835i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1519.48 | 3.74257 | ||||||||
\(407\) | − 593.936i | − 1.45930i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 601.798 | 1.47139 | 0.735695 | − | 0.677313i | \(-0.236856\pi\) | ||||
0.735695 | + | 0.677313i | \(0.236856\pi\) | |||||||
\(410\) | 222.742i | 0.543272i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 191.140 | 0.463931 | ||||||||
\(413\) | − 147.781i | − 0.357824i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −323.120 | −0.778602 | ||||||||
\(416\) | − 843.034i | − 2.02653i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 505.214 | 1.20865 | ||||||||
\(419\) | 242.412i | 0.578550i | 0.957246 | + | 0.289275i | \(0.0934142\pi\) | ||||
−0.957246 | + | 0.289275i | \(0.906586\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 76.6518 | 0.182071 | 0.0910354 | − | 0.995848i | \(-0.470982\pi\) | ||||
0.0910354 | + | 0.995848i | \(0.470982\pi\) | |||||||
\(422\) | − 773.975i | − 1.83406i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1252.32 | −2.95359 | ||||||||
\(425\) | − 10.4906i | − 0.0246836i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −575.750 | −1.34836 | ||||||||
\(428\) | − 947.440i | − 2.21364i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −272.855 | −0.634545 | ||||||||
\(431\) | 818.889i | 1.89997i | 0.312290 | + | 0.949987i | \(0.398904\pi\) | ||||
−0.312290 | + | 0.949987i | \(0.601096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.8770 | 0.0366674 | 0.0183337 | − | 0.999832i | \(-0.494164\pi\) | ||||
0.0183337 | + | 0.999832i | \(0.494164\pi\) | |||||||
\(434\) | − 439.613i | − 1.01293i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −928.178 | −2.12885 | ||||||||
\(437\) | 3.25746i | 0.00745414i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −617.332 | −1.40622 | −0.703111 | − | 0.711080i | \(-0.748206\pi\) | ||||
−0.703111 | + | 0.711080i | \(0.748206\pi\) | |||||||
\(440\) | 1269.34i | 2.88486i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −60.2481 | −0.136308 | ||||||||
\(443\) | 548.280i | 1.23765i | 0.785528 | + | 0.618826i | \(0.212392\pi\) | ||||
−0.785528 | + | 0.618826i | \(0.787608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.46391 | 0.0122785 | ||||||||
\(446\) | 945.941i | 2.12094i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 213.252 | 0.476008 | ||||||||
\(449\) | − 209.223i | − 0.465976i | −0.972480 | − | 0.232988i | \(-0.925150\pi\) | ||||
0.972480 | − | 0.232988i | \(-0.0748503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 333.828 | 0.740195 | ||||||||
\(452\) | 1090.14i | 2.41181i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −776.247 | −1.70980 | ||||||||
\(455\) | 679.299i | 1.49296i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −505.510 | −1.10615 | −0.553074 | − | 0.833132i | \(-0.686545\pi\) | ||||
−0.553074 | + | 0.833132i | \(0.686545\pi\) | |||||||
\(458\) | 263.422i | 0.575158i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.4303 | −0.0313702 | ||||||||
\(461\) | 839.959i | 1.82204i | 0.412366 | + | 0.911018i | \(0.364702\pi\) | ||||
−0.412366 | + | 0.911018i | \(0.635298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −287.564 | −0.621089 | −0.310545 | − | 0.950559i | \(-0.600511\pi\) | ||||
−0.310545 | + | 0.950559i | \(0.600511\pi\) | |||||||
\(464\) | − 1406.74i | − 3.03178i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 927.369 | 1.99006 | ||||||||
\(467\) | − 729.628i | − 1.56237i | −0.624298 | − | 0.781187i | \(-0.714615\pi\) | ||||
0.624298 | − | 0.781187i | \(-0.285385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 498.954 | 1.06387 | ||||||||
\(470\) | − 784.422i | − 1.66898i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −292.735 | −0.620202 | ||||||||
\(473\) | 408.933i | 0.864552i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 93.2546 | 0.196325 | ||||||||
\(476\) | − 72.9442i | − 0.153244i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 362.266 | 0.757878 | ||||||||
\(479\) | − 202.711i | − 0.423196i | −0.977357 | − | 0.211598i | \(-0.932133\pi\) | ||||
0.977357 | − | 0.211598i | \(-0.0678667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −629.622 | −1.30899 | ||||||||
\(482\) | − 1022.37i | − 2.12109i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2236.02 | 4.61989 | ||||||||
\(485\) | 142.701i | 0.294228i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 706.928 | 1.45160 | 0.725799 | − | 0.687907i | \(-0.241470\pi\) | ||||
0.725799 | + | 0.687907i | \(0.241470\pi\) | |||||||
\(488\) | 1140.49i | 2.33706i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −555.556 | −1.13379 | ||||||||
\(491\) | 246.901i | 0.502854i | 0.967876 | + | 0.251427i | \(0.0808999\pi\) | ||||
−0.967876 | + | 0.251427i | \(0.919100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.5541 | −0.0721179 | ||||||||
\(494\) | − 535.569i | − 1.08415i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −406.996 | −0.820556 | ||||||||
\(497\) | − 112.335i | − 0.226027i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 480.346 | 0.962618 | 0.481309 | − | 0.876551i | \(-0.340162\pi\) | ||||
0.481309 | + | 0.876551i | \(0.340162\pi\) | |||||||
\(500\) | 1220.19i | 2.44038i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1436.93 | 2.86240 | ||||||||
\(503\) | 955.396i | 1.89940i | 0.313167 | + | 0.949698i | \(0.398610\pi\) | ||||
−0.313167 | + | 0.949698i | \(0.601390\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 334.201 | 0.661783 | ||||||||
\(506\) | 30.9880i | 0.0612411i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 104.144 | 0.205008 | ||||||||
\(509\) | 666.159i | 1.30876i | 0.756166 | + | 0.654380i | \(0.227070\pi\) | ||||
−0.756166 | + | 0.654380i | \(0.772930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1191.84 | −2.33236 | ||||||||
\(512\) | 1120.59i | 2.18865i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −77.4017 | −0.150587 | ||||||||
\(515\) | 72.2537i | 0.140299i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1175.63 | −2.27395 | ||||||||
\(518\) | − 1092.26i | − 2.10860i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1345.60 | 2.58770 | ||||||||
\(521\) | 742.086i | 1.42435i | 0.702002 | + | 0.712175i | \(0.252290\pi\) | ||||
−0.702002 | + | 0.712175i | \(0.747710\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −171.187 | −0.327317 | −0.163659 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163659 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(524\) | 1664.50i | 3.17653i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1384.88 | −2.63285 | ||||||||
\(527\) | 10.2864i | 0.0195189i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.800 | 0.999622 | ||||||||
\(530\) | − 834.678i | − 1.57486i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 648.429 | 1.21885 | ||||||||
\(533\) | − 353.885i | − 0.663949i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 358.147 | 0.669434 | ||||||||
\(536\) | − 988.362i | − 1.84396i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 670.599 | 1.24647 | ||||||||
\(539\) | 832.624i | 1.54476i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −853.931 | −1.57843 | −0.789215 | − | 0.614117i | \(-0.789512\pi\) | ||||
−0.789215 | + | 0.614117i | \(0.789512\pi\) | |||||||
\(542\) | 1855.13i | 3.42274i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.2204 | −0.0629051 | ||||||||
\(545\) | − 350.866i | − 0.643791i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 304.847 | 0.557306 | 0.278653 | − | 0.960392i | \(-0.410112\pi\) | ||||
0.278653 | + | 0.960392i | \(0.410112\pi\) | |||||||
\(548\) | 1660.03i | 3.02926i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 887.124 | 1.61295 | ||||||||
\(551\) | − 316.055i | − 0.573602i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −504.100 | −0.911573 | ||||||||
\(554\) | − 283.963i | − 0.512569i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2202.65 | −3.96160 | ||||||||
\(557\) | − 376.762i | − 0.676413i | −0.941072 | − | 0.338207i | \(-0.890180\pi\) | ||||
0.941072 | − | 0.338207i | \(-0.109820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 433.503 | 0.775497 | ||||||||
\(560\) | 1091.00i | 1.94822i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −523.199 | −0.930959 | ||||||||
\(563\) | − 343.827i | − 0.610705i | −0.952239 | − | 0.305352i | \(-0.901226\pi\) | ||||
0.952239 | − | 0.305352i | \(-0.0987742\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −412.090 | −0.729363 | ||||||||
\(566\) | − 1001.71i | − 1.76980i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −222.521 | −0.391763 | ||||||||
\(569\) | − 601.227i | − 1.05664i | −0.849046 | − | 0.528319i | \(-0.822823\pi\) | ||||
0.849046 | − | 0.528319i | \(-0.177177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 595.727 | 1.04330 | 0.521652 | − | 0.853158i | \(-0.325316\pi\) | ||||
0.521652 | + | 0.853158i | \(0.325316\pi\) | |||||||
\(572\) | − 3555.75i | − 6.21635i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 613.914 | 1.06954 | ||||||||
\(575\) | 5.71990i | 0.00994765i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 68.3783 | 0.118507 | 0.0592533 | − | 0.998243i | \(-0.481128\pi\) | ||||
0.0592533 | + | 0.998243i | \(0.481128\pi\) | |||||||
\(578\) | − 1049.18i | − 1.81520i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1400.10 | 2.41396 | ||||||||
\(581\) | 890.572i | 1.53283i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1250.95 | −2.14571 | ||||||||
\(584\) | 2360.87i | 4.04259i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 973.939 | 1.66201 | ||||||||
\(587\) | − 651.244i | − 1.10944i | −0.832036 | − | 0.554722i | \(-0.812825\pi\) | ||||
0.832036 | − | 0.554722i | \(-0.187175\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −91.4401 | −0.155246 | ||||||||
\(590\) | − 195.110i | − 0.330695i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1011.22 | −1.70814 | ||||||||
\(593\) | − 12.2860i | − 0.0207183i | −0.999946 | − | 0.0103592i | \(-0.996703\pi\) | ||||
0.999946 | − | 0.0103592i | \(-0.00329748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.5740 | 0.0463429 | ||||||||
\(596\) | 1410.80i | 2.36712i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.8498 | 0.0549328 | ||||||||
\(599\) | − 10.2076i | − 0.0170410i | −0.999964 | − | 0.00852051i | \(-0.997288\pi\) | ||||
0.999964 | − | 0.00852051i | \(-0.00271220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −370.191 | −0.615959 | −0.307980 | − | 0.951393i | \(-0.599653\pi\) | ||||
−0.307980 | + | 0.951393i | \(0.599653\pi\) | |||||||
\(602\) | 752.033i | 1.24922i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2754.42 | −4.56030 | ||||||||
\(605\) | 845.252i | 1.39711i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 166.851 | 0.274878 | 0.137439 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137439 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(608\) | − 304.198i | − 0.500326i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −760.140 | −1.24613 | ||||||||
\(611\) | 1246.27i | 2.03971i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.09767 | 0.00994726 | 0.00497363 | − | 0.999988i | \(-0.498417\pi\) | ||||
0.00497363 | + | 0.999988i | \(0.498417\pi\) | |||||||
\(614\) | − 549.995i | − 0.895758i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3498.51 | 5.67939 | ||||||||
\(617\) | 304.059i | 0.492803i | 0.969168 | + | 0.246401i | \(0.0792482\pi\) | ||||
−0.969168 | + | 0.246401i | \(0.920752\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −446.526 | −0.721367 | −0.360683 | − | 0.932688i | \(-0.617457\pi\) | ||||
−0.360683 | + | 0.932688i | \(0.617457\pi\) | |||||||
\(620\) | − 405.072i | − 0.653342i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1794.92 | −2.88573 | ||||||||
\(623\) | − 15.0595i | − 0.0241725i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −141.339 | −0.226143 | ||||||||
\(626\) | − 360.719i | − 0.576229i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −834.049 | −1.32810 | ||||||||
\(629\) | 25.5576i | 0.0406320i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 786.982 | 1.24720 | 0.623599 | − | 0.781745i | \(-0.285670\pi\) | ||||
0.623599 | + | 0.781745i | \(0.285670\pi\) | |||||||
\(632\) | 998.556i | 1.57999i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 709.846 | 1.11963 | ||||||||
\(635\) | 39.3681i | 0.0619971i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 882.650 | 1.38564 | ||||||||
\(638\) | − 3006.60i | − 4.71254i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −301.735 | −0.471461 | ||||||||
\(641\) | 596.401i | 0.930423i | 0.885199 | + | 0.465212i | \(0.154022\pi\) | ||||
−0.885199 | + | 0.465212i | \(0.845978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 773.061 | 1.20227 | 0.601136 | − | 0.799146i | \(-0.294715\pi\) | ||||
0.601136 | + | 0.799146i | \(0.294715\pi\) | |||||||
\(644\) | 39.7723i | 0.0617582i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.7397 | −0.0336529 | ||||||||
\(647\) | − 112.273i | − 0.173529i | −0.996229 | − | 0.0867644i | \(-0.972347\pi\) | ||||
0.996229 | − | 0.0867644i | \(-0.0276527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −292.415 | −0.450563 | ||||||||
\(650\) | − 940.425i | − 1.44681i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2843.66 | −4.36144 | ||||||||
\(653\) | 1069.49i | 1.63781i | 0.573929 | + | 0.818905i | \(0.305419\pi\) | ||||
−0.573929 | + | 0.818905i | \(0.694581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −629.207 | −0.960622 | ||||||||
\(656\) | − 568.364i | − 0.866409i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2162.00 | −3.28571 | ||||||||
\(659\) | − 830.211i | − 1.25980i | −0.776675 | − | 0.629902i | \(-0.783095\pi\) | ||||
0.776675 | − | 0.629902i | \(-0.216905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −696.017 | −1.05298 | −0.526488 | − | 0.850183i | \(-0.676492\pi\) | ||||
−0.526488 | + | 0.850183i | \(0.676492\pi\) | |||||||
\(662\) | − 424.168i | − 0.640737i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1764.11 | 2.65679 | ||||||||
\(665\) | 245.116i | 0.368596i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.3856 | 0.0290639 | ||||||||
\(668\) | − 375.625i | − 0.562313i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 658.749 | 0.983207 | ||||||||
\(671\) | 1139.24i | 1.69782i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −122.055 | −0.181359 | −0.0906796 | − | 0.995880i | \(-0.528904\pi\) | ||||
−0.0906796 | + | 0.995880i | \(0.528904\pi\) | |||||||
\(674\) | 705.386i | 1.04657i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2207.61 | −3.26570 | ||||||||
\(677\) | 10.1764i | 0.0150317i | 0.999972 | + | 0.00751584i | \(0.00239239\pi\) | ||||
−0.999972 | + | 0.00751584i | \(0.997608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 393.307 | 0.579245 | ||||||||
\(680\) | − 54.6206i | − 0.0803243i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −869.863 | −1.27546 | ||||||||
\(683\) | − 356.039i | − 0.521287i | −0.965435 | − | 0.260643i | \(-0.916065\pi\) | ||||
0.965435 | − | 0.260643i | \(-0.0839347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −627.519 | −0.916086 | ||||||||
\(686\) | − 185.557i | − 0.270491i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 696.236 | 1.01197 | ||||||||
\(689\) | 1326.11i | 1.92469i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 707.950 | 1.02453 | 0.512265 | − | 0.858828i | \(-0.328807\pi\) | ||||
0.512265 | + | 0.858828i | \(0.328807\pi\) | |||||||
\(692\) | 2171.38i | 3.13783i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1328.52 | 1.91429 | ||||||||
\(695\) | − 832.636i | − 1.19804i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3649 | −0.0206096 | ||||||||
\(698\) | − 2255.14i | − 3.23087i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1138.60 | 1.62657 | ||||||||
\(701\) | 578.940i | 0.825877i | 0.910759 | + | 0.412939i | \(0.135498\pi\) | ||||
−0.910759 | + | 0.412939i | \(0.864502\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −227.191 | −0.323174 | ||||||||
\(704\) | − 421.962i | − 0.599377i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2015.00 | −2.85411 | ||||||||
\(707\) | − 921.113i | − 1.30285i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −115.048 | −0.162269 | −0.0811343 | − | 0.996703i | \(-0.525854\pi\) | ||||
−0.0811343 | + | 0.996703i | \(0.525854\pi\) | |||||||
\(710\) | − 148.312i | − 0.208890i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29.8308 | −0.0418972 | ||||||||
\(713\) | − 5.60861i | − 0.00786621i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1344.13 | 1.87990 | ||||||||
\(716\) | − 2352.28i | − 3.28531i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −354.290 | −0.493440 | ||||||||
\(719\) | 626.313i | 0.871089i | 0.900167 | + | 0.435545i | \(0.143444\pi\) | ||||
−0.900167 | + | 0.435545i | \(0.856556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 199.143 | 0.276205 | ||||||||
\(722\) | 1120.38i | 1.55177i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1484.89 | 2.05095 | ||||||||
\(725\) | − 554.972i | − 0.765479i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −773.461 | −1.06391 | −0.531954 | − | 0.846773i | \(-0.678542\pi\) | ||||
−0.531954 | + | 0.846773i | \(0.678542\pi\) | |||||||
\(728\) | − 3708.71i | − 5.09438i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1573.53 | −2.15553 | ||||||||
\(731\) | − 17.5967i | − 0.0240721i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 148.562 | 0.202677 | 0.101339 | − | 0.994852i | \(-0.467687\pi\) | ||||
0.101339 | + | 0.994852i | \(0.467687\pi\) | |||||||
\(734\) | 1789.98i | 2.43866i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.6584 | 0.0253511 | ||||||||
\(737\) | − 987.281i | − 1.33959i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1320.96 | −1.78749 | −0.893745 | − | 0.448575i | \(-0.851932\pi\) | ||||
−0.893745 | + | 0.448575i | \(0.851932\pi\) | |||||||
\(740\) | − 1006.44i | − 1.36005i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2300.51 | −3.10042 | ||||||||
\(743\) | − 674.905i | − 0.908352i | −0.890912 | − | 0.454176i | \(-0.849934\pi\) | ||||
0.890912 | − | 0.454176i | \(-0.150066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −533.306 | −0.715847 | ||||||||
\(746\) | − 1382.44i | − 1.85313i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −144.335 | −0.192961 | ||||||||
\(749\) | − 987.114i | − 1.31791i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −128.638 | −0.171289 | −0.0856446 | − | 0.996326i | \(-0.527295\pi\) | ||||
−0.0856446 | + | 0.996326i | \(0.527295\pi\) | |||||||
\(752\) | 2001.59i | 2.66169i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3187.25 | −4.22712 | ||||||||
\(755\) | − 1041.22i | − 1.37909i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −877.612 | −1.15933 | −0.579665 | − | 0.814855i | \(-0.696816\pi\) | ||||
−0.579665 | + | 0.814855i | \(0.696816\pi\) | |||||||
\(758\) | − 2351.58i | − 3.10234i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 485.543 | 0.638873 | ||||||||
\(761\) | − 379.587i | − 0.498800i | −0.968401 | − | 0.249400i | \(-0.919767\pi\) | ||||
0.968401 | − | 0.249400i | \(-0.0802334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −967.046 | −1.26743 | ||||||||
\(764\) | − 1556.48i | − 2.03728i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1321.70 | −1.72546 | ||||||||
\(767\) | 309.984i | 0.404152i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.2784 | −0.0484764 | −0.0242382 | − | 0.999706i | \(-0.507716\pi\) | ||||
−0.0242382 | + | 0.999706i | \(0.507716\pi\) | |||||||
\(770\) | 2331.77i | 3.02828i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3008.40 | −3.89689 | ||||||||
\(773\) | 90.6078i | 0.117216i | 0.998281 | + | 0.0586079i | \(0.0186662\pi\) | ||||
−0.998281 | + | 0.0586079i | \(0.981334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −160.563 | −0.207178 | ||||||||
\(776\) | − 779.090i | − 1.00398i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2412.10 | 3.10038 | ||||||||
\(779\) | − 127.695i | − 0.163922i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −222.278 | −0.284607 | ||||||||
\(782\) | − 1.33344i | − 0.00170516i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1417.60 | 1.80816 | ||||||||
\(785\) | − 315.283i | − 0.401635i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −605.048 | −0.768804 | −0.384402 | − | 0.923166i | \(-0.625592\pi\) | ||||
−0.384402 | + | 0.923166i | \(0.625592\pi\) | |||||||
\(788\) | − 1429.06i | − 1.81353i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −665.543 | −0.842459 | ||||||||
\(791\) | 1135.79i | 1.43589i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1207.69 | 1.52294 | ||||||||
\(794\) | − 89.6642i | − 0.112927i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2865.22 | 3.59952 | ||||||||
\(797\) | − 91.0829i | − 0.114282i | −0.998366 | − | 0.0571411i | \(-0.981802\pi\) | ||||
0.998366 | − | 0.0571411i | \(-0.0181985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.5883 | 0.0633145 | ||||||||
\(800\) | − 534.153i | − 0.667692i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 994.956 | 1.24059 | ||||||||
\(803\) | 2358.29i | 2.93685i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.0346 | −0.0186765 | ||||||||
\(806\) | 922.127i | 1.14408i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1824.60 | −2.25817 | ||||||||
\(809\) | 936.735i | 1.15789i | 0.815366 | + | 0.578947i | \(0.196536\pi\) | ||||
−0.815366 | + | 0.578947i | \(0.803464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −275.363 | −0.339536 | −0.169768 | − | 0.985484i | \(-0.554302\pi\) | ||||
−0.169768 | + | 0.985484i | \(0.554302\pi\) | |||||||
\(812\) | − 3858.90i | − 4.75234i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2161.25 | −2.65510 | ||||||||
\(815\) | − 1074.95i | − 1.31895i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 156.424 | 0.191461 | ||||||||
\(818\) | − 2189.86i | − 2.67709i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 565.678 | 0.689851 | ||||||||
\(821\) | − 243.447i | − 0.296525i | −0.988948 | − | 0.148263i | \(-0.952632\pi\) | ||||
0.988948 | − | 0.148263i | \(-0.0473681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −554.519 | −0.673777 | −0.336889 | − | 0.941545i | \(-0.609375\pi\) | ||||
−0.336889 | + | 0.941545i | \(0.609375\pi\) | |||||||
\(824\) | − 394.477i | − 0.478734i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −537.756 | −0.651036 | ||||||||
\(827\) | 1064.18i | 1.28680i | 0.765530 | + | 0.643400i | \(0.222477\pi\) | ||||
−0.765530 | + | 0.643400i | \(0.777523\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1090.98 | 1.31602 | 0.658012 | − | 0.753007i | \(-0.271397\pi\) | ||||
0.658012 | + | 0.753007i | \(0.271397\pi\) | |||||||
\(830\) | 1175.79i | 1.41661i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −447.314 | −0.537637 | ||||||||
\(833\) | − 35.8285i | − 0.0430113i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 141.992 | 0.170050 | ||||||||
\(836\) | − 1283.05i | − 1.53475i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 882.105 | 1.05263 | ||||||||
\(839\) | 978.978i | 1.16684i | 0.812171 | + | 0.583419i | \(0.198286\pi\) | ||||
−0.812171 | + | 0.583419i | \(0.801714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1039.89 | −1.23649 | ||||||||
\(842\) | − 278.925i | − 0.331265i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1965.60 | −2.32891 | ||||||||
\(845\) | − 834.513i | − 0.987589i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2329.66 | 2.75048 | ||||||||
\(848\) | 2129.83i | 2.51159i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −38.1736 | −0.0449102 | ||||||||
\(851\) | − 13.9351i | − 0.0163749i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 301.741 | 0.353741 | 0.176870 | − | 0.984234i | \(-0.443403\pi\) | ||||
0.176870 | + | 0.984234i | \(0.443403\pi\) | |||||||
\(854\) | 2095.08i | 2.45325i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1955.34 | −2.28428 | ||||||||
\(857\) | 1467.38i | 1.71222i | 0.516790 | + | 0.856112i | \(0.327127\pi\) | ||||
−0.516790 | + | 0.856112i | \(0.672873\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.3456 | 0.0143720 | 0.00718600 | − | 0.999974i | \(-0.497713\pi\) | ||||
0.00718600 | + | 0.999974i | \(0.497713\pi\) | |||||||
\(860\) | 692.945i | 0.805750i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2979.82 | 3.45687 | ||||||||
\(863\) | 10.8046i | 0.0125198i | 0.999980 | + | 0.00625990i | \(0.00199260\pi\) | ||||
−0.999980 | + | 0.00625990i | \(0.998007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −820.815 | −0.948919 | ||||||||
\(866\) | − 57.7742i | − 0.0667138i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1116.45 | −1.28623 | ||||||||
\(869\) | 997.463i | 1.14783i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1046.60 | −1.20161 | ||||||||
\(872\) | 1915.59i | 2.19678i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.8534 | 0.0135623 | ||||||||
\(875\) | 1271.28i | 1.45290i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 366.912 | 0.418372 | 0.209186 | − | 0.977876i | \(-0.432919\pi\) | ||||
0.209186 | + | 0.977876i | \(0.432919\pi\) | |||||||
\(878\) | 2246.38i | 2.55852i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2158.77 | 2.45314 | ||||||||
\(881\) | − 308.365i | − 0.350017i | −0.984567 | − | 0.175008i | \(-0.944005\pi\) | ||||
0.984567 | − | 0.175008i | \(-0.0559952\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −497.722 | −0.563672 | −0.281836 | − | 0.959463i | \(-0.590943\pi\) | ||||
−0.281836 | + | 0.959463i | \(0.590943\pi\) | |||||||
\(884\) | 153.007i | 0.173085i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1995.11 | 2.25182 | ||||||||
\(887\) | − 1001.96i | − 1.12961i | −0.825225 | − | 0.564805i | \(-0.808952\pi\) | ||||
0.825225 | − | 0.564805i | \(-0.191048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 108.505 | 0.122053 | ||||||||
\(890\) | − 19.8824i | − 0.0223398i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2402.32 | 2.69319 | ||||||||
\(893\) | 449.699i | 0.503582i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 889.199 | 0.993519 | ||||||||
\(896\) | 831.633i | 0.928162i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −761.334 | −0.847811 | ||||||||
\(899\) | 544.174i | 0.605310i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.8294 | 0.0597440 | ||||||||
\(902\) | − 1214.75i | − 1.34673i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2249.85 | 2.48877 | ||||||||
\(905\) | 561.310i | 0.620232i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 968.351 | 1.06764 | 0.533821 | − | 0.845598i | \(-0.320756\pi\) | ||||
0.533821 | + | 0.845598i | \(0.320756\pi\) | |||||||
\(908\) | 1971.37i | 2.17111i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2471.87 | 2.71635 | ||||||||
\(911\) | − 620.552i | − 0.681176i | −0.940213 | − | 0.340588i | \(-0.889374\pi\) | ||||
0.940213 | − | 0.340588i | \(-0.110626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1762.18 | 1.93010 | ||||||||
\(914\) | 1839.48i | 2.01256i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 668.992 | 0.730340 | ||||||||
\(917\) | 1734.20i | 1.89117i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 153.844 | 0.167403 | 0.0837016 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837016 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(920\) | 29.7815i | 0.0323712i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3056.49 | 3.31507 | ||||||||
\(923\) | 235.633i | 0.255290i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −398.933 | −0.431279 | ||||||||
\(926\) | 1046.41i | 1.13003i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1810.33 | −1.95079 | ||||||||
\(929\) | − 1440.34i | − 1.55042i | −0.631705 | − | 0.775209i | \(-0.717644\pi\) | ||||
0.631705 | − | 0.775209i | \(-0.282356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 318.493 | 0.342098 | ||||||||
\(932\) | − 2355.16i | − 2.52700i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2655.01 | −2.84263 | ||||||||
\(935\) | − 54.5608i | − 0.0583538i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1174.61 | −1.25359 | −0.626795 | − | 0.779184i | \(-0.715634\pi\) | ||||
−0.626795 | + | 0.779184i | \(0.715634\pi\) | |||||||
\(938\) | − 1815.62i | − 1.93563i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1992.13 | −2.11929 | ||||||||
\(941\) | − 1621.47i | − 1.72313i | −0.507644 | − | 0.861567i | \(-0.669484\pi\) | ||||
0.507644 | − | 0.861567i | \(-0.330516\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.83234 | 0.00830577 | ||||||||
\(944\) | 497.857i | 0.527390i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1488.05 | 1.57299 | ||||||||
\(947\) | − 642.612i | − 0.678576i | −0.940682 | − | 0.339288i | \(-0.889814\pi\) | ||||
0.940682 | − | 0.339288i | \(-0.110186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2499.98 | 2.63433 | ||||||||
\(950\) | − 339.340i | − 0.357200i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −150.543 | −0.158134 | ||||||||
\(953\) | − 447.223i | − 0.469279i | −0.972082 | − | 0.234639i | \(-0.924609\pi\) | ||||
0.972082 | − | 0.234639i | \(-0.0753909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 588.374 | 0.616098 | ||||||||
\(956\) | − 920.015i | − 0.962359i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −737.636 | −0.769975 | ||||||||
\(959\) | 1729.55i | 1.80349i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −803.561 | −0.836172 | ||||||||
\(962\) | 2291.11i | 2.38161i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2596.42 | −2.69338 | ||||||||
\(965\) | − 1137.22i | − 1.17847i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1084.47 | −1.12148 | −0.560742 | − | 0.827991i | \(-0.689484\pi\) | ||||
−0.560742 | + | 0.827991i | \(0.689484\pi\) | |||||||
\(968\) | − 4614.75i | − 4.76730i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 519.268 | 0.535328 | ||||||||
\(971\) | 202.150i | 0.208187i | 0.994567 | + | 0.104094i | \(0.0331942\pi\) | ||||
−0.994567 | + | 0.104094i | \(0.966806\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2294.89 | −2.35857 | ||||||||
\(974\) | − 2572.41i | − 2.64108i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1939.63 | 1.98733 | ||||||||
\(977\) | 443.613i | 0.454057i | 0.973888 | + | 0.227028i | \(0.0729010\pi\) | ||||
−0.973888 | + | 0.227028i | \(0.927099\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.7982 | −0.0304374 | ||||||||
\(980\) | 1410.90i | 1.43969i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 898.440 | 0.914908 | ||||||||
\(983\) | 350.462i | 0.356522i | 0.983983 | + | 0.178261i | \(0.0570472\pi\) | ||||
−0.983983 | + | 0.178261i | \(0.942953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 540.208 | 0.548435 | ||||||||
\(986\) | 129.377i | 0.131213i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1360.14 | −1.37666 | ||||||||
\(989\) | 9.59448i | 0.00970119i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −889.003 | −0.897076 | −0.448538 | − | 0.893764i | \(-0.648055\pi\) | ||||
−0.448538 | + | 0.893764i | \(0.648055\pi\) | |||||||
\(992\) | 523.760i | 0.527984i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −408.772 | −0.411240 | ||||||||
\(995\) | 1083.10i | 1.08854i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1156.35 | 1.15983 | 0.579913 | − | 0.814678i | \(-0.303086\pi\) | ||||
0.579913 | + | 0.814678i | \(0.303086\pi\) | |||||||
\(998\) | − 1747.91i | − 1.75142i | ||||||||
\(999\) | 0 | 0 |
(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 | 1143.3.b.a.890.5 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.80 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.5 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.80 | yes | 84 | 3.2 | odd | 2 | inner |