Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.167449\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.167449 | 0.118404 | 0.0592022 | − | 0.998246i | \(-0.481144\pi\) | ||||
0.0592022 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.97196 | −0.985980 | ||||||||
\(5\) | 3.80451 | 1.70143 | 0.850715 | − | 0.525628i | \(-0.176170\pi\) | ||||
0.850715 | + | 0.525628i | \(0.176170\pi\) | |||||||
\(6\) | −0.167449 | −0.0683608 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.665102 | −0.235149 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.637062 | 0.201457 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.97196 | 0.569256 | ||||||||
\(13\) | −3.80451 | −1.05518 | −0.527591 | − | 0.849499i | \(-0.676905\pi\) | ||||
−0.527591 | + | 0.849499i | \(0.676905\pi\) | |||||||
\(14\) | 0.167449 | 0.0447527 | ||||||||
\(15\) | −3.80451 | −0.982321 | ||||||||
\(16\) | 3.83255 | 0.958138 | ||||||||
\(17\) | −0.334898 | −0.0812248 | −0.0406124 | − | 0.999175i | \(-0.512931\pi\) | ||||
−0.0406124 | + | 0.999175i | \(0.512931\pi\) | |||||||
\(18\) | 0.167449 | 0.0394682 | ||||||||
\(19\) | −8.13941 | −1.86731 | −0.933654 | − | 0.358175i | \(-0.883399\pi\) | ||||
−0.933654 | + | 0.358175i | \(0.883399\pi\) | |||||||
\(20\) | −7.50235 | −1.67758 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.66510 | −0.347198 | −0.173599 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173599 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(24\) | 0.665102 | 0.135763 | ||||||||
\(25\) | 9.47431 | 1.89486 | ||||||||
\(26\) | −0.637062 | −0.124938 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.97196 | −0.372666 | ||||||||
\(29\) | −0.195488 | −0.0363013 | −0.0181506 | − | 0.999835i | \(-0.505778\pi\) | ||||
−0.0181506 | + | 0.999835i | \(0.505778\pi\) | |||||||
\(30\) | −0.637062 | −0.116311 | ||||||||
\(31\) | −9.94392 | −1.78598 | −0.892991 | − | 0.450075i | \(-0.851397\pi\) | ||||
−0.892991 | + | 0.450075i | \(0.851397\pi\) | |||||||
\(32\) | 1.97196 | 0.348597 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.0560785 | −0.00961738 | ||||||||
\(35\) | 3.80451 | 0.643080 | ||||||||
\(36\) | −1.97196 | −0.328660 | ||||||||
\(37\) | −4.47431 | −0.735572 | −0.367786 | − | 0.929911i | \(-0.619884\pi\) | ||||
−0.367786 | + | 0.929911i | \(0.619884\pi\) | |||||||
\(38\) | −1.36294 | −0.221098 | ||||||||
\(39\) | 3.80451 | 0.609209 | ||||||||
\(40\) | −2.53039 | −0.400089 | ||||||||
\(41\) | 6.27882 | 0.980587 | 0.490293 | − | 0.871557i | \(-0.336890\pi\) | ||||
0.490293 | + | 0.871557i | \(0.336890\pi\) | |||||||
\(42\) | −0.167449 | −0.0258380 | ||||||||
\(43\) | −2.33490 | −0.356069 | −0.178034 | − | 0.984024i | \(-0.556974\pi\) | ||||
−0.178034 | + | 0.984024i | \(0.556974\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.80451 | 0.567143 | ||||||||
\(46\) | −0.278820 | −0.0411098 | ||||||||
\(47\) | −12.1394 | −1.77071 | −0.885357 | − | 0.464911i | \(-0.846086\pi\) | ||||
−0.885357 | + | 0.464911i | \(0.846086\pi\) | |||||||
\(48\) | −3.83255 | −0.553181 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.58647 | 0.224360 | ||||||||
\(51\) | 0.334898 | 0.0468952 | ||||||||
\(52\) | 7.50235 | 1.04039 | ||||||||
\(53\) | 7.94392 | 1.09118 | 0.545591 | − | 0.838052i | \(-0.316305\pi\) | ||||
0.545591 | + | 0.838052i | \(0.316305\pi\) | |||||||
\(54\) | −0.167449 | −0.0227869 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.665102 | −0.0888779 | ||||||||
\(57\) | 8.13941 | 1.07809 | ||||||||
\(58\) | −0.0327344 | −0.00429823 | ||||||||
\(59\) | 3.74843 | 0.488004 | 0.244002 | − | 0.969775i | \(-0.421540\pi\) | ||||
0.244002 | + | 0.969775i | \(0.421540\pi\) | |||||||
\(60\) | 7.50235 | 0.968549 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | −1.66510 | −0.211468 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −7.33490 | −0.916862 | ||||||||
\(65\) | −14.4743 | −1.79532 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.139410 | −0.0170316 | −0.00851582 | − | 0.999964i | \(-0.502711\pi\) | ||||
−0.00851582 | + | 0.999964i | \(0.502711\pi\) | |||||||
\(68\) | 0.660406 | 0.0800860 | ||||||||
\(69\) | 1.66510 | 0.200455 | ||||||||
\(70\) | 0.637062 | 0.0761435 | ||||||||
\(71\) | 4.66980 | 0.554203 | 0.277101 | − | 0.960841i | \(-0.410626\pi\) | ||||
0.277101 | + | 0.960841i | \(0.410626\pi\) | |||||||
\(72\) | −0.665102 | −0.0783830 | ||||||||
\(73\) | −4.19549 | −0.491045 | −0.245522 | − | 0.969391i | \(-0.578959\pi\) | ||||
−0.245522 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(74\) | −0.749219 | −0.0870950 | ||||||||
\(75\) | −9.47431 | −1.09400 | ||||||||
\(76\) | 16.0506 | 1.84113 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.637062 | 0.0721331 | ||||||||
\(79\) | −3.33020 | −0.374677 | −0.187339 | − | 0.982295i | \(-0.559986\pi\) | ||||
−0.187339 | + | 0.982295i | \(0.559986\pi\) | |||||||
\(80\) | 14.5810 | 1.63020 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.05138 | 0.116106 | ||||||||
\(83\) | 13.9439 | 1.53054 | 0.765272 | − | 0.643707i | \(-0.222604\pi\) | ||||
0.765272 | + | 0.643707i | \(0.222604\pi\) | |||||||
\(84\) | 1.97196 | 0.215159 | ||||||||
\(85\) | −1.27412 | −0.138198 | ||||||||
\(86\) | −0.390977 | −0.0421601 | ||||||||
\(87\) | 0.195488 | 0.0209586 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.88784 | −1.04811 | −0.524055 | − | 0.851685i | \(-0.675581\pi\) | ||||
−0.524055 | + | 0.851685i | \(0.675581\pi\) | |||||||
\(90\) | 0.637062 | 0.0671523 | ||||||||
\(91\) | −3.80451 | −0.398821 | ||||||||
\(92\) | 3.28352 | 0.342330 | ||||||||
\(93\) | 9.94392 | 1.03114 | ||||||||
\(94\) | −2.03273 | −0.209661 | ||||||||
\(95\) | −30.9665 | −3.17709 | ||||||||
\(96\) | −1.97196 | −0.201262 | ||||||||
\(97\) | 0.0560785 | 0.00569391 | 0.00284695 | − | 0.999996i | \(-0.499094\pi\) | ||||
0.00284695 | + | 0.999996i | \(0.499094\pi\) | |||||||
\(98\) | 0.167449 | 0.0169149 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.6830 | −1.86830 | ||||||||
\(101\) | 18.8831 | 1.87894 | 0.939472 | − | 0.342626i | \(-0.111317\pi\) | ||||
0.939472 | + | 0.342626i | \(0.111317\pi\) | |||||||
\(102\) | 0.0560785 | 0.00555260 | ||||||||
\(103\) | −8.27882 | −0.815736 | −0.407868 | − | 0.913041i | \(-0.633728\pi\) | ||||
−0.407868 | + | 0.913041i | \(0.633728\pi\) | |||||||
\(104\) | 2.53039 | 0.248125 | ||||||||
\(105\) | −3.80451 | −0.371282 | ||||||||
\(106\) | 1.33020 | 0.129201 | ||||||||
\(107\) | 8.13941 | 0.786866 | 0.393433 | − | 0.919353i | \(-0.371287\pi\) | ||||
0.393433 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(108\) | 1.97196 | 0.189752 | ||||||||
\(109\) | −11.5529 | −1.10657 | −0.553286 | − | 0.832992i | \(-0.686626\pi\) | ||||
−0.553286 | + | 0.832992i | \(0.686626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.47431 | 0.424683 | ||||||||
\(112\) | 3.83255 | 0.362142 | ||||||||
\(113\) | −1.33020 | −0.125135 | −0.0625675 | − | 0.998041i | \(-0.519929\pi\) | ||||
−0.0625675 | + | 0.998041i | \(0.519929\pi\) | |||||||
\(114\) | 1.36294 | 0.127651 | ||||||||
\(115\) | −6.33490 | −0.590732 | ||||||||
\(116\) | 0.385496 | 0.0357924 | ||||||||
\(117\) | −3.80451 | −0.351727 | ||||||||
\(118\) | 0.627672 | 0.0577819 | ||||||||
\(119\) | −0.334898 | −0.0307001 | ||||||||
\(120\) | 2.53039 | 0.230992 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.00470 | −0.0909608 | ||||||||
\(123\) | −6.27882 | −0.566142 | ||||||||
\(124\) | 19.6090 | 1.76094 | ||||||||
\(125\) | 17.0226 | 1.52254 | ||||||||
\(126\) | 0.167449 | 0.0149176 | ||||||||
\(127\) | −14.6137 | −1.29676 | −0.648379 | − | 0.761318i | \(-0.724553\pi\) | ||||
−0.648379 | + | 0.761318i | \(0.724553\pi\) | |||||||
\(128\) | −5.17214 | −0.457157 | ||||||||
\(129\) | 2.33490 | 0.205576 | ||||||||
\(130\) | −2.42371 | −0.212574 | ||||||||
\(131\) | −20.5576 | −1.79613 | −0.898065 | − | 0.439863i | \(-0.855027\pi\) | ||||
−0.898065 | + | 0.439863i | \(0.855027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.13941 | −0.705776 | ||||||||
\(134\) | −0.0233441 | −0.00201662 | ||||||||
\(135\) | −3.80451 | −0.327440 | ||||||||
\(136\) | 0.222741 | 0.0190999 | ||||||||
\(137\) | −16.2227 | −1.38600 | −0.693001 | − | 0.720936i | \(-0.743712\pi\) | ||||
−0.693001 | + | 0.720936i | \(0.743712\pi\) | |||||||
\(138\) | 0.278820 | 0.0237347 | ||||||||
\(139\) | −22.5482 | −1.91252 | −0.956259 | − | 0.292522i | \(-0.905506\pi\) | ||||
−0.956259 | + | 0.292522i | \(0.905506\pi\) | |||||||
\(140\) | −7.50235 | −0.634064 | ||||||||
\(141\) | 12.1394 | 1.02232 | ||||||||
\(142\) | 0.781954 | 0.0656201 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.83255 | 0.319379 | ||||||||
\(145\) | −0.743738 | −0.0617641 | ||||||||
\(146\) | −0.702531 | −0.0581419 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 8.82316 | 0.725259 | ||||||||
\(149\) | −8.19549 | −0.671401 | −0.335700 | − | 0.941969i | \(-0.608973\pi\) | ||||
−0.335700 | + | 0.941969i | \(0.608973\pi\) | |||||||
\(150\) | −1.58647 | −0.129534 | ||||||||
\(151\) | 13.2741 | 1.08023 | 0.540116 | − | 0.841590i | \(-0.318380\pi\) | ||||
0.540116 | + | 0.841590i | \(0.318380\pi\) | |||||||
\(152\) | 5.41353 | 0.439096 | ||||||||
\(153\) | −0.334898 | −0.0270749 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.8318 | −3.03872 | ||||||||
\(156\) | −7.50235 | −0.600669 | ||||||||
\(157\) | −16.9392 | −1.35190 | −0.675949 | − | 0.736949i | \(-0.736266\pi\) | ||||
−0.675949 | + | 0.736949i | \(0.736266\pi\) | |||||||
\(158\) | −0.557640 | −0.0443634 | ||||||||
\(159\) | −7.94392 | −0.629994 | ||||||||
\(160\) | 7.50235 | 0.593113 | ||||||||
\(161\) | −1.66510 | −0.131228 | ||||||||
\(162\) | 0.167449 | 0.0131561 | ||||||||
\(163\) | −6.79982 | −0.532603 | −0.266301 | − | 0.963890i | \(-0.585802\pi\) | ||||
−0.266301 | + | 0.963890i | \(0.585802\pi\) | |||||||
\(164\) | −12.3816 | −0.966839 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.33490 | 0.181223 | ||||||||
\(167\) | 18.2227 | 1.41012 | 0.705059 | − | 0.709149i | \(-0.250920\pi\) | ||||
0.705059 | + | 0.709149i | \(0.250920\pi\) | |||||||
\(168\) | 0.665102 | 0.0513137 | ||||||||
\(169\) | 1.47431 | 0.113408 | ||||||||
\(170\) | −0.213351 | −0.0163633 | ||||||||
\(171\) | −8.13941 | −0.622436 | ||||||||
\(172\) | 4.60433 | 0.351077 | ||||||||
\(173\) | 1.72118 | 0.130859 | 0.0654294 | − | 0.997857i | \(-0.479158\pi\) | ||||
0.0654294 | + | 0.997857i | \(0.479158\pi\) | |||||||
\(174\) | 0.0327344 | 0.00248159 | ||||||||
\(175\) | 9.47431 | 0.716190 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.74843 | −0.281749 | ||||||||
\(178\) | −1.65571 | −0.124101 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | −7.50235 | −0.559192 | ||||||||
\(181\) | 0.725875 | 0.0539539 | 0.0269769 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269769 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(182\) | −0.637062 | −0.0472222 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 1.10746 | 0.0816432 | ||||||||
\(185\) | −17.0226 | −1.25152 | ||||||||
\(186\) | 1.66510 | 0.122091 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 23.9384 | 1.74589 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −5.18531 | −0.376182 | ||||||||
\(191\) | 5.27412 | 0.381622 | 0.190811 | − | 0.981627i | \(-0.438888\pi\) | ||||
0.190811 | + | 0.981627i | \(0.438888\pi\) | |||||||
\(192\) | 7.33490 | 0.529351 | ||||||||
\(193\) | 19.8318 | 1.42752 | 0.713761 | − | 0.700390i | \(-0.246990\pi\) | ||||
0.713761 | + | 0.700390i | \(0.246990\pi\) | |||||||
\(194\) | 0.00939029 | 0.000674184 0 | ||||||||
\(195\) | 14.4743 | 1.03653 | ||||||||
\(196\) | −1.97196 | −0.140854 | ||||||||
\(197\) | −2.66980 | −0.190215 | −0.0951076 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951076 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5529 | 0.960743 | 0.480371 | − | 0.877065i | \(-0.340502\pi\) | ||||
0.480371 | + | 0.877065i | \(0.340502\pi\) | |||||||
\(200\) | −6.30138 | −0.445575 | ||||||||
\(201\) | 0.139410 | 0.00983322 | ||||||||
\(202\) | 3.16197 | 0.222475 | ||||||||
\(203\) | −0.195488 | −0.0137206 | ||||||||
\(204\) | −0.660406 | −0.0462377 | ||||||||
\(205\) | 23.8878 | 1.66840 | ||||||||
\(206\) | −1.38628 | −0.0965868 | ||||||||
\(207\) | −1.66510 | −0.115733 | ||||||||
\(208\) | −14.5810 | −1.01101 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.637062 | −0.0439615 | ||||||||
\(211\) | 4.27882 | 0.294566 | 0.147283 | − | 0.989094i | \(-0.452947\pi\) | ||||
0.147283 | + | 0.989094i | \(0.452947\pi\) | |||||||
\(212\) | −15.6651 | −1.07588 | ||||||||
\(213\) | −4.66980 | −0.319969 | ||||||||
\(214\) | 1.36294 | 0.0931685 | ||||||||
\(215\) | −8.88315 | −0.605826 | ||||||||
\(216\) | 0.665102 | 0.0452544 | ||||||||
\(217\) | −9.94392 | −0.675037 | ||||||||
\(218\) | −1.93453 | −0.131023 | ||||||||
\(219\) | 4.19549 | 0.283505 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.27412 | 0.0857069 | ||||||||
\(222\) | 0.749219 | 0.0502843 | ||||||||
\(223\) | −10.2694 | −0.687692 | −0.343846 | − | 0.939026i | \(-0.611730\pi\) | ||||
−0.343846 | + | 0.939026i | \(0.611730\pi\) | |||||||
\(224\) | 1.97196 | 0.131757 | ||||||||
\(225\) | 9.47431 | 0.631621 | ||||||||
\(226\) | −0.222741 | −0.0148165 | ||||||||
\(227\) | 0.390977 | 0.0259500 | 0.0129750 | − | 0.999916i | \(-0.495870\pi\) | ||||
0.0129750 | + | 0.999916i | \(0.495870\pi\) | |||||||
\(228\) | −16.0506 | −1.06298 | ||||||||
\(229\) | 7.94392 | 0.524949 | 0.262475 | − | 0.964939i | \(-0.415461\pi\) | ||||
0.262475 | + | 0.964939i | \(0.415461\pi\) | |||||||
\(230\) | −1.06077 | −0.0699453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.130020 | 0.00853621 | ||||||||
\(233\) | −26.5576 | −1.73985 | −0.869924 | − | 0.493185i | \(-0.835833\pi\) | ||||
−0.869924 | + | 0.493185i | \(0.835833\pi\) | |||||||
\(234\) | −0.637062 | −0.0416461 | ||||||||
\(235\) | −46.1845 | −3.01275 | ||||||||
\(236\) | −7.39176 | −0.481163 | ||||||||
\(237\) | 3.33020 | 0.216320 | ||||||||
\(238\) | −0.0560785 | −0.00363503 | ||||||||
\(239\) | −10.7998 | −0.698582 | −0.349291 | − | 0.937014i | \(-0.613578\pi\) | ||||
−0.349291 | + | 0.937014i | \(0.613578\pi\) | |||||||
\(240\) | −14.5810 | −0.941198 | ||||||||
\(241\) | 12.0833 | 0.778356 | 0.389178 | − | 0.921163i | \(-0.372759\pi\) | ||||
0.389178 | + | 0.921163i | \(0.372759\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.8318 | 0.757451 | ||||||||
\(245\) | 3.80451 | 0.243061 | ||||||||
\(246\) | −1.05138 | −0.0670338 | ||||||||
\(247\) | 30.9665 | 1.97035 | ||||||||
\(248\) | 6.61372 | 0.419972 | ||||||||
\(249\) | −13.9439 | −0.883660 | ||||||||
\(250\) | 2.85041 | 0.180276 | ||||||||
\(251\) | 4.80921 | 0.303554 | 0.151777 | − | 0.988415i | \(-0.451500\pi\) | ||||
0.151777 | + | 0.988415i | \(0.451500\pi\) | |||||||
\(252\) | −1.97196 | −0.124222 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.44706 | −0.153542 | ||||||||
\(255\) | 1.27412 | 0.0797888 | ||||||||
\(256\) | 13.8037 | 0.862733 | ||||||||
\(257\) | −16.7531 | −1.04503 | −0.522516 | − | 0.852630i | \(-0.675006\pi\) | ||||
−0.522516 | + | 0.852630i | \(0.675006\pi\) | |||||||
\(258\) | 0.390977 | 0.0243412 | ||||||||
\(259\) | −4.47431 | −0.278020 | ||||||||
\(260\) | 28.5428 | 1.77015 | ||||||||
\(261\) | −0.195488 | −0.0121004 | ||||||||
\(262\) | −3.44236 | −0.212670 | ||||||||
\(263\) | 12.1394 | 0.748548 | 0.374274 | − | 0.927318i | \(-0.377892\pi\) | ||||
0.374274 | + | 0.927318i | \(0.377892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.2227 | 1.85657 | ||||||||
\(266\) | −1.36294 | −0.0835671 | ||||||||
\(267\) | 9.88784 | 0.605126 | ||||||||
\(268\) | 0.274911 | 0.0167929 | ||||||||
\(269\) | −25.2180 | −1.53757 | −0.768786 | − | 0.639506i | \(-0.779139\pi\) | ||||
−0.768786 | + | 0.639506i | \(0.779139\pi\) | |||||||
\(270\) | −0.637062 | −0.0387704 | ||||||||
\(271\) | −4.13941 | −0.251451 | −0.125726 | − | 0.992065i | \(-0.540126\pi\) | ||||
−0.125726 | + | 0.992065i | \(0.540126\pi\) | |||||||
\(272\) | −1.28352 | −0.0778245 | ||||||||
\(273\) | 3.80451 | 0.230260 | ||||||||
\(274\) | −2.71648 | −0.164109 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.28352 | −0.197644 | ||||||||
\(277\) | 18.2788 | 1.09827 | 0.549134 | − | 0.835734i | \(-0.314958\pi\) | ||||
0.549134 | + | 0.835734i | \(0.314958\pi\) | |||||||
\(278\) | −3.77569 | −0.226451 | ||||||||
\(279\) | −9.94392 | −0.595327 | ||||||||
\(280\) | −2.53039 | −0.151220 | ||||||||
\(281\) | −6.74374 | −0.402298 | −0.201149 | − | 0.979561i | \(-0.564467\pi\) | ||||
−0.201149 | + | 0.979561i | \(0.564467\pi\) | |||||||
\(282\) | 2.03273 | 0.121048 | ||||||||
\(283\) | −23.3575 | −1.38846 | −0.694228 | − | 0.719755i | \(-0.744254\pi\) | ||||
−0.694228 | + | 0.719755i | \(0.744254\pi\) | |||||||
\(284\) | −9.20866 | −0.546433 | ||||||||
\(285\) | 30.9665 | 1.83430 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.27882 | 0.370627 | ||||||||
\(288\) | 1.97196 | 0.116199 | ||||||||
\(289\) | −16.8878 | −0.993403 | ||||||||
\(290\) | −0.124538 | −0.00731314 | ||||||||
\(291\) | −0.0560785 | −0.00328738 | ||||||||
\(292\) | 8.27334 | 0.484161 | ||||||||
\(293\) | 14.1667 | 0.827625 | 0.413813 | − | 0.910362i | \(-0.364197\pi\) | ||||
0.413813 | + | 0.910362i | \(0.364197\pi\) | |||||||
\(294\) | −0.167449 | −0.00976584 | ||||||||
\(295\) | 14.2610 | 0.830305 | ||||||||
\(296\) | 2.97587 | 0.172969 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.37233 | −0.0794968 | ||||||||
\(299\) | 6.33490 | 0.366357 | ||||||||
\(300\) | 18.6830 | 1.07866 | ||||||||
\(301\) | −2.33490 | −0.134581 | ||||||||
\(302\) | 2.22274 | 0.127904 | ||||||||
\(303\) | −18.8831 | −1.08481 | ||||||||
\(304\) | −31.1947 | −1.78914 | ||||||||
\(305\) | −22.8271 | −1.30707 | ||||||||
\(306\) | −0.0560785 | −0.00320579 | ||||||||
\(307\) | 12.5576 | 0.716702 | 0.358351 | − | 0.933587i | \(-0.383339\pi\) | ||||
0.358351 | + | 0.933587i | \(0.383339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.27882 | 0.470966 | ||||||||
\(310\) | −6.33490 | −0.359798 | ||||||||
\(311\) | 9.33959 | 0.529600 | 0.264800 | − | 0.964303i | \(-0.414694\pi\) | ||||
0.264800 | + | 0.964303i | \(0.414694\pi\) | |||||||
\(312\) | −2.53039 | −0.143255 | ||||||||
\(313\) | −2.99530 | −0.169305 | −0.0846523 | − | 0.996411i | \(-0.526978\pi\) | ||||
−0.0846523 | + | 0.996411i | \(0.526978\pi\) | |||||||
\(314\) | −2.83646 | −0.160071 | ||||||||
\(315\) | 3.80451 | 0.214360 | ||||||||
\(316\) | 6.56703 | 0.369424 | ||||||||
\(317\) | 9.93453 | 0.557979 | 0.278989 | − | 0.960294i | \(-0.410001\pi\) | ||||
0.278989 | + | 0.960294i | \(0.410001\pi\) | |||||||
\(318\) | −1.33020 | −0.0745941 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −27.9057 | −1.55998 | ||||||||
\(321\) | −8.13941 | −0.454298 | ||||||||
\(322\) | −0.278820 | −0.0155380 | ||||||||
\(323\) | 2.72588 | 0.151672 | ||||||||
\(324\) | −1.97196 | −0.109553 | ||||||||
\(325\) | −36.0451 | −1.99942 | ||||||||
\(326\) | −1.13862 | −0.0630625 | ||||||||
\(327\) | 11.5529 | 0.638879 | ||||||||
\(328\) | −4.17605 | −0.230584 | ||||||||
\(329\) | −12.1394 | −0.669267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5482 | 1.23936 | 0.619682 | − | 0.784853i | \(-0.287262\pi\) | ||||
0.619682 | + | 0.784853i | \(0.287262\pi\) | |||||||
\(332\) | −27.4969 | −1.50909 | ||||||||
\(333\) | −4.47431 | −0.245191 | ||||||||
\(334\) | 3.05138 | 0.166964 | ||||||||
\(335\) | −0.530387 | −0.0289781 | ||||||||
\(336\) | −3.83255 | −0.209083 | ||||||||
\(337\) | −13.2835 | −0.723599 | −0.361800 | − | 0.932256i | \(-0.617838\pi\) | ||||
−0.361800 | + | 0.932256i | \(0.617838\pi\) | |||||||
\(338\) | 0.246872 | 0.0134281 | ||||||||
\(339\) | 1.33020 | 0.0722467 | ||||||||
\(340\) | 2.51252 | 0.136261 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.36294 | −0.0736992 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.55294 | 0.0837292 | ||||||||
\(345\) | 6.33490 | 0.341059 | ||||||||
\(346\) | 0.288210 | 0.0154943 | ||||||||
\(347\) | 27.7757 | 1.49108 | 0.745538 | − | 0.666463i | \(-0.232192\pi\) | ||||
0.745538 | + | 0.666463i | \(0.232192\pi\) | |||||||
\(348\) | −0.385496 | −0.0206647 | ||||||||
\(349\) | 2.85589 | 0.152873 | 0.0764363 | − | 0.997074i | \(-0.475646\pi\) | ||||
0.0764363 | + | 0.997074i | \(0.475646\pi\) | |||||||
\(350\) | 1.58647 | 0.0848001 | ||||||||
\(351\) | 3.80451 | 0.203070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.6410 | 1.31151 | 0.655753 | − | 0.754975i | \(-0.272351\pi\) | ||||
0.655753 | + | 0.754975i | \(0.272351\pi\) | |||||||
\(354\) | −0.627672 | −0.0333604 | ||||||||
\(355\) | 17.7663 | 0.942937 | ||||||||
\(356\) | 19.4984 | 1.03342 | ||||||||
\(357\) | 0.334898 | 0.0177247 | ||||||||
\(358\) | −2.00939 | −0.106200 | ||||||||
\(359\) | 11.8878 | 0.627416 | 0.313708 | − | 0.949519i | \(-0.398429\pi\) | ||||
0.313708 | + | 0.949519i | \(0.398429\pi\) | |||||||
\(360\) | −2.53039 | −0.133363 | ||||||||
\(361\) | 47.2500 | 2.48684 | ||||||||
\(362\) | 0.121547 | 0.00638838 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.50235 | 0.393230 | ||||||||
\(365\) | −15.9618 | −0.835478 | ||||||||
\(366\) | 1.00470 | 0.0525163 | ||||||||
\(367\) | 3.60902 | 0.188389 | 0.0941947 | − | 0.995554i | \(-0.469972\pi\) | ||||
0.0941947 | + | 0.995554i | \(0.469972\pi\) | |||||||
\(368\) | −6.38159 | −0.332663 | ||||||||
\(369\) | 6.27882 | 0.326862 | ||||||||
\(370\) | −2.85041 | −0.148186 | ||||||||
\(371\) | 7.94392 | 0.412428 | ||||||||
\(372\) | −19.6090 | −1.01668 | ||||||||
\(373\) | −12.3349 | −0.638677 | −0.319338 | − | 0.947641i | \(-0.603461\pi\) | ||||
−0.319338 | + | 0.947641i | \(0.603461\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.0226 | −0.879041 | ||||||||
\(376\) | 8.07394 | 0.416382 | ||||||||
\(377\) | 0.743738 | 0.0383045 | ||||||||
\(378\) | −0.167449 | −0.00861266 | ||||||||
\(379\) | 23.3575 | 1.19979 | 0.599896 | − | 0.800078i | \(-0.295209\pi\) | ||||
0.599896 | + | 0.800078i | \(0.295209\pi\) | |||||||
\(380\) | 61.0647 | 3.13255 | ||||||||
\(381\) | 14.6137 | 0.748683 | ||||||||
\(382\) | 0.883148 | 0.0451858 | ||||||||
\(383\) | −15.2180 | −0.777606 | −0.388803 | − | 0.921321i | \(-0.627111\pi\) | ||||
−0.388803 | + | 0.921321i | \(0.627111\pi\) | |||||||
\(384\) | 5.17214 | 0.263940 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.32081 | 0.169025 | ||||||||
\(387\) | −2.33490 | −0.118690 | ||||||||
\(388\) | −0.110585 | −0.00561408 | ||||||||
\(389\) | 3.73057 | 0.189147 | 0.0945737 | − | 0.995518i | \(-0.469851\pi\) | ||||
0.0945737 | + | 0.995518i | \(0.469851\pi\) | |||||||
\(390\) | 2.42371 | 0.122729 | ||||||||
\(391\) | 0.557640 | 0.0282011 | ||||||||
\(392\) | −0.665102 | −0.0335927 | ||||||||
\(393\) | 20.5576 | 1.03700 | ||||||||
\(394\) | −0.447055 | −0.0225223 | ||||||||
\(395\) | −12.6698 | −0.637487 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8925 | 1.04857 | 0.524283 | − | 0.851544i | \(-0.324333\pi\) | ||||
0.524283 | + | 0.851544i | \(0.324333\pi\) | |||||||
\(398\) | 2.26943 | 0.113756 | ||||||||
\(399\) | 8.13941 | 0.407480 | ||||||||
\(400\) | 36.3108 | 1.81554 | ||||||||
\(401\) | 23.2741 | 1.16225 | 0.581127 | − | 0.813813i | \(-0.302612\pi\) | ||||
0.581127 | + | 0.813813i | \(0.302612\pi\) | |||||||
\(402\) | 0.0233441 | 0.00116430 | ||||||||
\(403\) | 37.8318 | 1.88453 | ||||||||
\(404\) | −37.2368 | −1.85260 | ||||||||
\(405\) | 3.80451 | 0.189048 | ||||||||
\(406\) | −0.0327344 | −0.00162458 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.222741 | −0.0110273 | ||||||||
\(409\) | 23.8972 | 1.18164 | 0.590821 | − | 0.806803i | \(-0.298804\pi\) | ||||
0.590821 | + | 0.806803i | \(0.298804\pi\) | |||||||
\(410\) | 4.00000 | 0.197546 | ||||||||
\(411\) | 16.2227 | 0.800209 | ||||||||
\(412\) | 16.3255 | 0.804300 | ||||||||
\(413\) | 3.74843 | 0.184448 | ||||||||
\(414\) | −0.278820 | −0.0137033 | ||||||||
\(415\) | 53.0498 | 2.60411 | ||||||||
\(416\) | −7.50235 | −0.367833 | ||||||||
\(417\) | 22.5482 | 1.10419 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.2967 | −1.48009 | −0.740045 | − | 0.672557i | \(-0.765196\pi\) | ||||
−0.740045 | + | 0.672557i | \(0.765196\pi\) | |||||||
\(420\) | 7.50235 | 0.366077 | ||||||||
\(421\) | −15.5257 | −0.756676 | −0.378338 | − | 0.925668i | \(-0.623504\pi\) | ||||
−0.378338 | + | 0.925668i | \(0.623504\pi\) | |||||||
\(422\) | 0.716485 | 0.0348779 | ||||||||
\(423\) | −12.1394 | −0.590238 | ||||||||
\(424\) | −5.28352 | −0.256590 | ||||||||
\(425\) | −3.17293 | −0.153910 | ||||||||
\(426\) | −0.781954 | −0.0378858 | ||||||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | −16.0506 | −0.775835 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.48748 | −0.0717325 | ||||||||
\(431\) | −3.07864 | −0.148293 | −0.0741463 | − | 0.997247i | \(-0.523623\pi\) | ||||
−0.0741463 | + | 0.997247i | \(0.523623\pi\) | |||||||
\(432\) | −3.83255 | −0.184394 | ||||||||
\(433\) | 16.9392 | 0.814047 | 0.407024 | − | 0.913418i | \(-0.366567\pi\) | ||||
0.407024 | + | 0.913418i | \(0.366567\pi\) | |||||||
\(434\) | −1.66510 | −0.0799274 | ||||||||
\(435\) | 0.743738 | 0.0356595 | ||||||||
\(436\) | 22.7820 | 1.09106 | ||||||||
\(437\) | 13.5529 | 0.648325 | ||||||||
\(438\) | 0.702531 | 0.0335682 | ||||||||
\(439\) | 11.0786 | 0.528754 | 0.264377 | − | 0.964419i | \(-0.414834\pi\) | ||||
0.264377 | + | 0.964419i | \(0.414834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.213351 | 0.0101481 | ||||||||
\(443\) | −14.5482 | −0.691208 | −0.345604 | − | 0.938380i | \(-0.612326\pi\) | ||||
−0.345604 | + | 0.938380i | \(0.612326\pi\) | |||||||
\(444\) | −8.82316 | −0.418729 | ||||||||
\(445\) | −37.6184 | −1.78328 | ||||||||
\(446\) | −1.71961 | −0.0814258 | ||||||||
\(447\) | 8.19549 | 0.387633 | ||||||||
\(448\) | −7.33490 | −0.346541 | ||||||||
\(449\) | 27.4875 | 1.29721 | 0.648607 | − | 0.761123i | \(-0.275352\pi\) | ||||
0.648607 | + | 0.761123i | \(0.275352\pi\) | |||||||
\(450\) | 1.58647 | 0.0747867 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.62311 | 0.123381 | ||||||||
\(453\) | −13.2741 | −0.623673 | ||||||||
\(454\) | 0.0654688 | 0.00307260 | ||||||||
\(455\) | −14.4743 | −0.678566 | ||||||||
\(456\) | −5.41353 | −0.253512 | ||||||||
\(457\) | 7.94392 | 0.371601 | 0.185800 | − | 0.982587i | \(-0.440512\pi\) | ||||
0.185800 | + | 0.982587i | \(0.440512\pi\) | |||||||
\(458\) | 1.33020 | 0.0621563 | ||||||||
\(459\) | 0.334898 | 0.0156317 | ||||||||
\(460\) | 12.4922 | 0.582450 | ||||||||
\(461\) | −8.26943 | −0.385146 | −0.192573 | − | 0.981283i | \(-0.561683\pi\) | ||||
−0.192573 | + | 0.981283i | \(0.561683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.73904 | 0.452612 | 0.226306 | − | 0.974056i | \(-0.427335\pi\) | ||||
0.226306 | + | 0.974056i | \(0.427335\pi\) | |||||||
\(464\) | −0.749219 | −0.0347816 | ||||||||
\(465\) | 37.8318 | 1.75441 | ||||||||
\(466\) | −4.44706 | −0.206006 | ||||||||
\(467\) | −40.6970 | −1.88323 | −0.941617 | − | 0.336685i | \(-0.890694\pi\) | ||||
−0.941617 | + | 0.336685i | \(0.890694\pi\) | |||||||
\(468\) | 7.50235 | 0.346796 | ||||||||
\(469\) | −0.139410 | −0.00643735 | ||||||||
\(470\) | −7.73356 | −0.356723 | ||||||||
\(471\) | 16.9392 | 0.780518 | ||||||||
\(472\) | −2.49309 | −0.114754 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.557640 | 0.0256132 | ||||||||
\(475\) | −77.1153 | −3.53829 | ||||||||
\(476\) | 0.660406 | 0.0302697 | ||||||||
\(477\) | 7.94392 | 0.363727 | ||||||||
\(478\) | −1.80842 | −0.0827152 | ||||||||
\(479\) | −37.8318 | −1.72858 | −0.864289 | − | 0.502996i | \(-0.832231\pi\) | ||||
−0.864289 | + | 0.502996i | \(0.832231\pi\) | |||||||
\(480\) | −7.50235 | −0.342434 | ||||||||
\(481\) | 17.0226 | 0.776162 | ||||||||
\(482\) | 2.02334 | 0.0921608 | ||||||||
\(483\) | 1.66510 | 0.0757647 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.213351 | 0.00968778 | ||||||||
\(486\) | −0.167449 | −0.00759565 | ||||||||
\(487\) | 40.5576 | 1.83784 | 0.918921 | − | 0.394442i | \(-0.129062\pi\) | ||||
0.918921 | + | 0.394442i | \(0.129062\pi\) | |||||||
\(488\) | 3.99061 | 0.180646 | ||||||||
\(489\) | 6.79982 | 0.307498 | ||||||||
\(490\) | 0.637062 | 0.0287795 | ||||||||
\(491\) | −31.0786 | −1.40256 | −0.701280 | − | 0.712886i | \(-0.747388\pi\) | ||||
−0.701280 | + | 0.712886i | \(0.747388\pi\) | |||||||
\(492\) | 12.3816 | 0.558205 | ||||||||
\(493\) | 0.0654688 | 0.00294856 | ||||||||
\(494\) | 5.18531 | 0.233298 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −38.1106 | −1.71122 | ||||||||
\(497\) | 4.66980 | 0.209469 | ||||||||
\(498\) | −2.33490 | −0.104629 | ||||||||
\(499\) | 15.3575 | 0.687494 | 0.343747 | − | 0.939062i | \(-0.388304\pi\) | ||||
0.343747 | + | 0.939062i | \(0.388304\pi\) | |||||||
\(500\) | −33.5678 | −1.50120 | ||||||||
\(501\) | −18.2227 | −0.814132 | ||||||||
\(502\) | 0.805298 | 0.0359422 | ||||||||
\(503\) | −14.8925 | −0.664025 | −0.332013 | − | 0.943275i | \(-0.607728\pi\) | ||||
−0.332013 | + | 0.943275i | \(0.607728\pi\) | |||||||
\(504\) | −0.665102 | −0.0296260 | ||||||||
\(505\) | 71.8412 | 3.19689 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.47431 | −0.0654763 | ||||||||
\(508\) | 28.8177 | 1.27858 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0.213351 | 0.00944735 | ||||||||
\(511\) | −4.19549 | −0.185597 | ||||||||
\(512\) | 12.6557 | 0.559309 | ||||||||
\(513\) | 8.13941 | 0.359364 | ||||||||
\(514\) | −2.80530 | −0.123736 | ||||||||
\(515\) | −31.4969 | −1.38792 | ||||||||
\(516\) | −4.60433 | −0.202694 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.749219 | −0.0329188 | ||||||||
\(519\) | −1.72118 | −0.0755514 | ||||||||
\(520\) | 9.62689 | 0.422167 | ||||||||
\(521\) | 27.6924 | 1.21322 | 0.606612 | − | 0.794998i | \(-0.292528\pi\) | ||||
0.606612 | + | 0.794998i | \(0.292528\pi\) | |||||||
\(522\) | −0.0327344 | −0.00143274 | ||||||||
\(523\) | −18.4088 | −0.804962 | −0.402481 | − | 0.915428i | \(-0.631852\pi\) | ||||
−0.402481 | + | 0.915428i | \(0.631852\pi\) | |||||||
\(524\) | 40.5389 | 1.77095 | ||||||||
\(525\) | −9.47431 | −0.413493 | ||||||||
\(526\) | 2.03273 | 0.0886314 | ||||||||
\(527\) | 3.33020 | 0.145066 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2274 | −0.879454 | ||||||||
\(530\) | 5.06077 | 0.219826 | ||||||||
\(531\) | 3.74843 | 0.162668 | ||||||||
\(532\) | 16.0506 | 0.695882 | ||||||||
\(533\) | −23.8878 | −1.03470 | ||||||||
\(534\) | 1.65571 | 0.0716496 | ||||||||
\(535\) | 30.9665 | 1.33880 | ||||||||
\(536\) | 0.0927218 | 0.00400497 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | −4.22274 | −0.182055 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.50235 | 0.322850 | ||||||||
\(541\) | 4.26943 | 0.183557 | 0.0917786 | − | 0.995779i | \(-0.470745\pi\) | ||||
0.0917786 | + | 0.995779i | \(0.470745\pi\) | |||||||
\(542\) | −0.693141 | −0.0297729 | ||||||||
\(543\) | −0.725875 | −0.0311503 | ||||||||
\(544\) | −0.660406 | −0.0283147 | ||||||||
\(545\) | −43.9533 | −1.88275 | ||||||||
\(546\) | 0.637062 | 0.0272638 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 31.9906 | 1.36657 | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.59116 | 0.0677857 | ||||||||
\(552\) | −1.10746 | −0.0471367 | ||||||||
\(553\) | −3.33020 | −0.141615 | ||||||||
\(554\) | 3.06077 | 0.130040 | ||||||||
\(555\) | 17.0226 | 0.722567 | ||||||||
\(556\) | 44.4643 | 1.88570 | ||||||||
\(557\) | 12.4743 | 0.528553 | 0.264277 | − | 0.964447i | \(-0.414867\pi\) | ||||
0.264277 | + | 0.964447i | \(0.414867\pi\) | |||||||
\(558\) | −1.66510 | −0.0704894 | ||||||||
\(559\) | 8.88315 | 0.375717 | ||||||||
\(560\) | 14.5810 | 0.616159 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.12923 | −0.0476338 | ||||||||
\(563\) | 32.7710 | 1.38113 | 0.690566 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690566 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(564\) | −23.9384 | −1.00799 | ||||||||
\(565\) | −5.06077 | −0.212908 | ||||||||
\(566\) | −3.91119 | −0.164399 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −3.10589 | −0.130320 | ||||||||
\(569\) | 29.2180 | 1.22488 | 0.612442 | − | 0.790515i | \(-0.290187\pi\) | ||||
0.612442 | + | 0.790515i | \(0.290187\pi\) | |||||||
\(570\) | 5.18531 | 0.217189 | ||||||||
\(571\) | −32.4455 | −1.35780 | −0.678901 | − | 0.734230i | \(-0.737543\pi\) | ||||
−0.678901 | + | 0.734230i | \(0.737543\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.27412 | −0.220330 | ||||||||
\(574\) | 1.05138 | 0.0438839 | ||||||||
\(575\) | −15.7757 | −0.657892 | ||||||||
\(576\) | −7.33490 | −0.305621 | ||||||||
\(577\) | −14.8831 | −0.619594 | −0.309797 | − | 0.950803i | \(-0.600261\pi\) | ||||
−0.309797 | + | 0.950803i | \(0.600261\pi\) | |||||||
\(578\) | −2.82786 | −0.117623 | ||||||||
\(579\) | −19.8318 | −0.824180 | ||||||||
\(580\) | 1.46662 | 0.0608982 | ||||||||
\(581\) | 13.9439 | 0.578491 | ||||||||
\(582\) | −0.00939029 | −0.000389240 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.79043 | 0.115469 | ||||||||
\(585\) | −14.4743 | −0.598439 | ||||||||
\(586\) | 2.37220 | 0.0979945 | ||||||||
\(587\) | −4.53039 | −0.186989 | −0.0934945 | − | 0.995620i | \(-0.529804\pi\) | ||||
−0.0934945 | + | 0.995620i | \(0.529804\pi\) | |||||||
\(588\) | 1.97196 | 0.0813223 | ||||||||
\(589\) | 80.9377 | 3.33498 | ||||||||
\(590\) | 2.38799 | 0.0983118 | ||||||||
\(591\) | 2.66980 | 0.109821 | ||||||||
\(592\) | −17.1480 | −0.704779 | ||||||||
\(593\) | −8.28821 | −0.340356 | −0.170178 | − | 0.985413i | \(-0.554434\pi\) | ||||
−0.170178 | + | 0.985413i | \(0.554434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.27412 | −0.0522340 | ||||||||
\(596\) | 16.1612 | 0.661988 | ||||||||
\(597\) | −13.5529 | −0.554685 | ||||||||
\(598\) | 1.06077 | 0.0433783 | ||||||||
\(599\) | 1.99061 | 0.0813341 | 0.0406671 | − | 0.999173i | \(-0.487052\pi\) | ||||
0.0406671 | + | 0.999173i | \(0.487052\pi\) | |||||||
\(600\) | 6.30138 | 0.257253 | ||||||||
\(601\) | 8.47431 | 0.345674 | 0.172837 | − | 0.984950i | \(-0.444707\pi\) | ||||
0.172837 | + | 0.984950i | \(0.444707\pi\) | |||||||
\(602\) | −0.390977 | −0.0159350 | ||||||||
\(603\) | −0.139410 | −0.00567721 | ||||||||
\(604\) | −26.1761 | −1.06509 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.16197 | −0.128446 | ||||||||
\(607\) | 22.9665 | 0.932181 | 0.466090 | − | 0.884737i | \(-0.345662\pi\) | ||||
0.466090 | + | 0.884737i | \(0.345662\pi\) | |||||||
\(608\) | −16.0506 | −0.650938 | ||||||||
\(609\) | 0.195488 | 0.00792159 | ||||||||
\(610\) | −3.82237 | −0.154763 | ||||||||
\(611\) | 46.1845 | 1.86843 | ||||||||
\(612\) | 0.660406 | 0.0266953 | ||||||||
\(613\) | −3.55294 | −0.143502 | −0.0717510 | − | 0.997423i | \(-0.522859\pi\) | ||||
−0.0717510 | + | 0.997423i | \(0.522859\pi\) | |||||||
\(614\) | 2.10277 | 0.0848608 | ||||||||
\(615\) | −23.8878 | −0.963251 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.6698 | 0.912652 | 0.456326 | − | 0.889813i | \(-0.349165\pi\) | ||||
0.456326 | + | 0.889813i | \(0.349165\pi\) | |||||||
\(618\) | 1.38628 | 0.0557644 | ||||||||
\(619\) | 8.71648 | 0.350345 | 0.175173 | − | 0.984538i | \(-0.443952\pi\) | ||||
0.175173 | + | 0.984538i | \(0.443952\pi\) | |||||||
\(620\) | 74.6028 | 2.99612 | ||||||||
\(621\) | 1.66510 | 0.0668182 | ||||||||
\(622\) | 1.56391 | 0.0627070 | ||||||||
\(623\) | −9.88784 | −0.396148 | ||||||||
\(624\) | 14.5810 | 0.583707 | ||||||||
\(625\) | 17.3910 | 0.695639 | ||||||||
\(626\) | −0.501561 | −0.0200464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 33.4035 | 1.33294 | ||||||||
\(629\) | 1.49844 | 0.0597467 | ||||||||
\(630\) | 0.637062 | 0.0253812 | ||||||||
\(631\) | −11.8878 | −0.473248 | −0.236624 | − | 0.971601i | \(-0.576041\pi\) | ||||
−0.236624 | + | 0.971601i | \(0.576041\pi\) | |||||||
\(632\) | 2.21492 | 0.0881049 | ||||||||
\(633\) | −4.27882 | −0.170068 | ||||||||
\(634\) | 1.66353 | 0.0660672 | ||||||||
\(635\) | −55.5981 | −2.20634 | ||||||||
\(636\) | 15.6651 | 0.621162 | ||||||||
\(637\) | −3.80451 | −0.150740 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.66980 | 0.184734 | ||||||||
\(640\) | −19.6775 | −0.777821 | ||||||||
\(641\) | −4.89254 | −0.193244 | −0.0966218 | − | 0.995321i | \(-0.530804\pi\) | ||||
−0.0966218 | + | 0.995321i | \(0.530804\pi\) | |||||||
\(642\) | −1.36294 | −0.0537909 | ||||||||
\(643\) | 22.7804 | 0.898371 | 0.449185 | − | 0.893439i | \(-0.351714\pi\) | ||||
0.449185 | + | 0.893439i | \(0.351714\pi\) | |||||||
\(644\) | 3.28352 | 0.129389 | ||||||||
\(645\) | 8.88315 | 0.349774 | ||||||||
\(646\) | 0.456446 | 0.0179586 | ||||||||
\(647\) | 31.2453 | 1.22838 | 0.614190 | − | 0.789158i | \(-0.289483\pi\) | ||||
0.614190 | + | 0.789158i | \(0.289483\pi\) | |||||||
\(648\) | −0.665102 | −0.0261277 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.03573 | −0.236741 | ||||||||
\(651\) | 9.94392 | 0.389733 | ||||||||
\(652\) | 13.4090 | 0.525136 | ||||||||
\(653\) | 28.2882 | 1.10700 | 0.553502 | − | 0.832848i | \(-0.313291\pi\) | ||||
0.553502 | + | 0.832848i | \(0.313291\pi\) | |||||||
\(654\) | 1.93453 | 0.0756462 | ||||||||
\(655\) | −78.2118 | −3.05599 | ||||||||
\(656\) | 24.0639 | 0.939537 | ||||||||
\(657\) | −4.19549 | −0.163682 | ||||||||
\(658\) | −2.03273 | −0.0792442 | ||||||||
\(659\) | −30.2967 | −1.18019 | −0.590096 | − | 0.807333i | \(-0.700910\pi\) | ||||
−0.590096 | + | 0.807333i | \(0.700910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7196 | −1.38933 | −0.694666 | − | 0.719333i | \(-0.744448\pi\) | ||||
−0.694666 | + | 0.719333i | \(0.744448\pi\) | |||||||
\(662\) | 3.77569 | 0.146746 | ||||||||
\(663\) | −1.27412 | −0.0494829 | ||||||||
\(664\) | −9.27412 | −0.359906 | ||||||||
\(665\) | −30.9665 | −1.20083 | ||||||||
\(666\) | −0.749219 | −0.0290317 | ||||||||
\(667\) | 0.325508 | 0.0126037 | ||||||||
\(668\) | −35.9345 | −1.39035 | ||||||||
\(669\) | 10.2694 | 0.397039 | ||||||||
\(670\) | −0.0888128 | −0.00343114 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.97196 | −0.0760700 | ||||||||
\(673\) | −34.9377 | −1.34675 | −0.673374 | − | 0.739302i | \(-0.735156\pi\) | ||||
−0.673374 | + | 0.739302i | \(0.735156\pi\) | |||||||
\(674\) | −2.22431 | −0.0856774 | ||||||||
\(675\) | −9.47431 | −0.364666 | ||||||||
\(676\) | −2.90728 | −0.111818 | ||||||||
\(677\) | −20.0094 | −0.769023 | −0.384512 | − | 0.923120i | \(-0.625630\pi\) | ||||
−0.384512 | + | 0.923120i | \(0.625630\pi\) | |||||||
\(678\) | 0.222741 | 0.00855433 | ||||||||
\(679\) | 0.0560785 | 0.00215209 | ||||||||
\(680\) | 0.847422 | 0.0324972 | ||||||||
\(681\) | −0.390977 | −0.0149823 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0498 | 0.958504 | 0.479252 | − | 0.877677i | \(-0.340908\pi\) | ||||
0.479252 | + | 0.877677i | \(0.340908\pi\) | |||||||
\(684\) | 16.0506 | 0.613710 | ||||||||
\(685\) | −61.7196 | −2.35818 | ||||||||
\(686\) | 0.167449 | 0.00639324 | ||||||||
\(687\) | −7.94392 | −0.303080 | ||||||||
\(688\) | −8.94862 | −0.341163 | ||||||||
\(689\) | −30.2227 | −1.15139 | ||||||||
\(690\) | 1.06077 | 0.0403830 | ||||||||
\(691\) | −38.8271 | −1.47705 | −0.738526 | − | 0.674225i | \(-0.764478\pi\) | ||||
−0.738526 | + | 0.674225i | \(0.764478\pi\) | |||||||
\(692\) | −3.39410 | −0.129024 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.65102 | 0.176550 | ||||||||
\(695\) | −85.7851 | −3.25401 | ||||||||
\(696\) | −0.130020 | −0.00492838 | ||||||||
\(697\) | −2.10277 | −0.0796480 | ||||||||
\(698\) | 0.478217 | 0.0181008 | ||||||||
\(699\) | 26.5576 | 1.00450 | ||||||||
\(700\) | −18.6830 | −0.706150 | ||||||||
\(701\) | 41.7757 | 1.57785 | 0.788923 | − | 0.614492i | \(-0.210639\pi\) | ||||
0.788923 | + | 0.614492i | \(0.210639\pi\) | |||||||
\(702\) | 0.637062 | 0.0240444 | ||||||||
\(703\) | 36.4182 | 1.37354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.1845 | 1.73941 | ||||||||
\(706\) | 4.12611 | 0.155288 | ||||||||
\(707\) | 18.8831 | 0.710174 | ||||||||
\(708\) | 7.39176 | 0.277799 | ||||||||
\(709\) | −13.4041 | −0.503403 | −0.251702 | − | 0.967805i | \(-0.580990\pi\) | ||||
−0.251702 | + | 0.967805i | \(0.580990\pi\) | |||||||
\(710\) | 2.97495 | 0.111648 | ||||||||
\(711\) | −3.33020 | −0.124892 | ||||||||
\(712\) | 6.57642 | 0.246462 | ||||||||
\(713\) | 16.5576 | 0.620088 | ||||||||
\(714\) | 0.0560785 | 0.00209868 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.6635 | 0.884348 | ||||||||
\(717\) | 10.7998 | 0.403327 | ||||||||
\(718\) | 1.99061 | 0.0742889 | ||||||||
\(719\) | 5.47900 | 0.204332 | 0.102166 | − | 0.994767i | \(-0.467423\pi\) | ||||
0.102166 | + | 0.994767i | \(0.467423\pi\) | |||||||
\(720\) | 14.5810 | 0.543401 | ||||||||
\(721\) | −8.27882 | −0.308319 | ||||||||
\(722\) | 7.91197 | 0.294453 | ||||||||
\(723\) | −12.0833 | −0.449384 | ||||||||
\(724\) | −1.43140 | −0.0531975 | ||||||||
\(725\) | −1.85212 | −0.0687859 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.8831 | −1.21957 | −0.609784 | − | 0.792567i | \(-0.708744\pi\) | ||||
−0.609784 | + | 0.792567i | \(0.708744\pi\) | |||||||
\(728\) | 2.53039 | 0.0937824 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.67279 | −0.0989243 | ||||||||
\(731\) | 0.781954 | 0.0289216 | ||||||||
\(732\) | −11.8318 | −0.437315 | ||||||||
\(733\) | 35.8972 | 1.32589 | 0.662947 | − | 0.748666i | \(-0.269305\pi\) | ||||
0.662947 | + | 0.748666i | \(0.269305\pi\) | |||||||
\(734\) | 0.604328 | 0.0223062 | ||||||||
\(735\) | −3.80451 | −0.140332 | ||||||||
\(736\) | −3.28352 | −0.121032 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.05138 | 0.0387020 | ||||||||
\(739\) | −29.6651 | −1.09125 | −0.545624 | − | 0.838030i | \(-0.683707\pi\) | ||||
−0.545624 | + | 0.838030i | \(0.683707\pi\) | |||||||
\(740\) | 33.5678 | 1.23398 | ||||||||
\(741\) | −30.9665 | −1.13758 | ||||||||
\(742\) | 1.33020 | 0.0488333 | ||||||||
\(743\) | 18.7998 | 0.689698 | 0.344849 | − | 0.938658i | \(-0.387930\pi\) | ||||
0.344849 | + | 0.938658i | \(0.387930\pi\) | |||||||
\(744\) | −6.61372 | −0.242471 | ||||||||
\(745\) | −31.1798 | −1.14234 | ||||||||
\(746\) | −2.06547 | −0.0756222 | ||||||||
\(747\) | 13.9439 | 0.510181 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.13941 | 0.297408 | ||||||||
\(750\) | −2.85041 | −0.104082 | ||||||||
\(751\) | −9.59116 | −0.349986 | −0.174993 | − | 0.984570i | \(-0.555990\pi\) | ||||
−0.174993 | + | 0.984570i | \(0.555990\pi\) | |||||||
\(752\) | −46.5249 | −1.69659 | ||||||||
\(753\) | −4.80921 | −0.175257 | ||||||||
\(754\) | 0.124538 | 0.00453542 | ||||||||
\(755\) | 50.5016 | 1.83794 | ||||||||
\(756\) | 1.97196 | 0.0717195 | ||||||||
\(757\) | 2.74374 | 0.0997229 | 0.0498614 | − | 0.998756i | \(-0.484122\pi\) | ||||
0.0498614 | + | 0.998756i | \(0.484122\pi\) | |||||||
\(758\) | 3.91119 | 0.142061 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.5959 | 0.747090 | ||||||||
\(761\) | −6.39098 | −0.231673 | −0.115836 | − | 0.993268i | \(-0.536955\pi\) | ||||
−0.115836 | + | 0.993268i | \(0.536955\pi\) | |||||||
\(762\) | 2.44706 | 0.0886475 | ||||||||
\(763\) | −11.5529 | −0.418245 | ||||||||
\(764\) | −10.4004 | −0.376272 | ||||||||
\(765\) | −1.27412 | −0.0460661 | ||||||||
\(766\) | −2.54825 | −0.0920720 | ||||||||
\(767\) | −14.2610 | −0.514933 | ||||||||
\(768\) | −13.8037 | −0.498099 | ||||||||
\(769\) | −17.7951 | −0.641708 | −0.320854 | − | 0.947129i | \(-0.603970\pi\) | ||||
−0.320854 | + | 0.947129i | \(0.603970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.7531 | 0.603349 | ||||||||
\(772\) | −39.1075 | −1.40751 | ||||||||
\(773\) | −31.5257 | −1.13390 | −0.566950 | − | 0.823752i | \(-0.691877\pi\) | ||||
−0.566950 | + | 0.823752i | \(0.691877\pi\) | |||||||
\(774\) | −0.390977 | −0.0140534 | ||||||||
\(775\) | −94.2118 | −3.38419 | ||||||||
\(776\) | −0.0372979 | −0.00133892 | ||||||||
\(777\) | 4.47431 | 0.160515 | ||||||||
\(778\) | 0.624681 | 0.0223959 | ||||||||
\(779\) | −51.1059 | −1.83106 | ||||||||
\(780\) | −28.5428 | −1.02200 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.0933763 | 0.00333913 | ||||||||
\(783\) | 0.195488 | 0.00698619 | ||||||||
\(784\) | 3.83255 | 0.136877 | ||||||||
\(785\) | −64.4455 | −2.30016 | ||||||||
\(786\) | 3.44236 | 0.122785 | ||||||||
\(787\) | −31.8606 | −1.13571 | −0.567854 | − | 0.823130i | \(-0.692226\pi\) | ||||
−0.567854 | + | 0.823130i | \(0.692226\pi\) | |||||||
\(788\) | 5.26473 | 0.187548 | ||||||||
\(789\) | −12.1394 | −0.432174 | ||||||||
\(790\) | −2.12155 | −0.0754813 | ||||||||
\(791\) | −1.33020 | −0.0472966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.8271 | 0.810613 | ||||||||
\(794\) | 3.49844 | 0.124155 | ||||||||
\(795\) | −30.2227 | −1.07189 | ||||||||
\(796\) | −26.7259 | −0.947274 | ||||||||
\(797\) | 43.8590 | 1.55357 | 0.776783 | − | 0.629768i | \(-0.216850\pi\) | ||||
0.776783 | + | 0.629768i | \(0.216850\pi\) | |||||||
\(798\) | 1.36294 | 0.0482475 | ||||||||
\(799\) | 4.06547 | 0.143826 | ||||||||
\(800\) | 18.6830 | 0.660543 | ||||||||
\(801\) | −9.88784 | −0.349370 | ||||||||
\(802\) | 3.89723 | 0.137616 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.274911 | −0.00969536 | ||||||||
\(805\) | −6.33490 | −0.223276 | ||||||||
\(806\) | 6.33490 | 0.223137 | ||||||||
\(807\) | 25.2180 | 0.887717 | ||||||||
\(808\) | −12.5592 | −0.441832 | ||||||||
\(809\) | −6.74374 | −0.237097 | −0.118549 | − | 0.992948i | \(-0.537824\pi\) | ||||
−0.118549 | + | 0.992948i | \(0.537824\pi\) | |||||||
\(810\) | 0.637062 | 0.0223841 | ||||||||
\(811\) | −3.97275 | −0.139502 | −0.0697510 | − | 0.997564i | \(-0.522220\pi\) | ||||
−0.0697510 | + | 0.997564i | \(0.522220\pi\) | |||||||
\(812\) | 0.385496 | 0.0135282 | ||||||||
\(813\) | 4.13941 | 0.145175 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.8700 | −0.906186 | ||||||||
\(816\) | 1.28352 | 0.0449320 | ||||||||
\(817\) | 19.0047 | 0.664890 | ||||||||
\(818\) | 4.00157 | 0.139912 | ||||||||
\(819\) | −3.80451 | −0.132940 | ||||||||
\(820\) | −47.1059 | −1.64501 | ||||||||
\(821\) | −49.5896 | −1.73069 | −0.865344 | − | 0.501178i | \(-0.832900\pi\) | ||||
−0.865344 | + | 0.501178i | \(0.832900\pi\) | |||||||
\(822\) | 2.71648 | 0.0947483 | ||||||||
\(823\) | 23.1908 | 0.808380 | 0.404190 | − | 0.914675i | \(-0.367553\pi\) | ||||
0.404190 | + | 0.914675i | \(0.367553\pi\) | |||||||
\(824\) | 5.50626 | 0.191820 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.627672 | 0.0218395 | ||||||||
\(827\) | −27.7484 | −0.964908 | −0.482454 | − | 0.875921i | \(-0.660254\pi\) | ||||
−0.482454 | + | 0.875921i | \(0.660254\pi\) | |||||||
\(828\) | 3.28352 | 0.114110 | ||||||||
\(829\) | 0.269430 | 0.00935768 | 0.00467884 | − | 0.999989i | \(-0.498511\pi\) | ||||
0.00467884 | + | 0.999989i | \(0.498511\pi\) | |||||||
\(830\) | 8.88315 | 0.308339 | ||||||||
\(831\) | −18.2788 | −0.634085 | ||||||||
\(832\) | 27.9057 | 0.967456 | ||||||||
\(833\) | −0.334898 | −0.0116035 | ||||||||
\(834\) | 3.77569 | 0.130741 | ||||||||
\(835\) | 69.3286 | 2.39922 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.94392 | 0.343712 | ||||||||
\(838\) | −5.07316 | −0.175249 | ||||||||
\(839\) | −27.3575 | −0.944484 | −0.472242 | − | 0.881469i | \(-0.656555\pi\) | ||||
−0.472242 | + | 0.881469i | \(0.656555\pi\) | |||||||
\(840\) | 2.53039 | 0.0873066 | ||||||||
\(841\) | −28.9618 | −0.998682 | ||||||||
\(842\) | −2.59976 | −0.0895938 | ||||||||
\(843\) | 6.74374 | 0.232267 | ||||||||
\(844\) | −8.43767 | −0.290436 | ||||||||
\(845\) | 5.60902 | 0.192956 | ||||||||
\(846\) | −2.03273 | −0.0698868 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.4455 | 1.04550 | ||||||||
\(849\) | 23.3575 | 0.801626 | ||||||||
\(850\) | −0.531305 | −0.0182236 | ||||||||
\(851\) | 7.45018 | 0.255389 | ||||||||
\(852\) | 9.20866 | 0.315483 | ||||||||
\(853\) | 28.5482 | 0.977473 | 0.488737 | − | 0.872431i | \(-0.337458\pi\) | ||||
0.488737 | + | 0.872431i | \(0.337458\pi\) | |||||||
\(854\) | −1.00470 | −0.0343800 | ||||||||
\(855\) | −30.9665 | −1.05903 | ||||||||
\(856\) | −5.41353 | −0.185031 | ||||||||
\(857\) | 39.8972 | 1.36286 | 0.681432 | − | 0.731882i | \(-0.261358\pi\) | ||||
0.681432 | + | 0.731882i | \(0.261358\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5576 | 0.701418 | 0.350709 | − | 0.936485i | \(-0.385941\pi\) | ||||
0.350709 | + | 0.936485i | \(0.385941\pi\) | |||||||
\(860\) | 17.5172 | 0.597332 | ||||||||
\(861\) | −6.27882 | −0.213982 | ||||||||
\(862\) | −0.515515 | −0.0175585 | ||||||||
\(863\) | −9.66510 | −0.329004 | −0.164502 | − | 0.986377i | \(-0.552602\pi\) | ||||
−0.164502 | + | 0.986377i | \(0.552602\pi\) | |||||||
\(864\) | −1.97196 | −0.0670875 | ||||||||
\(865\) | 6.54825 | 0.222647 | ||||||||
\(866\) | 2.83646 | 0.0963868 | ||||||||
\(867\) | 16.8878 | 0.573541 | ||||||||
\(868\) | 19.6090 | 0.665574 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.124538 | 0.00422224 | ||||||||
\(871\) | 0.530387 | 0.0179715 | ||||||||
\(872\) | 7.68388 | 0.260209 | ||||||||
\(873\) | 0.0560785 | 0.00189797 | ||||||||
\(874\) | 2.26943 | 0.0767646 | ||||||||
\(875\) | 17.0226 | 0.575467 | ||||||||
\(876\) | −8.27334 | −0.279530 | ||||||||
\(877\) | 25.7212 | 0.868543 | 0.434271 | − | 0.900782i | \(-0.357006\pi\) | ||||
0.434271 | + | 0.900782i | \(0.357006\pi\) | |||||||
\(878\) | 1.85511 | 0.0626069 | ||||||||
\(879\) | −14.1667 | −0.477830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.6316 | −0.492950 | −0.246475 | − | 0.969149i | \(-0.579272\pi\) | ||||
−0.246475 | + | 0.969149i | \(0.579272\pi\) | |||||||
\(882\) | 0.167449 | 0.00563831 | ||||||||
\(883\) | 18.6877 | 0.628890 | 0.314445 | − | 0.949276i | \(-0.398182\pi\) | ||||
0.314445 | + | 0.949276i | \(0.398182\pi\) | |||||||
\(884\) | −2.51252 | −0.0845053 | ||||||||
\(885\) | −14.2610 | −0.479377 | ||||||||
\(886\) | −2.43609 | −0.0818421 | ||||||||
\(887\) | −38.6137 | −1.29652 | −0.648261 | − | 0.761418i | \(-0.724503\pi\) | ||||
−0.648261 | + | 0.761418i | \(0.724503\pi\) | |||||||
\(888\) | −2.97587 | −0.0998636 | ||||||||
\(889\) | −14.6137 | −0.490128 | ||||||||
\(890\) | −6.29917 | −0.211149 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.2509 | 0.678051 | ||||||||
\(893\) | 98.8076 | 3.30647 | ||||||||
\(894\) | 1.37233 | 0.0458975 | ||||||||
\(895\) | −45.6541 | −1.52605 | ||||||||
\(896\) | −5.17214 | −0.172789 | ||||||||
\(897\) | −6.33490 | −0.211516 | ||||||||
\(898\) | 4.60276 | 0.153596 | ||||||||
\(899\) | 1.94392 | 0.0648334 | ||||||||
\(900\) | −18.6830 | −0.622765 | ||||||||
\(901\) | −2.66041 | −0.0886310 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.33490 | 0.0777006 | ||||||||
\(904\) | 0.884720 | 0.0294254 | ||||||||
\(905\) | 2.76160 | 0.0917987 | ||||||||
\(906\) | −2.22274 | −0.0738456 | ||||||||
\(907\) | 49.0965 | 1.63022 | 0.815111 | − | 0.579304i | \(-0.196676\pi\) | ||||
0.815111 | + | 0.579304i | \(0.196676\pi\) | |||||||
\(908\) | −0.770991 | −0.0255862 | ||||||||
\(909\) | 18.8831 | 0.626314 | ||||||||
\(910\) | −2.42371 | −0.0803452 | ||||||||
\(911\) | 29.3753 | 0.973248 | 0.486624 | − | 0.873612i | \(-0.338228\pi\) | ||||
0.486624 | + | 0.873612i | \(0.338228\pi\) | |||||||
\(912\) | 31.1947 | 1.03296 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.33020 | 0.0439992 | ||||||||
\(915\) | 22.8271 | 0.754640 | ||||||||
\(916\) | −15.6651 | −0.517590 | ||||||||
\(917\) | −20.5576 | −0.678873 | ||||||||
\(918\) | 0.0560785 | 0.00185087 | ||||||||
\(919\) | 27.0047 | 0.890803 | 0.445401 | − | 0.895331i | \(-0.353061\pi\) | ||||
0.445401 | + | 0.895331i | \(0.353061\pi\) | |||||||
\(920\) | 4.21335 | 0.138910 | ||||||||
\(921\) | −12.5576 | −0.413788 | ||||||||
\(922\) | −1.38471 | −0.0456030 | ||||||||
\(923\) | −17.7663 | −0.584785 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.3910 | −1.39381 | ||||||||
\(926\) | 1.63079 | 0.0535912 | ||||||||
\(927\) | −8.27882 | −0.271912 | ||||||||
\(928\) | −0.385496 | −0.0126545 | ||||||||
\(929\) | 57.8496 | 1.89798 | 0.948992 | − | 0.315299i | \(-0.102105\pi\) | ||||
0.948992 | + | 0.315299i | \(0.102105\pi\) | |||||||
\(930\) | 6.33490 | 0.207730 | ||||||||
\(931\) | −8.13941 | −0.266758 | ||||||||
\(932\) | 52.3706 | 1.71546 | ||||||||
\(933\) | −9.33959 | −0.305765 | ||||||||
\(934\) | −6.81469 | −0.222983 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.53039 | 0.0827083 | ||||||||
\(937\) | −25.2180 | −0.823838 | −0.411919 | − | 0.911221i | \(-0.635141\pi\) | ||||
−0.411919 | + | 0.911221i | \(0.635141\pi\) | |||||||
\(938\) | −0.0233441 | −0.000762211 0 | ||||||||
\(939\) | 2.99530 | 0.0977481 | ||||||||
\(940\) | 91.0741 | 2.97051 | ||||||||
\(941\) | 34.2788 | 1.11746 | 0.558729 | − | 0.829350i | \(-0.311289\pi\) | ||||
0.558729 | + | 0.829350i | \(0.311289\pi\) | |||||||
\(942\) | 2.83646 | 0.0924169 | ||||||||
\(943\) | −10.4549 | −0.340458 | ||||||||
\(944\) | 14.3661 | 0.467575 | ||||||||
\(945\) | −3.80451 | −0.123761 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.1573 | −0.590032 | −0.295016 | − | 0.955492i | \(-0.595325\pi\) | ||||
−0.295016 | + | 0.955492i | \(0.595325\pi\) | |||||||
\(948\) | −6.56703 | −0.213287 | ||||||||
\(949\) | 15.9618 | 0.518141 | ||||||||
\(950\) | −12.9129 | −0.418950 | ||||||||
\(951\) | −9.93453 | −0.322149 | ||||||||
\(952\) | 0.222741 | 0.00721909 | ||||||||
\(953\) | 19.8045 | 0.641531 | 0.320766 | − | 0.947159i | \(-0.396060\pi\) | ||||
0.320766 | + | 0.947159i | \(0.396060\pi\) | |||||||
\(954\) | 1.33020 | 0.0430669 | ||||||||
\(955\) | 20.0655 | 0.649303 | ||||||||
\(956\) | 21.2968 | 0.688788 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.33490 | −0.204671 | ||||||||
\(959\) | −16.2227 | −0.523860 | ||||||||
\(960\) | 27.9057 | 0.900653 | ||||||||
\(961\) | 67.8816 | 2.18973 | ||||||||
\(962\) | 2.85041 | 0.0919010 | ||||||||
\(963\) | 8.13941 | 0.262289 | ||||||||
\(964\) | −23.8279 | −0.767444 | ||||||||
\(965\) | 75.4502 | 2.42883 | ||||||||
\(966\) | 0.278820 | 0.00897088 | ||||||||
\(967\) | 0.278820 | 0.00896624 | 0.00448312 | − | 0.999990i | \(-0.498573\pi\) | ||||
0.00448312 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.72588 | −0.0875677 | ||||||||
\(970\) | 0.0357255 | 0.00114708 | ||||||||
\(971\) | 25.3481 | 0.813458 | 0.406729 | − | 0.913549i | \(-0.366669\pi\) | ||||
0.406729 | + | 0.913549i | \(0.366669\pi\) | |||||||
\(972\) | 1.97196 | 0.0632507 | ||||||||
\(973\) | −22.5482 | −0.722864 | ||||||||
\(974\) | 6.79134 | 0.217609 | ||||||||
\(975\) | 36.0451 | 1.15437 | ||||||||
\(976\) | −22.9953 | −0.736062 | ||||||||
\(977\) | 6.71648 | 0.214879 | 0.107440 | − | 0.994212i | \(-0.465735\pi\) | ||||
0.107440 | + | 0.994212i | \(0.465735\pi\) | |||||||
\(978\) | 1.13862 | 0.0364092 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −7.50235 | −0.239654 | ||||||||
\(981\) | −11.5529 | −0.368857 | ||||||||
\(982\) | −5.20409 | −0.166069 | ||||||||
\(983\) | 9.99061 | 0.318651 | 0.159325 | − | 0.987226i | \(-0.449068\pi\) | ||||
0.159325 | + | 0.987226i | \(0.449068\pi\) | |||||||
\(984\) | 4.17605 | 0.133128 | ||||||||
\(985\) | −10.1573 | −0.323638 | ||||||||
\(986\) | 0.0109627 | 0.000349123 0 | ||||||||
\(987\) | 12.1394 | 0.386402 | ||||||||
\(988\) | −61.0647 | −1.94273 | ||||||||
\(989\) | 3.88784 | 0.123626 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.7064 | −0.848358 | −0.424179 | − | 0.905578i | \(-0.639437\pi\) | ||||
−0.424179 | + | 0.905578i | \(0.639437\pi\) | |||||||
\(992\) | −19.6090 | −0.622587 | ||||||||
\(993\) | −22.5482 | −0.715547 | ||||||||
\(994\) | 0.781954 | 0.0248021 | ||||||||
\(995\) | 51.5623 | 1.63464 | ||||||||
\(996\) | 27.4969 | 0.871272 | ||||||||
\(997\) | −54.3333 | −1.72075 | −0.860377 | − | 0.509658i | \(-0.829772\pi\) | ||||
−0.860377 | + | 0.509658i | \(0.829772\pi\) | |||||||
\(998\) | 2.57159 | 0.0814024 | ||||||||
\(999\) | 4.47431 | 0.141561 |
(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 | 2541.2.a.bi.1.2 | 3 | ||
3.2 | odd | 2 | 7623.2.a.cb.1.2 | 3 | |||
11.10 | odd | 2 | 231.2.a.d.1.2 | ✓ | 3 | ||
33.32 | even | 2 | 693.2.a.m.1.2 | 3 | |||
44.43 | even | 2 | 3696.2.a.bp.1.3 | 3 | |||
55.54 | odd | 2 | 5775.2.a.bw.1.2 | 3 | |||
77.76 | even | 2 | 1617.2.a.s.1.2 | 3 | |||
231.230 | odd | 2 | 4851.2.a.bp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.d.1.2 | ✓ | 3 | 11.10 | odd | 2 | ||
693.2.a.m.1.2 | 3 | 33.32 | even | 2 | |||
1617.2.a.s.1.2 | 3 | 77.76 | even | 2 | |||
2541.2.a.bi.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3696.2.a.bp.1.3 | 3 | 44.43 | even | 2 | |||
4851.2.a.bp.1.2 | 3 | 231.230 | odd | 2 | |||
5775.2.a.bw.1.2 | 3 | 55.54 | odd | 2 | |||
7623.2.a.cb.1.2 | 3 | 3.2 | odd | 2 |