Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41678 | −1.00181 | −0.500907 | − | 0.865501i | \(-0.667000\pi\) | ||||
−0.500907 | + | 0.865501i | \(0.667000\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.00726459 | 0.00363230 | ||||||||
\(5\) | 2.31073 | 1.03339 | 0.516695 | − | 0.856170i | \(-0.327162\pi\) | ||||
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(6\) | −1.41678 | −0.578398 | ||||||||
\(7\) | 2.67795 | 1.01217 | 0.506085 | − | 0.862484i | \(-0.331092\pi\) | ||||
0.506085 | + | 0.862484i | \(0.331092\pi\) | |||||||
\(8\) | 2.82327 | 0.998176 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.27380 | −1.03526 | ||||||||
\(11\) | −4.03181 | −1.21564 | −0.607818 | − | 0.794076i | \(-0.707955\pi\) | ||||
−0.607818 | + | 0.794076i | \(0.707955\pi\) | |||||||
\(12\) | 0.00726459 | 0.00209711 | ||||||||
\(13\) | −3.81653 | −1.05851 | −0.529257 | − | 0.848462i | \(-0.677529\pi\) | ||||
−0.529257 | + | 0.848462i | \(0.677529\pi\) | |||||||
\(14\) | −3.79406 | −1.01401 | ||||||||
\(15\) | 2.31073 | 0.596628 | ||||||||
\(16\) | −4.01448 | −1.00362 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.41678 | −0.333938 | ||||||||
\(19\) | −5.43435 | −1.24673 | −0.623363 | − | 0.781933i | \(-0.714234\pi\) | ||||
−0.623363 | + | 0.781933i | \(0.714234\pi\) | |||||||
\(20\) | 0.0167865 | 0.00375358 | ||||||||
\(21\) | 2.67795 | 0.584377 | ||||||||
\(22\) | 5.71219 | 1.21784 | ||||||||
\(23\) | −4.96423 | −1.03511 | −0.517556 | − | 0.855649i | \(-0.673158\pi\) | ||||
−0.517556 | + | 0.855649i | \(0.673158\pi\) | |||||||
\(24\) | 2.82327 | 0.576297 | ||||||||
\(25\) | 0.339473 | 0.0678945 | ||||||||
\(26\) | 5.40718 | 1.06043 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.0194542 | 0.00367650 | ||||||||
\(29\) | 7.33326 | 1.36175 | 0.680876 | − | 0.732399i | \(-0.261599\pi\) | ||||
0.680876 | + | 0.732399i | \(0.261599\pi\) | |||||||
\(30\) | −3.27380 | −0.597710 | ||||||||
\(31\) | 7.79303 | 1.39967 | 0.699835 | − | 0.714304i | \(-0.253257\pi\) | ||||
0.699835 | + | 0.714304i | \(0.253257\pi\) | |||||||
\(32\) | 0.0410945 | 0.00726456 | ||||||||
\(33\) | −4.03181 | −0.701848 | ||||||||
\(34\) | 1.41678 | 0.242976 | ||||||||
\(35\) | 6.18802 | 1.04597 | ||||||||
\(36\) | 0.00726459 | 0.00121077 | ||||||||
\(37\) | −4.21869 | −0.693548 | −0.346774 | − | 0.937949i | \(-0.612723\pi\) | ||||
−0.346774 | + | 0.937949i | \(0.612723\pi\) | |||||||
\(38\) | 7.69927 | 1.24899 | ||||||||
\(39\) | −3.81653 | −0.611133 | ||||||||
\(40\) | 6.52381 | 1.03150 | ||||||||
\(41\) | −0.767137 | −0.119807 | −0.0599034 | − | 0.998204i | \(-0.519079\pi\) | ||||
−0.0599034 | + | 0.998204i | \(0.519079\pi\) | |||||||
\(42\) | −3.79406 | −0.585437 | ||||||||
\(43\) | −0.0132232 | −0.00201652 | −0.00100826 | − | 0.999999i | \(-0.500321\pi\) | ||||
−0.00100826 | + | 0.999999i | \(0.500321\pi\) | |||||||
\(44\) | −0.0292895 | −0.00441555 | ||||||||
\(45\) | 2.31073 | 0.344463 | ||||||||
\(46\) | 7.03321 | 1.03699 | ||||||||
\(47\) | −4.65762 | −0.679383 | −0.339692 | − | 0.940537i | \(-0.610323\pi\) | ||||
−0.339692 | + | 0.940537i | \(0.610323\pi\) | |||||||
\(48\) | −4.01448 | −0.579440 | ||||||||
\(49\) | 0.171415 | 0.0244879 | ||||||||
\(50\) | −0.480958 | −0.0680177 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −0.0277255 | −0.00384483 | ||||||||
\(53\) | 7.15400 | 0.982677 | 0.491338 | − | 0.870969i | \(-0.336508\pi\) | ||||
0.491338 | + | 0.870969i | \(0.336508\pi\) | |||||||
\(54\) | −1.41678 | −0.192799 | ||||||||
\(55\) | −9.31643 | −1.25623 | ||||||||
\(56\) | 7.56057 | 1.01032 | ||||||||
\(57\) | −5.43435 | −0.719797 | ||||||||
\(58\) | −10.3896 | −1.36422 | ||||||||
\(59\) | −1.07505 | −0.139959 | −0.0699797 | − | 0.997548i | \(-0.522293\pi\) | ||||
−0.0699797 | + | 0.997548i | \(0.522293\pi\) | |||||||
\(60\) | 0.0167865 | 0.00216713 | ||||||||
\(61\) | 5.20154 | 0.665989 | 0.332994 | − | 0.942929i | \(-0.391941\pi\) | ||||
0.332994 | + | 0.942929i | \(0.391941\pi\) | |||||||
\(62\) | −11.0410 | −1.40221 | ||||||||
\(63\) | 2.67795 | 0.337390 | ||||||||
\(64\) | 7.97073 | 0.996341 | ||||||||
\(65\) | −8.81896 | −1.09386 | ||||||||
\(66\) | 5.71219 | 0.703122 | ||||||||
\(67\) | 11.7690 | 1.43781 | 0.718906 | − | 0.695107i | \(-0.244643\pi\) | ||||
0.718906 | + | 0.695107i | \(0.244643\pi\) | |||||||
\(68\) | −0.00726459 | −0.000880961 0 | ||||||||
\(69\) | −4.96423 | −0.597623 | ||||||||
\(70\) | −8.76706 | −1.04786 | ||||||||
\(71\) | 8.38610 | 0.995247 | 0.497623 | − | 0.867393i | \(-0.334206\pi\) | ||||
0.497623 | + | 0.867393i | \(0.334206\pi\) | |||||||
\(72\) | 2.82327 | 0.332725 | ||||||||
\(73\) | −15.9963 | −1.87222 | −0.936111 | − | 0.351705i | \(-0.885602\pi\) | ||||
−0.936111 | + | 0.351705i | \(0.885602\pi\) | |||||||
\(74\) | 5.97695 | 0.694806 | ||||||||
\(75\) | 0.339473 | 0.0391989 | ||||||||
\(76\) | −0.0394783 | −0.00452847 | ||||||||
\(77\) | −10.7970 | −1.23043 | ||||||||
\(78\) | 5.40718 | 0.612242 | ||||||||
\(79\) | 13.7133 | 1.54287 | 0.771433 | − | 0.636310i | \(-0.219540\pi\) | ||||
0.771433 | + | 0.636310i | \(0.219540\pi\) | |||||||
\(80\) | −9.27637 | −1.03713 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.08686 | 0.120024 | ||||||||
\(83\) | −5.99969 | −0.658551 | −0.329276 | − | 0.944234i | \(-0.606804\pi\) | ||||
−0.329276 | + | 0.944234i | \(0.606804\pi\) | |||||||
\(84\) | 0.0194542 | 0.00212263 | ||||||||
\(85\) | −2.31073 | −0.250634 | ||||||||
\(86\) | 0.0187344 | 0.00202018 | ||||||||
\(87\) | 7.33326 | 0.786208 | ||||||||
\(88\) | −11.3829 | −1.21342 | ||||||||
\(89\) | 13.1505 | 1.39395 | 0.696976 | − | 0.717094i | \(-0.254528\pi\) | ||||
0.696976 | + | 0.717094i | \(0.254528\pi\) | |||||||
\(90\) | −3.27380 | −0.345088 | ||||||||
\(91\) | −10.2205 | −1.07140 | ||||||||
\(92\) | −0.0360631 | −0.00375984 | ||||||||
\(93\) | 7.79303 | 0.808100 | ||||||||
\(94\) | 6.59882 | 0.680616 | ||||||||
\(95\) | −12.5573 | −1.28835 | ||||||||
\(96\) | 0.0410945 | 0.00419419 | ||||||||
\(97\) | −12.7568 | −1.29526 | −0.647631 | − | 0.761954i | \(-0.724240\pi\) | ||||
−0.647631 | + | 0.761954i | \(0.724240\pi\) | |||||||
\(98\) | −0.242858 | −0.0245324 | ||||||||
\(99\) | −4.03181 | −0.405212 | ||||||||
\(100\) | 0.00246613 | 0.000246613 0 | ||||||||
\(101\) | −5.53926 | −0.551177 | −0.275588 | − | 0.961276i | \(-0.588873\pi\) | ||||
−0.275588 | + | 0.961276i | \(0.588873\pi\) | |||||||
\(102\) | 1.41678 | 0.140282 | ||||||||
\(103\) | −12.5811 | −1.23965 | −0.619825 | − | 0.784740i | \(-0.712797\pi\) | ||||
−0.619825 | + | 0.784740i | \(0.712797\pi\) | |||||||
\(104\) | −10.7751 | −1.05658 | ||||||||
\(105\) | 6.18802 | 0.603889 | ||||||||
\(106\) | −10.1356 | −0.984460 | ||||||||
\(107\) | −15.9193 | −1.53898 | −0.769490 | − | 0.638659i | \(-0.779490\pi\) | ||||
−0.769490 | + | 0.638659i | \(0.779490\pi\) | |||||||
\(108\) | 0.00726459 | 0.000699036 0 | ||||||||
\(109\) | 10.3418 | 0.990569 | 0.495285 | − | 0.868731i | \(-0.335064\pi\) | ||||
0.495285 | + | 0.868731i | \(0.335064\pi\) | |||||||
\(110\) | 13.1993 | 1.25851 | ||||||||
\(111\) | −4.21869 | −0.400420 | ||||||||
\(112\) | −10.7506 | −1.01583 | ||||||||
\(113\) | −4.48878 | −0.422269 | −0.211134 | − | 0.977457i | \(-0.567716\pi\) | ||||
−0.211134 | + | 0.977457i | \(0.567716\pi\) | |||||||
\(114\) | 7.69927 | 0.721103 | ||||||||
\(115\) | −11.4710 | −1.06967 | ||||||||
\(116\) | 0.0532731 | 0.00494629 | ||||||||
\(117\) | −3.81653 | −0.352838 | ||||||||
\(118\) | 1.52311 | 0.140213 | ||||||||
\(119\) | −2.67795 | −0.245487 | ||||||||
\(120\) | 6.52381 | 0.595539 | ||||||||
\(121\) | 5.25550 | 0.477773 | ||||||||
\(122\) | −7.36943 | −0.667197 | ||||||||
\(123\) | −0.767137 | −0.0691704 | ||||||||
\(124\) | 0.0566132 | 0.00508402 | ||||||||
\(125\) | −10.7692 | −0.963228 | ||||||||
\(126\) | −3.79406 | −0.338002 | ||||||||
\(127\) | −11.5414 | −1.02414 | −0.512068 | − | 0.858945i | \(-0.671120\pi\) | ||||
−0.512068 | + | 0.858945i | \(0.671120\pi\) | |||||||
\(128\) | −11.3750 | −1.00541 | ||||||||
\(129\) | −0.0132232 | −0.00116424 | ||||||||
\(130\) | 12.4945 | 1.09584 | ||||||||
\(131\) | 1.04204 | 0.0910436 | 0.0455218 | − | 0.998963i | \(-0.485505\pi\) | ||||
0.0455218 | + | 0.998963i | \(0.485505\pi\) | |||||||
\(132\) | −0.0292895 | −0.00254932 | ||||||||
\(133\) | −14.5529 | −1.26190 | ||||||||
\(134\) | −16.6741 | −1.44042 | ||||||||
\(135\) | 2.31073 | 0.198876 | ||||||||
\(136\) | −2.82327 | −0.242093 | ||||||||
\(137\) | −5.64474 | −0.482263 | −0.241131 | − | 0.970493i | \(-0.577518\pi\) | ||||
−0.241131 | + | 0.970493i | \(0.577518\pi\) | |||||||
\(138\) | 7.03321 | 0.598707 | ||||||||
\(139\) | 10.1167 | 0.858088 | 0.429044 | − | 0.903284i | \(-0.358851\pi\) | ||||
0.429044 | + | 0.903284i | \(0.358851\pi\) | |||||||
\(140\) | 0.0449534 | 0.00379926 | ||||||||
\(141\) | −4.65762 | −0.392242 | ||||||||
\(142\) | −11.8813 | −0.997053 | ||||||||
\(143\) | 15.3875 | 1.28677 | ||||||||
\(144\) | −4.01448 | −0.334540 | ||||||||
\(145\) | 16.9452 | 1.40722 | ||||||||
\(146\) | 22.6632 | 1.87562 | ||||||||
\(147\) | 0.171415 | 0.0141381 | ||||||||
\(148\) | −0.0306470 | −0.00251917 | ||||||||
\(149\) | −12.1398 | −0.994534 | −0.497267 | − | 0.867598i | \(-0.665663\pi\) | ||||
−0.497267 | + | 0.867598i | \(0.665663\pi\) | |||||||
\(150\) | −0.480958 | −0.0392701 | ||||||||
\(151\) | −14.2187 | −1.15710 | −0.578552 | − | 0.815645i | \(-0.696382\pi\) | ||||
−0.578552 | + | 0.815645i | \(0.696382\pi\) | |||||||
\(152\) | −15.3426 | −1.24445 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 15.2970 | 1.23266 | ||||||||
\(155\) | 18.0076 | 1.44640 | ||||||||
\(156\) | −0.0277255 | −0.00221982 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −19.4287 | −1.54567 | ||||||||
\(159\) | 7.15400 | 0.567349 | ||||||||
\(160\) | 0.0949584 | 0.00750712 | ||||||||
\(161\) | −13.2939 | −1.04771 | ||||||||
\(162\) | −1.41678 | −0.111313 | ||||||||
\(163\) | −16.2976 | −1.27653 | −0.638263 | − | 0.769818i | \(-0.720347\pi\) | ||||
−0.638263 | + | 0.769818i | \(0.720347\pi\) | |||||||
\(164\) | −0.00557294 | −0.000435173 0 | ||||||||
\(165\) | −9.31643 | −0.725283 | ||||||||
\(166\) | 8.50023 | 0.659746 | ||||||||
\(167\) | −17.1057 | −1.32368 | −0.661839 | − | 0.749646i | \(-0.730224\pi\) | ||||
−0.661839 | + | 0.749646i | \(0.730224\pi\) | |||||||
\(168\) | 7.56057 | 0.583310 | ||||||||
\(169\) | 1.56586 | 0.120451 | ||||||||
\(170\) | 3.27380 | 0.251089 | ||||||||
\(171\) | −5.43435 | −0.415575 | ||||||||
\(172\) | −9.60612e−5 0 | −7.32460e−6 0 | ||||||||
\(173\) | −16.7942 | −1.27684 | −0.638420 | − | 0.769688i | \(-0.720412\pi\) | ||||
−0.638420 | + | 0.769688i | \(0.720412\pi\) | |||||||
\(174\) | −10.3896 | −0.787635 | ||||||||
\(175\) | 0.909091 | 0.0687208 | ||||||||
\(176\) | 16.1856 | 1.22004 | ||||||||
\(177\) | −1.07505 | −0.0808056 | ||||||||
\(178\) | −18.6314 | −1.39648 | ||||||||
\(179\) | −10.4357 | −0.780001 | −0.390001 | − | 0.920815i | \(-0.627525\pi\) | ||||
−0.390001 | + | 0.920815i | \(0.627525\pi\) | |||||||
\(180\) | 0.0167865 | 0.00125119 | ||||||||
\(181\) | −15.0002 | −1.11496 | −0.557479 | − | 0.830191i | \(-0.688231\pi\) | ||||
−0.557479 | + | 0.830191i | \(0.688231\pi\) | |||||||
\(182\) | 14.4801 | 1.07334 | ||||||||
\(183\) | 5.20154 | 0.384509 | ||||||||
\(184\) | −14.0153 | −1.03322 | ||||||||
\(185\) | −9.74825 | −0.716705 | ||||||||
\(186\) | −11.0410 | −0.809566 | ||||||||
\(187\) | 4.03181 | 0.294835 | ||||||||
\(188\) | −0.0338357 | −0.00246772 | ||||||||
\(189\) | 2.67795 | 0.194792 | ||||||||
\(190\) | 17.7909 | 1.29069 | ||||||||
\(191\) | −14.0987 | −1.02015 | −0.510073 | − | 0.860131i | \(-0.670382\pi\) | ||||
−0.510073 | + | 0.860131i | \(0.670382\pi\) | |||||||
\(192\) | 7.97073 | 0.575238 | ||||||||
\(193\) | −12.8316 | −0.923639 | −0.461820 | − | 0.886974i | \(-0.652803\pi\) | ||||
−0.461820 | + | 0.886974i | \(0.652803\pi\) | |||||||
\(194\) | 18.0736 | 1.29761 | ||||||||
\(195\) | −8.81896 | −0.631539 | ||||||||
\(196\) | 0.00124526 | 8.89474e−5 0 | ||||||||
\(197\) | 13.2413 | 0.943404 | 0.471702 | − | 0.881758i | \(-0.343640\pi\) | ||||
0.471702 | + | 0.881758i | \(0.343640\pi\) | |||||||
\(198\) | 5.71219 | 0.405947 | ||||||||
\(199\) | −7.79202 | −0.552362 | −0.276181 | − | 0.961106i | \(-0.589069\pi\) | ||||
−0.276181 | + | 0.961106i | \(0.589069\pi\) | |||||||
\(200\) | 0.958422 | 0.0677707 | ||||||||
\(201\) | 11.7690 | 0.830122 | ||||||||
\(202\) | 7.84791 | 0.552177 | ||||||||
\(203\) | 19.6381 | 1.37832 | ||||||||
\(204\) | −0.00726459 | −0.000508623 0 | ||||||||
\(205\) | −1.77265 | −0.123807 | ||||||||
\(206\) | 17.8246 | 1.24190 | ||||||||
\(207\) | −4.96423 | −0.345038 | ||||||||
\(208\) | 15.3213 | 1.06234 | ||||||||
\(209\) | 21.9103 | 1.51556 | ||||||||
\(210\) | −8.76706 | −0.604985 | ||||||||
\(211\) | 19.8034 | 1.36332 | 0.681660 | − | 0.731669i | \(-0.261258\pi\) | ||||
0.681660 | + | 0.731669i | \(0.261258\pi\) | |||||||
\(212\) | 0.0519709 | 0.00356937 | ||||||||
\(213\) | 8.38610 | 0.574606 | ||||||||
\(214\) | 22.5542 | 1.54177 | ||||||||
\(215\) | −0.0305553 | −0.00208385 | ||||||||
\(216\) | 2.82327 | 0.192099 | ||||||||
\(217\) | 20.8694 | 1.41670 | ||||||||
\(218\) | −14.6521 | −0.992367 | ||||||||
\(219\) | −15.9963 | −1.08093 | ||||||||
\(220\) | −0.0676800 | −0.00456299 | ||||||||
\(221\) | 3.81653 | 0.256727 | ||||||||
\(222\) | 5.97695 | 0.401147 | ||||||||
\(223\) | −13.2992 | −0.890583 | −0.445292 | − | 0.895386i | \(-0.646900\pi\) | ||||
−0.445292 | + | 0.895386i | \(0.646900\pi\) | |||||||
\(224\) | 0.110049 | 0.00735296 | ||||||||
\(225\) | 0.339473 | 0.0226315 | ||||||||
\(226\) | 6.35961 | 0.423035 | ||||||||
\(227\) | 0.285761 | 0.0189666 | 0.00948330 | − | 0.999955i | \(-0.496981\pi\) | ||||
0.00948330 | + | 0.999955i | \(0.496981\pi\) | |||||||
\(228\) | −0.0394783 | −0.00261452 | ||||||||
\(229\) | 15.0363 | 0.993629 | 0.496815 | − | 0.867857i | \(-0.334503\pi\) | ||||
0.496815 | + | 0.867857i | \(0.334503\pi\) | |||||||
\(230\) | 16.2519 | 1.07162 | ||||||||
\(231\) | −10.7970 | −0.710390 | ||||||||
\(232\) | 20.7038 | 1.35927 | ||||||||
\(233\) | 11.9182 | 0.780789 | 0.390394 | − | 0.920648i | \(-0.372339\pi\) | ||||
0.390394 | + | 0.920648i | \(0.372339\pi\) | |||||||
\(234\) | 5.40718 | 0.353478 | ||||||||
\(235\) | −10.7625 | −0.702068 | ||||||||
\(236\) | −0.00780979 | −0.000508374 0 | ||||||||
\(237\) | 13.7133 | 0.890774 | ||||||||
\(238\) | 3.79406 | 0.245933 | ||||||||
\(239\) | −19.2522 | −1.24532 | −0.622662 | − | 0.782491i | \(-0.713949\pi\) | ||||
−0.622662 | + | 0.782491i | \(0.713949\pi\) | |||||||
\(240\) | −9.27637 | −0.598787 | ||||||||
\(241\) | −2.32539 | −0.149792 | −0.0748958 | − | 0.997191i | \(-0.523862\pi\) | ||||
−0.0748958 | + | 0.997191i | \(0.523862\pi\) | |||||||
\(242\) | −7.44588 | −0.478639 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.0377871 | 0.00241907 | ||||||||
\(245\) | 0.396095 | 0.0253056 | ||||||||
\(246\) | 1.08686 | 0.0692960 | ||||||||
\(247\) | 20.7403 | 1.31968 | ||||||||
\(248\) | 22.0018 | 1.39712 | ||||||||
\(249\) | −5.99969 | −0.380215 | ||||||||
\(250\) | 15.2576 | 0.964976 | ||||||||
\(251\) | −16.4310 | −1.03711 | −0.518557 | − | 0.855043i | \(-0.673531\pi\) | ||||
−0.518557 | + | 0.855043i | \(0.673531\pi\) | |||||||
\(252\) | 0.0194542 | 0.00122550 | ||||||||
\(253\) | 20.0148 | 1.25832 | ||||||||
\(254\) | 16.3517 | 1.02599 | ||||||||
\(255\) | −2.31073 | −0.144704 | ||||||||
\(256\) | 0.174348 | 0.0108967 | ||||||||
\(257\) | −27.2932 | −1.70250 | −0.851250 | − | 0.524760i | \(-0.824155\pi\) | ||||
−0.851250 | + | 0.524760i | \(0.824155\pi\) | |||||||
\(258\) | 0.0187344 | 0.00116635 | ||||||||
\(259\) | −11.2974 | −0.701988 | ||||||||
\(260\) | −0.0640661 | −0.00397321 | ||||||||
\(261\) | 7.33326 | 0.453917 | ||||||||
\(262\) | −1.47634 | −0.0912088 | ||||||||
\(263\) | 23.0316 | 1.42019 | 0.710094 | − | 0.704107i | \(-0.248652\pi\) | ||||
0.710094 | + | 0.704107i | \(0.248652\pi\) | |||||||
\(264\) | −11.3829 | −0.700568 | ||||||||
\(265\) | 16.5310 | 1.01549 | ||||||||
\(266\) | 20.6183 | 1.26419 | ||||||||
\(267\) | 13.1505 | 0.804799 | ||||||||
\(268\) | 0.0854970 | 0.00522256 | ||||||||
\(269\) | −26.3989 | −1.60957 | −0.804786 | − | 0.593565i | \(-0.797720\pi\) | ||||
−0.804786 | + | 0.593565i | \(0.797720\pi\) | |||||||
\(270\) | −3.27380 | −0.199237 | ||||||||
\(271\) | 12.7225 | 0.772838 | 0.386419 | − | 0.922323i | \(-0.373712\pi\) | ||||
0.386419 | + | 0.922323i | \(0.373712\pi\) | |||||||
\(272\) | 4.01448 | 0.243413 | ||||||||
\(273\) | −10.2205 | −0.618571 | ||||||||
\(274\) | 7.99735 | 0.483138 | ||||||||
\(275\) | −1.36869 | −0.0825351 | ||||||||
\(276\) | −0.0360631 | −0.00217074 | ||||||||
\(277\) | −15.3201 | −0.920497 | −0.460249 | − | 0.887790i | \(-0.652240\pi\) | ||||
−0.460249 | + | 0.887790i | \(0.652240\pi\) | |||||||
\(278\) | −14.3331 | −0.859645 | ||||||||
\(279\) | 7.79303 | 0.466557 | ||||||||
\(280\) | 17.4704 | 1.04406 | ||||||||
\(281\) | 10.7031 | 0.638495 | 0.319248 | − | 0.947671i | \(-0.396570\pi\) | ||||
0.319248 | + | 0.947671i | \(0.396570\pi\) | |||||||
\(282\) | 6.59882 | 0.392954 | ||||||||
\(283\) | 6.66693 | 0.396308 | 0.198154 | − | 0.980171i | \(-0.436505\pi\) | ||||
0.198154 | + | 0.980171i | \(0.436505\pi\) | |||||||
\(284\) | 0.0609216 | 0.00361503 | ||||||||
\(285\) | −12.5573 | −0.743831 | ||||||||
\(286\) | −21.8007 | −1.28910 | ||||||||
\(287\) | −2.05436 | −0.121265 | ||||||||
\(288\) | 0.0410945 | 0.00242152 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −24.0076 | −1.40977 | ||||||||
\(291\) | −12.7568 | −0.747820 | ||||||||
\(292\) | −0.116206 | −0.00680046 | ||||||||
\(293\) | −0.808813 | −0.0472514 | −0.0236257 | − | 0.999721i | \(-0.507521\pi\) | ||||
−0.0236257 | + | 0.999721i | \(0.507521\pi\) | |||||||
\(294\) | −0.242858 | −0.0141638 | ||||||||
\(295\) | −2.48415 | −0.144633 | ||||||||
\(296\) | −11.9105 | −0.692283 | ||||||||
\(297\) | −4.03181 | −0.233949 | ||||||||
\(298\) | 17.1995 | 0.996338 | ||||||||
\(299\) | 18.9461 | 1.09568 | ||||||||
\(300\) | 0.00246613 | 0.000142382 0 | ||||||||
\(301\) | −0.0354111 | −0.00204106 | ||||||||
\(302\) | 20.1448 | 1.15920 | ||||||||
\(303\) | −5.53926 | −0.318222 | ||||||||
\(304\) | 21.8161 | 1.25124 | ||||||||
\(305\) | 12.0194 | 0.688226 | ||||||||
\(306\) | 1.41678 | 0.0809919 | ||||||||
\(307\) | 10.4262 | 0.595057 | 0.297528 | − | 0.954713i | \(-0.403838\pi\) | ||||
0.297528 | + | 0.954713i | \(0.403838\pi\) | |||||||
\(308\) | −0.0784357 | −0.00446929 | ||||||||
\(309\) | −12.5811 | −0.715712 | ||||||||
\(310\) | −25.5128 | −1.44903 | ||||||||
\(311\) | 15.5470 | 0.881588 | 0.440794 | − | 0.897608i | \(-0.354697\pi\) | ||||
0.440794 | + | 0.897608i | \(0.354697\pi\) | |||||||
\(312\) | −10.7751 | −0.610018 | ||||||||
\(313\) | 21.3908 | 1.20908 | 0.604540 | − | 0.796574i | \(-0.293357\pi\) | ||||
0.604540 | + | 0.796574i | \(0.293357\pi\) | |||||||
\(314\) | −1.41678 | −0.0799535 | ||||||||
\(315\) | 6.18802 | 0.348655 | ||||||||
\(316\) | 0.0996215 | 0.00560415 | ||||||||
\(317\) | −6.26249 | −0.351736 | −0.175868 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175868 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(318\) | −10.1356 | −0.568378 | ||||||||
\(319\) | −29.5663 | −1.65540 | ||||||||
\(320\) | 18.4182 | 1.02961 | ||||||||
\(321\) | −15.9193 | −0.888530 | ||||||||
\(322\) | 18.8346 | 1.04961 | ||||||||
\(323\) | 5.43435 | 0.302375 | ||||||||
\(324\) | 0.00726459 | 0.000403588 0 | ||||||||
\(325\) | −1.29561 | −0.0718673 | ||||||||
\(326\) | 23.0901 | 1.27884 | ||||||||
\(327\) | 10.3418 | 0.571905 | ||||||||
\(328\) | −2.16583 | −0.119588 | ||||||||
\(329\) | −12.4729 | −0.687651 | ||||||||
\(330\) | 13.1993 | 0.726599 | ||||||||
\(331\) | −4.36548 | −0.239949 | −0.119974 | − | 0.992777i | \(-0.538281\pi\) | ||||
−0.119974 | + | 0.992777i | \(0.538281\pi\) | |||||||
\(332\) | −0.0435853 | −0.00239205 | ||||||||
\(333\) | −4.21869 | −0.231183 | ||||||||
\(334\) | 24.2350 | 1.32608 | ||||||||
\(335\) | 27.1950 | 1.48582 | ||||||||
\(336\) | −10.7506 | −0.586491 | ||||||||
\(337\) | −15.2034 | −0.828181 | −0.414091 | − | 0.910236i | \(-0.635900\pi\) | ||||
−0.414091 | + | 0.910236i | \(0.635900\pi\) | |||||||
\(338\) | −2.21848 | −0.120670 | ||||||||
\(339\) | −4.48878 | −0.243797 | ||||||||
\(340\) | −0.0167865 | −0.000910376 0 | ||||||||
\(341\) | −31.4200 | −1.70149 | ||||||||
\(342\) | 7.69927 | 0.416329 | ||||||||
\(343\) | −18.2866 | −0.987384 | ||||||||
\(344\) | −0.0373326 | −0.00201284 | ||||||||
\(345\) | −11.4710 | −0.617577 | ||||||||
\(346\) | 23.7937 | 1.27916 | ||||||||
\(347\) | 25.1469 | 1.34996 | 0.674979 | − | 0.737837i | \(-0.264153\pi\) | ||||
0.674979 | + | 0.737837i | \(0.264153\pi\) | |||||||
\(348\) | 0.0532731 | 0.00285574 | ||||||||
\(349\) | 27.3184 | 1.46232 | 0.731161 | − | 0.682205i | \(-0.238979\pi\) | ||||
0.731161 | + | 0.682205i | \(0.238979\pi\) | |||||||
\(350\) | −1.28798 | −0.0688455 | ||||||||
\(351\) | −3.81653 | −0.203711 | ||||||||
\(352\) | −0.165685 | −0.00883106 | ||||||||
\(353\) | −31.0524 | −1.65275 | −0.826376 | − | 0.563119i | \(-0.809601\pi\) | ||||
−0.826376 | + | 0.563119i | \(0.809601\pi\) | |||||||
\(354\) | 1.52311 | 0.0809523 | ||||||||
\(355\) | 19.3780 | 1.02848 | ||||||||
\(356\) | 0.0955332 | 0.00506325 | ||||||||
\(357\) | −2.67795 | −0.141732 | ||||||||
\(358\) | 14.7851 | 0.781416 | ||||||||
\(359\) | 23.2162 | 1.22531 | 0.612653 | − | 0.790352i | \(-0.290102\pi\) | ||||
0.612653 | + | 0.790352i | \(0.290102\pi\) | |||||||
\(360\) | 6.52381 | 0.343835 | ||||||||
\(361\) | 10.5321 | 0.554324 | ||||||||
\(362\) | 21.2520 | 1.11698 | ||||||||
\(363\) | 5.25550 | 0.275842 | ||||||||
\(364\) | −0.0742475 | −0.00389163 | ||||||||
\(365\) | −36.9631 | −1.93474 | ||||||||
\(366\) | −7.36943 | −0.385207 | ||||||||
\(367\) | 32.8820 | 1.71643 | 0.858214 | − | 0.513292i | \(-0.171574\pi\) | ||||
0.858214 | + | 0.513292i | \(0.171574\pi\) | |||||||
\(368\) | 19.9288 | 1.03886 | ||||||||
\(369\) | −0.767137 | −0.0399356 | ||||||||
\(370\) | 13.8111 | 0.718006 | ||||||||
\(371\) | 19.1580 | 0.994636 | ||||||||
\(372\) | 0.0566132 | 0.00293526 | ||||||||
\(373\) | −30.9935 | −1.60478 | −0.802392 | − | 0.596798i | \(-0.796439\pi\) | ||||
−0.802392 | + | 0.596798i | \(0.796439\pi\) | |||||||
\(374\) | −5.71219 | −0.295370 | ||||||||
\(375\) | −10.7692 | −0.556120 | ||||||||
\(376\) | −13.1497 | −0.678144 | ||||||||
\(377\) | −27.9876 | −1.44143 | ||||||||
\(378\) | −3.79406 | −0.195146 | ||||||||
\(379\) | 14.7441 | 0.757353 | 0.378677 | − | 0.925529i | \(-0.376379\pi\) | ||||
0.378677 | + | 0.925529i | \(0.376379\pi\) | |||||||
\(380\) | −0.0912237 | −0.00467968 | ||||||||
\(381\) | −11.5414 | −0.591285 | ||||||||
\(382\) | 19.9748 | 1.02200 | ||||||||
\(383\) | −28.6639 | −1.46466 | −0.732329 | − | 0.680951i | \(-0.761567\pi\) | ||||
−0.732329 | + | 0.680951i | \(0.761567\pi\) | |||||||
\(384\) | −11.3750 | −0.580476 | ||||||||
\(385\) | −24.9489 | −1.27151 | ||||||||
\(386\) | 18.1796 | 0.925315 | ||||||||
\(387\) | −0.0132232 | −0.000672173 0 | ||||||||
\(388\) | −0.0926733 | −0.00470477 | ||||||||
\(389\) | −17.4660 | −0.885559 | −0.442780 | − | 0.896630i | \(-0.646008\pi\) | ||||
−0.442780 | + | 0.896630i | \(0.646008\pi\) | |||||||
\(390\) | 12.4945 | 0.632685 | ||||||||
\(391\) | 4.96423 | 0.251052 | ||||||||
\(392\) | 0.483951 | 0.0244432 | ||||||||
\(393\) | 1.04204 | 0.0525641 | ||||||||
\(394\) | −18.7600 | −0.945115 | ||||||||
\(395\) | 31.6877 | 1.59438 | ||||||||
\(396\) | −0.0292895 | −0.00147185 | ||||||||
\(397\) | −35.5696 | −1.78519 | −0.892595 | − | 0.450860i | \(-0.851117\pi\) | ||||
−0.892595 | + | 0.450860i | \(0.851117\pi\) | |||||||
\(398\) | 11.0396 | 0.553364 | ||||||||
\(399\) | −14.5529 | −0.728557 | ||||||||
\(400\) | −1.36281 | −0.0681403 | ||||||||
\(401\) | 2.08307 | 0.104024 | 0.0520118 | − | 0.998646i | \(-0.483437\pi\) | ||||
0.0520118 | + | 0.998646i | \(0.483437\pi\) | |||||||
\(402\) | −16.6741 | −0.831628 | ||||||||
\(403\) | −29.7423 | −1.48157 | ||||||||
\(404\) | −0.0402404 | −0.00200204 | ||||||||
\(405\) | 2.31073 | 0.114821 | ||||||||
\(406\) | −27.8229 | −1.38083 | ||||||||
\(407\) | 17.0089 | 0.843102 | ||||||||
\(408\) | −2.82327 | −0.139773 | ||||||||
\(409\) | 5.47665 | 0.270803 | 0.135401 | − | 0.990791i | \(-0.456768\pi\) | ||||
0.135401 | + | 0.990791i | \(0.456768\pi\) | |||||||
\(410\) | 2.51145 | 0.124032 | ||||||||
\(411\) | −5.64474 | −0.278434 | ||||||||
\(412\) | −0.0913964 | −0.00450278 | ||||||||
\(413\) | −2.87893 | −0.141663 | ||||||||
\(414\) | 7.03321 | 0.345664 | ||||||||
\(415\) | −13.8637 | −0.680540 | ||||||||
\(416\) | −0.156838 | −0.00768963 | ||||||||
\(417\) | 10.1167 | 0.495417 | ||||||||
\(418\) | −31.0420 | −1.51831 | ||||||||
\(419\) | −0.816347 | −0.0398812 | −0.0199406 | − | 0.999801i | \(-0.506348\pi\) | ||||
−0.0199406 | + | 0.999801i | \(0.506348\pi\) | |||||||
\(420\) | 0.0449534 | 0.00219350 | ||||||||
\(421\) | 0.230345 | 0.0112263 | 0.00561316 | − | 0.999984i | \(-0.498213\pi\) | ||||
0.00561316 | + | 0.999984i | \(0.498213\pi\) | |||||||
\(422\) | −28.0570 | −1.36579 | ||||||||
\(423\) | −4.65762 | −0.226461 | ||||||||
\(424\) | 20.1976 | 0.980884 | ||||||||
\(425\) | −0.339473 | −0.0164668 | ||||||||
\(426\) | −11.8813 | −0.575649 | ||||||||
\(427\) | 13.9295 | 0.674094 | ||||||||
\(428\) | −0.115647 | −0.00559003 | ||||||||
\(429\) | 15.3875 | 0.742916 | ||||||||
\(430\) | 0.0432901 | 0.00208763 | ||||||||
\(431\) | −25.5859 | −1.23243 | −0.616214 | − | 0.787579i | \(-0.711334\pi\) | ||||
−0.616214 | + | 0.787579i | \(0.711334\pi\) | |||||||
\(432\) | −4.01448 | −0.193147 | ||||||||
\(433\) | 8.75978 | 0.420968 | 0.210484 | − | 0.977597i | \(-0.432496\pi\) | ||||
0.210484 | + | 0.977597i | \(0.432496\pi\) | |||||||
\(434\) | −29.5673 | −1.41927 | ||||||||
\(435\) | 16.9452 | 0.812459 | ||||||||
\(436\) | 0.0751293 | 0.00359804 | ||||||||
\(437\) | 26.9773 | 1.29050 | ||||||||
\(438\) | 22.6632 | 1.08289 | ||||||||
\(439\) | 6.32351 | 0.301804 | 0.150902 | − | 0.988549i | \(-0.451782\pi\) | ||||
0.150902 | + | 0.988549i | \(0.451782\pi\) | |||||||
\(440\) | −26.3028 | −1.25393 | ||||||||
\(441\) | 0.171415 | 0.00816264 | ||||||||
\(442\) | −5.40718 | −0.257193 | ||||||||
\(443\) | −15.9795 | −0.759211 | −0.379606 | − | 0.925148i | \(-0.623940\pi\) | ||||
−0.379606 | + | 0.925148i | \(0.623940\pi\) | |||||||
\(444\) | −0.0306470 | −0.00145444 | ||||||||
\(445\) | 30.3873 | 1.44050 | ||||||||
\(446\) | 18.8421 | 0.892199 | ||||||||
\(447\) | −12.1398 | −0.574194 | ||||||||
\(448\) | 21.3452 | 1.00847 | ||||||||
\(449\) | 8.27207 | 0.390383 | 0.195192 | − | 0.980765i | \(-0.437467\pi\) | ||||
0.195192 | + | 0.980765i | \(0.437467\pi\) | |||||||
\(450\) | −0.480958 | −0.0226726 | ||||||||
\(451\) | 3.09295 | 0.145641 | ||||||||
\(452\) | −0.0326091 | −0.00153380 | ||||||||
\(453\) | −14.2187 | −0.668055 | ||||||||
\(454\) | −0.404860 | −0.0190010 | ||||||||
\(455\) | −23.6167 | −1.10717 | ||||||||
\(456\) | −15.3426 | −0.718484 | ||||||||
\(457\) | −9.56125 | −0.447256 | −0.223628 | − | 0.974675i | \(-0.571790\pi\) | ||||
−0.223628 | + | 0.974675i | \(0.571790\pi\) | |||||||
\(458\) | −21.3032 | −0.995432 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −0.0833320 | −0.00388538 | ||||||||
\(461\) | −5.59745 | −0.260699 | −0.130350 | − | 0.991468i | \(-0.541610\pi\) | ||||
−0.130350 | + | 0.991468i | \(0.541610\pi\) | |||||||
\(462\) | 15.2970 | 0.711679 | ||||||||
\(463\) | 23.1158 | 1.07428 | 0.537141 | − | 0.843492i | \(-0.319504\pi\) | ||||
0.537141 | + | 0.843492i | \(0.319504\pi\) | |||||||
\(464\) | −29.4392 | −1.36668 | ||||||||
\(465\) | 18.0076 | 0.835082 | ||||||||
\(466\) | −16.8855 | −0.782206 | ||||||||
\(467\) | −4.17250 | −0.193080 | −0.0965402 | − | 0.995329i | \(-0.530778\pi\) | ||||
−0.0965402 | + | 0.995329i | \(0.530778\pi\) | |||||||
\(468\) | −0.0277255 | −0.00128161 | ||||||||
\(469\) | 31.5168 | 1.45531 | ||||||||
\(470\) | 15.2481 | 0.703342 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −3.03515 | −0.139704 | ||||||||
\(473\) | 0.0533135 | 0.00245136 | ||||||||
\(474\) | −19.4287 | −0.892391 | ||||||||
\(475\) | −1.84481 | −0.0846458 | ||||||||
\(476\) | −0.0194542 | −0.000891682 0 | ||||||||
\(477\) | 7.15400 | 0.327559 | ||||||||
\(478\) | 27.2762 | 1.24758 | ||||||||
\(479\) | −12.9156 | −0.590131 | −0.295065 | − | 0.955477i | \(-0.595341\pi\) | ||||
−0.295065 | + | 0.955477i | \(0.595341\pi\) | |||||||
\(480\) | 0.0949584 | 0.00433424 | ||||||||
\(481\) | 16.1007 | 0.734130 | ||||||||
\(482\) | 3.29457 | 0.150063 | ||||||||
\(483\) | −13.2939 | −0.604896 | ||||||||
\(484\) | 0.0381790 | 0.00173541 | ||||||||
\(485\) | −29.4776 | −1.33851 | ||||||||
\(486\) | −1.41678 | −0.0642664 | ||||||||
\(487\) | 28.8019 | 1.30514 | 0.652570 | − | 0.757728i | \(-0.273691\pi\) | ||||
0.652570 | + | 0.757728i | \(0.273691\pi\) | |||||||
\(488\) | 14.6853 | 0.664774 | ||||||||
\(489\) | −16.2976 | −0.737003 | ||||||||
\(490\) | −0.561179 | −0.0253515 | ||||||||
\(491\) | −31.0266 | −1.40021 | −0.700106 | − | 0.714039i | \(-0.746864\pi\) | ||||
−0.700106 | + | 0.714039i | \(0.746864\pi\) | |||||||
\(492\) | −0.00557294 | −0.000251248 0 | ||||||||
\(493\) | −7.33326 | −0.330273 | ||||||||
\(494\) | −29.3845 | −1.32207 | ||||||||
\(495\) | −9.31643 | −0.418742 | ||||||||
\(496\) | −31.2850 | −1.40474 | ||||||||
\(497\) | 22.4576 | 1.00736 | ||||||||
\(498\) | 8.50023 | 0.380905 | ||||||||
\(499\) | −11.4975 | −0.514701 | −0.257350 | − | 0.966318i | \(-0.582849\pi\) | ||||
−0.257350 | + | 0.966318i | \(0.582849\pi\) | |||||||
\(500\) | −0.0782340 | −0.00349873 | ||||||||
\(501\) | −17.1057 | −0.764226 | ||||||||
\(502\) | 23.2791 | 1.03900 | ||||||||
\(503\) | 25.5582 | 1.13958 | 0.569791 | − | 0.821790i | \(-0.307024\pi\) | ||||
0.569791 | + | 0.821790i | \(0.307024\pi\) | |||||||
\(504\) | 7.56057 | 0.336774 | ||||||||
\(505\) | −12.7997 | −0.569580 | ||||||||
\(506\) | −28.3566 | −1.26060 | ||||||||
\(507\) | 1.56586 | 0.0695424 | ||||||||
\(508\) | −0.0838437 | −0.00371996 | ||||||||
\(509\) | 4.64105 | 0.205711 | 0.102856 | − | 0.994696i | \(-0.467202\pi\) | ||||
0.102856 | + | 0.994696i | \(0.467202\pi\) | |||||||
\(510\) | 3.27380 | 0.144966 | ||||||||
\(511\) | −42.8372 | −1.89501 | ||||||||
\(512\) | 22.5029 | 0.994497 | ||||||||
\(513\) | −5.43435 | −0.239932 | ||||||||
\(514\) | 38.6684 | 1.70559 | ||||||||
\(515\) | −29.0715 | −1.28104 | ||||||||
\(516\) | −9.60612e−5 0 | −4.22886e−6 0 | ||||||||
\(517\) | 18.7786 | 0.825883 | ||||||||
\(518\) | 16.0060 | 0.703262 | ||||||||
\(519\) | −16.7942 | −0.737184 | ||||||||
\(520\) | −24.8983 | −1.09186 | ||||||||
\(521\) | −27.7432 | −1.21545 | −0.607727 | − | 0.794146i | \(-0.707918\pi\) | ||||
−0.607727 | + | 0.794146i | \(0.707918\pi\) | |||||||
\(522\) | −10.3896 | −0.454741 | ||||||||
\(523\) | −12.2685 | −0.536465 | −0.268233 | − | 0.963354i | \(-0.586440\pi\) | ||||
−0.268233 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(524\) | 0.00757001 | 0.000330697 0 | ||||||||
\(525\) | 0.909091 | 0.0396760 | ||||||||
\(526\) | −32.6307 | −1.42277 | ||||||||
\(527\) | −7.79303 | −0.339470 | ||||||||
\(528\) | 16.1856 | 0.704388 | ||||||||
\(529\) | 1.64353 | 0.0714580 | ||||||||
\(530\) | −23.4207 | −1.01733 | ||||||||
\(531\) | −1.07505 | −0.0466532 | ||||||||
\(532\) | −0.105721 | −0.00458359 | ||||||||
\(533\) | 2.92780 | 0.126817 | ||||||||
\(534\) | −18.6314 | −0.806259 | ||||||||
\(535\) | −36.7853 | −1.59037 | ||||||||
\(536\) | 33.2270 | 1.43519 | ||||||||
\(537\) | −10.4357 | −0.450334 | ||||||||
\(538\) | 37.4015 | 1.61249 | ||||||||
\(539\) | −0.691115 | −0.0297684 | ||||||||
\(540\) | 0.0167865 | 0.000722376 0 | ||||||||
\(541\) | −7.52796 | −0.323652 | −0.161826 | − | 0.986819i | \(-0.551738\pi\) | ||||
−0.161826 | + | 0.986819i | \(0.551738\pi\) | |||||||
\(542\) | −18.0250 | −0.774240 | ||||||||
\(543\) | −15.0002 | −0.643722 | ||||||||
\(544\) | −0.0410945 | −0.00176191 | ||||||||
\(545\) | 23.8972 | 1.02364 | ||||||||
\(546\) | 14.4801 | 0.619693 | ||||||||
\(547\) | −7.18480 | −0.307200 | −0.153600 | − | 0.988133i | \(-0.549087\pi\) | ||||
−0.153600 | + | 0.988133i | \(0.549087\pi\) | |||||||
\(548\) | −0.0410067 | −0.00175172 | ||||||||
\(549\) | 5.20154 | 0.221996 | ||||||||
\(550\) | 1.93913 | 0.0826849 | ||||||||
\(551\) | −39.8515 | −1.69773 | ||||||||
\(552\) | −14.0153 | −0.596532 | ||||||||
\(553\) | 36.7235 | 1.56164 | ||||||||
\(554\) | 21.7052 | 0.922168 | ||||||||
\(555\) | −9.74825 | −0.413790 | ||||||||
\(556\) | 0.0734937 | 0.00311683 | ||||||||
\(557\) | −23.3722 | −0.990312 | −0.495156 | − | 0.868804i | \(-0.664889\pi\) | ||||
−0.495156 | + | 0.868804i | \(0.664889\pi\) | |||||||
\(558\) | −11.0410 | −0.467403 | ||||||||
\(559\) | 0.0504667 | 0.00213451 | ||||||||
\(560\) | −24.8417 | −1.04975 | ||||||||
\(561\) | 4.03181 | 0.170223 | ||||||||
\(562\) | −15.1640 | −0.639654 | ||||||||
\(563\) | −23.3413 | −0.983721 | −0.491860 | − | 0.870674i | \(-0.663683\pi\) | ||||
−0.491860 | + | 0.870674i | \(0.663683\pi\) | |||||||
\(564\) | −0.0338357 | −0.00142474 | ||||||||
\(565\) | −10.3724 | −0.436368 | ||||||||
\(566\) | −9.44558 | −0.397027 | ||||||||
\(567\) | 2.67795 | 0.112463 | ||||||||
\(568\) | 23.6762 | 0.993431 | ||||||||
\(569\) | −41.1586 | −1.72546 | −0.862730 | − | 0.505665i | \(-0.831247\pi\) | ||||
−0.862730 | + | 0.505665i | \(0.831247\pi\) | |||||||
\(570\) | 17.7909 | 0.745181 | ||||||||
\(571\) | 7.05391 | 0.295197 | 0.147598 | − | 0.989047i | \(-0.452846\pi\) | ||||
0.147598 | + | 0.989047i | \(0.452846\pi\) | |||||||
\(572\) | 0.111784 | 0.00467392 | ||||||||
\(573\) | −14.0987 | −0.588982 | ||||||||
\(574\) | 2.91057 | 0.121485 | ||||||||
\(575\) | −1.68522 | −0.0702785 | ||||||||
\(576\) | 7.97073 | 0.332114 | ||||||||
\(577\) | 40.4953 | 1.68584 | 0.842920 | − | 0.538039i | \(-0.180835\pi\) | ||||
0.842920 | + | 0.538039i | \(0.180835\pi\) | |||||||
\(578\) | −1.41678 | −0.0589303 | ||||||||
\(579\) | −12.8316 | −0.533263 | ||||||||
\(580\) | 0.123100 | 0.00511144 | ||||||||
\(581\) | −16.0669 | −0.666566 | ||||||||
\(582\) | 18.0736 | 0.749177 | ||||||||
\(583\) | −28.8436 | −1.19458 | ||||||||
\(584\) | −45.1617 | −1.86881 | ||||||||
\(585\) | −8.81896 | −0.364619 | ||||||||
\(586\) | 1.14591 | 0.0473371 | ||||||||
\(587\) | 2.52694 | 0.104298 | 0.0521490 | − | 0.998639i | \(-0.483393\pi\) | ||||
0.0521490 | + | 0.998639i | \(0.483393\pi\) | |||||||
\(588\) | 0.00124526 | 5.13538e−5 0 | ||||||||
\(589\) | −42.3501 | −1.74500 | ||||||||
\(590\) | 3.51949 | 0.144895 | ||||||||
\(591\) | 13.2413 | 0.544674 | ||||||||
\(592\) | 16.9358 | 0.696058 | ||||||||
\(593\) | 36.2539 | 1.48877 | 0.744386 | − | 0.667750i | \(-0.232743\pi\) | ||||
0.744386 | + | 0.667750i | \(0.232743\pi\) | |||||||
\(594\) | 5.71219 | 0.234374 | ||||||||
\(595\) | −6.18802 | −0.253684 | ||||||||
\(596\) | −0.0881909 | −0.00361244 | ||||||||
\(597\) | −7.79202 | −0.318906 | ||||||||
\(598\) | −26.8424 | −1.09767 | ||||||||
\(599\) | −43.1548 | −1.76326 | −0.881629 | − | 0.471944i | \(-0.843553\pi\) | ||||
−0.881629 | + | 0.471944i | \(0.843553\pi\) | |||||||
\(600\) | 0.958422 | 0.0391274 | ||||||||
\(601\) | 33.3337 | 1.35971 | 0.679854 | − | 0.733347i | \(-0.262043\pi\) | ||||
0.679854 | + | 0.733347i | \(0.262043\pi\) | |||||||
\(602\) | 0.0501697 | 0.00204476 | ||||||||
\(603\) | 11.7690 | 0.479271 | ||||||||
\(604\) | −0.103293 | −0.00420295 | ||||||||
\(605\) | 12.1440 | 0.493725 | ||||||||
\(606\) | 7.84791 | 0.318799 | ||||||||
\(607\) | 26.9211 | 1.09269 | 0.546347 | − | 0.837559i | \(-0.316018\pi\) | ||||
0.546347 | + | 0.837559i | \(0.316018\pi\) | |||||||
\(608\) | −0.223322 | −0.00905690 | ||||||||
\(609\) | 19.6381 | 0.795776 | ||||||||
\(610\) | −17.0288 | −0.689475 | ||||||||
\(611\) | 17.7759 | 0.719137 | ||||||||
\(612\) | −0.00726459 | −0.000293654 0 | ||||||||
\(613\) | −3.75524 | −0.151673 | −0.0758363 | − | 0.997120i | \(-0.524163\pi\) | ||||
−0.0758363 | + | 0.997120i | \(0.524163\pi\) | |||||||
\(614\) | −14.7717 | −0.596136 | ||||||||
\(615\) | −1.77265 | −0.0714800 | ||||||||
\(616\) | −30.4828 | −1.22819 | ||||||||
\(617\) | −30.1904 | −1.21542 | −0.607709 | − | 0.794160i | \(-0.707911\pi\) | ||||
−0.607709 | + | 0.794160i | \(0.707911\pi\) | |||||||
\(618\) | 17.8246 | 0.717011 | ||||||||
\(619\) | 19.9694 | 0.802637 | 0.401318 | − | 0.915939i | \(-0.368552\pi\) | ||||
0.401318 | + | 0.915939i | \(0.368552\pi\) | |||||||
\(620\) | 0.130818 | 0.00525377 | ||||||||
\(621\) | −4.96423 | −0.199208 | ||||||||
\(622\) | −22.0266 | −0.883188 | ||||||||
\(623\) | 35.2164 | 1.41092 | ||||||||
\(624\) | 15.3213 | 0.613345 | ||||||||
\(625\) | −26.5821 | −1.06328 | ||||||||
\(626\) | −30.3061 | −1.21127 | ||||||||
\(627\) | 21.9103 | 0.875012 | ||||||||
\(628\) | 0.00726459 | 0.000289889 0 | ||||||||
\(629\) | 4.21869 | 0.168210 | ||||||||
\(630\) | −8.76706 | −0.349288 | ||||||||
\(631\) | 13.6101 | 0.541810 | 0.270905 | − | 0.962606i | \(-0.412677\pi\) | ||||
0.270905 | + | 0.962606i | \(0.412677\pi\) | |||||||
\(632\) | 38.7163 | 1.54005 | ||||||||
\(633\) | 19.8034 | 0.787113 | ||||||||
\(634\) | 8.87257 | 0.352375 | ||||||||
\(635\) | −26.6691 | −1.05833 | ||||||||
\(636\) | 0.0519709 | 0.00206078 | ||||||||
\(637\) | −0.654211 | −0.0259208 | ||||||||
\(638\) | 41.8890 | 1.65840 | ||||||||
\(639\) | 8.38610 | 0.331749 | ||||||||
\(640\) | −26.2845 | −1.03898 | ||||||||
\(641\) | 44.7544 | 1.76769 | 0.883847 | − | 0.467776i | \(-0.154945\pi\) | ||||
0.883847 | + | 0.467776i | \(0.154945\pi\) | |||||||
\(642\) | 22.5542 | 0.890143 | ||||||||
\(643\) | −45.0643 | −1.77716 | −0.888581 | − | 0.458721i | \(-0.848308\pi\) | ||||
−0.888581 | + | 0.458721i | \(0.848308\pi\) | |||||||
\(644\) | −0.0965751 | −0.00380559 | ||||||||
\(645\) | −0.0305553 | −0.00120311 | ||||||||
\(646\) | −7.69927 | −0.302924 | ||||||||
\(647\) | 31.2551 | 1.22876 | 0.614382 | − | 0.789009i | \(-0.289406\pi\) | ||||
0.614382 | + | 0.789009i | \(0.289406\pi\) | |||||||
\(648\) | 2.82327 | 0.110908 | ||||||||
\(649\) | 4.33439 | 0.170140 | ||||||||
\(650\) | 1.83559 | 0.0719977 | ||||||||
\(651\) | 20.8694 | 0.817934 | ||||||||
\(652\) | −0.118395 | −0.00463672 | ||||||||
\(653\) | −24.7805 | −0.969735 | −0.484868 | − | 0.874587i | \(-0.661132\pi\) | ||||
−0.484868 | + | 0.874587i | \(0.661132\pi\) | |||||||
\(654\) | −14.6521 | −0.572943 | ||||||||
\(655\) | 2.40788 | 0.0940836 | ||||||||
\(656\) | 3.07965 | 0.120240 | ||||||||
\(657\) | −15.9963 | −0.624074 | ||||||||
\(658\) | 17.6713 | 0.688899 | ||||||||
\(659\) | −6.55239 | −0.255245 | −0.127622 | − | 0.991823i | \(-0.540735\pi\) | ||||
−0.127622 | + | 0.991823i | \(0.540735\pi\) | |||||||
\(660\) | −0.0676800 | −0.00263444 | ||||||||
\(661\) | 33.8232 | 1.31557 | 0.657786 | − | 0.753205i | \(-0.271493\pi\) | ||||
0.657786 | + | 0.753205i | \(0.271493\pi\) | |||||||
\(662\) | 6.18493 | 0.240384 | ||||||||
\(663\) | 3.81653 | 0.148222 | ||||||||
\(664\) | −16.9387 | −0.657350 | ||||||||
\(665\) | −33.6279 | −1.30403 | ||||||||
\(666\) | 5.97695 | 0.231602 | ||||||||
\(667\) | −36.4040 | −1.40957 | ||||||||
\(668\) | −0.124266 | −0.00480799 | ||||||||
\(669\) | −13.2992 | −0.514178 | ||||||||
\(670\) | −38.5293 | −1.48852 | ||||||||
\(671\) | −20.9716 | −0.809600 | ||||||||
\(672\) | 0.110049 | 0.00424524 | ||||||||
\(673\) | −0.526357 | −0.0202896 | −0.0101448 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101448 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(674\) | 21.5399 | 0.829684 | ||||||||
\(675\) | 0.339473 | 0.0130663 | ||||||||
\(676\) | 0.0113754 | 0.000437514 0 | ||||||||
\(677\) | −47.5145 | −1.82613 | −0.913066 | − | 0.407813i | \(-0.866292\pi\) | ||||
−0.913066 | + | 0.407813i | \(0.866292\pi\) | |||||||
\(678\) | 6.35961 | 0.244239 | ||||||||
\(679\) | −34.1622 | −1.31103 | ||||||||
\(680\) | −6.52381 | −0.250177 | ||||||||
\(681\) | 0.285761 | 0.0109504 | ||||||||
\(682\) | 44.5153 | 1.70458 | ||||||||
\(683\) | 11.1773 | 0.427687 | 0.213843 | − | 0.976868i | \(-0.431402\pi\) | ||||
0.213843 | + | 0.976868i | \(0.431402\pi\) | |||||||
\(684\) | −0.0394783 | −0.00150949 | ||||||||
\(685\) | −13.0435 | −0.498365 | ||||||||
\(686\) | 25.9081 | 0.989176 | ||||||||
\(687\) | 15.0363 | 0.573672 | ||||||||
\(688\) | 0.0530843 | 0.00202382 | ||||||||
\(689\) | −27.3034 | −1.04018 | ||||||||
\(690\) | 16.2519 | 0.618698 | ||||||||
\(691\) | 11.3158 | 0.430472 | 0.215236 | − | 0.976562i | \(-0.430948\pi\) | ||||
0.215236 | + | 0.976562i | \(0.430948\pi\) | |||||||
\(692\) | −0.122003 | −0.00463786 | ||||||||
\(693\) | −10.7970 | −0.410144 | ||||||||
\(694\) | −35.6276 | −1.35241 | ||||||||
\(695\) | 23.3770 | 0.886739 | ||||||||
\(696\) | 20.7038 | 0.784774 | ||||||||
\(697\) | 0.767137 | 0.0290574 | ||||||||
\(698\) | −38.7042 | −1.46497 | ||||||||
\(699\) | 11.9182 | 0.450789 | ||||||||
\(700\) | 0.00660417 | 0.000249614 0 | ||||||||
\(701\) | −31.2986 | −1.18213 | −0.591065 | − | 0.806624i | \(-0.701292\pi\) | ||||
−0.591065 | + | 0.806624i | \(0.701292\pi\) | |||||||
\(702\) | 5.40718 | 0.204081 | ||||||||
\(703\) | 22.9258 | 0.864664 | ||||||||
\(704\) | −32.1365 | −1.21119 | ||||||||
\(705\) | −10.7625 | −0.405339 | ||||||||
\(706\) | 43.9944 | 1.65575 | ||||||||
\(707\) | −14.8339 | −0.557884 | ||||||||
\(708\) | −0.00780979 | −0.000293510 0 | ||||||||
\(709\) | 11.5913 | 0.435320 | 0.217660 | − | 0.976025i | \(-0.430158\pi\) | ||||
0.217660 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(710\) | −27.4544 | −1.03034 | ||||||||
\(711\) | 13.7133 | 0.514289 | ||||||||
\(712\) | 37.1274 | 1.39141 | ||||||||
\(713\) | −38.6864 | −1.44882 | ||||||||
\(714\) | 3.79406 | 0.141989 | ||||||||
\(715\) | 35.5564 | 1.32973 | ||||||||
\(716\) | −0.0758111 | −0.00283319 | ||||||||
\(717\) | −19.2522 | −0.718988 | ||||||||
\(718\) | −32.8923 | −1.22753 | ||||||||
\(719\) | 18.8419 | 0.702686 | 0.351343 | − | 0.936247i | \(-0.385725\pi\) | ||||
0.351343 | + | 0.936247i | \(0.385725\pi\) | |||||||
\(720\) | −9.27637 | −0.345710 | ||||||||
\(721\) | −33.6915 | −1.25474 | ||||||||
\(722\) | −14.9217 | −0.555329 | ||||||||
\(723\) | −2.32539 | −0.0864822 | ||||||||
\(724\) | −0.108971 | −0.00404986 | ||||||||
\(725\) | 2.48944 | 0.0924555 | ||||||||
\(726\) | −7.44588 | −0.276343 | ||||||||
\(727\) | −33.2405 | −1.23282 | −0.616411 | − | 0.787425i | \(-0.711414\pi\) | ||||
−0.616411 | + | 0.787425i | \(0.711414\pi\) | |||||||
\(728\) | −28.8551 | −1.06944 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 52.3685 | 1.93825 | ||||||||
\(731\) | 0.0132232 | 0.000489078 0 | ||||||||
\(732\) | 0.0377871 | 0.00139665 | ||||||||
\(733\) | 33.5915 | 1.24073 | 0.620365 | − | 0.784313i | \(-0.286985\pi\) | ||||
0.620365 | + | 0.784313i | \(0.286985\pi\) | |||||||
\(734\) | −46.5866 | −1.71954 | ||||||||
\(735\) | 0.396095 | 0.0146102 | ||||||||
\(736\) | −0.204003 | −0.00751963 | ||||||||
\(737\) | −47.4504 | −1.74786 | ||||||||
\(738\) | 1.08686 | 0.0400080 | ||||||||
\(739\) | −0.813364 | −0.0299201 | −0.0149600 | − | 0.999888i | \(-0.504762\pi\) | ||||
−0.0149600 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(740\) | −0.0708170 | −0.00260329 | ||||||||
\(741\) | 20.7403 | 0.761915 | ||||||||
\(742\) | −27.1427 | −0.996441 | ||||||||
\(743\) | −4.43118 | −0.162564 | −0.0812820 | − | 0.996691i | \(-0.525901\pi\) | ||||
−0.0812820 | + | 0.996691i | \(0.525901\pi\) | |||||||
\(744\) | 22.0018 | 0.806626 | ||||||||
\(745\) | −28.0519 | −1.02774 | ||||||||
\(746\) | 43.9110 | 1.60770 | ||||||||
\(747\) | −5.99969 | −0.219517 | ||||||||
\(748\) | 0.0292895 | 0.00107093 | ||||||||
\(749\) | −42.6312 | −1.55771 | ||||||||
\(750\) | 15.2576 | 0.557129 | ||||||||
\(751\) | 2.64017 | 0.0963413 | 0.0481707 | − | 0.998839i | \(-0.484661\pi\) | ||||
0.0481707 | + | 0.998839i | \(0.484661\pi\) | |||||||
\(752\) | 18.6979 | 0.681842 | ||||||||
\(753\) | −16.4310 | −0.598778 | ||||||||
\(754\) | 39.6522 | 1.44405 | ||||||||
\(755\) | −32.8557 | −1.19574 | ||||||||
\(756\) | 0.0194542 | 0.000707543 0 | ||||||||
\(757\) | −1.93381 | −0.0702856 | −0.0351428 | − | 0.999382i | \(-0.511189\pi\) | ||||
−0.0351428 | + | 0.999382i | \(0.511189\pi\) | |||||||
\(758\) | −20.8891 | −0.758727 | ||||||||
\(759\) | 20.0148 | 0.726492 | ||||||||
\(760\) | −35.4526 | −1.28600 | ||||||||
\(761\) | 48.1701 | 1.74616 | 0.873082 | − | 0.487574i | \(-0.162118\pi\) | ||||
0.873082 | + | 0.487574i | \(0.162118\pi\) | |||||||
\(762\) | 16.3517 | 0.592358 | ||||||||
\(763\) | 27.6949 | 1.00262 | ||||||||
\(764\) | −0.102421 | −0.00370547 | ||||||||
\(765\) | −2.31073 | −0.0835446 | ||||||||
\(766\) | 40.6104 | 1.46732 | ||||||||
\(767\) | 4.10295 | 0.148149 | ||||||||
\(768\) | 0.174348 | 0.00629124 | ||||||||
\(769\) | 30.5605 | 1.10204 | 0.551020 | − | 0.834492i | \(-0.314239\pi\) | ||||
0.551020 | + | 0.834492i | \(0.314239\pi\) | |||||||
\(770\) | 35.3471 | 1.27382 | ||||||||
\(771\) | −27.2932 | −0.982939 | ||||||||
\(772\) | −0.0932164 | −0.00335493 | ||||||||
\(773\) | −33.2227 | −1.19494 | −0.597469 | − | 0.801892i | \(-0.703827\pi\) | ||||
−0.597469 | + | 0.801892i | \(0.703827\pi\) | |||||||
\(774\) | 0.0187344 | 0.000673393 0 | ||||||||
\(775\) | 2.64552 | 0.0950300 | ||||||||
\(776\) | −36.0160 | −1.29290 | ||||||||
\(777\) | −11.2974 | −0.405293 | ||||||||
\(778\) | 24.7454 | 0.887166 | ||||||||
\(779\) | 4.16889 | 0.149366 | ||||||||
\(780\) | −0.0640661 | −0.00229394 | ||||||||
\(781\) | −33.8112 | −1.20986 | ||||||||
\(782\) | −7.03321 | −0.251507 | ||||||||
\(783\) | 7.33326 | 0.262069 | ||||||||
\(784\) | −0.688143 | −0.0245765 | ||||||||
\(785\) | 2.31073 | 0.0824735 | ||||||||
\(786\) | −1.47634 | −0.0526594 | ||||||||
\(787\) | −2.99505 | −0.106762 | −0.0533810 | − | 0.998574i | \(-0.517000\pi\) | ||||
−0.0533810 | + | 0.998574i | \(0.517000\pi\) | |||||||
\(788\) | 0.0961926 | 0.00342672 | ||||||||
\(789\) | 23.0316 | 0.819946 | ||||||||
\(790\) | −44.8945 | −1.59728 | ||||||||
\(791\) | −12.0207 | −0.427408 | ||||||||
\(792\) | −11.3829 | −0.404473 | ||||||||
\(793\) | −19.8518 | −0.704958 | ||||||||
\(794\) | 50.3944 | 1.78843 | ||||||||
\(795\) | 16.5310 | 0.586292 | ||||||||
\(796\) | −0.0566059 | −0.00200634 | ||||||||
\(797\) | 23.7544 | 0.841422 | 0.420711 | − | 0.907195i | \(-0.361781\pi\) | ||||
0.420711 | + | 0.907195i | \(0.361781\pi\) | |||||||
\(798\) | 20.6183 | 0.729879 | ||||||||
\(799\) | 4.65762 | 0.164775 | ||||||||
\(800\) | 0.0139505 | 0.000493224 0 | ||||||||
\(801\) | 13.1505 | 0.464651 | ||||||||
\(802\) | −2.95125 | −0.104212 | ||||||||
\(803\) | 64.4939 | 2.27594 | ||||||||
\(804\) | 0.0854970 | 0.00301525 | ||||||||
\(805\) | −30.7187 | −1.08269 | ||||||||
\(806\) | 42.1383 | 1.48426 | ||||||||
\(807\) | −26.3989 | −0.929287 | ||||||||
\(808\) | −15.6388 | −0.550171 | ||||||||
\(809\) | 45.8999 | 1.61375 | 0.806877 | − | 0.590719i | \(-0.201156\pi\) | ||||
0.806877 | + | 0.590719i | \(0.201156\pi\) | |||||||
\(810\) | −3.27380 | −0.115029 | ||||||||
\(811\) | 39.2703 | 1.37897 | 0.689483 | − | 0.724302i | \(-0.257838\pi\) | ||||
0.689483 | + | 0.724302i | \(0.257838\pi\) | |||||||
\(812\) | 0.142663 | 0.00500648 | ||||||||
\(813\) | 12.7225 | 0.446198 | ||||||||
\(814\) | −24.0979 | −0.844632 | ||||||||
\(815\) | −37.6593 | −1.31915 | ||||||||
\(816\) | 4.01448 | 0.140535 | ||||||||
\(817\) | 0.0718595 | 0.00251405 | ||||||||
\(818\) | −7.75921 | −0.271294 | ||||||||
\(819\) | −10.2205 | −0.357132 | ||||||||
\(820\) | −0.0128776 | −0.000449704 0 | ||||||||
\(821\) | −23.3347 | −0.814385 | −0.407193 | − | 0.913342i | \(-0.633492\pi\) | ||||
−0.407193 | + | 0.913342i | \(0.633492\pi\) | |||||||
\(822\) | 7.99735 | 0.278940 | ||||||||
\(823\) | 26.0894 | 0.909419 | 0.454709 | − | 0.890640i | \(-0.349743\pi\) | ||||
0.454709 | + | 0.890640i | \(0.349743\pi\) | |||||||
\(824\) | −35.5197 | −1.23739 | ||||||||
\(825\) | −1.36869 | −0.0476517 | ||||||||
\(826\) | 4.07881 | 0.141920 | ||||||||
\(827\) | 5.87855 | 0.204417 | 0.102209 | − | 0.994763i | \(-0.467409\pi\) | ||||
0.102209 | + | 0.994763i | \(0.467409\pi\) | |||||||
\(828\) | −0.0360631 | −0.00125328 | ||||||||
\(829\) | −7.39304 | −0.256771 | −0.128385 | − | 0.991724i | \(-0.540979\pi\) | ||||
−0.128385 | + | 0.991724i | \(0.540979\pi\) | |||||||
\(830\) | 19.6417 | 0.681775 | ||||||||
\(831\) | −15.3201 | −0.531449 | ||||||||
\(832\) | −30.4205 | −1.05464 | ||||||||
\(833\) | −0.171415 | −0.00593919 | ||||||||
\(834\) | −14.3331 | −0.496316 | ||||||||
\(835\) | −39.5266 | −1.36788 | ||||||||
\(836\) | 0.159169 | 0.00550498 | ||||||||
\(837\) | 7.79303 | 0.269367 | ||||||||
\(838\) | 1.15658 | 0.0399535 | ||||||||
\(839\) | 17.8725 | 0.617029 | 0.308514 | − | 0.951220i | \(-0.400168\pi\) | ||||
0.308514 | + | 0.951220i | \(0.400168\pi\) | |||||||
\(840\) | 17.4704 | 0.602787 | ||||||||
\(841\) | 24.7767 | 0.854369 | ||||||||
\(842\) | −0.326348 | −0.0112467 | ||||||||
\(843\) | 10.7031 | 0.368635 | ||||||||
\(844\) | 0.143863 | 0.00495198 | ||||||||
\(845\) | 3.61829 | 0.124473 | ||||||||
\(846\) | 6.59882 | 0.226872 | ||||||||
\(847\) | 14.0740 | 0.483587 | ||||||||
\(848\) | −28.7195 | −0.986233 | ||||||||
\(849\) | 6.66693 | 0.228809 | ||||||||
\(850\) | 0.480958 | 0.0164967 | ||||||||
\(851\) | 20.9425 | 0.717900 | ||||||||
\(852\) | 0.0609216 | 0.00208714 | ||||||||
\(853\) | 11.3030 | 0.387007 | 0.193504 | − | 0.981100i | \(-0.438015\pi\) | ||||
0.193504 | + | 0.981100i | \(0.438015\pi\) | |||||||
\(854\) | −19.7350 | −0.675317 | ||||||||
\(855\) | −12.5573 | −0.429451 | ||||||||
\(856\) | −44.9445 | −1.53617 | ||||||||
\(857\) | −7.40474 | −0.252941 | −0.126471 | − | 0.991970i | \(-0.540365\pi\) | ||||
−0.126471 | + | 0.991970i | \(0.540365\pi\) | |||||||
\(858\) | −21.8007 | −0.744264 | ||||||||
\(859\) | 39.6964 | 1.35442 | 0.677211 | − | 0.735789i | \(-0.263188\pi\) | ||||
0.677211 | + | 0.735789i | \(0.263188\pi\) | |||||||
\(860\) | −0.000221972 0 | −7.56917e−6 0 | ||||||||
\(861\) | −2.05436 | −0.0700122 | ||||||||
\(862\) | 36.2495 | 1.23466 | ||||||||
\(863\) | 34.6242 | 1.17862 | 0.589311 | − | 0.807907i | \(-0.299399\pi\) | ||||
0.589311 | + | 0.807907i | \(0.299399\pi\) | |||||||
\(864\) | 0.0410945 | 0.00139806 | ||||||||
\(865\) | −38.8069 | −1.31947 | ||||||||
\(866\) | −12.4107 | −0.421732 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0.151607 | 0.00514589 | ||||||||
\(869\) | −55.2894 | −1.87556 | ||||||||
\(870\) | −24.0076 | −0.813934 | ||||||||
\(871\) | −44.9167 | −1.52194 | ||||||||
\(872\) | 29.1978 | 0.988762 | ||||||||
\(873\) | −12.7568 | −0.431754 | ||||||||
\(874\) | −38.2209 | −1.29284 | ||||||||
\(875\) | −28.8394 | −0.974951 | ||||||||
\(876\) | −0.116206 | −0.00392625 | ||||||||
\(877\) | 3.74564 | 0.126481 | 0.0632407 | − | 0.997998i | \(-0.479856\pi\) | ||||
0.0632407 | + | 0.997998i | \(0.479856\pi\) | |||||||
\(878\) | −8.95901 | −0.302352 | ||||||||
\(879\) | −0.808813 | −0.0272806 | ||||||||
\(880\) | 37.4006 | 1.26077 | ||||||||
\(881\) | 20.2039 | 0.680688 | 0.340344 | − | 0.940301i | \(-0.389457\pi\) | ||||
0.340344 | + | 0.940301i | \(0.389457\pi\) | |||||||
\(882\) | −0.242858 | −0.00817745 | ||||||||
\(883\) | 54.6753 | 1.83997 | 0.919986 | − | 0.391952i | \(-0.128200\pi\) | ||||
0.919986 | + | 0.391952i | \(0.128200\pi\) | |||||||
\(884\) | 0.0277255 | 0.000932509 0 | ||||||||
\(885\) | −2.48415 | −0.0835037 | ||||||||
\(886\) | 22.6395 | 0.760589 | ||||||||
\(887\) | 2.42654 | 0.0814752 | 0.0407376 | − | 0.999170i | \(-0.487029\pi\) | ||||
0.0407376 | + | 0.999170i | \(0.487029\pi\) | |||||||
\(888\) | −11.9105 | −0.399690 | ||||||||
\(889\) | −30.9074 | −1.03660 | ||||||||
\(890\) | −43.0521 | −1.44311 | ||||||||
\(891\) | −4.03181 | −0.135071 | ||||||||
\(892\) | −0.0966135 | −0.00323486 | ||||||||
\(893\) | 25.3111 | 0.847004 | ||||||||
\(894\) | 17.1995 | 0.575236 | ||||||||
\(895\) | −24.1141 | −0.806045 | ||||||||
\(896\) | −30.4616 | −1.01765 | ||||||||
\(897\) | 18.9461 | 0.632592 | ||||||||
\(898\) | −11.7197 | −0.391091 | ||||||||
\(899\) | 57.1483 | 1.90600 | ||||||||
\(900\) | 0.00246613 | 8.22044e−5 0 | ||||||||
\(901\) | −7.15400 | −0.238334 | ||||||||
\(902\) | −4.38203 | −0.145906 | ||||||||
\(903\) | −0.0354111 | −0.00117841 | ||||||||
\(904\) | −12.6730 | −0.421498 | ||||||||
\(905\) | −34.6615 | −1.15219 | ||||||||
\(906\) | 20.1448 | 0.669267 | ||||||||
\(907\) | 45.0778 | 1.49678 | 0.748391 | − | 0.663258i | \(-0.230827\pi\) | ||||
0.748391 | + | 0.663258i | \(0.230827\pi\) | |||||||
\(908\) | 0.00207593 | 6.88923e−5 0 | ||||||||
\(909\) | −5.53926 | −0.183726 | ||||||||
\(910\) | 33.4597 | 1.10918 | ||||||||
\(911\) | −9.02246 | −0.298927 | −0.149464 | − | 0.988767i | \(-0.547755\pi\) | ||||
−0.149464 | + | 0.988767i | \(0.547755\pi\) | |||||||
\(912\) | 21.8161 | 0.722402 | ||||||||
\(913\) | 24.1896 | 0.800559 | ||||||||
\(914\) | 13.5462 | 0.448068 | ||||||||
\(915\) | 12.0194 | 0.397348 | ||||||||
\(916\) | 0.109233 | 0.00360916 | ||||||||
\(917\) | 2.79054 | 0.0921516 | ||||||||
\(918\) | 1.41678 | 0.0467607 | ||||||||
\(919\) | 29.6673 | 0.978633 | 0.489317 | − | 0.872106i | \(-0.337246\pi\) | ||||
0.489317 | + | 0.872106i | \(0.337246\pi\) | |||||||
\(920\) | −32.3857 | −1.06772 | ||||||||
\(921\) | 10.4262 | 0.343556 | ||||||||
\(922\) | 7.93035 | 0.261172 | ||||||||
\(923\) | −32.0058 | −1.05348 | ||||||||
\(924\) | −0.0784357 | −0.00258035 | ||||||||
\(925\) | −1.43213 | −0.0470881 | ||||||||
\(926\) | −32.7500 | −1.07623 | ||||||||
\(927\) | −12.5811 | −0.413217 | ||||||||
\(928\) | 0.301357 | 0.00989252 | ||||||||
\(929\) | 19.3430 | 0.634623 | 0.317312 | − | 0.948321i | \(-0.397220\pi\) | ||||
0.317312 | + | 0.948321i | \(0.397220\pi\) | |||||||
\(930\) | −25.5128 | −0.836598 | ||||||||
\(931\) | −0.931531 | −0.0305297 | ||||||||
\(932\) | 0.0865810 | 0.00283606 | ||||||||
\(933\) | 15.5470 | 0.508985 | ||||||||
\(934\) | 5.91152 | 0.193431 | ||||||||
\(935\) | 9.31643 | 0.304680 | ||||||||
\(936\) | −10.7751 | −0.352194 | ||||||||
\(937\) | 15.9858 | 0.522233 | 0.261117 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261117 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(938\) | −44.6524 | −1.45795 | ||||||||
\(939\) | 21.3908 | 0.698063 | ||||||||
\(940\) | −0.0781851 | −0.00255012 | ||||||||
\(941\) | 32.7348 | 1.06712 | 0.533562 | − | 0.845761i | \(-0.320853\pi\) | ||||
0.533562 | + | 0.845761i | \(0.320853\pi\) | |||||||
\(942\) | −1.41678 | −0.0461612 | ||||||||
\(943\) | 3.80824 | 0.124013 | ||||||||
\(944\) | 4.31576 | 0.140466 | ||||||||
\(945\) | 6.18802 | 0.201296 | ||||||||
\(946\) | −0.0755334 | −0.00245580 | ||||||||
\(947\) | −53.6036 | −1.74188 | −0.870941 | − | 0.491388i | \(-0.836490\pi\) | ||||
−0.870941 | + | 0.491388i | \(0.836490\pi\) | |||||||
\(948\) | 0.0996215 | 0.00323556 | ||||||||
\(949\) | 61.0502 | 1.98177 | ||||||||
\(950\) | 2.61369 | 0.0847994 | ||||||||
\(951\) | −6.26249 | −0.203075 | ||||||||
\(952\) | −7.56057 | −0.245039 | ||||||||
\(953\) | −6.11836 | −0.198193 | −0.0990966 | − | 0.995078i | \(-0.531595\pi\) | ||||
−0.0990966 | + | 0.995078i | \(0.531595\pi\) | |||||||
\(954\) | −10.1356 | −0.328153 | ||||||||
\(955\) | −32.5783 | −1.05421 | ||||||||
\(956\) | −0.139860 | −0.00452338 | ||||||||
\(957\) | −29.5663 | −0.955743 | ||||||||
\(958\) | 18.2986 | 0.591202 | ||||||||
\(959\) | −15.1163 | −0.488132 | ||||||||
\(960\) | 18.4182 | 0.594445 | ||||||||
\(961\) | 29.7314 | 0.959077 | ||||||||
\(962\) | −22.8112 | −0.735462 | ||||||||
\(963\) | −15.9193 | −0.512993 | ||||||||
\(964\) | −0.0168930 | −0.000544087 0 | ||||||||
\(965\) | −29.6504 | −0.954479 | ||||||||
\(966\) | 18.8346 | 0.605993 | ||||||||
\(967\) | −46.7138 | −1.50221 | −0.751107 | − | 0.660181i | \(-0.770480\pi\) | ||||
−0.751107 | + | 0.660181i | \(0.770480\pi\) | |||||||
\(968\) | 14.8377 | 0.476901 | ||||||||
\(969\) | 5.43435 | 0.174576 | ||||||||
\(970\) | 41.7633 | 1.34094 | ||||||||
\(971\) | −41.8420 | −1.34277 | −0.671386 | − | 0.741108i | \(-0.734301\pi\) | ||||
−0.671386 | + | 0.741108i | \(0.734301\pi\) | |||||||
\(972\) | 0.00726459 | 0.000233012 0 | ||||||||
\(973\) | 27.0920 | 0.868530 | ||||||||
\(974\) | −40.8060 | −1.30751 | ||||||||
\(975\) | −1.29561 | −0.0414926 | ||||||||
\(976\) | −20.8815 | −0.668399 | ||||||||
\(977\) | 32.7492 | 1.04774 | 0.523869 | − | 0.851799i | \(-0.324488\pi\) | ||||
0.523869 | + | 0.851799i | \(0.324488\pi\) | |||||||
\(978\) | 23.0901 | 0.738340 | ||||||||
\(979\) | −53.0204 | −1.69454 | ||||||||
\(980\) | 0.00287747 | 9.19173e−5 0 | ||||||||
\(981\) | 10.3418 | 0.330190 | ||||||||
\(982\) | 43.9579 | 1.40275 | ||||||||
\(983\) | 1.85775 | 0.0592531 | 0.0296266 | − | 0.999561i | \(-0.490568\pi\) | ||||
0.0296266 | + | 0.999561i | \(0.490568\pi\) | |||||||
\(984\) | −2.16583 | −0.0690443 | ||||||||
\(985\) | 30.5971 | 0.974904 | ||||||||
\(986\) | 10.3896 | 0.330873 | ||||||||
\(987\) | −12.4729 | −0.397016 | ||||||||
\(988\) | 0.150670 | 0.00479345 | ||||||||
\(989\) | 0.0656430 | 0.00208733 | ||||||||
\(990\) | 13.1993 | 0.419502 | ||||||||
\(991\) | 12.6856 | 0.402972 | 0.201486 | − | 0.979491i | \(-0.435423\pi\) | ||||
0.201486 | + | 0.979491i | \(0.435423\pi\) | |||||||
\(992\) | 0.320251 | 0.0101680 | ||||||||
\(993\) | −4.36548 | −0.138534 | ||||||||
\(994\) | −31.8174 | −1.00919 | ||||||||
\(995\) | −18.0053 | −0.570805 | ||||||||
\(996\) | −0.0435853 | −0.00138105 | ||||||||
\(997\) | −62.4156 | −1.97672 | −0.988361 | − | 0.152128i | \(-0.951388\pi\) | ||||
−0.988361 | + | 0.152128i | \(0.951388\pi\) | |||||||
\(998\) | 16.2895 | 0.515635 | ||||||||
\(999\) | −4.21869 | −0.133473 |
(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 | 8007.2.a.e.1.16 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.16 | ✓ | 46 | 1.1 | even | 1 | trivial |