Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(1,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, 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("770.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.91729\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.406728 | −0.234825 | −0.117412 | − | 0.993083i | \(-0.537460\pi\) | ||||
−0.117412 | + | 0.993083i | \(0.537460\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.406728 | 0.166046 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.83457 | −0.944857 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.406728 | −0.117412 | ||||||||
\(13\) | −0.813457 | −0.225612 | −0.112806 | − | 0.993617i | \(-0.535984\pi\) | ||||
−0.112806 | + | 0.993617i | \(0.535984\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.406728 | 0.105017 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.83457 | 0.930020 | 0.465010 | − | 0.885305i | \(-0.346051\pi\) | ||||
0.465010 | + | 0.885305i | \(0.346051\pi\) | |||||||
\(18\) | 2.83457 | 0.668115 | ||||||||
\(19\) | 5.42784 | 1.24523 | 0.622616 | − | 0.782527i | \(-0.286070\pi\) | ||||
0.622616 | + | 0.782527i | \(0.286070\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.406728 | 0.0887554 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −5.42784 | −1.13178 | −0.565892 | − | 0.824480i | \(-0.691468\pi\) | ||||
−0.565892 | + | 0.824480i | \(0.691468\pi\) | |||||||
\(24\) | 0.406728 | 0.0830231 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.813457 | 0.159532 | ||||||||
\(27\) | 2.37309 | 0.456701 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 6.61439 | 1.22826 | 0.614130 | − | 0.789205i | \(-0.289507\pi\) | ||||
0.614130 | + | 0.789205i | \(0.289507\pi\) | |||||||
\(30\) | −0.406728 | −0.0742581 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.406728 | −0.0708023 | ||||||||
\(34\) | −3.83457 | −0.657624 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.83457 | −0.472429 | ||||||||
\(37\) | 8.24130 | 1.35486 | 0.677431 | − | 0.735587i | \(-0.263093\pi\) | ||||
0.677431 | + | 0.735587i | \(0.263093\pi\) | |||||||
\(38\) | −5.42784 | −0.880512 | ||||||||
\(39\) | 0.330856 | 0.0529794 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −5.59327 | −0.873522 | −0.436761 | − | 0.899578i | \(-0.643875\pi\) | ||||
−0.436761 | + | 0.899578i | \(0.643875\pi\) | |||||||
\(42\) | −0.406728 | −0.0627596 | ||||||||
\(43\) | −3.02112 | −0.460716 | −0.230358 | − | 0.973106i | \(-0.573990\pi\) | ||||
−0.230358 | + | 0.973106i | \(0.573990\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 2.83457 | 0.422553 | ||||||||
\(46\) | 5.42784 | 0.800292 | ||||||||
\(47\) | −5.02112 | −0.732405 | −0.366202 | − | 0.930535i | \(-0.619342\pi\) | ||||
−0.366202 | + | 0.930535i | \(0.619342\pi\) | |||||||
\(48\) | −0.406728 | −0.0587062 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.55963 | −0.218392 | ||||||||
\(52\) | −0.813457 | −0.112806 | ||||||||
\(53\) | 6.61439 | 0.908556 | 0.454278 | − | 0.890860i | \(-0.349897\pi\) | ||||
0.454278 | + | 0.890860i | \(0.349897\pi\) | |||||||
\(54\) | −2.37309 | −0.322936 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −2.20766 | −0.292411 | ||||||||
\(58\) | −6.61439 | −0.868512 | ||||||||
\(59\) | 10.6480 | 1.38626 | 0.693128 | − | 0.720815i | \(-0.256232\pi\) | ||||
0.693128 | + | 0.720815i | \(0.256232\pi\) | |||||||
\(60\) | 0.406728 | 0.0525084 | ||||||||
\(61\) | 0.978885 | 0.125333 | 0.0626667 | − | 0.998035i | \(-0.480039\pi\) | ||||
0.0626667 | + | 0.998035i | \(0.480039\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 2.83457 | 0.357123 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.813457 | 0.100897 | ||||||||
\(66\) | 0.406728 | 0.0500648 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 3.83457 | 0.465010 | ||||||||
\(69\) | 2.20766 | 0.265771 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 14.8557 | 1.76305 | 0.881523 | − | 0.472141i | \(-0.156519\pi\) | ||||
0.881523 | + | 0.472141i | \(0.156519\pi\) | |||||||
\(72\) | 2.83457 | 0.334058 | ||||||||
\(73\) | −6.20766 | −0.726551 | −0.363276 | − | 0.931682i | \(-0.618342\pi\) | ||||
−0.363276 | + | 0.931682i | \(0.618342\pi\) | |||||||
\(74\) | −8.24130 | −0.958032 | ||||||||
\(75\) | −0.406728 | −0.0469650 | ||||||||
\(76\) | 5.42784 | 0.622616 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −0.330856 | −0.0374621 | ||||||||
\(79\) | 17.0970 | 1.92356 | 0.961781 | − | 0.273821i | \(-0.0882876\pi\) | ||||
0.961781 | + | 0.273821i | \(0.0882876\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 7.53851 | 0.837613 | ||||||||
\(82\) | 5.59327 | 0.617674 | ||||||||
\(83\) | −8.81346 | −0.967403 | −0.483701 | − | 0.875233i | \(-0.660708\pi\) | ||||
−0.483701 | + | 0.875233i | \(0.660708\pi\) | |||||||
\(84\) | 0.406728 | 0.0443777 | ||||||||
\(85\) | −3.83457 | −0.415918 | ||||||||
\(86\) | 3.02112 | 0.325775 | ||||||||
\(87\) | −2.69026 | −0.288426 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −1.18654 | −0.125773 | −0.0628867 | − | 0.998021i | \(-0.520031\pi\) | ||||
−0.0628867 | + | 0.998021i | \(0.520031\pi\) | |||||||
\(90\) | −2.83457 | −0.298790 | ||||||||
\(91\) | 0.813457 | 0.0852734 | ||||||||
\(92\) | −5.42784 | −0.565892 | ||||||||
\(93\) | −2.44037 | −0.253055 | ||||||||
\(94\) | 5.02112 | 0.517888 | ||||||||
\(95\) | −5.42784 | −0.556885 | ||||||||
\(96\) | 0.406728 | 0.0415115 | ||||||||
\(97\) | −3.42784 | −0.348045 | −0.174022 | − | 0.984742i | \(-0.555677\pi\) | ||||
−0.174022 | + | 0.984742i | \(0.555677\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −2.83457 | −0.284885 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −18.6903 | −1.85975 | −0.929875 | − | 0.367875i | \(-0.880085\pi\) | ||||
−0.929875 | + | 0.367875i | \(0.880085\pi\) | |||||||
\(102\) | 1.55963 | 0.154426 | ||||||||
\(103\) | 15.4615 | 1.52347 | 0.761733 | − | 0.647891i | \(-0.224349\pi\) | ||||
0.761733 | + | 0.647891i | \(0.224349\pi\) | |||||||
\(104\) | 0.813457 | 0.0797660 | ||||||||
\(105\) | −0.406728 | −0.0396926 | ||||||||
\(106\) | −6.61439 | −0.642446 | ||||||||
\(107\) | −11.0211 | −1.06545 | −0.532726 | − | 0.846288i | \(-0.678832\pi\) | ||||
−0.532726 | + | 0.846288i | \(0.678832\pi\) | |||||||
\(108\) | 2.37309 | 0.228350 | ||||||||
\(109\) | 16.2413 | 1.55563 | 0.777817 | − | 0.628491i | \(-0.216327\pi\) | ||||
0.777817 | + | 0.628491i | \(0.216327\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | −3.35197 | −0.318155 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 2.20766 | 0.206766 | ||||||||
\(115\) | 5.42784 | 0.506149 | ||||||||
\(116\) | 6.61439 | 0.614130 | ||||||||
\(117\) | 2.30580 | 0.213171 | ||||||||
\(118\) | −10.6480 | −0.980231 | ||||||||
\(119\) | −3.83457 | −0.351515 | ||||||||
\(120\) | −0.406728 | −0.0371291 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.978885 | −0.0886241 | ||||||||
\(123\) | 2.27494 | 0.205125 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.83457 | −0.252524 | ||||||||
\(127\) | 17.2961 | 1.53478 | 0.767388 | − | 0.641182i | \(-0.221556\pi\) | ||||
0.767388 | + | 0.641182i | \(0.221556\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.22877 | 0.108187 | ||||||||
\(130\) | −0.813457 | −0.0713449 | ||||||||
\(131\) | 9.42784 | 0.823715 | 0.411857 | − | 0.911248i | \(-0.364880\pi\) | ||||
0.411857 | + | 0.911248i | \(0.364880\pi\) | |||||||
\(132\) | −0.406728 | −0.0354012 | ||||||||
\(133\) | −5.42784 | −0.470654 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −2.37309 | −0.204243 | ||||||||
\(136\) | −3.83457 | −0.328812 | ||||||||
\(137\) | 13.6691 | 1.16783 | 0.583917 | − | 0.811813i | \(-0.301519\pi\) | ||||
0.583917 | + | 0.811813i | \(0.301519\pi\) | |||||||
\(138\) | −2.20766 | −0.187928 | ||||||||
\(139\) | −11.8682 | −1.00665 | −0.503324 | − | 0.864098i | \(-0.667890\pi\) | ||||
−0.503324 | + | 0.864098i | \(0.667890\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 2.04223 | 0.171987 | ||||||||
\(142\) | −14.8557 | −1.24666 | ||||||||
\(143\) | −0.813457 | −0.0680247 | ||||||||
\(144\) | −2.83457 | −0.236214 | ||||||||
\(145\) | −6.61439 | −0.549295 | ||||||||
\(146\) | 6.20766 | 0.513749 | ||||||||
\(147\) | −0.406728 | −0.0335464 | ||||||||
\(148\) | 8.24130 | 0.677431 | ||||||||
\(149\) | −22.2835 | −1.82554 | −0.912769 | − | 0.408476i | \(-0.866060\pi\) | ||||
−0.912769 | + | 0.408476i | \(0.866060\pi\) | |||||||
\(150\) | 0.406728 | 0.0332092 | ||||||||
\(151\) | −3.05476 | −0.248593 | −0.124296 | − | 0.992245i | \(-0.539667\pi\) | ||||
−0.124296 | + | 0.992245i | \(0.539667\pi\) | |||||||
\(152\) | −5.42784 | −0.440256 | ||||||||
\(153\) | −10.8694 | −0.878737 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0.330856 | 0.0264897 | ||||||||
\(157\) | 4.85569 | 0.387526 | 0.193763 | − | 0.981048i | \(-0.437931\pi\) | ||||
0.193763 | + | 0.981048i | \(0.437931\pi\) | |||||||
\(158\) | −17.0970 | −1.36016 | ||||||||
\(159\) | −2.69026 | −0.213351 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.42784 | 0.427774 | ||||||||
\(162\) | −7.53851 | −0.592282 | ||||||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | −5.59327 | −0.436761 | ||||||||
\(165\) | 0.406728 | 0.0316638 | ||||||||
\(166\) | 8.81346 | 0.684057 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | −0.406728 | −0.0313798 | ||||||||
\(169\) | −12.3383 | −0.949099 | ||||||||
\(170\) | 3.83457 | 0.294098 | ||||||||
\(171\) | −15.3856 | −1.17657 | ||||||||
\(172\) | −3.02112 | −0.230358 | ||||||||
\(173\) | −19.0211 | −1.44615 | −0.723074 | − | 0.690770i | \(-0.757272\pi\) | ||||
−0.723074 | + | 0.690770i | \(0.757272\pi\) | |||||||
\(174\) | 2.69026 | 0.203948 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −4.33086 | −0.325527 | ||||||||
\(178\) | 1.18654 | 0.0889352 | ||||||||
\(179\) | 4.64803 | 0.347410 | 0.173705 | − | 0.984798i | \(-0.444426\pi\) | ||||
0.173705 | + | 0.984798i | \(0.444426\pi\) | |||||||
\(180\) | 2.83457 | 0.211277 | ||||||||
\(181\) | −25.3383 | −1.88338 | −0.941690 | − | 0.336482i | \(-0.890763\pi\) | ||||
−0.941690 | + | 0.336482i | \(0.890763\pi\) | |||||||
\(182\) | −0.813457 | −0.0602974 | ||||||||
\(183\) | −0.398140 | −0.0294314 | ||||||||
\(184\) | 5.42784 | 0.400146 | ||||||||
\(185\) | −8.24130 | −0.605912 | ||||||||
\(186\) | 2.44037 | 0.178937 | ||||||||
\(187\) | 3.83457 | 0.280412 | ||||||||
\(188\) | −5.02112 | −0.366202 | ||||||||
\(189\) | −2.37309 | −0.172617 | ||||||||
\(190\) | 5.42784 | 0.393777 | ||||||||
\(191\) | 15.6691 | 1.13378 | 0.566890 | − | 0.823794i | \(-0.308147\pi\) | ||||
0.566890 | + | 0.823794i | \(0.308147\pi\) | |||||||
\(192\) | −0.406728 | −0.0293531 | ||||||||
\(193\) | −2.16543 | −0.155871 | −0.0779355 | − | 0.996958i | \(-0.524833\pi\) | ||||
−0.0779355 | + | 0.996958i | \(0.524833\pi\) | |||||||
\(194\) | 3.42784 | 0.246105 | ||||||||
\(195\) | −0.330856 | −0.0236931 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.81346 | 0.200451 | 0.100225 | − | 0.994965i | \(-0.468044\pi\) | ||||
0.100225 | + | 0.994965i | \(0.468044\pi\) | |||||||
\(198\) | 2.83457 | 0.201444 | ||||||||
\(199\) | −13.0211 | −0.923042 | −0.461521 | − | 0.887129i | \(-0.652696\pi\) | ||||
−0.461521 | + | 0.887129i | \(0.652696\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −3.25383 | −0.229507 | ||||||||
\(202\) | 18.6903 | 1.31504 | ||||||||
\(203\) | −6.61439 | −0.464239 | ||||||||
\(204\) | −1.55963 | −0.109196 | ||||||||
\(205\) | 5.59327 | 0.390651 | ||||||||
\(206\) | −15.4615 | −1.07725 | ||||||||
\(207\) | 15.3856 | 1.06937 | ||||||||
\(208\) | −0.813457 | −0.0564031 | ||||||||
\(209\) | 5.42784 | 0.375452 | ||||||||
\(210\) | 0.406728 | 0.0280669 | ||||||||
\(211\) | 19.6691 | 1.35408 | 0.677040 | − | 0.735946i | \(-0.263262\pi\) | ||||
0.677040 | + | 0.735946i | \(0.263262\pi\) | |||||||
\(212\) | 6.61439 | 0.454278 | ||||||||
\(213\) | −6.04223 | −0.414007 | ||||||||
\(214\) | 11.0211 | 0.753388 | ||||||||
\(215\) | 3.02112 | 0.206038 | ||||||||
\(216\) | −2.37309 | −0.161468 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | −16.2413 | −1.10000 | ||||||||
\(219\) | 2.52483 | 0.170612 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −3.11926 | −0.209824 | ||||||||
\(222\) | 3.35197 | 0.224970 | ||||||||
\(223\) | −3.79234 | −0.253954 | −0.126977 | − | 0.991906i | \(-0.540527\pi\) | ||||
−0.126977 | + | 0.991906i | \(0.540527\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −2.83457 | −0.188971 | ||||||||
\(226\) | 14.0000 | 0.931266 | ||||||||
\(227\) | −14.0422 | −0.932016 | −0.466008 | − | 0.884781i | \(-0.654308\pi\) | ||||
−0.466008 | + | 0.884781i | \(0.654308\pi\) | |||||||
\(228\) | −2.20766 | −0.146206 | ||||||||
\(229\) | 1.83457 | 0.121232 | 0.0606160 | − | 0.998161i | \(-0.480694\pi\) | ||||
0.0606160 | + | 0.998161i | \(0.480694\pi\) | |||||||
\(230\) | −5.42784 | −0.357901 | ||||||||
\(231\) | 0.406728 | 0.0267608 | ||||||||
\(232\) | −6.61439 | −0.434256 | ||||||||
\(233\) | −8.04223 | −0.526864 | −0.263432 | − | 0.964678i | \(-0.584854\pi\) | ||||
−0.263432 | + | 0.964678i | \(0.584854\pi\) | |||||||
\(234\) | −2.30580 | −0.150735 | ||||||||
\(235\) | 5.02112 | 0.327541 | ||||||||
\(236\) | 10.6480 | 0.693128 | ||||||||
\(237\) | −6.95383 | −0.451700 | ||||||||
\(238\) | 3.83457 | 0.248558 | ||||||||
\(239\) | −15.4701 | −1.00068 | −0.500338 | − | 0.865830i | \(-0.666791\pi\) | ||||
−0.500338 | + | 0.865830i | \(0.666791\pi\) | |||||||
\(240\) | 0.406728 | 0.0262542 | ||||||||
\(241\) | 11.6355 | 0.749509 | 0.374754 | − | 0.927124i | \(-0.377727\pi\) | ||||
0.374754 | + | 0.927124i | \(0.377727\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −10.1854 | −0.653393 | ||||||||
\(244\) | 0.978885 | 0.0626667 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −2.27494 | −0.145045 | ||||||||
\(247\) | −4.41532 | −0.280940 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 3.58468 | 0.227170 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.35197 | 0.337813 | 0.168907 | − | 0.985632i | \(-0.445976\pi\) | ||||
0.168907 | + | 0.985632i | \(0.445976\pi\) | |||||||
\(252\) | 2.83457 | 0.178561 | ||||||||
\(253\) | −5.42784 | −0.341246 | ||||||||
\(254\) | −17.2961 | −1.08525 | ||||||||
\(255\) | 1.55963 | 0.0976678 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.7239 | 0.793695 | 0.396848 | − | 0.917885i | \(-0.370104\pi\) | ||||
0.396848 | + | 0.917885i | \(0.370104\pi\) | |||||||
\(258\) | −1.22877 | −0.0765001 | ||||||||
\(259\) | −8.24130 | −0.512089 | ||||||||
\(260\) | 0.813457 | 0.0504485 | ||||||||
\(261\) | −18.7490 | −1.16053 | ||||||||
\(262\) | −9.42784 | −0.582454 | ||||||||
\(263\) | −1.62691 | −0.100320 | −0.0501599 | − | 0.998741i | \(-0.515973\pi\) | ||||
−0.0501599 | + | 0.998741i | \(0.515973\pi\) | |||||||
\(264\) | 0.406728 | 0.0250324 | ||||||||
\(265\) | −6.61439 | −0.406319 | ||||||||
\(266\) | 5.42784 | 0.332802 | ||||||||
\(267\) | 0.482601 | 0.0295347 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | 23.8768 | 1.45579 | 0.727897 | − | 0.685686i | \(-0.240498\pi\) | ||||
0.727897 | + | 0.685686i | \(0.240498\pi\) | |||||||
\(270\) | 2.37309 | 0.144421 | ||||||||
\(271\) | 2.44037 | 0.148242 | 0.0741210 | − | 0.997249i | \(-0.476385\pi\) | ||||
0.0741210 | + | 0.997249i | \(0.476385\pi\) | |||||||
\(272\) | 3.83457 | 0.232505 | ||||||||
\(273\) | −0.330856 | −0.0200243 | ||||||||
\(274\) | −13.6691 | −0.825783 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 2.20766 | 0.132885 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 11.8682 | 0.711808 | ||||||||
\(279\) | −17.0074 | −1.01821 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −20.8557 | −1.24415 | −0.622073 | − | 0.782959i | \(-0.713709\pi\) | ||||
−0.622073 | + | 0.782959i | \(0.713709\pi\) | |||||||
\(282\) | −2.04223 | −0.121613 | ||||||||
\(283\) | 0.330856 | 0.0196673 | 0.00983367 | − | 0.999952i | \(-0.496870\pi\) | ||||
0.00983367 | + | 0.999952i | \(0.496870\pi\) | |||||||
\(284\) | 14.8557 | 0.881523 | ||||||||
\(285\) | 2.20766 | 0.130770 | ||||||||
\(286\) | 0.813457 | 0.0481007 | ||||||||
\(287\) | 5.59327 | 0.330160 | ||||||||
\(288\) | 2.83457 | 0.167029 | ||||||||
\(289\) | −2.29606 | −0.135062 | ||||||||
\(290\) | 6.61439 | 0.388410 | ||||||||
\(291\) | 1.39420 | 0.0817295 | ||||||||
\(292\) | −6.20766 | −0.363276 | ||||||||
\(293\) | −3.18654 | −0.186160 | −0.0930799 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930799 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(294\) | 0.406728 | 0.0237209 | ||||||||
\(295\) | −10.6480 | −0.619952 | ||||||||
\(296\) | −8.24130 | −0.479016 | ||||||||
\(297\) | 2.37309 | 0.137700 | ||||||||
\(298\) | 22.2835 | 1.29085 | ||||||||
\(299\) | 4.41532 | 0.255344 | ||||||||
\(300\) | −0.406728 | −0.0234825 | ||||||||
\(301\) | 3.02112 | 0.174134 | ||||||||
\(302\) | 3.05476 | 0.175782 | ||||||||
\(303\) | 7.60186 | 0.436715 | ||||||||
\(304\) | 5.42784 | 0.311308 | ||||||||
\(305\) | −0.978885 | −0.0560508 | ||||||||
\(306\) | 10.8694 | 0.621361 | ||||||||
\(307\) | 20.4826 | 1.16900 | 0.584502 | − | 0.811392i | \(-0.301290\pi\) | ||||
0.584502 | + | 0.811392i | \(0.301290\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | −6.28863 | −0.357747 | ||||||||
\(310\) | 6.00000 | 0.340777 | ||||||||
\(311\) | 3.62691 | 0.205663 | 0.102832 | − | 0.994699i | \(-0.467210\pi\) | ||||
0.102832 | + | 0.994699i | \(0.467210\pi\) | |||||||
\(312\) | −0.330856 | −0.0187310 | ||||||||
\(313\) | 20.7239 | 1.17138 | 0.585692 | − | 0.810534i | \(-0.300823\pi\) | ||||
0.585692 | + | 0.810534i | \(0.300823\pi\) | |||||||
\(314\) | −4.85569 | −0.274022 | ||||||||
\(315\) | −2.83457 | −0.159710 | ||||||||
\(316\) | 17.0970 | 0.961781 | ||||||||
\(317\) | −1.80093 | −0.101150 | −0.0505751 | − | 0.998720i | \(-0.516105\pi\) | ||||
−0.0505751 | + | 0.998720i | \(0.516105\pi\) | |||||||
\(318\) | 2.69026 | 0.150862 | ||||||||
\(319\) | 6.61439 | 0.370335 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 4.48260 | 0.250194 | ||||||||
\(322\) | −5.42784 | −0.302482 | ||||||||
\(323\) | 20.8135 | 1.15809 | ||||||||
\(324\) | 7.53851 | 0.418806 | ||||||||
\(325\) | −0.813457 | −0.0451225 | ||||||||
\(326\) | 8.00000 | 0.443079 | ||||||||
\(327\) | −6.60580 | −0.365301 | ||||||||
\(328\) | 5.59327 | 0.308837 | ||||||||
\(329\) | 5.02112 | 0.276823 | ||||||||
\(330\) | −0.406728 | −0.0223897 | ||||||||
\(331\) | −3.02112 | −0.166056 | −0.0830278 | − | 0.996547i | \(-0.526459\pi\) | ||||
−0.0830278 | + | 0.996547i | \(0.526459\pi\) | |||||||
\(332\) | −8.81346 | −0.483701 | ||||||||
\(333\) | −23.3606 | −1.28015 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0.406728 | 0.0221889 | ||||||||
\(337\) | −9.66914 | −0.526712 | −0.263356 | − | 0.964699i | \(-0.584829\pi\) | ||||
−0.263356 | + | 0.964699i | \(0.584829\pi\) | |||||||
\(338\) | 12.3383 | 0.671114 | ||||||||
\(339\) | 5.69420 | 0.309266 | ||||||||
\(340\) | −3.83457 | −0.207959 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 15.3856 | 0.831959 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.02112 | 0.162888 | ||||||||
\(345\) | −2.20766 | −0.118856 | ||||||||
\(346\) | 19.0211 | 1.02258 | ||||||||
\(347\) | 9.39420 | 0.504307 | 0.252154 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252154 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(348\) | −2.69026 | −0.144213 | ||||||||
\(349\) | −18.2077 | −0.974634 | −0.487317 | − | 0.873225i | \(-0.662024\pi\) | ||||
−0.487317 | + | 0.873225i | \(0.662024\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −1.93040 | −0.103037 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 12.7239 | 0.677225 | 0.338612 | − | 0.940926i | \(-0.390042\pi\) | ||||
0.338612 | + | 0.940926i | \(0.390042\pi\) | |||||||
\(354\) | 4.33086 | 0.230182 | ||||||||
\(355\) | −14.8557 | −0.788458 | ||||||||
\(356\) | −1.18654 | −0.0628867 | ||||||||
\(357\) | 1.55963 | 0.0825443 | ||||||||
\(358\) | −4.64803 | −0.245656 | ||||||||
\(359\) | 29.8432 | 1.57506 | 0.787531 | − | 0.616275i | \(-0.211359\pi\) | ||||
0.787531 | + | 0.616275i | \(0.211359\pi\) | |||||||
\(360\) | −2.83457 | −0.149395 | ||||||||
\(361\) | 10.4615 | 0.550605 | ||||||||
\(362\) | 25.3383 | 1.33175 | ||||||||
\(363\) | −0.406728 | −0.0213477 | ||||||||
\(364\) | 0.813457 | 0.0426367 | ||||||||
\(365\) | 6.20766 | 0.324924 | ||||||||
\(366\) | 0.398140 | 0.0208111 | ||||||||
\(367\) | 15.4615 | 0.807083 | 0.403541 | − | 0.914961i | \(-0.367779\pi\) | ||||
0.403541 | + | 0.914961i | \(0.367779\pi\) | |||||||
\(368\) | −5.42784 | −0.282946 | ||||||||
\(369\) | 15.8545 | 0.825354 | ||||||||
\(370\) | 8.24130 | 0.428445 | ||||||||
\(371\) | −6.61439 | −0.343402 | ||||||||
\(372\) | −2.44037 | −0.126527 | ||||||||
\(373\) | −8.10951 | −0.419895 | −0.209947 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209947 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(374\) | −3.83457 | −0.198281 | ||||||||
\(375\) | 0.406728 | 0.0210034 | ||||||||
\(376\) | 5.02112 | 0.258944 | ||||||||
\(377\) | −5.38052 | −0.277111 | ||||||||
\(378\) | 2.37309 | 0.122058 | ||||||||
\(379\) | 22.0422 | 1.13223 | 0.566117 | − | 0.824325i | \(-0.308445\pi\) | ||||
0.566117 | + | 0.824325i | \(0.308445\pi\) | |||||||
\(380\) | −5.42784 | −0.278442 | ||||||||
\(381\) | −7.03480 | −0.360404 | ||||||||
\(382\) | −15.6691 | −0.801703 | ||||||||
\(383\) | 38.2499 | 1.95448 | 0.977239 | − | 0.212141i | \(-0.0680437\pi\) | ||||
0.977239 | + | 0.212141i | \(0.0680437\pi\) | |||||||
\(384\) | 0.406728 | 0.0207558 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 2.16543 | 0.110217 | ||||||||
\(387\) | 8.56357 | 0.435311 | ||||||||
\(388\) | −3.42784 | −0.174022 | ||||||||
\(389\) | 16.8557 | 0.854617 | 0.427309 | − | 0.904106i | \(-0.359462\pi\) | ||||
0.427309 | + | 0.904106i | \(0.359462\pi\) | |||||||
\(390\) | 0.330856 | 0.0167535 | ||||||||
\(391\) | −20.8135 | −1.05258 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −3.83457 | −0.193429 | ||||||||
\(394\) | −2.81346 | −0.141740 | ||||||||
\(395\) | −17.0970 | −0.860243 | ||||||||
\(396\) | −2.83457 | −0.142443 | ||||||||
\(397\) | −4.44037 | −0.222856 | −0.111428 | − | 0.993773i | \(-0.535542\pi\) | ||||
−0.111428 | + | 0.993773i | \(0.535542\pi\) | |||||||
\(398\) | 13.0211 | 0.652690 | ||||||||
\(399\) | 2.20766 | 0.110521 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −3.46149 | −0.172858 | −0.0864292 | − | 0.996258i | \(-0.527546\pi\) | ||||
−0.0864292 | + | 0.996258i | \(0.527546\pi\) | |||||||
\(402\) | 3.25383 | 0.162286 | ||||||||
\(403\) | −4.88074 | −0.243127 | ||||||||
\(404\) | −18.6903 | −0.929875 | ||||||||
\(405\) | −7.53851 | −0.374592 | ||||||||
\(406\) | 6.61439 | 0.328267 | ||||||||
\(407\) | 8.24130 | 0.408506 | ||||||||
\(408\) | 1.55963 | 0.0772132 | ||||||||
\(409\) | −17.2624 | −0.853572 | −0.426786 | − | 0.904353i | \(-0.640354\pi\) | ||||
−0.426786 | + | 0.904353i | \(0.640354\pi\) | |||||||
\(410\) | −5.59327 | −0.276232 | ||||||||
\(411\) | −5.55963 | −0.274236 | ||||||||
\(412\) | 15.4615 | 0.761733 | ||||||||
\(413\) | −10.6480 | −0.523955 | ||||||||
\(414\) | −15.3856 | −0.756162 | ||||||||
\(415\) | 8.81346 | 0.432636 | ||||||||
\(416\) | 0.813457 | 0.0398830 | ||||||||
\(417\) | 4.82714 | 0.236386 | ||||||||
\(418\) | −5.42784 | −0.265485 | ||||||||
\(419\) | 9.02112 | 0.440710 | 0.220355 | − | 0.975420i | \(-0.429278\pi\) | ||||
0.220355 | + | 0.975420i | \(0.429278\pi\) | |||||||
\(420\) | −0.406728 | −0.0198463 | ||||||||
\(421\) | 31.7114 | 1.54552 | 0.772759 | − | 0.634700i | \(-0.218876\pi\) | ||||
0.772759 | + | 0.634700i | \(0.218876\pi\) | |||||||
\(422\) | −19.6691 | −0.957479 | ||||||||
\(423\) | 14.2327 | 0.692018 | ||||||||
\(424\) | −6.61439 | −0.321223 | ||||||||
\(425\) | 3.83457 | 0.186004 | ||||||||
\(426\) | 6.04223 | 0.292747 | ||||||||
\(427\) | −0.978885 | −0.0473716 | ||||||||
\(428\) | −11.0211 | −0.532726 | ||||||||
\(429\) | 0.330856 | 0.0159739 | ||||||||
\(430\) | −3.02112 | −0.145691 | ||||||||
\(431\) | −3.05476 | −0.147142 | −0.0735712 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735712 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(432\) | 2.37309 | 0.114175 | ||||||||
\(433\) | 27.9104 | 1.34129 | 0.670645 | − | 0.741778i | \(-0.266017\pi\) | ||||
0.670645 | + | 0.741778i | \(0.266017\pi\) | |||||||
\(434\) | 6.00000 | 0.288009 | ||||||||
\(435\) | 2.69026 | 0.128988 | ||||||||
\(436\) | 16.2413 | 0.777817 | ||||||||
\(437\) | −29.4615 | −1.40933 | ||||||||
\(438\) | −2.52483 | −0.120641 | ||||||||
\(439\) | −14.8557 | −0.709023 | −0.354512 | − | 0.935052i | \(-0.615353\pi\) | ||||
−0.354512 | + | 0.935052i | \(0.615353\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −2.83457 | −0.134980 | ||||||||
\(442\) | 3.11926 | 0.148368 | ||||||||
\(443\) | 0.746173 | 0.0354517 | 0.0177259 | − | 0.999843i | \(-0.494357\pi\) | ||||
0.0177259 | + | 0.999843i | \(0.494357\pi\) | |||||||
\(444\) | −3.35197 | −0.159078 | ||||||||
\(445\) | 1.18654 | 0.0562475 | ||||||||
\(446\) | 3.79234 | 0.179573 | ||||||||
\(447\) | 9.06335 | 0.428682 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 9.83457 | 0.464122 | 0.232061 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232061 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(450\) | 2.83457 | 0.133623 | ||||||||
\(451\) | −5.59327 | −0.263377 | ||||||||
\(452\) | −14.0000 | −0.658505 | ||||||||
\(453\) | 1.24246 | 0.0583757 | ||||||||
\(454\) | 14.0422 | 0.659035 | ||||||||
\(455\) | −0.813457 | −0.0381354 | ||||||||
\(456\) | 2.20766 | 0.103383 | ||||||||
\(457\) | 11.2961 | 0.528407 | 0.264204 | − | 0.964467i | \(-0.414891\pi\) | ||||
0.264204 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(458\) | −1.83457 | −0.0857239 | ||||||||
\(459\) | 9.09977 | 0.424741 | ||||||||
\(460\) | 5.42784 | 0.253075 | ||||||||
\(461\) | −7.41926 | −0.345549 | −0.172775 | − | 0.984961i | \(-0.555273\pi\) | ||||
−0.172775 | + | 0.984961i | \(0.555273\pi\) | |||||||
\(462\) | −0.406728 | −0.0189227 | ||||||||
\(463\) | −10.1740 | −0.472827 | −0.236413 | − | 0.971653i | \(-0.575972\pi\) | ||||
−0.236413 | + | 0.971653i | \(0.575972\pi\) | |||||||
\(464\) | 6.61439 | 0.307065 | ||||||||
\(465\) | 2.44037 | 0.113169 | ||||||||
\(466\) | 8.04223 | 0.372549 | ||||||||
\(467\) | −32.4912 | −1.50351 | −0.751756 | − | 0.659441i | \(-0.770793\pi\) | ||||
−0.751756 | + | 0.659441i | \(0.770793\pi\) | |||||||
\(468\) | 2.30580 | 0.106586 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | −5.02112 | −0.231607 | ||||||||
\(471\) | −1.97495 | −0.0910007 | ||||||||
\(472\) | −10.6480 | −0.490115 | ||||||||
\(473\) | −3.02112 | −0.138911 | ||||||||
\(474\) | 6.95383 | 0.319400 | ||||||||
\(475\) | 5.42784 | 0.249047 | ||||||||
\(476\) | −3.83457 | −0.175757 | ||||||||
\(477\) | −18.7490 | −0.858456 | ||||||||
\(478\) | 15.4701 | 0.707585 | ||||||||
\(479\) | −11.6691 | −0.533177 | −0.266588 | − | 0.963810i | \(-0.585896\pi\) | ||||
−0.266588 | + | 0.963810i | \(0.585896\pi\) | |||||||
\(480\) | −0.406728 | −0.0185645 | ||||||||
\(481\) | −6.70394 | −0.305673 | ||||||||
\(482\) | −11.6355 | −0.529983 | ||||||||
\(483\) | −2.20766 | −0.100452 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.42784 | 0.155650 | ||||||||
\(486\) | 10.1854 | 0.462019 | ||||||||
\(487\) | −5.49513 | −0.249008 | −0.124504 | − | 0.992219i | \(-0.539734\pi\) | ||||
−0.124504 | + | 0.992219i | \(0.539734\pi\) | |||||||
\(488\) | −0.978885 | −0.0443120 | ||||||||
\(489\) | 3.25383 | 0.147143 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −13.2961 | −0.600043 | −0.300021 | − | 0.953932i | \(-0.596994\pi\) | ||||
−0.300021 | + | 0.953932i | \(0.596994\pi\) | |||||||
\(492\) | 2.27494 | 0.102562 | ||||||||
\(493\) | 25.3633 | 1.14231 | ||||||||
\(494\) | 4.41532 | 0.198654 | ||||||||
\(495\) | 2.83457 | 0.127405 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −14.8557 | −0.666369 | ||||||||
\(498\) | −3.58468 | −0.160634 | ||||||||
\(499\) | −24.6480 | −1.10340 | −0.551699 | − | 0.834044i | \(-0.686020\pi\) | ||||
−0.551699 | + | 0.834044i | \(0.686020\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −3.25383 | −0.145370 | ||||||||
\(502\) | −5.35197 | −0.238870 | ||||||||
\(503\) | 38.9230 | 1.73549 | 0.867745 | − | 0.497010i | \(-0.165569\pi\) | ||||
0.867745 | + | 0.497010i | \(0.165569\pi\) | |||||||
\(504\) | −2.83457 | −0.126262 | ||||||||
\(505\) | 18.6903 | 0.831706 | ||||||||
\(506\) | 5.42784 | 0.241297 | ||||||||
\(507\) | 5.01833 | 0.222872 | ||||||||
\(508\) | 17.2961 | 0.767388 | ||||||||
\(509\) | −39.0497 | −1.73085 | −0.865423 | − | 0.501042i | \(-0.832950\pi\) | ||||
−0.865423 | + | 0.501042i | \(0.832950\pi\) | |||||||
\(510\) | −1.55963 | −0.0690616 | ||||||||
\(511\) | 6.20766 | 0.274611 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.8807 | 0.568699 | ||||||||
\(514\) | −12.7239 | −0.561227 | ||||||||
\(515\) | −15.4615 | −0.681314 | ||||||||
\(516\) | 1.22877 | 0.0540937 | ||||||||
\(517\) | −5.02112 | −0.220828 | ||||||||
\(518\) | 8.24130 | 0.362102 | ||||||||
\(519\) | 7.73643 | 0.339592 | ||||||||
\(520\) | −0.813457 | −0.0356724 | ||||||||
\(521\) | −33.2710 | −1.45763 | −0.728815 | − | 0.684711i | \(-0.759928\pi\) | ||||
−0.728815 | + | 0.684711i | \(0.759928\pi\) | |||||||
\(522\) | 18.7490 | 0.820619 | ||||||||
\(523\) | −40.2362 | −1.75941 | −0.879703 | − | 0.475523i | \(-0.842259\pi\) | ||||
−0.879703 | + | 0.475523i | \(0.842259\pi\) | |||||||
\(524\) | 9.42784 | 0.411857 | ||||||||
\(525\) | 0.406728 | 0.0177511 | ||||||||
\(526\) | 1.62691 | 0.0709368 | ||||||||
\(527\) | 23.0074 | 1.00222 | ||||||||
\(528\) | −0.406728 | −0.0177006 | ||||||||
\(529\) | 6.46149 | 0.280934 | ||||||||
\(530\) | 6.61439 | 0.287311 | ||||||||
\(531\) | −30.1826 | −1.30981 | ||||||||
\(532\) | −5.42784 | −0.235327 | ||||||||
\(533\) | 4.54989 | 0.197077 | ||||||||
\(534\) | −0.482601 | −0.0208842 | ||||||||
\(535\) | 11.0211 | 0.476484 | ||||||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | −1.89049 | −0.0815805 | ||||||||
\(538\) | −23.8768 | −1.02940 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −2.37309 | −0.102121 | ||||||||
\(541\) | 26.2835 | 1.13002 | 0.565009 | − | 0.825085i | \(-0.308873\pi\) | ||||
0.565009 | + | 0.825085i | \(0.308873\pi\) | |||||||
\(542\) | −2.44037 | −0.104823 | ||||||||
\(543\) | 10.3058 | 0.442264 | ||||||||
\(544\) | −3.83457 | −0.164406 | ||||||||
\(545\) | −16.2413 | −0.695701 | ||||||||
\(546\) | 0.330856 | 0.0141593 | ||||||||
\(547\) | 13.6269 | 0.582645 | 0.291322 | − | 0.956625i | \(-0.405905\pi\) | ||||
0.291322 | + | 0.956625i | \(0.405905\pi\) | |||||||
\(548\) | 13.6691 | 0.583917 | ||||||||
\(549\) | −2.77472 | −0.118422 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 35.9019 | 1.52947 | ||||||||
\(552\) | −2.20766 | −0.0939642 | ||||||||
\(553\) | −17.0970 | −0.727038 | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 3.35197 | 0.142283 | ||||||||
\(556\) | −11.8682 | −0.503324 | ||||||||
\(557\) | 14.8979 | 0.631245 | 0.315623 | − | 0.948885i | \(-0.397787\pi\) | ||||
0.315623 | + | 0.948885i | \(0.397787\pi\) | |||||||
\(558\) | 17.0074 | 0.719982 | ||||||||
\(559\) | 2.45755 | 0.103943 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −1.55963 | −0.0658476 | ||||||||
\(562\) | 20.8557 | 0.879744 | ||||||||
\(563\) | 39.7536 | 1.67541 | 0.837707 | − | 0.546119i | \(-0.183896\pi\) | ||||
0.837707 | + | 0.546119i | \(0.183896\pi\) | |||||||
\(564\) | 2.04223 | 0.0859934 | ||||||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | −0.330856 | −0.0139069 | ||||||||
\(567\) | −7.53851 | −0.316588 | ||||||||
\(568\) | −14.8557 | −0.623331 | ||||||||
\(569\) | 8.78840 | 0.368429 | 0.184215 | − | 0.982886i | \(-0.441026\pi\) | ||||
0.184215 | + | 0.982886i | \(0.441026\pi\) | |||||||
\(570\) | −2.20766 | −0.0924686 | ||||||||
\(571\) | −5.22877 | −0.218817 | −0.109409 | − | 0.993997i | \(-0.534896\pi\) | ||||
−0.109409 | + | 0.993997i | \(0.534896\pi\) | |||||||
\(572\) | −0.813457 | −0.0340123 | ||||||||
\(573\) | −6.37309 | −0.266239 | ||||||||
\(574\) | −5.59327 | −0.233459 | ||||||||
\(575\) | −5.42784 | −0.226357 | ||||||||
\(576\) | −2.83457 | −0.118107 | ||||||||
\(577\) | 5.80093 | 0.241496 | 0.120748 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120748 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(578\) | 2.29606 | 0.0955034 | ||||||||
\(579\) | 0.880741 | 0.0366024 | ||||||||
\(580\) | −6.61439 | −0.274647 | ||||||||
\(581\) | 8.81346 | 0.365644 | ||||||||
\(582\) | −1.39420 | −0.0577915 | ||||||||
\(583\) | 6.61439 | 0.273940 | ||||||||
\(584\) | 6.20766 | 0.256875 | ||||||||
\(585\) | −2.30580 | −0.0953332 | ||||||||
\(586\) | 3.18654 | 0.131635 | ||||||||
\(587\) | 25.3046 | 1.04443 | 0.522217 | − | 0.852812i | \(-0.325105\pi\) | ||||
0.522217 | + | 0.852812i | \(0.325105\pi\) | |||||||
\(588\) | −0.406728 | −0.0167732 | ||||||||
\(589\) | 32.5671 | 1.34190 | ||||||||
\(590\) | 10.6480 | 0.438372 | ||||||||
\(591\) | −1.14431 | −0.0470707 | ||||||||
\(592\) | 8.24130 | 0.338715 | ||||||||
\(593\) | −23.1729 | −0.951595 | −0.475798 | − | 0.879555i | \(-0.657841\pi\) | ||||
−0.475798 | + | 0.879555i | \(0.657841\pi\) | |||||||
\(594\) | −2.37309 | −0.0973689 | ||||||||
\(595\) | 3.83457 | 0.157202 | ||||||||
\(596\) | −22.2835 | −0.912769 | ||||||||
\(597\) | 5.29606 | 0.216753 | ||||||||
\(598\) | −4.41532 | −0.180556 | ||||||||
\(599\) | −8.48260 | −0.346590 | −0.173295 | − | 0.984870i | \(-0.555441\pi\) | ||||
−0.173295 | + | 0.984870i | \(0.555441\pi\) | |||||||
\(600\) | 0.406728 | 0.0166046 | ||||||||
\(601\) | −32.4490 | −1.32362 | −0.661810 | − | 0.749671i | \(-0.730212\pi\) | ||||
−0.661810 | + | 0.749671i | \(0.730212\pi\) | |||||||
\(602\) | −3.02112 | −0.123131 | ||||||||
\(603\) | −22.6766 | −0.923462 | ||||||||
\(604\) | −3.05476 | −0.124296 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −7.60186 | −0.308804 | ||||||||
\(607\) | −33.9441 | −1.37775 | −0.688874 | − | 0.724881i | \(-0.741895\pi\) | ||||
−0.688874 | + | 0.724881i | \(0.741895\pi\) | |||||||
\(608\) | −5.42784 | −0.220128 | ||||||||
\(609\) | 2.69026 | 0.109015 | ||||||||
\(610\) | 0.978885 | 0.0396339 | ||||||||
\(611\) | 4.08446 | 0.165240 | ||||||||
\(612\) | −10.8694 | −0.439368 | ||||||||
\(613\) | 8.77123 | 0.354267 | 0.177133 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177133 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(614\) | −20.4826 | −0.826610 | ||||||||
\(615\) | −2.27494 | −0.0917345 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −32.1095 | −1.29268 | −0.646340 | − | 0.763049i | \(-0.723701\pi\) | ||||
−0.646340 | + | 0.763049i | \(0.723701\pi\) | |||||||
\(618\) | 6.28863 | 0.252966 | ||||||||
\(619\) | −28.2749 | −1.13647 | −0.568233 | − | 0.822868i | \(-0.692373\pi\) | ||||
−0.568233 | + | 0.822868i | \(0.692373\pi\) | |||||||
\(620\) | −6.00000 | −0.240966 | ||||||||
\(621\) | −12.8807 | −0.516886 | ||||||||
\(622\) | −3.62691 | −0.145426 | ||||||||
\(623\) | 1.18654 | 0.0475378 | ||||||||
\(624\) | 0.330856 | 0.0132448 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −20.7239 | −0.828294 | ||||||||
\(627\) | −2.20766 | −0.0881654 | ||||||||
\(628\) | 4.85569 | 0.193763 | ||||||||
\(629\) | 31.6019 | 1.26005 | ||||||||
\(630\) | 2.83457 | 0.112932 | ||||||||
\(631\) | 34.9230 | 1.39026 | 0.695131 | − | 0.718883i | \(-0.255346\pi\) | ||||
0.695131 | + | 0.718883i | \(0.255346\pi\) | |||||||
\(632\) | −17.0970 | −0.680082 | ||||||||
\(633\) | −8.00000 | −0.317971 | ||||||||
\(634\) | 1.80093 | 0.0715241 | ||||||||
\(635\) | −17.2961 | −0.686373 | ||||||||
\(636\) | −2.69026 | −0.106676 | ||||||||
\(637\) | −0.813457 | −0.0322303 | ||||||||
\(638\) | −6.61439 | −0.261866 | ||||||||
\(639\) | −42.1095 | −1.66583 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −5.25383 | −0.207514 | −0.103757 | − | 0.994603i | \(-0.533086\pi\) | ||||
−0.103757 | + | 0.994603i | \(0.533086\pi\) | |||||||
\(642\) | −4.48260 | −0.176914 | ||||||||
\(643\) | −3.17796 | −0.125326 | −0.0626632 | − | 0.998035i | \(-0.519959\pi\) | ||||
−0.0626632 | + | 0.998035i | \(0.519959\pi\) | |||||||
\(644\) | 5.42784 | 0.213887 | ||||||||
\(645\) | −1.22877 | −0.0483829 | ||||||||
\(646\) | −20.8135 | −0.818895 | ||||||||
\(647\) | 37.9190 | 1.49075 | 0.745375 | − | 0.666645i | \(-0.232270\pi\) | ||||
0.745375 | + | 0.666645i | \(0.232270\pi\) | |||||||
\(648\) | −7.53851 | −0.296141 | ||||||||
\(649\) | 10.6480 | 0.417972 | ||||||||
\(650\) | 0.813457 | 0.0319064 | ||||||||
\(651\) | 2.44037 | 0.0956457 | ||||||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | 29.5374 | 1.15589 | 0.577943 | − | 0.816077i | \(-0.303856\pi\) | ||||
0.577943 | + | 0.816077i | \(0.303856\pi\) | |||||||
\(654\) | 6.60580 | 0.258307 | ||||||||
\(655\) | −9.42784 | −0.368376 | ||||||||
\(656\) | −5.59327 | −0.218381 | ||||||||
\(657\) | 17.5961 | 0.686487 | ||||||||
\(658\) | −5.02112 | −0.195743 | ||||||||
\(659\) | 15.1865 | 0.591584 | 0.295792 | − | 0.955252i | \(-0.404417\pi\) | ||||
0.295792 | + | 0.955252i | \(0.404417\pi\) | |||||||
\(660\) | 0.406728 | 0.0158319 | ||||||||
\(661\) | −44.6766 | −1.73772 | −0.868859 | − | 0.495060i | \(-0.835146\pi\) | ||||
−0.868859 | + | 0.495060i | \(0.835146\pi\) | |||||||
\(662\) | 3.02112 | 0.117419 | ||||||||
\(663\) | 1.26869 | 0.0492719 | ||||||||
\(664\) | 8.81346 | 0.342028 | ||||||||
\(665\) | 5.42784 | 0.210483 | ||||||||
\(666\) | 23.3606 | 0.905203 | ||||||||
\(667\) | −35.9019 | −1.39013 | ||||||||
\(668\) | 8.00000 | 0.309529 | ||||||||
\(669\) | 1.54245 | 0.0596347 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | 0.978885 | 0.0377894 | ||||||||
\(672\) | −0.406728 | −0.0156899 | ||||||||
\(673\) | 38.0000 | 1.46479 | 0.732396 | − | 0.680879i | \(-0.238402\pi\) | ||||
0.732396 | + | 0.680879i | \(0.238402\pi\) | |||||||
\(674\) | 9.66914 | 0.372442 | ||||||||
\(675\) | 2.37309 | 0.0913401 | ||||||||
\(676\) | −12.3383 | −0.474550 | ||||||||
\(677\) | −48.7325 | −1.87294 | −0.936471 | − | 0.350745i | \(-0.885928\pi\) | ||||
−0.936471 | + | 0.350745i | \(0.885928\pi\) | |||||||
\(678\) | −5.69420 | −0.218684 | ||||||||
\(679\) | 3.42784 | 0.131549 | ||||||||
\(680\) | 3.83457 | 0.147049 | ||||||||
\(681\) | 5.71137 | 0.218860 | ||||||||
\(682\) | −6.00000 | −0.229752 | ||||||||
\(683\) | −0.482601 | −0.0184662 | −0.00923310 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923310 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(684\) | −15.3856 | −0.588284 | ||||||||
\(685\) | −13.6691 | −0.522271 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −0.746173 | −0.0284683 | ||||||||
\(688\) | −3.02112 | −0.115179 | ||||||||
\(689\) | −5.38052 | −0.204981 | ||||||||
\(690\) | 2.20766 | 0.0840441 | ||||||||
\(691\) | −25.5037 | −0.970207 | −0.485104 | − | 0.874457i | \(-0.661218\pi\) | ||||
−0.485104 | + | 0.874457i | \(0.661218\pi\) | |||||||
\(692\) | −19.0211 | −0.723074 | ||||||||
\(693\) | 2.83457 | 0.107676 | ||||||||
\(694\) | −9.39420 | −0.356599 | ||||||||
\(695\) | 11.8682 | 0.450187 | ||||||||
\(696\) | 2.69026 | 0.101974 | ||||||||
\(697\) | −21.4478 | −0.812393 | ||||||||
\(698\) | 18.2077 | 0.689170 | ||||||||
\(699\) | 3.27100 | 0.123721 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 33.8682 | 1.27918 | 0.639592 | − | 0.768714i | \(-0.279103\pi\) | ||||
0.639592 | + | 0.768714i | \(0.279103\pi\) | |||||||
\(702\) | 1.93040 | 0.0728584 | ||||||||
\(703\) | 44.7325 | 1.68712 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −2.04223 | −0.0769148 | ||||||||
\(706\) | −12.7239 | −0.478870 | ||||||||
\(707\) | 18.6903 | 0.702920 | ||||||||
\(708\) | −4.33086 | −0.162764 | ||||||||
\(709\) | −15.9749 | −0.599952 | −0.299976 | − | 0.953947i | \(-0.596979\pi\) | ||||
−0.299976 | + | 0.953947i | \(0.596979\pi\) | |||||||
\(710\) | 14.8557 | 0.557524 | ||||||||
\(711\) | −48.4626 | −1.81749 | ||||||||
\(712\) | 1.18654 | 0.0444676 | ||||||||
\(713\) | −32.5671 | −1.21965 | ||||||||
\(714\) | −1.55963 | −0.0583677 | ||||||||
\(715\) | 0.813457 | 0.0304216 | ||||||||
\(716\) | 4.64803 | 0.173705 | ||||||||
\(717\) | 6.29212 | 0.234983 | ||||||||
\(718\) | −29.8432 | −1.11374 | ||||||||
\(719\) | −13.4364 | −0.501094 | −0.250547 | − | 0.968104i | \(-0.580611\pi\) | ||||
−0.250547 | + | 0.968104i | \(0.580611\pi\) | |||||||
\(720\) | 2.83457 | 0.105638 | ||||||||
\(721\) | −15.4615 | −0.575816 | ||||||||
\(722\) | −10.4615 | −0.389336 | ||||||||
\(723\) | −4.73249 | −0.176003 | ||||||||
\(724\) | −25.3383 | −0.941690 | ||||||||
\(725\) | 6.61439 | 0.245652 | ||||||||
\(726\) | 0.406728 | 0.0150951 | ||||||||
\(727\) | 6.64803 | 0.246562 | 0.123281 | − | 0.992372i | \(-0.460658\pi\) | ||||
0.123281 | + | 0.992372i | \(0.460658\pi\) | |||||||
\(728\) | −0.813457 | −0.0301487 | ||||||||
\(729\) | −18.4729 | −0.684180 | ||||||||
\(730\) | −6.20766 | −0.229756 | ||||||||
\(731\) | −11.5847 | −0.428475 | ||||||||
\(732\) | −0.398140 | −0.0147157 | ||||||||
\(733\) | 38.0285 | 1.40462 | 0.702308 | − | 0.711873i | \(-0.252153\pi\) | ||||
0.702308 | + | 0.711873i | \(0.252153\pi\) | |||||||
\(734\) | −15.4615 | −0.570694 | ||||||||
\(735\) | 0.406728 | 0.0150024 | ||||||||
\(736\) | 5.42784 | 0.200073 | ||||||||
\(737\) | 8.00000 | 0.294684 | ||||||||
\(738\) | −15.8545 | −0.583613 | ||||||||
\(739\) | −52.6343 | −1.93619 | −0.968093 | − | 0.250592i | \(-0.919375\pi\) | ||||
−0.968093 | + | 0.250592i | \(0.919375\pi\) | |||||||
\(740\) | −8.24130 | −0.302956 | ||||||||
\(741\) | 1.79583 | 0.0659716 | ||||||||
\(742\) | 6.61439 | 0.242822 | ||||||||
\(743\) | 28.0845 | 1.03032 | 0.515159 | − | 0.857094i | \(-0.327733\pi\) | ||||
0.515159 | + | 0.857094i | \(0.327733\pi\) | |||||||
\(744\) | 2.44037 | 0.0894683 | ||||||||
\(745\) | 22.2835 | 0.816405 | ||||||||
\(746\) | 8.10951 | 0.296910 | ||||||||
\(747\) | 24.9824 | 0.914057 | ||||||||
\(748\) | 3.83457 | 0.140206 | ||||||||
\(749\) | 11.0211 | 0.402703 | ||||||||
\(750\) | −0.406728 | −0.0148516 | ||||||||
\(751\) | 48.4826 | 1.76916 | 0.884578 | − | 0.466393i | \(-0.154447\pi\) | ||||
0.884578 | + | 0.466393i | \(0.154447\pi\) | |||||||
\(752\) | −5.02112 | −0.183101 | ||||||||
\(753\) | −2.17680 | −0.0793270 | ||||||||
\(754\) | 5.38052 | 0.195947 | ||||||||
\(755\) | 3.05476 | 0.111174 | ||||||||
\(756\) | −2.37309 | −0.0863083 | ||||||||
\(757\) | −11.8260 | −0.429823 | −0.214911 | − | 0.976634i | \(-0.568946\pi\) | ||||
−0.214911 | + | 0.976634i | \(0.568946\pi\) | |||||||
\(758\) | −22.0422 | −0.800610 | ||||||||
\(759\) | 2.20766 | 0.0801329 | ||||||||
\(760\) | 5.42784 | 0.196889 | ||||||||
\(761\) | −19.5510 | −0.708725 | −0.354362 | − | 0.935108i | \(-0.615302\pi\) | ||||
−0.354362 | + | 0.935108i | \(0.615302\pi\) | |||||||
\(762\) | 7.03480 | 0.254844 | ||||||||
\(763\) | −16.2413 | −0.587975 | ||||||||
\(764\) | 15.6691 | 0.566890 | ||||||||
\(765\) | 10.8694 | 0.392983 | ||||||||
\(766\) | −38.2499 | −1.38202 | ||||||||
\(767\) | −8.66171 | −0.312756 | ||||||||
\(768\) | −0.406728 | −0.0146765 | ||||||||
\(769\) | 6.07587 | 0.219102 | 0.109551 | − | 0.993981i | \(-0.465059\pi\) | ||||
0.109551 | + | 0.993981i | \(0.465059\pi\) | |||||||
\(770\) | −1.00000 | −0.0360375 | ||||||||
\(771\) | −5.17517 | −0.186379 | ||||||||
\(772\) | −2.16543 | −0.0779355 | ||||||||
\(773\) | −2.33086 | −0.0838351 | −0.0419175 | − | 0.999121i | \(-0.513347\pi\) | ||||
−0.0419175 | + | 0.999121i | \(0.513347\pi\) | |||||||
\(774\) | −8.56357 | −0.307811 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 3.42784 | 0.123052 | ||||||||
\(777\) | 3.35197 | 0.120251 | ||||||||
\(778\) | −16.8557 | −0.604306 | ||||||||
\(779\) | −30.3594 | −1.08774 | ||||||||
\(780\) | −0.330856 | −0.0118465 | ||||||||
\(781\) | 14.8557 | 0.531578 | ||||||||
\(782\) | 20.8135 | 0.744288 | ||||||||
\(783\) | 15.6965 | 0.560948 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −4.85569 | −0.173307 | ||||||||
\(786\) | 3.83457 | 0.136775 | ||||||||
\(787\) | −17.3805 | −0.619549 | −0.309774 | − | 0.950810i | \(-0.600253\pi\) | ||||
−0.309774 | + | 0.950810i | \(0.600253\pi\) | |||||||
\(788\) | 2.81346 | 0.100225 | ||||||||
\(789\) | 0.661712 | 0.0235576 | ||||||||
\(790\) | 17.0970 | 0.608284 | ||||||||
\(791\) | 14.0000 | 0.497783 | ||||||||
\(792\) | 2.83457 | 0.100722 | ||||||||
\(793\) | −0.796281 | −0.0282768 | ||||||||
\(794\) | 4.44037 | 0.157583 | ||||||||
\(795\) | 2.69026 | 0.0954137 | ||||||||
\(796\) | −13.0211 | −0.461521 | ||||||||
\(797\) | −15.6942 | −0.555917 | −0.277959 | − | 0.960593i | \(-0.589658\pi\) | ||||
−0.277959 | + | 0.960593i | \(0.589658\pi\) | |||||||
\(798\) | −2.20766 | −0.0781503 | ||||||||
\(799\) | −19.2538 | −0.681151 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 3.36334 | 0.118838 | ||||||||
\(802\) | 3.46149 | 0.122229 | ||||||||
\(803\) | −6.20766 | −0.219064 | ||||||||
\(804\) | −3.25383 | −0.114754 | ||||||||
\(805\) | −5.42784 | −0.191306 | ||||||||
\(806\) | 4.88074 | 0.171917 | ||||||||
\(807\) | −9.71137 | −0.341857 | ||||||||
\(808\) | 18.6903 | 0.657521 | ||||||||
\(809\) | 23.1443 | 0.813711 | 0.406855 | − | 0.913493i | \(-0.366625\pi\) | ||||
0.406855 | + | 0.913493i | \(0.366625\pi\) | |||||||
\(810\) | 7.53851 | 0.264876 | ||||||||
\(811\) | −27.6218 | −0.969933 | −0.484967 | − | 0.874533i | \(-0.661168\pi\) | ||||
−0.484967 | + | 0.874533i | \(0.661168\pi\) | |||||||
\(812\) | −6.61439 | −0.232119 | ||||||||
\(813\) | −0.992568 | −0.0348109 | ||||||||
\(814\) | −8.24130 | −0.288857 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | −1.55963 | −0.0545980 | ||||||||
\(817\) | −16.3981 | −0.573698 | ||||||||
\(818\) | 17.2624 | 0.603566 | ||||||||
\(819\) | −2.30580 | −0.0805712 | ||||||||
\(820\) | 5.59327 | 0.195326 | ||||||||
\(821\) | −39.5123 | −1.37899 | −0.689494 | − | 0.724291i | \(-0.742167\pi\) | ||||
−0.689494 | + | 0.724291i | \(0.742167\pi\) | |||||||
\(822\) | 5.55963 | 0.193914 | ||||||||
\(823\) | 13.5123 | 0.471009 | 0.235505 | − | 0.971873i | \(-0.424326\pi\) | ||||
0.235505 | + | 0.971873i | \(0.424326\pi\) | |||||||
\(824\) | −15.4615 | −0.538626 | ||||||||
\(825\) | −0.406728 | −0.0141605 | ||||||||
\(826\) | 10.6480 | 0.370492 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 15.3856 | 0.534687 | ||||||||
\(829\) | 13.8346 | 0.480495 | 0.240247 | − | 0.970712i | \(-0.422771\pi\) | ||||
0.240247 | + | 0.970712i | \(0.422771\pi\) | |||||||
\(830\) | −8.81346 | −0.305920 | ||||||||
\(831\) | −8.94803 | −0.310404 | ||||||||
\(832\) | −0.813457 | −0.0282015 | ||||||||
\(833\) | 3.83457 | 0.132860 | ||||||||
\(834\) | −4.82714 | −0.167150 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 5.42784 | 0.187726 | ||||||||
\(837\) | 14.2385 | 0.492155 | ||||||||
\(838\) | −9.02112 | −0.311629 | ||||||||
\(839\) | 44.0422 | 1.52051 | 0.760253 | − | 0.649627i | \(-0.225075\pi\) | ||||
0.760253 | + | 0.649627i | \(0.225075\pi\) | |||||||
\(840\) | 0.406728 | 0.0140335 | ||||||||
\(841\) | 14.7501 | 0.508625 | ||||||||
\(842\) | −31.7114 | −1.09285 | ||||||||
\(843\) | 8.48260 | 0.292156 | ||||||||
\(844\) | 19.6691 | 0.677040 | ||||||||
\(845\) | 12.3383 | 0.424450 | ||||||||
\(846\) | −14.2327 | −0.489331 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 6.61439 | 0.227139 | ||||||||
\(849\) | −0.134569 | −0.00461838 | ||||||||
\(850\) | −3.83457 | −0.131525 | ||||||||
\(851\) | −44.7325 | −1.53341 | ||||||||
\(852\) | −6.04223 | −0.207003 | ||||||||
\(853\) | −29.8095 | −1.02066 | −0.510329 | − | 0.859979i | \(-0.670476\pi\) | ||||
−0.510329 | + | 0.859979i | \(0.670476\pi\) | |||||||
\(854\) | 0.978885 | 0.0334968 | ||||||||
\(855\) | 15.3856 | 0.526177 | ||||||||
\(856\) | 11.0211 | 0.376694 | ||||||||
\(857\) | 42.7575 | 1.46057 | 0.730285 | − | 0.683143i | \(-0.239387\pi\) | ||||
0.730285 | + | 0.683143i | \(0.239387\pi\) | |||||||
\(858\) | −0.330856 | −0.0112952 | ||||||||
\(859\) | 6.31717 | 0.215539 | 0.107770 | − | 0.994176i | \(-0.465629\pi\) | ||||
0.107770 | + | 0.994176i | \(0.465629\pi\) | |||||||
\(860\) | 3.02112 | 0.103019 | ||||||||
\(861\) | −2.27494 | −0.0775298 | ||||||||
\(862\) | 3.05476 | 0.104045 | ||||||||
\(863\) | −48.3680 | −1.64647 | −0.823233 | − | 0.567704i | \(-0.807832\pi\) | ||||
−0.823233 | + | 0.567704i | \(0.807832\pi\) | |||||||
\(864\) | −2.37309 | −0.0807340 | ||||||||
\(865\) | 19.0211 | 0.646737 | ||||||||
\(866\) | −27.9104 | −0.948436 | ||||||||
\(867\) | 0.933872 | 0.0317160 | ||||||||
\(868\) | −6.00000 | −0.203653 | ||||||||
\(869\) | 17.0970 | 0.579976 | ||||||||
\(870\) | −2.69026 | −0.0912083 | ||||||||
\(871\) | −6.50765 | −0.220503 | ||||||||
\(872\) | −16.2413 | −0.550000 | ||||||||
\(873\) | 9.71647 | 0.328853 | ||||||||
\(874\) | 29.4615 | 0.996550 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 2.52483 | 0.0853061 | ||||||||
\(877\) | −24.1940 | −0.816972 | −0.408486 | − | 0.912764i | \(-0.633943\pi\) | ||||
−0.408486 | + | 0.912764i | \(0.633943\pi\) | |||||||
\(878\) | 14.8557 | 0.501355 | ||||||||
\(879\) | 1.29606 | 0.0437149 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 12.3731 | 0.416860 | 0.208430 | − | 0.978037i | \(-0.433165\pi\) | ||||
0.208430 | + | 0.978037i | \(0.433165\pi\) | |||||||
\(882\) | 2.83457 | 0.0954450 | ||||||||
\(883\) | −14.5248 | −0.488799 | −0.244400 | − | 0.969675i | \(-0.578591\pi\) | ||||
−0.244400 | + | 0.969675i | \(0.578591\pi\) | |||||||
\(884\) | −3.11926 | −0.104912 | ||||||||
\(885\) | 4.33086 | 0.145580 | ||||||||
\(886\) | −0.746173 | −0.0250682 | ||||||||
\(887\) | −25.3805 | −0.852194 | −0.426097 | − | 0.904677i | \(-0.640112\pi\) | ||||
−0.426097 | + | 0.904677i | \(0.640112\pi\) | |||||||
\(888\) | 3.35197 | 0.112485 | ||||||||
\(889\) | −17.2961 | −0.580091 | ||||||||
\(890\) | −1.18654 | −0.0397730 | ||||||||
\(891\) | 7.53851 | 0.252550 | ||||||||
\(892\) | −3.79234 | −0.126977 | ||||||||
\(893\) | −27.2538 | −0.912015 | ||||||||
\(894\) | −9.06335 | −0.303124 | ||||||||
\(895\) | −4.64803 | −0.155366 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −1.79583 | −0.0599612 | ||||||||
\(898\) | −9.83457 | −0.328184 | ||||||||
\(899\) | 39.6863 | 1.32361 | ||||||||
\(900\) | −2.83457 | −0.0944857 | ||||||||
\(901\) | 25.3633 | 0.844975 | ||||||||
\(902\) | 5.59327 | 0.186236 | ||||||||
\(903\) | −1.22877 | −0.0408910 | ||||||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 25.3383 | 0.842273 | ||||||||
\(906\) | −1.24246 | −0.0412779 | ||||||||
\(907\) | −7.93272 | −0.263402 | −0.131701 | − | 0.991290i | \(-0.542044\pi\) | ||||
−0.131701 | + | 0.991290i | \(0.542044\pi\) | |||||||
\(908\) | −14.0422 | −0.466008 | ||||||||
\(909\) | 52.9789 | 1.75720 | ||||||||
\(910\) | 0.813457 | 0.0269658 | ||||||||
\(911\) | 43.7364 | 1.44905 | 0.724526 | − | 0.689247i | \(-0.242059\pi\) | ||||
0.724526 | + | 0.689247i | \(0.242059\pi\) | |||||||
\(912\) | −2.20766 | −0.0731029 | ||||||||
\(913\) | −8.81346 | −0.291683 | ||||||||
\(914\) | −11.2961 | −0.373640 | ||||||||
\(915\) | 0.398140 | 0.0131621 | ||||||||
\(916\) | 1.83457 | 0.0606160 | ||||||||
\(917\) | −9.42784 | −0.311335 | ||||||||
\(918\) | −9.09977 | −0.300337 | ||||||||
\(919\) | −32.7661 | −1.08085 | −0.540427 | − | 0.841391i | \(-0.681737\pi\) | ||||
−0.540427 | + | 0.841391i | \(0.681737\pi\) | |||||||
\(920\) | −5.42784 | −0.178951 | ||||||||
\(921\) | −8.33086 | −0.274511 | ||||||||
\(922\) | 7.41926 | 0.244340 | ||||||||
\(923\) | −12.0845 | −0.397765 | ||||||||
\(924\) | 0.406728 | 0.0133804 | ||||||||
\(925\) | 8.24130 | 0.270972 | ||||||||
\(926\) | 10.1740 | 0.334339 | ||||||||
\(927\) | −43.8267 | −1.43946 | ||||||||
\(928\) | −6.61439 | −0.217128 | ||||||||
\(929\) | 59.4478 | 1.95042 | 0.975210 | − | 0.221283i | \(-0.0710246\pi\) | ||||
0.975210 | + | 0.221283i | \(0.0710246\pi\) | |||||||
\(930\) | −2.44037 | −0.0800229 | ||||||||
\(931\) | 5.42784 | 0.177890 | ||||||||
\(932\) | −8.04223 | −0.263432 | ||||||||
\(933\) | −1.47517 | −0.0482949 | ||||||||
\(934\) | 32.4912 | 1.06314 | ||||||||
\(935\) | −3.83457 | −0.125404 | ||||||||
\(936\) | −2.30580 | −0.0753675 | ||||||||
\(937\) | 53.2824 | 1.74066 | 0.870330 | − | 0.492470i | \(-0.163906\pi\) | ||||
0.870330 | + | 0.492470i | \(0.163906\pi\) | |||||||
\(938\) | 8.00000 | 0.261209 | ||||||||
\(939\) | −8.42900 | −0.275070 | ||||||||
\(940\) | 5.02112 | 0.163771 | ||||||||
\(941\) | −5.72506 | −0.186632 | −0.0933158 | − | 0.995637i | \(-0.529747\pi\) | ||||
−0.0933158 | + | 0.995637i | \(0.529747\pi\) | |||||||
\(942\) | 1.97495 | 0.0643472 | ||||||||
\(943\) | 30.3594 | 0.988638 | ||||||||
\(944\) | 10.6480 | 0.346564 | ||||||||
\(945\) | 2.37309 | 0.0771965 | ||||||||
\(946\) | 3.02112 | 0.0982249 | ||||||||
\(947\) | −27.4056 | −0.890561 | −0.445281 | − | 0.895391i | \(-0.646896\pi\) | ||||
−0.445281 | + | 0.895391i | \(0.646896\pi\) | |||||||
\(948\) | −6.95383 | −0.225850 | ||||||||
\(949\) | 5.04966 | 0.163919 | ||||||||
\(950\) | −5.42784 | −0.176102 | ||||||||
\(951\) | 0.732489 | 0.0237526 | ||||||||
\(952\) | 3.83457 | 0.124279 | ||||||||
\(953\) | −10.7998 | −0.349839 | −0.174919 | − | 0.984583i | \(-0.555967\pi\) | ||||
−0.174919 | + | 0.984583i | \(0.555967\pi\) | |||||||
\(954\) | 18.7490 | 0.607020 | ||||||||
\(955\) | −15.6691 | −0.507042 | ||||||||
\(956\) | −15.4701 | −0.500338 | ||||||||
\(957\) | −2.69026 | −0.0869637 | ||||||||
\(958\) | 11.6691 | 0.377013 | ||||||||
\(959\) | −13.6691 | −0.441400 | ||||||||
\(960\) | 0.406728 | 0.0131271 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 6.70394 | 0.216144 | ||||||||
\(963\) | 31.2401 | 1.00670 | ||||||||
\(964\) | 11.6355 | 0.374754 | ||||||||
\(965\) | 2.16543 | 0.0697076 | ||||||||
\(966\) | 2.20766 | 0.0710302 | ||||||||
\(967\) | 11.2538 | 0.361899 | 0.180949 | − | 0.983492i | \(-0.442083\pi\) | ||||
0.180949 | + | 0.983492i | \(0.442083\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −8.46542 | −0.271949 | ||||||||
\(970\) | −3.42784 | −0.110061 | ||||||||
\(971\) | 33.2401 | 1.06673 | 0.533363 | − | 0.845886i | \(-0.320928\pi\) | ||||
0.533363 | + | 0.845886i | \(0.320928\pi\) | |||||||
\(972\) | −10.1854 | −0.326696 | ||||||||
\(973\) | 11.8682 | 0.380477 | ||||||||
\(974\) | 5.49513 | 0.176075 | ||||||||
\(975\) | 0.330856 | 0.0105959 | ||||||||
\(976\) | 0.978885 | 0.0313333 | ||||||||
\(977\) | −2.74617 | −0.0878578 | −0.0439289 | − | 0.999035i | \(-0.513988\pi\) | ||||
−0.0439289 | + | 0.999035i | \(0.513988\pi\) | |||||||
\(978\) | −3.25383 | −0.104046 | ||||||||
\(979\) | −1.18654 | −0.0379221 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −46.0371 | −1.46985 | ||||||||
\(982\) | 13.2961 | 0.424294 | ||||||||
\(983\) | 39.4615 | 1.25863 | 0.629313 | − | 0.777152i | \(-0.283336\pi\) | ||||
0.629313 | + | 0.777152i | \(0.283336\pi\) | |||||||
\(984\) | −2.27494 | −0.0725225 | ||||||||
\(985\) | −2.81346 | −0.0896442 | ||||||||
\(986\) | −25.3633 | −0.807733 | ||||||||
\(987\) | −2.04223 | −0.0650049 | ||||||||
\(988\) | −4.41532 | −0.140470 | ||||||||
\(989\) | 16.3981 | 0.521431 | ||||||||
\(990\) | −2.83457 | −0.0900886 | ||||||||
\(991\) | 20.9652 | 0.665982 | 0.332991 | − | 0.942930i | \(-0.391942\pi\) | ||||
0.332991 | + | 0.942930i | \(0.391942\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | 1.22877 | 0.0389939 | ||||||||
\(994\) | 14.8557 | 0.471194 | ||||||||
\(995\) | 13.0211 | 0.412797 | ||||||||
\(996\) | 3.58468 | 0.113585 | ||||||||
\(997\) | 21.9441 | 0.694976 | 0.347488 | − | 0.937684i | \(-0.387035\pi\) | ||||
0.347488 | + | 0.937684i | \(0.387035\pi\) | |||||||
\(998\) | 24.6480 | 0.780220 | ||||||||
\(999\) | 19.5573 | 0.618766 |
(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 | 770.2.a.l.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 6930.2.a.cl.1.2 | 3 | |||
4.3 | odd | 2 | 6160.2.a.bi.1.2 | 3 | |||
5.2 | odd | 4 | 3850.2.c.z.1849.2 | 6 | |||
5.3 | odd | 4 | 3850.2.c.z.1849.5 | 6 | |||
5.4 | even | 2 | 3850.2.a.bu.1.2 | 3 | |||
7.6 | odd | 2 | 5390.2.a.bz.1.2 | 3 | |||
11.10 | odd | 2 | 8470.2.a.cl.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.l.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3850.2.a.bu.1.2 | 3 | 5.4 | even | 2 | |||
3850.2.c.z.1849.2 | 6 | 5.2 | odd | 4 | |||
3850.2.c.z.1849.5 | 6 | 5.3 | odd | 4 | |||
5390.2.a.bz.1.2 | 3 | 7.6 | odd | 2 | |||
6160.2.a.bi.1.2 | 3 | 4.3 | odd | 2 | |||
6930.2.a.cl.1.2 | 3 | 3.2 | odd | 2 | |||
8470.2.a.cl.1.2 | 3 | 11.10 | odd | 2 |