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 | 890.76 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.9 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.22737i | 1.61369i | 0.590766 | + | 0.806843i | \(0.298825\pi\) | ||||
−0.590766 | + | 0.806843i | \(0.701175\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.41592 | −1.60398 | ||||||||
\(5\) | − 1.45400i | − 0.290799i | −0.989373 | − | 0.145400i | \(-0.953553\pi\) | ||||
0.989373 | − | 0.145400i | \(-0.0464468\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.15873 | 0.308390 | 0.154195 | − | 0.988040i | \(-0.450722\pi\) | ||||
0.154195 | + | 0.988040i | \(0.450722\pi\) | |||||||
\(8\) | − 7.79707i | − 0.974634i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.69259 | 0.469259 | ||||||||
\(11\) | 6.04547i | 0.549588i | 0.961503 | + | 0.274794i | \(0.0886097\pi\) | ||||
−0.961503 | + | 0.274794i | \(0.911390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.2005 | 1.16927 | 0.584635 | − | 0.811297i | \(-0.301238\pi\) | ||||
0.584635 | + | 0.811297i | \(0.301238\pi\) | |||||||
\(14\) | 6.96703i | 0.497645i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.499646 | −0.0312279 | ||||||||
\(17\) | − 16.9441i | − 0.996713i | −0.866972 | − | 0.498356i | \(-0.833937\pi\) | ||||
0.866972 | − | 0.498356i | \(-0.166063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.63400 | −0.296527 | −0.148263 | − | 0.988948i | \(-0.547368\pi\) | ||||
−0.148263 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(20\) | 9.32873i | 0.466436i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −19.5110 | −0.886862 | ||||||||
\(23\) | − 12.2914i | − 0.534408i | −0.963640 | − | 0.267204i | \(-0.913900\pi\) | ||||
0.963640 | − | 0.267204i | \(-0.0860998\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.8859 | 0.915436 | ||||||||
\(26\) | 49.0577i | 1.88683i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.8503 | −0.494652 | ||||||||
\(29\) | − 20.9473i | − 0.722321i | −0.932504 | − | 0.361161i | \(-0.882381\pi\) | ||||
0.932504 | − | 0.361161i | \(-0.117619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.7052 | 1.44210 | 0.721052 | − | 0.692881i | \(-0.243659\pi\) | ||||
0.721052 | + | 0.692881i | \(0.243659\pi\) | |||||||
\(32\) | − 32.8008i | − 1.02503i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 54.6849 | 1.60838 | ||||||||
\(35\) | − 3.13879i | − 0.0896797i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 50.2331 | 1.35765 | 0.678826 | − | 0.734299i | \(-0.262489\pi\) | ||||
0.678826 | + | 0.734299i | \(0.262489\pi\) | |||||||
\(38\) | − 18.1830i | − 0.478501i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.3369 | −0.283423 | ||||||||
\(41\) | 45.3146i | 1.10523i | 0.833435 | + | 0.552617i | \(0.186371\pi\) | ||||
−0.833435 | + | 0.552617i | \(0.813629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 63.6233 | 1.47961 | 0.739806 | − | 0.672820i | \(-0.234917\pi\) | ||||
0.739806 | + | 0.672820i | \(0.234917\pi\) | |||||||
\(44\) | − 38.7873i | − 0.881529i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 39.6689 | 0.862367 | ||||||||
\(47\) | 57.8837i | 1.23157i | 0.787915 | + | 0.615784i | \(0.211161\pi\) | ||||
−0.787915 | + | 0.615784i | \(0.788839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.3399 | −0.904895 | ||||||||
\(50\) | 73.8613i | 1.47723i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −97.5252 | −1.87548 | ||||||||
\(53\) | 16.7003i | 0.315099i | 0.987511 | + | 0.157550i | \(0.0503594\pi\) | ||||
−0.987511 | + | 0.157550i | \(0.949641\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.79009 | 0.159820 | ||||||||
\(56\) | − 16.8318i | − 0.300568i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 67.6048 | 1.16560 | ||||||||
\(59\) | 111.728i | 1.89370i | 0.321682 | + | 0.946848i | \(0.395752\pi\) | ||||
−0.321682 | + | 0.946848i | \(0.604248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.642 | −1.68265 | −0.841325 | − | 0.540529i | \(-0.818224\pi\) | ||||
−0.841325 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(62\) | 144.280i | 2.32710i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 103.862 | 1.62284 | ||||||||
\(65\) | − 22.1015i | − 0.340023i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −69.5730 | −1.03840 | −0.519201 | − | 0.854652i | \(-0.673770\pi\) | ||||
−0.519201 | + | 0.854652i | \(0.673770\pi\) | |||||||
\(68\) | 108.712i | 1.59871i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.1300 | 0.144715 | ||||||||
\(71\) | − 87.3147i | − 1.22979i | −0.788611 | − | 0.614893i | \(-0.789199\pi\) | ||||
0.788611 | − | 0.614893i | \(-0.210801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.5578 | −0.199422 | −0.0997108 | − | 0.995016i | \(-0.531792\pi\) | ||||
−0.0997108 | + | 0.995016i | \(0.531792\pi\) | |||||||
\(74\) | 162.121i | 2.19082i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 36.1473 | 0.475623 | ||||||||
\(77\) | 13.0506i | 0.169488i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 146.673 | 1.85662 | 0.928310 | − | 0.371807i | \(-0.121262\pi\) | ||||
0.928310 | + | 0.371807i | \(0.121262\pi\) | |||||||
\(80\) | 0.726483i | 0.00908104i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −146.247 | −1.78350 | ||||||||
\(83\) | − 59.3483i | − 0.715040i | −0.933905 | − | 0.357520i | \(-0.883622\pi\) | ||||
0.933905 | − | 0.357520i | \(-0.116378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.6367 | −0.289843 | ||||||||
\(86\) | 205.336i | 2.38763i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 47.1370 | 0.535647 | ||||||||
\(89\) | 10.9134i | 0.122623i | 0.998119 | + | 0.0613114i | \(0.0195283\pi\) | ||||
−0.998119 | + | 0.0613114i | \(0.980472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.8138 | 0.360591 | ||||||||
\(92\) | 78.8606i | 0.857180i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −186.812 | −1.98736 | ||||||||
\(95\) | 8.19182i | 0.0862297i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21.3026 | 0.219614 | 0.109807 | − | 0.993953i | \(-0.464977\pi\) | ||||
0.109807 | + | 0.993953i | \(0.464977\pi\) | |||||||
\(98\) | − 143.101i | − 1.46022i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −146.834 | −1.46834 | ||||||||
\(101\) | 191.133i | 1.89240i | 0.323576 | + | 0.946202i | \(0.395115\pi\) | ||||
−0.323576 | + | 0.946202i | \(0.604885\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27.2875 | 0.264928 | 0.132464 | − | 0.991188i | \(-0.457711\pi\) | ||||
0.132464 | + | 0.991188i | \(0.457711\pi\) | |||||||
\(104\) | − 118.519i | − 1.13961i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −53.8980 | −0.508471 | ||||||||
\(107\) | − 77.1669i | − 0.721186i | −0.932723 | − | 0.360593i | \(-0.882574\pi\) | ||||
0.932723 | − | 0.360593i | \(-0.117426\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.49702 | −0.0137341 | −0.00686707 | − | 0.999976i | \(-0.502186\pi\) | ||||
−0.00686707 | + | 0.999976i | \(0.502186\pi\) | |||||||
\(110\) | 28.3689i | 0.257899i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.07860 | −0.00963037 | ||||||||
\(113\) | 131.194i | 1.16101i | 0.814256 | + | 0.580506i | \(0.197145\pi\) | ||||
−0.814256 | + | 0.580506i | \(0.802855\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.8716 | −0.155406 | ||||||||
\(116\) | 134.396i | 1.15859i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −360.588 | −3.05583 | ||||||||
\(119\) | − 36.5778i | − 0.307376i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 84.4523 | 0.697953 | ||||||||
\(122\) | − 331.263i | − 2.71527i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −286.825 | −2.31311 | ||||||||
\(125\) | − 69.6259i | − 0.557007i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2694 | −0.0887357 | ||||||||
\(128\) | 203.997i | 1.59373i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 71.3297 | 0.548690 | ||||||||
\(131\) | 143.034i | 1.09186i | 0.837830 | + | 0.545931i | \(0.183824\pi\) | ||||
−0.837830 | + | 0.545931i | \(0.816176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.1623 | −0.0914459 | ||||||||
\(134\) | − 224.538i | − 1.67565i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −132.114 | −0.971430 | ||||||||
\(137\) | 4.85061i | 0.0354059i | 0.999843 | + | 0.0177030i | \(0.00563532\pi\) | ||||
−0.999843 | + | 0.0177030i | \(0.994365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 115.522 | 0.831097 | 0.415548 | − | 0.909571i | \(-0.363590\pi\) | ||||
0.415548 | + | 0.909571i | \(0.363590\pi\) | |||||||
\(140\) | 20.1382i | 0.143844i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 281.797 | 1.98449 | ||||||||
\(143\) | 91.8942i | 0.642617i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.4573 | −0.210051 | ||||||||
\(146\) | − 46.9833i | − 0.321804i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −322.292 | −2.17765 | ||||||||
\(149\) | 101.662i | 0.682295i | 0.940010 | + | 0.341148i | \(0.110816\pi\) | ||||
−0.940010 | + | 0.341148i | \(0.889184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 147.676 | 0.977990 | 0.488995 | − | 0.872287i | \(-0.337364\pi\) | ||||
0.488995 | + | 0.872287i | \(0.337364\pi\) | |||||||
\(152\) | 43.9287i | 0.289005i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −42.1190 | −0.273500 | ||||||||
\(155\) | − 65.0012i | − 0.419363i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.8716 | −0.203004 | −0.101502 | − | 0.994835i | \(-0.532365\pi\) | ||||
−0.101502 | + | 0.994835i | \(0.532365\pi\) | |||||||
\(158\) | 473.368i | 2.99600i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −47.6923 | −0.298077 | ||||||||
\(161\) | − 26.5338i | − 0.164806i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.77669 | −0.0538447 | −0.0269224 | − | 0.999638i | \(-0.508571\pi\) | ||||
−0.0269224 | + | 0.999638i | \(0.508571\pi\) | |||||||
\(164\) | − 290.735i | − 1.77277i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 191.539 | 1.15385 | ||||||||
\(167\) | − 117.208i | − 0.701842i | −0.936405 | − | 0.350921i | \(-0.885869\pi\) | ||||
0.936405 | − | 0.350921i | \(-0.114131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 62.0553 | 0.367191 | ||||||||
\(170\) | − 79.5117i | − 0.467716i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −408.202 | −2.37327 | ||||||||
\(173\) | − 206.099i | − 1.19132i | −0.803235 | − | 0.595662i | \(-0.796890\pi\) | ||||
0.803235 | − | 0.595662i | \(-0.203110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 49.4045 | 0.282311 | ||||||||
\(176\) | − 3.02059i | − 0.0171625i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −35.2217 | −0.197875 | ||||||||
\(179\) | − 114.251i | − 0.638271i | −0.947709 | − | 0.319136i | \(-0.896607\pi\) | ||||
0.947709 | − | 0.319136i | \(-0.103393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 320.232 | 1.76923 | 0.884617 | − | 0.466317i | \(-0.154420\pi\) | ||||
0.884617 | + | 0.466317i | \(0.154420\pi\) | |||||||
\(182\) | 105.902i | 0.581881i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −95.8368 | −0.520852 | ||||||||
\(185\) | − 73.0388i | − 0.394804i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 102.435 | 0.547781 | ||||||||
\(188\) | − 371.377i | − 1.97541i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.4381 | −0.139148 | ||||||||
\(191\) | 104.041i | 0.544719i | 0.962196 | + | 0.272360i | \(0.0878040\pi\) | ||||
−0.962196 | + | 0.272360i | \(0.912196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −333.803 | −1.72955 | −0.864774 | − | 0.502162i | \(-0.832538\pi\) | ||||
−0.864774 | + | 0.502162i | \(0.832538\pi\) | |||||||
\(194\) | 68.7514i | 0.354389i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 284.481 | 1.45143 | ||||||||
\(197\) | − 111.309i | − 0.565020i | −0.959264 | − | 0.282510i | \(-0.908833\pi\) | ||||
0.959264 | − | 0.282510i | \(-0.0911670\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 179.209 | 0.900549 | 0.450274 | − | 0.892890i | \(-0.351326\pi\) | ||||
0.450274 | + | 0.892890i | \(0.351326\pi\) | |||||||
\(200\) | − 178.443i | − 0.892215i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −616.856 | −3.05374 | ||||||||
\(203\) | − 45.2196i | − 0.222757i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 65.8873 | 0.321401 | ||||||||
\(206\) | 88.0670i | 0.427510i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.59487 | −0.0365138 | ||||||||
\(209\) | − 34.0602i | − 0.162968i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −211.720 | −1.00341 | −0.501706 | − | 0.865038i | \(-0.667294\pi\) | ||||
−0.501706 | + | 0.865038i | \(0.667294\pi\) | |||||||
\(212\) | − 107.148i | − 0.505413i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 249.046 | 1.16377 | ||||||||
\(215\) | − 92.5081i | − 0.430270i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 96.5066 | 0.444731 | ||||||||
\(218\) | − 4.83144i | − 0.0221626i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −56.3965 | −0.256348 | ||||||||
\(221\) | − 257.559i | − 1.16543i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 252.821 | 1.13373 | 0.566864 | − | 0.823812i | \(-0.308157\pi\) | ||||
0.566864 | + | 0.823812i | \(0.308157\pi\) | |||||||
\(224\) | − 70.8082i | − 0.316108i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −423.413 | −1.87351 | ||||||||
\(227\) | − 160.992i | − 0.709217i | −0.935015 | − | 0.354609i | \(-0.884614\pi\) | ||||
0.935015 | − | 0.354609i | \(-0.115386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8026 | 0.0733739 | 0.0366870 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366870 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(230\) | − 57.6784i | − 0.250776i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −163.328 | −0.703999 | ||||||||
\(233\) | − 56.2312i | − 0.241336i | −0.992693 | − | 0.120668i | \(-0.961496\pi\) | ||||
0.992693 | − | 0.120668i | \(-0.0385036\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 84.1627 | 0.358139 | ||||||||
\(236\) | − 716.838i | − 3.03745i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 118.050 | 0.496009 | ||||||||
\(239\) | 365.589i | 1.52966i | 0.644232 | + | 0.764830i | \(0.277177\pi\) | ||||
−0.644232 | + | 0.764830i | \(0.722823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −314.533 | −1.30512 | −0.652558 | − | 0.757739i | \(-0.726304\pi\) | ||||
−0.652558 | + | 0.757739i | \(0.726304\pi\) | |||||||
\(242\) | 272.559i | 1.12628i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 658.541 | 2.69894 | ||||||||
\(245\) | 64.4700i | 0.263143i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −85.6397 | −0.346719 | ||||||||
\(248\) | − 348.570i | − 1.40552i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 224.709 | 0.898835 | ||||||||
\(251\) | 413.825i | 1.64871i | 0.566076 | + | 0.824353i | \(0.308461\pi\) | ||||
−0.566076 | + | 0.824353i | \(0.691539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 74.3072 | 0.293704 | ||||||||
\(254\) | − 36.3706i | − 0.143191i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −242.928 | −0.948936 | ||||||||
\(257\) | − 129.894i | − 0.505426i | −0.967541 | − | 0.252713i | \(-0.918677\pi\) | ||||
0.967541 | − | 0.252713i | \(-0.0813228\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 108.440 | 0.418687 | ||||||||
\(260\) | 141.801i | 0.545390i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −461.623 | −1.76192 | ||||||||
\(263\) | − 395.319i | − 1.50311i | −0.659668 | − | 0.751557i | \(-0.729303\pi\) | ||||
0.659668 | − | 0.751557i | \(-0.270697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.2821 | 0.0916307 | ||||||||
\(266\) | − 39.2523i | − 0.147565i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 446.375 | 1.66558 | ||||||||
\(269\) | − 424.438i | − 1.57784i | −0.614497 | − | 0.788919i | \(-0.710641\pi\) | ||||
0.614497 | − | 0.788919i | \(-0.289359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −296.500 | −1.09410 | −0.547048 | − | 0.837101i | \(-0.684248\pi\) | ||||
−0.547048 | + | 0.837101i | \(0.684248\pi\) | |||||||
\(272\) | 8.46606i | 0.0311252i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.6547 | −0.0571340 | ||||||||
\(275\) | 138.356i | 0.503113i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −111.921 | −0.404045 | −0.202023 | − | 0.979381i | \(-0.564751\pi\) | ||||
−0.202023 | + | 0.979381i | \(0.564751\pi\) | |||||||
\(278\) | 372.834i | 1.34113i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −24.4734 | −0.0874049 | ||||||||
\(281\) | 202.966i | 0.722298i | 0.932508 | + | 0.361149i | \(0.117615\pi\) | ||||
−0.932508 | + | 0.361149i | \(0.882385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8527 | 0.0736843 | 0.0368422 | − | 0.999321i | \(-0.488270\pi\) | ||||
0.0368422 | + | 0.999321i | \(0.488270\pi\) | |||||||
\(284\) | 560.204i | 1.97255i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −296.577 | −1.03698 | ||||||||
\(287\) | 97.8221i | 0.340844i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.89702 | 0.00656409 | ||||||||
\(290\) | − 98.2971i | − 0.338955i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 93.4015 | 0.319868 | ||||||||
\(293\) | 506.171i | 1.72755i | 0.503881 | + | 0.863773i | \(0.331905\pi\) | ||||
−0.503881 | + | 0.863773i | \(0.668095\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 162.452 | 0.550685 | ||||||||
\(296\) | − 391.671i | − 1.32321i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −328.101 | −1.10101 | ||||||||
\(299\) | − 186.835i | − 0.624867i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 137.346 | 0.456298 | ||||||||
\(302\) | 476.607i | 1.57817i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.81501 | 0.00925989 | ||||||||
\(305\) | 149.241i | 0.489314i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 446.721 | 1.45512 | 0.727559 | − | 0.686045i | \(-0.240655\pi\) | ||||
0.727559 | + | 0.686045i | \(0.240655\pi\) | |||||||
\(308\) | − 83.7313i | − 0.271855i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 209.783 | 0.676720 | ||||||||
\(311\) | − 523.253i | − 1.68249i | −0.540657 | − | 0.841243i | \(-0.681824\pi\) | ||||
0.540657 | − | 0.841243i | \(-0.318176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 354.860 | 1.13374 | 0.566869 | − | 0.823808i | \(-0.308155\pi\) | ||||
0.566869 | + | 0.823808i | \(0.308155\pi\) | |||||||
\(314\) | − 102.861i | − 0.327584i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −941.042 | −2.97798 | ||||||||
\(317\) | − 387.303i | − 1.22178i | −0.791717 | − | 0.610888i | \(-0.790813\pi\) | ||||
0.791717 | − | 0.610888i | \(-0.209187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 126.636 | 0.396979 | ||||||||
\(320\) | − 151.015i | − 0.471921i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 85.6344 | 0.265945 | ||||||||
\(323\) | 95.4632i | 0.295552i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 347.877 | 1.07039 | ||||||||
\(326\) | − 28.3256i | − 0.0868884i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 353.321 | 1.07720 | ||||||||
\(329\) | 124.955i | 0.379804i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −266.449 | −0.804981 | −0.402490 | − | 0.915424i | \(-0.631855\pi\) | ||||
−0.402490 | + | 0.915424i | \(0.631855\pi\) | |||||||
\(332\) | 380.774i | 1.14691i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 378.272 | 1.13255 | ||||||||
\(335\) | 101.159i | 0.301967i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 555.631 | 1.64876 | 0.824379 | − | 0.566039i | \(-0.191525\pi\) | ||||
0.824379 | + | 0.566039i | \(0.191525\pi\) | |||||||
\(338\) | 200.275i | 0.592531i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 158.067 | 0.464903 | ||||||||
\(341\) | 270.264i | 0.792563i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −201.496 | −0.587451 | ||||||||
\(344\) | − 496.076i | − 1.44208i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 665.158 | 1.92242 | ||||||||
\(347\) | 51.5775i | 0.148638i | 0.997235 | + | 0.0743192i | \(0.0236784\pi\) | ||||
−0.997235 | + | 0.0743192i | \(0.976322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 593.799 | 1.70143 | 0.850716 | − | 0.525626i | \(-0.176169\pi\) | ||||
0.850716 | + | 0.525626i | \(0.176169\pi\) | |||||||
\(350\) | 159.447i | 0.455562i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 198.296 | 0.563342 | ||||||||
\(353\) | 461.155i | 1.30639i | 0.757190 | + | 0.653195i | \(0.226572\pi\) | ||||
−0.757190 | + | 0.653195i | \(0.773428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −126.955 | −0.357621 | ||||||||
\(356\) | − 70.0197i | − 0.196685i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 368.729 | 1.02997 | ||||||||
\(359\) | 231.114i | 0.643771i | 0.946779 | + | 0.321885i | \(0.104317\pi\) | ||||
−0.946779 | + | 0.321885i | \(0.895683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −329.258 | −0.912072 | ||||||||
\(362\) | 1033.51i | 2.85499i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −210.531 | −0.578381 | ||||||||
\(365\) | 21.1670i | 0.0579916i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.4050 | −0.0719482 | −0.0359741 | − | 0.999353i | \(-0.511453\pi\) | ||||
−0.0359741 | + | 0.999353i | \(0.511453\pi\) | |||||||
\(368\) | 6.14134i | 0.0166884i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 235.723 | 0.637090 | ||||||||
\(371\) | 36.0514i | 0.0971736i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −529.266 | −1.41894 | −0.709472 | − | 0.704734i | \(-0.751066\pi\) | ||||
−0.709472 | + | 0.704734i | \(0.751066\pi\) | |||||||
\(374\) | 330.596i | 0.883947i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 451.323 | 1.20033 | ||||||||
\(377\) | − 318.410i | − 0.844588i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −361.693 | −0.954336 | −0.477168 | − | 0.878812i | \(-0.658337\pi\) | ||||
−0.477168 | + | 0.878812i | \(0.658337\pi\) | |||||||
\(380\) | − 52.5581i | − 0.138311i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −335.780 | −0.879005 | ||||||||
\(383\) | 93.1447i | 0.243198i | 0.992579 | + | 0.121599i | \(0.0388021\pi\) | ||||
−0.992579 | + | 0.121599i | \(0.961198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.9755 | 0.0492869 | ||||||||
\(386\) | − 1077.30i | − 2.79095i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −136.676 | −0.352257 | ||||||||
\(389\) | − 205.427i | − 0.528091i | −0.964510 | − | 0.264045i | \(-0.914943\pi\) | ||||
0.964510 | − | 0.264045i | \(-0.0850569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −208.267 | −0.532651 | ||||||||
\(392\) | 345.721i | 0.881942i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 359.235 | 0.911764 | ||||||||
\(395\) | − 213.262i | − 0.539904i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 178.575 | 0.449812 | 0.224906 | − | 0.974380i | \(-0.427793\pi\) | ||||
0.224906 | + | 0.974380i | \(0.427793\pi\) | |||||||
\(398\) | 578.375i | 1.45320i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.4348 | −0.0285871 | ||||||||
\(401\) | 80.5359i | 0.200838i | 0.994945 | + | 0.100419i | \(0.0320183\pi\) | ||||
−0.994945 | + | 0.100419i | \(0.967982\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 679.542 | 1.68621 | ||||||||
\(404\) | − 1226.29i | − 3.03538i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 145.941 | 0.359459 | ||||||||
\(407\) | 303.683i | 0.746149i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −50.7083 | −0.123981 | −0.0619906 | − | 0.998077i | \(-0.519745\pi\) | ||||
−0.0619906 | + | 0.998077i | \(0.519745\pi\) | |||||||
\(410\) | 212.643i | 0.518641i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −175.075 | −0.424939 | ||||||||
\(413\) | 241.191i | 0.583997i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −86.2923 | −0.207933 | ||||||||
\(416\) | − 498.589i | − 1.19853i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 109.925 | 0.262978 | ||||||||
\(419\) | − 421.505i | − 1.00598i | −0.864292 | − | 0.502990i | \(-0.832233\pi\) | ||||
0.864292 | − | 0.502990i | \(-0.167767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 126.531 | 0.300548 | 0.150274 | − | 0.988644i | \(-0.451984\pi\) | ||||
0.150274 | + | 0.988644i | \(0.451984\pi\) | |||||||
\(422\) | − 683.298i | − 1.61919i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 130.213 | 0.307107 | ||||||||
\(425\) | − 387.781i | − 0.912426i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −221.576 | −0.518913 | ||||||||
\(428\) | 495.097i | 1.15677i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 298.558 | 0.694321 | ||||||||
\(431\) | − 69.7232i | − 0.161771i | −0.996723 | − | 0.0808854i | \(-0.974225\pi\) | ||||
0.996723 | − | 0.0808854i | \(-0.0257748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 433.061 | 1.00014 | 0.500070 | − | 0.865985i | \(-0.333308\pi\) | ||||
0.500070 | + | 0.865985i | \(0.333308\pi\) | |||||||
\(434\) | 311.462i | 0.717656i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.60477 | 0.0220293 | ||||||||
\(437\) | 69.2497i | 0.158466i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 730.260 | 1.66346 | 0.831731 | − | 0.555179i | \(-0.187350\pi\) | ||||
0.831731 | + | 0.555179i | \(0.187350\pi\) | |||||||
\(440\) | − 68.5370i | − 0.155766i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 831.238 | 1.88063 | ||||||||
\(443\) | − 113.431i | − 0.256053i | −0.991771 | − | 0.128026i | \(-0.959136\pi\) | ||||
0.991771 | − | 0.128026i | \(-0.0408642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8681 | 0.0356586 | ||||||||
\(446\) | 815.948i | 1.82948i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 224.210 | 0.500468 | ||||||||
\(449\) | − 372.379i | − 0.829352i | −0.909969 | − | 0.414676i | \(-0.863895\pi\) | ||||
0.909969 | − | 0.414676i | \(-0.136105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −273.948 | −0.607424 | ||||||||
\(452\) | − 841.733i | − 1.86224i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 519.582 | 1.14445 | ||||||||
\(455\) | − 47.7112i | − 0.104860i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −525.639 | −1.15020 | −0.575098 | − | 0.818085i | \(-0.695036\pi\) | ||||
−0.575098 | + | 0.818085i | \(0.695036\pi\) | |||||||
\(458\) | 54.2283i | 0.118402i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 114.663 | 0.249267 | ||||||||
\(461\) | − 86.0937i | − 0.186754i | −0.995631 | − | 0.0933771i | \(-0.970234\pi\) | ||||
0.995631 | − | 0.0933771i | \(-0.0297662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 395.423 | 0.854046 | 0.427023 | − | 0.904241i | \(-0.359562\pi\) | ||||
0.427023 | + | 0.904241i | \(0.359562\pi\) | |||||||
\(464\) | 10.4662i | 0.0225566i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 181.479 | 0.389440 | ||||||||
\(467\) | − 398.158i | − 0.852587i | −0.904585 | − | 0.426294i | \(-0.859819\pi\) | ||||
0.904585 | − | 0.426294i | \(-0.140181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −150.189 | −0.320233 | ||||||||
\(470\) | 271.624i | 0.577924i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 871.151 | 1.84566 | ||||||||
\(473\) | 384.633i | 0.813177i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −128.939 | −0.271451 | ||||||||
\(476\) | 234.680i | 0.493026i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1179.89 | −2.46839 | ||||||||
\(479\) | − 298.231i | − 0.622611i | −0.950310 | − | 0.311305i | \(-0.899234\pi\) | ||||
0.950310 | − | 0.311305i | \(-0.100766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 763.568 | 1.58746 | ||||||||
\(482\) | − 1015.11i | − 2.10605i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −541.839 | −1.11950 | ||||||||
\(485\) | − 30.9739i | − 0.0638637i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.07802 | 0.00837376 | 0.00418688 | − | 0.999991i | \(-0.498667\pi\) | ||||
0.00418688 | + | 0.999991i | \(0.498667\pi\) | |||||||
\(488\) | 800.304i | 1.63997i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −208.069 | −0.424630 | ||||||||
\(491\) | 515.872i | 1.05065i | 0.850900 | + | 0.525327i | \(0.176057\pi\) | ||||
−0.850900 | + | 0.525327i | \(0.823943\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −354.934 | −0.719947 | ||||||||
\(494\) | − 276.391i | − 0.559496i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.3368 | −0.0450338 | ||||||||
\(497\) | − 188.489i | − 0.379254i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.3742 | −0.0528541 | −0.0264270 | − | 0.999651i | \(-0.508413\pi\) | ||||
−0.0264270 | + | 0.999651i | \(0.508413\pi\) | |||||||
\(500\) | 446.714i | 0.893429i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1335.57 | −2.66049 | ||||||||
\(503\) | − 11.6037i | − 0.0230690i | −0.999933 | − | 0.0115345i | \(-0.996328\pi\) | ||||
0.999933 | − | 0.0115345i | \(-0.00367163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 277.907 | 0.550310 | ||||||||
\(506\) | 239.817i | 0.473946i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 72.3038 | 0.142330 | ||||||||
\(509\) | − 623.478i | − 1.22491i | −0.790506 | − | 0.612454i | \(-0.790182\pi\) | ||||
0.790506 | − | 0.612454i | \(-0.209818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.4263 | −0.0614997 | ||||||||
\(512\) | 31.9719i | 0.0624451i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 419.218 | 0.815598 | ||||||||
\(515\) | − 39.6760i | − 0.0770408i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −349.934 | −0.676855 | ||||||||
\(518\) | 349.975i | 0.675628i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −172.327 | −0.331398 | ||||||||
\(521\) | − 126.020i | − 0.241881i | −0.992660 | − | 0.120941i | \(-0.961409\pi\) | ||||
0.992660 | − | 0.120941i | \(-0.0385911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 272.380 | 0.520802 | 0.260401 | − | 0.965500i | \(-0.416145\pi\) | ||||
0.260401 | + | 0.965500i | \(0.416145\pi\) | |||||||
\(524\) | − 917.694i | − 1.75132i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1275.84 | 2.42555 | ||||||||
\(527\) | − 757.490i | − 1.43736i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 377.922 | 0.714408 | ||||||||
\(530\) | 78.3674i | 0.147863i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 78.0324 | 0.146677 | ||||||||
\(533\) | 688.805i | 1.29232i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −112.200 | −0.209721 | ||||||||
\(536\) | 542.465i | 1.01206i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1369.82 | 2.54613 | ||||||||
\(539\) | − 268.055i | − 0.497320i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −893.640 | −1.65183 | −0.825915 | − | 0.563795i | \(-0.809341\pi\) | ||||
−0.825915 | + | 0.563795i | \(0.809341\pi\) | |||||||
\(542\) | − 956.915i | − 1.76553i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −555.781 | −1.02166 | ||||||||
\(545\) | 2.17666i | 0.00399388i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 271.399 | 0.496158 | 0.248079 | − | 0.968740i | \(-0.420201\pi\) | ||||
0.248079 | + | 0.968740i | \(0.420201\pi\) | |||||||
\(548\) | − 31.1211i | − 0.0567904i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −446.526 | −0.811866 | ||||||||
\(551\) | 118.017i | 0.214187i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 316.628 | 0.572564 | ||||||||
\(554\) | − 361.209i | − 0.652002i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −741.183 | −1.33306 | ||||||||
\(557\) | − 356.461i | − 0.639967i | −0.947423 | − | 0.319983i | \(-0.896323\pi\) | ||||
0.947423 | − | 0.319983i | \(-0.103677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 967.106 | 1.73007 | ||||||||
\(560\) | 1.56828i | 0.00280051i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −655.045 | −1.16556 | ||||||||
\(563\) | − 255.522i | − 0.453858i | −0.973911 | − | 0.226929i | \(-0.927131\pi\) | ||||
0.973911 | − | 0.226929i | \(-0.0728686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 190.756 | 0.337622 | ||||||||
\(566\) | 67.2993i | 0.118903i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −680.799 | −1.19859 | ||||||||
\(569\) | − 182.702i | − 0.321093i | −0.987028 | − | 0.160547i | \(-0.948674\pi\) | ||||
0.987028 | − | 0.160547i | \(-0.0513257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 159.637 | 0.279574 | 0.139787 | − | 0.990182i | \(-0.455358\pi\) | ||||
0.139787 | + | 0.990182i | \(0.455358\pi\) | |||||||
\(572\) | − 589.586i | − 1.03074i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −315.708 | −0.550014 | ||||||||
\(575\) | − 281.299i | − 0.489216i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −920.566 | −1.59543 | −0.797717 | − | 0.603031i | \(-0.793959\pi\) | ||||
−0.797717 | + | 0.603031i | \(0.793959\pi\) | |||||||
\(578\) | 6.12239i | 0.0105924i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 195.412 | 0.336917 | ||||||||
\(581\) | − 128.117i | − 0.220511i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −100.961 | −0.173175 | ||||||||
\(584\) | 113.508i | 0.194363i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1633.60 | −2.78772 | ||||||||
\(587\) | − 790.574i | − 1.34680i | −0.739276 | − | 0.673402i | \(-0.764832\pi\) | ||||
0.739276 | − | 0.673402i | \(-0.235168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −251.869 | −0.427622 | ||||||||
\(590\) | 524.293i | 0.888633i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25.0988 | −0.0423966 | ||||||||
\(593\) | 42.5943i | 0.0718285i | 0.999355 | + | 0.0359142i | \(0.0114343\pi\) | ||||
−0.999355 | + | 0.0359142i | \(0.988566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −53.1840 | −0.0893849 | ||||||||
\(596\) | − 652.255i | − 1.09439i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 602.987 | 1.00834 | ||||||||
\(599\) | − 532.138i | − 0.888378i | −0.895933 | − | 0.444189i | \(-0.853492\pi\) | ||||
0.895933 | − | 0.444189i | \(-0.146508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6373 | −0.0343382 | −0.0171691 | − | 0.999853i | \(-0.505465\pi\) | ||||
−0.0171691 | + | 0.999853i | \(0.505465\pi\) | |||||||
\(602\) | 443.265i | 0.736321i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −947.480 | −1.56868 | ||||||||
\(605\) | − 122.793i | − 0.202964i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 611.889 | 1.00805 | 0.504027 | − | 0.863688i | \(-0.331851\pi\) | ||||
0.504027 | + | 0.863688i | \(0.331851\pi\) | |||||||
\(608\) | 184.800i | 0.303947i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −481.655 | −0.789598 | ||||||||
\(611\) | 879.861i | 1.44003i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 939.218 | 1.53217 | 0.766083 | − | 0.642742i | \(-0.222203\pi\) | ||||
0.766083 | + | 0.642742i | \(0.222203\pi\) | |||||||
\(614\) | 1441.74i | 2.34810i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 101.756 | 0.165188 | ||||||||
\(617\) | 1182.83i | 1.91707i | 0.284978 | + | 0.958534i | \(0.408014\pi\) | ||||
−0.284978 | + | 0.958534i | \(0.591986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −535.727 | −0.865472 | −0.432736 | − | 0.901521i | \(-0.642452\pi\) | ||||
−0.432736 | + | 0.901521i | \(0.642452\pi\) | |||||||
\(620\) | 417.043i | 0.672650i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1688.73 | 2.71500 | ||||||||
\(623\) | 23.5592i | 0.0378157i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 470.911 | 0.753458 | ||||||||
\(626\) | 1145.26i | 1.82950i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 204.485 | 0.325614 | ||||||||
\(629\) | − 851.155i | − 1.35319i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −517.306 | −0.819819 | −0.409910 | − | 0.912126i | \(-0.634440\pi\) | ||||
−0.409910 | + | 0.912126i | \(0.634440\pi\) | |||||||
\(632\) | − 1143.62i | − 1.80952i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1249.97 | 1.97156 | ||||||||
\(635\) | 16.3857i | 0.0258043i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −673.988 | −1.05807 | ||||||||
\(638\) | 408.703i | 0.640600i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 296.611 | 0.463455 | ||||||||
\(641\) | − 289.081i | − 0.450984i | −0.974245 | − | 0.225492i | \(-0.927601\pi\) | ||||
0.974245 | − | 0.225492i | \(-0.0723989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −311.244 | −0.484050 | −0.242025 | − | 0.970270i | \(-0.577812\pi\) | ||||
−0.242025 | + | 0.970270i | \(0.577812\pi\) | |||||||
\(644\) | 170.239i | 0.264346i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −308.095 | −0.476928 | ||||||||
\(647\) | − 764.050i | − 1.18091i | −0.807070 | − | 0.590456i | \(-0.798948\pi\) | ||||
0.807070 | − | 0.590456i | \(-0.201052\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −675.449 | −1.04075 | ||||||||
\(650\) | 1122.73i | 1.72727i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 56.3105 | 0.0863659 | ||||||||
\(653\) | − 442.765i | − 0.678047i | −0.940778 | − | 0.339023i | \(-0.889903\pi\) | ||||
0.940778 | − | 0.339023i | \(-0.110097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 207.971 | 0.317513 | ||||||||
\(656\) | − 22.6413i | − 0.0345141i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −403.277 | −0.612883 | ||||||||
\(659\) | 67.8358i | 0.102937i | 0.998675 | + | 0.0514687i | \(0.0163903\pi\) | ||||
−0.998675 | + | 0.0514687i | \(0.983610\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 776.372 | 1.17454 | 0.587271 | − | 0.809391i | \(-0.300202\pi\) | ||||
0.587271 | + | 0.809391i | \(0.300202\pi\) | |||||||
\(662\) | − 859.929i | − 1.29899i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −462.743 | −0.696902 | ||||||||
\(665\) | 17.6840i | 0.0265924i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −257.472 | −0.386014 | ||||||||
\(668\) | 751.995i | 1.12574i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −326.477 | −0.487279 | ||||||||
\(671\) | − 620.517i | − 0.924765i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1207.59 | −1.79434 | −0.897172 | − | 0.441681i | \(-0.854382\pi\) | ||||
−0.897172 | + | 0.441681i | \(0.854382\pi\) | |||||||
\(674\) | 1793.23i | 2.66058i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −398.142 | −0.588967 | ||||||||
\(677\) | 920.516i | 1.35970i | 0.733352 | + | 0.679849i | \(0.237955\pi\) | ||||
−0.733352 | + | 0.679849i | \(0.762045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.9866 | 0.0677270 | ||||||||
\(680\) | 192.094i | 0.282491i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −872.242 | −1.27895 | ||||||||
\(683\) | 382.840i | 0.560528i | 0.959923 | + | 0.280264i | \(0.0904220\pi\) | ||||
−0.959923 | + | 0.280264i | \(0.909578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.05277 | 0.0102960 | ||||||||
\(686\) | − 650.302i | − 0.947961i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −31.7891 | −0.0462051 | ||||||||
\(689\) | 253.852i | 0.368436i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −678.861 | −0.982433 | −0.491217 | − | 0.871037i | \(-0.663448\pi\) | ||||
−0.491217 | + | 0.871037i | \(0.663448\pi\) | |||||||
\(692\) | 1322.31i | 1.91086i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −166.460 | −0.239856 | ||||||||
\(695\) | − 167.969i | − 0.241682i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 767.816 | 1.10160 | ||||||||
\(698\) | 1916.41i | 2.74557i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −316.975 | −0.452822 | ||||||||
\(701\) | − 684.318i | − 0.976202i | −0.872787 | − | 0.488101i | \(-0.837690\pi\) | ||||
0.872787 | − | 0.488101i | \(-0.162310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −283.014 | −0.402580 | ||||||||
\(704\) | 627.894i | 0.891894i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1488.32 | −2.10810 | ||||||||
\(707\) | 412.605i | 0.583599i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1302.62 | −1.83727 | −0.918633 | − | 0.395112i | \(-0.870706\pi\) | ||||
−0.918633 | + | 0.395112i | \(0.870706\pi\) | |||||||
\(710\) | − 409.732i | − 0.577087i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 85.0928 | 0.119512 | ||||||||
\(713\) | − 549.489i | − 0.770672i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 133.614 | 0.186873 | ||||||||
\(716\) | 733.023i | 1.02377i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −745.890 | −1.03884 | ||||||||
\(719\) | 733.683i | 1.02042i | 0.860050 | + | 0.510210i | \(0.170432\pi\) | ||||
−0.860050 | + | 0.510210i | \(0.829568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 58.9065 | 0.0817011 | ||||||||
\(722\) | − 1062.64i | − 1.47180i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2054.58 | −2.83782 | ||||||||
\(725\) | − 479.398i | − 0.661239i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −509.080 | −0.700247 | −0.350123 | − | 0.936704i | \(-0.613860\pi\) | ||||
−0.350123 | + | 0.936704i | \(0.613860\pi\) | |||||||
\(728\) | − 255.852i | − 0.351445i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −68.3136 | −0.0935803 | ||||||||
\(731\) | − 1078.04i | − 1.47475i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1281.50 | −1.74830 | −0.874149 | − | 0.485658i | \(-0.838580\pi\) | ||||
−0.874149 | + | 0.485658i | \(0.838580\pi\) | |||||||
\(734\) | − 85.2186i | − 0.116102i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −403.168 | −0.547782 | ||||||||
\(737\) | − 420.601i | − 0.570694i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −651.069 | −0.881013 | −0.440507 | − | 0.897749i | \(-0.645201\pi\) | ||||
−0.440507 | + | 0.897749i | \(0.645201\pi\) | |||||||
\(740\) | 468.611i | 0.633258i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −116.351 | −0.156808 | ||||||||
\(743\) | − 1290.81i | − 1.73730i | −0.495429 | − | 0.868649i | \(-0.664989\pi\) | ||||
0.495429 | − | 0.868649i | \(-0.335011\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 147.816 | 0.198411 | ||||||||
\(746\) | − 1708.14i | − 2.28973i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −657.216 | −0.878631 | ||||||||
\(749\) | − 166.583i | − 0.222407i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1270.00 | −1.69107 | −0.845536 | − | 0.533918i | \(-0.820719\pi\) | ||||
−0.845536 | + | 0.533918i | \(0.820719\pi\) | |||||||
\(752\) | − 28.9213i | − 0.0384592i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1027.63 | 1.36290 | ||||||||
\(755\) | − 214.721i | − 0.284399i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −835.003 | −1.10304 | −0.551521 | − | 0.834161i | \(-0.685952\pi\) | ||||
−0.551521 | + | 0.834161i | \(0.685952\pi\) | |||||||
\(758\) | − 1167.32i | − 1.54000i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 63.8722 | 0.0840424 | ||||||||
\(761\) | 907.753i | 1.19284i | 0.802672 | + | 0.596421i | \(0.203411\pi\) | ||||
−0.802672 | + | 0.596421i | \(0.796589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.23167 | −0.00423548 | ||||||||
\(764\) | − 667.521i | − 0.873719i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −300.613 | −0.392445 | ||||||||
\(767\) | 1698.32i | 2.21424i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −396.941 | −0.516178 | −0.258089 | − | 0.966121i | \(-0.583093\pi\) | ||||
−0.258089 | + | 0.966121i | \(0.583093\pi\) | |||||||
\(770\) | 61.2408i | 0.0795335i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2141.65 | 2.77416 | ||||||||
\(773\) | 1381.35i | 1.78700i | 0.449059 | + | 0.893502i | \(0.351759\pi\) | ||||
−0.449059 | + | 0.893502i | \(0.648241\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1023.12 | 1.32015 | ||||||||
\(776\) | − 166.098i | − 0.214044i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 662.990 | 0.852172 | ||||||||
\(779\) | − 255.303i | − 0.327731i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 527.859 | 0.675875 | ||||||||
\(782\) | − 672.154i | − 0.859532i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.1542 | 0.0282580 | ||||||||
\(785\) | 46.3412i | 0.0590333i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −113.599 | −0.144344 | −0.0721722 | − | 0.997392i | \(-0.522993\pi\) | ||||
−0.0721722 | + | 0.997392i | \(0.522993\pi\) | |||||||
\(788\) | 714.149i | 0.906281i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 688.276 | 0.871235 | ||||||||
\(791\) | 283.214i | 0.358045i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1560.20 | −1.96747 | ||||||||
\(794\) | 576.329i | 0.725855i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1149.79 | −1.44446 | ||||||||
\(797\) | 81.8545i | 0.102703i | 0.998681 | + | 0.0513516i | \(0.0163529\pi\) | ||||
−0.998681 | + | 0.0513516i | \(0.983647\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 980.788 | 1.22752 | ||||||||
\(800\) | − 750.676i | − 0.938345i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −259.919 | −0.324089 | ||||||||
\(803\) | − 88.0086i | − 0.109600i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.5801 | −0.0479256 | ||||||||
\(806\) | 2193.13i | 2.72101i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1490.28 | 1.84440 | ||||||||
\(809\) | − 330.667i | − 0.408735i | −0.978894 | − | 0.204368i | \(-0.934486\pi\) | ||||
0.978894 | − | 0.204368i | \(-0.0655138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1106.38 | −1.36422 | −0.682110 | − | 0.731249i | \(-0.738938\pi\) | ||||
−0.682110 | + | 0.731249i | \(0.738938\pi\) | |||||||
\(812\) | 290.126i | 0.357298i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −980.097 | −1.20405 | ||||||||
\(815\) | 12.7613i | 0.0156580i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −358.454 | −0.438744 | ||||||||
\(818\) | − 163.655i | − 0.200067i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −422.728 | −0.515521 | ||||||||
\(821\) | 1212.58i | 1.47696i | 0.674276 | + | 0.738479i | \(0.264456\pi\) | ||||
−0.674276 | + | 0.738479i | \(0.735544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 384.766 | 0.467517 | 0.233759 | − | 0.972295i | \(-0.424897\pi\) | ||||
0.233759 | + | 0.972295i | \(0.424897\pi\) | |||||||
\(824\) | − 212.763i | − 0.258207i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −778.412 | −0.942388 | ||||||||
\(827\) | − 836.135i | − 1.01105i | −0.862813 | − | 0.505523i | \(-0.831300\pi\) | ||||
0.862813 | − | 0.505523i | \(-0.168700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1008.06 | −1.21599 | −0.607995 | − | 0.793941i | \(-0.708026\pi\) | ||||
−0.607995 | + | 0.793941i | \(0.708026\pi\) | |||||||
\(830\) | − 278.497i | − 0.335539i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1578.75 | 1.89754 | ||||||||
\(833\) | 751.300i | 0.901921i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −170.419 | −0.204095 | ||||||||
\(836\) | 218.528i | 0.261397i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1360.35 | 1.62333 | ||||||||
\(839\) | − 788.289i | − 0.939558i | −0.882784 | − | 0.469779i | \(-0.844334\pi\) | ||||
0.882784 | − | 0.469779i | \(-0.155666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 402.210 | 0.478252 | ||||||||
\(842\) | 408.361i | 0.484990i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1358.38 | 1.60945 | ||||||||
\(845\) | − 90.2281i | − 0.106779i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 182.310 | 0.215242 | ||||||||
\(848\) | − 8.34422i | − 0.00983988i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1251.51 | 1.47237 | ||||||||
\(851\) | − 617.434i | − 0.725540i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −355.835 | −0.417157 | −0.208579 | − | 0.978006i | \(-0.566884\pi\) | ||||
−0.208579 | + | 0.978006i | \(0.566884\pi\) | |||||||
\(854\) | − 715.107i | − 0.837362i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −601.676 | −0.702893 | ||||||||
\(857\) | − 160.752i | − 0.187576i | −0.995592 | − | 0.0937878i | \(-0.970102\pi\) | ||||
0.995592 | − | 0.0937878i | \(-0.0298975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 378.660 | 0.440815 | 0.220408 | − | 0.975408i | \(-0.429261\pi\) | ||||
0.220408 | + | 0.975408i | \(0.429261\pi\) | |||||||
\(860\) | 593.525i | 0.690145i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 225.023 | 0.261047 | ||||||||
\(863\) | 116.099i | 0.134529i | 0.997735 | + | 0.0672646i | \(0.0214272\pi\) | ||||
−0.997735 | + | 0.0672646i | \(0.978573\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −299.667 | −0.346436 | ||||||||
\(866\) | 1397.65i | 1.61391i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −619.179 | −0.713339 | ||||||||
\(869\) | 886.707i | 1.02038i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1057.54 | −1.21417 | ||||||||
\(872\) | 11.6724i | 0.0133858i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −223.495 | −0.255715 | ||||||||
\(875\) | − 150.304i | − 0.171776i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.0296 | −0.0239790 | −0.0119895 | − | 0.999928i | \(-0.503816\pi\) | ||||
−0.0119895 | + | 0.999928i | \(0.503816\pi\) | |||||||
\(878\) | 2356.82i | 2.68430i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.39193 | −0.00499083 | ||||||||
\(881\) | 176.808i | 0.200690i | 0.994953 | + | 0.100345i | \(0.0319947\pi\) | ||||
−0.994953 | + | 0.100345i | \(0.968005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1552.93 | 1.75870 | 0.879349 | − | 0.476177i | \(-0.157978\pi\) | ||||
0.879349 | + | 0.476177i | \(0.157978\pi\) | |||||||
\(884\) | 1652.48i | 1.86932i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 366.085 | 0.413189 | ||||||||
\(887\) | − 1436.68i | − 1.61971i | −0.586631 | − | 0.809854i | \(-0.699546\pi\) | ||||
0.586631 | − | 0.809854i | \(-0.300454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.3277 | −0.0273652 | ||||||||
\(890\) | 51.2122i | 0.0575418i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1622.08 | −1.81848 | ||||||||
\(893\) | − 326.117i | − 0.365193i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −166.120 | −0.185609 | ||||||||
\(896\) | 440.376i | 0.491491i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1201.80 | 1.33831 | ||||||||
\(899\) | − 936.454i | − 1.04166i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 282.971 | 0.314064 | ||||||||
\(902\) | − 884.132i | − 0.980191i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1022.93 | 1.13156 | ||||||||
\(905\) | − 465.616i | − 0.514492i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1361.80 | −1.50144 | −0.750718 | − | 0.660623i | \(-0.770292\pi\) | ||||
−0.750718 | + | 0.660623i | \(0.770292\pi\) | |||||||
\(908\) | 1032.91i | 1.13757i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 153.982 | 0.169211 | ||||||||
\(911\) | 1434.07i | 1.57417i | 0.616844 | + | 0.787085i | \(0.288411\pi\) | ||||
−0.616844 | + | 0.787085i | \(0.711589\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 358.789 | 0.392978 | ||||||||
\(914\) | − 1696.43i | − 1.85605i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −107.804 | −0.117690 | ||||||||
\(917\) | 308.772i | 0.336720i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 752.268 | 0.818573 | 0.409286 | − | 0.912406i | \(-0.365778\pi\) | ||||
0.409286 | + | 0.912406i | \(0.365778\pi\) | |||||||
\(920\) | 139.346i | 0.151463i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 277.856 | 0.301363 | ||||||||
\(923\) | − 1327.23i | − 1.43795i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1149.63 | 1.24284 | ||||||||
\(926\) | 1276.18i | 1.37816i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −687.089 | −0.740398 | ||||||||
\(929\) | 74.4733i | 0.0801650i | 0.999196 | + | 0.0400825i | \(0.0127621\pi\) | ||||
−0.999196 | + | 0.0400825i | \(0.987238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 249.811 | 0.268326 | ||||||||
\(932\) | 360.775i | 0.387098i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1285.00 | 1.37581 | ||||||||
\(935\) | − 148.940i | − 0.159294i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 363.649 | 0.388099 | 0.194050 | − | 0.980992i | \(-0.437838\pi\) | ||||
0.194050 | + | 0.980992i | \(0.437838\pi\) | |||||||
\(938\) | − 484.717i | − 0.516756i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −539.981 | −0.574448 | ||||||||
\(941\) | 201.166i | 0.213779i | 0.994271 | + | 0.106890i | \(0.0340892\pi\) | ||||
−0.994271 | + | 0.106890i | \(0.965911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 556.979 | 0.590646 | ||||||||
\(944\) | − 55.8244i | − 0.0591361i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1241.35 | −1.31221 | ||||||||
\(947\) | 1001.85i | 1.05792i | 0.848647 | + | 0.528959i | \(0.177418\pi\) | ||||
−0.848647 | + | 0.528959i | \(0.822582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −221.285 | −0.233177 | ||||||||
\(950\) | − 416.135i | − 0.438037i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −285.200 | −0.299580 | ||||||||
\(953\) | 1431.96i | 1.50258i | 0.659971 | + | 0.751291i | \(0.270568\pi\) | ||||
−0.659971 | + | 0.751291i | \(0.729432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 151.276 | 0.158404 | ||||||||
\(956\) | − 2345.59i | − 2.45355i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 962.500 | 1.00470 | ||||||||
\(959\) | 10.4712i | 0.0109188i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1037.56 | 1.07966 | ||||||||
\(962\) | 2464.32i | 2.56166i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2018.02 | 2.09338 | ||||||||
\(965\) | 485.348i | 0.502951i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 812.242 | 0.839961 | 0.419980 | − | 0.907533i | \(-0.362037\pi\) | ||||
0.419980 | + | 0.907533i | \(0.362037\pi\) | |||||||
\(968\) | − 658.480i | − 0.680248i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 99.9643 | 0.103056 | ||||||||
\(971\) | − 1589.54i | − 1.63701i | −0.574496 | − | 0.818507i | \(-0.694802\pi\) | ||||
0.574496 | − | 0.818507i | \(-0.305198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 249.382 | 0.256302 | ||||||||
\(974\) | 13.1613i | 0.0135126i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 51.2845 | 0.0525456 | ||||||||
\(977\) | 1147.24i | 1.17425i | 0.809495 | + | 0.587126i | \(0.199741\pi\) | ||||
−0.809495 | + | 0.587126i | \(0.800259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −65.9768 | −0.0673920 | ||||||||
\(980\) | − 413.635i | − 0.422076i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1664.91 | −1.69543 | ||||||||
\(983\) | 1293.14i | 1.31551i | 0.753234 | + | 0.657753i | \(0.228493\pi\) | ||||
−0.753234 | + | 0.657753i | \(0.771507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −161.843 | −0.164307 | ||||||||
\(986\) | − 1145.50i | − 1.16177i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 549.458 | 0.556131 | ||||||||
\(989\) | − 782.019i | − 0.790717i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −605.355 | −0.610852 | −0.305426 | − | 0.952216i | \(-0.598799\pi\) | ||||
−0.305426 | + | 0.952216i | \(0.598799\pi\) | |||||||
\(992\) | − 1466.37i | − 1.47819i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 608.324 | 0.611996 | ||||||||
\(995\) | − 260.570i | − 0.261879i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 927.609 | 0.930400 | 0.465200 | − | 0.885206i | \(-0.345982\pi\) | ||||
0.465200 | + | 0.885206i | \(0.345982\pi\) | |||||||
\(998\) | − 85.1193i | − 0.0852898i | ||||||||
\(999\) | 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.890.76 | yes | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.9 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.9 | ✓ | 84 | 3.2 | odd | 2 | inner | |
1143.3.b.a.890.76 | yes | 84 | 1.1 | even | 1 | trivial |