Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.a (trivial) |
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: | yes |
Analytic conductor: | \(31.6926245622\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.59351616.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 21x^{2} - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.15750\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.239123 | 0.169086 | 0.0845428 | − | 0.996420i | \(-0.473057\pi\) | ||||
0.0845428 | + | 0.996420i | \(0.473057\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94282 | −0.971410 | ||||||||
\(5\) | 2.59179 | 1.15908 | 0.579542 | − | 0.814943i | \(-0.303232\pi\) | ||||
0.579542 | + | 0.814943i | \(0.303232\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.942820 | −0.333337 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.619757 | 0.195984 | ||||||||
\(11\) | 4.18194 | 1.26090 | 0.630452 | − | 0.776228i | \(-0.282870\pi\) | ||||
0.630452 | + | 0.776228i | \(0.282870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.68310 | −1.02151 | −0.510755 | − | 0.859726i | \(-0.670634\pi\) | ||||
−0.510755 | + | 0.859726i | \(0.670634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.66019 | 0.915047 | ||||||||
\(17\) | −1.71107 | −0.414996 | −0.207498 | − | 0.978235i | \(-0.566532\pi\) | ||||
−0.207498 | + | 0.978235i | \(0.566532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.15561 | 1.64161 | 0.820805 | − | 0.571209i | \(-0.193525\pi\) | ||||
0.820805 | + | 0.571209i | \(0.193525\pi\) | |||||||
\(20\) | −5.03538 | −1.12595 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.12476 | −1.06859 | −0.534294 | − | 0.845299i | \(-0.679422\pi\) | ||||
−0.534294 | + | 0.845299i | \(0.679422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.71737 | 0.343474 | ||||||||
\(26\) | −0.880716 | −0.172723 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.12476 | −0.394559 | −0.197279 | − | 0.980347i | \(-0.563211\pi\) | ||||
−0.197279 | + | 0.980347i | \(0.563211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.53585 | 1.17387 | 0.586937 | − | 0.809633i | \(-0.300334\pi\) | ||||
0.586937 | + | 0.809633i | \(0.300334\pi\) | |||||||
\(32\) | 2.76088 | 0.488059 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.409157 | −0.0701699 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.66019 | 0.272934 | 0.136467 | − | 0.990645i | \(-0.456425\pi\) | ||||
0.136467 | + | 0.990645i | \(0.456425\pi\) | |||||||
\(38\) | 1.71107 | 0.277573 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.44359 | −0.386366 | ||||||||
\(41\) | 10.2190 | 1.59593 | 0.797967 | − | 0.602702i | \(-0.205909\pi\) | ||||
0.797967 | + | 0.602702i | \(0.205909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66019 | −0.253177 | −0.126588 | − | 0.991955i | \(-0.540403\pi\) | ||||
−0.126588 | + | 0.991955i | \(0.540403\pi\) | |||||||
\(44\) | −8.12476 | −1.22485 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.22545 | −0.180683 | ||||||||
\(47\) | −9.33824 | −1.36212 | −0.681061 | − | 0.732226i | \(-0.738481\pi\) | ||||
−0.681061 | + | 0.732226i | \(0.738481\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.410663 | 0.0580765 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.15561 | 0.992305 | ||||||||
\(53\) | 10.6465 | 1.46241 | 0.731206 | − | 0.682157i | \(-0.238958\pi\) | ||||
0.731206 | + | 0.682157i | \(0.238958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8387 | 1.46149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.508080 | −0.0667142 | ||||||||
\(59\) | −6.06429 | −0.789504 | −0.394752 | − | 0.918788i | \(-0.629169\pi\) | ||||
−0.394752 | + | 0.918788i | \(0.629169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.98597 | 1.02250 | 0.511249 | − | 0.859433i | \(-0.329183\pi\) | ||||
0.511249 | + | 0.859433i | \(0.329183\pi\) | |||||||
\(62\) | 1.56287 | 0.198485 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.66019 | −0.832524 | ||||||||
\(65\) | −9.54583 | −1.18401 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.26320 | 1.00951 | 0.504755 | − | 0.863262i | \(-0.331583\pi\) | ||||
0.504755 | + | 0.863262i | \(0.331583\pi\) | |||||||
\(68\) | 3.32431 | 0.403131 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.23912 | 0.740448 | 0.370224 | − | 0.928943i | \(-0.379281\pi\) | ||||
0.370224 | + | 0.928943i | \(0.379281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.15561 | −0.837501 | −0.418750 | − | 0.908101i | \(-0.637532\pi\) | ||||
−0.418750 | + | 0.908101i | \(0.637532\pi\) | |||||||
\(74\) | 0.396990 | 0.0461492 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.9021 | −1.59468 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.82846 | −1.10579 | −0.552894 | − | 0.833252i | \(-0.686477\pi\) | ||||
−0.552894 | + | 0.833252i | \(0.686477\pi\) | |||||||
\(80\) | 9.48644 | 1.06062 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.44359 | 0.269849 | ||||||||
\(83\) | −6.89465 | −0.756786 | −0.378393 | − | 0.925645i | \(-0.623523\pi\) | ||||
−0.378393 | + | 0.925645i | \(0.623523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.43474 | −0.481015 | ||||||||
\(86\) | −0.396990 | −0.0428085 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.94282 | −0.420306 | ||||||||
\(89\) | 5.03538 | 0.533749 | 0.266875 | − | 0.963731i | \(-0.414009\pi\) | ||||
0.266875 | + | 0.963731i | \(0.414009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.95649 | 1.03804 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.23299 | −0.230315 | ||||||||
\(95\) | 18.5458 | 1.90276 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.06335 | −0.311036 | −0.155518 | − | 0.987833i | \(-0.549705\pi\) | ||||
−0.155518 | + | 0.987833i | \(0.549705\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.33654 | −0.333654 | ||||||||
\(101\) | 11.0997 | 1.10446 | 0.552229 | − | 0.833692i | \(-0.313777\pi\) | ||||
0.552229 | + | 0.833692i | \(0.313777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.98597 | −0.786881 | −0.393440 | − | 0.919350i | \(-0.628715\pi\) | ||||
−0.393440 | + | 0.919350i | \(0.628715\pi\) | |||||||
\(104\) | 3.47250 | 0.340507 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.54583 | 0.247273 | ||||||||
\(107\) | 3.95649 | 0.382489 | 0.191244 | − | 0.981542i | \(-0.438748\pi\) | ||||
0.191244 | + | 0.981542i | \(0.438748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.26320 | 0.695688 | 0.347844 | − | 0.937552i | \(-0.386914\pi\) | ||||
0.347844 | + | 0.937552i | \(0.386914\pi\) | |||||||
\(110\) | 2.59179 | 0.247117 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.92915 | 0.651839 | 0.325920 | − | 0.945397i | \(-0.394326\pi\) | ||||
0.325920 | + | 0.945397i | \(0.394326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.2823 | −1.23858 | ||||||||
\(116\) | 4.12803 | 0.383278 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.45011 | −0.133494 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.48865 | 0.589877 | ||||||||
\(122\) | 1.90963 | 0.172890 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.6980 | −1.14031 | ||||||||
\(125\) | −8.50788 | −0.760968 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.11109 | 0.808479 | 0.404239 | − | 0.914653i | \(-0.367536\pi\) | ||||
0.404239 | + | 0.914653i | \(0.367536\pi\) | |||||||
\(128\) | −7.11436 | −0.628827 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.28263 | −0.200200 | ||||||||
\(131\) | 4.30286 | 0.375943 | 0.187971 | − | 0.982175i | \(-0.439809\pi\) | ||||
0.187971 | + | 0.982175i | \(0.439809\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.97592 | 0.170694 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.61323 | 0.138334 | ||||||||
\(137\) | 20.5893 | 1.75907 | 0.879533 | − | 0.475838i | \(-0.157855\pi\) | ||||
0.879533 | + | 0.475838i | \(0.157855\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7613 | 1.33686 | 0.668429 | − | 0.743776i | \(-0.266967\pi\) | ||||
0.668429 | + | 0.743776i | \(0.266967\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.49192 | 0.125199 | ||||||||
\(143\) | −15.4025 | −1.28802 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.50694 | −0.457326 | ||||||||
\(146\) | −1.71107 | −0.141609 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.22545 | −0.265130 | ||||||||
\(149\) | 6.06758 | 0.497076 | 0.248538 | − | 0.968622i | \(-0.420050\pi\) | ||||
0.248538 | + | 0.968622i | \(0.420050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.48865 | 0.365281 | 0.182641 | − | 0.983180i | \(-0.441536\pi\) | ||||
0.182641 | + | 0.983180i | \(0.441536\pi\) | |||||||
\(152\) | −6.74645 | −0.547210 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.9396 | 1.36062 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.02891 | −0.0821163 | −0.0410582 | − | 0.999157i | \(-0.513073\pi\) | ||||
−0.0410582 | + | 0.999157i | \(0.513073\pi\) | |||||||
\(158\) | −2.35021 | −0.186973 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.15561 | 0.565701 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.82846 | 0.534846 | 0.267423 | − | 0.963579i | \(-0.413828\pi\) | ||||
0.267423 | + | 0.963579i | \(0.413828\pi\) | |||||||
\(164\) | −19.8536 | −1.55031 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.64867 | −0.127962 | ||||||||
\(167\) | −17.9943 | −1.39244 | −0.696221 | − | 0.717827i | \(-0.745137\pi\) | ||||
−0.696221 | + | 0.717827i | \(0.745137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.565260 | 0.0434816 | ||||||||
\(170\) | −1.06045 | −0.0813328 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.22545 | 0.245938 | ||||||||
\(173\) | 0.830357 | 0.0631309 | 0.0315654 | − | 0.999502i | \(-0.489951\pi\) | ||||
0.0315654 | + | 0.999502i | \(0.489951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.3067 | 1.15379 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.20408 | 0.0902493 | ||||||||
\(179\) | 7.57893 | 0.566476 | 0.283238 | − | 0.959050i | \(-0.408591\pi\) | ||||
0.283238 | + | 0.959050i | \(0.408591\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.409157 | −0.0304124 | −0.0152062 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152062 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.83173 | 0.356200 | ||||||||
\(185\) | 4.30286 | 0.316353 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.15561 | −0.523270 | ||||||||
\(188\) | 18.1425 | 1.32318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.43474 | 0.321730 | ||||||||
\(191\) | 16.0241 | 1.15946 | 0.579731 | − | 0.814808i | \(-0.303158\pi\) | ||||
0.579731 | + | 0.814808i | \(0.303158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3743 | −0.890721 | −0.445360 | − | 0.895351i | \(-0.646924\pi\) | ||||
−0.445360 | + | 0.895351i | \(0.646924\pi\) | |||||||
\(194\) | −0.732518 | −0.0525917 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.1021 | 1.64595 | 0.822977 | − | 0.568075i | \(-0.192312\pi\) | ||||
0.822977 | + | 0.568075i | \(0.192312\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.74645 | 0.478243 | 0.239122 | − | 0.970990i | \(-0.423141\pi\) | ||||
0.239122 | + | 0.970990i | \(0.423141\pi\) | |||||||
\(200\) | −1.61917 | −0.114493 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.65419 | 0.186748 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.4854 | 1.84982 | ||||||||
\(206\) | −1.90963 | −0.133050 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.4809 | −0.934730 | ||||||||
\(209\) | 29.9244 | 2.06991 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8856 | 1.16246 | 0.581228 | − | 0.813741i | \(-0.302573\pi\) | ||||
0.581228 | + | 0.813741i | \(0.302573\pi\) | |||||||
\(212\) | −20.6843 | −1.42060 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.946090 | 0.0646734 | ||||||||
\(215\) | −4.30286 | −0.293453 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.73680 | 0.117631 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −21.0577 | −1.41971 | ||||||||
\(221\) | 6.30206 | 0.423922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50142 | 0.301437 | 0.150719 | − | 0.988577i | \(-0.451841\pi\) | ||||
0.150719 | + | 0.988577i | \(0.451841\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.65692 | 0.110217 | ||||||||
\(227\) | 6.06429 | 0.402501 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0493 | 0.730159 | 0.365080 | − | 0.930976i | \(-0.381042\pi\) | ||||
0.365080 | + | 0.930976i | \(0.381042\pi\) | |||||||
\(230\) | −3.17611 | −0.209426 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00327 | 0.131521 | ||||||||
\(233\) | −8.13844 | −0.533167 | −0.266583 | − | 0.963812i | \(-0.585895\pi\) | ||||
−0.266583 | + | 0.963812i | \(0.585895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.2028 | −1.57881 | ||||||||
\(236\) | 11.7818 | 0.766932 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1625 | 1.36889 | 0.684445 | − | 0.729065i | \(-0.260045\pi\) | ||||
0.684445 | + | 0.729065i | \(0.260045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6915 | −0.881945 | −0.440972 | − | 0.897521i | \(-0.645366\pi\) | ||||
−0.440972 | + | 0.897521i | \(0.645366\pi\) | |||||||
\(242\) | 1.55159 | 0.0997398 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.5153 | −0.993265 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.3549 | −1.67692 | ||||||||
\(248\) | −6.16213 | −0.391296 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.03443 | −0.128669 | ||||||||
\(251\) | −15.2040 | −0.959667 | −0.479833 | − | 0.877360i | \(-0.659303\pi\) | ||||
−0.479833 | + | 0.877360i | \(0.659303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.4315 | −1.34738 | ||||||||
\(254\) | 2.17867 | 0.136702 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.6192 | 0.726198 | ||||||||
\(257\) | −25.6215 | −1.59822 | −0.799112 | − | 0.601182i | \(-0.794697\pi\) | ||||
−0.799112 | + | 0.601182i | \(0.794697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.5458 | 1.15016 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.02891 | 0.0635665 | ||||||||
\(263\) | 7.10069 | 0.437847 | 0.218924 | − | 0.975742i | \(-0.429745\pi\) | ||||
0.218924 | + | 0.975742i | \(0.429745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.5935 | 1.69506 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.0539 | −0.980649 | ||||||||
\(269\) | 16.4314 | 1.00184 | 0.500922 | − | 0.865493i | \(-0.332994\pi\) | ||||
0.500922 | + | 0.865493i | \(0.332994\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6980 | −0.771348 | −0.385674 | − | 0.922635i | \(-0.626031\pi\) | ||||
−0.385674 | + | 0.922635i | \(0.626031\pi\) | |||||||
\(272\) | −6.26285 | −0.379741 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.92339 | 0.297433 | ||||||||
\(275\) | 7.18194 | 0.433087 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.828460 | −0.0497773 | −0.0248887 | − | 0.999690i | \(-0.507923\pi\) | ||||
−0.0248887 | + | 0.999690i | \(0.507923\pi\) | |||||||
\(278\) | 3.76890 | 0.226044 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.21969 | 0.311381 | 0.155690 | − | 0.987806i | \(-0.450240\pi\) | ||||
0.155690 | + | 0.987806i | \(0.450240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.35417 | 0.437160 | 0.218580 | − | 0.975819i | \(-0.429858\pi\) | ||||
0.218580 | + | 0.975819i | \(0.429858\pi\) | |||||||
\(284\) | −12.1215 | −0.719278 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.68310 | −0.217787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0722 | −0.827778 | ||||||||
\(290\) | −1.31684 | −0.0773273 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.9021 | 0.813557 | ||||||||
\(293\) | −7.82573 | −0.457184 | −0.228592 | − | 0.973522i | \(-0.573412\pi\) | ||||
−0.228592 | + | 0.973522i | \(0.573412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.7174 | −0.915101 | ||||||||
\(296\) | −1.56526 | −0.0909789 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.45090 | 0.0840484 | ||||||||
\(299\) | 18.8750 | 1.09157 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.07334 | 0.0617638 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.1909 | 1.50215 | ||||||||
\(305\) | 20.6979 | 1.18516 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.6709 | −1.29390 | −0.646948 | − | 0.762534i | \(-0.723955\pi\) | ||||
−0.646948 | + | 0.762534i | \(0.723955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.05064 | 0.230061 | ||||||||
\(311\) | 32.3176 | 1.83256 | 0.916281 | − | 0.400536i | \(-0.131176\pi\) | ||||
0.916281 | + | 0.400536i | \(0.131176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3196 | 1.37462 | 0.687312 | − | 0.726362i | \(-0.258791\pi\) | ||||
0.687312 | + | 0.726362i | \(0.258791\pi\) | |||||||
\(314\) | −0.246037 | −0.0138847 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.0949 | 1.07417 | ||||||||
\(317\) | 5.13844 | 0.288603 | 0.144302 | − | 0.989534i | \(-0.453906\pi\) | ||||
0.144302 | + | 0.989534i | \(0.453906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.88564 | −0.497500 | ||||||||
\(320\) | −17.2618 | −0.964964 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.2438 | −0.681262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.32525 | −0.350862 | ||||||||
\(326\) | 1.63284 | 0.0904349 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.63464 | −0.531984 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6979 | −0.642977 | −0.321488 | − | 0.946913i | \(-0.604183\pi\) | ||||
−0.321488 | + | 0.946913i | \(0.604183\pi\) | |||||||
\(332\) | 13.3951 | 0.735150 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.30286 | −0.235442 | ||||||||
\(335\) | 21.4165 | 1.17011 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.6947 | −1.83547 | −0.917733 | − | 0.397198i | \(-0.869983\pi\) | ||||
−0.917733 | + | 0.397198i | \(0.869983\pi\) | |||||||
\(338\) | 0.135167 | 0.00735211 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.61590 | 0.467263 | ||||||||
\(341\) | 27.3326 | 1.48014 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.56526 | 0.0843932 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.198558 | 0.0106745 | ||||||||
\(347\) | 27.3114 | 1.46615 | 0.733075 | − | 0.680148i | \(-0.238084\pi\) | ||||
0.733075 | + | 0.680148i | \(0.238084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9169 | −1.22672 | −0.613358 | − | 0.789805i | \(-0.710182\pi\) | ||||
−0.613358 | + | 0.789805i | \(0.710182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.5458 | 0.615395 | ||||||||
\(353\) | −10.2693 | −0.546581 | −0.273290 | − | 0.961932i | \(-0.588112\pi\) | ||||
−0.273290 | + | 0.961932i | \(0.588112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.1705 | 0.858241 | ||||||||
\(356\) | −9.78284 | −0.518489 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.81230 | 0.0957830 | ||||||||
\(359\) | 10.1007 | 0.533094 | 0.266547 | − | 0.963822i | \(-0.414117\pi\) | ||||
0.266547 | + | 0.963822i | \(0.414117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.2028 | 1.69488 | ||||||||
\(362\) | −0.0978390 | −0.00514231 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.5458 | −0.970733 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.77537 | 0.405871 | 0.202935 | − | 0.979192i | \(-0.434952\pi\) | ||||
0.202935 | + | 0.979192i | \(0.434952\pi\) | |||||||
\(368\) | −18.7576 | −0.977808 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.02891 | 0.0534907 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.1111 | 1.24842 | 0.624212 | − | 0.781255i | \(-0.285420\pi\) | ||||
0.624212 | + | 0.781255i | \(0.285420\pi\) | |||||||
\(374\) | −1.71107 | −0.0884775 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.80428 | 0.454046 | ||||||||
\(377\) | 7.82573 | 0.403045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3581 | −0.686161 | −0.343081 | − | 0.939306i | \(-0.611470\pi\) | ||||
−0.343081 | + | 0.939306i | \(0.611470\pi\) | |||||||
\(380\) | −36.0312 | −1.84836 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.83173 | 0.196048 | ||||||||
\(383\) | 9.24040 | 0.472162 | 0.236081 | − | 0.971733i | \(-0.424137\pi\) | ||||
0.236081 | + | 0.971733i | \(0.424137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.95898 | −0.150608 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.95153 | 0.302143 | ||||||||
\(389\) | 10.4484 | 0.529756 | 0.264878 | − | 0.964282i | \(-0.414668\pi\) | ||||
0.264878 | + | 0.964282i | \(0.414668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.76884 | 0.443459 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.52424 | 0.278307 | ||||||||
\(395\) | −25.4733 | −1.28170 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.409157 | 0.0205350 | 0.0102675 | − | 0.999947i | \(-0.496732\pi\) | ||||
0.0102675 | + | 0.999947i | \(0.496732\pi\) | |||||||
\(398\) | 1.61323 | 0.0808641 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.28590 | 0.314295 | ||||||||
\(401\) | 15.2528 | 0.761688 | 0.380844 | − | 0.924639i | \(-0.375633\pi\) | ||||
0.380844 | + | 0.924639i | \(0.375633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0722 | −1.19912 | ||||||||
\(404\) | −21.5647 | −1.07288 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.94282 | 0.344143 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.12670 | 0.302946 | 0.151473 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151473 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(410\) | 6.33327 | 0.312778 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.5153 | 0.764384 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.8695 | −0.877178 | ||||||||
\(416\) | −10.1686 | −0.498557 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.15561 | 0.349992 | ||||||||
\(419\) | −1.56287 | −0.0763514 | −0.0381757 | − | 0.999271i | \(-0.512155\pi\) | ||||
−0.0381757 | + | 0.999271i | \(0.512155\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2632 | 1.13378 | 0.566889 | − | 0.823794i | \(-0.308147\pi\) | ||||
0.566889 | + | 0.823794i | \(0.308147\pi\) | |||||||
\(422\) | 4.03775 | 0.196555 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.0377 | −0.487476 | ||||||||
\(425\) | −2.93854 | −0.142540 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.68675 | −0.371553 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.02891 | −0.0496187 | ||||||||
\(431\) | 1.00576 | 0.0484456 | 0.0242228 | − | 0.999707i | \(-0.492289\pi\) | ||||
0.0242228 | + | 0.999707i | \(0.492289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.1071 | −0.629889 | −0.314945 | − | 0.949110i | \(-0.601986\pi\) | ||||
−0.314945 | + | 0.949110i | \(0.601986\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.1111 | −0.675799 | ||||||||
\(437\) | −36.6708 | −1.75420 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.6141 | −0.888402 | −0.444201 | − | 0.895927i | \(-0.646512\pi\) | ||||
−0.444201 | + | 0.895927i | \(0.646512\pi\) | |||||||
\(440\) | −10.2190 | −0.487170 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.50697 | 0.0716792 | ||||||||
\(443\) | −1.11901 | −0.0531656 | −0.0265828 | − | 0.999647i | \(-0.508463\pi\) | ||||
−0.0265828 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0506 | 0.618660 | ||||||||
\(446\) | 1.07639 | 0.0509687 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.4419 | −1.86138 | −0.930689 | − | 0.365813i | \(-0.880791\pi\) | ||||
−0.930689 | + | 0.365813i | \(0.880791\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.7351 | 2.01232 | ||||||||
\(452\) | −13.4621 | −0.633203 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.45011 | 0.0680572 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.2405 | −1.60170 | −0.800852 | − | 0.598863i | \(-0.795619\pi\) | ||||
−0.800852 | + | 0.598863i | \(0.795619\pi\) | |||||||
\(458\) | 2.64215 | 0.123459 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.8051 | 1.20317 | ||||||||
\(461\) | −20.3876 | −0.949543 | −0.474772 | − | 0.880109i | \(-0.657469\pi\) | ||||
−0.474772 | + | 0.880109i | \(0.657469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.80903 | 0.316442 | 0.158221 | − | 0.987404i | \(-0.449424\pi\) | ||||
0.158221 | + | 0.987404i | \(0.449424\pi\) | |||||||
\(464\) | −7.77704 | −0.361040 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.94609 | −0.0901509 | ||||||||
\(467\) | −24.7911 | −1.14720 | −0.573598 | − | 0.819137i | \(-0.694453\pi\) | ||||
−0.573598 | + | 0.819137i | \(0.694453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.78744 | −0.266955 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.71754 | 0.263171 | ||||||||
\(473\) | −6.94282 | −0.319231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.2888 | 0.563850 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.06045 | 0.231460 | ||||||||
\(479\) | 11.0997 | 0.507157 | 0.253579 | − | 0.967315i | \(-0.418392\pi\) | ||||
0.253579 | + | 0.967315i | \(0.418392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.11465 | −0.278804 | ||||||||
\(482\) | −3.27395 | −0.149124 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.6063 | −0.573013 | ||||||||
\(485\) | −7.93955 | −0.360516 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0377 | −0.454854 | −0.227427 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227427 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(488\) | −7.52933 | −0.340837 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3880 | −0.559061 | −0.279530 | − | 0.960137i | \(-0.590179\pi\) | ||||
−0.279530 | + | 0.960137i | \(0.590179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.63562 | 0.163740 | ||||||||
\(494\) | −6.30206 | −0.283543 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.9225 | 1.07415 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2222 | 0.457608 | 0.228804 | − | 0.973473i | \(-0.426519\pi\) | ||||
0.228804 | + | 0.973473i | \(0.426519\pi\) | |||||||
\(500\) | 16.5293 | 0.739212 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.63562 | −0.162266 | ||||||||
\(503\) | 8.45753 | 0.377102 | 0.188551 | − | 0.982063i | \(-0.439621\pi\) | ||||
0.188551 | + | 0.982063i | \(0.439621\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.7680 | 1.28016 | ||||||||
\(506\) | −5.12476 | −0.227824 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7012 | −0.785364 | ||||||||
\(509\) | 10.5657 | 0.468317 | 0.234159 | − | 0.972198i | \(-0.424767\pi\) | ||||
0.234159 | + | 0.972198i | \(0.424767\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.0071 | 0.751616 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.12670 | −0.270237 | ||||||||
\(515\) | −20.6979 | −0.912060 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.0520 | −1.71750 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | −19.7558 | −0.865515 | −0.432758 | − | 0.901510i | \(-0.642459\pi\) | ||||
−0.432758 | + | 0.901510i | \(0.642459\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.5282 | 1.42236 | 0.711179 | − | 0.703011i | \(-0.248161\pi\) | ||||
0.711179 | + | 0.703011i | \(0.248161\pi\) | |||||||
\(524\) | −8.35969 | −0.365195 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.69794 | 0.0740337 | ||||||||
\(527\) | −11.1833 | −0.487153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.26320 | 0.141878 | ||||||||
\(530\) | 6.59825 | 0.286610 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.6375 | −1.63026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.2544 | 0.443336 | ||||||||
\(536\) | −7.79071 | −0.336507 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.92914 | 0.169397 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2222 | 0.654453 | 0.327226 | − | 0.944946i | \(-0.393886\pi\) | ||||
0.327226 | + | 0.944946i | \(0.393886\pi\) | |||||||
\(542\) | −3.03638 | −0.130424 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.72406 | −0.202542 | ||||||||
\(545\) | 18.8247 | 0.806361 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3743 | 0.999412 | 0.499706 | − | 0.866195i | \(-0.333441\pi\) | ||||
0.499706 | + | 0.866195i | \(0.333441\pi\) | |||||||
\(548\) | −40.0014 | −1.70877 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.71737 | 0.0732289 | ||||||||
\(551\) | −15.2040 | −0.647711 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.198104 | −0.00841664 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.6214 | −1.29864 | ||||||||
\(557\) | 27.6673 | 1.17230 | 0.586151 | − | 0.810202i | \(-0.300643\pi\) | ||||
0.586151 | + | 0.810202i | \(0.300643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.11465 | 0.258622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.24815 | 0.0526500 | ||||||||
\(563\) | 8.55824 | 0.360687 | 0.180343 | − | 0.983604i | \(-0.442279\pi\) | ||||
0.180343 | + | 0.983604i | \(0.442279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.9589 | 0.755536 | ||||||||
\(566\) | 1.75855 | 0.0739175 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.88237 | −0.246819 | ||||||||
\(569\) | 13.7278 | 0.575498 | 0.287749 | − | 0.957706i | \(-0.407093\pi\) | ||||
0.287749 | + | 0.957706i | \(0.407093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7174 | 0.448508 | 0.224254 | − | 0.974531i | \(-0.428005\pi\) | ||||
0.224254 | + | 0.974531i | \(0.428005\pi\) | |||||||
\(572\) | 29.9244 | 1.25120 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.80111 | −0.367032 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.6353 | −1.89982 | −0.949912 | − | 0.312518i | \(-0.898827\pi\) | ||||
−0.949912 | + | 0.312518i | \(0.898827\pi\) | |||||||
\(578\) | −3.36500 | −0.139965 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.6990 | 0.444251 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.5231 | 1.84396 | ||||||||
\(584\) | 6.74645 | 0.279170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.87131 | −0.0773032 | ||||||||
\(587\) | −10.2190 | −0.421782 | −0.210891 | − | 0.977510i | \(-0.567636\pi\) | ||||
−0.210891 | + | 0.977510i | \(0.567636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.7680 | 1.92704 | ||||||||
\(590\) | −3.75839 | −0.154730 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.07661 | 0.249747 | ||||||||
\(593\) | 11.3961 | 0.467981 | 0.233990 | − | 0.972239i | \(-0.424822\pi\) | ||||
0.233990 | + | 0.972239i | \(0.424822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.7882 | −0.482864 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.51346 | 0.184569 | ||||||||
\(599\) | −34.5746 | −1.41268 | −0.706339 | − | 0.707874i | \(-0.749655\pi\) | ||||
−0.706339 | + | 0.707874i | \(0.749655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.8414 | −1.58437 | −0.792187 | − | 0.610279i | \(-0.791057\pi\) | ||||
−0.792187 | + | 0.610279i | \(0.791057\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.72064 | −0.354838 | ||||||||
\(605\) | 16.8172 | 0.683717 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.3325 | −1.67763 | −0.838817 | − | 0.544414i | \(-0.816752\pi\) | ||||
−0.838817 | + | 0.544414i | \(0.816752\pi\) | |||||||
\(608\) | 19.7558 | 0.801202 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.94936 | 0.200394 | ||||||||
\(611\) | 34.3937 | 1.39142 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.6569 | −1.15744 | −0.578721 | − | 0.815526i | \(-0.696448\pi\) | ||||
−0.578721 | + | 0.815526i | \(0.696448\pi\) | |||||||
\(614\) | −5.42114 | −0.218779 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.7037 | −1.35686 | −0.678430 | − | 0.734665i | \(-0.737339\pi\) | ||||
−0.678430 | + | 0.734665i | \(0.737339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.43807 | 0.0578010 | 0.0289005 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289005 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(620\) | −32.9105 | −1.32172 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.72789 | 0.309860 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6375 | −1.22550 | ||||||||
\(626\) | 5.81538 | 0.232429 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.99900 | 0.0797686 | ||||||||
\(629\) | −2.84071 | −0.113266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7680 | −1.22486 | −0.612428 | − | 0.790527i | \(-0.709807\pi\) | ||||
−0.612428 | + | 0.790527i | \(0.709807\pi\) | |||||||
\(632\) | 9.26647 | 0.368600 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.22872 | 0.0487987 | ||||||||
\(635\) | 23.6140 | 0.937094 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.12476 | −0.0841202 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.4389 | −0.728862 | ||||||||
\(641\) | 9.23912 | 0.364923 | 0.182462 | − | 0.983213i | \(-0.441593\pi\) | ||||
0.182462 | + | 0.983213i | \(0.441593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.5591 | −1.00795 | −0.503976 | − | 0.863718i | \(-0.668130\pi\) | ||||
−0.503976 | + | 0.863718i | \(0.668130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.92777 | −0.115192 | ||||||||
\(647\) | 28.3111 | 1.11302 | 0.556512 | − | 0.830839i | \(-0.312139\pi\) | ||||
0.556512 | + | 0.830839i | \(0.312139\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.3605 | −0.995488 | ||||||||
\(650\) | −1.51252 | −0.0593257 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.2665 | −0.519555 | ||||||||
\(653\) | −8.35021 | −0.326769 | −0.163385 | − | 0.986562i | \(-0.552241\pi\) | ||||
−0.163385 | + | 0.986562i | \(0.552241\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1521 | 0.435749 | ||||||||
\(656\) | 37.4033 | 1.46035 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.5724 | −1.30779 | −0.653897 | − | 0.756583i | \(-0.726867\pi\) | ||||
−0.653897 | + | 0.756583i | \(0.726867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.9534 | −0.659410 | −0.329705 | − | 0.944084i | \(-0.606949\pi\) | ||||
−0.329705 | + | 0.944084i | \(0.606949\pi\) | |||||||
\(662\) | −2.79725 | −0.108718 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.50041 | 0.252265 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.8889 | 0.421620 | ||||||||
\(668\) | 34.9597 | 1.35263 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.12118 | 0.197848 | ||||||||
\(671\) | 33.3969 | 1.28927 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4315 | −1.71271 | −0.856354 | − | 0.516390i | \(-0.827276\pi\) | ||||
−0.856354 | + | 0.516390i | \(0.827276\pi\) | |||||||
\(674\) | −8.05718 | −0.310351 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.09820 | −0.0422384 | ||||||||
\(677\) | −14.3736 | −0.552423 | −0.276212 | − | 0.961097i | \(-0.589079\pi\) | ||||
−0.276212 | + | 0.961097i | \(0.589079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.18116 | 0.160340 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.53585 | 0.250271 | ||||||||
\(683\) | −32.3092 | −1.23628 | −0.618138 | − | 0.786069i | \(-0.712113\pi\) | ||||
−0.618138 | + | 0.786069i | \(0.712113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.3632 | 2.03890 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.07661 | −0.231669 | ||||||||
\(689\) | −39.2122 | −1.49387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.9962 | −1.10307 | −0.551533 | − | 0.834153i | \(-0.685957\pi\) | ||||
−0.551533 | + | 0.834153i | \(0.685957\pi\) | |||||||
\(692\) | −1.61323 | −0.0613259 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.53078 | 0.247905 | ||||||||
\(695\) | 40.8500 | 1.54953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4854 | −0.662306 | ||||||||
\(698\) | −5.47997 | −0.207420 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.3912 | −0.996783 | −0.498392 | − | 0.866952i | \(-0.666076\pi\) | ||||
−0.498392 | + | 0.866952i | \(0.666076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.8797 | 0.448050 | ||||||||
\(704\) | −27.8525 | −1.04973 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.45563 | −0.0924190 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.88564 | −0.296151 | −0.148076 | − | 0.988976i | \(-0.547308\pi\) | ||||
−0.148076 | + | 0.988976i | \(0.547308\pi\) | |||||||
\(710\) | 3.86674 | 0.145116 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.74746 | −0.177918 | ||||||||
\(713\) | −33.4947 | −1.25439 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.9201 | −1.49293 | ||||||||
\(716\) | −14.7245 | −0.550281 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.41531 | 0.0901385 | ||||||||
\(719\) | −33.1508 | −1.23632 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.70043 | 0.286580 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.794919 | 0.0295429 | ||||||||
\(725\) | −3.64900 | −0.135521 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.1005 | 1.22763 | 0.613814 | − | 0.789451i | \(-0.289634\pi\) | ||||
0.613814 | + | 0.789451i | \(0.289634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.43474 | −0.164137 | ||||||||
\(731\) | 2.84071 | 0.105067 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.5589 | −1.64582 | −0.822911 | − | 0.568170i | \(-0.807651\pi\) | ||||
−0.822911 | + | 0.568170i | \(0.807651\pi\) | |||||||
\(734\) | 1.85927 | 0.0686270 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.1488 | −0.521533 | ||||||||
\(737\) | 34.5562 | 1.27290 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.8090 | 1.46440 | 0.732199 | − | 0.681090i | \(-0.238494\pi\) | ||||
0.732199 | + | 0.681090i | \(0.238494\pi\) | |||||||
\(740\) | −8.35969 | −0.307308 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7414 | 0.394065 | 0.197033 | − | 0.980397i | \(-0.436869\pi\) | ||||
0.197033 | + | 0.980397i | \(0.436869\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.7259 | 0.576152 | ||||||||
\(746\) | 5.76552 | 0.211091 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.9021 | 0.508310 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7141 | 0.719378 | 0.359689 | − | 0.933072i | \(-0.382883\pi\) | ||||
0.359689 | + | 0.933072i | \(0.382883\pi\) | |||||||
\(752\) | −34.1797 | −1.24641 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.87131 | 0.0681492 | ||||||||
\(755\) | 11.6336 | 0.423391 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3549 | 1.28499 | 0.642497 | − | 0.766288i | \(-0.277898\pi\) | ||||
0.642497 | + | 0.766288i | \(0.277898\pi\) | |||||||
\(758\) | −3.19424 | −0.116020 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.4854 | −0.634261 | ||||||||
\(761\) | −39.1144 | −1.41790 | −0.708948 | − | 0.705261i | \(-0.750830\pi\) | ||||
−0.708948 | + | 0.705261i | \(0.750830\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −31.1319 | −1.12631 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.20960 | 0.0798359 | ||||||||
\(767\) | 22.3354 | 0.806486 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.8479 | −1.36483 | −0.682415 | − | 0.730965i | \(-0.739070\pi\) | ||||
−0.682415 | + | 0.730965i | \(0.739070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.0410 | 0.865255 | ||||||||
\(773\) | 29.8265 | 1.07279 | 0.536393 | − | 0.843969i | \(-0.319787\pi\) | ||||
0.536393 | + | 0.843969i | \(0.319787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.2245 | 0.403195 | ||||||||
\(776\) | 2.88819 | 0.103680 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.49846 | 0.0895741 | ||||||||
\(779\) | 73.1229 | 2.61990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.0917 | 0.933633 | ||||||||
\(782\) | 2.09683 | 0.0749827 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.66673 | −0.0951796 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.6206 | 0.628107 | 0.314053 | − | 0.949405i | \(-0.398313\pi\) | ||||
0.314053 | + | 0.949405i | \(0.398313\pi\) | |||||||
\(788\) | −44.8832 | −1.59890 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.09126 | −0.216717 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.4132 | −1.04449 | ||||||||
\(794\) | 0.0978390 | 0.00347218 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.1071 | −0.464570 | ||||||||
\(797\) | 10.1211 | 0.358508 | 0.179254 | − | 0.983803i | \(-0.442632\pi\) | ||||
0.179254 | + | 0.983803i | \(0.442632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9784 | 0.565276 | ||||||||
\(800\) | 4.74145 | 0.167635 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.64730 | 0.128791 | ||||||||
\(803\) | −29.9244 | −1.05601 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.75623 | −0.202755 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.4650 | −0.368157 | ||||||||
\(809\) | −47.1469 | −1.65760 | −0.828799 | − | 0.559546i | \(-0.810975\pi\) | ||||
−0.828799 | + | 0.559546i | \(0.810975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0577 | 0.739435 | 0.369717 | − | 0.929144i | \(-0.379454\pi\) | ||||
0.369717 | + | 0.929144i | \(0.379454\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.66019 | 0.0581896 | ||||||||
\(815\) | 17.6979 | 0.619931 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.8797 | −0.415617 | ||||||||
\(818\) | 1.46504 | 0.0512238 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −51.4563 | −1.79693 | ||||||||
\(821\) | 11.1604 | 0.389499 | 0.194750 | − | 0.980853i | \(-0.437611\pi\) | ||||
0.194750 | + | 0.980853i | \(0.437611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.43474 | 0.328874 | 0.164437 | − | 0.986388i | \(-0.447419\pi\) | ||||
0.164437 | + | 0.986388i | \(0.447419\pi\) | |||||||
\(824\) | 7.52933 | 0.262297 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.2646 | 0.600348 | 0.300174 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300174 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.4526 | −1.68283 | −0.841415 | − | 0.540390i | \(-0.818277\pi\) | ||||
−0.841415 | + | 0.540390i | \(0.818277\pi\) | |||||||
\(830\) | −4.27301 | −0.148318 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.5302 | 0.850431 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46.6375 | −1.61396 | ||||||||
\(836\) | −58.1376 | −2.01073 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.373720 | −0.0129099 | ||||||||
\(839\) | −14.8686 | −0.513320 | −0.256660 | − | 0.966502i | \(-0.582622\pi\) | ||||
−0.256660 | + | 0.966502i | \(0.582622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4854 | −0.844323 | ||||||||
\(842\) | 5.56277 | 0.191706 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.8058 | −1.12922 | ||||||||
\(845\) | 1.46504 | 0.0503988 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 38.9683 | 1.33818 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.702674 | −0.0241015 | ||||||||
\(851\) | −8.50808 | −0.291653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.99801 | 0.273847 | 0.136923 | − | 0.990582i | \(-0.456279\pi\) | ||||
0.136923 | + | 0.990582i | \(0.456279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.73026 | −0.127498 | ||||||||
\(857\) | −43.1322 | −1.47337 | −0.736684 | − | 0.676237i | \(-0.763610\pi\) | ||||
−0.736684 | + | 0.676237i | \(0.763610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.44359 | −0.0833742 | −0.0416871 | − | 0.999131i | \(-0.513273\pi\) | ||||
−0.0416871 | + | 0.999131i | \(0.513273\pi\) | |||||||
\(860\) | 8.35969 | 0.285063 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.240500 | 0.00819146 | ||||||||
\(863\) | 25.7187 | 0.875476 | 0.437738 | − | 0.899103i | \(-0.355780\pi\) | ||||
0.437738 | + | 0.899103i | \(0.355780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.15211 | 0.0731739 | ||||||||
\(866\) | −3.13422 | −0.106505 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.1021 | −1.39429 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.4342 | −1.03122 | ||||||||
\(872\) | −6.84789 | −0.231899 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.76884 | −0.296611 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.9590 | −0.741502 | −0.370751 | − | 0.928732i | \(-0.620900\pi\) | ||||
−0.370751 | + | 0.928732i | \(0.620900\pi\) | |||||||
\(878\) | −4.45106 | −0.150216 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 39.6718 | 1.33733 | ||||||||
\(881\) | −35.0576 | −1.18112 | −0.590560 | − | 0.806994i | \(-0.701093\pi\) | ||||
−0.590560 | + | 0.806994i | \(0.701093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3009 | 0.885097 | 0.442549 | − | 0.896744i | \(-0.354074\pi\) | ||||
0.442549 | + | 0.896744i | \(0.354074\pi\) | |||||||
\(884\) | −12.2438 | −0.411803 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.267580 | −0.00898954 | ||||||||
\(887\) | 47.8180 | 1.60557 | 0.802785 | − | 0.596269i | \(-0.203351\pi\) | ||||
0.802785 | + | 0.596269i | \(0.203351\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.12071 | 0.104607 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.74545 | −0.292819 | ||||||||
\(893\) | −66.8208 | −2.23607 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.6430 | 0.656593 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.43147 | −0.314732 | ||||||||
\(899\) | −13.8871 | −0.463162 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.2170 | −0.606895 | ||||||||
\(902\) | 10.2190 | 0.340254 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.53294 | −0.217282 | ||||||||
\(905\) | −1.06045 | −0.0352505 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.1144 | −0.634682 | −0.317341 | − | 0.948312i | \(-0.602790\pi\) | ||||
−0.317341 | + | 0.948312i | \(0.602790\pi\) | |||||||
\(908\) | −11.7818 | −0.390994 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0586 | −0.598307 | −0.299153 | − | 0.954205i | \(-0.596704\pi\) | ||||
−0.299153 | + | 0.954205i | \(0.596704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.8330 | −0.954234 | ||||||||
\(914\) | −8.18770 | −0.270825 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.4668 | −0.709284 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.2093 | 0.534695 | 0.267348 | − | 0.963600i | \(-0.413853\pi\) | ||||
0.267348 | + | 0.963600i | \(0.413853\pi\) | |||||||
\(920\) | 12.5228 | 0.412865 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.87514 | −0.160554 | ||||||||
\(923\) | −22.9793 | −0.756374 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.85116 | 0.0937456 | ||||||||
\(926\) | 1.62820 | 0.0535059 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.86621 | −0.192568 | ||||||||
\(929\) | 22.6829 | 0.744203 | 0.372102 | − | 0.928192i | \(-0.378637\pi\) | ||||
0.372102 | + | 0.928192i | \(0.378637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.8115 | 0.517923 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.92814 | −0.193975 | ||||||||
\(935\) | −18.5458 | −0.606513 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.2933 | −1.67568 | −0.837840 | − | 0.545915i | \(-0.816182\pi\) | ||||
−0.837840 | + | 0.545915i | \(0.816182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 47.0216 | 1.53368 | ||||||||
\(941\) | 31.9318 | 1.04095 | 0.520474 | − | 0.853878i | \(-0.325755\pi\) | ||||
0.520474 | + | 0.853878i | \(0.325755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.3697 | −1.70539 | ||||||||
\(944\) | −22.1965 | −0.722433 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.66019 | −0.0539774 | ||||||||
\(947\) | −4.49330 | −0.146013 | −0.0730063 | − | 0.997331i | \(-0.523259\pi\) | ||||
−0.0730063 | + | 0.997331i | \(0.523259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.3549 | 0.855515 | ||||||||
\(950\) | 2.93854 | 0.0953390 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.14635 | 0.0371340 | 0.0185670 | − | 0.999828i | \(-0.494090\pi\) | ||||
0.0185670 | + | 0.999828i | \(0.494090\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.5310 | 1.34391 | ||||||||
\(956\) | −41.1150 | −1.32975 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.65419 | 0.0857530 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.7174 | 0.377980 | ||||||||
\(962\) | −1.46216 | −0.0471418 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.6000 | 0.856730 | ||||||||
\(965\) | −32.0715 | −1.03242 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.6159 | 1.59554 | 0.797770 | − | 0.602962i | \(-0.206013\pi\) | ||||
0.797770 | + | 0.602962i | \(0.206013\pi\) | |||||||
\(968\) | −6.11763 | −0.196628 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.89853 | −0.0609582 | ||||||||
\(971\) | 5.13322 | 0.164733 | 0.0823664 | − | 0.996602i | \(-0.473752\pi\) | ||||
0.0823664 | + | 0.996602i | \(0.473752\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.40026 | −0.0769093 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.2302 | 0.935634 | ||||||||
\(977\) | 31.1948 | 0.998011 | 0.499006 | − | 0.866599i | \(-0.333699\pi\) | ||||
0.499006 | + | 0.866599i | \(0.333699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.0577 | 0.673006 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.96225 | −0.0945292 | ||||||||
\(983\) | −20.3401 | −0.648748 | −0.324374 | − | 0.945929i | \(-0.605154\pi\) | ||||
−0.324374 | + | 0.945929i | \(0.605154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.8757 | 1.90780 | ||||||||
\(986\) | 0.869363 | 0.0276861 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 51.2028 | 1.62898 | ||||||||
\(989\) | 8.50808 | 0.270541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9655 | −0.411863 | −0.205932 | − | 0.978566i | \(-0.566022\pi\) | ||||
−0.205932 | + | 0.978566i | \(0.566022\pi\) | |||||||
\(992\) | 18.0447 | 0.572919 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4854 | 0.554324 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.4816 | 1.56710 | 0.783548 | − | 0.621331i | \(-0.213408\pi\) | ||||
0.783548 | + | 0.621331i | \(0.213408\pi\) | |||||||
\(998\) | 2.44436 | 0.0773749 | ||||||||
\(999\) | 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 | 3969.2.a.be.1.4 | 6 | ||
3.2 | odd | 2 | 3969.2.a.bd.1.3 | 6 | |||
7.6 | odd | 2 | inner | 3969.2.a.be.1.3 | 6 | ||
9.2 | odd | 6 | 1323.2.f.g.442.4 | 12 | |||
9.4 | even | 3 | 441.2.f.g.295.4 | yes | 12 | ||
9.5 | odd | 6 | 1323.2.f.g.883.4 | 12 | |||
9.7 | even | 3 | 441.2.f.g.148.4 | yes | 12 | ||
21.20 | even | 2 | 3969.2.a.bd.1.4 | 6 | |||
63.2 | odd | 6 | 1323.2.g.g.361.3 | 12 | |||
63.4 | even | 3 | 441.2.g.g.79.4 | 12 | |||
63.5 | even | 6 | 1323.2.h.g.802.3 | 12 | |||
63.11 | odd | 6 | 1323.2.h.g.226.4 | 12 | |||
63.13 | odd | 6 | 441.2.f.g.295.3 | yes | 12 | ||
63.16 | even | 3 | 441.2.g.g.67.4 | 12 | |||
63.20 | even | 6 | 1323.2.f.g.442.3 | 12 | |||
63.23 | odd | 6 | 1323.2.h.g.802.4 | 12 | |||
63.25 | even | 3 | 441.2.h.g.373.3 | 12 | |||
63.31 | odd | 6 | 441.2.g.g.79.3 | 12 | |||
63.32 | odd | 6 | 1323.2.g.g.667.3 | 12 | |||
63.34 | odd | 6 | 441.2.f.g.148.3 | ✓ | 12 | ||
63.38 | even | 6 | 1323.2.h.g.226.3 | 12 | |||
63.40 | odd | 6 | 441.2.h.g.214.4 | 12 | |||
63.41 | even | 6 | 1323.2.f.g.883.3 | 12 | |||
63.47 | even | 6 | 1323.2.g.g.361.4 | 12 | |||
63.52 | odd | 6 | 441.2.h.g.373.4 | 12 | |||
63.58 | even | 3 | 441.2.h.g.214.3 | 12 | |||
63.59 | even | 6 | 1323.2.g.g.667.4 | 12 | |||
63.61 | odd | 6 | 441.2.g.g.67.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.3 | ✓ | 12 | 63.34 | odd | 6 | ||
441.2.f.g.148.4 | yes | 12 | 9.7 | even | 3 | ||
441.2.f.g.295.3 | yes | 12 | 63.13 | odd | 6 | ||
441.2.f.g.295.4 | yes | 12 | 9.4 | even | 3 | ||
441.2.g.g.67.3 | 12 | 63.61 | odd | 6 | |||
441.2.g.g.67.4 | 12 | 63.16 | even | 3 | |||
441.2.g.g.79.3 | 12 | 63.31 | odd | 6 | |||
441.2.g.g.79.4 | 12 | 63.4 | even | 3 | |||
441.2.h.g.214.3 | 12 | 63.58 | even | 3 | |||
441.2.h.g.214.4 | 12 | 63.40 | odd | 6 | |||
441.2.h.g.373.3 | 12 | 63.25 | even | 3 | |||
441.2.h.g.373.4 | 12 | 63.52 | odd | 6 | |||
1323.2.f.g.442.3 | 12 | 63.20 | even | 6 | |||
1323.2.f.g.442.4 | 12 | 9.2 | odd | 6 | |||
1323.2.f.g.883.3 | 12 | 63.41 | even | 6 | |||
1323.2.f.g.883.4 | 12 | 9.5 | odd | 6 | |||
1323.2.g.g.361.3 | 12 | 63.2 | odd | 6 | |||
1323.2.g.g.361.4 | 12 | 63.47 | even | 6 | |||
1323.2.g.g.667.3 | 12 | 63.32 | odd | 6 | |||
1323.2.g.g.667.4 | 12 | 63.59 | even | 6 | |||
1323.2.h.g.226.3 | 12 | 63.38 | even | 6 | |||
1323.2.h.g.226.4 | 12 | 63.11 | odd | 6 | |||
1323.2.h.g.802.3 | 12 | 63.5 | even | 6 | |||
1323.2.h.g.802.4 | 12 | 63.23 | odd | 6 | |||
3969.2.a.bd.1.3 | 6 | 3.2 | odd | 2 | |||
3969.2.a.bd.1.4 | 6 | 21.20 | even | 2 | |||
3969.2.a.be.1.3 | 6 | 7.6 | odd | 2 | inner | ||
3969.2.a.be.1.4 | 6 | 1.1 | even | 1 | trivial |