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: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
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 | \(0.737640\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45589 | −1.02947 | −0.514734 | − | 0.857350i | \(-0.672109\pi\) | ||||
−0.514734 | + | 0.857350i | \(0.672109\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.119606 | 0.0598032 | ||||||||
\(5\) | 2.38705 | 1.06752 | 0.533762 | − | 0.845635i | \(-0.320778\pi\) | ||||
0.533762 | + | 0.845635i | \(0.320778\pi\) | |||||||
\(6\) | 1.45589 | 0.594363 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.73764 | 0.967902 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.47528 | −1.09898 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.119606 | −0.0345274 | ||||||||
\(13\) | 0.911774 | 0.252880 | 0.126440 | − | 0.991974i | \(-0.459645\pi\) | ||||
0.126440 | + | 0.991974i | \(0.459645\pi\) | |||||||
\(14\) | −1.45589 | −0.389102 | ||||||||
\(15\) | −2.38705 | −0.616335 | ||||||||
\(16\) | −4.22491 | −1.05623 | ||||||||
\(17\) | 2.18663 | 0.530335 | 0.265168 | − | 0.964202i | \(-0.414573\pi\) | ||||
0.265168 | + | 0.964202i | \(0.414573\pi\) | |||||||
\(18\) | −1.45589 | −0.343156 | ||||||||
\(19\) | −0.711349 | −0.163195 | −0.0815973 | − | 0.996665i | \(-0.526002\pi\) | ||||
−0.0815973 | + | 0.996665i | \(0.526002\pi\) | |||||||
\(20\) | 0.285507 | 0.0638413 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.80466 | −1.62738 | −0.813692 | − | 0.581296i | \(-0.802546\pi\) | ||||
−0.813692 | + | 0.581296i | \(0.802546\pi\) | |||||||
\(24\) | −2.73764 | −0.558818 | ||||||||
\(25\) | 0.698028 | 0.139606 | ||||||||
\(26\) | −1.32744 | −0.260332 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.119606 | 0.0226035 | ||||||||
\(29\) | −8.86742 | −1.64664 | −0.823320 | − | 0.567578i | \(-0.807880\pi\) | ||||
−0.823320 | + | 0.567578i | \(0.807880\pi\) | |||||||
\(30\) | 3.47528 | 0.634497 | ||||||||
\(31\) | −6.62627 | −1.19011 | −0.595056 | − | 0.803684i | \(-0.702870\pi\) | ||||
−0.595056 | + | 0.803684i | \(0.702870\pi\) | |||||||
\(32\) | 0.675706 | 0.119449 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.18348 | −0.545963 | ||||||||
\(35\) | 2.38705 | 0.403486 | ||||||||
\(36\) | 0.119606 | 0.0199344 | ||||||||
\(37\) | −4.20551 | −0.691382 | −0.345691 | − | 0.938348i | \(-0.612355\pi\) | ||||
−0.345691 | + | 0.938348i | \(0.612355\pi\) | |||||||
\(38\) | 1.03564 | 0.168003 | ||||||||
\(39\) | −0.911774 | −0.146001 | ||||||||
\(40\) | 6.53490 | 1.03326 | ||||||||
\(41\) | 11.9576 | 1.86746 | 0.933731 | − | 0.357975i | \(-0.116533\pi\) | ||||
0.933731 | + | 0.357975i | \(0.116533\pi\) | |||||||
\(42\) | 1.45589 | 0.224648 | ||||||||
\(43\) | −7.51601 | −1.14618 | −0.573091 | − | 0.819492i | \(-0.694256\pi\) | ||||
−0.573091 | + | 0.819492i | \(0.694256\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.38705 | 0.355841 | ||||||||
\(46\) | 11.3627 | 1.67534 | ||||||||
\(47\) | 6.27171 | 0.914823 | 0.457412 | − | 0.889255i | \(-0.348777\pi\) | ||||
0.457412 | + | 0.889255i | \(0.348777\pi\) | |||||||
\(48\) | 4.22491 | 0.609813 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.01625 | −0.143719 | ||||||||
\(51\) | −2.18663 | −0.306189 | ||||||||
\(52\) | 0.109054 | 0.0151231 | ||||||||
\(53\) | −6.56545 | −0.901834 | −0.450917 | − | 0.892566i | \(-0.648903\pi\) | ||||
−0.450917 | + | 0.892566i | \(0.648903\pi\) | |||||||
\(54\) | 1.45589 | 0.198121 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.73764 | 0.365833 | ||||||||
\(57\) | 0.711349 | 0.0942204 | ||||||||
\(58\) | 12.9100 | 1.69516 | ||||||||
\(59\) | −9.62312 | −1.25282 | −0.626412 | − | 0.779492i | \(-0.715477\pi\) | ||||
−0.626412 | + | 0.779492i | \(0.715477\pi\) | |||||||
\(60\) | −0.285507 | −0.0368588 | ||||||||
\(61\) | 0.0627598 | 0.00803556 | 0.00401778 | − | 0.999992i | \(-0.498721\pi\) | ||||
0.00401778 | + | 0.999992i | \(0.498721\pi\) | |||||||
\(62\) | 9.64709 | 1.22518 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 7.46606 | 0.933258 | ||||||||
\(65\) | 2.17645 | 0.269956 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3294 | −1.38410 | −0.692052 | − | 0.721847i | \(-0.743293\pi\) | ||||
−0.692052 | + | 0.721847i | \(0.743293\pi\) | |||||||
\(68\) | 0.261535 | 0.0317157 | ||||||||
\(69\) | 7.80466 | 0.939571 | ||||||||
\(70\) | −3.47528 | −0.415375 | ||||||||
\(71\) | −5.96945 | −0.708443 | −0.354221 | − | 0.935162i | \(-0.615254\pi\) | ||||
−0.354221 | + | 0.935162i | \(0.615254\pi\) | |||||||
\(72\) | 2.73764 | 0.322634 | ||||||||
\(73\) | 4.38705 | 0.513466 | 0.256733 | − | 0.966482i | \(-0.417354\pi\) | ||||
0.256733 | + | 0.966482i | \(0.417354\pi\) | |||||||
\(74\) | 6.12275 | 0.711755 | ||||||||
\(75\) | −0.698028 | −0.0806013 | ||||||||
\(76\) | −0.0850818 | −0.00975955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.32744 | 0.150303 | ||||||||
\(79\) | 4.85725 | 0.546483 | 0.273241 | − | 0.961945i | \(-0.411904\pi\) | ||||
0.273241 | + | 0.961945i | \(0.411904\pi\) | |||||||
\(80\) | −10.0851 | −1.12755 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.4089 | −1.92249 | ||||||||
\(83\) | −10.0490 | −1.10302 | −0.551509 | − | 0.834169i | \(-0.685948\pi\) | ||||
−0.551509 | + | 0.834169i | \(0.685948\pi\) | |||||||
\(84\) | −0.119606 | −0.0130501 | ||||||||
\(85\) | 5.21960 | 0.566145 | ||||||||
\(86\) | 10.9425 | 1.17996 | ||||||||
\(87\) | 8.86742 | 0.950688 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.261535 | −0.0277226 | −0.0138613 | − | 0.999904i | \(-0.504412\pi\) | ||||
−0.0138613 | + | 0.999904i | \(0.504412\pi\) | |||||||
\(90\) | −3.47528 | −0.366327 | ||||||||
\(91\) | 0.911774 | 0.0955798 | ||||||||
\(92\) | −0.933487 | −0.0973227 | ||||||||
\(93\) | 6.62627 | 0.687112 | ||||||||
\(94\) | −9.13090 | −0.941781 | ||||||||
\(95\) | −1.69803 | −0.174214 | ||||||||
\(96\) | −0.675706 | −0.0689639 | ||||||||
\(97\) | 9.88466 | 1.00363 | 0.501817 | − | 0.864974i | \(-0.332665\pi\) | ||||
0.501817 | + | 0.864974i | \(0.332665\pi\) | |||||||
\(98\) | −1.45589 | −0.147067 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0834885 | 0.00834885 | ||||||||
\(101\) | −9.94742 | −0.989805 | −0.494902 | − | 0.868949i | \(-0.664796\pi\) | ||||
−0.494902 | + | 0.868949i | \(0.664796\pi\) | |||||||
\(102\) | 3.18348 | 0.315212 | ||||||||
\(103\) | −0.658765 | −0.0649101 | −0.0324550 | − | 0.999473i | \(-0.510333\pi\) | ||||
−0.0324550 | + | 0.999473i | \(0.510333\pi\) | |||||||
\(104\) | 2.49611 | 0.244764 | ||||||||
\(105\) | −2.38705 | −0.232953 | ||||||||
\(106\) | 9.55855 | 0.928409 | ||||||||
\(107\) | −0.283088 | −0.0273672 | −0.0136836 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136836 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(108\) | −0.119606 | −0.0115091 | ||||||||
\(109\) | 8.97962 | 0.860092 | 0.430046 | − | 0.902807i | \(-0.358497\pi\) | ||||
0.430046 | + | 0.902807i | \(0.358497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.20551 | 0.399170 | ||||||||
\(112\) | −4.22491 | −0.399216 | ||||||||
\(113\) | 1.32938 | 0.125058 | 0.0625289 | − | 0.998043i | \(-0.480083\pi\) | ||||
0.0625289 | + | 0.998043i | \(0.480083\pi\) | |||||||
\(114\) | −1.03564 | −0.0969969 | ||||||||
\(115\) | −18.6302 | −1.73727 | ||||||||
\(116\) | −1.06060 | −0.0984742 | ||||||||
\(117\) | 0.911774 | 0.0842935 | ||||||||
\(118\) | 14.0102 | 1.28974 | ||||||||
\(119\) | 2.18663 | 0.200448 | ||||||||
\(120\) | −6.53490 | −0.596552 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −0.0913711 | −0.00827235 | ||||||||
\(123\) | −11.9576 | −1.07818 | ||||||||
\(124\) | −0.792543 | −0.0711725 | ||||||||
\(125\) | −10.2690 | −0.918491 | ||||||||
\(126\) | −1.45589 | −0.129701 | ||||||||
\(127\) | 21.8372 | 1.93773 | 0.968867 | − | 0.247580i | \(-0.0796354\pi\) | ||||
0.968867 | + | 0.247580i | \(0.0796354\pi\) | |||||||
\(128\) | −12.2212 | −1.08021 | ||||||||
\(129\) | 7.51601 | 0.661748 | ||||||||
\(130\) | −3.16867 | −0.277911 | ||||||||
\(131\) | 9.22227 | 0.805754 | 0.402877 | − | 0.915254i | \(-0.368010\pi\) | ||||
0.402877 | + | 0.915254i | \(0.368010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.711349 | −0.0616817 | ||||||||
\(134\) | 16.4943 | 1.42489 | ||||||||
\(135\) | −2.38705 | −0.205445 | ||||||||
\(136\) | 5.98620 | 0.513313 | ||||||||
\(137\) | −2.04750 | −0.174929 | −0.0874647 | − | 0.996168i | \(-0.527876\pi\) | ||||
−0.0874647 | + | 0.996168i | \(0.527876\pi\) | |||||||
\(138\) | −11.3627 | −0.967258 | ||||||||
\(139\) | 12.8454 | 1.08953 | 0.544766 | − | 0.838588i | \(-0.316618\pi\) | ||||
0.544766 | + | 0.838588i | \(0.316618\pi\) | |||||||
\(140\) | 0.285507 | 0.0241297 | ||||||||
\(141\) | −6.27171 | −0.528173 | ||||||||
\(142\) | 8.69084 | 0.729319 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.22491 | −0.352076 | ||||||||
\(145\) | −21.1670 | −1.75783 | ||||||||
\(146\) | −6.38705 | −0.528596 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −0.503006 | −0.0413468 | ||||||||
\(149\) | −15.3451 | −1.25712 | −0.628561 | − | 0.777761i | \(-0.716356\pi\) | ||||
−0.628561 | + | 0.777761i | \(0.716356\pi\) | |||||||
\(150\) | 1.01625 | 0.0829764 | ||||||||
\(151\) | 6.90936 | 0.562275 | 0.281138 | − | 0.959667i | \(-0.409288\pi\) | ||||
0.281138 | + | 0.959667i | \(0.409288\pi\) | |||||||
\(152\) | −1.94742 | −0.157956 | ||||||||
\(153\) | 2.18663 | 0.176778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.8173 | −1.27047 | ||||||||
\(156\) | −0.109054 | −0.00873130 | ||||||||
\(157\) | −9.33762 | −0.745223 | −0.372611 | − | 0.927987i | \(-0.621538\pi\) | ||||
−0.372611 | + | 0.927987i | \(0.621538\pi\) | |||||||
\(158\) | −7.07160 | −0.562586 | ||||||||
\(159\) | 6.56545 | 0.520674 | ||||||||
\(160\) | 1.61295 | 0.127515 | ||||||||
\(161\) | −7.80466 | −0.615094 | ||||||||
\(162\) | −1.45589 | −0.114385 | ||||||||
\(163\) | 10.4309 | 0.817013 | 0.408507 | − | 0.912755i | \(-0.366050\pi\) | ||||
0.408507 | + | 0.912755i | \(0.366050\pi\) | |||||||
\(164\) | 1.43020 | 0.111680 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.6302 | 1.13552 | ||||||||
\(167\) | −1.35141 | −0.104575 | −0.0522877 | − | 0.998632i | \(-0.516651\pi\) | ||||
−0.0522877 | + | 0.998632i | \(0.516651\pi\) | |||||||
\(168\) | −2.73764 | −0.211214 | ||||||||
\(169\) | −12.1687 | −0.936051 | ||||||||
\(170\) | −7.59915 | −0.582828 | ||||||||
\(171\) | −0.711349 | −0.0543982 | ||||||||
\(172\) | −0.898962 | −0.0685452 | ||||||||
\(173\) | −19.4855 | −1.48145 | −0.740726 | − | 0.671807i | \(-0.765518\pi\) | ||||
−0.740726 | + | 0.671807i | \(0.765518\pi\) | |||||||
\(174\) | −12.9100 | −0.978702 | ||||||||
\(175\) | 0.698028 | 0.0527659 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.62312 | 0.723318 | ||||||||
\(178\) | 0.380765 | 0.0285395 | ||||||||
\(179\) | −12.8541 | −0.960761 | −0.480380 | − | 0.877060i | \(-0.659501\pi\) | ||||
−0.480380 | + | 0.877060i | \(0.659501\pi\) | |||||||
\(180\) | 0.285507 | 0.0212804 | ||||||||
\(181\) | 14.3749 | 1.06848 | 0.534239 | − | 0.845333i | \(-0.320598\pi\) | ||||
0.534239 | + | 0.845333i | \(0.320598\pi\) | |||||||
\(182\) | −1.32744 | −0.0983963 | ||||||||
\(183\) | −0.0627598 | −0.00463933 | ||||||||
\(184\) | −21.3664 | −1.57515 | ||||||||
\(185\) | −10.0388 | −0.738066 | ||||||||
\(186\) | −9.64709 | −0.707359 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.750136 | 0.0547093 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 2.47214 | 0.179348 | ||||||||
\(191\) | −23.9520 | −1.73311 | −0.866554 | − | 0.499083i | \(-0.833670\pi\) | ||||
−0.866554 | + | 0.499083i | \(0.833670\pi\) | |||||||
\(192\) | −7.46606 | −0.538817 | ||||||||
\(193\) | −0.139609 | −0.0100493 | −0.00502463 | − | 0.999987i | \(-0.501599\pi\) | ||||
−0.00502463 | + | 0.999987i | \(0.501599\pi\) | |||||||
\(194\) | −14.3909 | −1.03321 | ||||||||
\(195\) | −2.17645 | −0.155859 | ||||||||
\(196\) | 0.119606 | 0.00854331 | ||||||||
\(197\) | −14.6113 | −1.04101 | −0.520505 | − | 0.853859i | \(-0.674256\pi\) | ||||
−0.520505 | + | 0.853859i | \(0.674256\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.4702 | −1.87642 | −0.938210 | − | 0.346066i | \(-0.887517\pi\) | ||||
−0.938210 | + | 0.346066i | \(0.887517\pi\) | |||||||
\(200\) | 1.91095 | 0.135124 | ||||||||
\(201\) | 11.3294 | 0.799113 | ||||||||
\(202\) | 14.4823 | 1.01897 | ||||||||
\(203\) | −8.86742 | −0.622371 | ||||||||
\(204\) | −0.261535 | −0.0183111 | ||||||||
\(205\) | 28.5434 | 1.99356 | ||||||||
\(206\) | 0.959087 | 0.0668228 | ||||||||
\(207\) | −7.80466 | −0.542462 | ||||||||
\(208\) | −3.85216 | −0.267099 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.47528 | 0.239817 | ||||||||
\(211\) | −17.5618 | −1.20901 | −0.604503 | − | 0.796603i | \(-0.706628\pi\) | ||||
−0.604503 | + | 0.796603i | \(0.706628\pi\) | |||||||
\(212\) | −0.785269 | −0.0539325 | ||||||||
\(213\) | 5.96945 | 0.409020 | ||||||||
\(214\) | 0.412145 | 0.0281736 | ||||||||
\(215\) | −17.9411 | −1.22357 | ||||||||
\(216\) | −2.73764 | −0.186273 | ||||||||
\(217\) | −6.62627 | −0.449820 | ||||||||
\(218\) | −13.0733 | −0.885436 | ||||||||
\(219\) | −4.38705 | −0.296450 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.99371 | 0.134111 | ||||||||
\(222\) | −6.12275 | −0.410932 | ||||||||
\(223\) | 22.5839 | 1.51233 | 0.756164 | − | 0.654383i | \(-0.227071\pi\) | ||||
0.756164 | + | 0.654383i | \(0.227071\pi\) | |||||||
\(224\) | 0.675706 | 0.0451475 | ||||||||
\(225\) | 0.698028 | 0.0465352 | ||||||||
\(226\) | −1.93543 | −0.128743 | ||||||||
\(227\) | −21.9714 | −1.45829 | −0.729146 | − | 0.684358i | \(-0.760083\pi\) | ||||
−0.729146 | + | 0.684358i | \(0.760083\pi\) | |||||||
\(228\) | 0.0850818 | 0.00563468 | ||||||||
\(229\) | 23.3803 | 1.54501 | 0.772507 | − | 0.635007i | \(-0.219003\pi\) | ||||
0.772507 | + | 0.635007i | \(0.219003\pi\) | |||||||
\(230\) | 27.1234 | 1.78846 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.2758 | −1.59379 | ||||||||
\(233\) | 1.04315 | 0.0683390 | 0.0341695 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341695 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(234\) | −1.32744 | −0.0867774 | ||||||||
\(235\) | 14.9709 | 0.976595 | ||||||||
\(236\) | −1.15099 | −0.0749228 | ||||||||
\(237\) | −4.85725 | −0.315512 | ||||||||
\(238\) | −3.18348 | −0.206355 | ||||||||
\(239\) | 12.4140 | 0.802994 | 0.401497 | − | 0.915860i | \(-0.368490\pi\) | ||||
0.401497 | + | 0.915860i | \(0.368490\pi\) | |||||||
\(240\) | 10.0851 | 0.650989 | ||||||||
\(241\) | −9.42435 | −0.607076 | −0.303538 | − | 0.952819i | \(-0.598168\pi\) | ||||
−0.303538 | + | 0.952819i | \(0.598168\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.00750646 | 0.000480552 0 | ||||||||
\(245\) | 2.38705 | 0.152503 | ||||||||
\(246\) | 17.4089 | 1.10995 | ||||||||
\(247\) | −0.648589 | −0.0412687 | ||||||||
\(248\) | −18.1403 | −1.15191 | ||||||||
\(249\) | 10.0490 | 0.636827 | ||||||||
\(250\) | 14.9506 | 0.945557 | ||||||||
\(251\) | −3.07219 | −0.193915 | −0.0969576 | − | 0.995289i | \(-0.530911\pi\) | ||||
−0.0969576 | + | 0.995289i | \(0.530911\pi\) | |||||||
\(252\) | 0.119606 | 0.00753449 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −31.7924 | −1.99483 | ||||||||
\(255\) | −5.21960 | −0.326864 | ||||||||
\(256\) | 2.86049 | 0.178781 | ||||||||
\(257\) | 0.626267 | 0.0390654 | 0.0195327 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195327 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(258\) | −10.9425 | −0.681248 | ||||||||
\(259\) | −4.20551 | −0.261318 | ||||||||
\(260\) | 0.260318 | 0.0161442 | ||||||||
\(261\) | −8.86742 | −0.548880 | ||||||||
\(262\) | −13.4266 | −0.829497 | ||||||||
\(263\) | −1.02517 | −0.0632149 | −0.0316074 | − | 0.999500i | \(-0.510063\pi\) | ||||
−0.0316074 | + | 0.999500i | \(0.510063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.6721 | −0.962729 | ||||||||
\(266\) | 1.03564 | 0.0634993 | ||||||||
\(267\) | 0.261535 | 0.0160057 | ||||||||
\(268\) | −1.35507 | −0.0827738 | ||||||||
\(269\) | 32.0066 | 1.95147 | 0.975737 | − | 0.218945i | \(-0.0702617\pi\) | ||||
0.975737 | + | 0.218945i | \(0.0702617\pi\) | |||||||
\(270\) | 3.47528 | 0.211499 | ||||||||
\(271\) | −5.95536 | −0.361762 | −0.180881 | − | 0.983505i | \(-0.557895\pi\) | ||||
−0.180881 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(272\) | −9.23830 | −0.560155 | ||||||||
\(273\) | −0.911774 | −0.0551830 | ||||||||
\(274\) | 2.98092 | 0.180084 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.933487 | 0.0561893 | ||||||||
\(277\) | 1.27771 | 0.0767700 | 0.0383850 | − | 0.999263i | \(-0.487779\pi\) | ||||
0.0383850 | + | 0.999263i | \(0.487779\pi\) | |||||||
\(278\) | −18.7014 | −1.12164 | ||||||||
\(279\) | −6.62627 | −0.396704 | ||||||||
\(280\) | 6.53490 | 0.390535 | ||||||||
\(281\) | 4.45011 | 0.265471 | 0.132736 | − | 0.991151i | \(-0.457624\pi\) | ||||
0.132736 | + | 0.991151i | \(0.457624\pi\) | |||||||
\(282\) | 9.13090 | 0.543737 | ||||||||
\(283\) | −22.7964 | −1.35511 | −0.677554 | − | 0.735473i | \(-0.736960\pi\) | ||||
−0.677554 | + | 0.735473i | \(0.736960\pi\) | |||||||
\(284\) | −0.713983 | −0.0423671 | ||||||||
\(285\) | 1.69803 | 0.100582 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.9576 | 0.705834 | ||||||||
\(288\) | 0.675706 | 0.0398163 | ||||||||
\(289\) | −12.2187 | −0.718744 | ||||||||
\(290\) | 30.8168 | 1.80962 | ||||||||
\(291\) | −9.88466 | −0.579449 | ||||||||
\(292\) | 0.524719 | 0.0307069 | ||||||||
\(293\) | 8.39334 | 0.490344 | 0.245172 | − | 0.969480i | \(-0.421156\pi\) | ||||
0.245172 | + | 0.969480i | \(0.421156\pi\) | |||||||
\(294\) | 1.45589 | 0.0849090 | ||||||||
\(295\) | −22.9709 | −1.33742 | ||||||||
\(296\) | −11.5132 | −0.669190 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.3408 | 1.29417 | ||||||||
\(299\) | −7.11609 | −0.411534 | ||||||||
\(300\) | −0.0834885 | −0.00482021 | ||||||||
\(301\) | −7.51601 | −0.433216 | ||||||||
\(302\) | −10.0592 | −0.578844 | ||||||||
\(303\) | 9.94742 | 0.571464 | ||||||||
\(304\) | 3.00538 | 0.172370 | ||||||||
\(305\) | 0.149811 | 0.00857815 | ||||||||
\(306\) | −3.18348 | −0.181988 | ||||||||
\(307\) | −11.0560 | −0.630999 | −0.315500 | − | 0.948926i | \(-0.602172\pi\) | ||||
−0.315500 | + | 0.948926i | \(0.602172\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.658765 | 0.0374758 | ||||||||
\(310\) | 23.0281 | 1.30791 | ||||||||
\(311\) | −22.5914 | −1.28104 | −0.640519 | − | 0.767942i | \(-0.721281\pi\) | ||||
−0.640519 | + | 0.767942i | \(0.721281\pi\) | |||||||
\(312\) | −2.49611 | −0.141314 | ||||||||
\(313\) | 2.54869 | 0.144061 | 0.0720303 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720303 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(314\) | 13.5945 | 0.767183 | ||||||||
\(315\) | 2.38705 | 0.134495 | ||||||||
\(316\) | 0.580957 | 0.0326814 | ||||||||
\(317\) | 31.3434 | 1.76042 | 0.880212 | − | 0.474581i | \(-0.157401\pi\) | ||||
0.880212 | + | 0.474581i | \(0.157401\pi\) | |||||||
\(318\) | −9.55855 | −0.536017 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 17.8219 | 0.996274 | ||||||||
\(321\) | 0.283088 | 0.0158005 | ||||||||
\(322\) | 11.3627 | 0.633219 | ||||||||
\(323\) | −1.55546 | −0.0865479 | ||||||||
\(324\) | 0.119606 | 0.00664480 | ||||||||
\(325\) | 0.636443 | 0.0353035 | ||||||||
\(326\) | −15.1863 | −0.841089 | ||||||||
\(327\) | −8.97962 | −0.496574 | ||||||||
\(328\) | 32.7356 | 1.80752 | ||||||||
\(329\) | 6.27171 | 0.345771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.82789 | −0.265365 | −0.132682 | − | 0.991159i | \(-0.542359\pi\) | ||||
−0.132682 | + | 0.991159i | \(0.542359\pi\) | |||||||
\(332\) | −1.20192 | −0.0659639 | ||||||||
\(333\) | −4.20551 | −0.230461 | ||||||||
\(334\) | 1.96750 | 0.107657 | ||||||||
\(335\) | −27.0438 | −1.47756 | ||||||||
\(336\) | 4.22491 | 0.230488 | ||||||||
\(337\) | −21.1153 | −1.15022 | −0.575112 | − | 0.818074i | \(-0.695042\pi\) | ||||
−0.575112 | + | 0.818074i | \(0.695042\pi\) | |||||||
\(338\) | 17.7162 | 0.963634 | ||||||||
\(339\) | −1.32938 | −0.0722022 | ||||||||
\(340\) | 0.624297 | 0.0338573 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.03564 | 0.0560012 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −20.5761 | −1.10939 | ||||||||
\(345\) | 18.6302 | 1.00301 | ||||||||
\(346\) | 28.3686 | 1.52511 | ||||||||
\(347\) | 12.4251 | 0.667015 | 0.333508 | − | 0.942747i | \(-0.391768\pi\) | ||||
0.333508 | + | 0.942747i | \(0.391768\pi\) | |||||||
\(348\) | 1.06060 | 0.0568541 | ||||||||
\(349\) | −16.9682 | −0.908289 | −0.454145 | − | 0.890928i | \(-0.650055\pi\) | ||||
−0.454145 | + | 0.890928i | \(0.650055\pi\) | |||||||
\(350\) | −1.01625 | −0.0543208 | ||||||||
\(351\) | −0.911774 | −0.0486669 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.57101 | −0.243291 | −0.121645 | − | 0.992574i | \(-0.538817\pi\) | ||||
−0.121645 | + | 0.992574i | \(0.538817\pi\) | |||||||
\(354\) | −14.0102 | −0.744632 | ||||||||
\(355\) | −14.2494 | −0.756279 | ||||||||
\(356\) | −0.0312812 | −0.00165790 | ||||||||
\(357\) | −2.18663 | −0.115729 | ||||||||
\(358\) | 18.7141 | 0.989072 | ||||||||
\(359\) | 30.9733 | 1.63471 | 0.817355 | − | 0.576134i | \(-0.195440\pi\) | ||||
0.817355 | + | 0.576134i | \(0.195440\pi\) | |||||||
\(360\) | 6.53490 | 0.344419 | ||||||||
\(361\) | −18.4940 | −0.973368 | ||||||||
\(362\) | −20.9282 | −1.09996 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.109054 | 0.00571598 | ||||||||
\(365\) | 10.4721 | 0.548137 | ||||||||
\(366\) | 0.0913711 | 0.00477604 | ||||||||
\(367\) | 14.7422 | 0.769536 | 0.384768 | − | 0.923013i | \(-0.374281\pi\) | ||||
0.384768 | + | 0.923013i | \(0.374281\pi\) | |||||||
\(368\) | 32.9740 | 1.71889 | ||||||||
\(369\) | 11.9576 | 0.622487 | ||||||||
\(370\) | 14.6153 | 0.759815 | ||||||||
\(371\) | −6.56545 | −0.340861 | ||||||||
\(372\) | 0.792543 | 0.0410915 | ||||||||
\(373\) | 12.5701 | 0.650853 | 0.325427 | − | 0.945567i | \(-0.394492\pi\) | ||||
0.325427 | + | 0.945567i | \(0.394492\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2690 | 0.530291 | ||||||||
\(376\) | 17.1697 | 0.885459 | ||||||||
\(377\) | −8.08508 | −0.416403 | ||||||||
\(378\) | 1.45589 | 0.0748827 | ||||||||
\(379\) | 16.0340 | 0.823610 | 0.411805 | − | 0.911272i | \(-0.364899\pi\) | ||||
0.411805 | + | 0.911272i | \(0.364899\pi\) | |||||||
\(380\) | −0.203095 | −0.0104185 | ||||||||
\(381\) | −21.8372 | −1.11875 | ||||||||
\(382\) | 34.8714 | 1.78418 | ||||||||
\(383\) | −2.81023 | −0.143596 | −0.0717979 | − | 0.997419i | \(-0.522874\pi\) | ||||
−0.0717979 | + | 0.997419i | \(0.522874\pi\) | |||||||
\(384\) | 12.2212 | 0.623658 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.203254 | 0.0103454 | ||||||||
\(387\) | −7.51601 | −0.382060 | ||||||||
\(388\) | 1.18227 | 0.0600205 | ||||||||
\(389\) | −20.6050 | −1.04471 | −0.522357 | − | 0.852727i | \(-0.674947\pi\) | ||||
−0.522357 | + | 0.852727i | \(0.674947\pi\) | |||||||
\(390\) | 3.16867 | 0.160452 | ||||||||
\(391\) | −17.0659 | −0.863060 | ||||||||
\(392\) | 2.73764 | 0.138272 | ||||||||
\(393\) | −9.22227 | −0.465202 | ||||||||
\(394\) | 21.2724 | 1.07169 | ||||||||
\(395\) | 11.5945 | 0.583383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6588 | 1.43834 | 0.719171 | − | 0.694833i | \(-0.244522\pi\) | ||||
0.719171 | + | 0.694833i | \(0.244522\pi\) | |||||||
\(398\) | 38.5376 | 1.93171 | ||||||||
\(399\) | 0.711349 | 0.0356120 | ||||||||
\(400\) | −2.94910 | −0.147455 | ||||||||
\(401\) | −22.3156 | −1.11439 | −0.557194 | − | 0.830383i | \(-0.688122\pi\) | ||||
−0.557194 | + | 0.830383i | \(0.688122\pi\) | |||||||
\(402\) | −16.4943 | −0.822661 | ||||||||
\(403\) | −6.04165 | −0.300956 | ||||||||
\(404\) | −1.18977 | −0.0591935 | ||||||||
\(405\) | 2.38705 | 0.118614 | ||||||||
\(406\) | 12.9100 | 0.640711 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.98620 | −0.296361 | ||||||||
\(409\) | −16.4360 | −0.812709 | −0.406354 | − | 0.913716i | \(-0.633200\pi\) | ||||
−0.406354 | + | 0.913716i | \(0.633200\pi\) | |||||||
\(410\) | −41.5560 | −2.05230 | ||||||||
\(411\) | 2.04750 | 0.100995 | ||||||||
\(412\) | −0.0787925 | −0.00388183 | ||||||||
\(413\) | −9.62312 | −0.473523 | ||||||||
\(414\) | 11.3627 | 0.558447 | ||||||||
\(415\) | −23.9874 | −1.17750 | ||||||||
\(416\) | 0.616090 | 0.0302063 | ||||||||
\(417\) | −12.8454 | −0.629042 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7725 | −0.623975 | −0.311988 | − | 0.950086i | \(-0.600995\pi\) | ||||
−0.311988 | + | 0.950086i | \(0.600995\pi\) | |||||||
\(420\) | −0.285507 | −0.0139313 | ||||||||
\(421\) | 10.8032 | 0.526514 | 0.263257 | − | 0.964726i | \(-0.415203\pi\) | ||||
0.263257 | + | 0.964726i | \(0.415203\pi\) | |||||||
\(422\) | 25.5680 | 1.24463 | ||||||||
\(423\) | 6.27171 | 0.304941 | ||||||||
\(424\) | −17.9738 | −0.872887 | ||||||||
\(425\) | 1.52633 | 0.0740378 | ||||||||
\(426\) | −8.69084 | −0.421072 | ||||||||
\(427\) | 0.0627598 | 0.00303716 | ||||||||
\(428\) | −0.0338592 | −0.00163664 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.1202 | 1.25963 | ||||||||
\(431\) | −27.5395 | −1.32653 | −0.663266 | − | 0.748384i | \(-0.730830\pi\) | ||||
−0.663266 | + | 0.748384i | \(0.730830\pi\) | |||||||
\(432\) | 4.22491 | 0.203271 | ||||||||
\(433\) | 15.2600 | 0.733351 | 0.366675 | − | 0.930349i | \(-0.380496\pi\) | ||||
0.366675 | + | 0.930349i | \(0.380496\pi\) | |||||||
\(434\) | 9.64709 | 0.463075 | ||||||||
\(435\) | 21.1670 | 1.01488 | ||||||||
\(436\) | 1.07402 | 0.0514362 | ||||||||
\(437\) | 5.55184 | 0.265580 | ||||||||
\(438\) | 6.38705 | 0.305185 | ||||||||
\(439\) | 28.5500 | 1.36262 | 0.681308 | − | 0.731997i | \(-0.261411\pi\) | ||||
0.681308 | + | 0.731997i | \(0.261411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −2.90262 | −0.138063 | ||||||||
\(443\) | 11.3310 | 0.538354 | 0.269177 | − | 0.963091i | \(-0.413248\pi\) | ||||
0.269177 | + | 0.963091i | \(0.413248\pi\) | |||||||
\(444\) | 0.503006 | 0.0238716 | ||||||||
\(445\) | −0.624297 | −0.0295945 | ||||||||
\(446\) | −32.8795 | −1.55689 | ||||||||
\(447\) | 15.3451 | 0.725799 | ||||||||
\(448\) | 7.46606 | 0.352738 | ||||||||
\(449\) | −26.8968 | −1.26934 | −0.634669 | − | 0.772784i | \(-0.718863\pi\) | ||||
−0.634669 | + | 0.772784i | \(0.718863\pi\) | |||||||
\(450\) | −1.01625 | −0.0479064 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.159003 | 0.00747885 | ||||||||
\(453\) | −6.90936 | −0.324630 | ||||||||
\(454\) | 31.9879 | 1.50126 | ||||||||
\(455\) | 2.17645 | 0.102034 | ||||||||
\(456\) | 1.94742 | 0.0911961 | ||||||||
\(457\) | 28.9694 | 1.35513 | 0.677567 | − | 0.735461i | \(-0.263034\pi\) | ||||
0.677567 | + | 0.735461i | \(0.263034\pi\) | |||||||
\(458\) | −34.0391 | −1.59054 | ||||||||
\(459\) | −2.18663 | −0.102063 | ||||||||
\(460\) | −2.22828 | −0.103894 | ||||||||
\(461\) | 41.9375 | 1.95322 | 0.976612 | − | 0.215008i | \(-0.0689778\pi\) | ||||
0.976612 | + | 0.215008i | \(0.0689778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.14904 | −0.0534005 | −0.0267003 | − | 0.999643i | \(-0.508500\pi\) | ||||
−0.0267003 | + | 0.999643i | \(0.508500\pi\) | |||||||
\(464\) | 37.4640 | 1.73922 | ||||||||
\(465\) | 15.8173 | 0.733508 | ||||||||
\(466\) | −1.51871 | −0.0703528 | ||||||||
\(467\) | 29.5887 | 1.36920 | 0.684600 | − | 0.728919i | \(-0.259977\pi\) | ||||
0.684600 | + | 0.728919i | \(0.259977\pi\) | |||||||
\(468\) | 0.109054 | 0.00504102 | ||||||||
\(469\) | −11.3294 | −0.523142 | ||||||||
\(470\) | −21.7960 | −1.00537 | ||||||||
\(471\) | 9.33762 | 0.430255 | ||||||||
\(472\) | −26.3446 | −1.21261 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7.07160 | 0.324809 | ||||||||
\(475\) | −0.496541 | −0.0227829 | ||||||||
\(476\) | 0.261535 | 0.0119874 | ||||||||
\(477\) | −6.56545 | −0.300611 | ||||||||
\(478\) | −18.0734 | −0.826656 | ||||||||
\(479\) | 10.1728 | 0.464809 | 0.232404 | − | 0.972619i | \(-0.425341\pi\) | ||||
0.232404 | + | 0.972619i | \(0.425341\pi\) | |||||||
\(480\) | −1.61295 | −0.0736206 | ||||||||
\(481\) | −3.83448 | −0.174837 | ||||||||
\(482\) | 13.7208 | 0.624965 | ||||||||
\(483\) | 7.80466 | 0.355124 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.5952 | 1.07140 | ||||||||
\(486\) | 1.45589 | 0.0660404 | ||||||||
\(487\) | 43.8320 | 1.98622 | 0.993110 | − | 0.117187i | \(-0.0373878\pi\) | ||||
0.993110 | + | 0.117187i | \(0.0373878\pi\) | |||||||
\(488\) | 0.171814 | 0.00777764 | ||||||||
\(489\) | −10.4309 | −0.471703 | ||||||||
\(490\) | −3.47528 | −0.156997 | ||||||||
\(491\) | −19.1207 | −0.862906 | −0.431453 | − | 0.902135i | \(-0.641999\pi\) | ||||
−0.431453 | + | 0.902135i | \(0.641999\pi\) | |||||||
\(492\) | −1.43020 | −0.0644786 | ||||||||
\(493\) | −19.3898 | −0.873271 | ||||||||
\(494\) | 0.944272 | 0.0424848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.9954 | 1.25703 | ||||||||
\(497\) | −5.96945 | −0.267766 | ||||||||
\(498\) | −14.6302 | −0.655593 | ||||||||
\(499\) | 20.4971 | 0.917576 | 0.458788 | − | 0.888546i | \(-0.348284\pi\) | ||||
0.458788 | + | 0.888546i | \(0.348284\pi\) | |||||||
\(500\) | −1.22824 | −0.0549287 | ||||||||
\(501\) | 1.35141 | 0.0603766 | ||||||||
\(502\) | 4.47277 | 0.199629 | ||||||||
\(503\) | −18.9794 | −0.846251 | −0.423126 | − | 0.906071i | \(-0.639067\pi\) | ||||
−0.423126 | + | 0.906071i | \(0.639067\pi\) | |||||||
\(504\) | 2.73764 | 0.121944 | ||||||||
\(505\) | −23.7450 | −1.05664 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1687 | 0.540430 | ||||||||
\(508\) | 2.61186 | 0.115883 | ||||||||
\(509\) | 23.5548 | 1.04405 | 0.522023 | − | 0.852931i | \(-0.325177\pi\) | ||||
0.522023 | + | 0.852931i | \(0.325177\pi\) | |||||||
\(510\) | 7.59915 | 0.336496 | ||||||||
\(511\) | 4.38705 | 0.194072 | ||||||||
\(512\) | 20.2778 | 0.896159 | ||||||||
\(513\) | 0.711349 | 0.0314068 | ||||||||
\(514\) | −0.911774 | −0.0402166 | ||||||||
\(515\) | −1.57251 | −0.0692930 | ||||||||
\(516\) | 0.898962 | 0.0395746 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.12275 | 0.269018 | ||||||||
\(519\) | 19.4855 | 0.855317 | ||||||||
\(520\) | 5.95835 | 0.261291 | ||||||||
\(521\) | −5.09046 | −0.223017 | −0.111509 | − | 0.993763i | \(-0.535568\pi\) | ||||
−0.111509 | + | 0.993763i | \(0.535568\pi\) | |||||||
\(522\) | 12.9100 | 0.565054 | ||||||||
\(523\) | −22.7768 | −0.995959 | −0.497979 | − | 0.867189i | \(-0.665925\pi\) | ||||
−0.497979 | + | 0.867189i | \(0.665925\pi\) | |||||||
\(524\) | 1.10304 | 0.0481866 | ||||||||
\(525\) | −0.698028 | −0.0304644 | ||||||||
\(526\) | 1.49254 | 0.0650777 | ||||||||
\(527\) | −14.4892 | −0.631159 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.9128 | 1.64838 | ||||||||
\(530\) | 22.8168 | 0.991098 | ||||||||
\(531\) | −9.62312 | −0.417608 | ||||||||
\(532\) | −0.0850818 | −0.00368876 | ||||||||
\(533\) | 10.9026 | 0.472245 | ||||||||
\(534\) | −0.380765 | −0.0164773 | ||||||||
\(535\) | −0.675747 | −0.0292151 | ||||||||
\(536\) | −31.0158 | −1.33968 | ||||||||
\(537\) | 12.8541 | 0.554695 | ||||||||
\(538\) | −46.5979 | −2.00898 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.285507 | −0.0122863 | ||||||||
\(541\) | 11.4416 | 0.491912 | 0.245956 | − | 0.969281i | \(-0.420898\pi\) | ||||
0.245956 | + | 0.969281i | \(0.420898\pi\) | |||||||
\(542\) | 8.67032 | 0.372422 | ||||||||
\(543\) | −14.3749 | −0.616886 | ||||||||
\(544\) | 1.47752 | 0.0633480 | ||||||||
\(545\) | 21.4348 | 0.918168 | ||||||||
\(546\) | 1.32744 | 0.0568091 | ||||||||
\(547\) | −3.79691 | −0.162344 | −0.0811720 | − | 0.996700i | \(-0.525866\pi\) | ||||
−0.0811720 | + | 0.996700i | \(0.525866\pi\) | |||||||
\(548\) | −0.244893 | −0.0104613 | ||||||||
\(549\) | 0.0627598 | 0.00267852 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.30783 | 0.268723 | ||||||||
\(552\) | 21.3664 | 0.909413 | ||||||||
\(553\) | 4.85725 | 0.206551 | ||||||||
\(554\) | −1.86020 | −0.0790322 | ||||||||
\(555\) | 10.0388 | 0.426123 | ||||||||
\(556\) | 1.53639 | 0.0651575 | ||||||||
\(557\) | 3.48937 | 0.147849 | 0.0739247 | − | 0.997264i | \(-0.476448\pi\) | ||||
0.0739247 | + | 0.997264i | \(0.476448\pi\) | |||||||
\(558\) | 9.64709 | 0.408394 | ||||||||
\(559\) | −6.85290 | −0.289847 | ||||||||
\(560\) | −10.0851 | −0.426172 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.47885 | −0.273294 | ||||||||
\(563\) | 28.1619 | 1.18688 | 0.593441 | − | 0.804877i | \(-0.297769\pi\) | ||||
0.593441 | + | 0.804877i | \(0.297769\pi\) | |||||||
\(564\) | −0.750136 | −0.0315864 | ||||||||
\(565\) | 3.17331 | 0.133502 | ||||||||
\(566\) | 33.1890 | 1.39504 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −16.3422 | −0.685703 | ||||||||
\(569\) | −21.5992 | −0.905483 | −0.452742 | − | 0.891642i | \(-0.649554\pi\) | ||||
−0.452742 | + | 0.891642i | \(0.649554\pi\) | |||||||
\(570\) | −2.47214 | −0.103546 | ||||||||
\(571\) | −14.4959 | −0.606636 | −0.303318 | − | 0.952889i | \(-0.598094\pi\) | ||||
−0.303318 | + | 0.952889i | \(0.598094\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.9520 | 1.00061 | ||||||||
\(574\) | −17.4089 | −0.726634 | ||||||||
\(575\) | −5.44787 | −0.227192 | ||||||||
\(576\) | 7.46606 | 0.311086 | ||||||||
\(577\) | 5.07081 | 0.211101 | 0.105550 | − | 0.994414i | \(-0.466340\pi\) | ||||
0.105550 | + | 0.994414i | \(0.466340\pi\) | |||||||
\(578\) | 17.7890 | 0.739924 | ||||||||
\(579\) | 0.139609 | 0.00580194 | ||||||||
\(580\) | −2.53171 | −0.105124 | ||||||||
\(581\) | −10.0490 | −0.416901 | ||||||||
\(582\) | 14.3909 | 0.596524 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.0102 | 0.496985 | ||||||||
\(585\) | 2.17645 | 0.0899853 | ||||||||
\(586\) | −12.2198 | −0.504794 | ||||||||
\(587\) | −43.3905 | −1.79092 | −0.895458 | − | 0.445146i | \(-0.853152\pi\) | ||||
−0.895458 | + | 0.445146i | \(0.853152\pi\) | |||||||
\(588\) | −0.119606 | −0.00493248 | ||||||||
\(589\) | 4.71359 | 0.194220 | ||||||||
\(590\) | 33.4430 | 1.37683 | ||||||||
\(591\) | 14.6113 | 0.601027 | ||||||||
\(592\) | 17.7679 | 0.730256 | ||||||||
\(593\) | 31.4532 | 1.29163 | 0.645815 | − | 0.763494i | \(-0.276518\pi\) | ||||
0.645815 | + | 0.763494i | \(0.276518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.21960 | 0.213983 | ||||||||
\(596\) | −1.83537 | −0.0751798 | ||||||||
\(597\) | 26.4702 | 1.08335 | ||||||||
\(598\) | 10.3602 | 0.423661 | ||||||||
\(599\) | −22.1842 | −0.906422 | −0.453211 | − | 0.891403i | \(-0.649722\pi\) | ||||
−0.453211 | + | 0.891403i | \(0.649722\pi\) | |||||||
\(600\) | −1.91095 | −0.0780141 | ||||||||
\(601\) | −32.2182 | −1.31421 | −0.657103 | − | 0.753800i | \(-0.728219\pi\) | ||||
−0.657103 | + | 0.753800i | \(0.728219\pi\) | |||||||
\(602\) | 10.9425 | 0.445981 | ||||||||
\(603\) | −11.3294 | −0.461368 | ||||||||
\(604\) | 0.826403 | 0.0336258 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.4823 | −0.588304 | ||||||||
\(607\) | −30.2533 | −1.22794 | −0.613971 | − | 0.789328i | \(-0.710429\pi\) | ||||
−0.613971 | + | 0.789328i | \(0.710429\pi\) | |||||||
\(608\) | −0.480662 | −0.0194934 | ||||||||
\(609\) | 8.86742 | 0.359326 | ||||||||
\(610\) | −0.218108 | −0.00883092 | ||||||||
\(611\) | 5.71838 | 0.231341 | ||||||||
\(612\) | 0.261535 | 0.0105719 | ||||||||
\(613\) | 4.18959 | 0.169216 | 0.0846080 | − | 0.996414i | \(-0.473036\pi\) | ||||
0.0846080 | + | 0.996414i | \(0.473036\pi\) | |||||||
\(614\) | 16.0963 | 0.649593 | ||||||||
\(615\) | −28.5434 | −1.15098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1457 | −1.25388 | −0.626939 | − | 0.779068i | \(-0.715693\pi\) | ||||
−0.626939 | + | 0.779068i | \(0.715693\pi\) | |||||||
\(618\) | −0.959087 | −0.0385802 | ||||||||
\(619\) | −47.8439 | −1.92301 | −0.961504 | − | 0.274790i | \(-0.911392\pi\) | ||||
−0.961504 | + | 0.274790i | \(0.911392\pi\) | |||||||
\(620\) | −1.89184 | −0.0759783 | ||||||||
\(621\) | 7.80466 | 0.313190 | ||||||||
\(622\) | 32.8905 | 1.31879 | ||||||||
\(623\) | −0.261535 | −0.0104782 | ||||||||
\(624\) | 3.85216 | 0.154210 | ||||||||
\(625\) | −28.0029 | −1.12012 | ||||||||
\(626\) | −3.71061 | −0.148306 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.11684 | −0.0445667 | ||||||||
\(629\) | −9.19590 | −0.366664 | ||||||||
\(630\) | −3.47528 | −0.138458 | ||||||||
\(631\) | 4.01691 | 0.159911 | 0.0799554 | − | 0.996798i | \(-0.474522\pi\) | ||||
0.0799554 | + | 0.996798i | \(0.474522\pi\) | |||||||
\(632\) | 13.2974 | 0.528942 | ||||||||
\(633\) | 17.5618 | 0.698020 | ||||||||
\(634\) | −45.6325 | −1.81230 | ||||||||
\(635\) | 52.1265 | 2.06858 | ||||||||
\(636\) | 0.785269 | 0.0311380 | ||||||||
\(637\) | 0.911774 | 0.0361258 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.96945 | −0.236148 | ||||||||
\(640\) | −29.1726 | −1.15315 | ||||||||
\(641\) | 27.6852 | 1.09350 | 0.546750 | − | 0.837296i | \(-0.315865\pi\) | ||||
0.546750 | + | 0.837296i | \(0.315865\pi\) | |||||||
\(642\) | −0.412145 | −0.0162661 | ||||||||
\(643\) | −4.25792 | −0.167916 | −0.0839579 | − | 0.996469i | \(-0.526756\pi\) | ||||
−0.0839579 | + | 0.996469i | \(0.526756\pi\) | |||||||
\(644\) | −0.933487 | −0.0367845 | ||||||||
\(645\) | 17.9411 | 0.706431 | ||||||||
\(646\) | 2.26457 | 0.0890982 | ||||||||
\(647\) | 5.24503 | 0.206203 | 0.103102 | − | 0.994671i | \(-0.467123\pi\) | ||||
0.103102 | + | 0.994671i | \(0.467123\pi\) | |||||||
\(648\) | 2.73764 | 0.107545 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.926589 | −0.0363438 | ||||||||
\(651\) | 6.62627 | 0.259704 | ||||||||
\(652\) | 1.24761 | 0.0488600 | ||||||||
\(653\) | −9.83716 | −0.384958 | −0.192479 | − | 0.981301i | \(-0.561653\pi\) | ||||
−0.192479 | + | 0.981301i | \(0.561653\pi\) | |||||||
\(654\) | 13.0733 | 0.511207 | ||||||||
\(655\) | 22.0141 | 0.860161 | ||||||||
\(656\) | −50.5197 | −1.97246 | ||||||||
\(657\) | 4.38705 | 0.171155 | ||||||||
\(658\) | −9.13090 | −0.355960 | ||||||||
\(659\) | −50.5575 | −1.96944 | −0.984720 | − | 0.174145i | \(-0.944284\pi\) | ||||
−0.984720 | + | 0.174145i | \(0.944284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.9751 | 0.893629 | 0.446814 | − | 0.894627i | \(-0.352558\pi\) | ||||
0.446814 | + | 0.894627i | \(0.352558\pi\) | |||||||
\(662\) | 7.02887 | 0.273185 | ||||||||
\(663\) | −1.99371 | −0.0774293 | ||||||||
\(664\) | −27.5104 | −1.06761 | ||||||||
\(665\) | −1.69803 | −0.0658467 | ||||||||
\(666\) | 6.12275 | 0.237252 | ||||||||
\(667\) | 69.2072 | 2.67972 | ||||||||
\(668\) | −0.161637 | −0.00625394 | ||||||||
\(669\) | −22.5839 | −0.873142 | ||||||||
\(670\) | 39.3728 | 1.52110 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.675706 | −0.0260659 | ||||||||
\(673\) | 21.8706 | 0.843048 | 0.421524 | − | 0.906817i | \(-0.361495\pi\) | ||||
0.421524 | + | 0.906817i | \(0.361495\pi\) | |||||||
\(674\) | 30.7415 | 1.18412 | ||||||||
\(675\) | −0.698028 | −0.0268671 | ||||||||
\(676\) | −1.45545 | −0.0559788 | ||||||||
\(677\) | 14.6716 | 0.563876 | 0.281938 | − | 0.959433i | \(-0.409023\pi\) | ||||
0.281938 | + | 0.959433i | \(0.409023\pi\) | |||||||
\(678\) | 1.93543 | 0.0743298 | ||||||||
\(679\) | 9.88466 | 0.379338 | ||||||||
\(680\) | 14.2894 | 0.547973 | ||||||||
\(681\) | 21.9714 | 0.841945 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.70579 | −0.371382 | −0.185691 | − | 0.982608i | \(-0.559452\pi\) | ||||
−0.185691 | + | 0.982608i | \(0.559452\pi\) | |||||||
\(684\) | −0.0850818 | −0.00325318 | ||||||||
\(685\) | −4.88748 | −0.186741 | ||||||||
\(686\) | −1.45589 | −0.0555860 | ||||||||
\(687\) | −23.3803 | −0.892014 | ||||||||
\(688\) | 31.7545 | 1.21063 | ||||||||
\(689\) | −5.98620 | −0.228056 | ||||||||
\(690\) | −27.1234 | −1.03257 | ||||||||
\(691\) | −43.6828 | −1.66177 | −0.830887 | − | 0.556441i | \(-0.812166\pi\) | ||||
−0.830887 | + | 0.556441i | \(0.812166\pi\) | |||||||
\(692\) | −2.33058 | −0.0885955 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.0896 | −0.686670 | ||||||||
\(695\) | 30.6627 | 1.16310 | ||||||||
\(696\) | 24.2758 | 0.920172 | ||||||||
\(697\) | 26.1468 | 0.990381 | ||||||||
\(698\) | 24.7038 | 0.935054 | ||||||||
\(699\) | −1.04315 | −0.0394555 | ||||||||
\(700\) | 0.0834885 | 0.00315557 | ||||||||
\(701\) | 20.7227 | 0.782687 | 0.391343 | − | 0.920245i | \(-0.372011\pi\) | ||||
0.391343 | + | 0.920245i | \(0.372011\pi\) | |||||||
\(702\) | 1.32744 | 0.0501010 | ||||||||
\(703\) | 2.99159 | 0.112830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.9709 | −0.563837 | ||||||||
\(706\) | 6.65488 | 0.250460 | ||||||||
\(707\) | −9.94742 | −0.374111 | ||||||||
\(708\) | 1.15099 | 0.0432567 | ||||||||
\(709\) | −19.2327 | −0.722301 | −0.361150 | − | 0.932508i | \(-0.617616\pi\) | ||||
−0.361150 | + | 0.932508i | \(0.617616\pi\) | |||||||
\(710\) | 20.7455 | 0.778565 | ||||||||
\(711\) | 4.85725 | 0.182161 | ||||||||
\(712\) | −0.715988 | −0.0268328 | ||||||||
\(713\) | 51.7158 | 1.93677 | ||||||||
\(714\) | 3.18348 | 0.119139 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.53743 | −0.0574565 | ||||||||
\(717\) | −12.4140 | −0.463609 | ||||||||
\(718\) | −45.0937 | −1.68288 | ||||||||
\(719\) | −5.36985 | −0.200261 | −0.100131 | − | 0.994974i | \(-0.531926\pi\) | ||||
−0.100131 | + | 0.994974i | \(0.531926\pi\) | |||||||
\(720\) | −10.0851 | −0.375849 | ||||||||
\(721\) | −0.658765 | −0.0245337 | ||||||||
\(722\) | 26.9251 | 1.00205 | ||||||||
\(723\) | 9.42435 | 0.350495 | ||||||||
\(724\) | 1.71933 | 0.0638984 | ||||||||
\(725\) | −6.18971 | −0.229880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.19052 | 0.303769 | 0.151885 | − | 0.988398i | \(-0.451466\pi\) | ||||
0.151885 | + | 0.988398i | \(0.451466\pi\) | |||||||
\(728\) | 2.49611 | 0.0925119 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.2462 | −0.564289 | ||||||||
\(731\) | −16.4347 | −0.607860 | ||||||||
\(732\) | −0.00750646 | −0.000277447 0 | ||||||||
\(733\) | −24.3265 | −0.898521 | −0.449260 | − | 0.893401i | \(-0.648312\pi\) | ||||
−0.449260 | + | 0.893401i | \(0.648312\pi\) | |||||||
\(734\) | −21.4630 | −0.792213 | ||||||||
\(735\) | −2.38705 | −0.0880478 | ||||||||
\(736\) | −5.27365 | −0.194389 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −17.4089 | −0.640831 | ||||||||
\(739\) | 18.9692 | 0.697795 | 0.348897 | − | 0.937161i | \(-0.386556\pi\) | ||||
0.348897 | + | 0.937161i | \(0.386556\pi\) | |||||||
\(740\) | −1.20070 | −0.0441387 | ||||||||
\(741\) | 0.648589 | 0.0238265 | ||||||||
\(742\) | 9.55855 | 0.350906 | ||||||||
\(743\) | 16.8997 | 0.619988 | 0.309994 | − | 0.950738i | \(-0.399673\pi\) | ||||
0.309994 | + | 0.950738i | \(0.399673\pi\) | |||||||
\(744\) | 18.1403 | 0.665057 | ||||||||
\(745\) | −36.6296 | −1.34201 | ||||||||
\(746\) | −18.3006 | −0.670032 | ||||||||
\(747\) | −10.0490 | −0.367672 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.283088 | −0.0103438 | ||||||||
\(750\) | −14.9506 | −0.545917 | ||||||||
\(751\) | −22.5942 | −0.824475 | −0.412237 | − | 0.911076i | \(-0.635253\pi\) | ||||
−0.412237 | + | 0.911076i | \(0.635253\pi\) | |||||||
\(752\) | −26.4974 | −0.966261 | ||||||||
\(753\) | 3.07219 | 0.111957 | ||||||||
\(754\) | 11.7710 | 0.428673 | ||||||||
\(755\) | 16.4930 | 0.600242 | ||||||||
\(756\) | −0.119606 | −0.00435004 | ||||||||
\(757\) | 3.87744 | 0.140928 | 0.0704640 | − | 0.997514i | \(-0.477552\pi\) | ||||
0.0704640 | + | 0.997514i | \(0.477552\pi\) | |||||||
\(758\) | −23.3436 | −0.847879 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.64859 | −0.168622 | ||||||||
\(761\) | −37.4591 | −1.35789 | −0.678945 | − | 0.734189i | \(-0.737563\pi\) | ||||
−0.678945 | + | 0.734189i | \(0.737563\pi\) | |||||||
\(762\) | 31.7924 | 1.15172 | ||||||||
\(763\) | 8.97962 | 0.325084 | ||||||||
\(764\) | −2.86481 | −0.103645 | ||||||||
\(765\) | 5.21960 | 0.188715 | ||||||||
\(766\) | 4.09137 | 0.147827 | ||||||||
\(767\) | −8.77411 | −0.316815 | ||||||||
\(768\) | −2.86049 | −0.103219 | ||||||||
\(769\) | 20.6137 | 0.743349 | 0.371674 | − | 0.928363i | \(-0.378784\pi\) | ||||
0.371674 | + | 0.928363i | \(0.378784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.626267 | −0.0225544 | ||||||||
\(772\) | −0.0166981 | −0.000600977 0 | ||||||||
\(773\) | 9.03686 | 0.325033 | 0.162517 | − | 0.986706i | \(-0.448039\pi\) | ||||
0.162517 | + | 0.986706i | \(0.448039\pi\) | |||||||
\(774\) | 10.9425 | 0.393319 | ||||||||
\(775\) | −4.62532 | −0.166146 | ||||||||
\(776\) | 27.0606 | 0.971420 | ||||||||
\(777\) | 4.20551 | 0.150872 | ||||||||
\(778\) | 29.9985 | 1.07550 | ||||||||
\(779\) | −8.50602 | −0.304760 | ||||||||
\(780\) | −0.260318 | −0.00932086 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 24.8460 | 0.888492 | ||||||||
\(783\) | 8.86742 | 0.316896 | ||||||||
\(784\) | −4.22491 | −0.150890 | ||||||||
\(785\) | −22.2894 | −0.795543 | ||||||||
\(786\) | 13.4266 | 0.478910 | ||||||||
\(787\) | 33.4585 | 1.19267 | 0.596333 | − | 0.802737i | \(-0.296624\pi\) | ||||
0.596333 | + | 0.802737i | \(0.296624\pi\) | |||||||
\(788\) | −1.74760 | −0.0622557 | ||||||||
\(789\) | 1.02517 | 0.0364971 | ||||||||
\(790\) | −16.8803 | −0.600574 | ||||||||
\(791\) | 1.32938 | 0.0472674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0572227 | 0.00203204 | ||||||||
\(794\) | −41.7239 | −1.48073 | ||||||||
\(795\) | 15.6721 | 0.555832 | ||||||||
\(796\) | −3.16600 | −0.112216 | ||||||||
\(797\) | 0.766169 | 0.0271391 | 0.0135695 | − | 0.999908i | \(-0.495681\pi\) | ||||
0.0135695 | + | 0.999908i | \(0.495681\pi\) | |||||||
\(798\) | −1.03564 | −0.0366614 | ||||||||
\(799\) | 13.7139 | 0.485163 | ||||||||
\(800\) | 0.471661 | 0.0166757 | ||||||||
\(801\) | −0.261535 | −0.00924087 | ||||||||
\(802\) | 32.4890 | 1.14723 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.35507 | 0.0477895 | ||||||||
\(805\) | −18.6302 | −0.656627 | ||||||||
\(806\) | 8.79597 | 0.309825 | ||||||||
\(807\) | −32.0066 | −1.12668 | ||||||||
\(808\) | −27.2324 | −0.958034 | ||||||||
\(809\) | 10.2311 | 0.359708 | 0.179854 | − | 0.983693i | \(-0.442438\pi\) | ||||
0.179854 | + | 0.983693i | \(0.442438\pi\) | |||||||
\(810\) | −3.47528 | −0.122109 | ||||||||
\(811\) | −10.4196 | −0.365880 | −0.182940 | − | 0.983124i | \(-0.558561\pi\) | ||||
−0.182940 | + | 0.983124i | \(0.558561\pi\) | |||||||
\(812\) | −1.06060 | −0.0372198 | ||||||||
\(813\) | 5.95536 | 0.208863 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.8992 | 0.872181 | ||||||||
\(816\) | 9.23830 | 0.323405 | ||||||||
\(817\) | 5.34650 | 0.187051 | ||||||||
\(818\) | 23.9290 | 0.836657 | ||||||||
\(819\) | 0.911774 | 0.0318599 | ||||||||
\(820\) | 3.41397 | 0.119221 | ||||||||
\(821\) | −27.7513 | −0.968527 | −0.484264 | − | 0.874922i | \(-0.660912\pi\) | ||||
−0.484264 | + | 0.874922i | \(0.660912\pi\) | |||||||
\(822\) | −2.98092 | −0.103972 | ||||||||
\(823\) | −18.7419 | −0.653302 | −0.326651 | − | 0.945145i | \(-0.605920\pi\) | ||||
−0.326651 | + | 0.945145i | \(0.605920\pi\) | |||||||
\(824\) | −1.80346 | −0.0628266 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.0102 | 0.487476 | ||||||||
\(827\) | 55.6432 | 1.93490 | 0.967451 | − | 0.253058i | \(-0.0814364\pi\) | ||||
0.967451 | + | 0.253058i | \(0.0814364\pi\) | |||||||
\(828\) | −0.933487 | −0.0324409 | ||||||||
\(829\) | −37.5600 | −1.30451 | −0.652257 | − | 0.757998i | \(-0.726178\pi\) | ||||
−0.652257 | + | 0.757998i | \(0.726178\pi\) | |||||||
\(830\) | 34.9230 | 1.21219 | ||||||||
\(831\) | −1.27771 | −0.0443232 | ||||||||
\(832\) | 6.80736 | 0.236003 | ||||||||
\(833\) | 2.18663 | 0.0757622 | ||||||||
\(834\) | 18.7014 | 0.647578 | ||||||||
\(835\) | −3.22589 | −0.111637 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.62627 | 0.229037 | ||||||||
\(838\) | 18.5953 | 0.642362 | ||||||||
\(839\) | −44.6850 | −1.54270 | −0.771348 | − | 0.636413i | \(-0.780417\pi\) | ||||
−0.771348 | + | 0.636413i | \(0.780417\pi\) | |||||||
\(840\) | −6.53490 | −0.225475 | ||||||||
\(841\) | 49.6312 | 1.71142 | ||||||||
\(842\) | −15.7282 | −0.542029 | ||||||||
\(843\) | −4.45011 | −0.153270 | ||||||||
\(844\) | −2.10051 | −0.0723024 | ||||||||
\(845\) | −29.0473 | −0.999257 | ||||||||
\(846\) | −9.13090 | −0.313927 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 27.7384 | 0.952541 | ||||||||
\(849\) | 22.7964 | 0.782371 | ||||||||
\(850\) | −2.22216 | −0.0762195 | ||||||||
\(851\) | 32.8226 | 1.12514 | ||||||||
\(852\) | 0.713983 | 0.0244607 | ||||||||
\(853\) | −55.6861 | −1.90666 | −0.953329 | − | 0.301934i | \(-0.902368\pi\) | ||||
−0.953329 | + | 0.301934i | \(0.902368\pi\) | |||||||
\(854\) | −0.0913711 | −0.00312665 | ||||||||
\(855\) | −1.69803 | −0.0580713 | ||||||||
\(856\) | −0.774994 | −0.0264888 | ||||||||
\(857\) | 37.5988 | 1.28435 | 0.642176 | − | 0.766557i | \(-0.278032\pi\) | ||||
0.642176 | + | 0.766557i | \(0.278032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.1084 | 1.50496 | 0.752479 | − | 0.658616i | \(-0.228858\pi\) | ||||
0.752479 | + | 0.658616i | \(0.228858\pi\) | |||||||
\(860\) | −2.14587 | −0.0731736 | ||||||||
\(861\) | −11.9576 | −0.407514 | ||||||||
\(862\) | 40.0944 | 1.36562 | ||||||||
\(863\) | −4.51049 | −0.153539 | −0.0767694 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767694 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(864\) | −0.675706 | −0.0229880 | ||||||||
\(865\) | −46.5128 | −1.58148 | ||||||||
\(866\) | −22.2169 | −0.754961 | ||||||||
\(867\) | 12.2187 | 0.414967 | ||||||||
\(868\) | −0.792543 | −0.0269007 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −30.8168 | −1.04479 | ||||||||
\(871\) | −10.3298 | −0.350013 | ||||||||
\(872\) | 24.5830 | 0.832485 | ||||||||
\(873\) | 9.88466 | 0.334545 | ||||||||
\(874\) | −8.08284 | −0.273406 | ||||||||
\(875\) | −10.2690 | −0.347157 | ||||||||
\(876\) | −0.524719 | −0.0177286 | ||||||||
\(877\) | 36.0877 | 1.21860 | 0.609298 | − | 0.792941i | \(-0.291451\pi\) | ||||
0.609298 | + | 0.792941i | \(0.291451\pi\) | |||||||
\(878\) | −41.5655 | −1.40277 | ||||||||
\(879\) | −8.39334 | −0.283100 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.8240 | −0.432052 | −0.216026 | − | 0.976388i | \(-0.569310\pi\) | ||||
−0.216026 | + | 0.976388i | \(0.569310\pi\) | |||||||
\(882\) | −1.45589 | −0.0490223 | ||||||||
\(883\) | −9.36217 | −0.315062 | −0.157531 | − | 0.987514i | \(-0.550353\pi\) | ||||
−0.157531 | + | 0.987514i | \(0.550353\pi\) | |||||||
\(884\) | 0.238460 | 0.00802029 | ||||||||
\(885\) | 22.9709 | 0.772159 | ||||||||
\(886\) | −16.4967 | −0.554217 | ||||||||
\(887\) | 9.91449 | 0.332896 | 0.166448 | − | 0.986050i | \(-0.446770\pi\) | ||||
0.166448 | + | 0.986050i | \(0.446770\pi\) | |||||||
\(888\) | 11.5132 | 0.386357 | ||||||||
\(889\) | 21.8372 | 0.732395 | ||||||||
\(890\) | 0.908906 | 0.0304666 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.70117 | 0.0904419 | ||||||||
\(893\) | −4.46137 | −0.149294 | ||||||||
\(894\) | −22.3408 | −0.747187 | ||||||||
\(895\) | −30.6834 | −1.02563 | ||||||||
\(896\) | −12.2212 | −0.408280 | ||||||||
\(897\) | 7.11609 | 0.237599 | ||||||||
\(898\) | 39.1587 | 1.30674 | ||||||||
\(899\) | 58.7579 | 1.95969 | ||||||||
\(900\) | 0.0834885 | 0.00278295 | ||||||||
\(901\) | −14.3562 | −0.478275 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.51601 | 0.250117 | ||||||||
\(904\) | 3.63937 | 0.121044 | ||||||||
\(905\) | 34.3137 | 1.14063 | ||||||||
\(906\) | 10.0592 | 0.334196 | ||||||||
\(907\) | −13.9881 | −0.464469 | −0.232234 | − | 0.972660i | \(-0.574604\pi\) | ||||
−0.232234 | + | 0.972660i | \(0.574604\pi\) | |||||||
\(908\) | −2.62792 | −0.0872105 | ||||||||
\(909\) | −9.94742 | −0.329935 | ||||||||
\(910\) | −3.16867 | −0.105040 | ||||||||
\(911\) | −27.1168 | −0.898419 | −0.449210 | − | 0.893426i | \(-0.648294\pi\) | ||||
−0.449210 | + | 0.893426i | \(0.648294\pi\) | |||||||
\(912\) | −3.00538 | −0.0995181 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −42.1762 | −1.39507 | ||||||||
\(915\) | −0.149811 | −0.00495260 | ||||||||
\(916\) | 2.79643 | 0.0923967 | ||||||||
\(917\) | 9.22227 | 0.304546 | ||||||||
\(918\) | 3.18348 | 0.105071 | ||||||||
\(919\) | −4.42881 | −0.146093 | −0.0730464 | − | 0.997329i | \(-0.523272\pi\) | ||||
−0.0730464 | + | 0.997329i | \(0.523272\pi\) | |||||||
\(920\) | −51.0027 | −1.68151 | ||||||||
\(921\) | 11.0560 | 0.364307 | ||||||||
\(922\) | −61.0563 | −2.01078 | ||||||||
\(923\) | −5.44278 | −0.179151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.93556 | −0.0965208 | ||||||||
\(926\) | 1.67288 | 0.0549741 | ||||||||
\(927\) | −0.658765 | −0.0216367 | ||||||||
\(928\) | −5.99177 | −0.196689 | ||||||||
\(929\) | −56.7744 | −1.86271 | −0.931353 | − | 0.364116i | \(-0.881371\pi\) | ||||
−0.931353 | + | 0.364116i | \(0.881371\pi\) | |||||||
\(930\) | −23.0281 | −0.755122 | ||||||||
\(931\) | −0.711349 | −0.0233135 | ||||||||
\(932\) | 0.124767 | 0.00408689 | ||||||||
\(933\) | 22.5914 | 0.739608 | ||||||||
\(934\) | −43.0777 | −1.40955 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.49611 | 0.0815878 | ||||||||
\(937\) | 2.85797 | 0.0933659 | 0.0466830 | − | 0.998910i | \(-0.485135\pi\) | ||||
0.0466830 | + | 0.998910i | \(0.485135\pi\) | |||||||
\(938\) | 16.4943 | 0.538558 | ||||||||
\(939\) | −2.54869 | −0.0831734 | ||||||||
\(940\) | 1.79062 | 0.0584034 | ||||||||
\(941\) | −24.2516 | −0.790580 | −0.395290 | − | 0.918556i | \(-0.629356\pi\) | ||||
−0.395290 | + | 0.918556i | \(0.629356\pi\) | |||||||
\(942\) | −13.5945 | −0.442933 | ||||||||
\(943\) | −93.3250 | −3.03908 | ||||||||
\(944\) | 40.6568 | 1.32327 | ||||||||
\(945\) | −2.38705 | −0.0776509 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.0901 | −1.46523 | −0.732616 | − | 0.680642i | \(-0.761701\pi\) | ||||
−0.732616 | + | 0.680642i | \(0.761701\pi\) | |||||||
\(948\) | −0.580957 | −0.0188686 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0.722907 | 0.0234542 | ||||||||
\(951\) | −31.3434 | −1.01638 | ||||||||
\(952\) | 5.98620 | 0.194014 | ||||||||
\(953\) | 37.7101 | 1.22155 | 0.610775 | − | 0.791804i | \(-0.290858\pi\) | ||||
0.610775 | + | 0.791804i | \(0.290858\pi\) | |||||||
\(954\) | 9.55855 | 0.309470 | ||||||||
\(955\) | −57.1748 | −1.85013 | ||||||||
\(956\) | 1.48479 | 0.0480216 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.8105 | −0.478505 | ||||||||
\(959\) | −2.04750 | −0.0661171 | ||||||||
\(960\) | −17.8219 | −0.575199 | ||||||||
\(961\) | 12.9074 | 0.416368 | ||||||||
\(962\) | 5.58256 | 0.179989 | ||||||||
\(963\) | −0.283088 | −0.00912240 | ||||||||
\(964\) | −1.12721 | −0.0363050 | ||||||||
\(965\) | −0.333254 | −0.0107278 | ||||||||
\(966\) | −11.3627 | −0.365589 | ||||||||
\(967\) | 60.7131 | 1.95240 | 0.976201 | − | 0.216870i | \(-0.0695846\pi\) | ||||
0.976201 | + | 0.216870i | \(0.0695846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.55546 | 0.0499684 | ||||||||
\(970\) | −34.3520 | −1.10297 | ||||||||
\(971\) | −29.4859 | −0.946247 | −0.473124 | − | 0.880996i | \(-0.656874\pi\) | ||||
−0.473124 | + | 0.880996i | \(0.656874\pi\) | |||||||
\(972\) | −0.119606 | −0.00383637 | ||||||||
\(973\) | 12.8454 | 0.411804 | ||||||||
\(974\) | −63.8145 | −2.04475 | ||||||||
\(975\) | −0.636443 | −0.0203825 | ||||||||
\(976\) | −0.265154 | −0.00848738 | ||||||||
\(977\) | 4.55016 | 0.145573 | 0.0727863 | − | 0.997348i | \(-0.476811\pi\) | ||||
0.0727863 | + | 0.997348i | \(0.476811\pi\) | |||||||
\(978\) | 15.1863 | 0.485603 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.285507 | 0.00912018 | ||||||||
\(981\) | 8.97962 | 0.286697 | ||||||||
\(982\) | 27.8376 | 0.888334 | ||||||||
\(983\) | −36.9736 | −1.17927 | −0.589637 | − | 0.807668i | \(-0.700729\pi\) | ||||
−0.589637 | + | 0.807668i | \(0.700729\pi\) | |||||||
\(984\) | −32.7356 | −1.04357 | ||||||||
\(985\) | −34.8779 | −1.11130 | ||||||||
\(986\) | 28.2293 | 0.899004 | ||||||||
\(987\) | −6.27171 | −0.199631 | ||||||||
\(988\) | −0.0775753 | −0.00246800 | ||||||||
\(989\) | 58.6599 | 1.86528 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.5701 | 0.971090 | 0.485545 | − | 0.874212i | \(-0.338621\pi\) | ||||
0.485545 | + | 0.874212i | \(0.338621\pi\) | |||||||
\(992\) | −4.47741 | −0.142158 | ||||||||
\(993\) | 4.82789 | 0.153209 | ||||||||
\(994\) | 8.69084 | 0.275657 | ||||||||
\(995\) | −63.1857 | −2.00312 | ||||||||
\(996\) | 1.20192 | 0.0380843 | ||||||||
\(997\) | 2.65445 | 0.0840671 | 0.0420336 | − | 0.999116i | \(-0.486616\pi\) | ||||
0.0420336 | + | 0.999116i | \(0.486616\pi\) | |||||||
\(998\) | −29.8415 | −0.944615 | ||||||||
\(999\) | 4.20551 | 0.133057 |
(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.bm.1.2 | 4 | ||
3.2 | odd | 2 | 7623.2.a.cl.1.3 | 4 | |||
11.7 | odd | 10 | 231.2.j.f.148.2 | yes | 8 | ||
11.8 | odd | 10 | 231.2.j.f.64.2 | ✓ | 8 | ||
11.10 | odd | 2 | 2541.2.a.bn.1.3 | 4 | |||
33.8 | even | 10 | 693.2.m.f.64.1 | 8 | |||
33.29 | even | 10 | 693.2.m.f.379.1 | 8 | |||
33.32 | even | 2 | 7623.2.a.ci.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.f.64.2 | ✓ | 8 | 11.8 | odd | 10 | ||
231.2.j.f.148.2 | yes | 8 | 11.7 | odd | 10 | ||
693.2.m.f.64.1 | 8 | 33.8 | even | 10 | |||
693.2.m.f.379.1 | 8 | 33.29 | even | 10 | |||
2541.2.a.bm.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2541.2.a.bn.1.3 | 4 | 11.10 | odd | 2 | |||
7623.2.a.ci.1.2 | 4 | 33.32 | even | 2 | |||
7623.2.a.cl.1.3 | 4 | 3.2 | odd | 2 |