Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + 5778 x^{8} - 5124 x^{7} - 9405 x^{6} + 8288 x^{5} + 6405 x^{4} - 6032 x^{3} + \cdots - 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.18082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18082 | −1.54207 | −0.771036 | − | 0.636792i | \(-0.780261\pi\) | ||||
−0.771036 | + | 0.636792i | \(0.780261\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.75597 | 1.37799 | ||||||||
\(5\) | −3.64804 | −1.63145 | −0.815726 | − | 0.578439i | \(-0.803662\pi\) | ||||
−0.815726 | + | 0.578439i | \(0.803662\pi\) | |||||||
\(6\) | −2.18082 | −0.890316 | ||||||||
\(7\) | 2.94825 | 1.11433 | 0.557167 | − | 0.830401i | \(-0.311888\pi\) | ||||
0.557167 | + | 0.830401i | \(0.311888\pi\) | |||||||
\(8\) | −1.64864 | −0.582881 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.95571 | 2.51582 | ||||||||
\(11\) | −2.90138 | −0.874798 | −0.437399 | − | 0.899268i | \(-0.644100\pi\) | ||||
−0.437399 | + | 0.899268i | \(0.644100\pi\) | |||||||
\(12\) | 2.75597 | 0.795580 | ||||||||
\(13\) | 1.83459 | 0.508823 | 0.254412 | − | 0.967096i | \(-0.418118\pi\) | ||||
0.254412 | + | 0.967096i | \(0.418118\pi\) | |||||||
\(14\) | −6.42960 | −1.71838 | ||||||||
\(15\) | −3.64804 | −0.941919 | ||||||||
\(16\) | −1.91657 | −0.479142 | ||||||||
\(17\) | 6.16079 | 1.49421 | 0.747105 | − | 0.664706i | \(-0.231443\pi\) | ||||
0.747105 | + | 0.664706i | \(0.231443\pi\) | |||||||
\(18\) | −2.18082 | −0.514024 | ||||||||
\(19\) | −7.26232 | −1.66609 | −0.833046 | − | 0.553204i | \(-0.813405\pi\) | ||||
−0.833046 | + | 0.553204i | \(0.813405\pi\) | |||||||
\(20\) | −10.0539 | −2.24812 | ||||||||
\(21\) | 2.94825 | 0.643361 | ||||||||
\(22\) | 6.32738 | 1.34900 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.64864 | −0.336526 | ||||||||
\(25\) | 8.30818 | 1.66164 | ||||||||
\(26\) | −4.00091 | −0.784642 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 8.12529 | 1.53554 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 7.95571 | 1.45251 | ||||||||
\(31\) | 9.78276 | 1.75704 | 0.878518 | − | 0.477710i | \(-0.158533\pi\) | ||||
0.878518 | + | 0.477710i | \(0.158533\pi\) | |||||||
\(32\) | 7.47695 | 1.32175 | ||||||||
\(33\) | −2.90138 | −0.505065 | ||||||||
\(34\) | −13.4356 | −2.30418 | ||||||||
\(35\) | −10.7553 | −1.81798 | ||||||||
\(36\) | 2.75597 | 0.459328 | ||||||||
\(37\) | −1.23929 | −0.203739 | −0.101869 | − | 0.994798i | \(-0.532482\pi\) | ||||
−0.101869 | + | 0.994798i | \(0.532482\pi\) | |||||||
\(38\) | 15.8378 | 2.56923 | ||||||||
\(39\) | 1.83459 | 0.293769 | ||||||||
\(40\) | 6.01428 | 0.950942 | ||||||||
\(41\) | −6.05736 | −0.946001 | −0.473001 | − | 0.881062i | \(-0.656829\pi\) | ||||
−0.473001 | + | 0.881062i | \(0.656829\pi\) | |||||||
\(42\) | −6.42960 | −0.992109 | ||||||||
\(43\) | 6.93454 | 1.05751 | 0.528754 | − | 0.848775i | \(-0.322660\pi\) | ||||
0.528754 | + | 0.848775i | \(0.322660\pi\) | |||||||
\(44\) | −7.99611 | −1.20546 | ||||||||
\(45\) | −3.64804 | −0.543817 | ||||||||
\(46\) | 2.18082 | 0.321544 | ||||||||
\(47\) | −6.40585 | −0.934389 | −0.467194 | − | 0.884155i | \(-0.654735\pi\) | ||||
−0.467194 | + | 0.884155i | \(0.654735\pi\) | |||||||
\(48\) | −1.91657 | −0.276632 | ||||||||
\(49\) | 1.69218 | 0.241739 | ||||||||
\(50\) | −18.1186 | −2.56236 | ||||||||
\(51\) | 6.16079 | 0.862683 | ||||||||
\(52\) | 5.05607 | 0.701151 | ||||||||
\(53\) | 4.62451 | 0.635226 | 0.317613 | − | 0.948220i | \(-0.397119\pi\) | ||||
0.317613 | + | 0.948220i | \(0.397119\pi\) | |||||||
\(54\) | −2.18082 | −0.296772 | ||||||||
\(55\) | 10.5843 | 1.42719 | ||||||||
\(56\) | −4.86059 | −0.649524 | ||||||||
\(57\) | −7.26232 | −0.961918 | ||||||||
\(58\) | 2.18082 | 0.286356 | ||||||||
\(59\) | −3.54179 | −0.461101 | −0.230551 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230551 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(60\) | −10.0539 | −1.29795 | ||||||||
\(61\) | −9.97508 | −1.27718 | −0.638589 | − | 0.769548i | \(-0.720482\pi\) | ||||
−0.638589 | + | 0.769548i | \(0.720482\pi\) | |||||||
\(62\) | −21.3344 | −2.70947 | ||||||||
\(63\) | 2.94825 | 0.371445 | ||||||||
\(64\) | −12.4728 | −1.55909 | ||||||||
\(65\) | −6.69265 | −0.830121 | ||||||||
\(66\) | 6.32738 | 0.778846 | ||||||||
\(67\) | 5.17176 | 0.631830 | 0.315915 | − | 0.948787i | \(-0.397688\pi\) | ||||
0.315915 | + | 0.948787i | \(0.397688\pi\) | |||||||
\(68\) | 16.9789 | 2.05900 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 23.4554 | 2.80346 | ||||||||
\(71\) | −4.85140 | −0.575755 | −0.287877 | − | 0.957667i | \(-0.592950\pi\) | ||||
−0.287877 | + | 0.957667i | \(0.592950\pi\) | |||||||
\(72\) | −1.64864 | −0.194294 | ||||||||
\(73\) | 7.56931 | 0.885921 | 0.442961 | − | 0.896541i | \(-0.353928\pi\) | ||||
0.442961 | + | 0.896541i | \(0.353928\pi\) | |||||||
\(74\) | 2.70268 | 0.314180 | ||||||||
\(75\) | 8.30818 | 0.959346 | ||||||||
\(76\) | −20.0148 | −2.29585 | ||||||||
\(77\) | −8.55398 | −0.974817 | ||||||||
\(78\) | −4.00091 | −0.453013 | ||||||||
\(79\) | 7.61876 | 0.857178 | 0.428589 | − | 0.903500i | \(-0.359011\pi\) | ||||
0.428589 | + | 0.903500i | \(0.359011\pi\) | |||||||
\(80\) | 6.99170 | 0.781696 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.2100 | 1.45880 | ||||||||
\(83\) | 11.2522 | 1.23508 | 0.617542 | − | 0.786538i | \(-0.288129\pi\) | ||||
0.617542 | + | 0.786538i | \(0.288129\pi\) | |||||||
\(84\) | 8.12529 | 0.886542 | ||||||||
\(85\) | −22.4748 | −2.43773 | ||||||||
\(86\) | −15.1230 | −1.63075 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 4.78331 | 0.509903 | ||||||||
\(89\) | 3.11532 | 0.330223 | 0.165111 | − | 0.986275i | \(-0.447202\pi\) | ||||
0.165111 | + | 0.986275i | \(0.447202\pi\) | |||||||
\(90\) | 7.95571 | 0.838605 | ||||||||
\(91\) | 5.40883 | 0.566999 | ||||||||
\(92\) | −2.75597 | −0.287330 | ||||||||
\(93\) | 9.78276 | 1.01442 | ||||||||
\(94\) | 13.9700 | 1.44089 | ||||||||
\(95\) | 26.4932 | 2.71815 | ||||||||
\(96\) | 7.47695 | 0.763114 | ||||||||
\(97\) | −1.36579 | −0.138674 | −0.0693372 | − | 0.997593i | \(-0.522088\pi\) | ||||
−0.0693372 | + | 0.997593i | \(0.522088\pi\) | |||||||
\(98\) | −3.69033 | −0.372780 | ||||||||
\(99\) | −2.90138 | −0.291599 | ||||||||
\(100\) | 22.8971 | 2.28971 | ||||||||
\(101\) | −3.09336 | −0.307801 | −0.153900 | − | 0.988086i | \(-0.549184\pi\) | ||||
−0.153900 | + | 0.988086i | \(0.549184\pi\) | |||||||
\(102\) | −13.4356 | −1.33032 | ||||||||
\(103\) | −5.80530 | −0.572013 | −0.286007 | − | 0.958228i | \(-0.592328\pi\) | ||||
−0.286007 | + | 0.958228i | \(0.592328\pi\) | |||||||
\(104\) | −3.02457 | −0.296583 | ||||||||
\(105\) | −10.7553 | −1.04961 | ||||||||
\(106\) | −10.0852 | −0.979564 | ||||||||
\(107\) | 13.4507 | 1.30033 | 0.650163 | − | 0.759795i | \(-0.274701\pi\) | ||||
0.650163 | + | 0.759795i | \(0.274701\pi\) | |||||||
\(108\) | 2.75597 | 0.265193 | ||||||||
\(109\) | 1.09175 | 0.104571 | 0.0522853 | − | 0.998632i | \(-0.483349\pi\) | ||||
0.0522853 | + | 0.998632i | \(0.483349\pi\) | |||||||
\(110\) | −23.0825 | −2.20083 | ||||||||
\(111\) | −1.23929 | −0.117629 | ||||||||
\(112\) | −5.65052 | −0.533923 | ||||||||
\(113\) | 17.7325 | 1.66814 | 0.834068 | − | 0.551661i | \(-0.186006\pi\) | ||||
0.834068 | + | 0.551661i | \(0.186006\pi\) | |||||||
\(114\) | 15.8378 | 1.48335 | ||||||||
\(115\) | 3.64804 | 0.340181 | ||||||||
\(116\) | −2.75597 | −0.255885 | ||||||||
\(117\) | 1.83459 | 0.169608 | ||||||||
\(118\) | 7.72399 | 0.711051 | ||||||||
\(119\) | 18.1635 | 1.66505 | ||||||||
\(120\) | 6.01428 | 0.549027 | ||||||||
\(121\) | −2.58201 | −0.234728 | ||||||||
\(122\) | 21.7538 | 1.96950 | ||||||||
\(123\) | −6.05736 | −0.546174 | ||||||||
\(124\) | 26.9610 | 2.42117 | ||||||||
\(125\) | −12.0684 | −1.07943 | ||||||||
\(126\) | −6.42960 | −0.572794 | ||||||||
\(127\) | 15.4962 | 1.37507 | 0.687533 | − | 0.726154i | \(-0.258694\pi\) | ||||
0.687533 | + | 0.726154i | \(0.258694\pi\) | |||||||
\(128\) | 12.2469 | 1.08248 | ||||||||
\(129\) | 6.93454 | 0.610552 | ||||||||
\(130\) | 14.5955 | 1.28011 | ||||||||
\(131\) | 10.5488 | 0.921657 | 0.460829 | − | 0.887489i | \(-0.347552\pi\) | ||||
0.460829 | + | 0.887489i | \(0.347552\pi\) | |||||||
\(132\) | −7.99611 | −0.695972 | ||||||||
\(133\) | −21.4111 | −1.85658 | ||||||||
\(134\) | −11.2787 | −0.974328 | ||||||||
\(135\) | −3.64804 | −0.313973 | ||||||||
\(136\) | −10.1569 | −0.870946 | ||||||||
\(137\) | −0.813436 | −0.0694965 | −0.0347483 | − | 0.999396i | \(-0.511063\pi\) | ||||
−0.0347483 | + | 0.999396i | \(0.511063\pi\) | |||||||
\(138\) | 2.18082 | 0.185644 | ||||||||
\(139\) | −17.3423 | −1.47096 | −0.735478 | − | 0.677549i | \(-0.763042\pi\) | ||||
−0.735478 | + | 0.677549i | \(0.763042\pi\) | |||||||
\(140\) | −29.6414 | −2.50515 | ||||||||
\(141\) | −6.40585 | −0.539470 | ||||||||
\(142\) | 10.5800 | 0.887855 | ||||||||
\(143\) | −5.32283 | −0.445118 | ||||||||
\(144\) | −1.91657 | −0.159714 | ||||||||
\(145\) | 3.64804 | 0.302953 | ||||||||
\(146\) | −16.5073 | −1.36615 | ||||||||
\(147\) | 1.69218 | 0.139568 | ||||||||
\(148\) | −3.41546 | −0.280749 | ||||||||
\(149\) | 21.0736 | 1.72641 | 0.863207 | − | 0.504850i | \(-0.168452\pi\) | ||||
0.863207 | + | 0.504850i | \(0.168452\pi\) | |||||||
\(150\) | −18.1186 | −1.47938 | ||||||||
\(151\) | −17.4071 | −1.41657 | −0.708286 | − | 0.705925i | \(-0.750531\pi\) | ||||
−0.708286 | + | 0.705925i | \(0.750531\pi\) | |||||||
\(152\) | 11.9729 | 0.971132 | ||||||||
\(153\) | 6.16079 | 0.498070 | ||||||||
\(154\) | 18.6547 | 1.50324 | ||||||||
\(155\) | −35.6879 | −2.86652 | ||||||||
\(156\) | 5.05607 | 0.404810 | ||||||||
\(157\) | 20.9775 | 1.67419 | 0.837095 | − | 0.547057i | \(-0.184252\pi\) | ||||
0.837095 | + | 0.547057i | \(0.184252\pi\) | |||||||
\(158\) | −16.6151 | −1.32183 | ||||||||
\(159\) | 4.62451 | 0.366748 | ||||||||
\(160\) | −27.2762 | −2.15637 | ||||||||
\(161\) | −2.94825 | −0.232355 | ||||||||
\(162\) | −2.18082 | −0.171341 | ||||||||
\(163\) | 3.29012 | 0.257702 | 0.128851 | − | 0.991664i | \(-0.458871\pi\) | ||||
0.128851 | + | 0.991664i | \(0.458871\pi\) | |||||||
\(164\) | −16.6939 | −1.30358 | ||||||||
\(165\) | 10.5843 | 0.823989 | ||||||||
\(166\) | −24.5389 | −1.90459 | ||||||||
\(167\) | 19.1189 | 1.47947 | 0.739733 | − | 0.672901i | \(-0.234952\pi\) | ||||
0.739733 | + | 0.672901i | \(0.234952\pi\) | |||||||
\(168\) | −4.86059 | −0.375003 | ||||||||
\(169\) | −9.63428 | −0.741099 | ||||||||
\(170\) | 49.0134 | 3.75916 | ||||||||
\(171\) | −7.26232 | −0.555364 | ||||||||
\(172\) | 19.1114 | 1.45723 | ||||||||
\(173\) | −4.38468 | −0.333361 | −0.166681 | − | 0.986011i | \(-0.553305\pi\) | ||||
−0.166681 | + | 0.986011i | \(0.553305\pi\) | |||||||
\(174\) | 2.18082 | 0.165327 | ||||||||
\(175\) | 24.4946 | 1.85162 | ||||||||
\(176\) | 5.56068 | 0.419152 | ||||||||
\(177\) | −3.54179 | −0.266217 | ||||||||
\(178\) | −6.79394 | −0.509227 | ||||||||
\(179\) | −21.2216 | −1.58618 | −0.793090 | − | 0.609104i | \(-0.791529\pi\) | ||||
−0.793090 | + | 0.609104i | \(0.791529\pi\) | |||||||
\(180\) | −10.0539 | −0.749372 | ||||||||
\(181\) | 19.4211 | 1.44356 | 0.721781 | − | 0.692121i | \(-0.243324\pi\) | ||||
0.721781 | + | 0.692121i | \(0.243324\pi\) | |||||||
\(182\) | −11.7957 | −0.874353 | ||||||||
\(183\) | −9.97508 | −0.737379 | ||||||||
\(184\) | 1.64864 | 0.121539 | ||||||||
\(185\) | 4.52099 | 0.332390 | ||||||||
\(186\) | −21.3344 | −1.56432 | ||||||||
\(187\) | −17.8748 | −1.30713 | ||||||||
\(188\) | −17.6543 | −1.28757 | ||||||||
\(189\) | 2.94825 | 0.214454 | ||||||||
\(190\) | −57.7769 | −4.19158 | ||||||||
\(191\) | 2.72682 | 0.197306 | 0.0986530 | − | 0.995122i | \(-0.468547\pi\) | ||||
0.0986530 | + | 0.995122i | \(0.468547\pi\) | |||||||
\(192\) | −12.4728 | −0.900143 | ||||||||
\(193\) | −2.27863 | −0.164019 | −0.0820097 | − | 0.996632i | \(-0.526134\pi\) | ||||
−0.0820097 | + | 0.996632i | \(0.526134\pi\) | |||||||
\(194\) | 2.97853 | 0.213846 | ||||||||
\(195\) | −6.69265 | −0.479270 | ||||||||
\(196\) | 4.66359 | 0.333113 | ||||||||
\(197\) | 11.3746 | 0.810408 | 0.405204 | − | 0.914226i | \(-0.367201\pi\) | ||||
0.405204 | + | 0.914226i | \(0.367201\pi\) | |||||||
\(198\) | 6.32738 | 0.449667 | ||||||||
\(199\) | 15.0746 | 1.06861 | 0.534306 | − | 0.845291i | \(-0.320573\pi\) | ||||
0.534306 | + | 0.845291i | \(0.320573\pi\) | |||||||
\(200\) | −13.6972 | −0.968535 | ||||||||
\(201\) | 5.17176 | 0.364787 | ||||||||
\(202\) | 6.74606 | 0.474651 | ||||||||
\(203\) | −2.94825 | −0.206927 | ||||||||
\(204\) | 16.9789 | 1.18876 | ||||||||
\(205\) | 22.0975 | 1.54336 | ||||||||
\(206\) | 12.6603 | 0.882086 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −3.51611 | −0.243798 | ||||||||
\(209\) | 21.0707 | 1.45749 | ||||||||
\(210\) | 23.4554 | 1.61858 | ||||||||
\(211\) | 20.6210 | 1.41961 | 0.709804 | − | 0.704399i | \(-0.248783\pi\) | ||||
0.709804 | + | 0.704399i | \(0.248783\pi\) | |||||||
\(212\) | 12.7450 | 0.875332 | ||||||||
\(213\) | −4.85140 | −0.332412 | ||||||||
\(214\) | −29.3335 | −2.00520 | ||||||||
\(215\) | −25.2975 | −1.72527 | ||||||||
\(216\) | −1.64864 | −0.112175 | ||||||||
\(217\) | 28.8420 | 1.95792 | ||||||||
\(218\) | −2.38091 | −0.161255 | ||||||||
\(219\) | 7.56931 | 0.511487 | ||||||||
\(220\) | 29.1701 | 1.96665 | ||||||||
\(221\) | 11.3025 | 0.760289 | ||||||||
\(222\) | 2.70268 | 0.181392 | ||||||||
\(223\) | 1.95442 | 0.130877 | 0.0654387 | − | 0.997857i | \(-0.479155\pi\) | ||||
0.0654387 | + | 0.997857i | \(0.479155\pi\) | |||||||
\(224\) | 22.0439 | 1.47287 | ||||||||
\(225\) | 8.30818 | 0.553878 | ||||||||
\(226\) | −38.6714 | −2.57239 | ||||||||
\(227\) | 21.4195 | 1.42166 | 0.710831 | − | 0.703362i | \(-0.248319\pi\) | ||||
0.710831 | + | 0.703362i | \(0.248319\pi\) | |||||||
\(228\) | −20.0148 | −1.32551 | ||||||||
\(229\) | 4.10165 | 0.271045 | 0.135522 | − | 0.990774i | \(-0.456729\pi\) | ||||
0.135522 | + | 0.990774i | \(0.456729\pi\) | |||||||
\(230\) | −7.95571 | −0.524584 | ||||||||
\(231\) | −8.55398 | −0.562811 | ||||||||
\(232\) | 1.64864 | 0.108238 | ||||||||
\(233\) | 16.6505 | 1.09081 | 0.545407 | − | 0.838171i | \(-0.316375\pi\) | ||||
0.545407 | + | 0.838171i | \(0.316375\pi\) | |||||||
\(234\) | −4.00091 | −0.261547 | ||||||||
\(235\) | 23.3688 | 1.52441 | ||||||||
\(236\) | −9.76106 | −0.635391 | ||||||||
\(237\) | 7.61876 | 0.494892 | ||||||||
\(238\) | −39.6114 | −2.56762 | ||||||||
\(239\) | 15.1886 | 0.982467 | 0.491234 | − | 0.871028i | \(-0.336546\pi\) | ||||
0.491234 | + | 0.871028i | \(0.336546\pi\) | |||||||
\(240\) | 6.99170 | 0.451313 | ||||||||
\(241\) | −6.49318 | −0.418262 | −0.209131 | − | 0.977888i | \(-0.567064\pi\) | ||||
−0.209131 | + | 0.977888i | \(0.567064\pi\) | |||||||
\(242\) | 5.63090 | 0.361968 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −27.4910 | −1.75993 | ||||||||
\(245\) | −6.17312 | −0.394386 | ||||||||
\(246\) | 13.2100 | 0.842240 | ||||||||
\(247\) | −13.3234 | −0.847746 | ||||||||
\(248\) | −16.1282 | −1.02414 | ||||||||
\(249\) | 11.2522 | 0.713076 | ||||||||
\(250\) | 26.3189 | 1.66455 | ||||||||
\(251\) | 26.2268 | 1.65542 | 0.827710 | − | 0.561157i | \(-0.189644\pi\) | ||||
0.827710 | + | 0.561157i | \(0.189644\pi\) | |||||||
\(252\) | 8.12529 | 0.511845 | ||||||||
\(253\) | 2.90138 | 0.182408 | ||||||||
\(254\) | −33.7944 | −2.12045 | ||||||||
\(255\) | −22.4748 | −1.40743 | ||||||||
\(256\) | −1.76277 | −0.110173 | ||||||||
\(257\) | 0.394588 | 0.0246137 | 0.0123069 | − | 0.999924i | \(-0.496083\pi\) | ||||
0.0123069 | + | 0.999924i | \(0.496083\pi\) | |||||||
\(258\) | −15.1230 | −0.941515 | ||||||||
\(259\) | −3.65375 | −0.227033 | ||||||||
\(260\) | −18.4447 | −1.14389 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −23.0051 | −1.42126 | ||||||||
\(263\) | 27.4775 | 1.69434 | 0.847168 | − | 0.531325i | \(-0.178306\pi\) | ||||
0.847168 | + | 0.531325i | \(0.178306\pi\) | |||||||
\(264\) | 4.78331 | 0.294393 | ||||||||
\(265\) | −16.8704 | −1.03634 | ||||||||
\(266\) | 46.6938 | 2.86298 | ||||||||
\(267\) | 3.11532 | 0.190654 | ||||||||
\(268\) | 14.2532 | 0.870653 | ||||||||
\(269\) | −12.5639 | −0.766037 | −0.383019 | − | 0.923741i | \(-0.625115\pi\) | ||||
−0.383019 | + | 0.923741i | \(0.625115\pi\) | |||||||
\(270\) | 7.95571 | 0.484169 | ||||||||
\(271\) | 3.16176 | 0.192063 | 0.0960316 | − | 0.995378i | \(-0.469385\pi\) | ||||
0.0960316 | + | 0.995378i | \(0.469385\pi\) | |||||||
\(272\) | −11.8076 | −0.715938 | ||||||||
\(273\) | 5.40883 | 0.327357 | ||||||||
\(274\) | 1.77396 | 0.107169 | ||||||||
\(275\) | −24.1052 | −1.45360 | ||||||||
\(276\) | −2.75597 | −0.165890 | ||||||||
\(277\) | 9.84864 | 0.591747 | 0.295874 | − | 0.955227i | \(-0.404389\pi\) | ||||
0.295874 | + | 0.955227i | \(0.404389\pi\) | |||||||
\(278\) | 37.8204 | 2.26832 | ||||||||
\(279\) | 9.78276 | 0.585678 | ||||||||
\(280\) | 17.7316 | 1.05967 | ||||||||
\(281\) | 18.5477 | 1.10646 | 0.553232 | − | 0.833027i | \(-0.313394\pi\) | ||||
0.553232 | + | 0.833027i | \(0.313394\pi\) | |||||||
\(282\) | 13.9700 | 0.831901 | ||||||||
\(283\) | 2.64756 | 0.157381 | 0.0786905 | − | 0.996899i | \(-0.474926\pi\) | ||||
0.0786905 | + | 0.996899i | \(0.474926\pi\) | |||||||
\(284\) | −13.3703 | −0.793382 | ||||||||
\(285\) | 26.4932 | 1.56932 | ||||||||
\(286\) | 11.6081 | 0.686403 | ||||||||
\(287\) | −17.8586 | −1.05416 | ||||||||
\(288\) | 7.47695 | 0.440584 | ||||||||
\(289\) | 20.9553 | 1.23266 | ||||||||
\(290\) | −7.95571 | −0.467175 | ||||||||
\(291\) | −1.36579 | −0.0800637 | ||||||||
\(292\) | 20.8608 | 1.22079 | ||||||||
\(293\) | −27.9274 | −1.63154 | −0.815768 | − | 0.578379i | \(-0.803685\pi\) | ||||
−0.815768 | + | 0.578379i | \(0.803685\pi\) | |||||||
\(294\) | −3.69033 | −0.215224 | ||||||||
\(295\) | 12.9206 | 0.752264 | ||||||||
\(296\) | 2.04315 | 0.118755 | ||||||||
\(297\) | −2.90138 | −0.168355 | ||||||||
\(298\) | −45.9576 | −2.66225 | ||||||||
\(299\) | −1.83459 | −0.106097 | ||||||||
\(300\) | 22.8971 | 1.32196 | ||||||||
\(301\) | 20.4447 | 1.17842 | ||||||||
\(302\) | 37.9618 | 2.18446 | ||||||||
\(303\) | −3.09336 | −0.177709 | ||||||||
\(304\) | 13.9187 | 0.798293 | ||||||||
\(305\) | 36.3895 | 2.08365 | ||||||||
\(306\) | −13.4356 | −0.768060 | ||||||||
\(307\) | −22.5768 | −1.28853 | −0.644263 | − | 0.764804i | \(-0.722836\pi\) | ||||
−0.644263 | + | 0.764804i | \(0.722836\pi\) | |||||||
\(308\) | −23.5745 | −1.34328 | ||||||||
\(309\) | −5.80530 | −0.330252 | ||||||||
\(310\) | 77.8288 | 4.42038 | ||||||||
\(311\) | 5.39270 | 0.305792 | 0.152896 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152896 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(312\) | −3.02457 | −0.171232 | ||||||||
\(313\) | −3.71684 | −0.210088 | −0.105044 | − | 0.994468i | \(-0.533498\pi\) | ||||
−0.105044 | + | 0.994468i | \(0.533498\pi\) | |||||||
\(314\) | −45.7482 | −2.58172 | ||||||||
\(315\) | −10.7553 | −0.605994 | ||||||||
\(316\) | 20.9971 | 1.18118 | ||||||||
\(317\) | −27.1940 | −1.52736 | −0.763682 | − | 0.645592i | \(-0.776611\pi\) | ||||
−0.763682 | + | 0.645592i | \(0.776611\pi\) | |||||||
\(318\) | −10.0852 | −0.565552 | ||||||||
\(319\) | 2.90138 | 0.162446 | ||||||||
\(320\) | 45.5011 | 2.54359 | ||||||||
\(321\) | 13.4507 | 0.750744 | ||||||||
\(322\) | 6.42960 | 0.358308 | ||||||||
\(323\) | −44.7416 | −2.48949 | ||||||||
\(324\) | 2.75597 | 0.153109 | ||||||||
\(325\) | 15.2421 | 0.845479 | ||||||||
\(326\) | −7.17515 | −0.397395 | ||||||||
\(327\) | 1.09175 | 0.0603738 | ||||||||
\(328\) | 9.98639 | 0.551406 | ||||||||
\(329\) | −18.8860 | −1.04122 | ||||||||
\(330\) | −23.0825 | −1.27065 | ||||||||
\(331\) | −13.7728 | −0.757020 | −0.378510 | − | 0.925597i | \(-0.623563\pi\) | ||||
−0.378510 | + | 0.925597i | \(0.623563\pi\) | |||||||
\(332\) | 31.0106 | 1.70193 | ||||||||
\(333\) | −1.23929 | −0.0679129 | ||||||||
\(334\) | −41.6949 | −2.28144 | ||||||||
\(335\) | −18.8668 | −1.03080 | ||||||||
\(336\) | −5.65052 | −0.308261 | ||||||||
\(337\) | −5.87686 | −0.320133 | −0.160066 | − | 0.987106i | \(-0.551171\pi\) | ||||
−0.160066 | + | 0.987106i | \(0.551171\pi\) | |||||||
\(338\) | 21.0106 | 1.14283 | ||||||||
\(339\) | 17.7325 | 0.963099 | ||||||||
\(340\) | −61.9398 | −3.35916 | ||||||||
\(341\) | −28.3835 | −1.53705 | ||||||||
\(342\) | 15.8378 | 0.856411 | ||||||||
\(343\) | −15.6488 | −0.844955 | ||||||||
\(344\) | −11.4325 | −0.616401 | ||||||||
\(345\) | 3.64804 | 0.196404 | ||||||||
\(346\) | 9.56220 | 0.514067 | ||||||||
\(347\) | −15.4892 | −0.831502 | −0.415751 | − | 0.909478i | \(-0.636481\pi\) | ||||
−0.415751 | + | 0.909478i | \(0.636481\pi\) | |||||||
\(348\) | −2.75597 | −0.147736 | ||||||||
\(349\) | 16.3066 | 0.872874 | 0.436437 | − | 0.899735i | \(-0.356240\pi\) | ||||
0.436437 | + | 0.899735i | \(0.356240\pi\) | |||||||
\(350\) | −53.4182 | −2.85532 | ||||||||
\(351\) | 1.83459 | 0.0979231 | ||||||||
\(352\) | −21.6935 | −1.15627 | ||||||||
\(353\) | −3.27199 | −0.174151 | −0.0870753 | − | 0.996202i | \(-0.527752\pi\) | ||||
−0.0870753 | + | 0.996202i | \(0.527752\pi\) | |||||||
\(354\) | 7.72399 | 0.410526 | ||||||||
\(355\) | 17.6981 | 0.939316 | ||||||||
\(356\) | 8.58572 | 0.455042 | ||||||||
\(357\) | 18.1635 | 0.961316 | ||||||||
\(358\) | 46.2806 | 2.44600 | ||||||||
\(359\) | 29.6747 | 1.56617 | 0.783085 | − | 0.621914i | \(-0.213645\pi\) | ||||
0.783085 | + | 0.621914i | \(0.213645\pi\) | |||||||
\(360\) | 6.01428 | 0.316981 | ||||||||
\(361\) | 33.7413 | 1.77586 | ||||||||
\(362\) | −42.3540 | −2.22608 | ||||||||
\(363\) | −2.58201 | −0.135520 | ||||||||
\(364\) | 14.9066 | 0.781316 | ||||||||
\(365\) | −27.6131 | −1.44534 | ||||||||
\(366\) | 21.7538 | 1.13709 | ||||||||
\(367\) | 14.2811 | 0.745467 | 0.372733 | − | 0.927938i | \(-0.378421\pi\) | ||||
0.372733 | + | 0.927938i | \(0.378421\pi\) | |||||||
\(368\) | 1.91657 | 0.0999079 | ||||||||
\(369\) | −6.05736 | −0.315334 | ||||||||
\(370\) | −9.85947 | −0.512569 | ||||||||
\(371\) | 13.6342 | 0.707854 | ||||||||
\(372\) | 26.9610 | 1.39786 | ||||||||
\(373\) | 22.9700 | 1.18934 | 0.594672 | − | 0.803968i | \(-0.297282\pi\) | ||||
0.594672 | + | 0.803968i | \(0.297282\pi\) | |||||||
\(374\) | 38.9816 | 2.01569 | ||||||||
\(375\) | −12.0684 | −0.623207 | ||||||||
\(376\) | 10.5609 | 0.544637 | ||||||||
\(377\) | −1.83459 | −0.0944861 | ||||||||
\(378\) | −6.42960 | −0.330703 | ||||||||
\(379\) | 0.488397 | 0.0250873 | 0.0125436 | − | 0.999921i | \(-0.496007\pi\) | ||||
0.0125436 | + | 0.999921i | \(0.496007\pi\) | |||||||
\(380\) | 73.0146 | 3.74557 | ||||||||
\(381\) | 15.4962 | 0.793894 | ||||||||
\(382\) | −5.94671 | −0.304260 | ||||||||
\(383\) | −18.6541 | −0.953182 | −0.476591 | − | 0.879125i | \(-0.658128\pi\) | ||||
−0.476591 | + | 0.879125i | \(0.658128\pi\) | |||||||
\(384\) | 12.2469 | 0.624972 | ||||||||
\(385\) | 31.2053 | 1.59037 | ||||||||
\(386\) | 4.96928 | 0.252930 | ||||||||
\(387\) | 6.93454 | 0.352502 | ||||||||
\(388\) | −3.76406 | −0.191091 | ||||||||
\(389\) | −10.6579 | −0.540375 | −0.270188 | − | 0.962808i | \(-0.587086\pi\) | ||||
−0.270188 | + | 0.962808i | \(0.587086\pi\) | |||||||
\(390\) | 14.5955 | 0.739069 | ||||||||
\(391\) | −6.16079 | −0.311564 | ||||||||
\(392\) | −2.78978 | −0.140905 | ||||||||
\(393\) | 10.5488 | 0.532119 | ||||||||
\(394\) | −24.8060 | −1.24971 | ||||||||
\(395\) | −27.7935 | −1.39844 | ||||||||
\(396\) | −7.99611 | −0.401820 | ||||||||
\(397\) | −18.4482 | −0.925890 | −0.462945 | − | 0.886387i | \(-0.653207\pi\) | ||||
−0.462945 | + | 0.886387i | \(0.653207\pi\) | |||||||
\(398\) | −32.8750 | −1.64788 | ||||||||
\(399\) | −21.4111 | −1.07190 | ||||||||
\(400\) | −15.9232 | −0.796158 | ||||||||
\(401\) | 14.9013 | 0.744134 | 0.372067 | − | 0.928206i | \(-0.378649\pi\) | ||||
0.372067 | + | 0.928206i | \(0.378649\pi\) | |||||||
\(402\) | −11.2787 | −0.562529 | ||||||||
\(403\) | 17.9473 | 0.894020 | ||||||||
\(404\) | −8.52521 | −0.424145 | ||||||||
\(405\) | −3.64804 | −0.181272 | ||||||||
\(406\) | 6.42960 | 0.319096 | ||||||||
\(407\) | 3.59566 | 0.178230 | ||||||||
\(408\) | −10.1569 | −0.502841 | ||||||||
\(409\) | 17.7732 | 0.878828 | 0.439414 | − | 0.898285i | \(-0.355186\pi\) | ||||
0.439414 | + | 0.898285i | \(0.355186\pi\) | |||||||
\(410\) | −48.1906 | −2.37996 | ||||||||
\(411\) | −0.813436 | −0.0401238 | ||||||||
\(412\) | −15.9992 | −0.788226 | ||||||||
\(413\) | −10.4421 | −0.513821 | ||||||||
\(414\) | 2.18082 | 0.107181 | ||||||||
\(415\) | −41.0483 | −2.01498 | ||||||||
\(416\) | 13.7171 | 0.672538 | ||||||||
\(417\) | −17.3423 | −0.849256 | ||||||||
\(418\) | −45.9515 | −2.24756 | ||||||||
\(419\) | −27.0503 | −1.32149 | −0.660746 | − | 0.750609i | \(-0.729760\pi\) | ||||
−0.660746 | + | 0.750609i | \(0.729760\pi\) | |||||||
\(420\) | −29.6414 | −1.44635 | ||||||||
\(421\) | −16.2889 | −0.793872 | −0.396936 | − | 0.917846i | \(-0.629927\pi\) | ||||
−0.396936 | + | 0.917846i | \(0.629927\pi\) | |||||||
\(422\) | −44.9707 | −2.18914 | ||||||||
\(423\) | −6.40585 | −0.311463 | ||||||||
\(424\) | −7.62414 | −0.370261 | ||||||||
\(425\) | 51.1849 | 2.48283 | ||||||||
\(426\) | 10.5800 | 0.512603 | ||||||||
\(427\) | −29.4090 | −1.42320 | ||||||||
\(428\) | 37.0697 | 1.79183 | ||||||||
\(429\) | −5.32283 | −0.256989 | ||||||||
\(430\) | 55.1692 | 2.66049 | ||||||||
\(431\) | −9.61562 | −0.463168 | −0.231584 | − | 0.972815i | \(-0.574391\pi\) | ||||
−0.231584 | + | 0.972815i | \(0.574391\pi\) | |||||||
\(432\) | −1.91657 | −0.0922108 | ||||||||
\(433\) | 24.8003 | 1.19183 | 0.595913 | − | 0.803049i | \(-0.296790\pi\) | ||||
0.595913 | + | 0.803049i | \(0.296790\pi\) | |||||||
\(434\) | −62.8992 | −3.01926 | ||||||||
\(435\) | 3.64804 | 0.174910 | ||||||||
\(436\) | 3.00883 | 0.144097 | ||||||||
\(437\) | 7.26232 | 0.347404 | ||||||||
\(438\) | −16.5073 | −0.788750 | ||||||||
\(439\) | −36.6776 | −1.75053 | −0.875263 | − | 0.483646i | \(-0.839312\pi\) | ||||
−0.875263 | + | 0.483646i | \(0.839312\pi\) | |||||||
\(440\) | −17.4497 | −0.831882 | ||||||||
\(441\) | 1.69218 | 0.0805798 | ||||||||
\(442\) | −24.6487 | −1.17242 | ||||||||
\(443\) | −8.45059 | −0.401499 | −0.200750 | − | 0.979643i | \(-0.564338\pi\) | ||||
−0.200750 | + | 0.979643i | \(0.564338\pi\) | |||||||
\(444\) | −3.41546 | −0.162091 | ||||||||
\(445\) | −11.3648 | −0.538743 | ||||||||
\(446\) | −4.26223 | −0.201822 | ||||||||
\(447\) | 21.0736 | 0.996746 | ||||||||
\(448\) | −36.7728 | −1.73735 | ||||||||
\(449\) | 10.7809 | 0.508782 | 0.254391 | − | 0.967102i | \(-0.418125\pi\) | ||||
0.254391 | + | 0.967102i | \(0.418125\pi\) | |||||||
\(450\) | −18.1186 | −0.854120 | ||||||||
\(451\) | 17.5747 | 0.827560 | ||||||||
\(452\) | 48.8704 | 2.29867 | ||||||||
\(453\) | −17.4071 | −0.817858 | ||||||||
\(454\) | −46.7121 | −2.19231 | ||||||||
\(455\) | −19.7316 | −0.925032 | ||||||||
\(456\) | 11.9729 | 0.560684 | ||||||||
\(457\) | −17.4004 | −0.813955 | −0.406978 | − | 0.913438i | \(-0.633417\pi\) | ||||
−0.406978 | + | 0.913438i | \(0.633417\pi\) | |||||||
\(458\) | −8.94495 | −0.417970 | ||||||||
\(459\) | 6.16079 | 0.287561 | ||||||||
\(460\) | 10.0539 | 0.468765 | ||||||||
\(461\) | −12.1558 | −0.566151 | −0.283076 | − | 0.959098i | \(-0.591355\pi\) | ||||
−0.283076 | + | 0.959098i | \(0.591355\pi\) | |||||||
\(462\) | 18.6547 | 0.867895 | ||||||||
\(463\) | −32.2609 | −1.49929 | −0.749645 | − | 0.661840i | \(-0.769776\pi\) | ||||
−0.749645 | + | 0.661840i | \(0.769776\pi\) | |||||||
\(464\) | 1.91657 | 0.0889743 | ||||||||
\(465\) | −35.6879 | −1.65499 | ||||||||
\(466\) | −36.3118 | −1.68211 | ||||||||
\(467\) | 3.87350 | 0.179244 | 0.0896222 | − | 0.995976i | \(-0.471434\pi\) | ||||
0.0896222 | + | 0.995976i | \(0.471434\pi\) | |||||||
\(468\) | 5.05607 | 0.233717 | ||||||||
\(469\) | 15.2476 | 0.704070 | ||||||||
\(470\) | −50.9631 | −2.35075 | ||||||||
\(471\) | 20.9775 | 0.966594 | ||||||||
\(472\) | 5.83911 | 0.268767 | ||||||||
\(473\) | −20.1197 | −0.925105 | ||||||||
\(474\) | −16.6151 | −0.763159 | ||||||||
\(475\) | −60.3367 | −2.76844 | ||||||||
\(476\) | 50.0582 | 2.29441 | ||||||||
\(477\) | 4.62451 | 0.211742 | ||||||||
\(478\) | −33.1235 | −1.51504 | ||||||||
\(479\) | −22.3385 | −1.02067 | −0.510337 | − | 0.859975i | \(-0.670479\pi\) | ||||
−0.510337 | + | 0.859975i | \(0.670479\pi\) | |||||||
\(480\) | −27.2762 | −1.24498 | ||||||||
\(481\) | −2.27360 | −0.103667 | ||||||||
\(482\) | 14.1604 | 0.644990 | ||||||||
\(483\) | −2.94825 | −0.134150 | ||||||||
\(484\) | −7.11595 | −0.323452 | ||||||||
\(485\) | 4.98244 | 0.226241 | ||||||||
\(486\) | −2.18082 | −0.0989240 | ||||||||
\(487\) | 11.6918 | 0.529804 | 0.264902 | − | 0.964275i | \(-0.414660\pi\) | ||||
0.264902 | + | 0.964275i | \(0.414660\pi\) | |||||||
\(488\) | 16.4453 | 0.744442 | ||||||||
\(489\) | 3.29012 | 0.148784 | ||||||||
\(490\) | 13.4625 | 0.608172 | ||||||||
\(491\) | 32.6810 | 1.47488 | 0.737438 | − | 0.675415i | \(-0.236036\pi\) | ||||
0.737438 | + | 0.675415i | \(0.236036\pi\) | |||||||
\(492\) | −16.6939 | −0.752620 | ||||||||
\(493\) | −6.16079 | −0.277468 | ||||||||
\(494\) | 29.0559 | 1.30729 | ||||||||
\(495\) | 10.5843 | 0.475730 | ||||||||
\(496\) | −18.7493 | −0.841868 | ||||||||
\(497\) | −14.3031 | −0.641583 | ||||||||
\(498\) | −24.5389 | −1.09961 | ||||||||
\(499\) | −26.3934 | −1.18153 | −0.590765 | − | 0.806844i | \(-0.701174\pi\) | ||||
−0.590765 | + | 0.806844i | \(0.701174\pi\) | |||||||
\(500\) | −33.2600 | −1.48743 | ||||||||
\(501\) | 19.1189 | 0.854170 | ||||||||
\(502\) | −57.1958 | −2.55278 | ||||||||
\(503\) | 30.8951 | 1.37754 | 0.688772 | − | 0.724978i | \(-0.258150\pi\) | ||||
0.688772 | + | 0.724978i | \(0.258150\pi\) | |||||||
\(504\) | −4.86059 | −0.216508 | ||||||||
\(505\) | 11.2847 | 0.502162 | ||||||||
\(506\) | −6.32738 | −0.281286 | ||||||||
\(507\) | −9.63428 | −0.427874 | ||||||||
\(508\) | 42.7071 | 1.89482 | ||||||||
\(509\) | 33.1618 | 1.46987 | 0.734936 | − | 0.678136i | \(-0.237212\pi\) | ||||
0.734936 | + | 0.678136i | \(0.237212\pi\) | |||||||
\(510\) | 49.0134 | 2.17035 | ||||||||
\(511\) | 22.3162 | 0.987212 | ||||||||
\(512\) | −20.6495 | −0.912588 | ||||||||
\(513\) | −7.26232 | −0.320639 | ||||||||
\(514\) | −0.860526 | −0.0379562 | ||||||||
\(515\) | 21.1780 | 0.933212 | ||||||||
\(516\) | 19.1114 | 0.841332 | ||||||||
\(517\) | 18.5858 | 0.817402 | ||||||||
\(518\) | 7.96817 | 0.350101 | ||||||||
\(519\) | −4.38468 | −0.192466 | ||||||||
\(520\) | 11.0337 | 0.483861 | ||||||||
\(521\) | −13.2878 | −0.582151 | −0.291075 | − | 0.956700i | \(-0.594013\pi\) | ||||
−0.291075 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(522\) | 2.18082 | 0.0954518 | ||||||||
\(523\) | −12.3035 | −0.537995 | −0.268997 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268997 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(524\) | 29.0723 | 1.27003 | ||||||||
\(525\) | 24.4946 | 1.06903 | ||||||||
\(526\) | −59.9235 | −2.61279 | ||||||||
\(527\) | 60.2695 | 2.62538 | ||||||||
\(528\) | 5.56068 | 0.241998 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 36.7913 | 1.59811 | ||||||||
\(531\) | −3.54179 | −0.153700 | ||||||||
\(532\) | −59.0085 | −2.55834 | ||||||||
\(533\) | −11.1128 | −0.481347 | ||||||||
\(534\) | −6.79394 | −0.294003 | ||||||||
\(535\) | −49.0686 | −2.12142 | ||||||||
\(536\) | −8.52634 | −0.368282 | ||||||||
\(537\) | −21.2216 | −0.915782 | ||||||||
\(538\) | 27.3997 | 1.18128 | ||||||||
\(539\) | −4.90964 | −0.211473 | ||||||||
\(540\) | −10.0539 | −0.432650 | ||||||||
\(541\) | 5.59393 | 0.240502 | 0.120251 | − | 0.992744i | \(-0.461630\pi\) | ||||
0.120251 | + | 0.992744i | \(0.461630\pi\) | |||||||
\(542\) | −6.89522 | −0.296175 | ||||||||
\(543\) | 19.4211 | 0.833441 | ||||||||
\(544\) | 46.0639 | 1.97497 | ||||||||
\(545\) | −3.98274 | −0.170602 | ||||||||
\(546\) | −11.7957 | −0.504808 | ||||||||
\(547\) | −22.5204 | −0.962904 | −0.481452 | − | 0.876472i | \(-0.659890\pi\) | ||||
−0.481452 | + | 0.876472i | \(0.659890\pi\) | |||||||
\(548\) | −2.24181 | −0.0957652 | ||||||||
\(549\) | −9.97508 | −0.425726 | ||||||||
\(550\) | 52.5690 | 2.24155 | ||||||||
\(551\) | 7.26232 | 0.309385 | ||||||||
\(552\) | 1.64864 | 0.0701706 | ||||||||
\(553\) | 22.4620 | 0.955182 | ||||||||
\(554\) | −21.4781 | −0.912517 | ||||||||
\(555\) | 4.52099 | 0.191905 | ||||||||
\(556\) | −47.7949 | −2.02696 | ||||||||
\(557\) | −21.5581 | −0.913448 | −0.456724 | − | 0.889608i | \(-0.650977\pi\) | ||||
−0.456724 | + | 0.889608i | \(0.650977\pi\) | |||||||
\(558\) | −21.3344 | −0.903158 | ||||||||
\(559\) | 12.7220 | 0.538084 | ||||||||
\(560\) | 20.6133 | 0.871071 | ||||||||
\(561\) | −17.8748 | −0.754673 | ||||||||
\(562\) | −40.4492 | −1.70625 | ||||||||
\(563\) | −21.7684 | −0.917430 | −0.458715 | − | 0.888583i | \(-0.651690\pi\) | ||||
−0.458715 | + | 0.888583i | \(0.651690\pi\) | |||||||
\(564\) | −17.6543 | −0.743381 | ||||||||
\(565\) | −64.6890 | −2.72148 | ||||||||
\(566\) | −5.77385 | −0.242693 | ||||||||
\(567\) | 2.94825 | 0.123815 | ||||||||
\(568\) | 7.99818 | 0.335596 | ||||||||
\(569\) | −15.5221 | −0.650719 | −0.325360 | − | 0.945590i | \(-0.605485\pi\) | ||||
−0.325360 | + | 0.945590i | \(0.605485\pi\) | |||||||
\(570\) | −57.7769 | −2.42001 | ||||||||
\(571\) | −13.0573 | −0.546430 | −0.273215 | − | 0.961953i | \(-0.588087\pi\) | ||||
−0.273215 | + | 0.961953i | \(0.588087\pi\) | |||||||
\(572\) | −14.6696 | −0.613366 | ||||||||
\(573\) | 2.72682 | 0.113915 | ||||||||
\(574\) | 38.9464 | 1.62559 | ||||||||
\(575\) | −8.30818 | −0.346475 | ||||||||
\(576\) | −12.4728 | −0.519698 | ||||||||
\(577\) | −4.59902 | −0.191460 | −0.0957299 | − | 0.995407i | \(-0.530519\pi\) | ||||
−0.0957299 | + | 0.995407i | \(0.530519\pi\) | |||||||
\(578\) | −45.6997 | −1.90086 | ||||||||
\(579\) | −2.27863 | −0.0946966 | ||||||||
\(580\) | 10.0539 | 0.417465 | ||||||||
\(581\) | 33.1742 | 1.37630 | ||||||||
\(582\) | 2.97853 | 0.123464 | ||||||||
\(583\) | −13.4175 | −0.555694 | ||||||||
\(584\) | −12.4790 | −0.516386 | ||||||||
\(585\) | −6.69265 | −0.276707 | ||||||||
\(586\) | 60.9046 | 2.51595 | ||||||||
\(587\) | −9.84048 | −0.406160 | −0.203080 | − | 0.979162i | \(-0.565095\pi\) | ||||
−0.203080 | + | 0.979162i | \(0.565095\pi\) | |||||||
\(588\) | 4.66359 | 0.192323 | ||||||||
\(589\) | −71.0455 | −2.92738 | ||||||||
\(590\) | −28.1774 | −1.16005 | ||||||||
\(591\) | 11.3746 | 0.467889 | ||||||||
\(592\) | 2.37519 | 0.0976197 | ||||||||
\(593\) | 43.2061 | 1.77426 | 0.887130 | − | 0.461519i | \(-0.152695\pi\) | ||||
0.887130 | + | 0.461519i | \(0.152695\pi\) | |||||||
\(594\) | 6.32738 | 0.259615 | ||||||||
\(595\) | −66.2612 | −2.71645 | ||||||||
\(596\) | 58.0781 | 2.37897 | ||||||||
\(597\) | 15.0746 | 0.616963 | ||||||||
\(598\) | 4.00091 | 0.163609 | ||||||||
\(599\) | 46.1400 | 1.88523 | 0.942615 | − | 0.333881i | \(-0.108359\pi\) | ||||
0.942615 | + | 0.333881i | \(0.108359\pi\) | |||||||
\(600\) | −13.6972 | −0.559184 | ||||||||
\(601\) | 31.5835 | 1.28832 | 0.644159 | − | 0.764891i | \(-0.277207\pi\) | ||||
0.644159 | + | 0.764891i | \(0.277207\pi\) | |||||||
\(602\) | −44.5863 | −1.81720 | ||||||||
\(603\) | 5.17176 | 0.210610 | ||||||||
\(604\) | −47.9735 | −1.95202 | ||||||||
\(605\) | 9.41927 | 0.382948 | ||||||||
\(606\) | 6.74606 | 0.274040 | ||||||||
\(607\) | 34.6230 | 1.40530 | 0.702652 | − | 0.711534i | \(-0.251999\pi\) | ||||
0.702652 | + | 0.711534i | \(0.251999\pi\) | |||||||
\(608\) | −54.3001 | −2.20216 | ||||||||
\(609\) | −2.94825 | −0.119469 | ||||||||
\(610\) | −79.3588 | −3.21314 | ||||||||
\(611\) | −11.7521 | −0.475439 | ||||||||
\(612\) | 16.9789 | 0.686333 | ||||||||
\(613\) | −17.1548 | −0.692877 | −0.346438 | − | 0.938073i | \(-0.612609\pi\) | ||||
−0.346438 | + | 0.938073i | \(0.612609\pi\) | |||||||
\(614\) | 49.2359 | 1.98700 | ||||||||
\(615\) | 22.0975 | 0.891057 | ||||||||
\(616\) | 14.1024 | 0.568202 | ||||||||
\(617\) | −37.5396 | −1.51129 | −0.755643 | − | 0.654984i | \(-0.772676\pi\) | ||||
−0.755643 | + | 0.654984i | \(0.772676\pi\) | |||||||
\(618\) | 12.6603 | 0.509272 | ||||||||
\(619\) | −23.3422 | −0.938204 | −0.469102 | − | 0.883144i | \(-0.655422\pi\) | ||||
−0.469102 | + | 0.883144i | \(0.655422\pi\) | |||||||
\(620\) | −98.3547 | −3.95002 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −11.7605 | −0.471553 | ||||||||
\(623\) | 9.18473 | 0.367978 | ||||||||
\(624\) | −3.51611 | −0.140757 | ||||||||
\(625\) | 2.48491 | 0.0993965 | ||||||||
\(626\) | 8.10576 | 0.323971 | ||||||||
\(627\) | 21.0707 | 0.841484 | ||||||||
\(628\) | 57.8135 | 2.30701 | ||||||||
\(629\) | −7.63503 | −0.304429 | ||||||||
\(630\) | 23.4554 | 0.934486 | ||||||||
\(631\) | 41.4409 | 1.64973 | 0.824867 | − | 0.565326i | \(-0.191250\pi\) | ||||
0.824867 | + | 0.565326i | \(0.191250\pi\) | |||||||
\(632\) | −12.5606 | −0.499632 | ||||||||
\(633\) | 20.6210 | 0.819611 | ||||||||
\(634\) | 59.3051 | 2.35531 | ||||||||
\(635\) | −56.5307 | −2.24335 | ||||||||
\(636\) | 12.7450 | 0.505373 | ||||||||
\(637\) | 3.10445 | 0.123003 | ||||||||
\(638\) | −6.32738 | −0.250503 | ||||||||
\(639\) | −4.85140 | −0.191918 | ||||||||
\(640\) | −44.6772 | −1.76602 | ||||||||
\(641\) | −33.3001 | −1.31527 | −0.657637 | − | 0.753335i | \(-0.728444\pi\) | ||||
−0.657637 | + | 0.753335i | \(0.728444\pi\) | |||||||
\(642\) | −29.3335 | −1.15770 | ||||||||
\(643\) | −17.4466 | −0.688025 | −0.344012 | − | 0.938965i | \(-0.611786\pi\) | ||||
−0.344012 | + | 0.938965i | \(0.611786\pi\) | |||||||
\(644\) | −8.12529 | −0.320181 | ||||||||
\(645\) | −25.2975 | −0.996086 | ||||||||
\(646\) | 97.5734 | 3.83897 | ||||||||
\(647\) | −16.1523 | −0.635012 | −0.317506 | − | 0.948256i | \(-0.602845\pi\) | ||||
−0.317506 | + | 0.948256i | \(0.602845\pi\) | |||||||
\(648\) | −1.64864 | −0.0647645 | ||||||||
\(649\) | 10.2761 | 0.403370 | ||||||||
\(650\) | −33.2402 | −1.30379 | ||||||||
\(651\) | 28.8420 | 1.13041 | ||||||||
\(652\) | 9.06747 | 0.355110 | ||||||||
\(653\) | −36.5084 | −1.42868 | −0.714342 | − | 0.699797i | \(-0.753274\pi\) | ||||
−0.714342 | + | 0.699797i | \(0.753274\pi\) | |||||||
\(654\) | −2.38091 | −0.0931008 | ||||||||
\(655\) | −38.4826 | −1.50364 | ||||||||
\(656\) | 11.6093 | 0.453268 | ||||||||
\(657\) | 7.56931 | 0.295307 | ||||||||
\(658\) | 41.1870 | 1.60564 | ||||||||
\(659\) | −34.0056 | −1.32467 | −0.662336 | − | 0.749207i | \(-0.730435\pi\) | ||||
−0.662336 | + | 0.749207i | \(0.730435\pi\) | |||||||
\(660\) | 29.1701 | 1.13545 | ||||||||
\(661\) | 4.58617 | 0.178381 | 0.0891906 | − | 0.996015i | \(-0.471572\pi\) | ||||
0.0891906 | + | 0.996015i | \(0.471572\pi\) | |||||||
\(662\) | 30.0359 | 1.16738 | ||||||||
\(663\) | 11.3025 | 0.438953 | ||||||||
\(664\) | −18.5507 | −0.719907 | ||||||||
\(665\) | 78.1086 | 3.02892 | ||||||||
\(666\) | 2.70268 | 0.104727 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 52.6911 | 2.03868 | ||||||||
\(669\) | 1.95442 | 0.0755621 | ||||||||
\(670\) | 41.1450 | 1.58957 | ||||||||
\(671\) | 28.9415 | 1.11727 | ||||||||
\(672\) | 22.0439 | 0.850363 | ||||||||
\(673\) | −10.9084 | −0.420488 | −0.210244 | − | 0.977649i | \(-0.567426\pi\) | ||||
−0.210244 | + | 0.977649i | \(0.567426\pi\) | |||||||
\(674\) | 12.8164 | 0.493668 | ||||||||
\(675\) | 8.30818 | 0.319782 | ||||||||
\(676\) | −26.5518 | −1.02122 | ||||||||
\(677\) | 3.91537 | 0.150480 | 0.0752400 | − | 0.997165i | \(-0.476028\pi\) | ||||
0.0752400 | + | 0.997165i | \(0.476028\pi\) | |||||||
\(678\) | −38.6714 | −1.48517 | ||||||||
\(679\) | −4.02668 | −0.154530 | ||||||||
\(680\) | 37.0527 | 1.42091 | ||||||||
\(681\) | 21.4195 | 0.820798 | ||||||||
\(682\) | 61.8992 | 2.37024 | ||||||||
\(683\) | −22.2311 | −0.850650 | −0.425325 | − | 0.905041i | \(-0.639840\pi\) | ||||
−0.425325 | + | 0.905041i | \(0.639840\pi\) | |||||||
\(684\) | −20.0148 | −0.765283 | ||||||||
\(685\) | 2.96745 | 0.113380 | ||||||||
\(686\) | 34.1272 | 1.30298 | ||||||||
\(687\) | 4.10165 | 0.156488 | ||||||||
\(688\) | −13.2905 | −0.506696 | ||||||||
\(689\) | 8.48408 | 0.323218 | ||||||||
\(690\) | −7.95571 | −0.302869 | ||||||||
\(691\) | 32.7261 | 1.24496 | 0.622479 | − | 0.782637i | \(-0.286126\pi\) | ||||
0.622479 | + | 0.782637i | \(0.286126\pi\) | |||||||
\(692\) | −12.0841 | −0.459367 | ||||||||
\(693\) | −8.55398 | −0.324939 | ||||||||
\(694\) | 33.7791 | 1.28224 | ||||||||
\(695\) | 63.2654 | 2.39979 | ||||||||
\(696\) | 1.64864 | 0.0624914 | ||||||||
\(697\) | −37.3181 | −1.41352 | ||||||||
\(698\) | −35.5618 | −1.34603 | ||||||||
\(699\) | 16.6505 | 0.629782 | ||||||||
\(700\) | 67.5063 | 2.55150 | ||||||||
\(701\) | 19.8786 | 0.750805 | 0.375402 | − | 0.926862i | \(-0.377505\pi\) | ||||
0.375402 | + | 0.926862i | \(0.377505\pi\) | |||||||
\(702\) | −4.00091 | −0.151004 | ||||||||
\(703\) | 9.00016 | 0.339447 | ||||||||
\(704\) | 36.1882 | 1.36389 | ||||||||
\(705\) | 23.3688 | 0.880119 | ||||||||
\(706\) | 7.13562 | 0.268553 | ||||||||
\(707\) | −9.12000 | −0.342993 | ||||||||
\(708\) | −9.76106 | −0.366843 | ||||||||
\(709\) | −34.8409 | −1.30848 | −0.654239 | − | 0.756288i | \(-0.727011\pi\) | ||||
−0.654239 | + | 0.756288i | \(0.727011\pi\) | |||||||
\(710\) | −38.5963 | −1.44849 | ||||||||
\(711\) | 7.61876 | 0.285726 | ||||||||
\(712\) | −5.13602 | −0.192481 | ||||||||
\(713\) | −9.78276 | −0.366367 | ||||||||
\(714\) | −39.6114 | −1.48242 | ||||||||
\(715\) | 19.4179 | 0.726188 | ||||||||
\(716\) | −58.4862 | −2.18573 | ||||||||
\(717\) | 15.1886 | 0.567228 | ||||||||
\(718\) | −64.7151 | −2.41515 | ||||||||
\(719\) | −42.3706 | −1.58016 | −0.790079 | − | 0.613005i | \(-0.789960\pi\) | ||||
−0.790079 | + | 0.613005i | \(0.789960\pi\) | |||||||
\(720\) | 6.99170 | 0.260565 | ||||||||
\(721\) | −17.1155 | −0.637414 | ||||||||
\(722\) | −73.5837 | −2.73850 | ||||||||
\(723\) | −6.49318 | −0.241484 | ||||||||
\(724\) | 53.5241 | 1.98921 | ||||||||
\(725\) | −8.30818 | −0.308558 | ||||||||
\(726\) | 5.63090 | 0.208982 | ||||||||
\(727\) | −7.10224 | −0.263408 | −0.131704 | − | 0.991289i | \(-0.542045\pi\) | ||||
−0.131704 | + | 0.991289i | \(0.542045\pi\) | |||||||
\(728\) | −8.91718 | −0.330493 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 60.2193 | 2.22881 | ||||||||
\(731\) | 42.7222 | 1.58014 | ||||||||
\(732\) | −27.4910 | −1.01610 | ||||||||
\(733\) | −2.19649 | −0.0811293 | −0.0405646 | − | 0.999177i | \(-0.512916\pi\) | ||||
−0.0405646 | + | 0.999177i | \(0.512916\pi\) | |||||||
\(734\) | −31.1445 | −1.14956 | ||||||||
\(735\) | −6.17312 | −0.227699 | ||||||||
\(736\) | −7.47695 | −0.275604 | ||||||||
\(737\) | −15.0052 | −0.552724 | ||||||||
\(738\) | 13.2100 | 0.486267 | ||||||||
\(739\) | 7.65800 | 0.281704 | 0.140852 | − | 0.990031i | \(-0.455016\pi\) | ||||
0.140852 | + | 0.990031i | \(0.455016\pi\) | |||||||
\(740\) | 12.4597 | 0.458029 | ||||||||
\(741\) | −13.3234 | −0.489446 | ||||||||
\(742\) | −29.7338 | −1.09156 | ||||||||
\(743\) | −0.670199 | −0.0245872 | −0.0122936 | − | 0.999924i | \(-0.503913\pi\) | ||||
−0.0122936 | + | 0.999924i | \(0.503913\pi\) | |||||||
\(744\) | −16.1282 | −0.591289 | ||||||||
\(745\) | −76.8772 | −2.81656 | ||||||||
\(746\) | −50.0935 | −1.83405 | ||||||||
\(747\) | 11.2522 | 0.411695 | ||||||||
\(748\) | −49.2623 | −1.80121 | ||||||||
\(749\) | 39.6560 | 1.44900 | ||||||||
\(750\) | 26.3189 | 0.961030 | ||||||||
\(751\) | −17.0871 | −0.623516 | −0.311758 | − | 0.950162i | \(-0.600918\pi\) | ||||
−0.311758 | + | 0.950162i | \(0.600918\pi\) | |||||||
\(752\) | 12.2772 | 0.447705 | ||||||||
\(753\) | 26.2268 | 0.955757 | ||||||||
\(754\) | 4.00091 | 0.145704 | ||||||||
\(755\) | 63.5019 | 2.31107 | ||||||||
\(756\) | 8.12529 | 0.295514 | ||||||||
\(757\) | 34.3726 | 1.24929 | 0.624646 | − | 0.780908i | \(-0.285243\pi\) | ||||
0.624646 | + | 0.780908i | \(0.285243\pi\) | |||||||
\(758\) | −1.06511 | −0.0386864 | ||||||||
\(759\) | 2.90138 | 0.105313 | ||||||||
\(760\) | −43.6777 | −1.58436 | ||||||||
\(761\) | −19.7508 | −0.715964 | −0.357982 | − | 0.933728i | \(-0.616535\pi\) | ||||
−0.357982 | + | 0.933728i | \(0.616535\pi\) | |||||||
\(762\) | −33.7944 | −1.22424 | ||||||||
\(763\) | 3.21875 | 0.116526 | ||||||||
\(764\) | 7.51505 | 0.271885 | ||||||||
\(765\) | −22.4748 | −0.812577 | ||||||||
\(766\) | 40.6813 | 1.46988 | ||||||||
\(767\) | −6.49772 | −0.234619 | ||||||||
\(768\) | −1.76277 | −0.0636086 | ||||||||
\(769\) | −24.9364 | −0.899231 | −0.449616 | − | 0.893222i | \(-0.648439\pi\) | ||||
−0.449616 | + | 0.893222i | \(0.648439\pi\) | |||||||
\(770\) | −68.0530 | −2.45246 | ||||||||
\(771\) | 0.394588 | 0.0142108 | ||||||||
\(772\) | −6.27984 | −0.226016 | ||||||||
\(773\) | 42.9566 | 1.54504 | 0.772520 | − | 0.634990i | \(-0.218996\pi\) | ||||
0.772520 | + | 0.634990i | \(0.218996\pi\) | |||||||
\(774\) | −15.1230 | −0.543584 | ||||||||
\(775\) | 81.2769 | 2.91955 | ||||||||
\(776\) | 2.25168 | 0.0808307 | ||||||||
\(777\) | −3.65375 | −0.131078 | ||||||||
\(778\) | 23.2429 | 0.833297 | ||||||||
\(779\) | 43.9905 | 1.57612 | ||||||||
\(780\) | −18.4447 | −0.660428 | ||||||||
\(781\) | 14.0757 | 0.503669 | ||||||||
\(782\) | 13.4356 | 0.480455 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −3.24317 | −0.115827 | ||||||||
\(785\) | −76.5269 | −2.73136 | ||||||||
\(786\) | −23.0051 | −0.820566 | ||||||||
\(787\) | −0.0246370 | −0.000878213 0 | −0.000439106 | − | 1.00000i | \(-0.500140\pi\) | ||||
−0.000439106 | 1.00000i | \(0.500140\pi\) | ||||||||
\(788\) | 31.3481 | 1.11673 | ||||||||
\(789\) | 27.4775 | 0.978225 | ||||||||
\(790\) | 60.6127 | 2.15650 | ||||||||
\(791\) | 52.2799 | 1.85886 | ||||||||
\(792\) | 4.78331 | 0.169968 | ||||||||
\(793\) | −18.3002 | −0.649858 | ||||||||
\(794\) | 40.2323 | 1.42779 | ||||||||
\(795\) | −16.8704 | −0.598332 | ||||||||
\(796\) | 41.5452 | 1.47253 | ||||||||
\(797\) | 44.0032 | 1.55867 | 0.779337 | − | 0.626605i | \(-0.215556\pi\) | ||||
0.779337 | + | 0.626605i | \(0.215556\pi\) | |||||||
\(798\) | 46.6938 | 1.65294 | ||||||||
\(799\) | −39.4651 | −1.39617 | ||||||||
\(800\) | 62.1199 | 2.19627 | ||||||||
\(801\) | 3.11532 | 0.110074 | ||||||||
\(802\) | −32.4970 | −1.14751 | ||||||||
\(803\) | −21.9614 | −0.775002 | ||||||||
\(804\) | 14.2532 | 0.502672 | ||||||||
\(805\) | 10.7553 | 0.379075 | ||||||||
\(806\) | −39.1399 | −1.37864 | ||||||||
\(807\) | −12.5639 | −0.442272 | ||||||||
\(808\) | 5.09982 | 0.179411 | ||||||||
\(809\) | −23.4278 | −0.823676 | −0.411838 | − | 0.911257i | \(-0.635113\pi\) | ||||
−0.411838 | + | 0.911257i | \(0.635113\pi\) | |||||||
\(810\) | 7.95571 | 0.279535 | ||||||||
\(811\) | 43.9171 | 1.54214 | 0.771069 | − | 0.636751i | \(-0.219722\pi\) | ||||
0.771069 | + | 0.636751i | \(0.219722\pi\) | |||||||
\(812\) | −8.12529 | −0.285142 | ||||||||
\(813\) | 3.16176 | 0.110888 | ||||||||
\(814\) | −7.84149 | −0.274844 | ||||||||
\(815\) | −12.0025 | −0.420428 | ||||||||
\(816\) | −11.8076 | −0.413347 | ||||||||
\(817\) | −50.3609 | −1.76190 | ||||||||
\(818\) | −38.7601 | −1.35522 | ||||||||
\(819\) | 5.40883 | 0.189000 | ||||||||
\(820\) | 60.9000 | 2.12672 | ||||||||
\(821\) | −9.21652 | −0.321659 | −0.160829 | − | 0.986982i | \(-0.551417\pi\) | ||||
−0.160829 | + | 0.986982i | \(0.551417\pi\) | |||||||
\(822\) | 1.77396 | 0.0618739 | ||||||||
\(823\) | 22.0721 | 0.769385 | 0.384692 | − | 0.923045i | \(-0.374308\pi\) | ||||
0.384692 | + | 0.923045i | \(0.374308\pi\) | |||||||
\(824\) | 9.57083 | 0.333416 | ||||||||
\(825\) | −24.1052 | −0.839234 | ||||||||
\(826\) | 22.7723 | 0.792348 | ||||||||
\(827\) | 6.11448 | 0.212621 | 0.106311 | − | 0.994333i | \(-0.466096\pi\) | ||||
0.106311 | + | 0.994333i | \(0.466096\pi\) | |||||||
\(828\) | −2.75597 | −0.0957766 | ||||||||
\(829\) | 0.991392 | 0.0344325 | 0.0172162 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172162 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(830\) | 89.5189 | 3.10724 | ||||||||
\(831\) | 9.84864 | 0.341646 | ||||||||
\(832\) | −22.8824 | −0.793303 | ||||||||
\(833\) | 10.4251 | 0.361209 | ||||||||
\(834\) | 37.8204 | 1.30961 | ||||||||
\(835\) | −69.7465 | −2.41368 | ||||||||
\(836\) | 58.0703 | 2.00840 | ||||||||
\(837\) | 9.78276 | 0.338142 | ||||||||
\(838\) | 58.9918 | 2.03784 | ||||||||
\(839\) | 48.3667 | 1.66980 | 0.834902 | − | 0.550399i | \(-0.185524\pi\) | ||||
0.834902 | + | 0.550399i | \(0.185524\pi\) | |||||||
\(840\) | 17.7316 | 0.611799 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 35.5231 | 1.22421 | ||||||||
\(843\) | 18.5477 | 0.638818 | ||||||||
\(844\) | 56.8309 | 1.95620 | ||||||||
\(845\) | 35.1462 | 1.20907 | ||||||||
\(846\) | 13.9700 | 0.480298 | ||||||||
\(847\) | −7.61241 | −0.261566 | ||||||||
\(848\) | −8.86319 | −0.304363 | ||||||||
\(849\) | 2.64756 | 0.0908640 | ||||||||
\(850\) | −111.625 | −3.82871 | ||||||||
\(851\) | 1.23929 | 0.0424825 | ||||||||
\(852\) | −13.3703 | −0.458059 | ||||||||
\(853\) | −25.5102 | −0.873452 | −0.436726 | − | 0.899595i | \(-0.643862\pi\) | ||||
−0.436726 | + | 0.899595i | \(0.643862\pi\) | |||||||
\(854\) | 64.1358 | 2.19468 | ||||||||
\(855\) | 26.4932 | 0.906049 | ||||||||
\(856\) | −22.1753 | −0.757935 | ||||||||
\(857\) | −50.0291 | −1.70896 | −0.854481 | − | 0.519483i | \(-0.826124\pi\) | ||||
−0.854481 | + | 0.519483i | \(0.826124\pi\) | |||||||
\(858\) | 11.6081 | 0.396295 | ||||||||
\(859\) | 2.36514 | 0.0806974 | 0.0403487 | − | 0.999186i | \(-0.487153\pi\) | ||||
0.0403487 | + | 0.999186i | \(0.487153\pi\) | |||||||
\(860\) | −69.7190 | −2.37740 | ||||||||
\(861\) | −17.8586 | −0.608620 | ||||||||
\(862\) | 20.9699 | 0.714239 | ||||||||
\(863\) | −33.5614 | −1.14244 | −0.571222 | − | 0.820796i | \(-0.693530\pi\) | ||||
−0.571222 | + | 0.820796i | \(0.693530\pi\) | |||||||
\(864\) | 7.47695 | 0.254371 | ||||||||
\(865\) | 15.9955 | 0.543863 | ||||||||
\(866\) | −54.0849 | −1.83788 | ||||||||
\(867\) | 20.9553 | 0.711679 | ||||||||
\(868\) | 79.4877 | 2.69799 | ||||||||
\(869\) | −22.1049 | −0.749858 | ||||||||
\(870\) | −7.95571 | −0.269724 | ||||||||
\(871\) | 9.48804 | 0.321490 | ||||||||
\(872\) | −1.79990 | −0.0609521 | ||||||||
\(873\) | −1.36579 | −0.0462248 | ||||||||
\(874\) | −15.8378 | −0.535722 | ||||||||
\(875\) | −35.5805 | −1.20284 | ||||||||
\(876\) | 20.8608 | 0.704822 | ||||||||
\(877\) | −7.13680 | −0.240993 | −0.120496 | − | 0.992714i | \(-0.538449\pi\) | ||||
−0.120496 | + | 0.992714i | \(0.538449\pi\) | |||||||
\(878\) | 79.9872 | 2.69944 | ||||||||
\(879\) | −27.9274 | −0.941968 | ||||||||
\(880\) | −20.2856 | −0.683826 | ||||||||
\(881\) | −44.4613 | −1.49794 | −0.748970 | − | 0.662604i | \(-0.769451\pi\) | ||||
−0.748970 | + | 0.662604i | \(0.769451\pi\) | |||||||
\(882\) | −3.69033 | −0.124260 | ||||||||
\(883\) | 40.1969 | 1.35274 | 0.676368 | − | 0.736564i | \(-0.263553\pi\) | ||||
0.676368 | + | 0.736564i | \(0.263553\pi\) | |||||||
\(884\) | 31.1494 | 1.04767 | ||||||||
\(885\) | 12.9206 | 0.434320 | ||||||||
\(886\) | 18.4292 | 0.619141 | ||||||||
\(887\) | 17.9446 | 0.602520 | 0.301260 | − | 0.953542i | \(-0.402593\pi\) | ||||
0.301260 | + | 0.953542i | \(0.402593\pi\) | |||||||
\(888\) | 2.04315 | 0.0685635 | ||||||||
\(889\) | 45.6867 | 1.53228 | ||||||||
\(890\) | 24.7845 | 0.830780 | ||||||||
\(891\) | −2.90138 | −0.0971998 | ||||||||
\(892\) | 5.38631 | 0.180347 | ||||||||
\(893\) | 46.5213 | 1.55678 | ||||||||
\(894\) | −45.9576 | −1.53705 | ||||||||
\(895\) | 77.4174 | 2.58778 | ||||||||
\(896\) | 36.1069 | 1.20625 | ||||||||
\(897\) | −1.83459 | −0.0612551 | ||||||||
\(898\) | −23.5112 | −0.784578 | ||||||||
\(899\) | −9.78276 | −0.326273 | ||||||||
\(900\) | 22.8971 | 0.763236 | ||||||||
\(901\) | 28.4906 | 0.949161 | ||||||||
\(902\) | −38.3272 | −1.27616 | ||||||||
\(903\) | 20.4447 | 0.680359 | ||||||||
\(904\) | −29.2345 | −0.972325 | ||||||||
\(905\) | −70.8491 | −2.35510 | ||||||||
\(906\) | 37.9618 | 1.26120 | ||||||||
\(907\) | 32.2495 | 1.07083 | 0.535414 | − | 0.844590i | \(-0.320156\pi\) | ||||
0.535414 | + | 0.844590i | \(0.320156\pi\) | |||||||
\(908\) | 59.0316 | 1.95903 | ||||||||
\(909\) | −3.09336 | −0.102600 | ||||||||
\(910\) | 43.0310 | 1.42647 | ||||||||
\(911\) | 53.0013 | 1.75601 | 0.878005 | − | 0.478652i | \(-0.158874\pi\) | ||||
0.878005 | + | 0.478652i | \(0.158874\pi\) | |||||||
\(912\) | 13.9187 | 0.460895 | ||||||||
\(913\) | −32.6467 | −1.08045 | ||||||||
\(914\) | 37.9471 | 1.25518 | ||||||||
\(915\) | 36.3895 | 1.20300 | ||||||||
\(916\) | 11.3040 | 0.373495 | ||||||||
\(917\) | 31.1006 | 1.02703 | ||||||||
\(918\) | −13.4356 | −0.443439 | ||||||||
\(919\) | −44.2461 | −1.45954 | −0.729772 | − | 0.683691i | \(-0.760374\pi\) | ||||
−0.729772 | + | 0.683691i | \(0.760374\pi\) | |||||||
\(920\) | −6.01428 | −0.198285 | ||||||||
\(921\) | −22.5768 | −0.743931 | ||||||||
\(922\) | 26.5096 | 0.873046 | ||||||||
\(923\) | −8.90032 | −0.292957 | ||||||||
\(924\) | −23.5745 | −0.775545 | ||||||||
\(925\) | −10.2963 | −0.338540 | ||||||||
\(926\) | 70.3552 | 2.31201 | ||||||||
\(927\) | −5.80530 | −0.190671 | ||||||||
\(928\) | −7.47695 | −0.245443 | ||||||||
\(929\) | 53.1570 | 1.74403 | 0.872013 | − | 0.489483i | \(-0.162814\pi\) | ||||
0.872013 | + | 0.489483i | \(0.162814\pi\) | |||||||
\(930\) | 77.8288 | 2.55211 | ||||||||
\(931\) | −12.2891 | −0.402760 | ||||||||
\(932\) | 45.8884 | 1.50313 | ||||||||
\(933\) | 5.39270 | 0.176549 | ||||||||
\(934\) | −8.44741 | −0.276408 | ||||||||
\(935\) | 65.2078 | 2.13252 | ||||||||
\(936\) | −3.02457 | −0.0988611 | ||||||||
\(937\) | 44.8870 | 1.46640 | 0.733198 | − | 0.680016i | \(-0.238027\pi\) | ||||
0.733198 | + | 0.680016i | \(0.238027\pi\) | |||||||
\(938\) | −33.2523 | −1.08573 | ||||||||
\(939\) | −3.71684 | −0.121295 | ||||||||
\(940\) | 64.4037 | 2.10062 | ||||||||
\(941\) | 7.11766 | 0.232029 | 0.116015 | − | 0.993248i | \(-0.462988\pi\) | ||||
0.116015 | + | 0.993248i | \(0.462988\pi\) | |||||||
\(942\) | −45.7482 | −1.49056 | ||||||||
\(943\) | 6.05736 | 0.197255 | ||||||||
\(944\) | 6.78807 | 0.220933 | ||||||||
\(945\) | −10.7553 | −0.349871 | ||||||||
\(946\) | 43.8774 | 1.42658 | ||||||||
\(947\) | −25.8079 | −0.838644 | −0.419322 | − | 0.907838i | \(-0.637732\pi\) | ||||
−0.419322 | + | 0.907838i | \(0.637732\pi\) | |||||||
\(948\) | 20.9971 | 0.681954 | ||||||||
\(949\) | 13.8866 | 0.450777 | ||||||||
\(950\) | 131.583 | 4.26913 | ||||||||
\(951\) | −27.1940 | −0.881824 | ||||||||
\(952\) | −29.9450 | −0.970525 | ||||||||
\(953\) | −2.86492 | −0.0928040 | −0.0464020 | − | 0.998923i | \(-0.514776\pi\) | ||||
−0.0464020 | + | 0.998923i | \(0.514776\pi\) | |||||||
\(954\) | −10.0852 | −0.326521 | ||||||||
\(955\) | −9.94755 | −0.321895 | ||||||||
\(956\) | 41.8593 | 1.35383 | ||||||||
\(957\) | 2.90138 | 0.0937882 | ||||||||
\(958\) | 48.7163 | 1.57395 | ||||||||
\(959\) | −2.39821 | −0.0774423 | ||||||||
\(960\) | 45.5011 | 1.46854 | ||||||||
\(961\) | 64.7023 | 2.08717 | ||||||||
\(962\) | 4.95830 | 0.159862 | ||||||||
\(963\) | 13.4507 | 0.433442 | ||||||||
\(964\) | −17.8950 | −0.576359 | ||||||||
\(965\) | 8.31253 | 0.267590 | ||||||||
\(966\) | 6.42960 | 0.206869 | ||||||||
\(967\) | 58.3742 | 1.87719 | 0.938594 | − | 0.345023i | \(-0.112129\pi\) | ||||
0.938594 | + | 0.345023i | \(0.112129\pi\) | |||||||
\(968\) | 4.25680 | 0.136819 | ||||||||
\(969\) | −44.7416 | −1.43731 | ||||||||
\(970\) | −10.8658 | −0.348879 | ||||||||
\(971\) | −39.9542 | −1.28219 | −0.641095 | − | 0.767461i | \(-0.721520\pi\) | ||||
−0.641095 | + | 0.767461i | \(0.721520\pi\) | |||||||
\(972\) | 2.75597 | 0.0883978 | ||||||||
\(973\) | −51.1295 | −1.63913 | ||||||||
\(974\) | −25.4976 | −0.816996 | ||||||||
\(975\) | 15.2421 | 0.488137 | ||||||||
\(976\) | 19.1179 | 0.611949 | ||||||||
\(977\) | −4.45659 | −0.142579 | −0.0712894 | − | 0.997456i | \(-0.522711\pi\) | ||||
−0.0712894 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(978\) | −7.17515 | −0.229436 | ||||||||
\(979\) | −9.03871 | −0.288878 | ||||||||
\(980\) | −17.0129 | −0.543459 | ||||||||
\(981\) | 1.09175 | 0.0348568 | ||||||||
\(982\) | −71.2714 | −2.27436 | ||||||||
\(983\) | 58.3721 | 1.86178 | 0.930891 | − | 0.365298i | \(-0.119033\pi\) | ||||
0.930891 | + | 0.365298i | \(0.119033\pi\) | |||||||
\(984\) | 9.98639 | 0.318354 | ||||||||
\(985\) | −41.4950 | −1.32214 | ||||||||
\(986\) | 13.4356 | 0.427875 | ||||||||
\(987\) | −18.8860 | −0.601149 | ||||||||
\(988\) | −36.7188 | −1.16818 | ||||||||
\(989\) | −6.93454 | −0.220505 | ||||||||
\(990\) | −23.0825 | −0.733610 | ||||||||
\(991\) | 12.6190 | 0.400856 | 0.200428 | − | 0.979708i | \(-0.435767\pi\) | ||||
0.200428 | + | 0.979708i | \(0.435767\pi\) | |||||||
\(992\) | 73.1452 | 2.32236 | ||||||||
\(993\) | −13.7728 | −0.437066 | ||||||||
\(994\) | 31.1925 | 0.989367 | ||||||||
\(995\) | −54.9928 | −1.74339 | ||||||||
\(996\) | 31.0106 | 0.982609 | ||||||||
\(997\) | 20.7247 | 0.656357 | 0.328178 | − | 0.944616i | \(-0.393565\pi\) | ||||
0.328178 | + | 0.944616i | \(0.393565\pi\) | |||||||
\(998\) | 57.5591 | 1.82200 | ||||||||
\(999\) | −1.23929 | −0.0392095 |
(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 | 2001.2.a.n.1.3 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.r.1.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.n.1.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.r.1.14 | 16 | 3.2 | odd | 2 |