Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 17x^{8} + 21x^{7} + 107x^{6} - 45x^{5} - 262x^{4} - 47x^{3} + 120x^{2} - 2x - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.274153\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.725847 | 0.419068 | 0.209534 | − | 0.977801i | \(-0.432805\pi\) | ||||
0.209534 | + | 0.977801i | \(0.432805\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.725847 | −0.296326 | ||||||||
\(7\) | −1.66243 | −0.628339 | −0.314169 | − | 0.949367i | \(-0.601726\pi\) | ||||
−0.314169 | + | 0.949367i | \(0.601726\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.47315 | −0.824382 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.725847 | 0.209534 | ||||||||
\(13\) | −1.34536 | −0.373137 | −0.186568 | − | 0.982442i | \(-0.559737\pi\) | ||||
−0.186568 | + | 0.982442i | \(0.559737\pi\) | |||||||
\(14\) | 1.66243 | 0.444303 | ||||||||
\(15\) | 0.725847 | 0.187413 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.15562 | −1.25042 | −0.625211 | − | 0.780456i | \(-0.714987\pi\) | ||||
−0.625211 | + | 0.780456i | \(0.714987\pi\) | |||||||
\(18\) | 2.47315 | 0.582926 | ||||||||
\(19\) | 1.16391 | 0.267019 | 0.133509 | − | 0.991048i | \(-0.457375\pi\) | ||||
0.133509 | + | 0.991048i | \(0.457375\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.20667 | −0.263317 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 7.78857 | 1.62403 | 0.812015 | − | 0.583637i | \(-0.198371\pi\) | ||||
0.812015 | + | 0.583637i | \(0.198371\pi\) | |||||||
\(24\) | −0.725847 | −0.148163 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.34536 | 0.263848 | ||||||||
\(27\) | −3.97267 | −0.764540 | ||||||||
\(28\) | −1.66243 | −0.314169 | ||||||||
\(29\) | 6.41615 | 1.19145 | 0.595724 | − | 0.803189i | \(-0.296865\pi\) | ||||
0.595724 | + | 0.803189i | \(0.296865\pi\) | |||||||
\(30\) | −0.725847 | −0.132521 | ||||||||
\(31\) | −8.67865 | −1.55873 | −0.779366 | − | 0.626569i | \(-0.784459\pi\) | ||||
−0.779366 | + | 0.626569i | \(0.784459\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.725847 | 0.126354 | ||||||||
\(34\) | 5.15562 | 0.884182 | ||||||||
\(35\) | −1.66243 | −0.281002 | ||||||||
\(36\) | −2.47315 | −0.412191 | ||||||||
\(37\) | 10.9749 | 1.80425 | 0.902127 | − | 0.431470i | \(-0.142005\pi\) | ||||
0.902127 | + | 0.431470i | \(0.142005\pi\) | |||||||
\(38\) | −1.16391 | −0.188811 | ||||||||
\(39\) | −0.976529 | −0.156370 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.51287 | −0.860966 | −0.430483 | − | 0.902599i | \(-0.641657\pi\) | ||||
−0.430483 | + | 0.902599i | \(0.641657\pi\) | |||||||
\(42\) | 1.20667 | 0.186193 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.47315 | −0.368675 | ||||||||
\(46\) | −7.78857 | −1.14836 | ||||||||
\(47\) | −2.09570 | −0.305689 | −0.152845 | − | 0.988250i | \(-0.548843\pi\) | ||||
−0.152845 | + | 0.988250i | \(0.548843\pi\) | |||||||
\(48\) | 0.725847 | 0.104767 | ||||||||
\(49\) | −4.23633 | −0.605190 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −3.74219 | −0.524012 | ||||||||
\(52\) | −1.34536 | −0.186568 | ||||||||
\(53\) | 1.29522 | 0.177912 | 0.0889561 | − | 0.996036i | \(-0.471647\pi\) | ||||
0.0889561 | + | 0.996036i | \(0.471647\pi\) | |||||||
\(54\) | 3.97267 | 0.540612 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 1.66243 | 0.222151 | ||||||||
\(57\) | 0.844819 | 0.111899 | ||||||||
\(58\) | −6.41615 | −0.842481 | ||||||||
\(59\) | 10.9331 | 1.42337 | 0.711683 | − | 0.702500i | \(-0.247933\pi\) | ||||
0.711683 | + | 0.702500i | \(0.247933\pi\) | |||||||
\(60\) | 0.725847 | 0.0937065 | ||||||||
\(61\) | 1.69522 | 0.217050 | 0.108525 | − | 0.994094i | \(-0.465387\pi\) | ||||
0.108525 | + | 0.994094i | \(0.465387\pi\) | |||||||
\(62\) | 8.67865 | 1.10219 | ||||||||
\(63\) | 4.11143 | 0.517991 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.34536 | −0.166872 | ||||||||
\(66\) | −0.725847 | −0.0893456 | ||||||||
\(67\) | 0.749628 | 0.0915817 | 0.0457908 | − | 0.998951i | \(-0.485419\pi\) | ||||
0.0457908 | + | 0.998951i | \(0.485419\pi\) | |||||||
\(68\) | −5.15562 | −0.625211 | ||||||||
\(69\) | 5.65331 | 0.680579 | ||||||||
\(70\) | 1.66243 | 0.198698 | ||||||||
\(71\) | −5.56121 | −0.659995 | −0.329997 | − | 0.943982i | \(-0.607048\pi\) | ||||
−0.329997 | + | 0.943982i | \(0.607048\pi\) | |||||||
\(72\) | 2.47315 | 0.291463 | ||||||||
\(73\) | 4.89194 | 0.572558 | 0.286279 | − | 0.958146i | \(-0.407582\pi\) | ||||
0.286279 | + | 0.958146i | \(0.407582\pi\) | |||||||
\(74\) | −10.9749 | −1.27580 | ||||||||
\(75\) | 0.725847 | 0.0838136 | ||||||||
\(76\) | 1.16391 | 0.133509 | ||||||||
\(77\) | −1.66243 | −0.189451 | ||||||||
\(78\) | 0.976529 | 0.110570 | ||||||||
\(79\) | −0.771969 | −0.0868533 | −0.0434266 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434266 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 4.53588 | 0.503987 | ||||||||
\(82\) | 5.51287 | 0.608795 | ||||||||
\(83\) | −4.41661 | −0.484786 | −0.242393 | − | 0.970178i | \(-0.577932\pi\) | ||||
−0.242393 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(84\) | −1.20667 | −0.131658 | ||||||||
\(85\) | −5.15562 | −0.559206 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | 4.65714 | 0.499298 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 7.92294 | 0.839830 | 0.419915 | − | 0.907563i | \(-0.362060\pi\) | ||||
0.419915 | + | 0.907563i | \(0.362060\pi\) | |||||||
\(90\) | 2.47315 | 0.260692 | ||||||||
\(91\) | 2.23657 | 0.234456 | ||||||||
\(92\) | 7.78857 | 0.812015 | ||||||||
\(93\) | −6.29938 | −0.653215 | ||||||||
\(94\) | 2.09570 | 0.216155 | ||||||||
\(95\) | 1.16391 | 0.119414 | ||||||||
\(96\) | −0.725847 | −0.0740815 | ||||||||
\(97\) | 5.76777 | 0.585629 | 0.292814 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292814 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(98\) | 4.23633 | 0.427934 | ||||||||
\(99\) | −2.47315 | −0.248560 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.94038 | 0.591090 | 0.295545 | − | 0.955329i | \(-0.404499\pi\) | ||||
0.295545 | + | 0.955329i | \(0.404499\pi\) | |||||||
\(102\) | 3.74219 | 0.370532 | ||||||||
\(103\) | 17.5535 | 1.72960 | 0.864798 | − | 0.502121i | \(-0.167447\pi\) | ||||
0.864798 | + | 0.502121i | \(0.167447\pi\) | |||||||
\(104\) | 1.34536 | 0.131924 | ||||||||
\(105\) | −1.20667 | −0.117759 | ||||||||
\(106\) | −1.29522 | −0.125803 | ||||||||
\(107\) | 8.34703 | 0.806938 | 0.403469 | − | 0.914993i | \(-0.367804\pi\) | ||||
0.403469 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(108\) | −3.97267 | −0.382270 | ||||||||
\(109\) | −10.2458 | −0.981370 | −0.490685 | − | 0.871337i | \(-0.663253\pi\) | ||||
−0.490685 | + | 0.871337i | \(0.663253\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 7.96607 | 0.756106 | ||||||||
\(112\) | −1.66243 | −0.157085 | ||||||||
\(113\) | 2.13157 | 0.200522 | 0.100261 | − | 0.994961i | \(-0.468032\pi\) | ||||
0.100261 | + | 0.994961i | \(0.468032\pi\) | |||||||
\(114\) | −0.844819 | −0.0791246 | ||||||||
\(115\) | 7.78857 | 0.726288 | ||||||||
\(116\) | 6.41615 | 0.595724 | ||||||||
\(117\) | 3.32728 | 0.307607 | ||||||||
\(118\) | −10.9331 | −1.00647 | ||||||||
\(119\) | 8.57085 | 0.785689 | ||||||||
\(120\) | −0.725847 | −0.0662605 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.69522 | −0.153478 | ||||||||
\(123\) | −4.00151 | −0.360804 | ||||||||
\(124\) | −8.67865 | −0.779366 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.11143 | −0.366275 | ||||||||
\(127\) | 15.5025 | 1.37562 | 0.687811 | − | 0.725890i | \(-0.258572\pi\) | ||||
0.687811 | + | 0.725890i | \(0.258572\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.725847 | 0.0639073 | ||||||||
\(130\) | 1.34536 | 0.117996 | ||||||||
\(131\) | −3.60750 | −0.315189 | −0.157594 | − | 0.987504i | \(-0.550374\pi\) | ||||
−0.157594 | + | 0.987504i | \(0.550374\pi\) | |||||||
\(132\) | 0.725847 | 0.0631769 | ||||||||
\(133\) | −1.93491 | −0.167778 | ||||||||
\(134\) | −0.749628 | −0.0647580 | ||||||||
\(135\) | −3.97267 | −0.341913 | ||||||||
\(136\) | 5.15562 | 0.442091 | ||||||||
\(137\) | 19.4879 | 1.66497 | 0.832483 | − | 0.554050i | \(-0.186918\pi\) | ||||
0.832483 | + | 0.554050i | \(0.186918\pi\) | |||||||
\(138\) | −5.65331 | −0.481242 | ||||||||
\(139\) | −8.10352 | −0.687332 | −0.343666 | − | 0.939092i | \(-0.611669\pi\) | ||||
−0.343666 | + | 0.939092i | \(0.611669\pi\) | |||||||
\(140\) | −1.66243 | −0.140501 | ||||||||
\(141\) | −1.52116 | −0.128105 | ||||||||
\(142\) | 5.56121 | 0.466687 | ||||||||
\(143\) | −1.34536 | −0.112505 | ||||||||
\(144\) | −2.47315 | −0.206095 | ||||||||
\(145\) | 6.41615 | 0.532832 | ||||||||
\(146\) | −4.89194 | −0.404860 | ||||||||
\(147\) | −3.07493 | −0.253616 | ||||||||
\(148\) | 10.9749 | 0.902127 | ||||||||
\(149\) | 17.2181 | 1.41056 | 0.705280 | − | 0.708928i | \(-0.250821\pi\) | ||||
0.705280 | + | 0.708928i | \(0.250821\pi\) | |||||||
\(150\) | −0.725847 | −0.0592652 | ||||||||
\(151\) | 3.10714 | 0.252856 | 0.126428 | − | 0.991976i | \(-0.459649\pi\) | ||||
0.126428 | + | 0.991976i | \(0.459649\pi\) | |||||||
\(152\) | −1.16391 | −0.0944053 | ||||||||
\(153\) | 12.7506 | 1.03082 | ||||||||
\(154\) | 1.66243 | 0.133962 | ||||||||
\(155\) | −8.67865 | −0.697086 | ||||||||
\(156\) | −0.976529 | −0.0781849 | ||||||||
\(157\) | 13.7020 | 1.09354 | 0.546770 | − | 0.837283i | \(-0.315857\pi\) | ||||
0.546770 | + | 0.837283i | \(0.315857\pi\) | |||||||
\(158\) | 0.771969 | 0.0614145 | ||||||||
\(159\) | 0.940133 | 0.0745574 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −12.9479 | −1.02044 | ||||||||
\(162\) | −4.53588 | −0.356373 | ||||||||
\(163\) | −8.87274 | −0.694966 | −0.347483 | − | 0.937686i | \(-0.612964\pi\) | ||||
−0.347483 | + | 0.937686i | \(0.612964\pi\) | |||||||
\(164\) | −5.51287 | −0.430483 | ||||||||
\(165\) | 0.725847 | 0.0565071 | ||||||||
\(166\) | 4.41661 | 0.342795 | ||||||||
\(167\) | −2.46104 | −0.190441 | −0.0952205 | − | 0.995456i | \(-0.530356\pi\) | ||||
−0.0952205 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(168\) | 1.20667 | 0.0930966 | ||||||||
\(169\) | −11.1900 | −0.860769 | ||||||||
\(170\) | 5.15562 | 0.395418 | ||||||||
\(171\) | −2.87851 | −0.220125 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −12.8786 | −0.979142 | −0.489571 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489571 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(174\) | −4.65714 | −0.353057 | ||||||||
\(175\) | −1.66243 | −0.125668 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 7.93575 | 0.596488 | ||||||||
\(178\) | −7.92294 | −0.593849 | ||||||||
\(179\) | −2.89487 | −0.216373 | −0.108186 | − | 0.994131i | \(-0.534504\pi\) | ||||
−0.108186 | + | 0.994131i | \(0.534504\pi\) | |||||||
\(180\) | −2.47315 | −0.184337 | ||||||||
\(181\) | −8.53765 | −0.634599 | −0.317299 | − | 0.948325i | \(-0.602776\pi\) | ||||
−0.317299 | + | 0.948325i | \(0.602776\pi\) | |||||||
\(182\) | −2.23657 | −0.165786 | ||||||||
\(183\) | 1.23047 | 0.0909589 | ||||||||
\(184\) | −7.78857 | −0.574181 | ||||||||
\(185\) | 10.9749 | 0.806887 | ||||||||
\(186\) | 6.29938 | 0.461893 | ||||||||
\(187\) | −5.15562 | −0.377016 | ||||||||
\(188\) | −2.09570 | −0.152845 | ||||||||
\(189\) | 6.60428 | 0.480391 | ||||||||
\(190\) | −1.16391 | −0.0844387 | ||||||||
\(191\) | 9.45261 | 0.683967 | 0.341983 | − | 0.939706i | \(-0.388901\pi\) | ||||
0.341983 | + | 0.939706i | \(0.388901\pi\) | |||||||
\(192\) | 0.725847 | 0.0523835 | ||||||||
\(193\) | 15.2682 | 1.09903 | 0.549516 | − | 0.835483i | \(-0.314812\pi\) | ||||
0.549516 | + | 0.835483i | \(0.314812\pi\) | |||||||
\(194\) | −5.76777 | −0.414102 | ||||||||
\(195\) | −0.976529 | −0.0699307 | ||||||||
\(196\) | −4.23633 | −0.302595 | ||||||||
\(197\) | 20.0157 | 1.42606 | 0.713031 | − | 0.701133i | \(-0.247322\pi\) | ||||
0.713031 | + | 0.701133i | \(0.247322\pi\) | |||||||
\(198\) | 2.47315 | 0.175759 | ||||||||
\(199\) | 5.22459 | 0.370361 | 0.185181 | − | 0.982705i | \(-0.440713\pi\) | ||||
0.185181 | + | 0.982705i | \(0.440713\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0.544116 | 0.0383790 | ||||||||
\(202\) | −5.94038 | −0.417964 | ||||||||
\(203\) | −10.6664 | −0.748633 | ||||||||
\(204\) | −3.74219 | −0.262006 | ||||||||
\(205\) | −5.51287 | −0.385036 | ||||||||
\(206\) | −17.5535 | −1.22301 | ||||||||
\(207\) | −19.2623 | −1.33882 | ||||||||
\(208\) | −1.34536 | −0.0932842 | ||||||||
\(209\) | 1.16391 | 0.0805091 | ||||||||
\(210\) | 1.20667 | 0.0832681 | ||||||||
\(211\) | 9.53438 | 0.656373 | 0.328187 | − | 0.944613i | \(-0.393562\pi\) | ||||
0.328187 | + | 0.944613i | \(0.393562\pi\) | |||||||
\(212\) | 1.29522 | 0.0889561 | ||||||||
\(213\) | −4.03659 | −0.276583 | ||||||||
\(214\) | −8.34703 | −0.570591 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 3.97267 | 0.270306 | ||||||||
\(217\) | 14.4276 | 0.979412 | ||||||||
\(218\) | 10.2458 | 0.693933 | ||||||||
\(219\) | 3.55080 | 0.239941 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 6.93618 | 0.466578 | ||||||||
\(222\) | −7.96607 | −0.534648 | ||||||||
\(223\) | 23.8079 | 1.59430 | 0.797148 | − | 0.603784i | \(-0.206341\pi\) | ||||
0.797148 | + | 0.603784i | \(0.206341\pi\) | |||||||
\(224\) | 1.66243 | 0.111076 | ||||||||
\(225\) | −2.47315 | −0.164876 | ||||||||
\(226\) | −2.13157 | −0.141790 | ||||||||
\(227\) | −13.3943 | −0.889009 | −0.444505 | − | 0.895777i | \(-0.646620\pi\) | ||||
−0.444505 | + | 0.895777i | \(0.646620\pi\) | |||||||
\(228\) | 0.844819 | 0.0559495 | ||||||||
\(229\) | 22.9682 | 1.51778 | 0.758889 | − | 0.651220i | \(-0.225742\pi\) | ||||
0.758889 | + | 0.651220i | \(0.225742\pi\) | |||||||
\(230\) | −7.78857 | −0.513563 | ||||||||
\(231\) | −1.20667 | −0.0793930 | ||||||||
\(232\) | −6.41615 | −0.421241 | ||||||||
\(233\) | 1.93058 | 0.126477 | 0.0632384 | − | 0.997998i | \(-0.479857\pi\) | ||||
0.0632384 | + | 0.997998i | \(0.479857\pi\) | |||||||
\(234\) | −3.32728 | −0.217511 | ||||||||
\(235\) | −2.09570 | −0.136708 | ||||||||
\(236\) | 10.9331 | 0.711683 | ||||||||
\(237\) | −0.560332 | −0.0363974 | ||||||||
\(238\) | −8.57085 | −0.555566 | ||||||||
\(239\) | 11.3596 | 0.734792 | 0.367396 | − | 0.930065i | \(-0.380249\pi\) | ||||
0.367396 | + | 0.930065i | \(0.380249\pi\) | |||||||
\(240\) | 0.725847 | 0.0468533 | ||||||||
\(241\) | 6.66307 | 0.429206 | 0.214603 | − | 0.976701i | \(-0.431154\pi\) | ||||
0.214603 | + | 0.976701i | \(0.431154\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 15.2104 | 0.975745 | ||||||||
\(244\) | 1.69522 | 0.108525 | ||||||||
\(245\) | −4.23633 | −0.270649 | ||||||||
\(246\) | 4.00151 | 0.255127 | ||||||||
\(247\) | −1.56588 | −0.0996345 | ||||||||
\(248\) | 8.67865 | 0.551095 | ||||||||
\(249\) | −3.20578 | −0.203158 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.1773 | 0.705506 | 0.352753 | − | 0.935716i | \(-0.385246\pi\) | ||||
0.352753 | + | 0.935716i | \(0.385246\pi\) | |||||||
\(252\) | 4.11143 | 0.258996 | ||||||||
\(253\) | 7.78857 | 0.489663 | ||||||||
\(254\) | −15.5025 | −0.972711 | ||||||||
\(255\) | −3.74219 | −0.234345 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.34928 | −0.208922 | −0.104461 | − | 0.994529i | \(-0.533312\pi\) | ||||
−0.104461 | + | 0.994529i | \(0.533312\pi\) | |||||||
\(258\) | −0.725847 | −0.0451893 | ||||||||
\(259\) | −18.2449 | −1.13368 | ||||||||
\(260\) | −1.34536 | −0.0834359 | ||||||||
\(261\) | −15.8681 | −0.982208 | ||||||||
\(262\) | 3.60750 | 0.222872 | ||||||||
\(263\) | −9.84688 | −0.607185 | −0.303592 | − | 0.952802i | \(-0.598186\pi\) | ||||
−0.303592 | + | 0.952802i | \(0.598186\pi\) | |||||||
\(264\) | −0.725847 | −0.0446728 | ||||||||
\(265\) | 1.29522 | 0.0795648 | ||||||||
\(266\) | 1.93491 | 0.118637 | ||||||||
\(267\) | 5.75085 | 0.351946 | ||||||||
\(268\) | 0.749628 | 0.0457908 | ||||||||
\(269\) | −9.33731 | −0.569306 | −0.284653 | − | 0.958631i | \(-0.591878\pi\) | ||||
−0.284653 | + | 0.958631i | \(0.591878\pi\) | |||||||
\(270\) | 3.97267 | 0.241769 | ||||||||
\(271\) | −1.10267 | −0.0669822 | −0.0334911 | − | 0.999439i | \(-0.510663\pi\) | ||||
−0.0334911 | + | 0.999439i | \(0.510663\pi\) | |||||||
\(272\) | −5.15562 | −0.312605 | ||||||||
\(273\) | 1.62341 | 0.0982532 | ||||||||
\(274\) | −19.4879 | −1.17731 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 5.65331 | 0.340290 | ||||||||
\(277\) | −12.3953 | −0.744759 | −0.372379 | − | 0.928081i | \(-0.621458\pi\) | ||||
−0.372379 | + | 0.928081i | \(0.621458\pi\) | |||||||
\(278\) | 8.10352 | 0.486017 | ||||||||
\(279\) | 21.4636 | 1.28499 | ||||||||
\(280\) | 1.66243 | 0.0993491 | ||||||||
\(281\) | −20.6616 | −1.23257 | −0.616283 | − | 0.787525i | \(-0.711362\pi\) | ||||
−0.616283 | + | 0.787525i | \(0.711362\pi\) | |||||||
\(282\) | 1.52116 | 0.0905837 | ||||||||
\(283\) | −24.0191 | −1.42779 | −0.713894 | − | 0.700254i | \(-0.753070\pi\) | ||||
−0.713894 | + | 0.700254i | \(0.753070\pi\) | |||||||
\(284\) | −5.56121 | −0.329997 | ||||||||
\(285\) | 0.844819 | 0.0500428 | ||||||||
\(286\) | 1.34536 | 0.0795530 | ||||||||
\(287\) | 9.16476 | 0.540979 | ||||||||
\(288\) | 2.47315 | 0.145731 | ||||||||
\(289\) | 9.58043 | 0.563554 | ||||||||
\(290\) | −6.41615 | −0.376769 | ||||||||
\(291\) | 4.18652 | 0.245418 | ||||||||
\(292\) | 4.89194 | 0.286279 | ||||||||
\(293\) | −27.3252 | −1.59635 | −0.798177 | − | 0.602423i | \(-0.794202\pi\) | ||||
−0.798177 | + | 0.602423i | \(0.794202\pi\) | |||||||
\(294\) | 3.07493 | 0.179334 | ||||||||
\(295\) | 10.9331 | 0.636549 | ||||||||
\(296\) | −10.9749 | −0.637900 | ||||||||
\(297\) | −3.97267 | −0.230518 | ||||||||
\(298\) | −17.2181 | −0.997417 | ||||||||
\(299\) | −10.4785 | −0.605985 | ||||||||
\(300\) | 0.725847 | 0.0419068 | ||||||||
\(301\) | −1.66243 | −0.0958208 | ||||||||
\(302\) | −3.10714 | −0.178796 | ||||||||
\(303\) | 4.31181 | 0.247707 | ||||||||
\(304\) | 1.16391 | 0.0667547 | ||||||||
\(305\) | 1.69522 | 0.0970679 | ||||||||
\(306\) | −12.7506 | −0.728903 | ||||||||
\(307\) | −33.9716 | −1.93886 | −0.969431 | − | 0.245363i | \(-0.921093\pi\) | ||||
−0.969431 | + | 0.245363i | \(0.921093\pi\) | |||||||
\(308\) | −1.66243 | −0.0947257 | ||||||||
\(309\) | 12.7411 | 0.724818 | ||||||||
\(310\) | 8.67865 | 0.492914 | ||||||||
\(311\) | −22.9168 | −1.29949 | −0.649746 | − | 0.760152i | \(-0.725125\pi\) | ||||
−0.649746 | + | 0.760152i | \(0.725125\pi\) | |||||||
\(312\) | 0.976529 | 0.0552851 | ||||||||
\(313\) | 23.0154 | 1.30091 | 0.650455 | − | 0.759545i | \(-0.274578\pi\) | ||||
0.650455 | + | 0.759545i | \(0.274578\pi\) | |||||||
\(314\) | −13.7020 | −0.773249 | ||||||||
\(315\) | 4.11143 | 0.231653 | ||||||||
\(316\) | −0.771969 | −0.0434266 | ||||||||
\(317\) | 2.65370 | 0.149047 | 0.0745233 | − | 0.997219i | \(-0.476256\pi\) | ||||
0.0745233 | + | 0.997219i | \(0.476256\pi\) | |||||||
\(318\) | −0.940133 | −0.0527200 | ||||||||
\(319\) | 6.41615 | 0.359235 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 6.05867 | 0.338162 | ||||||||
\(322\) | 12.9479 | 0.721561 | ||||||||
\(323\) | −6.00066 | −0.333886 | ||||||||
\(324\) | 4.53588 | 0.251994 | ||||||||
\(325\) | −1.34536 | −0.0746273 | ||||||||
\(326\) | 8.87274 | 0.491415 | ||||||||
\(327\) | −7.43689 | −0.411261 | ||||||||
\(328\) | 5.51287 | 0.304398 | ||||||||
\(329\) | 3.48395 | 0.192077 | ||||||||
\(330\) | −0.725847 | −0.0399566 | ||||||||
\(331\) | 16.8334 | 0.925245 | 0.462623 | − | 0.886555i | \(-0.346909\pi\) | ||||
0.462623 | + | 0.886555i | \(0.346909\pi\) | |||||||
\(332\) | −4.41661 | −0.242393 | ||||||||
\(333\) | −27.1424 | −1.48739 | ||||||||
\(334\) | 2.46104 | 0.134662 | ||||||||
\(335\) | 0.749628 | 0.0409566 | ||||||||
\(336\) | −1.20667 | −0.0658292 | ||||||||
\(337\) | −12.0727 | −0.657643 | −0.328821 | − | 0.944392i | \(-0.606651\pi\) | ||||
−0.328821 | + | 0.944392i | \(0.606651\pi\) | |||||||
\(338\) | 11.1900 | 0.608656 | ||||||||
\(339\) | 1.54720 | 0.0840322 | ||||||||
\(340\) | −5.15562 | −0.279603 | ||||||||
\(341\) | −8.67865 | −0.469975 | ||||||||
\(342\) | 2.87851 | 0.155652 | ||||||||
\(343\) | 18.6796 | 1.00860 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | 5.65331 | 0.304364 | ||||||||
\(346\) | 12.8786 | 0.692358 | ||||||||
\(347\) | 27.1039 | 1.45501 | 0.727507 | − | 0.686100i | \(-0.240679\pi\) | ||||
0.727507 | + | 0.686100i | \(0.240679\pi\) | |||||||
\(348\) | 4.65714 | 0.249649 | ||||||||
\(349\) | −2.80970 | −0.150400 | −0.0751999 | − | 0.997168i | \(-0.523959\pi\) | ||||
−0.0751999 | + | 0.997168i | \(0.523959\pi\) | |||||||
\(350\) | 1.66243 | 0.0888605 | ||||||||
\(351\) | 5.34468 | 0.285278 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −26.9343 | −1.43357 | −0.716783 | − | 0.697296i | \(-0.754386\pi\) | ||||
−0.716783 | + | 0.697296i | \(0.754386\pi\) | |||||||
\(354\) | −7.93575 | −0.421781 | ||||||||
\(355\) | −5.56121 | −0.295159 | ||||||||
\(356\) | 7.92294 | 0.419915 | ||||||||
\(357\) | 6.22113 | 0.329257 | ||||||||
\(358\) | 2.89487 | 0.152999 | ||||||||
\(359\) | 28.0499 | 1.48042 | 0.740209 | − | 0.672377i | \(-0.234727\pi\) | ||||
0.740209 | + | 0.672377i | \(0.234727\pi\) | |||||||
\(360\) | 2.47315 | 0.130346 | ||||||||
\(361\) | −17.6453 | −0.928701 | ||||||||
\(362\) | 8.53765 | 0.448729 | ||||||||
\(363\) | 0.725847 | 0.0380971 | ||||||||
\(364\) | 2.23657 | 0.117228 | ||||||||
\(365\) | 4.89194 | 0.256056 | ||||||||
\(366\) | −1.23047 | −0.0643177 | ||||||||
\(367\) | 22.3766 | 1.16805 | 0.584026 | − | 0.811735i | \(-0.301477\pi\) | ||||
0.584026 | + | 0.811735i | \(0.301477\pi\) | |||||||
\(368\) | 7.78857 | 0.406007 | ||||||||
\(369\) | 13.6341 | 0.709765 | ||||||||
\(370\) | −10.9749 | −0.570555 | ||||||||
\(371\) | −2.15321 | −0.111789 | ||||||||
\(372\) | −6.29938 | −0.326607 | ||||||||
\(373\) | 33.5261 | 1.73591 | 0.867957 | − | 0.496640i | \(-0.165433\pi\) | ||||
0.867957 | + | 0.496640i | \(0.165433\pi\) | |||||||
\(374\) | 5.15562 | 0.266591 | ||||||||
\(375\) | 0.725847 | 0.0374826 | ||||||||
\(376\) | 2.09570 | 0.108078 | ||||||||
\(377\) | −8.63205 | −0.444573 | ||||||||
\(378\) | −6.60428 | −0.339687 | ||||||||
\(379\) | 14.3694 | 0.738108 | 0.369054 | − | 0.929408i | \(-0.379682\pi\) | ||||
0.369054 | + | 0.929408i | \(0.379682\pi\) | |||||||
\(380\) | 1.16391 | 0.0597072 | ||||||||
\(381\) | 11.2524 | 0.576479 | ||||||||
\(382\) | −9.45261 | −0.483637 | ||||||||
\(383\) | 22.7826 | 1.16414 | 0.582069 | − | 0.813139i | \(-0.302243\pi\) | ||||
0.582069 | + | 0.813139i | \(0.302243\pi\) | |||||||
\(384\) | −0.725847 | −0.0370407 | ||||||||
\(385\) | −1.66243 | −0.0847252 | ||||||||
\(386\) | −15.2682 | −0.777133 | ||||||||
\(387\) | −2.47315 | −0.125717 | ||||||||
\(388\) | 5.76777 | 0.292814 | ||||||||
\(389\) | −39.0446 | −1.97964 | −0.989820 | − | 0.142327i | \(-0.954541\pi\) | ||||
−0.989820 | + | 0.142327i | \(0.954541\pi\) | |||||||
\(390\) | 0.976529 | 0.0494485 | ||||||||
\(391\) | −40.1549 | −2.03072 | ||||||||
\(392\) | 4.23633 | 0.213967 | ||||||||
\(393\) | −2.61849 | −0.132086 | ||||||||
\(394\) | −20.0157 | −1.00838 | ||||||||
\(395\) | −0.771969 | −0.0388420 | ||||||||
\(396\) | −2.47315 | −0.124280 | ||||||||
\(397\) | −3.27182 | −0.164208 | −0.0821040 | − | 0.996624i | \(-0.526164\pi\) | ||||
−0.0821040 | + | 0.996624i | \(0.526164\pi\) | |||||||
\(398\) | −5.22459 | −0.261885 | ||||||||
\(399\) | −1.40445 | −0.0703105 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 5.78768 | 0.289023 | 0.144512 | − | 0.989503i | \(-0.453839\pi\) | ||||
0.144512 | + | 0.989503i | \(0.453839\pi\) | |||||||
\(402\) | −0.544116 | −0.0271380 | ||||||||
\(403\) | 11.6759 | 0.581620 | ||||||||
\(404\) | 5.94038 | 0.295545 | ||||||||
\(405\) | 4.53588 | 0.225390 | ||||||||
\(406\) | 10.6664 | 0.529364 | ||||||||
\(407\) | 10.9749 | 0.544003 | ||||||||
\(408\) | 3.74219 | 0.185266 | ||||||||
\(409\) | −6.24178 | −0.308636 | −0.154318 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154318 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(410\) | 5.51287 | 0.272261 | ||||||||
\(411\) | 14.1453 | 0.697735 | ||||||||
\(412\) | 17.5535 | 0.864798 | ||||||||
\(413\) | −18.1755 | −0.894357 | ||||||||
\(414\) | 19.2623 | 0.946689 | ||||||||
\(415\) | −4.41661 | −0.216803 | ||||||||
\(416\) | 1.34536 | 0.0659619 | ||||||||
\(417\) | −5.88192 | −0.288039 | ||||||||
\(418\) | −1.16391 | −0.0569286 | ||||||||
\(419\) | 18.2981 | 0.893923 | 0.446961 | − | 0.894553i | \(-0.352506\pi\) | ||||
0.446961 | + | 0.894553i | \(0.352506\pi\) | |||||||
\(420\) | −1.20667 | −0.0588794 | ||||||||
\(421\) | 38.5499 | 1.87881 | 0.939403 | − | 0.342814i | \(-0.111380\pi\) | ||||
0.939403 | + | 0.342814i | \(0.111380\pi\) | |||||||
\(422\) | −9.53438 | −0.464126 | ||||||||
\(423\) | 5.18297 | 0.252005 | ||||||||
\(424\) | −1.29522 | −0.0629015 | ||||||||
\(425\) | −5.15562 | −0.250084 | ||||||||
\(426\) | 4.03659 | 0.195574 | ||||||||
\(427\) | −2.81818 | −0.136381 | ||||||||
\(428\) | 8.34703 | 0.403469 | ||||||||
\(429\) | −0.976529 | −0.0471473 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | −20.3620 | −0.980801 | −0.490401 | − | 0.871497i | \(-0.663150\pi\) | ||||
−0.490401 | + | 0.871497i | \(0.663150\pi\) | |||||||
\(432\) | −3.97267 | −0.191135 | ||||||||
\(433\) | −20.1175 | −0.966786 | −0.483393 | − | 0.875404i | \(-0.660596\pi\) | ||||
−0.483393 | + | 0.875404i | \(0.660596\pi\) | |||||||
\(434\) | −14.4276 | −0.692549 | ||||||||
\(435\) | 4.65714 | 0.223293 | ||||||||
\(436\) | −10.2458 | −0.490685 | ||||||||
\(437\) | 9.06517 | 0.433646 | ||||||||
\(438\) | −3.55080 | −0.169664 | ||||||||
\(439\) | 14.2368 | 0.679486 | 0.339743 | − | 0.940518i | \(-0.389660\pi\) | ||||
0.339743 | + | 0.940518i | \(0.389660\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 10.4771 | 0.498908 | ||||||||
\(442\) | −6.93618 | −0.329921 | ||||||||
\(443\) | −14.6856 | −0.697735 | −0.348867 | − | 0.937172i | \(-0.613434\pi\) | ||||
−0.348867 | + | 0.937172i | \(0.613434\pi\) | |||||||
\(444\) | 7.96607 | 0.378053 | ||||||||
\(445\) | 7.92294 | 0.375583 | ||||||||
\(446\) | −23.8079 | −1.12734 | ||||||||
\(447\) | 12.4977 | 0.591121 | ||||||||
\(448\) | −1.66243 | −0.0785424 | ||||||||
\(449\) | −3.04963 | −0.143921 | −0.0719605 | − | 0.997407i | \(-0.522926\pi\) | ||||
−0.0719605 | + | 0.997407i | \(0.522926\pi\) | |||||||
\(450\) | 2.47315 | 0.116585 | ||||||||
\(451\) | −5.51287 | −0.259591 | ||||||||
\(452\) | 2.13157 | 0.100261 | ||||||||
\(453\) | 2.25531 | 0.105964 | ||||||||
\(454\) | 13.3943 | 0.628625 | ||||||||
\(455\) | 2.23657 | 0.104852 | ||||||||
\(456\) | −0.844819 | −0.0395623 | ||||||||
\(457\) | 36.9106 | 1.72660 | 0.863301 | − | 0.504689i | \(-0.168393\pi\) | ||||
0.863301 | + | 0.504689i | \(0.168393\pi\) | |||||||
\(458\) | −22.9682 | −1.07323 | ||||||||
\(459\) | 20.4816 | 0.955998 | ||||||||
\(460\) | 7.78857 | 0.363144 | ||||||||
\(461\) | −14.3831 | −0.669889 | −0.334945 | − | 0.942238i | \(-0.608718\pi\) | ||||
−0.334945 | + | 0.942238i | \(0.608718\pi\) | |||||||
\(462\) | 1.20667 | 0.0561393 | ||||||||
\(463\) | 24.6421 | 1.14522 | 0.572608 | − | 0.819829i | \(-0.305932\pi\) | ||||
0.572608 | + | 0.819829i | \(0.305932\pi\) | |||||||
\(464\) | 6.41615 | 0.297862 | ||||||||
\(465\) | −6.29938 | −0.292127 | ||||||||
\(466\) | −1.93058 | −0.0894326 | ||||||||
\(467\) | −8.12080 | −0.375786 | −0.187893 | − | 0.982190i | \(-0.560166\pi\) | ||||
−0.187893 | + | 0.982190i | \(0.560166\pi\) | |||||||
\(468\) | 3.32728 | 0.153804 | ||||||||
\(469\) | −1.24620 | −0.0575443 | ||||||||
\(470\) | 2.09570 | 0.0966675 | ||||||||
\(471\) | 9.94557 | 0.458268 | ||||||||
\(472\) | −10.9331 | −0.503236 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 0.560332 | 0.0257369 | ||||||||
\(475\) | 1.16391 | 0.0534037 | ||||||||
\(476\) | 8.57085 | 0.392844 | ||||||||
\(477\) | −3.20327 | −0.146668 | ||||||||
\(478\) | −11.3596 | −0.519576 | ||||||||
\(479\) | 3.51328 | 0.160526 | 0.0802630 | − | 0.996774i | \(-0.474424\pi\) | ||||
0.0802630 | + | 0.996774i | \(0.474424\pi\) | |||||||
\(480\) | −0.725847 | −0.0331303 | ||||||||
\(481\) | −14.7652 | −0.673234 | ||||||||
\(482\) | −6.66307 | −0.303494 | ||||||||
\(483\) | −9.39823 | −0.427634 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 5.76777 | 0.261901 | ||||||||
\(486\) | −15.2104 | −0.689956 | ||||||||
\(487\) | 9.21794 | 0.417705 | 0.208852 | − | 0.977947i | \(-0.433027\pi\) | ||||
0.208852 | + | 0.977947i | \(0.433027\pi\) | |||||||
\(488\) | −1.69522 | −0.0767389 | ||||||||
\(489\) | −6.44025 | −0.291238 | ||||||||
\(490\) | 4.23633 | 0.191378 | ||||||||
\(491\) | −13.3645 | −0.603132 | −0.301566 | − | 0.953445i | \(-0.597509\pi\) | ||||
−0.301566 | + | 0.953445i | \(0.597509\pi\) | |||||||
\(492\) | −4.00151 | −0.180402 | ||||||||
\(493\) | −33.0792 | −1.48981 | ||||||||
\(494\) | 1.56588 | 0.0704522 | ||||||||
\(495\) | −2.47315 | −0.111160 | ||||||||
\(496\) | −8.67865 | −0.389683 | ||||||||
\(497\) | 9.24512 | 0.414700 | ||||||||
\(498\) | 3.20578 | 0.143655 | ||||||||
\(499\) | −33.2106 | −1.48671 | −0.743356 | − | 0.668896i | \(-0.766767\pi\) | ||||
−0.743356 | + | 0.668896i | \(0.766767\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −1.78634 | −0.0798077 | ||||||||
\(502\) | −11.1773 | −0.498868 | ||||||||
\(503\) | −3.60819 | −0.160881 | −0.0804407 | − | 0.996759i | \(-0.525633\pi\) | ||||
−0.0804407 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(504\) | −4.11143 | −0.183138 | ||||||||
\(505\) | 5.94038 | 0.264344 | ||||||||
\(506\) | −7.78857 | −0.346244 | ||||||||
\(507\) | −8.12223 | −0.360721 | ||||||||
\(508\) | 15.5025 | 0.687811 | ||||||||
\(509\) | 20.0548 | 0.888912 | 0.444456 | − | 0.895801i | \(-0.353397\pi\) | ||||
0.444456 | + | 0.895801i | \(0.353397\pi\) | |||||||
\(510\) | 3.74219 | 0.165707 | ||||||||
\(511\) | −8.13250 | −0.359761 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.62382 | −0.204147 | ||||||||
\(514\) | 3.34928 | 0.147730 | ||||||||
\(515\) | 17.5535 | 0.773499 | ||||||||
\(516\) | 0.725847 | 0.0319537 | ||||||||
\(517\) | −2.09570 | −0.0921688 | ||||||||
\(518\) | 18.2449 | 0.801635 | ||||||||
\(519\) | −9.34790 | −0.410327 | ||||||||
\(520\) | 1.34536 | 0.0589981 | ||||||||
\(521\) | −39.2837 | −1.72105 | −0.860524 | − | 0.509409i | \(-0.829864\pi\) | ||||
−0.860524 | + | 0.509409i | \(0.829864\pi\) | |||||||
\(522\) | 15.8681 | 0.694526 | ||||||||
\(523\) | 25.5670 | 1.11797 | 0.558984 | − | 0.829179i | \(-0.311191\pi\) | ||||
0.558984 | + | 0.829179i | \(0.311191\pi\) | |||||||
\(524\) | −3.60750 | −0.157594 | ||||||||
\(525\) | −1.20667 | −0.0526634 | ||||||||
\(526\) | 9.84688 | 0.429344 | ||||||||
\(527\) | 44.7438 | 1.94907 | ||||||||
\(528\) | 0.725847 | 0.0315885 | ||||||||
\(529\) | 37.6618 | 1.63747 | ||||||||
\(530\) | −1.29522 | −0.0562608 | ||||||||
\(531\) | −27.0391 | −1.17340 | ||||||||
\(532\) | −1.93491 | −0.0838891 | ||||||||
\(533\) | 7.41682 | 0.321258 | ||||||||
\(534\) | −5.75085 | −0.248863 | ||||||||
\(535\) | 8.34703 | 0.360874 | ||||||||
\(536\) | −0.749628 | −0.0323790 | ||||||||
\(537\) | −2.10123 | −0.0906749 | ||||||||
\(538\) | 9.33731 | 0.402560 | ||||||||
\(539\) | −4.23633 | −0.182472 | ||||||||
\(540\) | −3.97267 | −0.170956 | ||||||||
\(541\) | 3.79034 | 0.162959 | 0.0814797 | − | 0.996675i | \(-0.474035\pi\) | ||||
0.0814797 | + | 0.996675i | \(0.474035\pi\) | |||||||
\(542\) | 1.10267 | 0.0473636 | ||||||||
\(543\) | −6.19703 | −0.265940 | ||||||||
\(544\) | 5.15562 | 0.221045 | ||||||||
\(545\) | −10.2458 | −0.438882 | ||||||||
\(546\) | −1.62341 | −0.0694755 | ||||||||
\(547\) | 42.9493 | 1.83638 | 0.918189 | − | 0.396143i | \(-0.129651\pi\) | ||||
0.918189 | + | 0.396143i | \(0.129651\pi\) | |||||||
\(548\) | 19.4879 | 0.832483 | ||||||||
\(549\) | −4.19252 | −0.178932 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 7.46780 | 0.318139 | ||||||||
\(552\) | −5.65331 | −0.240621 | ||||||||
\(553\) | 1.28334 | 0.0545733 | ||||||||
\(554\) | 12.3953 | 0.526624 | ||||||||
\(555\) | 7.96607 | 0.338141 | ||||||||
\(556\) | −8.10352 | −0.343666 | ||||||||
\(557\) | 22.3786 | 0.948212 | 0.474106 | − | 0.880468i | \(-0.342771\pi\) | ||||
0.474106 | + | 0.880468i | \(0.342771\pi\) | |||||||
\(558\) | −21.4636 | −0.908625 | ||||||||
\(559\) | −1.34536 | −0.0569028 | ||||||||
\(560\) | −1.66243 | −0.0702504 | ||||||||
\(561\) | −3.74219 | −0.157996 | ||||||||
\(562\) | 20.6616 | 0.871556 | ||||||||
\(563\) | 39.7265 | 1.67427 | 0.837136 | − | 0.546994i | \(-0.184228\pi\) | ||||
0.837136 | + | 0.546994i | \(0.184228\pi\) | |||||||
\(564\) | −1.52116 | −0.0640523 | ||||||||
\(565\) | 2.13157 | 0.0896760 | ||||||||
\(566\) | 24.0191 | 1.00960 | ||||||||
\(567\) | −7.54058 | −0.316675 | ||||||||
\(568\) | 5.56121 | 0.233343 | ||||||||
\(569\) | −17.3076 | −0.725573 | −0.362786 | − | 0.931872i | \(-0.618175\pi\) | ||||
−0.362786 | + | 0.931872i | \(0.618175\pi\) | |||||||
\(570\) | −0.844819 | −0.0353856 | ||||||||
\(571\) | −14.7375 | −0.616747 | −0.308374 | − | 0.951265i | \(-0.599785\pi\) | ||||
−0.308374 | + | 0.951265i | \(0.599785\pi\) | |||||||
\(572\) | −1.34536 | −0.0562525 | ||||||||
\(573\) | 6.86115 | 0.286629 | ||||||||
\(574\) | −9.16476 | −0.382530 | ||||||||
\(575\) | 7.78857 | 0.324806 | ||||||||
\(576\) | −2.47315 | −0.103048 | ||||||||
\(577\) | 14.8862 | 0.619719 | 0.309859 | − | 0.950782i | \(-0.399718\pi\) | ||||
0.309859 | + | 0.950782i | \(0.399718\pi\) | |||||||
\(578\) | −9.58043 | −0.398493 | ||||||||
\(579\) | 11.0824 | 0.460570 | ||||||||
\(580\) | 6.41615 | 0.266416 | ||||||||
\(581\) | 7.34229 | 0.304610 | ||||||||
\(582\) | −4.18652 | −0.173537 | ||||||||
\(583\) | 1.29522 | 0.0536426 | ||||||||
\(584\) | −4.89194 | −0.202430 | ||||||||
\(585\) | 3.32728 | 0.137566 | ||||||||
\(586\) | 27.3252 | 1.12879 | ||||||||
\(587\) | 41.3213 | 1.70551 | 0.852756 | − | 0.522310i | \(-0.174929\pi\) | ||||
0.852756 | + | 0.522310i | \(0.174929\pi\) | |||||||
\(588\) | −3.07493 | −0.126808 | ||||||||
\(589\) | −10.1011 | −0.416210 | ||||||||
\(590\) | −10.9331 | −0.450108 | ||||||||
\(591\) | 14.5284 | 0.597617 | ||||||||
\(592\) | 10.9749 | 0.451064 | ||||||||
\(593\) | −16.5084 | −0.677918 | −0.338959 | − | 0.940801i | \(-0.610075\pi\) | ||||
−0.338959 | + | 0.940801i | \(0.610075\pi\) | |||||||
\(594\) | 3.97267 | 0.163001 | ||||||||
\(595\) | 8.57085 | 0.351371 | ||||||||
\(596\) | 17.2181 | 0.705280 | ||||||||
\(597\) | 3.79225 | 0.155207 | ||||||||
\(598\) | 10.4785 | 0.428496 | ||||||||
\(599\) | 37.2132 | 1.52049 | 0.760245 | − | 0.649637i | \(-0.225079\pi\) | ||||
0.760245 | + | 0.649637i | \(0.225079\pi\) | |||||||
\(600\) | −0.725847 | −0.0296326 | ||||||||
\(601\) | −7.05214 | −0.287663 | −0.143831 | − | 0.989602i | \(-0.545942\pi\) | ||||
−0.143831 | + | 0.989602i | \(0.545942\pi\) | |||||||
\(602\) | 1.66243 | 0.0677555 | ||||||||
\(603\) | −1.85394 | −0.0754983 | ||||||||
\(604\) | 3.10714 | 0.126428 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −4.31181 | −0.175155 | ||||||||
\(607\) | −24.1400 | −0.979814 | −0.489907 | − | 0.871775i | \(-0.662969\pi\) | ||||
−0.489907 | + | 0.871775i | \(0.662969\pi\) | |||||||
\(608\) | −1.16391 | −0.0472027 | ||||||||
\(609\) | −7.74217 | −0.313728 | ||||||||
\(610\) | −1.69522 | −0.0686374 | ||||||||
\(611\) | 2.81948 | 0.114064 | ||||||||
\(612\) | 12.7506 | 0.515412 | ||||||||
\(613\) | 5.92142 | 0.239164 | 0.119582 | − | 0.992824i | \(-0.461845\pi\) | ||||
0.119582 | + | 0.992824i | \(0.461845\pi\) | |||||||
\(614\) | 33.9716 | 1.37098 | ||||||||
\(615\) | −4.00151 | −0.161356 | ||||||||
\(616\) | 1.66243 | 0.0669812 | ||||||||
\(617\) | 28.2835 | 1.13865 | 0.569325 | − | 0.822112i | \(-0.307204\pi\) | ||||
0.569325 | + | 0.822112i | \(0.307204\pi\) | |||||||
\(618\) | −12.7411 | −0.512524 | ||||||||
\(619\) | 10.2965 | 0.413852 | 0.206926 | − | 0.978357i | \(-0.433654\pi\) | ||||
0.206926 | + | 0.978357i | \(0.433654\pi\) | |||||||
\(620\) | −8.67865 | −0.348543 | ||||||||
\(621\) | −30.9414 | −1.24164 | ||||||||
\(622\) | 22.9168 | 0.918879 | ||||||||
\(623\) | −13.1713 | −0.527698 | ||||||||
\(624\) | −0.976529 | −0.0390924 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.0154 | −0.919882 | ||||||||
\(627\) | 0.844819 | 0.0337388 | ||||||||
\(628\) | 13.7020 | 0.546770 | ||||||||
\(629\) | −56.5822 | −2.25608 | ||||||||
\(630\) | −4.11143 | −0.163803 | ||||||||
\(631\) | 11.9813 | 0.476970 | 0.238485 | − | 0.971146i | \(-0.423349\pi\) | ||||
0.238485 | + | 0.971146i | \(0.423349\pi\) | |||||||
\(632\) | 0.771969 | 0.0307073 | ||||||||
\(633\) | 6.92050 | 0.275065 | ||||||||
\(634\) | −2.65370 | −0.105392 | ||||||||
\(635\) | 15.5025 | 0.615197 | ||||||||
\(636\) | 0.940133 | 0.0372787 | ||||||||
\(637\) | 5.69941 | 0.225819 | ||||||||
\(638\) | −6.41615 | −0.254018 | ||||||||
\(639\) | 13.7537 | 0.544088 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −31.9150 | −1.26057 | −0.630284 | − | 0.776365i | \(-0.717062\pi\) | ||||
−0.630284 | + | 0.776365i | \(0.717062\pi\) | |||||||
\(642\) | −6.05867 | −0.239117 | ||||||||
\(643\) | −27.5708 | −1.08729 | −0.543643 | − | 0.839317i | \(-0.682955\pi\) | ||||
−0.543643 | + | 0.839317i | \(0.682955\pi\) | |||||||
\(644\) | −12.9479 | −0.510220 | ||||||||
\(645\) | 0.725847 | 0.0285802 | ||||||||
\(646\) | 6.00066 | 0.236093 | ||||||||
\(647\) | 16.4761 | 0.647743 | 0.323871 | − | 0.946101i | \(-0.395015\pi\) | ||||
0.323871 | + | 0.946101i | \(0.395015\pi\) | |||||||
\(648\) | −4.53588 | −0.178186 | ||||||||
\(649\) | 10.9331 | 0.429161 | ||||||||
\(650\) | 1.34536 | 0.0527695 | ||||||||
\(651\) | 10.4723 | 0.410440 | ||||||||
\(652\) | −8.87274 | −0.347483 | ||||||||
\(653\) | −17.3434 | −0.678698 | −0.339349 | − | 0.940661i | \(-0.610207\pi\) | ||||
−0.339349 | + | 0.940661i | \(0.610207\pi\) | |||||||
\(654\) | 7.43689 | 0.290805 | ||||||||
\(655\) | −3.60750 | −0.140957 | ||||||||
\(656\) | −5.51287 | −0.215242 | ||||||||
\(657\) | −12.0985 | −0.472007 | ||||||||
\(658\) | −3.48395 | −0.135819 | ||||||||
\(659\) | 31.9820 | 1.24584 | 0.622920 | − | 0.782286i | \(-0.285946\pi\) | ||||
0.622920 | + | 0.782286i | \(0.285946\pi\) | |||||||
\(660\) | 0.725847 | 0.0282536 | ||||||||
\(661\) | 26.6028 | 1.03473 | 0.517365 | − | 0.855765i | \(-0.326913\pi\) | ||||
0.517365 | + | 0.855765i | \(0.326913\pi\) | |||||||
\(662\) | −16.8334 | −0.654247 | ||||||||
\(663\) | 5.03461 | 0.195528 | ||||||||
\(664\) | 4.41661 | 0.171398 | ||||||||
\(665\) | −1.93491 | −0.0750327 | ||||||||
\(666\) | 27.1424 | 1.05175 | ||||||||
\(667\) | 49.9726 | 1.93495 | ||||||||
\(668\) | −2.46104 | −0.0952205 | ||||||||
\(669\) | 17.2809 | 0.668119 | ||||||||
\(670\) | −0.749628 | −0.0289607 | ||||||||
\(671\) | 1.69522 | 0.0654432 | ||||||||
\(672\) | 1.20667 | 0.0465483 | ||||||||
\(673\) | 9.46755 | 0.364947 | 0.182474 | − | 0.983211i | \(-0.441590\pi\) | ||||
0.182474 | + | 0.983211i | \(0.441590\pi\) | |||||||
\(674\) | 12.0727 | 0.465024 | ||||||||
\(675\) | −3.97267 | −0.152908 | ||||||||
\(676\) | −11.1900 | −0.430384 | ||||||||
\(677\) | −3.30003 | −0.126831 | −0.0634153 | − | 0.997987i | \(-0.520199\pi\) | ||||
−0.0634153 | + | 0.997987i | \(0.520199\pi\) | |||||||
\(678\) | −1.54720 | −0.0594197 | ||||||||
\(679\) | −9.58851 | −0.367973 | ||||||||
\(680\) | 5.15562 | 0.197709 | ||||||||
\(681\) | −9.72220 | −0.372556 | ||||||||
\(682\) | 8.67865 | 0.332323 | ||||||||
\(683\) | 27.8674 | 1.06632 | 0.533158 | − | 0.846016i | \(-0.321005\pi\) | ||||
0.533158 | + | 0.846016i | \(0.321005\pi\) | |||||||
\(684\) | −2.87851 | −0.110063 | ||||||||
\(685\) | 19.4879 | 0.744596 | ||||||||
\(686\) | −18.6796 | −0.713190 | ||||||||
\(687\) | 16.6714 | 0.636053 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −1.74254 | −0.0663856 | ||||||||
\(690\) | −5.65331 | −0.215218 | ||||||||
\(691\) | −16.2061 | −0.616508 | −0.308254 | − | 0.951304i | \(-0.599745\pi\) | ||||
−0.308254 | + | 0.951304i | \(0.599745\pi\) | |||||||
\(692\) | −12.8786 | −0.489571 | ||||||||
\(693\) | 4.11143 | 0.156180 | ||||||||
\(694\) | −27.1039 | −1.02885 | ||||||||
\(695\) | −8.10352 | −0.307384 | ||||||||
\(696\) | −4.65714 | −0.176529 | ||||||||
\(697\) | 28.4223 | 1.07657 | ||||||||
\(698\) | 2.80970 | 0.106349 | ||||||||
\(699\) | 1.40131 | 0.0530024 | ||||||||
\(700\) | −1.66243 | −0.0628339 | ||||||||
\(701\) | −9.47972 | −0.358044 | −0.179022 | − | 0.983845i | \(-0.557293\pi\) | ||||
−0.179022 | + | 0.983845i | \(0.557293\pi\) | |||||||
\(702\) | −5.34468 | −0.201722 | ||||||||
\(703\) | 12.7737 | 0.481770 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −1.52116 | −0.0572902 | ||||||||
\(706\) | 26.9343 | 1.01368 | ||||||||
\(707\) | −9.87546 | −0.371405 | ||||||||
\(708\) | 7.93575 | 0.298244 | ||||||||
\(709\) | −17.4239 | −0.654370 | −0.327185 | − | 0.944960i | \(-0.606100\pi\) | ||||
−0.327185 | + | 0.944960i | \(0.606100\pi\) | |||||||
\(710\) | 5.56121 | 0.208709 | ||||||||
\(711\) | 1.90919 | 0.0716002 | ||||||||
\(712\) | −7.92294 | −0.296925 | ||||||||
\(713\) | −67.5943 | −2.53143 | ||||||||
\(714\) | −6.22113 | −0.232820 | ||||||||
\(715\) | −1.34536 | −0.0503137 | ||||||||
\(716\) | −2.89487 | −0.108186 | ||||||||
\(717\) | 8.24534 | 0.307928 | ||||||||
\(718\) | −28.0499 | −1.04681 | ||||||||
\(719\) | −30.4682 | −1.13627 | −0.568136 | − | 0.822935i | \(-0.692335\pi\) | ||||
−0.568136 | + | 0.822935i | \(0.692335\pi\) | |||||||
\(720\) | −2.47315 | −0.0921687 | ||||||||
\(721\) | −29.1814 | −1.08677 | ||||||||
\(722\) | 17.6453 | 0.656691 | ||||||||
\(723\) | 4.83637 | 0.179867 | ||||||||
\(724\) | −8.53765 | −0.317299 | ||||||||
\(725\) | 6.41615 | 0.238290 | ||||||||
\(726\) | −0.725847 | −0.0269387 | ||||||||
\(727\) | −19.1274 | −0.709395 | −0.354697 | − | 0.934981i | \(-0.615416\pi\) | ||||
−0.354697 | + | 0.934981i | \(0.615416\pi\) | |||||||
\(728\) | −2.23657 | −0.0828928 | ||||||||
\(729\) | −2.56725 | −0.0950832 | ||||||||
\(730\) | −4.89194 | −0.181059 | ||||||||
\(731\) | −5.15562 | −0.190688 | ||||||||
\(732\) | 1.23047 | 0.0454795 | ||||||||
\(733\) | −21.3728 | −0.789423 | −0.394711 | − | 0.918805i | \(-0.629155\pi\) | ||||
−0.394711 | + | 0.918805i | \(0.629155\pi\) | |||||||
\(734\) | −22.3766 | −0.825937 | ||||||||
\(735\) | −3.07493 | −0.113421 | ||||||||
\(736\) | −7.78857 | −0.287091 | ||||||||
\(737\) | 0.749628 | 0.0276129 | ||||||||
\(738\) | −13.6341 | −0.501880 | ||||||||
\(739\) | 1.61737 | 0.0594958 | 0.0297479 | − | 0.999557i | \(-0.490530\pi\) | ||||
0.0297479 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(740\) | 10.9749 | 0.403444 | ||||||||
\(741\) | −1.13659 | −0.0417536 | ||||||||
\(742\) | 2.15321 | 0.0790469 | ||||||||
\(743\) | −25.8471 | −0.948239 | −0.474119 | − | 0.880461i | \(-0.657233\pi\) | ||||
−0.474119 | + | 0.880461i | \(0.657233\pi\) | |||||||
\(744\) | 6.29938 | 0.230946 | ||||||||
\(745\) | 17.2181 | 0.630822 | ||||||||
\(746\) | −33.5261 | −1.22748 | ||||||||
\(747\) | 10.9229 | 0.399648 | ||||||||
\(748\) | −5.15562 | −0.188508 | ||||||||
\(749\) | −13.8763 | −0.507030 | ||||||||
\(750\) | −0.725847 | −0.0265042 | ||||||||
\(751\) | 36.5242 | 1.33279 | 0.666393 | − | 0.745601i | \(-0.267837\pi\) | ||||
0.666393 | + | 0.745601i | \(0.267837\pi\) | |||||||
\(752\) | −2.09570 | −0.0764223 | ||||||||
\(753\) | 8.11303 | 0.295655 | ||||||||
\(754\) | 8.63205 | 0.314361 | ||||||||
\(755\) | 3.10714 | 0.113081 | ||||||||
\(756\) | 6.60428 | 0.240195 | ||||||||
\(757\) | −5.42796 | −0.197283 | −0.0986413 | − | 0.995123i | \(-0.531450\pi\) | ||||
−0.0986413 | + | 0.995123i | \(0.531450\pi\) | |||||||
\(758\) | −14.3694 | −0.521921 | ||||||||
\(759\) | 5.65331 | 0.205202 | ||||||||
\(760\) | −1.16391 | −0.0422193 | ||||||||
\(761\) | −25.1423 | −0.911407 | −0.455703 | − | 0.890132i | \(-0.650612\pi\) | ||||
−0.455703 | + | 0.890132i | \(0.650612\pi\) | |||||||
\(762\) | −11.2524 | −0.407632 | ||||||||
\(763\) | 17.0329 | 0.616633 | ||||||||
\(764\) | 9.45261 | 0.341983 | ||||||||
\(765\) | 12.7506 | 0.460999 | ||||||||
\(766\) | −22.7826 | −0.823170 | ||||||||
\(767\) | −14.7090 | −0.531110 | ||||||||
\(768\) | 0.725847 | 0.0261918 | ||||||||
\(769\) | −37.5144 | −1.35280 | −0.676401 | − | 0.736534i | \(-0.736461\pi\) | ||||
−0.676401 | + | 0.736534i | \(0.736461\pi\) | |||||||
\(770\) | 1.66243 | 0.0599098 | ||||||||
\(771\) | −2.43107 | −0.0875527 | ||||||||
\(772\) | 15.2682 | 0.549516 | ||||||||
\(773\) | −39.6749 | −1.42701 | −0.713503 | − | 0.700652i | \(-0.752892\pi\) | ||||
−0.713503 | + | 0.700652i | \(0.752892\pi\) | |||||||
\(774\) | 2.47315 | 0.0888954 | ||||||||
\(775\) | −8.67865 | −0.311746 | ||||||||
\(776\) | −5.76777 | −0.207051 | ||||||||
\(777\) | −13.2430 | −0.475091 | ||||||||
\(778\) | 39.0446 | 1.39982 | ||||||||
\(779\) | −6.41647 | −0.229894 | ||||||||
\(780\) | −0.976529 | −0.0349653 | ||||||||
\(781\) | −5.56121 | −0.198996 | ||||||||
\(782\) | 40.1549 | 1.43594 | ||||||||
\(783\) | −25.4892 | −0.910910 | ||||||||
\(784\) | −4.23633 | −0.151298 | ||||||||
\(785\) | 13.7020 | 0.489046 | ||||||||
\(786\) | 2.61849 | 0.0933986 | ||||||||
\(787\) | 4.79221 | 0.170824 | 0.0854119 | − | 0.996346i | \(-0.472779\pi\) | ||||
0.0854119 | + | 0.996346i | \(0.472779\pi\) | |||||||
\(788\) | 20.0157 | 0.713031 | ||||||||
\(789\) | −7.14733 | −0.254452 | ||||||||
\(790\) | 0.771969 | 0.0274654 | ||||||||
\(791\) | −3.54359 | −0.125995 | ||||||||
\(792\) | 2.47315 | 0.0878794 | ||||||||
\(793\) | −2.28068 | −0.0809895 | ||||||||
\(794\) | 3.27182 | 0.116113 | ||||||||
\(795\) | 0.940133 | 0.0333431 | ||||||||
\(796\) | 5.22459 | 0.185181 | ||||||||
\(797\) | −40.7575 | −1.44370 | −0.721852 | − | 0.692047i | \(-0.756709\pi\) | ||||
−0.721852 | + | 0.692047i | \(0.756709\pi\) | |||||||
\(798\) | 1.40445 | 0.0497170 | ||||||||
\(799\) | 10.8046 | 0.382241 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −19.5946 | −0.692340 | ||||||||
\(802\) | −5.78768 | −0.204370 | ||||||||
\(803\) | 4.89194 | 0.172633 | ||||||||
\(804\) | 0.544116 | 0.0191895 | ||||||||
\(805\) | −12.9479 | −0.456355 | ||||||||
\(806\) | −11.6759 | −0.411267 | ||||||||
\(807\) | −6.77746 | −0.238578 | ||||||||
\(808\) | −5.94038 | −0.208982 | ||||||||
\(809\) | 29.1429 | 1.02461 | 0.512306 | − | 0.858803i | \(-0.328791\pi\) | ||||
0.512306 | + | 0.858803i | \(0.328791\pi\) | |||||||
\(810\) | −4.53588 | −0.159375 | ||||||||
\(811\) | −16.3237 | −0.573202 | −0.286601 | − | 0.958050i | \(-0.592525\pi\) | ||||
−0.286601 | + | 0.958050i | \(0.592525\pi\) | |||||||
\(812\) | −10.6664 | −0.374317 | ||||||||
\(813\) | −0.800368 | −0.0280701 | ||||||||
\(814\) | −10.9749 | −0.384668 | ||||||||
\(815\) | −8.87274 | −0.310798 | ||||||||
\(816\) | −3.74219 | −0.131003 | ||||||||
\(817\) | 1.16391 | 0.0407200 | ||||||||
\(818\) | 6.24178 | 0.218239 | ||||||||
\(819\) | −5.53136 | −0.193282 | ||||||||
\(820\) | −5.51287 | −0.192518 | ||||||||
\(821\) | −40.6484 | −1.41864 | −0.709320 | − | 0.704887i | \(-0.750998\pi\) | ||||
−0.709320 | + | 0.704887i | \(0.750998\pi\) | |||||||
\(822\) | −14.1453 | −0.493373 | ||||||||
\(823\) | −23.5895 | −0.822280 | −0.411140 | − | 0.911572i | \(-0.634869\pi\) | ||||
−0.411140 | + | 0.911572i | \(0.634869\pi\) | |||||||
\(824\) | −17.5535 | −0.611504 | ||||||||
\(825\) | 0.725847 | 0.0252708 | ||||||||
\(826\) | 18.1755 | 0.632406 | ||||||||
\(827\) | 0.558107 | 0.0194073 | 0.00970363 | − | 0.999953i | \(-0.496911\pi\) | ||||
0.00970363 | + | 0.999953i | \(0.496911\pi\) | |||||||
\(828\) | −19.2623 | −0.669410 | ||||||||
\(829\) | 29.0461 | 1.00881 | 0.504407 | − | 0.863466i | \(-0.331711\pi\) | ||||
0.504407 | + | 0.863466i | \(0.331711\pi\) | |||||||
\(830\) | 4.41661 | 0.153303 | ||||||||
\(831\) | −8.99707 | −0.312105 | ||||||||
\(832\) | −1.34536 | −0.0466421 | ||||||||
\(833\) | 21.8409 | 0.756743 | ||||||||
\(834\) | 5.88192 | 0.203674 | ||||||||
\(835\) | −2.46104 | −0.0851678 | ||||||||
\(836\) | 1.16391 | 0.0402546 | ||||||||
\(837\) | 34.4774 | 1.19171 | ||||||||
\(838\) | −18.2981 | −0.632099 | ||||||||
\(839\) | −32.5345 | −1.12322 | −0.561608 | − | 0.827403i | \(-0.689817\pi\) | ||||
−0.561608 | + | 0.827403i | \(0.689817\pi\) | |||||||
\(840\) | 1.20667 | 0.0416341 | ||||||||
\(841\) | 12.1669 | 0.419549 | ||||||||
\(842\) | −38.5499 | −1.32852 | ||||||||
\(843\) | −14.9972 | −0.516529 | ||||||||
\(844\) | 9.53438 | 0.328187 | ||||||||
\(845\) | −11.1900 | −0.384948 | ||||||||
\(846\) | −5.18297 | −0.178194 | ||||||||
\(847\) | −1.66243 | −0.0571217 | ||||||||
\(848\) | 1.29522 | 0.0444781 | ||||||||
\(849\) | −17.4342 | −0.598340 | ||||||||
\(850\) | 5.15562 | 0.176836 | ||||||||
\(851\) | 85.4784 | 2.93016 | ||||||||
\(852\) | −4.03659 | −0.138291 | ||||||||
\(853\) | 31.1007 | 1.06487 | 0.532434 | − | 0.846471i | \(-0.321277\pi\) | ||||
0.532434 | + | 0.846471i | \(0.321277\pi\) | |||||||
\(854\) | 2.81818 | 0.0964361 | ||||||||
\(855\) | −2.87851 | −0.0984430 | ||||||||
\(856\) | −8.34703 | −0.285296 | ||||||||
\(857\) | −26.9867 | −0.921848 | −0.460924 | − | 0.887440i | \(-0.652482\pi\) | ||||
−0.460924 | + | 0.887440i | \(0.652482\pi\) | |||||||
\(858\) | 0.976529 | 0.0333381 | ||||||||
\(859\) | −1.97488 | −0.0673822 | −0.0336911 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336911 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | 6.65222 | 0.226707 | ||||||||
\(862\) | 20.3620 | 0.693531 | ||||||||
\(863\) | 25.4791 | 0.867320 | 0.433660 | − | 0.901077i | \(-0.357222\pi\) | ||||
0.433660 | + | 0.901077i | \(0.357222\pi\) | |||||||
\(864\) | 3.97267 | 0.135153 | ||||||||
\(865\) | −12.8786 | −0.437886 | ||||||||
\(866\) | 20.1175 | 0.683621 | ||||||||
\(867\) | 6.95393 | 0.236168 | ||||||||
\(868\) | 14.4276 | 0.489706 | ||||||||
\(869\) | −0.771969 | −0.0261872 | ||||||||
\(870\) | −4.65714 | −0.157892 | ||||||||
\(871\) | −1.00852 | −0.0341725 | ||||||||
\(872\) | 10.2458 | 0.346967 | ||||||||
\(873\) | −14.2645 | −0.482782 | ||||||||
\(874\) | −9.06517 | −0.306634 | ||||||||
\(875\) | −1.66243 | −0.0562003 | ||||||||
\(876\) | 3.55080 | 0.119970 | ||||||||
\(877\) | −34.5634 | −1.16712 | −0.583562 | − | 0.812068i | \(-0.698342\pi\) | ||||
−0.583562 | + | 0.812068i | \(0.698342\pi\) | |||||||
\(878\) | −14.2368 | −0.480469 | ||||||||
\(879\) | −19.8339 | −0.668981 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 46.2609 | 1.55857 | 0.779285 | − | 0.626670i | \(-0.215583\pi\) | ||||
0.779285 | + | 0.626670i | \(0.215583\pi\) | |||||||
\(882\) | −10.4771 | −0.352781 | ||||||||
\(883\) | −22.4064 | −0.754036 | −0.377018 | − | 0.926206i | \(-0.623051\pi\) | ||||
−0.377018 | + | 0.926206i | \(0.623051\pi\) | |||||||
\(884\) | 6.93618 | 0.233289 | ||||||||
\(885\) | 7.93575 | 0.266757 | ||||||||
\(886\) | 14.6856 | 0.493373 | ||||||||
\(887\) | −22.3812 | −0.751488 | −0.375744 | − | 0.926723i | \(-0.622613\pi\) | ||||
−0.375744 | + | 0.926723i | \(0.622613\pi\) | |||||||
\(888\) | −7.96607 | −0.267324 | ||||||||
\(889\) | −25.7717 | −0.864356 | ||||||||
\(890\) | −7.92294 | −0.265578 | ||||||||
\(891\) | 4.53588 | 0.151958 | ||||||||
\(892\) | 23.8079 | 0.797148 | ||||||||
\(893\) | −2.43920 | −0.0816247 | ||||||||
\(894\) | −12.4977 | −0.417986 | ||||||||
\(895\) | −2.89487 | −0.0967648 | ||||||||
\(896\) | 1.66243 | 0.0555378 | ||||||||
\(897\) | −7.60576 | −0.253949 | ||||||||
\(898\) | 3.04963 | 0.101767 | ||||||||
\(899\) | −55.6835 | −1.85715 | ||||||||
\(900\) | −2.47315 | −0.0824382 | ||||||||
\(901\) | −6.67767 | −0.222465 | ||||||||
\(902\) | 5.51287 | 0.183559 | ||||||||
\(903\) | −1.20667 | −0.0401554 | ||||||||
\(904\) | −2.13157 | −0.0708951 | ||||||||
\(905\) | −8.53765 | −0.283801 | ||||||||
\(906\) | −2.25531 | −0.0749277 | ||||||||
\(907\) | 42.3764 | 1.40709 | 0.703543 | − | 0.710653i | \(-0.251600\pi\) | ||||
0.703543 | + | 0.710653i | \(0.251600\pi\) | |||||||
\(908\) | −13.3943 | −0.444505 | ||||||||
\(909\) | −14.6914 | −0.487284 | ||||||||
\(910\) | −2.23657 | −0.0741416 | ||||||||
\(911\) | 13.6647 | 0.452733 | 0.226366 | − | 0.974042i | \(-0.427315\pi\) | ||||
0.226366 | + | 0.974042i | \(0.427315\pi\) | |||||||
\(912\) | 0.844819 | 0.0279748 | ||||||||
\(913\) | −4.41661 | −0.146168 | ||||||||
\(914\) | −36.9106 | −1.22089 | ||||||||
\(915\) | 1.23047 | 0.0406781 | ||||||||
\(916\) | 22.9682 | 0.758889 | ||||||||
\(917\) | 5.99721 | 0.198045 | ||||||||
\(918\) | −20.4816 | −0.675993 | ||||||||
\(919\) | −6.36128 | −0.209839 | −0.104920 | − | 0.994481i | \(-0.533459\pi\) | ||||
−0.104920 | + | 0.994481i | \(0.533459\pi\) | |||||||
\(920\) | −7.78857 | −0.256782 | ||||||||
\(921\) | −24.6582 | −0.812516 | ||||||||
\(922\) | 14.3831 | 0.473683 | ||||||||
\(923\) | 7.48185 | 0.246268 | ||||||||
\(924\) | −1.20667 | −0.0396965 | ||||||||
\(925\) | 10.9749 | 0.360851 | ||||||||
\(926\) | −24.6421 | −0.809790 | ||||||||
\(927\) | −43.4123 | −1.42585 | ||||||||
\(928\) | −6.41615 | −0.210620 | ||||||||
\(929\) | −46.5834 | −1.52835 | −0.764176 | − | 0.645007i | \(-0.776854\pi\) | ||||
−0.764176 | + | 0.645007i | \(0.776854\pi\) | |||||||
\(930\) | 6.29938 | 0.206565 | ||||||||
\(931\) | −4.93070 | −0.161597 | ||||||||
\(932\) | 1.93058 | 0.0632384 | ||||||||
\(933\) | −16.6341 | −0.544575 | ||||||||
\(934\) | 8.12080 | 0.265721 | ||||||||
\(935\) | −5.15562 | −0.168607 | ||||||||
\(936\) | −3.32728 | −0.108756 | ||||||||
\(937\) | 22.6834 | 0.741034 | 0.370517 | − | 0.928826i | \(-0.379181\pi\) | ||||
0.370517 | + | 0.928826i | \(0.379181\pi\) | |||||||
\(938\) | 1.24620 | 0.0406900 | ||||||||
\(939\) | 16.7057 | 0.545170 | ||||||||
\(940\) | −2.09570 | −0.0683542 | ||||||||
\(941\) | −40.0804 | −1.30658 | −0.653291 | − | 0.757107i | \(-0.726612\pi\) | ||||
−0.653291 | + | 0.757107i | \(0.726612\pi\) | |||||||
\(942\) | −9.94557 | −0.324044 | ||||||||
\(943\) | −42.9374 | −1.39823 | ||||||||
\(944\) | 10.9331 | 0.355842 | ||||||||
\(945\) | 6.60428 | 0.214837 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | −55.3428 | −1.79840 | −0.899199 | − | 0.437540i | \(-0.855850\pi\) | ||||
−0.899199 | + | 0.437540i | \(0.855850\pi\) | |||||||
\(948\) | −0.560332 | −0.0181987 | ||||||||
\(949\) | −6.58144 | −0.213642 | ||||||||
\(950\) | −1.16391 | −0.0377621 | ||||||||
\(951\) | 1.92618 | 0.0624607 | ||||||||
\(952\) | −8.57085 | −0.277783 | ||||||||
\(953\) | 55.5477 | 1.79937 | 0.899684 | − | 0.436542i | \(-0.143797\pi\) | ||||
0.899684 | + | 0.436542i | \(0.143797\pi\) | |||||||
\(954\) | 3.20327 | 0.103710 | ||||||||
\(955\) | 9.45261 | 0.305879 | ||||||||
\(956\) | 11.3596 | 0.367396 | ||||||||
\(957\) | 4.65714 | 0.150544 | ||||||||
\(958\) | −3.51328 | −0.113509 | ||||||||
\(959\) | −32.3973 | −1.04616 | ||||||||
\(960\) | 0.725847 | 0.0234266 | ||||||||
\(961\) | 44.3190 | 1.42964 | ||||||||
\(962\) | 14.7652 | 0.476048 | ||||||||
\(963\) | −20.6434 | −0.665225 | ||||||||
\(964\) | 6.66307 | 0.214603 | ||||||||
\(965\) | 15.2682 | 0.491502 | ||||||||
\(966\) | 9.39823 | 0.302383 | ||||||||
\(967\) | 18.0659 | 0.580960 | 0.290480 | − | 0.956881i | \(-0.406185\pi\) | ||||
0.290480 | + | 0.956881i | \(0.406185\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −4.35557 | −0.139921 | ||||||||
\(970\) | −5.76777 | −0.185192 | ||||||||
\(971\) | 16.2962 | 0.522971 | 0.261485 | − | 0.965207i | \(-0.415788\pi\) | ||||
0.261485 | + | 0.965207i | \(0.415788\pi\) | |||||||
\(972\) | 15.2104 | 0.487873 | ||||||||
\(973\) | 13.4715 | 0.431877 | ||||||||
\(974\) | −9.21794 | −0.295362 | ||||||||
\(975\) | −0.976529 | −0.0312739 | ||||||||
\(976\) | 1.69522 | 0.0542626 | ||||||||
\(977\) | 26.3379 | 0.842624 | 0.421312 | − | 0.906916i | \(-0.361570\pi\) | ||||
0.421312 | + | 0.906916i | \(0.361570\pi\) | |||||||
\(978\) | 6.44025 | 0.205937 | ||||||||
\(979\) | 7.92294 | 0.253218 | ||||||||
\(980\) | −4.23633 | −0.135325 | ||||||||
\(981\) | 25.3394 | 0.809024 | ||||||||
\(982\) | 13.3645 | 0.426479 | ||||||||
\(983\) | 11.0128 | 0.351255 | 0.175628 | − | 0.984457i | \(-0.443805\pi\) | ||||
0.175628 | + | 0.984457i | \(0.443805\pi\) | |||||||
\(984\) | 4.00151 | 0.127563 | ||||||||
\(985\) | 20.0157 | 0.637754 | ||||||||
\(986\) | 33.0792 | 1.05346 | ||||||||
\(987\) | 2.52882 | 0.0804932 | ||||||||
\(988\) | −1.56588 | −0.0498172 | ||||||||
\(989\) | 7.78857 | 0.247662 | ||||||||
\(990\) | 2.47315 | 0.0786017 | ||||||||
\(991\) | −18.6838 | −0.593512 | −0.296756 | − | 0.954953i | \(-0.595905\pi\) | ||||
−0.296756 | + | 0.954953i | \(0.595905\pi\) | |||||||
\(992\) | 8.67865 | 0.275547 | ||||||||
\(993\) | 12.2185 | 0.387741 | ||||||||
\(994\) | −9.24512 | −0.293237 | ||||||||
\(995\) | 5.22459 | 0.165631 | ||||||||
\(996\) | −3.20578 | −0.101579 | ||||||||
\(997\) | −51.8224 | −1.64123 | −0.820617 | − | 0.571479i | \(-0.806370\pi\) | ||||
−0.820617 | + | 0.571479i | \(0.806370\pi\) | |||||||
\(998\) | 33.2106 | 1.05126 | ||||||||
\(999\) | −43.5995 | −1.37943 |
(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 | 4730.2.a.z.1.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.z.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial |