Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.469.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.772866\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.772866 | 0.546498 | 0.273249 | − | 0.961943i | \(-0.411902\pi\) | ||||
0.273249 | + | 0.961943i | \(0.411902\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.40268 | −0.701339 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.772866 | 0.315521 | ||||||||
\(7\) | −1.62981 | −0.616012 | −0.308006 | − | 0.951384i | \(-0.599662\pi\) | ||||
−0.308006 | + | 0.951384i | \(0.599662\pi\) | |||||||
\(8\) | −2.62981 | −0.929779 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.772866 | 0.244402 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.40268 | −0.404918 | ||||||||
\(13\) | 4.80536 | 1.33277 | 0.666383 | − | 0.745609i | \(-0.267842\pi\) | ||||
0.666383 | + | 0.745609i | \(0.267842\pi\) | |||||||
\(14\) | −1.25963 | −0.336649 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0.772866 | 0.193216 | ||||||||
\(17\) | 2.17554 | 0.527647 | 0.263824 | − | 0.964571i | \(-0.415016\pi\) | ||||
0.263824 | + | 0.964571i | \(0.415016\pi\) | |||||||
\(18\) | 0.772866 | 0.182166 | ||||||||
\(19\) | −5.17554 | −1.18735 | −0.593676 | − | 0.804704i | \(-0.702324\pi\) | ||||
−0.593676 | + | 0.804704i | \(0.702324\pi\) | |||||||
\(20\) | −1.40268 | −0.313649 | ||||||||
\(21\) | −1.62981 | −0.355654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.62981 | 0.965383 | 0.482691 | − | 0.875791i | \(-0.339659\pi\) | ||||
0.482691 | + | 0.875791i | \(0.339659\pi\) | |||||||
\(24\) | −2.62981 | −0.536808 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.71390 | 0.728355 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.28610 | 0.432033 | ||||||||
\(29\) | 2.45427 | 0.455746 | 0.227873 | − | 0.973691i | \(-0.426823\pi\) | ||||
0.227873 | + | 0.973691i | \(0.426823\pi\) | |||||||
\(30\) | 0.772866 | 0.141105 | ||||||||
\(31\) | 5.80536 | 1.04267 | 0.521337 | − | 0.853351i | \(-0.325434\pi\) | ||||
0.521337 | + | 0.853351i | \(0.325434\pi\) | |||||||
\(32\) | 5.85695 | 1.03537 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.68140 | 0.288358 | ||||||||
\(35\) | −1.62981 | −0.275489 | ||||||||
\(36\) | −1.40268 | −0.233780 | ||||||||
\(37\) | 8.88944 | 1.46141 | 0.730707 | − | 0.682691i | \(-0.239190\pi\) | ||||
0.730707 | + | 0.682691i | \(0.239190\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 4.80536 | 0.769473 | ||||||||
\(40\) | −2.62981 | −0.415810 | ||||||||
\(41\) | −5.09146 | −0.795153 | −0.397576 | − | 0.917569i | \(-0.630149\pi\) | ||||
−0.397576 | + | 0.917569i | \(0.630149\pi\) | |||||||
\(42\) | −1.25963 | −0.194365 | ||||||||
\(43\) | 1.54573 | 0.235722 | 0.117861 | − | 0.993030i | \(-0.462396\pi\) | ||||
0.117861 | + | 0.993030i | \(0.462396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 3.57822 | 0.527580 | ||||||||
\(47\) | 9.72128 | 1.41799 | 0.708997 | − | 0.705212i | \(-0.249148\pi\) | ||||
0.708997 | + | 0.705212i | \(0.249148\pi\) | |||||||
\(48\) | 0.772866 | 0.111554 | ||||||||
\(49\) | −4.34371 | −0.620530 | ||||||||
\(50\) | 0.772866 | 0.109300 | ||||||||
\(51\) | 2.17554 | 0.304637 | ||||||||
\(52\) | −6.74037 | −0.934722 | ||||||||
\(53\) | −5.26701 | −0.723479 | −0.361739 | − | 0.932279i | \(-0.617817\pi\) | ||||
−0.361739 | + | 0.932279i | \(0.617817\pi\) | |||||||
\(54\) | 0.772866 | 0.105174 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.28610 | 0.572755 | ||||||||
\(57\) | −5.17554 | −0.685518 | ||||||||
\(58\) | 1.89682 | 0.249065 | ||||||||
\(59\) | −7.15645 | −0.931690 | −0.465845 | − | 0.884866i | \(-0.654250\pi\) | ||||
−0.465845 | + | 0.884866i | \(0.654250\pi\) | |||||||
\(60\) | −1.40268 | −0.181085 | ||||||||
\(61\) | 14.2596 | 1.82576 | 0.912879 | − | 0.408230i | \(-0.133854\pi\) | ||||
0.912879 | + | 0.408230i | \(0.133854\pi\) | |||||||
\(62\) | 4.48676 | 0.569819 | ||||||||
\(63\) | −1.62981 | −0.205337 | ||||||||
\(64\) | 2.98090 | 0.372613 | ||||||||
\(65\) | 4.80536 | 0.596031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.72128 | −0.576796 | −0.288398 | − | 0.957511i | \(-0.593123\pi\) | ||||
−0.288398 | + | 0.957511i | \(0.593123\pi\) | |||||||
\(68\) | −3.05159 | −0.370060 | ||||||||
\(69\) | 4.62981 | 0.557364 | ||||||||
\(70\) | −1.25963 | −0.150554 | ||||||||
\(71\) | 13.4426 | 1.59534 | 0.797669 | − | 0.603096i | \(-0.206066\pi\) | ||||
0.797669 | + | 0.603096i | \(0.206066\pi\) | |||||||
\(72\) | −2.62981 | −0.309926 | ||||||||
\(73\) | 1.17554 | 0.137587 | 0.0687935 | − | 0.997631i | \(-0.478085\pi\) | ||||
0.0687935 | + | 0.997631i | \(0.478085\pi\) | |||||||
\(74\) | 6.87034 | 0.798661 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 7.25963 | 0.832736 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.71390 | 0.420516 | ||||||||
\(79\) | −4.89682 | −0.550935 | −0.275468 | − | 0.961310i | \(-0.588833\pi\) | ||||
−0.275468 | + | 0.961310i | \(0.588833\pi\) | |||||||
\(80\) | 0.772866 | 0.0864090 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.93502 | −0.434550 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 2.28610 | 0.249434 | ||||||||
\(85\) | 2.17554 | 0.235971 | ||||||||
\(86\) | 1.19464 | 0.128822 | ||||||||
\(87\) | 2.45427 | 0.263125 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.5457 | 1.22385 | 0.611923 | − | 0.790918i | \(-0.290396\pi\) | ||||
0.611923 | + | 0.790918i | \(0.290396\pi\) | |||||||
\(90\) | 0.772866 | 0.0814672 | ||||||||
\(91\) | −7.83184 | −0.820999 | ||||||||
\(92\) | −6.49414 | −0.677061 | ||||||||
\(93\) | 5.80536 | 0.601988 | ||||||||
\(94\) | 7.51324 | 0.774931 | ||||||||
\(95\) | −5.17554 | −0.531000 | ||||||||
\(96\) | 5.85695 | 0.597772 | ||||||||
\(97\) | 4.72128 | 0.479373 | 0.239686 | − | 0.970850i | \(-0.422955\pi\) | ||||
0.239686 | + | 0.970850i | \(0.422955\pi\) | |||||||
\(98\) | −3.35710 | −0.339119 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.40268 | −0.140268 | ||||||||
\(101\) | −13.6107 | −1.35432 | −0.677158 | − | 0.735837i | \(-0.736789\pi\) | ||||
−0.677158 | + | 0.735837i | \(0.736789\pi\) | |||||||
\(102\) | 1.68140 | 0.166484 | ||||||||
\(103\) | 14.6181 | 1.44036 | 0.720182 | − | 0.693785i | \(-0.244058\pi\) | ||||
0.720182 | + | 0.693785i | \(0.244058\pi\) | |||||||
\(104\) | −12.6372 | −1.23918 | ||||||||
\(105\) | −1.62981 | −0.159053 | ||||||||
\(106\) | −4.07069 | −0.395380 | ||||||||
\(107\) | −19.3320 | −1.86889 | −0.934447 | − | 0.356102i | \(-0.884106\pi\) | ||||
−0.934447 | + | 0.356102i | \(0.884106\pi\) | |||||||
\(108\) | −1.40268 | −0.134973 | ||||||||
\(109\) | 8.78626 | 0.841571 | 0.420786 | − | 0.907160i | \(-0.361754\pi\) | ||||
0.420786 | + | 0.907160i | \(0.361754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.88944 | 0.843748 | ||||||||
\(112\) | −1.25963 | −0.119024 | ||||||||
\(113\) | 12.5266 | 1.17841 | 0.589203 | − | 0.807985i | \(-0.299442\pi\) | ||||
0.589203 | + | 0.807985i | \(0.299442\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | 4.62981 | 0.431732 | ||||||||
\(116\) | −3.44255 | −0.319633 | ||||||||
\(117\) | 4.80536 | 0.444255 | ||||||||
\(118\) | −5.53097 | −0.509167 | ||||||||
\(119\) | −3.54573 | −0.325037 | ||||||||
\(120\) | −2.62981 | −0.240068 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 11.0208 | 0.997774 | ||||||||
\(123\) | −5.09146 | −0.459082 | ||||||||
\(124\) | −8.14305 | −0.731268 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.25963 | −0.112216 | ||||||||
\(127\) | −17.2405 | −1.52985 | −0.764925 | − | 0.644120i | \(-0.777224\pi\) | ||||
−0.764925 | + | 0.644120i | \(0.777224\pi\) | |||||||
\(128\) | −9.41006 | −0.831740 | ||||||||
\(129\) | 1.54573 | 0.136094 | ||||||||
\(130\) | 3.71390 | 0.325730 | ||||||||
\(131\) | −15.6107 | −1.36391 | −0.681957 | − | 0.731392i | \(-0.738871\pi\) | ||||
−0.681957 | + | 0.731392i | \(0.738871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.43517 | 0.731422 | ||||||||
\(134\) | −3.64891 | −0.315218 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −5.72128 | −0.490595 | ||||||||
\(137\) | −10.6948 | −0.913718 | −0.456859 | − | 0.889539i | \(-0.651026\pi\) | ||||
−0.456859 | + | 0.889539i | \(0.651026\pi\) | |||||||
\(138\) | 3.57822 | 0.304599 | ||||||||
\(139\) | −6.98090 | −0.592112 | −0.296056 | − | 0.955171i | \(-0.595672\pi\) | ||||
−0.296056 | + | 0.955171i | \(0.595672\pi\) | |||||||
\(140\) | 2.28610 | 0.193211 | ||||||||
\(141\) | 9.72128 | 0.818679 | ||||||||
\(142\) | 10.3893 | 0.871849 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.772866 | 0.0644055 | ||||||||
\(145\) | 2.45427 | 0.203816 | ||||||||
\(146\) | 0.908538 | 0.0751911 | ||||||||
\(147\) | −4.34371 | −0.358263 | ||||||||
\(148\) | −12.4690 | −1.02495 | ||||||||
\(149\) | −3.89682 | −0.319240 | −0.159620 | − | 0.987179i | \(-0.551027\pi\) | ||||
−0.159620 | + | 0.987179i | \(0.551027\pi\) | |||||||
\(150\) | 0.772866 | 0.0631042 | ||||||||
\(151\) | −5.72128 | −0.465591 | −0.232795 | − | 0.972526i | \(-0.574787\pi\) | ||||
−0.232795 | + | 0.972526i | \(0.574787\pi\) | |||||||
\(152\) | 13.6107 | 1.10397 | ||||||||
\(153\) | 2.17554 | 0.175882 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.80536 | 0.466298 | ||||||||
\(156\) | −6.74037 | −0.539662 | ||||||||
\(157\) | −15.2405 | −1.21633 | −0.608163 | − | 0.793812i | \(-0.708093\pi\) | ||||
−0.608163 | + | 0.793812i | \(0.708093\pi\) | |||||||
\(158\) | −3.78458 | −0.301085 | ||||||||
\(159\) | −5.26701 | −0.417701 | ||||||||
\(160\) | 5.85695 | 0.463032 | ||||||||
\(161\) | −7.54573 | −0.594687 | ||||||||
\(162\) | 0.772866 | 0.0607221 | ||||||||
\(163\) | −17.2405 | −1.35038 | −0.675191 | − | 0.737643i | \(-0.735939\pi\) | ||||
−0.675191 | + | 0.737643i | \(0.735939\pi\) | |||||||
\(164\) | 7.14169 | 0.557672 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.09146 | 0.239944 | ||||||||
\(167\) | 5.53835 | 0.428570 | 0.214285 | − | 0.976771i | \(-0.431258\pi\) | ||||
0.214285 | + | 0.976771i | \(0.431258\pi\) | |||||||
\(168\) | 4.28610 | 0.330680 | ||||||||
\(169\) | 10.0915 | 0.776266 | ||||||||
\(170\) | 1.68140 | 0.128958 | ||||||||
\(171\) | −5.17554 | −0.395784 | ||||||||
\(172\) | −2.16816 | −0.165321 | ||||||||
\(173\) | 18.7022 | 1.42190 | 0.710950 | − | 0.703242i | \(-0.248265\pi\) | ||||
0.710950 | + | 0.703242i | \(0.248265\pi\) | |||||||
\(174\) | 1.89682 | 0.143798 | ||||||||
\(175\) | −1.62981 | −0.123202 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.15645 | −0.537911 | ||||||||
\(178\) | 8.92330 | 0.668829 | ||||||||
\(179\) | 1.19464 | 0.0892918 | 0.0446459 | − | 0.999003i | \(-0.485784\pi\) | ||||
0.0446459 | + | 0.999003i | \(0.485784\pi\) | |||||||
\(180\) | −1.40268 | −0.104550 | ||||||||
\(181\) | 15.3437 | 1.14049 | 0.570244 | − | 0.821475i | \(-0.306848\pi\) | ||||
0.570244 | + | 0.821475i | \(0.306848\pi\) | |||||||
\(182\) | −6.05296 | −0.448675 | ||||||||
\(183\) | 14.2596 | 1.05410 | ||||||||
\(184\) | −12.1755 | −0.897593 | ||||||||
\(185\) | 8.88944 | 0.653565 | ||||||||
\(186\) | 4.48676 | 0.328985 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −13.6358 | −0.994495 | ||||||||
\(189\) | −1.62981 | −0.118551 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 15.7139 | 1.13702 | 0.568509 | − | 0.822677i | \(-0.307521\pi\) | ||||
0.568509 | + | 0.822677i | \(0.307521\pi\) | |||||||
\(192\) | 2.98090 | 0.215128 | ||||||||
\(193\) | 11.2405 | 0.809111 | 0.404555 | − | 0.914513i | \(-0.367426\pi\) | ||||
0.404555 | + | 0.914513i | \(0.367426\pi\) | |||||||
\(194\) | 3.64891 | 0.261977 | ||||||||
\(195\) | 4.80536 | 0.344119 | ||||||||
\(196\) | 6.09283 | 0.435202 | ||||||||
\(197\) | −2.74037 | −0.195244 | −0.0976218 | − | 0.995224i | \(-0.531124\pi\) | ||||
−0.0976218 | + | 0.995224i | \(0.531124\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.0650 | −1.77681 | −0.888405 | − | 0.459061i | \(-0.848186\pi\) | ||||
−0.888405 | + | 0.459061i | \(0.848186\pi\) | |||||||
\(200\) | −2.62981 | −0.185956 | ||||||||
\(201\) | −4.72128 | −0.333013 | ||||||||
\(202\) | −10.5193 | −0.740132 | ||||||||
\(203\) | −4.00000 | −0.280745 | ||||||||
\(204\) | −3.05159 | −0.213654 | ||||||||
\(205\) | −5.09146 | −0.355603 | ||||||||
\(206\) | 11.2978 | 0.787157 | ||||||||
\(207\) | 4.62981 | 0.321794 | ||||||||
\(208\) | 3.71390 | 0.257512 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.25963 | −0.0869225 | ||||||||
\(211\) | 17.9735 | 1.23735 | 0.618674 | − | 0.785648i | \(-0.287670\pi\) | ||||
0.618674 | + | 0.785648i | \(0.287670\pi\) | |||||||
\(212\) | 7.38792 | 0.507404 | ||||||||
\(213\) | 13.4426 | 0.921068 | ||||||||
\(214\) | −14.9410 | −1.02135 | ||||||||
\(215\) | 1.54573 | 0.105418 | ||||||||
\(216\) | −2.62981 | −0.178936 | ||||||||
\(217\) | −9.46165 | −0.642299 | ||||||||
\(218\) | 6.79060 | 0.459917 | ||||||||
\(219\) | 1.17554 | 0.0794359 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4543 | 0.703230 | ||||||||
\(222\) | 6.87034 | 0.461107 | ||||||||
\(223\) | −12.7863 | −0.856231 | −0.428116 | − | 0.903724i | \(-0.640822\pi\) | ||||
−0.428116 | + | 0.903724i | \(0.640822\pi\) | |||||||
\(224\) | −9.54573 | −0.637801 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 9.68140 | 0.643997 | ||||||||
\(227\) | 14.2787 | 0.947712 | 0.473856 | − | 0.880602i | \(-0.342862\pi\) | ||||
0.473856 | + | 0.880602i | \(0.342862\pi\) | |||||||
\(228\) | 7.25963 | 0.480781 | ||||||||
\(229\) | −25.9692 | −1.71609 | −0.858046 | − | 0.513573i | \(-0.828322\pi\) | ||||
−0.858046 | + | 0.513573i | \(0.828322\pi\) | |||||||
\(230\) | 3.57822 | 0.235941 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.45427 | −0.423744 | ||||||||
\(233\) | −10.5648 | −0.692125 | −0.346062 | − | 0.938211i | \(-0.612481\pi\) | ||||
−0.346062 | + | 0.938211i | \(0.612481\pi\) | |||||||
\(234\) | 3.71390 | 0.242785 | ||||||||
\(235\) | 9.72128 | 0.634146 | ||||||||
\(236\) | 10.0382 | 0.653431 | ||||||||
\(237\) | −4.89682 | −0.318083 | ||||||||
\(238\) | −2.74037 | −0.177632 | ||||||||
\(239\) | −6.45427 | −0.417492 | −0.208746 | − | 0.977970i | \(-0.566938\pi\) | ||||
−0.208746 | + | 0.977970i | \(0.566938\pi\) | |||||||
\(240\) | 0.772866 | 0.0498883 | ||||||||
\(241\) | −25.6181 | −1.65021 | −0.825103 | − | 0.564982i | \(-0.808883\pi\) | ||||
−0.825103 | + | 0.564982i | \(0.808883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −20.0017 | −1.28048 | ||||||||
\(245\) | −4.34371 | −0.277509 | ||||||||
\(246\) | −3.93502 | −0.250887 | ||||||||
\(247\) | −24.8703 | −1.58246 | ||||||||
\(248\) | −15.2670 | −0.969456 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0.772866 | 0.0488803 | ||||||||
\(251\) | 4.80536 | 0.303311 | 0.151656 | − | 0.988433i | \(-0.451539\pi\) | ||||
0.151656 | + | 0.988433i | \(0.451539\pi\) | |||||||
\(252\) | 2.28610 | 0.144011 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.3246 | −0.836060 | ||||||||
\(255\) | 2.17554 | 0.136238 | ||||||||
\(256\) | −13.2345 | −0.827157 | ||||||||
\(257\) | 11.7863 | 0.735207 | 0.367603 | − | 0.929983i | \(-0.380178\pi\) | ||||
0.367603 | + | 0.929983i | \(0.380178\pi\) | |||||||
\(258\) | 1.19464 | 0.0743752 | ||||||||
\(259\) | −14.4881 | −0.900248 | ||||||||
\(260\) | −6.74037 | −0.418020 | ||||||||
\(261\) | 2.45427 | 0.151915 | ||||||||
\(262\) | −12.0650 | −0.745377 | ||||||||
\(263\) | 12.4235 | 0.766063 | 0.383031 | − | 0.923735i | \(-0.374880\pi\) | ||||
0.383031 | + | 0.923735i | \(0.374880\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.26701 | −0.323550 | ||||||||
\(266\) | 6.51925 | 0.399721 | ||||||||
\(267\) | 11.5457 | 0.706587 | ||||||||
\(268\) | 6.62243 | 0.404529 | ||||||||
\(269\) | 31.2214 | 1.90360 | 0.951802 | − | 0.306713i | \(-0.0992291\pi\) | ||||
0.951802 | + | 0.306713i | \(0.0992291\pi\) | |||||||
\(270\) | 0.772866 | 0.0470351 | ||||||||
\(271\) | −25.5002 | −1.54902 | −0.774512 | − | 0.632559i | \(-0.782005\pi\) | ||||
−0.774512 | + | 0.632559i | \(0.782005\pi\) | |||||||
\(272\) | 1.68140 | 0.101950 | ||||||||
\(273\) | −7.83184 | −0.474004 | ||||||||
\(274\) | −8.26564 | −0.499346 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.49414 | −0.390901 | ||||||||
\(277\) | 24.6033 | 1.47827 | 0.739136 | − | 0.673557i | \(-0.235234\pi\) | ||||
0.739136 | + | 0.673557i | \(0.235234\pi\) | |||||||
\(278\) | −5.39530 | −0.323589 | ||||||||
\(279\) | 5.80536 | 0.347558 | ||||||||
\(280\) | 4.28610 | 0.256144 | ||||||||
\(281\) | 11.5457 | 0.688761 | 0.344380 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344380 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(282\) | 7.51324 | 0.447407 | ||||||||
\(283\) | 6.09884 | 0.362539 | 0.181269 | − | 0.983434i | \(-0.441979\pi\) | ||||
0.181269 | + | 0.983434i | \(0.441979\pi\) | |||||||
\(284\) | −18.8556 | −1.11887 | ||||||||
\(285\) | −5.17554 | −0.306573 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.29813 | 0.489823 | ||||||||
\(288\) | 5.85695 | 0.345124 | ||||||||
\(289\) | −12.2670 | −0.721589 | ||||||||
\(290\) | 1.89682 | 0.111385 | ||||||||
\(291\) | 4.72128 | 0.276766 | ||||||||
\(292\) | −1.64891 | −0.0964952 | ||||||||
\(293\) | 5.82446 | 0.340268 | 0.170134 | − | 0.985421i | \(-0.445580\pi\) | ||||
0.170134 | + | 0.985421i | \(0.445580\pi\) | |||||||
\(294\) | −3.35710 | −0.195790 | ||||||||
\(295\) | −7.15645 | −0.416664 | ||||||||
\(296\) | −23.3776 | −1.35879 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.01172 | −0.174464 | ||||||||
\(299\) | 22.2479 | 1.28663 | ||||||||
\(300\) | −1.40268 | −0.0809837 | ||||||||
\(301\) | −2.51925 | −0.145207 | ||||||||
\(302\) | −4.42178 | −0.254445 | ||||||||
\(303\) | −13.6107 | −0.781915 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 14.2596 | 0.816504 | ||||||||
\(306\) | 1.68140 | 0.0961194 | ||||||||
\(307\) | −10.2670 | −0.585969 | −0.292985 | − | 0.956117i | \(-0.594648\pi\) | ||||
−0.292985 | + | 0.956117i | \(0.594648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6181 | 0.831594 | ||||||||
\(310\) | 4.48676 | 0.254831 | ||||||||
\(311\) | −0.454269 | −0.0257592 | −0.0128796 | − | 0.999917i | \(-0.504100\pi\) | ||||
−0.0128796 | + | 0.999917i | \(0.504100\pi\) | |||||||
\(312\) | −12.6372 | −0.715440 | ||||||||
\(313\) | 0.103180 | 0.00583208 | 0.00291604 | − | 0.999996i | \(-0.499072\pi\) | ||||
0.00291604 | + | 0.999996i | \(0.499072\pi\) | |||||||
\(314\) | −11.7789 | −0.664721 | ||||||||
\(315\) | −1.62981 | −0.0918296 | ||||||||
\(316\) | 6.86867 | 0.386393 | ||||||||
\(317\) | −19.0841 | −1.07187 | −0.535934 | − | 0.844260i | \(-0.680041\pi\) | ||||
−0.535934 | + | 0.844260i | \(0.680041\pi\) | |||||||
\(318\) | −4.07069 | −0.228273 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.98090 | 0.166637 | ||||||||
\(321\) | −19.3320 | −1.07901 | ||||||||
\(322\) | −5.83184 | −0.324995 | ||||||||
\(323\) | −11.2596 | −0.626502 | ||||||||
\(324\) | −1.40268 | −0.0779266 | ||||||||
\(325\) | 4.80536 | 0.266553 | ||||||||
\(326\) | −13.3246 | −0.737982 | ||||||||
\(327\) | 8.78626 | 0.485881 | ||||||||
\(328\) | 13.3896 | 0.739317 | ||||||||
\(329\) | −15.8439 | −0.873500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.45427 | −0.519654 | −0.259827 | − | 0.965655i | \(-0.583665\pi\) | ||||
−0.259827 | + | 0.965655i | \(0.583665\pi\) | |||||||
\(332\) | −5.61072 | −0.307928 | ||||||||
\(333\) | 8.88944 | 0.487138 | ||||||||
\(334\) | 4.28040 | 0.234213 | ||||||||
\(335\) | −4.72128 | −0.257951 | ||||||||
\(336\) | −1.25963 | −0.0687183 | ||||||||
\(337\) | 16.9544 | 0.923566 | 0.461783 | − | 0.886993i | \(-0.347210\pi\) | ||||
0.461783 | + | 0.886993i | \(0.347210\pi\) | |||||||
\(338\) | 7.79934 | 0.424228 | ||||||||
\(339\) | 12.5266 | 0.680353 | ||||||||
\(340\) | −3.05159 | −0.165496 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 18.4881 | 0.998265 | ||||||||
\(344\) | −4.06498 | −0.219169 | ||||||||
\(345\) | 4.62981 | 0.249261 | ||||||||
\(346\) | 14.4543 | 0.777066 | ||||||||
\(347\) | −28.0576 | −1.50621 | −0.753106 | − | 0.657900i | \(-0.771445\pi\) | ||||
−0.753106 | + | 0.657900i | \(0.771445\pi\) | |||||||
\(348\) | −3.44255 | −0.184540 | ||||||||
\(349\) | −17.5340 | −0.938574 | −0.469287 | − | 0.883046i | \(-0.655489\pi\) | ||||
−0.469287 | + | 0.883046i | \(0.655489\pi\) | |||||||
\(350\) | −1.25963 | −0.0673299 | ||||||||
\(351\) | 4.80536 | 0.256491 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.4884 | −1.09049 | −0.545245 | − | 0.838277i | \(-0.683563\pi\) | ||||
−0.545245 | + | 0.838277i | \(0.683563\pi\) | |||||||
\(354\) | −5.53097 | −0.293968 | ||||||||
\(355\) | 13.4426 | 0.713457 | ||||||||
\(356\) | −16.1950 | −0.858331 | ||||||||
\(357\) | −3.54573 | −0.187660 | ||||||||
\(358\) | 0.923298 | 0.0487978 | ||||||||
\(359\) | 28.6640 | 1.51283 | 0.756414 | − | 0.654094i | \(-0.226950\pi\) | ||||
0.756414 | + | 0.654094i | \(0.226950\pi\) | |||||||
\(360\) | −2.62981 | −0.138603 | ||||||||
\(361\) | 7.78626 | 0.409803 | ||||||||
\(362\) | 11.8586 | 0.623275 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.9856 | 0.575799 | ||||||||
\(365\) | 1.17554 | 0.0615308 | ||||||||
\(366\) | 11.0208 | 0.576065 | ||||||||
\(367\) | −22.5990 | −1.17966 | −0.589829 | − | 0.807528i | \(-0.700805\pi\) | ||||
−0.589829 | + | 0.807528i | \(0.700805\pi\) | |||||||
\(368\) | 3.57822 | 0.186528 | ||||||||
\(369\) | −5.09146 | −0.265051 | ||||||||
\(370\) | 6.87034 | 0.357172 | ||||||||
\(371\) | 8.58424 | 0.445671 | ||||||||
\(372\) | −8.14305 | −0.422198 | ||||||||
\(373\) | −26.0841 | −1.35058 | −0.675291 | − | 0.737551i | \(-0.735982\pi\) | ||||
−0.675291 | + | 0.737551i | \(0.735982\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −25.5651 | −1.31842 | ||||||||
\(377\) | 11.7936 | 0.607403 | ||||||||
\(378\) | −1.25963 | −0.0647882 | ||||||||
\(379\) | 9.16383 | 0.470714 | 0.235357 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235357 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(380\) | 7.25963 | 0.372411 | ||||||||
\(381\) | −17.2405 | −0.883259 | ||||||||
\(382\) | 12.1447 | 0.621378 | ||||||||
\(383\) | −18.3511 | −0.937697 | −0.468848 | − | 0.883279i | \(-0.655331\pi\) | ||||
−0.468848 | + | 0.883279i | \(0.655331\pi\) | |||||||
\(384\) | −9.41006 | −0.480205 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.68742 | 0.442178 | ||||||||
\(387\) | 1.54573 | 0.0785739 | ||||||||
\(388\) | −6.62243 | −0.336203 | ||||||||
\(389\) | −12.5990 | −0.638795 | −0.319397 | − | 0.947621i | \(-0.603480\pi\) | ||||
−0.319397 | + | 0.947621i | \(0.603480\pi\) | |||||||
\(390\) | 3.71390 | 0.188060 | ||||||||
\(391\) | 10.0724 | 0.509381 | ||||||||
\(392\) | 11.4231 | 0.576956 | ||||||||
\(393\) | −15.6107 | −0.787456 | ||||||||
\(394\) | −2.11794 | −0.106700 | ||||||||
\(395\) | −4.89682 | −0.246386 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6948 | −1.49034 | −0.745170 | − | 0.666875i | \(-0.767631\pi\) | ||||
−0.745170 | + | 0.666875i | \(0.767631\pi\) | |||||||
\(398\) | −19.3719 | −0.971024 | ||||||||
\(399\) | 8.43517 | 0.422287 | ||||||||
\(400\) | 0.772866 | 0.0386433 | ||||||||
\(401\) | 39.0533 | 1.95023 | 0.975114 | − | 0.221706i | \(-0.0711626\pi\) | ||||
0.975114 | + | 0.221706i | \(0.0711626\pi\) | |||||||
\(402\) | −3.64891 | −0.181991 | ||||||||
\(403\) | 27.8968 | 1.38964 | ||||||||
\(404\) | 19.0915 | 0.949836 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −3.09146 | −0.153427 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.72128 | −0.283245 | ||||||||
\(409\) | 29.5193 | 1.45963 | 0.729817 | − | 0.683643i | \(-0.239605\pi\) | ||||
0.729817 | + | 0.683643i | \(0.239605\pi\) | |||||||
\(410\) | −3.93502 | −0.194337 | ||||||||
\(411\) | −10.6948 | −0.527535 | ||||||||
\(412\) | −20.5045 | −1.01018 | ||||||||
\(413\) | 11.6637 | 0.573932 | ||||||||
\(414\) | 3.57822 | 0.175860 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 28.1447 | 1.37991 | ||||||||
\(417\) | −6.98090 | −0.341856 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.8703 | −1.11729 | −0.558645 | − | 0.829407i | \(-0.688678\pi\) | ||||
−0.558645 | + | 0.829407i | \(0.688678\pi\) | |||||||
\(420\) | 2.28610 | 0.111550 | ||||||||
\(421\) | −21.6033 | −1.05288 | −0.526441 | − | 0.850212i | \(-0.676474\pi\) | ||||
−0.526441 | + | 0.850212i | \(0.676474\pi\) | |||||||
\(422\) | 13.8911 | 0.676209 | ||||||||
\(423\) | 9.72128 | 0.472665 | ||||||||
\(424\) | 13.8512 | 0.672676 | ||||||||
\(425\) | 2.17554 | 0.105529 | ||||||||
\(426\) | 10.3893 | 0.503362 | ||||||||
\(427\) | −23.2405 | −1.12469 | ||||||||
\(428\) | 27.1166 | 1.31073 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.19464 | 0.0576108 | ||||||||
\(431\) | 34.4161 | 1.65776 | 0.828882 | − | 0.559424i | \(-0.188977\pi\) | ||||
0.828882 | + | 0.559424i | \(0.188977\pi\) | |||||||
\(432\) | 0.772866 | 0.0371845 | ||||||||
\(433\) | −20.2938 | −0.975258 | −0.487629 | − | 0.873051i | \(-0.662138\pi\) | ||||
−0.487629 | + | 0.873051i | \(0.662138\pi\) | |||||||
\(434\) | −7.31258 | −0.351015 | ||||||||
\(435\) | 2.45427 | 0.117673 | ||||||||
\(436\) | −12.3243 | −0.590227 | ||||||||
\(437\) | −23.9618 | −1.14625 | ||||||||
\(438\) | 0.908538 | 0.0434116 | ||||||||
\(439\) | 7.28610 | 0.347747 | 0.173873 | − | 0.984768i | \(-0.444372\pi\) | ||||
0.173873 | + | 0.984768i | \(0.444372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.34371 | −0.206843 | ||||||||
\(442\) | 8.07974 | 0.384314 | ||||||||
\(443\) | 7.25963 | 0.344915 | 0.172458 | − | 0.985017i | \(-0.444829\pi\) | ||||
0.172458 | + | 0.985017i | \(0.444829\pi\) | |||||||
\(444\) | −12.4690 | −0.591754 | ||||||||
\(445\) | 11.5457 | 0.547320 | ||||||||
\(446\) | −9.88206 | −0.467929 | ||||||||
\(447\) | −3.89682 | −0.184313 | ||||||||
\(448\) | −4.85831 | −0.229534 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0.772866 | 0.0364332 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −17.5708 | −0.826463 | ||||||||
\(453\) | −5.72128 | −0.268809 | ||||||||
\(454\) | 11.0355 | 0.517923 | ||||||||
\(455\) | −7.83184 | −0.367162 | ||||||||
\(456\) | 13.6107 | 0.637380 | ||||||||
\(457\) | −3.61072 | −0.168902 | −0.0844511 | − | 0.996428i | \(-0.526914\pi\) | ||||
−0.0844511 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(458\) | −20.0707 | −0.937842 | ||||||||
\(459\) | 2.17554 | 0.101546 | ||||||||
\(460\) | −6.49414 | −0.302791 | ||||||||
\(461\) | −20.1032 | −0.936298 | −0.468149 | − | 0.883649i | \(-0.655079\pi\) | ||||
−0.468149 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6874 | −0.961426 | −0.480713 | − | 0.876878i | \(-0.659622\pi\) | ||||
−0.480713 | + | 0.876878i | \(0.659622\pi\) | |||||||
\(464\) | 1.89682 | 0.0880577 | ||||||||
\(465\) | 5.80536 | 0.269217 | ||||||||
\(466\) | −8.16519 | −0.378245 | ||||||||
\(467\) | −0.850934 | −0.0393765 | −0.0196883 | − | 0.999806i | \(-0.506267\pi\) | ||||
−0.0196883 | + | 0.999806i | \(0.506267\pi\) | |||||||
\(468\) | −6.74037 | −0.311574 | ||||||||
\(469\) | 7.69480 | 0.355313 | ||||||||
\(470\) | 7.51324 | 0.346560 | ||||||||
\(471\) | −15.2405 | −0.702246 | ||||||||
\(472\) | 18.8201 | 0.866266 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3.78458 | −0.173832 | ||||||||
\(475\) | −5.17554 | −0.237470 | ||||||||
\(476\) | 4.97352 | 0.227961 | ||||||||
\(477\) | −5.26701 | −0.241160 | ||||||||
\(478\) | −4.98828 | −0.228159 | ||||||||
\(479\) | −28.4013 | −1.29769 | −0.648845 | − | 0.760921i | \(-0.724747\pi\) | ||||
−0.648845 | + | 0.760921i | \(0.724747\pi\) | |||||||
\(480\) | 5.85695 | 0.267332 | ||||||||
\(481\) | 42.7169 | 1.94772 | ||||||||
\(482\) | −19.7993 | −0.901835 | ||||||||
\(483\) | −7.54573 | −0.343343 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.72128 | 0.214382 | ||||||||
\(486\) | 0.772866 | 0.0350579 | ||||||||
\(487\) | 4.06498 | 0.184202 | 0.0921010 | − | 0.995750i | \(-0.470642\pi\) | ||||
0.0921010 | + | 0.995750i | \(0.470642\pi\) | |||||||
\(488\) | −37.5002 | −1.69755 | ||||||||
\(489\) | −17.2405 | −0.779644 | ||||||||
\(490\) | −3.35710 | −0.151658 | ||||||||
\(491\) | 27.9618 | 1.26190 | 0.630949 | − | 0.775824i | \(-0.282666\pi\) | ||||
0.630949 | + | 0.775824i | \(0.282666\pi\) | |||||||
\(492\) | 7.14169 | 0.321972 | ||||||||
\(493\) | 5.33937 | 0.240473 | ||||||||
\(494\) | −19.2214 | −0.864813 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.48676 | 0.201462 | ||||||||
\(497\) | −21.9088 | −0.982746 | ||||||||
\(498\) | 3.09146 | 0.138532 | ||||||||
\(499\) | 1.13735 | 0.0509147 | 0.0254574 | − | 0.999676i | \(-0.491896\pi\) | ||||
0.0254574 | + | 0.999676i | \(0.491896\pi\) | |||||||
\(500\) | −1.40268 | −0.0627297 | ||||||||
\(501\) | 5.53835 | 0.247435 | ||||||||
\(502\) | 3.71390 | 0.165759 | ||||||||
\(503\) | 21.8512 | 0.974299 | 0.487149 | − | 0.873319i | \(-0.338037\pi\) | ||||
0.487149 | + | 0.873319i | \(0.338037\pi\) | |||||||
\(504\) | 4.28610 | 0.190918 | ||||||||
\(505\) | −13.6107 | −0.605669 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0915 | 0.448178 | ||||||||
\(508\) | 24.1829 | 1.07294 | ||||||||
\(509\) | 18.2331 | 0.808170 | 0.404085 | − | 0.914721i | \(-0.367590\pi\) | ||||
0.404085 | + | 0.914721i | \(0.367590\pi\) | |||||||
\(510\) | 1.68140 | 0.0744538 | ||||||||
\(511\) | −1.91592 | −0.0847552 | ||||||||
\(512\) | 8.59162 | 0.379699 | ||||||||
\(513\) | −5.17554 | −0.228506 | ||||||||
\(514\) | 9.10919 | 0.401789 | ||||||||
\(515\) | 14.6181 | 0.644150 | ||||||||
\(516\) | −2.16816 | −0.0954481 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −11.1974 | −0.491984 | ||||||||
\(519\) | 18.7022 | 0.820934 | ||||||||
\(520\) | −12.6372 | −0.554178 | ||||||||
\(521\) | 37.1035 | 1.62553 | 0.812767 | − | 0.582589i | \(-0.197960\pi\) | ||||
0.812767 | + | 0.582589i | \(0.197960\pi\) | |||||||
\(522\) | 1.89682 | 0.0830216 | ||||||||
\(523\) | −15.1106 | −0.660739 | −0.330369 | − | 0.943852i | \(-0.607173\pi\) | ||||
−0.330369 | + | 0.943852i | \(0.607173\pi\) | |||||||
\(524\) | 21.8968 | 0.956567 | ||||||||
\(525\) | −1.62981 | −0.0711309 | ||||||||
\(526\) | 9.60166 | 0.418652 | ||||||||
\(527\) | 12.6298 | 0.550163 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.56483 | −0.0680360 | ||||||||
\(530\) | −4.07069 | −0.176819 | ||||||||
\(531\) | −7.15645 | −0.310563 | ||||||||
\(532\) | −11.8318 | −0.512975 | ||||||||
\(533\) | −24.4663 | −1.05975 | ||||||||
\(534\) | 8.92330 | 0.386149 | ||||||||
\(535\) | −19.3320 | −0.835795 | ||||||||
\(536\) | 12.4161 | 0.536293 | ||||||||
\(537\) | 1.19464 | 0.0515526 | ||||||||
\(538\) | 24.1300 | 1.04032 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.40268 | −0.0603617 | ||||||||
\(541\) | 3.27439 | 0.140777 | 0.0703884 | − | 0.997520i | \(-0.477576\pi\) | ||||
0.0703884 | + | 0.997520i | \(0.477576\pi\) | |||||||
\(542\) | −19.7082 | −0.846539 | ||||||||
\(543\) | 15.3437 | 0.658462 | ||||||||
\(544\) | 12.7420 | 0.546311 | ||||||||
\(545\) | 8.78626 | 0.376362 | ||||||||
\(546\) | −6.05296 | −0.259043 | ||||||||
\(547\) | −18.2479 | −0.780224 | −0.390112 | − | 0.920767i | \(-0.627564\pi\) | ||||
−0.390112 | + | 0.920767i | \(0.627564\pi\) | |||||||
\(548\) | 15.0014 | 0.640827 | ||||||||
\(549\) | 14.2596 | 0.608586 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7022 | −0.541131 | ||||||||
\(552\) | −12.1755 | −0.518226 | ||||||||
\(553\) | 7.98090 | 0.339382 | ||||||||
\(554\) | 19.0151 | 0.807873 | ||||||||
\(555\) | 8.88944 | 0.377336 | ||||||||
\(556\) | 9.79196 | 0.415272 | ||||||||
\(557\) | 16.3585 | 0.693131 | 0.346565 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346565 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(558\) | 4.48676 | 0.189940 | ||||||||
\(559\) | 7.42779 | 0.314162 | ||||||||
\(560\) | −1.25963 | −0.0532289 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.92330 | 0.376407 | ||||||||
\(563\) | −31.2214 | −1.31583 | −0.657913 | − | 0.753094i | \(-0.728561\pi\) | ||||
−0.657913 | + | 0.753094i | \(0.728561\pi\) | |||||||
\(564\) | −13.6358 | −0.574172 | ||||||||
\(565\) | 12.5266 | 0.526999 | ||||||||
\(566\) | 4.71359 | 0.198127 | ||||||||
\(567\) | −1.62981 | −0.0684457 | ||||||||
\(568\) | −35.3514 | −1.48331 | ||||||||
\(569\) | −8.97352 | −0.376190 | −0.188095 | − | 0.982151i | \(-0.560231\pi\) | ||||
−0.188095 | + | 0.982151i | \(0.560231\pi\) | |||||||
\(570\) | −4.00000 | −0.167542 | ||||||||
\(571\) | 19.5990 | 0.820193 | 0.410096 | − | 0.912042i | \(-0.365495\pi\) | ||||
0.410096 | + | 0.912042i | \(0.365495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.7139 | 0.656457 | ||||||||
\(574\) | 6.41334 | 0.267688 | ||||||||
\(575\) | 4.62981 | 0.193077 | ||||||||
\(576\) | 2.98090 | 0.124204 | ||||||||
\(577\) | 10.4204 | 0.433807 | 0.216904 | − | 0.976193i | \(-0.430404\pi\) | ||||
0.216904 | + | 0.976193i | \(0.430404\pi\) | |||||||
\(578\) | −9.48075 | −0.394347 | ||||||||
\(579\) | 11.2405 | 0.467140 | ||||||||
\(580\) | −3.44255 | −0.142944 | ||||||||
\(581\) | −6.51925 | −0.270464 | ||||||||
\(582\) | 3.64891 | 0.151252 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.09146 | −0.127926 | ||||||||
\(585\) | 4.80536 | 0.198677 | ||||||||
\(586\) | 4.50152 | 0.185956 | ||||||||
\(587\) | −4.59162 | −0.189516 | −0.0947582 | − | 0.995500i | \(-0.530208\pi\) | ||||
−0.0947582 | + | 0.995500i | \(0.530208\pi\) | |||||||
\(588\) | 6.09283 | 0.251264 | ||||||||
\(589\) | −30.0459 | −1.23802 | ||||||||
\(590\) | −5.53097 | −0.227706 | ||||||||
\(591\) | −2.74037 | −0.112724 | ||||||||
\(592\) | 6.87034 | 0.282369 | ||||||||
\(593\) | 16.1829 | 0.664553 | 0.332277 | − | 0.943182i | \(-0.392183\pi\) | ||||
0.332277 | + | 0.943182i | \(0.392183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.54573 | −0.145361 | ||||||||
\(596\) | 5.46599 | 0.223896 | ||||||||
\(597\) | −25.0650 | −1.02584 | ||||||||
\(598\) | 17.1946 | 0.703141 | ||||||||
\(599\) | −40.0120 | −1.63485 | −0.817424 | − | 0.576037i | \(-0.804598\pi\) | ||||
−0.817424 | + | 0.576037i | \(0.804598\pi\) | |||||||
\(600\) | −2.62981 | −0.107362 | ||||||||
\(601\) | −36.9162 | −1.50584 | −0.752922 | − | 0.658110i | \(-0.771356\pi\) | ||||
−0.752922 | + | 0.658110i | \(0.771356\pi\) | |||||||
\(602\) | −1.94704 | −0.0793556 | ||||||||
\(603\) | −4.72128 | −0.192265 | ||||||||
\(604\) | 8.02511 | 0.326537 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.5193 | −0.427315 | ||||||||
\(607\) | −19.7139 | −0.800162 | −0.400081 | − | 0.916480i | \(-0.631018\pi\) | ||||
−0.400081 | + | 0.916480i | \(0.631018\pi\) | |||||||
\(608\) | −30.3129 | −1.22935 | ||||||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 11.0208 | 0.446218 | ||||||||
\(611\) | 46.7142 | 1.88985 | ||||||||
\(612\) | −3.05159 | −0.123353 | ||||||||
\(613\) | 3.73299 | 0.150774 | 0.0753871 | − | 0.997154i | \(-0.475981\pi\) | ||||
0.0753871 | + | 0.997154i | \(0.475981\pi\) | |||||||
\(614\) | −7.93502 | −0.320231 | ||||||||
\(615\) | −5.09146 | −0.205308 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.8851 | −1.00184 | −0.500918 | − | 0.865495i | \(-0.667004\pi\) | ||||
−0.500918 | + | 0.865495i | \(0.667004\pi\) | |||||||
\(618\) | 11.2978 | 0.454465 | ||||||||
\(619\) | 29.9470 | 1.20367 | 0.601837 | − | 0.798619i | \(-0.294436\pi\) | ||||
0.601837 | + | 0.798619i | \(0.294436\pi\) | |||||||
\(620\) | −8.14305 | −0.327033 | ||||||||
\(621\) | 4.62981 | 0.185788 | ||||||||
\(622\) | −0.351089 | −0.0140774 | ||||||||
\(623\) | −18.8174 | −0.753903 | ||||||||
\(624\) | 3.71390 | 0.148675 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.0797444 | 0.00318723 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.3776 | 0.853058 | ||||||||
\(629\) | 19.3394 | 0.771111 | ||||||||
\(630\) | −1.25963 | −0.0501847 | ||||||||
\(631\) | −10.2787 | −0.409190 | −0.204595 | − | 0.978847i | \(-0.565588\pi\) | ||||
−0.204595 | + | 0.978847i | \(0.565588\pi\) | |||||||
\(632\) | 12.8777 | 0.512248 | ||||||||
\(633\) | 17.9735 | 0.714383 | ||||||||
\(634\) | −14.7494 | −0.585775 | ||||||||
\(635\) | −17.2405 | −0.684170 | ||||||||
\(636\) | 7.38792 | 0.292950 | ||||||||
\(637\) | −20.8731 | −0.827021 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.4426 | 0.531779 | ||||||||
\(640\) | −9.41006 | −0.371965 | ||||||||
\(641\) | −13.8586 | −0.547383 | −0.273691 | − | 0.961818i | \(-0.588245\pi\) | ||||
−0.273691 | + | 0.961818i | \(0.588245\pi\) | |||||||
\(642\) | −14.9410 | −0.589675 | ||||||||
\(643\) | −16.4499 | −0.648722 | −0.324361 | − | 0.945933i | \(-0.605149\pi\) | ||||
−0.324361 | + | 0.945933i | \(0.605149\pi\) | |||||||
\(644\) | 10.5842 | 0.417077 | ||||||||
\(645\) | 1.54573 | 0.0608631 | ||||||||
\(646\) | −8.70218 | −0.342383 | ||||||||
\(647\) | −15.3172 | −0.602182 | −0.301091 | − | 0.953595i | \(-0.597351\pi\) | ||||
−0.301091 | + | 0.953595i | \(0.597351\pi\) | |||||||
\(648\) | −2.62981 | −0.103309 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.71390 | 0.145671 | ||||||||
\(651\) | −9.46165 | −0.370831 | ||||||||
\(652\) | 24.1829 | 0.947076 | ||||||||
\(653\) | −37.2214 | −1.45659 | −0.728294 | − | 0.685265i | \(-0.759686\pi\) | ||||
−0.728294 | + | 0.685265i | \(0.759686\pi\) | |||||||
\(654\) | 6.79060 | 0.265533 | ||||||||
\(655\) | −15.6107 | −0.609961 | ||||||||
\(656\) | −3.93502 | −0.153637 | ||||||||
\(657\) | 1.17554 | 0.0458624 | ||||||||
\(658\) | −12.2452 | −0.477367 | ||||||||
\(659\) | 33.1564 | 1.29159 | 0.645796 | − | 0.763510i | \(-0.276526\pi\) | ||||
0.645796 | + | 0.763510i | \(0.276526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.2670 | 0.554922 | 0.277461 | − | 0.960737i | \(-0.410507\pi\) | ||||
0.277461 | + | 0.960737i | \(0.410507\pi\) | |||||||
\(662\) | −7.30688 | −0.283990 | ||||||||
\(663\) | 10.4543 | 0.406010 | ||||||||
\(664\) | −10.5193 | −0.408226 | ||||||||
\(665\) | 8.43517 | 0.327102 | ||||||||
\(666\) | 6.87034 | 0.266220 | ||||||||
\(667\) | 11.3628 | 0.439970 | ||||||||
\(668\) | −7.76853 | −0.300573 | ||||||||
\(669\) | −12.7863 | −0.494345 | ||||||||
\(670\) | −3.64891 | −0.140970 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −9.54573 | −0.368235 | ||||||||
\(673\) | 19.9427 | 0.768735 | 0.384367 | − | 0.923180i | \(-0.374420\pi\) | ||||
0.384367 | + | 0.923180i | \(0.374420\pi\) | |||||||
\(674\) | 13.1035 | 0.504728 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −14.1551 | −0.544426 | ||||||||
\(677\) | 25.6255 | 0.984867 | 0.492434 | − | 0.870350i | \(-0.336107\pi\) | ||||
0.492434 | + | 0.870350i | \(0.336107\pi\) | |||||||
\(678\) | 9.68140 | 0.371812 | ||||||||
\(679\) | −7.69480 | −0.295299 | ||||||||
\(680\) | −5.72128 | −0.219401 | ||||||||
\(681\) | 14.2787 | 0.547162 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.870342 | −0.0333027 | −0.0166514 | − | 0.999861i | \(-0.505301\pi\) | ||||
−0.0166514 | + | 0.999861i | \(0.505301\pi\) | |||||||
\(684\) | 7.25963 | 0.277579 | ||||||||
\(685\) | −10.6948 | −0.408627 | ||||||||
\(686\) | 14.2888 | 0.545550 | ||||||||
\(687\) | −25.9692 | −0.990786 | ||||||||
\(688\) | 1.19464 | 0.0455453 | ||||||||
\(689\) | −25.3099 | −0.964229 | ||||||||
\(690\) | 3.57822 | 0.136221 | ||||||||
\(691\) | 4.32461 | 0.164516 | 0.0822580 | − | 0.996611i | \(-0.473787\pi\) | ||||
0.0822580 | + | 0.996611i | \(0.473787\pi\) | |||||||
\(692\) | −26.2331 | −0.997235 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.6848 | −0.823142 | ||||||||
\(695\) | −6.98090 | −0.264801 | ||||||||
\(696\) | −6.45427 | −0.244648 | ||||||||
\(697\) | −11.0767 | −0.419560 | ||||||||
\(698\) | −13.5514 | −0.512929 | ||||||||
\(699\) | −10.5648 | −0.399599 | ||||||||
\(700\) | 2.28610 | 0.0864066 | ||||||||
\(701\) | 5.02648 | 0.189847 | 0.0949237 | − | 0.995485i | \(-0.469739\pi\) | ||||
0.0949237 | + | 0.995485i | \(0.469739\pi\) | |||||||
\(702\) | 3.71390 | 0.140172 | ||||||||
\(703\) | −46.0077 | −1.73521 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.72128 | 0.366124 | ||||||||
\(706\) | −15.8348 | −0.595951 | ||||||||
\(707\) | 22.1829 | 0.834275 | ||||||||
\(708\) | 10.0382 | 0.377259 | ||||||||
\(709\) | 32.1373 | 1.20694 | 0.603472 | − | 0.797384i | \(-0.293784\pi\) | ||||
0.603472 | + | 0.797384i | \(0.293784\pi\) | |||||||
\(710\) | 10.3893 | 0.389903 | ||||||||
\(711\) | −4.89682 | −0.183645 | ||||||||
\(712\) | −30.3631 | −1.13791 | ||||||||
\(713\) | 26.8777 | 1.00658 | ||||||||
\(714\) | −2.74037 | −0.102556 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.67570 | −0.0626238 | ||||||||
\(717\) | −6.45427 | −0.241039 | ||||||||
\(718\) | 22.1534 | 0.826758 | ||||||||
\(719\) | 42.6640 | 1.59110 | 0.795549 | − | 0.605889i | \(-0.207183\pi\) | ||||
0.795549 | + | 0.605889i | \(0.207183\pi\) | |||||||
\(720\) | 0.772866 | 0.0288030 | ||||||||
\(721\) | −23.8248 | −0.887281 | ||||||||
\(722\) | 6.01773 | 0.223957 | ||||||||
\(723\) | −25.6181 | −0.952747 | ||||||||
\(724\) | −21.5223 | −0.799870 | ||||||||
\(725\) | 2.45427 | 0.0911493 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.351089 | −0.0130212 | −0.00651058 | − | 0.999979i | \(-0.502072\pi\) | ||||
−0.00651058 | + | 0.999979i | \(0.502072\pi\) | |||||||
\(728\) | 20.5963 | 0.763348 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.908538 | 0.0336265 | ||||||||
\(731\) | 3.36281 | 0.124378 | ||||||||
\(732\) | −20.0017 | −0.739283 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | −17.4660 | −0.644681 | ||||||||
\(735\) | −4.34371 | −0.160220 | ||||||||
\(736\) | 27.1166 | 0.999530 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.93502 | −0.144850 | ||||||||
\(739\) | −15.2479 | −0.560903 | −0.280452 | − | 0.959868i | \(-0.590484\pi\) | ||||
−0.280452 | + | 0.959868i | \(0.590484\pi\) | |||||||
\(740\) | −12.4690 | −0.458371 | ||||||||
\(741\) | −24.8703 | −0.913635 | ||||||||
\(742\) | 6.63446 | 0.243559 | ||||||||
\(743\) | −4.11056 | −0.150802 | −0.0754009 | − | 0.997153i | \(-0.524024\pi\) | ||||
−0.0754009 | + | 0.997153i | \(0.524024\pi\) | |||||||
\(744\) | −15.2670 | −0.559716 | ||||||||
\(745\) | −3.89682 | −0.142768 | ||||||||
\(746\) | −20.1595 | −0.738091 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.5075 | 1.15126 | ||||||||
\(750\) | 0.772866 | 0.0282211 | ||||||||
\(751\) | −24.4928 | −0.893754 | −0.446877 | − | 0.894595i | \(-0.647464\pi\) | ||||
−0.446877 | + | 0.894595i | \(0.647464\pi\) | |||||||
\(752\) | 7.51324 | 0.273980 | ||||||||
\(753\) | 4.80536 | 0.175117 | ||||||||
\(754\) | 9.11490 | 0.331945 | ||||||||
\(755\) | −5.72128 | −0.208219 | ||||||||
\(756\) | 2.28610 | 0.0831448 | ||||||||
\(757\) | −1.03082 | −0.0374656 | −0.0187328 | − | 0.999825i | \(-0.505963\pi\) | ||||
−0.0187328 | + | 0.999825i | \(0.505963\pi\) | |||||||
\(758\) | 7.08241 | 0.257245 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.6107 | 0.493713 | ||||||||
\(761\) | 14.4161 | 0.522582 | 0.261291 | − | 0.965260i | \(-0.415852\pi\) | ||||
0.261291 | + | 0.965260i | \(0.415852\pi\) | |||||||
\(762\) | −13.3246 | −0.482700 | ||||||||
\(763\) | −14.3200 | −0.518417 | ||||||||
\(764\) | −22.0415 | −0.797435 | ||||||||
\(765\) | 2.17554 | 0.0786570 | ||||||||
\(766\) | −14.1829 | −0.512450 | ||||||||
\(767\) | −34.3893 | −1.24173 | ||||||||
\(768\) | −13.2345 | −0.477559 | ||||||||
\(769\) | 29.1447 | 1.05099 | 0.525493 | − | 0.850798i | \(-0.323881\pi\) | ||||
0.525493 | + | 0.850798i | \(0.323881\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7863 | 0.424472 | ||||||||
\(772\) | −15.7669 | −0.567461 | ||||||||
\(773\) | −44.3203 | −1.59409 | −0.797045 | − | 0.603920i | \(-0.793605\pi\) | ||||
−0.797045 | + | 0.603920i | \(0.793605\pi\) | |||||||
\(774\) | 1.19464 | 0.0429405 | ||||||||
\(775\) | 5.80536 | 0.208535 | ||||||||
\(776\) | −12.4161 | −0.445711 | ||||||||
\(777\) | −14.4881 | −0.519759 | ||||||||
\(778\) | −9.73733 | −0.349100 | ||||||||
\(779\) | 26.3511 | 0.944126 | ||||||||
\(780\) | −6.74037 | −0.241344 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 7.78458 | 0.278376 | ||||||||
\(783\) | 2.45427 | 0.0877084 | ||||||||
\(784\) | −3.35710 | −0.119897 | ||||||||
\(785\) | −15.2405 | −0.543958 | ||||||||
\(786\) | −12.0650 | −0.430344 | ||||||||
\(787\) | 9.03851 | 0.322188 | 0.161094 | − | 0.986939i | \(-0.448498\pi\) | ||||
0.161094 | + | 0.986939i | \(0.448498\pi\) | |||||||
\(788\) | 3.84386 | 0.136932 | ||||||||
\(789\) | 12.4235 | 0.442287 | ||||||||
\(790\) | −3.78458 | −0.134649 | ||||||||
\(791\) | −20.4161 | −0.725912 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.5226 | 2.43331 | ||||||||
\(794\) | −22.9501 | −0.814468 | ||||||||
\(795\) | −5.26701 | −0.186801 | ||||||||
\(796\) | 35.1581 | 1.24615 | ||||||||
\(797\) | −53.5873 | −1.89816 | −0.949079 | − | 0.315037i | \(-0.897983\pi\) | ||||
−0.949079 | + | 0.315037i | \(0.897983\pi\) | |||||||
\(798\) | 6.51925 | 0.230779 | ||||||||
\(799\) | 21.1491 | 0.748200 | ||||||||
\(800\) | 5.85695 | 0.207074 | ||||||||
\(801\) | 11.5457 | 0.407948 | ||||||||
\(802\) | 30.1829 | 1.06580 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.62243 | 0.233555 | ||||||||
\(805\) | −7.54573 | −0.265952 | ||||||||
\(806\) | 21.5605 | 0.759436 | ||||||||
\(807\) | 31.2214 | 1.09905 | ||||||||
\(808\) | 35.7936 | 1.25922 | ||||||||
\(809\) | 24.8703 | 0.874395 | 0.437197 | − | 0.899366i | \(-0.355971\pi\) | ||||
0.437197 | + | 0.899366i | \(0.355971\pi\) | |||||||
\(810\) | 0.772866 | 0.0271557 | ||||||||
\(811\) | 35.0415 | 1.23048 | 0.615238 | − | 0.788342i | \(-0.289060\pi\) | ||||
0.615238 | + | 0.788342i | \(0.289060\pi\) | |||||||
\(812\) | 5.61072 | 0.196898 | ||||||||
\(813\) | −25.5002 | −0.894329 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.2405 | −0.603909 | ||||||||
\(816\) | 1.68140 | 0.0588609 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 22.8144 | 0.797687 | ||||||||
\(819\) | −7.83184 | −0.273666 | ||||||||
\(820\) | 7.14169 | 0.249399 | ||||||||
\(821\) | 35.4044 | 1.23562 | 0.617810 | − | 0.786327i | \(-0.288020\pi\) | ||||
0.617810 | + | 0.786327i | \(0.288020\pi\) | |||||||
\(822\) | −8.26564 | −0.288297 | ||||||||
\(823\) | 27.4502 | 0.956855 | 0.478428 | − | 0.878127i | \(-0.341207\pi\) | ||||
0.478428 | + | 0.878127i | \(0.341207\pi\) | |||||||
\(824\) | −38.4429 | −1.33922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.01445 | 0.313653 | ||||||||
\(827\) | 21.7407 | 0.755998 | 0.377999 | − | 0.925806i | \(-0.376612\pi\) | ||||
0.377999 | + | 0.925806i | \(0.376612\pi\) | |||||||
\(828\) | −6.49414 | −0.225687 | ||||||||
\(829\) | 35.5193 | 1.23363 | 0.616817 | − | 0.787106i | \(-0.288422\pi\) | ||||
0.616817 | + | 0.787106i | \(0.288422\pi\) | |||||||
\(830\) | 3.09146 | 0.107306 | ||||||||
\(831\) | 24.6033 | 0.853480 | ||||||||
\(832\) | 14.3243 | 0.496606 | ||||||||
\(833\) | −9.44993 | −0.327421 | ||||||||
\(834\) | −5.39530 | −0.186824 | ||||||||
\(835\) | 5.53835 | 0.191663 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.80536 | 0.200663 | ||||||||
\(838\) | −17.6757 | −0.610597 | ||||||||
\(839\) | −18.6492 | −0.643843 | −0.321921 | − | 0.946766i | \(-0.604329\pi\) | ||||
−0.321921 | + | 0.946766i | \(0.604329\pi\) | |||||||
\(840\) | 4.28610 | 0.147885 | ||||||||
\(841\) | −22.9766 | −0.792295 | ||||||||
\(842\) | −16.6965 | −0.575398 | ||||||||
\(843\) | 11.5457 | 0.397656 | ||||||||
\(844\) | −25.2111 | −0.867801 | ||||||||
\(845\) | 10.0915 | 0.347157 | ||||||||
\(846\) | 7.51324 | 0.258310 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.07069 | −0.139788 | ||||||||
\(849\) | 6.09884 | 0.209312 | ||||||||
\(850\) | 1.68140 | 0.0576717 | ||||||||
\(851\) | 41.1564 | 1.41082 | ||||||||
\(852\) | −18.8556 | −0.645982 | ||||||||
\(853\) | −5.32027 | −0.182163 | −0.0910813 | − | 0.995843i | \(-0.529032\pi\) | ||||
−0.0910813 | + | 0.995843i | \(0.529032\pi\) | |||||||
\(854\) | −17.9618 | −0.614640 | ||||||||
\(855\) | −5.17554 | −0.177000 | ||||||||
\(856\) | 50.8395 | 1.73766 | ||||||||
\(857\) | −17.6181 | −0.601823 | −0.300911 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300911 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9012 | −0.406062 | −0.203031 | − | 0.979172i | \(-0.565079\pi\) | ||||
−0.203031 | + | 0.979172i | \(0.565079\pi\) | |||||||
\(860\) | −2.16816 | −0.0739338 | ||||||||
\(861\) | 8.29813 | 0.282800 | ||||||||
\(862\) | 26.5990 | 0.905965 | ||||||||
\(863\) | 21.7407 | 0.740061 | 0.370031 | − | 0.929020i | \(-0.379347\pi\) | ||||
0.370031 | + | 0.929020i | \(0.379347\pi\) | |||||||
\(864\) | 5.85695 | 0.199257 | ||||||||
\(865\) | 18.7022 | 0.635893 | ||||||||
\(866\) | −15.6844 | −0.532977 | ||||||||
\(867\) | −12.2670 | −0.416609 | ||||||||
\(868\) | 13.2717 | 0.450469 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.89682 | 0.0643082 | ||||||||
\(871\) | −22.6874 | −0.768734 | ||||||||
\(872\) | −23.1062 | −0.782475 | ||||||||
\(873\) | 4.72128 | 0.159791 | ||||||||
\(874\) | −18.5193 | −0.626423 | ||||||||
\(875\) | −1.62981 | −0.0550977 | ||||||||
\(876\) | −1.64891 | −0.0557115 | ||||||||
\(877\) | 39.8777 | 1.34657 | 0.673287 | − | 0.739381i | \(-0.264882\pi\) | ||||
0.673287 | + | 0.739381i | \(0.264882\pi\) | |||||||
\(878\) | 5.63118 | 0.190043 | ||||||||
\(879\) | 5.82446 | 0.196454 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.5873 | 1.73802 | 0.869010 | − | 0.494795i | \(-0.164757\pi\) | ||||
0.869010 | + | 0.494795i | \(0.164757\pi\) | |||||||
\(882\) | −3.35710 | −0.113040 | ||||||||
\(883\) | 24.1343 | 0.812184 | 0.406092 | − | 0.913832i | \(-0.366891\pi\) | ||||
0.406092 | + | 0.913832i | \(0.366891\pi\) | |||||||
\(884\) | −14.6640 | −0.493203 | ||||||||
\(885\) | −7.15645 | −0.240561 | ||||||||
\(886\) | 5.61072 | 0.188496 | ||||||||
\(887\) | 43.3896 | 1.45688 | 0.728440 | − | 0.685110i | \(-0.240246\pi\) | ||||
0.728440 | + | 0.685110i | \(0.240246\pi\) | |||||||
\(888\) | −23.3776 | −0.784500 | ||||||||
\(889\) | 28.0988 | 0.942405 | ||||||||
\(890\) | 8.92330 | 0.299110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.9350 | 0.600509 | ||||||||
\(893\) | −50.3129 | −1.68366 | ||||||||
\(894\) | −3.01172 | −0.100727 | ||||||||
\(895\) | 1.19464 | 0.0399325 | ||||||||
\(896\) | 15.3366 | 0.512361 | ||||||||
\(897\) | 22.2479 | 0.742836 | ||||||||
\(898\) | 17.0030 | 0.567399 | ||||||||
\(899\) | 14.2479 | 0.475194 | ||||||||
\(900\) | −1.40268 | −0.0467560 | ||||||||
\(901\) | −11.4586 | −0.381742 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.51925 | −0.0838355 | ||||||||
\(904\) | −32.9427 | −1.09566 | ||||||||
\(905\) | 15.3437 | 0.510042 | ||||||||
\(906\) | −4.42178 | −0.146904 | ||||||||
\(907\) | −28.6181 | −0.950248 | −0.475124 | − | 0.879919i | \(-0.657597\pi\) | ||||
−0.475124 | + | 0.879919i | \(0.657597\pi\) | |||||||
\(908\) | −20.0285 | −0.664668 | ||||||||
\(909\) | −13.6107 | −0.451439 | ||||||||
\(910\) | −6.05296 | −0.200654 | ||||||||
\(911\) | −19.3776 | −0.642007 | −0.321004 | − | 0.947078i | \(-0.604020\pi\) | ||||
−0.321004 | + | 0.947078i | \(0.604020\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.79060 | −0.0923048 | ||||||||
\(915\) | 14.2596 | 0.471409 | ||||||||
\(916\) | 36.4264 | 1.20356 | ||||||||
\(917\) | 25.4426 | 0.840187 | ||||||||
\(918\) | 1.68140 | 0.0554946 | ||||||||
\(919\) | −29.7096 | −0.980028 | −0.490014 | − | 0.871715i | \(-0.663008\pi\) | ||||
−0.490014 | + | 0.871715i | \(0.663008\pi\) | |||||||
\(920\) | −12.1755 | −0.401416 | ||||||||
\(921\) | −10.2670 | −0.338309 | ||||||||
\(922\) | −15.5371 | −0.511686 | ||||||||
\(923\) | 64.5963 | 2.12621 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.88944 | 0.292283 | ||||||||
\(926\) | −15.9886 | −0.525418 | ||||||||
\(927\) | 14.6181 | 0.480121 | ||||||||
\(928\) | 14.3745 | 0.471867 | ||||||||
\(929\) | 7.11490 | 0.233432 | 0.116716 | − | 0.993165i | \(-0.462763\pi\) | ||||
0.116716 | + | 0.993165i | \(0.462763\pi\) | |||||||
\(930\) | 4.48676 | 0.147127 | ||||||||
\(931\) | 22.4811 | 0.736787 | ||||||||
\(932\) | 14.8191 | 0.485415 | ||||||||
\(933\) | −0.454269 | −0.0148721 | ||||||||
\(934\) | −0.657657 | −0.0215192 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.6372 | −0.413060 | ||||||||
\(937\) | −8.68308 | −0.283664 | −0.141832 | − | 0.989891i | \(-0.545299\pi\) | ||||
−0.141832 | + | 0.989891i | \(0.545299\pi\) | |||||||
\(938\) | 5.94704 | 0.194178 | ||||||||
\(939\) | 0.103180 | 0.00336716 | ||||||||
\(940\) | −13.6358 | −0.444752 | ||||||||
\(941\) | 14.2861 | 0.465714 | 0.232857 | − | 0.972511i | \(-0.425193\pi\) | ||||
0.232857 | + | 0.972511i | \(0.425193\pi\) | |||||||
\(942\) | −11.7789 | −0.383777 | ||||||||
\(943\) | −23.5725 | −0.767627 | ||||||||
\(944\) | −5.53097 | −0.180018 | ||||||||
\(945\) | −1.62981 | −0.0530178 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.5916 | 1.57902 | 0.789508 | − | 0.613741i | \(-0.210336\pi\) | ||||
0.789508 | + | 0.613741i | \(0.210336\pi\) | |||||||
\(948\) | 6.86867 | 0.223084 | ||||||||
\(949\) | 5.64891 | 0.183371 | ||||||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | −19.0841 | −0.618844 | ||||||||
\(952\) | 9.32461 | 0.302212 | ||||||||
\(953\) | −50.0000 | −1.61966 | −0.809829 | − | 0.586665i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586665i | \(0.800440\pi\) | |||||||
\(954\) | −4.07069 | −0.131793 | ||||||||
\(955\) | 15.7139 | 0.508490 | ||||||||
\(956\) | 9.05327 | 0.292804 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.9504 | −0.709185 | ||||||||
\(959\) | 17.4305 | 0.562861 | ||||||||
\(960\) | 2.98090 | 0.0962082 | ||||||||
\(961\) | 2.70218 | 0.0871670 | ||||||||
\(962\) | 33.0144 | 1.06443 | ||||||||
\(963\) | −19.3320 | −0.622965 | ||||||||
\(964\) | 35.9340 | 1.15735 | ||||||||
\(965\) | 11.2405 | 0.361845 | ||||||||
\(966\) | −5.83184 | −0.187636 | ||||||||
\(967\) | 17.3819 | 0.558964 | 0.279482 | − | 0.960151i | \(-0.409837\pi\) | ||||
0.279482 | + | 0.960151i | \(0.409837\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.2596 | −0.361711 | ||||||||
\(970\) | 3.64891 | 0.117159 | ||||||||
\(971\) | 7.69046 | 0.246799 | 0.123399 | − | 0.992357i | \(-0.460620\pi\) | ||||
0.123399 | + | 0.992357i | \(0.460620\pi\) | |||||||
\(972\) | −1.40268 | −0.0449909 | ||||||||
\(973\) | 11.3776 | 0.364748 | ||||||||
\(974\) | 3.14169 | 0.100666 | ||||||||
\(975\) | 4.80536 | 0.153895 | ||||||||
\(976\) | 11.0208 | 0.352766 | ||||||||
\(977\) | −3.78626 | −0.121133 | −0.0605666 | − | 0.998164i | \(-0.519291\pi\) | ||||
−0.0605666 | + | 0.998164i | \(0.519291\pi\) | |||||||
\(978\) | −13.3246 | −0.426074 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.09283 | 0.194628 | ||||||||
\(981\) | 8.78626 | 0.280524 | ||||||||
\(982\) | 21.6107 | 0.689626 | ||||||||
\(983\) | −20.6446 | −0.658460 | −0.329230 | − | 0.944250i | \(-0.606789\pi\) | ||||
−0.329230 | + | 0.944250i | \(0.606789\pi\) | |||||||
\(984\) | 13.3896 | 0.426845 | ||||||||
\(985\) | −2.74037 | −0.0873156 | ||||||||
\(986\) | 4.12662 | 0.131418 | ||||||||
\(987\) | −15.8439 | −0.504316 | ||||||||
\(988\) | 34.8851 | 1.10984 | ||||||||
\(989\) | 7.15645 | 0.227562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.8130 | 0.883511 | 0.441755 | − | 0.897136i | \(-0.354356\pi\) | ||||
0.441755 | + | 0.897136i | \(0.354356\pi\) | |||||||
\(992\) | 34.0017 | 1.07955 | ||||||||
\(993\) | −9.45427 | −0.300022 | ||||||||
\(994\) | −16.9326 | −0.537069 | ||||||||
\(995\) | −25.0650 | −0.794613 | ||||||||
\(996\) | −5.61072 | −0.177782 | ||||||||
\(997\) | −30.7213 | −0.972953 | −0.486476 | − | 0.873694i | \(-0.661718\pi\) | ||||
−0.486476 | + | 0.873694i | \(0.661718\pi\) | |||||||
\(998\) | 0.879017 | 0.0278248 | ||||||||
\(999\) | 8.88944 | 0.281249 |
(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 | 1815.2.a.n.1.2 | yes | 3 | |
3.2 | odd | 2 | 5445.2.a.ba.1.2 | 3 | |||
5.4 | even | 2 | 9075.2.a.ce.1.2 | 3 | |||
11.10 | odd | 2 | 1815.2.a.l.1.2 | ✓ | 3 | ||
33.32 | even | 2 | 5445.2.a.bc.1.2 | 3 | |||
55.54 | odd | 2 | 9075.2.a.ci.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.l.1.2 | ✓ | 3 | 11.10 | odd | 2 | ||
1815.2.a.n.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
5445.2.a.ba.1.2 | 3 | 3.2 | odd | 2 | |||
5445.2.a.bc.1.2 | 3 | 33.32 | even | 2 | |||
9075.2.a.ce.1.2 | 3 | 5.4 | even | 2 | |||
9075.2.a.ci.1.2 | 3 | 55.54 | odd | 2 |