Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.77896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77896 | −1.25791 | −0.628956 | − | 0.777441i | \(-0.716517\pi\) | ||||
−0.628956 | + | 0.777441i | \(0.716517\pi\) | |||||||
\(3\) | −1.20779 | −0.697320 | −0.348660 | − | 0.937249i | \(-0.613363\pi\) | ||||
−0.348660 | + | 0.937249i | \(0.613363\pi\) | |||||||
\(4\) | 1.16468 | 0.582342 | ||||||||
\(5\) | 2.53283 | 1.13272 | 0.566359 | − | 0.824159i | \(-0.308352\pi\) | ||||
0.566359 | + | 0.824159i | \(0.308352\pi\) | |||||||
\(6\) | 2.14861 | 0.877168 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.48599 | 0.525377 | ||||||||
\(9\) | −1.54123 | −0.513744 | ||||||||
\(10\) | −4.50580 | −1.42486 | ||||||||
\(11\) | 4.69442 | 1.41542 | 0.707711 | − | 0.706502i | \(-0.249728\pi\) | ||||
0.707711 | + | 0.706502i | \(0.249728\pi\) | |||||||
\(12\) | −1.40670 | −0.406079 | ||||||||
\(13\) | 2.97799 | 0.825946 | 0.412973 | − | 0.910743i | \(-0.364490\pi\) | ||||
0.412973 | + | 0.910743i | \(0.364490\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.05914 | −0.789867 | ||||||||
\(16\) | −4.97288 | −1.24322 | ||||||||
\(17\) | 7.01187 | 1.70063 | 0.850315 | − | 0.526275i | \(-0.176412\pi\) | ||||
0.850315 | + | 0.526275i | \(0.176412\pi\) | |||||||
\(18\) | 2.74178 | 0.646245 | ||||||||
\(19\) | −2.78486 | −0.638891 | −0.319445 | − | 0.947605i | \(-0.603497\pi\) | ||||
−0.319445 | + | 0.947605i | \(0.603497\pi\) | |||||||
\(20\) | 2.94995 | 0.659629 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.35117 | −1.78048 | ||||||||
\(23\) | 4.04356 | 0.843140 | 0.421570 | − | 0.906796i | \(-0.361479\pi\) | ||||
0.421570 | + | 0.906796i | \(0.361479\pi\) | |||||||
\(24\) | −1.79477 | −0.366356 | ||||||||
\(25\) | 1.41524 | 0.283048 | ||||||||
\(26\) | −5.29771 | −1.03897 | ||||||||
\(27\) | 5.48488 | 1.05556 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.66082 | 1.42258 | 0.711289 | − | 0.702900i | \(-0.248112\pi\) | ||||
0.711289 | + | 0.702900i | \(0.248112\pi\) | |||||||
\(30\) | 5.44208 | 0.993583 | ||||||||
\(31\) | −1.24213 | −0.223092 | −0.111546 | − | 0.993759i | \(-0.535580\pi\) | ||||
−0.111546 | + | 0.993759i | \(0.535580\pi\) | |||||||
\(32\) | 5.87455 | 1.03848 | ||||||||
\(33\) | −5.66990 | −0.987003 | ||||||||
\(34\) | −12.4738 | −2.13924 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.79505 | −0.299175 | ||||||||
\(37\) | −5.48369 | −0.901514 | −0.450757 | − | 0.892647i | \(-0.648846\pi\) | ||||
−0.450757 | + | 0.892647i | \(0.648846\pi\) | |||||||
\(38\) | 4.95414 | 0.803668 | ||||||||
\(39\) | −3.59680 | −0.575949 | ||||||||
\(40\) | 3.76377 | 0.595104 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.18117 | 1.40012 | 0.700058 | − | 0.714086i | \(-0.253157\pi\) | ||||
0.700058 | + | 0.714086i | \(0.253157\pi\) | |||||||
\(44\) | 5.46752 | 0.824260 | ||||||||
\(45\) | −3.90368 | −0.581927 | ||||||||
\(46\) | −7.19331 | −1.06060 | ||||||||
\(47\) | 7.77039 | 1.13343 | 0.566714 | − | 0.823915i | \(-0.308214\pi\) | ||||
0.566714 | + | 0.823915i | \(0.308214\pi\) | |||||||
\(48\) | 6.00622 | 0.866923 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.51765 | −0.356050 | ||||||||
\(51\) | −8.46890 | −1.18588 | ||||||||
\(52\) | 3.46842 | 0.480983 | ||||||||
\(53\) | −9.44258 | −1.29704 | −0.648519 | − | 0.761198i | \(-0.724611\pi\) | ||||
−0.648519 | + | 0.761198i | \(0.724611\pi\) | |||||||
\(54\) | −9.75735 | −1.32781 | ||||||||
\(55\) | 11.8902 | 1.60327 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.36354 | 0.445512 | ||||||||
\(58\) | −13.6283 | −1.78948 | ||||||||
\(59\) | −1.63269 | −0.212559 | −0.106279 | − | 0.994336i | \(-0.533894\pi\) | ||||
−0.106279 | + | 0.994336i | \(0.533894\pi\) | |||||||
\(60\) | −3.56293 | −0.459973 | ||||||||
\(61\) | −13.9531 | −1.78651 | −0.893256 | − | 0.449548i | \(-0.851585\pi\) | ||||
−0.893256 | + | 0.449548i | \(0.851585\pi\) | |||||||
\(62\) | 2.20969 | 0.280631 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.504809 | −0.0631012 | ||||||||
\(65\) | 7.54275 | 0.935563 | ||||||||
\(66\) | 10.0865 | 1.24156 | ||||||||
\(67\) | −3.75824 | −0.459142 | −0.229571 | − | 0.973292i | \(-0.573732\pi\) | ||||
−0.229571 | + | 0.973292i | \(0.573732\pi\) | |||||||
\(68\) | 8.16662 | 0.990348 | ||||||||
\(69\) | −4.88379 | −0.587939 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.77038 | −0.803497 | −0.401748 | − | 0.915750i | \(-0.631597\pi\) | ||||
−0.401748 | + | 0.915750i | \(0.631597\pi\) | |||||||
\(72\) | −2.29026 | −0.269909 | ||||||||
\(73\) | −2.70572 | −0.316681 | −0.158340 | − | 0.987385i | \(-0.550614\pi\) | ||||
−0.158340 | + | 0.987385i | \(0.550614\pi\) | |||||||
\(74\) | 9.75525 | 1.13402 | ||||||||
\(75\) | −1.70932 | −0.197375 | ||||||||
\(76\) | −3.24348 | −0.372053 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.39855 | 0.724493 | ||||||||
\(79\) | 12.4767 | 1.40374 | 0.701870 | − | 0.712306i | \(-0.252349\pi\) | ||||
0.701870 | + | 0.712306i | \(0.252349\pi\) | |||||||
\(80\) | −12.5955 | −1.40822 | ||||||||
\(81\) | −2.00090 | −0.222323 | ||||||||
\(82\) | 1.77896 | 0.196453 | ||||||||
\(83\) | 0.292604 | 0.0321175 | 0.0160587 | − | 0.999871i | \(-0.494888\pi\) | ||||
0.0160587 | + | 0.999871i | \(0.494888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.7599 | 1.92633 | ||||||||
\(86\) | −16.3329 | −1.76122 | ||||||||
\(87\) | −9.25269 | −0.991993 | ||||||||
\(88\) | 6.97587 | 0.743630 | ||||||||
\(89\) | −2.99498 | −0.317467 | −0.158733 | − | 0.987321i | \(-0.550741\pi\) | ||||
−0.158733 | + | 0.987321i | \(0.550741\pi\) | |||||||
\(90\) | 6.94448 | 0.732013 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.70947 | 0.490996 | ||||||||
\(93\) | 1.50023 | 0.155567 | ||||||||
\(94\) | −13.8232 | −1.42575 | ||||||||
\(95\) | −7.05359 | −0.723683 | ||||||||
\(96\) | −7.09525 | −0.724156 | ||||||||
\(97\) | −11.1466 | −1.13176 | −0.565882 | − | 0.824486i | \(-0.691464\pi\) | ||||
−0.565882 | + | 0.824486i | \(0.691464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.23520 | −0.727165 | ||||||||
\(100\) | 1.64831 | 0.164831 | ||||||||
\(101\) | 1.72165 | 0.171311 | 0.0856553 | − | 0.996325i | \(-0.472702\pi\) | ||||
0.0856553 | + | 0.996325i | \(0.472702\pi\) | |||||||
\(102\) | 15.0658 | 1.49174 | ||||||||
\(103\) | −15.0433 | −1.48226 | −0.741128 | − | 0.671364i | \(-0.765709\pi\) | ||||
−0.741128 | + | 0.671364i | \(0.765709\pi\) | |||||||
\(104\) | 4.42526 | 0.433933 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.7979 | 1.63156 | ||||||||
\(107\) | 1.73679 | 0.167902 | 0.0839510 | − | 0.996470i | \(-0.473246\pi\) | ||||
0.0839510 | + | 0.996470i | \(0.473246\pi\) | |||||||
\(108\) | 6.38815 | 0.614700 | ||||||||
\(109\) | 18.1048 | 1.73413 | 0.867064 | − | 0.498196i | \(-0.166004\pi\) | ||||
0.867064 | + | 0.498196i | \(0.166004\pi\) | |||||||
\(110\) | −21.1521 | −2.01678 | ||||||||
\(111\) | 6.62317 | 0.628644 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.2644 | −1.43595 | −0.717976 | − | 0.696068i | \(-0.754931\pi\) | ||||
−0.717976 | + | 0.696068i | \(0.754931\pi\) | |||||||
\(114\) | −5.98359 | −0.560414 | ||||||||
\(115\) | 10.2417 | 0.955039 | ||||||||
\(116\) | 8.92243 | 0.828427 | ||||||||
\(117\) | −4.58977 | −0.424325 | ||||||||
\(118\) | 2.90449 | 0.267380 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.54585 | −0.414978 | ||||||||
\(121\) | 11.0376 | 1.00342 | ||||||||
\(122\) | 24.8220 | 2.24727 | ||||||||
\(123\) | 1.20779 | 0.108903 | ||||||||
\(124\) | −1.44668 | −0.129916 | ||||||||
\(125\) | −9.07960 | −0.812104 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.98507 | 0.531090 | 0.265545 | − | 0.964099i | \(-0.414448\pi\) | ||||
0.265545 | + | 0.964099i | \(0.414448\pi\) | |||||||
\(128\) | −10.8511 | −0.959108 | ||||||||
\(129\) | −11.0890 | −0.976329 | ||||||||
\(130\) | −13.4182 | −1.17686 | ||||||||
\(131\) | 6.99392 | 0.611061 | 0.305531 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305531 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(132\) | −6.60364 | −0.574773 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.68574 | 0.577560 | ||||||||
\(135\) | 13.8923 | 1.19566 | ||||||||
\(136\) | 10.4196 | 0.893471 | ||||||||
\(137\) | 8.30976 | 0.709951 | 0.354975 | − | 0.934876i | \(-0.384489\pi\) | ||||
0.354975 | + | 0.934876i | \(0.384489\pi\) | |||||||
\(138\) | 8.68804 | 0.739575 | ||||||||
\(139\) | 5.14052 | 0.436013 | 0.218007 | − | 0.975947i | \(-0.430045\pi\) | ||||
0.218007 | + | 0.975947i | \(0.430045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.38504 | −0.790363 | ||||||||
\(142\) | 12.0442 | 1.01073 | ||||||||
\(143\) | 13.9799 | 1.16906 | ||||||||
\(144\) | 7.66436 | 0.638697 | ||||||||
\(145\) | 19.4036 | 1.61138 | ||||||||
\(146\) | 4.81336 | 0.398356 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.38677 | −0.524989 | ||||||||
\(149\) | 15.0317 | 1.23144 | 0.615721 | − | 0.787964i | \(-0.288865\pi\) | ||||
0.615721 | + | 0.787964i | \(0.288865\pi\) | |||||||
\(150\) | 3.04080 | 0.248281 | ||||||||
\(151\) | 5.46293 | 0.444567 | 0.222284 | − | 0.974982i | \(-0.428649\pi\) | ||||
0.222284 | + | 0.974982i | \(0.428649\pi\) | |||||||
\(152\) | −4.13828 | −0.335659 | ||||||||
\(153\) | −10.8069 | −0.873688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.14610 | −0.252701 | ||||||||
\(156\) | −4.18913 | −0.335399 | ||||||||
\(157\) | −21.9068 | −1.74835 | −0.874177 | − | 0.485607i | \(-0.838599\pi\) | ||||
−0.874177 | + | 0.485607i | \(0.838599\pi\) | |||||||
\(158\) | −22.1955 | −1.76578 | ||||||||
\(159\) | 11.4047 | 0.904451 | ||||||||
\(160\) | 14.8793 | 1.17631 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.55952 | 0.279662 | ||||||||
\(163\) | 4.43254 | 0.347183 | 0.173592 | − | 0.984818i | \(-0.444463\pi\) | ||||
0.173592 | + | 0.984818i | \(0.444463\pi\) | |||||||
\(164\) | −1.16468 | −0.0909465 | ||||||||
\(165\) | −14.3609 | −1.11800 | ||||||||
\(166\) | −0.520530 | −0.0404009 | ||||||||
\(167\) | 18.3642 | 1.42107 | 0.710534 | − | 0.703663i | \(-0.248453\pi\) | ||||
0.710534 | + | 0.703663i | \(0.248453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.13158 | −0.317814 | ||||||||
\(170\) | −31.5941 | −2.42316 | ||||||||
\(171\) | 4.29212 | 0.328226 | ||||||||
\(172\) | 10.6932 | 0.815346 | ||||||||
\(173\) | −15.0583 | −1.14486 | −0.572430 | − | 0.819954i | \(-0.693999\pi\) | ||||
−0.572430 | + | 0.819954i | \(0.693999\pi\) | |||||||
\(174\) | 16.4601 | 1.24784 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −23.3448 | −1.75968 | ||||||||
\(177\) | 1.97196 | 0.148221 | ||||||||
\(178\) | 5.32793 | 0.399345 | ||||||||
\(179\) | 16.1292 | 1.20556 | 0.602778 | − | 0.797909i | \(-0.294060\pi\) | ||||
0.602778 | + | 0.797909i | \(0.294060\pi\) | |||||||
\(180\) | −4.54656 | −0.338880 | ||||||||
\(181\) | 2.53296 | 0.188273 | 0.0941366 | − | 0.995559i | \(-0.469991\pi\) | ||||
0.0941366 | + | 0.995559i | \(0.469991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.8525 | 1.24577 | ||||||||
\(184\) | 6.00869 | 0.442966 | ||||||||
\(185\) | −13.8893 | −1.02116 | ||||||||
\(186\) | −2.66885 | −0.195690 | ||||||||
\(187\) | 32.9167 | 2.40711 | ||||||||
\(188\) | 9.05005 | 0.660043 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.5480 | 0.910329 | ||||||||
\(191\) | 20.0577 | 1.45132 | 0.725660 | − | 0.688053i | \(-0.241534\pi\) | ||||
0.725660 | + | 0.688053i | \(0.241534\pi\) | |||||||
\(192\) | 0.609706 | 0.0440017 | ||||||||
\(193\) | 9.96154 | 0.717047 | 0.358524 | − | 0.933521i | \(-0.383280\pi\) | ||||
0.358524 | + | 0.933521i | \(0.383280\pi\) | |||||||
\(194\) | 19.8293 | 1.42366 | ||||||||
\(195\) | −9.11009 | −0.652387 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.6858 | 1.61630 | 0.808150 | − | 0.588977i | \(-0.200469\pi\) | ||||
0.808150 | + | 0.588977i | \(0.200469\pi\) | |||||||
\(198\) | 12.8711 | 0.914709 | ||||||||
\(199\) | 3.20741 | 0.227367 | 0.113684 | − | 0.993517i | \(-0.463735\pi\) | ||||
0.113684 | + | 0.993517i | \(0.463735\pi\) | |||||||
\(200\) | 2.10303 | 0.148707 | ||||||||
\(201\) | 4.53918 | 0.320169 | ||||||||
\(202\) | −3.06274 | −0.215493 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.86359 | −0.690590 | ||||||||
\(205\) | −2.53283 | −0.176901 | ||||||||
\(206\) | 26.7613 | 1.86455 | ||||||||
\(207\) | −6.23206 | −0.433158 | ||||||||
\(208\) | −14.8092 | −1.02683 | ||||||||
\(209\) | −13.0733 | −0.904300 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.40518 | 0.647479 | 0.323740 | − | 0.946146i | \(-0.395060\pi\) | ||||
0.323740 | + | 0.946146i | \(0.395060\pi\) | |||||||
\(212\) | −10.9976 | −0.755320 | ||||||||
\(213\) | 8.17723 | 0.560295 | ||||||||
\(214\) | −3.08968 | −0.211206 | ||||||||
\(215\) | 23.2544 | 1.58594 | ||||||||
\(216\) | 8.15047 | 0.554569 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −32.2077 | −2.18138 | ||||||||
\(219\) | 3.26796 | 0.220828 | ||||||||
\(220\) | 13.8483 | 0.933653 | ||||||||
\(221\) | 20.8813 | 1.40463 | ||||||||
\(222\) | −11.7823 | −0.790778 | ||||||||
\(223\) | −3.72574 | −0.249494 | −0.124747 | − | 0.992189i | \(-0.539812\pi\) | ||||
−0.124747 | + | 0.992189i | \(0.539812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.18121 | −0.145414 | ||||||||
\(226\) | 27.1547 | 1.80630 | ||||||||
\(227\) | 0.832706 | 0.0552687 | 0.0276343 | − | 0.999618i | \(-0.491203\pi\) | ||||
0.0276343 | + | 0.999618i | \(0.491203\pi\) | |||||||
\(228\) | 3.91746 | 0.259440 | ||||||||
\(229\) | 20.3333 | 1.34366 | 0.671831 | − | 0.740704i | \(-0.265508\pi\) | ||||
0.671831 | + | 0.740704i | \(0.265508\pi\) | |||||||
\(230\) | −18.2195 | −1.20136 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.3839 | 0.747390 | ||||||||
\(233\) | −3.59592 | −0.235576 | −0.117788 | − | 0.993039i | \(-0.537580\pi\) | ||||
−0.117788 | + | 0.993039i | \(0.537580\pi\) | |||||||
\(234\) | 8.16501 | 0.533763 | ||||||||
\(235\) | 19.6811 | 1.28385 | ||||||||
\(236\) | −1.90157 | −0.123782 | ||||||||
\(237\) | −15.0693 | −0.978856 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.82576 | 0.506206 | 0.253103 | − | 0.967439i | \(-0.418549\pi\) | ||||
0.253103 | + | 0.967439i | \(0.418549\pi\) | |||||||
\(240\) | 15.2127 | 0.981978 | ||||||||
\(241\) | 13.0500 | 0.840623 | 0.420311 | − | 0.907380i | \(-0.361921\pi\) | ||||
0.420311 | + | 0.907380i | \(0.361921\pi\) | |||||||
\(242\) | −19.6354 | −1.26221 | ||||||||
\(243\) | −14.0379 | −0.900535 | ||||||||
\(244\) | −16.2510 | −1.04036 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.14861 | −0.136991 | ||||||||
\(247\) | −8.29329 | −0.527689 | ||||||||
\(248\) | −1.84579 | −0.117208 | ||||||||
\(249\) | −0.353406 | −0.0223962 | ||||||||
\(250\) | 16.1522 | 1.02155 | ||||||||
\(251\) | 2.49236 | 0.157316 | 0.0786582 | − | 0.996902i | \(-0.474936\pi\) | ||||
0.0786582 | + | 0.996902i | \(0.474936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.9822 | 1.19340 | ||||||||
\(254\) | −10.6472 | −0.668064 | ||||||||
\(255\) | −21.4503 | −1.34327 | ||||||||
\(256\) | 20.3132 | 1.26957 | ||||||||
\(257\) | 20.3331 | 1.26834 | 0.634171 | − | 0.773193i | \(-0.281342\pi\) | ||||
0.634171 | + | 0.773193i | \(0.281342\pi\) | |||||||
\(258\) | 19.7268 | 1.22814 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.78492 | 0.544817 | ||||||||
\(261\) | −11.8071 | −0.730841 | ||||||||
\(262\) | −12.4419 | −0.768661 | ||||||||
\(263\) | −23.6495 | −1.45829 | −0.729144 | − | 0.684360i | \(-0.760082\pi\) | ||||
−0.729144 | + | 0.684360i | \(0.760082\pi\) | |||||||
\(264\) | −8.42542 | −0.518549 | ||||||||
\(265\) | −23.9165 | −1.46918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.61732 | 0.221376 | ||||||||
\(268\) | −4.37716 | −0.267378 | ||||||||
\(269\) | −4.03278 | −0.245883 | −0.122941 | − | 0.992414i | \(-0.539233\pi\) | ||||
−0.122941 | + | 0.992414i | \(0.539233\pi\) | |||||||
\(270\) | −24.7137 | −1.50403 | ||||||||
\(271\) | −17.7083 | −1.07570 | −0.537852 | − | 0.843039i | \(-0.680764\pi\) | ||||
−0.537852 | + | 0.843039i | \(0.680764\pi\) | |||||||
\(272\) | −34.8692 | −2.11426 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7827 | −0.893055 | ||||||||
\(275\) | 6.64374 | 0.400633 | ||||||||
\(276\) | −5.68807 | −0.342381 | ||||||||
\(277\) | 17.5596 | 1.05506 | 0.527528 | − | 0.849538i | \(-0.323119\pi\) | ||||
0.527528 | + | 0.849538i | \(0.323119\pi\) | |||||||
\(278\) | −9.14476 | −0.548466 | ||||||||
\(279\) | 1.91441 | 0.114612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2569 | −0.790843 | −0.395421 | − | 0.918500i | \(-0.629401\pi\) | ||||
−0.395421 | + | 0.918500i | \(0.629401\pi\) | |||||||
\(282\) | 16.6956 | 0.994206 | ||||||||
\(283\) | −9.58330 | −0.569668 | −0.284834 | − | 0.958577i | \(-0.591939\pi\) | ||||
−0.284834 | + | 0.958577i | \(0.591939\pi\) | |||||||
\(284\) | −7.88536 | −0.467910 | ||||||||
\(285\) | 8.51928 | 0.504639 | ||||||||
\(286\) | −24.8697 | −1.47058 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.05405 | −0.533515 | ||||||||
\(289\) | 32.1664 | 1.89214 | ||||||||
\(290\) | −34.5181 | −2.02697 | ||||||||
\(291\) | 13.4628 | 0.789202 | ||||||||
\(292\) | −3.15131 | −0.184417 | ||||||||
\(293\) | −19.5179 | −1.14025 | −0.570125 | − | 0.821558i | \(-0.693105\pi\) | ||||
−0.570125 | + | 0.821558i | \(0.693105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.13534 | −0.240769 | ||||||||
\(296\) | −8.14872 | −0.473634 | ||||||||
\(297\) | 25.7483 | 1.49407 | ||||||||
\(298\) | −26.7407 | −1.54904 | ||||||||
\(299\) | 12.0417 | 0.696388 | ||||||||
\(300\) | −1.99082 | −0.114940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.71831 | −0.559226 | ||||||||
\(303\) | −2.07940 | −0.119458 | ||||||||
\(304\) | 13.8488 | 0.794282 | ||||||||
\(305\) | −35.3409 | −2.02361 | ||||||||
\(306\) | 19.2250 | 1.09902 | ||||||||
\(307\) | −11.4155 | −0.651519 | −0.325759 | − | 0.945453i | \(-0.605620\pi\) | ||||
−0.325759 | + | 0.945453i | \(0.605620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.1692 | 1.03361 | ||||||||
\(310\) | 5.59677 | 0.317875 | ||||||||
\(311\) | −24.5477 | −1.39197 | −0.695985 | − | 0.718056i | \(-0.745032\pi\) | ||||
−0.695985 | + | 0.718056i | \(0.745032\pi\) | |||||||
\(312\) | −5.34481 | −0.302590 | ||||||||
\(313\) | −12.7014 | −0.717926 | −0.358963 | − | 0.933352i | \(-0.616870\pi\) | ||||
−0.358963 | + | 0.933352i | \(0.616870\pi\) | |||||||
\(314\) | 38.9713 | 2.19928 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.5314 | 0.817456 | ||||||||
\(317\) | 26.6083 | 1.49447 | 0.747237 | − | 0.664558i | \(-0.231380\pi\) | ||||
0.747237 | + | 0.664558i | \(0.231380\pi\) | |||||||
\(318\) | −20.2885 | −1.13772 | ||||||||
\(319\) | 35.9631 | 2.01355 | ||||||||
\(320\) | −1.27860 | −0.0714758 | ||||||||
\(321\) | −2.09769 | −0.117082 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5271 | −1.08652 | ||||||||
\(324\) | −2.33042 | −0.129468 | ||||||||
\(325\) | 4.21457 | 0.233782 | ||||||||
\(326\) | −7.88529 | −0.436726 | ||||||||
\(327\) | −21.8669 | −1.20924 | ||||||||
\(328\) | −1.48599 | −0.0820501 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 25.5474 | 1.40634 | ||||||||
\(331\) | −13.3106 | −0.731617 | −0.365809 | − | 0.930690i | \(-0.619207\pi\) | ||||
−0.365809 | + | 0.930690i | \(0.619207\pi\) | |||||||
\(332\) | 0.340791 | 0.0187033 | ||||||||
\(333\) | 8.45165 | 0.463147 | ||||||||
\(334\) | −32.6692 | −1.78758 | ||||||||
\(335\) | −9.51899 | −0.520078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.90555 | −0.376169 | −0.188085 | − | 0.982153i | \(-0.560228\pi\) | ||||
−0.188085 | + | 0.982153i | \(0.560228\pi\) | |||||||
\(338\) | 7.34990 | 0.399782 | ||||||||
\(339\) | 18.4362 | 1.00132 | ||||||||
\(340\) | 20.6847 | 1.12178 | ||||||||
\(341\) | −5.83107 | −0.315770 | ||||||||
\(342\) | −7.63549 | −0.412880 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 13.6431 | 0.735589 | ||||||||
\(345\) | −12.3698 | −0.665968 | ||||||||
\(346\) | 26.7880 | 1.44013 | ||||||||
\(347\) | 0.0561815 | 0.00301598 | 0.00150799 | − | 0.999999i | \(-0.499520\pi\) | ||||
0.00150799 | + | 0.999999i | \(0.499520\pi\) | |||||||
\(348\) | −10.7765 | −0.577679 | ||||||||
\(349\) | 6.22816 | 0.333386 | 0.166693 | − | 0.986009i | \(-0.446691\pi\) | ||||
0.166693 | + | 0.986009i | \(0.446691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.3339 | 0.871839 | ||||||||
\(352\) | 27.5776 | 1.46989 | ||||||||
\(353\) | 1.81469 | 0.0965863 | 0.0482932 | − | 0.998833i | \(-0.484622\pi\) | ||||
0.0482932 | + | 0.998833i | \(0.484622\pi\) | |||||||
\(354\) | −3.50803 | −0.186450 | ||||||||
\(355\) | −17.1482 | −0.910134 | ||||||||
\(356\) | −3.48820 | −0.184874 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.6932 | −1.51648 | ||||||||
\(359\) | −22.3519 | −1.17969 | −0.589845 | − | 0.807517i | \(-0.700811\pi\) | ||||
−0.589845 | + | 0.807517i | \(0.700811\pi\) | |||||||
\(360\) | −5.80084 | −0.305731 | ||||||||
\(361\) | −11.2445 | −0.591818 | ||||||||
\(362\) | −4.50602 | −0.236831 | ||||||||
\(363\) | −13.3312 | −0.699705 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.85314 | −0.358710 | ||||||||
\(366\) | −29.9798 | −1.56707 | ||||||||
\(367\) | −2.28250 | −0.119145 | −0.0595727 | − | 0.998224i | \(-0.518974\pi\) | ||||
−0.0595727 | + | 0.998224i | \(0.518974\pi\) | |||||||
\(368\) | −20.1081 | −1.04821 | ||||||||
\(369\) | 1.54123 | 0.0802334 | ||||||||
\(370\) | 24.7084 | 1.28453 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.74730 | 0.0905932 | ||||||||
\(373\) | −3.52330 | −0.182429 | −0.0912147 | − | 0.995831i | \(-0.529075\pi\) | ||||
−0.0912147 | + | 0.995831i | \(0.529075\pi\) | |||||||
\(374\) | −58.5574 | −3.02793 | ||||||||
\(375\) | 10.9663 | 0.566297 | ||||||||
\(376\) | 11.5467 | 0.595477 | ||||||||
\(377\) | 22.8138 | 1.17497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2688 | −0.784306 | −0.392153 | − | 0.919900i | \(-0.628270\pi\) | ||||
−0.392153 | + | 0.919900i | \(0.628270\pi\) | |||||||
\(380\) | −8.21520 | −0.421431 | ||||||||
\(381\) | −7.22874 | −0.370340 | ||||||||
\(382\) | −35.6817 | −1.82563 | ||||||||
\(383\) | 11.1027 | 0.567323 | 0.283661 | − | 0.958924i | \(-0.408451\pi\) | ||||
0.283661 | + | 0.958924i | \(0.408451\pi\) | |||||||
\(384\) | 13.1059 | 0.668806 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.7211 | −0.901982 | ||||||||
\(387\) | −14.1503 | −0.719301 | ||||||||
\(388\) | −12.9822 | −0.659074 | ||||||||
\(389\) | −16.4667 | −0.834892 | −0.417446 | − | 0.908702i | \(-0.637075\pi\) | ||||
−0.417446 | + | 0.908702i | \(0.637075\pi\) | |||||||
\(390\) | 16.2064 | 0.820645 | ||||||||
\(391\) | 28.3529 | 1.43387 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.44722 | −0.426106 | ||||||||
\(394\) | −40.3571 | −2.03316 | ||||||||
\(395\) | 31.6014 | 1.59004 | ||||||||
\(396\) | −8.42672 | −0.423459 | ||||||||
\(397\) | 20.1657 | 1.01209 | 0.506043 | − | 0.862509i | \(-0.331108\pi\) | ||||
0.506043 | + | 0.862509i | \(0.331108\pi\) | |||||||
\(398\) | −5.70584 | −0.286008 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.03782 | −0.351891 | ||||||||
\(401\) | −18.7090 | −0.934285 | −0.467143 | − | 0.884182i | \(-0.654717\pi\) | ||||
−0.467143 | + | 0.884182i | \(0.654717\pi\) | |||||||
\(402\) | −8.07500 | −0.402744 | ||||||||
\(403\) | −3.69904 | −0.184262 | ||||||||
\(404\) | 2.00518 | 0.0997613 | ||||||||
\(405\) | −5.06796 | −0.251829 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.7428 | −1.27602 | ||||||||
\(408\) | −12.5847 | −0.623036 | ||||||||
\(409\) | −5.36315 | −0.265191 | −0.132595 | − | 0.991170i | \(-0.542331\pi\) | ||||
−0.132595 | + | 0.991170i | \(0.542331\pi\) | |||||||
\(410\) | 4.50580 | 0.222525 | ||||||||
\(411\) | −10.0365 | −0.495063 | ||||||||
\(412\) | −17.5206 | −0.863180 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.0866 | 0.544875 | ||||||||
\(415\) | 0.741117 | 0.0363800 | ||||||||
\(416\) | 17.4944 | 0.857731 | ||||||||
\(417\) | −6.20870 | −0.304041 | ||||||||
\(418\) | 23.2569 | 1.13753 | ||||||||
\(419\) | −2.79177 | −0.136387 | −0.0681934 | − | 0.997672i | \(-0.521723\pi\) | ||||
−0.0681934 | + | 0.997672i | \(0.521723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.6956 | −1.05738 | −0.528689 | − | 0.848815i | \(-0.677316\pi\) | ||||
−0.528689 | + | 0.848815i | \(0.677316\pi\) | |||||||
\(422\) | −16.7314 | −0.814472 | ||||||||
\(423\) | −11.9760 | −0.582292 | ||||||||
\(424\) | −14.0316 | −0.681434 | ||||||||
\(425\) | 9.92349 | 0.481360 | ||||||||
\(426\) | −14.5469 | −0.704801 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.02281 | 0.0977764 | ||||||||
\(429\) | −16.8849 | −0.815211 | ||||||||
\(430\) | −41.3685 | −1.99497 | ||||||||
\(431\) | 4.61698 | 0.222392 | 0.111196 | − | 0.993798i | \(-0.464532\pi\) | ||||
0.111196 | + | 0.993798i | \(0.464532\pi\) | |||||||
\(432\) | −27.2756 | −1.31230 | ||||||||
\(433\) | 5.83701 | 0.280509 | 0.140254 | − | 0.990115i | \(-0.455208\pi\) | ||||
0.140254 | + | 0.990115i | \(0.455208\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.4355 | −1.12365 | ||||||||
\(436\) | 21.0864 | 1.00986 | ||||||||
\(437\) | −11.2607 | −0.538675 | ||||||||
\(438\) | −5.81355 | −0.277782 | ||||||||
\(439\) | 20.1437 | 0.961407 | 0.480703 | − | 0.876883i | \(-0.340381\pi\) | ||||
0.480703 | + | 0.876883i | \(0.340381\pi\) | |||||||
\(440\) | 17.6687 | 0.842323 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −37.1469 | −1.76690 | ||||||||
\(443\) | 5.14409 | 0.244403 | 0.122202 | − | 0.992505i | \(-0.461005\pi\) | ||||
0.122202 | + | 0.992505i | \(0.461005\pi\) | |||||||
\(444\) | 7.71390 | 0.366086 | ||||||||
\(445\) | −7.58577 | −0.359600 | ||||||||
\(446\) | 6.62792 | 0.313841 | ||||||||
\(447\) | −18.1552 | −0.858709 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.86081 | 0.323782 | 0.161891 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161891 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(450\) | 3.88029 | 0.182918 | ||||||||
\(451\) | −4.69442 | −0.221052 | ||||||||
\(452\) | −17.7782 | −0.836215 | ||||||||
\(453\) | −6.59810 | −0.310006 | ||||||||
\(454\) | −1.48135 | −0.0695231 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.99819 | 0.234062 | ||||||||
\(457\) | 7.22547 | 0.337993 | 0.168997 | − | 0.985617i | \(-0.445947\pi\) | ||||
0.168997 | + | 0.985617i | \(0.445947\pi\) | |||||||
\(458\) | −36.1721 | −1.69021 | ||||||||
\(459\) | 38.4593 | 1.79512 | ||||||||
\(460\) | 11.9283 | 0.556159 | ||||||||
\(461\) | −8.14091 | −0.379160 | −0.189580 | − | 0.981865i | \(-0.560713\pi\) | ||||
−0.189580 | + | 0.981865i | \(0.560713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0745 | 0.839993 | 0.419996 | − | 0.907526i | \(-0.362031\pi\) | ||||
0.419996 | + | 0.907526i | \(0.362031\pi\) | |||||||
\(464\) | −38.0963 | −1.76858 | ||||||||
\(465\) | 3.79984 | 0.176213 | ||||||||
\(466\) | 6.39698 | 0.296334 | ||||||||
\(467\) | 34.4162 | 1.59259 | 0.796296 | − | 0.604907i | \(-0.206790\pi\) | ||||
0.796296 | + | 0.604907i | \(0.206790\pi\) | |||||||
\(468\) | −5.34564 | −0.247102 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −35.0118 | −1.61497 | ||||||||
\(471\) | 26.4589 | 1.21916 | ||||||||
\(472\) | −2.42617 | −0.111673 | ||||||||
\(473\) | 43.1003 | 1.98176 | ||||||||
\(474\) | 26.8076 | 1.23131 | ||||||||
\(475\) | −3.94125 | −0.180837 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5532 | 0.666346 | ||||||||
\(478\) | −13.9217 | −0.636763 | ||||||||
\(479\) | 21.2341 | 0.970211 | 0.485105 | − | 0.874456i | \(-0.338781\pi\) | ||||
0.485105 | + | 0.874456i | \(0.338781\pi\) | |||||||
\(480\) | −17.9711 | −0.820264 | ||||||||
\(481\) | −16.3304 | −0.744601 | ||||||||
\(482\) | −23.2153 | −1.05743 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.8553 | 0.584334 | ||||||||
\(485\) | −28.2324 | −1.28197 | ||||||||
\(486\) | 24.9729 | 1.13279 | ||||||||
\(487\) | −24.8051 | −1.12403 | −0.562014 | − | 0.827128i | \(-0.689973\pi\) | ||||
−0.562014 | + | 0.827128i | \(0.689973\pi\) | |||||||
\(488\) | −20.7342 | −0.938592 | ||||||||
\(489\) | −5.35360 | −0.242098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.9360 | 1.71203 | 0.856014 | − | 0.516953i | \(-0.172934\pi\) | ||||
0.856014 | + | 0.516953i | \(0.172934\pi\) | |||||||
\(492\) | 1.40670 | 0.0634189 | ||||||||
\(493\) | 53.7167 | 2.41928 | ||||||||
\(494\) | 14.7534 | 0.663786 | ||||||||
\(495\) | −18.3256 | −0.823672 | ||||||||
\(496\) | 6.17694 | 0.277353 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.628693 | 0.0281724 | ||||||||
\(499\) | 24.0701 | 1.07752 | 0.538762 | − | 0.842458i | \(-0.318892\pi\) | ||||
0.538762 | + | 0.842458i | \(0.318892\pi\) | |||||||
\(500\) | −10.5749 | −0.472922 | ||||||||
\(501\) | −22.1802 | −0.990940 | ||||||||
\(502\) | −4.43380 | −0.197890 | ||||||||
\(503\) | −3.13580 | −0.139819 | −0.0699093 | − | 0.997553i | \(-0.522271\pi\) | ||||
−0.0699093 | + | 0.997553i | \(0.522271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.36065 | 0.194046 | ||||||||
\(506\) | −33.7685 | −1.50119 | ||||||||
\(507\) | 4.99010 | 0.221618 | ||||||||
\(508\) | 6.97072 | 0.309276 | ||||||||
\(509\) | −20.6034 | −0.913231 | −0.456616 | − | 0.889664i | \(-0.650939\pi\) | ||||
−0.456616 | + | 0.889664i | \(0.650939\pi\) | |||||||
\(510\) | 38.1592 | 1.68972 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.4341 | −0.637905 | ||||||||
\(513\) | −15.2746 | −0.674391 | ||||||||
\(514\) | −36.1716 | −1.59546 | ||||||||
\(515\) | −38.1021 | −1.67898 | ||||||||
\(516\) | −12.9151 | −0.568558 | ||||||||
\(517\) | 36.4775 | 1.60428 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.1873 | 0.798334 | ||||||||
\(520\) | 11.2085 | 0.491523 | ||||||||
\(521\) | 1.77725 | 0.0778629 | 0.0389314 | − | 0.999242i | \(-0.487605\pi\) | ||||
0.0389314 | + | 0.999242i | \(0.487605\pi\) | |||||||
\(522\) | 21.0043 | 0.919334 | ||||||||
\(523\) | 23.3930 | 1.02290 | 0.511452 | − | 0.859312i | \(-0.329108\pi\) | ||||
0.511452 | + | 0.859312i | \(0.329108\pi\) | |||||||
\(524\) | 8.14570 | 0.355847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.0713 | 1.83440 | ||||||||
\(527\) | −8.70963 | −0.379398 | ||||||||
\(528\) | 28.1957 | 1.22706 | ||||||||
\(529\) | −6.64964 | −0.289115 | ||||||||
\(530\) | 42.5464 | 1.84810 | ||||||||
\(531\) | 2.51636 | 0.109201 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.97799 | −0.128991 | ||||||||
\(534\) | −6.43504 | −0.278472 | ||||||||
\(535\) | 4.39900 | 0.190185 | ||||||||
\(536\) | −5.58471 | −0.241223 | ||||||||
\(537\) | −19.4808 | −0.840659 | ||||||||
\(538\) | 7.17414 | 0.309299 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.1801 | 0.696281 | ||||||||
\(541\) | 26.9238 | 1.15754 | 0.578772 | − | 0.815489i | \(-0.303532\pi\) | ||||
0.578772 | + | 0.815489i | \(0.303532\pi\) | |||||||
\(542\) | 31.5023 | 1.35314 | ||||||||
\(543\) | −3.05929 | −0.131287 | ||||||||
\(544\) | 41.1916 | 1.76608 | ||||||||
\(545\) | 45.8565 | 1.96428 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.3464 | −1.04098 | −0.520489 | − | 0.853869i | \(-0.674250\pi\) | ||||
−0.520489 | + | 0.853869i | \(0.674250\pi\) | |||||||
\(548\) | 9.67824 | 0.413434 | ||||||||
\(549\) | 21.5050 | 0.917810 | ||||||||
\(550\) | −11.8189 | −0.503960 | ||||||||
\(551\) | −21.3343 | −0.908872 | ||||||||
\(552\) | −7.25726 | −0.308890 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −31.2378 | −1.32717 | ||||||||
\(555\) | 16.7754 | 0.712076 | ||||||||
\(556\) | 5.98708 | 0.253909 | ||||||||
\(557\) | −39.4429 | −1.67125 | −0.835625 | − | 0.549301i | \(-0.814894\pi\) | ||||
−0.835625 | + | 0.549301i | \(0.814894\pi\) | |||||||
\(558\) | −3.40564 | −0.144172 | ||||||||
\(559\) | 27.3414 | 1.15642 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.7566 | −1.67853 | ||||||||
\(562\) | 23.5835 | 0.994811 | ||||||||
\(563\) | 4.52248 | 0.190600 | 0.0952998 | − | 0.995449i | \(-0.469619\pi\) | ||||
0.0952998 | + | 0.995449i | \(0.469619\pi\) | |||||||
\(564\) | −10.9306 | −0.460261 | ||||||||
\(565\) | −38.6621 | −1.62653 | ||||||||
\(566\) | 17.0483 | 0.716592 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.0607 | −0.422139 | ||||||||
\(569\) | −9.79397 | −0.410584 | −0.205292 | − | 0.978701i | \(-0.565814\pi\) | ||||
−0.205292 | + | 0.978701i | \(0.565814\pi\) | |||||||
\(570\) | −15.1554 | −0.634791 | ||||||||
\(571\) | 29.0757 | 1.21678 | 0.608390 | − | 0.793639i | \(-0.291816\pi\) | ||||
0.608390 | + | 0.793639i | \(0.291816\pi\) | |||||||
\(572\) | 16.2822 | 0.680794 | ||||||||
\(573\) | −24.2255 | −1.01204 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.72261 | 0.238649 | ||||||||
\(576\) | 0.778029 | 0.0324179 | ||||||||
\(577\) | −43.5350 | −1.81239 | −0.906193 | − | 0.422865i | \(-0.861024\pi\) | ||||
−0.906193 | + | 0.422865i | \(0.861024\pi\) | |||||||
\(578\) | −57.2225 | −2.38014 | ||||||||
\(579\) | −12.0315 | −0.500012 | ||||||||
\(580\) | 22.5990 | 0.938373 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −23.9497 | −0.992747 | ||||||||
\(583\) | −44.3275 | −1.83586 | ||||||||
\(584\) | −4.02068 | −0.166377 | ||||||||
\(585\) | −11.6251 | −0.480640 | ||||||||
\(586\) | 34.7215 | 1.43433 | ||||||||
\(587\) | −22.0541 | −0.910271 | −0.455135 | − | 0.890422i | \(-0.650409\pi\) | ||||
−0.455135 | + | 0.890422i | \(0.650409\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.45915 | 0.142532 | ||||||||
\(590\) | 7.35659 | 0.302866 | ||||||||
\(591\) | −27.3998 | −1.12708 | ||||||||
\(592\) | 27.2697 | 1.12078 | ||||||||
\(593\) | −34.7750 | −1.42804 | −0.714019 | − | 0.700126i | \(-0.753127\pi\) | ||||
−0.714019 | + | 0.700126i | \(0.753127\pi\) | |||||||
\(594\) | −45.8051 | −1.87941 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.5071 | 0.717120 | ||||||||
\(597\) | −3.87389 | −0.158548 | ||||||||
\(598\) | −21.4216 | −0.875994 | ||||||||
\(599\) | −27.8457 | −1.13775 | −0.568873 | − | 0.822425i | \(-0.692620\pi\) | ||||
−0.568873 | + | 0.822425i | \(0.692620\pi\) | |||||||
\(600\) | −2.54003 | −0.103696 | ||||||||
\(601\) | 6.64710 | 0.271141 | 0.135570 | − | 0.990768i | \(-0.456713\pi\) | ||||
0.135570 | + | 0.990768i | \(0.456713\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.79232 | 0.235881 | ||||||||
\(604\) | 6.36259 | 0.258890 | ||||||||
\(605\) | 27.9564 | 1.13659 | ||||||||
\(606\) | 3.69916 | 0.150268 | ||||||||
\(607\) | 11.9432 | 0.484760 | 0.242380 | − | 0.970181i | \(-0.422072\pi\) | ||||
0.242380 | + | 0.970181i | \(0.422072\pi\) | |||||||
\(608\) | −16.3598 | −0.663478 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 62.8699 | 2.54553 | ||||||||
\(611\) | 23.1401 | 0.936150 | ||||||||
\(612\) | −12.5867 | −0.508785 | ||||||||
\(613\) | −10.1793 | −0.411139 | −0.205570 | − | 0.978642i | \(-0.565905\pi\) | ||||
−0.205570 | + | 0.978642i | \(0.565905\pi\) | |||||||
\(614\) | 20.3077 | 0.819553 | ||||||||
\(615\) | 3.05914 | 0.123356 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.4430 | −1.14507 | −0.572536 | − | 0.819880i | \(-0.694040\pi\) | ||||
−0.572536 | + | 0.819880i | \(0.694040\pi\) | |||||||
\(618\) | −32.3221 | −1.30019 | ||||||||
\(619\) | −40.0289 | −1.60890 | −0.804448 | − | 0.594023i | \(-0.797539\pi\) | ||||
−0.804448 | + | 0.594023i | \(0.797539\pi\) | |||||||
\(620\) | −3.66421 | −0.147158 | ||||||||
\(621\) | 22.1784 | 0.889989 | ||||||||
\(622\) | 43.6692 | 1.75098 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.8864 | 0.716031 | ||||||||
\(625\) | −30.0733 | −1.20293 | ||||||||
\(626\) | 22.5952 | 0.903087 | ||||||||
\(627\) | 15.7899 | 0.630587 | ||||||||
\(628\) | −25.5145 | −1.01814 | ||||||||
\(629\) | −38.4510 | −1.53314 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5759 | −0.540446 | −0.270223 | − | 0.962798i | \(-0.587097\pi\) | ||||
−0.270223 | + | 0.962798i | \(0.587097\pi\) | |||||||
\(632\) | 18.5403 | 0.737492 | ||||||||
\(633\) | −11.3595 | −0.451501 | ||||||||
\(634\) | −47.3351 | −1.87992 | ||||||||
\(635\) | 15.1592 | 0.601574 | ||||||||
\(636\) | 13.2829 | 0.526700 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −63.9768 | −2.53287 | ||||||||
\(639\) | 10.4347 | 0.412792 | ||||||||
\(640\) | −27.4839 | −1.08640 | ||||||||
\(641\) | −5.11483 | −0.202024 | −0.101012 | − | 0.994885i | \(-0.532208\pi\) | ||||
−0.101012 | + | 0.994885i | \(0.532208\pi\) | |||||||
\(642\) | 3.73169 | 0.147278 | ||||||||
\(643\) | 24.0339 | 0.947804 | 0.473902 | − | 0.880578i | \(-0.342845\pi\) | ||||
0.473902 | + | 0.880578i | \(0.342845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.0865 | −1.10591 | ||||||||
\(646\) | 34.7378 | 1.36674 | ||||||||
\(647\) | 28.0872 | 1.10422 | 0.552111 | − | 0.833771i | \(-0.313822\pi\) | ||||
0.552111 | + | 0.833771i | \(0.313822\pi\) | |||||||
\(648\) | −2.97332 | −0.116803 | ||||||||
\(649\) | −7.66456 | −0.300860 | ||||||||
\(650\) | −7.49754 | −0.294078 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.16251 | 0.202179 | ||||||||
\(653\) | 29.8731 | 1.16903 | 0.584513 | − | 0.811385i | \(-0.301286\pi\) | ||||
0.584513 | + | 0.811385i | \(0.301286\pi\) | |||||||
\(654\) | 38.9003 | 1.52112 | ||||||||
\(655\) | 17.7144 | 0.692160 | ||||||||
\(656\) | 4.97288 | 0.194158 | ||||||||
\(657\) | 4.17015 | 0.162693 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.6367 | 0.998664 | 0.499332 | − | 0.866411i | \(-0.333579\pi\) | ||||
0.499332 | + | 0.866411i | \(0.333579\pi\) | |||||||
\(660\) | −16.7259 | −0.651055 | ||||||||
\(661\) | −15.0334 | −0.584733 | −0.292367 | − | 0.956306i | \(-0.594443\pi\) | ||||
−0.292367 | + | 0.956306i | \(0.594443\pi\) | |||||||
\(662\) | 23.6790 | 0.920310 | ||||||||
\(663\) | −25.2203 | −0.979475 | ||||||||
\(664\) | 0.434807 | 0.0168738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.0351 | −0.582598 | ||||||||
\(667\) | 30.9770 | 1.19943 | ||||||||
\(668\) | 21.3885 | 0.827547 | ||||||||
\(669\) | 4.49992 | 0.173977 | ||||||||
\(670\) | 16.9339 | 0.654212 | ||||||||
\(671\) | −65.5018 | −2.52867 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1067 | −0.697961 | −0.348981 | − | 0.937130i | \(-0.613472\pi\) | ||||
−0.348981 | + | 0.937130i | \(0.613472\pi\) | |||||||
\(674\) | 12.2847 | 0.473188 | ||||||||
\(675\) | 7.76242 | 0.298776 | ||||||||
\(676\) | −4.81198 | −0.185076 | ||||||||
\(677\) | 31.1567 | 1.19745 | 0.598725 | − | 0.800954i | \(-0.295674\pi\) | ||||
0.598725 | + | 0.800954i | \(0.295674\pi\) | |||||||
\(678\) | −32.7972 | −1.25957 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 26.3910 | 1.01205 | ||||||||
\(681\) | −1.00574 | −0.0385400 | ||||||||
\(682\) | 10.3732 | 0.397211 | ||||||||
\(683\) | −32.3923 | −1.23946 | −0.619728 | − | 0.784817i | \(-0.712757\pi\) | ||||
−0.619728 | + | 0.784817i | \(0.712757\pi\) | |||||||
\(684\) | 4.99896 | 0.191140 | ||||||||
\(685\) | 21.0472 | 0.804173 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.5585 | −0.936964 | ||||||||
\(688\) | −45.6569 | −1.74065 | ||||||||
\(689\) | −28.1199 | −1.07128 | ||||||||
\(690\) | 22.0054 | 0.837729 | ||||||||
\(691\) | 39.3721 | 1.49778 | 0.748892 | − | 0.662692i | \(-0.230586\pi\) | ||||
0.748892 | + | 0.662692i | \(0.230586\pi\) | |||||||
\(692\) | −17.5381 | −0.666700 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.0999444 | −0.00379384 | ||||||||
\(695\) | 13.0201 | 0.493880 | ||||||||
\(696\) | −13.7494 | −0.521170 | ||||||||
\(697\) | −7.01187 | −0.265594 | ||||||||
\(698\) | −11.0796 | −0.419370 | ||||||||
\(699\) | 4.34313 | 0.164272 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.4429 | −0.960966 | −0.480483 | − | 0.877004i | \(-0.659539\pi\) | ||||
−0.480483 | + | 0.877004i | \(0.659539\pi\) | |||||||
\(702\) | −29.0573 | −1.09670 | ||||||||
\(703\) | 15.2713 | 0.575969 | ||||||||
\(704\) | −2.36979 | −0.0893148 | ||||||||
\(705\) | −23.7707 | −0.895257 | ||||||||
\(706\) | −3.22826 | −0.121497 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.29671 | 0.0863156 | ||||||||
\(709\) | −23.9649 | −0.900022 | −0.450011 | − | 0.893023i | \(-0.648580\pi\) | ||||
−0.450011 | + | 0.893023i | \(0.648580\pi\) | |||||||
\(710\) | 30.5060 | 1.14487 | ||||||||
\(711\) | −19.2295 | −0.721163 | ||||||||
\(712\) | −4.45051 | −0.166790 | ||||||||
\(713\) | −5.02261 | −0.188098 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.4089 | 1.32422 | ||||||||
\(716\) | 18.7855 | 0.702046 | ||||||||
\(717\) | −9.45191 | −0.352988 | ||||||||
\(718\) | 39.7631 | 1.48394 | ||||||||
\(719\) | 28.2304 | 1.05282 | 0.526409 | − | 0.850232i | \(-0.323538\pi\) | ||||
0.526409 | + | 0.850232i | \(0.323538\pi\) | |||||||
\(720\) | 19.4125 | 0.723463 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.0036 | 0.744455 | ||||||||
\(723\) | −15.7617 | −0.586183 | ||||||||
\(724\) | 2.95009 | 0.109639 | ||||||||
\(725\) | 10.8419 | 0.402658 | ||||||||
\(726\) | 23.7156 | 0.880168 | ||||||||
\(727\) | −17.4611 | −0.647595 | −0.323798 | − | 0.946126i | \(-0.604960\pi\) | ||||
−0.323798 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.9577 | 0.850284 | ||||||||
\(730\) | 12.1914 | 0.451225 | ||||||||
\(731\) | 64.3772 | 2.38108 | ||||||||
\(732\) | 19.6278 | 0.725465 | ||||||||
\(733\) | −14.2857 | −0.527656 | −0.263828 | − | 0.964570i | \(-0.584985\pi\) | ||||
−0.263828 | + | 0.964570i | \(0.584985\pi\) | |||||||
\(734\) | 4.06046 | 0.149874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23.7541 | 0.875587 | ||||||||
\(737\) | −17.6428 | −0.649880 | ||||||||
\(738\) | −2.74178 | −0.100926 | ||||||||
\(739\) | 12.0944 | 0.444898 | 0.222449 | − | 0.974944i | \(-0.428595\pi\) | ||||
0.222449 | + | 0.974944i | \(0.428595\pi\) | |||||||
\(740\) | −16.1766 | −0.594664 | ||||||||
\(741\) | 10.0166 | 0.367968 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.11337 | 0.334337 | 0.167168 | − | 0.985928i | \(-0.446538\pi\) | ||||
0.167168 | + | 0.985928i | \(0.446538\pi\) | |||||||
\(744\) | 2.22933 | 0.0817313 | ||||||||
\(745\) | 38.0727 | 1.39487 | ||||||||
\(746\) | 6.26779 | 0.229480 | ||||||||
\(747\) | −0.450971 | −0.0165002 | ||||||||
\(748\) | 38.3376 | 1.40176 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.5085 | −0.712351 | ||||||||
\(751\) | −8.65418 | −0.315796 | −0.157898 | − | 0.987455i | \(-0.550472\pi\) | ||||
−0.157898 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(752\) | −38.6412 | −1.40910 | ||||||||
\(753\) | −3.01026 | −0.109700 | ||||||||
\(754\) | −40.5848 | −1.47801 | ||||||||
\(755\) | 13.8367 | 0.503569 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.7596 | 0.863556 | 0.431778 | − | 0.901980i | \(-0.357886\pi\) | ||||
0.431778 | + | 0.901980i | \(0.357886\pi\) | |||||||
\(758\) | 27.1625 | 0.986588 | ||||||||
\(759\) | −22.9266 | −0.832182 | ||||||||
\(760\) | −10.4816 | −0.380206 | ||||||||
\(761\) | 47.8706 | 1.73531 | 0.867655 | − | 0.497167i | \(-0.165627\pi\) | ||||
0.867655 | + | 0.497167i | \(0.165627\pi\) | |||||||
\(762\) | 12.8596 | 0.465854 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 23.3608 | 0.845165 | ||||||||
\(765\) | −27.3721 | −0.989642 | ||||||||
\(766\) | −19.7513 | −0.713642 | ||||||||
\(767\) | −4.86214 | −0.175562 | ||||||||
\(768\) | −24.5342 | −0.885300 | ||||||||
\(769\) | 37.0906 | 1.33752 | 0.668761 | − | 0.743478i | \(-0.266825\pi\) | ||||
0.668761 | + | 0.743478i | \(0.266825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.5582 | −0.884440 | ||||||||
\(772\) | 11.6020 | 0.417567 | ||||||||
\(773\) | 15.0756 | 0.542231 | 0.271115 | − | 0.962547i | \(-0.412607\pi\) | ||||
0.271115 | + | 0.962547i | \(0.412607\pi\) | |||||||
\(774\) | 25.1728 | 0.904818 | ||||||||
\(775\) | −1.75791 | −0.0631459 | ||||||||
\(776\) | −16.5637 | −0.594603 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.2934 | 1.05022 | ||||||||
\(779\) | 2.78486 | 0.0997780 | ||||||||
\(780\) | −10.6104 | −0.379912 | ||||||||
\(781\) | −31.7830 | −1.13729 | ||||||||
\(782\) | −50.4386 | −1.80368 | ||||||||
\(783\) | 42.0186 | 1.50162 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −55.4863 | −1.98039 | ||||||||
\(786\) | 15.0272 | 0.536003 | ||||||||
\(787\) | −44.0273 | −1.56940 | −0.784702 | − | 0.619874i | \(-0.787184\pi\) | ||||
−0.784702 | + | 0.619874i | \(0.787184\pi\) | |||||||
\(788\) | 26.4218 | 0.941239 | ||||||||
\(789\) | 28.5637 | 1.01689 | ||||||||
\(790\) | −56.2175 | −2.00013 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.7514 | −0.382036 | ||||||||
\(793\) | −41.5522 | −1.47556 | ||||||||
\(794\) | −35.8738 | −1.27311 | ||||||||
\(795\) | 28.8862 | 1.02449 | ||||||||
\(796\) | 3.73562 | 0.132406 | ||||||||
\(797\) | −12.7891 | −0.453015 | −0.226507 | − | 0.974009i | \(-0.572731\pi\) | ||||
−0.226507 | + | 0.974009i | \(0.572731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.4850 | 1.92754 | ||||||||
\(800\) | 8.31390 | 0.293941 | ||||||||
\(801\) | 4.61595 | 0.163097 | ||||||||
\(802\) | 33.2826 | 1.17525 | ||||||||
\(803\) | −12.7018 | −0.448237 | ||||||||
\(804\) | 5.28671 | 0.186448 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.58043 | 0.231786 | ||||||||
\(807\) | 4.87077 | 0.171459 | ||||||||
\(808\) | 2.55835 | 0.0900026 | ||||||||
\(809\) | 28.6918 | 1.00875 | 0.504375 | − | 0.863485i | \(-0.331723\pi\) | ||||
0.504375 | + | 0.863485i | \(0.331723\pi\) | |||||||
\(810\) | 9.01567 | 0.316778 | ||||||||
\(811\) | 19.8602 | 0.697385 | 0.348693 | − | 0.937237i | \(-0.386626\pi\) | ||||
0.348693 | + | 0.937237i | \(0.386626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.3880 | 0.750111 | ||||||||
\(814\) | 45.7953 | 1.60512 | ||||||||
\(815\) | 11.2269 | 0.393261 | ||||||||
\(816\) | 42.1148 | 1.47431 | ||||||||
\(817\) | −25.5683 | −0.894521 | ||||||||
\(818\) | 9.54080 | 0.333586 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.94995 | −0.103017 | ||||||||
\(821\) | −0.296096 | −0.0103338 | −0.00516690 | − | 0.999987i | \(-0.501645\pi\) | ||||
−0.00516690 | + | 0.999987i | \(0.501645\pi\) | |||||||
\(822\) | 17.8545 | 0.622746 | ||||||||
\(823\) | 3.66971 | 0.127918 | 0.0639590 | − | 0.997953i | \(-0.479627\pi\) | ||||
0.0639590 | + | 0.997953i | \(0.479627\pi\) | |||||||
\(824\) | −22.3541 | −0.778743 | ||||||||
\(825\) | −8.02427 | −0.279369 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.96494 | −0.137875 | −0.0689373 | − | 0.997621i | \(-0.521961\pi\) | ||||
−0.0689373 | + | 0.997621i | \(0.521961\pi\) | |||||||
\(828\) | −7.25838 | −0.252246 | ||||||||
\(829\) | −4.95467 | −0.172083 | −0.0860413 | − | 0.996292i | \(-0.527422\pi\) | ||||
−0.0860413 | + | 0.996292i | \(0.527422\pi\) | |||||||
\(830\) | −1.31841 | −0.0457628 | ||||||||
\(831\) | −21.2084 | −0.735712 | ||||||||
\(832\) | −1.50332 | −0.0521181 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.0450 | 0.382457 | ||||||||
\(835\) | 46.5136 | 1.60967 | ||||||||
\(836\) | −15.2263 | −0.526612 | ||||||||
\(837\) | −6.81291 | −0.235489 | ||||||||
\(838\) | 4.96643 | 0.171563 | ||||||||
\(839\) | −45.6338 | −1.57545 | −0.787726 | − | 0.616025i | \(-0.788742\pi\) | ||||
−0.787726 | + | 0.616025i | \(0.788742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6881 | 1.02373 | ||||||||
\(842\) | 38.5955 | 1.33009 | ||||||||
\(843\) | 16.0117 | 0.551471 | ||||||||
\(844\) | 10.9541 | 0.377054 | ||||||||
\(845\) | −10.4646 | −0.359993 | ||||||||
\(846\) | 21.3047 | 0.732472 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 46.9568 | 1.61250 | ||||||||
\(849\) | 11.5747 | 0.397241 | ||||||||
\(850\) | −17.6534 | −0.605508 | ||||||||
\(851\) | −22.1736 | −0.760102 | ||||||||
\(852\) | 9.52389 | 0.326283 | ||||||||
\(853\) | −13.8659 | −0.474759 | −0.237379 | − | 0.971417i | \(-0.576288\pi\) | ||||
−0.237379 | + | 0.971417i | \(0.576288\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8712 | 0.371788 | ||||||||
\(856\) | 2.58086 | 0.0882119 | ||||||||
\(857\) | −27.4574 | −0.937926 | −0.468963 | − | 0.883218i | \(-0.655372\pi\) | ||||
−0.468963 | + | 0.883218i | \(0.655372\pi\) | |||||||
\(858\) | 30.0375 | 1.02546 | ||||||||
\(859\) | −12.6561 | −0.431819 | −0.215910 | − | 0.976413i | \(-0.569272\pi\) | ||||
−0.215910 | + | 0.976413i | \(0.569272\pi\) | |||||||
\(860\) | 27.0840 | 0.923557 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.21341 | −0.279750 | ||||||||
\(863\) | 43.2918 | 1.47367 | 0.736834 | − | 0.676073i | \(-0.236320\pi\) | ||||
0.736834 | + | 0.676073i | \(0.236320\pi\) | |||||||
\(864\) | 32.2212 | 1.09619 | ||||||||
\(865\) | −38.1401 | −1.29680 | ||||||||
\(866\) | −10.3838 | −0.352855 | ||||||||
\(867\) | −38.8504 | −1.31943 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.5710 | 1.98688 | ||||||||
\(870\) | 41.6908 | 1.41345 | ||||||||
\(871\) | −11.1920 | −0.379226 | ||||||||
\(872\) | 26.9036 | 0.911071 | ||||||||
\(873\) | 17.1795 | 0.581437 | ||||||||
\(874\) | 20.0324 | 0.677605 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.80614 | 0.128597 | ||||||||
\(877\) | 50.3867 | 1.70144 | 0.850718 | − | 0.525622i | \(-0.176167\pi\) | ||||
0.850718 | + | 0.525622i | \(0.176167\pi\) | |||||||
\(878\) | −35.8348 | −1.20936 | ||||||||
\(879\) | 23.5736 | 0.795119 | ||||||||
\(880\) | −59.1285 | −1.99322 | ||||||||
\(881\) | 4.56171 | 0.153688 | 0.0768440 | − | 0.997043i | \(-0.475516\pi\) | ||||
0.0768440 | + | 0.997043i | \(0.475516\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.01017 | 0.303216 | 0.151608 | − | 0.988441i | \(-0.451555\pi\) | ||||
0.151608 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(884\) | 24.3201 | 0.817973 | ||||||||
\(885\) | 4.99464 | 0.167893 | ||||||||
\(886\) | −9.15111 | −0.307438 | ||||||||
\(887\) | −14.2743 | −0.479285 | −0.239642 | − | 0.970861i | \(-0.577030\pi\) | ||||
−0.239642 | + | 0.970861i | \(0.577030\pi\) | |||||||
\(888\) | 9.84197 | 0.330275 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.4948 | 0.452345 | ||||||||
\(891\) | −9.39309 | −0.314680 | ||||||||
\(892\) | −4.33930 | −0.145291 | ||||||||
\(893\) | −21.6395 | −0.724137 | ||||||||
\(894\) | 32.2972 | 1.08018 | ||||||||
\(895\) | 40.8527 | 1.36555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.5439 | −0.485606 | ||||||||
\(898\) | −12.2051 | −0.407289 | ||||||||
\(899\) | −9.51570 | −0.317366 | ||||||||
\(900\) | −2.54043 | −0.0846809 | ||||||||
\(901\) | −66.2102 | −2.20578 | ||||||||
\(902\) | 8.35117 | 0.278064 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.6827 | −0.754416 | ||||||||
\(905\) | 6.41556 | 0.213260 | ||||||||
\(906\) | 11.7377 | 0.389960 | ||||||||
\(907\) | −40.2553 | −1.33665 | −0.668327 | − | 0.743867i | \(-0.732990\pi\) | ||||
−0.668327 | + | 0.743867i | \(0.732990\pi\) | |||||||
\(908\) | 0.969840 | 0.0321853 | ||||||||
\(909\) | −2.65346 | −0.0880098 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.43178 | −0.246226 | −0.123113 | − | 0.992393i | \(-0.539288\pi\) | ||||
−0.123113 | + | 0.992393i | \(0.539288\pi\) | |||||||
\(912\) | −16.7265 | −0.553869 | ||||||||
\(913\) | 1.37361 | 0.0454598 | ||||||||
\(914\) | −12.8538 | −0.425165 | ||||||||
\(915\) | 42.6845 | 1.41111 | ||||||||
\(916\) | 23.6819 | 0.782471 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −68.4173 | −2.25811 | ||||||||
\(919\) | 2.77258 | 0.0914589 | 0.0457294 | − | 0.998954i | \(-0.485439\pi\) | ||||
0.0457294 | + | 0.998954i | \(0.485439\pi\) | |||||||
\(920\) | 15.2190 | 0.501756 | ||||||||
\(921\) | 13.7876 | 0.454317 | ||||||||
\(922\) | 14.4823 | 0.476950 | ||||||||
\(923\) | −20.1621 | −0.663644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.76074 | −0.255172 | ||||||||
\(926\) | −32.1537 | −1.05664 | ||||||||
\(927\) | 23.1852 | 0.761501 | ||||||||
\(928\) | 45.0039 | 1.47732 | ||||||||
\(929\) | 17.1310 | 0.562051 | 0.281025 | − | 0.959700i | \(-0.409325\pi\) | ||||
0.281025 | + | 0.959700i | \(0.409325\pi\) | |||||||
\(930\) | −6.75975 | −0.221661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.18811 | −0.137186 | ||||||||
\(933\) | 29.6485 | 0.970649 | ||||||||
\(934\) | −61.2249 | −2.00334 | ||||||||
\(935\) | 83.3725 | 2.72657 | ||||||||
\(936\) | −6.82036 | −0.222930 | ||||||||
\(937\) | −20.2782 | −0.662461 | −0.331231 | − | 0.943550i | \(-0.607464\pi\) | ||||
−0.331231 | + | 0.943550i | \(0.607464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3407 | 0.500624 | ||||||||
\(940\) | 22.9223 | 0.747642 | ||||||||
\(941\) | 9.63228 | 0.314003 | 0.157002 | − | 0.987598i | \(-0.449817\pi\) | ||||
0.157002 | + | 0.987598i | \(0.449817\pi\) | |||||||
\(942\) | −47.0693 | −1.53360 | ||||||||
\(943\) | −4.04356 | −0.131676 | ||||||||
\(944\) | 8.11919 | 0.264257 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −76.6736 | −2.49287 | ||||||||
\(947\) | −35.3846 | −1.14984 | −0.574922 | − | 0.818208i | \(-0.694968\pi\) | ||||
−0.574922 | + | 0.818208i | \(0.694968\pi\) | |||||||
\(948\) | −17.5510 | −0.570029 | ||||||||
\(949\) | −8.05761 | −0.261561 | ||||||||
\(950\) | 7.01131 | 0.227477 | ||||||||
\(951\) | −32.1374 | −1.04213 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.5962 | −0.796749 | −0.398374 | − | 0.917223i | \(-0.630426\pi\) | ||||
−0.398374 | + | 0.917223i | \(0.630426\pi\) | |||||||
\(954\) | −25.8895 | −0.838204 | ||||||||
\(955\) | 50.8027 | 1.64394 | ||||||||
\(956\) | 9.11454 | 0.294785 | ||||||||
\(957\) | −43.4361 | −1.40409 | ||||||||
\(958\) | −37.7745 | −1.22044 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.54428 | 0.0498415 | ||||||||
\(961\) | −29.4571 | −0.950230 | ||||||||
\(962\) | 29.0510 | 0.936643 | ||||||||
\(963\) | −2.67680 | −0.0862587 | ||||||||
\(964\) | 15.1991 | 0.489530 | ||||||||
\(965\) | 25.2309 | 0.812212 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.7607 | 1.05351 | 0.526757 | − | 0.850016i | \(-0.323408\pi\) | ||||
0.526757 | + | 0.850016i | \(0.323408\pi\) | |||||||
\(968\) | 16.4018 | 0.527174 | ||||||||
\(969\) | 23.5847 | 0.757650 | ||||||||
\(970\) | 50.2242 | 1.61260 | ||||||||
\(971\) | 46.1107 | 1.47976 | 0.739881 | − | 0.672738i | \(-0.234882\pi\) | ||||
0.739881 | + | 0.672738i | \(0.234882\pi\) | |||||||
\(972\) | −16.3498 | −0.524419 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 44.1272 | 1.41393 | ||||||||
\(975\) | −5.09034 | −0.163021 | ||||||||
\(976\) | 69.3871 | 2.22103 | ||||||||
\(977\) | 58.7400 | 1.87926 | 0.939629 | − | 0.342194i | \(-0.111170\pi\) | ||||
0.939629 | + | 0.342194i | \(0.111170\pi\) | |||||||
\(978\) | 9.52382 | 0.304538 | ||||||||
\(979\) | −14.0597 | −0.449350 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.9038 | −0.890899 | ||||||||
\(982\) | −67.4864 | −2.15358 | ||||||||
\(983\) | −25.4675 | −0.812286 | −0.406143 | − | 0.913810i | \(-0.633126\pi\) | ||||
−0.406143 | + | 0.913810i | \(0.633126\pi\) | |||||||
\(984\) | 1.79477 | 0.0572152 | ||||||||
\(985\) | 57.4595 | 1.83081 | ||||||||
\(986\) | −95.5596 | −3.04324 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.65906 | −0.307296 | ||||||||
\(989\) | 37.1246 | 1.18049 | ||||||||
\(990\) | 32.6003 | 1.03611 | ||||||||
\(991\) | 16.5141 | 0.524588 | 0.262294 | − | 0.964988i | \(-0.415521\pi\) | ||||
0.262294 | + | 0.964988i | \(0.415521\pi\) | |||||||
\(992\) | −7.29694 | −0.231678 | ||||||||
\(993\) | 16.0765 | 0.510171 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.12383 | 0.257543 | ||||||||
\(996\) | −0.411606 | −0.0130422 | ||||||||
\(997\) | 6.12265 | 0.193906 | 0.0969532 | − | 0.995289i | \(-0.469090\pi\) | ||||
0.0969532 | + | 0.995289i | \(0.469090\pi\) | |||||||
\(998\) | −42.8196 | −1.35543 | ||||||||
\(999\) | −30.0774 | −0.951606 |
(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 | 2009.2.a.r.1.4 | 17 | ||
7.3 | odd | 6 | 287.2.e.d.247.14 | yes | 34 | ||
7.5 | odd | 6 | 287.2.e.d.165.14 | ✓ | 34 | ||
7.6 | odd | 2 | 2009.2.a.s.1.4 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.14 | ✓ | 34 | 7.5 | odd | 6 | ||
287.2.e.d.247.14 | yes | 34 | 7.3 | odd | 6 | ||
2009.2.a.r.1.4 | 17 | 1.1 | even | 1 | trivial | ||
2009.2.a.s.1.4 | 17 | 7.6 | odd | 2 |